LMFDB - Embedded newform 414.2.e.e.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

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("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 4x^{10} - 3x^{9} + 22x^{8} - 9x^{7} + 69x^{6} - 27x^{5} + 198x^{4} - 81x^{3} + 324x^{2} + 729 $ x^12 + 4x^10 - 3x^9 + 22x^8 - 9x^7 + 69x^6 - 27x^5 + 198x^4 - 81x^3 + 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.2
Root			$1.20109 - 1.24795i$ of defining polynomial
Character	$\chi$	$=$	414.139
Dual form			414.2.e.e.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.20109 + 1.24795i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.39132 - 2.40983i) q^{5} +(-1.68130 - 0.416203i) q^{6} +(-1.77657 - 3.07710i) q^{7} -1.00000 q^{8} +(-0.114750 - 2.99780i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.20109 + 1.24795i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.39132 - 2.40983i) q^{5} +(-1.68130 - 0.416203i) q^{6} +(-1.77657 - 3.07710i) q^{7} -1.00000 q^{8} +(-0.114750 - 2.99780i) q^{9} +2.78263 q^{10} +(-2.05222 - 3.55455i) q^{11} +(-0.480208 - 1.66415i) q^{12} +(0.851125 - 1.47419i) q^{13} +(1.77657 - 3.07710i) q^{14} +(1.33624 + 4.63072i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.77050 q^{17} +(2.53880 - 1.59828i) q^{18} -3.17269 q^{19} +(1.39132 + 2.40983i) q^{20} +(5.97389 + 1.47883i) q^{21} +(2.05222 - 3.55455i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.20109 - 1.24795i) q^{24} +(-1.37153 - 2.37555i) q^{25} +1.70225 q^{26} +(3.87893 + 3.45744i) q^{27} +3.55313 q^{28} +(3.55222 + 6.15262i) q^{29} +(-3.34220 + 3.47258i) q^{30} +(-0.890708 + 1.54275i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.90079 + 1.70828i) q^{33} +(-0.885250 - 1.53330i) q^{34} -9.88707 q^{35} +(2.65355 + 1.39953i) q^{36} -1.29204 q^{37} +(-1.58634 - 2.74763i) q^{38} +(0.817434 + 2.83280i) q^{39} +(-1.39132 + 2.40983i) q^{40} +(4.67784 - 8.10225i) q^{41} +(1.70624 + 5.91295i) q^{42} +(-3.80661 - 6.59325i) q^{43} +4.10444 q^{44} +(-7.38386 - 3.89437i) q^{45} +1.00000 q^{46} +(5.11270 + 8.85546i) q^{47} +(1.68130 + 0.416203i) q^{48} +(-2.81238 + 4.87118i) q^{49} +(1.37153 - 2.37555i) q^{50} +(2.12654 - 2.20949i) q^{51} +(0.851125 + 1.47419i) q^{52} +10.8814 q^{53} +(-1.05477 + 5.08797i) q^{54} -11.4211 q^{55} +(1.77657 + 3.07710i) q^{56} +(3.81069 - 3.95935i) q^{57} +(-3.55222 + 6.15262i) q^{58} +(2.17463 - 3.76656i) q^{59} +(-4.67845 - 1.15814i) q^{60} +(-4.83454 - 8.37368i) q^{61} -1.78142 q^{62} +(-9.02070 + 5.67890i) q^{63} +1.00000 q^{64} +(-2.36837 - 4.10213i) q^{65} +(1.97098 + 6.83040i) q^{66} +(-0.446697 + 0.773701i) q^{67} +(0.885250 - 1.53330i) q^{68} +(0.480208 + 1.66415i) q^{69} +(-4.94353 - 8.56245i) q^{70} -9.82973 q^{71} +(0.114750 + 2.99780i) q^{72} -10.1956 q^{73} +(-0.646020 - 1.11894i) q^{74} +(4.61189 + 1.14167i) q^{75} +(1.58634 - 2.74763i) q^{76} +(-7.29180 + 12.6298i) q^{77} +(-2.04456 + 2.12432i) q^{78} +(-5.37347 - 9.30713i) q^{79} -2.78263 q^{80} +(-8.97366 + 0.687996i) q^{81} +9.35568 q^{82} +(6.68659 + 11.5815i) q^{83} +(-4.26764 + 4.43413i) q^{84} +(-2.46333 + 4.26661i) q^{85} +(3.80661 - 6.59325i) q^{86} +(-11.9447 - 2.95689i) q^{87} +(2.05222 + 3.55455i) q^{88} +15.2267 q^{89} +(-0.319307 - 8.34179i) q^{90} -6.04832 q^{91} +(0.500000 + 0.866025i) q^{92} +(-0.855451 - 2.96455i) q^{93} +(-5.11270 + 8.85546i) q^{94} +(-4.41421 + 7.64564i) q^{95} +(0.480208 + 1.66415i) q^{96} +(6.33599 + 10.9743i) q^{97} -5.62476 q^{98} +(-10.4203 + 6.56003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9} + 10 q^{10} + 6 q^{11} - 6 q^{13} + 3 q^{14} + 7 q^{15} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 4 q^{19} + 5 q^{20} + 17 q^{21} - 6 q^{22} + 6 q^{23} + q^{25} - 12 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} - q^{30} - 6 q^{31} + 6 q^{32} + 9 q^{33} - 4 q^{34} - 34 q^{35} - 2 q^{36} + 8 q^{37} + 2 q^{38} + 23 q^{39} - 5 q^{40} + 15 q^{41} + 7 q^{42} - 14 q^{43} - 12 q^{44} - 37 q^{45} + 12 q^{46} + 9 q^{47} - 5 q^{49} - q^{50} + 9 q^{51} - 6 q^{52} - 10 q^{53} - 9 q^{54} + 16 q^{55} + 3 q^{56} + 37 q^{57} - 12 q^{58} + 18 q^{59} - 8 q^{60} - 3 q^{61} - 12 q^{62} - 42 q^{63} + 12 q^{64} + 9 q^{65} + 3 q^{66} + 8 q^{67} + 4 q^{68} - 17 q^{70} - 18 q^{71} + 8 q^{72} - 32 q^{73} + 4 q^{74} + 34 q^{75} - 2 q^{76} - q^{77} + 22 q^{78} - 7 q^{79} - 10 q^{80} - 56 q^{81} + 30 q^{82} + 3 q^{83} - 10 q^{84} + 7 q^{85} + 14 q^{86} - 9 q^{87} - 6 q^{88} - 42 q^{89} - 17 q^{90} + 18 q^{91} + 6 q^{92} + 69 q^{93} - 9 q^{94} + 11 q^{95} + 13 q^{97} - 10 q^{98} - 60 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9 + 10 * q^10 + 6 * q^11 - 6 * q^13 + 3 * q^14 + 7 * q^15 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 4 * q^19 + 5 * q^20 + 17 * q^21 - 6 * q^22 + 6 * q^23 + q^25 - 12 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 - q^30 - 6 * q^31 + 6 * q^32 + 9 * q^33 - 4 * q^34 - 34 * q^35 - 2 * q^36 + 8 * q^37 + 2 * q^38 + 23 * q^39 - 5 * q^40 + 15 * q^41 + 7 * q^42 - 14 * q^43 - 12 * q^44 - 37 * q^45 + 12 * q^46 + 9 * q^47 - 5 * q^49 - q^50 + 9 * q^51 - 6 * q^52 - 10 * q^53 - 9 * q^54 + 16 * q^55 + 3 * q^56 + 37 * q^57 - 12 * q^58 + 18 * q^59 - 8 * q^60 - 3 * q^61 - 12 * q^62 - 42 * q^63 + 12 * q^64 + 9 * q^65 + 3 * q^66 + 8 * q^67 + 4 * q^68 - 17 * q^70 - 18 * q^71 + 8 * q^72 - 32 * q^73 + 4 * q^74 + 34 * q^75 - 2 * q^76 - q^77 + 22 * q^78 - 7 * q^79 - 10 * q^80 - 56 * q^81 + 30 * q^82 + 3 * q^83 - 10 * q^84 + 7 * q^85 + 14 * q^86 - 9 * q^87 - 6 * q^88 - 42 * q^89 - 17 * q^90 + 18 * q^91 + 6 * q^92 + 69 * q^93 - 9 * q^94 + 11 * q^95 + 13 * q^97 - 10 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.20109	+	1.24795i	−0.693452	+	0.720503i
$3$	−1.20109	+	1.24795i	−0.693452	+	0.720503i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.39132	−	2.40983i	0.622216	−	1.07771i	−0.366856	−	0.930278i	$-0.619566\pi$
$5$	1.39132	−	2.40983i	0.622216	−	1.07771i	0.989072	−	0.147432i	$-0.0471007\pi$
$6$	−1.68130	−	0.416203i	−0.686388	−	0.169914i
$7$	−1.77657	−	3.07710i	−0.671479	−	1.16304i	−0.977485	−	0.211006i	$-0.932326\pi$
$7$	−1.77657	−	3.07710i	−0.671479	−	1.16304i	0.306006	−	0.952030i	$-0.401007\pi$
$8$	−1.00000			−0.353553
$9$	−0.114750	−	2.99780i	−0.0382500	−	0.999268i
$10$	2.78263			0.879946
$11$	−2.05222	−	3.55455i	−0.618767	−	1.07174i	−0.989711	−	0.143081i	$-0.954299\pi$
$11$	−2.05222	−	3.55455i	−0.618767	−	1.07174i	0.370944	−	0.928655i	$-0.379034\pi$
$12$	−0.480208	−	1.66415i	−0.138624	−	0.480399i
$13$	0.851125	−	1.47419i	0.236059	−	0.408867i	−0.723521	−	0.690303i	$-0.757477\pi$
$13$	0.851125	−	1.47419i	0.236059	−	0.408867i	0.959580	+	0.281436i	$0.0908106\pi$
$14$	1.77657	−	3.07710i	0.474807	−	0.822391i
$15$	1.33624	+	4.63072i	0.345017	+	1.19565i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.77050			−0.429409			−0.214705	−	0.976679i	$-0.568879\pi$
$17$	−1.77050			−0.429409			−0.214705	+	0.976679i	$0.568879\pi$
$18$	2.53880	−	1.59828i	0.598401	−	0.376718i
$19$	−3.17269			−0.727864			−0.363932	−	0.931425i	$-0.618566\pi$
$19$	−3.17269			−0.727864			−0.363932	+	0.931425i	$0.618566\pi$
$20$	1.39132	+	2.40983i	0.311108	+	0.538855i
$21$	5.97389	+	1.47883i	1.30361	+	0.322706i
$22$	2.05222	−	3.55455i	0.437534	−	0.757832i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	1.20109	−	1.24795i	0.245172	−	0.254736i
$25$	−1.37153	−	2.37555i	−0.274305	−	0.475110i
$26$	1.70225			0.333839
$27$	3.87893	+	3.45744i	0.746501	+	0.665385i
$28$	3.55313			0.671479
$29$	3.55222	+	6.15262i	0.659630	+	1.14251i	0.980711	+	0.195461i	$0.0626205\pi$
$29$	3.55222	+	6.15262i	0.659630	+	1.14251i	−0.321081	+	0.947052i	$0.604046\pi$
$30$	−3.34220	+	3.47258i	−0.610200	+	0.634004i
$31$	−0.890708	+	1.54275i	−0.159976	+	0.277086i	−0.934860	−	0.355017i	$-0.884475\pi$
$31$	−0.890708	+	1.54275i	−0.159976	+	0.277086i	0.774884	+	0.632104i	$0.217808\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	6.90079	+	1.70828i	1.20127	+	0.297373i
$34$	−0.885250	−	1.53330i	−0.151819	−	0.262958i
$35$	−9.88707			−1.67122
$36$	2.65355	+	1.39953i	0.442258	+	0.233254i
$37$	−1.29204			−0.212410			−0.106205	−	0.994344i	$-0.533870\pi$
$37$	−1.29204			−0.212410			−0.106205	+	0.994344i	$0.533870\pi$
$38$	−1.58634	−	2.74763i	−0.257339	−	0.445724i
$39$	0.817434	+	2.83280i	0.130894	+	0.453611i
$40$	−1.39132	+	2.40983i	−0.219987	+	0.381028i
$41$	4.67784	−	8.10225i	0.730555	−	1.26536i	−0.226091	−	0.974106i	$-0.572595\pi$
$41$	4.67784	−	8.10225i	0.730555	−	1.26536i	0.956646	−	0.291253i	$-0.0940721\pi$
$42$	1.70624	+	5.91295i	0.263279	+	0.912388i
$43$	−3.80661	−	6.59325i	−0.580503	−	1.00546i	−0.995420	−	0.0956016i	$-0.969523\pi$
$43$	−3.80661	−	6.59325i	−0.580503	−	1.00546i	0.414916	−	0.909860i	$-0.363811\pi$
$44$	4.10444			0.618767
$45$	−7.38386	−	3.89437i	−1.10072	−	0.580538i
$46$	1.00000			0.147442
$47$	5.11270	+	8.85546i	0.745764	+	1.29170i	0.949837	+	0.312746i	$0.101249\pi$
$47$	5.11270	+	8.85546i	0.745764	+	1.29170i	−0.204073	+	0.978956i	$0.565418\pi$
$48$	1.68130	+	0.416203i	0.242675	+	0.0600737i
$49$	−2.81238	+	4.87118i	−0.401768	+	0.695883i
$50$	1.37153	−	2.37555i	0.193963	−	0.335954i
$51$	2.12654	−	2.20949i	0.297775	−	0.309391i
$52$	0.851125	+	1.47419i	0.118030	+	0.204434i
$53$	10.8814			1.49467			0.747335	−	0.664448i	$-0.231333\pi$
$53$	10.8814			1.49467			0.747335	+	0.664448i	$0.231333\pi$
$54$	−1.05477	+	5.08797i	−0.143535	+	0.692385i
$55$	−11.4211			−1.54003
$56$	1.77657	+	3.07710i	0.237404	+	0.411195i
$57$	3.81069	−	3.95935i	0.504739	−	0.524429i
$58$	−3.55222	+	6.15262i	−0.466429	+	0.807879i
$59$	2.17463	−	3.76656i	0.283112	−	0.490365i	−0.689037	−	0.724726i	$-0.741966\pi$
$59$	2.17463	−	3.76656i	0.283112	−	0.490365i	0.972150	+	0.234361i	$0.0752998\pi$
$60$	−4.67845	−	1.15814i	−0.603985	−	0.149515i
$61$	−4.83454	−	8.37368i	−0.619000	−	1.07214i	−0.989669	−	0.143374i	$-0.954205\pi$
$61$	−4.83454	−	8.37368i	−0.619000	−	1.07214i	0.370669	−	0.928765i	$-0.379129\pi$
$62$	−1.78142			−0.226240
$63$	−9.02070	+	5.67890i	−1.13650	+	0.715474i
$64$	1.00000			0.125000
$65$	−2.36837	−	4.10213i	−0.293760	−	0.508807i
$66$	1.97098	+	6.83040i	0.242611	+	0.840764i
$67$	−0.446697	+	0.773701i	−0.0545727	+	0.0945227i	−0.892021	−	0.451994i	$-0.850713\pi$
$67$	−0.446697	+	0.773701i	−0.0545727	+	0.0945227i	0.837449	+	0.546516i	$0.184046\pi$
$68$	0.885250	−	1.53330i	0.107352	−	0.185940i
$69$	0.480208	+	1.66415i	0.0578103	+	0.200340i
$70$	−4.94353	−	8.56245i	−0.590865	−	1.02341i
$71$	−9.82973			−1.16657			−0.583287	−	0.812266i	$-0.698234\pi$
$71$	−9.82973			−1.16657			−0.583287	+	0.812266i	$0.698234\pi$
$72$	0.114750	+	2.99780i	0.0135234	+	0.353295i
$73$	−10.1956			−1.19331			−0.596655	−	0.802498i	$-0.703504\pi$
$73$	−10.1956			−1.19331			−0.596655	+	0.802498i	$0.703504\pi$
$74$	−0.646020	−	1.11894i	−0.0750983	−	0.130074i
$75$	4.61189	+	1.14167i	0.532536	+	0.131828i
$76$	1.58634	−	2.74763i	0.181966	−	0.315174i
$77$	−7.29180	+	12.6298i	−0.830978	+	1.43930i
$78$	−2.04456	+	2.12432i	−0.231501	+	0.240532i
$79$	−5.37347	−	9.30713i	−0.604563	−	1.04713i	−0.992120	−	0.125288i	$-0.960014\pi$
$79$	−5.37347	−	9.30713i	−0.604563	−	1.04713i	0.387557	−	0.921846i	$-0.373319\pi$
$80$	−2.78263			−0.311108
$81$	−8.97366	+	0.687996i	−0.997074	+	0.0764441i
$82$	9.35568			1.03316
$83$	6.68659	+	11.5815i	0.733948	+	1.27124i	0.955183	+	0.296015i	$0.0956578\pi$
$83$	6.68659	+	11.5815i	0.733948	+	1.27124i	−0.221235	+	0.975220i	$0.571009\pi$
$84$	−4.26764	+	4.43413i	−0.465638	+	0.483803i
$85$	−2.46333	+	4.26661i	−0.267185	+	0.462778i
$86$	3.80661	−	6.59325i	0.410478	−	0.710968i
$87$	−11.9447	−	2.95689i	−1.28061	−	0.317012i
$88$	2.05222	+	3.55455i	0.218767	+	0.378916i
$89$	15.2267			1.61403			0.807015	−	0.590531i	$-0.201082\pi$
$89$	15.2267			1.61403			0.807015	+	0.590531i	$0.201082\pi$
$90$	−0.319307	−	8.34179i	−0.0336580	−	0.879302i
$91$	−6.04832			−0.634036
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	−0.855451	−	2.96455i	−0.0887061	−	0.307409i
$94$	−5.11270	+	8.85546i	−0.527335	+	0.913371i
$95$	−4.41421	+	7.64564i	−0.452889	+	0.784426i
$96$	0.480208	+	1.66415i	0.0490111	+	0.169847i
$97$	6.33599	+	10.9743i	0.643322	+	1.11427i	0.984686	+	0.174336i	$0.0557779\pi$
$97$	6.33599	+	10.9743i	0.643322	+	1.11427i	−0.341364	+	0.939931i	$0.610889\pi$
$98$	−5.62476			−0.568186
$99$	−10.4203	+	6.56003i	−1.04728	+	0.659308i
$100$	2.74305			0.274305
$101$	−3.51196	−	6.08290i	−0.349453	−	0.605271i	0.636699	−	0.771112i	$-0.280299\pi$
$101$	−3.51196	−	6.08290i	−0.349453	−	0.605271i	−0.986152	+	0.165841i	$0.946966\pi$
$102$	2.97674	+	0.736888i	0.294742	+	0.0729627i
$103$	7.56516	−	13.1032i	0.745417	−	1.29110i	−0.204582	−	0.978849i	$-0.565584\pi$
$103$	7.56516	−	13.1032i	0.745417	−	1.29110i	0.950000	−	0.312251i	$-0.101083\pi$
$104$	−0.851125	+	1.47419i	−0.0834596	+	0.144556i
$105$	11.8753	−	12.3386i	1.15891	−	1.20412i
$106$	5.44068	+	9.42353i	0.528446	+	0.915294i
$107$	7.83535			0.757472			0.378736	−	0.925505i	$-0.376359\pi$
$107$	7.83535			0.757472			0.378736	+	0.925505i	$0.376359\pi$
$108$	−4.93370	+	1.63053i	−0.474745	+	0.156898i
$109$	1.06132			0.101656			0.0508281	−	0.998707i	$-0.483814\pi$
$109$	1.06132			0.101656			0.0508281	+	0.998707i	$0.483814\pi$
$110$	−5.71057	−	9.89100i	−0.544482	−	0.943070i
$111$	1.55186	−	1.61240i	0.147296	−	0.153042i
$112$	−1.77657	+	3.07710i	−0.167870	+	0.290759i
$113$	−4.66618	+	8.08207i	−0.438958	+	0.760297i	−0.997609	−	0.0691053i	$-0.977986\pi$
$113$	−4.66618	+	8.08207i	−0.438958	+	0.760297i	0.558652	+	0.829402i	$0.311319\pi$
$114$	5.33424	+	1.32048i	0.499598	+	0.123674i
$115$	−1.39132	−	2.40983i	−0.129741	−	0.224718i
$116$	−7.10444			−0.659630
$117$	−4.51700	−	2.38234i	−0.417597	−	0.220248i
$118$	4.34925			0.400381
$119$	3.14541	+	5.44801i	0.288339	+	0.499418i
$120$	−1.33624	−	4.63072i	−0.121982	−	0.422725i
$121$	−2.92320	+	5.06312i	−0.265745	+	0.460284i
$122$	4.83454	−	8.37368i	0.437699	−	0.758117i
$123$	4.49267	+	15.5693i	0.405091	+	1.40383i
$124$	−0.890708	−	1.54275i	−0.0799879	−	0.138543i
$125$	6.28026			0.561724
$126$	−9.42842	−	4.97270i	−0.839950	−	0.443004i
$127$	8.84373			0.784754			0.392377	−	0.919804i	$-0.371653\pi$
$127$	8.84373			0.784754			0.392377	+	0.919804i	$0.371653\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	12.8001	+	3.16865i	1.12699	+	0.278984i
$130$	2.36837	−	4.10213i	0.207720	−	0.359781i
$131$	5.84578	−	10.1252i	0.510748	−	0.884642i	−0.489174	−	0.872186i	$-0.662702\pi$
$131$	5.84578	−	10.1252i	0.510748	−	0.884642i	0.999922	−	0.0124560i	$-0.00396496\pi$
$132$	−4.92981	+	5.12212i	−0.429085	+	0.445824i
$133$	5.63649	+	9.76269i	0.488746	+	0.846532i
$134$	−0.893393			−0.0771774
$135$	13.7287	−	4.53717i	1.18158	−	0.390498i
$136$	1.77050			0.151819
$137$	−7.19047	−	12.4543i	−0.614323	−	1.06404i	−0.990503	−	0.137493i	$-0.956096\pi$
$137$	−7.19047	−	12.4543i	−0.614323	−	1.06404i	0.376179	−	0.926547i	$-0.377238\pi$
$138$	−1.20109	+	1.24795i	−0.102244	+	0.106232i
$139$	3.60352	−	6.24148i	0.305647	−	0.529395i	−0.671759	−	0.740770i	$-0.734461\pi$
$139$	3.60352	−	6.24148i	0.305647	−	0.529395i	0.977405	+	0.211375i	$0.0677941\pi$
$140$	4.94353	−	8.56245i	0.417805	−	0.723659i
$141$	−17.1920	−	4.25585i	−1.44783	−	0.358407i
$142$	−4.91487	−	8.51280i	−0.412447	−	0.714378i
$143$	−6.98677			−0.584263
$144$	−2.53880	+	1.59828i	−0.211567	+	0.133190i
$145$	19.7690			1.64173
$146$	−5.09782	−	8.82969i	−0.421899	−	0.730750i
$147$	−2.70106	−	9.36045i	−0.222779	−	0.772037i
$148$	0.646020	−	1.11894i	0.0531025	−	0.0919763i
$149$	10.5105	−	18.2047i	0.861053	−	1.49139i	−0.00986095	−	0.999951i	$-0.503139\pi$
$149$	10.5105	−	18.2047i	0.861053	−	1.49139i	0.870914	−	0.491436i	$-0.163528\pi$
$150$	1.31724	+	4.56485i	0.107552	+	0.372719i
$151$	11.1760	+	19.3575i	0.909492	+	1.57529i	0.814771	+	0.579783i	$0.196863\pi$
$151$	11.1760	+	19.3575i	0.909492	+	1.57529i	0.0947218	+	0.995504i	$0.469804\pi$
$152$	3.17269			0.257339
$153$	0.203165	+	5.30761i	0.0164249	+	0.429095i
$154$	−14.5836			−1.17518
$155$	2.47851	+	4.29291i	0.199079	+	0.344815i
$156$	−2.86199	−	0.708481i	−0.229143	−	0.0567239i
$157$	−2.11914	+	3.67045i	−0.169126	+	0.292934i	−0.938113	−	0.346330i	$-0.887428\pi$
$157$	−2.11914	+	3.67045i	−0.169126	+	0.292934i	0.768987	+	0.639264i	$0.220761\pi$
$158$	5.37347	−	9.30713i	0.427491	−	0.740435i
$159$	−13.0695	+	13.5794i	−1.03648	+	1.07691i
$160$	−1.39132	−	2.40983i	−0.109993	−	0.190514i
$161$	−3.55313			−0.280026
$162$	−5.08265	−	7.42742i	−0.399331	−	0.583554i
$163$	−7.55605			−0.591835			−0.295918	−	0.955213i	$-0.595625\pi$
$163$	−7.55605			−0.591835			−0.295918	+	0.955213i	$0.595625\pi$
$164$	4.67784	+	8.10225i	0.365278	+	0.632680i
$165$	13.7179	−	14.2530i	1.06793	−	1.10959i
$166$	−6.68659	+	11.5815i	−0.518980	+	0.898899i
$167$	−4.79999	+	8.31383i	−0.371435	+	0.643344i	−0.989786	−	0.142558i	$-0.954467\pi$
$167$	−4.79999	+	8.31383i	−0.371435	+	0.643344i	0.618352	+	0.785901i	$0.287801\pi$
$168$	−5.97389	−	1.47883i	−0.460896	−	0.114094i
$169$	5.05117	+	8.74889i	0.388552	+	0.672992i
$170$	−4.92665			−0.377857
$171$	0.364066	+	9.51109i	0.0278408	+	0.727332i
$172$	7.61323			0.580503
$173$	5.23267	+	9.06325i	0.397833	+	0.689066i	0.993458	−	0.114196i	$-0.0364292\pi$
$173$	5.23267	+	9.06325i	0.397833	+	0.689066i	−0.595626	+	0.803262i	$0.703096\pi$
$174$	−3.41161	−	11.8229i	−0.258633	−	0.896288i
$175$	−4.87321	+	8.44065i	−0.368380	+	0.638053i
$176$	−2.05222	+	3.55455i	−0.154692	+	0.267934i
$177$	2.08855	+	7.23781i	0.156985	+	0.544027i
$178$	7.61337	+	13.1867i	0.570646	+	0.988388i
$179$	9.07927			0.678616			0.339308	−	0.940675i	$-0.389807\pi$
$179$	9.07927			0.678616			0.339308	+	0.940675i	$0.389807\pi$
$180$	7.06455	−	4.44742i	0.526560	−	0.331491i
$181$	−26.3796			−1.96078			−0.980391	−	0.197060i	$-0.936861\pi$
$181$	−26.3796			−1.96078			−0.980391	+	0.197060i	$0.936861\pi$
$182$	−3.02416	−	5.23800i	−0.224166	−	0.388266i
$183$	16.2567	+	4.02430i	1.20173	+	0.297485i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−1.79764	+	3.11360i	−0.132165	+	0.228916i
$186$	2.13965	−	2.22311i	0.156886	−	0.163007i
$187$	3.63345	+	6.29332i	0.265704	+	0.460213i
$188$	−10.2254			−0.745764
$189$	3.74772	−	18.0782i	0.272607	−	1.31500i
$190$	−8.82842			−0.640481
$191$	−1.03116	−	1.78602i	−0.0746123	−	0.129232i	0.826305	−	0.563222i	$-0.190439\pi$
$191$	−1.03116	−	1.78602i	−0.0746123	−	0.129232i	−0.900918	+	0.433990i	$0.857105\pi$
$192$	−1.20109	+	1.24795i	−0.0866814	+	0.0900629i
$193$	2.79416	−	4.83962i	0.201128	−	0.348364i	−0.747764	−	0.663964i	$-0.768873\pi$
$193$	2.79416	−	4.83962i	0.201128	−	0.348364i	0.948892	+	0.315601i	$0.102206\pi$
$194$	−6.33599	+	10.9743i	−0.454898	+	0.787906i
$195$	7.96388	+	1.97144i	0.570305	+	0.141178i
$196$	−2.81238	−	4.87118i	−0.200884	−	0.347942i
$197$	−23.6455			−1.68467			−0.842337	−	0.538951i	$-0.818821\pi$
$197$	−23.6455			−1.68467			−0.842337	+	0.538951i	$0.818821\pi$
$198$	−10.8913	−	5.74426i	−0.774013	−	0.408227i
$199$	3.42356			0.242690			0.121345	−	0.992610i	$-0.461279\pi$
$199$	3.42356			0.242690			0.121345	+	0.992610i	$0.461279\pi$
$200$	1.37153	+	2.37555i	0.0969815	+	0.167977i
$201$	−0.429015	−	1.48674i	−0.0302604	−	0.104867i
$202$	3.51196	−	6.08290i	0.247101	−	0.427991i
$203$	12.6215	−	21.8611i	0.885856	−	1.53435i
$204$	0.850209	+	2.94638i	0.0595265	+	0.206288i
$205$	−13.0167	−	22.5456i	−0.909126	−	1.57465i
$206$	15.1303			1.05418
$207$	−2.65355	−	1.39953i	−0.184434	−	0.0972738i
$208$	−1.70225			−0.118030
$209$	6.51104	+	11.2775i	0.450378	+	0.780078i
$210$	16.6231	+	4.11503i	1.14711	+	0.283964i
$211$	8.52713	−	14.7694i	0.587032	−	1.01677i	−0.407587	−	0.913166i	$-0.633630\pi$
$211$	8.52713	−	14.7694i	0.587032	−	1.01677i	0.994619	−	0.103603i	$-0.0330370\pi$
$212$	−5.44068	+	9.42353i	−0.373667	+	0.647211i
$213$	11.8064	−	12.2670i	0.808963	−	0.840521i
$214$	3.91768	+	6.78561i	0.267807	+	0.463855i
$215$	−21.1848			−1.44479
$216$	−3.87893	−	3.45744i	−0.263928	−	0.235249i
$217$	6.32961			0.429682
$218$	0.530661	+	0.919132i	0.0359409	+	0.0622515i
$219$	12.2459	−	12.7236i	0.827502	−	0.859784i
$220$	5.71057	−	9.89100i	0.385007	−	0.666851i
$221$	−1.50692	+	2.61006i	−0.101366	+	0.175571i
$222$	2.17231	+	0.537751i	0.145796	+	0.0360915i
$223$	11.7173	+	20.2950i	0.784650	+	1.35905i	0.929208	+	0.369557i	$0.120490\pi$
$223$	11.7173	+	20.2950i	0.784650	+	1.35905i	−0.144559	+	0.989496i	$0.546176\pi$
$224$	−3.55313			−0.237404
$225$	−6.96406	+	4.38416i	−0.464270	+	0.292277i
$226$	−9.33237			−0.620780
$227$	7.87710	+	13.6435i	0.522821	+	0.905553i	0.999647	+	0.0265556i	$0.00845389\pi$
$227$	7.87710	+	13.6435i	0.522821	+	0.905553i	−0.476826	+	0.878998i	$0.658213\pi$
$228$	1.52355	+	5.27983i	0.100900	+	0.349665i
$229$	5.92574	−	10.2637i	0.391584	−	0.678243i	−0.601075	−	0.799193i	$-0.705261\pi$
$229$	5.92574	−	10.2637i	0.391584	−	0.678243i	0.992659	+	0.120950i	$0.0385940\pi$
$230$	1.39132	−	2.40983i	0.0917407	−	0.158900i
$231$	−7.00317	−	24.2693i	−0.460775	−	1.59680i
$232$	−3.55222	−	6.15262i	−0.233215	−	0.403939i
$233$	1.98591			0.130101			0.0650507	−	0.997882i	$-0.479279\pi$
$233$	1.98591			0.130101			0.0650507	+	0.997882i	$0.479279\pi$
$234$	−0.195333	−	5.10301i	−0.0127693	−	0.333594i
$235$	28.4536			1.85611
$236$	2.17463	+	3.76656i	0.141556	+	0.245182i
$237$	18.0689	+	4.47291i	1.17370	+	0.290547i
$238$	−3.14541	+	5.44801i	−0.203887	+	0.353142i
$239$	−7.79942	+	13.5090i	−0.504502	+	0.873824i	0.495484	+	0.868617i	$0.334991\pi$
$239$	−7.79942	+	13.5090i	−0.504502	+	0.873824i	−0.999986	+	0.00520659i	$0.998343\pi$
$240$	3.34220	−	3.47258i	0.215738	−	0.224154i
$241$	−0.449125	−	0.777907i	−0.0289307	−	0.0501094i	0.851198	−	0.524845i	$-0.175877\pi$
$241$	−0.449125	−	0.777907i	−0.0289307	−	0.0501094i	−0.880128	+	0.474736i	$0.842544\pi$
$242$	−5.84639			−0.375820
$243$	9.91962	−	12.0250i	0.636344	−	0.771405i
$244$	9.66909			0.619000
$245$	7.82582	+	13.5547i	0.499973	+	0.865979i
$246$	−11.2370	+	11.6754i	−0.716447	+	0.744396i
$247$	−2.70035	+	4.67715i	−0.171819	+	0.297600i
$248$	0.890708	−	1.54275i	0.0565600	−	0.0979648i
$249$	−22.4843	−	5.56595i	−1.42489	−	0.352728i
$250$	3.14013	+	5.43887i	0.198599	+	0.343984i
$251$	−14.4019			−0.909042			−0.454521	−	0.890736i	$-0.650190\pi$
$251$	−14.4019			−0.909042			−0.454521	+	0.890736i	$0.650190\pi$
$252$	−0.407722	−	10.6516i	−0.0256841	−	0.670988i
$253$	−4.10444			−0.258044
$254$	4.42187	+	7.65890i	0.277452	+	0.480562i
$255$	−2.36582	−	8.19870i	−0.148153	−	0.513422i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.51981	−	2.63238i	0.0948030	−	0.164204i	−0.814723	−	0.579850i	$-0.803111\pi$
$257$	1.51981	−	2.63238i	0.0948030	−	0.164204i	0.909526	+	0.415646i	$0.136445\pi$
$258$	3.65594	+	12.6696i	0.227609	+	0.788773i
$259$	2.29540	+	3.97574i	0.142629	+	0.247041i
$260$	4.73674			0.293760
$261$	18.0367	−	11.3549i	1.11645	−	0.702849i
$262$	11.6916			0.722307
$263$	−3.26043	−	5.64724i	−0.201047	−	0.348223i	0.747819	−	0.663903i	$-0.231101\pi$
$263$	−3.26043	−	5.64724i	−0.201047	−	0.348223i	−0.948866	+	0.315679i	$0.897768\pi$
$264$	−6.90079	−	1.70828i	−0.424715	−	0.105137i
$265$	15.1394	−	26.2222i	0.930007	−	1.61082i
$266$	−5.63649	+	9.76269i	−0.345595	+	0.598589i
$267$	−18.2887	+	19.0022i	−1.11925	+	1.16291i
$268$	−0.446697	−	0.773701i	−0.0272863	−	0.0472613i
$269$	22.6509			1.38105			0.690524	−	0.723309i	$-0.257380\pi$
$269$	22.6509			1.38105			0.690524	+	0.723309i	$0.257380\pi$
$270$	10.7936	+	9.62079i	0.656880	+	0.585503i
$271$	−6.25005			−0.379664			−0.189832	−	0.981817i	$-0.560794\pi$
$271$	−6.25005			−0.379664			−0.189832	+	0.981817i	$0.560794\pi$
$272$	0.885250	+	1.53330i	0.0536762	+	0.0929698i
$273$	7.26459	−	7.54799i	0.439673	−	0.456825i
$274$	7.19047	−	12.4543i	0.434392	−	0.752390i
$275$	−5.62934	+	9.75030i	−0.339462	+	0.587965i
$276$	−1.68130	−	0.416203i	−0.101202	−	0.0250525i
$277$	−9.91276	−	17.1694i	−0.595600	−	1.03161i	−0.993462	−	0.114164i	$-0.963581\pi$
$277$	−9.91276	−	17.1694i	−0.595600	−	1.03161i	0.397862	−	0.917445i	$-0.369752\pi$
$278$	7.20704			0.432250
$279$	4.72708	+	2.49314i	0.283003	+	0.149260i
$280$	9.88707			0.590865
$281$	2.35490	+	4.07880i	0.140481	+	0.243321i	0.927678	−	0.373381i	$-0.121802\pi$
$281$	2.35490	+	4.07880i	0.140481	+	0.243321i	−0.787197	+	0.616702i	$0.788468\pi$
$282$	−4.91032	−	17.0166i	−0.292406	−	1.01333i
$283$	0.767952	−	1.33013i	0.0456500	−	0.0790681i	−0.842298	−	0.539013i	$-0.818797\pi$
$283$	0.767952	−	1.33013i	0.0456500	−	0.0790681i	0.887948	+	0.459945i	$0.152131\pi$
$284$	4.91487	−	8.51280i	0.291644	−	0.505142i
$285$	−4.23948	−	14.6918i	−0.251125	−	0.870269i
$286$	−3.49339	−	6.05072i	−0.206568	−	0.357787i
$287$	−33.2420			−1.96221
$288$	−2.65355	−	1.39953i	−0.156362	−	0.0824679i
$289$	−13.8653			−0.815608
$290$	9.88452	+	17.1205i	0.580439	+	1.00535i
$291$	−21.3054	−	5.27412i	−1.24895	−	0.309174i
$292$	5.09782	−	8.82969i	0.298327	−	0.516718i
$293$	−5.80357	+	10.0521i	−0.339048	+	0.587248i	−0.984254	−	0.176760i	$-0.943438\pi$
$293$	−5.80357	+	10.0521i	−0.339048	+	0.587248i	0.645206	+	0.764009i	$0.276772\pi$
$294$	6.75586	−	7.01941i	0.394010	−	0.409380i
$295$	−6.05119	−	10.4810i	−0.352314	−	0.610225i
$296$	1.29204			0.0750983
$297$	4.32922	−	20.8833i	0.251207	−	1.21177i
$298$	21.0210			1.21771
$299$	−0.851125	−	1.47419i	−0.0492218	−	0.0852547i
$300$	−3.29466	+	3.42319i	−0.190217	+	0.197638i
$301$	−13.5254	+	23.4267i	−0.779592	+	1.35029i
$302$	−11.1760	+	19.3575i	−0.643108	+	1.11390i
$303$	11.8093	+	2.92338i	0.678429	+	0.167944i
$304$	1.58634	+	2.74763i	0.0909830	+	0.157587i
$305$	−26.9055			−1.54061
$306$	−4.49494	+	2.82975i	−0.256959	+	0.161766i
$307$	33.8011			1.92913			0.964567	−	0.263839i	$-0.0849888\pi$
$307$	33.8011			1.92913			0.964567	+	0.263839i	$0.0849888\pi$
$308$	−7.29180	−	12.6298i	−0.415489	−	0.719648i
$309$	7.26570	+	25.1791i	0.413332	+	1.43239i
$310$	−2.47851	+	4.29291i	−0.140770	+	0.243821i
$311$	−2.38088	+	4.12380i	−0.135007	+	0.233839i	−0.925600	−	0.378503i	$-0.876439\pi$
$311$	−2.38088	+	4.12380i	−0.135007	+	0.233839i	0.790593	+	0.612342i	$0.209772\pi$
$312$	−0.817434	−	2.83280i	−0.0462781	−	0.160376i
$313$	11.9525	+	20.7023i	0.675594	+	1.17016i	0.976295	+	0.216444i	$0.0694460\pi$
$313$	11.9525	+	20.7023i	0.675594	+	1.17016i	−0.300701	+	0.953718i	$0.597221\pi$
$314$	−4.23828			−0.239180
$315$	1.13454	+	29.6395i	0.0639242	+	1.67000i
$316$	10.7469			0.604563
$317$	−12.1759	−	21.0894i	−0.683869	−	1.18450i	−0.973791	−	0.227446i	$-0.926962\pi$
$317$	−12.1759	−	21.0894i	−0.683869	−	1.18450i	0.289921	−	0.957050i	$-0.406371\pi$
$318$	−18.2948	−	4.52886i	−1.02592	−	0.253966i
$319$	14.5798	−	25.2530i	0.816315	−	1.41390i
$320$	1.39132	−	2.40983i	0.0777770	−	0.134714i
$321$	−9.41099	+	9.77811i	−0.525270	+	0.545761i
$322$	−1.77657	−	3.07710i	−0.0990042	−	0.171480i
$323$	5.61724			0.312552
$324$	3.89101	−	8.11542i	0.216167	−	0.450857i
$325$	−4.66936			−0.259009
$326$	−3.77802	−	6.54373i	−0.209245	−	0.362424i
$327$	−1.27475	+	1.32448i	−0.0704937	+	0.0732437i
$328$	−4.67784	+	8.10225i	−0.258290	+	0.447372i
$329$	18.1661	−	31.4646i	1.00153	−	1.73470i
$330$	19.2024	+	4.75351i	1.05706	+	0.261672i
$331$	−9.52877	−	16.5043i	−0.523749	−	0.907159i	−0.999618	−	0.0276433i	$-0.991200\pi$
$331$	−9.52877	−	16.5043i	−0.523749	−	0.907159i	0.475869	−	0.879516i	$-0.342134\pi$
$332$	−13.3732			−0.733948
$333$	0.148262	+	3.87329i	0.00812469	+	0.212255i
$334$	−9.59999			−0.525288
$335$	1.24299	+	2.15293i	0.0679120	+	0.117627i
$336$	−1.70624	−	5.91295i	−0.0930833	−	0.322578i
$337$	−12.7081	+	22.0110i	−0.692253	+	1.19902i	0.278845	+	0.960336i	$0.410048\pi$
$337$	−12.7081	+	22.0110i	−0.692253	+	1.19902i	−0.971098	+	0.238681i	$0.923285\pi$
$338$	−5.05117	+	8.74889i	−0.274748	+	0.475877i
$339$	−4.48148	−	15.5305i	−0.243401	−	0.843500i
$340$	−2.46333	−	4.26661i	−0.133593	−	0.231389i
$341$	7.31171			0.395951
$342$	−8.05482	+	5.07084i	−0.435555	+	0.274199i
$343$	−4.88642			−0.263842
$344$	3.80661	+	6.59325i	0.205239	+	0.355484i
$345$	4.67845	+	1.15814i	0.251879	+	0.0623522i
$346$	−5.23267	+	9.06325i	−0.281310	+	0.487243i
$347$	11.3339	−	19.6310i	0.608438	−	1.05385i	−0.383060	−	0.923723i	$-0.625130\pi$
$347$	11.3339	−	19.6310i	0.608438	−	1.05385i	0.991498	−	0.130122i	$-0.0415368\pi$
$348$	8.53309	−	8.86597i	0.457422	−	0.475266i
$349$	−6.76024	−	11.7091i	−0.361867	−	0.626772i	0.626401	−	0.779501i	$-0.284527\pi$
$349$	−6.76024	−	11.7091i	−0.361867	−	0.626772i	−0.988268	+	0.152729i	$0.951194\pi$
$350$	−9.74642			−0.520968
$351$	8.39838	−	2.77557i	0.448272	−	0.148149i
$352$	−4.10444			−0.218767
$353$	17.4879	+	30.2899i	0.930785	+	1.61217i	0.781984	+	0.623299i	$0.214208\pi$
$353$	17.4879	+	30.2899i	0.930785	+	1.61217i	0.148801	+	0.988867i	$0.452459\pi$
$354$	−5.22386	+	5.42764i	−0.277645	+	0.288476i
$355$	−13.6763	+	23.6880i	−0.725861	+	1.25723i
$356$	−7.61337	+	13.1867i	−0.403508	+	0.698896i
$357$	−10.5768	−	2.61826i	−0.559782	−	0.138573i
$358$	4.53963	+	7.86288i	0.239927	+	0.415566i
$359$	3.12656			0.165014			0.0825068	−	0.996590i	$-0.473707\pi$
$359$	3.12656			0.165014			0.0825068	+	0.996590i	$0.473707\pi$
$360$	7.38386	+	3.89437i	0.389163	+	0.205251i
$361$	−8.93406			−0.470214
$362$	−13.1898	−	22.8454i	−0.693241	−	1.20073i
$363$	−2.80749	−	9.72928i	−0.147355	−	0.510655i
$364$	3.02416	−	5.23800i	0.158509	−	0.274546i
$365$	−14.1854	+	24.5698i	−0.742496	+	1.28604i
$366$	4.64318	+	16.0908i	0.242703	+	0.841081i
$367$	9.60731	+	16.6403i	0.501498	+	0.868619i	0.999999	+	0.00173004i	$0.000550688\pi$
$367$	9.60731	+	16.6403i	0.501498	+	0.868619i	−0.498501	+	0.866889i	$0.666116\pi$
$368$	−1.00000			−0.0521286
$369$	−24.8258	−	13.0935i	−1.29238	−	0.681621i
$370$	−3.59528			−0.186909
$371$	−19.3315	−	33.4831i	−1.00364	−	1.73835i
$372$	2.99510	+	0.741431i	0.155289	+	0.0384414i
$373$	−5.36638	+	9.29484i	−0.277860	+	0.481268i	−0.970853	−	0.239676i	$-0.922959\pi$
$373$	−5.36638	+	9.29484i	−0.277860	+	0.481268i	0.692992	+	0.720945i	$0.256292\pi$
$374$	−3.63345	+	6.29332i	−0.187881	+	0.325420i
$375$	−7.54318	+	7.83745i	−0.389528	+	0.404724i
$376$	−5.11270	−	8.85546i	−0.263667	−	0.456685i
$377$	12.0935			0.622848
$378$	17.5301	−	5.79350i	0.901650	−	0.297985i
$379$	−26.2176			−1.34671			−0.673353	−	0.739321i	$-0.735147\pi$
$379$	−26.2176			−1.34671			−0.673353	+	0.739321i	$0.735147\pi$
$380$	−4.41421	−	7.64564i	−0.226444	−	0.392213i
$381$	−10.6221	+	11.0365i	−0.544189	+	0.565418i
$382$	1.03116	−	1.78602i	0.0527588	−	0.0913810i
$383$	−2.06077	+	3.56936i	−0.105301	+	0.182386i	−0.913861	−	0.406027i	$-0.866914\pi$
$383$	−2.06077	+	3.56936i	−0.105301	+	0.182386i	0.808560	+	0.588413i	$0.200247\pi$
$384$	−1.68130	−	0.416203i	−0.0857986	−	0.0212393i
$385$	20.2904	+	35.1440i	1.03410	+	1.79111i
$386$	5.58832			0.284438
$387$	−19.3285	+	12.1681i	−0.982521	+	0.618537i
$388$	−12.6720			−0.643322
$389$	7.81113	+	13.5293i	0.396040	+	0.685961i	0.993233	−	0.116136i	$-0.0370509\pi$
$389$	7.81113	+	13.5293i	0.396040	+	0.685961i	−0.597193	+	0.802097i	$0.703718\pi$
$390$	2.27462	+	7.88265i	0.115180	+	0.399153i
$391$	−0.885250	+	1.53330i	−0.0447690	+	0.0775422i
$392$	2.81238	−	4.87118i	0.142047	−	0.246032i
$393$	5.61439	+	19.4565i	0.283208	+	0.981452i
$394$	−11.8228	−	20.4776i	−0.595622	−	1.03165i
$395$	−29.9048			−1.50467
$396$	−0.470984	−	12.3043i	−0.0236678	−	0.618314i
$397$	15.8394			0.794955			0.397477	−	0.917612i	$-0.369886\pi$
$397$	15.8394			0.794955			0.397477	+	0.917612i	$0.369886\pi$
$398$	1.71178	+	2.96489i	0.0858038	+	0.148617i
$399$	−18.9533	−	4.69185i	−0.948851	−	0.234886i
$400$	−1.37153	+	2.37555i	−0.0685763	+	0.118778i
$401$	−1.42817	+	2.47367i	−0.0713196	+	0.123529i	−0.899480	−	0.436962i	$-0.856054\pi$
$401$	−1.42817	+	2.47367i	−0.0713196	+	0.123529i	0.828160	+	0.560491i	$0.189388\pi$
$402$	1.07305	−	1.11491i	0.0535188	−	0.0556066i
$403$	1.51621	+	2.62615i	0.0755276	+	0.130818i
$404$	7.02393			0.349453
$405$	−10.8273	+	22.5822i	−0.538011	+	1.12212i
$406$	25.2430			1.25279
$407$	2.65155	+	4.59262i	0.131432	+	0.227648i
$408$	−2.12654	+	2.20949i	−0.105279	+	0.109386i
$409$	9.73340	−	16.8587i	0.481286	−	0.833611i	−0.518484	−	0.855088i	$-0.673503\pi$
$409$	9.73340	−	16.8587i	0.481286	−	0.833611i	0.999769	+	0.0214761i	$0.00683658\pi$
$410$	13.0167	−	22.5456i	0.642849	−	1.11345i
$411$	24.1787	+	5.98539i	1.19265	+	0.295238i
$412$	7.56516	+	13.1032i	0.372709	+	0.645550i
$413$	−15.4535			−0.760416
$414$	−0.114750	−	2.99780i	−0.00563966	−	0.147334i
$415$	37.2126			1.82670
$416$	−0.851125	−	1.47419i	−0.0417298	−	0.0722782i
$417$	3.46088	+	11.9936i	0.169480	+	0.587329i
$418$	−6.51104	+	11.2775i	−0.318466	+	0.551599i
$419$	17.8208	−	30.8665i	0.870602	−	1.50793i	0.00922773	−	0.999957i	$-0.497063\pi$
$419$	17.8208	−	30.8665i	0.870602	−	1.50793i	0.861375	−	0.507970i	$-0.169604\pi$
$420$	4.74785	+	16.4536i	0.231672	+	0.802853i
$421$	−6.80073	−	11.7792i	−0.331447	−	0.574083i	0.651349	−	0.758779i	$-0.274204\pi$
$421$	−6.80073	−	11.7792i	−0.331447	−	0.574083i	−0.982796	+	0.184695i	$0.940870\pi$
$422$	17.0543			0.830188
$423$	25.9603	−	16.3430i	1.26223	−	0.794626i
$424$	−10.8814			−0.528446
$425$	2.42829	+	4.20591i	0.117789	+	0.204017i
$426$	16.5267	+	4.09117i	0.800724	+	0.198218i
$427$	−17.1778	+	29.7528i	−0.831291	+	1.43984i
$428$	−3.91768	+	6.78561i	−0.189368	+	0.327995i
$429$	8.39176	−	8.71913i	0.405158	−	0.420964i
$430$	−10.5924	−	18.3466i	−0.510812	−	0.884752i
$431$	−17.0437			−0.820966			−0.410483	−	0.911868i	$-0.634640\pi$
$431$	−17.0437			−0.820966			−0.410483	+	0.911868i	$0.634640\pi$
$432$	1.05477	−	5.08797i	0.0507475	−	0.244795i
$433$	−10.7139			−0.514878			−0.257439	−	0.966295i	$-0.582879\pi$
$433$	−10.7139			−0.514878			−0.257439	+	0.966295i	$0.582879\pi$
$434$	3.16480	+	5.48160i	0.151915	+	0.263125i
$435$	−23.7445	+	24.6707i	−1.13846	+	1.18287i
$436$	−0.530661	+	0.919132i	−0.0254141	+	0.0440185i
$437$	−1.58634	+	2.74763i	−0.0758851	+	0.131437i
$438$	17.1420	+	4.24346i	0.819074	+	0.202760i
$439$	15.9496	+	27.6255i	0.761234	+	1.31850i	0.942215	+	0.335009i	$0.108739\pi$
$439$	15.9496	+	27.6255i	0.761234	+	1.31850i	−0.180981	+	0.983487i	$0.557927\pi$
$440$	11.4211			0.544482
$441$	14.9256	+	7.87199i	0.710742	+	0.374857i
$442$	−3.01383			−0.143353
$443$	−1.90330	−	3.29661i	−0.0904283	−	0.156626i	0.817263	−	0.576265i	$-0.195490\pi$
$443$	−1.90330	−	3.29661i	−0.0904283	−	0.156626i	−0.907691	+	0.419638i	$0.862157\pi$
$444$	0.620449	+	2.15015i	0.0294452	+	0.102042i
$445$	21.1852	−	36.6939i	1.00428	−	1.73946i
$446$	−11.7173	+	20.2950i	−0.554831	+	0.960996i
$447$	10.0944	+	34.9821i	0.477451	+	1.65460i
$448$	−1.77657	−	3.07710i	−0.0839349	−	0.145379i
$449$	−11.0761			−0.522715			−0.261358	−	0.965242i	$-0.584170\pi$
$449$	−11.0761			−0.522715			−0.261358	+	0.965242i	$0.584170\pi$
$450$	−7.27882	−	3.83897i	−0.343127	−	0.180971i
$451$	−38.3998			−1.80817
$452$	−4.66618	−	8.08207i	−0.219479	−	0.380149i
$453$	−37.5806	−	9.30300i	−1.76569	−	0.437093i
$454$	−7.87710	+	13.6435i	−0.369691	+	0.640323i
$455$	−8.41513	+	14.5754i	−0.394507	+	0.683307i
$456$	−3.81069	+	3.95935i	−0.178452	+	0.185413i
$457$	8.43995	+	14.6184i	0.394804	+	0.683821i	0.993076	−	0.117472i	$-0.0374790\pi$
$457$	8.43995	+	14.6184i	0.394804	+	0.683821i	−0.598272	+	0.801293i	$0.704146\pi$
$458$	11.8515			0.553783
$459$	−6.86765	−	6.12140i	−0.320554	−	0.285722i
$460$	2.78263			0.129741
$461$	−8.64366	−	14.9713i	−0.402575	−	0.697281i	0.591461	−	0.806334i	$-0.298551\pi$
$461$	−8.64366	−	14.9713i	−0.402575	−	0.697281i	−0.994036	+	0.109053i	$0.965218\pi$
$462$	17.5163	−	18.1996i	0.814931	−	0.846722i
$463$	15.7710	−	27.3162i	0.732940	−	1.26949i	−0.222681	−	0.974891i	$-0.571481\pi$
$463$	15.7710	−	27.3162i	0.732940	−	1.26949i	0.955621	−	0.294599i	$-0.0951859\pi$
$464$	3.55222	−	6.15262i	0.164908	−	0.285628i
$465$	−8.33426	−	2.06313i	−0.386492	−	0.0956754i
$466$	0.992956	+	1.71985i	0.0459978	+	0.0796705i
$467$	−19.7008			−0.911642			−0.455821	−	0.890071i	$-0.650654\pi$
$467$	−19.7008			−0.911642			−0.455821	+	0.890071i	$0.650654\pi$
$468$	4.32167	−	2.72067i	0.199769	−	0.125763i
$469$	3.17435			0.146578
$470$	14.2268	+	24.6415i	0.656232	+	1.13663i
$471$	−2.03526	−	7.05313i	−0.0937796	−	0.324991i
$472$	−2.17463	+	3.76656i	−0.100095	+	0.173370i
$473$	−15.6240	+	27.0616i	−0.718392	+	1.24429i
$474$	5.16077	+	17.8845i	0.237042	+	0.821464i
$475$	4.35142	+	7.53688i	0.199657	+	0.345816i
$476$	−6.29082			−0.288339
$477$	−1.24864	−	32.6202i	−0.0571711	−	1.49358i
$478$	−15.5988			−0.713474
$479$	−8.22003	−	14.2375i	−0.375583	−	0.650529i	0.614831	−	0.788659i	$-0.289224\pi$
$479$	−8.22003	−	14.2375i	−0.375583	−	0.650529i	−0.990414	+	0.138130i	$0.955891\pi$
$480$	4.67845	+	1.15814i	0.213541	+	0.0528617i
$481$	−1.09969	+	1.90471i	−0.0501414	+	0.0868475i
$482$	0.449125	−	0.777907i	0.0204571	−	0.0354327i
$483$	4.26764	−	4.43413i	0.194185	−	0.201760i
$484$	−2.92320	−	5.06312i	−0.132873	−	0.230142i
$485$	35.2615			1.60114
$486$	15.3738	+	2.57814i	0.697369	+	0.116947i
$487$	−23.5907			−1.06899			−0.534497	−	0.845170i	$-0.679499\pi$
$487$	−23.5907			−1.06899			−0.534497	+	0.845170i	$0.679499\pi$
$488$	4.83454	+	8.37368i	0.218850	+	0.379059i
$489$	9.07552	−	9.42956i	0.410409	−	0.426419i
$490$	−7.82582	+	13.5547i	−0.353535	+	0.612340i
$491$	−1.60947	+	2.78769i	−0.0726346	+	0.125807i	−0.900055	−	0.435776i	$-0.856474\pi$
$491$	−1.60947	+	2.78769i	−0.0726346	+	0.125807i	0.827421	+	0.561583i	$0.189807\pi$
$492$	−15.7297	−	3.89386i	−0.709150	−	0.175549i
$493$	−6.28920	−	10.8932i	−0.283251	−	0.490606i
$494$	−5.40070			−0.242989
$495$	1.31058	+	34.2383i	0.0589060	+	1.53890i
$496$	1.78142			0.0799879
$497$	17.4632	+	30.2471i	0.783331	+	1.35677i
$498$	−6.42191	−	22.2550i	−0.287773	−	0.997270i
$499$	−4.47955	+	7.75881i	−0.200532	+	0.347332i	−0.948700	−	0.316177i	$-0.897601\pi$
$499$	−4.47955	+	7.75881i	−0.200532	+	0.347332i	0.748168	+	0.663510i	$0.230934\pi$
$500$	−3.14013	+	5.43887i	−0.140431	+	0.243234i
$501$	−4.60999	−	15.9758i	−0.205959	−	0.713747i
$502$	−7.20097	−	12.4724i	−0.321395	−	0.556672i
$503$	26.9673			1.20241			0.601205	−	0.799095i	$-0.294687\pi$
$503$	26.9673			1.20241			0.601205	+	0.799095i	$0.294687\pi$
$504$	9.02070	−	5.67890i	0.401814	−	0.252958i
$505$	−19.5450			−0.869742
$506$	−2.05222	−	3.55455i	−0.0912322	−	0.158019i
$507$	−16.9851	−	4.20463i	−0.754334	−	0.186734i
$508$	−4.42187	+	7.65890i	−0.196189	+	0.339809i
$509$	−15.7229	+	27.2328i	−0.696904	+	1.20707i	0.272630	+	0.962119i	$0.412106\pi$
$509$	−15.7229	+	27.2328i	−0.696904	+	1.20707i	−0.969535	+	0.244955i	$0.921227\pi$
$510$	5.91737	−	6.14821i	0.262026	−	0.272247i
$511$	18.1132	+	31.3731i	0.801283	+	1.38786i
$512$	−1.00000			−0.0441942
$513$	−12.3066	−	10.9694i	−0.543351	−	0.484310i
$514$	3.03962			0.134072
$515$	−21.0511	−	36.4615i	−0.927621	−	1.60669i
$516$	−9.14420	+	9.50092i	−0.402551	+	0.418255i
$517$	20.9848	−	36.3467i	0.922909	−	1.59852i
$518$	−2.29540	+	3.97574i	−0.100854	+	0.174684i
$519$	−17.5954	−	4.35571i	−0.772352	−	0.191194i
$520$	2.36837	+	4.10213i	0.103860	+	0.179890i
$521$	13.6965			0.600053			0.300026	−	0.953931i	$-0.403004\pi$
$521$	13.6965			0.600053			0.300026	+	0.953931i	$0.403004\pi$
$522$	18.8520	+	9.94284i	0.825129	+	0.435186i
$523$	25.9587			1.13509			0.567547	−	0.823341i	$-0.307893\pi$
$523$	25.9587			1.13509			0.567547	+	0.823341i	$0.307893\pi$
$524$	5.84578	+	10.1252i	0.255374	+	0.442321i
$525$	−4.68031	−	16.2195i	−0.204266	−	0.707878i
$526$	3.26043	−	5.64724i	0.142162	−	0.246231i
$527$	1.57700	−	2.73144i	0.0686951	−	0.118983i
$528$	−1.97098	−	6.83040i	−0.0857761	−	0.297255i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	30.2788			1.31523
$531$	−11.5410	−	6.08689i	−0.500835	−	0.264149i
$532$	−11.2730			−0.488746
$533$	−7.96285	−	13.7921i	−0.344909	−	0.597400i
$534$	−25.6007	−	6.33741i	−1.10785	−	0.274247i
$535$	10.9015	−	18.8819i	0.471311	−	0.816335i
$536$	0.446697	−	0.773701i	0.0192944	−	0.0334188i
$537$	−10.9050	+	11.3305i	−0.470587	+	0.488945i
$538$	11.3254	+	19.6162i	0.488274	+	0.845716i
$539$	23.0865			0.994404
$540$	−2.93503	+	14.1580i	−0.126303	+	0.609262i
$541$	−7.70265			−0.331163			−0.165581	−	0.986196i	$-0.552950\pi$
$541$	−7.70265			−0.331163			−0.165581	+	0.986196i	$0.552950\pi$
$542$	−3.12503	−	5.41271i	−0.134231	−	0.232496i
$543$	31.6844	−	32.9204i	1.35971	−	1.41275i
$544$	−0.885250	+	1.53330i	−0.0379548	+	0.0657396i
$545$	1.47664	−	2.55761i	0.0632521	−	0.109556i
$546$	10.1690	+	2.51733i	0.435195	+	0.107732i
$547$	−17.5774	−	30.4449i	−0.751553	−	1.30173i	−0.947070	−	0.321028i	$-0.895972\pi$
$547$	−17.5774	−	30.4449i	−0.751553	−	1.30173i	0.195516	−	0.980700i	$-0.437362\pi$
$548$	14.3809			0.614323
$549$	−24.5479	+	15.4539i	−1.04768	+	0.659556i
$550$	−11.2587			−0.480071
$551$	−11.2701	−	19.5203i	−0.480121	−	0.831594i
$552$	−0.480208	−	1.66415i	−0.0204390	−	0.0708310i
$553$	−19.0927	+	33.0695i	−0.811903	+	1.40626i
$554$	9.91276	−	17.1694i	0.421153	−	0.729458i
$555$	−1.72648	−	5.98308i	−0.0732851	−	0.253968i
$556$	3.60352	+	6.24148i	0.152823	+	0.264698i
$557$	34.3347			1.45481			0.727404	−	0.686210i	$-0.240727\pi$
$557$	34.3347			1.45481			0.727404	+	0.686210i	$0.240727\pi$
$558$	0.204418	+	5.34034i	0.00865369	+	0.226074i
$559$	−12.9596			−0.548133
$560$	4.94353	+	8.56245i	0.208902	+	0.361830i
$561$	−12.2179	−	3.02451i	−0.515838	−	0.127695i
$562$	−2.35490	+	4.07880i	−0.0993353	+	0.172054i
$563$	3.42054	−	5.92455i	0.144159	−	0.249690i	−0.784900	−	0.619622i	$-0.787286\pi$
$563$	3.42054	−	5.92455i	0.144159	−	0.249690i	0.929059	+	0.369932i	$0.120619\pi$
$564$	12.2817	−	12.7608i	0.517151	−	0.537326i
$565$	12.9843	+	22.4894i	0.546253	+	0.946138i
$566$	1.53590			0.0645588
$567$	18.0594	+	26.3906i	0.758421	+	1.10830i
$568$	9.82973			0.412447
$569$	−1.79047	−	3.10118i	−0.0750602	−	0.130008i	0.826052	−	0.563594i	$-0.190582\pi$
$569$	−1.79047	−	3.10118i	−0.0750602	−	0.130008i	−0.901112	+	0.433585i	$0.857248\pi$
$570$	10.6038	−	11.0174i	0.444143	−	0.461469i
$571$	23.3591	−	40.4592i	0.977549	−	1.69316i	0.306296	−	0.951936i	$-0.400910\pi$
$571$	23.3591	−	40.4592i	0.977549	−	1.69316i	0.671253	−	0.741228i	$-0.265756\pi$
$572$	3.49339	−	6.05072i	0.146066	−	0.252993i
$573$	3.46739	+	0.858346i	0.144852	+	0.0358579i
$574$	−16.6210	−	28.7884i	−0.693746	−	1.20160i
$575$	−2.74305			−0.114393
$576$	−0.114750	−	2.99780i	−0.00478125	−	0.124909i
$577$	−2.93068			−0.122006			−0.0610029	−	0.998138i	$-0.519430\pi$
$577$	−2.93068			−0.122006			−0.0610029	+	0.998138i	$0.519430\pi$
$578$	−6.93267	−	12.0077i	−0.288361	−	0.499456i
$579$	2.68356	+	9.29981i	0.111525	+	0.386487i
$580$	−9.88452	+	17.1205i	−0.410432	+	0.710890i
$581$	23.7583	−	41.1506i	0.985662	−	1.70722i
$582$	−6.08519	−	21.0881i	−0.252239	−	0.874130i
$583$	−22.3309	−	38.6783i	−0.924852	−	1.60189i
$584$	10.1956			0.421899
$585$	−12.0256	+	7.57062i	−0.497198	+	0.313007i
$586$	−11.6071			−0.479486
$587$	9.58395	+	16.5999i	0.395572	+	0.685151i	0.993174	−	0.116642i	$-0.0372130\pi$
$587$	9.58395	+	16.5999i	0.395572	+	0.685151i	−0.597602	+	0.801793i	$0.703880\pi$
$588$	9.45692	+	2.34104i	0.389997	+	0.0965429i
$589$	2.82594	−	4.89467i	0.116441	−	0.201681i
$590$	6.05119	−	10.4810i	0.249123	−	0.431494i
$591$	28.4005	−	29.5084i	1.16824	−	1.21381i
$592$	0.646020	+	1.11894i	0.0265513	+	0.0459881i
$593$	19.8234			0.814048			0.407024	−	0.913417i	$-0.366566\pi$
$593$	19.8234			0.814048			0.407024	+	0.913417i	$0.366566\pi$
$594$	20.2500	−	6.69241i	0.830869	−	0.274593i
$595$	17.5051			0.717637
$596$	10.5105	+	18.2047i	0.430526	+	0.745694i
$597$	−4.11202	+	4.27243i	−0.168294	+	0.174859i
$598$	0.851125	−	1.47419i	0.0348051	−	0.0602842i
$599$	17.6338	−	30.5426i	0.720496	−	1.24794i	−0.240305	−	0.970697i	$-0.577247\pi$
$599$	17.6338	−	30.5426i	0.720496	−	1.24794i	0.960801	−	0.277239i	$-0.0894192\pi$
$600$	−4.61189	−	1.14167i	−0.188280	−	0.0466083i
$601$	0.969650	+	1.67948i	0.0395529	+	0.0685076i	0.885124	−	0.465355i	$-0.154073\pi$
$601$	0.969650	+	1.67948i	0.0395529	+	0.0685076i	−0.845571	+	0.533863i	$0.820740\pi$
$602$	−27.0508			−1.10251
$603$	2.37066	+	1.25033i	0.0965409	+	0.0509173i
$604$	−22.3521			−0.909492
$605$	8.13418	+	14.0888i	0.330702	+	0.572792i
$606$	3.37295	+	11.6889i	0.137017	+	0.474828i
$607$	−2.24299	+	3.88498i	−0.0910402	+	0.157686i	−0.907949	−	0.419080i	$-0.862353\pi$
$607$	−2.24299	+	3.88498i	−0.0910402	+	0.157686i	0.816909	+	0.576767i	$0.195686\pi$
$608$	−1.58634	+	2.74763i	−0.0643347	+	0.111431i
$609$	12.1219	+	42.0082i	0.491204	+	1.70226i
$610$	−13.4528	−	23.3009i	−0.544687	−	0.943425i
$611$	17.4062			0.704179
$612$	−4.69811	−	2.47786i	−0.189910	−	0.100162i
$613$	−23.1365			−0.934474			−0.467237	−	0.884132i	$-0.654750\pi$
$613$	−23.1365			−0.934474			−0.467237	+	0.884132i	$0.654750\pi$
$614$	16.9006	+	29.2727i	0.682052	+	1.18135i
$615$	43.7700	+	10.8352i	1.76498	+	0.436917i
$616$	7.29180	−	12.6298i	0.293795	−	0.508868i
$617$	9.34249	−	16.1817i	0.376114	−	0.651449i	−0.614379	−	0.789011i	$-0.710593\pi$
$617$	9.34249	−	16.1817i	0.376114	−	0.651449i	0.990493	+	0.137562i	$0.0439266\pi$
$618$	−18.1729	+	18.8819i	−0.731022	+	0.759540i
$619$	6.23823	+	10.8049i	0.250736	+	0.434287i	0.963729	−	0.266884i	$-0.0859942\pi$
$619$	6.23823	+	10.8049i	0.250736	+	0.434287i	−0.712993	+	0.701171i	$0.752661\pi$
$620$	−4.95703			−0.199079
$621$	4.93370	−	1.63053i	0.197982	−	0.0654310i
$622$	−4.76176			−0.190929
$623$	−27.0513	−	46.8542i	−1.08379	−	1.87718i
$624$	2.04456	−	2.12432i	0.0818479	−	0.0850408i
$625$	15.5955	−	27.0121i	0.623819	−	1.08049i
$626$	−11.9525	+	20.7023i	−0.477717	+	0.827430i
$627$	−21.8941	−	5.41983i	−0.874364	−	0.216447i
$628$	−2.11914	−	3.67045i	−0.0845628	−	0.146467i
$629$	2.28756			0.0912109
$630$	−25.1013	+	15.8023i	−1.00006	+	0.629578i
$631$	34.2107			1.36191			0.680953	−	0.732327i	$-0.261566\pi$
$631$	34.2107			1.36191			0.680953	+	0.732327i	$0.261566\pi$
$632$	5.37347	+	9.30713i	0.213745	+	0.370218i
$633$	8.18960	+	28.3809i	0.325507	+	1.12804i
$634$	12.1759	−	21.0894i	0.483569	−	0.837566i
$635$	12.3044	−	21.3119i	0.488286	−	0.845737i
$636$	−5.22532	−	18.1082i	−0.207197	−	0.718038i
$637$	4.78737	+	8.29197i	0.189683	+	0.328540i
$638$	29.1597			1.15444
$639$	1.12796	+	29.4676i	0.0446215	+	1.16572i
$640$	2.78263			0.109993
$641$	−1.05824	−	1.83292i	−0.0417978	−	0.0723959i	0.844370	−	0.535761i	$-0.179975\pi$
$641$	−1.05824	−	1.83292i	−0.0417978	−	0.0723959i	−0.886167	+	0.463365i	$0.846642\pi$
$642$	−13.1736	−	3.26110i	−0.519920	−	0.128705i
$643$	−20.2717	+	35.1116i	−0.799438	+	1.38467i	0.120545	+	0.992708i	$0.461536\pi$
$643$	−20.2717	+	35.1116i	−0.799438	+	1.38467i	−0.919983	+	0.391959i	$0.871797\pi$
$644$	1.77657	−	3.07710i	0.0700065	−	0.121255i
$645$	25.4450	−	26.4376i	1.00189	−	1.04098i
$646$	2.80862	+	4.86467i	0.110504	+	0.191398i
$647$	27.1978			1.06925			0.534627	−	0.845088i	$-0.320452\pi$
$647$	27.1978			1.06925			0.534627	+	0.845088i	$0.320452\pi$
$648$	8.97366	−	0.687996i	0.352519	−	0.0270271i
$649$	−17.8512			−0.700722
$650$	−2.33468	−	4.04378i	−0.0915736	−	0.158610i
$651$	−7.60245	+	7.89902i	−0.297964	+	0.309587i
$652$	3.77802	−	6.54373i	0.147959	−	0.256272i
$653$	22.0042	−	38.1124i	0.861092	−	1.49145i	−0.00978470	−	0.999952i	$-0.503115\pi$
$653$	22.0042	−	38.1124i	0.861092	−	1.49145i	0.870876	−	0.491502i	$-0.163552\pi$
$654$	−1.78440	−	0.441726i	−0.0697757	−	0.0172728i
$655$	−16.2667	−	28.1747i	−0.635591	−	1.10088i
$656$	−9.35568			−0.365278
$657$	1.16995	+	30.5645i	0.0456441	+	1.19244i
$658$	36.3322			1.41638
$659$	−0.174968	−	0.303053i	−0.00681578	−	0.0118053i	0.862597	−	0.505891i	$-0.168836\pi$
$659$	−0.174968	−	0.303053i	−0.00681578	−	0.0118053i	−0.869413	+	0.494086i	$0.835503\pi$
$660$	5.48453	+	19.0065i	0.213485	+	0.739827i
$661$	−16.1774	+	28.0201i	−0.629228	+	1.08985i	0.358479	+	0.933538i	$0.383295\pi$
$661$	−16.1774	+	28.0201i	−0.629228	+	1.08985i	−0.987707	+	0.156317i	$0.950038\pi$
$662$	9.52877	−	16.5043i	0.370346	−	0.641459i
$663$	−1.44727	−	5.01547i	−0.0562072	−	0.194785i
$664$	−6.68659	−	11.5815i	−0.259490	−	0.449450i
$665$	31.3686			1.21642
$666$	−3.28023	+	2.06504i	−0.127106	+	0.0800187i
$667$	7.10444			0.275085
$668$	−4.79999	−	8.31383i	−0.185717	−	0.321672i
$669$	−39.4007	−	9.75357i	−1.52332	−	0.377095i
$670$	−1.24299	+	2.15293i	−0.0480210	+	0.0831748i
$671$	−19.8431	+	34.3692i	−0.766034	+	1.32681i
$672$	4.26764	−	4.43413i	0.164628	−	0.171050i
$673$	22.9616	+	39.7706i	0.885103	+	1.53304i	0.845595	+	0.533825i	$0.179246\pi$
$673$	22.9616	+	39.7706i	0.885103	+	1.53304i	0.0395084	+	0.999219i	$0.487421\pi$
$674$	−25.4161			−0.978993
$675$	2.89328	−	13.9566i	0.111362	−	0.537188i
$676$	−10.1023			−0.388552
$677$	−23.5854	−	40.8511i	−0.906460	−	1.57003i	−0.818946	−	0.573871i	$-0.805441\pi$
$677$	−23.5854	−	40.8511i	−0.906460	−	1.57003i	−0.0875139	−	0.996163i	$-0.527892\pi$
$678$	11.2090	−	11.6463i	0.430481	−	0.447274i
$679$	22.5126	−	38.9930i	0.863955	−	1.49641i
$680$	2.46333	−	4.26661i	0.0944643	−	0.163617i
$681$	−26.4876	−	6.55695i	−1.01501	−	0.251263i
$682$	3.65585	+	6.33212i	0.139990	+	0.242470i
$683$	3.71123			0.142006			0.0710032	−	0.997476i	$-0.477380\pi$
$683$	3.71123			0.142006			0.0710032	+	0.997476i	$0.477380\pi$
$684$	−8.41888	−	4.44026i	−0.321904	−	0.169777i
$685$	−40.0169			−1.52897
$686$	−2.44321	−	4.23176i	−0.0932821	−	0.161569i
$687$	5.69118	+	19.7226i	0.217132	+	0.752466i
$688$	−3.80661	+	6.59325i	−0.145126	+	0.251365i
$689$	9.26139	−	16.0412i	0.352831	−	0.611121i
$690$	1.33624	+	4.63072i	0.0508699	+	0.176289i
$691$	−7.48520	−	12.9647i	−0.284750	−	0.493202i	0.687798	−	0.725902i	$-0.258577\pi$
$691$	−7.48520	−	12.9647i	−0.284750	−	0.493202i	−0.972549	+	0.232700i	$0.925244\pi$
$692$	−10.4653			−0.397833
$693$	38.6983	+	20.4101i	1.47003	+	0.775317i
$694$	22.6679			0.860461
$695$	−10.0273	−	17.3678i	−0.380356	−	0.658796i
$696$	11.9447	+	2.95689i	0.452763	+	0.112081i
$697$	−8.28211	+	14.3450i	−0.313707	+	0.543357i
$698$	6.76024	−	11.7091i	0.255879	−	0.443195i
$699$	−2.38527	+	2.47832i	−0.0902190	+	0.0937385i
$700$	−4.87321	−	8.44065i	−0.184190	−	0.319027i
$701$	−28.3822			−1.07198			−0.535990	−	0.844224i	$-0.680062\pi$
$701$	−28.3822			−1.07198			−0.535990	+	0.844224i	$0.680062\pi$
$702$	6.60291	+	5.88543i	0.249211	+	0.222131i
$703$	4.09924			0.154606
$704$	−2.05222	−	3.55455i	−0.0773459	−	0.133967i
$705$	−34.1754	+	35.5086i	−1.28712	+	1.33733i
$706$	−17.4879	+	30.2899i	−0.658164	+	1.13997i
$707$	−12.4785	+	21.6134i	−0.469301	+	0.812854i
$708$	−7.31240	−	1.81017i	−0.274817	−	0.0680304i
$709$	17.7168	+	30.6864i	0.665369	+	1.15245i	0.979185	+	0.202970i	$0.0650593\pi$
$709$	17.7168	+	30.6864i	0.665369	+	1.15245i	−0.313816	+	0.949484i	$0.601607\pi$
$710$	−27.3526			−1.02652
$711$	−27.2843	+	17.1766i	−1.02324	+	0.644173i
$712$	−15.2267			−0.570646
$713$	0.890708	+	1.54275i	0.0333573	+	0.0577765i
$714$	−3.02091	−	10.4689i	−0.113055	−	0.391788i
$715$	−9.72081	+	16.8369i	−0.363538	+	0.629666i
$716$	−4.53963	+	7.86288i	−0.169654	+	0.293849i
$717$	−7.49069	−	25.9588i	−0.279745	−	0.969450i
$718$	1.56328	+	2.70768i	0.0583411	+	0.101050i
$719$	−12.4519			−0.464377			−0.232189	−	0.972671i	$-0.574589\pi$
$719$	−12.4519			−0.464377			−0.232189	+	0.972671i	$0.574589\pi$
$720$	0.319307	+	8.34179i	0.0118999	+	0.310880i
$721$	−53.7600			−2.00213
$722$	−4.46703	−	7.73712i	−0.166246	−	0.287946i
$723$	1.51023	+	0.373854i	0.0561660	+	0.0139038i
$724$	13.1898	−	22.8454i	0.490196	−	0.849044i
$725$	9.74391	−	16.8770i	0.361880	−	0.626794i
$726$	7.02206	−	7.29600i	0.260613	−	0.270780i
$727$	−19.0540	−	33.0026i	−0.706675	−	1.22400i	−0.966084	−	0.258230i	$-0.916861\pi$
$727$	−19.0540	−	33.0026i	−0.706675	−	1.22400i	0.259408	−	0.965768i	$-0.416472\pi$
$728$	6.04832			0.224166
$729$	3.09221	+	26.8223i	0.114526	+	0.993420i
$730$	−28.3707			−1.05005
$731$	6.73961	+	11.6733i	0.249273	+	0.431754i
$732$	−11.6135	+	12.0665i	−0.429246	+	0.445992i
$733$	2.14422	−	3.71389i	0.0791985	−	0.137176i	−0.823706	−	0.567017i	$-0.808097\pi$
$733$	2.14422	−	3.71389i	0.0791985	−	0.137176i	0.902904	+	0.429842i	$0.141431\pi$
$734$	−9.60731	+	16.6403i	−0.354612	+	0.614206i
$735$	−26.3151	−	6.51426i	−0.970648	−	0.240282i
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	3.66688			0.135071
$738$	−1.07356	−	28.0465i	−0.0395184	−	1.03241i
$739$	24.8250			0.913204			0.456602	−	0.889671i	$-0.349066\pi$
$739$	24.8250			0.913204			0.456602	+	0.889671i	$0.349066\pi$
$740$	−1.79764	−	3.11360i	−0.0660825	−	0.114458i
$741$	−2.59346	−	8.98759i	−0.0952732	−	0.330167i
$742$	19.3315	−	33.4831i	0.709680	−	1.22920i
$743$	6.42145	−	11.1223i	0.235580	−	0.408037i	−0.723861	−	0.689946i	$-0.757634\pi$
$743$	6.42145	−	11.1223i	0.235580	−	0.408037i	0.959441	+	0.281909i	$0.0909677\pi$
$744$	0.855451	+	2.96455i	0.0313623	+	0.108686i
$745$	−29.2468	−	50.6570i	−1.07152	−	1.85593i
$746$	−10.7328			−0.392954
$747$	33.9518	−	21.3741i	1.24223	−	0.782036i
$748$	−7.26690			−0.265704
$749$	−13.9200	−	24.1102i	−0.508627	−	0.880967i
$750$	−10.5590	−	2.61387i	−0.385561	−	0.0954449i
$751$	1.17145	−	2.02901i	0.0427468	−	0.0740397i	−0.843860	−	0.536563i	$-0.819722\pi$
$751$	1.17145	−	2.02901i	0.0427468	−	0.0740397i	0.886607	+	0.462523i	$0.153056\pi$
$752$	5.11270	−	8.85546i	0.186441	−	0.322925i
$753$	17.2981	−	17.9729i	0.630376	−	0.654968i
$754$	6.04676	+	10.4733i	0.220210	+	0.381415i
$755$	62.1976			2.26360
$756$	13.7824	+	12.2847i	0.501260	+	0.446792i
$757$	22.3582			0.812622			0.406311	−	0.913735i	$-0.366815\pi$
$757$	22.3582			0.812622			0.406311	+	0.913735i	$0.366815\pi$
$758$	−13.1088	−	22.7051i	−0.476133	−	0.824686i
$759$	4.92981	−	5.12212i	0.178941	−	0.185921i
$760$	4.41421	−	7.64564i	0.160120	−	0.277336i
$761$	−3.62069	+	6.27122i	−0.131250	+	0.227332i	−0.924159	−	0.382009i	$-0.875232\pi$
$761$	−3.62069	+	6.27122i	−0.131250	+	0.227332i	0.792909	+	0.609341i	$0.208566\pi$
$762$	−14.8690	−	3.68079i	−0.538646	−	0.133341i
$763$	−1.88551	−	3.26580i	−0.0682601	−	0.118230i
$764$	2.06232			0.0746123
$765$	13.0731	+	6.89498i	0.472660	+	0.249288i
$766$	−4.12154			−0.148917
$767$	−3.70175	−	6.41163i	−0.133663	−	0.231510i
$768$	−0.480208	−	1.66415i	−0.0173280	−	0.0600499i
$769$	−12.4106	+	21.4959i	−0.447539	+	0.775161i	−0.998225	−	0.0595518i	$-0.981033\pi$
$769$	−12.4106	+	21.4959i	−0.447539	+	0.775161i	0.550686	+	0.834712i	$0.314366\pi$
$770$	−20.2904	+	35.1440i	−0.731216	+	1.26650i
$771$	1.45965	+	5.05838i	0.0525680	+	0.182173i
$772$	2.79416	+	4.83962i	0.100564	+	0.174182i
$773$	30.3720			1.09241			0.546203	−	0.837653i	$-0.316073\pi$
$773$	30.3720			1.09241			0.546203	+	0.837653i	$0.316073\pi$
$774$	−20.2021	−	10.6549i	−0.726149	−	0.382983i
$775$	4.88651			0.175529
$776$	−6.33599	−	10.9743i	−0.227449	−	0.393953i
$777$	−7.71851	−	1.91070i	−0.276900	−	0.0685461i
$778$	−7.81113	+	13.5293i	−0.280042	+	0.485048i
$779$	−14.8413	+	25.7059i	−0.531745	+	0.921010i
$780$	−5.68926	+	5.91120i	−0.203708	+	0.211655i
$781$	20.1728	+	34.9402i	0.721838	+	1.25026i
$782$	−1.77050			−0.0633129
$783$	−7.49352	+	36.1472i	−0.267796	+	1.29179i
$784$	5.62476			0.200884
$785$	5.89678	+	10.2135i	0.210465	+	0.364536i
$786$	−14.0427	+	14.5905i	−0.500885	+	0.520425i
$787$	−15.1620	+	26.2613i	−0.540466	+	0.936114i	0.458411	+	0.888740i	$0.348419\pi$
$787$	−15.1620	+	26.2613i	−0.540466	+	0.936114i	−0.998877	+	0.0473743i	$0.984915\pi$
$788$	11.8228	−	20.4776i	0.421169	−	0.729486i
$789$	10.9635	+	2.71400i	0.390312	+	0.0966211i
$790$	−14.9524	−	25.8983i	−0.531983	−	0.921421i
$791$	33.1592			1.17900
$792$	10.4203	−	6.56003i	0.370271	−	0.233101i
$793$	−16.4592			−0.584483
$794$	7.91968	+	13.7173i	0.281059	+	0.486808i
$795$	14.5401	+	50.3886i	0.515686	+	1.78710i
$796$	−1.71178	+	2.96489i	−0.0606724	+	0.105088i
$797$	−10.4010	+	18.0151i	−0.368423	+	0.638128i	−0.989319	−	0.145765i	$-0.953436\pi$
$797$	−10.4010	+	18.0151i	−0.368423	+	0.638128i	0.620896	+	0.783893i	$0.286769\pi$
$798$	−5.41338	−	18.7599i	−0.191632	−	0.664095i
$799$	−9.05204	−	15.6786i	−0.320238	−	0.554669i
$800$	−2.74305			−0.0969815
$801$	−1.74727	−	45.6468i	−0.0617367	−	1.61285i
$802$	−2.85635			−0.100861
$803$	20.9237	+	36.2409i	0.738381	+	1.27891i
$804$	1.50206	+	0.371833i	0.0529737	+	0.0131135i
$805$	−4.94353	+	8.56245i	−0.174237	+	0.301787i
$806$	−1.51621	+	2.62615i	−0.0534061	+	0.0925021i
$807$	−27.2058	+	28.2671i	−0.957690	+	0.995050i
$808$	3.51196	+	6.08290i	0.123550	+	0.213996i
$809$	−8.08187			−0.284143			−0.142072	−	0.989856i	$-0.545376\pi$
$809$	−8.08187			−0.284143			−0.142072	+	0.989856i	$0.545376\pi$
$810$	−24.9704	+	1.91444i	−0.877371	+	0.0672666i
$811$	34.9201			1.22621			0.613106	−	0.790001i	$-0.289920\pi$
$811$	34.9201			1.22621			0.613106	+	0.790001i	$0.289920\pi$
$812$	12.6215	+	21.8611i	0.442928	+	0.767174i
$813$	7.50690	−	7.79974i	0.263278	−	0.273549i
$814$	−2.65155	+	4.59262i	−0.0929367	+	0.160971i
$815$	−10.5129	+	18.2088i	−0.368249	+	0.637827i
$816$	−2.97674	−	0.736888i	−0.104207	−	0.0257962i
$817$	12.0772	+	20.9183i	0.422528	+	0.731839i
$818$	19.4668			0.680641
$819$	0.694045	+	18.1317i	0.0242519	+	0.633572i
$820$	26.0334			0.909126
$821$	−6.07469	−	10.5217i	−0.212008	−	0.367209i	0.740335	−	0.672238i	$-0.234667\pi$
$821$	−6.07469	−	10.5217i	−0.212008	−	0.367209i	−0.952343	+	0.305029i	$0.901334\pi$
$822$	6.90585	+	23.9321i	0.240869	+	0.834727i
$823$	1.64369	−	2.84696i	0.0572955	−	0.0992387i	−0.835955	−	0.548798i	$-0.815086\pi$
$823$	1.64369	−	2.84696i	0.0572955	−	0.0992387i	0.893250	+	0.449559i	$0.148419\pi$
$824$	−7.56516	+	13.1032i	−0.263545	+	0.456473i
$825$	−5.40651	−	18.7361i	−0.188230	−	0.652309i
$826$	−7.72674	−	13.3831i	−0.268848	−	0.465658i
$827$	6.07229			0.211154			0.105577	−	0.994411i	$-0.466331\pi$
$827$	6.07229			0.211154			0.105577	+	0.994411i	$0.466331\pi$
$828$	2.53880	−	1.59828i	0.0882294	−	0.0555440i
$829$	−12.2327			−0.424858			−0.212429	−	0.977177i	$-0.568137\pi$
$829$	−12.2327			−0.424858			−0.212429	+	0.977177i	$0.568137\pi$
$830$	18.6063	+	32.2271i	0.645835	+	1.11862i
$831$	33.3327	+	8.25144i	1.15630	+	0.286239i
$832$	0.851125	−	1.47419i	0.0295074	−	0.0511084i
$833$	4.97932	−	8.62443i	0.172523	−	0.298819i
$834$	−8.65633	+	8.99401i	−0.299744	+	0.311437i
$835$	13.3566	+	23.1343i	0.462225	+	0.800597i
$836$	−13.0221			−0.450378
$837$	−8.78897	+	2.90466i	−0.303791	+	0.100400i
$838$	35.6416			1.23122
$839$	12.9001	+	22.3436i	0.445360	+	0.771386i	0.998077	−	0.0619829i	$-0.0197424\pi$
$839$	12.9001	+	22.3436i	0.445360	+	0.771386i	−0.552717	+	0.833369i	$0.686409\pi$
$840$	−11.8753	+	12.3386i	−0.409737	+	0.425720i
$841$	−10.7365	+	18.5962i	−0.370224	+	0.641247i
$842$	6.80073	−	11.7792i	0.234369	−	0.405938i
$843$	−7.91858	−	1.96023i	−0.272730	−	0.0675139i
$844$	8.52713	+	14.7694i	0.293516	+	0.508385i
$845$	28.1111			0.967052
$846$	27.1336	+	14.3107i	0.932873	+	0.492013i
$847$	20.7730			0.713769
$848$	−5.44068	−	9.42353i	−0.186834	−	0.323605i
$849$	0.737554	+	2.55598i	0.0253128	+	0.0877209i
$850$	−2.42829	+	4.20591i	−0.0832895	+	0.144262i
$851$	−0.646020	+	1.11894i	−0.0221453	+	0.0383568i
$852$	4.72032	+	16.3582i	0.161716	+	0.560422i
$853$	23.2329	+	40.2406i	0.795479	+	1.37781i	0.922534	+	0.385915i	$0.126114\pi$
$853$	23.2329	+	40.2406i	0.795479	+	1.37781i	−0.127055	+	0.991896i	$0.540552\pi$
$854$	−34.3556			−1.17562
$855$	23.4267	+	12.3556i	0.801175	+	0.422553i
$856$	−7.83535			−0.267807
$857$	0.779842	+	1.35073i	0.0266389	+	0.0461399i	0.879038	−	0.476753i	$-0.158186\pi$
$857$	0.779842	+	1.35073i	0.0266389	+	0.0461399i	−0.852399	+	0.522893i	$0.824853\pi$
$858$	11.7469	+	2.90792i	0.401032	+	0.0992746i
$859$	−20.2819	+	35.1293i	−0.692009	+	1.19859i	0.279170	+	0.960242i	$0.409941\pi$
$859$	−20.2819	+	35.1293i	−0.692009	+	1.19859i	−0.971179	+	0.238353i	$0.923393\pi$
$860$	10.5924	−	18.3466i	0.361198	−	0.625614i
$861$	39.9267	−	41.4843i	1.36070	−	1.41378i
$862$	−8.52184	−	14.7603i	−0.290255	−	0.502737i
$863$	−47.9157			−1.63107			−0.815534	−	0.578709i	$-0.803557\pi$
$863$	−47.9157			−1.63107			−0.815534	+	0.578709i	$0.803557\pi$
$864$	4.93370	−	1.63053i	0.167848	−	0.0554718i
$865$	29.1212			0.990151
$866$	−5.35696	−	9.27853i	−0.182037	−	0.315297i
$867$	16.6536	−	17.3032i	0.565584	−	0.587648i
$868$	−3.16480	+	5.48160i	−0.107420	+	0.186058i
$869$	−22.0551	+	38.2005i	−0.748167	+	1.29586i
$870$	−33.2377	−	8.22794i	−1.12686	−	0.278953i
$871$	0.760389	+	1.31703i	0.0257648	+	0.0446259i
$872$	−1.06132			−0.0359409
$873$	32.1716	−	20.2534i	1.08884	−	0.685472i
$874$	−3.17269			−0.107318
$875$	−11.1573	−	19.3250i	−0.377186	−	0.653305i
$876$	4.89603	+	16.9671i	0.165422	+	0.573265i
$877$	7.84509	−	13.5881i	0.264910	−	0.458837i	−0.702630	−	0.711555i	$-0.747991\pi$
$877$	7.84509	−	13.5881i	0.264910	−	0.458837i	0.967540	+	0.252718i	$0.0813245\pi$
$878$	−15.9496	+	27.6255i	−0.538274	+	0.932317i
$879$	−5.57384	−	19.3160i	−0.188001	−	0.651513i
$880$	5.71057	+	9.89100i	0.192503	+	0.333425i
$881$	15.9802			0.538385			0.269193	−	0.963086i	$-0.413243\pi$
$881$	15.9802			0.538385			0.269193	+	0.963086i	$0.413243\pi$
$882$	0.645441	+	16.8619i	0.0217331	+	0.567771i
$883$	50.2366			1.69060			0.845298	−	0.534296i	$-0.179423\pi$
$883$	50.2366			1.69060			0.845298	+	0.534296i	$0.179423\pi$
$884$	−1.50692	−	2.61006i	−0.0506831	−	0.0877857i
$885$	20.3477	+	5.03705i	0.683982	+	0.169318i
$886$	1.90330	−	3.29661i	0.0639425	−	0.110752i
$887$	−1.49885	+	2.59609i	−0.0503266	+	0.0871682i	−0.890091	−	0.455782i	$-0.849360\pi$
$887$	−1.49885	+	2.59609i	−0.0503266	+	0.0871682i	0.839765	+	0.542951i	$0.182693\pi$
$888$	−1.55186	+	1.61240i	−0.0520771	+	0.0541086i
$889$	−15.7115	−	27.2131i	−0.526946	−	0.912697i
$890$	42.3704			1.42026
$891$	20.8614	+	30.4854i	0.698884	+	1.02130i
$892$	−23.4346			−0.784650
$893$	−16.2210	−	28.0956i	−0.542815	−	0.940183i
$894$	−25.2482	+	26.2331i	−0.844425	+	0.877366i
$895$	12.6321	−	21.8795i	0.422246	−	0.731351i
$896$	1.77657	−	3.07710i	0.0593509	−	0.102799i
$897$	2.86199	+	0.708481i	0.0955592	+	0.0236555i
$898$	−5.53807	−	9.59222i	−0.184808	−	0.320096i
$899$	−12.6560			−0.422100
$900$	−0.314765	−	8.22313i	−0.0104922	−	0.274104i
$901$	−19.2654			−0.641825
$902$	−19.1999	−	33.2552i	−0.639286	−	1.10728i
$903$	−12.9900	−	45.0167i	−0.432281	−	1.49806i
$904$	4.66618	−	8.08207i	0.155195	−	0.268806i
$905$	−36.7024	+	63.5705i	−1.22003	+	2.11315i
$906$	−10.7336	−	37.1972i	−0.356602	−	1.23579i
$907$	−20.7754	−	35.9841i	−0.689837	−	1.19483i	−0.971890	−	0.235434i	$-0.924349\pi$
$907$	−20.7754	−	35.9841i	−0.689837	−	1.19483i	0.282053	−	0.959399i	$-0.408984\pi$
$908$	−15.7542			−0.522821
$909$	−17.8323	+	11.2262i	−0.591462	+	0.372349i
$910$	−16.8303			−0.557918
$911$	−0.685864	−	1.18795i	−0.0227237	−	0.0393586i	0.854440	−	0.519550i	$-0.173900\pi$
$911$	−0.685864	−	1.18795i	−0.0227237	−	0.0393586i	−0.877164	+	0.480192i	$0.840567\pi$
$912$	−5.33424	−	1.32048i	−0.176634	−	0.0437255i
$913$	27.4447	−	47.5355i	0.908286	−	1.57320i
$914$	−8.43995	+	14.6184i	−0.279169	+	0.483535i
$915$	32.3161	−	33.5767i	1.06834	−	1.11001i
$916$	5.92574	+	10.2637i	0.195792	+	0.339121i
$917$	−41.5417			−1.37183
$918$	1.86746	−	9.00826i	0.0616355	−	0.297317i
$919$	15.6120			0.514991			0.257496	−	0.966279i	$-0.417103\pi$
$919$	15.6120			0.514991			0.257496	+	0.966279i	$0.417103\pi$
$920$	1.39132	+	2.40983i	0.0458704	+	0.0794498i
$921$	−40.5983	+	42.1821i	−1.33776	+	1.38995i
$922$	8.64366	−	14.9713i	0.284664	−	0.493052i
$923$	−8.36633	+	14.4909i	−0.275381	+	0.476974i
$924$	24.5194	+	6.06974i	0.806630	+	0.199680i
$925$	1.77207	+	3.06931i	0.0582652	+	0.100918i
$926$	31.5420			1.03653
$927$	−40.1491	−	21.1753i	−1.31867	−	0.695487i
$928$	7.10444			0.233215
$929$	23.1938	+	40.1728i	0.760963	+	1.31803i	0.942355	+	0.334615i	$0.108606\pi$
$929$	23.1938	+	40.1728i	0.760963	+	1.31803i	−0.181392	+	0.983411i	$0.558060\pi$
$930$	−2.38041	−	8.24924i	−0.0780566	−	0.270503i
$931$	8.92280	−	15.4547i	0.292433	−	0.506509i
$932$	−0.992956	+	1.71985i	−0.0325254	+	0.0563356i
$933$	−2.28664	−	7.92428i	−0.0748611	−	0.259429i
$934$	−9.85038	−	17.0614i	−0.322314	−	0.558265i
$935$	20.2211			0.661302
$936$	4.51700	+	2.38234i	0.147643	+	0.0778693i
$937$	−26.9503			−0.880429			−0.440215	−	0.897893i	$-0.645098\pi$
$937$	−26.9503			−0.880429			−0.440215	+	0.897893i	$0.645098\pi$
$938$	1.58717	+	2.74906i	0.0518230	+	0.0897601i
$939$	−40.1914	−	9.94931i	−1.31160	−	0.324684i
$940$	−14.2268	+	24.6415i	−0.464026	+	0.803717i
$941$	5.27501	−	9.13659i	0.171961	−	0.297844i	−0.767145	−	0.641474i	$-0.778323\pi$
$941$	5.27501	−	9.13659i	0.171961	−	0.297844i	0.939105	+	0.343630i	$0.111656\pi$
$942$	5.09056	−	5.28915i	0.165860	−	0.172330i
$943$	−4.67784	−	8.10225i	−0.152331	−	0.263846i
$944$	−4.34925			−0.141556
$945$	−38.3513	−	34.1840i	−1.24757	−	1.11200i
$946$	−31.2480			−1.01596
$947$	−23.7353	−	41.1108i	−0.771294	−	1.33592i	−0.936854	−	0.349721i	$-0.886277\pi$
$947$	−23.7353	−	41.1108i	−0.771294	−	1.33592i	0.165560	−	0.986200i	$-0.447057\pi$
$948$	−12.9081	+	13.4116i	−0.419235	+	0.435590i
$949$	−8.67776	+	15.0303i	−0.281692	+	0.487905i
$950$	−4.35142	+	7.53688i	−0.141179	+	0.244529i
$951$	40.9429	+	10.1353i	1.32766	+	0.328661i
$952$	−3.14541	−	5.44801i	−0.101943	−	0.176571i
$953$	−35.8534			−1.16140			−0.580702	−	0.814116i	$-0.697222\pi$
$953$	−35.8534			−1.16140			−0.580702	+	0.814116i	$0.697222\pi$
$954$	27.6256	−	17.3914i	0.894412	−	0.563069i
$955$	−5.73869			−0.185700
$956$	−7.79942	−	13.5090i	−0.252251	−	0.436912i
$957$	14.0027	+	48.5262i	0.452644	+	1.56863i
$958$	8.22003	−	14.2375i	0.265577	−	0.459993i
$959$	−25.5487	+	44.2517i	−0.825011	+	1.42896i
$960$	1.33624	+	4.63072i	0.0431271	+	0.149456i
$961$	13.9133	+	24.0985i	0.448815	+	0.777371i
$962$	−2.19937			−0.0709107
$963$	−0.899107	−	23.4889i	−0.0289733	−	0.756918i
$964$	0.898250			0.0289307
$965$	−7.77512	−	13.4669i	−0.250290	−	0.433515i
$966$	5.97389	+	1.47883i	0.192207	+	0.0475804i
$967$	4.23819	−	7.34075i	0.136291	−	0.236063i	−0.789799	−	0.613366i	$-0.789815\pi$
$967$	4.23819	−	7.34075i	0.136291	−	0.236063i	0.926090	+	0.377303i	$0.123148\pi$
$968$	2.92320	−	5.06312i	0.0939551	−	0.162735i
$969$	−6.74683	+	7.01003i	−0.216739	+	0.225194i
$970$	17.6307	+	30.5373i	0.566089	+	0.980495i
$971$	34.5376			1.10836			0.554182	−	0.832395i	$-0.313031\pi$
$971$	34.5376			1.10836			0.554182	+	0.832395i	$0.313031\pi$
$972$	5.45416	+	14.6032i	0.174942	+	0.468396i
$973$	−25.6076			−0.820941
$974$	−11.7953	−	20.4301i	−0.377947	−	0.654623i
$975$	5.60833	−	5.82711i	0.179610	−	0.186617i
$976$	−4.83454	+	8.37368i	−0.154750	+	0.268035i
$977$	−21.9704	+	38.0538i	−0.702895	+	1.21745i	0.264551	+	0.964372i	$0.414776\pi$
$977$	−21.9704	+	38.0538i	−0.702895	+	1.21745i	−0.967446	+	0.253078i	$0.918557\pi$
$978$	12.7040	+	3.14485i	0.406229	+	0.100561i
$979$	−31.2486	−	54.1241i	−0.998709	−	1.72981i
$980$	−15.6516			−0.499973
$981$	−0.121787	−	3.18164i	−0.00388835	−	0.101582i
$982$	−3.21895			−0.102721
$983$	8.73641	+	15.1319i	0.278648	+	0.482633i	0.971049	−	0.238880i	$-0.0767804\pi$
$983$	8.73641	+	15.1319i	0.278648	+	0.482633i	−0.692401	+	0.721513i	$0.743447\pi$
$984$	−4.49267	−	15.5693i	−0.143221	−	0.496330i
$985$	−32.8984	+	56.9818i	−1.04823	+	1.81559i
$986$	6.28920	−	10.8932i	0.200289	−	0.346911i
$987$	17.4470	+	60.4623i	0.555345	+	1.92454i
$988$	−2.70035	−	4.67715i	−0.0859096	−	0.148800i
$989$	−7.61323			−0.242087
$990$	−28.9960	+	18.2542i	−0.921553	+	0.580156i
$991$	17.0866			0.542773			0.271386	−	0.962470i	$-0.412518\pi$
$991$	17.0866			0.542773			0.271386	+	0.962470i	$0.412518\pi$
$992$	0.890708	+	1.54275i	0.0282800	+	0.0489824i
$993$	32.0415	+	7.93181i	1.01681	+	0.251708i
$994$	−17.4632	+	30.2471i	−0.553898	+	0.959380i
$995$	4.76326	−	8.25020i	0.151005	−	0.261549i
$996$	16.0624	−	16.6890i	0.508957	−	0.528812i
$997$	−17.1355	−	29.6796i	−0.542688	−	0.939964i	−0.998748	−	0.0500146i	$-0.984073\pi$
$997$	−17.1355	−	29.6796i	−0.542688	−	0.939964i	0.456060	−	0.889949i	$-0.349260\pi$
$998$	−8.95911			−0.283596
$999$	−5.01174	−	4.46715i	−0.158564	−	0.141334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.e.139.2	✓	12
3.2	odd	2		1242.2.e.e.415.2		12
9.2	odd	6		1242.2.e.e.829.2		12
9.4	even	3		3726.2.a.w.1.2		6
9.5	odd	6		3726.2.a.x.1.5		6
9.7	even	3	inner	414.2.e.e.277.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.e.139.2	✓	12	1.1	even	1	trivial
414.2.e.e.277.2	yes	12	9.7	even	3	inner
1242.2.e.e.415.2		12	3.2	odd	2
1242.2.e.e.829.2		12	9.2	odd	6
3726.2.a.w.1.2		6	9.4	even	3
3726.2.a.x.1.5		6	9.5	odd	6

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.20109 + 1.24795i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.39132 - 2.40983i) q^{5} +(-1.68130 - 0.416203i) q^{6} +(-1.77657 - 3.07710i) q^{7} -1.00000 q^{8} +(-0.114750 - 2.99780i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.20109 + 1.24795i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.39132 - 2.40983i) q^{5} +(-1.68130 - 0.416203i) q^{6} +(-1.77657 - 3.07710i) q^{7} -1.00000 q^{8} +(-0.114750 - 2.99780i) q^{9} +2.78263 q^{10} +(-2.05222 - 3.55455i) q^{11} +(-0.480208 - 1.66415i) q^{12} +(0.851125 - 1.47419i) q^{13} +(1.77657 - 3.07710i) q^{14} +(1.33624 + 4.63072i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.77050 q^{17} +(2.53880 - 1.59828i) q^{18} -3.17269 q^{19} +(1.39132 + 2.40983i) q^{20} +(5.97389 + 1.47883i) q^{21} +(2.05222 - 3.55455i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.20109 - 1.24795i) q^{24} +(-1.37153 - 2.37555i) q^{25} +1.70225 q^{26} +(3.87893 + 3.45744i) q^{27} +3.55313 q^{28} +(3.55222 + 6.15262i) q^{29} +(-3.34220 + 3.47258i) q^{30} +(-0.890708 + 1.54275i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.90079 + 1.70828i) q^{33} +(-0.885250 - 1.53330i) q^{34} -9.88707 q^{35} +(2.65355 + 1.39953i) q^{36} -1.29204 q^{37} +(-1.58634 - 2.74763i) q^{38} +(0.817434 + 2.83280i) q^{39} +(-1.39132 + 2.40983i) q^{40} +(4.67784 - 8.10225i) q^{41} +(1.70624 + 5.91295i) q^{42} +(-3.80661 - 6.59325i) q^{43} +4.10444 q^{44} +(-7.38386 - 3.89437i) q^{45} +1.00000 q^{46} +(5.11270 + 8.85546i) q^{47} +(1.68130 + 0.416203i) q^{48} +(-2.81238 + 4.87118i) q^{49} +(1.37153 - 2.37555i) q^{50} +(2.12654 - 2.20949i) q^{51} +(0.851125 + 1.47419i) q^{52} +10.8814 q^{53} +(-1.05477 + 5.08797i) q^{54} -11.4211 q^{55} +(1.77657 + 3.07710i) q^{56} +(3.81069 - 3.95935i) q^{57} +(-3.55222 + 6.15262i) q^{58} +(2.17463 - 3.76656i) q^{59} +(-4.67845 - 1.15814i) q^{60} +(-4.83454 - 8.37368i) q^{61} -1.78142 q^{62} +(-9.02070 + 5.67890i) q^{63} +1.00000 q^{64} +(-2.36837 - 4.10213i) q^{65} +(1.97098 + 6.83040i) q^{66} +(-0.446697 + 0.773701i) q^{67} +(0.885250 - 1.53330i) q^{68} +(0.480208 + 1.66415i) q^{69} +(-4.94353 - 8.56245i) q^{70} -9.82973 q^{71} +(0.114750 + 2.99780i) q^{72} -10.1956 q^{73} +(-0.646020 - 1.11894i) q^{74} +(4.61189 + 1.14167i) q^{75} +(1.58634 - 2.74763i) q^{76} +(-7.29180 + 12.6298i) q^{77} +(-2.04456 + 2.12432i) q^{78} +(-5.37347 - 9.30713i) q^{79} -2.78263 q^{80} +(-8.97366 + 0.687996i) q^{81} +9.35568 q^{82} +(6.68659 + 11.5815i) q^{83} +(-4.26764 + 4.43413i) q^{84} +(-2.46333 + 4.26661i) q^{85} +(3.80661 - 6.59325i) q^{86} +(-11.9447 - 2.95689i) q^{87} +(2.05222 + 3.55455i) q^{88} +15.2267 q^{89} +(-0.319307 - 8.34179i) q^{90} -6.04832 q^{91} +(0.500000 + 0.866025i) q^{92} +(-0.855451 - 2.96455i) q^{93} +(-5.11270 + 8.85546i) q^{94} +(-4.41421 + 7.64564i) q^{95} +(0.480208 + 1.66415i) q^{96} +(6.33599 + 10.9743i) q^{97} -5.62476 q^{98} +(-10.4203 + 6.56003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9} + 10 q^{10} + 6 q^{11} - 6 q^{13} + 3 q^{14} + 7 q^{15} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 4 q^{19} + 5 q^{20} + 17 q^{21} - 6 q^{22} + 6 q^{23} + q^{25} - 12 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} - q^{30} - 6 q^{31} + 6 q^{32} + 9 q^{33} - 4 q^{34} - 34 q^{35} - 2 q^{36} + 8 q^{37} + 2 q^{38} + 23 q^{39} - 5 q^{40} + 15 q^{41} + 7 q^{42} - 14 q^{43} - 12 q^{44} - 37 q^{45} + 12 q^{46} + 9 q^{47} - 5 q^{49} - q^{50} + 9 q^{51} - 6 q^{52} - 10 q^{53} - 9 q^{54} + 16 q^{55} + 3 q^{56} + 37 q^{57} - 12 q^{58} + 18 q^{59} - 8 q^{60} - 3 q^{61} - 12 q^{62} - 42 q^{63} + 12 q^{64} + 9 q^{65} + 3 q^{66} + 8 q^{67} + 4 q^{68} - 17 q^{70} - 18 q^{71} + 8 q^{72} - 32 q^{73} + 4 q^{74} + 34 q^{75} - 2 q^{76} - q^{77} + 22 q^{78} - 7 q^{79} - 10 q^{80} - 56 q^{81} + 30 q^{82} + 3 q^{83} - 10 q^{84} + 7 q^{85} + 14 q^{86} - 9 q^{87} - 6 q^{88} - 42 q^{89} - 17 q^{90} + 18 q^{91} + 6 q^{92} + 69 q^{93} - 9 q^{94} + 11 q^{95} + 13 q^{97} - 10 q^{98} - 60 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9 + 10 * q^10 + 6 * q^11 - 6 * q^13 + 3 * q^14 + 7 * q^15 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 4 * q^19 + 5 * q^20 + 17 * q^21 - 6 * q^22 + 6 * q^23 + q^25 - 12 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 - q^30 - 6 * q^31 + 6 * q^32 + 9 * q^33 - 4 * q^34 - 34 * q^35 - 2 * q^36 + 8 * q^37 + 2 * q^38 + 23 * q^39 - 5 * q^40 + 15 * q^41 + 7 * q^42 - 14 * q^43 - 12 * q^44 - 37 * q^45 + 12 * q^46 + 9 * q^47 - 5 * q^49 - q^50 + 9 * q^51 - 6 * q^52 - 10 * q^53 - 9 * q^54 + 16 * q^55 + 3 * q^56 + 37 * q^57 - 12 * q^58 + 18 * q^59 - 8 * q^60 - 3 * q^61 - 12 * q^62 - 42 * q^63 + 12 * q^64 + 9 * q^65 + 3 * q^66 + 8 * q^67 + 4 * q^68 - 17 * q^70 - 18 * q^71 + 8 * q^72 - 32 * q^73 + 4 * q^74 + 34 * q^75 - 2 * q^76 - q^77 + 22 * q^78 - 7 * q^79 - 10 * q^80 - 56 * q^81 + 30 * q^82 + 3 * q^83 - 10 * q^84 + 7 * q^85 + 14 * q^86 - 9 * q^87 - 6 * q^88 - 42 * q^89 - 17 * q^90 + 18 * q^91 + 6 * q^92 + 69 * q^93 - 9 * q^94 + 11 * q^95 + 13 * q^97 - 10 * q^98 - 60 * q^99

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