LMFDB - Embedded newform 880.2.bi.d.219.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(219,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("880.219");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bi (of order $4$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			219.5
Character	$\chi$	$=$	880.219
Dual form			880.2.bi.d.659.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39809 + 0.212916i) q^{2} +(-1.56533 + 1.56533i) q^{3} +(1.90933 - 0.595354i) q^{4} +(-2.06921 - 0.847567i) q^{5} +(1.85519 - 2.52176i) q^{6} +3.42027 q^{7} +(-2.54267 + 1.23889i) q^{8} -1.90049i q^{9} +O(q^{10})$	\(q+(-1.39809 + 0.212916i) q^{2} +(-1.56533 + 1.56533i) q^{3} +(1.90933 - 0.595354i) q^{4} +(-2.06921 - 0.847567i) q^{5} +(1.85519 - 2.52176i) q^{6} +3.42027 q^{7} +(-2.54267 + 1.23889i) q^{8} -1.90049i q^{9} +(3.07341 + 0.744410i) q^{10} +(2.55906 - 2.10979i) q^{11} +(-2.05681 + 3.92065i) q^{12} +(-0.0456883 + 0.0456883i) q^{13} +(-4.78186 + 0.728231i) q^{14} +(4.56571 - 1.91227i) q^{15} +(3.29111 - 2.27346i) q^{16} -4.23540 q^{17} +(0.404646 + 2.65707i) q^{18} +(-5.23777 + 5.23777i) q^{19} +(-4.45541 - 0.386377i) q^{20} +(-5.35384 + 5.35384i) q^{21} +(-3.12860 + 3.49455i) q^{22} -4.53887i q^{23} +(2.04084 - 5.91937i) q^{24} +(3.56326 + 3.50759i) q^{25} +(0.0541487 - 0.0736043i) q^{26} +(-1.72109 - 1.72109i) q^{27} +(6.53044 - 2.03627i) q^{28} +(-4.51406 - 4.51406i) q^{29} +(-5.97614 + 3.64565i) q^{30} -7.51234i q^{31} +(-4.11722 + 3.87924i) q^{32} +(-0.703261 + 7.30827i) q^{33} +(5.92149 - 0.901785i) q^{34} +(-7.07726 - 2.89891i) q^{35} +(-1.13146 - 3.62867i) q^{36} +(-2.44770 + 2.44770i) q^{37} +(6.20768 - 8.43809i) q^{38} -0.143034i q^{39} +(6.31135 - 0.408438i) q^{40} +11.2312 q^{41} +(6.34525 - 8.62509i) q^{42} +(-0.823671 + 0.823671i) q^{43} +(3.63003 - 5.55183i) q^{44} +(-1.61080 + 3.93252i) q^{45} +(0.966399 + 6.34577i) q^{46} -9.31941 q^{47} +(-1.59296 + 8.71036i) q^{48} +4.69826 q^{49} +(-5.72859 - 4.14526i) q^{50} +(6.62979 - 6.62979i) q^{51} +(-0.0600335 + 0.114435i) q^{52} +(7.94399 - 7.94399i) q^{53} +(2.77269 + 2.03980i) q^{54} +(-7.08342 + 2.19662i) q^{55} +(-8.69661 + 4.23733i) q^{56} -16.3976i q^{57} +(7.27220 + 5.34997i) q^{58} +(-2.25266 + 2.25266i) q^{59} +(7.57898 - 6.36937i) q^{60} +(0.631557 + 0.631557i) q^{61} +(1.59950 + 10.5030i) q^{62} -6.50020i q^{63} +(4.93031 - 6.30016i) q^{64} +(0.133262 - 0.0558147i) q^{65} +(-0.572825 - 10.3674i) q^{66} +(6.60090 - 6.60090i) q^{67} +(-8.08680 + 2.52156i) q^{68} +(7.10481 + 7.10481i) q^{69} +(10.5119 + 2.54609i) q^{70} +3.46244 q^{71} +(2.35450 + 4.83232i) q^{72} -1.38474i q^{73} +(2.90096 - 3.94327i) q^{74} +(-11.0682 + 0.0871424i) q^{75} +(-6.88232 + 13.1190i) q^{76} +(8.75269 - 7.21605i) q^{77} +(0.0304543 + 0.199975i) q^{78} +7.15504 q^{79} +(-8.73690 + 1.91482i) q^{80} +11.0896 q^{81} +(-15.7022 + 2.39130i) q^{82} +(-8.46772 - 8.46772i) q^{83} +(-7.03484 + 13.4097i) q^{84} +(8.76394 + 3.58979i) q^{85} +(0.976196 - 1.32694i) q^{86} +14.1320 q^{87} +(-3.89305 + 8.53488i) q^{88} -9.53873i q^{89} +(1.41475 - 5.84099i) q^{90} +(-0.156266 + 0.156266i) q^{91} +(-2.70223 - 8.66622i) q^{92} +(11.7593 + 11.7593i) q^{93} +(13.0294 - 1.98425i) q^{94} +(15.2774 - 6.39868i) q^{95} +(0.372527 - 12.5171i) q^{96} -1.46575i q^{97} +(-6.56861 + 1.00034i) q^{98} +(-4.00964 - 4.86348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 8 q^{4} + 4 q^{5}+O(q^{10}) $ 256 * q - 8 * q^4 + 4 * q^5	$ 256 q - 8 q^{4} + 4 q^{5} + 12 q^{11} - 32 q^{14} + 24 q^{16} - 28 q^{20} - 80 q^{26} - 32 q^{34} + 24 q^{36} - 96 q^{44} + 4 q^{45} + 88 q^{49} - 4 q^{55} + 32 q^{56} + 96 q^{59} + 84 q^{60} - 104 q^{64} - 16 q^{66} - 8 q^{69} + 160 q^{70} - 216 q^{71} - 120 q^{80} - 160 q^{81} - 152 q^{86} - 80 q^{91} + 76 q^{99}+O(q^{100}) $ 256 * q - 8 * q^4 + 4 * q^5 + 12 * q^11 - 32 * q^14 + 24 * q^16 - 28 * q^20 - 80 * q^26 - 32 * q^34 + 24 * q^36 - 96 * q^44 + 4 * q^45 + 88 * q^49 - 4 * q^55 + 32 * q^56 + 96 * q^59 + 84 * q^60 - 104 * q^64 - 16 * q^66 - 8 * q^69 + 160 * q^70 - 216 * q^71 - 120 * q^80 - 160 * q^81 - 152 * q^86 - 80 * q^91 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.39809	+	0.212916i	−0.988602	+	0.150554i
$2$	−1.39809	+	0.212916i	−0.988602	+	0.150554i
$3$	−1.56533	+	1.56533i	−0.903742	+	0.903742i	−0.995758	−	0.0920160i	$-0.970669\pi$
$3$	−1.56533	+	1.56533i	−0.903742	+	0.903742i	0.0920160	+	0.995758i	$0.470669\pi$
$4$	1.90933	−	0.595354i	0.954667	−	0.297677i
$5$	−2.06921	−	0.847567i	−0.925379	−	0.379044i
$5$	−2.06921	−	0.847567i	−0.925379	−	0.379044i
$6$	1.85519	−	2.52176i	0.757378	−	1.02950i
$7$	3.42027			1.29274			0.646371	−	0.763024i	$-0.276286\pi$
$7$	3.42027			1.29274			0.646371	+	0.763024i	$0.276286\pi$
$8$	−2.54267	+	1.23889i	−0.898969	+	0.438013i
$9$		−	1.90049i		−	0.633498i
$10$	3.07341	+	0.744410i	0.971898	+	0.235403i
$11$	2.55906	−	2.10979i	0.771586	−	0.636125i
$11$	2.55906	−	2.10979i	0.771586	−	0.636125i
$12$	−2.05681	+	3.92065i	−0.593749	+	1.13179i
$13$	−0.0456883	+	0.0456883i	−0.0126716	+	0.0126716i	−0.713414	−	0.700743i	$-0.752852\pi$
$13$	−0.0456883	+	0.0456883i	−0.0126716	+	0.0126716i	0.700743	+	0.713414i	$0.252852\pi$
$14$	−4.78186	+	0.728231i	−1.27801	+	0.194628i
$15$	4.56571	−	1.91227i	1.17886	−	0.493746i
$16$	3.29111	−	2.27346i	0.822777	−	0.568364i
$17$	−4.23540			−1.02724			−0.513618	−	0.858019i	$-0.671695\pi$
$17$	−4.23540			−1.02724			−0.513618	+	0.858019i	$0.671695\pi$
$18$	0.404646	+	2.65707i	0.0953759	+	0.626277i
$19$	−5.23777	+	5.23777i	−1.20163	+	1.20163i	−0.227954	+	0.973672i	$0.573204\pi$
$19$	−5.23777	+	5.23777i	−1.20163	+	1.20163i	−0.973672	+	0.227954i	$0.926796\pi$
$20$	−4.45541	−	0.386377i	−0.996261	−	0.0863965i
$21$	−5.35384	+	5.35384i	−1.16830	+	1.16830i
$22$	−3.12860	+	3.49455i	−0.667020	+	0.745040i
$23$		−	4.53887i		−	0.946420i	−0.880950	−	0.473210i	$-0.843095\pi$
$23$		−	4.53887i		−	0.946420i	0.880950	−	0.473210i	$-0.156905\pi$
$24$	2.04084	−	5.91937i	0.416585	−	1.20829i
$25$	3.56326	+	3.50759i	0.712652	+	0.701518i
$26$	0.0541487	−	0.0736043i	0.0106194	−	0.0144350i
$27$	−1.72109	−	1.72109i	−0.331224	−	0.331224i
$28$	6.53044	−	2.03627i	1.23414	−	0.384819i
$29$	−4.51406	−	4.51406i	−0.838240	−	0.838240i	0.150387	−	0.988627i	$-0.451948\pi$
$29$	−4.51406	−	4.51406i	−0.838240	−	0.838240i	−0.988627	+	0.150387i	$0.951948\pi$
$30$	−5.97614	+	3.64565i	−1.09109	+	0.665601i
$31$		−	7.51234i		−	1.34926i	−0.738157	−	0.674628i	$-0.764304\pi$
$31$		−	7.51234i		−	1.34926i	0.738157	−	0.674628i	$-0.235696\pi$
$32$	−4.11722	+	3.87924i	−0.727829	+	0.685759i
$33$	−0.703261	+	7.30827i	−0.122422	+	1.27221i
$34$	5.92149	−	0.901785i	1.01553	−	0.154655i
$35$	−7.07726	−	2.89891i	−1.19628	−	0.490005i
$36$	−1.13146	−	3.62867i	−0.188577	−	0.604779i
$37$	−2.44770	+	2.44770i	−0.402399	+	0.402399i	−0.879078	−	0.476678i	$-0.841841\pi$
$37$	−2.44770	+	2.44770i	−0.402399	+	0.402399i	0.476678	+	0.879078i	$0.341841\pi$
$38$	6.20768	−	8.43809i	1.00702	−	1.36884i
$39$		−	0.143034i		−	0.0229038i
$40$	6.31135	−	0.408438i	0.997913	−	0.0645797i
$41$	11.2312			1.75401			0.877006	−	0.480479i	$-0.159537\pi$
$41$	11.2312			1.75401			0.877006	+	0.480479i	$0.159537\pi$
$42$	6.34525	−	8.62509i	0.979094	−	1.33088i
$43$	−0.823671	+	0.823671i	−0.125609	+	0.125609i	−0.767116	−	0.641508i	$-0.778309\pi$
$43$	−0.823671	+	0.823671i	−0.125609	+	0.125609i	0.641508	+	0.767116i	$0.278309\pi$
$44$	3.63003	−	5.55183i	0.547248	−	0.836971i
$45$	−1.61080	+	3.93252i	−0.240123	+	0.586225i
$46$	0.966399	+	6.34577i	0.142488	+	0.935633i
$47$	−9.31941			−1.35938			−0.679688	−	0.733502i	$-0.737885\pi$
$47$	−9.31941			−1.35938			−0.679688	+	0.733502i	$0.737885\pi$
$48$	−1.59296	+	8.71036i	−0.229924	+	1.25723i
$49$	4.69826			0.671180
$50$	−5.72859	−	4.14526i	−0.810146	−	0.586229i
$51$	6.62979	−	6.62979i	0.928356	−	0.928356i
$52$	−0.0600335	+	0.114435i	−0.00832514	+	0.0158693i
$53$	7.94399	−	7.94399i	1.09119	−	1.09119i	0.0957886	−	0.995402i	$-0.469463\pi$
$53$	7.94399	−	7.94399i	1.09119	−	1.09119i	0.995402	−	0.0957886i	$-0.0305373\pi$
$54$	2.77269	+	2.03980i	0.377315	+	0.277581i
$55$	−7.08342	+	2.19662i	−0.955129	+	0.296192i
$56$	−8.69661	+	4.23733i	−1.16213	+	0.566238i
$57$		−	16.3976i		−	2.17192i
$58$	7.27220	+	5.34997i	0.954887	+	0.702485i
$59$	−2.25266	+	2.25266i	−0.293271	+	0.293271i	−0.838371	−	0.545100i	$-0.816492\pi$
$59$	−2.25266	+	2.25266i	−0.293271	+	0.293271i	0.545100	+	0.838371i	$0.316492\pi$
$60$	7.57898	−	6.36937i	0.978442	−	0.822282i
$61$	0.631557	+	0.631557i	0.0808625	+	0.0808625i	0.746381	−	0.665519i	$-0.231790\pi$
$61$	0.631557	+	0.631557i	0.0808625	+	0.0808625i	−0.665519	+	0.746381i	$0.731790\pi$
$62$	1.59950	+	10.5030i	0.203137	+	1.33388i
$63$		−	6.50020i		−	0.818948i
$64$	4.93031	−	6.30016i	0.616289	−	0.787520i
$65$	0.133262	−	0.0558147i	0.0165292	−	0.00692297i
$66$	−0.572825	−	10.3674i	−0.0705098	−	1.27614i
$67$	6.60090	−	6.60090i	0.806428	−	0.806428i	−0.177663	−	0.984091i	$-0.556854\pi$
$67$	6.60090	−	6.60090i	0.806428	−	0.806428i	0.984091	+	0.177663i	$0.0568537\pi$
$68$	−8.08680	+	2.52156i	−0.980668	+	0.305784i
$69$	7.10481	+	7.10481i	0.855319	+	0.855319i
$70$	10.5119	+	2.54609i	1.25641	+	0.304316i
$71$	3.46244			0.410916			0.205458	−	0.978666i	$-0.434132\pi$
$71$	3.46244			0.410916			0.205458	+	0.978666i	$0.434132\pi$
$72$	2.35450	+	4.83232i	0.277480	+	0.569494i
$73$		−	1.38474i		−	0.162072i	−0.996711	−	0.0810360i	$-0.974177\pi$
$73$		−	1.38474i		−	0.162072i	0.996711	−	0.0810360i	$-0.0258229\pi$
$74$	2.90096	−	3.94327i	0.337230	−	0.458396i
$75$	−11.0682	+	0.0871424i	−1.27804	+	0.0100623i
$76$	−6.88232	+	13.1190i	−0.789456	+	1.50485i
$77$	8.75269	−	7.21605i	0.997461	−	0.822345i
$78$	0.0304543	+	0.199975i	0.00344827	+	0.0226427i
$79$	7.15504			0.805005			0.402503	−	0.915419i	$-0.368140\pi$
$79$	7.15504			0.805005			0.402503	+	0.915419i	$0.368140\pi$
$80$	−8.73690	+	1.91482i	−0.976815	+	0.214084i
$81$	11.0896			1.23218
$82$	−15.7022	+	2.39130i	−1.73402	+	0.264074i
$83$	−8.46772	−	8.46772i	−0.929453	−	0.929453i	0.0682173	−	0.997670i	$-0.478269\pi$
$83$	−8.46772	−	8.46772i	−0.929453	−	0.929453i	−0.997670	+	0.0682173i	$0.978269\pi$
$84$	−7.03484	+	13.4097i	−0.767564	+	1.46312i
$85$	8.76394	+	3.58979i	0.950582	+	0.389367i
$86$	0.976196	−	1.32694i	0.105266	−	0.143088i
$87$	14.1320			1.51511
$88$	−3.89305	+	8.53488i	−0.415001	+	0.909821i
$89$		−	9.53873i		−	1.01110i	−0.862796	−	0.505552i	$-0.831289\pi$
$89$		−	9.53873i		−	1.01110i	0.862796	−	0.505552i	$-0.168711\pi$
$90$	1.41475	−	5.84099i	0.149127	−	0.615695i
$91$	−0.156266	+	0.156266i	−0.0163812	+	0.0163812i
$92$	−2.70223	−	8.66622i	−0.281727	−	0.903516i
$93$	11.7593	+	11.7593i	1.21938	+	1.21938i
$94$	13.0294	−	1.98425i	1.34388	−	0.204660i
$95$	15.2774	−	6.39868i	1.56743	−	0.656491i
$96$	0.372527	−	12.5171i	0.0380209	−	1.27752i
$97$		−	1.46575i		−	0.148824i	−0.997228	−	0.0744120i	$-0.976292\pi$
$97$		−	1.46575i		−	0.148824i	0.997228	−	0.0744120i	$-0.0237080\pi$
$98$	−6.56861	+	1.00034i	−0.663530	+	0.101049i
$99$	−4.00964	−	4.86348i	−0.402984	−	0.488798i
$100$	8.89171	+	4.57576i	0.889171	+	0.457576i
$101$	2.98965	−	2.98965i	0.297481	−	0.297481i	−0.542546	−	0.840026i	$-0.682539\pi$
$101$	2.98965	−	2.98965i	0.297481	−	0.297481i	0.840026	+	0.542546i	$0.182539\pi$
$102$	−7.85748	+	10.6807i	−0.778006	+	1.05754i
$103$		−	15.8985i		−	1.56653i	−0.621688	−	0.783265i	$-0.713553\pi$
$103$		−	15.8985i		−	1.56653i	0.621688	−	0.783265i	$-0.286447\pi$
$104$	0.0595674	−	0.172773i	0.00584107	−	0.0169418i
$105$	15.6160	−	6.54048i	1.52396	−	0.638286i
$106$	−9.41504	+	12.7978i	−0.914469	+	1.24304i
$107$	3.57725	−	3.57725i	0.345826	−	0.345826i	−0.512726	−	0.858552i	$-0.671364\pi$
$107$	3.57725	−	3.57725i	0.345826	−	0.345826i	0.858552	+	0.512726i	$0.171364\pi$
$108$	−4.31079	−	2.26147i	−0.414806	−	0.217611i
$109$	−2.22261	−	2.22261i	−0.212887	−	0.212887i	0.592606	−	0.805493i	$-0.298099\pi$
$109$	−2.22261	−	2.22261i	−0.212887	−	0.212887i	−0.805493	+	0.592606i	$0.798099\pi$
$110$	9.43560	−	4.57925i	0.899649	−	0.436614i
$111$		−	7.66290i		−	0.727330i
$112$	11.2565	−	7.77584i	1.06364	−	0.734748i
$113$			9.26009i			0.871116i	0.900161	+	0.435558i	$0.143449\pi$
$113$			9.26009i			0.871116i	−0.900161	+	0.435558i	$0.856551\pi$
$114$	3.49132	+	22.9254i	0.326992	+	2.14716i
$115$	−3.84700	+	9.39188i	−0.358734	+	0.875797i
$116$	−11.3063	−	5.93139i	−1.04976	−	0.550716i
$117$	0.0868302	+	0.0868302i	0.00802746	+	0.00802746i
$118$	2.66980	−	3.62905i	0.245775	−	0.334081i
$119$	−14.4862			−1.32795
$120$	−9.23999	+	10.5187i	−0.843492	+	0.960218i
$121$	2.09759	−	10.7982i	0.190690	−	0.981650i
$122$	−1.01744	−	0.748507i	−0.0921150	−	0.0677666i
$123$	−17.5804	+	17.5804i	−1.58517	+	1.58517i
$124$	−4.47250	−	14.3436i	−0.401642	−	1.28809i
$125$	−4.40021	−	10.2780i	−0.393567	−	0.919296i
$126$	1.38400	+	9.08789i	0.123296	+	0.809614i
$127$		−	11.9342i		−	1.05899i	−0.848314	−	0.529493i	$-0.822382\pi$
$127$		−	11.9342i		−	1.05899i	0.848314	−	0.529493i	$-0.177618\pi$
$128$	−5.55163	+	9.85796i	−0.490700	+	0.871329i
$129$		−	2.57863i		−	0.227035i
$130$	−0.174430	+	0.106408i	−0.0152985	+	0.00933260i
$131$	−9.70195	+	9.70195i	−0.847663	+	0.847663i	−0.989841	−	0.142178i	$-0.954589\pi$
$131$	−9.70195	+	9.70195i	−0.847663	+	0.847663i	0.142178	+	0.989841i	$0.454589\pi$
$132$	3.00825	+	14.3726i	0.261834	+	1.25098i
$133$	−17.9146	+	17.9146i	−1.55339	+	1.55339i
$134$	−7.82324	+	10.6341i	−0.675825	+	0.918648i
$135$	2.10255	+	5.02003i	0.180959	+	0.432055i
$136$	10.7692	−	5.24719i	0.923453	−	0.449943i
$137$	−4.67562			−0.399465			−0.199733	−	0.979850i	$-0.564007\pi$
$137$	−4.67562			−0.399465			−0.199733	+	0.979850i	$0.564007\pi$
$138$	−11.4459	−	8.42047i	−0.974342	−	0.716798i
$139$	−13.4691	−	13.4691i	−1.14243	−	1.14243i	−0.988004	−	0.154427i	$-0.950647\pi$
$139$	−13.4691	−	13.4691i	−1.14243	−	1.14243i	−0.154427	−	0.988004i	$-0.549353\pi$
$140$	−15.2387	−	1.32151i	−1.28791	−	0.111688i
$141$	14.5879	−	14.5879i	1.22852	−	1.22852i
$142$	−4.84081	+	0.737209i	−0.406232	+	0.0618652i
$143$	−0.0205266	+	0.213312i	−0.00171652	+	0.0178380i
$144$	−4.32069	−	6.25473i	−0.360057	−	0.521227i
$145$	5.51457	+	13.1665i	0.457960	+	1.09342i
$146$	0.294834	+	1.93600i	0.0244007	+	0.160225i
$147$	−7.35431	+	7.35431i	−0.606573	+	0.606573i
$148$	−3.21623	+	6.13072i	−0.264372	+	0.503942i
$149$	−7.17389	+	7.17389i	−0.587708	+	0.587708i	−0.937010	−	0.349302i	$-0.886419\pi$
$149$	−7.17389	+	7.17389i	−0.587708	+	0.587708i	0.349302	+	0.937010i	$0.386419\pi$
$150$	15.4558	−	2.47843i	1.26196	−	0.202363i
$151$		−	12.6779i		−	1.03171i	−0.856676	−	0.515854i	$-0.827475\pi$
$151$		−	12.6779i		−	1.03171i	0.856676	−	0.515854i	$-0.172525\pi$
$152$	6.82889	−	19.8069i	0.553896	−	1.60655i
$153$			8.04935i			0.650751i
$154$	−10.7007	+	11.9523i	−0.862284	+	0.963144i
$155$	−6.36722	+	15.5446i	−0.511427	+	1.24857i
$156$	−0.0851559	−	0.273100i	−0.00681792	−	0.0218655i
$157$	−0.480603	−	0.480603i	−0.0383563	−	0.0383563i	0.687669	−	0.726025i	$-0.258634\pi$
$157$	−0.480603	−	0.480603i	−0.0383563	−	0.0383563i	−0.726025	+	0.687669i	$0.758634\pi$
$158$	−10.0034	+	1.52342i	−0.795830	+	0.121197i
$159$			24.8699i			1.97231i
$160$	11.8073	−	4.53733i	0.933450	−	0.358707i
$161$		−	15.5242i		−	1.22348i
$162$	−15.5043	+	2.36116i	−1.21813	+	0.185510i
$163$	12.6233	−	12.6233i	0.988733	−	0.988733i	−0.0112045	−	0.999937i	$-0.503567\pi$
$163$	12.6233	−	12.6233i	0.988733	−	0.988733i	0.999937	+	0.0112045i	$0.00356657\pi$
$164$	21.4440	−	6.68651i	1.67450	−	0.522129i
$165$	7.64945	−	14.5263i	0.595509	−	1.13087i
$166$	13.6416	+	10.0358i	1.05879	+	0.778926i
$167$	16.9179			1.30914			0.654572	−	0.756000i	$-0.272849\pi$
$167$	16.9179			1.30914			0.654572	+	0.756000i	$0.272849\pi$
$168$	6.98023	−	20.2458i	0.538536	−	1.56200i
$169$			12.9958i			0.999679i
$170$	−13.0171	−	3.15288i	−0.998368	−	0.241815i
$171$	9.95433	+	9.95433i	0.761227	+	0.761227i
$172$	−1.08229	+	2.06304i	−0.0825236	+	0.157305i
$173$	4.03554	−	4.03554i	0.306816	−	0.306816i	−0.536857	−	0.843673i	$-0.680389\pi$
$173$	4.03554	−	4.03554i	0.306816	−	0.306816i	0.843673	+	0.536857i	$0.180389\pi$
$174$	−19.7578	+	3.00892i	−1.49784	+	0.228106i
$175$	12.1873	+	11.9969i	0.921275	+	0.906881i
$176$	3.62564	−	12.7615i	0.273293	−	0.961931i
$177$		−	7.05228i		−	0.530082i
$178$	2.03095	+	13.3360i	0.152226	+	0.999578i
$179$	−15.5027	−	15.5027i	−1.15872	−	1.15872i	−0.984750	−	0.173973i	$-0.944339\pi$
$179$	−15.5027	−	15.5027i	−1.15872	−	1.15872i	−0.173973	−	0.984750i	$-0.555661\pi$
$180$	−0.734307	+	8.46748i	−0.0547320	+	0.631129i
$181$	5.20474	+	5.20474i	0.386865	+	0.386865i	0.873568	−	0.486703i	$-0.161800\pi$
$181$	5.20474	+	5.20474i	0.386865	+	0.386865i	−0.486703	+	0.873568i	$0.661800\pi$
$182$	0.185203	−	0.251747i	0.0137282	−	0.0186607i
$183$	−1.97718			−0.146158
$184$	5.62315	+	11.5408i	0.414544	+	0.850802i
$185$	7.13940	−	2.99022i	0.524899	−	0.219845i
$186$	−18.9443	−	13.9368i	−1.38906	−	1.02190i
$187$	−10.8387	+	8.93580i	−0.792601	+	0.653450i
$188$	−17.7939	+	5.54834i	−1.29775	+	0.404654i
$189$	−5.88659	−	5.88659i	−0.428186	−	0.428186i
$190$	−19.9969	+	12.1988i	−1.45072	+	0.884991i
$191$			19.6764i			1.42373i	0.702315	+	0.711866i	$0.252150\pi$
$191$			19.6764i			1.42373i	−0.702315	+	0.711866i	$0.747850\pi$
$192$	2.14426	+	17.5794i	0.154748	+	1.26868i
$193$	−15.6401			−1.12580			−0.562898	−	0.826526i	$-0.690314\pi$
$193$	−15.6401			−1.12580			−0.562898	+	0.826526i	$0.690314\pi$
$194$	0.312081	+	2.04925i	0.0224061	+	0.147128i
$195$	−0.121231	+	0.295968i	−0.00868153	+	0.0211947i
$196$	8.97055	−	2.79713i	0.640753	−	0.199795i
$197$	14.9181	+	14.9181i	1.06287	+	1.06287i	0.997886	+	0.0649821i	$0.0206990\pi$
$197$	14.9181	+	14.9181i	1.06287	+	1.06287i	0.0649821	+	0.997886i	$0.479301\pi$
$198$	6.64136	+	5.94588i	0.471981	+	0.422555i
$199$	−15.6588			−1.11002			−0.555010	−	0.831844i	$-0.687286\pi$
$199$	−15.6588			−1.11002			−0.555010	+	0.831844i	$0.687286\pi$
$200$	−13.4057	−	4.50415i	−0.947926	−	0.318492i
$201$			20.6651i			1.45761i
$202$	−3.54326	+	4.81635i	−0.249303	+	0.338877i
$203$	−15.4393	−	15.4393i	−1.08363	−	1.08363i
$204$	8.71141	−	16.6055i	0.609920	−	1.16262i
$205$	−23.2396	−	9.51916i	−1.62313	−	0.664847i
$206$	3.38506	+	22.2277i	0.235848	+	1.54867i
$207$	−8.62609			−0.599555
$208$	−0.0464947	+	0.254235i	−0.00322383	+	0.0176280i
$209$	−2.35319	+	24.4543i	−0.162774	+	1.69154i
$210$	−20.4400	+	12.4691i	−1.41049	+	0.860450i
$211$	5.21949	−	5.21949i	0.359324	−	0.359324i	−0.504239	−	0.863564i	$-0.668227\pi$
$211$	5.21949	−	5.21949i	0.359324	−	0.359324i	0.863564	+	0.504239i	$0.168227\pi$
$212$	10.4382	−	19.8972i	0.716901	−	1.36655i
$213$	−5.41985	+	5.41985i	−0.371362	+	0.371362i
$214$	−4.23968	+	5.76299i	−0.289819	+	0.393950i
$215$	2.40246	−	1.00623i	0.163847	−	0.0686244i
$216$	6.50839	+	2.24392i	0.442840	+	0.152679i
$217$		−	25.6943i		−	1.74424i
$218$	3.58064	+	2.63419i	0.242512	+	0.178410i
$219$	2.16758	+	2.16758i	0.146471	+	0.146471i
$220$	−12.2169	+	8.41121i	−0.823660	+	0.567084i
$221$	0.193508	−	0.193508i	0.0130168	−	0.0130168i
$222$	1.63156	+	10.7135i	0.109503	+	0.719040i
$223$	−1.37120			−0.0918225			−0.0459112	−	0.998946i	$-0.514619\pi$
$223$	−1.37120			−0.0918225			−0.0459112	+	0.998946i	$0.514619\pi$
$224$	−14.0820	+	13.2680i	−0.940895	+	0.886508i
$225$	6.66615	−	6.77195i	0.444410	−	0.451463i
$226$	−1.97162	−	12.9465i	−0.131150	−	0.861187i
$227$	−1.70218	−	1.70218i	−0.112977	−	0.112977i	0.648358	−	0.761336i	$-0.275456\pi$
$227$	−1.70218	−	1.70218i	−0.112977	−	0.112977i	−0.761336	+	0.648358i	$0.775456\pi$
$228$	−9.76238	−	31.3085i	−0.646530	−	2.07346i
$229$	20.3927	+	20.3927i	1.34758	+	1.34758i	0.888277	+	0.459308i	$0.151903\pi$
$229$	20.3927	+	20.3927i	1.34758	+	1.34758i	0.459308	+	0.888277i	$0.348097\pi$
$230$	3.37878	−	13.9498i	0.222790	−	0.919824i
$231$	−2.40534	+	24.9963i	−0.158260	+	1.64463i
$232$	17.0702	+	5.88534i	1.12071	+	0.386392i
$233$			18.2536i			1.19584i	0.801557	+	0.597918i	$0.204005\pi$
$233$			18.2536i			1.19584i	−0.801557	+	0.597918i	$0.795995\pi$
$234$	−0.139884	−	0.102909i	−0.00914453	−	0.00672739i
$235$	19.2838	+	7.89883i	1.25794	+	0.515263i
$236$	−2.95994	+	5.64220i	−0.192676	+	0.367276i
$237$	−11.2000	+	11.2000i	−0.727517	+	0.727517i
$238$	20.2531	−	3.08435i	1.31281	−	0.199929i
$239$	−1.21017			−0.0782797			−0.0391399	−	0.999234i	$-0.512462\pi$
$239$	−1.21017			−0.0782797			−0.0391399	+	0.999234i	$0.512462\pi$
$240$	10.6788	−	16.6734i	0.689312	−	1.07626i
$241$		−	18.5737i		−	1.19644i	−0.801333	−	0.598218i	$-0.795876\pi$
$241$		−	18.5737i		−	1.19644i	0.801333	−	0.598218i	$-0.204124\pi$
$242$	−0.633531	+	15.5434i	−0.0407249	+	0.999170i
$243$	−12.1956	+	12.1956i	−0.782347	+	0.782347i
$244$	1.58185	+	0.829853i	0.101268	+	0.0531259i
$245$	−9.72169	−	3.98209i	−0.621096	−	0.254407i
$246$	20.8359	−	28.3223i	1.32845	−	1.80576i
$247$		−	0.478609i		−	0.0304532i
$248$	9.30695	+	19.1014i	0.590992	+	1.21294i
$249$	26.5095			1.67997
$250$	8.34027	+	13.4328i	0.527485	+	0.849564i
$251$	−9.66599	+	9.66599i	−0.610112	+	0.610112i	−0.942975	−	0.332863i	$-0.891985\pi$
$251$	−9.66599	+	9.66599i	−0.610112	+	0.610112i	0.332863	+	0.942975i	$0.391985\pi$
$252$	−3.86992	−	12.4111i	−0.243782	−	0.781823i
$253$	−9.57605	−	11.6153i	−0.602041	−	0.730245i
$254$	2.54098	+	16.6851i	0.159435	+	1.04692i
$255$	−19.3376	+	8.09923i	−1.21097	+	0.507193i
$256$	5.66279	−	14.9644i	0.353924	−	0.935274i
$257$		−	0.110589i		−	0.00689838i	−0.999994	−	0.00344919i	$-0.998902\pi$
$257$		−	0.110589i		−	0.00689838i	0.999994	−	0.00344919i	$-0.00109791\pi$
$258$	0.549031	+	3.60516i	0.0341812	+	0.224448i
$259$	−8.37180	+	8.37180i	−0.520198	+	0.520198i
$260$	0.221213	−	0.185907i	0.0137191	−	0.0115295i
$261$	−8.57894	+	8.57894i	−0.531023	+	0.531023i
$262$	11.4985	−	15.6299i	0.710382	−	0.965621i
$263$	20.8626			1.28644			0.643221	−	0.765680i	$-0.277598\pi$
$263$	20.8626			1.28644			0.643221	+	0.765680i	$0.277598\pi$
$264$	−7.26597	−	19.4538i	−0.447190	−	1.19730i
$265$	−23.1708	+	9.70471i	−1.42337	+	0.596156i
$266$	21.2320	−	28.8606i	1.30182	−	1.76956i
$267$	14.9312	+	14.9312i	0.913776	+	0.913776i
$268$	8.67345	−	16.5332i	0.529815	−	1.00993i
$269$	10.1471	−	10.1471i	0.618677	−	0.618677i	−0.326515	−	0.945192i	$-0.605874\pi$
$269$	10.1471	−	10.1471i	0.618677	−	0.618677i	0.945192	+	0.326515i	$0.105874\pi$
$270$	−4.00841	−	6.57081i	−0.243944	−	0.399886i
$271$	−15.7456			−0.956479			−0.478240	−	0.878229i	$-0.658725\pi$
$271$	−15.7456			−0.956479			−0.478240	+	0.878229i	$0.658725\pi$
$272$	−13.9392	+	9.62900i	−0.845186	+	0.583844i
$273$		−	0.489216i		−	0.0296087i
$274$	6.53696	−	0.995516i	0.394912	−	0.0601413i
$275$	16.5189	+	1.45842i	0.996125	+	0.0879458i
$276$	17.7953	+	9.33558i	1.07115	+	0.561936i
$277$	0.0951882	+	0.0951882i	0.00571930	+	0.00571930i	0.709961	−	0.704241i	$-0.248713\pi$
$277$	0.0951882	+	0.0951882i	0.00571930	+	0.00571930i	−0.704241	+	0.709961i	$0.748713\pi$
$278$	21.6988	+	15.9632i	1.30141	+	0.957412i
$279$	−14.2772			−0.854751
$280$	21.5865	−	1.39697i	1.29004	−	0.0834849i
$281$	−22.1931			−1.32393			−0.661965	−	0.749534i	$-0.730277\pi$
$281$	−22.1931			−1.32393			−0.661965	+	0.749534i	$0.730277\pi$
$282$	−17.2893	+	23.5013i	−1.02956	+	1.39948i
$283$	4.69282	−	4.69282i	0.278959	−	0.278959i	−0.553734	−	0.832693i	$-0.686798\pi$
$283$	4.69282	−	4.69282i	0.278959	−	0.278959i	0.832693	+	0.553734i	$0.186798\pi$
$284$	6.61095	−	2.06137i	0.392288	−	0.122320i
$285$	−13.8981	+	33.9301i	−0.823252	+	2.00985i
$286$	−0.0167194	−	0.302600i	−0.000988641	−	0.0178931i
$287$	38.4136			2.26748
$288$	7.37246	+	7.82475i	0.434426	+	0.461078i
$289$	0.938632			0.0552136
$290$	−10.5133	−	17.2339i	−0.617360	−	1.01201i
$291$	2.29437	+	2.29437i	0.134499	+	0.134499i
$292$	−0.824412	−	2.64394i	−0.0482451	−	0.154725i
$293$	−7.97017	−	7.97017i	−0.465622	−	0.465622i	0.434871	−	0.900493i	$-0.356794\pi$
$293$	−7.97017	−	7.97017i	−0.465622	−	0.465622i	−0.900493	+	0.434871i	$0.856794\pi$
$294$	8.71617	−	11.8479i	0.508337	−	0.690982i
$295$	6.57050	−	2.75194i	0.382549	−	0.160224i
$296$	3.19126	−	9.25611i	0.185488	−	0.538001i
$297$	−8.03550	−	0.773240i	−0.466267	−	0.0448679i
$298$	8.50234	−	11.5572i	0.492527	−	0.669491i
$299$	0.207373	+	0.207373i	0.0119927	+	0.0119927i
$300$	−21.0810	+	6.75587i	−1.21711	+	0.390050i
$301$	−2.81718	+	2.81718i	−0.162379	+	0.162379i
$302$	2.69932	+	17.7248i	0.155328	+	1.01995i
$303$			9.35954i			0.537692i
$304$	−5.33022	+	29.1459i	−0.305709	+	1.67163i
$305$	−0.771536	−	1.84211i	−0.0441780	−	0.105479i
$306$	−1.71384	−	11.2537i	−0.0979735	−	0.643334i
$307$	−10.3368	−	10.3368i	−0.589950	−	0.589950i	0.347668	−	0.937618i	$-0.386974\pi$
$307$	−10.3368	−	10.3368i	−0.589950	−	0.589950i	−0.937618	+	0.347668i	$0.886974\pi$
$308$	12.4157	−	18.9888i	0.707450	−	1.08199i
$309$	24.8864	+	24.8864i	1.41574	+	1.41574i
$310$	5.59227	−	23.0885i	0.317619	−	1.31134i
$311$	6.58689			0.373508			0.186754	−	0.982407i	$-0.440203\pi$
$311$	6.58689			0.373508			0.186754	+	0.982407i	$0.440203\pi$
$312$	0.177203	+	0.363688i	0.0100322	+	0.0205898i
$313$	4.36850			0.246922			0.123461	−	0.992349i	$-0.460601\pi$
$313$	4.36850			0.246922			0.123461	+	0.992349i	$0.460601\pi$
$314$	0.774256	+	0.569600i	0.0436938	+	0.0321444i
$315$	−5.50936	+	13.4503i	−0.310417	+	0.757838i
$316$	13.6614	−	4.25978i	0.768512	−	0.239631i
$317$	0.932586	+	0.932586i	0.0523792	+	0.0523792i	0.732811	−	0.680432i	$-0.238208\pi$
$317$	0.932586	+	0.932586i	0.0523792	+	0.0523792i	−0.680432	+	0.732811i	$0.738208\pi$
$318$	−5.29519	−	34.7704i	−0.296940	−	1.94983i
$319$	−21.0755	−	2.02805i	−1.18000	−	0.113549i
$320$	−15.5417	+	8.85758i	−0.868805	+	0.495154i
$321$			11.1991i			0.625075i
$322$	3.30535	+	21.7043i	0.184200	+	1.20953i
$323$	22.1840	−	22.1840i	1.23435	−	1.23435i
$324$	21.1738	−	6.60224i	1.17632	−	0.366791i
$325$	−0.323055	+	0.00254349i	−0.0179199	+	0.000141087i
$326$	−14.9608	+	20.3363i	−0.828605	+	1.12632i
$327$	6.95821			0.384790
$328$	−28.5571	+	13.9142i	−1.57680	+	0.768281i
$329$	−31.8749			−1.75732
$330$	−7.60176	+	21.9378i	−0.418463	+	1.20764i
$331$	−1.02681	+	1.02681i	−0.0564386	+	0.0564386i	−0.734763	−	0.678324i	$-0.762707\pi$
$331$	−1.02681	+	1.02681i	−0.0564386	+	0.0564386i	0.678324	+	0.734763i	$0.262707\pi$
$332$	−21.2090	−	11.1264i	−1.16399	−	0.610641i
$333$	4.65184	+	4.65184i	0.254919	+	0.254919i
$334$	−23.6528	+	3.60209i	−1.29422	+	0.197097i
$335$	−19.2534	+	8.06394i	−1.05192	+	0.440580i
$336$	−5.44835	+	29.7918i	−0.297232	+	1.62528i
$337$	−5.05616			−0.275427			−0.137713	−	0.990472i	$-0.543975\pi$
$337$	−5.05616			−0.275427			−0.137713	+	0.990472i	$0.543975\pi$
$338$	−2.76702	−	18.1694i	−0.150506	−	0.988284i
$339$	−14.4951	−	14.4951i	−0.787264	−	0.787264i
$340$	18.8705	+	1.63646i	1.02339	+	0.0887496i
$341$	−15.8495	−	19.2246i	−0.858296	−	1.04107i
$342$	−16.0365	−	11.7977i	−0.867156	−	0.637944i
$343$	−7.87258			−0.425079
$344$	1.07388	−	3.11476i	0.0579000	−	0.167936i
$345$	−8.67954	−	20.7232i	−0.467291	−	1.11570i
$346$	−4.78283	+	6.50129i	−0.257126	+	0.349511i
$347$	9.65646	−	9.65646i	0.518386	−	0.518386i	−0.398697	−	0.917083i	$-0.630537\pi$
$347$	9.65646	−	9.65646i	0.518386	−	0.518386i	0.917083	+	0.398697i	$0.130537\pi$
$348$	26.9826	−	8.41351i	1.44642	−	0.451012i
$349$	−12.3365	−	12.3365i	−0.660359	−	0.660359i	0.295106	−	0.955465i	$-0.404645\pi$
$349$	−12.3365	−	12.3365i	−0.660359	−	0.660359i	−0.955465	+	0.295106i	$0.904645\pi$
$350$	−19.5933	−	14.1779i	−1.04731	−	0.757842i
$351$	0.157267			0.00839429
$352$	−2.35186	+	18.6137i	−0.125355	+	0.992112i
$353$		−	0.189733i		−	0.0100985i	−0.999987	−	0.00504924i	$-0.998393\pi$
$353$		−	0.189733i		−	0.0100985i	0.999987	−	0.00504924i	$-0.00160723\pi$
$354$	1.50154	+	9.85976i	0.0798062	+	0.524040i
$355$	−7.16451	−	2.93465i	−0.380253	−	0.155755i
$356$	−5.67892	−	18.2126i	−0.300982	−	0.965267i
$357$	22.6757	−	22.6757i	1.20012	−	1.20012i
$358$	24.9749	+	18.3734i	1.31997	+	0.971065i
$359$		−	7.08784i		−	0.374082i	−0.982352	−	0.187041i	$-0.940110\pi$
$359$		−	7.08784i		−	0.374082i	0.982352	−	0.187041i	$-0.0598897\pi$
$360$	−0.776234	−	11.9947i	−0.0409111	−	0.632175i
$361$		−	35.8684i		−	1.88781i
$362$	−8.38489	−	6.16854i	−0.440700	−	0.324211i
$363$	13.6192	+	20.1860i	0.714823	+	1.05949i
$364$	−0.205331	+	0.391398i	−0.0107623	+	0.0205148i
$365$	−1.17366	+	2.86533i	−0.0614324	+	0.149978i
$366$	2.76429	−	0.420974i	0.144492	−	0.0220047i
$367$	6.93730			0.362124			0.181062	−	0.983472i	$-0.442047\pi$
$367$	6.93730			0.362124			0.181062	+	0.983472i	$0.442047\pi$
$368$	−10.3189	−	14.9379i	−0.537911	−	0.778693i
$369$		−	21.3447i		−	1.11116i
$370$	−9.34488	+	5.70070i	−0.485817	+	0.296365i
$371$	27.1706	−	27.1706i	1.41063	−	1.41063i
$372$	29.4533	+	15.4514i	1.52708	+	0.801120i
$373$	12.3109	+	12.3109i	0.637436	+	0.637436i	0.949922	−	0.312486i	$-0.101162\pi$
$373$	12.3109	+	12.3109i	0.637436	+	0.637436i	−0.312486	+	0.949922i	$0.601162\pi$
$374$	13.2509	−	14.8008i	0.685187	−	0.765332i
$375$	22.9763	+	9.20072i	1.18649	+	0.475123i
$376$	23.6962	−	11.5457i	1.22204	−	0.595424i
$377$	0.412479			0.0212438
$378$	9.48335	+	6.97665i	0.487771	+	0.358840i
$379$	6.72090	−	6.72090i	0.345230	−	0.345230i	−0.513099	−	0.858329i	$-0.671503\pi$
$379$	6.72090	−	6.72090i	0.345230	−	0.345230i	0.858329	+	0.513099i	$0.171503\pi$
$380$	25.3602	−	21.3127i	1.30095	−	1.09332i
$381$	18.6809	+	18.6809i	0.957050	+	0.957050i
$382$	−4.18942	−	27.5094i	−0.214349	−	1.40750i
$383$	−7.34248			−0.375183			−0.187592	−	0.982247i	$-0.560068\pi$
$383$	−7.34248			−0.375183			−0.187592	+	0.982247i	$0.560068\pi$
$384$	−6.74080	−	24.1210i	−0.343990	−	1.23092i
$385$	−24.2272	+	7.51303i	−1.23473	+	0.382899i
$386$	21.8663	−	3.33002i	1.11296	−	0.169494i
$387$	1.56538	+	1.56538i	0.0795728	+	0.0795728i
$388$	−0.872638	−	2.79860i	−0.0443015	−	0.142077i
$389$	−14.9459	−	14.9459i	−0.757786	−	0.757786i	0.218133	−	0.975919i	$-0.430003\pi$
$389$	−14.9459	−	14.9459i	−0.757786	−	0.757786i	−0.975919	+	0.218133i	$0.930003\pi$
$390$	0.106476	−	0.439603i	0.00539163	−	0.0222601i
$391$			19.2239i			0.972197i
$392$	−11.9461	+	5.82062i	−0.603370	+	0.293986i
$393$		−	30.3734i		−	1.53214i
$394$	−24.0332	−	17.6806i	−1.21077	−	0.890734i
$395$	−14.8053	−	6.06438i	−0.744935	−	0.305132i
$396$	−10.5512	−	6.89885i	−0.530219	−	0.346680i
$397$	0.618034	+	0.618034i	0.0310183	+	0.0310183i	0.722446	−	0.691428i	$-0.243018\pi$
$397$	0.618034	+	0.618034i	0.0310183	+	0.0310183i	−0.691428	+	0.722446i	$0.743018\pi$
$398$	21.8924	−	3.33400i	1.09737	−	0.167119i
$399$		−	56.0843i		−	2.80773i
$400$	19.7014	+	3.44294i	0.985071	+	0.172147i
$401$	9.09945			0.454405			0.227202	−	0.973848i	$-0.427042\pi$
$401$	9.09945			0.454405			0.227202	+	0.973848i	$0.427042\pi$
$402$	−4.39994	−	28.8918i	−0.219449	−	1.44099i
$403$	0.343226	+	0.343226i	0.0170973	+	0.0170973i
$404$	3.92833	−	7.48813i	0.195442	−	0.372548i
$405$	−22.9467	−	9.39919i	−1.14023	−	0.467049i
$406$	24.8729	+	18.2983i	1.23442	+	0.908132i
$407$	−1.09969	+	11.4279i	−0.0545095	+	0.566462i
$408$	−8.64378	+	25.0709i	−0.427931	+	1.24119i
$409$	9.97728			0.493345			0.246672	−	0.969099i	$-0.420663\pi$
$409$	9.97728			0.493345			0.246672	+	0.969099i	$0.420663\pi$
$410$	34.5180	+	8.36059i	1.70472	+	0.412900i
$411$	7.31888	−	7.31888i	0.361013	−	0.361013i
$412$	−9.46526	−	30.3556i	−0.466320	−	1.49551i
$413$	−7.70470	+	7.70470i	−0.379123	+	0.379123i
$414$	12.0601	−	1.83663i	0.592721	−	0.0902656i
$415$	10.3445	+	24.6985i	0.507793	+	1.21240i
$416$	0.0108732	−	0.365344i	0.000533103	−	0.0179125i
$417$	42.1670			2.06493
$418$	−1.91674	−	34.6905i	−0.0937508	−	1.69677i
$419$	12.4664	+	12.4664i	0.609024	+	0.609024i	0.942691	−	0.333667i	$-0.108286\pi$
$419$	12.4664	+	12.4664i	0.609024	+	0.609024i	−0.333667	+	0.942691i	$0.608286\pi$
$420$	25.9222	−	21.7850i	1.26487	−	1.06300i
$421$	6.28410	+	6.28410i	0.306268	+	0.306268i	0.843460	−	0.537192i	$-0.180515\pi$
$421$	6.28410	+	6.28410i	0.306268	+	0.306268i	−0.537192	+	0.843460i	$0.680515\pi$
$422$	−6.18602	+	8.40865i	−0.301131	+	0.409327i
$423$			17.7115i			0.861161i
$424$	−10.3572	+	30.0406i	−0.502990	+	1.45890i
$425$	−15.0918	−	14.8561i	−0.732062	−	0.720624i
$426$	6.42348	−	8.73143i	0.311219	−	0.423039i
$427$	2.16010	+	2.16010i	0.104534	+	0.104534i
$428$	4.70044	−	8.95990i	0.227204	−	0.433093i
$429$	−0.301772	−	0.366033i	−0.0145697	−	0.0176722i
$430$	−3.14463	+	1.91833i	−0.151647	+	0.0925101i
$431$	−27.1745			−1.30895			−0.654475	−	0.756083i	$-0.727110\pi$
$431$	−27.1745			−1.30895			−0.654475	+	0.756083i	$0.727110\pi$
$432$	−9.57711	−	1.75147i	−0.460779	−	0.0842675i
$433$			18.8248i			0.904661i	0.891850	+	0.452330i	$0.149407\pi$
$433$			18.8248i			0.904661i	−0.891850	+	0.452330i	$0.850593\pi$
$434$	5.47072	+	35.9230i	0.262603	+	1.72436i
$435$	−29.2420	−	11.9778i	−1.40205	−	0.574291i
$436$	−5.56694	−	2.92046i	−0.266608	−	0.139865i
$437$	23.7735	+	23.7735i	1.13724	+	1.13724i
$438$	−3.49199	−	2.56896i	−0.166854	−	0.122750i
$439$			29.6690i			1.41602i	0.706201	+	0.708012i	$0.250408\pi$
$439$			29.6690i			1.41602i	−0.706201	+	0.708012i	$0.749592\pi$
$440$	15.2894	−	14.3608i	0.728895	−	0.684626i
$441$		−	8.92901i		−	0.425191i
$442$	−0.229342	+	0.311744i	−0.0109087	+	0.0148281i
$443$	−21.9275	−	21.9275i	−1.04180	−	1.04180i	−0.999087	−	0.0427177i	$-0.986398\pi$
$443$	−21.9275	−	21.9275i	−1.04180	−	1.04180i	−0.0427177	−	0.999087i	$-0.513602\pi$
$444$	−4.56213	−	14.6310i	−0.216509	−	0.694358i
$445$	−8.08471	+	19.7376i	−0.383252	+	0.935653i
$446$	1.91707	−	0.291951i	0.0907758	−	0.0138243i
$447$		−	22.4590i		−	1.06227i
$448$	16.8630	−	21.5483i	0.796702	−	1.01806i
$449$	−10.0115			−0.472471			−0.236236	−	0.971696i	$-0.575914\pi$
$449$	−10.0115			−0.472471			−0.236236	+	0.971696i	$0.575914\pi$
$450$	−7.87804	+	10.8872i	−0.371374	+	0.513225i
$451$	28.7412	−	23.6954i	1.35337	−	1.11577i
$452$	5.51303	+	17.6806i	0.259311	+	0.831626i
$453$	19.8450	+	19.8450i	0.932398	+	0.932398i
$454$	2.74222	+	2.01738i	0.128699	+	0.0946804i
$455$	0.455794	−	0.190902i	0.0213680	−	0.00894960i
$456$	20.3148	+	41.6937i	0.951329	+	1.95249i
$457$		−	12.0069i		−	0.561657i	−0.959758	−	0.280828i	$-0.909391\pi$
$457$		−	12.0069i		−	0.561657i	0.959758	−	0.280828i	$-0.0906092\pi$
$458$	−32.8528	−	24.1689i	−1.53511	−	1.12934i
$459$	7.28950	+	7.28950i	0.340245	+	0.340245i
$460$	−1.75372	+	20.2225i	−0.0817674	+	0.942881i
$461$	18.4668	+	18.4668i	0.860084	+	0.860084i	0.991348	−	0.131263i	$-0.0419033\pi$
$461$	18.4668	+	18.4668i	0.860084	+	0.860084i	−0.131263	+	0.991348i	$0.541903\pi$
$462$	−1.95922	−	35.4593i	−0.0911510	−	1.64972i
$463$	12.6625			0.588477			0.294238	−	0.955732i	$-0.404934\pi$
$463$	12.6625			0.588477			0.294238	+	0.955732i	$0.404934\pi$
$464$	−25.1188	−	4.59374i	−1.16611	−	0.213259i
$465$	−14.3656	−	34.2992i	−0.666190	−	1.59059i
$466$	−3.88649	−	25.5203i	−0.180038	−	1.18221i
$467$	−21.9912	+	21.9912i	−1.01763	+	1.01763i	−0.0177877	+	0.999842i	$0.505662\pi$
$467$	−21.9912	+	21.9912i	−1.01763	+	1.01763i	−0.999842	+	0.0177877i	$0.994338\pi$
$468$	0.217483	+	0.114093i	0.0100531	+	0.00527396i
$469$	22.5769	−	22.5769i	1.04250	−	1.04250i
$470$	−28.6424	−	6.93747i	−1.32117	−	0.320001i
$471$	1.50460			0.0693284
$472$	2.93697	−	8.51854i	0.135185	−	0.392098i
$473$	−0.370054	+	3.84560i	−0.0170151	+	0.176821i
$474$	13.2740	−	18.0433i	0.609693	−	0.828755i
$475$	−37.0354	+	0.291589i	−1.69930	+	0.0133790i
$476$	−27.6590	+	8.62443i	−1.26775	+	0.395300i
$477$	−15.0975	−	15.0975i	−0.691266	−	0.691266i
$478$	1.69194	−	0.257666i	0.0773874	−	0.0117854i
$479$	38.0454			1.73834			0.869170	−	0.494513i	$-0.164654\pi$
$479$	38.0454			1.73834			0.869170	+	0.494513i	$0.164654\pi$
$480$	−11.3799	+	25.5847i	−0.519419	+	1.16778i
$481$		−	0.223662i		−	0.0101981i
$482$	3.95464	+	25.9678i	0.180129	+	1.18280i
$483$	24.3004	+	24.3004i	1.10571	+	1.10571i
$484$	−2.42371	−	21.8661i	−0.110169	−	0.993913i
$485$	−1.24232	+	3.03294i	−0.0564108	+	0.137719i
$486$	14.4539	−	19.6472i	0.655644	−	0.891216i
$487$		−	11.4556i		−	0.519103i	−0.965729	−	0.259551i	$-0.916425\pi$
$487$		−	11.4556i		−	0.519103i	0.965729	−	0.259551i	$-0.0835747\pi$
$488$	−2.38827	−	0.823410i	−0.108112	−	0.0372740i
$489$			39.5191i			1.78712i
$490$	14.4397	+	3.49743i	0.652318	+	0.157998i
$491$	−12.9967	−	12.9967i	−0.586533	−	0.586533i	0.350158	−	0.936691i	$-0.386128\pi$
$491$	−12.9967	−	12.9967i	−0.586533	−	0.586533i	−0.936691	+	0.350158i	$0.886128\pi$
$492$	−23.1003	+	44.0335i	−1.04144	+	1.98518i
$493$	19.1189	+	19.1189i	0.861071	+	0.861071i
$494$	0.101904	+	0.669140i	0.00458486	+	0.0301060i
$495$	4.17465	+	13.4620i	0.187637	+	0.605072i
$496$	−17.0790	−	24.7239i	−0.766869	−	1.11014i
$497$	11.8425			0.531208
$498$	−37.0628	+	5.64430i	−1.66082	+	0.252927i
$499$	−6.91244	−	6.91244i	−0.309443	−	0.309443i	0.535250	−	0.844693i	$-0.320217\pi$
$499$	−6.91244	−	6.91244i	−0.309443	−	0.309443i	−0.844693	+	0.535250i	$0.820217\pi$
$500$	−14.5205	−	17.0045i	−0.649378	−	0.760465i
$501$	−26.4820	+	26.4820i	−1.18313	+	1.18313i
$502$	11.4559	−	15.5720i	0.511303	−	0.695013i
$503$	−38.3461			−1.70977			−0.854885	−	0.518818i	$-0.826372\pi$
$503$	−38.3461			−1.70977			−0.854885	+	0.518818i	$0.826372\pi$
$504$	8.05302	+	16.5278i	0.358710	+	0.736209i
$505$	−8.72013	+	3.65228i	−0.388041	+	0.162524i
$506$	15.8613	+	14.2003i	0.705121	+	0.631281i
$507$	−20.3427	−	20.3427i	−0.903451	−	0.903451i
$508$	−7.10505	−	22.7863i	−0.315236	−	1.01098i
$509$	−12.2916	+	12.2916i	−0.544815	+	0.544815i	−0.924936	−	0.380122i	$-0.875882\pi$
$509$	−12.2916	+	12.2916i	−0.544815	+	0.544815i	0.380122	+	0.924936i	$0.375882\pi$
$510$	25.3113	−	15.4408i	1.12080	−	0.683729i
$511$		−	4.73620i		−	0.209517i
$512$	−4.73095	+	22.1273i	−0.209081	+	0.977898i
$513$	18.0293			0.796013
$514$	0.0235463	+	0.154614i	0.00103858	+	0.00681975i
$515$	−13.4751	+	32.8974i	−0.593783	+	1.44963i
$516$	−1.53519	−	4.92346i	−0.0675832	−	0.216743i
$517$	−23.8489	+	19.6620i	−1.04888	+	0.864733i
$518$	9.92207	−	13.4871i	0.435951	−	0.592587i
$519$			12.6339i			0.554565i
$520$	−0.269694	+	0.307016i	−0.0118269	+	0.0134635i
$521$			14.7990i			0.648357i	0.945996	+	0.324179i	$0.105088\pi$
$521$			14.7990i			0.648357i	−0.945996	+	0.324179i	$0.894912\pi$
$522$	10.1676	−	13.8208i	0.445023	−	0.604918i
$523$	−3.73577	+	3.73577i	−0.163354	+	0.163354i	−0.784051	−	0.620697i	$-0.786850\pi$
$523$	−3.73577	+	3.73577i	−0.163354	+	0.163354i	0.620697	+	0.784051i	$0.286850\pi$
$524$	−12.7482	+	24.3003i	−0.556906	+	1.06157i
$525$	−37.8562	+	0.298051i	−1.65218	+	0.0130080i
$526$	−29.1679	+	4.44198i	−1.27178	+	0.193680i
$527$			31.8178i			1.38601i
$528$	14.3005	+	25.6511i	0.622351	+	1.11632i
$529$	2.39865			0.104289
$530$	30.3287	−	18.5015i	1.31740	−	0.803656i
$531$	4.28116	+	4.28116i	0.185786	+	0.185786i
$532$	−23.5394	+	44.8704i	−1.02056	+	1.94538i
$533$	−0.513132	+	0.513132i	−0.0222262	+	0.0222262i
$534$	−24.0543	−	17.6962i	−1.04093	−	0.765787i
$535$	−10.4341	+	4.37013i	−0.451103	+	0.188937i
$536$	−8.60612	+	24.9617i	−0.371728	+	1.07818i
$537$	48.5334			2.09437
$538$	−12.0261	+	16.3470i	−0.518481	+	0.704770i
$539$	12.0231	−	9.91233i	0.517873	−	0.426954i
$540$	7.00317	+	8.33315i	0.301368	+	0.358602i
$541$	1.02376	+	1.02376i	0.0440151	+	0.0440151i	0.728772	−	0.684757i	$-0.240092\pi$
$541$	1.02376	+	1.02376i	0.0440151	+	0.0440151i	−0.684757	+	0.728772i	$0.740092\pi$
$542$	22.0139	−	3.35250i	0.945577	−	0.144002i
$543$	−16.2942			−0.699252
$544$	17.4381	−	16.4301i	0.747652	−	0.704436i
$545$	2.71523	+	6.48285i	0.116308	+	0.277695i
$546$	0.104162	+	0.683969i	0.00445772	+	0.0292712i
$547$	11.6502	+	11.6502i	0.498127	+	0.498127i	0.910854	−	0.412728i	$-0.135424\pi$
$547$	11.6502	+	11.6502i	0.498127	+	0.498127i	−0.412728	+	0.910854i	$0.635424\pi$
$548$	−8.92732	+	2.78365i	−0.381356	+	0.118912i
$549$	1.20027	−	1.20027i	0.0512262	−	0.0512262i
$550$	−23.4055	+	1.47813i	−0.998012	+	0.0630277i
$551$	47.2872			2.01450
$552$	−26.8672	−	9.26311i	−1.14355	−	0.394264i
$553$	24.4722			1.04066
$554$	−0.153349	−	0.112815i	−0.00651518	−	0.00479305i
$555$	−6.49482	+	15.8561i	−0.275690	+	0.673056i
$556$	−33.7358	−	17.6981i	−1.43072	−	0.750566i
$557$	−0.762111	+	0.762111i	−0.0322917	+	0.0322917i	−0.723068	−	0.690777i	$-0.757269\pi$
$557$	−0.762111	+	0.762111i	−0.0322917	+	0.0322917i	0.690777	+	0.723068i	$0.257269\pi$
$558$	19.9608	−	3.03984i	0.845008	−	0.128687i
$559$		−	0.0752642i		−	0.00318334i
$560$	−29.8826	+	6.54922i	−1.26277	+	0.276755i
$561$	2.97859	−	30.9535i	0.125756	−	1.30686i
$562$	31.0281	−	4.72527i	1.30884	−	0.199324i
$563$	28.1426	+	28.1426i	1.18607	+	1.18607i	0.978145	+	0.207922i	$0.0666700\pi$
$563$	28.1426	+	28.1426i	1.18607	+	1.18607i	0.207922	+	0.978145i	$0.433330\pi$
$564$	19.1682	−	36.5382i	0.807128	−	1.53853i
$565$	7.84855	−	19.1611i	0.330191	−	0.806112i
$566$	−5.56182	+	7.56017i	−0.233781	+	0.317778i
$567$	37.9295			1.59289
$568$	−8.80383	+	4.28957i	−0.369400	+	0.179987i
$569$	11.9089			0.499247			0.249624	−	0.968343i	$-0.419693\pi$
$569$	11.9089			0.499247			0.249624	+	0.968343i	$0.419693\pi$
$570$	12.2066	−	50.3966i	0.511277	−	2.11088i
$571$	−29.9087	−	29.9087i	−1.25164	−	1.25164i	−0.954984	−	0.296658i	$-0.904128\pi$
$571$	−29.9087	−	29.9087i	−1.25164	−	1.25164i	−0.296658	−	0.954984i	$-0.595872\pi$
$572$	0.0878038	+	0.419504i	0.00367126	+	0.0175403i
$573$	−30.7999	−	30.7999i	−1.28669	−	1.28669i
$574$	−53.7059	+	8.17888i	−2.24164	+	0.341380i
$575$	15.9205	−	16.1732i	0.663931	−	0.674468i
$576$	−11.9734	−	9.37002i	−0.498892	−	0.390418i
$577$			37.3736i			1.55588i	0.628338	+	0.777941i	$0.283736\pi$
$577$			37.3736i			1.55588i	−0.628338	+	0.777941i	$0.716264\pi$
$578$	−1.31230	+	0.199850i	−0.0545843	+	0.00831266i
$579$	24.4818	−	24.4818i	1.01743	−	1.01743i
$580$	18.3679	+	21.8561i	0.762685	+	0.907527i
$581$	−28.9619	−	28.9619i	−1.20154	−	1.20154i
$582$	−3.69626	−	2.71924i	−0.153215	−	0.112716i
$583$	3.56903	−	37.0893i	0.147814	−	1.53608i
$584$	1.71554	+	3.52094i	0.0709897	+	0.145698i
$585$	−0.106075	−	0.253264i	−0.00438568	−	0.0104712i
$586$	12.8400	+	9.44607i	0.530416	+	0.390213i
$587$	3.42525	+	3.42525i	0.141375	+	0.141375i	0.774252	−	0.632877i	$-0.218126\pi$
$587$	3.42525	+	3.42525i	0.141375	+	0.141375i	−0.632877	+	0.774252i	$0.718126\pi$
$588$	−9.66342	+	18.4202i	−0.398513	+	0.759638i
$589$	39.3479	+	39.3479i	1.62130	+	1.62130i
$590$	−8.60024	+	5.24644i	−0.354066	+	0.215992i
$591$	−46.7033			−1.92112
$592$	−2.49091	+	13.6204i	−0.102376	+	0.559795i
$593$	−11.7388			−0.482056			−0.241028	−	0.970518i	$-0.577485\pi$
$593$	−11.7388			−0.482056			−0.241028	+	0.970518i	$0.577485\pi$
$594$	11.3990	−	0.629825i	0.467707	−	0.0258420i
$595$	29.9750	+	12.2781i	1.22886	+	0.503351i
$596$	−9.42635	+	17.9684i	−0.386118	+	0.736012i
$597$	24.5111	−	24.5111i	1.00317	−	1.00317i
$598$	−0.334080	−	0.245774i	−0.0136616	−	0.0100504i
$599$	−16.9294			−0.691715			−0.345857	−	0.938287i	$-0.612412\pi$
$599$	−16.9294			−0.691715			−0.345857	+	0.938287i	$0.612412\pi$
$600$	28.0348	−	13.9338i	1.14451	−	0.568846i
$601$	−10.4763			−0.427337			−0.213668	−	0.976906i	$-0.568541\pi$
$601$	−10.4763			−0.427337			−0.213668	+	0.976906i	$0.568541\pi$
$602$	3.33886	−	4.53850i	0.136082	−	0.184976i
$603$	−12.5450	−	12.5450i	−0.510870	−	0.510870i
$604$	−7.54780	−	24.2062i	−0.307116	−	0.984938i
$605$	−13.4925	+	20.5658i	−0.548549	+	0.836118i
$606$	−1.99280	−	13.0855i	−0.0809519	−	0.531563i
$607$		−	26.7401i		−	1.08535i	−0.839944	−	0.542673i	$-0.817412\pi$
$607$		−	26.7401i		−	1.08535i	0.839944	−	0.542673i	$-0.182588\pi$
$608$	1.24652	−	41.8836i	0.0505530	−	1.69860i
$609$	48.3352			1.95864
$610$	1.47090	+	2.41117i	0.0595548	+	0.0976254i
$611$	0.425788	−	0.425788i	0.0172255	−	0.0172255i
$612$	4.79221	+	15.3689i	0.193714	+	0.621251i
$613$	10.5489	+	10.5489i	0.426067	+	0.426067i	0.887286	−	0.461219i	$-0.152588\pi$
$613$	10.5489	+	10.5489i	0.426067	+	0.426067i	−0.461219	+	0.887286i	$0.652588\pi$
$614$	16.6526	+	12.2509i	0.672045	+	0.494406i
$615$	51.2782	−	21.4770i	2.06774	−	0.866037i
$616$	−13.3153	+	29.1916i	−0.536489	+	1.17616i
$617$	−10.3848			−0.418078			−0.209039	−	0.977907i	$-0.567033\pi$
$617$	−10.3848			−0.418078			−0.209039	+	0.977907i	$0.567033\pi$
$618$	−40.0923	−	29.4948i	−1.61275	−	1.18646i
$619$	30.9175	−	30.9175i	1.24268	−	1.24268i	0.283792	−	0.958886i	$-0.408407\pi$
$619$	30.9175	−	30.9175i	1.24268	−	1.24268i	0.958886	−	0.283792i	$-0.0915925\pi$
$620$	−2.90260	+	33.4706i	−0.116571	+	1.34421i
$621$	−7.81180	+	7.81180i	−0.313477	+	0.313477i
$622$	−9.20909	+	1.40245i	−0.369251	+	0.0562333i
$623$		−	32.6250i		−	1.30709i
$624$	−0.325182	−	0.470741i	−0.0130177	−	0.0188447i
$625$	0.393637	+	24.9969i	0.0157455	+	0.999876i
$626$	−6.10757	+	0.930123i	−0.244108	+	0.0371752i
$627$	−34.5955	−	41.9625i	−1.38161	−	1.67582i
$628$	−1.20376	−	0.631503i	−0.0480353	−	0.0251997i
$629$	10.3670	−	10.3670i	0.413359	−	0.413359i
$630$	4.83882	−	19.9778i	0.192783	−	0.795934i
$631$	−17.4165			−0.693338			−0.346669	−	0.937987i	$-0.612687\pi$
$631$	−17.4165			−0.693338			−0.346669	+	0.937987i	$0.612687\pi$
$632$	−18.1929	+	8.86430i	−0.723674	+	0.352603i
$633$			16.3404i			0.649473i
$634$	−1.50240	−	1.10528i	−0.0596681	−	0.0438963i
$635$	−10.1150	+	24.6943i	−0.401402	+	0.979964i
$636$	14.8064	+	47.4849i	0.587110	+	1.88290i
$637$	−0.214655	+	0.214655i	−0.00850496	+	0.00850496i
$638$	29.8973	−	1.65190i	1.18365	−	0.0653995i
$639$		−	6.58034i		−	0.260314i
$640$	19.8428	−	15.6928i	0.784355	−	0.620312i
$641$	−46.1486			−1.82276			−0.911380	−	0.411565i	$-0.864982\pi$
$641$	−46.1486			−1.82276			−0.911380	+	0.411565i	$0.864982\pi$
$642$	−2.38448	−	15.6575i	−0.0941078	−	0.617950i
$643$	−1.79738	+	1.79738i	−0.0708816	+	0.0708816i	−0.741659	−	0.670777i	$-0.765961\pi$
$643$	−1.79738	+	1.79738i	−0.0708816	+	0.0708816i	0.670777	+	0.741659i	$0.265961\pi$
$644$	−9.24237	−	29.6408i	−0.364200	−	1.16801i
$645$	−2.18556	+	5.33572i	−0.0860563	+	0.210094i
$646$	−26.2920	+	35.7387i	−1.03445	+	1.40612i
$647$		−	35.6004i		−	1.39959i	−0.714342	−	0.699797i	$-0.753274\pi$
$647$		−	35.6004i		−	1.39959i	0.714342	−	0.699797i	$-0.246726\pi$
$648$	−28.1972	+	13.7388i	−1.10769	+	0.539710i
$649$	−1.01206	+	10.5173i	−0.0397268	+	0.412841i
$650$	0.451119	−	0.0723396i	0.0176944	−	0.00283739i
$651$	40.2199	+	40.2199i	1.57634	+	1.57634i
$652$	16.5868	−	31.6174i	0.649587	−	1.23823i
$653$	34.8765	+	34.8765i	1.36482	+	1.36482i	0.867656	+	0.497166i	$0.165626\pi$
$653$	34.8765	+	34.8765i	1.36482	+	1.36482i	0.497166	+	0.867656i	$0.334374\pi$
$654$	−9.72824	+	1.48152i	−0.380404	+	0.0579319i
$655$	28.2984	−	11.8523i	1.10571	−	0.463108i
$656$	36.9630	−	25.5336i	1.44316	−	0.996918i
$657$	−2.63170			−0.102672
$658$	44.5641	−	6.78668i	1.73729	−	0.264572i
$659$	−7.45198	+	7.45198i	−0.290288	+	0.290288i	−0.837194	−	0.546906i	$-0.815805\pi$
$659$	−7.45198	+	7.45198i	−0.290288	+	0.290288i	0.546906	+	0.837194i	$0.315805\pi$
$660$	5.95707	−	32.2897i	0.231878	−	1.25687i
$661$	14.4421	+	14.4421i	0.561732	+	0.561732i	0.929799	−	0.368067i	$-0.119980\pi$
$661$	14.4421	+	14.4421i	0.561732	+	0.561732i	−0.368067	+	0.929799i	$0.619980\pi$
$662$	1.21695	−	1.65420i	0.0472982	−	0.0642924i
$663$			0.605807i			0.0235276i
$664$	32.0212	+	11.0400i	1.24266	+	0.428437i
$665$	52.2528	−	21.8852i	2.02628	−	0.848672i
$666$	−7.49416	−	5.51325i	−0.290393	−	0.213634i
$667$	−20.4888	+	20.4888i	−0.793328	+	0.793328i
$668$	32.3019	−	10.0721i	1.24980	−	0.389702i
$669$	2.14638	−	2.14638i	0.0829838	−	0.0829838i
$670$	25.2011	−	15.3735i	0.973602	−	0.593930i
$671$	2.94864	+	0.283742i	0.113831	+	0.0109537i
$672$	1.27414	−	42.8118i	0.0491512	−	1.65150i
$673$	−40.4628			−1.55973			−0.779864	−	0.625949i	$-0.784712\pi$
$673$	−40.4628			−1.55973			−0.779864	+	0.625949i	$0.784712\pi$
$674$	7.06899	−	1.07654i	0.272287	−	0.0414667i
$675$	−0.0958137	−	12.1696i	−0.00368787	−	0.468406i
$676$	7.73711	+	24.8134i	0.297581	+	0.954360i
$677$	−13.0846	−	13.0846i	−0.502884	−	0.502884i	0.409449	−	0.912333i	$-0.365721\pi$
$677$	−13.0846	−	13.0846i	−0.502884	−	0.502884i	−0.912333	+	0.409449i	$0.865721\pi$
$678$	23.3517	+	17.1792i	0.896816	+	0.659764i
$679$		−	5.01325i		−	0.192391i
$680$	−26.7311	+	1.72990i	−1.02509	+	0.0663386i
$681$	5.32892			0.204205
$682$	26.2522	+	23.5031i	1.00525	+	0.899981i
$683$	31.3465	+	31.3465i	1.19944	+	1.19944i	0.974334	+	0.225106i	$0.0722729\pi$
$683$	31.3465	+	31.3465i	1.19944	+	1.19944i	0.225106	+	0.974334i	$0.427727\pi$
$684$	24.9325	+	13.0798i	0.953318	+	0.500118i
$685$	9.67485	+	3.96290i	0.369657	+	0.151415i
$686$	11.0066	−	1.67620i	0.420234	−	0.0639975i
$687$	−63.8423			−2.43574
$688$	−0.838210	+	4.58337i	−0.0319565	+	0.174739i
$689$			0.725894i			0.0276544i
$690$	16.5471	+	27.1249i	0.629938	+	1.03263i
$691$	8.11085	+	8.11085i	0.308551	+	0.308551i	0.844347	−	0.535796i	$-0.179988\pi$
$691$	8.11085	+	8.11085i	0.308551	+	0.308551i	−0.535796	+	0.844347i	$0.679988\pi$
$692$	5.30261	−	10.1078i	0.201575	−	0.384239i
$693$	−13.7140	−	16.6344i	−0.520953	−	0.631889i
$694$	−11.4446	+	15.5567i	−0.434432	+	0.590522i
$695$	16.4544	+	39.2863i	0.624151	+	1.49021i
$696$	−35.9329	+	17.5079i	−1.36203	+	0.663636i
$697$	−47.5685			−1.80178
$698$	19.8743	+	14.6210i	0.752252	+	0.553412i
$699$	−28.5729	−	28.5729i	−1.08073	−	1.08073i
$700$	30.4121	+	15.6503i	1.14947	+	0.591527i
$701$	−2.68199	−	2.68199i	−0.101297	−	0.101297i	0.654642	−	0.755939i	$-0.272819\pi$
$701$	−2.68199	−	2.68199i	−0.101297	−	0.101297i	−0.755939	+	0.654642i	$0.772819\pi$
$702$	−0.219874	+	0.0334847i	−0.00829861	+	0.00126380i
$703$		−	25.6410i		−	0.967067i
$704$	−0.675025	−	26.5244i	−0.0254409	−	0.999676i
$705$	−42.5497	+	17.8212i	−1.60251	+	0.671186i
$706$	0.0403973	+	0.265265i	0.00152037	+	0.00998338i
$707$	10.2254	−	10.2254i	0.384566	−	0.384566i
$708$	−4.19860	−	13.4652i	−0.157793	−	0.506052i
$709$	−0.429802	−	0.429802i	−0.0161415	−	0.0161415i	0.698990	−	0.715131i	$-0.253633\pi$
$709$	−0.429802	−	0.429802i	−0.0161415	−	0.0161415i	−0.715131	+	0.698990i	$0.753633\pi$
$710$	10.6415	+	2.57748i	0.399368	+	0.0967309i
$711$		−	13.5981i		−	0.509969i
$712$	11.8174	+	24.2538i	0.442876	+	0.908950i
$713$	−34.0976			−1.27696
$714$	−26.8747	+	36.5307i	−1.00576	+	1.36713i
$715$	0.223270	−	0.423989i	0.00834981	−	0.0158563i
$716$	−38.8293	−	20.3702i	−1.45112	−	0.761270i
$717$	1.89432	−	1.89432i	0.0707446	−	0.0707446i
$718$	1.50912	+	9.90947i	0.0563197	+	0.369818i
$719$		−	5.10194i		−	0.190270i	−0.995464	−	0.0951351i	$-0.969672\pi$
$719$		−	5.10194i		−	0.190270i	0.995464	−	0.0951351i	$-0.0303283\pi$
$720$	3.63911	+	16.6044i	0.135622	+	0.618810i
$721$		−	54.3774i		−	2.02512i
$722$	7.63696	+	50.1474i	0.284218	+	1.86629i
$723$	29.0739	+	29.0739i	1.08127	+	1.08127i
$724$	13.0362	+	6.83892i	0.484488	+	0.254167i
$725$	−0.251300	−	31.9183i	−0.00933304	−	1.18541i
$726$	−23.3389	−	25.3222i	−0.866187	−	0.939797i
$727$			25.9257i			0.961531i	0.876849	+	0.480766i	$0.159641\pi$
$727$			25.9257i			0.961531i	−0.876849	+	0.480766i	$0.840359\pi$
$728$	0.203737	−	0.590930i	0.00755099	−	0.0219013i
$729$		−	4.91133i		−	0.181901i
$730$	1.03082	−	4.25589i	0.0381523	−	0.157517i
$731$	3.48858	−	3.48858i	0.129030	−	0.129030i
$732$	−3.77510	+	1.17712i	−0.139532	+	0.0435077i
$733$	−0.235908	+	0.235908i	−0.00871347	+	0.00871347i	−0.711450	−	0.702737i	$-0.751961\pi$
$733$	−0.235908	+	0.235908i	−0.00871347	+	0.00871347i	0.702737	+	0.711450i	$0.251961\pi$
$734$	−9.69900	+	1.47706i	−0.357997	+	0.0545194i
$735$	21.4509	−	8.98434i	0.791228	−	0.331392i
$736$	17.6074	+	18.6875i	0.649016	+	0.688832i
$737$	2.96561	−	30.8186i	0.109240	−	1.13522i
$738$	4.54464	+	29.8420i	0.167290	+	1.09850i
$739$	21.5170	−	21.5170i	0.791517	−	0.791517i	−0.190224	−	0.981741i	$-0.560921\pi$
$739$	21.5170	−	21.5170i	0.791517	−	0.791517i	0.981741	+	0.190224i	$0.0609214\pi$
$740$	11.8513	−	9.95978i	0.435661	−	0.366129i
$741$	0.749179	+	0.749179i	0.0275218	+	0.0275218i
$742$	−32.2020	+	43.7721i	−1.18217	+	1.60692i
$743$	−40.5421			−1.48735			−0.743673	−	0.668544i	$-0.766918\pi$
$743$	−40.5421			−1.48735			−0.743673	+	0.668544i	$0.766918\pi$
$744$	−44.4683	−	15.3315i	−1.63029	−	0.562080i
$745$	20.9246	−	8.76393i	0.766620	−	0.321086i
$746$	−19.8330	−	14.5906i	−0.726139	−	0.534202i
$747$	−16.0928	+	16.0928i	−0.588806	+	0.588806i
$748$	−15.3746	+	23.5143i	−0.562153	+	0.859766i
$749$	12.2352	−	12.2352i	0.447064	−	0.447064i
$750$	−34.0819	−	7.97145i	−1.24450	−	0.291076i
$751$			19.0350i			0.694599i	0.937754	+	0.347299i	$0.112901\pi$
$751$			19.0350i			0.694599i	−0.937754	+	0.347299i	$0.887099\pi$
$752$	−30.6712	+	21.1873i	−1.11846	+	0.772620i
$753$		−	30.2609i		−	1.10277i
$754$	−0.576685	+	0.0878235i	−0.0210016	+	0.00319834i
$755$	−10.7453	+	26.2331i	−0.391063	+	0.954721i
$756$	−14.7441	−	7.73486i	−0.536236	−	0.281314i
$757$	2.02730	−	2.02730i	0.0736833	−	0.0736833i	−0.669305	−	0.742988i	$-0.733408\pi$
$757$	2.02730	−	2.02730i	0.0736833	−	0.0736833i	0.742988	+	0.669305i	$0.233408\pi$
$758$	−7.96547	+	10.8274i	−0.289319	+	0.393270i
$759$	33.1713	+	3.19201i	1.20404	+	0.115863i
$760$	−30.9181	+	35.1967i	−1.12152	+	1.27672i
$761$	−25.3427			−0.918672			−0.459336	−	0.888262i	$-0.651913\pi$
$761$	−25.3427			−0.918672			−0.459336	+	0.888262i	$0.651913\pi$
$762$	−30.0951	−	22.1402i	−1.09023	−	0.802053i
$763$	−7.60192	−	7.60192i	−0.275208	−	0.275208i
$764$	11.7144	+	37.5688i	0.423812	+	1.35919i
$765$	6.82237	−	16.6558i	0.246663	−	0.602192i
$766$	10.2655	−	1.56333i	0.370907	−	0.0564855i
$767$		−	0.205840i		−	0.00743245i
$768$	14.5600	+	32.2883i	0.525390	+	1.16510i
$769$			1.76657i			0.0637043i	0.999493	+	0.0318521i	$0.0101406\pi$
$769$			1.76657i			0.0637043i	−0.999493	+	0.0318521i	$0.989859\pi$
$770$	32.2723	−	15.6623i	1.16301	−	0.564430i
$771$	0.173109	+	0.173109i	0.00623435	+	0.00623435i
$772$	−29.8621	+	9.31137i	−1.07476	+	0.335123i
$773$	22.7686	−	22.7686i	0.818931	−	0.818931i	−0.167022	−	0.985953i	$-0.553415\pi$
$773$	22.7686	−	22.7686i	0.818931	−	0.818931i	0.985953	+	0.167022i	$0.0534151\pi$
$774$	−2.52184	−	1.85525i	−0.0906458	−	0.0666857i
$775$	26.3502	−	26.7684i	0.946528	−	0.961551i
$776$	1.81590	+	3.72691i	0.0651869	+	0.133788i
$777$		−	26.2092i		−	0.940250i
$778$	24.0780	+	17.7135i	0.863237	+	0.635061i
$779$	−58.8262	+	58.8262i	−2.10767	+	2.10767i
$780$	−0.0552651	+	0.637276i	−0.00197881	+	0.0228181i
$781$	8.86059	−	7.30501i	0.317057	−	0.261394i
$782$	−4.09309	−	26.8769i	−0.146369	−	0.961115i
$783$			15.5382i			0.555290i
$784$	15.4625	−	10.6813i	0.552232	−	0.381475i
$785$	0.587125	+	1.40181i	0.0209554	+	0.0500328i
$786$	6.46699	+	42.4649i	0.230670	+	1.51467i
$787$	−11.2806	−	11.2806i	−0.402111	−	0.402111i	0.476865	−	0.878976i	$-0.341773\pi$
$787$	−11.2806	−	11.2806i	−0.402111	−	0.402111i	−0.878976	+	0.476865i	$0.841773\pi$
$788$	37.3651	+	19.6020i	1.33108	+	0.698294i
$789$	−32.6568	+	32.6568i	−1.16261	+	1.16261i
$790$	21.9904	+	5.32629i	0.782383	+	0.189501i
$791$			31.6720i			1.12613i
$792$	16.2205	+	7.39872i	0.576369	+	0.262902i
$793$	−0.0577095			−0.00204932
$794$	−0.995660	−	0.732481i	−0.0353346	−	0.0259948i
$795$	21.0789	−	51.4610i	0.747591	−	1.82513i
$796$	−29.8978	+	9.32250i	−1.05970	+	0.330427i
$797$	2.50495	+	2.50495i	0.0887299	+	0.0887299i	0.750079	−	0.661349i	$-0.230016\pi$
$797$	2.50495	+	2.50495i	0.0887299	+	0.0887299i	−0.661349	+	0.750079i	$0.730016\pi$
$798$	11.9413	+	78.4112i	0.422716	+	2.77573i
$799$	39.4714			1.39640
$800$	−28.2775	−	0.618801i	−0.999761	−	0.0218779i
$801$	−18.1283			−0.640531
$802$	−12.7219	+	1.93742i	−0.449226	+	0.0684127i
$803$	−2.92152	−	3.54365i	−0.103098	−	0.125053i
$804$	12.3031	+	39.4566i	0.433895	+	1.39153i
$805$	−13.1578	+	32.1228i	−0.463751	+	1.13218i
$806$	−0.552941	−	0.406784i	−0.0194765	−	0.0143284i
$807$			31.7669i			1.11825i
$808$	−3.89784	+	11.3055i	−0.137125	+	0.397726i
$809$	28.4857			1.00150			0.500752	−	0.865591i	$-0.333057\pi$
$809$	28.4857			1.00150			0.500752	+	0.865591i	$0.333057\pi$
$810$	34.0829	+	8.25522i	1.19755	+	0.290059i
$811$	20.9654	+	20.9654i	0.736194	+	0.736194i	0.971839	−	0.235645i	$-0.0757202\pi$
$811$	20.9654	+	20.9654i	0.736194	+	0.736194i	−0.235645	+	0.971839i	$0.575720\pi$
$812$	−38.6707	−	20.2870i	−1.35707	−	0.711933i
$813$	24.6471	−	24.6471i	0.864410	−	0.864410i
$814$	−0.895726	−	16.2115i	−0.0313952	−	0.568212i
$815$	−36.8193	+	15.4212i	−1.28973	+	0.540180i
$816$	6.74681	−	36.8919i	0.236186	−	1.29147i
$817$		−	8.62839i		−	0.301869i
$818$	−13.9492	+	2.12432i	−0.487722	+	0.0742752i
$819$	0.296983	+	0.296983i	0.0103774	+	0.0103774i
$820$	−50.0395	−	4.33946i	−1.74745	−	0.151541i
$821$	5.59608	−	5.59608i	0.195305	−	0.195305i	−0.602679	−	0.797984i	$-0.705900\pi$
$821$	5.59608	−	5.59608i	0.195305	−	0.195305i	0.797984	+	0.602679i	$0.205900\pi$
$822$	−8.67417	+	11.7908i	−0.302546	+	0.411251i
$823$			55.8811i			1.94789i	0.226779	+	0.973946i	$0.427181\pi$
$823$			55.8811i			1.94789i	−0.226779	+	0.973946i	$0.572819\pi$
$824$	19.6965	+	40.4247i	0.686161	+	1.40826i
$825$	−28.1403	+	23.5745i	−0.979720	+	0.820759i
$826$	9.13144	−	12.4123i	0.317723	−	0.431881i
$827$	31.6770	−	31.6770i	1.10152	−	1.10152i	0.107291	−	0.994228i	$-0.465782\pi$
$827$	31.6770	−	31.6770i	1.10152	−	1.10152i	0.994228	−	0.107291i	$-0.0342175\pi$
$828$	−16.4701	+	5.13557i	−0.572375	+	0.178474i
$829$	−16.7872	+	16.7872i	−0.583042	+	0.583042i	−0.935738	−	0.352696i	$-0.885265\pi$
$829$	−16.7872	+	16.7872i	−0.583042	+	0.583042i	0.352696	+	0.935738i	$0.385265\pi$
$830$	−19.7213	−	32.3282i	−0.684537	−	1.12213i
$831$	−0.298001			−0.0103375
$832$	0.0625859	+	0.513101i	0.00216978	+	0.0177886i
$833$	−19.8990			−0.689460
$834$	−58.9534	+	8.97803i	−2.04139	+	0.310884i
$835$	−35.0066	−	14.3390i	−1.21145	−	0.496223i
$836$	10.0659	+	48.0925i	0.348138	+	1.66331i
$837$	−12.9294	+	12.9294i	−0.446906	+	0.446906i
$838$	−20.0835	−	14.7749i	−0.693774	−	0.510391i
$839$	8.76079			0.302456			0.151228	−	0.988499i	$-0.451677\pi$
$839$	8.76079			0.302456			0.151228	+	0.988499i	$0.451677\pi$
$840$	−31.6033	+	35.9767i	−1.09042	+	1.24131i
$841$			11.7535i			0.405294i
$842$	−10.1238	−	7.44778i	−0.348888	−	0.256667i
$843$	34.7395	−	34.7395i	1.19649	−	1.19649i
$844$	6.85830	−	13.0732i	0.236073	−	0.449998i
$845$	11.0148	−	26.8911i	0.378922	−	0.925082i
$846$	−3.77106	−	24.7623i	−0.129652	−	0.851345i
$847$	7.17434	−	36.9326i	0.246513	−	1.26902i
$848$	8.08421	−	44.2048i	0.277613	−	1.51800i
$849$			14.6916i			0.504214i
$850$	24.2629	+	17.5569i	0.832211	+	0.602195i
$851$	11.1098	+	11.1098i	0.380839	+	0.380839i
$852$	−7.12157	+	13.5750i	−0.243981	+	0.465072i
$853$	−11.3018	−	11.3018i	−0.386965	−	0.386965i	0.486639	−	0.873603i	$-0.338223\pi$
$853$	−11.3018	−	11.3018i	−0.386965	−	0.386965i	−0.873603	+	0.486639i	$0.838223\pi$
$854$	−3.47994	−	2.56010i	−0.119081	−	0.0876047i
$855$	−12.1606	−	29.0346i	−0.415885	−	0.992962i
$856$	−4.66395	+	13.5276i	−0.159411	+	0.462363i
$857$			1.36548i			0.0466441i	0.999728	+	0.0233220i	$0.00742431\pi$
$857$			1.36548i			0.0466441i	−0.999728	+	0.0233220i	$0.992576\pi$
$858$	0.499839	+	0.447497i	0.0170642	+	0.0152773i
$859$	−11.4329	+	11.4329i	−0.390086	+	0.390086i	−0.874718	−	0.484632i	$-0.838953\pi$
$859$	−11.4329	+	11.4329i	−0.390086	+	0.390086i	0.484632	+	0.874718i	$0.338953\pi$
$860$	3.98804	−	3.35155i	0.135991	−	0.114287i
$861$	−60.1299	+	60.1299i	−2.04922	+	2.04922i
$862$	37.9925	−	5.78589i	1.29403	−	0.197068i
$863$	−10.3401			−0.351982			−0.175991	−	0.984392i	$-0.556313\pi$
$863$	−10.3401			−0.351982			−0.175991	+	0.984392i	$0.556313\pi$
$864$	13.7626	+	0.409596i	0.468213	+	0.0139348i
$865$	−11.7708	+	4.92998i	−0.400218	+	0.167624i
$866$	−4.00810	−	26.3188i	−0.136201	−	0.894349i
$867$	−1.46926	+	1.46926i	−0.0498989	+	0.0498989i
$868$	−15.2972	−	49.0589i	−0.519220	−	1.66517i
$869$	18.3102	−	15.0956i	0.621131	−	0.512084i
$870$	43.4333	+	10.5200i	1.47253	+	0.356661i
$871$			0.603168i			0.0204376i
$872$	8.40491	+	2.89779i	0.284626	+	0.0981315i
$873$	−2.78564			−0.0942797
$874$	−38.2994	−	28.1759i	−1.29550	−	0.953063i
$875$	−15.0499	−	35.1537i	−0.508781	−	1.18841i
$876$	5.42910	+	2.84815i	0.183432	+	0.0962301i
$877$	−29.9371	+	29.9371i	−1.01090	+	1.01090i	−0.0109627	+	0.999940i	$0.503490\pi$
$877$	−29.9371	+	29.9371i	−1.01090	+	1.01090i	−0.999940	+	0.0109627i	$0.996510\pi$
$878$	−6.31701	−	41.4800i	−0.213189	−	1.39988i
$879$	24.9518			0.841604
$880$	−18.3184	+	23.3332i	−0.617513	+	0.786561i
$881$	−49.6334			−1.67219			−0.836096	−	0.548583i	$-0.815167\pi$
$881$	−49.6334			−1.67219			−0.836096	+	0.548583i	$0.815167\pi$
$882$	1.90113	+	12.4836i	0.0640144	+	0.420344i
$883$	−33.0062	+	33.0062i	−1.11075	+	1.11075i	−0.117698	+	0.993049i	$0.537551\pi$
$883$	−33.0062	+	33.0062i	−1.11075	+	1.11075i	−0.993049	+	0.117698i	$0.962449\pi$
$884$	0.254266	−	0.484677i	0.00855189	−	0.0163015i
$885$	−5.97728	+	14.5927i	−0.200924	+	0.490527i
$886$	35.3254	+	25.9879i	1.18678	+	0.873082i
$887$	−0.133247			−0.00447400			−0.00223700	−	0.999997i	$-0.500712\pi$
$887$	−0.133247			−0.00447400			−0.00223700	+	0.999997i	$0.500712\pi$
$888$	9.49348	+	19.4842i	0.318580	+	0.653847i
$889$		−	40.8181i		−	1.36900i
$890$	7.10073	−	29.3164i	0.238017	−	0.982689i
$891$	28.3790	−	23.3967i	0.950732	−	0.783819i
$892$	−2.61808	+	0.816350i	−0.0876598	+	0.0273334i
$893$	48.8129	−	48.8129i	1.63346	−	1.63346i
$894$	4.78188	+	31.3997i	0.159930	+	1.05016i
$895$	18.9387	+	45.2178i	0.633051	+	1.51146i
$896$	−18.9881	+	33.7169i	−0.634348	+	1.12640i
$897$	−0.649213			−0.0216766
$898$	13.9970	−	2.13161i	0.467086	−	0.0711326i
$899$	−33.9112	+	33.9112i	−1.13100	+	1.13100i
$900$	8.69619	−	16.8986i	0.289873	−	0.563287i
$901$	−33.6460	+	33.6460i	−1.12091	+	1.12091i
$902$	−35.1378	+	39.2478i	−1.16996	+	1.30681i
$903$		−	8.81961i		−	0.293498i
$904$	−11.4722	−	23.5453i	−0.381560	−	0.783106i
$905$	−6.35833	−	15.1811i	−0.211358	−	0.504636i
$906$	−31.9705	−	23.5198i	−1.06215	−	0.781394i
$907$	2.51560	+	2.51560i	0.0835292	+	0.0835292i	0.747637	−	0.664108i	$-0.231188\pi$
$907$	2.51560	+	2.51560i	0.0835292	+	0.0835292i	−0.664108	+	0.747637i	$0.731188\pi$
$908$	−4.26342	−	2.23663i	−0.141487	−	0.0742250i
$909$	−5.68180	−	5.68180i	−0.188453	−	0.188453i
$910$	−0.596597	+	0.363944i	−0.0197770	+	0.0120646i
$911$			41.7978i			1.38482i	0.721503	+	0.692412i	$0.243452\pi$
$911$			41.7978i			1.38482i	−0.721503	+	0.692412i	$0.756548\pi$
$912$	−37.2793	−	53.9664i	−1.23444	−	1.78700i
$913$	−39.5345	−	3.80433i	−1.30840	−	0.125905i
$914$	2.55645	+	16.7867i	0.0845600	+	0.555255i
$915$	4.09121	+	1.67580i	0.135251	+	0.0554001i
$916$	51.0772	+	26.7955i	1.68764	+	0.885350i
$917$	−33.1833	+	33.1833i	−1.09581	+	1.09581i
$918$	−11.7435	−	8.63935i	−0.387592	−	0.285141i
$919$		−	28.5080i		−	0.940394i	−0.882562	−	0.470197i	$-0.844183\pi$
$919$		−	28.5080i		−	0.940394i	0.882562	−	0.470197i	$-0.155817\pi$
$920$	−1.85385	−	28.6464i	−0.0611196	−	0.944444i
$921$	32.3608			1.06632
$922$	−29.7502	−	21.8864i	−0.979770	−	0.720791i
$923$	−0.158193	+	0.158193i	−0.00520698	+	0.00520698i
$924$	10.2890	+	49.1583i	0.338484	+	1.61719i
$925$	−17.3073	+	0.136265i	−0.569061	+	0.00448035i
$926$	−17.7034	+	2.69605i	−0.581769	+	0.0885978i
$927$	−30.2151			−0.992393
$928$	36.0965	+	1.07429i	1.18493	+	0.0352652i
$929$	4.52908			0.148594			0.0742971	−	0.997236i	$-0.476329\pi$
$929$	4.52908			0.148594			0.0742971	+	0.997236i	$0.476329\pi$
$930$	27.3873	+	44.8948i	0.898066	+	1.47216i
$931$	−24.6084	+	24.6084i	−0.806507	+	0.806507i
$932$	10.8674	+	34.8523i	0.355972	+	1.14162i
$933$	−10.3106	+	10.3106i	−0.337555	+	0.337555i
$934$	26.0634	−	35.4280i	0.852822	−	1.15924i
$935$	30.0011	−	9.30355i	0.981142	−	0.304259i
$936$	−0.328353	−	0.113207i	−0.0107326	−	0.00370030i
$937$			20.9917i			0.685768i	0.939378	+	0.342884i	$0.111404\pi$
$937$			20.9917i			0.685768i	−0.939378	+	0.342884i	$0.888596\pi$
$938$	−26.7576	+	36.3716i	−0.873667	+	1.18757i
$939$	−6.83812	+	6.83812i	−0.223154	+	0.223154i
$940$	41.5218	+	3.60081i	1.35429	+	0.117445i
$941$	16.6454	+	16.6454i	0.542624	+	0.542624i	0.924297	−	0.381674i	$-0.124652\pi$
$941$	16.6454	+	16.6454i	0.542624	+	0.542624i	−0.381674	+	0.924297i	$0.624652\pi$
$942$	−2.10357	+	0.320354i	−0.0685381	+	0.0104377i
$943$		−	50.9768i		−	1.66003i
$944$	−2.29242	+	12.5351i	−0.0746119	+	0.407981i
$945$	7.19131	+	17.1699i	0.233933	+	0.558536i
$946$	−0.301419	−	5.45529i	−0.00979998	−	0.177367i
$947$	17.4125	−	17.4125i	0.565831	−	0.565831i	−0.365126	−	0.930958i	$-0.618974\pi$
$947$	17.4125	−	17.4125i	0.565831	−	0.565831i	0.930958	+	0.365126i	$0.118974\pi$
$948$	−14.7165	+	28.0524i	−0.477971	+	0.911101i
$949$	0.0632666	+	0.0632666i	0.00205372	+	0.00205372i
$950$	51.7170	−	8.29311i	1.67792	−	0.269064i
$951$	−2.91960			−0.0946746
$952$	36.8337	−	17.9468i	1.19379	−	0.581660i
$953$		−	57.8601i		−	1.87427i	−0.348962	−	0.937137i	$-0.613466\pi$
$953$		−	57.8601i		−	1.87427i	0.348962	−	0.937137i	$-0.386534\pi$
$954$	24.3222	+	17.8932i	0.787460	+	0.579314i
$955$	16.6770	−	40.7145i	0.539657	−	1.31749i
$956$	−2.31063	+	0.720482i	−0.0747310	+	0.0233020i
$957$	36.1646	−	29.8154i	1.16903	−	0.963796i
$958$	−53.1911	+	8.10049i	−1.71853	+	0.261715i
$959$	−15.9919			−0.516405
$960$	10.4628	−	38.1928i	0.337684	−	1.23267i
$961$	−25.4353			−0.820494
$962$	0.0476213	+	0.312701i	0.00153537	+	0.0100819i
$963$	−6.79855	−	6.79855i	−0.219080	−	0.219080i
$964$	−11.0579	−	35.4634i	−0.356151	−	1.14220i
$965$	32.3626	+	13.2560i	1.04179	+	0.426726i
$966$	−39.1482	−	28.8003i	−1.25957	−	0.926634i
$967$	−56.7080			−1.82361			−0.911803	−	0.410628i	$-0.865310\pi$
$967$	−56.7080			−1.82361			−0.911803	+	0.410628i	$0.865310\pi$
$968$	8.04422	+	30.0548i	0.258551	+	0.965998i
$969$			69.4505i			2.23107i
$970$	1.09112	−	4.50484i	0.0350337	−	0.144642i
$971$	−2.36739	+	2.36739i	−0.0759730	+	0.0759730i	−0.744072	−	0.668099i	$-0.767108\pi$
$971$	−2.36739	+	2.36739i	−0.0759730	+	0.0759730i	0.668099	+	0.744072i	$0.267108\pi$
$972$	−16.0248	+	30.5461i	−0.513994	+	0.979768i
$973$	−46.0679	−	46.0679i	−1.47687	−	1.47687i
$974$	2.43908	+	16.0160i	0.0781532	+	0.513186i
$975$	0.501705	−	0.509668i	0.0160674	−	0.0163224i
$976$	3.51434	+	0.642705i	0.112491	+	0.0205725i
$977$		−	28.5084i		−	0.912063i	−0.889964	−	0.456032i	$-0.849270\pi$
$977$		−	28.5084i		−	0.912063i	0.889964	−	0.456032i	$-0.150730\pi$
$978$	−8.41426	−	55.2515i	−0.269059	−	1.76675i
$979$	−20.1247	−	24.4102i	−0.643188	−	0.780153i
$980$	−20.9327	−	1.81530i	−0.668670	−	0.0579876i
$981$	−4.22405	+	4.22405i	−0.134864	+	0.134864i
$982$	20.9378	+	15.4034i	0.668153	+	0.491542i
$983$			21.5135i			0.686175i	0.939303	+	0.343088i	$0.111473\pi$
$983$			21.5135i			0.686175i	−0.939303	+	0.343088i	$0.888527\pi$
$984$	22.9210	−	66.4814i	0.730695	−	2.11935i
$985$	−18.2246	−	43.5127i	−0.580683	−	1.38643i
$986$	−30.8007	−	22.6593i	−0.980894	−	0.721618i
$987$	49.8946	−	49.8946i	1.58816	−	1.58816i
$988$	−0.284941	−	0.913824i	−0.00906520	−	0.0290726i
$989$	3.73854	+	3.73854i	0.118879	+	0.118879i
$990$	−8.70283	−	17.9323i	−0.276594	−	0.569925i
$991$		−	22.2526i		−	0.706877i	−0.935458	−	0.353438i	$-0.885012\pi$
$991$		−	22.2526i		−	0.706877i	0.935458	−	0.353438i	$-0.114988\pi$
$992$	29.1422	+	30.9300i	0.925264	+	0.982028i
$993$		−	3.21458i		−	0.102012i
$994$	−16.5569	+	2.52146i	−0.525153	+	0.0799757i
$995$	32.4013	+	13.2719i	1.02719	+	0.420746i
$996$	50.6155	−	15.7825i	1.60381	−	0.500088i
$997$	−26.4529	−	26.4529i	−0.837772	−	0.837772i	0.150793	−	0.988565i	$-0.451817\pi$
$997$	−26.4529	−	26.4529i	−0.837772	−	0.837772i	−0.988565	+	0.150793i	$0.951817\pi$
$998$	11.1360	+	8.19247i	0.352504	+	0.259328i
$999$	8.42542			0.266568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bi.d.219.5	✓	256
5.4	even	2	inner	880.2.bi.d.219.124	yes	256
11.10	odd	2	inner	880.2.bi.d.219.123	yes	256
16.3	odd	4	inner	880.2.bi.d.659.6	yes	256
55.54	odd	2	inner	880.2.bi.d.219.6	yes	256
80.19	odd	4	inner	880.2.bi.d.659.123	yes	256
176.131	even	4	inner	880.2.bi.d.659.124	yes	256
880.659	even	4	inner	880.2.bi.d.659.5	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.bi.d.219.5	✓	256	1.1	even	1	trivial
880.2.bi.d.219.6	yes	256	55.54	odd	2	inner
880.2.bi.d.219.123	yes	256	11.10	odd	2	inner
880.2.bi.d.219.124	yes	256	5.4	even	2	inner
880.2.bi.d.659.5	yes	256	880.659	even	4	inner
880.2.bi.d.659.6	yes	256	16.3	odd	4	inner
880.2.bi.d.659.123	yes	256	80.19	odd	4	inner
880.2.bi.d.659.124	yes	256	176.131	even	4	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bi (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39809 + 0.212916i) q^{2} +(-1.56533 + 1.56533i) q^{3} +(1.90933 - 0.595354i) q^{4} +(-2.06921 - 0.847567i) q^{5} +(1.85519 - 2.52176i) q^{6} +3.42027 q^{7} +(-2.54267 + 1.23889i) q^{8} -1.90049i q^{9} +O(q^{10})\)	\(q+(-1.39809 + 0.212916i) q^{2} +(-1.56533 + 1.56533i) q^{3} +(1.90933 - 0.595354i) q^{4} +(-2.06921 - 0.847567i) q^{5} +(1.85519 - 2.52176i) q^{6} +3.42027 q^{7} +(-2.54267 + 1.23889i) q^{8} -1.90049i q^{9} +(3.07341 + 0.744410i) q^{10} +(2.55906 - 2.10979i) q^{11} +(-2.05681 + 3.92065i) q^{12} +(-0.0456883 + 0.0456883i) q^{13} +(-4.78186 + 0.728231i) q^{14} +(4.56571 - 1.91227i) q^{15} +(3.29111 - 2.27346i) q^{16} -4.23540 q^{17} +(0.404646 + 2.65707i) q^{18} +(-5.23777 + 5.23777i) q^{19} +(-4.45541 - 0.386377i) q^{20} +(-5.35384 + 5.35384i) q^{21} +(-3.12860 + 3.49455i) q^{22} -4.53887i q^{23} +(2.04084 - 5.91937i) q^{24} +(3.56326 + 3.50759i) q^{25} +(0.0541487 - 0.0736043i) q^{26} +(-1.72109 - 1.72109i) q^{27} +(6.53044 - 2.03627i) q^{28} +(-4.51406 - 4.51406i) q^{29} +(-5.97614 + 3.64565i) q^{30} -7.51234i q^{31} +(-4.11722 + 3.87924i) q^{32} +(-0.703261 + 7.30827i) q^{33} +(5.92149 - 0.901785i) q^{34} +(-7.07726 - 2.89891i) q^{35} +(-1.13146 - 3.62867i) q^{36} +(-2.44770 + 2.44770i) q^{37} +(6.20768 - 8.43809i) q^{38} -0.143034i q^{39} +(6.31135 - 0.408438i) q^{40} +11.2312 q^{41} +(6.34525 - 8.62509i) q^{42} +(-0.823671 + 0.823671i) q^{43} +(3.63003 - 5.55183i) q^{44} +(-1.61080 + 3.93252i) q^{45} +(0.966399 + 6.34577i) q^{46} -9.31941 q^{47} +(-1.59296 + 8.71036i) q^{48} +4.69826 q^{49} +(-5.72859 - 4.14526i) q^{50} +(6.62979 - 6.62979i) q^{51} +(-0.0600335 + 0.114435i) q^{52} +(7.94399 - 7.94399i) q^{53} +(2.77269 + 2.03980i) q^{54} +(-7.08342 + 2.19662i) q^{55} +(-8.69661 + 4.23733i) q^{56} -16.3976i q^{57} +(7.27220 + 5.34997i) q^{58} +(-2.25266 + 2.25266i) q^{59} +(7.57898 - 6.36937i) q^{60} +(0.631557 + 0.631557i) q^{61} +(1.59950 + 10.5030i) q^{62} -6.50020i q^{63} +(4.93031 - 6.30016i) q^{64} +(0.133262 - 0.0558147i) q^{65} +(-0.572825 - 10.3674i) q^{66} +(6.60090 - 6.60090i) q^{67} +(-8.08680 + 2.52156i) q^{68} +(7.10481 + 7.10481i) q^{69} +(10.5119 + 2.54609i) q^{70} +3.46244 q^{71} +(2.35450 + 4.83232i) q^{72} -1.38474i q^{73} +(2.90096 - 3.94327i) q^{74} +(-11.0682 + 0.0871424i) q^{75} +(-6.88232 + 13.1190i) q^{76} +(8.75269 - 7.21605i) q^{77} +(0.0304543 + 0.199975i) q^{78} +7.15504 q^{79} +(-8.73690 + 1.91482i) q^{80} +11.0896 q^{81} +(-15.7022 + 2.39130i) q^{82} +(-8.46772 - 8.46772i) q^{83} +(-7.03484 + 13.4097i) q^{84} +(8.76394 + 3.58979i) q^{85} +(0.976196 - 1.32694i) q^{86} +14.1320 q^{87} +(-3.89305 + 8.53488i) q^{88} -9.53873i q^{89} +(1.41475 - 5.84099i) q^{90} +(-0.156266 + 0.156266i) q^{91} +(-2.70223 - 8.66622i) q^{92} +(11.7593 + 11.7593i) q^{93} +(13.0294 - 1.98425i) q^{94} +(15.2774 - 6.39868i) q^{95} +(0.372527 - 12.5171i) q^{96} -1.46575i q^{97} +(-6.56861 + 1.00034i) q^{98} +(-4.00964 - 4.86348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 8 q^{4} + 4 q^{5}+O(q^{10}) \) 256 * q - 8 * q^4 + 4 * q^5	\( 256 q - 8 q^{4} + 4 q^{5} + 12 q^{11} - 32 q^{14} + 24 q^{16} - 28 q^{20} - 80 q^{26} - 32 q^{34} + 24 q^{36} - 96 q^{44} + 4 q^{45} + 88 q^{49} - 4 q^{55} + 32 q^{56} + 96 q^{59} + 84 q^{60} - 104 q^{64} - 16 q^{66} - 8 q^{69} + 160 q^{70} - 216 q^{71} - 120 q^{80} - 160 q^{81} - 152 q^{86} - 80 q^{91} + 76 q^{99}+O(q^{100}) \) 256 * q - 8 * q^4 + 4 * q^5 + 12 * q^11 - 32 * q^14 + 24 * q^16 - 28 * q^20 - 80 * q^26 - 32 * q^34 + 24 * q^36 - 96 * q^44 + 4 * q^45 + 88 * q^49 - 4 * q^55 + 32 * q^56 + 96 * q^59 + 84 * q^60 - 104 * q^64 - 16 * q^66 - 8 * q^69 + 160 * q^70 - 216 * q^71 - 120 * q^80 - 160 * q^81 - 152 * q^86 - 80 * q^91 + 76 * q^99

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