LMFDB - Embedded newform 370.2.g.e.327.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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([3, 3]))

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.6
Root			$0.0477388 + 0.0477388i$ of defining polynomial
Character	$\chi$	$=$	370.327
Dual form			370.2.g.e.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.0477388	−	0.0477388i	−0.0275620	−	0.0275620i	0.693191	−	0.720753i	$-0.256204\pi$
$3$	−0.0477388	−	0.0477388i	−0.0275620	−	0.0275620i	−0.720753	+	0.693191i	$0.756204\pi$
$4$	−1.00000			−0.500000
$5$	2.17208	−	0.531109i	0.971383	−	0.237519i
$5$	2.17208	−	0.531109i	0.971383	−	0.237519i
$6$	−0.0477388	+	0.0477388i	−0.0194893	+	0.0194893i
$7$	−2.77997	−	2.77997i	−1.05073	−	1.05073i	−0.998643	−	0.0520865i	$-0.983413\pi$
$7$	−2.77997	−	2.77997i	−1.05073	−	1.05073i	−0.0520865	−	0.998643i	$-0.516587\pi$
$8$			1.00000i			0.353553i
$9$		−	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
$13$		−	3.32010i		−	0.920831i	−0.887703	−	0.460416i	$-0.847700\pi$
$13$		−	3.32010i		−	0.920831i	0.887703	−	0.460416i	$-0.152300\pi$
$14$	−2.77997	+	2.77997i	−0.742978	+	0.742978i
$15$	−0.129047	−	0.0783380i	−0.0333198	−	0.0202268i
$16$	1.00000			0.250000
$17$	3.64900			0.885013			0.442507	−	0.896765i	$-0.354089\pi$
$17$	3.64900			0.885013			0.442507	+	0.896765i	$0.354089\pi$
$18$	−2.99544			−0.706032
$19$	−4.65117	−	4.65117i	−1.06705	−	1.06705i	−0.997584	−	0.0694677i	$-0.977870\pi$
$19$	−4.65117	−	4.65117i	−1.06705	−	1.06705i	−0.0694677	−	0.997584i	$-0.522130\pi$
$20$	−2.17208	+	0.531109i	−0.485691	+	0.118760i
$21$			0.265425i			0.0579205i
$22$	4.24241			0.904484
$23$		−	3.99058i		−	0.832094i	−0.909343	−	0.416047i	$-0.863415\pi$
$23$		−	3.99058i		−	0.832094i	0.909343	−	0.416047i	$-0.136585\pi$
$24$	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	−0.817973	−	0.575256i	$-0.804902\pi$
$29$	−1.30707	+	1.30707i	−0.242717	+	0.242717i	0.575256	+	0.817973i	$0.304902\pi$
$30$	−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	$0.582141\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.202528	−	0.202528i	0.0352555	−	0.0352555i
$34$		−	3.64900i		−	0.625799i
$35$	−7.51477	−	4.56184i	−1.27023	−	0.771092i
$36$			2.99544i			0.499240i
$37$	−4.65727	−	3.91278i	−0.765650	−	0.643258i
$37$	−4.65727	−	3.91278i	−0.765650	−	0.643258i
$38$	−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	$0.932321\pi$
$42$	0.265425			0.0409560
$43$			6.95570i			1.06073i	0.847768	+	0.530367i	$0.177946\pi$
$43$			6.95570i			1.06073i	−0.847768	+	0.530367i	$0.822054\pi$
$44$		−	4.24241i		−	0.639567i
$45$	−1.59091	−	6.50633i	−0.237158	−	0.969907i
$46$	−3.99058			−0.588380
$47$	1.34199	+	1.34199i	0.195749	+	0.195749i	0.798175	−	0.602426i	$-0.205799\pi$
$47$	1.34199	+	1.34199i	0.195749	+	0.195749i	−0.602426	+	0.798175i	$0.705799\pi$
$48$	−0.0477388	−	0.0477388i	−0.00689051	−	0.00689051i
$49$			8.45644i			1.20806i
$50$	−2.30722	−	4.43585i	−0.326290	−	0.627324i
$51$	−0.174199	−	0.174199i	−0.0243928	−	0.0243928i
$52$			3.32010i			0.460416i
$53$	5.37378	−	5.37378i	0.738145	−	0.738145i	−0.234074	−	0.972219i	$-0.575206\pi$
$53$	5.37378	−	5.37378i	0.738145	−	0.738145i	0.972219	+	0.234074i	$0.0752057\pi$
$54$	0.286215	+	0.286215i	0.0389490	+	0.0389490i
$55$	2.25318	+	9.21484i	0.303819	+	1.24253i
$56$	2.77997	−	2.77997i	0.371489	−	0.371489i
$57$			0.444083i			0.0588202i
$58$	1.30707	+	1.30707i	0.171627	+	0.171627i
$59$	8.04404	+	8.04404i	1.04725	+	1.04725i	0.998827	+	0.0484179i	$0.0154179\pi$
$59$	8.04404	+	8.04404i	1.04725	+	1.04725i	0.0484179	+	0.998827i	$0.484582\pi$
$60$	0.129047	+	0.0783380i	0.0166599	+	0.0101134i
$61$	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	$-0.627645\pi$
$67$	4.34085	−	4.34085i	0.530320	−	0.530320i	0.920668	+	0.390348i	$0.127645\pi$
$68$	−3.64900			−0.442507
$69$	−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	$0.393222\pi$
$72$	2.99544			0.353016
$73$	11.1383	+	11.1383i	1.30364	+	1.30364i	0.925923	+	0.377712i	$0.123289\pi$
$73$	11.1383	+	11.1383i	1.30364	+	1.30364i	0.377712	+	0.925923i	$0.376711\pi$
$74$	−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	0.862864	−	0.505436i	$-0.168668\pi$
$79$	3.17689	+	3.17689i	0.357428	+	0.357428i	−0.505436	+	0.862864i	$0.668668\pi$
$80$	2.17208	−	0.531109i	0.242846	−	0.0593798i
$81$	−8.95900			−0.995444
$82$	2.70237			0.298427
$83$	7.08119	−	7.08119i	0.777261	−	0.777261i	−0.202103	−	0.979364i	$-0.564778\pi$
$83$	7.08119	−	7.08119i	0.777261	−	0.777261i	0.979364	+	0.202103i	$0.0647775\pi$
$84$		−	0.265425i		−	0.0289602i
$85$	7.92592	−	1.93802i	0.859687	−	0.210208i
$86$	6.95570			0.750053
$87$	0.124796			0.0133795
$88$	−4.24241			−0.452242
$89$	−7.75651	+	7.75651i	−0.822188	+	0.822188i	−0.986422	−	0.164233i	$-0.947485\pi$
$89$	−7.75651	+	7.75651i	−0.822188	+	0.822188i	0.164233	+	0.986422i	$0.447485\pi$
$90$	−6.50633	+	1.59091i	−0.685828	+	0.167696i
$91$	−9.22978	+	9.22978i	−0.967544	+	0.967544i
$92$			3.99058i			0.416047i
$93$		−	0.378332i		−	0.0392312i
$94$	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
$97$	10.0451			1.01992			0.509962	−	0.860197i	$-0.329660\pi$
$97$	10.0451			1.01992			0.509962	+	0.860197i	$0.329660\pi$
$98$	8.45644			0.854230
$99$	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
$103$	−3.88757			−0.383054			−0.191527	−	0.981487i	$-0.561344\pi$
$103$	−3.88757			−0.383054			−0.191527	+	0.981487i	$0.561344\pi$
$104$	3.32010			0.325563
$105$	0.140969	+	0.576524i	0.0137572	+	0.0562629i
$106$	−5.37378	−	5.37378i	−0.521948	−	0.521948i
$107$	0.736249	+	0.736249i	0.0711758	+	0.0711758i	0.741799	−	0.670623i	$-0.233973\pi$
$107$	0.736249	+	0.736249i	0.0711758	+	0.0711758i	−0.670623	+	0.741799i	$0.733973\pi$
$108$	0.286215	−	0.286215i	0.0275411	−	0.0275411i
$109$	−1.72705	−	1.72705i	−0.165422	−	0.165422i	0.619542	−	0.784964i	$-0.287318\pi$
$109$	−1.72705	−	1.72705i	−0.165422	−	0.165422i	−0.784964	+	0.619542i	$0.787318\pi$
$110$	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
$113$	−4.23008			−0.397933			−0.198966	−	0.980006i	$-0.563758\pi$
$113$	−4.23008			−0.397933			−0.198966	+	0.980006i	$0.563758\pi$
$114$	0.444083			0.0415922
$115$	−2.11943	−	8.66786i	−0.197638	−	0.808282i
$116$	1.30707	−	1.30707i	0.121358	−	0.121358i
$117$	−9.94518			−0.919432
$118$	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
$125$	8.40962	−	7.36738i	0.752179	−	0.658958i
$126$	8.32723	+	8.32723i	0.741849	+	0.741849i
$127$	0.683408	+	0.683408i	0.0606426	+	0.0606426i	0.736778	−	0.676135i	$-0.236346\pi$
$127$	0.683408	+	0.683408i	0.0606426	+	0.0606426i	−0.676135	+	0.736778i	$0.736346\pi$
$128$			1.00000i			0.0883883i
$129$	0.332057	−	0.332057i	0.0292360	−	0.0292360i
$130$	−7.21153	+	1.76334i	−0.632493	+	0.154655i
$131$	−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
$133$			25.8602i			2.24237i
$134$	−4.34085	−	4.34085i	−0.374993	−	0.374993i
$135$	−0.469671	+	0.773694i	−0.0404228	+	0.0665890i
$136$			3.64900i			0.312900i
$137$	15.4431	+	15.4431i	1.31939	+	1.31939i	0.914256	+	0.405138i	$0.132777\pi$
$137$	15.4431	+	15.4431i	1.31939	+	1.31939i	0.405138	+	0.914256i	$0.367223\pi$
$138$	0.190506	+	0.190506i	0.0162169	+	0.0162169i
$139$	−17.8399			−1.51316			−0.756582	−	0.653899i	$-0.773132\pi$
$139$	−17.8399			−1.51316			−0.756582	+	0.653899i	$0.773132\pi$
$140$	7.51477	+	4.56184i	0.635114	+	0.385546i
$141$		−	0.128130i		−	0.0107905i
$142$		−	5.54775i		−	0.465557i
$143$	14.0852			1.17787
$144$		−	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
$148$	4.65727	+	3.91278i	0.382825	+	0.321629i
$149$			17.7144i			1.45122i	0.688106	+	0.725610i	$0.258442\pi$
$149$			17.7144i			1.45122i	−0.688106	+	0.725610i	$0.741558\pi$
$150$	−0.101618	+	0.321906i	−0.00829709	+	0.0262835i
$151$			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
$153$		−	10.9304i		−	0.883669i
$154$	−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	0.554498	−	0.832185i	$-0.312910\pi$
$157$	−3.47940	−	3.47940i	−0.277687	−	0.277687i	−0.832185	+	0.554498i	$0.812910\pi$
$158$	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
$162$			8.95900i			0.703885i
$163$	−21.7952			−1.70713			−0.853566	−	0.520985i	$-0.825565\pi$
$163$	−21.7952			−1.70713			−0.853566	+	0.520985i	$0.825565\pi$
$164$		−	2.70237i		−	0.211020i
$165$	0.332342	−	0.547470i	0.0258728	−	0.0426205i
$166$	−7.08119	−	7.08119i	−0.549607	−	0.549607i
$167$	−11.1575			−0.863394			−0.431697	−	0.902019i	$-0.642085\pi$
$167$	−11.1575			−0.863394			−0.431697	+	0.902019i	$0.642085\pi$
$168$	−0.265425			−0.0204780
$169$	1.97691			0.152070
$170$	−1.93802	−	7.92592i	−0.148639	−	0.607890i
$171$	−13.9323	+	13.9323i	−1.06543	+	1.06543i
$172$		−	6.95570i		−	0.530367i
$173$	−14.4965	−	14.4965i	−1.10215	−	1.10215i	−0.994152	−	0.107994i	$-0.965557\pi$
$173$	−14.4965	−	14.4965i	−1.10215	−	1.10215i	−0.107994	−	0.994152i	$-0.534443\pi$
$174$		−	0.124796i		−	0.00946076i
$175$	−18.7455	−	5.91752i	−1.41703	−	0.447322i
$176$			4.24241i			0.319783i
$177$		−	0.768026i		−	0.0577284i
$178$	7.75651	+	7.75651i	0.581375	+	0.581375i
$179$	12.6119	−	12.6119i	0.942658	−	0.942658i	−0.0557848	−	0.998443i	$-0.517766\pi$
$179$	12.6119	−	12.6119i	0.942658	−	0.942658i	0.998443	+	0.0557848i	$0.0177661\pi$
$180$	1.59091	+	6.50633i	0.118579	+	0.484954i
$181$	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
$183$		−	0.148241i		−	0.0109583i
$184$	3.99058			0.294190
$185$	−12.1941	−	6.02536i	−0.896525	−	0.442993i
$186$	−0.378332			−0.0277406
$187$			15.4806i			1.13205i
$188$	−1.34199	−	1.34199i	−0.0978746	−	0.0978746i
$189$	1.59134			0.115753
$190$	−7.63243	+	12.5730i	−0.553715	+	0.912140i
$191$	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
$193$		−	7.58052i		−	0.545658i	−0.962063	−	0.272829i	$-0.912041\pi$
$193$		−	7.58052i		−	0.545658i	0.962063	−	0.272829i	$-0.0879593\pi$
$194$		−	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	−0.973037	−	0.230649i	$-0.925915\pi$
$197$	−16.8945	−	16.8945i	−1.20369	−	1.20369i	−0.230649	−	0.973037i	$-0.574085\pi$
$198$		−	12.7079i		−	0.903110i
$199$	−0.576031	+	0.576031i	−0.0408338	+	0.0408338i	−0.727229	−	0.686395i	$-0.759192\pi$
$199$	−0.576031	+	0.576031i	−0.0408338	+	0.0408338i	0.686395	+	0.727229i	$0.259192\pi$
$200$	2.30722	+	4.43585i	0.163145	+	0.313662i
$201$	−0.414455			−0.0292334
$202$	−1.51442			−0.106554
$203$	7.26722			0.510059
$204$	0.174199	+	0.174199i	0.0121964	+	0.0121964i
$205$	1.43525	+	5.86977i	0.100243	+	0.409962i
$206$			3.88757i			0.270860i
$207$	−11.9536			−0.830830
$208$		−	3.32010i		−	0.230208i
$209$	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
$217$		−	22.0313i		−	1.49559i
$218$	−1.72705	+	1.72705i	−0.116971	+	0.116971i
$219$		−	1.06346i		−	0.0718617i
$220$	−2.25318	−	9.21484i	−0.151909	−	0.621264i
$221$		−	12.1151i		−	0.814948i
$222$	0.409124	−	0.0355407i	0.0274586	−	0.00238534i
$223$	14.0320	−	14.0320i	0.939655	−	0.939655i	−0.0586249	−	0.998280i	$-0.518672\pi$
$223$	14.0320	−	14.0320i	0.939655	−	0.939655i	0.998280	+	0.0586249i	$0.0186716\pi$
$224$	−2.77997	+	2.77997i	−0.185744	+	0.185744i
$225$	−6.91114	−	13.2873i	−0.460743	−	0.885822i
$226$			4.23008i			0.281381i
$227$	−17.0093			−1.12895			−0.564475	−	0.825450i	$-0.690921\pi$
$227$	−17.0093			−1.12895			−0.564475	+	0.825450i	$0.690921\pi$
$228$		−	0.444083i		−	0.0294101i
$229$		−	8.49131i		−	0.561121i	−0.959836	−	0.280561i	$-0.909480\pi$
$229$		−	8.49131i		−	0.561121i	0.959836	−	0.280561i	$-0.0905204\pi$
$230$	−8.66786	+	2.11943i	−0.571542	+	0.139751i
$231$	−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	$-0.422263\pi$
$233$	−11.1205	−	11.1205i	−0.728530	−	0.728530i	−0.970327	+	0.241797i	$0.922263\pi$
$234$			9.94518i			0.650137i
$235$	3.62765	+	2.20216i	0.236642	+	0.143653i
$236$	−8.04404	−	8.04404i	−0.523623	−	0.523623i
$237$		−	0.303322i		−	0.0197029i
$238$	−10.1441	+	10.1441i	−0.657545	+	0.657545i
$239$	14.6371	+	14.6371i	0.946797	+	0.946797i	0.998654	−	0.0518580i	$-0.0165143\pi$
$239$	14.6371	+	14.6371i	0.946797	+	0.946797i	−0.0518580	+	0.998654i	$0.516514\pi$
$240$	−0.129047	−	0.0783380i	−0.00832995	−	0.00505669i
$241$	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	$0.0905560\pi$
$242$			6.99802i			0.449850i
$243$	1.28634	+	1.28634i	0.0825187	+	0.0825187i
$244$	−1.55262	−	1.55262i	−0.0993963	−	0.0993963i
$245$	4.49129	+	18.3681i	0.286938	+	1.17349i
$246$	−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
$253$	16.9297			1.06436
$254$	0.683408	−	0.683408i	0.0428808	−	0.0428808i
$255$	−0.470893	−	0.285856i	−0.0294885	−	0.0179010i
$256$	1.00000			0.0625000
$257$	5.00407			0.312145			0.156073	−	0.987746i	$-0.450117\pi$
$257$	5.00407			0.312145			0.156073	+	0.987746i	$0.450117\pi$
$258$	−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	$-0.0677477\pi$
$263$	12.4257	+	12.4257i	0.766203	+	0.766203i	−0.211233	+	0.977436i	$0.567748\pi$
$264$	0.202528	+	0.202528i	0.0124647	+	0.0124647i
$265$	8.81821	−	14.5263i	0.541698	−	0.892345i
$266$	25.8602			1.58559
$267$	0.740574			0.0453224
$268$	−4.34085	+	4.34085i	−0.265160	+	0.265160i
$269$			22.6019i			1.37806i	0.724732	+	0.689030i	$0.241963\pi$
$269$			22.6019i			1.37806i	−0.724732	+	0.689030i	$0.758037\pi$
$270$	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	$0.313647\pi$
$272$	3.64900			0.221253
$273$	0.881238			0.0533350
$274$	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
$277$			23.4453i			1.40869i	0.709857	+	0.704346i	$0.248759\pi$
$277$			23.4453i			1.40869i	−0.709857	+	0.704346i	$0.751241\pi$
$278$			17.8399i			1.06997i
$279$	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	$0.205253\pi$
$282$	−0.128130			−0.00763003
$283$	12.1785			0.723935			0.361968	−	0.932191i	$-0.382105\pi$
$283$	12.1785			0.723935			0.361968	+	0.932191i	$0.382105\pi$
$284$	−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
$288$	−2.99544			−0.176508
$289$	−3.68477			−0.216751
$290$	3.53325	+	2.14486i	0.207480	+	0.125951i
$291$	−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	−0.675315	−	0.737529i	$-0.735992\pi$
$293$	1.06493	−	1.06493i	0.0622140	−	0.0622140i	0.737529	+	0.675315i	$0.235992\pi$
$294$	−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
$298$	17.7144			1.02617
$299$	−13.2492			−0.766219
$300$	0.321906	+	0.101618i	0.0185853	+	0.00586693i
$301$	19.3366	−	19.3366i	1.11454	−	1.11454i
$302$	5.53031			0.318233
$303$	−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	$-0.975133\pi$
$307$	−16.1006	+	16.1006i	−0.918907	+	0.918907i	0.0780426	+	0.996950i	$0.475133\pi$
$308$	−11.7938	+	11.7938i	−0.672012	+	0.672012i
$309$	0.185588	+	0.185588i	0.0105577	+	0.0105577i
$310$	6.50237	−	10.7114i	0.369310	−	0.608368i
$311$	−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
$313$			21.7608i			1.22999i	0.788531	+	0.614995i	$0.210842\pi$
$313$			21.7608i			1.22999i	−0.788531	+	0.614995i	$0.789158\pi$
$314$	−3.47940	+	3.47940i	−0.196354	+	0.196354i
$315$	−13.6647	+	22.5101i	−0.769921	+	1.26830i
$316$	−3.17689	−	3.17689i	−0.178714	−	0.178714i
$317$	22.3061	−	22.3061i	1.25284	−	1.25284i	0.298392	−	0.954443i	$-0.403550\pi$
$317$	22.3061	−	22.3061i	1.25284	−	1.25284i	0.954443	−	0.298392i	$-0.0964504\pi$
$318$			0.513076i			0.0287719i
$319$	−5.54512	−	5.54512i	−0.310467	−	0.310467i
$320$	−2.17208	+	0.531109i	−0.121423	+	0.0296899i
$321$		−	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
$325$	−7.66021	−	14.7275i	−0.424912	−	0.816933i
$326$			21.7952i			1.20712i
$327$			0.164895i			0.00911871i
$328$	−2.70237			−0.149214
$329$		−	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
$333$	−11.7205	+	13.9506i	−0.642280	+	0.764486i
$334$			11.1575i			0.610512i
$335$	7.12321	−	11.7341i	0.389183	−	0.641105i
$336$			0.265425i			0.0144801i
$337$	−17.5570	+	17.5570i	−0.956390	+	0.956390i	−0.999088	−	0.0426980i	$-0.986405\pi$
$337$	−17.5570	+	17.5570i	−0.956390	+	0.956390i	0.0426980	+	0.999088i	$0.486405\pi$
$338$		−	1.97691i		−	0.107530i
$339$	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
$347$			11.0678i			0.594151i	0.954854	+	0.297075i	$0.0960112\pi$
$347$			11.0678i			0.594151i	−0.954854	+	0.297075i	$0.903989\pi$
$348$	−0.124796			−0.00668977
$349$			31.6855i			1.69609i	0.529926	+	0.848044i	$0.322220\pi$
$349$			31.6855i			1.69609i	−0.529926	+	0.848044i	$0.677780\pi$
$350$	−5.91752	+	18.7455i	−0.316305	+	1.00199i
$351$	0.950265	+	0.950265i	0.0507214	+	0.0507214i
$352$	4.24241			0.226121
$353$	−15.6047			−0.830555			−0.415278	−	0.909695i	$-0.636316\pi$
$353$	−15.6047			−0.830555			−0.415278	+	0.909695i	$0.636316\pi$
$354$	−0.768026			−0.0408201
$355$	12.0501	−	2.94646i	0.639555	−	0.156382i
$356$	7.75651	−	7.75651i	0.411094	−	0.411094i
$357$			0.968537i			0.0512604i
$358$	−12.6119	−	12.6119i	−0.666560	−	0.666560i
$359$		−	34.4499i		−	1.81820i	−0.416580	−	0.909099i	$-0.636771\pi$
$359$		−	34.4499i		−	1.81820i	0.416580	−	0.909099i	$-0.363229\pi$
$360$	6.50633	−	1.59091i	0.342914	−	0.0838481i
$361$			24.2668i			1.27720i
$362$		−	12.8145i		−	0.673515i
$363$	0.334077	+	0.334077i	0.0175345	+	0.0175345i
$364$	9.22978	−	9.22978i	0.483772	−	0.483772i
$365$	30.1088	+	18.2775i	1.57597	+	0.956691i
$366$	−0.148241			−0.00774866
$367$	−4.61443	−	4.61443i	−0.240871	−	0.240871i	0.576339	−	0.817211i	$-0.304481\pi$
$367$	−4.61443	−	4.61443i	−0.240871	−	0.240871i	−0.817211	+	0.576339i	$0.804481\pi$
$368$		−	3.99058i		−	0.208024i
$369$	8.09481			0.421399
$370$	−6.02536	+	12.1941i	−0.313243	+	0.633939i
$371$	−29.8779			−1.55118
$372$			0.378332i			0.0196156i
$373$	−15.3464	−	15.3464i	−0.794607	−	0.794607i	0.187632	−	0.982239i	$-0.439919\pi$
$373$	−15.3464	−	15.3464i	−0.794607	−	0.794607i	−0.982239	+	0.187632i	$0.939919\pi$
$374$	15.4806			0.800481
$375$	−0.753176	−	0.0497555i	−0.0388938	−	0.00256937i
$376$	−1.34199	+	1.34199i	−0.0692078	+	0.0692078i
$377$	4.33961	+	4.33961i	0.223501	+	0.223501i
$378$		−	1.59134i		−	0.0818497i
$379$			23.4892i			1.20656i	0.797531	+	0.603278i	$0.206139\pi$
$379$			23.4892i			1.20656i	−0.797531	+	0.603278i	$0.793861\pi$
$380$	12.5730	+	7.63243i	0.644981	+	0.391535i
$381$		−	0.0652502i		−	0.00334287i
$382$	−10.0822	−	10.0822i	−0.515850	−	0.515850i
$383$		−	0.480522i		−	0.0245535i	−0.999925	−	0.0122768i	$-0.996092\pi$
$383$		−	0.480522i		−	0.0245535i	0.999925	−	0.0122768i	$-0.00390791\pi$
$384$	0.0477388	−	0.0477388i	0.00243616	−	0.00243616i
$385$	19.3532	−	31.8807i	0.986330	−	1.62479i
$386$	−7.58052			−0.385838
$387$	20.8354			1.05912
$388$	−10.0451			−0.509962
$389$	11.0293	+	11.0293i	0.559208	+	0.559208i	0.929082	−	0.369874i	$-0.120599\pi$
$389$	11.0293	+	11.0293i	0.559208	+	0.559208i	−0.369874	+	0.929082i	$0.620599\pi$
$390$	0.428450	+	0.260090i	0.0216954	+	0.0131702i
$391$		−	14.5617i		−	0.736415i
$392$	−8.45644			−0.427115
$393$			0.320051i			0.0161444i
$394$	−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	$-0.980027\pi$
$397$	−18.6363	+	18.6363i	−0.935327	+	0.935327i	0.0627054	+	0.998032i	$0.480027\pi$
$398$	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	$0.439302\pi$
$402$			0.414455i			0.0206711i
$403$	13.1560	−	13.1560i	0.655346	−	0.655346i
$404$			1.51442i			0.0753454i
$405$	−19.4596	+	4.75820i	−0.966958	+	0.236437i
$406$		−	7.26722i		−	0.360666i
$407$	16.5996	−	19.7580i	0.822813	−	0.979369i
$408$	0.174199	−	0.174199i	0.00862415	−	0.00862415i
$409$	20.5642	−	20.5642i	1.01684	−	1.01684i	0.0169803	−	0.999856i	$-0.494595\pi$
$409$	20.5642	−	20.5642i	1.01684	−	1.01684i	0.999856	−	0.0169803i	$-0.00540527\pi$
$410$	5.86977	−	1.43525i	0.289887	−	0.0708822i
$411$		−	1.47447i		−	0.0727303i
$412$	3.88757			0.191527
$413$		−	44.7244i		−	2.20074i
$414$			11.9536i			0.587486i
$415$	11.6200	−	19.1418i	0.570404	−	0.939633i
$416$	−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	$0.376671\pi$
$419$			37.9044i			1.85175i	−0.377827	+	0.925876i	$0.623329\pi$
$420$	−0.140969	−	0.576524i	−0.00687861	−	0.0281315i
$421$	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	$0.430033\pi$
$422$			21.1449i			1.02932i
$423$	4.01985	−	4.01985i	0.195452	−	0.195452i
$424$	5.37378	+	5.37378i	0.260974	+	0.260974i
$425$	16.1864	−	8.41905i	0.785157	−	0.408384i
$426$	−0.264843	+	0.264843i	−0.0128317	+	0.0128317i
$427$		−	8.63247i		−	0.417754i
$428$	−0.736249	−	0.736249i	−0.0355879	−	0.0355879i
$429$	−0.672413	−	0.672413i	−0.0324644	−	0.0324644i
$430$	15.1083	−	3.69423i	0.728588	−	0.178152i
$431$	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	−0.981911	−	0.189341i	$-0.939365\pi$
$433$	−16.4923	+	16.4923i	−0.792570	+	0.792570i	0.189341	+	0.981911i	$0.439365\pi$
$434$	−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
$438$	−1.06346			−0.0508139
$439$	17.5768	−	17.5768i	0.838896	−	0.838896i	−0.149817	−	0.988714i	$-0.547869\pi$
$439$	17.5768	−	17.5768i	0.838896	−	0.838896i	0.988714	+	0.149817i	$0.0478686\pi$
$440$	−9.21484	+	2.25318i	−0.439300	+	0.107416i
$441$	25.3308			1.20623
$442$	−12.1151			−0.576255
$443$	14.2624	+	14.2624i	0.677629	+	0.677629i	0.959463	−	0.281834i	$-0.0909427\pi$
$443$	14.2624	+	14.2624i	0.677629	+	0.677629i	−0.281834	+	0.959463i	$0.590943\pi$
$444$	−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	0.156965	−	0.987604i	$-0.449829\pi$
$449$	−17.6009	−	17.6009i	−0.830639	−	0.830639i	−0.987604	+	0.156965i	$0.949829\pi$
$450$	−13.2873	+	6.91114i	−0.626370	+	0.325794i
$451$	−11.4646			−0.539846
$452$	4.23008			0.198966
$453$	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
$457$	−8.32533			−0.389443			−0.194721	−	0.980859i	$-0.562380\pi$
$457$	−8.32533			−0.389443			−0.194721	+	0.980859i	$0.562380\pi$
$458$	−8.49131			−0.396773
$459$	−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	$0.247616\pi$
$462$			1.12604i			0.0523881i
$463$		−	0.781658i		−	0.0363267i	−0.999835	−	0.0181634i	$-0.994218\pi$
$463$		−	0.781658i		−	0.0363267i	0.999835	−	0.0181634i	$-0.00578189\pi$
$464$	−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
$467$	−2.66280			−0.123220			−0.0616098	−	0.998100i	$-0.519623\pi$
$467$	−2.66280			−0.123220			−0.0616098	+	0.998100i	$0.519623\pi$
$468$	9.94518			0.459716
$469$	−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
$473$	−29.5089			−1.35682
$474$	−0.303322			−0.0139320
$475$	−31.3632	−	9.90061i	−1.43904	−	0.454271i
$476$	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	0.224294	−	0.974522i	$-0.427993\pi$
$479$	−16.4195	−	16.4195i	−0.750228	−	0.750228i	−0.974522	+	0.224294i	$0.927993\pi$
$480$	−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
$483$	1.05920			0.0481953
$484$	6.99802			0.318092
$485$	21.8187	−	5.33503i	0.990736	−	0.242251i
$486$	1.28634	−	1.28634i	0.0583495	−	0.0583495i
$487$	9.02775			0.409087			0.204543	−	0.978858i	$-0.434429\pi$
$487$	9.02775			0.409087			0.204543	+	0.978858i	$0.434429\pi$
$488$	−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
$495$	27.6025	−	6.74927i	1.24064	−	0.303357i
$496$	3.96252	+	3.96252i	0.177922	+	0.177922i
$497$	−15.4226	−	15.4226i	−0.691796	−	0.691796i
$498$			0.676095i			0.0302966i
$499$	11.5866	−	11.5866i	0.518686	−	0.518686i	−0.398487	−	0.917174i	$-0.630465\pi$
$499$	11.5866	−	11.5866i	0.518686	−	0.518686i	0.917174	+	0.398487i	$0.130465\pi$
$500$	−8.40962	+	7.36738i	−0.376090	+	0.329479i
$501$	0.532647	+	0.532647i	0.0237969	+	0.0237969i
$502$	−16.2391	+	16.2391i	−0.724784	+	0.724784i
$503$		−	19.3861i		−	0.864382i	−0.901782	−	0.432191i	$-0.857741\pi$
$503$		−	19.3861i		−	0.864382i	0.901782	−	0.432191i	$-0.142259\pi$
$504$	−8.32723	−	8.32723i	−0.370924	−	0.370924i
$505$	−0.804324	−	3.28945i	−0.0357919	−	0.146378i
$506$		−	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	$-0.554566\pi$
$509$	−7.69714			−0.341170			−0.170585	+	0.985343i	$0.554566\pi$
$510$	−0.285856	+	0.470893i	−0.0126579	+	0.0208515i
$511$		−	61.9280i		−	2.73953i
$512$		−	1.00000i		−	0.0441942i
$513$	2.66247			0.117551
$514$		−	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
$518$	23.8245	−	2.06964i	1.04679	−	0.0909346i
$519$			1.38409i			0.0607548i
$520$	7.21153	−	1.76334i	0.316246	−	0.0773274i
$521$			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
$523$		−	8.67427i		−	0.379299i	−0.981852	−	0.189650i	$-0.939265\pi$
$523$		−	8.67427i		−	0.379299i	0.981852	−	0.189650i	$-0.0607352\pi$
$524$	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
$532$		−	25.8602i		−	1.12118i
$533$	8.97216			0.388628
$534$		−	0.740574i		−	0.0320478i
$535$	1.99022	+	1.20816i	0.0860446	+	0.0522334i
$536$	4.34085	+	4.34085i	0.187496	+	0.187496i
$537$	−1.20416			−0.0519631
$538$	22.6019			0.974436
$539$	−35.8757			−1.54527
$540$	0.469671	−	0.773694i	0.0202114	−	0.0332945i
$541$	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	$0.0513477\pi$
$542$		−	18.1930i		−	0.781454i
$543$	−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
$547$			0.0420593i			0.00179833i	1.00000		0.000899163i	$0.000286213\pi$
$547$			0.0420593i			0.00179833i	−1.00000		0.000899163i	$0.999714\pi$
$548$	−15.4431	−	15.4431i	−0.659697	−	0.659697i
$549$	4.65078	−	4.65078i	0.198491	−	0.198491i
$550$	18.8187	−	9.78816i	0.802431	−	0.417369i
$551$	12.1588			0.517983
$552$	−0.190506	−	0.190506i	−0.00810847	−	0.00810847i
$553$		−	17.6633i		−	0.751120i
$554$	23.4453			0.996095
$555$	0.294487	+	0.869774i	0.0125003	+	0.0369198i
$556$	17.8399			0.756582
$557$		−	12.8111i		−	0.542823i	−0.962463	−	0.271412i	$-0.912509\pi$
$557$		−	12.8111i		−	0.542823i	0.962463	−	0.271412i	$-0.0874905\pi$
$558$	−11.8695	−	11.8695i	−0.502476	−	0.502476i
$559$	23.0937			0.976758
$560$	−7.51477	−	4.56184i	−0.317557	−	0.192773i
$561$	0.739024	−	0.739024i	0.0312016	−	0.0312016i
$562$	−3.32166	−	3.32166i	−0.140116	−	0.140116i
$563$			29.4317i			1.24040i	0.784444	+	0.620200i	$0.212949\pi$
$563$			29.4317i			1.24040i	−0.784444	+	0.620200i	$0.787051\pi$
$564$			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
$568$			5.54775i			0.232778i
$569$	−1.25554	+	1.25554i	−0.0526351	+	0.0526351i	−0.732934	−	0.680299i	$-0.761850\pi$
$569$	−1.25554	+	1.25554i	−0.0526351	+	0.0526351i	0.680299	+	0.732934i	$0.261850\pi$
$570$	0.964583	−	0.235856i	0.0404019	−	0.00987894i
$571$	−40.9624			−1.71422			−0.857111	−	0.515132i	$-0.827743\pi$
$571$	−40.9624			−1.71422			−0.857111	+	0.515132i	$0.827743\pi$
$572$	−14.0852			−0.588933
$573$	−0.962624			−0.0402142
$574$	−7.51251	−	7.51251i	−0.313566	−	0.313566i
$575$	−9.20715	−	17.7016i	−0.383965	−	0.738209i
$576$			2.99544i			0.124810i
$577$	−7.71924			−0.321356			−0.160678	−	0.987007i	$-0.551368\pi$
$577$	−7.71924			−0.321356			−0.160678	+	0.987007i	$0.551368\pi$
$578$			3.68477i			0.153266i
$579$	−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
$587$		−	5.39311i		−	0.222597i	−0.993787	−	0.111299i	$-0.964499\pi$
$587$		−	5.39311i		−	0.222597i	0.993787	−	0.111299i	$-0.0355010\pi$
$588$	−0.403701	+	0.403701i	−0.0166483	+	0.0166483i
$589$		−	36.8607i		−	1.51882i
$590$	13.2000	−	21.7445i	0.543437	−	0.895209i
$591$			1.61305i			0.0663521i
$592$	−4.65727	−	3.91278i	−0.191412	−	0.160814i
$593$	−10.4329	+	10.4329i	−0.428427	+	0.428427i	−0.888092	−	0.459665i	$-0.847969\pi$
$593$	−10.4329	+	10.4329i	−0.428427	+	0.428427i	0.459665	+	0.888092i	$0.347969\pi$
$594$	−1.21424	+	1.21424i	−0.0498210	+	0.0498210i
$595$	−27.4214	−	16.6462i	−1.12417	−	0.682427i
$596$		−	17.7144i		−	0.725610i
$597$	0.0549981			0.00225092
$598$			13.2492i			0.541798i
$599$			19.3788i			0.791798i	0.918294	+	0.395899i	$0.129567\pi$
$599$			19.3788i			0.791798i	−0.918294	+	0.395899i	$0.870433\pi$
$600$	0.101618	−	0.321906i	0.00414855	−	0.0131418i
$601$	−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
$605$	−15.2002	+	3.71671i	−0.617978	+	0.151106i
$606$	0.0722968	+	0.0722968i	0.00293686	+	0.00293686i
$607$			29.8434i			1.21131i	0.795729	+	0.605653i	$0.207088\pi$
$607$			29.8434i			1.21131i	−0.795729	+	0.605653i	$0.792912\pi$
$608$	−4.65117	+	4.65117i	−0.188630	+	0.188630i
$609$	−0.346929	−	0.346929i	−0.0140583	−	0.0140583i
$610$	2.54780	−	4.19702i	0.103158	−	0.169932i
$611$	4.45554	−	4.45554i	0.180252	−	0.180252i
$612$			10.9304i			0.441834i
$613$	−7.97850	−	7.97850i	−0.322248	−	0.322248i	0.527381	−	0.849629i	$-0.323174\pi$
$613$	−7.97850	−	7.97850i	−0.322248	−	0.322248i	−0.849629	+	0.527381i	$0.823174\pi$
$614$	16.1006	+	16.1006i	0.649766	+	0.649766i
$615$	0.211699	−	0.348733i	0.00853651	−	0.0140623i
$616$	11.7938	+	11.7938i	0.475184	+	0.475184i
$617$	−21.2579	+	21.2579i	−0.855812	+	0.855812i	−0.990842	−	0.135030i	$-0.956887\pi$
$617$	−21.2579	+	21.2579i	−0.855812	+	0.855812i	0.135030	+	0.990842i	$0.456887\pi$
$618$	0.185588	−	0.185588i	0.00746545	−	0.00746545i
$619$	7.54167			0.303125			0.151563	−	0.988448i	$-0.451569\pi$
$619$	7.54167			0.303125			0.151563	+	0.988448i	$0.451569\pi$
$620$	−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
$623$	43.1257			1.72779
$624$	−0.158498	+	0.158498i	−0.00634500	+	0.00634500i
$625$	14.3535	−	20.4689i	0.574139	−	0.818758i
$626$	21.7608			0.869735
$627$	−1.88398			−0.0752390
$628$	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
$635$	1.84738	+	1.12145i	0.0733110	+	0.0445034i
$636$	0.513076			0.0203448
$637$	28.0763			1.11242
$638$	−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	$0.577475\pi$
$642$	−0.0702953			−0.00277433
$643$	−26.4268			−1.04217			−0.521085	−	0.853505i	$-0.674472\pi$
$643$	−26.4268			−1.04217			−0.521085	+	0.853505i	$0.674472\pi$
$644$	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
$647$		−	23.6177i		−	0.928509i	−0.885702	−	0.464255i	$-0.846322\pi$
$647$		−	23.6177i		−	0.928509i	0.885702	−	0.464255i	$-0.153678\pi$
$648$		−	8.95900i		−	0.351943i
$649$	−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
$652$	21.7952			0.853566
$653$	−11.5143			−0.450588			−0.225294	−	0.974291i	$-0.572334\pi$
$653$	−11.5143			−0.450588			−0.225294	+	0.974291i	$0.572334\pi$
$654$	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
$658$	−7.46137			−0.290875
$659$	45.6299			1.77749			0.888744	−	0.458404i	$-0.151579\pi$
$659$	45.6299			1.77749			0.888744	+	0.458404i	$0.151579\pi$
$660$	−0.332342	+	0.547470i	−0.0129364	+	0.0213102i
$661$	−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
$668$	11.1575			0.431697
$669$	−1.33975			−0.0517976
$670$	−11.7341	−	7.12321i	−0.453329	−	0.275194i
$671$	−6.58685	+	6.58685i	−0.254282	+	0.254282i
$672$	0.265425			0.0102390
$673$	−25.0377	+	25.0377i	−0.965134	+	0.965134i	−0.999412	−	0.0342781i	$-0.989087\pi$
$673$	−25.0377	+	25.0377i	−0.965134	+	0.965134i	0.0342781	+	0.999412i	$0.489087\pi$
$674$	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	$-0.819967\pi$
$677$	−8.02326	+	8.02326i	−0.308359	+	0.308359i	0.535914	+	0.844273i	$0.319967\pi$
$678$	0.201939	−	0.201939i	0.00775543	−	0.00775543i
$679$	−27.9250	−	27.9250i	−1.07166	−	1.07166i
$680$	1.93802	+	7.92592i	0.0743196	+	0.303945i
$681$	0.812006	+	0.812006i	0.0311161	+	0.0311161i
$682$	16.8106	+	16.8106i	0.643712	+	0.643712i
$683$			14.7249i			0.563434i	0.959498	+	0.281717i	$0.0909039\pi$
$683$			14.7249i			0.563434i	−0.959498	+	0.281717i	$0.909096\pi$
$684$	13.9323	−	13.9323i	0.532715	−	0.532715i
$685$	41.7456	+	25.3417i	1.59502	+	0.968255i
$686$	−4.04887	−	4.04887i	−0.154586	−	0.154586i
$687$	−0.405365	+	0.405365i	−0.0154656	+	0.0154656i
$688$			6.95570i			0.265184i
$689$	−17.8415	−	17.8415i	−0.679707	−	0.679707i
$690$	0.514973	+	0.312614i	0.0196047	+	0.0119010i
$691$		−	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
$695$	−38.7497	+	9.47495i	−1.46986	+	0.359405i
$696$			0.124796i			0.00473038i
$697$			9.86097i			0.373511i
$698$	31.6855			1.19931
$699$			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
$703$	3.46271	+	39.8608i	0.130599	+	1.50338i
$704$		−	4.24241i		−	0.159892i
$705$	−0.0680510	−	0.278308i	−0.00256295	−	0.0104817i
$706$			15.6047i			0.587291i
$707$	−4.21005	+	4.21005i	−0.158335	+	0.158335i
$708$			0.768026i			0.0288642i
$709$	−24.5474	−	24.5474i	−0.921895	−	0.921895i	0.0752682	−	0.997163i	$-0.476019\pi$
$709$	−24.5474	−	24.5474i	−0.921895	−	0.921895i	−0.997163	+	0.0752682i	$0.976019\pi$
$710$	−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
$717$		−	1.39752i		−	0.0521913i
$718$	−34.4499			−1.28566
$719$			12.2897i			0.458329i	0.973388	+	0.229164i	$0.0735993\pi$
$719$			12.2897i			0.458329i	−0.973388	+	0.229164i	$0.926401\pi$
$720$	−1.59091	−	6.50633i	−0.0592895	−	0.242477i
$721$	10.8073	+	10.8073i	0.402486	+	0.402486i
$722$	24.2668			0.903116
$723$	−1.00663			−0.0374368
$724$	−12.8145			−0.476247
$725$	−2.78226	+	8.81366i	−0.103331	+	0.327331i
$726$	0.334077	−	0.334077i	0.0123988	−	0.0123988i
$727$			12.2686i			0.455016i	0.973776	+	0.227508i	$0.0730579\pi$
$727$			12.2686i			0.455016i	−0.973776	+	0.227508i	$0.926942\pi$
$728$	−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
$732$			0.148241i			0.00547913i
$733$	26.4738	+	26.4738i	0.977831	+	0.977831i	0.999760	−	0.0219285i	$-0.00698063\pi$
$733$	26.4738	+	26.4738i	0.977831	+	0.977831i	−0.0219285	+	0.999760i	$0.506981\pi$
$734$	−4.61443	+	4.61443i	−0.170322	+	0.170322i
$735$	0.662461	−	1.09128i	0.0244352	−	0.0402524i
$736$	−3.99058			−0.147095
$737$	18.4157	+	18.4157i	0.678350	+	0.678350i
$738$		−	8.09481i		−	0.297974i
$739$	23.9200			0.879912			0.439956	−	0.898019i	$-0.354994\pi$
$739$	23.9200			0.879912			0.439956	+	0.898019i	$0.354994\pi$
$740$	12.1941	+	6.02536i	0.448263	+	0.221497i
$741$	1.47440			0.0541635
$742$			29.8779i			1.09685i
$743$	8.98938	+	8.98938i	0.329788	+	0.329788i	0.852506	−	0.522718i	$-0.175082\pi$
$743$	8.98938	+	8.98938i	0.329788	+	0.329788i	−0.522718	+	0.852506i	$0.675082\pi$
$744$	0.378332			0.0138703
$745$	9.40827	+	38.4771i	0.344692	+	1.40969i
$746$	−15.3464	+	15.3464i	−0.561872	+	0.561872i
$747$	−21.2113	−	21.2113i	−0.776080	−	0.776080i
$748$		−	15.4806i		−	0.566025i
$749$		−	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
$753$			1.55047i			0.0565022i
$754$	4.33961	−	4.33961i	0.158039	−	0.158039i
$755$	2.93719	+	12.0123i	0.106895	+	0.437171i
$756$	−1.59134			−0.0578765
$757$	2.66868			0.0969950			0.0484975	−	0.998823i	$-0.484557\pi$
$757$	2.66868			0.0969950			0.0484975	+	0.998823i	$0.484557\pi$
$758$	23.4892			0.853164
$759$	−0.808204	−	0.808204i	−0.0293359	−	0.0293359i
$760$	7.63243	−	12.5730i	0.276857	−	0.456070i
$761$		−	50.1338i		−	1.81735i	−0.417507	−	0.908674i	$-0.637096\pi$
$761$		−	50.1338i		−	1.81735i	0.417507	−	0.908674i	$-0.362904\pi$
$762$	−0.0652502			−0.00236376
$763$			9.60230i			0.347626i
$764$	−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	$0.604346\pi$
$769$	−35.1828	+	35.1828i	−1.26872	+	1.26872i	−0.946748	+	0.321974i	$0.895654\pi$
$770$	−31.8807	−	19.3532i	−1.14890	−	0.697441i
$771$	−0.238888	−	0.238888i	−0.00860335	−	0.00860335i
$772$			7.58052i			0.272829i
$773$	−5.35033	+	5.35033i	−0.192438	+	0.192438i	−0.796749	−	0.604311i	$-0.793449\pi$
$773$	−5.35033	+	5.35033i	−0.192438	+	0.192438i	0.604311	+	0.796749i	$0.293449\pi$
$774$		−	20.8354i		−	0.748913i
$775$	26.7195	+	8.43473i	0.959793	+	0.302984i
$776$			10.0451i			0.360597i
$777$	1.03855	−	1.23615i	0.0372578	−	0.0443468i
$778$	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
$782$	−14.5617			−0.520724
$783$		−	0.748207i		−	0.0267387i
$784$			8.45644i			0.302016i
$785$	−9.40547	−	5.70959i	−0.335696	−	0.203784i
$786$	0.320051			0.0114158
$787$	−34.2308	−	34.2308i	−1.22020	−	1.22020i	−0.967561	−	0.252637i	$-0.918702\pi$
$787$	−34.2308	−	34.2308i	−1.22020	−	1.22020i	−0.252637	−	0.967561i	$-0.581298\pi$
$788$	16.8945	+	16.8945i	0.601843	+	0.601843i
$789$		−	1.18638i		−	0.0422362i
$790$	5.21318	−	8.58772i	0.185476	−	0.305537i
$791$	11.7595	+	11.7595i	0.418120	+	0.418120i
$792$			12.7079i			0.451555i
$793$	5.15486	−	5.15486i	0.183054	−	0.183054i
$794$	18.6363	+	18.6363i	0.661376	+	0.661376i
$795$	−1.11444	+	0.272499i	−0.0395252	+	0.00966455i
$796$	0.576031	−	0.576031i	0.0204169	−	0.0204169i
$797$		−	41.1330i		−	1.45700i	−0.685043	−	0.728502i	$-0.740217\pi$
$797$		−	41.1330i		−	1.45700i	0.685043	−	0.728502i	$-0.259783\pi$
$798$	−1.23454	−	1.23454i	−0.0437021	−	0.0437021i
$799$	4.89692	+	4.89692i	0.173241	+	0.173241i
$800$	−2.30722	−	4.43585i	−0.0815725	−	0.156831i
$801$	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
$808$	1.51442			0.0532772
$809$	−25.8572	+	25.8572i	−0.909092	+	0.909092i	−0.996199	−	0.0871071i	$-0.972238\pi$
$809$	−25.8572	+	25.8572i	−0.909092	+	0.909092i	0.0871071	+	0.996199i	$0.472238\pi$
$810$	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	$0.653929\pi$
$812$	−7.26722			−0.255030
$813$	−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
$820$	−1.43525	−	5.86977i	−0.0501213	−	0.204981i
$821$	31.1573			1.08740			0.543699	−	0.839280i	$-0.317023\pi$
$821$	31.1573			1.08740			0.543699	+	0.839280i	$0.317023\pi$
$822$	−1.47447			−0.0514281
$823$	26.4495	−	26.4495i	0.921971	−	0.921971i	−0.0751977	−	0.997169i	$-0.523959\pi$
$823$	26.4495	−	26.4495i	0.921971	−	0.921971i	0.997169	+	0.0751977i	$0.0239588\pi$
$824$		−	3.88757i		−	0.135430i
$825$	0.431106	−	1.36566i	0.0150092	−	0.0475461i
$826$	−44.7244			−1.55616
$827$	23.8982			0.831021			0.415510	−	0.909588i	$-0.363603\pi$
$827$	23.8982			0.831021			0.415510	+	0.909588i	$0.363603\pi$
$828$	11.9536			0.415415
$829$	7.39911	−	7.39911i	0.256982	−	0.256982i	−0.566844	−	0.823825i	$-0.691836\pi$
$829$	7.39911	−	7.39911i	0.256982	−	0.256982i	0.823825	+	0.566844i	$0.191836\pi$
$830$	−19.1418	−	11.6200i	−0.664421	−	0.403337i
$831$	1.11925	−	1.11925i	0.0388264	−	0.0388264i
$832$			3.32010i			0.115104i
$833$			30.8576i			1.06915i
$834$	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
$837$	−2.26827			−0.0784028
$838$	37.9044			1.30939
$839$	22.2697			0.768834			0.384417	−	0.923160i	$-0.374402\pi$
$839$	22.2697			0.768834			0.384417	+	0.923160i	$0.374402\pi$
$840$	−0.576524	+	0.140969i	−0.0198920	+	0.00486391i
$841$			25.5831i			0.882177i
$842$	24.4985	−	24.4985i	0.844273	−	0.844273i
$843$	−0.317145			−0.0109230
$844$	21.1449			0.727838
$845$	4.29399	−	1.04995i	0.147718	−	0.0361194i
$846$	−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
$853$	30.0733			1.02969			0.514845	−	0.857283i	$-0.327850\pi$
$853$	30.0733			1.02969			0.514845	+	0.857283i	$0.327850\pi$
$854$	−8.63247			−0.295397
$855$	−22.8625	+	37.6616i	−0.781881	+	1.28800i
$856$	−0.736249	+	0.736249i	−0.0251645	+	0.0251645i
$857$	19.5685			0.668446			0.334223	−	0.942494i	$-0.391526\pi$
$857$	19.5685			0.668446			0.334223	+	0.942494i	$0.391526\pi$
$858$	−0.672413	+	0.672413i	−0.0229558	+	0.0229558i
$859$	12.9463	+	12.9463i	0.441723	+	0.441723i	0.892591	−	0.450868i	$-0.148885\pi$
$859$	12.9463	+	12.9463i	0.441723	+	0.441723i	−0.450868	+	0.892591i	$0.648885\pi$
$860$	−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	−0.702335	−	0.711846i	$-0.747859\pi$
$863$	0.279402	−	0.279402i	0.00951094	−	0.00951094i	0.711846	+	0.702335i	$0.247859\pi$
$864$	0.286215	+	0.286215i	0.00973725	+	0.00973725i
$865$	−39.1867	−	23.7883i	−1.33239	−	0.808825i
$866$	16.4923	+	16.4923i	0.560432	+	0.560432i
$867$	0.175907	+	0.175907i	0.00597410	+	0.00597410i
$868$			22.0313i			0.747793i
$869$	−13.4777	+	13.4777i	−0.457198	+	0.457198i
$870$	−0.0662802	−	0.271067i	−0.00224711	−	0.00919002i
$871$	−14.4121	−	14.4121i	−0.488335	−	0.488335i
$872$	1.72705	−	1.72705i	0.0584853	−	0.0584853i
$873$		−	30.0895i		−	1.01837i
$874$	18.5609	+	18.5609i	0.627832	+	0.627832i
$875$	−43.8596	−	2.89741i	−1.48272	−	0.0979502i
$876$			1.06346i			0.0359308i
$877$	29.4697	+	29.4697i	0.995121	+	0.995121i	0.999988	−	0.00486751i	$-0.00154938\pi$
$877$	29.4697	+	29.4697i	0.995121	+	0.995121i	−0.00486751	+	0.999988i	$0.501549\pi$
$878$	−17.5768	−	17.5768i	−0.593189	−	0.593189i
$879$	−0.101677			−0.00342949
$880$	2.25318	+	9.21484i	0.0759547	+	0.310632i
$881$			41.3883i			1.39441i	0.716873	+	0.697204i	$0.245573\pi$
$881$			41.3883i			1.39441i	−0.716873	+	0.697204i	$0.754427\pi$
$882$		−	25.3308i		−	0.852932i
$883$	−16.0092			−0.538751			−0.269376	−	0.963035i	$-0.586817\pi$
$883$	−16.0092			−0.538751			−0.269376	+	0.963035i	$0.586817\pi$
$884$			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	$-0.741946\pi$
$887$	1.06556	−	1.06556i	0.0357779	−	0.0357779i	0.724769	+	0.688992i	$0.241946\pi$
$888$	−0.409124	+	0.0355407i	−0.0137293	+	0.00119267i
$889$		−	3.79970i		−	0.127438i
$890$	20.9673	+	12.7282i	0.702825	+	0.426650i
$891$		−	38.0077i		−	1.27331i
$892$	−14.0320	+	14.0320i	−0.469828	+	0.469828i
$893$		−	12.4836i		−	0.417749i
$894$	−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
$902$			11.4646i			0.381728i
$903$	−1.84622			−0.0614382
$904$		−	4.23008i		−	0.140691i
$905$	27.8341	−	6.80589i	0.925236	−	0.226235i
$906$	−0.264010	−	0.264010i	−0.00877116	−	0.00877116i
$907$	−0.646631			−0.0214710			−0.0107355	−	0.999942i	$-0.503417\pi$
$907$	−0.646631			−0.0214710			−0.0107355	+	0.999942i	$0.503417\pi$
$908$	17.0093			0.564475
$909$	−4.53637			−0.150462
$910$	24.9498	+	15.1458i	0.827079	+	0.502078i
$911$	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	$0.185777\pi$
$912$			0.444083i			0.0147051i
$913$	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
$917$			18.6375i			0.615464i
$918$	1.04440	+	1.04440i	0.0344704	+	0.0344704i
$919$	−2.27110	+	2.27110i	−0.0749167	+	0.0749167i	−0.743572	−	0.668656i	$-0.766870\pi$
$919$	−2.27110	+	2.27110i	−0.0749167	+	0.0749167i	0.668656	+	0.743572i	$0.266870\pi$
$920$	8.66786	−	2.11943i	0.285771	−	0.0698757i
$921$	1.53724			0.0506539
$922$	−0.227378	−	0.227378i	−0.00748828	−	0.00748828i
$923$		−	18.4191i		−	0.606272i
$924$	1.12604			0.0370440
$925$	−29.6866	−	6.61118i	−0.976088	−	0.217374i
$926$	−0.781658			−0.0256869
$927$			11.6450i			0.382472i
$928$	1.30707	+	1.30707i	0.0429067	+	0.0429067i
$929$	−7.69649			−0.252514			−0.126257	−	0.991998i	$-0.540296\pi$
$929$	−7.69649			−0.252514			−0.126257	+	0.991998i	$0.540296\pi$
$930$	−0.821767	+	0.200935i	−0.0269468	+	0.00658893i
$931$	39.3324	−	39.3324i	1.28907	−	1.28907i
$932$	11.1205	+	11.1205i	0.364265	+	0.364265i
$933$			1.77472i			0.0581018i
$934$			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	0.751295	−	0.659966i	$-0.229429\pi$
$937$	2.79563	+	2.79563i	0.0913291	+	0.0913291i	−0.659966	+	0.751295i	$0.729429\pi$
$938$			24.1349i			0.788032i
$939$	1.03883	−	1.03883i	0.0339010	−	0.0339010i
$940$	−3.62765	−	2.20216i	−0.118321	−	0.0718266i
$941$	−1.41774			−0.0462169			−0.0231085	−	0.999733i	$-0.507356\pi$
$941$	−1.41774			−0.0462169			−0.0231085	+	0.999733i	$0.507356\pi$
$942$	0.332205			0.0108238
$943$	10.7841			0.351177
$944$	8.04404	+	8.04404i	0.261811	+	0.261811i
$945$	3.45651	−	0.845174i	0.112440	−	0.0274935i
$946$			29.5089i			0.959418i
$947$	20.5099			0.666483			0.333242	−	0.942841i	$-0.391858\pi$
$947$	20.5099			0.666483			0.333242	+	0.942841i	$0.391858\pi$
$948$			0.303322i			0.00985144i
$949$	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	$-0.215322\pi$
$953$	4.74691	+	4.74691i	0.153768	+	0.153768i	−0.626031	+	0.779798i	$0.715322\pi$
$954$	−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
$957$			0.529435i			0.0171142i
$958$	−16.4195	+	16.4195i	−0.530491	+	0.530491i
$959$		−	85.8627i		−	2.77265i
$960$	0.129047	+	0.0783380i	0.00416497	+	0.00252835i
$961$			0.403092i			0.0130030i
$962$	15.4626	+	12.9909i	0.498535	+	0.418842i
$963$	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
$967$	51.7273			1.66344			0.831719	−	0.555197i	$-0.187357\pi$
$967$	51.7273			1.66344			0.831719	+	0.555197i	$0.187357\pi$
$968$		−	6.99802i		−	0.224925i
$969$			1.62046i			0.0520567i
$970$	−5.33503	−	21.8187i	−0.171297	−	0.700556i
$971$	−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
$975$	−0.337383	+	1.06876i	−0.0108049	+	0.0342278i
$976$	1.55262	+	1.55262i	0.0496982	+	0.0496982i
$977$		−	21.5483i		−	0.689390i	−0.938715	−	0.344695i	$-0.887982\pi$
$977$		−	21.5483i		−	0.689390i	0.938715	−	0.344695i	$-0.112018\pi$
$978$	1.04048	−	1.04048i	0.0332708	−	0.0332708i
$979$	−32.9063	−	32.9063i	−1.05169	−	1.05169i
$980$	−4.49129	−	18.3681i	−0.143469	−	0.586746i
$981$	−5.17328	+	5.17328i	−0.165170	+	0.165170i
$982$			2.91238i			0.0929378i
$983$	−9.09050	−	9.09050i	−0.289942	−	0.289942i	0.547115	−	0.837057i	$-0.315726\pi$
$983$	−9.09050	−	9.09050i	−0.289942	−	0.289942i	−0.837057	+	0.547115i	$0.815726\pi$
$984$	0.129008	+	0.129008i	0.00411263	+	0.00411263i
$985$	−45.6691	−	27.7234i	−1.45514	−	0.883342i
$986$	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
$993$	−2.29023			−0.0726783
$994$	−15.4226	+	15.4226i	−0.489174	+	0.489174i
$995$	−0.945250	+	1.55712i	−0.0299664	+	0.0493640i
$996$	0.676095			0.0214229
$997$	−49.7309			−1.57499			−0.787497	−	0.616318i	$-0.788623\pi$
$997$	−49.7309			−1.57499			−0.787497	+	0.616318i	$0.788623\pi$
$998$	−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.g.e.327.6	yes	20
5.3	odd	4		370.2.h.e.253.5	yes	20
37.6	odd	4		370.2.h.e.117.5	yes	20
185.43	even	4	inner	370.2.g.e.43.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.6	✓	20	185.43	even	4	inner
370.2.g.e.327.6	yes	20	1.1	even	1	trivial
370.2.h.e.117.5	yes	20	37.6	odd	4
370.2.h.e.253.5	yes	20	5.3	odd	4

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.g (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

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Database

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