LMFDB - Embedded newform 430.2.e.e.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.e (of order $3$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			251.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	430.251
Dual form			430.2.e.e.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.285997 + 0.495361i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.285997 + 0.495361i) q^{6} +(2.33641 - 4.04678i) q^{7} +1.00000 q^{8} +(1.33641 - 2.31473i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.285997 + 0.495361i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.285997 + 0.495361i) q^{6} +(2.33641 - 4.04678i) q^{7} +1.00000 q^{8} +(1.33641 - 2.31473i) q^{9} +(0.500000 + 0.866025i) q^{10} -1.57199 q^{11} +(0.285997 + 0.495361i) q^{12} +(-2.45882 + 4.25880i) q^{13} +(2.33641 - 4.04678i) q^{14} +(-0.285997 + 0.495361i) q^{15} +1.00000 q^{16} +(1.33641 - 2.31473i) q^{18} +(-0.214003 - 0.370665i) q^{19} +(0.500000 + 0.866025i) q^{20} +2.67282 q^{21} -1.57199 q^{22} +(0.336412 + 0.582682i) q^{23} +(0.285997 + 0.495361i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.45882 + 4.25880i) q^{26} +3.24482 q^{27} +(2.33641 - 4.04678i) q^{28} +(-2.47842 + 4.29275i) q^{29} +(-0.285997 + 0.495361i) q^{30} +(3.12241 + 5.40817i) q^{31} +1.00000 q^{32} +(-0.449585 - 0.778704i) q^{33} +4.67282 q^{35} +(1.33641 - 2.31473i) q^{36} +(2.78600 + 4.82549i) q^{37} +(-0.214003 - 0.370665i) q^{38} -2.81286 q^{39} +(0.500000 + 0.866025i) q^{40} -7.48963 q^{41} +2.67282 q^{42} +(1.90643 - 6.27420i) q^{43} -1.57199 q^{44} +2.67282 q^{45} +(0.336412 + 0.582682i) q^{46} -10.6336 q^{47} +(0.285997 + 0.495361i) q^{48} +(-7.41764 - 12.8477i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.45882 + 4.25880i) q^{52} +(-2.24482 - 3.88814i) q^{53} +3.24482 q^{54} +(-0.785997 - 1.36139i) q^{55} +(2.33641 - 4.04678i) q^{56} +(0.122408 - 0.212018i) q^{57} +(-2.47842 + 4.29275i) q^{58} -10.2017 q^{59} +(-0.285997 + 0.495361i) q^{60} +(3.90841 - 6.76956i) q^{61} +(3.12241 + 5.40817i) q^{62} +(-6.24482 - 10.8163i) q^{63} +1.00000 q^{64} -4.91764 q^{65} +(-0.449585 - 0.778704i) q^{66} +(5.63164 + 9.75429i) q^{67} +(-0.192425 + 0.333290i) q^{69} +4.67282 q^{70} +(-0.449585 + 0.778704i) q^{71} +(1.33641 - 2.31473i) q^{72} +(-7.22324 + 12.5110i) q^{73} +(2.78600 + 4.82549i) q^{74} -0.571993 q^{75} +(-0.214003 - 0.370665i) q^{76} +(-3.67282 + 6.36152i) q^{77} -2.81286 q^{78} +(6.48963 - 11.2404i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.08123 - 5.33684i) q^{81} -7.48963 q^{82} +(7.86723 + 13.6264i) q^{83} +2.67282 q^{84} +(1.90643 - 6.27420i) q^{86} -2.83528 q^{87} -1.57199 q^{88} +(-3.21598 - 5.57024i) q^{89} +2.67282 q^{90} +(11.4896 + 19.9006i) q^{91} +(0.336412 + 0.582682i) q^{92} +(-1.78600 + 3.09344i) q^{93} -10.6336 q^{94} +(0.214003 - 0.370665i) q^{95} +(0.285997 + 0.495361i) q^{96} -4.28797 q^{97} +(-7.41764 - 12.8477i) q^{98} +(-2.10083 + 3.63875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 3 q^{5} + q^{6} + 4 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 3 * q^5 + q^6 + 4 * q^7 + 6 * q^8 - 2 * q^9	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 3 q^{5} + q^{6} + 4 q^{7} + 6 q^{8} - 2 q^{9} + 3 q^{10} - 8 q^{11} + q^{12} + 6 q^{13} + 4 q^{14} - q^{15} + 6 q^{16} - 2 q^{18} - 2 q^{19} + 3 q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} + q^{24} - 3 q^{25} + 6 q^{26} - 2 q^{27} + 4 q^{28} - 7 q^{29} - q^{30} + 8 q^{31} + 6 q^{32} - 12 q^{33} + 8 q^{35} - 2 q^{36} + 16 q^{37} - 2 q^{38} - 4 q^{39} + 3 q^{40} - 2 q^{41} - 4 q^{42} + 5 q^{43} - 8 q^{44} - 4 q^{45} - 8 q^{46} - 18 q^{47} + q^{48} - 3 q^{49} - 3 q^{50} + 6 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} + 4 q^{56} - 10 q^{57} - 7 q^{58} - 24 q^{59} - q^{60} + 12 q^{61} + 8 q^{62} - 16 q^{63} + 6 q^{64} + 12 q^{65} - 12 q^{66} - 7 q^{67} + 6 q^{69} + 8 q^{70} - 12 q^{71} - 2 q^{72} - 14 q^{73} + 16 q^{74} - 2 q^{75} - 2 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} + 3 q^{80} + 13 q^{81} - 2 q^{82} + 15 q^{83} - 4 q^{84} + 5 q^{86} + 66 q^{87} - 8 q^{88} - 15 q^{89} - 4 q^{90} + 26 q^{91} - 8 q^{92} - 10 q^{93} - 18 q^{94} + 2 q^{95} + q^{96} - 20 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 3 * q^5 + q^6 + 4 * q^7 + 6 * q^8 - 2 * q^9 + 3 * q^10 - 8 * q^11 + q^12 + 6 * q^13 + 4 * q^14 - q^15 + 6 * q^16 - 2 * q^18 - 2 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 + q^24 - 3 * q^25 + 6 * q^26 - 2 * q^27 + 4 * q^28 - 7 * q^29 - q^30 + 8 * q^31 + 6 * q^32 - 12 * q^33 + 8 * q^35 - 2 * q^36 + 16 * q^37 - 2 * q^38 - 4 * q^39 + 3 * q^40 - 2 * q^41 - 4 * q^42 + 5 * q^43 - 8 * q^44 - 4 * q^45 - 8 * q^46 - 18 * q^47 + q^48 - 3 * q^49 - 3 * q^50 + 6 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 + 4 * q^56 - 10 * q^57 - 7 * q^58 - 24 * q^59 - q^60 + 12 * q^61 + 8 * q^62 - 16 * q^63 + 6 * q^64 + 12 * q^65 - 12 * q^66 - 7 * q^67 + 6 * q^69 + 8 * q^70 - 12 * q^71 - 2 * q^72 - 14 * q^73 + 16 * q^74 - 2 * q^75 - 2 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 + 3 * q^80 + 13 * q^81 - 2 * q^82 + 15 * q^83 - 4 * q^84 + 5 * q^86 + 66 * q^87 - 8 * q^88 - 15 * q^89 - 4 * q^90 + 26 * q^91 - 8 * q^92 - 10 * q^93 - 18 * q^94 + 2 * q^95 + q^96 - 20 * q^97 - 3 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.285997	+	0.495361i	0.165120	+	0.285997i	0.936698	−	0.350138i	$-0.113865\pi$
$3$	0.285997	+	0.495361i	0.165120	+	0.285997i	−0.771578	+	0.636135i	$0.780532\pi$
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.285997	+	0.495361i	0.116758	+	0.202230i
$7$	2.33641	−	4.04678i	0.883081	−	1.52954i	0.0351829	−	0.999381i	$-0.488799\pi$
$7$	2.33641	−	4.04678i	0.883081	−	1.52954i	0.847898	−	0.530160i	$-0.177868\pi$
$8$	1.00000			0.353553
$9$	1.33641	−	2.31473i	0.445471	−	0.771578i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−1.57199			−0.473974			−0.236987	−	0.971513i	$-0.576160\pi$
$11$	−1.57199			−0.473974			−0.236987	+	0.971513i	$0.576160\pi$
$12$	0.285997	+	0.495361i	0.0825601	+	0.142998i
$13$	−2.45882	+	4.25880i	−0.681954	+	1.18118i	0.292430	+	0.956287i	$0.405536\pi$
$13$	−2.45882	+	4.25880i	−0.681954	+	1.18118i	−0.974384	+	0.224892i	$0.927797\pi$
$14$	2.33641	−	4.04678i	0.624432	−	1.08155i
$15$	−0.285997	+	0.495361i	−0.0738440	+	0.127902i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	1.33641	−	2.31473i	0.314995	−	0.545588i
$19$	−0.214003	−	0.370665i	−0.0490957	−	0.0850363i	0.840433	−	0.541915i	$-0.182301\pi$
$19$	−0.214003	−	0.370665i	−0.0490957	−	0.0850363i	−0.889529	+	0.456879i	$0.848967\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	2.67282			0.583258
$22$	−1.57199			−0.335150
$23$	0.336412	+	0.582682i	0.0701467	+	0.121498i	0.898965	−	0.438020i	$-0.144320\pi$
$23$	0.336412	+	0.582682i	0.0701467	+	0.121498i	−0.828819	+	0.559517i	$0.810987\pi$
$24$	0.285997	+	0.495361i	0.0583788	+	0.101115i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.45882	+	4.25880i	−0.482214	+	0.835220i
$27$	3.24482			0.624465
$28$	2.33641	−	4.04678i	0.441540	−	0.764770i
$29$	−2.47842	+	4.29275i	−0.460231	+	0.797144i	−0.998972	−	0.0453274i	$-0.985567\pi$
$29$	−2.47842	+	4.29275i	−0.460231	+	0.797144i	0.538741	+	0.842472i	$0.318900\pi$
$30$	−0.285997	+	0.495361i	−0.0522156	+	0.0904401i
$31$	3.12241	+	5.40817i	0.560801	+	0.971336i	0.997427	+	0.0716927i	$0.0228401\pi$
$31$	3.12241	+	5.40817i	0.560801	+	0.971336i	−0.436626	+	0.899643i	$0.643827\pi$
$32$	1.00000			0.176777
$33$	−0.449585	−	0.778704i	−0.0782627	−	0.135555i
$34$		0			0
$35$	4.67282			0.789851
$36$	1.33641	−	2.31473i	0.222735	−	0.385789i
$37$	2.78600	+	4.82549i	0.458015	+	0.793305i	0.998856	−	0.0478196i	$-0.0152273\pi$
$37$	2.78600	+	4.82549i	0.458015	+	0.793305i	−0.540841	+	0.841125i	$0.681894\pi$
$38$	−0.214003	−	0.370665i	−0.0347159	−	0.0601298i
$39$	−2.81286			−0.450418
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−7.48963			−1.16968			−0.584842	−	0.811147i	$-0.698844\pi$
$41$	−7.48963			−1.16968			−0.584842	+	0.811147i	$0.698844\pi$
$42$	2.67282			0.412426
$43$	1.90643	−	6.27420i	0.290728	−	0.956806i
$43$	1.90643	−	6.27420i	0.290728	−	0.956806i
$44$	−1.57199			−0.236987
$45$	2.67282			0.398441
$46$	0.336412	+	0.582682i	0.0496012	+	0.0859118i
$47$	−10.6336			−1.55107			−0.775536	−	0.631303i	$-0.782521\pi$
$47$	−10.6336			−1.55107			−0.775536	+	0.631303i	$0.782521\pi$
$48$	0.285997	+	0.495361i	0.0412801	+	0.0714992i
$49$	−7.41764	−	12.8477i	−1.05966	−	1.83539i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−2.45882	+	4.25880i	−0.340977	+	0.590590i
$53$	−2.24482	−	3.88814i	−0.308349	−	0.534077i	0.669652	−	0.742675i	$-0.266443\pi$
$53$	−2.24482	−	3.88814i	−0.308349	−	0.534077i	−0.978001	+	0.208598i	$0.933110\pi$
$54$	3.24482			0.441564
$55$	−0.785997	−	1.36139i	−0.105984	−	0.183569i
$56$	2.33641	−	4.04678i	0.312216	−	0.540774i
$57$	0.122408	−	0.212018i	0.0162134	−	0.0280824i
$58$	−2.47842	+	4.29275i	−0.325433	+	0.563666i
$59$	−10.2017			−1.32814			−0.664072	−	0.747669i	$-0.731173\pi$
$59$	−10.2017			−1.32814			−0.664072	+	0.747669i	$0.731173\pi$
$60$	−0.285997	+	0.495361i	−0.0369220	+	0.0639508i
$61$	3.90841	−	6.76956i	0.500420	−	0.866753i	−0.499580	−	0.866268i	$-0.666512\pi$
$61$	3.90841	−	6.76956i	0.500420	−	0.866753i	1.00000		0.000485039i	$-0.000154393\pi$
$62$	3.12241	+	5.40817i	0.396546	+	0.686838i
$63$	−6.24482	−	10.8163i	−0.786773	−	1.36273i
$64$	1.00000			0.125000
$65$	−4.91764			−0.609958
$66$	−0.449585	−	0.778704i	−0.0553401	−	0.0958518i
$67$	5.63164	+	9.75429i	0.688015	+	1.19168i	0.972479	+	0.232990i	$0.0748509\pi$
$67$	5.63164	+	9.75429i	0.688015	+	1.19168i	−0.284464	+	0.958687i	$0.591816\pi$
$68$		0			0
$69$	−0.192425	+	0.333290i	−0.0231653	+	0.0401235i
$70$	4.67282			0.558509
$71$	−0.449585	+	0.778704i	−0.0533559	+	0.0924151i	−0.891470	−	0.453080i	$-0.850325\pi$
$71$	−0.449585	+	0.778704i	−0.0533559	+	0.0924151i	0.838114	+	0.545495i	$0.183658\pi$
$72$	1.33641	−	2.31473i	0.157498	−	0.272794i
$73$	−7.22324	+	12.5110i	−0.845416	+	1.46430i	0.0398431	+	0.999206i	$0.487314\pi$
$73$	−7.22324	+	12.5110i	−0.845416	+	1.46430i	−0.885259	+	0.465098i	$0.846019\pi$
$74$	2.78600	+	4.82549i	0.323866	+	0.560952i
$75$	−0.571993			−0.0660481
$76$	−0.214003	−	0.370665i	−0.0245479	−	0.0425182i
$77$	−3.67282	+	6.36152i	−0.418557	+	0.724962i
$78$	−2.81286			−0.318493
$79$	6.48963	−	11.2404i	0.730141	−	1.26464i	−0.226682	−	0.973969i	$-0.572788\pi$
$79$	6.48963	−	11.2404i	0.730141	−	1.26464i	0.956823	−	0.290672i	$-0.0938789\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.08123	−	5.33684i	−0.342359	−	0.592983i
$82$	−7.48963			−0.827092
$83$	7.86723	+	13.6264i	0.863540	+	1.49570i	0.868489	+	0.495708i	$0.165091\pi$
$83$	7.86723	+	13.6264i	0.863540	+	1.49570i	−0.00494923	+	0.999988i	$0.501575\pi$
$84$	2.67282			0.291629
$85$		0			0
$86$	1.90643	−	6.27420i	0.205575	−	0.676564i
$87$	−2.83528			−0.303974
$88$	−1.57199			−0.167575
$89$	−3.21598	−	5.57024i	−0.340893	−	0.590444i	0.643706	−	0.765273i	$-0.277396\pi$
$89$	−3.21598	−	5.57024i	−0.340893	−	0.590444i	−0.984599	+	0.174829i	$0.944063\pi$
$90$	2.67282			0.281740
$91$	11.4896	+	19.9006i	1.20444	+	2.08615i
$92$	0.336412	+	0.582682i	0.0350734	+	0.0607488i
$93$	−1.78600	+	3.09344i	−0.185199	+	0.320774i
$94$	−10.6336			−1.09677
$95$	0.214003	−	0.370665i	0.0219563	−	0.0380294i
$96$	0.285997	+	0.495361i	0.0291894	+	0.0505575i
$97$	−4.28797			−0.435378			−0.217689	−	0.976018i	$-0.569852\pi$
$97$	−4.28797			−0.435378			−0.217689	+	0.976018i	$0.569852\pi$
$98$	−7.41764	−	12.8477i	−0.749295	−	1.29782i
$99$	−2.10083	+	3.63875i	−0.211141	+	0.365708i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−0.570017	+	0.987298i	−0.0567188	+	0.0982398i	−0.892991	−	0.450075i	$-0.851397\pi$
$101$	−0.570017	+	0.987298i	−0.0567188	+	0.0982398i	0.836272	+	0.548315i	$0.184731\pi$
$102$		0			0
$103$	3.98040	−	6.89425i	0.392200	−	0.679311i	−0.600539	−	0.799595i	$-0.705047\pi$
$103$	3.98040	−	6.89425i	0.392200	−	0.679311i	0.992739	+	0.120284i	$0.0383807\pi$
$104$	−2.45882	+	4.25880i	−0.241107	+	0.417610i
$105$	1.33641	+	2.31473i	0.130420	+	0.225895i
$106$	−2.24482	−	3.88814i	−0.218036	−	0.377649i
$107$	6.30249			0.609285			0.304642	−	0.952467i	$-0.401463\pi$
$107$	6.30249			0.609285			0.304642	+	0.952467i	$0.401463\pi$
$108$	3.24482			0.312233
$109$	−10.1512	−	17.5825i	−0.972313	−	1.68410i	−0.688531	−	0.725207i	$-0.741744\pi$
$109$	−10.1512	−	17.5825i	−0.972313	−	1.68410i	−0.283782	−	0.958889i	$-0.591589\pi$
$110$	−0.785997	−	1.36139i	−0.0749418	−	0.129803i
$111$	−1.59357	+	2.76015i	−0.151255	+	0.261982i
$112$	2.33641	−	4.04678i	0.220770	−	0.382385i
$113$	−1.95684			−0.184084			−0.0920422	−	0.995755i	$-0.529339\pi$
$113$	−1.95684			−0.184084			−0.0920422	+	0.995755i	$0.529339\pi$
$114$	0.122408	−	0.212018i	0.0114646	−	0.0198573i
$115$	−0.336412	+	0.582682i	−0.0313706	+	0.0543354i
$116$	−2.47842	+	4.29275i	−0.230116	+	0.398572i
$117$	6.57199	+	11.3830i	0.607581	+	1.05236i
$118$	−10.2017			−0.939139
$119$		0			0
$120$	−0.285997	+	0.495361i	−0.0261078	+	0.0452200i
$121$	−8.52884			−0.775349
$122$	3.90841	−	6.76956i	0.353850	−	0.612887i
$123$	−2.14201	−	3.71007i	−0.193139	−	0.334526i
$124$	3.12241	+	5.40817i	0.280401	+	0.485668i
$125$	−1.00000			−0.0894427
$126$	−6.24482	−	10.8163i	−0.556333	−	0.963596i
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	1.00000			0.0883883
$129$	3.65322	−	0.850029i	0.321648	−	0.0748409i
$130$	−4.91764			−0.431306
$131$	7.05767			0.616632			0.308316	−	0.951284i	$-0.400235\pi$
$131$	7.05767			0.616632			0.308316	+	0.951284i	$0.400235\pi$
$132$	−0.449585	−	0.778704i	−0.0391313	−	0.0677775i
$133$	−2.00000			−0.173422
$134$	5.63164	+	9.75429i	0.486500	+	0.842643i
$135$	1.62241	+	2.81009i	0.139635	+	0.241854i
$136$		0			0
$137$	13.7921			1.17834			0.589170	−	0.808009i	$-0.299455\pi$
$137$	13.7921			1.17834			0.589170	+	0.808009i	$0.299455\pi$
$138$	−0.192425	+	0.333290i	−0.0163803	+	0.0283716i
$139$	−4.52884	−	7.84418i	−0.384131	−	0.665334i	0.607517	−	0.794306i	$-0.292166\pi$
$139$	−4.52884	−	7.84418i	−0.384131	−	0.665334i	−0.991648	+	0.128972i	$0.958832\pi$
$140$	4.67282			0.394926
$141$	−3.04118	−	5.26748i	−0.256114	−	0.443602i
$142$	−0.449585	+	0.778704i	−0.0377283	+	0.0653474i
$143$	3.86525	−	6.69481i	0.323228	−	0.559848i
$144$	1.33641	−	2.31473i	0.111368	−	0.192894i
$145$	−4.95684			−0.411643
$146$	−7.22324	+	12.5110i	−0.597800	+	1.03542i
$147$	4.24284	−	7.34882i	0.349944	−	0.606120i
$148$	2.78600	+	4.82549i	0.229008	+	0.396653i
$149$	4.72324	+	8.18089i	0.386943	+	0.670205i	0.992037	−	0.125950i	$-0.0401977\pi$
$149$	4.72324	+	8.18089i	0.386943	+	0.670205i	−0.605094	+	0.796154i	$0.706864\pi$
$150$	−0.571993			−0.0467031
$151$	5.75518			0.468350			0.234175	−	0.972194i	$-0.424761\pi$
$151$	5.75518			0.468350			0.234175	+	0.972194i	$0.424761\pi$
$152$	−0.214003	−	0.370665i	−0.0173580	−	0.0300649i
$153$		0			0
$154$	−3.67282	+	6.36152i	−0.295965	+	0.512626i
$155$	−3.12241	+	5.40817i	−0.250798	+	0.434395i
$156$	−2.81286			−0.225209
$157$	−3.35799	+	5.81621i	−0.267997	+	0.464184i	−0.968344	−	0.249618i	$-0.919695\pi$
$157$	−3.35799	+	5.81621i	−0.267997	+	0.464184i	0.700348	+	0.713802i	$0.253028\pi$
$158$	6.48963	−	11.2404i	0.516288	−	0.894236i
$159$	1.28402	−	2.22399i	0.101829	−	0.176374i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	3.14399			0.247781
$162$	−3.08123	−	5.33684i	−0.242084	−	0.419302i
$163$	6.30447	−	10.9197i	0.493804	−	0.855294i	−0.506170	−	0.862433i	$-0.668939\pi$
$163$	6.30447	−	10.9197i	0.493804	−	0.855294i	0.999975	+	0.00713978i	$0.00227268\pi$
$164$	−7.48963			−0.584842
$165$	0.449585	−	0.778704i	0.0350001	−	0.0606220i
$166$	7.86723	+	13.6264i	0.610615	+	1.05762i
$167$	12.6625	+	21.9320i	0.979850	+	1.69715i	0.662899	+	0.748709i	$0.269326\pi$
$167$	12.6625	+	21.9320i	0.979850	+	1.69715i	0.316951	+	0.948442i	$0.397341\pi$
$168$	2.67282			0.206213
$169$	−5.59159	−	9.68493i	−0.430123	−	0.744994i
$170$		0			0
$171$	−1.14399			−0.0874828
$172$	1.90643	−	6.27420i	0.145364	−	0.478403i
$173$	9.91369			0.753724			0.376862	−	0.926269i	$-0.377003\pi$
$173$	9.91369			0.753724			0.376862	+	0.926269i	$0.377003\pi$
$174$	−2.83528			−0.214942
$175$	2.33641	+	4.04678i	0.176616	+	0.305908i
$176$	−1.57199			−0.118493
$177$	−2.91764	−	5.05350i	−0.219303	−	0.379844i
$178$	−3.21598	−	5.57024i	−0.241048	−	0.417507i
$179$	−1.95684	+	3.38935i	−0.146261	+	0.253332i	−0.929843	−	0.367957i	$-0.880057\pi$
$179$	−1.95684	+	3.38935i	−0.146261	+	0.253332i	0.783581	+	0.621289i	$0.213391\pi$
$180$	2.67282			0.199221
$181$	−1.28797	+	2.23083i	−0.0957343	+	0.165817i	−0.909915	−	0.414795i	$-0.863853\pi$
$181$	−1.28797	+	2.23083i	−0.0957343	+	0.165817i	0.814181	+	0.580612i	$0.197187\pi$
$182$	11.4896	+	19.9006i	0.851668	+	1.47513i
$183$	4.47116			0.330518
$184$	0.336412	+	0.582682i	0.0248006	+	0.0429559i
$185$	−2.78600	+	4.82549i	−0.204831	+	0.354777i
$186$	−1.78600	+	3.09344i	−0.130956	+	0.226822i
$187$		0			0
$188$	−10.6336			−0.775536
$189$	7.58123	−	13.1311i	0.551453	−	0.955145i
$190$	0.214003	−	0.370665i	0.0155254	−	0.0268908i
$191$	−5.91764	−	10.2497i	−0.428185	−	0.741639i	0.568527	−	0.822665i	$-0.307514\pi$
$191$	−5.91764	−	10.2497i	−0.428185	−	0.741639i	−0.996712	+	0.0810260i	$0.974180\pi$
$192$	0.285997	+	0.495361i	0.0206400	+	0.0357496i
$193$	−9.25934			−0.666502			−0.333251	−	0.942838i	$-0.608146\pi$
$193$	−9.25934			−0.666502			−0.333251	+	0.942838i	$0.608146\pi$
$194$	−4.28797			−0.307859
$195$	−1.40643	−	2.43601i	−0.100716	−	0.174446i
$196$	−7.41764	−	12.8477i	−0.529831	−	0.917695i
$197$	0.528837	−	0.915973i	0.0376781	−	0.0652604i	−0.846571	−	0.532275i	$-0.821337\pi$
$197$	0.528837	−	0.915973i	0.0376781	−	0.0652604i	0.884250	+	0.467015i	$0.154671\pi$
$198$	−2.10083	+	3.63875i	−0.149300	+	0.258594i
$199$	10.5328			0.746650			0.373325	−	0.927701i	$-0.378218\pi$
$199$	10.5328			0.746650			0.373325	+	0.927701i	$0.378218\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−3.22126	+	5.57939i	−0.227210	+	0.393540i
$202$	−0.570017	+	0.987298i	−0.0401062	+	0.0694661i
$203$	11.5812	+	20.0593i	0.812843	+	1.40789i
$204$		0			0
$205$	−3.74482	−	6.48621i	−0.261549	−	0.453017i
$206$	3.98040	−	6.89425i	0.277327	−	0.480345i
$207$	1.79834			0.124993
$208$	−2.45882	+	4.25880i	−0.170489	+	0.295295i
$209$	0.336412	+	0.582682i	0.0232701	+	0.0403050i
$210$	1.33641	+	2.31473i	0.0922212	+	0.159732i
$211$	3.85997			0.265731			0.132866	−	0.991134i	$-0.457582\pi$
$211$	3.85997			0.265731			0.132866	+	0.991134i	$0.457582\pi$
$212$	−2.24482	−	3.88814i	−0.154175	−	0.267038i
$213$	−0.514319			−0.0352406
$214$	6.30249			0.430829
$215$	6.38683	−	1.48608i	0.435578	−	0.101350i
$216$	3.24482			0.220782
$217$	29.1809			1.98093
$218$	−10.1512	−	17.5825i	−0.687529	−	1.19084i
$219$	−8.26329			−0.558381
$220$	−0.785997	−	1.36139i	−0.0529919	−	0.0917846i
$221$		0			0
$222$	−1.59357	+	2.76015i	−0.106954	+	0.185249i
$223$	25.0185			1.67536			0.837680	−	0.546161i	$-0.183911\pi$
$223$	25.0185			1.67536			0.837680	+	0.546161i	$0.183911\pi$
$224$	2.33641	−	4.04678i	0.156108	−	0.270387i
$225$	1.33641	+	2.31473i	0.0890941	+	0.154316i
$226$	−1.95684			−0.130167
$227$	−6.48766	−	11.2370i	−0.430601	−	0.745823i	0.566324	−	0.824183i	$-0.308365\pi$
$227$	−6.48766	−	11.2370i	−0.430601	−	0.745823i	−0.996925	+	0.0783598i	$0.975032\pi$
$228$	0.122408	−	0.212018i	0.00810670	−	0.0140412i
$229$	−10.3569	+	17.9386i	−0.684401	+	1.18542i	0.289224	+	0.957261i	$0.406603\pi$
$229$	−10.3569	+	17.9386i	−0.684401	+	1.18542i	−0.973625	+	0.228155i	$0.926731\pi$
$230$	−0.336412	+	0.582682i	−0.0221823	+	0.0384209i
$231$	−4.20166			−0.276449
$232$	−2.47842	+	4.29275i	−0.162716	+	0.281833i
$233$	−11.1625	+	19.3339i	−0.731277	+	1.26661i	0.225061	+	0.974345i	$0.427742\pi$
$233$	−11.1625	+	19.3339i	−0.731277	+	1.26661i	−0.956338	+	0.292264i	$0.905591\pi$
$234$	6.57199	+	11.3830i	0.429625	+	0.744132i
$235$	−5.31681	−	9.20899i	−0.346830	−	0.600728i
$236$	−10.2017			−0.664072
$237$	7.42405			0.482244
$238$		0			0
$239$	−11.3857	−	19.7206i	−0.736479	−	1.27562i	−0.954071	−	0.299580i	$-0.903153\pi$
$239$	−11.3857	−	19.7206i	−0.736479	−	1.27562i	0.217592	−	0.976040i	$-0.430180\pi$
$240$	−0.285997	+	0.495361i	−0.0184610	+	0.0319754i
$241$	12.4793	−	21.6147i	0.803860	−	1.39233i	−0.113197	−	0.993573i	$-0.536109\pi$
$241$	12.4793	−	21.6147i	0.803860	−	1.39233i	0.917058	−	0.398754i	$-0.130557\pi$
$242$	−8.52884			−0.548254
$243$	6.62967	−	11.4829i	0.425293	−	0.736630i
$244$	3.90841	−	6.76956i	0.250210	−	0.433376i
$245$	7.41764	−	12.8477i	0.473896	−	0.820811i
$246$	−2.14201	−	3.71007i	−0.136570	−	0.236545i
$247$	2.10478			0.133924
$248$	3.12241	+	5.40817i	0.198273	+	0.343419i
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$	−1.00000			−0.0632456
$251$	−0.929983	+	1.61078i	−0.0587000	+	0.101671i	−0.893882	−	0.448302i	$-0.852029\pi$
$251$	−0.929983	+	1.61078i	−0.0587000	+	0.101671i	0.835182	+	0.549974i	$0.185362\pi$
$252$	−6.24482	−	10.8163i	−0.393386	−	0.681365i
$253$	−0.528837	−	0.915973i	−0.0332477	−	0.0575867i
$254$	−1.00000			−0.0627456
$255$		0			0
$256$	1.00000			0.0625000
$257$	−26.3681			−1.64480			−0.822398	−	0.568913i	$-0.807364\pi$
$257$	−26.3681			−1.64480			−0.822398	+	0.568913i	$0.807364\pi$
$258$	3.65322	−	0.850029i	0.227440	−	0.0529205i
$259$	26.0369			1.61786
$260$	−4.91764			−0.304979
$261$	6.62438	+	11.4738i	0.410039	+	0.710209i
$262$	7.05767			0.436025
$263$	3.40841	+	5.90353i	0.210171	+	0.364027i	0.951768	−	0.306819i	$-0.0992645\pi$
$263$	3.40841	+	5.90353i	0.210171	+	0.364027i	−0.741597	+	0.670846i	$0.765931\pi$
$264$	−0.449585	−	0.778704i	−0.0276700	−	0.0479259i
$265$	2.24482	−	3.88814i	0.137898	−	0.238846i
$266$	−2.00000			−0.122628
$267$	1.83952	−	3.18614i	0.112577	−	0.194989i
$268$	5.63164	+	9.75429i	0.344007	+	0.595838i
$269$	−3.22635			−0.196714			−0.0983569	−	0.995151i	$-0.531359\pi$
$269$	−3.22635			−0.196714			−0.0983569	+	0.995151i	$0.531359\pi$
$270$	1.62241	+	2.81009i	0.0987366	+	0.171017i
$271$	13.1008	−	22.6913i	0.795819	−	1.37840i	−0.126499	−	0.991967i	$-0.540374\pi$
$271$	13.1008	−	22.6913i	0.795819	−	1.37840i	0.922318	−	0.386432i	$-0.126293\pi$
$272$		0			0
$273$	−6.57199	+	11.3830i	−0.397755	+	0.688932i
$274$	13.7921			0.833213
$275$	0.785997	−	1.36139i	0.0473974	−	0.0820947i
$276$	−0.192425	+	0.333290i	−0.0115826	+	0.0200617i
$277$	0.715980	+	1.24011i	0.0430191	+	0.0745112i	0.886733	−	0.462282i	$-0.152969\pi$
$277$	0.715980	+	1.24011i	0.0430191	+	0.0745112i	−0.843714	+	0.536793i	$0.819636\pi$
$278$	−4.52884	−	7.84418i	−0.271622	−	0.470462i
$279$	16.6913			0.999282
$280$	4.67282			0.279255
$281$	−0.0823593	−	0.142651i	−0.00491315	−	0.00850982i	0.863558	−	0.504249i	$-0.168231\pi$
$281$	−0.0823593	−	0.142651i	−0.00491315	−	0.00850982i	−0.868472	+	0.495739i	$0.834897\pi$
$282$	−3.04118	−	5.26748i	−0.181100	−	0.313674i
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$	−0.449585	+	0.778704i	−0.0266779	+	0.0462076i
$285$	0.244817			0.0145017
$286$	3.86525	−	6.69481i	0.228557	−	0.395872i
$287$	−17.4989	+	30.3089i	−1.03293	+	1.78908i
$288$	1.33641	−	2.31473i	0.0787488	−	0.136397i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−4.95684			−0.291076
$291$	−1.22635	−	2.12409i	−0.0718897	−	0.124517i
$292$	−7.22324	+	12.5110i	−0.422708	+	0.732152i
$293$	26.1153			1.52567			0.762837	−	0.646590i	$-0.223806\pi$
$293$	26.1153			1.52567			0.762837	+	0.646590i	$0.223806\pi$
$294$	4.24284	−	7.34882i	0.247447	−	0.428592i
$295$	−5.10083	−	8.83490i	−0.296982	−	0.514388i
$296$	2.78600	+	4.82549i	0.161933	+	0.280476i
$297$	−5.10083			−0.295980
$298$	4.72324	+	8.18089i	0.273610	+	0.473906i
$299$	−3.30871			−0.191347
$300$	−0.571993			−0.0330240
$301$	−20.9361	−	22.3740i	−1.20674	−	1.28962i
$302$	5.75518			0.331174
$303$	−0.652092			−0.0374617
$304$	−0.214003	−	0.370665i	−0.0122739	−	0.0212591i
$305$	7.81681			0.447589
$306$		0			0
$307$	0.112042	+	0.194063i	0.00639460	+	0.0110758i	0.869205	−	0.494452i	$-0.164631\pi$
$307$	0.112042	+	0.194063i	0.00639460	+	0.0110758i	−0.862810	+	0.505528i	$0.831298\pi$
$308$	−3.67282	+	6.36152i	−0.209279	+	0.362481i
$309$	4.55352			0.259041
$310$	−3.12241	+	5.40817i	−0.177341	+	0.307163i
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	−2.81286			−0.159247
$313$	6.71287	+	11.6270i	0.379434	+	0.657199i	0.990980	−	0.134010i	$-0.0427854\pi$
$313$	6.71287	+	11.6270i	0.379434	+	0.657199i	−0.611546	+	0.791209i	$0.709452\pi$
$314$	−3.35799	+	5.81621i	−0.189502	+	0.328228i
$315$	6.24482	−	10.8163i	0.351856	−	0.609432i
$316$	6.48963	−	11.2404i	0.365070	−	0.632321i
$317$	19.6952			1.10620			0.553098	−	0.833116i	$-0.313446\pi$
$317$	19.6952			1.10620			0.553098	+	0.833116i	$0.313446\pi$
$318$	1.28402	−	2.22399i	0.0720043	−	0.124715i
$319$	3.89606	−	6.74818i	0.218138	−	0.377825i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	1.80249	+	3.12201i	0.100605	+	0.174253i
$322$	3.14399			0.175208
$323$		0			0
$324$	−3.08123	−	5.33684i	−0.171179	−	0.296491i
$325$	−2.45882	−	4.25880i	−0.136391	−	0.236236i
$326$	6.30447	−	10.9197i	0.349172	−	0.604784i
$327$	5.80644	−	10.0571i	0.321097	−	0.556156i
$328$	−7.48963			−0.413546
$329$	−24.8445	+	43.0320i	−1.36972	+	2.37243i
$330$	0.449585	−	0.778704i	0.0247488	−	0.0428662i
$331$	−4.96080	+	8.59235i	−0.272670	+	0.472278i	−0.969545	−	0.244915i	$-0.921240\pi$
$331$	−4.96080	+	8.59235i	−0.272670	+	0.472278i	0.696875	+	0.717193i	$0.254573\pi$
$332$	7.86723	+	13.6264i	0.431770	+	0.747848i
$333$	14.8930			0.816129
$334$	12.6625	+	21.9320i	0.692859	+	1.20007i
$335$	−5.63164	+	9.75429i	−0.307690	+	0.532934i
$336$	2.67282			0.145814
$337$	−6.18008	+	10.7042i	−0.336651	+	0.583096i	−0.983800	−	0.179267i	$-0.942627\pi$
$337$	−6.18008	+	10.7042i	−0.336651	+	0.583096i	0.647150	+	0.762363i	$0.275961\pi$
$338$	−5.59159	−	9.68493i	−0.304143	−	0.526791i
$339$	−0.559651	−	0.969344i	−0.0303961	−	0.0526475i
$340$		0			0
$341$	−4.90841	−	8.50161i	−0.265805	−	0.460388i
$342$	−1.14399			−0.0618597
$343$	−36.6129			−1.97691
$344$	1.90643	−	6.27420i	0.102788	−	0.338282i
$345$	−0.384851			−0.0207197
$346$	9.91369			0.532963
$347$	−15.2468	−	26.4082i	−0.818491	−	1.41767i	−0.906794	−	0.421574i	$-0.861478\pi$
$347$	−15.2468	−	26.4082i	−0.818491	−	1.41767i	0.0883033	−	0.996094i	$-0.471856\pi$
$348$	−2.83528			−0.151987
$349$	0.901146	+	1.56083i	0.0482372	+	0.0835494i	0.889136	−	0.457643i	$-0.151306\pi$
$349$	0.901146	+	1.56083i	0.0482372	+	0.0835494i	−0.840899	+	0.541193i	$0.817973\pi$
$350$	2.33641	+	4.04678i	0.124886	+	0.216310i
$351$	−7.97842	+	13.8190i	−0.425857	+	0.737605i
$352$	−1.57199			−0.0837875
$353$	10.7129	−	18.5552i	0.570189	−	0.987596i	−0.426357	−	0.904555i	$-0.640203\pi$
$353$	10.7129	−	18.5552i	0.570189	−	0.987596i	0.996546	−	0.0830410i	$-0.0264632\pi$
$354$	−2.91764	−	5.05350i	−0.155071	−	0.268591i
$355$	−0.899170			−0.0477230
$356$	−3.21598	−	5.57024i	−0.170447	−	0.295222i
$357$		0			0
$358$	−1.95684	+	3.38935i	−0.103422	+	0.179133i
$359$	4.18404	−	7.24696i	0.220825	−	0.382480i	−0.734234	−	0.678897i	$-0.762458\pi$
$359$	4.18404	−	7.24696i	0.220825	−	0.382480i	0.955059	+	0.296417i	$0.0957917\pi$
$360$	2.67282			0.140870
$361$	9.40841	−	16.2958i	0.495179	−	0.857676i
$362$	−1.28797	+	2.23083i	−0.0676944	+	0.117250i
$363$	−2.43922	−	4.22485i	−0.128026	−	0.221747i
$364$	11.4896	+	19.9006i	0.602220	+	1.04308i
$365$	−14.4465			−0.756163
$366$	4.47116			0.233711
$367$	−10.1585	−	17.5950i	−0.530270	−	0.918454i	−0.999376	−	0.0353124i	$-0.988757\pi$
$367$	−10.1585	−	17.5950i	−0.530270	−	0.918454i	0.469107	−	0.883142i	$-0.344576\pi$
$368$	0.336412	+	0.582682i	0.0175367	+	0.0303744i
$369$	−10.0092	+	17.3365i	−0.521060	+	0.902502i
$370$	−2.78600	+	4.82549i	−0.144837	+	0.250865i
$371$	−20.9793			−1.08919
$372$	−1.78600	+	3.09344i	−0.0925996	+	0.160387i
$373$	14.2056	−	24.6048i	0.735539	−	1.27399i	−0.218948	−	0.975737i	$-0.570262\pi$
$373$	14.2056	−	24.6048i	0.735539	−	1.27399i	0.954487	−	0.298254i	$-0.0964042\pi$
$374$		0			0
$375$	−0.285997	−	0.495361i	−0.0147688	−	0.0255803i
$376$	−10.6336			−0.548387
$377$	−12.1880	−	21.1102i	−0.627713	−	1.08723i
$378$	7.58123	−	13.1311i	0.389936	−	0.675390i
$379$	6.42801			0.330185			0.165092	−	0.986278i	$-0.447208\pi$
$379$	6.42801			0.330185			0.165092	+	0.986278i	$0.447208\pi$
$380$	0.214003	−	0.370665i	0.0109781	−	0.0190147i
$381$	−0.285997	−	0.495361i	−0.0146521	−	0.0253781i
$382$	−5.91764	−	10.2497i	−0.302773	−	0.524418i
$383$	17.3064			0.884318			0.442159	−	0.896937i	$-0.354213\pi$
$383$	17.3064			0.884318			0.442159	+	0.896937i	$0.354213\pi$
$384$	0.285997	+	0.495361i	0.0145947	+	0.0252788i
$385$	−7.34565			−0.374369
$386$	−9.25934			−0.471288
$387$	−11.9753	−	12.7978i	−0.608739	−	0.650548i
$388$	−4.28797			−0.217689
$389$	−20.2386			−1.02614			−0.513069	−	0.858347i	$-0.671491\pi$
$389$	−20.2386			−1.02614			−0.513069	+	0.858347i	$0.671491\pi$
$390$	−1.40643	−	2.43601i	−0.0712173	−	0.123352i
$391$		0			0
$392$	−7.41764	−	12.8477i	−0.374647	−	0.648908i
$393$	2.01847	+	3.49609i	0.101818	+	0.176355i
$394$	0.528837	−	0.915973i	0.0266424	−	0.0461460i
$395$	12.9793			0.653058
$396$	−2.10083	+	3.63875i	−0.105571	+	0.182854i
$397$	−4.75518	−	8.23622i	−0.238656	−	0.413364i	0.721673	−	0.692234i	$-0.243373\pi$
$397$	−4.75518	−	8.23622i	−0.238656	−	0.413364i	−0.960329	+	0.278870i	$0.910040\pi$
$398$	10.5328			0.527961
$399$	−0.571993	−	0.990721i	−0.0286355	−	0.0495981i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−15.1101	+	26.1714i	−0.754561	+	1.30694i	0.191032	+	0.981584i	$0.438817\pi$
$401$	−15.1101	+	26.1714i	−0.754561	+	1.30694i	−0.945592	+	0.325354i	$0.894517\pi$
$402$	−3.22126	+	5.57939i	−0.160662	+	0.278275i
$403$	−30.7098			−1.52976
$404$	−0.570017	+	0.987298i	−0.0283594	+	0.0491199i
$405$	3.08123	−	5.33684i	0.153107	−	0.265190i
$406$	11.5812	+	20.0593i	0.574767	+	0.995525i
$407$	−4.37957	−	7.58563i	−0.217087	−	0.376006i
$408$		0			0
$409$	13.4712			0.666106			0.333053	−	0.942908i	$-0.391921\pi$
$409$	13.4712			0.666106			0.333053	+	0.942908i	$0.391921\pi$
$410$	−3.74482	−	6.48621i	−0.184943	−	0.320331i
$411$	3.94450	+	6.83208i	0.194568	+	0.337001i
$412$	3.98040	−	6.89425i	0.196100	−	0.339655i
$413$	−23.8353	+	41.2839i	−1.17286	+	2.03145i
$414$	1.79834			0.0883835
$415$	−7.86723	+	13.6264i	−0.386187	+	0.668895i
$416$	−2.45882	+	4.25880i	−0.120554	+	0.208805i
$417$	2.59046	−	4.48682i	0.126856	−	0.219720i
$418$	0.336412	+	0.582682i	0.0164544	+	0.0284999i
$419$	−18.5759			−0.907494			−0.453747	−	0.891130i	$-0.649913\pi$
$419$	−18.5759			−0.907494			−0.453747	+	0.891130i	$0.649913\pi$
$420$	1.33641	+	2.31473i	0.0652102	+	0.112947i
$421$	−10.1028	+	17.4986i	−0.492381	+	0.852828i	−0.999961	−	0.00877580i	$-0.997207\pi$
$421$	−10.1028	+	17.4986i	−0.492381	+	0.852828i	0.507581	+	0.861604i	$0.330540\pi$
$422$	3.85997			0.187900
$423$	−14.2109	+	24.6140i	−0.690957	+	1.19677i
$424$	−2.24482	−	3.88814i	−0.109018	−	0.188825i
$425$		0			0
$426$	−0.514319			−0.0249188
$427$	−18.2633	−	31.6329i	−0.883822	−	1.53083i
$428$	6.30249			0.304642
$429$	4.42179			0.213486
$430$	6.38683	−	1.48608i	0.308000	−	0.0716652i
$431$	36.7345			1.76944			0.884718	−	0.466126i	$-0.154351\pi$
$431$	36.7345			1.76944			0.884718	+	0.466126i	$0.154351\pi$
$432$	3.24482			0.156116
$433$	−16.5728	−	28.7050i	−0.796440	−	1.37947i	−0.921921	−	0.387378i	$-0.873381\pi$
$433$	−16.5728	−	28.7050i	−0.796440	−	1.37947i	0.125481	−	0.992096i	$-0.459953\pi$
$434$	29.1809			1.40073
$435$	−1.41764	−	2.45543i	−0.0679707	−	0.117729i
$436$	−10.1512	−	17.5825i	−0.486156	−	0.842048i
$437$	0.143987	−	0.249392i	0.00688781	−	0.0119300i
$438$	−8.26329			−0.394835
$439$	−1.52884	+	2.64802i	−0.0729674	+	0.126383i	−0.900201	−	0.435476i	$-0.856580\pi$
$439$	−1.52884	+	2.64802i	−0.0729674	+	0.126383i	0.827233	+	0.561859i	$0.189914\pi$
$440$	−0.785997	−	1.36139i	−0.0374709	−	0.0649015i
$441$	−39.6521			−1.88819
$442$		0			0
$443$	−4.38683	+	7.59821i	−0.208424	+	0.361002i	−0.951218	−	0.308518i	$-0.900167\pi$
$443$	−4.38683	+	7.59821i	−0.208424	+	0.361002i	0.742794	+	0.669520i	$0.233500\pi$
$444$	−1.59357	+	2.76015i	−0.0756275	+	0.130991i
$445$	3.21598	−	5.57024i	0.152452	−	0.264055i
$446$	25.0185			1.18466
$447$	−2.70166	+	4.67941i	−0.127784	+	0.221329i
$448$	2.33641	−	4.04678i	0.110385	−	0.191193i
$449$	−8.74877	−	15.1533i	−0.412880	−	0.715129i	0.582323	−	0.812957i	$-0.302144\pi$
$449$	−8.74877	−	15.1533i	−0.412880	−	0.715129i	−0.995203	+	0.0978282i	$0.968810\pi$
$450$	1.33641	+	2.31473i	0.0629991	+	0.109118i
$451$	11.7737			0.554400
$452$	−1.95684			−0.0920422
$453$	1.64596	+	2.85089i	0.0773341	+	0.133947i
$454$	−6.48766	−	11.2370i	−0.304481	−	0.527376i
$455$	−11.4896	+	19.9006i	−0.538642	+	0.932956i
$456$	0.122408	−	0.212018i	0.00573230	−	0.00992864i
$457$	−2.07841			−0.0972238			−0.0486119	−	0.998818i	$-0.515480\pi$
$457$	−2.07841			−0.0972238			−0.0486119	+	0.998818i	$0.515480\pi$
$458$	−10.3569	+	17.9386i	−0.483944	+	0.838216i
$459$		0			0
$460$	−0.336412	+	0.582682i	−0.0156853	+	0.0271677i
$461$	−0.151246	−	0.261965i	−0.00704421	−	0.0122009i	0.862482	−	0.506088i	$-0.168909\pi$
$461$	−0.151246	−	0.261965i	−0.00704421	−	0.0122009i	−0.869526	+	0.493887i	$0.835576\pi$
$462$	−4.20166			−0.195479
$463$	2.85488	+	4.94480i	0.132678	+	0.229804i	0.924708	−	0.380677i	$-0.124309\pi$
$463$	2.85488	+	4.94480i	0.132678	+	0.229804i	−0.792030	+	0.610482i	$0.790976\pi$
$464$	−2.47842	+	4.29275i	−0.115058	+	0.199286i
$465$	−3.57199			−0.165647
$466$	−11.1625	+	19.3339i	−0.517091	+	0.895628i
$467$	3.87844	+	6.71765i	0.179473	+	0.310856i	0.941700	−	0.336454i	$-0.109228\pi$
$467$	3.87844	+	6.71765i	0.179473	+	0.310856i	−0.762227	+	0.647309i	$0.775894\pi$
$468$	6.57199	+	11.3830i	0.303790	+	0.526181i
$469$	52.6314			2.43029
$470$	−5.31681	−	9.20899i	−0.245246	−	0.424779i
$471$	−3.84150			−0.177007
$472$	−10.2017			−0.469570
$473$	−2.99689	+	9.86299i	−0.137797	+	0.453501i
$474$	7.42405			0.340998
$475$	0.428007			0.0196383
$476$		0			0
$477$	−12.0000			−0.549442
$478$	−11.3857	−	19.7206i	−0.520770	−	0.901999i
$479$	−14.5944	−	25.2783i	−0.666836	−	1.15499i	−0.978784	−	0.204895i	$-0.934315\pi$
$479$	−14.5944	−	25.2783i	−0.666836	−	1.15499i	0.311948	−	0.950099i	$-0.399018\pi$
$480$	−0.285997	+	0.495361i	−0.0130539	+	0.0226100i
$481$	−27.4011			−1.24938
$482$	12.4793	−	21.6147i	0.568415	−	0.984524i
$483$	0.899170	+	1.55741i	0.0409136	+	0.0708645i
$484$	−8.52884			−0.387674
$485$	−2.14399	−	3.71349i	−0.0973534	−	0.168621i
$486$	6.62967	−	11.4829i	0.300728	−	0.520876i
$487$	0.705614	−	1.22216i	0.0319744	−	0.0553813i	−0.849595	−	0.527435i	$-0.823154\pi$
$487$	0.705614	−	1.22216i	0.0319744	−	0.0553813i	0.881570	+	0.472054i	$0.156487\pi$
$488$	3.90841	−	6.76956i	0.176925	−	0.306443i
$489$	7.21223			0.326148
$490$	7.41764	−	12.8477i	0.335095	−	0.580401i
$491$	−7.45882	+	12.9191i	−0.336612	+	0.583029i	−0.983793	−	0.179307i	$-0.942614\pi$
$491$	−7.45882	+	12.9191i	−0.336612	+	0.583029i	0.647181	+	0.762336i	$0.275948\pi$
$492$	−2.14201	−	3.71007i	−0.0965693	−	0.167263i
$493$		0			0
$494$	2.10478			0.0946987
$495$	−4.20166			−0.188851
$496$	3.12241	+	5.40817i	0.140200	+	0.242834i
$497$	2.10083	+	3.63875i	0.0942351	+	0.163220i
$498$	−4.50000	+	7.79423i	−0.201650	+	0.349268i
$499$	−10.4157	+	18.0405i	−0.466269	+	0.807602i	−0.999258	−	0.0385205i	$-0.987736\pi$
$499$	−10.4157	+	18.0405i	−0.466269	+	0.807602i	0.532989	+	0.846122i	$0.321069\pi$
$500$	−1.00000			−0.0447214
$501$	−7.24284	+	12.5450i	−0.323586	+	0.560468i
$502$	−0.929983	+	1.61078i	−0.0415072	+	0.0718925i
$503$	3.01037	−	5.21411i	0.134226	−	0.232486i	−0.791076	−	0.611718i	$-0.790479\pi$
$503$	3.01037	−	5.21411i	0.134226	−	0.232486i	0.925301	+	0.379233i	$0.123812\pi$
$504$	−6.24482	−	10.8163i	−0.278166	−	0.481798i
$505$	−1.14003			−0.0507308
$506$	−0.528837	−	0.915973i	−0.0235097	−	0.0407200i
$507$	3.19835	−	5.53971i	0.142044	−	0.246027i
$508$	−1.00000			−0.0443678
$509$	−3.05437	+	5.29032i	−0.135382	+	0.234489i	−0.925744	−	0.378152i	$-0.876560\pi$
$509$	−3.05437	+	5.29032i	−0.135382	+	0.234489i	0.790361	+	0.612641i	$0.209893\pi$
$510$		0			0
$511$	33.7529	+	58.4618i	1.49314	+	2.58620i
$512$	1.00000			0.0441942
$513$	−0.694402	−	1.20274i	−0.0306586	−	0.0531022i
$514$	−26.3681			−1.16305
$515$	7.96080			0.350795
$516$	3.65322	−	0.850029i	0.160824	−	0.0374204i
$517$	16.7160			0.735168
$518$	26.0369			1.14400
$519$	2.83528	+	4.91085i	0.124455	+	0.215562i
$520$	−4.91764			−0.215653
$521$	−2.72522	−	4.72021i	−0.119394	−	0.206796i	0.800134	−	0.599822i	$-0.204762\pi$
$521$	−2.72522	−	4.72021i	−0.119394	−	0.206796i	−0.919528	+	0.393025i	$0.871428\pi$
$522$	6.62438	+	11.4738i	0.289941	+	0.502193i
$523$	−18.1081	+	31.3641i	−0.791811	+	1.37146i	0.133033	+	0.991112i	$0.457528\pi$
$523$	−18.1081	+	31.3641i	−0.791811	+	1.37146i	−0.924844	+	0.380346i	$0.875805\pi$
$524$	7.05767			0.308316
$525$	−1.33641	+	2.31473i	−0.0583258	+	0.101023i
$526$	3.40841	+	5.90353i	0.148614	+	0.257406i
$527$		0			0
$528$	−0.449585	−	0.778704i	−0.0195657	−	0.0338887i
$529$	11.2737	−	19.5265i	0.490159	−	0.848980i
$530$	2.24482	−	3.88814i	0.0975086	−	0.168890i
$531$	−13.6336	+	23.6141i	−0.591649	+	1.02477i
$532$	−2.00000			−0.0867110
$533$	18.4157	−	31.8969i	0.797671	−	1.38161i
$534$	1.83952	−	3.18614i	0.0796038	−	0.137878i
$535$	3.15125	+	5.45812i	0.136240	+	0.235975i
$536$	5.63164	+	9.75429i	0.243250	+	0.421321i
$537$	−2.23860			−0.0966029
$538$	−3.22635			−0.139098
$539$	11.6605	+	20.1965i	0.502252	+	0.869927i
$540$	1.62241	+	2.81009i	0.0698173	+	0.120927i
$541$	0.854037	−	1.47924i	0.0367179	−	0.0635973i	−0.847082	−	0.531461i	$-0.821643\pi$
$541$	0.854037	−	1.47924i	0.0367179	−	0.0635973i	0.883800	+	0.467864i	$0.154976\pi$
$542$	13.1008	−	22.6913i	0.562729	−	0.974675i
$543$	−1.47342			−0.0632307
$544$		0			0
$545$	10.1512	−	17.5825i	0.434832	−	0.753150i
$546$	−6.57199	+	11.3830i	−0.281255	+	0.487149i
$547$	−20.4145	−	35.3590i	−0.872862	−	1.51184i	−0.859022	−	0.511938i	$-0.828928\pi$
$547$	−20.4145	−	35.3590i	−0.872862	−	1.51184i	−0.0138399	−	0.999904i	$-0.504406\pi$
$548$	13.7921			0.589170
$549$	−10.4465	−	18.0938i	−0.445845	−	0.772226i
$550$	0.785997	−	1.36139i	0.0335150	−	0.0580497i
$551$	2.12156			0.0903816
$552$	−0.192425	+	0.333290i	−0.00819017	+	0.0141858i
$553$	−30.3249	−	52.5243i	−1.28955	−	2.23356i
$554$	0.715980	+	1.24011i	0.0304191	+	0.0526874i
$555$	−3.18714			−0.135287
$556$	−4.52884	−	7.84418i	−0.192065	−	0.332667i
$557$	−36.6050			−1.55100			−0.775501	−	0.631346i	$-0.782503\pi$
$557$	−36.6050			−1.55100			−0.775501	+	0.631346i	$0.782503\pi$
$558$	16.6913			0.706599
$559$	22.0330	+	23.5462i	0.931896	+	0.995899i
$560$	4.67282			0.197463
$561$		0			0
$562$	−0.0823593	−	0.142651i	−0.00347412	−	0.00601735i
$563$	31.8946			1.34420			0.672100	−	0.740461i	$-0.265393\pi$
$563$	31.8946			1.34420			0.672100	+	0.740461i	$0.265393\pi$
$564$	−3.04118	−	5.26748i	−0.128057	−	0.221801i
$565$	−0.978422	−	1.69468i	−0.0411625	−	0.0712956i
$566$	−10.0000	+	17.3205i	−0.420331	+	0.728035i
$567$	−28.7961			−1.20932
$568$	−0.449585	+	0.778704i	−0.0188642	+	0.0326737i
$569$	13.7056	+	23.7388i	0.574569	+	0.995183i	0.996088	+	0.0883635i	$0.0281637\pi$
$569$	13.7056	+	23.7388i	0.574569	+	0.995183i	−0.421519	+	0.906820i	$0.638503\pi$
$570$	0.244817			0.0102543
$571$	−20.1501	−	34.9010i	−0.843256	−	1.46056i	−0.887127	−	0.461525i	$-0.847302\pi$
$571$	−20.1501	−	34.9010i	−0.843256	−	1.46056i	0.0438710	−	0.999037i	$-0.486031\pi$
$572$	3.86525	−	6.69481i	0.161614	−	0.279924i
$573$	3.38485	−	5.86273i	0.141404	−	0.244919i
$574$	−17.4989	+	30.3089i	−0.730389	+	1.26507i
$575$	−0.672824			−0.0280587
$576$	1.33641	−	2.31473i	0.0556838	−	0.0964472i
$577$	8.69045	−	15.0523i	0.361788	−	0.626635i	−0.626467	−	0.779448i	$-0.715500\pi$
$577$	8.69045	−	15.0523i	0.361788	−	0.626635i	0.988255	+	0.152812i	$0.0488330\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−2.64814	−	4.58671i	−0.110053	−	0.190617i
$580$	−4.95684			−0.205822
$581$	73.5243			3.05030
$582$	−1.22635	−	2.12409i	−0.0508337	−	0.0880465i
$583$	3.52884	+	6.11213i	0.146150	+	0.253138i
$584$	−7.22324	+	12.5110i	−0.298900	+	0.517710i
$585$	−6.57199	+	11.3830i	−0.271718	+	0.470630i
$586$	26.1153			1.07882
$587$	3.72719	−	6.45569i	0.153838	−	0.266455i	−0.778798	−	0.627275i	$-0.784170\pi$
$587$	3.72719	−	6.45569i	0.153838	−	0.266455i	0.932635	+	0.360821i	$0.117503\pi$
$588$	4.24284	−	7.34882i	0.174972	−	0.303060i
$589$	1.33641	−	2.31473i	0.0550659	−	0.0953769i
$590$	−5.10083	−	8.83490i	−0.209998	−	0.363727i
$591$	0.604983			0.0248857
$592$	2.78600	+	4.82549i	0.114504	+	0.198326i
$593$	8.48568	−	14.6976i	0.348465	−	0.603559i	−0.637512	−	0.770441i	$-0.720036\pi$
$593$	8.48568	−	14.6976i	0.348465	−	0.603559i	0.985977	+	0.166881i	$0.0533696\pi$
$594$	−5.10083			−0.209290
$595$		0			0
$596$	4.72324	+	8.18089i	0.193471	+	0.335102i
$597$	3.01234	+	5.21753i	0.123287	+	0.213539i
$598$	−3.30871			−0.135303
$599$	−6.69045	−	11.5882i	−0.273364	−	0.473481i	0.696357	−	0.717696i	$-0.254803\pi$
$599$	−6.69045	−	11.5882i	−0.273364	−	0.473481i	−0.969721	+	0.244215i	$0.921470\pi$
$600$	−0.571993			−0.0233515
$601$	34.9585			1.42599			0.712994	−	0.701170i	$-0.247339\pi$
$601$	34.9585			1.42599			0.712994	+	0.701170i	$0.247339\pi$
$602$	−20.9361	−	22.3740i	−0.853292	−	0.911897i
$603$	30.1048			1.22596
$604$	5.75518			0.234175
$605$	−4.26442	−	7.38619i	−0.173373	−	0.300291i
$606$	−0.652092			−0.0264894
$607$	1.28289	+	2.22203i	0.0520709	+	0.0901894i	0.890886	−	0.454227i	$-0.150084\pi$
$607$	1.28289	+	2.22203i	0.0520709	+	0.0901894i	−0.838815	+	0.544416i	$0.816751\pi$
$608$	−0.214003	−	0.370665i	−0.00867898	−	0.0150324i
$609$	−6.62438	+	11.4738i	−0.268434	+	0.464941i
$610$	7.81681			0.316493
$611$	26.1462	−	45.2865i	1.05776	−	1.83209i
$612$		0			0
$613$	13.7120			0.553824			0.276912	−	0.960895i	$-0.410689\pi$
$613$	13.7120			0.553824			0.276912	+	0.960895i	$0.410689\pi$
$614$	0.112042	+	0.194063i	0.00452166	+	0.00783175i
$615$	2.14201	−	3.71007i	0.0863742	−	0.149604i
$616$	−3.67282	+	6.36152i	−0.147982	+	0.256313i
$617$	−20.0832	+	34.7851i	−0.808519	+	1.40040i	0.105370	+	0.994433i	$0.466397\pi$
$617$	−20.0832	+	34.7851i	−0.808519	+	1.40040i	−0.913889	+	0.405964i	$0.866936\pi$
$618$	4.55352			0.183170
$619$	−8.29410	+	14.3658i	−0.333368	+	0.577410i	−0.983170	−	0.182693i	$-0.941519\pi$
$619$	−8.29410	+	14.3658i	−0.333368	+	0.577410i	0.649802	+	0.760104i	$0.274852\pi$
$620$	−3.12241	+	5.40817i	−0.125399	+	0.217197i
$621$	1.09159	+	1.89070i	0.0438042	+	0.0758711i
$622$	9.00000	+	15.5885i	0.360867	+	0.625040i
$623$	−30.0554			−1.20414
$624$	−2.81286			−0.112604
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.71287	+	11.6270i	0.268300	+	0.464710i
$627$	−0.192425	+	0.333290i	−0.00768473	+	0.0133103i
$628$	−3.35799	+	5.81621i	−0.133998	+	0.232092i
$629$		0			0
$630$	6.24482	−	10.8163i	0.248799	−	0.430933i
$631$	14.5081	−	25.1288i	0.577559	−	1.00036i	−0.418200	−	0.908355i	$-0.637339\pi$
$631$	14.5081	−	25.1288i	0.577559	−	1.00036i	0.995758	−	0.0920057i	$-0.0293278\pi$
$632$	6.48963	−	11.2404i	0.258144	−	0.447118i
$633$	1.10394	+	1.91208i	0.0438776	+	0.0759982i
$634$	19.6952			0.782198
$635$	−0.500000	−	0.866025i	−0.0198419	−	0.0343672i
$636$	1.28402	−	2.22399i	0.0509147	−	0.0881869i
$637$	72.9546			2.89057
$638$	3.89606	−	6.74818i	0.154247	−	0.267163i
$639$	1.20166	+	2.08134i	0.0475370	+	0.0823364i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−49.6419			−1.96074			−0.980369	−	0.197171i	$-0.936825\pi$
$641$	−49.6419			−1.96074			−0.980369	+	0.197171i	$0.936825\pi$
$642$	1.80249	+	3.12201i	0.0711387	+	0.123216i
$643$	−5.81286			−0.229237			−0.114618	−	0.993410i	$-0.536565\pi$
$643$	−5.81286			−0.229237			−0.114618	+	0.993410i	$0.536565\pi$
$644$	3.14399			0.123890
$645$	2.56276	+	2.73877i	0.100908	+	0.107839i
$646$		0			0
$647$	−17.2122			−0.676682			−0.338341	−	0.941023i	$-0.609866\pi$
$647$	−17.2122			−0.676682			−0.338341	+	0.941023i	$0.609866\pi$
$648$	−3.08123	−	5.33684i	−0.121042	−	0.209651i
$649$	16.0369			0.629505
$650$	−2.45882	−	4.25880i	−0.0964429	−	0.167044i
$651$	8.34565	+	14.4551i	0.327092	+	0.566539i
$652$	6.30447	−	10.9197i	0.246902	−	0.427647i
$653$	38.4033			1.50284			0.751419	−	0.659825i	$-0.229370\pi$
$653$	38.4033			1.50284			0.751419	+	0.659825i	$0.229370\pi$
$654$	5.80644	−	10.0571i	0.227050	−	0.393262i
$655$	3.52884	+	6.11213i	0.137883	+	0.238820i
$656$	−7.48963			−0.292421
$657$	19.3064	+	33.4397i	0.753216	+	1.30461i
$658$	−24.8445	+	43.0320i	−0.968540	+	1.67756i
$659$	6.22635	−	10.7843i	0.242544	−	0.420099i	−0.718894	−	0.695119i	$-0.755351\pi$
$659$	6.22635	−	10.7843i	0.242544	−	0.420099i	0.961438	+	0.275021i	$0.0886848\pi$
$660$	0.449585	−	0.778704i	0.0175001	−	0.0303110i
$661$	46.7177			1.81711			0.908553	−	0.417769i	$-0.137188\pi$
$661$	46.7177			1.81711			0.908553	+	0.417769i	$0.137188\pi$
$662$	−4.96080	+	8.59235i	−0.192807	+	0.333951i
$663$		0			0
$664$	7.86723	+	13.6264i	0.305308	+	0.528808i
$665$	−1.00000	−	1.73205i	−0.0387783	−	0.0671660i
$666$	14.8930			0.577090
$667$	−3.33508			−0.129135
$668$	12.6625	+	21.9320i	0.489925	+	0.848575i
$669$	7.15520	+	12.3932i	0.276636	+	0.479148i
$670$	−5.63164	+	9.75429i	−0.217569	+	0.376841i
$671$	−6.14399	+	10.6417i	−0.237186	+	0.410818i
$672$	2.67282			0.103106
$673$	11.4936	−	19.9075i	0.443045	−	0.767377i	−0.554869	−	0.831938i	$-0.687231\pi$
$673$	11.4936	−	19.9075i	0.443045	−	0.767377i	0.997914	+	0.0645612i	$0.0205648\pi$
$674$	−6.18008	+	10.7042i	−0.238048	+	0.412311i
$675$	−1.62241	+	2.81009i	−0.0624465	+	0.108161i
$676$	−5.59159	−	9.68493i	−0.215061	−	0.372497i
$677$	−13.6010			−0.522730			−0.261365	−	0.965240i	$-0.584173\pi$
$677$	−13.6010			−0.522730			−0.261365	+	0.965240i	$0.584173\pi$
$678$	−0.559651	−	0.969344i	−0.0214933	−	0.0372274i
$679$	−10.0185	+	17.3525i	−0.384474	+	0.665928i
$680$		0			0
$681$	3.71090	−	6.42746i	0.142202	−	0.246301i
$682$	−4.90841	−	8.50161i	−0.187953	−	0.325543i
$683$	7.18714	+	12.4485i	0.275008	+	0.476328i	0.970137	−	0.242557i	$-0.0779860\pi$
$683$	7.18714	+	12.4485i	0.275008	+	0.476328i	−0.695129	+	0.718885i	$0.744653\pi$
$684$	−1.14399			−0.0437414
$685$	6.89606	+	11.9443i	0.263485	+	0.456369i
$686$	−36.6129			−1.39789
$687$	−11.8481			−0.452034
$688$	1.90643	−	6.27420i	0.0726819	−	0.239201i
$689$	22.0784			0.841120
$690$	−0.384851			−0.0146510
$691$	10.8868	+	18.8565i	0.414154	+	0.717336i	0.995339	−	0.0964351i	$-0.0307440\pi$
$691$	10.8868	+	18.8565i	0.414154	+	0.717336i	−0.581185	+	0.813772i	$0.697411\pi$
$692$	9.91369			0.376862
$693$	9.81681	+	17.0032i	0.372910	+	0.645899i
$694$	−15.2468	−	26.4082i	−0.578760	−	1.00244i
$695$	4.52884	−	7.84418i	0.171789	−	0.297547i
$696$	−2.83528			−0.107471
$697$		0			0
$698$	0.901146	+	1.56083i	0.0341089	+	0.0590783i
$699$	−12.7697			−0.482994
$700$	2.33641	+	4.04678i	0.0883081	+	0.152954i
$701$	22.8672	−	39.6072i	0.863683	−	1.49594i	−0.00466559	−	0.999989i	$-0.501485\pi$
$701$	22.8672	−	39.6072i	0.863683	−	1.49594i	0.868349	−	0.495954i	$-0.165182\pi$
$702$	−7.97842	+	13.8190i	−0.301126	+	0.521566i
$703$	1.19243	−	2.06534i	0.0449732	−	0.0778958i
$704$	−1.57199			−0.0592467
$705$	3.04118	−	5.26748i	0.114537	−	0.198385i
$706$	10.7129	−	18.5552i	0.403184	−	0.698336i
$707$	2.66359	+	4.61347i	0.100175	+	0.173507i
$708$	−2.91764	−	5.05350i	−0.109652	−	0.189922i
$709$	24.5042			0.920273			0.460136	−	0.887848i	$-0.347801\pi$
$709$	24.5042			0.920273			0.460136	+	0.887848i	$0.347801\pi$
$710$	−0.899170			−0.0337452
$711$	−17.3456	−	30.0435i	−0.650513	−	1.12672i
$712$	−3.21598	−	5.57024i	−0.120524	−	0.208754i
$713$	−2.10083	+	3.63875i	−0.0786767	+	0.136272i
$714$		0			0
$715$	7.73050			0.289104
$716$	−1.95684	+	3.38935i	−0.0731307	+	0.126666i
$717$	6.51254	−	11.2801i	0.243215	−	0.421261i
$718$	4.18404	−	7.24696i	0.156147	−	0.270454i
$719$	−2.30644	−	3.99488i	−0.0860159	−	0.148984i	0.819808	−	0.572639i	$-0.194080\pi$
$719$	−2.30644	−	3.99488i	−0.0860159	−	0.148984i	−0.905824	+	0.423655i	$0.860747\pi$
$720$	2.67282			0.0996103
$721$	−18.5997	−	32.2156i	−0.692689	−	1.19977i
$722$	9.40841	−	16.2958i	0.350145	−	0.606468i
$723$	14.2761			0.530934
$724$	−1.28797	+	2.23083i	−0.0478671	+	0.0829083i
$725$	−2.47842	−	4.29275i	−0.0920463	−	0.159429i
$726$	−2.43922	−	4.22485i	−0.0905279	−	0.156799i
$727$	−12.4297			−0.460992			−0.230496	−	0.973073i	$-0.574035\pi$
$727$	−12.4297			−0.460992			−0.230496	+	0.973073i	$0.574035\pi$
$728$	11.4896	+	19.9006i	0.425834	+	0.737566i
$729$	−10.9031			−0.403819
$730$	−14.4465			−0.534688
$731$		0			0
$732$	4.47116			0.165259
$733$	13.1272			0.484864			0.242432	−	0.970168i	$-0.422055\pi$
$733$	13.1272			0.484864			0.242432	+	0.970168i	$0.422055\pi$
$734$	−10.1585	−	17.5950i	−0.374957	−	0.649445i
$735$	8.48568			0.312999
$736$	0.336412	+	0.582682i	0.0124003	+	0.0214780i
$737$	−8.85291	−	15.3337i	−0.326101	−	0.564824i
$738$	−10.0092	+	17.3365i	−0.368445	+	0.638166i
$739$	−35.2426			−1.29642			−0.648209	−	0.761462i	$-0.724482\pi$
$739$	−35.2426			−1.29642			−0.648209	+	0.761462i	$0.724482\pi$
$740$	−2.78600	+	4.82549i	−0.102415	+	0.177388i
$741$	0.601961	+	1.04263i	0.0221136	+	0.0383019i
$742$	−20.9793			−0.770173
$743$	−20.4033	−	35.3396i	−0.748525	−	1.29648i	−0.948530	−	0.316689i	$-0.897429\pi$
$743$	−20.4033	−	35.3396i	−0.748525	−	1.29648i	0.200004	−	0.979795i	$-0.435904\pi$
$744$	−1.78600	+	3.09344i	−0.0654778	+	0.113411i
$745$	−4.72324	+	8.18089i	−0.173046	+	0.299725i
$746$	14.2056	−	24.6048i	0.520104	−	0.900847i
$747$	42.0554			1.53873
$748$		0			0
$749$	14.7252	−	25.5048i	0.538048	−	0.931926i
$750$	−0.285997	−	0.495361i	−0.0104431	−	0.0180880i
$751$	1.34480	+	2.32926i	0.0490725	+	0.0849961i	0.889518	−	0.456900i	$-0.151040\pi$
$751$	1.34480	+	2.32926i	0.0490725	+	0.0849961i	−0.840446	+	0.541896i	$0.817707\pi$
$752$	−10.6336			−0.387768
$753$	−1.06389			−0.0387702
$754$	−12.1880	−	21.1102i	−0.443860	−	0.768789i
$755$	2.87759	+	4.98413i	0.104726	+	0.181391i
$756$	7.58123	−	13.1311i	0.275727	−	0.477573i
$757$	−26.3412	+	45.6243i	−0.957388	+	1.65824i	−0.228580	+	0.973525i	$0.573408\pi$
$757$	−26.3412	+	45.6243i	−0.957388	+	1.65824i	−0.728807	+	0.684719i	$0.759925\pi$
$758$	6.42801			0.233476
$759$	0.302491	−	0.523930i	0.0109797	−	0.0190175i
$760$	0.214003	−	0.370665i	0.00776272	−	0.0134454i
$761$	−1.45156	+	2.51418i	−0.0526191	+	0.0911389i	−0.891135	−	0.453738i	$-0.850090\pi$
$761$	−1.45156	+	2.51418i	−0.0526191	+	0.0911389i	0.838516	+	0.544877i	$0.183424\pi$
$762$	−0.285997	−	0.495361i	−0.0103606	−	0.0179450i
$763$	−94.8700			−3.43452
$764$	−5.91764	−	10.2497i	−0.214093	−	0.370819i
$765$		0			0
$766$	17.3064			0.625307
$767$	25.0841	−	43.4469i	0.905733	−	1.56877i
$768$	0.285997	+	0.495361i	0.0103200	+	0.0178748i
$769$	6.23558	+	10.8003i	0.224861	+	0.389470i	0.956278	−	0.292460i	$-0.0944739\pi$
$769$	6.23558	+	10.8003i	0.224861	+	0.389470i	−0.731417	+	0.681931i	$0.761141\pi$
$770$	−7.34565			−0.264719
$771$	−7.54118	−	13.0617i	−0.271589	−	0.470406i
$772$	−9.25934			−0.333251
$773$	4.71598			0.169622			0.0848110	−	0.996397i	$-0.472971\pi$
$773$	4.71598			0.169622			0.0848110	+	0.996397i	$0.472971\pi$
$774$	−11.9753	−	12.7978i	−0.430444	−	0.460007i
$775$	−6.24482			−0.224320
$776$	−4.28797			−0.153929
$777$	7.44648	+	12.8977i	0.267141	+	0.462702i
$778$	−20.2386			−0.725589
$779$	1.60281	+	2.77614i	0.0574265	+	0.0994656i
$780$	−1.40643	−	2.43601i	−0.0503582	−	0.0872230i
$781$	0.706744	−	1.22412i	0.0252893	−	0.0438023i
$782$		0			0
$783$	−8.04203	+	13.9292i	−0.287399	+	0.497789i
$784$	−7.41764	−	12.8477i	−0.264916	−	0.458848i
$785$	−6.71598			−0.239704
$786$	2.01847	+	3.49609i	0.0719965	+	0.124702i
$787$	14.6933	−	25.4495i	0.523759	−	0.907176i	−0.475859	−	0.879522i	$-0.657863\pi$
$787$	14.6933	−	25.4495i	0.523759	−	0.907176i	0.999618	−	0.0276548i	$-0.00880393\pi$
$788$	0.528837	−	0.915973i	0.0188390	−	0.0326302i
$789$	−1.94958	+	3.37678i	−0.0694071	+	0.120217i
$790$	12.9793			0.461782
$791$	−4.57199	+	7.91892i	−0.162561	+	0.281565i
$792$	−2.10083	+	3.63875i	−0.0746498	+	0.129297i
$793$	19.2201	+	33.2902i	0.682527	+	1.18217i
$794$	−4.75518	−	8.23622i	−0.168755	−	0.292292i
$795$	2.56804			0.0910790
$796$	10.5328			0.373325
$797$	25.7406	+	44.5840i	0.911778	+	1.57925i	0.811551	+	0.584281i	$0.198624\pi$
$797$	25.7406	+	44.5840i	0.911778	+	1.57925i	0.100227	+	0.994965i	$0.468043\pi$
$798$	−0.571993	−	0.990721i	−0.0202483	−	0.0350712i
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−17.1915			−0.607432
$802$	−15.1101	+	26.1714i	−0.533555	+	0.924144i
$803$	11.3549	−	19.6672i	0.400705	−	0.694042i
$804$	−3.22126	+	5.57939i	−0.113605	+	0.196770i
$805$	1.57199	+	2.72277i	0.0554055	+	0.0959651i
$806$	−30.7098			−1.08171
$807$	−0.922724	−	1.59820i	−0.0324814	−	0.0562595i
$808$	−0.570017	+	0.987298i	−0.0200531	+	0.0347330i
$809$	29.9793			1.05401			0.527007	−	0.849861i	$-0.323314\pi$
$809$	29.9793			1.05401			0.527007	+	0.849861i	$0.323314\pi$
$810$	3.08123	−	5.33684i	0.108263	−	0.187518i
$811$	21.4896	+	37.2211i	0.754603	+	1.30701i	0.945571	+	0.325415i	$0.105504\pi$
$811$	21.4896	+	37.2211i	0.754603	+	1.30701i	−0.190968	+	0.981596i	$0.561163\pi$
$812$	11.5812	+	20.0593i	0.406421	+	0.703943i
$813$	14.9872			0.525623
$814$	−4.37957	−	7.58563i	−0.153504	−	0.265876i
$815$	12.6089			0.441672
$816$		0			0
$817$	−2.73360	+	0.636053i	−0.0956367	+	0.0222527i
$818$	13.4712			0.471008
$819$	61.4195			2.14617
$820$	−3.74482	−	6.48621i	−0.130775	−	0.226508i
$821$	−7.53940			−0.263127			−0.131563	−	0.991308i	$-0.542000\pi$
$821$	−7.53940			−0.263127			−0.131563	+	0.991308i	$0.542000\pi$
$822$	3.94450	+	6.83208i	0.137580	+	0.238296i
$823$	−3.49472	−	6.05303i	−0.121818	−	0.210995i	0.798667	−	0.601774i	$-0.205539\pi$
$823$	−3.49472	−	6.05303i	−0.121818	−	0.210995i	−0.920485	+	0.390779i	$0.872206\pi$
$824$	3.98040	−	6.89425i	0.138664	−	0.240173i
$825$	0.899170			0.0313051
$826$	−23.8353	+	41.2839i	−0.829336	+	1.43645i
$827$	−17.6429	−	30.5583i	−0.613502	−	1.06262i	−0.990645	−	0.136462i	$-0.956427\pi$
$827$	−17.6429	−	30.5583i	−0.613502	−	1.06262i	0.377143	−	0.926155i	$-0.376906\pi$
$828$	1.79834			0.0624966
$829$	18.4969	+	32.0376i	0.642424	+	1.11271i	0.984890	+	0.173180i	$0.0554044\pi$
$829$	18.4969	+	32.0376i	0.642424	+	1.11271i	−0.342466	+	0.939530i	$0.611262\pi$
$830$	−7.86723	+	13.6264i	−0.273075	+	0.472980i
$831$	−0.409536	+	0.709337i	−0.0142066	+	0.0246066i
$832$	−2.45882	+	4.25880i	−0.0852443	+	0.147647i
$833$		0			0
$834$	2.59046	−	4.48682i	0.0897004	−	0.155366i
$835$	−12.6625	+	21.9320i	−0.438202	+	0.758989i
$836$	0.336412	+	0.582682i	0.0116350	+	0.0201525i
$837$	10.1316	+	17.5485i	0.350201	+	0.606566i
$838$	−18.5759			−0.641695
$839$	−16.0722			−0.554874			−0.277437	−	0.960744i	$-0.589485\pi$
$839$	−16.0722			−0.554874			−0.277437	+	0.960744i	$0.589485\pi$
$840$	1.33641	+	2.31473i	0.0461106	+	0.0798659i
$841$	2.21485	+	3.83623i	0.0763741	+	0.132284i
$842$	−10.1028	+	17.4986i	−0.348166	+	0.603041i
$843$	0.0471090	−	0.0815952i	0.00162252	−	0.00281029i
$844$	3.85997			0.132866
$845$	5.59159	−	9.68493i	0.192357	−	0.333172i
$846$	−14.2109	+	24.6140i	−0.488581	+	0.846247i
$847$	−19.9269	+	34.5144i	−0.684696	+	1.18593i
$848$	−2.24482	−	3.88814i	−0.0770873	−	0.133519i
$849$	−11.4399			−0.392615
$850$		0			0
$851$	−1.87448	+	3.24670i	−0.0642565	+	0.111296i
$852$	−0.514319			−0.0176203
$853$	−24.4812	+	42.4028i	−0.838222	+	1.45184i	0.0531582	+	0.998586i	$0.483071\pi$
$853$	−24.4812	+	42.4028i	−0.838222	+	1.45184i	−0.891380	+	0.453257i	$0.850262\pi$
$854$	−18.2633	−	31.6329i	−0.624957	−	1.08246i
$855$	−0.571993	−	0.990721i	−0.0195618	−	0.0338820i
$856$	6.30249			0.215415
$857$	−15.4496	−	26.7595i	−0.527748	−	0.914086i	−0.999477	−	0.0323424i	$-0.989703\pi$
$857$	−15.4496	−	26.7595i	−0.527748	−	0.914086i	0.471729	−	0.881744i	$-0.343630\pi$
$858$	4.42179			0.150958
$859$	−35.6336			−1.21580			−0.607902	−	0.794012i	$-0.707989\pi$
$859$	−35.6336			−1.21580			−0.607902	+	0.794012i	$0.707989\pi$
$860$	6.38683	−	1.48608i	0.217789	−	0.0506750i
$861$	−20.0185			−0.682228
$862$	36.7345			1.25118
$863$	4.88767	+	8.46570i	0.166378	+	0.288176i	0.937144	−	0.348943i	$-0.113459\pi$
$863$	4.88767	+	8.46570i	0.166378	+	0.288176i	−0.770766	+	0.637119i	$0.780126\pi$
$864$	3.24482			0.110391
$865$	4.95684	+	8.58551i	0.168538	+	0.291916i
$866$	−16.5728	−	28.7050i	−0.563168	−	0.975436i
$867$	−4.86194	+	8.42113i	−0.165120	+	0.285997i
$868$	29.1809			0.990465
$869$	−10.2017	+	17.6698i	−0.346068	+	0.599407i
$870$	−1.41764	−	2.45543i	−0.0480625	−	0.0832467i
$871$	−55.3888			−1.87678
$872$	−10.1512	−	17.5825i	−0.343765	−	0.595418i
$873$	−5.73050	+	9.92551i	−0.193948	+	0.335928i
$874$	0.143987	−	0.249392i	0.00487042	−	0.00843581i
$875$	−2.33641	+	4.04678i	−0.0789851	+	0.136806i
$876$	−8.26329			−0.279191
$877$	16.9322	−	29.3274i	0.571758	−	0.990315i	−0.424627	−	0.905368i	$-0.639595\pi$
$877$	16.9322	−	29.3274i	0.571758	−	0.990315i	0.996386	−	0.0849463i	$-0.0270719\pi$
$878$	−1.52884	+	2.64802i	−0.0515958	+	0.0893665i
$879$	7.46890	+	12.9365i	0.251920	+	0.436338i
$880$	−0.785997	−	1.36139i	−0.0264959	−	0.0458923i
$881$	6.77535			0.228267			0.114134	−	0.993465i	$-0.463591\pi$
$881$	6.77535			0.228267			0.114134	+	0.993465i	$0.463591\pi$
$882$	−39.6521			−1.33516
$883$	−16.2600	−	28.1631i	−0.547192	−	0.947764i	−0.998465	−	0.0553786i	$-0.982363\pi$
$883$	−16.2600	−	28.1631i	−0.547192	−	0.947764i	0.451273	−	0.892386i	$-0.350970\pi$
$884$		0			0
$885$	2.91764	−	5.05350i	0.0980754	−	0.169872i
$886$	−4.38683	+	7.59821i	−0.147378	+	0.255267i
$887$	−13.3720			−0.448989			−0.224494	−	0.974475i	$-0.572073\pi$
$887$	−13.3720			−0.448989			−0.224494	+	0.974475i	$0.572073\pi$
$888$	−1.59357	+	2.76015i	−0.0534768	+	0.0926245i
$889$	−2.33641	+	4.04678i	−0.0783607	+	0.135725i
$890$	3.21598	−	5.57024i	0.107800	−	0.186715i
$891$	4.84367	+	8.38948i	0.162269	+	0.281058i
$892$	25.0185			0.837680
$893$	2.27563	+	3.94151i	0.0761511	+	0.131898i
$894$	−2.70166	+	4.67941i	−0.0903571	+	0.156503i
$895$	−3.91369			−0.130820
$896$	2.33641	−	4.04678i	0.0780540	−	0.135194i
$897$	−0.946279	−	1.63900i	−0.0315953	−	0.0547247i
$898$	−8.74877	−	15.1533i	−0.291950	−	0.505673i
$899$	−30.9546			−1.03239
$900$	1.33641	+	2.31473i	0.0445471	+	0.0771578i
$901$		0			0
$902$	11.7737			0.392020
$903$	5.09555	−	16.7698i	0.169569	−	0.558065i
$904$	−1.95684			−0.0650837
$905$	−2.57595			−0.0856273
$906$	1.64596	+	2.85089i	0.0546835	+	0.0947145i
$907$	−14.6544			−0.486590			−0.243295	−	0.969952i	$-0.578228\pi$
$907$	−14.6544			−0.486590			−0.243295	+	0.969952i	$0.578228\pi$
$908$	−6.48766	−	11.2370i	−0.215300	−	0.372911i
$909$	1.52355	+	2.63887i	0.0505331	+	0.0875259i
$910$	−11.4896	+	19.9006i	−0.380878	+	0.659699i
$911$	−15.1792			−0.502911			−0.251455	−	0.967869i	$-0.580909\pi$
$911$	−15.1792			−0.502911			−0.251455	+	0.967869i	$0.580909\pi$
$912$	0.122408	−	0.212018i	0.00405335	−	0.00702061i
$913$	−12.3672	−	21.4207i	−0.409295	−	0.708920i
$914$	−2.07841			−0.0687476
$915$	2.23558	+	3.87214i	0.0739060	+	0.128009i
$916$	−10.3569	+	17.9386i	−0.342200	+	0.592708i
$917$	16.4896	−	28.5609i	0.544536	−	0.943163i
$918$		0			0
$919$	−25.3905			−0.837555			−0.418778	−	0.908089i	$-0.637541\pi$
$919$	−25.3905			−0.837555			−0.418778	+	0.908089i	$0.637541\pi$
$920$	−0.336412	+	0.582682i	−0.0110912	+	0.0192105i
$921$	−0.0640875	+	0.111003i	−0.00211176	+	0.00365767i
$922$	−0.151246	−	0.261965i	−0.00498101	−	0.00862736i
$923$	−2.21090	−	3.82938i	−0.0727725	−	0.126046i
$924$	−4.20166			−0.138224
$925$	−5.57199			−0.183206
$926$	2.85488	+	4.94480i	0.0938173	+	0.162496i
$927$	−10.6389	−	18.4271i	−0.349427	−	0.605226i
$928$	−2.47842	+	4.29275i	−0.0813582	+	0.140917i
$929$	−13.4764	+	23.3419i	−0.442148	+	0.765823i	−0.997849	−	0.0655598i	$-0.979117\pi$
$929$	−13.4764	+	23.3419i	−0.442148	+	0.765823i	0.555701	+	0.831382i	$0.312450\pi$
$930$	−3.57199			−0.117130
$931$	−3.17480	+	5.49892i	−0.104050	+	0.180220i
$932$	−11.1625	+	19.3339i	−0.365638	+	0.633304i
$933$	−5.14794	+	8.91649i	−0.168536	+	0.291913i
$934$	3.87844	+	6.71765i	0.126906	+	0.219808i
$935$		0			0
$936$	6.57199	+	11.3830i	0.214812	+	0.372066i
$937$	−7.28797	+	12.6231i	−0.238088	+	0.412380i	−0.960166	−	0.279432i	$-0.909854\pi$
$937$	−7.28797	+	12.6231i	−0.238088	+	0.412380i	0.722078	+	0.691812i	$0.243187\pi$
$938$	52.6314			1.71847
$939$	−3.83972	+	6.65059i	−0.125304	+	0.217034i
$940$	−5.31681	−	9.20899i	−0.173415	−	0.300364i
$941$	−20.0317	−	34.6959i	−0.653013	−	1.13105i	−0.982388	−	0.186853i	$-0.940171\pi$
$941$	−20.0317	−	34.6959i	−0.653013	−	1.13105i	0.329374	−	0.944199i	$-0.393162\pi$
$942$	−3.84150			−0.125163
$943$	−2.51960	−	4.36408i	−0.0820495	−	0.142114i
$944$	−10.2017			−0.332036
$945$	15.1625			0.493235
$946$	−2.99689	+	9.86299i	−0.0974374	+	0.320674i
$947$	37.2751			1.21128			0.605640	−	0.795739i	$-0.292917\pi$
$947$	37.2751			1.21128			0.605640	+	0.795739i	$0.292917\pi$
$948$	7.42405			0.241122
$949$	−35.5213	−	61.5247i	−1.15307	−	1.99718i
$950$	0.428007			0.0138864
$951$	5.63277	+	9.75625i	0.182655	+	0.316368i
$952$		0			0
$953$	12.8137	−	22.1940i	0.415077	−	0.718934i	−0.580360	−	0.814360i	$-0.697088\pi$
$953$	12.8137	−	22.1940i	0.415077	−	0.718934i	0.995436	+	0.0954264i	$0.0304215\pi$
$954$	−12.0000			−0.388514
$955$	5.91764	−	10.2497i	0.191490	−	0.331671i
$956$	−11.3857	−	19.7206i	−0.368240	−	0.637810i
$957$	4.45704			0.144076
$958$	−14.5944	−	25.2783i	−0.471524	−	0.816704i
$959$	32.2241	−	55.8138i	1.04057	−	1.80232i
$960$	−0.285997	+	0.495361i	−0.00923050	+	0.0159877i
$961$	−3.99887	+	6.92625i	−0.128996	+	0.223427i
$962$	−27.4011			−0.883446
$963$	8.42272	−	14.5886i	0.271418	−	0.470111i
$964$	12.4793	−	21.6147i	0.401930	−	0.696163i
$965$	−4.62967	−	8.01882i	−0.149034	−	0.258135i
$966$	0.899170	+	1.55741i	0.0289303	+	0.0501088i
$967$	43.6442			1.40350			0.701751	−	0.712422i	$-0.252402\pi$
$967$	43.6442			1.40350			0.701751	+	0.712422i	$0.252402\pi$
$968$	−8.52884			−0.274127
$969$		0			0
$970$	−2.14399	−	3.71349i	−0.0688393	−	0.119233i
$971$	−18.4773	+	32.0036i	−0.592965	+	1.02704i	0.400866	+	0.916137i	$0.368709\pi$
$971$	−18.4773	+	32.0036i	−0.592965	+	1.02704i	−0.993831	+	0.110908i	$0.964624\pi$
$972$	6.62967	−	11.4829i	0.212647	−	0.368315i
$973$	−42.3249			−1.35687
$974$	0.705614	−	1.22216i	0.0226093	−	0.0391605i
$975$	1.40643	−	2.43601i	0.0450418	−	0.0780146i
$976$	3.90841	−	6.76956i	0.125105	−	0.216688i
$977$	30.5257	+	52.8721i	0.976605	+	1.69153i	0.674535	+	0.738243i	$0.264344\pi$
$977$	30.5257	+	52.8721i	0.976605	+	1.69153i	0.302070	+	0.953286i	$0.402322\pi$
$978$	7.21223			0.230622
$979$	5.05550	+	8.75638i	0.161574	+	0.279855i
$980$	7.41764	−	12.8477i	0.236948	−	0.410406i
$981$	−54.2650			−1.73255
$982$	−7.45882	+	12.9191i	−0.238021	+	0.412264i
$983$	−21.6964	−	37.5792i	−0.692007	−	1.19859i	−0.971179	−	0.238350i	$-0.923393\pi$
$983$	−21.6964	−	37.5792i	−0.692007	−	1.19859i	0.279172	−	0.960241i	$-0.409940\pi$
$984$	−2.14201	−	3.71007i	−0.0682848	−	0.118273i
$985$	1.05767			0.0337003
$986$		0			0
$987$	−28.4218			−0.904676
$988$	2.10478			0.0669621
$989$	4.29721	−	0.999871i	0.136643	−	0.0317941i
$990$	−4.20166			−0.133538
$991$	−6.52658			−0.207324			−0.103662	−	0.994613i	$-0.533056\pi$
$991$	−6.52658			−0.207324			−0.103662	+	0.994613i	$0.533056\pi$
$992$	3.12241	+	5.40817i	0.0991366	+	0.171710i
$993$	−5.67508			−0.180093
$994$	2.10083	+	3.63875i	0.0666343	+	0.115414i
$995$	5.26640	+	9.12166i	0.166956	+	0.289176i
$996$	−4.50000	+	7.79423i	−0.142588	+	0.246970i
$997$	20.0000			0.633406			0.316703	−	0.948525i	$-0.397424\pi$
$997$	20.0000			0.633406			0.316703	+	0.948525i	$0.397424\pi$
$998$	−10.4157	+	18.0405i	−0.329702	+	0.571061i
$999$	9.04005	+	15.6578i	0.286014	+	0.495392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.e.251.2	yes	6
43.6	even	3	inner	430.2.e.e.221.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.e.221.2	✓	6	43.6	even	3	inner
430.2.e.e.251.2	yes	6	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.285997 + 0.495361i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.285997 + 0.495361i) q^{6} +(2.33641 - 4.04678i) q^{7} +1.00000 q^{8} +(1.33641 - 2.31473i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.285997 + 0.495361i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.285997 + 0.495361i) q^{6} +(2.33641 - 4.04678i) q^{7} +1.00000 q^{8} +(1.33641 - 2.31473i) q^{9} +(0.500000 + 0.866025i) q^{10} -1.57199 q^{11} +(0.285997 + 0.495361i) q^{12} +(-2.45882 + 4.25880i) q^{13} +(2.33641 - 4.04678i) q^{14} +(-0.285997 + 0.495361i) q^{15} +1.00000 q^{16} +(1.33641 - 2.31473i) q^{18} +(-0.214003 - 0.370665i) q^{19} +(0.500000 + 0.866025i) q^{20} +2.67282 q^{21} -1.57199 q^{22} +(0.336412 + 0.582682i) q^{23} +(0.285997 + 0.495361i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.45882 + 4.25880i) q^{26} +3.24482 q^{27} +(2.33641 - 4.04678i) q^{28} +(-2.47842 + 4.29275i) q^{29} +(-0.285997 + 0.495361i) q^{30} +(3.12241 + 5.40817i) q^{31} +1.00000 q^{32} +(-0.449585 - 0.778704i) q^{33} +4.67282 q^{35} +(1.33641 - 2.31473i) q^{36} +(2.78600 + 4.82549i) q^{37} +(-0.214003 - 0.370665i) q^{38} -2.81286 q^{39} +(0.500000 + 0.866025i) q^{40} -7.48963 q^{41} +2.67282 q^{42} +(1.90643 - 6.27420i) q^{43} -1.57199 q^{44} +2.67282 q^{45} +(0.336412 + 0.582682i) q^{46} -10.6336 q^{47} +(0.285997 + 0.495361i) q^{48} +(-7.41764 - 12.8477i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.45882 + 4.25880i) q^{52} +(-2.24482 - 3.88814i) q^{53} +3.24482 q^{54} +(-0.785997 - 1.36139i) q^{55} +(2.33641 - 4.04678i) q^{56} +(0.122408 - 0.212018i) q^{57} +(-2.47842 + 4.29275i) q^{58} -10.2017 q^{59} +(-0.285997 + 0.495361i) q^{60} +(3.90841 - 6.76956i) q^{61} +(3.12241 + 5.40817i) q^{62} +(-6.24482 - 10.8163i) q^{63} +1.00000 q^{64} -4.91764 q^{65} +(-0.449585 - 0.778704i) q^{66} +(5.63164 + 9.75429i) q^{67} +(-0.192425 + 0.333290i) q^{69} +4.67282 q^{70} +(-0.449585 + 0.778704i) q^{71} +(1.33641 - 2.31473i) q^{72} +(-7.22324 + 12.5110i) q^{73} +(2.78600 + 4.82549i) q^{74} -0.571993 q^{75} +(-0.214003 - 0.370665i) q^{76} +(-3.67282 + 6.36152i) q^{77} -2.81286 q^{78} +(6.48963 - 11.2404i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.08123 - 5.33684i) q^{81} -7.48963 q^{82} +(7.86723 + 13.6264i) q^{83} +2.67282 q^{84} +(1.90643 - 6.27420i) q^{86} -2.83528 q^{87} -1.57199 q^{88} +(-3.21598 - 5.57024i) q^{89} +2.67282 q^{90} +(11.4896 + 19.9006i) q^{91} +(0.336412 + 0.582682i) q^{92} +(-1.78600 + 3.09344i) q^{93} -10.6336 q^{94} +(0.214003 - 0.370665i) q^{95} +(0.285997 + 0.495361i) q^{96} -4.28797 q^{97} +(-7.41764 - 12.8477i) q^{98} +(-2.10083 + 3.63875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 3 q^{5} + q^{6} + 4 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 3 * q^5 + q^6 + 4 * q^7 + 6 * q^8 - 2 * q^9	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 3 q^{5} + q^{6} + 4 q^{7} + 6 q^{8} - 2 q^{9} + 3 q^{10} - 8 q^{11} + q^{12} + 6 q^{13} + 4 q^{14} - q^{15} + 6 q^{16} - 2 q^{18} - 2 q^{19} + 3 q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} + q^{24} - 3 q^{25} + 6 q^{26} - 2 q^{27} + 4 q^{28} - 7 q^{29} - q^{30} + 8 q^{31} + 6 q^{32} - 12 q^{33} + 8 q^{35} - 2 q^{36} + 16 q^{37} - 2 q^{38} - 4 q^{39} + 3 q^{40} - 2 q^{41} - 4 q^{42} + 5 q^{43} - 8 q^{44} - 4 q^{45} - 8 q^{46} - 18 q^{47} + q^{48} - 3 q^{49} - 3 q^{50} + 6 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} + 4 q^{56} - 10 q^{57} - 7 q^{58} - 24 q^{59} - q^{60} + 12 q^{61} + 8 q^{62} - 16 q^{63} + 6 q^{64} + 12 q^{65} - 12 q^{66} - 7 q^{67} + 6 q^{69} + 8 q^{70} - 12 q^{71} - 2 q^{72} - 14 q^{73} + 16 q^{74} - 2 q^{75} - 2 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} + 3 q^{80} + 13 q^{81} - 2 q^{82} + 15 q^{83} - 4 q^{84} + 5 q^{86} + 66 q^{87} - 8 q^{88} - 15 q^{89} - 4 q^{90} + 26 q^{91} - 8 q^{92} - 10 q^{93} - 18 q^{94} + 2 q^{95} + q^{96} - 20 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 3 * q^5 + q^6 + 4 * q^7 + 6 * q^8 - 2 * q^9 + 3 * q^10 - 8 * q^11 + q^12 + 6 * q^13 + 4 * q^14 - q^15 + 6 * q^16 - 2 * q^18 - 2 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 + q^24 - 3 * q^25 + 6 * q^26 - 2 * q^27 + 4 * q^28 - 7 * q^29 - q^30 + 8 * q^31 + 6 * q^32 - 12 * q^33 + 8 * q^35 - 2 * q^36 + 16 * q^37 - 2 * q^38 - 4 * q^39 + 3 * q^40 - 2 * q^41 - 4 * q^42 + 5 * q^43 - 8 * q^44 - 4 * q^45 - 8 * q^46 - 18 * q^47 + q^48 - 3 * q^49 - 3 * q^50 + 6 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 + 4 * q^56 - 10 * q^57 - 7 * q^58 - 24 * q^59 - q^60 + 12 * q^61 + 8 * q^62 - 16 * q^63 + 6 * q^64 + 12 * q^65 - 12 * q^66 - 7 * q^67 + 6 * q^69 + 8 * q^70 - 12 * q^71 - 2 * q^72 - 14 * q^73 + 16 * q^74 - 2 * q^75 - 2 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 + 3 * q^80 + 13 * q^81 - 2 * q^82 + 15 * q^83 - 4 * q^84 + 5 * q^86 + 66 * q^87 - 8 * q^88 - 15 * q^89 - 4 * q^90 + 26 * q^91 - 8 * q^92 - 10 * q^93 - 18 * q^94 + 2 * q^95 + q^96 - 20 * q^97 - 3 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

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