LMFDB - Embedded newform 406.2.e.a.291.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(233,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, 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("406.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.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:	$3.24192632206$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			291.1
Root			$-0.359001 - 0.701254i$ of defining polynomial
Character	$\chi$	$=$	406.291
Dual form			406.2.e.a.233.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.61748 + 2.80156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.572197 - 0.991074i) q^{5} +3.23497 q^{6} +(0.469216 - 2.60381i) q^{7} +1.00000 q^{8} +(-3.73251 - 6.46489i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.61748 + 2.80156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.572197 - 0.991074i) q^{5} +3.23497 q^{6} +(0.469216 - 2.60381i) q^{7} +1.00000 q^{8} +(-3.73251 - 6.46489i) q^{9} +(-0.572197 + 0.991074i) q^{10} +(0.425341 - 0.736713i) q^{11} +(-1.61748 - 2.80156i) q^{12} +3.66136 q^{13} +(-2.48958 + 0.895553i) q^{14} +3.70208 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0971241 + 0.168224i) q^{17} +(-3.73251 + 6.46489i) q^{18} +(3.49684 + 6.05671i) q^{19} +1.14439 q^{20} +(6.53580 + 5.52616i) q^{21} -0.850683 q^{22} +(1.73109 + 2.99834i) q^{23} +(-1.61748 + 2.80156i) q^{24} +(1.84518 - 3.19595i) q^{25} +(-1.83068 - 3.17083i) q^{26} +14.4442 q^{27} +(2.02036 + 1.70826i) q^{28} -1.00000 q^{29} +(-1.85104 - 3.20609i) q^{30} +(1.98711 - 3.44178i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.37597 + 2.38324i) q^{33} +0.194248 q^{34} +(-2.84905 + 1.02487i) q^{35} +7.46501 q^{36} +(-3.60460 - 6.24335i) q^{37} +(3.49684 - 6.05671i) q^{38} +(-5.92219 + 10.2575i) q^{39} +(-0.572197 - 0.991074i) q^{40} +4.04493 q^{41} +(1.51790 - 8.42325i) q^{42} +9.77788 q^{43} +(0.425341 + 0.736713i) q^{44} +(-4.27146 + 7.39838i) q^{45} +(1.73109 - 2.99834i) q^{46} +(-0.0269105 - 0.0466104i) q^{47} +3.23497 q^{48} +(-6.55967 - 2.44350i) q^{49} -3.69036 q^{50} +(-0.314193 - 0.544199i) q^{51} +(-1.83068 + 3.17083i) q^{52} +(1.33549 - 2.31313i) q^{53} +(-7.22208 - 12.5090i) q^{54} -0.973516 q^{55} +(0.469216 - 2.60381i) q^{56} -22.6244 q^{57} +(0.500000 + 0.866025i) q^{58} +(4.02177 - 6.96591i) q^{59} +(-1.85104 + 3.20609i) q^{60} +(2.54072 + 4.40065i) q^{61} -3.97423 q^{62} +(-18.5847 + 6.68531i) q^{63} +1.00000 q^{64} +(-2.09502 - 3.62868i) q^{65} +(1.37597 - 2.38324i) q^{66} +(5.80013 - 10.0461i) q^{67} +(-0.0971241 - 0.168224i) q^{68} -11.2001 q^{69} +(2.31209 + 1.95492i) q^{70} -11.2825 q^{71} +(-3.73251 - 6.46489i) q^{72} +(3.65539 - 6.33131i) q^{73} +(-3.60460 + 6.24335i) q^{74} +(5.96910 + 10.3388i) q^{75} -6.99369 q^{76} +(-1.71868 - 1.45319i) q^{77} +11.8444 q^{78} +(6.67821 + 11.5670i) q^{79} +(-0.572197 + 0.991074i) q^{80} +(-12.1657 + 21.0716i) q^{81} +(-2.02247 - 3.50301i) q^{82} +9.04564 q^{83} +(-8.05369 + 2.89708i) q^{84} +0.222296 q^{85} +(-4.88894 - 8.46789i) q^{86} +(1.61748 - 2.80156i) q^{87} +(0.425341 - 0.736713i) q^{88} +(-7.11526 - 12.3240i) q^{89} +8.54291 q^{90} +(1.71797 - 9.53349i) q^{91} -3.46219 q^{92} +(6.42825 + 11.1340i) q^{93} +(-0.0269105 + 0.0466104i) q^{94} +(4.00177 - 6.93126i) q^{95} +(-1.61748 - 2.80156i) q^{96} +18.7779 q^{97} +(1.16370 + 6.90259i) q^{98} -6.35036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/406\mathbb{Z}\right)^\times$.

$n$	$59$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.61748	+	2.80156i	−0.933854	+	1.61748i	−0.157191	+	0.987568i	$0.550244\pi$
$3$	−1.61748	+	2.80156i	−0.933854	+	1.61748i	−0.776664	+	0.629915i	$0.783090\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.572197	−	0.991074i	−0.255894	−	0.443222i	0.709244	−	0.704963i	$-0.249037\pi$
$5$	−0.572197	−	0.991074i	−0.255894	−	0.443222i	−0.965138	+	0.261741i	$0.915703\pi$
$6$	3.23497			1.32067
$7$	0.469216	−	2.60381i	0.177347	−	0.984148i
$7$	0.469216	−	2.60381i	0.177347	−	0.984148i
$8$	1.00000			0.353553
$9$	−3.73251	−	6.46489i	−1.24417	−	2.15496i
$10$	−0.572197	+	0.991074i	−0.180945	+	0.313405i
$11$	0.425341	−	0.736713i	0.128245	−	0.222127i	−0.794752	−	0.606935i	$-0.792399\pi$
$11$	0.425341	−	0.736713i	0.128245	−	0.222127i	0.922997	+	0.384808i	$0.125732\pi$
$12$	−1.61748	−	2.80156i	−0.466927	−	0.808742i
$13$	3.66136			1.01548			0.507739	−	0.861511i	$-0.330481\pi$
$13$	3.66136			1.01548			0.507739	+	0.861511i	$0.330481\pi$
$14$	−2.48958	+	0.895553i	−0.665367	+	0.239347i
$15$	3.70208			0.955872
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.0971241	+	0.168224i	−0.0235561	+	0.0408003i	−0.877563	−	0.479461i	$-0.840832\pi$
$17$	−0.0971241	+	0.168224i	−0.0235561	+	0.0408003i	0.854007	+	0.520261i	$0.174165\pi$
$18$	−3.73251	+	6.46489i	−0.879760	+	1.52379i
$19$	3.49684	+	6.05671i	0.802231	+	1.38950i	0.918145	+	0.396246i	$0.129687\pi$
$19$	3.49684	+	6.05671i	0.802231	+	1.38950i	−0.115913	+	0.993259i	$0.536980\pi$
$20$	1.14439			0.255894
$21$	6.53580	+	5.52616i	1.42623	+	1.20591i
$22$	−0.850683			−0.181366
$23$	1.73109	+	2.99834i	0.360958	+	0.625197i	0.988119	−	0.153692i	$-0.0491165\pi$
$23$	1.73109	+	2.99834i	0.360958	+	0.625197i	−0.627161	+	0.778890i	$0.715783\pi$
$24$	−1.61748	+	2.80156i	−0.330167	+	0.571867i
$25$	1.84518	−	3.19595i	0.369036	−	0.639190i
$26$	−1.83068	−	3.17083i	−0.359026	−	0.621851i
$27$	14.4442			2.77978
$28$	2.02036	+	1.70826i	0.381812	+	0.322831i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	−1.85104	−	3.20609i	−0.337952	−	0.585350i
$31$	1.98711	−	3.44178i	0.356896	−	0.618162i	−0.630544	−	0.776153i	$-0.717168\pi$
$31$	1.98711	−	3.44178i	0.356896	−	0.618162i	0.987441	+	0.157991i	$0.0505017\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.37597	+	2.38324i	0.239525	+	0.414869i
$34$	0.194248			0.0333133
$35$	−2.84905	+	1.02487i	−0.481578	+	0.173234i
$36$	7.46501			1.24417
$37$	−3.60460	−	6.24335i	−0.592592	−	1.02640i	−0.993882	−	0.110448i	$-0.964771\pi$
$37$	−3.60460	−	6.24335i	−0.592592	−	1.02640i	0.401290	−	0.915951i	$-0.368562\pi$
$38$	3.49684	−	6.05671i	0.567263	−	0.982528i
$39$	−5.92219	+	10.2575i	−0.948309	+	1.64252i
$40$	−0.572197	−	0.991074i	−0.0904723	−	0.156703i
$41$	4.04493			0.631712			0.315856	−	0.948807i	$-0.397708\pi$
$41$	4.04493			0.631712			0.315856	+	0.948807i	$0.397708\pi$
$42$	1.51790	−	8.42325i	0.234217	−	1.29973i
$43$	9.77788			1.49111			0.745556	−	0.666443i	$-0.232184\pi$
$43$	9.77788			1.49111			0.745556	+	0.666443i	$0.232184\pi$
$44$	0.425341	+	0.736713i	0.0641226	+	0.111064i
$45$	−4.27146	+	7.39838i	−0.636751	+	1.10289i
$46$	1.73109	−	2.99834i	0.255236	−	0.442081i
$47$	−0.0269105	−	0.0466104i	−0.00392531	−	0.00679883i	0.864056	−	0.503396i	$-0.167916\pi$
$47$	−0.0269105	−	0.0466104i	−0.00392531	−	0.00679883i	−0.867981	+	0.496597i	$0.834583\pi$
$48$	3.23497			0.466927
$49$	−6.55967	−	2.44350i	−0.937096	−	0.349071i
$50$	−3.69036			−0.521896
$51$	−0.314193	−	0.544199i	−0.0439958	−	0.0762030i
$52$	−1.83068	+	3.17083i	−0.253869	+	0.439715i
$53$	1.33549	−	2.31313i	0.183443	−	0.317733i	−0.759608	−	0.650382i	$-0.774609\pi$
$53$	1.33549	−	2.31313i	0.183443	−	0.317733i	0.943051	+	0.332649i	$0.107942\pi$
$54$	−7.22208	−	12.5090i	−0.982801	−	1.70226i
$55$	−0.973516			−0.131269
$56$	0.469216	−	2.60381i	0.0627016	−	0.347949i
$57$	−22.6244			−2.99667
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	4.02177	−	6.96591i	0.523590	−	0.906885i	−0.476033	−	0.879427i	$-0.657926\pi$
$59$	4.02177	−	6.96591i	0.523590	−	0.906885i	0.999623	−	0.0274571i	$-0.00874096\pi$
$60$	−1.85104	+	3.20609i	−0.238968	+	0.413905i
$61$	2.54072	+	4.40065i	0.325306	+	0.563446i	0.981574	−	0.191081i	$-0.0611995\pi$
$61$	2.54072	+	4.40065i	0.325306	+	0.563446i	−0.656268	+	0.754527i	$0.727866\pi$
$62$	−3.97423			−0.504727
$63$	−18.5847	+	6.68531i	−2.34145	+	0.842270i
$64$	1.00000			0.125000
$65$	−2.09502	−	3.62868i	−0.259855	−	0.450082i
$66$	1.37597	−	2.38324i	0.169370	−	0.293357i
$67$	5.80013	−	10.0461i	0.708599	−	1.22733i	−0.256778	−	0.966471i	$-0.582661\pi$
$67$	5.80013	−	10.0461i	0.708599	−	1.22733i	0.965377	−	0.260859i	$-0.0840059\pi$
$68$	−0.0971241	−	0.168224i	−0.0117780	−	0.0204001i
$69$	−11.2001			−1.34833
$70$	2.31209	+	1.95492i	0.276347	+	0.233658i
$71$	−11.2825			−1.33898			−0.669492	−	0.742819i	$-0.733488\pi$
$71$	−11.2825			−1.33898			−0.669492	+	0.742819i	$0.733488\pi$
$72$	−3.73251	−	6.46489i	−0.439880	−	0.761894i
$73$	3.65539	−	6.33131i	0.427830	−	0.741024i	−0.568850	−	0.822442i	$-0.692611\pi$
$73$	3.65539	−	6.33131i	0.427830	−	0.741024i	0.996680	+	0.0814175i	$0.0259447\pi$
$74$	−3.60460	+	6.24335i	−0.419026	+	0.725774i
$75$	5.96910	+	10.3388i	0.689252	+	1.19382i
$76$	−6.99369			−0.802231
$77$	−1.71868	−	1.45319i	−0.195862	−	0.165606i
$78$	11.8444			1.34111
$79$	6.67821	+	11.5670i	0.751357	+	1.30139i	0.947165	+	0.320746i	$0.103934\pi$
$79$	6.67821	+	11.5670i	0.751357	+	1.30139i	−0.195808	+	0.980642i	$0.562733\pi$
$80$	−0.572197	+	0.991074i	−0.0639736	+	0.110805i
$81$	−12.1657	+	21.0716i	−1.35174	+	2.34129i
$82$	−2.02247	−	3.50301i	−0.223344	−	0.386843i
$83$	9.04564			0.992888			0.496444	−	0.868069i	$-0.334639\pi$
$83$	9.04564			0.992888			0.496444	+	0.868069i	$0.334639\pi$
$84$	−8.05369	+	2.89708i	−0.878730	+	0.316098i
$85$	0.222296			0.0241114
$86$	−4.88894	−	8.46789i	−0.527188	−	0.913116i
$87$	1.61748	−	2.80156i	0.173412	−	0.300359i
$88$	0.425341	−	0.736713i	0.0453415	−	0.0785339i
$89$	−7.11526	−	12.3240i	−0.754216	−	1.30634i	−0.945763	−	0.324857i	$-0.894684\pi$
$89$	−7.11526	−	12.3240i	−0.754216	−	1.30634i	0.191547	−	0.981483i	$-0.438650\pi$
$90$	8.54291			0.900502
$91$	1.71797	−	9.53349i	0.180092	−	0.999381i
$92$	−3.46219			−0.360958
$93$	6.42825	+	11.1340i	0.666578	+	1.15455i
$94$	−0.0269105	+	0.0466104i	−0.00277561	+	0.00480750i
$95$	4.00177	−	6.93126i	0.410573	−	0.711133i
$96$	−1.61748	−	2.80156i	−0.165084	−	0.285933i
$97$	18.7779			1.90660			0.953302	−	0.302017i	$-0.0976601\pi$
$97$	18.7779			1.90660			0.953302	+	0.302017i	$0.0976601\pi$
$98$	1.16370	+	6.90259i	0.117552	+	0.697267i
$99$	−6.35036			−0.638235
$100$	1.84518	+	3.19595i	0.184518	+	0.319595i
$101$	−6.85968	+	11.8813i	−0.682564	+	1.18224i	0.291632	+	0.956531i	$0.405802\pi$
$101$	−6.85968	+	11.8813i	−0.682564	+	1.18224i	−0.974196	+	0.225705i	$0.927531\pi$
$102$	−0.314193	+	0.544199i	−0.0311098	+	0.0538837i
$103$	−0.590573	−	1.02290i	−0.0581909	−	0.100790i	0.835462	−	0.549548i	$-0.185200\pi$
$103$	−0.590573	−	1.02290i	−0.0581909	−	0.100790i	−0.893653	+	0.448758i	$0.851867\pi$
$104$	3.66136			0.359026
$105$	1.73707	−	9.63951i	0.169521	−	0.940720i
$106$	−2.67097			−0.259428
$107$	0.896121	+	1.55213i	0.0866313	+	0.150050i	0.906085	−	0.423095i	$-0.139056\pi$
$107$	0.896121	+	1.55213i	0.0866313	+	0.150050i	−0.819454	+	0.573145i	$0.805723\pi$
$108$	−7.22208	+	12.5090i	−0.694945	+	1.20368i
$109$	−1.82095	+	3.15397i	−0.174415	+	0.302096i	−0.939959	−	0.341288i	$-0.889137\pi$
$109$	−1.82095	+	3.15397i	−0.174415	+	0.302096i	0.765544	+	0.643384i	$0.222470\pi$
$110$	0.486758	+	0.843090i	0.0464106	+	0.0803855i
$111$	23.3215			2.21358
$112$	−2.48958	+	0.895553i	−0.235243	+	0.0846218i
$113$	−17.7718			−1.67183			−0.835915	−	0.548859i	$-0.815063\pi$
$113$	−17.7718			−1.67183			−0.835915	+	0.548859i	$0.815063\pi$
$114$	11.3122	+	19.5933i	1.05948	+	1.83508i
$115$	1.98105	−	3.43128i	0.184734	−	0.319969i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	−13.6660	−	23.6703i	−1.26343	−	2.18832i
$118$	−8.04354			−0.740468
$119$	0.392451	+	0.331826i	0.0359759	+	0.0304185i
$120$	3.70208			0.337952
$121$	5.13817	+	8.89957i	0.467106	+	0.809052i
$122$	2.54072	−	4.40065i	0.230026	−	0.398416i
$123$	−6.54261	+	11.3321i	−0.589927	+	1.02178i
$124$	1.98711	+	3.44178i	0.178448	+	0.309081i
$125$	−9.94520			−0.889526
$126$	15.0820	+	12.7522i	1.34361	+	1.13605i
$127$	−11.5789			−1.02746			−0.513732	−	0.857950i	$-0.671738\pi$
$127$	−11.5789			−1.02746			−0.513732	+	0.857950i	$0.671738\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−15.8156	+	27.3934i	−1.39248	+	2.41185i
$130$	−2.09502	+	3.62868i	−0.183745	+	0.318256i
$131$	8.09878	+	14.0275i	0.707593	+	1.22559i	0.965747	+	0.259484i	$0.0835524\pi$
$131$	8.09878	+	14.0275i	0.707593	+	1.22559i	−0.258154	+	0.966104i	$0.583114\pi$
$132$	−2.75193			−0.239525
$133$	17.4113	−	6.26322i	1.50975	−	0.543090i
$134$	−11.6003			−1.00211
$135$	−8.26491	−	14.3152i	−0.711330	−	1.23206i
$136$	−0.0971241	+	0.168224i	−0.00832832	+	0.0144251i
$137$	6.39212	−	11.0715i	0.546116	−	0.945900i	−0.452420	−	0.891805i	$-0.649439\pi$
$137$	6.39212	−	11.0715i	0.546116	−	0.945900i	0.998536	−	0.0540951i	$-0.0172274\pi$
$138$	5.60003	+	9.69954i	0.476706	+	0.825679i
$139$	0.170575			0.0144679			0.00723397	−	0.999974i	$-0.497697\pi$
$139$	0.170575			0.0144679			0.00723397	+	0.999974i	$0.497697\pi$
$140$	0.536968	−	2.97979i	0.0453821	−	0.251838i
$141$	0.174109			0.0146627
$142$	5.64124	+	9.77091i	0.473402	+	0.819957i
$143$	1.55733	−	2.69737i	0.130230	−	0.225565i
$144$	−3.73251	+	6.46489i	−0.311042	+	0.538741i
$145$	0.572197	+	0.991074i	0.0475184	+	0.0823042i
$146$	−7.31077			−0.605044
$147$	17.4558	−	14.4250i	1.43973	−	1.18976i
$148$	7.20919			0.592592
$149$	−7.02198	−	12.1624i	−0.575263	−	0.996384i	−0.996013	−	0.0892077i	$-0.971567\pi$
$149$	−7.02198	−	12.1624i	−0.575263	−	0.996384i	0.420750	−	0.907176i	$-0.361767\pi$
$150$	5.96910	−	10.3388i	0.487375	−	0.844158i
$151$	−6.09878	+	10.5634i	−0.496311	+	0.859636i	−0.999991	−	0.00425408i	$-0.998646\pi$
$151$	−6.09878	+	10.5634i	−0.496311	+	0.859636i	0.503680	+	0.863891i	$0.331979\pi$
$152$	3.49684	+	6.05671i	0.283632	+	0.491264i
$153$	1.45006			0.117231
$154$	−0.399154	+	2.21502i	−0.0321647	+	0.178491i
$155$	−4.54808			−0.365311
$156$	−5.92219	−	10.2575i	−0.474154	−	0.821259i
$157$	−7.19485	+	12.4618i	−0.574212	+	0.994564i	0.421915	+	0.906635i	$0.361358\pi$
$157$	−7.19485	+	12.4618i	−0.574212	+	0.994564i	−0.996127	+	0.0879283i	$0.971975\pi$
$158$	6.67821	−	11.5670i	0.531290	−	0.920220i
$159$	4.32025	+	7.48290i	0.342618	+	0.593433i
$160$	1.14439			0.0904723
$161$	8.61937	−	3.10057i	0.679302	−	0.244359i
$162$	24.3314			1.91165
$163$	−8.38368	−	14.5210i	−0.656660	−	1.13737i	−0.981475	−	0.191591i	$-0.938635\pi$
$163$	−8.38368	−	14.5210i	−0.656660	−	1.13737i	0.324814	−	0.945778i	$-0.394698\pi$
$164$	−2.02247	+	3.50301i	−0.157928	+	0.273539i
$165$	1.57465	−	2.72737i	0.122586	−	0.212325i
$166$	−4.52282	−	7.83376i	−0.351039	−	0.608017i
$167$	−10.6555			−0.824544			−0.412272	−	0.911061i	$-0.635265\pi$
$167$	−10.6555			−0.824544			−0.412272	+	0.911061i	$0.635265\pi$
$168$	6.53580	+	5.52616i	0.504248	+	0.426353i
$169$	0.405541			0.0311955
$170$	−0.111148	−	0.192514i	−0.00852468	−	0.0147652i
$171$	26.1040	−	45.2134i	1.99622	−	3.45756i
$172$	−4.88894	+	8.46789i	−0.372778	+	0.645671i
$173$	−8.96254	−	15.5236i	−0.681409	−	1.18024i	−0.974551	−	0.224167i	$-0.928034\pi$
$173$	−8.96254	−	15.5236i	−0.681409	−	1.18024i	0.293141	−	0.956069i	$-0.405299\pi$
$174$	−3.23497			−0.245242
$175$	−7.45586	−	6.30409i	−0.563610	−	0.476545i
$176$	−0.850683			−0.0641226
$177$	13.0103	+	22.5345i	0.977914	+	1.69380i
$178$	−7.11526	+	12.3240i	−0.533311	+	0.923722i
$179$	−2.64460	+	4.58058i	−0.197667	+	0.342368i	−0.947771	−	0.318950i	$-0.896670\pi$
$179$	−2.64460	+	4.58058i	−0.197667	+	0.342368i	0.750105	+	0.661319i	$0.230003\pi$
$180$	−4.27146	−	7.39838i	−0.318376	−	0.551443i
$181$	13.1711			0.978997			0.489498	−	0.872004i	$-0.337180\pi$
$181$	13.1711			0.978997			0.489498	+	0.872004i	$0.337180\pi$
$182$	−9.11523	+	3.27894i	−0.675665	+	0.243051i
$183$	−16.4383			−1.21515
$184$	1.73109	+	2.99834i	0.127618	+	0.221041i
$185$	−4.12508	+	7.14485i	−0.303282	+	0.525300i
$186$	6.42825	−	11.1340i	0.471342	−	0.816388i
$187$	0.0826218	+	0.143105i	0.00604190	+	0.0104649i
$188$	0.0538211			0.00392531
$189$	6.77743	−	37.6099i	0.492985	−	2.73572i
$190$	−8.00353			−0.580637
$191$	−4.95435	−	8.58118i	−0.358484	−	0.620912i	0.629224	−	0.777224i	$-0.283373\pi$
$191$	−4.95435	−	8.58118i	−0.358484	−	0.620912i	−0.987708	+	0.156312i	$0.950040\pi$
$192$	−1.61748	+	2.80156i	−0.116732	+	0.202185i
$193$	8.69752	−	15.0645i	0.626061	−	1.08437i	−0.362274	−	0.932072i	$-0.617999\pi$
$193$	8.69752	−	15.0645i	0.626061	−	1.08437i	0.988335	−	0.152298i	$-0.0486672\pi$
$194$	−9.38894	−	16.2621i	−0.674087	−	1.16755i
$195$	13.5546			0.970667
$196$	5.39597	−	4.45909i	0.385426	−	0.318507i
$197$	17.5961			1.25367			0.626834	−	0.779153i	$-0.284350\pi$
$197$	17.5961			1.25367			0.626834	+	0.779153i	$0.284350\pi$
$198$	3.17518	+	5.49957i	0.225650	+	0.390837i
$199$	−5.64229	+	9.77274i	−0.399972	+	0.692771i	−0.993722	−	0.111878i	$-0.964313\pi$
$199$	−5.64229	+	9.77274i	−0.399972	+	0.692771i	0.593750	+	0.804649i	$0.297647\pi$
$200$	1.84518	−	3.19595i	0.130474	−	0.225988i
$201$	18.7632	+	32.4989i	1.32346	+	2.29229i
$202$	13.7194			0.965291
$203$	−0.469216	+	2.60381i	−0.0329325	+	0.182752i
$204$	0.628386			0.0439958
$205$	−2.31450	−	4.00883i	−0.161652	−	0.279989i
$206$	−0.590573	+	1.02290i	−0.0411472	+	0.0712690i
$207$	12.9226	−	22.3827i	0.898185	−	1.55570i
$208$	−1.83068	−	3.17083i	−0.126935	−	0.219857i
$209$	5.94941			0.411529
$210$	−9.21660	+	3.31541i	−0.636006	+	0.228785i
$211$	−9.87572			−0.679873			−0.339936	−	0.940448i	$-0.610406\pi$
$211$	−9.87572			−0.679873			−0.339936	+	0.940448i	$0.610406\pi$
$212$	1.33549	+	2.31313i	0.0917216	+	0.158866i
$213$	18.2492	−	31.6086i	1.25042	−	2.16578i
$214$	0.896121	−	1.55213i	0.0612576	−	0.106101i
$215$	−5.59487	−	9.69060i	−0.381567	−	0.660894i
$216$	14.4442			0.982801
$217$	−8.02937	−	6.78901i	−0.545069	−	0.460868i
$218$	3.64190			0.246660
$219$	11.8250	+	20.4816i	0.799063	+	1.38402i
$220$	0.486758	−	0.843090i	0.0328172	−	0.0568411i
$221$	−0.355606	+	0.615928i	−0.0239207	+	0.0414318i
$222$	−11.6608	−	20.1970i	−0.782618	−	1.35553i
$223$	−16.5982			−1.11150			−0.555748	−	0.831351i	$-0.687568\pi$
$223$	−16.5982			−1.11150			−0.555748	+	0.831351i	$0.687568\pi$
$224$	2.02036	+	1.70826i	0.134991	+	0.114138i
$225$	−27.5486			−1.83657
$226$	8.88590	+	15.3908i	0.591081	+	1.02378i
$227$	−8.99651	+	15.5824i	−0.597120	+	1.03424i	0.396125	+	0.918197i	$0.370355\pi$
$227$	−8.99651	+	15.5824i	−0.597120	+	1.03424i	−0.993244	+	0.116045i	$0.962978\pi$
$228$	11.3122	−	19.5933i	0.749167	−	1.29760i
$229$	1.01911	+	1.76514i	0.0673444	+	0.116644i	0.897732	−	0.440543i	$-0.145214\pi$
$229$	1.01911	+	1.76514i	0.0673444	+	0.116644i	−0.830387	+	0.557187i	$0.811881\pi$
$230$	−3.96211			−0.261253
$231$	6.85114	−	2.46450i	0.450772	−	0.162152i
$232$	−1.00000			−0.0656532
$233$	8.24947	+	14.2885i	0.540441	+	0.936071i	0.998879	+	0.0473443i	$0.0150758\pi$
$233$	8.24947	+	14.2885i	0.540441	+	0.936071i	−0.458438	+	0.888726i	$0.651591\pi$
$234$	−13.6660	+	23.6703i	−0.893377	+	1.54737i
$235$	−0.0307963	+	0.0533407i	−0.00200893	+	0.00347956i
$236$	4.02177	+	6.96591i	0.261795	+	0.453442i
$237$	−43.2075			−2.80663
$238$	0.0911443	−	0.505786i	0.00590801	−	0.0327852i
$239$	18.7414			1.21228			0.606141	−	0.795357i	$-0.292717\pi$
$239$	18.7414			1.21228			0.606141	+	0.795357i	$0.292717\pi$
$240$	−1.85104	−	3.20609i	−0.119484	−	0.206952i
$241$	−8.93903	+	15.4828i	−0.575813	+	0.997338i	0.420139	+	0.907460i	$0.361981\pi$
$241$	−8.93903	+	15.4828i	−0.575813	+	0.997338i	−0.995953	+	0.0898784i	$0.971352\pi$
$242$	5.13817	−	8.89957i	0.330294	−	0.572086i
$243$	−17.6893	−	30.6388i	−1.13477	−	1.96548i
$244$	−5.08144			−0.325306
$245$	1.33174	+	7.89929i	0.0850815	+	0.504667i
$246$	13.0852			0.834283
$247$	12.8032	+	22.1758i	0.814648	+	1.41101i
$248$	1.98711	−	3.44178i	0.126182	−	0.218553i
$249$	−14.6312	+	25.3419i	−0.927213	+	1.60598i
$250$	4.97260	+	8.61279i	0.314495	+	0.544721i
$251$	−1.69249			−0.106829			−0.0534144	−	0.998572i	$-0.517010\pi$
$251$	−1.69249			−0.106829			−0.0534144	+	0.998572i	$0.517010\pi$
$252$	3.50270	−	19.4375i	0.220649	−	1.22445i
$253$	2.94522			0.185165
$254$	5.78947	+	10.0277i	0.363264	+	0.629191i
$255$	−0.359561	+	0.622778i	−0.0225166	+	0.0389998i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.77662	−	3.07719i	−0.110822	−	0.191950i	0.805280	−	0.592895i	$-0.202015\pi$
$257$	−1.77662	−	3.07719i	−0.110822	−	0.191950i	−0.916102	+	0.400945i	$0.868682\pi$
$258$	31.6311			1.96927
$259$	−17.9478	+	6.45622i	−1.11522	+	0.401170i
$260$	4.19004			0.259855
$261$	3.73251	+	6.46489i	0.231036	+	0.400167i
$262$	8.09878	−	14.0275i	0.500344	−	0.866621i
$263$	9.18136	−	15.9026i	0.566147	−	0.980595i	−0.430795	−	0.902450i	$-0.641767\pi$
$263$	9.18136	−	15.9026i	0.566147	−	0.980595i	0.996942	−	0.0781456i	$-0.0248999\pi$
$264$	1.37597	+	2.38324i	0.0846848	+	0.146678i
$265$	−3.05665			−0.187768
$266$	−14.1298	−	11.9470i	−0.866351	−	0.732519i
$267$	46.0353			2.81731
$268$	5.80013	+	10.0461i	0.354300	+	0.613665i
$269$	−9.09102	+	15.7461i	−0.554289	+	0.960057i	0.443669	+	0.896191i	$0.353676\pi$
$269$	−9.09102	+	15.7461i	−0.554289	+	0.960057i	−0.997958	+	0.0638663i	$0.979657\pi$
$270$	−8.26491	+	14.3152i	−0.502986	+	0.871198i
$271$	3.65352	+	6.32808i	0.221935	+	0.384403i	0.955396	−	0.295329i	$-0.0954293\pi$
$271$	3.65352	+	6.32808i	0.221935	+	0.384403i	−0.733460	+	0.679732i	$0.762096\pi$
$272$	0.194248			0.0117780
$273$	23.9299	+	20.2333i	1.44830	+	1.22457i
$274$	−12.7842			−0.772324
$275$	−1.56966	−	2.71874i	−0.0946543	−	0.163946i
$276$	5.60003	−	9.69954i	0.337082	−	0.583843i
$277$	8.32098	−	14.4124i	0.499959	−	0.865955i	−0.500041	−	0.866002i	$-0.666682\pi$
$277$	8.32098	−	14.4124i	0.499959	−	0.865955i	1.00000		4.71482e-5i	$1.50077e-5\pi$
$278$	−0.0852873	−	0.147722i	−0.00511519	−	0.00885977i
$279$	−29.6676			−1.77616
$280$	−2.84905	+	1.02487i	−0.170264	+	0.0612474i
$281$	13.2562			0.790800			0.395400	−	0.918509i	$-0.370606\pi$
$281$	13.2562			0.790800			0.395400	+	0.918509i	$0.370606\pi$
$282$	−0.0870547	−	0.150783i	−0.00518403	−	0.00897901i
$283$	7.63929	−	13.2316i	0.454109	−	0.786539i	−0.544528	−	0.838743i	$-0.683291\pi$
$283$	7.63929	−	13.2316i	0.454109	−	0.786539i	0.998636	+	0.0522035i	$0.0166244\pi$
$284$	5.64124	−	9.77091i	0.334746	−	0.579797i
$285$	12.9456	+	22.4224i	0.766830	+	1.32819i
$286$	−3.11465			−0.184173
$287$	1.89795	−	10.5322i	0.112032	−	0.621698i
$288$	7.46501			0.439880
$289$	8.48113	+	14.6898i	0.498890	+	0.864103i
$290$	0.572197	−	0.991074i	0.0336006	−	0.0581979i
$291$	−30.3729	+	52.6074i	−1.78049	+	3.08390i
$292$	3.65539	+	6.33131i	0.213915	+	0.370512i
$293$	−15.5191			−0.906637			−0.453318	−	0.891349i	$-0.649760\pi$
$293$	−15.5191			−0.906637			−0.453318	+	0.891349i	$0.649760\pi$
$294$	−21.2203	−	7.90464i	−1.23759	−	0.461008i
$295$	−9.20498			−0.535935
$296$	−3.60460	−	6.24335i	−0.209513	−	0.362887i
$297$	6.14370	−	10.6412i	0.356494	−	0.617465i
$298$	−7.02198	+	12.1624i	−0.406772	+	0.704550i
$299$	6.33815	+	10.9780i	0.366545	+	0.634874i
$300$	−11.9382			−0.689252
$301$	4.58794	−	25.4598i	0.264444	−	1.46748i
$302$	12.1976			0.701890
$303$	−22.1908	−	38.4357i	−1.27483	−	2.20807i
$304$	3.49684	−	6.05671i	0.200558	−	0.347376i
$305$	2.90758	−	5.03608i	0.166488	−	0.288365i
$306$	−0.725032	−	1.25579i	−0.0414473	−	0.0717889i
$307$	3.14277			0.179368			0.0896838	−	0.995970i	$-0.471414\pi$
$307$	3.14277			0.179368			0.0896838	+	0.995970i	$0.471414\pi$
$308$	2.11784	−	0.761832i	0.120675	−	0.0434094i
$309$	3.82097			0.217367
$310$	2.27404	+	3.93875i	0.129157	+	0.223706i
$311$	−12.1080	+	20.9717i	−0.686581	+	1.18919i	0.286356	+	0.958123i	$0.407556\pi$
$311$	−12.1080	+	20.9717i	−0.686581	+	1.18919i	−0.972937	+	0.231070i	$0.925777\pi$
$312$	−5.92219	+	10.2575i	−0.335278	+	0.580718i
$313$	5.17640	+	8.96579i	0.292588	+	0.506777i	0.974421	−	0.224731i	$-0.0721504\pi$
$313$	5.17640	+	8.96579i	0.292588	+	0.506777i	−0.681833	+	0.731508i	$0.738817\pi$
$314$	14.3897			0.812058
$315$	17.2598	+	14.5935i	0.972477	+	0.822251i
$316$	−13.3564			−0.751357
$317$	17.2664	+	29.9063i	0.969780	+	1.67971i	0.696185	+	0.717862i	$0.254879\pi$
$317$	17.2664	+	29.9063i	0.969780	+	1.67971i	0.273594	+	0.961845i	$0.411787\pi$
$318$	4.32025	−	7.48290i	0.242268	−	0.419620i
$319$	−0.425341	+	0.736713i	−0.0238145	+	0.0412480i
$320$	−0.572197	−	0.991074i	−0.0319868	−	0.0554027i
$321$	−5.79784			−0.323604
$322$	−6.99486	−	5.91431i	−0.389808	−	0.329592i
$323$	−1.35851			−0.0755896
$324$	−12.1657	−	21.0716i	−0.675871	−	1.17064i
$325$	6.75587	−	11.7015i	0.374748	−	0.649083i
$326$	−8.38368	+	14.5210i	−0.464329	+	0.804241i
$327$	−5.89071	−	10.2030i	−0.325757	−	0.564227i
$328$	4.04493			0.223344
$329$	−0.133992	+	0.0481996i	−0.00738720	+	0.00265733i
$330$	−3.14929			−0.173363
$331$	−2.55022	−	4.41710i	−0.140173	−	0.242786i	0.787389	−	0.616457i	$-0.211432\pi$
$331$	−2.55022	−	4.41710i	−0.140173	−	0.242786i	−0.927562	+	0.373671i	$0.878099\pi$
$332$	−4.52282	+	7.83376i	−0.248222	+	0.429933i
$333$	−26.9084	+	46.6066i	−1.47457	+	2.55403i
$334$	5.32773	+	9.22789i	0.291520	+	0.504928i
$335$	−13.2753			−0.725306
$336$	1.51790	−	8.42325i	0.0828081	−	0.459526i
$337$	24.7613			1.34884			0.674418	−	0.738350i	$-0.264394\pi$
$337$	24.7613			1.34884			0.674418	+	0.738350i	$0.264394\pi$
$338$	−0.202771	−	0.351209i	−0.0110293	−	0.0191033i
$339$	28.7456	−	49.7888i	1.56125	−	2.70416i
$340$	−0.111148	+	0.192514i	−0.00602786	+	0.0104406i
$341$	−1.69040	−	2.92786i	−0.0915405	−	0.158553i
$342$	−52.2080			−2.82308
$343$	−9.44032	+	15.9336i	−0.509729	+	0.860335i
$344$	9.77788			0.527188
$345$	6.40864	+	11.1001i	0.345030	+	0.597609i
$346$	−8.96254	+	15.5236i	−0.481829	+	0.834553i
$347$	−3.21016	+	5.56016i	−0.172331	+	0.298485i	−0.939234	−	0.343277i	$-0.888463\pi$
$347$	−3.21016	+	5.56016i	−0.172331	+	0.298485i	0.766904	+	0.641762i	$0.221796\pi$
$348$	1.61748	+	2.80156i	0.0867062	+	0.150180i
$349$	−2.54039			−0.135984			−0.0679920	−	0.997686i	$-0.521659\pi$
$349$	−2.54039			−0.135984			−0.0679920	+	0.997686i	$0.521659\pi$
$350$	−1.73158	+	9.60901i	−0.0925567	+	0.513623i
$351$	52.8852			2.82281
$352$	0.425341	+	0.736713i	0.0226708	+	0.0392669i
$353$	0.603140	−	1.04467i	0.0321019	−	0.0556021i	−0.849528	−	0.527543i	$-0.823113\pi$
$353$	0.603140	−	1.04467i	0.0321019	−	0.0556021i	0.881630	+	0.471941i	$0.156447\pi$
$354$	13.0103	−	22.5345i	0.691489	−	1.19769i
$355$	6.45580	+	11.1818i	0.342638	+	0.593467i
$356$	14.2305			0.754216
$357$	−1.56442	+	0.562753i	−0.0827976	+	0.0297841i
$358$	5.28920			0.279543
$359$	−0.157998	−	0.273661i	−0.00833883	−	0.0144433i	0.861826	−	0.507204i	$-0.169321\pi$
$359$	−0.157998	−	0.273661i	−0.00833883	−	0.0144433i	−0.870165	+	0.492761i	$0.835988\pi$
$360$	−4.27146	+	7.39838i	−0.225126	+	0.389929i
$361$	−14.9558	+	25.9043i	−0.787149	+	1.36338i
$362$	−6.58553	−	11.4065i	−0.346128	−	0.599511i
$363$	−33.2436			−1.74484
$364$	7.39726	+	6.25455i	0.387722	+	0.327827i
$365$	−8.36640			−0.437917
$366$	8.21914	+	14.2360i	0.429621	+	0.744126i
$367$	−12.1499	+	21.0442i	−0.634217	+	1.09850i	0.352463	+	0.935826i	$0.385344\pi$
$367$	−12.1499	+	21.0442i	−0.634217	+	1.09850i	−0.986680	+	0.162671i	$0.947989\pi$
$368$	1.73109	−	2.99834i	0.0902395	−	0.156299i
$369$	−15.0977	−	26.1500i	−0.785956	−	1.36132i
$370$	8.25016			0.428905
$371$	−5.39632	−	4.56271i	−0.280163	−	0.236884i
$372$	−12.8565			−0.666578
$373$	4.99255	+	8.64735i	0.258504	+	0.447743i	0.965841	−	0.259134i	$-0.0834370\pi$
$373$	4.99255	+	8.64735i	0.258504	+	0.447743i	−0.707337	+	0.706876i	$0.750104\pi$
$374$	0.0826218	−	0.143105i	0.00427227	−	0.00739979i
$375$	16.0862	−	27.8621i	0.830687	−	1.43879i
$376$	−0.0269105	−	0.0466104i	−0.00138781	−	0.00240375i
$377$	−3.66136			−0.188570
$378$	−35.9598	+	12.9355i	−1.84957	+	0.665331i
$379$	−13.0891			−0.672343			−0.336172	−	0.941801i	$-0.609132\pi$
$379$	−13.0891			−0.672343			−0.336172	+	0.941801i	$0.609132\pi$
$380$	4.00177	+	6.93126i	0.205286	+	0.355566i
$381$	18.7287	−	32.4391i	0.959503	−	1.66191i
$382$	−4.95435	+	8.58118i	−0.253486	+	0.439051i
$383$	1.48195	+	2.56681i	0.0757241	+	0.131158i	0.901401	−	0.432985i	$-0.142540\pi$
$383$	1.48195	+	2.56681i	0.0757241	+	0.131158i	−0.825677	+	0.564143i	$0.809206\pi$
$384$	3.23497			0.165084
$385$	−0.456789	+	2.53485i	−0.0232801	+	0.129188i
$386$	−17.3950			−0.885384
$387$	−36.4960	−	63.2129i	−1.85520	−	3.21329i
$388$	−9.38894	+	16.2621i	−0.476651	+	0.825584i
$389$	17.4557	−	30.2342i	0.885040	−	1.53293i	0.0393729	−	0.999225i	$-0.487464\pi$
$389$	17.4557	−	30.2342i	0.885040	−	1.53293i	0.845667	−	0.533710i	$-0.179203\pi$
$390$	−6.77731	−	11.7387i	−0.343183	−	0.594410i
$391$	−0.672523			−0.0340110
$392$	−6.55967	−	2.44350i	−0.331314	−	0.123415i
$393$	−52.3985			−2.64316
$394$	−8.79804	−	15.2386i	−0.443239	−	0.767712i
$395$	7.64250	−	13.2372i	0.384536	−	0.666036i
$396$	3.17518	−	5.49957i	0.159559	−	0.276364i
$397$	−7.70778	−	13.3503i	−0.386842	−	0.670031i	0.605180	−	0.796088i	$-0.293101\pi$
$397$	−7.70778	−	13.3503i	−0.386842	−	0.670031i	−0.992023	+	0.126057i	$0.959768\pi$
$398$	11.2846			0.565645
$399$	−10.6157	+	58.9096i	−0.531450	+	2.94917i
$400$	−3.69036			−0.184518
$401$	−19.0183	−	32.9406i	−0.949728	−	1.64498i	−0.745996	−	0.665950i	$-0.768026\pi$
$401$	−19.0183	−	32.9406i	−0.949728	−	1.64498i	−0.203731	−	0.979027i	$-0.565307\pi$
$402$	18.7632	−	32.4989i	0.935825	−	1.62090i
$403$	7.27553	−	12.6016i	0.362420	−	0.627730i
$404$	−6.85968	−	11.8813i	−0.341282	−	0.591118i
$405$	27.8447			1.38361
$406$	2.48958	−	0.895553i	0.123556	−	0.0444456i
$407$	−6.13274			−0.303989
$408$	−0.314193	−	0.544199i	−0.0155549	−	0.0269418i
$409$	14.6428	−	25.3621i	0.724041	−	1.25408i	−0.235327	−	0.971916i	$-0.575616\pi$
$409$	14.6428	−	25.3621i	0.724041	−	1.25408i	0.959368	−	0.282159i	$-0.0910506\pi$
$410$	−2.31450	+	4.00883i	−0.114305	+	0.197982i
$411$	20.6783	+	35.8159i	1.01999	+	1.76667i
$412$	1.18115			0.0581909
$413$	−16.2508	−	13.7405i	−0.799652	−	0.676123i
$414$	−25.8453			−1.27023
$415$	−5.17589	−	8.96490i	−0.254074	−	0.440070i
$416$	−1.83068	+	3.17083i	−0.0897564	+	0.155463i
$417$	−0.275902	+	0.477875i	−0.0135110	+	0.0234017i
$418$	−2.97471	−	5.15234i	−0.145498	−	0.252009i
$419$	−6.29412			−0.307488			−0.153744	−	0.988111i	$-0.549133\pi$
$419$	−6.29412			−0.307488			−0.153744	+	0.988111i	$0.549133\pi$
$420$	7.47952	+	6.32410i	0.364963	+	0.308585i
$421$	2.94479			0.143520			0.0717602	−	0.997422i	$-0.477138\pi$
$421$	2.94479			0.143520			0.0717602	+	0.997422i	$0.477138\pi$
$422$	4.93786	+	8.55262i	0.240371	+	0.416335i
$423$	−0.200887	+	0.347947i	−0.00976748	+	0.0169178i
$424$	1.33549	−	2.31313i	0.0648570	−	0.112336i
$425$	0.358423	+	0.620807i	0.0173861	+	0.0301136i
$426$	−36.4984			−1.76836
$427$	12.6506	−	4.55070i	0.612206	−	0.220224i
$428$	−1.79224			−0.0866313
$429$	5.03790	+	8.72590i	0.243232	+	0.421290i
$430$	−5.59487	+	9.69060i	−0.269809	+	0.467322i
$431$	−2.72971	+	4.72800i	−0.131486	+	0.227740i	−0.924249	−	0.381789i	$-0.875308\pi$
$431$	−2.72971	+	4.72800i	−0.131486	+	0.227740i	0.792764	+	0.609529i	$0.208641\pi$
$432$	−7.22208	−	12.5090i	−0.347473	−	0.601840i
$433$	−16.9899			−0.816482			−0.408241	−	0.912874i	$-0.633858\pi$
$433$	−16.9899			−0.816482			−0.408241	+	0.912874i	$0.633858\pi$
$434$	−1.86477	+	10.3481i	−0.0895118	+	0.496727i
$435$	−3.70208			−0.177501
$436$	−1.82095	−	3.15397i	−0.0872076	−	0.151048i
$437$	−12.1067	+	20.9695i	−0.579143	+	1.00311i
$438$	11.8250	−	20.4816i	0.565023	−	0.978648i
$439$	11.3210	+	19.6085i	0.540321	+	0.935863i	0.998885	+	0.0472016i	$0.0150303\pi$
$439$	11.3210	+	19.6085i	0.540321	+	0.935863i	−0.458565	+	0.888661i	$0.651636\pi$
$440$	−0.973516			−0.0464106
$441$	8.68706	+	51.5279i	0.413670	+	2.45371i
$442$	0.711212			0.0338289
$443$	8.56936	+	14.8426i	0.407143	+	0.705192i	0.994568	−	0.104086i	$-0.0331919\pi$
$443$	8.56936	+	14.8426i	0.407143	+	0.705192i	−0.587426	+	0.809278i	$0.699859\pi$
$444$	−11.6608	+	20.1970i	−0.553395	+	0.958508i
$445$	−8.14266	+	14.1035i	−0.385999	+	0.668570i
$446$	8.29908	+	14.3744i	0.392973	+	0.680649i
$447$	45.4317			2.14885
$448$	0.469216	−	2.60381i	0.0221684	−	0.123019i
$449$	−12.1802			−0.574818			−0.287409	−	0.957808i	$-0.592794\pi$
$449$	−12.1802			−0.574818			−0.287409	+	0.957808i	$0.592794\pi$
$450$	13.7743	+	23.8578i	0.649327	+	1.12467i
$451$	1.72048	−	2.97995i	0.0810141	−	0.140321i
$452$	8.88590	−	15.3908i	0.417958	−	0.723924i
$453$	−19.7293	−	34.1722i	−0.926965	−	1.60555i
$454$	17.9930			0.844455
$455$	−10.4314	+	3.75240i	−0.489032	+	0.175915i
$456$	−22.6244			−1.05948
$457$	−15.7551	−	27.2886i	−0.736991	−	1.27651i	−0.953844	−	0.300302i	$-0.902912\pi$
$457$	−15.7551	−	27.2886i	−0.736991	−	1.27651i	0.216853	−	0.976204i	$-0.430421\pi$
$458$	1.01911	−	1.76514i	0.0476197	−	0.0824797i
$459$	−1.40288	+	2.42985i	−0.0654806	+	0.113416i
$460$	1.98105	+	3.43128i	0.0923671	+	0.159984i
$461$	−6.40796			−0.298448			−0.149224	−	0.988803i	$-0.547678\pi$
$461$	−6.40796			−0.298448			−0.149224	+	0.988803i	$0.547678\pi$
$462$	−5.55989	−	4.70101i	−0.258669	−	0.218711i
$463$	−0.902939			−0.0419632			−0.0209816	−	0.999780i	$-0.506679\pi$
$463$	−0.902939			−0.0419632			−0.0209816	+	0.999780i	$0.506679\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	7.35645	−	12.7417i	0.341147	−	0.590884i
$466$	8.24947	−	14.2885i	0.382149	−	0.661902i
$467$	18.2056	+	31.5330i	0.842454	+	1.45917i	0.887814	+	0.460202i	$0.152223\pi$
$467$	18.2056	+	31.5330i	0.842454	+	1.45917i	−0.0453601	+	0.998971i	$0.514444\pi$
$468$	27.3321			1.26343
$469$	−23.4367	−	19.8163i	−1.08221	−	0.915030i
$470$	0.0615925			0.00284105
$471$	−23.2751	−	40.3137i	−1.07246	−	1.85756i
$472$	4.02177	−	6.96591i	0.185117	−	0.320632i
$473$	4.15894	−	7.20349i	0.191228	−	0.331217i
$474$	21.6038	+	37.4188i	0.992294	+	1.71870i
$475$	25.8092			1.18421
$476$	−0.483595	+	0.173960i	−0.0221656	+	0.00797342i
$477$	−19.9388			−0.912937
$478$	−9.37071	−	16.2305i	−0.428606	−	0.742368i
$479$	−15.7142	+	27.2177i	−0.717998	+	1.24361i	0.243794	+	0.969827i	$0.421608\pi$
$479$	−15.7142	+	27.2177i	−0.717998	+	1.24361i	−0.961792	+	0.273782i	$0.911725\pi$
$480$	−1.85104	+	3.20609i	−0.0844880	+	0.146337i
$481$	−13.1977	−	22.8591i	−0.601764	−	1.04229i
$482$	17.8781			0.814323
$483$	−5.25525	+	29.1628i	−0.239122	+	1.32696i
$484$	−10.2763			−0.467106
$485$	−10.7446	−	18.6103i	−0.487889	−	0.845049i
$486$	−17.6893	+	30.6388i	−0.802404	+	1.38980i
$487$	−7.22298	+	12.5106i	−0.327304	+	0.566908i	−0.981976	−	0.189006i	$-0.939474\pi$
$487$	−7.22298	+	12.5106i	−0.327304	+	0.566908i	0.654672	+	0.755913i	$0.272807\pi$
$488$	2.54072	+	4.40065i	0.115013	+	0.199208i
$489$	54.2418			2.45290
$490$	6.17511	−	5.10296i	0.278963	−	0.230528i
$491$	29.2405			1.31961			0.659803	−	0.751439i	$-0.270640\pi$
$491$	29.2405			1.31961			0.659803	+	0.751439i	$0.270640\pi$
$492$	−6.54261	−	11.3321i	−0.294964	−	0.510892i
$493$	0.0971241	−	0.168224i	0.00437425	−	0.00757642i
$494$	12.8032	−	22.1758i	0.576043	−	0.997736i
$495$	3.63365	+	6.29367i	0.163321	+	0.282880i
$496$	−3.97423			−0.178448
$497$	−5.29392	+	29.3774i	−0.237465	+	1.31776i
$498$	29.2624			1.31128
$499$	−14.2452	−	24.6735i	−0.637704	−	1.10454i	−0.985935	−	0.167127i	$-0.946551\pi$
$499$	−14.2452	−	24.6735i	−0.637704	−	1.10454i	0.348231	−	0.937409i	$-0.386782\pi$
$500$	4.97260	−	8.61279i	0.222381	−	0.385176i
$501$	17.2350	−	29.8519i	0.770004	−	1.33369i
$502$	0.846243	+	1.46574i	0.0377697	+	0.0654190i
$503$	19.9091			0.887701			0.443850	−	0.896101i	$-0.353612\pi$
$503$	19.9091			0.887701			0.443850	+	0.896101i	$0.353612\pi$
$504$	−18.5847	+	6.68531i	−0.827829	+	0.297788i
$505$	15.7004			0.698657
$506$	−1.47261	−	2.55064i	−0.0654656	−	0.113390i
$507$	−0.655956	+	1.13615i	−0.0291321	+	0.0504582i
$508$	5.78947	−	10.0277i	0.256866	−	0.444905i
$509$	−1.78599	−	3.09343i	−0.0791628	−	0.137114i	0.823726	−	0.566988i	$-0.191891\pi$
$509$	−1.78599	−	3.09343i	−0.0791628	−	0.137114i	−0.902889	+	0.429874i	$0.858558\pi$
$510$	0.719122			0.0318432
$511$	−14.7704	−	12.4887i	−0.653403	−	0.552467i
$512$	1.00000			0.0441942
$513$	50.5090	+	87.4841i	2.23003	+	3.86252i
$514$	−1.77662	+	3.07719i	−0.0783633	+	0.135729i
$515$	−0.675848	+	1.17060i	−0.0297814	+	0.0515829i
$516$	−15.8156	−	27.3934i	−0.696241	−	1.20593i
$517$	−0.0457847			−0.00201361
$518$	14.5652	+	12.3152i	0.639956	+	0.541097i
$519$	57.9871			2.54535
$520$	−2.09502	−	3.62868i	−0.0918726	−	0.159128i
$521$	4.68438	−	8.11359i	0.205227	−	0.355463i	−0.744978	−	0.667089i	$-0.767540\pi$
$521$	4.68438	−	8.11359i	0.205227	−	0.355463i	0.950205	+	0.311626i	$0.100874\pi$
$522$	3.73251	−	6.46489i	0.163367	−	0.282960i
$523$	6.80794	+	11.7917i	0.297690	+	0.515615i	0.975607	−	0.219524i	$-0.0704504\pi$
$523$	6.80794	+	11.7917i	0.297690	+	0.515615i	−0.677917	+	0.735139i	$0.737117\pi$
$524$	−16.1976			−0.707593
$525$	29.7210	−	10.6913i	1.29713	−	0.466606i
$526$	−18.3627			−0.800653
$527$	0.385993	+	0.668560i	0.0168141	+	0.0291229i
$528$	1.37597	−	2.38324i	0.0598812	−	0.103717i
$529$	5.50663	−	9.53777i	0.239419	−	0.414686i
$530$	1.52832	+	2.64713i	0.0663861	+	0.114984i
$531$	−60.0451			−2.60574
$532$	−3.28155	+	18.2102i	−0.142273	+	0.789514i
$533$	14.8099			0.641490
$534$	−23.0176	−	39.8677i	−0.996070	−	1.72524i
$535$	1.02552	−	1.77624i	0.0443369	−	0.0767937i
$536$	5.80013	−	10.0461i	0.250528	−	0.433927i
$537$	−8.55519	−	14.8180i	−0.369184	−	0.639445i
$538$	18.1820			0.783883
$539$	−4.59026	+	3.79327i	−0.197716	+	0.163388i
$540$	16.5298			0.711330
$541$	−5.34851	−	9.26389i	−0.229951	−	0.398286i	0.727843	−	0.685744i	$-0.240523\pi$
$541$	−5.34851	−	9.26389i	−0.229951	−	0.398286i	−0.957793	+	0.287458i	$0.907190\pi$
$542$	3.65352	−	6.32808i	0.156932	−	0.271814i
$543$	−21.3040	+	36.8995i	−0.914240	+	1.58351i
$544$	−0.0971241	−	0.168224i	−0.00416416	−	0.00721254i
$545$	4.16776			0.178527
$546$	5.55757	−	30.8405i	0.237842	−	1.31985i
$547$	−23.6925			−1.01302			−0.506509	−	0.862235i	$-0.669064\pi$
$547$	−23.6925			−1.01302			−0.506509	+	0.862235i	$0.669064\pi$
$548$	6.39212	+	11.0715i	0.273058	+	0.472950i
$549$	18.9665	−	32.8509i	0.809470	−	1.40204i
$550$	−1.56966	+	2.71874i	−0.0669307	+	0.115927i
$551$	−3.49684	−	6.05671i	−0.148971	−	0.258025i
$552$	−11.2001			−0.476706
$553$	33.2518	−	11.9614i	1.41401	−	0.508649i
$554$	−16.6420			−0.707049
$555$	−13.3445	−	23.1133i	−0.566442	−	0.981107i
$556$	−0.0852873	+	0.147722i	−0.00361699	+	0.00626480i
$557$	−6.13907	+	10.6332i	−0.260121	+	0.450543i	−0.966274	−	0.257517i	$-0.917096\pi$
$557$	−6.13907	+	10.6332i	−0.260121	+	0.450543i	0.706153	+	0.708059i	$0.250429\pi$
$558$	14.8338	+	25.6929i	0.627966	+	1.08767i
$559$	35.8003			1.51419
$560$	2.31209	+	1.95492i	0.0977035	+	0.0826105i
$561$	−0.534558			−0.0225690
$562$	−6.62811	−	11.4802i	−0.279590	−	0.484264i
$563$	−18.6915	+	32.3747i	−0.787755	+	1.36443i	0.139585	+	0.990210i	$0.455423\pi$
$563$	−18.6915	+	32.3747i	−0.787755	+	1.36443i	−0.927340	+	0.374221i	$0.877910\pi$
$564$	−0.0870547	+	0.150783i	−0.00366566	+	0.00634912i
$565$	10.1690	+	17.6132i	0.427812	+	0.740992i
$566$	−15.2786			−0.642207
$567$	49.1581	+	41.5642i	2.06444	+	1.74553i
$568$	−11.2825			−0.473402
$569$	7.12391	+	12.3390i	0.298650	+	0.517277i	0.975827	−	0.218543i	$-0.0701304\pi$
$569$	7.12391	+	12.3390i	0.298650	+	0.517277i	−0.677177	+	0.735820i	$0.736797\pi$
$570$	12.9456	−	22.4224i	0.542231	−	0.939171i
$571$	3.29932	−	5.71460i	0.138072	−	0.239148i	−0.788695	−	0.614785i	$-0.789243\pi$
$571$	3.29932	−	5.71460i	0.138072	−	0.239148i	0.926767	+	0.375637i	$0.122576\pi$
$572$	1.55733	+	2.69737i	0.0651151	+	0.112783i
$573$	32.0543			1.33909
$574$	−10.0702	+	3.62245i	−0.420320	+	0.151198i
$575$	12.7767			0.532826
$576$	−3.73251	−	6.46489i	−0.155521	−	0.269370i
$577$	10.5455	−	18.2654i	0.439016	−	0.760398i	−0.558598	−	0.829439i	$-0.688660\pi$
$577$	10.5455	−	18.2654i	0.439016	−	0.760398i	0.997614	+	0.0690406i	$0.0219938\pi$
$578$	8.48113	−	14.6898i	0.352769	−	0.611013i
$579$	28.1362	+	48.7333i	1.16930	+	2.02529i
$580$	−1.14439			−0.0475184
$581$	4.24436	−	23.5532i	0.176086	−	0.977149i
$582$	60.7458			2.51800
$583$	−1.13608	−	1.96774i	−0.0470514	−	0.0814955i
$584$	3.65539	−	6.33131i	0.151261	−	0.261992i
$585$	−15.6393	+	27.0881i	−0.646607	+	1.11996i
$586$	7.75956	+	13.4400i	0.320545	+	0.555199i
$587$	23.5851			0.973459			0.486730	−	0.873553i	$-0.338190\pi$
$587$	23.5851			0.973459			0.486730	+	0.873553i	$0.338190\pi$
$588$	3.76454	+	22.3297i	0.155247	+	0.920860i
$589$	27.7945			1.14525
$590$	4.60249	+	7.97175i	0.189482	+	0.328192i
$591$	−28.4614	+	49.2965i	−1.17074	+	2.02779i
$592$	−3.60460	+	6.24335i	−0.148148	+	0.256600i
$593$	12.4404	+	21.5474i	0.510865	+	0.884844i	0.999921	+	0.0125916i	$0.00400813\pi$
$593$	12.4404	+	21.5474i	0.510865	+	0.884844i	−0.489056	+	0.872253i	$0.662659\pi$
$594$	−12.2874			−0.504158
$595$	0.104305	−	0.578818i	0.00427609	−	0.0237292i
$596$	14.0440			0.575263
$597$	−18.2526	−	31.6145i	−0.747031	−	1.29390i
$598$	6.33815	−	10.9780i	0.259186	−	0.448924i
$599$	−2.38954	+	4.13880i	−0.0976338	+	0.169107i	−0.910705	−	0.413058i	$-0.864461\pi$
$599$	−2.38954	+	4.13880i	−0.0976338	+	0.169107i	0.813071	+	0.582165i	$0.197794\pi$
$600$	5.96910	+	10.3388i	0.243687	+	0.422079i
$601$	−44.3292			−1.80823			−0.904113	−	0.427292i	$-0.859467\pi$
$601$	−44.3292			−1.80823			−0.904113	+	0.427292i	$0.859467\pi$
$602$	−24.3428	+	8.75661i	−0.992137	+	0.356893i
$603$	−86.5961			−3.52647
$604$	−6.09878	−	10.5634i	−0.248156	−	0.429818i
$605$	5.88009	−	10.1846i	0.239060	−	0.414063i
$606$	−22.1908	+	38.4357i	−0.901442	+	1.56134i
$607$	−21.4496	−	37.1518i	−0.870613	−	1.50795i	−0.861364	−	0.507989i	$-0.830389\pi$
$607$	−21.4496	−	37.1518i	−0.870613	−	1.50795i	−0.00924938	−	0.999957i	$-0.502944\pi$
$608$	−6.99369			−0.283632
$609$	−6.53580	−	5.52616i	−0.264844	−	0.223931i
$610$	−5.81517			−0.235449
$611$	−0.0985291	−	0.170657i	−0.00398606	−	0.00690406i
$612$	−0.725032	+	1.25579i	−0.0293077	+	0.0507624i
$613$	−13.0203	+	22.5518i	−0.525884	+	0.910857i	0.473662	+	0.880707i	$0.342932\pi$
$613$	−13.0203	+	22.5518i	−0.525884	+	0.910857i	−0.999545	+	0.0301503i	$0.990401\pi$
$614$	−1.57139	−	2.72172i	−0.0634160	−	0.109840i
$615$	14.9746			0.603836
$616$	−1.71868	−	1.45319i	−0.0692478	−	0.0585505i
$617$	−38.2301			−1.53909			−0.769543	−	0.638595i	$-0.779516\pi$
$617$	−38.2301			−1.53909			−0.769543	+	0.638595i	$0.779516\pi$
$618$	−1.91048	−	3.30905i	−0.0768509	−	0.133110i
$619$	−16.9206	+	29.3074i	−0.680098	+	1.17796i	0.294853	+	0.955543i	$0.404729\pi$
$619$	−16.9206	+	29.3074i	−0.680098	+	1.17796i	−0.974951	+	0.222421i	$0.928604\pi$
$620$	2.27404	−	3.93875i	0.0913277	−	0.158184i
$621$	25.0042	+	43.3085i	1.00338	+	1.73791i
$622$	24.2160			0.970973
$623$	−35.4280	+	12.7442i	−1.41939	+	0.510585i
$624$	11.8444			0.474154
$625$	−3.53529	−	6.12331i	−0.141412	−	0.244932i
$626$	5.17640	−	8.96579i	0.206891	−	0.358345i
$627$	−9.62307	+	16.6677i	−0.384309	+	0.665642i
$628$	−7.19485	−	12.4618i	−0.287106	−	0.497282i
$629$	1.40037			0.0558365
$630$	4.00847	−	22.2441i	0.159701	−	0.886228i
$631$	−36.3237			−1.44602			−0.723012	−	0.690835i	$-0.757243\pi$
$631$	−36.3237			−1.44602			−0.723012	+	0.690835i	$0.757243\pi$
$632$	6.67821	+	11.5670i	0.265645	+	0.460110i
$633$	15.9738	−	27.6675i	0.634902	−	1.09968i
$634$	17.2664	−	29.9063i	0.685738	−	1.18773i
$635$	6.62543	+	11.4756i	0.262922	+	0.455395i
$636$	−8.64051			−0.342618
$637$	−24.0173	−	8.94653i	−0.951600	−	0.354474i
$638$	0.850683			0.0336789
$639$	42.1119	+	72.9400i	1.66592	+	2.88546i
$640$	−0.572197	+	0.991074i	−0.0226181	+	0.0391756i
$641$	2.50688	−	4.34204i	0.0990157	−	0.171500i	−0.812262	−	0.583293i	$-0.801764\pi$
$641$	2.50688	−	4.34204i	0.0990157	−	0.171500i	0.911278	+	0.411793i	$0.135097\pi$
$642$	2.89892	+	5.02108i	0.114411	+	0.198166i
$643$	−21.6758			−0.854811			−0.427406	−	0.904060i	$-0.640572\pi$
$643$	−21.6758			−0.854811			−0.427406	+	0.904060i	$0.640572\pi$
$644$	−1.62451	+	9.01488i	−0.0640148	+	0.355236i
$645$	36.1985			1.42531
$646$	0.679256	+	1.17651i	0.0267250	+	0.0462890i
$647$	11.5473	−	20.0005i	0.453970	−	0.786299i	−0.544658	−	0.838658i	$-0.683341\pi$
$647$	11.5473	−	20.0005i	0.453970	−	0.786299i	0.998628	+	0.0523591i	$0.0166740\pi$
$648$	−12.1657	+	21.0716i	−0.477913	+	0.827769i
$649$	−3.42125	−	5.92578i	−0.134296	−	0.232607i
$650$	−13.5117			−0.529974
$651$	32.0072	−	11.5137i	1.25446	−	0.451256i
$652$	16.7674			0.656660
$653$	16.9620	+	29.3790i	0.663774	+	1.14969i	0.979616	+	0.200879i	$0.0643798\pi$
$653$	16.9620	+	29.3790i	0.663774	+	1.14969i	−0.315842	+	0.948812i	$0.602287\pi$
$654$	−5.89071	+	10.2030i	−0.230345	+	0.398969i
$655$	9.26819	−	16.0530i	0.362138	−	0.627242i
$656$	−2.02247	−	3.50301i	−0.0789640	−	0.136770i
$657$	−54.5750			−2.12917
$658$	0.108738	+	0.0919403i	0.00423905	+	0.00358421i
$659$	−5.52520			−0.215231			−0.107616	−	0.994193i	$-0.534322\pi$
$659$	−5.52520			−0.215231			−0.107616	+	0.994193i	$0.534322\pi$
$660$	1.57465	+	2.72737i	0.0612930	+	0.106163i
$661$	0.811825	−	1.40612i	0.0315763	−	0.0546918i	−0.849805	−	0.527097i	$-0.823281\pi$
$661$	0.811825	−	1.40612i	0.0315763	−	0.0546918i	0.881382	+	0.472405i	$0.156614\pi$
$662$	−2.55022	+	4.41710i	−0.0991170	+	0.171676i
$663$	−1.15037	−	1.99251i	−0.0446768	−	0.0773825i
$664$	9.04564			0.351039
$665$	−16.1700	−	13.6721i	−0.627046	−	0.530182i
$666$	53.8167			2.08536
$667$	−1.73109	−	2.99834i	−0.0670282	−	0.116096i
$668$	5.32773	−	9.22789i	0.206136	−	0.357038i
$669$	26.8473	−	46.5008i	1.03798	−	1.79783i
$670$	6.63764	+	11.4967i	0.256434	+	0.444157i
$671$	4.32269			0.166876
$672$	−8.05369	+	2.89708i	−0.310678	+	0.111757i
$673$	−1.69886			−0.0654862			−0.0327431	−	0.999464i	$-0.510424\pi$
$673$	−1.69886			−0.0654862			−0.0327431	+	0.999464i	$0.510424\pi$
$674$	−12.3807	−	21.4440i	−0.476886	−	0.825990i
$675$	26.6521	−	46.1628i	1.02584	−	1.77681i
$676$	−0.202771	+	0.351209i	−0.00779887	+	0.0135080i
$677$	−10.3638	−	17.9507i	−0.398314	−	0.689900i	0.595204	−	0.803575i	$-0.297071\pi$
$677$	−10.3638	−	17.9507i	−0.398314	−	0.689900i	−0.993518	+	0.113674i	$0.963738\pi$
$678$	−57.4912			−2.20794
$679$	8.81088	−	48.8941i	0.338130	−	1.87638i
$680$	0.222296			0.00852468
$681$	−29.1034	−	50.4086i	−1.11525	−	1.93166i
$682$	−1.69040	+	2.92786i	−0.0647289	+	0.112114i
$683$	15.1908	−	26.3113i	0.581261	−	1.00677i	−0.414069	−	0.910246i	$-0.635893\pi$
$683$	15.1908	−	26.3113i	0.581261	−	1.00677i	0.995330	−	0.0965286i	$-0.0307739\pi$
$684$	26.1040	+	45.2134i	0.998111	+	1.72878i
$685$	−14.6302			−0.558991
$686$	18.5191	+	0.208741i	0.707062	+	0.00796975i
$687$	−6.59355			−0.251560
$688$	−4.88894	−	8.46789i	−0.186389	−	0.322835i
$689$	4.88969	−	8.46920i	0.186282	−	0.322651i
$690$	6.40864	−	11.1001i	0.243973	−	0.422573i
$691$	2.31023	+	4.00144i	0.0878853	+	0.152222i	0.906617	−	0.421954i	$-0.138656\pi$
$691$	2.31023	+	4.00144i	0.0878853	+	0.152222i	−0.818732	+	0.574176i	$0.805322\pi$
$692$	17.9251			0.681409
$693$	−2.97969	+	16.5351i	−0.113189	+	0.628118i
$694$	6.42032			0.243712
$695$	−0.0976022	−	0.169052i	−0.00370226	−	0.00641251i
$696$	1.61748	−	2.80156i	0.0613106	−	0.106193i
$697$	−0.392860	+	0.680454i	−0.0148806	+	0.0257740i
$698$	1.27020	+	2.20004i	0.0480776	+	0.0832729i
$699$	−53.3735			−2.01877
$700$	9.18743	−	3.30492i	0.347252	−	0.124914i
$701$	36.9179			1.39437			0.697186	−	0.716890i	$-0.254435\pi$
$701$	36.9179			1.39437			0.697186	+	0.716890i	$0.254435\pi$
$702$	−26.4426	−	45.8000i	−0.998012	−	1.72861i
$703$	25.2094	−	43.6640i	0.950792	−	1.64682i
$704$	0.425341	−	0.736713i	0.0160307	−	0.0277659i
$705$	−0.0996249	−	0.172555i	−0.00375209	−	0.00649881i
$706$	−1.20628			−0.0453989
$707$	27.7181	+	23.4362i	1.04244	+	0.881410i
$708$	−26.0206			−0.977914
$709$	16.0371	+	27.7771i	0.602286	+	1.04319i	0.992474	+	0.122454i	$0.0390765\pi$
$709$	16.0371	+	27.7771i	0.602286	+	1.04319i	−0.390189	+	0.920735i	$0.627590\pi$
$710$	6.45580	−	11.1818i	0.242282	−	0.419644i
$711$	49.8529	−	86.3477i	1.86963	−	3.23829i
$712$	−7.11526	−	12.3240i	−0.266656	−	0.461861i
$713$	13.7595			0.515298
$714$	1.26957	+	1.07345i	0.0475123	+	0.0401727i
$715$	−3.56439			−0.133301
$716$	−2.64460	−	4.58058i	−0.0988333	−	0.171184i
$717$	−30.3139	+	52.5053i	−1.13209	+	1.96085i
$718$	−0.157998	+	0.273661i	−0.00589644	+	0.0102129i
$719$	−17.9177	−	31.0344i	−0.668218	−	1.15739i	−0.978402	−	0.206711i	$-0.933724\pi$
$719$	−17.9177	−	31.0344i	−0.668218	−	1.15739i	0.310184	−	0.950676i	$-0.399609\pi$
$720$	8.54291			0.318376
$721$	−2.94055	+	1.05778i	−0.109512	+	0.0393937i
$722$	29.9117			1.11320
$723$	−28.9175	−	50.0865i	−1.07545	−	1.86274i
$724$	−6.58553	+	11.4065i	−0.244749	+	0.423918i
$725$	−1.84518	+	3.19595i	−0.0685283	+	0.118695i
$726$	16.6218	+	28.7898i	0.616893	+	1.06849i
$727$	−12.8401			−0.476215			−0.238107	−	0.971239i	$-0.576527\pi$
$727$	−12.8401			−0.476215			−0.238107	+	0.971239i	$0.576527\pi$
$728$	1.71797	−	9.53349i	0.0636721	−	0.353335i
$729$	41.4546			1.53536
$730$	4.18320	+	7.24552i	0.154827	+	0.268169i
$731$	−0.949668	+	1.64487i	−0.0351247	+	0.0608378i
$732$	8.21914	−	14.2360i	0.303788	−	0.526177i
$733$	4.56646	+	7.90935i	0.168666	+	0.292138i	0.937951	−	0.346767i	$-0.112721\pi$
$733$	4.56646	+	7.90935i	0.168666	+	0.292138i	−0.769285	+	0.638906i	$0.779387\pi$
$734$	24.2997			0.896919
$735$	−24.2844	−	9.04602i	−0.895744	−	0.333668i
$736$	−3.46219			−0.127618
$737$	−4.93407	−	8.54607i	−0.181749	−	0.314798i
$738$	−15.0977	+	26.1500i	−0.555755	+	0.962596i
$739$	−3.16227	+	5.47721i	−0.116326	+	0.201482i	−0.918309	−	0.395864i	$-0.870445\pi$
$739$	−3.16227	+	5.47721i	−0.116326	+	0.201482i	0.801983	+	0.597347i	$0.203778\pi$
$740$	−4.12508	−	7.14485i	−0.151641	−	0.262650i
$741$	−82.8358			−3.04305
$742$	−1.25326	+	6.95471i	−0.0460087	+	0.255315i
$743$	32.2973			1.18487			0.592436	−	0.805618i	$-0.298166\pi$
$743$	32.2973			1.18487			0.592436	+	0.805618i	$0.298166\pi$
$744$	6.42825	+	11.1340i	0.235671	+	0.408194i
$745$	−8.03591	+	13.9186i	−0.294413	+	0.509938i
$746$	4.99255	−	8.64735i	0.182790	−	0.316602i
$747$	−33.7629	−	58.4791i	−1.23532	−	2.13964i
$748$	−0.165244			−0.00604190
$749$	4.46192	−	1.60505i	0.163035	−	0.0586472i
$750$	−32.1724			−1.17477
$751$	−9.93095	−	17.2009i	−0.362385	−	0.627670i	0.625968	−	0.779849i	$-0.284704\pi$
$751$	−9.93095	−	17.2009i	−0.362385	−	0.627670i	−0.988353	+	0.152179i	$0.951371\pi$
$752$	−0.0269105	+	0.0466104i	−0.000981327	+	0.00169971i
$753$	2.73757	−	4.74161i	0.0997625	−	0.172794i
$754$	1.83068	+	3.17083i	0.0666694	+	0.115475i
$755$	13.9588			0.508013
$756$	29.1824	+	24.6744i	1.06135	+	0.897398i
$757$	24.1136			0.876425			0.438213	−	0.898871i	$-0.355612\pi$
$757$	24.1136			0.876425			0.438213	+	0.898871i	$0.355612\pi$
$758$	6.54456	+	11.3355i	0.237709	+	0.411725i
$759$	−4.76385	+	8.25123i	−0.172917	+	0.299501i
$760$	4.00177	−	6.93126i	0.145159	−	0.251423i
$761$	−19.8123	−	34.3158i	−0.718194	−	1.24395i	−0.961715	−	0.274052i	$-0.911636\pi$
$761$	−19.8123	−	34.3158i	−0.718194	−	1.24395i	0.243521	−	0.969896i	$-0.421697\pi$
$762$	−37.4575			−1.35694
$763$	7.35794	+	6.22130i	0.266375	+	0.225226i
$764$	9.90869			0.358484
$765$	−0.829723	−	1.43712i	−0.0299987	−	0.0519592i
$766$	1.48195	−	2.56681i	0.0535451	−	0.0927428i
$767$	14.7251	−	25.5047i	0.531694	−	0.920921i
$768$	−1.61748	−	2.80156i	−0.0583659	−	0.101093i
$769$	−11.8143			−0.426034			−0.213017	−	0.977049i	$-0.568329\pi$
$769$	−11.8143			−0.426034			−0.213017	+	0.977049i	$0.568329\pi$
$770$	2.42364	−	0.871836i	0.0873420	−	0.0314188i
$771$	11.4946			0.413968
$772$	8.69752	+	15.0645i	0.313030	+	0.542185i
$773$	−9.01041	+	15.6065i	−0.324082	+	0.561327i	−0.981326	−	0.192351i	$-0.938389\pi$
$773$	−9.01041	+	15.6065i	−0.324082	+	0.561327i	0.657244	+	0.753678i	$0.271722\pi$
$774$	−36.4960	+	63.2129i	−1.31182	+	2.27214i
$775$	−7.33317	−	12.7014i	−0.263415	−	0.456249i
$776$	18.7779			0.674087
$777$	10.9428	−	60.7248i	0.392571	−	2.17849i
$778$	−34.9114			−1.25164
$779$	14.1445	+	24.4990i	0.506779	+	0.877767i
$780$	−6.77731	+	11.7387i	−0.242667	+	0.420311i
$781$	−4.79890	+	8.31195i	−0.171718	+	0.297425i
$782$	0.336262	+	0.582422i	0.0120247	+	0.0208274i
$783$	−14.4442			−0.516192
$784$	1.16370	+	6.90259i	0.0415608	+	0.246521i
$785$	16.4675			0.587750
$786$	26.1993	+	45.3785i	0.934497	+	1.61860i
$787$	3.65922	−	6.33795i	0.130437	−	0.225923i	−0.793408	−	0.608690i	$-0.791695\pi$
$787$	3.65922	−	6.33795i	0.130437	−	0.225923i	0.923845	+	0.382767i	$0.125029\pi$
$788$	−8.79804	+	15.2386i	−0.313417	+	0.542854i
$789$	29.7014	+	51.4443i	1.05740	+	1.83147i
$790$	−15.2850			−0.543816
$791$	−8.33881	+	46.2744i	−0.296494	+	1.64533i
$792$	−6.35036			−0.225650
$793$	9.30248	+	16.1124i	0.330341	+	0.572167i
$794$	−7.70778	+	13.3503i	−0.273539	+	0.473783i
$795$	4.94407	−	8.56339i	0.175348	−	0.303712i
$796$	−5.64229	−	9.77274i	−0.199986	−	0.346386i
$797$	53.5394			1.89646			0.948232	−	0.317578i	$-0.102869\pi$
$797$	53.5394			1.89646			0.948232	+	0.317578i	$0.102869\pi$
$798$	56.3250	−	20.2613i	1.99388	−	0.717242i
$799$	0.0104546			0.000369859
$800$	1.84518	+	3.19595i	0.0652370	+	0.112994i
$801$	−53.1155	+	91.9987i	−1.87674	+	3.25062i
$802$	−19.0183	+	32.9406i	−0.671559	+	1.16317i
$803$	−3.10957	−	5.38594i	−0.109734	−	0.190066i
$804$	−37.5265			−1.32346
$805$	−8.00488	−	6.76830i	−0.282135	−	0.238551i
$806$	−14.5511			−0.512540
$807$	−29.4091	−	50.9381i	−1.03525	−	1.79311i
$808$	−6.85968	+	11.8813i	−0.241323	+	0.417983i
$809$	−4.44663	+	7.70178i	−0.156335	+	0.270780i	−0.933544	−	0.358462i	$-0.883301\pi$
$809$	−4.44663	+	7.70178i	−0.156335	+	0.270780i	0.777209	+	0.629242i	$0.216635\pi$
$810$	−13.9223	−	24.1142i	−0.489181	−	0.847286i
$811$	4.11053			0.144340			0.0721701	−	0.997392i	$-0.477008\pi$
$811$	4.11053			0.144340			0.0721701	+	0.997392i	$0.477008\pi$
$812$	−2.02036	−	1.70826i	−0.0709007	−	0.0599481i
$813$	−23.6380			−0.829021
$814$	3.06637	+	5.31111i	0.107476	+	0.186154i
$815$	−9.59423	+	16.6177i	−0.336071	+	0.582092i
$816$	−0.314193	+	0.544199i	−0.0109990	+	0.0190508i
$817$	34.1917	+	59.2218i	1.19622	+	2.07191i
$818$	−29.2856			−1.02395
$819$	−68.0453	+	24.4773i	−2.37769	+	0.855307i
$820$	4.62899			0.161652
$821$	−7.10319	−	12.3031i	−0.247903	−	0.429381i	0.715041	−	0.699083i	$-0.246408\pi$
$821$	−7.10319	−	12.3031i	−0.247903	−	0.429381i	−0.962944	+	0.269702i	$0.913075\pi$
$822$	20.6783	−	35.8159i	0.721238	−	1.24922i
$823$	−9.42010	+	16.3161i	−0.328364	+	0.568743i	−0.982187	−	0.187904i	$-0.939831\pi$
$823$	−9.42010	+	16.3161i	−0.328364	+	0.568743i	0.653823	+	0.756647i	$0.273164\pi$
$824$	−0.590573	−	1.02290i	−0.0205736	−	0.0356345i
$825$	10.1556			0.353573
$826$	−3.77416	+	20.9439i	−0.131320	+	0.728731i
$827$	7.13405			0.248075			0.124038	−	0.992278i	$-0.460416\pi$
$827$	7.13405			0.248075			0.124038	+	0.992278i	$0.460416\pi$
$828$	12.9226	+	22.3827i	0.449092	+	0.777851i
$829$	−0.606016	+	1.04965i	−0.0210478	+	0.0364559i	−0.876357	−	0.481661i	$-0.840034\pi$
$829$	−0.606016	+	1.04965i	−0.0210478	+	0.0364559i	0.855310	+	0.518117i	$0.173367\pi$
$830$	−5.17589	+	8.96490i	−0.179658	+	0.311176i
$831$	26.9181	+	46.6235i	0.933778	+	1.61735i
$832$	3.66136			0.126935
$833$	1.04816	−	0.866171i	0.0363165	−	0.0300110i
$834$	0.551803			0.0191074
$835$	6.09702	+	10.5603i	0.210996	+	0.365456i
$836$	−2.97471	+	5.15234i	−0.102882	+	0.178197i
$837$	28.7022	−	49.7136i	0.992093	−	1.71836i
$838$	3.14706	+	5.45087i	0.108713	+	0.188297i
$839$	13.0004			0.448823			0.224412	−	0.974494i	$-0.427954\pi$
$839$	13.0004			0.448823			0.224412	+	0.974494i	$0.427954\pi$
$840$	1.73707	−	9.63951i	0.0599347	−	0.332595i
$841$	1.00000			0.0344828
$842$	−1.47240	−	2.55026i	−0.0507421	−	0.0878879i
$843$	−21.4417	+	37.1382i	−0.738492	+	1.27911i
$844$	4.93786	−	8.55262i	0.169968	−	0.294393i
$845$	−0.232050	−	0.401922i	−0.00798275	−	0.0138265i
$846$	0.401775			0.0138133
$847$	25.5837	−	9.20301i	0.879067	−	0.316219i
$848$	−2.67097			−0.0917216
$849$	24.7129	+	42.8039i	0.848143	+	1.46903i
$850$	0.358423	−	0.620807i	0.0122938	−	0.0212935i
$851$	12.4798	−	21.6156i	0.427802	−	0.740974i
$852$	18.2492	+	31.6086i	0.625208	+	1.08289i
$853$	23.8201			0.815584			0.407792	−	0.913075i	$-0.366299\pi$
$853$	23.8201			0.815584			0.407792	+	0.913075i	$0.366299\pi$
$854$	−10.2663	−	8.68041i	−0.351307	−	0.297038i
$855$	−59.7465			−2.04329
$856$	0.896121	+	1.55213i	0.0306288	+	0.0530506i
$857$	3.63570	−	6.29722i	0.124193	−	0.215109i	−0.797224	−	0.603683i	$-0.793699\pi$
$857$	3.63570	−	6.29722i	0.124193	−	0.215109i	0.921417	+	0.388575i	$0.127032\pi$
$858$	5.03790	−	8.72590i	0.171991	−	0.297897i
$859$	−4.91631	−	8.51531i	−0.167742	−	0.290539i	0.769883	−	0.638185i	$-0.220314\pi$
$859$	−4.91631	−	8.51531i	−0.167742	−	0.290539i	−0.937626	+	0.347646i	$0.886981\pi$
$860$	11.1897			0.381567
$861$	26.4368	+	22.3529i	0.900965	+	0.761786i
$862$	5.45942			0.185949
$863$	−10.9706	−	19.0017i	−0.373445	−	0.646826i	0.616648	−	0.787239i	$-0.288490\pi$
$863$	−10.9706	−	19.0017i	−0.373445	−	0.646826i	−0.990093	+	0.140413i	$0.955157\pi$
$864$	−7.22208	+	12.5090i	−0.245700	+	0.425565i
$865$	−10.2567	+	17.7651i	−0.348738	+	0.604031i
$866$	8.49495	+	14.7137i	0.288670	+	0.499991i
$867$	−54.8724			−1.86356
$868$	9.89414	−	3.55913i	0.335829	−	0.120805i
$869$	11.3621			0.385432
$870$	1.85104	+	3.20609i	0.0627561	+	0.108697i
$871$	21.2364	−	36.7825i	0.719567	−	1.24633i
$872$	−1.82095	+	3.15397i	−0.0616651	+	0.106807i
$873$	−70.0885	−	121.397i	−2.37214	−	4.10866i
$874$	24.2135			0.819032
$875$	−4.66644	+	25.8954i	−0.157755	+	0.875425i
$876$	−23.6501			−0.799063
$877$	−18.2830	−	31.6670i	−0.617372	−	1.06932i	−0.989963	−	0.141324i	$-0.954864\pi$
$877$	−18.2830	−	31.6670i	−0.617372	−	1.06932i	0.372592	−	0.927995i	$-0.378469\pi$
$878$	11.3210	−	19.6085i	0.382064	−	0.661755i
$879$	25.1019	−	43.4778i	0.846667	−	1.46647i
$880$	0.486758	+	0.843090i	0.0164086	+	0.0284206i
$881$	−33.4505			−1.12698			−0.563489	−	0.826124i	$-0.690541\pi$
$881$	−33.4505			−1.12698			−0.563489	+	0.826124i	$0.690541\pi$
$882$	40.2810	−	33.2872i	1.35633	−	1.12084i
$883$	−23.9555			−0.806166			−0.403083	−	0.915163i	$-0.632061\pi$
$883$	−23.9555			−0.806166			−0.403083	+	0.915163i	$0.632061\pi$
$884$	−0.355606	−	0.615928i	−0.0119603	−	0.0207159i
$885$	14.8889	−	25.7883i	0.500485	−	0.866866i
$886$	8.56936	−	14.8426i	0.287893	−	0.498646i
$887$	−3.69777	−	6.40472i	−0.124159	−	0.215049i	0.797245	−	0.603656i	$-0.206290\pi$
$887$	−3.69777	−	6.40472i	−0.124159	−	0.215049i	−0.921404	+	0.388606i	$0.872957\pi$
$888$	23.3215			0.782618
$889$	−5.43302	+	30.1494i	−0.182218	+	1.01118i
$890$	16.2853			0.545885
$891$	10.3491	+	17.9252i	0.346709	+	0.600517i
$892$	8.29908	−	14.3744i	0.277874	−	0.481292i
$893$	0.188204	−	0.325979i	0.00629801	−	0.0109085i
$894$	−22.7159	−	39.3450i	−0.759732	−	1.31589i
$895$	6.05292			0.202327
$896$	−2.48958	+	0.895553i	−0.0831709	+	0.0299183i
$897$	−41.0074			−1.36920
$898$	6.09008	+	10.5483i	0.203229	+	0.352002i
$899$	−1.98711	+	3.44178i	−0.0662739	+	0.114790i
$900$	13.7743	−	23.8578i	0.459143	−	0.795259i
$901$	0.259416	+	0.449321i	0.00864239	+	0.0149691i
$902$	−3.44095			−0.114571
$903$	63.9062	+	54.0341i	2.12667	+	1.79814i
$904$	−17.7718			−0.591081
$905$	−7.53644	−	13.0535i	−0.250520	−	0.433913i
$906$	−19.7293	+	34.1722i	−0.655463	+	1.13530i
$907$	−14.2946	+	24.7590i	−0.474644	+	0.822108i	−0.999578	−	0.0290348i	$-0.990757\pi$
$907$	−14.2946	+	24.7590i	−0.474644	+	0.822108i	0.524934	+	0.851143i	$0.324090\pi$
$908$	−8.99651	−	15.5824i	−0.298560	−	0.517121i
$909$	102.415			3.39690
$910$	8.46538	+	7.15767i	0.280625	+	0.237274i
$911$	−15.2600			−0.505587			−0.252793	−	0.967520i	$-0.581349\pi$
$911$	−15.2600			−0.505587			−0.252793	+	0.967520i	$0.581349\pi$
$912$	11.3122	+	19.5933i	0.374584	+	0.648798i
$913$	3.84749	−	6.66404i	0.127333	−	0.220548i
$914$	−15.7551	+	27.2886i	−0.521132	+	0.902626i
$915$	9.40593	+	16.2916i	0.310951	+	0.538582i
$916$	−2.03821			−0.0673444
$917$	40.3250	−	14.5058i	1.33165	−	0.479023i
$918$	2.80575			0.0926036
$919$	11.1510	+	19.3140i	0.367836	+	0.637111i	0.989227	−	0.146390i	$-0.0467654\pi$
$919$	11.1510	+	19.3140i	0.367836	+	0.637111i	−0.621391	+	0.783501i	$0.713432\pi$
$920$	1.98105	−	3.43128i	0.0653134	−	0.113126i
$921$	−5.08339	+	8.80468i	−0.167503	+	0.290124i
$922$	3.20398	+	5.54945i	0.105517	+	0.182762i
$923$	−41.3092			−1.35971
$924$	−1.29125	+	7.16551i	−0.0424790	+	0.235728i
$925$	−26.6045			−0.874752
$926$	0.451470	+	0.781968i	0.0148362	+	0.0256971i
$927$	−4.40863	+	7.63598i	−0.144798	+	0.250798i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	22.4850	+	38.9452i	0.737710	+	1.27775i	0.953524	+	0.301316i	$0.0974259\pi$
$929$	22.4850	+	38.9452i	0.737710	+	1.27775i	−0.215815	+	0.976434i	$0.569241\pi$
$930$	−14.7129			−0.482455
$931$	−8.13858	−	48.2746i	−0.266731	−	1.58214i
$932$	−16.4989			−0.540441
$933$	−39.1690	−	67.8426i	−1.28233	−	2.22107i
$934$	18.2056	−	31.5330i	0.595705	−	1.03179i
$935$	0.0945519	−	0.163769i	0.00309218	−	0.00535581i
$936$	−13.6660	−	23.6703i	−0.446688	−	0.773687i
$937$	20.6347			0.674105			0.337053	−	0.941486i	$-0.390570\pi$
$937$	20.6347			0.674105			0.337053	+	0.941486i	$0.390570\pi$
$938$	−5.44303	+	30.2049i	−0.177721	+	0.986226i
$939$	−33.4910			−1.09294
$940$	−0.0307963	−	0.0533407i	−0.00100446	−	0.00173978i
$941$	−16.6294	+	28.8030i	−0.542103	+	0.938950i	0.456680	+	0.889631i	$0.349038\pi$
$941$	−16.6294	+	28.8030i	−0.542103	+	0.938950i	−0.998783	+	0.0493189i	$0.984295\pi$
$942$	−23.2751	+	40.3137i	−0.758344	+	1.31349i
$943$	7.00215	+	12.1281i	0.228021	+	0.394945i
$944$	−8.04354			−0.261795
$945$	−41.1522	+	14.8033i	−1.33868	+	0.481552i
$946$	−8.31787			−0.270437
$947$	−0.0479947	−	0.0831292i	−0.00155962	−	0.00270134i	0.865245	−	0.501350i	$-0.167163\pi$
$947$	−0.0479947	−	0.0831292i	−0.00155962	−	0.00270134i	−0.866804	+	0.498649i	$0.833830\pi$
$948$	21.6038	−	37.4188i	0.701658	−	1.21531i
$949$	13.3837	−	23.1812i	0.434452	−	0.752494i
$950$	−12.9046	−	22.3515i	−0.418681	−	0.725177i
$951$	−111.713			−3.62253
$952$	0.392451	+	0.331826i	0.0127194	+	0.0107545i
$953$	−11.4213			−0.369974			−0.184987	−	0.982741i	$-0.559224\pi$
$953$	−11.4213			−0.369974			−0.184987	+	0.982741i	$0.559224\pi$
$954$	9.96942	+	17.2675i	0.322772	+	0.559057i
$955$	−5.66972	+	9.82025i	−0.183468	+	0.317776i
$956$	−9.37071	+	16.2305i	−0.303070	+	0.524933i
$957$	−1.37597	−	2.38324i	−0.0444786	−	0.0770393i
$958$	31.4283			1.01540
$959$	−25.8288	−	21.8388i	−0.834054	−	0.705211i
$960$	3.70208			0.119484
$961$	7.60276	+	13.1684i	0.245250	+	0.424786i
$962$	−13.1977	+	22.8591i	−0.425512	+	0.737008i
$963$	6.68955	−	11.5866i	0.215568	−	0.373374i
$964$	−8.93903	−	15.4828i	−0.287907	−	0.498669i
$965$	−19.9068			−0.640822
$966$	27.8834	−	10.0302i	0.897133	−	0.322718i
$967$	−9.43755			−0.303491			−0.151746	−	0.988420i	$-0.548489\pi$
$967$	−9.43755			−0.303491			−0.151746	+	0.988420i	$0.548489\pi$
$968$	5.13817	+	8.89957i	0.165147	+	0.286043i
$969$	2.19737	−	3.80596i	0.0705897	−	0.122265i
$970$	−10.7446	+	18.6103i	−0.344990	+	0.597540i
$971$	9.26400	+	16.0457i	0.297296	+	0.514932i	0.975516	−	0.219927i	$-0.0705819\pi$
$971$	9.26400	+	16.0457i	0.297296	+	0.514932i	−0.678220	+	0.734859i	$0.737249\pi$
$972$	35.3786			1.13477
$973$	0.0800363	−	0.444144i	0.00256585	−	0.0142386i
$974$	14.4460			0.462878
$975$	21.8550	+	37.8540i	0.699921	+	1.21230i
$976$	2.54072	−	4.40065i	0.0813264	−	0.140861i
$977$	20.3383	−	35.2270i	0.650680	−	1.12701i	−0.332279	−	0.943181i	$-0.607817\pi$
$977$	20.3383	−	35.2270i	0.650680	−	1.12701i	0.982958	−	0.183829i	$-0.0588492\pi$
$978$	−27.1209	−	46.9748i	−0.867231	−	1.50209i
$979$	−12.1057			−0.386899
$980$	−7.50685	−	2.79633i	−0.239798	−	0.0893254i
$981$	27.1868			0.868008
$982$	−14.6203	−	25.3230i	−0.466551	−	0.808090i
$983$	−26.3075	+	45.5659i	−0.839078	+	1.45332i	0.0515893	+	0.998668i	$0.483571\pi$
$983$	−26.3075	+	45.5659i	−0.839078	+	1.45332i	−0.890667	+	0.454657i	$0.849762\pi$
$984$	−6.54261	+	11.3321i	−0.208571	+	0.361255i
$985$	−10.0684	−	17.4390i	−0.320806	−	0.555653i
$986$	−0.194248			−0.00618612
$987$	0.0816949	−	0.453348i	0.00260038	−	0.0144302i
$988$	−25.6064			−0.814648
$989$	16.9264	+	29.3174i	0.538229	+	0.932240i
$990$	3.63365	−	6.29367i	0.115485	−	0.200026i
$991$	12.3917	−	21.4631i	0.393637	−	0.681799i	−0.599290	−	0.800532i	$-0.704550\pi$
$991$	12.3917	−	21.4631i	0.393637	−	0.681799i	0.992926	+	0.118734i	$0.0378835\pi$
$992$	1.98711	+	3.44178i	0.0630909	+	0.109277i
$993$	16.4997			0.523603
$994$	28.0886	−	10.1041i	0.890915	−	0.320481i
$995$	12.9140			0.409402
$996$	−14.6312	−	25.3419i	−0.463607	−	0.802990i
$997$	−8.09453	+	14.0201i	−0.256356	+	0.444022i	−0.965263	−	0.261280i	$-0.915855\pi$
$997$	−8.09453	+	14.0201i	−0.256356	+	0.444022i	0.708907	+	0.705302i	$0.249189\pi$
$998$	−14.2452	+	24.6735i	−0.450925	+	0.781025i
$999$	−52.0654	−	90.1799i	−1.64728	−	2.85317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.e.a.291.1	yes	10
7.2	even	3	inner	406.2.e.a.233.1	✓	10
7.3	odd	6		2842.2.a.x.1.1		5
7.4	even	3		2842.2.a.z.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.1	✓	10	7.2	even	3	inner
406.2.e.a.291.1	yes	10	1.1	even	1	trivial
2842.2.a.x.1.1		5	7.3	odd	6
2842.2.a.z.1.5		5	7.4	even	3

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:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.61748 + 2.80156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.572197 - 0.991074i) q^{5} +3.23497 q^{6} +(0.469216 - 2.60381i) q^{7} +1.00000 q^{8} +(-3.73251 - 6.46489i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.61748 + 2.80156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.572197 - 0.991074i) q^{5} +3.23497 q^{6} +(0.469216 - 2.60381i) q^{7} +1.00000 q^{8} +(-3.73251 - 6.46489i) q^{9} +(-0.572197 + 0.991074i) q^{10} +(0.425341 - 0.736713i) q^{11} +(-1.61748 - 2.80156i) q^{12} +3.66136 q^{13} +(-2.48958 + 0.895553i) q^{14} +3.70208 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0971241 + 0.168224i) q^{17} +(-3.73251 + 6.46489i) q^{18} +(3.49684 + 6.05671i) q^{19} +1.14439 q^{20} +(6.53580 + 5.52616i) q^{21} -0.850683 q^{22} +(1.73109 + 2.99834i) q^{23} +(-1.61748 + 2.80156i) q^{24} +(1.84518 - 3.19595i) q^{25} +(-1.83068 - 3.17083i) q^{26} +14.4442 q^{27} +(2.02036 + 1.70826i) q^{28} -1.00000 q^{29} +(-1.85104 - 3.20609i) q^{30} +(1.98711 - 3.44178i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.37597 + 2.38324i) q^{33} +0.194248 q^{34} +(-2.84905 + 1.02487i) q^{35} +7.46501 q^{36} +(-3.60460 - 6.24335i) q^{37} +(3.49684 - 6.05671i) q^{38} +(-5.92219 + 10.2575i) q^{39} +(-0.572197 - 0.991074i) q^{40} +4.04493 q^{41} +(1.51790 - 8.42325i) q^{42} +9.77788 q^{43} +(0.425341 + 0.736713i) q^{44} +(-4.27146 + 7.39838i) q^{45} +(1.73109 - 2.99834i) q^{46} +(-0.0269105 - 0.0466104i) q^{47} +3.23497 q^{48} +(-6.55967 - 2.44350i) q^{49} -3.69036 q^{50} +(-0.314193 - 0.544199i) q^{51} +(-1.83068 + 3.17083i) q^{52} +(1.33549 - 2.31313i) q^{53} +(-7.22208 - 12.5090i) q^{54} -0.973516 q^{55} +(0.469216 - 2.60381i) q^{56} -22.6244 q^{57} +(0.500000 + 0.866025i) q^{58} +(4.02177 - 6.96591i) q^{59} +(-1.85104 + 3.20609i) q^{60} +(2.54072 + 4.40065i) q^{61} -3.97423 q^{62} +(-18.5847 + 6.68531i) q^{63} +1.00000 q^{64} +(-2.09502 - 3.62868i) q^{65} +(1.37597 - 2.38324i) q^{66} +(5.80013 - 10.0461i) q^{67} +(-0.0971241 - 0.168224i) q^{68} -11.2001 q^{69} +(2.31209 + 1.95492i) q^{70} -11.2825 q^{71} +(-3.73251 - 6.46489i) q^{72} +(3.65539 - 6.33131i) q^{73} +(-3.60460 + 6.24335i) q^{74} +(5.96910 + 10.3388i) q^{75} -6.99369 q^{76} +(-1.71868 - 1.45319i) q^{77} +11.8444 q^{78} +(6.67821 + 11.5670i) q^{79} +(-0.572197 + 0.991074i) q^{80} +(-12.1657 + 21.0716i) q^{81} +(-2.02247 - 3.50301i) q^{82} +9.04564 q^{83} +(-8.05369 + 2.89708i) q^{84} +0.222296 q^{85} +(-4.88894 - 8.46789i) q^{86} +(1.61748 - 2.80156i) q^{87} +(0.425341 - 0.736713i) q^{88} +(-7.11526 - 12.3240i) q^{89} +8.54291 q^{90} +(1.71797 - 9.53349i) q^{91} -3.46219 q^{92} +(6.42825 + 11.1340i) q^{93} +(-0.0269105 + 0.0466104i) q^{94} +(4.00177 - 6.93126i) q^{95} +(-1.61748 - 2.80156i) q^{96} +18.7779 q^{97} +(1.16370 + 6.90259i) q^{98} -6.35036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

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