LMFDB - Embedded newform 255.2.bi.a.22.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [255,2,Mod(22,255)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(255, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("255.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 255 = 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	255.bi (of order $16$, degree $8$, 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:	$2.03618525154$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			22.18
Character	$\chi$	$=$	255.22
Dual form			255.2.bi.a.58.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03325 - 2.49449i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-3.74064 - 3.74064i) q^{4} +(-1.65882 - 1.49944i) q^{5} +(1.50005 - 2.24498i) q^{6} +(-0.128784 + 0.192738i) q^{7} +(-8.20701 + 3.39946i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})$	\(q+(1.03325 - 2.49449i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-3.74064 - 3.74064i) q^{4} +(-1.65882 - 1.49944i) q^{5} +(1.50005 - 2.24498i) q^{6} +(-0.128784 + 0.192738i) q^{7} +(-8.20701 + 3.39946i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-5.45431 + 2.58860i) q^{10} +(1.99662 + 1.33410i) q^{11} +(-2.93900 - 4.39853i) q^{12} +4.63849 q^{13} +(0.347717 + 0.520396i) q^{14} +(-1.33442 - 1.79425i) q^{15} +13.4046i q^{16} +(1.87483 - 3.67219i) q^{17} +(1.90920 - 1.90920i) q^{18} +(-3.42730 + 1.41963i) q^{19} +(0.596172 + 11.8139i) q^{20} +(-0.163910 + 0.163910i) q^{21} +(5.39089 - 3.60208i) q^{22} +(-0.825706 - 4.15110i) q^{23} +(-8.71252 + 1.73303i) q^{24} +(0.503354 + 4.97460i) q^{25} +(4.79272 - 11.5707i) q^{26} +(0.831470 + 0.555570i) q^{27} +(1.20270 - 0.239231i) q^{28} +(1.70788 - 8.58610i) q^{29} +(-5.85451 + 1.47478i) q^{30} +(2.18280 - 1.45850i) q^{31} +(17.0236 + 7.05142i) q^{32} +(1.69798 + 1.69798i) q^{33} +(-7.22307 - 8.47103i) q^{34} +(0.502628 - 0.126614i) q^{35} +(-2.02442 - 4.88738i) q^{36} +(-1.72339 + 8.66406i) q^{37} +10.0162i q^{38} +(4.54937 + 0.904925i) q^{39} +(18.7112 + 6.66685i) q^{40} +(0.945732 + 4.75451i) q^{41} +(0.239512 + 0.578233i) q^{42} +(0.153752 + 0.371191i) q^{43} +(-2.47825 - 12.4590i) q^{44} +(-0.958737 - 2.02010i) q^{45} +(-11.2080 - 2.22942i) q^{46} +9.73422i q^{47} +(-2.61511 + 13.1471i) q^{48} +(2.65822 + 6.41751i) q^{49} +(12.9292 + 3.88439i) q^{50} +(2.55521 - 3.23587i) q^{51} +(-17.3509 - 17.3509i) q^{52} +(10.6910 + 4.42835i) q^{53} +(2.24498 - 1.50005i) q^{54} +(-1.31163 - 5.20683i) q^{55} +(0.401723 - 2.01960i) q^{56} +(-3.63840 + 0.723722i) q^{57} +(-19.6532 - 13.1319i) q^{58} +(-0.594386 + 1.43498i) q^{59} +(-1.72006 + 11.7032i) q^{60} +(-4.69467 + 0.933828i) q^{61} +(-1.38283 - 6.95195i) q^{62} +(-0.192738 + 0.128784i) q^{63} +(16.2223 - 16.2223i) q^{64} +(-7.69442 - 6.95515i) q^{65} +(5.99004 - 2.48115i) q^{66} +(1.69680 - 1.69680i) q^{67} +(-20.7494 + 6.72330i) q^{68} -4.23243i q^{69} +(0.203503 - 1.38462i) q^{70} +(-8.33019 - 12.4670i) q^{71} -8.88321 q^{72} +(0.341001 + 0.510345i) q^{73} +(19.8317 + 13.2511i) q^{74} +(-0.476814 + 4.97721i) q^{75} +(18.1306 + 7.50994i) q^{76} +(-0.514263 + 0.213015i) q^{77} +(6.95796 - 10.4133i) q^{78} +(-1.83806 + 2.75085i) q^{79} +(20.0995 - 22.2358i) q^{80} +(0.707107 + 0.707107i) q^{81} +(12.8372 + 2.55349i) q^{82} +(-4.21219 + 10.1691i) q^{83} +1.22626 q^{84} +(-8.61624 + 3.28031i) q^{85} +1.08479 q^{86} +(3.35013 - 8.08793i) q^{87} +(-20.9215 - 4.16154i) q^{88} +(1.93036 + 1.93036i) q^{89} +(-6.02974 + 0.304282i) q^{90} +(-0.597362 + 0.894016i) q^{91} +(-12.4391 + 18.6165i) q^{92} +(2.42540 - 1.00463i) q^{93} +(24.2819 + 10.0579i) q^{94} +(7.81391 + 2.78412i) q^{95} +(15.3209 + 10.2371i) q^{96} +(-1.26576 - 1.89434i) q^{97} +18.7550 q^{98} +(1.33410 + 1.99662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q+O(q^{10}) $ 144 * q	$ 144 q - 16 q^{10} + 64 q^{14} - 32 q^{19} - 32 q^{20} - 16 q^{25} - 64 q^{26} - 64 q^{28} - 64 q^{30} - 32 q^{31} + 16 q^{33} + 32 q^{34} - 16 q^{36} - 32 q^{37} + 112 q^{40} - 80 q^{41} - 16 q^{46} - 64 q^{50} - 64 q^{52} + 48 q^{53} + 16 q^{54} - 64 q^{55} - 32 q^{57} - 112 q^{58} + 32 q^{59} - 32 q^{64} + 64 q^{67} - 272 q^{68} - 32 q^{70} + 32 q^{71} + 48 q^{72} - 80 q^{73} + 80 q^{74} + 32 q^{75} + 64 q^{76} - 96 q^{77} + 64 q^{78} + 32 q^{79} + 336 q^{80} - 16 q^{83} - 96 q^{84} + 32 q^{85} + 64 q^{86} + 48 q^{87} - 80 q^{88} + 320 q^{92} + 128 q^{93} + 16 q^{94} - 64 q^{95} + 64 q^{96} - 16 q^{97} + 144 q^{98}+O(q^{100}) $ 144 * q - 16 * q^10 + 64 * q^14 - 32 * q^19 - 32 * q^20 - 16 * q^25 - 64 * q^26 - 64 * q^28 - 64 * q^30 - 32 * q^31 + 16 * q^33 + 32 * q^34 - 16 * q^36 - 32 * q^37 + 112 * q^40 - 80 * q^41 - 16 * q^46 - 64 * q^50 - 64 * q^52 + 48 * q^53 + 16 * q^54 - 64 * q^55 - 32 * q^57 - 112 * q^58 + 32 * q^59 - 32 * q^64 + 64 * q^67 - 272 * q^68 - 32 * q^70 + 32 * q^71 + 48 * q^72 - 80 * q^73 + 80 * q^74 + 32 * q^75 + 64 * q^76 - 96 * q^77 + 64 * q^78 + 32 * q^79 + 336 * q^80 - 16 * q^83 - 96 * q^84 + 32 * q^85 + 64 * q^86 + 48 * q^87 - 80 * q^88 + 320 * q^92 + 128 * q^93 + 16 * q^94 - 64 * q^95 + 64 * q^96 - 16 * q^97 + 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/255\mathbb{Z}\right)^\times$.

$n$	$52$	$86$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	1.03325	−	2.49449i	0.730618	−	1.76387i	0.0900886	−	0.995934i	$-0.471285\pi$
$2$	1.03325	−	2.49449i	0.730618	−	1.76387i	0.640529	−	0.767934i	$-0.278715\pi$
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$4$	−3.74064	−	3.74064i	−1.87032	−	1.87032i
$5$	−1.65882	−	1.49944i	−0.741846	−	0.670570i
$5$	−1.65882	−	1.49944i	−0.741846	−	0.670570i
$6$	1.50005	−	2.24498i	0.612391	−	0.916508i
$7$	−0.128784	+	0.192738i	−0.0486756	+	0.0728482i	−0.855009	−	0.518613i	$-0.826449\pi$
$7$	−0.128784	+	0.192738i	−0.0486756	+	0.0728482i	0.806334	+	0.591461i	$0.201449\pi$
$8$	−8.20701	+	3.39946i	−2.90162	+	1.20189i
$9$	0.923880	+	0.382683i	0.307960	+	0.127561i
$10$	−5.45431	+	2.58860i	−1.72480	+	0.818587i
$11$	1.99662	+	1.33410i	0.602003	+	0.402245i	0.818889	−	0.573951i	$-0.194590\pi$
$11$	1.99662	+	1.33410i	0.602003	+	0.402245i	−0.216887	+	0.976197i	$0.569590\pi$
$12$	−2.93900	−	4.39853i	−0.848417	−	1.26975i
$13$	4.63849			1.28649			0.643244	−	0.765662i	$-0.277588\pi$
$13$	4.63849			1.28649			0.643244	+	0.765662i	$0.277588\pi$
$14$	0.347717	+	0.520396i	0.0929313	+	0.139082i
$15$	−1.33442	−	1.79425i	−0.344545	−	0.463273i
$16$			13.4046i			3.35116i
$17$	1.87483	−	3.67219i	0.454713	−	0.890638i
$17$	1.87483	−	3.67219i	0.454713	−	0.890638i
$18$	1.90920	−	1.90920i	0.450002	−	0.450002i
$19$	−3.42730	+	1.41963i	−0.786275	+	0.325686i	−0.739445	−	0.673217i	$-0.764912\pi$
$19$	−3.42730	+	1.41963i	−0.786275	+	0.325686i	−0.0468304	+	0.998903i	$0.514912\pi$
$20$	0.596172	+	11.8139i	0.133308	+	2.64167i
$21$	−0.163910	+	0.163910i	−0.0357682	+	0.0357682i
$22$	5.39089	−	3.60208i	1.14934	−	0.767966i
$23$	−0.825706	−	4.15110i	−0.172172	−	0.865565i	−0.966222	−	0.257713i	$-0.917031\pi$
$23$	−0.825706	−	4.15110i	−0.172172	−	0.865565i	0.794050	−	0.607853i	$-0.207969\pi$
$24$	−8.71252	+	1.73303i	−1.77844	+	0.353753i
$25$	0.503354	+	4.97460i	0.100671	+	0.994920i
$26$	4.79272	−	11.5707i	0.939930	−	2.26919i
$27$	0.831470	+	0.555570i	0.160016	+	0.106920i
$28$	1.20270	−	0.239231i	0.227288	−	0.0452105i
$29$	1.70788	−	8.58610i	0.317146	−	1.59440i	−0.412753	−	0.910843i	$-0.635433\pi$
$29$	1.70788	−	8.58610i	0.317146	−	1.59440i	0.729899	−	0.683555i	$-0.239567\pi$
$30$	−5.85451	+	1.47478i	−1.06888	+	0.269257i
$31$	2.18280	−	1.45850i	0.392042	−	0.261954i	−0.343889	−	0.939010i	$-0.611745\pi$
$31$	2.18280	−	1.45850i	0.392042	−	0.261954i	0.735931	+	0.677056i	$0.236745\pi$
$32$	17.0236	+	7.05142i	3.00938	+	1.24653i
$33$	1.69798	+	1.69798i	0.295581	+	0.295581i
$34$	−7.22307	−	8.47103i	−1.23875	−	1.45277i
$35$	0.502628	−	0.126614i	0.0849597	−	0.0214017i
$36$	−2.02442	−	4.88738i	−0.337403	−	0.814563i
$37$	−1.72339	+	8.66406i	−0.283323	+	1.42436i	0.532681	+	0.846316i	$0.321185\pi$
$37$	−1.72339	+	8.66406i	−0.283323	+	1.42436i	−0.816004	+	0.578046i	$0.803815\pi$
$38$			10.0162i			1.62484i
$39$	4.54937	+	0.904925i	0.728482	+	0.144904i
$40$	18.7112	+	6.66685i	2.95850	+	1.05412i
$41$	0.945732	+	4.75451i	0.147698	+	0.742530i	0.981650	+	0.190692i	$0.0610733\pi$
$41$	0.945732	+	4.75451i	0.147698	+	0.742530i	−0.833951	+	0.551838i	$0.813927\pi$
$42$	0.239512	+	0.578233i	0.0369575	+	0.0892232i
$43$	0.153752	+	0.371191i	0.0234470	+	0.0566061i	0.935169	−	0.354201i	$-0.115247\pi$
$43$	0.153752	+	0.371191i	0.0234470	+	0.0566061i	−0.911722	+	0.410807i	$0.865247\pi$
$44$	−2.47825	−	12.4590i	−0.373610	−	1.87827i
$45$	−0.958737	−	2.02010i	−0.142920	−	0.301139i
$46$	−11.2080	−	2.22942i	−1.65253	−	0.328709i
$47$			9.73422i			1.41988i	0.704261	+	0.709941i	$0.251278\pi$
$47$			9.73422i			1.41988i	−0.704261	+	0.709941i	$0.748722\pi$
$48$	−2.61511	+	13.1471i	−0.377459	+	1.89762i
$49$	2.65822	+	6.41751i	0.379746	+	0.916788i
$50$	12.9292	+	3.88439i	1.82846	+	0.549336i
$51$	2.55521	−	3.23587i	0.357802	−	0.453113i
$52$	−17.3509	−	17.3509i	−2.40614	−	2.40614i
$53$	10.6910	+	4.42835i	1.46852	+	0.608280i	0.966521	−	0.256588i	$-0.0825984\pi$
$53$	10.6910	+	4.42835i	1.46852	+	0.608280i	0.501998	+	0.864869i	$0.332598\pi$
$54$	2.24498	−	1.50005i	0.305503	−	0.204130i
$55$	−1.31163	−	5.20683i	−0.176859	−	0.702089i
$56$	0.401723	−	2.01960i	0.0536825	−	0.269880i
$57$	−3.63840	+	0.723722i	−0.481917	+	0.0958593i
$58$	−19.6532	−	13.1319i	−2.58059	−	1.72430i
$59$	−0.594386	+	1.43498i	−0.0773825	+	0.186818i	−0.957837	−	0.287314i	$-0.907238\pi$
$59$	−0.594386	+	1.43498i	−0.0773825	+	0.186818i	0.880454	+	0.474131i	$0.157238\pi$
$60$	−1.72006	+	11.7032i	−0.222059	+	1.51088i
$61$	−4.69467	+	0.933828i	−0.601091	+	0.119564i	−0.486250	−	0.873820i	$-0.661636\pi$
$61$	−4.69467	+	0.933828i	−0.601091	+	0.119564i	−0.114841	+	0.993384i	$0.536636\pi$
$62$	−1.38283	−	6.95195i	−0.175619	−	0.882899i
$63$	−0.192738	+	0.128784i	−0.0242827	+	0.0162252i
$64$	16.2223	−	16.2223i	2.02779	−	2.02779i
$65$	−7.69442	−	6.95515i	−0.954375	−	0.862680i
$66$	5.99004	−	2.48115i	0.737323	−	0.305409i
$67$	1.69680	−	1.69680i	0.207297	−	0.207297i	−0.595820	−	0.803118i	$-0.703173\pi$
$67$	1.69680	−	1.69680i	0.207297	−	0.207297i	0.803118	+	0.595820i	$0.203173\pi$
$68$	−20.7494	+	6.72330i	−2.51624	+	0.815319i
$69$		−	4.23243i		−	0.509525i
$70$	0.203503	−	1.38462i	0.0243232	−	0.165494i
$71$	−8.33019	−	12.4670i	−0.988612	−	1.47956i	−0.873866	−	0.486167i	$-0.838395\pi$
$71$	−8.33019	−	12.4670i	−0.988612	−	1.47956i	−0.114746	−	0.993395i	$-0.536605\pi$
$72$	−8.88321			−1.04690
$73$	0.341001	+	0.510345i	0.0399112	+	0.0597313i	0.850889	−	0.525346i	$-0.176064\pi$
$73$	0.341001	+	0.510345i	0.0399112	+	0.0597313i	−0.810977	+	0.585077i	$0.801064\pi$
$74$	19.8317	+	13.2511i	2.30539	+	1.54041i
$75$	−0.476814	+	4.97721i	−0.0550577	+	0.574719i
$76$	18.1306	+	7.50994i	2.07972	+	0.861449i
$77$	−0.514263	+	0.213015i	−0.0586057	+	0.0242753i
$78$	6.95796	−	10.4133i	0.787833	−	1.17908i
$79$	−1.83806	+	2.75085i	−0.206798	+	0.309495i	−0.920341	−	0.391116i	$-0.872089\pi$
$79$	−1.83806	+	2.75085i	−0.206798	+	0.309495i	0.713543	+	0.700611i	$0.247089\pi$
$80$	20.0995	−	22.2358i	2.24719	−	2.48604i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	12.8372	+	2.55349i	1.41764	+	0.281985i
$83$	−4.21219	+	10.1691i	−0.462348	+	1.11621i	0.505082	+	0.863071i	$0.331462\pi$
$83$	−4.21219	+	10.1691i	−0.462348	+	1.11621i	−0.967431	+	0.253136i	$0.918538\pi$
$84$	1.22626			0.133796
$85$	−8.61624	+	3.28031i	−0.934562	+	0.355799i
$86$	1.08479			0.116976
$87$	3.35013	−	8.08793i	0.359172	−	0.867117i
$88$	−20.9215	−	4.16154i	−2.23024	−	0.443622i
$89$	1.93036	+	1.93036i	0.204618	+	0.204618i	0.801975	−	0.597357i	$-0.203783\pi$
$89$	1.93036	+	1.93036i	0.204618	+	0.204618i	−0.597357	+	0.801975i	$0.703783\pi$
$90$	−6.02974	+	0.304282i	−0.635590	+	0.0320741i
$91$	−0.597362	+	0.894016i	−0.0626206	+	0.0937183i
$92$	−12.4391	+	18.6165i	−1.29687	+	1.94090i
$93$	2.42540	−	1.00463i	0.251502	−	0.104175i
$94$	24.2819	+	10.0579i	2.50448	+	1.03739i
$95$	7.81391	+	2.78412i	0.801691	+	0.285644i
$96$	15.3209	+	10.2371i	1.56368	+	1.04482i
$97$	−1.26576	−	1.89434i	−0.128518	−	0.192341i	0.761630	−	0.648012i	$-0.224399\pi$
$97$	−1.26576	−	1.89434i	−0.128518	−	0.192341i	−0.890148	+	0.455671i	$0.849399\pi$
$98$	18.7550			1.89454
$99$	1.33410	+	1.99662i	0.134082	+	0.200668i
$100$	16.7253	−	20.4910i	1.67253	−	2.04910i
$101$		−	13.3521i		−	1.32858i	−0.747474	−	0.664291i	$-0.768733\pi$
$101$		−	13.3521i		−	1.32858i	0.747474	−	0.664291i	$-0.231267\pi$
$102$	−5.43167	−	9.71741i	−0.537815	−	0.962167i
$103$	−2.55818	+	2.55818i	−0.252065	+	0.252065i	−0.821817	−	0.569752i	$-0.807039\pi$
$103$	−2.55818	+	2.55818i	−0.252065	+	0.252065i	0.569752	+	0.821817i	$0.307039\pi$
$104$	−38.0682	+	15.7684i	−3.73289	+	1.54621i
$105$	0.517672	−	0.0261236i	0.0505196	−	0.00254940i
$106$	22.0929	−	22.0929i	2.14585	−	2.14585i
$107$	−10.6901	+	7.14290i	−1.03345	+	0.690531i	−0.951985	−	0.306145i	$-0.900961\pi$
$107$	−10.6901	+	7.14290i	−1.03345	+	0.690531i	−0.0814674	+	0.996676i	$0.525961\pi$
$108$	−1.03204	−	5.18842i	−0.0993081	−	0.499255i
$109$	4.78880	−	0.952552i	0.458684	−	0.0912379i	0.0396603	−	0.999213i	$-0.487372\pi$
$109$	4.78880	−	0.952552i	0.458684	−	0.0912379i	0.419024	+	0.907975i	$0.362372\pi$
$110$	−14.3436	−	2.10813i	−1.36761	−	0.201002i
$111$	−3.38055	+	8.16136i	−0.320867	+	0.774642i
$112$	−2.58359	−	1.72630i	−0.244126	−	0.163120i
$113$	−7.23760	+	1.43965i	−0.680856	+	0.135431i	−0.523389	−	0.852094i	$-0.675333\pi$
$113$	−7.23760	+	1.43965i	−0.680856	+	0.135431i	−0.157467	+	0.987524i	$0.550333\pi$
$114$	−1.95406	+	9.82371i	−0.183014	+	0.920075i
$115$	−4.85464	+	8.12402i	−0.452698	+	0.757569i
$116$	−38.5061	+	25.7289i	−3.57520	+	2.38887i
$117$	4.28541	+	1.77508i	0.396186	+	0.164106i
$118$	2.96538	+	2.96538i	0.272985	+	0.272985i
$119$	0.466325	+	0.834270i	0.0427480	+	0.0764774i
$120$	17.0511	+	10.1891i	1.55654	+	0.930136i
$121$	−2.00285	−	4.83531i	−0.182077	−	0.439574i
$122$	−2.52135	+	12.6757i	−0.228272	+	1.14760i
$123$			4.84766i			0.437099i
$124$	−13.6208	−	2.70934i	−1.22318	−	0.243306i
$125$	6.62414	−	9.00670i	0.592481	−	0.805584i
$126$	0.122102	+	0.613848i	0.0108777	+	0.0546860i
$127$	3.42848	+	8.27709i	0.304229	+	0.734473i	0.999871	+	0.0160846i	$0.00512010\pi$
$127$	3.42848	+	8.27709i	0.304229	+	0.734473i	−0.695642	+	0.718389i	$0.744880\pi$
$128$	−9.60179	−	23.1808i	−0.848687	−	2.04891i
$129$	0.0783823	+	0.394054i	0.00690117	+	0.0346945i
$130$	−25.2998	+	12.0072i	−2.21894	+	1.05310i
$131$	0.825089	+	0.164120i	0.0720884	+	0.0143393i	0.231003	−	0.972953i	$-0.425799\pi$
$131$	0.825089	+	0.164120i	0.0720884	+	0.0143393i	−0.158914	+	0.987292i	$0.550799\pi$
$132$		−	12.7031i		−	1.10566i
$133$	0.167762	−	0.843396i	0.0145468	−	0.0731317i
$134$	−2.47943	−	5.98586i	−0.214190	−	0.517100i
$135$	−0.546212	−	2.16833i	−0.0470104	−	0.186620i
$136$	−2.90328	+	36.5111i	−0.248954	+	3.13080i
$137$	−7.82486	−	7.82486i	−0.668523	−	0.668523i	0.288851	−	0.957374i	$-0.406727\pi$
$137$	−7.82486	−	7.82486i	−0.668523	−	0.668523i	−0.957374	+	0.288851i	$0.906727\pi$
$138$	−10.5577	−	4.37316i	−0.898734	−	0.372268i
$139$	5.08042	−	3.39463i	0.430916	−	0.287929i	−0.321136	−	0.947033i	$-0.604065\pi$
$139$	5.08042	−	3.39463i	0.430916	−	0.287929i	0.752051	+	0.659105i	$0.229065\pi$
$140$	−2.35377	−	1.40653i	−0.198930	−	0.118874i
$141$	−1.89905	+	9.54718i	−0.159929	+	0.804018i
$142$	−39.7059	+	7.89800i	−3.33205	+	0.662786i
$143$	9.26130	+	6.18820i	0.774469	+	0.517484i
$144$	−5.12973	+	12.3843i	−0.427478	+	1.03202i
$145$	−15.7074	+	11.6819i	−1.30443	+	0.970129i
$146$	1.62539	−	0.323309i	0.134518	−	0.0267573i
$147$	1.35515	+	6.81280i	0.111771	+	0.561910i
$148$	38.8557	−	25.9625i	3.19392	−	2.13411i
$149$	7.15371	−	7.15371i	0.586055	−	0.586055i	−0.350506	−	0.936560i	$-0.613990\pi$
$149$	7.15371	−	7.15371i	0.586055	−	0.586055i	0.936560	+	0.350506i	$0.113990\pi$
$150$	11.9229	+	6.33211i	0.973502	+	0.517015i
$151$	−16.7122	+	6.92240i	−1.36002	+	0.563337i	−0.939063	−	0.343746i	$-0.888304\pi$
$151$	−16.7122	+	6.92240i	−1.36002	+	0.563337i	−0.420953	+	0.907083i	$0.638304\pi$
$152$	23.3019	−	23.3019i	1.89003	−	1.89003i
$153$	3.13740	−	2.67520i	0.253644	−	0.216277i
$154$			1.50292i			0.121109i
$155$	−5.80780	−	0.853592i	−0.466494	−	0.0685622i
$156$	−13.6325	−	20.4025i	−1.09148	−	1.63351i
$157$	10.2083			0.814707			0.407354	−	0.913270i	$-0.366452\pi$
$157$	10.2083			0.814707			0.407354	+	0.913270i	$0.366452\pi$
$158$	4.96279	+	7.42734i	0.394818	+	0.590887i
$159$	9.62163	+	6.42897i	0.763045	+	0.509850i
$160$	−17.6659	−	37.2230i	−1.39661	−	2.94273i
$161$	0.906414	+	0.375449i	0.0714355	+	0.0295895i
$162$	2.49449	−	1.03325i	0.195985	−	0.0811798i
$163$	−8.51972	+	12.7507i	−0.667316	+	0.998709i	0.331163	+	0.943574i	$0.392559\pi$
$163$	−8.51972	+	12.7507i	−0.667316	+	0.998709i	−0.998479	+	0.0551356i	$0.982441\pi$
$164$	14.2473	−	21.3226i	1.11253	−	1.66501i
$165$	−0.270620	−	5.36267i	−0.0210677	−	0.417483i
$166$	21.0145	+	21.0145i	1.63104	+	1.63104i
$167$	21.4623	+	4.26911i	1.66080	+	0.330354i	0.934212	−	0.356719i	$-0.116104\pi$
$167$	21.4623	+	4.26911i	1.66080	+	0.330354i	0.726589	+	0.687072i	$0.241104\pi$
$168$	0.788009	−	1.90242i	0.0607962	−	0.146775i
$169$	8.51564			0.655049
$170$	−0.720047	+	24.8825i	−0.0552251	+	1.90840i
$171$	−3.70968			−0.283686
$172$	0.813359	−	1.96362i	0.0620181	−	0.149725i
$173$	−10.0169	−	1.99249i	−0.761574	−	0.151486i	−0.201000	−	0.979591i	$-0.564419\pi$
$173$	−10.0169	−	1.99249i	−0.761574	−	0.151486i	−0.560573	+	0.828105i	$0.689419\pi$
$174$	−16.7137	−	16.7137i	−1.26706	−	1.26706i
$175$	−1.02362	−	0.543631i	−0.0773784	−	0.0410947i
$176$	−17.8831	+	26.7639i	−1.34799	+	2.01741i
$177$	−0.862915	+	1.29144i	−0.0648607	+	0.0970709i
$178$	6.80980	−	2.82071i	0.510416	−	0.211421i
$179$	−13.0625	−	5.41068i	−0.976340	−	0.404413i	−0.163271	−	0.986581i	$-0.552205\pi$
$179$	−13.0625	−	5.41068i	−0.976340	−	0.404413i	−0.813069	+	0.582168i	$0.802205\pi$
$180$	−3.97019	+	11.1428i	−0.295921	+	0.830533i
$181$	−10.2379	−	6.84076i	−0.760979	−	0.508470i	0.113497	−	0.993538i	$-0.463795\pi$
$181$	−10.2379	−	6.84076i	−0.760979	−	0.508470i	−0.874476	+	0.485068i	$0.838795\pi$
$182$	1.61288	+	2.41385i	0.119555	+	0.178927i
$183$	−4.78664			−0.353839
$184$	20.8881	+	31.2612i	1.53989	+	2.30461i
$185$	15.8500	−	11.7880i	1.16532	−	0.866669i
$186$		−	7.08815i		−	0.519728i
$187$	8.64238	−	4.83076i	0.631994	−	0.353261i
$188$	36.4122	−	36.4122i	2.65563	−	2.65563i
$189$	−0.214159	+	0.0887077i	−0.0155778	+	0.00645254i
$190$	15.0187	−	16.6150i	1.08957	−	1.20538i
$191$	3.47438	−	3.47438i	0.251397	−	0.251397i	−0.570146	−	0.821543i	$-0.693113\pi$
$191$	3.47438	−	3.47438i	0.251397	−	0.251397i	0.821543	+	0.570146i	$0.193113\pi$
$192$	19.0754	−	12.7458i	1.37665	−	0.919849i
$193$	−1.21425	−	6.10445i	−0.0874037	−	0.439408i	−0.999563	−	0.0295714i	$-0.990586\pi$
$193$	−1.21425	−	6.10445i	−0.0874037	−	0.439408i	0.912159	−	0.409836i	$-0.134414\pi$
$194$	−6.03324	+	1.20009i	−0.433162	+	0.0861612i
$195$	−6.18969	−	8.32261i	−0.443253	−	0.595995i
$196$	14.0622	−	33.9490i	1.00444	−	2.42493i
$197$	−3.62031	−	2.41901i	−0.257936	−	0.172348i	0.419878	−	0.907580i	$-0.362073\pi$
$197$	−3.62031	−	2.41901i	−0.257936	−	0.172348i	−0.677815	+	0.735233i	$0.737073\pi$
$198$	6.35899	−	1.26488i	0.451914	−	0.0898912i
$199$	−1.40541	+	7.06547i	−0.0996268	+	0.500858i	0.898461	+	0.439053i	$0.144686\pi$
$199$	−1.40541	+	7.06547i	−0.0996268	+	0.500858i	−0.998088	+	0.0618053i	$0.980314\pi$
$200$	−21.0420	−	39.1155i	−1.48789	−	2.76588i
$201$	1.99523	−	1.33317i	0.140732	−	0.0940344i
$202$	−33.3066	−	13.7960i	−2.34344	−	0.970686i
$203$	1.43492	+	1.43492i	0.100712	+	0.100712i
$204$	−21.6624	+	2.54610i	−1.51667	+	0.178263i
$205$	5.56032	−	9.30494i	0.388349	−	0.649885i
$206$	3.73810	+	9.02458i	0.260446	+	0.628772i
$207$	0.825706	−	4.15110i	0.0573905	−	0.288522i
$208$			62.1773i			4.31122i
$209$	−8.73692	−	1.73788i	−0.604346	−	0.120212i
$210$	0.469719	−	1.31832i	0.0324137	−	0.0909725i
$211$	−3.61185	−	18.1580i	−0.248650	−	1.25005i	−0.880159	−	0.474680i	$-0.842564\pi$
$211$	−3.61185	−	18.1580i	−0.248650	−	1.25005i	0.631509	−	0.775369i	$-0.282436\pi$
$212$	−23.4262	−	56.5559i	−1.60892	−	3.88428i
$213$	−5.73793	−	13.8526i	−0.393157	−	0.949165i
$214$	6.77232	+	34.0467i	0.462946	+	2.32739i
$215$	0.301532	−	0.846281i	0.0205643	−	0.0577159i
$216$	−8.71252	−	1.73303i	−0.592812	−	0.117918i
$217$			0.608540i			0.0413104i
$218$	2.57190	−	12.9298i	0.174191	−	0.875718i
$219$	0.234886	+	0.567064i	0.0158721	+	0.0383187i
$220$	−14.5706	+	24.3832i	−0.982348	+	1.64392i
$221$	8.69639	−	17.0335i	0.584982	−	1.14579i
$222$	16.8655	+	16.8655i	1.13194	+	1.13194i
$223$	24.5599	+	10.1730i	1.64465	+	0.681236i	0.996755	−	0.0804938i	$-0.0256497\pi$
$223$	24.5599	+	10.1730i	1.64465	+	0.681236i	0.647895	+	0.761730i	$0.275650\pi$
$224$	−3.55144	+	2.37300i	−0.237291	+	0.158553i
$225$	−1.43866	+	4.78856i	−0.0959105	+	0.319237i
$226$	−3.88707	+	19.5416i	−0.258564	+	1.29989i
$227$	−7.09032	+	1.41035i	−0.470601	+	0.0936084i	−0.424693	−	0.905337i	$-0.639618\pi$
$227$	−7.09032	+	1.41035i	−0.470601	+	0.0936084i	−0.0459080	+	0.998946i	$0.514618\pi$
$228$	16.3171	+	10.9027i	1.08063	+	0.722052i
$229$	6.34424	−	15.3163i	0.419239	−	1.01213i	−0.563330	−	0.826232i	$-0.690480\pi$
$229$	6.34424	−	15.3163i	0.419239	−	1.01213i	0.982569	−	0.185900i	$-0.0595202\pi$
$230$	15.2492	+	20.5040i	1.00550	+	1.35199i
$231$	−0.545939	+	0.108594i	−0.0359201	+	0.00714496i
$232$	15.1715	+	76.2721i	0.996055	+	5.00751i
$233$	−18.1414	+	12.1217i	−1.18848	+	0.794119i	−0.982831	−	0.184506i	$-0.940931\pi$
$233$	−18.1414	+	12.1217i	−1.18848	+	0.794119i	−0.205651	+	0.978625i	$0.565931\pi$
$234$	8.85580	−	8.85580i	0.578922	−	0.578922i
$235$	14.5959	−	16.1473i	0.952131	−	1.05333i
$236$	7.59111	−	3.14434i	0.494139	−	0.204679i
$237$	−2.33941	+	2.33941i	−0.151961	+	0.151961i
$238$	2.56290	−	0.301233i	0.166128	−	0.0195260i
$239$		−	2.31380i		−	0.149667i	−0.997196	−	0.0748336i	$-0.976157\pi$
$239$		−	2.31380i		−	0.149667i	0.997196	−	0.0748336i	$-0.0238426\pi$
$240$	24.0512	−	17.8874i	1.55250	−	1.15463i
$241$	3.85243	+	5.76557i	0.248157	+	0.371393i	0.934547	−	0.355841i	$-0.115805\pi$
$241$	3.85243	+	5.76557i	0.248157	+	0.371393i	−0.686390	+	0.727234i	$0.740805\pi$
$242$	−14.1311			−0.908379
$243$	0.555570	+	0.831470i	0.0356398	+	0.0533388i
$244$	21.0542	+	14.0680i	1.34786	+	0.900608i
$245$	5.21318	−	14.6313i	0.333058	−	0.934762i
$246$	12.0924	+	5.00884i	0.770985	+	0.319352i
$247$	−15.8975	+	6.58496i	−1.01153	+	0.418991i
$248$	−12.9561	+	19.3902i	−0.822716	+	1.23128i
$249$	−6.11516	+	9.15198i	−0.387532	+	0.579983i
$250$	−15.6227	−	25.8300i	−0.988066	−	1.63363i
$251$	13.3925	+	13.3925i	0.845329	+	0.845329i	0.989546	−	0.144217i	$-0.0460662\pi$
$251$	13.3925	+	13.3925i	0.845329	+	0.845329i	−0.144217	+	0.989546i	$0.546066\pi$
$252$	1.20270	+	0.239231i	0.0757628	+	0.0150702i
$253$	3.88936	−	9.38974i	0.244522	−	0.590328i
$254$	24.1896			1.51779
$255$	−9.09064	+	1.53633i	−0.569278	+	0.0962089i
$256$	−21.8615			−1.36634
$257$	−0.233227	+	0.563059i	−0.0145483	+	0.0351227i	−0.930987	−	0.365053i	$-0.881051\pi$
$257$	−0.233227	+	0.563059i	−0.0145483	+	0.0351227i	0.916438	+	0.400176i	$0.131051\pi$
$258$	1.06395	+	0.211633i	0.0662387	+	0.0131757i
$259$	−1.44795	−	1.44795i	−0.0899713	−	0.0899713i
$260$	2.76534	+	54.7987i	0.171499	+	3.39847i
$261$	4.86363	−	7.27894i	0.301051	−	0.450555i
$262$	1.26192	−	1.88860i	0.0779616	−	0.116678i
$263$	−24.9396	+	10.3303i	−1.53784	+	0.636994i	−0.981067	−	0.193670i	$-0.937961\pi$
$263$	−24.9396	+	10.3303i	−1.53784	+	0.636994i	−0.556774	+	0.830664i	$0.687961\pi$
$264$	−19.7076	−	8.16315i	−1.21292	−	0.502407i
$265$	−11.0943	−	23.3763i	−0.681520	−	1.43600i
$266$	−1.93050	−	1.28992i	−0.118367	−	0.0790900i
$267$	1.51667	+	2.26986i	0.0928190	+	0.138913i
$268$	−12.6942			−0.775424
$269$	−3.70109	−	5.53907i	−0.225659	−	0.337723i	0.701312	−	0.712854i	$-0.252598\pi$
$269$	−3.70109	−	5.53907i	−0.225659	−	0.337723i	−0.926972	+	0.375131i	$0.877598\pi$
$270$	−5.97324	−	0.877908i	−0.363520	−	0.0534278i
$271$		−	14.8170i		−	0.900067i	−0.893012	−	0.450033i	$-0.851412\pi$
$271$		−	14.8170i		−	0.900067i	0.893012	−	0.450033i	$-0.148588\pi$
$272$	49.2244	+	25.1314i	2.98467	+	1.52381i
$273$	−0.760298	+	0.760298i	−0.0460153	+	0.0460153i
$274$	−27.6040	+	11.4340i	−1.66762	+	0.690751i
$275$	−5.63159	+	10.6039i	−0.339598	+	0.639439i
$276$	−15.8320	+	15.8320i	−0.952974	+	0.952974i
$277$	20.8247	−	13.9146i	1.25124	−	0.836050i	0.259676	−	0.965696i	$-0.416384\pi$
$277$	20.8247	−	13.9146i	1.25124	−	0.836050i	0.991560	+	0.129646i	$0.0413841\pi$
$278$	−3.21851	−	16.1805i	−0.193033	−	0.970444i
$279$	2.57479	−	0.512157i	0.154148	−	0.0306620i
$280$	−3.69466	+	2.74779i	−0.220798	+	0.164212i
$281$	−9.79616	+	23.6500i	−0.584390	+	1.41084i	0.304407	+	0.952542i	$0.401542\pi$
$281$	−9.79616	+	23.6500i	−0.584390	+	1.41084i	−0.888797	+	0.458300i	$0.848458\pi$
$282$	21.8531	+	14.6018i	1.30133	+	0.869523i
$283$	14.7852	−	2.94095i	0.878886	−	0.174821i	0.265031	−	0.964240i	$-0.414618\pi$
$283$	14.7852	−	2.94095i	0.878886	−	0.174821i	0.613855	+	0.789419i	$0.289618\pi$
$284$	−15.4744	+	77.7948i	−0.918234	+	4.61627i
$285$	7.12062	+	4.25504i	0.421789	+	0.252047i
$286$	25.0056	−	16.7082i	1.47861	−	0.987978i
$287$	−1.03817	−	0.430025i	−0.0612813	−	0.0253836i
$288$	13.0293	+	13.0293i	0.767761	+	0.767761i
$289$	−9.97003	−	13.7695i	−0.586472	−	0.809969i
$290$	12.9107	+	51.2522i	0.758140	+	3.00963i
$291$	−0.871868	−	2.10488i	−0.0511098	−	0.123390i
$292$	0.633452	−	3.18458i	0.0370700	−	0.186363i
$293$		−	20.3722i		−	1.19015i	−0.803669	−	0.595077i	$-0.797121\pi$
$293$		−	20.3722i		−	1.19015i	0.803669	−	0.595077i	$-0.202879\pi$
$294$	18.3946	+	3.65892i	1.07280	+	0.213392i
$295$	3.13764	−	1.48912i	0.182680	−	0.0866997i
$296$	−15.3092	−	76.9646i	−0.889830	−	4.47348i
$297$	0.918942	+	2.21852i	0.0533224	+	0.128732i
$298$	−10.4533	−	25.2364i	−0.605541	−	1.46190i
$299$	−3.83003	−	19.2549i	−0.221497	−	1.11354i
$300$	20.4015	−	16.8344i	1.17788	−	0.971933i
$301$	−0.0913435	−	0.0181694i	−0.00526495	−	0.00104726i
$302$			48.8408i			2.81047i
$303$	2.60486	−	13.0955i	0.149646	−	0.752319i
$304$	−19.0296	−	45.9416i	−1.09143	−	2.63493i
$305$	9.18782	+	5.49033i	0.526093	+	0.314375i
$306$	−3.43152	−	10.5904i	−0.196167	−	0.605411i
$307$	12.1383	+	12.1383i	0.692769	+	0.692769i	0.962840	−	0.270071i	$-0.0870473\pi$
$307$	12.1383	+	12.1383i	0.692769	+	0.692769i	−0.270071	+	0.962840i	$0.587047\pi$
$308$	2.72048	+	1.12686i	0.155014	+	0.0642089i
$309$	−3.00810	+	2.00995i	−0.171125	+	0.114342i
$310$	−8.13018	+	13.6055i	−0.461763	+	0.772740i
$311$	1.88449	−	9.47397i	0.106860	−	0.537220i	−0.889856	−	0.456241i	$-0.849195\pi$
$311$	1.88449	−	9.47397i	0.106860	−	0.537220i	0.996716	−	0.0809787i	$-0.0258046\pi$
$312$	−40.4130	+	8.03864i	−2.28793	+	0.455098i
$313$	7.25785	+	4.84954i	0.410238	+	0.274112i	0.743518	−	0.668715i	$-0.233156\pi$
$313$	7.25785	+	4.84954i	0.410238	+	0.274112i	−0.333280	+	0.942828i	$0.608156\pi$
$314$	10.5477	−	25.4643i	0.595240	−	1.43704i
$315$	0.512821	+	0.0753711i	0.0288942	+	0.00424668i
$316$	17.1655	−	3.41443i	0.965634	−	0.192076i
$317$	−2.89628	−	14.5606i	−0.162671	−	0.817804i	−0.972817	−	0.231576i	$-0.925612\pi$
$317$	−2.89628	−	14.5606i	−0.162671	−	0.817804i	0.810145	−	0.586229i	$-0.199388\pi$
$318$	25.9785	−	17.3583i	1.45680	−	0.973404i
$319$	14.8647	−	14.8647i	0.832262	−	0.832262i
$320$	−51.2343	+	2.58547i	−2.86408	+	0.144532i
$321$	−11.8782	+	4.92012i	−0.662977	+	0.274614i
$322$	1.87310	−	1.87310i	0.104384	−	0.104384i
$323$	−1.21243	+	15.2473i	−0.0674612	+	0.848380i
$324$		−	5.29006i		−	0.293892i
$325$	2.33480	+	23.0747i	0.129512	+	1.27995i
$326$	23.0033	+	34.4269i	1.27404	+	1.90673i
$327$	4.88262			0.270010
$328$	−23.9244	−	35.8054i	−1.32100	−	1.97702i
$329$	−1.87616	−	1.25361i	−0.103436	−	0.0691136i
$330$	−13.6567	−	4.86592i	−0.751778	−	0.267860i
$331$	−9.13247	−	3.78279i	−0.501966	−	0.207921i	0.117309	−	0.993095i	$-0.462573\pi$
$331$	−9.13247	−	3.78279i	−0.501966	−	0.207921i	−0.619275	+	0.785174i	$0.712573\pi$
$332$	53.7954	−	22.2828i	2.95240	−	1.22293i
$333$	−4.90779	+	7.34503i	−0.268945	+	0.402505i
$334$	32.8251	−	49.1263i	1.79611	−	2.68807i
$335$	−5.35894	+	0.270431i	−0.292790	+	0.0147752i
$336$	−2.19716	−	2.19716i	−0.119865	−	0.119865i
$337$	7.03011	+	1.39838i	0.382954	+	0.0761744i	0.382814	−	0.923826i	$-0.374955\pi$
$337$	7.03011	+	1.39838i	0.382954	+	0.0761744i	0.000140879		1.00000i	$0.499955\pi$
$338$	8.79878	−	21.2421i	0.478590	−	1.15542i
$339$	−7.37939			−0.400794
$340$	44.5007	+	19.9598i	2.41339	+	1.08247i
$341$	6.30399			0.341380
$342$	−3.83302	+	9.25374i	−0.207266	+	0.500385i
$343$	−3.17069	−	0.630689i	−0.171201	−	0.0340540i
$344$	−2.52369	−	2.52369i	−0.136068	−	0.136068i
$345$	−6.34628	+	7.02083i	−0.341672	+	0.377989i
$346$	−15.3202	+	22.9284i	−0.823622	+	1.23264i
$347$	−6.06926	+	9.08329i	−0.325815	+	0.487617i	−0.957828	−	0.287341i	$-0.907229\pi$
$347$	−6.06926	+	9.08329i	−0.325815	+	0.487617i	0.632013	+	0.774958i	$0.282229\pi$
$348$	−42.7856	+	17.7224i	−2.29355	+	0.950020i
$349$	−10.0229	−	4.15161i	−0.536512	−	0.222231i	0.0979405	−	0.995192i	$-0.468775\pi$
$349$	−10.0229	−	4.15161i	−0.536512	−	0.222231i	−0.634453	+	0.772962i	$0.718775\pi$
$350$	−2.41373	+	1.99170i	−0.129020	+	0.106461i
$351$	3.85677	+	2.57701i	0.205859	+	0.137551i
$352$	24.5824	+	36.7902i	1.31025	+	1.96092i
$353$	8.66257			0.461062			0.230531	−	0.973065i	$-0.425954\pi$
$353$	8.66257			0.461062			0.230531	+	0.973065i	$0.425954\pi$
$354$	2.32988	+	3.48691i	0.123832	+	0.185327i
$355$	−4.87528	+	33.1711i	−0.258753	+	1.76054i
$356$		−	14.4416i		−	0.765401i
$357$	0.294607	+	0.909215i	0.0155923	+	0.0481208i
$358$	−26.9937	+	26.9937i	−1.42666	+	1.42666i
$359$	−26.0893	+	10.8065i	−1.37694	+	0.570347i	−0.943661	−	0.330913i	$-0.892643\pi$
$359$	−26.0893	+	10.8065i	−1.37694	+	0.570347i	−0.433278	+	0.901260i	$0.642643\pi$
$360$	14.7356	+	13.3198i	0.776635	+	0.702017i
$361$	−3.70403	+	3.70403i	−0.194949	+	0.194949i
$362$	−27.6425	+	18.4701i	−1.45286	+	0.970769i
$363$	−1.02104	−	5.13314i	−0.0535910	−	0.269420i
$364$	5.57871	−	1.10967i	0.292404	−	0.0581627i
$365$	0.199572	−	1.35788i	0.0104461	−	0.0710747i
$366$	−4.94580	+	11.9402i	−0.258521	+	0.624125i
$367$	−12.9000	−	8.61949i	−0.673373	−	0.449934i	0.171298	−	0.985219i	$-0.445204\pi$
$367$	−12.9000	−	8.61949i	−0.673373	−	0.449934i	−0.844671	+	0.535286i	$0.820204\pi$
$368$	55.6440	−	11.0683i	2.90065	−	0.576974i
$369$	−0.945732	+	4.75451i	−0.0492328	+	0.247510i
$370$	−13.0279	−	51.7176i	−0.677288	−	2.68867i
$371$	−2.23034	+	1.49026i	−0.115793	+	0.0773706i
$372$	−12.8305	−	5.31456i	−0.665230	−	0.275547i
$373$	−12.1420	−	12.1420i	−0.628686	−	0.628686i	0.319051	−	0.947738i	$-0.396636\pi$
$373$	−12.1420	−	12.1420i	−0.628686	−	0.628686i	−0.947738	+	0.319051i	$0.896636\pi$
$374$	−3.12053	−	26.5497i	−0.161359	−	1.37285i
$375$	8.25398	−	7.54134i	0.426234	−	0.389433i
$376$	−33.0911	−	79.8889i	−1.70654	−	4.11995i
$377$	7.92200	−	39.8266i	0.408004	−	2.05117i
$378$			0.625874i			0.0321915i
$379$	4.77160	+	0.949130i	0.245100	+	0.0487535i	0.316112	−	0.948722i	$-0.397623\pi$
$379$	4.77160	+	0.949130i	0.245100	+	0.0487535i	−0.0710111	+	0.997476i	$0.522623\pi$
$380$	−18.8147	−	39.6434i	−0.965172	−	2.03366i
$381$	1.74783	+	8.78692i	0.0895439	+	0.450167i
$382$	−5.07688	−	12.2567i	−0.259756	−	0.627106i
$383$	9.90180	+	23.9051i	0.505959	+	1.22149i	0.946191	+	0.323608i	$0.104896\pi$
$383$	9.90180	+	23.9051i	0.505959	+	1.22149i	−0.440233	+	0.897884i	$0.645104\pi$
$384$	−4.89495	−	24.6086i	−0.249794	−	1.25580i
$385$	1.17247	+	0.417755i	0.0597547	+	0.0212907i
$386$	−16.4821	−	3.27849i	−0.838916	−	0.166871i
$387$			0.401774i			0.0204233i
$388$	−2.35130	+	11.8208i	−0.119369	+	0.600109i
$389$	1.50465	+	3.63255i	0.0762889	+	0.184178i	0.957423	−	0.288689i	$-0.0932193\pi$
$389$	1.50465	+	3.63255i	0.0762889	+	0.184178i	−0.881134	+	0.472866i	$0.843219\pi$
$390$	−27.1561	+	6.84075i	−1.37510	+	0.346395i
$391$	−16.7917	−	4.75046i	−0.849194	−	0.240241i
$392$	−43.6321	−	43.6321i	−2.20375	−	2.20375i
$393$	0.777217	+	0.321934i	0.0392054	+	0.0162394i
$394$	−9.77487	+	6.53136i	−0.492451	+	0.329045i
$395$	7.17375	−	1.80710i	0.360951	−	0.0909251i
$396$	2.47825	−	12.4590i	0.124537	−	0.626088i
$397$	32.0455	−	6.37424i	1.60832	−	0.319914i	0.692470	−	0.721446i	$-0.256522\pi$
$397$	32.0455	−	6.37424i	1.60832	−	0.319914i	0.915845	+	0.401532i	$0.131522\pi$
$398$	16.1726	+	10.8062i	0.810658	+	0.541664i
$399$	0.329077	−	0.794462i	0.0164745	−	0.0397728i
$400$	−66.6827	+	6.74728i	−3.33413	+	0.337364i
$401$	−12.5954	+	2.50539i	−0.628986	+	0.125113i	−0.499282	−	0.866440i	$-0.666403\pi$
$401$	−12.5954	+	2.50539i	−0.628986	+	0.125113i	−0.129704	+	0.991553i	$0.541403\pi$
$402$	−1.26400	−	6.35456i	−0.0630426	−	0.316937i
$403$	10.1249	−	6.76524i	0.504357	−	0.337001i
$404$	−49.9454	+	49.9454i	−2.48487	+	2.48487i
$405$	−0.112697	−	2.23323i	−0.00559994	−	0.110970i
$406$	5.06203	−	2.09676i	0.251224	−	0.104060i
$407$	−14.9996	+	14.9996i	−0.743505	+	0.743505i
$408$	−9.97047	+	35.2432i	−0.493612	+	1.74480i
$409$			5.19675i			0.256963i	0.991712	+	0.128481i	$0.0410102\pi$
$409$			5.19675i			0.256963i	−0.991712	+	0.128481i	$0.958990\pi$
$410$	−17.4658	−	23.4845i	−0.862577	−	1.15981i
$411$	−6.14795	−	9.20106i	−0.303256	−	0.453855i
$412$	19.1384			0.942883
$413$	−0.200028	−	0.299362i	−0.00984271	−	0.0147307i
$414$	−9.50171	−	6.34884i	−0.466984	−	0.312028i
$415$	22.2353	−	10.5528i	1.09149	−	0.518017i
$416$	78.9641	+	32.7080i	3.87153	+	1.60364i
$417$	5.64506	−	2.33826i	0.276440	−	0.114505i
$418$	−13.3625	+	19.9985i	−0.653584	+	0.978157i
$419$	−6.48950	+	9.71223i	−0.317033	+	0.474473i	−0.955423	−	0.295239i	$-0.904601\pi$
$419$	−6.48950	+	9.71223i	−0.317033	+	0.474473i	0.638390	+	0.769713i	$0.279601\pi$
$420$	−2.03414	−	1.83870i	−0.0992559	−	0.0897196i
$421$	20.9588	+	20.9588i	1.02147	+	1.02147i	0.999764	+	0.0217040i	$0.00690915\pi$
$421$	20.9588	+	20.9588i	1.02147	+	1.02147i	0.0217040	+	0.999764i	$0.493091\pi$
$422$	−49.0268	−	9.75204i	−2.38659	−	0.474722i
$423$	−3.72512	+	8.99325i	−0.181122	+	0.437267i
$424$	−102.795			−4.99217
$425$	19.2114	+	7.47811i	0.931890	+	0.362742i
$426$	−40.4838			−1.96145
$427$	0.424612	−	1.02510i	0.0205484	−	0.0496083i
$428$	66.7069	+	13.2688i	3.22440	+	0.641373i
$429$	7.87609	+	7.87609i	0.380261	+	0.380261i
$430$	−1.79948	−	1.62659i	−0.0867785	−	0.0784409i
$431$	5.39807	−	8.07878i	0.260016	−	0.389141i	−0.678376	−	0.734715i	$-0.737316\pi$
$431$	5.39807	−	8.07878i	0.260016	−	0.389141i	0.938391	+	0.345574i	$0.112316\pi$
$432$	−7.44722	+	11.1455i	−0.358304	+	0.536240i
$433$	7.43813	−	3.08097i	0.357454	−	0.148062i	−0.196728	−	0.980458i	$-0.563031\pi$
$433$	7.43813	−	3.08097i	0.357454	−	0.148062i	0.554181	+	0.832396i	$0.313031\pi$
$434$	1.51799	+	0.628773i	0.0728660	+	0.0301821i
$435$	−17.6846	+	8.39308i	−0.847913	+	0.402417i
$436$	−21.4763	−	14.3500i	−1.02853	−	0.687242i
$437$	8.72298	+	13.0549i	0.417277	+	0.624499i
$438$	1.65723			0.0791855
$439$	3.26022	+	4.87926i	0.155602	+	0.232875i	0.901077	−	0.433658i	$-0.142778\pi$
$439$	3.26022	+	4.87926i	0.155602	+	0.232875i	−0.745476	+	0.666533i	$0.767778\pi$
$440$	28.4649	+	38.2737i	1.35701	+	1.82463i
$441$			6.94627i			0.330775i
$442$	−33.5042	−	39.2928i	−1.59363	−	1.86897i
$443$	−4.70713	+	4.70713i	−0.223642	+	0.223642i	−0.810030	−	0.586388i	$-0.800549\pi$
$443$	−4.70713	+	4.70713i	−0.223642	+	0.223642i	0.586388	+	0.810030i	$0.300549\pi$
$444$	43.1741	−	17.8833i	2.04895	−	0.848704i
$445$	−0.307655	−	6.09658i	−0.0145843	−	0.289005i
$446$	50.7529	−	50.7529i	2.40322	−	2.40322i
$447$	8.41187	−	5.62063i	0.397868	−	0.265847i
$448$	1.03749	+	5.21583i	0.0490170	+	0.246425i
$449$	2.61208	−	0.519574i	0.123271	−	0.0245202i	−0.133069	−	0.991107i	$-0.542483\pi$
$449$	2.61208	−	0.519574i	0.123271	−	0.0245202i	0.256340	+	0.966587i	$0.417483\pi$
$450$	10.4585	+	8.53649i	0.493018	+	0.402414i
$451$	−4.45472	+	10.7546i	−0.209765	+	0.506416i
$452$	32.4584	+	21.6880i	1.52672	+	1.02012i
$453$	−17.7415	+	3.52901i	−0.833570	+	0.165807i
$454$	−3.80797	+	19.1440i	−0.178717	+	0.898471i
$455$	2.33144	−	0.587300i	0.109300	−	0.0275330i
$456$	27.4001	−	18.3082i	1.28313	−	0.857358i
$457$	−10.2716	−	4.25465i	−0.480486	−	0.199024i	0.129275	−	0.991609i	$-0.458735\pi$
$457$	−10.2716	−	4.25465i	−0.480486	−	0.199024i	−0.609762	+	0.792585i	$0.708735\pi$
$458$	−31.6512	−	31.6512i	−1.47896	−	1.47896i
$459$	3.59903	−	2.01172i	0.167988	−	0.0938990i
$460$	48.5485	−	12.2296i	2.26359	−	0.570207i
$461$	14.4449	+	34.8732i	0.672768	+	1.62421i	0.776886	+	0.629641i	$0.216798\pi$
$461$	14.4449	+	34.8732i	0.672768	+	1.62421i	−0.104118	+	0.994565i	$0.533202\pi$
$462$	−0.293205	+	1.47404i	−0.0136411	+	0.0685786i
$463$		−	6.44300i		−	0.299432i	−0.988729	−	0.149716i	$-0.952164\pi$
$463$		−	6.44300i		−	0.299432i	0.988729	−	0.149716i	$-0.0478359\pi$
$464$	115.093	+	22.8935i	5.34308	+	1.06280i
$465$	−5.52967	−	1.97024i	−0.256433	−	0.0913675i
$466$	11.4928	+	57.7782i	0.532394	+	2.67652i
$467$	1.85150	+	4.46992i	0.0856774	+	0.206843i	0.960911	−	0.276856i	$-0.0892926\pi$
$467$	1.85150	+	4.46992i	0.0856774	+	0.206843i	−0.875234	+	0.483700i	$0.839293\pi$
$468$	−9.39026	−	22.6701i	−0.434065	−	1.04793i
$469$	0.108518	+	0.545559i	0.00501091	+	0.0251916i
$470$	−25.1980	−	53.0934i	−1.16230	−	2.44902i
$471$	10.0121	+	1.99153i	0.461333	+	0.0917649i
$472$		−	13.7975i		−	0.635079i
$473$	−0.188220	+	0.946247i	−0.00865437	+	0.0435085i
$474$	3.41843	+	8.25282i	0.157014	+	0.379064i
$475$	−8.78724	−	16.3348i	−0.403186	−	0.749494i
$476$	1.37635	−	4.86506i	0.0630848	−	0.222990i
$477$	8.18252	+	8.18252i	0.374652	+	0.374652i
$478$	−5.77174	−	2.39073i	−0.263993	−	0.109350i
$479$	−19.4825	+	13.0178i	−0.890177	+	0.594797i	−0.914356	−	0.404910i	$-0.867303\pi$
$479$	−19.4825	+	13.0178i	−0.890177	+	0.594797i	0.0241791	+	0.999708i	$0.492303\pi$
$480$	−10.0646	−	39.9542i	−0.459386	−	1.82365i
$481$	−7.99393	+	40.1882i	−0.364492	+	1.83242i
$482$	18.3627	−	3.65256i	0.836396	−	0.166370i
$483$	0.815751	+	0.545068i	0.0371180	+	0.0248014i
$484$	−10.5952	+	25.5791i	−0.481600	+	1.16269i
$485$	−0.740789	+	5.04029i	−0.0336375	+	0.228868i
$486$	2.64813	−	0.526746i	0.120122	−	0.0238937i
$487$	2.55488	+	12.8443i	0.115773	+	0.582029i	0.994503	+	0.104710i	$0.0333914\pi$
$487$	2.55488	+	12.8443i	0.115773	+	0.582029i	−0.878730	+	0.477319i	$0.841609\pi$
$488$	35.3547	−	23.6233i	1.60043	−	1.06937i
$489$	−10.8436	+	10.8436i	−0.490362	+	0.490362i
$490$	−31.1111	−	28.1220i	−1.40546	−	1.27042i
$491$	36.2266	−	15.0056i	1.63488	−	0.677191i	0.639118	−	0.769109i	$-0.279300\pi$
$491$	36.2266	−	15.0056i	1.63488	−	0.677191i	0.995767	+	0.0919174i	$0.0292996\pi$
$492$	18.1334	−	18.1334i	0.817515	−	0.817515i
$493$	−28.3278	−	22.3691i	−1.27582	−	1.00746i
$494$			46.4600i			2.09033i
$495$	0.780786	−	5.31242i	0.0350937	−	0.238776i
$496$	19.5506	+	29.2596i	0.877850	+	1.31380i
$497$	3.47566			0.155905
$498$	16.5110	+	24.7105i	0.739875	+	1.10730i
$499$	0.628901	+	0.420218i	0.0281535	+	0.0188115i	0.569567	−	0.821945i	$-0.307111\pi$
$499$	0.628901	+	0.420218i	0.0281535	+	0.0188115i	−0.541414	+	0.840756i	$0.682111\pi$
$500$	−58.4694	+	8.91229i	−2.61483	+	0.398570i
$501$	20.2170	+	8.37416i	0.903230	+	0.374130i
$502$	47.2453	−	19.5697i	2.10866	−	0.873436i
$503$	−6.06211	+	9.07259i	−0.270296	+	0.404527i	−0.941641	−	0.336618i	$-0.890717\pi$
$503$	−6.06211	+	9.07259i	−0.270296	+	0.404527i	0.671345	+	0.741145i	$0.265717\pi$
$504$	1.14401	−	1.71213i	0.0509583	−	0.0762645i
$505$	−20.0207	+	22.1487i	−0.890908	+	0.985604i
$506$	−19.4039	−	19.4039i	−0.862608	−	0.862608i
$507$	8.35201	+	1.66132i	0.370926	+	0.0737817i
$508$	18.1369	−	43.7863i	0.804695	−	1.94270i
$509$	4.10691			0.182036			0.0910178	−	0.995849i	$-0.470988\pi$
$509$	4.10691			0.182036			0.0910178	+	0.995849i	$0.470988\pi$
$510$	−5.56054	+	24.2639i	−0.246225	+	1.07442i
$511$	−0.142278			−0.00629402
$512$	−3.38481	+	8.17165i	−0.149589	+	0.361140i
$513$	−3.63840	−	0.723722i	−0.160639	−	0.0319531i
$514$	1.16356	+	1.16356i	0.0513225	+	0.0513225i
$515$	8.07939	−	0.407715i	0.356020	−	0.0179661i
$516$	1.18081	−	1.76721i	0.0519825	−	0.0777973i
$517$	−12.9864	+	19.4355i	−0.571141	+	0.854773i
$518$	−5.10799	+	2.11580i	−0.224432	+	0.0929629i
$519$	−9.43575	−	3.90842i	−0.414184	−	0.171560i
$520$	86.7919	+	30.9242i	3.80608	+	1.35611i
$521$	−11.2256	−	7.50073i	−0.491804	−	0.328613i	0.284816	−	0.958582i	$-0.408067\pi$
$521$	−11.2256	−	7.50073i	−0.491804	−	0.328613i	−0.776620	+	0.629969i	$0.783067\pi$
$522$	−13.1319	−	19.6532i	−0.574766	−	0.860198i
$523$	−2.98052			−0.130329			−0.0651645	−	0.997875i	$-0.520757\pi$
$523$	−2.98052			−0.130329			−0.0651645	+	0.997875i	$0.520757\pi$
$524$	−2.47244	−	3.70028i	−0.108009	−	0.161647i
$525$	−0.897894	−	0.732884i	−0.0391873	−	0.0319857i
$526$			72.8852i			3.17795i
$527$	−1.26352	−	10.7501i	−0.0550398	−	0.468282i
$528$	−22.7608	+	22.7608i	−0.990539	+	0.990539i
$529$	4.69935	−	1.94653i	0.204319	−	0.0846319i
$530$	−69.7751	+	3.52110i	−3.03084	+	0.152947i
$531$	−1.09828	+	1.09828i	−0.0476614	+	0.0476614i
$532$	−3.78238	+	2.52730i	−0.163987	+	0.109573i
$533$	4.38677	+	22.0538i	0.190012	+	0.955256i
$534$	7.22924	−	1.43799i	0.312840	−	0.0622277i
$535$	28.4433	+	4.18041i	1.22971	+	0.180735i
$536$	−8.15747	+	19.6939i	−0.352349	+	0.850645i
$537$	−11.7560	−	7.85509i	−0.507308	−	0.338972i
$538$	−17.6413	+	3.50907i	−0.760570	+	0.151287i
$539$	−3.25414	+	16.3596i	−0.140166	+	0.704660i
$540$	−6.06776	+	10.1541i	−0.261115	+	0.436964i
$541$	−12.5466	+	8.38339i	−0.539422	+	0.360430i	−0.795240	−	0.606295i	$-0.792655\pi$
$541$	−12.5466	+	8.38339i	−0.539422	+	0.360430i	0.255818	+	0.966725i	$0.417655\pi$
$542$	−36.9607	−	15.3096i	−1.58760	−	0.657605i
$543$	−8.70664	−	8.70664i	−0.373638	−	0.373638i
$544$	57.8106	−	49.2939i	2.47861	−	2.11346i
$545$	−9.37205	−	5.60042i	−0.401454	−	0.239895i
$546$	1.11097	+	2.68213i	0.0475453	+	0.114785i
$547$	8.11597	−	40.8017i	0.347014	−	1.74456i	−0.274902	−	0.961472i	$-0.588645\pi$
$547$	8.11597	−	40.8017i	0.347014	−	1.74456i	0.621916	−	0.783084i	$-0.286355\pi$
$548$			58.5400i			2.50070i
$549$	−4.69467	−	0.933828i	−0.200364	−	0.0398548i
$550$	20.6324	+	25.0044i	0.879769	+	1.06619i
$551$	6.33569	+	31.8517i	0.269909	+	1.35693i
$552$	14.3880	+	34.7356i	0.612392	+	1.47845i
$553$	−0.293483	−	0.708530i	−0.0124802	−	0.0301298i
$554$	−13.1927	−	66.3243i	−0.560505	−	2.81785i
$555$	17.8452	−	8.46929i	0.757486	−	0.359501i
$556$	−31.7021	−	6.30594i	−1.34447	−	0.267431i
$557$		−	5.57074i		−	0.236040i	−0.993011	−	0.118020i	$-0.962345\pi$
$557$		−	5.57074i		−	0.236040i	0.993011	−	0.118020i	$-0.0376546\pi$
$558$	1.38283	−	6.95195i	0.0585398	−	0.294300i
$559$	0.713179	+	1.72177i	0.0301643	+	0.0728230i
$560$	1.69722	+	6.73755i	0.0717206	+	0.284713i
$561$	9.41876	−	3.05190i	0.397660	−	0.128851i
$562$	48.8728	+	48.8728i	2.06157	+	2.06157i
$563$	10.5768	+	4.38107i	0.445761	+	0.184640i	0.594261	−	0.804272i	$-0.297445\pi$
$563$	10.5768	+	4.38107i	0.445761	+	0.184640i	−0.148500	+	0.988912i	$0.547445\pi$
$564$	42.8162	−	28.6089i	1.80289	−	1.20465i
$565$	14.1645	+	8.46424i	0.595906	+	0.356093i
$566$	7.94060	−	39.9201i	0.333768	−	1.67797i
$567$	−0.227350	+	0.0452228i	−0.00954782	+	0.00189918i
$568$	110.747	+	73.9988i	4.64684	+	3.10492i
$569$	−2.89254	+	6.98321i	−0.121262	+	0.292751i	−0.972841	−	0.231474i	$-0.925645\pi$
$569$	−2.89254	+	6.98321i	−0.121262	+	0.292751i	0.851579	+	0.524226i	$0.175645\pi$
$570$	17.9715	−	13.3658i	0.752744	−	0.559830i
$571$	−14.8956	+	2.96293i	−0.623363	+	0.123995i	−0.496659	−	0.867946i	$-0.665440\pi$
$571$	−14.8956	+	2.96293i	−0.623363	+	0.123995i	−0.126704	+	0.991941i	$0.540440\pi$
$572$	−11.4953	−	57.7910i	−0.480645	−	2.41636i
$573$	4.08544	−	2.72980i	0.170672	−	0.114039i
$574$	−2.14538	+	2.14538i	−0.0895465	+	0.0895465i
$575$	20.2345	−	6.19703i	0.843835	−	0.258434i
$576$	21.1955	−	8.77946i	0.883145	−	0.365811i
$577$	−1.61896	+	1.61896i	−0.0673983	+	0.0673983i	−0.740002	−	0.672604i	$-0.765176\pi$
$577$	−1.61896	+	1.61896i	−0.0673983	+	0.0673983i	0.672604	+	0.740002i	$0.265176\pi$
$578$	−44.6493	+	10.6428i	−1.85717	+	0.442682i
$579$		−	6.22404i		−	0.258662i
$580$	102.454	+	15.0580i	4.25415	+	0.625247i
$581$	−1.41752	−	2.12147i	−0.0588087	−	0.0880134i
$582$	−6.15144			−0.254985
$583$	15.4379	+	23.1045i	0.639375	+	0.956892i
$584$	−4.53350	−	3.02918i	−0.187597	−	0.125349i
$585$	−4.44710	−	9.37025i	−0.183865	−	0.387412i
$586$	−50.8181	−	21.0495i	−2.09927	−	0.869548i
$587$	−21.2630	+	8.80743i	−0.877618	+	0.363521i	−0.775573	−	0.631258i	$-0.782539\pi$
$587$	−21.2630	+	8.80743i	−0.877618	+	0.363521i	−0.102046	+	0.994780i	$0.532539\pi$
$588$	20.4151	−	30.5533i	0.841904	−	1.26000i
$589$	−5.41056	+	8.09748i	−0.222938	+	0.333651i
$590$	−0.472613	−	9.36543i	−0.0194572	−	0.385568i
$591$	−3.07882	−	3.07882i	−0.126646	−	0.126646i
$592$	−116.139	−	23.1014i	−4.77326	−	0.949461i
$593$	3.03115	−	7.31785i	0.124474	−	0.300508i	−0.849342	−	0.527843i	$-0.823001\pi$
$593$	3.03115	−	7.31785i	0.124474	−	0.300508i	0.973817	+	0.227335i	$0.0730011\pi$
$594$	6.48357			0.266024
$595$	0.477390	−	2.08313i	0.0195711	−	0.0854000i
$596$	−53.5189			−2.19222
$597$	−2.75681	+	6.65553i	−0.112829	+	0.272393i
$598$	−51.9884	−	10.3411i	−2.12596	−	0.422880i
$599$	−20.5921	−	20.5921i	−0.841371	−	0.841371i	0.147666	−	0.989037i	$-0.452824\pi$
$599$	−20.5921	−	20.5921i	−0.841371	−	0.841371i	−0.989037	+	0.147666i	$0.952824\pi$
$600$	−13.0066	−	42.4690i	−0.530992	−	1.73379i
$601$	−8.73137	+	13.0674i	−0.356160	+	0.533031i	−0.965678	−	0.259741i	$-0.916363\pi$
$601$	−8.73137	+	13.0674i	−0.356160	+	0.533031i	0.609518	+	0.792772i	$0.291363\pi$
$602$	−0.139704	+	0.209082i	−0.00569390	+	0.00852153i
$603$	2.21698	−	0.918302i	0.0902823	−	0.0373962i
$604$	88.4083	+	36.6199i	3.59728	+	1.49004i
$605$	−3.92790	+	11.0241i	−0.159692	+	0.448192i
$606$	−29.9751	−	20.0288i	−1.21766	−	0.813612i
$607$	−3.73293	−	5.58672i	−0.151515	−	0.226758i	0.747946	−	0.663760i	$-0.231040\pi$
$607$	−3.73293	−	5.58672i	−0.151515	−	0.226758i	−0.899461	+	0.437002i	$0.856040\pi$
$608$	−68.3555			−2.77218
$609$	1.12741	+	1.68729i	0.0456850	+	0.0683725i
$610$	23.1889	−	17.2460i	0.938890	−	0.698270i
$611$			45.1521i			1.82666i
$612$	−21.7429	−	1.72894i	−0.878903	−	0.0698883i
$613$	12.5690	−	12.5690i	0.507656	−	0.507656i	−0.406150	−	0.913806i	$-0.633129\pi$
$613$	12.5690	−	12.5690i	0.507656	−	0.507656i	0.913806	+	0.406150i	$0.133129\pi$
$614$	42.8207	−	17.7369i	1.72810	−	0.715803i
$615$	7.26878	−	8.04139i	0.293106	−	0.324260i
$616$	3.49643	−	3.49643i	0.140875	−	0.140875i
$617$	−4.08683	+	2.73074i	−0.164530	+	0.109935i	−0.635109	−	0.772422i	$-0.719045\pi$
$617$	−4.08683	+	2.73074i	−0.164530	+	0.109935i	0.470579	+	0.882358i	$0.344045\pi$
$618$	1.90567	+	9.58044i	0.0766572	+	0.385382i
$619$	−39.6838	+	7.89360i	−1.59503	+	0.317271i	−0.911070	−	0.412252i	$-0.864742\pi$
$619$	−39.6838	+	7.89360i	−1.59503	+	0.317271i	−0.683957	+	0.729522i	$0.739742\pi$
$620$	18.5319	+	24.9179i	0.744259	+	1.00073i
$621$	1.61968	−	3.91026i	0.0649956	−	0.156913i
$622$	−21.6855	−	14.4898i	−0.869511	−	0.580989i
$623$	−0.620653	+	0.123456i	−0.0248659	+	0.00494614i
$624$	−12.1302	+	60.9826i	−0.485596	+	2.44126i
$625$	−24.4933	+	5.00797i	−0.979731	+	0.200319i
$626$	19.5963	−	13.0938i	0.783225	−	0.523334i
$627$	−8.23000	−	3.40898i	−0.328675	−	0.136142i
$628$	−38.1854	−	38.1854i	−1.52376	−	1.52376i
$629$	28.5851	+	22.5722i	1.13976	+	0.900014i
$630$	0.717884	−	1.20135i	0.0286012	−	0.0478628i
$631$	−7.13656	−	17.2292i	−0.284102	−	0.685883i	0.715821	−	0.698284i	$-0.246053\pi$
$631$	−7.13656	−	17.2292i	−0.284102	−	0.685883i	−0.999923	+	0.0124010i	$0.996053\pi$
$632$	5.73359	−	28.8247i	0.228070	−	1.14659i
$633$		−	18.5137i		−	0.735855i
$634$	−39.3138	−	7.82000i	−1.56135	−	0.310572i
$635$	6.72378	−	18.8710i	0.266825	−	0.748873i
$636$	−11.9426	−	60.0395i	−0.473555	−	2.38072i
$637$	12.3301	+	29.7676i	0.488538	+	1.17944i
$638$	−21.7208	−	52.4386i	−0.859934	−	2.07607i
$639$	−2.92517	−	14.7058i	−0.115718	−	0.581754i
$640$	−18.8306	+	52.8500i	−0.744344	+	2.08908i
$641$	−34.2513	−	6.81301i	−1.35285	−	0.269098i	−0.535154	−	0.844754i	$-0.679747\pi$
$641$	−34.2513	−	6.81301i	−1.35285	−	0.269098i	−0.817692	+	0.575656i	$0.804747\pi$
$642$			34.7137i			1.37004i
$643$	4.49010	−	22.5732i	0.177072	−	0.890202i	−0.785435	−	0.618945i	$-0.787561\pi$
$643$	4.49010	−	22.5732i	0.177072	−	0.890202i	0.962507	−	0.271257i	$-0.0874395\pi$
$644$	−1.98615	−	4.79499i	−0.0782652	−	0.188949i
$645$	0.460839	−	0.771194i	0.0181455	−	0.0303657i
$646$	36.7813	+	18.7786i	1.44714	+	0.738835i
$647$	−13.6212	−	13.6212i	−0.535506	−	0.535506i	0.386700	−	0.922206i	$-0.373615\pi$
$647$	−13.6212	−	13.6212i	−0.535506	−	0.535506i	−0.922206	+	0.386700i	$0.873615\pi$
$648$	−8.20701	−	3.39946i	−0.322402	−	0.133543i
$649$	−3.10116	+	2.07213i	−0.121731	+	0.0813381i
$650$	59.9718	+	18.0177i	2.35229	+	0.706714i
$651$	−0.118720	+	0.596847i	−0.00465301	+	0.0233923i
$652$	79.5648	−	15.8264i	3.11600	−	0.619811i
$653$	−15.7505	−	10.5242i	−0.616365	−	0.411842i	0.207816	−	0.978168i	$-0.433364\pi$
$653$	−15.7505	−	10.5242i	−0.616365	−	0.411842i	−0.824181	+	0.566326i	$0.808364\pi$
$654$	5.04497	−	12.1796i	0.197274	−	0.476261i
$655$	−1.12258	−	1.50942i	−0.0438630	−	0.0589778i
$656$	−63.7325	+	12.6772i	−2.48834	+	0.494961i
$657$	0.119744	+	0.601992i	0.00467165	+	0.0234860i
$658$	−5.06565	+	3.38476i	−0.197479	+	0.131952i
$659$	35.9699	−	35.9699i	1.40119	−	1.40119i	0.604845	−	0.796343i	$-0.293235\pi$
$659$	35.9699	−	35.9699i	1.40119	−	1.40119i	0.796343	−	0.604845i	$-0.206765\pi$
$660$	−19.0475	+	21.0721i	−0.741424	+	0.820231i
$661$	36.3654	−	15.0630i	1.41445	−	0.585884i	0.460990	−	0.887406i	$-0.347495\pi$
$661$	36.3654	−	15.0630i	1.41445	−	0.585884i	0.953459	+	0.301522i	$0.0974945\pi$
$662$	−18.8722	+	18.8722i	−0.733490	+	0.733490i
$663$	11.8523	−	15.0096i	0.460307	−	0.582924i
$664$		−	97.7774i		−	3.79450i
$665$	−1.54291	+	1.14749i	−0.0598315	+	0.0444978i
$666$	13.2511	+	19.8317i	0.513470	+	0.768462i
$667$	−37.0520			−1.43466
$668$	−64.3134	−	96.2518i	−2.48836	−	3.72410i
$669$	22.1033	+	14.7689i	0.854562	+	0.571000i
$670$	−4.86253	+	13.6472i	−0.187856	+	0.527238i
$671$	−10.6193	−	4.39865i	−0.409953	−	0.169808i
$672$	−3.94615	+	1.63455i	−0.152226	+	0.0630542i
$673$	7.63240	−	11.4227i	0.294207	−	0.440312i	−0.654690	−	0.755898i	$-0.727201\pi$
$673$	7.63240	−	11.4227i	0.294207	−	0.440312i	0.948897	+	0.315585i	$0.102201\pi$
$674$	10.7521	−	16.0916i	0.414155	−	0.619827i
$675$	−2.34522	+	4.41588i	−0.0902674	+	0.169967i
$676$	−31.8539	−	31.8539i	−1.22515	−	1.22515i
$677$	14.5438	+	2.89294i	0.558963	+	0.111185i	0.466483	−	0.884530i	$-0.345521\pi$
$677$	14.5438	+	2.89294i	0.558963	+	0.111185i	0.0924795	+	0.995715i	$0.470521\pi$
$678$	−7.62475	+	18.4078i	−0.292827	+	0.706947i
$679$	0.528120			0.0202674
$680$	59.5623	−	56.2120i	2.28411	−	2.15563i
$681$	−7.22923			−0.277025
$682$	6.51360	−	15.7252i	0.249419	−	0.602150i
$683$	31.0373	+	6.17370i	1.18761	+	0.236230i	0.749075	−	0.662485i	$-0.230498\pi$
$683$	31.0373	+	6.17370i	1.18761	+	0.236230i	0.438533	+	0.898715i	$0.355498\pi$
$684$	13.8766	+	13.8766i	0.530584	+	0.530584i
$685$	1.24710	+	24.7129i	0.0476494	+	0.944233i
$686$	−4.84936	+	7.25758i	−0.185149	+	0.277096i
$687$	9.21041	−	13.7843i	0.351399	−	0.525906i
$688$	−4.97568	+	2.06099i	−0.189696	+	0.0785746i
$689$	49.5901	+	20.5409i	1.88923	+	0.782545i
$690$	10.9561	+	23.0850i	0.417090	+	0.878830i
$691$	−5.63634	−	3.76608i	−0.214417	−	0.143269i	0.443724	−	0.896163i	$-0.353657\pi$
$691$	−5.63634	−	3.76608i	−0.214417	−	0.143269i	−0.658141	+	0.752895i	$0.728657\pi$
$692$	30.0166	+	44.9230i	1.14106	+	1.70771i
$693$	−0.556635			−0.0211448
$694$	16.3871	+	24.5250i	0.622045	+	0.930956i
$695$	−13.5175	−	1.98672i	−0.512749	−	0.0753606i
$696$			77.7663i			2.94772i
$697$	19.2326	+	5.44099i	0.728486	+	0.206092i
$698$	−20.7123	+	20.7123i	−0.783971	+	0.783971i
$699$	−20.1576	+	8.34957i	−0.762432	+	0.315810i
$700$	1.79546	+	5.86252i	0.0678621	+	0.221582i
$701$	11.9002	−	11.9002i	0.449464	−	0.449464i	−0.445712	−	0.895176i	$-0.647049\pi$
$701$	11.9002	−	11.9002i	0.449464	−	0.449464i	0.895176	+	0.445712i	$0.147049\pi$
$702$	10.4133	−	6.95796i	0.393025	−	0.262611i
$703$	−6.39321	−	32.1409i	−0.241125	−	1.21222i
$704$	54.0319	−	10.7476i	2.03640	−	0.405066i
$705$	17.4656	−	12.9895i	0.657793	−	0.489214i
$706$	8.95060	−	21.6087i	0.336860	−	0.813253i
$707$	2.57346	+	1.71953i	0.0967849	+	0.0646696i
$708$	8.05868	−	1.60297i	0.302864	−	0.0602433i
$709$	4.09610	−	20.5925i	0.153832	−	0.773368i	−0.824425	−	0.565972i	$-0.808501\pi$
$709$	4.09610	−	20.5925i	0.153832	−	0.773368i	0.978257	−	0.207396i	$-0.0664989\pi$
$710$	77.7075	+	46.4354i	2.91631	+	1.74269i
$711$	−2.75085	+	1.83806i	−0.103165	+	0.0689327i
$712$	−22.4047	−	9.28032i	−0.839650	−	0.347795i
$713$	−7.85673	−	7.85673i	−0.294237	−	0.294237i
$714$	2.57243	+	0.204553i	0.0962706	+	0.00765522i
$715$	−6.08397	−	24.1519i	−0.227527	−	0.903229i
$716$	28.6228	+	69.1016i	1.06969	+	2.58245i
$717$	0.451400	−	2.26934i	0.0168578	−	0.0847501i
$718$			76.2452i			2.84544i
$719$	−20.5699	−	4.09161i	−0.767128	−	0.152591i	−0.204011	−	0.978969i	$-0.565398\pi$
$719$	−20.5699	−	4.09161i	−0.767128	−	0.152591i	−0.563117	+	0.826377i	$0.690398\pi$
$720$	27.0788	−	12.8515i	1.00917	−	0.478948i
$721$	−0.163608	−	0.822510i	−0.00609306	−	0.0306319i
$722$	5.41246	+	13.0668i	0.201431	+	0.486298i
$723$	2.65360	+	6.40636i	0.0986885	+	0.238255i
$724$	12.7076	+	63.8852i	0.472273	+	2.37428i
$725$	43.5721	+	4.17418i	1.61823	+	0.155025i
$726$	−13.8595	−	2.75683i	−0.514376	−	0.102316i
$727$			45.5044i			1.68767i	0.536606	+	0.843833i	$0.319706\pi$
$727$			45.5044i			1.68767i	−0.536606	+	0.843833i	$0.680294\pi$
$728$	1.86339	−	9.36790i	0.0690619	−	0.347198i
$729$	0.382683	+	0.923880i	0.0141735	+	0.0342178i
$730$	−3.18100	−	1.90086i	−0.117734	−	0.0703540i
$731$	1.65134	+	0.131311i	0.0610772	+	0.00485672i
$732$	17.9051	+	17.9051i	0.661792	+	0.661792i
$733$	−33.0977	−	13.7095i	−1.22249	−	0.506372i	−0.324289	−	0.945958i	$-0.605125\pi$
$733$	−33.0977	−	13.7095i	−1.22249	−	0.506372i	−0.898200	+	0.439586i	$0.855125\pi$
$734$	−34.8301	+	23.2727i	−1.28560	+	0.859011i
$735$	7.96744	−	13.3332i	0.293883	−	0.491801i
$736$	15.2147	−	76.4893i	0.560820	−	2.81943i
$737$	5.65156	−	1.12417i	0.208178	−	0.0414092i
$738$	10.8829	+	7.27172i	0.400605	+	0.267676i
$739$	0.607382	−	1.46635i	0.0223429	−	0.0539405i	−0.912314	−	0.409491i	$-0.865706\pi$
$739$	0.607382	−	1.46635i	0.0223429	−	0.0539405i	0.934657	+	0.355550i	$0.115706\pi$
$740$	−103.384	−	15.1947i	−3.80046	−	0.558567i
$741$	−16.8767	+	3.35698i	−0.619981	+	0.123322i
$742$	1.41294	+	7.10335i	0.0518708	+	0.260772i
$743$	13.4664	−	8.99795i	0.494034	−	0.330103i	−0.283470	−	0.958981i	$-0.591486\pi$
$743$	13.4664	−	8.99795i	0.494034	−	0.330103i	0.777504	+	0.628878i	$0.216486\pi$
$744$	−16.4900	+	16.4900i	−0.604554	+	0.604554i
$745$	−22.5933	+	1.14014i	−0.827753	+	0.0417714i
$746$	−42.8336	+	17.7423i	−1.56825	+	0.649590i
$747$	−7.78312	+	7.78312i	−0.284769	+	0.284769i
$748$	−50.3982	−	14.2579i	−1.84274	−	0.521320i
$749$		−	2.98028i		−	0.108897i
$750$	−10.2833	−	28.3815i	−0.375494	−	1.03635i
$751$	3.97323	+	5.94636i	0.144985	+	0.216986i	0.896854	−	0.442328i	$-0.145847\pi$
$751$	3.97323	+	5.94636i	0.144985	+	0.216986i	−0.751868	+	0.659313i	$0.770847\pi$
$752$	−130.484			−4.75825
$753$	10.5224	+	15.7480i	0.383459	+	0.573887i
$754$	−91.1614	−	60.9121i	−3.31990	−	2.21829i
$755$	38.1021	+	13.5759i	1.38668	+	0.494077i
$756$	1.13292	+	0.469269i	0.0412038	+	0.0170672i
$757$	−38.1876	+	15.8178i	−1.38795	+	0.574908i	−0.946595	−	0.322424i	$-0.895502\pi$
$757$	−38.1876	+	15.8178i	−1.38795	+	0.574908i	−0.441356	+	0.897332i	$0.645502\pi$
$758$	7.29784	−	10.9220i	0.265070	−	0.396705i
$759$	5.64647	−	8.45054i	0.204954	−	0.306735i
$760$	−73.5934	+	3.71378i	−2.66951	+	0.134713i
$761$	19.6987	+	19.6987i	0.714077	+	0.714077i	0.967385	−	0.253309i	$-0.0815189\pi$
$761$	19.6987	+	19.6987i	0.714077	+	0.714077i	−0.253309	+	0.967385i	$0.581519\pi$
$762$	23.7248	+	4.71915i	0.859458	+	0.170957i
$763$	−0.433126	+	1.04566i	−0.0156802	+	0.0378554i
$764$	−25.9928			−0.940386
$765$	−9.21569	−	0.266683i	−0.333194	−	0.00964195i
$766$	69.8619			2.52421
$767$	−2.75706	+	6.65613i	−0.0995516	+	0.240339i
$768$	−21.4414	−	4.26497i	−0.773702	−	0.153899i
$769$	−1.46441	−	1.46441i	−0.0528080	−	0.0528080i	0.680210	−	0.733018i	$-0.261889\pi$
$769$	−1.46441	−	1.46441i	−0.0528080	−	0.0528080i	−0.733018	+	0.680210i	$0.761889\pi$
$770$	2.25354	−	2.49307i	0.0812119	−	0.0898440i
$771$	−0.338593	+	0.506740i	−0.0121941	+	0.0182498i
$772$	−18.2925	+	27.3766i	−0.658360	+	0.985306i
$773$	−40.9343	+	16.9555i	−1.47231	+	0.609849i	−0.967383	−	0.253316i	$-0.918479\pi$
$773$	−40.9343	+	16.9555i	−1.47231	+	0.609849i	−0.504922	+	0.863165i	$0.668479\pi$
$774$	1.00222	+	0.415133i	0.0360240	+	0.0149216i
$775$	8.35417	+	10.1244i	0.300091	+	0.363679i
$776$	16.8278	+	11.2440i	0.604083	+	0.403635i
$777$	−1.13765	−	1.70261i	−0.0408129	−	0.0610808i
$778$	10.6160			0.380603
$779$	−9.99096	−	14.9525i	−0.357963	−	0.535730i
$780$	−7.97850	+	54.2853i	−0.285676	+	1.94373i
$781$		−	36.0051i		−	1.28837i
$782$	−29.2000	+	36.9783i	−1.04419	+	1.32234i
$783$	6.19023	−	6.19023i	0.221221	−	0.221221i
$784$	−86.0244	+	35.6325i	−3.07230	+	1.27259i
$785$	−16.9336	−	15.3067i	−0.604387	−	0.546319i
$786$	1.60612	−	1.60612i	0.0572883	−	0.0572883i
$787$	42.7335	−	28.5536i	1.52328	−	1.01783i	0.538782	−	0.842445i	$-0.318885\pi$
$787$	42.7335	−	28.5536i	1.52328	−	1.01783i	0.984501	−	0.175380i	$-0.0561155\pi$
$788$	4.49361	+	22.5909i	0.160078	+	0.804768i
$789$	−26.4757	+	5.26635i	−0.942560	+	0.187487i
$790$	2.90449	−	19.7620i	0.103337	−	0.703101i
$791$	0.654609	−	1.58037i	0.0232752	−	0.0561913i
$792$	−17.7364	−	11.8511i	−0.630234	−	0.421109i
$793$	−21.7762	+	4.33156i	−0.773296	+	0.153818i
$794$	17.2105	−	86.5231i	0.610778	−	3.07059i
$795$	−6.32067	−	25.0915i	−0.224171	−	0.889905i
$796$	31.6865	−	21.1722i	1.12310	−	0.750430i
$797$	2.64102	+	1.09395i	0.0935497	+	0.0387496i	0.428968	−	0.903320i	$-0.358877\pi$
$797$	2.64102	+	1.09395i	0.0935497	+	0.0387496i	−0.335418	+	0.942069i	$0.608877\pi$
$798$	−1.64176	−	1.64176i	−0.0581175	−	0.0581175i
$799$	35.7460	+	18.2500i	1.26460	+	0.645639i
$800$	−26.5091	+	88.2351i	−0.937237	+	3.11958i
$801$	1.04470	+	2.52214i	0.0369128	+	0.0891153i
$802$	−6.76458	+	34.0078i	−0.238866	+	1.20086i
$803$			1.47389i			0.0520125i
$804$	−12.4503	−	2.47652i	−0.439089	−	0.0873402i
$805$	−0.940613	−	1.98192i	−0.0331522	−	0.0698534i
$806$	−6.41425	−	32.2466i	−0.225932	−	1.13584i
$807$	−2.54936	−	6.15469i	−0.0897416	−	0.216655i
$808$	45.3898	+	109.581i	1.59681	+	3.85504i
$809$	−4.67677	−	23.5117i	−0.164427	−	0.826628i	−0.971658	−	0.236393i	$-0.924035\pi$
$809$	−4.67677	−	23.5117i	−0.164427	−	0.826628i	0.807231	−	0.590236i	$-0.200965\pi$
$810$	−5.68719	−	2.02636i	−0.199828	−	0.0711990i
$811$	37.3936	+	7.43805i	1.31307	+	0.261185i	0.801467	−	0.598039i	$-0.204053\pi$
$811$	37.3936	+	7.43805i	1.31307	+	0.261185i	0.511599	+	0.859224i	$0.329053\pi$
$812$		−	10.7351i		−	0.376727i
$813$	2.89065	−	14.5323i	0.101379	−	0.509669i
$814$	21.9180	+	52.9148i	0.768226	+	1.85466i
$815$	33.2515	−	8.37621i	1.16475	−	0.293406i
$816$	43.3757	+	34.2517i	1.51845	+	1.19905i
$817$	−1.05391	−	1.05391i	−0.0368716	−	0.0368716i
$818$	12.9632	+	5.36954i	0.453248	+	0.187741i
$819$	−0.894016	+	0.597362i	−0.0312394	+	0.0208735i
$820$	−55.6056	+	14.0073i	−1.94183	+	0.489156i
$821$	4.19072	−	21.0682i	0.146257	−	0.735285i	−0.836145	−	0.548508i	$-0.815196\pi$
$821$	4.19072	−	21.0682i	0.146257	−	0.735285i	0.982402	−	0.186777i	$-0.0598041\pi$
$822$	−29.3043	+	5.82899i	−1.02210	+	0.203309i
$823$	−4.97024	−	3.32101i	−0.173252	−	0.115763i	0.465921	−	0.884826i	$-0.345723\pi$
$823$	−4.97024	−	3.32101i	−0.173252	−	0.115763i	−0.639173	+	0.769063i	$0.720723\pi$
$824$	12.2986	−	29.6914i	0.428442	−	1.03435i
$825$	−7.59210	+	9.30147i	−0.264323	+	0.323836i
$826$	−0.953433	+	0.189650i	−0.0331742	+	0.00659876i
$827$	8.76311	+	44.0551i	0.304723	+	1.53195i	0.764917	+	0.644128i	$0.222780\pi$
$827$	8.76311	+	44.0551i	0.304723	+	1.53195i	−0.460194	+	0.887818i	$0.652220\pi$
$828$	−18.6165	+	12.4391i	−0.646966	+	0.432289i
$829$	−27.0517	+	27.0517i	−0.939546	+	0.939546i	−0.998274	−	0.0587284i	$-0.981295\pi$
$829$	−27.0517	+	27.0517i	−0.939546	+	0.939546i	0.0587284	+	0.998274i	$0.481295\pi$
$830$	−3.34923	−	66.3693i	−0.116254	−	2.30371i
$831$	23.1392	−	9.58457i	0.802690	−	0.332485i
$832$	75.2472	−	75.2472i	2.60873	−	2.60873i
$833$	28.5501	+	2.27023i	0.989201	+	0.0786590i
$834$		−	16.4975i		−	0.571263i
$835$	−29.2007	−	39.2631i	−1.01053	−	1.35876i
$836$	26.1809	+	39.1825i	0.905485	+	1.35515i
$837$	2.62523			0.0907412
$838$	17.5217	+	26.2231i	0.605278	+	0.905863i
$839$	−17.0696	−	11.4056i	−0.589309	−	0.393764i	0.224860	−	0.974391i	$-0.427807\pi$
$839$	−17.0696	−	11.4056i	−0.589309	−	0.393764i	−0.814170	+	0.580627i	$0.802807\pi$
$840$	−4.15973	+	1.97420i	−0.143524	+	0.0681163i
$841$	−44.0117	−	18.2302i	−1.51764	−	0.628629i
$842$	73.9370	−	30.6257i	2.54804	−	1.05543i
$843$	−14.2218	+	21.2845i	−0.489826	+	0.733076i
$844$	−54.4119	+	81.4332i	−1.87293	+	2.80305i
$845$	−14.1259	−	12.7687i	−0.485945	−	0.439256i
$846$	18.5845	+	18.5845i	0.638950	+	0.638950i
$847$	1.18988	+	0.236683i	0.0408849	+	0.00813251i
$848$	−59.3604	+	143.309i	−2.03844	+	4.92124i
$849$	15.0748			0.517366
$850$	38.5042	−	40.1958i	1.32068	−	1.37870i
$851$	37.3884			1.28166
$852$	−30.3540	+	73.2811i	−1.03991	+	2.51057i
$853$	20.5757	+	4.09276i	0.704499	+	0.140134i	0.534323	−	0.845280i	$-0.320566\pi$
$853$	20.5757	+	4.09276i	0.704499	+	0.140134i	0.170176	+	0.985414i	$0.445566\pi$
$854$	−2.11838	−	2.11838i	−0.0724894	−	0.0724894i
$855$	6.15368	+	5.56244i	0.210451	+	0.190232i
$856$	63.4519	−	94.9625i	2.16874	−	3.24575i
$857$	25.3643	−	37.9604i	0.866428	−	1.29670i	−0.0873459	−	0.996178i	$-0.527839\pi$
$857$	25.3643	−	37.9604i	0.866428	−	1.29670i	0.953774	−	0.300524i	$-0.0971615\pi$
$858$	27.7848	−	11.5088i	0.948556	−	0.392905i
$859$	14.4972	+	6.00493i	0.494637	+	0.204885i	0.616035	−	0.787718i	$-0.288738\pi$
$859$	14.4972	+	6.00493i	0.494637	+	0.204885i	−0.121398	+	0.992604i	$0.538738\pi$
$860$	−4.29355	+	2.03771i	−0.146409	+	0.0694853i
$861$	−0.934330	−	0.624299i	−0.0318419	−	0.0212761i
$862$	−14.5748	−	21.8128i	−0.496421	−	0.742947i
$863$	14.5702			0.495975			0.247988	−	0.968763i	$-0.420231\pi$
$863$	14.5702			0.495975			0.247988	+	0.968763i	$0.420231\pi$
$864$	10.2371	+	15.3209i	0.348272	+	0.521227i
$865$	13.6287	+	18.3250i	0.463388	+	0.623068i
$866$		−	21.7377i		−	0.738678i
$867$	−7.09217	−	15.4500i	−0.240863	−	0.524708i
$868$	2.27633	−	2.27633i	0.0772636	−	0.0772636i
$869$	−7.33981	+	3.04025i	−0.248986	+	0.103133i
$870$	2.66378	+	52.7862i	0.0903106	+	1.78962i
$871$	7.87060	−	7.87060i	0.266685	−	0.266685i
$872$	−36.0636	+	24.0969i	−1.22127	+	0.816025i
$873$	−0.444475	−	2.23453i	−0.0150432	−	0.0756272i
$874$	41.5782	−	8.27041i	1.40640	−	0.279751i
$875$	0.882855	+	2.43664i	0.0298460	+	0.0823735i
$876$	1.24256	−	2.99981i	0.0419822	−	0.101354i
$877$	18.2754	+	12.2112i	0.617117	+	0.412345i	0.824457	−	0.565924i	$-0.191481\pi$
$877$	18.2754	+	12.2112i	0.617117	+	0.412345i	−0.207340	+	0.978269i	$0.566481\pi$
$878$	15.5399	−	3.09107i	0.524445	−	0.104319i
$879$	3.97441	−	19.9807i	0.134054	−	0.673933i
$880$	69.7957	−	17.5819i	2.35281	−	0.592684i
$881$	−12.7703	+	8.53282i	−0.430241	+	0.287478i	−0.751774	−	0.659420i	$-0.770802\pi$
$881$	−12.7703	+	8.53282i	−0.430241	+	0.287478i	0.321533	+	0.946898i	$0.395802\pi$
$882$	17.3274	+	7.17723i	0.583443	+	0.241670i
$883$	13.3887	+	13.3887i	0.450567	+	0.450567i	0.895543	−	0.444976i	$-0.146788\pi$
$883$	13.3887	+	13.3887i	0.450567	+	0.450567i	−0.444976	+	0.895543i	$0.646788\pi$
$884$	−96.2460	+	31.1860i	−3.23710	+	1.04890i
$885$	3.36786	−	0.848380i	0.113209	−	0.0285180i
$886$	6.87822	+	16.6055i	0.231078	+	0.557872i
$887$	7.62909	−	38.3540i	0.256160	−	1.28780i	−0.611738	−	0.791060i	$-0.709529\pi$
$887$	7.62909	−	38.3540i	0.256160	−	1.28780i	0.867898	−	0.496742i	$-0.165471\pi$
$888$		−	78.4724i		−	2.63336i
$889$	−2.03685	−	0.405154i	−0.0683136	−	0.0135884i
$890$	−15.5257	−	5.53185i	−0.520423	−	0.185428i
$891$	0.468473	+	2.35517i	0.0156944	+	0.0789012i
$892$	−53.8159	−	129.923i	−1.80189	−	4.35015i
$893$	−13.8190	−	33.3620i	−0.462436	−	1.11642i
$894$	−5.32902	−	26.7908i	−0.178229	−	0.896018i
$895$	13.5554	+	28.5618i	0.453106	+	0.954717i
$896$	5.70438	+	1.13467i	0.190570	+	0.0379067i
$897$		−	19.6321i		−	0.655497i
$898$	1.40286	−	7.05263i	0.0468139	−	0.235349i
$899$	−8.79485	−	21.2327i	−0.293325	−	0.708149i
$900$	23.2938	−	12.5308i	0.776459	−	0.417692i
$901$	36.3055	−	30.9570i	1.20951	−	1.03133i
$902$	22.2245	+	22.2245i	0.739994	+	0.739994i
$903$	−0.0860437	−	0.0356405i	−0.00286335	−	0.00118604i
$904$	54.5050	−	36.4191i	1.81281	−	1.21128i
$905$	6.72554	+	26.6987i	0.223564	+	0.887496i
$906$	−9.52836	+	47.9023i	−0.316559	+	1.59145i
$907$	−29.3742	+	5.84288i	−0.975353	+	0.194010i	−0.656940	−	0.753943i	$-0.728150\pi$
$907$	−29.3742	+	5.84288i	−0.975353	+	0.194010i	−0.318412	+	0.947952i	$0.603150\pi$
$908$	31.7980	+	21.2467i	1.05525	+	0.705097i
$909$	5.10962	−	12.3357i	0.169476	−	0.409150i
$910$	0.943947	−	6.42257i	0.0312915	−	0.212906i
$911$	−34.1209	+	6.78706i	−1.13047	+	0.224865i	−0.724671	−	0.689095i	$-0.758008\pi$
$911$	−34.1209	+	6.78706i	−1.13047	+	0.224865i	−0.405803	+	0.913960i	$0.633008\pi$
$912$	−9.70123	−	48.7714i	−0.321240	−	1.61498i
$913$	−21.9768	+	14.6844i	−0.727324	+	0.485983i
$914$	−21.2263	+	21.2263i	−0.702104	+	0.702104i
$915$	7.94017	+	7.17729i	0.262494	+	0.237274i
$916$	−81.0244	+	33.5614i	−2.67712	+	1.10890i
$917$	−0.137890	+	0.137890i	−0.00455354	+	0.00455354i
$918$	−1.29951	−	11.0563i	−0.0428903	−	0.364913i
$919$		−	29.8893i		−	0.985957i	−0.870041	−	0.492979i	$-0.835908\pi$
$919$		−	29.8893i		−	0.985957i	0.870041	−	0.492979i	$-0.164092\pi$
$920$	12.2248	−	83.1771i	0.403041	−	2.74227i
$921$	9.53699	+	14.2731i	0.314255	+	0.470315i
$922$	101.916			3.35642
$923$	−38.6395	−	57.8282i	−1.27184	−	1.90344i
$924$	2.44837	+	1.63595i	0.0805455	+	0.0538188i
$925$	−43.9677	−	4.21208i	−1.44565	−	0.138492i
$926$	−16.0720	−	6.65723i	−0.528158	−	0.218770i
$927$	−3.34242	+	1.38448i	−0.109780	+	0.0454722i
$928$	89.6185	−	134.124i	2.94187	−	4.40282i
$929$	−15.4822	+	23.1707i	−0.507953	+	0.760206i	−0.993479	−	0.114016i	$-0.963628\pi$
$929$	−15.4822	+	23.1707i	−0.507953	+	0.760206i	0.485525	+	0.874223i	$0.338628\pi$
$930$	−10.6283	+	11.7579i	−0.348514	+	0.385558i
$931$	−18.2210	−	18.2210i	−0.597170	−	0.597170i
$932$	113.203	+	22.5175i	3.70810	+	0.737587i
$933$	3.69656	−	8.92429i	0.121020	−	0.292168i
$934$	13.0632			0.427442
$935$	−21.5796	−	4.94538i	−0.705728	−	0.161731i
$936$	−41.2047			−1.34682
$937$	−0.339978	+	0.820779i	−0.0111066	+	0.0268137i	−0.929336	−	0.369236i	$-0.879619\pi$
$937$	−0.339978	+	0.820779i	−0.0111066	+	0.0268137i	0.918229	+	0.396050i	$0.129619\pi$
$938$	1.47301	+	0.293001i	0.0480956	+	0.00956682i
$939$	6.17230	+	6.17230i	0.201425	+	0.201425i
$940$	−114.999	+	5.80327i	−3.75086	+	0.189282i
$941$	−2.61006	+	3.90624i	−0.0850856	+	0.127340i	−0.871571	−	0.490269i	$-0.836898\pi$
$941$	−2.61006	+	3.90624i	−0.0850856	+	0.127340i	0.786485	+	0.617609i	$0.211898\pi$
$942$	15.3128	−	22.9173i	0.498920	−	0.746686i
$943$	18.9556	−	7.85166i	0.617279	−	0.255685i
$944$	−19.2353	−	7.96753i	−0.626056	−	0.259321i
$945$	0.488263	+	0.173969i	0.0158832	+	0.00565922i
$946$	2.16592	+	1.44722i	0.0704202	+	0.0470532i
$947$	−20.3956	−	30.5241i	−0.662767	−	0.991900i	−0.998748	−	0.0500317i	$-0.984068\pi$
$947$	−20.3956	−	30.5241i	−0.662767	−	0.991900i	0.335981	−	0.941869i	$-0.390932\pi$
$948$	17.5018			0.568431
$949$	1.58173	+	2.36723i	0.0513452	+	0.0768436i
$950$	−49.8264	+	5.04168i	−1.61658	+	0.163574i
$951$		−	14.8459i		−	0.481410i
$952$	−6.66320	−	5.26161i	−0.215956	−	0.170530i
$953$	−20.8325	+	20.8325i	−0.674831	+	0.674831i	−0.958826	−	0.283995i	$-0.908340\pi$
$953$	−20.8325	+	20.8325i	−0.674831	+	0.674831i	0.283995	+	0.958826i	$0.408340\pi$
$954$	28.8658	−	11.9566i	0.934564	−	0.387109i
$955$	−10.9730	+	0.553736i	−0.355077	+	0.0179185i
$956$	−8.65509	+	8.65509i	−0.279926	+	0.279926i
$957$	17.4790	−	11.6791i	0.565016	−	0.377532i
$958$	12.3424	+	62.0494i	0.398765	+	2.00472i
$959$	2.51586	−	0.500437i	0.0812415	−	0.0161599i
$960$	−50.7542	−	7.45953i	−1.63809	−	0.240755i
$961$	−9.22580	+	22.2730i	−0.297606	+	0.718485i
$962$	91.9891	+	61.4652i	2.96585	+	1.98172i
$963$	−12.6098	+	2.50825i	−0.406347	+	0.0808274i
$964$	7.15637	−	35.9775i	0.230491	−	1.15876i
$965$	−7.13904	+	11.9469i	−0.229814	+	0.384583i
$966$	2.20254	−	1.47169i	0.0708655	−	0.0473508i
$967$	−47.9926	−	19.8792i	−1.54334	−	0.639272i	−0.561243	−	0.827651i	$-0.689677\pi$
$967$	−47.9926	−	19.8792i	−1.54334	−	0.639272i	−0.982096	+	0.188379i	$0.939677\pi$
$968$	32.8749	+	32.8749i	1.05664	+	1.05664i
$969$	−4.16372	+	14.7178i	−0.133758	+	0.472803i
$970$	11.8075	+	7.05577i	0.379116	+	0.226547i
$971$	6.87896	+	16.6073i	0.220756	+	0.532953i	0.994993	−	0.0999431i	$-0.0318661\pi$
$971$	6.87896	+	16.6073i	0.220756	+	0.532953i	−0.774237	+	0.632896i	$0.781866\pi$
$972$	1.03204	−	5.18842i	0.0331027	−	0.166418i
$973$			1.41636i			0.0454066i
$974$	34.6797	+	6.89821i	1.11121	+	0.221033i
$975$	−2.21170	+	23.0868i	−0.0708311	+	0.739369i
$976$	−12.5176	−	62.9303i	−0.400679	−	2.01435i
$977$	0.429605	+	1.03716i	0.0137443	+	0.0331816i	0.930603	−	0.366031i	$-0.119284\pi$
$977$	0.429605	+	1.03716i	0.0137443	+	0.0331816i	−0.916858	+	0.399213i	$0.869284\pi$
$978$	15.8450	+	38.2532i	0.506667	+	1.22320i
$979$	1.27890	+	6.42948i	0.0408739	+	0.205487i
$980$	−74.2311	+	35.2299i	−2.37123	+	1.12538i
$981$	4.78880	+	0.952552i	0.152895	+	0.0304126i
$982$		−	105.871i		−	3.37849i
$983$	−10.6986	+	53.7855i	−0.341232	+	1.71549i	0.305001	+	0.952352i	$0.401343\pi$
$983$	−10.6986	+	53.7855i	−0.341232	+	1.71549i	−0.646234	+	0.763140i	$0.723657\pi$
$984$	−16.4794	−	39.7848i	−0.525344	−	1.26829i
$985$	2.37827	+	9.44114i	0.0757778	+	0.300820i
$986$	−85.0692	+	47.5505i	−2.70916	+	1.51432i
$987$	−1.59554	−	1.59554i	−0.0507866	−	0.0507866i
$988$	84.0987	+	34.8348i	2.67554	+	1.10824i
$989$	1.41390	−	0.944737i	0.0449594	−	0.0300409i
$990$	−12.4450	−	7.43672i	−0.395529	−	0.236354i
$991$	−1.54751	+	7.77984i	−0.0491581	+	0.247135i	−0.997549	−	0.0699684i	$-0.977710\pi$
$991$	−1.54751	+	7.77984i	−0.0491581	+	0.247135i	0.948391	+	0.317103i	$0.102710\pi$
$992$	47.4437	−	9.43713i	1.50634	−	0.299629i
$993$	−8.21900	−	5.49176i	−0.260822	−	0.174276i
$994$	3.59123	−	8.66999i	0.113907	−	0.274995i
$995$	12.9256	−	9.61300i	0.409768	−	0.304753i
$996$	57.1089	−	11.3597i	1.80956	−	0.359944i
$997$	0.809494	+	4.06960i	0.0256369	+	0.128886i	0.991484	−	0.130226i	$-0.0415703\pi$
$997$	0.809494	+	4.06960i	0.0256369	+	0.128886i	−0.965847	+	0.259112i	$0.916570\pi$
$998$	1.69804	−	1.13459i	0.0537505	−	0.0359149i
$999$	−6.24644	+	6.24644i	−0.197629	+	0.197629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	255.2.bi.a.22.18	yes	144
3.2	odd	2		765.2.cc.b.532.1		144
5.3	odd	4		255.2.bd.a.73.1	yes	144
15.8	even	4		765.2.bx.b.73.18		144
17.7	odd	16		255.2.bd.a.7.1	✓	144
51.41	even	16		765.2.bx.b.262.18		144
85.58	even	16	inner	255.2.bi.a.58.18	yes	144
255.143	odd	16		765.2.cc.b.568.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
255.2.bd.a.7.1	✓	144	17.7	odd	16
255.2.bd.a.73.1	yes	144	5.3	odd	4
255.2.bi.a.22.18	yes	144	1.1	even	1	trivial
255.2.bi.a.58.18	yes	144	85.58	even	16	inner
765.2.bx.b.73.18		144	15.8	even	4
765.2.bx.b.262.18		144	51.41	even	16
765.2.cc.b.532.1		144	3.2	odd	2
765.2.cc.b.568.1		144	255.143	odd	16

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:	\( N \)	\(=\)	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	255.bi (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03325 - 2.49449i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-3.74064 - 3.74064i) q^{4} +(-1.65882 - 1.49944i) q^{5} +(1.50005 - 2.24498i) q^{6} +(-0.128784 + 0.192738i) q^{7} +(-8.20701 + 3.39946i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})\)	\(q+(1.03325 - 2.49449i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-3.74064 - 3.74064i) q^{4} +(-1.65882 - 1.49944i) q^{5} +(1.50005 - 2.24498i) q^{6} +(-0.128784 + 0.192738i) q^{7} +(-8.20701 + 3.39946i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-5.45431 + 2.58860i) q^{10} +(1.99662 + 1.33410i) q^{11} +(-2.93900 - 4.39853i) q^{12} +4.63849 q^{13} +(0.347717 + 0.520396i) q^{14} +(-1.33442 - 1.79425i) q^{15} +13.4046i q^{16} +(1.87483 - 3.67219i) q^{17} +(1.90920 - 1.90920i) q^{18} +(-3.42730 + 1.41963i) q^{19} +(0.596172 + 11.8139i) q^{20} +(-0.163910 + 0.163910i) q^{21} +(5.39089 - 3.60208i) q^{22} +(-0.825706 - 4.15110i) q^{23} +(-8.71252 + 1.73303i) q^{24} +(0.503354 + 4.97460i) q^{25} +(4.79272 - 11.5707i) q^{26} +(0.831470 + 0.555570i) q^{27} +(1.20270 - 0.239231i) q^{28} +(1.70788 - 8.58610i) q^{29} +(-5.85451 + 1.47478i) q^{30} +(2.18280 - 1.45850i) q^{31} +(17.0236 + 7.05142i) q^{32} +(1.69798 + 1.69798i) q^{33} +(-7.22307 - 8.47103i) q^{34} +(0.502628 - 0.126614i) q^{35} +(-2.02442 - 4.88738i) q^{36} +(-1.72339 + 8.66406i) q^{37} +10.0162i q^{38} +(4.54937 + 0.904925i) q^{39} +(18.7112 + 6.66685i) q^{40} +(0.945732 + 4.75451i) q^{41} +(0.239512 + 0.578233i) q^{42} +(0.153752 + 0.371191i) q^{43} +(-2.47825 - 12.4590i) q^{44} +(-0.958737 - 2.02010i) q^{45} +(-11.2080 - 2.22942i) q^{46} +9.73422i q^{47} +(-2.61511 + 13.1471i) q^{48} +(2.65822 + 6.41751i) q^{49} +(12.9292 + 3.88439i) q^{50} +(2.55521 - 3.23587i) q^{51} +(-17.3509 - 17.3509i) q^{52} +(10.6910 + 4.42835i) q^{53} +(2.24498 - 1.50005i) q^{54} +(-1.31163 - 5.20683i) q^{55} +(0.401723 - 2.01960i) q^{56} +(-3.63840 + 0.723722i) q^{57} +(-19.6532 - 13.1319i) q^{58} +(-0.594386 + 1.43498i) q^{59} +(-1.72006 + 11.7032i) q^{60} +(-4.69467 + 0.933828i) q^{61} +(-1.38283 - 6.95195i) q^{62} +(-0.192738 + 0.128784i) q^{63} +(16.2223 - 16.2223i) q^{64} +(-7.69442 - 6.95515i) q^{65} +(5.99004 - 2.48115i) q^{66} +(1.69680 - 1.69680i) q^{67} +(-20.7494 + 6.72330i) q^{68} -4.23243i q^{69} +(0.203503 - 1.38462i) q^{70} +(-8.33019 - 12.4670i) q^{71} -8.88321 q^{72} +(0.341001 + 0.510345i) q^{73} +(19.8317 + 13.2511i) q^{74} +(-0.476814 + 4.97721i) q^{75} +(18.1306 + 7.50994i) q^{76} +(-0.514263 + 0.213015i) q^{77} +(6.95796 - 10.4133i) q^{78} +(-1.83806 + 2.75085i) q^{79} +(20.0995 - 22.2358i) q^{80} +(0.707107 + 0.707107i) q^{81} +(12.8372 + 2.55349i) q^{82} +(-4.21219 + 10.1691i) q^{83} +1.22626 q^{84} +(-8.61624 + 3.28031i) q^{85} +1.08479 q^{86} +(3.35013 - 8.08793i) q^{87} +(-20.9215 - 4.16154i) q^{88} +(1.93036 + 1.93036i) q^{89} +(-6.02974 + 0.304282i) q^{90} +(-0.597362 + 0.894016i) q^{91} +(-12.4391 + 18.6165i) q^{92} +(2.42540 - 1.00463i) q^{93} +(24.2819 + 10.0579i) q^{94} +(7.81391 + 2.78412i) q^{95} +(15.3209 + 10.2371i) q^{96} +(-1.26576 - 1.89434i) q^{97} +18.7550 q^{98} +(1.33410 + 1.99662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q+O(q^{10}) \) 144 * q	\( 144 q - 16 q^{10} + 64 q^{14} - 32 q^{19} - 32 q^{20} - 16 q^{25} - 64 q^{26} - 64 q^{28} - 64 q^{30} - 32 q^{31} + 16 q^{33} + 32 q^{34} - 16 q^{36} - 32 q^{37} + 112 q^{40} - 80 q^{41} - 16 q^{46} - 64 q^{50} - 64 q^{52} + 48 q^{53} + 16 q^{54} - 64 q^{55} - 32 q^{57} - 112 q^{58} + 32 q^{59} - 32 q^{64} + 64 q^{67} - 272 q^{68} - 32 q^{70} + 32 q^{71} + 48 q^{72} - 80 q^{73} + 80 q^{74} + 32 q^{75} + 64 q^{76} - 96 q^{77} + 64 q^{78} + 32 q^{79} + 336 q^{80} - 16 q^{83} - 96 q^{84} + 32 q^{85} + 64 q^{86} + 48 q^{87} - 80 q^{88} + 320 q^{92} + 128 q^{93} + 16 q^{94} - 64 q^{95} + 64 q^{96} - 16 q^{97} + 144 q^{98}+O(q^{100}) \) 144 * q - 16 * q^10 + 64 * q^14 - 32 * q^19 - 32 * q^20 - 16 * q^25 - 64 * q^26 - 64 * q^28 - 64 * q^30 - 32 * q^31 + 16 * q^33 + 32 * q^34 - 16 * q^36 - 32 * q^37 + 112 * q^40 - 80 * q^41 - 16 * q^46 - 64 * q^50 - 64 * q^52 + 48 * q^53 + 16 * q^54 - 64 * q^55 - 32 * q^57 - 112 * q^58 + 32 * q^59 - 32 * q^64 + 64 * q^67 - 272 * q^68 - 32 * q^70 + 32 * q^71 + 48 * q^72 - 80 * q^73 + 80 * q^74 + 32 * q^75 + 64 * q^76 - 96 * q^77 + 64 * q^78 + 32 * q^79 + 336 * q^80 - 16 * q^83 - 96 * q^84 + 32 * q^85 + 64 * q^86 + 48 * q^87 - 80 * q^88 + 320 * q^92 + 128 * q^93 + 16 * q^94 - 64 * q^95 + 64 * q^96 - 16 * q^97 + 144 * q^98

Introduction

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