LMFDB - Embedded newform 483.2.q.c.463.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 295 x^{16} - 575 x^{15} + 1777 x^{14} - 1560 x^{13} + \cdots + 2374681 $ x^20 - 8x^19 + 40x^18 - 117x^17 + 295x^16 - 575x^15 + 1777x^14 - 1560x^13 + 4383x^12 - 6446x^11 + 7261x^10 + 7700x^9 + 7852x^8 - 39430x^7 - 101709x^6 + 156742x^5 + 999838x^4 + 2029154x^3 + 3616480x^2 + 4299390*x + 2374681
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.2
Root			$-0.318425 + 2.21469i$ of defining polynomial
Character	$\chi$	$=$	483.463
Dual form			483.2.q.c.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.186393 + 1.29639i) q^{2} +(0.415415 - 0.909632i) q^{3} +(0.273100 - 0.0801894i) q^{4} +(1.65162 - 1.90608i) q^{5} +(1.25667 + 0.368991i) q^{6} +(0.841254 - 0.540641i) q^{7} +(1.24302 + 2.72183i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(2.77887 + 1.78587i) q^{10} +(0.470231 - 3.27053i) q^{11} +(0.0405070 - 0.281733i) q^{12} +(-2.21826 - 1.42559i) q^{13} +(0.857685 + 0.989821i) q^{14} +(-1.04772 - 2.29418i) q^{15} +(-2.81797 + 1.81100i) q^{16} +(-2.87118 - 0.843054i) q^{17} +(0.857685 - 0.989821i) q^{18} +(-4.39983 + 1.29191i) q^{19} +(0.298212 - 0.652992i) q^{20} +(-0.142315 - 0.989821i) q^{21} +4.32753 q^{22} +(4.63215 + 1.24226i) q^{23} +2.99223 q^{24} +(-0.193688 - 1.34713i) q^{25} +(1.43465 - 3.14145i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.186393 - 0.215109i) q^{28} +(8.79997 + 2.58390i) q^{29} +(2.77887 - 1.78587i) q^{30} +(-0.0842219 - 0.184420i) q^{31} +(1.04598 + 1.20712i) q^{32} +(-2.77963 - 1.78636i) q^{33} +(0.557760 - 3.87931i) q^{34} +(0.358932 - 2.49643i) q^{35} +(-0.239446 - 0.153882i) q^{36} +(-1.42086 - 1.63976i) q^{37} +(-2.49491 - 5.46310i) q^{38} +(-2.21826 + 1.42559i) q^{39} +(7.24100 + 2.12615i) q^{40} +(-8.17344 + 9.43265i) q^{41} +(1.25667 - 0.368991i) q^{42} +(-3.94480 + 8.63790i) q^{43} +(-0.133842 - 0.930889i) q^{44} -2.52210 q^{45} +(-0.747049 + 6.23662i) q^{46} +5.57125 q^{47} +(0.476716 + 3.31563i) q^{48} +(0.415415 - 0.909632i) q^{49} +(1.71030 - 0.502190i) q^{50} +(-1.95960 + 2.26150i) q^{51} +(-0.720124 - 0.211448i) q^{52} +(8.67612 - 5.57580i) q^{53} +(-0.544078 - 1.19136i) q^{54} +(-5.45722 - 6.29797i) q^{55} +(2.51722 + 1.61772i) q^{56} +(-0.652596 + 4.53891i) q^{57} +(-1.70950 + 11.8898i) q^{58} +(1.24495 + 0.800081i) q^{59} +(-0.470101 - 0.542526i) q^{60} +(1.38782 + 3.03890i) q^{61} +(0.223382 - 0.143559i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-5.75714 + 6.64410i) q^{64} +(-6.38101 + 1.87363i) q^{65} +(1.79772 - 3.93646i) q^{66} +(1.58647 + 11.0342i) q^{67} -0.851723 q^{68} +(3.05426 - 3.69750i) q^{69} +3.30325 q^{70} +(1.08372 + 7.53743i) q^{71} +(1.24302 - 2.72183i) q^{72} +(4.67859 - 1.37376i) q^{73} +(1.86093 - 2.14763i) q^{74} +(-1.30585 - 0.383433i) q^{75} +(-1.09800 + 0.705640i) q^{76} +(-1.37260 - 3.00557i) q^{77} +(-2.26159 - 2.61001i) q^{78} +(-14.2391 - 9.15090i) q^{79} +(-1.20232 + 8.36235i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-13.7519 - 8.83779i) q^{82} +(-3.75858 - 4.33764i) q^{83} +(-0.118239 - 0.258908i) q^{84} +(-6.34903 + 4.08027i) q^{85} +(-11.9334 - 3.50395i) q^{86} +(6.00604 - 6.93134i) q^{87} +(9.48631 - 2.78543i) q^{88} +(5.48049 - 12.0006i) q^{89} +(-0.470101 - 3.26962i) q^{90} -2.63685 q^{91} +(1.36466 - 0.0321892i) q^{92} -0.202742 q^{93} +(1.03844 + 7.22251i) q^{94} +(-4.80439 + 10.5202i) q^{95} +(1.53255 - 0.449997i) q^{96} +(-4.55992 + 5.26243i) q^{97} +(1.25667 + 0.368991i) q^{98} +(-2.77963 + 1.78636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots + 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	0.186393	+	1.29639i	0.131800	+	0.916686i	0.943207	+	0.332205i	$0.107793\pi$
$2$	0.186393	+	1.29639i	0.131800	+	0.916686i	−0.811407	+	0.584481i	$0.801298\pi$
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	0.273100	−	0.0801894i	0.136550	−	0.0400947i
$5$	1.65162	−	1.90608i	0.738628	−	0.852423i	−0.254786	−	0.966997i	$-0.582005\pi$
$5$	1.65162	−	1.90608i	0.738628	−	0.852423i	0.993415	+	0.114575i	$0.0365505\pi$
$6$	1.25667	+	0.368991i	0.513033	+	0.150640i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	1.24302	+	2.72183i	0.439473	+	0.962311i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	2.77887	+	1.78587i	0.878755	+	0.564742i
$11$	0.470231	−	3.27053i	0.141780	−	0.986100i	−0.787392	−	0.616453i	$-0.788569\pi$
$11$	0.470231	−	3.27053i	0.141780	−	0.986100i	0.929172	−	0.369648i	$-0.120522\pi$
$12$	0.0405070	−	0.281733i	0.0116934	−	0.0813292i
$13$	−2.21826	−	1.42559i	−0.615234	−	0.395387i	0.195582	−	0.980687i	$-0.437340\pi$
$13$	−2.21826	−	1.42559i	−0.615234	−	0.395387i	−0.810817	+	0.585300i	$0.800977\pi$
$14$	0.857685	+	0.989821i	0.229226	+	0.264541i
$15$	−1.04772	−	2.29418i	−0.270520	−	0.592355i
$16$	−2.81797	+	1.81100i	−0.704492	+	0.452750i
$17$	−2.87118	−	0.843054i	−0.696363	−	0.204471i	−0.0856531	−	0.996325i	$-0.527298\pi$
$17$	−2.87118	−	0.843054i	−0.696363	−	0.204471i	−0.610710	+	0.791854i	$0.709116\pi$
$18$	0.857685	−	0.989821i	0.202158	−	0.233303i
$19$	−4.39983	+	1.29191i	−1.00939	+	0.296384i	−0.744304	−	0.667841i	$-0.767219\pi$
$19$	−4.39983	+	1.29191i	−1.00939	+	0.296384i	−0.265087	+	0.964225i	$0.585401\pi$
$20$	0.298212	−	0.652992i	0.0666821	−	0.146013i
$21$	−0.142315	−	0.989821i	−0.0310556	−	0.215997i
$22$	4.32753			0.922631
$23$	4.63215	+	1.24226i	0.965870	+	0.259028i
$23$	4.63215	+	1.24226i	0.965870	+	0.259028i
$24$	2.99223			0.610786
$25$	−0.193688	−	1.34713i	−0.0387376	−	0.269426i
$26$	1.43465	−	3.14145i	0.281358	−	0.616089i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	0.186393	−	0.215109i	0.0352249	−	0.0406517i
$29$	8.79997	+	2.58390i	1.63411	+	0.479819i	0.964761	−	0.263127i	$-0.0847538\pi$
$29$	8.79997	+	2.58390i	1.63411	+	0.479819i	0.669352	+	0.742946i	$0.266572\pi$
$30$	2.77887	−	1.78587i	0.507350	−	0.326054i
$31$	−0.0842219	−	0.184420i	−0.0151267	−	0.0331229i	0.901918	−	0.431908i	$-0.142159\pi$
$31$	−0.0842219	−	0.184420i	−0.0151267	−	0.0331229i	−0.917045	+	0.398785i	$0.869432\pi$
$32$	1.04598	+	1.20712i	0.184904	+	0.213391i
$33$	−2.77963	−	1.78636i	−0.483872	−	0.310966i
$34$	0.557760	−	3.87931i	0.0956551	−	0.665296i
$35$	0.358932	−	2.49643i	0.0606706	−	0.421973i
$36$	−0.239446	−	0.153882i	−0.0399076	−	0.0256471i
$37$	−1.42086	−	1.63976i	−0.233588	−	0.269575i	0.626839	−	0.779149i	$-0.284349\pi$
$37$	−1.42086	−	1.63976i	−0.233588	−	0.269575i	−0.860427	+	0.509574i	$0.829803\pi$
$38$	−2.49491	−	5.46310i	−0.404728	−	0.886232i
$39$	−2.21826	+	1.42559i	−0.355206	+	0.228277i
$40$	7.24100	+	2.12615i	1.14490	+	0.336174i
$41$	−8.17344	+	9.43265i	−1.27648	+	1.47313i	−0.469040	+	0.883177i	$0.655400\pi$
$41$	−8.17344	+	9.43265i	−1.27648	+	1.47313i	−0.807436	+	0.589955i	$0.799145\pi$
$42$	1.25667	−	0.368991i	0.193908	−	0.0569366i
$43$	−3.94480	+	8.63790i	−0.601576	+	1.31727i	0.326613	+	0.945158i	$0.394093\pi$
$43$	−3.94480	+	8.63790i	−0.601576	+	1.31727i	−0.928189	+	0.372109i	$0.878635\pi$
$44$	−0.133842	−	0.930889i	−0.0201774	−	0.140337i
$45$	−2.52210			−0.375972
$46$	−0.747049	+	6.23662i	−0.110146	+	0.919540i
$47$	5.57125			0.812650			0.406325	−	0.913729i	$-0.366810\pi$
$47$	5.57125			0.812650			0.406325	+	0.913729i	$0.366810\pi$
$48$	0.476716	+	3.31563i	0.0688080	+	0.478570i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	1.71030	−	0.502190i	0.241873	−	0.0710204i
$51$	−1.95960	+	2.26150i	−0.274399	+	0.316673i
$52$	−0.720124	−	0.211448i	−0.0998633	−	0.0293225i
$53$	8.67612	−	5.57580i	1.19176	−	0.765895i	0.214245	−	0.976780i	$-0.431271\pi$
$53$	8.67612	−	5.57580i	1.19176	−	0.765895i	0.977511	+	0.210885i	$0.0676345\pi$
$54$	−0.544078	−	1.19136i	−0.0740396	−	0.162124i
$55$	−5.45722	−	6.29797i	−0.735852	−	0.849218i
$56$	2.51722	+	1.61772i	0.336378	+	0.216177i
$57$	−0.652596	+	4.53891i	−0.0864385	+	0.601193i
$58$	−1.70950	+	11.8898i	−0.224468	+	1.56121i
$59$	1.24495	+	0.800081i	0.162079	+	0.104162i	0.619166	−	0.785260i	$-0.287471\pi$
$59$	1.24495	+	0.800081i	0.162079	+	0.104162i	−0.457087	+	0.889422i	$0.651107\pi$
$60$	−0.470101	−	0.542526i	−0.0606898	−	0.0700397i
$61$	1.38782	+	3.03890i	0.177692	+	0.389092i	0.977431	−	0.211257i	$-0.0677557\pi$
$61$	1.38782	+	3.03890i	0.177692	+	0.389092i	−0.799738	+	0.600349i	$0.795028\pi$
$62$	0.223382	−	0.143559i	0.0283696	−	0.0182320i
$63$	−0.959493	−	0.281733i	−0.120885	−	0.0354950i
$64$	−5.75714	+	6.64410i	−0.719643	+	0.830512i
$65$	−6.38101	+	1.87363i	−0.791467	+	0.232396i
$66$	1.79772	−	3.93646i	0.221284	−	0.484544i
$67$	1.58647	+	11.0342i	0.193819	+	1.34804i	0.821785	+	0.569798i	$0.192979\pi$
$67$	1.58647	+	11.0342i	0.193819	+	1.34804i	−0.627966	+	0.778241i	$0.716112\pi$
$68$	−0.851723			−0.103287
$69$	3.05426	−	3.69750i	0.367690	−	0.445127i
$70$	3.30325			0.394814
$71$	1.08372	+	7.53743i	0.128614	+	0.894528i	0.947314	+	0.320307i	$0.103786\pi$
$71$	1.08372	+	7.53743i	0.128614	+	0.894528i	−0.818700	+	0.574221i	$0.805305\pi$
$72$	1.24302	−	2.72183i	0.146491	−	0.320770i
$73$	4.67859	−	1.37376i	0.547588	−	0.160786i	0.00377516	−	0.999993i	$-0.498798\pi$
$73$	4.67859	−	1.37376i	0.547588	−	0.160786i	0.543813	+	0.839207i	$0.316980\pi$
$74$	1.86093	−	2.14763i	0.216329	−	0.249657i
$75$	−1.30585	−	0.383433i	−0.150787	−	0.0442750i
$76$	−1.09800	+	0.705640i	−0.125949	+	0.0809425i
$77$	−1.37260	−	3.00557i	−0.156422	−	0.342516i
$78$	−2.26159	−	2.61001i	−0.256074	−	0.295526i
$79$	−14.2391	−	9.15090i	−1.60202	−	1.02956i	−0.966225	−	0.257699i	$-0.917036\pi$
$79$	−14.2391	−	9.15090i	−1.60202	−	1.02956i	−0.635796	−	0.771858i	$-0.719328\pi$
$80$	−1.20232	+	8.36235i	−0.134424	+	0.934939i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−13.7519	−	8.83779i	−1.51864	−	0.975970i
$83$	−3.75858	−	4.33764i	−0.412558	−	0.476117i	0.510997	−	0.859582i	$-0.329276\pi$
$83$	−3.75858	−	4.33764i	−0.412558	−	0.476117i	−0.923555	+	0.383465i	$0.874731\pi$
$84$	−0.118239	−	0.258908i	−0.0129010	−	0.0282492i
$85$	−6.34903	+	4.08027i	−0.688649	+	0.442568i
$86$	−11.9334	−	3.50395i	−1.28681	−	0.377841i
$87$	6.00604	−	6.93134i	0.643915	−	0.743118i
$88$	9.48631	−	2.78543i	1.01124	−	0.296928i
$89$	5.48049	−	12.0006i	0.580931	−	1.27206i	−0.359839	−	0.933015i	$-0.617168\pi$
$89$	5.48049	−	12.0006i	0.580931	−	1.27206i	0.940770	−	0.339047i	$-0.110104\pi$
$90$	−0.470101	−	3.26962i	−0.0495530	−	0.344649i
$91$	−2.63685			−0.276417
$92$	1.36466	−	0.0321892i	0.142275	−	0.00335595i
$93$	−0.202742			−0.0210233
$94$	1.03844	+	7.22251i	0.107107	+	0.744945i
$95$	−4.80439	+	10.5202i	−0.492920	+	1.07935i
$96$	1.53255	−	0.449997i	0.156415	−	0.0459276i
$97$	−4.55992	+	5.26243i	−0.462990	+	0.534319i	−0.938449	−	0.345419i	$-0.887737\pi$
$97$	−4.55992	+	5.26243i	−0.462990	+	0.534319i	0.475458	+	0.879738i	$0.342282\pi$
$98$	1.25667	+	0.368991i	0.126943	+	0.0372737i
$99$	−2.77963	+	1.78636i	−0.279364	+	0.179536i
$100$	−0.160922	−	0.352370i	−0.0160922	−	0.0352370i
$101$	−1.49221	−	1.72210i	−0.148480	−	0.171356i	0.676637	−	0.736317i	$-0.263437\pi$
$101$	−1.49221	−	1.72210i	−0.148480	−	0.171356i	−0.825118	+	0.564961i	$0.808891\pi$
$102$	−3.29704	−	2.11888i	−0.326456	−	0.209800i
$103$	−0.468013	+	3.25510i	−0.0461147	+	0.320735i	0.953687	+	0.300802i	$0.0972543\pi$
$103$	−0.468013	+	3.25510i	−0.0461147	+	0.320735i	−0.999801	+	0.0199329i	$0.993655\pi$
$104$	1.12287	−	7.80975i	0.110107	−	0.765809i
$105$	−2.12172	−	1.36355i	−0.207059	−	0.133069i
$106$	8.84558	+	10.2083i	0.859159	+	0.991522i
$107$	−4.00784	−	8.77594i	−0.387452	−	0.848402i	−0.998390	−	0.0567236i	$-0.981935\pi$
$107$	−4.00784	−	8.77594i	−0.387452	−	0.848402i	0.610938	−	0.791679i	$-0.290793\pi$
$108$	−0.239446	+	0.153882i	−0.0230407	+	0.0148073i
$109$	−12.7008	−	3.72928i	−1.21651	−	0.357201i	−0.390369	−	0.920659i	$-0.627652\pi$
$109$	−12.7008	−	3.72928i	−1.21651	−	0.357201i	−0.826145	+	0.563458i	$0.809471\pi$
$110$	7.14744	−	8.24859i	0.681482	−	0.786472i
$111$	−2.08183	+	0.611280i	−0.197598	+	0.0580201i
$112$	−1.39153	+	3.04702i	−0.131487	+	0.287916i
$113$	−1.43771	−	9.99948i	−0.135248	−	0.940672i	−0.938561	−	0.345114i	$-0.887840\pi$
$113$	−1.43771	−	9.99948i	−0.135248	−	0.940672i	0.803313	−	0.595558i	$-0.203069\pi$
$114$	−6.00583			−0.562498
$115$	10.0184	−	6.77748i	0.934220	−	0.632004i
$116$	2.61047			0.242376
$117$	0.375263	+	2.61001i	0.0346931	+	0.241296i
$118$	−0.805168	+	1.76307i	−0.0741217	+	0.162304i
$119$	−2.87118	+	0.843054i	−0.263200	+	0.0772826i
$120$	4.94203	−	5.70341i	0.451144	−	0.520648i
$121$	0.0792039	+	0.0232563i	0.00720035	+	0.00211421i
$122$	−3.68092	+	2.36559i	−0.333255	+	0.214170i
$123$	5.18487	+	11.3533i	0.467504	+	1.02369i
$124$	−0.0377896	−	0.0436115i	−0.00339360	−	0.00391643i
$125$	7.72099	+	4.96198i	0.690587	+	0.443813i
$126$	0.186393	−	1.29639i	0.0166052	−	0.115492i
$127$	1.32005	−	9.18113i	0.117135	−	0.814694i	−0.843549	−	0.537052i	$-0.819538\pi$
$127$	1.32005	−	9.18113i	0.117135	−	0.814694i	0.960685	−	0.277642i	$-0.0895529\pi$
$128$	−6.99906	−	4.49802i	−0.618635	−	0.397573i
$129$	6.21858	+	7.17663i	0.547516	+	0.631867i
$130$	−3.61833	−	7.92305i	−0.317349	−	0.694897i
$131$	−16.8739	+	10.8442i	−1.47428	+	0.947460i	−0.476614	+	0.879113i	$0.658136\pi$
$131$	−16.8739	+	10.8442i	−1.47428	+	0.947460i	−0.997662	+	0.0683471i	$0.978227\pi$
$132$	−0.902366	−	0.264959i	−0.0785409	−	0.0230617i
$133$	−3.00292	+	3.46555i	−0.260386	+	0.300501i
$134$	−14.0089	+	4.11338i	−1.21018	+	0.355342i
$135$	−1.04772	+	2.29418i	−0.0901732	+	0.197452i
$136$	−1.27428	−	8.86278i	−0.109268	−	0.759977i
$137$	8.77044			0.749310			0.374655	−	0.927164i	$-0.377761\pi$
$137$	8.77044			0.749310			0.374655	+	0.927164i	$0.377761\pi$
$138$	5.36269	+	3.27033i	0.456503	+	0.278389i
$139$	−0.374915			−0.0317999			−0.0158999	−	0.999874i	$-0.505061\pi$
$139$	−0.374915			−0.0317999			−0.0158999	+	0.999874i	$0.505061\pi$
$140$	−0.102163	−	0.710557i	−0.00863433	−	0.0600531i
$141$	2.31438	−	5.06779i	0.194906	−	0.426784i
$142$	−9.56945	+	2.80984i	−0.803051	+	0.235797i
$143$	−5.70552	+	6.58452i	−0.477119	+	0.550625i
$144$	3.21404	+	0.943727i	0.267837	+	0.0786439i
$145$	19.4593	−	12.5058i	1.61601	−	1.03855i
$146$	2.65298	+	5.80923i	0.219563	+	0.480775i
$147$	−0.654861	−	0.755750i	−0.0540120	−	0.0623332i
$148$	−0.519529	−	0.333881i	−0.0427050	−	0.0274449i
$149$	−1.40976	+	9.80512i	−0.115492	+	0.803267i	0.846929	+	0.531706i	$0.178449\pi$
$149$	−1.40976	+	9.80512i	−0.115492	+	0.803267i	−0.962421	+	0.271561i	$0.912460\pi$
$150$	0.253677	−	1.76436i	0.0207127	−	0.144060i
$151$	0.955818	+	0.614267i	0.0777833	+	0.0499883i	0.578954	−	0.815360i	$-0.303461\pi$
$151$	0.955818	+	0.614267i	0.0777833	+	0.0499883i	−0.501171	+	0.865348i	$0.667097\pi$
$152$	−8.98541	−	10.3697i	−0.728813	−	0.841095i
$153$	1.24308	+	2.72197i	0.100497	+	0.220059i
$154$	3.64055	−	2.33964i	0.293364	−	0.188533i
$155$	−0.490622	−	0.144060i	−0.0394077	−	0.0115711i
$156$	−0.491490	+	0.567210i	−0.0393507	+	0.0454131i
$157$	4.65872	−	1.36792i	0.371807	−	0.109172i	−0.0904906	−	0.995897i	$-0.528844\pi$
$157$	4.65872	−	1.36792i	0.371807	−	0.109172i	0.462297	+	0.886725i	$0.347025\pi$
$158$	9.20907	−	20.1651i	0.732635	−	1.60425i
$159$	−1.46774	−	10.2083i	−0.116399	−	0.809574i
$160$	4.02842			0.318474
$161$	4.56843	−	1.45928i	0.360042	−	0.115007i
$162$	−1.30972			−0.102901
$163$	2.38814	+	16.6099i	0.187054	+	1.30099i	0.839587	+	0.543226i	$0.182797\pi$
$163$	2.38814	+	16.6099i	0.187054	+	1.30099i	−0.652533	+	0.757760i	$0.726294\pi$
$164$	−1.47577	+	3.23148i	−0.115238	+	0.252336i
$165$	−7.99585	+	2.34779i	−0.622476	+	0.182775i
$166$	4.92270	−	5.68110i	0.382075	−	0.440939i
$167$	−21.1766	−	6.21800i	−1.63869	−	0.481164i	−0.672739	−	0.739880i	$-0.734882\pi$
$167$	−21.1766	−	6.21800i	−1.63869	−	0.481164i	−0.965953	+	0.258716i	$0.916701\pi$
$168$	2.51722	−	1.61772i	0.194208	−	0.124810i
$169$	−2.51202	−	5.50056i	−0.193233	−	0.423120i
$170$	−6.47304	−	7.47029i	−0.496460	−	0.572945i
$171$	3.85764	+	2.47915i	0.295001	+	0.189586i
$172$	−0.384656	+	2.67534i	−0.0293298	+	0.203993i
$173$	0.766000	−	5.32765i	0.0582379	−	0.405054i	−0.939762	−	0.341831i	$-0.888953\pi$
$173$	0.766000	−	5.32765i	0.0582379	−	0.405054i	0.997999	−	0.0632228i	$-0.0201379\pi$
$174$	10.1052	+	6.49422i	0.766074	+	0.492326i
$175$	−0.891254	−	1.02856i	−0.0673724	−	0.0777520i
$176$	4.59782	+	10.0678i	0.346574	+	0.758891i
$177$	1.24495	−	0.800081i	0.0935762	−	0.0601378i
$178$	16.5790	+	4.86803i	1.24265	+	0.364874i
$179$	4.47124	−	5.16009i	0.334197	−	0.385683i	−0.563634	−	0.826025i	$-0.690597\pi$
$179$	4.47124	−	5.16009i	0.334197	−	0.385683i	0.897830	+	0.440341i	$0.145143\pi$
$180$	−0.688786	+	0.202246i	−0.0513390	+	0.0150745i
$181$	4.26883	−	9.34743i	0.317300	−	0.694789i	−0.682033	−	0.731321i	$-0.738904\pi$
$181$	4.26883	−	9.34743i	0.317300	−	0.694789i	0.999332	+	0.0365324i	$0.0116312\pi$
$182$	−0.491490	−	3.41839i	−0.0364317	−	0.253388i
$183$	3.34080			0.246959
$184$	2.37663	+	14.1521i	0.175208	+	1.04330i
$185$	−5.47224			−0.402327
$186$	−0.0377896	−	0.262832i	−0.00277087	−	0.0192718i
$187$	−4.10734	+	8.99383i	−0.300359	+	0.657694i
$188$	1.52151	−	0.446755i	0.110967	−	0.0325830i
$189$	−0.654861	+	0.755750i	−0.0476341	+	0.0549727i
$190$	−14.5337	−	4.26749i	−1.05439	−	0.309596i
$191$	−21.3802	+	13.7402i	−1.54702	+	0.994207i	−0.560951	+	0.827849i	$0.689565\pi$
$191$	−21.3802	+	13.7402i	−1.54702	+	0.994207i	−0.986065	+	0.166359i	$0.946799\pi$
$192$	3.65208	+	7.99694i	0.263566	+	0.577130i
$193$	−13.7810	−	15.9041i	−0.991979	−	1.14480i	−0.989460	−	0.144808i	$-0.953744\pi$
$193$	−13.7810	−	15.9041i	−0.991979	−	1.14480i	−0.00251935	−	0.999997i	$-0.500802\pi$
$194$	−7.67210	−	4.93056i	−0.550825	−	0.353994i
$195$	−0.946450	+	6.58270i	−0.0677767	+	0.471397i
$196$	0.0405070	−	0.281733i	0.00289336	−	0.0201238i
$197$	−3.66346	−	2.35436i	−0.261011	−	0.167742i	0.403590	−	0.914940i	$-0.367762\pi$
$197$	−3.66346	−	2.35436i	−0.261011	−	0.167742i	−0.664601	+	0.747198i	$0.731399\pi$
$198$	−2.83393	−	3.27053i	−0.201398	−	0.232426i
$199$	−1.44805	−	3.17078i	−0.102649	−	0.224771i	0.851338	−	0.524618i	$-0.175792\pi$
$199$	−1.44805	−	3.17078i	−0.102649	−	0.224771i	−0.953987	+	0.299847i	$0.903064\pi$
$200$	3.42590	−	2.20169i	0.242247	−	0.155683i
$201$	10.6961	+	3.14065i	0.754443	+	0.221525i
$202$	1.95438	−	2.25547i	0.137510	−	0.158695i
$203$	8.79997	−	2.58390i	0.617637	−	0.181354i
$204$	−0.353819	+	0.774755i	−0.0247723	+	0.0542437i
$205$	4.47990	+	31.1584i	0.312890	+	2.17619i
$206$	−4.30712			−0.300091
$207$	−2.09458	−	4.31425i	−0.145583	−	0.299861i
$208$	8.83273			0.612439
$209$	2.15628	+	14.9973i	0.149153	+	1.03738i
$210$	1.37222	−	3.00474i	0.0946921	−	0.207347i
$211$	−2.00966	+	0.590091i	−0.138351	+	0.0406235i	−0.350175	−	0.936684i	$-0.613878\pi$
$211$	−2.00966	+	0.590091i	−0.138351	+	0.0406235i	0.211824	+	0.977308i	$0.432060\pi$
$212$	1.92233	−	2.21849i	0.132026	−	0.152366i
$213$	7.30648	+	2.14538i	0.500632	+	0.146999i
$214$	10.6300	−	6.83150i	0.726653	−	0.466991i
$215$	9.94917	+	21.7856i	0.678528	+	1.48577i
$216$	−1.95949	−	2.26138i	−0.133327	−	0.153867i
$217$	−0.170557	−	0.109610i	−0.0115782	−	0.00744084i
$218$	2.46727	−	17.1603i	0.167105	−	1.16224i
$219$	0.693943	−	4.82648i	0.0468923	−	0.326143i
$220$	−1.99540	−	1.28237i	−0.134530	−	0.0864570i
$221$	5.16717	+	5.96323i	0.347581	+	0.401130i
$222$	−1.18049	−	2.58492i	−0.0792296	−	0.173489i
$223$	1.31799	−	0.847020i	0.0882591	−	0.0567207i	−0.495767	−	0.868456i	$-0.665113\pi$
$223$	1.31799	−	0.847020i	0.0882591	−	0.0567207i	0.584026	+	0.811735i	$0.301477\pi$
$224$	1.53255	+	0.449997i	0.102398	+	0.0300667i
$225$	−0.891254	+	1.02856i	−0.0594169	+	0.0685708i
$226$	12.6952	−	3.72766i	0.844475	−	0.247960i
$227$	7.70344	−	16.8682i	0.511295	−	1.11958i	−0.461336	−	0.887226i	$-0.652630\pi$
$227$	7.70344	−	16.8682i	0.511295	−	1.11958i	0.972631	−	0.232355i	$-0.0746431\pi$
$228$	0.185748	+	1.29191i	0.0123015	+	0.0855587i
$229$	22.5410			1.48955			0.744775	−	0.667316i	$-0.232557\pi$
$229$	22.5410			1.48955			0.744775	+	0.667316i	$0.232557\pi$
$230$	10.6536	+	11.7245i	0.702479	+	0.773089i
$231$	−3.30416			−0.217398
$232$	3.90557	+	27.1638i	0.256413	+	1.78339i
$233$	−2.49059	+	5.45364i	−0.163164	+	0.357280i	−0.973500	−	0.228686i	$-0.926557\pi$
$233$	−2.49059	+	5.45364i	−0.163164	+	0.357280i	0.810336	+	0.585965i	$0.199285\pi$
$234$	−3.31365	+	0.972974i	−0.216620	+	0.0636053i
$235$	9.20160	−	10.6192i	0.600246	−	0.692721i
$236$	0.404154	+	0.118670i	0.0263082	+	0.00772478i
$237$	−14.2391	+	9.15090i	−0.924927	+	0.594415i
$238$	−1.62809	−	3.56503i	−0.105534	−	0.231086i
$239$	−0.803055	−	0.926775i	−0.0519453	−	0.0599481i	0.729182	−	0.684320i	$-0.239901\pi$
$239$	−0.803055	−	0.926775i	−0.0519453	−	0.0599481i	−0.781128	+	0.624371i	$0.785355\pi$
$240$	7.10720	+	4.56752i	0.458768	+	0.294832i
$241$	0.631571	−	4.39267i	0.0406831	−	0.282957i	−0.959317	−	0.282332i	$-0.908892\pi$
$241$	0.631571	−	4.39267i	0.0406831	−	0.282957i	1.00000		0.000624904i	$-0.000198913\pi$
$242$	−0.0153863	+	0.107014i	−0.000989068	+	0.00687912i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	0.622702	+	0.718636i	0.0398644	+	0.0460060i
$245$	−1.04772	−	2.29418i	−0.0669362	−	0.146570i
$246$	−13.7519	+	8.83779i	−0.876787	+	0.563477i
$247$	11.6017	+	3.40657i	0.738198	+	0.216755i
$248$	0.397271	−	0.458475i	0.0252267	−	0.0291132i
$249$	−5.50703	+	1.61701i	−0.348994	+	0.102474i
$250$	−4.99353	+	10.9343i	−0.315818	+	0.691546i
$251$	4.09327	+	28.4693i	0.258365	+	1.79697i	0.544482	+	0.838773i	$0.316726\pi$
$251$	4.09327	+	28.4693i	0.258365	+	1.79697i	−0.286117	+	0.958195i	$0.592365\pi$
$252$	−0.284630			−0.0179300
$253$	6.24101	−	14.5654i	0.392369	−	0.915720i
$254$	12.1484			0.762257
$255$	1.07407	+	7.47029i	0.0672606	+	0.467807i
$256$	−2.77755	+	6.08198i	−0.173597	+	0.380124i
$257$	2.75513	−	0.808978i	0.171860	−	0.0504626i	−0.194670	−	0.980869i	$-0.562364\pi$
$257$	2.75513	−	0.808978i	0.171860	−	0.0504626i	0.366530	+	0.930406i	$0.380546\pi$
$258$	−8.14461	+	9.39938i	−0.507061	+	0.585180i
$259$	−2.08183	−	0.611280i	−0.129358	−	0.0379831i
$260$	−1.59241	+	1.02338i	−0.0987570	+	0.0634673i
$261$	−3.80997	−	8.34267i	−0.235831	−	0.516398i
$262$	−17.2034	−	19.8538i	−1.06283	−	1.22657i
$263$	26.2897	+	16.8954i	1.62109	+	1.04181i	0.955283	+	0.295692i	$0.0955502\pi$
$263$	26.2897	+	16.8954i	1.62109	+	1.04181i	0.665810	+	0.746121i	$0.268086\pi$
$264$	1.40704	−	9.78616i	0.0865972	−	0.602296i
$265$	3.70178	−	25.7465i	0.227399	−	1.58159i
$266$	−5.05243	−	3.24700i	−0.309784	−	0.199086i
$267$	−8.63945	−	9.97046i	−0.528726	−	0.610182i
$268$	1.31809	+	2.88622i	0.0805152	+	0.176304i
$269$	12.7375	−	8.18588i	0.776618	−	0.499102i	−0.0912919	−	0.995824i	$-0.529100\pi$
$269$	12.7375	−	8.18588i	0.776618	−	0.499102i	0.867909	+	0.496722i	$0.165463\pi$
$270$	−3.16944	−	0.930632i	−0.192886	−	0.0566365i
$271$	−15.3456	+	17.7097i	−0.932176	+	1.07579i	0.0647855	+	0.997899i	$0.479364\pi$
$271$	−15.3456	+	17.7097i	−0.932176	+	1.07579i	−0.996962	+	0.0778898i	$0.975182\pi$
$272$	9.61766	−	2.82400i	0.583156	−	0.171230i
$273$	−1.09539	+	2.39856i	−0.0662958	+	0.145168i
$274$	1.63475	+	11.3699i	0.0987587	+	0.686882i
$275$	−4.49690			−0.271173
$276$	0.537618	−	1.25471i	0.0323608	−	0.0755245i
$277$	−4.56128			−0.274060			−0.137030	−	0.990567i	$-0.543756\pi$
$277$	−4.56128			−0.274060			−0.137030	+	0.990567i	$0.543756\pi$
$278$	−0.0698814	−	0.486036i	−0.00419121	−	0.0291505i
$279$	−0.0842219	+	0.184420i	−0.00504223	+	0.0110410i
$280$	7.24100	−	2.12615i	0.432733	−	0.127062i
$281$	4.82033	−	5.56296i	0.287557	−	0.331858i	−0.593531	−	0.804811i	$-0.702267\pi$
$281$	4.82033	−	5.56296i	0.287557	−	0.331858i	0.881088	+	0.472953i	$0.156812\pi$
$282$	7.00121	+	2.05574i	0.416916	+	0.122418i
$283$	17.6435	−	11.3388i	1.04880	−	0.674023i	0.101652	−	0.994820i	$-0.467587\pi$
$283$	17.6435	−	11.3388i	1.04880	−	0.674023i	0.947148	+	0.320797i	$0.103951\pi$
$284$	0.900386	+	1.97157i	0.0534281	+	0.116991i
$285$	7.57365	+	8.74046i	0.448624	+	0.517740i
$286$	−9.59957	−	6.16927i	−0.567635	−	0.364797i
$287$	−1.77626	+	12.3541i	−0.104849	+	0.729242i
$288$	0.227312	−	1.58099i	0.0133945	−	0.0931608i
$289$	−6.76839	−	4.34978i	−0.398140	−	0.255869i
$290$	19.8394	+	22.8959i	1.16501	+	1.34450i
$291$	2.89262	+	6.33395i	0.169568	+	0.371302i
$292$	1.16756	−	0.750348i	0.0683265	−	0.0439108i
$293$	4.43145	+	1.30119i	0.258888	+	0.0760164i	0.408601	−	0.912713i	$-0.366017\pi$
$293$	4.43145	+	1.30119i	0.258888	+	0.0760164i	−0.149713	+	0.988729i	$0.547835\pi$
$294$	0.857685	−	0.989821i	0.0500212	−	0.0577276i
$295$	3.58120	−	1.05154i	0.208506	−	0.0612228i
$296$	2.69699	−	5.90559i	0.156760	−	0.343256i
$297$	0.470231	+	3.27053i	0.0272855	+	0.189775i
$298$	−12.9740			−0.751566
$299$	−8.50436	−	9.35918i	−0.491820	−	0.541256i
$300$	−0.387376			−0.0223652
$301$	1.35143	+	9.39938i	0.0778950	+	0.541771i
$302$	−0.618172	+	1.35361i	−0.0355718	+	0.0778914i
$303$	−2.18637	+	0.641975i	−0.125603	+	0.0368805i
$304$	10.0590	−	11.6086i	0.576920	−	0.665802i
$305$	8.08453	+	2.37383i	0.462919	+	0.135925i
$306$	−3.29704	+	2.11888i	−0.188479	+	0.121128i
$307$	−10.4397	−	22.8598i	−0.595827	−	1.30468i	−0.931856	−	0.362828i	$-0.881811\pi$
$307$	−10.4397	−	22.8598i	−0.595827	−	1.30468i	0.336029	−	0.941852i	$-0.390916\pi$
$308$	−0.615871	−	0.710753i	−0.0350925	−	0.0404989i
$309$	2.76653	+	1.77794i	0.157382	+	0.101143i
$310$	0.0953090	−	0.662889i	0.00541319	−	0.0376496i
$311$	2.43854	−	16.9604i	0.138277	−	0.961737i	−0.796027	−	0.605261i	$-0.793069\pi$
$311$	2.43854	−	16.9604i	0.138277	−	0.961737i	0.934304	−	0.356476i	$-0.116022\pi$
$312$	−6.63754	−	4.26569i	−0.375777	−	0.241497i
$313$	2.17026	+	2.50461i	0.122670	+	0.141569i	0.813762	−	0.581198i	$-0.197416\pi$
$313$	2.17026	+	2.50461i	0.122670	+	0.141569i	−0.691092	+	0.722767i	$0.742870\pi$
$314$	2.64172	+	5.78455i	0.149081	+	0.326441i
$315$	−2.12172	+	1.36355i	−0.119546	+	0.0768273i
$316$	−4.62250	−	1.35729i	−0.260036	−	0.0763534i
$317$	−2.34826	+	2.71004i	−0.131891	+	0.152211i	−0.817854	−	0.575426i	$-0.804836\pi$
$317$	−2.34826	+	2.71004i	−0.131891	+	0.152211i	0.685962	+	0.727637i	$0.259382\pi$
$318$	12.9604	−	3.80552i	0.726784	−	0.213403i
$319$	12.5887	−	27.5655i	0.704834	−	1.54337i
$320$	3.15552	+	21.9471i	0.176399	+	1.22688i
$321$	−9.64779			−0.538487
$322$	2.74331	+	5.65046i	0.152879	+	0.314888i
$323$	13.7219			0.763504
$324$	0.0405070	+	0.281733i	0.00225039	+	0.0156518i
$325$	−1.49080	+	3.26440i	−0.0826948	+	0.181076i
$326$	−21.0878	+	6.19192i	−1.16794	+	0.342939i
$327$	−8.66837	+	10.0038i	−0.479362	+	0.553213i
$328$	−35.8337	−	10.5217i	−1.97859	−	0.580966i
$329$	4.68683	−	3.01204i	0.258393	−	0.166059i
$330$	−4.53402	−	9.92813i	−0.249590	−	0.546526i
$331$	12.3090	+	14.2053i	0.676562	+	0.780794i	0.985388	−	0.170325i	$-0.0544816\pi$
$331$	12.3090	+	14.2053i	0.676562	+	0.780794i	−0.308826	+	0.951118i	$0.599936\pi$
$332$	−1.37430	−	0.883211i	−0.0754247	−	0.0484725i
$333$	−0.308783	+	2.14763i	−0.0169212	+	0.117689i
$334$	4.11380	−	28.6121i	0.225097	−	1.56558i
$335$	23.6522	+	15.2004i	1.29226	+	0.830484i
$336$	2.19360	+	2.53155i	0.119671	+	0.138108i
$337$	−12.3013	−	26.9360i	−0.670093	−	1.46730i	−0.872809	−	0.488062i	$-0.837704\pi$
$337$	−12.3013	−	26.9360i	−0.670093	−	1.46730i	0.202715	−	0.979238i	$-0.435023\pi$
$338$	6.66266	−	4.28183i	0.362401	−	0.232901i
$339$	−9.69309	−	2.84615i	−0.526456	−	0.154582i
$340$	−1.40673	+	1.62345i	−0.0762904	+	0.0880439i
$341$	−0.642755	+	0.188730i	−0.0348071	+	0.0102203i
$342$	−2.49491	+	5.46310i	−0.134909	+	0.295411i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	−28.4143			−1.53200
$345$	−2.00322	−	11.9285i	−0.107850	−	0.642210i
$346$	7.04949			0.378983
$347$	2.07532	+	14.4342i	0.111409	+	0.774867i	0.966551	+	0.256473i	$0.0825606\pi$
$347$	2.07532	+	14.4342i	0.111409	+	0.774867i	−0.855142	+	0.518393i	$0.826530\pi$
$348$	1.08443	−	2.37457i	0.0581316	−	0.127290i
$349$	−4.53253	+	1.33087i	−0.242621	+	0.0712399i	−0.400782	−	0.916173i	$-0.631262\pi$
$349$	−4.53253	+	1.33087i	−0.242621	+	0.0712399i	0.158161	+	0.987413i	$0.449443\pi$
$350$	1.16729	−	1.34713i	0.0623945	−	0.0720071i
$351$	2.53004	+	0.742887i	0.135043	+	0.0396523i
$352$	4.43976	−	2.85326i	0.236640	−	0.152079i
$353$	−3.40829	−	7.46310i	−0.181405	−	0.397221i	0.796982	−	0.604003i	$-0.206428\pi$
$353$	−3.40829	−	7.46310i	−0.181405	−	0.397221i	−0.978387	+	0.206782i	$0.933701\pi$
$354$	1.26927	+	1.46481i	0.0674608	+	0.0778539i
$355$	16.1568	+	10.3833i	0.857514	+	0.551091i
$356$	0.534401	−	3.71684i	0.0283232	−	0.196992i
$357$	−0.425862	+	2.96193i	−0.0225390	+	0.156762i
$358$	7.52290	+	4.83467i	0.397598	+	0.255520i
$359$	−6.56431	−	7.57562i	−0.346451	−	0.399826i	0.555604	−	0.831447i	$-0.312487\pi$
$359$	−6.56431	−	7.57562i	−0.346451	−	0.399826i	−0.902055	+	0.431621i	$0.857942\pi$
$360$	−3.13501	−	6.86472i	−0.165230	−	0.361802i
$361$	1.70568	−	1.09618i	0.0897729	−	0.0576935i
$362$	12.9136	+	3.79177i	0.678724	+	0.199291i
$363$	0.0540572	−	0.0623853i	0.00283727	−	0.00327438i
$364$	−0.720124	+	0.211448i	−0.0377448	+	0.0110829i
$365$	5.10879	−	11.1867i	0.267406	−	0.585538i
$366$	0.622702	+	4.33099i	0.0325491	+	0.226384i
$367$	−12.0408			−0.628523			−0.314262	−	0.949336i	$-0.601757\pi$
$367$	−12.0408			−0.628523			−0.314262	+	0.949336i	$0.601757\pi$
$368$	−15.3030	+	4.88818i	−0.797723	+	0.254814i
$369$	12.4812			0.649744
$370$	−1.01999	−	7.09416i	−0.0530265	−	0.368808i
$371$	4.28431	−	9.38132i	0.222430	−	0.487054i
$372$	−0.0553688	+	0.0162577i	−0.00287074	+	0.000842924i
$373$	22.7774	−	26.2865i	1.17937	−	1.36106i	0.260997	−	0.965340i	$-0.415949\pi$
$373$	22.7774	−	26.2865i	1.17937	−	1.36106i	0.918370	−	0.395722i	$-0.129506\pi$
$374$	−12.4251	−	3.64834i	−0.642486	−	0.188651i
$375$	7.72099	−	4.96198i	0.398710	−	0.256236i
$376$	6.92515	+	15.1640i	0.357138	+	0.782022i
$377$	−15.8370	−	18.2769i	−0.815648	−	0.941308i
$378$	−1.10181	−	0.708089i	−0.0566709	−	0.0364202i
$379$	0.816121	−	5.67625i	0.0419213	−	0.291569i	−0.958066	−	0.286547i	$-0.907492\pi$
$379$	0.816121	−	5.67625i	0.0419213	−	0.291569i	0.999987	−	0.00502178i	$-0.00159849\pi$
$380$	−0.468475	+	3.25832i	−0.0240323	+	0.167148i
$381$	−7.80308	−	5.01474i	−0.399764	−	0.256913i
$382$	−21.7978	−	25.1560i	−1.11527	−	1.28709i
$383$	−5.00784	−	10.9656i	−0.255889	−	0.560318i	0.737470	−	0.675380i	$-0.236021\pi$
$383$	−5.00784	−	10.9656i	−0.255889	−	0.560318i	−0.993358	+	0.115062i	$0.963293\pi$
$384$	−6.99906	+	4.49802i	−0.357169	+	0.229539i
$385$	−7.99585	−	2.34779i	−0.407506	−	0.119655i
$386$	18.0493	−	20.8300i	0.918685	−	1.06022i
$387$	9.11138	−	2.67534i	0.463158	−	0.135995i
$388$	−0.823324	+	1.80283i	−0.0417980	+	0.0915248i
$389$	−0.186520	−	1.29728i	−0.00945694	−	0.0657745i	0.984546	−	0.175124i	$-0.0560325\pi$
$389$	−0.186520	−	1.29728i	−0.00945694	−	0.0657745i	−0.994003	+	0.109349i	$0.965123\pi$
$390$	−8.71017			−0.441056
$391$	−12.2524	−	7.47189i	−0.619632	−	0.377870i
$392$	2.99223			0.151130
$393$	2.85455	+	19.8538i	0.143993	+	1.00149i
$394$	2.36933	−	5.18811i	0.119365	−	0.261373i
$395$	−40.9599	+	12.0269i	−2.06092	+	0.605139i
$396$	−0.615871	+	0.710753i	−0.0309487	+	0.0357167i
$397$	6.06013	+	1.77941i	0.304149	+	0.0893062i	0.430246	−	0.902712i	$-0.358427\pi$
$397$	6.06013	+	1.77941i	0.304149	+	0.0893062i	−0.126097	+	0.992018i	$0.540245\pi$
$398$	3.84067	−	2.46825i	0.192515	−	0.123722i
$399$	1.90492	+	4.17119i	0.0953652	+	0.208821i
$400$	2.98546	+	3.44540i	0.149273	+	0.172270i
$401$	−3.11533	−	2.00210i	−0.155572	−	0.0999801i	0.460539	−	0.887640i	$-0.347656\pi$
$401$	−3.11533	−	2.00210i	−0.155572	−	0.0999801i	−0.616111	+	0.787660i	$0.711293\pi$
$402$	−2.07784	+	14.4517i	−0.103633	+	0.720785i
$403$	−0.0760814	+	0.529158i	−0.00378988	+	0.0263592i
$404$	−0.545617	−	0.350647i	−0.0271455	−	0.0174453i
$405$	1.65162	+	1.90608i	0.0820698	+	0.0947136i
$406$	4.99000	+	10.9266i	0.247649	+	0.542277i
$407$	−6.03102	+	3.87590i	−0.298946	+	0.192121i
$408$	−8.59122	−	2.52261i	−0.425329	−	0.124888i
$409$	3.53251	−	4.07673i	0.174671	−	0.201581i	−0.661663	−	0.749801i	$-0.730149\pi$
$409$	3.53251	−	4.07673i	0.174671	−	0.201581i	0.836334	+	0.548220i	$0.184694\pi$
$410$	−39.5584	+	11.6154i	−1.95365	+	0.573643i
$411$	3.64337	−	7.97788i	0.179714	−	0.393520i
$412$	0.133210	+	0.926499i	0.00656281	+	0.0456453i
$413$	1.47988			0.0728199
$414$	5.20254	−	3.51954i	0.255691	−	0.172976i
$415$	−14.4756			−0.710581
$416$	−0.599388	−	4.16884i	−0.0293874	−	0.204394i
$417$	−0.155745	+	0.341035i	−0.00762688	+	0.0167005i
$418$	−19.0404	+	5.59076i	−0.931296	+	0.273453i
$419$	−16.6696	+	19.2377i	−0.814363	+	0.939825i	−0.999076	−	0.0429670i	$-0.986319\pi$
$419$	−16.6696	+	19.2377i	−0.814363	+	0.939825i	0.184713	+	0.982792i	$0.440864\pi$
$420$	−0.688786	−	0.202246i	−0.0336093	−	0.00986858i
$421$	17.7987	−	11.4385i	0.867456	−	0.557480i	−0.0295176	−	0.999564i	$-0.509397\pi$
$421$	17.7987	−	11.4385i	0.867456	−	0.557480i	0.896974	+	0.442084i	$0.145761\pi$
$422$	−1.13957	−	2.49532i	−0.0554736	−	0.121470i
$423$	−3.64839	−	4.21047i	−0.177391	−	0.204720i
$424$	25.9609	+	16.6841i	1.26077	+	0.810250i
$425$	−0.579590	+	4.03114i	−0.0281142	+	0.195539i
$426$	−1.41937	+	9.87193i	−0.0687687	+	0.478297i
$427$	2.81046	+	1.80618i	0.136008	+	0.0874069i
$428$	−1.79828	−	2.07533i	−0.0869231	−	0.100315i
$429$	3.61933	+	7.92523i	0.174743	+	0.382634i
$430$	−26.3882	+	16.9587i	−1.27255	+	0.817821i
$431$	−29.9982	−	8.80828i	−1.44496	−	0.424280i	−0.537091	−	0.843524i	$-0.680477\pi$
$431$	−29.9982	−	8.80828i	−1.44496	−	0.424280i	−0.907874	+	0.419244i	$0.862295\pi$
$432$	2.19360	−	2.53155i	0.105540	−	0.121799i
$433$	−1.87865	+	0.551623i	−0.0902823	+	0.0265093i	−0.326562	−	0.945176i	$-0.605890\pi$
$433$	−1.87865	+	0.551623i	−0.0902823	+	0.0265093i	0.236279	+	0.971685i	$0.424072\pi$
$434$	0.110307	−	0.241539i	0.00529492	−	0.0115942i
$435$	−3.29194	−	22.8959i	−0.157836	−	1.09778i
$436$	−3.76763			−0.180437
$437$	−21.9856	+	0.518590i	−1.05171	+	0.0248075i
$438$	6.38635			0.305151
$439$	−0.629598	−	4.37895i	−0.0300491	−	0.208996i	0.969265	−	0.246017i	$-0.0791221\pi$
$439$	−0.629598	−	4.37895i	−0.0300491	−	0.208996i	−0.999314	+	0.0370216i	$0.988213\pi$
$440$	10.3586	−	22.6821i	0.493825	−	1.08133i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	−6.76755	+	7.81017i	−0.321900	+	0.371492i
$443$	18.3412	+	5.38546i	0.871416	+	0.255871i	0.686717	−	0.726924i	$-0.259051\pi$
$443$	18.3412	+	5.38546i	0.871416	+	0.255871i	0.184698	+	0.982795i	$0.440869\pi$
$444$	−0.519529	+	0.333881i	−0.0246558	+	0.0158453i
$445$	−13.8223	−	30.2667i	−0.655242	−	1.43478i
$446$	1.34373	+	1.55075i	0.0636276	+	0.0734302i
$447$	8.33342	+	5.35556i	0.394157	+	0.253309i
$448$	−1.25115	+	8.70192i	−0.0591111	+	0.411127i
$449$	2.03194	−	14.1324i	0.0958930	−	0.666951i	−0.884009	−	0.467470i	$-0.845166\pi$
$449$	2.03194	−	14.1324i	0.0958930	−	0.666951i	0.979902	−	0.199480i	$-0.0639254\pi$
$450$	−1.49954	−	0.963696i	−0.0706890	−	0.0454291i
$451$	27.0063	+	31.1669i	1.27168	+	1.46759i
$452$	−1.19449	−	2.61557i	−0.0561841	−	0.123026i
$453$	0.955818	−	0.614267i	0.0449082	−	0.0288608i
$454$	23.3036	+	6.84256i	1.09369	+	0.321137i
$455$	−4.35508	+	5.02603i	−0.204169	+	0.235624i
$456$	−13.1653	+	3.86568i	−0.616522	+	0.181027i
$457$	6.13016	−	13.4232i	0.286757	−	0.627910i	−0.710356	−	0.703842i	$-0.751466\pi$
$457$	6.13016	−	13.4232i	0.286757	−	0.627910i	0.997113	+	0.0759326i	$0.0241934\pi$
$458$	4.20147	+	29.2219i	0.196322	+	1.36545i
$459$	2.99239			0.139673
$460$	2.19254	−	2.65430i	0.102228	−	0.123757i
$461$	31.1011			1.44852			0.724261	−	0.689526i	$-0.242181\pi$
$461$	31.1011			1.44852			0.724261	+	0.689526i	$0.242181\pi$
$462$	−0.615871	−	4.28348i	−0.0286529	−	0.199285i
$463$	−10.4127	+	22.8006i	−0.483919	+	1.05964i	0.497448	+	0.867494i	$0.334271\pi$
$463$	−10.4127	+	22.8006i	−0.483919	+	1.05964i	−0.981367	+	0.192142i	$0.938457\pi$
$464$	−29.4775	+	8.65537i	−1.36846	+	0.401815i
$465$	−0.334853	+	0.386441i	−0.0155284	+	0.0179208i
$466$	−7.53427	−	2.21226i	−0.349019	−	0.102481i
$467$	−0.0524443	+	0.0337039i	−0.00242683	+	0.00155963i	−0.541854	−	0.840473i	$-0.682277\pi$
$467$	−0.0524443	+	0.0337039i	−0.00242683	+	0.00155963i	0.539427	+	0.842032i	$0.318641\pi$
$468$	0.311780	+	0.682702i	0.0144120	+	0.0315579i
$469$	7.30015	+	8.42482i	0.337090	+	0.389022i
$470$	15.4818	+	9.94952i	0.714120	+	0.458937i
$471$	0.690996	−	4.80598i	0.0318394	−	0.221448i
$472$	−0.630188	+	4.38305i	−0.0290068	+	0.201746i
$473$	26.3955	+	16.9634i	1.21367	+	0.779976i
$474$	−14.5172	−	16.7537i	−0.666797	−	0.769525i
$475$	2.59256	+	5.67692i	0.118955	+	0.260475i
$476$	−0.716515	+	0.460476i	−0.0328414	+	0.0211059i
$477$	−9.89556	−	2.90560i	−0.453086	−	0.133038i
$478$	1.05178	−	1.21382i	0.0481072	−	0.0555187i
$479$	15.1748	−	4.45571i	0.693352	−	0.203587i	0.0839760	−	0.996468i	$-0.473238\pi$
$479$	15.1748	−	4.45571i	0.693352	−	0.203587i	0.609376	+	0.792881i	$0.291420\pi$
$480$	1.67347	−	3.66438i	0.0763829	−	0.167255i
$481$	0.814214	+	5.66298i	0.0371250	+	0.258210i
$482$	5.81234			0.264745
$483$	0.570388	−	4.76179i	0.0259535	−	0.216669i
$484$	0.0234955			0.00106798
$485$	2.49931	+	17.3831i	0.113488	+	0.789327i
$486$	−0.544078	+	1.19136i	−0.0246799	+	0.0540414i
$487$	7.46889	−	2.19306i	0.338448	−	0.0993772i	−0.108092	−	0.994141i	$-0.534474\pi$
$487$	7.46889	−	2.19306i	0.338448	−	0.0993772i	0.446540	+	0.894764i	$0.352656\pi$
$488$	−6.54628	+	7.55481i	−0.296336	+	0.341990i
$489$	16.1009	+	4.72766i	0.728110	+	0.213792i
$490$	2.77887	−	1.78587i	0.125536	−	0.0806774i
$491$	−4.49390	−	9.84026i	−0.202807	−	0.444085i	0.780712	−	0.624891i	$-0.214857\pi$
$491$	−4.49390	−	9.84026i	−0.202807	−	0.444085i	−0.983519	+	0.180806i	$0.942129\pi$
$492$	2.32640	+	2.68481i	0.104882	+	0.121041i
$493$	−23.0879	−	14.8377i	−1.03983	−	0.668256i
$494$	−2.25377	+	15.6753i	−0.101402	+	0.705265i
$495$	−1.18597	+	8.24859i	−0.0533053	+	0.370746i
$496$	0.571320	+	0.367165i	0.0256530	+	0.0164862i
$497$	4.98672	+	5.75499i	0.223685	+	0.258146i
$498$	−3.12274	−	6.83786i	−0.139934	−	0.306412i
$499$	−23.4986	+	15.1016i	−1.05194	+	0.676043i	−0.947912	−	0.318532i	$-0.896810\pi$
$499$	−23.4986	+	15.1016i	−1.05194	+	0.676043i	−0.104031	+	0.994574i	$0.533174\pi$
$500$	2.50650	+	0.735976i	0.112094	+	0.0329138i
$501$	−14.4532	+	16.6798i	−0.645720	+	0.745200i
$502$	−36.1444	+	10.6130i	−1.61320	+	0.473679i
$503$	5.26285	−	11.5240i	0.234659	−	0.513831i	−0.755267	−	0.655417i	$-0.772493\pi$
$503$	5.26285	−	11.5240i	0.234659	−	0.513831i	0.989926	+	0.141586i	$0.0452201\pi$
$504$	−0.425839	−	2.96177i	−0.0189684	−	0.131928i
$505$	−5.74703			−0.255739
$506$	20.0457	+	5.37589i	0.891142	+	0.238988i
$507$	−6.04702			−0.268558
$508$	−0.375725	−	2.61322i	−0.0166701	−	0.115943i
$509$	−18.0043	+	39.4239i	−0.798026	+	1.74743i	−0.145934	+	0.989294i	$0.546619\pi$
$509$	−18.0043	+	39.4239i	−0.798026	+	1.74743i	−0.652092	+	0.758140i	$0.726108\pi$
$510$	−9.48421	+	2.78482i	−0.419968	+	0.123314i
$511$	3.19317	−	3.68512i	0.141258	−	0.163020i
$512$	−24.3679	−	7.15506i	−1.07692	−	0.316212i
$513$	3.85764	−	2.47915i	0.170319	−	0.109457i
$514$	1.56229	+	3.42093i	0.0689095	+	0.150891i
$515$	5.43149	+	6.26827i	0.239340	+	0.276213i
$516$	2.27379	+	1.46127i	0.100098	+	0.0643290i
$517$	2.61977	−	18.2209i	0.115217	−	0.801355i
$518$	0.404419	−	2.81280i	0.0177692	−	0.123587i
$519$	−4.52799	−	2.90996i	−0.198757	−	0.127733i
$520$	−13.0314	−	15.0390i	−0.571465	−	0.659506i
$521$	4.15968	+	9.10843i	0.182239	+	0.399047i	0.978599	−	0.205775i	$-0.0659714\pi$
$521$	4.15968	+	9.10843i	0.182239	+	0.399047i	−0.796361	+	0.604822i	$0.793244\pi$
$522$	10.1052	−	6.49422i	0.442293	−	0.284244i
$523$	4.27279	+	1.25461i	0.186836	+	0.0548600i	0.373812	−	0.927504i	$-0.378050\pi$
$523$	4.27279	+	1.25461i	0.186836	+	0.0548600i	−0.186976	+	0.982364i	$0.559869\pi$
$524$	−3.73867	+	4.31465i	−0.163324	+	0.188486i
$525$	−1.30585	+	0.383433i	−0.0569921	+	0.0167344i
$526$	−17.0028	+	37.2309i	−0.741357	+	1.62334i
$527$	0.0863399	+	0.600507i	0.00376102	+	0.0261585i
$528$	11.0680			0.481674
$529$	19.9136	+	11.5086i	0.865809	+	0.500375i
$530$	34.0674			1.47979
$531$	−0.210608	−	1.46481i	−0.00913962	−	0.0635674i
$532$	−0.542197	+	1.18724i	−0.0235072	+	0.0514736i
$533$	31.5779	−	9.27210i	1.36779	−	0.401619i
$534$	11.3153	−	13.0585i	0.489660	−	0.565098i
$535$	−23.3470	−	6.85531i	−1.00938	−	0.296381i
$536$	−28.0611	+	18.0338i	−1.21205	+	0.778940i
$537$	−2.83636	−	6.21077i	−0.122398	−	0.268014i
$538$	12.9863	+	14.9870i	0.559878	+	0.646133i
$539$	−2.77963	−	1.78636i	−0.119727	−	0.0769441i
$540$	−0.102163	+	0.710557i	−0.00439638	+	0.0305775i
$541$	−5.70598	+	39.6860i	−0.245319	+	1.70623i	0.379275	+	0.925284i	$0.376173\pi$
$541$	−5.70598	+	39.6860i	−0.245319	+	1.70623i	−0.624594	+	0.780949i	$0.714736\pi$
$542$	−25.8190	−	16.5929i	−1.10902	−	0.712725i
$543$	−6.72939	−	7.76613i	−0.288786	−	0.333276i
$544$	−1.98551	−	4.34767i	−0.0851282	−	0.186405i
$545$	−28.0852	+	18.0493i	−1.20304	+	0.773145i
$546$	−3.31365	−	0.972974i	−0.141811	−	0.0416395i
$547$	27.1099	−	31.2865i	1.15914	−	1.33772i	0.227735	−	0.973723i	$-0.426868\pi$
$547$	27.1099	−	31.2865i	1.15914	−	1.33772i	0.931402	−	0.363993i	$-0.118587\pi$
$548$	2.39521	−	0.703297i	0.102318	−	0.0300434i
$549$	1.38782	−	3.03890i	0.0592307	−	0.129697i
$550$	−0.838189	−	5.82974i	−0.0357405	−	0.248581i
$551$	−42.0565			−1.79167
$552$	13.8604	+	3.71711i	0.589940	+	0.158211i
$553$	−16.9260			−0.719768
$554$	−0.850189	−	5.91319i	−0.0361211	−	0.251228i
$555$	−2.27325	+	4.97772i	−0.0964941	+	0.211293i
$556$	−0.102389	+	0.0300642i	−0.00434227	+	0.00127501i
$557$	18.2912	−	21.1092i	0.775024	−	0.894425i	−0.221716	−	0.975111i	$-0.571166\pi$
$557$	18.2912	−	21.1092i	0.775024	−	0.894425i	0.996740	+	0.0806863i	$0.0257112\pi$
$558$	−0.254779	−	0.0748099i	−0.0107857	−	0.00316695i
$559$	21.0647	−	13.5374i	0.890941	−	0.572573i
$560$	3.50957	+	7.68488i	0.148306	+	0.324746i
$561$	6.47482	+	7.47234i	0.273367	+	0.315483i
$562$	8.11024	+	5.21213i	0.342110	+	0.219861i
$563$	2.27463	−	15.8204i	0.0958642	−	0.666750i	−0.884059	−	0.467375i	$-0.845200\pi$
$563$	2.27463	−	15.8204i	0.0958642	−	0.666750i	0.979923	−	0.199375i	$-0.0638912\pi$
$564$	0.225675	−	1.56960i	0.00950262	−	0.0660922i
$565$	−21.4343	−	13.7750i	−0.901748	−	0.579518i
$566$	17.9882	+	20.7594i	0.756099	+	0.872585i
$567$	0.415415	+	0.909632i	0.0174458	+	0.0382010i
$568$	−19.1685	+	12.3188i	−0.804292	+	0.516887i
$569$	12.5407	+	3.68229i	0.525734	+	0.154370i	0.533821	−	0.845598i	$-0.320756\pi$
$569$	12.5407	+	3.68229i	0.525734	+	0.154370i	−0.00808620	+	0.999967i	$0.502574\pi$
$570$	−9.91938	+	11.4476i	−0.415477	+	0.479486i
$571$	−9.89261	+	2.90473i	−0.413993	+	0.121559i	−0.482095	−	0.876119i	$-0.660124\pi$
$571$	−9.89261	+	2.90473i	−0.413993	+	0.121559i	0.0681020	+	0.997678i	$0.478306\pi$
$572$	−1.03017	+	2.25576i	−0.0430735	+	0.0943179i
$573$	3.61689	+	25.1560i	0.151098	+	1.05091i
$574$	−16.3469			−0.682305
$575$	0.776288	−	6.48071i	0.0323734	−	0.270264i
$576$	8.79140			0.366308
$577$	−3.17575	−	22.0878i	−0.132208	−	0.919529i	−0.942667	−	0.333733i	$-0.891691\pi$
$577$	−3.17575	−	22.0878i	−0.132208	−	0.919529i	0.810459	−	0.585795i	$-0.199218\pi$
$578$	4.37743	−	9.58524i	0.182077	−	0.398693i
$579$	−20.1918	+	5.92883i	−0.839141	+	0.246394i
$580$	4.31152	−	4.97576i	0.179026	−	0.206607i
$581$	−5.50703	−	1.61701i	−0.228470	−	0.0670848i
$582$	−7.67210	+	4.93056i	−0.318019	+	0.204378i
$583$	−14.1560	−	30.9974i	−0.586283	−	1.28378i
$584$	9.55470	+	11.0267i	0.395376	+	0.456289i
$585$	5.59467	+	3.59548i	0.231311	+	0.148655i
$586$	−0.860861	+	5.98742i	−0.0355618	+	0.247338i
$587$	4.01482	−	27.9237i	0.165709	−	1.15253i	−0.721921	−	0.691976i	$-0.756740\pi$
$587$	4.01482	−	27.9237i	0.165709	−	1.15253i	0.887630	−	0.460557i	$-0.152350\pi$
$588$	−0.239446	−	0.153882i	−0.00987458	−	0.00634600i
$589$	0.608816	+	0.702611i	0.0250858	+	0.0289506i
$590$	2.03071	+	4.44664i	0.0836031	+	0.183065i
$591$	−3.66346	+	2.35436i	−0.150695	+	0.0968456i
$592$	6.97355	+	2.04762i	0.286611	+	0.0841566i
$593$	10.6300	−	12.2677i	0.436521	−	0.503772i	−0.494278	−	0.869304i	$-0.664567\pi$
$593$	10.6300	−	12.2677i	0.436521	−	0.503772i	0.930799	+	0.365532i	$0.119113\pi$
$594$	−4.15223	+	1.21920i	−0.170368	+	0.0500246i
$595$	−3.13518	+	6.86509i	−0.128530	+	0.281441i
$596$	0.401261	+	2.79083i	0.0164363	+	0.114317i
$597$	−3.48579			−0.142664
$598$	10.5480	−	12.7695i	0.431340	−	0.522182i
$599$	−17.3022			−0.706950			−0.353475	−	0.935444i	$-0.615000\pi$
$599$	−17.3022			−0.706950			−0.353475	+	0.935444i	$0.615000\pi$
$600$	−0.579559	−	4.03092i	−0.0236604	−	0.164562i
$601$	−1.28248	+	2.80824i	−0.0523135	+	0.114551i	−0.933984	−	0.357315i	$-0.883692\pi$
$601$	−1.28248	+	2.80824i	−0.0523135	+	0.114551i	0.881670	+	0.471866i	$0.156419\pi$
$602$	−11.9334	+	3.50395i	−0.486368	+	0.142811i
$603$	7.30015	−	8.42482i	0.297285	−	0.343085i
$604$	0.310292	+	0.0911098i	0.0126256	+	0.00370721i
$605$	0.175143	−	0.112558i	0.00712059	−	0.00457612i
$606$	−1.23977	−	2.71472i	−0.0503623	−	0.110278i
$607$	28.8973	+	33.3493i	1.17291	+	1.35361i	0.922750	+	0.385400i	$0.125937\pi$
$607$	28.8973	+	33.3493i	1.17291	+	1.35361i	0.250156	+	0.968205i	$0.419518\pi$
$608$	−6.16160	−	3.95982i	−0.249886	−	0.160592i
$609$	1.30524	−	9.07812i	0.0528909	−	0.367864i
$610$	−1.57052	+	10.9232i	−0.0635883	+	0.442266i
$611$	−12.3585	−	7.94231i	−0.499970	−	0.321311i
$612$	0.557760	+	0.643689i	0.0225461	+	0.0260196i
$613$	1.57867	+	3.45681i	0.0637620	+	0.139619i	0.938830	−	0.344380i	$-0.111911\pi$
$613$	1.57867	+	3.45681i	0.0637620	+	0.139619i	−0.875068	+	0.483999i	$0.839184\pi$
$614$	27.6894	−	17.7949i	1.11745	−	0.718143i
$615$	30.2037	+	8.86859i	1.21793	+	0.357616i
$616$	6.47447	−	7.47194i	0.260864	−	0.301053i
$617$	16.9638	−	4.98102i	0.682937	−	0.200528i	0.0781810	−	0.996939i	$-0.475089\pi$
$617$	16.9638	−	4.98102i	0.682937	−	0.200528i	0.604756	+	0.796411i	$0.293271\pi$
$618$	−1.78924	+	3.91789i	−0.0719739	+	0.157601i
$619$	2.07272	+	14.4161i	0.0833097	+	0.579431i	0.988128	+	0.153633i	$0.0490975\pi$
$619$	2.07272	+	14.4161i	0.0833097	+	0.579431i	−0.904818	+	0.425798i	$0.859993\pi$
$620$	−0.145541			−0.00584506
$621$	−4.79450	+	0.113091i	−0.192397	+	0.00453820i
$622$	22.4418			0.899836
$623$	−1.87753	−	13.0585i	−0.0752217	−	0.523179i
$624$	3.66925	−	8.03453i	0.146887	−	0.321639i
$625$	28.7393	−	8.43863i	1.14957	−	0.337545i
$626$	−2.84243	+	3.28034i	−0.113606	+	0.131109i
$627$	14.5377	+	4.26866i	0.580581	+	0.170474i
$628$	1.16261	−	0.747161i	0.0463930	−	0.0298150i
$629$	2.69714	+	5.90591i	0.107542	+	0.235484i
$630$	−2.16317	−	2.49643i	−0.0861826	−	0.0994600i
$631$	−11.4500	−	7.35845i	−0.455816	−	0.292935i	0.292514	−	0.956261i	$-0.405508\pi$
$631$	−11.4500	−	7.35845i	−0.455816	−	0.292935i	−0.748331	+	0.663326i	$0.769144\pi$
$632$	7.20775	−	50.1310i	0.286709	−	1.99410i
$633$	−0.298079	+	2.07319i	−0.0118476	+	0.0824018i
$634$	−3.95096	−	2.53913i	−0.156913	−	0.100842i
$635$	−15.3197	−	17.6799i	−0.607944	−	0.701605i
$636$	−1.21944	−	2.67020i	−0.0483540	−	0.105880i
$637$	−2.21826	+	1.42559i	−0.0878906	+	0.0564839i
$638$	38.0821	+	11.1819i	1.50768	+	0.442696i
$639$	4.98672	−	5.75499i	0.197272	−	0.227664i
$640$	−20.1334	+	5.91169i	−0.795841	+	0.233680i
$641$	7.58613	−	16.6113i	0.299634	−	0.656107i	−0.698600	−	0.715512i	$-0.746193\pi$
$641$	7.58613	−	16.6113i	0.299634	−	0.656107i	0.998234	+	0.0594056i	$0.0189205\pi$
$642$	−1.79828	−	12.5073i	−0.0709724	−	0.493624i
$643$	−46.0420			−1.81572			−0.907859	−	0.419275i	$-0.862284\pi$
$643$	−46.0420			−1.81572			−0.907859	+	0.419275i	$0.862284\pi$
$644$	1.13062	−	0.764868i	0.0445526	−	0.0301400i
$645$	23.9499			0.943028
$646$	2.55765	+	17.7889i	0.100630	+	0.699894i
$647$	17.5091	−	38.3397i	0.688355	−	1.50729i	−0.165187	−	0.986262i	$-0.552823\pi$
$647$	17.5091	−	38.3397i	0.688355	−	1.50729i	0.853542	−	0.521025i	$-0.174450\pi$
$648$	−2.87102	+	0.843008i	−0.112784	+	0.0331165i
$649$	3.20210	−	3.69542i	0.125693	−	0.145058i
$650$	−4.50981	−	1.32420i	−0.176889	−	0.0519394i
$651$	−0.170557	+	0.109610i	−0.00668466	+	0.00429597i
$652$	1.98414	+	4.34466i	0.0777049	+	0.170150i
$653$	−26.1701	−	30.2019i	−1.02411	−	1.18189i	−0.983163	−	0.182729i	$-0.941507\pi$
$653$	−26.1701	−	30.2019i	−1.02411	−	1.18189i	−0.0409500	−	0.999161i	$-0.513038\pi$
$654$	−14.5846	−	9.37294i	−0.570302	−	0.366511i
$655$	−7.19946	+	50.0733i	−0.281306	+	1.95653i
$656$	5.94998	−	41.3830i	0.232308	−	1.61573i
$657$	−4.10205	−	2.63622i	−0.160036	−	0.102849i
$658$	4.77838	+	5.51454i	0.186281	+	0.214979i
$659$	4.28633	+	9.38574i	0.166972	+	0.365617i	0.974559	−	0.224131i	$-0.0719544\pi$
$659$	4.28633	+	9.38574i	0.166972	+	0.365617i	−0.807587	+	0.589748i	$0.799227\pi$
$660$	−1.99540	+	1.28237i	−0.0776708	+	0.0499160i
$661$	−8.52557	−	2.50333i	−0.331606	−	0.0973684i	0.111691	−	0.993743i	$-0.464373\pi$
$661$	−8.52557	−	2.50333i	−0.331606	−	0.0973684i	−0.443297	+	0.896375i	$0.646191\pi$
$662$	−16.1213	+	18.6050i	−0.626573	+	0.723103i
$663$	7.57087	−	2.22301i	0.294028	−	0.0863344i
$664$	7.13431	−	15.6220i	0.276865	−	0.606250i
$665$	1.64591	+	11.4476i	0.0638257	+	0.443918i
$666$	−2.84172			−0.110115
$667$	37.5529	+	22.9008i	1.45405	+	0.886724i
$668$	−6.28194			−0.243056
$669$	−0.222964	−	1.55075i	−0.00862030	−	0.0599555i
$670$	−15.2970	+	33.4957i	−0.590974	+	1.29405i
$671$	10.5914	−	3.10992i	0.408877	−	0.120057i
$672$	1.04598	−	1.20712i	0.0403494	−	0.0465657i
$673$	40.0901	+	11.7715i	1.54536	+	0.453759i	0.939710	−	0.341973i	$-0.111095\pi$
$673$	40.0901	+	11.7715i	1.54536	+	0.453759i	0.605650	+	0.795731i	$0.292913\pi$
$674$	32.6268	−	20.9679i	1.25674	−	0.807655i
$675$	0.565372	+	1.23799i	0.0217612	+	0.0476504i
$676$	−1.12712	−	1.30077i	−0.0433508	−	0.0500295i
$677$	3.48970	+	2.24269i	0.134120	+	0.0861937i	0.605980	−	0.795480i	$-0.292781\pi$
$677$	3.48970	+	2.24269i	0.134120	+	0.0861937i	−0.471860	+	0.881673i	$0.656417\pi$
$678$	1.88300	−	13.0965i	0.0723160	−	0.502969i
$679$	−0.990966	+	6.89232i	−0.0380298	+	0.264503i
$680$	−18.9977	−	12.2091i	−0.728530	−	0.468198i
$681$	−12.1437	−	14.0146i	−0.465348	−	0.537040i
$682$	−0.364472	−	0.798083i	−0.0139564	−	0.0305602i
$683$	1.38359	−	0.889182i	0.0529418	−	0.0340236i	−0.513902	−	0.857849i	$-0.671801\pi$
$683$	1.38359	−	0.889182i	0.0529418	−	0.0340236i	0.566844	+	0.823825i	$0.308164\pi$
$684$	1.25232	+	0.367715i	0.0478838	+	0.0140599i
$685$	14.4855	−	16.7171i	0.553461	−	0.638728i
$686$	1.25667	−	0.368991i	0.0479798	−	0.0140881i
$687$	9.36386	−	20.5040i	0.357253	−	0.782276i
$688$	−4.52691	−	31.4854i	−0.172587	−	1.20037i
$689$	−27.1947			−1.03603
$690$	15.0906	−	4.82035i	0.574491	−	0.183508i
$691$	−38.3026			−1.45710			−0.728550	−	0.684993i	$-0.759805\pi$
$691$	−38.3026			−1.45710			−0.728550	+	0.684993i	$0.759805\pi$
$692$	−0.218026	−	1.51641i	−0.00828812	−	0.0576451i
$693$	−1.37260	+	3.00557i	−0.0521406	+	0.114172i
$694$	−18.3255	+	5.38085i	−0.695626	+	0.204254i
$695$	−0.619218	+	0.714616i	−0.0234883	+	0.0271069i
$696$	26.3315	+	7.73163i	0.998093	+	0.293067i
$697$	31.4196	−	20.1922i	1.19010	−	0.764833i
$698$	−2.57016	−	5.62786i	−0.0972820	−	0.213018i
$699$	3.92617	+	4.53105i	0.148502	+	0.171380i
$700$	−0.325881	−	0.209431i	−0.0123172	−	0.00791576i
$701$	−0.215004	+	1.49539i	−0.00812060	+	0.0564800i	−0.993479	−	0.114017i	$-0.963628\pi$
$701$	−0.215004	+	1.49539i	−0.00812060	+	0.0564800i	0.985358	+	0.170497i	$0.0545373\pi$
$702$	−0.491490	+	3.41839i	−0.0185501	+	0.129019i
$703$	8.36997	+	5.37906i	0.315680	+	0.202875i
$704$	19.0225	+	21.9531i	0.716938	+	0.827390i
$705$	−5.83709	−	12.7815i	−0.219838	−	0.481377i
$706$	9.03982	−	5.80954i	0.340218	−	0.218645i
$707$	−2.18637	−	0.641975i	−0.0822268	−	0.0241440i
$708$	0.275838	−	0.318334i	0.0103666	−	0.0119637i
$709$	6.39523	−	1.87781i	0.240178	−	0.0705226i	−0.159428	−	0.987210i	$-0.550965\pi$
$709$	6.39523	−	1.87781i	0.240178	−	0.0705226i	0.399606	+	0.916687i	$0.369147\pi$
$710$	−10.4494	+	22.8809i	−0.392157	+	0.858705i
$711$	2.40882	+	16.7537i	0.0903379	+	0.628314i
$712$	39.4759			1.47942
$713$	−0.161031	−	0.958887i	−0.00603067	−	0.0359106i
$714$	−3.91920			−0.146672
$715$	3.12722	+	21.7503i	0.116951	+	0.813415i
$716$	0.807313	−	1.76777i	0.0301707	−	0.0660646i
$717$	−1.17662	+	0.345488i	−0.0439419	+	0.0129025i
$718$	8.59742	−	9.92195i	0.320853	−	0.370284i
$719$	−47.6209	−	13.9828i	−1.77596	−	0.521469i	−0.781252	−	0.624216i	$-0.785418\pi$
$719$	−47.6209	−	13.9828i	−1.77596	−	0.521469i	−0.994707	+	0.102748i	$0.967237\pi$
$720$	7.10720	−	4.56752i	0.264870	−	0.170221i
$721$	1.36612	+	2.99139i	0.0508771	+	0.111405i
$722$	1.73900	+	2.00691i	0.0647189	+	0.0746896i
$723$	−3.73335	−	2.39928i	−0.138845	−	0.0892302i
$724$	0.416253	−	2.89510i	0.0154699	−	0.107596i
$725$	1.77640	−	12.3552i	0.0659740	−	0.458859i
$726$	0.0909516	+	0.0584510i	0.00337553	+	0.00216932i
$727$	21.6998	+	25.0429i	0.804802	+	0.928790i	0.998634	−	0.0522441i	$-0.0166374\pi$
$727$	21.6998	+	25.0429i	0.804802	+	0.928790i	−0.193833	+	0.981035i	$0.562092\pi$
$728$	−3.27765	−	7.17705i	−0.121478	−	0.265999i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	15.4546	+	4.53787i	0.571999	+	0.167954i
$731$	18.6084	−	21.4753i	0.688258	−	0.794292i
$732$	0.912374	−	0.267897i	0.0337223	−	0.00990177i
$733$	−20.1278	+	44.0738i	−0.743438	+	1.62790i	0.0343783	+	0.999409i	$0.489055\pi$
$733$	−20.1278	+	44.0738i	−0.743438	+	1.62790i	−0.777816	+	0.628492i	$0.783672\pi$
$734$	−2.24431	−	15.6095i	−0.0828391	−	0.576159i
$735$	−2.52210			−0.0930290
$736$	3.34556	+	6.89093i	0.123319	+	0.254003i
$737$	36.8335			1.35678
$738$	2.32640	+	16.1805i	0.0856360	+	0.595612i
$739$	−14.0636	+	30.7950i	−0.517339	+	1.13281i	0.453099	+	0.891460i	$0.350319\pi$
$739$	−14.0636	+	30.7950i	−0.517339	+	1.13281i	−0.970437	+	0.241353i	$0.922409\pi$
$740$	−1.49447	+	0.438816i	−0.0549378	+	0.0161312i
$741$	7.91824	−	9.13814i	0.290884	−	0.335698i
$742$	12.9604	+	3.80552i	0.475792	+	0.139705i
$743$	−29.9633	+	19.2562i	−1.09925	+	0.706443i	−0.958924	−	0.283663i	$-0.908450\pi$
$743$	−29.9633	+	19.2562i	−1.09925	+	0.706443i	−0.140323	+	0.990106i	$0.544814\pi$
$744$	−0.252011	−	0.551827i	−0.00923918	−	0.0202310i
$745$	16.3609	+	18.8815i	0.599417	+	0.691764i
$746$	38.3231	+	24.6287i	1.40311	+	0.901722i
$747$	−0.816818	+	5.68110i	−0.0298858	+	0.207860i
$748$	−0.400506	+	2.78558i	−0.0146440	+	0.101851i
$749$	−8.11624	−	5.21599i	−0.296561	−	0.190588i
$750$	7.87180	+	9.08454i	0.287438	+	0.331721i
$751$	12.7324	+	27.8800i	0.464611	+	1.01736i	0.986412	+	0.164289i	$0.0525330\pi$
$751$	12.7324	+	27.8800i	0.464611	+	1.01736i	−0.521801	+	0.853067i	$0.674740\pi$
$752$	−15.6996	+	10.0895i	−0.572506	+	0.367927i
$753$	27.5970	+	8.10321i	1.00569	+	0.295297i
$754$	20.7421	−	23.9377i	0.755383	−	0.871758i
$755$	2.74949	−	0.807323i	0.100064	−	0.0293815i
$756$	−0.118239	+	0.258908i	−0.00430033	+	0.00941640i
$757$	1.14421	+	7.95819i	0.0415872	+	0.289245i	0.999993	+	0.00383507i	$0.00122074\pi$
$757$	1.14421	+	7.95819i	0.0415872	+	0.289245i	−0.958405	+	0.285410i	$0.907870\pi$
$758$	7.51075			0.272803
$759$	−10.6566	−	11.7277i	−0.386809	−	0.425689i
$760$	−34.6060			−1.25529
$761$	6.84705	+	47.6223i	0.248206	+	1.72631i	0.608574	+	0.793497i	$0.291742\pi$
$761$	6.84705	+	47.6223i	0.248206	+	1.72631i	−0.360368	+	0.932810i	$0.617349\pi$
$762$	5.04662	−	11.0506i	0.182820	−	0.400319i
$763$	−12.7008	+	3.72928i	−0.459799	+	0.135009i
$764$	−4.73711	+	5.46692i	−0.171383	+	0.197786i
$765$	7.24139	+	2.12627i	0.261813	+	0.0768753i
$766$	13.2823	−	8.53604i	0.479910	−	0.308419i
$767$	−1.62104	−	3.54957i	−0.0585322	−	0.128168i
$768$	4.37853	+	5.05309i	0.157996	+	0.182338i
$769$	−17.3137	−	11.1269i	−0.624349	−	0.401245i	0.189864	−	0.981810i	$-0.439195\pi$
$769$	−17.3137	−	11.1269i	−0.624349	−	0.401245i	−0.814214	+	0.580565i	$0.802832\pi$
$770$	1.55329	−	10.8034i	0.0559766	−	0.389326i
$771$	0.408648	−	2.84221i	0.0147171	−	0.102360i
$772$	−5.03894	−	3.23833i	−0.181355	−	0.116550i
$773$	7.79761	+	8.99892i	0.280460	+	0.323669i	0.878449	−	0.477836i	$-0.158579\pi$
$773$	7.79761	+	8.99892i	0.280460	+	0.323669i	−0.597989	+	0.801505i	$0.704033\pi$
$774$	5.16659	+	11.3132i	0.185709	+	0.406646i
$775$	−0.232125	+	0.149178i	−0.00833818	+	0.00535862i
$776$	−19.9915	−	5.87003i	−0.717653	−	0.210722i
$777$	−1.42086	+	1.63976i	−0.0509731	+	0.0588261i
$778$	1.64701	−	0.483606i	0.0590482	−	0.0173381i
$779$	23.7756	−	52.0614i	0.851851	−	1.86529i
$780$	0.269388	+	1.87363i	0.00964563	+	0.0670868i
$781$	25.1609			0.900330
$782$	7.40272	−	17.2766i	0.264721	−	0.617812i
$783$	−9.17148			−0.327762
$784$	0.476716	+	3.31563i	0.0170256	+	0.118415i
$785$	5.08709	−	11.1392i	0.181566	−	0.397574i
$786$	−25.2063	+	7.40122i	−0.899077	+	0.263993i
$787$	−24.8327	+	28.6585i	−0.885192	+	1.02157i	0.114413	+	0.993433i	$0.463501\pi$
$787$	−24.8327	+	28.6585i	−0.885192	+	1.02157i	−0.999604	+	0.0281323i	$0.991044\pi$
$788$	−1.18929	−	0.349206i	−0.0423666	−	0.0124400i
$789$	26.2897	−	16.8954i	0.935939	−	0.601491i
$790$	−23.2262	−	50.8583i	−0.826351	−	1.80946i
$791$	−6.61560	−	7.63481i	−0.235224	−	0.271463i
$792$	−8.31730	−	5.34520i	−0.295542	−	0.189934i
$793$	1.25368	−	8.71954i	0.0445195	−	0.309640i
$794$	−1.17725	+	8.18796i	−0.0417791	+	0.290580i
$795$	−21.8820	−	14.0627i	−0.776075	−	0.498753i
$796$	−0.649726	−	0.749823i	−0.0230289	−	0.0265768i
$797$	13.1235	+	28.7364i	0.464858	+	1.01790i	0.986353	+	0.164643i	$0.0526471\pi$
$797$	13.1235	+	28.7364i	0.464858	+	1.01790i	−0.521495	+	0.853254i	$0.674626\pi$
$798$	−5.05243	+	3.24700i	−0.178854	+	0.114943i
$799$	−15.9960	−	4.69686i	−0.565899	−	0.166163i
$800$	1.42355	−	1.64287i	0.0503302	−	0.0580842i
$801$	−12.6584	+	3.71684i	−0.447263	+	0.131328i
$802$	2.01483	−	4.41186i	0.0711460	−	0.155788i
$803$	−2.29290	−	15.9474i	−0.0809145	−	0.562773i
$804$	3.17295			0.111901
$805$	4.76383	−	11.1179i	0.167903	−	0.391856i
$806$	−0.700176			−0.0246626
$807$	−2.15480	−	14.9870i	−0.0758525	−	0.527566i
$808$	2.83242	−	6.20214i	0.0996443	−	0.218191i
$809$	−34.5904	+	10.1567i	−1.21613	+	0.357089i	−0.826001	−	0.563669i	$-0.809389\pi$
$809$	−34.5904	+	10.1567i	−1.21613	+	0.357089i	−0.390134	+	0.920758i	$0.627571\pi$
$810$	−2.16317	+	2.49643i	−0.0760059	+	0.0877155i
$811$	51.3652	+	15.0822i	1.80368	+	0.529607i	0.998027	−	0.0627875i	$-0.0199990\pi$
$811$	51.3652	+	15.0822i	1.80368	+	0.529607i	0.805648	+	0.592394i	$0.201817\pi$
$812$	2.19607	−	1.41133i	0.0770670	−	0.0495279i
$813$	9.73455	+	21.3157i	0.341406	+	0.747574i
$814$	−6.14882	−	7.09611i	−0.215516	−	0.248719i
$815$	35.6040	+	22.8813i	1.24715	+	0.801497i
$816$	1.42652	−	9.92166i	0.0499382	−	0.347328i
$817$	6.19708	−	43.1016i	0.216808	−	1.50794i
$818$	5.94347	+	3.81963i	0.207808	+	0.133550i
$819$	1.72677	+	1.99280i	0.0603382	+	0.0696340i
$820$	3.72203	+	8.15011i	0.129979	+	0.284614i
$821$	33.8258	−	21.7385i	1.18053	−	0.758680i	0.205046	−	0.978752i	$-0.434266\pi$
$821$	33.8258	−	21.7385i	1.18053	−	0.758680i	0.975484	+	0.220072i	$0.0706292\pi$
$822$	11.0215	+	3.23622i	0.384420	+	0.112876i
$823$	−1.63966	+	1.89227i	−0.0571550	+	0.0659604i	−0.783607	−	0.621257i	$-0.786622\pi$
$823$	−1.63966	+	1.89227i	−0.0571550	+	0.0659604i	0.726452	+	0.687217i	$0.241168\pi$
$824$	−9.44158	+	2.77230i	−0.328913	+	0.0965776i
$825$	−1.86808	+	4.09052i	−0.0650382	+	0.142414i
$826$	0.275838	+	1.91850i	0.00959764	+	0.0667530i
$827$	−10.6733			−0.371147			−0.185573	−	0.982630i	$-0.559414\pi$
$827$	−10.6733			−0.371147			−0.185573	+	0.982630i	$0.559414\pi$
$828$	−0.917987	−	1.01026i	−0.0319022	−	0.0351089i
$829$	−46.5506			−1.61677			−0.808385	−	0.588654i	$-0.799658\pi$
$829$	−46.5506			−1.61677			−0.808385	+	0.588654i	$0.799658\pi$
$830$	−2.69815	−	18.7661i	−0.0936542	−	0.651380i
$831$	−1.89482	+	4.14908i	−0.0657307	+	0.143930i
$832$	22.2426	−	6.53102i	0.771123	−	0.226422i
$833$	−1.95960	+	2.26150i	−0.0678961	+	0.0783563i
$834$	−0.471144	−	0.138340i	−0.0163144	−	0.00479033i
$835$	−46.8277	+	30.0943i	−1.62054	+	1.04146i
$836$	1.79150	+	3.92284i	0.0619604	+	0.135674i
$837$	0.132768	+	0.153222i	0.00458912	+	0.00529612i
$838$	−28.0467	−	18.0245i	−0.968858	−	0.622647i
$839$	5.49119	−	38.1920i	0.189577	−	1.31854i	−0.643529	−	0.765422i	$-0.722530\pi$
$839$	5.49119	−	38.1920i	0.189577	−	1.31854i	0.833106	−	0.553114i	$-0.186560\pi$
$840$	1.07401	−	7.46988i	0.0370568	−	0.257735i
$841$	46.3665	+	29.7980i	1.59885	+	1.02752i
$842$	18.1464	+	20.9420i	0.625365	+	0.721709i
$843$	−3.05781	−	6.69566i	−0.105316	−	0.230611i
$844$	−0.501520	+	0.322308i	−0.0172630	+	0.0110943i
$845$	−14.6334	−	4.29676i	−0.503404	−	0.147813i
$846$	4.77838	−	5.51454i	0.164284	−	0.189594i
$847$	0.0792039	−	0.0232563i	0.00272148	−	0.000799098i
$848$	−14.3513	+	31.4249i	−0.492824	+	1.07913i
$849$	−2.98476	−	20.7594i	−0.102437	−	0.712462i
$850$	−5.33396			−0.182953
$851$	−4.54464	−	9.36069i	−0.155788	−	0.320880i
$852$	2.16744			0.0742552
$853$	3.48496	+	24.2385i	0.119323	+	0.829909i	0.958304	+	0.285749i	$0.0922424\pi$
$853$	3.48496	+	24.2385i	0.119323	+	0.829909i	−0.838982	+	0.544160i	$0.816849\pi$
$854$	−1.81766	+	3.98012i	−0.0621990	+	0.136197i
$855$	11.0968	−	3.25832i	0.379503	−	0.111432i
$856$	18.9048	−	21.8173i	0.646152	−	0.745700i
$857$	13.2432	+	3.88857i	0.452381	+	0.132831i	0.499983	−	0.866035i	$-0.333340\pi$
$857$	13.2432	+	3.88857i	0.452381	+	0.132831i	−0.0476019	+	0.998866i	$0.515158\pi$
$858$	−9.59957	+	6.16927i	−0.327724	+	0.210615i
$859$	−1.31133	−	2.87141i	−0.0447420	−	0.0979714i	0.885941	−	0.463798i	$-0.153514\pi$
$859$	−1.31133	−	2.87141i	−0.0447420	−	0.0979714i	−0.930683	+	0.365827i	$0.880786\pi$
$860$	4.46410	+	5.15184i	0.152224	+	0.175676i
$861$	10.4998	+	6.74784i	0.357833	+	0.229966i
$862$	5.82751	−	40.5312i	0.198486	−	1.38050i
$863$	−5.11346	+	35.5649i	−0.174064	+	1.21064i	0.696123	+	0.717922i	$0.254907\pi$
$863$	−5.11346	+	35.5649i	−0.174064	+	1.21064i	−0.870188	+	0.492721i	$0.836002\pi$
$864$	−1.34369	−	0.863538i	−0.0457133	−	0.0293781i
$865$	−8.88975	−	10.2593i	−0.302261	−	0.348827i
$866$	−1.06529	−	2.33265i	−0.0361999	−	0.0792667i
$867$	−6.76839	+	4.34978i	−0.229866	+	0.147726i
$868$	−0.0553688	−	0.0162577i	−0.00187934	−	0.000551823i
$869$	−36.6239	+	42.2662i	−1.24238	+	1.43378i
$870$	29.0685	−	8.53527i	0.985513	−	0.289373i
$871$	12.2110	−	26.7383i	0.413753	−	0.905993i
$872$	−5.63681	−	39.2049i	−0.190886	−	1.32764i
$873$	6.96320			0.235668
$874$	−4.77024	−	28.4052i	−0.161356	−	0.960820i
$875$	9.17796			0.310272
$876$	−0.197517	−	1.37376i	−0.00667347	−	0.0464150i
$877$	−6.94981	+	15.2180i	−0.234678	+	0.513874i	−0.989929	−	0.141562i	$-0.954788\pi$
$877$	−6.94981	+	15.2180i	−0.234678	+	0.513874i	0.755251	+	0.655436i	$0.227515\pi$
$878$	5.55948	−	1.63241i	0.187623	−	0.0550912i
$879$	3.02449	−	3.49045i	0.102014	−	0.117730i
$880$	26.7839	+	7.86446i	0.902885	+	0.265111i
$881$	−19.6619	+	12.6359i	−0.662426	+	0.425715i	−0.828188	−	0.560450i	$-0.810628\pi$
$881$	−19.6619	+	12.6359i	−0.662426	+	0.425715i	0.165762	+	0.986166i	$0.446992\pi$
$882$	−0.544078	−	1.19136i	−0.0183201	−	0.0401153i
$883$	3.56380	+	4.11285i	0.119932	+	0.138408i	0.812540	−	0.582905i	$-0.198084\pi$
$883$	3.56380	+	4.11285i	0.119932	+	0.138408i	−0.692609	+	0.721314i	$0.743539\pi$
$884$	1.88934	+	1.21421i	0.0635455	+	0.0408382i
$885$	0.531175	−	3.69440i	0.0178552	−	0.124186i
$886$	−3.56299	+	24.7811i	−0.119701	+	0.832539i
$887$	0.494927	+	0.318071i	0.0166180	+	0.0106798i	0.548923	−	0.835873i	$-0.315038\pi$
$887$	0.494927	+	0.318071i	0.0166180	+	0.0106798i	−0.532305	+	0.846552i	$0.678674\pi$
$888$	−4.25154	−	4.90654i	−0.142672	−	0.164653i
$889$	−3.85320	−	8.43733i	−0.129232	−	0.282979i
$890$	36.6611	−	23.5606i	1.22888	−	0.789754i
$891$	3.17032	+	0.930889i	0.106210	+	0.0311859i
$892$	0.292021	−	0.337010i	0.00977759	−	0.0112839i
$893$	−24.5126	+	7.19754i	−0.820281	+	0.240856i
$894$	−5.38961	+	11.8016i	−0.180255	+	0.394704i
$895$	−2.45071	−	17.0451i	−0.0819182	−	0.569753i
$896$	−8.31979			−0.277945
$897$	−12.0463	+	3.84789i	−0.402213	+	0.128477i
$898$	18.6999			0.624023
$899$	−0.264626	−	1.84051i	−0.00882577	−	0.0613846i
$900$	−0.160922	+	0.352370i	−0.00536406	+	0.0117457i
$901$	−29.6114	+	8.69468i	−0.986498	+	0.289662i
$902$	−35.3707	+	40.8200i	−1.17772	+	1.35916i
$903$	9.11138	+	2.67534i	0.303208	+	0.0890299i
$904$	25.4297	−	16.3427i	0.845781	−	0.543550i
$905$	−10.7664	−	23.5751i	−0.357887	−	0.783664i
$906$	0.974487	+	1.12462i	0.0323752	+	0.0373629i
$907$	−20.9221	−	13.4458i	−0.694706	−	0.446461i	0.145050	−	0.989424i	$-0.453666\pi$
$907$	−20.9221	−	13.4458i	−0.694706	−	0.446461i	−0.839756	+	0.542964i	$0.817302\pi$
$908$	0.751161	−	5.22444i	0.0249282	−	0.173379i
$909$	−0.324288	+	2.25547i	−0.0107560	+	0.0748094i
$910$	−7.32746	−	4.70907i	−0.242903	−	0.156104i
$911$	−3.08440	−	3.55958i	−0.102191	−	0.117934i	0.702350	−	0.711831i	$-0.252134\pi$
$911$	−3.08440	−	3.55958i	−0.102191	−	0.117934i	−0.804541	+	0.593897i	$0.797589\pi$
$912$	−6.38096	−	13.9723i	−0.211295	−	0.462671i
$913$	−15.9538	+	10.2529i	−0.527992	+	0.339320i
$914$	18.5443	+	5.44510i	0.613391	+	0.180108i
$915$	5.51775	−	6.36782i	0.182411	−	0.210514i
$916$	6.15594	−	1.80755i	0.203398	−	0.0597231i
$917$	−8.33239	+	18.2454i	−0.275160	+	0.602516i
$918$	0.557760	+	3.87931i	0.0184088	+	0.128036i
$919$	−15.2585			−0.503331			−0.251665	−	0.967814i	$-0.580978\pi$
$919$	−15.2585			−0.503331			−0.251665	+	0.967814i	$0.580978\pi$
$920$	30.9002	+	18.8438i	1.01875	+	0.621262i
$921$	−25.1309			−0.828090
$922$	5.79702	+	40.3192i	0.190915	+	1.32784i
$923$	8.34130	−	18.2649i	0.274557	−	0.601197i
$924$	−0.902366	+	0.264959i	−0.0296857	+	0.00871649i
$925$	−1.93377	+	2.23169i	−0.0635819	+	0.0733774i
$926$	−31.4994	−	9.24906i	−1.03513	−	0.303943i
$927$	2.76653	−	1.77794i	0.0908647	−	0.0583952i
$928$	6.08547	+	13.3253i	0.199765	+	0.437425i
$929$	20.4640	+	23.6167i	0.671402	+	0.774839i	0.984595	−	0.174850i	$-0.0559442\pi$
$929$	20.4640	+	23.6167i	0.671402	+	0.774839i	−0.313193	+	0.949689i	$0.601399\pi$
$930$	−0.563392	−	0.362070i	−0.0184744	−	0.0118727i
$931$	−0.652596	+	4.53891i	−0.0213880	+	0.148757i
$932$	−0.242857	+	1.68911i	−0.00795505	+	0.0553286i
$933$	−14.4147	−	9.26378i	−0.471917	−	0.303283i
$934$	−0.0534687	−	0.0617062i	−0.00174955	−	0.00201909i
$935$	10.3591	+	22.6833i	0.338780	+	0.741824i
$936$	−6.63754	+	4.26569i	−0.216955	+	0.139428i
$937$	−23.0629	−	6.77188i	−0.753433	−	0.221228i	−0.117607	−	0.993060i	$-0.537522\pi$
$937$	−23.0629	−	6.77188i	−0.753433	−	0.221228i	−0.635826	+	0.771833i	$0.719340\pi$
$938$	−9.56116	+	11.0342i	−0.312183	+	0.360279i
$939$	3.17983	−	0.933682i	0.103770	−	0.0304696i
$940$	1.66141	−	3.63798i	0.0541892	−	0.118658i
$941$	4.94144	+	34.3685i	0.161086	+	1.12038i	0.896591	+	0.442860i	$0.146036\pi$
$941$	4.94144	+	34.3685i	0.161086	+	1.12038i	−0.735504	+	0.677520i	$0.763055\pi$
$942$	6.35922			0.207195
$943$	−49.5783	+	33.5399i	−1.61449	+	1.09221i
$944$	−4.95718			−0.161342
$945$	0.358932	+	2.49643i	0.0116761	+	0.0812088i
$946$	−17.0712	+	37.3807i	−0.555033	+	1.21535i
$947$	47.8497	−	14.0499i	1.55491	−	0.456561i	0.612343	−	0.790592i	$-0.290227\pi$
$947$	47.8497	−	14.0499i	1.55491	−	0.456561i	0.942562	+	0.334031i	$0.108409\pi$
$948$	−3.15489	+	3.64093i	−0.102466	+	0.118252i
$949$	−12.3368	−	3.62240i	−0.400468	−	0.117588i
$950$	−6.87626	+	4.41911i	−0.223095	+	0.143375i
$951$	1.48963	+	3.26184i	0.0483047	+	0.105773i
$952$	−5.86357	−	6.76692i	−0.190039	−	0.219317i
$953$	−10.8854	−	6.99565i	−0.352614	−	0.226611i	0.352327	−	0.935877i	$-0.385390\pi$
$953$	−10.8854	−	6.99565i	−0.352614	−	0.226611i	−0.704941	+	0.709266i	$0.749027\pi$
$954$	1.92233	−	13.3701i	0.0622377	−	0.432873i
$955$	−9.12215	+	63.4459i	−0.295186	+	2.05306i
$956$	−0.293632	−	0.188706i	−0.00949674	−	0.00610318i
$957$	−19.8449	−	22.9022i	−0.641494	−	0.740324i
$958$	8.60481	+	18.8419i	0.278009	+	0.608754i
$959$	7.37817	−	4.74166i	0.238253	−	0.153116i
$960$	21.2746	+	6.24680i	0.686636	+	0.201614i
$961$	20.2738	−	23.3972i	0.653992	−	0.754747i
$962$	−7.18967	+	2.11108i	−0.231804	+	0.0680639i
$963$	−4.00784	+	8.77594i	−0.129151	+	0.282801i
$964$	−0.179764	−	1.25029i	−0.00578981	−	0.0402690i
$965$	−53.0755			−1.70856
$966$	6.27946	−	0.148118i	0.202038	−	0.00476563i
$967$	22.5885			0.726397			0.363199	−	0.931712i	$-0.381685\pi$
$967$	22.5885			0.726397			0.363199	+	0.931712i	$0.381685\pi$
$968$	0.0351520	+	0.244487i	0.00112983	+	0.00785812i
$969$	5.70026	−	12.4818i	0.183119	−	0.400974i
$970$	−22.0694	+	6.48017i	−0.708607	+	0.208066i
$971$	−11.1665	+	12.8868i	−0.358349	+	0.413557i	−0.906086	−	0.423094i	$-0.860944\pi$
$971$	−11.1665	+	12.8868i	−0.358349	+	0.413557i	0.547737	+	0.836651i	$0.315490\pi$
$972$	0.273100	+	0.0801894i	0.00875969	+	0.00257208i
$973$	−0.315398	+	0.202694i	−0.0101112	+	0.00649808i
$974$	4.23522	+	9.27383i	0.135705	+	0.297153i
$975$	2.35010	+	2.71216i	0.0752635	+	0.0868587i
$976$	−9.41428	−	6.05019i	−0.301344	−	0.193662i
$977$	6.12745	−	42.6173i	0.196034	−	1.36345i	−0.619616	−	0.784905i	$-0.712712\pi$
$977$	6.12745	−	42.6173i	0.196034	−	1.36345i	0.815651	−	0.578545i	$-0.196379\pi$
$978$	−3.12780	+	21.7543i	−0.100016	+	0.695626i
$979$	−36.6712	−	23.5671i	−1.17202	−	0.753209i
$980$	−0.470101	−	0.542526i	−0.0150168	−	0.0173303i
$981$	5.49883	+	12.0408i	0.175564	+	0.384432i
$982$	11.9192	−	7.66000i	0.380357	−	0.244440i
$983$	9.92229	+	2.91345i	0.316472	+	0.0929245i	0.436111	−	0.899893i	$-0.356356\pi$
$983$	9.92229	+	2.91345i	0.316472	+	0.0929245i	−0.119639	+	0.992817i	$0.538174\pi$
$984$	−24.4568	+	28.2246i	−0.779654	+	0.899769i
$985$	−10.5383	+	3.09431i	−0.335777	+	0.0985930i
$986$	14.9320	−	32.6966i	0.475533	−	1.04127i
$987$	−0.792871	−	5.51454i	−0.0252374	−	0.175530i
$988$	3.44160			0.109492
$989$	−29.0034	+	35.1116i	−0.922254	+	1.11648i
$990$	−10.9144			−0.346884
$991$	1.32458	+	9.21263i	0.0420765	+	0.292649i	0.999984	+	0.00557318i	$0.00177401\pi$
$991$	1.32458	+	9.21263i	0.0420765	+	0.292649i	−0.957908	+	0.287076i	$0.907317\pi$
$992$	0.134523	−	0.294565i	0.00427112	−	0.00935244i
$993$	18.0349	−	5.29553i	0.572321	−	0.168049i
$994$	−6.53122	+	7.53743i	−0.207158	+	0.239073i
$995$	−8.43538	−	2.47685i	−0.267420	−	0.0785215i
$996$	−1.37430	+	0.883211i	−0.0435464	+	0.0279856i
$997$	25.6784	+	56.2279i	0.813244	+	1.78076i	0.592786	+	0.805360i	$0.298028\pi$
$997$	25.6784	+	56.2279i	0.813244	+	1.78076i	0.220458	+	0.975396i	$0.429245\pi$
$998$	−23.9576	−	27.6485i	−0.758365	−	0.875200i
$999$	1.82528	+	1.17304i	0.0577493	+	0.0371132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.463.2	yes	20
23.8	even	11	inner	483.2.q.c.169.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.169.2	✓	20	23.8	even	11	inner
483.2.q.c.463.2	yes	20	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.186393 + 1.29639i) q^{2} +(0.415415 - 0.909632i) q^{3} +(0.273100 - 0.0801894i) q^{4} +(1.65162 - 1.90608i) q^{5} +(1.25667 + 0.368991i) q^{6} +(0.841254 - 0.540641i) q^{7} +(1.24302 + 2.72183i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(2.77887 + 1.78587i) q^{10} +(0.470231 - 3.27053i) q^{11} +(0.0405070 - 0.281733i) q^{12} +(-2.21826 - 1.42559i) q^{13} +(0.857685 + 0.989821i) q^{14} +(-1.04772 - 2.29418i) q^{15} +(-2.81797 + 1.81100i) q^{16} +(-2.87118 - 0.843054i) q^{17} +(0.857685 - 0.989821i) q^{18} +(-4.39983 + 1.29191i) q^{19} +(0.298212 - 0.652992i) q^{20} +(-0.142315 - 0.989821i) q^{21} +4.32753 q^{22} +(4.63215 + 1.24226i) q^{23} +2.99223 q^{24} +(-0.193688 - 1.34713i) q^{25} +(1.43465 - 3.14145i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.186393 - 0.215109i) q^{28} +(8.79997 + 2.58390i) q^{29} +(2.77887 - 1.78587i) q^{30} +(-0.0842219 - 0.184420i) q^{31} +(1.04598 + 1.20712i) q^{32} +(-2.77963 - 1.78636i) q^{33} +(0.557760 - 3.87931i) q^{34} +(0.358932 - 2.49643i) q^{35} +(-0.239446 - 0.153882i) q^{36} +(-1.42086 - 1.63976i) q^{37} +(-2.49491 - 5.46310i) q^{38} +(-2.21826 + 1.42559i) q^{39} +(7.24100 + 2.12615i) q^{40} +(-8.17344 + 9.43265i) q^{41} +(1.25667 - 0.368991i) q^{42} +(-3.94480 + 8.63790i) q^{43} +(-0.133842 - 0.930889i) q^{44} -2.52210 q^{45} +(-0.747049 + 6.23662i) q^{46} +5.57125 q^{47} +(0.476716 + 3.31563i) q^{48} +(0.415415 - 0.909632i) q^{49} +(1.71030 - 0.502190i) q^{50} +(-1.95960 + 2.26150i) q^{51} +(-0.720124 - 0.211448i) q^{52} +(8.67612 - 5.57580i) q^{53} +(-0.544078 - 1.19136i) q^{54} +(-5.45722 - 6.29797i) q^{55} +(2.51722 + 1.61772i) q^{56} +(-0.652596 + 4.53891i) q^{57} +(-1.70950 + 11.8898i) q^{58} +(1.24495 + 0.800081i) q^{59} +(-0.470101 - 0.542526i) q^{60} +(1.38782 + 3.03890i) q^{61} +(0.223382 - 0.143559i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-5.75714 + 6.64410i) q^{64} +(-6.38101 + 1.87363i) q^{65} +(1.79772 - 3.93646i) q^{66} +(1.58647 + 11.0342i) q^{67} -0.851723 q^{68} +(3.05426 - 3.69750i) q^{69} +3.30325 q^{70} +(1.08372 + 7.53743i) q^{71} +(1.24302 - 2.72183i) q^{72} +(4.67859 - 1.37376i) q^{73} +(1.86093 - 2.14763i) q^{74} +(-1.30585 - 0.383433i) q^{75} +(-1.09800 + 0.705640i) q^{76} +(-1.37260 - 3.00557i) q^{77} +(-2.26159 - 2.61001i) q^{78} +(-14.2391 - 9.15090i) q^{79} +(-1.20232 + 8.36235i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-13.7519 - 8.83779i) q^{82} +(-3.75858 - 4.33764i) q^{83} +(-0.118239 - 0.258908i) q^{84} +(-6.34903 + 4.08027i) q^{85} +(-11.9334 - 3.50395i) q^{86} +(6.00604 - 6.93134i) q^{87} +(9.48631 - 2.78543i) q^{88} +(5.48049 - 12.0006i) q^{89} +(-0.470101 - 3.26962i) q^{90} -2.63685 q^{91} +(1.36466 - 0.0321892i) q^{92} -0.202742 q^{93} +(1.03844 + 7.22251i) q^{94} +(-4.80439 + 10.5202i) q^{95} +(1.53255 - 0.449997i) q^{96} +(-4.55992 + 5.26243i) q^{97} +(1.25667 + 0.368991i) q^{98} +(-2.77963 + 1.78636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more