LMFDB - Embedded newform 630.2.i.h.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 36 x^{8} - 24 x^{7} + 33 x^{6} + 42 x^{5} + 114 x^{4} + \cdots + 79 $ x^12 - 5x^11 + 14x^10 - 28x^9 + 36x^8 - 24x^7 + 33x^6 + 42x^5 + 114x^4 + 104x^3 + 197x^2 + 166*x + 79
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.6
Root			$0.737753 + 1.71208i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.h.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.73202 - 0.0100417i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73202 - 0.0100417i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(2.99980 - 0.0347849i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.73202 - 0.0100417i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73202 - 0.0100417i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(2.99980 - 0.0347849i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.771481 + 1.33624i) q^{11} +(1.73202 - 0.0100417i) q^{12} +(-3.10276 - 5.37414i) q^{13} +(-0.710533 + 2.54856i) q^{14} +(0.857314 - 1.50500i) q^{15} +1.00000 q^{16} +(2.90844 - 5.03756i) q^{17} +(2.99980 - 0.0347849i) q^{18} +(3.46705 + 6.00511i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.20507 + 4.42129i) q^{21} +(0.771481 + 1.33624i) q^{22} +(-3.62333 + 6.27579i) q^{23} +(1.73202 - 0.0100417i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.10276 - 5.37414i) q^{26} +(5.19537 - 0.0903714i) q^{27} +(-0.710533 + 2.54856i) q^{28} +(-1.25691 + 2.17703i) q^{29} +(0.857314 - 1.50500i) q^{30} -8.09078 q^{31} +1.00000 q^{32} +(1.34964 + 2.30666i) q^{33} +(2.90844 - 5.03756i) q^{34} +(1.85185 + 1.88962i) q^{35} +(2.99980 - 0.0347849i) q^{36} +(-4.38024 - 7.58679i) q^{37} +(3.46705 + 6.00511i) q^{38} +(-5.42801 - 9.27696i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.70890 - 2.95990i) q^{41} +(-1.20507 + 4.42129i) q^{42} +(2.75052 - 4.76404i) q^{43} +(0.771481 + 1.33624i) q^{44} +(1.46977 - 2.61529i) q^{45} +(-3.62333 + 6.27579i) q^{46} +5.63858 q^{47} +(1.73202 - 0.0100417i) q^{48} +(-5.99028 - 3.62167i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.98689 - 8.75437i) q^{51} +(-3.10276 - 5.37414i) q^{52} +(-2.96378 + 5.13341i) q^{53} +(5.19537 - 0.0903714i) q^{54} +1.54296 q^{55} +(-0.710533 + 2.54856i) q^{56} +(6.06531 + 10.3662i) q^{57} +(-1.25691 + 2.17703i) q^{58} -8.45100 q^{59} +(0.857314 - 1.50500i) q^{60} +4.82092 q^{61} -8.09078 q^{62} +(-2.04281 + 7.66987i) q^{63} +1.00000 q^{64} -6.20552 q^{65} +(1.34964 + 2.30666i) q^{66} -2.09156 q^{67} +(2.90844 - 5.03756i) q^{68} +(-6.21267 + 10.9062i) q^{69} +(1.85185 + 1.88962i) q^{70} -7.31869 q^{71} +(2.99980 - 0.0347849i) q^{72} +(-1.97220 + 3.41595i) q^{73} +(-4.38024 - 7.58679i) q^{74} +(-0.874707 - 1.49495i) q^{75} +(3.46705 + 6.00511i) q^{76} +(-3.95366 + 1.01672i) q^{77} +(-5.42801 - 9.27696i) q^{78} -2.25380 q^{79} +(0.500000 - 0.866025i) q^{80} +(8.99758 - 0.208696i) q^{81} +(-1.70890 - 2.95990i) q^{82} +(-4.13650 + 7.16463i) q^{83} +(-1.20507 + 4.42129i) q^{84} +(-2.90844 - 5.03756i) q^{85} +(2.75052 - 4.76404i) q^{86} +(-2.15513 + 3.78328i) q^{87} +(0.771481 + 1.33624i) q^{88} +(2.13541 + 3.69864i) q^{89} +(1.46977 - 2.61529i) q^{90} +(15.9009 - 4.08906i) q^{91} +(-3.62333 + 6.27579i) q^{92} +(-14.0134 + 0.0812453i) q^{93} +5.63858 q^{94} +6.93410 q^{95} +(1.73202 - 0.0100417i) q^{96} +(6.52492 - 11.3015i) q^{97} +(-5.99028 - 3.62167i) q^{98} +(2.36077 + 3.98163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	1.73202	−	0.0100417i	0.999983	−	0.00579759i
$3$	1.73202	−	0.0100417i	0.999983	−	0.00579759i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.73202	−	0.0100417i	0.707095	−	0.00409951i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$8$	1.00000			0.353553
$9$	2.99980	−	0.0347849i	0.999933	−	0.0115950i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.771481	+	1.33624i	0.232610	+	0.402893i	0.958576	−	0.284839i	$-0.0919400\pi$
$11$	0.771481	+	1.33624i	0.232610	+	0.402893i	−0.725965	+	0.687731i	$0.758607\pi$
$12$	1.73202	−	0.0100417i	0.499992	−	0.00289879i
$13$	−3.10276	−	5.37414i	−0.860551	−	1.49052i	−0.871398	−	0.490576i	$-0.836786\pi$
$13$	−3.10276	−	5.37414i	−0.860551	−	1.49052i	0.0108477	−	0.999941i	$-0.496547\pi$
$14$	−0.710533	+	2.54856i	−0.189898	+	0.681130i
$15$	0.857314	−	1.50500i	0.221358	−	0.388588i
$16$	1.00000			0.250000
$17$	2.90844	−	5.03756i	0.705399	−	1.22179i	−0.261148	−	0.965299i	$-0.584101\pi$
$17$	2.90844	−	5.03756i	0.705399	−	1.22179i	0.966547	−	0.256489i	$-0.0825656\pi$
$18$	2.99980	−	0.0347849i	0.707059	−	0.00819889i
$19$	3.46705	+	6.00511i	0.795396	+	1.37767i	0.922588	+	0.385788i	$0.126070\pi$
$19$	3.46705	+	6.00511i	0.795396	+	1.37767i	−0.127192	+	0.991878i	$0.540596\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.20507	+	4.42129i	−0.262967	+	0.964805i
$22$	0.771481	+	1.33624i	0.164480	+	0.284888i
$23$	−3.62333	+	6.27579i	−0.755516	+	1.30859i	0.189601	+	0.981861i	$0.439281\pi$
$23$	−3.62333	+	6.27579i	−0.755516	+	1.30859i	−0.945117	+	0.326732i	$0.894053\pi$
$24$	1.73202	−	0.0100417i	0.353547	−	0.00204976i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.10276	−	5.37414i	−0.608501	−	1.05395i
$27$	5.19537	−	0.0903714i	0.999849	−	0.0173920i
$28$	−0.710533	+	2.54856i	−0.134278	+	0.481632i
$29$	−1.25691	+	2.17703i	−0.233402	+	0.404264i	−0.958807	−	0.284058i	$-0.908319\pi$
$29$	−1.25691	+	2.17703i	−0.233402	+	0.404264i	0.725405	+	0.688322i	$0.241652\pi$
$30$	0.857314	−	1.50500i	0.156523	−	0.274773i
$31$	−8.09078			−1.45315			−0.726573	−	0.687089i	$-0.758888\pi$
$31$	−8.09078			−1.45315			−0.726573	+	0.687089i	$0.758888\pi$
$32$	1.00000			0.176777
$33$	1.34964	+	2.30666i	0.234942	+	0.401538i
$34$	2.90844	−	5.03756i	0.498793	−	0.863934i
$35$	1.85185	+	1.88962i	0.313020	+	0.319404i
$36$	2.99980	−	0.0347849i	0.499966	−	0.00579749i
$37$	−4.38024	−	7.58679i	−0.720106	−	1.24726i	−0.960957	−	0.276699i	$-0.910760\pi$
$37$	−4.38024	−	7.58679i	−0.720106	−	1.24726i	0.240850	−	0.970562i	$-0.422574\pi$
$38$	3.46705	+	6.00511i	0.562430	+	0.974157i
$39$	−5.42801	−	9.27696i	−0.869178	−	1.48550i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−1.70890	−	2.95990i	−0.266885	−	0.462258i	0.701171	−	0.712993i	$-0.252661\pi$
$41$	−1.70890	−	2.95990i	−0.266885	−	0.462258i	−0.968056	+	0.250735i	$0.919328\pi$
$42$	−1.20507	+	4.42129i	−0.185946	+	0.682220i
$43$	2.75052	−	4.76404i	0.419450	−	0.726509i	−0.576434	−	0.817144i	$-0.695556\pi$
$43$	2.75052	−	4.76404i	0.419450	−	0.726509i	0.995884	+	0.0906345i	$0.0288895\pi$
$44$	0.771481	+	1.33624i	0.116305	+	0.201446i
$45$	1.46977	−	2.61529i	0.219101	−	0.389865i
$46$	−3.62333	+	6.27579i	−0.534231	+	0.925315i
$47$	5.63858			0.822471			0.411236	−	0.911529i	$-0.365097\pi$
$47$	5.63858			0.822471			0.411236	+	0.911529i	$0.365097\pi$
$48$	1.73202	−	0.0100417i	0.249996	−	0.00144940i
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	4.98689	−	8.75437i	0.698304	−	1.22586i
$52$	−3.10276	−	5.37414i	−0.430275	−	0.745259i
$53$	−2.96378	+	5.13341i	−0.407106	+	0.705129i	−0.994564	−	0.104126i	$-0.966795\pi$
$53$	−2.96378	+	5.13341i	−0.407106	+	0.705129i	0.587458	+	0.809255i	$0.300129\pi$
$54$	5.19537	−	0.0903714i	0.707000	−	0.0122980i
$55$	1.54296			0.208053
$56$	−0.710533	+	2.54856i	−0.0949490	+	0.340565i
$57$	6.06531	+	10.3662i	0.803369	+	1.37303i
$58$	−1.25691	+	2.17703i	−0.165040	+	0.285858i
$59$	−8.45100			−1.10023			−0.550113	−	0.835090i	$-0.685415\pi$
$59$	−8.45100			−1.10023			−0.550113	+	0.835090i	$0.685415\pi$
$60$	0.857314	−	1.50500i	0.110679	−	0.194294i
$61$	4.82092			0.617256			0.308628	−	0.951183i	$-0.400130\pi$
$61$	4.82092			0.617256			0.308628	+	0.951183i	$0.400130\pi$
$62$	−8.09078			−1.02753
$63$	−2.04281	+	7.66987i	−0.257369	+	0.966313i
$64$	1.00000			0.125000
$65$	−6.20552			−0.769700
$66$	1.34964	+	2.30666i	0.166129	+	0.283930i
$67$	−2.09156			−0.255525			−0.127762	−	0.991805i	$-0.540780\pi$
$67$	−2.09156			−0.255525			−0.127762	+	0.991805i	$0.540780\pi$
$68$	2.90844	−	5.03756i	0.352700	−	0.610894i
$69$	−6.21267	+	10.9062i	−0.747917	+	1.31295i
$70$	1.85185	+	1.88962i	0.221338	+	0.225853i
$71$	−7.31869			−0.868569			−0.434285	−	0.900776i	$-0.642999\pi$
$71$	−7.31869			−0.868569			−0.434285	+	0.900776i	$0.642999\pi$
$72$	2.99980	−	0.0347849i	0.353530	−	0.00409944i
$73$	−1.97220	+	3.41595i	−0.230829	+	0.399807i	−0.958052	−	0.286594i	$-0.907477\pi$
$73$	−1.97220	+	3.41595i	−0.230829	+	0.399807i	0.727223	+	0.686401i	$0.240810\pi$
$74$	−4.38024	−	7.58679i	−0.509192	−	0.881947i
$75$	−0.874707	−	1.49495i	−0.101002	−	0.172622i
$76$	3.46705	+	6.00511i	0.397698	+	0.688833i
$77$	−3.95366	+	1.01672i	−0.450561	+	0.115866i
$78$	−5.42801	−	9.27696i	−0.614601	−	1.05041i
$79$	−2.25380			−0.253572			−0.126786	−	0.991930i	$-0.540466\pi$
$79$	−2.25380			−0.253572			−0.126786	+	0.991930i	$0.540466\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	8.99758	−	0.208696i	0.999731	−	0.0231884i
$82$	−1.70890	−	2.95990i	−0.188716	−	0.326866i
$83$	−4.13650	+	7.16463i	−0.454040	+	0.786421i	−0.998632	−	0.0522804i	$-0.983351\pi$
$83$	−4.13650	+	7.16463i	−0.454040	+	0.786421i	0.544592	+	0.838701i	$0.316684\pi$
$84$	−1.20507	+	4.42129i	−0.131484	+	0.482402i
$85$	−2.90844	−	5.03756i	−0.315464	−	0.546400i
$86$	2.75052	−	4.76404i	0.296596	−	0.513720i
$87$	−2.15513	+	3.78328i	−0.231054	+	0.405610i
$88$	0.771481	+	1.33624i	0.0822402	+	0.142444i
$89$	2.13541	+	3.69864i	0.226353	+	0.392055i	0.956725	−	0.290995i	$-0.0939863\pi$
$89$	2.13541	+	3.69864i	0.226353	+	0.392055i	−0.730371	+	0.683050i	$0.760653\pi$
$90$	1.46977	−	2.61529i	0.154928	−	0.275676i
$91$	15.9009	−	4.08906i	1.66687	−	0.428649i
$92$	−3.62333	+	6.27579i	−0.377758	+	0.654296i
$93$	−14.0134	+	0.0812453i	−1.45312	+	0.00842474i
$94$	5.63858			0.581575
$95$	6.93410			0.711424
$96$	1.73202	−	0.0100417i	0.176774	−	0.00102488i
$97$	6.52492	−	11.3015i	0.662505	−	1.14749i	−0.317451	−	0.948275i	$-0.602827\pi$
$97$	6.52492	−	11.3015i	0.662505	−	1.14749i	0.979955	−	0.199217i	$-0.0638399\pi$
$98$	−5.99028	−	3.62167i	−0.605110	−	0.365844i
$99$	2.36077	+	3.98163i	0.237266	+	0.400169i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	0.549052	+	0.950986i	0.0546327	+	0.0946266i	0.892048	−	0.451940i	$-0.149268\pi$
$101$	0.549052	+	0.950986i	0.0546327	+	0.0946266i	−0.837416	+	0.546567i	$0.815935\pi$
$102$	4.98689	−	8.75437i	0.493775	−	0.866811i
$103$	3.68749	−	6.38692i	0.363339	−	0.629321i	−0.625169	−	0.780489i	$-0.714970\pi$
$103$	3.68749	−	6.38692i	0.363339	−	0.629321i	0.988508	+	0.151168i	$0.0483034\pi$
$104$	−3.10276	−	5.37414i	−0.304251	−	0.526977i
$105$	3.22642	+	3.25426i	0.314866	+	0.317584i
$106$	−2.96378	+	5.13341i	−0.287868	+	0.498601i
$107$	−2.12699	−	3.68406i	−0.205624	−	0.356151i	0.744707	−	0.667391i	$-0.232589\pi$
$107$	−2.12699	−	3.68406i	−0.205624	−	0.356151i	−0.950331	+	0.311240i	$0.899256\pi$
$108$	5.19537	−	0.0903714i	0.499924	−	0.00869599i
$109$	−7.57730	+	13.1243i	−0.725773	+	1.25708i	0.232882	+	0.972505i	$0.425185\pi$
$109$	−7.57730	+	13.1243i	−0.725773	+	1.25708i	−0.958655	+	0.284571i	$0.908149\pi$
$110$	1.54296			0.147116
$111$	−7.66285	−	13.0965i	−0.727325	−	1.24307i
$112$	−0.710533	+	2.54856i	−0.0671391	+	0.240816i
$113$	8.11693	+	14.0589i	0.763577	+	1.32255i	0.940996	+	0.338418i	$0.109892\pi$
$113$	8.11693	+	14.0589i	0.763577	+	1.32255i	−0.177419	+	0.984135i	$0.556775\pi$
$114$	6.06531	+	10.3662i	0.568068	+	0.970880i
$115$	3.62333	+	6.27579i	0.337877	+	0.585221i
$116$	−1.25691	+	2.17703i	−0.116701	+	0.202132i
$117$	−9.49459	−	16.0134i	−0.877775	−	1.48044i
$118$	−8.45100			−0.777977
$119$	10.7720	+	10.9917i	0.987464	+	1.00760i
$120$	0.857314	−	1.50500i	0.0782617	−	0.137387i
$121$	4.30963	−	7.46450i	0.391785	−	0.678591i
$122$	4.82092			0.436466
$123$	−2.98957	−	5.10945i	−0.269560	−	0.460703i
$124$	−8.09078			−0.726573
$125$	−1.00000			−0.0894427
$126$	−2.04281	+	7.66987i	−0.181988	+	0.683287i
$127$	−7.19028			−0.638034			−0.319017	−	0.947749i	$-0.603353\pi$
$127$	−7.19028			−0.638034			−0.319017	+	0.947749i	$0.603353\pi$
$128$	1.00000			0.0883883
$129$	4.71612	−	8.27904i	0.415231	−	0.728929i
$130$	−6.20552			−0.544260
$131$	−4.49687	+	7.78881i	−0.392893	+	0.680511i	−0.992830	−	0.119536i	$-0.961859\pi$
$131$	−4.49687	+	7.78881i	−0.392893	+	0.680511i	0.599936	+	0.800048i	$0.295193\pi$
$132$	1.34964	+	2.30666i	0.117471	+	0.200769i
$133$	−17.7678	+	4.56915i	−1.54066	+	0.396195i
$134$	−2.09156			−0.180683
$135$	2.51942	−	4.54451i	0.216837	−	0.391129i
$136$	2.90844	−	5.03756i	0.249396	−	0.431967i
$137$	−3.43969	−	5.95772i	−0.293873	−	0.509002i	0.680849	−	0.732423i	$-0.261611\pi$
$137$	−3.43969	−	5.95772i	−0.293873	−	0.509002i	−0.974722	+	0.223421i	$0.928277\pi$
$138$	−6.21267	+	10.9062i	−0.528857	+	0.928397i
$139$	−9.10281	−	15.7665i	−0.772090	−	1.33730i	−0.936416	−	0.350893i	$-0.885878\pi$
$139$	−9.10281	−	15.7665i	−0.772090	−	1.33730i	0.164325	−	0.986406i	$-0.447455\pi$
$140$	1.85185	+	1.88962i	0.156510	+	0.159702i
$141$	9.76614	−	0.0566210i	0.822457	−	0.00476835i
$142$	−7.31869			−0.614171
$143$	4.78744	−	8.29209i	0.400346	−	0.693419i
$144$	2.99980	−	0.0347849i	0.249983	−	0.00289874i
$145$	1.25691	+	2.17703i	0.104380	+	0.180792i
$146$	−1.97220	+	3.41595i	−0.163221	+	0.282706i
$147$	−10.4117	−	6.21266i	−0.858740	−	0.512411i
$148$	−4.38024	−	7.58679i	−0.360053	−	0.623631i
$149$	−3.23664	+	5.60603i	−0.265156	+	0.459264i	−0.967605	−	0.252471i	$-0.918757\pi$
$149$	−3.23664	+	5.60603i	−0.265156	+	0.459264i	0.702448	+	0.711735i	$0.252090\pi$
$150$	−0.874707	−	1.49495i	−0.0714195	−	0.122062i
$151$	−11.1363	−	19.2886i	−0.906255	−	1.56968i	−0.819223	−	0.573475i	$-0.805595\pi$
$151$	−11.1363	−	19.2886i	−0.906255	−	1.56968i	−0.0870324	−	0.996205i	$-0.527738\pi$
$152$	3.46705	+	6.00511i	0.281215	+	0.487078i
$153$	8.54949	−	15.2128i	0.691185	−	1.22988i
$154$	−3.95366	+	1.01672i	−0.318595	+	0.0819294i
$155$	−4.04539	+	7.00682i	−0.324934	+	0.562801i
$156$	−5.42801	−	9.27696i	−0.434589	−	0.742752i
$157$	17.2654			1.37793			0.688964	−	0.724795i	$-0.258066\pi$
$157$	17.2654			1.37793			0.688964	+	0.724795i	$0.258066\pi$
$158$	−2.25380			−0.179302
$159$	−5.08178	+	8.92095i	−0.403011	+	0.707477i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−13.4197	−	13.6934i	−1.05762	−	1.07919i
$162$	8.99758	−	0.208696i	0.706917	−	0.0163967i
$163$	2.65916	+	4.60580i	0.208281	+	0.360754i	0.951173	−	0.308657i	$-0.0998797\pi$
$163$	2.65916	+	4.60580i	0.208281	+	0.360754i	−0.742892	+	0.669412i	$0.766546\pi$
$164$	−1.70890	−	2.95990i	−0.133442	−	0.231129i
$165$	2.67244	−	0.0154940i	0.208050	−	0.00120621i
$166$	−4.13650	+	7.16463i	−0.321055	+	0.556083i
$167$	5.88405	+	10.1915i	0.455322	+	0.788640i	0.998707	−	0.0508434i	$-0.0161909\pi$
$167$	5.88405	+	10.1915i	0.455322	+	0.788640i	−0.543385	+	0.839484i	$0.682858\pi$
$168$	−1.20507	+	4.42129i	−0.0929730	+	0.341110i
$169$	−12.7542	+	22.0910i	−0.981095	+	1.69931i
$170$	−2.90844	−	5.03756i	−0.223067	−	0.386363i
$171$	10.6093	+	17.8935i	0.811316	+	1.36835i
$172$	2.75052	−	4.76404i	0.209725	−	0.363255i
$173$	22.7593			1.73036			0.865178	−	0.501465i	$-0.167205\pi$
$173$	22.7593			1.73036			0.865178	+	0.501465i	$0.167205\pi$
$174$	−2.15513	+	3.78328i	−0.163380	+	0.286810i
$175$	2.56238	−	0.658939i	0.193698	−	0.0498111i
$176$	0.771481	+	1.33624i	0.0581526	+	0.100723i
$177$	−14.6373	+	0.0848625i	−1.10021	+	0.00637866i
$178$	2.13541	+	3.69864i	0.160056	+	0.277225i
$179$	−5.64468	+	9.77687i	−0.421903	+	0.730758i	−0.996126	−	0.0879416i	$-0.971971\pi$
$179$	−5.64468	+	9.77687i	−0.421903	+	0.730758i	0.574223	+	0.818699i	$0.305304\pi$
$180$	1.46977	−	2.61529i	0.109551	−	0.194933i
$181$	8.38765			0.623449			0.311725	−	0.950173i	$-0.399093\pi$
$181$	8.38765			0.623449			0.311725	+	0.950173i	$0.399093\pi$
$182$	15.9009	−	4.08906i	1.17865	−	0.303101i
$183$	8.34995	−	0.0484103i	0.617246	−	0.00357860i
$184$	−3.62333	+	6.27579i	−0.267115	+	0.462657i
$185$	−8.76047			−0.644083
$186$	−14.0134	+	0.0812453i	−1.02751	+	0.00595719i
$187$	8.97521			0.656333
$188$	5.63858			0.411236
$189$	−3.46116	+	13.3049i	−0.251763	+	0.967789i
$190$	6.93410			0.503052
$191$	3.17491			0.229728			0.114864	−	0.993381i	$-0.463357\pi$
$191$	3.17491			0.229728			0.114864	+	0.993381i	$0.463357\pi$
$192$	1.73202	−	0.0100417i	0.124998	−	0.000724698i
$193$	−7.78050			−0.560052			−0.280026	−	0.959992i	$-0.590343\pi$
$193$	−7.78050			−0.560052			−0.280026	+	0.959992i	$0.590343\pi$
$194$	6.52492	−	11.3015i	0.468462	−	0.811399i
$195$	−10.7481	+	0.0623140i	−0.769687	+	0.00446240i
$196$	−5.99028	−	3.62167i	−0.427877	−	0.258691i
$197$	12.3809			0.882104			0.441052	−	0.897482i	$-0.354605\pi$
$197$	12.3809			0.882104			0.441052	+	0.897482i	$0.354605\pi$
$198$	2.36077	+	3.98163i	0.167773	+	0.282962i
$199$	6.84286	−	11.8522i	0.485078	−	0.840179i	−0.514775	−	0.857325i	$-0.672125\pi$
$199$	6.84286	−	11.8522i	0.485078	−	0.840179i	0.999853	+	0.0171458i	$0.00545795\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−3.62263	+	0.0210029i	−0.255521	+	0.00148143i
$202$	0.549052	+	0.950986i	0.0386312	+	0.0669111i
$203$	−4.65520	−	4.75015i	−0.326731	−	0.333395i
$204$	4.98689	−	8.75437i	0.349152	−	0.612928i
$205$	−3.41780			−0.238709
$206$	3.68749	−	6.38692i	0.256919	−	0.444997i
$207$	−10.6510	+	18.9521i	−0.740293	+	1.31727i
$208$	−3.10276	−	5.37414i	−0.215138	−	0.372629i
$209$	−5.34953	+	9.26565i	−0.370034	+	0.640919i
$210$	3.22642	+	3.25426i	0.222644	+	0.224566i
$211$	4.95466	+	8.58172i	0.341093	+	0.590790i	0.984636	−	0.174620i	$-0.0558697\pi$
$211$	4.95466	+	8.58172i	0.341093	+	0.590790i	−0.643543	+	0.765410i	$0.722536\pi$
$212$	−2.96378	+	5.13341i	−0.203553	+	0.352564i
$213$	−12.6761	+	0.0734922i	−0.868554	+	0.00503560i
$214$	−2.12699	−	3.68406i	−0.145398	−	0.251837i
$215$	−2.75052	−	4.76404i	−0.187584	−	0.324905i
$216$	5.19537	−	0.0903714i	0.353500	−	0.00614899i
$217$	5.74877	−	20.6198i	0.390252	−	1.39976i
$218$	−7.57730	+	13.1243i	−0.513199	+	0.888887i
$219$	−3.38159	+	5.93631i	−0.228507	+	0.401139i
$220$	1.54296			0.104027
$221$	−36.0967			−2.42813
$222$	−7.66285	−	13.0965i	−0.514297	−	0.878980i
$223$	8.60737	−	14.9084i	0.576392	−	0.998340i	−0.419497	−	0.907757i	$-0.637793\pi$
$223$	8.60737	−	14.9084i	0.576392	−	0.998340i	0.995889	−	0.0905834i	$-0.0288732\pi$
$224$	−0.710533	+	2.54856i	−0.0474745	+	0.170283i
$225$	−1.53002	−	2.58051i	−0.102002	−	0.172034i
$226$	8.11693	+	14.0589i	0.539930	+	0.935186i
$227$	−2.86190	−	4.95696i	−0.189951	−	0.329005i	0.755282	−	0.655399i	$-0.227500\pi$
$227$	−2.86190	−	4.95696i	−0.189951	−	0.329005i	−0.945234	+	0.326394i	$0.894166\pi$
$228$	6.06531	+	10.3662i	0.401685	+	0.686516i
$229$	2.30893	−	3.99919i	0.152579	−	0.264274i	−0.779596	−	0.626283i	$-0.784576\pi$
$229$	2.30893	−	3.99919i	0.152579	−	0.264274i	0.932175	+	0.362009i	$0.117909\pi$
$230$	3.62333	+	6.27579i	0.238915	+	0.413813i
$231$	−6.83761	+	1.80068i	−0.449882	+	0.118476i
$232$	−1.25691	+	2.17703i	−0.0825200	+	0.142929i
$233$	1.25932	+	2.18121i	0.0825011	+	0.142896i	0.904324	−	0.426847i	$-0.140376\pi$
$233$	1.25932	+	2.18121i	0.0825011	+	0.142896i	−0.821823	+	0.569744i	$0.807043\pi$
$234$	−9.49459	−	16.0134i	−0.620681	−	1.04683i
$235$	2.81929	−	4.88315i	0.183910	−	0.318542i
$236$	−8.45100			−0.550113
$237$	−3.90362	+	0.0226320i	−0.253568	+	0.00147010i
$238$	10.7720	+	10.9917i	0.698243	+	0.712484i
$239$	4.43364	+	7.67928i	0.286788	+	0.496732i	0.973041	−	0.230631i	$-0.0740791\pi$
$239$	4.43364	+	7.67928i	0.286788	+	0.496732i	−0.686253	+	0.727363i	$0.740746\pi$
$240$	0.857314	−	1.50500i	0.0553394	−	0.0971471i
$241$	6.90302	+	11.9564i	0.444663	+	0.770178i	0.998029	−	0.0627600i	$-0.0199903\pi$
$241$	6.90302	+	11.9564i	0.444663	+	0.770178i	−0.553366	+	0.832938i	$0.686657\pi$
$242$	4.30963	−	7.46450i	0.277034	−	0.479837i
$243$	15.5819	−	0.451816i	0.999580	−	0.0289840i
$244$	4.82092			0.308628
$245$	−6.13160	+	3.37690i	−0.391734	+	0.215742i
$246$	−2.98957	−	5.10945i	−0.190608	−	0.325766i
$247$	21.5148	−	37.2648i	1.36896	−	2.37110i
$248$	−8.09078			−0.513765
$249$	−7.09257	+	12.4508i	−0.449473	+	0.789040i
$250$	−1.00000			−0.0632456
$251$	24.4674			1.54437			0.772186	−	0.635397i	$-0.219164\pi$
$251$	24.4674			1.54437			0.772186	+	0.635397i	$0.219164\pi$
$252$	−2.04281	+	7.66987i	−0.128685	+	0.483157i
$253$	−11.1813			−0.702964
$254$	−7.19028			−0.451158
$255$	−5.08806	−	8.69595i	−0.318627	−	0.544562i
$256$	1.00000			0.0625000
$257$	15.4089	−	26.6890i	0.961182	−	1.66482i	0.241642	−	0.970366i	$-0.422314\pi$
$257$	15.4089	−	26.6890i	0.961182	−	1.66482i	0.719540	−	0.694451i	$-0.244352\pi$
$258$	4.71612	−	8.27904i	0.293613	−	0.515431i
$259$	22.4477	−	5.77261i	1.39483	−	0.358693i
$260$	−6.20552			−0.384850
$261$	−3.69474	+	6.57436i	−0.228699	+	0.406943i
$262$	−4.49687	+	7.78881i	−0.277818	+	0.481194i
$263$	9.93518	+	17.2082i	0.612629	+	1.06110i	0.990795	+	0.135367i	$0.0432214\pi$
$263$	9.93518	+	17.2082i	0.612629	+	1.06110i	−0.378166	+	0.925738i	$0.623445\pi$
$264$	1.34964	+	2.30666i	0.0830646	+	0.141965i
$265$	2.96378	+	5.13341i	0.182063	+	0.315343i
$266$	−17.7678	+	4.56915i	−1.08941	+	0.280152i
$267$	3.73572	+	6.38469i	0.228622	+	0.390736i
$268$	−2.09156			−0.127762
$269$	−8.59058	+	14.8793i	−0.523777	+	0.907208i	0.475840	+	0.879532i	$0.342144\pi$
$269$	−8.59058	+	14.8793i	−0.523777	+	0.907208i	−0.999617	+	0.0276764i	$0.991189\pi$
$270$	2.51942	−	4.54451i	0.153327	−	0.276570i
$271$	8.49672	+	14.7167i	0.516139	+	0.893979i	0.999824	+	0.0187368i	$0.00596446\pi$
$271$	8.49672	+	14.7167i	0.516139	+	0.893979i	−0.483686	+	0.875242i	$0.660702\pi$
$272$	2.90844	−	5.03756i	0.176350	−	0.305447i
$273$	27.4997	−	7.24201i	1.66435	−	0.438306i
$274$	−3.43969	−	5.95772i	−0.207799	−	0.359919i
$275$	0.771481	−	1.33624i	0.0465221	−	0.0805786i
$276$	−6.21267	+	10.9062i	−0.373959	+	0.656476i
$277$	5.05302	+	8.75208i	0.303606	+	0.525862i	0.976950	−	0.213468i	$-0.0684759\pi$
$277$	5.05302	+	8.75208i	0.303606	+	0.525862i	−0.673344	+	0.739330i	$0.735143\pi$
$278$	−9.10281	−	15.7665i	−0.545950	−	0.945613i
$279$	−24.2707	+	0.281437i	−1.45305	+	0.0168492i
$280$	1.85185	+	1.88962i	0.110669	+	0.112926i
$281$	−3.90526	+	6.76411i	−0.232968	+	0.403513i	−0.958680	−	0.284486i	$-0.908177\pi$
$281$	−3.90526	+	6.76411i	−0.232968	+	0.403513i	0.725712	+	0.687999i	$0.241511\pi$
$282$	9.76614	−	0.0566210i	0.581565	−	0.00337173i
$283$	−27.1446			−1.61358			−0.806789	−	0.590840i	$-0.798796\pi$
$283$	−27.1446			−1.61358			−0.806789	+	0.590840i	$0.798796\pi$
$284$	−7.31869			−0.434285
$285$	12.0100	−	0.0696302i	0.711412	−	0.00412454i
$286$	4.78744	−	8.29209i	0.283087	−	0.490322i
$287$	8.75770	−	2.25212i	0.516951	−	0.132938i
$288$	2.99980	−	0.0347849i	0.176765	−	0.00204972i
$289$	−8.41799	−	14.5804i	−0.495176	−	0.857670i
$290$	1.25691	+	2.17703i	0.0738081	+	0.127839i
$291$	11.1878	−	19.6399i	0.655841	−	1.15131i
$292$	−1.97220	+	3.41595i	−0.115414	+	0.199904i
$293$	−8.63571	−	14.9575i	−0.504504	−	0.873826i	−0.999986	−	0.00520815i	$-0.998342\pi$
$293$	−8.63571	−	14.9575i	−0.504504	−	0.873826i	0.495483	−	0.868618i	$-0.334991\pi$
$294$	−10.4117	−	6.21266i	−0.607221	−	0.362330i
$295$	−4.22550	+	7.31878i	−0.246018	+	0.426116i
$296$	−4.38024	−	7.58679i	−0.254596	−	0.440973i
$297$	4.12889	+	6.87256i	0.239582	+	0.398786i
$298$	−3.23664	+	5.60603i	−0.187494	+	0.324749i
$299$	44.9693			2.60064
$300$	−0.874707	−	1.49495i	−0.0505012	−	0.0863112i
$301$	10.1871	+	10.3949i	0.587174	+	0.599150i
$302$	−11.1363	−	19.2886i	−0.640819	−	1.10993i
$303$	0.960520	+	1.64162i	0.0551804	+	0.0943083i
$304$	3.46705	+	6.00511i	0.198849	+	0.344416i
$305$	2.41046	−	4.17504i	0.138023	−	0.239062i
$306$	8.54949	−	15.2128i	0.488742	−	0.869660i
$307$	−7.78197			−0.444140			−0.222070	−	0.975031i	$-0.571281\pi$
$307$	−7.78197			−0.444140			−0.222070	+	0.975031i	$0.571281\pi$
$308$	−3.95366	+	1.01672i	−0.225281	+	0.0579329i
$309$	6.32267	−	11.0993i	0.359684	−	0.631417i
$310$	−4.04539	+	7.00682i	−0.229763	+	0.397961i
$311$	17.9716			1.01908			0.509538	−	0.860448i	$-0.329816\pi$
$311$	17.9716			1.01908			0.509538	+	0.860448i	$0.329816\pi$
$312$	−5.42801	−	9.27696i	−0.307301	−	0.525205i
$313$	−10.6635			−0.602734			−0.301367	−	0.953508i	$-0.597443\pi$
$313$	−10.6635			−0.602734			−0.301367	+	0.953508i	$0.597443\pi$
$314$	17.2654			0.974343
$315$	5.62090	+	5.60406i	0.316702	+	0.315753i
$316$	−2.25380			−0.126786
$317$	32.5627			1.82891			0.914453	−	0.404692i	$-0.132621\pi$
$317$	32.5627			1.82891			0.914453	+	0.404692i	$0.132621\pi$
$318$	−5.08178	+	8.92095i	−0.284972	+	0.500262i
$319$	−3.87872			−0.217167
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−3.72099	−	6.35951i	−0.207685	−	0.354953i
$322$	−13.4197	−	13.6934i	−0.747851	−	0.763104i
$323$	40.3348			2.24429
$324$	8.99758	−	0.208696i	0.499866	−	0.0115942i
$325$	−3.10276	+	5.37414i	−0.172110	+	0.298103i
$326$	2.65916	+	4.60580i	0.147277	+	0.255092i
$327$	−12.9923	+	22.8076i	−0.718473	+	1.26126i
$328$	−1.70890	−	2.95990i	−0.0943581	−	0.163433i
$329$	−4.00640	+	14.3702i	−0.220880	+	0.792257i
$330$	2.67244	−	0.0154940i	0.147113	−	0.000852916i
$331$	16.9247			0.930264			0.465132	−	0.885241i	$-0.346007\pi$
$331$	16.9247			0.930264			0.465132	+	0.885241i	$0.346007\pi$
$332$	−4.13650	+	7.16463i	−0.227020	+	0.393210i
$333$	−13.4037	−	22.6065i	−0.734520	−	1.23883i
$334$	5.88405	+	10.1915i	0.321961	+	0.557653i
$335$	−1.04578	+	1.81135i	−0.0571371	+	0.0989644i
$336$	−1.20507	+	4.42129i	−0.0657418	+	0.241201i
$337$	−1.43560	−	2.48654i	−0.0782022	−	0.135450i	0.824272	−	0.566194i	$-0.191585\pi$
$337$	−1.43560	−	2.48654i	−0.0782022	−	0.135450i	−0.902474	+	0.430744i	$0.858251\pi$
$338$	−12.7542	+	22.0910i	−0.693739	+	1.20159i
$339$	14.1999	+	24.2689i	0.771231	+	1.31810i
$340$	−2.90844	−	5.03756i	−0.157732	−	0.273200i
$341$	−6.24188	−	10.8113i	−0.338017	−	0.585463i
$342$	10.6093	+	17.8935i	0.573687	+	0.967570i
$343$	13.4863	−	12.6933i	0.728193	−	0.685372i
$344$	2.75052	−	4.76404i	0.148298	−	0.256860i
$345$	6.33871	+	10.8334i	0.341264	+	0.583252i
$346$	22.7593			1.22355
$347$	2.87948			0.154578			0.0772892	−	0.997009i	$-0.475374\pi$
$347$	2.87948			0.154578			0.0772892	+	0.997009i	$0.475374\pi$
$348$	−2.15513	+	3.78328i	−0.115527	+	0.202805i
$349$	−15.3092	+	26.5164i	−0.819484	+	1.41939i	0.0865789	+	0.996245i	$0.472407\pi$
$349$	−15.3092	+	26.5164i	−0.819484	+	1.41939i	−0.906063	+	0.423143i	$0.860927\pi$
$350$	2.56238	−	0.658939i	0.136965	−	0.0352217i
$351$	−16.6056	−	27.6402i	−0.886343	−	1.47533i
$352$	0.771481	+	1.33624i	0.0411201	+	0.0712221i
$353$	−9.01525	−	15.6149i	−0.479834	−	0.831096i	0.519899	−	0.854228i	$-0.325970\pi$
$353$	−9.01525	−	15.6149i	−0.479834	−	0.831096i	−0.999732	+	0.0231317i	$0.992636\pi$
$354$	−14.6373	+	0.0848625i	−0.777964	+	0.00451039i
$355$	−3.65935	+	6.33817i	−0.194218	+	0.336395i
$356$	2.13541	+	3.69864i	0.113177	+	0.196028i
$357$	18.7676	+	18.9296i	0.993289	+	1.00186i
$358$	−5.64468	+	9.77687i	−0.298331	+	0.516724i
$359$	−1.97671	−	3.42376i	−0.104327	−	0.180699i	0.809136	−	0.587621i	$-0.199935\pi$
$359$	−1.97671	−	3.42376i	−0.104327	−	0.180699i	−0.913463	+	0.406922i	$0.866602\pi$
$360$	1.46977	−	2.61529i	0.0774639	−	0.137838i
$361$	−14.5409	+	25.1855i	−0.765309	+	1.32555i
$362$	8.38765			0.440845
$363$	7.38942	−	12.9720i	0.387844	−	0.680851i
$364$	15.9009	−	4.08906i	0.833434	−	0.214325i
$365$	1.97220	+	3.41595i	0.103230	+	0.178799i
$366$	8.34995	−	0.0484103i	0.436459	−	0.00253045i
$367$	3.97656	+	6.88760i	0.207575	+	0.359530i	0.950950	−	0.309345i	$-0.100110\pi$
$367$	3.97656	+	6.88760i	0.207575	+	0.359530i	−0.743375	+	0.668875i	$0.766776\pi$
$368$	−3.62333	+	6.27579i	−0.188879	+	0.327148i
$369$	−5.22931	−	8.81965i	−0.272227	−	0.459133i
$370$	−8.76047			−0.455435
$371$	−10.9769	−	11.2008i	−0.569894	−	0.581518i
$372$	−14.0134	+	0.0812453i	−0.726561	+	0.00421237i
$373$	4.69137	−	8.12570i	0.242910	−	0.420733i	−0.718632	−	0.695391i	$-0.755231\pi$
$373$	4.69137	−	8.12570i	0.242910	−	0.420733i	0.961542	+	0.274658i	$0.0885647\pi$
$374$	8.97521			0.464097
$375$	−1.73202	+	0.0100417i	−0.0894412	+	0.000518552i
$376$	5.63858			0.290787
$377$	15.5995			0.803416
$378$	−3.46116	+	13.3049i	−0.178023	+	0.684330i
$379$	18.5648			0.953608			0.476804	−	0.879010i	$-0.341795\pi$
$379$	18.5648			0.953608			0.476804	+	0.879010i	$0.341795\pi$
$380$	6.93410			0.355712
$381$	−12.4537	+	0.0722027i	−0.638024	+	0.00369906i
$382$	3.17491			0.162442
$383$	0.930769	−	1.61214i	0.0475601	−	0.0823764i	−0.841265	−	0.540622i	$-0.818189\pi$
$383$	0.930769	−	1.61214i	0.0475601	−	0.0823764i	0.888825	+	0.458246i	$0.151522\pi$
$384$	1.73202	−	0.0100417i	0.0883869	−	0.000512439i
$385$	−1.09633	+	3.93233i	−0.0558740	+	0.200410i
$386$	−7.78050			−0.396017
$387$	8.08529	−	14.3868i	0.410998	−	0.731324i
$388$	6.52492	−	11.3015i	0.331252	−	0.573746i
$389$	−17.4663	−	30.2526i	−0.885579	−	1.53387i	−0.845049	−	0.534690i	$-0.820429\pi$
$389$	−17.4663	−	30.2526i	−0.885579	−	1.53387i	−0.0405305	−	0.999178i	$-0.512905\pi$
$390$	−10.7481	+	0.0623140i	−0.544251	+	0.00315539i
$391$	21.0764	+	36.5055i	1.06588	+	1.84616i
$392$	−5.99028	−	3.62167i	−0.302555	−	0.182922i
$393$	−7.71047	+	13.5355i	−0.388942	+	0.682778i
$394$	12.3809			0.623742
$395$	−1.12690	+	1.95184i	−0.0567004	+	0.0982080i
$396$	2.36077	+	3.98163i	0.118633	+	0.200084i
$397$	−5.08328	−	8.80450i	−0.255122	−	0.441885i	0.709806	−	0.704397i	$-0.248782\pi$
$397$	−5.08328	−	8.80450i	−0.255122	−	0.441885i	−0.964929	+	0.262512i	$0.915449\pi$
$398$	6.84286	−	11.8522i	0.343002	−	0.594097i
$399$	−30.7283	+	8.09228i	−1.53834	+	0.405121i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−7.15000	+	12.3842i	−0.357054	+	0.618436i	−0.987467	−	0.157824i	$-0.949552\pi$
$401$	−7.15000	+	12.3842i	−0.357054	+	0.618436i	0.630413	+	0.776260i	$0.282885\pi$
$402$	−3.62263	+	0.0210029i	−0.180680	+	0.00104753i
$403$	25.1037	+	43.4810i	1.25051	+	2.16594i
$404$	0.549052	+	0.950986i	0.0273164	+	0.0473133i
$405$	4.31805	−	7.89648i	0.214566	−	0.392379i
$406$	−4.65520	−	4.75015i	−0.231034	−	0.235746i
$407$	6.75854	−	11.7061i	0.335008	−	0.580252i
$408$	4.98689	−	8.75437i	0.246888	−	0.433406i
$409$	16.1964			0.800861			0.400431	−	0.916327i	$-0.368861\pi$
$409$	16.1964			0.800861			0.400431	+	0.916327i	$0.368861\pi$
$410$	−3.41780			−0.168793
$411$	−6.01744	−	10.2844i	−0.296819	−	0.507290i
$412$	3.68749	−	6.38692i	0.181669	−	0.314661i
$413$	6.00471	−	21.5378i	0.295473	−	1.05981i
$414$	−10.6510	+	18.9521i	−0.523466	+	0.931447i
$415$	4.13650	+	7.16463i	0.203053	+	0.351698i
$416$	−3.10276	−	5.37414i	−0.152125	−	0.263489i
$417$	−15.9246	−	27.2166i	−0.779830	−	1.33280i
$418$	−5.34953	+	9.26565i	−0.261654	+	0.453198i
$419$	0.0855194	+	0.148124i	0.00417789	+	0.00723632i	0.868107	−	0.496377i	$-0.165337\pi$
$419$	0.0855194	+	0.148124i	0.00417789	+	0.00723632i	−0.863929	+	0.503614i	$0.832003\pi$
$420$	3.22642	+	3.25426i	0.157433	+	0.158792i
$421$	7.19459	−	12.4614i	0.350643	−	0.607331i	−0.635720	−	0.771920i	$-0.719297\pi$
$421$	7.19459	−	12.4614i	0.350643	−	0.607331i	0.986362	+	0.164589i	$0.0526299\pi$
$422$	4.95466	+	8.58172i	0.241189	+	0.417751i
$423$	16.9146	−	0.196138i	0.822416	−	0.00953653i
$424$	−2.96378	+	5.13341i	−0.143934	+	0.249301i
$425$	−5.81687			−0.282160
$426$	−12.6761	+	0.0734922i	−0.614161	+	0.00356071i
$427$	−3.42543	+	12.2864i	−0.165768	+	0.594581i
$428$	−2.12699	−	3.68406i	−0.102812	−	0.178076i
$429$	8.20868	−	14.4102i	0.396319	−	0.695729i
$430$	−2.75052	−	4.76404i	−0.132642	−	0.229742i
$431$	2.89574	−	5.01558i	0.139483	−	0.241592i	−0.787818	−	0.615908i	$-0.788789\pi$
$431$	2.89574	−	5.01558i	0.139483	−	0.241592i	0.927301	+	0.374316i	$0.122123\pi$
$432$	5.19537	−	0.0903714i	0.249962	−	0.00434799i
$433$	34.0010			1.63398			0.816991	−	0.576650i	$-0.195640\pi$
$433$	34.0010			1.63398			0.816991	+	0.576650i	$0.195640\pi$
$434$	5.74877	−	20.6198i	0.275950	−	0.989783i
$435$	2.19885	+	3.75804i	0.105427	+	0.180184i
$436$	−7.57730	+	13.1243i	−0.362887	+	0.628538i
$437$	−50.2490			−2.40374
$438$	−3.38159	+	5.93631i	−0.161579	+	0.283648i
$439$	−12.1404			−0.579431			−0.289715	−	0.957113i	$-0.593561\pi$
$439$	−12.1404			−0.579431			−0.289715	+	0.957113i	$0.593561\pi$
$440$	1.54296			0.0735578
$441$	−18.0956	−	10.6559i	−0.861696	−	0.507424i
$442$	−36.0967			−1.71695
$443$	5.37339			0.255297			0.127649	−	0.991819i	$-0.459257\pi$
$443$	5.37339			0.255297			0.127649	+	0.991819i	$0.459257\pi$
$444$	−7.66285	−	13.0965i	−0.363663	−	0.621533i
$445$	4.27082			0.202457
$446$	8.60737	−	14.9084i	0.407571	−	0.705933i
$447$	−5.54964	+	9.74227i	−0.262489	+	0.460794i
$448$	−0.710533	+	2.54856i	−0.0335695	+	0.120408i
$449$	23.7693			1.12174			0.560870	−	0.827904i	$-0.310467\pi$
$449$	23.7693			1.12174			0.560870	+	0.827904i	$0.310467\pi$
$450$	−1.53002	−	2.58051i	−0.0721260	−	0.121646i
$451$	2.63676	−	4.56701i	0.124160	−	0.215052i
$452$	8.11693	+	14.0589i	0.381788	+	0.661277i
$453$	−19.4819	−	33.2964i	−0.915341	−	1.56440i
$454$	−2.86190	−	4.95696i	−0.134316	−	0.232642i
$455$	4.40923	−	15.8151i	0.206708	−	0.741424i
$456$	6.06531	+	10.3662i	0.284034	+	0.485440i
$457$	−9.69872			−0.453687			−0.226843	−	0.973931i	$-0.572841\pi$
$457$	−9.69872			−0.453687			−0.226843	+	0.973931i	$0.572841\pi$
$458$	2.30893	−	3.99919i	0.107889	−	0.186870i
$459$	14.6551	−	26.4348i	0.684043	−	1.23387i
$460$	3.62333	+	6.27579i	0.168939	+	0.292610i
$461$	−18.0316	+	31.2316i	−0.839814	+	1.45460i	0.0502359	+	0.998737i	$0.484003\pi$
$461$	−18.0316	+	31.2316i	−0.839814	+	1.45460i	−0.890050	+	0.455863i	$0.849331\pi$
$462$	−6.83761	+	1.80068i	−0.318115	+	0.0837751i
$463$	−8.40491	−	14.5577i	−0.390610	−	0.676556i	0.601921	−	0.798556i	$-0.294402\pi$
$463$	−8.40491	−	14.5577i	−0.390610	−	0.676556i	−0.992530	+	0.122000i	$0.961069\pi$
$464$	−1.25691	+	2.17703i	−0.0583504	+	0.101066i
$465$	−6.93634	+	12.1766i	−0.321665	+	0.564676i
$466$	1.25932	+	2.18121i	0.0583371	+	0.101043i
$467$	−2.70979	−	4.69349i	−0.125394	−	0.217189i	0.796493	−	0.604648i	$-0.206686\pi$
$467$	−2.70979	−	4.69349i	−0.125394	−	0.217189i	−0.921887	+	0.387459i	$0.873353\pi$
$468$	−9.49459	−	16.0134i	−0.438888	−	0.740220i
$469$	1.48612	−	5.33047i	0.0686229	−	0.246138i
$470$	2.81929	−	4.88315i	0.130044	−	0.225243i
$471$	29.9040	−	0.173374i	1.37791	−	0.00798866i
$472$	−8.45100			−0.388989
$473$	8.48790			0.390274
$474$	−3.90362	+	0.0226320i	−0.179299	+	0.00103952i
$475$	3.46705	−	6.00511i	0.159079	−	0.275533i
$476$	10.7720	+	10.9917i	0.493732	+	0.503802i
$477$	−8.71217	+	15.5023i	−0.398903	+	0.709802i
$478$	4.43364	+	7.67928i	0.202790	+	0.351242i
$479$	−10.6632	−	18.4692i	−0.487215	−	0.843881i	0.512677	−	0.858582i	$-0.328654\pi$
$479$	−10.6632	−	18.4692i	−0.487215	−	0.843881i	−0.999892	+	0.0147003i	$0.995321\pi$
$480$	0.857314	−	1.50500i	0.0391309	−	0.0686933i
$481$	−27.1816	+	47.0800i	−1.23938	+	2.14666i
$482$	6.90302	+	11.9564i	0.314424	+	0.544598i
$483$	−23.3807	−	23.5825i	−1.06386	−	1.07304i
$484$	4.30963	−	7.46450i	0.195892	−	0.339296i
$485$	−6.52492	−	11.3015i	−0.296281	−	0.513174i
$486$	15.5819	−	0.451816i	0.706810	−	0.0204948i
$487$	4.46333	−	7.73071i	0.202253	−	0.350312i	−0.747001	−	0.664823i	$-0.768507\pi$
$487$	4.46333	−	7.73071i	0.202253	−	0.350312i	0.949254	+	0.314511i	$0.101840\pi$
$488$	4.82092			0.218233
$489$	4.65197	+	7.95064i	0.210369	+	0.359541i
$490$	−6.13160	+	3.37690i	−0.276997	+	0.152553i
$491$	4.97746	+	8.62122i	0.224630	+	0.389070i	0.956208	−	0.292687i	$-0.0945494\pi$
$491$	4.97746	+	8.62122i	0.224630	+	0.389070i	−0.731579	+	0.681757i	$0.761216\pi$
$492$	−2.98957	−	5.10945i	−0.134780	−	0.230352i
$493$	7.31127	+	12.6635i	0.329283	+	0.570335i
$494$	21.5148	−	37.2648i	0.967998	−	1.67662i
$495$	4.62858	−	0.0536718i	0.208039	−	0.00241237i
$496$	−8.09078			−0.363287
$497$	5.20018	−	18.6521i	0.233260	−	0.836661i
$498$	−7.09257	+	12.4508i	−0.317825	+	0.557935i
$499$	−15.3925	+	26.6607i	−0.689065	+	1.19350i	0.283076	+	0.959098i	$0.408645\pi$
$499$	−15.3925	+	26.6607i	−0.689065	+	1.19350i	−0.972141	+	0.234398i	$0.924688\pi$
$500$	−1.00000			−0.0447214
$501$	10.2936	+	17.5928i	0.459886	+	0.785987i
$502$	24.4674			1.09204
$503$	−27.1915			−1.21241			−0.606204	−	0.795309i	$-0.707308\pi$
$503$	−27.1915			−1.21241			−0.606204	+	0.795309i	$0.707308\pi$
$504$	−2.04281	+	7.66987i	−0.0909938	+	0.341643i
$505$	1.09810			0.0488650
$506$	−11.1813			−0.497070
$507$	−21.8688	+	38.3901i	−0.971226	+	1.70497i
$508$	−7.19028			−0.319017
$509$	21.2588	−	36.8214i	0.942282	−	1.63208i	0.181178	−	0.983450i	$-0.442009\pi$
$509$	21.2588	−	36.8214i	0.942282	−	1.63208i	0.761104	−	0.648630i	$-0.224658\pi$
$510$	−5.08806	−	8.69595i	−0.225303	−	0.385063i
$511$	−7.30444	−	7.45342i	−0.323129	−	0.329720i
$512$	1.00000			0.0441942
$513$	18.5553	+	30.8854i	0.819236	+	1.36362i
$514$	15.4089	−	26.6890i	0.679658	−	1.17720i
$515$	−3.68749	−	6.38692i	−0.162490	−	0.281441i
$516$	4.71612	−	8.27904i	0.207616	−	0.364464i
$517$	4.35006	+	7.53452i	0.191315	+	0.331368i
$518$	22.4477	−	5.77261i	0.986294	−	0.253634i
$519$	39.4196	−	0.228542i	1.73033	−	0.0100319i
$520$	−6.20552			−0.272130
$521$	6.77599	−	11.7364i	0.296862	−	0.514179i	−0.678555	−	0.734550i	$-0.737393\pi$
$521$	6.77599	−	11.7364i	0.296862	−	0.514179i	0.975416	+	0.220371i	$0.0707267\pi$
$522$	−3.69474	+	6.57436i	−0.161714	+	0.287752i
$523$	−1.34200	−	2.32440i	−0.0586813	−	0.101639i	0.835192	−	0.549958i	$-0.185356\pi$
$523$	−1.34200	−	2.32440i	−0.0586813	−	0.101639i	−0.893874	+	0.448319i	$0.852023\pi$
$524$	−4.49687	+	7.78881i	−0.196447	+	0.340256i
$525$	4.43148	−	1.16703i	0.193406	−	0.0509332i
$526$	9.93518	+	17.2082i	0.433194	+	0.750314i
$527$	−23.5315	+	40.7578i	−1.02505	+	1.77544i
$528$	1.34964	+	2.30666i	0.0587356	+	0.100384i
$529$	−14.7570	−	25.5599i	−0.641610	−	1.11130i
$530$	2.96378	+	5.13341i	0.128738	+	0.222981i
$531$	−25.3513	+	0.293967i	−1.10015	+	0.0127571i
$532$	−17.7678	+	4.56915i	−0.770332	+	0.198098i
$533$	−10.6046	+	18.3677i	−0.459336	+	0.795593i
$534$	3.73572	+	6.38469i	0.161660	+	0.276292i
$535$	−4.25398			−0.183916
$536$	−2.09156			−0.0903417
$537$	−9.67853	+	16.9904i	−0.417659	+	0.733191i
$538$	−8.59058	+	14.8793i	−0.370366	+	0.641493i
$539$	0.218044	−	10.7985i	0.00939181	−	0.465126i
$540$	2.51942	−	4.54451i	0.108419	−	0.195564i
$541$	7.96591	+	13.7974i	0.342481	+	0.593195i	0.984893	−	0.173165i	$-0.0553994\pi$
$541$	7.96591	+	13.7974i	0.342481	+	0.593195i	−0.642412	+	0.766360i	$0.722066\pi$
$542$	8.49672	+	14.7167i	0.364965	+	0.632138i
$543$	14.5276	−	0.0842264i	0.623439	−	0.00361450i
$544$	2.90844	−	5.03756i	0.124698	−	0.215984i
$545$	7.57730	+	13.1243i	0.324576	+	0.562182i
$546$	27.4997	−	7.24201i	1.17688	−	0.309929i
$547$	−10.3885	+	17.9934i	−0.444179	+	0.769340i	−0.997995	−	0.0632988i	$-0.979838\pi$
$547$	−10.3885	+	17.9934i	−0.444179	+	0.769340i	0.553816	+	0.832639i	$0.313171\pi$
$548$	−3.43969	−	5.95772i	−0.146936	−	0.254501i
$549$	14.4618	−	0.167696i	0.617215	−	0.00715707i
$550$	0.771481	−	1.33624i	0.0328961	−	0.0569777i
$551$	−17.4310			−0.742587
$552$	−6.21267	+	10.9062i	−0.264429	+	0.464198i
$553$	1.60140	−	5.74393i	0.0680983	−	0.244257i
$554$	5.05302	+	8.75208i	0.214682	+	0.371840i
$555$	−15.1733	+	0.0879702i	−0.644072	+	0.00373413i
$556$	−9.10281	−	15.7665i	−0.386045	−	0.668650i
$557$	8.90674	−	15.4269i	0.377391	−	0.653660i	−0.613291	−	0.789857i	$-0.710155\pi$
$557$	8.90674	−	15.4269i	0.377391	−	0.653660i	0.990682	+	0.136197i	$0.0434880\pi$
$558$	−24.2707	+	0.281437i	−1.02746	+	0.0119142i
$559$	−34.1368			−1.44383
$560$	1.85185	+	1.88962i	0.0782549	+	0.0798509i
$561$	15.5453	−	0.0901265i	0.656322	−	0.00380514i
$562$	−3.90526	+	6.76411i	−0.164733	+	0.285327i
$563$	−12.1696			−0.512889			−0.256445	−	0.966559i	$-0.582551\pi$
$563$	−12.1696			−0.512889			−0.256445	+	0.966559i	$0.582551\pi$
$564$	9.76614	−	0.0566210i	0.411229	−	0.00238417i
$565$	16.2339			0.682964
$566$	−27.1446			−1.14097
$567$	−5.86121	+	23.0791i	−0.246148	+	0.969232i
$568$	−7.31869			−0.307086
$569$	27.8955			1.16944			0.584721	−	0.811235i	$-0.301204\pi$
$569$	27.8955			1.16944			0.584721	+	0.811235i	$0.301204\pi$
$570$	12.0100	−	0.0696302i	0.503044	−	0.00291649i
$571$	11.2403			0.470393			0.235197	−	0.971948i	$-0.424427\pi$
$571$	11.2403			0.470393			0.235197	+	0.971948i	$0.424427\pi$
$572$	4.78744	−	8.29209i	0.200173	−	0.346710i
$573$	5.49901	−	0.0318815i	0.229724	−	0.00133187i
$574$	8.75770	−	2.25212i	0.365539	−	0.0940016i
$575$	7.24666			0.302207
$576$	2.99980	−	0.0347849i	0.124992	−	0.00144937i
$577$	−7.44028	+	12.8869i	−0.309743	+	0.536491i	−0.978306	−	0.207165i	$-0.933576\pi$
$577$	−7.44028	+	12.8869i	−0.309743	+	0.536491i	0.668563	+	0.743655i	$0.266910\pi$
$578$	−8.41799	−	14.5804i	−0.350142	−	0.606464i
$579$	−13.4760	+	0.0781295i	−0.560043	+	0.00324695i
$580$	1.25691	+	2.17703i	0.0521902	+	0.0903961i
$581$	−15.3203	−	15.6328i	−0.635595	−	0.648559i
$582$	11.1878	−	19.6399i	0.463750	−	0.814102i
$583$	−9.14600			−0.378788
$584$	−1.97220	+	3.41595i	−0.0816103	+	0.141353i
$585$	−18.6153	+	0.215859i	−0.769648	+	0.00892465i
$586$	−8.63571	−	14.9575i	−0.356738	−	0.617888i
$587$	5.35630	−	9.27739i	0.221078	−	0.382919i	−0.734057	−	0.679087i	$-0.762376\pi$
$587$	5.35630	−	9.27739i	0.221078	−	0.382919i	0.955136	+	0.296169i	$0.0957090\pi$
$588$	−10.4117	−	6.21266i	−0.429370	−	0.256206i
$589$	−28.0511	−	48.5860i	−1.15583	−	2.00195i
$590$	−4.22550	+	7.31878i	−0.173961	+	0.301309i
$591$	21.4440	−	0.124326i	0.882089	−	0.00511407i
$592$	−4.38024	−	7.58679i	−0.180027	−	0.311815i
$593$	0.229321	+	0.397195i	0.00941708	+	0.0163109i	0.870696	−	0.491822i	$-0.163669\pi$
$593$	0.229321	+	0.397195i	0.00941708	+	0.0163109i	−0.861278	+	0.508133i	$0.830336\pi$
$594$	4.12889	+	6.87256i	0.169410	+	0.281985i
$595$	14.9050	−	3.83296i	0.611047	−	0.157136i
$596$	−3.23664	+	5.60603i	−0.132578	+	0.229632i
$597$	11.7330	−	20.5970i	0.480199	−	0.842978i
$598$	44.9693			1.83893
$599$	17.7420			0.724920			0.362460	−	0.931999i	$-0.381937\pi$
$599$	17.7420			0.724920			0.362460	+	0.931999i	$0.381937\pi$
$600$	−0.874707	−	1.49495i	−0.0357098	−	0.0610312i
$601$	4.77382	−	8.26849i	0.194728	−	0.337279i	−0.752083	−	0.659068i	$-0.770951\pi$
$601$	4.77382	−	8.26849i	0.194728	−	0.337279i	0.946811	+	0.321789i	$0.104284\pi$
$602$	10.1871	+	10.3949i	0.415195	+	0.423663i
$603$	−6.27426	+	0.0727548i	−0.255508	+	0.00296281i
$604$	−11.1363	−	19.2886i	−0.453128	−	0.784840i
$605$	−4.30963	−	7.46450i	−0.175212	−	0.303475i
$606$	0.960520	+	1.64162i	0.0390184	+	0.0666861i
$607$	−6.09444	+	10.5559i	−0.247366	+	0.428450i	−0.962794	−	0.270236i	$-0.912898\pi$
$607$	−6.09444	+	10.5559i	−0.247366	+	0.428450i	0.715428	+	0.698686i	$0.246232\pi$
$608$	3.46705	+	6.00511i	0.140607	+	0.243539i
$609$	−8.11061	−	8.18062i	−0.328659	−	0.331495i
$610$	2.41046	−	4.17504i	0.0975968	−	0.169043i
$611$	−17.4951	−	30.3025i	−0.707778	−	1.22591i
$612$	8.54949	−	15.2128i	0.345593	−	0.614942i
$613$	−12.6045	+	21.8316i	−0.509090	+	0.881771i	0.490854	+	0.871242i	$0.336685\pi$
$613$	−12.6045	+	21.8316i	−0.509090	+	0.881771i	−0.999945	+	0.0105288i	$0.996649\pi$
$614$	−7.78197			−0.314055
$615$	−5.91970	+	0.0343205i	−0.238705	+	0.00138394i
$616$	−3.95366	+	1.01672i	−0.159297	+	0.0409647i
$617$	−8.41154	−	14.5692i	−0.338636	−	0.586534i	0.645541	−	0.763726i	$-0.276632\pi$
$617$	−8.41154	−	14.5692i	−0.338636	−	0.586534i	−0.984176	+	0.177192i	$0.943299\pi$
$618$	6.32267	−	11.0993i	0.254335	−	0.446480i
$619$	−14.7716	−	25.5851i	−0.593720	−	1.02835i	−0.993726	−	0.111840i	$-0.964326\pi$
$619$	−14.7716	−	25.5851i	−0.593720	−	1.02835i	0.400007	−	0.916512i	$-0.369008\pi$
$620$	−4.04539	+	7.00682i	−0.162467	+	0.281401i
$621$	−18.2574	+	32.9325i	−0.732643	+	1.32153i
$622$	17.9716			0.720595
$623$	−10.9435	+	2.81421i	−0.438441	+	0.112749i
$624$	−5.42801	−	9.27696i	−0.217294	−	0.371376i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−10.6635			−0.426197
$627$	−9.17245	+	16.1020i	−0.366312	+	0.643053i
$628$	17.2654			0.688964
$629$	−50.9585			−2.03185
$630$	5.62090	+	5.60406i	0.223942	+	0.223271i
$631$	−22.1608			−0.882206			−0.441103	−	0.897457i	$-0.645413\pi$
$631$	−22.1608			−0.882206			−0.441103	+	0.897457i	$0.645413\pi$
$632$	−2.25380			−0.0896512
$633$	8.66775	+	14.8140i	0.344512	+	0.588802i
$634$	32.5627			1.29323
$635$	−3.59514	+	6.22697i	−0.142669	+	0.247110i
$636$	−5.08178	+	8.92095i	−0.201506	+	0.353739i
$637$	−0.876933	+	43.4298i	−0.0347454	+	1.72075i
$638$	−3.87872			−0.153560
$639$	−21.9546	+	0.254580i	−0.868511	+	0.0100710i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	2.38574	+	4.13223i	0.0942312	+	0.163213i	0.909287	−	0.416169i	$-0.136627\pi$
$641$	2.38574	+	4.13223i	0.0942312	+	0.163213i	−0.815056	+	0.579382i	$0.803294\pi$
$642$	−3.72099	−	6.35951i	−0.146856	−	0.250990i
$643$	−15.2908	−	26.4845i	−0.603011	−	1.04444i	−0.992363	−	0.123356i	$-0.960634\pi$
$643$	−15.2908	−	26.4845i	−0.603011	−	1.04444i	0.389352	−	0.921089i	$-0.372699\pi$
$644$	−13.4197	−	13.6934i	−0.528811	−	0.539596i
$645$	−4.81180	−	8.22380i	−0.189464	−	0.323812i
$646$	40.3348			1.58695
$647$	−13.6741	+	23.6843i	−0.537586	+	0.931127i	0.461447	+	0.887168i	$0.347330\pi$
$647$	−13.6741	+	23.6843i	−0.537586	+	0.931127i	−0.999033	+	0.0439590i	$0.986003\pi$
$648$	8.99758	−	0.208696i	0.353458	−	0.00819834i
$649$	−6.51979	−	11.2926i	−0.255924	−	0.443273i
$650$	−3.10276	+	5.37414i	−0.121700	+	0.210791i
$651$	9.74993	−	35.7717i	0.382130	−	1.40200i
$652$	2.65916	+	4.60580i	0.104141	+	0.180377i
$653$	−4.52327	+	7.83453i	−0.177009	+	0.306589i	−0.940855	−	0.338810i	$-0.889976\pi$
$653$	−4.52327	+	7.83453i	−0.177009	+	0.306589i	0.763846	+	0.645399i	$0.223309\pi$
$654$	−12.9923	+	22.8076i	−0.508037	+	0.891847i
$655$	4.49687	+	7.78881i	0.175707	+	0.304334i
$656$	−1.70890	−	2.95990i	−0.0667212	−	0.115565i
$657$	−5.79738	+	10.3158i	−0.226178	+	0.402457i
$658$	−4.00640	+	14.3702i	−0.156186	+	0.560210i
$659$	−17.6976	+	30.6532i	−0.689401	+	1.19408i	0.282631	+	0.959229i	$0.408793\pi$
$659$	−17.6976	+	30.6532i	−0.689401	+	1.19408i	−0.972032	+	0.234849i	$0.924540\pi$
$660$	2.67244	−	0.0154940i	0.104025	−	0.000603103i
$661$	−8.20464			−0.319123			−0.159562	−	0.987188i	$-0.551008\pi$
$661$	−8.20464			−0.319123			−0.159562	+	0.987188i	$0.551008\pi$
$662$	16.9247			0.657796
$663$	−62.5203	+	0.362473i	−2.42809	+	0.0140773i
$664$	−4.13650	+	7.16463i	−0.160527	+	0.278042i
$665$	−4.92691	+	17.6719i	−0.191057	+	0.685289i
$666$	−13.4037	−	22.6065i	−0.519384	−	0.875983i
$667$	−9.10838	−	15.7762i	−0.352678	−	0.610856i
$668$	5.88405	+	10.1915i	0.227661	+	0.394320i
$669$	14.7584	−	25.9081i	0.570594	−	1.00167i
$670$	−1.04578	+	1.81135i	−0.0404020	+	0.0699784i
$671$	3.71925	+	6.44193i	0.143580	+	0.248688i
$672$	−1.20507	+	4.42129i	−0.0464865	+	0.170555i
$673$	−15.6349	+	27.0805i	−0.602681	+	1.04387i	0.389732	+	0.920928i	$0.372568\pi$
$673$	−15.6349	+	27.0805i	−0.602681	+	1.04387i	−0.992413	+	0.122946i	$0.960766\pi$
$674$	−1.43560	−	2.48654i	−0.0552973	−	0.0957778i
$675$	−2.67595	−	4.45413i	−0.102997	−	0.171440i
$676$	−12.7542	+	22.0910i	−0.490547	+	0.849653i
$677$	−31.8139			−1.22271			−0.611353	−	0.791358i	$-0.709374\pi$
$677$	−31.8139			−1.22271			−0.611353	+	0.791358i	$0.709374\pi$
$678$	14.1999	+	24.2689i	0.545343	+	0.932040i
$679$	24.1663	+	24.6592i	0.927418	+	0.946333i
$680$	−2.90844	−	5.03756i	−0.111533	−	0.193182i
$681$	−5.00666	−	8.55683i	−0.191856	−	0.327898i
$682$	−6.24188	−	10.8113i	−0.239014	−	0.413985i
$683$	0.963470	−	1.66878i	0.0368661	−	0.0638540i	−0.847004	−	0.531587i	$-0.821596\pi$
$683$	0.963470	−	1.66878i	0.0368661	−	0.0638540i	0.883870	+	0.467733i	$0.154929\pi$
$684$	10.6093	+	17.8935i	0.405658	+	0.684175i
$685$	−6.87938			−0.262848
$686$	13.4863	−	12.6933i	0.514910	−	0.484631i
$687$	3.95896	−	6.94987i	0.151044	−	0.265154i
$688$	2.75052	−	4.76404i	0.104863	−	0.181627i
$689$	36.7836			1.40134
$690$	6.33871	+	10.8334i	0.241310	+	0.412421i
$691$	−36.9635			−1.40616			−0.703078	−	0.711112i	$-0.748192\pi$
$691$	−36.9635			−1.40616			−0.703078	+	0.711112i	$0.748192\pi$
$692$	22.7593			0.865178
$693$	−11.8248	+	3.18747i	−0.449187	+	0.121082i
$694$	2.87948			0.109303
$695$	−18.2056			−0.690578
$696$	−2.15513	+	3.78328i	−0.0816900	+	0.143405i
$697$	−19.8809			−0.753042
$698$	−15.3092	+	26.5164i	−0.579463	+	1.00366i
$699$	2.20308	+	3.76527i	0.0833282	+	0.142415i
$700$	2.56238	−	0.658939i	0.0968489	−	0.0249055i
$701$	−5.97352			−0.225617			−0.112808	−	0.993617i	$-0.535985\pi$
$701$	−5.97352			−0.225617			−0.112808	+	0.993617i	$0.535985\pi$
$702$	−16.6056	−	27.6402i	−0.626739	−	1.04321i
$703$	30.3730	−	52.6076i	1.14554	−	1.98413i
$704$	0.771481	+	1.33624i	0.0290763	+	0.0503616i
$705$	4.83403	−	8.48603i	0.182060	−	0.319603i
$706$	−9.01525	−	15.6149i	−0.339294	−	0.587674i
$707$	−2.81376	+	0.723583i	−0.105822	+	0.0272131i
$708$	−14.6373	+	0.0848625i	−0.550104	+	0.00318933i
$709$	−13.3965			−0.503115			−0.251557	−	0.967842i	$-0.580943\pi$
$709$	−13.3965			−0.503115			−0.251557	+	0.967842i	$0.580943\pi$
$710$	−3.65935	+	6.33817i	−0.137333	+	0.237867i
$711$	−6.76093	+	0.0783981i	−0.253555	+	0.00294016i
$712$	2.13541	+	3.69864i	0.0800280	+	0.138612i
$713$	29.3156	−	50.7760i	1.09788	−	1.90158i
$714$	18.7676	+	18.9296i	0.702362	+	0.708424i
$715$	−4.78744	−	8.29209i	−0.179040	−	0.310107i
$716$	−5.64468	+	9.77687i	−0.210952	+	0.365379i
$717$	7.75627	+	13.2562i	0.289663	+	0.495061i
$718$	−1.97671	−	3.42376i	−0.0737701	−	0.127774i
$719$	20.4220	+	35.3719i	0.761612	+	1.31915i	0.942019	+	0.335559i	$0.108925\pi$
$719$	20.4220	+	35.3719i	0.761612	+	1.31915i	−0.180407	+	0.983592i	$0.557742\pi$
$720$	1.46977	−	2.61529i	0.0547753	−	0.0974663i
$721$	13.6573	+	13.9359i	0.508626	+	0.519000i
$722$	−14.5409	+	25.1855i	−0.541155	+	0.937308i
$723$	12.0762	+	20.6394i	0.449120	+	0.767587i
$724$	8.38765			0.311725
$725$	2.51381			0.0933607
$726$	7.38942	−	12.9720i	0.274247	−	0.481435i
$727$	16.3277	−	28.2803i	0.605559	−	1.04886i	−0.386403	−	0.922330i	$-0.626283\pi$
$727$	16.3277	−	28.2803i	0.605559	−	1.04886i	0.991963	−	0.126530i	$-0.0403840\pi$
$728$	15.9009	−	4.08906i	0.589327	−	0.151550i
$729$	26.9837	−	0.939025i	0.999395	−	0.0347787i
$730$	1.97220	+	3.41595i	0.0729945	+	0.126430i
$731$	−15.9994	−	27.7118i	−0.591760	−	1.02496i
$732$	8.34995	−	0.0484103i	0.308623	−	0.00178930i
$733$	−9.86377	+	17.0846i	−0.364327	+	0.631033i	−0.988668	−	0.150119i	$-0.952034\pi$
$733$	−9.86377	+	17.0846i	−0.364327	+	0.631033i	0.624341	+	0.781152i	$0.285368\pi$
$734$	3.97656	+	6.88760i	0.146778	+	0.254226i
$735$	−10.5862	+	5.91044i	−0.390476	+	0.218010i
$736$	−3.62333	+	6.27579i	−0.133558	+	0.231329i
$737$	−1.61360	−	2.79484i	−0.0594377	−	0.102949i
$738$	−5.22931	−	8.81965i	−0.192494	−	0.324656i
$739$	2.35401	−	4.07726i	0.0865935	−	0.149984i	−0.819476	−	0.573114i	$-0.805735\pi$
$739$	2.35401	−	4.07726i	0.0865935	−	0.149984i	0.906069	+	0.423130i	$0.139069\pi$
$740$	−8.76047			−0.322041
$741$	36.8900	−	64.7595i	1.35519	−	2.37900i
$742$	−10.9769	−	11.2008i	−0.402976	−	0.411195i
$743$	−19.2174	−	33.2856i	−0.705019	−	1.22113i	−0.966685	−	0.255970i	$-0.917605\pi$
$743$	−19.2174	−	33.2856i	−0.705019	−	1.22113i	0.261666	−	0.965159i	$-0.415728\pi$
$744$	−14.0134	+	0.0812453i	−0.513756	+	0.00297860i
$745$	3.23664	+	5.60603i	0.118581	+	0.205389i
$746$	4.69137	−	8.12570i	0.171763	−	0.297503i
$747$	−12.1595	+	21.6363i	−0.444891	+	0.791632i
$748$	8.97521			0.328166
$749$	10.9003	−	2.80311i	0.398289	−	0.102424i
$750$	−1.73202	+	0.0100417i	−0.0632445	+	0.000366672i
$751$	7.83405	−	13.5690i	0.285869	−	0.495139i	−0.686951	−	0.726704i	$-0.741051\pi$
$751$	7.83405	−	13.5690i	0.285869	−	0.495139i	0.972819	+	0.231565i	$0.0743846\pi$
$752$	5.63858			0.205618
$753$	42.3781	−	0.245695i	1.54435	−	0.00895362i
$754$	15.5995			0.568101
$755$	−22.2725			−0.810580
$756$	−3.46116	+	13.3049i	−0.125881	+	0.483895i
$757$	−12.4460			−0.452358			−0.226179	−	0.974086i	$-0.572623\pi$
$757$	−12.4460			−0.452358			−0.226179	+	0.974086i	$0.572623\pi$
$758$	18.5648			0.674303
$759$	−19.3663	+	0.112280i	−0.702952	+	0.00407549i
$760$	6.93410			0.251526
$761$	20.0202	−	34.6760i	0.725732	−	1.25701i	−0.232939	−	0.972491i	$-0.574834\pi$
$761$	20.0202	−	34.6760i	0.725732	−	1.25701i	0.958672	−	0.284514i	$-0.0918323\pi$
$762$	−12.4537	+	0.0722027i	−0.451151	+	0.00261563i
$763$	−28.0640	−	28.6364i	−1.01599	−	1.03671i
$764$	3.17491			0.114864
$765$	−8.89995	−	15.0105i	−0.321778	−	0.542705i
$766$	0.930769	−	1.61214i	0.0336300	−	0.0582489i
$767$	26.2214	+	45.4168i	0.946800	+	1.63991i
$768$	1.73202	−	0.0100417i	0.0624989	−	0.000362349i
$769$	15.4719	+	26.7981i	0.557931	+	0.966364i	0.997669	+	0.0682382i	$0.0217378\pi$
$769$	15.4719	+	26.7981i	0.557931	+	0.966364i	−0.439739	+	0.898126i	$0.644929\pi$
$770$	−1.09633	+	3.93233i	−0.0395089	+	0.141711i
$771$	26.4206	−	46.3807i	0.951514	−	1.67036i
$772$	−7.78050			−0.280026
$773$	−18.7768	+	32.5224i	−0.675355	+	1.16975i	0.301010	+	0.953621i	$0.402676\pi$
$773$	−18.7768	+	32.5224i	−0.675355	+	1.16975i	−0.976365	+	0.216129i	$0.930657\pi$
$774$	8.08529	−	14.3868i	0.290620	−	0.517124i
$775$	4.04539	+	7.00682i	0.145315	+	0.251692i
$776$	6.52492	−	11.3015i	0.234231	−	0.405700i
$777$	38.8219	−	10.2237i	1.39273	−	0.366773i
$778$	−17.4663	−	30.2526i	−0.626199	−	1.08461i
$779$	11.8497	−	20.5242i	0.424558	−	0.735357i
$780$	−10.7481	+	0.0623140i	−0.384843	+	0.00223120i
$781$	−5.64623	−	9.77956i	−0.202038	−	0.349940i
$782$	21.0764	+	36.5055i	0.753692	+	1.30543i
$783$	−6.33335	+	11.4240i	−0.226336	+	0.408262i
$784$	−5.99028	−	3.62167i	−0.213939	−	0.129345i
$785$	8.63270	−	14.9523i	0.308114	−	0.533670i
$786$	−7.71047	+	13.5355i	−0.275023	+	0.482797i
$787$	−19.1946			−0.684213			−0.342107	−	0.939661i	$-0.611140\pi$
$787$	−19.1946			−0.684213			−0.342107	+	0.939661i	$0.611140\pi$
$788$	12.3809			0.441052
$789$	17.3807	+	29.7053i	0.618771	+	1.05754i
$790$	−1.12690	+	1.95184i	−0.0400932	+	0.0694435i
$791$	−41.5973	+	10.6971i	−1.47903	+	0.380346i
$792$	2.36077	+	3.98163i	0.0838863	+	0.141481i
$793$	−14.9582	−	25.9083i	−0.531180	−	0.920031i
$794$	−5.08328	−	8.80450i	−0.180399	−	0.312460i
$795$	5.18488	+	8.86142i	0.183889	+	0.314282i
$796$	6.84286	−	11.8522i	0.242539	−	0.420090i
$797$	6.70543	+	11.6141i	0.237518	+	0.411394i	0.960002	−	0.279995i	$-0.0903326\pi$
$797$	6.70543	+	11.6141i	0.237518	+	0.411394i	−0.722483	+	0.691389i	$0.756999\pi$
$798$	−30.7283	+	8.09228i	−1.08777	+	0.286464i
$799$	16.3994	−	28.4047i	0.580170	−	1.00488i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	6.53446	+	11.0209i	0.230884	+	0.389404i
$802$	−7.15000	+	12.3842i	−0.252475	+	0.437300i
$803$	−6.08607			−0.214773
$804$	−3.62263	+	0.0210029i	−0.127760	+	0.000740714i
$805$	−18.5687	+	4.77510i	−0.654461	+	0.168300i
$806$	25.1037	+	43.4810i	0.884242	+	1.53155i
$807$	−14.7297	+	25.8576i	−0.518509	+	0.910230i
$808$	0.549052	+	0.950986i	0.0193156	+	0.0334556i
$809$	−16.4388	+	28.4729i	−0.577959	+	1.00105i	0.417754	+	0.908560i	$0.362817\pi$
$809$	−16.4388	+	28.4729i	−0.577959	+	1.00105i	−0.995713	+	0.0924944i	$0.970516\pi$
$810$	4.31805	−	7.89648i	0.151721	−	0.277454i
$811$	−31.3557			−1.10105			−0.550523	−	0.834820i	$-0.685572\pi$
$811$	−31.3557			−1.10105			−0.550523	+	0.834820i	$0.685572\pi$
$812$	−4.65520	−	4.75015i	−0.163366	−	0.166698i
$813$	14.8643	+	25.4044i	0.521313	+	0.890971i
$814$	6.75854	−	11.7061i	0.236887	−	0.410300i
$815$	5.31832			0.186293
$816$	4.98689	−	8.75437i	0.174576	−	0.306464i
$817$	38.1448			1.33452
$818$	16.1964			0.566295
$819$	47.5573	−	12.8195i	1.66179	−	0.447948i
$820$	−3.41780			−0.119355
$821$	−6.27339			−0.218943			−0.109471	−	0.993990i	$-0.534916\pi$
$821$	−6.27339			−0.218943			−0.109471	+	0.993990i	$0.534916\pi$
$822$	−6.01744	−	10.2844i	−0.209882	−	0.358708i
$823$	14.7466			0.514034			0.257017	−	0.966407i	$-0.417260\pi$
$823$	14.7466			0.514034			0.257017	+	0.966407i	$0.417260\pi$
$824$	3.68749	−	6.38692i	0.128460	−	0.222499i
$825$	1.32280	−	2.32215i	0.0460541	−	0.0808469i
$826$	6.00471	−	21.5378i	0.208931	−	0.749398i
$827$	−14.5322			−0.505333			−0.252666	−	0.967553i	$-0.581307\pi$
$827$	−14.5322			−0.505333			−0.252666	+	0.967553i	$0.581307\pi$
$828$	−10.6510	+	18.9521i	−0.370146	+	0.658633i
$829$	−6.46322	+	11.1946i	−0.224477	+	0.388806i	−0.956162	−	0.292837i	$-0.905401\pi$
$829$	−6.46322	+	11.1946i	−0.224477	+	0.388806i	0.731685	+	0.681642i	$0.238734\pi$
$830$	4.13650	+	7.16463i	0.143580	+	0.248688i
$831$	8.83982	+	15.1081i	0.306650	+	0.524093i
$832$	−3.10276	−	5.37414i	−0.107569	−	0.186315i
$833$	−35.6667	+	19.6430i	−1.23578	+	0.680590i
$834$	−15.9246	−	27.2166i	−0.551423	−	0.942432i
$835$	11.7681			0.407252
$836$	−5.34953	+	9.26565i	−0.185017	+	0.320459i
$837$	−42.0346	+	0.731175i	−1.45293	+	0.0252731i
$838$	0.0855194	+	0.148124i	0.00295422	+	0.00511685i
$839$	−12.6427	+	21.8978i	−0.436475	+	0.755998i	−0.997415	−	0.0718593i	$-0.977107\pi$
$839$	−12.6427	+	21.8978i	−0.436475	+	0.755998i	0.560939	+	0.827857i	$0.310440\pi$
$840$	3.22642	+	3.25426i	0.111322	+	0.112283i
$841$	11.3404	+	19.6421i	0.391047	+	0.677314i
$842$	7.19459	−	12.4614i	0.247942	−	0.429448i
$843$	−6.69607	+	11.7548i	−0.230625	+	0.404857i
$844$	4.95466	+	8.58172i	0.170546	+	0.295395i
$845$	12.7542	+	22.0910i	0.438759	+	0.759953i
$846$	16.9146	−	0.196138i	0.581536	−	0.00674335i
$847$	15.9616	+	16.2871i	0.548446	+	0.559632i
$848$	−2.96378	+	5.13341i	−0.101777	+	0.176282i
$849$	−47.0150	+	0.272578i	−1.61355	+	0.00935485i
$850$	−5.81687			−0.199517
$851$	63.4842			2.17621
$852$	−12.6761	+	0.0734922i	−0.434277	+	0.00251780i
$853$	−13.4673	+	23.3260i	−0.461111	+	0.798668i	−0.999017	−	0.0443370i	$-0.985882\pi$
$853$	−13.4673	+	23.3260i	−0.461111	+	0.798668i	0.537905	+	0.843005i	$0.319216\pi$
$854$	−3.42543	+	12.2864i	−0.117216	+	0.420432i
$855$	20.8009	−	0.241202i	0.711376	−	0.00824894i
$856$	−2.12699	−	3.68406i	−0.0726991	−	0.125918i
$857$	−15.1577	−	26.2538i	−0.517775	−	0.896813i	−0.999787	−	0.0206484i	$-0.993427\pi$
$857$	−15.1577	−	26.2538i	−0.517775	−	0.896813i	0.482011	−	0.876165i	$-0.339906\pi$
$858$	8.20868	−	14.4102i	0.280240	−	0.491955i
$859$	−21.0935	+	36.5351i	−0.719702	+	1.24656i	0.241415	+	0.970422i	$0.422388\pi$
$859$	−21.0935	+	36.5351i	−0.719702	+	1.24656i	−0.961118	+	0.276139i	$0.910945\pi$
$860$	−2.75052	−	4.76404i	−0.0937919	−	0.162452i
$861$	15.1459	−	3.98866i	0.516171	−	0.135933i
$862$	2.89574	−	5.01558i	0.0986295	−	0.170831i
$863$	−4.35704	−	7.54661i	−0.148315	−	0.256890i	0.782290	−	0.622915i	$-0.214052\pi$
$863$	−4.35704	−	7.54661i	−0.148315	−	0.256890i	−0.930605	+	0.366025i	$0.880718\pi$
$864$	5.19537	−	0.0903714i	0.176750	−	0.00307450i
$865$	11.3796	−	19.7101i	0.386919	−	0.670164i
$866$	34.0010			1.15540
$867$	−14.7266	−	25.1690i	−0.500140	−	0.854785i
$868$	5.74877	−	20.6198i	0.195126	−	0.699882i
$869$	−1.73876	−	3.01162i	−0.0589834	−	0.102162i
$870$	2.19885	+	3.75804i	0.0745480	+	0.127409i
$871$	6.48961	+	11.2403i	0.219892	+	0.380864i
$872$	−7.57730	+	13.1243i	−0.256600	+	0.444444i
$873$	19.1803	−	34.1291i	0.649155	−	1.15510i
$874$	−50.2490			−1.69970
$875$	0.710533	−	2.54856i	0.0240204	−	0.0861569i
$876$	−3.38159	+	5.93631i	−0.114254	+	0.200569i
$877$	6.80059	−	11.7790i	0.229639	−	0.397747i	−0.728062	−	0.685511i	$-0.759579\pi$
$877$	6.80059	−	11.7790i	0.229639	−	0.397747i	0.957701	+	0.287764i	$0.0929120\pi$
$878$	−12.1404			−0.409719
$879$	−15.1074	−	25.8200i	−0.509561	−	0.870886i
$880$	1.54296			0.0520133
$881$	32.5677			1.09723			0.548616	−	0.836074i	$-0.315155\pi$
$881$	32.5677			1.09723			0.548616	+	0.836074i	$0.315155\pi$
$882$	−18.0956	−	10.6559i	−0.609311	−	0.358803i
$883$	32.1269			1.08116			0.540578	−	0.841294i	$-0.318206\pi$
$883$	32.1269			1.08116			0.540578	+	0.841294i	$0.318206\pi$
$884$	−36.0967			−1.21406
$885$	−7.24516	+	12.7187i	−0.243543	+	0.427535i
$886$	5.37339			0.180523
$887$	−17.8166	+	30.8593i	−0.598223	+	1.03615i	0.394860	+	0.918741i	$0.370793\pi$
$887$	−17.8166	+	30.8593i	−0.598223	+	1.03615i	−0.993083	+	0.117412i	$0.962540\pi$
$888$	−7.66285	−	13.0965i	−0.257148	−	0.439490i
$889$	5.10893	−	18.3248i	0.171348	−	0.614595i
$890$	4.27082			0.143158
$891$	7.22033	+	11.8620i	0.241890	+	0.397391i
$892$	8.60737	−	14.9084i	0.288196	−	0.499170i
$893$	19.5492	+	33.8603i	0.654190	+	1.13309i
$894$	−5.54964	+	9.74227i	−0.185608	+	0.325830i
$895$	5.64468	+	9.77687i	0.188681	+	0.326805i
$896$	−0.710533	+	2.54856i	−0.0237373	+	0.0851413i
$897$	77.8878	−	0.451569i	2.60060	−	0.0150774i
$898$	23.7693			0.793190
$899$	10.1694	−	17.6138i	0.339167	−	0.587455i
$900$	−1.53002	−	2.58051i	−0.0510008	−	0.0860170i
$901$	17.2399	+	29.8604i	0.574345	+	0.994795i
$902$	2.63676	−	4.56701i	0.0877947	−	0.152065i
$903$	17.7486	+	17.9018i	0.590638	+	0.595736i
$904$	8.11693	+	14.0589i	0.269965	+	0.467593i
$905$	4.19382	−	7.26392i	0.139407	−	0.241461i
$906$	−19.4819	−	33.2964i	−0.647244	−	1.10620i
$907$	−11.0914	−	19.2109i	−0.368285	−	0.637889i	0.621012	−	0.783801i	$-0.286722\pi$
$907$	−11.0914	−	19.2109i	−0.368285	−	0.637889i	−0.989298	+	0.145912i	$0.953388\pi$
$908$	−2.86190	−	4.95696i	−0.0949756	−	0.164503i
$909$	1.68013	+	2.83367i	0.0557262	+	0.0939868i
$910$	4.40923	−	15.8151i	0.146164	−	0.524266i
$911$	−16.0034	+	27.7187i	−0.530216	+	0.918362i	0.469162	+	0.883112i	$0.344556\pi$
$911$	−16.0034	+	27.7187i	−0.530216	+	0.918362i	−0.999379	+	0.0352498i	$0.988777\pi$
$912$	6.06531	+	10.3662i	0.200842	+	0.343258i
$913$	−12.7649			−0.422458
$914$	−9.69872			−0.320805
$915$	4.13305	−	7.25547i	0.136634	−	0.239858i
$916$	2.30893	−	3.99919i	0.0762893	−	0.132137i
$917$	−16.6550	−	16.9947i	−0.549998	−	0.561216i
$918$	14.6551	−	26.4348i	0.483692	−	0.872478i
$919$	−8.48951	−	14.7043i	−0.280043	−	0.485049i	0.691352	−	0.722518i	$-0.257015\pi$
$919$	−8.48951	−	14.7043i	−0.280043	−	0.485049i	−0.971395	+	0.237469i	$0.923682\pi$
$920$	3.62333	+	6.27579i	0.119458	+	0.206907i
$921$	−13.4785	+	0.0781443i	−0.444133	+	0.00257494i
$922$	−18.0316	+	31.2316i	−0.593838	+	1.02856i
$923$	22.7081	+	39.3317i	0.747448	+	1.29462i
$924$	−6.83761	+	1.80068i	−0.224941	+	0.0592380i
$925$	−4.38024	+	7.58679i	−0.144021	+	0.249452i
$926$	−8.40491	−	14.5577i	−0.276203	−	0.478397i
$927$	10.8395	−	19.2877i	0.356018	−	0.633492i
$928$	−1.25691	+	2.17703i	−0.0412600	+	0.0714644i
$929$	−6.09369			−0.199927			−0.0999637	−	0.994991i	$-0.531873\pi$
$929$	−6.09369			−0.199927			−0.0999637	+	0.994991i	$0.531873\pi$
$930$	−6.93634	+	12.1766i	−0.227452	+	0.399286i
$931$	0.979893	−	48.5288i	0.0321147	−	1.59047i
$932$	1.25932	+	2.18121i	0.0412506	+	0.0714481i
$933$	31.1272	−	0.180466i	1.01906	−	0.00590818i
$934$	−2.70979	−	4.69349i	−0.0886670	−	0.153576i
$935$	4.48761	−	7.77276i	0.146760	−	0.254197i
$936$	−9.49459	−	16.0134i	−0.310340	−	0.523414i
$937$	−36.0008			−1.17609			−0.588047	−	0.808826i	$-0.700103\pi$
$937$	−36.0008			−1.17609			−0.588047	+	0.808826i	$0.700103\pi$
$938$	1.48612	−	5.33047i	0.0485237	−	0.174046i
$939$	−18.4693	+	0.107079i	−0.602724	+	0.00349440i
$940$	2.81929	−	4.88315i	0.0919551	−	0.159271i
$941$	−7.52937			−0.245450			−0.122725	−	0.992441i	$-0.539163\pi$
$941$	−7.52937			−0.245450			−0.122725	+	0.992441i	$0.539163\pi$
$942$	29.9040	−	0.173374i	0.974326	−	0.00564884i
$943$	24.7676			0.806544
$944$	−8.45100			−0.275057
$945$	9.79180	+	9.64991i	0.318527	+	0.313911i
$946$	8.48790			0.275965
$947$	−7.10952			−0.231028			−0.115514	−	0.993306i	$-0.536852\pi$
$947$	−7.10952			−0.231028			−0.115514	+	0.993306i	$0.536852\pi$
$948$	−3.90362	+	0.0226320i	−0.126784	+	0.000735052i
$949$	24.4771			0.794559
$950$	3.46705	−	6.00511i	0.112486	−	0.194831i
$951$	56.3994	−	0.326986i	1.82888	−	0.0106032i
$952$	10.7720	+	10.9917i	0.349121	+	0.356242i
$953$	−2.96281			−0.0959750			−0.0479875	−	0.998848i	$-0.515281\pi$
$953$	−2.96281			−0.0959750			−0.0479875	+	0.998848i	$0.515281\pi$
$954$	−8.71217	+	15.5023i	−0.282067	+	0.501906i
$955$	1.58745	−	2.74955i	0.0513688	−	0.0889734i
$956$	4.43364	+	7.67928i	0.143394	+	0.248366i
$957$	−6.71803	+	0.0389490i	−0.217163	+	0.00125904i
$958$	−10.6632	−	18.4692i	−0.344513	−	0.596714i
$959$	17.6276	−	4.53309i	0.569225	−	0.146381i
$960$	0.857314	−	1.50500i	0.0276697	−	0.0485735i
$961$	34.4607			1.11164
$962$	−27.1816	+	47.0800i	−0.876371	+	1.51792i
$963$	−6.50870	−	10.9774i	−0.209740	−	0.353743i
$964$	6.90302	+	11.9564i	0.222331	+	0.385089i
$965$	−3.89025	+	6.73811i	−0.125232	+	0.216907i
$966$	−23.3807	−	23.5825i	−0.752263	−	0.758756i
$967$	−23.4494	−	40.6156i	−0.754083	−	1.30611i	−0.945829	−	0.324666i	$-0.894748\pi$
$967$	−23.4494	−	40.6156i	−0.754083	−	1.30611i	0.191746	−	0.981445i	$-0.438585\pi$
$968$	4.30963	−	7.46450i	0.138517	−	0.239918i
$969$	69.8607	−	0.405030i	2.24425	−	0.0130114i
$970$	−6.52492	−	11.3015i	−0.209502	−	0.362869i
$971$	11.3903	+	19.7286i	0.365533	+	0.633122i	0.988862	−	0.148838i	$-0.0475533\pi$
$971$	11.3903	+	19.7286i	0.365533	+	0.633122i	−0.623328	+	0.781960i	$0.714220\pi$
$972$	15.5819	−	0.451816i	0.499790	−	0.0144920i
$973$	46.6497	−	11.9964i	1.49552	−	0.384586i
$974$	4.46333	−	7.73071i	0.143014	−	0.247708i
$975$	−5.32008	+	9.33928i	−0.170379	+	0.299096i
$976$	4.82092			0.154314
$977$	56.6089			1.81108			0.905539	−	0.424263i	$-0.139467\pi$
$977$	56.6089			1.81108			0.905539	+	0.424263i	$0.139467\pi$
$978$	4.65197	+	7.95064i	0.148754	+	0.254234i
$979$	−3.29486	+	5.70687i	−0.105304	+	0.182392i
$980$	−6.13160	+	3.37690i	−0.195867	+	0.107871i
$981$	−22.2738	+	39.6337i	−0.711149	+	1.26541i
$982$	4.97746	+	8.62122i	0.158837	+	0.275114i
$983$	8.70756	+	15.0819i	0.277728	+	0.481039i	0.970820	−	0.239810i	$-0.0770852\pi$
$983$	8.70756	+	15.0819i	0.277728	+	0.481039i	−0.693092	+	0.720849i	$0.743752\pi$
$984$	−2.98957	−	5.10945i	−0.0953040	−	0.162883i
$985$	6.19046	−	10.7222i	0.197244	−	0.341637i
$986$	7.31127	+	12.6635i	0.232838	+	0.403288i
$987$	−6.79487	+	24.9298i	−0.216283	+	0.793524i
$988$	21.5148	−	37.2648i	0.684478	−	1.18555i
$989$	19.9321	+	34.5234i	0.633803	+	1.09778i
$990$	4.62858	−	0.0536718i	0.147106	−	0.00170580i
$991$	28.7894	−	49.8647i	0.914526	−	1.58401i	0.106932	−	0.994266i	$-0.465897\pi$
$991$	28.7894	−	49.8647i	0.914526	−	1.58401i	0.807594	−	0.589739i	$-0.200769\pi$
$992$	−8.09078			−0.256883
$993$	29.3139	−	0.169953i	0.930248	−	0.00539328i
$994$	5.20018	−	18.6521i	0.164940	−	0.591609i
$995$	−6.84286	−	11.8522i	−0.216933	−	0.375740i
$996$	−7.09257	+	12.4508i	−0.224737	+	0.394520i
$997$	−8.94008	−	15.4847i	−0.283135	−	0.490404i	0.689020	−	0.724742i	$-0.258041\pi$
$997$	−8.94008	−	15.4847i	−0.283135	−	0.490404i	−0.972155	+	0.234338i	$0.924708\pi$
$998$	−15.3925	+	26.6607i	−0.487242	+	0.843929i
$999$	−23.4426	−	39.0203i	−0.741690	−	1.23455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.h.151.6	yes	12
3.2	odd	2		1890.2.i.f.991.1		12
7.2	even	3		630.2.l.f.331.3	yes	12
9.4	even	3		630.2.l.f.571.3	yes	12
9.5	odd	6		1890.2.l.h.361.2		12
21.2	odd	6		1890.2.l.h.1801.2		12
63.23	odd	6		1890.2.i.f.1171.1		12
63.58	even	3	inner	630.2.i.h.121.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.6	✓	12	63.58	even	3	inner
630.2.i.h.151.6	yes	12	1.1	even	1	trivial
630.2.l.f.331.3	yes	12	7.2	even	3
630.2.l.f.571.3	yes	12	9.4	even	3
1890.2.i.f.991.1		12	3.2	odd	2
1890.2.i.f.1171.1		12	63.23	odd	6
1890.2.l.h.361.2		12	9.5	odd	6
1890.2.l.h.1801.2		12	21.2	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.73202 - 0.0100417i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73202 - 0.0100417i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(2.99980 - 0.0347849i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.73202 - 0.0100417i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73202 - 0.0100417i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(2.99980 - 0.0347849i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.771481 + 1.33624i) q^{11} +(1.73202 - 0.0100417i) q^{12} +(-3.10276 - 5.37414i) q^{13} +(-0.710533 + 2.54856i) q^{14} +(0.857314 - 1.50500i) q^{15} +1.00000 q^{16} +(2.90844 - 5.03756i) q^{17} +(2.99980 - 0.0347849i) q^{18} +(3.46705 + 6.00511i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.20507 + 4.42129i) q^{21} +(0.771481 + 1.33624i) q^{22} +(-3.62333 + 6.27579i) q^{23} +(1.73202 - 0.0100417i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.10276 - 5.37414i) q^{26} +(5.19537 - 0.0903714i) q^{27} +(-0.710533 + 2.54856i) q^{28} +(-1.25691 + 2.17703i) q^{29} +(0.857314 - 1.50500i) q^{30} -8.09078 q^{31} +1.00000 q^{32} +(1.34964 + 2.30666i) q^{33} +(2.90844 - 5.03756i) q^{34} +(1.85185 + 1.88962i) q^{35} +(2.99980 - 0.0347849i) q^{36} +(-4.38024 - 7.58679i) q^{37} +(3.46705 + 6.00511i) q^{38} +(-5.42801 - 9.27696i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.70890 - 2.95990i) q^{41} +(-1.20507 + 4.42129i) q^{42} +(2.75052 - 4.76404i) q^{43} +(0.771481 + 1.33624i) q^{44} +(1.46977 - 2.61529i) q^{45} +(-3.62333 + 6.27579i) q^{46} +5.63858 q^{47} +(1.73202 - 0.0100417i) q^{48} +(-5.99028 - 3.62167i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.98689 - 8.75437i) q^{51} +(-3.10276 - 5.37414i) q^{52} +(-2.96378 + 5.13341i) q^{53} +(5.19537 - 0.0903714i) q^{54} +1.54296 q^{55} +(-0.710533 + 2.54856i) q^{56} +(6.06531 + 10.3662i) q^{57} +(-1.25691 + 2.17703i) q^{58} -8.45100 q^{59} +(0.857314 - 1.50500i) q^{60} +4.82092 q^{61} -8.09078 q^{62} +(-2.04281 + 7.66987i) q^{63} +1.00000 q^{64} -6.20552 q^{65} +(1.34964 + 2.30666i) q^{66} -2.09156 q^{67} +(2.90844 - 5.03756i) q^{68} +(-6.21267 + 10.9062i) q^{69} +(1.85185 + 1.88962i) q^{70} -7.31869 q^{71} +(2.99980 - 0.0347849i) q^{72} +(-1.97220 + 3.41595i) q^{73} +(-4.38024 - 7.58679i) q^{74} +(-0.874707 - 1.49495i) q^{75} +(3.46705 + 6.00511i) q^{76} +(-3.95366 + 1.01672i) q^{77} +(-5.42801 - 9.27696i) q^{78} -2.25380 q^{79} +(0.500000 - 0.866025i) q^{80} +(8.99758 - 0.208696i) q^{81} +(-1.70890 - 2.95990i) q^{82} +(-4.13650 + 7.16463i) q^{83} +(-1.20507 + 4.42129i) q^{84} +(-2.90844 - 5.03756i) q^{85} +(2.75052 - 4.76404i) q^{86} +(-2.15513 + 3.78328i) q^{87} +(0.771481 + 1.33624i) q^{88} +(2.13541 + 3.69864i) q^{89} +(1.46977 - 2.61529i) q^{90} +(15.9009 - 4.08906i) q^{91} +(-3.62333 + 6.27579i) q^{92} +(-14.0134 + 0.0812453i) q^{93} +5.63858 q^{94} +6.93410 q^{95} +(1.73202 - 0.0100417i) q^{96} +(6.52492 - 11.3015i) q^{97} +(-5.99028 - 3.62167i) q^{98} +(2.36077 + 3.98163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

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