LMFDB - Embedded newform 950.2.h.d.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	950.191
Dual form			950.2.h.d.761.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.00220 - 3.08444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.22762 + 0.194172i) q^{5} +(1.00220 - 3.08444i) q^{6} -1.89338 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.08232 + 4.41906i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.00220 - 3.08444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.22762 + 0.194172i) q^{5} +(1.00220 - 3.08444i) q^{6} -1.89338 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.08232 + 4.41906i) q^{9} +(-1.91632 - 1.15227i) q^{10} +(0.464150 + 0.337224i) q^{11} +(2.62378 - 1.90629i) q^{12} +(3.33739 - 2.42476i) q^{13} +(-1.53178 - 1.11290i) q^{14} +(2.83142 + 6.67636i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.87262 + 5.76335i) q^{17} -7.51816 q^{18} +(-0.309017 + 0.951057i) q^{19} +(-0.873042 - 2.05859i) q^{20} +(1.89754 + 5.84002i) q^{21} +(0.177289 + 0.545640i) q^{22} +(3.33360 + 2.42200i) q^{23} +3.24317 q^{24} +(4.92459 - 0.865085i) q^{25} +4.12524 q^{26} +(11.8547 + 8.61292i) q^{27} +(-0.585087 - 1.80071i) q^{28} +(-1.75171 - 5.39122i) q^{29} +(-1.63360 + 7.06556i) q^{30} +(-3.14712 + 9.68584i) q^{31} -1.00000 q^{32} +(0.574980 - 1.76961i) q^{33} +(-4.90259 + 3.56194i) q^{34} +(4.21774 - 0.367642i) q^{35} +(-6.08232 - 4.41906i) q^{36} +(5.44549 - 3.95638i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-10.8237 - 7.86390i) q^{39} +(0.503704 - 2.17860i) q^{40} +(-0.476860 + 0.346459i) q^{41} +(-1.89754 + 5.84002i) q^{42} -7.31897 q^{43} +(-0.177289 + 0.545640i) q^{44} +(12.6910 - 11.0250i) q^{45} +(1.27332 + 3.91888i) q^{46} +(4.19065 + 12.8975i) q^{47} +(2.62378 + 1.90629i) q^{48} -3.41511 q^{49} +(4.49256 + 2.19474i) q^{50} +19.6534 q^{51} +(3.33739 + 2.42476i) q^{52} +(1.12441 + 3.46056i) q^{53} +(4.52808 + 13.9360i) q^{54} +(-1.09943 - 0.661083i) q^{55} +(0.585087 - 1.80071i) q^{56} +3.24317 q^{57} +(1.75171 - 5.39122i) q^{58} +(-3.71145 + 2.69653i) q^{59} +(-5.47464 + 4.75595i) q^{60} +(-7.49765 - 5.44737i) q^{61} +(-8.23927 + 5.98618i) q^{62} +(11.5162 - 8.36697i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-6.96362 + 6.04947i) q^{65} +(1.50532 - 1.09368i) q^{66} +(2.54706 - 7.83905i) q^{67} -6.05994 q^{68} +(4.12960 - 12.7096i) q^{69} +(3.62832 + 2.18169i) q^{70} +(1.93827 + 5.96539i) q^{71} +(-2.32324 - 7.15020i) q^{72} +(-2.13653 - 1.55228i) q^{73} +6.73099 q^{74} +(-7.60371 - 14.3226i) q^{75} -1.00000 q^{76} +(-0.878812 - 0.638494i) q^{77} +(-4.13430 - 12.7241i) q^{78} +(2.49118 + 7.66705i) q^{79} +(1.68805 - 1.46645i) q^{80} +(7.71562 - 23.7462i) q^{81} -0.589431 q^{82} +(-2.72143 + 8.37571i) q^{83} +(-4.96782 + 3.60933i) q^{84} +(3.05242 - 13.2022i) q^{85} +(-5.92117 - 4.30198i) q^{86} +(-14.8733 + 10.8061i) q^{87} +(-0.464150 + 0.337224i) q^{88} +(0.613119 + 0.445457i) q^{89} +(16.7476 - 1.45982i) q^{90} +(-6.31895 + 4.59099i) q^{91} +(-1.27332 + 3.91888i) q^{92} +33.0294 q^{93} +(-4.19065 + 12.8975i) q^{94} +(0.503704 - 2.17860i) q^{95} +(1.00220 + 3.08444i) q^{96} +(4.71836 + 14.5216i) q^{97} +(-2.76288 - 2.00735i) q^{98} -4.31332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.00220	−	3.08444i	−0.578618	−	1.78080i	−0.623516	−	0.781810i	$-0.714296\pi$
$3$	−1.00220	−	3.08444i	−0.578618	−	1.78080i	0.0448987	−	0.998992i	$-0.485704\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.22762	+	0.194172i	−0.996223	+	0.0868365i
$5$	−2.22762	+	0.194172i	−0.996223	+	0.0868365i
$6$	1.00220	−	3.08444i	0.409144	−	1.25922i
$7$	−1.89338			−0.715631			−0.357815	−	0.933792i	$-0.616478\pi$
$7$	−1.89338			−0.715631			−0.357815	+	0.933792i	$0.616478\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−6.08232	+	4.41906i	−2.02744	+	1.47302i
$10$	−1.91632	−	1.15227i	−0.605992	−	0.364381i
$11$	0.464150	+	0.337224i	0.139946	+	0.101677i	0.655556	−	0.755147i	$-0.272434\pi$
$11$	0.464150	+	0.337224i	0.139946	+	0.101677i	−0.515609	+	0.856824i	$0.672434\pi$
$12$	2.62378	−	1.90629i	0.757420	−	0.550298i
$13$	3.33739	−	2.42476i	0.925626	−	0.672506i	−0.0192923	−	0.999814i	$-0.506141\pi$
$13$	3.33739	−	2.42476i	0.925626	−	0.672506i	0.944918	+	0.327308i	$0.106141\pi$
$14$	−1.53178	−	1.11290i	−0.409385	−	0.297435i
$15$	2.83142	+	6.67636i	0.731071	+	1.72383i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.87262	+	5.76335i	−0.454178	+	1.39782i	0.417919	+	0.908484i	$0.362760\pi$
$17$	−1.87262	+	5.76335i	−0.454178	+	1.39782i	−0.872097	+	0.489332i	$0.837240\pi$
$18$	−7.51816			−1.77205
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	−0.873042	−	2.05859i	−0.195218	−	0.460315i
$21$	1.89754	+	5.84002i	0.414077	+	1.27440i
$22$	0.177289	+	0.545640i	0.0377982	+	0.116331i
$23$	3.33360	+	2.42200i	0.695104	+	0.505023i	0.878334	−	0.478047i	$-0.158655\pi$
$23$	3.33360	+	2.42200i	0.695104	+	0.505023i	−0.183230	+	0.983070i	$0.558655\pi$
$24$	3.24317			0.662010
$25$	4.92459	−	0.865085i	0.984919	−	0.173017i
$26$	4.12524			0.809026
$27$	11.8547	+	8.61292i	2.28143	+	1.65756i
$28$	−0.585087	−	1.80071i	−0.110571	−	0.340303i
$29$	−1.75171	−	5.39122i	−0.325285	−	1.00112i	−0.971312	−	0.237809i	$-0.923571\pi$
$29$	−1.75171	−	5.39122i	−0.325285	−	1.00112i	0.646027	−	0.763314i	$-0.276429\pi$
$30$	−1.63360	+	7.06556i	−0.298253	+	1.28999i
$31$	−3.14712	+	9.68584i	−0.565240	+	1.73963i	0.101999	+	0.994784i	$0.467476\pi$
$31$	−3.14712	+	9.68584i	−0.565240	+	1.73963i	−0.667239	+	0.744844i	$0.732524\pi$
$32$	−1.00000			−0.176777
$33$	0.574980	−	1.76961i	0.100091	−	0.308049i
$34$	−4.90259	+	3.56194i	−0.840788	+	0.610868i
$35$	4.21774	−	0.367642i	0.712928	−	0.0621429i
$36$	−6.08232	−	4.41906i	−1.01372	−	0.736511i
$37$	5.44549	−	3.95638i	0.895232	−	0.650424i	−0.0420047	−	0.999117i	$-0.513374\pi$
$37$	5.44549	−	3.95638i	0.895232	−	0.650424i	0.937237	+	0.348693i	$0.113374\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	−10.8237	−	7.86390i	−1.73318	−	1.25923i
$40$	0.503704	−	2.17860i	0.0796426	−	0.344466i
$41$	−0.476860	+	0.346459i	−0.0744730	+	0.0541078i	−0.624399	−	0.781106i	$-0.714656\pi$
$41$	−0.476860	+	0.346459i	−0.0744730	+	0.0541078i	0.549926	+	0.835213i	$0.314656\pi$
$42$	−1.89754	+	5.84002i	−0.292796	+	0.901135i
$43$	−7.31897			−1.11613			−0.558066	−	0.829797i	$-0.688456\pi$
$43$	−7.31897			−1.11613			−0.558066	+	0.829797i	$0.688456\pi$
$44$	−0.177289	+	0.545640i	−0.0267274	+	0.0822584i
$45$	12.6910	−	11.0250i	1.89187	−	1.64351i
$46$	1.27332	+	3.91888i	0.187741	+	0.577808i
$47$	4.19065	+	12.8975i	0.611269	+	1.88129i	0.445967	+	0.895050i	$0.352860\pi$
$47$	4.19065	+	12.8975i	0.611269	+	1.88129i	0.165302	+	0.986243i	$0.447140\pi$
$48$	2.62378	+	1.90629i	0.378710	+	0.275149i
$49$	−3.41511			−0.487872
$50$	4.49256	+	2.19474i	0.635345	+	0.310382i
$51$	19.6534			2.75203
$52$	3.33739	+	2.42476i	0.462813	+	0.336253i
$53$	1.12441	+	3.46056i	0.154449	+	0.475345i	0.998105	−	0.0615397i	$-0.0196011\pi$
$53$	1.12441	+	3.46056i	0.154449	+	0.475345i	−0.843656	+	0.536885i	$0.819601\pi$
$54$	4.52808	+	13.9360i	0.616194	+	1.89645i
$55$	−1.09943	−	0.661083i	−0.148247	−	0.0891404i
$56$	0.585087	−	1.80071i	0.0781855	−	0.240630i
$57$	3.24317			0.429569
$58$	1.75171	−	5.39122i	0.230011	−	0.707901i
$59$	−3.71145	+	2.69653i	−0.483190	+	0.351058i	−0.802559	−	0.596572i	$-0.796529\pi$
$59$	−3.71145	+	2.69653i	−0.483190	+	0.351058i	0.319370	+	0.947630i	$0.396529\pi$
$60$	−5.47464	+	4.75595i	−0.706773	+	0.613991i
$61$	−7.49765	−	5.44737i	−0.959976	−	0.697464i	−0.00683108	−	0.999977i	$-0.502174\pi$
$61$	−7.49765	−	5.44737i	−0.959976	−	0.697464i	−0.953145	+	0.302513i	$0.902174\pi$
$62$	−8.23927	+	5.98618i	−1.04639	+	0.760245i
$63$	11.5162	−	8.36697i	1.45090	−	1.05414i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−6.96362	+	6.04947i	−0.863731	+	0.750344i
$66$	1.50532	−	1.09368i	0.185292	−	0.134622i
$67$	2.54706	−	7.83905i	0.311173	−	0.957692i	−0.666128	−	0.745837i	$-0.732050\pi$
$67$	2.54706	−	7.83905i	0.311173	−	0.957692i	0.977301	−	0.211855i	$-0.0679503\pi$
$68$	−6.05994			−0.734876
$69$	4.12960	−	12.7096i	0.497146	−	1.53006i
$70$	3.62832	+	2.18169i	0.433667	+	0.260762i
$71$	1.93827	+	5.96539i	0.230031	+	0.707962i	0.997742	+	0.0671657i	$0.0213956\pi$
$71$	1.93827	+	5.96539i	0.230031	+	0.707962i	−0.767711	+	0.640796i	$0.778604\pi$
$72$	−2.32324	−	7.15020i	−0.273796	−	0.842659i
$73$	−2.13653	−	1.55228i	−0.250062	−	0.181681i	0.455692	−	0.890137i	$-0.349392\pi$
$73$	−2.13653	−	1.55228i	−0.250062	−	0.181681i	−0.705754	+	0.708457i	$0.749392\pi$
$74$	6.73099			0.782462
$75$	−7.60371	−	14.3226i	−0.878000	−	1.65383i
$76$	−1.00000			−0.114708
$77$	−0.878812	−	0.638494i	−0.100150	−	0.0727632i
$78$	−4.13430	−	12.7241i	−0.468117	−	1.44072i
$79$	2.49118	+	7.66705i	0.280279	+	0.862611i	0.987774	+	0.155892i	$0.0498253\pi$
$79$	2.49118	+	7.66705i	0.280279	+	0.862611i	−0.707495	+	0.706719i	$0.750175\pi$
$80$	1.68805	−	1.46645i	0.188730	−	0.163954i
$81$	7.71562	−	23.7462i	0.857291	−	2.63847i
$82$	−0.589431			−0.0650917
$83$	−2.72143	+	8.37571i	−0.298716	+	0.919353i	0.683232	+	0.730202i	$0.260574\pi$
$83$	−2.72143	+	8.37571i	−0.298716	+	0.919353i	−0.981948	+	0.189152i	$0.939426\pi$
$84$	−4.96782	+	3.60933i	−0.542033	+	0.393810i
$85$	3.05242	−	13.2022i	0.331081	−	1.43198i
$86$	−5.92117	−	4.30198i	−0.638496	−	0.463895i
$87$	−14.8733	+	10.8061i	−1.59459	+	1.15854i
$88$	−0.464150	+	0.337224i	−0.0494785	+	0.0359482i
$89$	0.613119	+	0.445457i	0.0649905	+	0.0472184i	0.619806	−	0.784755i	$-0.287211\pi$
$89$	0.613119	+	0.445457i	0.0649905	+	0.0472184i	−0.554816	+	0.831973i	$0.687211\pi$
$90$	16.7476	−	1.45982i	1.76535	−	0.153878i
$91$	−6.31895	+	4.59099i	−0.662406	+	0.481266i
$92$	−1.27332	+	3.91888i	−0.132753	+	0.408572i
$93$	33.0294			3.42499
$94$	−4.19065	+	12.8975i	−0.432232	+	1.33027i
$95$	0.503704	−	2.17860i	0.0516789	−	0.223519i
$96$	1.00220	+	3.08444i	0.102286	+	0.314804i
$97$	4.71836	+	14.5216i	0.479077	+	1.47445i	0.840379	+	0.541999i	$0.182332\pi$
$97$	4.71836	+	14.5216i	0.479077	+	1.47445i	−0.361302	+	0.932449i	$0.617668\pi$
$98$	−2.76288	−	2.00735i	−0.279093	−	0.202773i
$99$	−4.31332			−0.433505
$100$	2.34453	+	4.41624i	0.234453	+	0.441624i
$101$	−14.2152			−1.41447			−0.707233	−	0.706980i	$-0.750057\pi$
$101$	−14.2152			−1.41447			−0.707233	+	0.706980i	$0.750057\pi$
$102$	15.9000	+	11.5520i	1.57433	+	1.14382i
$103$	4.36637	+	13.4383i	0.430231	+	1.32412i	0.897895	+	0.440209i	$0.145096\pi$
$103$	4.36637	+	13.4383i	0.430231	+	1.32412i	−0.467664	+	0.883906i	$0.654904\pi$
$104$	1.27477	+	3.92334i	0.125001	+	0.384715i
$105$	−5.36097	−	12.6409i	−0.523177	−	1.23363i
$106$	−1.12441	+	3.46056i	−0.109212	+	0.336120i
$107$	0.459792			0.0444498			0.0222249	−	0.999753i	$-0.492925\pi$
$107$	0.459792			0.0444498			0.0222249	+	0.999753i	$0.492925\pi$
$108$	−4.52808	+	13.9360i	−0.435715	+	1.34099i
$109$	−4.34202	+	3.15466i	−0.415890	+	0.302162i	−0.775982	−	0.630755i	$-0.782745\pi$
$109$	−4.34202	+	3.15466i	−0.415890	+	0.302162i	0.360092	+	0.932917i	$0.382745\pi$
$110$	−0.500882	−	1.18106i	−0.0477572	−	0.112609i
$111$	−17.6606	−	12.8312i	−1.67627	−	1.21788i
$112$	1.53178	−	1.11290i	0.144739	−	0.105159i
$113$	−3.66902	+	2.66570i	−0.345152	+	0.250768i	−0.746833	−	0.665012i	$-0.768426\pi$
$113$	−3.66902	+	2.66570i	−0.345152	+	0.250768i	0.401680	+	0.915780i	$0.368426\pi$
$114$	2.62378	+	1.90629i	0.245740	+	0.178540i
$115$	−7.89629	−	4.74801i	−0.736333	−	0.442755i
$116$	4.58604	−	3.33195i	0.425803	−	0.309364i
$117$	−9.58392	+	29.4963i	−0.886034	+	2.72693i
$118$	−4.58761			−0.422323
$119$	3.54559	−	10.9122i	0.325024	−	1.00032i
$120$	−7.22456	+	0.629734i	−0.659509	+	0.0574866i
$121$	−3.29747	−	10.1486i	−0.299770	−	0.922598i
$122$	−2.86385	−	8.81402i	−0.259281	−	0.797984i
$123$	1.54654	+	1.12363i	0.139447	+	0.101314i
$124$	−10.1843			−0.914577
$125$	−10.8022	+	2.88330i	−0.966174	+	0.257890i
$126$	14.2347			1.26813
$127$	−10.8319	−	7.86986i	−0.961179	−	0.698337i	−0.00775476	−	0.999970i	$-0.502468\pi$
$127$	−10.8319	−	7.86986i	−0.961179	−	0.698337i	−0.953424	+	0.301632i	$0.902468\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	7.33503	+	22.5749i	0.645814	+	1.98761i
$130$	−9.18948	+	0.801008i	−0.805970	+	0.0702531i
$131$	−2.57262	+	7.91771i	−0.224771	+	0.691774i	0.773544	+	0.633743i	$0.218482\pi$
$131$	−2.57262	+	7.91771i	−0.224771	+	0.691774i	−0.998315	+	0.0580311i	$0.981518\pi$
$132$	1.86067			0.161951
$133$	0.585087	−	1.80071i	0.0507335	−	0.156142i
$134$	6.66829	−	4.84480i	0.576053	−	0.418527i
$135$	−28.0801	−	16.8845i	−2.41675	−	1.45318i
$136$	−4.90259	−	3.56194i	−0.420394	−	0.305434i
$137$	10.2693	−	7.46105i	0.877362	−	0.637441i	−0.0551904	−	0.998476i	$-0.517577\pi$
$137$	10.2693	−	7.46105i	0.877362	−	0.637441i	0.932552	+	0.361035i	$0.117577\pi$
$138$	10.8114	−	7.85497i	0.920331	−	0.668660i
$139$	−5.47992	−	3.98139i	−0.464800	−	0.337697i	0.330611	−	0.943767i	$-0.392745\pi$
$139$	−5.47992	−	3.98139i	−0.464800	−	0.337697i	−0.795411	+	0.606070i	$0.792745\pi$
$140$	1.65300	+	3.89770i	0.139704	+	0.329416i
$141$	35.5817	−	25.8516i	2.99652	−	2.17710i
$142$	−1.93827	+	5.96539i	−0.162656	+	0.500605i
$143$	2.36673			0.197916
$144$	2.32324	−	7.15020i	0.193603	−	0.595850i
$145$	4.94898	+	11.6695i	0.410990	+	0.969095i
$146$	−0.816082	−	2.51164i	−0.0675394	−	0.207865i
$147$	3.42260	+	10.5337i	0.282292	+	0.868804i
$148$	5.44549	+	3.95638i	0.447616	+	0.325212i
$149$	−9.44267			−0.773574			−0.386787	−	0.922169i	$-0.626415\pi$
$149$	−9.44267			−0.773574			−0.386787	+	0.922169i	$0.626415\pi$
$150$	2.26710	−	16.0566i	0.185108	−	1.31102i
$151$	−16.1723			−1.31608			−0.658041	−	0.752982i	$-0.728615\pi$
$151$	−16.1723			−1.31608			−0.658041	+	0.752982i	$0.728615\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−14.0787	−	43.3298i	−1.13819	−	3.50300i
$154$	−0.335676	−	1.03311i	−0.0270496	−	0.0832500i
$155$	5.12987	−	22.1875i	0.412041	−	1.78214i
$156$	4.13430	−	12.7241i	0.331009	−	1.01874i
$157$	−15.7303			−1.25541			−0.627707	−	0.778450i	$-0.716006\pi$
$157$	−15.7303			−1.25541			−0.627707	+	0.778450i	$0.716006\pi$
$158$	−2.49118	+	7.66705i	−0.198187	+	0.609958i
$159$	9.54702	−	6.93632i	0.757128	−	0.550086i
$160$	2.22762	−	0.194172i	0.176109	−	0.0153507i
$161$	−6.31178	−	4.58578i	−0.497438	−	0.361410i
$162$	20.1998	−	14.6760i	1.58704	−	1.15305i
$163$	1.95207	−	1.41826i	0.152898	−	0.111087i	−0.508706	−	0.860940i	$-0.669876\pi$
$163$	1.95207	−	1.41826i	0.152898	−	0.111087i	0.661604	+	0.749854i	$0.269876\pi$
$164$	−0.476860	−	0.346459i	−0.0372365	−	0.0270539i
$165$	−0.937229	+	4.05366i	−0.0729631	+	0.315577i
$166$	−7.12480	+	5.17647i	−0.552992	+	0.401772i
$167$	6.37907	−	19.6328i	0.493628	−	1.51923i	−0.325457	−	0.945557i	$-0.605518\pi$
$167$	6.37907	−	19.6328i	0.493628	−	1.51923i	0.819085	−	0.573673i	$-0.194482\pi$
$168$	−6.14056			−0.473755
$169$	1.24151	−	3.82098i	0.0955009	−	0.293922i
$170$	10.2295	−	8.88661i	0.784566	−	0.681572i
$171$	−2.32324	−	7.15020i	−0.177663	−	0.546789i
$172$	−2.26169	−	6.96075i	−0.172452	−	0.530752i
$173$	−1.14971	−	0.835313i	−0.0874109	−	0.0635077i	0.543221	−	0.839589i	$-0.317204\pi$
$173$	−1.14971	−	0.835313i	−0.0874109	−	0.0635077i	−0.630632	+	0.776082i	$0.717204\pi$
$174$	−18.3844			−1.39372
$175$	−9.32413	+	1.63794i	−0.704838	+	0.123816i
$176$	−0.573720			−0.0432458
$177$	12.0369	+	8.74530i	0.904747	+	0.657337i
$178$	0.234191	+	0.720765i	0.0175533	+	0.0540236i
$179$	4.42881	+	13.6305i	0.331025	+	1.01879i	0.968647	+	0.248441i	$0.0799181\pi$
$179$	4.42881	+	13.6305i	0.331025	+	1.01879i	−0.637622	+	0.770349i	$0.720082\pi$
$180$	14.4072	+	8.66298i	1.07385	+	0.645701i
$181$	6.35387	−	19.5552i	0.472279	−	1.45353i	−0.377313	−	0.926086i	$-0.623152\pi$
$181$	6.35387	−	19.5552i	0.472279	−	1.45353i	0.849592	−	0.527440i	$-0.176848\pi$
$182$	−7.81066			−0.578964
$183$	−9.28795	+	28.5854i	−0.686585	+	2.11309i
$184$	−3.33360	+	2.42200i	−0.245756	+	0.178553i
$185$	−11.3623	+	9.87067i	−0.835370	+	0.725706i
$186$	26.7214	+	19.4142i	1.95931	+	1.42352i
$187$	−2.81272	+	2.04356i	−0.205686	+	0.149440i
$188$	−10.9713	+	7.97109i	−0.800161	+	0.581351i
$189$	−22.4454	−	16.3075i	−1.63266	−	1.18620i
$190$	1.68805	−	1.46645i	0.122464	−	0.106388i
$191$	2.57419	−	1.87026i	0.186262	−	0.135327i	−0.490747	−	0.871302i	$-0.663276\pi$
$191$	2.57419	−	1.87026i	0.186262	−	0.135327i	0.677009	+	0.735975i	$0.263276\pi$
$192$	−1.00220	+	3.08444i	−0.0723272	+	0.222600i
$193$	19.6231			1.41250			0.706252	−	0.707961i	$-0.250385\pi$
$193$	19.6231			1.41250			0.706252	+	0.707961i	$0.250385\pi$
$194$	−4.71836	+	14.5216i	−0.338759	+	1.04259i
$195$	25.6381	+	15.4161i	1.83598	+	1.10397i
$196$	−1.05533	−	3.24796i	−0.0753804	−	0.231997i
$197$	−2.87298	−	8.84213i	−0.204692	−	0.629976i	−0.999726	−	0.0234114i	$-0.992547\pi$
$197$	−2.87298	−	8.84213i	−0.204692	−	0.629976i	0.795034	−	0.606564i	$-0.207453\pi$
$198$	−3.48955	−	2.53531i	−0.247992	−	0.180176i
$199$	2.06025			0.146047			0.0730236	−	0.997330i	$-0.476735\pi$
$199$	2.06025			0.146047			0.0730236	+	0.997330i	$0.476735\pi$
$200$	−0.699038	+	4.95089i	−0.0494295	+	0.350081i
$201$	−26.7317			−1.88551
$202$	−11.5004	−	8.35549i	−0.809162	−	0.587891i
$203$	3.31666	+	10.2076i	0.232784	+	0.716435i
$204$	6.07324	+	18.6915i	0.425212	+	1.30867i
$205$	0.994990	−	0.864372i	0.0694931	−	0.0603704i
$206$	−4.36637	+	13.4383i	−0.304219	+	0.936291i
$207$	−30.9790			−2.15319
$208$	−1.27477	+	3.92334i	−0.0883894	+	0.272035i
$209$	−0.464150	+	0.337224i	−0.0321059	+	0.0233263i
$210$	3.09302	−	13.3778i	0.213439	−	0.923156i
$211$	11.4274	+	8.30252i	0.786697	+	0.571569i	0.906981	−	0.421170i	$-0.138381\pi$
$211$	11.4274	+	8.30252i	0.786697	+	0.571569i	−0.120284	+	0.992739i	$0.538381\pi$
$212$	−2.94373	+	2.13875i	−0.202176	+	0.146890i
$213$	16.4574	−	11.9570i	1.12764	−	0.819278i
$214$	0.371980	+	0.270259i	0.0254280	+	0.0184745i
$215$	16.3039	−	1.42114i	1.11192	−	0.0969211i
$216$	−11.8547	+	8.61292i	−0.806608	+	0.586035i
$217$	5.95870	−	18.3390i	0.404503	−	1.24493i
$218$	−5.36703			−0.363501
$219$	−2.64669	+	8.14569i	−0.178847	+	0.550435i
$220$	0.288985	−	1.24991i	0.0194834	−	0.0842686i
$221$	7.72503	+	23.7752i	0.519642	+	1.59929i
$222$	−6.74577	−	20.7613i	−0.452746	−	1.39341i
$223$	−17.3538	−	12.6083i	−1.16210	−	0.844313i	−0.172055	−	0.985087i	$-0.555041\pi$
$223$	−17.3538	−	12.6083i	−1.16210	−	0.844313i	−0.990042	+	0.140774i	$0.955041\pi$
$224$	1.89338			0.126507
$225$	−26.1301	+	27.0238i	−1.74201	+	1.80159i
$226$	−4.53516			−0.301674
$227$	6.49428	+	4.71837i	0.431040	+	0.313169i	0.782065	−	0.623197i	$-0.214167\pi$
$227$	6.49428	+	4.71837i	0.431040	+	0.313169i	−0.351024	+	0.936366i	$0.614167\pi$
$228$	1.00220	+	3.08444i	0.0663720	+	0.204272i
$229$	6.68159	+	20.5638i	0.441532	+	1.35889i	0.886243	+	0.463221i	$0.153306\pi$
$229$	6.68159	+	20.5638i	0.441532	+	1.35889i	−0.444711	+	0.895674i	$0.646694\pi$
$230$	−3.59742	−	8.48255i	−0.237207	−	0.559323i
$231$	−1.08866	+	3.35054i	−0.0716283	+	0.220449i
$232$	5.66866			0.372166
$233$	0.308466	−	0.949360i	0.0202083	−	0.0621946i	−0.940444	−	0.339949i	$-0.889590\pi$
$233$	0.308466	−	0.949360i	0.0202083	−	0.0621946i	0.960652	+	0.277754i	$0.0895902\pi$
$234$	−25.0910	+	18.2297i	−1.64025	+	1.19171i
$235$	−11.8395	−	27.9170i	−0.772325	−	1.82111i
$236$	−3.71145	−	2.69653i	−0.241595	−	0.175529i
$237$	21.1519	−	15.3678i	1.37396	−	0.998244i
$238$	9.28248	−	6.74412i	0.601694	−	0.437156i
$239$	−0.884928	−	0.642938i	−0.0572412	−	0.0415882i	0.558797	−	0.829305i	$-0.311263\pi$
$239$	−0.884928	−	0.642938i	−0.0572412	−	0.0415882i	−0.616038	+	0.787716i	$0.711263\pi$
$240$	−6.21494	−	3.73702i	−0.401173	−	0.241224i
$241$	0.359780	−	0.261395i	0.0231755	−	0.0168380i	−0.576137	−	0.817353i	$-0.695441\pi$
$241$	0.359780	−	0.261395i	0.0231755	−	0.0168380i	0.599313	+	0.800515i	$0.295441\pi$
$242$	3.29747	−	10.1486i	0.211970	−	0.652375i
$243$	−37.0169			−2.37463
$244$	2.86385	−	8.81402i	0.183339	−	0.564260i
$245$	7.60757	−	0.663120i	0.486030	−	0.0423652i
$246$	0.590725	+	1.81806i	0.0376632	+	0.115916i
$247$	1.27477	+	3.92334i	0.0811117	+	0.249636i
$248$	−8.23927	−	5.98618i	−0.523194	−	0.380123i
$249$	28.5618			1.81003
$250$	−10.4339	−	4.01671i	−0.659897	−	0.254039i
$251$	28.3292			1.78812			0.894061	−	0.447944i	$-0.147844\pi$
$251$	28.3292			1.78812			0.894061	+	0.447944i	$0.147844\pi$
$252$	11.5162	+	8.36697i	0.725449	+	0.527070i
$253$	0.730531	+	2.24834i	0.0459281	+	0.141352i
$254$	−4.13743	−	12.7337i	−0.259606	−	0.798984i
$255$	−43.7804	+	3.81615i	−2.74163	+	0.238977i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	14.8139			0.924068			0.462034	−	0.886862i	$-0.347120\pi$
$257$	14.8139			0.924068			0.462034	+	0.886862i	$0.347120\pi$
$258$	−7.33503	+	22.5749i	−0.456659	+	1.40545i
$259$	−10.3104	+	7.49093i	−0.640656	+	0.465464i
$260$	−7.90526	−	4.75341i	−0.490264	−	0.294794i
$261$	34.4786	+	25.0502i	2.13417	+	1.55057i
$262$	−6.73521	+	4.89342i	−0.416103	+	0.302316i
$263$	−14.5965	+	10.6050i	−0.900060	+	0.653932i	−0.938481	−	0.345330i	$-0.887767\pi$
$263$	−14.5965	+	10.6050i	−0.900060	+	0.653932i	0.0384213	+	0.999262i	$0.487767\pi$
$264$	1.50532	+	1.09368i	0.0926458	+	0.0673111i
$265$	−3.17669	−	7.49050i	−0.195143	−	0.460138i
$266$	1.53178	−	1.11290i	0.0939193	−	0.0682364i
$267$	0.759521	−	2.33756i	0.0464819	−	0.143057i
$268$	8.24246			0.503488
$269$	−4.95494	+	15.2497i	−0.302108	+	0.929792i	0.678633	+	0.734478i	$0.262573\pi$
$269$	−4.95494	+	15.2497i	−0.302108	+	0.929792i	−0.980741	+	0.195315i	$0.937427\pi$
$270$	−12.7928	−	30.1649i	−0.778547	−	1.83578i
$271$	1.52016	+	4.67857i	0.0923431	+	0.284203i	0.986552	−	0.163447i	$-0.0522612\pi$
$271$	1.52016	+	4.67857i	0.0923431	+	0.284203i	−0.894209	+	0.447650i	$0.852261\pi$
$272$	−1.87262	−	5.76335i	−0.113545	−	0.349454i
$273$	20.4934	+	14.8894i	1.24032	+	0.901145i
$274$	12.6935			0.766842
$275$	2.57748	+	1.25916i	0.155428	+	0.0759305i
$276$	13.3637			0.804399
$277$	14.5481	+	10.5698i	0.874111	+	0.635079i	0.931687	−	0.363262i	$-0.118337\pi$
$277$	14.5481	+	10.5698i	0.874111	+	0.635079i	−0.0575759	+	0.998341i	$0.518337\pi$
$278$	−2.09314	−	6.44203i	−0.125538	−	0.386367i
$279$	−23.6606	−	72.8197i	−1.41652	−	4.35960i
$280$	−0.953704	+	4.12491i	−0.0569947	+	0.246511i
$281$	0.217428	−	0.669176i	0.0129707	−	0.0399197i	−0.944362	−	0.328909i	$-0.893319\pi$
$281$	0.217428	−	0.669176i	0.0129707	−	0.0399197i	0.957332	+	0.288989i	$0.0933191\pi$
$282$	43.9814			2.61905
$283$	−2.19426	+	6.75324i	−0.130435	+	0.401439i	−0.994852	−	0.101337i	$-0.967688\pi$
$283$	−2.19426	+	6.75324i	−0.130435	+	0.401439i	0.864417	+	0.502776i	$0.167688\pi$
$284$	−5.07447	+	3.68682i	−0.301114	+	0.218772i
$285$	−7.22456	+	0.629734i	−0.427946	+	0.0373022i
$286$	1.91473	+	1.39113i	0.113220	+	0.0822594i
$287$	0.902877	−	0.655979i	0.0532951	−	0.0387212i
$288$	6.08232	−	4.41906i	0.358404	−	0.260396i
$289$	−15.9561	−	11.5928i	−0.938597	−	0.681930i
$290$	−2.85533	+	12.3497i	−0.167671	+	0.725201i
$291$	40.0624	−	29.1070i	2.34850	−	1.70628i
$292$	0.816082	−	2.51164i	0.0477576	−	0.146983i
$293$	8.35405			0.488049			0.244025	−	0.969769i	$-0.421532\pi$
$293$	8.35405			0.488049			0.244025	+	0.969769i	$0.421532\pi$
$294$	−3.42260	+	10.5337i	−0.199610	+	0.614337i
$295$	7.74412	−	6.72750i	0.450880	−	0.391690i
$296$	2.07999	+	6.40155i	0.120897	+	0.372083i
$297$	2.59785	+	7.99536i	0.150743	+	0.463938i
$298$	−7.63928	−	5.55026i	−0.442532	−	0.321518i
$299$	16.9983			0.983037
$300$	11.2720	−	11.6575i	0.650787	−	0.673046i
$301$	13.8576			0.798739
$302$	−13.0837	−	9.50583i	−0.752880	−	0.546999i
$303$	14.2464	+	43.8460i	0.818435	+	2.51889i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	17.7597	+	10.6788i	1.01692	+	0.611468i
$306$	14.0787	−	43.3298i	0.804825	−	2.47700i
$307$	−23.0443			−1.31521			−0.657604	−	0.753364i	$-0.728430\pi$
$307$	−23.0443			−1.31521			−0.657604	+	0.753364i	$0.728430\pi$
$308$	0.335676	−	1.03311i	0.0191269	−	0.0588666i
$309$	37.0737	−	26.9356i	2.10905	−	1.53231i
$310$	17.1916	−	14.9348i	0.976418	−	0.848238i
$311$	3.08550	+	2.24175i	0.174963	+	0.127118i	0.671820	−	0.740714i	$-0.265513\pi$
$311$	3.08550	+	2.24175i	0.174963	+	0.127118i	−0.496857	+	0.867832i	$0.665513\pi$
$312$	10.8237	−	7.86390i	0.612773	−	0.445206i
$313$	13.1964	−	9.58772i	0.745903	−	0.541930i	−0.148651	−	0.988890i	$-0.547493\pi$
$313$	13.1964	−	9.58772i	0.745903	−	0.541930i	0.894554	+	0.446960i	$0.147493\pi$
$314$	−12.7261	−	9.24603i	−0.718174	−	0.521784i
$315$	−24.0290	+	20.8746i	−1.35388	+	1.17615i
$316$	−6.52198	+	4.73850i	−0.366890	+	0.266561i
$317$	2.84290	−	8.74954i	0.159673	−	0.491423i	−0.838931	−	0.544237i	$-0.816819\pi$
$317$	2.84290	−	8.74954i	0.159673	−	0.491423i	0.998604	+	0.0528143i	$0.0168192\pi$
$318$	11.8008			0.661754
$319$	1.00499	−	3.09305i	0.0562688	−	0.173178i
$320$	1.91632	+	1.15227i	0.107125	+	0.0644141i
$321$	−0.460802	−	1.41820i	−0.0257194	−	0.0791563i
$322$	−2.41089	−	7.41994i	−0.134353	−	0.413497i
$323$	−4.90259	−	3.56194i	−0.272788	−	0.198192i
$324$	24.9683			1.38713
$325$	14.3377	−	14.8281i	0.795311	−	0.822513i
$326$	2.41289			0.133637
$327$	14.0819	+	10.2311i	0.778731	+	0.565781i
$328$	−0.182144	−	0.560582i	−0.0100572	−	0.0309530i
$329$	−7.93450	−	24.4199i	−0.437443	−	1.34631i
$330$	−3.14091	+	2.72859i	−0.172902	+	0.150204i
$331$	5.54865	−	17.0770i	0.304982	−	0.938637i	−0.674702	−	0.738090i	$-0.735728\pi$
$331$	5.54865	−	17.0770i	0.304982	−	0.938637i	0.979684	−	0.200547i	$-0.0642719\pi$
$332$	−8.80674			−0.483333
$333$	−15.6377	+	48.1279i	−0.856941	+	2.63739i
$334$	16.7006	−	12.1337i	0.913818	−	0.663928i
$335$	−4.15176	+	17.9570i	−0.226835	+	0.981095i
$336$	−4.96782	−	3.60933i	−0.271017	−	0.196905i
$337$	3.86237	−	2.80618i	0.210397	−	0.152862i	−0.477596	−	0.878579i	$-0.658492\pi$
$337$	3.86237	−	2.80618i	0.210397	−	0.152862i	0.687993	+	0.725717i	$0.258492\pi$
$338$	3.25032	−	2.36150i	0.176794	−	0.128448i
$339$	11.8993	+	8.64532i	0.646279	+	0.469549i
$340$	13.4993	−	1.17667i	0.732100	−	0.0638141i
$341$	−4.72704	+	3.43439i	−0.255983	+	0.185983i
$342$	2.32324	−	7.15020i	0.125626	−	0.386638i
$343$	19.7198			1.06477
$344$	2.26169	−	6.96075i	0.121942	−	0.375299i
$345$	−6.73134	+	29.1141i	−0.362403	+	1.56745i
$346$	−0.439150	−	1.35157i	−0.0236089	−	0.0726606i
$347$	−1.54092	−	4.74248i	−0.0827211	−	0.254589i	0.901139	−	0.433531i	$-0.142733\pi$
$347$	−1.54092	−	4.74248i	−0.0827211	−	0.254589i	−0.983860	+	0.178942i	$0.942733\pi$
$348$	−14.8733	−	10.8061i	−0.797294	−	0.579268i
$349$	−30.0102			−1.60641			−0.803204	−	0.595704i	$-0.796873\pi$
$349$	−30.0102			−1.60641			−0.803204	+	0.595704i	$0.796873\pi$
$350$	−8.50614	−	4.15547i	−0.454672	−	0.222119i
$351$	60.4479			3.22647
$352$	−0.464150	−	0.337224i	−0.0247393	−	0.0179741i
$353$	2.77384	+	8.53701i	0.147637	+	0.454379i	0.997341	−	0.0728809i	$-0.0232193\pi$
$353$	2.77384	+	8.53701i	0.147637	+	0.454379i	−0.849704	+	0.527260i	$0.823219\pi$
$354$	4.59768	+	14.1502i	0.244364	+	0.752074i
$355$	−5.47605	−	12.9123i	−0.290639	−	0.685313i
$356$	−0.234191	+	0.720765i	−0.0124121	+	0.0382005i
$357$	−37.2114			−1.96944
$358$	−4.42881	+	13.6305i	−0.234070	+	0.720393i
$359$	1.44358	−	1.04882i	0.0761891	−	0.0553546i	−0.549039	−	0.835797i	$-0.685006\pi$
$359$	1.44358	−	1.04882i	0.0761891	−	0.0553546i	0.625228	+	0.780442i	$0.285006\pi$
$360$	6.56367	+	15.4768i	0.345936	+	0.815700i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	16.6346	−	12.0858i	0.874297	−	0.635214i
$363$	−27.9980	+	20.3417i	−1.46951	+	1.06766i
$364$	−6.31895	−	4.59099i	−0.331203	−	0.240633i
$365$	5.06079	+	3.04304i	0.264894	+	0.159280i
$366$	−24.3162	+	17.6667i	−1.27103	+	0.923455i
$367$	1.12032	−	3.44800i	0.0584805	−	0.179984i	−0.917549	−	0.397623i	$-0.869835\pi$
$367$	1.12032	−	3.44800i	0.0584805	−	0.179984i	0.976029	+	0.217638i	$0.0698353\pi$
$368$	−4.12056			−0.214799
$369$	1.36939	−	4.21455i	0.0712876	−	0.219401i
$370$	−14.9941	+	1.30697i	−0.779506	+	0.0679463i
$371$	−2.12893	−	6.55217i	−0.110528	−	0.340172i
$372$	10.2067	+	31.4128i	0.529190	+	1.62868i
$373$	−18.4823	−	13.4282i	−0.956975	−	0.695283i	−0.00452901	−	0.999990i	$-0.501442\pi$
$373$	−18.4823	−	13.4282i	−0.956975	−	0.695283i	−0.952446	+	0.304706i	$0.901442\pi$
$374$	−3.47671			−0.179776
$375$	19.7192	+	30.4290i	1.01830	+	1.57134i
$376$	−13.5612			−0.699367
$377$	−18.9185	−	13.7451i	−0.974354	−	0.707910i
$378$	−8.57338	−	26.3862i	−0.440967	−	1.35716i
$379$	−4.13524	−	12.7270i	−0.212413	−	0.653740i	−0.999327	−	0.0366777i	$-0.988323\pi$
$379$	−4.13524	−	12.7270i	−0.212413	−	0.653740i	0.786914	−	0.617063i	$-0.211677\pi$
$380$	2.22762	−	0.194172i	0.114275	−	0.00996083i
$381$	−13.4184	+	41.2976i	−0.687446	+	2.11574i
$382$	3.18187			0.162799
$383$	−9.91233	+	30.5070i	−0.506497	+	1.55884i	0.291743	+	0.956497i	$0.405765\pi$
$383$	−9.91233	+	30.5070i	−0.506497	+	1.55884i	−0.798240	+	0.602340i	$0.794235\pi$
$384$	−2.62378	+	1.90629i	−0.133894	+	0.0972799i
$385$	2.08164	+	1.25168i	0.106090	+	0.0637917i
$386$	15.8754	+	11.5342i	0.808039	+	0.587075i
$387$	44.5163	−	32.3430i	2.26289	−	1.64409i
$388$	−12.3528	+	8.97486i	−0.627120	+	0.455630i
$389$	18.6623	+	13.5590i	0.946216	+	0.687466i	0.949909	−	0.312527i	$-0.101175\pi$
$389$	18.6623	+	13.5590i	0.946216	+	0.687466i	−0.00369265	+	0.999993i	$0.501175\pi$
$390$	11.6803	+	27.5416i	0.591455	+	1.39462i
$391$	−20.2014	+	14.6772i	−1.02163	+	0.742258i
$392$	1.05533	−	3.24796i	0.0533020	−	0.164047i
$393$	27.0000			1.36197
$394$	2.87298	−	8.84213i	0.144739	−	0.445460i
$395$	−7.03813	−	16.5956i	−0.354127	−	0.835014i
$396$	−1.33289	−	4.10221i	−0.0669802	−	0.206144i
$397$	7.07148	+	21.7638i	0.354907	+	1.09229i	0.956063	+	0.293161i	$0.0947072\pi$
$397$	7.07148	+	21.7638i	0.354907	+	1.09229i	−0.601156	+	0.799132i	$0.705293\pi$
$398$	1.66678	+	1.21098i	0.0835480	+	0.0607012i
$399$	−6.14056			−0.307413
$400$	−3.47560	+	3.59447i	−0.173780	+	0.179724i
$401$	−18.9544			−0.946535			−0.473268	−	0.880919i	$-0.656926\pi$
$401$	−18.9544			−0.946535			−0.473268	+	0.880919i	$0.656926\pi$
$402$	−21.6264	−	15.7125i	−1.07863	−	0.783669i
$403$	12.9826	+	39.9564i	0.646711	+	1.99037i
$404$	−4.39274	−	13.5195i	−0.218547	−	0.672619i
$405$	−12.5766	+	54.3958i	−0.624937	+	2.70295i
$406$	−3.31666	+	10.2076i	−0.164603	+	0.506596i
$407$	3.86171			0.191418
$408$	−6.07324	+	18.6915i	−0.300670	+	0.925368i
$409$	26.5553	−	19.2935i	1.31307	−	0.954005i	0.313084	−	0.949725i	$-0.398638\pi$
$409$	26.5553	−	19.2935i	1.31307	−	0.954005i	0.999991	−	0.00427910i	$-0.00136208\pi$
$410$	1.31303	−	0.114451i	0.0648459	−	0.00565234i
$411$	−33.3050	−	24.1975i	−1.64281	−	1.19357i
$412$	−11.4313	+	8.30533i	−0.563180	+	0.409174i
$413$	7.02719	−	5.10555i	0.345786	−	0.251228i
$414$	−25.0626	−	18.2090i	−1.23176	−	0.894924i
$415$	4.43599	−	19.1863i	0.217754	−	0.941820i
$416$	−3.33739	+	2.42476i	−0.163629	+	0.118883i
$417$	−6.78842	+	20.8926i	−0.332430	+	1.02311i
$418$	−0.573720			−0.0280616
$419$	7.59100	−	23.3627i	0.370844	−	1.14134i	−0.575395	−	0.817875i	$-0.695152\pi$
$419$	7.59100	−	23.3627i	0.370844	−	1.14134i	0.946240	−	0.323466i	$-0.104848\pi$
$420$	10.3656	−	9.00484i	0.505789	−	0.439391i
$421$	−1.97747	−	6.08602i	−0.0963758	−	0.296614i	0.891234	−	0.453544i	$-0.149840\pi$
$421$	−1.97747	−	6.08602i	−0.0963758	−	0.296614i	−0.987610	+	0.156930i	$0.949840\pi$
$422$	4.36489	+	13.4338i	0.212480	+	0.653945i
$423$	−82.4837	−	59.9279i	−4.01050	−	2.91380i
$424$	−3.63865			−0.176709
$425$	−4.23613	+	30.0021i	−0.205483	+	1.45532i
$426$	20.3424			0.985594
$427$	14.1959	+	10.3139i	0.686989	+	0.499127i
$428$	0.142084	+	0.437289i	0.00686787	+	0.0211371i
$429$	−2.37193	−	7.30005i	−0.114518	−	0.352450i
$430$	14.0255	+	8.43346i	0.676367	+	0.406697i
$431$	−4.43608	+	13.6529i	−0.213679	+	0.657635i	0.785566	+	0.618778i	$0.212372\pi$
$431$	−4.43608	+	13.6529i	−0.213679	+	0.657635i	−0.999245	+	0.0388574i	$0.987628\pi$
$432$	−14.6532			−0.705001
$433$	−0.939853	+	2.89257i	−0.0451665	+	0.139008i	−0.971097	−	0.238687i	$-0.923283\pi$
$433$	−0.939853	+	2.89257i	−0.0451665	+	0.139008i	0.925930	+	0.377695i	$0.123283\pi$
$434$	15.6001	−	11.3341i	0.748828	−	0.544055i
$435$	31.0339	−	26.9599i	1.48796	−	1.29263i
$436$	−4.34202	−	3.15466i	−0.207945	−	0.151081i
$437$	−3.33360	+	2.42200i	−0.159468	+	0.115860i
$438$	−6.92914	+	5.03431i	−0.331087	+	0.240549i
$439$	−27.1710	−	19.7409i	−1.29680	−	0.942181i	−0.296883	−	0.954914i	$-0.595947\pi$
$439$	−27.1710	−	19.7409i	−1.29680	−	0.942181i	−0.999919	+	0.0127325i	$0.995947\pi$
$440$	0.968470	−	0.841333i	0.0461700	−	0.0401090i
$441$	20.7718	−	15.0916i	0.989132	−	0.718647i
$442$	−7.72503	+	23.7752i	−0.367442	+	1.13087i
$443$	17.2535			0.819739			0.409870	−	0.912144i	$-0.365574\pi$
$443$	17.2535			0.819739			0.409870	+	0.912144i	$0.365574\pi$
$444$	6.74577	−	20.7613i	0.320140	−	0.985289i
$445$	−1.45229	−	0.873259i	−0.0688453	−	0.0413965i
$446$	−6.62856	−	20.4006i	−0.313872	−	0.965998i
$447$	9.46340	+	29.1253i	0.447603	+	1.37758i
$448$	1.53178	+	1.11290i	0.0723697	+	0.0525797i
$449$	16.4111			0.774489			0.387244	−	0.921977i	$-0.373427\pi$
$449$	16.4111			0.774489			0.387244	+	0.921977i	$0.373427\pi$
$450$	−37.0239	+	6.50385i	−1.74532	+	0.306594i
$451$	−0.338168			−0.0159237
$452$	−3.66902	−	2.66570i	−0.172576	−	0.125384i
$453$	16.2078	+	49.8824i	0.761508	+	2.34368i
$454$	2.48059	+	7.63448i	0.116420	+	0.358304i
$455$	13.1848	−	11.4539i	0.618113	−	0.536969i
$456$	−1.00220	+	3.08444i	−0.0469321	+	0.144442i
$457$	−38.4737			−1.79972			−0.899862	−	0.436174i	$-0.856333\pi$
$457$	−38.4737			−1.79972			−0.899862	+	0.436174i	$0.856333\pi$
$458$	−6.68159	+	20.5638i	−0.312210	+	0.960884i
$459$	−71.8386	+	52.1938i	−3.35314	+	2.43620i
$460$	2.07554	−	8.97704i	0.0967726	−	0.418556i
$461$	17.1465	+	12.4576i	0.798590	+	0.580210i	0.910500	−	0.413509i	$-0.135697\pi$
$461$	17.1465	+	12.4576i	0.798590	+	0.580210i	−0.111910	+	0.993718i	$0.535697\pi$
$462$	−2.85014	+	2.07075i	−0.132600	+	0.0963399i
$463$	23.9946	−	17.4331i	1.11512	−	0.810184i	0.131660	−	0.991295i	$-0.457969\pi$
$463$	23.9946	−	17.4331i	1.11512	−	0.810184i	0.983463	+	0.181111i	$0.0579694\pi$
$464$	4.58604	+	3.33195i	0.212902	+	0.154682i
$465$	−73.5770	+	6.41340i	−3.41205	+	0.297414i
$466$	0.807574	−	0.586737i	0.0374101	−	0.0271801i
$467$	−5.07738	+	15.6266i	−0.234953	+	0.723112i	0.762174	+	0.647372i	$0.224132\pi$
$467$	−5.07738	+	15.6266i	−0.234953	+	0.723112i	−0.997128	+	0.0757401i	$0.975868\pi$
$468$	−31.0142			−1.43363
$469$	−4.82256	+	14.8423i	−0.222685	+	0.685354i
$470$	6.83084	−	29.5444i	0.315083	−	1.36278i
$471$	15.7648	+	48.5191i	0.726405	+	2.23564i
$472$	−1.41765	−	4.36307i	−0.0652526	−	0.200827i
$473$	−3.39710	−	2.46813i	−0.156199	−	0.113485i
$474$	26.1452			1.20089
$475$	−0.699038	+	4.95089i	−0.0320741	+	0.227163i
$476$	11.4738			0.525900
$477$	−22.1314	−	16.0794i	−1.01333	−	0.736227i
$478$	−0.338012	−	1.04030i	−0.0154603	−	0.0475820i
$479$	8.07187	+	24.8426i	0.368813	+	1.13509i	0.947559	+	0.319582i	$0.103542\pi$
$479$	8.07187	+	24.8426i	0.368813	+	1.13509i	−0.578746	+	0.815508i	$0.696458\pi$
$480$	−2.83142	−	6.67636i	−0.129236	−	0.304733i
$481$	8.58046	−	26.4079i	0.391235	−	1.20410i
$482$	0.444712			0.0202561
$483$	−7.81892	+	24.0641i	−0.355773	+	1.09496i
$484$	8.63289	−	6.27217i	0.392404	−	0.285098i
$485$	−13.3304	−	31.4325i	−0.605304	−	1.42728i
$486$	−29.9473	−	21.7580i	−1.35844	−	0.986961i
$487$	6.32551	−	4.59576i	0.286636	−	0.208254i	−0.435170	−	0.900348i	$-0.643312\pi$
$487$	6.32551	−	4.59576i	0.286636	−	0.208254i	0.721807	+	0.692095i	$0.243312\pi$
$488$	7.49765	−	5.44737i	0.339403	−	0.246591i
$489$	−6.33089	−	4.59966i	−0.286293	−	0.208004i
$490$	6.54442	+	3.93514i	0.295647	+	0.177771i
$491$	−2.31720	+	1.68354i	−0.104574	+	0.0759773i	−0.638843	−	0.769337i	$-0.720587\pi$
$491$	−2.31720	+	1.68354i	−0.104574	+	0.0759773i	0.534270	+	0.845314i	$0.320587\pi$
$492$	−0.590725	+	1.81806i	−0.0266319	+	0.0819646i
$493$	34.3517			1.54712
$494$	−1.27477	+	3.92334i	−0.0573546	+	0.176519i
$495$	9.60845	−	0.837528i	0.431868	−	0.0376441i
$496$	−3.14712	−	9.68584i	−0.141310	−	0.434907i
$497$	−3.66989	−	11.2948i	−0.164617	−	0.506639i
$498$	23.1070	+	16.7882i	1.03545	+	0.752297i
$499$	39.1002			1.75036			0.875182	−	0.483794i	$-0.160742\pi$
$499$	39.1002			1.75036			0.875182	+	0.483794i	$0.160742\pi$
$500$	−6.08023	−	9.38247i	−0.271916	−	0.419597i
$501$	−66.9492			−2.99107
$502$	22.9188	+	16.6515i	1.02292	+	0.743192i
$503$	2.38177	+	7.33034i	0.106198	+	0.326843i	0.990010	−	0.140999i	$-0.0450314\pi$
$503$	2.38177	+	7.33034i	0.106198	+	0.326843i	−0.883812	+	0.467843i	$0.845031\pi$
$504$	4.39878	+	13.5380i	0.195937	+	0.603033i
$505$	31.6661	−	2.76020i	1.40912	−	0.122827i
$506$	−0.730531	+	2.24834i	−0.0324761	+	0.0999511i
$507$	−13.0298			−0.578675
$508$	4.13743	−	12.7337i	0.183569	−	0.564967i
$509$	−25.6845	+	18.6609i	−1.13845	+	0.827129i	−0.986902	−	0.161321i	$-0.948424\pi$
$509$	−25.6845	+	18.6609i	−1.13845	+	0.827129i	−0.151544	+	0.988451i	$0.548424\pi$
$510$	−37.6622	−	22.6461i	−1.66771	−	1.00279i
$511$	4.04527	+	2.93906i	0.178952	+	0.130016i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−11.8547	+	8.61292i	−0.523396	+	0.380270i
$514$	11.9847	+	8.70741i	0.528624	+	0.384068i
$515$	−12.3360	−	29.0876i	−0.543588	−	1.28175i
$516$	−19.2034	+	13.9521i	−0.845381	+	0.614205i
$517$	−2.40426	+	7.39955i	−0.105739	+	0.325432i
$518$	−12.7443			−0.559954
$519$	−1.42424	+	4.38336i	−0.0625172	+	0.192408i
$520$	−3.60151	−	8.49219i	−0.157937	−	0.372407i
$521$	−9.38617	−	28.8877i	−0.411216	−	1.26559i	−0.915592	−	0.402108i	$-0.868278\pi$
$521$	−9.38617	−	28.8877i	−0.411216	−	1.26559i	0.504377	−	0.863484i	$-0.331722\pi$
$522$	13.1697	+	40.5320i	0.576420	+	1.77404i
$523$	−2.34980	−	1.70723i	−0.102750	−	0.0746520i	0.535224	−	0.844710i	$-0.320227\pi$
$523$	−2.34980	−	1.70723i	−0.102750	−	0.0746520i	−0.637974	+	0.770058i	$0.720227\pi$
$524$	−8.32518			−0.363687
$525$	14.3967	+	27.1182i	0.628324	+	1.18354i
$526$	−18.0423			−0.786681
$527$	−49.9295	−	36.2759i	−2.17496	−	1.58020i
$528$	0.574980	+	1.76961i	0.0250228	+	0.0770122i
$529$	−1.86059	−	5.72630i	−0.0808952	−	0.248970i
$530$	1.83280	−	7.92715i	0.0796119	−	0.344334i
$531$	10.6581	−	32.8023i	0.462523	−	1.42350i
$532$	1.89338			0.0820885
$533$	−0.751389	+	2.31254i	−0.0325463	+	0.100167i
$534$	1.98845	−	1.44469i	0.0860487	−	0.0625180i
$535$	−1.02424	+	0.0892790i	−0.0442819	+	0.00385987i
$536$	6.66829	+	4.84480i	0.288026	+	0.209263i
$537$	37.6039	−	27.3208i	1.62273	−	1.17898i
$538$	−12.9722	+	9.42485i	−0.559271	+	0.406334i
$539$	−1.58512	−	1.15166i	−0.0682760	−	0.0496054i
$540$	7.38086	−	31.9233i	0.317622	−	1.37376i
$541$	−36.2149	+	26.3117i	−1.55700	+	1.13123i	−0.618588	+	0.785716i	$0.712295\pi$
$541$	−36.2149	+	26.3117i	−1.55700	+	1.13123i	−0.938414	+	0.345512i	$0.887705\pi$
$542$	−1.52016	+	4.67857i	−0.0652964	+	0.200962i
$543$	−66.6846			−2.86171
$544$	1.87262	−	5.76335i	0.0802881	−	0.247101i
$545$	9.05982	−	7.87049i	0.388080	−	0.337135i
$546$	7.82780	+	24.0915i	0.334999	+	1.03102i
$547$	−11.7668	−	36.2146i	−0.503114	−	1.54843i	−0.803918	−	0.594740i	$-0.797255\pi$
$547$	−11.7668	−	36.2146i	−0.503114	−	1.54843i	0.300804	−	0.953686i	$-0.402745\pi$
$548$	10.2693	+	7.46105i	0.438681	+	0.318720i
$549$	69.6754			2.97367
$550$	1.34510	+	2.53369i	0.0573554	+	0.108037i
$551$	5.66866			0.241493
$552$	10.8114	+	7.85497i	0.460166	+	0.334330i
$553$	−4.71675	−	14.5167i	−0.200576	−	0.617311i
$554$	5.55688	+	17.1023i	0.236089	+	0.726608i
$555$	41.8327	+	25.1539i	1.77570	+	1.06772i
$556$	2.09314	−	6.44203i	0.0887690	−	0.273203i
$557$	−18.8060			−0.796838			−0.398419	−	0.917204i	$-0.630441\pi$
$557$	−18.8060			−0.796838			−0.398419	+	0.917204i	$0.630441\pi$
$558$	23.6606	−	72.8197i	1.00163	−	3.08270i
$559$	−24.4263	+	17.7467i	−1.03312	+	0.750606i
$560$	−3.19613	+	2.77655i	−0.135061	+	0.117331i
$561$	9.12213	+	6.62761i	0.385137	+	0.279818i
$562$	0.569235	−	0.413573i	0.0240117	−	0.0174455i
$563$	−8.31605	+	6.04196i	−0.350480	+	0.254638i	−0.749070	−	0.662491i	$-0.769499\pi$
$563$	−8.31605	+	6.04196i	−0.350480	+	0.254638i	0.398591	+	0.917129i	$0.369499\pi$
$564$	35.5817	+	25.8516i	1.49826	+	1.08855i
$565$	7.65558	−	6.65059i	0.322073	−	0.279792i
$566$	−5.74465	+	4.17373i	−0.241466	+	0.175435i
$567$	−14.6086	+	44.9607i	−0.613504	+	1.88817i
$568$	−6.27239			−0.263183
$569$	−7.51991	+	23.1439i	−0.315251	+	0.970243i	0.660400	+	0.750914i	$0.270387\pi$
$569$	−7.51991	+	23.1439i	−0.315251	+	0.970243i	−0.975651	+	0.219329i	$0.929613\pi$
$570$	−6.21494	−	3.73702i	−0.260315	−	0.156527i
$571$	−4.58932	−	14.1245i	−0.192057	−	0.591091i	−0.999998	−	0.00182796i	$-0.999418\pi$
$571$	−4.58932	−	14.1245i	−0.192057	−	0.591091i	0.807941	−	0.589263i	$-0.200582\pi$
$572$	0.731361	+	2.25090i	0.0305798	+	0.0941148i
$573$	−8.34854	−	6.06557i	−0.348765	−	0.253393i
$574$	1.11602			0.0465817
$575$	18.5119	+	9.04354i	0.771999	+	0.377142i
$576$	7.51816			0.313257
$577$	−24.1822	−	17.5694i	−1.00672	−	0.731423i	−0.0431995	−	0.999066i	$-0.513755\pi$
$577$	−24.1822	−	17.5694i	−1.00672	−	0.731423i	−0.963518	+	0.267643i	$0.913755\pi$
$578$	−6.09470	−	18.7576i	−0.253506	−	0.780212i
$579$	−19.6662	−	60.5264i	−0.817300	−	2.51539i
$580$	−9.56899	+	8.31282i	−0.397331	+	0.345171i
$581$	5.15271	−	15.8584i	0.213770	−	0.657918i
$582$	49.5198			2.05266
$583$	−0.645094	+	1.98540i	−0.0267171	+	0.0822267i
$584$	2.13653	−	1.55228i	0.0884103	−	0.0642338i
$585$	15.6220	−	67.5675i	0.645890	−	2.79357i
$586$	6.75857	+	4.91039i	0.279194	+	0.202846i
$587$	−25.7455	+	18.7052i	−1.06263	+	0.772047i	−0.974573	−	0.224069i	$-0.928066\pi$
$587$	−25.7455	+	18.7052i	−1.06263	+	0.772047i	−0.0880578	+	0.996115i	$0.528066\pi$
$588$	−8.96049	+	6.51018i	−0.369524	+	0.268475i
$589$	−8.23927	−	5.98618i	−0.339493	−	0.246656i
$590$	10.2195	−	0.890787i	0.420728	−	0.0366731i
$591$	−24.3937	+	17.7231i	−1.00342	+	0.729030i
$592$	−2.07999	+	6.40155i	−0.0854871	+	0.263102i
$593$	−0.0881275			−0.00361896			−0.00180948	−	0.999998i	$-0.500576\pi$
$593$	−0.0881275			−0.00361896			−0.00180948	+	0.999998i	$0.500576\pi$
$594$	−2.59785	+	7.99536i	−0.106591	+	0.328054i
$595$	−5.77939	+	24.9967i	−0.236932	+	1.02477i
$596$	−2.91795	−	8.98051i	−0.119524	−	0.367856i
$597$	−2.06477	−	6.35472i	−0.0845055	−	0.260081i
$598$	13.7519	+	9.99135i	0.562358	+	0.408577i
$599$	−10.4277			−0.426065			−0.213033	−	0.977045i	$-0.568334\pi$
$599$	−10.4277			−0.426065			−0.213033	+	0.977045i	$0.568334\pi$
$600$	15.9713	−	2.80562i	0.652026	−	0.114539i
$601$	7.45955			0.304282			0.152141	−	0.988359i	$-0.451383\pi$
$601$	7.45955			0.304282			0.152141	+	0.988359i	$0.451383\pi$
$602$	11.2110	+	8.14529i	0.456928	+	0.331977i
$603$	19.1492	+	58.9352i	0.779816	+	2.40003i
$604$	−4.99751	−	15.3808i	−0.203346	−	0.625834i
$605$	9.31609	+	21.9669i	0.378753	+	0.893082i
$606$	−14.2464	+	43.8460i	−0.578721	+	1.78112i
$607$	26.9823			1.09518			0.547590	−	0.836747i	$-0.315546\pi$
$607$	26.9823			1.09518			0.547590	+	0.836747i	$0.315546\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	28.1609	−	20.4601i	1.14114	−	0.829084i
$610$	8.09101	+	19.0782i	0.327595	+	0.772455i
$611$	45.2591	+	32.8827i	1.83099	+	1.33029i
$612$	36.8585	−	26.7793i	1.48992	−	1.08249i
$613$	10.3233	−	7.50031i	0.416954	−	0.302935i	−0.359457	−	0.933162i	$-0.617038\pi$
$613$	10.3233	−	7.50031i	0.416954	−	0.302935i	0.776411	+	0.630227i	$0.217038\pi$
$614$	−18.6432	−	13.5451i	−0.752379	−	0.546636i
$615$	−3.66328	−	2.20272i	−0.147718	−	0.0888221i
$616$	0.878812	−	0.638494i	0.0354083	−	0.0257257i
$617$	1.87269	−	5.76356i	0.0753918	−	0.232032i	−0.906258	−	0.422725i	$-0.861074\pi$
$617$	1.87269	−	5.76356i	0.0753918	−	0.232032i	0.981650	+	0.190693i	$0.0610736\pi$
$618$	45.8256			1.84338
$619$	−6.06318	+	18.6606i	−0.243700	+	0.750031i	0.752148	+	0.658995i	$0.229018\pi$
$619$	−6.06318	+	18.6606i	−0.243700	+	0.750031i	−0.995848	+	0.0910365i	$0.970982\pi$
$620$	22.6868	−	1.97751i	0.911122	−	0.0794187i
$621$	18.6582	+	57.4241i	0.748729	+	2.30435i
$622$	1.17856	+	3.62723i	0.0472558	+	0.145439i
$623$	−1.16087	−	0.843420i	−0.0465092	−	0.0337909i
$624$	13.3789			0.535583
$625$	23.5033	−	8.52039i	0.940130	−	0.340815i
$626$	16.3116			0.651943
$627$	1.50532	+	1.09368i	0.0601165	+	0.0436772i
$628$	−4.86093	−	14.9604i	−0.193972	−	0.596985i
$629$	12.6046	+	38.7930i	0.502579	+	1.54678i
$630$	−31.7096	+	2.76400i	−1.26334	+	0.110120i
$631$	−12.0376	+	37.0479i	−0.479209	+	1.47485i	0.360987	+	0.932571i	$0.382440\pi$
$631$	−12.0376	+	37.0479i	−0.479209	+	1.47485i	−0.840196	+	0.542282i	$0.817560\pi$
$632$	−8.06162			−0.320674
$633$	14.1561	−	43.5680i	0.562654	−	1.73167i
$634$	7.44280	−	5.40751i	0.295591	−	0.214760i
$635$	25.6576	+	15.4278i	1.01819	+	0.612234i
$636$	9.54702	+	6.93632i	0.378564	+	0.275043i
$637$	−11.3975	+	8.28080i	−0.451587	+	0.328097i
$638$	2.63111	−	1.91161i	0.104166	−	0.0756814i
$639$	−38.1507	−	27.7181i	−1.50922	−	1.09651i
$640$	0.873042	+	2.05859i	0.0345100	+	0.0813730i
$641$	−7.37373	+	5.35733i	−0.291245	+	0.211602i	−0.723807	−	0.690002i	$-0.757610\pi$
$641$	−7.37373	+	5.35733i	−0.291245	+	0.211602i	0.432562	+	0.901604i	$0.357610\pi$
$642$	0.460802	−	1.41820i	0.0181864	−	0.0559720i
$643$	35.0792			1.38339			0.691695	−	0.722190i	$-0.256864\pi$
$643$	35.0792			1.38339			0.691695	+	0.722190i	$0.256864\pi$
$644$	2.41089	−	7.41994i	0.0950022	−	0.292387i
$645$	−20.7231	−	48.8641i	−0.815971	−	1.92402i
$646$	−1.87262	−	5.76335i	−0.0736774	−	0.226756i
$647$	−8.11194	−	24.9660i	−0.318913	−	0.981514i	−0.974114	−	0.226059i	$-0.927416\pi$
$647$	−8.11194	−	24.9660i	−0.318913	−	0.981514i	0.655200	−	0.755455i	$-0.272584\pi$
$648$	20.1998	+	14.6760i	0.793521	+	0.576527i
$649$	−2.63200			−0.103315
$650$	20.3151	−	3.56869i	0.796825	−	0.139975i
$651$	−62.5373			−2.45103
$652$	1.95207	+	1.41826i	0.0764488	+	0.0555433i
$653$	12.3756	+	38.0881i	0.484294	+	1.49050i	0.833001	+	0.553272i	$0.186621\pi$
$653$	12.3756	+	38.0881i	0.484294	+	1.49050i	−0.348706	+	0.937232i	$0.613379\pi$
$654$	5.37881	+	16.5543i	0.210328	+	0.647323i
$655$	4.19342	−	18.1372i	0.163851	−	0.708679i
$656$	0.182144	−	0.560582i	0.00711153	−	0.0218871i
$657$	19.8547			0.774605
$658$	7.93450	−	24.4199i	0.309319	−	0.951986i
$659$	−35.1331	+	25.5257i	−1.36859	+	0.994339i	−0.370745	+	0.928735i	$0.620897\pi$
$659$	−35.1331	+	25.5257i	−1.36859	+	0.994339i	−0.997846	+	0.0656043i	$0.979103\pi$
$660$	−4.14488	+	0.361291i	−0.161339	+	0.0140633i
$661$	−0.196513	−	0.142775i	−0.00764347	−	0.00555330i	0.583957	−	0.811785i	$-0.301504\pi$
$661$	−0.196513	−	0.142775i	−0.00764347	−	0.00555330i	−0.591600	+	0.806231i	$0.701504\pi$
$662$	14.5266	−	10.5542i	0.564591	−	0.410199i
$663$	65.5912	−	47.6548i	2.54735	−	1.85076i
$664$	−7.12480	−	5.17647i	−0.276496	−	0.200886i
$665$	−0.953704	+	4.12491i	−0.0369830	+	0.159957i
$666$	−40.9400	+	29.7447i	−1.58639	+	1.15258i
$667$	7.21803	−	22.2148i	0.279483	−	0.860161i
$668$	20.6431			0.798706
$669$	−21.4976	+	66.1627i	−0.831144	+	2.55800i
$670$	−13.9137	+	12.0872i	−0.537533	+	0.466968i
$671$	−1.64305	−	5.05678i	−0.0634292	−	0.195215i
$672$	−1.89754	−	5.84002i	−0.0731991	−	0.225284i
$673$	6.88431	+	5.00174i	0.265371	+	0.192803i	0.712511	−	0.701661i	$-0.247558\pi$
$673$	6.88431	+	5.00174i	0.265371	+	0.192803i	−0.447141	+	0.894464i	$0.647558\pi$
$674$	4.77415			0.183894
$675$	65.8303	+	32.1598i	2.53381	+	1.23783i
$676$	4.01762			0.154524
$677$	3.90270	+	2.83548i	0.149993	+	0.108976i	0.660251	−	0.751045i	$-0.270450\pi$
$677$	3.90270	+	2.83548i	0.149993	+	0.108976i	−0.510258	+	0.860021i	$0.670450\pi$
$678$	4.54511	+	13.9884i	0.174554	+	0.537222i
$679$	−8.93366	−	27.4950i	−0.342842	−	1.05516i
$680$	11.6128	+	6.98271i	0.445329	+	0.267775i
$681$	8.04499	−	24.7599i	0.308285	−	0.948802i
$682$	−5.84294			−0.223738
$683$	2.86001	−	8.80220i	0.109435	−	0.336807i	−0.881311	−	0.472537i	$-0.843338\pi$
$683$	2.86001	−	8.80220i	0.109435	−	0.336807i	0.990746	+	0.135731i	$0.0433382\pi$
$684$	6.08232	−	4.41906i	0.232563	−	0.168967i
$685$	−21.4273	+	18.6144i	−0.818694	+	0.711220i
$686$	15.9536	+	11.5910i	0.609112	+	0.442546i
$687$	56.7316	−	41.2179i	2.16444	−	1.57256i
$688$	5.92117	−	4.30198i	0.225742	−	0.164012i
$689$	12.1436	+	8.82284i	0.462634	+	0.336124i
$690$	−22.5586	+	19.5972i	−0.858791	+	0.746052i
$691$	20.2111	−	14.6843i	0.768868	−	0.558615i	−0.132749	−	0.991150i	$-0.542381\pi$
$691$	20.2111	−	14.6843i	0.768868	−	0.558615i	0.901617	+	0.432534i	$0.142381\pi$
$692$	0.439150	−	1.35157i	0.0166940	−	0.0513788i
$693$	8.16676			0.310230
$694$	1.54092	−	4.74248i	0.0584927	−	0.180022i
$695$	12.9803	+	7.80499i	0.492369	+	0.296060i
$696$	−5.68110	−	17.4846i	−0.215342	−	0.662753i
$697$	−1.10378	−	3.39709i	−0.0418087	−	0.128674i
$698$	−24.2788	−	17.6395i	−0.918964	−	0.667667i
$699$	−3.23739			−0.122449
$700$	−4.43909	−	8.36163i	−0.167782	−	0.316040i
$701$	26.0406			0.983541			0.491770	−	0.870725i	$-0.336350\pi$
$701$	26.0406			0.983541			0.491770	+	0.870725i	$0.336350\pi$
$702$	48.9034	+	35.5304i	1.84574	+	1.34101i
$703$	2.07999	+	6.40155i	0.0784483	+	0.241439i
$704$	−0.177289	−	0.545640i	−0.00668184	−	0.0205646i
$705$	−74.2428	+	64.4966i	−2.79615	+	2.42908i
$706$	−2.77384	+	8.53701i	−0.104395	+	0.321295i
$707$	26.9148			1.01224
$708$	−4.59768	+	14.1502i	−0.172791	+	0.531797i
$709$	−13.5436	+	9.83997i	−0.508639	+	0.369548i	−0.812307	−	0.583230i	$-0.801789\pi$
$709$	−13.5436	+	9.83997i	−0.508639	+	0.369548i	0.303668	+	0.952778i	$0.401789\pi$
$710$	3.15943	−	13.6650i	0.118571	−	0.512838i
$711$	−49.0333	−	35.6248i	−1.83889	−	1.33603i
$712$	−0.613119	+	0.445457i	−0.0229776	+	0.0166942i
$713$	−33.9504	+	24.6664i	−1.27145	+	0.923764i
$714$	−30.1047	−	21.8723i	−1.12664	−	0.818551i
$715$	−5.27219	+	0.459555i	−0.197169	+	0.0171864i
$716$	−11.5948	+	8.42410i	−0.433317	+	0.314823i
$717$	−1.09623	+	3.37386i	−0.0409395	+	0.125999i
$718$	1.78436			0.0665917
$719$	4.90732	−	15.1032i	0.183012	−	0.563253i	−0.816896	−	0.576784i	$-0.804307\pi$
$719$	4.90732	−	15.1032i	0.183012	−	0.563253i	0.999908	+	0.0135313i	$0.00430729\pi$
$720$	−3.78693	+	16.3790i	−0.141130	+	0.610411i
$721$	−8.26720	−	25.4438i	−0.307887	−	0.947578i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	−1.16683	−	0.847750i	−0.0433948	−	0.0315282i
$724$	20.5615			0.764164
$725$	−13.2903	−	25.0342i	−0.493591	−	0.929746i
$726$	−34.6074			−1.28440
$727$	26.9381	+	19.5717i	0.999079	+	0.725873i	0.961890	−	0.273435i	$-0.0881599\pi$
$727$	26.9381	+	19.5717i	0.999079	+	0.725873i	0.0371881	+	0.999308i	$0.488160\pi$
$728$	−2.41363	−	7.42837i	−0.0894549	−	0.275314i
$729$	13.9513	+	42.9376i	0.516713	+	1.59028i
$730$	2.30561	+	5.43653i	0.0853346	+	0.201215i
$731$	13.7057	−	42.1817i	0.506923	−	1.56015i
$732$	−30.0565			−1.11092
$733$	7.10475	−	21.8662i	0.262420	−	0.807646i	−0.729857	−	0.683600i	$-0.760413\pi$
$733$	7.10475	−	21.8662i	0.262420	−	0.807646i	0.992277	−	0.124045i	$-0.0395868\pi$
$734$	2.93305	−	2.13098i	0.108261	−	0.0786560i
$735$	−9.66962	−	22.8005i	−0.356669	−	0.841009i
$736$	−3.33360	−	2.42200i	−0.122878	−	0.0892763i
$737$	3.82573	−	2.77956i	0.140923	−	0.102386i
$738$	3.58511	−	2.60473i	0.131970	−	0.0958815i
$739$	−21.8434	−	15.8702i	−0.803524	−	0.583794i	0.108422	−	0.994105i	$-0.465420\pi$
$739$	−21.8434	−	15.8702i	−0.803524	−	0.583794i	−0.911946	+	0.410311i	$0.865420\pi$
$740$	−12.8987	−	7.75595i	−0.474166	−	0.285114i
$741$	10.8237	−	7.86390i	0.397620	−	0.288888i
$742$	2.12893	−	6.55217i	0.0781554	−	0.240538i
$743$	37.6912			1.38275			0.691377	−	0.722494i	$-0.257004\pi$
$743$	37.6912			1.38275			0.691377	+	0.722494i	$0.257004\pi$
$744$	−10.2067	+	31.4128i	−0.374194	+	1.15165i
$745$	21.0347	−	1.83351i	0.770652	−	0.0671745i
$746$	−7.05960	−	21.7272i	−0.258470	−	0.795489i
$747$	−20.4602	−	62.9699i	−0.748598	−	2.30395i
$748$	−2.81272	−	2.04356i	−0.102843	−	0.0747199i
$749$	−0.870562			−0.0318097
$750$	−1.93250	+	36.2082i	−0.0705648	+	1.32214i
$751$	18.3752			0.670519			0.335259	−	0.942126i	$-0.391176\pi$
$751$	18.3752			0.670519			0.335259	+	0.942126i	$0.391176\pi$
$752$	−10.9713	−	7.97109i	−0.400081	−	0.290676i
$753$	−28.3914	−	87.3797i	−1.03464	−	3.18429i
$754$	−7.22624	−	22.2401i	−0.263164	−	0.809935i
$755$	36.0257	−	3.14021i	1.31111	−	0.114284i
$756$	8.57338	−	26.3862i	0.311811	−	0.959655i
$757$	−28.5442			−1.03746			−0.518729	−	0.854939i	$-0.673595\pi$
$757$	−28.5442			−1.03746			−0.518729	+	0.854939i	$0.673595\pi$
$758$	4.13524	−	12.7270i	0.150199	−	0.462264i
$759$	6.20275	−	4.50656i	0.225145	−	0.163578i
$760$	1.91632	+	1.15227i	0.0695121	+	0.0417974i
$761$	10.3498	+	7.51956i	0.375179	+	0.272584i	0.759355	−	0.650676i	$-0.225514\pi$
$761$	10.3498	+	7.51956i	0.375179	+	0.272584i	−0.384176	+	0.923260i	$0.625514\pi$
$762$	−35.1298	+	25.5233i	−1.27262	+	0.924612i
$763$	8.22110	−	5.97298i	0.297624	−	0.216236i
$764$	2.57419	+	1.87026i	0.0931310	+	0.0676636i
$765$	39.7754	+	93.7886i	1.43808	+	3.39093i
$766$	−25.9508	+	18.8544i	−0.937641	+	0.681236i
$767$	−5.84814	+	17.9987i	−0.211164	+	0.649896i
$768$	−3.24317			−0.117028
$769$	4.44445	−	13.6786i	0.160271	−	0.493263i	−0.838386	−	0.545077i	$-0.816500\pi$
$769$	4.44445	−	13.6786i	0.160271	−	0.493263i	0.998657	+	0.0518141i	$0.0165003\pi$
$770$	0.948360	+	2.23619i	0.0341765	+	0.0805867i
$771$	−14.8465	−	45.6927i	−0.534682	−	1.64558i
$772$	6.06388	+	18.6627i	0.218244	+	0.671685i
$773$	15.0235	+	10.9152i	0.540358	+	0.392593i	0.824218	−	0.566273i	$-0.191615\pi$
$773$	15.0235	+	10.9152i	0.540358	+	0.392593i	−0.283860	+	0.958866i	$0.591615\pi$
$774$	55.0252			1.97784
$775$	−7.11921	+	50.4214i	−0.255730	+	1.81119i
$776$	−15.2689			−0.548123
$777$	33.4383	+	24.2944i	1.19959	+	0.871556i
$778$	7.12837	+	21.9389i	0.255564	+	0.786546i
$779$	−0.182144	−	0.560582i	−0.00652599	−	0.0200849i
$780$	−6.73899	+	29.1471i	−0.241294	+	1.04364i
$781$	−1.11203	+	3.42247i	−0.0397915	+	0.122466i
$782$	−24.9703			−0.892938
$783$	25.6681	−	78.9984i	0.917305	−	2.82317i
$784$	2.76288	−	2.00735i	0.0986743	−	0.0716911i
$785$	35.0411	−	3.05439i	1.25067	−	0.109016i
$786$	21.8434	+	15.8702i	0.779130	+	0.566071i
$787$	20.0756	−	14.5858i	0.715617	−	0.519926i	−0.169364	−	0.985554i	$-0.554171\pi$
$787$	20.0756	−	14.5858i	0.715617	−	0.519926i	0.884981	+	0.465627i	$0.154171\pi$
$788$	7.52157	−	5.46474i	0.267945	−	0.194673i
$789$	47.3390	+	34.3938i	1.68531	+	1.22445i
$790$	4.06067	−	17.5630i	0.144472	−	0.624864i
$791$	6.94685	−	5.04718i	0.247002	−	0.179457i
$792$	1.33289	−	4.10221i	0.0473622	−	0.145766i
$793$	−38.2311			−1.35763
$794$	−7.07148	+	21.7638i	−0.250957	+	0.772368i
$795$	−19.9203	+	17.3053i	−0.706501	+	0.613754i
$796$	0.636652	+	1.95941i	0.0225655	+	0.0694496i
$797$	−0.0107365	−	0.0330436i	−0.000380307	−	0.00117046i	0.950866	−	0.309602i	$-0.100196\pi$
$797$	−0.0107365	−	0.0330436i	−0.000380307	−	0.00117046i	−0.951246	+	0.308432i	$0.900196\pi$
$798$	−4.96782	−	3.60933i	−0.175859	−	0.127769i
$799$	−82.1802			−2.90733
$800$	−4.92459	+	0.865085i	−0.174111	+	0.0305854i
$801$	−5.69769			−0.201318
$802$	−15.3344	−	11.1411i	−0.541476	−	0.393405i
$803$	−0.468203	−	1.44098i	−0.0165225	−	0.0508511i
$804$	−8.26055	−	25.4234i	−0.291327	−	0.896613i
$805$	14.9507	+	8.98980i	0.526943	+	0.316849i
$806$	−12.9826	+	39.9564i	−0.457294	+	1.40741i
$807$	52.0027			1.83058
$808$	4.39274	−	13.5195i	0.154536	−	0.475613i
$809$	7.83146	−	5.68989i	0.275340	−	0.200046i	−0.441543	−	0.897240i	$-0.645569\pi$
$809$	7.83146	−	5.68989i	0.275340	−	0.200046i	0.716882	+	0.697194i	$0.245569\pi$
$810$	−42.1477	+	36.6148i	−1.48092	+	1.28651i
$811$	4.97682	+	3.61587i	0.174760	+	0.126970i	0.671727	−	0.740799i	$-0.265553\pi$
$811$	4.97682	+	3.61587i	0.174760	+	0.126970i	−0.496967	+	0.867769i	$0.665553\pi$
$812$	−8.68313	+	6.30866i	−0.304718	+	0.221391i
$813$	12.9073	−	9.37768i	0.452678	−	0.328890i
$814$	3.12419	+	2.26985i	0.109503	+	0.0795583i
$815$	−4.07308	+	3.53838i	−0.142674	+	0.123944i
$816$	−15.9000	+	11.5520i	−0.556610	+	0.404401i
$817$	2.26169	−	6.96075i	0.0791264	−	0.243526i
$818$	32.8241			1.14767
$819$	18.1460	−	55.8477i	0.634073	−	1.95148i
$820$	1.12954	+	0.679186i	0.0394451	+	0.0237182i
$821$	4.52842	+	13.9370i	0.158043	+	0.486406i	0.998456	−	0.0555395i	$-0.0176879\pi$
$821$	4.52842	+	13.9370i	0.158043	+	0.486406i	−0.840414	+	0.541946i	$0.817688\pi$
$822$	−12.7214	−	39.1523i	−0.443708	−	1.36559i
$823$	4.33625	+	3.15047i	0.151152	+	0.109818i	0.660791	−	0.750570i	$-0.270221\pi$
$823$	4.33625	+	3.15047i	0.151152	+	0.109818i	−0.509639	+	0.860388i	$0.670221\pi$
$824$	−14.1299			−0.492237
$825$	1.30068	−	9.21200i	0.0452839	−	0.320721i
$826$	8.68609			0.302228
$827$	32.1379	+	23.3495i	1.11754	+	0.811943i	0.983835	−	0.179078i	$-0.0573114\pi$
$827$	32.1379	+	23.3495i	1.11754	+	0.811943i	0.133708	+	0.991021i	$0.457311\pi$
$828$	−9.57305	−	29.4628i	−0.332686	−	1.02390i
$829$	7.70189	+	23.7040i	0.267498	+	0.823273i	0.991107	+	0.133064i	$0.0424816\pi$
$829$	7.70189	+	23.7040i	0.267498	+	0.823273i	−0.723610	+	0.690209i	$0.757518\pi$
$830$	14.8662	−	12.9147i	0.516015	−	0.448274i
$831$	18.0219	−	55.4658i	0.625174	−	1.92409i
$832$	−4.12524			−0.143017
$833$	6.39521	−	19.6824i	0.221581	−	0.681956i
$834$	−17.7723	+	12.9123i	−0.615405	+	0.447118i
$835$	−10.3980	+	44.9730i	−0.359838	+	1.55636i
$836$	−0.464150	−	0.337224i	−0.0160529	−	0.0116631i
$837$	−120.731	+	87.7165i	−4.17309	+	3.03193i
$838$	19.8735	−	14.4389i	0.686518	−	0.498785i
$839$	−14.9175	−	10.8382i	−0.515009	−	0.374176i	0.299712	−	0.954030i	$-0.403110\pi$
$839$	−14.9175	−	10.8382i	−0.515009	−	0.374176i	−0.814720	+	0.579854i	$0.803110\pi$
$840$	13.6788	−	1.19233i	0.471965	−	0.0411392i
$841$	−2.53522	+	1.84194i	−0.0874214	+	0.0635153i
$842$	1.97747	−	6.08602i	0.0681480	−	0.209738i
$843$	−2.28194			−0.0785941
$844$	−4.36489	+	13.4338i	−0.150246	+	0.462409i
$845$	−2.02369	+	8.75277i	−0.0696170	+	0.301104i
$846$	−31.5060	−	96.9654i	−1.08320	−	3.33374i
$847$	6.24337	+	19.2151i	0.214525	+	0.660240i
$848$	−2.94373	−	2.13875i	−0.101088	−	0.0734448i
$849$	23.0290			0.790355
$850$	−21.0619	+	21.7823i	−0.722417	+	0.747126i
$851$	27.7354			0.950759
$852$	16.4574	+	11.9570i	0.563820	+	0.409639i
$853$	−6.33094	−	19.4846i	−0.216767	−	0.667141i	−0.999023	−	0.0441843i	$-0.985931\pi$
$853$	−6.33094	−	19.4846i	−0.216767	−	0.667141i	0.782256	−	0.622957i	$-0.214069\pi$
$854$	5.42236	+	16.6883i	0.185549	+	0.571062i
$855$	6.56367	+	15.4768i	0.224473	+	0.529296i
$856$	−0.142084	+	0.437289i	−0.00485632	+	0.0149462i
$857$	34.7818			1.18812			0.594061	−	0.804420i	$-0.297524\pi$
$857$	34.7818			1.18812			0.594061	+	0.804420i	$0.297524\pi$
$858$	2.37193	−	7.30005i	0.0809764	−	0.249220i
$859$	−45.4807	+	33.0437i	−1.55178	+	1.12744i	−0.609416	+	0.792850i	$0.708596\pi$
$859$	−45.4807	+	33.0437i	−1.55178	+	1.12744i	−0.942365	+	0.334585i	$0.891404\pi$
$860$	6.38977	+	15.0668i	0.217889	+	0.513772i
$861$	−2.92819	−	2.12745i	−0.0997923	−	0.0725033i
$862$	−11.6138	+	8.43793i	−0.395568	+	0.287397i
$863$	1.00573	−	0.730707i	0.0342355	−	0.0248736i	−0.570536	−	0.821273i	$-0.693264\pi$
$863$	1.00573	−	0.730707i	0.0342355	−	0.0248736i	0.604771	+	0.796399i	$0.293264\pi$
$864$	−11.8547	−	8.61292i	−0.403304	−	0.293017i
$865$	2.72331	+	1.63752i	0.0925955	+	0.0556774i
$866$	−2.46057	+	1.78771i	−0.0836135	+	0.0607488i
$867$	−19.7662	+	60.8340i	−0.671294	+	2.06603i
$868$	19.2828			0.654499
$869$	−1.42924	+	4.39874i	−0.0484836	+	0.149217i
$870$	40.9536	−	3.56975i	1.38846	−	0.121026i
$871$	−10.5072	−	32.3380i	−0.356024	−	1.09573i
$872$	−1.65850	−	5.10435i	−0.0561640	−	0.172855i
$873$	−92.8706	−	67.4745i	−3.14319	−	2.28366i
$874$	−4.12056			−0.139380
$875$	20.4526	−	5.45919i	0.691424	−	0.184554i
$876$	−8.56488			−0.289381
$877$	−33.4077	−	24.2721i	−1.12810	−	0.819611i	−0.142681	−	0.989769i	$-0.545572\pi$
$877$	−33.4077	−	24.2721i	−1.12810	−	0.819611i	−0.985417	+	0.170158i	$0.945572\pi$
$878$	−10.3784	−	31.9414i	−0.350254	−	1.07797i
$879$	−8.37239	−	25.7676i	−0.282394	−	0.869119i
$880$	1.27803	−	0.111401i	0.0430824	−	0.00375532i
$881$	−0.443765	+	1.36577i	−0.0149508	+	0.0460139i	−0.958254	−	0.285920i	$-0.907701\pi$
$881$	−0.443765	+	1.36577i	−0.0149508	+	0.0460139i	0.943303	+	0.331934i	$0.107701\pi$
$882$	25.6753			0.864533
$883$	−5.02120	+	15.4537i	−0.168977	+	0.520057i	−0.999307	−	0.0372141i	$-0.988152\pi$
$883$	−5.02120	+	15.4537i	−0.168977	+	0.520057i	0.830331	+	0.557271i	$0.188152\pi$
$884$	−20.2244	+	14.6939i	−0.680220	+	0.494209i
$885$	−28.5117	−	17.1440i	−0.958410	−	0.576289i
$886$	13.9584	+	10.1414i	0.468941	+	0.340706i
$887$	−23.2919	+	16.9226i	−0.782066	+	0.568204i	−0.905598	−	0.424136i	$-0.860578\pi$
$887$	−23.2919	+	16.9226i	−0.782066	+	0.568204i	0.123532	+	0.992341i	$0.460578\pi$
$888$	17.6606	−	12.8312i	0.592652	−	0.430587i
$889$	20.5090	+	14.9007i	0.687849	+	0.499752i
$890$	−0.661641	−	1.56012i	−0.0221783	−	0.0522953i
$891$	11.5890	−	8.41991i	0.388246	−	0.282078i
$892$	6.62856	−	20.4006i	0.221941	−	0.683063i
$893$	−13.5612			−0.453809
$894$	−9.46340	+	29.1253i	−0.316503	+	0.974097i
$895$	−12.5124	−	29.5036i	−0.418243	−	0.986196i
$896$	0.585087	+	1.80071i	0.0195464	+	0.0601576i
$897$	−17.0356	−	52.4302i	−0.568803	−	1.75059i
$898$	13.2769	+	9.64622i	0.443055	+	0.321898i
$899$	57.7313			1.92545
$900$	−33.7758	−	16.5004i	−1.12586	−	0.550012i
$901$	−22.0500			−0.734592
$902$	−0.273584	−	0.198770i	−0.00910935	−	0.00661833i
$903$	−13.8880	−	42.7429i	−0.462164	−	1.42240i
$904$	−1.40144	−	4.31319i	−0.0466112	−	0.143455i
$905$	−10.3569	+	44.7953i	−0.344276	+	1.48905i
$906$	−16.2078	+	49.8824i	−0.538468	+	1.65723i
$907$	−3.78140			−0.125559			−0.0627797	−	0.998027i	$-0.519997\pi$
$907$	−3.78140			−0.125559			−0.0627797	+	0.998027i	$0.519997\pi$
$908$	−2.48059	+	7.63448i	−0.0823214	+	0.253359i
$909$	86.4615	−	62.8180i	2.86775	−	2.08354i
$910$	17.3992	−	1.51661i	0.576777	−	0.0502753i
$911$	−39.6286	−	28.7918i	−1.31295	−	0.953916i	−0.999991	−	0.00415022i	$-0.998679\pi$
$911$	−39.6286	−	28.7918i	−1.31295	−	0.953916i	−0.312961	−	0.949766i	$-0.601321\pi$
$912$	−2.62378	+	1.90629i	−0.0868821	+	0.0631235i
$913$	−4.08764	+	2.96985i	−0.135281	+	0.0982876i
$914$	−31.1259	−	22.6143i	−1.02955	−	0.748014i
$915$	15.1396	−	65.4809i	0.500498	−	2.16473i
$916$	−17.4926	+	12.7091i	−0.577972	+	0.419922i
$917$	4.87095	−	14.9913i	0.160853	−	0.495055i
$918$	−88.7974			−2.93075
$919$	−10.2494	+	31.5443i	−0.338095	+	1.04055i	0.627082	+	0.778953i	$0.284249\pi$
$919$	−10.2494	+	31.5443i	−0.338095	+	1.04055i	−0.965177	+	0.261596i	$0.915751\pi$
$920$	6.95572	−	6.04260i	0.229323	−	0.199219i
$921$	23.0949	+	71.0787i	0.761002	+	2.34212i
$922$	6.54937	+	20.1569i	0.215692	+	0.663831i
$923$	20.9334	+	15.2090i	0.689031	+	0.500610i
$924$	−3.52296			−0.115897
$925$	23.3942	−	24.1944i	0.769197	−	0.795506i
$926$	29.6589			0.974653
$927$	−85.9424	−	62.4408i	−2.82272	−	2.05083i
$928$	1.75171	+	5.39122i	0.0575028	+	0.176975i
$929$	−2.54041	−	7.81857i	−0.0833480	−	0.256519i	0.900694	−	0.434453i	$-0.143058\pi$
$929$	−2.54041	−	7.81857i	−0.0833480	−	0.256519i	−0.984042	+	0.177935i	$0.943058\pi$
$930$	−63.2948	−	38.0589i	−2.07552	−	1.24800i
$931$	1.05533	−	3.24796i	0.0345869	−	0.106448i
$932$	0.998216			0.0326977
$933$	3.82226	−	11.7637i	0.125135	−	0.385127i
$934$	−13.2928	+	9.65776i	−0.434953	+	0.316012i
$935$	5.86887	−	5.09843i	0.191933	−	0.166736i
$936$	−25.0910	−	18.2297i	−0.820126	−	0.595857i
$937$	27.4307	−	19.9296i	0.896122	−	0.651071i	−0.0413451	−	0.999145i	$-0.513164\pi$
$937$	27.4307	−	19.9296i	0.896122	−	0.651071i	0.937467	+	0.348074i	$0.113164\pi$
$938$	−12.6256	+	9.17305i	−0.412241	+	0.299511i
$939$	−42.7981	−	31.0946i	−1.39666	−	1.01473i
$940$	22.8921	−	19.8869i	0.746656	−	0.648639i
$941$	40.3101	−	29.2870i	1.31407	−	0.954729i	0.314086	−	0.949394i	$-0.398302\pi$
$941$	40.3101	−	29.2870i	1.31407	−	0.954729i	0.999986	−	0.00533479i	$-0.00169813\pi$
$942$	−15.7648	+	48.5191i	−0.513646	+	1.58084i
$943$	−2.42878			−0.0790921
$944$	1.41765	−	4.36307i	0.0461405	−	0.142006i
$945$	53.1663	+	31.9687i	1.72950	+	1.03994i
$946$	−1.29757	−	3.99353i	−0.0421878	−	0.129841i
$947$	−7.01613	−	21.5934i	−0.227994	−	0.701693i	−0.997974	−	0.0636248i	$-0.979734\pi$
$947$	−7.01613	−	21.5934i	−0.227994	−	0.701693i	0.769980	−	0.638068i	$-0.220266\pi$
$948$	21.1519	+	15.3678i	0.686982	+	0.499122i
$949$	−10.8943			−0.353645
$950$	−3.47560	+	3.59447i	−0.112763	+	0.116620i
$951$	−29.8365			−0.967516
$952$	9.28248	+	6.74412i	0.300847	+	0.218578i
$953$	−3.41016	−	10.4954i	−0.110466	−	0.339979i	0.880509	−	0.474030i	$-0.157201\pi$
$953$	−3.41016	−	10.4954i	−0.110466	−	0.339979i	−0.990974	+	0.134051i	$0.957201\pi$
$954$	−8.45346	−	26.0171i	−0.273691	−	0.842334i
$955$	−5.37117	+	4.66607i	−0.173807	+	0.150990i
$956$	0.338012	−	1.04030i	0.0109321	−	0.0336455i
$957$	−10.5475			−0.340953
$958$	−8.07187	+	24.8426i	−0.260790	+	0.802630i
$959$	−19.4436	+	14.1266i	−0.627867	+	0.456172i
$960$	1.63360	−	7.06556i	0.0527242	−	0.228040i
$961$	−58.8316	−	42.7437i	−1.89779	−	1.37883i
$962$	22.4639	−	16.3210i	0.724267	−	0.526210i
$963$	−2.79660	+	2.03185i	−0.0901193	+	0.0654755i
$964$	0.359780	+	0.261395i	0.0115877	+	0.00841898i
$965$	−43.7129	+	3.81027i	−1.40717	+	0.122657i
$966$	−20.4702	+	14.8725i	−0.658618	+	0.478514i
$967$	0.104684	−	0.322185i	0.00336642	−	0.0103608i	−0.949359	−	0.314193i	$-0.898266\pi$
$967$	0.104684	−	0.322185i	0.00336642	−	0.0103608i	0.952726	+	0.303832i	$0.0982662\pi$
$968$	10.6708			0.342974
$969$	−6.07324	+	18.6915i	−0.195101	+	0.600458i
$970$	7.69103	−	33.2649i	0.246944	−	1.06807i
$971$	15.2511	+	46.9380i	0.489430	+	1.50631i	0.825461	+	0.564460i	$0.190915\pi$
$971$	15.2511	+	46.9380i	0.489430	+	1.50631i	−0.336031	+	0.941851i	$0.609085\pi$
$972$	−11.4388	−	35.2051i	−0.366901	−	1.12920i
$973$	10.3756	+	7.53829i	0.332626	+	0.241667i
$974$	7.81877			0.250529
$975$	−60.1054	−	29.3631i	−1.92491	−	0.940371i
$976$	9.26761			0.296649
$977$	32.4259	+	23.5588i	1.03740	+	0.753712i	0.969776	−	0.243999i	$-0.0784593\pi$
$977$	32.4259	+	23.5588i	1.03740	+	0.753712i	0.0676205	+	0.997711i	$0.478459\pi$
$978$	−2.41818	−	7.44240i	−0.0773250	−	0.237982i
$979$	0.134360	+	0.413518i	0.00429416	+	0.0132161i
$980$	2.98153	+	7.03031i	0.0952415	+	0.224575i
$981$	12.4689	−	38.3753i	0.398101	−	1.22523i
$982$	−2.86422			−0.0914008
$983$	6.21823	−	19.1377i	0.198331	−	0.610399i	−0.801591	−	0.597873i	$-0.796013\pi$
$983$	6.21823	−	19.1377i	0.198331	−	0.610399i	0.999922	−	0.0125263i	$-0.00398734\pi$
$984$	−1.54654	+	1.12363i	−0.0493018	+	0.0358199i
$985$	8.11681	+	19.1391i	0.258623	+	0.609821i
$986$	27.7911	+	20.1914i	0.885050	+	0.643027i
$987$	−67.3697	+	48.9469i	−2.14440	+	1.55800i
$988$	−3.33739	+	2.42476i	−0.106177	+	0.0771418i
$989$	−24.3985	−	17.7266i	−0.775828	−	0.563672i
$990$	8.26568	+	4.97013i	0.262701	+	0.157961i
$991$	−37.7319	+	27.4139i	−1.19859	+	0.870830i	−0.994146	−	0.108047i	$-0.965540\pi$
$991$	−37.7319	+	27.4139i	−1.19859	+	0.870830i	−0.204449	+	0.978877i	$0.565540\pi$
$992$	3.14712	−	9.68584i	0.0999212	−	0.307526i
$993$	−58.2338			−1.84799
$994$	3.66989	−	11.2948i	0.116402	−	0.358248i
$995$	−4.58946	+	0.400044i	−0.145496	+	0.0126822i
$996$	8.82607	+	27.1639i	0.279665	+	0.860720i
$997$	−16.8515	−	51.8636i	−0.533693	−	1.64254i	−0.746457	−	0.665434i	$-0.768247\pi$
$997$	−16.8515	−	51.8636i	−0.533693	−	1.64254i	0.212764	−	0.977104i	$-0.431753\pi$
$998$	31.6327	+	22.9825i	1.00132	+	0.727498i
$999$	98.6304			3.12053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.d.191.1	✓	44
25.11	even	5	inner	950.2.h.d.761.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.d.191.1	✓	44	1.1	even	1	trivial
950.2.h.d.761.1	yes	44	25.11	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.00220 - 3.08444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.22762 + 0.194172i) q^{5} +(1.00220 - 3.08444i) q^{6} -1.89338 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.08232 + 4.41906i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.00220 - 3.08444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.22762 + 0.194172i) q^{5} +(1.00220 - 3.08444i) q^{6} -1.89338 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.08232 + 4.41906i) q^{9} +(-1.91632 - 1.15227i) q^{10} +(0.464150 + 0.337224i) q^{11} +(2.62378 - 1.90629i) q^{12} +(3.33739 - 2.42476i) q^{13} +(-1.53178 - 1.11290i) q^{14} +(2.83142 + 6.67636i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.87262 + 5.76335i) q^{17} -7.51816 q^{18} +(-0.309017 + 0.951057i) q^{19} +(-0.873042 - 2.05859i) q^{20} +(1.89754 + 5.84002i) q^{21} +(0.177289 + 0.545640i) q^{22} +(3.33360 + 2.42200i) q^{23} +3.24317 q^{24} +(4.92459 - 0.865085i) q^{25} +4.12524 q^{26} +(11.8547 + 8.61292i) q^{27} +(-0.585087 - 1.80071i) q^{28} +(-1.75171 - 5.39122i) q^{29} +(-1.63360 + 7.06556i) q^{30} +(-3.14712 + 9.68584i) q^{31} -1.00000 q^{32} +(0.574980 - 1.76961i) q^{33} +(-4.90259 + 3.56194i) q^{34} +(4.21774 - 0.367642i) q^{35} +(-6.08232 - 4.41906i) q^{36} +(5.44549 - 3.95638i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-10.8237 - 7.86390i) q^{39} +(0.503704 - 2.17860i) q^{40} +(-0.476860 + 0.346459i) q^{41} +(-1.89754 + 5.84002i) q^{42} -7.31897 q^{43} +(-0.177289 + 0.545640i) q^{44} +(12.6910 - 11.0250i) q^{45} +(1.27332 + 3.91888i) q^{46} +(4.19065 + 12.8975i) q^{47} +(2.62378 + 1.90629i) q^{48} -3.41511 q^{49} +(4.49256 + 2.19474i) q^{50} +19.6534 q^{51} +(3.33739 + 2.42476i) q^{52} +(1.12441 + 3.46056i) q^{53} +(4.52808 + 13.9360i) q^{54} +(-1.09943 - 0.661083i) q^{55} +(0.585087 - 1.80071i) q^{56} +3.24317 q^{57} +(1.75171 - 5.39122i) q^{58} +(-3.71145 + 2.69653i) q^{59} +(-5.47464 + 4.75595i) q^{60} +(-7.49765 - 5.44737i) q^{61} +(-8.23927 + 5.98618i) q^{62} +(11.5162 - 8.36697i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-6.96362 + 6.04947i) q^{65} +(1.50532 - 1.09368i) q^{66} +(2.54706 - 7.83905i) q^{67} -6.05994 q^{68} +(4.12960 - 12.7096i) q^{69} +(3.62832 + 2.18169i) q^{70} +(1.93827 + 5.96539i) q^{71} +(-2.32324 - 7.15020i) q^{72} +(-2.13653 - 1.55228i) q^{73} +6.73099 q^{74} +(-7.60371 - 14.3226i) q^{75} -1.00000 q^{76} +(-0.878812 - 0.638494i) q^{77} +(-4.13430 - 12.7241i) q^{78} +(2.49118 + 7.66705i) q^{79} +(1.68805 - 1.46645i) q^{80} +(7.71562 - 23.7462i) q^{81} -0.589431 q^{82} +(-2.72143 + 8.37571i) q^{83} +(-4.96782 + 3.60933i) q^{84} +(3.05242 - 13.2022i) q^{85} +(-5.92117 - 4.30198i) q^{86} +(-14.8733 + 10.8061i) q^{87} +(-0.464150 + 0.337224i) q^{88} +(0.613119 + 0.445457i) q^{89} +(16.7476 - 1.45982i) q^{90} +(-6.31895 + 4.59099i) q^{91} +(-1.27332 + 3.91888i) q^{92} +33.0294 q^{93} +(-4.19065 + 12.8975i) q^{94} +(0.503704 - 2.17860i) q^{95} +(1.00220 + 3.08444i) q^{96} +(4.71836 + 14.5216i) q^{97} +(-2.76288 - 2.00735i) q^{98} -4.31332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

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