LMFDB - Embedded newform 55.3.f.a.23.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,3,Mod(12,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.12"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49864145398$
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} + 212 x^{16} - 792 x^{15} + 1480 x^{14} + 148 x^{13} + \cdots + 38416 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 212x^16 - 792x^15 + 1480x^14 + 148x^13 + 11654x^12 - 43032x^11 + 79360x^10 - 4948x^9 + 109988x^8 - 423032x^7 + 812488x^6 - 86868x^5 - 87295x^4 + 20876x^3 + 561800x^2 + 207760*x + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.6
Root			$-0.188102 - 0.188102i$ of defining polynomial
Character	$\chi$	$=$	55.23
Dual form			55.3.f.a.12.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.188102 - 0.188102i) q^{2} +(0.812414 + 0.812414i) q^{3} +3.92923i q^{4} +(-1.21594 + 4.84990i) q^{5} +0.305634 q^{6} +(5.94455 - 5.94455i) q^{7} +(1.49151 + 1.49151i) q^{8} -7.67997i q^{9} +(0.683556 + 1.14100i) q^{10} -3.31662 q^{11} +(-3.19216 + 3.19216i) q^{12} +(3.02318 + 3.02318i) q^{13} -2.23637i q^{14} +(-4.92797 + 2.95227i) q^{15} -15.1558 q^{16} +(0.878385 - 0.878385i) q^{17} +(-1.44462 - 1.44462i) q^{18} -29.2386i q^{19} +(-19.0564 - 4.77772i) q^{20} +9.65887 q^{21} +(-0.623865 + 0.623865i) q^{22} +(11.8993 + 11.8993i) q^{23} +2.42344i q^{24} +(-22.0430 - 11.7944i) q^{25} +1.13733 q^{26} +(13.5510 - 13.5510i) q^{27} +(23.3575 + 23.3575i) q^{28} +15.7896i q^{29} +(-0.371633 + 1.48229i) q^{30} -14.3621 q^{31} +(-8.81688 + 8.81688i) q^{32} +(-2.69447 - 2.69447i) q^{33} -0.330453i q^{34} +(21.6022 + 36.0587i) q^{35} +30.1764 q^{36} +(36.1210 - 36.1210i) q^{37} +(-5.49985 - 5.49985i) q^{38} +4.91214i q^{39} +(-9.04725 + 5.42007i) q^{40} -57.6501 q^{41} +(1.81686 - 1.81686i) q^{42} +(58.0890 + 58.0890i) q^{43} -13.0318i q^{44} +(37.2470 + 9.33839i) q^{45} +4.47659 q^{46} +(-29.8948 + 29.8948i) q^{47} +(-12.3128 - 12.3128i) q^{48} -21.6754i q^{49} +(-6.36489 + 1.92779i) q^{50} +1.42722 q^{51} +(-11.8788 + 11.8788i) q^{52} +(-59.0764 - 59.0764i) q^{53} -5.09797i q^{54} +(4.03282 - 16.0853i) q^{55} +17.7327 q^{56} +(23.7538 - 23.7538i) q^{57} +(2.97007 + 2.97007i) q^{58} +61.7604i q^{59} +(-11.6002 - 19.3631i) q^{60} +1.59704 q^{61} +(-2.70154 + 2.70154i) q^{62} +(-45.6540 - 45.6540i) q^{63} -57.3064i q^{64} +(-18.3381 + 10.9861i) q^{65} -1.01367 q^{66} +(-32.7908 + 32.7908i) q^{67} +(3.45138 + 3.45138i) q^{68} +19.3344i q^{69} +(10.8462 + 2.71929i) q^{70} -12.4615 q^{71} +(11.4547 - 11.4547i) q^{72} +(-74.3641 - 74.3641i) q^{73} -13.5889i q^{74} +(-8.32610 - 27.4899i) q^{75} +114.885 q^{76} +(-19.7158 + 19.7158i) q^{77} +(0.923986 + 0.923986i) q^{78} +21.8223i q^{79} +(18.4286 - 73.5042i) q^{80} -47.1016 q^{81} +(-10.8441 + 10.8441i) q^{82} +(45.9955 + 45.9955i) q^{83} +37.9520i q^{84} +(3.19201 + 5.32814i) q^{85} +21.8534 q^{86} +(-12.8277 + 12.8277i) q^{87} +(-4.94677 - 4.94677i) q^{88} +89.4219i q^{89} +(8.76283 - 5.24969i) q^{90} +35.9429 q^{91} +(-46.7553 + 46.7553i) q^{92} +(-11.6679 - 11.6679i) q^{93} +11.2466i q^{94} +(141.804 + 35.5524i) q^{95} -14.3259 q^{96} +(-62.6170 + 62.6170i) q^{97} +(-4.07719 - 4.07719i) q^{98} +25.4716i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 8 q^{6} + 12 q^{8} + 12 q^{10} - 16 q^{12} + 4 q^{13} - 20 q^{15} - 16 q^{16} + 24 q^{17} - 24 q^{18} - 8 q^{20} - 64 q^{21} - 86 q^{23} + 90 q^{25} + 96 q^{26} - 50 q^{27}+ \cdots + 620 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 8 * q^6 + 12 * q^8 + 12 * q^10 - 16 * q^12 + 4 * q^13 - 20 * q^15 - 16 * q^16 + 24 * q^17 - 24 * q^18 - 8 * q^20 - 64 * q^21 - 86 * q^23 + 90 * q^25 + 96 * q^26 - 50 * q^27 + 76 * q^28 - 56 * q^30 - 40 * q^31 + 184 * q^32 - 22 * q^33 - 60 * q^35 - 168 * q^36 - 126 * q^37 + 184 * q^38 + 64 * q^40 - 56 * q^41 + 32 * q^42 - 24 * q^43 + 278 * q^45 + 168 * q^46 + 156 * q^47 + 8 * q^48 - 352 * q^50 + 304 * q^51 - 100 * q^52 - 52 * q^53 + 66 * q^55 + 216 * q^56 - 80 * q^57 - 344 * q^58 - 224 * q^60 - 120 * q^61 - 540 * q^62 + 388 * q^63 - 56 * q^65 - 242 * q^67 + 204 * q^68 + 112 * q^70 - 204 * q^71 + 612 * q^72 - 228 * q^73 - 116 * q^75 - 504 * q^76 - 880 * q^78 + 640 * q^80 + 152 * q^81 + 256 * q^82 + 464 * q^83 - 532 * q^85 - 128 * q^86 + 496 * q^87 - 264 * q^88 - 112 * q^90 - 96 * q^91 - 168 * q^92 + 346 * q^93 + 508 * q^95 - 112 * q^96 + 290 * q^97 + 620 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.188102	−	0.188102i	0.0940512	−	0.0940512i	−0.658516	−	0.752567i	$-0.728815\pi$
$2$	0.188102	−	0.188102i	0.0940512	−	0.0940512i	0.752567	+	0.658516i	$0.228815\pi$
$3$	0.812414	+	0.812414i	0.270805	+	0.270805i	0.829424	−	0.558619i	$-0.188669\pi$
$3$	0.812414	+	0.812414i	0.270805	+	0.270805i	−0.558619	+	0.829424i	$0.688669\pi$
$4$			3.92923i			0.982309i
$5$	−1.21594	+	4.84990i	−0.243188	+	0.969979i
$5$	−1.21594	+	4.84990i	−0.243188	+	0.969979i
$6$	0.305634			0.0509390
$7$	5.94455	−	5.94455i	0.849222	−	0.849222i	−0.140814	−	0.990036i	$-0.544972\pi$
$7$	5.94455	−	5.94455i	0.849222	−	0.849222i	0.990036	+	0.140814i	$0.0449721\pi$
$8$	1.49151	+	1.49151i	0.186439	+	0.186439i
$9$		−	7.67997i		−	0.853330i
$10$	0.683556	+	1.14100i	0.0683556	+	0.114100i
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$	−3.19216	+	3.19216i	−0.266014	+	0.266014i
$13$	3.02318	+	3.02318i	0.232552	+	0.232552i	0.813757	−	0.581205i	$-0.197419\pi$
$13$	3.02318	+	3.02318i	0.232552	+	0.232552i	−0.581205	+	0.813757i	$0.697419\pi$
$14$		−	2.23637i		−	0.159741i
$15$	−4.92797	+	2.95227i	−0.328531	+	0.196818i
$16$	−15.1558			−0.947239
$17$	0.878385	−	0.878385i	0.0516697	−	0.0516697i	−0.680800	−	0.732470i	$-0.738368\pi$
$17$	0.878385	−	0.878385i	0.0516697	−	0.0516697i	0.732470	+	0.680800i	$0.238368\pi$
$18$	−1.44462	−	1.44462i	−0.0802567	−	0.0802567i
$19$		−	29.2386i		−	1.53887i	−0.638723	−	0.769437i	$-0.720537\pi$
$19$		−	29.2386i		−	1.53887i	0.638723	−	0.769437i	$-0.279463\pi$
$20$	−19.0564	−	4.77772i	−0.952819	−	0.238886i
$21$	9.65887			0.459946
$22$	−0.623865	+	0.623865i	−0.0283575	+	0.0283575i
$23$	11.8993	+	11.8993i	0.517362	+	0.517362i	0.916772	−	0.399410i	$-0.130785\pi$
$23$	11.8993	+	11.8993i	0.517362	+	0.517362i	−0.399410	+	0.916772i	$0.630785\pi$
$24$			2.42344i			0.100977i
$25$	−22.0430	−	11.7944i	−0.881719	−	0.471775i
$26$	1.13733			0.0437436
$27$	13.5510	−	13.5510i	0.501890	−	0.501890i
$28$	23.3575	+	23.3575i	0.834198	+	0.834198i
$29$			15.7896i			0.544470i	0.962231	+	0.272235i	$0.0877629\pi$
$29$			15.7896i			0.544470i	−0.962231	+	0.272235i	$0.912237\pi$
$30$	−0.371633	+	1.48229i	−0.0123878	+	0.0494098i
$31$	−14.3621			−0.463293			−0.231646	−	0.972800i	$-0.574411\pi$
$31$	−14.3621			−0.463293			−0.231646	+	0.972800i	$0.574411\pi$
$32$	−8.81688	+	8.81688i	−0.275528	+	0.275528i
$33$	−2.69447	−	2.69447i	−0.0816506	−	0.0816506i
$34$		−	0.330453i		−	0.00971919i
$35$	21.6022	+	36.0587i	0.617207	+	1.03025i
$36$	30.1764			0.838233
$37$	36.1210	−	36.1210i	0.976244	−	0.976244i	−0.0234804	−	0.999724i	$-0.507475\pi$
$37$	36.1210	−	36.1210i	0.976244	−	0.976244i	0.999724	+	0.0234804i	$0.00747473\pi$
$38$	−5.49985	−	5.49985i	−0.144733	−	0.144733i
$39$			4.91214i			0.125952i
$40$	−9.04725	+	5.42007i	−0.226181	+	0.135502i
$41$	−57.6501			−1.40610			−0.703050	−	0.711141i	$-0.748179\pi$
$41$	−57.6501			−1.40610			−0.703050	+	0.711141i	$0.748179\pi$
$42$	1.81686	−	1.81686i	0.0432585	−	0.0432585i
$43$	58.0890	+	58.0890i	1.35091	+	1.35091i	0.884648	+	0.466259i	$0.154399\pi$
$43$	58.0890	+	58.0890i	1.35091	+	1.35091i	0.466259	+	0.884648i	$0.345601\pi$
$44$		−	13.0318i		−	0.296177i
$45$	37.2470	+	9.33839i	0.827712	+	0.207520i
$46$	4.47659			0.0973171
$47$	−29.8948	+	29.8948i	−0.636060	+	0.636060i	−0.949581	−	0.313522i	$-0.898491\pi$
$47$	−29.8948	+	29.8948i	−0.636060	+	0.636060i	0.313522	+	0.949581i	$0.398491\pi$
$48$	−12.3128	−	12.3128i	−0.256517	−	0.256517i
$49$		−	21.6754i		−	0.442355i
$50$	−6.36489	+	1.92779i	−0.127298	+	0.0385557i
$51$	1.42722			0.0279848
$52$	−11.8788	+	11.8788i	−0.228438	+	0.228438i
$53$	−59.0764	−	59.0764i	−1.11465	−	1.11465i	−0.992514	−	0.122135i	$-0.961026\pi$
$53$	−59.0764	−	59.0764i	−1.11465	−	1.11465i	−0.122135	−	0.992514i	$-0.538974\pi$
$54$		−	5.09797i		−	0.0944068i
$55$	4.03282	−	16.0853i	0.0733240	−	0.292460i
$56$	17.7327			0.316655
$57$	23.7538	−	23.7538i	0.416734	−	0.416734i
$58$	2.97007	+	2.97007i	0.0512081	+	0.0512081i
$59$			61.7604i			1.04679i	0.852091	+	0.523393i	$0.175334\pi$
$59$			61.7604i			1.04679i	−0.852091	+	0.523393i	$0.824666\pi$
$60$	−11.6002	−	19.3631i	−0.193336	−	0.322719i
$61$	1.59704			0.0261810			0.0130905	−	0.999914i	$-0.495833\pi$
$61$	1.59704			0.0261810			0.0130905	+	0.999914i	$0.495833\pi$
$62$	−2.70154	+	2.70154i	−0.0435733	+	0.0435733i
$63$	−45.6540	−	45.6540i	−0.724666	−	0.724666i
$64$		−	57.3064i		−	0.895412i
$65$	−18.3381	+	10.9861i	−0.282125	+	0.169017i
$66$	−1.01367			−0.0153587
$67$	−32.7908	+	32.7908i	−0.489415	+	0.489415i	−0.908122	−	0.418706i	$-0.862484\pi$
$67$	−32.7908	+	32.7908i	−0.489415	+	0.489415i	0.418706	+	0.908122i	$0.362484\pi$
$68$	3.45138	+	3.45138i	0.0507556	+	0.0507556i
$69$			19.3344i			0.280208i
$70$	10.8462	+	2.71929i	0.154945	+	0.0388470i
$71$	−12.4615			−0.175514			−0.0877571	−	0.996142i	$-0.527970\pi$
$71$	−12.4615			−0.175514			−0.0877571	+	0.996142i	$0.527970\pi$
$72$	11.4547	−	11.4547i	0.159094	−	0.159094i
$73$	−74.3641	−	74.3641i	−1.01869	−	1.01869i	−0.999822	−	0.0188637i	$-0.993995\pi$
$73$	−74.3641	−	74.3641i	−1.01869	−	1.01869i	−0.0188637	−	0.999822i	$-0.506005\pi$
$74$		−	13.5889i		−	0.183634i
$75$	−8.32610	−	27.4899i	−0.111015	−	0.366532i
$76$	114.885			1.51165
$77$	−19.7158	+	19.7158i	−0.256050	+	0.256050i
$78$	0.923986	+	0.923986i	0.0118460	+	0.0118460i
$79$			21.8223i			0.276232i	0.990416	+	0.138116i	$0.0441046\pi$
$79$			21.8223i			0.276232i	−0.990416	+	0.138116i	$0.955895\pi$
$80$	18.4286	−	73.5042i	0.230357	−	0.918802i
$81$	−47.1016			−0.581502
$82$	−10.8441	+	10.8441i	−0.132245	+	0.132245i
$83$	45.9955	+	45.9955i	0.554163	+	0.554163i	0.927640	−	0.373477i	$-0.121834\pi$
$83$	45.9955	+	45.9955i	0.554163	+	0.554163i	−0.373477	+	0.927640i	$0.621834\pi$
$84$			37.9520i			0.451809i
$85$	3.19201	+	5.32814i	0.0375531	+	0.0626840i
$86$	21.8534			0.254109
$87$	−12.8277	+	12.8277i	−0.147445	+	0.147445i
$88$	−4.94677	−	4.94677i	−0.0562133	−	0.0562133i
$89$			89.4219i			1.00474i	0.864652	+	0.502370i	$0.167539\pi$
$89$			89.4219i			1.00474i	−0.864652	+	0.502370i	$0.832461\pi$
$90$	8.76283	−	5.24969i	0.0973648	−	0.0583299i
$91$	35.9429			0.394977
$92$	−46.7553	+	46.7553i	−0.508209	+	0.508209i
$93$	−11.6679	−	11.6679i	−0.125462	−	0.125462i
$94$			11.2466i			0.119644i
$95$	141.804	+	35.5524i	1.49268	+	0.374236i
$96$	−14.3259			−0.149228
$97$	−62.6170	+	62.6170i	−0.645536	+	0.645536i	−0.951911	−	0.306375i	$-0.900884\pi$
$97$	−62.6170	+	62.6170i	−0.645536	+	0.645536i	0.306375	+	0.951911i	$0.400884\pi$
$98$	−4.07719	−	4.07719i	−0.0416040	−	0.0416040i
$99$			25.4716i			0.257289i
$100$	46.3429	−	86.6120i	0.463429	−	0.866120i
$101$	61.9216			0.613085			0.306543	−	0.951857i	$-0.400828\pi$
$101$	61.9216			0.613085			0.306543	+	0.951857i	$0.400828\pi$
$102$	0.268464	−	0.268464i	0.00263200	−	0.00263200i
$103$	22.9870	+	22.9870i	0.223174	+	0.223174i	0.809834	−	0.586659i	$-0.199557\pi$
$103$	22.9870	+	22.9870i	0.223174	+	0.223174i	−0.586659	+	0.809834i	$0.699557\pi$
$104$			9.01819i			0.0867134i
$105$	−11.7446	+	46.8445i	−0.111853	+	0.446138i
$106$	−22.2248			−0.209668
$107$	129.770	−	129.770i	1.21281	−	1.21281i	0.242705	−	0.970100i	$-0.421965\pi$
$107$	129.770	−	129.770i	1.21281	−	1.21281i	0.970100	−	0.242705i	$-0.0780347\pi$
$108$	53.2452	+	53.2452i	0.493011	+	0.493011i
$109$			23.0533i			0.211498i	0.994393	+	0.105749i	$0.0337240\pi$
$109$			23.0533i			0.211498i	−0.994393	+	0.105749i	$0.966276\pi$
$110$	−2.26710	−	3.78426i	−0.0206100	−	0.0344024i
$111$	58.6904			0.528743
$112$	−90.0946	+	90.0946i	−0.804416	+	0.804416i
$113$	−49.9313	−	49.9313i	−0.441870	−	0.441870i	0.450770	−	0.892640i	$-0.351149\pi$
$113$	−49.9313	−	49.9313i	−0.441870	−	0.441870i	−0.892640	+	0.450770i	$0.851149\pi$
$114$		−	8.93631i		−	0.0783887i
$115$	−72.1794	+	43.2416i	−0.627647	+	0.376014i
$116$	−62.0412			−0.534838
$117$	23.2179	−	23.2179i	0.198444	−	0.198444i
$118$	11.6173	+	11.6173i	0.0984515	+	0.0984515i
$119$		−	10.4432i		−	0.0877580i
$120$	−11.7534	−	2.94676i	−0.0979454	−	0.0245564i
$121$	11.0000			0.0909091
$122$	0.300408	−	0.300408i	0.00246236	−	0.00246236i
$123$	−46.8357	−	46.8357i	−0.380778	−	0.380778i
$124$		−	56.4320i		−	0.455097i
$125$	84.0044	−	92.5649i	0.672035	−	0.740519i
$126$	−17.1752			−0.136311
$127$	71.1676	−	71.1676i	0.560374	−	0.560374i	−0.369039	−	0.929414i	$-0.620313\pi$
$127$	71.1676	−	71.1676i	0.560374	−	0.560374i	0.929414	+	0.369039i	$0.120313\pi$
$128$	−46.0470	−	46.0470i	−0.359742	−	0.359742i
$129$			94.3846i			0.731664i
$130$	−1.38293	+	5.51595i	−0.0106379	+	0.0424304i
$131$	−176.911			−1.35047			−0.675234	−	0.737603i	$-0.735957\pi$
$131$	−176.911			−1.35047			−0.675234	+	0.737603i	$0.735957\pi$
$132$	10.5872	−	10.5872i	0.0802061	−	0.0802061i
$133$	−173.810	−	173.810i	−1.30685	−	1.30685i
$134$			12.3361i			0.0920602i
$135$	49.2438	+	82.1984i	0.364769	+	0.608877i
$136$	2.62024			0.0192664
$137$	40.2015	−	40.2015i	0.293442	−	0.293442i	−0.544997	−	0.838438i	$-0.683469\pi$
$137$	40.2015	−	40.2015i	0.293442	−	0.293442i	0.838438	+	0.544997i	$0.183469\pi$
$138$	3.63684	+	3.63684i	0.0263539	+	0.0263539i
$139$			4.34004i			0.0312233i	0.999878	+	0.0156117i	$0.00496955\pi$
$139$			4.34004i			0.0312233i	−0.999878	+	0.0156117i	$0.995030\pi$
$140$	−141.683	+	84.8802i	−1.01202	+	0.606287i
$141$	−48.5739			−0.344496
$142$	−2.34404	+	2.34404i	−0.0165073	+	0.0165073i
$143$	−10.0267	−	10.0267i	−0.0701171	−	0.0701171i
$144$			116.396i			0.808307i
$145$	−76.5781	−	19.1993i	−0.528125	−	0.132409i
$146$	−27.9761			−0.191617
$147$	17.6094	−	17.6094i	0.119792	−	0.119792i
$148$	141.928	+	141.928i	0.958973	+	0.958973i
$149$		−	237.366i		−	1.59306i	−0.604597	−	0.796531i	$-0.706666\pi$
$149$		−	237.366i		−	1.59306i	0.604597	−	0.796531i	$-0.293334\pi$
$150$	−6.73708	−	3.60476i	−0.0449139	−	0.0240317i
$151$	110.122			0.729288			0.364644	−	0.931147i	$-0.381191\pi$
$151$	110.122			0.729288			0.364644	+	0.931147i	$0.381191\pi$
$152$	43.6096	−	43.6096i	0.286906	−	0.286906i
$153$	−6.74597	−	6.74597i	−0.0440913	−	0.0440913i
$154$			7.41720i			0.0481636i
$155$	17.4634	−	69.6546i	0.112667	−	0.449384i
$156$	−19.3010			−0.123724
$157$	−112.345	+	112.345i	−0.715572	+	0.715572i	−0.967695	−	0.252123i	$-0.918871\pi$
$157$	−112.345	+	112.345i	−0.715572	+	0.715572i	0.252123	+	0.967695i	$0.418871\pi$
$158$	4.10483	+	4.10483i	0.0259799	+	0.0259799i
$159$		−	95.9889i		−	0.603704i
$160$	−32.0402	−	53.4818i	−0.200251	−	0.334261i
$161$	141.472			0.878710
$162$	−8.85993	+	8.85993i	−0.0546909	+	0.0546909i
$163$	150.557	+	150.557i	0.923661	+	0.923661i	0.997286	−	0.0736248i	$-0.0234567\pi$
$163$	150.557	+	150.557i	0.923661	+	0.923661i	−0.0736248	+	0.997286i	$0.523457\pi$
$164$		−	226.521i		−	1.38122i
$165$	16.3442	−	9.79159i	0.0990559	−	0.0593429i
$166$	17.3037			0.104239
$167$	127.791	−	127.791i	0.765219	−	0.765219i	−0.212042	−	0.977261i	$-0.568011\pi$
$167$	127.791	−	127.791i	0.765219	−	0.765219i	0.977261	+	0.212042i	$0.0680114\pi$
$168$	14.4063	+	14.4063i	0.0857517	+	0.0857517i
$169$		−	150.721i		−	0.891839i
$170$	1.60266	+	0.401811i	0.00942742	+	0.00236359i
$171$	−224.552			−1.31317
$172$	−228.245	+	228.245i	−1.32701	+	1.32701i
$173$	228.084	+	228.084i	1.31840	+	1.31840i	0.915041	+	0.403361i	$0.132158\pi$
$173$	228.084	+	228.084i	1.31840	+	1.31840i	0.403361	+	0.915041i	$0.367842\pi$
$174$			4.82585i			0.0277348i
$175$	−201.148	+	60.9233i	−1.14942	+	0.348133i
$176$	50.2662			0.285603
$177$	−50.1750	+	50.1750i	−0.283474	+	0.283474i
$178$	16.8205	+	16.8205i	0.0944971	+	0.0944971i
$179$			188.436i			1.05272i	0.850263	+	0.526358i	$0.176443\pi$
$179$			188.436i			1.05272i	−0.850263	+	0.526358i	$0.823557\pi$
$180$	−36.6927	+	146.352i	−0.203848	+	0.813069i
$181$	136.162			0.752277			0.376139	−	0.926563i	$-0.377252\pi$
$181$	136.162			0.752277			0.376139	+	0.926563i	$0.377252\pi$
$182$	6.76094	−	6.76094i	0.0371480	−	0.0371480i
$183$	1.29746	+	1.29746i	0.00708994	+	0.00708994i
$184$			35.4959i			0.192912i
$185$	131.262	+	219.104i	0.709525	+	1.18435i
$186$	−4.38954			−0.0235997
$187$	−2.91327	+	2.91327i	−0.0155790	+	0.0155790i
$188$	−117.464	−	117.464i	−0.624807	−	0.624807i
$189$		−	161.110i		−	0.852432i
$190$	33.3612	−	19.9862i	0.175585	−	0.105191i
$191$	−25.7594			−0.134866			−0.0674330	−	0.997724i	$-0.521481\pi$
$191$	−25.7594			−0.134866			−0.0674330	+	0.997724i	$0.521481\pi$
$192$	46.5565	−	46.5565i	0.242482	−	0.242482i
$193$	203.382	+	203.382i	1.05379	+	1.05379i	0.998469	+	0.0553218i	$0.0176185\pi$
$193$	203.382	+	203.382i	1.05379	+	1.05379i	0.0553218	+	0.998469i	$0.482382\pi$
$194$			23.5568i			0.121427i
$195$	−23.8234	−	5.97287i	−0.122171	−	0.0306301i
$196$	85.1677			0.434529
$197$	170.916	−	170.916i	0.867592	−	0.867592i	−0.124613	−	0.992205i	$-0.539769\pi$
$197$	170.916	−	170.916i	0.867592	−	0.867592i	0.992205	+	0.124613i	$0.0397689\pi$
$198$	4.79127	+	4.79127i	0.0241983	+	0.0241983i
$199$			56.5696i			0.284269i	0.989847	+	0.142135i	$0.0453966\pi$
$199$			56.5696i			0.284269i	−0.989847	+	0.142135i	$0.954603\pi$
$200$	−15.2859	−	50.4687i	−0.0764294	−	0.252343i
$201$	−53.2794			−0.265072
$202$	11.6476	−	11.6476i	0.0576614	−	0.0576614i
$203$	93.8623	+	93.8623i	0.462376	+	0.462376i
$204$			5.60790i			0.0274897i
$205$	70.0991	−	279.597i	0.341947	−	1.36389i
$206$	8.64781			0.0419797
$207$	91.3865	−	91.3865i	0.441480	−	0.441480i
$208$	−45.8188	−	45.8188i	−0.220282	−	0.220282i
$209$			96.9735i			0.463988i
$210$	6.60238	+	11.0208i	0.0314399	+	0.0524798i
$211$	−144.139			−0.683125			−0.341563	−	0.939859i	$-0.610956\pi$
$211$	−144.139			−0.683125			−0.341563	+	0.939859i	$0.610956\pi$
$212$	232.125	−	232.125i	1.09493	−	1.09493i
$213$	−10.1239	−	10.1239i	−0.0475300	−	0.0475300i
$214$		−	48.8202i		−	0.228132i
$215$	−352.359	+	211.093i	−1.63888	+	0.981827i
$216$	40.4230			0.187143
$217$	−85.3761	+	85.3761i	−0.393438	+	0.393438i
$218$	4.33638	+	4.33638i	0.0198916	+	0.0198916i
$219$		−	120.829i		−	0.551729i
$220$	63.2029	+	15.8459i	0.287286	+	0.0720268i
$221$	5.31102			0.0240318
$222$	11.0398	−	11.0398i	0.0497289	−	0.0497289i
$223$	−127.020	−	127.020i	−0.569597	−	0.569597i	0.362419	−	0.932015i	$-0.381951\pi$
$223$	−127.020	−	127.020i	−0.569597	−	0.569597i	−0.932015	+	0.362419i	$0.881951\pi$
$224$			104.825i			0.467968i
$225$	−90.5804	+	169.289i	−0.402580	+	0.752397i
$226$	−18.7844			−0.0831169
$227$	−33.3387	+	33.3387i	−0.146866	+	0.146866i	−0.776717	−	0.629850i	$-0.783116\pi$
$227$	−33.3387	+	33.3387i	−0.146866	+	0.146866i	0.629850	+	0.776717i	$0.283116\pi$
$228$	93.3344	+	93.3344i	0.409362	+	0.409362i
$229$			257.494i			1.12443i	0.826992	+	0.562214i	$0.190050\pi$
$229$			257.494i			1.12443i	−0.826992	+	0.562214i	$0.809950\pi$
$230$	−5.44326	+	21.7110i	−0.0236664	+	0.0943955i
$231$	−32.0348			−0.138679
$232$	−23.5504	+	23.5504i	−0.101510	+	0.101510i
$233$	−92.1414	−	92.1414i	−0.395457	−	0.395457i	0.481170	−	0.876627i	$-0.340212\pi$
$233$	−92.1414	−	92.1414i	−0.395457	−	0.395457i	−0.876627	+	0.481170i	$0.840212\pi$
$234$		−	8.73469i		−	0.0373277i
$235$	−108.636	−	181.337i	−0.462282	−	0.771647i
$236$	−242.671			−1.02827
$237$	−17.7287	+	17.7287i	−0.0748048	+	0.0748048i
$238$	−1.96439	−	1.96439i	−0.00825375	−	0.00825375i
$239$		−	276.668i		−	1.15761i	−0.815467	−	0.578804i	$-0.803520\pi$
$239$		−	276.668i		−	1.15761i	0.815467	−	0.578804i	$-0.196480\pi$
$240$	74.6874	−	44.7442i	0.311198	−	0.186434i
$241$	−443.392			−1.83980			−0.919900	−	0.392153i	$-0.871731\pi$
$241$	−443.392			−1.83980			−0.919900	+	0.392153i	$0.871731\pi$
$242$	2.06913	−	2.06913i	0.00855011	−	0.00855011i
$243$	−160.225	−	160.225i	−0.659363	−	0.659363i
$244$			6.27515i			0.0257178i
$245$	105.123	+	26.3560i	0.429075	+	0.107575i
$246$	−17.6198			−0.0716253
$247$	88.3935	−	88.3935i	0.357868	−	0.357868i
$248$	−21.4212	−	21.4212i	−0.0863757	−	0.0863757i
$249$			74.7348i			0.300140i
$250$	−1.61024	−	33.2131i	−0.00644096	−	0.132852i
$251$	102.835			0.409702			0.204851	−	0.978793i	$-0.434329\pi$
$251$	102.835			0.409702			0.204851	+	0.978793i	$0.434329\pi$
$252$	179.385	−	179.385i	0.711846	−	0.711846i
$253$	−39.4656	−	39.4656i	−0.155991	−	0.155991i
$254$		−	26.7736i		−	0.105408i
$255$	−1.73542	+	6.92188i	−0.00680556	+	0.0271446i
$256$	211.902			0.827743
$257$	−156.554	+	156.554i	−0.609161	+	0.609161i	−0.942727	−	0.333566i	$-0.891748\pi$
$257$	−156.554	+	156.554i	−0.609161	+	0.609161i	0.333566	+	0.942727i	$0.391748\pi$
$258$	17.7540	+	17.7540i	0.0688139	+	0.0688139i
$259$		−	429.447i		−	1.65809i
$260$	−43.1669	−	72.0547i	−0.166027	−	0.277133i
$261$	121.264			0.464613
$262$	−33.2775	+	33.2775i	−0.127013	+	0.127013i
$263$	96.0051	+	96.0051i	0.365039	+	0.365039i	0.865664	−	0.500625i	$-0.166897\pi$
$263$	96.0051	+	96.0051i	0.365039	+	0.365039i	−0.500625	+	0.865664i	$0.666897\pi$
$264$		−	8.03765i		−	0.0304457i
$265$	358.348	−	214.681i	1.35225	−	0.810116i
$266$	−65.3883			−0.245821
$267$	−72.6476	+	72.6476i	−0.272088	+	0.272088i
$268$	−128.843	−	128.843i	−0.480757	−	0.480757i
$269$			231.025i			0.858831i	0.903107	+	0.429415i	$0.141280\pi$
$269$			231.025i			0.858831i	−0.903107	+	0.429415i	$0.858720\pi$
$270$	24.7246	+	6.19882i	0.0915726	+	0.0229586i
$271$	147.528			0.544384			0.272192	−	0.962243i	$-0.412251\pi$
$271$	147.528			0.544384			0.272192	+	0.962243i	$0.412251\pi$
$272$	−13.3126	+	13.3126i	−0.0489435	+	0.0489435i
$273$	29.2005	+	29.2005i	0.106961	+	0.106961i
$274$		−	15.1240i		−	0.0551971i
$275$	73.1083	+	39.1175i	0.265848	+	0.142245i
$276$	−75.9692			−0.275251
$277$	−218.892	+	218.892i	−0.790223	+	0.790223i	−0.981530	−	0.191307i	$-0.938727\pi$
$277$	−218.892	+	218.892i	−0.790223	+	0.790223i	0.191307	+	0.981530i	$0.438727\pi$
$278$	0.816372	+	0.816372i	0.00293659	+	0.00293659i
$279$			110.300i			0.395342i
$280$	−21.5619	+	86.0017i	−0.0770068	+	0.307149i
$281$	219.613			0.781541			0.390771	−	0.920488i	$-0.372209\pi$
$281$	219.613			0.781541			0.390771	+	0.920488i	$0.372209\pi$
$282$	−9.13687	+	9.13687i	−0.0324002	+	0.0324002i
$283$	147.560	+	147.560i	0.521414	+	0.521414i	0.917998	−	0.396584i	$-0.129805\pi$
$283$	147.560	+	147.560i	0.521414	+	0.521414i	−0.396584	+	0.917998i	$0.629805\pi$
$284$		−	48.9642i		−	0.172409i
$285$	86.3204	+	144.087i	0.302879	+	0.505568i
$286$	−3.77211			−0.0131892
$287$	−342.704	+	342.704i	−1.19409	+	1.19409i
$288$	67.7134	+	67.7134i	0.235116	+	0.235116i
$289$			287.457i			0.994660i
$290$	−18.0160	+	10.7931i	−0.0621240	+	0.0372176i
$291$	−101.742			−0.349628
$292$	292.194	−	292.194i	1.00066	−	1.00066i
$293$	−272.170	−	272.170i	−0.928907	−	0.928907i	0.0687286	−	0.997635i	$-0.478106\pi$
$293$	−272.170	−	272.170i	−0.928907	−	0.928907i	−0.997635	+	0.0687286i	$0.978106\pi$
$294$		−	6.62474i		−	0.0225331i
$295$	−299.531	−	75.0969i	−1.01536	−	0.254566i
$296$	107.750			0.364019
$297$	−44.9437	+	44.9437i	−0.151326	+	0.151326i
$298$	−44.6492	−	44.6492i	−0.149830	−	0.149830i
$299$			71.9476i			0.240627i
$300$	108.014	−	32.7152i	0.360048	−	0.109051i
$301$	690.626			2.29444
$302$	20.7143	−	20.7143i	0.0685904	−	0.0685904i
$303$	50.3060	+	50.3060i	0.166026	+	0.166026i
$304$			443.135i			1.45768i
$305$	−1.94191	+	7.74549i	−0.00636691	+	0.0253950i
$306$	−2.53787			−0.00829368
$307$	−89.4740	+	89.4740i	−0.291446	+	0.291446i	−0.837651	−	0.546205i	$-0.816072\pi$
$307$	−89.4740	+	89.4740i	−0.291446	+	0.291446i	0.546205	+	0.837651i	$0.316072\pi$
$308$	−77.4682	−	77.4682i	−0.251520	−	0.251520i
$309$			37.3499i			0.120873i
$310$	−9.81728	−	16.3871i	−0.0316687	−	0.0528617i
$311$	−198.596			−0.638571			−0.319286	−	0.947659i	$-0.603443\pi$
$311$	−198.596			−0.638571			−0.319286	+	0.947659i	$0.603443\pi$
$312$	−7.32650	+	7.32650i	−0.0234824	+	0.0234824i
$313$	128.282	+	128.282i	0.409846	+	0.409846i	0.881685	−	0.471839i	$-0.156410\pi$
$313$	128.282	+	128.282i	0.409846	+	0.409846i	−0.471839	+	0.881685i	$0.656410\pi$
$314$			42.2647i			0.134601i
$315$	276.930	−	165.904i	0.879141	−	0.526681i
$316$	−85.7449			−0.271345
$317$	79.3104	−	79.3104i	0.250191	−	0.250191i	−0.570858	−	0.821049i	$-0.693389\pi$
$317$	79.3104	−	79.3104i	0.250191	−	0.250191i	0.821049	+	0.570858i	$0.193389\pi$
$318$	−18.0557	−	18.0557i	−0.0567791	−	0.0567791i
$319$		−	52.3683i		−	0.164164i
$320$	277.930	+	69.6811i	0.868531	+	0.217754i
$321$	210.854			0.656866
$322$	26.6113	−	26.6113i	0.0826438	−	0.0826438i
$323$	−25.6827	−	25.6827i	−0.0795131	−	0.0795131i
$324$		−	185.073i		−	0.571214i
$325$	−30.9833	−	102.296i	−0.0953334	−	0.314758i
$326$	56.6402			0.173743
$327$	−18.7288	+	18.7288i	−0.0572746	+	0.0572746i
$328$	−85.9856	−	85.9856i	−0.262151	−	0.262151i
$329$			355.422i			1.08031i
$330$	1.23257	−	4.91621i	0.00373505	−	0.0148976i
$331$	478.725			1.44630			0.723149	−	0.690692i	$-0.242694\pi$
$331$	478.725			1.44630			0.723149	+	0.690692i	$0.242694\pi$
$332$	−180.727	+	180.727i	−0.544359	+	0.544359i
$333$	−277.408	−	277.408i	−0.833058	−	0.833058i
$334$		−	48.0758i		−	0.143939i
$335$	−119.160	−	198.904i	−0.355703	−	0.593742i
$336$	−146.388			−0.435679
$337$	−189.268	+	189.268i	−0.561626	+	0.561626i	−0.929769	−	0.368143i	$-0.879994\pi$
$337$	−189.268	+	189.268i	−0.561626	+	0.561626i	0.368143	+	0.929769i	$0.379994\pi$
$338$	−28.3510	−	28.3510i	−0.0838786	−	0.0838786i
$339$		−	81.1298i		−	0.239321i
$340$	−20.9355	+	12.5422i	−0.0615750	+	0.0368887i
$341$	47.6336			0.139688
$342$	−42.2387	+	42.2387i	−0.123505	+	0.123505i
$343$	162.433	+	162.433i	0.473564	+	0.473564i
$344$			173.281i			0.503723i
$345$	−93.7696	−	23.5094i	−0.271796	−	0.0681433i
$346$	85.8061			0.247995
$347$	−116.951	+	116.951i	−0.337034	+	0.337034i	−0.855250	−	0.518216i	$-0.826596\pi$
$347$	−116.951	+	116.951i	−0.337034	+	0.337034i	0.518216	+	0.855250i	$0.326596\pi$
$348$	−50.4031	−	50.4031i	−0.144837	−	0.144837i
$349$		−	517.882i		−	1.48390i	−0.670454	−	0.741951i	$-0.733901\pi$
$349$		−	517.882i		−	1.48390i	0.670454	−	0.741951i	$-0.266099\pi$
$350$	−26.3766	+	49.2962i	−0.0753616	+	0.140846i
$351$	81.9344			0.233431
$352$	29.2423	−	29.2423i	0.0830747	−	0.0830747i
$353$	−290.305	−	290.305i	−0.822395	−	0.822395i	0.164056	−	0.986451i	$-0.447542\pi$
$353$	−290.305	−	290.305i	−0.822395	−	0.822395i	−0.986451	+	0.164056i	$0.947542\pi$
$354$			18.8761i			0.0533222i
$355$	15.1525	−	60.4370i	0.0426830	−	0.170245i
$356$	−351.360			−0.986966
$357$	8.48420	−	8.48420i	0.0237653	−	0.0237653i
$358$	35.4453	+	35.4453i	0.0990093	+	0.0990093i
$359$		−	25.7739i		−	0.0717937i	−0.999355	−	0.0358969i	$-0.988571\pi$
$359$		−	25.7739i		−	0.0717937i	0.999355	−	0.0358969i	$-0.0114288\pi$
$360$	41.6260	+	69.4826i	0.115628	+	0.193007i
$361$	−493.896			−1.36813
$362$	25.6124	−	25.6124i	0.0707526	−	0.0707526i
$363$	8.93655	+	8.93655i	0.0246186	+	0.0246186i
$364$			141.228i			0.387989i
$365$	451.080	−	270.236i	1.23584	−	0.740372i
$366$	0.488110			0.00133363
$367$	139.007	−	139.007i	0.378766	−	0.378766i	−0.491891	−	0.870657i	$-0.663694\pi$
$367$	139.007	−	139.007i	0.378766	−	0.378766i	0.870657	+	0.491891i	$0.163694\pi$
$368$	−180.344	−	180.344i	−0.490066	−	0.490066i
$369$			442.751i			1.19987i
$370$	65.9048	+	16.5233i	0.178121	+	0.0446576i
$371$	−702.365			−1.89317
$372$	45.8461	−	45.8461i	0.123242	−	0.123242i
$373$	238.874	+	238.874i	0.640413	+	0.640413i	0.950657	−	0.310244i	$-0.100411\pi$
$373$	238.874	+	238.874i	0.640413	+	0.640413i	−0.310244	+	0.950657i	$0.600411\pi$
$374$			1.09599i			0.00293045i
$375$	143.447	−	6.95462i	0.382526	−	0.0185456i
$376$	−89.1767			−0.237172
$377$	−47.7349	+	47.7349i	−0.126618	+	0.126618i
$378$	−30.3051	−	30.3051i	−0.0801723	−	0.0801723i
$379$		−	698.963i		−	1.84423i	−0.386917	−	0.922115i	$-0.626460\pi$
$379$		−	698.963i		−	1.84423i	0.386917	−	0.922115i	$-0.373540\pi$
$380$	−139.694	+	557.182i	−0.367615	+	1.46627i
$381$	115.635			0.303504
$382$	−4.84541	+	4.84541i	−0.0126843	+	0.0126843i
$383$	−256.886	−	256.886i	−0.670721	−	0.670721i	0.287161	−	0.957882i	$-0.407288\pi$
$383$	−256.886	−	256.886i	−0.670721	−	0.670721i	−0.957882	+	0.287161i	$0.907288\pi$
$384$		−	74.8184i		−	0.194840i
$385$	−71.6465	−	119.593i	−0.186095	−	0.310631i
$386$	76.5131			0.198221
$387$	446.122	−	446.122i	1.15277	−	1.15277i
$388$	−246.037	−	246.037i	−0.634116	−	0.634116i
$389$			40.8358i			0.104976i	0.998622	+	0.0524881i	$0.0167152\pi$
$389$			40.8358i			0.104976i	−0.998622	+	0.0524881i	$0.983285\pi$
$390$	−5.60475	+	3.35772i	−0.0143711	+	0.00860954i
$391$	20.9044			0.0534639
$392$	32.3290	−	32.3290i	0.0824720	−	0.0824720i
$393$	−143.725	−	143.725i	−0.365713	−	0.365713i
$394$		−	64.2993i		−	0.163196i
$395$	−105.836	−	26.5346i	−0.267939	−	0.0671763i
$396$	−100.084			−0.252737
$397$	−41.8862	+	41.8862i	−0.105507	+	0.105507i	−0.757890	−	0.652383i	$-0.773769\pi$
$397$	−41.8862	+	41.8862i	−0.105507	+	0.105507i	0.652383	+	0.757890i	$0.273769\pi$
$398$	10.6409	+	10.6409i	0.0267359	+	0.0267359i
$399$		−	282.412i		−	0.707799i
$400$	334.080	+	178.753i	0.835199	+	0.446884i
$401$	142.121			0.354417			0.177208	−	0.984173i	$-0.443293\pi$
$401$	142.121			0.354417			0.177208	+	0.984173i	$0.443293\pi$
$402$	−10.0220	+	10.0220i	−0.0249303	+	0.0249303i
$403$	−43.4191	−	43.4191i	−0.107740	−	0.107740i
$404$			243.305i			0.602239i
$405$	57.2728	−	228.438i	0.141414	−	0.564044i
$406$	35.3115			0.0869741
$407$	−119.800	+	119.800i	−0.294349	+	0.294349i
$408$	2.12872	+	2.12872i	0.00521744	+	0.00521744i
$409$			342.570i			0.837579i	0.908083	+	0.418789i	$0.137545\pi$
$409$			342.570i			0.837579i	−0.908083	+	0.418789i	$0.862455\pi$
$410$	−39.4071	−	65.7787i	−0.0961148	−	0.160436i
$411$	65.3205			0.158931
$412$	−90.3212	+	90.3212i	−0.219226	+	0.219226i
$413$	367.138	+	367.138i	0.888953	+	0.888953i
$414$		−	34.3800i		−	0.0830436i
$415$	−279.001	+	167.146i	−0.672292	+	0.402761i
$416$	−53.3100			−0.128149
$417$	−3.52591	+	3.52591i	−0.00845541	+	0.00845541i
$418$	18.2410	+	18.2410i	0.0436386	+	0.0436386i
$419$			710.505i			1.69572i	0.530224	+	0.847858i	$0.322108\pi$
$419$			710.505i			1.69572i	−0.530224	+	0.847858i	$0.677892\pi$
$420$	−184.063	−	46.1474i	−0.438245	−	0.109875i
$421$	32.6639			0.0775865			0.0387933	−	0.999247i	$-0.487649\pi$
$421$	32.6639			0.0775865			0.0387933	+	0.999247i	$0.487649\pi$
$422$	−27.1130	+	27.1130i	−0.0642488	+	0.0642488i
$423$	229.591	+	229.591i	0.542769	+	0.542769i
$424$		−	176.226i		−	0.415627i
$425$	−29.7222	+	9.00221i	−0.0699346	+	0.0211817i
$426$	−3.80866			−0.00894051
$427$	9.49370	−	9.49370i	0.0222335	−	0.0222335i
$428$	509.897	+	509.897i	1.19135	+	1.19135i
$429$		−	16.2917i		−	0.0379761i
$430$	−26.5724	+	105.987i	−0.0617963	+	0.246480i
$431$	363.111			0.842485			0.421242	−	0.906948i	$-0.361594\pi$
$431$	363.111			0.842485			0.421242	+	0.906948i	$0.361594\pi$
$432$	−205.377	+	205.377i	−0.475410	+	0.475410i
$433$	91.1972	+	91.1972i	0.210617	+	0.210617i	0.804530	−	0.593913i	$-0.202417\pi$
$433$	91.1972	+	91.1972i	0.210617	+	0.210617i	−0.593913	+	0.804530i	$0.702417\pi$
$434$			32.1189i			0.0740067i
$435$	−46.6154	−	77.8109i	−0.107162	−	0.178876i
$436$	−90.5817			−0.207756
$437$	347.920	−	347.920i	0.796155	−	0.796155i
$438$	−22.7282	−	22.7282i	−0.0518908	−	0.0518908i
$439$		−	236.126i		−	0.537871i	−0.963158	−	0.268936i	$-0.913328\pi$
$439$		−	236.126i		−	0.537871i	0.963158	−	0.268936i	$-0.0866719\pi$
$440$	30.0063	−	17.9764i	0.0681962	−	0.0408554i
$441$	−166.466			−0.377475
$442$	0.999017	−	0.999017i	0.00226022	−	0.00226022i
$443$	521.493	+	521.493i	1.17719	+	1.17719i	0.980458	+	0.196728i	$0.0630315\pi$
$443$	521.493	+	521.493i	1.17719	+	1.17719i	0.196728	+	0.980458i	$0.436969\pi$
$444$			230.608i			0.519388i
$445$	−433.687	−	108.732i	−0.974578	−	0.244341i
$446$	−47.7856			−0.107143
$447$	192.840	−	192.840i	0.431409	−	0.431409i
$448$	−340.661	−	340.661i	−0.760403	−	0.760403i
$449$		−	485.876i		−	1.08213i	−0.840981	−	0.541065i	$-0.818021\pi$
$449$		−	485.876i		−	1.08213i	0.840981	−	0.541065i	$-0.181979\pi$
$450$	14.8053	+	48.8821i	0.0329008	+	0.108627i
$451$	191.204			0.423955
$452$	196.192	−	196.192i	0.434053	−	0.434053i
$453$	89.4650	+	89.4650i	0.197495	+	0.197495i
$454$			12.5422i			0.0276259i
$455$	−43.7044	+	174.319i	−0.0960536	+	0.383119i
$456$	70.8581			0.155391
$457$	198.466	−	198.466i	0.434280	−	0.434280i	−0.455802	−	0.890081i	$-0.650647\pi$
$457$	198.466	−	198.466i	0.434280	−	0.434280i	0.890081	+	0.455802i	$0.150647\pi$
$458$	48.4352	+	48.4352i	0.105754	+	0.105754i
$459$		−	23.8060i		−	0.0518650i
$460$	−169.906	−	283.610i	−0.369362	−	0.616543i
$461$	629.839			1.36625			0.683123	−	0.730304i	$-0.260621\pi$
$461$	629.839			1.36625			0.683123	+	0.730304i	$0.260621\pi$
$462$	−6.02583	+	6.02583i	−0.0130429	+	0.0130429i
$463$	416.661	+	416.661i	0.899915	+	0.899915i	0.995428	−	0.0955133i	$-0.0304493\pi$
$463$	416.661	+	416.661i	0.899915	+	0.899915i	−0.0955133	+	0.995428i	$0.530449\pi$
$464$		−	239.305i		−	0.515744i
$465$	70.7759	−	42.4008i	0.152206	−	0.0911845i
$466$	−34.6641			−0.0743864
$467$	−55.8562	+	55.8562i	−0.119606	+	0.119606i	−0.764377	−	0.644770i	$-0.776953\pi$
$467$	−55.8562	+	55.8562i	−0.119606	+	0.119606i	0.644770	+	0.764377i	$0.276953\pi$
$468$	91.2286	+	91.2286i	0.194933	+	0.194933i
$469$			389.853i			0.831244i
$470$	−54.5447	−	13.6752i	−0.116053	−	0.0290961i
$471$	−182.541			−0.387560
$472$	−92.1161	+	92.1161i	−0.195161	+	0.195161i
$473$	−192.659	−	192.659i	−0.407314	−	0.407314i
$474$			6.66964i			0.0140710i
$475$	−344.851	+	644.506i	−0.726002	+	1.35685i
$476$	41.0338			0.0862055
$477$	−453.705	+	453.705i	−0.951163	+	0.951163i
$478$	−52.0420	−	52.0420i	−0.108874	−	0.108874i
$479$		−	509.457i		−	1.06358i	−0.846875	−	0.531792i	$-0.821519\pi$
$479$		−	509.457i		−	1.06358i	0.846875	−	0.531792i	$-0.178481\pi$
$480$	17.4195	−	69.4792i	0.0362905	−	0.144748i
$481$	218.401			0.454055
$482$	−83.4031	+	83.4031i	−0.173035	+	0.173035i
$483$	114.934	+	114.934i	0.237959	+	0.237959i
$484$			43.2216i			0.0893008i
$485$	−227.547	−	379.825i	−0.469170	−	0.783143i
$486$	−60.2775			−0.124028
$487$	−203.040	+	203.040i	−0.416919	+	0.416919i	−0.884140	−	0.467221i	$-0.845255\pi$
$487$	−203.040	+	203.040i	−0.416919	+	0.416919i	0.467221	+	0.884140i	$0.345255\pi$
$488$	2.38200	+	2.38200i	0.00488115	+	0.00488115i
$489$			244.629i			0.500263i
$490$	24.7316	−	14.8163i	0.0504726	−	0.0302374i
$491$	−421.861			−0.859188			−0.429594	−	0.903022i	$-0.641343\pi$
$491$	−421.861			−0.859188			−0.429594	+	0.903022i	$0.641343\pi$
$492$	184.029	−	184.029i	0.374042	−	0.374042i
$493$	13.8694	+	13.8694i	0.0281326	+	0.0281326i
$494$		−	33.2541i		−	0.0673159i
$495$	−123.534	−	30.9719i	−0.249565	−	0.0625695i
$496$	217.669			0.438849
$497$	−74.0780	+	74.0780i	−0.149050	+	0.149050i
$498$	14.0578	+	14.0578i	0.0282285	+	0.0282285i
$499$		−	757.843i		−	1.51872i	−0.650669	−	0.759362i	$-0.725511\pi$
$499$		−	757.843i		−	1.51872i	0.650669	−	0.759362i	$-0.274489\pi$
$500$	363.709	+	330.073i	0.727418	+	0.660146i
$501$	207.639			0.414449
$502$	19.3436	−	19.3436i	0.0385330	−	0.0385330i
$503$	−43.4433	−	43.4433i	−0.0863684	−	0.0863684i	0.662603	−	0.748971i	$-0.269452\pi$
$503$	−43.4433	−	43.4433i	−0.0863684	−	0.0863684i	−0.748971	+	0.662603i	$0.769452\pi$
$504$		−	136.187i		−	0.270211i
$505$	−75.2930	+	300.313i	−0.149095	+	0.594680i
$506$	−14.8472			−0.0293422
$507$	122.448	−	122.448i	0.241514	−	0.241514i
$508$	279.634	+	279.634i	0.550461	+	0.550461i
$509$		−	581.790i		−	1.14301i	−0.820600	−	0.571503i	$-0.806361\pi$
$509$		−	581.790i		−	1.14301i	0.820600	−	0.571503i	$-0.193639\pi$
$510$	0.975587	+	1.62846i	0.00191292	+	0.00319306i
$511$	−884.122			−1.73018
$512$	224.047	−	224.047i	0.437592	−	0.437592i
$513$	−396.213	−	396.213i	−0.772346	−	0.772346i
$514$			58.8965i			0.114585i
$515$	−139.435	+	83.5336i	−0.270748	+	0.162201i
$516$	−370.859			−0.718720
$517$	99.1498	−	99.1498i	0.191779	−	0.191779i
$518$	−80.7800	−	80.7800i	−0.155946	−	0.155946i
$519$			370.596i			0.714058i
$520$	−43.7373	−	10.9656i	−0.0841102	−	0.0210877i
$521$	−481.328			−0.923855			−0.461927	−	0.886918i	$-0.652842\pi$
$521$	−481.328			−0.923855			−0.461927	+	0.886918i	$0.652842\pi$
$522$	22.8100	−	22.8100i	0.0436974	−	0.0436974i
$523$	−35.2579	−	35.2579i	−0.0674148	−	0.0674148i	0.672596	−	0.740010i	$-0.265179\pi$
$523$	−35.2579	−	35.2579i	−0.0674148	−	0.0674148i	−0.740010	+	0.672596i	$0.765179\pi$
$524$		−	695.126i		−	1.32658i
$525$	−212.910	−	113.920i	−0.405543	−	0.216991i
$526$	36.1176			0.0686646
$527$	−12.6154	+	12.6154i	−0.0239382	+	0.0239382i
$528$	40.8369	+	40.8369i	0.0773427	+	0.0773427i
$529$		−	245.812i		−	0.464673i
$530$	27.0241	−	107.788i	0.0509888	−	0.203374i
$531$	474.318			0.893253
$532$	682.942	−	682.942i	1.28373	−	1.28373i
$533$	−174.286	−	174.286i	−0.326991	−	0.326991i
$534$			27.3304i			0.0511805i
$535$	471.579	+	787.164i	0.881456	+	1.47134i
$536$	−97.8156			−0.182492
$537$	−153.088	+	153.088i	−0.285080	+	0.285080i
$538$	43.4564	+	43.4564i	0.0807741	+	0.0807741i
$539$			71.8891i			0.133375i
$540$	−322.977	+	193.491i	−0.598105	+	0.358316i
$541$	−1005.22			−1.85808			−0.929039	−	0.369983i	$-0.879363\pi$
$541$	−1005.22			−1.85808			−0.929039	+	0.369983i	$0.879363\pi$
$542$	27.7504	−	27.7504i	0.0511999	−	0.0511999i
$543$	110.620	+	110.620i	0.203720	+	0.203720i
$544$			15.4892i			0.0284728i
$545$	−111.806	−	28.0314i	−0.205149	−	0.0514338i
$546$	10.9854			0.0201197
$547$	−21.0865	+	21.0865i	−0.0385494	+	0.0385494i	−0.726119	−	0.687569i	$-0.758678\pi$
$547$	−21.0865	+	21.0865i	−0.0385494	+	0.0385494i	0.687569	+	0.726119i	$0.258678\pi$
$548$	157.961	+	157.961i	0.288250	+	0.288250i
$549$		−	12.2652i		−	0.0223410i
$550$	21.1099	−	6.39375i	0.0383817	−	0.0116250i
$551$	461.667			0.837872
$552$	−28.8374	+	28.8374i	−0.0522416	+	0.0522416i
$553$	129.724	+	129.724i	0.234582	+	0.234582i
$554$			82.3482i			0.148643i
$555$	−71.3641	+	284.642i	−0.128584	+	0.512869i
$556$	−17.0530			−0.0306709
$557$	180.472	−	180.472i	0.324008	−	0.324008i	−0.526295	−	0.850302i	$-0.676419\pi$
$557$	180.472	−	180.472i	0.324008	−	0.324008i	0.850302	+	0.526295i	$0.176419\pi$
$558$	20.7478	+	20.7478i	0.0371824	+	0.0371824i
$559$			351.227i			0.628313i
$560$	−327.400	−	546.499i	−0.584642	−	0.975891i
$561$	−4.73356			−0.00843773
$562$	41.3098	−	41.3098i	0.0735049	−	0.0735049i
$563$	−547.914	−	547.914i	−0.973204	−	0.973204i	0.0264467	−	0.999650i	$-0.491581\pi$
$563$	−547.914	−	547.914i	−0.973204	−	0.973204i	−0.999650	+	0.0264467i	$0.991581\pi$
$564$		−	190.858i		−	0.338401i
$565$	302.875	−	181.448i	0.536062	−	0.321147i
$566$	55.5128			0.0980792
$567$	−279.998	+	279.998i	−0.493824	+	0.493824i
$568$	−18.5864	−	18.5864i	−0.0327226	−	0.0327226i
$569$			209.473i			0.368142i	0.982913	+	0.184071i	$0.0589277\pi$
$569$			209.473i			0.368142i	−0.982913	+	0.184071i	$0.941072\pi$
$570$	43.3402	+	10.8660i	0.0760354	+	0.0190632i
$571$	155.583			0.272474			0.136237	−	0.990676i	$-0.456499\pi$
$571$	155.583			0.272474			0.136237	+	0.990676i	$0.456499\pi$
$572$	39.3974	−	39.3974i	0.0688766	−	0.0688766i
$573$	−20.9273	−	20.9273i	−0.0365223	−	0.0365223i
$574$			128.927i			0.224611i
$575$	−121.951	−	402.642i	−0.212090	−	0.700246i
$576$	−440.111			−0.764082
$577$	436.706	−	436.706i	0.756856	−	0.756856i	−0.218893	−	0.975749i	$-0.570245\pi$
$577$	436.706	−	436.706i	0.756856	−	0.756856i	0.975749	+	0.218893i	$0.0702446\pi$
$578$	54.0713	+	54.0713i	0.0935490	+	0.0935490i
$579$			330.460i			0.570742i
$580$	75.4384	−	300.893i	0.130066	−	0.518782i
$581$	546.846			0.941214
$582$	−19.1379	+	19.1379i	−0.0328830	+	0.0328830i
$583$	195.934	+	195.934i	0.336079	+	0.336079i
$584$		−	221.829i		−	0.379845i
$585$	84.3728	+	140.836i	0.144227	+	0.240745i
$586$	−102.392			−0.174730
$587$	−160.160	+	160.160i	−0.272844	+	0.272844i	−0.830244	−	0.557400i	$-0.811799\pi$
$587$	−160.160	+	160.160i	−0.272844	+	0.272844i	0.557400	+	0.830244i	$0.311799\pi$
$588$	69.1914	+	69.1914i	0.117672	+	0.117672i
$589$			419.927i			0.712949i
$590$	−70.4685	+	42.2167i	−0.119438	+	0.0715536i
$591$	277.709			0.469896
$592$	−547.444	+	547.444i	−0.924736	+	0.924736i
$593$	−501.168	−	501.168i	−0.845140	−	0.845140i	0.144382	−	0.989522i	$-0.453881\pi$
$593$	−501.168	−	501.168i	−0.845140	−	0.845140i	−0.989522	+	0.144382i	$0.953881\pi$
$594$			16.9080i			0.0284647i
$595$	50.6485	+	12.6983i	0.0851235	+	0.0213417i
$596$	932.668			1.56488
$597$	−45.9579	+	45.9579i	−0.0769815	+	0.0769815i
$598$	13.5335	+	13.5335i	0.0226313	+	0.0226313i
$599$			233.877i			0.390445i	0.980759	+	0.195223i	$0.0625429\pi$
$599$			233.877i			0.390445i	−0.980759	+	0.195223i	$0.937457\pi$
$600$	28.5830	−	53.4199i	0.0476383	−	0.0890332i
$601$	−523.655			−0.871306			−0.435653	−	0.900115i	$-0.643483\pi$
$601$	−523.655			−0.871306			−0.435653	+	0.900115i	$0.643483\pi$
$602$	129.909	−	129.909i	0.215795	−	0.215795i
$603$	251.832	+	251.832i	0.417633	+	0.417633i
$604$			432.697i			0.716386i
$605$	−13.3753	+	53.3489i	−0.0221080	+	0.0881799i
$606$	18.9254			0.0312300
$607$	303.496	−	303.496i	0.499993	−	0.499993i	−0.411442	−	0.911436i	$-0.634975\pi$
$607$	303.496	−	303.496i	0.499993	−	0.499993i	0.911436	+	0.411442i	$0.134975\pi$
$608$	257.793	+	257.793i	0.424002	+	0.424002i
$609$			152.510i			0.250427i
$610$	1.09167	+	1.82222i	0.00178962	+	0.00298725i
$611$	−180.755			−0.295834
$612$	26.5065	−	26.5065i	0.0433112	−	0.0433112i
$613$	290.162	+	290.162i	0.473348	+	0.473348i	0.902996	−	0.429648i	$-0.141362\pi$
$613$	290.162	+	290.162i	0.473348	+	0.473348i	−0.429648	+	0.902996i	$0.641362\pi$
$614$			33.6605i			0.0548217i
$615$	284.098	−	170.199i	0.461948	−	0.276746i
$616$	−58.8127			−0.0954752
$617$	−410.213	+	410.213i	−0.664850	+	0.664850i	−0.956519	−	0.291669i	$-0.905789\pi$
$617$	−410.213	+	410.213i	−0.664850	+	0.664850i	0.291669	+	0.956519i	$0.405789\pi$
$618$	7.02560	+	7.02560i	0.0113683	+	0.0113683i
$619$			224.045i			0.361946i	0.983488	+	0.180973i	$0.0579247\pi$
$619$			224.045i			0.361946i	−0.983488	+	0.180973i	$0.942075\pi$
$620$	273.689	+	68.6179i	0.441434	+	0.110674i
$621$	322.496			0.519318
$622$	−37.3563	+	37.3563i	−0.0600584	+	0.0600584i
$623$	531.573	+	531.573i	0.853248	+	0.853248i
$624$		−	74.4476i		−	0.119307i
$625$	346.786	+	519.966i	0.554857	+	0.831946i
$626$	48.2602			0.0770930
$627$	−78.7826	+	78.7826i	−0.125650	+	0.125650i
$628$	−441.429	−	441.429i	−0.702913	−	0.702913i
$629$		−	63.4563i		−	0.100884i
$630$	20.8841	−	83.2982i	0.0331493	−	0.132219i
$631$	228.193			0.361636			0.180818	−	0.983517i	$-0.442125\pi$
$631$	228.193			0.361636			0.180818	+	0.983517i	$0.442125\pi$
$632$	−32.5481	+	32.5481i	−0.0515002	+	0.0515002i
$633$	−117.101	−	117.101i	−0.184993	−	0.184993i
$634$		−	29.8370i		−	0.0470615i
$635$	258.620	+	431.691i	0.407275	+	0.679828i
$636$	377.163			0.593023
$637$	65.5285	−	65.5285i	0.102871	−	0.102871i
$638$	−9.85061	−	9.85061i	−0.0154398	−	0.0154398i
$639$			95.7039i			0.149771i
$640$	279.314	−	167.333i	0.436427	−	0.261457i
$641$	−376.921			−0.588020			−0.294010	−	0.955802i	$-0.594990\pi$
$641$	−376.921			−0.588020			−0.294010	+	0.955802i	$0.594990\pi$
$642$	39.6622	−	39.6622i	0.0617791	−	0.0617791i
$643$	−2.85853	−	2.85853i	−0.00444562	−	0.00444562i	0.704880	−	0.709326i	$-0.251001\pi$
$643$	−2.85853	−	2.85853i	−0.00444562	−	0.00444562i	−0.709326	+	0.704880i	$0.751001\pi$
$644$			555.878i			0.863165i
$645$	−457.756	−	114.766i	−0.709699	−	0.177932i
$646$	−9.66198			−0.0149566
$647$	761.351	−	761.351i	1.17674	−	1.17674i	0.196171	−	0.980570i	$-0.437149\pi$
$647$	761.351	−	761.351i	1.17674	−	1.17674i	0.980570	−	0.196171i	$-0.0628507\pi$
$648$	−70.2525	−	70.2525i	−0.108414	−	0.108414i
$649$		−	204.836i		−	0.315618i
$650$	−25.0702	−	13.4141i	−0.0385696	−	0.0206371i
$651$	−138.721			−0.213090
$652$	−591.573	+	591.573i	−0.907321	+	0.907321i
$653$	−154.965	−	154.965i	−0.237312	−	0.237312i	0.578424	−	0.815736i	$-0.303668\pi$
$653$	−154.965	−	154.965i	−0.237312	−	0.237312i	−0.815736	+	0.578424i	$0.803668\pi$
$654$			7.04586i			0.0107735i
$655$	215.114	−	858.002i	0.328418	−	1.30993i
$656$	873.735			1.33191
$657$	−571.114	+	571.114i	−0.869275	+	0.869275i
$658$	66.8558	+	66.8558i	0.101605	+	0.101605i
$659$		−	1011.53i		−	1.53494i	−0.641084	−	0.767471i	$-0.721515\pi$
$659$		−	1011.53i		−	1.53494i	0.641084	−	0.767471i	$-0.278485\pi$
$660$	38.4734	+	64.2203i	0.0582931	+	0.0973035i
$661$	−1052.50			−1.59229			−0.796144	−	0.605107i	$-0.793130\pi$
$661$	−1052.50			−1.59229			−0.796144	+	0.605107i	$0.793130\pi$
$662$	90.0493	−	90.0493i	0.136026	−	0.136026i
$663$	4.31475	+	4.31475i	0.00650792	+	0.00650792i
$664$			137.205i			0.206635i
$665$	1054.31	−	631.619i	1.58542	−	0.949803i
$666$	−104.362			−0.156700
$667$	−187.886	+	187.886i	−0.281688	+	0.281688i
$668$	502.123	+	502.123i	0.751681	+	0.751681i
$669$		−	206.386i		−	0.308499i
$670$	−59.8286	−	14.9999i	−0.0892965	−	0.0223880i
$671$	−5.29679			−0.00789387
$672$	−85.1611	+	85.1611i	−0.126728	+	0.126728i
$673$	−766.388	−	766.388i	−1.13876	−	1.13876i	−0.988672	−	0.150091i	$-0.952043\pi$
$673$	−766.388	−	766.388i	−1.13876	−	1.13876i	−0.150091	−	0.988672i	$-0.547957\pi$
$674$			71.2036i			0.105643i
$675$	−458.531	+	138.879i	−0.679305	+	0.205747i
$676$	592.217			0.876061
$677$	−533.292	+	533.292i	−0.787728	+	0.787728i	−0.981121	−	0.193393i	$-0.938051\pi$
$677$	−533.292	+	533.292i	−0.787728	+	0.787728i	0.193393	+	0.981121i	$0.438051\pi$
$678$	−15.2607	−	15.2607i	−0.0225084	−	0.0225084i
$679$			744.460i			1.09641i
$680$	−3.18605	+	12.7079i	−0.00468537	+	0.0186880i
$681$	−54.1696			−0.0795441
$682$	8.96000	−	8.96000i	0.0131378	−	0.0131378i
$683$	457.630	+	457.630i	0.670030	+	0.670030i	0.957723	−	0.287693i	$-0.0928882\pi$
$683$	457.630	+	457.630i	0.670030	+	0.670030i	−0.287693	+	0.957723i	$0.592888\pi$
$684$		−	882.316i		−	1.28994i
$685$	146.091	+	243.856i	0.213271	+	0.355994i
$686$	61.1079			0.0890786
$687$	−209.191	+	209.191i	−0.304500	+	0.304500i
$688$	−880.387	−	880.387i	−1.27963	−	1.27963i
$689$		−	357.197i		−	0.518428i
$690$	−22.0605	+	13.2161i	−0.0319717	+	0.0191538i
$691$	190.118			0.275135			0.137567	−	0.990492i	$-0.456072\pi$
$691$	190.118			0.275135			0.137567	+	0.990492i	$0.456072\pi$
$692$	−896.194	+	896.194i	−1.29508	+	1.29508i
$693$	151.417	+	151.417i	0.218495	+	0.218495i
$694$			43.9974i			0.0633968i
$695$	−21.0487	−	5.27723i	−0.0302860	−	0.00759314i
$696$	−38.2653			−0.0549789
$697$	−50.6389	+	50.6389i	−0.0726527	+	0.0726527i
$698$	−97.4148	−	97.4148i	−0.139563	−	0.139563i
$699$		−	149.714i		−	0.214183i
$700$	−239.382	−	790.357i	−0.341975	−	1.12908i
$701$	268.036			0.382363			0.191181	−	0.981555i	$-0.438768\pi$
$701$	268.036			0.382363			0.191181	+	0.981555i	$0.438768\pi$
$702$	15.4121	−	15.4121i	0.0219545	−	0.0219545i
$703$	−1056.13	−	1056.13i	−1.50232	−	1.50232i
$704$			190.064i			0.269977i
$705$	59.0630	−	235.578i	0.0837773	−	0.334154i
$706$	−109.214			−0.154694
$707$	368.096	−	368.096i	0.520645	−	0.520645i
$708$	−197.149	−	197.149i	−0.278459	−	0.278459i
$709$			818.058i			1.15382i	0.816808	+	0.576910i	$0.195742\pi$
$709$			818.058i			1.15382i	−0.816808	+	0.576910i	$0.804258\pi$
$710$	−8.51813	−	14.2186i	−0.0119974	−	0.0200261i
$711$	167.595			0.235717
$712$	−133.374	+	133.374i	−0.187322	+	0.187322i
$713$	−170.899	−	170.899i	−0.239690	−	0.239690i
$714$		−	3.19180i		−	0.00447031i
$715$	60.8206	−	36.4367i	0.0850638	−	0.0509605i
$716$	−740.410			−1.03409
$717$	224.769	−	224.769i	0.313485	−	0.313485i
$718$	−4.84814	−	4.84814i	−0.00675229	−	0.00675229i
$719$			977.894i			1.36007i	0.733177	+	0.680037i	$0.238037\pi$
$719$			977.894i			1.36007i	−0.733177	+	0.680037i	$0.761963\pi$
$720$	−564.510	−	141.531i	−0.784041	−	0.196571i
$721$	273.294			0.379049
$722$	−92.9031	+	92.9031i	−0.128675	+	0.128675i
$723$	−360.218	−	360.218i	−0.498226	−	0.498226i
$724$			535.013i			0.738968i
$725$	186.229	−	348.051i	0.256867	−	0.480070i
$726$	3.36197			0.00463082
$727$	814.957	−	814.957i	1.12099	−	1.12099i	0.129392	−	0.991593i	$-0.458697\pi$
$727$	814.957	−	814.957i	1.12099	−	1.12099i	0.991593	−	0.129392i	$-0.0413027\pi$
$728$	53.6091	+	53.6091i	0.0736389	+	0.0736389i
$729$			163.576i			0.224384i
$730$	34.0173	−	135.681i	0.0465991	−	0.185865i
$731$	102.049			0.139602
$732$	−5.09802	+	5.09802i	−0.00696451	+	0.00696451i
$733$	−94.7594	−	94.7594i	−0.129276	−	0.129276i	0.639508	−	0.768784i	$-0.279138\pi$
$733$	−94.7594	−	94.7594i	−0.129276	−	0.129276i	−0.768784	+	0.639508i	$0.779138\pi$
$734$		−	52.2951i		−	0.0712467i
$735$	63.9917	+	106.816i	0.0870635	+	0.145327i
$736$	−209.830			−0.285095
$737$	108.755	−	108.755i	0.147564	−	0.147564i
$738$	83.2825	+	83.2825i	0.112849	+	0.112849i
$739$		−	344.985i		−	0.466827i	−0.972378	−	0.233413i	$-0.925010\pi$
$739$		−	344.985i		−	0.466827i	0.972378	−	0.233413i	$-0.0749895\pi$
$740$	−860.912	+	515.760i	−1.16339	+	0.696973i
$741$	143.624			0.193825
$742$	−132.117	+	132.117i	−0.178055	+	0.178055i
$743$	−409.342	−	409.342i	−0.550931	−	0.550931i	0.375778	−	0.926710i	$-0.377375\pi$
$743$	−409.342	−	409.342i	−0.550931	−	0.550931i	−0.926710	+	0.375778i	$0.877375\pi$
$744$		−	34.8057i		−	0.0467818i
$745$	1151.20	+	288.623i	1.54524	+	0.387414i
$746$	89.8656			0.120463
$747$	353.244	−	353.244i	0.472884	−	0.472884i
$748$	−11.4469	−	11.4469i	−0.0153034	−	0.0153034i
$749$		−	1542.85i		−	2.05988i
$750$	25.6746	−	28.2910i	0.0342328	−	0.0377213i
$751$	553.227			0.736654			0.368327	−	0.929696i	$-0.379931\pi$
$751$	553.227			0.736654			0.368327	+	0.929696i	$0.379931\pi$
$752$	453.080	−	453.080i	0.602501	−	0.602501i
$753$	83.5448	+	83.5448i	0.110949	+	0.110949i
$754$			17.9581i			0.0238171i
$755$	−133.902	+	534.083i	−0.177354	+	0.707394i
$756$	633.038			0.837351
$757$	61.6367	−	61.6367i	0.0814224	−	0.0814224i	−0.665223	−	0.746645i	$-0.731663\pi$
$757$	61.6367	−	61.6367i	0.0814224	−	0.0814224i	0.746645	+	0.665223i	$0.231663\pi$
$758$	−131.477	−	131.477i	−0.173452	−	0.173452i
$759$		−	64.1248i		−	0.0844859i
$760$	158.475	+	264.529i	0.208520	+	0.348064i
$761$	23.5586			0.0309574			0.0154787	−	0.999880i	$-0.495073\pi$
$761$	23.5586			0.0309574			0.0154787	+	0.999880i	$0.495073\pi$
$762$	21.7512	−	21.7512i	0.0285449	−	0.0285449i
$763$	137.041	+	137.041i	0.179609	+	0.179609i
$764$		−	101.215i		−	0.132480i
$765$	40.9199	−	24.5145i	0.0534901	−	0.0320451i
$766$	−96.6418			−0.126164
$767$	−186.713	+	186.713i	−0.243432	+	0.243432i
$768$	172.152	+	172.152i	0.224157	+	0.224157i
$769$			879.915i			1.14423i	0.820172	+	0.572117i	$0.193878\pi$
$769$			879.915i			1.14423i	−0.820172	+	0.572117i	$0.806122\pi$
$770$	−35.9726	−	9.01888i	−0.0467177	−	0.0117128i
$771$	−254.374			−0.329927
$772$	−799.134	+	799.134i	−1.03515	+	1.03515i
$773$	−756.338	−	756.338i	−0.978445	−	0.978445i	0.0213279	−	0.999773i	$-0.493211\pi$
$773$	−756.338	−	756.338i	−0.978445	−	0.978445i	−0.999773	+	0.0213279i	$0.993211\pi$
$774$		−	167.833i		−	0.216839i
$775$	316.583	+	169.392i	0.408494	+	0.218570i
$776$	−186.788			−0.240706
$777$	348.888	−	348.888i	0.449020	−	0.449020i
$778$	7.68131	+	7.68131i	0.00987314	+	0.00987314i
$779$			1685.61i			2.16381i
$780$	23.4688	−	93.6076i	0.0300882	−	0.120010i
$781$	41.3301			0.0529195
$782$	3.93216	−	3.93216i	0.00502834	−	0.00502834i
$783$	213.966	+	213.966i	0.273264	+	0.273264i
$784$			328.508i			0.419016i
$785$	−408.256	−	681.465i	−0.520071	−	0.868108i
$786$	−54.0701			−0.0687915
$787$	413.849	−	413.849i	0.525857	−	0.525857i	−0.393477	−	0.919334i	$-0.628728\pi$
$787$	413.849	−	413.849i	0.525857	−	0.525857i	0.919334	+	0.393477i	$0.128728\pi$
$788$	671.568	+	671.568i	0.852244	+	0.852244i
$789$			155.992i			0.197708i
$790$	−24.8992	+	14.9168i	−0.0315180	+	0.0188820i
$791$	−593.639			−0.750492
$792$	−37.9911	+	37.9911i	−0.0479685	+	0.0479685i
$793$	4.82814	+	4.82814i	0.00608845	+	0.00608845i
$794$			15.7578i			0.0198461i
$795$	465.536	+	116.717i	0.585580	+	0.146814i
$796$	−222.275			−0.279240
$797$	−626.179	+	626.179i	−0.785670	+	0.785670i	−0.980781	−	0.195111i	$-0.937493\pi$
$797$	−626.179	+	626.179i	−0.785670	+	0.785670i	0.195111	+	0.980781i	$0.437493\pi$
$798$	−53.1224	−	53.1224i	−0.0665694	−	0.0665694i
$799$			52.5183i			0.0657300i
$800$	298.340	−	90.3607i	0.372925	−	0.112951i
$801$	686.758			0.857375
$802$	26.7333	−	26.7333i	0.0333333	−	0.0333333i
$803$	246.638	+	246.638i	0.307145	+	0.307145i
$804$		−	209.347i		−	0.260382i
$805$	−172.022	+	686.126i	−0.213692	+	0.852331i
$806$	−16.3345			−0.0202661
$807$	−187.688	+	187.688i	−0.232575	+	0.232575i
$808$	92.3566	+	92.3566i	0.114303	+	0.114303i
$809$		−	17.3326i		−	0.0214247i	−0.999943	−	0.0107123i	$-0.996590\pi$
$809$		−	17.3326i		−	0.0214247i	0.999943	−	0.0107123i	$-0.00340991\pi$
$810$	−32.1966	−	53.7429i	−0.0397489	−	0.0663493i
$811$	−183.396			−0.226135			−0.113068	−	0.993587i	$-0.536068\pi$
$811$	−183.396			−0.226135			−0.113068	+	0.993587i	$0.536068\pi$
$812$	−368.807	+	368.807i	−0.454196	+	0.454196i
$813$	119.854	+	119.854i	0.147422	+	0.147422i
$814$			45.0693i			0.0553677i
$815$	−913.253	+	547.117i	−1.12056	+	0.671309i
$816$	−21.6307			−0.0265083
$817$	1698.44	−	1698.44i	2.07888	−	2.07888i
$818$	64.4382	+	64.4382i	0.0787753	+	0.0787753i
$819$		−	276.040i		−	0.337045i
$820$	1098.60	+	275.436i	1.33976	+	0.335897i
$821$	−477.313			−0.581380			−0.290690	−	0.956817i	$-0.593885\pi$
$821$	−477.313			−0.581380			−0.290690	+	0.956817i	$0.593885\pi$
$822$	12.2870	−	12.2870i	0.0149476	−	0.0149476i
$823$	2.56546	+	2.56546i	0.00311720	+	0.00311720i	0.708664	−	0.705546i	$-0.249298\pi$
$823$	2.56546	+	2.56546i	0.00311720	+	0.00311720i	−0.705546	+	0.708664i	$0.749298\pi$
$824$			68.5705i			0.0832167i
$825$	27.6146	+	91.1738i	0.0334722	+	0.110514i
$826$	138.119			0.167214
$827$	−909.533	+	909.533i	−1.09980	+	1.09980i	−0.105365	+	0.994434i	$0.533601\pi$
$827$	−909.533	+	909.533i	−1.09980	+	1.09980i	−0.994434	+	0.105365i	$0.966399\pi$
$828$	359.079	+	359.079i	0.433670	+	0.433670i
$829$		−	790.117i		−	0.953096i	−0.879148	−	0.476548i	$-0.841888\pi$
$829$		−	790.117i		−	0.953096i	0.879148	−	0.476548i	$-0.158112\pi$
$830$	−21.0403	+	83.9213i	−0.0253498	+	0.101110i
$831$	−355.662			−0.427992
$832$	173.247	−	173.247i	0.208230	−	0.208230i
$833$	−19.0393	−	19.0393i	−0.0228563	−	0.0228563i
$834$			1.32646i			0.00159048i
$835$	464.389	+	775.162i	0.556154	+	0.928338i
$836$	−381.032			−0.455780
$837$	−194.621	+	194.621i	−0.232522	+	0.232522i
$838$	133.648	+	133.648i	0.159484	+	0.159484i
$839$		−	60.7879i		−	0.0724528i	−0.999344	−	0.0362264i	$-0.988466\pi$
$839$		−	60.7879i		−	0.0724528i	0.999344	−	0.0362264i	$-0.0115338\pi$
$840$	−87.3862	+	52.3518i	−0.104031	+	0.0623236i
$841$	591.687			0.703552
$842$	6.14416	−	6.14416i	0.00729711	−	0.00729711i
$843$	178.417	+	178.417i	0.211645	+	0.211645i
$844$		−	566.358i		−	0.671040i
$845$	730.980	+	183.268i	0.865065	+	0.216885i
$846$	86.3733			0.102096
$847$	65.3901	−	65.3901i	0.0772020	−	0.0772020i
$848$	895.351	+	895.351i	1.05584	+	1.05584i
$849$			239.760i			0.282403i
$850$	−3.89748	+	7.28416i	−0.00458527	+	0.00856960i
$851$	859.632			1.01014
$852$	39.7792	−	39.7792i	0.0466892	−	0.0466892i
$853$	359.951	+	359.951i	0.421982	+	0.421982i	0.885886	−	0.463904i	$-0.153552\pi$
$853$	359.951	+	359.951i	0.421982	+	0.421982i	−0.463904	+	0.885886i	$0.653552\pi$
$854$		−	3.57158i		−	0.00418217i
$855$	273.041	−	1089.05i	0.319347	−	1.27374i
$856$	387.107			0.452227
$857$	527.644	−	527.644i	0.615687	−	0.615687i	−0.328735	−	0.944422i	$-0.606622\pi$
$857$	527.644	−	527.644i	0.615687	−	0.615687i	0.944422	+	0.328735i	$0.106622\pi$
$858$	−3.06451	−	3.06451i	−0.00357169	−	0.00357169i
$859$		−	670.563i		−	0.780633i	−0.920681	−	0.390316i	$-0.872366\pi$
$859$		−	670.563i		−	0.780633i	0.920681	−	0.390316i	$-0.127634\pi$
$860$	−829.434	−	1384.50i	−0.964458	−	1.60988i
$861$	−556.835			−0.646730
$862$	68.3021	−	68.3021i	0.0792367	−	0.0792367i
$863$	−579.728	−	579.728i	−0.671759	−	0.671759i	0.286363	−	0.958121i	$-0.407554\pi$
$863$	−579.728	−	579.728i	−0.671759	−	0.671759i	−0.958121	+	0.286363i	$0.907554\pi$
$864$			238.956i			0.276569i
$865$	−1383.52	+	828.845i	−1.59944	+	0.958203i
$866$	34.3088			0.0396176
$867$	−233.534	+	233.534i	−0.269359	+	0.269359i
$868$	−335.463	−	335.463i	−0.386478	−	0.386478i
$869$		−	72.3764i		−	0.0832870i
$870$	−23.4049	−	5.86795i	−0.0269022	−	0.00674477i
$871$	−198.265			−0.227629
$872$	−34.3842	+	34.3842i	−0.0394314	+	0.0394314i
$873$	480.897	+	480.897i	0.550855	+	0.550855i
$874$		−	130.889i		−	0.149759i
$875$	−50.8880	−	1049.63i	−0.0581577	−	1.19957i
$876$	474.765			0.541969
$877$	−528.672	+	528.672i	−0.602819	+	0.602819i	−0.941060	−	0.338241i	$-0.890168\pi$
$877$	−528.672	+	528.672i	−0.602819	+	0.602819i	0.338241	+	0.941060i	$0.390168\pi$
$878$	−44.4158	−	44.4158i	−0.0505875	−	0.0505875i
$879$		−	442.229i		−	0.503104i
$880$	−61.1207	+	243.786i	−0.0694554	+	0.277029i
$881$	−275.976			−0.313253			−0.156627	−	0.987658i	$-0.550062\pi$
$881$	−275.976			−0.313253			−0.156627	+	0.987658i	$0.550062\pi$
$882$	−31.3127	+	31.3127i	−0.0355020	+	0.0355020i
$883$	266.103	+	266.103i	0.301362	+	0.301362i	0.841547	−	0.540185i	$-0.181646\pi$
$883$	266.103	+	266.103i	0.301362	+	0.301362i	−0.540185	+	0.841547i	$0.681646\pi$
$884$			20.8683i			0.0236066i
$885$	−182.334	−	304.353i	−0.206027	−	0.343902i
$886$	196.188			0.221432
$887$	289.867	−	289.867i	0.326795	−	0.326795i	−0.524572	−	0.851366i	$-0.675775\pi$
$887$	289.867	−	289.867i	0.326795	−	0.326795i	0.851366	+	0.524572i	$0.175775\pi$
$888$	87.5373	+	87.5373i	0.0985780	+	0.0985780i
$889$		−	846.118i		−	0.951764i
$890$	−102.030	+	61.1249i	−0.114641	+	0.0686797i
$891$	156.218			0.175329
$892$	499.092	−	499.092i	0.559520	−	0.559520i
$893$	874.082	+	874.082i	0.978816	+	0.978816i
$894$		−	72.5472i		−	0.0811490i
$895$	−913.896	−	229.127i	−1.02111	−	0.256008i
$896$	−547.458			−0.611002
$897$	−58.4512	+	58.4512i	−0.0651630	+	0.0651630i
$898$	−91.3946	−	91.3946i	−0.101776	−	0.101776i
$899$		−	226.772i		−	0.252249i
$900$	−665.178	−	355.912i	−0.739086	−	0.395457i
$901$	−103.784			−0.115187
$902$	35.9659	−	35.9659i	0.0398735	−	0.0398735i
$903$	561.074	+	561.074i	0.621345	+	0.621345i
$904$		−	148.946i		−	0.164763i
$905$	−165.565	+	660.372i	−0.182945	+	0.729693i
$906$	33.6572			0.0371492
$907$	−133.317	+	133.317i	−0.146987	+	0.146987i	−0.776771	−	0.629784i	$-0.783144\pi$
$907$	−133.317	+	133.317i	−0.146987	+	0.146987i	0.629784	+	0.776771i	$0.283144\pi$
$908$	−130.995	−	130.995i	−0.144268	−	0.144268i
$909$		−	475.556i		−	0.523164i
$910$	24.5690	+	41.0108i	0.0269989	+	0.0450668i
$911$	−1504.93			−1.65195			−0.825976	−	0.563706i	$-0.809375\pi$
$911$	−1504.93			−1.65195			−0.825976	+	0.563706i	$0.809375\pi$
$912$	−360.009	+	360.009i	−0.394747	+	0.394747i
$913$	−152.550	−	152.550i	−0.167086	−	0.167086i
$914$		−	74.6638i		−	0.0816891i
$915$	−7.87017	+	4.71491i	−0.00860128	+	0.00515290i
$916$	−1011.75			−1.10453
$917$	−1051.66	+	1051.66i	−1.14685	+	1.14685i
$918$	−4.47797	−	4.47797i	−0.00487797	−	0.00487797i
$919$			749.075i			0.815098i	0.913183	+	0.407549i	$0.133616\pi$
$919$			749.075i			0.815098i	−0.913183	+	0.407549i	$0.866384\pi$
$920$	−172.151	−	43.1609i	−0.187121	−	0.0469140i
$921$	−145.380			−0.157850
$922$	118.474	−	118.474i	0.128497	−	0.128497i
$923$	−37.6733	−	37.6733i	−0.0408162	−	0.0408162i
$924$		−	125.872i		−	0.136226i
$925$	−1222.24	+	370.190i	−1.32134	+	0.400205i
$926$	156.750			0.169276
$927$	176.539	−	176.539i	0.190441	−	0.190441i
$928$	−139.215	−	139.215i	−0.150017	−	0.150017i
$929$			1130.03i			1.21640i	0.793785	+	0.608199i	$0.208108\pi$
$929$			1130.03i			1.21640i	−0.793785	+	0.608199i	$0.791892\pi$
$930$	5.33742	−	21.2888i	0.00573916	−	0.0228912i
$931$	−633.758			−0.680729
$932$	362.045	−	362.045i	0.388461	−	0.388461i
$933$	−161.342	−	161.342i	−0.172928	−	0.172928i
$934$			21.0134i			0.0224983i
$935$	−10.5867	−	17.6714i	−0.0113227	−	0.0188999i
$936$	69.2594			0.0739951
$937$	824.469	−	824.469i	0.879903	−	0.879903i	−0.113621	−	0.993524i	$-0.536245\pi$
$937$	824.469	−	824.469i	0.879903	−	0.879903i	0.993524	+	0.113621i	$0.0362450\pi$
$938$	73.3324	+	73.3324i	0.0781795	+	0.0781795i
$939$			208.436i			0.221976i
$940$	712.516	−	426.858i	0.757995	−	0.454104i
$941$	417.653			0.443840			0.221920	−	0.975065i	$-0.428768\pi$
$941$	417.653			0.443840			0.221920	+	0.975065i	$0.428768\pi$
$942$	−34.3364	+	34.3364i	−0.0364505	+	0.0364505i
$943$	−685.997	−	685.997i	−0.727463	−	0.727463i
$944$		−	936.029i		−	0.991556i
$945$	781.365	+	195.900i	0.826841	+	0.207301i
$946$	−72.4794			−0.0766168
$947$	496.138	−	496.138i	0.523905	−	0.523905i	−0.394843	−	0.918748i	$-0.629201\pi$
$947$	496.138	−	496.138i	0.523905	−	0.523905i	0.918748	+	0.394843i	$0.129201\pi$
$948$	−69.6604	−	69.6604i	−0.0734814	−	0.0734814i
$949$		−	449.631i		−	0.473795i
$950$	56.3658	+	186.101i	0.0593324	+	0.195895i
$951$	128.866			0.135506
$952$	15.5761	−	15.5761i	0.0163615	−	0.0163615i
$953$	354.080	+	354.080i	0.371543	+	0.371543i	0.868039	−	0.496496i	$-0.165380\pi$
$953$	354.080	+	354.080i	0.371543	+	0.371543i	−0.496496	+	0.868039i	$0.665380\pi$
$954$			170.686i			0.178916i
$955$	31.3219	−	124.930i	0.0327978	−	0.130817i
$956$	1087.09			1.13713
$957$	42.5447	−	42.5447i	0.0444564	−	0.0444564i
$958$	−95.8301	−	95.8301i	−0.100031	−	0.100031i
$959$		−	477.960i		−	0.498394i
$960$	169.184	+	282.404i	0.176233	+	0.294171i
$961$	−754.731			−0.785360
$962$	41.0817	−	41.0817i	0.0427044	−	0.0427044i
$963$	−996.631	−	996.631i	−1.03492	−	1.03492i
$964$		−	1742.19i		−	1.80725i
$965$	−1233.68	+	739.079i	−1.27842	+	0.765885i
$966$	43.2388			0.0447606
$967$	530.697	−	530.697i	0.548808	−	0.548808i	−0.377288	−	0.926096i	$-0.623143\pi$
$967$	530.697	−	530.697i	0.548808	−	0.548808i	0.926096	+	0.377288i	$0.123143\pi$
$968$	16.4066	+	16.4066i	0.0169490	+	0.0169490i
$969$		−	41.7300i		−	0.0430650i
$970$	−114.248	−	28.6437i	−0.117782	−	0.0295296i
$971$	178.795			0.184135			0.0920676	−	0.995753i	$-0.470652\pi$
$971$	178.795			0.184135			0.0920676	+	0.995753i	$0.470652\pi$
$972$	629.563	−	629.563i	0.647698	−	0.647698i
$973$	25.7996	+	25.7996i	0.0265155	+	0.0265155i
$974$			76.3845i			0.0784235i
$975$	57.9356	−	108.278i	0.0594211	−	0.111055i
$976$	−24.2045			−0.0247997
$977$	911.070	−	911.070i	0.932518	−	0.932518i	−0.0653447	−	0.997863i	$-0.520815\pi$
$977$	911.070	−	911.070i	0.932518	−	0.932518i	0.997863	+	0.0653447i	$0.0208147\pi$
$978$	46.0153	+	46.0153i	0.0470504	+	0.0470504i
$979$		−	296.579i		−	0.302941i
$980$	−103.559	+	413.054i	−0.105672	+	0.421484i
$981$	177.048			0.180477
$982$	−79.3531	+	79.3531i	−0.0808077	+	0.0808077i
$983$	735.682	+	735.682i	0.748405	+	0.748405i	0.974180	−	0.225775i	$-0.0724913\pi$
$983$	735.682	+	735.682i	0.748405	+	0.748405i	−0.225775	+	0.974180i	$0.572491\pi$
$984$		−	139.712i		−	0.141983i
$985$	621.100	+	1036.75i	0.630558	+	1.05253i
$986$	5.21773			0.00529181
$987$	−288.750	+	288.750i	−0.292553	+	0.292553i
$988$	347.319	+	347.319i	0.351537	+	0.351537i
$989$			1382.44i			1.39782i
$990$	−29.0630	+	17.4112i	−0.0293566	+	0.0175871i
$991$	−92.7479			−0.0935903			−0.0467951	−	0.998905i	$-0.514901\pi$
$991$	−92.7479			−0.0935903			−0.0467951	+	0.998905i	$0.514901\pi$
$992$	126.629	−	126.629i	0.127650	−	0.127650i
$993$	388.923	+	388.923i	0.391664	+	0.391664i
$994$			27.8685i			0.0280367i
$995$	−274.357	−	68.7853i	−0.275735	−	0.0691310i
$996$	−293.651			−0.294830
$997$	91.8082	−	91.8082i	0.0920844	−	0.0920844i	−0.659564	−	0.751648i	$-0.729259\pi$
$997$	91.8082	−	91.8082i	0.0920844	−	0.0920844i	0.751648	+	0.659564i	$0.229259\pi$
$998$	−142.552	−	142.552i	−0.142838	−	0.142838i
$999$		−	978.954i		−	0.979934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.f.a.23.6	yes	20
3.2	odd	2		495.3.j.a.298.5		20
5.2	odd	4	inner	55.3.f.a.12.6	✓	20
5.3	odd	4		275.3.f.b.232.5		20
5.4	even	2		275.3.f.b.243.5		20
15.2	even	4		495.3.j.a.397.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.f.a.12.6	✓	20	5.2	odd	4	inner
55.3.f.a.23.6	yes	20	1.1	even	1	trivial
275.3.f.b.232.5		20	5.3	odd	4
275.3.f.b.243.5		20	5.4	even	2
495.3.j.a.298.5		20	3.2	odd	2
495.3.j.a.397.5		20	15.2	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.188102 - 0.188102i) q^{2} +(0.812414 + 0.812414i) q^{3} +3.92923i q^{4} +(-1.21594 + 4.84990i) q^{5} +0.305634 q^{6} +(5.94455 - 5.94455i) q^{7} +(1.49151 + 1.49151i) q^{8} -7.67997i q^{9} +(0.683556 + 1.14100i) q^{10} -3.31662 q^{11} +(-3.19216 + 3.19216i) q^{12} +(3.02318 + 3.02318i) q^{13} -2.23637i q^{14} +(-4.92797 + 2.95227i) q^{15} -15.1558 q^{16} +(0.878385 - 0.878385i) q^{17} +(-1.44462 - 1.44462i) q^{18} -29.2386i q^{19} +(-19.0564 - 4.77772i) q^{20} +9.65887 q^{21} +(-0.623865 + 0.623865i) q^{22} +(11.8993 + 11.8993i) q^{23} +2.42344i q^{24} +(-22.0430 - 11.7944i) q^{25} +1.13733 q^{26} +(13.5510 - 13.5510i) q^{27} +(23.3575 + 23.3575i) q^{28} +15.7896i q^{29} +(-0.371633 + 1.48229i) q^{30} -14.3621 q^{31} +(-8.81688 + 8.81688i) q^{32} +(-2.69447 - 2.69447i) q^{33} -0.330453i q^{34} +(21.6022 + 36.0587i) q^{35} +30.1764 q^{36} +(36.1210 - 36.1210i) q^{37} +(-5.49985 - 5.49985i) q^{38} +4.91214i q^{39} +(-9.04725 + 5.42007i) q^{40} -57.6501 q^{41} +(1.81686 - 1.81686i) q^{42} +(58.0890 + 58.0890i) q^{43} -13.0318i q^{44} +(37.2470 + 9.33839i) q^{45} +4.47659 q^{46} +(-29.8948 + 29.8948i) q^{47} +(-12.3128 - 12.3128i) q^{48} -21.6754i q^{49} +(-6.36489 + 1.92779i) q^{50} +1.42722 q^{51} +(-11.8788 + 11.8788i) q^{52} +(-59.0764 - 59.0764i) q^{53} -5.09797i q^{54} +(4.03282 - 16.0853i) q^{55} +17.7327 q^{56} +(23.7538 - 23.7538i) q^{57} +(2.97007 + 2.97007i) q^{58} +61.7604i q^{59} +(-11.6002 - 19.3631i) q^{60} +1.59704 q^{61} +(-2.70154 + 2.70154i) q^{62} +(-45.6540 - 45.6540i) q^{63} -57.3064i q^{64} +(-18.3381 + 10.9861i) q^{65} -1.01367 q^{66} +(-32.7908 + 32.7908i) q^{67} +(3.45138 + 3.45138i) q^{68} +19.3344i q^{69} +(10.8462 + 2.71929i) q^{70} -12.4615 q^{71} +(11.4547 - 11.4547i) q^{72} +(-74.3641 - 74.3641i) q^{73} -13.5889i q^{74} +(-8.32610 - 27.4899i) q^{75} +114.885 q^{76} +(-19.7158 + 19.7158i) q^{77} +(0.923986 + 0.923986i) q^{78} +21.8223i q^{79} +(18.4286 - 73.5042i) q^{80} -47.1016 q^{81} +(-10.8441 + 10.8441i) q^{82} +(45.9955 + 45.9955i) q^{83} +37.9520i q^{84} +(3.19201 + 5.32814i) q^{85} +21.8534 q^{86} +(-12.8277 + 12.8277i) q^{87} +(-4.94677 - 4.94677i) q^{88} +89.4219i q^{89} +(8.76283 - 5.24969i) q^{90} +35.9429 q^{91} +(-46.7553 + 46.7553i) q^{92} +(-11.6679 - 11.6679i) q^{93} +11.2466i q^{94} +(141.804 + 35.5524i) q^{95} -14.3259 q^{96} +(-62.6170 + 62.6170i) q^{97} +(-4.07719 - 4.07719i) q^{98} +25.4716i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 8 q^{6} + 12 q^{8} + 12 q^{10} - 16 q^{12} + 4 q^{13} - 20 q^{15} - 16 q^{16} + 24 q^{17} - 24 q^{18} - 8 q^{20} - 64 q^{21} - 86 q^{23} + 90 q^{25} + 96 q^{26} - 50 q^{27}+ \cdots + 620 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 8 * q^6 + 12 * q^8 + 12 * q^10 - 16 * q^12 + 4 * q^13 - 20 * q^15 - 16 * q^16 + 24 * q^17 - 24 * q^18 - 8 * q^20 - 64 * q^21 - 86 * q^23 + 90 * q^25 + 96 * q^26 - 50 * q^27 + 76 * q^28 - 56 * q^30 - 40 * q^31 + 184 * q^32 - 22 * q^33 - 60 * q^35 - 168 * q^36 - 126 * q^37 + 184 * q^38 + 64 * q^40 - 56 * q^41 + 32 * q^42 - 24 * q^43 + 278 * q^45 + 168 * q^46 + 156 * q^47 + 8 * q^48 - 352 * q^50 + 304 * q^51 - 100 * q^52 - 52 * q^53 + 66 * q^55 + 216 * q^56 - 80 * q^57 - 344 * q^58 - 224 * q^60 - 120 * q^61 - 540 * q^62 + 388 * q^63 - 56 * q^65 - 242 * q^67 + 204 * q^68 + 112 * q^70 - 204 * q^71 + 612 * q^72 - 228 * q^73 - 116 * q^75 - 504 * q^76 - 880 * q^78 + 640 * q^80 + 152 * q^81 + 256 * q^82 + 464 * q^83 - 532 * q^85 - 128 * q^86 + 496 * q^87 - 264 * q^88 - 112 * q^90 - 96 * q^91 - 168 * q^92 + 346 * q^93 + 508 * q^95 - 112 * q^96 + 290 * q^97 + 620 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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