LMFDB - Embedded newform 231.2.l.b.65.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(32,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.20
Character	$\chi$	$=$	231.65
Dual form			231.2.l.b.32.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939478 - 1.62722i) q^{2} +(1.16688 - 1.27999i) q^{3} +(-0.765237 - 1.32543i) q^{4} +(-2.63713 - 1.52255i) q^{5} +(-0.986571 - 3.10131i) q^{6} +(-0.738610 + 2.54056i) q^{7} +0.882219 q^{8} +(-0.276760 - 2.98721i) q^{9} +O(q^{10})$	\(q+(0.939478 - 1.62722i) q^{2} +(1.16688 - 1.27999i) q^{3} +(-0.765237 - 1.32543i) q^{4} +(-2.63713 - 1.52255i) q^{5} +(-0.986571 - 3.10131i) q^{6} +(-0.738610 + 2.54056i) q^{7} +0.882219 q^{8} +(-0.276760 - 2.98721i) q^{9} +(-4.95505 + 2.86080i) q^{10} +(0.988816 - 3.16579i) q^{11} +(-2.58948 - 0.567126i) q^{12} +1.24436i q^{13} +(3.44015 + 3.58868i) q^{14} +(-5.02608 + 1.59887i) q^{15} +(2.35930 - 4.08643i) q^{16} +(2.83407 + 4.90876i) q^{17} +(-5.12086 - 2.35606i) q^{18} +(0.532275 + 0.307309i) q^{19} +4.66044i q^{20} +(2.39003 + 3.90996i) q^{21} +(-4.22248 - 4.58322i) q^{22} +(4.41744 + 2.55041i) q^{23} +(1.02945 - 1.12923i) q^{24} +(2.13630 + 3.70019i) q^{25} +(2.02485 + 1.16905i) q^{26} +(-4.14655 - 3.13147i) q^{27} +(3.93255 - 0.965157i) q^{28} +1.47768 q^{29} +(-2.12017 + 9.68065i) q^{30} +(3.18007 + 5.50805i) q^{31} +(-3.55080 - 6.15016i) q^{32} +(-2.89836 - 4.95979i) q^{33} +10.6502 q^{34} +(5.81594 - 5.57522i) q^{35} +(-3.74754 + 2.65275i) q^{36} +(-3.15832 + 5.47036i) q^{37} +(1.00012 - 0.577420i) q^{38} +(1.59277 + 1.45202i) q^{39} +(-2.32653 - 1.34322i) q^{40} -10.3640 q^{41} +(8.60775 - 0.215789i) q^{42} -2.31140i q^{43} +(-4.95271 + 1.11198i) q^{44} +(-3.81831 + 8.29903i) q^{45} +(8.30018 - 4.79211i) q^{46} +(-9.35776 - 5.40270i) q^{47} +(-2.47756 - 7.78827i) q^{48} +(-5.90891 - 3.75297i) q^{49} +8.02804 q^{50} +(9.59020 + 2.10036i) q^{51} +(1.64931 - 0.952228i) q^{52} +(2.58050 - 1.48985i) q^{53} +(-8.99120 + 3.80541i) q^{54} +(-7.42771 + 6.84309i) q^{55} +(-0.651616 + 2.24133i) q^{56} +(1.01446 - 0.322713i) q^{57} +(1.38825 - 2.40451i) q^{58} +(5.38180 - 3.10718i) q^{59} +(5.96533 + 5.43819i) q^{60} +(8.24852 + 4.76229i) q^{61} +11.9504 q^{62} +(7.79360 + 1.50325i) q^{63} -3.90639 q^{64} +(1.89459 - 3.28153i) q^{65} +(-10.7936 + 0.0566571i) q^{66} +(2.31763 + 4.01426i) q^{67} +(4.33747 - 7.51272i) q^{68} +(8.41916 - 2.67826i) q^{69} +(-3.60819 - 14.7016i) q^{70} +7.90967i q^{71} +(-0.244163 - 2.63537i) q^{72} +(-1.01586 + 0.586510i) q^{73} +(5.93434 + 10.2786i) q^{74} +(7.22903 + 1.58324i) q^{75} -0.940657i q^{76} +(7.31254 + 4.85043i) q^{77} +(3.85913 - 1.22765i) q^{78} +(-3.34216 - 1.92960i) q^{79} +(-12.4436 + 7.18429i) q^{80} +(-8.84681 + 1.65348i) q^{81} +(-9.73679 + 16.8646i) q^{82} -15.6693 q^{83} +(3.35344 - 6.15986i) q^{84} -17.2600i q^{85} +(-3.76117 - 2.17151i) q^{86} +(1.72428 - 1.89142i) q^{87} +(0.872352 - 2.79292i) q^{88} +(1.19552 + 0.690235i) q^{89} +(9.91716 + 14.0100i) q^{90} +(-3.16137 - 0.919095i) q^{91} -7.80668i q^{92} +(10.7610 + 2.35679i) q^{93} +(-17.5828 + 10.1514i) q^{94} +(-0.935785 - 1.62083i) q^{95} +(-12.0155 - 2.63154i) q^{96} +9.19643 q^{97} +(-11.6582 + 6.08929i) q^{98} +(-9.73054 - 2.07763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9	$ 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9} + 14 q^{12} + 4 q^{15} - 28 q^{16} - 24 q^{22} - 36 q^{27} - 4 q^{31} - 26 q^{33} + 56 q^{34} + 12 q^{36} - 28 q^{37} + 96 q^{42} + 30 q^{45} - 72 q^{48} + 24 q^{49} - 80 q^{55} + 16 q^{58} - 32 q^{60} + 256 q^{64} - 42 q^{66} + 16 q^{67} + 36 q^{69} - 76 q^{70} + 34 q^{75} + 104 q^{78} - 26 q^{81} - 4 q^{82} - 16 q^{88} - 36 q^{91} + 52 q^{93} - 144 q^{97} - 36 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9 + 14 * q^12 + 4 * q^15 - 28 * q^16 - 24 * q^22 - 36 * q^27 - 4 * q^31 - 26 * q^33 + 56 * q^34 + 12 * q^36 - 28 * q^37 + 96 * q^42 + 30 * q^45 - 72 * q^48 + 24 * q^49 - 80 * q^55 + 16 * q^58 - 32 * q^60 + 256 * q^64 - 42 * q^66 + 16 * q^67 + 36 * q^69 - 76 * q^70 + 34 * q^75 + 104 * q^78 - 26 * q^81 - 4 * q^82 - 16 * q^88 - 36 * q^91 + 52 * q^93 - 144 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.939478	−	1.62722i	0.664311	−	1.15062i	−0.315161	−	0.949038i	$-0.602058\pi$
$2$	0.939478	−	1.62722i	0.664311	−	1.15062i	0.979472	−	0.201582i	$-0.0646083\pi$
$3$	1.16688	−	1.27999i	0.673701	−	0.739004i
$3$	1.16688	−	1.27999i	0.673701	−	0.739004i
$4$	−0.765237	−	1.32543i	−0.382618	−	0.662715i
$5$	−2.63713	−	1.52255i	−1.17936	−	0.680904i	−0.223494	−	0.974705i	$-0.571746\pi$
$5$	−2.63713	−	1.52255i	−1.17936	−	0.680904i	−0.955867	+	0.293801i	$0.905080\pi$
$6$	−0.986571	−	3.10131i	−0.402766	−	1.26610i
$7$	−0.738610	+	2.54056i	−0.279168	+	0.960242i
$7$	−0.738610	+	2.54056i	−0.279168	+	0.960242i
$8$	0.882219			0.311911
$9$	−0.276760	−	2.98721i	−0.0922534	−	0.995736i
$10$	−4.95505	+	2.86080i	−1.56692	+	0.904664i
$11$	0.988816	−	3.16579i	0.298139	−	0.954522i
$11$	0.988816	−	3.16579i	0.298139	−	0.954522i
$12$	−2.58948	−	0.567126i	−0.747519	−	0.163715i
$13$			1.24436i			0.345123i	0.984999	+	0.172561i	$0.0552043\pi$
$13$			1.24436i			0.345123i	−0.984999	+	0.172561i	$0.944796\pi$
$14$	3.44015	+	3.58868i	0.919420	+	0.959116i
$15$	−5.02608	+	1.59887i	−1.29773	+	0.412826i
$16$	2.35930	−	4.08643i	0.589825	−	1.02161i
$17$	2.83407	+	4.90876i	0.687363	+	1.19055i	0.972688	+	0.232117i	$0.0745653\pi$
$17$	2.83407	+	4.90876i	0.687363	+	1.19055i	−0.285325	+	0.958431i	$0.592101\pi$
$18$	−5.12086	−	2.35606i	−1.20700	−	0.555330i
$19$	0.532275	+	0.307309i	0.122112	+	0.0705015i	0.559812	−	0.828620i	$-0.310873\pi$
$19$	0.532275	+	0.307309i	0.122112	+	0.0705015i	−0.437700	+	0.899121i	$0.644207\pi$
$20$			4.66044i			1.04211i
$21$	2.39003	+	3.90996i	0.521547	+	0.853223i
$22$	−4.22248	−	4.58322i	−0.900236	−	0.977145i
$23$	4.41744	+	2.55041i	0.921101	+	0.531798i	0.883986	−	0.467513i	$-0.154850\pi$
$23$	4.41744	+	2.55041i	0.921101	+	0.531798i	0.0371147	+	0.999311i	$0.488183\pi$
$24$	1.02945	−	1.12923i	0.210135	−	0.230504i
$25$	2.13630	+	3.70019i	0.427261	+	0.740037i
$26$	2.02485	+	1.16905i	0.397105	+	0.229269i
$27$	−4.14655	−	3.13147i	−0.798004	−	0.602653i
$28$	3.93255	−	0.965157i	0.743181	−	0.182397i
$29$	1.47768			0.274398			0.137199	−	0.990544i	$-0.456190\pi$
$29$	1.47768			0.274398			0.137199	+	0.990544i	$0.456190\pi$
$30$	−2.12017	+	9.68065i	−0.387089	+	1.76744i
$31$	3.18007	+	5.50805i	0.571158	+	0.989275i	0.996447	+	0.0842172i	$0.0268390\pi$
$31$	3.18007	+	5.50805i	0.571158	+	0.989275i	−0.425289	+	0.905057i	$0.639828\pi$
$32$	−3.55080	−	6.15016i	−0.627698	−	1.08721i
$33$	−2.89836	−	4.95979i	−0.504539	−	0.863389i
$34$	10.6502			1.82649
$35$	5.81594	−	5.57522i	0.983073	−	0.942385i
$36$	−3.74754	+	2.65275i	−0.624591	+	0.442124i
$37$	−3.15832	+	5.47036i	−0.519224	+	0.899322i	0.480526	+	0.876980i	$0.340446\pi$
$37$	−3.15832	+	5.47036i	−0.519224	+	0.899322i	−0.999750	+	0.0223421i	$0.992888\pi$
$38$	1.00012	−	0.577420i	0.162241	−	0.0936699i
$39$	1.59277	+	1.45202i	0.255047	+	0.232510i
$40$	−2.32653	−	1.34322i	−0.367856	−	0.212382i
$41$	−10.3640			−1.61859			−0.809296	−	0.587401i	$-0.800151\pi$
$41$	−10.3640			−1.61859			−0.809296	+	0.587401i	$0.800151\pi$
$42$	8.60775	−	0.215789i	1.32820	−	0.0332970i
$43$		−	2.31140i		−	0.352486i	−0.984347	−	0.176243i	$-0.943606\pi$
$43$		−	2.31140i		−	0.352486i	0.984347	−	0.176243i	$-0.0563944\pi$
$44$	−4.95271	+	1.11198i	−0.746649	+	0.167637i
$45$	−3.81831	+	8.29903i	−0.569200	+	1.23715i
$46$	8.30018	−	4.79211i	1.22379	−	0.706558i
$47$	−9.35776	−	5.40270i	−1.36497	−	0.788065i	−0.374689	−	0.927151i	$-0.622250\pi$
$47$	−9.35776	−	5.40270i	−1.36497	−	0.788065i	−0.990280	+	0.139086i	$0.955584\pi$
$48$	−2.47756	−	7.78827i	−0.357605	−	1.12414i
$49$	−5.90891	−	3.75297i	−0.844130	−	0.536138i
$50$	8.02804			1.13534
$51$	9.59020	+	2.10036i	1.34290	+	0.294110i
$52$	1.64931	−	0.952228i	0.228718	−	0.132050i
$53$	2.58050	−	1.48985i	0.354459	−	0.204647i	−0.312189	−	0.950020i	$-0.601062\pi$
$53$	2.58050	−	1.48985i	0.354459	−	0.204647i	0.666647	+	0.745373i	$0.267729\pi$
$54$	−8.99120	+	3.80541i	−1.22355	+	0.517851i
$55$	−7.42771	+	6.84309i	−1.00155	+	0.922722i
$56$	−0.651616	+	2.24133i	−0.0870758	+	0.299511i
$57$	1.01446	−	0.322713i	0.134368	−	0.0427444i
$58$	1.38825	−	2.40451i	0.182286	−	0.315728i
$59$	5.38180	−	3.10718i	0.700650	−	0.404521i	−0.106939	−	0.994266i	$-0.534105\pi$
$59$	5.38180	−	3.10718i	0.700650	−	0.404521i	0.807590	+	0.589745i	$0.200772\pi$
$60$	5.96533	+	5.43819i	0.770120	+	0.702068i
$61$	8.24852	+	4.76229i	1.05612	+	0.609749i	0.924355	−	0.381533i	$-0.124604\pi$
$61$	8.24852	+	4.76229i	1.05612	+	0.609749i	0.131760	+	0.991282i	$0.457937\pi$
$62$	11.9504			1.51771
$63$	7.79360	+	1.50325i	0.981902	+	0.189392i
$64$	−3.90639			−0.488299
$65$	1.89459	−	3.28153i	0.234995	−	0.407024i
$66$	−10.7936	+	0.0566571i	−1.32860	+	0.00697401i
$67$	2.31763	+	4.01426i	0.283144	+	0.490420i	0.972157	−	0.234329i	$-0.0752893\pi$
$67$	2.31763	+	4.01426i	0.283144	+	0.490420i	−0.689013	+	0.724749i	$0.741956\pi$
$68$	4.33747	−	7.51272i	0.525996	−	0.911051i
$69$	8.41916	−	2.67826i	1.01355	−	0.322424i
$70$	−3.60819	−	14.7016i	−0.431261	−	1.75718i
$71$			7.90967i			0.938705i	0.883011	+	0.469353i	$0.155513\pi$
$71$			7.90967i			0.938705i	−0.883011	+	0.469353i	$0.844487\pi$
$72$	−0.244163	−	2.63537i	−0.0287749	−	0.310581i
$73$	−1.01586	+	0.586510i	−0.118898	+	0.0686458i	−0.558270	−	0.829660i	$-0.688534\pi$
$73$	−1.01586	+	0.586510i	−0.118898	+	0.0686458i	0.439372	+	0.898305i	$0.355201\pi$
$74$	5.93434	+	10.2786i	0.689853	+	1.19486i
$75$	7.22903	+	1.58324i	0.834736	+	0.182817i
$76$		−	0.940657i		−	0.107901i
$77$	7.31254	+	4.85043i	0.833342	+	0.552758i
$78$	3.85913	−	1.22765i	0.436961	−	0.139004i
$79$	−3.34216	−	1.92960i	−0.376022	−	0.217097i	0.300064	−	0.953919i	$-0.402992\pi$
$79$	−3.34216	−	1.92960i	−0.376022	−	0.217097i	−0.676086	+	0.736822i	$0.736325\pi$
$80$	−12.4436	+	7.18429i	−1.39123	+	0.803228i
$81$	−8.84681	+	1.65348i	−0.982979	+	0.183720i
$82$	−9.73679	+	16.8646i	−1.07525	+	1.86238i
$83$	−15.6693			−1.71993			−0.859966	−	0.510352i	$-0.829515\pi$
$83$	−15.6693			−1.71993			−0.859966	+	0.510352i	$0.829515\pi$
$84$	3.35344	−	6.15986i	0.365890	−	0.672095i
$85$		−	17.2600i		−	1.87211i
$86$	−3.76117	−	2.17151i	−0.405577	−	0.234160i
$87$	1.72428	−	1.89142i	0.184862	−	0.202781i
$88$	0.872352	−	2.79292i	0.0929931	−	0.297726i
$89$	1.19552	+	0.690235i	0.126725	+	0.0731648i	0.562022	−	0.827122i	$-0.310023\pi$
$89$	1.19552	+	0.690235i	0.126725	+	0.0731648i	−0.435297	+	0.900287i	$0.643357\pi$
$90$	9.91716	+	14.0100i	1.04536	+	1.47678i
$91$	−3.16137	−	0.919095i	−0.331401	−	0.0963473i
$92$		−	7.80668i		−	0.813903i
$93$	10.7610	+	2.35679i	1.11587	+	0.244388i
$94$	−17.5828	+	10.1514i	−1.81353	+	1.04704i
$95$	−0.935785	−	1.62083i	−0.0960095	−	0.166293i
$96$	−12.0155	−	2.63154i	−1.22633	−	0.268580i
$97$	9.19643			0.933756			0.466878	−	0.884322i	$-0.345379\pi$
$97$	9.19643			0.933756			0.466878	+	0.884322i	$0.345379\pi$
$98$	−11.6582	+	6.08929i	−1.17766	+	0.615111i
$99$	−9.73054	−	2.07763i	−0.977956	−	0.208810i
$100$	3.26956	−	5.66304i	0.326956	−	0.566304i
$101$	−5.50095	−	9.52793i	−0.547365	−	0.948064i	−0.998454	−	0.0555851i	$-0.982298\pi$
$101$	−5.50095	−	9.52793i	−0.547365	−	0.948064i	0.451089	−	0.892479i	$-0.351036\pi$
$102$	12.4275	−	13.6322i	1.23051	−	1.34978i
$103$	−1.24322	+	2.15333i	−0.122499	+	0.212174i	−0.920752	−	0.390148i	$-0.872424\pi$
$103$	−1.24322	+	2.15333i	−0.122499	+	0.212174i	0.798254	+	0.602321i	$0.205757\pi$
$104$			1.09780i			0.107648i
$105$	−0.349715	−	13.9500i	−0.0341286	−	1.36138i
$106$		−	5.59873i		−	0.543797i
$107$	−6.89744	+	11.9467i	−0.666800	+	1.15493i	0.311994	+	0.950084i	$0.399003\pi$
$107$	−6.89744	+	11.9467i	−0.666800	+	1.15493i	−0.978794	+	0.204848i	$0.934330\pi$
$108$	−0.977456	+	7.89228i	−0.0940558	+	0.759435i
$109$	−2.99294	+	1.72797i	−0.286671	+	0.165510i	−0.636440	−	0.771326i	$-0.719594\pi$
$109$	−2.99294	+	1.72797i	−0.286671	+	0.165510i	0.349768	+	0.936836i	$0.386260\pi$
$110$	4.15706	+	18.5155i	0.396361	+	1.76538i
$111$	3.31663	+	10.4259i	0.314801	+	0.989583i
$112$	8.63922	+	9.01222i	0.816329	+	0.851575i
$113$		−	7.98997i		−	0.751633i	−0.926694	−	0.375817i	$-0.877362\pi$
$113$		−	7.98997i		−	0.751633i	0.926694	−	0.375817i	$-0.122638\pi$
$114$	0.427933	−	1.95393i	0.0400796	−	0.183002i
$115$	−7.76625	−	13.4515i	−0.724207	−	1.25436i
$116$	−1.13077	−	1.95856i	−0.104990	−	0.181847i
$117$	3.71715	−	0.344389i	0.343651	−	0.0318387i
$118$		−	11.6765i		−	1.07491i
$119$	−14.5643	+	3.57448i	−1.33510	+	0.327672i
$120$	−4.43410	+	1.41055i	−0.404776	+	0.128765i
$121$	−9.04449	−	6.26077i	−0.822226	−	0.569161i
$122$	15.4986	−	8.94813i	1.40318	−	0.810125i
$123$	−12.0936	+	13.2659i	−1.09045	+	1.19615i
$124$	4.86702	−	8.42992i	0.437071	−	0.757029i
$125$			2.21498i			0.198114i
$126$	9.76805	−	11.2697i	0.870207	−	1.00398i
$127$			11.9269i			1.05834i	0.848514	+	0.529172i	$0.177498\pi$
$127$			11.9269i			1.05834i	−0.848514	+	0.529172i	$0.822502\pi$
$128$	3.43163	−	5.94376i	0.303316	−	0.525359i
$129$	−2.95858	−	2.69714i	−0.260488	−	0.237470i
$130$	−3.55986	−	6.16585i	−0.312220	−	0.540781i
$131$	1.54608	−	2.67789i	0.135082	−	0.233968i	−0.790547	−	0.612401i	$-0.790204\pi$
$131$	1.54608	−	2.67789i	0.135082	−	0.233968i	0.925629	+	0.378433i	$0.123537\pi$
$132$	−4.35592	+	7.63698i	−0.379135	+	0.664714i
$133$	−1.17388	+	1.12530i	−0.101788	+	0.0975755i
$134$	8.70946			0.752383
$135$	6.16717	+	14.5714i	0.530785	+	1.25411i
$136$	2.50027	+	4.33060i	0.214396	+	0.371346i
$137$	−2.68265	+	1.54883i	−0.229194	+	0.132325i	−0.610200	−	0.792247i	$-0.708911\pi$
$137$	−2.68265	+	1.54883i	−0.229194	+	0.132325i	0.381006	+	0.924573i	$0.375578\pi$
$138$	3.55149	−	16.2160i	0.302323	−	1.38040i
$139$		−	12.1764i		−	1.03279i	−0.856351	−	0.516394i	$-0.827274\pi$
$139$		−	12.1764i		−	1.03279i	0.856351	−	0.516394i	$-0.172726\pi$
$140$	−11.8401	−	3.44225i	−1.00067	−	0.290923i
$141$	−17.8348	+	5.67352i	−1.50196	+	0.477797i
$142$	12.8708	+	7.43096i	1.08009	+	0.623592i
$143$	3.93938	+	1.23044i	0.329427	+	0.102895i
$144$	−12.8600	−	5.91675i	−1.07166	−	0.493063i
$145$	−3.89683	−	2.24983i	−0.323614	−	0.186839i
$146$			2.20405i			0.182409i
$147$	−11.6988	+	3.18408i	−0.964900	+	0.262618i
$148$	9.66744			0.794659
$149$	10.7473	−	18.6148i	0.880452	−	1.52499i	0.0296119	−	0.999561i	$-0.490573\pi$
$149$	10.7473	−	18.6148i	0.880452	−	1.52499i	0.850840	−	0.525425i	$-0.176094\pi$
$150$	9.36780	−	10.2758i	0.764877	−	0.839018i
$151$	−19.8835	+	11.4797i	−1.61810	+	0.934208i	−0.630683	+	0.776040i	$0.717225\pi$
$151$	−19.8835	+	11.4797i	−1.61810	+	0.934208i	−0.987412	+	0.158168i	$0.949441\pi$
$152$	0.469583	+	0.271114i	0.0380882	+	0.0219902i
$153$	13.8791	−	9.82450i	1.12206	−	0.794264i
$154$	14.7627	−	7.34226i	1.18961	−	0.591657i
$155$		−	19.3673i		−	1.55562i
$156$	0.705707	−	3.22224i	0.0565018	−	0.257986i
$157$	5.67235	+	9.82480i	0.452703	+	0.784105i	0.998553	−	0.0537783i	$-0.0171264\pi$
$157$	5.67235	+	9.82480i	0.452703	+	0.784105i	−0.545850	+	0.837883i	$0.683793\pi$
$158$	−6.27977	+	3.62563i	−0.499592	+	0.288439i
$159$	1.10415	−	5.04150i	0.0875645	−	0.399817i
$160$			21.6250i			1.70961i
$161$	−9.74225	+	9.33903i	−0.767797	+	0.736019i
$162$	−5.62080	+	15.9491i	−0.441612	+	1.25308i
$163$	6.79598	−	11.7710i	0.532302	−	0.921975i	−0.466986	−	0.884265i	$-0.654660\pi$
$163$	6.79598	−	11.7710i	0.532302	−	0.921975i	0.999289	−	0.0377102i	$-0.0120064\pi$
$164$	7.93095	+	13.7368i	0.619303	+	1.07266i
$165$	0.0918203	+	17.4925i	0.00714820	+	1.36179i
$166$	−14.7210	+	25.4975i	−1.14257	+	1.97899i
$167$	6.57900			0.509099			0.254549	−	0.967060i	$-0.418073\pi$
$167$	6.57900			0.509099			0.254549	+	0.967060i	$0.418073\pi$
$168$	2.10853	+	3.44944i	0.162676	+	0.266130i
$169$	11.4516			0.880890
$170$	−28.0859	−	16.2154i	−2.15409	−	1.24367i
$171$	0.770683	−	1.67507i	0.0589356	−	0.128095i
$172$	−3.06360	+	1.76877i	−0.233597	+	0.134867i
$173$	1.14593	−	1.98481i	0.0871234	−	0.150902i	−0.819171	−	0.573550i	$-0.805566\pi$
$173$	1.14593	−	1.98481i	0.0871234	−	0.150902i	0.906294	+	0.422648i	$0.138899\pi$
$174$	−1.45783	−	4.58273i	−0.110518	−	0.347416i
$175$	−10.9784	+	2.69442i	−0.829893	+	0.203679i
$176$	−10.6039	−	11.5098i	−0.799296	−	0.867582i
$177$	2.30277	−	10.5144i	0.173087	−	0.790310i
$178$	2.24633	−	1.29692i	0.168370	−	0.0972083i
$179$	−12.2722	+	7.08537i	−0.917269	+	0.529585i	−0.882763	−	0.469819i	$-0.844319\pi$
$179$	−12.2722	+	7.08537i	−0.917269	+	0.529585i	−0.0345062	+	0.999404i	$0.510986\pi$
$180$	13.9217	−	1.28982i	1.03766	−	0.0961378i
$181$	9.13748			0.679184			0.339592	−	0.940573i	$-0.389711\pi$
$181$	9.13748			0.679184			0.339592	+	0.940573i	$0.389711\pi$
$182$	−4.46561	+	4.28078i	−0.331013	+	0.317313i
$183$	15.7208	−	5.00101i	1.16211	−	0.369685i
$184$	3.89715	+	2.25002i	0.287302	+	0.165874i
$185$	16.6578	−	9.61738i	1.22470	−	0.707084i
$186$	13.9448	−	15.2965i	1.02248	−	1.12159i
$187$	18.3425	−	4.11823i	1.34133	−	0.301154i
$188$			16.5374i			1.20611i
$189$	11.0184	−	8.22163i	0.801470	−	0.598035i
$190$	−3.51660			−0.255121
$191$	1.37505	+	0.793888i	0.0994954	+	0.0574437i	0.548922	−	0.835874i	$-0.315038\pi$
$191$	1.37505	+	0.793888i	0.0994954	+	0.0574437i	−0.449427	+	0.893317i	$0.648372\pi$
$192$	−4.55831	+	5.00015i	−0.328967	+	0.360855i
$193$	11.2686	−	6.50595i	0.811135	−	0.468309i	−0.0362150	−	0.999344i	$-0.511530\pi$
$193$	11.2686	−	6.50595i	0.811135	−	0.468309i	0.847350	+	0.531035i	$0.178197\pi$
$194$	8.63984	−	14.9646i	0.620305	−	1.07440i
$195$	−1.98956	−	6.25423i	−0.142476	−	0.447875i
$196$	−0.452577	+	10.7038i	−0.0323270	+	0.764554i
$197$	0.114518			0.00815905			0.00407953	−	0.999992i	$-0.498701\pi$
$197$	0.114518			0.00815905			0.00407953	+	0.999992i	$0.498701\pi$
$198$	−12.5224	+	13.8819i	−0.889928	+	0.986542i
$199$	−11.9254	−	20.6554i	−0.845370	−	1.46422i	−0.885299	−	0.465021i	$-0.846047\pi$
$199$	−11.9254	−	20.6554i	−0.845370	−	1.46422i	0.0399293	−	0.999203i	$-0.487287\pi$
$200$	1.88469	+	3.26437i	0.133268	+	0.230826i
$201$	7.84263	+	1.71762i	0.553176	+	0.121152i
$202$	−20.6721			−1.45448
$203$	−1.09143	+	3.75413i	−0.0766032	+	0.263488i
$204$	−4.55490	−	14.3184i	−0.318906	−	1.00249i
$205$	27.3313	+	15.7798i	1.90890	+	1.10211i
$206$	2.33596	+	4.04601i	0.162754	+	0.281899i
$207$	6.39604	−	13.9017i	0.444555	−	0.966233i
$208$	5.08497	+	2.93581i	0.352579	+	0.203562i
$209$	1.49920	−	1.38120i	0.103702	−	0.0955396i
$210$	−23.0283	−	12.5366i	−1.58910	−	0.865111i
$211$		−	5.75491i		−	0.396184i	−0.980183	−	0.198092i	$-0.936525\pi$
$211$		−	5.75491i		−	0.396184i	0.980183	−	0.198092i	$-0.0634746\pi$
$212$	−3.94939	−	2.28018i	−0.271245	−	0.156603i
$213$	10.1243	+	9.22968i	0.693707	+	0.632407i
$214$	12.9600	+	22.4473i	0.885926	+	1.53447i
$215$	−3.51922	+	6.09547i	−0.240009	+	0.415708i
$216$	−3.65816	−	2.76265i	−0.248906	−	0.187974i
$217$	−16.3424	+	4.01087i	−1.10939	+	0.272276i
$218$			6.49357i			0.439800i
$219$	−0.434669	+	1.98469i	−0.0293722	+	0.134113i
$220$	14.7540	+	4.60832i	0.994713	+	0.310693i
$221$	−6.10825	+	3.52660i	−0.410885	+	0.237225i
$222$	20.0812	+	4.39800i	1.34776	+	0.295175i
$223$	−10.9109			−0.730650			−0.365325	−	0.930880i	$-0.619042\pi$
$223$	−10.9109			−0.730650			−0.365325	+	0.930880i	$0.619042\pi$
$224$	18.2475	−	4.47845i	1.21921	−	0.299229i
$225$	10.4620	−	7.40564i	0.697465	−	0.493710i
$226$	−13.0015	−	7.50640i	−0.864845	−	0.499318i
$227$	4.04895	+	7.01299i	0.268739	+	0.465469i	0.968536	−	0.248872i	$-0.0800599\pi$
$227$	4.04895	+	7.01299i	0.268739	+	0.465469i	−0.699798	+	0.714341i	$0.746727\pi$
$228$	−1.20403	−	1.09764i	−0.0797391	−	0.0726929i
$229$	−0.452439	+	0.783647i	−0.0298980	+	0.0517848i	−0.880587	−	0.473884i	$-0.842852\pi$
$229$	−0.452439	+	0.783647i	−0.0298980	+	0.0517848i	0.850689	+	0.525669i	$0.176185\pi$
$230$	−29.1849			−1.92439
$231$	14.7414	−	3.70010i	0.969914	−	0.243449i
$232$	1.30363			0.0855878
$233$	0.199109	−	0.344867i	0.0130441	−	0.0225930i	−0.859430	−	0.511254i	$-0.829181\pi$
$233$	0.199109	−	0.344867i	0.0130441	−	0.0225930i	0.872474	+	0.488661i	$0.162514\pi$
$234$	2.93179	−	6.37218i	0.191657	−	0.416563i
$235$	16.4517	+	28.4953i	1.07319	+	1.85883i
$236$	−8.23670	−	4.75546i	−0.536164	−	0.309554i
$237$	−6.36978	+	2.02632i	−0.413762	+	0.131624i
$238$	−7.86633	+	27.0575i	−0.509899	+	1.75387i
$239$	−18.8807			−1.22129			−0.610647	−	0.791903i	$-0.709091\pi$
$239$	−18.8807			−1.22129			−0.610647	+	0.791903i	$0.709091\pi$
$240$	−5.32436	+	24.3109i	−0.343686	+	1.56926i
$241$	2.61969	−	1.51248i	0.168749	−	0.0974274i	−0.413247	−	0.910619i	$-0.635605\pi$
$241$	2.61969	−	1.51248i	0.168749	−	0.0974274i	0.581996	+	0.813192i	$0.302272\pi$
$242$	−18.6848	+	8.83554i	−1.20110	+	0.567970i
$243$	−8.20676	+	13.2533i	−0.526464	+	0.850197i
$244$		−	14.5771i		−	0.933204i
$245$	9.86849	+	18.8937i	0.630475	+	1.20707i
$246$	10.2249	+	32.1421i	0.651913	+	2.04930i
$247$	−0.382402	+	0.662340i	−0.0243317	+	0.0421437i
$248$	2.80552	+	4.85930i	0.178151	+	0.308566i
$249$	−18.2843	+	20.0566i	−1.15872	+	1.27104i
$250$	3.60427	+	2.08092i	0.227954	+	0.131609i
$251$		−	7.80267i		−	0.492500i	−0.969206	−	0.246250i	$-0.920802\pi$
$251$		−	7.80267i		−	0.492500i	0.969206	−	0.246250i	$-0.0791985\pi$
$252$	−3.97149	−	11.4802i	−0.250181	−	0.723185i
$253$	12.4421	−	11.4628i	0.782229	−	0.720661i
$254$	19.4078	+	11.2051i	1.21775	+	0.703070i
$255$	−22.0927	−	20.1405i	−1.38350	−	1.26125i
$256$	−10.3543	−	17.9341i	−0.647142	−	1.12088i
$257$	9.02456	+	5.21033i	0.562937	+	0.325012i	0.754323	−	0.656503i	$-0.227965\pi$
$257$	9.02456	+	5.21033i	0.562937	+	0.325012i	−0.191387	+	0.981515i	$0.561298\pi$
$258$	−7.16837	+	2.28036i	−0.446283	+	0.141969i
$259$	−11.5650	−	12.0644i	−0.718616	−	0.749643i
$260$	−5.79925			−0.359654
$261$	−0.408962	−	4.41413i	−0.0253141	−	0.273228i
$262$	−2.90501	−	5.03163i	−0.179472	−	0.310855i
$263$	15.4549	+	26.7686i	0.952989	+	1.65062i	0.738905	+	0.673809i	$0.235343\pi$
$263$	15.4549	+	26.7686i	0.952989	+	1.65062i	0.214083	+	0.976815i	$0.431324\pi$
$264$	−2.55698	−	4.37562i	−0.157371	−	0.269301i
$265$	−9.07348			−0.557380
$266$	0.728272	+	2.96736i	0.0446532	+	0.181940i
$267$	2.27853	−	0.724834i	0.139444	−	0.0443591i
$268$	3.54708	−	6.14372i	0.216672	−	0.375287i
$269$	7.00519	−	4.04445i	0.427114	−	0.246594i	−0.271002	−	0.962579i	$-0.587355\pi$
$269$	7.00519	−	4.04445i	0.427114	−	0.246594i	0.698116	+	0.715984i	$0.254022\pi$
$270$	29.5049	+	3.65417i	1.79561	+	0.222386i
$271$	−11.9023	−	6.87180i	−0.723014	−	0.417432i	0.0928473	−	0.995680i	$-0.470403\pi$
$271$	−11.9023	−	6.87180i	−0.723014	−	0.417432i	−0.815861	+	0.578248i	$0.803736\pi$
$272$	26.7457			1.62170
$273$	−4.86538	+	2.97405i	−0.294466	+	0.179998i
$274$			5.82036i			0.351621i
$275$	13.8264	−	3.10429i	0.833765	−	0.187196i
$276$	−9.99249	−	9.10949i	−0.601477	−	0.548327i
$277$	23.6582	−	13.6590i	1.42148	−	0.820692i	0.425055	−	0.905167i	$-0.360255\pi$
$277$	23.6582	−	13.6590i	1.42148	−	0.820692i	0.996426	+	0.0844752i	$0.0269214\pi$
$278$	−19.8137	−	11.4394i	−1.18835	−	0.686092i
$279$	15.5736	−	11.0239i	0.932365	−	0.659986i
$280$	5.13093	−	4.91857i	0.306632	−	0.293941i
$281$	0.129664			0.00773512			0.00386756	−	0.999993i	$-0.498769\pi$
$281$	0.129664			0.00773512			0.00386756	+	0.999993i	$0.498769\pi$
$282$	−7.52335	+	34.3514i	−0.448009	+	2.04560i
$283$	25.0814	−	14.4807i	1.49093	−	0.860790i	0.490986	−	0.871168i	$-0.336637\pi$
$283$	25.0814	−	14.4807i	1.49093	−	0.860790i	0.999946	+	0.0103778i	$0.00330341\pi$
$284$	10.4837	−	6.05277i	0.622094	−	0.359166i
$285$	−3.16660	−	0.693521i	−0.187573	−	0.0410806i
$286$	5.70316	−	5.25427i	0.337235	−	0.310692i
$287$	7.65499	−	26.3305i	0.451859	−	1.55424i
$288$	−17.3891	+	12.3091i	−1.02466	+	0.725320i
$289$	−7.56392	+	13.1011i	−0.444936	+	0.770653i
$290$	−7.32197	+	4.22734i	−0.429961	+	0.248238i
$291$	10.7312	−	11.7714i	0.629073	−	0.690049i
$292$	1.55475	+	0.897638i	0.0909851	+	0.0525303i
$293$	4.79018			0.279845			0.139923	−	0.990162i	$-0.455315\pi$
$293$	4.79018			0.279845			0.139923	+	0.990162i	$0.455315\pi$
$294$	−5.80955	+	22.0279i	−0.338820	+	1.28469i
$295$	−18.9233			−1.10176
$296$	−2.78633	+	4.82606i	−0.161952	+	0.280509i
$297$	−14.0138	+	10.0307i	−0.813162	+	0.582038i
$298$	−20.1937	−	34.9764i	−1.16979	−	2.02613i
$299$	−3.17362	+	5.49688i	−0.183535	+	0.317893i
$300$	−3.43345	−	10.7931i	−0.198230	−	0.623141i
$301$	5.87226	+	1.70722i	0.338471	+	0.0984028i
$302$			43.1398i			2.48242i
$303$	−18.6146	−	4.07682i	−1.06938	−	0.234207i
$304$	2.51159	−	1.45007i	0.144050	−	0.0831671i
$305$	−14.5016	−	25.1175i	−0.830360	−	1.43823i
$306$	−2.94755	−	31.8143i	−0.168500	−	1.81870i
$307$			14.6773i			0.837677i	0.908061	+	0.418839i	$0.137563\pi$
$307$			14.6773i			0.837677i	−0.908061	+	0.418839i	$0.862437\pi$
$308$	0.833080	−	13.4040i	0.0474691	−	0.763763i
$309$	1.30554	+	4.10400i	0.0742697	+	0.233468i
$310$	−31.5148	−	18.1951i	−1.78992	−	1.03341i
$311$	−13.2520	+	7.65105i	−0.751453	+	0.433852i	−0.826219	−	0.563350i	$-0.809512\pi$
$311$	−13.2520	+	7.65105i	−0.751453	+	0.433852i	0.0747658	+	0.997201i	$0.476179\pi$
$312$	1.40517	+	1.28100i	0.0795521	+	0.0725224i
$313$	9.92967	−	17.1987i	0.561258	−	0.972127i	−0.436129	−	0.899884i	$-0.643651\pi$
$313$	9.92967	−	17.1987i	0.561258	−	0.972127i	0.997387	−	0.0722432i	$-0.0230158\pi$
$314$	21.3162			1.20294
$315$	−18.2640	−	15.8304i	−1.02906	−	0.891942i
$316$			5.90639i			0.332261i
$317$	−15.6174	−	9.01672i	−0.877161	−	0.506429i	−0.00743978	−	0.999972i	$-0.502368\pi$
$317$	−15.6174	−	9.01672i	−0.877161	−	0.506429i	−0.869721	+	0.493543i	$0.835702\pi$
$318$	−7.16633	−	6.53307i	−0.401868	−	0.366356i
$319$	1.46115	−	4.67802i	0.0818088	−	0.261919i
$320$	10.3017	+	5.94767i	0.575880	+	0.332485i
$321$	7.24318	+	22.7691i	0.404275	+	1.27085i
$322$	6.04406	+	24.6266i	0.336822	+	1.37239i
$323$			3.48374i			0.193841i
$324$	8.96147	+	10.4605i	0.497860	+	0.581140i
$325$	−4.60435	+	2.65833i	−0.255404	+	0.147457i
$326$	−12.7693	−	22.1172i	−0.707229	−	1.22496i
$327$	−1.28062	+	5.84728i	−0.0708184	+	0.323355i
$328$	−9.14336			−0.504857
$329$	20.6376	−	19.7835i	1.13779	−	1.09070i
$330$	28.5505	+	16.2844i	1.57165	+	0.896427i
$331$	−8.50642	+	14.7336i	−0.467555	+	0.809830i	−0.999313	−	0.0370671i	$-0.988198\pi$
$331$	−8.50642	+	14.7336i	−0.467555	+	0.809830i	0.531757	+	0.846897i	$0.321532\pi$
$332$	11.9907	+	20.7686i	0.658078	+	1.13982i
$333$	17.2152	+	7.92057i	0.943387	+	0.434044i
$334$	6.18083	−	10.7055i	0.338200	−	0.585779i
$335$		−	14.1148i		−	0.771175i
$336$	21.6165	−	0.541908i	1.17928	−	0.0295635i
$337$			23.4102i			1.27523i	0.770354	+	0.637616i	$0.220079\pi$
$337$			23.4102i			1.27523i	−0.770354	+	0.637616i	$0.779921\pi$
$338$	10.7585	−	18.6343i	0.585185	−	1.01357i
$339$	−10.2271	−	9.32337i	−0.555460	−	0.506376i
$340$	−22.8770	+	13.2080i	−1.24068	+	0.716305i
$341$	20.5818	−	4.62100i	1.11457	−	0.250241i
$342$	−2.00167	−	2.82776i	−0.108238	−	0.152908i
$343$	13.8990	−	12.2400i	0.750477	−	0.660897i
$344$		−	2.03916i		−	0.109944i
$345$	−26.2802	−	5.75566i	−1.41488	−	0.309874i
$346$	−2.15315	−	3.72937i	−0.115754	−	0.200492i
$347$	−11.4850	−	19.8925i	−0.616545	−	1.06789i	−0.990111	−	0.140283i	$-0.955199\pi$
$347$	−11.4850	−	19.8925i	−0.616545	−	1.06789i	0.373567	−	0.927603i	$-0.378135\pi$
$348$	−3.82642	−	0.838029i	−0.205118	−	0.0449231i
$349$		−	10.0181i		−	0.536258i	−0.963383	−	0.268129i	$-0.913595\pi$
$349$		−	10.0181i		−	0.536258i	0.963383	−	0.268129i	$-0.0864053\pi$
$350$	−5.92959	+	20.3957i	−0.316950	+	1.09020i
$351$	3.89667	−	5.15979i	0.207989	−	0.275409i
$352$	−22.9812	+	5.15971i	−1.22490	+	0.275014i
$353$	4.58642	−	2.64797i	0.244110	−	0.140937i	−0.372954	−	0.927850i	$-0.621655\pi$
$353$	4.58642	−	2.64797i	0.244110	−	0.140937i	0.617064	+	0.786913i	$0.288322\pi$
$354$	−14.9459	−	13.6251i	−0.794363	−	0.724168i
$355$	12.0429	−	20.8588i	0.639168	−	1.10707i
$356$		−	2.11277i		−	0.111977i
$357$	−12.4195	+	22.8132i	−0.657311	+	1.20740i
$358$			26.6262i			1.40724i
$359$	2.99188	−	5.18209i	0.157905	−	0.273500i	−0.776208	−	0.630477i	$-0.782859\pi$
$359$	2.99188	−	5.18209i	0.157905	−	0.273500i	0.934113	+	0.356977i	$0.116193\pi$
$360$	−3.36859	+	7.32156i	−0.177540	+	0.385880i
$361$	−9.31112	−	16.1273i	−0.490059	−	0.848807i
$362$	8.58446	−	14.8687i	0.451189	−	0.781483i
$363$	−18.5676	+	4.27127i	−0.974547	+	0.224184i
$364$	1.20100	+	4.89349i	0.0629495	+	0.256489i
$365$	3.57196			0.186965
$366$	6.63156	−	30.2795i	0.346637	−	1.58274i
$367$	−9.83094	−	17.0277i	−0.513171	−	0.888838i	−0.999883	−	0.0152759i	$-0.995137\pi$
$367$	−9.83094	−	17.0277i	−0.513171	−	0.888838i	0.486712	−	0.873562i	$-0.338196\pi$
$368$	20.8441	−	12.0344i	1.08658	−	0.627335i
$369$	2.86835	+	30.9595i	0.149321	+	1.61169i
$370$		−	36.1412i		−	1.87889i
$371$	1.87908	+	7.65634i	0.0975569	+	0.397497i
$372$	−5.11099	−	16.0665i	−0.264992	−	0.833009i
$373$	−16.8118	−	9.70627i	−0.870480	−	0.502572i	−0.00297207	−	0.999996i	$-0.500946\pi$
$373$	−16.8118	−	9.70627i	−0.870480	−	0.502572i	−0.867508	+	0.497424i	$0.834279\pi$
$374$	10.5311	−	33.7163i	0.544549	−	1.74343i
$375$	2.83516	+	2.58463i	0.146407	+	0.133470i
$376$	−8.25559	−	4.76637i	−0.425749	−	0.245807i
$377$			1.83876i			0.0947009i
$378$	−3.02689	−	25.6534i	−0.155686	−	1.31947i
$379$	2.78311			0.142959			0.0714795	−	0.997442i	$-0.477228\pi$
$379$	2.78311			0.142959			0.0714795	+	0.997442i	$0.477228\pi$
$380$	−1.43219	+	2.48063i	−0.0734700	+	0.127254i
$381$	15.2664	+	13.9174i	0.782121	+	0.713008i
$382$	2.58366	−	1.49168i	0.132192	−	0.0763210i
$383$	−7.16366	−	4.13594i	−0.366046	−	0.211337i	0.305684	−	0.952133i	$-0.401115\pi$
$383$	−7.16366	−	4.13594i	−0.366046	−	0.211337i	−0.671730	+	0.740796i	$0.734448\pi$
$384$	−3.60365	−	11.3281i	−0.183898	−	0.578087i
$385$	−11.8991	−	23.9249i	−0.606435	−	1.21933i
$386$		−	24.4488i		−	1.24441i
$387$	−6.90464	+	0.639704i	−0.350982	+	0.0325180i
$388$	−7.03745	−	12.1892i	−0.357272	−	0.618814i
$389$	−16.7647	+	9.67910i	−0.850004	+	0.490750i	−0.860652	−	0.509193i	$-0.829944\pi$
$389$	−16.7647	+	9.67910i	−0.850004	+	0.490750i	0.0106482	+	0.999943i	$0.496610\pi$
$390$	−12.0462	−	2.63825i	−0.609982	−	0.133593i
$391$			28.9122i			1.46215i
$392$	−5.21295	−	3.31094i	−0.263294	−	0.167228i
$393$	−1.62358	−	5.10375i	−0.0818987	−	0.257450i
$394$	0.107587	−	0.186346i	0.00542015	−	0.00938797i
$395$	5.87581	+	10.1772i	0.295644	+	0.512070i
$396$	4.69241	+	14.4870i	0.235803	+	0.728000i
$397$	7.01674	−	12.1534i	0.352160	−	0.609959i	−0.634467	−	0.772950i	$-0.718781\pi$
$397$	7.01674	−	12.1534i	0.352160	−	0.609959i	0.986628	+	0.162990i	$0.0521139\pi$
$398$	−44.8146			−2.24635
$399$	0.0705859	+	2.81565i	0.00353372	+	0.140959i
$400$	20.1607			1.00804
$401$	11.1606	+	6.44358i	0.557334	+	0.321777i	0.752075	−	0.659078i	$-0.229053\pi$
$401$	11.1606	+	6.44358i	0.557334	+	0.321777i	−0.194741	+	0.980855i	$0.562387\pi$
$402$	10.1629	−	11.1480i	0.506881	−	0.556014i
$403$	−6.85398	+	3.95715i	−0.341421	+	0.197120i
$404$	−8.41906	+	14.5822i	−0.418864	+	0.725494i
$405$	25.8477	+	9.10925i	1.28438	+	0.452642i
$406$	5.08344	+	5.30292i	0.252287	+	0.263179i
$407$	14.1950	+	15.4078i	0.703622	+	0.763734i
$408$	8.46066	+	1.85298i	0.418865	+	0.0917362i
$409$	6.17168	−	3.56322i	0.305170	−	0.176190i	−0.339593	−	0.940572i	$-0.610289\pi$
$409$	6.17168	−	3.56322i	0.305170	−	0.176190i	0.644763	+	0.764382i	$0.276956\pi$
$410$	51.3544	−	29.6495i	2.53621	−	1.46428i
$411$	−1.14785	+	5.24107i	−0.0566195	+	0.258523i
$412$	3.80544			0.187481
$413$	3.91894	+	15.9678i	0.192838	+	0.785724i
$414$	−16.6122	−	23.4681i	−0.816444	−	1.15339i
$415$	41.3220	+	23.8573i	2.02842	+	1.17111i
$416$	7.65300	−	4.41846i	0.375219	−	0.216633i
$417$	−15.5857	−	14.2084i	−0.763234	−	0.695790i
$418$	−0.839056	−	3.73714i	−0.0410396	−	0.182789i
$419$			27.8186i			1.35903i	0.733663	+	0.679514i	$0.237809\pi$
$419$			27.8186i			1.35903i	−0.733663	+	0.679514i	$0.762191\pi$
$420$	−18.2221	+	11.1386i	−0.889148	+	0.543507i
$421$	−17.5302			−0.854369			−0.427185	−	0.904164i	$-0.640495\pi$
$421$	−17.5302			−0.854369			−0.427185	+	0.904164i	$0.640495\pi$
$422$	−9.36453	−	5.40661i	−0.455858	−	0.263190i
$423$	−13.5491	+	29.4488i	−0.658781	+	1.43185i
$424$	2.27656	−	1.31438i	0.110560	−	0.0638317i
$425$	−12.1089	+	20.9732i	−0.587367	+	1.01735i
$426$	24.5303	−	7.80345i	1.18850	−	0.378078i
$427$	−18.1913	+	17.4384i	−0.880340	+	0.843904i
$428$	21.1127			1.02052
$429$	6.17175	−	3.60659i	0.297975	−	0.174128i
$430$	6.61246	+	11.4531i	0.318881	+	0.552318i
$431$	6.45778	+	11.1852i	0.311060	+	0.538772i	0.978592	−	0.205809i	$-0.0659826\pi$
$431$	6.45778	+	11.1852i	0.311060	+	0.538772i	−0.667532	+	0.744581i	$0.732649\pi$
$432$	−22.5795	+	9.55648i	−1.08636	+	0.459786i
$433$	6.99731			0.336269			0.168135	−	0.985764i	$-0.446226\pi$
$433$	6.99731			0.336269			0.168135	+	0.985764i	$0.446226\pi$
$434$	−8.82671	+	30.3608i	−0.423695	+	1.45737i
$435$	−7.42692	+	2.36261i	−0.356094	+	0.113279i
$436$	4.58061	+	2.64462i	0.219371	+	0.126654i
$437$	1.56753	+	2.71504i	0.0749851	+	0.129878i
$438$	2.82117	+	2.57187i	0.134801	+	0.122889i
$439$	10.1810	+	5.87802i	0.485914	+	0.280543i	0.722878	−	0.690976i	$-0.242819\pi$
$439$	10.1810	+	5.87802i	0.485914	+	0.280543i	−0.236964	+	0.971519i	$0.576152\pi$
$440$	−6.55286	+	6.03710i	−0.312396	+	0.287807i
$441$	−9.57554	+	18.6898i	−0.455978	+	0.889991i
$442$			13.2526i			0.630364i
$443$	−8.29921	−	4.79155i	−0.394307	−	0.227653i	0.289717	−	0.957112i	$-0.406439\pi$
$443$	−8.29921	−	4.79155i	−0.394307	−	0.227653i	−0.684025	+	0.729459i	$0.739772\pi$
$444$	11.2808	−	12.3742i	0.535363	−	0.587256i
$445$	−2.10183	−	3.64048i	−0.0996364	−	0.172575i
$446$	−10.2506	+	17.7545i	−0.485379	+	0.840701i
$447$	−11.2860	−	35.4778i	−0.533810	−	1.67804i
$448$	2.88530	−	9.92443i	0.136318	−	0.468885i
$449$			30.0895i			1.42001i	0.704197	+	0.710005i	$0.251307\pi$
$449$			30.0895i			1.42001i	−0.704197	+	0.710005i	$0.748693\pi$
$450$	−2.22184	−	23.9814i	−0.104739	−	1.13049i
$451$	−10.2481	+	32.8104i	−0.482566	+	1.54498i
$452$	−10.5901	+	6.11422i	−0.498118	+	0.287589i
$453$	−8.50777	+	38.8462i	−0.399730	+	1.82516i
$454$	15.2156			0.714104
$455$	6.93757	+	7.23710i	0.325238	+	0.339281i
$456$	0.894973	−	0.284704i	0.0419109	−	0.0133325i
$457$	−35.4804	−	20.4846i	−1.65970	−	0.958230i	−0.972851	−	0.231434i	$-0.925658\pi$
$457$	−35.4804	−	20.4846i	−1.65970	−	0.958230i	−0.686853	−	0.726796i	$-0.741008\pi$
$458$	0.850112	+	1.47244i	0.0397231	+	0.0688025i
$459$	3.62003	−	29.2292i	0.168969	−	1.36430i
$460$	−11.8860	+	20.5872i	−0.554190	+	0.959884i
$461$	−5.45941			−0.254270			−0.127135	−	0.991885i	$-0.540578\pi$
$461$	−5.45941			−0.254270			−0.127135	+	0.991885i	$0.540578\pi$
$462$	7.82834	−	27.4637i	0.364207	−	1.27773i
$463$	6.44042			0.299312			0.149656	−	0.988738i	$-0.452183\pi$
$463$	6.44042			0.299312			0.149656	+	0.988738i	$0.452183\pi$
$464$	3.48628	−	6.03842i	0.161847	−	0.280327i
$465$	−24.7899	−	22.5993i	−1.14961	−	1.04802i
$466$	−0.374117	−	0.647990i	−0.0173306	−	0.0300176i
$467$	2.59974	+	1.50096i	0.120301	+	0.0694561i	0.558943	−	0.829206i	$-0.311207\pi$
$467$	2.59974	+	1.50096i	0.120301	+	0.0694561i	−0.438642	+	0.898662i	$0.644540\pi$
$468$	−3.30096	−	4.66328i	−0.152587	−	0.215560i
$469$	−11.9103	+	2.92312i	−0.549966	+	0.134977i
$470$	61.8242			2.85174
$471$	19.1947	+	4.20385i	0.884443	+	0.193703i
$472$	4.74792	−	2.74122i	0.218541	−	0.126175i
$473$	−7.31742	−	2.28555i	−0.336455	−	0.105090i
$474$	−2.68699	+	12.2687i	−0.123418	+	0.563522i
$475$			2.62602i			0.120490i
$476$	15.8828	+	16.5686i	0.727989	+	0.759420i
$477$	−5.16467	−	7.29615i	−0.236474	−	0.334068i
$478$	−17.7380	+	30.7232i	−0.811319	+	1.40525i
$479$	−10.7538	−	18.6261i	−0.491353	−	0.851049i	0.508597	−	0.861005i	$-0.330164\pi$
$479$	−10.7538	−	18.6261i	−0.491353	−	0.851049i	−0.999950	+	0.00995594i	$0.996831\pi$
$480$	27.6799	+	25.2339i	1.26341	+	1.15177i
$481$	−6.80709	−	3.93007i	−0.310377	−	0.179196i
$482$		−	5.68377i		−	0.258888i
$483$	0.585805	+	23.3676i	0.0266551	+	1.06326i
$484$	−1.37704	+	16.7788i	−0.0625926	+	0.762673i
$485$	−24.2522	−	14.0020i	−1.10124	−	0.635798i
$486$	13.8559	+	25.8054i	0.628519	+	1.17056i
$487$	16.6319	+	28.8073i	0.753665	+	1.30539i	0.946035	+	0.324063i	$0.105049\pi$
$487$	16.6319	+	28.8073i	0.753665	+	1.30539i	−0.192371	+	0.981322i	$0.561618\pi$
$488$	7.27700	+	4.20138i	0.329415	+	0.190188i
$489$	−7.13664	−	22.4342i	−0.322730	−	1.01451i
$490$	40.0154	+	1.69194i	1.80771	+	0.0764340i
$491$	3.76057			0.169712			0.0848562	−	0.996393i	$-0.472957\pi$
$491$	3.76057			0.169712			0.0848562	+	0.996393i	$0.472957\pi$
$492$	26.8375	+	5.87772i	1.20993	+	0.264988i
$493$	4.18784	+	7.25356i	0.188611	+	0.326684i
$494$	0.718517	+	1.24451i	0.0323276	+	0.0559930i
$495$	22.4974	+	20.2942i	1.01118	+	0.912157i
$496$	30.0110			1.34753
$497$	−20.0950	−	5.84216i	−0.901385	−	0.262057i
$498$	15.4589	+	48.5954i	0.692730	+	2.17761i
$499$	−1.01365	+	1.75570i	−0.0453773	+	0.0785958i	−0.887822	−	0.460187i	$-0.847782\pi$
$499$	−1.01365	+	1.75570i	−0.0453773	+	0.0785958i	0.842445	+	0.538783i	$0.181116\pi$
$500$	2.93580	−	1.69498i	0.131293	−	0.0758020i
$501$	7.67694	−	8.42107i	0.342980	−	0.376226i
$502$	−12.6967	−	7.33044i	−0.566681	−	0.327173i
$503$	12.6627			0.564602			0.282301	−	0.959326i	$-0.408902\pi$
$503$	12.6627			0.564602			0.282301	+	0.959326i	$0.408902\pi$
$504$	6.87566	+	1.32620i	0.306266	+	0.0590736i
$505$			33.5018i			1.49081i
$506$	−6.96348	−	31.0152i	−0.309564	−	1.37879i
$507$	13.3627	−	14.6579i	0.593457	−	0.650981i
$508$	15.8083	−	9.12693i	0.701381	−	0.404942i
$509$	−24.5196	−	14.1564i	−1.08681	−	0.627471i	−0.154086	−	0.988057i	$-0.549243\pi$
$509$	−24.5196	−	14.1564i	−1.08681	−	0.627471i	−0.932726	+	0.360586i	$0.882577\pi$
$510$	−53.5287	+	17.0282i	−2.37029	+	0.754023i
$511$	−0.739737	−	3.01407i	−0.0327240	−	0.133335i
$512$	−25.1839			−1.11298
$513$	−1.24477	−	2.94108i	−0.0549581	−	0.129852i
$514$	16.9568	−	9.78999i	0.747930	−	0.431818i
$515$	6.55709	−	3.78574i	0.288940	−	0.166819i
$516$	−1.31086	+	5.98534i	−0.0577072	+	0.263490i
$517$	−26.3569	+	24.2824i	−1.15918	+	1.06794i
$518$	−30.4965	+	7.48469i	−1.33994	+	0.328859i
$519$	−1.20337	−	3.78282i	−0.0528221	−	0.166047i
$520$	1.67145	−	2.89503i	0.0732978	−	0.126955i
$521$	4.46847	−	2.57987i	0.195767	−	0.113026i	−0.398912	−	0.916989i	$-0.630612\pi$
$521$	4.46847	−	2.57987i	0.195767	−	0.113026i	0.594680	+	0.803963i	$0.297279\pi$
$522$	−7.56698	−	3.48150i	−0.331198	−	0.152381i
$523$	−1.50137	−	0.866814i	−0.0656502	−	0.0379031i	0.466816	−	0.884355i	$-0.345401\pi$
$523$	−1.50137	−	0.866814i	−0.0656502	−	0.0379031i	−0.532466	+	0.846452i	$0.678735\pi$
$524$	−4.73247			−0.206739
$525$	−9.36175	+	17.1964i	−0.408580	+	0.750513i
$526$	58.0781			2.53232
$527$	−18.0251	+	31.2204i	−0.785186	+	1.35998i
$528$	−27.1059	+	0.142282i	−1.17963	+	0.00619204i
$529$	1.50921	+	2.61402i	0.0656177	+	0.113653i
$530$	−8.52433	+	14.7646i	−0.370273	+	0.641332i
$531$	−10.7713	−	15.2166i	−0.467433	−	0.660344i
$532$	2.38980	+	0.694778i	0.103611	+	0.0301225i
$533$		−	12.8966i		−	0.558613i
$534$	0.961163	−	4.38865i	0.0415936	−	0.189915i
$535$	36.3789	−	21.0034i	1.57280	−	0.908054i
$536$	2.04466	+	3.54145i	0.0883158	+	0.152968i
$537$	−5.25105	+	23.9762i	−0.226599	+	1.03465i
$538$		−	15.1987i		−	0.655262i
$539$	−17.7239	+	14.9954i	−0.763424	+	0.645897i
$540$	14.5940	−	19.3247i	0.628028	−	0.831604i
$541$	21.1393	+	12.2048i	0.908850	+	0.524725i	0.880061	−	0.474861i	$-0.157502\pi$
$541$	21.1393	+	12.2048i	0.908850	+	0.524725i	0.0287892	+	0.999586i	$0.490835\pi$
$542$	−22.3639	+	12.9118i	−0.960612	+	0.554610i
$543$	10.6624	−	11.6959i	0.457567	−	0.501919i
$544$	20.1264	−	34.8600i	0.862914	−	1.49461i
$545$	10.5237			0.450785
$546$	0.268519	+	10.7111i	0.0114915	+	0.458394i
$547$		−	22.7953i		−	0.974657i	−0.873219	−	0.487329i	$-0.837971\pi$
$547$		−	22.7953i		−	0.974657i	0.873219	−	0.487329i	$-0.162029\pi$
$548$	4.10572	+	2.37044i	0.175388	+	0.101260i
$549$	11.9431	−	25.9581i	0.509718	−	1.10786i
$550$	7.93825	−	25.4151i	0.338488	−	1.08370i
$551$	0.786530	+	0.454104i	0.0335073	+	0.0193455i
$552$	7.42754	−	2.36281i	0.316137	−	0.100568i
$553$	7.37081	−	7.06575i	0.313439	−	0.300466i
$554$		−	51.3295i		−	2.18078i
$555$	7.12755	−	32.5442i	0.302547	−	1.38142i
$556$	−16.1389	+	9.31782i	−0.684443	+	0.395163i
$557$	−9.05269	−	15.6797i	−0.383575	−	0.664371i	0.607995	−	0.793941i	$-0.291974\pi$
$557$	−9.05269	−	15.6797i	−0.383575	−	0.664371i	−0.991570	+	0.129569i	$0.958641\pi$
$558$	−3.30740	−	35.6984i	−0.140014	−	1.51123i
$559$	2.87621			0.121651
$560$	−9.06120	−	36.9200i	−0.382906	−	1.56016i
$561$	16.1323	−	28.2837i	0.681105	−	1.19414i
$562$	0.121817	−	0.210993i	0.00513853	−	0.00890019i
$563$	12.5996	+	21.8232i	0.531011	+	0.919737i	0.999345	+	0.0361860i	$0.0115209\pi$
$563$	12.5996	+	21.8232i	0.531011	+	0.919737i	−0.468335	+	0.883551i	$0.655146\pi$
$564$	21.1677	+	19.2972i	0.891322	+	0.812560i
$565$	−12.1651	+	21.0706i	−0.511790	+	0.886446i
$566$		−	54.4173i		−	2.28733i
$567$	2.33357	−	23.6971i	0.0980008	−	0.995186i
$568$			6.97806i			0.292793i
$569$	−5.47239	+	9.47846i	−0.229415	+	0.397358i	−0.957635	−	0.287986i	$-0.907014\pi$
$569$	−5.47239	+	9.47846i	−0.229415	+	0.397358i	0.728220	+	0.685343i	$0.240348\pi$
$570$	−4.10346	+	4.50122i	−0.171875	+	0.188535i
$571$	−13.1413	+	7.58714i	−0.549946	+	0.317512i	−0.749100	−	0.662456i	$-0.769514\pi$
$571$	−13.1413	+	7.58714i	−0.549946	+	0.317512i	0.199154	+	0.979968i	$0.436181\pi$
$572$	−1.38369	−	6.16294i	−0.0578552	−	0.257686i
$573$	2.62070	−	0.833683i	0.109481	−	0.0348276i
$574$	−35.6539	−	37.1933i	−1.48817	−	1.55242i
$575$			21.7938i			0.908865i
$576$	1.08113	+	11.6692i	0.0450472	+	0.486216i
$577$	−0.568986	−	0.985512i	−0.0236872	−	0.0410274i	0.853939	−	0.520373i	$-0.174207\pi$
$577$	−0.568986	−	0.985512i	−0.0236872	−	0.0410274i	−0.877626	+	0.479346i	$0.840874\pi$
$578$	14.2123	+	24.6164i	0.591152	+	1.02391i
$579$	4.82164	−	22.0155i	0.200380	−	0.914932i
$580$			6.88663i			0.285952i
$581$	11.5735	−	39.8089i	0.480150	−	1.65155i
$582$	−9.07293	−	28.5209i	−0.376085	−	1.18223i
$583$	−2.16492	−	9.64251i	−0.0896619	−	0.399352i
$584$	−0.896215	+	0.517430i	−0.0370856	+	0.0214114i
$585$	−10.3270	−	4.75135i	−0.426967	−	0.196444i
$586$	4.50027	−	7.79470i	0.185904	−	0.321996i
$587$			21.1025i			0.870991i	0.900191	+	0.435496i	$0.143427\pi$
$587$			21.1025i			0.870991i	−0.900191	+	0.435496i	$0.856573\pi$
$588$	13.1726	+	13.0693i	0.543229	+	0.538971i
$589$			3.90906i			0.161070i
$590$	−17.7781	+	30.7925i	−0.731911	+	1.26771i
$591$	0.133629	−	0.146582i	0.00549676	−	0.00602957i
$592$	14.9028	+	25.8124i	0.612502	+	1.06089i
$593$	17.5906	−	30.4678i	0.722359	−	1.25116i	−0.237692	−	0.971341i	$-0.576391\pi$
$593$	17.5906	−	30.4678i	0.722359	−	1.25116i	0.960052	−	0.279823i	$-0.0902757\pi$
$594$	3.15649	+	32.2271i	0.129512	+	1.32229i
$595$	43.8502	+	12.7484i	1.79768	+	0.522635i
$596$	−32.8969			−1.34751
$597$	−40.3544	−	8.83806i	−1.65159	−	0.361718i
$598$	5.96310	+	10.3284i	0.243849	+	0.422359i
$599$	−5.52855	+	3.19191i	−0.225890	+	0.130418i	−0.608675	−	0.793420i	$-0.708299\pi$
$599$	−5.52855	+	3.19191i	−0.225890	+	0.130418i	0.382784	+	0.923838i	$0.374965\pi$
$600$	6.37759	+	1.39676i	0.260364	+	0.0570226i
$601$			10.8370i			0.442050i	0.975268	+	0.221025i	$0.0709402\pi$
$601$			10.8370i			0.442050i	−0.975268	+	0.221025i	$0.929060\pi$
$602$	8.29489	−	7.95158i	0.338075	−	0.324082i
$603$	11.3500	−	8.03424i	0.462207	−	0.327179i
$604$	30.4312	+	17.5694i	1.23823	+	0.714890i
$605$	14.3192	+	30.2811i	0.582157	+	1.23110i
$606$	−24.1219	+	26.4601i	−0.979887	+	1.07487i
$607$	−19.0804	−	11.0161i	−0.774450	−	0.447129i	0.0600101	−	0.998198i	$-0.480887\pi$
$607$	−19.0804	−	11.0161i	−0.774450	−	0.447129i	−0.834460	+	0.551069i	$0.814220\pi$
$608$		−	4.36477i		−	0.177015i
$609$	3.53169	+	5.77766i	0.143111	+	0.234122i
$610$	−54.4958			−2.20647
$611$	6.72289	−	11.6444i	0.271979	−	0.471082i
$612$	−23.6425	−	10.8777i	−0.955691	−	0.439705i
$613$	−2.01225	+	1.16177i	−0.0812739	+	0.0469235i	−0.540086	−	0.841610i	$-0.681608\pi$
$613$	−2.01225	+	1.16177i	−0.0812739	+	0.0469235i	0.458812	+	0.888533i	$0.348275\pi$
$614$	23.8832	+	13.7890i	0.963849	+	0.556478i
$615$	52.0905	−	16.5707i	2.10049	−	0.668197i
$616$	6.45126	+	4.27914i	0.259929	+	0.172412i
$617$			6.99701i			0.281689i	0.990032	+	0.140845i	$0.0449818\pi$
$617$			6.99701i			0.281689i	−0.990032	+	0.140845i	$0.955018\pi$
$618$	7.90466	+	1.73121i	0.317972	+	0.0696394i
$619$	6.40585	+	11.0953i	0.257473	+	0.445956i	0.965564	−	0.260165i	$-0.0837768\pi$
$619$	6.40585	+	11.0953i	0.257473	+	0.445956i	−0.708091	+	0.706121i	$0.750444\pi$
$620$	−25.6699	+	14.8205i	−1.03093	+	0.595207i
$621$	−10.3306	−	24.4085i	−0.414552	−	0.979480i
$622$			28.7520i			1.15285i
$623$	−2.63661	+	2.52748i	−0.105634	+	0.101262i
$624$	9.69139	−	3.08297i	0.387966	−	0.123418i
$625$	14.0539	−	24.3421i	0.562157	−	0.973685i
$626$	−18.6574	−	32.3156i	−0.745700	−	1.29159i
$627$	−0.0185329	−	3.53066i	−0.000740132	−	0.141001i
$628$	8.68139	−	15.0366i	0.346425	−	0.600026i
$629$	−35.8036			−1.42758
$630$	−42.9182	+	14.8472i	−1.70990	+	0.591528i
$631$	−40.1391			−1.59791			−0.798957	−	0.601388i	$-0.794615\pi$
$631$	−40.1391			−1.59791			−0.798957	+	0.601388i	$0.794615\pi$
$632$	−2.94852	−	1.70233i	−0.117286	−	0.0677149i
$633$	−7.36624	−	6.71532i	−0.292782	−	0.266910i
$634$	−29.3444	+	16.9420i	−1.16542	+	0.672853i
$635$	18.1593	−	31.4529i	0.720631	−	1.24817i
$636$	−7.52709	+	2.39448i	−0.298468	+	0.0949472i
$637$	4.67003	−	7.35280i	0.185033	−	0.291328i
$638$	−6.23946	−	6.77251i	−0.247023	−	0.268126i
$639$	23.6278	−	2.18908i	0.934702	−	0.0865988i
$640$	−18.0993	+	10.4496i	−0.715438	+	0.413058i
$641$	42.8336	−	24.7300i	1.69183	−	0.976776i	0.738781	−	0.673946i	$-0.235402\pi$
$641$	42.8336	−	24.7300i	1.69183	−	0.976776i	0.953045	−	0.302830i	$-0.0979314\pi$
$642$	43.8552	+	9.60479i	1.73083	+	0.379071i
$643$	−9.38943			−0.370283			−0.185141	−	0.982712i	$-0.559274\pi$
$643$	−9.38943			−0.370283			−0.185141	+	0.982712i	$0.559274\pi$
$644$	19.8334	+	5.76609i	0.781544	+	0.227216i
$645$	3.69563	+	11.6173i	0.145515	+	0.457430i
$646$	5.66883	+	3.27290i	0.223037	+	0.128770i
$647$	−26.9444	+	15.5564i	−1.05929	+	0.611584i	−0.925237	−	0.379390i	$-0.876134\pi$
$647$	−26.9444	+	15.5564i	−1.05929	+	0.611584i	−0.134058	+	0.990974i	$0.542801\pi$
$648$	−7.80482	+	1.45873i	−0.306602	+	0.0573044i
$649$	−4.51509	−	20.1101i	−0.177233	−	0.789390i
$650$			9.98975i			0.391830i
$651$	−13.9358	+	25.5983i	−0.546186	+	1.00328i
$652$	−20.8021			−0.814675
$653$	40.2088	+	23.2146i	1.57349	+	0.908456i	0.995736	+	0.0922467i	$0.0294048\pi$
$653$	40.2088	+	23.2146i	1.57349	+	0.908456i	0.577756	+	0.816210i	$0.303929\pi$
$654$	8.31171	+	7.57724i	0.325014	+	0.296294i
$655$	−8.15442	+	4.70796i	−0.318620	+	0.183955i
$656$	−24.4519	+	42.3519i	−0.954685	+	1.65356i
$657$	2.03318	+	2.87227i	0.0793218	+	0.112058i
$658$	−12.8035	−	52.1682i	−0.499133	−	2.03373i
$659$	0.495294			0.0192939			0.00964695	−	0.999953i	$-0.496929\pi$
$659$	0.495294			0.0192939			0.00964695	+	0.999953i	$0.496929\pi$
$660$	23.1148	−	13.5076i	0.899743	−	0.525783i
$661$	20.7038	+	35.8600i	0.805283	+	1.39479i	0.916100	+	0.400951i	$0.131320\pi$
$661$	20.7038	+	35.8600i	0.805283	+	1.39479i	−0.110816	+	0.993841i	$0.535346\pi$
$662$	15.9832	+	27.6837i	0.621204	+	1.07596i
$663$	−2.61360	+	11.9336i	−0.101504	+	0.463464i
$664$	−13.8238			−0.536466
$665$	4.80899	−	1.18026i	0.186485	−	0.0457686i
$666$	29.0618	−	20.5718i	1.12612	−	0.797141i
$667$	6.52756	+	3.76869i	0.252748	+	0.145924i
$668$	−5.03450	−	8.72000i	−0.194791	−	0.337387i
$669$	−12.7318	+	13.9659i	−0.492240	+	0.539953i
$670$	−22.9680	−	13.2606i	−0.887330	−	0.512300i
$671$	23.2327	−	21.4041i	0.896888	−	0.826296i
$672$	15.5604	−	28.5825i	0.600255	−	1.10260i
$673$		−	16.3937i		−	0.631930i	−0.948771	−	0.315965i	$-0.897672\pi$
$673$		−	16.3937i		−	0.631930i	0.948771	−	0.315965i	$-0.102328\pi$
$674$	38.0936	+	21.9933i	1.46731	+	0.847151i
$675$	2.72875	−	22.0328i	0.105030	−	0.848042i
$676$	−8.76317	−	15.1783i	−0.337045	−	0.583779i
$677$	3.90912	−	6.77079i	0.150239	−	0.260222i	−0.781076	−	0.624436i	$-0.785329\pi$
$677$	3.90912	−	6.77079i	0.150239	−	0.260222i	0.931315	+	0.364214i	$0.118662\pi$
$678$	−24.7793	+	7.88267i	−0.951645	+	0.302732i
$679$	−6.79258	+	23.3641i	−0.260675	+	0.896632i
$680$		−	15.2271i		−	0.583934i
$681$	13.7012	+	3.00073i	0.525033	+	0.114988i
$682$	11.8168	−	37.8326i	0.452488	−	1.44868i
$683$	−25.9035	+	14.9554i	−0.991171	+	0.572253i	−0.905624	−	0.424081i	$-0.860597\pi$
$683$	−25.9035	+	14.9554i	−0.991171	+	0.572253i	−0.0855471	+	0.996334i	$0.527264\pi$
$684$	−2.80994	+	0.260336i	−0.107441	+	0.00995421i
$685$	9.43266			0.360403
$686$	−6.85934	−	34.1160i	−0.261891	−	1.30256i
$687$	0.475118	+	1.49354i	0.0181269	+	0.0569822i
$688$	−9.44537	−	5.45329i	−0.360101	−	0.207905i
$689$	1.85391	+	3.21106i	0.0706283	+	0.122332i
$690$	−34.0554	+	37.3564i	−1.29647	+	1.42213i
$691$	−8.58042	+	14.8617i	−0.326415	+	0.565367i	−0.981798	−	0.189930i	$-0.939174\pi$
$691$	−8.58042	+	14.8617i	−0.326415	+	0.565367i	0.655383	+	0.755297i	$0.272507\pi$
$692$	−3.50763			−0.133340
$693$	12.4654	−	23.1865i	0.473523	−	0.880782i
$694$	−43.1594			−1.63831
$695$	−18.5391	+	32.1107i	−0.703229	+	1.21803i
$696$	1.52119	−	1.66864i	0.0576606	−	0.0632497i
$697$	−29.3724	−	50.8746i	−1.11256	−	1.92701i
$698$	−16.3017	−	9.41180i	−0.617029	−	0.356242i
$699$	−0.209090	−	0.657278i	−0.00790851	−	0.0248606i
$700$	11.9724	+	12.4893i	0.452513	+	0.472051i
$701$	−26.0963			−0.985644			−0.492822	−	0.870130i	$-0.664035\pi$
$701$	−26.0963			−0.985644			−0.492822	+	0.870130i	$0.664035\pi$
$702$	−4.73529	−	11.1883i	−0.178722	−	0.422274i
$703$	−3.36218	+	1.94116i	−0.126807	+	0.0732122i
$704$	−3.86270	+	12.3668i	−0.145581	+	0.466092i
$705$	55.6710	+	12.1926i	2.09669	+	0.459199i
$706$		−	9.95083i		−	0.374505i
$707$	28.2693	−	6.93809i	1.06318	−	0.260934i
$708$	−15.6982	+	4.99384i	−0.589976	+	0.187680i
$709$	−17.8611	+	30.9363i	−0.670786	+	1.16184i	0.306895	+	0.951743i	$0.400710\pi$
$709$	−17.8611	+	30.9363i	−0.670786	+	1.16184i	−0.977681	+	0.210093i	$0.932623\pi$
$710$	−22.6280	−	39.1928i	−0.849213	−	1.47088i
$711$	−4.83913	+	10.5178i	−0.181481	+	0.394447i
$712$	1.05471	+	0.608938i	0.0395270	+	0.0228209i
$713$			32.4420i			1.21496i
$714$	25.4542	+	41.6418i	0.952601	+	1.55840i
$715$	−8.51525	−	9.24272i	−0.318452	−	0.345658i
$716$	18.7823	+	10.8440i	0.701928	+	0.405258i
$717$	−22.0317	+	24.1672i	−0.822787	+	0.902541i
$718$	−5.62161	−	9.73692i	−0.209797	−	0.363378i
$719$	−15.2790	−	8.82134i	−0.569811	−	0.328980i	0.187263	−	0.982310i	$-0.440038\pi$
$719$	−15.2790	−	8.82134i	−0.569811	−	0.328980i	−0.757074	+	0.653329i	$0.773372\pi$
$720$	24.9048	+	35.1831i	0.928149	+	1.31120i
$721$	−4.55240	−	4.74896i	−0.169540	−	0.176860i
$722$	−34.9904			−1.30221
$723$	1.12092	−	5.11808i	0.0416873	−	0.190343i
$724$	−6.99234	−	12.1111i	−0.259868	−	0.450105i
$725$	3.15677	+	5.46768i	0.117239	+	0.203065i
$726$	−10.4935	+	34.2264i	−0.389452	+	1.27026i
$727$	−9.23458			−0.342492			−0.171246	−	0.985228i	$-0.554779\pi$
$727$	−9.23458			−0.342492			−0.171246	+	0.985228i	$0.554779\pi$
$728$	−2.78902	−	0.810843i	−0.103368	−	0.0300518i
$729$	7.38773	+	25.9696i	0.273620	+	0.961838i
$730$	3.35577	−	5.81237i	0.124203	−	0.215125i
$731$	11.3461	−	6.55068i	0.419651	−	0.242286i
$732$	−18.6586	−	17.0098i	−0.689641	−	0.628701i
$733$	−6.55078	−	3.78209i	−0.241958	−	0.139695i	0.374118	−	0.927381i	$-0.377945\pi$
$733$	−6.55078	−	3.78209i	−0.241958	−	0.139695i	−0.616077	+	0.787686i	$0.711279\pi$
$734$	−36.9438			−1.36362
$735$	35.6991	+	9.41514i	1.31678	+	0.347282i
$736$		−	36.2240i		−	1.33523i
$737$	15.0000	−	3.36778i	0.552533	−	0.124054i
$738$	53.0728	+	24.4183i	1.95364	+	0.898852i
$739$	−10.4826	+	6.05211i	−0.385607	+	0.222631i	−0.680255	−	0.732975i	$-0.738131\pi$
$739$	−10.4826	+	6.05211i	−0.385607	+	0.222631i	0.294648	+	0.955606i	$0.404798\pi$
$740$	−25.4943	−	14.7191i	−0.937189	−	0.541086i
$741$	0.401571	+	1.26235i	0.0147521	+	0.0463735i
$742$	14.2239	+	4.13528i	0.522177	+	0.151811i
$743$	−42.7206			−1.56727			−0.783633	−	0.621224i	$-0.786636\pi$
$743$	−42.7206			−1.56727			−0.783633	+	0.621224i	$0.786636\pi$
$744$	9.49359	+	2.07920i	0.348052	+	0.0762273i
$745$	−56.6840	+	32.7265i	−2.07674	+	1.19901i
$746$	−31.5885	+	18.2377i	−1.15654	+	0.667728i
$747$	4.33664	+	46.8075i	0.158670	+	1.71260i
$748$	−19.4948	−	21.1602i	−0.712799	−	0.773695i
$749$	−25.2568	−	26.3473i	−0.922865	−	0.962710i
$750$	6.86933	−	2.18524i	0.250833	−	0.0797935i
$751$	22.0949	−	38.2695i	0.806255	−	1.39647i	−0.109186	−	0.994021i	$-0.534824\pi$
$751$	22.0949	−	38.2695i	0.806255	−	1.39647i	0.915441	−	0.402453i	$-0.131842\pi$
$752$	−44.1555	+	25.4932i	−1.61018	+	0.929641i
$753$	−9.98736	−	9.10482i	−0.363960	−	0.331798i
$754$	2.99207	+	1.72747i	0.108965	+	0.0629109i
$755$	69.9138			2.54442
$756$	−19.3289	−	8.31260i	−0.702984	−	0.302326i
$757$	41.7862			1.51875			0.759373	−	0.650656i	$-0.225506\pi$
$757$	41.7862			1.51875			0.759373	+	0.650656i	$0.225506\pi$
$758$	2.61467	−	4.52875i	0.0949692	−	0.164491i
$759$	−0.153808	−	29.3016i	−0.00558287	−	1.06358i
$760$	−0.825567	−	1.42992i	−0.0299465	−	0.0518688i
$761$	19.0611	−	33.0148i	0.690965	−	1.19679i	−0.280556	−	0.959838i	$-0.590519\pi$
$761$	19.0611	−	33.0148i	0.690965	−	1.19679i	0.971522	−	0.236950i	$-0.0761477\pi$
$762$	36.9891	−	11.7668i	1.33997	−	0.426265i
$763$	−2.17941	−	8.88004i	−0.0788999	−	0.321479i
$764$		−	2.43005i		−	0.0879161i
$765$	−51.5593	+	4.77689i	−1.86413	+	0.172709i
$766$	−13.4602	+	7.77125i	−0.486337	+	0.280787i
$767$	3.86645	+	6.69688i	0.139609	+	0.241810i
$768$	−35.0378	−	7.67367i	−1.26432	−	0.276900i
$769$			36.9953i			1.33408i	0.745020	+	0.667042i	$0.232440\pi$
$769$			36.9953i			1.33408i	−0.745020	+	0.667042i	$0.767560\pi$
$770$	−50.1101	−	3.11443i	−1.80584	−	0.112236i
$771$	17.1998	−	5.47151i	0.619436	−	0.197052i
$772$	−17.2464	−	9.95719i	−0.620710	−	0.358367i
$773$	36.9288	−	21.3208i	1.32824	−	0.766857i	0.343209	−	0.939259i	$-0.388486\pi$
$773$	36.9288	−	21.3208i	1.32824	−	0.766857i	0.985027	+	0.172402i	$0.0551527\pi$
$774$	−5.44581	+	11.8364i	−0.195746	+	0.425450i
$775$	−13.5872	+	23.5337i	−0.488067	+	0.845356i
$776$	8.11327			0.291249
$777$	−28.9374	+	0.725435i	−1.03812	+	0.0260248i
$778$			36.3732i			1.30404i
$779$	−5.51652	−	3.18496i	−0.197650	−	0.114113i
$780$	−6.76706	+	7.42300i	−0.242300	+	0.265786i
$781$	25.0404	+	7.82121i	0.896015	+	0.279865i
$782$	47.0466	+	27.1624i	1.68238	+	0.971324i
$783$	−6.12726	−	4.62731i	−0.218970	−	0.165367i
$784$	−29.2771	+	15.2919i	−1.04561	+	0.546141i
$785$		−	34.5457i		−	1.23299i
$786$	−9.83026	−	2.15294i	−0.350634	−	0.0767928i
$787$	40.3211	−	23.2794i	1.43729	−	0.829820i	0.439630	−	0.898179i	$-0.355110\pi$
$787$	40.3211	−	23.2794i	1.43729	−	0.829820i	0.997661	+	0.0683592i	$0.0217764\pi$
$788$	−0.0876332	−	0.151785i	−0.00312180	−	0.00540712i
$789$	52.2977	+	11.4538i	1.86185	+	0.407766i
$790$	22.0808			0.785598
$791$	20.2990	+	5.90147i	0.721750	+	0.209832i
$792$	−8.58447	−	1.83293i	−0.305036	−	0.0651302i
$793$	−5.92599	+	10.2641i	−0.210438	+	0.364489i
$794$	−13.1841	−	22.8356i	−0.467888	−	0.810406i
$795$	−10.5877	+	11.6140i	−0.375507	+	0.411906i
$796$	−18.2515	+	31.6126i	−0.646908	+	1.12048i
$797$			43.3952i			1.53714i	0.639768	+	0.768568i	$0.279030\pi$
$797$			43.3952i			1.53714i	−0.639768	+	0.768568i	$0.720970\pi$
$798$	4.64800	+	2.53038i	0.164538	+	0.0895745i
$799$		−	61.2466i		−	2.16675i
$800$	15.1712	−	26.2772i	0.536382	−	0.929040i
$801$	1.73100	−	3.76230i	0.0611620	−	0.132934i
$802$	20.9703	−	12.1072i	0.740487	−	0.427520i
$803$	0.852265	+	3.79597i	0.0300758	+	0.133957i
$804$	−3.72488	−	11.7092i	−0.131366	−	0.412953i
$805$	39.9107	−	9.79520i	1.40667	−	0.345235i
$806$			14.8706i			0.523795i
$807$	2.99739	−	13.6860i	0.105513	−	0.481770i
$808$	−4.85304	−	8.40572i	−0.170729	−	0.295712i
$809$	21.0777	+	36.5077i	0.741053	+	1.28354i	0.952016	+	0.306048i	$0.0990067\pi$
$809$	21.0777	+	36.5077i	0.741053	+	1.28354i	−0.210963	+	0.977494i	$0.567660\pi$
$810$	39.1061	−	33.5020i	1.37405	−	1.17714i
$811$		−	37.2022i		−	1.30635i	−0.757209	−	0.653173i	$-0.773437\pi$
$811$		−	37.2022i		−	1.30635i	0.757209	−	0.653173i	$-0.226563\pi$
$812$	5.81104	−	1.42619i	0.203927	−	0.0500495i
$813$	−22.6845	+	7.21626i	−0.795579	+	0.253085i
$814$	38.4078	−	8.62326i	1.34619	−	0.302245i
$815$	−35.8438	+	20.6944i	−1.25555	+	0.724894i
$816$	31.2091	−	34.2343i	1.09254	−	1.19844i
$817$	0.710315	−	1.23030i	0.0248508	−	0.0430428i
$818$		−	13.3903i		−	0.468180i
$819$	−1.87059	+	9.69803i	−0.0653635	+	0.338876i
$820$		−	48.3010i		−	1.68674i
$821$	−10.8482	+	18.7896i	−0.378604	+	0.655761i	−0.990859	−	0.134899i	$-0.956929\pi$
$821$	−10.8482	+	18.7896i	−0.378604	+	0.655761i	0.612256	+	0.790660i	$0.290262\pi$
$822$	7.45001	+	6.79169i	0.259849	+	0.236887i
$823$	9.74375	+	16.8767i	0.339646	+	0.588284i	0.984366	−	0.176135i	$-0.0563595\pi$
$823$	9.74375	+	16.8767i	0.339646	+	0.588284i	−0.644720	+	0.764419i	$0.723026\pi$
$824$	−1.09680	+	1.89971i	−0.0382087	+	0.0661794i
$825$	12.1604	−	21.3201i	0.423370	−	0.742270i
$826$	29.6649	+	8.62439i	1.03217	+	0.300081i
$827$	38.2080			1.32862			0.664311	−	0.747457i	$-0.268725\pi$
$827$	38.2080			1.32862			0.664311	+	0.747457i	$0.268725\pi$
$828$	−23.3202	+	2.16058i	−0.810432	+	0.0750853i
$829$	−7.92313	−	13.7233i	−0.275182	−	0.476629i	0.694999	−	0.719010i	$-0.255405\pi$
$829$	−7.92313	−	13.7233i	−0.275182	−	0.476629i	−0.970181	+	0.242382i	$0.922071\pi$
$830$	77.6423	−	44.8268i	2.69500	−	1.55596i
$831$	10.1229	−	46.2208i	0.351159	−	1.60338i
$832$		−	4.86094i		−	0.168523i
$833$	1.67613	−	39.6416i	0.0580745	−	1.37350i
$834$	−37.7627	+	12.0129i	−1.30761	+	0.415971i
$835$	−17.3497	−	10.0168i	−0.600411	−	0.346647i
$836$	−2.97792	−	0.930137i	−0.102994	−	0.0321694i
$837$	4.06199	−	32.7977i	0.140403	−	1.13365i
$838$	45.2671	+	26.1350i	1.56372	+	0.902817i
$839$		−	20.1527i		−	0.695748i	−0.937541	−	0.347874i	$-0.886904\pi$
$839$		−	20.1527i		−	0.695748i	0.937541	−	0.347874i	$-0.113096\pi$
$840$	−0.308525	−	12.3070i	−0.0106451	−	0.424630i
$841$	−26.8165			−0.924706
$842$	−16.4692	+	28.5255i	−0.567567	+	0.983055i
$843$	0.151303	−	0.165969i	0.00521116	−	0.00571628i
$844$	−7.62773	+	4.40387i	−0.262557	+	0.151587i
$845$	−30.1993	−	17.4356i	−1.03889	−	0.599802i
$846$	35.1907	+	49.7140i	1.20988	+	1.70920i
$847$	22.5862	−	18.3538i	0.776072	−	0.630644i
$848$		−	14.0600i		−	0.482823i
$849$	10.7318	−	49.0013i	0.368316	−	1.68172i
$850$	22.7520	+	39.4077i	0.780388	+	1.35167i
$851$	−27.9034	+	16.1100i	−0.956515	+	0.552244i
$852$	4.48578	−	20.4820i	0.153680	−	0.701700i
$853$		−	20.6654i		−	0.707570i	−0.935327	−	0.353785i	$-0.884894\pi$
$853$		−	20.6654i		−	0.707570i	0.935327	−	0.353785i	$-0.115106\pi$
$854$	11.2858	+	45.9844i	0.386194	+	1.57355i
$855$	−4.58276	+	3.24396i	−0.156727	+	0.110941i
$856$	−6.08505	+	10.5396i	−0.207983	+	0.360237i
$857$	2.12306	+	3.67725i	0.0725224	+	0.125612i	0.900006	−	0.435877i	$-0.143562\pi$
$857$	2.12306	+	3.67725i	0.0725224	+	0.125612i	−0.827484	+	0.561490i	$0.810228\pi$
$858$	−0.0705017	−	13.4311i	−0.00240689	−	0.458531i
$859$	11.1034	−	19.2317i	0.378844	−	0.656177i	−0.612050	−	0.790819i	$-0.709655\pi$
$859$	11.1034	−	19.2317i	0.378844	−	0.656177i	0.990894	+	0.134642i	$0.0429884\pi$
$860$	10.7721			0.367327
$861$	−24.7703	−	40.5230i	−0.844171	−	1.38102i
$862$	24.2677			0.826563
$863$	15.9992	+	9.23715i	0.544619	+	0.314436i	0.746949	−	0.664881i	$-0.231518\pi$
$863$	15.9992	+	9.23715i	0.544619	+	0.314436i	−0.202330	+	0.979317i	$0.564851\pi$
$864$	−4.53552	+	36.6212i	−0.154302	+	1.24588i
$865$	−6.04393	+	3.48946i	−0.205500	+	0.118645i
$866$	6.57381	−	11.3862i	0.223387	−	0.386918i
$867$	7.94308	+	24.9692i	0.269761	+	0.847999i
$868$	17.8219	+	18.5914i	0.604915	+	0.631033i
$869$	−9.41349	+	8.67257i	−0.319331	+	0.294197i
$870$	−3.13293	+	14.3049i	−0.106216	+	0.484981i
$871$	−4.99517	+	2.88396i	−0.169255	+	0.0977194i
$872$	−2.64042	+	1.52445i	−0.0894160	+	0.0516244i
$873$	−2.54521	−	27.4716i	−0.0861422	−	0.929774i
$874$	5.89064			0.199254
$875$	−5.62730	−	1.63601i	−0.190237	−	0.0553071i
$876$	2.96319	−	0.942633i	0.100117	−	0.0318486i
$877$	−13.8416	−	7.99143i	−0.467396	−	0.269851i	0.247753	−	0.968823i	$-0.420308\pi$
$877$	−13.8416	−	7.99143i	−0.467396	−	0.269851i	−0.715149	+	0.698972i	$0.753641\pi$
$878$	19.1297	−	11.0445i	0.645596	−	0.372735i
$879$	5.58959	−	6.13140i	0.188532	−	0.206807i
$880$	10.4396	+	46.4977i	0.351918	+	1.56744i
$881$		−	12.5797i		−	0.423819i	−0.977289	−	0.211910i	$-0.932032\pi$
$881$		−	12.5797i		−	0.423819i	0.977289	−	0.211910i	$-0.0679683\pi$
$882$	21.4165	+	33.1402i	0.721131	+	1.11589i
$883$	4.39614			0.147942			0.0739710	−	0.997260i	$-0.476433\pi$
$883$	4.39614			0.147942			0.0739710	+	0.997260i	$0.476433\pi$
$884$	9.34851	+	5.39736i	0.314424	+	0.181533i
$885$	−22.0814	+	24.2217i	−0.742257	+	0.814204i
$886$	−15.5938	+	9.00311i	−0.523885	+	0.302465i
$887$	−4.55516	+	7.88976i	−0.152947	+	0.264912i	−0.932310	−	0.361661i	$-0.882210\pi$
$887$	−4.55516	+	7.88976i	−0.152947	+	0.264912i	0.779362	+	0.626573i	$0.215543\pi$
$888$	2.92600	+	9.19793i	0.0981900	+	0.308662i
$889$	−30.3011	−	8.80936i	−1.01627	−	0.295456i
$890$	−7.89850			−0.264758
$891$	−3.51329	+	29.6421i	−0.117700	+	0.993049i
$892$	8.34944	+	14.4617i	0.279560	+	0.484212i
$893$	−3.32060	−	5.75145i	−0.111120	−	0.192465i
$894$	−68.3333	−	14.9658i	−2.28541	−	0.500530i
$895$	43.1513			1.44239
$896$	12.5659	+	13.1084i	0.419796	+	0.437921i
$897$	3.33271	+	10.4764i	0.111276	+	0.349798i
$898$	48.9623	+	28.2684i	1.63389	+	0.943328i
$899$	4.69912	+	8.13912i	0.156724	+	0.271455i
$900$	−17.8215	−	8.19954i	−0.594052	−	0.273318i
$901$	14.6266	+	8.44469i	0.487284	+	0.281333i
$902$	43.7620	+	47.5007i	1.45711	+	1.58160i
$903$	9.03749	−	5.52431i	0.300749	−	0.183838i
$904$		−	7.04890i		−	0.234443i
$905$	−24.0967	−	13.9123i	−0.801003	−	0.462459i
$906$	55.2187	+	50.3392i	1.83452	+	1.67241i
$907$	15.1268	+	26.2004i	0.502278	+	0.869970i	0.999997	+	0.00263193i	$0.000837770\pi$
$907$	15.1268	+	26.2004i	0.502278	+	0.869970i	−0.497719	+	0.867338i	$0.665829\pi$
$908$	6.19682	−	10.7332i	0.205649	−	0.356194i
$909$	−26.9394	+	19.0694i	−0.893525	+	0.632493i
$910$	18.2941	−	4.48988i	0.606443	−	0.148838i
$911$		−	19.0232i		−	0.630267i	−0.949047	−	0.315134i	$-0.897951\pi$
$911$		−	19.0232i		−	0.630267i	0.949047	−	0.315134i	$-0.102049\pi$
$912$	1.07466	−	4.90688i	0.0355856	−	0.162483i
$913$	−15.4941	+	49.6058i	−0.512779	+	1.64171i
$914$	−66.6661	+	38.4897i	−2.20512	+	1.27313i
$915$	−49.0720	−	10.7473i	−1.62227	−	0.355295i
$916$	1.38489			0.0457581
$917$	5.66139	+	5.90582i	0.186956	+	0.195027i
$918$	−44.1615	−	33.3508i	−1.45755	−	1.10074i
$919$	23.5991	+	13.6250i	0.778463	+	0.449446i	0.835885	−	0.548904i	$-0.184955\pi$
$919$	23.5991	+	13.6250i	0.778463	+	0.449446i	−0.0574223	+	0.998350i	$0.518288\pi$
$920$	−6.85153	−	11.8672i	−0.225888	−	0.391250i
$921$	18.7868	+	17.1267i	0.619047	+	0.564344i
$922$	−5.12899	+	8.88368i	−0.168914	+	0.292568i
$923$	−9.84246			−0.323968
$924$	−16.1849	−	16.7072i	−0.532444	−	0.549628i
$925$	−26.9885			−0.887376
$926$	6.05063	−	10.4800i	0.198836	−	0.344394i
$927$	6.77651	+	3.11781i	0.222570	+	0.102402i
$928$	−5.24693	−	9.08796i	−0.172239	−	0.298327i
$929$	16.4471	+	9.49571i	0.539610	+	0.311544i	0.744921	−	0.667153i	$-0.232487\pi$
$929$	16.4471	+	9.49571i	0.539610	+	0.311544i	−0.205311	+	0.978697i	$0.565820\pi$
$930$	−60.0638	+	19.1072i	−1.96957	+	0.626549i
$931$	−1.99184	−	3.81347i	−0.0652800	−	0.124982i
$932$	−0.609463			−0.0199636
$933$	−5.67028	+	25.8904i	−0.185637	+	0.847613i
$934$	4.88479	−	2.82023i	0.159835	−	0.0922809i
$935$	−54.6417	−	17.0670i	−1.78697	−	0.558151i
$936$	3.27934	−	0.303826i	0.107189	−	0.00993087i
$937$			33.4823i			1.09382i	0.837192	+	0.546909i	$0.184196\pi$
$937$			33.4823i			1.09382i	−0.837192	+	0.546909i	$0.815804\pi$
$938$	−6.43289	+	22.1269i	−0.210041	+	0.722469i
$939$	−10.4274	−	32.7788i	−0.340286	−	1.06970i
$940$	25.1790	−	43.6112i	0.821247	−	1.42244i
$941$	10.3259	+	17.8849i	0.336613	+	0.583031i	0.983793	−	0.179306i	$-0.0573852\pi$
$941$	10.3259	+	17.8849i	0.336613	+	0.583031i	−0.647180	+	0.762337i	$0.724052\pi$
$942$	24.8735	−	27.2846i	0.810424	−	0.888979i
$943$	−45.7826	−	26.4326i	−1.49089	−	0.860763i
$944$		−	29.3231i		−	0.954385i
$945$	−41.5747	+	4.90547i	−1.35243	+	0.159575i
$946$	−10.5937	+	9.75985i	−0.344429	+	0.317320i
$947$	−34.0101	−	19.6358i	−1.10518	−	0.638077i	−0.167604	−	0.985854i	$-0.553603\pi$
$947$	−34.0101	−	19.6358i	−1.10518	−	0.638077i	−0.937577	+	0.347778i	$0.886936\pi$
$948$	7.56014	+	6.89208i	0.245542	+	0.223844i
$949$	−0.729828	−	1.26410i	−0.0236912	−	0.0410344i
$950$	4.27312	+	2.46709i	0.138638	+	0.0800429i
$951$	−29.7650	+	9.46870i	−0.965198	+	0.307043i
$952$	−12.8489	+	3.15347i	−0.416434	+	0.102205i
$953$	7.71381			0.249875			0.124937	−	0.992165i	$-0.460127\pi$
$953$	7.71381			0.249875			0.124937	+	0.992165i	$0.460127\pi$
$954$	−16.7246	+	1.54951i	−0.541478	+	0.0501671i
$955$	−2.41746	−	4.18717i	−0.0782273	−	0.135494i
$956$	14.4482	+	25.0251i	0.467290	+	0.809369i
$957$	−4.28283	−	7.32897i	−0.138444	−	0.236912i
$958$	−40.4118			−1.30565
$959$	−1.95346	−	7.95941i	−0.0630806	−	0.257023i
$960$	19.6338	−	6.24580i	0.633679	−	0.201582i
$961$	−4.72573	+	8.18520i	−0.152443	+	0.264039i
$962$	−12.7902	+	7.38443i	−0.412373	+	0.238084i
$963$	37.5962	+	17.2977i	1.21152	+	0.557410i
$964$	−4.00937	−	2.31481i	−0.129133	−	0.0745551i
$965$	−39.6225			−1.27549
$966$	38.5746	+	21.0001i	1.24112	+	0.675667i
$967$		−	15.1529i		−	0.487283i	−0.969865	−	0.243642i	$-0.921658\pi$
$967$		−	15.1529i		−	0.487283i	0.969865	−	0.243642i	$-0.0783421\pi$
$968$	−7.97922	−	5.52337i	−0.256462	−	0.177528i
$969$	4.45916	+	4.06513i	0.143249	+	0.130591i
$970$	−45.5688	+	26.3091i	−1.46313	+	0.844736i
$971$	24.0452	+	13.8825i	0.771648	+	0.445511i	0.833462	−	0.552576i	$-0.186355\pi$
$971$	24.0452	+	13.8825i	0.771648	+	0.445511i	−0.0618141	+	0.998088i	$0.519689\pi$
$972$	23.8464	+	0.735596i	0.764873	+	0.0235943i
$973$	30.9349	+	8.99360i	0.991726	+	0.288321i
$974$	62.5013			2.00267
$975$	−1.97011	+	8.99550i	−0.0630942	+	0.288086i
$976$	38.9215	−	22.4713i	1.24585	−	0.719289i
$977$	44.2071	−	25.5230i	1.41431	−	0.816553i	0.418520	−	0.908208i	$-0.362549\pi$
$977$	44.2071	−	25.5230i	1.41431	−	0.816553i	0.995791	+	0.0916549i	$0.0292157\pi$
$978$	−43.2101	−	9.46351i	−1.38171	−	0.302610i
$979$	3.36729	−	3.10226i	0.107619	−	0.0991487i
$980$	17.4905	−	27.5381i	0.558713	−	0.879673i
$981$	5.99014	+	8.46228i	0.191250	+	0.270180i
$982$	3.53298	−	6.11929i	0.112742	−	0.195275i
$983$	9.49000	−	5.47905i	0.302684	−	0.174755i	−0.340964	−	0.940076i	$-0.610753\pi$
$983$	9.49000	−	5.47905i	0.302684	−	0.174755i	0.643648	+	0.765322i	$0.277420\pi$
$984$	−10.6692	+	11.7034i	−0.340123	+	0.373092i
$985$	−0.301998	−	0.174359i	−0.00962246	−	0.00555553i
$986$	15.7375			0.501185
$987$	−1.24095	−	49.5010i	−0.0394998	−	1.57564i
$988$	1.17051			0.0372390
$989$	5.89503	−	10.2105i	0.187451	−	0.324675i
$990$	54.1590	−	17.5424i	1.72129	−	0.557533i
$991$	9.46591	+	16.3954i	0.300695	+	0.520818i	0.976293	−	0.216451i	$-0.0694482\pi$
$991$	9.46591	+	16.3954i	0.300695	+	0.520818i	−0.675599	+	0.737269i	$0.736115\pi$
$992$	22.5836	−	39.1159i	0.717030	−	1.24193i
$993$	8.93282	+	28.0805i	0.283475	+	0.891108i
$994$	−28.3853	+	27.2105i	−0.900328	+	0.863064i
$995$			72.6280i			2.30246i
$996$	40.5754	+	8.88648i	1.28568	+	0.281579i
$997$	−24.8780	+	14.3633i	−0.787895	+	0.454891i	−0.839221	−	0.543791i	$-0.816989\pi$
$997$	−24.8780	+	14.3633i	−0.787895	+	0.454891i	0.0513262	+	0.998682i	$0.483655\pi$
$998$	1.90461	+	3.29888i	0.0602893	+	0.104424i
$999$	30.2264	−	12.7929i	0.956322	−	0.404751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.l.b.65.20	yes	48
3.2	odd	2	inner	231.2.l.b.65.5	yes	48
7.4	even	3	inner	231.2.l.b.32.19	yes	48
11.10	odd	2	inner	231.2.l.b.65.6	yes	48
21.11	odd	6	inner	231.2.l.b.32.6	yes	48
33.32	even	2	inner	231.2.l.b.65.19	yes	48
77.32	odd	6	inner	231.2.l.b.32.5	✓	48
231.32	even	6	inner	231.2.l.b.32.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.l.b.32.5	✓	48	77.32	odd	6	inner
231.2.l.b.32.6	yes	48	21.11	odd	6	inner
231.2.l.b.32.19	yes	48	7.4	even	3	inner
231.2.l.b.32.20	yes	48	231.32	even	6	inner
231.2.l.b.65.5	yes	48	3.2	odd	2	inner
231.2.l.b.65.6	yes	48	11.10	odd	2	inner
231.2.l.b.65.19	yes	48	33.32	even	2	inner
231.2.l.b.65.20	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939478 - 1.62722i) q^{2} +(1.16688 - 1.27999i) q^{3} +(-0.765237 - 1.32543i) q^{4} +(-2.63713 - 1.52255i) q^{5} +(-0.986571 - 3.10131i) q^{6} +(-0.738610 + 2.54056i) q^{7} +0.882219 q^{8} +(-0.276760 - 2.98721i) q^{9} +O(q^{10})\)	\(q+(0.939478 - 1.62722i) q^{2} +(1.16688 - 1.27999i) q^{3} +(-0.765237 - 1.32543i) q^{4} +(-2.63713 - 1.52255i) q^{5} +(-0.986571 - 3.10131i) q^{6} +(-0.738610 + 2.54056i) q^{7} +0.882219 q^{8} +(-0.276760 - 2.98721i) q^{9} +(-4.95505 + 2.86080i) q^{10} +(0.988816 - 3.16579i) q^{11} +(-2.58948 - 0.567126i) q^{12} +1.24436i q^{13} +(3.44015 + 3.58868i) q^{14} +(-5.02608 + 1.59887i) q^{15} +(2.35930 - 4.08643i) q^{16} +(2.83407 + 4.90876i) q^{17} +(-5.12086 - 2.35606i) q^{18} +(0.532275 + 0.307309i) q^{19} +4.66044i q^{20} +(2.39003 + 3.90996i) q^{21} +(-4.22248 - 4.58322i) q^{22} +(4.41744 + 2.55041i) q^{23} +(1.02945 - 1.12923i) q^{24} +(2.13630 + 3.70019i) q^{25} +(2.02485 + 1.16905i) q^{26} +(-4.14655 - 3.13147i) q^{27} +(3.93255 - 0.965157i) q^{28} +1.47768 q^{29} +(-2.12017 + 9.68065i) q^{30} +(3.18007 + 5.50805i) q^{31} +(-3.55080 - 6.15016i) q^{32} +(-2.89836 - 4.95979i) q^{33} +10.6502 q^{34} +(5.81594 - 5.57522i) q^{35} +(-3.74754 + 2.65275i) q^{36} +(-3.15832 + 5.47036i) q^{37} +(1.00012 - 0.577420i) q^{38} +(1.59277 + 1.45202i) q^{39} +(-2.32653 - 1.34322i) q^{40} -10.3640 q^{41} +(8.60775 - 0.215789i) q^{42} -2.31140i q^{43} +(-4.95271 + 1.11198i) q^{44} +(-3.81831 + 8.29903i) q^{45} +(8.30018 - 4.79211i) q^{46} +(-9.35776 - 5.40270i) q^{47} +(-2.47756 - 7.78827i) q^{48} +(-5.90891 - 3.75297i) q^{49} +8.02804 q^{50} +(9.59020 + 2.10036i) q^{51} +(1.64931 - 0.952228i) q^{52} +(2.58050 - 1.48985i) q^{53} +(-8.99120 + 3.80541i) q^{54} +(-7.42771 + 6.84309i) q^{55} +(-0.651616 + 2.24133i) q^{56} +(1.01446 - 0.322713i) q^{57} +(1.38825 - 2.40451i) q^{58} +(5.38180 - 3.10718i) q^{59} +(5.96533 + 5.43819i) q^{60} +(8.24852 + 4.76229i) q^{61} +11.9504 q^{62} +(7.79360 + 1.50325i) q^{63} -3.90639 q^{64} +(1.89459 - 3.28153i) q^{65} +(-10.7936 + 0.0566571i) q^{66} +(2.31763 + 4.01426i) q^{67} +(4.33747 - 7.51272i) q^{68} +(8.41916 - 2.67826i) q^{69} +(-3.60819 - 14.7016i) q^{70} +7.90967i q^{71} +(-0.244163 - 2.63537i) q^{72} +(-1.01586 + 0.586510i) q^{73} +(5.93434 + 10.2786i) q^{74} +(7.22903 + 1.58324i) q^{75} -0.940657i q^{76} +(7.31254 + 4.85043i) q^{77} +(3.85913 - 1.22765i) q^{78} +(-3.34216 - 1.92960i) q^{79} +(-12.4436 + 7.18429i) q^{80} +(-8.84681 + 1.65348i) q^{81} +(-9.73679 + 16.8646i) q^{82} -15.6693 q^{83} +(3.35344 - 6.15986i) q^{84} -17.2600i q^{85} +(-3.76117 - 2.17151i) q^{86} +(1.72428 - 1.89142i) q^{87} +(0.872352 - 2.79292i) q^{88} +(1.19552 + 0.690235i) q^{89} +(9.91716 + 14.0100i) q^{90} +(-3.16137 - 0.919095i) q^{91} -7.80668i q^{92} +(10.7610 + 2.35679i) q^{93} +(-17.5828 + 10.1514i) q^{94} +(-0.935785 - 1.62083i) q^{95} +(-12.0155 - 2.63154i) q^{96} +9.19643 q^{97} +(-11.6582 + 6.08929i) q^{98} +(-9.73054 - 2.07763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9	\( 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9} + 14 q^{12} + 4 q^{15} - 28 q^{16} - 24 q^{22} - 36 q^{27} - 4 q^{31} - 26 q^{33} + 56 q^{34} + 12 q^{36} - 28 q^{37} + 96 q^{42} + 30 q^{45} - 72 q^{48} + 24 q^{49} - 80 q^{55} + 16 q^{58} - 32 q^{60} + 256 q^{64} - 42 q^{66} + 16 q^{67} + 36 q^{69} - 76 q^{70} + 34 q^{75} + 104 q^{78} - 26 q^{81} - 4 q^{82} - 16 q^{88} - 36 q^{91} + 52 q^{93} - 144 q^{97} - 36 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9 + 14 * q^12 + 4 * q^15 - 28 * q^16 - 24 * q^22 - 36 * q^27 - 4 * q^31 - 26 * q^33 + 56 * q^34 + 12 * q^36 - 28 * q^37 + 96 * q^42 + 30 * q^45 - 72 * q^48 + 24 * q^49 - 80 * q^55 + 16 * q^58 - 32 * q^60 + 256 * q^64 - 42 * q^66 + 16 * q^67 + 36 * q^69 - 76 * q^70 + 34 * q^75 + 104 * q^78 - 26 * q^81 - 4 * q^82 - 16 * q^88 - 36 * q^91 + 52 * q^93 - 144 * q^97 - 36 * q^99

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