LMFDB - Embedded newform 78.2.i.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(43,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("78.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.43
Dual form			78.2.i.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.866025 + 1.50000i) q^{10} +(-1.09808 - 0.633975i) q^{11} +1.00000 q^{12} +(1.59808 + 3.23205i) q^{13} -1.26795 q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(-4.09808 + 2.36603i) q^{19} +(1.50000 - 0.866025i) q^{20} -1.26795i q^{21} +(0.633975 + 1.09808i) q^{22} +(-4.09808 + 7.09808i) q^{23} +(-0.866025 - 0.500000i) q^{24} +2.00000 q^{25} +(0.232051 - 3.59808i) q^{26} -1.00000 q^{27} +(1.09808 + 0.633975i) q^{28} +(1.50000 - 2.59808i) q^{29} +(0.866025 + 1.50000i) q^{30} -9.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09808 + 0.633975i) q^{33} -5.19615i q^{34} +(-1.09808 - 1.90192i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.59808 - 1.50000i) q^{37} +4.73205 q^{38} +(3.59808 + 0.232051i) q^{39} -1.73205 q^{40} +(5.59808 + 3.23205i) q^{41} +(-0.633975 + 1.09808i) q^{42} +(-2.09808 - 3.63397i) q^{43} -1.26795i q^{44} +(-1.50000 + 0.866025i) q^{45} +(7.09808 - 4.09808i) q^{46} -4.73205i q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.69615 + 4.66987i) q^{49} +(-1.73205 - 1.00000i) q^{50} +5.19615 q^{51} +(-2.00000 + 3.00000i) q^{52} +3.00000 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.09808 + 1.90192i) q^{55} +(-0.633975 - 1.09808i) q^{56} +4.73205i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-12.0000 + 6.92820i) q^{59} -1.73205i q^{60} +(-7.59808 - 13.1603i) q^{61} +(-4.73205 + 8.19615i) q^{62} +(-1.09808 - 0.633975i) q^{63} -1.00000 q^{64} +(5.59808 - 2.76795i) q^{65} +1.26795 q^{66} +(6.29423 + 3.63397i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(4.09808 + 7.09808i) q^{69} +2.19615i q^{70} +(1.90192 - 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 + 2.59808i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-4.09808 - 2.36603i) q^{76} -1.60770 q^{77} +(-3.00000 - 2.00000i) q^{78} +8.39230 q^{79} +(1.50000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.23205 - 5.59808i) q^{82} -5.66025i q^{83} +(1.09808 - 0.633975i) q^{84} +(7.79423 - 4.50000i) q^{85} +4.19615i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} +1.73205 q^{90} +(3.80385 + 2.53590i) q^{91} -8.19615 q^{92} +(-8.19615 - 4.73205i) q^{93} +(-2.36603 + 4.09808i) q^{94} +(4.09808 + 7.09808i) q^{95} -1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(4.66987 - 2.69615i) q^{98} +1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 4 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{19} + 6 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} + 6 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^12 - 4 * q^13 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 6 * q^19 + 6 * q^20 + 6 * q^22 - 6 * q^23 + 8 * q^25 - 6 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^33 + 6 * q^35 + 2 * q^36 + 12 * q^38 + 4 * q^39 + 12 * q^41 - 6 * q^42 + 2 * q^43 - 6 * q^45 + 18 * q^46 + 2 * q^48 + 10 * q^49 - 8 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 48 * q^59 - 20 * q^61 - 12 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^65 + 12 * q^66 - 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 + 4 * q^75 - 6 * q^76 - 48 * q^77 - 12 * q^78 - 8 * q^79 + 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^84 - 6 * q^87 - 6 * q^88 - 12 * q^89 + 36 * q^91 - 12 * q^92 - 12 * q^93 - 6 * q^94 + 6 * q^95 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	1.09808	−	0.633975i	0.415034	−	0.239620i	−0.277916	−	0.960605i	$-0.589644\pi$
$7$	1.09808	−	0.633975i	0.415034	−	0.239620i	0.692950	+	0.720985i	$0.256311\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.866025	+	1.50000i	−0.273861	+	0.474342i
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	0.325239	−	0.945632i	$-0.394555\pi$
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	−0.656322	+	0.754481i	$0.727889\pi$
$12$	1.00000			0.288675
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$14$	−1.26795			−0.338874
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	0.987526	+	0.157459i	$0.0503301\pi$
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	−0.357400	+	0.933952i	$0.616337\pi$
$18$			1.00000i			0.235702i
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.890011	−	0.455938i	$-0.849304\pi$
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.0501517	+	0.998742i	$0.515970\pi$
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$		−	1.26795i		−	0.276689i
$22$	0.633975	+	1.09808i	0.135164	+	0.234111i
$23$	−4.09808	+	7.09808i	−0.854508	+	1.48005i	0.0225928	+	0.999745i	$0.492808\pi$
$23$	−4.09808	+	7.09808i	−0.854508	+	1.48005i	−0.877101	+	0.480306i	$0.840525\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	2.00000			0.400000
$26$	0.232051	−	3.59808i	0.0455089	−	0.705641i
$27$	−1.00000			−0.192450
$28$	1.09808	+	0.633975i	0.207517	+	0.119810i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	0.866025	+	1.50000i	0.158114	+	0.273861i
$31$		−	9.46410i		−	1.69980i	−0.526942	−	0.849901i	$-0.676661\pi$
$31$		−	9.46410i		−	1.69980i	0.526942	−	0.849901i	$-0.323339\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.09808	+	0.633975i	−0.191151	+	0.110361i
$34$		−	5.19615i		−	0.891133i
$35$	−1.09808	−	1.90192i	−0.185609	−	0.321484i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.59808	−	1.50000i	−0.427121	−	0.246598i	0.270998	−	0.962580i	$-0.412646\pi$
$37$	−2.59808	−	1.50000i	−0.427121	−	0.246598i	−0.698119	+	0.715981i	$0.745980\pi$
$38$	4.73205			0.767640
$39$	3.59808	+	0.232051i	0.576153	+	0.0371579i
$40$	−1.73205			−0.273861
$41$	5.59808	+	3.23205i	0.874273	+	0.504762i	0.868766	−	0.495223i	$-0.164914\pi$
$41$	5.59808	+	3.23205i	0.874273	+	0.504762i	0.00550690	+	0.999985i	$0.498247\pi$
$42$	−0.633975	+	1.09808i	−0.0978244	+	0.169437i
$43$	−2.09808	−	3.63397i	−0.319954	−	0.554176i	0.660524	−	0.750805i	$-0.270334\pi$
$43$	−2.09808	−	3.63397i	−0.319954	−	0.554176i	−0.980478	+	0.196629i	$0.937001\pi$
$44$		−	1.26795i		−	0.191151i
$45$	−1.50000	+	0.866025i	−0.223607	+	0.129099i
$46$	7.09808	−	4.09808i	1.04655	−	0.604228i
$47$		−	4.73205i		−	0.690241i	−0.938558	−	0.345120i	$-0.887838\pi$
$47$		−	4.73205i		−	0.690241i	0.938558	−	0.345120i	$-0.112162\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−2.69615	+	4.66987i	−0.385165	+	0.667125i
$50$	−1.73205	−	1.00000i	−0.244949	−	0.141421i
$51$	5.19615			0.727607
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−1.09808	+	1.90192i	−0.148065	+	0.256455i
$56$	−0.633975	−	1.09808i	−0.0847184	−	0.146737i
$57$			4.73205i			0.626775i
$58$	−2.59808	+	1.50000i	−0.341144	+	0.196960i
$59$	−12.0000	+	6.92820i	−1.56227	+	0.901975i	−0.565240	+	0.824927i	$0.691216\pi$
$59$	−12.0000	+	6.92820i	−1.56227	+	0.901975i	−0.997027	+	0.0770484i	$0.975450\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−7.59808	−	13.1603i	−0.972834	−	1.68500i	−0.686905	−	0.726747i	$-0.741031\pi$
$61$	−7.59808	−	13.1603i	−0.972834	−	1.68500i	−0.285929	−	0.958251i	$-0.592302\pi$
$62$	−4.73205	+	8.19615i	−0.600971	+	1.04091i
$63$	−1.09808	−	0.633975i	−0.138345	−	0.0798733i
$64$	−1.00000			−0.125000
$65$	5.59808	−	2.76795i	0.694356	−	0.343322i
$66$	1.26795			0.156074
$67$	6.29423	+	3.63397i	0.768962	+	0.443961i	0.832504	−	0.554019i	$-0.186906\pi$
$67$	6.29423	+	3.63397i	0.768962	+	0.443961i	−0.0635419	+	0.997979i	$0.520240\pi$
$68$	−2.59808	+	4.50000i	−0.315063	+	0.545705i
$69$	4.09808	+	7.09808i	0.493350	+	0.854508i
$70$			2.19615i			0.262490i
$71$	1.90192	−	1.09808i	0.225717	−	0.130318i	−0.382878	−	0.923799i	$-0.625067\pi$
$71$	1.90192	−	1.09808i	0.225717	−	0.130318i	0.608595	+	0.793481i	$0.291734\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			12.1244i			1.41905i	0.704681	+	0.709524i	$0.251090\pi$
$73$			12.1244i			1.41905i	−0.704681	+	0.709524i	$0.748910\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	−4.09808	−	2.36603i	−0.470082	−	0.271402i
$77$	−1.60770			−0.183214
$78$	−3.00000	−	2.00000i	−0.339683	−	0.226455i
$79$	8.39230			0.944208			0.472104	−	0.881543i	$-0.343495\pi$
$79$	8.39230			0.944208			0.472104	+	0.881543i	$0.343495\pi$
$80$	1.50000	+	0.866025i	0.167705	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.23205	−	5.59808i	−0.356920	−	0.618204i
$83$		−	5.66025i		−	0.621294i	−0.950525	−	0.310647i	$-0.899454\pi$
$83$		−	5.66025i		−	0.621294i	0.950525	−	0.310647i	$-0.100546\pi$
$84$	1.09808	−	0.633975i	0.119810	−	0.0691723i
$85$	7.79423	−	4.50000i	0.845403	−	0.488094i
$86$			4.19615i			0.452483i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	−0.633975	+	1.09808i	−0.0675819	+	0.117055i
$89$	−8.19615	−	4.73205i	−0.868790	−	0.501596i	−0.00184433	−	0.999998i	$-0.500587\pi$
$89$	−8.19615	−	4.73205i	−0.868790	−	0.501596i	−0.866946	+	0.498402i	$0.833920\pi$
$90$	1.73205			0.182574
$91$	3.80385	+	2.53590i	0.398752	+	0.265834i
$92$	−8.19615			−0.854508
$93$	−8.19615	−	4.73205i	−0.849901	−	0.490691i
$94$	−2.36603	+	4.09808i	−0.244037	+	0.422684i
$95$	4.09808	+	7.09808i	0.420454	+	0.728247i
$96$		−	1.00000i		−	0.102062i
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	−0.740034	−	0.672569i	$-0.765191\pi$
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	0.212445	+	0.977173i	$0.431857\pi$
$98$	4.66987	−	2.69615i	0.471728	−	0.272353i
$99$			1.26795i			0.127434i
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	9.69615	−	16.7942i	0.964803	−	1.67109i	0.254660	−	0.967031i	$-0.418036\pi$
$101$	9.69615	−	16.7942i	0.964803	−	1.67109i	0.710143	−	0.704058i	$-0.248630\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	−6.19615			−0.610525			−0.305263	−	0.952268i	$-0.598744\pi$
$103$	−6.19615			−0.610525			−0.305263	+	0.952268i	$0.598744\pi$
$104$	3.23205	−	1.59808i	0.316929	−	0.156704i
$105$	−2.19615			−0.214323
$106$	−2.59808	−	1.50000i	−0.252347	−	0.145693i
$107$	1.09808	−	1.90192i	0.106155	−	0.183866i	−0.808054	−	0.589108i	$-0.799479\pi$
$107$	1.09808	−	1.90192i	0.106155	−	0.183866i	0.914210	+	0.405242i	$0.132813\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			4.39230i			0.420707i	0.977625	+	0.210353i	$0.0674614\pi$
$109$			4.39230i			0.420707i	−0.977625	+	0.210353i	$0.932539\pi$
$110$	1.90192	−	1.09808i	0.181341	−	0.104697i
$111$	−2.59808	+	1.50000i	−0.246598	+	0.142374i
$112$			1.26795i			0.119810i
$113$	−0.401924	−	0.696152i	−0.0378098	−	0.0654885i	0.846501	−	0.532387i	$-0.178705\pi$
$113$	−0.401924	−	0.696152i	−0.0378098	−	0.0654885i	−0.884311	+	0.466898i	$0.845371\pi$
$114$	2.36603	−	4.09808i	0.221599	−	0.383820i
$115$	12.2942	+	7.09808i	1.14644	+	0.661899i
$116$	3.00000			0.278543
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$	13.8564			1.27559
$119$	5.70577	+	3.29423i	0.523047	+	0.301981i
$120$	−0.866025	+	1.50000i	−0.0790569	+	0.136931i
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$			15.1962i			1.37579i
$123$	5.59808	−	3.23205i	0.504762	−	0.291424i
$124$	8.19615	−	4.73205i	0.736036	−	0.424951i
$125$		−	12.1244i		−	1.08444i
$126$	0.633975	+	1.09808i	0.0564789	+	0.0978244i
$127$	−2.00000	+	3.46410i	−0.177471	+	0.307389i	−0.941014	−	0.338368i	$-0.890125\pi$
$127$	−2.00000	+	3.46410i	−0.177471	+	0.307389i	0.763542	+	0.645758i	$0.223458\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.19615			−0.369451
$130$	−6.23205	−	0.401924i	−0.546587	−	0.0352510i
$131$	−4.39230			−0.383757			−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230			−0.383757			−0.191879	+	0.981419i	$0.561458\pi$
$132$	−1.09808	−	0.633975i	−0.0955753	−	0.0551804i
$133$	−3.00000	+	5.19615i	−0.260133	+	0.450564i
$134$	−3.63397	−	6.29423i	−0.313928	−	0.543739i
$135$			1.73205i			0.149071i
$136$	4.50000	−	2.59808i	0.385872	−	0.222783i
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	−0.794524	−	0.607233i	$-0.792279\pi$
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	0.128618	+	0.991694i	$0.458946\pi$
$138$		−	8.19615i		−	0.697703i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	1.09808	−	1.90192i	0.0928044	−	0.160742i
$141$	−4.09808	−	2.36603i	−0.345120	−	0.199255i
$142$	−2.19615			−0.184297
$143$	0.294229	−	4.56218i	0.0246046	−	0.381508i
$144$	1.00000			0.0833333
$145$	−4.50000	−	2.59808i	−0.373705	−	0.215758i
$146$	6.06218	−	10.5000i	0.501709	−	0.868986i
$147$	2.69615	+	4.66987i	0.222375	+	0.385165i
$148$		−	3.00000i		−	0.246598i
$149$	−5.30385	+	3.06218i	−0.434508	+	0.250863i	−0.701265	−	0.712900i	$-0.747381\pi$
$149$	−5.30385	+	3.06218i	−0.434508	+	0.250863i	0.266757	+	0.963764i	$0.414048\pi$
$150$	−1.73205	+	1.00000i	−0.141421	+	0.0816497i
$151$			10.7321i			0.873362i	0.899616	+	0.436681i	$0.143846\pi$
$151$			10.7321i			0.873362i	−0.899616	+	0.436681i	$0.856154\pi$
$152$	2.36603	+	4.09808i	0.191910	+	0.332398i
$153$	2.59808	−	4.50000i	0.210042	−	0.363803i
$154$	1.39230	+	0.803848i	0.112195	+	0.0647759i
$155$	−16.3923			−1.31666
$156$	1.59808	+	3.23205i	0.127948	+	0.258771i
$157$	7.19615			0.574315			0.287158	−	0.957883i	$-0.407290\pi$
$157$	7.19615			0.574315			0.287158	+	0.957883i	$0.407290\pi$
$158$	−7.26795	−	4.19615i	−0.578207	−	0.333828i
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$	−0.866025	−	1.50000i	−0.0684653	−	0.118585i
$161$			10.3923i			0.819028i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	2.19615	−	1.26795i	0.172016	−	0.0993134i	−0.411520	−	0.911401i	$-0.635002\pi$
$163$	2.19615	−	1.26795i	0.172016	−	0.0993134i	0.583536	+	0.812087i	$0.301669\pi$
$164$			6.46410i			0.504762i
$165$	1.09808	+	1.90192i	0.0854851	+	0.148065i
$166$	−2.83013	+	4.90192i	−0.219660	+	0.380463i
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	0.782391	−	0.622787i	$-0.214000\pi$
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	−0.148154	+	0.988964i	$0.547333\pi$
$168$	−1.26795			−0.0978244
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$	−9.00000			−0.690268
$171$	4.09808	+	2.36603i	0.313388	+	0.180934i
$172$	2.09808	−	3.63397i	0.159977	−	0.277088i
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	0.770383	−	0.637582i	$-0.220065\pi$
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	−0.937353	+	0.348380i	$0.886732\pi$
$174$			3.00000i			0.227429i
$175$	2.19615	−	1.26795i	0.166014	−	0.0958479i
$176$	1.09808	−	0.633975i	0.0827706	−	0.0477876i
$177$			13.8564i			1.04151i
$178$	4.73205	+	8.19615i	0.354682	+	0.614328i
$179$	1.09808	−	1.90192i	0.0820741	−	0.142156i	−0.822067	−	0.569391i	$-0.807179\pi$
$179$	1.09808	−	1.90192i	0.0820741	−	0.142156i	0.904141	+	0.427235i	$0.140512\pi$
$180$	−1.50000	−	0.866025i	−0.111803	−	0.0645497i
$181$	−19.5885			−1.45600			−0.727999	−	0.685578i	$-0.759550\pi$
$181$	−19.5885			−1.45600			−0.727999	+	0.685578i	$0.759550\pi$
$182$	−2.02628	−	4.09808i	−0.150198	−	0.303770i
$183$	−15.1962			−1.12333
$184$	7.09808	+	4.09808i	0.523277	+	0.302114i
$185$	−2.59808	+	4.50000i	−0.191014	+	0.330847i
$186$	4.73205	+	8.19615i	0.346971	+	0.600971i
$187$		−	6.58846i		−	0.481796i
$188$	4.09808	−	2.36603i	0.298883	−	0.172560i
$189$	−1.09808	+	0.633975i	−0.0798733	+	0.0461149i
$190$		−	8.19615i		−	0.594611i
$191$	10.3923	+	18.0000i	0.751961	+	1.30243i	0.946871	+	0.321613i	$0.104225\pi$
$191$	10.3923	+	18.0000i	0.751961	+	1.30243i	−0.194910	+	0.980821i	$0.562442\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	20.0885	+	11.5981i	1.44600	+	0.834848i	0.998240	−	0.0593065i	$-0.0188889\pi$
$193$	20.0885	+	11.5981i	1.44600	+	0.834848i	0.447759	+	0.894154i	$0.352222\pi$
$194$	6.00000			0.430775
$195$	0.401924	−	6.23205i	0.0287824	−	0.446286i
$196$	−5.39230			−0.385165
$197$	−6.00000	−	3.46410i	−0.427482	−	0.246807i	0.270791	−	0.962638i	$-0.412715\pi$
$197$	−6.00000	−	3.46410i	−0.427482	−	0.246807i	−0.698273	+	0.715831i	$0.746048\pi$
$198$	0.633975	−	1.09808i	0.0450546	−	0.0780369i
$199$	−11.2942	−	19.5622i	−0.800627	−	1.38673i	−0.919204	−	0.393781i	$-0.871167\pi$
$199$	−11.2942	−	19.5622i	−0.800627	−	1.38673i	0.118578	−	0.992945i	$-0.462167\pi$
$200$		−	2.00000i		−	0.141421i
$201$	6.29423	−	3.63397i	0.443961	−	0.256321i
$202$	−16.7942	+	9.69615i	−1.18164	+	0.682219i
$203$		−	3.80385i		−	0.266978i
$204$	2.59808	+	4.50000i	0.181902	+	0.315063i
$205$	5.59808	−	9.69615i	0.390987	−	0.677209i
$206$	5.36603	+	3.09808i	0.373869	+	0.215853i
$207$	8.19615			0.569672
$208$	−3.59808	−	0.232051i	−0.249482	−	0.0160898i
$209$	6.00000			0.415029
$210$	1.90192	+	1.09808i	0.131245	+	0.0757745i
$211$	12.1962	−	21.1244i	0.839618	−	1.45426i	−0.0505968	−	0.998719i	$-0.516112\pi$
$211$	12.1962	−	21.1244i	0.839618	−	1.45426i	0.890215	−	0.455541i	$-0.150554\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$		−	2.19615i		−	0.150478i
$214$	−1.90192	+	1.09808i	−0.130013	+	0.0750629i
$215$	−6.29423	+	3.63397i	−0.429263	+	0.247835i
$216$			1.00000i			0.0680414i
$217$	−6.00000	−	10.3923i	−0.407307	−	0.705476i
$218$	2.19615	−	3.80385i	0.148742	−	0.257629i
$219$	10.5000	+	6.06218i	0.709524	+	0.409644i
$220$	−2.19615			−0.148065
$221$	−10.3923	+	15.5885i	−0.699062	+	1.04859i
$222$	3.00000			0.201347
$223$	−4.39230	−	2.53590i	−0.294130	−	0.169816i	0.345673	−	0.938355i	$-0.387651\pi$
$223$	−4.39230	−	2.53590i	−0.294130	−	0.169816i	−0.639803	+	0.768539i	$0.720984\pi$
$224$	0.633975	−	1.09808i	0.0423592	−	0.0733683i
$225$	−1.00000	−	1.73205i	−0.0666667	−	0.115470i
$226$			0.803848i			0.0534711i
$227$	17.4904	−	10.0981i	1.16088	−	0.670233i	0.209363	−	0.977838i	$-0.432861\pi$
$227$	17.4904	−	10.0981i	1.16088	−	0.670233i	0.951514	+	0.307605i	$0.0995276\pi$
$228$	−4.09808	+	2.36603i	−0.271402	+	0.156694i
$229$		−	7.85641i		−	0.519166i	−0.965721	−	0.259583i	$-0.916415\pi$
$229$		−	7.85641i		−	0.519166i	0.965721	−	0.259583i	$-0.0835851\pi$
$230$	−7.09808	−	12.2942i	−0.468033	−	0.810657i
$231$	−0.803848	+	1.39230i	−0.0528893	+	0.0916069i
$232$	−2.59808	−	1.50000i	−0.170572	−	0.0984798i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	−3.23205	+	1.59808i	−0.211286	+	0.104470i
$235$	−8.19615			−0.534658
$236$	−12.0000	−	6.92820i	−0.781133	−	0.450988i
$237$	4.19615	−	7.26795i	0.272569	−	0.472104i
$238$	−3.29423	−	5.70577i	−0.213533	−	0.369850i
$239$		−	6.58846i		−	0.426172i	−0.977033	−	0.213086i	$-0.931649\pi$
$239$		−	6.58846i		−	0.426172i	0.977033	−	0.213086i	$-0.0683514\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	9.69615	−	5.59808i	0.624584	−	0.360604i	−0.154068	−	0.988060i	$-0.549237\pi$
$241$	9.69615	−	5.59808i	0.624584	−	0.360604i	0.778652	+	0.627457i	$0.215904\pi$
$242$			9.39230i			0.603760i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	7.59808	−	13.1603i	0.486417	−	0.842499i
$245$	8.08846	+	4.66987i	0.516753	+	0.298347i
$246$	−6.46410			−0.412136
$247$	−14.1962	−	9.46410i	−0.903280	−	0.602186i
$248$	−9.46410			−0.600971
$249$	−4.90192	−	2.83013i	−0.310647	−	0.179352i
$250$	−6.06218	+	10.5000i	−0.383406	+	0.664078i
$251$	8.19615	+	14.1962i	0.517337	+	0.896053i	0.999797	+	0.0201356i	$0.00640979\pi$
$251$	8.19615	+	14.1962i	0.517337	+	0.896053i	−0.482461	+	0.875918i	$0.660257\pi$
$252$		−	1.26795i		−	0.0798733i
$253$	9.00000	−	5.19615i	0.565825	−	0.326679i
$254$	3.46410	−	2.00000i	0.217357	−	0.125491i
$255$		−	9.00000i		−	0.563602i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.5981	−	20.0885i	0.723468	−	1.25308i	−0.236133	−	0.971721i	$-0.575880\pi$
$257$	11.5981	−	20.0885i	0.723468	−	1.25308i	0.959601	−	0.281363i	$-0.0907865\pi$
$258$	3.63397	+	2.09808i	0.226241	+	0.130621i
$259$	−3.80385			−0.236360
$260$	5.19615	+	3.46410i	0.322252	+	0.214834i
$261$	−3.00000			−0.185695
$262$	3.80385	+	2.19615i	0.235002	+	0.135679i
$263$	−4.09808	+	7.09808i	−0.252698	+	0.437686i	−0.964268	−	0.264930i	$-0.914651\pi$
$263$	−4.09808	+	7.09808i	−0.252698	+	0.437686i	0.711570	+	0.702616i	$0.247985\pi$
$264$	0.633975	+	1.09808i	0.0390184	+	0.0675819i
$265$		−	5.19615i		−	0.319197i
$266$	5.19615	−	3.00000i	0.318597	−	0.183942i
$267$	−8.19615	+	4.73205i	−0.501596	+	0.289597i
$268$			7.26795i			0.443961i
$269$	3.80385	+	6.58846i	0.231925	+	0.401705i	0.958374	−	0.285514i	$-0.0921644\pi$
$269$	3.80385	+	6.58846i	0.231925	+	0.401705i	−0.726450	+	0.687220i	$0.758831\pi$
$270$	0.866025	−	1.50000i	0.0527046	−	0.0912871i
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$	−5.19615			−0.315063
$273$	4.09808	−	2.02628i	0.248027	−	0.122636i
$274$	9.00000			0.543710
$275$	−2.19615	−	1.26795i	−0.132433	−	0.0764602i
$276$	−4.09808	+	7.09808i	−0.246675	+	0.427254i
$277$	2.40192	+	4.16025i	0.144318	+	0.249965i	0.929118	−	0.369783i	$-0.120568\pi$
$277$	2.40192	+	4.16025i	0.144318	+	0.249965i	−0.784801	+	0.619748i	$0.787235\pi$
$278$		−	4.00000i		−	0.239904i
$279$	−8.19615	+	4.73205i	−0.490691	+	0.283300i
$280$	−1.90192	+	1.09808i	−0.113662	+	0.0656226i
$281$			17.5359i			1.04610i	0.852301	+	0.523052i	$0.175207\pi$
$281$			17.5359i			1.04610i	−0.852301	+	0.523052i	$0.824793\pi$
$282$	2.36603	+	4.09808i	0.140895	+	0.244037i
$283$	−9.90192	+	17.1506i	−0.588608	+	1.01950i	0.405807	+	0.913959i	$0.366991\pi$
$283$	−9.90192	+	17.1506i	−0.588608	+	1.01950i	−0.994415	+	0.105541i	$0.966343\pi$
$284$	1.90192	+	1.09808i	0.112858	+	0.0651588i
$285$	8.19615			0.485498
$286$	−2.53590	+	3.80385i	−0.149951	+	0.224926i
$287$	8.19615			0.483804
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	2.59808	+	4.50000i	0.152564	+	0.264249i
$291$			6.00000i			0.351726i
$292$	−10.5000	+	6.06218i	−0.614466	+	0.354762i
$293$	2.30385	−	1.33013i	0.134592	−	0.0777069i	−0.431192	−	0.902260i	$-0.641907\pi$
$293$	2.30385	−	1.33013i	0.134592	−	0.0777069i	0.565784	+	0.824553i	$0.308574\pi$
$294$		−	5.39230i		−	0.314486i
$295$	12.0000	+	20.7846i	0.698667	+	1.21013i
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$	1.09808	+	0.633975i	0.0637168	+	0.0367869i
$298$	6.12436			0.354774
$299$	−29.4904	−	1.90192i	−1.70547	−	0.109991i
$300$	2.00000			0.115470
$301$	−4.60770	−	2.66025i	−0.265583	−	0.153334i
$302$	5.36603	−	9.29423i	0.308780	−	0.534823i
$303$	−9.69615	−	16.7942i	−0.557029	−	0.964803i
$304$		−	4.73205i		−	0.271402i
$305$	−22.7942	+	13.1603i	−1.30519	+	0.753554i
$306$	−4.50000	+	2.59808i	−0.257248	+	0.148522i
$307$			7.26795i			0.414804i	0.978256	+	0.207402i	$0.0665008\pi$
$307$			7.26795i			0.414804i	−0.978256	+	0.207402i	$0.933499\pi$
$308$	−0.803848	−	1.39230i	−0.0458035	−	0.0793339i
$309$	−3.09808	+	5.36603i	−0.176243	+	0.305263i
$310$	14.1962	+	8.19615i	0.806287	+	0.465510i
$311$	8.19615			0.464761			0.232381	−	0.972625i	$-0.425349\pi$
$311$	8.19615			0.464761			0.232381	+	0.972625i	$0.425349\pi$
$312$	0.232051	−	3.59808i	0.0131373	−	0.203701i
$313$	−3.60770			−0.203919			−0.101959	−	0.994789i	$-0.532511\pi$
$313$	−3.60770			−0.203919			−0.101959	+	0.994789i	$0.532511\pi$
$314$	−6.23205	−	3.59808i	−0.351695	−	0.203051i
$315$	−1.09808	+	1.90192i	−0.0618696	+	0.107161i
$316$	4.19615	+	7.26795i	0.236052	+	0.408854i
$317$			18.1244i			1.01797i	0.860777	+	0.508983i	$0.169978\pi$
$317$			18.1244i			1.01797i	−0.860777	+	0.508983i	$0.830022\pi$
$318$	−2.59808	+	1.50000i	−0.145693	+	0.0841158i
$319$	−3.29423	+	1.90192i	−0.184441	+	0.106487i
$320$			1.73205i			0.0968246i
$321$	−1.09808	−	1.90192i	−0.0612886	−	0.106155i
$322$	5.19615	−	9.00000i	0.289570	−	0.501550i
$323$	−21.2942	−	12.2942i	−1.18484	−	0.684069i
$324$	−1.00000			−0.0555556
$325$	3.19615	+	6.46410i	0.177291	+	0.358564i
$326$	−2.53590			−0.140450
$327$	3.80385	+	2.19615i	0.210353	+	0.121448i
$328$	3.23205	−	5.59808i	0.178460	−	0.309102i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		−	2.19615i		−	0.120894i
$331$	−10.3923	+	6.00000i	−0.571213	+	0.329790i	−0.757634	−	0.652680i	$-0.773645\pi$
$331$	−10.3923	+	6.00000i	−0.571213	+	0.329790i	0.186421	+	0.982470i	$0.440311\pi$
$332$	4.90192	−	2.83013i	0.269028	−	0.155323i
$333$			3.00000i			0.164399i
$334$	−4.73205	−	8.19615i	−0.258926	−	0.448474i
$335$	6.29423	−	10.9019i	0.343890	−	0.595636i
$336$	1.09808	+	0.633975i	0.0599050	+	0.0345861i
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$	−0.803848			−0.0436590
$340$	7.79423	+	4.50000i	0.422701	+	0.244047i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$	−2.36603	−	4.09808i	−0.127940	−	0.221599i
$343$			15.7128i			0.848412i
$344$	−3.63397	+	2.09808i	−0.195931	+	0.113121i
$345$	12.2942	−	7.09808i	0.661899	−	0.382148i
$346$			4.39230i			0.236132i
$347$	−9.29423	−	16.0981i	−0.498940	−	0.864190i	0.501059	−	0.865413i	$-0.332944\pi$
$347$	−9.29423	−	16.0981i	−0.498940	−	0.864190i	−0.999999	+	0.00122316i	$0.999611\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	−8.19615	−	4.73205i	−0.438730	−	0.253301i	0.264329	−	0.964433i	$-0.414850\pi$
$349$	−8.19615	−	4.73205i	−0.438730	−	0.253301i	−0.703059	+	0.711132i	$0.748183\pi$
$350$	−2.53590			−0.135549
$351$	−1.59808	−	3.23205i	−0.0852990	−	0.172514i
$352$	−1.26795			−0.0675819
$353$	−30.9904	−	17.8923i	−1.64945	−	0.952311i	−0.977290	−	0.211907i	$-0.932033\pi$
$353$	−30.9904	−	17.8923i	−1.64945	−	0.952311i	−0.672162	−	0.740404i	$-0.734634\pi$
$354$	6.92820	−	12.0000i	0.368230	−	0.637793i
$355$	−1.90192	−	3.29423i	−0.100944	−	0.174840i
$356$		−	9.46410i		−	0.501596i
$357$	5.70577	−	3.29423i	0.301981	−	0.174349i
$358$	−1.90192	+	1.09808i	−0.100520	+	0.0580351i
$359$		−	16.0526i		−	0.847222i	−0.905844	−	0.423611i	$-0.860762\pi$
$359$		−	16.0526i		−	0.847222i	0.905844	−	0.423611i	$-0.139238\pi$
$360$	0.866025	+	1.50000i	0.0456435	+	0.0790569i
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	16.9641	+	9.79423i	0.891613	+	0.514773i
$363$	−9.39230			−0.492968
$364$	−0.294229	+	4.56218i	−0.0154218	+	0.239123i
$365$	21.0000			1.09919
$366$	13.1603	+	7.59808i	0.687897	+	0.397158i
$367$	6.90192	−	11.9545i	0.360277	−	0.624019i	−0.627729	−	0.778432i	$-0.716015\pi$
$367$	6.90192	−	11.9545i	0.360277	−	0.624019i	0.988006	+	0.154413i	$0.0493487\pi$
$368$	−4.09808	−	7.09808i	−0.213627	−	0.370013i
$369$		−	6.46410i		−	0.336508i
$370$	4.50000	−	2.59808i	0.233944	−	0.135068i
$371$	3.29423	−	1.90192i	0.171028	−	0.0987430i
$372$		−	9.46410i		−	0.490691i
$373$	13.9904	+	24.2321i	0.724394	+	1.25469i	0.959223	+	0.282651i	$0.0912139\pi$
$373$	13.9904	+	24.2321i	0.724394	+	1.25469i	−0.234828	+	0.972037i	$0.575453\pi$
$374$	−3.29423	+	5.70577i	−0.170341	+	0.295038i
$375$	−10.5000	−	6.06218i	−0.542218	−	0.313050i
$376$	−4.73205			−0.244037
$377$	10.7942	+	0.696152i	0.555931	+	0.0358537i
$378$	1.26795			0.0652163
$379$	26.1962	+	15.1244i	1.34561	+	0.776886i	0.987624	−	0.156842i	$-0.0501315\pi$
$379$	26.1962	+	15.1244i	1.34561	+	0.776886i	0.357982	+	0.933728i	$0.383465\pi$
$380$	−4.09808	+	7.09808i	−0.210227	+	0.364124i
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$		−	20.7846i		−	1.06343i
$383$	20.1962	−	11.6603i	1.03198	−	0.595811i	0.114425	−	0.993432i	$-0.463497\pi$
$383$	20.1962	−	11.6603i	1.03198	−	0.595811i	0.917550	+	0.397621i	$0.130164\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$			2.78461i			0.141917i
$386$	−11.5981	−	20.0885i	−0.590327	−	1.02248i
$387$	−2.09808	+	3.63397i	−0.106651	+	0.184725i
$388$	−5.19615	−	3.00000i	−0.263795	−	0.152302i
$389$	−7.39230			−0.374805			−0.187402	−	0.982283i	$-0.560007\pi$
$389$	−7.39230			−0.374805			−0.187402	+	0.982283i	$0.560007\pi$
$390$	−3.46410	+	5.19615i	−0.175412	+	0.263117i
$391$	−42.5885			−2.15379
$392$	4.66987	+	2.69615i	0.235864	+	0.136176i
$393$	−2.19615	+	3.80385i	−0.110781	+	0.191879i
$394$	3.46410	+	6.00000i	0.174519	+	0.302276i
$395$		−	14.5359i		−	0.731380i
$396$	−1.09808	+	0.633975i	−0.0551804	+	0.0318584i
$397$	3.80385	−	2.19615i	0.190910	−	0.110222i	−0.401499	−	0.915860i	$-0.631511\pi$
$397$	3.80385	−	2.19615i	0.190910	−	0.110222i	0.592408	+	0.805638i	$0.298177\pi$
$398$			22.5885i			1.13226i
$399$	3.00000	+	5.19615i	0.150188	+	0.260133i
$400$	−1.00000	+	1.73205i	−0.0500000	+	0.0866025i
$401$	−18.1865	−	10.5000i	−0.908192	−	0.524345i	−0.0283431	−	0.999598i	$-0.509023\pi$
$401$	−18.1865	−	10.5000i	−0.908192	−	0.524345i	−0.879849	+	0.475253i	$0.842356\pi$
$402$	−7.26795			−0.362492
$403$	30.5885	−	15.1244i	1.52372	−	0.753398i
$404$	19.3923			0.964803
$405$	1.50000	+	0.866025i	0.0745356	+	0.0430331i
$406$	−1.90192	+	3.29423i	−0.0943909	+	0.163490i
$407$	1.90192	+	3.29423i	0.0942749	+	0.163289i
$408$		−	5.19615i		−	0.257248i
$409$	17.8923	−	10.3301i	0.884718	−	0.510792i	0.0125066	−	0.999922i	$-0.496019\pi$
$409$	17.8923	−	10.3301i	0.884718	−	0.510792i	0.872211	+	0.489130i	$0.162686\pi$
$410$	−9.69615	+	5.59808i	−0.478859	+	0.276469i
$411$			9.00000i			0.443937i
$412$	−3.09808	−	5.36603i	−0.152631	−	0.264365i
$413$	−8.78461	+	15.2154i	−0.432262	+	0.748700i
$414$	−7.09808	−	4.09808i	−0.348851	−	0.201409i
$415$	−9.80385			−0.481252
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$	4.00000			0.195881
$418$	−5.19615	−	3.00000i	−0.254152	−	0.146735i
$419$	2.19615	−	3.80385i	0.107289	−	0.185830i	−0.807382	−	0.590029i	$-0.799116\pi$
$419$	2.19615	−	3.80385i	0.107289	−	0.185830i	0.914671	+	0.404199i	$0.132450\pi$
$420$	−1.09808	−	1.90192i	−0.0535806	−	0.0928044i
$421$			6.46410i			0.315041i	0.987516	+	0.157521i	$0.0503500\pi$
$421$			6.46410i			0.315041i	−0.987516	+	0.157521i	$0.949650\pi$
$422$	−21.1244	+	12.1962i	−1.02832	+	0.593699i
$423$	−4.09808	+	2.36603i	−0.199255	+	0.115040i
$424$		−	3.00000i		−	0.145693i
$425$	5.19615	+	9.00000i	0.252050	+	0.436564i
$426$	−1.09808	+	1.90192i	−0.0532020	+	0.0921485i
$427$	−16.6865	−	9.63397i	−0.807518	−	0.466221i
$428$	2.19615			0.106155
$429$	−3.80385	−	2.53590i	−0.183651	−	0.122434i
$430$	7.26795			0.350492
$431$	33.0788	+	19.0981i	1.59335	+	0.919922i	0.992727	+	0.120391i	$0.0384149\pi$
$431$	33.0788	+	19.0981i	1.59335	+	0.919922i	0.600625	+	0.799531i	$0.294918\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	3.89230	+	6.74167i	0.187052	+	0.323984i	0.944266	−	0.329183i	$-0.106773\pi$
$433$	3.89230	+	6.74167i	0.187052	+	0.323984i	−0.757214	+	0.653167i	$0.773440\pi$
$434$			12.0000i			0.576018i
$435$	−4.50000	+	2.59808i	−0.215758	+	0.124568i
$436$	−3.80385	+	2.19615i	−0.182171	+	0.105177i
$437$		−	38.7846i		−	1.85532i
$438$	−6.06218	−	10.5000i	−0.289662	−	0.501709i
$439$	−7.29423	+	12.6340i	−0.348135	+	0.602987i	−0.985918	−	0.167229i	$-0.946518\pi$
$439$	−7.29423	+	12.6340i	−0.348135	+	0.602987i	0.637784	+	0.770216i	$0.279851\pi$
$440$	1.90192	+	1.09808i	0.0906707	+	0.0523487i
$441$	5.39230			0.256776
$442$	16.7942	−	8.30385i	0.798820	−	0.394974i
$443$	16.3923			0.778822			0.389411	−	0.921064i	$-0.372679\pi$
$443$	16.3923			0.778822			0.389411	+	0.921064i	$0.372679\pi$
$444$	−2.59808	−	1.50000i	−0.123299	−	0.0711868i
$445$	−8.19615	+	14.1962i	−0.388535	+	0.672962i
$446$	2.53590	+	4.39230i	0.120078	+	0.207982i
$447$			6.12436i			0.289672i
$448$	−1.09808	+	0.633975i	−0.0518792	+	0.0299525i
$449$	22.9808	−	13.2679i	1.08453	−	0.626153i	0.152415	−	0.988317i	$-0.451295\pi$
$449$	22.9808	−	13.2679i	1.08453	−	0.626153i	0.932115	+	0.362163i	$0.117962\pi$
$450$			2.00000i			0.0942809i
$451$	−4.09808	−	7.09808i	−0.192971	−	0.334235i
$452$	0.401924	−	0.696152i	0.0189049	−	0.0327443i
$453$	9.29423	+	5.36603i	0.436681	+	0.252118i
$454$	−20.1962			−0.947852
$455$	4.39230	−	6.58846i	0.205914	−	0.308872i
$456$	4.73205			0.221599
$457$	−27.6962	−	15.9904i	−1.29557	−	0.747998i	−0.315935	−	0.948781i	$-0.602318\pi$
$457$	−27.6962	−	15.9904i	−1.29557	−	0.747998i	−0.979636	+	0.200782i	$0.935652\pi$
$458$	−3.92820	+	6.80385i	−0.183553	+	0.317923i
$459$	−2.59808	−	4.50000i	−0.121268	−	0.210042i
$460$			14.1962i			0.661899i
$461$	−27.6962	+	15.9904i	−1.28994	+	0.744746i	−0.978643	−	0.205567i	$-0.934096\pi$
$461$	−27.6962	+	15.9904i	−1.28994	+	0.744746i	−0.311295	+	0.950313i	$0.600763\pi$
$462$	1.39230	−	0.803848i	0.0647759	−	0.0373984i
$463$		−	15.8038i		−	0.734467i	−0.930129	−	0.367234i	$-0.880305\pi$
$463$		−	15.8038i		−	0.734467i	0.930129	−	0.367234i	$-0.119695\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	−8.19615	+	14.1962i	−0.380087	+	0.658331i
$466$	−15.5885	−	9.00000i	−0.722121	−	0.416917i
$467$	−5.41154			−0.250416			−0.125208	−	0.992130i	$-0.539960\pi$
$467$	−5.41154			−0.250416			−0.125208	+	0.992130i	$0.539960\pi$
$468$	3.59808	+	0.232051i	0.166321	+	0.0107266i
$469$	9.21539			0.425527
$470$	7.09808	+	4.09808i	0.327410	+	0.189030i
$471$	3.59808	−	6.23205i	0.165791	−	0.287158i
$472$	6.92820	+	12.0000i	0.318896	+	0.552345i
$473$			5.32051i			0.244637i
$474$	−7.26795	+	4.19615i	−0.333828	+	0.192736i
$475$	−8.19615	+	4.73205i	−0.376065	+	0.217121i
$476$			6.58846i			0.301981i
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	−3.29423	+	5.70577i	−0.150675	+	0.260976i
$479$	0.588457	+	0.339746i	0.0268873	+	0.0155234i	0.513383	−	0.858159i	$-0.328392\pi$
$479$	0.588457	+	0.339746i	0.0268873	+	0.0155234i	−0.486496	+	0.873683i	$0.661725\pi$
$480$	−1.73205			−0.0790569
$481$	0.696152	−	10.7942i	0.0317418	−	0.492174i
$482$	−11.1962			−0.509971
$483$	9.00000	+	5.19615i	0.409514	+	0.236433i
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	5.19615	+	9.00000i	0.235945	+	0.408669i
$486$		−	1.00000i		−	0.0453609i
$487$	13.0981	−	7.56218i	0.593530	−	0.342675i	−0.172962	−	0.984929i	$-0.555334\pi$
$487$	13.0981	−	7.56218i	0.593530	−	0.342675i	0.766492	+	0.642254i	$0.222000\pi$
$488$	−13.1603	+	7.59808i	−0.595737	+	0.343949i
$489$		−	2.53590i		−	0.114677i
$490$	−4.66987	−	8.08846i	−0.210963	−	0.365399i
$491$	−15.2942	+	26.4904i	−0.690219	+	1.19549i	0.281547	+	0.959547i	$0.409152\pi$
$491$	−15.2942	+	26.4904i	−0.690219	+	1.19549i	−0.971766	+	0.235947i	$0.924181\pi$
$492$	5.59808	+	3.23205i	0.252381	+	0.145712i
$493$	15.5885			0.702069
$494$	7.56218	+	15.2942i	0.340238	+	0.688120i
$495$	2.19615			0.0987097
$496$	8.19615	+	4.73205i	0.368018	+	0.212475i
$497$	1.39230	−	2.41154i	0.0624534	−	0.108172i
$498$	2.83013	+	4.90192i	0.126821	+	0.219660i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	10.5000	−	6.06218i	0.469574	−	0.271109i
$501$	8.19615	−	4.73205i	0.366177	−	0.211412i
$502$		−	16.3923i		−	0.731624i
$503$	−6.29423	−	10.9019i	−0.280646	−	0.486093i	0.690898	−	0.722952i	$-0.257215\pi$
$503$	−6.29423	−	10.9019i	−0.280646	−	0.486093i	−0.971544	+	0.236859i	$0.923882\pi$
$504$	−0.633975	+	1.09808i	−0.0282395	+	0.0489122i
$505$	−29.0885	−	16.7942i	−1.29442	−	0.747333i
$506$	−10.3923			−0.461994
$507$	5.00000	+	12.0000i	0.222058	+	0.532939i
$508$	−4.00000			−0.177471
$509$	23.0885	+	13.3301i	1.02338	+	0.590847i	0.915081	−	0.403271i	$-0.132127\pi$
$509$	23.0885	+	13.3301i	1.02338	+	0.590847i	0.108297	+	0.994119i	$0.465460\pi$
$510$	−4.50000	+	7.79423i	−0.199263	+	0.345134i
$511$	7.68653	+	13.3135i	0.340032	+	0.588953i
$512$			1.00000i			0.0441942i
$513$	4.09808	−	2.36603i	0.180934	−	0.104463i
$514$	−20.0885	+	11.5981i	−0.886064	+	0.511569i
$515$			10.7321i			0.472911i
$516$	−2.09808	−	3.63397i	−0.0923627	−	0.159977i
$517$	−3.00000	+	5.19615i	−0.131940	+	0.228527i
$518$	3.29423	+	1.90192i	0.144740	+	0.0835657i
$519$	−4.39230			−0.192801
$520$	−2.76795	−	5.59808i	−0.121383	−	0.245492i
$521$	−29.1962			−1.27911			−0.639553	−	0.768747i	$-0.720881\pi$
$521$	−29.1962			−1.27911			−0.639553	+	0.768747i	$0.720881\pi$
$522$	2.59808	+	1.50000i	0.113715	+	0.0656532i
$523$	−16.2942	+	28.2224i	−0.712497	+	1.23408i	0.251420	+	0.967878i	$0.419102\pi$
$523$	−16.2942	+	28.2224i	−0.712497	+	1.23408i	−0.963917	+	0.266203i	$0.914231\pi$
$524$	−2.19615	−	3.80385i	−0.0959394	−	0.166172i
$525$		−	2.53590i		−	0.110676i
$526$	7.09808	−	4.09808i	0.309491	−	0.178685i
$527$	42.5885	−	24.5885i	1.85518	−	1.07109i
$528$		−	1.26795i		−	0.0551804i
$529$	−22.0885	−	38.2583i	−0.960368	−	1.66341i
$530$	−2.59808	+	4.50000i	−0.112853	+	0.195468i
$531$	12.0000	+	6.92820i	0.520756	+	0.300658i
$532$	−6.00000			−0.260133
$533$	−1.50000	+	23.2583i	−0.0649722	+	1.00743i
$534$	9.46410			0.409552
$535$	−3.29423	−	1.90192i	−0.142422	−	0.0822273i
$536$	3.63397	−	6.29423i	0.156964	−	0.271869i
$537$	−1.09808	−	1.90192i	−0.0473855	−	0.0820741i
$538$		−	7.60770i		−	0.327991i
$539$	5.92116	−	3.41858i	0.255042	−	0.147249i
$540$	−1.50000	+	0.866025i	−0.0645497	+	0.0372678i
$541$		−	10.8564i		−	0.466753i	−0.972386	−	0.233377i	$-0.925022\pi$
$541$		−	10.8564i		−	0.466753i	0.972386	−	0.233377i	$-0.0749775\pi$
$542$		0			0
$543$	−9.79423	+	16.9641i	−0.420311	+	0.727999i
$544$	4.50000	+	2.59808i	0.192936	+	0.111392i
$545$	7.60770			0.325878
$546$	−4.56218	−	0.294229i	−0.195243	−	0.0125918i
$547$	4.19615			0.179415			0.0897073	−	0.995968i	$-0.471407\pi$
$547$	4.19615			0.179415			0.0897073	+	0.995968i	$0.471407\pi$
$548$	−7.79423	−	4.50000i	−0.332953	−	0.192230i
$549$	−7.59808	+	13.1603i	−0.324278	+	0.561666i
$550$	1.26795	+	2.19615i	0.0540655	+	0.0936443i
$551$			14.1962i			0.604776i
$552$	7.09808	−	4.09808i	0.302114	−	0.174426i
$553$	9.21539	−	5.32051i	0.391878	−	0.226251i
$554$		−	4.80385i		−	0.204096i
$555$	2.59808	+	4.50000i	0.110282	+	0.191014i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−22.2846	−	12.8660i	−0.944229	−	0.545151i	−0.0529457	−	0.998597i	$-0.516861\pi$
$557$	−22.2846	−	12.8660i	−0.944229	−	0.545151i	−0.891284	+	0.453446i	$0.850194\pi$
$558$	9.46410			0.400647
$559$	8.39230	−	12.5885i	0.354957	−	0.532435i
$560$	2.19615			0.0928044
$561$	−5.70577	−	3.29423i	−0.240898	−	0.139082i
$562$	8.76795	−	15.1865i	0.369854	−	0.640605i
$563$	−16.3923	−	28.3923i	−0.690853	−	1.19659i	−0.971559	−	0.236799i	$-0.923902\pi$
$563$	−16.3923	−	28.3923i	−0.690853	−	1.19659i	0.280705	−	0.959794i	$-0.409432\pi$
$564$		−	4.73205i		−	0.199255i
$565$	−1.20577	+	0.696152i	−0.0507272	+	0.0292874i
$566$	17.1506	−	9.90192i	0.720895	−	0.416209i
$567$			1.26795i			0.0532489i
$568$	−1.09808	−	1.90192i	−0.0460743	−	0.0798029i
$569$	4.39230	−	7.60770i	0.184135	−	0.318931i	−0.759150	−	0.650916i	$-0.774385\pi$
$569$	4.39230	−	7.60770i	0.184135	−	0.318931i	0.943285	+	0.331985i	$0.107718\pi$
$570$	−7.09808	−	4.09808i	−0.297306	−	0.171650i
$571$	24.1962			1.01258			0.506289	−	0.862364i	$-0.331017\pi$
$571$	24.1962			1.01258			0.506289	+	0.862364i	$0.331017\pi$
$572$	4.09808	−	2.02628i	0.171349	−	0.0847230i
$573$	20.7846			0.868290
$574$	−7.09808	−	4.09808i	−0.296268	−	0.171050i
$575$	−8.19615	+	14.1962i	−0.341803	+	0.592020i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			19.7321i			0.821456i	0.911758	+	0.410728i	$0.134725\pi$
$577$			19.7321i			0.821456i	−0.911758	+	0.410728i	$0.865275\pi$
$578$	8.66025	−	5.00000i	0.360219	−	0.207973i
$579$	20.0885	−	11.5981i	0.834848	−	0.482000i
$580$		−	5.19615i		−	0.215758i
$581$	−3.58846	−	6.21539i	−0.148874	−	0.257858i
$582$	3.00000	−	5.19615i	0.124354	−	0.215387i
$583$	−3.29423	−	1.90192i	−0.136433	−	0.0787696i
$584$	12.1244			0.501709
$585$	−5.19615	−	3.46410i	−0.214834	−	0.143223i
$586$	−2.66025			−0.109894
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	−2.69615	+	4.66987i	−0.111187	+	0.192582i
$589$	22.3923	+	38.7846i	0.922659	+	1.59809i
$590$		−	24.0000i		−	0.988064i
$591$	−6.00000	+	3.46410i	−0.246807	+	0.142494i
$592$	2.59808	−	1.50000i	0.106780	−	0.0616496i
$593$		−	19.1436i		−	0.786133i	−0.919510	−	0.393067i	$-0.871414\pi$
$593$		−	19.1436i		−	0.786133i	0.919510	−	0.393067i	$-0.128586\pi$
$594$	−0.633975	−	1.09808i	−0.0260123	−	0.0450546i
$595$	5.70577	−	9.88269i	0.233914	−	0.405151i
$596$	−5.30385	−	3.06218i	−0.217254	−	0.125432i
$597$	−22.5885			−0.924484
$598$	24.5885	+	16.3923i	1.00550	+	0.670331i
$599$	16.3923			0.669771			0.334886	−	0.942259i	$-0.391302\pi$
$599$	16.3923			0.669771			0.334886	+	0.942259i	$0.391302\pi$
$600$	−1.73205	−	1.00000i	−0.0707107	−	0.0408248i
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	−0.590632	−	0.806941i	$-0.701121\pi$
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	0.994147	+	0.108032i	$0.0344548\pi$
$602$	2.66025	+	4.60770i	0.108424	+	0.187796i
$603$		−	7.26795i		−	0.295974i
$604$	−9.29423	+	5.36603i	−0.378177	+	0.218340i
$605$	−14.0885	+	8.13397i	−0.572777	+	0.330693i
$606$			19.3923i			0.787759i
$607$	3.60770	+	6.24871i	0.146432	+	0.253627i	0.929906	−	0.367797i	$-0.119888\pi$
$607$	3.60770	+	6.24871i	0.146432	+	0.253627i	−0.783474	+	0.621424i	$0.786554\pi$
$608$	−2.36603	+	4.09808i	−0.0959550	+	0.166199i
$609$	−3.29423	−	1.90192i	−0.133489	−	0.0770698i
$610$	26.3205			1.06569
$611$	15.2942	−	7.56218i	0.618738	−	0.305933i
$612$	5.19615			0.210042
$613$	−11.3827	−	6.57180i	−0.459742	−	0.265432i	0.252194	−	0.967677i	$-0.418848\pi$
$613$	−11.3827	−	6.57180i	−0.459742	−	0.265432i	−0.711936	+	0.702244i	$0.752181\pi$
$614$	3.63397	−	6.29423i	0.146655	−	0.254014i
$615$	−5.59808	−	9.69615i	−0.225736	−	0.390987i
$616$			1.60770i			0.0647759i
$617$	−27.1865	+	15.6962i	−1.09449	+	0.631903i	−0.934768	−	0.355259i	$-0.884393\pi$
$617$	−27.1865	+	15.6962i	−1.09449	+	0.631903i	−0.159721	+	0.987162i	$0.551059\pi$
$618$	5.36603	−	3.09808i	0.215853	−	0.124623i
$619$		−	28.3923i		−	1.14118i	−0.821234	−	0.570592i	$-0.806714\pi$
$619$		−	28.3923i		−	1.14118i	0.821234	−	0.570592i	$-0.193286\pi$
$620$	−8.19615	−	14.1962i	−0.329165	−	0.570131i
$621$	4.09808	−	7.09808i	0.164450	−	0.284836i
$622$	−7.09808	−	4.09808i	−0.284607	−	0.164318i
$623$	−12.0000			−0.480770
$624$	−2.00000	+	3.00000i	−0.0800641	+	0.120096i
$625$	−11.0000			−0.440000
$626$	3.12436	+	1.80385i	0.124874	+	0.0720962i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	3.59808	+	6.23205i	0.143579	+	0.248686i
$629$		−	15.5885i		−	0.621552i
$630$	1.90192	−	1.09808i	0.0757745	−	0.0437484i
$631$	−1.60770	+	0.928203i	−0.0640013	+	0.0369512i	−0.531659	−	0.846958i	$-0.678431\pi$
$631$	−1.60770	+	0.928203i	−0.0640013	+	0.0369512i	0.467658	+	0.883910i	$0.345098\pi$
$632$		−	8.39230i		−	0.333828i
$633$	−12.1962	−	21.1244i	−0.484754	−	0.839618i
$634$	9.06218	−	15.6962i	0.359905	−	0.623374i
$635$	6.00000	+	3.46410i	0.238103	+	0.137469i
$636$	3.00000			0.118958
$637$	−19.4019	−	1.25129i	−0.768732	−	0.0495779i
$638$	3.80385			0.150596
$639$	−1.90192	−	1.09808i	−0.0752389	−	0.0434392i
$640$	0.866025	−	1.50000i	0.0342327	−	0.0592927i
$641$	−20.5981	−	35.6769i	−0.813575	−	1.40915i	−0.910347	−	0.413847i	$-0.864185\pi$
$641$	−20.5981	−	35.6769i	−0.813575	−	1.40915i	0.0967715	−	0.995307i	$-0.469148\pi$
$642$			2.19615i			0.0866752i
$643$	−24.0000	+	13.8564i	−0.946468	+	0.546443i	−0.891982	−	0.452071i	$-0.850685\pi$
$643$	−24.0000	+	13.8564i	−0.946468	+	0.546443i	−0.0544858	+	0.998515i	$0.517352\pi$
$644$	−9.00000	+	5.19615i	−0.354650	+	0.204757i
$645$			7.26795i			0.286175i
$646$	12.2942	+	21.2942i	0.483710	+	0.837810i
$647$	−24.5885	+	42.5885i	−0.966672	+	1.67433i	−0.261618	+	0.965172i	$0.584256\pi$
$647$	−24.5885	+	42.5885i	−0.966672	+	1.67433i	−0.705054	+	0.709153i	$0.749077\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	17.5692			0.689652
$650$	0.464102	−	7.19615i	0.0182036	−	0.282256i
$651$	−12.0000			−0.470317
$652$	2.19615	+	1.26795i	0.0860080	+	0.0496567i
$653$	−6.58846	+	11.4115i	−0.257826	+	0.446568i	−0.965659	−	0.259812i	$-0.916340\pi$
$653$	−6.58846	+	11.4115i	−0.257826	+	0.446568i	0.707833	+	0.706380i	$0.249673\pi$
$654$	−2.19615	−	3.80385i	−0.0858764	−	0.148742i
$655$			7.60770i			0.297257i
$656$	−5.59808	+	3.23205i	−0.218568	+	0.126190i
$657$	10.5000	−	6.06218i	0.409644	−	0.236508i
$658$			6.00000i			0.233904i
$659$	18.5885	+	32.1962i	0.724103	+	1.25418i	0.959342	+	0.282246i	$0.0910796\pi$
$659$	18.5885	+	32.1962i	0.724103	+	1.25418i	−0.235238	+	0.971938i	$0.575587\pi$
$660$	−1.09808	+	1.90192i	−0.0427426	+	0.0740323i
$661$	−7.79423	−	4.50000i	−0.303160	−	0.175030i	0.340701	−	0.940172i	$-0.389335\pi$
$661$	−7.79423	−	4.50000i	−0.303160	−	0.175030i	−0.643862	+	0.765142i	$0.722669\pi$
$662$	12.0000			0.466393
$663$	8.30385	+	16.7942i	0.322495	+	0.652234i
$664$	−5.66025			−0.219660
$665$	9.00000	+	5.19615i	0.349005	+	0.201498i
$666$	1.50000	−	2.59808i	0.0581238	−	0.100673i
$667$	12.2942	+	21.2942i	0.476034	+	0.824516i
$668$			9.46410i			0.366177i
$669$	−4.39230	+	2.53590i	−0.169816	+	0.0980435i
$670$	−10.9019	+	6.29423i	−0.421178	+	0.243167i
$671$			19.2679i			0.743831i
$672$	−0.633975	−	1.09808i	−0.0244561	−	0.0423592i
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	−26.8468	−	15.5000i	−1.03410	−	0.597038i
$675$	−2.00000			−0.0769800
$676$	−12.8923	−	1.66987i	−0.495858	−	0.0642259i
$677$	−16.3923			−0.630007			−0.315004	−	0.949090i	$-0.602006\pi$
$677$	−16.3923			−0.630007			−0.315004	+	0.949090i	$0.602006\pi$
$678$	0.696152	+	0.401924i	0.0267356	+	0.0154358i
$679$	−3.80385	+	6.58846i	−0.145978	+	0.252842i
$680$	−4.50000	−	7.79423i	−0.172567	−	0.298895i
$681$		−	20.1962i		−	0.773918i
$682$	10.3923	−	6.00000i	0.397942	−	0.229752i
$683$	−24.0000	+	13.8564i	−0.918334	+	0.530201i	−0.883103	−	0.469179i	$-0.844550\pi$
$683$	−24.0000	+	13.8564i	−0.918334	+	0.530201i	−0.0352311	+	0.999379i	$0.511217\pi$
$684$			4.73205i			0.180934i
$685$	7.79423	+	13.5000i	0.297802	+	0.515808i
$686$	7.85641	−	13.6077i	0.299959	−	0.519544i
$687$	−6.80385	−	3.92820i	−0.259583	−	0.149870i
$688$	4.19615			0.159977
$689$	4.79423	+	9.69615i	0.182646	+	0.369394i
$690$	−14.1962			−0.540438
$691$	22.0981	+	12.7583i	0.840650	+	0.485350i	0.857485	−	0.514509i	$-0.172026\pi$
$691$	22.0981	+	12.7583i	0.840650	+	0.485350i	−0.0168348	+	0.999858i	$0.505359\pi$
$692$	2.19615	−	3.80385i	0.0834852	−	0.144601i
$693$	0.803848	+	1.39230i	0.0305356	+	0.0528893i
$694$			18.5885i			0.705608i
$695$	6.00000	−	3.46410i	0.227593	−	0.131401i
$696$	−2.59808	+	1.50000i	−0.0984798	+	0.0568574i
$697$			33.5885i			1.27225i
$698$	4.73205	+	8.19615i	0.179111	+	0.310229i
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$	2.19615	+	1.26795i	0.0830068	+	0.0479240i
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$	−0.232051	+	3.59808i	−0.00875819	+	0.135801i
$703$	14.1962			0.535418
$704$	1.09808	+	0.633975i	0.0413853	+	0.0238938i
$705$	−4.09808	+	7.09808i	−0.154342	+	0.267329i
$706$	17.8923	+	30.9904i	0.673386	+	1.16634i
$707$		−	24.5885i		−	0.924744i
$708$	−12.0000	+	6.92820i	−0.450988	+	0.260378i
$709$	−39.1865	+	22.6244i	−1.47168	+	0.849676i	−0.999494	−	0.0318226i	$-0.989869\pi$
$709$	−39.1865	+	22.6244i	−1.47168	+	0.849676i	−0.472188	+	0.881498i	$0.656536\pi$
$710$			3.80385i			0.142756i
$711$	−4.19615	−	7.26795i	−0.157368	−	0.272569i
$712$	−4.73205	+	8.19615i	−0.177341	+	0.307164i
$713$	67.1769	+	38.7846i	2.51580	+	1.45250i
$714$	−6.58846			−0.246567
$715$	−7.90192	−	0.509619i	−0.295515	−	0.0190587i
$716$	2.19615			0.0820741
$717$	−5.70577	−	3.29423i	−0.213086	−	0.123025i
$718$	−8.02628	+	13.9019i	−0.299538	+	0.518815i
$719$	15.8038	+	27.3731i	0.589384	+	1.02084i	0.994313	+	0.106495i	$0.0339628\pi$
$719$	15.8038	+	27.3731i	0.589384	+	1.02084i	−0.404929	+	0.914348i	$0.632704\pi$
$720$		−	1.73205i		−	0.0645497i
$721$	−6.80385	+	3.92820i	−0.253389	+	0.146294i
$722$	−2.93782	+	1.69615i	−0.109334	+	0.0631243i
$723$		−	11.1962i		−	0.416389i
$724$	−9.79423	−	16.9641i	−0.364000	−	0.630466i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	8.13397	+	4.69615i	0.301880	+	0.174291i
$727$	13.8038			0.511956			0.255978	−	0.966683i	$-0.417602\pi$
$727$	13.8038			0.511956			0.255978	+	0.966683i	$0.417602\pi$
$728$	2.53590	−	3.80385i	0.0939866	−	0.140980i
$729$	1.00000			0.0370370
$730$	−18.1865	−	10.5000i	−0.673114	−	0.388622i
$731$	10.9019	−	18.8827i	0.403222	−	0.698401i
$732$	−7.59808	−	13.1603i	−0.280833	−	0.486417i
$733$		−	20.3205i		−	0.750555i	−0.926912	−	0.375278i	$-0.877547\pi$
$733$		−	20.3205i		−	0.750555i	0.926912	−	0.375278i	$-0.122453\pi$
$734$	−11.9545	+	6.90192i	−0.441248	+	0.254755i
$735$	8.08846	−	4.66987i	0.298347	−	0.172251i
$736$			8.19615i			0.302114i
$737$	−4.60770	−	7.98076i	−0.169727	−	0.293975i
$738$	−3.23205	+	5.59808i	−0.118973	+	0.206068i
$739$	4.39230	+	2.53590i	0.161574	+	0.0932845i	0.578607	−	0.815607i	$-0.303597\pi$
$739$	4.39230	+	2.53590i	0.161574	+	0.0932845i	−0.417033	+	0.908891i	$0.636930\pi$
$740$	−5.19615			−0.191014
$741$	−15.2942	+	7.56218i	−0.561848	+	0.277804i
$742$	−3.80385			−0.139644
$743$	−14.1962	−	8.19615i	−0.520806	−	0.300688i	0.216458	−	0.976292i	$-0.430550\pi$
$743$	−14.1962	−	8.19615i	−0.520806	−	0.300688i	−0.737264	+	0.675604i	$0.763883\pi$
$744$	−4.73205	+	8.19615i	−0.173485	+	0.300486i
$745$	5.30385	+	9.18653i	0.194318	+	0.336569i
$746$		−	27.9808i		−	1.02445i
$747$	−4.90192	+	2.83013i	−0.179352	+	0.103549i
$748$	5.70577	−	3.29423i	0.208624	−	0.120449i
$749$		−	2.78461i		−	0.101747i
$750$	6.06218	+	10.5000i	0.221359	+	0.383406i
$751$	13.4904	−	23.3660i	0.492271	−	0.852638i	−0.507689	−	0.861540i	$-0.669500\pi$
$751$	13.4904	−	23.3660i	0.492271	−	0.852638i	0.999960	+	0.00890181i	$0.00283357\pi$
$752$	4.09808	+	2.36603i	0.149441	+	0.0862801i
$753$	16.3923			0.597369
$754$	−9.00000	−	6.00000i	−0.327761	−	0.218507i
$755$	18.5885			0.676503
$756$	−1.09808	−	0.633975i	−0.0399366	−	0.0230574i
$757$	11.3923	−	19.7321i	0.414060	−	0.717174i	−0.581269	−	0.813712i	$-0.697444\pi$
$757$	11.3923	−	19.7321i	0.414060	−	0.717174i	0.995329	+	0.0965379i	$0.0307769\pi$
$758$	−15.1244	−	26.1962i	−0.549341	−	0.951487i
$759$		−	10.3923i		−	0.377217i
$760$	7.09808	−	4.09808i	0.257474	−	0.148653i
$761$	14.1962	−	8.19615i	0.514610	−	0.297110i	−0.220117	−	0.975474i	$-0.570644\pi$
$761$	14.1962	−	8.19615i	0.514610	−	0.297110i	0.734727	+	0.678363i	$0.237310\pi$
$762$		−	4.00000i		−	0.144905i
$763$	2.78461	+	4.82309i	0.100810	+	0.174607i
$764$	−10.3923	+	18.0000i	−0.375980	+	0.651217i
$765$	−7.79423	−	4.50000i	−0.281801	−	0.162698i
$766$	−23.3205			−0.842604
$767$	−41.5692	−	27.7128i	−1.50098	−	1.00065i
$768$	−1.00000			−0.0360844
$769$	−18.8038	−	10.8564i	−0.678084	−	0.391492i	0.121049	−	0.992647i	$-0.461374\pi$
$769$	−18.8038	−	10.8564i	−0.678084	−	0.391492i	−0.799133	+	0.601155i	$0.794708\pi$
$770$	1.39230	−	2.41154i	0.0501752	−	0.0869060i
$771$	−11.5981	−	20.0885i	−0.417695	−	0.723468i
$772$			23.1962i			0.834848i
$773$	7.98076	−	4.60770i	0.287048	−	0.165727i	−0.349562	−	0.936913i	$-0.613670\pi$
$773$	7.98076	−	4.60770i	0.287048	−	0.165727i	0.636610	+	0.771186i	$0.280336\pi$
$774$	3.63397	−	2.09808i	0.130621	−	0.0754138i
$775$		−	18.9282i		−	0.679921i
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	−1.90192	+	3.29423i	−0.0682311	+	0.118180i
$778$	6.40192	+	3.69615i	0.229520	+	0.132513i
$779$	−30.5885			−1.09595
$780$	5.59808	−	2.76795i	0.200443	−	0.0991085i
$781$	−2.78461			−0.0996412
$782$	36.8827	+	21.2942i	1.31892	+	0.761480i
$783$	−1.50000	+	2.59808i	−0.0536056	+	0.0928477i
$784$	−2.69615	−	4.66987i	−0.0962912	−	0.166781i
$785$		−	12.4641i		−	0.444863i
$786$	3.80385	−	2.19615i	0.135679	−	0.0783342i
$787$	−18.5885	+	10.7321i	−0.662607	+	0.382556i	−0.793270	−	0.608871i	$-0.791623\pi$
$787$	−18.5885	+	10.7321i	−0.662607	+	0.382556i	0.130663	+	0.991427i	$0.458290\pi$
$788$		−	6.92820i		−	0.246807i
$789$	4.09808	+	7.09808i	0.145895	+	0.252698i
$790$	−7.26795	+	12.5885i	−0.258582	+	0.447877i
$791$	−0.882686	−	0.509619i	−0.0313847	−	0.0181200i
$792$	1.26795			0.0450546
$793$	30.3923	−	45.5885i	1.07926	−	1.61889i
$794$	−4.39230			−0.155877
$795$	−4.50000	−	2.59808i	−0.159599	−	0.0921443i
$796$	11.2942	−	19.5622i	0.400313	−	0.693363i
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	0.914255	−	0.405140i	$-0.132777\pi$
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	−0.807989	+	0.589197i	$0.799444\pi$
$798$		−	6.00000i		−	0.212398i
$799$	21.2942	−	12.2942i	0.753336	−	0.434939i
$800$	1.73205	−	1.00000i	0.0612372	−	0.0353553i
$801$			9.46410i			0.334398i
$802$	10.5000	+	18.1865i	0.370768	+	0.642189i
$803$	7.68653	−	13.3135i	0.271252	−	0.469822i
$804$	6.29423	+	3.63397i	0.221980	+	0.128160i
$805$	18.0000			0.634417
$806$	−34.0526	−	2.19615i	−1.19945	−	0.0773562i
$807$	7.60770			0.267804
$808$	−16.7942	−	9.69615i	−0.590819	−	0.341109i
$809$	18.4019	−	31.8731i	0.646977	−	1.12060i	−0.336864	−	0.941553i	$-0.609366\pi$
$809$	18.4019	−	31.8731i	0.646977	−	1.12060i	0.983841	−	0.179044i	$-0.0573004\pi$
$810$	−0.866025	−	1.50000i	−0.0304290	−	0.0527046i
$811$			16.3923i			0.575612i	0.957689	+	0.287806i	$0.0929258\pi$
$811$			16.3923i			0.575612i	−0.957689	+	0.287806i	$0.907074\pi$
$812$	3.29423	−	1.90192i	0.115605	−	0.0667444i
$813$		0			0
$814$		−	3.80385i		−	0.133325i
$815$	−2.19615	−	3.80385i	−0.0769279	−	0.133243i
$816$	−2.59808	+	4.50000i	−0.0909509	+	0.157532i
$817$	17.1962	+	9.92820i	0.601617	+	0.347344i
$818$	−20.6603			−0.722369
$819$	0.294229	−	4.56218i	0.0102812	−	0.159415i
$820$	11.1962			0.390987
$821$	24.8038	+	14.3205i	0.865660	+	0.499789i	0.865904	−	0.500211i	$-0.166744\pi$
$821$	24.8038	+	14.3205i	0.865660	+	0.499789i	−0.000243419		1.00000i	$0.500077\pi$
$822$	4.50000	−	7.79423i	0.156956	−	0.271855i
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$			6.19615i			0.215853i
$825$	−2.19615	+	1.26795i	−0.0764602	+	0.0441443i
$826$	15.2154	−	8.78461i	0.529411	−	0.305656i
$827$			44.1051i			1.53369i	0.641835	+	0.766843i	$0.278173\pi$
$827$			44.1051i			1.53369i	−0.641835	+	0.766843i	$0.721827\pi$
$828$	4.09808	+	7.09808i	0.142418	+	0.246675i
$829$	19.9904	−	34.6244i	0.694295	−	1.20255i	−0.276123	−	0.961122i	$-0.589050\pi$
$829$	19.9904	−	34.6244i	0.694295	−	1.20255i	0.970418	−	0.241431i	$-0.0776169\pi$
$830$	8.49038	+	4.90192i	0.294705	+	0.170148i
$831$	4.80385			0.166644
$832$	−1.59808	−	3.23205i	−0.0554033	−	0.112051i
$833$	−28.0192			−0.970809
$834$	−3.46410	−	2.00000i	−0.119952	−	0.0692543i
$835$	8.19615	−	14.1962i	0.283640	−	0.491278i
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$			9.46410i			0.327127i
$838$	−3.80385	+	2.19615i	−0.131402	+	0.0758648i
$839$	−10.3923	+	6.00000i	−0.358782	+	0.207143i	−0.668546	−	0.743670i	$-0.733083\pi$
$839$	−10.3923	+	6.00000i	−0.358782	+	0.207143i	0.309764	+	0.950813i	$0.399750\pi$
$840$			2.19615i			0.0757745i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	3.23205	−	5.59808i	0.111384	−	0.192922i
$843$	15.1865	+	8.76795i	0.523052	+	0.301984i
$844$	24.3923			0.839618
$845$	17.8923	+	13.6699i	0.615514	+	0.470258i
$846$	4.73205			0.162691
$847$	−10.3135	−	5.95448i	−0.354375	−	0.204598i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$	9.90192	+	17.1506i	0.339833	+	0.588608i
$850$		−	10.3923i		−	0.356453i
$851$	21.2942	−	12.2942i	0.729957	−	0.421441i
$852$	1.90192	−	1.09808i	0.0651588	−	0.0376195i
$853$			9.00000i			0.308154i	0.988059	+	0.154077i	$0.0492404\pi$
$853$			9.00000i			0.308154i	−0.988059	+	0.154077i	$0.950760\pi$
$854$	9.63397	+	16.6865i	0.329668	+	0.571001i
$855$	4.09808	−	7.09808i	0.140151	−	0.242749i
$856$	−1.90192	−	1.09808i	−0.0650064	−	0.0375315i
$857$	−18.3731			−0.627612			−0.313806	−	0.949487i	$-0.601604\pi$
$857$	−18.3731			−0.627612			−0.313806	+	0.949487i	$0.601604\pi$
$858$	2.02628	+	4.09808i	0.0691760	+	0.139906i
$859$	−20.5885			−0.702469			−0.351235	−	0.936288i	$-0.614238\pi$
$859$	−20.5885			−0.702469			−0.351235	+	0.936288i	$0.614238\pi$
$860$	−6.29423	−	3.63397i	−0.214631	−	0.123918i
$861$	4.09808	−	7.09808i	0.139662	−	0.241902i
$862$	−19.0981	−	33.0788i	−0.650483	−	1.12667i
$863$		−	49.5167i		−	1.68557i	−0.538253	−	0.842783i	$-0.680915\pi$
$863$		−	49.5167i		−	1.68557i	0.538253	−	0.842783i	$-0.319085\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−6.58846	+	3.80385i	−0.224014	+	0.129335i
$866$		−	7.78461i		−	0.264532i
$867$	5.00000	+	8.66025i	0.169809	+	0.294118i
$868$	6.00000	−	10.3923i	0.203653	−	0.352738i
$869$	−9.21539	−	5.32051i	−0.312611	−	0.180486i
$870$	5.19615			0.176166
$871$	−1.68653	+	26.1506i	−0.0571460	+	0.886080i
$872$	4.39230			0.148742
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	−19.3923	+	33.5885i	−0.655954	+	1.13615i
$875$	−7.68653	−	13.3135i	−0.259852	−	0.450077i
$876$			12.1244i			0.409644i
$877$	−19.5788	+	11.3038i	−0.661130	+	0.381704i	−0.792708	−	0.609602i	$-0.791329\pi$
$877$	−19.5788	+	11.3038i	−0.661130	+	0.381704i	0.131577	+	0.991306i	$0.457996\pi$
$878$	12.6340	−	7.29423i	0.426376	−	0.246168i
$879$		−	2.66025i		−	0.0897281i
$880$	−1.09808	−	1.90192i	−0.0370161	−	0.0641138i
$881$	−6.99038	+	12.1077i	−0.235512	+	0.407919i	−0.959421	−	0.281976i	$-0.909010\pi$
$881$	−6.99038	+	12.1077i	−0.235512	+	0.407919i	0.723909	+	0.689895i	$0.242343\pi$
$882$	−4.66987	−	2.69615i	−0.157243	−	0.0907842i
$883$	−16.7846			−0.564847			−0.282424	−	0.959290i	$-0.591138\pi$
$883$	−16.7846			−0.564847			−0.282424	+	0.959290i	$0.591138\pi$
$884$	−18.6962	−	1.20577i	−0.628820	−	0.0405545i
$885$	24.0000			0.806751
$886$	−14.1962	−	8.19615i	−0.476929	−	0.275355i
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$	1.50000	+	2.59808i	0.0503367	+	0.0871857i
$889$			5.07180i			0.170103i
$890$	14.1962	−	8.19615i	0.475856	−	0.274736i
$891$	1.09808	−	0.633975i	0.0367869	−	0.0212389i
$892$		−	5.07180i		−	0.169816i
$893$	11.1962	+	19.3923i	0.374665	+	0.648939i
$894$	3.06218	−	5.30385i	0.102415	−	0.177387i
$895$	−3.29423	−	1.90192i	−0.110114	−	0.0635743i
$896$	1.26795			0.0423592
$897$	−16.3923	+	24.5885i	−0.547323	+	0.820985i
$898$	−26.5359			−0.885514
$899$	−24.5885	−	14.1962i	−0.820071	−	0.473468i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	7.79423	+	13.5000i	0.259663	+	0.449750i
$902$			8.19615i			0.272902i
$903$	−4.60770	+	2.66025i	−0.153334	+	0.0885277i
$904$	−0.696152	+	0.401924i	−0.0231537	+	0.0133678i
$905$			33.9282i			1.12781i
$906$	−5.36603	−	9.29423i	−0.178274	−	0.308780i
$907$	10.5885	−	18.3397i	0.351584	−	0.608961i	−0.634943	−	0.772559i	$-0.718977\pi$
$907$	10.5885	−	18.3397i	0.351584	−	0.608961i	0.986527	+	0.163598i	$0.0523098\pi$
$908$	17.4904	+	10.0981i	0.580439	+	0.335116i
$909$	−19.3923			−0.643202
$910$	−7.09808	+	3.50962i	−0.235299	+	0.116343i
$911$	−25.1769			−0.834148			−0.417074	−	0.908872i	$-0.636944\pi$
$911$	−25.1769			−0.834148			−0.417074	+	0.908872i	$0.636944\pi$
$912$	−4.09808	−	2.36603i	−0.135701	−	0.0783469i
$913$	−3.58846	+	6.21539i	−0.118761	+	0.205699i
$914$	15.9904	+	27.6962i	0.528915	+	0.916107i
$915$			26.3205i			0.870129i
$916$	6.80385	−	3.92820i	0.224805	−	0.129791i
$917$	−4.82309	+	2.78461i	−0.159272	+	0.0919559i
$918$			5.19615i			0.171499i
$919$	−5.80385	−	10.0526i	−0.191451	−	0.331603i	0.754280	−	0.656553i	$-0.227986\pi$
$919$	−5.80385	−	10.0526i	−0.191451	−	0.331603i	−0.945731	+	0.324949i	$0.894653\pi$
$920$	7.09808	−	12.2942i	0.234017	−	0.405329i
$921$	6.29423	+	3.63397i	0.207402	+	0.119744i
$922$	31.9808			1.05323
$923$	6.58846	+	4.39230i	0.216862	+	0.144574i
$924$	−1.60770			−0.0528893
$925$	−5.19615	−	3.00000i	−0.170848	−	0.0986394i
$926$	−7.90192	+	13.6865i	−0.259673	+	0.449767i
$927$	3.09808	+	5.36603i	0.101754	+	0.176243i
$928$		−	3.00000i		−	0.0984798i
$929$	47.9711	−	27.6962i	1.57388	−	0.908681i	0.578196	−	0.815898i	$-0.303757\pi$
$929$	47.9711	−	27.6962i	1.57388	−	0.908681i	0.995686	−	0.0927833i	$-0.0295764\pi$
$930$	14.1962	−	8.19615i	0.465510	−	0.268762i
$931$		−	25.5167i		−	0.836275i
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$	4.09808	−	7.09808i	0.134165	−	0.232381i
$934$	4.68653	+	2.70577i	0.153348	+	0.0885355i
$935$	−11.4115			−0.373197
$936$	−3.00000	−	2.00000i	−0.0980581	−	0.0653720i
$937$	−15.3923			−0.502845			−0.251422	−	0.967877i	$-0.580898\pi$
$937$	−15.3923			−0.502845			−0.251422	+	0.967877i	$0.580898\pi$
$938$	−7.98076	−	4.60770i	−0.260581	−	0.150447i
$939$	−1.80385	+	3.12436i	−0.0588663	+	0.101959i
$940$	−4.09808	−	7.09808i	−0.133665	−	0.231514i
$941$			38.7846i			1.26434i	0.774829	+	0.632171i	$0.217836\pi$
$941$			38.7846i			1.26434i	−0.774829	+	0.632171i	$0.782164\pi$
$942$	−6.23205	+	3.59808i	−0.203051	+	0.117232i
$943$	−45.8827	+	26.4904i	−1.49415	+	0.862645i
$944$		−	13.8564i		−	0.450988i
$945$	1.09808	+	1.90192i	0.0357204	+	0.0618696i
$946$	2.66025	−	4.60770i	0.0864923	−	0.149809i
$947$	25.1769	+	14.5359i	0.818140	+	0.472353i	0.849775	−	0.527146i	$-0.176738\pi$
$947$	25.1769	+	14.5359i	0.818140	+	0.472353i	−0.0316348	+	0.999499i	$0.510071\pi$
$948$	8.39230			0.272569
$949$	−39.1865	+	19.3756i	−1.27205	+	0.628960i
$950$	9.46410			0.307056
$951$	15.6962	+	9.06218i	0.508983	+	0.293861i
$952$	3.29423	−	5.70577i	0.106767	−	0.184925i
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	0.603559	−	0.797318i	$-0.293749\pi$
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	−0.992277	+	0.124039i	$0.960415\pi$
$954$			3.00000i			0.0971286i
$955$	31.1769	−	18.0000i	1.00886	−	0.582466i
$956$	5.70577	−	3.29423i	0.184538	−	0.106543i
$957$			3.80385i			0.122961i
$958$	−0.339746	−	0.588457i	−0.0109767	−	0.0190122i
$959$	−5.70577	+	9.88269i	−0.184249	+	0.319129i
$960$	1.50000	+	0.866025i	0.0484123	+	0.0279508i
$961$	−58.5692			−1.88933
$962$	−6.00000	+	9.00000i	−0.193448	+	0.290172i
$963$	−2.19615			−0.0707700
$964$	9.69615	+	5.59808i	0.312292	+	0.180302i
$965$	20.0885	−	34.7942i	0.646670	−	1.12007i
$966$	−5.19615	−	9.00000i	−0.167183	−	0.289570i
$967$			39.1244i			1.25815i	0.777343	+	0.629077i	$0.216567\pi$
$967$			39.1244i			1.25815i	−0.777343	+	0.629077i	$0.783433\pi$
$968$	−8.13397	+	4.69615i	−0.261436	+	0.150940i
$969$	−21.2942	+	12.2942i	−0.684069	+	0.394948i
$970$		−	10.3923i		−	0.333677i
$971$	−24.5885	−	42.5885i	−0.789081	−	1.36673i	−0.926530	−	0.376220i	$-0.877224\pi$
$971$	−24.5885	−	42.5885i	−0.789081	−	1.36673i	0.137449	−	0.990509i	$-0.456110\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	4.39230	+	2.53590i	0.140811	+	0.0812972i
$974$	−15.1244			−0.484616
$975$	7.19615	+	0.464102i	0.230461	+	0.0148631i
$976$	15.1962			0.486417
$977$	9.40192	+	5.42820i	0.300794	+	0.173664i	0.642800	−	0.766034i	$-0.277773\pi$
$977$	9.40192	+	5.42820i	0.300794	+	0.173664i	−0.342005	+	0.939698i	$0.611106\pi$
$978$	−1.26795	+	2.19615i	−0.0405445	+	0.0702252i
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$			9.33975i			0.298347i
$981$	3.80385	−	2.19615i	0.121448	−	0.0701178i
$982$	26.4904	−	15.2942i	0.845342	−	0.488058i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$	−3.23205	−	5.59808i	−0.103034	−	0.178460i
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$	−13.5000	−	7.79423i	−0.429928	−	0.248219i
$987$	−6.00000			−0.190982
$988$	1.09808	−	17.0263i	0.0349345	−	0.541678i
$989$	34.3923			1.09361
$990$	−1.90192	−	1.09808i	−0.0604471	−	0.0348992i
$991$	21.6865	−	37.5622i	0.688895	−	1.19320i	−0.283300	−	0.959031i	$-0.591429\pi$
$991$	21.6865	−	37.5622i	0.688895	−	1.19320i	0.972196	−	0.234171i	$-0.0752374\pi$
$992$	−4.73205	−	8.19615i	−0.150243	−	0.260228i
$993$			12.0000i			0.380808i
$994$	−2.41154	+	1.39230i	−0.0764895	+	0.0441612i
$995$	−33.8827	+	19.5622i	−1.07415	+	0.620163i
$996$		−	5.66025i		−	0.179352i
$997$	−1.40192	−	2.42820i	−0.0443994	−	0.0769020i	0.842972	−	0.537958i	$-0.180804\pi$
$997$	−1.40192	−	2.42820i	−0.0443994	−	0.0769020i	−0.887371	+	0.461056i	$0.847471\pi$
$998$		0			0
$999$	2.59808	+	1.50000i	0.0821995	+	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.i.b.43.1	✓	4
3.2	odd	2		234.2.l.a.199.2		4
4.3	odd	2		624.2.bv.d.433.1		4
5.2	odd	4		1950.2.y.h.199.1		4
5.3	odd	4		1950.2.y.a.199.2		4
5.4	even	2		1950.2.bc.c.901.2		4
12.11	even	2		1872.2.by.k.433.1		4
13.2	odd	12		1014.2.e.h.991.1		4
13.3	even	3		1014.2.i.f.361.2		4
13.4	even	6		1014.2.b.d.337.2		4
13.5	odd	4		1014.2.e.h.529.1		4
13.6	odd	12		1014.2.a.j.1.1		2
13.7	odd	12		1014.2.a.h.1.2		2
13.8	odd	4		1014.2.e.j.529.2		4
13.9	even	3		1014.2.b.d.337.3		4
13.10	even	6	inner	78.2.i.b.49.1	yes	4
13.11	odd	12		1014.2.e.j.991.2		4
13.12	even	2		1014.2.i.f.823.2		4
39.17	odd	6		3042.2.b.l.1351.3		4
39.20	even	12		3042.2.a.v.1.1		2
39.23	odd	6		234.2.l.a.127.2		4
39.32	even	12		3042.2.a.s.1.2		2
39.35	odd	6		3042.2.b.l.1351.2		4
52.7	even	12		8112.2.a.bq.1.2		2
52.19	even	12		8112.2.a.bx.1.1		2
52.23	odd	6		624.2.bv.d.49.1		4
65.23	odd	12		1950.2.y.h.49.1		4
65.49	even	6		1950.2.bc.c.751.2		4
65.62	odd	12		1950.2.y.a.49.2		4
156.23	even	6		1872.2.by.k.1297.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.1	✓	4	1.1	even	1	trivial
78.2.i.b.49.1	yes	4	13.10	even	6	inner
234.2.l.a.127.2		4	39.23	odd	6
234.2.l.a.199.2		4	3.2	odd	2
624.2.bv.d.49.1		4	52.23	odd	6
624.2.bv.d.433.1		4	4.3	odd	2
1014.2.a.h.1.2		2	13.7	odd	12
1014.2.a.j.1.1		2	13.6	odd	12
1014.2.b.d.337.2		4	13.4	even	6
1014.2.b.d.337.3		4	13.9	even	3
1014.2.e.h.529.1		4	13.5	odd	4
1014.2.e.h.991.1		4	13.2	odd	12
1014.2.e.j.529.2		4	13.8	odd	4
1014.2.e.j.991.2		4	13.11	odd	12
1014.2.i.f.361.2		4	13.3	even	3
1014.2.i.f.823.2		4	13.12	even	2
1872.2.by.k.433.1		4	12.11	even	2
1872.2.by.k.1297.1		4	156.23	even	6
1950.2.y.a.49.2		4	65.62	odd	12
1950.2.y.a.199.2		4	5.3	odd	4
1950.2.y.h.49.1		4	65.23	odd	12
1950.2.y.h.199.1		4	5.2	odd	4
1950.2.bc.c.751.2		4	65.49	even	6
1950.2.bc.c.901.2		4	5.4	even	2
3042.2.a.s.1.2		2	39.32	even	12
3042.2.a.v.1.1		2	39.20	even	12
3042.2.b.l.1351.2		4	39.35	odd	6
3042.2.b.l.1351.3		4	39.17	odd	6
8112.2.a.bq.1.2		2	52.7	even	12
8112.2.a.bx.1.1		2	52.19	even	12

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.866025 + 1.50000i) q^{10} +(-1.09808 - 0.633975i) q^{11} +1.00000 q^{12} +(1.59808 + 3.23205i) q^{13} -1.26795 q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(-4.09808 + 2.36603i) q^{19} +(1.50000 - 0.866025i) q^{20} -1.26795i q^{21} +(0.633975 + 1.09808i) q^{22} +(-4.09808 + 7.09808i) q^{23} +(-0.866025 - 0.500000i) q^{24} +2.00000 q^{25} +(0.232051 - 3.59808i) q^{26} -1.00000 q^{27} +(1.09808 + 0.633975i) q^{28} +(1.50000 - 2.59808i) q^{29} +(0.866025 + 1.50000i) q^{30} -9.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09808 + 0.633975i) q^{33} -5.19615i q^{34} +(-1.09808 - 1.90192i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.59808 - 1.50000i) q^{37} +4.73205 q^{38} +(3.59808 + 0.232051i) q^{39} -1.73205 q^{40} +(5.59808 + 3.23205i) q^{41} +(-0.633975 + 1.09808i) q^{42} +(-2.09808 - 3.63397i) q^{43} -1.26795i q^{44} +(-1.50000 + 0.866025i) q^{45} +(7.09808 - 4.09808i) q^{46} -4.73205i q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.69615 + 4.66987i) q^{49} +(-1.73205 - 1.00000i) q^{50} +5.19615 q^{51} +(-2.00000 + 3.00000i) q^{52} +3.00000 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.09808 + 1.90192i) q^{55} +(-0.633975 - 1.09808i) q^{56} +4.73205i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-12.0000 + 6.92820i) q^{59} -1.73205i q^{60} +(-7.59808 - 13.1603i) q^{61} +(-4.73205 + 8.19615i) q^{62} +(-1.09808 - 0.633975i) q^{63} -1.00000 q^{64} +(5.59808 - 2.76795i) q^{65} +1.26795 q^{66} +(6.29423 + 3.63397i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(4.09808 + 7.09808i) q^{69} +2.19615i q^{70} +(1.90192 - 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 + 2.59808i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-4.09808 - 2.36603i) q^{76} -1.60770 q^{77} +(-3.00000 - 2.00000i) q^{78} +8.39230 q^{79} +(1.50000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.23205 - 5.59808i) q^{82} -5.66025i q^{83} +(1.09808 - 0.633975i) q^{84} +(7.79423 - 4.50000i) q^{85} +4.19615i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} +1.73205 q^{90} +(3.80385 + 2.53590i) q^{91} -8.19615 q^{92} +(-8.19615 - 4.73205i) q^{93} +(-2.36603 + 4.09808i) q^{94} +(4.09808 + 7.09808i) q^{95} -1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(4.66987 - 2.69615i) q^{98} +1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 4 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{19} + 6 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} + 6 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^12 - 4 * q^13 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 6 * q^19 + 6 * q^20 + 6 * q^22 - 6 * q^23 + 8 * q^25 - 6 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^33 + 6 * q^35 + 2 * q^36 + 12 * q^38 + 4 * q^39 + 12 * q^41 - 6 * q^42 + 2 * q^43 - 6 * q^45 + 18 * q^46 + 2 * q^48 + 10 * q^49 - 8 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 48 * q^59 - 20 * q^61 - 12 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^65 + 12 * q^66 - 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 + 4 * q^75 - 6 * q^76 - 48 * q^77 - 12 * q^78 - 8 * q^79 + 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^84 - 6 * q^87 - 6 * q^88 - 12 * q^89 + 36 * q^91 - 12 * q^92 - 12 * q^93 - 6 * q^94 + 6 * q^95 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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