LMFDB - Embedded newform 504.2.bf.b.115.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (of order $6$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.8
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37865 + 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 - 0.869029i) q^{4} +(1.58477 - 2.74491i) q^{5} +(-0.173654 - 2.44333i) q^{6} +(-2.63076 - 0.281244i) q^{7} +(-2.20950 + 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +O(q^{10})$	\(q+(-1.37865 + 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 - 0.869029i) q^{4} +(1.58477 - 2.74491i) q^{5} +(-0.173654 - 2.44333i) q^{6} +(-2.63076 - 0.281244i) q^{7} +(-2.20950 + 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +(-1.31972 + 4.28374i) q^{10} +(2.67808 + 4.63857i) q^{11} +(1.00948 + 3.31375i) q^{12} +(-0.893100 - 1.54689i) q^{13} +(3.71553 - 0.441413i) q^{14} +(4.27771 + 3.44083i) q^{15} +(2.48958 - 3.13081i) q^{16} +(4.04061 + 2.33285i) q^{17} +(4.22809 + 0.351071i) q^{18} +(2.36047 - 1.36282i) q^{19} +(0.469296 - 6.32170i) q^{20} +(1.17941 - 4.42820i) q^{21} +(-5.15409 - 5.55089i) q^{22} +(4.01783 + 2.31970i) q^{23} +(-2.43613 - 4.25033i) q^{24} +(-2.52301 - 4.36999i) q^{25} +(1.71881 + 1.85114i) q^{26} +(2.31328 - 4.65282i) q^{27} +(-4.98328 + 1.77959i) q^{28} +(2.85231 + 1.64678i) q^{29} +(-6.98191 - 3.39546i) q^{30} +9.98908 q^{31} +(-2.44549 + 5.10094i) q^{32} +(-8.65000 + 3.35305i) q^{33} +(-6.30583 - 1.94267i) q^{34} +(-4.94115 + 6.77549i) q^{35} +(-5.93969 + 0.848585i) q^{36} +(2.33249 - 1.34666i) q^{37} +(-2.82473 + 2.62281i) q^{38} +(2.88464 - 1.11819i) q^{39} +(1.34545 + 8.86329i) q^{40} +(4.34585 - 2.50908i) q^{41} +(-0.230330 + 6.47665i) q^{42} +(-0.212741 + 0.368479i) q^{43} +(8.85516 + 6.02827i) q^{44} +(-7.02436 + 6.40879i) q^{45} +(-6.27028 - 1.93172i) q^{46} -2.98331 q^{47} +(4.69815 + 5.09189i) q^{48} +(6.84180 + 1.47977i) q^{49} +(4.85565 + 5.22948i) q^{50} +(-5.06503 + 6.29696i) q^{51} +(-2.95306 - 2.01034i) q^{52} +(5.19961 + 3.00200i) q^{53} +(-1.72275 + 7.14368i) q^{54} +16.9766 q^{55} +(6.30929 - 4.02403i) q^{56} +(1.70630 + 4.40180i) q^{57} +(-4.45135 - 1.37135i) q^{58} +4.47279i q^{59} +(10.6957 + 2.48061i) q^{60} -11.6099 q^{61} +(-13.7714 + 3.14830i) q^{62} +(7.26641 + 3.19364i) q^{63} +(1.76378 - 7.80314i) q^{64} -5.66144 q^{65} +(10.8685 - 7.34893i) q^{66} -12.7934 q^{67} +(9.30579 + 0.690822i) q^{68} +(-5.03648 + 6.26146i) q^{69} +(4.67663 - 10.8983i) q^{70} +2.92741i q^{71} +(7.92128 - 3.04194i) q^{72} +(-0.864336 - 0.499025i) q^{73} +(-2.79124 + 2.59171i) q^{74} +(8.14914 - 3.15890i) q^{75} +(3.06766 - 4.50621i) q^{76} +(-5.74082 - 12.9562i) q^{77} +(-3.62448 + 2.45076i) q^{78} -7.46476i q^{79} +(-4.64838 - 11.7953i) q^{80} +(7.35000 + 5.19398i) q^{81} +(-5.20059 + 4.82883i) q^{82} +(-7.03493 - 4.06162i) q^{83} +(-1.72373 - 9.00160i) q^{84} +(12.8069 - 7.39407i) q^{85} +(0.177160 - 0.575052i) q^{86} +(-3.57546 + 4.44509i) q^{87} +(-14.1081 - 5.51993i) q^{88} +(6.04395 - 3.48948i) q^{89} +(7.66422 - 11.0494i) q^{90} +(1.91448 + 4.32069i) q^{91} +(9.25333 + 0.686927i) q^{92} +(-2.65044 + 17.0974i) q^{93} +(4.11293 - 0.940264i) q^{94} -8.63904i q^{95} +(-8.08193 - 5.53918i) q^{96} +(11.7930 + 6.80869i) q^{97} +(-9.89881 + 0.116282i) q^{98} +(-3.44397 - 15.6951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.37865	+	0.315175i	−0.974850	+	0.222862i
$2$	−1.37865	+	0.315175i	−0.974850	+	0.222862i
$3$	−0.265334	+	1.71161i	−0.153191	+	0.988197i
$3$	−0.265334	+	1.71161i	−0.153191	+	0.988197i
$4$	1.80133	−	0.869029i	0.900665	−	0.434514i
$5$	1.58477	−	2.74491i	0.708732	−	1.22756i	−0.256595	−	0.966519i	$-0.582601\pi$
$5$	1.58477	−	2.74491i	0.708732	−	1.22756i	0.965328	−	0.261041i	$-0.0840659\pi$
$6$	−0.173654	−	2.44333i	−0.0708938	−	0.997484i
$7$	−2.63076	−	0.281244i	−0.994334	−	0.106300i
$7$	−2.63076	−	0.281244i	−0.994334	−	0.106300i
$8$	−2.20950	+	1.76582i	−0.781176	+	0.624310i
$9$	−2.85920	−	0.908295i	−0.953065	−	0.302765i
$10$	−1.31972	+	4.28374i	−0.417331	+	1.35464i
$11$	2.67808	+	4.63857i	0.807472	+	1.39858i	0.914610	+	0.404338i	$0.132498\pi$
$11$	2.67808	+	4.63857i	0.807472	+	1.39858i	−0.107138	+	0.994244i	$0.534169\pi$
$12$	1.00948	+	3.31375i	0.291412	+	0.956598i
$13$	−0.893100	−	1.54689i	−0.247701	−	0.429031i	0.715186	−	0.698934i	$-0.246342\pi$
$13$	−0.893100	−	1.54689i	−0.247701	−	0.429031i	−0.962888	+	0.269903i	$0.913009\pi$
$14$	3.71553	−	0.441413i	0.993017	−	0.117973i
$15$	4.27771	+	3.44083i	1.10450	+	0.888417i
$16$	2.48958	−	3.13081i	0.622395	−	0.782704i
$17$	4.04061	+	2.33285i	0.979993	+	0.565799i	0.902268	−	0.431176i	$-0.141901\pi$
$17$	4.04061	+	2.33285i	0.979993	+	0.565799i	0.0777247	+	0.996975i	$0.475234\pi$
$18$	4.22809	+	0.351071i	0.996570	+	0.0827481i
$19$	2.36047	−	1.36282i	0.541530	−	0.312652i	−0.204169	−	0.978936i	$-0.565449\pi$
$19$	2.36047	−	1.36282i	0.541530	−	0.312652i	0.745699	+	0.666283i	$0.232116\pi$
$20$	0.469296	−	6.32170i	0.104938	−	1.41357i
$21$	1.17941	−	4.42820i	0.257368	−	0.966313i
$22$	−5.15409	−	5.55089i	−1.09886	−	1.18345i
$23$	4.01783	+	2.31970i	0.837776	+	0.483690i	0.856508	−	0.516134i	$-0.172629\pi$
$23$	4.01783	+	2.31970i	0.837776	+	0.483690i	−0.0187314	+	0.999825i	$0.505963\pi$
$24$	−2.43613	−	4.25033i	−0.497273	−	0.867594i
$25$	−2.52301	−	4.36999i	−0.504603	−	0.873997i
$26$	1.71881	+	1.85114i	0.337086	+	0.363038i
$27$	2.31328	−	4.65282i	0.445192	−	0.895435i
$28$	−4.98328	+	1.77959i	−0.941751	+	0.336311i
$29$	2.85231	+	1.64678i	0.529661	+	0.305800i	0.740878	−	0.671639i	$-0.234409\pi$
$29$	2.85231	+	1.64678i	0.529661	+	0.305800i	−0.211217	+	0.977439i	$0.567743\pi$
$30$	−6.98191	−	3.39546i	−1.27472	−	0.619923i
$31$	9.98908			1.79409			0.897046	−	0.441938i	$-0.145709\pi$
$31$	9.98908			1.79409			0.897046	+	0.441938i	$0.145709\pi$
$32$	−2.44549	+	5.10094i	−0.432306	+	0.901727i
$33$	−8.65000	+	3.35305i	−1.50577	+	0.583691i
$34$	−6.30583	−	1.94267i	−1.08144	−	0.333166i
$35$	−4.94115	+	6.77549i	−0.835207	+	1.14527i
$36$	−5.93969	+	0.848585i	−0.989948	+	0.141431i
$37$	2.33249	−	1.34666i	0.383458	−	0.221390i	−0.295864	−	0.955230i	$-0.595607\pi$
$37$	2.33249	−	1.34666i	0.383458	−	0.221390i	0.679322	+	0.733840i	$0.262274\pi$
$38$	−2.82473	+	2.62281i	−0.458232	+	0.425476i
$39$	2.88464	−	1.11819i	0.461913	−	0.179054i
$40$	1.34545	+	8.86329i	0.212734	+	1.40141i
$41$	4.34585	−	2.50908i	0.678707	−	0.391852i	−0.120660	−	0.992694i	$-0.538501\pi$
$41$	4.34585	−	2.50908i	0.678707	−	0.391852i	0.799368	+	0.600842i	$0.205168\pi$
$42$	−0.230330	+	6.47665i	−0.0355407	+	0.999368i
$43$	−0.212741	+	0.368479i	−0.0324427	+	0.0561925i	−0.881791	−	0.471641i	$-0.843662\pi$
$43$	−0.212741	+	0.368479i	−0.0324427	+	0.0561925i	0.849348	+	0.527833i	$0.176995\pi$
$44$	8.85516	+	6.02827i	1.33497	+	0.908796i
$45$	−7.02436	+	6.40879i	−1.04713	+	0.955366i
$46$	−6.27028	−	1.93172i	−0.924503	−	0.284817i
$47$	−2.98331			−0.435161			−0.217580	−	0.976042i	$-0.569816\pi$
$47$	−2.98331			−0.435161			−0.217580	+	0.976042i	$0.569816\pi$
$48$	4.69815	+	5.09189i	0.678120	+	0.734951i
$49$	6.84180	+	1.47977i	0.977401	+	0.211396i
$50$	4.85565	+	5.22948i	0.686693	+	0.739560i
$51$	−5.06503	+	6.29696i	−0.709246	+	0.881750i
$52$	−2.95306	−	2.01034i	−0.409516	−	0.278784i
$53$	5.19961	+	3.00200i	0.714221	+	0.412356i	0.812622	−	0.582791i	$-0.198039\pi$
$53$	5.19961	+	3.00200i	0.714221	+	0.412356i	−0.0984008	+	0.995147i	$0.531373\pi$
$54$	−1.72275	+	7.14368i	−0.234437	+	0.972131i
$55$	16.9766			2.28913
$56$	6.30929	−	4.02403i	0.843115	−	0.537734i
$57$	1.70630	+	4.40180i	0.226005	+	0.583033i
$58$	−4.45135	−	1.37135i	−0.584491	−	0.180068i
$59$			4.47279i			0.582308i	0.956676	+	0.291154i	$0.0940392\pi$
$59$			4.47279i			0.582308i	−0.956676	+	0.291154i	$0.905961\pi$
$60$	10.6957	+	2.48061i	1.38081	+	0.320245i
$61$	−11.6099			−1.48650			−0.743248	−	0.669016i	$-0.766716\pi$
$61$	−11.6099			−1.48650			−0.743248	+	0.669016i	$0.766716\pi$
$62$	−13.7714	+	3.14830i	−1.74897	+	0.399835i
$63$	7.26641	+	3.19364i	0.915481	+	0.402361i
$64$	1.76378	−	7.80314i	0.220473	−	0.975393i
$65$	−5.66144			−0.702216
$66$	10.8685	−	7.34893i	1.33782	−	0.904591i
$67$	−12.7934			−1.56296			−0.781480	−	0.623930i	$-0.785535\pi$
$67$	−12.7934			−1.56296			−0.781480	+	0.623930i	$0.785535\pi$
$68$	9.30579	+	0.690822i	1.12849	+	0.0837745i
$69$	−5.03648	+	6.26146i	−0.606321	+	0.753791i
$70$	4.67663	−	10.8983i	0.558965	−	1.30260i
$71$			2.92741i			0.347420i	0.984797	+	0.173710i	$0.0555755\pi$
$71$			2.92741i			0.347420i	−0.984797	+	0.173710i	$0.944424\pi$
$72$	7.92128	−	3.04194i	0.933531	−	0.358496i
$73$	−0.864336	−	0.499025i	−0.101163	−	0.0584064i	0.448565	−	0.893750i	$-0.351935\pi$
$73$	−0.864336	−	0.499025i	−0.101163	−	0.0584064i	−0.549728	+	0.835344i	$0.685269\pi$
$74$	−2.79124	+	2.59171i	−0.324475	+	0.301280i
$75$	8.14914	−	3.15890i	0.940982	−	0.364758i
$76$	3.06766	−	4.50621i	0.351885	−	0.516897i
$77$	−5.74082	−	12.9562i	−0.654227	−	1.47649i
$78$	−3.62448	+	2.45076i	−0.410391	+	0.277494i
$79$		−	7.46476i		−	0.839851i	−0.907559	−	0.419925i	$-0.862056\pi$
$79$		−	7.46476i		−	0.839851i	0.907559	−	0.419925i	$-0.137944\pi$
$80$	−4.64838	−	11.7953i	−0.519705	−	1.31875i
$81$	7.35000	+	5.19398i	0.816667	+	0.577109i
$82$	−5.20059	+	4.82883i	−0.574309	+	0.533255i
$83$	−7.03493	−	4.06162i	−0.772184	−	0.445821i	0.0614690	−	0.998109i	$-0.480421\pi$
$83$	−7.03493	−	4.06162i	−0.772184	−	0.445821i	−0.833653	+	0.552288i	$0.813755\pi$
$84$	−1.72373	−	9.00160i	−0.188075	−	0.982155i
$85$	12.8069	−	7.39407i	1.38910	−	0.802000i
$86$	0.177160	−	0.575052i	0.0191036	−	0.0620095i
$87$	−3.57546	+	4.44509i	−0.383330	+	0.476564i
$88$	−14.1081	−	5.51993i	−1.50393	−	0.588426i
$89$	6.04395	−	3.48948i	0.640658	−	0.369884i	−0.144210	−	0.989547i	$-0.546064\pi$
$89$	6.04395	−	3.48948i	0.640658	−	0.369884i	0.784868	+	0.619663i	$0.212731\pi$
$90$	7.66422	−	11.0494i	0.807880	−	1.16470i
$91$	1.91448	+	4.32069i	0.200692	+	0.452931i
$92$	9.25333	+	0.686927i	0.964726	+	0.0716171i
$93$	−2.65044	+	17.0974i	−0.274838	+	1.77292i
$94$	4.11293	−	0.940264i	0.424216	−	0.0969808i
$95$		−	8.63904i		−	0.886347i
$96$	−8.08193	−	5.53918i	−0.824858	−	0.565340i
$97$	11.7930	+	6.80869i	1.19740	+	0.691318i	0.959974	−	0.280089i	$-0.0903639\pi$
$97$	11.7930	+	6.80869i	1.19740	+	0.691318i	0.237423	+	0.971406i	$0.423697\pi$
$98$	−9.89881	+	0.116282i	−0.999931	+	0.0117462i
$99$	−3.44397	−	15.6951i	−0.346132	−	1.57741i
$100$	−8.34242	−	5.67922i	−0.834242	−	0.567922i
$101$	0.434202	+	0.752060i	0.0432047	+	0.0748327i	0.886819	−	0.462117i	$-0.152910\pi$
$101$	0.434202	+	0.752060i	0.0432047	+	0.0748327i	−0.843614	+	0.536949i	$0.819577\pi$
$102$	4.99824	−	10.2776i	0.494900	−	1.01764i
$103$	−8.35409	+	14.4697i	−0.823153	+	1.42574i	0.0801693	+	0.996781i	$0.474454\pi$
$103$	−8.35409	+	14.4697i	−0.823153	+	1.42574i	−0.903323	+	0.428962i	$0.858879\pi$
$104$	4.70484	+	1.84081i	0.461347	+	0.180507i
$105$	−10.2859	−	10.2551i	−1.00380	−	1.00079i
$106$	−8.11457	−	2.49990i	−0.788157	−	0.242812i
$107$	−7.16839	−	12.4160i	−0.692994	−	1.20030i	−0.970852	−	0.239679i	$-0.922958\pi$
$107$	−7.16839	−	12.4160i	−0.692994	−	1.20030i	0.277858	−	0.960622i	$-0.410376\pi$
$108$	0.123557	−	10.3916i	0.0118893	−	0.999929i
$109$	−15.6663	−	9.04494i	−1.50056	−	0.866348i	−1.00000		0.000646449i	$-0.999794\pi$
$109$	−15.6663	−	9.04494i	−1.50056	−	0.866348i	−0.500560	−	0.865702i	$-0.666872\pi$
$110$	−23.4047	+	5.35060i	−2.23155	+	0.510159i
$111$	1.68607	+	4.34961i	0.160034	+	0.412847i
$112$	−7.43001	+	7.53624i	−0.702070	+	0.712108i
$113$	−2.83892	−	4.91715i	−0.267063	−	0.462567i	0.701039	−	0.713123i	$-0.252720\pi$
$113$	−2.83892	−	4.91715i	−0.267063	−	0.462567i	−0.968102	+	0.250556i	$0.919387\pi$
$114$	−3.73972	−	5.53075i	−0.350257	−	0.518002i
$115$	12.7347	−	7.35239i	1.18752	−	0.685614i
$116$	6.56906	+	0.487659i	0.609922	+	0.0452780i
$117$	1.14851	+	5.23407i	0.106180	+	0.483890i
$118$	−1.40971	−	6.16639i	−0.129774	−	0.567663i
$119$	−9.97379	−	7.27357i	−0.914295	−	0.666767i
$120$	−15.5275	−	0.0488571i	−1.41746	−	0.00446002i
$121$	−8.84424	+	15.3187i	−0.804022	+	1.39261i
$122$	16.0060	−	3.65915i	1.44911	−	0.331284i
$123$	3.14145	+	8.10413i	0.283255	+	0.730724i
$124$	17.9936	−	8.68079i	1.61588	−	0.779558i
$125$	−0.145884			−0.0130483
$126$	−11.0244	−	2.11271i	−0.982128	−	0.188215i
$127$			4.54442i			0.403252i	0.979463	+	0.201626i	$0.0646226\pi$
$127$			4.54442i			0.403252i	−0.979463	+	0.201626i	$0.935377\pi$
$128$	0.0277197	+	11.3137i	0.00245010	+	0.999997i
$129$	−0.574243	−	0.461899i	−0.0505593	−	0.0406680i
$130$	7.80513	−	1.78434i	0.684555	−	0.156497i
$131$	19.5820	+	11.3056i	1.71088	+	0.987779i	0.933373	+	0.358909i	$0.116851\pi$
$131$	19.5820	+	11.3056i	1.71088	+	0.987779i	0.777510	+	0.628870i	$0.216482\pi$
$132$	−12.6676	+	13.5570i	−1.10257	+	1.17999i
$133$	−6.59313	+	2.92138i	−0.571697	+	0.253316i
$134$	17.6375	−	4.03215i	1.52365	−	0.348325i
$135$	−9.10552	−	13.7234i	−0.783679	−	1.18112i
$136$	−13.0471	+	1.98055i	−1.11878	+	0.169831i
$137$	0.166825	+	0.288950i	0.0142528	+	0.0246867i	0.873064	−	0.487606i	$-0.162130\pi$
$137$	0.166825	+	0.288950i	0.0142528	+	0.0246867i	−0.858811	+	0.512293i	$0.828796\pi$
$138$	4.97007	−	10.2197i	0.423080	−	0.869959i
$139$	−1.30955	+	0.756069i	−0.111075	+	0.0641289i	−0.554508	−	0.832178i	$-0.687094\pi$
$139$	−1.30955	+	0.756069i	−0.111075	+	0.0641289i	0.443434	+	0.896307i	$0.353760\pi$
$140$	−3.01255	+	16.4989i	−0.254607	+	1.39441i
$141$	0.791573	−	5.10626i	0.0666625	−	0.430024i
$142$	−0.922647	−	4.03587i	−0.0774268	−	0.338682i
$143$	4.78359	−	8.28542i	0.400024	−	0.692861i
$144$	−9.96189	+	6.69034i	−0.830158	+	0.557528i
$145$	9.04054	−	5.21956i	0.750776	−	0.433461i
$146$	1.34889	+	0.415562i	0.111635	+	0.0343921i
$147$	−4.34815	+	11.3178i	−0.358629	+	0.933480i
$148$	3.03129	−	4.45278i	0.249170	−	0.366016i
$149$	−15.4464	−	8.91798i	−1.26542	−	0.730590i	−0.291301	−	0.956631i	$-0.594088\pi$
$149$	−15.4464	−	8.91798i	−1.26542	−	0.730590i	−0.974118	+	0.226042i	$0.927421\pi$
$150$	−10.2392	+	6.92341i	−0.836025	+	0.565294i
$151$	11.4870	−	6.63202i	0.934799	−	0.539706i	0.0464728	−	0.998920i	$-0.485202\pi$
$151$	11.4870	−	6.63202i	0.934799	−	0.539706i	0.888326	+	0.459213i	$0.151869\pi$
$152$	−2.80898	+	7.17931i	−0.227838	+	0.582319i
$153$	−9.43399	−	10.3401i	−0.762693	−	0.835951i
$154$	11.9980	+	16.0526i	0.966828	+	1.29356i
$155$	15.8304	−	27.4191i	1.27153	−	2.20236i
$156$	4.22445	−	4.52107i	0.338227	−	0.361975i
$157$	−5.84007			−0.466088			−0.233044	−	0.972466i	$-0.574869\pi$
$157$	−5.84007			−0.466088			−0.233044	+	0.972466i	$0.574869\pi$
$158$	2.35270	+	10.2913i	0.187171	+	0.818729i
$159$	−6.51787	+	8.10316i	−0.516901	+	0.642622i
$160$	10.1260	+	14.7965i	0.800535	+	1.16976i
$161$	−9.91756	−	7.23256i	−0.781613	−	0.570006i
$162$	−11.7701	−	4.84413i	−0.924744	−	0.380591i
$163$	2.06173	+	3.57103i	0.161488	+	0.279705i	0.935402	−	0.353585i	$-0.115038\pi$
$163$	2.06173	+	3.57103i	0.161488	+	0.279705i	−0.773915	+	0.633290i	$0.781704\pi$
$164$	5.64785	−	8.29634i	0.441023	−	0.647835i
$165$	−4.50447	+	29.0573i	−0.350673	+	2.26211i
$166$	10.9788	+	3.38230i	0.852120	+	0.262518i
$167$	−5.25195	−	9.09665i	−0.406408	−	0.703920i	0.588076	−	0.808806i	$-0.299886\pi$
$167$	−5.25195	−	9.09665i	−0.406408	−	0.703920i	−0.994484	+	0.104886i	$0.966552\pi$
$168$	5.21349	+	11.8667i	0.402230	+	0.915539i
$169$	4.90475	−	8.49527i	0.377288	−	0.653482i
$170$	−15.3258	+	14.2302i	−1.17543	+	1.09141i
$171$	−7.98690	+	1.75256i	−0.610773	+	0.134022i
$172$	−0.0629987	+	0.848630i	−0.00480360	+	0.0647074i
$173$	−3.11457			−0.236796			−0.118398	−	0.992966i	$-0.537776\pi$
$173$	−3.11457			−0.236796			−0.118398	+	0.992966i	$0.537776\pi$
$174$	3.52832	−	7.25510i	0.267481	−	0.550008i
$175$	5.40841	+	12.2060i	0.408837	+	0.922685i
$176$	21.1898	+	3.16351i	1.59724	+	0.238459i
$177$	−7.65566	−	1.18678i	−0.575435	−	0.0892041i
$178$	−7.23268	+	6.71566i	−0.542112	+	0.503360i
$179$	0.757866	−	1.31266i	0.0566456	−	0.0981130i	−0.836312	−	0.548254i	$-0.815293\pi$
$179$	0.757866	−	1.31266i	0.0566456	−	0.0981130i	0.892958	+	0.450141i	$0.148626\pi$
$180$	−7.08377	+	17.6487i	−0.527993	+	1.31546i
$181$	2.75740			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$181$	2.75740			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$182$	−4.00116	−	5.35330i	−0.296586	−	0.396813i
$183$	3.08050	−	19.8716i	0.227717	−	1.46895i
$184$	−12.9736	+	1.96939i	−0.956424	+	0.145185i
$185$		−	8.53661i		−	0.627624i
$186$	−1.73464	−	24.4066i	−0.127190	−	1.78958i
$187$			24.9902i			1.82747i
$188$	−5.37393	+	2.59258i	−0.391934	+	0.189084i
$189$	−7.39428	+	11.5899i	−0.537854	+	0.843038i
$190$	2.72281	+	11.9102i	0.197533	+	0.864056i
$191$			7.75689i			0.561269i	0.959815	+	0.280634i	$0.0905448\pi$
$191$			7.75689i			0.561269i	−0.959815	+	0.280634i	$0.909455\pi$
$192$	12.8879	+	5.08934i	0.930106	+	0.367292i
$193$	−4.94596			−0.356018			−0.178009	−	0.984029i	$-0.556966\pi$
$193$	−4.94596			−0.356018			−0.178009	+	0.984029i	$0.556966\pi$
$194$	−18.4043	−	5.66992i	−1.32135	−	0.407076i
$195$	1.50217	−	9.69017i	0.107573	−	0.693927i
$196$	13.6103	−	3.28017i	0.972165	−	0.234298i
$197$			7.54976i			0.537898i	0.963154	+	0.268949i	$0.0866763\pi$
$197$			7.54976i			0.537898i	−0.963154	+	0.268949i	$0.913324\pi$
$198$	9.69470	+	20.5525i	0.688973	+	1.46060i
$199$	7.62668	−	13.2098i	0.540641	−	0.936418i	−0.458226	−	0.888836i	$-0.651515\pi$
$199$	7.62668	−	13.2098i	0.540641	−	0.936418i	0.998867	−	0.0475821i	$-0.0151516\pi$
$200$	13.2912	+	5.20031i	0.939829	+	0.367717i
$201$	3.39452	−	21.8972i	0.239431	−	1.54451i
$202$	−0.835641	−	0.899975i	−0.0587955	−	0.0633220i
$203$	−7.04060	−	5.13449i	−0.494154	−	0.360371i
$204$	−3.65156	+	15.7446i	−0.255660	+	1.10234i
$205$		−	15.9053i		−	1.11087i
$206$	6.95685	−	22.5816i	0.484707	−	1.57334i
$207$	−9.38081	−	10.2818i	−0.652011	−	0.714638i
$208$	−7.06648	−	1.05498i	−0.489972	−	0.0731500i
$209$	12.6431	+	7.29949i	0.874540	+	0.504916i
$210$	17.4128	+	10.8963i	1.20160	+	0.751913i
$211$	−0.449200	−	0.778038i	−0.0309242	−	0.0535623i	0.850149	−	0.526542i	$-0.176512\pi$
$211$	−0.449200	−	0.778038i	−0.0309242	−	0.0535623i	−0.881073	+	0.472980i	$0.843178\pi$
$212$	11.9750	+	0.888975i	0.822449	+	0.0610551i
$213$	−5.01058	−	0.776742i	−0.343319	−	0.0532215i
$214$	13.7959	+	14.8580i	0.943067	+	1.01567i
$215$	0.674294	+	1.16791i	0.0459864	+	0.0796509i
$216$	3.10482	+	14.3652i	0.211256	+	0.977431i
$217$	−26.2789	−	2.80937i	−1.78393	−	0.190712i
$218$	24.4490	+	7.53215i	1.65590	+	0.510142i
$219$	1.08347	−	1.34700i	0.0732142	−	0.0910215i
$220$	30.5805	−	14.7532i	2.06174	−	0.994658i
$221$		−	8.33387i		−	0.560597i
$222$	−3.69538	−	5.46517i	−0.248018	−	0.366798i
$223$	6.78219	−	11.7471i	0.454169	−	0.786644i	−0.544471	−	0.838780i	$-0.683269\pi$
$223$	6.78219	−	11.7471i	0.454169	−	0.786644i	0.998640	+	0.0521356i	$0.0166028\pi$
$224$	7.86812	−	12.7316i	0.525711	−	0.850663i
$225$	3.24455	+	14.7863i	0.216304	+	0.985753i
$226$	5.46363	+	5.88426i	0.363435	+	0.391415i
$227$	−3.04590	+	1.75855i	−0.202164	+	0.116719i	−0.597664	−	0.801746i	$-0.703904\pi$
$227$	−3.04590	+	1.75855i	−0.202164	+	0.116719i	0.395501	+	0.918466i	$0.370571\pi$
$228$	6.89890	+	6.44628i	0.456891	+	0.426915i
$229$	11.6852	−	20.2394i	0.772181	−	1.33746i	−0.164184	−	0.986430i	$-0.552499\pi$
$229$	11.6852	−	20.2394i	0.772181	−	1.33746i	0.936365	−	0.351027i	$-0.114167\pi$
$230$	−15.2394	+	14.1500i	−1.00485	+	0.933024i
$231$	23.6991	−	6.38832i	1.55929	−	0.420320i
$232$	−9.21010	+	1.39809i	−0.604673	+	0.0917892i
$233$	6.13808	+	10.6315i	0.402119	+	0.696491i	0.993981	−	0.109548i	$-0.0349404\pi$
$233$	6.13808	+	10.6315i	0.402119	+	0.696491i	−0.591862	+	0.806039i	$0.701607\pi$
$234$	−3.23304	−	6.85395i	−0.211350	−	0.448057i
$235$	−4.72787	+	8.18891i	−0.308412	+	0.534186i
$236$	3.88698	+	8.05697i	0.253021	+	0.524464i
$237$	12.7767	+	1.98065i	0.829938	+	0.128657i
$238$	16.0428	+	6.88419i	1.03990	+	0.446236i
$239$	−25.0467	+	14.4607i	−1.62014	+	0.935387i	−0.633257	+	0.773942i	$0.718282\pi$
$239$	−25.0467	+	14.4607i	−1.62014	+	0.935387i	−0.986882	+	0.161446i	$0.948384\pi$
$240$	21.4223	−	4.82651i	1.38280	−	0.311550i
$241$	3.52556	−	2.03548i	0.227101	−	0.131117i	−0.382133	−	0.924107i	$-0.624810\pi$
$241$	3.52556	−	2.03548i	0.227101	−	0.131117i	0.609234	+	0.792990i	$0.291477\pi$
$242$	7.36502	−	23.9065i	0.473441	−	1.53677i
$243$	−10.8403	+	11.2022i	−0.695403	+	0.718620i
$244$	−20.9133	+	10.0893i	−1.33884	+	0.645904i
$245$	14.9045	−	16.4350i	0.952216	−	1.04999i
$246$	−6.88517	−	10.1826i	−0.438982	−	0.649220i
$247$	−4.21628	−	2.43427i	−0.268275	−	0.154889i
$248$	−22.0709	+	17.6389i	−1.40150	+	1.12007i
$249$	8.81850	−	10.9634i	0.558850	−	0.694774i
$250$	0.201123	−	0.0459790i	0.0127201	−	0.00290797i
$251$			16.9156i			1.06770i	0.845578	+	0.533852i	$0.179256\pi$
$251$			16.9156i			1.06770i	−0.845578	+	0.533852i	$0.820744\pi$
$252$	15.8646	−	0.561922i	0.999373	−	0.0353977i
$253$			24.8494i			1.56227i
$254$	−1.43229	−	6.26515i	−0.0898696	−	0.393110i
$255$	9.25764	+	23.8823i	0.579736	+	1.49557i
$256$	−3.60400	−	15.5888i	−0.225250	−	0.974301i
$257$	2.21508	+	1.27887i	0.138173	+	0.0797740i	0.567493	−	0.823378i	$-0.307913\pi$
$257$	2.21508	+	1.27887i	0.138173	+	0.0797740i	−0.429320	+	0.903152i	$0.641247\pi$
$258$	0.937257	+	0.455809i	0.0583511	+	0.0283774i
$259$	−6.51495	+	2.88675i	−0.404819	+	0.179374i
$260$	−10.1981	+	4.91996i	−0.632461	+	0.305123i
$261$	−6.65956	−	7.29922i	−0.412216	−	0.451810i
$262$	−30.5598	−	9.41475i	−1.88799	−	0.581645i
$263$	−18.9865	+	10.9619i	−1.17076	+	0.675938i	−0.953859	−	0.300256i	$-0.902928\pi$
$263$	−18.9865	+	10.9619i	−1.17076	+	0.675938i	−0.216900	+	0.976194i	$0.569594\pi$
$264$	13.1913	−	22.6829i	0.811869	−	1.39603i
$265$	16.4804	−	9.51497i	1.01238	−	0.584500i
$266$	8.16884	−	6.10554i	0.500864	−	0.374355i
$267$	4.36895	+	11.2707i	0.267375	+	0.689759i
$268$	−23.0451	+	11.1178i	−1.40770	+	0.679128i
$269$	6.10379	−	10.5721i	0.372155	−	0.644591i	−0.617742	−	0.786381i	$-0.711952\pi$
$269$	6.10379	−	10.5721i	0.372155	−	0.644591i	0.989897	+	0.141790i	$0.0452858\pi$
$270$	16.8786	+	16.0499i	1.02720	+	0.976766i
$271$	12.1660	+	21.0722i	0.739034	+	1.28004i	0.952931	+	0.303188i	$0.0980509\pi$
$271$	12.1660	+	21.0722i	0.739034	+	1.28004i	−0.213897	+	0.976856i	$0.568616\pi$
$272$	17.3631	−	6.84260i	1.05280	−	0.414894i
$273$	−7.90329	+	2.13041i	−0.478329	+	0.128938i
$274$	−0.321063	−	0.345781i	−0.0193961	−	0.0208894i
$275$	13.5137	−	23.4064i	0.814905	−	1.41146i
$276$	−3.63097	+	15.6558i	−0.218559	+	0.942368i
$277$	8.84759	−	5.10816i	0.531600	−	0.306919i	−0.210068	−	0.977687i	$-0.567368\pi$
$277$	8.84759	−	5.10816i	0.531600	−	0.306919i	0.741668	+	0.670767i	$0.234035\pi$
$278$	1.56711	−	1.45509i	0.0939891	−	0.0872704i
$279$	−28.5607	−	9.07303i	−1.70989	−	0.543188i
$280$	−1.04680	−	23.6956i	−0.0625582	−	1.41608i
$281$	−14.3951	+	24.9330i	−0.858738	+	1.48738i	0.0143945	+	0.999896i	$0.495418\pi$
$281$	−14.3951	+	24.9330i	−0.858738	+	1.48738i	−0.873133	+	0.487482i	$0.837915\pi$
$282$	0.518063	+	7.28920i	0.0308502	+	0.434066i
$283$			8.63820i			0.513488i	0.966479	+	0.256744i	$0.0826497\pi$
$283$			8.63820i			0.513488i	−0.966479	+	0.256744i	$0.917350\pi$
$284$	2.54401	+	5.27324i	0.150959	+	0.312909i
$285$	14.7866	+	2.29223i	0.875885	+	0.135780i
$286$	−3.98352	+	12.9303i	−0.235551	+	0.764586i
$287$	−12.1385	+	5.37854i	−0.716516	+	0.317485i
$288$	11.6253	−	12.3633i	0.685027	−	0.728517i
$289$	2.38437	+	4.12985i	0.140257	+	0.242932i
$290$	−10.8186	+	10.0453i	−0.635292	+	0.589879i
$291$	−14.7829	+	18.3784i	−0.866588	+	1.07736i
$292$	−1.99062	−	0.147775i	−0.116492	−	0.00864789i
$293$	5.36418	+	9.29102i	0.313378	+	0.542787i	0.979091	−	0.203420i	$-0.0652058\pi$
$293$	5.36418	+	9.29102i	0.313378	+	0.542787i	−0.665713	+	0.746208i	$0.731872\pi$
$294$	2.42746	−	16.9737i	0.141572	−	0.989928i
$295$	12.2774	+	7.08836i	0.714818	+	0.412700i
$296$	−2.77567	+	7.09419i	−0.161333	+	0.412341i
$297$	27.7776	−	1.73028i	1.61182	−	0.100401i
$298$	24.1058	+	7.42643i	1.39641	+	0.430201i
$299$		−	8.28689i		−	0.479243i
$300$	11.9341	−	12.7721i	0.689016	−	0.737395i
$301$	0.663304	−	0.909547i	0.0382322	−	0.0524254i
$302$	−13.7463	+	12.7636i	−0.791009	+	0.734464i
$303$	−1.40244	+	0.543636i	−0.0805680	+	0.0312311i
$304$	1.60985	−	10.7831i	0.0923311	−	0.618450i
$305$	−18.3991	+	31.8681i	−1.05353	+	1.82476i
$306$	16.2651	+	11.2820i	0.929813	+	0.644951i
$307$		−	28.5013i		−	1.62666i	−0.581805	−	0.813328i	$-0.697653\pi$
$307$		−	28.5013i		−	1.62666i	0.581805	−	0.813328i	$-0.302347\pi$
$308$	−21.6004	−	18.3494i	−1.23080	−	1.04555i
$309$	−22.5498	−	18.1382i	−1.28282	−	1.03185i
$310$	−13.1827	+	42.7906i	−0.748730	+	2.43034i
$311$	−31.6953			−1.79728			−0.898639	−	0.438689i	$-0.855443\pi$
$311$	−31.6953			−1.79728			−0.898639	+	0.438689i	$0.855443\pi$
$312$	−4.39910	+	7.56440i	−0.249050	+	0.428250i
$313$		−	10.9088i		−	0.616603i	−0.951289	−	0.308302i	$-0.900239\pi$
$313$		−	10.9088i		−	0.616603i	0.951289	−	0.308302i	$-0.0997606\pi$
$314$	8.05139	−	1.84064i	0.454366	−	0.103873i
$315$	20.2819	−	14.8844i	1.14275	−	0.838643i
$316$	−6.48709	−	13.4465i	−0.364927	−	0.756424i
$317$		−	11.5402i		−	0.648162i	−0.946029	−	0.324081i	$-0.894945\pi$
$317$		−	11.5402i		−	0.648162i	0.946029	−	0.324081i	$-0.105055\pi$
$318$	6.43193	−	13.2257i	0.360684	−	0.741658i
$319$			17.6409i			0.987700i
$320$	−18.6237	−	17.2076i	−1.04110	−	0.961936i
$321$	23.1534	−	8.97508i	1.29229	−	0.500940i
$322$	15.9523	+	6.84538i	0.888988	+	0.381478i
$323$	12.7170			0.707594
$324$	17.7535	+	2.96872i	0.986305	+	0.164929i
$325$	−4.50661	+	7.80567i	−0.249982	+	0.432981i
$326$	−3.96790	−	4.27338i	−0.219762	−	0.236681i
$327$	19.6382	−	24.4146i	1.08599	−	1.35013i
$328$	−5.17158	+	13.2178i	−0.285553	+	0.729830i
$329$	7.84838	+	0.839039i	0.432695	+	0.0462577i
$330$	−2.94805	−	41.4794i	−0.162285	−	2.28337i
$331$	−0.928777			−0.0510502			−0.0255251	−	0.999674i	$-0.508126\pi$
$331$	−0.928777			−0.0510502			−0.0255251	+	0.999674i	$0.508126\pi$
$332$	−16.2019	−	1.20276i	−0.889195	−	0.0660100i
$333$	−7.89220	+	1.73178i	−0.432490	+	0.0949012i
$334$	10.1076	+	10.8858i	0.553064	+	0.595643i
$335$	−20.2746	+	35.1166i	−1.10772	+	1.91863i
$336$	−10.9277	−	14.7169i	−0.596152	−	0.802871i
$337$	0.718049	+	1.24370i	0.0391146	+	0.0677485i	0.884920	−	0.465743i	$-0.154213\pi$
$337$	0.718049	+	1.24370i	0.0391146	+	0.0677485i	−0.845805	+	0.533492i	$0.820880\pi$
$338$	−4.08441	+	13.2578i	−0.222163	+	0.721130i
$339$	9.16950	−	3.55443i	0.498019	−	0.193050i
$340$	16.6438	−	24.4487i	0.902637	−	1.32592i
$341$	26.7516	+	46.3351i	1.44868	+	2.50918i
$342$	10.4587	−	4.93343i	0.565544	−	0.266770i
$343$	−17.5830	−	5.81714i	−0.949391	−	0.314096i
$344$	−0.180614	−	1.18982i	−0.00973805	−	0.0641506i
$345$	9.20545	+	23.7477i	0.495605	+	1.27853i
$346$	4.29388	−	0.981632i	0.230841	−	0.0527729i
$347$	−14.7107			−0.789714			−0.394857	−	0.918743i	$-0.629206\pi$
$347$	−14.7107			−0.789714			−0.394857	+	0.918743i	$0.629206\pi$
$348$	−2.57767	+	11.1143i	−0.138178	+	0.595786i
$349$	−11.1777	+	19.3603i	−0.598328	+	1.03633i	0.394740	+	0.918793i	$0.370835\pi$
$349$	−11.1777	+	19.3603i	−0.598328	+	1.03633i	−0.993068	+	0.117541i	$0.962499\pi$
$350$	−11.3033	−	15.1231i	−0.604187	−	0.808365i
$351$	−9.26341	+	0.577024i	−0.494444	+	0.0307992i
$352$	−30.2103	+	2.31712i	−1.61021	+	0.123503i
$353$	3.96945	−	2.29176i	0.211272	−	0.121978i	−0.390630	−	0.920548i	$-0.627743\pi$
$353$	3.96945	−	2.29176i	0.211272	−	0.121978i	0.601903	+	0.798570i	$0.294410\pi$
$354$	10.9285	−	0.776716i	0.580843	−	0.0412820i
$355$	8.03548	+	4.63929i	0.426479	+	0.246228i
$356$	7.85470	−	11.5381i	0.416298	−	0.611516i
$357$	15.0959	−	15.1413i	0.798958	−	0.801361i
$358$	−0.631111	+	2.04856i	−0.0333553	+	0.108270i
$359$	14.2343	−	8.21816i	0.751256	−	0.433738i	−0.0748915	−	0.997192i	$-0.523861\pi$
$359$	14.2343	−	8.21816i	0.751256	−	0.433738i	0.826148	+	0.563454i	$0.190528\pi$
$360$	4.20359	−	26.5640i	0.221549	−	1.40004i
$361$	−5.78544	+	10.0207i	−0.304497	+	0.527404i
$362$	−3.80148	+	0.869063i	−0.199801	+	0.0456769i
$363$	−23.8729	−	19.2024i	−1.25300	−	1.00787i
$364$	7.20341	+	6.11925i	0.377561	+	0.320736i
$365$	−2.73955	+	1.58168i	−0.143395	+	0.0827890i
$366$	2.01610	+	28.3668i	0.105383	+	1.48276i
$367$	6.68954	+	11.5866i	0.349191	+	0.604817i	0.986106	−	0.166118i	$-0.0531231\pi$
$367$	6.68954	+	11.5866i	0.349191	+	0.604817i	−0.636915	+	0.770934i	$0.719790\pi$
$368$	17.2653	−	6.80402i	0.900014	−	0.354684i
$369$	−14.7046	+	3.22663i	−0.765492	+	0.167972i
$370$	2.69052	+	11.7690i	0.139874	+	0.611839i
$371$	−12.8346	−	9.35989i	−0.666341	−	0.485941i
$372$	10.0838	+	33.1013i	0.522820	+	1.71622i
$373$	15.5628	+	8.98519i	0.805811	+	0.465235i	0.845499	−	0.533977i	$-0.179303\pi$
$373$	15.5628	+	8.98519i	0.805811	+	0.465235i	−0.0396879	+	0.999212i	$0.512636\pi$
$374$	−7.87629	−	34.4527i	−0.407273	−	1.78151i
$375$	0.0387080	−	0.249697i	0.00199887	−	0.0128943i
$376$	6.59163	−	5.26798i	0.339937	−	0.271675i
$377$		−	5.88297i		−	0.302988i
$378$	6.54126	−	18.3088i	0.336446	−	0.941703i
$379$	−16.4196			−0.843420			−0.421710	−	0.906731i	$-0.638570\pi$
$379$	−16.4196			−0.843420			−0.421710	+	0.906731i	$0.638570\pi$
$380$	−7.50758	−	15.5618i	−0.385131	−	0.798302i
$381$	−7.77826	−	1.20579i	−0.398492	−	0.0617744i
$382$	−2.44478	−	10.6940i	−0.125086	−	0.547153i
$383$	11.0723	−	19.1778i	0.565770	−	0.979942i	−0.431208	−	0.902253i	$-0.641912\pi$
$383$	11.0723	−	19.1778i	0.565770	−	0.979942i	0.996978	−	0.0776894i	$-0.0247542\pi$
$384$	−19.3719	−	2.95446i	−0.988569	−	0.150769i
$385$	−44.6614	−	4.77457i	−2.27616	−	0.243335i
$386$	6.81873	−	1.55884i	0.347064	−	0.0793430i
$387$	0.942956	−	0.860321i	0.0479332	−	0.0437326i
$388$	27.1600	+	2.01624i	1.37884	+	0.102359i
$389$	0.0236594	−	0.0136597i	0.00119958	−	0.000692576i	−0.499400	−	0.866371i	$-0.666446\pi$
$389$	0.0236594	−	0.0136597i	0.00119958	−	0.000692576i	0.500600	+	0.865679i	$0.333113\pi$
$390$	0.983130	+	13.8328i	0.0497827	+	0.700449i
$391$	10.8230	+	18.7460i	0.547343	+	0.948026i
$392$	−17.7300	+	8.81181i	−0.895499	+	0.445064i
$393$	−24.5466	+	30.5168i	−1.23821	+	1.53937i
$394$	−2.37949	−	10.4084i	−0.119877	−	0.524370i
$395$	−20.4901	−	11.8299i	−1.03097	−	0.595229i
$396$	−19.8432	−	25.2791i	−0.997158	−	1.27032i
$397$	−12.3558	−	21.4009i	−0.620121	−	1.07408i	−0.989463	−	0.144787i	$-0.953750\pi$
$397$	−12.3558	−	21.4009i	−0.620121	−	1.07408i	0.369342	−	0.929294i	$-0.379583\pi$
$398$	−6.35110	+	20.6154i	−0.318352	+	1.03336i
$399$	−3.25088	−	12.0600i	−0.162748	−	0.603754i
$400$	−19.9629	−	2.98034i	−0.998143	−	0.149017i
$401$	14.5787	−	25.2511i	0.728027	−	1.26098i	−0.229688	−	0.973264i	$-0.573771\pi$
$401$	14.5787	−	25.2511i	0.728027	−	1.26098i	0.957716	−	0.287716i	$-0.0928960\pi$
$402$	2.22162	+	31.2584i	0.110804	+	1.55903i
$403$	−8.92124	−	15.4520i	−0.444399	−	0.769721i
$404$	1.43570	+	0.977374i	0.0714288	+	0.0486262i
$405$	25.9051	−	11.9438i	1.28723	−	0.593492i
$406$	11.3248	+	4.85962i	0.562039	+	0.241179i
$407$	12.4932	+	7.21294i	0.619264	+	0.357532i
$408$	0.0719195	−	22.8570i	0.00356055	−	1.13159i
$409$			0.135526i			0.00670134i	0.999994	+	0.00335067i	$0.00106655\pi$
$409$			0.135526i			0.00670134i	−0.999994	+	0.00335067i	$0.998933\pi$
$410$	5.01294	+	21.9277i	0.247571	+	1.08293i
$411$	−0.538833	+	0.208871i	−0.0265787	+	0.0103029i
$412$	−2.47388	+	33.3247i	−0.121879	+	1.64179i
$413$	1.25795	−	11.7668i	0.0618995	−	0.579008i
$414$	16.1734	+	11.2184i	0.794879	+	0.551356i
$415$	−22.2975	+	12.8735i	−1.09454	+	0.631935i
$416$	10.0747	−	0.772726i	0.493952	−	0.0378860i
$417$	−0.946625	−	2.44205i	−0.0463564	−	0.119587i
$418$	−19.7309	−	6.07863i	−0.965072	−	0.297315i
$419$	−10.2755	+	5.93257i	−0.501991	+	0.289825i	−0.729536	−	0.683943i	$-0.760264\pi$
$419$	−10.2755	+	5.93257i	−0.501991	+	0.289825i	0.227544	+	0.973768i	$0.426930\pi$
$420$	−27.4403	−	9.53401i	−1.33895	−	0.465212i
$421$	−22.5571	−	13.0233i	−1.09936	−	0.634719i	−0.163311	−	0.986575i	$-0.552217\pi$
$421$	−22.5571	−	13.0233i	−1.09936	−	0.634719i	−0.936054	+	0.351856i	$0.885551\pi$
$422$	0.864506	+	0.931062i	0.0420835	+	0.0453234i
$423$	8.52987	+	2.70973i	0.414736	+	0.131751i
$424$	−16.7895	+	2.54865i	−0.815371	+	0.123773i
$425$		−	23.5432i		−	1.14201i
$426$	7.15263	−	0.508356i	0.346546	−	0.0246299i
$427$	30.5429	+	3.26522i	1.47807	+	0.158015i
$428$	−23.7025	−	16.1358i	−1.14570	−	0.779953i
$429$	12.9121	+	10.3860i	0.623404	+	0.501442i
$430$	−1.29771	−	1.39762i	−0.0625810	−	0.0673990i
$431$	−31.6669	−	18.2829i	−1.52534	−	0.880655i	−0.999549	−	0.0300416i	$-0.990436\pi$
$431$	−31.6669	−	18.2829i	−1.52534	−	0.880655i	−0.525791	−	0.850614i	$-0.676231\pi$
$432$	−8.80801	−	18.8260i	−0.423775	−	0.905767i
$433$		−	12.0347i		−	0.578349i	−0.957276	−	0.289174i	$-0.906619\pi$
$433$		−	12.0347i		−	0.578349i	0.957276	−	0.289174i	$-0.0933808\pi$
$434$	37.1147	−	4.40931i	1.78156	−	0.211654i
$435$	6.53507	+	16.8588i	0.313333	+	0.808316i
$436$	−36.0805	−	2.67846i	−1.72794	−	0.128275i
$437$	12.6453			0.604908
$438$	−1.06919	+	2.19851i	−0.0510877	+	0.105049i
$439$	−6.93057			−0.330778			−0.165389	−	0.986228i	$-0.552888\pi$
$439$	−6.93057			−0.330778			−0.165389	+	0.986228i	$0.552888\pi$
$440$	−37.5098	+	29.9776i	−1.78821	+	1.42912i
$441$	−18.2180	−	10.4453i	−0.867523	−	0.497397i
$442$	2.62662	+	11.4895i	0.124936	+	0.546498i
$443$	−30.3331			−1.44117			−0.720584	−	0.693367i	$-0.756126\pi$
$443$	−30.3331			−1.44117			−0.720584	+	0.693367i	$0.756126\pi$
$444$	6.81710	+	6.36985i	0.323525	+	0.302300i
$445$		−	22.1201i		−	1.04859i
$446$	−5.64785	+	18.3327i	−0.267434	+	0.868077i
$447$	19.3625	−	24.0719i	0.915817	−	1.13856i
$448$	−6.83468	+	20.0322i	−0.322908	+	0.946430i
$449$	22.7034			1.07144			0.535721	−	0.844395i	$-0.320040\pi$
$449$	22.7034			1.07144			0.535721	+	0.844395i	$0.320040\pi$
$450$	−9.13335	−	19.3625i	−0.430550	−	0.912755i
$451$	23.2771	+	13.4390i	1.09607	+	0.632819i
$452$	−9.38698	−	6.39031i	−0.441526	−	0.300575i
$453$	8.30353	+	21.4209i	0.390134	+	1.00644i
$454$	3.64497	−	3.38441i	0.171067	−	0.158838i
$455$	14.8939	+	1.59225i	0.698237	+	0.0746457i
$456$	−11.5428	−	6.71278i	−0.540543	−	0.314355i
$457$	27.1520			1.27012			0.635059	−	0.772464i	$-0.280976\pi$
$457$	27.1520			1.27012			0.635059	+	0.772464i	$0.280976\pi$
$458$	−9.73084	+	31.5858i	−0.454692	+	1.47591i
$459$	20.2014	−	13.4037i	0.942921	−	0.625631i
$460$	16.5500	−	24.3109i	0.771647	−	1.13350i
$461$	−0.861717	+	1.49254i	−0.0401342	+	0.0695144i	−0.885395	−	0.464840i	$-0.846112\pi$
$461$	−0.861717	+	1.49254i	−0.0401342	+	0.0695144i	0.845261	+	0.534354i	$0.179445\pi$
$462$	−30.6592	+	16.2766i	−1.42640	+	0.757255i
$463$	9.97910	−	5.76144i	0.463768	−	0.267757i	−0.249859	−	0.968282i	$-0.580384\pi$
$463$	9.97910	−	5.76144i	0.463768	−	0.267757i	0.713627	+	0.700525i	$0.247051\pi$
$464$	12.2568	−	4.83027i	0.569009	−	0.224239i
$465$	42.7304	+	34.3707i	1.98157	+	1.59390i
$466$	−11.8130	−	12.7225i	−0.547227	−	0.589357i
$467$	16.4233	−	9.48200i	0.759980	−	0.438775i	−0.0693086	−	0.997595i	$-0.522079\pi$
$467$	16.4233	−	9.48200i	0.759980	−	0.438775i	0.829289	+	0.558821i	$0.188746\pi$
$468$	6.61741	+	8.43020i	0.305890	+	0.389686i
$469$	33.6563	+	3.59806i	1.55410	+	0.166143i
$470$	3.93712	−	12.7797i	0.181606	−	0.589484i
$471$	1.54957	−	9.99590i	0.0714003	−	0.460587i
$472$	−7.89813	−	9.88263i	−0.363541	−	0.454885i
$473$	−2.27895			−0.104786
$474$	−18.2388	+	1.29628i	−0.837738	+	0.0595402i
$475$	−11.9110	−	6.87683i	−0.546515	−	0.315530i
$476$	−24.2870	−	4.43459i	−1.11319	−	0.203259i
$477$	−12.1400	−	13.3061i	−0.555853	−	0.609243i
$478$	29.9729	−	27.8303i	1.37093	−	1.27293i
$479$	−0.225098	−	0.389881i	−0.0102850	−	0.0178141i	0.860837	−	0.508881i	$-0.169941\pi$
$479$	−0.225098	−	0.389881i	−0.0102850	−	0.0178141i	−0.871122	+	0.491067i	$0.836607\pi$
$480$	−28.0125	+	13.4058i	−1.27859	+	0.611889i
$481$	−4.16629	−	2.40541i	−0.189966	−	0.109677i
$482$	−4.21896	+	3.91738i	−0.192169	+	0.178432i
$483$	15.0108	−	15.0559i	0.683014	−	0.685068i
$484$	−2.61903	+	35.2799i	−0.119047	+	1.60363i
$485$	37.3785	−	21.5805i	1.69727	−	0.979918i
$486$	11.4142	−	18.8604i	0.517761	−	0.855525i
$487$	−20.8671	−	12.0476i	−0.945577	−	0.545929i	−0.0538731	−	0.998548i	$-0.517157\pi$
$487$	−20.8671	−	12.0476i	−0.945577	−	0.545929i	−0.891704	+	0.452618i	$0.850490\pi$
$488$	25.6521	−	20.5010i	1.16122	−	0.928035i
$489$	−6.65925	+	2.58136i	−0.301141	+	0.116733i
$490$	−15.3682	+	27.3556i	−0.694264	+	1.23580i
$491$	−13.3040	−	23.0432i	−0.600402	−	1.03993i	−0.992760	−	0.120114i	$-0.961674\pi$
$491$	−13.3040	−	23.0432i	−0.600402	−	1.03993i	0.392358	−	0.919812i	$-0.371659\pi$
$492$	12.7015	+	11.8682i	0.572628	+	0.535059i
$493$	7.68339	+	13.3080i	0.346043	+	0.599364i
$494$	6.57997	+	2.02713i	0.296047	+	0.0912049i
$495$	−48.5395	−	15.4198i	−2.18169	−	0.693067i
$496$	24.8686	−	31.2739i	1.11663	−	1.40424i
$497$	0.823318	−	7.70132i	0.0369308	−	0.345452i
$498$	−8.70222	+	17.8940i	−0.389956	+	0.801847i
$499$	6.47254	−	11.2108i	0.289751	−	0.501863i	−0.684000	−	0.729482i	$-0.739761\pi$
$499$	6.47254	−	11.2108i	0.289751	−	0.501863i	0.973750	+	0.227620i	$0.0730943\pi$
$500$	−0.262786	+	0.126778i	−0.0117521	+	0.00566967i
$501$	16.9634	−	6.57563i	0.757869	−	0.293777i
$502$	−5.33137	−	23.3206i	−0.237951	−	1.04085i
$503$	19.2426			0.857984			0.428992	−	0.903308i	$-0.358869\pi$
$503$	19.2426			0.857984			0.428992	+	0.903308i	$0.358869\pi$
$504$	−21.6945	+	5.77480i	−0.966350	+	0.257230i
$505$	2.75245			0.122482
$506$	−7.83189	−	34.2585i	−0.348170	−	1.52297i
$507$	13.2392	+	10.6491i	0.587972	+	0.472942i
$508$	3.94923	+	8.18600i	0.175219	+	0.363195i
$509$	−1.92253	+	3.32991i	−0.0852145	+	0.147596i	−0.905483	−	0.424383i	$-0.860491\pi$
$509$	−1.92253	+	3.32991i	−0.0852145	+	0.147596i	0.820268	+	0.571979i	$0.193824\pi$
$510$	−20.2901	−	30.0075i	−0.898461	−	1.32875i
$511$	2.13351	+	1.55590i	0.0943811	+	0.0688292i
$512$	9.88184	+	20.3556i	0.436720	+	0.899598i
$513$	−0.880506	−	14.1354i	−0.0388753	−	0.624095i
$514$	−3.45687	−	1.06498i	−0.152476	−	0.0469742i
$515$	26.4787	+	45.8624i	1.16679	+	2.02094i
$516$	−1.43581	−	0.332999i	−0.0632078	−	0.0146595i
$517$	−7.98955	−	13.8383i	−0.351380	−	0.608608i
$518$	8.07198	−	6.03315i	0.354663	−	0.265081i
$519$	0.826400	−	5.33091i	0.0362749	−	0.234001i
$520$	12.5090	−	9.99707i	0.548554	−	0.438401i
$521$	−6.35138	−	3.66697i	−0.278259	−	0.160653i	0.354376	−	0.935103i	$-0.384693\pi$
$521$	−6.35138	−	3.66697i	−0.278259	−	0.160653i	−0.632635	+	0.774450i	$0.718027\pi$
$522$	11.4817	+	7.96411i	0.502540	+	0.348580i
$523$	−22.2694	+	12.8572i	−0.973772	+	0.562207i	−0.900384	−	0.435096i	$-0.856714\pi$
$523$	−22.2694	+	12.8572i	−0.973772	+	0.562207i	−0.0733878	+	0.997303i	$0.523381\pi$
$524$	45.0985	+	3.34792i	1.97014	+	0.146254i
$525$	−22.3269	+	6.01842i	−0.974424	+	0.262665i
$526$	22.7208	−	21.0966i	0.990673	−	0.919855i
$527$	40.3620	+	23.3030i	1.75820	+	1.01510i
$528$	−11.0371	+	35.4292i	−0.480327	+	1.54186i
$529$	−0.738006	−	1.27826i	−0.0320872	−	0.0555767i
$530$	−19.7218	+	18.3120i	−0.856659	+	0.795421i
$531$	4.06261	−	12.7886i	0.176302	−	0.554977i
$532$	−9.33763	+	10.9920i	−0.404838	+	0.476563i
$533$	−7.76255	−	4.48171i	−0.336233	−	0.194124i
$534$	−9.57549	−	14.1614i	−0.414372	−	0.612823i
$535$	−45.4411			−1.96459
$536$	28.2670	−	22.5908i	1.22095	−	0.975772i
$537$	2.04567	+	1.64546i	0.0882774	+	0.0710070i
$538$	−5.08292	+	16.4989i	−0.219140	+	0.711318i
$539$	11.4589	+	35.6992i	0.493569	+	1.53767i
$540$	−28.3281	−	16.8074i	−1.21905	−	0.723277i
$541$	−24.8063	+	14.3219i	−1.06650	+	0.615747i	−0.927224	−	0.374506i	$-0.877812\pi$
$541$	−24.8063	+	14.3219i	−1.06650	+	0.615747i	−0.139280	+	0.990253i	$0.544479\pi$
$542$	−23.4141	−	25.2167i	−1.00572	−	1.08315i
$543$	−0.731632	+	4.71959i	−0.0313973	+	0.202537i
$544$	−21.7810	+	14.9059i	−0.933853	+	0.639087i
$545$	−49.6551	+	28.6684i	−2.12699	+	1.22802i
$546$	10.2244	−	5.42800i	0.437564	−	0.232297i
$547$	19.2927	−	33.4159i	0.824896	−	1.42876i	−0.0771029	−	0.997023i	$-0.524567\pi$
$547$	19.2927	−	33.4159i	0.824896	−	1.42876i	0.901999	−	0.431739i	$-0.142100\pi$
$548$	0.551613	+	0.375518i	0.0235637	+	0.0160413i
$549$	33.1950	+	10.5452i	1.41673	+	0.450059i
$550$	−11.2535	+	36.5283i	−0.479850	+	1.55757i
$551$	8.97708			0.382436
$552$	0.0715141	−	22.7282i	0.00304384	−	0.967376i
$553$	−2.09942	+	19.6380i	−0.0892764	+	0.835092i
$554$	−10.5877	+	9.83088i	−0.449829	+	0.417674i
$555$	14.6113	+	2.26505i	0.620216	+	0.0961461i
$556$	−1.70189	+	2.49997i	−0.0721760	+	0.106022i
$557$	−12.7001	−	7.33238i	−0.538119	−	0.310683i	0.206197	−	0.978510i	$-0.433891\pi$
$557$	−12.7001	−	7.33238i	−0.538119	−	0.310683i	−0.744316	+	0.667827i	$0.767224\pi$
$558$	42.2347	+	3.50687i	1.78794	+	0.148458i
$559$	0.759997			0.0321444
$560$	8.91142	+	32.3379i	0.376576	+	1.36653i
$561$	−42.7735	−	6.63076i	−1.80590	−	0.279951i
$562$	11.9875	−	38.9108i	0.505661	−	1.64135i
$563$			29.1210i			1.22730i	0.789577	+	0.613651i	$0.210300\pi$
$563$			29.1210i			1.22730i	−0.789577	+	0.613651i	$0.789700\pi$
$564$	−3.01160	−	9.88595i	−0.126811	−	0.416274i
$565$	−17.9962			−0.757105
$566$	−2.72254	−	11.9090i	−0.114437	−	0.500573i
$567$	−17.8753	−	15.7313i	−0.750693	−	0.660651i
$568$	−5.16927	−	6.46812i	−0.216898	−	0.271396i
$569$	−20.6987			−0.867734			−0.433867	−	0.900977i	$-0.642851\pi$
$569$	−20.6987			−0.867734			−0.433867	+	0.900977i	$0.642851\pi$
$570$	−21.1080	+	1.50020i	−0.884117	+	0.0628365i
$571$	−8.00204			−0.334875			−0.167438	−	0.985883i	$-0.553549\pi$
$571$	−8.00204			−0.334875			−0.167438	+	0.985883i	$0.553549\pi$
$572$	1.41655	−	19.0818i	0.0592291	−	0.797852i
$573$	−13.2767	−	2.05817i	−0.554644	−	0.0859811i
$574$	15.0396	−	11.2409i	0.627740	−	0.469184i
$575$		−	23.4105i		−	0.976286i
$576$	−12.1306	+	20.7087i	−0.505440	+	0.862862i
$577$	25.7178	+	14.8482i	1.07065	+	0.618139i	0.928358	−	0.371686i	$-0.121220\pi$
$577$	25.7178	+	14.8482i	1.07065	+	0.618139i	0.142289	+	0.989825i	$0.454554\pi$
$578$	−4.58882	−	4.94211i	−0.190870	−	0.205565i
$579$	1.31233	−	8.46554i	0.0545386	−	0.351816i
$580$	11.7490	−	17.2586i	0.487853	−	0.716626i
$581$	17.3649	+	12.6637i	0.720418	+	0.525378i
$582$	14.5880	−	29.9965i	0.604690	−	1.24339i
$583$			32.1584i			1.33186i
$584$	2.79094	−	0.423664i	0.115490	−	0.0175313i
$585$	16.1872	+	5.14226i	0.669257	+	0.212606i
$586$	−10.3236	−	11.1184i	−0.426464	−	0.459296i
$587$	−9.59608	−	5.54030i	−0.396072	−	0.228673i	0.288715	−	0.957415i	$-0.406772\pi$
$587$	−9.59608	−	5.54030i	−0.396072	−	0.228673i	−0.684788	+	0.728742i	$0.740105\pi$
$588$	2.00308	+	24.1658i	0.0826056	+	0.996582i
$589$	23.5790	−	13.6133i	0.971554	−	0.560927i
$590$	−19.1603	−	5.90281i	−0.788815	−	0.243015i
$591$	−12.9222	−	2.00321i	−0.531549	−	0.0824009i
$592$	1.59076	−	10.6552i	0.0653798	−	0.437926i
$593$	30.1862	−	17.4280i	1.23960	−	0.715682i	0.270585	−	0.962696i	$-0.412783\pi$
$593$	30.1862	−	17.4280i	1.23960	−	0.715682i	0.969012	+	0.247014i	$0.0794494\pi$
$594$	−37.7501	+	11.1402i	−1.54891	+	0.457090i
$595$	−35.7715	+	15.8502i	−1.46649	+	0.649794i
$596$	−35.5740	−	2.64087i	−1.45717	−	0.108174i
$597$	20.5864	+	16.5589i	0.842544	+	0.677710i
$598$	2.61182	+	11.4247i	0.106805	+	0.467190i
$599$			33.2106i			1.35695i	0.734624	+	0.678475i	$0.237359\pi$
$599$			33.2106i			1.35695i	−0.734624	+	0.678475i	$0.762641\pi$
$600$	−12.4275	+	21.3695i	−0.507350	+	0.872405i
$601$	14.6277	+	8.44532i	0.596677	+	0.344492i	0.767733	−	0.640770i	$-0.221385\pi$
$601$	14.6277	+	8.44532i	0.596677	+	0.344492i	−0.171056	+	0.985261i	$0.554718\pi$
$602$	−0.627795	+	1.46300i	−0.0255870	+	0.0596274i
$603$	36.5788	+	11.6202i	1.48960	+	0.473209i
$604$	14.9285	−	21.9290i	0.607430	−	0.892278i
$605$	28.0322	+	48.5533i	1.13967	+	1.97397i
$606$	1.76213	−	1.19149i	0.0715815	−	0.0484012i
$607$	−0.322354	+	0.558333i	−0.0130839	+	0.0226620i	−0.872493	−	0.488626i	$-0.837498\pi$
$607$	−0.322354	+	0.558333i	−0.0130839	+	0.0226620i	0.859409	+	0.511288i	$0.170832\pi$
$608$	1.17914	+	15.3734i	0.0478203	+	0.623473i
$609$	10.6563	−	10.6884i	0.431817	−	0.433116i
$610$	15.3218	−	49.7338i	0.620361	−	2.01366i
$611$	2.66439	+	4.61487i	0.107790	+	0.186698i
$612$	−25.9796	−	10.4276i	−1.05016	−	0.421510i
$613$	12.0000	+	6.92823i	0.484677	+	0.279829i	0.722364	−	0.691513i	$-0.243056\pi$
$613$	12.0000	+	6.92823i	0.484677	+	0.279829i	−0.237686	+	0.971342i	$0.576389\pi$
$614$	8.98289	+	39.2932i	0.362520	+	1.58575i
$615$	27.2236	+	4.22021i	1.09776	+	0.170175i
$616$	35.5626	+	18.4894i	1.43286	+	0.744960i
$617$	21.7443	+	37.6623i	0.875394	+	1.51623i	0.856343	+	0.516408i	$0.172731\pi$
$617$	21.7443	+	37.6623i	0.875394	+	1.51623i	0.0190506	+	0.999819i	$0.493936\pi$
$618$	36.8050	+	17.8991i	1.48051	+	0.720006i
$619$	−7.18168	+	4.14635i	−0.288656	+	0.166656i	−0.637336	−	0.770586i	$-0.719964\pi$
$619$	−7.18168	+	4.14635i	−0.288656	+	0.166656i	0.348679	+	0.937242i	$0.386630\pi$
$620$	4.68783	−	63.1479i	0.188268	−	2.53608i
$621$	20.0875	−	13.3281i	0.806085	−	0.534839i
$622$	43.6967	−	9.98957i	1.75208	−	0.400545i
$623$	−16.8816	+	7.48015i	−0.676347	+	0.299686i
$624$	3.68070	−	11.8151i	0.147346	−	0.472983i
$625$	12.3839	−	21.4495i	0.495355	−	0.857980i
$626$	3.43819	+	15.0394i	0.137418	+	0.601096i
$627$	−15.8485	+	19.7032i	−0.632928	+	0.786869i
$628$	−10.5199	+	5.07519i	−0.419789	+	0.202522i
$629$	12.5662			0.501048
$630$	−23.2703	+	26.9127i	−0.927111	+	1.07223i
$631$		−	13.1848i		−	0.524877i	−0.964949	−	0.262439i	$-0.915473\pi$
$631$		−	13.1848i		−	0.524877i	0.964949	−	0.262439i	$-0.0845267\pi$
$632$	13.1814	+	16.4934i	0.524328	+	0.656072i
$633$	1.45088	−	0.562414i	0.0576674	−	0.0223540i
$634$	3.63718	+	15.9098i	0.144451	+	0.631860i
$635$	12.4740	+	7.20188i	0.495016	+	0.285798i
$636$	−4.69896	+	20.2607i	−0.186326	+	0.803388i
$637$	−3.82136	−	11.9051i	−0.151408	−	0.471698i
$638$	−5.55996	−	24.3205i	−0.220121	−	0.962859i
$639$	2.65895	−	8.37005i	0.105187	−	0.331114i
$640$	31.0989	+	17.8535i	1.22929	+	0.705722i
$641$	−22.6543	−	39.2383i	−0.894790	−	1.54982i	−0.834065	−	0.551666i	$-0.813992\pi$
$641$	−22.6543	−	39.2383i	−0.894790	−	1.54982i	−0.0607246	−	0.998155i	$-0.519341\pi$
$642$	−29.0916	+	19.6708i	−1.14815	+	0.776345i
$643$	−35.4400	+	20.4613i	−1.39762	+	0.806914i	−0.994142	−	0.108078i	$-0.965530\pi$
$643$	−35.4400	+	20.4613i	−1.39762	+	0.806914i	−0.403473	+	0.914991i	$0.632197\pi$
$644$	−24.1501	−	4.40959i	−0.951647	−	0.173762i
$645$	−2.17792	+	0.844239i	−0.0857554	+	0.0332419i
$646$	−17.5323	+	4.00808i	−0.689798	+	0.157696i
$647$	−4.58077	+	7.93413i	−0.180089	+	0.311923i	−0.941911	−	0.335864i	$-0.890972\pi$
$647$	−4.58077	+	7.93413i	−0.180089	+	0.311923i	0.761822	+	0.647787i	$0.224305\pi$
$648$	−25.4115	+	1.50264i	−0.998256	+	0.0590294i
$649$	−20.7474	+	11.9785i	−0.814405	+	0.470197i
$650$	3.75286	−	12.1816i	0.147199	−	0.477803i
$651$	11.7812	−	44.2337i	0.461742	−	1.73365i
$652$	6.81719	+	4.64089i	0.266982	+	0.181751i
$653$	5.94553	+	3.43265i	0.232666	+	0.134330i	0.611802	−	0.791011i	$-0.290445\pi$
$653$	5.94553	+	3.43265i	0.232666	+	0.134330i	−0.379135	+	0.925341i	$0.623778\pi$
$654$	−19.3792	+	39.8486i	−0.757788	+	1.55820i
$655$	62.0659	−	35.8338i	2.42512	−	1.40014i
$656$	2.96388	−	19.8526i	0.115720	−	0.775113i
$657$	2.01805	+	2.21188i	0.0787314	+	0.0862937i
$658$	−11.0846	+	1.31687i	−0.432122	+	0.0513370i
$659$	−21.7591	+	37.6878i	−0.847613	+	1.46811i	0.0357196	+	0.999362i	$0.488628\pi$
$659$	−21.7591	+	37.6878i	−0.847613	+	1.46811i	−0.883333	+	0.468747i	$0.844706\pi$
$660$	17.1376	+	56.2563i	0.667079	+	2.18977i
$661$	−8.49405			−0.330380			−0.165190	−	0.986262i	$-0.552824\pi$
$661$	−8.49405			−0.330380			−0.165190	+	0.986262i	$0.552824\pi$
$662$	1.28045	−	0.292727i	0.0497663	−	0.0113772i
$663$	14.2643	+	2.21126i	0.553980	+	0.0858781i
$664$	22.7158	−	3.44825i	0.881543	−	0.133818i
$665$	−2.42968	+	22.7273i	−0.0942189	+	0.881325i
$666$	10.3347	−	4.87494i	0.400463	−	0.188900i
$667$	7.64008	+	13.2330i	0.295825	+	0.512384i
$668$	−17.3658	−	11.8220i	−0.671901	−	0.457406i
$669$	18.3069	+	14.7254i	0.707785	+	0.569315i
$670$	16.8836	−	54.8035i	0.652271	−	2.11724i
$671$	−31.0923	−	53.8534i	−1.20030	−	2.07899i
$672$	19.7038	+	16.8452i	0.760089	+	0.649819i
$673$	−9.53159	+	16.5092i	−0.367416	+	0.636383i	−0.989161	−	0.146837i	$-0.953091\pi$
$673$	−9.53159	+	16.5092i	−0.367416	+	0.636383i	0.621745	+	0.783220i	$0.286424\pi$
$674$	−1.38192	−	1.48831i	−0.0532294	−	0.0573274i
$675$	−26.1692	+	1.63010i	−1.00725	+	0.0627424i
$676$	1.45243	−	19.5651i	0.0558628	−	0.752506i
$677$	−16.5958			−0.637829			−0.318915	−	0.947783i	$-0.603318\pi$
$677$	−16.5958			−0.637829			−0.318915	+	0.947783i	$0.603318\pi$
$678$	−11.5212	+	7.79029i	−0.442470	+	0.299184i
$679$	−29.1096	−	21.2287i	−1.11713	−	0.814684i
$680$	−15.2403	+	38.9519i	−0.584439	+	1.49374i
$681$	−2.20177	−	5.67999i	−0.0843720	−	0.217658i
$682$	−51.4846	−	55.4482i	−1.97145	−	2.12322i
$683$	2.60938	−	4.51957i	0.0998451	−	0.172937i	−0.811775	−	0.583970i	$-0.801499\pi$
$683$	2.60938	−	4.51957i	0.0998451	−	0.172937i	0.911620	+	0.411033i	$0.134832\pi$
$684$	−12.8640	+	10.0978i	−0.491868	+	0.386099i
$685$	1.05752			0.0404058
$686$	26.0741	+	2.47807i	0.995514	+	0.0946133i
$687$	31.5414	+	25.3707i	1.20338	+	0.967952i
$688$	0.624003	+	1.58341i	0.0237899	+	0.0603670i
$689$		−	10.7243i		−	0.408564i
$690$	−20.1757	−	29.8383i	−0.768077	−	1.13592i
$691$			21.7803i			0.828562i	0.910149	+	0.414281i	$0.135967\pi$
$691$			21.7803i			0.828562i	−0.910149	+	0.414281i	$0.864033\pi$
$692$	−5.61036	+	2.70665i	−0.213274	+	0.102891i
$693$	4.64611	+	42.2586i	0.176491	+	1.60527i
$694$	20.2809	−	4.63645i	0.769852	−	0.175997i
$695$			4.79279i			0.181801i
$696$	0.0507688	−	16.1350i	0.00192439	−	0.611597i
$697$	23.4132			0.886838
$698$	9.30819	−	30.2139i	0.352320	−	1.14361i
$699$	−19.8255	+	7.68510i	−0.749871	+	0.290677i
$700$	20.3497	+	17.2869i	0.769145	+	0.653384i
$701$			32.2438i			1.21783i	0.793235	+	0.608915i	$0.208395\pi$
$701$			32.2438i			1.21783i	−0.793235	+	0.608915i	$0.791605\pi$
$702$	12.5891	−	3.71510i	0.475145	−	0.140218i
$703$	3.67051	−	6.35752i	0.138436	−	0.239778i
$704$	40.9190	−	12.7160i	1.54219	−	0.479253i
$705$	−12.7617	−	10.2651i	−0.480635	−	0.386604i
$706$	−4.75016	+	4.41060i	−0.178774	+	0.165995i
$707$	−0.930769	−	2.10061i	−0.0350052	−	0.0790014i
$708$	−14.8217	+	4.51520i	−0.557034	+	0.169692i
$709$			24.2078i			0.909142i	0.890710	+	0.454571i	$0.150207\pi$
$709$			24.2078i			0.909142i	−0.890710	+	0.454571i	$0.849793\pi$
$710$	−12.5403	−	3.86335i	−0.470628	−	0.144989i
$711$	−6.78020	+	21.3432i	−0.254277	+	0.800433i
$712$	−7.19234	+	18.3825i	−0.269544	+	0.688914i
$713$	40.1345	+	23.1716i	1.50305	+	0.867785i
$714$	−16.0397	+	25.6323i	−0.600271	+	0.959265i
$715$	−15.1618	−	26.2610i	−0.567019	−	0.982106i
$716$	0.224425	−	3.02315i	0.00838717	−	0.112980i
$717$	−18.1053	−	46.7071i	−0.676157	−	1.74431i
$718$	−17.0339	+	15.8162i	−0.635698	+	0.590256i
$719$	7.32742	+	12.6915i	0.273267	+	0.473312i	0.969696	−	0.244313i	$-0.0785625\pi$
$719$	7.32742	+	12.6915i	0.273267	+	0.473312i	−0.696430	+	0.717625i	$0.745229\pi$
$720$	2.57703	+	37.9472i	0.0960401	+	1.41421i
$721$	26.0471	−	35.7168i	0.970046	−	1.33016i
$722$	4.81781	−	15.6384i	0.179300	−	0.582001i
$723$	2.54849	+	6.57445i	0.0947795	+	0.244507i
$724$	4.96699	−	2.39626i	0.184597	−	0.0890563i
$725$		−	16.6194i		−	0.617230i
$726$	38.9644	+	18.9492i	1.44610	+	0.703272i
$727$	−10.3117	+	17.8604i	−0.382439	+	0.662404i	−0.991410	−	0.130788i	$-0.958249\pi$
$727$	−10.3117	+	17.8604i	−0.382439	+	0.662404i	0.608971	+	0.793192i	$0.291583\pi$
$728$	−11.8596	−	6.16595i	−0.439545	−	0.228525i
$729$	−16.2974	−	21.5266i	−0.603608	−	0.797281i
$730$	3.27837	−	3.04402i	0.121338	−	0.112664i
$731$	−1.71921	+	0.992587i	−0.0635873	+	0.0367121i
$732$	−11.7200	−	38.4723i	−0.433183	−	1.42198i
$733$	2.17331	−	3.76428i	0.0802730	−	0.139037i	−0.823094	−	0.567905i	$-0.807754\pi$
$733$	2.17331	−	3.76428i	0.0802730	−	0.139037i	0.903367	+	0.428868i	$0.141087\pi$
$734$	−12.8743	−	13.8655i	−0.475200	−	0.511784i
$735$	24.1756	+	29.8715i	0.891731	+	1.10183i
$736$	−21.6582	+	14.8219i	−0.798333	+	0.546343i
$737$	−34.2617	−	59.3430i	−1.26205	−	2.18593i
$738$	19.2555	−	9.08290i	0.708805	−	0.334346i
$739$	21.9380	−	37.9978i	0.807004	−	1.39777i	−0.107926	−	0.994159i	$-0.534421\pi$
$739$	21.9380	−	37.9978i	0.807004	−	1.39777i	0.914930	−	0.403612i	$-0.132246\pi$
$740$	−7.41856	−	15.3773i	−0.272712	−	0.565279i
$741$	5.28523	−	6.57071i	0.194158	−	0.241381i
$742$	20.6444	+	8.85883i	0.757880	+	0.325218i
$743$	37.5962	−	21.7062i	1.37927	−	0.796323i	0.387200	−	0.921996i	$-0.373442\pi$
$743$	37.5962	−	21.7062i	1.37927	−	0.796323i	0.992072	+	0.125673i	$0.0401091\pi$
$744$	−24.3347	−	42.4568i	−0.892152	−	1.55654i
$745$	−48.9581	+	28.2660i	−1.79369	+	1.03558i
$746$	−24.2875	−	7.48239i	−0.889228	−	0.273950i
$747$	16.4251	+	18.0028i	0.600963	+	0.658687i
$748$	21.7172	+	45.0157i	0.794061	+	1.64594i
$749$	15.3664	+	34.6796i	0.561476	+	1.26717i
$750$	0.0253333	+	0.356443i	0.000925042	+	0.0130155i
$751$	−22.9059	−	13.2247i	−0.835847	−	0.482577i	0.0200031	−	0.999800i	$-0.493632\pi$
$751$	−22.9059	−	13.2247i	−0.835847	−	0.482577i	−0.855851	+	0.517223i	$0.826966\pi$
$752$	−7.42719	+	9.34019i	−0.270842	+	0.340602i
$753$	−28.9529	−	4.48828i	−1.05510	−	0.163562i
$754$	1.85416	+	8.11053i	0.0675246	+	0.295368i
$755$		−	42.0410i		−	1.53003i
$756$	−3.24762	+	27.3030i	−0.118115	+	0.993000i
$757$			24.3621i			0.885454i	0.896656	+	0.442727i	$0.145989\pi$
$757$			24.3621i			0.885454i	−0.896656	+	0.442727i	$0.854011\pi$
$758$	22.6369	−	5.17505i	0.822208	−	0.187966i
$759$	−42.5323	−	6.59338i	−1.54383	−	0.239324i
$760$	15.2550	+	19.0880i	0.553356	+	0.692393i
$761$	3.57672	+	2.06502i	0.129656	+	0.0748569i	0.563425	−	0.826167i	$-0.309483\pi$
$761$	3.57672	+	2.06502i	0.129656	+	0.0748569i	−0.433769	+	0.901024i	$0.642817\pi$
$762$	11.1035	−	0.789155i	0.402238	−	0.0285881i
$763$	38.6705	+	28.2011i	1.39996	+	1.02095i
$764$	6.74096	+	13.9727i	0.243879	+	0.505515i
$765$	−43.3335	+	9.50866i	−1.56672	+	0.343786i
$766$	−9.22046	+	29.9292i	−0.333149	+	1.08139i
$767$	6.91893	−	3.99465i	0.249828	−	0.144238i
$768$	27.6382	−	2.03239i	0.997307	−	0.0733375i
$769$	0.551842	−	0.318606i	0.0198999	−	0.0114892i	−0.490017	−	0.871713i	$-0.663009\pi$
$769$	0.551842	−	0.318606i	0.0198999	−	0.0114892i	0.509917	+	0.860224i	$0.329676\pi$
$770$	63.0771	−	7.49370i	2.27314	−	0.270054i
$771$	−2.77666	+	3.45201i	−0.0999991	+	0.124321i
$772$	−8.90931	+	4.29818i	−0.320653	+	0.154695i
$773$	18.4194	−	31.9033i	0.662500	−	1.14748i	−0.317457	−	0.948273i	$-0.602829\pi$
$773$	18.4194	−	31.9033i	0.662500	−	1.14748i	0.979957	−	0.199211i	$-0.0638379\pi$
$774$	−1.02885	+	1.48327i	−0.0369813	+	0.0533152i
$775$	−25.2026	−	43.6521i	−0.905303	−	1.56803i
$776$	−38.0795	+	5.78046i	−1.36698	+	0.207507i
$777$	−3.21234	−	11.9170i	−0.115242	−	0.427520i
$778$	−0.0283127	+	0.0262888i	−0.00101506	+	0.000942498i
$779$	6.83884	−	11.8452i	0.245027	−	0.424399i
$780$	−5.71512	−	18.7606i	−0.204634	−	0.671738i
$781$	−13.5790	+	7.83985i	−0.485896	+	0.280532i
$782$	−20.8294	−	22.4330i	−0.744857	−	0.802201i
$783$	14.2604	−	9.46181i	0.509625	−	0.338138i
$784$	21.6661	−	17.7364i	0.773789	−	0.633443i
$785$	−9.25519	+	16.0305i	−0.330332	+	0.572151i
$786$	24.2229	−	49.8084i	0.864002	−	1.77661i
$787$		−	32.8255i		−	1.17010i	−0.810997	−	0.585051i	$-0.801075\pi$
$787$		−	32.8255i		−	1.17010i	0.810997	−	0.585051i	$-0.198925\pi$
$788$	6.56096	+	13.5996i	0.233724	+	0.484466i
$789$	−13.7246	−	35.4060i	−0.488610	−	1.26049i
$790$	31.9771	+	9.85136i	1.13769	+	0.350496i
$791$	6.08560	+	13.7343i	0.216379	+	0.488335i
$792$	35.3241	+	28.5969i	1.25519	+	1.01615i
$793$	10.3688	+	17.9593i	0.368207	+	0.637753i
$794$	23.7793	+	25.6100i	0.843897	+	0.908866i
$795$	11.9131	+	30.7326i	0.422513	+	1.08997i
$796$	2.25847	−	30.4230i	0.0800495	−	1.07831i
$797$	−15.9448	−	27.6173i	−0.564795	−	0.978254i	−0.997069	−	0.0765115i	$-0.975622\pi$
$797$	−15.9448	−	27.6173i	−0.564795	−	0.978254i	0.432273	−	0.901743i	$-0.357712\pi$
$798$	8.28282	+	15.6019i	0.293208	+	0.552300i
$799$	−12.0544	−	6.95961i	−0.426454	−	0.246213i
$800$	28.4610	−	2.18296i	1.00625	−	0.0771791i
$801$	−20.4503	+	4.48741i	−0.722576	+	0.158555i
$802$	−12.1404	+	39.4072i	−0.428693	+	1.39152i
$803$		−	5.34572i		−	0.188646i
$804$	−12.9147	−	42.3941i	−0.455466	−	1.49512i
$805$	−35.5698	+	15.7608i	−1.25367	+	0.555496i
$806$	17.1693	+	18.4912i	0.604764	+	0.651323i
$807$	16.4757	+	13.2524i	0.579972	+	0.466507i
$808$	−2.28737	−	0.894955i	−0.0804693	−	0.0314844i
$809$	−11.3674	+	19.6890i	−0.399658	+	0.692228i	−0.993684	−	0.112218i	$-0.964205\pi$
$809$	−11.3674	+	19.6890i	−0.399658	+	0.692228i	0.594025	+	0.804446i	$0.297538\pi$
$810$	−31.9496	+	24.6309i	−1.12259	+	0.865441i
$811$		−	48.6530i		−	1.70844i	−0.519914	−	0.854218i	$-0.674036\pi$
$811$		−	48.6530i		−	1.70844i	0.519914	−	0.854218i	$-0.325964\pi$
$812$	−17.1445	−	3.13042i	−0.601653	−	0.109856i
$813$	−39.2954	+	15.2323i	−1.37815	+	0.534220i
$814$	−19.4970	−	6.00656i	−0.683370	−	0.210530i
$815$	13.0695			0.457806
$816$	7.10481	+	31.5344i	0.248718	+	1.10393i
$817$			1.15971i			0.0405732i
$818$	−0.0427144	−	0.186843i	−0.00149347	−	0.00653280i
$819$	−1.54941	−	14.0926i	−0.0541407	−	0.492435i
$820$	−13.8221	−	28.6506i	−0.482690	−	1.00052i
$821$			30.9122i			1.07884i	0.842036	+	0.539421i	$0.181357\pi$
$821$			30.9122i			1.07884i	−0.842036	+	0.539421i	$0.818643\pi$
$822$	0.677029	−	0.457786i	0.0236141	−	0.0159671i
$823$			46.9111i			1.63522i	0.575774	+	0.817609i	$0.304701\pi$
$823$			46.9111i			1.63522i	−0.575774	+	0.817609i	$0.695299\pi$
$824$	−7.09249	−	46.7226i	−0.247078	−	1.62766i
$825$	36.4769	+	29.3406i	1.26996	+	1.02151i
$826$	1.97435	+	16.6188i	0.0686964	+	0.578241i
$827$	14.2867			0.496798			0.248399	−	0.968658i	$-0.420096\pi$
$827$	14.2867			0.496798			0.248399	+	0.968658i	$0.420096\pi$
$828$	−25.8331	−	10.3688i	−0.897764	−	0.360341i
$829$	−12.1872	+	21.1088i	−0.423279	+	0.733140i	−0.996258	−	0.0864296i	$-0.972454\pi$
$829$	−12.1872	+	21.1088i	−0.423279	+	0.733140i	0.572979	+	0.819570i	$0.305788\pi$
$830$	26.6830	−	24.7756i	0.926181	−	0.859974i
$831$	6.39559	+	16.4990i	0.221861	+	0.572342i
$832$	−13.6459	+	4.24060i	−0.473086	+	0.147016i
$833$	24.1930	+	21.9401i	0.838238	+	0.760179i
$834$	2.07473	+	3.06836i	0.0718421	+	0.106249i
$835$	−33.2926			−1.15214
$836$	29.1178	+	2.16158i	1.00706	+	0.0747599i
$837$	23.1076	−	46.4774i	0.798715	−	1.60649i
$838$	12.2965	−	11.4175i	0.424775	−	0.394411i
$839$	5.21888	−	9.03937i	0.180176	−	0.312074i	−0.761764	−	0.647854i	$-0.775667\pi$
$839$	5.21888	−	9.03937i	0.180176	−	0.312074i	0.941940	+	0.335780i	$0.109000\pi$
$840$	40.8353	+	4.49554i	1.40895	+	0.155111i
$841$	−9.07621	−	15.7205i	−0.312973	−	0.542085i
$842$	35.2029	+	10.8452i	1.21317	+	0.373749i
$843$	−38.8560	−	31.2543i	−1.33827	−	1.07645i
$844$	−1.48529	−	1.01113i	−0.0511260	−	0.0348047i
$845$	−15.5458	−	26.9262i	−0.534792	−	0.926288i
$846$	−12.6137	−	1.04735i	−0.433668	−	0.0360087i
$847$	27.5754	−	37.8124i	0.947501	−	1.29925i
$848$	22.3435	−	8.80531i	0.767280	−	0.302376i
$849$	−14.7852	−	2.29201i	−0.507427	−	0.0786615i
$850$	7.42023	+	32.4578i	0.254512	+	1.11329i
$851$	12.4954			0.428336
$852$	−9.70072	+	2.95517i	−0.332341	+	0.101242i
$853$	−5.10824	+	8.84772i	−0.174903	+	0.302940i	−0.940128	−	0.340823i	$-0.889294\pi$
$853$	−5.10824	+	8.84772i	−0.174903	+	0.302940i	0.765225	+	0.643763i	$0.222628\pi$
$854$	−43.1369	+	5.12477i	−1.47612	+	0.175366i
$855$	−7.84680	+	24.7007i	−0.268355	+	0.844747i
$856$	37.7630	+	14.7751i	1.29071	+	0.505004i
$857$	30.8384	−	17.8046i	1.05342	−	0.608193i	0.129816	−	0.991538i	$-0.458561\pi$
$857$	30.8384	−	17.8046i	1.05342	−	0.608193i	0.923605	+	0.383345i	$0.125228\pi$
$858$	−21.0747	−	10.2491i	−0.719477	−	0.349898i
$859$	−19.2042	−	11.0876i	−0.655240	−	0.378303i	0.135221	−	0.990815i	$-0.456826\pi$
$859$	−19.2042	−	11.0876i	−0.655240	−	0.378303i	−0.790461	+	0.612513i	$0.790159\pi$
$860$	2.22957	+	1.51781i	0.0760278	+	0.0517570i
$861$	−5.98517	−	22.2035i	−0.203974	−	0.756694i
$862$	49.4197	+	15.2250i	1.68324	+	0.518566i
$863$	−6.83577	+	3.94664i	−0.232692	+	0.134345i	−0.611814	−	0.791002i	$-0.709560\pi$
$863$	−6.83577	+	3.94664i	−0.232692	+	0.134345i	0.379121	+	0.925347i	$0.376226\pi$
$864$	18.0766	+	23.1784i	0.614979	+	0.788544i
$865$	−4.93588	+	8.54920i	−0.167825	+	0.290681i
$866$	3.79302	+	16.5915i	0.128892	+	0.563803i
$867$	−7.70133	+	2.98531i	−0.261551	+	0.101387i
$868$	−49.7783	+	17.7765i	−1.68959	+	0.603373i
$869$	34.6258	−	19.9912i	1.17460	−	0.678156i
$870$	−14.3230	−	21.1826i	−0.485595	−	0.718157i
$871$	11.4258	+	19.7900i	0.387147	+	0.670559i
$872$	50.5864	−	7.67901i	1.71307	−	0.260044i
$873$	−27.5342	−	30.1789i	−0.931891	−	1.02140i
$874$	−17.4334	+	3.98549i	−0.589694	+	0.134811i
$875$	0.383787	+	0.0410291i	0.0129744	+	0.00138704i
$876$	0.781112	−	3.36795i	0.0263913	−	0.113793i
$877$	−27.3184	−	15.7723i	−0.922477	−	0.532592i	−0.0380523	−	0.999276i	$-0.512115\pi$
$877$	−27.3184	−	15.7723i	−0.922477	−	0.532592i	−0.884424	+	0.466684i	$0.845449\pi$
$878$	9.55481	−	2.18434i	0.322459	−	0.0737180i
$879$	−17.3259	+	6.71614i	−0.584387	+	0.226530i
$880$	42.2646	−	53.1506i	1.42474	−	1.79171i
$881$			37.4546i			1.26188i	0.775832	+	0.630939i	$0.217330\pi$
$881$			37.4546i			1.26188i	−0.775832	+	0.630939i	$0.782670\pi$
$882$	28.4083	+	8.65857i	0.956556	+	0.291549i
$883$	50.0676			1.68491			0.842454	−	0.538769i	$-0.181110\pi$
$883$	50.0676			1.68491			0.842454	+	0.538769i	$0.181110\pi$
$884$	−7.24237	−	15.0120i	−0.243587	−	0.504910i
$885$	−15.3901	+	19.1333i	−0.517332	+	0.643159i
$886$	41.8186	−	9.56022i	1.40492	−	0.321182i
$887$	−12.6301	+	21.8759i	−0.424076	+	0.734522i	−0.996334	−	0.0855523i	$-0.972735\pi$
$887$	−12.6301	+	21.8759i	−0.424076	+	0.734522i	0.572257	+	0.820074i	$0.306068\pi$
$888$	−11.4060	−	6.63319i	−0.382760	−	0.222595i
$889$	1.27809	−	11.9553i	0.0428658	−	0.400967i
$890$	6.97170	+	30.4958i	0.233692	+	1.02222i
$891$	−4.40877	+	48.0034i	−0.147699	+	1.60818i
$892$	2.00840	−	27.0543i	0.0672461	−	0.905846i
$893$	−7.04203	+	4.06572i	−0.235652	+	0.136054i
$894$	−19.1072	+	39.2892i	−0.639041	+	1.31403i
$895$	−2.40209	−	4.16055i	−0.0802931	−	0.139072i
$896$	3.10898	−	29.7714i	0.103864	−	0.994592i
$897$	14.1839	+	2.19879i	0.473586	+	0.0734155i
$898$	−31.3000	+	7.15555i	−1.04449	+	0.238784i
$899$	28.4920	+	16.4498i	0.950261	+	0.548633i
$900$	18.6942	+	23.8154i	0.623141	+	0.793846i
$901$	14.0064	+	24.2598i	0.466621	+	0.808211i
$902$	−36.3265	−	11.1913i	−1.20954	−	0.372630i
$903$	1.38079	+	1.37665i	0.0459498	+	0.0458120i
$904$	14.9554	+	5.85144i	0.497409	+	0.194616i
$905$	4.36985	−	7.56881i	0.145259	−	0.251596i
$906$	−18.1990	−	26.9148i	−0.604620	−	0.894185i
$907$	−22.3047	−	38.6328i	−0.740615	−	1.28278i	−0.952216	−	0.305426i	$-0.901201\pi$
$907$	−22.3047	−	38.6328i	−0.740615	−	1.28278i	0.211601	−	0.977356i	$-0.432132\pi$
$908$	−3.95844	+	5.81471i	−0.131366	+	0.192968i
$909$	−0.558376	−	2.54467i	−0.0185202	−	0.0844013i
$910$	−21.0353	+	2.49904i	−0.697312	+	0.0828422i
$911$	12.9121	+	7.45481i	0.427797	+	0.246989i	0.698408	−	0.715700i	$-0.253892\pi$
$911$	12.9121	+	7.45481i	0.427797	+	0.246989i	−0.270611	+	0.962689i	$0.587226\pi$
$912$	18.0292	+	5.61653i	0.597006	+	0.185982i
$913$		−	43.5094i		−	1.43995i
$914$	−37.4330	+	8.55763i	−1.23817	+	0.283061i
$915$	−49.6638	−	39.9477i	−1.64183	−	1.32063i
$916$	3.46032	−	46.6126i	0.114332	−	1.54012i
$917$	−48.3358	−	35.2498i	−1.59619	−	1.16405i
$918$	−23.6261	+	24.8459i	−0.779777	+	0.820038i
$919$	−4.04861	+	2.33746i	−0.133551	+	0.0771058i	−0.565287	−	0.824894i	$-0.691235\pi$
$919$	−4.04861	+	2.33746i	−0.133551	+	0.0771058i	0.431736	+	0.902000i	$0.357901\pi$
$920$	−15.1544	+	38.7323i	−0.499625	+	1.27697i
$921$	48.7831	+	7.56237i	1.60746	+	0.249188i
$922$	0.717593	−	2.32927i	0.0236327	−	0.0767105i
$923$	4.52840	−	2.61447i	0.149054	−	0.0860564i
$924$	37.1383	−	32.1027i	1.22176	−	1.05610i
$925$	−11.7698	−	6.79529i	−0.386988	−	0.223428i
$926$	−11.9418	+	11.0881i	−0.392432	+	0.364379i
$927$	37.0287	−	33.7838i	1.21618	−	1.10960i
$928$	−15.3755	+	10.5223i	−0.504724	+	0.345410i
$929$			1.35417i			0.0444290i	0.999753	+	0.0222145i	$0.00707168\pi$
$929$			1.35417i			0.0444290i	−0.999753	+	0.0222145i	$0.992928\pi$
$930$	−69.7428	−	33.9175i	−2.28696	−	1.11220i
$931$	18.1666	−	5.83118i	0.595385	−	0.191109i
$932$	20.2958	+	13.8166i	0.664810	+	0.452578i
$933$	8.40985	−	54.2500i	0.275326	−	1.77606i
$934$	−19.6534	+	18.2485i	−0.643080	+	0.597110i
$935$	68.5959	+	39.6039i	2.24333	+	1.29518i
$936$	−11.7800	−	9.53662i	−0.385043	−	0.311714i
$937$		−	26.0498i		−	0.851009i	−0.904956	−	0.425505i	$-0.860097\pi$
$937$		−	26.0498i		−	0.851009i	0.904956	−	0.425505i	$-0.139903\pi$
$938$	−47.5342	+	5.64716i	−1.55205	+	0.184386i
$939$	18.6716	+	2.89448i	0.609325	+	0.0944578i
$940$	−1.40006	+	18.8596i	−0.0456648	+	0.615132i
$941$	−27.8960			−0.909383			−0.454691	−	0.890649i	$-0.650250\pi$
$941$	−27.8960			−0.909383			−0.454691	+	0.890649i	$0.650250\pi$
$942$	1.01415	+	14.2692i	0.0330428	+	0.464915i
$943$	23.2812			0.758140
$944$	14.0035	+	11.1354i	0.455774	+	0.362425i
$945$	20.0948	+	38.6639i	0.653685	+	1.25774i
$946$	3.14187	−	0.718269i	0.102151	−	0.0233529i
$947$	12.2487			0.398029			0.199015	−	0.979997i	$-0.436226\pi$
$947$	12.2487			0.398029			0.199015	+	0.979997i	$0.436226\pi$
$948$	24.7363	−	7.53553i	0.803399	−	0.244743i
$949$			1.78272i			0.0578694i
$950$	18.5885	+	5.72666i	0.603090	+	0.185797i
$951$	19.7523	+	3.06200i	0.640511	+	0.0992923i
$952$	34.8809	−	1.54093i	1.13050	−	0.0499418i
$953$	−16.7007			−0.540987			−0.270494	−	0.962722i	$-0.587187\pi$
$953$	−16.7007			−0.540987			−0.270494	+	0.962722i	$0.587187\pi$
$954$	20.9305	+	14.5181i	0.677650	+	0.470042i
$955$	21.2919	+	12.2929i	0.688991	+	0.397789i
$956$	−32.5506	+	47.8149i	−1.05276	+	1.54644i
$957$	−30.1943	−	4.68072i	−0.976042	−	0.151306i
$958$	0.433211	+	0.466562i	0.0139964	+	0.0150739i
$959$	−0.357612	−	0.807077i	−0.0115479	−	0.0260619i
$960$	34.3942	−	27.3107i	1.11007	−	0.881449i
$961$	68.7817			2.21876
$962$	6.50196	+	2.00310i	0.209631	+	0.0645824i
$963$	9.21843	+	42.0108i	0.297060	+	1.35378i
$964$	4.58180	−	6.73039i	0.147570	−	0.216771i
$965$	−7.83823	+	13.5762i	−0.252321	+	0.437034i
$966$	−15.9493	+	25.4878i	−0.513160	+	0.820056i
$967$	0.261329	−	0.150878i	0.00840376	−	0.00485191i	−0.495792	−	0.868441i	$-0.665122\pi$
$967$	0.261329	−	0.150878i	0.00840376	−	0.00485191i	0.504196	+	0.863589i	$0.331789\pi$
$968$	−7.50861	−	49.4639i	−0.241336	−	1.58983i
$969$	−3.37425	+	21.7665i	−0.108397	+	0.699242i
$970$	−44.7300	+	41.5326i	−1.43620	+	1.33353i
$971$	−30.4664	+	17.5898i	−0.977713	+	0.564483i	−0.901579	−	0.432615i	$-0.857591\pi$
$971$	−30.4664	+	17.5898i	−0.977713	+	0.564483i	−0.0761342	+	0.997098i	$0.524258\pi$
$972$	−9.79188	+	29.5993i	−0.314075	+	0.949398i
$973$	3.65775	−	1.62073i	0.117262	−	0.0519583i
$974$	32.5654	+	10.0326i	1.04346	+	0.321466i
$975$	−12.1645	−	9.78465i	−0.389575	−	0.313359i
$976$	−28.9038	+	36.3485i	−0.925187	+	1.16349i
$977$	−19.4750			−0.623060			−0.311530	−	0.950236i	$-0.600841\pi$
$977$	−19.4750			−0.623060			−0.311530	+	0.950236i	$0.600841\pi$
$978$	8.36716	−	5.65761i	0.267552	−	0.180910i
$979$	32.3724	+	18.6902i	1.03463	+	0.597342i
$980$	12.5655	−	42.5574i	0.401390	−	1.35945i
$981$	36.5776	+	40.0909i	1.16783	+	1.28000i
$982$	25.6042	+	27.5754i	0.817062	+	0.879965i
$983$	−13.6550	−	23.6512i	−0.435528	−	0.754357i	0.561810	−	0.827266i	$-0.310105\pi$
$983$	−13.6550	−	23.6512i	−0.435528	−	0.754357i	−0.997339	+	0.0729091i	$0.976772\pi$
$984$	−21.2514	−	12.3588i	−0.677471	−	0.393986i
$985$	20.7234	+	11.9647i	0.660302	+	0.381226i
$986$	−14.7870	−	15.9255i	−0.470915	−	0.507170i
$987$	−3.51854	+	13.2107i	−0.111997	+	0.420502i
$988$	−9.71035	−	0.720855i	−0.308928	−	0.0229335i
$989$	−1.70952	+	0.986991i	−0.0543595	+	0.0313845i
$990$	71.7786	+	5.95999i	2.28127	+	0.189421i
$991$	−15.3988	−	8.89049i	−0.489158	−	0.282416i	0.235067	−	0.971979i	$-0.424469\pi$
$991$	−15.3988	−	8.89049i	−0.489158	−	0.282416i	−0.724225	+	0.689563i	$0.757802\pi$
$992$	−24.4282	+	50.9537i	−0.775597	+	1.61778i
$993$	0.246436	−	1.58970i	0.00782041	−	0.0504476i
$994$	1.29220	+	10.8769i	0.0409860	+	0.344994i
$995$	−24.1731	−	41.8691i	−0.766339	−	1.32734i
$996$	6.35756	−	27.4121i	0.201447	−	0.868587i
$997$	−21.3724	−	37.0182i	−0.676872	−	1.17238i	−0.975918	−	0.218138i	$-0.930002\pi$
$997$	−21.3724	−	37.0182i	−0.676872	−	1.17238i	0.299046	−	0.954239i	$-0.403332\pi$
$998$	−5.38999	+	17.4957i	−0.170617	+	0.553815i
$999$	−0.870066	−	13.9678i	−0.0275277	−	0.441923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.8	yes	180
7.5	odd	6		504.2.cz.b.187.65	yes	180
8.3	odd	2	inner	504.2.bf.b.115.7	✓	180
9.4	even	3		504.2.cz.b.283.53	yes	180
56.19	even	6		504.2.cz.b.187.53	yes	180
63.40	odd	6	inner	504.2.bf.b.355.8	yes	180
72.67	odd	6		504.2.cz.b.283.65	yes	180
504.355	even	6	inner	504.2.bf.b.355.7	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.7	✓	180	8.3	odd	2	inner
504.2.bf.b.115.8	yes	180	1.1	even	1	trivial
504.2.bf.b.355.7	yes	180	504.355	even	6	inner
504.2.bf.b.355.8	yes	180	63.40	odd	6	inner
504.2.cz.b.187.53	yes	180	56.19	even	6
504.2.cz.b.187.65	yes	180	7.5	odd	6
504.2.cz.b.283.53	yes	180	9.4	even	3
504.2.cz.b.283.65	yes	180	72.67	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37865 + 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 - 0.869029i) q^{4} +(1.58477 - 2.74491i) q^{5} +(-0.173654 - 2.44333i) q^{6} +(-2.63076 - 0.281244i) q^{7} +(-2.20950 + 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +O(q^{10})\)	\(q+(-1.37865 + 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 - 0.869029i) q^{4} +(1.58477 - 2.74491i) q^{5} +(-0.173654 - 2.44333i) q^{6} +(-2.63076 - 0.281244i) q^{7} +(-2.20950 + 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +(-1.31972 + 4.28374i) q^{10} +(2.67808 + 4.63857i) q^{11} +(1.00948 + 3.31375i) q^{12} +(-0.893100 - 1.54689i) q^{13} +(3.71553 - 0.441413i) q^{14} +(4.27771 + 3.44083i) q^{15} +(2.48958 - 3.13081i) q^{16} +(4.04061 + 2.33285i) q^{17} +(4.22809 + 0.351071i) q^{18} +(2.36047 - 1.36282i) q^{19} +(0.469296 - 6.32170i) q^{20} +(1.17941 - 4.42820i) q^{21} +(-5.15409 - 5.55089i) q^{22} +(4.01783 + 2.31970i) q^{23} +(-2.43613 - 4.25033i) q^{24} +(-2.52301 - 4.36999i) q^{25} +(1.71881 + 1.85114i) q^{26} +(2.31328 - 4.65282i) q^{27} +(-4.98328 + 1.77959i) q^{28} +(2.85231 + 1.64678i) q^{29} +(-6.98191 - 3.39546i) q^{30} +9.98908 q^{31} +(-2.44549 + 5.10094i) q^{32} +(-8.65000 + 3.35305i) q^{33} +(-6.30583 - 1.94267i) q^{34} +(-4.94115 + 6.77549i) q^{35} +(-5.93969 + 0.848585i) q^{36} +(2.33249 - 1.34666i) q^{37} +(-2.82473 + 2.62281i) q^{38} +(2.88464 - 1.11819i) q^{39} +(1.34545 + 8.86329i) q^{40} +(4.34585 - 2.50908i) q^{41} +(-0.230330 + 6.47665i) q^{42} +(-0.212741 + 0.368479i) q^{43} +(8.85516 + 6.02827i) q^{44} +(-7.02436 + 6.40879i) q^{45} +(-6.27028 - 1.93172i) q^{46} -2.98331 q^{47} +(4.69815 + 5.09189i) q^{48} +(6.84180 + 1.47977i) q^{49} +(4.85565 + 5.22948i) q^{50} +(-5.06503 + 6.29696i) q^{51} +(-2.95306 - 2.01034i) q^{52} +(5.19961 + 3.00200i) q^{53} +(-1.72275 + 7.14368i) q^{54} +16.9766 q^{55} +(6.30929 - 4.02403i) q^{56} +(1.70630 + 4.40180i) q^{57} +(-4.45135 - 1.37135i) q^{58} +4.47279i q^{59} +(10.6957 + 2.48061i) q^{60} -11.6099 q^{61} +(-13.7714 + 3.14830i) q^{62} +(7.26641 + 3.19364i) q^{63} +(1.76378 - 7.80314i) q^{64} -5.66144 q^{65} +(10.8685 - 7.34893i) q^{66} -12.7934 q^{67} +(9.30579 + 0.690822i) q^{68} +(-5.03648 + 6.26146i) q^{69} +(4.67663 - 10.8983i) q^{70} +2.92741i q^{71} +(7.92128 - 3.04194i) q^{72} +(-0.864336 - 0.499025i) q^{73} +(-2.79124 + 2.59171i) q^{74} +(8.14914 - 3.15890i) q^{75} +(3.06766 - 4.50621i) q^{76} +(-5.74082 - 12.9562i) q^{77} +(-3.62448 + 2.45076i) q^{78} -7.46476i q^{79} +(-4.64838 - 11.7953i) q^{80} +(7.35000 + 5.19398i) q^{81} +(-5.20059 + 4.82883i) q^{82} +(-7.03493 - 4.06162i) q^{83} +(-1.72373 - 9.00160i) q^{84} +(12.8069 - 7.39407i) q^{85} +(0.177160 - 0.575052i) q^{86} +(-3.57546 + 4.44509i) q^{87} +(-14.1081 - 5.51993i) q^{88} +(6.04395 - 3.48948i) q^{89} +(7.66422 - 11.0494i) q^{90} +(1.91448 + 4.32069i) q^{91} +(9.25333 + 0.686927i) q^{92} +(-2.65044 + 17.0974i) q^{93} +(4.11293 - 0.940264i) q^{94} -8.63904i q^{95} +(-8.08193 - 5.53918i) q^{96} +(11.7930 + 6.80869i) q^{97} +(-9.89881 + 0.116282i) q^{98} +(-3.44397 - 15.6951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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