LMFDB - Embedded newform 483.2.q.c.127.1

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			127.1
Root			$-1.02673 - 0.659842i$ of defining polynomial
Character	$\chi$	$=$	483.127
Dual form			483.2.q.c.232.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(-2.78540 + 0.817866i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(-2.78540 + 0.817866i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(3.64809 - 4.21012i) q^{10} +(-1.01130 - 0.649920i) q^{11} +(1.41542 + 0.909632i) q^{12} +(2.65446 - 3.06341i) q^{13} +(1.84125 + 0.540641i) q^{14} +(-0.413138 - 2.87344i) q^{15} +(2.96926 + 3.42671i) q^{16} +(-0.185587 - 0.406379i) q^{17} +(1.84125 - 0.540641i) q^{18} +(-0.122970 + 0.269268i) q^{19} +(-0.695108 + 4.83458i) q^{20} +(0.841254 - 0.540641i) q^{21} +2.30687 q^{22} +(3.14576 + 3.61997i) q^{23} +0.609264 q^{24} +(2.88326 - 1.85296i) q^{25} +(-1.10700 + 7.69937i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-1.61435 + 0.474017i) q^{28} +(-1.93907 - 4.24598i) q^{29} +(3.64809 + 4.21012i) q^{30} +(-0.518984 - 3.60962i) q^{31} +(-7.17941 - 2.10807i) q^{32} +(0.787227 - 0.908508i) q^{33} +(0.721214 + 0.463496i) q^{34} +(2.44215 + 1.56947i) q^{35} +(-1.10181 + 1.27155i) q^{36} +(5.35680 + 1.57290i) q^{37} +(-0.0808426 - 0.562273i) q^{38} +(2.65446 + 3.06341i) q^{39} +(0.734739 + 1.60885i) q^{40} +(1.51933 - 0.446116i) q^{41} +(-0.797176 + 1.74557i) q^{42} +(0.200691 - 1.39584i) q^{43} +(-1.70151 + 1.09349i) q^{44} +2.90299 q^{45} +(-8.83402 - 2.58025i) q^{46} -3.48129 q^{47} +(-3.81440 + 2.45137i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-2.73219 + 5.98266i) q^{50} +(0.428654 - 0.125864i) q^{51} +(-2.83313 - 6.20368i) q^{52} +(7.57328 + 8.74004i) q^{53} +(0.273100 + 1.89945i) q^{54} +(3.34841 + 0.983181i) q^{55} +(-0.398983 + 0.460451i) q^{56} +(-0.249026 - 0.160040i) q^{57} +(7.53547 + 4.84275i) q^{58} +(8.82892 - 10.1891i) q^{59} +(-4.68645 - 1.37607i) q^{60} +(-0.602744 - 4.19218i) q^{61} +(4.58274 + 5.28876i) q^{62} +(0.415415 + 0.909632i) q^{63} +(5.07616 - 1.49049i) q^{64} +(-4.88826 + 10.7038i) q^{65} +(-0.328302 + 2.28339i) q^{66} +(3.01093 - 1.93501i) q^{67} -0.751662 q^{68} +(-4.03082 + 2.59856i) q^{69} -5.57079 q^{70} +(10.0099 - 6.43295i) q^{71} +(-0.0867074 + 0.603063i) q^{72} +(4.65850 - 10.2007i) q^{73} +(-10.2796 + 3.01837i) q^{74} +(1.42377 + 3.11762i) q^{75} +(0.326155 + 0.376403i) q^{76} +(0.171081 + 1.18989i) q^{77} +(-7.46346 - 2.19147i) q^{78} +(-4.68236 + 5.40373i) q^{79} +(-11.0732 - 7.11628i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-1.98990 + 2.29647i) q^{82} +(-0.0254587 - 0.00747534i) q^{83} +(-0.239446 - 1.66538i) q^{84} +(0.849297 + 0.980141i) q^{85} +(1.12417 + 2.46159i) q^{86} +(4.47872 - 1.31507i) q^{87} +(-0.304256 + 0.666228i) q^{88} +(1.50411 - 10.4613i) q^{89} +(-4.68645 + 3.01180i) q^{90} -4.05347 q^{91} +(7.73893 - 2.28432i) q^{92} +3.64673 q^{93} +(5.62003 - 3.61177i) q^{94} +(0.122296 - 0.850591i) q^{95} +(3.10835 - 6.80633i) q^{96} +(0.0741642 - 0.0217766i) q^{97} +(-0.797176 - 1.74557i) q^{98} +(0.787227 + 0.908508i) 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}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−1.61435	+	1.03748i	−1.14152	+	0.733611i	−0.967933	−	0.251208i	$-0.919172\pi$
$2$	−1.61435	+	1.03748i	−1.14152	+	0.733611i	−0.173587	+	0.984818i	$0.555536\pi$
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	0.698939	−	1.53046i	0.349469	−	0.765231i
$5$	−2.78540	+	0.817866i	−1.24567	+	0.365761i	−0.837142	−	0.546986i	$-0.815775\pi$
$5$	−2.78540	+	0.817866i	−1.24567	+	0.365761i	−0.408525	+	0.912747i	$0.633957\pi$
$6$	−0.797176	−	1.74557i	−0.325446	−	0.712626i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.0867074	−	0.603063i	−0.0306557	−	0.213215i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	3.64809	−	4.21012i	1.15363	−	1.33136i
$11$	−1.01130	−	0.649920i	−0.304917	−	0.195958i	0.379230	−	0.925302i	$-0.376189\pi$
$11$	−1.01130	−	0.649920i	−0.304917	−	0.195958i	−0.684147	+	0.729344i	$0.739825\pi$
$12$	1.41542	+	0.909632i	0.408595	+	0.262588i
$13$	2.65446	−	3.06341i	0.736214	−	0.849636i	−0.256943	−	0.966427i	$-0.582715\pi$
$13$	2.65446	−	3.06341i	0.736214	−	0.849636i	0.993157	+	0.116791i	$0.0372606\pi$
$14$	1.84125	+	0.540641i	0.492096	+	0.144492i
$15$	−0.413138	−	2.87344i	−0.106672	−	0.741919i
$16$	2.96926	+	3.42671i	0.742315	+	0.856677i
$17$	−0.185587	−	0.406379i	−0.0450115	−	0.0985614i	0.885790	−	0.464086i	$-0.153617\pi$
$17$	−0.185587	−	0.406379i	−0.0450115	−	0.0985614i	−0.930802	+	0.365524i	$0.880890\pi$
$18$	1.84125	−	0.540641i	0.433988	−	0.127430i
$19$	−0.122970	+	0.269268i	−0.0282114	+	0.0617742i	−0.923213	−	0.384288i	$-0.874447\pi$
$19$	−0.122970	+	0.269268i	−0.0282114	+	0.0617742i	0.895002	+	0.446063i	$0.147174\pi$
$20$	−0.695108	+	4.83458i	−0.155431	+	1.08105i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	2.30687			0.491826
$23$	3.14576	+	3.61997i	0.655936	+	0.754817i
$23$	3.14576	+	3.61997i	0.655936	+	0.754817i
$24$	0.609264			0.124366
$25$	2.88326	−	1.85296i	0.576652	−	0.370592i
$26$	−1.10700	+	7.69937i	−0.217101	+	1.50997i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−1.61435	+	0.474017i	−0.305084	+	0.0895808i
$29$	−1.93907	−	4.24598i	−0.360077	−	0.788458i	−0.999803	−	0.0198550i	$-0.993680\pi$
$29$	−1.93907	−	4.24598i	−0.360077	−	0.788458i	0.639726	−	0.768603i	$-0.279048\pi$
$30$	3.64809	+	4.21012i	0.666048	+	0.768660i
$31$	−0.518984	−	3.60962i	−0.0932123	−	0.648306i	−0.981845	−	0.189686i	$-0.939253\pi$
$31$	−0.518984	−	3.60962i	−0.0932123	−	0.648306i	0.888632	−	0.458620i	$-0.151656\pi$
$32$	−7.17941	−	2.10807i	−1.26915	−	0.372657i
$33$	0.787227	−	0.908508i	0.137039	−	0.158151i
$34$	0.721214	+	0.463496i	0.123687	+	0.0794889i
$35$	2.44215	+	1.56947i	0.412798	+	0.265289i
$36$	−1.10181	+	1.27155i	−0.183635	+	0.211926i
$37$	5.35680	+	1.57290i	0.880652	+	0.258583i	0.690640	−	0.723199i	$-0.257329\pi$
$37$	5.35680	+	1.57290i	0.880652	+	0.258583i	0.190012	+	0.981782i	$0.439147\pi$
$38$	−0.0808426	−	0.562273i	−0.0131144	−	0.0912127i
$39$	2.65446	+	3.06341i	0.425053	+	0.490538i
$40$	0.734739	+	1.60885i	0.116172	+	0.254382i
$41$	1.51933	−	0.446116i	0.237280	−	0.0696716i	−0.160931	−	0.986966i	$-0.551450\pi$
$41$	1.51933	−	0.446116i	0.237280	−	0.0696716i	0.398210	+	0.917294i	$0.369631\pi$
$42$	−0.797176	+	1.74557i	−0.123007	+	0.269347i
$43$	0.200691	−	1.39584i	0.0306051	−	0.212863i	−0.968780	−	0.247921i	$-0.920253\pi$
$43$	0.200691	−	1.39584i	0.0306051	−	0.212863i	0.999385	+	0.0350582i	$0.0111616\pi$
$44$	−1.70151	+	1.09349i	−0.256512	+	0.164851i
$45$	2.90299			0.432752
$46$	−8.83402	−	2.58025i	−1.30251	−	0.380438i
$47$	−3.48129			−0.507798			−0.253899	−	0.967231i	$-0.581713\pi$
$47$	−3.48129			−0.507798			−0.253899	+	0.967231i	$0.581713\pi$
$48$	−3.81440	+	2.45137i	−0.550561	+	0.353824i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−2.73219	+	5.98266i	−0.386390	+	0.846076i
$51$	0.428654	−	0.125864i	0.0600236	−	0.0176245i
$52$	−2.83313	−	6.20368i	−0.392884	−	0.860295i
$53$	7.57328	+	8.74004i	1.04027	+	1.20054i	0.979304	+	0.202397i	$0.0648730\pi$
$53$	7.57328	+	8.74004i	1.04027	+	1.20054i	0.0609670	+	0.998140i	$0.480582\pi$
$54$	0.273100	+	1.89945i	0.0371642	+	0.258483i
$55$	3.34841	+	0.983181i	0.451499	+	0.132572i
$56$	−0.398983	+	0.460451i	−0.0533164	+	0.0615304i
$57$	−0.249026	−	0.160040i	−0.0329844	−	0.0211978i
$58$	7.53547	+	4.84275i	0.989456	+	0.635885i
$59$	8.82892	−	10.1891i	1.14943	−	1.32651i	0.212429	−	0.977177i	$-0.431863\pi$
$59$	8.82892	−	10.1891i	1.14943	−	1.32651i	0.936999	−	0.349333i	$-0.113592\pi$
$60$	−4.68645	−	1.37607i	−0.605018	−	0.177649i
$61$	−0.602744	−	4.19218i	−0.0771735	−	0.536753i	−0.991330	−	0.131393i	$-0.958055\pi$
$61$	−0.602744	−	4.19218i	−0.0771735	−	0.536753i	0.914157	−	0.405361i	$-0.132854\pi$
$62$	4.58274	+	5.28876i	0.582008	+	0.671673i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	5.07616	−	1.49049i	0.634520	−	0.186312i
$65$	−4.88826	+	10.7038i	−0.606314	+	1.32764i
$66$	−0.328302	+	2.28339i	−0.0404111	+	0.281066i
$67$	3.01093	−	1.93501i	0.367844	−	0.236399i	−0.343640	−	0.939102i	$-0.611660\pi$
$67$	3.01093	−	1.93501i	0.367844	−	0.236399i	0.711484	+	0.702703i	$0.248024\pi$
$68$	−0.751662			−0.0911523
$69$	−4.03082	+	2.59856i	−0.485253	+	0.312830i
$70$	−5.57079			−0.665837
$71$	10.0099	−	6.43295i	1.18795	−	0.763451i	0.211121	−	0.977460i	$-0.432289\pi$
$71$	10.0099	−	6.43295i	1.18795	−	0.763451i	0.976832	+	0.214009i	$0.0686522\pi$
$72$	−0.0867074	+	0.603063i	−0.0102186	+	0.0710717i
$73$	4.65850	−	10.2007i	0.545236	−	1.19390i	−0.413736	−	0.910397i	$-0.635776\pi$
$73$	4.65850	−	10.2007i	0.545236	−	1.19390i	0.958971	−	0.283503i	$-0.0914965\pi$
$74$	−10.2796	+	3.01837i	−1.19498	+	0.350878i
$75$	1.42377	+	3.11762i	0.164403	+	0.359991i
$76$	0.326155	+	0.376403i	0.0374126	+	0.0431764i
$77$	0.171081	+	1.18989i	0.0194965	+	0.135601i
$78$	−7.46346	−	2.19147i	−0.845071	−	0.248135i
$79$	−4.68236	+	5.40373i	−0.526807	+	0.607967i	−0.955322	−	0.295567i	$-0.904491\pi$
$79$	−4.68236	+	5.40373i	−0.526807	+	0.607967i	0.428515	+	0.903535i	$0.359037\pi$
$80$	−11.0732	−	7.11628i	−1.23802	−	0.795625i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−1.98990	+	2.29647i	−0.219748	+	0.253602i
$83$	−0.0254587	−	0.00747534i	−0.00279445	−	0.000820525i	0.280335	−	0.959902i	$-0.409554\pi$
$83$	−0.0254587	−	0.00747534i	−0.00279445	−	0.000820525i	−0.283129	+	0.959082i	$0.591373\pi$
$84$	−0.239446	−	1.66538i	−0.0261257	−	0.181708i
$85$	0.849297	+	0.980141i	0.0921192	+	0.106311i
$86$	1.12417	+	2.46159i	0.121222	+	0.265440i
$87$	4.47872	−	1.31507i	0.480169	−	0.140990i
$88$	−0.304256	+	0.666228i	−0.0324338	+	0.0710201i
$89$	1.50411	−	10.4613i	0.159435	−	1.10890i	−0.740242	−	0.672340i	$-0.765289\pi$
$89$	1.50411	−	10.4613i	0.159435	−	1.10890i	0.899677	−	0.436555i	$-0.143802\pi$
$90$	−4.68645	+	3.01180i	−0.493995	+	0.317471i
$91$	−4.05347			−0.424919
$92$	7.73893	−	2.28432i	0.806839	−	0.238157i
$93$	3.64673			0.378149
$94$	5.62003	−	3.61177i	0.579662	−	0.372526i
$95$	0.122296	−	0.850591i	0.0125474	−	0.0872688i
$96$	3.10835	−	6.80633i	0.317244	−	0.694668i
$97$	0.0741642	−	0.0217766i	0.00753024	−	0.00221108i	−0.277965	−	0.960591i	$-0.589660\pi$
$97$	0.0741642	−	0.0217766i	0.00753024	−	0.00221108i	0.285496	+	0.958380i	$0.407842\pi$
$98$	−0.797176	−	1.74557i	−0.0805269	−	0.176329i
$99$	0.787227	+	0.908508i	0.0791193	+	0.0913085i
$100$	−0.820661	−	5.70783i	−0.0820661	−	0.570783i
$101$	−16.9464	−	4.97591i	−1.68623	−	0.495122i	−0.708628	−	0.705582i	$-0.750685\pi$
$101$	−16.9464	−	4.97591i	−1.68623	−	0.495122i	−0.977602	+	0.210461i	$0.932504\pi$
$102$	−0.561418	+	0.647911i	−0.0555886	+	0.0641527i
$103$	3.33681	+	2.14444i	0.328786	+	0.211298i	0.694611	−	0.719386i	$-0.255577\pi$
$103$	3.33681	+	2.14444i	0.328786	+	0.211298i	−0.365825	+	0.930684i	$0.619213\pi$
$104$	−2.07759	−	1.33518i	−0.203724	−	0.130926i
$105$	−1.90105	+	2.19393i	−0.185524	+	0.214106i
$106$	−21.2936	−	6.25236i	−2.06822	−	0.607283i
$107$	0.0744754	+	0.517988i	0.00719981	+	0.0500758i	0.993105	−	0.117231i	$-0.0374019\pi$
$107$	0.0744754	+	0.517988i	0.00719981	+	0.0500758i	−0.985905	+	0.167307i	$0.946493\pi$
$108$	−1.10181	−	1.27155i	−0.106022	−	0.122355i
$109$	−2.40391	−	5.26384i	−0.230253	−	0.504184i	0.758876	−	0.651235i	$-0.225749\pi$
$109$	−2.40391	−	5.26384i	−0.230253	−	0.504184i	−0.989129	+	0.147051i	$0.953022\pi$
$110$	−6.42554	+	1.88671i	−0.612651	+	0.179891i
$111$	−2.31924	+	5.07843i	−0.220133	+	0.482023i
$112$	0.645282	−	4.48803i	0.0609734	−	0.424079i
$113$	15.2240	−	9.78385i	1.43215	−	0.920387i	0.432325	−	0.901718i	$-0.357693\pi$
$113$	15.2240	−	9.78385i	1.43215	−	0.920387i	0.999826	−	0.0186690i	$-0.00594288\pi$
$114$	0.568055			0.0532032
$115$	−11.7228	−	7.51026i	−1.09316	−	0.700335i
$116$	−7.85360			−0.729188
$117$	−3.40999	+	2.19147i	−0.315254	+	0.202601i
$118$	−3.68197	+	25.6087i	−0.338953	+	2.35747i
$119$	−0.185587	+	0.406379i	−0.0170127	+	0.0372527i
$120$	−1.69704	+	0.498297i	−0.154918	+	0.0454881i
$121$	−3.96924	−	8.69143i	−0.360840	−	0.790130i
$122$	5.32235	+	6.14232i	0.481863	+	0.556100i
$123$	0.225352	+	1.56736i	0.0203193	+	0.141324i
$124$	−5.88712	−	1.72861i	−0.528679	−	0.155234i
$125$	2.98971	−	3.45031i	0.267408	−	0.308605i
$126$	−1.61435	−	1.03748i	−0.143818	−	0.0924263i
$127$	−11.8527	−	7.61725i	−1.05175	−	0.675922i	−0.103888	−	0.994589i	$-0.533128\pi$
$127$	−11.8527	−	7.61725i	−1.05175	−	0.675922i	−0.947867	+	0.318667i	$0.896765\pi$
$128$	3.15165	−	3.63720i	0.278569	−	0.321486i
$129$	1.35307	+	0.397297i	0.119131	+	0.0349800i
$130$	−3.21362	−	22.3512i	−0.281853	−	1.96033i
$131$	−10.3363	−	11.9287i	−0.903085	−	1.04222i	−0.998903	−	0.0468170i	$-0.985092\pi$
$131$	−10.3363	−	11.9287i	−0.903085	−	1.04222i	0.0958183	−	0.995399i	$-0.469453\pi$
$132$	−0.840214	−	1.83981i	−0.0731313	−	0.160135i
$133$	0.284027	−	0.0833980i	0.0246283	−	0.00723152i
$134$	−2.85317	+	6.24758i	−0.246477	+	0.539709i
$135$	−0.413138	+	2.87344i	−0.0355573	+	0.247306i
$136$	−0.228980	+	0.147157i	−0.0196349	+	0.0126186i
$137$	3.02092			0.258095			0.129047	−	0.991638i	$-0.458808\pi$
$137$	3.02092			0.258095			0.129047	+	0.991638i	$0.458808\pi$
$138$	3.81120	−	8.37690i	0.324431	−	0.713089i
$139$	−11.3664			−0.964085			−0.482043	−	0.876148i	$-0.660105\pi$
$139$	−11.3664			−0.964085			−0.482043	+	0.876148i	$0.660105\pi$
$140$	4.10893	−	2.64065i	0.347268	−	0.223176i
$141$	0.495439	−	3.44585i	0.0417235	−	0.290193i
$142$	−9.48539	+	20.7701i	−0.795997	+	1.74299i
$143$	−4.67541	+	1.37282i	−0.390977	+	0.114801i
$144$	−1.88357	−	4.12444i	−0.156964	−	0.343703i
$145$	8.87372	+	10.2408i	0.736923	+	0.850454i
$146$	3.06257	+	21.3006i	0.253460	+	1.76285i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	6.15133	−	7.09902i	0.505637	−	0.583536i
$149$	−15.2467	−	9.79845i	−1.24906	−	0.802720i	−0.262309	−	0.964984i	$-0.584484\pi$
$149$	−15.2467	−	9.79845i	−1.24906	−	0.802720i	−0.986747	+	0.162264i	$0.948120\pi$
$150$	−5.53294	−	3.55580i	−0.451762	−	0.290330i
$151$	2.89891	−	3.34552i	0.235910	−	0.272254i	−0.625434	−	0.780277i	$-0.715078\pi$
$151$	2.89891	−	3.34552i	0.235910	−	0.272254i	0.861344	+	0.508023i	$0.169623\pi$
$152$	0.173048	+	0.0508114i	0.0140360	+	0.00412135i
$153$	0.0635793	+	0.442204i	0.00514008	+	0.0357500i
$154$	−1.51068	−	1.74341i	−0.121734	−	0.140488i
$155$	4.39776	+	9.62975i	0.353237	+	0.773480i
$156$	6.54373	−	1.92141i	0.523918	−	0.153836i
$157$	−6.59036	+	14.4309i	−0.525968	+	1.15171i	0.441162	+	0.897427i	$0.354566\pi$
$157$	−6.59036	+	14.4309i	−0.525968	+	1.15171i	−0.967130	+	0.254282i	$0.918161\pi$
$158$	1.95271	−	13.5814i	0.155349	−	1.08048i
$159$	−9.72887	+	6.25236i	−0.771549	+	0.495845i
$160$	21.7216			1.71725
$161$	0.675762	−	4.74798i	0.0532575	−	0.374194i
$162$	−1.91899			−0.150770
$163$	1.66312	−	1.06882i	0.130265	−	0.0837164i	−0.473885	−	0.880587i	$-0.657149\pi$
$163$	1.66312	−	1.06882i	0.130265	−	0.0837164i	0.604151	+	0.796870i	$0.293513\pi$
$164$	0.379156	−	2.63709i	0.0296071	−	0.205922i
$165$	−1.44970	+	3.17440i	−0.112859	+	0.247127i
$166$	0.0488548	−	0.0143451i	0.00379187	−	0.00111339i
$167$	5.83085	+	12.7678i	0.451204	+	0.988000i	0.989405	+	0.145183i	$0.0463771\pi$
$167$	5.83085	+	12.7678i	0.451204	+	0.988000i	−0.538200	+	0.842817i	$0.680896\pi$
$168$	−0.398983	−	0.460451i	−0.0307822	−	0.0355246i
$169$	−0.488225	−	3.39568i	−0.0375558	−	0.261206i
$170$	−2.38794	−	0.701164i	−0.183147	−	0.0537768i
$171$	0.193851	−	0.223716i	0.0148241	−	0.0171080i
$172$	−1.99601	−	1.28275i	−0.152194	−	0.0978091i
$173$	−5.56630	−	3.57724i	−0.423198	−	0.271973i	0.311660	−	0.950194i	$-0.399115\pi$
$173$	−5.56630	−	3.57724i	−0.423198	−	0.271973i	−0.734858	+	0.678221i	$0.762751\pi$
$174$	−5.86587	+	6.76958i	−0.444690	+	0.513200i
$175$	−3.28851	−	0.965593i	−0.248588	−	0.0729919i
$176$	−0.775712	−	5.39519i	−0.0584715	−	0.406678i
$177$	8.82892	+	10.1891i	0.663622	+	0.765861i
$178$	8.42525	+	18.4487i	0.631499	+	1.38279i
$179$	21.6136	−	6.34632i	1.61548	−	0.474347i	0.655678	−	0.755040i	$-0.272383\pi$
$179$	21.6136	−	6.34632i	1.61548	−	0.474347i	0.959797	+	0.280694i	$0.0905645\pi$
$180$	2.02901	−	4.44291i	0.151234	−	0.331155i
$181$	1.20178	−	8.35854i	0.0893274	−	0.621286i	−0.895149	−	0.445767i	$-0.852931\pi$
$181$	1.20178	−	8.35854i	0.0893274	−	0.621286i	0.984476	−	0.175518i	$-0.0561601\pi$
$182$	6.54373	−	4.20540i	0.485054	−	0.311725i
$183$	4.23529			0.313081
$184$	1.91031	−	2.21097i	0.140830	−	0.162995i
$185$	−16.2072			−1.19158
$186$	−5.88712	+	3.78342i	−0.431664	+	0.277414i
$187$	−0.0764305	+	0.531586i	−0.00558915	+	0.0388734i
$188$	−2.43321	+	5.32798i	−0.177460	+	0.388583i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	0.685043	+	1.50003i	0.0496982	+	0.108824i
$191$	14.1995	+	16.3872i	1.02744	+	1.18573i	0.982408	+	0.186747i	$0.0597946\pi$
$191$	14.1995	+	16.3872i	1.02744	+	1.18573i	0.0450353	+	0.998985i	$0.485660\pi$
$192$	0.752911	+	5.23661i	0.0543366	+	0.377920i
$193$	18.6865	+	5.48686i	1.34509	+	0.394953i	0.873482	−	0.486857i	$-0.161857\pi$
$193$	18.6865	+	5.48686i	1.34509	+	0.394953i	0.471605	+	0.881810i	$0.343675\pi$
$194$	−0.0971345	+	0.112099i	−0.00697385	+	0.00804825i
$195$	−9.89917	−	6.36181i	−0.708894	−	0.455579i
$196$	1.41542	+	0.909632i	0.101101	+	0.0649737i
$197$	6.61609	−	7.63537i	0.471377	−	0.543998i	−0.469417	−	0.882976i	$-0.655536\pi$
$197$	6.61609	−	7.63537i	0.471377	−	0.543998i	0.940794	+	0.338979i	$0.110081\pi$
$198$	−2.21342	−	0.649920i	−0.157301	−	0.0461878i
$199$	0.584439	+	4.06486i	0.0414298	+	0.288151i	0.999995	+	0.00327615i	$0.00104283\pi$
$199$	0.584439	+	4.06486i	0.0414298	+	0.288151i	−0.958565	+	0.284874i	$0.908048\pi$
$200$	−1.36745	−	1.57812i	−0.0966934	−	0.111590i
$201$	1.48681	+	3.25567i	0.104872	+	0.229637i
$202$	32.5199	−	9.54871i	2.28809	−	0.671845i
$203$	−1.93907	+	4.24598i	−0.136096	+	0.298009i
$204$	0.106973	−	0.744011i	0.00748958	−	0.0520912i
$205$	−3.86708	+	2.48522i	−0.270088	+	0.173575i
$206$	−7.61161			−0.530326
$207$	−1.99847	−	4.35960i	−0.138903	−	0.303013i
$208$	18.3792			1.27437
$209$	0.299362	−	0.192388i	0.0207073	−	0.0133078i
$210$	0.792806	−	5.51409i	0.0547088	−	0.380508i
$211$	−9.46499	+	20.7254i	−0.651597	+	1.42680i	0.238553	+	0.971129i	$0.423327\pi$
$211$	−9.46499	+	20.7254i	−0.651597	+	1.42680i	−0.890150	+	0.455668i	$0.849400\pi$
$212$	18.6696	−	5.48188i	1.28223	−	0.376497i
$213$	4.94292	+	10.8235i	0.338683	+	0.741613i
$214$	−0.657632	−	0.758948i	−0.0449548	−	0.0518806i
$215$	0.582604	+	4.05210i	0.0397332	+	0.276351i
$216$	−0.584585	−	0.171650i	−0.0397760	−	0.0116793i
$217$	−2.38810	+	2.75602i	−0.162115	+	0.187091i
$218$	9.34190	+	6.00368i	0.632713	+	0.406620i
$219$	9.43388	+	6.06279i	0.637483	+	0.409685i
$220$	3.84505	−	4.43743i	0.259233	−	0.299171i
$221$	−1.73754	−	0.510187i	−0.116879	−	0.0343189i
$222$	−1.52470	−	10.6045i	−0.102331	−	0.711731i
$223$	10.5014	+	12.1192i	0.703224	+	0.811564i	0.989184	−	0.146678i	$-0.0468580\pi$
$223$	10.5014	+	12.1192i	0.703224	+	0.811564i	−0.285960	+	0.958242i	$0.592313\pi$
$224$	3.10835	+	6.80633i	0.207685	+	0.454767i
$225$	−3.28851	+	0.965593i	−0.219234	+	0.0643728i
$226$	−14.4263	+	31.5892i	−0.959623	+	2.10128i
$227$	−0.591691	+	4.11530i	−0.0392719	+	0.273142i	−0.999990	−	0.00438268i	$-0.998605\pi$
$227$	−0.591691	+	4.11530i	−0.0392719	+	0.273142i	0.960719	+	0.277525i	$0.0895140\pi$
$228$	−0.418989	+	0.269268i	−0.0277482	+	0.0178327i
$229$	14.7545			0.975002			0.487501	−	0.873122i	$-0.337909\pi$
$229$	14.7545			0.975002			0.487501	+	0.873122i	$0.337909\pi$
$230$	26.7166	−	0.0380204i	1.76164	−	0.00250699i
$231$	−1.20213			−0.0790943
$232$	−2.39246	+	1.53754i	−0.157073	+	0.100944i
$233$	−1.45568	+	10.1245i	−0.0953650	+	0.663278i	0.884928	+	0.465728i	$0.154208\pi$
$233$	−1.45568	+	10.1245i	−0.0953650	+	0.663278i	−0.980293	+	0.197550i	$0.936702\pi$
$234$	3.23133	−	7.07562i	0.211238	−	0.462547i
$235$	9.69677	−	2.84723i	0.632547	−	0.185733i
$236$	−9.42318	−	20.6339i	−0.613397	−	1.34315i
$237$	−4.68236	−	5.40373i	−0.304152	−	0.351010i
$238$	−0.122008	−	0.848582i	−0.00790859	−	0.0550054i
$239$	3.49850	+	1.02725i	0.226299	+	0.0664475i	0.392916	−	0.919574i	$-0.371466\pi$
$239$	3.49850	+	1.02725i	0.226299	+	0.0664475i	−0.166617	+	0.986022i	$0.553284\pi$
$240$	8.61972	−	9.94769i	0.556401	−	0.642121i
$241$	−13.1849	−	8.47343i	−0.849315	−	0.545822i	0.0420461	−	0.999116i	$-0.486612\pi$
$241$	−13.1849	−	8.47343i	−0.849315	−	0.545822i	−0.891361	+	0.453294i	$0.850249\pi$
$242$	15.4250	+	9.91302i	0.991554	+	0.637233i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	−6.83725	−	2.00760i	−0.437710	−	0.128523i
$245$	−0.413138	−	2.87344i	−0.0263944	−	0.183577i
$246$	−1.98990	−	2.29647i	−0.126871	−	0.146417i
$247$	0.498457	+	1.09147i	0.0317160	+	0.0694484i
$248$	−2.13183	+	0.625961i	−0.135371	+	0.0397485i
$249$	0.0110224	−	0.0241357i	0.000698516	−	0.00152954i
$250$	−1.24682	+	8.67180i	−0.0788556	+	0.548453i
$251$	−10.4770	+	6.73318i	−0.661305	+	0.424995i	−0.827781	−	0.561051i	$-0.810397\pi$
$251$	−10.4770	+	6.73318i	−0.661305	+	0.424995i	0.166477	+	0.986045i	$0.446761\pi$
$252$	1.68251			0.105988
$253$	−0.828595	−	5.70535i	−0.0520933	−	0.358692i
$254$	27.0372			1.69646
$255$	−1.09103	+	0.701164i	−0.0683231	+	0.0439086i
$256$	−2.82017	+	19.6147i	−0.176261	+	1.22592i
$257$	9.21150	−	20.1704i	0.574598	−	1.25819i	−0.369715	−	0.929145i	$-0.620545\pi$
$257$	9.21150	−	20.1704i	0.574598	−	1.25819i	0.944313	−	0.329049i	$-0.106728\pi$
$258$	−2.59652	+	0.762407i	−0.161652	+	0.0474654i
$259$	−2.31924	−	5.07843i	−0.144111	−	0.315558i
$260$	12.9652	+	14.9626i	0.804065	+	0.927940i
$261$	0.664296	+	4.62028i	0.0411189	+	0.285988i
$262$	29.0622	+	8.53344i	1.79547	+	0.527198i
$263$	−5.63899	+	6.50774i	−0.347715	+	0.401285i	−0.902486	−	0.430718i	$-0.858260\pi$
$263$	−5.63899	+	6.50774i	−0.347715	+	0.401285i	0.554771	+	0.832003i	$0.312806\pi$
$264$	−0.616146	−	0.395973i	−0.0379212	−	0.0243705i
$265$	−28.2428	−	18.1505i	−1.73494	−	1.11498i
$266$	−0.371997	+	0.429307i	−0.0228086	+	0.0263225i
$267$	10.1408	+	2.97760i	0.620604	+	0.182226i
$268$	−0.857001	−	5.96057i	−0.0523497	−	0.364100i
$269$	−14.8106	−	17.0924i	−0.903019	−	1.04214i	−0.998907	−	0.0467472i	$-0.985114\pi$
$269$	−14.8106	−	17.0924i	−0.903019	−	1.04214i	0.0958879	−	0.995392i	$-0.469431\pi$
$270$	−2.31419	−	5.06737i	−0.140837	−	0.308390i
$271$	−14.2737	+	4.19113i	−0.867065	+	0.254593i	−0.684867	−	0.728668i	$-0.740140\pi$
$271$	−14.2737	+	4.19113i	−0.867065	+	0.254593i	−0.182199	+	0.983262i	$0.558321\pi$
$272$	0.841486	−	1.84260i	0.0510226	−	0.111724i
$273$	0.576869	−	4.01221i	0.0349137	−	0.242830i
$274$	−4.87683	+	3.13415i	−0.294620	+	0.189341i
$275$	−4.12010			−0.248451
$276$	1.15971	+	7.98525i	0.0698061	+	0.480655i
$277$	−26.3243			−1.58167			−0.790837	−	0.612027i	$-0.790354\pi$
$277$	−26.3243			−1.58167			−0.790837	+	0.612027i	$0.790354\pi$
$278$	18.3494	−	11.7924i	1.10052	−	0.707263i
$279$	−0.518984	+	3.60962i	−0.0310708	+	0.216102i
$280$	0.734739	−	1.60885i	0.0439091	−	0.0961475i
$281$	18.2275	−	5.35207i	1.08736	−	0.319278i	0.311540	−	0.950233i	$-0.399155\pi$
$281$	18.2275	−	5.35207i	1.08736	−	0.319278i	0.775819	+	0.630955i	$0.217337\pi$
$282$	2.77520	+	6.07684i	0.165261	+	0.361870i
$283$	13.7978	+	15.9235i	0.820194	+	0.946554i	0.999305	−	0.0372750i	$-0.0118678\pi$
$283$	13.7978	+	15.9235i	0.820194	+	0.946554i	−0.179112	+	0.983829i	$0.557322\pi$
$284$	−2.84911	−	19.8160i	−0.169063	−	1.17586i
$285$	0.824528	+	0.242103i	0.0488408	+	0.0143410i
$286$	6.12348	−	7.06688i	0.362089	−	0.417873i
$287$	−1.33210	−	0.856090i	−0.0786315	−	0.0505334i
$288$	6.29469	+	4.04535i	0.370918	+	0.238374i
$289$	11.0019	−	12.6969i	0.647172	−	0.746877i
$290$	−24.9500	−	7.32598i	−1.46511	−	0.430196i
$291$	0.0110003	+	0.0765085i	0.000644847	+	0.00448501i
$292$	−12.3558	−	14.2593i	−0.723066	−	0.834463i
$293$	−11.5235	−	25.2329i	−0.673209	−	1.47412i	−0.869682	−	0.493612i	$-0.835676\pi$
$293$	−11.5235	−	25.2329i	−0.673209	−	1.47412i	0.196474	−	0.980509i	$-0.437051\pi$
$294$	1.84125	−	0.540641i	0.107384	−	0.0315308i
$295$	−16.2587	+	35.6016i	−0.946618	+	2.07281i
$296$	0.484083	−	3.36687i	0.0281367	−	0.195695i
$297$	−1.01130	+	0.649920i	−0.0586813	+	0.0377122i
$298$	34.7792			2.01471
$299$	19.4397	−	0.0276647i	1.12423	−	0.00159989i
$300$	5.76652			0.332930
$301$	−1.18633	+	0.762407i	−0.0683788	+	0.0439444i
$302$	−1.20895	+	8.40841i	−0.0695671	+	0.483850i
$303$	7.33699	−	16.0658i	0.421499	−	0.922954i
$304$	−1.28783	+	0.378142i	−0.0738623	+	0.0216879i
$305$	5.10752	+	11.1839i	0.292456	+	0.640389i
$306$	−0.561418	−	0.647911i	−0.0320941	−	0.0370386i
$307$	1.09159	+	7.59220i	0.0623005	+	0.433310i	0.996970	+	0.0777911i	$0.0247867\pi$
$307$	1.09159	+	7.59220i	0.0623005	+	0.433310i	−0.934669	+	0.355519i	$0.884304\pi$
$308$	1.94066	+	0.569830i	0.110579	+	0.0324691i
$309$	−2.59749	+	2.99766i	−0.147766	+	0.170531i
$310$	−17.0902	−	10.9832i	−0.970660	−	0.623805i
$311$	−12.1727	−	7.82290i	−0.690249	−	0.443596i	0.147925	−	0.988999i	$-0.452740\pi$
$311$	−12.1727	−	7.82290i	−0.690249	−	0.443596i	−0.838174	+	0.545402i	$0.816377\pi$
$312$	1.61727	−	1.86642i	0.0915597	−	0.105665i
$313$	−13.5303	−	3.97286i	−0.764779	−	0.224560i	−0.123998	−	0.992283i	$-0.539572\pi$
$313$	−13.5303	−	3.97286i	−0.764779	−	0.224560i	−0.640782	+	0.767723i	$0.721390\pi$
$314$	−4.33260	−	30.1339i	−0.244503	−	1.70056i
$315$	−1.90105	−	2.19393i	−0.107112	−	0.123614i
$316$	4.99753	+	10.9431i	0.281133	+	0.615595i
$317$	−22.9933	+	6.75144i	−1.29143	+	0.379199i	−0.854104	−	0.520103i	$-0.825894\pi$
$317$	−22.9933	+	6.75144i	−1.29143	+	0.379199i	−0.437329	+	0.899302i	$0.644075\pi$
$318$	9.21912	−	20.1870i	0.516982	−	1.13203i
$319$	−0.798570	+	5.55418i	−0.0447113	+	0.310974i
$320$	−12.9201	+	8.30323i	−0.722255	+	0.464165i
$321$	−0.523314			−0.0292085
$322$	3.83503	+	8.36602i	0.213718	+	0.466220i
$323$	0.132246			0.00735839
$324$	1.41542	−	0.909632i	0.0786342	−	0.0505351i
$325$	1.97712	−	13.7512i	0.109671	−	0.762779i
$326$	−1.57598	+	3.45090i	−0.0872852	+	0.191128i
$327$	5.55237	−	1.63032i	0.307047	−	0.0901571i
$328$	−0.400773	−	0.877571i	−0.0221290	−	0.0484557i
$329$	2.27976	+	2.63098i	0.125687	+	0.145051i
$330$	−0.953056	−	6.62865i	−0.0524640	−	0.364895i
$331$	−20.0779	−	5.89539i	−1.10358	−	0.324040i	−0.321306	−	0.946975i	$-0.604122\pi$
$331$	−20.0779	−	5.89539i	−1.10358	−	0.324040i	−0.782273	+	0.622935i	$0.785940\pi$
$332$	−0.0292348	+	0.0337387i	−0.00160447	+	0.00185165i
$333$	−4.69667	−	3.01837i	−0.257376	−	0.165406i
$334$	−22.6594	−	14.5623i	−1.23987	−	0.796814i
$335$	−6.80407	+	7.85231i	−0.371746	+	0.429018i
$336$	4.35052	+	1.27743i	0.237340	+	0.0696894i
$337$	2.03640	+	14.1634i	0.110930	+	0.771532i	0.967019	+	0.254704i	$0.0819782\pi$
$337$	2.03640	+	14.1634i	0.110930	+	0.771532i	−0.856089	+	0.516828i	$0.827113\pi$
$338$	4.31112	+	4.97530i	0.234494	+	0.270621i
$339$	7.51767	+	16.4614i	0.408304	+	0.894060i
$340$	2.09368	−	0.614759i	0.113545	−	0.0333400i
$341$	−1.82111	+	3.98768i	−0.0986189	+	0.215945i
$342$	−0.0808426	+	0.562273i	−0.00437147	+	0.0304042i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	−0.859179			−0.0463238
$345$	9.10215	−	10.5347i	0.490043	−	0.567169i
$346$	12.6973			0.682611
$347$	16.2732	−	10.4582i	0.873591	−	0.561423i	−0.0252580	−	0.999681i	$-0.508041\pi$
$347$	16.2732	−	10.4582i	0.873591	−	0.561423i	0.898849	+	0.438258i	$0.144404\pi$
$348$	1.11768	−	7.77366i	0.0599141	−	0.416712i
$349$	0.384187	−	0.841253i	0.0205651	−	0.0450312i	−0.899071	−	0.437803i	$-0.855757\pi$
$349$	0.384187	−	0.841253i	0.0205651	−	0.0450312i	0.919636	+	0.392772i	$0.128484\pi$
$350$	6.31060	−	1.85296i	0.337316	−	0.0990448i
$351$	−1.68387	−	3.68716i	−0.0898784	−	0.196806i
$352$	5.89043	+	6.79792i	0.313961	+	0.362330i
$353$	2.65353	+	18.4557i	0.141233	+	0.982297i	0.929988	+	0.367590i	$0.119817\pi$
$353$	2.65353	+	18.4557i	0.141233	+	0.982297i	−0.788755	+	0.614708i	$0.789274\pi$
$354$	−24.8240	−	7.28899i	−1.31938	−	0.387405i
$355$	−22.6202	+	26.1051i	−1.20055	+	1.38551i
$356$	−14.9593	−	9.61378i	−0.792844	−	0.509530i
$357$	−0.375831	−	0.241532i	−0.0198911	−	0.0127832i
$358$	−28.3078	+	32.6689i	−1.49611	+	1.72661i
$359$	−1.19924	−	0.352130i	−0.0632937	−	0.0185847i	0.249932	−	0.968263i	$-0.419592\pi$
$359$	−1.19924	−	0.352130i	−0.0632937	−	0.0185847i	−0.313226	+	0.949679i	$0.601410\pi$
$360$	−0.251710	−	1.75068i	−0.0132663	−	0.0922692i
$361$	12.3850	+	14.2930i	0.651841	+	0.752264i
$362$	6.73175	+	14.7405i	0.353813	+	0.774742i
$363$	9.16785	−	2.69192i	0.481187	−	0.141289i
$364$	−2.83313	+	6.20368i	−0.148496	+	0.325161i
$365$	−4.63296	+	32.2230i	−0.242500	+	1.68663i
$366$	−6.83725	+	4.39404i	−0.357389	+	0.229680i
$367$	18.0114			0.940185			0.470093	−	0.882617i	$-0.344221\pi$
$367$	18.0114			0.940185			0.470093	+	0.882617i	$0.344221\pi$
$368$	−3.06403	+	21.5282i	−0.159724	+	1.12224i
$369$	−1.58347			−0.0824323
$370$	26.1642	−	16.8147i	1.36021	−	0.874155i
$371$	1.64583	−	11.4470i	0.0854473	−	0.594299i
$372$	2.54884	−	5.58119i	0.132151	−	0.289371i
$373$	20.7698	−	6.09857i	1.07542	−	0.315772i	0.304375	−	0.952552i	$-0.401552\pi$
$373$	20.7698	−	6.09857i	1.07542	−	0.315772i	0.771045	+	0.636780i	$0.219734\pi$
$374$	−0.428125	−	0.937463i	−0.0221378	−	0.0484750i
$375$	2.98971	+	3.45031i	0.154388	+	0.178173i
$376$	0.301853	+	2.09944i	0.0155669	+	0.108270i
$377$	−18.1543	−	5.33059i	−0.934996	−	0.274539i
$378$	1.25667	−	1.45027i	0.0646361	−	0.0745940i
$379$	11.4115	+	7.33373i	0.586170	+	0.376709i	0.799854	−	0.600194i	$-0.204910\pi$
$379$	11.4115	+	7.33373i	0.586170	+	0.376709i	−0.213684	+	0.976903i	$0.568546\pi$
$380$	−1.21632	−	0.781681i	−0.0623959	−	0.0400994i
$381$	9.22653	−	10.6480i	0.472689	−	0.545513i
$382$	−39.9245	−	11.7229i	−2.04271	−	0.599795i
$383$	1.21662	+	8.46177i	0.0621663	+	0.432376i	0.997007	+	0.0773091i	$0.0246328\pi$
$383$	1.21662	+	8.46177i	0.0621663	+	0.432376i	−0.934841	+	0.355067i	$0.884458\pi$
$384$	3.15165	+	3.63720i	0.160832	+	0.185610i
$385$	−1.44970	−	3.17440i	−0.0738836	−	0.161783i
$386$	−35.8592	+	10.5292i	−1.82519	+	0.535923i
$387$	−0.585814	+	1.28275i	−0.0297786	+	0.0652061i
$388$	0.0185080	−	0.128726i	0.000939602	−	0.00653508i
$389$	−0.165993	+	0.106677i	−0.00841618	+	0.00540875i	−0.544842	−	0.838539i	$-0.683410\pi$
$389$	−0.165993	+	0.106677i	−0.00841618	+	0.00540875i	0.536426	+	0.843947i	$0.319774\pi$
$390$	22.5810			1.14343
$391$	0.887270	−	1.95019i	0.0448712	−	0.0986253i
$392$	0.609264			0.0307725
$393$	13.2783	−	8.53344i	0.669801	−	0.430455i
$394$	−2.75914	+	19.1903i	−0.139004	+	0.966792i
$395$	8.62270	−	18.8811i	0.433855	−	0.950010i
$396$	1.94066	−	0.569830i	0.0975219	−	0.0286350i
$397$	−13.6949	−	29.9876i	−0.687326	−	1.50503i	−0.854690	−	0.519139i	$-0.826253\pi$
$397$	−13.6949	−	29.9876i	−0.687326	−	1.50503i	0.167363	−	0.985895i	$-0.446475\pi$
$398$	−5.16072	−	5.95578i	−0.258683	−	0.298537i
$399$	0.0421278	+	0.293005i	0.00210903	+	0.0146686i
$400$	14.9107	+	4.37817i	0.745535	+	0.218909i
$401$	−17.5850	+	20.2942i	−0.878154	+	1.01344i	0.121628	+	0.992576i	$0.461189\pi$
$401$	−17.5850	+	20.2942i	−0.878154	+	1.01344i	−0.999782	+	0.0208683i	$0.993357\pi$
$402$	−5.77794	−	3.71326i	−0.288177	−	0.185200i
$403$	−12.4353	−	7.99171i	−0.619448	−	0.398095i
$404$	−19.4599	+	22.4580i	−0.968168	+	1.11733i
$405$	−2.78540	−	0.817866i	−0.138407	−	0.0406401i
$406$	−1.27478	−	8.86626i	−0.0632660	−	0.440025i
$407$	−4.39505	−	5.07215i	−0.217854	−	0.251417i
$408$	−0.113072	−	0.247592i	−0.00559788	−	0.0122576i
$409$	6.43959	−	1.89084i	0.318417	−	0.0934958i	−0.118618	−	0.992940i	$-0.537847\pi$
$409$	6.43959	−	1.89084i	0.318417	−	0.0934958i	0.437036	+	0.899444i	$0.356028\pi$
$410$	3.66446	−	8.02404i	0.180975	−	0.396279i
$411$	−0.429922	+	2.99017i	−0.0212065	+	0.147494i
$412$	5.61421	−	3.60803i	0.276592	−	0.177755i
$413$	−13.4821			−0.663412
$414$	7.74924	+	4.96457i	0.380854	+	0.243995i
$415$	0.0770263			0.00378107
$416$	−25.5153	+	16.3977i	−1.25099	+	0.803963i
$417$	1.61761	−	11.2507i	0.0792146	−	0.550949i
$418$	−0.283677	+	0.621165i	−0.0138751	+	0.0303822i
$419$	4.30211	−	1.26321i	0.210172	−	0.0617120i	−0.174952	−	0.984577i	$-0.555977\pi$
$419$	4.30211	−	1.26321i	0.210172	−	0.0617120i	0.385124	+	0.922865i	$0.374159\pi$
$420$	2.02901	+	4.44291i	0.0990056	+	0.216792i
$421$	−26.7489	−	30.8698i	−1.30366	−	1.50450i	−0.724459	−	0.689318i	$-0.757910\pi$
$421$	−26.7489	−	30.8698i	−1.30366	−	1.50450i	−0.579200	−	0.815185i	$-0.696635\pi$
$422$	−6.22243	−	43.2779i	−0.302903	−	2.10674i
$423$	3.34027	+	0.980792i	0.162410	+	0.0476878i
$424$	4.61413	−	5.32499i	0.224082	−	0.258605i
$425$	−1.28810	−	0.827811i	−0.0624820	−	0.0401547i
$426$	−19.2088	−	12.3447i	−0.930669	−	0.598105i
$427$	−2.77352	+	3.20082i	−0.134220	+	0.154898i
$428$	0.844814	+	0.248060i	0.0408356	+	0.0119904i
$429$	−0.693470	−	4.82319i	−0.0334811	−	0.232866i
$430$	−5.14451	−	5.93708i	−0.248090	−	0.286311i
$431$	16.9646	+	37.1474i	0.817158	+	1.78933i	0.572922	+	0.819610i	$0.305810\pi$
$431$	16.9646	+	37.1474i	0.817158	+	1.78933i	0.244236	+	0.969716i	$0.421463\pi$
$432$	4.35052	−	1.27743i	0.209314	−	0.0614602i
$433$	16.3503	−	35.8022i	0.785746	−	1.72054i	0.0973023	−	0.995255i	$-0.468979\pi$
$433$	16.3503	−	35.8022i	0.785746	−	1.72054i	0.688444	−	0.725290i	$-0.258294\pi$
$434$	0.995924	−	6.92680i	0.0478059	−	0.332497i
$435$	−11.3994	+	7.32598i	−0.546562	+	0.351254i
$436$	−9.73629			−0.466284
$437$	−1.36158	+	0.401901i	−0.0651331	+	0.0192255i
$438$	−21.5197			−1.02825
$439$	16.5106	−	10.6107i	0.788007	−	0.506421i	−0.0836753	−	0.996493i	$-0.526666\pi$
$439$	16.5106	−	10.6107i	0.788007	−	0.506421i	0.871682	+	0.490072i	$0.163029\pi$
$440$	0.302588	−	2.10455i	0.0144253	−	0.100330i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	3.33431	−	0.979041i	0.158597	−	0.0465682i
$443$	−9.85390	−	21.5770i	−0.468173	−	1.02516i	−0.985548	−	0.169397i	$-0.945818\pi$
$443$	−9.85390	−	21.5770i	−0.468173	−	1.02516i	0.517375	−	0.855759i	$-0.326909\pi$
$444$	6.15133	+	7.09902i	0.291929	+	0.336905i
$445$	4.36641	+	30.3690i	0.206987	+	1.43963i
$446$	−29.5264	−	8.66974i	−1.39812	−	0.410524i
$447$	11.8685	−	13.6970i	0.561363	−	0.647847i
$448$	−4.45062	−	2.86024i	−0.210272	−	0.135133i
$449$	14.5774	+	9.36836i	0.687952	+	0.442120i	0.837357	−	0.546656i	$-0.184099\pi$
$449$	14.5774	+	9.36836i	0.687952	+	0.442120i	−0.149405	+	0.988776i	$0.547736\pi$
$450$	4.30703	−	4.97057i	0.203035	−	0.234315i
$451$	−1.82643	−	0.536289i	−0.0860033	−	0.0252528i
$452$	−4.33319	−	30.1380i	−0.203816	−	1.41757i
$453$	2.89891	+	3.34552i	0.136202	+	0.157186i
$454$	−3.31435	−	7.25742i	−0.155550	−	0.340607i
$455$	11.2905	−	3.31519i	0.529307	−	0.155419i
$456$	−0.0749215	+	0.164055i	−0.00350852	+	0.00768259i
$457$	1.91255	−	13.3021i	0.0894653	−	0.622245i	−0.894921	−	0.446224i	$-0.852768\pi$
$457$	1.91255	−	13.3021i	0.0894653	−	0.622245i	0.984386	−	0.176021i	$-0.0563226\pi$
$458$	−23.8189	+	15.3075i	−1.11298	+	0.715272i
$459$	−0.446751			−0.0208525
$460$	−19.6877	+	12.6921i	−0.917944	+	0.591774i
$461$	−21.9771			−1.02357			−0.511787	−	0.859112i	$-0.671016\pi$
$461$	−21.9771			−1.02357			−0.511787	+	0.859112i	$0.671016\pi$
$462$	1.94066	−	1.24719i	0.0902877	−	0.0580244i
$463$	1.20109	−	8.35379i	0.0558196	−	0.388234i	−0.942691	−	0.333668i	$-0.891714\pi$
$463$	1.20109	−	8.35379i	0.0558196	−	0.388234i	0.998510	−	0.0545655i	$-0.0173774\pi$
$464$	8.79211	−	19.2520i	0.408163	−	0.893753i
$465$	−10.1576	+	2.98254i	−0.471047	+	0.138312i
$466$	−8.15400	−	17.8548i	−0.377727	−	0.827106i
$467$	18.5490	+	21.4067i	0.858347	+	0.990586i	1.00000		0.000669154i	$0.000212998\pi$
$467$	18.5490	+	21.4067i	0.858347	+	0.990586i	−0.141652	+	0.989916i	$0.545242\pi$
$468$	0.970585	+	6.75057i	0.0448653	+	0.312045i
$469$	−3.43413	−	1.00835i	−0.158573	−	0.0465613i
$470$	−12.7001	+	14.6567i	−0.585810	+	0.676061i
$471$	−13.3461	−	8.57701i	−0.614955	−	0.395208i
$472$	−6.91021	−	4.44092i	−0.318068	−	0.204410i
$473$	−1.11014	+	1.28117i	−0.0510443	+	0.0589083i
$474$	13.1653	+	3.86567i	0.604701	+	0.177556i
$475$	0.144386	+	1.00423i	0.00662489	+	0.0460771i
$476$	0.492234	+	0.568068i	0.0225615	+	0.0260373i
$477$	−4.80416	−	10.5196i	−0.219967	−	0.481661i
$478$	−6.71358	+	1.97129i	−0.307072	+	0.0901645i
$479$	−13.9645	+	30.5781i	−0.638056	+	1.39715i	0.263575	+	0.964639i	$0.415098\pi$
$479$	−13.9645	+	30.5781i	−0.638056	+	1.39715i	−0.901630	+	0.432508i	$0.857629\pi$
$480$	−3.09131	+	21.5005i	−0.141098	+	0.981360i
$481$	19.0378	−	12.2349i	0.868050	−	0.557862i
$482$	30.0761			1.36993
$483$	4.60348	+	1.34459i	0.209466	+	0.0611811i
$484$	−16.0762			−0.730735
$485$	−0.188766	+	0.121313i	−0.00857144	+	0.00550853i
$486$	0.273100	−	1.89945i	0.0123881	−	0.0861610i
$487$	−3.75489	+	8.22206i	−0.170150	+	0.372577i	−0.975427	−	0.220322i	$-0.929289\pi$
$487$	−3.75489	+	8.22206i	−0.170150	+	0.372577i	0.805277	+	0.592899i	$0.202017\pi$
$488$	−2.47589	+	0.726986i	−0.112078	+	0.0329091i
$489$	0.821254	+	1.79830i	0.0371384	+	0.0813218i
$490$	3.64809	+	4.21012i	0.164804	+	0.190194i
$491$	−0.832831	−	5.79247i	−0.0375852	−	0.261410i	0.962361	−	0.271774i	$-0.0876103\pi$
$491$	−0.832831	−	5.79247i	−0.0375852	−	0.261410i	−0.999946	+	0.0103634i	$0.996701\pi$
$492$	2.55628	+	0.750593i	0.115246	+	0.0338393i
$493$	−1.36561	+	1.57600i	−0.0615039	+	0.0709793i
$494$	−1.93706	−	1.24488i	−0.0871526	−	0.0560096i
$495$	−2.93578	−	1.88671i	−0.131953	−	0.0848013i
$496$	10.8281	−	12.4963i	0.486196	−	0.561100i
$497$	−11.4168	−	3.35227i	−0.512112	−	0.150370i
$498$	0.00724629	+	0.0503991i	0.000324714	+	0.00225844i
$499$	24.7024	+	28.5080i	1.10583	+	1.27620i	0.957870	+	0.287202i	$0.0927250\pi$
$499$	24.7024	+	28.5080i	1.10583	+	1.27620i	0.147959	+	0.988993i	$0.452730\pi$
$500$	−3.19095	−	6.98720i	−0.142704	−	0.312477i
$501$	−13.4676	+	3.95445i	−0.601689	+	0.176672i
$502$	9.92809	−	21.7395i	0.443112	−	0.970280i
$503$	−2.80101	+	19.4815i	−0.124891	+	0.868636i	0.827001	+	0.562201i	$0.190045\pi$
$503$	−2.80101	+	19.4815i	−0.124891	+	0.868636i	−0.951892	+	0.306435i	$0.900864\pi$
$504$	0.512546	−	0.329393i	0.0228306	−	0.0146723i
$505$	51.2721			2.28158
$506$	7.25685	+	8.35080i	0.322606	+	0.371239i
$507$	3.43060			0.152358
$508$	−19.9422	+	12.8161i	−0.884792	+	0.568621i
$509$	4.29334	−	29.8608i	0.190299	−	1.32356i	−0.640918	−	0.767609i	$-0.721446\pi$
$509$	4.29334	−	29.8608i	0.190299	−	1.32356i	0.831217	−	0.555948i	$-0.187645\pi$
$510$	1.03387	−	2.26385i	0.0457804	−	0.100245i
$511$	−10.7598	+	3.15937i	−0.475987	+	0.139762i
$512$	−11.7986	−	25.8354i	−0.521431	−	1.14177i
$513$	0.193851	+	0.223716i	0.00855872	+	0.00987729i
$514$	6.05578	+	42.1189i	0.267109	+	1.85779i
$515$	−11.0482	−	3.24405i	−0.486842	−	0.142950i
$516$	1.55376	−	1.79313i	0.0684004	−	0.0789383i
$517$	3.52061	+	2.26256i	0.154836	+	0.0995072i
$518$	9.01285	+	5.79221i	0.396002	+	0.254495i
$519$	4.33300	−	5.00054i	0.190197	−	0.219500i
$520$	6.87891	+	2.01983i	0.301660	+	0.0885754i
$521$	2.26432	+	15.7487i	0.0992019	+	0.689964i	0.977358	+	0.211591i	$0.0678644\pi$
$521$	2.26432	+	15.7487i	0.0992019	+	0.689964i	−0.878157	+	0.478373i	$0.841227\pi$
$522$	−5.86587	−	6.76958i	−0.256742	−	0.296296i
$523$	−13.5710	−	29.7164i	−0.593420	−	1.29941i	−0.933353	−	0.358959i	$-0.883132\pi$
$523$	−13.5710	−	29.7164i	−0.593420	−	1.29941i	0.339933	−	0.940450i	$-0.389596\pi$
$524$	−25.4809	+	7.48186i	−1.11314	+	0.326846i
$525$	1.42377	−	3.11762i	0.0621383	−	0.136064i
$526$	2.35166	−	16.3561i	0.102537	−	0.713162i
$527$	−1.37055	+	0.880802i	−0.0597023	+	0.0383683i
$528$	5.45067			0.237210
$529$	−3.20843	+	22.7751i	−0.139497	+	0.990222i
$530$	64.4247			2.79843
$531$	−11.3419	+	7.28899i	−0.492196	+	0.316315i
$532$	0.0708803	−	0.492983i	0.00307305	−	0.0213735i
$533$	2.66636	−	5.83852i	0.115493	−	0.252894i
$534$	−19.4600	+	5.71396i	−0.842115	+	0.247267i
$535$	−0.631088	−	1.38189i	−0.0272843	−	0.0597443i
$536$	−1.42800	−	1.64800i	−0.0616803	−	0.0711829i
$537$	3.20579	+	22.2968i	0.138340	+	0.962177i
$538$	41.6426	+	12.2274i	1.79534	+	0.527159i
$539$	0.787227	−	0.908508i	0.0339083	−	0.0391322i
$540$	4.10893	+	2.64065i	0.176820	+	0.113636i
$541$	−20.0450	−	12.8821i	−0.861801	−	0.553846i	0.0334337	−	0.999441i	$-0.489356\pi$
$541$	−20.0450	−	12.8821i	−0.861801	−	0.553846i	−0.895235	+	0.445595i	$0.852992\pi$
$542$	18.6946	−	21.5747i	0.803000	−	0.926712i
$543$	8.10243	+	2.37909i	0.347709	+	0.102096i
$544$	0.475732	+	3.30879i	0.0203969	+	0.141863i
$545$	11.0010	+	12.6958i	0.471229	+	0.543828i
$546$	3.23133	+	7.07562i	0.138288	+	0.302808i
$547$	−20.9981	+	6.16561i	−0.897816	+	0.263622i	−0.697904	−	0.716191i	$-0.745884\pi$
$547$	−20.9981	+	6.16561i	−0.897816	+	0.263622i	−0.199912	+	0.979814i	$0.564066\pi$
$548$	2.11144	−	4.62340i	0.0901962	−	0.197502i
$549$	−0.602744	+	4.19218i	−0.0257245	+	0.178918i
$550$	6.65130	−	4.27453i	0.283612	−	0.182267i
$551$	1.38175			0.0588646
$552$	1.91660	+	2.20552i	0.0815758	+	0.0938732i
$553$	7.15016			0.304056
$554$	42.4967	−	27.3110i	1.80551	−	1.16033i
$555$	2.30653	−	16.0423i	0.0979067	−	0.680956i
$556$	−7.94442	+	17.3958i	−0.336918	+	0.737748i
$557$	−34.7233	+	10.1957i	−1.47127	+	0.432004i	−0.916512	−	0.400006i	$-0.869008\pi$
$557$	−34.7233	+	10.1957i	−1.47127	+	0.432004i	−0.554760	+	0.832011i	$0.687190\pi$
$558$	−2.90709	−	6.36563i	−0.123067	−	0.269479i
$559$	−3.74329	−	4.31999i	−0.158324	−	0.182716i
$560$	1.87324	+	13.0287i	0.0791590	+	0.550563i
$561$	−0.515298	−	0.151305i	−0.0217559	−	0.00638811i
$562$	−23.8729	+	27.5508i	−1.00702	+	1.16216i
$563$	32.5347	+	20.9088i	1.37117	+	0.881201i	0.998899	−	0.0469213i	$-0.0149410\pi$
$563$	32.5347	+	20.9088i	1.37117	+	0.881201i	0.372276	+	0.928122i	$0.378577\pi$
$564$	−4.92747	−	3.16669i	−0.207484	−	0.133342i
$565$	−34.4029	+	39.7031i	−1.44734	+	1.67032i
$566$	−38.7949	−	11.3912i	−1.63067	−	0.478808i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	−4.74740	−	5.47880i	−0.199197	−	0.229885i
$569$	3.78035	+	8.27782i	0.158481	+	0.347024i	0.972170	−	0.234275i	$-0.0752717\pi$
$569$	3.78035	+	8.27782i	0.158481	+	0.347024i	−0.813690	+	0.581300i	$0.802544\pi$
$570$	−1.58226	+	0.464593i	−0.0662735	+	0.0194597i
$571$	14.9750	−	32.7907i	0.626685	−	1.37225i	−0.283872	−	0.958862i	$-0.591619\pi$
$571$	14.9750	−	32.7907i	0.626685	−	1.37225i	0.910556	−	0.413385i	$-0.135654\pi$
$572$	−1.16677	+	8.11505i	−0.0487851	+	0.339307i
$573$	−18.2412	+	11.7229i	−0.762035	+	0.489730i
$574$	3.03866			0.126831
$575$	15.7777	+	4.60837i	0.657975	+	0.192182i
$576$	−5.29046			−0.220436
$577$	28.8955	−	18.5700i	1.20294	−	0.773081i	0.223475	−	0.974710i	$-0.428260\pi$
$577$	28.8955	−	18.5700i	1.20294	−	0.773081i	0.979462	+	0.201629i	$0.0646235\pi$
$578$	−4.58820	+	31.9116i	−0.190844	+	1.32735i
$579$	−8.09039	+	17.7155i	−0.336225	+	0.736230i
$580$	21.8754	−	6.42319i	0.908326	−	0.266709i
$581$	0.0110224	+	0.0241357i	0.000457286	+	0.00100132i
$582$	−0.0971345	−	0.112099i	−0.00402635	−	0.00464666i
$583$	−1.97850	−	13.7608i	−0.0819412	−	0.569913i
$584$	−6.55558	−	1.92489i	−0.271272	−	0.0796526i
$585$	7.70586	−	8.89303i	0.318598	−	0.367682i
$586$	44.7816	+	28.7794i	1.84991	+	1.18887i
$587$	−6.87638	−	4.41918i	−0.283818	−	0.182399i	0.390984	−	0.920397i	$-0.372135\pi$
$587$	−6.87638	−	4.41918i	−0.283818	−	0.182399i	−0.674802	+	0.737998i	$0.735771\pi$
$588$	−1.10181	+	1.27155i	−0.0454378	+	0.0524380i
$589$	1.03577	+	0.304130i	0.0426783	+	0.0125315i
$590$	−10.6887	−	74.3417i	−0.440048	−	3.06060i
$591$	6.61609	+	7.63537i	0.272150	+	0.314077i
$592$	10.5159	+	23.0265i	0.432199	+	0.946384i
$593$	25.4459	−	7.47159i	1.04494	−	0.306821i	0.286167	−	0.958180i	$-0.407619\pi$
$593$	25.4459	−	7.47159i	1.04494	−	0.306821i	0.758770	+	0.651359i	$0.225801\pi$
$594$	0.958308	−	2.09840i	0.0393198	−	0.0860984i
$595$	0.184570	−	1.28371i	0.00756663	−	0.0526270i
$596$	−25.6526	+	16.4860i	−1.05077	+	0.675291i
$597$	−4.10666			−0.168075
$598$	−31.3539	+	20.2130i	−1.28216	+	0.826572i
$599$	19.5398			0.798375			0.399188	−	0.916869i	$-0.369292\pi$
$599$	19.5398			0.798375			0.399188	+	0.916869i	$0.369292\pi$
$600$	1.75667	−	1.12894i	0.0717157	−	0.0460889i
$601$	−2.83902	+	19.7458i	−0.115806	+	0.805448i	0.846287	+	0.532727i	$0.178833\pi$
$601$	−2.83902	+	19.7458i	−0.115806	+	0.805448i	−0.962093	+	0.272721i	$0.912076\pi$
$602$	1.12417	−	2.46159i	0.0458177	−	0.100327i
$603$	−3.43413	+	1.00835i	−0.139848	+	0.0410632i
$604$	−3.09403	−	6.77498i	−0.125894	−	0.275670i
$605$	18.1643	+	20.9628i	0.738486	+	0.852258i
$606$	4.82345	+	33.5478i	0.195939	+	1.36279i
$607$	−29.2282	−	8.58218i	−1.18634	−	0.348340i	−0.371723	−	0.928344i	$-0.621233\pi$
$607$	−29.2282	−	8.58218i	−1.18634	−	0.348340i	−0.814614	+	0.580004i	$0.803051\pi$
$608$	1.45049	−	1.67395i	0.0588251	−	0.0678878i
$609$	−3.92680	−	2.52360i	−0.159122	−	0.102261i
$610$	−19.8485	−	12.7558i	−0.803641	−	0.516468i
$611$	−9.24093	+	10.6646i	−0.373848	+	0.431444i
$612$	0.721214	+	0.211768i	0.0291533	+	0.00856019i
$613$	2.23998	+	15.5794i	0.0904721	+	0.629247i	0.983723	+	0.179690i	$0.0575093\pi$
$613$	2.23998	+	15.5794i	0.0904721	+	0.629247i	−0.893251	+	0.449558i	$0.851582\pi$
$614$	−9.63899	−	11.1240i	−0.388998	−	0.448928i
$615$	−1.90958	−	4.18140i	−0.0770017	−	0.168610i
$616$	0.702746	−	0.206345i	0.0283145	−	0.00831388i
$617$	−6.18378	+	13.5406i	−0.248950	+	0.545124i	−0.992311	−	0.123766i	$-0.960503\pi$
$617$	−6.18378	+	13.5406i	−0.248950	+	0.545124i	0.743362	+	0.668890i	$0.233230\pi$
$618$	1.08325	−	7.53414i	0.0435745	−	0.303068i
$619$	20.7947	−	13.3639i	0.835810	−	0.537142i	−0.0513094	−	0.998683i	$-0.516339\pi$
$619$	20.7947	−	13.3639i	0.835810	−	0.537142i	0.887119	+	0.461540i	$0.152703\pi$
$620$	17.8117			0.715336
$621$	4.59964	−	1.35769i	0.184577	−	0.0544822i
$622$	27.7671			1.11336
$623$	−8.89110	+	5.71396i	−0.356214	+	0.228925i
$624$	−2.61563	+	18.1921i	−0.104709	+	0.728267i
$625$	−12.6245	+	27.6438i	−0.504979	+	1.10575i
$626$	25.9645	−	7.62387i	1.03775	−	0.304711i
$627$	0.147826	+	0.323694i	0.00590361	+	0.0129271i
$628$	17.4797	+	20.1726i	0.697514	+	0.804974i
$629$	−0.354960	−	2.46880i	−0.0141532	−	0.0984375i
$630$	5.34514	+	1.56947i	0.212955	+	0.0625293i
$631$	7.82029	−	9.02509i	0.311321	−	0.359283i	−0.578428	−	0.815733i	$-0.696334\pi$
$631$	7.82029	−	9.02509i	0.311321	−	0.359283i	0.889749	+	0.456450i	$0.150879\pi$
$632$	3.66479	+	2.35522i	0.145777	+	0.0936854i
$633$	−19.1675	−	12.3182i	−0.761838	−	0.489604i
$634$	30.1148	−	34.7544i	1.19601	−	1.38027i
$635$	39.2443	+	11.5232i	1.55736	+	0.457283i
$636$	2.76912	+	19.2597i	0.109803	+	0.763696i
$637$	2.65446	+	3.06341i	0.105173	+	0.121377i
$638$	−4.47318	−	9.79491i	−0.177095	−	0.387784i
$639$	−11.4168	+	3.35227i	−0.451640	+	0.132614i
$640$	−5.80385	+	12.7087i	−0.229417	+	0.502354i
$641$	−2.31863	+	16.1264i	−0.0915802	+	0.636954i	0.891397	+	0.453224i	$0.149726\pi$
$641$	−2.31863	+	16.1264i	−0.0915802	+	0.636954i	−0.982977	+	0.183730i	$0.941183\pi$
$642$	0.844814	−	0.542929i	0.0333422	−	0.0214277i
$643$	−34.3064			−1.35291			−0.676455	−	0.736484i	$-0.736485\pi$
$643$	−34.3064			−1.35291			−0.676455	+	0.736484i	$0.736485\pi$
$644$	−6.79429	−	4.35278i	−0.267733	−	0.171523i
$645$	−4.09377			−0.161192
$646$	−0.213492	+	0.137203i	−0.00839975	+	0.00539819i
$647$	0.710436	−	4.94119i	0.0279301	−	0.194258i	−0.971079	−	0.238757i	$-0.923260\pi$
$647$	0.710436	−	4.94119i	0.0279301	−	0.194258i	0.999009	+	0.0444989i	$0.0141691\pi$
$648$	0.253098	−	0.554206i	0.00994261	−	0.0217713i
$649$	−15.5508	+	4.56611i	−0.610420	+	0.179236i
$650$	11.0748	+	24.2505i	0.434391	+	0.951184i
$651$	−2.38810	−	2.75602i	−0.0935971	−	0.108017i
$652$	−0.473372	−	3.29237i	−0.0185387	−	0.128939i
$653$	15.9815	+	4.69258i	0.625403	+	0.183635i	0.579052	−	0.815290i	$-0.303423\pi$
$653$	15.9815	+	4.69258i	0.625403	+	0.183635i	0.0463505	+	0.998925i	$0.485241\pi$
$654$	−7.27206	+	8.39240i	−0.284360	+	0.328169i
$655$	38.5467	+	24.7725i	1.50615	+	0.967941i
$656$	6.04000	+	3.88167i	0.235822	+	0.151554i
$657$	−7.34366	+	8.47503i	−0.286503	+	0.330643i
$658$	−6.40993	−	1.88213i	−0.249885	−	0.0733729i
$659$	−1.74111	−	12.1097i	−0.0678240	−	0.471726i	−0.995221	−	0.0976477i	$-0.968868\pi$
$659$	−1.74111	−	12.1097i	−0.0678240	−	0.471726i	0.927397	−	0.374078i	$-0.122041\pi$
$660$	3.84505	+	4.43743i	0.149668	+	0.172727i
$661$	−13.2195	−	28.9467i	−0.514179	−	1.12590i	−0.971597	−	0.236644i	$-0.923953\pi$
$661$	−13.2195	−	28.9467i	−0.514179	−	1.12590i	0.457417	−	0.889252i	$-0.348775\pi$
$662$	38.5291	−	11.3132i	1.49748	−	0.439699i
$663$	0.752271	−	1.64724i	0.0292158	−	0.0639736i
$664$	−0.00230065	+	0.0160013i	−8.92824e−5	+	0.000620973i
$665$	−0.722921	+	0.464593i	−0.0280337	+	0.0180161i
$666$	10.7136			0.415143
$667$	9.27047	−	20.3762i	0.358954	−	0.788969i
$668$	23.6160			0.913730
$669$	−13.4904	+	8.66974i	−0.521568	+	0.335192i
$670$	2.83754	−	19.7355i	0.109624	−	0.762449i
$671$	−2.11503	+	4.63127i	−0.0816497	+	0.178788i
$672$	−7.17941	+	2.10807i	−0.276952	+	0.0813204i
$673$	−21.0071	−	45.9991i	−0.809764	−	1.77314i	−0.608419	−	0.793616i	$-0.708196\pi$
$673$	−21.0071	−	45.9991i	−0.809764	−	1.77314i	−0.201345	−	0.979520i	$-0.564531\pi$
$674$	−17.9818	−	20.7521i	−0.692633	−	0.799341i
$675$	−0.487761	−	3.39245i	−0.0187739	−	0.130576i
$676$	−5.53820	−	1.62616i	−0.213008	−	0.0625447i
$677$	−8.38542	+	9.67728i	−0.322278	+	0.371928i	−0.893651	−	0.448762i	$-0.851865\pi$
$677$	−8.38542	+	9.67728i	−0.322278	+	0.371928i	0.571374	+	0.820690i	$0.306411\pi$
$678$	−29.2146	−	18.7751i	−1.12198	−	0.721052i
$679$	−0.0650249	−	0.0417890i	−0.00249543	−	0.00160371i
$680$	0.517446	−	0.597165i	0.0198432	−	0.0229002i
$681$	−3.98921	−	1.17134i	−0.152867	−	0.0448857i
$682$	−1.19723	−	8.32691i	−0.0458442	−	0.318854i
$683$	−0.436006	−	0.503178i	−0.0166833	−	0.0192536i	0.747347	−	0.664434i	$-0.231327\pi$
$683$	−0.436006	−	0.503178i	−0.0166833	−	0.0192536i	−0.764030	+	0.645181i	$0.776782\pi$
$684$	−0.206899	−	0.453045i	−0.00791097	−	0.0173226i
$685$	−8.41446	+	2.47071i	−0.321500	+	0.0944009i
$686$	−0.797176	+	1.74557i	−0.0304363	+	0.0666462i
$687$	−2.09978	+	14.6043i	−0.0801115	+	0.557188i
$688$	5.37903	−	3.45689i	0.205074	−	0.131793i
$689$	46.8772			1.78588
$690$	−3.76453	+	26.4500i	−0.143313	+	1.00694i
$691$	−26.3499			−1.00240			−0.501198	−	0.865333i	$-0.667107\pi$
$691$	−26.3499			−1.00240			−0.501198	+	0.865333i	$0.667107\pi$
$692$	−9.36533	+	6.01873i	−0.356017	+	0.228798i
$693$	0.171081	−	1.18989i	0.00649882	−	0.0452003i
$694$	−15.4206	+	33.7663i	−0.585356	+	1.28175i
$695$	31.6599	−	9.29619i	1.20093	−	0.352625i
$696$	−1.18141	−	2.58692i	−0.0447811	−	0.0980570i
$697$	−0.463260	−	0.534631i	−0.0175472	−	0.0202506i
$698$	0.252571	+	1.75667i	0.00955994	+	0.0664908i
$699$	−9.81428	−	2.88173i	−0.371210	−	0.108997i
$700$	−3.77627	+	4.35805i	−0.142729	+	0.164719i
$701$	13.0382	+	8.37915i	0.492447	+	0.316476i	0.763189	−	0.646176i	$-0.223633\pi$
$701$	13.0382	+	8.37915i	0.492447	+	0.316476i	−0.270742	+	0.962652i	$0.587269\pi$
$702$	6.54373	+	4.20540i	0.246977	+	0.158723i
$703$	−1.08226	+	1.24899i	−0.0408181	+	0.0471067i
$704$	−6.10219	−	1.79177i	−0.229985	−	0.0675297i
$705$	1.43825	+	10.0033i	0.0541678	+	0.376745i
$706$	−23.4312	−	27.0410i	−0.881844	−	1.01770i
$707$	7.33699	+	16.0658i	0.275936	+	0.604215i
$708$	21.7649	−	6.39076i	0.817976	−	0.240179i
$709$	9.65095	−	21.1326i	0.362449	−	0.793653i	−0.637286	−	0.770628i	$-0.719943\pi$
$709$	9.65095	−	21.1326i	0.362449	−	0.793653i	0.999735	−	0.0230254i	$-0.00732985\pi$
$710$	9.43341	−	65.6108i	0.354029	−	2.46233i
$711$	6.01510	−	3.86567i	0.225584	−	0.144974i
$712$	−6.43924			−0.241321
$713$	11.4341	−	13.2337i	0.428211	−	0.495605i
$714$	0.857309			0.0320840
$715$	11.9001	−	7.64772i	0.445038	−	0.286008i
$716$	5.39377	−	37.5145i	0.201575	−	1.40198i
$717$	−1.51469	+	3.31670i	−0.0565670	+	0.123864i
$718$	2.30133	−	0.675732i	0.0858850	−	0.0252181i
$719$	−5.36515	−	11.7480i	−0.200086	−	0.438128i	0.782817	−	0.622252i	$-0.213782\pi$
$719$	−5.36515	−	11.7480i	−0.200086	−	0.438128i	−0.982903	+	0.184125i	$0.941055\pi$
$720$	8.61972	+	9.94769i	0.321238	+	0.370729i
$721$	−0.564489	−	3.92610i	−0.0210227	−	0.146216i
$722$	−34.8225	−	10.2248i	−1.29596	−	0.380528i
$723$	10.2636	−	11.8448i	0.381707	−	0.440513i
$724$	−11.9525	−	7.68138i	−0.444210	−	0.285476i
$725$	−13.4585	−	8.64923i	−0.499835	−	0.321224i
$726$	−12.0073	+	13.8572i	−0.445634	+	0.514289i
$727$	39.9866	+	11.7411i	1.48302	+	0.435454i	0.920307	−	0.391197i	$-0.127939\pi$
$727$	39.9866	+	11.7411i	1.48302	+	0.435454i	0.562714	+	0.826652i	$0.309757\pi$
$728$	0.351466	+	2.44450i	0.0130262	+	0.0905991i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−25.9515	−	56.8259i	−0.960509	−	2.10322i
$731$	−0.604484	+	0.177493i	−0.0223577	+	0.00656480i
$732$	2.96021	−	6.48195i	0.109412	−	0.239580i
$733$	0.137962	−	0.959545i	0.00509573	−	0.0354416i	−0.987115	−	0.160013i	$-0.948846\pi$
$733$	0.137962	−	0.959545i	0.00509573	−	0.0354416i	0.992211	+	0.124571i	$0.0397555\pi$
$734$	−29.0767	+	18.6865i	−1.07324	+	0.689730i
$735$	2.90299			0.107078
$736$	−14.9535	−	32.6208i	−0.551195	−	1.20242i
$737$	−4.30254			−0.158486
$738$	2.55628	−	1.64282i	0.0940981	−	0.0604732i
$739$	3.45488	−	24.0292i	0.127090	−	0.883930i	−0.822126	−	0.569305i	$-0.807212\pi$
$739$	3.45488	−	24.0292i	0.127090	−	0.883930i	0.949216	−	0.314625i	$-0.101879\pi$
$740$	−11.3279	+	24.8045i	−0.416420	+	0.911833i
$741$	−1.15130	+	0.338051i	−0.0422939	+	0.0124186i
$742$	9.21912	+	20.1870i	0.338444	+	0.741090i
$743$	−24.2420	−	27.9767i	−0.889352	−	1.02637i	−0.999473	−	0.0324492i	$-0.989669\pi$
$743$	−24.2420	−	27.9767i	−0.889352	−	1.02637i	0.110121	−	0.993918i	$-0.464876\pi$
$744$	−0.316199	−	2.19921i	−0.0115924	−	0.0806270i
$745$	50.4819	+	14.8228i	1.84951	+	0.543066i
$746$	−27.2027	+	31.3936i	−0.995961	+	1.14940i
$747$	0.0223214	+	0.0143451i	0.000816696	+	0.000524859i
$748$	0.760152	+	0.488520i	0.0277939	+	0.0178621i
$749$	0.342698	−	0.395494i	0.0125219	−	0.0144511i
$750$	−8.40609	−	2.46825i	−0.306947	−	0.0901278i
$751$	−0.791946	−	5.50811i	−0.0288985	−	0.200994i	0.970257	−	0.242076i	$-0.0778284\pi$
$751$	−0.791946	−	5.50811i	−0.0288985	−	0.200994i	−0.999156	+	0.0410826i	$0.986919\pi$
$752$	−10.3368	−	11.9294i	−0.376946	−	0.435019i
$753$	−5.17361	−	11.3286i	−0.188537	−	0.412838i
$754$	34.8379	−	10.2293i	1.26872	−	0.372530i
$755$	−5.33842	+	11.6895i	−0.194285	+	0.425425i
$756$	−0.239446	+	1.66538i	−0.00870856	+	0.0605693i
$757$	−11.6133	+	7.46341i	−0.422093	+	0.271262i	−0.734398	−	0.678719i	$-0.762535\pi$
$757$	−11.6133	+	7.46341i	−0.422093	+	0.271262i	0.312305	+	0.949982i	$0.398899\pi$
$758$	−26.0308			−0.945482
$759$	5.76520	−	0.00820448i	0.209264	−	0.000297804i
$760$	−0.523564			−0.0189917
$761$	14.4210	−	9.26784i	0.522762	−	0.335959i	−0.252501	−	0.967597i	$-0.581253\pi$
$761$	14.4210	−	9.26784i	0.522762	−	0.335959i	0.775264	+	0.631638i	$0.217617\pi$
$762$	−3.84779	+	26.7620i	−0.139391	+	0.969484i
$763$	−2.40391	+	5.26384i	−0.0870275	+	0.190564i
$764$	35.0045	−	10.2783i	1.26642	−	0.371854i
$765$	−0.538757	−	1.17971i	−0.0194788	−	0.0426526i
$766$	−10.7430	−	12.3981i	−0.388160	−	0.447960i
$767$	−7.77742	−	54.0931i	−0.280826	−	1.95319i
$768$	−19.0137	−	5.58293i	−0.686098	−	0.201457i
$769$	−5.31096	+	6.12917i	−0.191518	+	0.221024i	−0.843385	−	0.537310i	$-0.819441\pi$
$769$	−5.31096	+	6.12917i	−0.191518	+	0.221024i	0.651867	+	0.758333i	$0.273986\pi$
$770$	5.63372	+	3.62057i	0.203025	+	0.130476i
$771$	18.6541	+	11.9883i	0.671813	+	0.431748i
$772$	21.4582	−	24.7641i	0.772297	−	0.891278i
$773$	−37.0149	−	10.8685i	−1.33133	−	0.390914i	−0.462763	−	0.886482i	$-0.653142\pi$
$773$	−37.0149	−	10.8685i	−1.33133	−	0.390914i	−0.868569	+	0.495568i	$0.834960\pi$
$774$	−0.385123	−	2.67859i	−0.0138430	−	0.0962800i
$775$	−8.18483	−	9.44580i	−0.294008	−	0.339303i
$776$	−0.0195632	−	0.0428375i	−0.000702279	−	0.00153778i
$777$	5.35680	−	1.57290i	0.192174	−	0.0564274i
$778$	0.157296	−	0.344429i	0.00563932	−	0.0123484i
$779$	−0.0667082	+	0.463966i	−0.00239007	+	0.0166233i
$780$	−16.6554	+	10.7038i	−0.596360	+	0.383257i
$781$	−14.3038			−0.511831
$782$	0.590920	+	4.06882i	0.0211312	+	0.145501i
$783$	−4.66779			−0.166813
$784$	−3.81440	+	2.45137i	−0.136229	+	0.0875488i
$785$	6.55424	−	45.5857i	0.233931	−	1.62702i
$786$	−12.5826	+	27.5520i	−0.448805	+	0.982747i
$787$	−12.9819	+	3.81184i	−0.462756	+	0.135877i	−0.504796	−	0.863238i	$-0.668432\pi$
$787$	−12.9819	+	3.81184i	−0.462756	+	0.135877i	0.0420402	+	0.999116i	$0.486614\pi$
$788$	−7.06141	−	15.4623i	−0.251552	−	0.550823i
$789$	−5.63899	−	6.50774i	−0.200753	−	0.231682i
$790$	5.66870	+	39.4266i	0.201683	+	1.40274i
$791$	−17.3637	−	5.09845i	−0.617383	−	0.181280i
$792$	0.479629	−	0.553522i	0.0170429	−	0.0196685i
$793$	−14.4423	−	9.28151i	−0.512861	−	0.329596i
$794$	53.2200	+	34.2024i	1.88871	+	1.21380i
$795$	21.9852	−	25.3722i	0.779733	−	0.899860i
$796$	6.62961	+	1.94663i	0.234980	+	0.0689964i
$797$	2.98799	+	20.7819i	0.105840	+	0.736134i	0.971763	+	0.235957i	$0.0758225\pi$
$797$	2.98799	+	20.7819i	0.105840	+	0.736134i	−0.865923	+	0.500177i	$0.833268\pi$
$798$	−0.371997	−	0.429307i	−0.0131685	−	0.0151973i
$799$	0.646082	+	1.41472i	0.0228567	+	0.0500493i
$800$	−24.6063	+	7.22505i	−0.869963	+	0.255444i
$801$	−4.39047	+	9.61378i	−0.155130	+	0.339686i
$802$	7.33358	−	51.0062i	0.258958	−	1.80109i
$803$	−11.3407	+	7.28825i	−0.400206	+	0.257197i
$804$	6.02187			0.212375
$805$	2.00095	+	13.7777i	0.0705242	+	0.485600i
$806$	28.3663			0.999160
$807$	19.0261	−	12.2274i	0.669752	−	0.430424i
$808$	−1.53141	+	10.6512i	−0.0538749	+	0.374708i
$809$	−1.56325	+	3.42303i	−0.0549609	+	0.120347i	−0.935120	−	0.354331i	$-0.884709\pi$
$809$	−1.56325	+	3.42303i	−0.0549609	+	0.120347i	0.880159	+	0.474679i	$0.157436\pi$
$810$	5.34514	−	1.56947i	0.187809	−	0.0551457i
$811$	−5.28315	−	11.5685i	−0.185516	−	0.406224i	0.793907	−	0.608039i	$-0.208043\pi$
$811$	−5.28315	−	11.5685i	−0.185516	−	0.406224i	−0.979424	+	0.201815i	$0.935316\pi$
$812$	5.14301	+	5.93535i	0.180484	+	0.208290i
$813$	−2.11712	−	14.7249i	−0.0742505	−	0.516424i
$814$	12.3574	+	3.62847i	0.433128	+	0.127178i
$815$	−3.75828	+	4.33729i	−0.131647	+	0.151929i
$816$	1.70409	+	1.09515i	0.0596549	+	0.0383379i
$817$	0.351175	+	0.225686i	0.0122860	+	0.00789576i
$818$	−8.43407	+	9.73344i	−0.294890	+	0.340322i
$819$	3.88927	+	1.14199i	0.135902	+	0.0399045i
$820$	1.10068	+	7.65543i	0.0384376	+	0.267339i
$821$	22.5552	+	26.0301i	0.787182	+	0.908457i	0.997606	−	0.0691536i	$-0.0220299\pi$
$821$	22.5552	+	26.0301i	0.787182	+	0.908457i	−0.210424	+	0.977610i	$0.567484\pi$
$822$	−2.40820	−	5.27323i	−0.0839957	−	0.183925i
$823$	4.78390	−	1.40468i	0.166756	−	0.0489640i	−0.197289	−	0.980345i	$-0.563214\pi$
$823$	4.78390	−	1.40468i	0.166756	−	0.0489640i	0.364045	+	0.931381i	$0.381395\pi$
$824$	1.00391	−	2.19825i	0.0349727	−	0.0765796i
$825$	0.586352	−	4.07817i	0.0204141	−	0.141983i
$826$	21.7649	−	13.9875i	0.757299	−	0.486686i
$827$	−2.16673			−0.0753447			−0.0376724	−	0.999290i	$-0.511994\pi$
$827$	−2.16673			−0.0753447			−0.0376724	+	0.999290i	$0.511994\pi$
$828$	−8.06901	+	0.0114830i	−0.280418	+	0.000399063i
$829$	37.0342			1.28625			0.643126	−	0.765760i	$-0.277637\pi$
$829$	37.0342			1.28625			0.643126	+	0.765760i	$0.277637\pi$
$830$	−0.124348	+	0.0799134i	−0.00431617	+	0.00277383i
$831$	3.74634	−	26.0564i	0.129959	−	0.903885i
$832$	8.90845	−	19.5068i	0.308845	−	0.676276i
$833$	0.428654	−	0.125864i	0.0148520	−	0.00436094i
$834$	9.06102	+	19.8409i	0.313757	+	0.687033i
$835$	−26.6835	−	30.7945i	−0.923422	−	1.06569i
$836$	−0.0852073	−	0.592630i	−0.00294695	−	0.0204965i
$837$	−3.49902	−	1.02740i	−0.120944	−	0.0355123i
$838$	−5.63456	+	6.50263i	−0.194643	+	0.224630i
$839$	14.8879	+	9.56785i	0.513986	+	0.330319i	0.771789	−	0.635879i	$-0.219362\pi$
$839$	14.8879	+	9.56785i	0.513986	+	0.330319i	−0.257803	+	0.966198i	$0.582999\pi$
$840$	1.48791	+	0.956225i	0.0513379	+	0.0329929i
$841$	4.72266	−	5.45024i	0.162850	−	0.187939i
$842$	75.2090	+	22.0834i	2.59187	+	0.761043i
$843$	2.70355	+	18.8036i	0.0931153	+	0.647631i
$844$	25.1040	+	28.9716i	0.864117	+	0.997244i
$845$	4.13711	+	9.05901i	0.142321	+	0.311639i
$846$	−6.40993	+	1.88213i	−0.220378	+	0.0647088i
$847$	−3.96924	+	8.69143i	−0.136385	+	0.298641i
$848$	−7.46251	+	51.9029i	−0.256263	+	1.78235i
$849$	−17.7251	+	11.3912i	−0.608322	+	0.390945i
$850$	2.93829			0.100782
$851$	11.1573	+	24.3394i	0.382468	+	0.834345i
$852$	20.0197			0.685865
$853$	9.57364	−	6.15260i	0.327795	−	0.210661i	−0.366383	−	0.930464i	$-0.619404\pi$
$853$	9.57364	−	6.15260i	0.327795	−	0.210661i	0.694179	+	0.719803i	$0.255768\pi$
$854$	1.15666	−	8.04473i	0.0395800	−	0.275285i
$855$	−0.356982	+	0.781681i	−0.0122085	+	0.0267329i
$856$	0.305922	−	0.0898267i	0.0104562	−	0.00307021i
$857$	6.94015	+	15.1968i	0.237071	+	0.519113i	0.990350	−	0.138588i	$-0.0442564\pi$
$857$	6.94015	+	15.1968i	0.237071	+	0.519113i	−0.753279	+	0.657701i	$0.771529\pi$
$858$	6.12348	+	7.06688i	0.209052	+	0.241259i
$859$	8.04242	+	55.9362i	0.274404	+	1.90852i	0.400137	+	0.916455i	$0.368963\pi$
$859$	8.04242	+	55.9362i	0.274404	+	1.90852i	−0.125733	+	0.992064i	$0.540128\pi$
$860$	6.60879	+	1.94051i	0.225358	+	0.0661710i
$861$	1.03695	−	1.19671i	0.0353393	−	0.0407837i
$862$	−65.9267	−	42.3685i	−2.24547	−	1.44308i
$863$	12.4175	+	7.98022i	0.422696	+	0.271650i	0.734649	−	0.678447i	$-0.237347\pi$
$863$	12.4175	+	7.98022i	0.422696	+	0.271650i	−0.311953	+	0.950097i	$0.600983\pi$
$864$	−4.90000	+	5.65490i	−0.166701	+	0.192384i
$865$	18.4300	+	5.41155i	0.626640	+	0.183998i
$866$	10.7490	+	74.7606i	0.365264	+	2.54047i
$867$	11.0019	+	12.6969i	0.373645	+	0.431210i
$868$	2.54884	+	5.58119i	0.0865134	+	0.189438i
$869$	8.24724	−	2.42161i	0.279769	−	0.0821475i
$870$	10.8022	−	23.6534i	0.366228	−	0.801927i
$871$	2.06467	−	14.3601i	0.0699588	−	0.486574i
$872$	−2.96599	+	1.90612i	−0.100441	+	0.0645495i
$873$	−0.0772952			−0.00261605
$874$	1.78110	−	2.06142i	0.0602467	−	0.0697286i
$875$	−4.56542			−0.154339
$876$	15.8726	−	10.2007i	0.536285	−	0.344649i
$877$	−6.67962	+	46.4577i	−0.225555	+	1.56877i	0.490952	+	0.871186i	$0.336649\pi$
$877$	−6.67962	+	46.4577i	−0.225555	+	1.56877i	−0.716507	+	0.697580i	$0.754260\pi$
$878$	−15.6455	+	34.2588i	−0.528010	+	1.15618i
$879$	26.6160	−	7.81517i	0.897736	−	0.263599i
$880$	6.57321	+	14.3933i	0.221583	+	0.485199i
$881$	−15.1944	−	17.5353i	−0.511912	−	0.590778i	0.439675	−	0.898157i	$-0.355094\pi$
$881$	−15.1944	−	17.5353i	−0.511912	−	0.590778i	−0.951587	+	0.307379i	$0.900548\pi$
$882$	0.273100	+	1.89945i	0.00919576	+	0.0639579i
$883$	36.7922	+	10.8032i	1.23816	+	0.363555i	0.834322	−	0.551277i	$-0.185859\pi$
$883$	36.7922	+	10.8032i	1.23816	+	0.363555i	0.403833	+	0.914833i	$0.367678\pi$
$884$	−1.99525	+	2.30264i	−0.0671076	+	0.0774463i
$885$	−32.9254	−	21.1599i	−1.10677	−	0.711281i
$886$	38.2935	+	24.6097i	1.28649	+	0.826780i
$887$	−9.25951	+	10.6860i	−0.310904	+	0.358802i	−0.889599	−	0.456741i	$-0.849016\pi$
$887$	−9.25951	+	10.6860i	−0.310904	+	0.358802i	0.578696	+	0.815544i	$0.303562\pi$
$888$	3.26371	+	0.958311i	0.109523	+	0.0321588i
$889$	2.00512	+	13.9459i	0.0672494	+	0.467730i
$890$	−38.5562	−	44.4963i	−1.29241	−	1.49152i
$891$	−0.499382	−	1.09349i	−0.0167299	−	0.0366335i
$892$	25.8878	−	7.60136i	0.866789	−	0.254512i
$893$	0.428096	−	0.937398i	0.0143257	−	0.0313688i
$894$	−4.94960	+	34.4252i	−0.165539	+	1.15135i
$895$	−55.0120	+	35.3541i	−1.83885	+	1.18176i
$896$	−4.81270			−0.160781
$897$	−2.73918	+	19.2458i	−0.0914585	+	0.642598i
$898$	−33.2527			−1.10966
$899$	−14.3200	+	9.20290i	−0.477598	+	0.306934i
$900$	−0.820661	+	5.70783i	−0.0273554	+	0.190261i
$901$	2.14626	−	4.69966i	0.0715024	−	0.156568i
$902$	3.50490	−	1.02913i	0.116700	−	0.0342663i
$903$	−0.585814	−	1.28275i	−0.0194947	−	0.0426874i
$904$	−7.22031	−	8.33268i	−0.240144	−	0.277141i
$905$	3.48874	+	24.2647i	0.115970	+	0.806587i
$906$	−8.15077	−	2.39328i	−0.270791	−	0.0795115i
$907$	9.65301	−	11.1402i	0.320523	−	0.369903i	−0.572507	−	0.819899i	$-0.694029\pi$
$907$	9.65301	−	11.1402i	0.320523	−	0.369903i	0.893030	+	0.449996i	$0.148575\pi$
$908$	5.88476	+	3.78190i	0.195292	+	0.125507i
$909$	14.8581	+	9.54871i	0.492811	+	0.316711i
$910$	−14.7874	+	17.0656i	−0.490198	+	0.565719i
$911$	−40.2965	−	11.8321i	−1.33508	−	0.392016i	−0.465170	−	0.885221i	$-0.654007\pi$
$911$	−40.2965	−	11.8321i	−1.33508	−	0.392016i	−0.869913	+	0.493205i	$0.835825\pi$
$912$	−0.191015	−	1.32854i	−0.00632514	−	0.0439923i
$913$	0.0208879	+	0.0241059i	0.000691287	+	0.000797788i
$914$	10.7131	+	23.4585i	0.354359	+	0.775938i
$915$	−11.7970	+	3.46390i	−0.389995	+	0.114513i
$916$	10.3125	−	22.5811i	0.340733	−	0.746102i
$917$	−2.24629	+	15.6233i	−0.0741790	+	0.515926i
$918$	0.721214	−	0.463496i	0.0238036	−	0.0152976i
$919$	−48.6165			−1.60371			−0.801855	−	0.597518i	$-0.796154\pi$
$919$	−48.6165			−1.60371			−0.801855	+	0.597518i	$0.796154\pi$
$920$	−3.51270	+	7.72080i	−0.115810	+	0.254547i
$921$	−7.67027			−0.252744
$922$	35.4788	−	22.8008i	1.16843	−	0.750905i
$923$	6.86402	−	47.7403i	0.225932	−	1.57139i
$924$	−0.840214	+	1.83981i	−0.0276410	+	0.0605254i
$925$	18.3596	−	5.39085i	0.603659	−	0.177250i
$926$	6.72792	+	14.7321i	0.221093	+	0.484126i
$927$	−2.59749	−	2.99766i	−0.0853128	−	0.0984562i
$928$	4.97060	+	34.5713i	0.163168	+	1.13486i
$929$	−17.7633	−	5.21577i	−0.582794	−	0.171124i	−0.0229713	−	0.999736i	$-0.507313\pi$
$929$	−17.7633	−	5.21577i	−0.582794	−	0.171124i	−0.559823	+	0.828612i	$0.689131\pi$
$930$	13.3036	−	15.3532i	0.436243	−	0.503451i
$931$	−0.249026	−	0.160040i	−0.00816151	−	0.00524508i
$932$	14.4777	+	9.30427i	0.474234	+	0.304772i
$933$	9.47563	−	10.9355i	0.310218	−	0.358011i
$934$	−52.1538	−	15.3137i	−1.70653	−	0.501081i
$935$	−0.221877	−	1.54319i	−0.00725615	−	0.0504676i
$936$	1.61727	+	1.86642i	0.0528620	+	0.0610060i
$937$	6.49063	+	14.2125i	0.212040	+	0.464302i	0.985529	−	0.169507i	$-0.0542177\pi$
$937$	6.49063	+	14.2125i	0.212040	+	0.464302i	−0.773489	+	0.633809i	$0.781490\pi$
$938$	6.59004	−	1.93501i	0.215172	−	0.0631803i
$939$	5.85799	−	12.8272i	0.191168	−	0.418600i
$940$	2.41987	−	16.8306i	0.0789275	−	0.548953i
$941$	38.5934	−	24.8025i	1.25811	−	0.808537i	0.270085	−	0.962837i	$-0.412948\pi$
$941$	38.5934	−	24.8025i	1.25811	−	0.808537i	0.988024	+	0.154299i	$0.0493120\pi$
$942$	30.4438			0.991912
$943$	6.39437	+	4.09657i	0.208229	+	0.133403i
$944$	61.1305			1.98963
$945$	2.44215	−	1.56947i	0.0794431	−	0.0510550i
$946$	0.462968	−	3.22001i	0.0150524	−	0.104692i
$947$	2.63521	−	5.77030i	0.0856327	−	0.187509i	−0.861971	−	0.506957i	$-0.830770\pi$
$947$	2.63521	−	5.77030i	0.0856327	−	0.187509i	0.947604	+	0.319448i	$0.103497\pi$
$948$	−11.5429	+	3.38930i	−0.374896	+	0.110079i
$949$	−18.8831	−	41.3481i	−0.612970	−	1.34222i
$950$	−1.27496	−	1.47138i	−0.0413651	−	0.0477379i
$951$	−3.41044	−	23.7201i	−0.110591	−	0.769177i
$952$	0.261164	+	0.0766846i	0.00846437	+	0.00248536i
$953$	13.2712	−	15.3158i	0.429897	−	0.496127i	−0.498930	−	0.866642i	$-0.666273\pi$
$953$	13.2712	−	15.3158i	0.429897	−	0.496127i	0.928826	+	0.370515i	$0.120819\pi$
$954$	18.6696	+	11.9982i	0.604449	+	0.388456i
$955$	−52.9539	−	34.0314i	−1.71355	−	1.10123i
$956$	4.01741	−	4.63634i	0.129932	−	0.149950i
$957$	−5.38399	−	1.58088i	−0.174040	−	0.0511027i
$958$	−9.18049	−	63.8517i	−0.296608	−	2.06296i
$959$	−1.97828	−	2.28306i	−0.0638821	−	0.0737238i
$960$	−6.38000	−	13.9702i	−0.205914	−	0.450888i
$961$	16.9843	−	4.98704i	0.547881	−	0.160872i
$962$	−18.0403	+	39.5028i	−0.581643	+	1.27362i
$963$	0.0744754	−	0.517988i	0.00239994	−	0.0166919i
$964$	−22.1837	+	14.2566i	−0.714489	+	0.459174i
$965$	−56.5369			−1.81999
$966$	−8.82664	+	2.60539i	−0.283993	+	0.0838269i
$967$	24.6358			0.792233			0.396117	−	0.918200i	$-0.370358\pi$
$967$	24.6358			0.792233			0.396117	+	0.918200i	$0.370358\pi$
$968$	−4.89732	+	3.14731i	−0.157406	+	0.101159i
$969$	−0.0188206	+	0.130900i	−0.000604606	+	0.00420512i
$970$	0.178876	−	0.391684i	0.00574336	−	0.0125762i
$971$	−41.8085	+	12.2761i	−1.34170	+	0.393958i	−0.872275	−	0.489015i	$-0.837356\pi$
$971$	−41.8085	+	12.2761i	−1.34170	+	0.393958i	−0.469423	+	0.882973i	$0.655538\pi$
$972$	0.698939	+	1.53046i	0.0224185	+	0.0490896i
$973$	7.44341	+	8.59015i	0.238625	+	0.275388i
$974$	−2.46852	−	17.1689i	−0.0790965	−	0.550128i
$975$	13.3299	+	3.91400i	0.426897	+	0.125348i
$976$	12.5757	−	14.5131i	0.402537	−	0.464553i
$977$	−23.9802	−	15.4111i	−0.767194	−	0.493046i	0.0975669	−	0.995229i	$-0.468894\pi$
$977$	−23.9802	−	15.4111i	−0.767194	−	0.493046i	−0.864761	+	0.502183i	$0.832530\pi$
$978$	−3.19149	−	2.05105i	−0.102053	−	0.0655853i
$979$	−8.32010	+	9.60191i	−0.265912	+	0.306878i
$980$	−4.68645	−	1.37607i	−0.149703	−	0.0439568i
$981$	0.823544	+	5.72787i	0.0262937	+	0.182877i
$982$	7.35407	+	8.48705i	0.234678	+	0.270833i
$983$	21.5788	+	47.2509i	0.688256	+	1.50707i	0.853653	+	0.520843i	$0.174382\pi$
$983$	21.5788	+	47.2509i	0.688256	+	1.50707i	−0.165397	+	0.986227i	$0.552890\pi$
$984$	0.925674	−	0.271802i	0.0295094	−	0.00866475i
$985$	−12.1837	+	26.6786i	−0.388206	+	0.850052i
$986$	0.569507	−	3.96101i	0.0181368	−	0.126144i
$987$	−2.92865	+	1.88213i	−0.0932198	+	0.0599087i
$988$	2.01884			0.0642279
$989$	5.68422	−	3.66447i	0.180748	−	0.116523i
$990$	6.69681			0.212839
$991$	4.85669	−	3.12121i	0.154278	−	0.0991484i	−0.461224	−	0.887284i	$-0.652590\pi$
$991$	4.85669	−	3.12121i	0.154278	−	0.0991484i	0.615502	+	0.788135i	$0.288953\pi$
$992$	−3.88330	+	27.0090i	−0.123295	+	0.857536i
$993$	8.69277	−	19.0345i	0.275857	−	0.604042i
$994$	21.9086	−	6.43295i	0.694899	−	0.204041i
$995$	−4.95241	−	10.8443i	−0.157002	−	0.343786i
$996$	−0.0292348	−	0.0337387i	−0.000926339	−	0.00106905i
$997$	0.559857	+	3.89389i	0.0177308	+	0.123321i	0.996764	−	0.0803781i	$-0.0256128\pi$
$997$	0.559857	+	3.89389i	0.0177308	+	0.123321i	−0.979034	+	0.203699i	$0.934704\pi$
$998$	−69.4549	−	20.3938i	−2.19856	−	0.645555i
$999$	3.65605	−	4.21931i	0.115672	−	0.133493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.127.1	✓	20
23.2	even	11	inner	483.2.q.c.232.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.127.1	✓	20	1.1	even	1	trivial
483.2.q.c.232.1	yes	20	23.2	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(-2.78540 + 0.817866i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(-2.78540 + 0.817866i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(3.64809 - 4.21012i) q^{10} +(-1.01130 - 0.649920i) q^{11} +(1.41542 + 0.909632i) q^{12} +(2.65446 - 3.06341i) q^{13} +(1.84125 + 0.540641i) q^{14} +(-0.413138 - 2.87344i) q^{15} +(2.96926 + 3.42671i) q^{16} +(-0.185587 - 0.406379i) q^{17} +(1.84125 - 0.540641i) q^{18} +(-0.122970 + 0.269268i) q^{19} +(-0.695108 + 4.83458i) q^{20} +(0.841254 - 0.540641i) q^{21} +2.30687 q^{22} +(3.14576 + 3.61997i) q^{23} +0.609264 q^{24} +(2.88326 - 1.85296i) q^{25} +(-1.10700 + 7.69937i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-1.61435 + 0.474017i) q^{28} +(-1.93907 - 4.24598i) q^{29} +(3.64809 + 4.21012i) q^{30} +(-0.518984 - 3.60962i) q^{31} +(-7.17941 - 2.10807i) q^{32} +(0.787227 - 0.908508i) q^{33} +(0.721214 + 0.463496i) q^{34} +(2.44215 + 1.56947i) q^{35} +(-1.10181 + 1.27155i) q^{36} +(5.35680 + 1.57290i) q^{37} +(-0.0808426 - 0.562273i) q^{38} +(2.65446 + 3.06341i) q^{39} +(0.734739 + 1.60885i) q^{40} +(1.51933 - 0.446116i) q^{41} +(-0.797176 + 1.74557i) q^{42} +(0.200691 - 1.39584i) q^{43} +(-1.70151 + 1.09349i) q^{44} +2.90299 q^{45} +(-8.83402 - 2.58025i) q^{46} -3.48129 q^{47} +(-3.81440 + 2.45137i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-2.73219 + 5.98266i) q^{50} +(0.428654 - 0.125864i) q^{51} +(-2.83313 - 6.20368i) q^{52} +(7.57328 + 8.74004i) q^{53} +(0.273100 + 1.89945i) q^{54} +(3.34841 + 0.983181i) q^{55} +(-0.398983 + 0.460451i) q^{56} +(-0.249026 - 0.160040i) q^{57} +(7.53547 + 4.84275i) q^{58} +(8.82892 - 10.1891i) q^{59} +(-4.68645 - 1.37607i) q^{60} +(-0.602744 - 4.19218i) q^{61} +(4.58274 + 5.28876i) q^{62} +(0.415415 + 0.909632i) q^{63} +(5.07616 - 1.49049i) q^{64} +(-4.88826 + 10.7038i) q^{65} +(-0.328302 + 2.28339i) q^{66} +(3.01093 - 1.93501i) q^{67} -0.751662 q^{68} +(-4.03082 + 2.59856i) q^{69} -5.57079 q^{70} +(10.0099 - 6.43295i) q^{71} +(-0.0867074 + 0.603063i) q^{72} +(4.65850 - 10.2007i) q^{73} +(-10.2796 + 3.01837i) q^{74} +(1.42377 + 3.11762i) q^{75} +(0.326155 + 0.376403i) q^{76} +(0.171081 + 1.18989i) q^{77} +(-7.46346 - 2.19147i) q^{78} +(-4.68236 + 5.40373i) q^{79} +(-11.0732 - 7.11628i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-1.98990 + 2.29647i) q^{82} +(-0.0254587 - 0.00747534i) q^{83} +(-0.239446 - 1.66538i) q^{84} +(0.849297 + 0.980141i) q^{85} +(1.12417 + 2.46159i) q^{86} +(4.47872 - 1.31507i) q^{87} +(-0.304256 + 0.666228i) q^{88} +(1.50411 - 10.4613i) q^{89} +(-4.68645 + 3.01180i) q^{90} -4.05347 q^{91} +(7.73893 - 2.28432i) q^{92} +3.64673 q^{93} +(5.62003 - 3.61177i) q^{94} +(0.122296 - 0.850591i) q^{95} +(3.10835 - 6.80633i) q^{96} +(0.0741642 - 0.0217766i) q^{97} +(-0.797176 - 1.74557i) q^{98} +(0.787227 + 0.908508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 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

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