LMFDB - Embedded newform 105.3.l.a.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(22,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.l (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.3
Character	$\chi$	$=$	105.22
Dual form			105.3.l.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36784 - 1.36784i) q^{2} +(-1.22474 + 1.22474i) q^{3} -0.258033i q^{4} +(3.39663 + 3.66919i) q^{5} +3.35051 q^{6} +(1.87083 + 1.87083i) q^{7} +(-5.82430 + 5.82430i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.36784 - 1.36784i) q^{2} +(-1.22474 + 1.22474i) q^{3} -0.258033i q^{4} +(3.39663 + 3.66919i) q^{5} +3.35051 q^{6} +(1.87083 + 1.87083i) q^{7} +(-5.82430 + 5.82430i) q^{8} -3.00000i q^{9} +(0.372817 - 9.66489i) q^{10} +17.6130 q^{11} +(0.316024 + 0.316024i) q^{12} +(12.1245 - 12.1245i) q^{13} -5.11799i q^{14} +(-8.65382 - 0.333816i) q^{15} +14.9013 q^{16} +(13.8772 + 13.8772i) q^{17} +(-4.10352 + 4.10352i) q^{18} -18.3068i q^{19} +(0.946770 - 0.876441i) q^{20} -4.58258 q^{21} +(-24.0917 - 24.0917i) q^{22} +(-26.3956 + 26.3956i) q^{23} -14.2666i q^{24} +(-1.92585 + 24.9257i) q^{25} -33.1686 q^{26} +(3.67423 + 3.67423i) q^{27} +(0.482735 - 0.482735i) q^{28} -2.87815i q^{29} +(11.3804 + 12.2936i) q^{30} +16.1149 q^{31} +(2.91465 + 2.91465i) q^{32} +(-21.5714 + 21.5714i) q^{33} -37.9637i q^{34} +(-0.509912 + 13.2189i) q^{35} -0.774098 q^{36} +(2.52440 + 2.52440i) q^{37} +(-25.0408 + 25.0408i) q^{38} +29.6988i q^{39} +(-41.1534 - 1.58747i) q^{40} -1.89828 q^{41} +(6.26823 + 6.26823i) q^{42} +(-42.5974 + 42.5974i) q^{43} -4.54472i q^{44} +(11.0076 - 10.1899i) q^{45} +72.2098 q^{46} +(-57.7457 - 57.7457i) q^{47} +(-18.2503 + 18.2503i) q^{48} +7.00000i q^{49} +(36.7286 - 31.4601i) q^{50} -33.9922 q^{51} +(-3.12851 - 3.12851i) q^{52} +(66.5567 - 66.5567i) q^{53} -10.0515i q^{54} +(59.8247 + 64.6253i) q^{55} -21.7925 q^{56} +(22.4212 + 22.4212i) q^{57} +(-3.93685 + 3.93685i) q^{58} +16.4673i q^{59} +(-0.0861354 + 2.23297i) q^{60} -7.37026 q^{61} +(-22.0426 - 22.0426i) q^{62} +(5.61249 - 5.61249i) q^{63} -67.5787i q^{64} +(85.6692 + 3.30464i) q^{65} +59.0124 q^{66} +(-27.2024 - 27.2024i) q^{67} +(3.58078 - 3.58078i) q^{68} -64.6557i q^{69} +(18.7788 - 17.3839i) q^{70} -79.5984 q^{71} +(17.4729 + 17.4729i) q^{72} +(63.3051 - 63.3051i) q^{73} -6.90594i q^{74} +(-28.1690 - 32.8863i) q^{75} -4.72376 q^{76} +(32.9508 + 32.9508i) q^{77} +(40.6231 - 40.6231i) q^{78} +2.48684i q^{79} +(50.6141 + 54.6756i) q^{80} -9.00000 q^{81} +(2.59655 + 2.59655i) q^{82} +(-29.0421 + 29.0421i) q^{83} +1.18245i q^{84} +(-3.78237 + 98.0540i) q^{85} +116.533 q^{86} +(3.52500 + 3.52500i) q^{87} +(-102.583 + 102.583i) q^{88} +29.3345i q^{89} +(-28.9947 - 1.11845i) q^{90} +45.3656 q^{91} +(6.81092 + 6.81092i) q^{92} +(-19.7367 + 19.7367i) q^{93} +157.974i q^{94} +(67.1711 - 62.1814i) q^{95} -7.13941 q^{96} +(-89.1223 - 89.1223i) q^{97} +(9.57487 - 9.57487i) q^{98} -52.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−1.36784	−	1.36784i	−0.683920	−	0.683920i	0.276961	−	0.960881i	$-0.410673\pi$
$2$	−1.36784	−	1.36784i	−0.683920	−	0.683920i	−0.960881	+	0.276961i	$0.910673\pi$
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		−	0.258033i		−	0.0645082i
$5$	3.39663	+	3.66919i	0.679325	+	0.733837i
$5$	3.39663	+	3.66919i	0.679325	+	0.733837i
$6$	3.35051			0.558418
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	−5.82430	+	5.82430i	−0.728038	+	0.728038i
$9$		−	3.00000i		−	0.333333i
$10$	0.372817	−	9.66489i	0.0372817	−	0.966489i
$11$	17.6130			1.60118			0.800589	−	0.599213i	$-0.204520\pi$
$11$	17.6130			1.60118			0.800589	+	0.599213i	$0.204520\pi$
$12$	0.316024	+	0.316024i	0.0263354	+	0.0263354i
$13$	12.1245	−	12.1245i	0.932651	−	0.932651i	−0.0652196	−	0.997871i	$-0.520775\pi$
$13$	12.1245	−	12.1245i	0.932651	−	0.932651i	0.997871	+	0.0652196i	$0.0207748\pi$
$14$		−	5.11799i		−	0.365570i
$15$	−8.65382	−	0.333816i	−0.576921	−	0.0222544i
$16$	14.9013			0.931331
$17$	13.8772	+	13.8772i	0.816309	+	0.816309i	0.985571	−	0.169262i	$-0.0541385\pi$
$17$	13.8772	+	13.8772i	0.816309	+	0.816309i	−0.169262	+	0.985571i	$0.554138\pi$
$18$	−4.10352	+	4.10352i	−0.227973	+	0.227973i
$19$		−	18.3068i		−	0.963516i	−0.876304	−	0.481758i	$-0.839998\pi$
$19$		−	18.3068i		−	0.963516i	0.876304	−	0.481758i	$-0.160002\pi$
$20$	0.946770	−	0.876441i	0.0473385	−	0.0438220i
$21$	−4.58258			−0.218218
$22$	−24.0917	−	24.0917i	−1.09508	−	1.09508i
$23$	−26.3956	+	26.3956i	−1.14763	+	1.14763i	−0.160617	+	0.987017i	$0.551348\pi$
$23$	−26.3956	+	26.3956i	−1.14763	+	1.14763i	−0.987017	+	0.160617i	$0.948652\pi$
$24$		−	14.2666i		−	0.594440i
$25$	−1.92585	+	24.9257i	−0.0770341	+	0.997028i
$26$	−33.1686			−1.27572
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	0.482735	−	0.482735i	0.0172405	−	0.0172405i
$29$		−	2.87815i		−	0.0992467i	−0.998768	−	0.0496234i	$-0.984198\pi$
$29$		−	2.87815i		−	0.0992467i	0.998768	−	0.0496234i	$-0.0158021\pi$
$30$	11.3804	+	12.2936i	0.379347	+	0.409788i
$31$	16.1149			0.519836			0.259918	−	0.965631i	$-0.416304\pi$
$31$	16.1149			0.519836			0.259918	+	0.965631i	$0.416304\pi$
$32$	2.91465	+	2.91465i	0.0910828	+	0.0910828i
$33$	−21.5714	+	21.5714i	−0.653679	+	0.653679i
$34$		−	37.9637i		−	1.11658i
$35$	−0.509912	+	13.2189i	−0.0145689	+	0.377684i
$36$	−0.774098			−0.0215027
$37$	2.52440	+	2.52440i	0.0682270	+	0.0682270i	0.740397	−	0.672170i	$-0.234638\pi$
$37$	2.52440	+	2.52440i	0.0682270	+	0.0682270i	−0.672170	+	0.740397i	$0.734638\pi$
$38$	−25.0408	+	25.0408i	−0.658968	+	0.658968i
$39$			29.6988i			0.761507i
$40$	−41.1534	−	1.58747i	−1.02884	−	0.0396867i
$41$	−1.89828			−0.0462996			−0.0231498	−	0.999732i	$-0.507369\pi$
$41$	−1.89828			−0.0462996			−0.0231498	+	0.999732i	$0.507369\pi$
$42$	6.26823	+	6.26823i	0.149243	+	0.149243i
$43$	−42.5974	+	42.5974i	−0.990637	+	0.990637i	−0.999957	−	0.00931954i	$-0.997033\pi$
$43$	−42.5974	+	42.5974i	−0.990637	+	0.990637i	0.00931954	+	0.999957i	$0.497033\pi$
$44$		−	4.54472i		−	0.103289i
$45$	11.0076	−	10.1899i	0.244612	−	0.226442i
$46$	72.2098			1.56978
$47$	−57.7457	−	57.7457i	−1.22863	−	1.22863i	−0.964482	−	0.264150i	$-0.914909\pi$
$47$	−57.7457	−	57.7457i	−1.22863	−	1.22863i	−0.264150	−	0.964482i	$-0.585091\pi$
$48$	−18.2503	+	18.2503i	−0.380214	+	0.380214i
$49$			7.00000i			0.142857i
$50$	36.7286	−	31.4601i	0.734572	−	0.629202i
$51$	−33.9922			−0.666513
$52$	−3.12851	−	3.12851i	−0.0601636	−	0.0601636i
$53$	66.5567	−	66.5567i	1.25579	−	1.25579i	0.302701	−	0.953086i	$-0.402112\pi$
$53$	66.5567	−	66.5567i	1.25579	−	1.25579i	0.953086	−	0.302701i	$-0.0978883\pi$
$54$		−	10.0515i		−	0.186139i
$55$	59.8247	+	64.6253i	1.08772	+	1.17500i
$56$	−21.7925			−0.389153
$57$	22.4212	+	22.4212i	0.393354	+	0.393354i
$58$	−3.93685	+	3.93685i	−0.0678768	+	0.0678768i
$59$			16.4673i			0.279107i	0.990215	+	0.139554i	$0.0445668\pi$
$59$			16.4673i			0.279107i	−0.990215	+	0.139554i	$0.955433\pi$
$60$	−0.0861354	+	2.23297i	−0.00143559	+	0.0372161i
$61$	−7.37026			−0.120824			−0.0604119	−	0.998174i	$-0.519241\pi$
$61$	−7.37026			−0.120824			−0.0604119	+	0.998174i	$0.519241\pi$
$62$	−22.0426	−	22.0426i	−0.355526	−	0.355526i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$		−	67.5787i		−	1.05592i
$65$	85.6692	+	3.30464i	1.31799	+	0.0508406i
$66$	59.0124			0.894127
$67$	−27.2024	−	27.2024i	−0.406006	−	0.406006i	0.474337	−	0.880343i	$-0.342688\pi$
$67$	−27.2024	−	27.2024i	−0.406006	−	0.406006i	−0.880343	+	0.474337i	$0.842688\pi$
$68$	3.58078	−	3.58078i	0.0526586	−	0.0526586i
$69$		−	64.6557i		−	0.937039i
$70$	18.7788	−	17.3839i	0.268269	−	0.248341i
$71$	−79.5984			−1.12110			−0.560552	−	0.828119i	$-0.689411\pi$
$71$	−79.5984			−1.12110			−0.560552	+	0.828119i	$0.689411\pi$
$72$	17.4729	+	17.4729i	0.242679	+	0.242679i
$73$	63.3051	−	63.3051i	0.867193	−	0.867193i	−0.124968	−	0.992161i	$-0.539883\pi$
$73$	63.3051	−	63.3051i	0.867193	−	0.867193i	0.992161	+	0.124968i	$0.0398827\pi$
$74$		−	6.90594i		−	0.0933235i
$75$	−28.1690	−	32.8863i	−0.375586	−	0.438484i
$76$	−4.72376			−0.0621547
$77$	32.9508	+	32.9508i	0.427933	+	0.427933i
$78$	40.6231	−	40.6231i	0.520809	−	0.520809i
$79$			2.48684i			0.0314790i	0.999876	+	0.0157395i	$0.00501024\pi$
$79$			2.48684i			0.0314790i	−0.999876	+	0.0157395i	$0.994990\pi$
$80$	50.6141	+	54.6756i	0.632676	+	0.683445i
$81$	−9.00000			−0.111111
$82$	2.59655	+	2.59655i	0.0316652	+	0.0316652i
$83$	−29.0421	+	29.0421i	−0.349905	+	0.349905i	−0.860074	−	0.510169i	$-0.829583\pi$
$83$	−29.0421	+	29.0421i	−0.349905	+	0.349905i	0.510169	+	0.860074i	$0.329583\pi$
$84$			1.18245i			0.0140768i
$85$	−3.78237	+	98.0540i	−0.0444985	+	1.15358i
$86$	116.533			1.35503
$87$	3.52500	+	3.52500i	0.0405173	+	0.0405173i
$88$	−102.583	+	102.583i	−1.16572	+	1.16572i
$89$			29.3345i			0.329601i	0.986327	+	0.164800i	$0.0526980\pi$
$89$			29.3345i			0.329601i	−0.986327	+	0.164800i	$0.947302\pi$
$90$	−28.9947	−	1.11845i	−0.322163	−	0.0124272i
$91$	45.3656			0.498523
$92$	6.81092	+	6.81092i	0.0740318	+	0.0740318i
$93$	−19.7367	+	19.7367i	−0.212222	+	0.212222i
$94$			157.974i			1.68057i
$95$	67.1711	−	62.1814i	0.707064	−	0.654541i
$96$	−7.13941			−0.0743688
$97$	−89.1223	−	89.1223i	−0.918786	−	0.918786i	0.0781549	−	0.996941i	$-0.475097\pi$
$97$	−89.1223	−	89.1223i	−0.918786	−	0.918786i	−0.996941	+	0.0781549i	$0.975097\pi$
$98$	9.57487	−	9.57487i	0.0977028	−	0.0977028i
$99$		−	52.8389i		−	0.533726i
$100$	6.43165	+	0.496933i	0.0643165	+	0.00496933i
$101$	−87.3306			−0.864660			−0.432330	−	0.901716i	$-0.642308\pi$
$101$	−87.3306			−0.864660			−0.432330	+	0.901716i	$0.642308\pi$
$102$	46.4958	+	46.4958i	0.455841	+	0.455841i
$103$	36.7417	−	36.7417i	0.356715	−	0.356715i	−0.505885	−	0.862601i	$-0.668834\pi$
$103$	36.7417	−	36.7417i	0.356715	−	0.356715i	0.862601	+	0.505885i	$0.168834\pi$
$104$			141.233i			1.35801i
$105$	−15.5653	−	16.8143i	−0.148241	−	0.160136i
$106$	−182.078			−1.71771
$107$	−91.9855	−	91.9855i	−0.859677	−	0.859677i	0.131622	−	0.991300i	$-0.457981\pi$
$107$	−91.9855	−	91.9855i	−0.859677	−	0.859677i	−0.991300	+	0.131622i	$0.957981\pi$
$108$	0.948073	−	0.948073i	0.00877845	−	0.00877845i
$109$			144.628i			1.32686i	0.748237	+	0.663432i	$0.230901\pi$
$109$			144.628i			1.32686i	−0.748237	+	0.663432i	$0.769099\pi$
$110$	6.56642	−	170.227i	0.0596947	−	1.54752i
$111$	−6.18349			−0.0557071
$112$	27.8778	+	27.8778i	0.248909	+	0.248909i
$113$	28.6801	−	28.6801i	0.253806	−	0.253806i	−0.568723	−	0.822529i	$-0.692562\pi$
$113$	28.6801	−	28.6801i	0.253806	−	0.253806i	0.822529	+	0.568723i	$0.192562\pi$
$114$		−	61.3371i		−	0.538045i
$115$	−186.506	−	7.19436i	−1.62179	−	0.0625597i
$116$	−0.742658			−0.00640222
$117$	−36.3734	−	36.3734i	−0.310884	−	0.310884i
$118$	22.5247	−	22.5247i	0.190887	−	0.190887i
$119$			51.9239i			0.436335i
$120$	52.3467	−	48.4582i	0.436223	−	0.403818i
$121$	189.217			1.56377
$122$	10.0813	+	10.0813i	0.0826338	+	0.0826338i
$123$	2.32491	−	2.32491i	0.0189017	−	0.0189017i
$124$		−	4.15818i		−	0.0335337i
$125$	−97.9985	+	77.5970i	−0.783988	+	0.620776i
$126$	−15.3540			−0.121857
$127$	12.2062	+	12.2062i	0.0961116	+	0.0961116i	0.753528	−	0.657416i	$-0.228351\pi$
$127$	12.2062	+	12.2062i	0.0961116	+	0.0961116i	−0.657416	+	0.753528i	$0.728351\pi$
$128$	−80.7782	+	80.7782i	−0.631080	+	0.631080i
$129$		−	104.342i		−	0.808852i
$130$	−112.661	−	121.702i	−0.866627	−	0.936169i
$131$	−23.2249			−0.177290			−0.0886448	−	0.996063i	$-0.528254\pi$
$131$	−23.2249			−0.177290			−0.0886448	+	0.996063i	$0.528254\pi$
$132$	5.56613	+	5.56613i	0.0421676	+	0.0421676i
$133$	34.2489	−	34.2489i	0.257511	−	0.257511i
$134$			74.4170i			0.555351i
$135$	−1.00145	+	25.9615i	−0.00741813	+	0.192307i
$136$	−161.651			−1.18861
$137$	−17.2588	−	17.2588i	−0.125977	−	0.125977i	0.641307	−	0.767284i	$-0.278392\pi$
$137$	−17.2588	−	17.2588i	−0.125977	−	0.125977i	−0.767284	+	0.641307i	$0.778392\pi$
$138$	−88.4386	+	88.4386i	−0.640859	+	0.640859i
$139$		−	29.4799i		−	0.212085i	−0.994362	−	0.106043i	$-0.966182\pi$
$139$		−	29.4799i		−	0.212085i	0.994362	−	0.106043i	$-0.0338180\pi$
$140$	3.41092	+	0.131574i	0.0243637	+	0.000939814i
$141$	141.447			1.00317
$142$	108.878	+	108.878i	0.766745	+	0.766745i
$143$	213.548	−	213.548i	1.49334	−	1.49334i
$144$		−	44.7039i		−	0.310444i
$145$	10.5605	−	9.77602i	0.0728309	−	0.0674208i
$146$	−173.182			−1.18618
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	0.651377	−	0.651377i	0.00440120	−	0.00440120i
$149$		−	14.3848i		−	0.0965421i	−0.998834	−	0.0482710i	$-0.984629\pi$
$149$		−	14.3848i		−	0.0965421i	0.998834	−	0.0482710i	$-0.0153711\pi$
$150$	−6.45259	+	83.5138i	−0.0430172	+	0.556759i
$151$	15.3569			0.101701			0.0508506	−	0.998706i	$-0.483807\pi$
$151$	15.3569			0.101701			0.0508506	+	0.998706i	$0.483807\pi$
$152$	106.624	+	106.624i	0.701476	+	0.701476i
$153$	41.6317	−	41.6317i	0.272103	−	0.272103i
$154$		−	90.1429i		−	0.585344i
$155$	54.7364	+	59.1286i	0.353138	+	0.381475i
$156$	7.66325			0.0491234
$157$	63.2769	+	63.2769i	0.403037	+	0.403037i	0.879302	−	0.476265i	$-0.158010\pi$
$157$	63.2769	+	63.2769i	0.403037	+	0.403037i	−0.476265	+	0.879302i	$0.658010\pi$
$158$	3.40160	−	3.40160i	0.0215291	−	0.0215291i
$159$			163.030i			1.02535i
$160$	−0.794415	+	20.5944i	−0.00496509	+	0.128715i
$161$	−98.7632			−0.613436
$162$	12.3106	+	12.3106i	0.0759911	+	0.0759911i
$163$	−121.254	+	121.254i	−0.743890	+	0.743890i	−0.973324	−	0.229434i	$-0.926312\pi$
$163$	−121.254	+	121.254i	−0.743890	+	0.743890i	0.229434	+	0.973324i	$0.426312\pi$
$164$			0.489819i			0.00298670i
$165$	−152.419	−	5.87948i	−0.923754	−	0.0356332i
$166$	79.4498			0.478613
$167$	−51.2223	−	51.2223i	−0.306720	−	0.306720i	0.536916	−	0.843636i	$-0.319589\pi$
$167$	−51.2223	−	51.2223i	−0.306720	−	0.306720i	−0.843636	+	0.536916i	$0.819589\pi$
$168$	26.6903	−	26.6903i	0.158871	−	0.158871i
$169$		−	125.005i		−	0.739677i
$170$	139.296	−	128.948i	0.819387	−	0.758520i
$171$	−54.9204			−0.321172
$172$	10.9915	+	10.9915i	0.0639042	+	0.0639042i
$173$	78.5418	−	78.5418i	0.453999	−	0.453999i	−0.442681	−	0.896679i	$-0.645972\pi$
$173$	78.5418	−	78.5418i	0.453999	−	0.453999i	0.896679	+	0.442681i	$0.145972\pi$
$174$		−	9.64328i		−	0.0554211i
$175$	−50.2347	+	43.0288i	−0.287055	+	0.245879i
$176$	262.456			1.49123
$177$	−20.1683	−	20.1683i	−0.113945	−	0.113945i
$178$	40.1248	−	40.1248i	0.225420	−	0.225420i
$179$			162.375i			0.907125i	0.891224	+	0.453563i	$0.149847\pi$
$179$			162.375i			0.907125i	−0.891224	+	0.453563i	$0.850153\pi$
$180$	−2.62932	−	2.84031i	−0.0146073	−	0.0157795i
$181$	257.224			1.42113			0.710564	−	0.703633i	$-0.248440\pi$
$181$	257.224			1.42113			0.710564	+	0.703633i	$0.248440\pi$
$182$	−62.0528	−	62.0528i	−0.340950	−	0.340950i
$183$	9.02668	−	9.02668i	0.0493261	−	0.0493261i
$184$		−	307.472i		−	1.67104i
$185$	−0.688048	+	17.8369i	−0.00371918	+	0.0964158i
$186$	53.9932			0.290286
$187$	244.420	+	244.420i	1.30706	+	1.30706i
$188$	−14.9003	+	14.9003i	−0.0792568	+	0.0792568i
$189$			13.7477i			0.0727393i
$190$	−176.933	−	6.82510i	−0.931228	−	0.0359216i
$191$	−334.101			−1.74922			−0.874610	−	0.484827i	$-0.838883\pi$
$191$	−334.101			−1.74922			−0.874610	+	0.484827i	$0.838883\pi$
$192$	82.7667	+	82.7667i	0.431076	+	0.431076i
$193$	19.9582	−	19.9582i	0.103410	−	0.103410i	−0.653509	−	0.756919i	$-0.726704\pi$
$193$	19.9582	−	19.9582i	0.103410	−	0.103410i	0.756919	+	0.653509i	$0.226704\pi$
$194$			243.810i			1.25675i
$195$	−108.970	+	100.876i	−0.558822	+	0.517311i
$196$	1.80623			0.00921545
$197$	36.5252	+	36.5252i	0.185407	+	0.185407i	0.793707	−	0.608300i	$-0.208148\pi$
$197$	36.5252	+	36.5252i	0.185407	+	0.185407i	−0.608300	+	0.793707i	$0.708148\pi$
$198$	−72.2751	+	72.2751i	−0.365026	+	0.365026i
$199$		−	187.619i		−	0.942810i	−0.881917	−	0.471405i	$-0.843747\pi$
$199$		−	187.619i		−	0.942810i	0.881917	−	0.471405i	$-0.156253\pi$
$200$	−133.958	−	156.392i	−0.669791	−	0.781958i
$201$	66.6320			0.331502
$202$	119.454	+	119.454i	0.591358	+	0.591358i
$203$	5.38453	−	5.38453i	0.0265248	−	0.0265248i
$204$			8.77110i			0.0429956i
$205$	−6.44776	−	6.96516i	−0.0314525	−	0.0339764i
$206$	−100.513			−0.487929
$207$	79.1867	+	79.1867i	0.382545	+	0.382545i
$208$	180.670	−	180.670i	0.868607	−	0.868607i
$209$		−	322.437i		−	1.54276i
$210$	−1.70846	+	44.2901i	−0.00813554	+	0.210905i
$211$	−73.6409			−0.349009			−0.174505	−	0.984656i	$-0.555832\pi$
$211$	−73.6409			−0.349009			−0.174505	+	0.984656i	$0.555832\pi$
$212$	−17.1738	−	17.1738i	−0.0810085	−	0.0810085i
$213$	97.4878	−	97.4878i	0.457689	−	0.457689i
$214$			251.643i			1.17590i
$215$	−300.985	−	11.6103i	−1.39993	−	0.0540015i
$216$	−42.7997			−0.198147
$217$	30.1483	+	30.1483i	0.138932	+	0.138932i
$218$	197.828	−	197.828i	0.907468	−	0.907468i
$219$			155.065i			0.708060i
$220$	16.6754	−	15.4367i	0.0757974	−	0.0701669i
$221$	336.509			1.52266
$222$	8.45801	+	8.45801i	0.0380992	+	0.0380992i
$223$	258.221	−	258.221i	1.15794	−	1.15794i	0.173025	−	0.984917i	$-0.444646\pi$
$223$	258.221	−	258.221i	1.15794	−	1.15794i	0.984917	−	0.173025i	$-0.0553542\pi$
$224$			10.9056i			0.0486858i
$225$	74.7771	+	5.77756i	0.332343	+	0.0256780i
$226$	−78.4596			−0.347166
$227$	−9.72923	−	9.72923i	−0.0428601	−	0.0428601i	0.685352	−	0.728212i	$-0.259648\pi$
$227$	−9.72923	−	9.72923i	−0.0428601	−	0.0428601i	−0.728212	+	0.685352i	$0.759648\pi$
$228$	5.78540	−	5.78540i	0.0253745	−	0.0253745i
$229$		−	108.047i		−	0.471822i	−0.971775	−	0.235911i	$-0.924193\pi$
$229$		−	108.047i		−	0.471822i	0.971775	−	0.235911i	$-0.0758074\pi$
$230$	245.270	+	264.951i	1.06639	+	1.15196i
$231$	−80.7128			−0.349406
$232$	16.7632	+	16.7632i	0.0722554	+	0.0722554i
$233$	−2.47323	+	2.47323i	−0.0106147	+	0.0106147i	−0.712394	−	0.701779i	$-0.752389\pi$
$233$	−2.47323	+	2.47323i	−0.0106147	+	0.0106147i	0.701779	+	0.712394i	$0.252389\pi$
$234$			99.5059i			0.425239i
$235$	15.7391	−	408.020i	0.0669750	−	1.73626i
$236$	4.24911			0.0180047
$237$	−3.04574	−	3.04574i	−0.0128512	−	0.0128512i
$238$	71.0236	−	71.0236i	0.298418	−	0.298418i
$239$			230.974i			0.966417i	0.875505	+	0.483209i	$0.160529\pi$
$239$			230.974i			0.966417i	−0.875505	+	0.483209i	$0.839471\pi$
$240$	−128.953	−	4.97428i	−0.537304	−	0.0207262i
$241$	−280.404			−1.16350			−0.581752	−	0.813366i	$-0.697633\pi$
$241$	−280.404			−1.16350			−0.581752	+	0.813366i	$0.697633\pi$
$242$	−258.818	−	258.818i	−1.06950	−	1.06950i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			1.90177i			0.00779413i
$245$	−25.6843	+	23.7764i	−0.104834	+	0.0970465i
$246$	−6.36022			−0.0258545
$247$	−221.960	−	221.960i	−0.898625	−	0.898625i
$248$	−93.8582	+	93.8582i	−0.378460	+	0.378460i
$249$		−	71.1383i		−	0.285696i
$250$	240.186	+	27.9059i	0.960746	+	0.111624i
$251$	53.4737			0.213043			0.106521	−	0.994310i	$-0.466029\pi$
$251$	53.4737			0.213043			0.106521	+	0.994310i	$0.466029\pi$
$252$	−1.44821	−	1.44821i	−0.00574685	−	0.00574685i
$253$	−464.904	+	464.904i	−1.83757	+	1.83757i
$254$		−	33.3921i		−	0.131465i
$255$	−115.459	−	124.724i	−0.452779	−	0.489112i
$256$	−49.3317			−0.192702
$257$	78.9368	+	78.9368i	0.307147	+	0.307147i	0.843802	−	0.536655i	$-0.180312\pi$
$257$	78.9368	+	78.9368i	0.307147	+	0.307147i	−0.536655	+	0.843802i	$0.680312\pi$
$258$	−142.723	+	142.723i	−0.553189	+	0.553189i
$259$			9.44543i			0.0364688i
$260$	0.852705	−	22.1055i	0.00327963	−	0.0850210i
$261$	−8.63446			−0.0330822
$262$	31.7680	+	31.7680i	0.121252	+	0.121252i
$263$	−323.863	+	323.863i	−1.23142	+	1.23142i	−0.268002	+	0.963418i	$0.586363\pi$
$263$	−323.863	+	323.863i	−1.23142	+	1.23142i	−0.963418	+	0.268002i	$0.913637\pi$
$264$		−	251.277i		−	0.951806i
$265$	470.277	+	18.1406i	1.77463	+	0.0684553i
$266$	−93.6940			−0.352233
$267$	−35.9272	−	35.9272i	−0.134559	−	0.134559i
$268$	−7.01911	+	7.01911i	−0.0261907	+	0.0261907i
$269$			119.052i			0.442573i	0.975209	+	0.221286i	$0.0710256\pi$
$269$			119.052i			0.442573i	−0.975209	+	0.221286i	$0.928974\pi$
$270$	36.8809	−	34.1413i	0.136596	−	0.126449i
$271$	380.174			1.40286			0.701429	−	0.712740i	$-0.252546\pi$
$271$	380.174			1.40286			0.701429	+	0.712740i	$0.252546\pi$
$272$	206.789	+	206.789i	0.760253	+	0.760253i
$273$	−55.5613	+	55.5613i	−0.203521	+	0.203521i
$274$			47.2146i			0.172316i
$275$	−33.9200	+	439.016i	−0.123345	+	1.59642i
$276$	−16.6833			−0.0604467
$277$	−374.455	−	374.455i	−1.35182	−	1.35182i	−0.883624	−	0.468198i	$-0.844903\pi$
$277$	−374.455	−	374.455i	−1.35182	−	1.35182i	−0.468198	−	0.883624i	$-0.655097\pi$
$278$	−40.3237	+	40.3237i	−0.145049	+	0.145049i
$279$		−	48.3448i		−	0.173279i
$280$	−74.0212	−	79.9609i	−0.264361	−	0.285575i
$281$	−300.844			−1.07062			−0.535309	−	0.844656i	$-0.679805\pi$
$281$	−300.844			−1.07062			−0.535309	+	0.844656i	$0.679805\pi$
$282$	−193.477	−	193.477i	−0.686090	−	0.686090i
$283$	−137.166	+	137.166i	−0.484686	+	0.484686i	−0.906624	−	0.421938i	$-0.861350\pi$
$283$	−137.166	+	137.166i	−0.484686	+	0.484686i	0.421938	+	0.906624i	$0.361350\pi$
$284$			20.5390i			0.0723204i
$285$	−6.11110	+	158.424i	−0.0214425	+	0.555873i
$286$	−584.198			−2.04265
$287$	−3.55136	−	3.55136i	−0.0123741	−	0.0123741i
$288$	8.74395	−	8.74395i	0.0303609	−	0.0303609i
$289$			96.1561i			0.332720i
$290$	−27.8171	−	1.07303i	−0.0959209	−	0.00370009i
$291$	218.304			0.750186
$292$	−16.3348	−	16.3348i	−0.0559411	−	0.0559411i
$293$	193.498	−	193.498i	0.660403	−	0.660403i	−0.295072	−	0.955475i	$-0.595344\pi$
$293$	193.498	−	193.498i	0.660403	−	0.660403i	0.955475	+	0.295072i	$0.0953436\pi$
$294$			23.4536i			0.0797740i
$295$	−60.4217	+	55.9334i	−0.204819	+	0.189605i
$296$	−29.4057			−0.0993436
$297$	64.7142	+	64.7142i	0.217893	+	0.217893i
$298$	−19.6761	+	19.6761i	−0.0660270	+	0.0660270i
$299$			640.065i			2.14068i
$300$	−8.48575	+	7.26851i	−0.0282858	+	0.0242284i
$301$	−159.385			−0.529518
$302$	−21.0057	−	21.0057i	−0.0695554	−	0.0695554i
$303$	106.958	−	106.958i	0.352996	−	0.352996i
$304$		−	272.795i		−	0.897352i
$305$	−25.0340	−	27.0428i	−0.0820787	−	0.0886650i
$306$	−113.891			−0.372193
$307$	122.528	+	122.528i	0.399115	+	0.399115i	0.877921	−	0.478806i	$-0.158930\pi$
$307$	122.528	+	122.528i	0.399115	+	0.399115i	−0.478806	+	0.877921i	$0.658930\pi$
$308$	8.50240	−	8.50240i	0.0276052	−	0.0276052i
$309$			89.9984i			0.291257i
$310$	6.00792	−	155.749i	0.0193804	−	0.502416i
$311$	118.050			0.379582			0.189791	−	0.981825i	$-0.439219\pi$
$311$	118.050			0.379582			0.189791	+	0.981825i	$0.439219\pi$
$312$	−172.975	−	172.975i	−0.554406	−	0.554406i
$313$	−289.482	+	289.482i	−0.924861	+	0.924861i	−0.997368	−	0.0725069i	$-0.976900\pi$
$313$	−289.482	+	289.482i	−0.924861	+	0.924861i	0.0725069	+	0.997368i	$0.476900\pi$
$314$		−	173.105i		−	0.551290i
$315$	39.6568	+	1.52974i	0.125895	+	0.00485630i
$316$	0.641686			0.00203065
$317$	−292.255	−	292.255i	−0.921942	−	0.921942i	0.0752250	−	0.997167i	$-0.476032\pi$
$317$	−292.255	−	292.255i	−0.921942	−	0.921942i	−0.997167	+	0.0752250i	$0.976032\pi$
$318$	222.999	−	222.999i	0.701254	−	0.701254i
$319$		−	50.6928i		−	0.158912i
$320$	247.959	−	229.540i	0.774871	−	0.717311i
$321$	225.318			0.701924
$322$	135.092	+	135.092i	0.419541	+	0.419541i
$323$	254.048	−	254.048i	0.786527	−	0.786527i
$324$			2.32229i			0.00716758i
$325$	278.861	+	325.561i	0.858034	+	1.00173i
$326$	331.712			1.01752
$327$	−177.133	−	177.133i	−0.541690	−	0.541690i
$328$	11.0562	−	11.0562i	0.0337079	−	0.0337079i
$329$		−	216.065i		−	0.656731i
$330$	200.443	+	216.527i	0.607403	+	0.656144i
$331$	580.718			1.75443			0.877217	−	0.480093i	$-0.159397\pi$
$331$	580.718			1.75443			0.877217	+	0.480093i	$0.159397\pi$
$332$	7.49381	+	7.49381i	0.0225717	+	0.0225717i
$333$	7.57319	−	7.57319i	0.0227423	−	0.0227423i
$334$			140.128i			0.419544i
$335$	7.41427	−	192.207i	0.0221321	−	0.573752i
$336$	−68.2863			−0.203233
$337$	253.637	+	253.637i	0.752631	+	0.752631i	0.974970	−	0.222339i	$-0.0713690\pi$
$337$	253.637	+	253.637i	0.752631	+	0.752631i	−0.222339	+	0.974970i	$0.571369\pi$
$338$	−170.987	+	170.987i	−0.505880	+	0.505880i
$339$			70.2516i			0.207232i
$340$	25.3012	+	0.975976i	0.0744152	+	0.00287052i
$341$	283.832			0.832351
$342$	75.1223	+	75.1223i	0.219656	+	0.219656i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	496.200i		−	1.44244i
$345$	237.234	−	219.611i	0.687634	−	0.636554i
$346$	−214.865			−0.620997
$347$	60.2580	+	60.2580i	0.173654	+	0.173654i	0.788583	−	0.614929i	$-0.210815\pi$
$347$	60.2580	+	60.2580i	0.173654	+	0.173654i	−0.614929	+	0.788583i	$0.710815\pi$
$348$	0.909567	−	0.909567i	0.00261370	−	0.00261370i
$349$			348.191i			0.997681i	0.866694	+	0.498841i	$0.166241\pi$
$349$			348.191i			0.997681i	−0.866694	+	0.498841i	$0.833759\pi$
$350$	127.569	+	9.85649i	0.364484	+	0.0281614i
$351$	89.0963			0.253836
$352$	51.3356	+	51.3356i	0.145840	+	0.145840i
$353$	113.128	−	113.128i	0.320476	−	0.320476i	−0.528474	−	0.848950i	$-0.677235\pi$
$353$	113.128	−	113.128i	0.320476	−	0.320476i	0.848950	+	0.528474i	$0.177235\pi$
$354$			55.1740i			0.155859i
$355$	−270.366	−	292.061i	−0.761595	−	0.822708i
$356$	7.56925			0.0212619
$357$	−63.5935	−	63.5935i	−0.178133	−	0.178133i
$358$	222.103	−	222.103i	0.620401	−	0.620401i
$359$			105.651i			0.294293i	0.989115	+	0.147147i	$0.0470089\pi$
$359$			105.651i			0.294293i	−0.989115	+	0.147147i	$0.952991\pi$
$360$	−4.76241	+	123.460i	−0.0132289	+	0.342945i
$361$	25.8608			0.0716365
$362$	−351.841	−	351.841i	−0.971937	−	0.971937i
$363$	−231.742	+	231.742i	−0.638408	+	0.638408i
$364$		−	11.7058i		−	0.0321588i
$365$	447.302	+	17.2544i	1.22548	+	0.0472723i
$366$	−24.6941			−0.0674702
$367$	−230.168	−	230.168i	−0.627161	−	0.627161i	0.320191	−	0.947353i	$-0.396253\pi$
$367$	−230.168	−	230.168i	−0.627161	−	0.627161i	−0.947353	+	0.320191i	$0.896253\pi$
$368$	−393.328	+	393.328i	−1.06883	+	1.06883i
$369$			5.69485i			0.0154332i
$370$	25.3392	−	23.4569i	0.0684843	−	0.0633970i
$371$	249.032			0.671246
$372$	5.09271	+	5.09271i	0.0136901	+	0.0136901i
$373$	−211.456	+	211.456i	−0.566906	+	0.566906i	−0.931260	−	0.364355i	$-0.881290\pi$
$373$	−211.456	+	211.456i	−0.566906	+	0.566906i	0.364355	+	0.931260i	$0.381290\pi$
$374$		−	668.653i		−	1.78784i
$375$	24.9866	−	215.060i	0.0666309	−	0.573493i
$376$	672.657			1.78898
$377$	−34.8961	−	34.8961i	−0.0925626	−	0.0925626i
$378$	18.8047	−	18.8047i	0.0497478	−	0.0497478i
$379$		−	132.280i		−	0.349024i	−0.984655	−	0.174512i	$-0.944165\pi$
$379$		−	132.280i		−	0.349024i	0.984655	−	0.174512i	$-0.0558347\pi$
$380$	−16.0448	−	17.3323i	−0.0422233	−	0.0456114i
$381$	−29.8989			−0.0784748
$382$	456.997	+	456.997i	1.19633	+	1.19633i
$383$	149.538	−	149.538i	0.390438	−	0.390438i	−0.484406	−	0.874844i	$-0.660964\pi$
$383$	149.538	−	149.538i	0.390438	−	0.390438i	0.874844	+	0.484406i	$0.160964\pi$
$384$		−	197.865i		−	0.515274i
$385$	−8.98106	+	232.825i	−0.0233274	+	0.604739i
$386$	−54.5991			−0.141448
$387$	127.792	+	127.792i	0.330212	+	0.330212i
$388$	−22.9965	+	22.9965i	−0.0592692	+	0.0592692i
$389$		−	289.081i		−	0.743140i	−0.928405	−	0.371570i	$-0.878820\pi$
$389$		−	289.081i		−	0.743140i	0.928405	−	0.371570i	$-0.121180\pi$
$390$	287.035	+	11.0722i	0.735988	+	0.0283903i
$391$	−732.596			−1.87365
$392$	−40.7701	−	40.7701i	−0.104005	−	0.104005i
$393$	28.4446	−	28.4446i	0.0723781	−	0.0723781i
$394$		−	99.9213i		−	0.253607i
$395$	−9.12468	+	8.44687i	−0.0231005	+	0.0213845i
$396$	−13.6342			−0.0344297
$397$	−502.891	−	502.891i	−1.26673	−	1.26673i	−0.947768	−	0.318961i	$-0.896666\pi$
$397$	−502.891	−	502.891i	−1.26673	−	1.26673i	−0.318961	−	0.947768i	$-0.603334\pi$
$398$	−256.633	+	256.633i	−0.644806	+	0.644806i
$399$			83.8923i			0.210256i
$400$	−28.6977	+	371.425i	−0.0717442	+	0.928563i
$401$	405.912			1.01225			0.506125	−	0.862460i	$-0.331078\pi$
$401$	405.912			1.01225			0.506125	+	0.862460i	$0.331078\pi$
$402$	−91.1418	−	91.1418i	−0.226721	−	0.226721i
$403$	195.385	−	195.385i	0.484826	−	0.484826i
$404$			22.5342i			0.0557776i
$405$	−30.5696	−	33.0227i	−0.0754806	−	0.0815375i
$406$	−14.7304			−0.0362817
$407$	44.4621	+	44.4621i	0.109244	+	0.109244i
$408$	197.981	−	197.981i	0.485247	−	0.485247i
$409$			505.400i			1.23570i	0.786297	+	0.617849i	$0.211996\pi$
$409$			505.400i			1.23570i	−0.786297	+	0.617849i	$0.788004\pi$
$410$	−0.707713	+	18.3467i	−0.00172613	+	0.0447481i
$411$	42.2753			0.102860
$412$	−9.48056	−	9.48056i	−0.0230111	−	0.0230111i
$413$	−30.8076	+	30.8076i	−0.0745946	+	0.0745946i
$414$		−	216.629i		−	0.523259i
$415$	−205.206	−	7.91569i	−0.494472	−	0.0190740i
$416$	70.6772			0.169897
$417$	36.1053	+	36.1053i	0.0865834	+	0.0865834i
$418$	−441.042	+	441.042i	−1.05512	+	1.05512i
$419$		−	553.591i		−	1.32122i	−0.750729	−	0.660610i	$-0.770298\pi$
$419$		−	553.591i		−	1.32122i	0.750729	−	0.660610i	$-0.229702\pi$
$420$	−4.33865	+	4.01636i	−0.0103301	+	0.00956275i
$421$	−320.444			−0.761150			−0.380575	−	0.924750i	$-0.624274\pi$
$421$	−320.444			−0.761150			−0.380575	+	0.924750i	$0.624274\pi$
$422$	100.729	+	100.729i	0.238694	+	0.238694i
$423$	−173.237	+	173.237i	−0.409544	+	0.409544i
$424$			775.293i			1.82852i
$425$	−372.626	+	319.175i	−0.876767	+	0.750999i
$426$	−266.695			−0.626045
$427$	−13.7885	−	13.7885i	−0.0322915	−	0.0322915i
$428$	−23.7353	+	23.7353i	−0.0554562	+	0.0554562i
$429$			523.083i			1.21931i
$430$	395.818	+	427.580i	0.920508	+	0.994373i
$431$	221.870			0.514780			0.257390	−	0.966308i	$-0.417138\pi$
$431$	221.870			0.514780			0.257390	+	0.966308i	$0.417138\pi$
$432$	54.7508	+	54.7508i	0.126738	+	0.126738i
$433$	−162.133	+	162.133i	−0.374440	+	0.374440i	−0.869091	−	0.494651i	$-0.835296\pi$
$433$	−162.133	+	162.133i	−0.374440	+	0.374440i	0.494651	+	0.869091i	$0.335296\pi$
$434$		−	82.4759i		−	0.190037i
$435$	−0.960773	+	24.9070i	−0.00220867	+	0.0572575i
$436$	37.3188			0.0855936
$437$	483.219	+	483.219i	1.10576	+	1.10576i
$438$	212.104	−	212.104i	0.484256	−	0.484256i
$439$		−	606.504i		−	1.38156i	−0.723066	−	0.690779i	$-0.757268\pi$
$439$		−	606.504i		−	1.38156i	0.723066	−	0.690779i	$-0.242732\pi$
$440$	−724.834	−	27.9600i	−1.64735	−	0.0635455i
$441$	21.0000			0.0476190
$442$	−460.289	−	460.289i	−1.04138	−	1.04138i
$443$	−9.75385	+	9.75385i	−0.0220177	+	0.0220177i	−0.718030	−	0.696012i	$-0.754956\pi$
$443$	−9.75385	+	9.75385i	−0.0220177	+	0.0220177i	0.696012	+	0.718030i	$0.254956\pi$
$444$			1.59554i			0.00359356i
$445$	−107.634	+	99.6382i	−0.241873	+	0.223906i
$446$	−706.410			−1.58388
$447$	17.6177	+	17.6177i	0.0394131	+	0.0394131i
$448$	126.428	−	126.428i	0.282206	−	0.282206i
$449$		−	448.959i		−	0.999908i	−0.866052	−	0.499954i	$-0.833350\pi$
$449$		−	448.959i		−	0.999908i	0.866052	−	0.499954i	$-0.166650\pi$
$450$	−94.3803	−	110.186i	−0.209734	−	0.244857i
$451$	−33.4344			−0.0741340
$452$	−7.40041	−	7.40041i	−0.0163726	−	0.0163726i
$453$	−18.8083	+	18.8083i	−0.0415193	+	0.0415193i
$454$			26.6161i			0.0586257i
$455$	154.090	+	166.455i	0.338659	+	0.365835i
$456$	−261.175			−0.572753
$457$	368.860	+	368.860i	0.807133	+	0.807133i	0.984199	−	0.177066i	$-0.0566606\pi$
$457$	368.860	+	368.860i	0.807133	+	0.807133i	−0.177066	+	0.984199i	$0.556661\pi$
$458$	−147.791	+	147.791i	−0.322688	+	0.322688i
$459$			101.977i			0.222171i
$460$	−1.85638	+	48.1247i	−0.00403561	+	0.104619i
$461$	−507.955			−1.10186			−0.550928	−	0.834553i	$-0.685726\pi$
$461$	−507.955			−1.10186			−0.550928	+	0.834553i	$0.685726\pi$
$462$	110.402	+	110.402i	0.238966	+	0.238966i
$463$	255.428	−	255.428i	0.551681	−	0.551681i	−0.375245	−	0.926926i	$-0.622441\pi$
$463$	255.428	−	255.428i	0.551681	−	0.551681i	0.926926	+	0.375245i	$0.122441\pi$
$464$		−	42.8882i		−	0.0924315i
$465$	−139.456	−	5.37941i	−0.299904	−	0.0115686i
$466$	6.76597			0.0145192
$467$	408.350	+	408.350i	0.874411	+	0.874411i	0.992950	−	0.118538i	$-0.0378208\pi$
$467$	408.350	+	408.350i	0.874411	+	0.874411i	−0.118538	+	0.992950i	$0.537821\pi$
$468$	−9.38553	+	9.38553i	−0.0200545	+	0.0200545i
$469$		−	101.782i		−	0.217019i
$470$	−579.635	+	536.577i	−1.23326	+	1.14165i
$471$	−154.996			−0.329079
$472$	−95.9108	−	95.9108i	−0.203201	−	0.203201i
$473$	−750.267	+	750.267i	−1.58619	+	1.58619i
$474$			8.33218i			0.0175784i
$475$	456.310	+	35.2562i	0.960653	+	0.0742236i
$476$	13.3981			0.0281472
$477$	−199.670	−	199.670i	−0.418595	−	0.418595i
$478$	315.935	−	315.935i	0.660952	−	0.660952i
$479$		−	664.740i		−	1.38777i	−0.720087	−	0.693883i	$-0.755898\pi$
$479$		−	664.740i		−	1.38777i	0.720087	−	0.693883i	$-0.244102\pi$
$480$	−24.2499	−	26.1958i	−0.0505206	−	0.0545746i
$481$	61.2140			0.127264
$482$	383.548	+	383.548i	0.795743	+	0.795743i
$483$	120.960	−	120.960i	0.250434	−	0.250434i
$484$		−	48.8241i		−	0.100876i
$485$	24.2911	−	629.721i	0.0500848	−	1.29839i
$486$	−30.1546			−0.0620464
$487$	−334.715	−	334.715i	−0.687300	−	0.687300i	0.274334	−	0.961634i	$-0.411543\pi$
$487$	−334.715	−	334.715i	−0.687300	−	0.687300i	−0.961634	+	0.274334i	$0.911543\pi$
$488$	42.9266	−	42.9266i	0.0879643	−	0.0879643i
$489$		−	297.010i		−	0.607383i
$490$	67.6543	+	2.60972i	0.138070	+	0.00532596i
$491$	−312.255			−0.635958			−0.317979	−	0.948098i	$-0.603004\pi$
$491$	−312.255			−0.635958			−0.317979	+	0.948098i	$0.603004\pi$
$492$	−0.599904	−	0.599904i	−0.00121932	−	0.00121932i
$493$	39.9409	−	39.9409i	0.0810160	−	0.0810160i
$494$			607.212i			1.22917i
$495$	193.876	−	179.474i	0.391668	−	0.362574i
$496$	240.133			0.484139
$497$	−148.915	−	148.915i	−0.299628	−	0.299628i
$498$	−97.3057	+	97.3057i	−0.195393	+	0.195393i
$499$			89.3669i			0.179092i	0.995983	+	0.0895460i	$0.0285416\pi$
$499$			89.3669i			0.179092i	−0.995983	+	0.0895460i	$0.971458\pi$
$500$	20.0226	+	25.2868i	0.0400451	+	0.0505736i
$501$	125.469			0.250436
$502$	−73.1434	−	73.1434i	−0.145704	−	0.145704i
$503$	627.521	−	627.521i	1.24756	−	1.24756i	0.290761	−	0.956796i	$-0.406092\pi$
$503$	627.521	−	627.521i	1.24756	−	1.24756i	0.956796	−	0.290761i	$-0.0939085\pi$
$504$			65.3776i			0.129718i
$505$	−296.630	−	320.432i	−0.587385	−	0.634520i
$506$	1271.83			2.51350
$507$	153.100	+	153.100i	0.301972	+	0.301972i
$508$	3.14959	−	3.14959i	0.00619998	−	0.00619998i
$509$		−	556.945i		−	1.09420i	−0.837069	−	0.547098i	$-0.815733\pi$
$509$		−	556.945i		−	1.09420i	0.837069	−	0.547098i	$-0.184267\pi$
$510$	−12.6729	+	328.531i	−0.0248488	+	0.644178i
$511$	236.866			0.463534
$512$	390.591	+	390.591i	0.762872	+	0.762872i
$513$	67.2635	−	67.2635i	0.131118	−	0.131118i
$514$		−	215.946i		−	0.420128i
$515$	259.610	+	10.0143i	0.504097	+	0.0194452i
$516$	−26.9236			−0.0521776
$517$	−1017.07	−	1017.07i	−1.96726	−	1.96726i
$518$	12.9198	−	12.9198i	0.0249418	−	0.0249418i
$519$			192.387i			0.370688i
$520$	−518.211	+	479.716i	−0.996559	+	0.922531i
$521$	−64.5705			−0.123936			−0.0619679	−	0.998078i	$-0.519738\pi$
$521$	−64.5705			−0.123936			−0.0619679	+	0.998078i	$0.519738\pi$
$522$	11.8106	+	11.8106i	0.0226256	+	0.0226256i
$523$	−431.531	+	431.531i	−0.825107	+	0.825107i	−0.986835	−	0.161728i	$-0.948293\pi$
$523$	−431.531	+	431.531i	−0.825107	+	0.825107i	0.161728	+	0.986835i	$0.448293\pi$
$524$			5.99279i			0.0114366i
$525$	8.82537	−	114.224i	0.0168102	−	0.217569i
$526$	885.986			1.68438
$527$	223.631	+	223.631i	0.424347	+	0.424347i
$528$	−321.442	+	321.442i	−0.608791	+	0.608791i
$529$		−	864.452i		−	1.63413i
$530$	−618.450	−	668.077i	−1.16689	−	1.26052i
$531$	49.4020			0.0930358
$532$	−8.83734	−	8.83734i	−0.0166115	−	0.0166115i
$533$	−23.0157	+	23.0157i	−0.0431814	+	0.0431814i
$534$			98.2854i			0.184055i
$535$	25.0715	−	649.952i	0.0468626	−	1.21486i
$536$	316.870			0.591175
$537$	−198.868	−	198.868i	−0.370332	−	0.370332i
$538$	162.844	−	162.844i	0.302684	−	0.302684i
$539$			123.291i			0.228740i
$540$	6.69891	+	0.258406i	0.0124054	+	0.000478530i
$541$	−571.616			−1.05659			−0.528295	−	0.849061i	$-0.677169\pi$
$541$	−571.616			−1.05659			−0.528295	+	0.849061i	$0.677169\pi$
$542$	−520.017	−	520.017i	−0.959441	−	0.959441i
$543$	−315.034	+	315.034i	−0.580173	+	0.580173i
$544$			80.8946i			0.148703i
$545$	−530.667	+	491.248i	−0.973702	+	0.901372i
$546$	151.998			0.278384
$547$	259.835	+	259.835i	0.475017	+	0.475017i	0.903534	−	0.428516i	$-0.140964\pi$
$547$	259.835	+	259.835i	0.475017	+	0.475017i	−0.428516	+	0.903534i	$0.640964\pi$
$548$	−4.45334	+	4.45334i	−0.00812653	+	0.00812653i
$549$			22.1108i			0.0402746i
$550$	646.900	−	554.106i	1.17618	−	1.00747i
$551$	−52.6898			−0.0956258
$552$	376.574	+	376.574i	0.682200	+	0.682200i
$553$	−4.65245	+	4.65245i	−0.00841311	+	0.00841311i
$554$			1024.39i			1.84907i
$555$	−21.0030	−	22.6884i	−0.0378432	−	0.0408799i
$556$	−7.60677			−0.0136812
$557$	503.660	+	503.660i	0.904237	+	0.904237i	0.995799	−	0.0915625i	$-0.0291861\pi$
$557$	503.660	+	503.660i	0.904237	+	0.904237i	−0.0915625	+	0.995799i	$0.529186\pi$
$558$	−66.1278	+	66.1278i	−0.118509	+	0.118509i
$559$			1032.94i			1.84784i
$560$	−7.59834	+	196.979i	−0.0135685	+	0.351748i
$561$	−598.703			−1.06721
$562$	411.506	+	411.506i	0.732216	+	0.732216i
$563$	−405.076	+	405.076i	−0.719495	+	0.719495i	−0.968502	−	0.249007i	$-0.919896\pi$
$563$	−405.076	+	405.076i	−0.719495	+	0.719495i	0.249007	+	0.968502i	$0.419896\pi$
$564$		−	36.4981i		−	0.0647129i
$565$	202.648	+	7.81703i	0.358670	+	0.0138355i
$566$	375.242			0.662972
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	463.605	−	463.605i	0.816207	−	0.816207i
$569$			674.447i			1.18532i	0.805453	+	0.592660i	$0.201922\pi$
$569$			674.447i			1.18532i	−0.805453	+	0.592660i	$0.798078\pi$
$570$	225.057	−	208.339i	0.394837	−	0.365507i
$571$	825.137			1.44507			0.722537	−	0.691333i	$-0.242976\pi$
$571$	825.137			1.44507			0.722537	+	0.691333i	$0.242976\pi$
$572$	−55.1023	−	55.1023i	−0.0963328	−	0.0963328i
$573$	409.189	−	409.189i	0.714116	−	0.714116i
$574$			9.71539i			0.0169258i
$575$	−607.094	−	708.762i	−1.05582	−	1.23263i
$576$	−202.736			−0.351972
$577$	532.596	+	532.596i	0.923043	+	0.923043i	0.997243	−	0.0742001i	$-0.0236403\pi$
$577$	532.596	+	532.596i	0.923043	+	0.923043i	−0.0742001	+	0.997243i	$0.523640\pi$
$578$	131.526	−	131.526i	0.227554	−	0.227554i
$579$			48.8873i			0.0844340i
$580$	−2.52253	−	2.72495i	−0.00434919	−	0.00469819i
$581$	−108.666			−0.187032
$582$	−298.605	−	298.605i	−0.513067	−	0.513067i
$583$	1172.26	−	1172.26i	2.01074	−	2.01074i
$584$			737.416i			1.26270i
$585$	9.91391	−	257.008i	0.0169469	−	0.439329i
$586$	−529.349			−0.903325
$587$	800.352	+	800.352i	1.36346	+	1.36346i	0.869463	+	0.493999i	$0.164465\pi$
$587$	800.352	+	800.352i	1.36346	+	1.36346i	0.493999	+	0.869463i	$0.335535\pi$
$588$	−2.21217	+	2.21217i	−0.00376219	+	0.00376219i
$589$		−	295.013i		−	0.500871i
$590$	159.155	+	6.13931i	0.269754	+	0.0104056i
$591$	−89.4682			−0.151384
$592$	37.6168	+	37.6168i	0.0635419	+	0.0635419i
$593$	254.908	−	254.908i	0.429862	−	0.429862i	−0.458719	−	0.888581i	$-0.651692\pi$
$593$	254.908	−	254.908i	0.429862	−	0.429862i	0.888581	+	0.458719i	$0.151692\pi$
$594$		−	177.037i		−	0.298042i
$595$	−190.518	+	176.366i	−0.320199	+	0.296414i
$596$	−3.71174			−0.00622775
$597$	229.786	+	229.786i	0.384900	+	0.384900i
$598$	875.505	−	875.505i	1.46406	−	1.46406i
$599$		−	661.029i		−	1.10355i	−0.833991	−	0.551777i	$-0.813950\pi$
$599$		−	661.029i		−	1.10355i	0.833991	−	0.551777i	$-0.186050\pi$
$600$	355.604	+	27.4753i	0.592674	+	0.0457922i
$601$	−410.580			−0.683162			−0.341581	−	0.939852i	$-0.610962\pi$
$601$	−410.580			−0.683162			−0.341581	+	0.939852i	$0.610962\pi$
$602$	218.013	+	218.013i	0.362148	+	0.362148i
$603$	−81.6072	+	81.6072i	−0.135335	+	0.135335i
$604$		−	3.96258i		−	0.00656056i
$605$	642.698	+	694.271i	1.06231	+	1.14756i
$606$	−292.602			−0.482842
$607$	−604.297	−	604.297i	−0.995548	−	0.995548i	0.00444263	−	0.999990i	$-0.498586\pi$
$607$	−604.297	−	604.297i	−0.995548	−	0.995548i	−0.999990	+	0.00444263i	$0.998586\pi$
$608$	53.3579	−	53.3579i	0.0877598	−	0.0877598i
$609$			13.1894i			0.0216574i
$610$	−2.74776	+	71.2327i	−0.00450452	+	0.116775i
$611$	−1400.27			−2.29177
$612$	−10.7424	−	10.7424i	−0.0175529	−	0.0175529i
$613$	−61.4626	+	61.4626i	−0.100265	+	0.100265i	−0.755460	−	0.655195i	$-0.772587\pi$
$613$	−61.4626	+	61.4626i	−0.100265	+	0.100265i	0.655195	+	0.755460i	$0.272587\pi$
$614$		−	335.198i		−	0.545926i
$615$	16.4274	+	0.633677i	0.0267112	+	0.00103037i
$616$	−383.831			−0.623103
$617$	−509.151	−	509.151i	−0.825204	−	0.825204i	0.161645	−	0.986849i	$-0.448320\pi$
$617$	−509.151	−	509.151i	−0.825204	−	0.825204i	−0.986849	+	0.161645i	$0.948320\pi$
$618$	123.103	−	123.103i	0.199196	−	0.199196i
$619$			735.555i			1.18830i	0.804356	+	0.594148i	$0.202511\pi$
$619$			735.555i			1.18830i	−0.804356	+	0.594148i	$0.797489\pi$
$620$	15.2571	−	14.1238i	0.0246083	−	0.0227803i
$621$	−193.967			−0.312346
$622$	−161.473	−	161.473i	−0.259603	−	0.259603i
$623$	−54.8798	+	54.8798i	−0.0880895	+	0.0880895i
$624$			442.550i			0.709214i
$625$	−617.582	−	96.0065i	−0.988131	−	0.153610i
$626$	791.928			1.26506
$627$	394.903	+	394.903i	0.629830	+	0.629830i
$628$	16.3275	−	16.3275i	0.0259992	−	0.0259992i
$629$			70.0634i			0.111389i
$630$	−52.1517	−	56.3365i	−0.0827804	−	0.0894230i
$631$	649.002			1.02853			0.514265	−	0.857631i	$-0.328065\pi$
$631$	649.002			1.02853			0.514265	+	0.857631i	$0.328065\pi$
$632$	−14.4841	−	14.4841i	−0.0229179	−	0.0229179i
$633$	90.1914	−	90.1914i	0.142482	−	0.142482i
$634$			799.517i			1.26107i
$635$	−3.32691	+	86.2465i	−0.00523922	+	0.135821i
$636$	42.0671			0.0661432
$637$	84.8713	+	84.8713i	0.133236	+	0.133236i
$638$	−69.3396	+	69.3396i	−0.108683	+	0.108683i
$639$			238.795i			0.373702i
$640$	−570.763	−	22.0168i	−0.891818	−	0.0344013i
$641$	−103.576			−0.161585			−0.0807925	−	0.996731i	$-0.525745\pi$
$641$	−103.576			−0.161585			−0.0807925	+	0.996731i	$0.525745\pi$
$642$	−308.198	−	308.198i	−0.480059	−	0.480059i
$643$	504.926	−	504.926i	0.785266	−	0.785266i	−0.195448	−	0.980714i	$-0.562616\pi$
$643$	504.926	−	504.926i	0.785266	−	0.785266i	0.980714	+	0.195448i	$0.0626160\pi$
$644$			25.4841i			0.0395716i
$645$	382.850	−	354.410i	0.593566	−	0.549473i
$646$	−694.994			−1.07584
$647$	134.888	+	134.888i	0.208482	+	0.208482i	0.803622	−	0.595140i	$-0.202903\pi$
$647$	134.888	+	134.888i	0.208482	+	0.208482i	−0.595140	+	0.803622i	$0.702903\pi$
$648$	52.4187	−	52.4187i	0.0808931	−	0.0808931i
$649$			290.039i			0.446901i
$650$	63.8779	−	826.752i	0.0982738	−	1.27193i
$651$	−73.8478			−0.113438
$652$	31.2875	+	31.2875i	0.0479870	+	0.0479870i
$653$	−123.054	+	123.054i	−0.188444	+	0.188444i	−0.795023	−	0.606579i	$-0.792541\pi$
$653$	−123.054	+	123.054i	−0.188444	+	0.188444i	0.606579	+	0.795023i	$0.292541\pi$
$654$			484.578i			0.740944i
$655$	−78.8864	−	85.2166i	−0.120437	−	0.130102i
$656$	−28.2869			−0.0431202
$657$	−189.915	−	189.915i	−0.289064	−	0.289064i
$658$	−295.542	+	295.542i	−0.449151	+	0.449151i
$659$			811.814i			1.23189i	0.787790	+	0.615944i	$0.211225\pi$
$659$			811.814i			1.23189i	−0.787790	+	0.615944i	$0.788775\pi$
$660$	−1.51710	+	39.3292i	−0.00229864	+	0.0595897i
$661$	979.510			1.48186			0.740930	−	0.671582i	$-0.234385\pi$
$661$	979.510			1.48186			0.740930	+	0.671582i	$0.234385\pi$
$662$	−794.329	−	794.329i	−1.19989	−	1.19989i
$663$	−412.137	+	412.137i	−0.621625	+	0.621625i
$664$		−	338.300i		−	0.509488i
$665$	241.996	+	9.33486i	0.363904	+	0.0140374i
$666$	−20.7178			−0.0311078
$667$	75.9705	+	75.9705i	0.113899	+	0.113899i
$668$	−13.2170	+	13.2170i	−0.0197860	+	0.0197860i
$669$			632.510i			0.945456i
$670$	−273.050	+	252.767i	−0.407537	+	0.377264i
$671$	−129.812			−0.193461
$672$	−13.3566	−	13.3566i	−0.0198759	−	0.0198759i
$673$	−327.449	+	327.449i	−0.486552	+	0.486552i	−0.907216	−	0.420664i	$-0.861797\pi$
$673$	−327.449	+	327.449i	−0.486552	+	0.486552i	0.420664	+	0.907216i	$0.361797\pi$
$674$		−	693.868i		−	1.02948i
$675$	−98.6589	+	84.5069i	−0.146161	+	0.125195i
$676$	−32.2555			−0.0477152
$677$	463.677	+	463.677i	0.684900	+	0.684900i	0.961100	−	0.276200i	$-0.0890754\pi$
$677$	463.677	+	463.677i	0.684900	+	0.684900i	−0.276200	+	0.961100i	$0.589075\pi$
$678$	96.0929	−	96.0929i	0.141730	−	0.141730i
$679$		−	333.465i		−	0.491112i
$680$	−549.067	−	593.126i	−0.807451	−	0.872244i
$681$	23.8317			0.0349951
$682$	−388.236	−	388.236i	−0.569261	−	0.569261i
$683$	667.534	−	667.534i	0.977356	−	0.977356i	−0.0223933	−	0.999749i	$-0.507129\pi$
$683$	667.534	−	667.534i	0.977356	−	0.977356i	0.999749	+	0.0223933i	$0.00712859\pi$
$684$			14.1713i			0.0207182i
$685$	4.70405	−	121.948i	0.00686723	−	0.178026i
$686$	35.8259			0.0522243
$687$	132.330	+	132.330i	0.192621	+	0.192621i
$688$	−634.756	+	634.756i	−0.922610	+	0.922610i
$689$		−	1613.93i		−	2.34242i
$690$	−624.890	−	24.1048i	−0.905638	−	0.0349344i
$691$	−622.518			−0.900895			−0.450447	−	0.892803i	$-0.648736\pi$
$691$	−622.518			−0.900895			−0.450447	+	0.892803i	$0.648736\pi$
$692$	−20.2663	−	20.2663i	−0.0292866	−	0.0292866i
$693$	98.8525	−	98.8525i	0.142644	−	0.142644i
$694$		−	164.846i		−	0.237531i
$695$	108.167	−	100.132i	0.155636	−	0.144075i
$696$	−41.0614			−0.0589963
$697$	−26.3430	−	26.3430i	−0.0377948	−	0.0377948i
$698$	476.269	−	476.269i	0.682334	−	0.682334i
$699$		−	6.05816i		−	0.00866689i
$700$	11.1028	+	12.9622i	0.0158612	+	0.0185174i
$701$	−821.585			−1.17202			−0.586009	−	0.810304i	$-0.699302\pi$
$701$	−821.585			−1.17202			−0.586009	+	0.810304i	$0.699302\pi$
$702$	−121.869	−	121.869i	−0.173603	−	0.173603i
$703$	46.2137	−	46.2137i	0.0657378	−	0.0657378i
$704$		−	1190.26i		−	1.69071i
$705$	480.444	+	518.997i	0.681481	+	0.736166i
$706$	−309.482			−0.438359
$707$	−163.381	−	163.381i	−0.231090	−	0.231090i
$708$	−5.20408	+	5.20408i	−0.00735039	+	0.00735039i
$709$			1124.01i			1.58535i	0.609647	+	0.792673i	$0.291311\pi$
$709$			1124.01i			1.58535i	−0.609647	+	0.792673i	$0.708689\pi$
$710$	−29.6757	+	769.310i	−0.0417967	+	1.08354i
$711$	7.46052			0.0104930
$712$	−170.853	−	170.853i	−0.239962	−	0.239962i
$713$	−425.363	+	425.363i	−0.596581	+	0.596581i
$714$			173.971i			0.243658i
$715$	1508.89	+	58.2045i	2.11033	+	0.0814048i
$716$	41.8982			0.0585170
$717$	−282.884	−	282.884i	−0.394538	−	0.394538i
$718$	144.514	−	144.514i	0.201273	−	0.201273i
$719$			826.757i			1.14987i	0.818199	+	0.574936i	$0.194973\pi$
$719$			826.757i			1.14987i	−0.818199	+	0.574936i	$0.805027\pi$
$720$	164.027	−	151.842i	0.227815	−	0.210892i
$721$	137.475			0.190672
$722$	−35.3734	−	35.3734i	−0.0489936	−	0.0489936i
$723$	343.424	−	343.424i	0.474998	−	0.474998i
$724$		−	66.3722i		−	0.0916744i
$725$	71.7400	+	5.54290i	0.0989518	+	0.00764538i
$726$	633.972			0.873239
$727$	829.278	+	829.278i	1.14069	+	1.14069i	0.988325	+	0.152360i	$0.0486874\pi$
$727$	829.278	+	829.278i	1.14069	+	1.14069i	0.152360	+	0.988325i	$0.451313\pi$
$728$	−264.223	+	264.223i	−0.362944	+	0.362944i
$729$			27.0000i			0.0370370i
$730$	−588.236	−	635.438i	−0.805803	−	0.870463i
$731$	−1182.27			−1.61733
$732$	−2.32918	−	2.32918i	−0.00318194	−	0.00318194i
$733$	−306.100	+	306.100i	−0.417599	+	0.417599i	−0.884375	−	0.466776i	$-0.845415\pi$
$733$	−306.100	+	306.100i	−0.417599	+	0.417599i	0.466776	+	0.884375i	$0.345415\pi$
$734$			629.666i			0.857856i
$735$	2.33671	−	60.5767i	0.00317920	−	0.0824173i
$736$	−153.868			−0.209059
$737$	−479.115	−	479.115i	−0.650088	−	0.650088i
$738$	7.78964	−	7.78964i	0.0105551	−	0.0105551i
$739$			1152.24i			1.55919i	0.626283	+	0.779596i	$0.284575\pi$
$739$			1152.24i			1.55919i	−0.626283	+	0.779596i	$0.715425\pi$
$740$	4.60251	+	0.177539i	0.00621961	+	0.000239918i
$741$	543.689			0.733724
$742$	−340.636	−	340.636i	−0.459078	−	0.459078i
$743$	−87.8428	+	87.8428i	−0.118227	+	0.118227i	−0.763745	−	0.645518i	$-0.776642\pi$
$743$	−87.8428	+	87.8428i	−0.118227	+	0.118227i	0.645518	+	0.763745i	$0.276642\pi$
$744$		−	229.905i		−	0.309012i
$745$	52.7804	−	48.8597i	0.0708462	−	0.0655835i
$746$	578.475			0.775436
$747$	87.1263	+	87.1263i	0.116635	+	0.116635i
$748$	63.0682	−	63.0682i	0.0843158	−	0.0843158i
$749$		−	344.178i		−	0.459517i
$750$	−328.345	+	259.989i	−0.437793	+	0.346653i
$751$	−601.083			−0.800377			−0.400189	−	0.916433i	$-0.631055\pi$
$751$	−601.083			−0.800377			−0.400189	+	0.916433i	$0.631055\pi$
$752$	−860.485	−	860.485i	−1.14426	−	1.14426i
$753$	−65.4916	+	65.4916i	−0.0869743	+	0.0869743i
$754$			95.4645i			0.126611i
$755$	52.1616	+	56.3472i	0.0690882	+	0.0746321i
$756$	3.54736			0.00469228
$757$	650.454	+	650.454i	0.859252	+	0.859252i	0.991250	−	0.131998i	$-0.0421393\pi$
$757$	650.454	+	650.454i	0.859252	+	0.859252i	−0.131998	+	0.991250i	$0.542139\pi$
$758$	−180.938	+	180.938i	−0.238704	+	0.238704i
$759$		−	1138.78i		−	1.50037i
$760$	−29.0615	+	753.388i	−0.0382388	+	0.991300i
$761$	344.833			0.453131			0.226566	−	0.973996i	$-0.427250\pi$
$761$	344.833			0.453131			0.226566	+	0.973996i	$0.427250\pi$
$762$	40.8969	+	40.8969i	0.0536704	+	0.0536704i
$763$	−270.574	+	270.574i	−0.354619	+	0.354619i
$764$			86.2090i			0.112839i
$765$	294.162	+	11.3471i	0.384526	+	0.0148328i
$766$	−409.087			−0.534056
$767$	199.658	+	199.658i	0.260310	+	0.260310i
$768$	60.4187	−	60.4187i	0.0786702	−	0.0786702i
$769$			953.105i			1.23941i	0.784836	+	0.619704i	$0.212747\pi$
$769$			953.105i			1.23941i	−0.784836	+	0.619704i	$0.787253\pi$
$770$	330.751	−	306.182i	0.429547	−	0.397639i
$771$	−193.355			−0.250785
$772$	−5.14986	−	5.14986i	−0.00667080	−	0.00667080i
$773$	−716.434	+	716.434i	−0.926823	+	0.926823i	−0.997499	−	0.0706765i	$-0.977484\pi$
$773$	−716.434	+	716.434i	−0.926823	+	0.926823i	0.0706765	+	0.997499i	$0.477484\pi$
$774$		−	349.598i		−	0.451677i
$775$	−31.0350	+	401.676i	−0.0400451	+	0.518291i
$776$	1038.15			1.33782
$777$	−11.5682	−	11.5682i	−0.0148883	−	0.0148883i
$778$	−395.417	+	395.417i	−0.508248	+	0.508248i
$779$			34.7515i			0.0446104i
$780$	26.0292	+	28.1179i	0.0333708	+	0.0360486i
$781$	−1401.96			−1.79509
$782$	1002.07	+	1002.07i	1.28142	+	1.28142i
$783$	10.5750	−	10.5750i	0.0135058	−	0.0135058i
$784$			104.309i			0.133047i
$785$	−17.2467	+	447.103i	−0.0219703	+	0.569557i
$786$	−77.8153			−0.0990017
$787$	475.797	+	475.797i	0.604570	+	0.604570i	0.941522	−	0.336952i	$-0.109396\pi$
$787$	475.797	+	475.797i	0.604570	+	0.604570i	−0.336952	+	0.941522i	$0.609396\pi$
$788$	9.42471	−	9.42471i	0.0119603	−	0.0119603i
$789$		−	793.300i		−	1.00545i
$790$	24.0350	+	0.927137i	0.0304241	+	0.00117359i
$791$	107.311			0.135665
$792$	307.750	+	307.750i	0.388573	+	0.388573i
$793$	−89.3604	+	89.3604i	−0.112687	+	0.112687i
$794$			1375.75i			1.73268i
$795$	−598.187	+	553.752i	−0.752437	+	0.696543i
$796$	−48.4119			−0.0608189
$797$	−523.540	−	523.540i	−0.656889	−	0.656889i	0.297754	−	0.954643i	$-0.403762\pi$
$797$	−523.540	−	523.540i	−0.656889	−	0.656889i	−0.954643	+	0.297754i	$0.903762\pi$
$798$	114.751	−	114.751i	0.143799	−	0.143799i
$799$		−	1602.70i		−	2.00589i
$800$	−78.2629	+	67.0365i	−0.0978286	+	0.0837957i
$801$	88.0034			0.109867
$802$	−555.222	−	555.222i	−0.692297	−	0.692297i
$803$	1114.99	−	1114.99i	1.38853	−	1.38853i
$804$		−	17.1932i		−	0.0213846i
$805$	−335.462	−	362.381i	−0.416723	−	0.450162i
$806$	−534.510			−0.663164
$807$	−145.808	−	145.808i	−0.180680	−	0.180680i
$808$	508.640	−	508.640i	0.629505	−	0.629505i
$809$		−	801.958i		−	0.991295i	−0.868524	−	0.495648i	$-0.834931\pi$
$809$		−	801.958i		−	0.991295i	0.868524	−	0.495648i	$-0.165069\pi$
$810$	−3.35536	+	86.9841i	−0.00414241	+	0.107388i
$811$	56.4562			0.0696130			0.0348065	−	0.999394i	$-0.488919\pi$
$811$	56.4562			0.0696130			0.0348065	+	0.999394i	$0.488919\pi$
$812$	−1.38939	−	1.38939i	−0.00171107	−	0.00171107i
$813$	−465.616	+	465.616i	−0.572714	+	0.572714i
$814$		−	121.634i		−	0.149428i
$815$	−856.758	−	33.0489i	−1.05124	−	0.0405508i
$816$	−506.527			−0.620744
$817$	779.822	+	779.822i	0.954495	+	0.954495i
$818$	691.306	−	691.306i	0.845118	−	0.845118i
$819$		−	136.097i		−	0.166174i
$820$	−1.79724	+	1.66373i	−0.00219175	+	0.00202894i
$821$	983.386			1.19779			0.598896	−	0.800827i	$-0.295606\pi$
$821$	983.386			1.19779			0.598896	+	0.800827i	$0.295606\pi$
$822$	−57.8258	−	57.8258i	−0.0703477	−	0.0703477i
$823$	8.06828	−	8.06828i	0.00980350	−	0.00980350i	−0.702188	−	0.711992i	$-0.747793\pi$
$823$	8.06828	−	8.06828i	0.00980350	−	0.00980350i	0.711992	+	0.702188i	$0.247793\pi$
$824$			427.989i			0.519405i
$825$	−496.139	−	579.226i	−0.601381	−	0.702092i
$826$	84.2796			0.102033
$827$	917.498	+	917.498i	1.10943	+	1.10943i	0.993225	+	0.116204i	$0.0370725\pi$
$827$	917.498	+	917.498i	1.10943	+	1.10943i	0.116204	+	0.993225i	$0.462927\pi$
$828$	20.4328	−	20.4328i	0.0246773	−	0.0246773i
$829$		−	589.450i		−	0.711037i	−0.934669	−	0.355518i	$-0.884304\pi$
$829$		−	589.450i		−	0.711037i	0.934669	−	0.355518i	$-0.115696\pi$
$830$	269.861	+	291.516i	0.325134	+	0.351224i
$831$	917.223			1.10376
$832$	−819.356	−	819.356i	−0.984803	−	0.984803i
$833$	−97.1407	+	97.1407i	−0.116616	+	0.116616i
$834$		−	98.7725i		−	0.118432i
$835$	13.9611	−	361.927i	0.0167199	−	0.433446i
$836$	−83.1994			−0.0995208
$837$	59.2100	+	59.2100i	0.0707407	+	0.0707407i
$838$	−757.224	+	757.224i	−0.903609	+	0.903609i
$839$			230.274i			0.274463i	0.990539	+	0.137231i	$0.0438204\pi$
$839$			230.274i			0.274463i	−0.990539	+	0.137231i	$0.956180\pi$
$840$	188.589	+	7.27469i	0.224510	+	0.00866035i
$841$	832.716			0.990150
$842$	438.316	+	438.316i	0.520566	+	0.520566i
$843$	368.457	−	368.457i	0.437078	−	0.437078i
$844$			19.0018i			0.0225140i
$845$	458.668	−	424.597i	0.542803	−	0.502481i
$846$	473.921			0.560190
$847$	353.992	+	353.992i	0.417936	+	0.417936i
$848$	991.780	−	991.780i	1.16955	−	1.16955i
$849$		−	335.987i		−	0.395744i
$850$	946.272	+	73.1125i	1.11326	+	0.0860147i
$851$	−133.266			−0.156599
$852$	−25.1550	−	25.1550i	−0.0295247	−	0.0295247i
$853$	−843.744	+	843.744i	−0.989148	+	0.989148i	−0.999942	−	0.0107933i	$-0.996564\pi$
$853$	−843.744	+	843.744i	−0.989148	+	0.989148i	0.0107933	+	0.999942i	$0.496564\pi$
$854$			37.7209i			0.0441696i
$855$	−186.544	−	201.513i	−0.218180	−	0.235688i
$856$	1071.50			1.25176
$857$	437.772	+	437.772i	0.510819	+	0.510819i	0.914777	−	0.403959i	$-0.132366\pi$
$857$	437.772	+	437.772i	0.510819	+	0.510819i	−0.403959	+	0.914777i	$0.632366\pi$
$858$	715.494	−	715.494i	0.833909	−	0.833909i
$859$		−	1402.95i		−	1.63324i	−0.577175	−	0.816621i	$-0.695845\pi$
$859$		−	1402.95i		−	1.63324i	0.577175	−	0.816621i	$-0.304155\pi$
$860$	−2.99584	+	77.6640i	−0.00348354	+	0.0903070i
$861$	8.69903			0.0101034
$862$	−303.482	−	303.482i	−0.352068	−	0.352068i
$863$	1049.60	−	1049.60i	1.21622	−	1.21622i	0.247281	−	0.968944i	$-0.420463\pi$
$863$	1049.60	−	1049.60i	1.21622	−	1.21622i	0.968944	−	0.247281i	$-0.0795369\pi$
$864$			21.4182i			0.0247896i
$865$	554.961	+	21.4073i	0.641574	+	0.0247483i
$866$	443.543			0.512174
$867$	−117.767	−	117.767i	−0.135832	−	0.135832i
$868$	7.77924	−	7.77924i	0.00896225	−	0.00896225i
$869$			43.8006i			0.0504035i
$870$	35.3830	−	32.7546i	0.0406701	−	0.0376490i
$871$	−659.629			−0.757324
$872$	−842.358	−	842.358i	−0.966007	−	0.966007i
$873$	−267.367	+	267.367i	−0.306262	+	0.306262i
$874$		−	1321.93i		−	1.51251i
$875$	−328.509	−	38.1676i	−0.375439	−	0.0436201i
$876$	40.0119			0.0456757
$877$	−236.787	−	236.787i	−0.269996	−	0.269996i	0.559102	−	0.829099i	$-0.311146\pi$
$877$	−236.787	−	236.787i	−0.269996	−	0.269996i	−0.829099	+	0.559102i	$0.811146\pi$
$878$	−829.599	+	829.599i	−0.944874	+	0.944874i
$879$			473.972i			0.539217i
$880$	891.465	+	963.000i	1.01303	+	1.09432i
$881$	311.627			0.353720			0.176860	−	0.984236i	$-0.443406\pi$
$881$	311.627			0.353720			0.176860	+	0.984236i	$0.443406\pi$
$882$	−28.7246	−	28.7246i	−0.0325676	−	0.0325676i
$883$	−54.4472	+	54.4472i	−0.0616616	+	0.0616616i	−0.737265	−	0.675604i	$-0.763883\pi$
$883$	−54.4472	+	54.4472i	−0.0616616	+	0.0616616i	0.675604	+	0.737265i	$0.263883\pi$
$884$		−	86.8302i		−	0.0982242i
$885$	5.49706	−	142.505i	0.00621136	−	0.161023i
$886$	26.6834			0.0301167
$887$	−485.748	−	485.748i	−0.547631	−	0.547631i	0.378124	−	0.925755i	$-0.376569\pi$
$887$	−485.748	−	485.748i	−0.547631	−	0.547631i	−0.925755	+	0.378124i	$0.876569\pi$
$888$	36.0145	−	36.0145i	0.0405569	−	0.0405569i
$889$			45.6713i			0.0513738i
$890$	283.515	+	10.9364i	0.318556	+	0.0122881i
$891$	−158.517			−0.177909
$892$	−66.6295	−	66.6295i	−0.0746968	−	0.0746968i
$893$	−1057.14	+	1057.14i	−1.18381	+	1.18381i
$894$		−	48.1963i		−	0.0539108i
$895$	−595.786	+	551.529i	−0.665682	+	0.616233i
$896$	−302.244			−0.337326
$897$	−783.916	−	783.916i	−0.873931	−	0.873931i
$898$	−614.103	+	614.103i	−0.683856	+	0.683856i
$899$		−	46.3812i		−	0.0515920i
$900$	1.49080	−	19.2949i	0.00165644	−	0.0214388i
$901$	1847.25			2.05022
$902$	45.7329	+	45.7329i	0.0507017	+	0.0507017i
$903$	195.206	−	195.206i	0.216175	−	0.216175i
$904$			334.083i			0.369561i
$905$	873.694	+	943.803i	0.965408	+	1.04288i
$906$	51.4533			0.0567918
$907$	355.846	+	355.846i	0.392334	+	0.392334i	0.875518	−	0.483185i	$-0.160520\pi$
$907$	355.846	+	355.846i	0.392334	+	0.392334i	−0.483185	+	0.875518i	$0.660520\pi$
$908$	−2.51046	+	2.51046i	−0.00276482	+	0.00276482i
$909$			261.992i			0.288220i
$910$	16.9131	−	438.454i	0.0185858	−	0.481817i
$911$	440.542			0.483581			0.241790	−	0.970329i	$-0.422265\pi$
$911$	440.542			0.483581			0.241790	+	0.970329i	$0.422265\pi$
$912$	334.104	+	334.104i	0.366342	+	0.366342i
$913$	−511.517	+	511.517i	−0.560260	+	0.560260i
$914$		−	1009.08i		−	1.10403i
$915$	63.7808	+	2.46031i	0.0697058	+	0.00268886i
$916$	−27.8797			−0.0304364
$917$	−43.4499	−	43.4499i	−0.0473826	−	0.0473826i
$918$	139.487	−	139.487i	0.151947	−	0.151947i
$919$		−	576.067i		−	0.626841i	−0.949614	−	0.313420i	$-0.898525\pi$
$919$		−	576.067i		−	0.626841i	0.949614	−	0.313420i	$-0.101475\pi$
$920$	1128.17	−	1044.37i	1.22627	−	1.13518i
$921$	−300.132			−0.325876
$922$	694.801	+	694.801i	0.753580	+	0.753580i
$923$	−965.089	+	965.089i	−1.04560	+	1.04560i
$924$			20.8265i			0.0225395i
$925$	−67.7840	+	58.0608i	−0.0732800	+	0.0627684i
$926$	−698.769			−0.754611
$927$	−110.225	−	110.225i	−0.118905	−	0.118905i
$928$	8.38881	−	8.38881i	0.00903967	−	0.00903967i
$929$			513.292i			0.552521i	0.961083	+	0.276260i	$0.0890952\pi$
$929$			513.292i			0.552521i	−0.961083	+	0.276260i	$0.910905\pi$
$930$	183.395	+	198.111i	0.197199	+	0.213023i
$931$	128.148			0.137645
$932$	0.638175	+	0.638175i	0.000684737	+	0.000684737i
$933$	−144.581	+	144.581i	−0.154964	+	0.154964i
$934$		−	1117.11i		−	1.19605i
$935$	−66.6188	+	1727.02i	−0.0712501	+	1.84708i
$936$	423.699			0.452670
$937$	−224.557	−	224.557i	−0.239655	−	0.239655i	0.577052	−	0.816707i	$-0.304203\pi$
$937$	−224.557	−	224.557i	−0.239655	−	0.239655i	−0.816707	+	0.577052i	$0.804203\pi$
$938$	−139.221	+	139.221i	−0.148424	+	0.148424i
$939$		−	709.082i		−	0.755146i
$940$	−105.283	−	4.06121i	−0.112003	−	0.00432044i
$941$	595.500			0.632838			0.316419	−	0.948620i	$-0.397519\pi$
$941$	595.500			0.632838			0.316419	+	0.948620i	$0.397519\pi$
$942$	212.010	+	212.010i	0.225063	+	0.225063i
$943$	50.1063	−	50.1063i	0.0531350	−	0.0531350i
$944$			245.385i			0.259941i
$945$	−50.4430	+	46.6959i	−0.0533788	+	0.0494136i
$946$	2052.49			2.16965
$947$	−890.942	−	890.942i	−0.940805	−	0.940805i	0.0575384	−	0.998343i	$-0.481675\pi$
$947$	−890.942	−	890.942i	−0.940805	−	0.940805i	−0.998343	+	0.0575384i	$0.981675\pi$
$948$	−0.785902	+	0.785902i	−0.000829010	+	0.000829010i
$949$		−	1535.08i		−	1.61758i
$950$	−575.934	−	672.384i	−0.606246	−	0.707772i
$951$	715.877			0.752762
$952$	−302.421	−	302.421i	−0.317669	−	0.317669i
$953$	270.103	−	270.103i	0.283424	−	0.283424i	−0.551049	−	0.834473i	$-0.685772\pi$
$953$	270.103	−	270.103i	0.283424	−	0.283424i	0.834473	+	0.551049i	$0.185772\pi$
$954$			546.233i			0.572571i
$955$	−1134.82	−	1225.88i	−1.18829	−	1.28364i
$956$	59.5988			0.0623418
$957$	62.0858	+	62.0858i	0.0648754	+	0.0648754i
$958$	−909.258	+	909.258i	−0.949121	+	0.949121i
$959$		−	64.5766i		−	0.0673374i
$960$	−22.5588	+	584.814i	−0.0234988	+	0.609181i
$961$	−701.309			−0.729770
$962$	−83.7308	−	83.7308i	−0.0870383	−	0.0870383i
$963$	−275.956	+	275.956i	−0.286559	+	0.286559i
$964$			72.3535i			0.0750555i
$965$	141.021	+	5.43978i	0.146135	+	0.00563708i
$966$	−330.907			−0.342554
$967$	1139.02	+	1139.02i	1.17789	+	1.17789i	0.980281	+	0.197611i	$0.0633182\pi$
$967$	1139.02	+	1139.02i	1.17789	+	1.17789i	0.197611	+	0.980281i	$0.436682\pi$
$968$	−1102.06	+	1102.06i	−1.13849	+	1.13849i
$969$			622.288i			0.642196i
$970$	−894.584	+	828.131i	−0.922251	+	0.853743i
$971$	−736.722			−0.758725			−0.379363	−	0.925248i	$-0.623857\pi$
$971$	−736.722			−0.758725			−0.379363	+	0.925248i	$0.623857\pi$
$972$	−2.84422	−	2.84422i	−0.00292615	−	0.00292615i
$973$	55.1518	−	55.1518i	0.0566822	−	0.0566822i
$974$			915.673i			0.940116i
$975$	−740.263	−	57.1955i	−0.759244	−	0.0586620i
$976$	−109.826			−0.112527
$977$	−993.980	−	993.980i	−1.01738	−	1.01738i	−0.999846	−	0.0175332i	$-0.994419\pi$
$977$	−993.980	−	993.980i	−1.01738	−	1.01738i	−0.0175332	−	0.999846i	$-0.505581\pi$
$978$	−406.263	+	406.263i	−0.415401	+	0.415401i
$979$			516.667i			0.527750i
$980$	6.13509	+	6.62739i	0.00626029	+	0.00676264i
$981$	433.884			0.442288
$982$	427.115	+	427.115i	0.434944	+	0.434944i
$983$	−546.928	+	546.928i	−0.556387	+	0.556387i	−0.928277	−	0.371890i	$-0.878710\pi$
$983$	−546.928	+	546.928i	−0.556387	+	0.556387i	0.371890	+	0.928277i	$0.378710\pi$
$984$			27.0820i			0.0275224i
$985$	−9.95530	+	258.081i	−0.0101069	+	0.262011i
$986$	−109.265			−0.110817
$987$	264.624	+	264.624i	0.268109	+	0.268109i
$988$	−57.2730	+	57.2730i	−0.0579686	+	0.0579686i
$989$		−	2248.77i		−	2.27378i
$990$	−510.682	−	19.6993i	−0.515841	−	0.0198982i
$991$	−1132.40			−1.14269			−0.571343	−	0.820711i	$-0.693577\pi$
$991$	−1132.40			−1.14269			−0.571343	+	0.820711i	$0.693577\pi$
$992$	46.9694	+	46.9694i	0.0473481	+	0.0473481i
$993$	−711.231	+	711.231i	−0.716245	+	0.716245i
$994$			407.384i			0.409843i
$995$	688.409	−	637.272i	0.691869	−	0.640474i
$996$	−18.3560			−0.0184297
$997$	−44.1992	−	44.1992i	−0.0443322	−	0.0443322i	0.684593	−	0.728925i	$-0.259980\pi$
$997$	−44.1992	−	44.1992i	−0.0443322	−	0.0443322i	−0.728925	+	0.684593i	$0.759980\pi$
$998$	122.239	−	122.239i	0.122484	−	0.122484i
$999$			18.5505i			0.0185690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.22.3	✓	24
3.2	odd	2		315.3.o.b.127.10		24
5.2	odd	4		525.3.l.e.43.10		24
5.3	odd	4	inner	105.3.l.a.43.3	yes	24
5.4	even	2		525.3.l.e.232.10		24
15.8	even	4		315.3.o.b.253.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.3	✓	24	1.1	even	1	trivial
105.3.l.a.43.3	yes	24	5.3	odd	4	inner
315.3.o.b.127.10		24	3.2	odd	2
315.3.o.b.253.10		24	15.8	even	4
525.3.l.e.43.10		24	5.2	odd	4
525.3.l.e.232.10		24	5.4	even	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36784 - 1.36784i) q^{2} +(-1.22474 + 1.22474i) q^{3} -0.258033i q^{4} +(3.39663 + 3.66919i) q^{5} +3.35051 q^{6} +(1.87083 + 1.87083i) q^{7} +(-5.82430 + 5.82430i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.36784 - 1.36784i) q^{2} +(-1.22474 + 1.22474i) q^{3} -0.258033i q^{4} +(3.39663 + 3.66919i) q^{5} +3.35051 q^{6} +(1.87083 + 1.87083i) q^{7} +(-5.82430 + 5.82430i) q^{8} -3.00000i q^{9} +(0.372817 - 9.66489i) q^{10} +17.6130 q^{11} +(0.316024 + 0.316024i) q^{12} +(12.1245 - 12.1245i) q^{13} -5.11799i q^{14} +(-8.65382 - 0.333816i) q^{15} +14.9013 q^{16} +(13.8772 + 13.8772i) q^{17} +(-4.10352 + 4.10352i) q^{18} -18.3068i q^{19} +(0.946770 - 0.876441i) q^{20} -4.58258 q^{21} +(-24.0917 - 24.0917i) q^{22} +(-26.3956 + 26.3956i) q^{23} -14.2666i q^{24} +(-1.92585 + 24.9257i) q^{25} -33.1686 q^{26} +(3.67423 + 3.67423i) q^{27} +(0.482735 - 0.482735i) q^{28} -2.87815i q^{29} +(11.3804 + 12.2936i) q^{30} +16.1149 q^{31} +(2.91465 + 2.91465i) q^{32} +(-21.5714 + 21.5714i) q^{33} -37.9637i q^{34} +(-0.509912 + 13.2189i) q^{35} -0.774098 q^{36} +(2.52440 + 2.52440i) q^{37} +(-25.0408 + 25.0408i) q^{38} +29.6988i q^{39} +(-41.1534 - 1.58747i) q^{40} -1.89828 q^{41} +(6.26823 + 6.26823i) q^{42} +(-42.5974 + 42.5974i) q^{43} -4.54472i q^{44} +(11.0076 - 10.1899i) q^{45} +72.2098 q^{46} +(-57.7457 - 57.7457i) q^{47} +(-18.2503 + 18.2503i) q^{48} +7.00000i q^{49} +(36.7286 - 31.4601i) q^{50} -33.9922 q^{51} +(-3.12851 - 3.12851i) q^{52} +(66.5567 - 66.5567i) q^{53} -10.0515i q^{54} +(59.8247 + 64.6253i) q^{55} -21.7925 q^{56} +(22.4212 + 22.4212i) q^{57} +(-3.93685 + 3.93685i) q^{58} +16.4673i q^{59} +(-0.0861354 + 2.23297i) q^{60} -7.37026 q^{61} +(-22.0426 - 22.0426i) q^{62} +(5.61249 - 5.61249i) q^{63} -67.5787i q^{64} +(85.6692 + 3.30464i) q^{65} +59.0124 q^{66} +(-27.2024 - 27.2024i) q^{67} +(3.58078 - 3.58078i) q^{68} -64.6557i q^{69} +(18.7788 - 17.3839i) q^{70} -79.5984 q^{71} +(17.4729 + 17.4729i) q^{72} +(63.3051 - 63.3051i) q^{73} -6.90594i q^{74} +(-28.1690 - 32.8863i) q^{75} -4.72376 q^{76} +(32.9508 + 32.9508i) q^{77} +(40.6231 - 40.6231i) q^{78} +2.48684i q^{79} +(50.6141 + 54.6756i) q^{80} -9.00000 q^{81} +(2.59655 + 2.59655i) q^{82} +(-29.0421 + 29.0421i) q^{83} +1.18245i q^{84} +(-3.78237 + 98.0540i) q^{85} +116.533 q^{86} +(3.52500 + 3.52500i) q^{87} +(-102.583 + 102.583i) q^{88} +29.3345i q^{89} +(-28.9947 - 1.11845i) q^{90} +45.3656 q^{91} +(6.81092 + 6.81092i) q^{92} +(-19.7367 + 19.7367i) q^{93} +157.974i q^{94} +(67.1711 - 62.1814i) q^{95} -7.13941 q^{96} +(-89.1223 - 89.1223i) q^{97} +(9.57487 - 9.57487i) q^{98} -52.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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