LMFDB - Embedded newform 430.2.q.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	430.81
Dual form			430.2.q.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(0.269177 + 0.0830302i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.140846 + 0.243953i) q^{6} +(-0.703462 - 1.21843i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-2.41315 - 1.64526i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(0.269177 + 0.0830302i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.140846 + 0.243953i) q^{6} +(-0.703462 - 1.21843i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-2.41315 - 1.64526i) q^{9} +(0.988831 - 0.149042i) q^{10} +(-3.05456 + 1.47100i) q^{11} +(-0.206495 - 0.191599i) q^{12} +(-5.47469 - 0.825177i) q^{13} +(1.34442 - 0.414698i) q^{14} +(-0.0210509 - 0.280904i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-2.08019 + 5.30023i) q^{17} +(2.14099 - 1.98655i) q^{18} +(-2.81653 + 1.92028i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(-0.0881893 - 0.386383i) q^{21} +(-0.754415 - 3.30531i) q^{22} +(0.530858 - 7.08380i) q^{23} +(0.232745 - 0.158683i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(2.02272 - 5.15381i) q^{26} +(-1.03986 - 1.30394i) q^{27} +(0.105140 + 1.40299i) q^{28} +(8.07434 - 2.49060i) q^{29} +(0.278546 + 0.0419840i) q^{30} +(0.0828697 + 0.0768919i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.944357 + 0.142339i) q^{33} +(-4.70446 - 3.20745i) q^{34} +(-0.877202 + 1.09998i) q^{35} +(1.46032 + 2.52936i) q^{36} +(-3.53605 + 6.12463i) q^{37} +(-1.24539 - 3.17321i) q^{38} +(-1.40515 - 0.676684i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(0.772627 - 3.38510i) q^{41} +0.396319 q^{42} +(6.17285 - 2.21266i) q^{43} +3.39031 q^{44} +(-0.649906 + 2.84742i) q^{45} +(6.78807 + 2.09384i) q^{46} +(-10.2380 - 4.93037i) q^{47} +(0.102914 + 0.262220i) q^{48} +(2.51028 - 4.34794i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00002 + 1.25398i) q^{51} +(4.57450 + 3.11884i) q^{52} +(7.24312 - 1.09172i) q^{53} +(1.50264 - 0.723631i) q^{54} +(2.48527 + 2.30600i) q^{55} +(-1.39121 - 0.209691i) q^{56} +(-0.917586 + 0.283038i) q^{57} +(0.631450 + 8.42611i) q^{58} +(3.61003 + 4.52683i) q^{59} +(-0.102914 + 0.262220i) q^{60} +(6.08870 - 5.64949i) q^{61} +(-0.0934043 + 0.0636819i) q^{62} +(-0.307076 + 4.09764i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(1.23199 + 5.39772i) q^{65} +(0.0713690 - 0.952353i) q^{66} +(-10.0292 + 6.83782i) q^{67} +(4.17387 - 3.87279i) q^{68} +(0.731065 - 1.86272i) q^{69} +(-0.877202 - 1.09998i) q^{70} +(0.393492 + 5.25079i) q^{71} +(-2.79089 + 0.860877i) q^{72} +(-5.80830 - 0.875461i) q^{73} +(-5.18422 - 4.81026i) q^{74} +(-0.253796 + 0.122222i) q^{75} +(3.37078 - 0.508063i) q^{76} +(3.94108 + 2.68698i) q^{77} +(0.972393 - 1.21934i) q^{78} +(-6.81661 - 11.8067i) q^{79} +(0.500000 - 0.866025i) q^{80} +(3.02946 + 7.71894i) q^{81} +(3.12830 + 1.50651i) q^{82} +(-7.14886 - 2.20513i) q^{83} +(-0.0881893 + 0.386383i) q^{84} +5.69383 q^{85} +(0.783598 + 6.51045i) q^{86} +2.38022 q^{87} +(-0.754415 + 3.30531i) q^{88} +(8.17260 + 2.52091i) q^{89} +(-2.63141 - 1.26722i) q^{90} +(2.84581 + 7.25102i) q^{91} +(-3.55183 + 6.15196i) q^{92} +(0.0159223 + 0.0275782i) q^{93} +(7.08492 - 8.88421i) q^{94} +(2.81653 + 1.92028i) q^{95} +(-0.278546 + 0.0419840i) q^{96} +(-6.59420 + 3.17560i) q^{97} +(3.68034 + 3.41485i) q^{98} +(9.79131 + 1.47580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	0.269177	+	0.0830302i	0.155410	+	0.0479375i	0.371484	−	0.928439i	$-0.378849\pi$
$3$	0.269177	+	0.0830302i	0.155410	+	0.0479375i	−0.216074	+	0.976377i	$0.569325\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$6$	−0.140846	+	0.243953i	−0.0575002	+	0.0995932i
$7$	−0.703462	−	1.21843i	−0.265883	−	0.460524i	0.701911	−	0.712264i	$-0.252330\pi$
$7$	−0.703462	−	1.21843i	−0.265883	−	0.460524i	−0.967795	+	0.251741i	$0.918997\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	−2.41315	−	1.64526i	−0.804385	−	0.548420i
$10$	0.988831	−	0.149042i	0.312696	−	0.0471313i
$11$	−3.05456	+	1.47100i	−0.920986	+	0.443523i	−0.833423	−	0.552636i	$-0.813622\pi$
$11$	−3.05456	+	1.47100i	−0.920986	+	0.443523i	−0.0875628	+	0.996159i	$0.527908\pi$
$12$	−0.206495	−	0.191599i	−0.0596099	−	0.0553099i
$13$	−5.47469	−	0.825177i	−1.51841	−	0.228863i	−0.663709	−	0.747990i	$-0.731019\pi$
$13$	−5.47469	−	0.825177i	−1.51841	−	0.228863i	−0.854697	+	0.519128i	$0.826257\pi$
$14$	1.34442	−	0.414698i	0.359311	−	0.110833i
$15$	−0.0210509	−	0.280904i	−0.00543531	−	0.0725292i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−2.08019	+	5.30023i	−0.504520	+	1.28550i	0.421091	+	0.907018i	$0.361647\pi$
$17$	−2.08019	+	5.30023i	−0.504520	+	1.28550i	−0.925611	+	0.378477i	$0.876448\pi$
$18$	2.14099	−	1.98655i	0.504636	−	0.468233i
$19$	−2.81653	+	1.92028i	−0.646156	+	0.440541i	−0.841547	−	0.540184i	$-0.818355\pi$
$19$	−2.81653	+	1.92028i	−0.646156	+	0.440541i	0.195391	+	0.980725i	$0.437402\pi$
$20$	−0.0747301	+	0.997204i	−0.0167102	+	0.222982i
$21$	−0.0881893	−	0.386383i	−0.0192445	−	0.0843156i
$22$	−0.754415	−	3.30531i	−0.160842	−	0.704694i
$23$	0.530858	−	7.08380i	0.110691	−	1.47708i	−0.614712	−	0.788752i	$-0.710728\pi$
$23$	0.530858	−	7.08380i	0.110691	−	1.47708i	0.725404	−	0.688324i	$-0.241653\pi$
$24$	0.232745	−	0.158683i	0.0475089	−	0.0323910i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	2.02272	−	5.15381i	0.396688	−	1.01075i
$27$	−1.03986	−	1.30394i	−0.200120	−	0.250943i
$28$	0.105140	+	1.40299i	0.0198695	+	0.265140i
$29$	8.07434	−	2.49060i	1.49937	−	0.462494i	0.566912	−	0.823778i	$-0.308138\pi$
$29$	8.07434	−	2.49060i	1.49937	−	0.462494i	0.932456	+	0.361285i	$0.117662\pi$
$30$	0.278546	+	0.0419840i	0.0508553	+	0.00766520i
$31$	0.0828697	+	0.0768919i	0.0148838	+	0.0138102i	0.687580	−	0.726109i	$-0.258673\pi$
$31$	0.0828697	+	0.0768919i	0.0148838	+	0.0138102i	−0.672696	+	0.739919i	$0.734864\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	−0.944357	+	0.142339i	−0.164391	+	0.0247780i
$34$	−4.70446	−	3.20745i	−0.806808	−	0.550073i
$35$	−0.877202	+	1.09998i	−0.148274	+	0.185930i
$36$	1.46032	+	2.52936i	0.243387	+	0.421559i
$37$	−3.53605	+	6.12463i	−0.581324	+	1.00688i	0.413999	+	0.910277i	$0.364132\pi$
$37$	−3.53605	+	6.12463i	−0.581324	+	1.00688i	−0.995323	+	0.0966049i	$0.969202\pi$
$38$	−1.24539	−	3.17321i	−0.202030	−	0.514763i
$39$	−1.40515	−	0.676684i	−0.225004	−	0.108356i
$40$	−0.955573	−	0.294755i	−0.151089	−	0.0466049i
$41$	0.772627	−	3.38510i	0.120664	−	0.528664i	−0.878078	−	0.478518i	$-0.841174\pi$
$41$	0.772627	−	3.38510i	0.120664	−	0.528664i	0.998742	−	0.0501459i	$-0.0159686\pi$
$42$	0.396319			0.0611534
$43$	6.17285	−	2.21266i	0.941351	−	0.337428i
$43$	6.17285	−	2.21266i	0.941351	−	0.337428i
$44$	3.39031			0.511109
$45$	−0.649906	+	2.84742i	−0.0968822	+	0.424469i
$46$	6.78807	+	2.09384i	1.00085	+	0.308720i
$47$	−10.2380	−	4.93037i	−1.49337	−	0.719168i	−0.503878	−	0.863775i	$-0.668094\pi$
$47$	−10.2380	−	4.93037i	−1.49337	−	0.719168i	−0.989489	+	0.144607i	$0.953808\pi$
$48$	0.102914	+	0.262220i	0.0148543	+	0.0378482i
$49$	2.51028	−	4.34794i	0.358612	−	0.621134i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−1.00002	+	1.25398i	−0.140031	+	0.175593i
$52$	4.57450	+	3.11884i	0.634368	+	0.432505i
$53$	7.24312	−	1.09172i	0.994919	−	0.149960i	0.368651	−	0.929568i	$-0.379820\pi$
$53$	7.24312	−	1.09172i	0.994919	−	0.149960i	0.626268	+	0.779608i	$0.284582\pi$
$54$	1.50264	−	0.723631i	0.204483	−	0.0984738i
$55$	2.48527	+	2.30600i	0.335114	+	0.310941i
$56$	−1.39121	−	0.209691i	−0.185908	−	0.0280211i
$57$	−0.917586	+	0.283038i	−0.121537	+	0.0374893i
$58$	0.631450	+	8.42611i	0.0829134	+	1.10640i
$59$	3.61003	+	4.52683i	0.469985	+	0.589343i	0.959167	−	0.282839i	$-0.0912761\pi$
$59$	3.61003	+	4.52683i	0.469985	+	0.589343i	−0.489182	+	0.872182i	$0.662705\pi$
$60$	−0.102914	+	0.262220i	−0.0132861	+	0.0338524i
$61$	6.08870	−	5.64949i	0.779578	−	0.723343i	−0.186256	−	0.982501i	$-0.559636\pi$
$61$	6.08870	−	5.64949i	0.779578	−	0.723343i	0.965835	+	0.259158i	$0.0834450\pi$
$62$	−0.0934043	+	0.0636819i	−0.0118624	+	0.00808762i
$63$	−0.307076	+	4.09764i	−0.0386879	+	0.516254i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	1.23199	+	5.39772i	0.152810	+	0.669504i
$66$	0.0713690	−	0.952353i	0.00878492	−	0.117227i
$67$	−10.0292	+	6.83782i	−1.22527	+	0.835373i	−0.990612	−	0.136706i	$-0.956348\pi$
$67$	−10.0292	+	6.83782i	−1.22527	+	0.835373i	−0.234655	+	0.972079i	$0.575396\pi$
$68$	4.17387	−	3.87279i	0.506156	−	0.469644i
$69$	0.731065	−	1.86272i	0.0880098	−	0.224245i
$70$	−0.877202	−	1.09998i	−0.104846	−	0.131472i
$71$	0.393492	+	5.25079i	0.0466990	+	0.623154i	0.970627	+	0.240589i	$0.0773404\pi$
$71$	0.393492	+	5.25079i	0.0466990	+	0.623154i	−0.923928	+	0.382566i	$0.875041\pi$
$72$	−2.79089	+	0.860877i	−0.328910	+	0.101455i
$73$	−5.80830	−	0.875461i	−0.679810	−	0.102465i	−0.199945	−	0.979807i	$-0.564076\pi$
$73$	−5.80830	−	0.875461i	−0.679810	−	0.102465i	−0.479865	+	0.877342i	$0.659314\pi$
$74$	−5.18422	−	4.81026i	−0.602654	−	0.559181i
$75$	−0.253796	+	0.122222i	−0.0293058	+	0.0141129i
$76$	3.37078	−	0.508063i	0.386655	−	0.0582788i
$77$	3.94108	+	2.68698i	0.449128	+	0.306210i
$78$	0.972393	−	1.21934i	0.110102	−	0.138063i
$79$	−6.81661	−	11.8067i	−0.766929	−	1.32836i	−0.939221	−	0.343313i	$-0.888451\pi$
$79$	−6.81661	−	11.8067i	−0.766929	−	1.32836i	0.172292	−	0.985046i	$-0.444883\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	3.02946	+	7.71894i	0.336607	+	0.857660i
$82$	3.12830	+	1.50651i	0.345463	+	0.166366i
$83$	−7.14886	−	2.20513i	−0.784690	−	0.242045i	−0.123581	−	0.992335i	$-0.539438\pi$
$83$	−7.14886	−	2.20513i	−0.784690	−	0.242045i	−0.661109	+	0.750290i	$0.729914\pi$
$84$	−0.0881893	+	0.386383i	−0.00962224	+	0.0421578i
$85$	5.69383			0.617582
$86$	0.783598	+	6.51045i	0.0844975	+	0.702040i
$87$	2.38022			0.255187
$88$	−0.754415	+	3.30531i	−0.0804209	+	0.352347i
$89$	8.17260	+	2.52091i	0.866294	+	0.267216i	0.695882	−	0.718156i	$-0.255014\pi$
$89$	8.17260	+	2.52091i	0.866294	+	0.267216i	0.170412	+	0.985373i	$0.445490\pi$
$90$	−2.63141	−	1.26722i	−0.277375	−	0.133577i
$91$	2.84581	+	7.25102i	0.298322	+	0.760113i
$92$	−3.55183	+	6.15196i	−0.370304	+	0.641386i
$93$	0.0159223	+	0.0275782i	0.00165107	+	0.00285973i
$94$	7.08492	−	8.88421i	0.730754	−	0.916337i
$95$	2.81653	+	1.92028i	0.288970	+	0.197016i
$96$	−0.278546	+	0.0419840i	−0.0284290	+	0.00428498i
$97$	−6.59420	+	3.17560i	−0.669540	+	0.322433i	−0.737590	−	0.675249i	$-0.764036\pi$
$97$	−6.59420	+	3.17560i	−0.669540	+	0.322433i	0.0680505	+	0.997682i	$0.478322\pi$
$98$	3.68034	+	3.41485i	0.371770	+	0.344952i
$99$	9.79131	+	1.47580i	0.984064	+	0.148324i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	−1.28866	−	17.1959i	−0.128226	−	1.71106i	−0.576445	−	0.817136i	$-0.695561\pi$
$101$	−1.28866	−	17.1959i	−0.128226	−	1.71106i	0.448219	−	0.893924i	$-0.352058\pi$
$102$	−1.00002	−	1.25398i	−0.0990166	−	0.124163i
$103$	−5.53305	+	14.0980i	−0.545187	+	1.38911i	0.347178	+	0.937799i	$0.387140\pi$
$103$	−5.53305	+	14.0980i	−0.545187	+	1.38911i	−0.892365	+	0.451315i	$0.850955\pi$
$104$	−4.05856	+	3.76580i	−0.397975	+	0.369267i
$105$	−0.327454	+	0.223255i	−0.0319563	+	0.0217874i
$106$	−0.547393	+	7.30445i	−0.0531675	+	0.709471i
$107$	−1.53242	−	6.71397i	−0.148145	−	0.649064i	−0.993400	−	0.114702i	$-0.963409\pi$
$107$	−1.53242	−	6.71397i	−0.148145	−	0.649064i	0.845255	−	0.534363i	$-0.179448\pi$
$108$	0.371120	+	1.62598i	0.0357111	+	0.156460i
$109$	−1.17099	+	15.6258i	−0.112160	+	1.49668i	0.603014	+	0.797731i	$0.293966\pi$
$109$	−1.17099	+	15.6258i	−0.112160	+	1.49668i	−0.715174	+	0.698946i	$0.753653\pi$
$110$	−2.80121	+	1.90983i	−0.267085	+	0.182095i
$111$	−1.46035	+	1.35501i	−0.138611	+	0.128612i
$112$	0.514007	−	1.30967i	0.0485691	−	0.123752i
$113$	−5.95098	−	7.46229i	−0.559821	−	0.701993i	0.418704	−	0.908123i	$-0.362485\pi$
$113$	−5.95098	−	7.46229i	−0.559821	−	0.701993i	−0.978525	+	0.206130i	$0.933913\pi$
$114$	−0.0717593	−	0.957562i	−0.00672088	−	0.0896839i
$115$	−6.78807	+	2.09384i	−0.632991	+	0.195252i
$116$	−8.35536	−	1.25937i	−0.775776	−	0.116929i
$117$	11.8536	+	10.9986i	1.09587	+	1.01682i
$118$	−5.21664	+	2.51220i	−0.480230	+	0.231267i
$119$	7.92130	−	1.19394i	0.726145	−	0.109449i
$120$	−0.232745	−	0.158683i	−0.0212466	−	0.0144857i
$121$	0.308132	−	0.386385i	0.0280120	−	0.0351259i
$122$	4.15298	+	7.19318i	0.375993	+	0.651240i
$123$	0.489039	−	0.847041i	0.0440952	−	0.0763751i
$124$	−0.0413009	−	0.105233i	−0.00370893	−	0.00945020i
$125$	0.900969	+	0.433884i	0.0805851	+	0.0388077i
$126$	−3.92657	−	1.21119i	−0.349807	−	0.107901i
$127$	−2.74578	+	12.0301i	−0.243649	+	1.06749i	0.694018	+	0.719958i	$0.255839\pi$
$127$	−2.74578	+	12.0301i	−0.243649	+	1.06749i	−0.937666	+	0.347537i	$0.887018\pi$
$128$	1.00000			0.0883883
$129$	1.84531	−	0.0830654i	0.162470	−	0.00731350i
$130$	−5.53653			−0.485586
$131$	−0.114273	+	0.500663i	−0.00998409	+	0.0437431i	−0.979675	−	0.200593i	$-0.935713\pi$
$131$	−0.114273	+	0.500663i	−0.00998409	+	0.0437431i	0.969691	+	0.244337i	$0.0785701\pi$
$132$	0.912595	+	0.281498i	0.0794312	+	0.0245013i
$133$	4.32104	+	2.08090i	0.374682	+	0.180437i
$134$	−4.43467	−	11.2993i	−0.383097	−	0.976115i
$135$	−0.833900	+	1.44436i	−0.0717707	+	0.124310i
$136$	2.84691	+	4.93100i	0.244121	+	0.422830i
$137$	6.58184	−	8.25337i	0.562324	−	0.705133i	−0.416661	−	0.909062i	$-0.636800\pi$
$137$	6.58184	−	8.25337i	0.562324	−	0.705133i	0.978986	+	0.203929i	$0.0653713\pi$
$138$	1.65334	+	1.12723i	0.140742	+	0.0959562i
$139$	−5.66761	+	0.854255i	−0.480721	+	0.0724570i	−0.384932	−	0.922945i	$-0.625775\pi$
$139$	−5.66761	+	0.854255i	−0.480721	+	0.0724570i	−0.0957882	+	0.995402i	$0.530537\pi$
$140$	1.26759	−	0.610441i	0.107131	−	0.0515917i
$141$	−2.34647	−	2.17721i	−0.197609	−	0.183354i
$142$	−5.20670	−	0.784784i	−0.436937	−	0.0658576i
$143$	17.9366	−	5.53272i	1.49994	−	0.462669i
$144$	−0.218260	−	2.91248i	−0.0181884	−	0.242707i
$145$	−5.26833	−	6.60627i	−0.437511	−	0.548621i
$146$	2.14598	−	5.46787i	0.177603	−	0.452524i
$147$	1.03672	−	0.961937i	0.0855074	−	0.0793392i
$148$	5.84325	−	3.98386i	0.480312	−	0.327471i
$149$	−0.418423	+	5.58347i	−0.0342786	+	0.457416i	0.953483	+	0.301446i	$0.0974693\pi$
$149$	−0.418423	+	5.58347i	−0.0342786	+	0.457416i	−0.987762	+	0.155970i	$0.950150\pi$
$150$	−0.0626824	−	0.274629i	−0.00511800	−	0.0224234i
$151$	−3.11694	−	13.6562i	−0.253653	−	1.11132i	−0.927903	−	0.372822i	$-0.878390\pi$
$151$	−3.11694	−	13.6562i	−0.253653	−	1.11132i	0.674250	−	0.738503i	$-0.264467\pi$
$152$	−0.254744	+	3.39932i	−0.0206625	+	0.275721i
$153$	13.7401	−	9.36783i	1.11082	−	0.757344i
$154$	−3.49659	+	3.24436i	−0.281763	+	0.261438i
$155$	0.0413009	−	0.105233i	0.00331737	−	0.00845252i
$156$	0.972393	+	1.21934i	0.0778537	+	0.0976255i
$157$	1.40410	+	18.7364i	0.112059	+	1.49533i	0.715888	+	0.698215i	$0.246022\pi$
$157$	1.40410	+	18.7364i	0.112059	+	1.49533i	−0.603829	+	0.797114i	$0.706359\pi$
$158$	13.0275	−	4.01846i	1.03642	−	0.319692i
$159$	2.04033	+	0.307530i	0.161809	+	0.0243887i
$160$	0.733052	+	0.680173i	0.0579528	+	0.0537724i
$161$	−9.00457	+	4.33637i	−0.709659	+	0.341754i
$162$	−8.19953	+	1.23588i	−0.644216	+	0.0970999i
$163$	−10.4758	−	7.14230i	−0.820530	−	0.559428i	0.0787027	−	0.996898i	$-0.474922\pi$
$163$	−10.4758	−	7.14230i	−0.820530	−	0.559428i	−0.899233	+	0.437470i	$0.855875\pi$
$164$	−2.16485	+	2.71464i	−0.169047	+	0.211978i
$165$	0.477512	+	0.827075i	0.0371742	+	0.0643877i
$166$	3.74062	−	6.47894i	0.290328	−	0.502863i
$167$	−0.596737	−	1.52046i	−0.0461769	−	0.117657i	0.905925	−	0.423439i	$-0.139177\pi$
$167$	−0.596737	−	1.52046i	−0.0461769	−	0.117657i	−0.952101	+	0.305782i	$0.901082\pi$
$168$	−0.357071	−	0.171956i	−0.0275486	−	0.0132667i
$169$	16.8689	+	5.20336i	1.29761	+	0.400259i
$170$	−1.26700	+	5.55107i	−0.0971741	+	0.425748i
$171$	9.95607			0.761359
$172$	−6.52159	−	0.684760i	−0.497266	−	0.0522125i
$173$	−5.42294			−0.412298			−0.206149	−	0.978521i	$-0.566093\pi$
$173$	−5.42294			−0.412298			−0.206149	+	0.978521i	$0.566093\pi$
$174$	−0.529650	+	2.32055i	−0.0401527	+	0.175920i
$175$	1.34442	+	0.414698i	0.101628	+	0.0313482i
$176$	−3.05456	−	1.47100i	−0.230246	−	0.110881i
$177$	0.595873	+	1.51826i	0.0447886	+	0.114119i
$178$	−4.27628	+	7.40674i	−0.320521	+	0.555159i
$179$	−11.6928	−	20.2525i	−0.873960	−	1.51374i	−0.857867	−	0.513872i	$-0.828211\pi$
$179$	−11.6928	−	20.2525i	−0.873960	−	1.51374i	−0.0160926	−	0.999871i	$-0.505123\pi$
$180$	1.82100	−	2.28346i	0.135729	−	0.170199i
$181$	4.70405	+	3.20717i	0.349649	+	0.238387i	0.725390	−	0.688338i	$-0.241659\pi$
$181$	4.70405	+	3.20717i	0.349649	+	0.238387i	−0.375741	+	0.926725i	$0.622612\pi$
$182$	−7.70247	+	1.16096i	−0.570945	+	0.0860561i
$183$	2.10802	−	1.01517i	0.155829	−	0.0750434i
$184$	−5.20736	−	4.83172i	−0.383891	−	0.356199i
$185$	6.99312	+	1.05404i	0.514144	+	0.0774948i
$186$	−0.0304298	+	0.00938636i	−0.00223122	+	0.000688241i
$187$	−1.44258	−	19.2499i	−0.105492	−	1.40769i
$188$	7.08492	+	8.88421i	0.516721	+	0.647948i
$189$	−0.857261	+	2.18426i	−0.0623565	+	0.158882i
$190$	−2.49887	+	2.31861i	−0.181287	+	0.168210i
$191$	−7.79700	+	5.31591i	−0.564171	+	0.384645i	−0.811558	−	0.584271i	$-0.801380\pi$
$191$	−7.79700	+	5.31591i	−0.564171	+	0.384645i	0.247387	+	0.968917i	$0.420428\pi$
$192$	0.0210509	−	0.280904i	0.00151922	−	0.0202725i
$193$	−5.92655	−	25.9659i	−0.426603	−	1.86907i	−0.491025	−	0.871146i	$-0.663378\pi$
$193$	−5.92655	−	25.9659i	−0.426603	−	1.86907i	0.0644223	−	0.997923i	$-0.479480\pi$
$194$	−1.62863	−	7.13551i	−0.116929	−	0.512300i
$195$	−0.116549	+	1.55524i	−0.00834623	+	0.111373i
$196$	−4.14819	+	2.82819i	−0.296299	+	0.202013i
$197$	11.5067	−	10.6766i	0.819817	−	0.760679i	−0.153986	−	0.988073i	$-0.549211\pi$
$197$	11.5067	−	10.6766i	0.819817	−	0.760679i	0.973803	+	0.227394i	$0.0730205\pi$
$198$	−3.61757	+	9.21743i	−0.257090	+	0.655054i
$199$	1.28600	+	1.61260i	0.0911623	+	0.114314i	0.825321	−	0.564664i	$-0.190994\pi$
$199$	1.28600	+	1.61260i	0.0911623	+	0.114314i	−0.734158	+	0.678978i	$0.762423\pi$
$200$	0.0747301	+	0.997204i	0.00528422	+	0.0705130i
$201$	−3.26739	+	1.00786i	−0.230464	+	0.0710887i
$202$	17.0516	+	2.57011i	1.19974	+	0.180832i
$203$	−8.71462	−	8.08599i	−0.611646	−	0.567525i
$204$	1.44507	−	0.695909i	0.101175	−	0.0487233i
$205$	−3.43337	+	0.517498i	−0.239797	+	0.0361436i
$206$	−12.5133	−	8.53141i	−0.871842	−	0.594412i
$207$	−12.9357	+	16.2209i	−0.899096	+	1.12743i
$208$	−2.76827	−	4.79478i	−0.191945	−	0.332458i
$209$	5.77854	−	10.0087i	0.399710	−	0.692317i
$210$	−0.144792	−	0.368923i	−0.00999157	−	0.0254581i
$211$	−12.5159	−	6.02734i	−0.861629	−	0.414939i	−0.0497484	−	0.998762i	$-0.515842\pi$
$211$	−12.5159	−	6.02734i	−0.861629	−	0.414939i	−0.811881	+	0.583823i	$0.801556\pi$
$212$	−6.99951	−	2.15906i	−0.480728	−	0.148285i
$213$	−0.330055	+	1.44607i	−0.0226150	+	0.0990828i
$214$	6.88663			0.470761
$215$	−4.31491	−	4.93777i	−0.294274	−	0.336753i
$216$	−1.66780			−0.113479
$217$	0.0353918	−	0.155062i	0.00240255	−	0.0105263i
$218$	−14.9734	−	4.61869i	−1.01413	−	0.312817i
$219$	−1.49077	−	0.717919i	−0.100737	−	0.0485125i
$220$	−1.23862	−	3.15595i	−0.0835077	−	0.212774i
$221$	15.7620	−	27.3006i	1.06027	−	1.83644i
$222$	−0.996079	−	1.72526i	−0.0668524	−	0.115792i
$223$	−10.2359	+	12.8354i	−0.685445	+	0.859521i	−0.995843	−	0.0910858i	$-0.970966\pi$
$223$	−10.2359	+	12.8354i	−0.685445	+	0.859521i	0.310398	+	0.950607i	$0.399538\pi$
$224$	1.16245	+	0.792548i	0.0776698	+	0.0529543i
$225$	2.88803	−	0.435300i	0.192535	−	0.0290200i
$226$	8.59941	−	4.14126i	0.572025	−	0.275472i
$227$	−1.31345	−	1.21870i	−0.0871765	−	0.0808879i	0.635381	−	0.772199i	$-0.280843\pi$
$227$	−1.31345	−	1.21870i	−0.0871765	−	0.0808879i	−0.722557	+	0.691311i	$0.757034\pi$
$228$	0.949522	+	0.143117i	0.0628836	+	0.00947818i
$229$	13.9027	−	4.28841i	0.918715	−	0.283386i	0.200893	−	0.979613i	$-0.435616\pi$
$229$	13.9027	−	4.28841i	0.918715	−	0.283386i	0.717821	+	0.696227i	$0.245139\pi$
$230$	−0.530858	−	7.08380i	−0.0350037	−	0.467092i
$231$	0.837749	+	1.05050i	0.0551198	+	0.0691181i
$232$	3.08704	−	7.86564i	0.202674	−	0.516405i
$233$	−5.36197	+	4.97518i	−0.351274	+	0.325935i	−0.835998	−	0.548732i	$-0.815111\pi$
$233$	−5.36197	+	4.97518i	−0.351274	+	0.325935i	0.484724	+	0.874667i	$0.338920\pi$
$234$	−13.3605	+	9.10903i	−0.873403	+	0.595476i
$235$	−0.849183	+	11.3316i	−0.0553946	+	0.739190i
$236$	−1.28840	−	5.64486i	−0.0838679	−	0.367449i
$237$	−0.854563	−	3.74408i	−0.0555098	−	0.243204i
$238$	−0.598646	+	7.98838i	−0.0388045	+	0.517810i
$239$	23.4317	−	15.9754i	1.51567	−	1.03336i	0.533404	−	0.845861i	$-0.320913\pi$
$239$	23.4317	−	15.9754i	1.51567	−	1.03336i	0.982264	−	0.187504i	$-0.0600398\pi$
$240$	0.206495	−	0.191599i	0.0133292	−	0.0123677i
$241$	1.24201	−	3.16460i	0.0800052	−	0.203850i	−0.885274	−	0.465069i	$-0.846029\pi$
$241$	1.24201	−	3.16460i	0.0800052	−	0.203850i	0.965279	+	0.261219i	$0.0841246\pi$
$242$	0.308132	+	0.386385i	0.0198075	+	0.0248378i
$243$	0.548461	+	7.31871i	0.0351838	+	0.469495i
$244$	−7.93695	+	2.44823i	−0.508111	+	0.156732i
$245$	−4.96449	−	0.748277i	−0.317170	−	0.0478056i
$246$	0.716982	+	0.665262i	0.0457131	+	0.0424156i
$247$	17.0042	−	8.18878i	1.08195	−	0.521040i
$248$	0.111785	−	0.0168489i	0.00709835	−	0.00106990i
$249$	−1.74122	−	1.18714i	−0.110345	−	0.0752322i
$250$	−0.623490	+	0.781831i	−0.0394330	+	0.0494474i
$251$	3.96219	+	6.86272i	0.250091	+	0.433171i	0.963551	−	0.267526i	$-0.0862060\pi$
$251$	3.96219	+	6.86272i	0.250091	+	0.433171i	−0.713459	+	0.700697i	$0.752873\pi$
$252$	2.05456	−	3.55861i	0.129425	−	0.224171i
$253$	8.79874	+	22.4188i	0.553172	+	1.40946i
$254$	−11.1174	−	5.35388i	−0.697570	−	0.335932i
$255$	1.53265	+	0.472760i	0.0959782	+	0.0296053i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−8.81300			−0.549740			−0.274870	−	0.961481i	$-0.588635\pi$
$257$	−8.81300			−0.549740			−0.274870	+	0.961481i	$0.588635\pi$
$258$	−0.329637	+	1.81753i	−0.0205223	+	0.113154i
$259$	9.94991			0.618258
$260$	1.23199	−	5.39772i	0.0764050	−	0.334752i
$261$	−23.5823	−	7.27418i	−1.45971	−	0.450261i
$262$	−0.462682	−	0.222816i	−0.0285846	−	0.0137656i
$263$	−7.27709	−	18.5417i	−0.448725	−	1.14333i	−0.959022	−	0.283333i	$-0.908560\pi$
$263$	−7.27709	−	18.5417i	−0.448725	−	1.14333i	0.510297	−	0.859998i	$-0.329535\pi$
$264$	−0.477512	+	0.827075i	−0.0293888	+	0.0509029i
$265$	−3.66247	−	6.34358i	−0.224984	−	0.389683i
$266$	−2.99025	+	3.74966i	−0.183344	+	0.229906i
$267$	1.99057	+	1.35715i	0.121821	+	0.0830560i
$268$	12.0029	−	1.80914i	0.733191	−	0.110511i
$269$	−0.179462	+	0.0864245i	−0.0109420	+	0.00526940i	−0.439347	−	0.898318i	$-0.644790\pi$
$269$	−0.179462	+	0.0864245i	−0.0109420	+	0.00526940i	0.428405	+	0.903587i	$0.359076\pi$
$270$	−1.22258	−	1.13439i	−0.0744041	−	0.0690369i
$271$	−31.0201	−	4.67552i	−1.88434	−	0.284018i	−0.896923	−	0.442186i	$-0.854203\pi$
$271$	−31.0201	−	4.67552i	−1.88434	−	0.284018i	−0.987412	+	0.158168i	$0.949441\pi$
$272$	−5.44087	+	1.67828i	−0.329901	+	0.101761i
$273$	0.163975	+	2.18810i	0.00992423	+	0.132430i
$274$	6.58184	+	8.25337i	0.397623	+	0.498604i
$275$	1.23862	−	3.15595i	0.0746916	−	0.190311i
$276$	−1.46687	+	1.36106i	−0.0882953	+	0.0819260i
$277$	22.2461	−	15.1671i	1.33664	−	0.911303i	0.337091	−	0.941472i	$-0.390557\pi$
$277$	22.2461	−	15.1671i	1.33664	−	0.911303i	0.999545	+	0.0301692i	$0.00960462\pi$
$278$	0.428325	−	5.71560i	0.0256892	−	0.342799i
$279$	−0.0734702	−	0.321894i	−0.00439855	−	0.0192713i
$280$	0.313070	+	1.37165i	0.0187095	+	0.0819717i
$281$	−1.88902	+	25.2072i	−0.112690	+	1.50374i	0.598719	+	0.800959i	$0.295676\pi$
$281$	−1.88902	+	25.2072i	−0.112690	+	1.50374i	−0.711409	+	0.702778i	$0.751943\pi$
$282$	2.64476	−	1.80317i	0.157493	−	0.107377i
$283$	−3.20047	+	2.96961i	−0.190248	+	0.176525i	−0.769546	−	0.638591i	$-0.779517\pi$
$283$	−3.20047	+	2.96961i	−0.190248	+	0.176525i	0.579298	+	0.815116i	$0.303327\pi$
$284$	1.92371	−	4.90153i	0.114151	−	0.290852i
$285$	0.598704	+	0.750751i	0.0354642	+	0.0444707i
$286$	1.40273	+	18.7181i	0.0829449	+	1.10682i
$287$	−4.66802	+	1.43989i	−0.275545	+	0.0849943i
$288$	2.88803	+	0.435300i	0.170179	+	0.0256503i
$289$	−11.3034	−	10.4880i	−0.664906	−	0.616943i
$290$	7.61295	−	3.66620i	0.447048	−	0.215287i
$291$	−2.03868	+	0.307282i	−0.119510	+	0.0180132i
$292$	4.85325	+	3.30889i	0.284015	+	0.193638i
$293$	3.65061	−	4.57772i	0.213271	−	0.267433i	−0.663676	−	0.748020i	$-0.731005\pi$
$293$	3.65061	−	4.57772i	0.213271	−	0.267433i	0.876947	+	0.480587i	$0.159576\pi$
$294$	0.707127	+	1.22478i	0.0412405	+	0.0714306i
$295$	2.89502	−	5.01431i	0.168554	−	0.291945i
$296$	2.58373	+	6.58324i	0.150176	+	0.382643i
$297$	5.09440	+	2.45334i	0.295607	+	0.142357i
$298$	−5.35037	−	1.65037i	−0.309939	−	0.0956034i
$299$	−8.75167	+	38.3436i	−0.506122	+	2.21747i
$300$	0.281692			0.0162635
$301$	−7.03834	−	5.96467i	−0.405683	−	0.343798i
$302$	14.0074			0.806034
$303$	1.08090	−	4.73575i	0.0620964	−	0.272062i
$304$	−3.25741	−	1.00478i	−0.186825	−	0.0576279i
$305$	−7.48342	−	3.60382i	−0.428499	−	0.206354i
$306$	6.07550	+	15.4801i	0.347313	+	0.884940i
$307$	−0.0451903	+	0.0782719i	−0.00257915	+	0.00446721i	−0.867312	−	0.497765i	$-0.834154\pi$
$307$	−0.0451903	+	0.0782719i	−0.00257915	+	0.00446721i	0.864733	+	0.502232i	$0.167488\pi$
$308$	−2.38495	−	4.13086i	−0.135895	−	0.235378i
$309$	−2.65993	+	3.33544i	−0.151318	+	0.189747i
$310$	0.0934043	+	0.0636819i	0.00530501	+	0.00361689i
$311$	7.67936	−	1.15748i	0.435457	−	0.0656345i	0.0723439	−	0.997380i	$-0.476952\pi$
$311$	7.67936	−	1.15748i	0.435457	−	0.0656345i	0.363113	+	0.931745i	$0.381714\pi$
$312$	−1.40515	+	0.676684i	−0.0795508	+	0.0383097i
$313$	4.37927	+	4.06337i	0.247531	+	0.229675i	0.794174	−	0.607691i	$-0.207904\pi$
$313$	4.37927	+	4.06337i	0.247531	+	0.229675i	−0.546643	+	0.837366i	$0.684094\pi$
$314$	−18.5791	−	2.80035i	−1.04848	−	0.158033i
$315$	3.92657	−	1.21119i	0.221237	−	0.0682427i
$316$	1.01881	+	13.5951i	0.0573126	+	0.764784i
$317$	−6.57561	−	8.24556i	−0.369323	−	0.463117i	0.562092	−	0.827075i	$-0.309997\pi$
$317$	−6.57561	−	8.24556i	−0.369323	−	0.463117i	−0.931415	+	0.363958i	$0.881425\pi$
$318$	−0.753836	+	1.92074i	−0.0422730	+	0.107710i
$319$	−20.9999	+	19.4851i	−1.17577	+	1.09095i
$320$	−0.826239	+	0.563320i	−0.0461882	+	0.0314905i
$321$	0.144970	−	1.93449i	0.00809142	−	0.107972i
$322$	−2.22394	−	9.74374i	−0.123936	−	0.542997i
$323$	−4.31900	−	18.9228i	−0.240316	−	1.05289i
$324$	0.619673	−	8.26896i	0.0344263	−	0.459386i
$325$	4.57450	−	3.11884i	0.253747	−	0.173002i
$326$	9.29432	−	8.62387i	0.514765	−	0.477632i
$327$	−1.61261	+	4.10887i	−0.0891778	+	0.227221i
$328$	−2.16485	−	2.71464i	−0.119534	−	0.149891i
$329$	1.19474	+	15.9426i	0.0658679	+	0.878946i
$330$	−0.912595	+	0.281498i	−0.0502367	+	0.0154960i
$331$	5.89326	+	0.888266i	0.323923	+	0.0488235i	0.308991	−	0.951065i	$-0.400009\pi$
$331$	5.89326	+	0.888266i	0.323923	+	0.0488235i	0.0149320	+	0.999889i	$0.495247\pi$
$332$	5.48413	+	5.08853i	0.300981	+	0.279269i
$333$	18.6096	−	8.96193i	1.01980	−	0.491111i
$334$	1.61513	−	0.243441i	0.0883757	−	0.0133205i
$335$	10.0292	+	6.83782i	0.547956	+	0.373590i
$336$	0.247101	−	0.309855i	0.0134805	−	0.0169040i
$337$	4.56078	+	7.89951i	0.248442	+	0.430314i	0.963094	−	0.269167i	$-0.0867482\pi$
$337$	4.56078	+	7.89951i	0.248442	+	0.430314i	−0.714652	+	0.699480i	$0.753415\pi$
$338$	−8.82658	+	15.2881i	−0.480103	+	0.831562i
$339$	−0.982273	−	2.50279i	−0.0533497	−	0.135933i
$340$	−5.12996	−	2.47046i	−0.278211	−	0.133979i
$341$	−0.366239	−	0.112970i	−0.0198329	−	0.00611765i
$342$	−2.21543	+	9.70645i	−0.119797	+	0.524864i
$343$	−16.9120			−0.913163
$344$	2.11878	−	6.20570i	0.114237	−	0.334589i
$345$	−2.00105			−0.107733
$346$	1.20672	−	5.28697i	0.0648735	−	0.284229i
$347$	31.2279	+	9.63253i	1.67640	+	0.517101i	0.979736	−	0.200294i	$-0.0641898\pi$
$347$	31.2279	+	9.63253i	1.67640	+	0.517101i	0.696666	+	0.717396i	$0.254666\pi$
$348$	−2.14451	−	1.03274i	−0.114958	−	0.0553607i
$349$	11.4691	+	29.2227i	0.613924	+	1.56425i	0.811743	+	0.584015i	$0.198519\pi$
$349$	11.4691	+	29.2227i	0.613924	+	1.56425i	−0.197819	+	0.980239i	$0.563386\pi$
$350$	−0.703462	+	1.21843i	−0.0376016	+	0.0651279i
$351$	4.61691	+	7.99673i	0.246433	+	0.426834i
$352$	2.11382	−	2.65065i	0.112667	−	0.141280i
$353$	18.9291	+	12.9057i	1.00750	+	0.686899i	0.950259	−	0.311462i	$-0.100819\pi$
$353$	18.9291	+	12.9057i	1.00750	+	0.686899i	0.0572367	+	0.998361i	$0.481771\pi$
$354$	−1.61279	+	0.243089i	−0.0857188	+	0.0129200i
$355$	4.74407	−	2.28462i	0.251789	−	0.121255i
$356$	−6.26948	−	5.81722i	−0.332282	−	0.308312i
$357$	2.23137	+	0.336325i	0.118097	+	0.0178002i
$358$	22.3466	−	6.89302i	1.18105	−	0.364307i
$359$	2.12673	+	28.3792i	0.112245	+	1.49780i	0.714579	+	0.699555i	$0.246618\pi$
$359$	2.12673	+	28.3792i	0.112245	+	1.49780i	−0.602334	+	0.798244i	$0.705762\pi$
$360$	1.82100	+	2.28346i	0.0959749	+	0.120349i
$361$	−2.69611	+	6.86959i	−0.141901	+	0.361557i
$362$	−4.17351	+	3.87245i	−0.219355	+	0.203531i
$363$	0.115024	−	0.0784218i	0.00603718	−	0.00411608i
$364$	0.582108	−	7.76769i	0.0305108	−	0.407138i
$365$	1.30707	+	5.72664i	0.0684151	+	0.299746i
$366$	0.520638	+	2.28106i	0.0272142	+	0.119233i
$367$	1.44662	−	19.3038i	0.0755130	−	1.00765i	−0.822810	−	0.568316i	$-0.807595\pi$
$367$	1.44662	−	19.3038i	0.0755130	−	1.00765i	0.898323	−	0.439335i	$-0.144786\pi$
$368$	5.86933	−	4.00164i	0.305960	−	0.208600i
$369$	−7.43384	+	6.89759i	−0.386990	+	0.359074i
$370$	−2.58373	+	6.58324i	−0.134322	+	0.342246i
$371$	−6.42545	−	8.05726i	−0.333593	−	0.418312i
$372$	−0.00237975	−	0.0317556i	−0.000123384	−	0.00164645i
$373$	−16.8980	+	5.21233i	−0.874944	+	0.269884i	−0.699524	−	0.714609i	$-0.746604\pi$
$373$	−16.8980	+	5.21233i	−0.874944	+	0.269884i	−0.175420	+	0.984494i	$0.556128\pi$
$374$	19.0882	+	2.87709i	0.987029	+	0.148771i
$375$	0.206495	+	0.191599i	0.0106634	+	0.00989414i
$376$	−10.2380	+	4.93037i	−0.527985	+	0.254264i
$377$	−46.2597	+	6.97253i	−2.38250	+	0.359104i
$378$	−1.93874	−	1.32181i	−0.0997181	−	0.0679867i
$379$	−5.15761	+	6.46744i	−0.264929	+	0.332210i	−0.896447	−	0.443151i	$-0.853861\pi$
$379$	−5.15761	+	6.46744i	−0.264929	+	0.332210i	0.631518	+	0.775361i	$0.282432\pi$
$380$	−1.70443	−	2.95215i	−0.0874352	−	0.151442i
$381$	−1.73796	+	3.01023i	−0.0890384	+	0.154219i
$382$	−3.44763	−	8.78441i	−0.176396	−	0.449450i
$383$	−19.3508	−	9.31884i	−0.988778	−	0.476171i	−0.131663	−	0.991295i	$-0.542032\pi$
$383$	−19.3508	−	9.31884i	−0.988778	−	0.476171i	−0.857116	+	0.515124i	$0.827746\pi$
$384$	0.269177	+	0.0830302i	0.0137364	+	0.00423712i
$385$	1.06140	−	4.65031i	0.0540942	−	0.237002i
$386$	26.6337			1.35562
$387$	−18.5365	−	4.81646i	−0.942261	−	0.244834i
$388$	7.31901			0.371567
$389$	−4.96170	+	21.7386i	−0.251568	+	1.10219i	0.678440	+	0.734655i	$0.262656\pi$
$389$	−4.96170	+	21.7386i	−0.251568	+	1.10219i	−0.930009	+	0.367537i	$0.880201\pi$
$390$	−1.49031	−	0.459699i	−0.0754647	−	0.0232778i
$391$	36.4415	+	17.5493i	1.84293	+	0.887507i
$392$	−1.83422	−	4.67351i	−0.0926421	−	0.236048i
$393$	−0.0723299	+	0.125279i	−0.00364856	+	0.00631949i
$394$	7.84848	+	13.5940i	0.395401	+	0.684854i
$395$	−8.50017	+	10.6589i	−0.427690	+	0.536307i
$396$	−8.18134	−	5.57794i	−0.411128	−	0.280302i
$397$	20.9029	−	3.15061i	1.04909	−	0.158125i	0.398200	−	0.917299i	$-0.369635\pi$
$397$	20.9029	−	3.15061i	1.04909	−	0.158125i	0.650888	+	0.759174i	$0.274397\pi$
$398$	−1.85833	+	0.894924i	−0.0931496	+	0.0448585i
$399$	0.990349	+	0.918909i	0.0495794	+	0.0460030i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	−9.52143	+	2.93697i	−0.475477	+	0.146665i	−0.523226	−	0.852194i	$-0.675272\pi$
$401$	−9.52143	+	2.93697i	−0.475477	+	0.146665i	0.0477484	+	0.998859i	$0.484795\pi$
$402$	−0.255525	−	3.40974i	−0.0127444	−	0.170062i
$403$	−0.390237	−	0.489341i	−0.0194391	−	0.0243758i
$404$	−6.30000	+	16.0521i	−0.313437	+	0.798623i
$405$	6.07857	−	5.64009i	0.302047	−	0.280258i
$406$	9.82244	−	6.69682i	0.487479	−	0.332358i
$407$	1.79178	−	23.9096i	0.0888151	−	1.18515i
$408$	0.356903	+	1.56369i	0.0176693	+	0.0774143i
$409$	−7.18572	−	31.4827i	−0.355311	−	1.55672i	−0.764717	−	0.644366i	$-0.777121\pi$
$409$	−7.18572	−	31.4827i	−0.355311	−	1.55672i	0.409406	−	0.912352i	$-0.365736\pi$
$410$	0.259474	−	3.46244i	0.0128145	−	0.170998i
$411$	2.45696	−	1.67513i	0.121193	−	0.0826279i
$412$	11.1020	−	10.3011i	0.546955	−	0.507500i
$413$	2.97612	−	7.58302i	0.146445	−	0.373136i
$414$	−12.9357	−	16.2209i	−0.635757	−	0.797214i
$415$	0.559073	+	7.46032i	0.0274438	+	0.366213i
$416$	5.29056	−	1.63192i	0.259391	−	0.0800115i
$417$	−1.59652	−	0.240637i	−0.0781820	−	0.0117840i
$418$	8.47193	+	7.86080i	0.414376	+	0.384485i
$419$	0.981756	−	0.472789i	0.0479619	−	0.0230972i	−0.409749	−	0.912198i	$-0.634384\pi$
$419$	0.981756	−	0.472789i	0.0479619	−	0.0230972i	0.457711	+	0.889101i	$0.348669\pi$
$420$	0.391893	−	0.0590683i	0.0191224	−	0.00288224i
$421$	7.23386	+	4.93196i	0.352557	+	0.240369i	0.726628	−	0.687031i	$-0.241086\pi$
$421$	7.23386	+	4.93196i	0.352557	+	0.240369i	−0.374072	+	0.927400i	$0.622039\pi$
$422$	8.66127	−	10.8609i	0.421624	−	0.528700i
$423$	16.5942	+	28.7419i	0.806836	+	1.39748i
$424$	3.66247	−	6.34358i	0.177865	−	0.308071i
$425$	−2.08019	−	5.30023i	−0.100904	−	0.257099i
$426$	−1.33637	−	0.643560i	−0.0647471	−	0.0311806i
$427$	−11.1667	−	3.44447i	−0.540394	−	0.166689i
$428$	−1.53242	+	6.71397i	−0.0740723	+	0.324532i
$429$	5.28752			0.255284
$430$	5.77413	−	3.10797i	0.278453	−	0.149879i
$431$	11.9625			0.576214			0.288107	−	0.957598i	$-0.406974\pi$
$431$	11.9625			0.576214			0.288107	+	0.957598i	$0.406974\pi$
$432$	0.371120	−	1.62598i	0.0178555	−	0.0782302i
$433$	−22.4947	−	6.93870i	−1.08103	−	0.333453i	−0.297443	−	0.954739i	$-0.596134\pi$
$433$	−22.4947	−	6.93870i	−1.08103	−	0.333453i	−0.783583	+	0.621287i	$0.786610\pi$
$434$	0.143298	+	0.0690089i	0.00687854	+	0.00331253i
$435$	−0.869594	−	2.21569i	−0.0416938	−	0.106234i
$436$	7.83479	−	13.5703i	0.375218	−	0.649897i
$437$	12.1077	+	20.9711i	0.579189	+	1.00318i
$438$	1.03165	−	1.29364i	0.0492940	−	0.0618127i
$439$	−17.3461	−	11.8264i	−0.827886	−	0.564443i	0.0735818	−	0.997289i	$-0.476557\pi$
$439$	−17.3461	−	11.8264i	−0.827886	−	0.564443i	−0.901468	+	0.432846i	$0.857509\pi$
$440$	3.35244	−	0.505300i	0.159821	−	0.0240892i
$441$	−13.2112	+	6.36217i	−0.629104	+	0.302961i
$442$	23.1088	+	21.4418i	1.09917	+	1.01988i
$443$	21.9808	+	3.31307i	1.04434	+	0.157409i	0.648736	−	0.761014i	$-0.275298\pi$
$443$	21.9808	+	3.31307i	1.04434	+	0.157409i	0.395602	+	0.918422i	$0.370536\pi$
$444$	1.90365	−	0.587199i	0.0903433	−	0.0278672i
$445$	−0.639134	−	8.52865i	−0.0302979	−	0.404297i
$446$	−10.2359	−	12.8354i	−0.484683	−	0.607773i
$447$	−0.576227	+	1.46820i	−0.0272546	+	0.0694435i
$448$	−1.03135	+	0.956951i	−0.0487266	+	0.0452117i
$449$	−20.5734	+	14.0267i	−0.970920	+	0.661962i	−0.941290	−	0.337599i	$-0.890385\pi$
$449$	−20.5734	+	14.0267i	−0.970920	+	0.661962i	−0.0296300	+	0.999561i	$0.509433\pi$
$450$	−0.218260	+	2.91248i	−0.0102889	+	0.137296i
$451$	2.61944	+	11.4765i	0.123345	+	0.540409i
$452$	2.12388	+	9.30533i	0.0998989	+	0.437686i
$453$	0.294868	−	3.93474i	0.0138541	−	0.184870i
$454$	1.48041	−	1.00933i	0.0694792	−	0.0473701i
$455$	5.71009	−	5.29819i	0.267693	−	0.248383i
$456$	−0.350818	+	0.893869i	−0.0164285	+	0.0418592i
$457$	−8.58937	−	10.7707i	−0.401794	−	0.503834i	0.539237	−	0.842154i	$-0.318713\pi$
$457$	−8.58937	−	10.7707i	−0.401794	−	0.503834i	−0.941031	+	0.338320i	$0.890141\pi$
$458$	1.08725	+	14.5084i	0.0508039	+	0.677931i
$459$	9.07428	−	2.79904i	0.423551	−	0.130648i
$460$	7.02433	+	1.05875i	0.327511	+	0.0493643i
$461$	10.4344	+	9.68175i	0.485981	+	0.450924i	0.884708	−	0.466145i	$-0.154358\pi$
$461$	10.4344	+	9.68175i	0.485981	+	0.450924i	−0.398728	+	0.917069i	$0.630548\pi$
$462$	−1.21058	+	0.582986i	−0.0563214	+	0.0271229i
$463$	1.58358	−	0.238687i	0.0735954	−	0.0110927i	−0.112141	−	0.993692i	$-0.535771\pi$
$463$	1.58358	−	0.238687i	0.0735954	−	0.0110927i	0.185737	+	0.982600i	$0.440533\pi$
$464$	6.98150	+	4.75991i	0.324108	+	0.220973i
$465$	0.0198548	−	0.0248971i	0.000920743	−	0.00115458i
$466$	−3.65729	−	6.33461i	−0.169421	−	0.293445i
$467$	3.92101	−	6.79140i	0.181443	−	0.314268i	−0.760929	−	0.648835i	$-0.775257\pi$
$467$	3.92101	−	6.79140i	0.181443	−	0.314268i	0.942372	+	0.334567i	$0.108590\pi$
$468$	−5.90766	−	15.0525i	−0.273082	−	0.695801i
$469$	15.3866	+	7.40979i	0.710487	+	0.342153i
$470$	−10.8585	−	3.34940i	−0.500865	−	0.154496i
$471$	−1.17774	+	5.16000i	−0.0542673	+	0.237760i
$472$	5.79003			0.266508
$473$	−15.6005	+	15.8390i	−0.717314	+	0.728278i
$474$	3.84037			0.176394
$475$	0.758541	−	3.32339i	0.0348043	−	0.152487i
$476$	−7.65488	−	2.36122i	−0.350861	−	0.108226i
$477$	−19.2749	−	9.28232i	−0.882539	−	0.425008i
$478$	10.3609	+	26.3990i	0.473895	+	1.20746i
$479$	13.0567	−	22.6149i	0.596576	−	1.03330i	−0.396747	−	0.917928i	$-0.629861\pi$
$479$	13.0567	−	22.6149i	0.596576	−	1.03330i	0.993322	−	0.115371i	$-0.0368058\pi$
$480$	0.140846	+	0.243953i	0.00642871	+	0.0111349i
$481$	24.4127	−	30.6126i	1.11312	−	1.39581i
$482$	2.80888	+	1.91506i	0.127941	+	0.0872288i
$483$	−2.78387	+	0.419602i	−0.126671	+	0.0190925i
$484$	−0.445263	+	0.214428i	−0.0202392	+	0.00974670i
$485$	5.36522	+	4.97819i	0.243622	+	0.226048i
$486$	−7.25726	−	1.09386i	−0.329196	−	0.0496183i
$487$	27.4556	−	8.46893i	1.24413	−	0.383764i	0.398321	−	0.917246i	$-0.369593\pi$
$487$	27.4556	−	8.46893i	1.24413	−	0.383764i	0.845811	+	0.533482i	$0.179117\pi$
$488$	−0.620705	−	8.28274i	−0.0280980	−	0.374942i
$489$	−2.22683	−	2.79236i	−0.100701	−	0.126275i
$490$	1.83422	−	4.67351i	0.0828616	−	0.211128i
$491$	−6.66467	+	6.18391i	−0.300773	+	0.279076i	−0.816092	−	0.577922i	$-0.803864\pi$
$491$	−6.66467	+	6.18391i	−0.300773	+	0.279076i	0.515319	+	0.856998i	$0.327673\pi$
$492$	−0.808126	+	0.550971i	−0.0364331	+	0.0248397i
$493$	−3.59537	+	47.9768i	−0.161927	+	2.16077i
$494$	4.19969	+	18.4000i	0.188953	+	0.827856i
$495$	−2.20338	−	9.65365i	−0.0990347	−	0.433899i
$496$	−0.00844805	+	0.112731i	−0.000379329	+	0.00506179i
$497$	6.12092	−	4.17317i	0.274561	−	0.187192i
$498$	1.54484	−	1.43340i	0.0692258	−	0.0642322i
$499$	3.70466	−	9.43931i	0.165843	−	0.422562i	−0.823658	−	0.567087i	$-0.808070\pi$
$499$	3.70466	−	9.43931i	0.165843	−	0.422562i	0.989501	+	0.144525i	$0.0461655\pi$
$500$	−0.623490	−	0.781831i	−0.0278833	−	0.0349646i
$501$	−0.0343838	−	0.458821i	−0.00153616	−	0.0204986i
$502$	−7.57232	+	2.33575i	−0.337969	+	0.104250i
$503$	−19.5241	−	2.94279i	−0.870538	−	0.131212i	−0.301443	−	0.953484i	$-0.597468\pi$
$503$	−19.5241	−	2.94279i	−0.870538	−	0.131212i	−0.569095	+	0.822272i	$0.692706\pi$
$504$	3.01221	+	2.79492i	0.134174	+	0.124496i
$505$	−15.5364	+	7.48196i	−0.691363	+	0.332943i
$506$	−23.8146	+	3.58948i	−1.05869	+	0.159572i
$507$	4.10868	+	2.80125i	0.182473	+	0.124408i
$508$	7.69351	−	9.64735i	0.341344	−	0.428032i
$509$	3.43591	+	5.95117i	0.152294	+	0.263781i	0.932070	−	0.362277i	$-0.118001\pi$
$509$	3.43591	+	5.95117i	0.152294	+	0.263781i	−0.779776	+	0.626058i	$0.784667\pi$
$510$	−0.801953	+	1.38902i	−0.0355111	+	0.0615070i
$511$	3.01923	+	7.69287i	0.133563	+	0.340313i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	5.43270	+	1.67577i	0.239860	+	0.0739869i
$514$	1.96108	−	8.59204i	0.0864994	−	0.378979i
$515$	15.1449			0.667363
$516$	−1.69861	−	0.725811i	−0.0747770	−	0.0319520i
$517$	38.5252			1.69434
$518$	−2.21406	+	9.70045i	−0.0972804	+	0.426213i
$519$	−1.45973	−	0.450268i	−0.0640751	−	0.0197646i
$520$	4.98824	+	2.40221i	0.218749	+	0.105344i
$521$	−12.1075	−	30.8495i	−0.530440	−	1.35154i	−0.905424	−	0.424508i	$-0.860447\pi$
$521$	−12.1075	−	30.8495i	−0.530440	−	1.35154i	0.374984	−	0.927031i	$-0.377648\pi$
$522$	12.3394	−	21.3724i	0.540079	−	0.935445i
$523$	−3.42987	−	5.94070i	−0.149978	−	0.259769i	0.781241	−	0.624229i	$-0.214587\pi$
$523$	−3.42987	−	5.94070i	−0.149978	−	0.259769i	−0.931219	+	0.364460i	$0.881253\pi$
$524$	0.320186	−	0.401501i	0.0139874	−	0.0175396i
$525$	0.327454	+	0.223255i	0.0142913	+	0.00974363i
$526$	19.6961	−	2.96872i	0.858793	−	0.129442i
$527$	−0.579929	+	0.279279i	−0.0252621	+	0.0121656i
$528$	−0.700082	−	0.649581i	−0.0304672	−	0.0282694i
$529$	−27.1554	−	4.09301i	−1.18067	−	0.177957i
$530$	6.99951	−	2.15906i	0.304039	−	0.0937837i
$531$	−1.26373	−	16.8634i	−0.0548414	−	0.731808i
$532$	−2.99025	−	3.74966i	−0.129644	−	0.162568i
$533$	−7.02320	+	17.8948i	−0.304209	+	0.775111i
$534$	−1.76606	+	1.63867i	−0.0764250	+	0.0709120i
$535$	−5.69000	+	3.87938i	−0.246000	+	0.167720i
$536$	−0.907106	+	12.1045i	−0.0391810	+	0.522834i
$537$	−1.46586	−	6.42237i	−0.0632567	−	0.277146i
$538$	−0.0443236	−	0.194194i	−0.00191092	−	0.00837231i
$539$	−1.27200	+	16.9737i	−0.0547890	+	0.731108i
$540$	1.37800	−	0.939505i	0.0592997	−	0.0404299i
$541$	8.09459	−	7.51068i	0.348014	−	0.322909i	−0.486726	−	0.873555i	$-0.661809\pi$
$541$	8.09459	−	7.51068i	0.348014	−	0.322909i	0.834739	+	0.550646i	$0.185618\pi$
$542$	11.4609	−	29.2019i	0.492288	−	1.25433i
$543$	0.999932	+	1.25387i	0.0429112	+	0.0538089i
$544$	−0.425500	−	5.67790i	−0.0182432	−	0.243438i
$545$	14.9734	−	4.61869i	0.641391	−	0.197843i
$546$	−2.16973	−	0.327033i	−0.0928557	−	0.0139957i
$547$	−25.1995	−	23.3817i	−1.07745	−	0.999731i	−0.999996	−	0.00273487i	$-0.999129\pi$
$547$	−25.1995	−	23.3817i	−1.07745	−	0.999731i	−0.0774570	−	0.996996i	$-0.524680\pi$
$548$	−9.51103	+	4.58027i	−0.406291	+	0.195660i
$549$	−23.9879	+	3.61559i	−1.02378	+	0.154310i
$550$	2.80121	+	1.90983i	0.119444	+	0.0814354i
$551$	−17.9590	+	22.5198i	−0.765077	+	0.959376i
$552$	−1.00052	−	1.73296i	−0.0425851	−	0.0737596i
$553$	−9.59045	+	16.6111i	−0.407827	+	0.706378i
$554$	9.83662	+	25.0633i	0.417918	+	1.06484i
$555$	1.79487	+	0.864365i	0.0761881	+	0.0366902i
$556$	5.47699	+	1.68943i	0.232276	+	0.0716477i
$557$	0.242864	−	1.06406i	0.0102905	−	0.0450856i	−0.969522	−	0.245004i	$-0.921211\pi$
$557$	0.242864	−	1.06406i	0.0102905	−	0.0450856i	0.979813	+	0.199919i	$0.0640678\pi$
$558$	0.330172			0.0139773
$559$	−35.6203	+	7.01995i	−1.50658	+	0.296912i
$560$	−1.40692			−0.0594534
$561$	1.21001	−	5.30140i	0.0510867	−	0.223825i
$562$	−24.1549	−	7.45079i	−1.01891	−	0.314293i
$563$	1.36804	+	0.658814i	0.0576560	+	0.0277657i	0.462490	−	0.886625i	$-0.346956\pi$
$563$	1.36804	+	0.658814i	0.0576560	+	0.0277657i	−0.404834	+	0.914390i	$0.632671\pi$
$564$	1.16944	+	2.97969i	0.0492424	+	0.125468i
$565$	−4.77231	+	8.26589i	−0.200773	+	0.347749i
$566$	−2.18298	−	3.78103i	−0.0917575	−	0.158929i
$567$	7.27389	−	9.12116i	0.305475	−	0.383053i
$568$	4.35057	+	2.96617i	0.182546	+	0.124458i
$569$	7.58763	−	1.14365i	0.318090	−	0.0479444i	0.0119432	−	0.999929i	$-0.496198\pi$
$569$	7.58763	−	1.14365i	0.318090	−	0.0479444i	0.306147	+	0.951984i	$0.400960\pi$
$570$	−0.865153	+	0.416636i	−0.0362373	+	0.0174509i
$571$	−4.66722	−	4.33055i	−0.195317	−	0.181228i	0.576451	−	0.817132i	$-0.304437\pi$
$571$	−4.66722	−	4.33055i	−0.195317	−	0.181228i	−0.771768	+	0.635904i	$0.780628\pi$
$572$	−18.5609	−	2.79761i	−0.776070	−	0.116974i
$573$	−2.54016	+	0.783534i	−0.106117	+	0.0327326i
$574$	−0.365060	−	4.87139i	−0.0152373	−	0.203328i
$575$	4.42906	+	5.55387i	0.184705	+	0.231612i
$576$	−1.06703	+	2.71876i	−0.0444597	+	0.113282i
$577$	−7.50217	+	6.96099i	−0.312319	+	0.289790i	−0.820720	−	0.571331i	$-0.806427\pi$
$577$	−7.50217	+	6.96099i	−0.312319	+	0.289790i	0.508401	+	0.861121i	$0.330237\pi$
$578$	12.7403	−	8.68620i	0.529927	−	0.361298i
$579$	0.560662	−	7.48152i	0.0233003	−	0.310921i
$580$	1.88024	+	8.23789i	0.0780729	+	0.342060i
$581$	2.34215	+	10.2616i	0.0971687	+	0.425724i
$582$	0.154072	−	2.05594i	0.00638647	−	0.0852216i
$583$	−20.5186	+	13.9894i	−0.849796	+	0.579381i
$584$	−4.30588	+	3.99527i	−0.178179	+	0.165326i
$585$	5.90766	−	15.0525i	0.244252	−	0.622343i
$586$	3.65061	+	4.57772i	0.150805	+	0.189104i
$587$	−0.910723	−	12.1528i	−0.0375896	−	0.501598i	−0.983945	−	0.178471i	$-0.942885\pi$
$587$	−0.910723	−	12.1528i	−0.0375896	−	0.501598i	0.946356	−	0.323127i	$-0.104734\pi$
$588$	−1.35142	+	0.416859i	−0.0557317	+	0.0171910i
$589$	−0.381058	−	0.0574353i	−0.0157012	−	0.00236658i
$590$	4.24439	+	3.93822i	0.174739	+	0.162134i
$591$	3.98382	−	1.91851i	0.163872	−	0.0789168i
$592$	−6.99312	+	1.05404i	−0.287415	+	0.0433209i
$593$	−25.2940	−	17.2452i	−1.03870	−	0.708174i	−0.0812269	−	0.996696i	$-0.525884\pi$
$593$	−25.2940	−	17.2452i	−1.03870	−	0.708174i	−0.957473	+	0.288522i	$0.906836\pi$
$594$	−3.52544	+	4.42076i	−0.144650	+	0.181386i
$595$	−4.00539	−	6.93754i	−0.164205	−	0.284411i
$596$	2.79956	−	4.84898i	0.114675	−	0.198622i
$597$	0.212269	+	0.540851i	0.00868757	+	0.0221356i
$598$	−35.4348	−	17.0645i	−1.44904	−	0.697819i
$599$	−9.59244	−	2.95888i	−0.391936	−	0.120896i	0.0925220	−	0.995711i	$-0.470507\pi$
$599$	−9.59244	−	2.95888i	−0.391936	−	0.120896i	−0.484458	+	0.874814i	$0.660983\pi$
$600$	−0.0626824	+	0.274629i	−0.00255900	+	0.0112117i
$601$	8.10109			0.330450			0.165225	−	0.986256i	$-0.447165\pi$
$601$	8.10109			0.330450			0.165225	+	0.986256i	$0.447165\pi$
$602$	7.38131	−	5.53461i	0.300840	−	0.225574i
$603$	35.4521			1.44372
$604$	−3.11694	+	13.6562i	−0.126826	+	0.555662i
$605$	−0.472249	−	0.145669i	−0.0191996	−	0.00592231i
$606$	4.37649	+	2.10761i	0.177783	+	0.0856157i
$607$	−7.99692	−	20.3758i	−0.324585	−	0.827029i	−0.996278	−	0.0861993i	$-0.972528\pi$
$607$	−7.99692	−	20.3758i	−0.324585	−	0.827029i	0.671693	−	0.740830i	$-0.265567\pi$
$608$	1.70443	−	2.95215i	0.0691236	−	0.119726i
$609$	−1.67440	−	2.90014i	−0.0678500	−	0.117520i
$610$	5.17868	−	6.49386i	0.209679	−	0.262929i
$611$	51.9815	+	35.4404i	2.10295	+	1.43377i
$612$	−16.4439	+	2.47852i	−0.664706	+	0.100188i
$613$	10.1327	−	4.87965i	0.409256	−	0.197087i	−0.217917	−	0.975967i	$-0.569926\pi$
$613$	10.1327	−	4.87965i	0.409256	−	0.197087i	0.627173	+	0.778880i	$0.284212\pi$
$614$	−0.0662536	−	0.0614744i	−0.00267378	−	0.00248090i
$615$	−0.967154	−	0.145775i	−0.0389994	−	0.00587821i
$616$	4.55799	−	1.40595i	0.183647	−	0.0566475i
$617$	−0.584871	−	7.80455i	−0.0235460	−	0.314200i	−0.996524	−	0.0833029i	$-0.973453\pi$
$617$	−0.584871	−	7.80455i	−0.0235460	−	0.314200i	0.972978	−	0.230897i	$-0.0741659\pi$
$618$	−2.65993	−	3.33544i	−0.106998	−	0.134171i
$619$	−10.4562	+	26.6418i	−0.420268	+	1.07083i	0.551351	+	0.834274i	$0.314113\pi$
$619$	−10.4562	+	26.6418i	−0.420268	+	1.07083i	−0.971619	+	0.236552i	$0.923983\pi$
$620$	−0.0828697	+	0.0768919i	−0.00332813	+	0.00308805i
$621$	−9.78886	+	6.67393i	−0.392814	+	0.267816i
$622$	−0.580362	+	7.74439i	−0.0232704	+	0.310522i
$623$	−2.67755	−	11.7311i	−0.107274	−	0.469997i
$624$	−0.347043	−	1.52049i	−0.0138928	−	0.0608685i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	−4.93597	+	3.36529i	−0.197281	+	0.134504i
$627$	2.38648	−	2.21433i	0.0953067	−	0.0884317i
$628$	6.86438	−	17.4901i	0.273918	−	0.697933i
$629$	−25.1063	−	31.4823i	−1.00105	−	1.25528i
$630$	0.307076	+	4.09764i	0.0122342	+	0.163254i
$631$	24.2914	−	7.49291i	0.967026	−	0.298288i	0.229276	−	0.973362i	$-0.426364\pi$
$631$	24.2914	−	7.49291i	0.967026	−	0.298288i	0.737751	+	0.675073i	$0.235888\pi$
$632$	−13.4809	−	2.03193i	−0.536243	−	0.0808257i
$633$	−2.86854	−	2.66162i	−0.114014	−	0.105790i
$634$	9.50203	−	4.57594i	0.377374	−	0.181734i
$635$	12.2016	−	1.83910i	0.484206	−	0.0729823i
$636$	−1.70484	−	1.16234i	−0.0676013	−	0.0460898i
$637$	−17.3308	+	21.7322i	−0.686673	+	0.861061i
$638$	−14.3236	−	24.8092i	−0.567078	−	0.982207i
$639$	7.68936	−	13.3184i	0.304187	−	0.526866i
$640$	−0.365341	−	0.930874i	−0.0144414	−	0.0367960i
$641$	−41.0948	−	19.7902i	−1.62315	−	0.781667i	−0.623149	−	0.782103i	$-0.714147\pi$
$641$	−41.0948	−	19.7902i	−1.62315	−	0.781667i	−1.00000		0.000435841i	$0.999861\pi$
$642$	1.85373	+	0.571799i	0.0731607	+	0.0225671i
$643$	−1.53699	+	6.73398i	−0.0606129	+	0.265562i	−0.996150	−	0.0876663i	$-0.972059\pi$
$643$	−1.53699	+	6.73398i	−0.0606129	+	0.265562i	0.935537	+	0.353229i	$0.114916\pi$
$644$	9.99431			0.393831
$645$	−0.751491	−	1.68740i	−0.0295899	−	0.0664414i
$646$	19.4094			0.763653
$647$	−2.65388	+	11.6274i	−0.104335	+	0.457121i	0.895590	+	0.444880i	$0.146754\pi$
$647$	−2.65388	+	11.6274i	−0.104335	+	0.457121i	−0.999925	+	0.0122409i	$0.996104\pi$
$648$	7.92375	+	2.44415i	0.311274	+	0.0960154i
$649$	−17.6860	−	8.51714i	−0.694237	−	0.334327i
$650$	2.02272	+	5.15381i	0.0793377	+	0.202149i
$651$	0.0224015	−	0.0388005i	0.000877982	−	0.00152071i
$652$	6.33947	+	10.9803i	0.248273	+	0.430021i
$653$	25.1952	−	31.5938i	0.985964	−	1.23636i	0.0143236	−	0.999897i	$-0.495440\pi$
$653$	25.1952	−	31.5938i	0.985964	−	1.23636i	0.971641	−	0.236463i	$-0.0759881\pi$
$654$	−3.64702	−	2.48649i	−0.142610	−	0.0972296i
$655$	0.507803	−	0.0765390i	0.0198415	−	0.00299062i
$656$	3.12830	−	1.50651i	0.122140	−	0.0588194i
$657$	12.5760	+	11.6688i	0.490635	+	0.455243i
$658$	−15.8088	−	2.38279i	−0.616290	−	0.0928908i
$659$	28.1688	−	8.68893i	1.09730	−	0.338473i	0.307321	−	0.951606i	$-0.400567\pi$
$659$	28.1688	−	8.68893i	1.09730	−	0.338473i	0.789980	+	0.613133i	$0.210091\pi$
$660$	−0.0713690	−	0.952353i	−0.00277803	−	0.0370703i
$661$	−23.7957	−	29.8389i	−0.925547	−	1.16060i	−0.986713	−	0.162472i	$-0.948053\pi$
$661$	−23.7957	−	29.8389i	−0.925547	−	1.16060i	0.0611658	−	0.998128i	$-0.480518\pi$
$662$	−2.17737	+	5.54785i	−0.0846259	+	0.215623i
$663$	6.50955	−	6.03998i	0.252810	−	0.234574i
$664$	−6.18129	+	4.21433i	−0.239880	+	0.163548i
$665$	0.358405	−	4.78258i	0.0138984	−	0.185461i
$666$	4.59620	+	20.1373i	0.178099	+	0.780304i
$667$	−13.3566	−	58.5192i	−0.517171	−	2.26587i
$668$	−0.122062	+	1.62880i	−0.00472271	+	0.0630202i
$669$	−3.82099	+	2.60511i	−0.147728	+	0.100719i
$670$	−8.89810	+	8.25623i	−0.343763	+	0.318966i
$671$	−10.2879	+	26.2132i	−0.397161	+	1.01195i
$672$	0.247101	+	0.309855i	0.00953213	+	0.0119529i
$673$	0.675627	+	9.01562i	0.0260435	+	0.347527i	0.994970	+	0.100176i	$0.0319407\pi$
$673$	0.675627	+	9.01562i	0.0260435	+	0.347527i	−0.968926	+	0.247350i	$0.920440\pi$
$674$	−8.71632	+	2.68863i	−0.335740	+	0.103562i
$675$	1.64917	+	0.248573i	0.0634767	+	0.00956757i
$676$	−12.9407	−	12.0072i	−0.497719	−	0.461815i
$677$	−20.3315	+	9.79112i	−0.781402	+	0.376303i	−0.781666	−	0.623697i	$-0.785630\pi$
$677$	−20.3315	+	9.79112i	−0.781402	+	0.376303i	0.000264725		1.00000i	$0.499916\pi$
$678$	2.65862	−	0.400722i	0.102104	−	0.0153896i
$679$	8.50802	+	5.80067i	0.326508	+	0.222609i
$680$	3.55004	−	4.45161i	0.136138	−	0.170712i
$681$	−0.252361	−	0.437102i	−0.00967049	−	0.0167498i
$682$	0.191633	−	0.331918i	0.00733801	−	0.0127098i
$683$	12.7296	+	32.4344i	0.487083	+	1.24107i	0.937418	+	0.348207i	$0.113210\pi$
$683$	12.7296	+	32.4344i	0.487083	+	1.24107i	−0.450334	+	0.892860i	$0.648695\pi$
$684$	−8.97010	−	4.31977i	−0.342981	−	0.165171i
$685$	−10.0875	−	3.11157i	−0.385422	−	0.118887i
$686$	3.76328	−	16.4880i	0.143683	−	0.629515i
$687$	4.09835			0.156362
$688$	5.57864	+	3.44656i	0.212684	+	0.131399i
$689$	−40.5547			−1.54501
$690$	0.445275	−	1.95088i	0.0169513	−	0.0742686i
$691$	0.0268615	+	0.00828568i	0.00102186	+	0.000315202i	0.295266	−	0.955415i	$-0.404592\pi$
$691$	0.0268615	+	0.00828568i	0.00102186	+	0.000315202i	−0.294244	+	0.955730i	$0.595068\pi$
$692$	4.88590	+	2.35292i	0.185734	+	0.0894448i
$693$	−5.08965	−	12.9682i	−0.193340	−	0.492622i
$694$	−16.3399	+	28.3015i	−0.620254	+	1.07431i
$695$	2.86582	+	4.96374i	0.108707	+	0.188285i
$696$	1.48405	−	1.86093i	0.0562526	−	0.0705385i
$697$	16.3346	+	11.1367i	0.618717	+	0.421834i
$698$	−31.0421	+	4.67884i	−1.17496	+	0.177097i
$699$	−1.85641	+	0.894000i	−0.0702159	+	0.0338142i
$700$	−1.03135	−	0.956951i	−0.0389813	−	0.0361693i
$701$	12.0862	+	1.82170i	0.456490	+	0.0688048i	0.373263	−	0.927726i	$-0.378239\pi$
$701$	12.0862	+	1.82170i	0.456490	+	0.0688048i	0.0832276	+	0.996531i	$0.473477\pi$
$702$	−8.82359	+	2.72172i	−0.333025	+	0.102725i
$703$	−1.80158	−	24.0404i	−0.0679477	−	0.906700i
$704$	2.11382	+	2.65065i	0.0796677	+	0.0999002i
$705$	−1.16944	+	2.97969i	−0.0440438	+	0.112222i
$706$	−16.7942	+	15.5827i	−0.632058	+	0.586464i
$707$	−20.0455	+	13.6668i	−0.753890	+	0.513994i
$708$	0.121885	−	1.62645i	0.00458073	−	0.0611256i
$709$	1.07973	+	4.73062i	0.0405502	+	0.177662i	0.991148	−	0.132764i	$-0.0423853\pi$
$709$	1.07973	+	4.73062i	0.0405502	+	0.177662i	−0.950597	+	0.310426i	$0.899528\pi$
$710$	1.17169	+	5.13350i	0.0439726	+	0.192657i
$711$	−2.97559	+	39.7065i	−0.111593	+	1.48911i
$712$	7.06646	−	4.81783i	0.264827	−	0.180556i
$713$	0.588679	−	0.546214i	0.0220462	−	0.0204559i
$714$	−0.824418	+	2.10058i	−0.0308531	+	0.0786124i
$715$	−11.7033	−	14.6754i	−0.437677	−	0.548829i
$716$	1.74761	+	23.3202i	0.0653111	+	0.871516i
$717$	7.63371	−	2.35469i	0.285086	−	0.0879375i
$718$	−28.1410	−	4.24157i	−1.05021	−	0.158294i
$719$	0.898580	+	0.833760i	0.0335114	+	0.0310940i	0.696751	−	0.717313i	$-0.254628\pi$
$719$	0.898580	+	0.833760i	0.0335114	+	0.0310940i	−0.663239	+	0.748407i	$0.730819\pi$
$720$	−2.63141	+	1.26722i	−0.0980670	+	0.0472266i
$721$	21.0697	−	3.17574i	0.784676	−	0.118271i
$722$	−6.09741	−	4.15714i	−0.226922	−	0.154713i
$723$	0.597080	−	0.748714i	0.0222056	−	0.0278450i
$724$	−2.84666	−	4.93057i	−0.105795	−	0.183243i
$725$	−4.22487	+	7.31769i	−0.156908	+	0.271772i
$726$	0.0508605	+	0.129590i	0.00188761	+	0.00480955i
$727$	7.92932	+	3.81856i	0.294082	+	0.141623i	0.575108	−	0.818078i	$-0.304960\pi$
$727$	7.92932	+	3.81856i	0.294082	+	0.141623i	−0.281025	+	0.959700i	$0.590674\pi$
$728$	7.44341	+	2.29599i	0.275871	+	0.0850950i
$729$	5.07549	−	22.2372i	0.187981	−	0.823598i
$730$	−5.87391			−0.217403
$731$	−1.11307	+	37.3203i	−0.0411683	+	1.38034i
$732$	−2.33972			−0.0864787
$733$	6.57542	−	28.8088i	0.242869	−	1.06408i	−0.695523	−	0.718504i	$-0.744827\pi$
$733$	6.57542	−	28.8088i	0.242869	−	1.06408i	0.938392	−	0.345573i	$-0.112315\pi$
$734$	18.4979	+	5.70585i	0.682771	+	0.210607i
$735$	−1.27420	−	0.613622i	−0.0469995	−	0.0226338i
$736$	2.59526	+	6.61262i	0.0956626	+	0.243744i
$737$	20.5765	−	35.6396i	0.757946	−	1.31280i
$738$	−5.07047	−	8.78231i	−0.186647	−	0.323281i
$739$	17.5313	−	21.9835i	0.644898	−	0.808676i	−0.346708	−	0.937973i	$-0.612701\pi$
$739$	17.5313	−	21.9835i	0.644898	−	0.808676i	0.991606	+	0.129297i	$0.0412721\pi$
$740$	−5.84325	−	3.98386i	−0.214802	−	0.146450i
$741$	5.25706	−	0.792374i	0.193123	−	0.0291086i
$742$	9.28504	−	4.47144i	0.340865	−	0.164152i
$743$	32.9195	+	30.5448i	1.20770	+	1.12058i	0.989479	+	0.144680i	$0.0462152\pi$
$743$	32.9195	+	30.5448i	1.20770	+	1.12058i	0.218219	+	0.975900i	$0.429975\pi$
$744$	0.0314889	+	0.00474619i	0.00115444	+	0.000174004i
$745$	5.35037	−	1.65037i	0.196022	−	0.0604649i
$746$	−1.32150	−	17.6342i	−0.0483834	−	0.645632i
$747$	13.6233	+	17.0831i	0.498450	+	0.625037i
$748$	−7.05248	+	17.9694i	−0.257864	+	0.657028i
$749$	−7.10251	+	6.59017i	−0.259520	+	0.240800i
$750$	−0.232745	+	0.158683i	−0.00849864	+	0.00579428i
$751$	2.99229	−	39.9293i	0.109190	−	1.45704i	−0.626340	−	0.779550i	$-0.715448\pi$
$751$	2.99229	−	39.9293i	0.109190	−	1.45704i	0.735530	−	0.677492i	$-0.236933\pi$
$752$	−2.52858	−	11.0784i	−0.0922078	−	0.403989i
$753$	0.496719	+	2.17627i	0.0181015	+	0.0793077i
$754$	3.49604	−	46.6514i	0.127318	−	1.69894i
$755$	−11.5734	+	7.89064i	−0.421201	+	0.287170i
$756$	1.72008	−	1.59600i	0.0625588	−	0.0580461i
$757$	−9.66403	+	24.6235i	−0.351245	+	0.894958i	0.640642	+	0.767839i	$0.278668\pi$
$757$	−9.66403	+	24.6235i	−0.351245	+	0.894958i	−0.991888	+	0.127119i	$0.959427\pi$
$758$	−5.15761	−	6.46744i	−0.187333	−	0.234908i
$759$	0.506982	+	6.76520i	0.0184023	+	0.245561i
$760$	3.25741	−	1.00478i	0.118159	−	0.0364471i
$761$	−30.8661	−	4.65231i	−1.11889	−	0.168646i	−0.436552	−	0.899679i	$-0.643800\pi$
$761$	−30.8661	−	4.65231i	−1.11889	−	0.168646i	−0.682342	+	0.731033i	$0.739039\pi$
$762$	−2.54803	−	2.36423i	−0.0923053	−	0.0856468i
$763$	19.8627	−	9.56536i	0.719077	−	0.346289i
$764$	9.33134	−	1.40647i	0.337596	−	0.0508844i
$765$	−13.7401	−	9.36783i	−0.496774	−	0.338694i
$766$	13.3912	−	16.7920i	0.483842	−	0.606719i
$767$	−16.0283	−	27.7619i	−0.578750	−	1.00242i
$768$	−0.140846	+	0.243953i	−0.00508234	+	0.00880288i
$769$	1.69064	+	4.30769i	0.0609662	+	0.155339i	0.958111	−	0.286397i	$-0.0924578\pi$
$769$	1.69064	+	4.30769i	0.0609662	+	0.155339i	−0.897145	+	0.441737i	$0.854363\pi$
$770$	4.29754	+	2.06958i	0.154872	+	0.0745827i
$771$	−2.37226	−	0.731745i	−0.0854349	−	0.0263532i
$772$	−5.92655	+	25.9659i	−0.213301	+	0.934534i
$773$	12.9326			0.465153			0.232576	−	0.972578i	$-0.425284\pi$
$773$	12.9326			0.465153			0.232576	+	0.972578i	$0.425284\pi$
$774$	8.82045	−	16.9999i	0.317044	−	0.611050i
$775$	−0.113048			−0.00406079
$776$	−1.62863	+	7.13551i	−0.0584645	+	0.256150i
$777$	2.67829	+	0.826143i	0.0960832	+	0.0296377i
$778$	−20.0895	−	9.67460i	−0.720244	−	0.346851i
$779$	4.32420	+	11.0179i	0.154930	+	0.394756i
$780$	0.779798	−	1.35065i	0.0279213	−	0.0483610i
$781$	−8.92587	−	15.4601i	−0.319393	−	0.553204i
$782$	−25.2183	+	31.6228i	−0.901805	+	1.13083i
$783$	−11.6438	−	7.93858i	−0.416114	−	0.283702i
$784$	4.96449	−	0.748277i	0.177303	−	0.0267242i
$785$	16.9283	−	8.15222i	0.604196	−	0.290965i
$786$	−0.106043	−	0.0983936i	−0.00378243	−	0.00350958i
$787$	26.6816	+	4.02161i	0.951097	+	0.143355i	0.606223	−	0.795295i	$-0.292684\pi$
$787$	26.6816	+	4.02161i	0.951097	+	0.143355i	0.344873	+	0.938649i	$0.387922\pi$
$788$	−14.9996	+	4.62676i	−0.534338	+	0.164821i
$789$	−0.419304	−	5.59523i	−0.0149276	−	0.199195i
$790$	−8.50017	−	10.6589i	−0.302423	−	0.379226i
$791$	−4.90600	+	12.5003i	−0.174437	+	0.444459i
$792$	7.25861	−	6.73501i	0.257924	−	0.239318i
$793$	−37.9956	+	25.9050i	−1.34926	+	0.919912i
$794$	−1.57972	+	21.0799i	−0.0560622	+	0.748098i
$795$	−0.459144	−	2.01164i	−0.0162842	−	0.0713456i
$796$	−0.458969	−	2.01087i	−0.0162677	−	0.0712736i
$797$	−2.00760	+	26.7896i	−0.0711128	+	0.948935i	0.841539	+	0.540196i	$0.181650\pi$
$797$	−2.00760	+	26.7896i	−0.0711128	+	0.948935i	−0.912652	+	0.408738i	$0.865969\pi$
$798$	−1.11624	+	0.761042i	−0.0395146	+	0.0269406i
$799$	47.4291	−	44.0078i	1.67792	−	1.55688i
$800$	0.365341	−	0.930874i	0.0129168	−	0.0329114i
$801$	−15.5742	−	19.5294i	−0.550287	−	0.690038i
$802$	−0.744619	−	9.93624i	−0.0262934	−	0.350861i
$803$	19.0296	−	5.86987i	0.671541	−	0.207143i
$804$	3.38111	+	0.509620i	0.119242	+	0.0179729i
$805$	7.32635	+	6.79786i	0.258220	+	0.239593i
$806$	0.563908	−	0.271564i	0.0198628	−	0.00956543i
$807$	−0.0554831	+	0.00836273i	−0.00195310	+	0.000294382i
$808$	−14.2478	−	9.71398i	−0.501235	−	0.341737i
$809$	9.58908	−	12.0243i	0.337134	−	0.422753i	−0.584148	−	0.811647i	$-0.698571\pi$
$809$	9.58908	−	12.0243i	0.337134	−	0.422753i	0.921282	+	0.388894i	$0.127143\pi$
$810$	4.14607	+	7.18121i	0.145678	+	0.252322i
$811$	−14.0387	+	24.3158i	−0.492966	+	0.853842i	−0.999967	−	0.00810347i	$-0.997421\pi$
$811$	−14.0387	+	24.3158i	−0.492966	+	0.853842i	0.507001	+	0.861945i	$0.330754\pi$
$812$	4.34322	+	11.0664i	0.152417	+	0.388353i
$813$	−7.96169	−	3.83415i	−0.279229	−	0.134469i
$814$	22.9114	+	7.06724i	0.803045	+	0.247707i
$815$	−2.82133	+	12.3611i	−0.0988268	+	0.432989i
$816$	−1.60391			−0.0561479
$817$	−13.1371	+	18.0856i	−0.459608	+	0.632735i
$818$	32.2923			1.12907
$819$	5.06242	−	22.1799i	0.176895	−	0.775029i
$820$	3.31790	+	1.02344i	0.115866	+	0.0357399i
$821$	−29.7144	−	14.3097i	−1.03704	−	0.499412i	−0.163694	−	0.986511i	$-0.552341\pi$
$821$	−29.7144	−	14.3097i	−1.03704	−	0.499412i	−0.873347	+	0.487099i	$0.838055\pi$
$822$	1.08640	+	2.76811i	0.0378927	+	0.0965489i
$823$	−1.08033	+	1.87118i	−0.0376578	+	0.0652252i	−0.884240	−	0.467033i	$-0.845323\pi$
$823$	−1.08033	+	1.87118i	−0.0376578	+	0.0652252i	0.846582	+	0.532258i	$0.178656\pi$
$824$	7.57244	+	13.1158i	0.263798	+	0.456912i
$825$	0.595448	−	0.746668i	0.0207308	−	0.0259956i
$826$	6.73065	+	4.58888i	0.234189	+	0.159667i
$827$	−13.2296	+	1.99403i	−0.460037	+	0.0693394i	−0.374972	−	0.927036i	$-0.622348\pi$
$827$	−13.2296	+	1.99403i	−0.460037	+	0.0693394i	−0.0850645	+	0.996375i	$0.527110\pi$
$828$	18.6927	−	9.00193i	0.649616	−	0.312839i
$829$	28.7079	+	26.6370i	0.997067	+	0.925143i	0.997194	−	0.0748573i	$-0.0238501\pi$
$829$	28.7079	+	26.6370i	0.997067	+	0.925143i	−0.000127537		1.00000i	$0.500041\pi$
$830$	−7.39768	−	1.11502i	−0.256777	−	0.0387029i
$831$	7.24746	−	2.23555i	0.251412	−	0.0775502i
$832$	0.413745	+	5.52105i	0.0143440	+	0.191408i
$833$	17.8232	+	22.3496i	0.617538	+	0.774368i
$834$	0.589863	−	1.50295i	0.0204253	−	0.0520428i
$835$	−1.19734	+	1.11097i	−0.0414358	+	0.0384468i
$836$	−9.54890	+	6.51033i	−0.330256	+	0.225164i
$837$	0.0140897	−	0.188014i	0.000487010	−	0.00649870i
$838$	0.242474	+	1.06235i	0.00837611	+	0.0366982i
$839$	−5.86459	−	25.6944i	−0.202468	−	0.887070i	−0.969428	−	0.245375i	$-0.921089\pi$
$839$	−5.86459	−	25.6944i	−0.202468	−	0.887070i	0.766960	−	0.641695i	$-0.221768\pi$
$840$	−0.0296170	+	0.395211i	−0.00102188	+	0.0136361i
$841$	35.0310	−	23.8837i	1.20796	−	0.823576i
$842$	−6.41800	+	5.95503i	−0.221179	+	0.205224i
$843$	−2.60144	+	6.62837i	−0.0895984	+	0.228293i
$844$	8.66127	+	10.8609i	0.298133	+	0.373847i
$845$	−1.31922	−	17.6038i	−0.0453826	−	0.605589i
$846$	−31.7139	+	9.78243i	−1.09035	+	0.336327i
$847$	−0.687542	−	0.103630i	−0.0236242	−	0.00356078i
$848$	5.36956	+	4.98222i	0.184391	+	0.171090i
$849$	−1.10806	+	0.533615i	−0.0380286	+	0.0183136i
$850$	5.63023	−	0.848621i	0.193115	−	0.0291075i
$851$	41.5085	+	28.3000i	1.42289	+	0.970112i
$852$	0.924794	−	1.15965i	0.0316829	−	0.0397291i
$853$	−2.98355	−	5.16767i	−0.102155	−	0.176938i	0.810417	−	0.585853i	$-0.199240\pi$
$853$	−2.98355	−	5.16767i	−0.102155	−	0.176938i	−0.912572	+	0.408915i	$0.865907\pi$
$854$	5.84293	−	10.1202i	0.199941	−	0.346308i
$855$	−3.63736	−	9.26784i	−0.124395	−	0.316953i
$856$	−6.20464	−	2.98800i	−0.212070	−	0.102128i
$857$	43.3233	+	13.3635i	1.47990	+	0.456488i	0.926457	−	0.376401i	$-0.122839\pi$
$857$	43.3233	+	13.3635i	1.47990	+	0.456488i	0.553440	+	0.832889i	$0.313315\pi$
$858$	−1.17658	+	5.15495i	−0.0401679	+	0.175987i
$859$	−19.3440			−0.660010			−0.330005	−	0.943979i	$-0.607050\pi$
$859$	−19.3440			−0.660010			−0.330005	+	0.943979i	$0.607050\pi$
$860$	1.74518	+	6.32095i	0.0595101	+	0.215542i
$861$	−1.37608			−0.0468967
$862$	−2.66191	+	11.6626i	−0.0906650	+	0.397229i
$863$	45.2825	+	13.9678i	1.54143	+	0.475470i	0.944966	−	0.327167i	$-0.106094\pi$
$863$	45.2825	+	13.9678i	1.54143	+	0.475470i	0.596468	+	0.802637i	$0.296570\pi$
$864$	1.50264	+	0.723631i	0.0511207	+	0.0246184i
$865$	1.98122	+	5.04807i	0.0673636	+	0.171640i
$866$	11.7703	−	20.3867i	0.399970	−	0.692769i
$867$	−2.17180	−	3.76166i	−0.0737581	−	0.127753i
$868$	−0.0991656	+	0.124350i	−0.00336590	+	0.00422070i
$869$	38.1895	+	26.0371i	1.29549	+	0.883249i
$870$	2.35364	−	0.354754i	0.0797959	−	0.0120273i
$871$	60.5494	−	29.1591i	2.05164	−	0.988017i
$872$	11.4866	+	10.6580i	0.388986	+	0.360926i
$873$	21.1375	+	3.18597i	0.715396	+	0.107829i
$874$	−23.1395	+	7.13760i	−0.782707	+	0.241433i
$875$	−0.105140	−	1.40299i	−0.00355436	−	0.0474297i
$876$	1.03165	+	1.29364i	0.0348561	+	0.0437082i
$877$	−10.3882	+	26.4688i	−0.350786	+	0.893787i	0.641193	+	0.767380i	$0.278440\pi$
$877$	−10.3882	+	26.4688i	−0.350786	+	0.893787i	−0.991978	+	0.126407i	$0.959655\pi$
$878$	15.3898	−	14.2796i	0.519379	−	0.481914i
$879$	1.36275	−	0.929107i	0.0459644	−	0.0313380i
$880$	−0.253358	+	3.38083i	−0.00854070	+	0.113968i
$881$	4.30784	+	18.8739i	0.145135	+	0.635877i	0.994196	+	0.107583i	$0.0343110\pi$
$881$	4.30784	+	18.8739i	0.145135	+	0.635877i	−0.849061	+	0.528294i	$0.822832\pi$
$882$	−3.26289	−	14.2957i	−0.109867	−	0.481360i
$883$	0.896519	−	11.9632i	0.0301703	−	0.402594i	−0.961590	−	0.274489i	$-0.911491\pi$
$883$	0.896519	−	11.9632i	0.0301703	−	0.402594i	0.991761	−	0.128105i	$-0.0408896\pi$
$884$	−26.0464	+	17.7581i	−0.876035	+	0.597270i
$885$	1.19561	−	1.10937i	0.0401901	−	0.0372909i
$886$	−8.12118	+	20.6924i	−0.272836	+	0.695176i
$887$	27.8785	+	34.9585i	0.936068	+	1.17379i	0.984574	+	0.174969i	$0.0559826\pi$
$887$	27.8785	+	34.9585i	0.936068	+	1.17379i	−0.0485059	+	0.998823i	$0.515446\pi$
$888$	0.148874	+	1.98659i	0.00499589	+	0.0666655i
$889$	16.5893	−	5.11713i	0.556389	−	0.171623i
$890$	8.45704	+	1.27469i	0.283481	+	0.0427278i
$891$	−20.6082	−	19.1217i	−0.690402	−	0.640600i
$892$	14.7913	−	7.12310i	0.495248	−	0.238499i
$893$	38.3033	−	5.77329i	1.28177	−	0.193196i
$894$	−1.30317	−	0.888485i	−0.0435845	−	0.0297154i
$895$	−14.5807	+	18.2836i	−0.487378	+	0.611152i
$896$	−0.703462	−	1.21843i	−0.0235010	−	0.0407049i
$897$	−5.53943	+	9.59457i	−0.184956	+	0.320353i
$898$	−9.09703	−	23.1789i	−0.303572	−	0.773488i
$899$	0.860626	+	0.414455i	0.0287035	+	0.0138229i
$900$	−2.79089	−	0.860877i	−0.0930298	−	0.0286959i
$901$	−9.28066	+	40.6612i	−0.309184	+	1.35462i
$902$	−11.7717			−0.391954
$903$	−1.39931	−	2.18995i	−0.0465663	−	0.0728770i
$904$	−9.54463			−0.317450
$905$	1.26688	−	5.55059i	0.0421127	−	0.184508i
$906$	3.77047	+	1.16304i	0.125265	+	0.0386393i
$907$	−31.6289	−	15.2317i	−1.05022	−	0.505759i	−0.172537	−	0.985003i	$-0.555197\pi$
$907$	−31.6289	−	15.2317i	−1.05022	−	0.505759i	−0.877682	+	0.479244i	$0.840911\pi$
$908$	0.654600	+	1.66789i	0.0217237	+	0.0553510i
$909$	−25.1821	+	43.6166i	−0.835236	+	1.44667i
$910$	3.89474	+	6.74588i	0.129109	+	0.223624i
$911$	−13.5228	+	16.9570i	−0.448030	+	0.561812i	−0.953640	−	0.300950i	$-0.902696\pi$
$911$	−13.5228	+	16.9570i	−0.448030	+	0.561812i	0.505610	+	0.862762i	$0.331268\pi$
$912$	−0.793393	−	0.540926i	−0.0262719	−	0.0179119i
$913$	25.0804	−	3.78026i	0.830041	−	0.125109i
$914$	12.4120	−	5.97731i	0.410553	−	0.197712i
$915$	−1.71514	−	1.59142i	−0.0567008	−	0.0526106i
$916$	−14.3865	−	2.16842i	−0.475345	−	0.0716467i
$917$	0.690410	−	0.212963i	0.0227994	−	0.00703267i
$918$	0.709649	+	9.46961i	0.0234219	+	0.312544i
$919$	−19.6460	−	24.6353i	−0.648061	−	0.812643i	0.343924	−	0.938997i	$-0.388244\pi$
$919$	−19.6460	−	24.6353i	−0.648061	−	0.812643i	−0.991985	+	0.126355i	$0.959672\pi$
$920$	−2.59526	+	6.61262i	−0.0855632	+	0.218012i
$921$	−0.0186631	+	0.0173168i	−0.000614971	+	0.000570610i
$922$	−11.7609	+	8.01844i	−0.387324	+	0.264073i
$923$	2.17858	−	29.0712i	0.0717089	−	0.956889i
$924$	−0.298989	−	1.30996i	−0.00983602	−	0.0430944i
$925$	−1.57369	−	6.89480i	−0.0517427	−	0.226699i
$926$	−0.119678	+	1.59699i	−0.00393287	+	0.0524805i
$927$	36.5469	−	24.9173i	1.20036	−	0.818390i
$928$	−6.19410	+	5.74728i	−0.203331	+	0.188664i
$929$	10.8568	−	27.6626i	0.356199	−	0.907581i	−0.634673	−	0.772780i	$-0.718865\pi$
$929$	10.8568	−	27.6626i	0.356199	−	0.907581i	0.990873	−	0.134801i	$-0.0430394\pi$
$930$	0.0198548	+	0.0248971i	0.000651064	+	0.000816408i
$931$	1.27896	+	17.0665i	0.0419162	+	0.559333i
$932$	6.98962	−	2.15601i	0.228952	−	0.0706225i
$933$	2.16322	+	0.326052i	0.0708205	+	0.0106745i
$934$	5.74861	+	5.33393i	0.188100	+	0.174532i
$935$	−17.3922	+	8.37562i	−0.568784	+	0.273912i
$936$	15.9897	−	2.41005i	0.522638	−	0.0787750i
$937$	−9.16919	−	6.25145i	−0.299544	−	0.204226i	0.404216	−	0.914664i	$-0.367545\pi$
$937$	−9.16919	−	6.25145i	−0.299544	−	0.204226i	−0.703760	+	0.710438i	$0.748497\pi$
$938$	−10.6479	+	13.3520i	−0.347665	+	0.435958i
$939$	0.841418	+	1.45738i	0.0274586	+	0.0475598i
$940$	5.68167	−	9.84094i	0.185316	−	0.320976i
$941$	2.22125	+	5.65965i	0.0724106	+	0.184499i	0.962497	−	0.271293i	$-0.0874512\pi$
$941$	2.22125	+	5.65965i	0.0724106	+	0.184499i	−0.890086	+	0.455792i	$0.849356\pi$
$942$	−4.76856	−	2.29642i	−0.155368	−	0.0748213i
$943$	−23.5692	−	7.27014i	−0.767520	−	0.236748i
$944$	−1.28840	+	5.64486i	−0.0419339	+	0.183725i
$945$	2.34647			0.0763306
$946$	−11.9704	−	18.7339i	−0.389192	−	0.609092i
$947$	9.45546			0.307261			0.153631	−	0.988128i	$-0.450903\pi$
$947$	9.45546			0.307261			0.153631	+	0.988128i	$0.450903\pi$
$948$	−0.854563	+	3.74408i	−0.0277549	+	0.121602i
$949$	31.0763	+	9.58576i	1.00878	+	0.311167i
$950$	3.07127	+	1.47905i	0.0996452	+	0.0479866i
$951$	−1.08538	−	2.76549i	−0.0351957	−	0.0896772i
$952$	4.00539	−	6.93754i	0.129815	−	0.224847i
$953$	−0.661345	−	1.14548i	−0.0214231	−	0.0371058i	0.855115	−	0.518438i	$-0.173486\pi$
$953$	−0.661345	−	1.14548i	−0.0214231	−	0.0371058i	−0.876538	+	0.481332i	$0.840153\pi$
$954$	13.3387	−	16.7262i	0.431855	−	0.541529i
$955$	7.79700	+	5.31591i	0.252305	+	0.172019i
$956$	−28.0427	+	4.22675i	−0.906965	+	0.136703i
$957$	−7.27055	+	3.50131i	−0.235023	+	0.113181i
$958$	19.1425	+	17.7616i	0.618465	+	0.573852i
$959$	−14.6862	−	2.21359i	−0.474243	−	0.0714806i
$960$	−0.269177	+	0.0830302i	−0.00868766	+	0.00267979i
$961$	−2.31568	−	30.9006i	−0.0746993	−	0.996793i
$962$	24.4127	+	30.6126i	0.787097	+	0.986989i
$963$	−7.34827	+	18.7231i	−0.236795	+	0.603343i
$964$	−2.49209	+	2.31232i	−0.0802647	+	0.0744747i
$965$	−22.0058	+	15.0033i	−0.708391	+	0.482973i
$966$	0.210389	−	2.80745i	0.00676916	−	0.0903281i
$967$	2.01925	+	8.84691i	0.0649347	+	0.284498i	0.996962	−	0.0778908i	$-0.0248185\pi$
$967$	2.01925	+	8.84691i	0.0649347	+	0.284498i	−0.932027	+	0.362388i	$0.881961\pi$
$968$	−0.109971	−	0.481814i	−0.00353460	−	0.0154861i
$969$	0.408585	−	5.45219i	0.0131256	−	0.175150i
$970$	−6.04725	+	4.12295i	−0.194166	+	0.132380i
$971$	−3.63600	+	3.37372i	−0.116685	+	0.108268i	−0.736358	−	0.676593i	$-0.763456\pi$
$971$	−3.63600	+	3.37372i	−0.116685	+	0.108268i	0.619673	+	0.784860i	$0.287265\pi$
$972$	2.68132	−	6.83190i	0.0860035	−	0.219133i
$973$	5.02780	+	6.30466i	0.161184	+	0.202118i
$974$	2.14715	+	28.6517i	0.0687992	+	0.918061i
$975$	1.49031	−	0.459699i	0.0477281	−	0.0147222i
$976$	8.21319	+	1.23794i	0.262898	+	0.0396255i
$977$	−13.3045	−	12.3448i	−0.425650	−	0.394945i	0.438051	−	0.898950i	$-0.355669\pi$
$977$	−13.3045	−	12.3448i	−0.425650	−	0.394945i	−0.863701	+	0.504005i	$0.831859\pi$
$978$	3.21786	−	1.54964i	0.102896	−	0.0495520i
$979$	−28.6720	+	4.32161i	−0.916361	+	0.138119i
$980$	4.14819	+	2.82819i	0.132509	+	0.0903431i
$981$	28.5342	−	35.7808i	0.911028	−	1.14239i
$982$	−4.54584	−	7.87363i	−0.145064	−	0.251258i
$983$	−7.57031	+	13.1122i	−0.241455	+	0.418213i	−0.961129	−	0.276100i	$-0.910958\pi$
$983$	−7.57031	+	13.1122i	−0.241455	+	0.418213i	0.719674	+	0.694312i	$0.244291\pi$
$984$	−0.357332	−	0.910467i	−0.0113913	−	0.0290246i
$985$	−14.1425	−	6.81065i	−0.450616	−	0.217005i
$986$	−45.9739	−	14.1811i	−1.46411	−	0.451617i
$987$	−1.00212	+	4.39060i	−0.0318980	+	0.139754i
$988$	−18.8732			−0.600437
$989$	−12.3972	−	44.9019i	−0.394207	−	1.42780i
$990$	9.90191			0.314703
$991$	5.59833	−	24.5279i	0.177837	−	0.779153i	−0.804790	−	0.593560i	$-0.797722\pi$
$991$	5.59833	−	24.5279i	0.177837	−	0.779153i	0.982627	−	0.185594i	$-0.0594208\pi$
$992$	−0.108025	−	0.0333213i	−0.00342980	−	0.00105795i
$993$	1.51258	+	0.728420i	0.0480002	+	0.0231157i
$994$	2.70651	+	6.89608i	0.0858453	+	0.218730i
$995$	1.03129	−	1.78625i	0.0326942	−	0.0566281i
$996$	1.05370	+	1.82507i	0.0333878	+	0.0578294i
$997$	−14.3368	+	17.9777i	−0.454050	+	0.569361i	−0.955185	−	0.296008i	$-0.904344\pi$
$997$	−14.3368	+	17.9777i	−0.454050	+	0.569361i	0.501135	+	0.865369i	$0.332916\pi$
$998$	8.37829	+	5.71222i	0.265210	+	0.180817i
$999$	11.6631	−	1.75793i	0.369005	−	0.0556185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.81.2	✓	48
43.17	even	21	inner	430.2.q.b.361.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.81.2	✓	48	1.1	even	1	trivial
430.2.q.b.361.2	yes	48	43.17	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(0.269177 + 0.0830302i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.140846 + 0.243953i) q^{6} +(-0.703462 - 1.21843i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-2.41315 - 1.64526i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(0.269177 + 0.0830302i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.140846 + 0.243953i) q^{6} +(-0.703462 - 1.21843i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-2.41315 - 1.64526i) q^{9} +(0.988831 - 0.149042i) q^{10} +(-3.05456 + 1.47100i) q^{11} +(-0.206495 - 0.191599i) q^{12} +(-5.47469 - 0.825177i) q^{13} +(1.34442 - 0.414698i) q^{14} +(-0.0210509 - 0.280904i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-2.08019 + 5.30023i) q^{17} +(2.14099 - 1.98655i) q^{18} +(-2.81653 + 1.92028i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(-0.0881893 - 0.386383i) q^{21} +(-0.754415 - 3.30531i) q^{22} +(0.530858 - 7.08380i) q^{23} +(0.232745 - 0.158683i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(2.02272 - 5.15381i) q^{26} +(-1.03986 - 1.30394i) q^{27} +(0.105140 + 1.40299i) q^{28} +(8.07434 - 2.49060i) q^{29} +(0.278546 + 0.0419840i) q^{30} +(0.0828697 + 0.0768919i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.944357 + 0.142339i) q^{33} +(-4.70446 - 3.20745i) q^{34} +(-0.877202 + 1.09998i) q^{35} +(1.46032 + 2.52936i) q^{36} +(-3.53605 + 6.12463i) q^{37} +(-1.24539 - 3.17321i) q^{38} +(-1.40515 - 0.676684i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(0.772627 - 3.38510i) q^{41} +0.396319 q^{42} +(6.17285 - 2.21266i) q^{43} +3.39031 q^{44} +(-0.649906 + 2.84742i) q^{45} +(6.78807 + 2.09384i) q^{46} +(-10.2380 - 4.93037i) q^{47} +(0.102914 + 0.262220i) q^{48} +(2.51028 - 4.34794i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00002 + 1.25398i) q^{51} +(4.57450 + 3.11884i) q^{52} +(7.24312 - 1.09172i) q^{53} +(1.50264 - 0.723631i) q^{54} +(2.48527 + 2.30600i) q^{55} +(-1.39121 - 0.209691i) q^{56} +(-0.917586 + 0.283038i) q^{57} +(0.631450 + 8.42611i) q^{58} +(3.61003 + 4.52683i) q^{59} +(-0.102914 + 0.262220i) q^{60} +(6.08870 - 5.64949i) q^{61} +(-0.0934043 + 0.0636819i) q^{62} +(-0.307076 + 4.09764i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(1.23199 + 5.39772i) q^{65} +(0.0713690 - 0.952353i) q^{66} +(-10.0292 + 6.83782i) q^{67} +(4.17387 - 3.87279i) q^{68} +(0.731065 - 1.86272i) q^{69} +(-0.877202 - 1.09998i) q^{70} +(0.393492 + 5.25079i) q^{71} +(-2.79089 + 0.860877i) q^{72} +(-5.80830 - 0.875461i) q^{73} +(-5.18422 - 4.81026i) q^{74} +(-0.253796 + 0.122222i) q^{75} +(3.37078 - 0.508063i) q^{76} +(3.94108 + 2.68698i) q^{77} +(0.972393 - 1.21934i) q^{78} +(-6.81661 - 11.8067i) q^{79} +(0.500000 - 0.866025i) q^{80} +(3.02946 + 7.71894i) q^{81} +(3.12830 + 1.50651i) q^{82} +(-7.14886 - 2.20513i) q^{83} +(-0.0881893 + 0.386383i) q^{84} +5.69383 q^{85} +(0.783598 + 6.51045i) q^{86} +2.38022 q^{87} +(-0.754415 + 3.30531i) q^{88} +(8.17260 + 2.52091i) q^{89} +(-2.63141 - 1.26722i) q^{90} +(2.84581 + 7.25102i) q^{91} +(-3.55183 + 6.15196i) q^{92} +(0.0159223 + 0.0275782i) q^{93} +(7.08492 - 8.88421i) q^{94} +(2.81653 + 1.92028i) q^{95} +(-0.278546 + 0.0419840i) q^{96} +(-6.59420 + 3.17560i) q^{97} +(3.68034 + 3.41485i) q^{98} +(9.79131 + 1.47580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

L-functions

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