LMFDB - Embedded newform 430.2.e.e.251.1

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			251.1
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	430.251
Dual form			430.2.e.e.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.04307 - 1.80664i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.80664i) q^{6} +(0.324030 - 0.561237i) q^{7} +1.00000 q^{8} +(-0.675970 + 1.17081i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.04307 - 1.80664i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.80664i) q^{6} +(0.324030 - 0.561237i) q^{7} +1.00000 q^{8} +(-0.675970 + 1.17081i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.08613 q^{11} +(-1.04307 - 1.80664i) q^{12} +(2.89500 - 5.01429i) q^{13} +(0.324030 - 0.561237i) q^{14} +(1.04307 - 1.80664i) q^{15} +1.00000 q^{16} +(-0.675970 + 1.17081i) q^{18} +(-1.54307 - 2.67267i) q^{19} +(0.500000 + 0.866025i) q^{20} -1.35194 q^{21} +1.08613 q^{22} +(-1.67597 - 2.90286i) q^{23} +(-1.04307 - 1.80664i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.89500 - 5.01429i) q^{26} -3.43807 q^{27} +(0.324030 - 0.561237i) q^{28} +(-4.45323 + 7.71321i) q^{29} +(1.04307 - 1.80664i) q^{30} +(-0.219035 - 0.379379i) q^{31} +1.00000 q^{32} +(-1.13290 - 1.96225i) q^{33} +0.648061 q^{35} +(-0.675970 + 1.17081i) q^{36} +(1.45693 + 2.52349i) q^{37} +(-1.54307 - 2.67267i) q^{38} -12.0787 q^{39} +(0.500000 + 0.866025i) q^{40} +5.87614 q^{41} -1.35194 q^{42} +(6.53936 - 0.486646i) q^{43} +1.08613 q^{44} -1.35194 q^{45} +(-1.67597 - 2.90286i) q^{46} +8.04840 q^{47} +(-1.04307 - 1.80664i) q^{48} +(3.29001 + 5.69846i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.89500 - 5.01429i) q^{52} +(4.43807 + 7.68696i) q^{53} -3.43807 q^{54} +(0.543065 + 0.940616i) q^{55} +(0.324030 - 0.561237i) q^{56} +(-3.21903 + 5.57553i) q^{57} +(-4.45323 + 7.71321i) q^{58} -7.46838 q^{59} +(1.04307 - 1.80664i) q^{60} +(-0.762100 + 1.32000i) q^{61} +(-0.219035 - 0.379379i) q^{62} +(0.438069 + 0.758758i) q^{63} +1.00000 q^{64} +5.79001 q^{65} +(-1.13290 - 1.96225i) q^{66} +(-3.74694 - 6.48990i) q^{67} +(-3.49629 + 6.05575i) q^{69} +0.648061 q^{70} +(-1.13290 + 1.96225i) q^{71} +(-0.675970 + 1.17081i) q^{72} +(-2.51516 + 4.35638i) q^{73} +(1.45693 + 2.52349i) q^{74} +2.08613 q^{75} +(-1.54307 - 2.67267i) q^{76} +(0.351939 - 0.609577i) q^{77} -12.0787 q^{78} +(-6.87614 + 11.9098i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.61404 + 9.72380i) q^{81} +5.87614 q^{82} +(-2.15710 - 3.73621i) q^{83} -1.35194 q^{84} +(6.53936 - 0.486646i) q^{86} +18.5800 q^{87} +1.08613 q^{88} +(4.75839 + 8.24177i) q^{89} -1.35194 q^{90} +(-1.87614 - 3.24957i) q^{91} +(-1.67597 - 2.90286i) q^{92} +(-0.456935 + 0.791434i) q^{93} +8.04840 q^{94} +(1.54307 - 2.67267i) q^{95} +(-1.04307 - 1.80664i) q^{96} +6.34452 q^{97} +(3.29001 + 5.69846i) q^{98} +(-0.734191 + 1.27166i) 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
$3$	−1.04307	−	1.80664i	−0.602214	−	1.04307i	−0.992485	−	0.122365i	$-0.960952\pi$
$3$	−1.04307	−	1.80664i	−0.602214	−	1.04307i	0.390271	−	0.920700i	$-0.372381\pi$
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.04307	−	1.80664i	−0.425830	−	0.737558i
$7$	0.324030	−	0.561237i	0.122472	−	0.212128i	−0.798270	−	0.602300i	$-0.794251\pi$
$7$	0.324030	−	0.561237i	0.122472	−	0.212128i	0.920742	+	0.390172i	$0.127585\pi$
$8$	1.00000			0.353553
$9$	−0.675970	+	1.17081i	−0.225323	+	0.390271i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.08613			0.327481			0.163740	−	0.986503i	$-0.447644\pi$
$11$	1.08613			0.327481			0.163740	+	0.986503i	$0.447644\pi$
$12$	−1.04307	−	1.80664i	−0.301107	−	0.521533i
$13$	2.89500	−	5.01429i	0.802930	−	1.39072i	−0.114750	−	0.993394i	$-0.536607\pi$
$13$	2.89500	−	5.01429i	0.802930	−	1.39072i	0.917680	−	0.397321i	$-0.130060\pi$
$14$	0.324030	−	0.561237i	0.0866008	−	0.149997i
$15$	1.04307	−	1.80664i	0.269318	−	0.466473i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−0.675970	+	1.17081i	−0.159328	+	0.275963i
$19$	−1.54307	−	2.67267i	−0.354003	−	0.613152i	0.632943	−	0.774198i	$-0.281847\pi$
$19$	−1.54307	−	2.67267i	−0.354003	−	0.613152i	−0.986947	+	0.161046i	$0.948513\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.35194			−0.295017
$22$	1.08613			0.231564
$23$	−1.67597	−	2.90286i	−0.349464	−	0.605289i	0.636690	−	0.771119i	$-0.280303\pi$
$23$	−1.67597	−	2.90286i	−0.349464	−	0.605289i	−0.986154	+	0.165830i	$0.946970\pi$
$24$	−1.04307	−	1.80664i	−0.212915	−	0.368779i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.89500	−	5.01429i	0.567757	−	0.983384i
$27$	−3.43807			−0.661657
$28$	0.324030	−	0.561237i	0.0612360	−	0.106064i
$29$	−4.45323	+	7.71321i	−0.826943	+	1.43231i	0.0734818	+	0.997297i	$0.476589\pi$
$29$	−4.45323	+	7.71321i	−0.826943	+	1.43231i	−0.900425	+	0.435011i	$0.856744\pi$
$30$	1.04307	−	1.80664i	0.190437	−	0.329846i
$31$	−0.219035	−	0.379379i	−0.0393398	−	0.0681385i	0.845685	−	0.533682i	$-0.179192\pi$
$31$	−0.219035	−	0.379379i	−0.0393398	−	0.0681385i	−0.885025	+	0.465544i	$0.845859\pi$
$32$	1.00000			0.176777
$33$	−1.13290	−	1.96225i	−0.197213	−	0.341584i
$34$		0			0
$35$	0.648061			0.109542
$36$	−0.675970	+	1.17081i	−0.112662	+	0.195136i
$37$	1.45693	+	2.52349i	0.239519	+	0.414858i	0.960576	−	0.278017i	$-0.0896771\pi$
$37$	1.45693	+	2.52349i	0.239519	+	0.414858i	−0.721058	+	0.692875i	$0.756344\pi$
$38$	−1.54307	−	2.67267i	−0.250318	−	0.433564i
$39$	−12.0787			−1.93414
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	5.87614			0.917699			0.458849	−	0.888514i	$-0.348262\pi$
$41$	5.87614			0.917699			0.458849	+	0.888514i	$0.348262\pi$
$42$	−1.35194			−0.208609
$43$	6.53936	−	0.486646i	0.997242	−	0.0742128i
$43$	6.53936	−	0.486646i	0.997242	−	0.0742128i
$44$	1.08613			0.163740
$45$	−1.35194			−0.201535
$46$	−1.67597	−	2.90286i	−0.247108	−	0.428004i
$47$	8.04840			1.17398			0.586990	−	0.809594i	$-0.300313\pi$
$47$	8.04840			1.17398			0.586990	+	0.809594i	$0.300313\pi$
$48$	−1.04307	−	1.80664i	−0.150553	−	0.260766i
$49$	3.29001	+	5.69846i	0.470001	+	0.814066i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	2.89500	−	5.01429i	0.401465	−	0.695358i
$53$	4.43807	+	7.68696i	0.609616	+	1.05589i	0.991304	+	0.131594i	$0.0420096\pi$
$53$	4.43807	+	7.68696i	0.609616	+	1.05589i	−0.381688	+	0.924291i	$0.624657\pi$
$54$	−3.43807			−0.467862
$55$	0.543065	+	0.940616i	0.0732269	+	0.126833i
$56$	0.324030	−	0.561237i	0.0433004	−	0.0749985i
$57$	−3.21903	+	5.57553i	−0.426372	+	0.738497i
$58$	−4.45323	+	7.71321i	−0.584737	+	1.01279i
$59$	−7.46838			−0.972301			−0.486150	−	0.873875i	$-0.661599\pi$
$59$	−7.46838			−0.972301			−0.486150	+	0.873875i	$0.661599\pi$
$60$	1.04307	−	1.80664i	0.134659	−	0.233236i
$61$	−0.762100	+	1.32000i	−0.0975769	+	0.169008i	−0.910681	−	0.413110i	$-0.864443\pi$
$61$	−0.762100	+	1.32000i	−0.0975769	+	0.169008i	0.813104	+	0.582118i	$0.197776\pi$
$62$	−0.219035	−	0.379379i	−0.0278174	−	0.0481812i
$63$	0.438069	+	0.758758i	0.0551916	+	0.0955946i
$64$	1.00000			0.125000
$65$	5.79001			0.718162
$66$	−1.13290	−	1.96225i	−0.139451	−	0.241536i
$67$	−3.74694	−	6.48990i	−0.457762	−	0.792867i	0.541080	−	0.840971i	$-0.318015\pi$
$67$	−3.74694	−	6.48990i	−0.457762	−	0.792867i	−0.998842	+	0.0481039i	$0.984682\pi$
$68$		0			0
$69$	−3.49629	+	6.05575i	−0.420904	+	0.729027i
$70$	0.648061			0.0774581
$71$	−1.13290	+	1.96225i	−0.134451	+	0.232876i	−0.925388	−	0.379022i	$-0.876260\pi$
$71$	−1.13290	+	1.96225i	−0.134451	+	0.232876i	0.790937	+	0.611898i	$0.209594\pi$
$72$	−0.675970	+	1.17081i	−0.0796638	+	0.137982i
$73$	−2.51516	+	4.35638i	−0.294377	+	0.509876i	−0.974840	−	0.222907i	$-0.928445\pi$
$73$	−2.51516	+	4.35638i	−0.294377	+	0.509876i	0.680463	+	0.732782i	$0.261779\pi$
$74$	1.45693	+	2.52349i	0.169365	+	0.293349i
$75$	2.08613			0.240886
$76$	−1.54307	−	2.67267i	−0.177002	−	0.306576i
$77$	0.351939	−	0.609577i	0.0401072	−	0.0694677i
$78$	−12.0787			−1.36764
$79$	−6.87614	+	11.9098i	−0.773626	+	1.33996i	0.161937	+	0.986801i	$0.448226\pi$
$79$	−6.87614	+	11.9098i	−0.773626	+	1.33996i	−0.935563	+	0.353159i	$0.885108\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	5.61404	+	9.72380i	0.623782	+	1.08042i
$82$	5.87614			0.648911
$83$	−2.15710	−	3.73621i	−0.236773	−	0.410103i	0.723014	−	0.690834i	$-0.242756\pi$
$83$	−2.15710	−	3.73621i	−0.236773	−	0.410103i	−0.959786	+	0.280731i	$0.909423\pi$
$84$	−1.35194			−0.147509
$85$		0			0
$86$	6.53936	−	0.486646i	0.705157	−	0.0524764i
$87$	18.5800			1.99199
$88$	1.08613			0.115782
$89$	4.75839	+	8.24177i	0.504388	+	0.873626i	0.999987	+	0.00507472i	$0.00161534\pi$
$89$	4.75839	+	8.24177i	0.504388	+	0.873626i	−0.495599	+	0.868552i	$0.665051\pi$
$90$	−1.35194			−0.142507
$91$	−1.87614	−	3.24957i	−0.196673	−	0.340647i
$92$	−1.67597	−	2.90286i	−0.174732	−	0.302645i
$93$	−0.456935	+	0.791434i	−0.0473819	+	0.0820679i
$94$	8.04840			0.830129
$95$	1.54307	−	2.67267i	0.158315	−	0.274210i
$96$	−1.04307	−	1.80664i	−0.106457	−	0.184390i
$97$	6.34452			0.644188			0.322094	−	0.946708i	$-0.395613\pi$
$97$	6.34452			0.644188			0.322094	+	0.946708i	$0.395613\pi$
$98$	3.29001	+	5.69846i	0.332341	+	0.575632i
$99$	−0.734191	+	1.27166i	−0.0737890	+	0.127806i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.21533	+	12.4973i	−0.717952	+	1.24353i	0.243858	+	0.969811i	$0.421587\pi$
$101$	−7.21533	+	12.4973i	−0.717952	+	1.24353i	−0.961810	+	0.273718i	$0.911747\pi$
$102$		0			0
$103$	−3.34823	+	5.79930i	−0.329911	+	0.571422i	−0.982494	−	0.186295i	$-0.940352\pi$
$103$	−3.34823	+	5.79930i	−0.329911	+	0.571422i	0.652583	+	0.757717i	$0.273685\pi$
$104$	2.89500	−	5.01429i	0.283879	−	0.491692i
$105$	−0.675970	−	1.17081i	−0.0659679	−	0.114260i
$106$	4.43807	+	7.68696i	0.431063	+	0.746624i
$107$	2.20257			0.212931			0.106465	−	0.994316i	$-0.466047\pi$
$107$	2.20257			0.212931			0.106465	+	0.994316i	$0.466047\pi$
$108$	−3.43807			−0.330828
$109$	−8.10129	−	14.0318i	−0.775963	−	1.34401i	−0.934252	−	0.356614i	$-0.883931\pi$
$109$	−8.10129	−	14.0318i	−0.775963	−	1.34401i	0.158289	−	0.987393i	$-0.449402\pi$
$110$	0.543065	+	0.940616i	0.0517792	+	0.0896842i
$111$	3.03936	−	5.26432i	0.288483	−	0.499667i
$112$	0.324030	−	0.561237i	0.0306180	−	0.0530319i
$113$	−5.90645			−0.555632			−0.277816	−	0.960634i	$-0.589611\pi$
$113$	−5.90645			−0.555632			−0.277816	+	0.960634i	$0.589611\pi$
$114$	−3.21903	+	5.57553i	−0.301490	+	0.522196i
$115$	1.67597	−	2.90286i	0.156285	−	0.270694i
$116$	−4.45323	+	7.71321i	−0.413472	+	0.716154i
$117$	3.91387	+	6.77902i	0.361837	+	0.626721i
$118$	−7.46838			−0.687520
$119$		0			0
$120$	1.04307	−	1.80664i	0.0952184	−	0.164923i
$121$	−9.82032			−0.892756
$122$	−0.762100	+	1.32000i	−0.0689973	+	0.119507i
$123$	−6.12920	−	10.6161i	−0.552651	−	0.957219i
$124$	−0.219035	−	0.379379i	−0.0196699	−	0.0340693i
$125$	−1.00000			−0.0894427
$126$	0.438069	+	0.758758i	0.0390263	+	0.0675956i
$127$	−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
$129$	−7.70017	−	11.3067i	−0.677962	−	0.995497i
$130$	5.79001			0.507817
$131$	9.64064			0.842307			0.421153	−	0.906989i	$-0.361625\pi$
$131$	9.64064			0.842307			0.421153	+	0.906989i	$0.361625\pi$
$132$	−1.13290	−	1.96225i	−0.0986067	−	0.170792i
$133$	−2.00000			−0.173422
$134$	−3.74694	−	6.48990i	−0.323687	−	0.560642i
$135$	−1.71903	−	2.97746i	−0.147951	−	0.256259i
$136$		0			0
$137$	−3.67357			−0.313854			−0.156927	−	0.987610i	$-0.550159\pi$
$137$	−3.67357			−0.313854			−0.156927	+	0.987610i	$0.550159\pi$
$138$	−3.49629	+	6.05575i	−0.297624	+	0.515500i
$139$	−5.82032	−	10.0811i	−0.493673	−	0.855067i	0.506300	−	0.862357i	$-0.331013\pi$
$139$	−5.82032	−	10.0811i	−0.493673	−	0.855067i	−0.999973	+	0.00729022i	$0.997679\pi$
$140$	0.648061			0.0547711
$141$	−8.39500	−	14.5406i	−0.706987	−	1.22454i
$142$	−1.13290	+	1.96225i	−0.0950712	+	0.164668i
$143$	3.14435	−	5.44618i	0.262944	−	0.455432i
$144$	−0.675970	+	1.17081i	−0.0563308	+	0.0975678i
$145$	−8.90645			−0.739641
$146$	−2.51516	+	4.35638i	−0.208156	+	0.360536i
$147$	6.86339	−	11.8877i	0.566083	−	0.980484i
$148$	1.45693	+	2.52349i	0.119759	+	0.207429i
$149$	0.0151563	+	0.0262515i	0.00124165	+	0.00215060i	0.866646	−	0.498924i	$-0.166271\pi$
$149$	0.0151563	+	0.0262515i	0.00124165	+	0.00215060i	−0.865404	+	0.501075i	$0.832938\pi$
$150$	2.08613			0.170332
$151$	12.4381			1.01220			0.506098	−	0.862476i	$-0.331087\pi$
$151$	12.4381			1.01220			0.506098	+	0.862476i	$0.331087\pi$
$152$	−1.54307	−	2.67267i	−0.125159	−	0.216782i
$153$		0			0
$154$	0.351939	−	0.609577i	0.0283601	−	0.0491211i
$155$	0.219035	−	0.379379i	0.0175933	−	0.0304725i
$156$	−12.0787			−0.967071
$157$	0.629195	−	1.08980i	0.0502153	−	0.0869754i	−0.839825	−	0.542857i	$-0.817343\pi$
$157$	0.629195	−	1.08980i	0.0502153	−	0.0869754i	0.890040	+	0.455882i	$0.150676\pi$
$158$	−6.87614	+	11.9098i	−0.547036	+	0.947495i
$159$	9.25839	−	16.0360i	0.734238	−	1.27174i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−2.17226			−0.171198
$162$	5.61404	+	9.72380i	0.441081	+	0.763974i
$163$	−7.09888	+	12.2956i	−0.556027	+	0.963068i	0.441795	+	0.897116i	$0.354342\pi$
$163$	−7.09888	+	12.2956i	−0.556027	+	0.963068i	−0.997823	+	0.0659519i	$0.978992\pi$
$164$	5.87614			0.458849
$165$	1.13290	−	1.96225i	0.0881965	−	0.152761i
$166$	−2.15710	−	3.73621i	−0.167424	−	0.289986i
$167$	−4.72808	−	8.18927i	−0.365870	−	0.633705i	0.623046	−	0.782185i	$-0.285895\pi$
$167$	−4.72808	−	8.18927i	−0.365870	−	0.633705i	−0.988915	+	0.148481i	$0.952562\pi$
$168$	−1.35194			−0.104304
$169$	−10.2621	−	17.7745i	−0.789392	−	1.36727i
$170$		0			0
$171$	4.17226			0.319061
$172$	6.53936	−	0.486646i	0.498621	−	0.0371064i
$173$	17.8129			1.35429			0.677145	−	0.735850i	$-0.263217\pi$
$173$	17.8129			1.35429			0.677145	+	0.735850i	$0.263217\pi$
$174$	18.5800			1.40855
$175$	0.324030	+	0.561237i	0.0244944	+	0.0424255i
$176$	1.08613			0.0818701
$177$	7.79001	+	13.4927i	0.585533	+	1.01417i
$178$	4.75839	+	8.24177i	0.356656	+	0.617747i
$179$	−5.90645	+	10.2303i	−0.441469	+	0.764647i	−0.997799	−	0.0663150i	$-0.978876\pi$
$179$	−5.90645	+	10.2303i	−0.441469	+	0.764647i	0.556330	+	0.830962i	$0.312209\pi$
$180$	−1.35194			−0.100768
$181$	9.34452	−	16.1852i	0.694573	−	1.20304i	−0.275752	−	0.961229i	$-0.588927\pi$
$181$	9.34452	−	16.1852i	0.694573	−	1.20304i	0.970325	−	0.241806i	$-0.0777399\pi$
$182$	−1.87614	−	3.24957i	−0.139069	−	0.240874i
$183$	3.17968			0.235049
$184$	−1.67597	−	2.90286i	−0.123554	−	0.214002i
$185$	−1.45693	+	2.52349i	−0.107116	+	0.185530i
$186$	−0.456935	+	0.791434i	−0.0335041	+	0.0580308i
$187$		0			0
$188$	8.04840			0.586990
$189$	−1.11404	+	1.92957i	−0.0810344	+	0.140356i
$190$	1.54307	−	2.67267i	0.111946	−	0.193896i
$191$	4.79001	+	8.29654i	0.346593	+	0.600316i	0.985642	−	0.168850i	$-0.0540052\pi$
$191$	4.79001	+	8.29654i	0.346593	+	0.600316i	−0.639049	+	0.769166i	$0.720672\pi$
$192$	−1.04307	−	1.80664i	−0.0752767	−	0.130383i
$193$	−9.10902			−0.655682			−0.327841	−	0.944733i	$-0.606321\pi$
$193$	−9.10902			−0.655682			−0.327841	+	0.944733i	$0.606321\pi$
$194$	6.34452			0.455510
$195$	−6.03936	−	10.4605i	−0.432487	−	0.749090i
$196$	3.29001	+	5.69846i	0.235001	+	0.407033i
$197$	1.82032	−	3.15289i	0.129693	−	0.224634i	−0.793865	−	0.608094i	$-0.791934\pi$
$197$	1.82032	−	3.15289i	0.129693	−	0.224634i	0.923557	+	0.383460i	$0.125268\pi$
$198$	−0.734191	+	1.27166i	−0.0521767	+	0.0903727i
$199$	−6.78259			−0.480805			−0.240403	−	0.970673i	$-0.577279\pi$
$199$	−6.78259			−0.480805			−0.240403	+	0.970673i	$0.577279\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−7.81661	+	13.5388i	−0.551341	+	0.954951i
$202$	−7.21533	+	12.4973i	−0.507669	+	0.879308i
$203$	2.88596	+	4.99863i	0.202555	+	0.350835i
$204$		0			0
$205$	2.93807	+	5.08889i	0.205204	+	0.355423i
$206$	−3.34823	+	5.79930i	−0.233282	+	0.404057i
$207$	4.53162			0.314969
$208$	2.89500	−	5.01429i	0.200732	−	0.347679i
$209$	−1.67597	−	2.90286i	−0.115929	−	0.200795i
$210$	−0.675970	−	1.17081i	−0.0466463	−	0.0807938i
$211$	−9.43065			−0.649233			−0.324616	−	0.945846i	$-0.605235\pi$
$211$	−9.43065			−0.649233			−0.324616	+	0.945846i	$0.605235\pi$
$212$	4.43807	+	7.68696i	0.304808	+	0.527943i
$213$	4.72677			0.323873
$214$	2.20257			0.150565
$215$	3.69113	+	5.41993i	0.251733	+	0.369636i
$216$	−3.43807			−0.233931
$217$	−0.283896			−0.0192721
$218$	−8.10129	−	14.0318i	−0.548688	−	0.950356i
$219$	10.4939			0.709111
$220$	0.543065	+	0.940616i	0.0366134	+	0.0634163i
$221$		0			0
$222$	3.03936	−	5.26432i	0.203988	−	0.353318i
$223$	12.9442			0.866807			0.433403	−	0.901200i	$-0.357313\pi$
$223$	12.9442			0.866807			0.433403	+	0.901200i	$0.357313\pi$
$224$	0.324030	−	0.561237i	0.0216502	−	0.0374992i
$225$	−0.675970	−	1.17081i	−0.0450646	−	0.0780542i
$226$	−5.90645			−0.392891
$227$	−2.42532	−	4.20077i	−0.160974	−	0.278815i	0.774244	−	0.632887i	$-0.218130\pi$
$227$	−2.42532	−	4.20077i	−0.160974	−	0.278815i	−0.935218	+	0.354072i	$0.884797\pi$
$228$	−3.21903	+	5.57553i	−0.213186	+	0.369249i
$229$	13.0332	−	22.5742i	0.861261	−	1.49175i	−0.00945158	−	0.999955i	$-0.503009\pi$
$229$	13.0332	−	22.5742i	0.861261	−	1.49175i	0.870713	−	0.491792i	$-0.163658\pi$
$230$	1.67597	−	2.90286i	0.110510	−	0.191409i
$231$	−1.46838			−0.0966124
$232$	−4.45323	+	7.71321i	−0.292369	+	0.506397i
$233$	6.22808	−	10.7873i	0.408015	−	0.706703i	−0.586652	−	0.809839i	$-0.699554\pi$
$233$	6.22808	−	10.7873i	0.408015	−	0.706703i	0.994667	+	0.103136i	$0.0328878\pi$
$234$	3.91387	+	6.77902i	0.255858	+	0.443158i
$235$	4.02420	+	6.97012i	0.262510	+	0.454680i
$236$	−7.46838			−0.486150
$237$	28.6890			1.86355
$238$		0			0
$239$	10.7129	+	18.5553i	0.692961	+	1.20024i	0.970863	+	0.239635i	$0.0770277\pi$
$239$	10.7129	+	18.5553i	0.692961	+	1.20024i	−0.277902	+	0.960609i	$0.589639\pi$
$240$	1.04307	−	1.80664i	0.0673296	−	0.116618i
$241$	−14.2523	+	24.6857i	−0.918070	+	1.59014i	−0.115726	+	0.993281i	$0.536920\pi$
$241$	−14.2523	+	24.6857i	−0.918070	+	1.59014i	−0.802343	+	0.596863i	$0.796414\pi$
$242$	−9.82032			−0.631274
$243$	6.55451	−	11.3527i	0.420472	−	0.728279i
$244$	−0.762100	+	1.32000i	−0.0487884	+	0.0845041i
$245$	−3.29001	+	5.69846i	−0.210191	+	0.364061i
$246$	−6.12920	−	10.6161i	−0.390783	−	0.676856i
$247$	−17.8687			−1.13696
$248$	−0.219035	−	0.379379i	−0.0139087	−	0.0240906i
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$	−1.00000			−0.0632456
$251$	5.71533	−	9.89923i	0.360748	−	0.624834i	−0.627336	−	0.778749i	$-0.715855\pi$
$251$	5.71533	−	9.89923i	0.360748	−	0.624834i	0.988084	+	0.153915i	$0.0491881\pi$
$252$	0.438069	+	0.758758i	0.0275958	+	0.0477973i
$253$	−1.82032	−	3.15289i	−0.114443	−	0.198220i
$254$	−1.00000			−0.0627456
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.3626			0.771158			0.385579	−	0.922675i	$-0.374002\pi$
$257$	12.3626			0.771158			0.385579	+	0.922675i	$0.374002\pi$
$258$	−7.70017	−	11.3067i	−0.479392	−	0.703923i
$259$	1.88836			0.117337
$260$	5.79001			0.359081
$261$	−6.02049	−	10.4278i	−0.372659	−	0.645464i
$262$	9.64064			0.595601
$263$	−1.26210	−	2.18602i	−0.0778244	−	0.134796i	0.824487	−	0.565881i	$-0.191464\pi$
$263$	−1.26210	−	2.18602i	−0.0778244	−	0.134796i	−0.902311	+	0.431086i	$0.858131\pi$
$264$	−1.13290	−	1.96225i	−0.0697255	−	0.120768i
$265$	−4.43807	+	7.68696i	−0.272628	+	0.472206i
$266$	−2.00000			−0.122628
$267$	9.92662	−	17.1934i	0.607499	−	1.05222i
$268$	−3.74694	−	6.48990i	−0.228881	−	0.396434i
$269$	−8.61775			−0.525433			−0.262717	−	0.964873i	$-0.584618\pi$
$269$	−8.61775			−0.525433			−0.262717	+	0.964873i	$0.584618\pi$
$270$	−1.71903	−	2.97746i	−0.104617	−	0.181202i
$271$	11.7342	−	20.3242i	0.712801	−	1.23461i	−0.251000	−	0.967987i	$-0.580759\pi$
$271$	11.7342	−	20.3242i	0.712801	−	1.23461i	0.963801	−	0.266621i	$-0.0859072\pi$
$272$		0			0
$273$	−3.91387	+	6.77902i	−0.236878	+	0.410285i
$274$	−3.67357			−0.221928
$275$	−0.543065	+	0.940616i	−0.0327481	+	0.0567213i
$276$	−3.49629	+	6.05575i	−0.210452	+	0.364514i
$277$	−7.25839	−	12.5719i	−0.436114	−	0.755372i	0.561271	−	0.827632i	$-0.310312\pi$
$277$	−7.25839	−	12.5719i	−0.436114	−	0.755372i	−0.997386	+	0.0722594i	$0.976979\pi$
$278$	−5.82032	−	10.0811i	−0.349080	−	0.604624i
$279$	0.592243			0.0354567
$280$	0.648061			0.0387290
$281$	−10.7900	−	18.6888i	−0.643678	−	1.11488i	−0.984605	−	0.174793i	$-0.944074\pi$
$281$	−10.7900	−	18.6888i	−0.643678	−	1.11488i	0.340927	−	0.940090i	$-0.389259\pi$
$282$	−8.39500	−	14.5406i	−0.499915	−	0.865879i
$283$	−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	$0.964041\pi$
$284$	−1.13290	+	1.96225i	−0.0672255	+	0.116438i
$285$	−6.43807			−0.381358
$286$	3.14435	−	5.44618i	0.185929	−	0.322039i
$287$	1.90405	−	3.29791i	0.112392	−	0.194669i
$288$	−0.675970	+	1.17081i	−0.0398319	+	0.0689909i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−8.90645			−0.523005
$291$	−6.61775	−	11.4623i	−0.387939	−	0.671931i
$292$	−2.51516	+	4.35638i	−0.147188	+	0.254938i
$293$	31.2813			1.82747			0.913736	−	0.406308i	$-0.133184\pi$
$293$	31.2813			1.82747			0.913736	+	0.406308i	$0.133184\pi$
$294$	6.86339	−	11.8877i	0.400281	−	0.693307i
$295$	−3.73419	−	6.46781i	−0.217413	−	0.376570i
$296$	1.45693	+	2.52349i	0.0846826	+	0.146675i
$297$	−3.73419			−0.216680
$298$	0.0151563	+	0.0262515i	0.000877981	+	0.00152071i
$299$	−19.4078			−1.12238
$300$	2.08613			0.120443
$301$	1.84583	−	3.82782i	0.106392	−	0.220632i
$302$	12.4381			0.715730
$303$	30.1042			1.72944
$304$	−1.54307	−	2.67267i	−0.0885009	−	0.153288i
$305$	−1.52420			−0.0872754
$306$		0			0
$307$	−16.5952	−	28.7437i	−0.947137	−	1.64049i	−0.751416	−	0.659829i	$-0.770629\pi$
$307$	−16.5952	−	28.7437i	−0.947137	−	1.64049i	−0.195721	−	0.980660i	$-0.562705\pi$
$308$	0.351939	−	0.609577i	0.0200536	−	0.0347338i
$309$	13.9697			0.794708
$310$	0.219035	−	0.379379i	0.0124403	−	0.0215473i
$311$	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	$0.662852\pi$
$312$	−12.0787			−0.683822
$313$	−11.3610	−	19.6778i	−0.642161	−	1.11225i	−0.984949	−	0.172842i	$-0.944705\pi$
$313$	−11.3610	−	19.6778i	−0.642161	−	1.11225i	0.342789	−	0.939413i	$-0.388628\pi$
$314$	0.629195	−	1.08980i	0.0355075	−	0.0615009i
$315$	−0.438069	+	0.758758i	−0.0246824	+	0.0427512i
$316$	−6.87614	+	11.9098i	−0.386813	+	0.669980i
$317$	−15.0107			−0.843083			−0.421542	−	0.906809i	$-0.638511\pi$
$317$	−15.0107			−0.843083			−0.421542	+	0.906809i	$0.638511\pi$
$318$	9.25839	−	16.0360i	0.519185	−	0.899254i
$319$	−4.83678	+	8.37755i	−0.270808	+	0.469053i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−2.29743	−	3.97926i	−0.128230	−	0.222101i
$322$	−2.17226			−0.121055
$323$		0			0
$324$	5.61404	+	9.72380i	0.311891	+	0.540211i
$325$	2.89500	+	5.01429i	0.160586	+	0.278143i
$326$	−7.09888	+	12.2956i	−0.393171	+	0.680992i
$327$	−16.9003	+	29.2722i	−0.934591	+	1.61876i
$328$	5.87614			0.324455
$329$	2.60793	−	4.51706i	0.143780	−	0.249034i
$330$	1.13290	−	1.96225i	0.0623643	−	0.108018i
$331$	9.69646	−	16.7948i	0.532966	−	0.923124i	−0.466293	−	0.884630i	$-0.654411\pi$
$331$	9.69646	−	16.7948i	0.532966	−	0.923124i	0.999259	−	0.0384933i	$-0.0122558\pi$
$332$	−2.15710	−	3.73621i	−0.118386	−	0.205051i
$333$	−3.93937			−0.215876
$334$	−4.72808	−	8.18927i	−0.258709	−	0.448097i
$335$	3.74694	−	6.48990i	0.204717	−	0.354581i
$336$	−1.35194			−0.0737543
$337$	−5.42161	+	9.39050i	−0.295334	+	0.511533i	−0.975062	−	0.221931i	$-0.928764\pi$
$337$	−5.42161	+	9.39050i	−0.295334	+	0.511533i	0.679729	+	0.733464i	$0.262098\pi$
$338$	−10.2621	−	17.7745i	−0.558185	−	0.966804i
$339$	6.16081	+	10.6708i	0.334609	+	0.579561i
$340$		0			0
$341$	−0.237900	−	0.412055i	−0.0128830	−	0.0223140i
$342$	4.17226			0.225610
$343$	8.80068			0.475192
$344$	6.53936	−	0.486646i	0.352578	−	0.0262382i
$345$	−6.99258			−0.376468
$346$	17.8129			0.957628
$347$	0.739525	+	1.28090i	0.0396998	+	0.0687620i	0.885193	−	0.465225i	$-0.154027\pi$
$347$	0.739525	+	1.28090i	0.0396998	+	0.0687620i	−0.845493	+	0.533987i	$0.820693\pi$
$348$	18.5800			0.995993
$349$	−7.03565	−	12.1861i	−0.376610	−	0.652307i	0.613957	−	0.789339i	$-0.289577\pi$
$349$	−7.03565	−	12.1861i	−0.376610	−	0.652307i	−0.990567	+	0.137033i	$0.956243\pi$
$350$	0.324030	+	0.561237i	0.0173202	+	0.0299994i
$351$	−9.95323	+	17.2395i	−0.531264	+	0.920176i
$352$	1.08613			0.0578909
$353$	−7.36098	+	12.7496i	−0.391786	+	0.678593i	−0.992685	−	0.120732i	$-0.961476\pi$
$353$	−7.36098	+	12.7496i	−0.391786	+	0.678593i	0.600900	+	0.799325i	$0.294809\pi$
$354$	7.79001	+	13.4927i	0.414034	+	0.717128i
$355$	−2.26581			−0.120257
$356$	4.75839	+	8.24177i	0.252194	+	0.436813i
$357$		0			0
$358$	−5.90645	+	10.2303i	−0.312166	+	0.540687i
$359$	−15.1813	+	26.2948i	−0.801239	+	1.38779i	0.117563	+	0.993065i	$0.462492\pi$
$359$	−15.1813	+	26.2948i	−0.801239	+	1.38779i	−0.918801	+	0.394720i	$0.870841\pi$
$360$	−1.35194			−0.0712535
$361$	4.73790	−	8.20628i	0.249363	−	0.431910i
$362$	9.34452	−	16.1852i	0.491137	−	0.850674i
$363$	10.2432	+	17.7418i	0.537630	+	0.931203i
$364$	−1.87614	−	3.24957i	−0.0983364	−	0.170324i
$365$	−5.03031			−0.263299
$366$	3.17968			0.166204
$367$	−11.3748	−	19.7018i	−0.593761	−	1.02843i	−0.993720	−	0.111892i	$-0.964309\pi$
$367$	−11.3748	−	19.7018i	−0.593761	−	1.02843i	0.399959	−	0.916533i	$-0.369024\pi$
$368$	−1.67597	−	2.90286i	−0.0873660	−	0.151322i
$369$	−3.97209	+	6.87986i	−0.206779	+	0.358151i
$370$	−1.45693	+	2.52349i	−0.0757424	+	0.131190i
$371$	5.75228			0.298643
$372$	−0.456935	+	0.791434i	−0.0236910	+	0.0410340i
$373$	−7.13453	+	12.3574i	−0.369412	+	0.639840i	−0.989474	−	0.144713i	$-0.953774\pi$
$373$	−7.13453	+	12.3574i	−0.369412	+	0.639840i	0.620062	+	0.784553i	$0.287108\pi$
$374$		0			0
$375$	1.04307	+	1.80664i	0.0538637	+	0.0932946i
$376$	8.04840			0.415064
$377$	25.7842	+	44.6596i	1.32795	+	2.30008i
$378$	−1.11404	+	1.92957i	−0.0573000	+	0.0992465i
$379$	9.08613			0.466723			0.233362	−	0.972390i	$-0.425027\pi$
$379$	9.08613			0.466723			0.233362	+	0.972390i	$0.425027\pi$
$380$	1.54307	−	2.67267i	0.0791576	−	0.137105i
$381$	1.04307	+	1.80664i	0.0534378	+	0.0925571i
$382$	4.79001	+	8.29654i	0.245078	+	0.424488i
$383$	−5.40034			−0.275944			−0.137972	−	0.990436i	$-0.544058\pi$
$383$	−5.40034			−0.275944			−0.137972	+	0.990436i	$0.544058\pi$
$384$	−1.04307	−	1.80664i	−0.0532287	−	0.0921948i
$385$	0.703878			0.0358730
$386$	−9.10902			−0.463637
$387$	−3.85063	+	7.98533i	−0.195739	+	0.405917i
$388$	6.34452			0.322094
$389$	6.64325			0.336826			0.168413	−	0.985716i	$-0.446136\pi$
$389$	6.64325			0.336826			0.168413	+	0.985716i	$0.446136\pi$
$390$	−6.03936	−	10.4605i	−0.305815	−	0.529687i
$391$		0			0
$392$	3.29001	+	5.69846i	0.166171	+	0.287816i
$393$	−10.0558	−	17.4172i	−0.507249	−	0.878581i
$394$	1.82032	−	3.15289i	0.0917065	−	0.158840i
$395$	−13.7523			−0.691952
$396$	−0.734191	+	1.27166i	−0.0368945	+	0.0639031i
$397$	−11.4381	−	19.8113i	−0.574060	−	0.994302i	−0.996143	−	0.0877442i	$-0.972034\pi$
$397$	−11.4381	−	19.8113i	−0.574060	−	0.994302i	0.422083	−	0.906557i	$-0.361299\pi$
$398$	−6.78259			−0.339981
$399$	2.08613	+	3.61328i	0.104437	+	0.180890i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−7.70628	+	13.3477i	−0.384833	+	0.666551i	−0.991746	−	0.128218i	$-0.959074\pi$
$401$	−7.70628	+	13.3477i	−0.384833	+	0.666551i	0.606913	+	0.794769i	$0.292408\pi$
$402$	−7.81661	+	13.5388i	−0.389857	+	0.675252i
$403$	−2.53643			−0.126348
$404$	−7.21533	+	12.4973i	−0.358976	+	0.621764i
$405$	−5.61404	+	9.72380i	−0.278964	+	0.483180i
$406$	2.88596	+	4.99863i	0.143228	+	0.248078i
$407$	1.58242	+	2.74083i	0.0784377	+	0.135858i
$408$		0			0
$409$	12.1797			0.602246			0.301123	−	0.953585i	$-0.402638\pi$
$409$	12.1797			0.602246			0.301123	+	0.953585i	$0.402638\pi$
$410$	2.93807	+	5.08889i	0.145101	+	0.251322i
$411$	3.83177	+	6.63682i	0.189007	+	0.327370i
$412$	−3.34823	+	5.79930i	−0.164955	+	0.285711i
$413$	−2.41998	+	4.19153i	−0.119080	+	0.206252i
$414$	4.53162			0.222717
$415$	2.15710	−	3.73621i	0.105888	−	0.183404i
$416$	2.89500	−	5.01429i	0.141939	−	0.245846i
$417$	−12.1419	+	21.0305i	−0.594594	+	1.02987i
$418$	−1.67597	−	2.90286i	−0.0819744	−	0.141984i
$419$	2.68904			0.131368			0.0656841	−	0.997840i	$-0.479077\pi$
$419$	2.68904			0.131368			0.0656841	+	0.997840i	$0.479077\pi$
$420$	−0.675970	−	1.17081i	−0.0329839	−	0.0571299i
$421$	0.567265	−	0.982531i	0.0276468	−	0.0478856i	−0.851871	−	0.523752i	$-0.824532\pi$
$421$	0.567265	−	0.982531i	0.0276468	−	0.0478856i	0.879518	+	0.475866i	$0.157865\pi$
$422$	−9.43065			−0.459077
$423$	−5.44047	+	9.42318i	−0.264525	+	0.458170i
$424$	4.43807	+	7.68696i	0.215532	+	0.373312i
$425$		0			0
$426$	4.72677			0.229013
$427$	0.493887	+	0.855437i	0.0239009	+	0.0413975i
$428$	2.20257			0.106465
$429$	−13.1191			−0.633394
$430$	3.69113	+	5.41993i	0.178002	+	0.261372i
$431$	16.6858			0.803726			0.401863	−	0.915700i	$-0.368363\pi$
$431$	16.6858			0.803726			0.401863	+	0.915700i	$0.368363\pi$
$432$	−3.43807			−0.165414
$433$	14.7916	+	25.6199i	0.710841	+	1.23121i	0.964542	+	0.263929i	$0.0850186\pi$
$433$	14.7916	+	25.6199i	0.710841	+	1.23121i	−0.253701	+	0.967283i	$0.581648\pi$
$434$	−0.283896			−0.0136274
$435$	9.29001	+	16.0908i	0.445422	+	0.771493i
$436$	−8.10129	−	14.0318i	−0.387981	−	0.672003i
$437$	−5.17226	+	8.95862i	−0.247423	+	0.428549i
$438$	10.4939			0.501417
$439$	−2.82032	+	4.88494i	−0.134607	+	0.233145i	−0.925447	−	0.378877i	$-0.876310\pi$
$439$	−2.82032	+	4.88494i	−0.134607	+	0.233145i	0.790841	+	0.612022i	$0.209644\pi$
$440$	0.543065	+	0.940616i	0.0258896	+	0.0448421i
$441$	−8.89578			−0.423609
$442$		0			0
$443$	−1.69113	+	2.92912i	−0.0803478	+	0.139166i	−0.903399	−	0.428800i	$-0.858936\pi$
$443$	−1.69113	+	2.92912i	−0.0803478	+	0.139166i	0.823052	+	0.567967i	$0.192270\pi$
$444$	3.03936	−	5.26432i	0.144241	−	0.249834i
$445$	−4.75839	+	8.24177i	−0.225569	+	0.390698i
$446$	12.9442			0.612925
$447$	0.0316180	−	0.0547640i	0.00149548	−	0.00259025i
$448$	0.324030	−	0.561237i	0.0153090	−	0.0265160i
$449$	16.5410	+	28.6498i	0.780617	+	1.35207i	0.931583	+	0.363530i	$0.118428\pi$
$449$	16.5410	+	28.6498i	0.780617	+	1.35207i	−0.150966	+	0.988539i	$0.548238\pi$
$450$	−0.675970	−	1.17081i	−0.0318655	−	0.0551927i
$451$	6.38225			0.300528
$452$	−5.90645			−0.277816
$453$	−12.9737	−	22.4711i	−0.609558	−	1.05579i
$454$	−2.42532	−	4.20077i	−0.113826	−	0.197152i
$455$	1.87614	−	3.24957i	0.0879547	−	0.152342i
$456$	−3.21903	+	5.57553i	−0.150745	+	0.261098i
$457$	−31.3929			−1.46850			−0.734249	−	0.678880i	$-0.762466\pi$
$457$	−31.3929			−1.46850			−0.734249	+	0.678880i	$0.762466\pi$
$458$	13.0332	−	22.5742i	0.609003	−	1.05482i
$459$		0			0
$460$	1.67597	−	2.90286i	0.0781425	−	0.135347i
$461$	1.89871	+	3.28867i	0.0884319	+	0.153169i	0.906848	−	0.421457i	$-0.138481\pi$
$461$	1.89871	+	3.28867i	0.0884319	+	0.153169i	−0.818417	+	0.574625i	$0.805148\pi$
$462$	−1.46838			−0.0683153
$463$	−11.2318	−	19.4540i	−0.521985	−	0.904105i	−0.999673	−	0.0255754i	$-0.991858\pi$
$463$	−11.2318	−	19.4540i	−0.521985	−	0.904105i	0.477687	−	0.878530i	$-0.341475\pi$
$464$	−4.45323	+	7.71321i	−0.206736	+	0.358077i
$465$	−0.913870			−0.0423797
$466$	6.22808	−	10.7873i	0.288510	−	0.499714i
$467$	−21.4865	−	37.2157i	−0.994275	−	1.72214i	−0.589672	−	0.807643i	$-0.700743\pi$
$467$	−21.4865	−	37.2157i	−0.994275	−	1.72214i	−0.404603	−	0.914492i	$-0.632590\pi$
$468$	3.91387	+	6.77902i	0.180919	+	0.313360i
$469$	−4.85649			−0.224252
$470$	4.02420	+	6.97012i	0.185622	+	0.321508i
$471$	−2.62517			−0.120961
$472$	−7.46838			−0.343760
$473$	7.10259	−	0.528561i	0.326578	−	0.0243033i
$474$	28.6890			1.31773
$475$	3.08613			0.141601
$476$		0			0
$477$	−12.0000			−0.549442
$478$	10.7129	+	18.5553i	0.489998	+	0.848701i
$479$	18.7449	+	32.4670i	0.856474	+	1.48346i	0.875270	+	0.483634i	$0.160683\pi$
$479$	18.7449	+	32.4670i	0.856474	+	1.48346i	−0.0187959	+	0.999823i	$0.505983\pi$
$480$	1.04307	−	1.80664i	0.0476092	−	0.0824615i
$481$	16.8713			0.769266
$482$	−14.2523	+	24.6857i	−0.649173	+	1.12440i
$483$	2.26581	+	3.92450i	0.103098	+	0.178571i
$484$	−9.82032			−0.446378
$485$	3.17226	+	5.49452i	0.144045	+	0.249493i
$486$	6.55451	−	11.3527i	0.297319	−	0.514971i
$487$	−20.6345	+	35.7401i	−0.935040	+	1.61954i	−0.160477	+	0.987040i	$0.551303\pi$
$487$	−20.6345	+	35.7401i	−0.935040	+	1.61954i	−0.774563	+	0.632497i	$0.782030\pi$
$488$	−0.762100	+	1.32000i	−0.0344986	+	0.0597534i
$489$	29.6184			1.33939
$490$	−3.29001	+	5.69846i	−0.148627	+	0.257430i
$491$	−2.10500	+	3.64596i	−0.0949971	+	0.164540i	−0.909607	−	0.415469i	$-0.863618\pi$
$491$	−2.10500	+	3.64596i	−0.0949971	+	0.164540i	0.814610	+	0.580009i	$0.196951\pi$
$492$	−6.12920	−	10.6161i	−0.276325	−	0.478610i
$493$		0			0
$494$	−17.8687			−0.803952
$495$	−1.46838			−0.0659989
$496$	−0.219035	−	0.379379i	−0.00983495	−	0.0170346i
$497$	0.734191	+	1.27166i	0.0329330	+	0.0570416i
$498$	−4.50000	+	7.79423i	−0.201650	+	0.349268i
$499$	−9.01145	+	15.6083i	−0.403408	+	0.698723i	−0.994135	−	0.108149i	$-0.965508\pi$
$499$	−9.01145	+	15.6083i	−0.403408	+	0.698723i	0.590727	+	0.806872i	$0.298841\pi$
$500$	−1.00000			−0.0447214
$501$	−9.86339	+	17.0839i	−0.440664	+	0.763252i
$502$	5.71533	−	9.89923i	0.255087	−	0.441824i
$503$	16.3761	−	28.3643i	0.730176	−	1.26470i	−0.226632	−	0.973980i	$-0.572771\pi$
$503$	16.3761	−	28.3643i	0.730176	−	1.26470i	0.956808	−	0.290721i	$-0.0938953\pi$
$504$	0.438069	+	0.758758i	0.0195132	+	0.0337978i
$505$	−14.4307			−0.642156
$506$	−1.82032	−	3.15289i	−0.0809231	−	0.140163i
$507$	−21.4081	+	37.0799i	−0.950766	+	1.64678i
$508$	−1.00000			−0.0443678
$509$	16.2358	−	28.1213i	0.719640	−	1.24645i	−0.241503	−	0.970400i	$-0.577640\pi$
$509$	16.2358	−	28.1213i	0.719640	−	1.24645i	0.961143	−	0.276053i	$-0.0890264\pi$
$510$		0			0
$511$	1.62997	+	2.82320i	0.0721058	+	0.124891i
$512$	1.00000			0.0441942
$513$	5.30516	+	9.18882i	0.234229	+	0.405696i
$514$	12.3626			0.545291
$515$	−6.69646			−0.295081
$516$	−7.70017	−	11.3067i	−0.338981	−	0.497748i
$517$	8.74161			0.384456
$518$	1.88836			0.0829700
$519$	−18.5800	−	32.1815i	−0.815572	−	1.41261i
$520$	5.79001			0.253909
$521$	11.2863	+	19.5484i	0.494462	+	0.856433i	0.999980	−	0.00638325i	$-0.00203187\pi$
$521$	11.2863	+	19.5484i	0.494462	+	0.856433i	−0.505518	+	0.862816i	$0.668699\pi$
$522$	−6.02049	−	10.4278i	−0.263510	−	0.456412i
$523$	−20.0077	+	34.6544i	−0.874877	+	1.51533i	−0.0179839	+	0.999838i	$0.505725\pi$
$523$	−20.0077	+	34.6544i	−0.874877	+	1.51533i	−0.856893	+	0.515494i	$0.827609\pi$
$524$	9.64064			0.421153
$525$	0.675970	−	1.17081i	0.0295017	−	0.0510985i
$526$	−1.26210	−	2.18602i	−0.0550302	−	0.0953150i
$527$		0			0
$528$	−1.13290	−	1.96225i	−0.0493033	−	0.0853959i
$529$	5.88225	−	10.1884i	0.255750	−	0.442972i
$530$	−4.43807	+	7.68696i	−0.192777	+	0.333900i
$531$	5.04840	−	8.74408i	0.219082	−	0.379461i
$532$	−2.00000			−0.0867110
$533$	17.0114	−	29.4647i	0.736848	−	1.27626i
$534$	9.92662	−	17.1934i	0.429567	−	0.744032i
$535$	1.10129	+	1.90748i	0.0476128	+	0.0824677i
$536$	−3.74694	−	6.48990i	−0.161843	−	0.280321i
$537$	24.6433			1.06343
$538$	−8.61775			−0.371538
$539$	3.57338	+	6.18927i	0.153916	+	0.266591i
$540$	−1.71903	−	2.97746i	−0.0739755	−	0.128129i
$541$	15.4737	−	26.8013i	0.665267	−	1.15228i	−0.313946	−	0.949441i	$-0.601651\pi$
$541$	15.4737	−	26.8013i	0.665267	−	1.15228i	0.979213	−	0.202835i	$-0.0650156\pi$
$542$	11.7342	−	20.3242i	0.504027	−	0.873000i
$543$	−38.9878			−1.67313
$544$		0			0
$545$	8.10129	−	14.0318i	0.347021	−	0.601058i
$546$	−3.91387	+	6.77902i	−0.167498	+	0.290115i
$547$	0.392601	+	0.680004i	0.0167864	+	0.0290749i	0.874297	−	0.485392i	$-0.161323\pi$
$547$	0.392601	+	0.680004i	0.0167864	+	0.0290749i	−0.857510	+	0.514467i	$0.827990\pi$
$548$	−3.67357			−0.156927
$549$	−1.03031	−	1.78455i	−0.0439727	−	0.0761629i
$550$	−0.543065	+	0.940616i	−0.0231564	+	0.0401080i
$551$	27.4865			1.17096
$552$	−3.49629	+	6.05575i	−0.148812	+	0.257750i
$553$	4.45616	+	7.71829i	0.189495	+	0.328215i
$554$	−7.25839	−	12.5719i	−0.308379	−	0.534129i
$555$	6.07871			0.258027
$556$	−5.82032	−	10.0811i	−0.246837	−	0.427534i
$557$	−28.4051			−1.20356			−0.601782	−	0.798660i	$-0.705543\pi$
$557$	−28.4051			−1.20356			−0.601782	+	0.798660i	$0.705543\pi$
$558$	0.592243			0.0250717
$559$	16.4913	−	34.1991i	0.697507	−	1.44647i
$560$	0.648061			0.0273856
$561$		0			0
$562$	−10.7900	−	18.6888i	−0.455149	−	0.788341i
$563$	−44.3504			−1.86915			−0.934573	−	0.355772i	$-0.884218\pi$
$563$	−44.3504			−1.86915			−0.934573	+	0.355772i	$0.884218\pi$
$564$	−8.39500	−	14.5406i	−0.353493	−	0.612269i
$565$	−2.95323	−	5.11514i	−0.124243	−	0.215195i
$566$	−10.0000	+	17.3205i	−0.420331	+	0.728035i
$567$	7.27648			0.305583
$568$	−1.13290	+	1.96225i	−0.0475356	+	0.0823341i
$569$	−7.63453	−	13.2234i	−0.320056	−	0.554353i	0.660443	−	0.750876i	$-0.270368\pi$
$569$	−7.63453	−	13.2234i	−0.320056	−	0.554353i	−0.980499	+	0.196523i	$0.937035\pi$
$570$	−6.43807			−0.269661
$571$	1.30276	+	2.25645i	0.0545189	+	0.0944294i	0.891997	−	0.452042i	$-0.149304\pi$
$571$	1.30276	+	2.25645i	0.0545189	+	0.0944294i	−0.837478	+	0.546471i	$0.815971\pi$
$572$	3.14435	−	5.44618i	0.131472	−	0.227716i
$573$	9.99258	−	17.3077i	0.417446	−	0.723038i
$574$	1.90405	−	3.29791i	0.0794734	−	0.137652i
$575$	3.35194			0.139786
$576$	−0.675970	+	1.17081i	−0.0281654	+	0.0487839i
$577$	21.2977	−	36.8888i	0.886637	−	1.53570i	0.0428107	−	0.999083i	$-0.486369\pi$
$577$	21.2977	−	36.8888i	0.886637	−	1.53570i	0.843826	−	0.536617i	$-0.180298\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	9.50131	+	16.4567i	0.394861	+	0.683919i
$580$	−8.90645			−0.369820
$581$	−2.79587			−0.115992
$582$	−6.61775	−	11.4623i	−0.274314	−	0.475127i
$583$	4.82032	+	8.34904i	0.199637	+	0.345782i
$584$	−2.51516	+	4.35638i	−0.104078	+	0.180268i
$585$	−3.91387	+	6.77902i	−0.161819	+	0.280278i
$586$	31.2813			1.29222
$587$	−19.5878	+	33.9270i	−0.808473	+	1.40032i	0.105448	+	0.994425i	$0.466372\pi$
$587$	−19.5878	+	33.9270i	−0.808473	+	1.40032i	−0.913921	+	0.405892i	$0.866961\pi$
$588$	6.86339	−	11.8877i	0.283041	−	0.490242i
$589$	−0.675970	+	1.17081i	−0.0278528	+	0.0482425i
$590$	−3.73419	−	6.46781i	−0.153734	−	0.266275i
$591$	−7.59485			−0.312411
$592$	1.45693	+	2.52349i	0.0598797	+	0.103715i
$593$	13.7268	−	23.7755i	0.563691	−	0.976341i	−0.433479	−	0.901164i	$-0.642714\pi$
$593$	13.7268	−	23.7755i	0.563691	−	0.976341i	0.997170	−	0.0751778i	$-0.0239524\pi$
$594$	−3.73419			−0.153216
$595$		0			0
$596$	0.0151563	+	0.0262515i	0.000620826	+	0.00107530i
$597$	7.07468	+	12.2537i	0.289548	+	0.501511i
$598$	−19.4078			−0.793642
$599$	−19.2977	−	33.4247i	−0.788485	−	1.36570i	−0.926895	−	0.375320i	$-0.877533\pi$
$599$	−19.2977	−	33.4247i	−0.788485	−	1.36570i	0.138411	−	0.990375i	$-0.455801\pi$
$600$	2.08613			0.0851659
$601$	−18.5046			−0.754817			−0.377408	−	0.926047i	$-0.623185\pi$
$601$	−18.5046			−0.754817			−0.377408	+	0.926047i	$0.623185\pi$
$602$	1.84583	−	3.82782i	0.0752303	−	0.156010i
$603$	10.1313			0.412578
$604$	12.4381			0.506098
$605$	−4.91016	−	8.50465i	−0.199626	−	0.345763i
$606$	30.1042			1.22290
$607$	−10.1457	−	17.5728i	−0.411800	−	0.713258i	0.583287	−	0.812266i	$-0.301766\pi$
$607$	−10.1457	−	17.5728i	−0.411800	−	0.713258i	−0.995087	+	0.0990084i	$0.968433\pi$
$608$	−1.54307	−	2.67267i	−0.0625796	−	0.108391i
$609$	6.02049	−	10.4278i	0.243963	−	0.422556i
$610$	−1.52420			−0.0617130
$611$	23.3002	−	40.3570i	0.942623	−	1.63267i
$612$		0			0
$613$	24.3445			0.983266			0.491633	−	0.870803i	$-0.336400\pi$
$613$	24.3445			0.983266			0.491633	+	0.870803i	$0.336400\pi$
$614$	−16.5952	−	28.7437i	−0.669727	−	1.16000i
$615$	6.12920	−	10.6161i	0.247153	−	0.428082i
$616$	0.351939	−	0.609577i	0.0141800	−	0.0245605i
$617$	−2.08451	+	3.61047i	−0.0839190	+	0.145352i	−0.904930	−	0.425560i	$-0.860077\pi$
$617$	−2.08451	+	3.61047i	−0.0839190	+	0.145352i	0.821011	+	0.570912i	$0.193410\pi$
$618$	13.9697			0.561943
$619$	18.4750	−	31.9997i	0.742574	−	1.28618i	−0.208746	−	0.977970i	$-0.566938\pi$
$619$	18.4750	−	31.9997i	0.742574	−	1.28618i	0.951320	−	0.308206i	$-0.0997285\pi$
$620$	0.219035	−	0.379379i	0.00879665	−	0.0152362i
$621$	5.76210	+	9.98025i	0.231225	+	0.400494i
$622$	9.00000	+	15.5885i	0.360867	+	0.625040i
$623$	6.16745			0.247094
$624$	−12.0787			−0.483535
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.3610	−	19.6778i	−0.454076	−	0.786483i
$627$	−3.49629	+	6.05575i	−0.139628	+	0.241843i
$628$	0.629195	−	1.08980i	0.0251076	−	0.0434877i
$629$		0			0
$630$	−0.438069	+	0.758758i	−0.0174531	+	0.0302297i
$631$	−10.9320	+	18.9347i	−0.435194	+	0.753779i	−0.997311	−	0.0732789i	$-0.976654\pi$
$631$	−10.9320	+	18.9347i	−0.435194	+	0.753779i	0.562117	+	0.827058i	$0.309987\pi$
$632$	−6.87614	+	11.9098i	−0.273518	+	0.473747i
$633$	9.83678	+	17.0378i	0.390977	+	0.677192i
$634$	−15.0107			−0.596150
$635$	−0.500000	−	0.866025i	−0.0198419	−	0.0343672i
$636$	9.25839	−	16.0360i	0.367119	−	0.635869i
$637$	38.0984			1.50951
$638$	−4.83678	+	8.37755i	−0.191490	+	0.331671i
$639$	−1.53162	−	2.65284i	−0.0605899	−	0.104945i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−17.2935			−0.683053			−0.341526	−	0.939872i	$-0.610944\pi$
$641$	−17.2935			−0.683053			−0.341526	+	0.939872i	$0.610944\pi$
$642$	−2.29743	−	3.97926i	−0.0906722	−	0.157049i
$643$	−15.0787			−0.594646			−0.297323	−	0.954777i	$-0.596094\pi$
$643$	−15.0787			−0.594646			−0.297323	+	0.954777i	$0.596094\pi$
$644$	−2.17226			−0.0855991
$645$	5.94178	−	12.3219i	0.233957	−	0.485173i
$646$		0			0
$647$	−39.6184			−1.55756			−0.778780	−	0.627297i	$-0.784161\pi$
$647$	−39.6184			−1.55756			−0.778780	+	0.627297i	$0.784161\pi$
$648$	5.61404	+	9.72380i	0.220540	+	0.381987i
$649$	−8.11164			−0.318410
$650$	2.89500	+	5.01429i	0.113551	+	0.196677i
$651$	0.296122	+	0.512898i	0.0116059	+	0.0201020i
$652$	−7.09888	+	12.2956i	−0.278014	+	0.481534i
$653$	32.9368			1.28892			0.644458	−	0.764640i	$-0.277083\pi$
$653$	32.9368			1.28892			0.644458	+	0.764640i	$0.277083\pi$
$654$	−16.9003	+	29.2722i	−0.660856	+	1.14464i
$655$	4.82032	+	8.34904i	0.188346	+	0.326224i
$656$	5.87614			0.229425
$657$	−3.40034	−	5.88956i	−0.132660	−	0.229774i
$658$	2.60793	−	4.51706i	0.101668	−	0.176093i
$659$	11.6177	−	20.1225i	0.452563	−	0.783862i	−0.545981	−	0.837797i	$-0.683843\pi$
$659$	11.6177	−	20.1225i	0.452563	−	0.783862i	0.998544	+	0.0539349i	$0.0171764\pi$
$660$	1.13290	−	1.96225i	0.0440982	−	0.0763804i
$661$	−18.6694			−0.726155			−0.363078	−	0.931759i	$-0.618274\pi$
$661$	−18.6694			−0.726155			−0.363078	+	0.931759i	$0.618274\pi$
$662$	9.69646	−	16.7948i	0.376864	−	0.652747i
$663$		0			0
$664$	−2.15710	−	3.73621i	−0.0837119	−	0.144993i
$665$	−1.00000	−	1.73205i	−0.0387783	−	0.0671660i
$666$	−3.93937			−0.152648
$667$	29.8539			1.15595
$668$	−4.72808	−	8.18927i	−0.182935	−	0.316852i
$669$	−13.5016	−	23.3855i	−0.522003	−	0.904136i
$670$	3.74694	−	6.48990i	0.144757	−	0.250727i
$671$	−0.827740	+	1.43369i	−0.0319545	+	0.0553469i
$672$	−1.35194			−0.0521522
$673$	−20.4791	+	35.4708i	−0.789409	+	1.36730i	0.136920	+	0.990582i	$0.456280\pi$
$673$	−20.4791	+	35.4708i	−0.789409	+	1.36730i	−0.926329	+	0.376715i	$0.877054\pi$
$674$	−5.42161	+	9.39050i	−0.208833	+	0.361709i
$675$	1.71903	−	2.97746i	0.0661657	−	0.114602i
$676$	−10.2621	−	17.7745i	−0.394696	−	0.683634i
$677$	−24.0081			−0.922705			−0.461352	−	0.887217i	$-0.652636\pi$
$677$	−24.0081			−0.922705			−0.461352	+	0.887217i	$0.652636\pi$
$678$	6.16081	+	10.6708i	0.236605	+	0.409811i
$679$	2.05582	−	3.56078i	0.0788950	−	0.136650i
$680$		0			0
$681$	−5.05953	+	8.76336i	−0.193881	+	0.335813i
$682$	−0.237900	−	0.412055i	−0.00910967	−	0.0157784i
$683$	−2.07871	−	3.60043i	−0.0795397	−	0.137767i	0.823512	−	0.567299i	$-0.192012\pi$
$683$	−2.07871	−	3.60043i	−0.0795397	−	0.137767i	−0.903051	+	0.429532i	$0.858678\pi$
$684$	4.17226			0.159530
$685$	−1.83678	−	3.18140i	−0.0701799	−	0.121555i
$686$	8.80068			0.336011
$687$	−54.3781			−2.07465
$688$	6.53936	−	0.486646i	0.249311	−	0.0185532i
$689$	51.3929			1.95791
$690$	−6.99258			−0.266203
$691$	8.19113	+	14.1874i	0.311605	+	0.539716i	0.978710	−	0.205248i	$-0.0658001\pi$
$691$	8.19113	+	14.1874i	0.311605	+	0.539716i	−0.667105	+	0.744964i	$0.732467\pi$
$692$	17.8129			0.677145
$693$	0.475800	+	0.824110i	0.0180742	+	0.0313054i
$694$	0.739525	+	1.28090i	0.0280720	+	0.0486221i
$695$	5.82032	−	10.0811i	0.220777	−	0.382398i
$696$	18.5800			0.704274
$697$		0			0
$698$	−7.03565	−	12.1861i	−0.266303	−	0.461251i
$699$	−25.9852			−0.982849
$700$	0.324030	+	0.561237i	0.0122472	+	0.0212128i
$701$	12.8429	−	22.2445i	0.485069	−	0.840165i	−0.514783	−	0.857320i	$-0.672128\pi$
$701$	12.8429	−	22.2445i	0.485069	−	0.840165i	0.999853	+	0.0171553i	$0.00546097\pi$
$702$	−9.95323	+	17.2395i	−0.375660	+	0.650663i
$703$	4.49629	−	7.78780i	0.169581	−	0.293723i
$704$	1.08613			0.0409351
$705$	8.39500	−	14.5406i	0.316174	−	0.547630i
$706$	−7.36098	+	12.7496i	−0.277034	+	0.479837i
$707$	4.67597	+	8.09902i	0.175858	+	0.304595i
$708$	7.79001	+	13.4927i	0.292766	+	0.507086i
$709$	17.6710			0.663647			0.331823	−	0.943342i	$-0.392336\pi$
$709$	17.6710			0.663647			0.331823	+	0.943342i	$0.392336\pi$
$710$	−2.26581			−0.0850343
$711$	−9.29612	−	16.1014i	−0.348632	−	0.603848i
$712$	4.75839	+	8.24177i	0.178328	+	0.308874i
$713$	−0.734191	+	1.27166i	−0.0274957	+	0.0476239i
$714$		0			0
$715$	6.28870			0.235184
$716$	−5.90645	+	10.2303i	−0.220734	+	0.382323i
$717$	22.3485	−	38.7088i	0.834622	−	1.44561i
$718$	−15.1813	+	26.2948i	−0.566561	+	0.981313i
$719$	20.4003	+	35.3344i	0.760804	+	1.31775i	0.942437	+	0.334385i	$0.108529\pi$
$719$	20.4003	+	35.3344i	0.760804	+	1.31775i	−0.181632	+	0.983367i	$0.558138\pi$
$720$	−1.35194			−0.0503838
$721$	2.16986	+	3.75830i	0.0808097	+	0.139966i
$722$	4.73790	−	8.20628i	0.176326	−	0.305406i
$723$	59.4642			2.21150
$724$	9.34452	−	16.1852i	0.347286	−	0.601518i
$725$	−4.45323	−	7.71321i	−0.165389	−	0.286462i
$726$	10.2432	+	17.7418i	0.380162	+	0.658460i
$727$	42.3249			1.56974			0.784871	−	0.619659i	$-0.212729\pi$
$727$	42.3249			1.56974			0.784871	+	0.619659i	$0.212729\pi$
$728$	−1.87614	−	3.24957i	−0.0695343	−	0.120437i
$729$	6.33710			0.234707
$730$	−5.03031			−0.186180
$731$		0			0
$732$	3.17968			0.117524
$733$	−37.5274			−1.38611			−0.693054	−	0.720886i	$-0.743735\pi$
$733$	−37.5274			−1.38611			−0.693054	+	0.720886i	$0.743735\pi$
$734$	−11.3748	−	19.7018i	−0.419853	−	0.727206i
$735$	13.7268			0.506320
$736$	−1.67597	−	2.90286i	−0.0617771	−	0.107001i
$737$	−4.06967	−	7.04887i	−0.149908	−	0.259649i
$738$	−3.97209	+	6.87986i	−0.146215	+	0.253251i
$739$	10.2462			0.376911			0.188456	−	0.982082i	$-0.439652\pi$
$739$	10.2462			0.376911			0.188456	+	0.982082i	$0.439652\pi$
$740$	−1.45693	+	2.52349i	−0.0535580	+	0.0927652i
$741$	18.6382	+	32.2824i	0.684693	+	1.18592i
$742$	5.75228			0.211173
$743$	−14.9368	−	25.8712i	−0.547977	−	0.949124i	−0.998413	−	0.0563150i	$-0.982065\pi$
$743$	−14.9368	−	25.8712i	−0.547977	−	0.949124i	0.450436	−	0.892809i	$-0.351268\pi$
$744$	−0.456935	+	0.791434i	−0.0167520	+	0.0290154i
$745$	−0.0151563	+	0.0262515i	−0.000555284	+	0.000961780i
$746$	−7.13453	+	12.3574i	−0.261214	+	0.452435i
$747$	5.83255			0.213402
$748$		0			0
$749$	0.713701	−	1.23617i	0.0260781	−	0.0451685i
$750$	1.04307	+	1.80664i	0.0380874	+	0.0659692i
$751$	22.0016	+	38.1079i	0.802851	+	1.39058i	0.917732	+	0.397199i	$0.130018\pi$
$751$	22.0016	+	38.1079i	0.802851	+	1.39058i	−0.114882	+	0.993379i	$0.536649\pi$
$752$	8.04840			0.293495
$753$	−23.8458			−0.868990
$754$	25.7842	+	44.6596i	0.939006	+	1.62641i
$755$	6.21903	+	10.7717i	0.226334	+	0.392022i
$756$	−1.11404	+	1.92957i	−0.0405172	+	0.0701779i
$757$	22.9844	−	39.8101i	0.835382	−	1.44692i	−0.0583377	−	0.998297i	$-0.518580\pi$
$757$	22.9844	−	39.8101i	0.835382	−	1.44692i	0.893719	−	0.448627i	$-0.148087\pi$
$758$	9.08613			0.330023
$759$	−3.79743	+	6.57734i	−0.137838	+	0.238742i
$760$	1.54307	−	2.67267i	0.0559729	−	0.0969478i
$761$	7.16855	−	12.4163i	0.259860	−	0.450090i	−0.706344	−	0.707868i	$-0.749657\pi$
$761$	7.16855	−	12.4163i	0.259860	−	0.450090i	0.966204	+	0.257778i	$0.0829903\pi$
$762$	1.04307	+	1.80664i	0.0377863	+	0.0654477i
$763$	−10.5003			−0.380135
$764$	4.79001	+	8.29654i	0.173296	+	0.300158i
$765$		0			0
$766$	−5.40034			−0.195122
$767$	−21.6210	+	37.4487i	−0.780689	+	1.35219i
$768$	−1.04307	−	1.80664i	−0.0376384	−	0.0651916i
$769$	5.58984	+	9.68189i	0.201575	+	0.349138i	0.949036	−	0.315168i	$-0.102061\pi$
$769$	5.58984	+	9.68189i	0.201575	+	0.349138i	−0.747461	+	0.664305i	$0.768727\pi$
$770$	0.703878			0.0253660
$771$	−12.8950	−	22.3348i	−0.464402	−	0.804368i
$772$	−9.10902			−0.327841
$773$	−3.25839			−0.117196			−0.0585981	−	0.998282i	$-0.518663\pi$
$773$	−3.25839			−0.117196			−0.0585981	+	0.998282i	$0.518663\pi$
$774$	−3.85063	+	7.98533i	−0.138408	+	0.287027i
$775$	0.438069			0.0157359
$776$	6.34452			0.227755
$777$	−1.96969	−	3.41160i	−0.0706621	−	0.122390i
$778$	6.64325			0.238172
$779$	−9.06726	−	15.7050i	−0.324868	−	0.562689i
$780$	−6.03936	−	10.4605i	−0.216244	−	0.374545i
$781$	−1.23048	+	2.13126i	−0.0440301	+	0.0762624i
$782$		0			0
$783$	15.3105	−	26.5186i	0.547153	−	0.947696i
$784$	3.29001	+	5.69846i	0.117500	+	0.203517i
$785$	1.25839			0.0449139
$786$	−10.0558	−	17.4172i	−0.358679	−	0.621250i
$787$	−10.7092	+	18.5489i	−0.381742	+	0.661197i	−0.991311	−	0.131536i	$-0.958009\pi$
$787$	−10.7092	+	18.5489i	−0.381742	+	0.661197i	0.609569	+	0.792733i	$0.291342\pi$
$788$	1.82032	−	3.15289i	0.0648463	−	0.112317i
$789$	−2.63290	+	4.56032i	−0.0937339	+	0.162352i
$790$	−13.7523			−0.489284
$791$	−1.91387	+	3.31492i	−0.0680494	+	0.117865i
$792$	−0.734191	+	1.27166i	−0.0260883	+	0.0451863i
$793$	4.41256	+	7.64279i	0.156695	+	0.271403i
$794$	−11.4381	−	19.8113i	−0.405922	−	0.703077i
$795$	18.5168			0.656723
$796$	−6.78259			−0.240403
$797$	−10.4447	−	18.0908i	−0.369971	−	0.640808i	0.619590	−	0.784926i	$-0.287299\pi$
$797$	−10.4447	−	18.0908i	−0.369971	−	0.640808i	−0.989561	+	0.144118i	$0.953966\pi$
$798$	2.08613	+	3.61328i	0.0738482	+	0.127909i
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−12.8661			−0.454602
$802$	−7.70628	+	13.3477i	−0.272118	+	0.471323i
$803$	−2.73179	+	4.73159i	−0.0964027	+	0.166974i
$804$	−7.81661	+	13.5388i	−0.275671	+	0.477476i
$805$	−1.08613	−	1.88123i	−0.0382811	−	0.0663047i
$806$	−2.53643			−0.0893418
$807$	8.98887	+	15.5692i	0.316423	+	0.548061i
$808$	−7.21533	+	12.4973i	−0.253834	+	0.439654i
$809$	3.24772			0.114184			0.0570919	−	0.998369i	$-0.481817\pi$
$809$	3.24772			0.114184			0.0570919	+	0.998369i	$0.481817\pi$
$810$	−5.61404	+	9.72380i	−0.197257	+	0.341660i
$811$	8.12386	+	14.0709i	0.285267	+	0.494098i	0.972674	−	0.232175i	$-0.0745843\pi$
$811$	8.12386	+	14.0709i	0.285267	+	0.494098i	−0.687407	+	0.726273i	$0.741251\pi$
$812$	2.88596	+	4.99863i	0.101277	+	0.175418i
$813$	−48.9581			−1.71704
$814$	1.58242	+	2.74083i	0.0554638	+	0.0960662i
$815$	−14.1978			−0.497326
$816$		0			0
$817$	−11.3913	−	16.7266i	−0.398531	−	0.585189i
$818$	12.1797			0.425852
$819$	5.07285			0.177260
$820$	2.93807	+	5.08889i	0.102602	+	0.177712i
$821$	−33.9703			−1.18557			−0.592786	−	0.805360i	$-0.701972\pi$
$821$	−33.9703			−1.18557			−0.592786	+	0.805360i	$0.701972\pi$
$822$	3.83177	+	6.63682i	0.133648	+	0.231486i
$823$	9.07500	+	15.7184i	0.316335	+	0.547908i	0.979720	−	0.200370i	$-0.0642144\pi$
$823$	9.07500	+	15.7184i	0.316335	+	0.547908i	−0.663386	+	0.748278i	$0.730881\pi$
$824$	−3.34823	+	5.79930i	−0.116641	+	0.202028i
$825$	2.26581			0.0788853
$826$	−2.41998	+	4.19153i	−0.0842020	+	0.145842i
$827$	7.07631	+	12.2565i	0.246067	+	0.426201i	0.962431	−	0.271526i	$-0.0875282\pi$
$827$	7.07631	+	12.2565i	0.246067	+	0.426201i	−0.716364	+	0.697727i	$0.754195\pi$
$828$	4.53162			0.157485
$829$	8.39741	+	14.5447i	0.291654	+	0.505160i	0.974201	−	0.225682i	$-0.0724611\pi$
$829$	8.39741	+	14.5447i	0.291654	+	0.505160i	−0.682547	+	0.730842i	$0.739128\pi$
$830$	2.15710	−	3.73621i	0.0748742	−	0.129686i
$831$	−15.1419	+	26.2266i	−0.525268	+	0.909791i
$832$	2.89500	−	5.01429i	0.100366	−	0.173839i
$833$		0			0
$834$	−12.1419	+	21.0305i	−0.420441	+	0.728226i
$835$	4.72808	−	8.18927i	0.163622	−	0.283401i
$836$	−1.67597	−	2.90286i	−0.0579646	−	0.100398i
$837$	0.753056	+	1.30433i	0.0260294	+	0.0450843i
$838$	2.68904			0.0928914
$839$	−25.1877			−0.869577			−0.434789	−	0.900533i	$-0.643177\pi$
$839$	−25.1877			−0.869577			−0.434789	+	0.900533i	$0.643177\pi$
$840$	−0.675970	−	1.17081i	−0.0233232	−	0.0403969i
$841$	−25.1624	−	43.5826i	−0.867670	−	1.50285i
$842$	0.567265	−	0.982531i	0.0195492	−	0.0338603i
$843$	−22.5094	+	38.9874i	−0.775264	+	1.34280i
$844$	−9.43065			−0.324616
$845$	10.2621	−	17.7745i	0.353027	−	0.611461i
$846$	−5.44047	+	9.42318i	−0.187047	+	0.323975i
$847$	−3.18208	+	5.51153i	−0.109338	+	0.189378i
$848$	4.43807	+	7.68696i	0.152404	+	0.263971i
$849$	41.7226			1.43192
$850$		0			0
$851$	4.88356	−	8.45857i	0.167406	−	0.289956i
$852$	4.72677			0.161937
$853$	11.5537	−	20.0117i	0.395592	−	0.685186i	−0.597584	−	0.801806i	$-0.703873\pi$
$853$	11.5537	−	20.0117i	0.395592	−	0.685186i	0.993177	+	0.116620i	$0.0372060\pi$
$854$	0.493887	+	0.855437i	0.0169005	+	0.0292725i
$855$	2.08613	+	3.61328i	0.0713441	+	0.123572i
$856$	2.20257			0.0752824
$857$	−16.1329	−	27.9430i	−0.551090	−	0.954515i	−0.998196	−	0.0600345i	$-0.980879\pi$
$857$	−16.1329	−	27.9430i	−0.551090	−	0.954515i	0.447107	−	0.894481i	$-0.352454\pi$
$858$	−13.1191			−0.447877
$859$	−16.9516			−0.578381			−0.289191	−	0.957272i	$-0.593386\pi$
$859$	−16.9516			−0.578381			−0.289191	+	0.957272i	$0.593386\pi$
$860$	3.69113	+	5.41993i	0.125866	+	0.184818i
$861$	−7.94418			−0.270737
$862$	16.6858			0.568320
$863$	−26.5144	−	45.9242i	−0.902560	−	1.56328i	−0.824160	−	0.566358i	$-0.808352\pi$
$863$	−26.5144	−	45.9242i	−0.902560	−	1.56328i	−0.0784003	−	0.996922i	$-0.524981\pi$
$864$	−3.43807			−0.116965
$865$	8.90645	+	15.4264i	0.302828	+	0.524514i
$866$	14.7916	+	25.6199i	0.502640	+	0.870598i
$867$	17.7321	−	30.7129i	0.602214	−	1.04307i
$868$	−0.283896			−0.00963604
$869$	−7.46838	+	12.9356i	−0.253348	+	0.438811i
$870$	9.29001	+	16.0908i	0.314961	+	0.545528i
$871$	−43.3897			−1.47020
$872$	−8.10129	−	14.0318i	−0.274344	−	0.475178i
$873$	−4.28870	+	7.42825i	−0.145151	+	0.251408i
$874$	−5.17226	+	8.95862i	−0.174954	+	0.303030i
$875$	−0.324030	+	0.561237i	−0.0109542	+	0.0189733i
$876$	10.4939			0.354556
$877$	12.7571	−	22.0959i	0.430776	−	0.746126i	−0.566164	−	0.824293i	$-0.691573\pi$
$877$	12.7571	−	22.0959i	0.430776	−	0.746126i	0.996940	+	0.0781663i	$0.0249065\pi$
$878$	−2.82032	+	4.88494i	−0.0951812	+	0.164859i
$879$	−32.6284	−	56.5141i	−1.10053	−	1.90617i
$880$	0.543065	+	0.940616i	0.0183067	+	0.0317082i
$881$	−56.0288			−1.88766			−0.943828	−	0.330436i	$-0.892804\pi$
$881$	−56.0288			−1.88766			−0.943828	+	0.330436i	$0.892804\pi$
$882$	−8.89578			−0.299537
$883$	24.3703	+	42.2107i	0.820127	+	1.42050i	0.905587	+	0.424161i	$0.139431\pi$
$883$	24.3703	+	42.2107i	0.820127	+	1.42050i	−0.0854595	+	0.996342i	$0.527236\pi$
$884$		0			0
$885$	−7.79001	+	13.4927i	−0.261858	+	0.453552i
$886$	−1.69113	+	2.92912i	−0.0568145	+	0.0984056i
$887$	43.9655			1.47622			0.738109	−	0.674682i	$-0.235719\pi$
$887$	43.9655			1.47622			0.738109	+	0.674682i	$0.235719\pi$
$888$	3.03936	−	5.26432i	0.101994	−	0.176659i
$889$	−0.324030	+	0.561237i	−0.0108676	+	0.0188233i
$890$	−4.75839	+	8.24177i	−0.159502	+	0.276265i
$891$	6.09758	+	10.5613i	0.204277	+	0.353817i
$892$	12.9442			0.433403
$893$	−12.4192	−	21.5107i	−0.415593	−	0.719828i
$894$	0.0316180	−	0.0547640i	0.00105746	−	0.00183158i
$895$	−11.8129			−0.394862
$896$	0.324030	−	0.561237i	0.0108251	−	0.0187496i
$897$	20.2436	+	35.0629i	0.675913	+	1.17071i
$898$	16.5410	+	28.6498i	0.551980	+	0.956057i
$899$	3.90164			0.130127
$900$	−0.675970	−	1.17081i	−0.0225323	−	0.0390271i
$901$		0			0
$902$	6.38225			0.212506
$903$	−8.84081	+	0.657916i	−0.294204	+	0.0218941i
$904$	−5.90645			−0.196446
$905$	18.6890			0.621245
$906$	−12.9737	−	22.4711i	−0.431023	−	0.746553i
$907$	−22.7039			−0.753870			−0.376935	−	0.926240i	$-0.623022\pi$
$907$	−22.7039			−0.753870			−0.376935	+	0.926240i	$0.623022\pi$
$908$	−2.42532	−	4.20077i	−0.0804870	−	0.139408i
$909$	−9.75468	−	16.8956i	−0.323542	−	0.560392i
$910$	1.87614	−	3.24957i	0.0621934	−	0.107722i
$911$	−43.1271			−1.42886			−0.714432	−	0.699704i	$-0.753315\pi$
$911$	−43.1271			−1.42886			−0.714432	+	0.699704i	$0.753315\pi$
$912$	−3.21903	+	5.57553i	−0.106593	+	0.184624i
$913$	−2.34290	−	4.05801i	−0.0775385	−	0.134301i
$914$	−31.3929			−1.03839
$915$	1.58984	+	2.75368i	0.0525585	+	0.0910339i
$916$	13.0332	−	22.5742i	0.430630	−	0.745874i
$917$	3.12386	−	5.41069i	0.103159	−	0.178677i
$918$		0			0
$919$	44.0213			1.45213			0.726065	−	0.687626i	$-0.241347\pi$
$919$	44.0213			1.45213			0.726065	+	0.687626i	$0.241347\pi$
$920$	1.67597	−	2.90286i	0.0552551	−	0.0957046i
$921$	−34.6197	+	59.9631i	−1.14076	+	1.97585i
$922$	1.89871	+	3.28867i	0.0625308	+	0.108307i
$923$	6.55953	+	11.3614i	0.215909	+	0.373966i
$924$	−1.46838			−0.0483062
$925$	−2.91387			−0.0958074
$926$	−11.2318	−	19.4540i	−0.369099	−	0.639299i
$927$	−4.52660	−	7.84031i	−0.148673	−	0.257509i
$928$	−4.45323	+	7.71321i	−0.146184	+	0.253199i
$929$	−24.7547	+	42.8764i	−0.812175	+	1.40673i	0.0991642	+	0.995071i	$0.468383\pi$
$929$	−24.7547	+	42.8764i	−0.812175	+	1.40673i	−0.911339	+	0.411657i	$0.864950\pi$
$930$	−0.913870			−0.0299670
$931$	10.1534	−	17.5862i	0.332764	−	0.576364i
$932$	6.22808	−	10.7873i	0.204007	−	0.353351i
$933$	18.7752	−	32.5196i	0.614672	−	1.06464i
$934$	−21.4865	−	37.2157i	−0.703059	−	1.21773i
$935$		0			0
$936$	3.91387	+	6.77902i	0.127929	+	0.221579i
$937$	3.34452	−	5.79288i	0.109261	−	0.189245i	−0.806210	−	0.591629i	$-0.798485\pi$
$937$	3.34452	−	5.79288i	0.109261	−	0.189245i	0.915471	+	0.402384i	$0.131818\pi$
$938$	−4.85649			−0.158570
$939$	−23.7005	+	41.0505i	−0.773436	+	1.33963i
$940$	4.02420	+	6.97012i	0.131255	+	0.227340i
$941$	16.6866	+	28.9021i	0.543969	+	0.942182i	0.998671	+	0.0515381i	$0.0164124\pi$
$941$	16.6866	+	28.9021i	0.543969	+	0.942182i	−0.454702	+	0.890644i	$0.650254\pi$
$942$	−2.62517			−0.0855326
$943$	−9.84823	−	17.0576i	−0.320702	−	0.555473i
$944$	−7.46838			−0.243075
$945$	−2.22808			−0.0724794
$946$	7.10259	−	0.528561i	0.230925	−	0.0171850i
$947$	−37.3026			−1.21217			−0.606086	−	0.795399i	$-0.707261\pi$
$947$	−37.3026			−1.21217			−0.606086	+	0.795399i	$0.707261\pi$
$948$	28.6890			0.931777
$949$	14.5628	+	25.2235i	0.472728	+	0.818788i
$950$	3.08613			0.100127
$951$	15.6571	+	27.1189i	0.507716	+	0.879391i
$952$		0			0
$953$	−6.62679	+	11.4779i	−0.214663	+	0.371807i	−0.953168	−	0.302441i	$-0.902199\pi$
$953$	−6.62679	+	11.4779i	−0.214663	+	0.371807i	0.738505	+	0.674248i	$0.235532\pi$
$954$	−12.0000			−0.388514
$955$	−4.79001	+	8.29654i	−0.155001	+	0.268470i
$956$	10.7129	+	18.5553i	0.346481	+	0.600122i
$957$	20.1803			0.652337
$958$	18.7449	+	32.4670i	0.605619	+	1.04896i
$959$	−1.19035	+	2.06174i	−0.0384383	+	0.0665771i
$960$	1.04307	−	1.80664i	0.0336648	−	0.0583091i
$961$	15.4040	−	26.6806i	0.496905	−	0.860664i
$962$	16.8713			0.543954
$963$	−1.48887	+	2.57880i	−0.0479782	+	0.0831008i
$964$	−14.2523	+	24.6857i	−0.459035	+	0.795072i
$965$	−4.55451	−	7.88865i	−0.146615	−	0.253945i
$966$	2.26581	+	3.92450i	0.0729012	+	0.126269i
$967$	50.1016			1.61116			0.805580	−	0.592488i	$-0.201854\pi$
$967$	50.1016			1.61116			0.805580	+	0.592488i	$0.201854\pi$
$968$	−9.82032			−0.315637
$969$		0			0
$970$	3.17226	+	5.49452i	0.101855	+	0.176418i
$971$	−1.04918	+	1.81723i	−0.0336697	+	0.0583177i	−0.882369	−	0.470558i	$-0.844053\pi$
$971$	−1.04918	+	1.81723i	−0.0336697	+	0.0583177i	0.848700	+	0.528875i	$0.177386\pi$
$972$	6.55451	−	11.3527i	0.210236	−	0.364140i
$973$	−7.54384			−0.241845
$974$	−20.6345	+	35.7401i	−0.661173	+	1.14519i
$975$	6.03936	−	10.4605i	0.193414	−	0.335003i
$976$	−0.762100	+	1.32000i	−0.0243942	+	0.0422520i
$977$	21.7177	+	37.6162i	0.694812	+	1.20345i	0.970244	+	0.242129i	$0.0778456\pi$
$977$	21.7177	+	37.6162i	0.694812	+	1.20345i	−0.275432	+	0.961320i	$0.588821\pi$
$978$	29.6184			0.947092
$979$	5.16823	+	8.95164i	0.165177	+	0.286096i
$980$	−3.29001	+	5.69846i	−0.105095	+	0.182031i
$981$	21.9049			0.699369
$982$	−2.10500	+	3.64596i	−0.0671731	+	0.116347i
$983$	−6.39338	−	11.0737i	−0.203917	−	0.353195i	0.745870	−	0.666091i	$-0.232034\pi$
$983$	−6.39338	−	11.0737i	−0.203917	−	0.353195i	−0.949787	+	0.312897i	$0.898701\pi$
$984$	−6.12920	−	10.6161i	−0.195392	−	0.338428i
$985$	3.64064			0.116001
$986$		0			0
$987$	−10.8809			−0.346344
$988$	−17.8687			−0.568480
$989$	−12.3724	−	18.1673i	−0.393420	−	0.577685i
$990$	−1.46838			−0.0466682
$991$	30.9878			0.984359			0.492180	−	0.870494i	$-0.336200\pi$
$991$	30.9878			0.984359			0.492180	+	0.870494i	$0.336200\pi$
$992$	−0.219035	−	0.379379i	−0.00695436	−	0.0120453i
$993$	−40.4562			−1.28384
$994$	0.734191	+	1.27166i	0.0232871	+	0.0403345i
$995$	−3.39130	−	5.87390i	−0.107511	−	0.186215i
$996$	−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	$0.397424\pi$
$998$	−9.01145	+	15.6083i	−0.285252	+	0.494072i
$999$	−5.00904	−	8.67592i	−0.158479	−	0.274494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.e.251.1	yes	6
43.6	even	3	inner	430.2.e.e.221.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.e.221.1	✓	6	43.6	even	3	inner
430.2.e.e.251.1	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.04307 - 1.80664i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.80664i) q^{6} +(0.324030 - 0.561237i) q^{7} +1.00000 q^{8} +(-0.675970 + 1.17081i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.04307 - 1.80664i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.80664i) q^{6} +(0.324030 - 0.561237i) q^{7} +1.00000 q^{8} +(-0.675970 + 1.17081i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.08613 q^{11} +(-1.04307 - 1.80664i) q^{12} +(2.89500 - 5.01429i) q^{13} +(0.324030 - 0.561237i) q^{14} +(1.04307 - 1.80664i) q^{15} +1.00000 q^{16} +(-0.675970 + 1.17081i) q^{18} +(-1.54307 - 2.67267i) q^{19} +(0.500000 + 0.866025i) q^{20} -1.35194 q^{21} +1.08613 q^{22} +(-1.67597 - 2.90286i) q^{23} +(-1.04307 - 1.80664i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.89500 - 5.01429i) q^{26} -3.43807 q^{27} +(0.324030 - 0.561237i) q^{28} +(-4.45323 + 7.71321i) q^{29} +(1.04307 - 1.80664i) q^{30} +(-0.219035 - 0.379379i) q^{31} +1.00000 q^{32} +(-1.13290 - 1.96225i) q^{33} +0.648061 q^{35} +(-0.675970 + 1.17081i) q^{36} +(1.45693 + 2.52349i) q^{37} +(-1.54307 - 2.67267i) q^{38} -12.0787 q^{39} +(0.500000 + 0.866025i) q^{40} +5.87614 q^{41} -1.35194 q^{42} +(6.53936 - 0.486646i) q^{43} +1.08613 q^{44} -1.35194 q^{45} +(-1.67597 - 2.90286i) q^{46} +8.04840 q^{47} +(-1.04307 - 1.80664i) q^{48} +(3.29001 + 5.69846i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.89500 - 5.01429i) q^{52} +(4.43807 + 7.68696i) q^{53} -3.43807 q^{54} +(0.543065 + 0.940616i) q^{55} +(0.324030 - 0.561237i) q^{56} +(-3.21903 + 5.57553i) q^{57} +(-4.45323 + 7.71321i) q^{58} -7.46838 q^{59} +(1.04307 - 1.80664i) q^{60} +(-0.762100 + 1.32000i) q^{61} +(-0.219035 - 0.379379i) q^{62} +(0.438069 + 0.758758i) q^{63} +1.00000 q^{64} +5.79001 q^{65} +(-1.13290 - 1.96225i) q^{66} +(-3.74694 - 6.48990i) q^{67} +(-3.49629 + 6.05575i) q^{69} +0.648061 q^{70} +(-1.13290 + 1.96225i) q^{71} +(-0.675970 + 1.17081i) q^{72} +(-2.51516 + 4.35638i) q^{73} +(1.45693 + 2.52349i) q^{74} +2.08613 q^{75} +(-1.54307 - 2.67267i) q^{76} +(0.351939 - 0.609577i) q^{77} -12.0787 q^{78} +(-6.87614 + 11.9098i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.61404 + 9.72380i) q^{81} +5.87614 q^{82} +(-2.15710 - 3.73621i) q^{83} -1.35194 q^{84} +(6.53936 - 0.486646i) q^{86} +18.5800 q^{87} +1.08613 q^{88} +(4.75839 + 8.24177i) q^{89} -1.35194 q^{90} +(-1.87614 - 3.24957i) q^{91} +(-1.67597 - 2.90286i) q^{92} +(-0.456935 + 0.791434i) q^{93} +8.04840 q^{94} +(1.54307 - 2.67267i) q^{95} +(-1.04307 - 1.80664i) q^{96} +6.34452 q^{97} +(3.29001 + 5.69846i) q^{98} +(-0.734191 + 1.27166i) 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

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