LMFDB - Embedded newform 930.2.n.e.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} + \cdots + 25 $ x^12 - x^11 + 16x^10 - 6x^9 + 161x^8 - 180x^7 + 1725x^6 - 2255x^5 + 17635x^4 - 18375x^3 + 60975x^2 + 2000x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			841.1
Root			$1.05776 - 3.25545i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.e.721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.96024 + 1.42420i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.96024 + 1.42420i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(-1.46024 + 1.06092i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-1.45758 + 4.48597i) q^{13} +(1.96024 + 1.42420i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.05638 + 2.94713i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-0.100180 - 0.308322i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(0.748744 + 2.30440i) q^{21} +(1.46024 + 1.06092i) q^{22} +(-0.902476 - 0.655687i) q^{23} +(0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +4.71683 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.748744 - 2.30440i) q^{28} +(2.50698 + 7.71569i) q^{29} -1.00000 q^{30} +(-3.74736 + 4.11792i) q^{31} -1.00000 q^{32} +(0.557761 + 1.71661i) q^{33} +(1.54940 - 4.76856i) q^{34} +(-1.96024 + 1.42420i) q^{35} +1.00000 q^{36} +8.55247 q^{37} +(-0.262274 + 0.190553i) q^{38} +(3.81600 + 2.77248i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-0.649419 - 1.99870i) q^{41} +(1.96024 - 1.42420i) q^{42} +(-1.66907 - 5.13688i) q^{43} +(0.557761 - 1.71661i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(-0.344715 + 1.06092i) q^{46} +(-1.86006 + 5.72467i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.348924 + 1.07388i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(4.05638 - 2.94713i) q^{51} +(-1.45758 - 4.48597i) q^{52} +(-1.13590 - 0.825283i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-1.46024 + 1.06092i) q^{55} -2.42299 q^{56} -0.324189 q^{57} +(6.56336 - 4.76856i) q^{58} +(-2.07310 + 6.38035i) q^{59} +(0.309017 + 0.951057i) q^{60} -15.5525 q^{61} +(5.07438 + 2.29144i) q^{62} +2.42299 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.45758 + 4.48597i) q^{65} +(1.46024 - 1.06092i) q^{66} +16.3524 q^{67} -5.01396 q^{68} +(-0.902476 + 0.655687i) q^{69} +(1.96024 + 1.42420i) q^{70} +(8.91048 + 6.47384i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(4.87235 - 3.53997i) q^{73} +(-2.64286 - 8.13388i) q^{74} +(0.309017 - 0.951057i) q^{75} +(0.262274 + 0.190553i) q^{76} +(1.35145 - 4.15932i) q^{77} +(1.45758 - 4.48597i) q^{78} +(-3.44939 - 2.50613i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.70020 + 1.23527i) q^{82} +(-2.69898 - 8.30660i) q^{83} +(-1.96024 - 1.42420i) q^{84} +(4.05638 + 2.94713i) q^{85} +(-4.36969 + 3.17477i) q^{86} +8.11276 q^{87} -1.80495 q^{88} +(-7.37667 + 5.35947i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(-3.53170 - 10.8694i) q^{91} +1.11552 q^{92} +(2.75838 + 4.83646i) q^{93} +6.01927 q^{94} +(-0.100180 - 0.308322i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(14.2119 - 10.3256i) q^{97} +1.12914 q^{98} +1.80495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	−1.96024	+	1.42420i	−0.740900	+	0.538295i	−0.892993	−	0.450071i	$-0.851399\pi$
$7$	−1.96024	+	1.42420i	−0.740900	+	0.538295i	0.152093	+	0.988366i	$0.451399\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.309017	−	0.951057i	−0.0977198	−	0.300750i
$11$	−1.46024	+	1.06092i	−0.440278	+	0.319881i	−0.785745	−	0.618550i	$-0.787720\pi$
$11$	−1.46024	+	1.06092i	−0.440278	+	0.319881i	0.345467	+	0.938431i	$0.387720\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	−1.45758	+	4.48597i	−0.404260	+	1.24419i	0.517251	+	0.855834i	$0.326955\pi$
$13$	−1.45758	+	4.48597i	−0.404260	+	1.24419i	−0.921511	+	0.388351i	$0.873045\pi$
$14$	1.96024	+	1.42420i	0.523895	+	0.380632i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.05638	+	2.94713i	0.983816	+	0.714784i	0.958558	−	0.284897i	$-0.0919593\pi$
$17$	4.05638	+	2.94713i	0.983816	+	0.714784i	0.0252579	+	0.999681i	$0.491959\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	−0.100180	−	0.308322i	−0.0229828	−	0.0707339i	0.938907	−	0.344170i	$-0.111840\pi$
$19$	−0.100180	−	0.308322i	−0.0229828	−	0.0707339i	−0.961890	+	0.273436i	$0.911840\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	0.748744	+	2.30440i	0.163389	+	0.502861i
$22$	1.46024	+	1.06092i	0.311323	+	0.226190i
$23$	−0.902476	−	0.655687i	−0.188179	−	0.136720i	0.489707	−	0.871887i	$-0.337104\pi$
$23$	−0.902476	−	0.655687i	−0.188179	−	0.136720i	−0.677886	+	0.735167i	$0.737104\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	1.00000			0.200000
$26$	4.71683			0.925047
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.748744	−	2.30440i	0.141499	−	0.435490i
$29$	2.50698	+	7.71569i	0.465534	+	1.43277i	0.858309	+	0.513133i	$0.171515\pi$
$29$	2.50698	+	7.71569i	0.465534	+	1.43277i	−0.392775	+	0.919635i	$0.628485\pi$
$30$	−1.00000			−0.182574
$31$	−3.74736	+	4.11792i	−0.673046	+	0.739601i
$31$	−3.74736	+	4.11792i	−0.673046	+	0.739601i
$32$	−1.00000			−0.176777
$33$	0.557761	+	1.71661i	0.0970937	+	0.298824i
$34$	1.54940	−	4.76856i	0.265720	−	0.817801i
$35$	−1.96024	+	1.42420i	−0.331340	+	0.240733i
$36$	1.00000			0.166667
$37$	8.55247			1.40602			0.703008	−	0.711182i	$-0.251840\pi$
$37$	8.55247			1.40602			0.703008	+	0.711182i	$0.251840\pi$
$38$	−0.262274	+	0.190553i	−0.0425465	+	0.0309118i
$39$	3.81600	+	2.77248i	0.611048	+	0.443953i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−0.649419	−	1.99870i	−0.101422	−	0.312145i	0.887452	−	0.460900i	$-0.152473\pi$
$41$	−0.649419	−	1.99870i	−0.101422	−	0.312145i	−0.988874	+	0.148755i	$0.952473\pi$
$42$	1.96024	−	1.42420i	0.302471	−	0.219758i
$43$	−1.66907	−	5.13688i	−0.254531	−	0.783367i	−0.993922	−	0.110090i	$-0.964886\pi$
$43$	−1.66907	−	5.13688i	−0.254531	−	0.783367i	0.739390	−	0.673277i	$-0.235114\pi$
$44$	0.557761	−	1.71661i	0.0840856	−	0.258789i
$45$	−0.809017	−	0.587785i	−0.120601	−	0.0876219i
$46$	−0.344715	+	1.06092i	−0.0508255	+	0.156425i
$47$	−1.86006	+	5.72467i	−0.271317	+	0.835028i	0.718853	+	0.695162i	$0.244667\pi$
$47$	−1.86006	+	5.72467i	−0.271317	+	0.835028i	−0.990170	+	0.139866i	$0.955333\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−0.348924	+	1.07388i	−0.0498462	+	0.153411i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	4.05638	−	2.94713i	0.568007	−	0.412681i
$52$	−1.45758	−	4.48597i	−0.202130	−	0.622093i
$53$	−1.13590	−	0.825283i	−0.156029	−	0.113361i	0.507032	−	0.861927i	$-0.330743\pi$
$53$	−1.13590	−	0.825283i	−0.156029	−	0.113361i	−0.663060	+	0.748566i	$0.730743\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	−1.46024	+	1.06092i	−0.196898	+	0.143055i
$56$	−2.42299			−0.323785
$57$	−0.324189			−0.0429398
$58$	6.56336	−	4.76856i	0.861811	−	0.626142i
$59$	−2.07310	+	6.38035i	−0.269895	+	0.830651i	0.720630	+	0.693320i	$0.243853\pi$
$59$	−2.07310	+	6.38035i	−0.269895	+	0.830651i	−0.990525	+	0.137332i	$0.956147\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	−15.5525			−1.99129			−0.995645	−	0.0932298i	$-0.970281\pi$
$61$	−15.5525			−1.99129			−0.995645	+	0.0932298i	$0.970281\pi$
$62$	5.07438	+	2.29144i	0.644446	+	0.291014i
$63$	2.42299			0.305268
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.45758	+	4.48597i	−0.180791	+	0.556416i
$66$	1.46024	−	1.06092i	0.179743	−	0.130591i
$67$	16.3524			1.99776			0.998881	−	0.0472865i	$-0.0150574\pi$
$67$	16.3524			1.99776			0.998881	+	0.0472865i	$0.0150574\pi$
$68$	−5.01396			−0.608032
$69$	−0.902476	+	0.655687i	−0.108645	+	0.0789354i
$70$	1.96024	+	1.42420i	0.234293	+	0.170224i
$71$	8.91048	+	6.47384i	1.05748	+	0.768304i	0.973620	−	0.228174i	$-0.0732755\pi$
$71$	8.91048	+	6.47384i	1.05748	+	0.768304i	0.0838590	+	0.996478i	$0.473275\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	4.87235	−	3.53997i	0.570265	−	0.414322i	−0.264936	−	0.964266i	$-0.585351\pi$
$73$	4.87235	−	3.53997i	0.570265	−	0.414322i	0.835202	+	0.549944i	$0.185351\pi$
$74$	−2.64286	−	8.13388i	−0.307226	−	0.945544i
$75$	0.309017	−	0.951057i	0.0356822	−	0.109819i
$76$	0.262274	+	0.190553i	0.0300849	+	0.0218580i
$77$	1.35145	−	4.15932i	0.154012	−	0.473999i
$78$	1.45758	−	4.48597i	0.165039	−	0.507936i
$79$	−3.44939	−	2.50613i	−0.388087	−	0.281961i	0.376584	−	0.926382i	$-0.377098\pi$
$79$	−3.44939	−	2.50613i	−0.388087	−	0.281961i	−0.764671	+	0.644421i	$0.777098\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−1.70020	+	1.23527i	−0.187756	+	0.136412i
$83$	−2.69898	−	8.30660i	−0.296251	−	0.911767i	−0.982798	−	0.184682i	$-0.940874\pi$
$83$	−2.69898	−	8.30660i	−0.296251	−	0.911767i	0.686547	−	0.727085i	$-0.259126\pi$
$84$	−1.96024	−	1.42420i	−0.213879	−	0.155392i
$85$	4.05638	+	2.94713i	0.439976	+	0.319661i
$86$	−4.36969	+	3.17477i	−0.471196	+	0.342344i
$87$	8.11276			0.869779
$88$	−1.80495			−0.192408
$89$	−7.37667	+	5.35947i	−0.781926	+	0.568102i	−0.905556	−	0.424226i	$-0.860546\pi$
$89$	−7.37667	+	5.35947i	−0.781926	+	0.568102i	0.123631	+	0.992328i	$0.460546\pi$
$90$	−0.309017	+	0.951057i	−0.0325733	+	0.100250i
$91$	−3.53170	−	10.8694i	−0.370223	−	1.13943i
$92$	1.11552			0.116301
$93$	2.75838	+	4.83646i	0.286031	+	0.501518i
$94$	6.01927			0.620840
$95$	−0.100180	−	0.308322i	−0.0102782	−	0.0316331i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	14.2119	−	10.3256i	1.44300	−	1.04840i	0.455600	−	0.890185i	$-0.349425\pi$
$97$	14.2119	−	10.3256i	1.44300	−	1.04840i	0.987404	−	0.158219i	$-0.0505751\pi$
$98$	1.12914			0.114060
$99$	1.80495			0.181404
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	14.1775	+	10.3006i	1.41071	+	1.02494i	0.993218	+	0.116264i	$0.0370920\pi$
$101$	14.1775	+	10.3006i	1.41071	+	1.02494i	0.417495	+	0.908679i	$0.362908\pi$
$102$	−4.05638	−	2.94713i	−0.401641	−	0.291809i
$103$	−5.45135	−	16.7775i	−0.537137	−	1.65314i	−0.738986	−	0.673721i	$-0.764695\pi$
$103$	−5.45135	−	16.7775i	−0.537137	−	1.65314i	0.201848	−	0.979417i	$-0.435305\pi$
$104$	−3.81600	+	2.77248i	−0.374189	+	0.271864i
$105$	0.748744	+	2.30440i	0.0730699	+	0.224886i
$106$	−0.433877	+	1.33534i	−0.0421419	+	0.129699i
$107$	−2.69184	−	1.95573i	−0.260230	−	0.189068i	0.450019	−	0.893019i	$-0.351417\pi$
$107$	−2.69184	−	1.95573i	−0.260230	−	0.189068i	−0.710248	+	0.703951i	$0.751417\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	0.978026	−	3.01005i	0.0936779	−	0.288311i	−0.893229	−	0.449602i	$-0.851566\pi$
$109$	0.978026	−	3.01005i	0.0936779	−	0.288311i	0.986907	+	0.161291i	$0.0515658\pi$
$110$	1.46024	+	1.06092i	0.139228	+	0.101155i
$111$	2.64286	−	8.13388i	0.250849	−	0.772034i
$112$	0.748744	+	2.30440i	0.0707496	+	0.217745i
$113$	−5.51661	+	4.00806i	−0.518959	+	0.377046i	−0.816212	−	0.577753i	$-0.803930\pi$
$113$	−5.51661	+	4.00806i	−0.518959	+	0.377046i	0.297252	+	0.954799i	$0.403930\pi$
$114$	0.100180	+	0.308322i	0.00938270	+	0.0288770i
$115$	−0.902476	−	0.655687i	−0.0841563	−	0.0611431i
$116$	−6.56336	−	4.76856i	−0.609392	−	0.442750i
$117$	3.81600	−	2.77248i	0.352789	−	0.256316i
$118$	6.70870			0.617586
$119$	−12.1488			−1.11367
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	−2.39246	+	7.36322i	−0.217496	+	0.669384i
$122$	4.80598	+	14.7913i	0.435113	+	1.33914i
$123$	−2.10156			−0.189492
$124$	0.611225	−	5.53411i	0.0548896	−	0.496978i
$125$	1.00000			0.0894427
$126$	−0.748744	−	2.30440i	−0.0667034	−	0.205292i
$127$	−3.62388	+	11.1532i	−0.321568	+	0.989684i	0.651398	+	0.758736i	$0.274183\pi$
$127$	−3.62388	+	11.1532i	−0.321568	+	0.989684i	−0.972966	+	0.230948i	$0.925817\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−5.40124			−0.475552
$130$	4.71683			0.413693
$131$	−7.29944	+	5.30335i	−0.637755	+	0.463356i	−0.859078	−	0.511844i	$-0.828962\pi$
$131$	−7.29944	+	5.30335i	−0.637755	+	0.463356i	0.221323	+	0.975201i	$0.428962\pi$
$132$	−1.46024	−	1.06092i	−0.127097	−	0.0923416i
$133$	0.635487	+	0.461708i	0.0551037	+	0.0400352i
$134$	−5.05317	−	15.5520i	−0.436527	−	1.34349i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	1.54940	+	4.76856i	0.132860	+	0.408900i
$137$	−1.21313	+	3.73364i	−0.103645	+	0.318987i	−0.989410	−	0.145147i	$-0.953634\pi$
$137$	−1.21313	+	3.73364i	−0.103645	+	0.318987i	0.885765	+	0.464134i	$0.153634\pi$
$138$	0.902476	+	0.655687i	0.0768238	+	0.0558158i
$139$	2.18271	−	6.71769i	0.185135	−	0.569787i	−0.814816	−	0.579720i	$-0.803162\pi$
$139$	2.18271	−	6.71769i	0.185135	−	0.569787i	0.999951	+	0.00993322i	$0.00316190\pi$
$140$	0.748744	−	2.30440i	0.0632804	−	0.194757i
$141$	4.86969	+	3.53804i	0.410102	+	0.297957i
$142$	3.40350	−	10.4749i	0.285615	−	0.879034i
$143$	−2.63086	−	8.09696i	−0.220004	−	0.677102i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	2.50698	+	7.71569i	0.208193	+	0.640753i
$146$	−4.87235	−	3.53997i	−0.403238	−	0.292970i
$147$	0.913494	+	0.663692i	0.0753437	+	0.0547404i
$148$	−6.91909	+	5.02701i	−0.568746	+	0.413218i
$149$	−12.0385			−0.986236			−0.493118	−	0.869963i	$-0.664143\pi$
$149$	−12.0385			−0.986236			−0.493118	+	0.869963i	$0.664143\pi$
$150$	−1.00000			−0.0816497
$151$	−3.08961	+	2.24473i	−0.251429	+	0.182674i	−0.706360	−	0.707853i	$-0.749664\pi$
$151$	−3.08961	+	2.24473i	−0.251429	+	0.182674i	0.454931	+	0.890527i	$0.349664\pi$
$152$	0.100180	−	0.308322i	0.00812566	−	0.0250082i
$153$	−1.54940	−	4.76856i	−0.125261	−	0.385515i
$154$	−4.37337			−0.352416
$155$	−3.74736	+	4.11792i	−0.300995	+	0.330759i
$156$	−4.71683			−0.377649
$157$	−5.35410	−	16.4782i	−0.427304	−	1.31511i	−0.900771	−	0.434295i	$-0.856998\pi$
$157$	−5.35410	−	16.4782i	−0.427304	−	1.31511i	0.473467	−	0.880812i	$-0.343002\pi$
$158$	−1.31755	+	4.05500i	−0.104819	+	0.322598i
$159$	−1.13590	+	0.825283i	−0.0900831	+	0.0654492i
$160$	−1.00000			−0.0790569
$161$	2.70289			0.213018
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	3.64244	+	2.64639i	0.285298	+	0.207281i	0.721225	−	0.692701i	$-0.243579\pi$
$163$	3.64244	+	2.64639i	0.285298	+	0.207281i	−0.435927	+	0.899982i	$0.643579\pi$
$164$	1.70020	+	1.23527i	0.132763	+	0.0964582i
$165$	0.557761	+	1.71661i	0.0434216	+	0.133638i
$166$	−7.06601	+	5.13376i	−0.548429	+	0.398457i
$167$	4.33386	+	13.3382i	0.335364	+	1.03214i	0.966543	+	0.256506i	$0.0825715\pi$
$167$	4.33386	+	13.3382i	0.335364	+	1.03214i	−0.631179	+	0.775638i	$0.717429\pi$
$168$	−0.748744	+	2.30440i	−0.0577668	+	0.177788i
$169$	−7.48219	−	5.43613i	−0.575553	−	0.418164i
$170$	1.54940	−	4.76856i	0.118833	−	0.365732i
$171$	−0.100180	+	0.308322i	−0.00766094	+	0.0235780i
$172$	4.36969	+	3.17477i	0.333186	+	0.242074i
$173$	−4.16908	+	12.8311i	−0.316970	+	0.975532i	0.657967	+	0.753047i	$0.271417\pi$
$173$	−4.16908	+	12.8311i	−0.316970	+	0.975532i	−0.974936	+	0.222485i	$0.928583\pi$
$174$	−2.50698	−	7.71569i	−0.190054	−	0.584925i
$175$	−1.96024	+	1.42420i	−0.148180	+	0.107659i
$176$	0.557761	+	1.71661i	0.0420428	+	0.129394i
$177$	5.42745	+	3.94328i	0.407952	+	0.296395i
$178$	7.37667	+	5.35947i	0.552905	+	0.401709i
$179$	0.653457	−	0.474764i	0.0488417	−	0.0354856i	−0.563097	−	0.826391i	$-0.690390\pi$
$179$	0.653457	−	0.474764i	0.0488417	−	0.0354856i	0.611938	+	0.790906i	$0.290390\pi$
$180$	1.00000			0.0745356
$181$	13.7986			1.02564			0.512820	−	0.858496i	$-0.328601\pi$
$181$	13.7986			1.02564			0.512820	+	0.858496i	$0.328601\pi$
$182$	−9.24610	+	6.71769i	−0.685367	+	0.497948i
$183$	−4.80598	+	14.7913i	−0.355268	+	1.09340i
$184$	−0.344715	−	1.06092i	−0.0254127	−	0.0782124i
$185$	8.55247			0.628790
$186$	3.74736	−	4.11792i	0.274770	−	0.301941i
$187$	−9.04995			−0.661798
$188$	−1.86006	−	5.72467i	−0.135659	−	0.417514i
$189$	0.748744	−	2.30440i	0.0544631	−	0.167620i
$190$	−0.262274	+	0.190553i	−0.0190274	+	0.0138242i
$191$	4.61521			0.333945			0.166973	−	0.985962i	$-0.446601\pi$
$191$	4.61521			0.333945			0.166973	+	0.985962i	$0.446601\pi$
$192$	1.00000			0.0721688
$193$	−14.7913	+	10.7465i	−1.06470	+	0.773548i	−0.974952	−	0.222417i	$-0.928605\pi$
$193$	−14.7913	+	10.7465i	−1.06470	+	0.773548i	−0.0897459	+	0.995965i	$0.528605\pi$
$194$	−14.2119	−	10.3256i	−1.02036	−	0.741333i
$195$	3.81600	+	2.77248i	0.273269	+	0.198542i
$196$	−0.348924	−	1.07388i	−0.0249231	−	0.0767055i
$197$	−1.82112	+	1.32312i	−0.129750	+	0.0942685i	−0.650767	−	0.759277i	$-0.725553\pi$
$197$	−1.82112	+	1.32312i	−0.129750	+	0.0942685i	0.521018	+	0.853546i	$0.325553\pi$
$198$	−0.557761	−	1.71661i	−0.0396383	−	0.121994i
$199$	2.20376	−	6.78247i	0.156220	−	0.480796i	−0.842062	−	0.539380i	$-0.818659\pi$
$199$	2.20376	−	6.78247i	0.156220	−	0.480796i	0.998282	+	0.0585839i	$0.0186585\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	5.05317	−	15.5520i	0.356423	−	1.09696i
$202$	5.41532	−	16.6666i	0.381021	−	1.17266i
$203$	−15.9029	−	11.5541i	−1.11617	−	0.810942i
$204$	−1.54940	+	4.76856i	−0.108480	+	0.333866i
$205$	−0.649419	−	1.99870i	−0.0453574	−	0.139596i
$206$	−14.2718	+	10.3691i	−0.994364	+	0.722448i
$207$	0.344715	+	1.06092i	0.0239594	+	0.0737393i
$208$	3.81600	+	2.77248i	0.264592	+	0.192237i
$209$	0.473392	+	0.343940i	0.0327452	+	0.0237908i
$210$	1.96024	−	1.42420i	0.135269	−	0.0982788i
$211$	−25.7779			−1.77463			−0.887313	−	0.461167i	$-0.847431\pi$
$211$	−25.7779			−1.77463			−0.887313	+	0.461167i	$0.847431\pi$
$212$	1.40406			0.0964309
$213$	8.91048	−	6.47384i	0.610536	−	0.443580i
$214$	−1.02819	+	3.16444i	−0.0702857	+	0.216317i
$215$	−1.66907	−	5.13688i	−0.113830	−	0.350332i
$216$	−1.00000			−0.0680414
$217$	1.48099	−	13.4091i	0.100536	−	0.910267i
$218$	−3.16496			−0.214358
$219$	−1.86107	−	5.72779i	−0.125760	−	0.387048i
$220$	0.557761	−	1.71661i	0.0376042	−	0.115734i
$221$	−19.1332	+	13.9011i	−1.28704	+	0.935090i
$222$	−8.55247			−0.574004
$223$	−4.09935			−0.274513			−0.137256	−	0.990536i	$-0.543828\pi$
$223$	−4.09935			−0.274513			−0.137256	+	0.990536i	$0.543828\pi$
$224$	1.96024	−	1.42420i	0.130974	−	0.0951580i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	5.51661	+	4.00806i	0.366960	+	0.266612i
$227$	−4.57067	−	14.0671i	−0.303366	−	0.933664i	−0.980282	−	0.197604i	$-0.936684\pi$
$227$	−4.57067	−	14.0671i	−0.303366	−	0.933664i	0.676916	−	0.736060i	$-0.263316\pi$
$228$	0.262274	−	0.190553i	0.0173695	−	0.0126197i
$229$	−0.501543	−	1.54359i	−0.0331429	−	0.102003i	0.933117	−	0.359574i	$-0.117078\pi$
$229$	−0.501543	−	1.54359i	−0.0331429	−	0.102003i	−0.966259	+	0.257571i	$0.917078\pi$
$230$	−0.344715	+	1.06092i	−0.0227298	+	0.0699553i
$231$	−3.53813	−	2.57060i	−0.232792	−	0.169133i
$232$	−2.50698	+	7.71569i	−0.164591	+	0.506560i
$233$	7.62781	−	23.4760i	0.499715	−	1.53796i	−0.309764	−	0.950814i	$-0.600250\pi$
$233$	7.62781	−	23.4760i	0.499715	−	1.53796i	0.809478	−	0.587150i	$-0.199750\pi$
$234$	−3.81600	−	2.77248i	−0.249459	−	0.181243i
$235$	−1.86006	+	5.72467i	−0.121337	+	0.373436i
$236$	−2.07310	−	6.38035i	−0.134947	−	0.415326i
$237$	−3.44939	+	2.50613i	−0.224062	+	0.162790i
$238$	3.75417	+	11.5541i	0.243347	+	0.748944i
$239$	−4.92480	−	3.57807i	−0.318559	−	0.231446i	0.417002	−	0.908906i	$-0.363081\pi$
$239$	−4.92480	−	3.57807i	−0.318559	−	0.231446i	−0.735560	+	0.677459i	$0.763081\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	−4.21977	+	3.06584i	−0.271819	+	0.197488i	−0.715341	−	0.698775i	$-0.753729\pi$
$241$	−4.21977	+	3.06584i	−0.271819	+	0.197488i	0.443522	+	0.896263i	$0.353729\pi$
$242$	7.74215			0.497684
$243$	1.00000			0.0641500
$244$	12.5822	−	9.14151i	0.805493	−	0.585225i
$245$	−0.348924	+	1.07388i	−0.0222919	+	0.0686074i
$246$	0.649419	+	1.99870i	0.0414054	+	0.127433i
$247$	1.52914			0.0972971
$248$	−5.45213	+	1.12883i	−0.346211	+	0.0716805i
$249$	−8.73407			−0.553499
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−0.776676	+	2.39036i	−0.0490233	+	0.150878i	−0.972571	−	0.232604i	$-0.925275\pi$
$251$	−0.776676	+	2.39036i	−0.0490233	+	0.150878i	0.923548	+	0.383482i	$0.125275\pi$
$252$	−1.96024	+	1.42420i	−0.123483	+	0.0897159i
$253$	2.01346			0.126585
$254$	11.7271			0.735826
$255$	4.05638	−	2.94713i	0.254020	−	0.184557i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	22.5899	+	16.4126i	1.40912	+	1.02379i	0.993449	+	0.114272i	$0.0364536\pi$
$257$	22.5899	+	16.4126i	1.40912	+	1.02379i	0.415672	+	0.909515i	$0.363546\pi$
$258$	1.66907	+	5.13688i	0.103912	+	0.319808i
$259$	−16.7649	+	12.1804i	−1.04172	+	0.756852i
$260$	−1.45758	−	4.48597i	−0.0903953	−	0.278208i
$261$	2.50698	−	7.71569i	0.155178	−	0.477589i
$262$	7.29944	+	5.30335i	0.450961	+	0.327642i
$263$	−0.720991	+	2.21898i	−0.0444582	+	0.136828i	−0.970822	−	0.239802i	$-0.922917\pi$
$263$	−0.720991	+	2.21898i	−0.0444582	+	0.136828i	0.926364	+	0.376631i	$0.122917\pi$
$264$	−0.557761	+	1.71661i	−0.0343278	+	0.105650i
$265$	−1.13590	−	0.825283i	−0.0697781	−	0.0506967i
$266$	0.242734	−	0.747059i	0.0148830	−	0.0458051i
$267$	2.81764	+	8.67180i	0.172437	+	0.530705i
$268$	−13.2294	+	9.61170i	−0.808112	+	0.587128i
$269$	5.61719	+	17.2879i	0.342486	+	1.05406i	0.962916	+	0.269802i	$0.0869582\pi$
$269$	5.61719	+	17.2879i	0.342486	+	1.05406i	−0.620430	+	0.784262i	$0.713042\pi$
$270$	0.809017	+	0.587785i	0.0492352	+	0.0357715i
$271$	−16.1899	−	11.7626i	−0.983465	−	0.714529i	−0.0249846	−	0.999688i	$-0.507954\pi$
$271$	−16.1899	−	11.7626i	−0.983465	−	0.714529i	−0.958480	+	0.285159i	$0.907954\pi$
$272$	4.05638	−	2.94713i	0.245954	−	0.178696i
$273$	−11.4288			−0.691703
$274$	3.92578			0.237165
$275$	−1.46024	+	1.06092i	−0.0880556	+	0.0639761i
$276$	0.344715	−	1.06092i	0.0207494	−	0.0638601i
$277$	8.75742	+	26.9526i	0.526182	+	1.61942i	0.761966	+	0.647617i	$0.224234\pi$
$277$	8.75742	+	26.9526i	0.526182	+	1.61942i	−0.235784	+	0.971806i	$0.575766\pi$
$278$	−7.06340			−0.423634
$279$	5.45213	−	1.12883i	0.326411	−	0.0675810i
$280$	−2.42299			−0.144801
$281$	−5.80800	−	17.8752i	−0.346476	−	1.06634i	−0.960789	−	0.277282i	$-0.910566\pi$
$281$	−5.80800	−	17.8752i	−0.346476	−	1.06634i	0.614312	−	0.789063i	$-0.289434\pi$
$282$	1.86006	−	5.72467i	0.110765	−	0.340899i
$283$	−9.00698	+	6.54395i	−0.535409	+	0.388998i	−0.822377	−	0.568943i	$-0.807353\pi$
$283$	−9.00698	+	6.54395i	−0.535409	+	0.388998i	0.286968	+	0.957940i	$0.407353\pi$
$284$	−11.0140			−0.653558
$285$	−0.324189			−0.0192033
$286$	−6.88769	+	5.00420i	−0.407278	+	0.295904i
$287$	4.11956	+	2.99304i	0.243170	+	0.176673i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	2.51533	+	7.74139i	0.147961	+	0.455376i
$290$	6.56336	−	4.76856i	0.385414	−	0.280019i
$291$	−5.42848	−	16.7071i	−0.318223	−	0.979390i
$292$	−1.86107	+	5.72779i	−0.108911	+	0.335193i
$293$	−6.04511	−	4.39203i	−0.353159	−	0.256585i	0.397034	−	0.917804i	$-0.370040\pi$
$293$	−6.04511	−	4.39203i	−0.353159	−	0.256585i	−0.750193	+	0.661219i	$0.770040\pi$
$294$	0.348924	−	1.07388i	0.0203496	−	0.0626297i
$295$	−2.07310	+	6.38035i	−0.120701	+	0.371479i
$296$	6.91909	+	5.02701i	0.402164	+	0.292189i
$297$	0.557761	−	1.71661i	0.0323646	−	0.0996079i
$298$	3.72011	+	11.4493i	0.215500	+	0.663242i
$299$	4.25683	−	3.09277i	0.246179	−	0.178859i
$300$	0.309017	+	0.951057i	0.0178411	+	0.0549093i
$301$	10.5877	+	7.69241i	0.610265	+	0.443383i
$302$	3.08961	+	2.24473i	0.177787	+	0.129170i
$303$	14.1775	−	10.3006i	0.814476	−	0.591751i
$304$	−0.324189			−0.0185935
$305$	−15.5525			−0.890532
$306$	−4.05638	+	2.94713i	−0.231888	+	0.168476i
$307$	−1.63840	+	5.04248i	−0.0935085	+	0.287789i	−0.986862	−	0.161565i	$-0.948346\pi$
$307$	−1.63840	+	5.04248i	−0.0935085	+	0.287789i	0.893354	+	0.449354i	$0.148346\pi$
$308$	1.35145	+	4.15932i	0.0770058	+	0.236999i
$309$	−17.6409			−1.00356
$310$	5.07438	+	2.29144i	0.288205	+	0.130145i
$311$	23.9381			1.35740			0.678702	−	0.734414i	$-0.262543\pi$
$311$	23.9381			1.35740			0.678702	+	0.734414i	$0.262543\pi$
$312$	1.45758	+	4.48597i	0.0825193	+	0.253968i
$313$	1.06712	−	3.28426i	0.0603172	−	0.185637i	−0.916358	−	0.400360i	$-0.868885\pi$
$313$	1.06712	−	3.28426i	0.0603172	−	0.185637i	0.976675	+	0.214723i	$0.0688849\pi$
$314$	−14.0172	+	10.1841i	−0.791038	+	0.574722i
$315$	2.42299			0.136520
$316$	4.26368			0.239851
$317$	11.3941	−	8.27831i	0.639957	−	0.464956i	−0.219878	−	0.975527i	$-0.570566\pi$
$317$	11.3941	−	8.27831i	0.639957	−	0.464956i	0.859835	+	0.510571i	$0.170566\pi$
$318$	1.13590	+	0.825283i	0.0636984	+	0.0462796i
$319$	−11.8465	−	8.60702i	−0.663279	−	0.481900i
$320$	0.309017	+	0.951057i	0.0172746	+	0.0531657i
$321$	−2.69184	+	1.95573i	−0.150244	+	0.109158i
$322$	−0.835240	−	2.57060i	−0.0465461	−	0.143254i
$323$	0.502297	−	1.54591i	0.0279486	−	0.0860169i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−1.45758	+	4.48597i	−0.0808520	+	0.248837i
$326$	1.39129	−	4.28194i	0.0770563	−	0.237155i
$327$	−2.56050	−	1.86032i	−0.141596	−	0.102876i
$328$	0.649419	−	1.99870i	0.0358581	−	0.110360i
$329$	−4.50689	−	13.8708i	−0.248473	−	0.764721i
$330$	1.46024	−	1.06092i	0.0803834	−	0.0584019i
$331$	−4.50567	−	13.8670i	−0.247654	−	0.762200i	−0.995189	−	0.0979777i	$-0.968763\pi$
$331$	−4.50567	−	13.8670i	−0.247654	−	0.762200i	0.747535	−	0.664223i	$-0.231237\pi$
$332$	7.06601	+	5.13376i	0.387798	+	0.281752i
$333$	−6.91909	−	5.02701i	−0.379164	−	0.275479i
$334$	11.3462	−	8.24349i	0.620836	−	0.451063i
$335$	16.3524			0.893427
$336$	2.42299			0.132185
$337$	21.3796	−	15.5332i	1.16462	−	0.846147i	0.174266	−	0.984699i	$-0.444245\pi$
$337$	21.3796	−	15.5332i	1.16462	−	0.846147i	0.990355	+	0.138552i	$0.0442448\pi$
$338$	−2.85794	+	8.79584i	−0.155452	+	0.478431i
$339$	2.10716	+	6.48517i	0.114445	+	0.352226i
$340$	−5.01396			−0.271920
$341$	1.10323	−	9.98881i	0.0597433	−	0.540924i
$342$	0.324189			0.0175301
$343$	−6.08664	−	18.7328i	−0.328648	−	1.01147i
$344$	1.66907	−	5.13688i	0.0899904	−	0.276962i
$345$	−0.902476	+	0.655687i	−0.0485877	+	0.0353010i
$346$	13.4914			0.725304
$347$	13.9275			0.747668			0.373834	−	0.927496i	$-0.378043\pi$
$347$	13.9275			0.747668			0.373834	+	0.927496i	$0.378043\pi$
$348$	−6.56336	+	4.76856i	−0.351833	+	0.255622i
$349$	−10.6818	−	7.76080i	−0.571785	−	0.415426i	0.263968	−	0.964531i	$-0.414969\pi$
$349$	−10.6818	−	7.76080i	−0.571785	−	0.415426i	−0.835753	+	0.549105i	$0.814969\pi$
$350$	1.96024	+	1.42420i	0.104779	+	0.0761264i
$351$	−1.45758	−	4.48597i	−0.0777999	−	0.239444i
$352$	1.46024	−	1.06092i	0.0778309	−	0.0565474i
$353$	3.78675	+	11.6544i	0.201549	+	0.620303i	0.999837	+	0.0180281i	$0.00573883\pi$
$353$	3.78675	+	11.6544i	0.201549	+	0.620303i	−0.798289	+	0.602275i	$0.794261\pi$
$354$	2.07310	−	6.38035i	0.110184	−	0.339112i
$355$	8.91048	+	6.47384i	0.472919	+	0.343596i
$356$	2.81764	−	8.67180i	0.149335	−	0.459604i
$357$	−3.75417	+	11.5541i	−0.198692	+	0.611510i
$358$	−0.653457	−	0.474764i	−0.0345363	−	0.0250921i
$359$	3.23374	−	9.95242i	0.170670	−	0.525268i	−0.828739	−	0.559635i	$-0.810941\pi$
$359$	3.23374	−	9.95242i	0.170670	−	0.525268i	0.999409	+	0.0343665i	$0.0109414\pi$
$360$	−0.309017	−	0.951057i	−0.0162866	−	0.0501251i
$361$	15.2863	−	11.1061i	0.804542	−	0.584534i
$362$	−4.26400	−	13.1232i	−0.224111	−	0.689742i
$363$	6.26353	+	4.55072i	0.328750	+	0.238851i
$364$	9.24610	+	6.71769i	0.484628	+	0.352103i
$365$	4.87235	−	3.53997i	0.255030	−	0.185290i
$366$	15.5525			0.812940
$367$	−30.1192			−1.57221			−0.786104	−	0.618094i	$-0.787905\pi$
$367$	−30.1192			−1.57221			−0.786104	+	0.618094i	$0.787905\pi$
$368$	−0.902476	+	0.655687i	−0.0470448	+	0.0341801i
$369$	−0.649419	+	1.99870i	−0.0338074	+	0.104048i
$370$	−2.64286	−	8.13388i	−0.137396	−	0.422860i
$371$	3.40201			0.176623
$372$	−5.07438	−	2.29144i	−0.263094	−	0.118806i
$373$	20.2901			1.05058			0.525290	−	0.850923i	$-0.323957\pi$
$373$	20.2901			1.05058			0.525290	+	0.850923i	$0.323957\pi$
$374$	2.79659	+	8.60702i	0.144608	+	0.445058i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	−4.86969	+	3.53804i	−0.251135	+	0.182460i
$377$	−38.2665			−1.97082
$378$	−2.42299			−0.124625
$379$	13.5373	−	9.83542i	0.695364	−	0.505212i	−0.183055	−	0.983103i	$-0.558599\pi$
$379$	13.5373	−	9.83542i	0.695364	−	0.505212i	0.878419	+	0.477891i	$0.158599\pi$
$380$	0.262274	+	0.190553i	0.0134544	+	0.00977518i
$381$	9.48745	+	6.89304i	0.486057	+	0.353141i
$382$	−1.42618	−	4.38933i	−0.0729697	−	0.224578i
$383$	5.96204	−	4.33168i	0.304646	−	0.221338i	−0.424950	−	0.905217i	$-0.639708\pi$
$383$	5.96204	−	4.33168i	0.304646	−	0.221338i	0.729596	+	0.683879i	$0.239708\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$	1.35145	−	4.15932i	0.0688761	−	0.211979i
$386$	14.7913	+	10.7465i	0.752855	+	0.546981i
$387$	−1.66907	+	5.13688i	−0.0848438	+	0.261122i
$388$	−5.42848	+	16.7071i	−0.275589	+	0.848176i
$389$	22.1971	+	16.1271i	1.12544	+	0.817677i	0.985024	−	0.172417i	$-0.0551576\pi$
$389$	22.1971	+	16.1271i	1.12544	+	0.817677i	0.140411	+	0.990093i	$0.455158\pi$
$390$	1.45758	−	4.48597i	0.0738075	−	0.227156i
$391$	−1.72839	−	5.31943i	−0.0874083	−	0.269015i
$392$	−0.913494	+	0.663692i	−0.0461384	+	0.0335215i
$393$	2.78814	+	8.58101i	0.140643	+	0.432855i
$394$	1.82112	+	1.32312i	0.0917468	+	0.0666579i
$395$	−3.44939	−	2.50613i	−0.173558	−	0.126097i
$396$	−1.46024	+	1.06092i	−0.0733796	+	0.0533134i
$397$	−9.17272			−0.460365			−0.230183	−	0.973147i	$-0.573932\pi$
$397$	−9.17272			−0.460365			−0.230183	+	0.973147i	$0.573932\pi$
$398$	−7.13151			−0.357470
$399$	0.635487	−	0.461708i	0.0318141	−	0.0231143i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−5.54794	−	17.0748i	−0.277051	−	0.852676i	−0.988669	−	0.150109i	$-0.952037\pi$
$401$	−5.54794	−	17.0748i	−0.277051	−	0.852676i	0.711618	−	0.702566i	$-0.247963\pi$
$402$	−16.3524			−0.815583
$403$	−13.0108	−	22.8128i	−0.648114	−	1.13638i
$404$	−17.5243			−0.871869
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	−6.07438	+	18.6950i	−0.301466	+	0.927818i
$407$	−12.4886	+	9.07352i	−0.619038	+	0.449758i
$408$	5.01396			0.248228
$409$	32.8063			1.62217			0.811083	−	0.584931i	$-0.198878\pi$
$409$	32.8063			1.62217			0.811083	+	0.584931i	$0.198878\pi$
$410$	−1.70020	+	1.23527i	−0.0839669	+	0.0610055i
$411$	3.17603	+	2.30752i	0.156662	+	0.113821i
$412$	14.2718	+	10.3691i	0.703122	+	0.510848i
$413$	−5.02310	−	15.4595i	−0.247170	−	0.760712i
$414$	0.902476	−	0.655687i	0.0443543	−	0.0322253i
$415$	−2.69898	−	8.30660i	−0.132488	−	0.407755i
$416$	1.45758	−	4.48597i	0.0714638	−	0.219943i
$417$	−5.71441	−	4.15176i	−0.279836	−	0.203313i
$418$	0.180820	−	0.556506i	0.00884418	−	0.0272196i
$419$	4.58941	−	14.1248i	0.224207	−	0.690039i	−0.774164	−	0.632985i	$-0.781829\pi$
$419$	4.58941	−	14.1248i	0.224207	−	0.690039i	0.998371	−	0.0570539i	$-0.0181707\pi$
$420$	−1.96024	−	1.42420i	−0.0956498	−	0.0694936i
$421$	−2.71404	+	8.35295i	−0.132274	+	0.407098i	−0.995156	−	0.0983076i	$-0.968657\pi$
$421$	−2.71404	+	8.35295i	−0.132274	+	0.407098i	0.862882	+	0.505406i	$0.168657\pi$
$422$	7.96582	+	24.5163i	0.387770	+	1.19343i
$423$	4.86969	−	3.53804i	0.236773	−	0.172025i
$424$	−0.433877	−	1.33534i	−0.0210709	−	0.0648497i
$425$	4.05638	+	2.94713i	0.196763	+	0.142957i
$426$	−8.91048	−	6.47384i	−0.431714	−	0.313659i
$427$	30.4865	−	22.1497i	1.47535	−	1.07190i
$428$	3.32729			0.160831
$429$	−8.51365			−0.411043
$430$	−4.36969	+	3.17477i	−0.210725	+	0.153101i
$431$	7.34746	−	22.6132i	0.353915	−	1.08924i	−0.602721	−	0.797952i	$-0.705917\pi$
$431$	7.34746	−	22.6132i	0.353915	−	1.08924i	0.956636	−	0.291286i	$-0.0940831\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	10.1903			0.489714			0.244857	−	0.969559i	$-0.421259\pi$
$433$	10.1903			0.489714			0.244857	+	0.969559i	$0.421259\pi$
$434$	−13.2104	+	2.73513i	−0.634121	+	0.131290i
$435$	8.11276			0.388977
$436$	0.978026	+	3.01005i	0.0468389	+	0.144155i
$437$	−0.111753	+	0.343940i	−0.00534586	+	0.0164529i
$438$	−4.87235	+	3.53997i	−0.232810	+	0.169146i
$439$	11.7134			0.559050			0.279525	−	0.960138i	$-0.409823\pi$
$439$	11.7134			0.559050			0.279525	+	0.960138i	$0.409823\pi$
$440$	−1.80495			−0.0860477
$441$	0.913494	−	0.663692i	0.0434997	−	0.0316044i
$442$	19.1332	+	13.9011i	0.910076	+	0.661209i
$443$	29.9228	+	21.7402i	1.42168	+	1.03291i	0.991492	+	0.130168i	$0.0415516\pi$
$443$	29.9228	+	21.7402i	1.42168	+	1.03291i	0.430185	+	0.902741i	$0.358448\pi$
$444$	2.64286	+	8.13388i	0.125424	+	0.386017i
$445$	−7.37667	+	5.35947i	−0.349688	+	0.254063i
$446$	1.26677	+	3.89871i	0.0599832	+	0.184609i
$447$	−3.72011	+	11.4493i	−0.175955	+	0.541535i
$448$	−1.96024	−	1.42420i	−0.0926125	−	0.0672869i
$449$	6.03928	−	18.5870i	0.285011	−	0.877174i	−0.701384	−	0.712784i	$-0.747434\pi$
$449$	6.03928	−	18.5870i	0.285011	−	0.877174i	0.986395	−	0.164391i	$-0.0525658\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	3.06878	+	2.22960i	0.144503	+	0.104988i
$452$	2.10716	−	6.48517i	0.0991124	−	0.305037i
$453$	1.18012	+	3.63205i	0.0554471	+	0.170649i
$454$	−11.9662	+	8.69393i	−0.561600	+	0.408026i
$455$	−3.53170	−	10.8694i	−0.165569	−	0.509568i
$456$	−0.262274	−	0.190553i	−0.0122821	−	0.00892348i
$457$	26.8230	+	19.4881i	1.25473	+	0.911613i	0.998486	−	0.0549996i	$-0.0175158\pi$
$457$	26.8230	+	19.4881i	1.25473	+	0.911613i	0.256242	+	0.966613i	$0.417516\pi$
$458$	−1.31306	+	0.953991i	−0.0613551	+	0.0445771i
$459$	−5.01396			−0.234032
$460$	1.11552			0.0520115
$461$	3.43399	−	2.49494i	0.159937	−	0.116201i	−0.504938	−	0.863155i	$-0.668485\pi$
$461$	3.43399	−	2.49494i	0.159937	−	0.116201i	0.664875	+	0.746955i	$0.268485\pi$
$462$	−1.35145	+	4.15932i	−0.0628750	+	0.193509i
$463$	−0.925426	−	2.84817i	−0.0430082	−	0.132366i	0.927247	−	0.374451i	$-0.122169\pi$
$463$	−0.925426	−	2.84817i	−0.0430082	−	0.132366i	−0.970255	+	0.242085i	$0.922169\pi$
$464$	8.11276			0.376625
$465$	2.75838	+	4.83646i	0.127917	+	0.224285i
$466$	−24.6841			−1.14347
$467$	−1.42206	−	4.37664i	−0.0658049	−	0.202527i	0.912748	−	0.408524i	$-0.133956\pi$
$467$	−1.42206	−	4.37664i	−0.0658049	−	0.202527i	−0.978553	+	0.205997i	$0.933956\pi$
$468$	−1.45758	+	4.48597i	−0.0673767	+	0.207364i
$469$	−32.0546	+	23.2890i	−1.48014	+	1.07539i
$470$	6.01927			0.277648
$471$	−17.3262			−0.798351
$472$	−5.42745	+	3.94328i	−0.249819	+	0.181504i
$473$	7.88708	+	5.73030i	0.362648	+	0.263480i
$474$	3.44939	+	2.50613i	0.158436	+	0.115110i
$475$	−0.100180	−	0.308322i	−0.00459657	−	0.0141468i
$476$	9.82855	−	7.14086i	0.450491	−	0.327301i
$477$	0.433877	+	1.33534i	0.0198659	+	0.0611408i
$478$	−1.88111	+	5.78945i	−0.0860397	+	0.264803i
$479$	6.58800	+	4.78646i	0.301014	+	0.218699i	0.728031	−	0.685544i	$-0.240436\pi$
$479$	6.58800	+	4.78646i	0.301014	+	0.218699i	−0.427017	+	0.904243i	$0.640436\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	−12.4659	+	38.3661i	−0.568397	+	1.74934i
$482$	4.21977	+	3.06584i	0.192205	+	0.139645i
$483$	0.835240	−	2.57060i	0.0380047	−	0.116967i
$484$	−2.39246	−	7.36322i	−0.108748	−	0.334692i
$485$	14.2119	−	10.3256i	0.645331	−	0.468860i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	28.0537	+	20.3822i	1.27124	+	0.923607i	0.999251	−	0.0386950i	$-0.0123201\pi$
$487$	28.0537	+	20.3822i	1.27124	+	0.923607i	0.271984	+	0.962302i	$0.412320\pi$
$488$	−12.5822	−	9.14151i	−0.569570	−	0.413817i
$489$	3.64244	−	2.64639i	0.164717	−	0.119674i
$490$	1.12914			0.0510094
$491$	21.1104			0.952698			0.476349	−	0.879256i	$-0.341960\pi$
$491$	21.1104			0.952698			0.476349	+	0.879256i	$0.341960\pi$
$492$	1.70020	−	1.23527i	0.0766509	−	0.0556902i
$493$	−12.5699	+	38.6861i	−0.566119	+	1.74234i
$494$	−0.472531	−	1.45430i	−0.0212602	−	0.0654321i
$495$	1.80495			0.0811265
$496$	2.75838	+	4.83646i	0.123855	+	0.217163i
$497$	−26.6867			−1.19706
$498$	2.69898	+	8.30660i	0.120944	+	0.372227i
$499$	−7.66259	+	23.5830i	−0.343024	+	1.05572i	0.619608	+	0.784911i	$0.287291\pi$
$499$	−7.66259	+	23.5830i	−0.343024	+	1.05572i	−0.962633	+	0.270810i	$0.912709\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	14.0247			0.626575
$502$	2.51338			0.112177
$503$	25.1874	−	18.2997i	1.12305	−	0.815943i	0.138381	−	0.990379i	$-0.455810\pi$
$503$	25.1874	−	18.2997i	1.12305	−	0.815943i	0.984669	+	0.174436i	$0.0558101\pi$
$504$	1.96024	+	1.42420i	0.0873159	+	0.0634387i
$505$	14.1775	+	10.3006i	0.630890	+	0.458369i
$506$	−0.622194	−	1.91492i	−0.0276599	−	0.0851284i
$507$	−7.48219	+	5.43613i	−0.332296	+	0.241427i
$508$	−3.62388	−	11.1532i	−0.160784	−	0.494842i
$509$	−7.38814	+	22.7383i	−0.327473	+	1.00786i	0.642838	+	0.766002i	$0.277757\pi$
$509$	−7.38814	+	22.7383i	−0.327473	+	1.00786i	−0.970312	+	0.241858i	$0.922243\pi$
$510$	−4.05638	−	2.94713i	−0.179619	−	0.130501i
$511$	−4.50935	+	13.8783i	−0.199482	+	0.613942i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	0.262274	+	0.190553i	0.0115797	+	0.00841313i
$514$	8.62859	−	26.5561i	0.380591	−	1.17134i
$515$	−5.45135	−	16.7775i	−0.240215	−	0.739306i
$516$	4.36969	−	3.17477i	0.192365	−	0.139761i
$517$	−3.35731	−	10.3327i	−0.147654	−	0.454434i
$518$	16.7649	+	12.1804i	0.736606	+	0.535175i
$519$	10.9148	+	7.93007i	0.479107	+	0.348091i
$520$	−3.81600	+	2.77248i	−0.167343	+	0.121581i
$521$	28.0331			1.22815			0.614075	−	0.789248i	$-0.289529\pi$
$521$	28.0331			1.22815			0.614075	+	0.789248i	$0.289529\pi$
$522$	−8.11276			−0.355086
$523$	13.1521	−	9.55557i	0.575102	−	0.417836i	−0.261853	−	0.965108i	$-0.584334\pi$
$523$	13.1521	−	9.55557i	0.575102	−	0.417836i	0.836955	+	0.547272i	$0.184334\pi$
$524$	2.78814	−	8.58101i	0.121800	−	0.374863i
$525$	0.748744	+	2.30440i	0.0326779	+	0.100572i
$526$	2.33318			0.101731
$527$	−27.3368	+	5.65989i	−1.19081	+	0.246549i
$528$	1.80495			0.0785504
$529$	−6.72285	−	20.6908i	−0.292298	−	0.899601i
$530$	−0.433877	+	1.33534i	−0.0188464	+	0.0580033i
$531$	5.42745	−	3.94328i	0.235531	−	0.171124i
$532$	−0.785505			−0.0340559
$533$	9.91272			0.429367
$534$	7.37667	−	5.35947i	0.319220	−	0.231927i
$535$	−2.69184	−	1.95573i	−0.116378	−	0.0845538i
$536$	13.2294	+	9.61170i	0.571421	+	0.415162i
$537$	−0.249598	−	0.768185i	−0.0107710	−	0.0331496i
$538$	14.7060	−	10.6845i	0.634020	−	0.460643i
$539$	−0.629790	−	1.93829i	−0.0271270	−	0.0834883i
$540$	0.309017	−	0.951057i	0.0132980	−	0.0409270i
$541$	−4.25960	−	3.09478i	−0.183135	−	0.133055i	0.492441	−	0.870346i	$-0.336105\pi$
$541$	−4.25960	−	3.09478i	−0.183135	−	0.133055i	−0.675576	+	0.737291i	$0.736105\pi$
$542$	−6.18398	+	19.0323i	−0.265625	+	0.817509i
$543$	4.26400	−	13.1232i	0.182986	−	0.563172i
$544$	−4.05638	−	2.94713i	−0.173916	−	0.126357i
$545$	0.978026	−	3.01005i	0.0418940	−	0.128937i
$546$	3.53170	+	10.8694i	0.151143	+	0.465169i
$547$	8.74771	−	6.35558i	0.374025	−	0.271745i	−0.384853	−	0.922978i	$-0.625748\pi$
$547$	8.74771	−	6.35558i	0.374025	−	0.271745i	0.758878	+	0.651233i	$0.225748\pi$
$548$	−1.21313	−	3.73364i	−0.0518225	−	0.159493i
$549$	12.5822	+	9.14151i	0.536996	+	0.390150i
$550$	1.46024	+	1.06092i	0.0622647	+	0.0452380i
$551$	2.12777	−	1.54591i	0.0906459	−	0.0658581i
$552$	−1.11552			−0.0474797
$553$	10.3308			0.439312
$554$	22.9272	−	16.6576i	0.974084	−	0.707714i
$555$	2.64286	−	8.13388i	0.112183	−	0.345264i
$556$	2.18271	+	6.71769i	0.0925675	+	0.284893i
$557$	15.2354			0.645543			0.322771	−	0.946477i	$-0.395385\pi$
$557$	15.2354			0.645543			0.322771	+	0.946477i	$0.395385\pi$
$558$	−2.75838	−	4.83646i	−0.116771	−	0.204744i
$559$	25.4767			1.07755
$560$	0.748744	+	2.30440i	0.0316402	+	0.0973785i
$561$	−2.79659	+	8.60702i	−0.118072	+	0.363389i
$562$	−15.2055	+	11.0475i	−0.641407	+	0.466010i
$563$	6.07239			0.255921			0.127960	−	0.991779i	$-0.459157\pi$
$563$	6.07239			0.255921			0.127960	+	0.991779i	$0.459157\pi$
$564$	−6.01927			−0.253457
$565$	−5.51661	+	4.00806i	−0.232086	+	0.168620i
$566$	9.00698	+	6.54395i	0.378592	+	0.275063i
$567$	−1.96024	−	1.42420i	−0.0823222	−	0.0598106i
$568$	3.40350	+	10.4749i	0.142808	+	0.439517i
$569$	−19.7611	+	14.3573i	−0.828429	+	0.601889i	−0.919115	−	0.393990i	$-0.871094\pi$
$569$	−19.7611	+	14.3573i	−0.828429	+	0.601889i	0.0906852	+	0.995880i	$0.471094\pi$
$570$	0.100180	+	0.308322i	0.00419607	+	0.0129142i
$571$	5.41561	−	16.6675i	0.226636	−	0.697515i	−0.771485	−	0.636247i	$-0.780486\pi$
$571$	5.41561	−	16.6675i	0.226636	−	0.697515i	0.998121	−	0.0612673i	$-0.0195142\pi$
$572$	6.88769	+	5.00420i	0.287989	+	0.209236i
$573$	1.42618	−	4.38933i	0.0595795	−	0.183367i
$574$	1.57353	−	4.84283i	0.0656780	−	0.202136i
$575$	−0.902476	−	0.655687i	−0.0376358	−	0.0273440i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−10.4038	−	32.0197i	−0.433117	−	1.33300i	−0.895004	−	0.446059i	$-0.852827\pi$
$577$	−10.4038	−	32.0197i	−0.433117	−	1.33300i	0.461886	−	0.886939i	$-0.347173\pi$
$578$	6.58522	−	4.78444i	0.273909	−	0.199007i
$579$	5.64976	+	17.3882i	0.234796	+	0.722627i
$580$	−6.56336	−	4.76856i	−0.272529	−	0.198004i
$581$	17.1208	+	12.4390i	0.710292	+	0.516058i
$582$	−14.2119	+	10.3256i	−0.589104	+	0.428009i
$583$	2.53425			0.104958
$584$	6.02255			0.249215
$585$	3.81600	−	2.77248i	0.157772	−	0.114628i
$586$	−2.30903	+	7.10646i	−0.0953850	+	0.293565i
$587$	2.86701	+	8.82375i	0.118334	+	0.364195i	0.992628	−	0.121202i	$-0.0386750\pi$
$587$	2.86701	+	8.82375i	0.118334	+	0.364195i	−0.874294	+	0.485397i	$0.838675\pi$
$588$	−1.12914			−0.0465650
$589$	1.64506	+	0.742860i	0.0677833	+	0.0306090i
$590$	6.70870			0.276193
$591$	0.695606	+	2.14086i	0.0286134	+	0.0880631i
$592$	2.64286	−	8.13388i	0.108621	−	0.334300i
$593$	−3.35825	+	2.43991i	−0.137907	+	0.100195i	−0.654600	−	0.755976i	$-0.727163\pi$
$593$	−3.35825	+	2.43991i	−0.137907	+	0.100195i	0.516693	+	0.856171i	$0.327163\pi$
$594$	−1.80495			−0.0740581
$595$	−12.1488			−0.498050
$596$	9.73938	−	7.07608i	0.398941	−	0.289847i
$597$	−5.76951	−	4.19180i	−0.236130	−	0.171559i
$598$	−4.25683	−	3.09277i	−0.174075	−	0.126473i
$599$	8.65424	+	26.6350i	0.353603	+	1.08828i	0.956815	+	0.290697i	$0.0938870\pi$
$599$	8.65424	+	26.6350i	0.353603	+	1.08828i	−0.603213	+	0.797580i	$0.706113\pi$
$600$	0.809017	−	0.587785i	0.0330280	−	0.0239962i
$601$	6.74578	+	20.7614i	0.275166	+	0.846874i	0.989175	+	0.146738i	$0.0468774\pi$
$601$	6.74578	+	20.7614i	0.275166	+	0.846874i	−0.714009	+	0.700136i	$0.753123\pi$
$602$	4.04414	−	12.4466i	0.164827	−	0.507285i
$603$	−13.2294	−	9.61170i	−0.538741	−	0.391418i
$604$	1.18012	−	3.63205i	0.0480186	−	0.147786i
$605$	−2.39246	+	7.36322i	−0.0972672	+	0.299358i
$606$	−14.1775	−	10.3006i	−0.575921	−	0.418431i
$607$	0.844896	−	2.60032i	0.0342933	−	0.105544i	−0.932445	−	0.361313i	$-0.882329\pi$
$607$	0.844896	−	2.60032i	0.0342933	−	0.105544i	0.966738	+	0.255769i	$0.0823286\pi$
$608$	0.100180	+	0.308322i	0.00406283	+	0.0125041i
$609$	−15.9029	+	11.5541i	−0.644419	+	0.468198i
$610$	4.80598	+	14.7913i	0.194588	+	0.598881i
$611$	−22.9695	−	16.6883i	−0.929247	−	0.675138i
$612$	4.05638	+	2.94713i	0.163969	+	0.119131i
$613$	−23.5616	+	17.1185i	−0.951645	+	0.691410i	−0.951195	−	0.308590i	$-0.900143\pi$
$613$	−23.5616	+	17.1185i	−0.951645	+	0.691410i	−0.000449259		1.00000i	$0.500143\pi$
$614$	5.30198			0.213970
$615$	−2.10156			−0.0847432
$616$	3.53813	−	2.57060i	0.142555	−	0.103573i
$617$	2.54647	−	7.83723i	0.102517	−	0.315515i	−0.886623	−	0.462494i	$-0.846955\pi$
$617$	2.54647	−	7.83723i	0.102517	−	0.315515i	0.989140	+	0.146978i	$0.0469548\pi$
$618$	5.45135	+	16.7775i	0.219285	+	0.674891i
$619$	−41.0774			−1.65104			−0.825520	−	0.564373i	$-0.809118\pi$
$619$	−41.0774			−1.65104			−0.825520	+	0.564373i	$0.809118\pi$
$620$	0.611225	−	5.53411i	0.0245474	−	0.222255i
$621$	1.11552			0.0447643
$622$	−7.39728	−	22.7665i	−0.296604	−	0.912852i
$623$	6.82710	−	21.0116i	0.273522	−	0.841814i
$624$	3.81600	−	2.77248i	0.152762	−	0.110988i
$625$	1.00000			0.0400000
$626$	−3.45328			−0.138021
$627$	0.473392	−	0.343940i	0.0189055	−	0.0137356i
$628$	14.0172	+	10.1841i	0.559348	+	0.406390i
$629$	34.6920	+	25.2052i	1.38326	+	1.00500i
$630$	−0.748744	−	2.30440i	−0.0298307	−	0.0918093i
$631$	17.3436	−	12.6009i	0.690438	−	0.501633i	−0.186366	−	0.982480i	$-0.559671\pi$
$631$	17.3436	−	12.6009i	0.690438	−	0.501633i	0.876804	+	0.480848i	$0.159671\pi$
$632$	−1.31755	−	4.05500i	−0.0524093	−	0.161299i
$633$	−7.96582	+	24.5163i	−0.316613	+	0.974435i
$634$	−11.3941	−	8.27831i	−0.452518	−	0.328774i
$635$	−3.62388	+	11.1532i	−0.143809	+	0.442600i
$636$	0.433877	−	1.33534i	0.0172043	−	0.0529495i
$637$	−4.30880	−	3.13052i	−0.170721	−	0.124036i
$638$	−4.52498	+	13.9264i	−0.179146	+	0.551353i
$639$	−3.40350	−	10.4749i	−0.134640	−	0.414381i
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	7.95563	+	24.4849i	0.314228	+	0.967095i	0.976071	+	0.217453i	$0.0697747\pi$
$641$	7.95563	+	24.4849i	0.314228	+	0.967095i	−0.661843	+	0.749643i	$0.730225\pi$
$642$	2.69184	+	1.95573i	0.106238	+	0.0771867i
$643$	−10.3053	−	7.48725i	−0.406402	−	0.295268i	0.365742	−	0.930716i	$-0.380815\pi$
$643$	−10.3053	−	7.48725i	−0.406402	−	0.295268i	−0.772144	+	0.635448i	$0.780815\pi$
$644$	−2.18669	+	1.58872i	−0.0861675	+	0.0626044i
$645$	−5.40124			−0.212673
$646$	−1.62547			−0.0639532
$647$	36.9577	−	26.8513i	1.45296	−	1.05563i	0.467826	−	0.883820i	$-0.345037\pi$
$647$	36.9577	−	26.8513i	1.45296	−	1.05563i	0.985129	−	0.171814i	$-0.0549628\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	−3.74185	−	11.5162i	−0.146880	−	0.452052i
$650$	4.71683			0.185009
$651$	−12.2951	−	5.55214i	−0.481884	−	0.217605i
$652$	−4.50230			−0.176324
$653$	−14.9951	−	46.1503i	−0.586805	−	1.80600i	−0.591898	−	0.806013i	$-0.701621\pi$
$653$	−14.9951	−	46.1503i	−0.586805	−	1.80600i	0.00509251	−	0.999987i	$-0.498379\pi$
$654$	−0.978026	+	3.01005i	−0.0382438	+	0.117702i
$655$	−7.29944	+	5.30335i	−0.285213	+	0.207219i
$656$	−2.10156			−0.0820522
$657$	−6.02255			−0.234962
$658$	−11.7992	+	8.57262i	−0.459980	+	0.334195i
$659$	−2.98330	−	2.16749i	−0.116213	−	0.0844335i	0.528161	−	0.849144i	$-0.322882\pi$
$659$	−2.98330	−	2.16749i	−0.116213	−	0.0844335i	−0.644374	+	0.764711i	$0.722882\pi$
$660$	−1.46024	−	1.06092i	−0.0568396	−	0.0412964i
$661$	−6.82942	−	21.0188i	−0.265634	−	0.817537i	−0.991547	−	0.129750i	$-0.958583\pi$
$661$	−6.82942	−	21.0188i	−0.265634	−	0.817537i	0.725913	−	0.687787i	$-0.241417\pi$
$662$	−11.7960	+	8.57029i	−0.458464	+	0.333094i
$663$	7.30825	+	22.4925i	0.283829	+	0.873536i
$664$	2.69898	−	8.30660i	0.104741	−	0.322358i
$665$	0.635487	+	0.461708i	0.0246431	+	0.0179043i
$666$	−2.64286	+	8.13388i	−0.102409	+	0.315181i
$667$	2.79659	−	8.60702i	0.108284	−	0.333265i
$668$	−11.3462	−	8.24349i	−0.438997	−	0.318950i
$669$	−1.26677	+	3.89871i	−0.0489761	+	0.150733i
$670$	−5.05317	−	15.5520i	−0.195221	−	0.600828i
$671$	22.7103	−	16.5000i	0.876721	−	0.636975i
$672$	−0.748744	−	2.30440i	−0.0288834	−	0.0888940i
$673$	−20.2474	−	14.7106i	−0.780480	−	0.567052i	0.124643	−	0.992202i	$-0.460222\pi$
$673$	−20.2474	−	14.7106i	−0.780480	−	0.567052i	−0.905123	+	0.425149i	$0.860222\pi$
$674$	−21.3796	−	15.5332i	−0.823512	−	0.598316i
$675$	−0.809017	+	0.587785i	−0.0311391	+	0.0226239i
$676$	9.24849			0.355711
$677$	8.10371			0.311451			0.155726	−	0.987800i	$-0.450228\pi$
$677$	8.10371			0.311451			0.155726	+	0.987800i	$0.450228\pi$
$678$	5.51661	−	4.00806i	0.211864	−	0.153928i
$679$	−13.1531	+	40.4811i	−0.504771	+	1.55352i
$680$	1.54940	+	4.76856i	0.0594167	+	0.182866i
$681$	−14.7910			−0.566792
$682$	−9.84084	+	2.03748i	−0.376825	+	0.0780190i
$683$	−30.4097			−1.16359			−0.581797	−	0.813334i	$-0.697650\pi$
$683$	−30.4097			−1.16359			−0.581797	+	0.813334i	$0.697650\pi$
$684$	−0.100180	−	0.308322i	−0.00383047	−	0.0117890i
$685$	−1.21313	+	3.73364i	−0.0463515	+	0.142655i
$686$	−15.9350	+	11.5775i	−0.608403	+	0.442030i
$687$	−1.62303			−0.0619223
$688$	−5.40124			−0.205920
$689$	5.35787	−	3.89272i	0.204119	−	0.148301i
$690$	0.902476	+	0.655687i	0.0343567	+	0.0249616i
$691$	−19.9287	−	14.4790i	−0.758122	−	0.550808i	0.140212	−	0.990122i	$-0.455222\pi$
$691$	−19.9287	−	14.4790i	−0.758122	−	0.550808i	−0.898334	+	0.439314i	$0.855222\pi$
$692$	−4.16908	−	12.8311i	−0.158485	−	0.487766i
$693$	−3.53813	+	2.57060i	−0.134403	+	0.0976492i
$694$	−4.30384	−	13.2459i	−0.163371	−	0.502806i
$695$	2.18271	−	6.71769i	0.0827949	−	0.254816i
$696$	6.56336	+	4.76856i	0.248783	+	0.180752i
$697$	3.25616	−	10.0214i	0.123336	−	0.379588i
$698$	−4.08009	+	12.5572i	−0.154434	+	0.475298i
$699$	−19.9699	−	14.5090i	−0.755330	−	0.548779i
$700$	0.748744	−	2.30440i	0.0282999	−	0.0870980i
$701$	8.26991	+	25.4522i	0.312350	+	0.961315i	0.976831	+	0.214010i	$0.0686526\pi$
$701$	8.26991	+	25.4522i	0.312350	+	0.961315i	−0.664481	+	0.747305i	$0.731347\pi$
$702$	−3.81600	+	2.77248i	−0.144026	+	0.104641i
$703$	−0.856784	−	2.63691i	−0.0323142	−	0.0994530i
$704$	−1.46024	−	1.06092i	−0.0550347	−	0.0399851i
$705$	4.86969	+	3.53804i	0.183403	+	0.133250i
$706$	9.91385	−	7.20284i	0.373113	−	0.271082i
$707$	−42.4612			−1.59692
$708$	−6.70870			−0.252128
$709$	23.6152	−	17.1574i	0.886886	−	0.644361i	−0.0481779	−	0.998839i	$-0.515341\pi$
$709$	23.6152	−	17.1574i	0.886886	−	0.644361i	0.935064	+	0.354478i	$0.115341\pi$
$710$	3.40350	−	10.4749i	0.127731	−	0.393116i
$711$	1.31755	+	4.05500i	0.0494120	+	0.152074i
$712$	−9.11807			−0.341714
$713$	6.08197	−	1.25923i	0.227772	−	0.0471585i
$714$	12.1488			0.454656
$715$	−2.63086	−	8.09696i	−0.0983887	−	0.302809i
$716$	−0.249598	+	0.768185i	−0.00932793	+	0.0287084i
$717$	−4.92480	+	3.57807i	−0.183920	+	0.133626i
$718$	−10.4646			−0.390535
$719$	24.5029			0.913804			0.456902	−	0.889517i	$-0.348959\pi$
$719$	24.5029			0.913804			0.456902	+	0.889517i	$0.348959\pi$
$720$	−0.809017	+	0.587785i	−0.0301503	+	0.0219055i
$721$	34.5804	+	25.1241i	1.28784	+	0.935671i
$722$	−15.2863	−	11.1061i	−0.568897	−	0.413328i
$723$	1.61181	+	4.96064i	0.0599438	+	0.184488i
$724$	−11.1633	+	8.11060i	−0.414880	+	0.301428i
$725$	2.50698	+	7.71569i	0.0931069	+	0.286554i
$726$	2.39246	−	7.36322i	0.0887924	−	0.273275i
$727$	−19.2013	−	13.9505i	−0.712136	−	0.517397i	0.171726	−	0.985145i	$-0.445066\pi$
$727$	−19.2013	−	13.9505i	−0.712136	−	0.517397i	−0.883862	+	0.467748i	$0.845066\pi$
$728$	3.53170	−	10.8694i	0.130893	−	0.402849i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−4.87235	−	3.53997i	−0.180334	−	0.131020i
$731$	8.36867	−	25.7561i	0.309526	−	0.952624i
$732$	−4.80598	−	14.7913i	−0.177634	−	0.546701i
$733$	10.1816	−	7.39739i	0.376067	−	0.273229i	−0.383655	−	0.923476i	$-0.625335\pi$
$733$	10.1816	−	7.39739i	0.376067	−	0.273229i	0.759722	+	0.650248i	$0.225335\pi$
$734$	9.30734	+	28.6450i	0.343540	+	1.05731i
$735$	0.913494	+	0.663692i	0.0336947	+	0.0244807i
$736$	0.902476	+	0.655687i	0.0332657	+	0.0241689i
$737$	−23.8784	+	17.3486i	−0.879571	+	0.639046i
$738$	2.10156			0.0773596
$739$	−29.7735			−1.09524			−0.547618	−	0.836728i	$-0.684465\pi$
$739$	−29.7735			−1.09524			−0.547618	+	0.836728i	$0.684465\pi$
$740$	−6.91909	+	5.02701i	−0.254351	+	0.184797i
$741$	0.472531	−	1.45430i	0.0173589	−	0.0534251i
$742$	−1.05128	−	3.23550i	−0.0385936	−	0.118779i
$743$	1.68416			0.0617859			0.0308930	−	0.999523i	$-0.490165\pi$
$743$	1.68416			0.0617859			0.0308930	+	0.999523i	$0.490165\pi$
$744$	−0.611225	+	5.53411i	−0.0224086	+	0.202890i
$745$	−12.0385			−0.441058
$746$	−6.26998	−	19.2970i	−0.229560	−	0.706514i
$747$	−2.69898	+	8.30660i	−0.0987504	+	0.303922i
$748$	7.32157	−	5.31943i	0.267703	−	0.194498i
$749$	8.06199			0.294579
$750$	−1.00000			−0.0365148
$751$	−11.4137	+	8.29254i	−0.416492	+	0.302599i	−0.776225	−	0.630456i	$-0.782868\pi$
$751$	−11.4137	+	8.29254i	−0.416492	+	0.302599i	0.359733	+	0.933055i	$0.382868\pi$
$752$	4.86969	+	3.53804i	0.177579	+	0.129019i
$753$	2.03336	+	1.47733i	0.0740999	+	0.0538367i
$754$	11.8250	+	36.3936i	0.430641	+	1.32538i
$755$	−3.08961	+	2.24473i	−0.112442	+	0.0816941i
$756$	0.748744	+	2.30440i	0.0272315	+	0.0838101i
$757$	−0.493620	+	1.51921i	−0.0179409	+	0.0552165i	−0.959626	−	0.281279i	$-0.909242\pi$
$757$	−0.493620	+	1.51921i	−0.0179409	+	0.0552165i	0.941685	+	0.336495i	$0.109242\pi$
$758$	−13.5373	−	9.83542i	−0.491697	−	0.357239i
$759$	0.622194	−	1.91492i	0.0225842	−	0.0695071i
$760$	0.100180	−	0.308322i	0.00363390	−	0.0111840i
$761$	−19.5514	−	14.2049i	−0.708738	−	0.514928i	0.174028	−	0.984741i	$-0.444322\pi$
$761$	−19.5514	−	14.2049i	−0.708738	−	0.514928i	−0.882766	+	0.469812i	$0.844322\pi$
$762$	3.62388	−	11.1532i	0.131279	−	0.404037i
$763$	2.36974	+	7.29332i	0.0857904	+	0.264036i
$764$	−3.73379	+	2.71276i	−0.135084	+	0.0981440i
$765$	−1.54940	−	4.76856i	−0.0560186	−	0.172408i
$766$	−5.96204	−	4.33168i	−0.215417	−	0.156510i
$767$	−25.6004	−	18.5998i	−0.924376	−	0.671598i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	7.98207			0.287841			0.143920	−	0.989589i	$-0.454029\pi$
$769$	7.98207			0.287841			0.143920	+	0.989589i	$0.454029\pi$
$770$	−4.37337			−0.157605
$771$	22.5899	−	16.4126i	0.813557	−	0.591084i
$772$	5.64976	−	17.3882i	0.203339	−	0.625814i
$773$	−2.81150	−	8.65290i	−0.101123	−	0.311223i	0.887678	−	0.460464i	$-0.152317\pi$
$773$	−2.81150	−	8.65290i	−0.101123	−	0.311223i	−0.988801	+	0.149241i	$0.952317\pi$
$774$	5.40124			0.194143
$775$	−3.74736	+	4.11792i	−0.134609	+	0.147920i
$776$	17.5669			0.630616
$777$	6.40361	+	19.7083i	0.229728	+	0.707030i
$778$	8.47852	−	26.0942i	0.303970	−	0.935522i
$779$	−0.551186	+	0.400460i	−0.0197483	+	0.0143480i
$780$	−4.71683			−0.168890
$781$	−19.8797			−0.711350
$782$	−4.52498	+	3.28759i	−0.161813	+	0.117564i
$783$	−6.56336	−	4.76856i	−0.234555	−	0.170414i
$784$	0.913494	+	0.663692i	0.0326248	+	0.0237033i
$785$	−5.35410	−	16.4782i	−0.191096	−	0.588133i
$786$	7.29944	−	5.30335i	0.260362	−	0.189164i
$787$	4.85077	+	14.9291i	0.172911	+	0.532166i	0.999532	−	0.0305936i	$-0.00973976\pi$
$787$	4.85077	+	14.9291i	0.172911	+	0.532166i	−0.826621	+	0.562759i	$0.809740\pi$
$788$	0.695606	−	2.14086i	0.0247800	−	0.0762648i
$789$	1.88758	+	1.37141i	0.0671996	+	0.0488234i
$790$	−1.31755	+	4.05500i	−0.0468763	+	0.144270i
$791$	5.10562	−	15.7135i	0.181535	−	0.558707i
$792$	1.46024	+	1.06092i	0.0518872	+	0.0376983i
$793$	22.6690	−	69.7679i	0.804999	−	2.47753i
$794$	2.83452	+	8.72377i	0.100594	+	0.309595i
$795$	−1.13590	+	0.825283i	−0.0402864	+	0.0292698i
$796$	2.20376	+	6.78247i	0.0781101	+	0.240398i
$797$	−22.3483	−	16.2370i	−0.791617	−	0.575143i	0.116826	−	0.993152i	$-0.462728\pi$
$797$	−22.3483	−	16.2370i	−0.791617	−	0.575143i	−0.908443	+	0.418009i	$0.862728\pi$
$798$	−0.635487	−	0.461708i	−0.0224960	−	0.0163443i
$799$	−24.4164	+	17.7396i	−0.863791	+	0.627581i
$800$	−1.00000			−0.0353553
$801$	9.11807			0.322171
$802$	−14.5247	+	10.5528i	−0.512885	+	0.372633i
$803$	−3.35914	+	10.3384i	−0.118542	+	0.364834i
$804$	5.05317	+	15.5520i	0.178211	+	0.548479i
$805$	2.70289			0.0952644
$806$	−17.6757	+	19.4235i	−0.622599	+	0.684165i
$807$	18.1776			0.639882
$808$	5.41532	+	16.6666i	0.190510	+	0.586331i
$809$	−13.2674	+	40.8328i	−0.466456	+	1.43560i	0.390686	+	0.920524i	$0.372238\pi$
$809$	−13.2674	+	40.8328i	−0.466456	+	1.43560i	−0.857142	+	0.515080i	$0.827762\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	−53.0390			−1.86245			−0.931226	−	0.364442i	$-0.881260\pi$
$811$	−53.0390			−1.86245			−0.931226	+	0.364442i	$0.881260\pi$
$812$	19.6571			0.689829
$813$	−16.1899	+	11.7626i	−0.567804	+	0.412534i
$814$	12.4886	+	9.07352i	0.437726	+	0.318027i
$815$	3.64244	+	2.64639i	0.127589	+	0.0926989i
$816$	−1.54940	−	4.76856i	−0.0542398	−	0.166933i
$817$	−1.41660	+	1.02922i	−0.0495607	+	0.0360080i
$818$	−10.1377	−	31.2006i	−0.354456	−	1.09090i
$819$	−3.53170	+	10.8694i	−0.123408	+	0.379809i
$820$	1.70020	+	1.23527i	0.0593736	+	0.0431374i
$821$	2.39687	−	7.37680i	0.0836513	−	0.257452i	−0.900479	−	0.434899i	$-0.856784\pi$
$821$	2.39687	−	7.37680i	0.0836513	−	0.257452i	0.984130	+	0.177447i	$0.0567839\pi$
$822$	1.21313	−	3.73364i	0.0423129	−	0.130226i
$823$	42.3576	+	30.7746i	1.47649	+	1.07273i	0.978666	+	0.205458i	$0.0658683\pi$
$823$	42.3576	+	30.7746i	1.47649	+	1.07273i	0.497826	+	0.867277i	$0.334132\pi$
$824$	5.45135	−	16.7775i	0.189907	−	0.584473i
$825$	0.557761	+	1.71661i	0.0194187	+	0.0597647i
$826$	−13.1506	+	9.55450i	−0.457569	+	0.332444i
$827$	0.408959	+	1.25865i	0.0142209	+	0.0437674i	0.957915	−	0.287051i	$-0.0926751\pi$
$827$	0.408959	+	1.25865i	0.0142209	+	0.0437674i	−0.943694	+	0.330819i	$0.892675\pi$
$828$	−0.902476	−	0.655687i	−0.0313632	−	0.0227867i
$829$	15.6629	+	11.3798i	0.543996	+	0.395236i	0.825567	−	0.564304i	$-0.190856\pi$
$829$	15.6629	+	11.3798i	0.543996	+	0.395236i	−0.281571	+	0.959540i	$0.590856\pi$
$830$	−7.06601	+	5.13376i	−0.245265	+	0.178195i
$831$	28.3396			0.983090
$832$	−4.71683			−0.163527
$833$	−4.58022	+	3.32772i	−0.158695	+	0.115299i
$834$	−2.18271	+	6.71769i	−0.0755810	+	0.232615i
$835$	4.33386	+	13.3382i	0.149979	+	0.461589i
$836$	−0.585145			−0.0202377
$837$	0.611225	−	5.53411i	0.0211270	−	0.191287i
$838$	−14.8516			−0.513041
$839$	10.5086	+	32.3423i	0.362799	+	1.11658i	0.951348	+	0.308118i	$0.0996993\pi$
$839$	10.5086	+	32.3423i	0.362799	+	1.11658i	−0.588549	+	0.808461i	$0.700301\pi$
$840$	−0.748744	+	2.30440i	−0.0258341	+	0.0795092i
$841$	−29.7854	+	21.6404i	−1.02708	+	0.746220i
$842$	8.78281			0.302676
$843$	−18.7951			−0.647337
$844$	20.8548	−	15.1519i	0.717852	−	0.521550i
$845$	−7.48219	−	5.43613i	−0.257395	−	0.187009i
$846$	−4.86969	−	3.53804i	−0.167423	−	0.121640i
$847$	−5.79689	−	17.8410i	−0.199183	−	0.613023i
$848$	−1.13590	+	0.825283i	−0.0390071	+	0.0283403i
$849$	3.44036	+	10.5883i	0.118073	+	0.363391i
$850$	1.54940	−	4.76856i	0.0531439	−	0.163560i
$851$	−7.71839	−	5.60774i	−0.264583	−	0.192231i
$852$	−3.40350	+	10.4749i	−0.116602	+	0.358864i
$853$	16.0919	−	49.5257i	0.550975	−	1.69573i	−0.155367	−	0.987857i	$-0.549656\pi$
$853$	16.0919	−	49.5257i	0.550975	−	1.69573i	0.706342	−	0.707870i	$-0.250344\pi$
$854$	−30.4865	−	22.1497i	−1.04323	−	0.757949i
$855$	−0.100180	+	0.308322i	−0.00342608	+	0.0105444i
$856$	−1.02819	−	3.16444i	−0.0351428	−	0.108159i
$857$	−43.7750	+	31.8044i	−1.49533	+	1.08642i	−0.523129	+	0.852253i	$0.675236\pi$
$857$	−43.7750	+	31.8044i	−1.49533	+	1.08642i	−0.972197	+	0.234165i	$0.924764\pi$
$858$	2.63086	+	8.09696i	0.0898162	+	0.276426i
$859$	26.1411	+	18.9926i	0.891923	+	0.648020i	0.936379	−	0.350992i	$-0.114155\pi$
$859$	26.1411	+	18.9926i	0.891923	+	0.648020i	−0.0444560	+	0.999011i	$0.514155\pi$
$860$	4.36969	+	3.17477i	0.149005	+	0.108259i
$861$	4.11956	−	2.99304i	0.140394	−	0.102002i
$862$	−23.7769			−0.809844
$863$	10.0039			0.340538			0.170269	−	0.985398i	$-0.445536\pi$
$863$	10.0039			0.340538			0.170269	+	0.985398i	$0.445536\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	−4.16908	+	12.8311i	−0.141753	+	0.436271i
$866$	−3.14897	−	9.69154i	−0.107006	−	0.329332i
$867$	8.13978			0.276442
$868$	6.68351	+	11.7187i	0.226853	+	0.397758i
$869$	7.69573			0.261060
$870$	−2.50698	−	7.71569i	−0.0849946	−	0.261586i
$871$	−23.8349	+	73.3564i	−0.807616	+	2.48559i
$872$	2.56050	−	1.86032i	0.0867096	−	0.0629982i
$873$	−17.5669			−0.594550
$874$	0.361639			0.0122326
$875$	−1.96024	+	1.42420i	−0.0662681	+	0.0481466i
$876$	4.87235	+	3.53997i	0.164621	+	0.119604i
$877$	−2.74491	−	1.99429i	−0.0926890	−	0.0673425i	0.540476	−	0.841360i	$-0.318244\pi$
$877$	−2.74491	−	1.99429i	−0.0926890	−	0.0673425i	−0.633165	+	0.774017i	$0.718244\pi$
$878$	−3.61964	−	11.1401i	−0.122157	−	0.375960i
$879$	−6.04511	+	4.39203i	−0.203897	+	0.148140i
$880$	0.557761	+	1.71661i	0.0188021	+	0.0578669i
$881$	10.2312	−	31.4885i	0.344699	−	1.06087i	−0.617046	−	0.786927i	$-0.711671\pi$
$881$	10.2312	−	31.4885i	0.344699	−	1.06087i	0.961745	−	0.273946i	$-0.0883291\pi$
$882$	−0.913494	−	0.663692i	−0.0307589	−	0.0223477i
$883$	−2.99169	+	9.20746i	−0.100678	+	0.309856i	−0.988692	−	0.149961i	$-0.952085\pi$
$883$	−2.99169	+	9.20746i	−0.100678	+	0.309856i	0.888014	+	0.459817i	$0.152085\pi$
$884$	7.30825	−	22.4925i	0.245803	−	0.756504i
$885$	5.42745	+	3.94328i	0.182442	+	0.132552i
$886$	11.4295	−	35.1764i	0.383982	−	1.18177i
$887$	11.3960	+	35.0732i	0.382639	+	1.17764i	0.938179	+	0.346151i	$0.112512\pi$
$887$	11.3960	+	35.0732i	0.382639	+	1.17764i	−0.555540	+	0.831490i	$0.687488\pi$
$888$	6.91909	−	5.02701i	0.232189	−	0.168696i
$889$	−8.78062	−	27.0240i	−0.294492	−	0.906355i
$890$	7.37667	+	5.35947i	0.247267	+	0.179650i
$891$	−1.46024	−	1.06092i	−0.0489198	−	0.0355423i
$892$	3.31644	−	2.40954i	0.111043	−	0.0806772i
$893$	1.95138			0.0653004
$894$	12.0385			0.402629
$895$	0.653457	−	0.474764i	0.0218427	−	0.0158696i
$896$	−0.748744	+	2.30440i	−0.0250138	+	0.0769845i
$897$	−1.62596	−	5.00420i	−0.0542893	−	0.167085i
$898$	−19.5435			−0.652176
$899$	−41.1672	−	18.5899i	−1.37300	−	0.620009i
$900$	1.00000			0.0333333
$901$	−2.17544	−	6.69532i	−0.0724745	−	0.223053i
$902$	1.17217	−	3.60757i	0.0390290	−	0.120119i
$903$	10.5877	−	7.69241i	0.352337	−	0.255988i
$904$	−6.81891			−0.226794
$905$	13.7986			0.458680
$906$	3.08961	−	2.24473i	0.102645	−	0.0745762i
$907$	−17.2831	−	12.5569i	−0.573875	−	0.416945i	0.262636	−	0.964895i	$-0.415408\pi$
$907$	−17.2831	−	12.5569i	−0.573875	−	0.416945i	−0.836511	+	0.547950i	$0.815408\pi$
$908$	11.9662	+	8.69393i	0.397111	+	0.288518i
$909$	−5.41532	−	16.6666i	−0.179615	−	0.552798i
$910$	−9.24610	+	6.71769i	−0.306505	+	0.222689i
$911$	7.40895	+	22.8024i	0.245469	+	0.755477i	0.995559	+	0.0941408i	$0.0300104\pi$
$911$	7.40895	+	22.8024i	0.245469	+	0.755477i	−0.750089	+	0.661336i	$0.769990\pi$
$912$	−0.100180	+	0.308322i	−0.00331729	+	0.0102096i
$913$	12.7538	+	9.26619i	0.422090	+	0.306666i
$914$	10.2455	−	31.5324i	0.338890	−	1.04300i
$915$	−4.80598	+	14.7913i	−0.158881	+	0.488984i
$916$	1.31306	+	0.953991i	0.0433846	+	0.0315207i
$917$	6.75562	−	20.7917i	0.223090	−	0.686601i
$918$	1.54940	+	4.76856i	0.0511378	+	0.157386i
$919$	30.1080	−	21.8747i	0.993170	−	0.721580i	0.0325570	−	0.999470i	$-0.489635\pi$
$919$	30.1080	−	21.8747i	0.993170	−	0.721580i	0.960613	+	0.277890i	$0.0896349\pi$
$920$	−0.344715	−	1.06092i	−0.0113649	−	0.0349776i
$921$	4.28939	+	3.11642i	0.141340	+	0.102690i
$922$	−3.43399	−	2.49494i	−0.113092	−	0.0821664i
$923$	−42.0292	+	30.5360i	−1.38341	+	1.00511i
$924$	4.37337			0.143873
$925$	8.55247			0.281203
$926$	−2.42280	+	1.76027i	−0.0796181	+	0.0578459i
$927$	−5.45135	+	16.7775i	−0.179046	+	0.551046i
$928$	−2.50698	−	7.71569i	−0.0822956	−	0.253280i
$929$	5.38273			0.176602			0.0883009	−	0.996094i	$-0.471856\pi$
$929$	5.38273			0.176602			0.0883009	+	0.996094i	$0.471856\pi$
$930$	3.74736	−	4.11792i	0.122881	−	0.135032i
$931$	0.366055			0.0119970
$932$	7.62781	+	23.4760i	0.249857	+	0.768982i
$933$	7.39728	−	22.7665i	0.242176	−	0.745341i
$934$	−3.72299	+	2.70491i	−0.121820	+	0.0885074i
$935$	−9.04995			−0.295965
$936$	4.71683			0.154174
$937$	16.6234	−	12.0776i	0.543063	−	0.394558i	−0.282159	−	0.959368i	$-0.591050\pi$
$937$	16.6234	−	12.0776i	0.543063	−	0.394558i	0.825221	+	0.564810i	$0.191050\pi$
$938$	32.0546	+	23.2890i	1.04662	+	0.760413i
$939$	−2.79376	−	2.02978i	−0.0911709	−	0.0662395i
$940$	−1.86006	−	5.72467i	−0.0606684	−	0.186718i
$941$	−39.0622	+	28.3803i	−1.27339	+	0.925172i	−0.999332	−	0.0365408i	$-0.988366\pi$
$941$	−39.0622	+	28.3803i	−1.27339	+	0.925172i	−0.274058	+	0.961713i	$0.588366\pi$
$942$	5.35410	+	16.4782i	0.174446	+	0.536890i
$943$	−0.724440	+	2.22960i	−0.0235910	+	0.0726057i
$944$	5.42745	+	3.94328i	0.176649	+	0.128343i
$945$	0.748744	−	2.30440i	0.0243566	−	0.0749620i
$946$	3.01260	−	9.27182i	0.0979480	−	0.301453i
$947$	−5.63111	−	4.09124i	−0.182986	−	0.132947i	0.492521	−	0.870301i	$-0.336075\pi$
$947$	−5.63111	−	4.09124i	−0.182986	−	0.132947i	−0.675508	+	0.737353i	$0.736075\pi$
$948$	1.31755	−	4.05500i	0.0427920	−	0.131700i
$949$	8.77836	+	27.0170i	0.284958	+	0.877009i
$950$	−0.262274	+	0.190553i	−0.00850930	+	0.00618237i
$951$	−4.35216	−	13.3946i	−0.141129	−	0.434349i
$952$	−9.82855	−	7.14086i	−0.318545	−	0.231436i
$953$	21.3565	+	15.5164i	0.691806	+	0.502627i	0.877253	−	0.480028i	$-0.159373\pi$
$953$	21.3565	+	15.5164i	0.691806	+	0.502627i	−0.185447	+	0.982654i	$0.559373\pi$
$954$	1.13590	−	0.825283i	0.0367763	−	0.0267195i
$955$	4.61521			0.149345
$956$	6.08738			0.196880
$957$	−11.8465	+	8.60702i	−0.382944	+	0.278225i
$958$	2.51639	−	7.74466i	0.0813010	−	0.250219i
$959$	−2.93941	−	9.04656i	−0.0949184	−	0.292129i
$960$	1.00000			0.0322749
$961$	−2.91457	−	30.8627i	−0.0940185	−	0.995570i
$962$	40.3405			1.30063
$963$	1.02819	+	3.16444i	0.0331330	+	0.101973i
$964$	1.61181	−	4.96064i	0.0519129	−	0.159771i
$965$	−14.7913	+	10.7465i	−0.476147	+	0.345941i
$966$	−2.70289			−0.0869641
$967$	24.0701			0.774043			0.387021	−	0.922071i	$-0.373504\pi$
$967$	24.0701			0.774043			0.387021	+	0.922071i	$0.373504\pi$
$968$	−6.26353	+	4.55072i	−0.201317	+	0.146266i
$969$	−1.31503	−	0.955427i	−0.0422449	−	0.0306927i
$970$	−14.2119	−	10.3256i	−0.456318	−	0.331534i
$971$	−12.9516	−	39.8608i	−0.415636	−	1.27920i	−0.911681	−	0.410899i	$-0.865215\pi$
$971$	−12.9516	−	39.8608i	−0.415636	−	1.27920i	0.496045	−	0.868297i	$-0.334785\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	5.28867	+	16.2769i	0.169547	+	0.521812i
$974$	10.7156	−	32.9791i	0.343349	−	1.05672i
$975$	3.81600	+	2.77248i	0.122210	+	0.0887905i
$976$	−4.80598	+	14.7913i	−0.153836	+	0.473457i
$977$	6.07981	−	18.7117i	0.194510	−	0.598641i	−0.805472	−	0.592634i	$-0.798088\pi$
$977$	6.07981	−	18.7117i	0.194510	−	0.598641i	0.999982	−	0.00600699i	$-0.00191210\pi$
$978$	−3.64244	−	2.64639i	−0.116472	−	0.0846221i
$979$	5.08570	−	15.6522i	0.162540	−	0.500246i
$980$	−0.348924	−	1.07388i	−0.0111460	−	0.0343037i
$981$	−2.56050	+	1.86032i	−0.0817506	+	0.0593953i
$982$	−6.52347	−	20.0772i	−0.208172	−	0.640688i
$983$	44.3552	+	32.2259i	1.41471	+	1.02785i	0.992617	+	0.121295i	$0.0387046\pi$
$983$	44.3552	+	32.2259i	1.41471	+	1.02785i	0.422094	+	0.906552i	$0.361295\pi$
$984$	−1.70020	−	1.23527i	−0.0542004	−	0.0393789i
$985$	−1.82112	+	1.32312i	−0.0580257	+	0.0421582i
$986$	40.6770			1.29542
$987$	−14.5846			−0.464233
$988$	−1.23710	+	0.898808i	−0.0393575	+	0.0285949i
$989$	−1.86189	+	5.73030i	−0.0592046	+	0.182213i
$990$	−0.557761	−	1.71661i	−0.0177268	−	0.0545575i
$991$	−5.41290			−0.171947			−0.0859733	−	0.996297i	$-0.527400\pi$
$991$	−5.41290			−0.171947			−0.0859733	+	0.996297i	$0.527400\pi$
$992$	3.74736	−	4.11792i	0.118979	−	0.130744i
$993$	−14.5806			−0.462703
$994$	8.24663	+	25.3805i	0.261567	+	0.805021i
$995$	2.20376	−	6.78247i	0.0698638	−	0.215019i
$996$	7.06601	−	5.13376i	0.223895	−	0.162669i
$997$	−31.3340			−0.992356			−0.496178	−	0.868221i	$-0.665264\pi$
$997$	−31.3340			−0.992356			−0.496178	+	0.868221i	$0.665264\pi$
$998$	24.7967			0.784924
$999$	−6.91909	+	5.02701i	−0.218910	+	0.159048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.e.841.1	yes	12
31.8	even	5	inner	930.2.n.e.721.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.e.721.1	✓	12	31.8	even	5	inner
930.2.n.e.841.1	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.96024 + 1.42420i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.96024 + 1.42420i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(-1.46024 + 1.06092i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-1.45758 + 4.48597i) q^{13} +(1.96024 + 1.42420i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.05638 + 2.94713i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-0.100180 - 0.308322i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(0.748744 + 2.30440i) q^{21} +(1.46024 + 1.06092i) q^{22} +(-0.902476 - 0.655687i) q^{23} +(0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +4.71683 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.748744 - 2.30440i) q^{28} +(2.50698 + 7.71569i) q^{29} -1.00000 q^{30} +(-3.74736 + 4.11792i) q^{31} -1.00000 q^{32} +(0.557761 + 1.71661i) q^{33} +(1.54940 - 4.76856i) q^{34} +(-1.96024 + 1.42420i) q^{35} +1.00000 q^{36} +8.55247 q^{37} +(-0.262274 + 0.190553i) q^{38} +(3.81600 + 2.77248i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-0.649419 - 1.99870i) q^{41} +(1.96024 - 1.42420i) q^{42} +(-1.66907 - 5.13688i) q^{43} +(0.557761 - 1.71661i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(-0.344715 + 1.06092i) q^{46} +(-1.86006 + 5.72467i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.348924 + 1.07388i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(4.05638 - 2.94713i) q^{51} +(-1.45758 - 4.48597i) q^{52} +(-1.13590 - 0.825283i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-1.46024 + 1.06092i) q^{55} -2.42299 q^{56} -0.324189 q^{57} +(6.56336 - 4.76856i) q^{58} +(-2.07310 + 6.38035i) q^{59} +(0.309017 + 0.951057i) q^{60} -15.5525 q^{61} +(5.07438 + 2.29144i) q^{62} +2.42299 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.45758 + 4.48597i) q^{65} +(1.46024 - 1.06092i) q^{66} +16.3524 q^{67} -5.01396 q^{68} +(-0.902476 + 0.655687i) q^{69} +(1.96024 + 1.42420i) q^{70} +(8.91048 + 6.47384i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(4.87235 - 3.53997i) q^{73} +(-2.64286 - 8.13388i) q^{74} +(0.309017 - 0.951057i) q^{75} +(0.262274 + 0.190553i) q^{76} +(1.35145 - 4.15932i) q^{77} +(1.45758 - 4.48597i) q^{78} +(-3.44939 - 2.50613i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.70020 + 1.23527i) q^{82} +(-2.69898 - 8.30660i) q^{83} +(-1.96024 - 1.42420i) q^{84} +(4.05638 + 2.94713i) q^{85} +(-4.36969 + 3.17477i) q^{86} +8.11276 q^{87} -1.80495 q^{88} +(-7.37667 + 5.35947i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(-3.53170 - 10.8694i) q^{91} +1.11552 q^{92} +(2.75838 + 4.83646i) q^{93} +6.01927 q^{94} +(-0.100180 - 0.308322i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(14.2119 - 10.3256i) q^{97} +1.12914 q^{98} +1.80495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more