LMFDB - Embedded newform 896.2.bn.b.29.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$784$
Relative dimension:	$49$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			29.32
Character	$\chi$	$=$	896.29
Dual form			896.2.bn.b.309.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.616695 - 1.27267i) q^{2} +(-0.0275048 + 0.279261i) q^{3} +(-1.23938 - 1.56970i) q^{4} +(-0.347914 + 0.185964i) q^{5} +(0.338445 + 0.207223i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.76202 + 0.609291i) q^{8} +(2.86513 + 0.569909i) q^{9} +O(q^{10})$	\(q+(0.616695 - 1.27267i) q^{2} +(-0.0275048 + 0.279261i) q^{3} +(-1.23938 - 1.56970i) q^{4} +(-0.347914 + 0.185964i) q^{5} +(0.338445 + 0.207223i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.76202 + 0.609291i) q^{8} +(2.86513 + 0.569909i) q^{9} +(0.0221139 + 0.557462i) q^{10} +(-3.65531 + 4.45401i) q^{11} +(0.472444 - 0.302935i) q^{12} +(-1.89582 + 3.54683i) q^{13} +(1.36853 + 0.356560i) q^{14} +(-0.0423631 - 0.102274i) q^{15} +(-0.927897 + 3.89089i) q^{16} +(-1.36012 + 3.28363i) q^{17} +(2.49221 - 3.29490i) q^{18} +(-1.57404 - 5.18892i) q^{19} +(0.723103 + 0.315640i) q^{20} +(-0.279261 + 0.0275048i) q^{21} +(3.41427 + 7.39877i) q^{22} +(-4.39844 + 2.93894i) q^{23} +(-0.0941824 - 0.788083i) q^{24} +(-2.69139 + 4.02795i) q^{25} +(3.34480 + 4.60007i) q^{26} +(-0.482330 + 1.59003i) q^{27} +(1.29775 - 1.52179i) q^{28} +(5.30890 - 4.35690i) q^{29} +(-0.156286 - 0.00915735i) q^{30} +(1.20966 - 1.20966i) q^{31} +(4.37958 + 3.58040i) q^{32} +(-1.14329 - 1.14329i) q^{33} +(3.34019 + 3.75598i) q^{34} +(-0.250265 - 0.304949i) q^{35} +(-2.65638 - 5.20371i) q^{36} +(-3.01638 - 0.915009i) q^{37} +(-7.57448 - 1.19674i) q^{38} +(-0.938348 - 0.626984i) q^{39} +(0.847640 - 0.725617i) q^{40} +(5.56411 + 8.32728i) q^{41} +(-0.137214 + 0.372369i) q^{42} +(-0.737278 - 7.48570i) q^{43} +(11.5218 + 0.217542i) q^{44} +(-1.10280 + 0.334531i) q^{45} +(1.02781 + 7.41019i) q^{46} +(8.67379 + 3.59280i) q^{47} +(-1.06105 - 0.366144i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(3.46648 + 5.90926i) q^{50} +(-0.879579 - 0.470145i) q^{51} +(7.91709 - 1.41999i) q^{52} +(-4.15094 - 3.40659i) q^{53} +(1.72613 + 1.59441i) q^{54} +(0.443449 - 2.22937i) q^{55} +(-1.13643 - 2.59008i) q^{56} +(1.49236 - 0.296848i) q^{57} +(-2.27092 - 9.44334i) q^{58} +(2.37410 + 4.44164i) q^{59} +(-0.108035 + 0.193253i) q^{60} +(10.1692 + 1.00158i) q^{61} +(-0.793507 - 2.28549i) q^{62} +2.92126i q^{63} +(7.25753 - 3.36575i) q^{64} -1.58655i q^{65} +(-2.16010 + 0.749972i) q^{66} +(-12.1910 - 1.20070i) q^{67} +(6.84001 - 1.93467i) q^{68} +(-0.699754 - 1.30915i) q^{69} +(-0.542437 + 0.130444i) q^{70} +(-1.96809 + 0.391476i) q^{71} +(-8.26078 + 0.171596i) q^{72} +(-2.57065 + 12.9235i) q^{73} +(-3.02469 + 3.27457i) q^{74} +(-1.05082 - 0.862388i) q^{75} +(-6.19420 + 8.90178i) q^{76} +(-5.08155 - 2.71614i) q^{77} +(-1.37662 + 0.807549i) q^{78} +(-6.27687 + 2.59997i) q^{79} +(-0.400736 - 1.52625i) q^{80} +(7.66590 + 3.17532i) q^{81} +(14.0292 - 1.94589i) q^{82} +(3.10200 - 0.940983i) q^{83} +(0.389283 + 0.404266i) q^{84} +(-0.137430 - 1.39535i) q^{85} +(-9.98150 - 3.67808i) q^{86} +(1.07069 + 1.60240i) q^{87} +(7.38227 - 14.5292i) q^{88} +(-4.45037 - 2.97364i) q^{89} +(-0.254344 + 1.60980i) q^{90} +(-3.84854 - 1.16744i) q^{91} +(10.0646 + 3.26176i) q^{92} +(0.304540 + 0.371083i) q^{93} +(9.92153 - 8.82321i) q^{94} +(1.51258 + 1.51258i) q^{95} +(-1.12032 + 1.12457i) q^{96} +(-2.76382 + 2.76382i) q^{97} +(-0.0827221 + 1.41179i) q^{98} +(-13.0113 + 10.6781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 784 q+O(q^{10}) $ 784 * q	$ 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) $ 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{32}\right)$

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 $

$2$	0.616695	−	1.27267i	0.436069	−	0.899913i
$2$	0.616695	−	1.27267i	0.436069	−	0.899913i
$3$	−0.0275048	+	0.279261i	−0.0158799	+	0.161231i	−0.999854	−	0.0170793i	$-0.994563\pi$
$3$	−0.0275048	+	0.279261i	−0.0158799	+	0.161231i	0.983974	+	0.178311i	$0.0570632\pi$
$4$	−1.23938	−	1.56970i	−0.619688	−	0.784849i
$5$	−0.347914	+	0.185964i	−0.155592	+	0.0831656i	−0.547355	−	0.836901i	$-0.684365\pi$
$5$	−0.347914	+	0.185964i	−0.155592	+	0.0831656i	0.391763	+	0.920066i	$0.371865\pi$
$6$	0.338445	+	0.207223i	0.138170	+	0.0845985i
$7$	0.195090	+	0.980785i	0.0737372	+	0.370702i
$7$	0.195090	+	0.980785i	0.0737372	+	0.370702i
$8$	−2.76202	+	0.609291i	−0.976522	+	0.215417i
$9$	2.86513	+	0.569909i	0.955042	+	0.189970i
$10$	0.0221139	+	0.557462i	0.00699302	+	0.176285i
$11$	−3.65531	+	4.45401i	−1.10212	+	1.34294i	−0.168076	+	0.985774i	$0.553755\pi$
$11$	−3.65531	+	4.45401i	−1.10212	+	1.34294i	−0.934043	+	0.357162i	$0.883745\pi$
$12$	0.472444	−	0.302935i	0.136383	−	0.0874498i
$13$	−1.89582	+	3.54683i	−0.525806	+	0.983715i	0.469122	+	0.883133i	$0.344570\pi$
$13$	−1.89582	+	3.54683i	−0.525806	+	0.983715i	−0.994929	+	0.100581i	$0.967930\pi$
$14$	1.36853	+	0.356560i	0.365754	+	0.0952946i
$15$	−0.0423631	−	0.102274i	−0.0109381	−	0.0264069i
$16$	−0.927897	+	3.89089i	−0.231974	+	0.972722i
$17$	−1.36012	+	3.28363i	−0.329878	+	0.796397i	0.668722	+	0.743512i	$0.266842\pi$
$17$	−1.36012	+	3.28363i	−0.329878	+	0.796397i	−0.998601	+	0.0528847i	$0.983158\pi$
$18$	2.49221	−	3.29490i	0.587420	−	0.776615i
$19$	−1.57404	−	5.18892i	−0.361110	−	1.19042i	−0.929861	−	0.367910i	$-0.880073\pi$
$19$	−1.57404	−	5.18892i	−0.361110	−	1.19042i	0.568752	−	0.822509i	$-0.307427\pi$
$20$	0.723103	+	0.315640i	0.161691	+	0.0705793i
$21$	−0.279261	+	0.0275048i	−0.0609397	+	0.00600204i
$22$	3.41427	+	7.39877i	0.727926	+	1.57742i
$23$	−4.39844	+	2.93894i	−0.917138	+	0.612812i	−0.922006	−	0.387176i	$-0.873451\pi$
$23$	−4.39844	+	2.93894i	−0.917138	+	0.612812i	0.00486753	+	0.999988i	$0.498451\pi$
$24$	−0.0941824	−	0.788083i	−0.0192249	−	0.160867i
$25$	−2.69139	+	4.02795i	−0.538278	+	0.805590i
$26$	3.34480	+	4.60007i	0.655970	+	0.902148i
$27$	−0.482330	+	1.59003i	−0.0928245	+	0.306001i
$28$	1.29775	−	1.52179i	0.245251	−	0.287592i
$29$	5.30890	−	4.35690i	0.985837	−	0.809056i	0.00423447	−	0.999991i	$-0.498652\pi$
$29$	5.30890	−	4.35690i	0.985837	−	0.809056i	0.981603	+	0.190935i	$0.0611521\pi$
$30$	−0.156286	−	0.00915735i	−0.0285337	−	0.00167190i
$31$	1.20966	−	1.20966i	0.217262	−	0.217262i	−0.590082	−	0.807343i	$-0.700905\pi$
$31$	1.20966	−	1.20966i	0.217262	−	0.217262i	0.807343	+	0.590082i	$0.200905\pi$
$32$	4.37958	+	3.58040i	0.774208	+	0.632931i
$33$	−1.14329	−	1.14329i	−0.199022	−	0.199022i
$34$	3.34019	+	3.75598i	0.572839	+	0.644146i
$35$	−0.250265	−	0.304949i	−0.0423025	−	0.0515458i
$36$	−2.65638	−	5.20371i	−0.442730	−	0.867285i
$37$	−3.01638	−	0.915009i	−0.495890	−	0.150427i	0.0324265	−	0.999474i	$-0.489677\pi$
$37$	−3.01638	−	0.915009i	−0.495890	−	0.150427i	−0.528316	+	0.849048i	$0.677177\pi$
$38$	−7.57448	−	1.19674i	−1.22874	−	0.194137i
$39$	−0.938348	−	0.626984i	−0.150256	−	0.100398i
$40$	0.847640	−	0.725617i	0.134024	−	0.114730i
$41$	5.56411	+	8.32728i	0.868969	+	1.30050i	0.952668	+	0.304012i	$0.0983264\pi$
$41$	5.56411	+	8.32728i	0.868969	+	1.30050i	−0.0836995	+	0.996491i	$0.526674\pi$
$42$	−0.137214	+	0.372369i	−0.0211726	+	0.0574578i
$43$	−0.737278	−	7.48570i	−0.112434	−	1.14156i	−0.871449	−	0.490486i	$-0.836819\pi$
$43$	−0.737278	−	7.48570i	−0.112434	−	1.14156i	0.759015	−	0.651073i	$-0.225681\pi$
$44$	11.5218	+	0.217542i	1.73697	+	0.0327956i
$45$	−1.10280	+	0.334531i	−0.164396	+	0.0498689i
$46$	1.02781	+	7.41019i	0.151542	+	1.09257i
$47$	8.67379	+	3.59280i	1.26520	+	0.524064i	0.911502	−	0.411295i	$-0.134923\pi$
$47$	8.67379	+	3.59280i	1.26520	+	0.524064i	0.353700	+	0.935359i	$0.384923\pi$
$48$	−1.06105	−	0.366144i	−0.153150	−	0.0528483i
$49$	−0.923880	+	0.382683i	−0.131983	+	0.0546691i
$50$	3.46648	+	5.90926i	0.490235	+	0.835696i
$51$	−0.879579	−	0.470145i	−0.123166	−	0.0658335i
$52$	7.91709	−	1.41999i	1.09790	−	0.196917i
$53$	−4.15094	−	3.40659i	−0.570175	−	0.467931i	0.304586	−	0.952485i	$-0.401482\pi$
$53$	−4.15094	−	3.40659i	−0.570175	−	0.467931i	−0.874761	+	0.484554i	$0.838982\pi$
$54$	1.72613	+	1.59441i	0.234897	+	0.216972i
$55$	0.443449	−	2.22937i	0.0597947	−	0.300608i
$56$	−1.13643	−	2.59008i	−0.151862	−	0.346114i
$57$	1.49236	−	0.296848i	0.197667	−	0.0393185i
$58$	−2.27092	−	9.44334i	−0.298187	−	1.23997i
$59$	2.37410	+	4.44164i	0.309082	+	0.578252i	0.987722	−	0.156219i	$-0.0499305\pi$
$59$	2.37410	+	4.44164i	0.309082	+	0.578252i	−0.678640	+	0.734471i	$0.737431\pi$
$60$	−0.108035	+	0.193253i	−0.0139472	+	0.0249488i
$61$	10.1692	+	1.00158i	1.30204	+	0.128239i	0.725154	−	0.688587i	$-0.241769\pi$
$61$	10.1692	+	1.00158i	1.30204	+	0.128239i	0.576883	+	0.816826i	$0.304269\pi$
$62$	−0.793507	−	2.28549i	−0.100776	−	0.290258i
$63$			2.92126i			0.368044i
$64$	7.25753	−	3.36575i	0.907191	−	0.420719i
$65$		−	1.58655i		−	0.196787i
$66$	−2.16010	+	0.749972i	−0.265890	+	0.0923151i
$67$	−12.1910	−	1.20070i	−1.48936	−	0.146689i	−0.679659	−	0.733528i	$-0.737872\pi$
$67$	−12.1910	−	1.20070i	−1.48936	−	0.146689i	−0.809704	+	0.586839i	$0.800372\pi$
$68$	6.84001	−	1.93467i	0.829473	−	0.234613i
$69$	−0.699754	−	1.30915i	−0.0842405	−	0.157603i
$70$	−0.542437	+	0.130444i	−0.0648336	+	0.0155911i
$71$	−1.96809	+	0.391476i	−0.233569	+	0.0464597i	−0.310487	−	0.950578i	$-0.600492\pi$
$71$	−1.96809	+	0.391476i	−0.233569	+	0.0464597i	0.0769180	+	0.997037i	$0.475492\pi$
$72$	−8.26078	+	0.171596i	−0.973542	+	0.0202227i
$73$	−2.57065	+	12.9235i	−0.300872	+	1.51259i	0.474032	+	0.880508i	$0.342798\pi$
$73$	−2.57065	+	12.9235i	−0.300872	+	1.51259i	−0.774904	+	0.632079i	$0.782202\pi$
$74$	−3.02469	+	3.27457i	−0.351613	+	0.380662i
$75$	−1.05082	−	0.862388i	−0.121339	−	0.0995800i
$76$	−6.19420	+	8.90178i	−0.710523	+	1.02110i
$77$	−5.08155	−	2.71614i	−0.579096	−	0.309533i
$78$	−1.37662	+	0.807549i	−0.155871	+	0.0914369i
$79$	−6.27687	+	2.59997i	−0.706203	+	0.292519i	−0.706733	−	0.707481i	$-0.749832\pi$
$79$	−6.27687	+	2.59997i	−0.706203	+	0.292519i	0.000529117		1.00000i	$0.499832\pi$
$80$	−0.400736	−	1.52625i	−0.0448036	−	0.170640i
$81$	7.66590	+	3.17532i	0.851767	+	0.352813i
$82$	14.0292	−	1.94589i	1.54927	−	0.214887i
$83$	3.10200	−	0.940983i	0.340489	−	0.103286i	−0.115409	−	0.993318i	$-0.536818\pi$
$83$	3.10200	−	0.940983i	0.340489	−	0.103286i	0.455899	+	0.890032i	$0.349318\pi$
$84$	0.389283	+	0.404266i	0.0424743	+	0.0441091i
$85$	−0.137430	−	1.39535i	−0.0149064	−	0.151347i
$86$	−9.98150	−	3.67808i	−1.07633	−	0.396618i
$87$	1.07069	+	1.60240i	0.114790	+	0.171796i
$88$	7.38227	−	14.5292i	0.786952	−	1.54882i
$89$	−4.45037	−	2.97364i	−0.471738	−	0.315205i	0.296878	−	0.954915i	$-0.404054\pi$
$89$	−4.45037	−	2.97364i	−0.471738	−	0.315205i	−0.768616	+	0.639710i	$0.779054\pi$
$90$	−0.254344	+	1.60980i	−0.0268102	+	0.169688i
$91$	−3.84854	−	1.16744i	−0.403436	−	0.122381i
$92$	10.0646	+	3.26176i	1.04930	+	0.340062i
$93$	0.304540	+	0.371083i	0.0315793	+	0.0384795i
$94$	9.92153	−	8.82321i	1.02333	−	0.910044i
$95$	1.51258	+	1.51258i	0.155188	+	0.155188i
$96$	−1.12032	+	1.12457i	−0.114343	+	0.114776i
$97$	−2.76382	+	2.76382i	−0.280623	+	0.280623i	−0.833358	−	0.552734i	$-0.813584\pi$
$97$	−2.76382	+	2.76382i	−0.280623	+	0.280623i	0.552734	+	0.833358i	$0.313584\pi$
$98$	−0.0827221	+	1.41179i	−0.00835619	+	0.142613i
$99$	−13.0113	+	10.6781i	−1.30769	+	1.07319i
$100$	9.65830	−	0.767475i	0.965830	−	0.0767475i
$101$	2.90864	−	9.58849i	0.289420	−	0.954091i	−0.684846	−	0.728688i	$-0.740130\pi$
$101$	2.90864	−	9.58849i	0.289420	−	0.954091i	0.974266	−	0.225402i	$-0.0723696\pi$
$102$	−1.14077	+	0.829478i	−0.112953	+	0.0821306i
$103$	4.52303	−	6.76920i	0.445668	−	0.666989i	−0.538824	−	0.842418i	$-0.681131\pi$
$103$	4.52303	−	6.76920i	0.445668	−	0.666989i	0.984492	+	0.175429i	$0.0561314\pi$
$104$	3.07525	−	10.9515i	0.301553	−	1.07389i
$105$	0.0920439	−	0.0615017i	0.00898256	−	0.00600195i
$106$	−6.89532	+	3.18195i	−0.669733	+	0.309058i
$107$	3.81956	−	0.376194i	0.369251	−	0.0363681i	0.0883099	−	0.996093i	$-0.471853\pi$
$107$	3.81956	−	0.376194i	0.369251	−	0.0363681i	0.280941	+	0.959725i	$0.409353\pi$
$108$	3.09365	−	1.21353i	0.297687	−	0.116772i
$109$	−0.704328	−	2.32186i	−0.0674624	−	0.222394i	0.916727	−	0.399515i	$-0.130821\pi$
$109$	−0.704328	−	2.32186i	−0.0674624	−	0.222394i	−0.984189	+	0.177121i	$0.943321\pi$
$110$	−2.56378	−	1.93920i	−0.244447	−	0.184896i
$111$	0.338491	−	0.817190i	0.0321282	−	0.0775643i
$112$	−3.99715	−	0.150994i	−0.377695	−	0.0142676i
$113$	−3.16521	−	7.64150i	−0.297758	−	0.718852i	−0.999976	−	0.00689004i	$-0.997807\pi$
$113$	−3.16521	−	7.64150i	−0.297758	−	0.718852i	0.702218	−	0.711962i	$-0.252193\pi$
$114$	0.542538	−	2.08234i	0.0508134	−	0.195029i
$115$	0.983741	−	1.84045i	0.0917343	−	0.171623i
$116$	−13.4187	−	2.93353i	−1.24590	−	0.272371i
$117$	−7.45314	+	9.08168i	−0.689043	+	0.839601i
$118$	7.11683	−	0.282316i	0.655158	−	0.0259893i
$119$	−3.48588	−	0.693385i	−0.319550	−	0.0635625i
$120$	0.179322	+	0.256671i	0.0163698	+	0.0234307i
$121$	−4.33092	−	21.7730i	−0.393720	−	1.97936i
$122$	7.54600	−	12.3244i	0.683182	−	1.11580i
$123$	−2.47852	+	1.32480i	−0.223481	+	0.119453i
$124$	−3.39803	−	0.399577i	−0.305152	−	0.0358831i
$125$	0.380655	−	3.86486i	0.0340469	−	0.345684i
$126$	3.71779	+	1.80152i	0.331207	+	0.160492i
$127$	−13.5550			−1.20281			−0.601405	−	0.798945i	$-0.705392\pi$
$127$	−13.5550			−1.20281			−0.601405	+	0.798945i	$0.705392\pi$
$128$	0.192189	−	11.3121i	0.0169872	−	0.999856i
$129$	2.11074			0.185841
$130$	−2.01915	−	0.978415i	−0.177091	−	0.0858127i
$131$	−0.407111	+	4.13347i	−0.0355695	+	0.361143i	0.960881	+	0.276962i	$0.0893275\pi$
$131$	−0.407111	+	4.13347i	−0.0355695	+	0.361143i	−0.996450	+	0.0841814i	$0.973172\pi$
$132$	−0.377655	+	3.21159i	−0.0328706	+	0.279533i
$133$	4.78213	−	2.55610i	0.414664	−	0.221642i
$134$	−9.04620	+	14.7746i	−0.781473	+	1.27633i
$135$	−0.127879	−	0.642889i	−0.0110060	−	0.0553311i
$136$	1.75600	−	9.89817i	0.150576	−	0.848761i
$137$	12.8910	+	2.56417i	1.10135	+	0.219072i	0.712112	−	0.702066i	$-0.247739\pi$
$137$	12.8910	+	2.56417i	1.10135	+	0.219072i	0.389237	+	0.921138i	$0.372739\pi$
$138$	−2.09765	+	0.0832112i	−0.178564	+	0.00708341i
$139$	−13.4266	+	16.3603i	−1.13883	+	1.38766i	−0.228617	+	0.973516i	$0.573420\pi$
$139$	−13.4266	+	16.3603i	−1.13883	+	1.38766i	−0.910210	+	0.414148i	$0.864080\pi$
$140$	−0.168505	+	0.770787i	−0.0142413	+	0.0651434i
$141$	−1.24190	+	2.32343i	−0.104587	+	0.195668i
$142$	−0.715487	+	2.74614i	−0.0600424	+	0.230451i
$143$	−8.86782	−	21.4088i	−0.741564	−	1.79029i
$144$	−4.87599	+	10.6191i	−0.406333	+	0.884922i
$145$	−1.03681	+	2.50309i	−0.0861026	+	0.207870i
$146$	14.8621	+	11.2415i	1.23000	+	0.930351i
$147$	−0.0814574	−	0.268529i	−0.00671849	−	0.0221479i
$148$	2.30214	+	5.86884i	0.189235	+	0.482416i
$149$	3.69601	−	0.364026i	0.302789	−	0.0298221i	0.0545183	−	0.998513i	$-0.482638\pi$
$149$	3.69601	−	0.364026i	0.302789	−	0.0298221i	0.248271	+	0.968691i	$0.420138\pi$
$150$	−1.74557	+	0.805520i	−0.142525	+	0.0657704i
$151$	3.18729	−	2.12968i	0.259378	−	0.173311i	−0.419082	−	0.907949i	$-0.637648\pi$
$151$	3.18729	−	2.12968i	0.259378	−	0.173311i	0.678459	+	0.734638i	$0.262648\pi$
$152$	7.50910	+	13.3729i	0.609068	+	1.08468i
$153$	−5.76830	+	8.63286i	−0.466339	+	0.697926i
$154$	−6.59052	+	4.79210i	−0.531079	+	0.386158i
$155$	−0.195905	+	0.645811i	−0.0157354	+	0.0518728i
$156$	0.178790	+	2.24999i	0.0143147	+	0.180143i
$157$	−2.73618	+	2.24553i	−0.218371	+	0.179213i	−0.737219	−	0.675654i	$-0.763861\pi$
$157$	−2.73618	+	2.24553i	−0.218371	+	0.179213i	0.518848	+	0.854867i	$0.326361\pi$
$158$	−0.562017	+	9.59177i	−0.0447117	+	0.763080i
$159$	1.06550	−	1.06550i	0.0844994	−	0.0844994i
$160$	−2.18954	−	0.431225i	−0.173099	−	0.0340914i
$161$	−3.74057	−	3.74057i	−0.294798	−	0.294798i
$162$	8.76865	−	7.79796i	0.688931	−	0.612665i
$163$	−6.67484	−	8.13332i	−0.522814	−	0.637051i	0.442927	−	0.896558i	$-0.353940\pi$
$163$	−6.67484	−	8.13332i	−0.522814	−	0.637051i	−0.965741	+	0.259507i	$0.916440\pi$
$164$	6.17529	−	19.0546i	0.482209	−	1.48791i
$165$	0.610379	+	0.185156i	0.0475179	+	0.0144144i
$166$	0.715430	−	4.52813i	0.0555281	−	0.351451i
$167$	−9.85567	−	6.58535i	−0.762654	−	0.509589i	0.112371	−	0.993666i	$-0.464155\pi$
$167$	−9.85567	−	6.58535i	−0.762654	−	0.509589i	−0.875025	+	0.484077i	$0.839155\pi$
$168$	0.754566	−	0.246120i	0.0582161	−	0.0189886i
$169$	−1.76347	−	2.63922i	−0.135652	−	0.203017i
$170$	−1.86058	−	0.685604i	−0.142700	−	0.0525834i
$171$	−1.55261	−	15.7640i	−0.118731	−	1.20550i
$172$	−10.8365	+	10.4349i	−0.826277	+	0.795654i
$173$	9.15099	−	2.77592i	0.695737	−	0.211049i	0.0774432	−	0.996997i	$-0.475324\pi$
$173$	9.15099	−	2.77592i	0.695737	−	0.211049i	0.618293	+	0.785947i	$0.287824\pi$
$174$	2.69962	−	0.374443i	0.204658	−	0.0283864i
$175$	−4.47562	−	1.85386i	−0.338325	−	0.140139i
$176$	−13.9383	−	18.3553i	−1.05064	−	1.38358i
$177$	−1.30567	+	0.540828i	−0.0981405	+	0.0406511i
$178$	−6.52898	+	3.83002i	−0.489368	+	0.287072i
$179$	0.832553	+	0.445009i	0.0622279	+	0.0332615i	0.502217	−	0.864741i	$-0.332518\pi$
$179$	0.832553	+	0.445009i	0.0622279	+	0.0332615i	−0.439989	+	0.898003i	$0.645018\pi$
$180$	1.89189	+	1.31645i	0.141013	+	0.0981225i
$181$	14.6912	+	12.0567i	1.09198	+	0.896169i	0.995075	−	0.0991245i	$-0.0316042\pi$
$181$	14.6912	+	12.0567i	1.09198	+	0.896169i	0.0969097	+	0.995293i	$0.469104\pi$
$182$	−3.85914	+	4.17796i	−0.286059	+	0.309691i
$183$	−0.559406	+	2.81232i	−0.0413524	+	0.207893i
$184$	10.3579	−	10.7974i	0.763596	−	0.795992i
$185$	1.21960	−	0.242593i	0.0896667	−	0.0178358i
$186$	0.660074	−	0.158734i	0.0483989	−	0.0116389i
$187$	−9.65365	−	18.0607i	−0.705945	−	1.32073i
$188$	−5.11047	−	18.0681i	−0.372720	−	1.31775i
$189$	−1.65358	−	0.162863i	−0.120280	−	0.0118465i
$190$	2.85782	−	0.992215i	0.207328	−	0.0719829i
$191$		−	10.1522i		−	0.734590i	−0.930105	−	0.367295i	$-0.880284\pi$
$191$		−	10.1522i		−	0.734590i	0.930105	−	0.367295i	$-0.119716\pi$
$192$	0.740306	+	2.11932i	0.0534270	+	0.152949i
$193$			8.50910i			0.612499i	0.951951	+	0.306249i	$0.0990741\pi$
$193$			8.50910i			0.612499i	−0.951951	+	0.306249i	$0.900926\pi$
$194$	1.81300	+	5.22186i	0.130166	+	0.374908i
$195$	0.443061	+	0.0436377i	0.0317282	+	0.00312496i
$196$	1.74573	+	0.975923i	0.124695	+	0.0697088i
$197$	12.5048	+	23.3949i	0.890934	+	1.66682i	0.733934	+	0.679221i	$0.237682\pi$
$197$	12.5048	+	23.3949i	0.890934	+	1.66682i	0.157000	+	0.987599i	$0.449818\pi$
$198$	5.56570	+	23.1442i	0.395537	+	1.64479i
$199$	24.9201	−	4.95691i	1.76654	−	0.351386i	0.798461	−	0.602047i	$-0.205648\pi$
$199$	24.9201	−	4.95691i	1.76654	−	0.351386i	0.968075	+	0.250661i	$0.0806480\pi$
$200$	4.97948	−	12.7651i	0.352103	−	0.902631i
$201$	0.670620	−	3.37143i	0.0473019	−	0.237803i
$202$	−10.4092	−	9.61491i	−0.732392	−	0.676502i
$203$	5.30890	+	4.35690i	0.372611	+	0.305794i
$204$	0.352144	+	1.96336i	0.0246550	+	0.137463i
$205$	−3.48441	−	1.86245i	−0.243362	−	0.130079i
$206$	−5.82562	−	9.93085i	−0.405890	−	0.691915i
$207$	−14.2770	+	5.91373i	−0.992321	+	0.411033i
$208$	−12.0412	−	10.6675i	−0.834907	−	0.739660i
$209$	28.8651	+	11.9563i	1.99664	+	0.827036i
$210$	−0.0215084	−	0.155069i	−0.00148422	−	0.0107008i
$211$	−4.25792	+	1.29163i	−0.293127	+	0.0889192i	−0.433424	−	0.901190i	$-0.642695\pi$
$211$	−4.25792	+	1.29163i	−0.293127	+	0.0889192i	0.140296	+	0.990110i	$0.455195\pi$
$212$	−0.202739	+	10.7378i	−0.0139242	+	0.737472i
$213$	−0.0551923	−	0.560377i	−0.00378171	−	0.0383964i
$214$	1.87673	−	5.09304i	0.128291	−	0.348153i
$215$	1.64858	+	2.46727i	0.112432	+	0.168267i
$216$	0.363415	−	4.68558i	0.0247273	−	0.318813i
$217$	1.42241	+	0.950425i	0.0965596	+	0.0645190i
$218$	−3.38931	−	0.535501i	−0.229553	−	0.0362687i
$219$	−3.53833	−	1.07334i	−0.239099	−	0.0725297i
$220$	−4.04903	+	2.06694i	−0.272986	+	0.139353i
$221$	−9.06793	−	11.0493i	−0.609975	−	0.743257i
$222$	−0.831267	−	0.934744i	−0.0557910	−	0.0627359i
$223$	9.49504	+	9.49504i	0.635835	+	0.635835i	0.949525	−	0.313691i	$-0.101565\pi$
$223$	9.49504	+	9.49504i	0.635835	+	0.635835i	−0.313691	+	0.949525i	$0.601565\pi$
$224$	−2.65719	+	4.99393i	−0.177541	+	0.333671i
$225$	−10.0067	+	10.0067i	−0.667116	+	0.667116i
$226$	−11.6771	−	0.684203i	−0.776748	−	0.0455125i
$227$	−3.29157	+	2.70132i	−0.218469	+	0.179293i	−0.737262	−	0.675607i	$-0.763882\pi$
$227$	−3.29157	+	2.70132i	−0.218469	+	0.179293i	0.518793	+	0.854900i	$0.326382\pi$
$228$	−2.31555	−	1.97464i	−0.153351	−	0.130774i
$229$	−1.74983	+	5.76842i	−0.115632	+	0.381188i	−0.995584	−	0.0938748i	$-0.970075\pi$
$229$	−1.74983	+	5.76842i	−0.115632	+	0.381188i	0.879952	+	0.475063i	$0.157575\pi$
$230$	−1.73562	−	2.38697i	−0.114443	−	0.157392i
$231$	0.898280	−	1.34437i	0.0591025	−	0.0884531i
$232$	−12.0087	+	15.2685i	−0.788407	+	1.00243i
$233$	0.491938	−	0.328702i	0.0322279	−	0.0215340i	−0.539352	−	0.842080i	$-0.681331\pi$
$233$	0.491938	−	0.328702i	0.0322279	−	0.0215340i	0.571580	+	0.820546i	$0.306331\pi$
$234$	6.96166	+	15.0860i	0.455098	+	0.986203i
$235$	−3.68586	+	0.363026i	−0.240439	+	0.0236812i
$236$	4.02962	−	9.23148i	0.262306	−	0.600918i
$237$	−0.553425	−	1.82440i	−0.0359488	−	0.118507i
$238$	−3.03218	+	4.00877i	−0.196547	+	0.259850i
$239$	−3.17502	+	7.66517i	−0.205375	+	0.495818i	−0.992684	−	0.120740i	$-0.961473\pi$
$239$	−3.17502	+	7.66517i	−0.205375	+	0.495818i	0.787310	+	0.616558i	$0.211473\pi$
$240$	0.437244	−	0.0699307i	0.0282240	−	0.00451401i
$241$	2.09816	+	5.06541i	0.135154	+	0.326291i	0.976938	−	0.213524i	$-0.0684941\pi$
$241$	2.09816	+	5.06541i	0.135154	+	0.326291i	−0.841784	+	0.539815i	$0.818494\pi$
$242$	−30.3807	−	7.91547i	−1.95294	−	0.508825i
$243$	−3.44738	+	6.44959i	−0.221149	+	0.413741i
$244$	−11.0313	−	17.2040i	−0.706208	−	1.10137i
$245$	0.250265	−	0.304949i	0.0159889	−	0.0194825i
$246$	0.157538	+	3.97134i	0.0100443	+	0.253203i
$247$	21.3883	+	4.25440i	1.36091	+	0.270701i
$248$	−2.60407	+	4.07815i	−0.165359	+	0.258963i
$249$	0.177460	+	0.892150i	0.0112461	+	0.0565377i
$250$	−4.68394	−	2.86789i	−0.296238	−	0.181381i
$251$	−15.9406	+	8.52045i	−1.00616	+	0.537806i	−0.890259	−	0.455454i	$-0.849477\pi$
$251$	−15.9406	+	8.52045i	−1.00616	+	0.537806i	−0.115905	+	0.993260i	$0.536977\pi$
$252$	4.58549	−	3.62053i	0.288859	−	0.228072i
$253$	2.98759	−	30.3335i	0.187828	−	1.90705i
$254$	−8.35928	+	17.2510i	−0.524508	+	1.08242i
$255$	0.393448			0.0246387
$256$	−14.2780	−	7.22069i	−0.892376	−	0.451293i
$257$	30.5793			1.90749			0.953743	−	0.300623i	$-0.0971946\pi$
$257$	30.5793			1.90749			0.953743	+	0.300623i	$0.0971946\pi$
$258$	1.30168	−	2.68628i	0.0810393	−	0.167240i
$259$	0.308961	−	3.13693i	0.0191979	−	0.194919i
$260$	−2.49040	+	1.96633i	−0.154448	+	0.121946i
$261$	17.6937	−	9.45747i	1.09521	−	0.585403i
$262$	5.00948	+	3.06721i	0.309487	+	0.189493i
$263$	−0.850571	−	4.27611i	−0.0524484	−	0.263676i	0.945660	−	0.325158i	$-0.105417\pi$
$263$	−0.850571	−	4.27611i	−0.0524484	−	0.263676i	−0.998108	+	0.0614817i	$0.980417\pi$
$264$	3.85440	+	2.46120i	0.237222	+	0.151477i
$265$	2.07767	+	0.413274i	0.127630	+	0.0253872i
$266$	−0.303959	−	7.66241i	−0.0186369	−	0.469813i
$267$	0.952828	−	1.16102i	0.0583121	−	0.0710536i
$268$	13.2244	+	20.6242i	0.807811	+	1.25983i
$269$	12.6412	−	23.6500i	0.770748	−	1.44197i	−0.122531	−	0.992465i	$-0.539101\pi$
$269$	12.6412	−	23.6500i	0.770748	−	1.44197i	0.893279	−	0.449503i	$-0.148399\pi$
$270$	−0.897048	−	0.233719i	−0.0545926	−	0.0142237i
$271$	−1.07944	−	2.60599i	−0.0655711	−	0.158303i	0.887697	−	0.460428i	$-0.152304\pi$
$271$	−1.07944	−	2.60599i	−0.0655711	−	0.158303i	−0.953268	+	0.302125i	$0.902304\pi$
$272$	−11.5142	−	8.33896i	−0.698150	−	0.505624i
$273$	0.431874	−	1.04264i	0.0261382	−	0.0631032i
$274$	11.2131	−	14.8246i	0.677410	−	0.895588i
$275$	−8.10267	−	26.7109i	−0.488609	−	1.61073i
$276$	−1.18771	+	2.72093i	−0.0714916	+	0.163781i
$277$	−21.4101	+	2.10871i	−1.28641	+	0.126700i	−0.717997	−	0.696046i	$-0.754941\pi$
$277$	−21.4101	+	2.10871i	−1.28641	+	0.126700i	−0.568409	+	0.822746i	$0.692441\pi$
$278$	12.5412	+	27.1769i	0.752171	+	1.62996i
$279$	4.15523	−	2.77644i	0.248767	−	0.166221i
$280$	0.877041	+	0.689792i	0.0524132	+	0.0412229i
$281$	−12.3801	+	18.5282i	−0.738537	+	1.10530i	0.251957	+	0.967739i	$0.418926\pi$
$281$	−12.3801	+	18.5282i	−0.738537	+	1.10530i	−0.990493	+	0.137560i	$0.956074\pi$
$282$	2.19109	+	3.01338i	0.130477	+	0.179444i
$283$	−9.24773	+	30.4857i	−0.549720	+	1.81218i	0.0329243	+	0.999458i	$0.489518\pi$
$283$	−9.24773	+	30.4857i	−0.549720	+	1.81218i	−0.582645	+	0.812727i	$0.697982\pi$
$284$	3.05370	+	2.60411i	0.181203	+	0.154526i
$285$	−0.464008	+	0.380802i	−0.0274855	+	0.0225567i
$286$	−32.7151	−	1.91690i	−1.93448	−	0.113348i
$287$	−7.08177	+	7.08177i	−0.418024	+	0.418024i
$288$	10.5076	+	12.7543i	0.619164	+	0.751551i
$289$	3.08853	+	3.08853i	0.181678	+	0.181678i
$290$	2.54621	+	2.86316i	0.149518	+	0.168131i
$291$	−0.695809	−	0.847845i	−0.0407890	−	0.0497016i
$292$	23.4720	−	11.9820i	1.37360	−	0.701192i
$293$	2.28171	+	0.692148i	0.133299	+	0.0404357i	0.356229	−	0.934399i	$-0.384062\pi$
$293$	2.28171	+	0.692148i	0.133299	+	0.0404357i	−0.222930	+	0.974834i	$0.571562\pi$
$294$	−0.391983	−	0.0619321i	−0.0228609	−	0.00361195i
$295$	−1.65197	−	1.10381i	−0.0961813	−	0.0642663i
$296$	8.88882	+	0.689420i	0.516652	+	0.0400717i
$297$	−5.31894	−	7.96036i	−0.308636	−	0.461907i
$298$	1.81603	−	4.92830i	0.105200	−	0.285489i
$299$	−2.08528	−	21.1723i	−0.120595	−	1.22442i
$300$	−0.0513240	+	2.71830i	−0.00296319	+	0.156941i
$301$	7.19803	−	2.18350i	0.414888	−	0.125855i
$302$	−0.744792	−	5.36972i	−0.0428580	−	0.308993i
$303$	2.59769	+	1.07600i	0.149233	+	0.0618145i
$304$	21.6500	−	1.30963i	1.24171	−	0.0751126i
$305$	−3.72428	+	1.54265i	−0.213251	+	0.0883316i
$306$	7.42951	+	12.6650i	0.424717	+	0.724008i
$307$	−5.20607	−	2.78270i	−0.297126	−	0.158817i	0.316097	−	0.948727i	$-0.397627\pi$
$307$	−5.20607	−	2.78270i	−0.297126	−	0.158817i	−0.613223	+	0.789910i	$0.710127\pi$
$308$	2.03442	+	11.3428i	0.115922	+	0.646317i
$309$	1.76597	+	1.44929i	0.100462	+	0.0824473i
$310$	0.701091	+	0.647590i	0.0398193	+	0.0367807i
$311$	0.715206	−	3.59559i	0.0405556	−	0.203887i	−0.955195	−	0.295977i	$-0.904355\pi$
$311$	0.715206	−	3.59559i	0.0405556	−	0.203887i	0.995751	+	0.0920901i	$0.0293548\pi$
$312$	2.97375	+	1.16002i	0.168356	+	0.0656730i
$313$	−30.4621	+	6.05928i	−1.72182	+	0.342491i	−0.954371	−	0.298623i	$-0.903473\pi$
$313$	−30.4621	+	6.05928i	−1.72182	+	0.342491i	−0.767446	+	0.641114i	$0.778473\pi$
$314$	1.17042	+	4.86706i	0.0660509	+	0.274664i
$315$	−0.543248	−	1.01635i	−0.0306086	−	0.0572646i
$316$	11.8606	+	6.63046i	0.667209	+	0.372992i
$317$	−20.0259	−	1.97238i	−1.12477	−	0.110780i	−0.481517	−	0.876437i	$-0.659914\pi$
$317$	−20.0259	−	1.97238i	−1.12477	−	0.110780i	−0.643249	+	0.765657i	$0.722414\pi$
$318$	−0.698939	−	2.01311i	−0.0391946	−	0.112890i
$319$			39.5717i			2.21559i
$320$	−1.89909	+	2.52063i	−0.106162	+	0.140907i
$321$			1.07700i			0.0601124i
$322$	−7.06729	+	2.45372i	−0.393845	+	0.136740i
$323$	19.1794	+	1.88900i	1.06717	+	0.105107i
$324$	−4.51664	−	15.9686i	−0.250924	−	0.887142i
$325$	−9.18407	−	17.1822i	−0.509440	−	0.953096i
$326$	−14.4674	+	3.47909i	−0.801273	+	0.192689i
$327$	0.667777	−	0.132829i	0.0369281	−	0.00734546i
$328$	−20.4419	−	19.6100i	−1.12872	−	1.08278i
$329$	−1.83159	+	9.20805i	−0.100979	+	0.507656i
$330$	0.612060	−	0.662626i	0.0336928	−	0.0364763i
$331$	8.58768	+	7.04773i	0.472022	+	0.387378i	0.840113	−	0.542412i	$-0.182489\pi$
$331$	8.58768	+	7.04773i	0.472022	+	0.387378i	−0.368091	+	0.929790i	$0.619989\pi$
$332$	−5.32161	−	3.70298i	−0.292061	−	0.203227i
$333$	−8.12084	−	4.34068i	−0.445019	−	0.237868i
$334$	−14.4589	+	8.48186i	−0.791156	+	0.464107i
$335$	4.46469	−	1.84934i	0.243932	−	0.101040i
$336$	0.152107	−	1.11209i	0.00829814	−	0.0606697i
$337$	8.76284	+	3.62969i	0.477342	+	0.197722i	0.608364	−	0.793658i	$-0.291826\pi$
$337$	8.76284	+	3.62969i	0.477342	+	0.197722i	−0.131022	+	0.991379i	$0.541826\pi$
$338$	−4.44638	+	0.616723i	−0.241851	+	0.0335453i
$339$	2.22103	−	0.673742i	0.120630	−	0.0365927i
$340$	−2.01996	+	1.94509i	−0.109547	+	0.105487i
$341$	0.966156	+	9.80954i	0.0523203	+	0.531216i
$342$	−21.0198	−	7.74558i	−1.13662	−	0.418833i
$343$	−0.555570	−	0.831470i	−0.0299980	−	0.0448951i
$344$	6.59735	+	20.2265i	0.355705	+	1.09054i
$345$	0.486908	+	0.325342i	0.0262143	+	0.0175158i
$346$	2.11053	−	13.3581i	0.113463	−	0.718135i
$347$	28.7256	+	8.71381i	1.54207	+	0.467782i	0.942966	−	0.332890i	$-0.108024\pi$
$347$	28.7256	+	8.71381i	1.54207	+	0.467782i	0.599104	+	0.800672i	$0.295524\pi$
$348$	1.18830	−	3.66664i	0.0636995	−	0.196552i
$349$	−17.4114	−	21.2158i	−0.932010	−	1.13566i	−0.990520	−	0.137371i	$-0.956135\pi$
$349$	−17.4114	−	21.2158i	−0.932010	−	1.13566i	0.0585098	−	0.998287i	$-0.481365\pi$
$350$	−5.11944	+	4.55272i	−0.273646	+	0.243353i
$351$	−4.72516	−	4.72516i	−0.252210	−	0.252210i
$352$	−31.9559	+	6.41925i	−1.70325	+	0.342147i
$353$	18.2950	−	18.2950i	0.973746	−	0.973746i	−0.0259179	−	0.999664i	$-0.508251\pi$
$353$	18.2950	−	18.2950i	0.973746	−	0.973746i	0.999664	+	0.0259179i	$0.00825083\pi$
$354$	−0.116907	+	1.99522i	−0.00621354	+	0.106045i
$355$	0.611924	−	0.502193i	0.0324775	−	0.0266536i
$356$	0.847961	+	10.6712i	0.0449419	+	0.565572i
$357$	0.289514	−	0.954399i	0.0153227	−	0.0505122i
$358$	1.07978	−	0.785130i	0.0570681	−	0.0414954i
$359$	−4.01484	+	6.00864i	−0.211895	+	0.317124i	−0.922158	−	0.386813i	$-0.873576\pi$
$359$	−4.01484	+	6.00864i	−0.211895	+	0.317124i	0.710263	+	0.703936i	$0.248576\pi$
$360$	2.84213	−	1.59591i	0.149793	−	0.0841117i
$361$	−8.64933	+	5.77930i	−0.455228	+	0.304174i
$362$	24.4042	−	11.2617i	1.28265	−	0.591900i
$363$	6.19947	−	0.610594i	0.325388	−	0.0320479i
$364$	2.93725	+	7.48794i	0.153954	+	0.392475i
$365$	−1.50895	−	4.97433i	−0.0789818	−	0.260368i
$366$	3.23417	+	2.44628i	0.169053	+	0.127869i
$367$	−5.38586	+	13.0026i	−0.281140	+	0.678731i	−0.999863	−	0.0165653i	$-0.994727\pi$
$367$	−5.38586	+	13.0026i	−0.281140	+	0.678731i	0.718723	+	0.695296i	$0.244727\pi$
$368$	−7.35380	−	19.8409i	−0.383343	−	1.03428i
$369$	11.1961	+	27.0298i	0.582845	+	1.40711i
$370$	0.443379	−	1.70175i	0.0230502	−	0.0884699i
$371$	2.53132	−	4.73577i	0.131420	−	0.245869i
$372$	0.205048	−	0.937946i	0.0106313	−	0.0486302i
$373$	14.5250	−	17.6987i	0.752074	−	0.916405i	−0.246535	−	0.969134i	$-0.579292\pi$
$373$	14.5250	−	17.6987i	0.752074	−	0.916405i	0.998609	+	0.0527291i	$0.0167920\pi$
$374$	−28.9387	+	1.14796i	−1.49638	+	0.0593598i
$375$	1.06883	+	0.212604i	0.0551944	+	0.0109788i
$376$	−26.1463	−	4.63853i	−1.34839	−	0.239214i
$377$	5.38847	+	27.0897i	0.277520	+	1.39519i
$378$	−1.22702	+	2.00402i	−0.0631112	+	0.103076i
$379$	12.3894	−	6.62227i	0.636401	−	0.340163i	−0.121444	−	0.992598i	$-0.538752\pi$
$379$	12.3894	−	6.62227i	0.636401	−	0.340163i	0.757845	+	0.652435i	$0.226252\pi$
$380$	0.499638	−	4.24895i	0.0256309	−	0.217967i
$381$	0.372827	−	3.78537i	0.0191005	−	0.193931i
$382$	−12.9204	−	6.26083i	−0.661067	−	0.320332i
$383$	16.1248			0.823941			0.411970	−	0.911197i	$-0.364841\pi$
$383$	16.1248			0.823941			0.411970	+	0.911197i	$0.364841\pi$
$384$	3.15373	+	0.364807i	0.160938	+	0.0186165i
$385$	2.27305			0.115845
$386$	10.8293	+	5.24752i	0.551196	+	0.267092i
$387$	2.15378	−	21.8677i	0.109483	−	1.11160i
$388$	7.76377	+	0.912950i	0.394146	+	0.0463480i
$389$	16.0375	−	8.57221i	0.813132	−	0.434628i	−0.0117514	−	0.999931i	$-0.503741\pi$
$389$	16.0375	−	8.57221i	0.813132	−	0.434628i	0.824883	+	0.565303i	$0.191241\pi$
$390$	0.328769	−	0.536959i	0.0166479	−	0.0271900i
$391$	−3.66798	−	18.4402i	−0.185498	−	0.932560i
$392$	2.31861	−	1.61989i	0.117107	−	0.0818169i
$393$	−1.14312	−	0.227381i	−0.0576628	−	0.0114698i
$394$	37.4857	−	1.48701i	1.88850	−	0.0749146i
$395$	1.70031	−	2.07184i	0.0855520	−	0.104245i
$396$	32.8873	+	7.18964i	1.65265	+	0.361293i
$397$	−0.490794	+	0.918210i	−0.0246322	+	0.0460837i	−0.893936	−	0.448194i	$-0.852067\pi$
$397$	−0.490794	+	0.918210i	−0.0246322	+	0.0460837i	0.869304	+	0.494278i	$0.164567\pi$
$398$	9.05956	−	34.7719i	0.454115	−	1.74296i
$399$	0.582288	+	1.40577i	0.0291509	+	0.0703764i
$400$	−13.1750	−	14.2094i	−0.658748	−	0.710471i
$401$	−0.0844426	+	0.203863i	−0.00421686	+	0.0101804i	−0.925974	−	0.377587i	$-0.876754\pi$
$401$	−0.0844426	+	0.203863i	−0.00421686	+	0.0101804i	0.921757	+	0.387768i	$0.126754\pi$
$402$	−3.87715	−	2.93262i	−0.193375	−	0.146266i
$403$	1.99716	+	6.58377i	0.0994859	+	0.327961i
$404$	−18.6559	+	7.31806i	−0.928167	+	0.364087i
$405$	−3.25757	+	0.320842i	−0.161870	+	0.0159428i
$406$	8.81886	−	4.06959i	0.437673	−	0.201971i
$407$	15.1013	−	10.0904i	0.748543	−	0.500160i
$408$	2.71587	+	0.762630i	0.134456	+	0.0377558i
$409$	19.5618	−	29.2763i	0.967268	−	1.44762i	0.0744383	−	0.997226i	$-0.476284\pi$
$409$	19.5618	−	29.2763i	0.967268	−	1.44762i	0.892830	−	0.450394i	$-0.148716\pi$
$410$	−4.51910	+	3.28593i	−0.223183	+	0.162281i
$411$	−1.07064	+	3.52941i	−0.0528106	+	0.174093i
$412$	−16.2313	+	1.28978i	−0.799660	+	0.0635431i
$413$	−3.89313	+	3.19501i	−0.191568	+	0.157216i
$414$	−1.27833	+	21.8169i	−0.0628266	+	1.07224i
$415$	−0.904242	+	0.904242i	−0.0443875	+	0.0443875i
$416$	−21.0020	+	8.74586i	−1.02971	+	0.428801i
$417$	−4.19950	−	4.19950i	−0.205651	−	0.205651i
$418$	33.0174	−	29.3624i	1.61493	−	1.43616i
$419$	6.43212	+	7.83756i	0.314230	+	0.382890i	0.906043	−	0.423185i	$-0.139088\pi$
$419$	6.43212	+	7.83756i	0.314230	+	0.382890i	−0.591814	+	0.806075i	$0.701588\pi$
$420$	−0.210616	−	0.0682572i	−0.0102770	−	0.00333061i
$421$	5.07424	+	1.53925i	0.247303	+	0.0750186i	0.411503	−	0.911409i	$-0.365004\pi$
$421$	5.07424	+	1.53925i	0.247303	+	0.0750186i	−0.164199	+	0.986427i	$0.552504\pi$
$422$	−0.982024	+	6.21547i	−0.0478042	+	0.302564i
$423$	22.8039	+	15.2371i	1.10877	+	0.740853i
$424$	13.5406	+	6.87994i	0.657589	+	0.334119i
$425$	−9.56567	−	14.3160i	−0.464003	−	0.694430i
$426$	−0.747211	−	0.275340i	−0.0362025	−	0.0133403i
$427$	1.00158	+	10.1692i	0.0484700	+	0.492124i
$428$	−5.32438	−	5.52931i	−0.257364	−	0.267269i
$429$	6.22255	−	1.88759i	0.300428	−	0.0911337i
$430$	4.15669	−	0.576542i	0.200454	−	0.0278033i
$431$	20.2914	+	8.40498i	0.977403	+	0.404854i	0.813463	−	0.581617i	$-0.197580\pi$
$431$	20.2914	+	8.40498i	0.977403	+	0.404854i	0.163940	+	0.986470i	$0.447580\pi$
$432$	−5.73907	−	3.35208i	−0.276121	−	0.161277i
$433$	2.55454	−	1.05813i	0.122763	−	0.0508503i	−0.320456	−	0.947263i	$-0.603836\pi$
$433$	2.55454	−	1.05813i	0.122763	−	0.0508503i	0.443220	+	0.896413i	$0.353836\pi$
$434$	2.08677	−	1.22414i	0.100168	−	0.0587605i
$435$	−0.670497	−	0.358388i	−0.0321479	−	0.0171834i
$436$	−2.77169	+	3.98324i	−0.132740	+	0.190762i
$437$	22.1733	+	18.1971i	1.06069	+	0.870487i
$438$	−3.54808	+	3.84121i	−0.169534	+	0.183540i
$439$	6.62167	−	33.2894i	0.316035	−	1.58882i	−0.417184	−	0.908822i	$-0.636983\pi$
$439$	6.62167	−	33.2894i	0.316035	−	1.58882i	0.733219	−	0.679993i	$-0.238017\pi$
$440$	0.133519	+	6.42776i	0.00636529	+	0.306431i
$441$	−2.86513	+	0.569909i	−0.136435	+	0.0271385i
$442$	−19.6543	+	4.72643i	−0.934858	+	0.224813i
$443$	7.57476	+	14.1714i	0.359888	+	0.673303i	0.995083	−	0.0990493i	$-0.0315802\pi$
$443$	7.57476	+	14.1714i	0.359888	+	0.673303i	−0.635195	+	0.772352i	$0.719080\pi$
$444$	−1.70226	+	0.481477i	−0.0807856	+	0.0228499i
$445$	2.10133	+	0.206963i	0.0996128	+	0.00981101i
$446$	17.9396	−	6.22850i	0.849464	−	0.294928i
$447$			1.04216i			0.0492927i
$448$	4.71695	+	6.46145i	0.222855	+	0.305275i
$449$			28.7382i			1.35624i	0.734951	+	0.678120i	$0.237205\pi$
$449$			28.7382i			1.35624i	−0.734951	+	0.678120i	$0.762795\pi$
$450$	6.56417	+	18.9064i	0.309438	+	0.891255i
$451$	−57.4284	−	5.65621i	−2.70420	−	0.266340i
$452$	−8.07195	+	14.4391i	−0.379673	+	0.679159i
$453$	0.507070	+	0.948661i	0.0238242	+	0.0445720i
$454$	1.40799	+	5.85496i	0.0660804	+	0.274787i
$455$	1.55606	−	0.309520i	0.0729493	−	0.0145105i
$456$	−3.94105	+	1.72918i	−0.184557	+	0.0809763i
$457$	1.57526	−	7.91938i	0.0736877	−	0.370453i	−0.926292	−	0.376806i	$-0.877022\pi$
$457$	1.57526	−	7.91938i	0.0736877	−	0.370453i	0.999980	+	0.00635312i	$0.00202227\pi$
$458$	6.26218	+	5.78431i	0.292613	+	0.270283i
$459$	−4.56504	−	3.74643i	−0.213078	−	0.174868i
$460$	−4.10817	+	0.736833i	−0.191545	+	0.0343550i
$461$	23.1190	+	12.3574i	1.07676	+	0.575541i	0.911748	−	0.410751i	$-0.134733\pi$
$461$	23.1190	+	12.3574i	1.07676	+	0.575541i	0.165013	+	0.986291i	$0.447233\pi$
$462$	−1.15698	−	1.97228i	−0.0538274	−	0.0917587i
$463$	35.0345	−	14.5118i	1.62819	−	0.674419i	0.633163	−	0.774018i	$-0.281756\pi$
$463$	35.0345	−	14.5118i	1.62819	−	0.674419i	0.995028	+	0.0995994i	$0.0317561\pi$
$464$	12.0261	+	24.6991i	0.558297	+	1.14663i
$465$	−0.174962	−	0.0724714i	−0.00811365	−	0.00336078i
$466$	−0.114954	−	0.828783i	−0.00532514	−	0.0383926i
$467$	−18.4090	+	5.58431i	−0.851867	+	0.258411i	−0.685878	−	0.727717i	$-0.740582\pi$
$467$	−18.4090	+	5.58431i	−0.851867	+	0.258411i	−0.165989	+	0.986128i	$0.553082\pi$
$468$	23.4927	+	0.443565i	1.08595	+	0.0205038i
$469$	−1.20070	−	12.1910i	−0.0554434	−	0.562926i
$470$	−1.81104	+	4.91476i	−0.0835371	+	0.226701i
$471$	−0.551830	−	0.825871i	−0.0254270	−	0.0380541i
$472$	−9.26358	−	10.8214i	−0.426391	−	0.498094i
$473$	36.0364	+	24.0788i	1.65696	+	1.10714i
$474$	−2.66315	−	0.420769i	−0.122322	−	0.0193266i
$475$	25.1370	+	7.62524i	1.15337	+	0.349870i
$476$	3.23191	+	6.33114i	0.148134	+	0.290187i
$477$	−9.95152	−	12.1260i	−0.455649	−	0.555209i
$478$	7.79721	+	8.76781i	0.356636	+	0.401030i
$479$	6.39570	+	6.39570i	0.292227	+	0.292227i	0.837959	−	0.545733i	$-0.183749\pi$
$479$	6.39570	+	6.39570i	0.292227	+	0.292227i	−0.545733	+	0.837959i	$0.683749\pi$
$480$	0.180647	−	0.599593i	0.00824538	−	0.0273675i
$481$	8.96391	−	8.96391i	0.408719	−	0.408719i
$482$	7.74051	+	0.453545i	0.352571	+	0.0206584i
$483$	1.14748	−	0.941710i	0.0522120	−	0.0428493i
$484$	−28.8094	+	33.7832i	−1.30952	+	1.53560i
$485$	0.447601	−	1.47554i	0.0203245	−	0.0670009i
$486$	6.08222	+	8.36480i	0.275895	+	0.379435i
$487$	13.7600	−	20.5933i	0.623525	−	0.933171i	−0.376452	−	0.926436i	$-0.622856\pi$
$487$	13.7600	−	20.5933i	0.623525	−	0.933171i	0.999977	−	0.00673496i	$-0.00214382\pi$
$488$	−28.6979	+	3.42964i	−1.29909	+	0.155252i
$489$	2.45491	−	1.64032i	0.111015	−	0.0741777i
$490$	−0.233762	−	0.506565i	−0.0105603	−	0.0228843i
$491$	10.2010	−	1.00471i	0.460363	−	0.0453418i	0.134822	−	0.990870i	$-0.456954\pi$
$491$	10.2010	−	1.00471i	0.460363	−	0.0453418i	0.325541	+	0.945528i	$0.394454\pi$
$492$	5.15136	+	2.24861i	0.232241	+	0.101375i
$493$	7.08568	+	23.3584i	0.319123	+	1.05201i
$494$	18.6045	−	24.5966i	0.837057	−	1.10665i
$495$	2.54108	−	6.13470i	0.114213	−	0.275734i
$496$	3.58422	+	5.82910i	0.160936	+	0.261734i
$497$	−0.767909	−	1.85390i	−0.0344454	−	0.0831586i
$498$	1.24485	+	0.324337i	0.0557831	+	0.0145339i
$499$	−12.0151	+	22.4787i	−0.537871	+	1.00629i	0.455380	+	0.890297i	$0.349503\pi$
$499$	−12.0151	+	22.4787i	−0.537871	+	1.00629i	−0.993251	+	0.115988i	$0.962997\pi$
$500$	−6.53843	+	4.19250i	−0.292408	+	0.187494i
$501$	2.11011	−	2.57117i	0.0942727	−	0.114872i
$502$	1.01321	+	25.5417i	0.0452217	+	1.13998i
$503$	43.3005	+	8.61301i	1.93067	+	0.384035i	0.999826	+	0.0186287i	$0.00593004\pi$
$503$	43.3005	+	8.61301i	1.93067	+	0.384035i	0.930848	+	0.365406i	$0.119070\pi$
$504$	−1.77990	−	8.06857i	−0.0792829	−	0.359403i
$505$	0.771158	+	3.87687i	0.0343161	+	0.172518i
$506$	−36.7621	−	22.5087i	−1.63427	−	1.00063i
$507$	0.785536	−	0.419878i	0.0348869	−	0.0186474i
$508$	16.7997	+	21.2772i	0.745366	+	0.944023i
$509$	−0.978169	+	9.93152i	−0.0433566	+	0.440207i	0.948861	+	0.315693i	$0.102237\pi$
$509$	−0.978169	+	9.93152i	−0.0433566	+	0.440207i	−0.992218	+	0.124514i	$0.960263\pi$
$510$	0.242637	−	0.500729i	0.0107442	−	0.0221727i
$511$	−13.1767			−0.582904
$512$	−17.9947	+	13.7182i	−0.795262	+	0.606266i
$513$	9.00974			0.397790
$514$	18.8581	−	38.9174i	0.831796	−	1.71657i
$515$	−0.314800	+	3.19622i	−0.0138717	+	0.140842i
$516$	−2.61600	−	3.31323i	−0.115163	−	0.145857i
$517$	−47.7078	+	25.5004i	−2.09819	+	1.12150i
$518$	−3.80174	−	2.32773i	−0.167039	−	0.102275i
$519$	0.523510	+	2.63186i	0.0229796	+	0.115526i
$520$	0.966669	+	4.38208i	0.0423913	+	0.192167i
$521$	3.52665	+	0.701495i	0.154505	+	0.0307330i	0.271737	−	0.962372i	$-0.412402\pi$
$521$	3.52665	+	0.701495i	0.154505	+	0.0307330i	−0.117231	+	0.993105i	$0.537402\pi$
$522$	−1.12463	−	28.3506i	−0.0492239	−	1.24087i
$523$	2.60566	−	3.17501i	0.113938	−	0.138834i	−0.712918	−	0.701247i	$-0.752627\pi$
$523$	2.60566	−	3.17501i	0.113938	−	0.138834i	0.826856	+	0.562413i	$0.190127\pi$
$524$	6.99286	−	4.48388i	0.305485	−	0.195879i
$525$	0.640812	−	1.19887i	0.0279673	−	0.0523232i
$526$	−5.96661	−	1.55456i	−0.260157	−	0.0677819i
$527$	2.32679	+	5.61737i	0.101357	+	0.244696i
$528$	5.50928	−	3.38757i	0.239761	−	0.147425i
$529$	1.90717	−	4.60432i	0.0829204	−	0.200188i
$530$	1.80725	−	2.38932i	0.0785019	−	0.103786i
$531$	4.27078	+	14.0789i	0.185336	+	0.610971i
$532$	−9.93917	−	4.33853i	−0.430917	−	0.188099i
$533$	−40.0841	+	3.94794i	−1.73623	+	0.171004i
$534$	−0.889996	−	1.92863i	−0.0385139	−	0.0834601i
$535$	−1.25892	+	0.841184i	−0.0544279	+	0.0363675i
$536$	34.4033	−	4.11147i	1.48599	−	0.177589i
$537$	−0.147173	+	0.220260i	−0.00635097	+	0.00950490i
$538$	−22.3029	−	30.6729i	−0.961547	−	1.32240i
$539$	1.67259	−	5.51380i	0.0720437	−	0.237496i
$540$	−0.850652	+	0.997512i	−0.0366062	+	0.0429261i
$541$	6.85987	−	5.62975i	0.294929	−	0.242042i	−0.475278	−	0.879835i	$-0.657653\pi$
$541$	6.85987	−	5.62975i	0.294929	−	0.242042i	0.770207	+	0.637794i	$0.220153\pi$
$542$	−3.98225	−	0.233334i	−0.171052	−	0.0100226i
$543$	−3.77105	+	3.77105i	−0.161831	+	0.161831i
$544$	−17.7135	+	9.51115i	−0.759459	+	0.407787i
$545$	0.676827	+	0.676827i	0.0289921	+	0.0289921i
$546$	−1.06060	−	1.19262i	−0.0453894	−	0.0510395i
$547$	−27.2656	−	33.2232i	−1.16579	−	1.42052i	−0.887978	−	0.459887i	$-0.847890\pi$
$547$	−27.2656	−	33.2232i	−1.16579	−	1.42052i	−0.277814	−	0.960635i	$-0.589610\pi$
$548$	−11.9518	−	23.4129i	−0.510554	−	1.00015i
$549$	28.5653	+	8.66520i	1.21914	+	0.369822i
$550$	−38.9910	−	6.16046i	−1.66258	−	0.262683i
$551$	−30.9640	−	20.6895i	−1.31911	−	0.881401i
$552$	2.73039	+	3.18954i	0.116213	+	0.135756i
$553$	−3.77457	−	5.64904i	−0.160511	−	0.240221i
$554$	−10.5198	+	28.5484i	−0.446943	+	1.21290i
$555$	0.0342020	+	0.347259i	0.00145179	+	0.0147403i
$556$	42.3213	+	0.799066i	1.79482	+	0.0338879i
$557$	28.3079	−	8.58711i	1.19944	−	0.363848i	0.373517	−	0.927623i	$-0.378152\pi$
$557$	28.3079	−	8.58711i	1.19944	−	0.363848i	0.825928	+	0.563776i	$0.190652\pi$
$558$	−0.970977	−	7.00045i	−0.0411047	−	0.296353i
$559$	27.9483	+	11.5766i	1.18209	+	0.489636i
$560$	1.41874	−	0.690792i	0.0599528	−	0.0291913i
$561$	5.30917	−	2.19913i	0.224153	−	0.0928474i
$562$	15.9455	+	27.1820i	0.672620	+	1.14661i
$563$	7.75815	+	4.14682i	0.326967	+	0.174768i	0.626710	−	0.779252i	$-0.284401\pi$
$563$	7.75815	+	4.14682i	0.326967	+	0.174768i	−0.299743	+	0.954020i	$0.596901\pi$
$564$	5.18626	−	0.930197i	0.218381	−	0.0391684i
$565$	2.52226	+	2.06997i	0.106112	+	0.0870843i
$566$	33.0952	+	30.5696i	1.39109	+	1.28494i
$567$	−1.61876	+	8.13808i	−0.0679817	+	0.341767i
$568$	5.19737	−	2.28040i	0.218077	−	0.0956836i
$569$	−35.9208	+	7.14509i	−1.50588	+	0.299538i	−0.877957	−	0.478740i	$-0.841094\pi$
$569$	−35.9208	+	7.14509i	−1.50588	+	0.299538i	−0.627921	+	0.778277i	$0.716094\pi$
$570$	0.198483	+	0.825367i	0.00831355	+	0.0345708i
$571$	8.71162	+	16.2983i	0.364570	+	0.682062i	0.995601	−	0.0936954i	$-0.0298680\pi$
$571$	8.71162	+	16.2983i	0.364570	+	0.682062i	−0.631031	+	0.775758i	$0.717368\pi$
$572$	−22.6148	+	40.4533i	−0.945572	+	1.69144i
$573$	2.83512	+	0.279235i	0.118439	+	0.0116652i
$574$	4.64547	+	13.3800i	0.193898	+	0.558472i
$575$		−	25.6265i		−	1.06870i
$576$	22.7119	−	5.50717i	0.946329	−	0.229466i
$577$		−	16.7877i		−	0.698882i	−0.936958	−	0.349441i	$-0.886371\pi$
$577$		−	16.7877i		−	0.698882i	0.936958	−	0.349441i	$-0.113629\pi$
$578$	5.83536	−	2.02600i	0.242719	−	0.0842704i
$579$	−2.37626	−	0.234041i	−0.0987540	−	0.00972642i
$580$	5.21409	−	1.47478i	0.216503	−	0.0612370i
$581$	1.52807	+	2.85882i	0.0633952	+	0.118604i
$582$	−1.50813	+	0.362673i	−0.0625139	+	0.0150333i
$583$	30.3460	−	6.03619i	1.25680	−	0.249993i
$584$	−0.774006	−	37.2614i	−0.0320286	−	1.54189i
$585$	0.904187	−	4.54566i	0.0373835	−	0.187940i
$586$	2.28799	−	2.47701i	0.0945161	−	0.102325i
$587$	−2.88207	−	2.36526i	−0.118956	−	0.0976246i	0.573035	−	0.819531i	$-0.305766\pi$
$587$	−2.88207	−	2.36526i	−0.118956	−	0.0976246i	−0.691991	+	0.721907i	$0.743266\pi$
$588$	−0.320553	+	0.460672i	−0.0132194	+	0.0189978i
$589$	−8.18089	−	4.37278i	−0.337088	−	0.180177i
$590$	−2.42354	+	1.42170i	−0.0997758	+	0.0585303i
$591$	−6.87723	+	2.84864i	−0.282892	+	0.117178i
$592$	6.35909	−	10.8874i	0.261357	−	0.447468i
$593$	−1.41270	−	0.585159i	−0.0580126	−	0.0240296i	0.353488	−	0.935439i	$-0.384995\pi$
$593$	−1.41270	−	0.585159i	−0.0580126	−	0.0240296i	−0.411501	+	0.911409i	$0.634995\pi$
$594$	−13.4111	+	1.86015i	−0.550263	+	0.0763227i
$595$	1.34173	−	0.407010i	0.0550056	−	0.0166858i
$596$	−5.15216	−	5.35046i	−0.211041	−	0.219163i
$597$	0.698849	+	7.09554i	0.0286020	+	0.290401i
$598$	−28.2313	−	10.4029i	−1.15446	−	0.425408i
$599$	8.94514	+	13.3873i	0.365488	+	0.546992i	0.967946	−	0.251159i	$-0.0808117\pi$
$599$	8.94514	+	13.3873i	0.365488	+	0.546992i	−0.602457	+	0.798151i	$0.705812\pi$
$600$	3.42784	+	1.74168i	0.139941	+	0.0711037i
$601$	−20.1565	−	13.4682i	−0.822202	−	0.549378i	0.0718111	−	0.997418i	$-0.477122\pi$
$601$	−20.1565	−	13.4682i	−0.822202	−	0.549378i	−0.894013	+	0.448040i	$0.852122\pi$
$602$	1.66012	−	10.5073i	0.0676613	−	0.428244i
$603$	−34.2443	−	10.3879i	−1.39454	−	0.423028i
$604$	−7.29319	−	2.36361i	−0.296756	−	0.0961737i
$605$	5.55578	+	6.76974i	0.225875	+	0.275229i
$606$	2.97137	−	2.64244i	0.120704	−	0.107342i
$607$	−20.5215	−	20.5215i	−0.832943	−	0.832943i	0.154976	−	0.987918i	$-0.450470\pi$
$607$	−20.5215	−	20.5215i	−0.832943	−	0.832943i	−0.987918	+	0.154976i	$0.950470\pi$
$608$	11.6847	−	28.3610i	0.473879	−	1.15019i
$609$	−1.36273	+	1.36273i	−0.0552207	+	0.0552207i
$610$	−0.333463	+	5.69111i	−0.0135015	+	0.230426i
$611$	−29.1870	+	23.9532i	−1.18078	+	0.969042i
$612$	20.7001	−	1.64488i	0.836751	−	0.0664905i
$613$	1.36699	−	4.50635i	0.0552120	−	0.182010i	−0.924997	−	0.379974i	$-0.875933\pi$
$613$	1.36699	−	4.50635i	0.0552120	−	0.182010i	0.980209	+	0.197964i	$0.0634330\pi$
$614$	−6.75202	+	4.90953i	−0.272489	+	0.198132i
$615$	0.615949	−	0.921832i	0.0248374	−	0.0371719i
$616$	15.6903	+	4.40590i	0.632179	+	0.177519i
$617$	9.28376	−	6.20321i	0.373750	−	0.249732i	−0.354481	−	0.935063i	$-0.615343\pi$
$617$	9.28376	−	6.20321i	0.373750	−	0.249732i	0.728231	+	0.685331i	$0.240343\pi$
$618$	2.93353	−	1.35372i	0.118004	−	0.0544547i
$619$	5.62263	−	0.553781i	0.225993	−	0.0222583i	0.0156130	−	0.999878i	$-0.495030\pi$
$619$	5.62263	−	0.553781i	0.225993	−	0.0222583i	0.210380	+	0.977620i	$0.432530\pi$
$620$	1.25653	−	0.492892i	0.0504634	−	0.0197950i
$621$	−2.55151	−	8.41119i	−0.102388	−	0.337530i
$622$	−4.13493	−	3.12760i	−0.165796	−	0.125405i
$623$	2.04828	−	4.94498i	0.0820626	−	0.198117i
$624$	3.31021	−	3.06923i	0.132515	−	0.122867i
$625$	−8.68302	−	20.9627i	−0.347321	−	0.838506i
$626$	−11.0743	+	42.5049i	−0.442619	+	1.69884i
$627$	−4.13286	+	7.73204i	−0.165051	+	0.308788i
$628$	6.91595	+	1.51193i	0.275977	+	0.0603324i
$629$	7.10720	−	8.66015i	0.283383	−	0.345303i
$630$	−1.62849	+	0.0646003i	−0.0648806	+	0.00257374i
$631$	−23.8270	−	4.73949i	−0.948540	−	0.188676i	−0.303505	−	0.952830i	$-0.598157\pi$
$631$	−23.8270	−	4.73949i	−0.948540	−	0.188676i	−0.645034	+	0.764154i	$0.723157\pi$
$632$	15.7527	−	11.0056i	0.626610	−	0.437780i
$633$	−0.243588	−	1.22460i	−0.00968173	−	0.0486734i
$634$	−14.8600	+	24.2700i	−0.590168	+	0.963884i
$635$	4.71596	−	2.52074i	0.187147	−	0.100032i
$636$	−2.99306	−	0.351957i	−0.118683	−	0.0139560i
$637$	0.394197	−	4.00235i	0.0156186	−	0.158579i
$638$	50.3617	+	24.4037i	1.99384	+	0.966151i
$639$	−5.86192			−0.231894
$640$	2.03677	+	3.97137i	0.0805105	+	0.156982i
$641$	−37.5484			−1.48307			−0.741536	−	0.670913i	$-0.765902\pi$
$641$	−37.5484			−1.48307			−0.741536	+	0.670913i	$0.765902\pi$
$642$	1.37067	+	0.664181i	0.0540959	+	0.0262131i
$643$	1.88652	−	19.1542i	0.0743972	−	0.755367i	−0.883534	−	0.468368i	$-0.844842\pi$
$643$	1.88652	−	19.1542i	0.0743972	−	0.755367i	0.957931	−	0.286999i	$-0.0926578\pi$
$644$	−1.23559	+	10.5075i	−0.0486891	+	0.414054i
$645$	−0.734357	+	0.392522i	−0.0289153	+	0.0154555i
$646$	14.2319	−	23.2441i	0.559946	−	0.914525i
$647$	6.48777	+	32.6162i	0.255061	+	1.28228i	0.869744	+	0.493503i	$0.164284\pi$
$647$	6.48777	+	32.6162i	0.255061	+	1.28228i	−0.614684	+	0.788774i	$0.710716\pi$
$648$	−23.1081	−	4.09954i	−0.907771	−	0.161045i
$649$	−28.4612	−	5.66129i	−1.11720	−	0.222225i
$650$	−27.5310	+	1.09212i	−1.07986	+	0.0428366i
$651$	−0.304540	+	0.371083i	−0.0119359	+	0.0145439i
$652$	−4.49421	+	20.5577i	−0.176007	+	0.805102i
$653$	−12.6507	+	23.6678i	−0.495060	+	0.926193i	0.503021	+	0.864274i	$0.332222\pi$
$653$	−12.6507	+	23.6678i	−0.495060	+	0.926193i	−0.998081	+	0.0619184i	$0.980278\pi$
$654$	0.242767	−	0.931774i	0.00949294	−	0.0364353i
$655$	−0.627037	−	1.51380i	−0.0245003	−	0.0591491i
$656$	−37.5635	+	13.9225i	−1.46661	+	0.543581i
$657$	−14.7305	+	35.5625i	−0.574691	+	1.38743i
$658$	10.5893	+	8.00957i	0.412813	+	0.312245i
$659$	−9.82230	−	32.3798i	−0.382623	−	1.26134i	−0.911028	−	0.412345i	$-0.864710\pi$
$659$	−9.82230	−	32.3798i	−0.382623	−	1.26134i	0.528405	−	0.848992i	$-0.322790\pi$
$660$	−0.465849	−	1.18759i	−0.0181331	−	0.0462268i
$661$	4.44678	−	0.437969i	0.172960	−	0.0170350i	−0.0111666	−	0.999938i	$-0.503555\pi$
$661$	4.44678	−	0.437969i	0.172960	−	0.0170350i	0.184126	+	0.982903i	$0.441055\pi$
$662$	14.2654	−	6.58298i	0.554441	−	0.255855i
$663$	3.33505	−	2.22841i	0.129523	−	0.0865443i
$664$	−7.99447	+	4.48904i	−0.310246	+	0.174209i
$665$	−1.18843	+	1.77861i	−0.0460852	+	0.0689714i
$666$	−10.5323	+	7.65827i	−0.408119	+	0.296752i
$667$	−10.5462	+	34.7661i	−0.408350	+	1.34615i
$668$	1.87787	+	23.6321i	0.0726571	+	0.914354i
$669$	−2.91275	+	2.39043i	−0.112613	+	0.0924195i
$670$	0.399758	−	6.82255i	0.0154440	−	0.263578i
$671$	−41.6328	+	41.6328i	−1.60722	+	1.60722i
$672$	−1.32152	−	0.879405i	−0.0509789	−	0.0339238i
$673$	−6.74474	−	6.74474i	−0.259991	−	0.259991i	0.565060	−	0.825050i	$-0.308853\pi$
$673$	−6.74474	−	6.74474i	−0.259991	−	0.259991i	−0.825050	+	0.565060i	$0.808853\pi$
$674$	10.0234	−	8.91379i	0.386087	−	0.343346i
$675$	−5.10642	−	6.22219i	−0.196546	−	0.239492i
$676$	−1.95718	+	6.03911i	−0.0752760	+	0.232273i
$677$	−18.5372	−	5.62320i	−0.712442	−	0.216117i	−0.0867985	−	0.996226i	$-0.527664\pi$
$677$	−18.5372	−	5.62320i	−0.712442	−	0.216117i	−0.625644	+	0.780109i	$0.715164\pi$
$678$	0.512247	−	3.24213i	0.0196727	−	0.124513i
$679$	−3.24991	−	2.17152i	−0.124720	−	0.0833353i
$680$	1.22976	+	3.77026i	0.0471593	+	0.144583i
$681$	−0.663839	−	0.993505i	−0.0254384	−	0.0380712i
$682$	13.0801	+	4.81990i	0.500864	+	0.184563i
$683$	3.84624	+	39.0515i	0.147172	+	1.49427i	0.730994	+	0.682384i	$0.239057\pi$
$683$	3.84624	+	39.0515i	0.147172	+	1.49427i	−0.583822	+	0.811882i	$0.698443\pi$
$684$	−22.8204	+	21.9746i	−0.872559	+	0.840220i
$685$	−4.96179	+	1.50514i	−0.189580	+	0.0575085i
$686$	−1.40080	+	0.194294i	−0.0534829	+	0.00741820i
$687$	−1.56277	−	0.647319i	−0.0596232	−	0.0246968i
$688$	29.8102	+	4.07730i	1.13650	+	0.155446i
$689$	19.9520	−	8.26440i	0.760112	−	0.314849i
$690$	0.714326	−	0.419037i	0.0271939	−	0.0159525i
$691$	31.0918	+	16.6189i	1.18279	+	0.632213i	0.941096	−	0.338140i	$-0.109798\pi$
$691$	31.0918	+	16.6189i	1.18279	+	0.632213i	0.241691	+	0.970353i	$0.422298\pi$
$692$	−15.6989	−	10.9239i	−0.596781	−	0.415263i
$693$	−13.0113	−	10.6781i	−0.494259	−	0.405628i
$694$	28.8047	−	31.1844i	1.09341	−	1.18374i
$695$	1.62886	−	8.18884i	0.0617862	−	0.310620i
$696$	−3.93360	−	3.77351i	−0.149103	−	0.143034i
$697$	−34.9116	+	6.94435i	−1.32237	+	0.263036i
$698$	−37.7382	+	9.07525i	−1.42841	+	0.343503i
$699$	0.0782631	+	0.146420i	0.00296018	+	0.00553811i
$700$	2.63697	+	9.32299i	0.0996681	+	0.352376i
$701$	−20.5012	−	2.01920i	−0.774321	−	0.0762640i	−0.296865	−	0.954919i	$-0.595941\pi$
$701$	−20.5012	−	2.01920i	−0.774321	−	0.0762640i	−0.477456	+	0.878655i	$0.658441\pi$
$702$	−8.92754	+	3.09958i	−0.336948	+	0.116986i
$703$			17.0920i			0.644637i
$704$	−11.5374	+	44.6280i	−0.434834	+	1.68198i
$705$		−	1.03930i		−	0.0391424i
$706$	−12.0011	−	34.5660i	−0.451667	−	1.30091i
$707$	9.97170	+	0.982127i	0.375024	+	0.0369367i
$708$	2.46716	+	1.37922i	0.0927215	+	0.0518344i
$709$	−21.7685	−	40.7260i	−0.817533	−	1.52950i	−0.848021	−	0.529962i	$-0.822206\pi$
$709$	−21.7685	−	40.7260i	−0.817533	−	1.52950i	0.0304880	−	0.999535i	$-0.490294\pi$
$710$	−0.261755	−	1.08848i	−0.00982350	−	0.0408498i
$711$	−19.4658	+	3.87198i	−0.730024	+	0.145211i
$712$	14.1038	+	5.50169i	0.528563	+	0.206185i
$713$	−1.76550	+	8.87575i	−0.0661184	+	0.332400i
$714$	−1.03609	−	0.957028i	−0.0387748	−	0.0358159i
$715$	7.06650	+	5.79933i	0.264272	+	0.216883i
$716$	−0.333317	−	1.85839i	−0.0124566	−	0.0694512i
$717$	−2.05325	−	1.09749i	−0.0766801	−	0.0409864i
$718$	5.17108	+	8.81506i	0.192983	+	0.328975i
$719$	49.3569	−	20.4443i	1.84070	−	0.762444i	0.886937	−	0.461891i	$-0.152829\pi$
$719$	49.3569	−	20.4443i	1.84070	−	0.762444i	0.953765	−	0.300553i	$-0.0971712\pi$
$720$	−0.278336	−	4.60128i	−0.0103730	−	0.171480i
$721$	7.52153	+	3.11552i	0.280116	+	0.116028i
$722$	2.02114	+	14.5718i	0.0752190	+	0.542306i
$723$	−1.47228	+	0.446611i	−0.0547547	+	0.0166096i
$724$	0.717541	−	38.0035i	0.0266672	−	1.41239i
$725$	3.26106	+	33.1101i	0.121113	+	1.22968i
$726$	3.04610	−	8.26643i	0.113051	−	0.306796i
$727$	11.5742	+	17.3220i	0.429262	+	0.642436i	0.981547	−	0.191219i	$-0.0612442\pi$
$727$	11.5742	+	17.3220i	0.429262	+	0.642436i	−0.552286	+	0.833655i	$0.686244\pi$
$728$	11.3411	+	0.879617i	0.420328	+	0.0326008i
$729$	18.9911	+	12.6894i	0.703374	+	0.469979i
$730$	−7.26123	−	1.14725i	−0.268750	−	0.0424617i
$731$	25.5831	+	7.76054i	0.946224	+	0.287034i
$732$	5.10781	−	2.60742i	0.188790	−	0.0963732i
$733$	2.55088	+	3.10826i	0.0942189	+	0.114806i	0.817986	−	0.575239i	$-0.195091\pi$
$733$	2.55088	+	3.10826i	0.0942189	+	0.114806i	−0.723767	+	0.690045i	$0.757591\pi$
$734$	13.2266	+	14.8731i	0.488203	+	0.548975i
$735$	0.0782769	+	0.0782769i	0.00288729	+	0.00288729i
$736$	−29.7859	−	2.87681i	−1.09792	−	0.106041i
$737$	49.9097	−	49.9097i	1.83845	−	1.83845i
$738$	41.3045	+	2.42018i	1.52044	+	0.0890881i
$739$	40.2035	−	32.9942i	1.47891	−	1.21371i	0.554571	−	0.832137i	$-0.312883\pi$
$739$	40.2035	−	32.9942i	1.47891	−	1.21371i	0.924339	−	0.381573i	$-0.124617\pi$
$740$	−1.89234	−	1.61374i	−0.0695638	−	0.0593222i
$741$	−1.77637	+	5.85591i	−0.0652566	+	0.215122i
$742$	−4.46602	−	6.14206i	−0.163953	−	0.225482i
$743$	17.5853	−	26.3182i	0.645141	−	0.965521i	−0.354396	−	0.935095i	$-0.615314\pi$
$743$	17.5853	−	26.3182i	0.645141	−	0.965521i	0.999537	−	0.0304258i	$-0.00968633\pi$
$744$	−1.06724	−	0.839385i	−0.0391270	−	0.0307733i
$745$	−1.21820	+	0.813974i	−0.0446314	+	0.0298217i
$746$	−13.5672	−	29.4002i	−0.496729	−	1.07642i
$747$	9.42391	−	0.928174i	0.344803	−	0.0339601i
$748$	−16.3853	+	37.5373i	−0.599108	+	1.37250i
$749$	1.11413	+	3.67278i	0.0407093	+	0.134200i
$750$	0.929720	−	1.22916i	0.0339486	−	0.0448826i
$751$	3.80142	−	9.17744i	0.138716	−	0.334890i	−0.839221	−	0.543790i	$-0.816989\pi$
$751$	3.80142	−	9.17744i	0.138716	−	0.334890i	0.977937	+	0.208901i	$0.0669886\pi$
$752$	−22.0276	+	30.4150i	−0.803263	+	1.10912i
$753$	−1.94099	−	4.68595i	−0.0707334	−	0.170766i
$754$	37.7992	+	9.84831i	1.37657	+	0.358654i
$755$	−0.712858	+	1.33366i	−0.0259436	+	0.0485370i
$756$	1.79376	+	2.79746i	0.0652382	+	0.101743i
$757$	−23.0993	+	28.1465i	−0.839557	+	1.02300i	0.159800	+	0.987149i	$0.448915\pi$
$757$	−23.0993	+	28.1465i	−0.839557	+	1.02300i	−0.999357	+	0.0358540i	$0.988585\pi$
$758$	−0.787487	−	19.8515i	−0.0286028	−	0.721040i
$759$	8.38878	+	1.66863i	0.304494	+	0.0605675i
$760$	−5.09939	−	3.25618i	−0.184974	−	0.118114i
$761$	1.57404	+	7.91322i	0.0570588	+	0.286854i	0.998771	−	0.0495660i	$-0.0157838\pi$
$761$	1.57404	+	7.91322i	0.0570588	+	0.286854i	−0.941712	+	0.336420i	$0.890784\pi$
$762$	−4.58761	−	2.80891i	−0.166192	−	0.101756i
$763$	2.13984	−	1.14377i	0.0774673	−	0.0414071i
$764$	−15.9359	+	12.5824i	−0.576542	+	0.455216i
$765$	0.401469	−	4.07619i	0.0145152	−	0.147375i
$766$	9.94410	−	20.5216i	0.359295	−	0.741475i
$767$	−20.2546			−0.731352
$768$	2.40917	−	3.78869i	0.0869334	−	0.136712i
$769$	−35.3404			−1.27441			−0.637204	−	0.770696i	$-0.719909\pi$
$769$	−35.3404			−1.27441			−0.637204	+	0.770696i	$0.719909\pi$
$770$	1.40178	−	2.89284i	0.0505165	−	0.104251i
$771$	−0.841078	+	8.53961i	−0.0302907	+	0.307547i
$772$	13.3567	−	10.5460i	0.480719	−	0.379558i
$773$	−37.2439	+	19.9073i	−1.33957	+	0.716015i	−0.976453	−	0.215729i	$-0.930787\pi$
$773$	−37.2439	+	19.9073i	−1.33957	+	0.716015i	−0.363116	+	0.931744i	$0.618287\pi$
$774$	−26.5021	−	16.2267i	−0.952598	−	0.583257i
$775$	1.61678	+	8.12813i	0.0580766	+	0.291971i
$776$	5.94976	−	9.31770i	0.213584	−	0.334486i
$777$	0.867524	+	0.172561i	0.0311223	+	0.00619060i
$778$	−1.01936	−	25.6968i	−0.0365459	−	0.921276i
$779$	34.4514	−	41.9792i	1.23435	−	1.50406i
$780$	−0.480620	−	0.749554i	−0.0172090	−	0.0268383i
$781$	5.45033	−	10.1968i	0.195028	−	0.364872i
$782$	−25.7303	−	6.70383i	−0.920113	−	0.239729i
$783$	4.36696	+	10.5428i	0.156062	+	0.376768i
$784$	−0.631713	−	3.94980i	−0.0225612	−	0.141064i
$785$	0.534369	−	1.29008i	0.0190724	−	0.0460450i
$786$	−0.994336	+	1.31459i	−0.0354668	+	0.0468898i
$787$	13.6612	+	45.0350i	0.486970	+	1.60532i	0.764511	+	0.644610i	$0.222980\pi$
$787$	13.6612	+	45.0350i	0.486970	+	1.60532i	−0.277542	+	0.960714i	$0.589520\pi$
$788$	21.2247	−	48.6239i	0.756100	−	1.73216i
$789$	1.21754	−	0.119918i	0.0433457	−	0.00426918i
$790$	−1.58819	−	3.44162i	−0.0565052	−	0.122448i
$791$	6.87717	−	4.59518i	0.244524	−	0.163386i
$792$	29.4315	−	37.4209i	1.04580	−	1.32969i
$793$	−22.8315	+	34.1698i	−0.810770	+	1.21340i
$794$	0.865909	+	1.19087i	0.0307299	+	0.0422625i
$795$	−0.172557	+	0.568845i	−0.00611998	+	0.0201749i
$796$	−38.6661	−	32.9735i	−1.37049	−	1.16871i
$797$	17.9531	−	14.7337i	0.635931	−	0.521895i	−0.260274	−	0.965535i	$-0.583813\pi$
$797$	17.9531	−	14.7337i	0.635931	−	0.521895i	0.896205	+	0.443640i	$0.146313\pi$
$798$	2.14817	+	0.125869i	0.0760445	+	0.00445572i
$799$	−23.5949	+	23.5949i	−0.834726	+	0.834726i
$800$	−26.2088	+	8.00450i	−0.926622	+	0.283002i
$801$	−11.0562	−	11.0562i	−0.390650	−	0.390650i
$802$	0.207374	+	0.233189i	0.00732264	+	0.00823417i
$803$	−48.1651	−	58.6893i	−1.69971	−	2.07110i
$804$	−6.12328	+	3.12580i	−0.215951	+	0.110238i
$805$	1.99701	+	0.605785i	0.0703852	+	0.0213511i
$806$	9.61060	+	1.51845i	0.338519	+	0.0534850i
$807$	6.25684	+	4.18068i	0.220251	+	0.147167i
$808$	−2.19153	+	28.2558i	−0.0770979	+	0.994037i
$809$	−3.22527	−	4.82695i	−0.113394	−	0.169707i	0.770431	−	0.637523i	$-0.220041\pi$
$809$	−3.22527	−	4.82695i	−0.113394	−	0.169707i	−0.883826	+	0.467816i	$0.845041\pi$
$810$	−1.60060	+	4.34367i	−0.0562393	+	0.152621i
$811$	−2.09948	−	21.3164i	−0.0737229	−	0.748521i	−0.958990	−	0.283439i	$-0.908525\pi$
$811$	−2.09948	−	21.3164i	−0.0737229	−	0.748521i	0.885268	−	0.465082i	$-0.153975\pi$
$812$	0.259295	−	13.7332i	0.00909949	−	0.481940i
$813$	0.757441	−	0.229767i	0.0265646	−	0.00805829i
$814$	−3.52881	−	25.4416i	−0.123685	−	0.891728i
$815$	3.83477	+	1.58842i	0.134326	+	0.0556398i
$816$	2.64544	−	2.98610i	0.0926089	−	0.104534i
$817$	−37.6822	+	15.6085i	−1.31833	+	0.546071i
$818$	−25.1954	−	42.9502i	−0.880936	−	1.50172i
$819$	−10.3612	−	5.53818i	−0.362050	−	0.193520i
$820$	1.39500	+	7.77774i	0.0487155	+	0.271611i
$821$	3.59506	+	2.95039i	0.125468	+	0.102969i	0.695035	−	0.718976i	$-0.255389\pi$
$821$	3.59506	+	2.95039i	0.125468	+	0.102969i	−0.569567	+	0.821945i	$0.692889\pi$
$822$	3.83152	+	3.53914i	0.133640	+	0.123442i
$823$	−9.63895	+	48.4583i	−0.335993	+	1.68915i	0.330636	+	0.943758i	$0.392737\pi$
$823$	−9.63895	+	48.4583i	−0.335993	+	1.68915i	−0.666628	+	0.745390i	$0.732263\pi$
$824$	−8.36830	+	21.4525i	−0.291524	+	0.747334i
$825$	7.68217	−	1.52808i	0.267459	−	0.0532009i
$826$	1.66532	+	6.92501i	0.0579438	+	0.240952i
$827$	11.3725	+	21.2764i	0.395460	+	0.739853i	0.998317	−	0.0579960i	$-0.0184711\pi$
$827$	11.3725	+	21.2764i	0.395460	+	0.739853i	−0.602857	+	0.797849i	$0.705971\pi$
$828$	26.9774	+	15.0813i	0.937528	+	0.524110i
$829$	−35.3804	−	3.48467i	−1.22881	−	0.121028i	−0.537300	−	0.843391i	$-0.680556\pi$
$829$	−35.3804	−	3.48467i	−1.22881	−	0.121028i	−0.691513	+	0.722364i	$0.743056\pi$
$830$	0.593160	+	1.70844i	0.0205889	+	0.0593009i
$831$		−	6.03700i		−	0.209421i
$832$	−1.82122	+	32.1221i	−0.0631394	+	1.11363i
$833$		−	3.55417i		−	0.123145i
$834$	−7.93439	+	2.75477i	−0.274745	+	0.0953898i
$835$	4.65356	+	0.458336i	0.161043	+	0.0158614i
$836$	−17.0069	−	60.1279i	−0.588196	−	2.07957i
$837$	1.33994	+	2.50685i	0.0463151	+	0.0866495i
$838$	13.9413	−	3.35258i	0.481593	−	0.115813i
$839$	−54.7810	+	10.8966i	−1.89125	+	0.376193i	−0.997393	−	0.0721596i	$-0.977011\pi$
$839$	−54.7810	+	10.8966i	−1.89125	+	0.376193i	−0.893857	+	0.448353i	$0.852011\pi$
$840$	−0.216755	+	0.225951i	−0.00747875	+	0.00779604i
$841$	3.54419	−	17.8179i	0.122213	−	0.614409i
$842$	5.08822	−	5.50858i	0.175351	−	0.189838i
$843$	−4.83368	−	3.96690i	−0.166481	−	0.136627i
$844$	7.30463	+	5.08284i	0.251436	+	0.174958i
$845$	1.10434	+	0.590280i	0.0379903	+	0.0203063i
$846$	33.4549	−	19.6252i	1.15020	−	0.674729i
$847$	20.5097	−	8.49540i	0.704722	−	0.291906i
$848$	17.1063	−	12.9899i	0.587432	−	0.446074i
$849$	−8.25910	−	3.42103i	−0.283452	−	0.117409i
$850$	−24.1187	+	3.34531i	−0.827264	+	0.114743i
$851$	15.9565	−	4.84036i	0.546983	−	0.165925i
$852$	−0.811218	+	0.781152i	−0.0277919	+	0.0267618i
$853$	5.43942	+	55.2273i	0.186242	+	1.89095i	0.403720	+	0.914882i	$0.367717\pi$
$853$	5.43942	+	55.2273i	0.186242	+	1.89095i	−0.217478	+	0.976065i	$0.569783\pi$
$854$	13.5597	+	4.99663i	0.464005	+	0.170981i
$855$	3.47170	+	5.19577i	0.118730	+	0.177692i
$856$	−10.3205	+	3.36628i	−0.352748	+	0.115057i
$857$	−38.4292	−	25.6776i	−1.31272	−	0.877130i	−0.315303	−	0.948991i	$-0.602106\pi$
$857$	−38.4292	−	25.6776i	−1.31272	−	0.877130i	−0.997415	+	0.0718609i	$0.977106\pi$
$858$	1.43514	−	9.08332i	0.0489947	−	0.310099i
$859$	25.8893	+	7.85342i	0.883330	+	0.267955i	0.699183	−	0.714943i	$-0.253547\pi$
$859$	25.8893	+	7.85342i	0.883330	+	0.267955i	0.184148	+	0.982899i	$0.441047\pi$
$860$	1.82966	−	5.64565i	0.0623910	−	0.192515i
$861$	−1.78288	−	2.17245i	−0.0607604	−	0.0740367i
$862$	23.2104	−	20.6410i	0.790548	−	0.703034i
$863$	−11.9875	−	11.9875i	−0.408059	−	0.408059i	0.473002	−	0.881061i	$-0.343170\pi$
$863$	−11.9875	−	11.9875i	−0.408059	−	0.408059i	−0.881061	+	0.473002i	$0.843170\pi$
$864$	−7.80534	+	5.23674i	−0.265543	+	0.178157i
$865$	−2.66753	+	2.66753i	−0.0906989	+	0.0906989i
$866$	0.228728	−	3.90363i	0.00777248	−	0.132651i
$867$	−0.947455	+	0.777556i	−0.0321773	+	0.0264072i
$868$	−0.271022	−	3.41069i	−0.00919910	−	0.115766i
$869$	11.3637	−	37.4610i	0.385486	−	1.27078i
$870$	−0.869602	+	0.632305i	−0.0294823	+	0.0214372i
$871$	27.3706	−	40.9630i	0.927417	−	1.38798i
$872$	3.36006	+	5.98388i	0.113786	+	0.202640i
$873$	−9.49382	+	6.34357i	−0.321317	+	0.214697i
$874$	36.8331	−	16.9972i	1.24590	−	0.574938i
$875$	3.86486	−	0.380655i	0.130656	−	0.0128685i
$876$	2.70050	+	6.88439i	0.0912415	+	0.232602i
$877$	−8.52466	−	28.1020i	−0.287857	−	0.948939i	−0.974960	−	0.222379i	$-0.928618\pi$
$877$	−8.52466	−	28.1020i	−0.287857	−	0.948939i	0.687103	−	0.726560i	$-0.258882\pi$
$878$	−38.2828	−	28.9566i	−1.29198	−	0.977237i
$879$	−0.256048	+	0.618154i	−0.00863628	+	0.0208498i
$880$	8.26275	+	3.79404i	0.278537	+	0.127897i
$881$	−8.04251	−	19.4163i	−0.270959	−	0.654153i	0.728566	−	0.684976i	$-0.240187\pi$
$881$	−8.04251	−	19.4163i	−0.270959	−	0.654153i	−0.999525	+	0.0308230i	$0.990187\pi$
$882$	−1.04160	+	3.99782i	−0.0350726	+	0.134614i
$883$	9.39627	−	17.5792i	0.316210	−	0.591587i	−0.672733	−	0.739885i	$-0.734880\pi$
$883$	9.39627	−	17.5792i	0.316210	−	0.591587i	0.988943	+	0.148299i	$0.0473797\pi$
$884$	−6.10549	+	27.9281i	−0.205350	+	0.939325i
$885$	0.353688	−	0.430970i	0.0118891	−	0.0144869i
$886$	22.7068	−	0.900752i	0.762850	−	0.0302614i
$887$	−42.4679	−	8.44739i	−1.42593	−	0.283636i	−0.578997	−	0.815330i	$-0.696556\pi$
$887$	−42.4679	−	8.44739i	−1.42593	−	0.283636i	−0.846936	+	0.531694i	$0.821556\pi$
$888$	−0.437013	+	2.46334i	−0.0146652	+	0.0826642i
$889$	−2.64444	−	13.2945i	−0.0886918	−	0.445884i
$890$	1.55928	−	2.54667i	0.0522671	−	0.0853646i
$891$	−42.1642	+	22.5372i	−1.41255	+	0.755026i
$892$	3.13642	−	26.6722i	0.105015	−	0.893053i
$893$	4.98985	−	50.6628i	0.166979	−	1.69537i
$894$	1.32633	+	0.642697i	0.0443591	+	0.0214950i
$895$	−0.372412			−0.0124484
$896$	11.1322	−	2.01838i	0.371901	−	0.0674294i
$897$	5.96994			0.199330
$898$	36.5742	+	17.7227i	1.22050	+	0.591414i
$899$	1.15159	−	11.6923i	0.0384078	−	0.389961i
$900$	28.1096	+	3.30544i	0.936988	+	0.110181i
$901$	16.8318	−	8.99676i	0.560747	−	0.299726i
$902$	−42.6143	+	69.5993i	−1.41890	+	2.31740i
$903$	0.411786	+	2.07019i	0.0137034	+	0.0688915i
$904$	13.3983	+	19.1775i	0.445621	+	0.637833i
$905$	−7.35337	−	1.46268i	−0.244434	−	0.0486210i
$906$	1.52004	−	0.0602982i	0.0504999	−	0.00200327i
$907$	−5.87594	+	7.15986i	−0.195107	+	0.237739i	−0.861370	−	0.507978i	$-0.830393\pi$
$907$	−5.87594	+	7.15986i	−0.195107	+	0.237739i	0.666262	+	0.745717i	$0.267893\pi$
$908$	8.31973	+	1.81881i	0.276100	+	0.0603594i
$909$	13.7982	−	25.8146i	0.457657	−	0.856215i
$910$	0.565698	−	2.17123i	0.0187527	−	0.0719756i
$911$	−1.14767	−	2.77073i	−0.0380241	−	0.0917984i	0.903727	−	0.428110i	$-0.140820\pi$
$911$	−1.14767	−	2.77073i	−0.0380241	−	0.0917984i	−0.941751	+	0.336312i	$0.890820\pi$
$912$	−0.229751	+	6.08203i	−0.00760781	+	0.201396i
$913$	−7.14765	+	17.2560i	−0.236553	+	0.571089i
$914$	−9.10730	−	6.88863i	−0.301243	−	0.227856i
$915$	−0.328365	−	1.08247i	−0.0108554	−	0.0357855i
$916$	11.2234	−	4.40253i	0.370831	−	0.145464i
$917$	−4.13347	+	0.407111i	−0.136499	+	0.0134440i
$918$	−7.58320	+	3.49938i	−0.250283	+	0.115497i
$919$	23.5494	−	15.7352i	0.776824	−	0.519057i	−0.102814	−	0.994701i	$-0.532785\pi$
$919$	23.5494	−	15.7352i	0.776824	−	0.519057i	0.879638	+	0.475644i	$0.157785\pi$
$920$	−1.59574	+	5.68275i	−0.0526101	+	0.187355i
$921$	0.920292	−	1.37731i	0.0303247	−	0.0453840i
$922$	29.9843	−	21.8022i	0.987479	−	0.718016i
$923$	2.34264	−	7.72264i	0.0771088	−	0.254194i
$924$	−3.22356	+	0.256153i	−0.106047	+	0.00842681i
$925$	11.8039	−	9.68718i	0.388109	−	0.318513i
$926$	3.13691	−	53.5367i	0.103085	−	1.75932i
$927$	16.8169	−	16.8169i	0.552339	−	0.552339i
$928$	38.8502	−	0.0734521i	1.27532	−	0.00241118i
$929$	24.1518	+	24.1518i	0.792396	+	0.792396i	0.981883	−	0.189487i	$-0.0606825\pi$
$929$	24.1518	+	24.1518i	0.792396	+	0.792396i	−0.189487	+	0.981883i	$0.560682\pi$
$930$	−0.200130	+	0.177975i	−0.00656252	+	0.00583605i
$931$	3.43994	+	4.19157i	0.112739	+	0.137373i
$932$	−1.12566	−	0.364808i	−0.0368722	−	0.0119497i
$933$	0.984435	+	0.298625i	0.0322290	+	0.00977655i
$934$	−4.24575	+	26.8724i	−0.138925	+	0.879291i
$935$	6.71728	+	4.48834i	0.219678	+	0.146784i
$936$	15.0523	−	29.6249i	0.492001	−	0.968321i
$937$	5.35062	+	8.00777i	0.174797	+	0.261602i	0.908515	−	0.417852i	$-0.137217\pi$
$937$	5.35062	+	8.00777i	0.174797	+	0.261602i	−0.733718	+	0.679454i	$0.762217\pi$
$938$	−16.2555	−	5.99000i	−0.530762	−	0.195580i
$939$	−0.854267	−	8.67352i	−0.0278780	−	0.283050i
$940$	5.13801	+	5.33576i	0.167583	+	0.174033i
$941$	14.4840	−	4.39366i	0.472164	−	0.143229i	−0.0452303	−	0.998977i	$-0.514402\pi$
$941$	14.4840	−	4.39366i	0.472164	−	0.143229i	0.517394	+	0.855747i	$0.326902\pi$
$942$	−1.39137	+	0.192986i	−0.0453333	+	0.00628783i
$943$	−48.9469	−	20.2745i	−1.59393	−	0.660227i
$944$	−19.4848	+	5.11599i	−0.634177	+	0.166511i
$945$	0.605589	−	0.250843i	0.0196998	−	0.00815992i
$946$	52.8678	−	31.0132i	1.71888	−	1.00833i
$947$	−8.16782	−	4.36579i	−0.265419	−	0.141869i	0.333320	−	0.942814i	$-0.391831\pi$
$947$	−8.16782	−	4.36579i	−0.265419	−	0.141869i	−0.598738	+	0.800945i	$0.704331\pi$
$948$	−2.17785	+	3.12982i	−0.0707333	+	0.101652i
$949$	−40.9641	−	33.6184i	−1.32975	−	1.09130i
$950$	25.2063	−	27.2887i	0.817800	−	0.885363i
$951$	1.10162	−	5.53820i	0.0357223	−	0.179588i
$952$	10.0506	−	0.208773i	0.325740	−	0.00676639i
$953$	−36.6164	+	7.28345i	−1.18612	+	0.235934i	−0.748444	−	0.663198i	$-0.769199\pi$
$953$	−36.6164	+	7.28345i	−1.18612	+	0.235934i	−0.437677	+	0.899132i	$0.644199\pi$
$954$	−21.5694	+	5.18698i	−0.698335	+	0.167935i
$955$	1.88795	+	3.53210i	0.0610926	+	0.114296i
$956$	15.9670	−	4.51621i	0.516411	−	0.146065i
$957$	−11.0508	−	1.08841i	−0.357223	−	0.0351834i
$958$	12.0838	−	4.19542i	0.390410	−	0.135548i
$959$			13.1435i			0.424426i
$960$	−0.651679	−	0.599670i	−0.0210329	−	0.0193543i
$961$			28.0734i			0.905595i
$962$	−5.88010	−	16.9361i	−0.189582	−	0.546041i
$963$	11.1579	+	1.09896i	0.359559	+	0.0354135i
$964$	5.35074	−	9.57141i	0.172336	−	0.308274i
$965$	−1.58239	−	2.96044i	−0.0509388	−	0.0952998i
$966$	−0.490843	−	2.04111i	−0.0157926	−	0.0656716i
$967$	−25.2298	+	5.01852i	−0.811336	+	0.161385i	−0.583288	−	0.812265i	$-0.698234\pi$
$967$	−25.2298	+	5.01852i	−0.811336	+	0.161385i	−0.228048	+	0.973650i	$0.573234\pi$
$968$	25.2282	+	57.4987i	0.810865	+	1.84808i
$969$	−1.05505	+	5.30409i	−0.0338931	+	0.170392i
$970$	−1.60184	−	1.47961i	−0.0514321	−	0.0475073i
$971$	11.4870	+	9.42710i	0.368634	+	0.302530i	0.800413	−	0.599450i	$-0.204614\pi$
$971$	11.4870	+	9.42710i	0.368634	+	0.302530i	−0.431779	+	0.901980i	$0.642114\pi$
$972$	14.3965	−	2.58212i	0.461768	−	0.0828217i
$973$	−18.6654	−	9.97684i	−0.598384	−	0.319843i
$974$	−17.7227	−	30.2117i	−0.567873	−	0.968045i
$975$	5.05092	−	2.09216i	0.161759	−	0.0670027i
$976$	−13.3331	+	38.6380i	−0.426781	+	1.23677i
$977$	22.4928	+	9.31684i	0.719610	+	0.298072i	0.712274	−	0.701901i	$-0.247665\pi$
$977$	22.4928	+	9.31684i	0.719610	+	0.298072i	0.00733509	+	0.999973i	$0.497665\pi$
$978$	−0.573653	−	4.13586i	−0.0183434	−	0.132250i
$979$	29.5121	−	8.95241i	0.943212	−	0.286120i
$980$	−0.788850	−	0.0148942i	−0.0251989	−	0.000475779i
$981$	−0.694741	−	7.05382i	−0.0221814	−	0.225211i
$982$	5.01222	−	13.6020i	0.159946	−	0.434059i
$983$	−9.03226	−	13.5177i	−0.288084	−	0.431149i	0.658995	−	0.752147i	$-0.270982\pi$
$983$	−9.03226	−	13.5177i	−0.288084	−	0.431149i	−0.947080	+	0.320998i	$0.895982\pi$
$984$	6.03855	−	5.16927i	0.192502	−	0.164790i
$985$	−8.70122	−	5.81397i	−0.277244	−	0.185248i
$986$	34.0972	+	5.38725i	1.08588	+	0.171565i
$987$	−2.52107	−	0.764758i	−0.0802465	−	0.0243425i
$988$	−19.8300	−	38.8460i	−0.630878	−	1.23586i
$989$	25.2429	+	30.7586i	0.802679	+	0.978067i
$990$	−6.24038	−	7.01718i	−0.198332	−	0.223021i
$991$	−6.72382	−	6.72382i	−0.213589	−	0.213589i	0.592201	−	0.805790i	$-0.298259\pi$
$991$	−6.72382	−	6.72382i	−0.213589	−	0.213589i	−0.805790	+	0.592201i	$0.798259\pi$
$992$	9.62888	−	0.966747i	0.305717	−	0.0306942i
$993$	−2.20436	+	2.20436i	−0.0699532	+	0.0699532i
$994$	−2.83296	−	0.165994i	−0.0898561	−	0.00526500i
$995$	−7.74823	+	6.35881i	−0.245635	+	0.201588i
$996$	1.18047	−	1.38427i	0.0374045	−	0.0438622i
$997$	−3.65036	+	12.0336i	−0.115608	+	0.381109i	−0.995580	−	0.0939168i	$-0.970061\pi$
$997$	−3.65036	+	12.0336i	−0.115608	+	0.381109i	0.879972	+	0.475026i	$0.157561\pi$
$998$	21.1983	+	29.1538i	0.671021	+	0.922847i
$999$	2.90978	−	4.35480i	0.0920615	−	0.137780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.b.29.32	✓	784
128.53	even	32	inner	896.2.bn.b.309.32	yes	784

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.b.29.32	✓	784	1.1	even	1	trivial
896.2.bn.b.309.32	yes	784	128.53	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.616695 - 1.27267i) q^{2} +(-0.0275048 + 0.279261i) q^{3} +(-1.23938 - 1.56970i) q^{4} +(-0.347914 + 0.185964i) q^{5} +(0.338445 + 0.207223i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.76202 + 0.609291i) q^{8} +(2.86513 + 0.569909i) q^{9} +O(q^{10})\)	\(q+(0.616695 - 1.27267i) q^{2} +(-0.0275048 + 0.279261i) q^{3} +(-1.23938 - 1.56970i) q^{4} +(-0.347914 + 0.185964i) q^{5} +(0.338445 + 0.207223i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.76202 + 0.609291i) q^{8} +(2.86513 + 0.569909i) q^{9} +(0.0221139 + 0.557462i) q^{10} +(-3.65531 + 4.45401i) q^{11} +(0.472444 - 0.302935i) q^{12} +(-1.89582 + 3.54683i) q^{13} +(1.36853 + 0.356560i) q^{14} +(-0.0423631 - 0.102274i) q^{15} +(-0.927897 + 3.89089i) q^{16} +(-1.36012 + 3.28363i) q^{17} +(2.49221 - 3.29490i) q^{18} +(-1.57404 - 5.18892i) q^{19} +(0.723103 + 0.315640i) q^{20} +(-0.279261 + 0.0275048i) q^{21} +(3.41427 + 7.39877i) q^{22} +(-4.39844 + 2.93894i) q^{23} +(-0.0941824 - 0.788083i) q^{24} +(-2.69139 + 4.02795i) q^{25} +(3.34480 + 4.60007i) q^{26} +(-0.482330 + 1.59003i) q^{27} +(1.29775 - 1.52179i) q^{28} +(5.30890 - 4.35690i) q^{29} +(-0.156286 - 0.00915735i) q^{30} +(1.20966 - 1.20966i) q^{31} +(4.37958 + 3.58040i) q^{32} +(-1.14329 - 1.14329i) q^{33} +(3.34019 + 3.75598i) q^{34} +(-0.250265 - 0.304949i) q^{35} +(-2.65638 - 5.20371i) q^{36} +(-3.01638 - 0.915009i) q^{37} +(-7.57448 - 1.19674i) q^{38} +(-0.938348 - 0.626984i) q^{39} +(0.847640 - 0.725617i) q^{40} +(5.56411 + 8.32728i) q^{41} +(-0.137214 + 0.372369i) q^{42} +(-0.737278 - 7.48570i) q^{43} +(11.5218 + 0.217542i) q^{44} +(-1.10280 + 0.334531i) q^{45} +(1.02781 + 7.41019i) q^{46} +(8.67379 + 3.59280i) q^{47} +(-1.06105 - 0.366144i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(3.46648 + 5.90926i) q^{50} +(-0.879579 - 0.470145i) q^{51} +(7.91709 - 1.41999i) q^{52} +(-4.15094 - 3.40659i) q^{53} +(1.72613 + 1.59441i) q^{54} +(0.443449 - 2.22937i) q^{55} +(-1.13643 - 2.59008i) q^{56} +(1.49236 - 0.296848i) q^{57} +(-2.27092 - 9.44334i) q^{58} +(2.37410 + 4.44164i) q^{59} +(-0.108035 + 0.193253i) q^{60} +(10.1692 + 1.00158i) q^{61} +(-0.793507 - 2.28549i) q^{62} +2.92126i q^{63} +(7.25753 - 3.36575i) q^{64} -1.58655i q^{65} +(-2.16010 + 0.749972i) q^{66} +(-12.1910 - 1.20070i) q^{67} +(6.84001 - 1.93467i) q^{68} +(-0.699754 - 1.30915i) q^{69} +(-0.542437 + 0.130444i) q^{70} +(-1.96809 + 0.391476i) q^{71} +(-8.26078 + 0.171596i) q^{72} +(-2.57065 + 12.9235i) q^{73} +(-3.02469 + 3.27457i) q^{74} +(-1.05082 - 0.862388i) q^{75} +(-6.19420 + 8.90178i) q^{76} +(-5.08155 - 2.71614i) q^{77} +(-1.37662 + 0.807549i) q^{78} +(-6.27687 + 2.59997i) q^{79} +(-0.400736 - 1.52625i) q^{80} +(7.66590 + 3.17532i) q^{81} +(14.0292 - 1.94589i) q^{82} +(3.10200 - 0.940983i) q^{83} +(0.389283 + 0.404266i) q^{84} +(-0.137430 - 1.39535i) q^{85} +(-9.98150 - 3.67808i) q^{86} +(1.07069 + 1.60240i) q^{87} +(7.38227 - 14.5292i) q^{88} +(-4.45037 - 2.97364i) q^{89} +(-0.254344 + 1.60980i) q^{90} +(-3.84854 - 1.16744i) q^{91} +(10.0646 + 3.26176i) q^{92} +(0.304540 + 0.371083i) q^{93} +(9.92153 - 8.82321i) q^{94} +(1.51258 + 1.51258i) q^{95} +(-1.12032 + 1.12457i) q^{96} +(-2.76382 + 2.76382i) q^{97} +(-0.0827221 + 1.41179i) q^{98} +(-13.0113 + 10.6781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 784 q+O(q^{10}) \) 784 * q	\( 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) \) 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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