LMFDB - Embedded newform 370.2.h.e.253.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (of order $4$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.5
Root			$0.0477388 + 0.0477388i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.0477388 - 0.0477388i) q^{3} +1.00000 q^{4} +(0.531109 - 2.17208i) q^{5} +(-0.0477388 + 0.0477388i) q^{6} +(-2.77997 + 2.77997i) q^{7} -1.00000 q^{8} +2.99544i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.0477388 - 0.0477388i) q^{3} +1.00000 q^{4} +(0.531109 - 2.17208i) q^{5} +(-0.0477388 + 0.0477388i) q^{6} +(-2.77997 + 2.77997i) q^{7} -1.00000 q^{8} +2.99544i q^{9} +(-0.531109 + 2.17208i) q^{10} +4.24241i q^{11} +(0.0477388 - 0.0477388i) q^{12} +3.32010 q^{13} +(2.77997 - 2.77997i) q^{14} +(-0.0783380 - 0.129047i) q^{15} +1.00000 q^{16} -3.64900i q^{17} -2.99544i q^{18} +(4.65117 + 4.65117i) q^{19} +(0.531109 - 2.17208i) q^{20} +0.265425i q^{21} -4.24241i q^{22} +3.99058 q^{23} +(-0.0477388 + 0.0477388i) q^{24} +(-4.43585 - 2.30722i) q^{25} -3.32010 q^{26} +(0.286215 + 0.286215i) q^{27} +(-2.77997 + 2.77997i) q^{28} +(1.30707 - 1.30707i) q^{29} +(0.0783380 + 0.129047i) q^{30} +(3.96252 + 3.96252i) q^{31} -1.00000 q^{32} +(0.202528 + 0.202528i) q^{33} +3.64900i q^{34} +(4.56184 + 7.51477i) q^{35} +2.99544i q^{36} +(-3.91278 + 4.65727i) q^{37} +(-4.65117 - 4.65117i) q^{38} +(0.158498 - 0.158498i) q^{39} +(-0.531109 + 2.17208i) q^{40} +2.70237i q^{41} -0.265425i q^{42} -6.95570 q^{43} +4.24241i q^{44} +(6.50633 + 1.59091i) q^{45} -3.99058 q^{46} +(1.34199 - 1.34199i) q^{47} +(0.0477388 - 0.0477388i) q^{48} -8.45644i q^{49} +(4.43585 + 2.30722i) q^{50} +(-0.174199 - 0.174199i) q^{51} +3.32010 q^{52} +(5.37378 + 5.37378i) q^{53} +(-0.286215 - 0.286215i) q^{54} +(9.21484 + 2.25318i) q^{55} +(2.77997 - 2.77997i) q^{56} +0.444083 q^{57} +(-1.30707 + 1.30707i) q^{58} +(-8.04404 - 8.04404i) q^{59} +(-0.0783380 - 0.129047i) q^{60} +(1.55262 + 1.55262i) q^{61} +(-3.96252 - 3.96252i) q^{62} +(-8.32723 - 8.32723i) q^{63} +1.00000 q^{64} +(1.76334 - 7.21153i) q^{65} +(-0.202528 - 0.202528i) q^{66} +(-4.34085 - 4.34085i) q^{67} -3.64900i q^{68} +(0.190506 - 0.190506i) q^{69} +(-4.56184 - 7.51477i) q^{70} +5.54775 q^{71} -2.99544i q^{72} +(-11.1383 + 11.1383i) q^{73} +(3.91278 - 4.65727i) q^{74} +(-0.321906 + 0.101618i) q^{75} +(4.65117 + 4.65117i) q^{76} +(-11.7938 - 11.7938i) q^{77} +(-0.158498 + 0.158498i) q^{78} +(-3.17689 - 3.17689i) q^{79} +(0.531109 - 2.17208i) q^{80} -8.95900 q^{81} -2.70237i q^{82} +(7.08119 + 7.08119i) q^{83} +0.265425i q^{84} +(-7.92592 - 1.93802i) q^{85} +6.95570 q^{86} -0.124796i q^{87} -4.24241i q^{88} +(7.75651 - 7.75651i) q^{89} +(-6.50633 - 1.59091i) q^{90} +(-9.22978 + 9.22978i) q^{91} +3.99058 q^{92} +0.378332 q^{93} +(-1.34199 + 1.34199i) q^{94} +(12.5730 - 7.63243i) q^{95} +(-0.0477388 + 0.0477388i) q^{96} -10.0451i q^{97} +8.45644i q^{98} -12.7079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.0477388	−	0.0477388i	0.0275620	−	0.0275620i	−0.693191	−	0.720753i	$-0.743796\pi$
$3$	0.0477388	−	0.0477388i	0.0275620	−	0.0275620i	0.720753	+	0.693191i	$0.243796\pi$
$4$	1.00000			0.500000
$5$	0.531109	−	2.17208i	0.237519	−	0.971383i
$5$	0.531109	−	2.17208i	0.237519	−	0.971383i
$6$	−0.0477388	+	0.0477388i	−0.0194893	+	0.0194893i
$7$	−2.77997	+	2.77997i	−1.05073	+	1.05073i	−0.0520865	+	0.998643i	$0.516587\pi$
$7$	−2.77997	+	2.77997i	−1.05073	+	1.05073i	−0.998643	+	0.0520865i	$0.983413\pi$
$8$	−1.00000			−0.353553
$9$			2.99544i			0.998481i
$10$	−0.531109	+	2.17208i	−0.167951	+	0.686871i
$11$			4.24241i			1.27913i	0.768735	+	0.639567i	$0.220886\pi$
$11$			4.24241i			1.27913i	−0.768735	+	0.639567i	$0.779114\pi$
$12$	0.0477388	−	0.0477388i	0.0137810	−	0.0137810i
$13$	3.32010			0.920831			0.460416	−	0.887703i	$-0.347700\pi$
$13$	3.32010			0.920831			0.460416	+	0.887703i	$0.347700\pi$
$14$	2.77997	−	2.77997i	0.742978	−	0.742978i
$15$	−0.0783380	−	0.129047i	−0.0202268	−	0.0333198i
$16$	1.00000			0.250000
$17$		−	3.64900i		−	0.885013i	−0.896765	−	0.442507i	$-0.854089\pi$
$17$		−	3.64900i		−	0.885013i	0.896765	−	0.442507i	$-0.145911\pi$
$18$		−	2.99544i		−	0.706032i
$19$	4.65117	+	4.65117i	1.06705	+	1.06705i	0.997584	+	0.0694677i	$0.0221301\pi$
$19$	4.65117	+	4.65117i	1.06705	+	1.06705i	0.0694677	+	0.997584i	$0.477870\pi$
$20$	0.531109	−	2.17208i	0.118760	−	0.485691i
$21$			0.265425i			0.0579205i
$22$		−	4.24241i		−	0.904484i
$23$	3.99058			0.832094			0.416047	−	0.909343i	$-0.363415\pi$
$23$	3.99058			0.832094			0.416047	+	0.909343i	$0.363415\pi$
$24$	−0.0477388	+	0.0477388i	−0.00974465	+	0.00974465i
$25$	−4.43585	−	2.30722i	−0.887169	−	0.461444i
$26$	−3.32010			−0.651126
$27$	0.286215	+	0.286215i	0.0550822	+	0.0550822i
$28$	−2.77997	+	2.77997i	−0.525365	+	0.525365i
$29$	1.30707	−	1.30707i	0.242717	−	0.242717i	−0.575256	−	0.817973i	$-0.695098\pi$
$29$	1.30707	−	1.30707i	0.242717	−	0.242717i	0.817973	+	0.575256i	$0.195098\pi$
$30$	0.0783380	+	0.129047i	0.0143025	+	0.0235607i
$31$	3.96252	+	3.96252i	0.711689	+	0.711689i	0.966888	−	0.255199i	$-0.0821411\pi$
$31$	3.96252	+	3.96252i	0.711689	+	0.711689i	−0.255199	+	0.966888i	$0.582141\pi$
$32$	−1.00000			−0.176777
$33$	0.202528	+	0.202528i	0.0352555	+	0.0352555i
$34$			3.64900i			0.625799i
$35$	4.56184	+	7.51477i	0.771092	+	1.27023i
$36$			2.99544i			0.499240i
$37$	−3.91278	+	4.65727i	−0.643258	+	0.765650i
$37$	−3.91278	+	4.65727i	−0.643258	+	0.765650i
$38$	−4.65117	−	4.65117i	−0.754520	−	0.754520i
$39$	0.158498	−	0.158498i	0.0253800	−	0.0253800i
$40$	−0.531109	+	2.17208i	−0.0839757	+	0.343436i
$41$			2.70237i			0.422040i	0.977482	+	0.211020i	$0.0676785\pi$
$41$			2.70237i			0.422040i	−0.977482	+	0.211020i	$0.932321\pi$
$42$		−	0.265425i		−	0.0409560i
$43$	−6.95570			−1.06073			−0.530367	−	0.847768i	$-0.677946\pi$
$43$	−6.95570			−1.06073			−0.530367	+	0.847768i	$0.677946\pi$
$44$			4.24241i			0.639567i
$45$	6.50633	+	1.59091i	0.969907	+	0.237158i
$46$	−3.99058			−0.588380
$47$	1.34199	−	1.34199i	0.195749	−	0.195749i	−0.602426	−	0.798175i	$-0.705799\pi$
$47$	1.34199	−	1.34199i	0.195749	−	0.195749i	0.798175	+	0.602426i	$0.205799\pi$
$48$	0.0477388	−	0.0477388i	0.00689051	−	0.00689051i
$49$		−	8.45644i		−	1.20806i
$50$	4.43585	+	2.30722i	0.627324	+	0.326290i
$51$	−0.174199	−	0.174199i	−0.0243928	−	0.0243928i
$52$	3.32010			0.460416
$53$	5.37378	+	5.37378i	0.738145	+	0.738145i	0.972219	−	0.234074i	$-0.0752057\pi$
$53$	5.37378	+	5.37378i	0.738145	+	0.738145i	−0.234074	+	0.972219i	$0.575206\pi$
$54$	−0.286215	−	0.286215i	−0.0389490	−	0.0389490i
$55$	9.21484	+	2.25318i	1.24253	+	0.303819i
$56$	2.77997	−	2.77997i	0.371489	−	0.371489i
$57$	0.444083			0.0588202
$58$	−1.30707	+	1.30707i	−0.171627	+	0.171627i
$59$	−8.04404	−	8.04404i	−1.04725	−	1.04725i	−0.998827	−	0.0484179i	$-0.984582\pi$
$59$	−8.04404	−	8.04404i	−1.04725	−	1.04725i	−0.0484179	−	0.998827i	$-0.515418\pi$
$60$	−0.0783380	−	0.129047i	−0.0101134	−	0.0166599i
$61$	1.55262	+	1.55262i	0.198793	+	0.198793i	0.799482	−	0.600690i	$-0.205107\pi$
$61$	1.55262	+	1.55262i	0.198793	+	0.198793i	−0.600690	+	0.799482i	$0.705107\pi$
$62$	−3.96252	−	3.96252i	−0.503240	−	0.503240i
$63$	−8.32723	−	8.32723i	−1.04913	−	1.04913i
$64$	1.00000			0.125000
$65$	1.76334	−	7.21153i	0.218715	−	0.894480i
$66$	−0.202528	−	0.202528i	−0.0249294	−	0.0249294i
$67$	−4.34085	−	4.34085i	−0.530320	−	0.530320i	0.390348	−	0.920668i	$-0.372355\pi$
$67$	−4.34085	−	4.34085i	−0.530320	−	0.530320i	−0.920668	+	0.390348i	$0.872355\pi$
$68$		−	3.64900i		−	0.442507i
$69$	0.190506	−	0.190506i	0.0229342	−	0.0229342i
$70$	−4.56184	−	7.51477i	−0.545244	−	0.898187i
$71$	5.54775			0.658397			0.329198	−	0.944261i	$-0.393222\pi$
$71$	5.54775			0.658397			0.329198	+	0.944261i	$0.393222\pi$
$72$		−	2.99544i		−	0.353016i
$73$	−11.1383	+	11.1383i	−1.30364	+	1.30364i	−0.377712	+	0.925923i	$0.623289\pi$
$73$	−11.1383	+	11.1383i	−1.30364	+	1.30364i	−0.925923	+	0.377712i	$0.876711\pi$
$74$	3.91278	−	4.65727i	0.454852	−	0.541396i
$75$	−0.321906	+	0.101618i	−0.0371705	+	0.0117339i
$76$	4.65117	+	4.65117i	0.533526	+	0.533526i
$77$	−11.7938	−	11.7938i	−1.34402	−	1.34402i
$78$	−0.158498	+	0.158498i	−0.0179464	+	0.0179464i
$79$	−3.17689	−	3.17689i	−0.357428	−	0.357428i	0.505436	−	0.862864i	$-0.331332\pi$
$79$	−3.17689	−	3.17689i	−0.357428	−	0.357428i	−0.862864	+	0.505436i	$0.831332\pi$
$80$	0.531109	−	2.17208i	0.0593798	−	0.242846i
$81$	−8.95900			−0.995444
$82$		−	2.70237i		−	0.298427i
$83$	7.08119	+	7.08119i	0.777261	+	0.777261i	0.979364	−	0.202103i	$-0.0647775\pi$
$83$	7.08119	+	7.08119i	0.777261	+	0.777261i	−0.202103	+	0.979364i	$0.564778\pi$
$84$			0.265425i			0.0289602i
$85$	−7.92592	−	1.93802i	−0.859687	−	0.210208i
$86$	6.95570			0.750053
$87$		−	0.124796i		−	0.0133795i
$88$		−	4.24241i		−	0.452242i
$89$	7.75651	−	7.75651i	0.822188	−	0.822188i	−0.164233	−	0.986422i	$-0.552515\pi$
$89$	7.75651	−	7.75651i	0.822188	−	0.822188i	0.986422	+	0.164233i	$0.0525149\pi$
$90$	−6.50633	−	1.59091i	−0.685828	−	0.167696i
$91$	−9.22978	+	9.22978i	−0.967544	+	0.967544i
$92$	3.99058			0.416047
$93$	0.378332			0.0392312
$94$	−1.34199	+	1.34199i	−0.138416	+	0.138416i
$95$	12.5730	−	7.63243i	1.28996	−	0.783071i
$96$	−0.0477388	+	0.0477388i	−0.00487233	+	0.00487233i
$97$		−	10.0451i		−	1.01992i	−0.860197	−	0.509962i	$-0.829660\pi$
$97$		−	10.0451i		−	1.01992i	0.860197	−	0.509962i	$-0.170340\pi$
$98$			8.45644i			0.854230i
$99$	−12.7079			−1.27719
$100$	−4.43585	−	2.30722i	−0.443585	−	0.230722i
$101$		−	1.51442i		−	0.150691i	−0.997157	−	0.0753454i	$-0.975994\pi$
$101$		−	1.51442i		−	0.150691i	0.997157	−	0.0753454i	$-0.0240059\pi$
$102$	0.174199	+	0.174199i	0.0172483	+	0.0172483i
$103$		−	3.88757i		−	0.383054i	−0.981487	−	0.191527i	$-0.938656\pi$
$103$		−	3.88757i		−	0.383054i	0.981487	−	0.191527i	$-0.0613439\pi$
$104$	−3.32010			−0.325563
$105$	0.576524	+	0.140969i	0.0562629	+	0.0137572i
$106$	−5.37378	−	5.37378i	−0.521948	−	0.521948i
$107$	0.736249	−	0.736249i	0.0711758	−	0.0711758i	−0.670623	−	0.741799i	$-0.733973\pi$
$107$	0.736249	−	0.736249i	0.0711758	−	0.0711758i	0.741799	+	0.670623i	$0.233973\pi$
$108$	0.286215	+	0.286215i	0.0275411	+	0.0275411i
$109$	1.72705	+	1.72705i	0.165422	+	0.165422i	0.784964	−	0.619542i	$-0.212682\pi$
$109$	1.72705	+	1.72705i	0.165422	+	0.165422i	−0.619542	+	0.784964i	$0.712682\pi$
$110$	−9.21484	−	2.25318i	−0.878600	−	0.214832i
$111$	0.0355407	+	0.409124i	0.00337337	+	0.0388324i
$112$	−2.77997	+	2.77997i	−0.262682	+	0.262682i
$113$		−	4.23008i		−	0.397933i	−0.980006	−	0.198966i	$-0.936242\pi$
$113$		−	4.23008i		−	0.397933i	0.980006	−	0.198966i	$-0.0637585\pi$
$114$	−0.444083			−0.0415922
$115$	2.11943	−	8.66786i	0.197638	−	0.808282i
$116$	1.30707	−	1.30707i	0.121358	−	0.121358i
$117$			9.94518i			0.919432i
$118$	8.04404	+	8.04404i	0.740514	+	0.740514i
$119$	10.1441	+	10.1441i	0.929909	+	0.929909i
$120$	0.0783380	+	0.129047i	0.00715125	+	0.0117803i
$121$	−6.99802			−0.636183
$122$	−1.55262	−	1.55262i	−0.140568	−	0.140568i
$123$	0.129008	+	0.129008i	0.0116323	+	0.0116323i
$124$	3.96252	+	3.96252i	0.355845	+	0.355845i
$125$	−7.36738	+	8.40962i	−0.658958	+	0.752179i
$126$	8.32723	+	8.32723i	0.741849	+	0.741849i
$127$	0.683408	−	0.683408i	0.0606426	−	0.0606426i	−0.676135	−	0.736778i	$-0.736346\pi$
$127$	0.683408	−	0.683408i	0.0606426	−	0.0606426i	0.736778	+	0.676135i	$0.236346\pi$
$128$	−1.00000			−0.0883883
$129$	−0.332057	+	0.332057i	−0.0292360	+	0.0292360i
$130$	−1.76334	+	7.21153i	−0.154655	+	0.632493i
$131$	−3.35210	−	3.35210i	−0.292875	−	0.292875i	0.545340	−	0.838215i	$-0.316400\pi$
$131$	−3.35210	−	3.35210i	−0.292875	−	0.292875i	−0.838215	+	0.545340i	$0.816400\pi$
$132$	0.202528	+	0.202528i	0.0176278	+	0.0176278i
$133$	−25.8602			−2.24237
$134$	4.34085	+	4.34085i	0.374993	+	0.374993i
$135$	0.773694	−	0.469671i	0.0665890	−	0.0404228i
$136$			3.64900i			0.312900i
$137$	15.4431	−	15.4431i	1.31939	−	1.31939i	0.405138	−	0.914256i	$-0.367223\pi$
$137$	15.4431	−	15.4431i	1.31939	−	1.31939i	0.914256	−	0.405138i	$-0.132777\pi$
$138$	−0.190506	+	0.190506i	−0.0162169	+	0.0162169i
$139$	17.8399			1.51316			0.756582	−	0.653899i	$-0.226868\pi$
$139$	17.8399			1.51316			0.756582	+	0.653899i	$0.226868\pi$
$140$	4.56184	+	7.51477i	0.385546	+	0.635114i
$141$		−	0.128130i		−	0.0107905i
$142$	−5.54775			−0.465557
$143$			14.0852i			1.17787i
$144$			2.99544i			0.249620i
$145$	−2.14486	−	3.53325i	−0.178121	−	0.293421i
$146$	11.1383	−	11.1383i	0.921809	−	0.921809i
$147$	−0.403701	−	0.403701i	−0.0332967	−	0.0332967i
$148$	−3.91278	+	4.65727i	−0.321629	+	0.382825i
$149$		−	17.7144i		−	1.45122i	−0.688106	−	0.725610i	$-0.741558\pi$
$149$		−	17.7144i		−	1.45122i	0.688106	−	0.725610i	$-0.258442\pi$
$150$	0.321906	−	0.101618i	0.0262835	−	0.00829709i
$151$			5.53031i			0.450050i	0.974353	+	0.225025i	$0.0722464\pi$
$151$			5.53031i			0.450050i	−0.974353	+	0.225025i	$0.927754\pi$
$152$	−4.65117	−	4.65117i	−0.377260	−	0.377260i
$153$	10.9304			0.883669
$154$	11.7938	+	11.7938i	0.950368	+	0.950368i
$155$	10.7114	−	6.50237i	0.860362	−	0.522283i
$156$	0.158498	−	0.158498i	0.0126900	−	0.0126900i
$157$	−3.47940	+	3.47940i	−0.277687	+	0.277687i	−0.832185	−	0.554498i	$-0.812910\pi$
$157$	−3.47940	+	3.47940i	−0.277687	+	0.277687i	0.554498	+	0.832185i	$0.312910\pi$
$158$	3.17689	+	3.17689i	0.252740	+	0.252740i
$159$	0.513076			0.0406896
$160$	−0.531109	+	2.17208i	−0.0419878	+	0.171718i
$161$	−11.0937	+	11.0937i	−0.874306	+	0.874306i
$162$	8.95900			0.703885
$163$		−	21.7952i		−	1.70713i	−0.520985	−	0.853566i	$-0.674435\pi$
$163$		−	21.7952i		−	1.70713i	0.520985	−	0.853566i	$-0.325565\pi$
$164$			2.70237i			0.211020i
$165$	0.547470	−	0.332342i	0.0426205	−	0.0258728i
$166$	−7.08119	−	7.08119i	−0.549607	−	0.549607i
$167$			11.1575i			0.863394i	0.902019	+	0.431697i	$0.142085\pi$
$167$			11.1575i			0.863394i	−0.902019	+	0.431697i	$0.857915\pi$
$168$		−	0.265425i		−	0.0204780i
$169$	−1.97691			−0.152070
$170$	7.92592	+	1.93802i	0.607890	+	0.148639i
$171$	−13.9323	+	13.9323i	−1.06543	+	1.06543i
$172$	−6.95570			−0.530367
$173$	14.4965	−	14.4965i	1.10215	−	1.10215i	0.107994	−	0.994152i	$-0.465557\pi$
$173$	14.4965	−	14.4965i	1.10215	−	1.10215i	0.994152	−	0.107994i	$-0.0344428\pi$
$174$			0.124796i			0.00946076i
$175$	18.7455	−	5.91752i	1.41703	−	0.447322i
$176$			4.24241i			0.319783i
$177$	−0.768026			−0.0577284
$178$	−7.75651	+	7.75651i	−0.581375	+	0.581375i
$179$	−12.6119	+	12.6119i	−0.942658	+	0.942658i	−0.998443	−	0.0557848i	$-0.982234\pi$
$179$	−12.6119	+	12.6119i	−0.942658	+	0.942658i	0.0557848	+	0.998443i	$0.482234\pi$
$180$	6.50633	+	1.59091i	0.484954	+	0.118579i
$181$	12.8145			0.952494			0.476247	−	0.879312i	$-0.341997\pi$
$181$	12.8145			0.952494			0.476247	+	0.879312i	$0.341997\pi$
$182$	9.22978	−	9.22978i	0.684157	−	0.684157i
$183$	0.148241			0.0109583
$184$	−3.99058			−0.294190
$185$	8.03783	+	10.9724i	0.590953	+	0.806706i
$186$	−0.378332			−0.0277406
$187$	15.4806			1.13205
$188$	1.34199	−	1.34199i	0.0978746	−	0.0978746i
$189$	−1.59134			−0.115753
$190$	−12.5730	+	7.63243i	−0.912140	+	0.553715i
$191$	10.0822	−	10.0822i	0.729521	−	0.729521i	−0.241003	−	0.970524i	$-0.577476\pi$
$191$	10.0822	−	10.0822i	0.729521	−	0.729521i	0.970524	+	0.241003i	$0.0774763\pi$
$192$	0.0477388	−	0.0477388i	0.00344525	−	0.00344525i
$193$	7.58052			0.545658			0.272829	−	0.962063i	$-0.412041\pi$
$193$	7.58052			0.545658			0.272829	+	0.962063i	$0.412041\pi$
$194$			10.0451i			0.721195i
$195$	−0.260090	−	0.428450i	−0.0186255	−	0.0306819i
$196$		−	8.45644i		−	0.604032i
$197$	−16.8945	+	16.8945i	−1.20369	+	1.20369i	−0.230649	+	0.973037i	$0.574085\pi$
$197$	−16.8945	+	16.8945i	−1.20369	+	1.20369i	−0.973037	+	0.230649i	$0.925915\pi$
$198$	12.7079			0.903110
$199$	0.576031	−	0.576031i	0.0408338	−	0.0408338i	−0.686395	−	0.727229i	$-0.740808\pi$
$199$	0.576031	−	0.576031i	0.0408338	−	0.0408338i	0.727229	+	0.686395i	$0.240808\pi$
$200$	4.43585	+	2.30722i	0.313662	+	0.163145i
$201$	−0.414455			−0.0292334
$202$			1.51442i			0.106554i
$203$			7.26722i			0.510059i
$204$	−0.174199	−	0.174199i	−0.0121964	−	0.0121964i
$205$	5.86977	+	1.43525i	0.409962	+	0.100243i
$206$			3.88757i			0.270860i
$207$			11.9536i			0.830830i
$208$	3.32010			0.230208
$209$	−19.7322	+	19.7322i	−1.36490	+	1.36490i
$210$	−0.576524	−	0.140969i	−0.0397839	−	0.00972782i
$211$	−21.1449			−1.45568			−0.727838	−	0.685749i	$-0.759475\pi$
$211$	−21.1449			−1.45568			−0.727838	+	0.685749i	$0.759475\pi$
$212$	5.37378	+	5.37378i	0.369073	+	0.369073i
$213$	0.264843	−	0.264843i	0.0181467	−	0.0181467i
$214$	−0.736249	+	0.736249i	−0.0503289	+	0.0503289i
$215$	−3.69423	+	15.1083i	−0.251945	+	1.03038i
$216$	−0.286215	−	0.286215i	−0.0194745	−	0.0194745i
$217$	−22.0313			−1.49559
$218$	−1.72705	−	1.72705i	−0.116971	−	0.116971i
$219$			1.06346i			0.0718617i
$220$	9.21484	+	2.25318i	0.621264	+	0.151909i
$221$		−	12.1151i		−	0.814948i
$222$	−0.0355407	−	0.409124i	−0.00238534	−	0.0274586i
$223$	14.0320	+	14.0320i	0.939655	+	0.939655i	0.998280	−	0.0586249i	$-0.0186716\pi$
$223$	14.0320	+	14.0320i	0.939655	+	0.939655i	−0.0586249	+	0.998280i	$0.518672\pi$
$224$	2.77997	−	2.77997i	0.185744	−	0.185744i
$225$	6.91114	−	13.2873i	0.460743	−	0.885822i
$226$			4.23008i			0.281381i
$227$			17.0093i			1.12895i	0.825450	+	0.564475i	$0.190921\pi$
$227$			17.0093i			1.12895i	−0.825450	+	0.564475i	$0.809079\pi$
$228$	0.444083			0.0294101
$229$			8.49131i			0.561121i	0.959836	+	0.280561i	$0.0905204\pi$
$229$			8.49131i			0.561121i	−0.959836	+	0.280561i	$0.909480\pi$
$230$	−2.11943	+	8.66786i	−0.139751	+	0.571542i
$231$	−1.12604			−0.0740880
$232$	−1.30707	+	1.30707i	−0.0858133	+	0.0858133i
$233$	11.1205	−	11.1205i	0.728530	−	0.728530i	−0.241797	−	0.970327i	$-0.577737\pi$
$233$	11.1205	−	11.1205i	0.728530	−	0.728530i	0.970327	+	0.241797i	$0.0777367\pi$
$234$		−	9.94518i		−	0.650137i
$235$	−2.20216	−	3.62765i	−0.143653	−	0.236642i
$236$	−8.04404	−	8.04404i	−0.523623	−	0.523623i
$237$	−0.303322			−0.0197029
$238$	−10.1441	−	10.1441i	−0.657545	−	0.657545i
$239$	−14.6371	−	14.6371i	−0.946797	−	0.946797i	0.0518580	−	0.998654i	$-0.483486\pi$
$239$	−14.6371	−	14.6371i	−0.946797	−	0.946797i	−0.998654	+	0.0518580i	$0.983486\pi$
$240$	−0.0783380	−	0.129047i	−0.00505669	−	0.00832995i
$241$	10.5430	−	10.5430i	0.679137	−	0.679137i	−0.280668	−	0.959805i	$-0.590556\pi$
$241$	10.5430	−	10.5430i	0.679137	−	0.679137i	0.959805	+	0.280668i	$0.0905560\pi$
$242$	6.99802			0.449850
$243$	−1.28634	+	1.28634i	−0.0825187	+	0.0825187i
$244$	1.55262	+	1.55262i	0.0993963	+	0.0993963i
$245$	−18.3681	−	4.49129i	−1.17349	−	0.286938i
$246$	−0.129008	−	0.129008i	−0.00822526	−	0.00822526i
$247$	15.4424	+	15.4424i	0.982575	+	0.982575i
$248$	−3.96252	−	3.96252i	−0.251620	−	0.251620i
$249$	0.676095			0.0428458
$250$	7.36738	−	8.40962i	0.465954	−	0.531871i
$251$	−16.2391	−	16.2391i	−1.02500	−	1.02500i	−0.999679	−	0.0253206i	$-0.991939\pi$
$251$	−16.2391	−	16.2391i	−1.02500	−	1.02500i	−0.0253206	−	0.999679i	$-0.508061\pi$
$252$	−8.32723	−	8.32723i	−0.524566	−	0.524566i
$253$			16.9297i			1.06436i
$254$	−0.683408	+	0.683408i	−0.0428808	+	0.0428808i
$255$	−0.470893	+	0.285856i	−0.0294885	+	0.0179010i
$256$	1.00000			0.0625000
$257$		−	5.00407i		−	0.312145i	−0.987746	−	0.156073i	$-0.950117\pi$
$257$		−	5.00407i		−	0.312145i	0.987746	−	0.156073i	$-0.0498834\pi$
$258$	0.332057	−	0.332057i	0.0206730	−	0.0206730i
$259$	−2.06964	−	23.8245i	−0.128601	−	1.48038i
$260$	1.76334	−	7.21153i	0.109357	−	0.447240i
$261$	3.91525	+	3.91525i	0.242348	+	0.242348i
$262$	3.35210	+	3.35210i	0.207094	+	0.207094i
$263$	−12.4257	+	12.4257i	−0.766203	+	0.766203i	−0.977436	−	0.211233i	$-0.932252\pi$
$263$	−12.4257	+	12.4257i	−0.766203	+	0.766203i	0.211233	+	0.977436i	$0.432252\pi$
$264$	−0.202528	−	0.202528i	−0.0124647	−	0.0124647i
$265$	14.5263	−	8.81821i	0.892345	−	0.541698i
$266$	25.8602			1.58559
$267$		−	0.740574i		−	0.0453224i
$268$	−4.34085	−	4.34085i	−0.265160	−	0.265160i
$269$		−	22.6019i		−	1.37806i	−0.724732	−	0.689030i	$-0.758037\pi$
$269$		−	22.6019i		−	1.37806i	0.724732	−	0.689030i	$-0.241963\pi$
$270$	−0.773694	+	0.469671i	−0.0470855	+	0.0285833i
$271$	18.1930			1.10514			0.552572	−	0.833465i	$-0.313647\pi$
$271$	18.1930			1.10514			0.552572	+	0.833465i	$0.313647\pi$
$272$		−	3.64900i		−	0.221253i
$273$			0.881238i			0.0533350i
$274$	−15.4431	+	15.4431i	−0.932952	+	0.932952i
$275$	9.78816	−	18.8187i	0.590248	−	1.13481i
$276$	0.190506	−	0.190506i	0.0114671	−	0.0114671i
$277$	23.4453			1.40869			0.704346	−	0.709857i	$-0.251241\pi$
$277$	23.4453			1.40869			0.704346	+	0.709857i	$0.251241\pi$
$278$	−17.8399			−1.06997
$279$	−11.8695	+	11.8695i	−0.710608	+	0.710608i
$280$	−4.56184	−	7.51477i	−0.272622	−	0.449094i
$281$	3.32166	−	3.32166i	0.198154	−	0.198154i	−0.601054	−	0.799208i	$-0.705253\pi$
$281$	3.32166	−	3.32166i	0.198154	−	0.198154i	0.799208	+	0.601054i	$0.205253\pi$
$282$			0.128130i			0.00763003i
$283$			12.1785i			0.723935i	0.932191	+	0.361968i	$0.117895\pi$
$283$			12.1785i			0.723935i	−0.932191	+	0.361968i	$0.882105\pi$
$284$	5.54775			0.329198
$285$	0.235856	−	0.964583i	0.0139709	−	0.0571370i
$286$		−	14.0852i		−	0.832877i
$287$	−7.51251	−	7.51251i	−0.443450	−	0.443450i
$288$		−	2.99544i		−	0.176508i
$289$	3.68477			0.216751
$290$	2.14486	+	3.53325i	0.125951	+	0.207480i
$291$	−0.479541	−	0.479541i	−0.0281112	−	0.0281112i
$292$	−11.1383	+	11.1383i	−0.651818	+	0.651818i
$293$	1.06493	+	1.06493i	0.0622140	+	0.0622140i	0.737529	−	0.675315i	$-0.235992\pi$
$293$	1.06493	+	1.06493i	0.0622140	+	0.0622140i	−0.675315	+	0.737529i	$0.735992\pi$
$294$	0.403701	+	0.403701i	0.0235443	+	0.0235443i
$295$	−21.7445	+	13.2000i	−1.26602	+	0.768535i
$296$	3.91278	−	4.65727i	0.227426	−	0.270698i
$297$	−1.21424	+	1.21424i	−0.0704575	+	0.0704575i
$298$			17.7144i			1.02617i
$299$	13.2492			0.766219
$300$	−0.321906	+	0.101618i	−0.0185853	+	0.00586693i
$301$	19.3366	−	19.3366i	1.11454	−	1.11454i
$302$		−	5.53031i		−	0.318233i
$303$	−0.0722968	−	0.0722968i	−0.00415334	−	0.00415334i
$304$	4.65117	+	4.65117i	0.266763	+	0.266763i
$305$	4.19702	−	2.54780i	0.240321	−	0.145887i
$306$	−10.9304			−0.624848
$307$	16.1006	+	16.1006i	0.918907	+	0.918907i	0.996950	−	0.0780426i	$-0.0248670\pi$
$307$	16.1006	+	16.1006i	0.918907	+	0.918907i	−0.0780426	+	0.996950i	$0.524867\pi$
$308$	−11.7938	−	11.7938i	−0.672012	−	0.672012i
$309$	−0.185588	−	0.185588i	−0.0105577	−	0.0105577i
$310$	−10.7114	+	6.50237i	−0.608368	+	0.369310i
$311$	−18.5878	−	18.5878i	−1.05402	−	1.05402i	−0.998455	−	0.0555639i	$-0.982304\pi$
$311$	−18.5878	−	18.5878i	−1.05402	−	1.05402i	−0.0555639	−	0.998455i	$-0.517696\pi$
$312$	−0.158498	+	0.158498i	−0.00897318	+	0.00897318i
$313$	−21.7608			−1.22999			−0.614995	−	0.788531i	$-0.710842\pi$
$313$	−21.7608			−1.22999			−0.614995	+	0.788531i	$0.710842\pi$
$314$	3.47940	−	3.47940i	0.196354	−	0.196354i
$315$	−22.5101	+	13.6647i	−1.26830	+	0.769921i
$316$	−3.17689	−	3.17689i	−0.178714	−	0.178714i
$317$	−22.3061	−	22.3061i	−1.25284	−	1.25284i	−0.954443	−	0.298392i	$-0.903550\pi$
$317$	−22.3061	−	22.3061i	−1.25284	−	1.25284i	−0.298392	−	0.954443i	$-0.596450\pi$
$318$	−0.513076			−0.0287719
$319$	5.54512	+	5.54512i	0.310467	+	0.310467i
$320$	0.531109	−	2.17208i	0.0296899	−	0.121423i
$321$		−	0.0702953i		−	0.00392350i
$322$	11.0937	−	11.0937i	0.618228	−	0.618228i
$323$	16.9721	−	16.9721i	0.944355	−	0.944355i
$324$	−8.95900			−0.497722
$325$	−14.7275	−	7.66021i	−0.816933	−	0.424912i
$326$			21.7952i			1.20712i
$327$	0.164895			0.00911871
$328$		−	2.70237i		−	0.149214i
$329$			7.46137i			0.411359i
$330$	−0.547470	+	0.332342i	−0.0301372	+	0.0182948i
$331$	23.9871	−	23.9871i	1.31845	−	1.31845i	0.403447	−	0.915003i	$-0.367812\pi$
$331$	23.9871	−	23.9871i	1.31845	−	1.31845i	0.915003	−	0.403447i	$-0.132188\pi$
$332$	7.08119	+	7.08119i	0.388631	+	0.388631i
$333$	−13.9506	−	11.7205i	−0.764486	−	0.642280i
$334$		−	11.1575i		−	0.610512i
$335$	−11.7341	+	7.12321i	−0.641105	+	0.389183i
$336$			0.265425i			0.0144801i
$337$	17.5570	+	17.5570i	0.956390	+	0.956390i	0.999088	−	0.0426980i	$-0.0135953\pi$
$337$	17.5570	+	17.5570i	0.956390	+	0.956390i	−0.0426980	+	0.999088i	$0.513595\pi$
$338$	1.97691			0.107530
$339$	−0.201939	−	0.201939i	−0.0109678	−	0.0109678i
$340$	−7.92592	−	1.93802i	−0.429843	−	0.105104i
$341$	−16.8106	+	16.8106i	−0.910346	+	0.910346i
$342$	13.9323	−	13.9323i	0.753373	−	0.753373i
$343$	4.04887	+	4.04887i	0.218618	+	0.218618i
$344$	6.95570			0.375026
$345$	−0.312614	−	0.514973i	−0.0168306	−	0.0277252i
$346$	−14.4965	+	14.4965i	−0.779335	+	0.779335i
$347$	11.0678			0.594151			0.297075	−	0.954854i	$-0.403989\pi$
$347$	11.0678			0.594151			0.297075	+	0.954854i	$0.403989\pi$
$348$		−	0.124796i		−	0.00668977i
$349$		−	31.6855i		−	1.69609i	−0.529926	−	0.848044i	$-0.677780\pi$
$349$		−	31.6855i		−	1.69609i	0.529926	−	0.848044i	$-0.322220\pi$
$350$	−18.7455	+	5.91752i	−1.00199	+	0.316305i
$351$	0.950265	+	0.950265i	0.0507214	+	0.0507214i
$352$		−	4.24241i		−	0.226121i
$353$		−	15.6047i		−	0.830555i	−0.909695	−	0.415278i	$-0.863684\pi$
$353$		−	15.6047i		−	0.830555i	0.909695	−	0.415278i	$-0.136316\pi$
$354$	0.768026			0.0408201
$355$	2.94646	−	12.0501i	0.156382	−	0.639555i
$356$	7.75651	−	7.75651i	0.411094	−	0.411094i
$357$	0.968537			0.0512604
$358$	12.6119	−	12.6119i	0.666560	−	0.666560i
$359$			34.4499i			1.81820i	0.416580	+	0.909099i	$0.363229\pi$
$359$			34.4499i			1.81820i	−0.416580	+	0.909099i	$0.636771\pi$
$360$	−6.50633	−	1.59091i	−0.342914	−	0.0838481i
$361$			24.2668i			1.27720i
$362$	−12.8145			−0.673515
$363$	−0.334077	+	0.334077i	−0.0175345	+	0.0175345i
$364$	−9.22978	+	9.22978i	−0.483772	+	0.483772i
$365$	18.2775	+	30.1088i	0.956691	+	1.57597i
$366$	−0.148241			−0.00774866
$367$	−4.61443	+	4.61443i	−0.240871	+	0.240871i	−0.817211	−	0.576339i	$-0.804481\pi$
$367$	−4.61443	+	4.61443i	−0.240871	+	0.240871i	0.576339	+	0.817211i	$0.304481\pi$
$368$	3.99058			0.208024
$369$	−8.09481			−0.421399
$370$	−8.03783	−	10.9724i	−0.417867	−	0.570427i
$371$	−29.8779			−1.55118
$372$	0.378332			0.0196156
$373$	15.3464	−	15.3464i	0.794607	−	0.794607i	−0.187632	−	0.982239i	$-0.560081\pi$
$373$	15.3464	−	15.3464i	0.794607	−	0.794607i	0.982239	+	0.187632i	$0.0600813\pi$
$374$	−15.4806			−0.800481
$375$	0.0497555	+	0.753176i	0.00256937	+	0.0388938i
$376$	−1.34199	+	1.34199i	−0.0692078	+	0.0692078i
$377$	4.33961	−	4.33961i	0.223501	−	0.223501i
$378$	1.59134			0.0818497
$379$		−	23.4892i		−	1.20656i	−0.797531	−	0.603278i	$-0.793861\pi$
$379$		−	23.4892i		−	1.20656i	0.797531	−	0.603278i	$-0.206139\pi$
$380$	12.5730	−	7.63243i	0.644981	−	0.391535i
$381$		−	0.0652502i		−	0.00334287i
$382$	−10.0822	+	10.0822i	−0.515850	+	0.515850i
$383$	0.480522			0.0245535			0.0122768	−	0.999925i	$-0.496092\pi$
$383$	0.480522			0.0245535			0.0122768	+	0.999925i	$0.496092\pi$
$384$	−0.0477388	+	0.0477388i	−0.00243616	+	0.00243616i
$385$	−31.8807	+	19.3532i	−1.62479	+	0.986330i
$386$	−7.58052			−0.385838
$387$		−	20.8354i		−	1.05912i
$388$		−	10.0451i		−	0.509962i
$389$	−11.0293	−	11.0293i	−0.559208	−	0.559208i	0.369874	−	0.929082i	$-0.379401\pi$
$389$	−11.0293	−	11.0293i	−0.559208	−	0.559208i	−0.929082	+	0.369874i	$0.879401\pi$
$390$	0.260090	+	0.428450i	0.0131702	+	0.0216954i
$391$		−	14.5617i		−	0.736415i
$392$			8.45644i			0.427115i
$393$	−0.320051			−0.0161444
$394$	16.8945	−	16.8945i	0.851134	−	0.851134i
$395$	−8.58772	+	5.21318i	−0.432095	+	0.262303i
$396$	−12.7079			−0.638595
$397$	18.6363	+	18.6363i	0.935327	+	0.935327i	0.998032	−	0.0627054i	$-0.0199729\pi$
$397$	18.6363	+	18.6363i	0.935327	+	0.935327i	−0.0627054	+	0.998032i	$0.519973\pi$
$398$	−0.576031	+	0.576031i	−0.0288738	+	0.0288738i
$399$	−1.23454	+	1.23454i	−0.0618041	+	0.0618041i
$400$	−4.43585	−	2.30722i	−0.221792	−	0.115361i
$401$	23.4574	+	23.4574i	1.17141	+	1.17141i	0.981874	+	0.189535i	$0.0606980\pi$
$401$	23.4574	+	23.4574i	1.17141	+	1.17141i	0.189535	+	0.981874i	$0.439302\pi$
$402$	0.414455			0.0206711
$403$	13.1560	+	13.1560i	0.655346	+	0.655346i
$404$		−	1.51442i		−	0.0753454i
$405$	−4.75820	+	19.4596i	−0.236437	+	0.966958i
$406$		−	7.26722i		−	0.360666i
$407$	−19.7580	−	16.5996i	−0.979369	−	0.822813i
$408$	0.174199	+	0.174199i	0.00862415	+	0.00862415i
$409$	−20.5642	+	20.5642i	−1.01684	+	1.01684i	−0.0169803	+	0.999856i	$0.505405\pi$
$409$	−20.5642	+	20.5642i	−1.01684	+	1.01684i	−0.999856	+	0.0169803i	$0.994595\pi$
$410$	−5.86977	−	1.43525i	−0.289887	−	0.0708822i
$411$		−	1.47447i		−	0.0727303i
$412$		−	3.88757i		−	0.191527i
$413$	44.7244			2.20074
$414$		−	11.9536i		−	0.587486i
$415$	19.1418	−	11.6200i	0.939633	−	0.570404i
$416$	−3.32010			−0.162782
$417$	0.851658	−	0.851658i	0.0417059	−	0.0417059i
$418$	19.7322	−	19.7322i	0.965132	−	0.965132i
$419$		−	37.9044i		−	1.85175i	−0.377827	−	0.925876i	$-0.623329\pi$
$419$		−	37.9044i		−	1.85175i	0.377827	−	0.925876i	$-0.376671\pi$
$420$	0.576524	+	0.140969i	0.0281315	+	0.00687861i
$421$	24.4985	+	24.4985i	1.19398	+	1.19398i	0.975939	+	0.218043i	$0.0699674\pi$
$421$	24.4985	+	24.4985i	1.19398	+	1.19398i	0.218043	+	0.975939i	$0.430033\pi$
$422$	21.1449			1.02932
$423$	4.01985	+	4.01985i	0.195452	+	0.195452i
$424$	−5.37378	−	5.37378i	−0.260974	−	0.260974i
$425$	−8.41905	+	16.1864i	−0.408384	+	0.785157i
$426$	−0.264843	+	0.264843i	−0.0128317	+	0.0128317i
$427$	−8.63247			−0.417754
$428$	0.736249	−	0.736249i	0.0355879	−	0.0355879i
$429$	0.672413	+	0.672413i	0.0324644	+	0.0324644i
$430$	3.69423	−	15.1083i	0.178152	−	0.728588i
$431$	15.3753	+	15.3753i	0.740601	+	0.740601i	0.972694	−	0.232092i	$-0.0745571\pi$
$431$	15.3753	+	15.3753i	0.740601	+	0.740601i	−0.232092	+	0.972694i	$0.574557\pi$
$432$	0.286215	+	0.286215i	0.0137705	+	0.0137705i
$433$	−16.4923	−	16.4923i	−0.792570	−	0.792570i	0.189341	−	0.981911i	$-0.439365\pi$
$433$	−16.4923	−	16.4923i	−0.792570	−	0.792570i	−0.981911	+	0.189341i	$0.939365\pi$
$434$	22.0313			1.05754
$435$	−0.271067	−	0.0662802i	−0.0129966	−	0.00317789i
$436$	1.72705	+	1.72705i	0.0827108	+	0.0827108i
$437$	18.5609	+	18.5609i	0.887888	+	0.887888i
$438$		−	1.06346i		−	0.0508139i
$439$	−17.5768	+	17.5768i	−0.838896	+	0.838896i	−0.988714	−	0.149817i	$-0.952131\pi$
$439$	−17.5768	+	17.5768i	−0.838896	+	0.838896i	0.149817	+	0.988714i	$0.452131\pi$
$440$	−9.21484	−	2.25318i	−0.439300	−	0.107416i
$441$	25.3308			1.20623
$442$			12.1151i			0.576255i
$443$	−14.2624	+	14.2624i	−0.677629	+	0.677629i	−0.959463	−	0.281834i	$-0.909057\pi$
$443$	−14.2624	+	14.2624i	−0.677629	+	0.677629i	0.281834	+	0.959463i	$0.409057\pi$
$444$	0.0355407	+	0.409124i	0.00168669	+	0.0194162i
$445$	−12.7282	−	20.9673i	−0.603374	−	0.993945i
$446$	−14.0320	−	14.0320i	−0.664437	−	0.664437i
$447$	−0.845665	−	0.845665i	−0.0399986	−	0.0399986i
$448$	−2.77997	+	2.77997i	−0.131341	+	0.131341i
$449$	17.6009	+	17.6009i	0.830639	+	0.830639i	0.987604	−	0.156965i	$-0.0501709\pi$
$449$	17.6009	+	17.6009i	0.830639	+	0.830639i	−0.156965	+	0.987604i	$0.550171\pi$
$450$	−6.91114	+	13.2873i	−0.325794	+	0.626370i
$451$	−11.4646			−0.539846
$452$		−	4.23008i		−	0.198966i
$453$	0.264010	+	0.264010i	0.0124043	+	0.0124043i
$454$		−	17.0093i		−	0.798288i
$455$	15.1458	+	24.9498i	0.710046	+	1.16967i
$456$	−0.444083			−0.0207961
$457$			8.32533i			0.389443i	0.980859	+	0.194721i	$0.0623802\pi$
$457$			8.32533i			0.389443i	−0.980859	+	0.194721i	$0.937620\pi$
$458$		−	8.49131i		−	0.396773i
$459$	1.04440	−	1.04440i	0.0487485	−	0.0487485i
$460$	2.11943	−	8.66786i	0.0988191	−	0.404141i
$461$	0.227378	−	0.227378i	0.0105900	−	0.0105900i	−0.701792	−	0.712382i	$-0.747616\pi$
$461$	0.227378	−	0.227378i	0.0105900	−	0.0105900i	0.712382	+	0.701792i	$0.247616\pi$
$462$	1.12604			0.0523881
$463$	0.781658			0.0363267			0.0181634	−	0.999835i	$-0.494218\pi$
$463$	0.781658			0.0363267			0.0181634	+	0.999835i	$0.494218\pi$
$464$	1.30707	−	1.30707i	0.0606792	−	0.0606792i
$465$	0.200935	−	0.821767i	0.00931816	−	0.0381085i
$466$	−11.1205	+	11.1205i	−0.515149	+	0.515149i
$467$			2.66280i			0.123220i	0.998100	+	0.0616098i	$0.0196235\pi$
$467$			2.66280i			0.123220i	−0.998100	+	0.0616098i	$0.980377\pi$
$468$			9.94518i			0.459716i
$469$	24.1349			1.11444
$470$	2.20216	+	3.62765i	0.101578	+	0.167331i
$471$			0.332205i			0.0153072i
$472$	8.04404	+	8.04404i	0.370257	+	0.370257i
$473$		−	29.5089i		−	1.35682i
$474$	0.303322			0.0139320
$475$	−9.90061	−	31.3632i	−0.454271	−	1.43904i
$476$	10.1441	+	10.1441i	0.464955	+	0.464955i
$477$	−16.0968	+	16.0968i	−0.737024	+	0.737024i
$478$	14.6371	+	14.6371i	0.669486	+	0.669486i
$479$	16.4195	+	16.4195i	0.750228	+	0.750228i	0.974522	−	0.224294i	$-0.0720075\pi$
$479$	16.4195	+	16.4195i	0.750228	+	0.750228i	−0.224294	+	0.974522i	$0.572007\pi$
$480$	0.0783380	+	0.129047i	0.00357562	+	0.00589016i
$481$	−12.9909	+	15.4626i	−0.592332	+	0.705034i
$482$	−10.5430	+	10.5430i	−0.480222	+	0.480222i
$483$			1.05920i			0.0481953i
$484$	−6.99802			−0.318092
$485$	−21.8187	−	5.33503i	−0.990736	−	0.242251i
$486$	1.28634	−	1.28634i	0.0583495	−	0.0583495i
$487$		−	9.02775i		−	0.409087i	−0.978858	−	0.204543i	$-0.934429\pi$
$487$		−	9.02775i		−	0.409087i	0.978858	−	0.204543i	$-0.0655709\pi$
$488$	−1.55262	−	1.55262i	−0.0702838	−	0.0702838i
$489$	−1.04048	−	1.04048i	−0.0470520	−	0.0470520i
$490$	18.3681	+	4.49129i	0.829784	+	0.202896i
$491$	−2.91238			−0.131434			−0.0657169	−	0.997838i	$-0.520933\pi$
$491$	−2.91238			−0.131434			−0.0657169	+	0.997838i	$0.520933\pi$
$492$	0.129008	+	0.129008i	0.00581614	+	0.00581614i
$493$	−4.76950	−	4.76950i	−0.214808	−	0.214808i
$494$	−15.4424	−	15.4424i	−0.694785	−	0.694785i
$495$	−6.74927	+	27.6025i	−0.303357	+	1.24064i
$496$	3.96252	+	3.96252i	0.177922	+	0.177922i
$497$	−15.4226	+	15.4226i	−0.691796	+	0.691796i
$498$	−0.676095			−0.0302966
$499$	−11.5866	+	11.5866i	−0.518686	+	0.518686i	−0.917174	−	0.398487i	$-0.869535\pi$
$499$	−11.5866	+	11.5866i	−0.518686	+	0.518686i	0.398487	+	0.917174i	$0.369535\pi$
$500$	−7.36738	+	8.40962i	−0.329479	+	0.376090i
$501$	0.532647	+	0.532647i	0.0237969	+	0.0237969i
$502$	16.2391	+	16.2391i	0.724784	+	0.724784i
$503$	19.3861			0.864382			0.432191	−	0.901782i	$-0.357741\pi$
$503$	19.3861			0.864382			0.432191	+	0.901782i	$0.357741\pi$
$504$	8.32723	+	8.32723i	0.370924	+	0.370924i
$505$	−3.28945	−	0.804324i	−0.146378	−	0.0357919i
$506$		−	16.9297i		−	0.752616i
$507$	−0.0943752	+	0.0943752i	−0.00419135	+	0.00419135i
$508$	0.683408	−	0.683408i	0.0303213	−	0.0303213i
$509$	7.69714			0.341170			0.170585	−	0.985343i	$-0.445434\pi$
$509$	7.69714			0.341170			0.170585	+	0.985343i	$0.445434\pi$
$510$	0.470893	−	0.285856i	0.0208515	−	0.0126579i
$511$		−	61.9280i		−	2.73953i
$512$	−1.00000			−0.0441942
$513$			2.66247i			0.117551i
$514$			5.00407i			0.220720i
$515$	−8.44410	−	2.06472i	−0.372092	−	0.0909825i
$516$	−0.332057	+	0.332057i	−0.0146180	+	0.0146180i
$517$	5.69326	+	5.69326i	0.250389	+	0.250389i
$518$	2.06964	+	23.8245i	0.0909346	+	1.04679i
$519$		−	1.38409i		−	0.0607548i
$520$	−1.76334	+	7.21153i	−0.0773274	+	0.316246i
$521$			15.1959i			0.665746i	0.942972	+	0.332873i	$0.108018\pi$
$521$			15.1959i			0.665746i	−0.942972	+	0.332873i	$0.891982\pi$
$522$	−3.91525	−	3.91525i	−0.171366	−	0.171366i
$523$	8.67427			0.379299			0.189650	−	0.981852i	$-0.439265\pi$
$523$	8.67427			0.379299			0.189650	+	0.981852i	$0.439265\pi$
$524$	−3.35210	−	3.35210i	−0.146437	−	0.146437i
$525$	0.612393	−	1.17738i	0.0267270	−	0.0513853i
$526$	12.4257	−	12.4257i	0.541788	−	0.541788i
$527$	14.4592	−	14.4592i	0.629855	−	0.629855i
$528$	0.202528	+	0.202528i	0.00881388	+	0.00881388i
$529$	−7.07523			−0.307619
$530$	−14.5263	+	8.81821i	−0.630983	+	0.383038i
$531$	24.0955	−	24.0955i	1.04565	−	1.04565i
$532$	−25.8602			−1.12118
$533$			8.97216i			0.388628i
$534$			0.740574i			0.0320478i
$535$	−1.20816	−	1.99022i	−0.0522334	−	0.0860446i
$536$	4.34085	+	4.34085i	0.187496	+	0.187496i
$537$			1.20416i			0.0519631i
$538$			22.6019i			0.974436i
$539$	35.8757			1.54527
$540$	0.773694	−	0.469671i	0.0332945	−	0.0202114i
$541$	19.2216	−	19.2216i	0.826402	−	0.826402i	−0.160615	−	0.987017i	$-0.551348\pi$
$541$	19.2216	−	19.2216i	0.826402	−	0.826402i	0.987017	+	0.160615i	$0.0513477\pi$
$542$	−18.1930			−0.781454
$543$	0.611749	−	0.611749i	0.0262527	−	0.0262527i
$544$			3.64900i			0.156450i
$545$	4.66854	−	2.83404i	0.199978	−	0.121397i
$546$		−	0.881238i		−	0.0377135i
$547$	0.0420593			0.00179833			0.000899163	−	1.00000i	$-0.499714\pi$
$547$	0.0420593			0.00179833			0.000899163		1.00000i	$0.499714\pi$
$548$	15.4431	−	15.4431i	0.659697	−	0.659697i
$549$	−4.65078	+	4.65078i	−0.198491	+	0.198491i
$550$	−9.78816	+	18.8187i	−0.417369	+	0.802431i
$551$	12.1588			0.517983
$552$	−0.190506	+	0.190506i	−0.00810847	+	0.00810847i
$553$	17.6633			0.751120
$554$	−23.4453			−0.996095
$555$	0.907526	+	0.140092i	0.0385223	+	0.00594659i
$556$	17.8399			0.756582
$557$	−12.8111			−0.542823			−0.271412	−	0.962463i	$-0.587491\pi$
$557$	−12.8111			−0.542823			−0.271412	+	0.962463i	$0.587491\pi$
$558$	11.8695	−	11.8695i	0.502476	−	0.502476i
$559$	−23.0937			−0.976758
$560$	4.56184	+	7.51477i	0.192773	+	0.317557i
$561$	0.739024	−	0.739024i	0.0312016	−	0.0312016i
$562$	−3.32166	+	3.32166i	−0.140116	+	0.140116i
$563$	−29.4317			−1.24040			−0.620200	−	0.784444i	$-0.712949\pi$
$563$	−29.4317			−1.24040			−0.620200	+	0.784444i	$0.712949\pi$
$564$		−	0.128130i		−	0.00539525i
$565$	−9.18807	−	2.24663i	−0.386545	−	0.0945166i
$566$		−	12.1785i		−	0.511900i
$567$	24.9057	−	24.9057i	1.04594	−	1.04594i
$568$	−5.54775			−0.232778
$569$	1.25554	−	1.25554i	0.0526351	−	0.0526351i	−0.680299	−	0.732934i	$-0.738150\pi$
$569$	1.25554	−	1.25554i	0.0526351	−	0.0526351i	0.732934	+	0.680299i	$0.238150\pi$
$570$	−0.235856	+	0.964583i	−0.00987894	+	0.0404019i
$571$	−40.9624			−1.71422			−0.857111	−	0.515132i	$-0.827743\pi$
$571$	−40.9624			−1.71422			−0.857111	+	0.515132i	$0.827743\pi$
$572$			14.0852i			0.588933i
$573$		−	0.962624i		−	0.0402142i
$574$	7.51251	+	7.51251i	0.313566	+	0.313566i
$575$	−17.7016	−	9.20715i	−0.738209	−	0.383965i
$576$			2.99544i			0.124810i
$577$			7.71924i			0.321356i	0.987007	+	0.160678i	$0.0513681\pi$
$577$			7.71924i			0.321356i	−0.987007	+	0.160678i	$0.948632\pi$
$578$	−3.68477			−0.153266
$579$	0.361885	−	0.361885i	0.0150394	−	0.0150394i
$580$	−2.14486	−	3.53325i	−0.0890605	−	0.146710i
$581$	−39.3710			−1.63338
$582$	0.479541	+	0.479541i	0.0198776	+	0.0198776i
$583$	−22.7978	+	22.7978i	−0.944187	+	0.944187i
$584$	11.1383	−	11.1383i	0.460905	−	0.460905i
$585$	21.6017	+	5.28197i	0.893121	+	0.218383i
$586$	−1.06493	−	1.06493i	−0.0439919	−	0.0439919i
$587$	−5.39311			−0.222597			−0.111299	−	0.993787i	$-0.535501\pi$
$587$	−5.39311			−0.222597			−0.111299	+	0.993787i	$0.535501\pi$
$588$	−0.403701	−	0.403701i	−0.0166483	−	0.0166483i
$589$			36.8607i			1.51882i
$590$	21.7445	−	13.2000i	0.895209	−	0.543437i
$591$			1.61305i			0.0663521i
$592$	−3.91278	+	4.65727i	−0.160814	+	0.191412i
$593$	−10.4329	−	10.4329i	−0.428427	−	0.428427i	0.459665	−	0.888092i	$-0.347969\pi$
$593$	−10.4329	−	10.4329i	−0.428427	−	0.428427i	−0.888092	+	0.459665i	$0.847969\pi$
$594$	1.21424	−	1.21424i	0.0498210	−	0.0498210i
$595$	27.4214	−	16.6462i	1.12417	−	0.682427i
$596$		−	17.7144i		−	0.725610i
$597$		−	0.0549981i		−	0.00225092i
$598$	−13.2492			−0.541798
$599$		−	19.3788i		−	0.791798i	−0.918294	−	0.395899i	$-0.870433\pi$
$599$		−	19.3788i		−	0.791798i	0.918294	−	0.395899i	$-0.129567\pi$
$600$	0.321906	−	0.101618i	0.0131418	−	0.00414855i
$601$	−4.17046			−0.170117			−0.0850583	−	0.996376i	$-0.527108\pi$
$601$	−4.17046			−0.170117			−0.0850583	+	0.996376i	$0.527108\pi$
$602$	−19.3366	+	19.3366i	−0.788102	+	0.788102i
$603$	13.0028	−	13.0028i	0.529514	−	0.529514i
$604$			5.53031i			0.225025i
$605$	−3.71671	+	15.2002i	−0.151106	+	0.617978i
$606$	0.0722968	+	0.0722968i	0.00293686	+	0.00293686i
$607$	29.8434			1.21131			0.605653	−	0.795729i	$-0.292912\pi$
$607$	29.8434			1.21131			0.605653	+	0.795729i	$0.292912\pi$
$608$	−4.65117	−	4.65117i	−0.188630	−	0.188630i
$609$	0.346929	+	0.346929i	0.0140583	+	0.0140583i
$610$	−4.19702	+	2.54780i	−0.169932	+	0.103158i
$611$	4.45554	−	4.45554i	0.180252	−	0.180252i
$612$	10.9304			0.441834
$613$	7.97850	−	7.97850i	0.322248	−	0.322248i	−0.527381	−	0.849629i	$-0.676826\pi$
$613$	7.97850	−	7.97850i	0.322248	−	0.322248i	0.849629	+	0.527381i	$0.176826\pi$
$614$	−16.1006	−	16.1006i	−0.649766	−	0.649766i
$615$	0.348733	−	0.211699i	0.0140623	−	0.00853651i
$616$	11.7938	+	11.7938i	0.475184	+	0.475184i
$617$	21.2579	+	21.2579i	0.855812	+	0.855812i	0.990842	−	0.135030i	$-0.0431130\pi$
$617$	21.2579	+	21.2579i	0.855812	+	0.855812i	−0.135030	+	0.990842i	$0.543113\pi$
$618$	0.185588	+	0.185588i	0.00746545	+	0.00746545i
$619$	−7.54167			−0.303125			−0.151563	−	0.988448i	$-0.548431\pi$
$619$	−7.54167			−0.303125			−0.151563	+	0.988448i	$0.548431\pi$
$620$	10.7114	−	6.50237i	0.430181	−	0.261141i
$621$	1.14217	+	1.14217i	0.0458336	+	0.0458336i
$622$	18.5878	+	18.5878i	0.745304	+	0.745304i
$623$			43.1257i			1.72779i
$624$	0.158498	−	0.158498i	0.00634500	−	0.00634500i
$625$	14.3535	+	20.4689i	0.574139	+	0.818758i
$626$	21.7608			0.869735
$627$			1.88398i			0.0752390i
$628$	−3.47940	+	3.47940i	−0.138843	+	0.138843i
$629$	16.9944	+	14.2778i	0.677610	+	0.569292i
$630$	22.5101	−	13.6647i	0.896822	−	0.544416i
$631$	23.1881	+	23.1881i	0.923103	+	0.923103i	0.997247	−	0.0741448i	$-0.0236227\pi$
$631$	23.1881	+	23.1881i	0.923103	+	0.923103i	−0.0741448	+	0.997247i	$0.523623\pi$
$632$	3.17689	+	3.17689i	0.126370	+	0.126370i
$633$	−1.00943	+	1.00943i	−0.0401214	+	0.0401214i
$634$	22.3061	+	22.3061i	0.885889	+	0.885889i
$635$	−1.12145	−	1.84738i	−0.0445034	−	0.0733110i
$636$	0.513076			0.0203448
$637$		−	28.0763i		−	1.11242i
$638$	−5.54512	−	5.54512i	−0.219533	−	0.219533i
$639$			16.6180i			0.657396i
$640$	−0.531109	+	2.17208i	−0.0209939	+	0.0858589i
$641$	−12.2032			−0.481999			−0.240999	−	0.970525i	$-0.577475\pi$
$641$	−12.2032			−0.481999			−0.240999	+	0.970525i	$0.577475\pi$
$642$			0.0702953i			0.00277433i
$643$		−	26.4268i		−	1.04217i	−0.853505	−	0.521085i	$-0.825528\pi$
$643$		−	26.4268i		−	1.04217i	0.853505	−	0.521085i	$-0.174472\pi$
$644$	−11.0937	+	11.0937i	−0.437153	+	0.437153i
$645$	0.544896	+	0.897613i	0.0214552	+	0.0353435i
$646$	−16.9721	+	16.9721i	−0.667760	+	0.667760i
$647$	−23.6177			−0.928509			−0.464255	−	0.885702i	$-0.653678\pi$
$647$	−23.6177			−0.928509			−0.464255	+	0.885702i	$0.653678\pi$
$648$	8.95900			0.351943
$649$	34.1261	−	34.1261i	1.33957	−	1.33957i
$650$	14.7275	+	7.66021i	0.577659	+	0.300458i
$651$	−1.05175	+	1.05175i	−0.0412214	+	0.0412214i
$652$		−	21.7952i		−	0.853566i
$653$		−	11.5143i		−	0.450588i	−0.974291	−	0.225294i	$-0.927666\pi$
$653$		−	11.5143i		−	0.450588i	0.974291	−	0.225294i	$-0.0723342\pi$
$654$	−0.164895			−0.00644790
$655$	−9.06136	+	5.50070i	−0.354057	+	0.214930i
$656$			2.70237i			0.105510i
$657$	−33.3640	−	33.3640i	−1.30165	−	1.30165i
$658$		−	7.46137i		−	0.290875i
$659$	−45.6299			−1.77749			−0.888744	−	0.458404i	$-0.848421\pi$
$659$	−45.6299			−1.77749			−0.888744	+	0.458404i	$0.848421\pi$
$660$	0.547470	−	0.332342i	0.0213102	−	0.0129364i
$661$	−8.90268	−	8.90268i	−0.346274	−	0.346274i	0.512446	−	0.858720i	$-0.328740\pi$
$661$	−8.90268	−	8.90268i	−0.346274	−	0.346274i	−0.858720	+	0.512446i	$0.828740\pi$
$662$	−23.9871	+	23.9871i	−0.932285	+	0.932285i
$663$	−0.578360	−	0.578360i	−0.0224616	−	0.0224616i
$664$	−7.08119	−	7.08119i	−0.274803	−	0.274803i
$665$	−13.7346	+	56.1704i	−0.532604	+	2.17819i
$666$	13.9506	+	11.7205i	0.540574	+	0.454161i
$667$	5.21597	−	5.21597i	0.201963	−	0.201963i
$668$			11.1575i			0.431697i
$669$	1.33975			0.0517976
$670$	11.7341	−	7.12321i	0.453329	−	0.275194i
$671$	−6.58685	+	6.58685i	−0.254282	+	0.254282i
$672$		−	0.265425i		−	0.0102390i
$673$	−25.0377	−	25.0377i	−0.965134	−	0.965134i	0.0342781	−	0.999412i	$-0.489087\pi$
$673$	−25.0377	−	25.0377i	−0.965134	−	0.965134i	−0.999412	+	0.0342781i	$0.989087\pi$
$674$	−17.5570	−	17.5570i	−0.676270	−	0.676270i
$675$	−0.609246	−	1.92997i	−0.0234499	−	0.0742846i
$676$	−1.97691			−0.0760348
$677$	8.02326	+	8.02326i	0.308359	+	0.308359i	0.844273	−	0.535914i	$-0.180033\pi$
$677$	8.02326	+	8.02326i	0.308359	+	0.308359i	−0.535914	+	0.844273i	$0.680033\pi$
$678$	0.201939	+	0.201939i	0.00775543	+	0.00775543i
$679$	27.9250	+	27.9250i	1.07166	+	1.07166i
$680$	7.92592	+	1.93802i	0.303945	+	0.0743196i
$681$	0.812006	+	0.812006i	0.0311161	+	0.0311161i
$682$	16.8106	−	16.8106i	0.643712	−	0.643712i
$683$	−14.7249			−0.563434			−0.281717	−	0.959498i	$-0.590904\pi$
$683$	−14.7249			−0.563434			−0.281717	+	0.959498i	$0.590904\pi$
$684$	−13.9323	+	13.9323i	−0.532715	+	0.532715i
$685$	−25.3417	−	41.7456i	−0.968255	−	1.59502i
$686$	−4.04887	−	4.04887i	−0.154586	−	0.154586i
$687$	0.405365	+	0.405365i	0.0154656	+	0.0154656i
$688$	−6.95570			−0.265184
$689$	17.8415	+	17.8415i	0.679707	+	0.679707i
$690$	0.312614	+	0.514973i	0.0119010	+	0.0196047i
$691$		−	7.03274i		−	0.267538i	−0.991013	−	0.133769i	$-0.957292\pi$
$691$		−	7.03274i		−	0.267538i	0.991013	−	0.133769i	$-0.0427080\pi$
$692$	14.4965	−	14.4965i	0.551073	−	0.551073i
$693$	35.3275	−	35.3275i	1.34198	−	1.34198i
$694$	−11.0678			−0.420128
$695$	9.47495	−	38.7497i	0.359405	−	1.46986i
$696$			0.124796i			0.00473038i
$697$	9.86097			0.373511
$698$			31.6855i			1.19931i
$699$		−	1.06176i		−	0.0401595i
$700$	18.7455	−	5.91752i	0.708514	−	0.223661i
$701$	−18.7062	+	18.7062i	−0.706523	+	0.706523i	−0.965802	−	0.259279i	$-0.916515\pi$
$701$	−18.7062	+	18.7062i	−0.706523	+	0.706523i	0.259279	+	0.965802i	$0.416515\pi$
$702$	−0.950265	−	0.950265i	−0.0358654	−	0.0358654i
$703$	−39.8608	+	3.46271i	−1.50338	+	0.130599i
$704$			4.24241i			0.159892i
$705$	−0.278308	−	0.0680510i	−0.0104817	−	0.00256295i
$706$			15.6047i			0.587291i
$707$	4.21005	+	4.21005i	0.158335	+	0.158335i
$708$	−0.768026			−0.0288642
$709$	24.5474	+	24.5474i	0.921895	+	0.921895i	0.997163	−	0.0752682i	$-0.0239813\pi$
$709$	24.5474	+	24.5474i	0.921895	+	0.921895i	−0.0752682	+	0.997163i	$0.523981\pi$
$710$	−2.94646	+	12.0501i	−0.110579	+	0.452234i
$711$	9.51618	−	9.51618i	0.356885	−	0.356885i
$712$	−7.75651	+	7.75651i	−0.290688	+	0.290688i
$713$	15.8128	+	15.8128i	0.592193	+	0.592193i
$714$	−0.968537			−0.0362466
$715$	30.5942	+	7.48079i	1.14416	+	0.279766i
$716$	−12.6119	+	12.6119i	−0.471329	+	0.471329i
$717$	−1.39752			−0.0521913
$718$		−	34.4499i		−	1.28566i
$719$		−	12.2897i		−	0.458329i	−0.973388	−	0.229164i	$-0.926401\pi$
$719$		−	12.2897i		−	0.458329i	0.973388	−	0.229164i	$-0.0735993\pi$
$720$	6.50633	+	1.59091i	0.242477	+	0.0592895i
$721$	10.8073	+	10.8073i	0.402486	+	0.402486i
$722$		−	24.2668i		−	0.903116i
$723$		−	1.00663i		−	0.0374368i
$724$	12.8145			0.476247
$725$	−8.81366	+	2.78226i	−0.327331	+	0.103331i
$726$	0.334077	−	0.334077i	0.0123988	−	0.0123988i
$727$	12.2686			0.455016			0.227508	−	0.973776i	$-0.426942\pi$
$727$	12.2686			0.455016			0.227508	+	0.973776i	$0.426942\pi$
$728$	9.22978	−	9.22978i	0.342079	−	0.342079i
$729$		−	26.7542i		−	0.990896i
$730$	−18.2775	−	30.1088i	−0.676482	−	1.11438i
$731$			25.3814i			0.938765i
$732$	0.148241			0.00547913
$733$	−26.4738	+	26.4738i	−0.977831	+	0.977831i	−0.999760	−	0.0219285i	$-0.993019\pi$
$733$	−26.4738	+	26.4738i	−0.977831	+	0.977831i	0.0219285	+	0.999760i	$0.493019\pi$
$734$	4.61443	−	4.61443i	0.170322	−	0.170322i
$735$	−1.09128	+	0.662461i	−0.0402524	+	0.0244352i
$736$	−3.99058			−0.147095
$737$	18.4157	−	18.4157i	0.678350	−	0.678350i
$738$	8.09481			0.297974
$739$	−23.9200			−0.879912			−0.439956	−	0.898019i	$-0.645006\pi$
$739$	−23.9200			−0.879912			−0.439956	+	0.898019i	$0.645006\pi$
$740$	8.03783	+	10.9724i	0.295477	+	0.403353i
$741$	1.47440			0.0541635
$742$	29.8779			1.09685
$743$	−8.98938	+	8.98938i	−0.329788	+	0.329788i	−0.852506	−	0.522718i	$-0.824918\pi$
$743$	−8.98938	+	8.98938i	−0.329788	+	0.329788i	0.522718	+	0.852506i	$0.324918\pi$
$744$	−0.378332			−0.0138703
$745$	−38.4771	−	9.40827i	−1.40969	−	0.344692i
$746$	−15.3464	+	15.3464i	−0.561872	+	0.561872i
$747$	−21.2113	+	21.2113i	−0.776080	+	0.776080i
$748$	15.4806			0.566025
$749$			4.09349i			0.149573i
$750$	−0.0497555	−	0.753176i	−0.00181682	−	0.0275021i
$751$		−	34.7552i		−	1.26824i	−0.773236	−	0.634118i	$-0.781363\pi$
$751$		−	34.7552i		−	1.26824i	0.773236	−	0.634118i	$-0.218637\pi$
$752$	1.34199	−	1.34199i	0.0489373	−	0.0489373i
$753$	−1.55047			−0.0565022
$754$	−4.33961	+	4.33961i	−0.158039	+	0.158039i
$755$	12.0123	+	2.93719i	0.437171	+	0.106895i
$756$	−1.59134			−0.0578765
$757$		−	2.66868i		−	0.0969950i	−0.998823	−	0.0484975i	$-0.984557\pi$
$757$		−	2.66868i		−	0.0969950i	0.998823	−	0.0484975i	$-0.0154433\pi$
$758$			23.4892i			0.853164i
$759$	0.808204	+	0.808204i	0.0293359	+	0.0293359i
$760$	−12.5730	+	7.63243i	−0.456070	+	0.276857i
$761$		−	50.1338i		−	1.81735i	−0.417507	−	0.908674i	$-0.637096\pi$
$761$		−	50.1338i		−	1.81735i	0.417507	−	0.908674i	$-0.362904\pi$
$762$			0.0652502i			0.00236376i
$763$	−9.60230			−0.347626
$764$	10.0822	−	10.0822i	0.364761	−	0.364761i
$765$	5.80522	−	23.7416i	0.209888	−	0.858381i
$766$	−0.480522			−0.0173620
$767$	−26.7071	−	26.7071i	−0.964336	−	0.964336i
$768$	0.0477388	−	0.0477388i	0.00172263	−	0.00172263i
$769$	35.1828	−	35.1828i	1.26872	−	1.26872i	0.321974	−	0.946748i	$-0.395654\pi$
$769$	35.1828	−	35.1828i	1.26872	−	1.26872i	0.946748	−	0.321974i	$-0.104346\pi$
$770$	31.8807	−	19.3532i	1.14890	−	0.697441i
$771$	−0.238888	−	0.238888i	−0.00860335	−	0.00860335i
$772$	7.58052			0.272829
$773$	−5.35033	−	5.35033i	−0.192438	−	0.192438i	0.604311	−	0.796749i	$-0.293449\pi$
$773$	−5.35033	−	5.35033i	−0.192438	−	0.192438i	−0.796749	+	0.604311i	$0.793449\pi$
$774$			20.8354i			0.748913i
$775$	−8.43473	−	26.7195i	−0.302984	−	0.959793i
$776$			10.0451i			0.360597i
$777$	−1.23615	−	1.03855i	−0.0443468	−	0.0372578i
$778$	11.0293	+	11.0293i	0.395420	+	0.395420i
$779$	−12.5692	+	12.5692i	−0.450339	+	0.450339i
$780$	−0.260090	−	0.428450i	−0.00931273	−	0.0153410i
$781$			23.5358i			0.842177i
$782$			14.5617i			0.520724i
$783$	0.748207			0.0267387
$784$		−	8.45644i		−	0.302016i
$785$	5.70959	+	9.40547i	0.203784	+	0.335696i
$786$	0.320051			0.0114158
$787$	−34.2308	+	34.2308i	−1.22020	+	1.22020i	−0.252637	+	0.967561i	$0.581298\pi$
$787$	−34.2308	+	34.2308i	−1.22020	+	1.22020i	−0.967561	+	0.252637i	$0.918702\pi$
$788$	−16.8945	+	16.8945i	−0.601843	+	0.601843i
$789$			1.18638i			0.0422362i
$790$	8.58772	−	5.21318i	0.305537	−	0.185476i
$791$	11.7595	+	11.7595i	0.418120	+	0.418120i
$792$	12.7079			0.451555
$793$	5.15486	+	5.15486i	0.183054	+	0.183054i
$794$	−18.6363	−	18.6363i	−0.661376	−	0.661376i
$795$	0.272499	−	1.11444i	0.00966455	−	0.0395252i
$796$	0.576031	−	0.576031i	0.0204169	−	0.0204169i
$797$	−41.1330			−1.45700			−0.728502	−	0.685043i	$-0.759783\pi$
$797$	−41.1330			−1.45700			−0.728502	+	0.685043i	$0.759783\pi$
$798$	1.23454	−	1.23454i	0.0437021	−	0.0437021i
$799$	−4.89692	−	4.89692i	−0.173241	−	0.173241i
$800$	4.43585	+	2.30722i	0.156831	+	0.0815725i
$801$	23.2342	+	23.2342i	0.820939	+	0.820939i
$802$	−23.4574	−	23.4574i	−0.828311	−	0.828311i
$803$	−47.2530	−	47.2530i	−1.66752	−	1.66752i
$804$	−0.414455			−0.0146167
$805$	18.2044	+	29.9883i	0.641621	+	1.05695i
$806$	−13.1560	−	13.1560i	−0.463399	−	0.463399i
$807$	−1.07899	−	1.07899i	−0.0379822	−	0.0379822i
$808$			1.51442i			0.0532772i
$809$	25.8572	−	25.8572i	0.909092	−	0.909092i	−0.0871071	−	0.996199i	$-0.527762\pi$
$809$	25.8572	−	25.8572i	0.909092	−	0.909092i	0.996199	+	0.0871071i	$0.0277622\pi$
$810$	4.75820	−	19.4596i	0.167186	−	0.683742i
$811$	−26.4820			−0.929907			−0.464954	−	0.885335i	$-0.653929\pi$
$811$	−26.4820			−0.929907			−0.464954	+	0.885335i	$0.653929\pi$
$812$			7.26722i			0.255030i
$813$	0.868510	−	0.868510i	0.0304600	−	0.0304600i
$814$	19.7580	+	16.5996i	0.692518	+	0.581816i
$815$	−47.3409	−	11.5756i	−1.65828	−	0.405476i
$816$	−0.174199	−	0.174199i	−0.00609819	−	0.00609819i
$817$	−32.3522	−	32.3522i	−1.13186	−	1.13186i
$818$	20.5642	−	20.5642i	0.719012	−	0.719012i
$819$	−27.6473	−	27.6473i	−0.966074	−	0.966074i
$820$	5.86977	+	1.43525i	0.204981	+	0.0501213i
$821$	31.1573			1.08740			0.543699	−	0.839280i	$-0.317023\pi$
$821$	31.1573			1.08740			0.543699	+	0.839280i	$0.317023\pi$
$822$			1.47447i			0.0514281i
$823$	26.4495	+	26.4495i	0.921971	+	0.921971i	0.997169	−	0.0751977i	$-0.0239588\pi$
$823$	26.4495	+	26.4495i	0.921971	+	0.921971i	−0.0751977	+	0.997169i	$0.523959\pi$
$824$			3.88757i			0.135430i
$825$	−0.431106	−	1.36566i	−0.0150092	−	0.0475461i
$826$	−44.7244			−1.55616
$827$		−	23.8982i		−	0.831021i	−0.909588	−	0.415510i	$-0.863603\pi$
$827$		−	23.8982i		−	0.831021i	0.909588	−	0.415510i	$-0.136397\pi$
$828$			11.9536i			0.415415i
$829$	−7.39911	+	7.39911i	−0.256982	+	0.256982i	−0.823825	−	0.566844i	$-0.808164\pi$
$829$	−7.39911	+	7.39911i	−0.256982	+	0.256982i	0.566844	+	0.823825i	$0.308164\pi$
$830$	−19.1418	+	11.6200i	−0.664421	+	0.403337i
$831$	1.11925	−	1.11925i	0.0388264	−	0.0388264i
$832$	3.32010			0.115104
$833$	−30.8576			−1.06915
$834$	−0.851658	+	0.851658i	−0.0294905	+	0.0294905i
$835$	24.2350	+	5.92585i	0.838687	+	0.205073i
$836$	−19.7322	+	19.7322i	−0.682451	+	0.682451i
$837$			2.26827i			0.0784028i
$838$			37.9044i			1.30939i
$839$	−22.2697			−0.768834			−0.384417	−	0.923160i	$-0.625598\pi$
$839$	−22.2697			−0.768834			−0.384417	+	0.923160i	$0.625598\pi$
$840$	−0.576524	−	0.140969i	−0.0198920	−	0.00486391i
$841$			25.5831i			0.882177i
$842$	−24.4985	−	24.4985i	−0.844273	−	0.844273i
$843$		−	0.317145i		−	0.0109230i
$844$	−21.1449			−0.727838
$845$	−1.04995	+	4.29399i	−0.0361194	+	0.147718i
$846$	−4.01985	−	4.01985i	−0.138205	−	0.138205i
$847$	19.4543	−	19.4543i	0.668456	−	0.668456i
$848$	5.37378	+	5.37378i	0.184536	+	0.184536i
$849$	0.581386	+	0.581386i	0.0199531	+	0.0199531i
$850$	8.41905	−	16.1864i	0.288771	−	0.555190i
$851$	−15.6143	+	18.5852i	−0.535251	+	0.637093i
$852$	0.264843	−	0.264843i	0.00907337	−	0.00907337i
$853$			30.0733i			1.02969i	0.857283	+	0.514845i	$0.172150\pi$
$853$			30.0733i			1.02969i	−0.857283	+	0.514845i	$0.827850\pi$
$854$	8.63247			0.295397
$855$	22.8625	+	37.6616i	0.781881	+	1.28800i
$856$	−0.736249	+	0.736249i	−0.0251645	+	0.0251645i
$857$		−	19.5685i		−	0.668446i	−0.942494	−	0.334223i	$-0.891526\pi$
$857$		−	19.5685i		−	0.668446i	0.942494	−	0.334223i	$-0.108474\pi$
$858$	−0.672413	−	0.672413i	−0.0229558	−	0.0229558i
$859$	−12.9463	−	12.9463i	−0.441723	−	0.441723i	0.450868	−	0.892591i	$-0.351115\pi$
$859$	−12.9463	−	12.9463i	−0.441723	−	0.441723i	−0.892591	+	0.450868i	$0.851115\pi$
$860$	−3.69423	+	15.1083i	−0.125972	+	0.515190i
$861$	−0.717277			−0.0244447
$862$	−15.3753	−	15.3753i	−0.523684	−	0.523684i
$863$	0.279402	+	0.279402i	0.00951094	+	0.00951094i	0.711846	−	0.702335i	$-0.247859\pi$
$863$	0.279402	+	0.279402i	0.00951094	+	0.00951094i	−0.702335	+	0.711846i	$0.747859\pi$
$864$	−0.286215	−	0.286215i	−0.00973725	−	0.00973725i
$865$	−23.7883	−	39.1867i	−0.808825	−	1.33239i
$866$	16.4923	+	16.4923i	0.560432	+	0.560432i
$867$	0.175907	−	0.175907i	0.00597410	−	0.00597410i
$868$	−22.0313			−0.747793
$869$	13.4777	−	13.4777i	0.457198	−	0.457198i
$870$	0.271067	+	0.0662802i	0.00919002	+	0.00224711i
$871$	−14.4121	−	14.4121i	−0.488335	−	0.488335i
$872$	−1.72705	−	1.72705i	−0.0584853	−	0.0584853i
$873$	30.0895			1.01837
$874$	−18.5609	−	18.5609i	−0.627832	−	0.627832i
$875$	−2.89741	−	43.8596i	−0.0979502	−	1.48272i
$876$			1.06346i			0.0359308i
$877$	29.4697	−	29.4697i	0.995121	−	0.995121i	−0.00486751	−	0.999988i	$-0.501549\pi$
$877$	29.4697	−	29.4697i	0.995121	−	0.995121i	0.999988	+	0.00486751i	$0.00154938\pi$
$878$	17.5768	−	17.5768i	0.593189	−	0.593189i
$879$	0.101677			0.00342949
$880$	9.21484	+	2.25318i	0.310632	+	0.0759547i
$881$			41.3883i			1.39441i	0.716873	+	0.697204i	$0.245573\pi$
$881$			41.3883i			1.39441i	−0.716873	+	0.697204i	$0.754427\pi$
$882$	−25.3308			−0.852932
$883$		−	16.0092i		−	0.538751i	−0.963035	−	0.269376i	$-0.913183\pi$
$883$		−	16.0092i		−	0.538751i	0.963035	−	0.269376i	$-0.0868173\pi$
$884$		−	12.1151i		−	0.407474i
$885$	−0.407906	+	1.66821i	−0.0137116	+	0.0560764i
$886$	14.2624	−	14.2624i	0.479156	−	0.479156i
$887$	−1.06556	−	1.06556i	−0.0357779	−	0.0357779i	0.688992	−	0.724769i	$-0.258054\pi$
$887$	−1.06556	−	1.06556i	−0.0357779	−	0.0357779i	−0.724769	+	0.688992i	$0.758054\pi$
$888$	−0.0355407	−	0.409124i	−0.00119267	−	0.0137293i
$889$			3.79970i			0.127438i
$890$	12.7282	+	20.9673i	0.426650	+	0.702825i
$891$		−	38.0077i		−	1.27331i
$892$	14.0320	+	14.0320i	0.469828	+	0.469828i
$893$	12.4836			0.417749
$894$	0.845665	+	0.845665i	0.0282833	+	0.0282833i
$895$	20.6958	+	34.0923i	0.691783	+	1.13958i
$896$	2.77997	−	2.77997i	0.0928722	−	0.0928722i
$897$	0.632499	−	0.632499i	0.0211185	−	0.0211185i
$898$	−17.6009	−	17.6009i	−0.587351	−	0.587351i
$899$	10.3586			0.345478
$900$	6.91114	−	13.2873i	0.230371	−	0.442911i
$901$	19.6089	−	19.6089i	0.653269	−	0.653269i
$902$	11.4646			0.381728
$903$		−	1.84622i		−	0.0614382i
$904$			4.23008i			0.140691i
$905$	6.80589	−	27.8341i	0.226235	−	0.925236i
$906$	−0.264010	−	0.264010i	−0.00877116	−	0.00877116i
$907$			0.646631i			0.0214710i	0.999942	+	0.0107355i	$0.00341728\pi$
$907$			0.646631i			0.0214710i	−0.999942	+	0.0107355i	$0.996583\pi$
$908$			17.0093i			0.564475i
$909$	4.53637			0.150462
$910$	−15.1458	−	24.9498i	−0.502078	−	0.827079i
$911$	8.55384	−	8.55384i	0.283401	−	0.283401i	−0.551063	−	0.834464i	$-0.685777\pi$
$911$	8.55384	−	8.55384i	0.283401	−	0.283401i	0.834464	+	0.551063i	$0.185777\pi$
$912$	0.444083			0.0147051
$913$	−30.0413	+	30.0413i	−0.994221	+	0.994221i
$914$		−	8.32533i		−	0.275377i
$915$	0.0787319	−	0.321990i	0.00260280	−	0.0106447i
$916$			8.49131i			0.280561i
$917$	18.6375			0.615464
$918$	−1.04440	+	1.04440i	−0.0344704	+	0.0344704i
$919$	2.27110	−	2.27110i	0.0749167	−	0.0749167i	−0.668656	−	0.743572i	$-0.733130\pi$
$919$	2.27110	−	2.27110i	0.0749167	−	0.0749167i	0.743572	+	0.668656i	$0.233130\pi$
$920$	−2.11943	+	8.66786i	−0.0698757	+	0.285771i
$921$	1.53724			0.0506539
$922$	−0.227378	+	0.227378i	−0.00748828	+	0.00748828i
$923$	18.4191			0.606272
$924$	−1.12604			−0.0370440
$925$	28.1018	−	11.6313i	0.923983	−	0.382434i
$926$	−0.781658			−0.0256869
$927$	11.6450			0.382472
$928$	−1.30707	+	1.30707i	−0.0429067	+	0.0429067i
$929$	7.69649			0.252514			0.126257	−	0.991998i	$-0.459704\pi$
$929$	7.69649			0.252514			0.126257	+	0.991998i	$0.459704\pi$
$930$	−0.200935	+	0.821767i	−0.00658893	+	0.0269468i
$931$	39.3324	−	39.3324i	1.28907	−	1.28907i
$932$	11.1205	−	11.1205i	0.364265	−	0.364265i
$933$	−1.77472			−0.0581018
$934$		−	2.66280i		−	0.0871295i
$935$	8.22186	−	33.6250i	0.268884	−	1.09965i
$936$		−	9.94518i		−	0.325068i
$937$	2.79563	−	2.79563i	0.0913291	−	0.0913291i	−0.659966	−	0.751295i	$-0.729429\pi$
$937$	2.79563	−	2.79563i	0.0913291	−	0.0913291i	0.751295	+	0.659966i	$0.229429\pi$
$938$	−24.1349			−0.788032
$939$	−1.03883	+	1.03883i	−0.0339010	+	0.0339010i
$940$	−2.20216	−	3.62765i	−0.0718266	−	0.118321i
$941$	−1.41774			−0.0462169			−0.0231085	−	0.999733i	$-0.507356\pi$
$941$	−1.41774			−0.0462169			−0.0231085	+	0.999733i	$0.507356\pi$
$942$		−	0.332205i		−	0.0108238i
$943$			10.7841i			0.351177i
$944$	−8.04404	−	8.04404i	−0.261811	−	0.261811i
$945$	−0.845174	+	3.45651i	−0.0274935	+	0.112440i
$946$			29.5089i			0.959418i
$947$		−	20.5099i		−	0.666483i	−0.942841	−	0.333242i	$-0.891858\pi$
$947$		−	20.5099i		−	0.666483i	0.942841	−	0.333242i	$-0.108142\pi$
$948$	−0.303322			−0.00985144
$949$	−36.9802	+	36.9802i	−1.20043	+	1.20043i
$950$	9.90061	+	31.3632i	0.321218	+	1.01756i
$951$	−2.12974			−0.0690614
$952$	−10.1441	−	10.1441i	−0.328773	−	0.328773i
$953$	−4.74691	+	4.74691i	−0.153768	+	0.153768i	−0.779798	−	0.626031i	$-0.784678\pi$
$953$	−4.74691	+	4.74691i	−0.153768	+	0.153768i	0.626031	+	0.779798i	$0.284678\pi$
$954$	16.0968	−	16.0968i	0.521155	−	0.521155i
$955$	−16.5446	−	27.2540i	−0.535369	−	0.881920i
$956$	−14.6371	−	14.6371i	−0.473398	−	0.473398i
$957$	0.529435			0.0171142
$958$	−16.4195	−	16.4195i	−0.530491	−	0.530491i
$959$			85.8627i			2.77265i
$960$	−0.0783380	−	0.129047i	−0.00252835	−	0.00416497i
$961$			0.403092i			0.0130030i
$962$	12.9909	−	15.4626i	0.418842	−	0.498535i
$963$	2.20539	+	2.20539i	0.0710677	+	0.0710677i
$964$	10.5430	−	10.5430i	0.339569	−	0.339569i
$965$	4.02608	−	16.4655i	0.129604	−	0.530042i
$966$		−	1.05920i		−	0.0340792i
$967$		−	51.7273i		−	1.66344i	−0.555197	−	0.831719i	$-0.687357\pi$
$967$		−	51.7273i		−	1.66344i	0.555197	−	0.831719i	$-0.312643\pi$
$968$	6.99802			0.224925
$969$		−	1.62046i		−	0.0520567i
$970$	21.8187	+	5.33503i	0.700556	+	0.171297i
$971$	−20.2722			−0.650566			−0.325283	−	0.945617i	$-0.605460\pi$
$971$	−20.2722			−0.650566			−0.325283	+	0.945617i	$0.605460\pi$
$972$	−1.28634	+	1.28634i	−0.0412593	+	0.0412593i
$973$	−49.5945	+	49.5945i	−1.58993	+	1.58993i
$974$			9.02775i			0.289268i
$975$	−1.06876	+	0.337383i	−0.0342278	+	0.0108049i
$976$	1.55262	+	1.55262i	0.0496982	+	0.0496982i
$977$	−21.5483			−0.689390			−0.344695	−	0.938715i	$-0.612018\pi$
$977$	−21.5483			−0.689390			−0.344695	+	0.938715i	$0.612018\pi$
$978$	1.04048	+	1.04048i	0.0332708	+	0.0332708i
$979$	32.9063	+	32.9063i	1.05169	+	1.05169i
$980$	−18.3681	−	4.49129i	−0.586746	−	0.143469i
$981$	−5.17328	+	5.17328i	−0.165170	+	0.165170i
$982$	2.91238			0.0929378
$983$	9.09050	−	9.09050i	0.289942	−	0.289942i	−0.547115	−	0.837057i	$-0.684274\pi$
$983$	9.09050	−	9.09050i	0.289942	−	0.289942i	0.837057	+	0.547115i	$0.184274\pi$
$984$	−0.129008	−	0.129008i	−0.00411263	−	0.00411263i
$985$	27.7234	+	45.6691i	0.883342	+	1.45514i
$986$	4.76950	+	4.76950i	0.151892	+	0.151892i
$987$	0.356197	+	0.356197i	0.0113379	+	0.0113379i
$988$	15.4424	+	15.4424i	0.491287	+	0.491287i
$989$	−27.7573			−0.882632
$990$	6.74927	−	27.6025i	0.214506	−	0.877266i
$991$	12.2842	+	12.2842i	0.390219	+	0.390219i	0.874766	−	0.484546i	$-0.161015\pi$
$991$	12.2842	+	12.2842i	0.390219	+	0.390219i	−0.484546	+	0.874766i	$0.661015\pi$
$992$	−3.96252	−	3.96252i	−0.125810	−	0.125810i
$993$		−	2.29023i		−	0.0726783i
$994$	15.4226	−	15.4226i	0.489174	−	0.489174i
$995$	−0.945250	−	1.55712i	−0.0299664	−	0.0493640i
$996$	0.676095			0.0214229
$997$			49.7309i			1.57499i	0.616318	+	0.787497i	$0.288623\pi$
$997$			49.7309i			1.57499i	−0.616318	+	0.787497i	$0.711377\pi$
$998$	11.5866	−	11.5866i	0.366767	−	0.366767i
$999$	−2.45288	+	0.213082i	−0.0776057	+	0.00674162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.253.5	yes	20
5.2	odd	4		370.2.g.e.327.6	yes	20
37.6	odd	4		370.2.g.e.43.6	✓	20
185.117	even	4	inner	370.2.h.e.117.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.6	✓	20	37.6	odd	4
370.2.g.e.327.6	yes	20	5.2	odd	4
370.2.h.e.117.5	yes	20	185.117	even	4	inner
370.2.h.e.253.5	yes	20	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.0477388 - 0.0477388i) q^{3} +1.00000 q^{4} +(0.531109 - 2.17208i) q^{5} +(-0.0477388 + 0.0477388i) q^{6} +(-2.77997 + 2.77997i) q^{7} -1.00000 q^{8} +2.99544i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.0477388 - 0.0477388i) q^{3} +1.00000 q^{4} +(0.531109 - 2.17208i) q^{5} +(-0.0477388 + 0.0477388i) q^{6} +(-2.77997 + 2.77997i) q^{7} -1.00000 q^{8} +2.99544i q^{9} +(-0.531109 + 2.17208i) q^{10} +4.24241i q^{11} +(0.0477388 - 0.0477388i) q^{12} +3.32010 q^{13} +(2.77997 - 2.77997i) q^{14} +(-0.0783380 - 0.129047i) q^{15} +1.00000 q^{16} -3.64900i q^{17} -2.99544i q^{18} +(4.65117 + 4.65117i) q^{19} +(0.531109 - 2.17208i) q^{20} +0.265425i q^{21} -4.24241i q^{22} +3.99058 q^{23} +(-0.0477388 + 0.0477388i) q^{24} +(-4.43585 - 2.30722i) q^{25} -3.32010 q^{26} +(0.286215 + 0.286215i) q^{27} +(-2.77997 + 2.77997i) q^{28} +(1.30707 - 1.30707i) q^{29} +(0.0783380 + 0.129047i) q^{30} +(3.96252 + 3.96252i) q^{31} -1.00000 q^{32} +(0.202528 + 0.202528i) q^{33} +3.64900i q^{34} +(4.56184 + 7.51477i) q^{35} +2.99544i q^{36} +(-3.91278 + 4.65727i) q^{37} +(-4.65117 - 4.65117i) q^{38} +(0.158498 - 0.158498i) q^{39} +(-0.531109 + 2.17208i) q^{40} +2.70237i q^{41} -0.265425i q^{42} -6.95570 q^{43} +4.24241i q^{44} +(6.50633 + 1.59091i) q^{45} -3.99058 q^{46} +(1.34199 - 1.34199i) q^{47} +(0.0477388 - 0.0477388i) q^{48} -8.45644i q^{49} +(4.43585 + 2.30722i) q^{50} +(-0.174199 - 0.174199i) q^{51} +3.32010 q^{52} +(5.37378 + 5.37378i) q^{53} +(-0.286215 - 0.286215i) q^{54} +(9.21484 + 2.25318i) q^{55} +(2.77997 - 2.77997i) q^{56} +0.444083 q^{57} +(-1.30707 + 1.30707i) q^{58} +(-8.04404 - 8.04404i) q^{59} +(-0.0783380 - 0.129047i) q^{60} +(1.55262 + 1.55262i) q^{61} +(-3.96252 - 3.96252i) q^{62} +(-8.32723 - 8.32723i) q^{63} +1.00000 q^{64} +(1.76334 - 7.21153i) q^{65} +(-0.202528 - 0.202528i) q^{66} +(-4.34085 - 4.34085i) q^{67} -3.64900i q^{68} +(0.190506 - 0.190506i) q^{69} +(-4.56184 - 7.51477i) q^{70} +5.54775 q^{71} -2.99544i q^{72} +(-11.1383 + 11.1383i) q^{73} +(3.91278 - 4.65727i) q^{74} +(-0.321906 + 0.101618i) q^{75} +(4.65117 + 4.65117i) q^{76} +(-11.7938 - 11.7938i) q^{77} +(-0.158498 + 0.158498i) q^{78} +(-3.17689 - 3.17689i) q^{79} +(0.531109 - 2.17208i) q^{80} -8.95900 q^{81} -2.70237i q^{82} +(7.08119 + 7.08119i) q^{83} +0.265425i q^{84} +(-7.92592 - 1.93802i) q^{85} +6.95570 q^{86} -0.124796i q^{87} -4.24241i q^{88} +(7.75651 - 7.75651i) q^{89} +(-6.50633 - 1.59091i) q^{90} +(-9.22978 + 9.22978i) q^{91} +3.99058 q^{92} +0.378332 q^{93} +(-1.34199 + 1.34199i) q^{94} +(12.5730 - 7.63243i) q^{95} +(-0.0477388 + 0.0477388i) q^{96} -10.0451i q^{97} +8.45644i q^{98} -12.7079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Introduction

L-functions

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Database

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