LMFDB - Embedded newform 430.2.e.d.221.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.2
Root			$1.58114 + 2.73861i$ of defining polynomial
Character	$\chi$	$=$	430.221
Dual form			430.2.e.d.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.00000 - 1.73205i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} +(1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.00000 - 1.73205i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} +(1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +2.16228 q^{11} +(1.00000 - 1.73205i) q^{12} +(1.58114 + 2.73861i) q^{13} +(-1.58114 - 2.73861i) q^{14} +(1.00000 + 1.73205i) q^{15} +1.00000 q^{16} +(1.08114 + 1.87259i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.08114 + 3.60464i) q^{19} +(-0.500000 + 0.866025i) q^{20} +6.32456 q^{21} -2.16228 q^{22} +(-1.00000 + 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.58114 - 2.73861i) q^{26} +4.00000 q^{27} +(1.58114 + 2.73861i) q^{28} +(-5.16228 - 8.94133i) q^{29} +(-1.00000 - 1.73205i) q^{30} +(4.58114 - 7.93477i) q^{31} -1.00000 q^{32} +(2.16228 - 3.74517i) q^{33} +(-1.08114 - 1.87259i) q^{34} -3.16228 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.08114 - 3.60464i) q^{38} +6.32456 q^{39} +(0.500000 - 0.866025i) q^{40} +1.32456 q^{41} -6.32456 q^{42} +(1.66228 + 6.34325i) q^{43} +2.16228 q^{44} +1.00000 q^{45} -4.32456 q^{47} +(1.00000 - 1.73205i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +4.32456 q^{51} +(1.58114 + 2.73861i) q^{52} +(5.16228 - 8.94133i) q^{53} -4.00000 q^{54} +(-1.08114 + 1.87259i) q^{55} +(-1.58114 - 2.73861i) q^{56} +(4.16228 + 7.20928i) q^{57} +(5.16228 + 8.94133i) q^{58} +3.83772 q^{59} +(1.00000 + 1.73205i) q^{60} +(-0.581139 - 1.00656i) q^{61} +(-4.58114 + 7.93477i) q^{62} +(1.58114 - 2.73861i) q^{63} +1.00000 q^{64} -3.16228 q^{65} +(-2.16228 + 3.74517i) q^{66} +(-6.82456 + 11.8205i) q^{67} +(1.08114 + 1.87259i) q^{68} +3.16228 q^{70} +(-5.58114 - 9.66682i) q^{71} +(0.500000 + 0.866025i) q^{72} +(0.0811388 + 0.140537i) q^{73} +(1.00000 - 1.73205i) q^{74} -2.00000 q^{75} +(-2.08114 + 3.60464i) q^{76} +(3.41886 + 5.92164i) q^{77} -6.32456 q^{78} +(1.58114 + 2.73861i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} -1.32456 q^{82} +(-3.00000 + 5.19615i) q^{83} +6.32456 q^{84} -2.16228 q^{85} +(-1.66228 - 6.34325i) q^{86} -20.6491 q^{87} -2.16228 q^{88} +(-1.50000 + 2.59808i) q^{89} -1.00000 q^{90} +(-5.00000 + 8.66025i) q^{91} +(-9.16228 - 15.8695i) q^{93} +4.32456 q^{94} +(-2.08114 - 3.60464i) q^{95} +(-1.00000 + 1.73205i) q^{96} +10.1623 q^{97} +(1.50000 - 2.59808i) q^{98} +(-1.08114 - 1.87259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{24} - 2 q^{25} + 16 q^{27} - 8 q^{29} - 4 q^{30} + 12 q^{31} - 4 q^{32} - 4 q^{33} + 2 q^{34} - 2 q^{36} - 4 q^{37} + 2 q^{38} + 2 q^{40} - 20 q^{41} - 6 q^{43} - 4 q^{44} + 4 q^{45} + 8 q^{47} + 4 q^{48} - 6 q^{49} + 2 q^{50} - 8 q^{51} + 8 q^{53} - 16 q^{54} + 2 q^{55} + 4 q^{57} + 8 q^{58} + 28 q^{59} + 4 q^{60} + 4 q^{61} - 12 q^{62} + 4 q^{64} + 4 q^{66} - 2 q^{67} - 2 q^{68} - 16 q^{71} + 2 q^{72} - 6 q^{73} + 4 q^{74} - 8 q^{75} - 2 q^{76} + 20 q^{77} - 2 q^{80} + 22 q^{81} + 20 q^{82} - 12 q^{83} + 4 q^{85} + 6 q^{86} - 32 q^{87} + 4 q^{88} - 6 q^{89} - 4 q^{90} - 20 q^{91} - 24 q^{93} - 8 q^{94} - 2 q^{95} - 4 q^{96} + 28 q^{97} + 6 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 + 4 * q^22 - 4 * q^24 - 2 * q^25 + 16 * q^27 - 8 * q^29 - 4 * q^30 + 12 * q^31 - 4 * q^32 - 4 * q^33 + 2 * q^34 - 2 * q^36 - 4 * q^37 + 2 * q^38 + 2 * q^40 - 20 * q^41 - 6 * q^43 - 4 * q^44 + 4 * q^45 + 8 * q^47 + 4 * q^48 - 6 * q^49 + 2 * q^50 - 8 * q^51 + 8 * q^53 - 16 * q^54 + 2 * q^55 + 4 * q^57 + 8 * q^58 + 28 * q^59 + 4 * q^60 + 4 * q^61 - 12 * q^62 + 4 * q^64 + 4 * q^66 - 2 * q^67 - 2 * q^68 - 16 * q^71 + 2 * q^72 - 6 * q^73 + 4 * q^74 - 8 * q^75 - 2 * q^76 + 20 * q^77 - 2 * q^80 + 22 * q^81 + 20 * q^82 - 12 * q^83 + 4 * q^85 + 6 * q^86 - 32 * q^87 + 4 * q^88 - 6 * q^89 - 4 * q^90 - 20 * q^91 - 24 * q^93 - 8 * q^94 - 2 * q^95 - 4 * q^96 + 28 * q^97 + 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	1.58114	+	2.73861i	0.597614	+	1.03510i	0.993172	+	0.116657i	$0.0372179\pi$
$7$	1.58114	+	2.73861i	0.597614	+	1.03510i	−0.395558	+	0.918441i	$0.629449\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.16228			0.651951			0.325976	−	0.945378i	$-0.394307\pi$
$11$	2.16228			0.651951			0.325976	+	0.945378i	$0.394307\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	1.58114	+	2.73861i	0.438529	+	0.759555i	0.997576	−	0.0695813i	$-0.0221663\pi$
$13$	1.58114	+	2.73861i	0.438529	+	0.759555i	−0.559047	+	0.829136i	$0.688833\pi$
$14$	−1.58114	−	2.73861i	−0.422577	−	0.731925i
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	1.00000			0.250000
$17$	1.08114	+	1.87259i	0.262215	+	0.454169i	0.966830	−	0.255420i	$-0.0822138\pi$
$17$	1.08114	+	1.87259i	0.262215	+	0.454169i	−0.704615	+	0.709589i	$0.748880\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.08114	+	3.60464i	−0.477446	+	0.826961i	−0.999666	−	0.0258502i	$-0.991771\pi$
$19$	−2.08114	+	3.60464i	−0.477446	+	0.826961i	0.522220	+	0.852811i	$0.325104\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	6.32456			1.38013
$22$	−2.16228			−0.460999
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.58114	−	2.73861i	−0.310087	−	0.537086i
$27$	4.00000			0.769800
$28$	1.58114	+	2.73861i	0.298807	+	0.517549i
$29$	−5.16228	−	8.94133i	−0.958611	−	1.66036i	−0.725880	−	0.687822i	$-0.758567\pi$
$29$	−5.16228	−	8.94133i	−0.958611	−	1.66036i	−0.232731	−	0.972541i	$-0.574766\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$	4.58114	−	7.93477i	0.822797	−	1.42513i	−0.0807947	−	0.996731i	$-0.525746\pi$
$31$	4.58114	−	7.93477i	0.822797	−	1.42513i	0.903592	−	0.428395i	$-0.140921\pi$
$32$	−1.00000			−0.176777
$33$	2.16228	−	3.74517i	0.376404	−	0.651951i
$34$	−1.08114	−	1.87259i	−0.185414	−	0.321146i
$35$	−3.16228			−0.534522
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	2.08114	−	3.60464i	0.337605	−	0.584750i
$39$	6.32456			1.01274
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.32456			0.206861			0.103430	−	0.994637i	$-0.467018\pi$
$41$	1.32456			0.206861			0.103430	+	0.994637i	$0.467018\pi$
$42$	−6.32456			−0.975900
$43$	1.66228	+	6.34325i	0.253495	+	0.967337i
$43$	1.66228	+	6.34325i	0.253495	+	0.967337i
$44$	2.16228			0.325976
$45$	1.00000			0.149071
$46$		0			0
$47$	−4.32456			−0.630801			−0.315401	−	0.948959i	$-0.602139\pi$
$47$	−4.32456			−0.630801			−0.315401	+	0.948959i	$0.602139\pi$
$48$	1.00000	−	1.73205i	0.144338	−	0.250000i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	4.32456			0.605559
$52$	1.58114	+	2.73861i	0.219265	+	0.379777i
$53$	5.16228	−	8.94133i	0.709093	−	1.22819i	−0.256100	−	0.966650i	$-0.582438\pi$
$53$	5.16228	−	8.94133i	0.709093	−	1.22819i	0.965194	−	0.261536i	$-0.0842289\pi$
$54$	−4.00000			−0.544331
$55$	−1.08114	+	1.87259i	−0.145781	+	0.252500i
$56$	−1.58114	−	2.73861i	−0.211289	−	0.365963i
$57$	4.16228	+	7.20928i	0.551307	+	0.954892i
$58$	5.16228	+	8.94133i	0.677840	+	1.17405i
$59$	3.83772			0.499629			0.249814	−	0.968294i	$-0.419630\pi$
$59$	3.83772			0.499629			0.249814	+	0.968294i	$0.419630\pi$
$60$	1.00000	+	1.73205i	0.129099	+	0.223607i
$61$	−0.581139	−	1.00656i	−0.0744072	−	0.128877i	0.826421	−	0.563052i	$-0.190373\pi$
$61$	−0.581139	−	1.00656i	−0.0744072	−	0.128877i	−0.900828	+	0.434175i	$0.857040\pi$
$62$	−4.58114	+	7.93477i	−0.581805	+	1.00772i
$63$	1.58114	−	2.73861i	0.199205	−	0.345033i
$64$	1.00000			0.125000
$65$	−3.16228			−0.392232
$66$	−2.16228	+	3.74517i	−0.266158	+	0.460999i
$67$	−6.82456	+	11.8205i	−0.833752	+	1.44410i	0.0612903	+	0.998120i	$0.480478\pi$
$67$	−6.82456	+	11.8205i	−0.833752	+	1.44410i	−0.895042	+	0.445981i	$0.852855\pi$
$68$	1.08114	+	1.87259i	0.131107	+	0.227085i
$69$		0			0
$70$	3.16228			0.377964
$71$	−5.58114	−	9.66682i	−0.662359	−	1.14724i	−0.979994	−	0.199027i	$-0.936222\pi$
$71$	−5.58114	−	9.66682i	−0.662359	−	1.14724i	0.317635	−	0.948213i	$-0.397111\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	0.0811388	+	0.140537i	0.00949658	+	0.0164486i	0.870735	−	0.491753i	$-0.163644\pi$
$73$	0.0811388	+	0.140537i	0.00949658	+	0.0164486i	−0.861238	+	0.508202i	$0.830310\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−2.00000			−0.230940
$76$	−2.08114	+	3.60464i	−0.238723	+	0.413480i
$77$	3.41886	+	5.92164i	0.389615	+	0.674834i
$78$	−6.32456			−0.716115
$79$	1.58114	+	2.73861i	0.177892	+	0.308118i	0.941158	−	0.337966i	$-0.109739\pi$
$79$	1.58114	+	2.73861i	0.177892	+	0.308118i	−0.763266	+	0.646084i	$0.776406\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−1.32456			−0.146273
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	−0.982372	−	0.186938i	$-0.940144\pi$
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	0.653079	+	0.757290i	$0.273477\pi$
$84$	6.32456			0.690066
$85$	−2.16228			−0.234532
$86$	−1.66228	−	6.34325i	−0.179248	−	0.684010i
$87$	−20.6491			−2.21382
$88$	−2.16228			−0.230500
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$	−1.00000			−0.105409
$91$	−5.00000	+	8.66025i	−0.524142	+	0.907841i
$92$		0			0
$93$	−9.16228	−	15.8695i	−0.950084	−	1.64559i
$94$	4.32456			0.446044
$95$	−2.08114	−	3.60464i	−0.213520	−	0.369828i
$96$	−1.00000	+	1.73205i	−0.102062	+	0.176777i
$97$	10.1623			1.03182			0.515911	−	0.856642i	$-0.327453\pi$
$97$	10.1623			1.03182			0.515911	+	0.856642i	$0.327453\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−1.08114	−	1.87259i	−0.108659	−	0.188202i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.41886	+	5.92164i	0.340189	+	0.589225i	0.984468	−	0.175566i	$-0.0561755\pi$
$101$	3.41886	+	5.92164i	0.340189	+	0.589225i	−0.644278	+	0.764791i	$0.722842\pi$
$102$	−4.32456			−0.428195
$103$	−7.90569	−	13.6931i	−0.778971	−	1.34922i	−0.932535	−	0.361079i	$-0.882408\pi$
$103$	−7.90569	−	13.6931i	−0.778971	−	1.34922i	0.153564	−	0.988139i	$-0.450925\pi$
$104$	−1.58114	−	2.73861i	−0.155043	−	0.268543i
$105$	−3.16228	+	5.47723i	−0.308607	+	0.534522i
$106$	−5.16228	+	8.94133i	−0.501405	+	0.868458i
$107$	−11.6491			−1.12616			−0.563081	−	0.826402i	$-0.690384\pi$
$107$	−11.6491			−1.12616			−0.563081	+	0.826402i	$0.690384\pi$
$108$	4.00000			0.384900
$109$	4.58114	−	7.93477i	0.438794	−	0.760013i	−0.558803	−	0.829300i	$-0.688739\pi$
$109$	4.58114	−	7.93477i	0.438794	−	0.760013i	0.997597	+	0.0692876i	$0.0220726\pi$
$110$	1.08114	−	1.87259i	0.103083	−	0.178544i
$111$	2.00000	+	3.46410i	0.189832	+	0.328798i
$112$	1.58114	+	2.73861i	0.149404	+	0.258775i
$113$	−0.486833			−0.0457974			−0.0228987	−	0.999738i	$-0.507290\pi$
$113$	−0.486833			−0.0457974			−0.0228987	+	0.999738i	$0.507290\pi$
$114$	−4.16228	−	7.20928i	−0.389833	−	0.675211i
$115$		0			0
$116$	−5.16228	−	8.94133i	−0.479305	−	0.830181i
$117$	1.58114	−	2.73861i	0.146176	−	0.253185i
$118$	−3.83772			−0.353291
$119$	−3.41886	+	5.92164i	−0.313406	+	0.542836i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−6.32456			−0.574960
$122$	0.581139	+	1.00656i	0.0526138	+	0.0911298i
$123$	1.32456	−	2.29420i	0.119431	−	0.206861i
$124$	4.58114	−	7.93477i	0.411398	−	0.712563i
$125$	1.00000			0.0894427
$126$	−1.58114	+	2.73861i	−0.140859	+	0.243975i
$127$	−18.6491			−1.65484			−0.827420	−	0.561583i	$-0.810193\pi$
$127$	−18.6491			−1.65484			−0.827420	+	0.561583i	$0.810193\pi$
$128$	−1.00000			−0.0883883
$129$	12.6491	+	3.46410i	1.11369	+	0.304997i
$130$	3.16228			0.277350
$131$	−12.4868			−1.09098			−0.545490	−	0.838117i	$-0.683656\pi$
$131$	−12.4868			−1.09098			−0.545490	+	0.838117i	$0.683656\pi$
$132$	2.16228	−	3.74517i	0.188202	−	0.325976i
$133$	−13.1623			−1.14131
$134$	6.82456	−	11.8205i	0.589552	−	1.02113i
$135$	−2.00000	+	3.46410i	−0.172133	+	0.298142i
$136$	−1.08114	−	1.87259i	−0.0927069	−	0.160573i
$137$	−7.67544			−0.655757			−0.327879	−	0.944720i	$-0.606334\pi$
$137$	−7.67544			−0.655757			−0.327879	+	0.944720i	$0.606334\pi$
$138$		0			0
$139$	−1.24342	+	2.15366i	−0.105465	+	0.182671i	−0.913928	−	0.405876i	$-0.866966\pi$
$139$	−1.24342	+	2.15366i	−0.105465	+	0.182671i	0.808463	+	0.588547i	$0.200300\pi$
$140$	−3.16228			−0.267261
$141$	−4.32456	+	7.49035i	−0.364193	+	0.630801i
$142$	5.58114	+	9.66682i	0.468359	+	0.811221i
$143$	3.41886	+	5.92164i	0.285900	+	0.495193i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	10.3246			0.857408
$146$	−0.0811388	−	0.140537i	−0.00671510	−	0.0116309i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	−2.58114	+	4.47066i	−0.211455	+	0.366251i	−0.952170	−	0.305568i	$-0.901154\pi$
$149$	−2.58114	+	4.47066i	−0.211455	+	0.366251i	0.740715	+	0.671819i	$0.234487\pi$
$150$	2.00000			0.163299
$151$	6.32456			0.514685			0.257343	−	0.966320i	$-0.417153\pi$
$151$	6.32456			0.514685			0.257343	+	0.966320i	$0.417153\pi$
$152$	2.08114	−	3.60464i	0.168803	−	0.292375i
$153$	1.08114	−	1.87259i	0.0874049	−	0.151390i
$154$	−3.41886	−	5.92164i	−0.275500	−	0.477179i
$155$	4.58114	+	7.93477i	0.367966	+	0.637336i
$156$	6.32456			0.506370
$157$	−2.25658	−	3.90852i	−0.180095	−	0.311934i	0.761818	−	0.647791i	$-0.224307\pi$
$157$	−2.25658	−	3.90852i	−0.180095	−	0.311934i	−0.941913	+	0.335858i	$0.890974\pi$
$158$	−1.58114	−	2.73861i	−0.125789	−	0.217872i
$159$	−10.3246	−	17.8827i	−0.818790	−	1.41819i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	−5.50000	+	9.52628i	−0.432121	+	0.748455i
$163$	10.8246	+	18.7487i	0.847845	+	1.46851i	0.883128	+	0.469133i	$0.155433\pi$
$163$	10.8246	+	18.7487i	0.847845	+	1.46851i	−0.0352831	+	0.999377i	$0.511233\pi$
$164$	1.32456			0.103430
$165$	2.16228	+	3.74517i	0.168333	+	0.291561i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	12.0000	−	20.7846i	0.928588	−	1.60836i	0.142901	−	0.989737i	$-0.454357\pi$
$167$	12.0000	−	20.7846i	0.928588	−	1.60836i	0.785687	−	0.618624i	$-0.212310\pi$
$168$	−6.32456			−0.487950
$169$	1.50000	−	2.59808i	0.115385	−	0.199852i
$170$	2.16228			0.165839
$171$	4.16228			0.318297
$172$	1.66228	+	6.34325i	0.126747	+	0.483668i
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$	20.6491			1.56541
$175$	1.58114	−	2.73861i	0.119523	−	0.207020i
$176$	2.16228			0.162988
$177$	3.83772	−	6.64713i	0.288461	−	0.499629i
$178$	1.50000	−	2.59808i	0.112430	−	0.194734i
$179$	−2.75658	−	4.77454i	−0.206037	−	0.356866i	0.744426	−	0.667705i	$-0.232723\pi$
$179$	−2.75658	−	4.77454i	−0.206037	−	0.356866i	−0.950463	+	0.310839i	$0.899390\pi$
$180$	1.00000			0.0745356
$181$	−0.162278	−	0.281073i	−0.0120620	−	0.0208920i	0.859931	−	0.510410i	$-0.170506\pi$
$181$	−0.162278	−	0.281073i	−0.0120620	−	0.0208920i	−0.871993	+	0.489518i	$0.837173\pi$
$182$	5.00000	−	8.66025i	0.370625	−	0.641941i
$183$	−2.32456			−0.171836
$184$		0			0
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	9.16228	+	15.8695i	0.671811	+	1.16361i
$187$	2.33772	+	4.04905i	0.170951	+	0.296096i
$188$	−4.32456			−0.315401
$189$	6.32456	+	10.9545i	0.460044	+	0.796819i
$190$	2.08114	+	3.60464i	0.150982	+	0.261508i
$191$	3.90569	−	6.76486i	0.282606	−	0.489488i	−0.689420	−	0.724362i	$-0.742134\pi$
$191$	3.90569	−	6.76486i	0.282606	−	0.489488i	0.972026	+	0.234874i	$0.0754677\pi$
$192$	1.00000	−	1.73205i	0.0721688	−	0.125000i
$193$	26.9737			1.94161			0.970803	−	0.239876i	$-0.0771069\pi$
$193$	26.9737			1.94161			0.970803	+	0.239876i	$0.0771069\pi$
$194$	−10.1623			−0.729609
$195$	−3.16228	+	5.47723i	−0.226455	+	0.392232i
$196$	−1.50000	+	2.59808i	−0.107143	+	0.185577i
$197$	5.16228	+	8.94133i	0.367797	+	0.637043i	0.989221	−	0.146431i	$-0.0467788\pi$
$197$	5.16228	+	8.94133i	0.367797	+	0.637043i	−0.621424	+	0.783475i	$0.713445\pi$
$198$	1.08114	+	1.87259i	0.0768332	+	0.133079i
$199$	24.3246			1.72432			0.862161	−	0.506634i	$-0.169111\pi$
$199$	24.3246			1.72432			0.862161	+	0.506634i	$0.169111\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	13.6491	+	23.6410i	0.962734	+	1.66750i
$202$	−3.41886	−	5.92164i	−0.240550	−	0.416645i
$203$	16.3246	−	28.2750i	1.14576	−	1.98451i
$204$	4.32456			0.302779
$205$	−0.662278	+	1.14710i	−0.0462555	+	0.0801168i
$206$	7.90569	+	13.6931i	0.550816	+	0.954041i
$207$		0			0
$208$	1.58114	+	2.73861i	0.109632	+	0.189889i
$209$	−4.50000	+	7.79423i	−0.311272	+	0.539138i
$210$	3.16228	−	5.47723i	0.218218	−	0.377964i
$211$	−22.9737			−1.58157			−0.790786	−	0.612092i	$-0.790328\pi$
$211$	−22.9737			−1.58157			−0.790786	+	0.612092i	$0.790328\pi$
$212$	5.16228	−	8.94133i	0.354547	−	0.614093i
$213$	−22.3246			−1.52965
$214$	11.6491			0.796317
$215$	−6.32456	−	1.73205i	−0.431331	−	0.118125i
$216$	−4.00000			−0.272166
$217$	28.9737			1.96686
$218$	−4.58114	+	7.93477i	−0.310274	+	0.537410i
$219$	0.324555			0.0219314
$220$	−1.08114	+	1.87259i	−0.0728904	+	0.126250i
$221$	−3.41886	+	5.92164i	−0.229977	+	0.398333i
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	−15.1623			−1.01534			−0.507671	−	0.861551i	$-0.669493\pi$
$223$	−15.1623			−1.01534			−0.507671	+	0.861551i	$0.669493\pi$
$224$	−1.58114	−	2.73861i	−0.105644	−	0.182981i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	0.486833			0.0323836
$227$	2.82456	−	4.89227i	0.187472	−	0.324712i	−0.756935	−	0.653491i	$-0.773304\pi$
$227$	2.82456	−	4.89227i	0.187472	−	0.324712i	0.944407	+	0.328779i	$0.106637\pi$
$228$	4.16228	+	7.20928i	0.275654	+	0.477446i
$229$	−0.162278	−	0.281073i	−0.0107236	−	0.0185738i	0.860614	−	0.509258i	$-0.170080\pi$
$229$	−0.162278	−	0.281073i	−0.0107236	−	0.0185738i	−0.871337	+	0.490684i	$0.836747\pi$
$230$		0			0
$231$	13.6754			0.899778
$232$	5.16228	+	8.94133i	0.338920	+	0.587027i
$233$	2.40569	+	4.16678i	0.157602	+	0.272975i	0.934004	−	0.357264i	$-0.116290\pi$
$233$	2.40569	+	4.16678i	0.157602	+	0.272975i	−0.776401	+	0.630239i	$0.782957\pi$
$234$	−1.58114	+	2.73861i	−0.103362	+	0.179029i
$235$	2.16228	−	3.74517i	0.141051	−	0.244308i
$236$	3.83772			0.249814
$237$	6.32456			0.410824
$238$	3.41886	−	5.92164i	0.221612	−	0.383843i
$239$	−14.1623	+	24.5298i	−0.916082	+	1.58670i	−0.110772	+	0.993846i	$0.535332\pi$
$239$	−14.1623	+	24.5298i	−0.916082	+	1.58670i	−0.805310	+	0.592854i	$0.798001\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	−8.32456	−	14.4186i	−0.536232	−	0.928781i	−0.999103	−	0.0423549i	$-0.986514\pi$
$241$	−8.32456	−	14.4186i	−0.536232	−	0.928781i	0.462871	−	0.886426i	$-0.346819\pi$
$242$	6.32456			0.406558
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$	−0.581139	−	1.00656i	−0.0372036	−	0.0644385i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−1.32456	+	2.29420i	−0.0844506	+	0.146273i
$247$	−13.1623			−0.837496
$248$	−4.58114	+	7.93477i	−0.290903	+	0.503858i
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	−1.00000			−0.0632456
$251$	−10.9189	−	18.9120i	−0.689192	−	1.19372i	−0.972099	−	0.234569i	$-0.924632\pi$
$251$	−10.9189	−	18.9120i	−0.689192	−	1.19372i	0.282907	−	0.959147i	$-0.408701\pi$
$252$	1.58114	−	2.73861i	0.0996024	−	0.172516i
$253$		0			0
$254$	18.6491			1.17015
$255$	−2.16228	+	3.74517i	−0.135407	+	0.234532i
$256$	1.00000			0.0625000
$257$	−9.83772			−0.613660			−0.306830	−	0.951764i	$-0.599268\pi$
$257$	−9.83772			−0.613660			−0.306830	+	0.951764i	$0.599268\pi$
$258$	−12.6491	−	3.46410i	−0.787499	−	0.215666i
$259$	−6.32456			−0.392989
$260$	−3.16228			−0.196116
$261$	−5.16228	+	8.94133i	−0.319537	+	0.553454i
$262$	12.4868			0.771439
$263$	4.74342	−	8.21584i	0.292492	−	0.506610i	−0.681907	−	0.731439i	$-0.738849\pi$
$263$	4.74342	−	8.21584i	0.292492	−	0.506610i	0.974398	+	0.224829i	$0.0721823\pi$
$264$	−2.16228	+	3.74517i	−0.133079	+	0.230500i
$265$	5.16228	+	8.94133i	0.317116	+	0.549261i
$266$	13.1623			0.807031
$267$	3.00000	+	5.19615i	0.183597	+	0.317999i
$268$	−6.82456	+	11.8205i	−0.416876	+	0.722051i
$269$	2.51317			0.153230			0.0766152	−	0.997061i	$-0.475589\pi$
$269$	2.51317			0.153230			0.0766152	+	0.997061i	$0.475589\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	−11.3246	−	19.6147i	−0.687918	−	1.19151i	−0.972510	−	0.232860i	$-0.925192\pi$
$271$	−11.3246	−	19.6147i	−0.687918	−	1.19151i	0.284593	−	0.958649i	$-0.408142\pi$
$272$	1.08114	+	1.87259i	0.0655537	+	0.113542i
$273$	10.0000	+	17.3205i	0.605228	+	1.04828i
$274$	7.67544			0.463691
$275$	−1.08114	−	1.87259i	−0.0651951	−	0.112921i
$276$		0			0
$277$	8.48683	−	14.6996i	0.509924	−	0.883215i	−0.490010	−	0.871717i	$-0.663007\pi$
$277$	8.48683	−	14.6996i	0.509924	−	0.883215i	0.999934	−	0.0114978i	$-0.00365996\pi$
$278$	1.24342	−	2.15366i	0.0745752	−	0.129168i
$279$	−9.16228			−0.548531
$280$	3.16228			0.188982
$281$	4.50000	−	7.79423i	0.268447	−	0.464965i	−0.700014	−	0.714130i	$-0.746823\pi$
$281$	4.50000	−	7.79423i	0.268447	−	0.464965i	0.968461	+	0.249165i	$0.0801561\pi$
$282$	4.32456	−	7.49035i	0.257524	−	0.446044i
$283$	1.82456	+	3.16022i	0.108459	+	0.187856i	0.915146	−	0.403123i	$-0.132075\pi$
$283$	1.82456	+	3.16022i	0.108459	+	0.187856i	−0.806687	+	0.590978i	$0.798742\pi$
$284$	−5.58114	−	9.66682i	−0.331180	−	0.573620i
$285$	−8.32456			−0.493104
$286$	−3.41886	−	5.92164i	−0.202161	−	0.350154i
$287$	2.09431	+	3.62744i	0.123623	+	0.214121i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	6.16228	−	10.6734i	0.362487	−	0.627846i
$290$	−10.3246			−0.606279
$291$	10.1623	−	17.6016i	0.595723	−	1.03182i
$292$	0.0811388	+	0.140537i	0.00474829	+	0.00822428i
$293$	21.4868			1.25527			0.627637	−	0.778506i	$-0.284022\pi$
$293$	21.4868			1.25527			0.627637	+	0.778506i	$0.284022\pi$
$294$	−3.00000	−	5.19615i	−0.174964	−	0.303046i
$295$	−1.91886	+	3.32357i	−0.111720	+	0.193505i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	8.64911			0.501872
$298$	2.58114	−	4.47066i	0.149521	−	0.258979i
$299$		0			0
$300$	−2.00000			−0.115470
$301$	−14.7434	+	14.5819i	−0.849796	+	0.840486i
$302$	−6.32456			−0.363937
$303$	13.6754			0.785634
$304$	−2.08114	+	3.60464i	−0.119361	+	0.206740i
$305$	1.16228			0.0665518
$306$	−1.08114	+	1.87259i	−0.0618046	+	0.107049i
$307$	−6.33772	+	10.9773i	−0.361713	+	0.626505i	−0.988243	−	0.152892i	$-0.951141\pi$
$307$	−6.33772	+	10.9773i	−0.361713	+	0.626505i	0.626530	+	0.779397i	$0.284475\pi$
$308$	3.41886	+	5.92164i	0.194808	+	0.337417i
$309$	−31.6228			−1.79896
$310$	−4.58114	−	7.93477i	−0.260191	−	0.450664i
$311$	−0.837722	+	1.45098i	−0.0475029	+	0.0822774i	−0.888799	−	0.458297i	$-0.848460\pi$
$311$	−0.837722	+	1.45098i	−0.0475029	+	0.0822774i	0.841296	+	0.540574i	$0.181793\pi$
$312$	−6.32456			−0.358057
$313$	9.32456	−	16.1506i	0.527055	−	0.912886i	−0.472448	−	0.881359i	$-0.656629\pi$
$313$	9.32456	−	16.1506i	0.527055	−	0.912886i	0.999503	−	0.0315275i	$-0.0100372\pi$
$314$	2.25658	+	3.90852i	0.127346	+	0.220570i
$315$	1.58114	+	2.73861i	0.0890871	+	0.154303i
$316$	1.58114	+	2.73861i	0.0889460	+	0.154059i
$317$	−1.67544			−0.0941023			−0.0470512	−	0.998892i	$-0.514982\pi$
$317$	−1.67544			−0.0941023			−0.0470512	+	0.998892i	$0.514982\pi$
$318$	10.3246	+	17.8827i	0.578972	+	1.00281i
$319$	−11.1623	−	19.3336i	−0.624968	−	1.08248i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−11.6491	+	20.1769i	−0.650190	+	1.12616i
$322$		0			0
$323$	−9.00000			−0.500773
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$	1.58114	−	2.73861i	0.0877058	−	0.151911i
$326$	−10.8246	−	18.7487i	−0.599517	−	1.03839i
$327$	−9.16228	−	15.8695i	−0.506675	−	0.877587i
$328$	−1.32456			−0.0731363
$329$	−6.83772	−	11.8433i	−0.376976	−	0.652941i
$330$	−2.16228	−	3.74517i	−0.119029	−	0.206165i
$331$	−7.24342	−	12.5460i	−0.398134	−	0.689589i	0.595362	−	0.803458i	$-0.297009\pi$
$331$	−7.24342	−	12.5460i	−0.398134	−	0.689589i	−0.993496	+	0.113869i	$0.963675\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	2.00000			0.109599
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$	−6.82456	−	11.8205i	−0.372865	−	0.645822i
$336$	6.32456			0.345033
$337$	−14.5680	−	25.2325i	−0.793568	−	1.37450i	−0.923745	−	0.383009i	$-0.874888\pi$
$337$	−14.5680	−	25.2325i	−0.793568	−	1.37450i	0.130177	−	0.991491i	$-0.458446\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	−0.486833	+	0.843219i	−0.0264411	+	0.0457974i
$340$	−2.16228			−0.117266
$341$	9.90569	−	17.1572i	0.536423	−	0.929113i
$342$	−4.16228			−0.225070
$343$	12.6491			0.682988
$344$	−1.66228	−	6.34325i	−0.0896240	−	0.342005i
$345$		0			0
$346$		0			0
$347$	−10.9868	+	19.0298i	−0.589804	+	1.02157i	0.404454	+	0.914559i	$0.367462\pi$
$347$	−10.9868	+	19.0298i	−0.589804	+	1.02157i	−0.994258	+	0.107012i	$0.965872\pi$
$348$	−20.6491			−1.10691
$349$	−5.32456	+	9.22240i	−0.285017	+	0.493664i	−0.972613	−	0.232429i	$-0.925333\pi$
$349$	−5.32456	+	9.22240i	−0.285017	+	0.493664i	0.687596	+	0.726093i	$0.258666\pi$
$350$	−1.58114	+	2.73861i	−0.0845154	+	0.146385i
$351$	6.32456	+	10.9545i	0.337580	+	0.584705i
$352$	−2.16228			−0.115250
$353$	−10.9189	−	18.9120i	−0.581152	−	1.00659i	−0.995343	−	0.0963953i	$-0.969269\pi$
$353$	−10.9189	−	18.9120i	−0.581152	−	1.00659i	0.414191	−	0.910190i	$-0.364065\pi$
$354$	−3.83772	+	6.64713i	−0.203973	+	0.353291i
$355$	11.1623			0.592432
$356$	−1.50000	+	2.59808i	−0.0794998	+	0.137698i
$357$	6.83772	+	11.8433i	0.361891	+	0.626813i
$358$	2.75658	+	4.77454i	0.145690	+	0.252342i
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$	−1.00000			−0.0527046
$361$	0.837722	+	1.45098i	0.0440906	+	0.0763672i
$362$	0.162278	+	0.281073i	0.00852912	+	0.0147729i
$363$	−6.32456	+	10.9545i	−0.331953	+	0.574960i
$364$	−5.00000	+	8.66025i	−0.262071	+	0.453921i
$365$	−0.162278			−0.00849400
$366$	2.32456			0.121506
$367$	−4.41886	+	7.65369i	−0.230663	+	0.399519i	−0.958003	−	0.286757i	$-0.907423\pi$
$367$	−4.41886	+	7.65369i	−0.230663	+	0.399519i	0.727341	+	0.686277i	$0.240756\pi$
$368$		0			0
$369$	−0.662278	−	1.14710i	−0.0344768	−	0.0597156i
$370$	1.00000	+	1.73205i	0.0519875	+	0.0900450i
$371$	32.6491			1.69506
$372$	−9.16228	−	15.8695i	−0.475042	−	0.822797i
$373$	6.25658	+	10.8367i	0.323954	+	0.561104i	0.981300	−	0.192484i	$-0.0616545\pi$
$373$	6.25658	+	10.8367i	0.323954	+	0.561104i	−0.657346	+	0.753589i	$0.728321\pi$
$374$	−2.33772	−	4.04905i	−0.120881	−	0.209372i
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$	4.32456			0.223022
$377$	16.3246	−	28.2750i	0.840757	−	1.45623i
$378$	−6.32456	−	10.9545i	−0.325300	−	0.563436i
$379$	11.8377			0.608063			0.304031	−	0.952662i	$-0.401667\pi$
$379$	11.8377			0.608063			0.304031	+	0.952662i	$0.401667\pi$
$380$	−2.08114	−	3.60464i	−0.106760	−	0.184914i
$381$	−18.6491	+	32.3012i	−0.955423	+	1.65484i
$382$	−3.90569	+	6.76486i	−0.199833	+	0.346120i
$383$	−24.0000			−1.22634			−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000			−1.22634			−0.613171	+	0.789950i	$0.710106\pi$
$384$	−1.00000	+	1.73205i	−0.0510310	+	0.0883883i
$385$	−6.83772			−0.348483
$386$	−26.9737			−1.37292
$387$	4.66228	−	4.61120i	0.236997	−	0.234400i
$388$	10.1623			0.515911
$389$	−24.1359			−1.22374			−0.611870	−	0.790958i	$-0.709583\pi$
$389$	−24.1359			−1.22374			−0.611870	+	0.790958i	$0.709583\pi$
$390$	3.16228	−	5.47723i	0.160128	−	0.277350i
$391$		0			0
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	−12.4868	+	21.6278i	−0.629877	+	1.09098i
$394$	−5.16228	−	8.94133i	−0.260072	−	0.450458i
$395$	−3.16228			−0.159111
$396$	−1.08114	−	1.87259i	−0.0543293	−	0.0941011i
$397$	15.7434	−	27.2684i	0.790139	−	1.36856i	−0.135741	−	0.990744i	$-0.543341\pi$
$397$	15.7434	−	27.2684i	0.790139	−	1.36856i	0.925880	−	0.377817i	$-0.123325\pi$
$398$	−24.3246			−1.21928
$399$	−13.1623	+	22.7977i	−0.658938	+	1.14131i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	9.48683	+	16.4317i	0.473750	+	0.820559i	0.999548	−	0.0300503i	$-0.00956676\pi$
$401$	9.48683	+	16.4317i	0.473750	+	0.820559i	−0.525799	+	0.850609i	$0.676233\pi$
$402$	−13.6491	−	23.6410i	−0.680756	−	1.17910i
$403$	28.9737			1.44328
$404$	3.41886	+	5.92164i	0.170095	+	0.294613i
$405$	5.50000	+	9.52628i	0.273297	+	0.473365i
$406$	−16.3246	+	28.2750i	−0.810174	+	1.40326i
$407$	−2.16228	+	3.74517i	−0.107180	+	0.185641i
$408$	−4.32456			−0.214097
$409$	−39.6491			−1.96052			−0.980261	−	0.197707i	$-0.936651\pi$
$409$	−39.6491			−1.96052			−0.980261	+	0.197707i	$0.936651\pi$
$410$	0.662278	−	1.14710i	0.0327076	−	0.0566512i
$411$	−7.67544	+	13.2943i	−0.378602	+	0.655757i
$412$	−7.90569	−	13.6931i	−0.389486	−	0.674609i
$413$	6.06797	+	10.5100i	0.298585	+	0.517165i
$414$		0			0
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	−1.58114	−	2.73861i	−0.0775217	−	0.134272i
$417$	2.48683	+	4.30732i	0.121781	+	0.210930i
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	−17.2982			−0.845073			−0.422537	−	0.906346i	$-0.638860\pi$
$419$	−17.2982			−0.845073			−0.422537	+	0.906346i	$0.638860\pi$
$420$	−3.16228	+	5.47723i	−0.154303	+	0.267261i
$421$	−2.74342	−	4.75174i	−0.133706	−	0.231585i	0.791396	−	0.611303i	$-0.209354\pi$
$421$	−2.74342	−	4.75174i	−0.133706	−	0.231585i	−0.925102	+	0.379718i	$0.876021\pi$
$422$	22.9737			1.11834
$423$	2.16228	+	3.74517i	0.105134	+	0.182097i
$424$	−5.16228	+	8.94133i	−0.250702	+	0.434229i
$425$	1.08114	−	1.87259i	0.0524429	−	0.0908338i
$426$	22.3246			1.08163
$427$	1.83772	−	3.18303i	0.0889336	−	0.154038i
$428$	−11.6491			−0.563081
$429$	13.6754			0.660257
$430$	6.32456	+	1.73205i	0.304997	+	0.0835269i
$431$	28.4605			1.37089			0.685447	−	0.728123i	$-0.259607\pi$
$431$	28.4605			1.37089			0.685447	+	0.728123i	$0.259607\pi$
$432$	4.00000			0.192450
$433$	5.48683	−	9.50347i	0.263680	−	0.456708i	−0.703537	−	0.710659i	$-0.748397\pi$
$433$	5.48683	−	9.50347i	0.263680	−	0.456708i	0.967217	+	0.253951i	$0.0817303\pi$
$434$	−28.9737			−1.39078
$435$	10.3246	−	17.8827i	0.495025	−	0.857408i
$436$	4.58114	−	7.93477i	0.219397	−	0.380006i
$437$		0			0
$438$	−0.324555			−0.0155079
$439$	14.0680	+	24.3664i	0.671428	+	1.16295i	0.977499	+	0.210938i	$0.0676519\pi$
$439$	14.0680	+	24.3664i	0.671428	+	1.16295i	−0.306072	+	0.952008i	$0.599015\pi$
$440$	1.08114	−	1.87259i	0.0515413	−	0.0892721i
$441$	3.00000			0.142857
$442$	3.41886	−	5.92164i	0.162619	−	0.281664i
$443$	11.6491	+	20.1769i	0.553466	+	0.958631i	0.998021	+	0.0628797i	$0.0200284\pi$
$443$	11.6491	+	20.1769i	0.553466	+	0.958631i	−0.444555	+	0.895751i	$0.646638\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	−1.50000	−	2.59808i	−0.0711068	−	0.123161i
$446$	15.1623			0.717955
$447$	5.16228	+	8.94133i	0.244167	+	0.422910i
$448$	1.58114	+	2.73861i	0.0747018	+	0.129387i
$449$	9.66228	−	16.7356i	0.455991	−	0.789800i	−0.542754	−	0.839892i	$-0.682618\pi$
$449$	9.66228	−	16.7356i	0.455991	−	0.789800i	0.998745	+	0.0500923i	$0.0159516\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	2.86406			0.134863
$452$	−0.486833			−0.0228987
$453$	6.32456	−	10.9545i	0.297154	−	0.514685i
$454$	−2.82456	+	4.89227i	−0.132563	+	0.229606i
$455$	−5.00000	−	8.66025i	−0.234404	−	0.405999i
$456$	−4.16228	−	7.20928i	−0.194917	−	0.337605i
$457$	28.1623			1.31738			0.658688	−	0.752416i	$-0.271112\pi$
$457$	28.1623			1.31738			0.658688	+	0.752416i	$0.271112\pi$
$458$	0.162278	+	0.281073i	0.00758274	+	0.0131337i
$459$	4.32456	+	7.49035i	0.201853	+	0.349620i
$460$		0			0
$461$	10.2566	−	17.7649i	0.477697	−	0.827395i	−0.521976	−	0.852960i	$-0.674805\pi$
$461$	10.2566	−	17.7649i	0.477697	−	0.827395i	0.999673	+	0.0255649i	$0.00813845\pi$
$462$	−13.6754			−0.636239
$463$	−14.8114	+	25.6541i	−0.688344	+	1.19225i	0.284030	+	0.958815i	$0.408329\pi$
$463$	−14.8114	+	25.6541i	−0.688344	+	1.19225i	−0.972373	+	0.233431i	$0.925005\pi$
$464$	−5.16228	−	8.94133i	−0.239653	−	0.415091i
$465$	18.3246			0.849781
$466$	−2.40569	−	4.16678i	−0.111442	−	0.193023i
$467$	−12.6623	+	21.9317i	−0.585940	+	1.01488i	0.408817	+	0.912616i	$0.365941\pi$
$467$	−12.6623	+	21.9317i	−0.585940	+	1.01488i	−0.994757	+	0.102262i	$0.967392\pi$
$468$	1.58114	−	2.73861i	0.0730882	−	0.126592i
$469$	−43.1623			−1.99305
$470$	−2.16228	+	3.74517i	−0.0997384	+	0.172752i
$471$	−9.02633			−0.415912
$472$	−3.83772			−0.176645
$473$	3.59431	+	13.7159i	0.165266	+	0.630656i
$474$	−6.32456			−0.290496
$475$	4.16228			0.190978
$476$	−3.41886	+	5.92164i	−0.156703	+	0.271418i
$477$	−10.3246			−0.472729
$478$	14.1623	−	24.5298i	0.647768	−	1.12197i
$479$	−1.74342	+	3.01969i	−0.0796587	+	0.137973i	−0.903103	−	0.429425i	$-0.858716\pi$
$479$	−1.74342	+	3.01969i	−0.0796587	+	0.137973i	0.823444	+	0.567398i	$0.192050\pi$
$480$	−1.00000	−	1.73205i	−0.0456435	−	0.0790569i
$481$	−6.32456			−0.288375
$482$	8.32456	+	14.4186i	0.379173	+	0.656747i
$483$		0			0
$484$	−6.32456			−0.287480
$485$	−5.08114	+	8.80079i	−0.230723	+	0.399623i
$486$	5.00000	+	8.66025i	0.226805	+	0.392837i
$487$	−7.83772	−	13.5753i	−0.355161	−	0.615157i	0.631984	−	0.774981i	$-0.282241\pi$
$487$	−7.83772	−	13.5753i	−0.355161	−	0.615157i	−0.987146	+	0.159824i	$0.948907\pi$
$488$	0.581139	+	1.00656i	0.0263069	+	0.0455649i
$489$	43.2982			1.95801
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	12.2434	+	21.2062i	0.552538	+	0.957023i	0.998091	+	0.0617677i	$0.0196738\pi$
$491$	12.2434	+	21.2062i	0.552538	+	0.957023i	−0.445553	+	0.895256i	$0.646993\pi$
$492$	1.32456	−	2.29420i	0.0597156	−	0.103430i
$493$	11.1623	−	19.3336i	0.502724	−	0.870743i
$494$	13.1623			0.592199
$495$	2.16228			0.0971872
$496$	4.58114	−	7.93477i	0.205699	−	0.356281i
$497$	17.6491	−	30.5692i	0.791671	−	1.37121i
$498$	−6.00000	−	10.3923i	−0.268866	−	0.465690i
$499$	−4.24342	−	7.34981i	−0.189961	−	0.329023i	0.755276	−	0.655407i	$-0.227503\pi$
$499$	−4.24342	−	7.34981i	−0.189961	−	0.329023i	−0.945237	+	0.326384i	$0.894170\pi$
$500$	1.00000			0.0447214
$501$	−24.0000	−	41.5692i	−1.07224	−	1.85718i
$502$	10.9189	+	18.9120i	0.487333	+	0.844085i
$503$	−4.74342	−	8.21584i	−0.211498	−	0.366326i	0.740685	−	0.671852i	$-0.234501\pi$
$503$	−4.74342	−	8.21584i	−0.211498	−	0.366326i	−0.952184	+	0.305526i	$0.901168\pi$
$504$	−1.58114	+	2.73861i	−0.0704295	+	0.121988i
$505$	−6.83772			−0.304275
$506$		0			0
$507$	−3.00000	−	5.19615i	−0.133235	−	0.230769i
$508$	−18.6491			−0.827420
$509$	14.5811	+	25.2553i	0.646298	+	1.11942i	0.984000	+	0.178167i	$0.0570169\pi$
$509$	14.5811	+	25.2553i	0.646298	+	1.11942i	−0.337703	+	0.941253i	$0.609650\pi$
$510$	2.16228	−	3.74517i	0.0957473	−	0.165839i
$511$	−0.256584	+	0.444416i	−0.0113506	+	0.0196598i
$512$	−1.00000			−0.0441942
$513$	−8.32456	+	14.4186i	−0.367538	+	0.636595i
$514$	9.83772			0.433923
$515$	15.8114			0.696733
$516$	12.6491	+	3.46410i	0.556846	+	0.152499i
$517$	−9.35089			−0.411252
$518$	6.32456			0.277885
$519$		0			0
$520$	3.16228			0.138675
$521$	−21.6623	+	37.5202i	−0.949042	+	1.64379i	−0.201592	+	0.979470i	$0.564612\pi$
$521$	−21.6623	+	37.5202i	−0.949042	+	1.64379i	−0.747449	+	0.664319i	$0.768722\pi$
$522$	5.16228	−	8.94133i	0.225947	−	0.391351i
$523$	−16.6623	−	28.8599i	−0.728591	−	1.26196i	−0.957479	−	0.288503i	$-0.906842\pi$
$523$	−16.6623	−	28.8599i	−0.728591	−	1.26196i	0.228888	−	0.973453i	$-0.426491\pi$
$524$	−12.4868			−0.545490
$525$	−3.16228	−	5.47723i	−0.138013	−	0.239046i
$526$	−4.74342	+	8.21584i	−0.206823	+	0.358228i
$527$	19.8114			0.862998
$528$	2.16228	−	3.74517i	0.0941011	−	0.162988i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−5.16228	−	8.94133i	−0.224235	−	0.388386i
$531$	−1.91886	−	3.32357i	−0.0832715	−	0.144230i
$532$	−13.1623			−0.570657
$533$	2.09431	+	3.62744i	0.0907145	+	0.157122i
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	5.82456	−	10.0884i	0.251817	−	0.436161i
$536$	6.82456	−	11.8205i	0.294776	−	0.510567i
$537$	−11.0263			−0.475821
$538$	−2.51317			−0.108350
$539$	−3.24342	+	5.61776i	−0.139704	+	0.241974i
$540$	−2.00000	+	3.46410i	−0.0860663	+	0.149071i
$541$	−20.8114	−	36.0464i	−0.894751	−	1.54976i	−0.834112	−	0.551595i	$-0.814019\pi$
$541$	−20.8114	−	36.0464i	−0.894751	−	1.54976i	−0.0606396	−	0.998160i	$-0.519314\pi$
$542$	11.3246	+	19.6147i	0.486431	+	0.842524i
$543$	−0.649111			−0.0278560
$544$	−1.08114	−	1.87259i	−0.0463534	−	0.0802865i
$545$	4.58114	+	7.93477i	0.196234	+	0.339888i
$546$	−10.0000	−	17.3205i	−0.427960	−	0.741249i
$547$	−10.4868	+	18.1637i	−0.448385	+	0.776625i	−0.998281	−	0.0586079i	$-0.981334\pi$
$547$	−10.4868	+	18.1637i	−0.448385	+	0.776625i	0.549896	+	0.835233i	$0.314667\pi$
$548$	−7.67544			−0.327879
$549$	−0.581139	+	1.00656i	−0.0248024	+	0.0429590i
$550$	1.08114	+	1.87259i	0.0460999	+	0.0798474i
$551$	42.9737			1.83074
$552$		0			0
$553$	−5.00000	+	8.66025i	−0.212622	+	0.368271i
$554$	−8.48683	+	14.6996i	−0.360571	+	0.624527i
$555$	−4.00000			−0.169791
$556$	−1.24342	+	2.15366i	−0.0527326	+	0.0913356i
$557$	5.16228			0.218733			0.109366	−	0.994002i	$-0.465118\pi$
$557$	5.16228			0.218733			0.109366	+	0.994002i	$0.465118\pi$
$558$	9.16228			0.387870
$559$	−14.7434	+	14.5819i	−0.623580	+	0.616748i
$560$	−3.16228			−0.133631
$561$	9.35089			0.394795
$562$	−4.50000	+	7.79423i	−0.189821	+	0.328780i
$563$	6.00000			0.252870			0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000			0.252870			0.126435	+	0.991975i	$0.459647\pi$
$564$	−4.32456	+	7.49035i	−0.182097	+	0.315401i
$565$	0.243416	−	0.421610i	0.0102406	−	0.0177373i
$566$	−1.82456	−	3.16022i	−0.0766918	−	0.132834i
$567$	34.7851			1.46083
$568$	5.58114	+	9.66682i	0.234179	+	0.405611i
$569$	2.33772	−	4.04905i	0.0980024	−	0.169745i	−0.812855	−	0.582466i	$-0.802088\pi$
$569$	2.33772	−	4.04905i	0.0980024	−	0.169745i	0.910858	+	0.412721i	$0.135421\pi$
$570$	8.32456			0.348677
$571$	0.324555	−	0.562146i	0.0135822	−	0.0235251i	−0.859154	−	0.511716i	$-0.829010\pi$
$571$	0.324555	−	0.562146i	0.0135822	−	0.0235251i	0.872737	+	0.488191i	$0.162343\pi$
$572$	3.41886	+	5.92164i	0.142950	+	0.247596i
$573$	−7.81139	−	13.5297i	−0.326325	−	0.565212i
$574$	−2.09431	−	3.62744i	−0.0874146	−	0.151407i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−19.9737	−	34.5954i	−0.831515	−	1.44023i	−0.896837	−	0.442361i	$-0.854141\pi$
$577$	−19.9737	−	34.5954i	−0.831515	−	1.44023i	0.0653223	−	0.997864i	$-0.479192\pi$
$578$	−6.16228	+	10.6734i	−0.256317	+	0.443954i
$579$	26.9737	−	46.7198i	1.12099	−	1.94161i
$580$	10.3246			0.428704
$581$	−18.9737			−0.787160
$582$	−10.1623	+	17.6016i	−0.421240	+	0.729609i
$583$	11.1623	−	19.3336i	0.462294	−	0.800717i
$584$	−0.0811388	−	0.140537i	−0.00335755	−	0.00581544i
$585$	1.58114	+	2.73861i	0.0653720	+	0.113228i
$586$	−21.4868			−0.887613
$587$	−10.9868	−	19.0298i	−0.453475	−	0.785442i	0.545124	−	0.838355i	$-0.316483\pi$
$587$	−10.9868	−	19.0298i	−0.453475	−	0.785442i	−0.998599	+	0.0529135i	$0.983149\pi$
$588$	3.00000	+	5.19615i	0.123718	+	0.214286i
$589$	19.0680	+	33.0267i	0.785682	+	1.36084i
$590$	1.91886	−	3.32357i	0.0789983	−	0.136829i
$591$	20.6491			0.849391
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	2.75658	+	4.77454i	0.113199	+	0.196067i	0.917059	−	0.398753i	$-0.130557\pi$
$593$	2.75658	+	4.77454i	0.113199	+	0.196067i	−0.803859	+	0.594820i	$0.797223\pi$
$594$	−8.64911			−0.354877
$595$	−3.41886	−	5.92164i	−0.140160	−	0.242764i
$596$	−2.58114	+	4.47066i	−0.105728	+	0.183126i
$597$	24.3246	−	42.1314i	0.995538	−	1.72432i
$598$		0			0
$599$	−7.74342	+	13.4120i	−0.316387	+	0.547999i	−0.979731	−	0.200315i	$-0.935803\pi$
$599$	−7.74342	+	13.4120i	−0.316387	+	0.547999i	0.663344	+	0.748315i	$0.269137\pi$
$600$	2.00000			0.0816497
$601$	−13.0000			−0.530281			−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000			−0.530281			−0.265141	+	0.964210i	$0.585418\pi$
$602$	14.7434	−	14.5819i	0.600897	−	0.594314i
$603$	13.6491			0.555835
$604$	6.32456			0.257343
$605$	3.16228	−	5.47723i	0.128565	−	0.222681i
$606$	−13.6754			−0.555527
$607$	1.09431	−	1.89539i	0.0444165	−	0.0769316i	−0.842962	−	0.537972i	$-0.819190\pi$
$607$	1.09431	−	1.89539i	0.0444165	−	0.0769316i	0.887379	+	0.461041i	$0.152524\pi$
$608$	2.08114	−	3.60464i	0.0844013	−	0.146187i
$609$	−32.6491	−	56.5499i	−1.32301	−	2.29152i
$610$	−1.16228			−0.0470592
$611$	−6.83772	−	11.8433i	−0.276625	−	0.479128i
$612$	1.08114	−	1.87259i	0.0437024	−	0.0756949i
$613$	−31.4868			−1.27174			−0.635871	−	0.771796i	$-0.719359\pi$
$613$	−31.4868			−1.27174			−0.635871	+	0.771796i	$0.719359\pi$
$614$	6.33772	−	10.9773i	0.255770	−	0.443006i
$615$	1.32456	+	2.29420i	0.0534112	+	0.0925110i
$616$	−3.41886	−	5.92164i	−0.137750	−	0.238590i
$617$	13.8114	+	23.9220i	0.556026	+	0.963065i	0.997823	+	0.0659497i	$0.0210077\pi$
$617$	13.8114	+	23.9220i	0.556026	+	0.963065i	−0.441797	+	0.897115i	$0.645659\pi$
$618$	31.6228			1.27205
$619$	9.32456	+	16.1506i	0.374786	+	0.649148i	0.990295	−	0.138982i	$-0.0443830\pi$
$619$	9.32456	+	16.1506i	0.374786	+	0.649148i	−0.615509	+	0.788130i	$0.711050\pi$
$620$	4.58114	+	7.93477i	0.183983	+	0.318668i
$621$		0			0
$622$	0.837722	−	1.45098i	0.0335896	−	0.0581789i
$623$	−9.48683			−0.380082
$624$	6.32456			0.253185
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−9.32456	+	16.1506i	−0.372684	+	0.645508i
$627$	9.00000	+	15.5885i	0.359425	+	0.622543i
$628$	−2.25658	−	3.90852i	−0.0900475	−	0.155967i
$629$	−4.32456			−0.172431
$630$	−1.58114	−	2.73861i	−0.0629941	−	0.109109i
$631$	11.0680	+	19.1703i	0.440609	+	0.763157i	0.997735	−	0.0672710i	$-0.0214292\pi$
$631$	11.0680	+	19.1703i	0.440609	+	0.763157i	−0.557126	+	0.830428i	$0.688096\pi$
$632$	−1.58114	−	2.73861i	−0.0628943	−	0.108936i
$633$	−22.9737	+	39.7916i	−0.913121	+	1.58157i
$634$	1.67544			0.0665404
$635$	9.32456	−	16.1506i	0.370034	−	0.640917i
$636$	−10.3246	−	17.8827i	−0.409395	−	0.709093i
$637$	−9.48683			−0.375882
$638$	11.1623	+	19.3336i	0.441919	+	0.765426i
$639$	−5.58114	+	9.66682i	−0.220786	+	0.382413i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	36.6228			1.44651			0.723256	−	0.690580i	$-0.242645\pi$
$641$	36.6228			1.44651			0.723256	+	0.690580i	$0.242645\pi$
$642$	11.6491	−	20.1769i	0.459754	−	0.796317i
$643$	0.675445			0.0266369			0.0133185	−	0.999911i	$-0.495760\pi$
$643$	0.675445			0.0266369			0.0133185	+	0.999911i	$0.495760\pi$
$644$		0			0
$645$	−9.32456	+	9.22240i	−0.367154	+	0.363132i
$646$	9.00000			0.354100
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	−5.50000	+	9.52628i	−0.216060	+	0.374228i
$649$	8.29822			0.325734
$650$	−1.58114	+	2.73861i	−0.0620174	+	0.107417i
$651$	28.9737	−	50.1839i	1.13557	−	1.96686i
$652$	10.8246	+	18.7487i	0.423922	+	0.734255i
$653$	−34.4605			−1.34854			−0.674272	−	0.738483i	$-0.735542\pi$
$653$	−34.4605			−1.34854			−0.674272	+	0.738483i	$0.735542\pi$
$654$	9.16228	+	15.8695i	0.358273	+	0.620548i
$655$	6.24342	−	10.8139i	0.243950	−	0.422535i
$656$	1.32456			0.0517152
$657$	0.0811388	−	0.140537i	0.00316553	−	0.00548285i
$658$	6.83772	+	11.8433i	0.266562	+	0.461699i
$659$	4.32456	+	7.49035i	0.168461	+	0.291783i	0.937879	−	0.346963i	$-0.112787\pi$
$659$	4.32456	+	7.49035i	0.168461	+	0.291783i	−0.769418	+	0.638745i	$0.779454\pi$
$660$	2.16228	+	3.74517i	0.0841665	+	0.145781i
$661$	−40.2719			−1.56639			−0.783197	−	0.621773i	$-0.786413\pi$
$661$	−40.2719			−1.56639			−0.783197	+	0.621773i	$0.786413\pi$
$662$	7.24342	+	12.5460i	0.281523	+	0.487613i
$663$	6.83772	+	11.8433i	0.265555	+	0.459955i
$664$	3.00000	−	5.19615i	0.116423	−	0.201650i
$665$	6.58114	−	11.3989i	0.255206	−	0.442029i
$666$	−2.00000			−0.0774984
$667$		0			0
$668$	12.0000	−	20.7846i	0.464294	−	0.804181i
$669$	−15.1623	+	26.2618i	−0.586208	+	1.01534i
$670$	6.82456	+	11.8205i	0.263656	+	0.456665i
$671$	−1.25658	−	2.17647i	−0.0485099	−	0.0840216i
$672$	−6.32456			−0.243975
$673$	−2.08114	−	3.60464i	−0.0802220	−	0.138949i	0.823123	−	0.567863i	$-0.192230\pi$
$673$	−2.08114	−	3.60464i	−0.0802220	−	0.138949i	−0.903345	+	0.428914i	$0.858896\pi$
$674$	14.5680	+	25.2325i	0.561137	+	0.971918i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	1.50000	−	2.59808i	0.0576923	−	0.0999260i
$677$	−48.1359			−1.85001			−0.925007	−	0.379949i	$-0.875941\pi$
$677$	−48.1359			−1.85001			−0.925007	+	0.379949i	$0.875941\pi$
$678$	0.486833	−	0.843219i	0.0186967	−	0.0323836i
$679$	16.0680	+	27.8305i	0.616632	+	1.06804i
$680$	2.16228			0.0829196
$681$	−5.64911	−	9.78455i	−0.216474	−	0.374945i
$682$	−9.90569	+	17.1572i	−0.379309	+	0.656982i
$683$	−12.4868	+	21.6278i	−0.477795	+	0.827566i	−0.999676	−	0.0254526i	$-0.991897\pi$
$683$	−12.4868	+	21.6278i	−0.477795	+	0.827566i	0.521881	+	0.853019i	$0.325231\pi$
$684$	4.16228			0.159149
$685$	3.83772	−	6.64713i	0.146632	−	0.253974i
$686$	−12.6491			−0.482945
$687$	−0.649111			−0.0247651
$688$	1.66228	+	6.34325i	0.0633737	+	0.241834i
$689$	32.6491			1.24383
$690$		0			0
$691$	3.08114	−	5.33669i	0.117212	−	0.203017i	−0.801450	−	0.598062i	$-0.795938\pi$
$691$	3.08114	−	5.33669i	0.117212	−	0.203017i	0.918662	+	0.395045i	$0.129271\pi$
$692$		0			0
$693$	3.41886	−	5.92164i	0.129872	−	0.224945i
$694$	10.9868	−	19.0298i	0.417054	−	0.722360i
$695$	−1.24342	−	2.15366i	−0.0471655	−	0.0816930i
$696$	20.6491			0.782703
$697$	1.43203	+	2.48035i	0.0542419	+	0.0939498i
$698$	5.32456	−	9.22240i	0.201537	−	0.349073i
$699$	9.62278			0.363967
$700$	1.58114	−	2.73861i	0.0597614	−	0.103510i
$701$	20.2302	+	35.0398i	0.764086	+	1.32344i	0.940728	+	0.339161i	$0.110143\pi$
$701$	20.2302	+	35.0398i	0.764086	+	1.32344i	−0.176642	+	0.984275i	$0.556524\pi$
$702$	−6.32456	−	10.9545i	−0.238705	−	0.413449i
$703$	−4.16228	−	7.20928i	−0.156983	−	0.271903i
$704$	2.16228			0.0814939
$705$	−4.32456	−	7.49035i	−0.162872	−	0.282103i
$706$	10.9189	+	18.9120i	0.410937	+	0.711763i
$707$	−10.8114	+	18.7259i	−0.406604	+	0.704259i
$708$	3.83772	−	6.64713i	0.144230	−	0.249814i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−11.1623			−0.418913
$711$	1.58114	−	2.73861i	0.0592973	−	0.102706i
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$		0			0
$714$	−6.83772	−	11.8433i	−0.255895	−	0.443224i
$715$	−6.83772			−0.255716
$716$	−2.75658	−	4.77454i	−0.103018	−	0.178433i
$717$	28.3246	+	49.0596i	1.05780	+	1.83216i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	−0.438141	−	0.898906i	$-0.644363\pi$
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	0.997546	−	0.0700124i	$-0.0223039\pi$
$720$	1.00000			0.0372678
$721$	25.0000	−	43.3013i	0.931049	−	1.61262i
$722$	−0.837722	−	1.45098i	−0.0311768	−	0.0539998i
$723$	−33.2982			−1.23837
$724$	−0.162278	−	0.281073i	−0.00603100	−	0.0104460i
$725$	−5.16228	+	8.94133i	−0.191722	+	0.332073i
$726$	6.32456	−	10.9545i	0.234726	−	0.406558i
$727$	−9.02633			−0.334768			−0.167384	−	0.985892i	$-0.553532\pi$
$727$	−9.02633			−0.334768			−0.167384	+	0.985892i	$0.553532\pi$
$728$	5.00000	−	8.66025i	0.185312	−	0.320970i
$729$	13.0000			0.481481
$730$	0.162278			0.00600617
$731$	−10.0811	+	9.97070i	−0.372864	+	0.368779i
$732$	−2.32456			−0.0859180
$733$	48.4605			1.78993			0.894965	−	0.446137i	$-0.147201\pi$
$733$	48.4605			1.78993			0.894965	+	0.446137i	$0.147201\pi$
$734$	4.41886	−	7.65369i	0.163103	−	0.282503i
$735$	−6.00000			−0.221313
$736$		0			0
$737$	−14.7566	+	25.5592i	−0.543566	+	0.941483i
$738$	0.662278	+	1.14710i	0.0243788	+	0.0422253i
$739$	38.9737			1.43367			0.716835	−	0.697243i	$-0.245590\pi$
$739$	38.9737			1.43367			0.716835	+	0.697243i	$0.245590\pi$
$740$	−1.00000	−	1.73205i	−0.0367607	−	0.0636715i
$741$	−13.1623	+	22.7977i	−0.483528	+	0.837496i
$742$	−32.6491			−1.19859
$743$	−22.8114	+	39.5105i	−0.836869	+	1.44950i	0.0556312	+	0.998451i	$0.482283\pi$
$743$	−22.8114	+	39.5105i	−0.836869	+	1.44950i	−0.892500	+	0.451048i	$0.851050\pi$
$744$	9.16228	+	15.8695i	0.335905	+	0.581805i
$745$	−2.58114	−	4.47066i	−0.0945656	−	0.163792i
$746$	−6.25658	−	10.8367i	−0.229070	−	0.396761i
$747$	6.00000			0.219529
$748$	2.33772	+	4.04905i	0.0854756	+	0.148048i
$749$	−18.4189	−	31.9024i	−0.673011	−	1.16569i
$750$	−1.00000	+	1.73205i	−0.0365148	+	0.0632456i
$751$	−4.48683	+	7.77142i	−0.163727	+	0.283583i	−0.936202	−	0.351461i	$-0.885685\pi$
$751$	−4.48683	+	7.77142i	−0.163727	+	0.283583i	0.772476	+	0.635044i	$0.219018\pi$
$752$	−4.32456			−0.157700
$753$	−43.6754			−1.59162
$754$	−16.3246	+	28.2750i	−0.594505	+	1.02971i
$755$	−3.16228	+	5.47723i	−0.115087	+	0.199337i
$756$	6.32456	+	10.9545i	0.230022	+	0.398410i
$757$	−3.16228	−	5.47723i	−0.114935	−	0.199073i	0.802819	−	0.596223i	$-0.203333\pi$
$757$	−3.16228	−	5.47723i	−0.114935	−	0.199073i	−0.917754	+	0.397150i	$0.869999\pi$
$758$	−11.8377			−0.429965
$759$		0			0
$760$	2.08114	+	3.60464i	0.0754908	+	0.130754i
$761$	12.9737	+	22.4710i	0.470295	+	0.814575i	0.999423	−	0.0339672i	$-0.0108142\pi$
$761$	12.9737	+	22.4710i	0.470295	+	0.814575i	−0.529128	+	0.848542i	$0.677481\pi$
$762$	18.6491	−	32.3012i	0.675586	−	1.17015i
$763$	28.9737			1.04892
$764$	3.90569	−	6.76486i	0.141303	−	0.244744i
$765$	1.08114	+	1.87259i	0.0390887	+	0.0677035i
$766$	24.0000			0.867155
$767$	6.06797	+	10.5100i	0.219102	+	0.379495i
$768$	1.00000	−	1.73205i	0.0360844	−	0.0625000i
$769$	21.6359	−	37.4746i	0.780212	−	1.35137i	−0.151606	−	0.988441i	$-0.548444\pi$
$769$	21.6359	−	37.4746i	0.780212	−	1.35137i	0.931818	−	0.362926i	$-0.118222\pi$
$770$	6.83772			0.246414
$771$	−9.83772	+	17.0394i	−0.354297	+	0.613660i
$772$	26.9737			0.970803
$773$	−20.7851			−0.747586			−0.373793	−	0.927512i	$-0.621943\pi$
$773$	−20.7851			−0.747586			−0.373793	+	0.927512i	$0.621943\pi$
$774$	−4.66228	+	4.61120i	−0.167582	+	0.165746i
$775$	−9.16228			−0.329119
$776$	−10.1623			−0.364805
$777$	−6.32456	+	10.9545i	−0.226892	+	0.392989i
$778$	24.1359			0.865316
$779$	−2.75658	+	4.77454i	−0.0987649	+	0.171066i
$780$	−3.16228	+	5.47723i	−0.113228	+	0.196116i
$781$	−12.0680	−	20.9023i	−0.431826	−	0.747945i
$782$		0			0
$783$	−20.6491	−	35.7653i	−0.737939	−	1.27815i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$	4.51317			0.161082
$786$	12.4868	−	21.6278i	0.445391	−	0.771439i
$787$	17.8377	+	30.8958i	0.635846	+	1.10132i	0.986335	+	0.164751i	$0.0526820\pi$
$787$	17.8377	+	30.8958i	0.635846	+	1.10132i	−0.350489	+	0.936567i	$0.613985\pi$
$788$	5.16228	+	8.94133i	0.183899	+	0.318522i
$789$	−9.48683	−	16.4317i	−0.337740	−	0.584983i
$790$	3.16228			0.112509
$791$	−0.769751	−	1.33325i	−0.0273692	−	0.0474048i
$792$	1.08114	+	1.87259i	0.0384166	+	0.0665395i
$793$	1.83772	−	3.18303i	0.0652594	−	0.113033i
$794$	−15.7434	+	27.2684i	−0.558713	+	0.967719i
$795$	20.6491			0.732348
$796$	24.3246			0.862161
$797$	−25.7434	+	44.5889i	−0.911879	+	1.57942i	−0.100470	+	0.994940i	$0.532035\pi$
$797$	−25.7434	+	44.5889i	−0.911879	+	1.57942i	−0.811408	+	0.584480i	$0.801299\pi$
$798$	13.1623	−	22.7977i	0.465940	−	0.807031i
$799$	−4.67544	−	8.09811i	−0.165405	−	0.286490i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	3.00000			0.106000
$802$	−9.48683	−	16.4317i	−0.334992	−	0.580223i
$803$	0.175445	+	0.303879i	0.00619131	+	0.0107237i
$804$	13.6491	+	23.6410i	0.481367	+	0.833752i
$805$		0			0
$806$	−28.9737			−1.02055
$807$	2.51317	−	4.35293i	0.0884677	−	0.153230i
$808$	−3.41886	−	5.92164i	−0.120275	−	0.208323i
$809$	46.3246			1.62868			0.814342	−	0.580385i	$-0.197098\pi$
$809$	46.3246			1.62868			0.814342	+	0.580385i	$0.197098\pi$
$810$	−5.50000	−	9.52628i	−0.193250	−	0.334719i
$811$	−11.9189	+	20.6441i	−0.418528	+	0.724911i	−0.995792	−	0.0916463i	$-0.970787\pi$
$811$	−11.9189	+	20.6441i	−0.418528	+	0.724911i	0.577264	+	0.816558i	$0.304120\pi$
$812$	16.3246	−	28.2750i	0.572880	−	0.992257i
$813$	−45.2982			−1.58868
$814$	2.16228	−	3.74517i	0.0757878	−	0.131268i
$815$	−21.6491			−0.758335
$816$	4.32456			0.151390
$817$	−26.3246	−	7.20928i	−0.920980	−	0.252221i
$818$	39.6491			1.38630
$819$	10.0000			0.349428
$820$	−0.662278	+	1.14710i	−0.0231277	+	0.0400584i
$821$	32.7851			1.14421			0.572103	−	0.820182i	$-0.306128\pi$
$821$	32.7851			1.14421			0.572103	+	0.820182i	$0.306128\pi$
$822$	7.67544	−	13.2943i	0.267712	−	0.463691i
$823$	−9.23025	+	15.9873i	−0.321746	+	0.557281i	−0.980848	−	0.194773i	$-0.937603\pi$
$823$	−9.23025	+	15.9873i	−0.321746	+	0.557281i	0.659102	+	0.752053i	$0.270936\pi$
$824$	7.90569	+	13.6931i	0.275408	+	0.477020i
$825$	−4.32456			−0.150562
$826$	−6.06797	−	10.5100i	−0.211132	−	0.365691i
$827$	21.6623	−	37.5202i	0.753271	−	1.30470i	−0.192958	−	0.981207i	$-0.561808\pi$
$827$	21.6623	−	37.5202i	0.753271	−	1.30470i	0.946229	−	0.323497i	$-0.104859\pi$
$828$		0			0
$829$	3.81139	−	6.60152i	0.132375	−	0.229280i	−0.792217	−	0.610240i	$-0.791073\pi$
$829$	3.81139	−	6.60152i	0.132375	−	0.229280i	0.924592	+	0.380960i	$0.124406\pi$
$830$	3.00000	+	5.19615i	0.104132	+	0.180361i
$831$	−16.9737	−	29.3993i	−0.588810	−	1.01985i
$832$	1.58114	+	2.73861i	0.0548161	+	0.0949443i
$833$	−6.48683			−0.224755
$834$	−2.48683	−	4.30732i	−0.0861120	−	0.149150i
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	−4.50000	+	7.79423i	−0.155636	+	0.269569i
$837$	18.3246	−	31.7391i	0.633389	−	1.09706i
$838$	17.2982			0.597557
$839$	47.4342			1.63761			0.818805	−	0.574072i	$-0.194637\pi$
$839$	47.4342			1.63761			0.818805	+	0.574072i	$0.194637\pi$
$840$	3.16228	−	5.47723i	0.109109	−	0.188982i
$841$	−38.7982	+	67.2005i	−1.33787	+	2.31726i
$842$	2.74342	+	4.75174i	0.0945444	+	0.163756i
$843$	−9.00000	−	15.5885i	−0.309976	−	0.536895i
$844$	−22.9737			−0.790786
$845$	1.50000	+	2.59808i	0.0516016	+	0.0893765i
$846$	−2.16228	−	3.74517i	−0.0743406	−	0.128762i
$847$	−10.0000	−	17.3205i	−0.343604	−	0.595140i
$848$	5.16228	−	8.94133i	0.177273	−	0.307046i
$849$	7.29822			0.250474
$850$	−1.08114	+	1.87259i	−0.0370828	+	0.0642292i
$851$		0			0
$852$	−22.3246			−0.764827
$853$	14.0000	+	24.2487i	0.479351	+	0.830260i	0.999720	−	0.0236816i	$-0.00753881\pi$
$853$	14.0000	+	24.2487i	0.479351	+	0.830260i	−0.520369	+	0.853942i	$0.674205\pi$
$854$	−1.83772	+	3.18303i	−0.0628856	+	0.108921i
$855$	−2.08114	+	3.60464i	−0.0711734	+	0.123276i
$856$	11.6491			0.398158
$857$	8.16228	−	14.1375i	0.278818	−	0.482927i	−0.692273	−	0.721636i	$-0.743391\pi$
$857$	8.16228	−	14.1375i	0.278818	−	0.482927i	0.971091	+	0.238708i	$0.0767240\pi$
$858$	−13.6754			−0.466872
$859$	−7.13594			−0.243475			−0.121738	−	0.992562i	$-0.538847\pi$
$859$	−7.13594			−0.243475			−0.121738	+	0.992562i	$0.538847\pi$
$860$	−6.32456	−	1.73205i	−0.215666	−	0.0590624i
$861$	8.37722			0.285495
$862$	−28.4605			−0.969368
$863$	−12.4868	+	21.6278i	−0.425057	+	0.736220i	−0.996426	−	0.0844734i	$-0.973079\pi$
$863$	−12.4868	+	21.6278i	−0.425057	+	0.736220i	0.571369	+	0.820693i	$0.306413\pi$
$864$	−4.00000			−0.136083
$865$		0			0
$866$	−5.48683	+	9.50347i	−0.186450	+	0.322941i
$867$	−12.3246	−	21.3468i	−0.418564	−	0.724974i
$868$	28.9737			0.983430
$869$	3.41886	+	5.92164i	0.115977	+	0.200878i
$870$	−10.3246	+	17.8827i	−0.350035	+	0.606279i
$871$	−43.1623			−1.46250
$872$	−4.58114	+	7.93477i	−0.155137	+	0.268705i
$873$	−5.08114	−	8.80079i	−0.171970	−	0.297862i
$874$		0			0
$875$	1.58114	+	2.73861i	0.0534522	+	0.0925820i
$876$	0.324555			0.0109657
$877$	−12.2302	−	21.1834i	−0.412986	−	0.715313i	0.582229	−	0.813025i	$-0.302181\pi$
$877$	−12.2302	−	21.1834i	−0.412986	−	0.715313i	−0.995215	+	0.0977121i	$0.968848\pi$
$878$	−14.0680	−	24.3664i	−0.474771	−	0.822328i
$879$	21.4868	−	37.2163i	0.724733	−	1.25527i
$880$	−1.08114	+	1.87259i	−0.0364452	+	0.0631249i
$881$	−46.9473			−1.58170			−0.790848	−	0.612013i	$-0.790360\pi$
$881$	−46.9473			−1.58170			−0.790848	+	0.612013i	$0.790360\pi$
$882$	−3.00000			−0.101015
$883$	12.8114	−	22.1900i	0.431138	−	0.746752i	−0.565834	−	0.824519i	$-0.691446\pi$
$883$	12.8114	−	22.1900i	0.431138	−	0.746752i	0.996972	+	0.0777670i	$0.0247790\pi$
$884$	−3.41886	+	5.92164i	−0.114989	+	0.199166i
$885$	3.83772	+	6.64713i	0.129004	+	0.223441i
$886$	−11.6491	−	20.1769i	−0.391360	−	0.677855i
$887$	10.1886			0.342100			0.171050	−	0.985262i	$-0.445284\pi$
$887$	10.1886			0.342100			0.171050	+	0.985262i	$0.445284\pi$
$888$	−2.00000	−	3.46410i	−0.0671156	−	0.116248i
$889$	−29.4868	−	51.0727i	−0.988957	−	1.71292i
$890$	1.50000	+	2.59808i	0.0502801	+	0.0870877i
$891$	11.8925	−	20.5985i	0.398415	−	0.690074i
$892$	−15.1623			−0.507671
$893$	9.00000	−	15.5885i	0.301174	−	0.521648i
$894$	−5.16228	−	8.94133i	−0.172652	−	0.299043i
$895$	5.51317			0.184285
$896$	−1.58114	−	2.73861i	−0.0528221	−	0.0914906i
$897$		0			0
$898$	−9.66228	+	16.7356i	−0.322434	+	0.558473i
$899$	−94.5964			−3.15497
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	22.3246			0.743739
$902$	−2.86406			−0.0953626
$903$	10.5132	+	40.1182i	0.349856	+	1.33505i
$904$	0.486833			0.0161918
$905$	0.324555			0.0107886
$906$	−6.32456	+	10.9545i	−0.210119	+	0.363937i
$907$	42.6754			1.41701			0.708507	−	0.705703i	$-0.249369\pi$
$907$	42.6754			1.41701			0.708507	+	0.705703i	$0.249369\pi$
$908$	2.82456	−	4.89227i	0.0937362	−	0.162356i
$909$	3.41886	−	5.92164i	0.113396	−	0.196408i
$910$	5.00000	+	8.66025i	0.165748	+	0.287085i
$911$	43.8114			1.45154			0.725768	−	0.687940i	$-0.241485\pi$
$911$	43.8114			1.45154			0.725768	+	0.687940i	$0.241485\pi$
$912$	4.16228	+	7.20928i	0.137827	+	0.238723i
$913$	−6.48683	+	11.2355i	−0.214683	+	0.371842i
$914$	−28.1623			−0.931525
$915$	1.16228	−	2.01312i	0.0384237	−	0.0665518i
$916$	−0.162278	−	0.281073i	−0.00536180	−	0.00928692i
$917$	−19.7434	−	34.1966i	−0.651985	−	1.12927i
$918$	−4.32456	−	7.49035i	−0.142732	−	0.247218i
$919$	13.0263			0.429699			0.214850	−	0.976647i	$-0.431074\pi$
$919$	13.0263			0.429699			0.214850	+	0.976647i	$0.431074\pi$
$920$		0			0
$921$	12.6754	+	21.9545i	0.417670	+	0.723426i
$922$	−10.2566	+	17.7649i	−0.337783	+	0.585057i
$923$	17.6491	−	30.5692i	0.580928	−	1.00620i
$924$	13.6754			0.449889
$925$	2.00000			0.0657596
$926$	14.8114	−	25.6541i	0.486732	−	0.843045i
$927$	−7.90569	+	13.6931i	−0.259657	+	0.449739i
$928$	5.16228	+	8.94133i	0.169460	+	0.293513i
$929$	−17.3377	−	30.0298i	−0.568832	−	0.985246i	−0.996682	−	0.0813964i	$-0.974062\pi$
$929$	−17.3377	−	30.0298i	−0.568832	−	0.985246i	0.427850	−	0.903850i	$-0.359271\pi$
$930$	−18.3246			−0.600886
$931$	−6.24342	−	10.8139i	−0.204620	−	0.354412i
$932$	2.40569	+	4.16678i	0.0788011	+	0.136488i
$933$	1.67544	+	2.90196i	0.0548516	+	0.0950058i
$934$	12.6623	−	21.9317i	0.414322	−	0.717627i
$935$	−4.67544			−0.152903
$936$	−1.58114	+	2.73861i	−0.0516811	+	0.0895144i
$937$	13.4057	+	23.2193i	0.437945	+	0.758543i	0.997531	−	0.0702295i	$-0.0223731\pi$
$937$	13.4057	+	23.2193i	0.437945	+	0.758543i	−0.559586	+	0.828772i	$0.689040\pi$
$938$	43.1623			1.40930
$939$	−18.6491	−	32.3012i	−0.608591	−	1.05411i
$940$	2.16228	−	3.74517i	0.0705257	−	0.122154i
$941$	−18.9737	+	32.8634i	−0.618524	+	1.07131i	0.371231	+	0.928540i	$0.378936\pi$
$941$	−18.9737	+	32.8634i	−0.618524	+	1.07131i	−0.989755	+	0.142774i	$0.954398\pi$
$942$	9.02633			0.294094
$943$		0			0
$944$	3.83772			0.124907
$945$	−12.6491			−0.411476
$946$	−3.59431	−	13.7159i	−0.116861	−	0.445941i
$947$	−51.9737			−1.68892			−0.844459	−	0.535621i	$-0.820078\pi$
$947$	−51.9737			−1.68892			−0.844459	+	0.535621i	$0.820078\pi$
$948$	6.32456			0.205412
$949$	−0.256584	+	0.444416i	−0.00832905	+	0.0144263i
$950$	−4.16228			−0.135042
$951$	−1.67544	+	2.90196i	−0.0543300	+	0.0941023i
$952$	3.41886	−	5.92164i	0.110806	−	0.191921i
$953$	13.8114	+	23.9220i	0.447395	+	0.774910i	0.998216	−	0.0597131i	$-0.0190186\pi$
$953$	13.8114	+	23.9220i	0.447395	+	0.774910i	−0.550821	+	0.834624i	$0.685685\pi$
$954$	10.3246			0.334270
$955$	3.90569	+	6.76486i	0.126385	+	0.218906i
$956$	−14.1623	+	24.5298i	−0.458041	+	0.793350i
$957$	−44.6491			−1.44330
$958$	1.74342	−	3.01969i	0.0563272	−	0.0975616i
$959$	−12.1359	−	21.0201i	−0.391890	−	0.678773i
$960$	1.00000	+	1.73205i	0.0322749	+	0.0559017i
$961$	−26.4737	−	45.8537i	−0.853989	−	1.47915i
$962$	6.32456			0.203912
$963$	5.82456	+	10.0884i	0.187694	+	0.325095i
$964$	−8.32456	−	14.4186i	−0.268116	−	0.464390i
$965$	−13.4868	+	23.3599i	−0.434157	+	0.751981i
$966$		0			0
$967$	20.8377			0.670096			0.335048	−	0.942201i	$-0.391247\pi$
$967$	20.8377			0.670096			0.335048	+	0.942201i	$0.391247\pi$
$968$	6.32456			0.203279
$969$	−9.00000	+	15.5885i	−0.289122	+	0.500773i
$970$	5.08114	−	8.80079i	0.163146	−	0.282576i
$971$	7.32456	+	12.6865i	0.235056	+	0.407129i	0.959289	−	0.282426i	$-0.0911393\pi$
$971$	7.32456	+	12.6865i	0.235056	+	0.407129i	−0.724233	+	0.689556i	$0.757806\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$	−7.86406			−0.252110
$974$	7.83772	+	13.5753i	0.251137	+	0.434982i
$975$	−3.16228	−	5.47723i	−0.101274	−	0.175412i
$976$	−0.581139	−	1.00656i	−0.0186018	−	0.0322193i
$977$	−24.2434	+	41.9908i	−0.775616	+	1.34341i	0.158832	+	0.987306i	$0.449227\pi$
$977$	−24.2434	+	41.9908i	−0.775616	+	1.34341i	−0.934448	+	0.356100i	$0.884106\pi$
$978$	−43.2982			−1.38452
$979$	−3.24342	+	5.61776i	−0.103660	+	0.179544i
$980$	−1.50000	−	2.59808i	−0.0479157	−	0.0829925i
$981$	−9.16228			−0.292529
$982$	−12.2434	−	21.2062i	−0.390703	−	0.676718i
$983$	−14.0943	+	24.4121i	−0.449539	+	0.778624i	−0.998356	−	0.0573187i	$-0.981745\pi$
$983$	−14.0943	+	24.4121i	−0.449539	+	0.778624i	0.548817	+	0.835942i	$0.315078\pi$
$984$	−1.32456	+	2.29420i	−0.0422253	+	0.0731363i
$985$	−10.3246			−0.328968
$986$	−11.1623	+	19.3336i	−0.355479	+	0.615708i
$987$	−27.3509			−0.870588
$988$	−13.1623			−0.418748
$989$		0			0
$990$	−2.16228			−0.0687217
$991$	15.8114			0.502265			0.251133	−	0.967953i	$-0.419197\pi$
$991$	15.8114			0.502265			0.251133	+	0.967953i	$0.419197\pi$
$992$	−4.58114	+	7.93477i	−0.145451	+	0.251929i
$993$	−28.9737			−0.919451
$994$	−17.6491	+	30.5692i	−0.559796	+	0.969595i
$995$	−12.1623	+	21.0657i	−0.385570	+	0.667827i
$996$	6.00000	+	10.3923i	0.190117	+	0.329293i
$997$	−50.4605			−1.59810			−0.799050	−	0.601265i	$-0.794664\pi$
$997$	−50.4605			−1.59810			−0.799050	+	0.601265i	$0.794664\pi$
$998$	4.24342	+	7.34981i	0.134323	+	0.232654i
$999$	−4.00000	+	6.92820i	−0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.d.221.2	✓	4
43.36	even	3	inner	430.2.e.d.251.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.d.221.2	✓	4	1.1	even	1	trivial
430.2.e.d.251.2	yes	4	43.36	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.00000 - 1.73205i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} +(1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.00000 - 1.73205i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} +(1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +2.16228 q^{11} +(1.00000 - 1.73205i) q^{12} +(1.58114 + 2.73861i) q^{13} +(-1.58114 - 2.73861i) q^{14} +(1.00000 + 1.73205i) q^{15} +1.00000 q^{16} +(1.08114 + 1.87259i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.08114 + 3.60464i) q^{19} +(-0.500000 + 0.866025i) q^{20} +6.32456 q^{21} -2.16228 q^{22} +(-1.00000 + 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.58114 - 2.73861i) q^{26} +4.00000 q^{27} +(1.58114 + 2.73861i) q^{28} +(-5.16228 - 8.94133i) q^{29} +(-1.00000 - 1.73205i) q^{30} +(4.58114 - 7.93477i) q^{31} -1.00000 q^{32} +(2.16228 - 3.74517i) q^{33} +(-1.08114 - 1.87259i) q^{34} -3.16228 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.08114 - 3.60464i) q^{38} +6.32456 q^{39} +(0.500000 - 0.866025i) q^{40} +1.32456 q^{41} -6.32456 q^{42} +(1.66228 + 6.34325i) q^{43} +2.16228 q^{44} +1.00000 q^{45} -4.32456 q^{47} +(1.00000 - 1.73205i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +4.32456 q^{51} +(1.58114 + 2.73861i) q^{52} +(5.16228 - 8.94133i) q^{53} -4.00000 q^{54} +(-1.08114 + 1.87259i) q^{55} +(-1.58114 - 2.73861i) q^{56} +(4.16228 + 7.20928i) q^{57} +(5.16228 + 8.94133i) q^{58} +3.83772 q^{59} +(1.00000 + 1.73205i) q^{60} +(-0.581139 - 1.00656i) q^{61} +(-4.58114 + 7.93477i) q^{62} +(1.58114 - 2.73861i) q^{63} +1.00000 q^{64} -3.16228 q^{65} +(-2.16228 + 3.74517i) q^{66} +(-6.82456 + 11.8205i) q^{67} +(1.08114 + 1.87259i) q^{68} +3.16228 q^{70} +(-5.58114 - 9.66682i) q^{71} +(0.500000 + 0.866025i) q^{72} +(0.0811388 + 0.140537i) q^{73} +(1.00000 - 1.73205i) q^{74} -2.00000 q^{75} +(-2.08114 + 3.60464i) q^{76} +(3.41886 + 5.92164i) q^{77} -6.32456 q^{78} +(1.58114 + 2.73861i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} -1.32456 q^{82} +(-3.00000 + 5.19615i) q^{83} +6.32456 q^{84} -2.16228 q^{85} +(-1.66228 - 6.34325i) q^{86} -20.6491 q^{87} -2.16228 q^{88} +(-1.50000 + 2.59808i) q^{89} -1.00000 q^{90} +(-5.00000 + 8.66025i) q^{91} +(-9.16228 - 15.8695i) q^{93} +4.32456 q^{94} +(-2.08114 - 3.60464i) q^{95} +(-1.00000 + 1.73205i) q^{96} +10.1623 q^{97} +(1.50000 - 2.59808i) q^{98} +(-1.08114 - 1.87259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{24} - 2 q^{25} + 16 q^{27} - 8 q^{29} - 4 q^{30} + 12 q^{31} - 4 q^{32} - 4 q^{33} + 2 q^{34} - 2 q^{36} - 4 q^{37} + 2 q^{38} + 2 q^{40} - 20 q^{41} - 6 q^{43} - 4 q^{44} + 4 q^{45} + 8 q^{47} + 4 q^{48} - 6 q^{49} + 2 q^{50} - 8 q^{51} + 8 q^{53} - 16 q^{54} + 2 q^{55} + 4 q^{57} + 8 q^{58} + 28 q^{59} + 4 q^{60} + 4 q^{61} - 12 q^{62} + 4 q^{64} + 4 q^{66} - 2 q^{67} - 2 q^{68} - 16 q^{71} + 2 q^{72} - 6 q^{73} + 4 q^{74} - 8 q^{75} - 2 q^{76} + 20 q^{77} - 2 q^{80} + 22 q^{81} + 20 q^{82} - 12 q^{83} + 4 q^{85} + 6 q^{86} - 32 q^{87} + 4 q^{88} - 6 q^{89} - 4 q^{90} - 20 q^{91} - 24 q^{93} - 8 q^{94} - 2 q^{95} - 4 q^{96} + 28 q^{97} + 6 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 + 4 * q^22 - 4 * q^24 - 2 * q^25 + 16 * q^27 - 8 * q^29 - 4 * q^30 + 12 * q^31 - 4 * q^32 - 4 * q^33 + 2 * q^34 - 2 * q^36 - 4 * q^37 + 2 * q^38 + 2 * q^40 - 20 * q^41 - 6 * q^43 - 4 * q^44 + 4 * q^45 + 8 * q^47 + 4 * q^48 - 6 * q^49 + 2 * q^50 - 8 * q^51 + 8 * q^53 - 16 * q^54 + 2 * q^55 + 4 * q^57 + 8 * q^58 + 28 * q^59 + 4 * q^60 + 4 * q^61 - 12 * q^62 + 4 * q^64 + 4 * q^66 - 2 * q^67 - 2 * q^68 - 16 * q^71 + 2 * q^72 - 6 * q^73 + 4 * q^74 - 8 * q^75 - 2 * q^76 + 20 * q^77 - 2 * q^80 + 22 * q^81 + 20 * q^82 - 12 * q^83 + 4 * q^85 + 6 * q^86 - 32 * q^87 + 4 * q^88 - 6 * q^89 - 4 * q^90 - 20 * q^91 - 24 * q^93 - 8 * q^94 - 2 * q^95 - 4 * q^96 + 28 * q^97 + 6 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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