LMFDB - Embedded newform 414.2.e.d.139.3

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.3
Root			$-0.539982 - 0.935277i$ of defining polynomial
Character	$\chi$	$=$	414.139
Dual form			414.2.e.d.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.376855 + 1.69056i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.990153 + 1.71499i) q^{5} +(-1.65249 + 0.518912i) q^{6} +(0.245502 + 0.425221i) q^{7} -1.00000 q^{8} +(-2.71596 - 1.27419i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.376855 + 1.69056i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.990153 + 1.71499i) q^{5} +(-1.65249 + 0.518912i) q^{6} +(0.245502 + 0.425221i) q^{7} -1.00000 q^{8} +(-2.71596 - 1.27419i) q^{9} -1.98031 q^{10} +(-1.91763 - 3.32142i) q^{11} +(-1.27564 - 1.17164i) q^{12} +(-2.84575 + 4.92899i) q^{13} +(-0.245502 + 0.425221i) q^{14} +(-2.52615 - 2.32021i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.35597 q^{17} +(-0.254498 - 2.98919i) q^{18} +4.40294 q^{19} +(-0.990153 - 1.71499i) q^{20} +(-0.811379 + 0.254787i) q^{21} +(1.91763 - 3.32142i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.376855 - 1.69056i) q^{24} +(0.539195 + 0.933913i) q^{25} -5.69151 q^{26} +(3.17762 - 4.11130i) q^{27} -0.491003 q^{28} +(-4.47632 - 7.75322i) q^{29} +(0.746289 - 3.34782i) q^{30} +(-4.82606 + 8.35898i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.33772 - 1.99016i) q^{33} +(2.17799 + 3.77238i) q^{34} -0.972336 q^{35} +(2.46146 - 1.71499i) q^{36} -9.12212 q^{37} +(2.20147 + 3.81306i) q^{38} +(-7.26030 - 6.66842i) q^{39} +(0.990153 - 1.71499i) q^{40} +(-1.69182 + 2.93032i) q^{41} +(-0.626342 - 0.575281i) q^{42} +(4.76500 + 8.25323i) q^{43} +3.83525 q^{44} +(4.87445 - 3.39621i) q^{45} -1.00000 q^{46} +(6.30759 + 10.9251i) q^{47} +(1.65249 - 0.518912i) q^{48} +(3.37946 - 5.85339i) q^{49} +(-0.539195 + 0.933913i) q^{50} +(-1.64157 + 7.36402i) q^{51} +(-2.84575 - 4.92899i) q^{52} -0.481721 q^{53} +(5.14930 + 0.696247i) q^{54} +7.59497 q^{55} +(-0.245502 - 0.425221i) q^{56} +(-1.65927 + 7.44342i) q^{57} +(4.47632 - 7.75322i) q^{58} +(-1.38506 + 2.39900i) q^{59} +(3.27244 - 1.02760i) q^{60} +(1.41327 + 2.44785i) q^{61} -9.65212 q^{62} +(-0.124960 - 1.46770i) q^{63} +1.00000 q^{64} +(-5.63546 - 9.76091i) q^{65} +(4.89239 + 4.49355i) q^{66} +(0.245502 - 0.425221i) q^{67} +(-2.17799 + 3.77238i) q^{68} +(-1.27564 - 1.17164i) q^{69} +(-0.486168 - 0.842068i) q^{70} +5.93089 q^{71} +(2.71596 + 1.27419i) q^{72} +6.59667 q^{73} +(-4.56106 - 7.89998i) q^{74} +(-1.78203 + 0.559589i) q^{75} +(-2.20147 + 3.81306i) q^{76} +(0.941560 - 1.63083i) q^{77} +(2.14488 - 9.62182i) q^{78} +(6.68166 + 11.5730i) q^{79} +1.98031 q^{80} +(5.75288 + 6.92130i) q^{81} -3.38364 q^{82} +(-0.956164 - 1.65612i) q^{83} +(0.185037 - 0.830068i) q^{84} +(-4.31308 + 7.47047i) q^{85} +(-4.76500 + 8.25323i) q^{86} +(14.7942 - 4.64563i) q^{87} +(1.91763 + 3.32142i) q^{88} -5.17284 q^{89} +(5.37843 + 2.52329i) q^{90} -2.79455 q^{91} +(-0.500000 - 0.866025i) q^{92} +(-12.3126 - 11.3089i) q^{93} +(-6.30759 + 10.9251i) q^{94} +(-4.35959 + 7.55102i) q^{95} +(1.27564 + 1.17164i) q^{96} +(6.47632 + 11.2173i) q^{97} +6.75892 q^{98} +(0.976065 + 11.4643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * 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
$3$	−0.376855	+	1.69056i	−0.217578	+	0.976043i
$3$	−0.376855	+	1.69056i	−0.217578	+	0.976043i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.990153	+	1.71499i	−0.442810	+	0.766969i	−0.997897	−	0.0648233i	$-0.979352\pi$
$5$	−0.990153	+	1.71499i	−0.442810	+	0.766969i	0.555087	+	0.831792i	$0.312685\pi$
$6$	−1.65249	+	0.518912i	−0.674627	+	0.211845i
$7$	0.245502	+	0.425221i	0.0927909	+	0.160719i	0.908684	−	0.417484i	$-0.137088\pi$
$7$	0.245502	+	0.425221i	0.0927909	+	0.160719i	−0.815894	+	0.578202i	$0.803755\pi$
$8$	−1.00000			−0.353553
$9$	−2.71596	−	1.27419i	−0.905320	−	0.424730i
$10$	−1.98031			−0.626228
$11$	−1.91763	−	3.32142i	−0.578186	−	1.00145i	−0.995687	−	0.0927710i	$-0.970428\pi$
$11$	−1.91763	−	3.32142i	−0.578186	−	1.00145i	0.417502	−	0.908676i	$-0.362906\pi$
$12$	−1.27564	−	1.17164i	−0.368245	−	0.338225i
$13$	−2.84575	+	4.92899i	−0.789270	+	1.36706i	0.137144	+	0.990551i	$0.456208\pi$
$13$	−2.84575	+	4.92899i	−0.789270	+	1.36706i	−0.926415	+	0.376505i	$0.877126\pi$
$14$	−0.245502	+	0.425221i	−0.0656131	+	0.113645i
$15$	−2.52615	−	2.32021i	−0.652249	−	0.599077i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.35597			1.05648			0.528239	−	0.849096i	$-0.322852\pi$
$17$	4.35597			1.05648			0.528239	+	0.849096i	$0.322852\pi$
$18$	−0.254498	−	2.98919i	−0.0599859	−	0.704558i
$19$	4.40294			1.01010			0.505052	−	0.863089i	$-0.331473\pi$
$19$	4.40294			1.01010			0.505052	+	0.863089i	$0.331473\pi$
$20$	−0.990153	−	1.71499i	−0.221405	−	0.383485i
$21$	−0.811379	+	0.254787i	−0.177057	+	0.0555991i
$22$	1.91763	−	3.32142i	0.408839	−	0.708130i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	0.376855	−	1.69056i	0.0769253	−	0.345083i
$25$	0.539195	+	0.933913i	0.107839	+	0.186783i
$26$	−5.69151			−1.11620
$27$	3.17762	−	4.11130i	0.611532	−	0.791219i
$28$	−0.491003			−0.0927909
$29$	−4.47632	−	7.75322i	−0.831232	−	1.43974i	−0.897062	−	0.441905i	$-0.854303\pi$
$29$	−4.47632	−	7.75322i	−0.831232	−	1.43974i	0.0658299	−	0.997831i	$-0.479031\pi$
$30$	0.746289	−	3.34782i	0.136253	−	0.611225i
$31$	−4.82606	+	8.35898i	−0.866786	+	1.50132i	−0.00152311	+	0.999999i	$0.500485\pi$
$31$	−4.82606	+	8.35898i	−0.866786	+	1.50132i	−0.865263	+	0.501318i	$0.832849\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	6.33772	−	1.99016i	1.10326	−	0.346442i
$34$	2.17799	+	3.77238i	0.373522	+	0.646958i
$35$	−0.972336			−0.164355
$36$	2.46146	−	1.71499i	0.410244	−	0.285832i
$37$	−9.12212			−1.49967			−0.749833	−	0.661627i	$-0.769866\pi$
$37$	−9.12212			−1.49967			−0.749833	+	0.661627i	$0.769866\pi$
$38$	2.20147	+	3.81306i	0.357126	+	0.618560i
$39$	−7.26030	−	6.66842i	−1.16258	−	1.06780i
$40$	0.990153	−	1.71499i	0.156557	−	0.271165i
$41$	−1.69182	+	2.93032i	−0.264218	+	0.457638i	−0.967358	−	0.253412i	$-0.918447\pi$
$41$	−1.69182	+	2.93032i	−0.264218	+	0.457638i	0.703141	+	0.711051i	$0.251780\pi$
$42$	−0.626342	−	0.575281i	−0.0966466	−	0.0887678i
$43$	4.76500	+	8.25323i	0.726656	+	1.25861i	0.958289	+	0.285802i	$0.0922599\pi$
$43$	4.76500	+	8.25323i	0.726656	+	1.25861i	−0.231633	+	0.972803i	$0.574407\pi$
$44$	3.83525			0.578186
$45$	4.87445	−	3.39621i	0.726639	−	0.506278i
$46$	−1.00000			−0.147442
$47$	6.30759	+	10.9251i	0.920056	+	1.59358i	0.799325	+	0.600899i	$0.205190\pi$
$47$	6.30759	+	10.9251i	0.920056	+	1.59358i	0.120731	+	0.992685i	$0.461476\pi$
$48$	1.65249	−	0.518912i	0.238517	−	0.0748984i
$49$	3.37946	−	5.85339i	0.482780	−	0.836199i
$50$	−0.539195	+	0.933913i	−0.0762537	+	0.132075i
$51$	−1.64157	+	7.36402i	−0.229866	+	1.03117i
$52$	−2.84575	−	4.92899i	−0.394635	−	0.683528i
$53$	−0.481721			−0.0661695			−0.0330847	−	0.999453i	$-0.510533\pi$
$53$	−0.481721			−0.0661695			−0.0330847	+	0.999453i	$0.510533\pi$
$54$	5.14930	+	0.696247i	0.700730	+	0.0947472i
$55$	7.59497			1.02411
$56$	−0.245502	−	0.425221i	−0.0328065	−	0.0568226i
$57$	−1.65927	+	7.44342i	−0.219776	+	0.985905i
$58$	4.47632	−	7.75322i	0.587770	−	1.01805i
$59$	−1.38506	+	2.39900i	−0.180320	+	0.312324i	−0.941990	−	0.335642i	$-0.891047\pi$
$59$	−1.38506	+	2.39900i	−0.180320	+	0.312324i	0.761669	+	0.647966i	$0.224380\pi$
$60$	3.27244	−	1.02760i	0.422470	−	0.132663i
$61$	1.41327	+	2.44785i	0.180951	+	0.313416i	0.942205	−	0.335038i	$-0.108749\pi$
$61$	1.41327	+	2.44785i	0.180951	+	0.313416i	−0.761254	+	0.648454i	$0.775416\pi$
$62$	−9.65212			−1.22582
$63$	−0.124960	−	1.46770i	−0.0157434	−	0.184913i
$64$	1.00000			0.125000
$65$	−5.63546	−	9.76091i	−0.698993	−	1.21069i
$66$	4.89239	+	4.49355i	0.602211	+	0.553118i
$67$	0.245502	−	0.425221i	0.0299928	−	0.0519490i	−0.850639	−	0.525750i	$-0.823785\pi$
$67$	0.245502	−	0.425221i	0.0299928	−	0.0519490i	0.880632	+	0.473801i	$0.157118\pi$
$68$	−2.17799	+	3.77238i	−0.264120	+	0.457469i
$69$	−1.27564	−	1.17164i	−0.153569	−	0.141049i
$70$	−0.486168	−	0.842068i	−0.0581082	−	0.100646i
$71$	5.93089			0.703867			0.351934	−	0.936025i	$-0.385524\pi$
$71$	5.93089			0.703867			0.351934	+	0.936025i	$0.385524\pi$
$72$	2.71596	+	1.27419i	0.320079	+	0.150165i
$73$	6.59667			0.772082			0.386041	−	0.922482i	$-0.373842\pi$
$73$	6.59667			0.772082			0.386041	+	0.922482i	$0.373842\pi$
$74$	−4.56106	−	7.89998i	−0.530212	−	0.918354i
$75$	−1.78203	+	0.559589i	−0.205771	+	0.0646158i
$76$	−2.20147	+	3.81306i	−0.252526	+	0.437388i
$77$	0.941560	−	1.63083i	0.107301	−	0.185850i
$78$	2.14488	−	9.62182i	0.242859	−	1.08946i
$79$	6.68166	+	11.5730i	0.751746	+	1.30206i	0.946976	+	0.321304i	$0.104121\pi$
$79$	6.68166	+	11.5730i	0.751746	+	1.30206i	−0.195230	+	0.980757i	$0.562545\pi$
$80$	1.98031			0.221405
$81$	5.75288	+	6.92130i	0.639208	+	0.769034i
$82$	−3.38364			−0.373660
$83$	−0.956164	−	1.65612i	−0.104953	−	0.181783i	0.808766	−	0.588130i	$-0.200136\pi$
$83$	−0.956164	−	1.65612i	−0.104953	−	0.181783i	−0.913719	+	0.406347i	$0.866802\pi$
$84$	0.185037	−	0.830068i	0.0201892	−	0.0905679i
$85$	−4.31308	+	7.47047i	−0.467819	+	0.810286i
$86$	−4.76500	+	8.25323i	−0.513823	+	0.889968i
$87$	14.7942	−	4.64563i	1.58610	−	0.498064i
$88$	1.91763	+	3.32142i	0.204420	+	0.354065i
$89$	−5.17284			−0.548320			−0.274160	−	0.961684i	$-0.588400\pi$
$89$	−5.17284			−0.548320			−0.274160	+	0.961684i	$0.588400\pi$
$90$	5.37843	+	2.52329i	0.566936	+	0.265978i
$91$	−2.79455			−0.292948
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	−12.3126	−	11.3089i	−1.27676	−	1.17267i
$94$	−6.30759	+	10.9251i	−0.650578	+	1.12683i
$95$	−4.35959	+	7.55102i	−0.447284	+	0.774719i
$96$	1.27564	+	1.17164i	0.130194	+	0.119580i
$97$	6.47632	+	11.2173i	0.657571	+	1.13895i	0.981243	+	0.192777i	$0.0617493\pi$
$97$	6.47632	+	11.2173i	0.657571	+	1.13895i	−0.323672	+	0.946169i	$0.604917\pi$
$98$	6.75892			0.682754
$99$	0.976065	+	11.4643i	0.0980982	+	1.15220i
$100$	−1.07839			−0.107839
$101$	−7.03237	−	12.1804i	−0.699747	−	1.21200i	−0.968554	−	0.248803i	$-0.919963\pi$
$101$	−7.03237	−	12.1804i	−0.699747	−	1.21200i	0.268808	−	0.963194i	$-0.413370\pi$
$102$	−7.19821	+	2.26036i	−0.712729	+	0.223809i
$103$	8.28251	−	14.3457i	0.816100	−	1.41353i	−0.0924356	−	0.995719i	$-0.529465\pi$
$103$	8.28251	−	14.3457i	0.816100	−	1.41353i	0.908535	−	0.417808i	$-0.137201\pi$
$104$	2.84575	−	4.92899i	0.279049	−	0.483327i
$105$	0.366430	−	1.64379i	0.0357599	−	0.160417i
$106$	−0.240860	−	0.417183i	−0.0233944	−	0.0405204i
$107$	6.19254			0.598655			0.299328	−	0.954150i	$-0.403238\pi$
$107$	6.19254			0.598655			0.299328	+	0.954150i	$0.403238\pi$
$108$	1.97168	+	4.80754i	0.189725	+	0.462606i
$109$	4.67294			0.447587			0.223793	−	0.974637i	$-0.428156\pi$
$109$	4.67294			0.447587			0.223793	+	0.974637i	$0.428156\pi$
$110$	3.79748	+	6.57744i	0.362076	+	0.627134i
$111$	3.43772	−	15.4214i	0.326294	−	1.46374i
$112$	0.245502	−	0.425221i	0.0231977	−	0.0401796i
$113$	−2.36980	+	4.10462i	−0.222932	+	0.386130i	−0.955697	−	0.294352i	$-0.904896\pi$
$113$	−2.36980	+	4.10462i	−0.222932	+	0.386130i	0.732765	+	0.680482i	$0.238230\pi$
$114$	−7.27583	+	2.28474i	−0.681444	+	0.213985i
$115$	−0.990153	−	1.71499i	−0.0923322	−	0.159924i
$116$	8.95264			0.831232
$117$	14.0094	−	9.76091i	1.29517	−	0.902396i
$118$	−2.77013			−0.255011
$119$	1.06940	+	1.85225i	0.0980316	+	0.169796i
$120$	2.52615	+	2.32021i	0.230605	+	0.211806i
$121$	−1.85457	+	3.21222i	−0.168598	+	0.292020i
$122$	−1.41327	+	2.44785i	−0.127951	+	0.221618i
$123$	−4.31629	−	3.96442i	−0.389187	−	0.357460i
$124$	−4.82606	−	8.35898i	−0.433393	−	0.750659i
$125$	−12.0371			−1.07663
$126$	1.20859	−	0.842068i	0.107669	−	0.0750174i
$127$	5.87595			0.521406			0.260703	−	0.965419i	$-0.416046\pi$
$127$	5.87595			0.521406			0.260703	+	0.965419i	$0.416046\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−15.7483	+	4.94523i	−1.38656	+	0.435403i
$130$	5.63546	−	9.76091i	0.494263	−	0.856088i
$131$	−1.16862	+	2.02411i	−0.102103	+	0.176847i	−0.912551	−	0.408963i	$-0.865890\pi$
$131$	−1.16862	+	2.02411i	−0.102103	+	0.176847i	0.810448	+	0.585810i	$0.199224\pi$
$132$	−1.44534	+	6.48371i	−0.125800	+	0.564334i
$133$	1.08093	+	1.87222i	0.0937285	+	0.162342i
$134$	0.491003			0.0424162
$135$	3.90453	+	9.52041i	0.336048	+	0.819386i
$136$	−4.35597			−0.373522
$137$	−1.30317	−	2.25716i	−0.111337	−	0.192842i	0.804972	−	0.593312i	$-0.202180\pi$
$137$	−1.30317	−	2.25716i	−0.111337	−	0.192842i	−0.916310	+	0.400470i	$0.868847\pi$
$138$	0.376855	−	1.69056i	0.0320801	−	0.143910i
$139$	5.42794	−	9.40146i	0.460391	−	0.797421i	−0.538589	−	0.842569i	$-0.681042\pi$
$139$	5.42794	−	9.40146i	0.460391	−	0.797421i	0.998980	+	0.0451473i	$0.0143757\pi$
$140$	0.486168	−	0.842068i	0.0410887	−	0.0711677i
$141$	−20.8465	+	6.54616i	−1.75559	+	0.551286i
$142$	2.96545	+	5.13630i	0.248855	+	0.431029i
$143$	21.8284			1.82538
$144$	0.254498	+	2.98919i	0.0212082	+	0.249099i
$145$	17.7290			1.47231
$146$	3.29833	+	5.71288i	0.272972	+	0.472802i
$147$	8.62192	+	7.91905i	0.711124	+	0.653152i
$148$	4.56106	−	7.89998i	0.374917	−	0.649375i
$149$	4.13281	−	7.15824i	0.338573	−	0.586426i	−0.645591	−	0.763683i	$-0.723389\pi$
$149$	4.13281	−	7.15824i	0.338573	−	0.586426i	0.984165	+	0.177257i	$0.0567224\pi$
$150$	−1.37563	−	1.26349i	−0.112320	−	0.103164i
$151$	−3.03757	−	5.26123i	−0.247194	−	0.428153i	0.715552	−	0.698559i	$-0.246175\pi$
$151$	−3.03757	−	5.26123i	−0.247194	−	0.428153i	−0.962746	+	0.270407i	$0.912842\pi$
$152$	−4.40294			−0.357126
$153$	−11.8306	−	5.55034i	−0.956451	−	0.448718i
$154$	1.88312			0.151746
$155$	−9.55707	−	16.5533i	−0.767643	−	1.32960i
$156$	9.40517	−	2.95339i	0.753017	−	0.236460i
$157$	−3.82728	+	6.62905i	−0.305450	+	0.529055i	−0.977361	−	0.211576i	$-0.932140\pi$
$157$	−3.82728	+	6.62905i	−0.305450	+	0.529055i	0.671911	+	0.740632i	$0.265474\pi$
$158$	−6.68166	+	11.5730i	−0.531564	+	0.920697i
$159$	0.181539	−	0.814376i	0.0143970	−	0.0645842i
$160$	0.990153	+	1.71499i	0.0782784	+	0.135582i
$161$	−0.491003			−0.0386965
$162$	−3.11759	+	8.44279i	−0.244941	+	0.663328i
$163$	−19.8556			−1.55521			−0.777607	−	0.628751i	$-0.783567\pi$
$163$	−19.8556			−1.55521			−0.777607	+	0.628751i	$0.783567\pi$
$164$	−1.69182	−	2.93032i	−0.132109	−	0.228819i
$165$	−2.86221	+	12.8397i	−0.222822	+	0.999571i
$166$	0.956164	−	1.65612i	0.0742127	−	0.128540i
$167$	−2.18300	+	3.78106i	−0.168926	+	0.292588i	−0.938042	−	0.346521i	$-0.887363\pi$
$167$	−2.18300	+	3.78106i	−0.168926	+	0.292588i	0.769117	+	0.639108i	$0.220696\pi$
$168$	0.811379	−	0.254787i	0.0625992	−	0.0196573i
$169$	−9.69664	−	16.7951i	−0.745895	−	1.29193i
$170$	−8.62616			−0.661596
$171$	−11.9582	−	5.61019i	−0.914468	−	0.429022i
$172$	−9.53000			−0.726656
$173$	−3.42292	−	5.92868i	−0.260240	−	0.450749i	0.706066	−	0.708146i	$-0.250468\pi$
$173$	−3.42292	−	5.92868i	−0.260240	−	0.450749i	−0.966306	+	0.257398i	$0.917135\pi$
$174$	11.4203	+	10.4893i	0.865772	+	0.795193i
$175$	−0.264746	+	0.458554i	−0.0200130	+	0.0346634i
$176$	−1.91763	+	3.32142i	−0.144546	+	0.250362i
$177$	−3.53368	−	3.24561i	−0.265608	−	0.243955i
$178$	−2.58642	−	4.47981i	−0.193860	−	0.335776i
$179$	11.4029			0.852296			0.426148	−	0.904653i	$-0.359870\pi$
$179$	11.4029			0.852296			0.426148	+	0.904653i	$0.359870\pi$
$180$	0.503985	+	5.91950i	0.0375648	+	0.441214i
$181$	15.7382			1.16981			0.584907	−	0.811100i	$-0.301131\pi$
$181$	15.7382			1.16981			0.584907	+	0.811100i	$0.301131\pi$
$182$	−1.39727	−	2.42015i	−0.103573	−	0.179393i
$183$	−4.67083	+	1.46672i	−0.345278	+	0.108423i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	9.03229	−	15.6444i	0.664067	−	1.15020i
$186$	3.63745	−	16.3175i	0.266711	−	1.19645i
$187$	−8.35312	−	14.4680i	−0.610841	−	1.05801i
$188$	−12.6152			−0.920056
$189$	2.52832	+	0.341860i	0.183908	+	0.0248666i
$190$	−8.71917			−0.632555
$191$	8.87075	+	15.3646i	0.641865	+	1.11174i	0.985016	+	0.172462i	$0.0551723\pi$
$191$	8.87075	+	15.3646i	0.641865	+	1.11174i	−0.343151	+	0.939280i	$0.611494\pi$
$192$	−0.376855	+	1.69056i	−0.0271972	+	0.122005i
$193$	2.95227	−	5.11348i	0.212509	−	0.368077i	−0.739990	−	0.672618i	$-0.765170\pi$
$193$	2.95227	−	5.11348i	0.212509	−	0.368077i	0.952499	+	0.304541i	$0.0985032\pi$
$194$	−6.47632	+	11.2173i	−0.464973	+	0.805356i
$195$	18.6251	−	5.84861i	1.33377	−	0.418828i
$196$	3.37946	+	5.85339i	0.241390	+	0.418099i
$197$	10.0295			0.714571			0.357286	−	0.933995i	$-0.383702\pi$
$197$	10.0295			0.714571			0.357286	+	0.933995i	$0.383702\pi$
$198$	−9.44032	+	6.57744i	−0.670894	+	0.467438i
$199$	−18.6534			−1.32231			−0.661153	−	0.750251i	$-0.729933\pi$
$199$	−18.6534			−1.32231			−0.661153	+	0.750251i	$0.729933\pi$
$200$	−0.539195	−	0.933913i	−0.0381268	−	0.0660376i
$201$	0.626342	+	0.575281i	0.0441787	+	0.0405772i
$202$	7.03237	−	12.1804i	0.494796	−	0.857011i
$203$	2.19789	−	3.80685i	0.154261	−	0.267189i
$204$	−5.55664	−	5.10365i	−0.389043	−	0.357327i
$205$	−3.35032	−	5.80292i	−0.233996	−	0.405293i
$206$	16.5650			1.15414
$207$	2.46146	−	1.71499i	0.171083	−	0.119200i
$208$	5.69151			0.394635
$209$	−8.44320	−	14.6240i	−0.584028	−	1.01157i
$210$	1.60678	−	0.504557i	0.110878	−	0.0348177i
$211$	4.71584	−	8.16808i	0.324652	−	0.562314i	−0.656790	−	0.754074i	$-0.728086\pi$
$211$	4.71584	−	8.16808i	0.324652	−	0.562314i	0.981442	+	0.191760i	$0.0614194\pi$
$212$	0.240860	−	0.417183i	0.0165424	−	0.0286522i
$213$	−2.23509	+	10.0265i	−0.153146	+	0.687005i
$214$	3.09627	+	5.36289i	0.211657	+	0.366600i
$215$	−18.8723			−1.28708
$216$	−3.17762	+	4.11130i	−0.216209	+	0.279738i
$217$	−4.73922			−0.321719
$218$	2.33647	+	4.04689i	0.158246	+	0.274090i
$219$	−2.48599	+	11.1520i	−0.167988	+	0.753585i
$220$	−3.79748	+	6.57744i	−0.256026	+	0.443451i
$221$	−12.3960	+	21.4706i	−0.833847	+	1.44427i
$222$	15.0742	−	4.73357i	1.01172	−	0.317697i
$223$	1.72239	+	2.98326i	0.115340	+	0.199774i	0.917915	−	0.396776i	$-0.129871\pi$
$223$	1.72239	+	2.98326i	0.115340	+	0.199774i	−0.802576	+	0.596550i	$0.796538\pi$
$224$	0.491003			0.0328065
$225$	−0.274449	−	3.22351i	−0.0182966	−	0.214901i
$226$	−4.73961			−0.315274
$227$	8.69217	+	15.0553i	0.576919	+	0.999253i	0.995830	+	0.0912262i	$0.0290786\pi$
$227$	8.69217	+	15.0553i	0.576919	+	0.999253i	−0.418911	+	0.908027i	$0.637588\pi$
$228$	−5.61656	−	5.15868i	−0.371966	−	0.341642i
$229$	−1.23488	+	2.13888i	−0.0816033	+	0.141341i	−0.903939	−	0.427662i	$-0.859337\pi$
$229$	−1.23488	+	2.13888i	−0.0816033	+	0.141341i	0.822335	+	0.569003i	$0.192671\pi$
$230$	0.990153	−	1.71499i	0.0652887	−	0.113083i
$231$	2.40218	+	2.20635i	0.158052	+	0.145167i
$232$	4.47632	+	7.75322i	0.293885	+	0.509024i
$233$	7.45708			0.488530			0.244265	−	0.969709i	$-0.421453\pi$
$233$	7.45708			0.488530			0.244265	+	0.969709i	$0.421453\pi$
$234$	15.4579	+	7.25207i	1.01052	+	0.474082i
$235$	−24.9819			−1.62964
$236$	−1.38506	−	2.39900i	−0.0901600	−	0.156162i
$237$	−22.0828	+	6.93438i	−1.43443	+	0.450437i
$238$	−1.06940	+	1.85225i	−0.0693188	+	0.120064i
$239$	13.0680	−	22.6345i	0.845301	−	1.46410i	−0.0400582	−	0.999197i	$-0.512754\pi$
$239$	13.0680	−	22.6345i	0.845301	−	1.46410i	0.885359	−	0.464907i	$-0.153912\pi$
$240$	−0.746289	+	3.34782i	−0.0481727	+	0.216101i
$241$	−5.14759	−	8.91589i	−0.331585	−	0.574323i	0.651238	−	0.758874i	$-0.274250\pi$
$241$	−5.14759	−	8.91589i	−0.331585	−	0.574323i	−0.982823	+	0.184551i	$0.940917\pi$
$242$	−3.70915			−0.238433
$243$	−13.8689	+	7.11723i	−0.889687	+	0.456570i
$244$	−2.82654			−0.180951
$245$	6.69236	+	11.5915i	0.427559	+	0.740554i
$246$	1.27514	−	5.72023i	0.0813001	−	0.364708i
$247$	−12.5297	+	21.7021i	−0.797245	+	1.38087i
$248$	4.82606	−	8.35898i	0.306455	−	0.530796i
$249$	3.16011	−	0.992329i	0.200264	−	0.0628863i
$250$	−6.01853	−	10.4244i	−0.380646	−	0.659297i
$251$	14.0776			0.888570			0.444285	−	0.895886i	$-0.353458\pi$
$251$	14.0776			0.888570			0.444285	+	0.895886i	$0.353458\pi$
$252$	1.33354	+	0.625632i	0.0840054	+	0.0394111i
$253$	3.83525			0.241120
$254$	2.93798	+	5.08872i	0.184345	+	0.319295i
$255$	−11.0038	−	10.1068i	−0.689087	−	0.632912i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.6086	−	20.1066i	0.724123	−	1.25422i	−0.235211	−	0.971944i	$-0.575578\pi$
$257$	11.6086	−	20.1066i	0.724123	−	1.25422i	0.959334	−	0.282273i	$-0.0910884\pi$
$258$	−12.1568	−	11.1658i	−0.756851	−	0.695151i
$259$	−2.23949	−	3.87892i	−0.139155	−	0.241024i
$260$	11.2709			0.698993
$261$	2.27843	+	26.7611i	0.141031	+	1.65647i
$262$	−2.33724			−0.144395
$263$	−6.46220	−	11.1929i	−0.398477	−	0.690182i	0.595062	−	0.803680i	$-0.297128\pi$
$263$	−6.46220	−	11.1929i	−0.398477	−	0.690182i	−0.993538	+	0.113498i	$0.963794\pi$
$264$	−6.33772	+	1.99016i	−0.390060	+	0.122486i
$265$	0.476977	−	0.826149i	0.0293005	−	0.0507499i
$266$	−1.08093	+	1.87222i	−0.0662760	+	0.114793i
$267$	1.94941	−	8.74498i	0.119302	−	0.535184i
$268$	0.245502	+	0.425221i	0.0149964	+	0.0259745i
$269$	−28.1514			−1.71642			−0.858212	−	0.513295i	$-0.828425\pi$
$269$	−28.1514			−1.71642			−0.858212	+	0.513295i	$0.828425\pi$
$270$	−6.29265	+	8.14162i	−0.382958	+	0.495483i
$271$	−6.12742			−0.372214			−0.186107	−	0.982529i	$-0.559587\pi$
$271$	−6.12742			−0.372214			−0.186107	+	0.982529i	$0.559587\pi$
$272$	−2.17799	−	3.77238i	−0.132060	−	0.228734i
$273$	1.05314	−	4.72434i	0.0637390	−	0.285930i
$274$	1.30317	−	2.25716i	0.0787274	−	0.136360i
$275$	2.06795	−	3.58179i	0.124702	−	0.215990i
$276$	1.65249	−	0.518912i	0.0994683	−	0.0312348i
$277$	−12.4804	−	21.6168i	−0.749877	−	1.29883i	−0.947881	−	0.318624i	$-0.896779\pi$
$277$	−12.4804	−	21.6168i	−0.749877	−	1.29883i	0.198004	−	0.980201i	$-0.436554\pi$
$278$	10.8559			0.651092
$279$	23.7583	−	16.5533i	1.42237	−	0.991022i
$280$	0.972336			0.0581082
$281$	12.4119	+	21.4981i	0.740433	+	1.28247i	0.952298	+	0.305168i	$0.0987128\pi$
$281$	12.4119	+	21.4981i	0.740433	+	1.28247i	−0.211866	+	0.977299i	$0.567954\pi$
$282$	−16.0924	−	14.7805i	−0.958287	−	0.880166i
$283$	8.55622	−	14.8198i	0.508615	−	0.880946i	−0.491336	−	0.870970i	$-0.663491\pi$
$283$	8.55622	−	14.8198i	0.508615	−	0.880946i	0.999950	−	0.00997607i	$-0.00317554\pi$
$284$	−2.96545	+	5.13630i	−0.175967	+	0.304784i
$285$	−11.1225	−	10.2158i	−0.658840	−	0.605130i
$286$	10.9142	+	18.9039i	0.645369	+	1.11781i
$287$	−1.66138			−0.0980679
$288$	−2.46146	+	1.71499i	−0.145043	+	0.101057i
$289$	1.97450			0.116147
$290$	8.86448	+	15.3537i	0.520540	+	0.901602i
$291$	−21.4041	+	6.72128i	−1.25473	+	0.394008i
$292$	−3.29833	+	5.71288i	−0.193020	+	0.334321i
$293$	−1.12470	+	1.94804i	−0.0657059	+	0.113806i	−0.897007	−	0.442017i	$-0.854263\pi$
$293$	−1.12470	+	1.94804i	−0.0657059	+	0.113806i	0.831301	+	0.555822i	$0.187597\pi$
$294$	−2.54713	+	11.4263i	−0.148552	+	0.666397i
$295$	−2.74285	−	4.75076i	−0.159695	−	0.276600i
$296$	9.12212			0.530212
$297$	−19.7488	−	2.67028i	−1.14594	−	0.154946i
$298$	8.26563			0.478815
$299$	−2.84575	−	4.92899i	−0.164574	−	0.285051i
$300$	0.406397	−	1.82308i	0.0234634	−	0.105256i
$301$	−2.33963	+	4.05236i	−0.134854	+	0.233574i
$302$	3.03757	−	5.26123i	0.174793	−	0.302750i
$303$	23.2419	−	7.29835i	1.33521	−	0.419279i
$304$	−2.20147	−	3.81306i	−0.126263	−	0.218694i
$305$	−5.59741			−0.320507
$306$	−1.10859	−	13.0208i	−0.0633738	−	0.744350i
$307$	25.6490			1.46387			0.731933	−	0.681377i	$-0.238618\pi$
$307$	25.6490			1.46387			0.731933	+	0.681377i	$0.238618\pi$
$308$	0.941560	+	1.63083i	0.0536504	+	0.0929252i
$309$	21.1309	+	19.4083i	1.20210	+	1.10410i
$310$	9.55707	−	16.5533i	0.542805	−	0.940166i
$311$	−9.92819	+	17.1961i	−0.562976	+	0.975103i	0.434259	+	0.900788i	$0.357010\pi$
$311$	−9.92819	+	17.1961i	−0.562976	+	0.975103i	−0.997235	+	0.0743150i	$0.976323\pi$
$312$	7.26030	+	6.66842i	0.411033	+	0.377525i
$313$	−5.45361	−	9.44593i	−0.308256	−	0.533915i	0.669725	−	0.742609i	$-0.266412\pi$
$313$	−5.45361	−	9.44593i	−0.308256	−	0.533915i	−0.977981	+	0.208694i	$0.933079\pi$
$314$	−7.65456			−0.431972
$315$	2.64083	+	1.23894i	0.148794	+	0.0698065i
$316$	−13.3633			−0.751746
$317$	−8.28174	−	14.3444i	−0.465149	−	0.805662i	0.534059	−	0.845447i	$-0.320666\pi$
$317$	−8.28174	−	14.3444i	−0.465149	−	0.805662i	−0.999208	+	0.0397852i	$0.987333\pi$
$318$	0.796040	−	0.249971i	0.0446397	−	0.0140177i
$319$	−17.1678	+	29.7355i	−0.961213	+	1.66487i
$320$	−0.990153	+	1.71499i	−0.0553512	+	0.0958711i
$321$	−2.33369	+	10.4688i	−0.130254	+	0.584313i
$322$	−0.245502	−	0.425221i	−0.0136813	−	0.0236967i
$323$	19.1791			1.06715
$324$	−8.87046	+	1.52149i	−0.492803	+	0.0845270i
$325$	−6.13767			−0.340456
$326$	−9.92782	−	17.1955i	−0.549851	−	0.952370i
$327$	−1.76102	+	7.89987i	−0.0973849	+	0.436864i
$328$	1.69182	−	2.93032i	0.0934150	−	0.161800i
$329$	−3.09705	+	5.36424i	−0.170746	+	0.295740i
$330$	−12.5506	+	3.94112i	−0.690889	+	0.216951i
$331$	0.974042	+	1.68709i	0.0535382	+	0.0927309i	0.891552	−	0.452917i	$-0.149617\pi$
$331$	0.974042	+	1.68709i	0.0535382	+	0.0927309i	−0.838014	+	0.545648i	$0.816283\pi$
$332$	1.91233			0.104953
$333$	24.7753	+	11.6233i	1.35768	+	0.636954i
$334$	−4.36600			−0.238897
$335$	0.486168	+	0.842068i	0.0265622	+	0.0460071i
$336$	0.626342	+	0.575281i	0.0341697	+	0.0313842i
$337$	−1.68898	+	2.92539i	−0.0920044	+	0.159356i	−0.908354	−	0.418201i	$-0.862661\pi$
$337$	−1.68898	+	2.92539i	−0.0920044	+	0.159356i	0.816350	+	0.577557i	$0.195994\pi$
$338$	9.69664	−	16.7951i	0.527427	−	0.913531i
$339$	−6.04602	−	5.55314i	−0.328375	−	0.301605i
$340$	−4.31308	−	7.47047i	−0.233910	−	0.405143i
$341$	37.0183			2.00465
$342$	−1.12054	−	13.1612i	−0.0605920	−	0.711677i
$343$	6.75567			0.364772
$344$	−4.76500	−	8.25323i	−0.256912	−	0.444984i
$345$	3.27244	−	1.02760i	0.176182	−	0.0553243i
$346$	3.42292	−	5.92868i	0.184017	−	0.318728i
$347$	−5.27605	+	9.13839i	−0.283233	+	0.490574i	−0.972179	−	0.234238i	$-0.924740\pi$
$347$	−5.27605	+	9.13839i	−0.283233	+	0.490574i	0.688946	+	0.724813i	$0.258074\pi$
$348$	−3.37385	+	15.1349i	−0.180857	+	0.811318i
$349$	−0.196204	−	0.339835i	−0.0105025	−	0.0181909i	0.860726	−	0.509068i	$-0.170010\pi$
$349$	−0.196204	−	0.339835i	−0.0105025	−	0.0181909i	−0.871229	+	0.490877i	$0.836676\pi$
$350$	−0.529493			−0.0283026
$351$	11.2218	+	27.3622i	0.598977	+	1.46049i
$352$	−3.83525			−0.204420
$353$	−0.936949	−	1.62284i	−0.0498687	−	0.0863752i	0.840014	−	0.542565i	$-0.182547\pi$
$353$	−0.936949	−	1.62284i	−0.0498687	−	0.0863752i	−0.889882	+	0.456190i	$0.849214\pi$
$354$	1.04394	−	4.68306i	0.0554847	−	0.248902i
$355$	−5.87249	+	10.1714i	−0.311679	+	0.539845i
$356$	2.58642	−	4.47981i	0.137080	−	0.237430i
$357$	−3.53434	+	1.10985i	−0.187057	+	0.0587393i
$358$	5.70147	+	9.87524i	0.301332	+	0.521923i
$359$	22.3446			1.17930			0.589651	−	0.807658i	$-0.299265\pi$
$359$	22.3446			1.17930			0.589651	+	0.807658i	$0.299265\pi$
$360$	−4.87445	+	3.39621i	−0.256906	+	0.178996i
$361$	0.385908			0.0203109
$362$	7.86912	+	13.6297i	0.413592	+	0.716362i
$363$	−4.73153	−	4.34580i	−0.248341	−	0.228096i
$364$	1.39727	−	2.42015i	0.0732371	−	0.126850i
$365$	−6.53171	+	11.3133i	−0.341885	+	0.592163i
$366$	−3.60564	−	3.31170i	−0.188470	−	0.173105i
$367$	7.49849	+	12.9878i	0.391418	+	0.677956i	0.992637	−	0.121128i	$-0.0386513\pi$
$367$	7.49849	+	12.9878i	0.391418	+	0.677956i	−0.601219	+	0.799085i	$0.705318\pi$
$368$	1.00000			0.0521286
$369$	8.32869	−	5.80292i	0.433574	−	0.302088i
$370$	18.0646			0.939133
$371$	−0.118263	−	0.204838i	−0.00613992	−	0.0106347i
$372$	15.9501	−	5.00860i	0.826972	−	0.259684i
$373$	−15.3152	+	26.5266i	−0.792989	+	1.37350i	0.131119	+	0.991367i	$0.458143\pi$
$373$	−15.3152	+	26.5266i	−0.792989	+	1.37350i	−0.924108	+	0.382131i	$0.875190\pi$
$374$	8.35312	−	14.4680i	0.431930	−	0.748124i
$375$	4.53624	−	20.3493i	0.234250	−	1.05084i
$376$	−6.30759	−	10.9251i	−0.325289	−	0.563417i
$377$	50.9540			2.62427
$378$	0.968101	+	2.36052i	0.0497937	+	0.121412i
$379$	18.2092			0.935342			0.467671	−	0.883903i	$-0.345093\pi$
$379$	18.2092			0.935342			0.467671	+	0.883903i	$0.345093\pi$
$380$	−4.35959	−	7.55102i	−0.223642	−	0.387359i
$381$	−2.21439	+	9.93363i	−0.113446	+	0.508915i
$382$	−8.87075	+	15.3646i	−0.453867	+	0.786120i
$383$	13.2106	−	22.8815i	0.675032	−	1.16919i	−0.301427	−	0.953489i	$-0.597463\pi$
$383$	13.2106	−	22.8815i	0.675032	−	1.16919i	0.976459	−	0.215701i	$-0.0692037\pi$
$384$	−1.65249	+	0.518912i	−0.0843284	+	0.0264806i
$385$	1.86458	+	3.22954i	0.0950276	+	0.164593i
$386$	5.90454			0.300533
$387$	−2.42537	−	28.4870i	−0.123289	−	1.44807i
$388$	−12.9526			−0.657571
$389$	−5.03171	−	8.71518i	−0.255118	−	0.441877i	0.709810	−	0.704394i	$-0.248781\pi$
$389$	−5.03171	−	8.71518i	−0.255118	−	0.441877i	−0.964928	+	0.262516i	$0.915448\pi$
$390$	14.3776	+	13.2055i	0.728039	+	0.668687i
$391$	−2.17799	+	3.77238i	−0.110146	+	0.190778i
$392$	−3.37946	+	5.85339i	−0.170688	+	0.295641i
$393$	−2.98147	−	2.73841i	−0.150395	−	0.138135i
$394$	5.01474	+	8.68579i	0.252639	+	0.437584i
$395$	−26.4635			−1.33152
$396$	−10.4164	−	4.88684i	−0.523443	−	0.245573i
$397$	10.0383			0.503806			0.251903	−	0.967753i	$-0.418944\pi$
$397$	10.0383			0.503806			0.251903	+	0.967753i	$0.418944\pi$
$398$	−9.32672	−	16.1543i	−0.467506	−	0.809744i
$399$	−3.57246	+	1.12181i	−0.178846	+	0.0561609i
$400$	0.539195	−	0.933913i	0.0269598	−	0.0466957i
$401$	−17.5822	+	30.4533i	−0.878015	+	1.52077i	−0.0244997	+	0.999700i	$0.507799\pi$
$401$	−17.5822	+	30.4533i	−0.878015	+	1.52077i	−0.853516	+	0.521067i	$0.825534\pi$
$402$	−0.185037	+	0.830068i	−0.00922882	+	0.0414000i
$403$	−27.4676	−	47.5752i	−1.36826	−	2.36989i
$404$	14.0647			0.699747
$405$	−17.5662	+	3.01301i	−0.872873	+	0.149718i
$406$	4.39578			0.218159
$407$	17.4928	+	30.2984i	0.867086	+	1.50184i
$408$	1.64157	−	7.36402i	0.0812699	−	0.364573i
$409$	−3.54061	+	6.13252i	−0.175072	+	0.303233i	−0.940186	−	0.340661i	$-0.889349\pi$
$409$	−3.54061	+	6.13252i	−0.175072	+	0.303233i	0.765114	+	0.643895i	$0.222682\pi$
$410$	3.35032	−	5.80292i	0.165460	−	0.286586i
$411$	4.30696	−	1.35246i	0.212446	−	0.0667119i
$412$	8.28251	+	14.3457i	0.408050	+	0.706763i
$413$	−1.36014			−0.0669282
$414$	2.71596	+	1.27419i	0.133482	+	0.0626231i
$415$	3.78699			0.185896
$416$	2.84575	+	4.92899i	0.139525	+	0.241664i
$417$	13.8481	+	12.7192i	0.678147	+	0.622863i
$418$	8.44320	−	14.6240i	0.412970	−	0.715285i
$419$	6.26384	−	10.8493i	0.306009	−	0.530023i	−0.671477	−	0.741026i	$-0.734340\pi$
$419$	6.26384	−	10.8493i	0.306009	−	0.530023i	0.977485	+	0.211003i	$0.0676730\pi$
$420$	1.24035	+	1.13923i	0.0605228	+	0.0555889i
$421$	16.2278	+	28.1074i	0.790897	+	1.36987i	0.925412	+	0.378962i	$0.123719\pi$
$421$	16.2278	+	28.1074i	0.790897	+	1.36987i	−0.134516	+	0.990911i	$0.542948\pi$
$422$	9.43169			0.459127
$423$	−3.21054	−	37.7091i	−0.156102	−	1.83348i
$424$	0.481721			0.0233944
$425$	2.34872	+	4.06810i	0.113930	+	0.197332i
$426$	−9.80075	+	3.07761i	−0.474848	+	0.149111i
$427$	−0.693920	+	1.20190i	−0.0335811	+	0.0581642i
$428$	−3.09627	+	5.36289i	−0.149664	+	0.259225i
$429$	−8.22614	+	36.9021i	−0.397162	+	1.78165i
$430$	−9.43616	−	16.3439i	−0.455052	−	0.788173i
$431$	−7.22801			−0.348161			−0.174081	−	0.984731i	$-0.555695\pi$
$431$	−7.22801			−0.348161			−0.174081	+	0.984731i	$0.555695\pi$
$432$	−5.14930	−	0.696247i	−0.247746	−	0.0334982i
$433$	37.0157			1.77886			0.889430	−	0.457072i	$-0.151102\pi$
$433$	37.0157			1.77886			0.889430	+	0.457072i	$0.151102\pi$
$434$	−2.36961	−	4.10429i	−0.113745	−	0.197012i
$435$	−6.68126	+	29.9718i	−0.320342	+	1.43704i
$436$	−2.33647	+	4.04689i	−0.111897	+	0.193811i
$437$	−2.20147	+	3.81306i	−0.105311	+	0.182403i
$438$	−10.9009	+	3.42309i	−0.520867	+	0.163561i
$439$	9.41544	+	16.3080i	0.449374	+	0.778339i	0.998345	−	0.0575021i	$-0.0183136\pi$
$439$	9.41544	+	16.3080i	0.449374	+	0.778339i	−0.548971	+	0.835841i	$0.684980\pi$
$440$	−7.59497			−0.362076
$441$	−16.6368	+	11.5915i	−0.792229	+	0.551976i
$442$	−24.7921			−1.17924
$443$	4.76549	+	8.25407i	0.226415	+	0.392163i	0.956743	−	0.290934i	$-0.0939660\pi$
$443$	4.76549	+	8.25407i	0.226415	+	0.392163i	−0.730328	+	0.683097i	$0.760633\pi$
$444$	11.6365	+	10.6879i	0.552244	+	0.507224i
$445$	5.12190	−	8.87140i	0.242802	−	0.420545i
$446$	−1.72239	+	2.98326i	−0.0815574	+	0.141262i
$447$	10.5439	+	9.68438i	0.498711	+	0.458055i
$448$	0.245502	+	0.425221i	0.0115989	+	0.0200898i
$449$	−7.11135			−0.335606			−0.167803	−	0.985821i	$-0.553667\pi$
$449$	−7.11135			−0.335606			−0.167803	+	0.985821i	$0.553667\pi$
$450$	2.65442	−	1.84943i	0.125130	−	0.0871831i
$451$	12.9771			0.611068
$452$	−2.36980	−	4.10462i	−0.111466	−	0.193065i
$453$	10.0391	−	3.15246i	0.471680	−	0.148116i
$454$	−8.69217	+	15.0553i	−0.407944	+	0.706579i
$455$	2.76703	−	4.79264i	0.129720	−	0.224682i
$456$	1.65927	−	7.44342i	0.0777026	−	0.348570i
$457$	−2.76634	−	4.79144i	−0.129404	−	0.224134i	0.794042	−	0.607863i	$-0.207973\pi$
$457$	−2.76634	−	4.79144i	−0.129404	−	0.224134i	−0.923446	+	0.383729i	$0.874640\pi$
$458$	−2.46976			−0.115405
$459$	13.8416	−	17.9087i	0.646071	−	0.835906i
$460$	1.98031			0.0923322
$461$	7.97263	+	13.8090i	0.371322	+	0.643149i	0.989769	−	0.142678i	$-0.0455712\pi$
$461$	7.97263	+	13.8090i	0.371322	+	0.643149i	−0.618447	+	0.785827i	$0.712238\pi$
$462$	−0.709664	+	3.18352i	−0.0330166	+	0.148111i
$463$	2.93221	−	5.07873i	0.136271	−	0.236029i	−0.789811	−	0.613350i	$-0.789822\pi$
$463$	2.93221	−	5.07873i	0.136271	−	0.236029i	0.926082	+	0.377322i	$0.123155\pi$
$464$	−4.47632	+	7.75322i	−0.207808	+	0.359934i
$465$	31.5860	−	9.91855i	1.46476	−	0.459962i
$466$	3.72854	+	6.45802i	0.172721	+	0.299162i
$467$	5.82468			0.269534			0.134767	−	0.990877i	$-0.456971\pi$
$467$	5.82468			0.269534			0.134767	+	0.990877i	$0.456971\pi$
$468$	1.44848	+	17.0130i	0.0669560	+	0.786425i
$469$	0.241084			0.0111322
$470$	−12.4909	−	21.6350i	−0.576165	−	0.997946i
$471$	−9.76444	−	8.96843i	−0.449922	−	0.413243i
$472$	1.38506	−	2.39900i	0.0637528	−	0.110423i
$473$	18.2750	−	31.6532i	0.840284	−	1.45542i
$474$	−17.0467	−	15.6571i	−0.782983	−	0.719153i
$475$	2.37404	+	4.11197i	0.108929	+	0.188670i
$476$	−2.13880			−0.0980316
$477$	1.30833	+	0.613804i	0.0599045	+	0.0281042i
$478$	26.1361			1.19544
$479$	11.3864	+	19.7218i	0.520258	+	0.901114i	0.999723	+	0.0235524i	$0.00749764\pi$
$479$	11.3864	+	19.7218i	0.520258	+	0.901114i	−0.479464	+	0.877561i	$0.659169\pi$
$480$	−3.27244	+	1.02760i	−0.149366	+	0.0469035i
$481$	25.9593	−	44.9628i	1.18364	−	2.05013i
$482$	5.14759	−	8.91589i	0.234466	−	0.406107i
$483$	0.185037	−	0.830068i	0.00841949	−	0.0377694i
$484$	−1.85457	−	3.21222i	−0.0842988	−	0.146010i
$485$	−25.6502			−1.16472
$486$	−13.0981	−	8.45216i	−0.594143	−	0.383398i
$487$	−8.84186			−0.400663			−0.200332	−	0.979728i	$-0.564202\pi$
$487$	−8.84186			−0.400663			−0.200332	+	0.979728i	$0.564202\pi$
$488$	−1.41327	−	2.44785i	−0.0639757	−	0.110809i
$489$	7.48271	−	33.5671i	0.338380	−	1.51796i
$490$	−6.69236	+	11.5915i	−0.302330	+	0.523651i
$491$	−10.8533	+	18.7985i	−0.489803	+	0.848363i	−0.999931	−	0.0117352i	$-0.996264\pi$
$491$	−10.8533	+	18.7985i	−0.489803	+	0.848363i	0.510129	+	0.860098i	$0.329598\pi$
$492$	5.59143	−	1.75581i	0.252081	−	0.0791580i
$493$	−19.4987	−	33.7728i	−0.878179	−	1.52105i
$494$	−25.0594			−1.12748
$495$	−20.6276	−	9.67744i	−0.927143	−	0.434968i
$496$	9.65212			0.433393
$497$	1.45604	+	2.52194i	0.0653125	+	0.113125i
$498$	2.43944	+	2.24057i	0.109314	+	0.100402i
$499$	−9.67125	+	16.7511i	−0.432945	+	0.749882i	−0.997125	−	0.0757693i	$-0.975859\pi$
$499$	−9.67125	+	16.7511i	−0.432945	+	0.749882i	0.564181	+	0.825651i	$0.309192\pi$
$500$	6.01853	−	10.4244i	0.269157	−	0.466194i
$501$	−5.56943	−	5.11540i	−0.248824	−	0.228539i
$502$	7.03879	+	12.1915i	0.314157	+	0.544135i
$503$	−9.04690			−0.403381			−0.201691	−	0.979449i	$-0.564644\pi$
$503$	−9.04690			−0.403381			−0.201691	+	0.979449i	$0.564644\pi$
$504$	0.124960	+	1.46770i	0.00556614	+	0.0653765i
$505$	27.8525			1.23942
$506$	1.91763	+	3.32142i	0.0852488	+	0.147655i
$507$	32.0472	−	10.0634i	1.42327	−	0.446931i
$508$	−2.93798	+	5.08872i	−0.130352	+	0.225776i
$509$	−6.18528	+	10.7132i	−0.274158	+	0.474855i	−0.969922	−	0.243415i	$-0.921732\pi$
$509$	−6.18528	+	10.7132i	−0.274158	+	0.474855i	0.695765	+	0.718270i	$0.255066\pi$
$510$	3.25081	−	14.5830i	0.143948	−	0.645746i
$511$	1.61949	+	2.80504i	0.0716421	+	0.124088i
$512$	−1.00000			−0.0441942
$513$	13.9909	−	18.1018i	0.617712	−	0.799214i
$514$	23.2171			1.02406
$515$	16.4019	+	28.4089i	0.722754	+	1.25185i
$516$	3.59143	−	16.1110i	0.158104	−	0.709248i
$517$	24.1912	−	41.9003i	1.06393	−	1.84278i
$518$	2.23949	−	3.87892i	0.0983977	−	0.170430i
$519$	11.3127	−	3.55239i	0.496573	−	0.155933i
$520$	5.63546	+	9.76091i	0.247131	+	0.428044i
$521$	−34.6704			−1.51894			−0.759470	−	0.650543i	$-0.774541\pi$
$521$	−34.6704			−1.51894			−0.759470	+	0.650543i	$0.774541\pi$
$522$	−22.0366	+	15.3537i	−0.964515	+	0.672015i
$523$	−36.3144			−1.58792			−0.793959	−	0.607971i	$-0.791984\pi$
$523$	−36.3144			−1.58792			−0.793959	+	0.607971i	$0.791984\pi$
$524$	−1.16862	−	2.02411i	−0.0510513	−	0.0884235i
$525$	−0.675441	−	0.620377i	−0.0294786	−	0.0270755i
$526$	6.46220	−	11.1929i	0.281765	−	0.488032i
$527$	−21.0222	+	36.4115i	−0.915741	+	1.58611i
$528$	−4.89239	−	4.49355i	−0.212914	−	0.195557i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	0.953955			0.0414371
$531$	6.81857	−	4.75076i	0.295901	−	0.206165i
$532$	−2.16186			−0.0937285
$533$	−9.62900	−	16.6779i	−0.417078	−	0.722401i
$534$	8.54808	−	2.68425i	0.369912	−	0.116159i
$535$	−6.13156	+	10.6202i	−0.265090	+	0.459150i
$536$	−0.245502	+	0.425221i	−0.0106041	+	0.0183668i
$537$	−4.29726	+	19.2773i	−0.185441	+	0.831878i
$538$	−14.0757	−	24.3799i	−0.606848	−	1.05109i
$539$	−25.9221			−1.11655
$540$	−10.1972	−	1.37878i	−0.438817	−	0.0593333i
$541$	40.1250			1.72511			0.862555	−	0.505964i	$-0.168863\pi$
$541$	40.1250			1.72511			0.862555	+	0.505964i	$0.168863\pi$
$542$	−3.06371	−	5.30650i	−0.131598	−	0.227934i
$543$	−5.93105	+	26.6064i	−0.254526	+	1.14179i
$544$	2.17799	−	3.77238i	0.0933804	−	0.161740i
$545$	−4.62693	+	8.01408i	−0.198196	+	0.343285i
$546$	4.61797	−	1.45012i	0.197631	−	0.0620596i
$547$	−9.25852	−	16.0362i	−0.395866	−	0.685660i	0.597346	−	0.801984i	$-0.296222\pi$
$547$	−9.25852	−	16.0362i	−0.395866	−	0.685660i	−0.993211	+	0.116324i	$0.962889\pi$
$548$	2.60634			0.111337
$549$	−0.719350	−	8.44905i	−0.0307011	−	0.360597i
$550$	4.13590			0.176355
$551$	−19.7090	−	34.1370i	−0.839631	−	1.45428i
$552$	1.27564	+	1.17164i	0.0542947	+	0.0498685i
$553$	−3.28072	+	5.68237i	−0.139510	+	0.241639i
$554$	12.4804	−	21.6168i	0.530243	−	0.918408i
$555$	23.0438	+	21.1653i	0.978156	+	0.898415i
$556$	5.42794	+	9.40146i	0.230196	+	0.398711i
$557$	−13.4234			−0.568767			−0.284383	−	0.958711i	$-0.591789\pi$
$557$	−13.4234			−0.568767			−0.284383	+	0.958711i	$0.591789\pi$
$558$	26.2148	+	12.2986i	1.10976	+	0.520643i
$559$	−54.2401			−2.29411
$560$	0.486168	+	0.842068i	0.0205444	+	0.0355839i
$561$	27.6069	−	8.66907i	1.16557	−	0.366008i
$562$	−12.4119	+	21.4981i	−0.523565	+	0.906841i
$563$	−19.7884	+	34.2744i	−0.833980	+	1.44450i	0.0608787	+	0.998145i	$0.480610\pi$
$563$	−19.7884	+	34.2744i	−0.833980	+	1.44450i	−0.894858	+	0.446350i	$0.852724\pi$
$564$	4.75410	−	21.3267i	0.200184	−	0.898014i
$565$	−4.69294	−	8.12841i	−0.197433	−	0.341965i
$566$	17.1124			0.719290
$567$	−1.53074	+	4.14544i	−0.0642852	+	0.174092i
$568$	−5.93089			−0.248855
$569$	−11.3717	−	19.6963i	−0.476725	−	0.825711i	0.522920	−	0.852382i	$-0.324843\pi$
$569$	−11.3717	−	19.6963i	−0.476725	−	0.825711i	−0.999644	+	0.0266706i	$0.991509\pi$
$570$	3.28587	−	14.7403i	0.137630	−	0.617401i
$571$	−3.89161	+	6.74046i	−0.162859	+	0.282079i	−0.935893	−	0.352285i	$-0.885405\pi$
$571$	−3.89161	+	6.74046i	−0.162859	+	0.282079i	0.773034	+	0.634364i	$0.218738\pi$
$572$	−10.9142	+	18.9039i	−0.456345	+	0.790412i
$573$	−29.3177	+	9.20627i	−1.22476	+	0.384597i
$574$	−0.830688	−	1.43879i	−0.0346723	−	0.0600541i
$575$	−1.07839			−0.0449720
$576$	−2.71596	−	1.27419i	−0.113165	−	0.0530913i
$577$	−36.0241			−1.49970			−0.749852	−	0.661605i	$-0.769875\pi$
$577$	−36.0241			−1.49970			−0.749852	+	0.661605i	$0.769875\pi$
$578$	0.987249	+	1.70997i	0.0410642	+	0.0711252i
$579$	7.53205	+	6.91802i	0.313021	+	0.287503i
$580$	−8.86448	+	15.3537i	−0.368078	+	0.637529i
$581$	0.469480	−	0.813162i	0.0194773	−	0.0337357i
$582$	−16.5229	−	15.1759i	−0.684895	−	0.629061i
$583$	0.923760	+	1.60000i	0.0382582	+	0.0662652i
$584$	−6.59667			−0.272972
$585$	2.86843	+	33.6909i	0.118595	+	1.39295i
$586$	−2.24941			−0.0929222
$587$	2.50701	+	4.34226i	0.103475	+	0.179224i	0.913114	−	0.407704i	$-0.133670\pi$
$587$	2.50701	+	4.34226i	0.103475	+	0.179224i	−0.809639	+	0.586928i	$0.800337\pi$
$588$	−11.1691	+	3.50728i	−0.460604	+	0.144638i
$589$	−21.2489	+	36.8041i	−0.875544	+	1.51649i
$590$	2.74285	−	4.75076i	0.112921	−	0.195586i
$591$	−3.77967	+	16.9554i	−0.155475	+	0.697452i
$592$	4.56106	+	7.89998i	0.187458	+	0.324687i
$593$	−13.7000			−0.562594			−0.281297	−	0.959621i	$-0.590765\pi$
$593$	−13.7000			−0.562594			−0.281297	+	0.959621i	$0.590765\pi$
$594$	−7.56189	−	18.4381i	−0.310268	−	0.756526i
$595$	−4.23547			−0.173637
$596$	4.13281	+	7.15824i	0.169287	+	0.293213i
$597$	7.02965	−	31.5347i	0.287704	−	1.29063i
$598$	2.84575	−	4.92899i	0.116372	−	0.201561i
$599$	−0.508335	+	0.880463i	−0.0207700	+	0.0359747i	−0.876224	−	0.481905i	$-0.839945\pi$
$599$	−0.508335	+	0.880463i	−0.0207700	+	0.0359747i	0.855454	+	0.517880i	$0.173278\pi$
$600$	1.78203	−	0.559589i	0.0727511	−	0.0228451i
$601$	−0.747033	−	1.29390i	−0.0304721	−	0.0527792i	0.850387	−	0.526157i	$-0.176368\pi$
$601$	−0.747033	−	1.29390i	−0.0304721	−	0.0527792i	−0.880859	+	0.473378i	$0.843034\pi$
$602$	−4.67926			−0.190712
$603$	−1.20859	+	0.842068i	−0.0492174	+	0.0342917i
$604$	6.07515			0.247194
$605$	−3.67262	−	6.36117i	−0.149313	−	0.258618i
$606$	17.9415	+	16.4789i	0.728823	+	0.669408i
$607$	6.35637	−	11.0096i	0.257997	−	0.446864i	−0.707708	−	0.706505i	$-0.750271\pi$
$607$	6.35637	−	11.0096i	0.257997	−	0.446864i	0.965705	+	0.259641i	$0.0836041\pi$
$608$	2.20147	−	3.81306i	0.0892815	−	0.154640i
$609$	5.60741	+	5.15029i	0.227224	+	0.208700i
$610$	−2.79871	−	4.84750i	−0.113316	−	0.196270i
$611$	−71.7994			−2.90469
$612$	10.7221	−	7.47047i	0.433414	−	0.301976i
$613$	11.8172			0.477292			0.238646	−	0.971107i	$-0.423296\pi$
$613$	11.8172			0.477292			0.238646	+	0.971107i	$0.423296\pi$
$614$	12.8245	+	22.2127i	0.517555	+	0.896431i
$615$	11.0727	−	3.47704i	0.446496	−	0.140208i
$616$	−0.941560	+	1.63083i	−0.0379365	+	0.0657080i
$617$	19.1596	−	33.1854i	0.771336	−	1.33599i	−0.165495	−	0.986211i	$-0.552922\pi$
$617$	19.1596	−	33.1854i	0.771336	−	1.33599i	0.936831	−	0.349782i	$-0.113744\pi$
$618$	−6.24262	+	28.0041i	−0.251115	+	1.12649i
$619$	−8.98993	−	15.5710i	−0.361336	−	0.625852i	0.626845	−	0.779144i	$-0.284346\pi$
$619$	−8.98993	−	15.5710i	−0.361336	−	0.625852i	−0.988181	+	0.153292i	$0.951013\pi$
$620$	19.1141			0.767643
$621$	1.97168	+	4.80754i	0.0791208	+	0.192920i
$622$	−19.8564			−0.796168
$623$	−1.26994	−	2.19960i	−0.0508791	−	0.0881252i
$624$	−2.14488	+	9.62182i	−0.0858638	+	0.385181i
$625$	9.22256	−	15.9739i	0.368902	−	0.638958i
$626$	5.45361	−	9.44593i	0.217970	−	0.377535i
$627$	27.9046	−	8.76254i	1.11440	−	0.349942i
$628$	−3.82728	−	6.62905i	−0.152725	−	0.264528i
$629$	−39.7357			−1.58437
$630$	0.247458	+	2.90649i	0.00985896	+	0.115797i
$631$	15.9861			0.636398			0.318199	−	0.948024i	$-0.396922\pi$
$631$	15.9861			0.636398			0.318199	+	0.948024i	$0.396922\pi$
$632$	−6.68166	−	11.5730i	−0.265782	−	0.460348i
$633$	12.0314	+	11.0506i	0.478206	+	0.439221i
$634$	8.28174	−	14.3444i	0.328910	−	0.569689i
$635$	−5.81809	+	10.0772i	−0.230884	+	0.399903i
$636$	0.614501	+	0.564406i	0.0243666	+	0.0223801i
$637$	19.2342	+	33.3146i	0.762087	+	1.31997i
$638$	−34.3356			−1.35936
$639$	−16.1081	−	7.55709i	−0.637225	−	0.298954i
$640$	−1.98031			−0.0782784
$641$	−12.8109	−	22.1892i	−0.506002	−	0.876421i	−0.999976	−	0.00694409i	$-0.997790\pi$
$641$	−12.8109	−	22.1892i	−0.506002	−	0.876421i	0.493974	−	0.869477i	$-0.335544\pi$
$642$	−10.2331	+	3.21338i	−0.403869	+	0.126822i
$643$	−2.27841	+	3.94632i	−0.0898517	+	0.155628i	−0.907448	−	0.420164i	$-0.861973\pi$
$643$	−2.27841	+	3.94632i	−0.0898517	+	0.155628i	0.817597	+	0.575791i	$0.195306\pi$
$644$	0.245502	−	0.425221i	0.00967412	−	0.0167561i
$645$	7.11214	−	31.9047i	0.280040	−	1.25625i
$646$	9.58955	+	16.6096i	0.377296	+	0.653496i
$647$	−29.1999			−1.14796			−0.573982	−	0.818868i	$-0.694602\pi$
$647$	−29.1999			−1.14796			−0.573982	+	0.818868i	$0.694602\pi$
$648$	−5.75288	−	6.92130i	−0.225994	−	0.271894i
$649$	10.6241			0.417034
$650$	−3.06883	−	5.31537i	−0.120370	−	0.208486i
$651$	1.78600	−	8.01192i	0.0699989	−	0.314012i
$652$	9.92782	−	17.1955i	0.388803	−	0.673427i
$653$	−12.3427	+	21.3782i	−0.483007	+	0.836592i	−0.999810	−	0.0195123i	$-0.993789\pi$
$653$	−12.3427	+	21.3782i	−0.483007	+	0.836592i	0.516803	+	0.856104i	$0.327122\pi$
$654$	−7.72200	+	2.42485i	−0.301954	+	0.0948190i
$655$	−2.31422	−	4.00835i	−0.0904241	−	0.156619i
$656$	3.38364			0.132109
$657$	−17.9163	−	8.40541i	−0.698981	−	0.327926i
$658$	−6.19409			−0.241471
$659$	−2.39420	−	4.14688i	−0.0932649	−	0.161539i	0.815618	−	0.578590i	$-0.196397\pi$
$659$	−2.39420	−	4.14688i	−0.0932649	−	0.161539i	−0.908883	+	0.417051i	$0.863064\pi$
$660$	−9.68842	−	8.89860i	−0.377121	−	0.346378i
$661$	−17.3401	+	30.0340i	−0.674453	+	1.16819i	0.302176	+	0.953252i	$0.402287\pi$
$661$	−17.3401	+	30.0340i	−0.674453	+	1.16819i	−0.976629	+	0.214934i	$0.931046\pi$
$662$	−0.974042	+	1.68709i	−0.0378572	+	0.0655706i
$663$	−31.6257	−	29.0475i	−1.22824	−	1.12811i
$664$	0.956164	+	1.65612i	0.0371064	+	0.0642701i
$665$	−4.28114			−0.166016
$666$	2.32156	+	27.2677i	0.0899588	+	1.05660i
$667$	8.95264			0.346648
$668$	−2.18300	−	3.78106i	−0.0844628	−	0.146294i
$669$	−5.69246	+	1.78753i	−0.220083	+	0.0691101i
$670$	−0.486168	+	0.842068i	−0.0187823	+	0.0325319i
$671$	5.42024	−	9.38814i	0.209246	−	0.362425i
$672$	−0.185037	+	0.830068i	−0.00713797	+	0.0320206i
$673$	15.6099	+	27.0372i	0.601719	+	1.04221i	0.992561	+	0.121750i	$0.0388506\pi$
$673$	15.6099	+	27.0372i	0.601719	+	1.04221i	−0.390842	+	0.920458i	$0.627816\pi$
$674$	−3.37795			−0.130114
$675$	5.55295	+	0.750826i	0.213733	+	0.0288993i
$676$	19.3933			0.745895
$677$	11.3284	+	19.6214i	0.435387	+	0.754112i	0.997327	−	0.0730658i	$-0.0232783\pi$
$677$	11.3284	+	19.6214i	0.435387	+	0.754112i	−0.561940	+	0.827178i	$0.689945\pi$
$678$	1.78615	−	8.01258i	0.0685966	−	0.307721i
$679$	−3.17989	+	5.50774i	−0.122033	+	0.211368i
$680$	4.31308	−	7.47047i	0.165399	−	0.286479i
$681$	−28.7275	+	9.02093i	−1.10084	+	0.345683i
$682$	18.5091	+	32.0588i	0.708752	+	1.22759i
$683$	4.28796			0.164074			0.0820371	−	0.996629i	$-0.473857\pi$
$683$	4.28796			0.164074			0.0820371	+	0.996629i	$0.473857\pi$
$684$	10.8377	−	7.55102i	0.414389	−	0.288721i
$685$	5.16135			0.197205
$686$	3.37784	+	5.85058i	0.128966	+	0.223376i
$687$	−3.15052	−	2.89369i	−0.120200	−	0.110401i
$688$	4.76500	−	8.25323i	0.181664	−	0.314651i
$689$	1.37086	−	2.37440i	0.0522256	−	0.0904574i
$690$	2.52615	+	2.32021i	0.0961689	+	0.0883290i
$691$	13.6137	+	23.5797i	0.517891	+	0.897014i	0.999784	+	0.0207838i	$0.00661616\pi$
$691$	13.6137	+	23.5797i	0.517891	+	0.897014i	−0.481893	+	0.876230i	$0.660051\pi$
$692$	6.84585			0.260240
$693$	−4.63523	+	3.22954i	−0.176078	+	0.122680i
$694$	−10.5521			−0.400552
$695$	10.7490	+	18.6178i	0.407732	+	0.706212i
$696$	−14.7942	+	4.64563i	−0.560772	+	0.176092i
$697$	−7.36951	+	12.7644i	−0.279140	+	0.483485i
$698$	0.196204	−	0.339835i	0.00742642	−	0.0128629i
$699$	−2.81024	+	12.6066i	−0.106293	+	0.476826i
$700$	−0.264746	−	0.458554i	−0.0100065	−	0.0173317i
$701$	29.0558			1.09742			0.548711	−	0.836012i	$-0.315119\pi$
$701$	29.0558			1.09742			0.548711	+	0.836012i	$0.315119\pi$
$702$	−18.0854	+	23.3995i	−0.682590	+	0.883157i
$703$	−40.1642			−1.51482
$704$	−1.91763	−	3.32142i	−0.0722732	−	0.125181i
$705$	9.41457	−	42.2333i	0.354573	−	1.59060i
$706$	0.936949	−	1.62284i	0.0352625	−	0.0610765i
$707$	3.45291	−	5.98062i	0.129860	−	0.224924i
$708$	4.57762	−	1.43745i	0.172037	−	0.0540228i
$709$	−3.10441	−	5.37700i	−0.116589	−	0.201938i	0.801825	−	0.597559i	$-0.203863\pi$
$709$	−3.10441	−	5.37700i	−0.116589	−	0.201938i	−0.918414	+	0.395621i	$0.870529\pi$
$710$	−11.7450			−0.440781
$711$	−3.40094	−	39.9455i	−0.127545	−	1.49807i
$712$	5.17284			0.193860
$713$	−4.82606	−	8.35898i	−0.180737	−	0.313046i
$714$	−2.72833	−	2.50591i	−0.102105	−	0.0937813i
$715$	−21.6134	+	37.4355i	−0.808296	+	1.40001i
$716$	−5.70147	+	9.87524i	−0.213074	+	0.369055i
$717$	33.3401	+	30.6222i	1.24511	+	1.14361i
$718$	11.1723	+	19.3510i	0.416946	+	0.722172i
$719$	2.20314			0.0821633			0.0410817	−	0.999156i	$-0.486920\pi$
$719$	2.20314			0.0821633			0.0410817	+	0.999156i	$0.486920\pi$
$720$	−5.37843	−	2.52329i	−0.200442	−	0.0940374i
$721$	8.13348			0.302906
$722$	0.192954	+	0.334206i	0.00718100	+	0.0124379i
$723$	17.0127	−	5.34229i	0.632709	−	0.198682i
$724$	−7.86912	+	13.6297i	−0.292454	+	0.506545i
$725$	4.82722	−	8.36099i	0.179278	−	0.310519i
$726$	1.39781	−	6.27052i	0.0518777	−	0.232721i
$727$	−8.80940	−	15.2583i	−0.326723	−	0.565900i	0.655137	−	0.755510i	$-0.272611\pi$
$727$	−8.80940	−	15.2583i	−0.326723	−	0.565900i	−0.981859	+	0.189610i	$0.939278\pi$
$728$	2.79455			0.103573
$729$	−6.80552	−	26.1282i	−0.252056	−	0.967713i
$730$	−13.0634			−0.483499
$731$	20.7562	+	35.9508i	0.767697	+	1.32969i
$732$	1.06520	−	4.77842i	0.0393708	−	0.176616i
$733$	25.4504	−	44.0815i	0.940033	−	1.62819i	0.174631	−	0.984634i	$-0.444127\pi$
$733$	25.4504	−	44.0815i	0.940033	−	1.62819i	0.765403	−	0.643552i	$-0.222540\pi$
$734$	−7.49849	+	12.9878i	−0.276774	+	0.479387i
$735$	−22.1181	+	6.94549i	−0.815840	+	0.256188i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−1.88312			−0.0693656
$738$	9.18982	+	4.31140i	0.338282	+	0.158705i
$739$	6.05374			0.222690			0.111345	−	0.993782i	$-0.464484\pi$
$739$	6.05374			0.222690			0.111345	+	0.993782i	$0.464484\pi$
$740$	9.03229	+	15.6444i	0.332034	+	0.575099i
$741$	−31.9667	−	29.3607i	−1.17433	−	1.07859i
$742$	0.118263	−	0.204838i	0.00434158	−	0.00751984i
$743$	23.4669	−	40.6459i	0.860917	−	1.49115i	−0.0101274	−	0.999949i	$-0.503224\pi$
$743$	23.4669	−	40.6459i	0.860917	−	1.49115i	0.871045	−	0.491204i	$-0.163443\pi$
$744$	12.3126	+	11.3089i	0.451402	+	0.414603i
$745$	8.18423	+	14.1755i	0.299847	+	0.519350i
$746$	−30.6303			−1.12146
$747$	0.486684	+	5.71630i	0.0178069	+	0.209149i
$748$	16.7062			0.610841
$749$	1.52028	+	2.63320i	0.0555497	+	0.0962150i
$750$	19.8912	−	6.24618i	0.726323	−	0.228078i
$751$	18.6436	−	32.2917i	0.680315	−	1.17834i	−0.294570	−	0.955630i	$-0.595176\pi$
$751$	18.6436	−	32.2917i	0.680315	−	1.17834i	0.974885	−	0.222710i	$-0.0714903\pi$
$752$	6.30759	−	10.9251i	0.230014	−	0.398396i
$753$	−5.30522	+	23.7990i	−0.193333	+	0.867282i
$754$	25.4770	+	44.1275i	0.927818	+	1.60703i
$755$	12.0306			0.437840
$756$	−1.56022	+	2.01866i	−0.0567446	+	0.0734179i
$757$	−45.8083			−1.66493			−0.832465	−	0.554077i	$-0.813071\pi$
$757$	−45.8083			−1.66493			−0.832465	+	0.554077i	$0.813071\pi$
$758$	9.10458	+	15.7696i	0.330693	+	0.572778i
$759$	−1.44534	+	6.48371i	−0.0524623	+	0.235344i
$760$	4.35959	−	7.55102i	0.158139	−	0.273904i
$761$	8.32774	−	14.4241i	0.301880	−	0.522872i	−0.674681	−	0.738109i	$-0.735719\pi$
$761$	8.32774	−	14.4241i	0.301880	−	0.522872i	0.976562	+	0.215237i	$0.0690523\pi$
$762$	−9.70997	+	3.04910i	−0.351755	+	0.110457i
$763$	1.14722	+	1.98704i	0.0415320	+	0.0719355i
$764$	−17.7415			−0.641865
$765$	21.2330	−	14.7938i	0.767679	−	0.534872i
$766$	26.4213			0.954640
$767$	−7.88311	−	13.6539i	−0.284643	−	0.493015i
$768$	−1.27564	−	1.17164i	−0.0460306	−	0.0422781i
$769$	11.3048	−	19.5805i	0.407663	−	0.706092i	−0.586965	−	0.809612i	$-0.699677\pi$
$769$	11.3048	−	19.5805i	0.407663	−	0.706092i	0.994627	+	0.103520i	$0.0330106\pi$
$770$	−1.86458	+	3.22954i	−0.0671947	+	0.116385i
$771$	29.6166	+	27.2022i	1.06662	+	0.979664i
$772$	2.95227	+	5.11348i	0.106255	+	0.184038i
$773$	39.7217			1.42869			0.714345	−	0.699794i	$-0.246725\pi$
$773$	39.7217			1.42869			0.714345	+	0.699794i	$0.246725\pi$
$774$	23.4577	−	16.3439i	0.843171	−	0.587470i
$775$	−10.4087			−0.373893
$776$	−6.47632	−	11.2173i	−0.232486	−	0.402678i
$777$	7.40149	−	2.32420i	0.265527	−	0.0833802i
$778$	5.03171	−	8.71518i	0.180396	−	0.312454i
$779$	−7.44898	+	12.9020i	−0.266887	+	0.462263i
$780$	−4.24751	+	19.0541i	−0.152085	+	0.682247i
$781$	−11.3732	−	19.6990i	−0.406966	−	0.704886i
$782$	−4.35597			−0.155769
$783$	−46.0998	−	6.23325i	−1.64747	−	0.222758i
$784$	−6.75892			−0.241390
$785$	−7.57919	−	13.1275i	−0.270513	−	0.468542i
$786$	0.880801	−	3.95123i	0.0314171	−	0.140936i
$787$	5.07395	−	8.78834i	0.180867	−	0.313270i	−0.761309	−	0.648389i	$-0.775443\pi$
$787$	5.07395	−	8.78834i	0.180867	−	0.313270i	0.942176	+	0.335119i	$0.108776\pi$
$788$	−5.01474	+	8.68579i	−0.178643	+	0.309419i
$789$	21.3575	−	6.70663i	0.760347	−	0.238762i
$790$	−13.2317	−	22.9180i	−0.470764	−	0.815387i
$791$	−2.32716			−0.0827444
$792$	−0.976065	−	11.4643i	−0.0346830	−	0.407365i
$793$	−16.0873			−0.571276
$794$	5.01913	+	8.69339i	0.178122	+	0.308517i
$795$	1.21690	+	1.11770i	0.0431590	+	0.0396406i
$796$	9.32672	−	16.1543i	0.330577	−	0.572576i
$797$	−1.73392	+	3.00323i	−0.0614185	+	0.106380i	−0.895100	−	0.445866i	$-0.852896\pi$
$797$	−1.73392	+	3.00323i	−0.0614185	+	0.106380i	0.833681	+	0.552246i	$0.186229\pi$
$798$	−2.75775	−	2.53293i	−0.0976232	−	0.0896648i
$799$	27.4757	+	47.5893i	0.972020	+	1.68359i
$800$	1.07839			0.0381268
$801$	14.0492	+	6.59119i	0.496405	+	0.232888i
$802$	−35.1645			−1.24170
$803$	−12.6499	−	21.9103i	−0.446407	−	0.773199i
$804$	−0.811379	+	0.254787i	−0.0286151	+	0.00898565i
$805$	0.486168	−	0.842068i	0.0171352	−	0.0296790i
$806$	27.4676	−	47.5752i	0.967504	−	1.67577i
$807$	10.6090	−	47.5916i	0.373455	−	1.67530i
$808$	7.03237	+	12.1804i	0.247398	+	0.428506i
$809$	−46.5003			−1.63486			−0.817431	−	0.576027i	$-0.804602\pi$
$809$	−46.5003			−1.63486			−0.817431	+	0.576027i	$0.804602\pi$
$810$	−11.3925	−	13.7063i	−0.400290	−	0.481590i
$811$	−9.96119			−0.349785			−0.174892	−	0.984588i	$-0.555958\pi$
$811$	−9.96119			−0.349785			−0.174892	+	0.984588i	$0.555958\pi$
$812$	2.19789	+	3.80685i	0.0771307	+	0.133594i
$813$	2.30915	−	10.3587i	0.0809854	−	0.363297i
$814$	−17.4928	+	30.2984i	−0.613122	+	1.06196i
$815$	19.6601	−	34.0523i	0.688664	−	1.19280i
$816$	7.19821	−	2.26036i	0.251988	−	0.0791286i
$817$	20.9800	+	36.3385i	0.733998	+	1.27132i
$818$	−7.08122			−0.247589
$819$	7.58988	+	3.56079i	0.265212	+	0.124424i
$820$	6.70063			0.233996
$821$	9.00462	+	15.5965i	0.314263	+	0.544320i	0.979281	−	0.202508i	$-0.0649092\pi$
$821$	9.00462	+	15.5965i	0.314263	+	0.544320i	−0.665017	+	0.746828i	$0.731576\pi$
$822$	3.32474	+	3.05370i	0.115964	+	0.106510i
$823$	21.9227	−	37.9712i	0.764176	−	1.32359i	−0.176505	−	0.984300i	$-0.556479\pi$
$823$	21.9227	−	37.9712i	0.764176	−	1.32359i	0.940681	−	0.339292i	$-0.110188\pi$
$824$	−8.28251	+	14.3457i	−0.288535	+	0.499757i
$825$	5.27590	+	4.84580i	0.183683	+	0.168709i
$826$	−0.680071	−	1.17792i	−0.0236627	−	0.0409850i
$827$	−40.1574			−1.39641			−0.698205	−	0.715898i	$-0.746018\pi$
$827$	−40.1574			−1.39641			−0.698205	+	0.715898i	$0.746018\pi$
$828$	0.254498	+	2.98919i	0.00884443	+	0.103881i
$829$	35.0885			1.21868			0.609338	−	0.792911i	$-0.291435\pi$
$829$	35.0885			1.21868			0.609338	+	0.792911i	$0.291435\pi$
$830$	1.89350	+	3.27963i	0.0657242	+	0.113838i
$831$	41.2477	−	12.9525i	1.43087	−	0.449317i
$832$	−2.84575	+	4.92899i	−0.0986588	+	0.170882i
$833$	14.7208	−	25.4972i	0.510046	−	0.883426i
$834$	−4.09109	+	18.3525i	−0.141663	+	0.635494i
$835$	−4.32300	−	7.48766i	−0.149604	−	0.259121i
$836$	16.8864			0.584028
$837$	19.0309	+	46.4030i	0.657804	+	1.60392i
$838$	12.5277			0.432762
$839$	−23.4482	−	40.6135i	−0.809523	−	1.40214i	−0.913195	−	0.407523i	$-0.866392\pi$
$839$	−23.4482	−	40.6135i	−0.809523	−	1.40214i	0.103672	−	0.994612i	$-0.466941\pi$
$840$	−0.366430	+	1.64379i	−0.0126430	+	0.0567161i
$841$	−25.5749	+	44.2970i	−0.881893	+	1.52748i
$842$	−16.2278	+	28.1074i	−0.559248	+	0.968647i
$843$	−41.0212	+	12.8814i	−1.41284	+	0.443658i
$844$	4.71584	+	8.16808i	0.162326	+	0.281157i
$845$	38.4046			1.32116
$846$	31.0518	−	21.6350i	1.06758	−	0.743825i
$847$	−1.82120			−0.0625773
$848$	0.240860	+	0.417183i	0.00827118	+	0.0143261i
$849$	21.8293	+	20.0497i	0.749178	+	0.688104i
$850$	−2.34872	+	4.06810i	−0.0805604	+	0.139535i
$851$	4.56106	−	7.89998i	0.156351	−	0.270808i
$852$	−7.56566	−	6.94890i	−0.259195	−	0.238065i
$853$	−1.40121	−	2.42696i	−0.0479764	−	0.0830975i	0.841040	−	0.540973i	$-0.181944\pi$
$853$	−1.40121	−	2.42696i	−0.0479764	−	0.0830975i	−0.889016	+	0.457875i	$0.848611\pi$
$854$	−1.38784			−0.0474909
$855$	21.4619	−	14.9533i	0.733982	−	0.511393i
$856$	−6.19254			−0.211657
$857$	11.4343	+	19.8048i	0.390588	+	0.676518i	0.992527	−	0.122024i	$-0.0389385\pi$
$857$	11.4343	+	19.8048i	0.390588	+	0.676518i	−0.601940	+	0.798542i	$0.705605\pi$
$858$	−36.0712	+	11.3270i	−1.23145	+	0.386697i
$859$	26.7021	−	46.2494i	0.911063	−	1.57801i	0.0984988	−	0.995137i	$-0.468596\pi$
$859$	26.7021	−	46.2494i	0.911063	−	1.57801i	0.812565	−	0.582871i	$-0.198071\pi$
$860$	9.43616	−	16.3439i	0.321770	−	0.557323i
$861$	0.626099	−	2.80865i	0.0213374	−	0.0957185i
$862$	−3.61401	−	6.25964i	−0.123094	−	0.213204i
$863$	−31.9394			−1.08723			−0.543614	−	0.839335i	$-0.682945\pi$
$863$	−31.9394			−1.08723			−0.543614	+	0.839335i	$0.682945\pi$
$864$	−1.97168	−	4.80754i	−0.0670779	−	0.163556i
$865$	13.5569			0.460947
$866$	18.5078	+	32.0565i	0.628922	+	1.08932i
$867$	−0.744101	+	3.33800i	−0.0252710	+	0.113364i
$868$	2.36961	−	4.10429i	0.0804298	−	0.139309i
$869$	25.6258	−	44.3853i	0.869297	−	1.50567i
$870$	−29.2970	+	9.19977i	−0.993261	+	0.311901i
$871$	1.39727	+	2.42015i	0.0473448	+	0.0820037i
$872$	−4.67294			−0.158246
$873$	−3.29643	−	38.7179i	−0.111567	−	1.31040i
$874$	−4.40294			−0.148932
$875$	−2.95512	−	5.11842i	−0.0999013	−	0.173034i
$876$	−8.41495	−	7.72895i	−0.284315	−	0.261137i
$877$	11.6178	−	20.1227i	0.392307	−	0.679495i	−0.600447	−	0.799665i	$-0.705011\pi$
$877$	11.6178	−	20.1227i	0.392307	−	0.679495i	0.992753	+	0.120170i	$0.0383439\pi$
$878$	−9.41544	+	16.3080i	−0.317756	+	0.550369i
$879$	−2.86943	−	2.63551i	−0.0967834	−	0.0888934i
$880$	−3.79748	−	6.57744i	−0.128013	−	0.221725i
$881$	42.8183			1.44259			0.721293	−	0.692630i	$-0.243548\pi$
$881$	42.8183			1.44259			0.721293	+	0.692630i	$0.243548\pi$
$882$	−18.3569	−	8.61215i	−0.618110	−	0.289986i
$883$	49.9493			1.68093			0.840465	−	0.541866i	$-0.182282\pi$
$883$	49.9493			1.68093			0.840465	+	0.541866i	$0.182282\pi$
$884$	−12.3960	−	21.4706i	−0.416924	−	0.722133i
$885$	9.06508	−	2.84660i	0.304719	−	0.0956873i
$886$	−4.76549	+	8.25407i	−0.160100	+	0.277301i
$887$	−9.77329	+	16.9278i	−0.328155	+	0.568381i	−0.982146	−	0.188122i	$-0.939760\pi$
$887$	−9.77329	+	16.9278i	−0.328155	+	0.568381i	0.653991	+	0.756502i	$0.273093\pi$
$888$	−3.43772	+	15.4214i	−0.115362	+	0.517510i
$889$	1.44256	+	2.49858i	0.0483818	+	0.0837997i
$890$	10.2438			0.343373
$891$	11.9567	−	32.3802i	0.400565	−	1.08478i
$892$	−3.44478			−0.115340
$893$	27.7719	+	48.1024i	0.929353	+	1.60969i
$894$	−3.11495	+	13.9735i	−0.104179	+	0.467344i
$895$	−11.2907	+	19.5560i	−0.377405	+	0.653685i
$896$	−0.245502	+	0.425221i	−0.00820163	+	0.0142056i
$897$	9.40517	−	2.95339i	0.314030	−	0.0986108i
$898$	−3.55568	−	6.15861i	−0.118654	−	0.205516i
$899$	86.4120			2.88200
$900$	2.92886	+	1.37407i	0.0976288	+	0.0458025i
$901$	−2.09836			−0.0699066
$902$	6.48855	+	11.2385i	0.216045	+	0.374201i
$903$	−5.96904	−	5.48243i	−0.198637	−	0.182444i
$904$	2.36980	−	4.10462i	0.0788185	−	0.136518i
$905$	−15.5833	+	26.9910i	−0.518005	+	0.897212i
$906$	7.74968	+	7.11791i	0.257466	+	0.236477i
$907$	−27.0689	−	46.8848i	−0.898810	−	1.55678i	−0.829018	−	0.559223i	$-0.811100\pi$
$907$	−27.0689	−	46.8848i	−0.898810	−	1.55678i	−0.0697921	−	0.997562i	$-0.522234\pi$
$908$	−17.3843			−0.576919
$909$	3.57945	+	42.0421i	0.118723	+	1.39445i
$910$	5.53406			0.183452
$911$	19.9195	+	34.5016i	0.659963	+	1.14309i	0.980625	+	0.195895i	$0.0627613\pi$
$911$	19.9195	+	34.5016i	0.659963	+	1.14309i	−0.320662	+	0.947194i	$0.603905\pi$
$912$	7.27583	−	2.28474i	0.240927	−	0.0756552i
$913$	−3.66713	+	6.35165i	−0.121364	+	0.210209i
$914$	2.76634	−	4.79144i	0.0915024	−	0.158487i
$915$	2.10942	−	9.46274i	0.0697351	−	0.312828i
$916$	−1.23488	−	2.13888i	−0.0408017	−	0.0706706i
$917$	−1.14759			−0.0378968
$918$	22.4302	+	3.03283i	0.740307	+	0.100098i
$919$	−32.7115			−1.07905			−0.539527	−	0.841968i	$-0.681397\pi$
$919$	−32.7115			−1.07905			−0.539527	+	0.841968i	$0.681397\pi$
$920$	0.990153	+	1.71499i	0.0326444	+	0.0565417i
$921$	−9.66597	+	43.3611i	−0.318504	+	1.42880i
$922$	−7.97263	+	13.8090i	−0.262564	+	0.454775i
$923$	−16.8779	+	29.2333i	−0.555542	+	0.962226i
$924$	−3.11184	+	0.977173i	−0.102372	+	0.0321466i
$925$	−4.91860	−	8.51926i	−0.161723	−	0.280112i
$926$	5.86441			0.192716
$927$	−40.7742	+	28.4089i	−1.33920	+	0.933071i
$928$	−8.95264			−0.293885
$929$	−18.6194	−	32.2497i	−0.610881	−	1.05808i	−0.991092	−	0.133177i	$-0.957482\pi$
$929$	−18.6194	−	32.2497i	−0.610881	−	1.05808i	0.380211	−	0.924900i	$-0.375851\pi$
$930$	24.3827	+	22.3950i	0.799541	+	0.734360i
$931$	14.8796	−	25.7722i	0.487658	−	0.844648i
$932$	−3.72854	+	6.45802i	−0.122132	+	0.211540i
$933$	−25.3295	−	23.2646i	−0.829252	−	0.761649i
$934$	2.91234	+	5.04432i	0.0952947	+	0.165055i
$935$	33.0835			1.08195
$936$	−14.0094	+	9.76091i	−0.457913	+	0.319045i
$937$	41.3670			1.35140			0.675700	−	0.737177i	$-0.263842\pi$
$937$	41.3670			1.35140			0.675700	+	0.737177i	$0.263842\pi$
$938$	0.120542	+	0.208785i	0.00393584	+	0.00681707i
$939$	18.0241	−	5.65988i	0.588194	−	0.184703i
$940$	12.4909	−	21.6350i	0.407410	−	0.705655i
$941$	−3.96496	+	6.86751i	−0.129254	+	0.223874i	−0.923388	−	0.383869i	$-0.874592\pi$
$941$	−3.96496	+	6.86751i	−0.129254	+	0.223874i	0.794134	+	0.607743i	$0.207925\pi$
$942$	2.88466	−	12.9405i	0.0939874	−	0.421623i
$943$	−1.69182	−	2.93032i	−0.0550932	−	0.0954242i
$944$	2.77013			0.0901600
$945$	−3.08971	+	3.99756i	−0.100508	+	0.130041i
$946$	36.5500			1.18834
$947$	−3.24044	−	5.61261i	−0.105300	−	0.182385i	0.808561	−	0.588413i	$-0.200247\pi$
$947$	−3.24044	−	5.61261i	−0.105300	−	0.182385i	−0.913861	+	0.406028i	$0.866914\pi$
$948$	5.03604	−	22.5914i	0.163563	−	0.733736i
$949$	−18.7725	+	32.5149i	−0.609381	+	1.05548i
$950$	−2.37404	+	4.11197i	−0.0770242	+	0.133410i
$951$	27.3710	−	8.59499i	0.887567	−	0.278712i
$952$	−1.06940	−	1.85225i	−0.0346594	−	0.0600318i
$953$	−3.25690			−0.105501			−0.0527507	−	0.998608i	$-0.516799\pi$
$953$	−3.25690			−0.105501			−0.0527507	+	0.998608i	$0.516799\pi$
$954$	0.122597	+	1.43995i	0.00396923	+	0.0466202i
$955$	−35.1336			−1.13690
$956$	13.0680	+	22.6345i	0.422651	+	0.732052i
$957$	−43.7998	−	40.2291i	−1.41585	−	1.30042i
$958$	−11.3864	+	19.7218i	−0.367878	+	0.637184i
$959$	0.639860	−	1.10827i	0.0206622	−	0.0357879i
$960$	−2.52615	−	2.32021i	−0.0815312	−	0.0748846i
$961$	−31.0817	−	53.8351i	−1.00264	−	1.73662i
$962$	51.9186			1.67392
$963$	−16.8187	−	7.89047i	−0.541974	−	0.254267i
$964$	10.2952			0.331585
$965$	5.84640	+	10.1263i	0.188202	+	0.325976i
$966$	0.811379	−	0.254787i	0.0261057	−	0.00819765i
$967$	−2.46810	+	4.27487i	−0.0793686	+	0.137470i	−0.902978	−	0.429687i	$-0.858624\pi$
$967$	−2.46810	+	4.27487i	−0.0793686	+	0.137470i	0.823609	+	0.567158i	$0.191957\pi$
$968$	1.85457	−	3.21222i	0.0596083	−	0.103245i
$969$	−7.22775	+	32.4233i	−0.232189	+	1.04159i
$970$	−12.8251	−	22.2137i	−0.411789	−	0.713239i
$971$	3.10588			0.0996725			0.0498363	−	0.998757i	$-0.484130\pi$
$971$	3.10588			0.0996725			0.0498363	+	0.998757i	$0.484130\pi$
$972$	0.770725	−	15.5694i	0.0247210	−	0.499388i
$973$	5.33027			0.170881
$974$	−4.42093	−	7.65728i	−0.141656	−	0.245355i
$975$	2.31301	−	10.3761i	0.0740757	−	0.332300i
$976$	1.41327	−	2.44785i	0.0452377	−	0.0783539i
$977$	−8.46066	+	14.6543i	−0.270680	+	0.468832i	−0.969036	−	0.246918i	$-0.920582\pi$
$977$	−8.46066	+	14.6543i	−0.270680	+	0.468832i	0.698356	+	0.715751i	$0.253915\pi$
$978$	32.8113	−	10.3033i	1.04919	−	0.329464i
$979$	9.91957	+	17.1812i	0.317031	+	0.549114i
$980$	−13.3847			−0.427559
$981$	−12.6915	−	5.95422i	−0.405209	−	0.190104i
$982$	−21.7066			−0.692686
$983$	15.6073	+	27.0326i	0.497794	+	0.862205i	0.999997	−	0.00254491i	$-0.000810072\pi$
$983$	15.6073	+	27.0326i	0.497794	+	0.862205i	−0.502202	+	0.864750i	$0.667477\pi$
$984$	4.31629	+	3.96442i	0.137598	+	0.126381i
$985$	−9.93073	+	17.2005i	−0.316419	+	0.548054i
$986$	19.4987	−	33.7728i	0.620966	−	1.07554i
$987$	−7.90141	−	7.25727i	−0.251505	−	0.231002i
$988$	−12.5297	−	21.7021i	−0.398623	−	0.690435i
$989$	−9.53000			−0.303037
$990$	−1.93291	−	22.7028i	−0.0614318	−	0.721541i
$991$	−8.49533			−0.269863			−0.134931	−	0.990855i	$-0.543081\pi$
$991$	−8.49533			−0.269863			−0.134931	+	0.990855i	$0.543081\pi$
$992$	4.82606	+	8.35898i	0.153228	+	0.265398i
$993$	−3.21919	+	1.01088i	−0.102158	+	0.0320794i
$994$	−1.45604	+	2.52194i	−0.0461829	+	0.0799911i
$995$	18.4697	−	31.9905i	0.585530	−	1.01417i
$996$	−0.720671	+	3.23290i	−0.0228353	+	0.102438i
$997$	16.7617	+	29.0321i	0.530848	+	0.919457i	0.999352	+	0.0359949i	$0.0114600\pi$
$997$	16.7617	+	29.0321i	0.530848	+	0.919457i	−0.468503	+	0.883462i	$0.655207\pi$
$998$	−19.3425			−0.612276
$999$	−28.9866	+	37.5037i	−0.917095	+	1.18657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.d.139.3	✓	10
3.2	odd	2		1242.2.e.b.415.4		10
9.2	odd	6		1242.2.e.b.829.4		10
9.4	even	3		3726.2.a.r.1.4		5
9.5	odd	6		3726.2.a.u.1.2		5
9.7	even	3	inner	414.2.e.d.277.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.3	✓	10	1.1	even	1	trivial
414.2.e.d.277.3	yes	10	9.7	even	3	inner
1242.2.e.b.415.4		10	3.2	odd	2
1242.2.e.b.829.4		10	9.2	odd	6
3726.2.a.r.1.4		5	9.4	even	3
3726.2.a.u.1.2		5	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.376855 + 1.69056i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.990153 + 1.71499i) q^{5} +(-1.65249 + 0.518912i) q^{6} +(0.245502 + 0.425221i) q^{7} -1.00000 q^{8} +(-2.71596 - 1.27419i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.376855 + 1.69056i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.990153 + 1.71499i) q^{5} +(-1.65249 + 0.518912i) q^{6} +(0.245502 + 0.425221i) q^{7} -1.00000 q^{8} +(-2.71596 - 1.27419i) q^{9} -1.98031 q^{10} +(-1.91763 - 3.32142i) q^{11} +(-1.27564 - 1.17164i) q^{12} +(-2.84575 + 4.92899i) q^{13} +(-0.245502 + 0.425221i) q^{14} +(-2.52615 - 2.32021i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.35597 q^{17} +(-0.254498 - 2.98919i) q^{18} +4.40294 q^{19} +(-0.990153 - 1.71499i) q^{20} +(-0.811379 + 0.254787i) q^{21} +(1.91763 - 3.32142i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.376855 - 1.69056i) q^{24} +(0.539195 + 0.933913i) q^{25} -5.69151 q^{26} +(3.17762 - 4.11130i) q^{27} -0.491003 q^{28} +(-4.47632 - 7.75322i) q^{29} +(0.746289 - 3.34782i) q^{30} +(-4.82606 + 8.35898i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.33772 - 1.99016i) q^{33} +(2.17799 + 3.77238i) q^{34} -0.972336 q^{35} +(2.46146 - 1.71499i) q^{36} -9.12212 q^{37} +(2.20147 + 3.81306i) q^{38} +(-7.26030 - 6.66842i) q^{39} +(0.990153 - 1.71499i) q^{40} +(-1.69182 + 2.93032i) q^{41} +(-0.626342 - 0.575281i) q^{42} +(4.76500 + 8.25323i) q^{43} +3.83525 q^{44} +(4.87445 - 3.39621i) q^{45} -1.00000 q^{46} +(6.30759 + 10.9251i) q^{47} +(1.65249 - 0.518912i) q^{48} +(3.37946 - 5.85339i) q^{49} +(-0.539195 + 0.933913i) q^{50} +(-1.64157 + 7.36402i) q^{51} +(-2.84575 - 4.92899i) q^{52} -0.481721 q^{53} +(5.14930 + 0.696247i) q^{54} +7.59497 q^{55} +(-0.245502 - 0.425221i) q^{56} +(-1.65927 + 7.44342i) q^{57} +(4.47632 - 7.75322i) q^{58} +(-1.38506 + 2.39900i) q^{59} +(3.27244 - 1.02760i) q^{60} +(1.41327 + 2.44785i) q^{61} -9.65212 q^{62} +(-0.124960 - 1.46770i) q^{63} +1.00000 q^{64} +(-5.63546 - 9.76091i) q^{65} +(4.89239 + 4.49355i) q^{66} +(0.245502 - 0.425221i) q^{67} +(-2.17799 + 3.77238i) q^{68} +(-1.27564 - 1.17164i) q^{69} +(-0.486168 - 0.842068i) q^{70} +5.93089 q^{71} +(2.71596 + 1.27419i) q^{72} +6.59667 q^{73} +(-4.56106 - 7.89998i) q^{74} +(-1.78203 + 0.559589i) q^{75} +(-2.20147 + 3.81306i) q^{76} +(0.941560 - 1.63083i) q^{77} +(2.14488 - 9.62182i) q^{78} +(6.68166 + 11.5730i) q^{79} +1.98031 q^{80} +(5.75288 + 6.92130i) q^{81} -3.38364 q^{82} +(-0.956164 - 1.65612i) q^{83} +(0.185037 - 0.830068i) q^{84} +(-4.31308 + 7.47047i) q^{85} +(-4.76500 + 8.25323i) q^{86} +(14.7942 - 4.64563i) q^{87} +(1.91763 + 3.32142i) q^{88} -5.17284 q^{89} +(5.37843 + 2.52329i) q^{90} -2.79455 q^{91} +(-0.500000 - 0.866025i) q^{92} +(-12.3126 - 11.3089i) q^{93} +(-6.30759 + 10.9251i) q^{94} +(-4.35959 + 7.55102i) q^{95} +(1.27564 + 1.17164i) q^{96} +(6.47632 + 11.2173i) q^{97} +6.75892 q^{98} +(0.976065 + 11.4643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

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