LMFDB - Embedded newform 45.4.e.c.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.3
Root			$-0.785104 + 1.35984i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.4.e.c.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.785104 - 1.35984i) q^{2} +(-3.89934 + 3.43441i) q^{3} +(2.76722 - 4.79297i) q^{4} +(2.50000 - 4.33013i) q^{5} +(7.73164 + 2.60611i) q^{6} +(-17.1199 - 29.6525i) q^{7} -21.2519 q^{8} +(3.40971 - 26.7838i) q^{9} +O(q^{10})$	\(q+(-0.785104 - 1.35984i) q^{2} +(-3.89934 + 3.43441i) q^{3} +(2.76722 - 4.79297i) q^{4} +(2.50000 - 4.33013i) q^{5} +(7.73164 + 2.60611i) q^{6} +(-17.1199 - 29.6525i) q^{7} -21.2519 q^{8} +(3.40971 - 26.7838i) q^{9} -7.85104 q^{10} +(13.4480 + 23.2926i) q^{11} +(5.67066 + 28.1932i) q^{12} +(9.74401 - 16.8771i) q^{13} +(-26.8818 + 46.5607i) q^{14} +(5.12307 + 25.4707i) q^{15} +(-5.45281 - 9.44454i) q^{16} +29.1232 q^{17} +(-39.0987 + 16.3915i) q^{18} +47.1006 q^{19} +(-13.8361 - 23.9648i) q^{20} +(168.595 + 56.8286i) q^{21} +(21.1162 - 36.5743i) q^{22} +(-56.6083 + 98.0485i) q^{23} +(82.8684 - 72.9877i) q^{24} +(-12.5000 - 21.6506i) q^{25} -30.6003 q^{26} +(78.6910 + 116.150i) q^{27} -189.498 q^{28} +(-40.6219 - 70.3593i) q^{29} +(30.6139 - 26.9637i) q^{30} +(5.41811 - 9.38445i) q^{31} +(-93.5697 + 162.067i) q^{32} +(-132.435 - 44.6399i) q^{33} +(-22.8648 - 39.6029i) q^{34} -171.199 q^{35} +(-118.939 - 90.4594i) q^{36} +410.002 q^{37} +(-36.9789 - 64.0493i) q^{38} +(19.9677 + 99.2746i) q^{39} +(-53.1298 + 92.0234i) q^{40} +(221.755 - 384.091i) q^{41} +(-55.0869 - 273.879i) q^{42} +(-169.748 - 294.012i) q^{43} +148.854 q^{44} +(-107.453 - 81.7240i) q^{45} +177.774 q^{46} +(-118.121 - 204.591i) q^{47} +(53.6988 + 18.1003i) q^{48} +(-414.681 + 718.249i) q^{49} +(-19.6276 + 33.9960i) q^{50} +(-113.561 + 100.021i) q^{51} +(-53.9277 - 93.4055i) q^{52} +609.634 q^{53} +(96.1643 - 198.197i) q^{54} +134.480 q^{55} +(363.830 + 630.173i) q^{56} +(-183.661 + 161.763i) q^{57} +(-63.7849 + 110.479i) q^{58} +(-7.77272 + 13.4627i) q^{59} +(136.257 + 45.9283i) q^{60} +(-30.5255 - 52.8717i) q^{61} -17.0151 q^{62} +(-852.582 + 357.430i) q^{63} +206.603 q^{64} +(-48.7201 - 84.3856i) q^{65} +(43.2718 + 215.137i) q^{66} +(-108.445 + 187.832i) q^{67} +(80.5903 - 139.587i) q^{68} +(-116.003 - 576.740i) q^{69} +(134.409 + 232.803i) q^{70} +65.4315 q^{71} +(-72.4627 + 569.208i) q^{72} +711.811 q^{73} +(-321.895 - 557.538i) q^{74} +(123.099 + 41.4931i) q^{75} +(130.338 - 225.752i) q^{76} +(460.457 - 797.534i) q^{77} +(119.321 - 105.094i) q^{78} +(478.876 + 829.438i) q^{79} -54.5281 q^{80} +(-705.748 - 182.650i) q^{81} -696.404 q^{82} +(261.220 + 452.446i) q^{83} +(738.918 - 650.814i) q^{84} +(72.8080 - 126.107i) q^{85} +(-266.540 + 461.660i) q^{86} +(400.041 + 134.842i) q^{87} +(-285.796 - 495.012i) q^{88} -1602.24 q^{89} +(-26.7697 + 210.281i) q^{90} -667.266 q^{91} +(313.296 + 542.644i) q^{92} +(11.1029 + 55.2011i) q^{93} +(-185.474 + 321.251i) q^{94} +(117.751 - 203.952i) q^{95} +(-191.745 - 953.312i) q^{96} +(-400.969 - 694.499i) q^{97} +1302.27 q^{98} +(669.719 - 280.768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.785104	−	1.35984i	−0.277576	−	0.480776i	0.693206	−	0.720740i	$-0.256198\pi$
$2$	−0.785104	−	1.35984i	−0.277576	−	0.480776i	−0.970782	+	0.239964i	$0.922864\pi$
$3$	−3.89934	+	3.43441i	−0.750428	+	0.660952i
$3$	−3.89934	+	3.43441i	−0.750428	+	0.660952i
$4$	2.76722	−	4.79297i	0.345903	−	0.599121i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	7.73164	+	2.60611i	0.526071	+	0.177324i
$7$	−17.1199	−	29.6525i	−0.924387	−	1.60109i	−0.792544	−	0.609815i	$-0.791244\pi$
$7$	−17.1199	−	29.6525i	−0.924387	−	1.60109i	−0.131844	−	0.991271i	$-0.542090\pi$
$8$	−21.2519			−0.939210
$9$	3.40971	−	26.7838i	0.126285	−	0.991994i
$10$	−7.85104			−0.248272
$11$	13.4480	+	23.2926i	0.368611	+	0.638453i	0.989349	−	0.145565i	$-0.0465000\pi$
$11$	13.4480	+	23.2926i	0.368611	+	0.638453i	−0.620737	+	0.784019i	$0.713167\pi$
$12$	5.67066	+	28.1932i	0.136415	+	0.678223i
$13$	9.74401	−	16.8771i	0.207885	−	0.360067i	−0.743163	−	0.669110i	$-0.766675\pi$
$13$	9.74401	−	16.8771i	0.207885	−	0.360067i	0.951048	+	0.309043i	$0.100009\pi$
$14$	−26.8818	+	46.5607i	−0.513176	+	0.888847i
$15$	5.12307	+	25.4707i	0.0881847	+	0.438433i
$16$	−5.45281	−	9.44454i	−0.0852001	−	0.147571i
$17$	29.1232			0.415495			0.207747	−	0.978182i	$-0.433387\pi$
$17$	29.1232			0.415495			0.207747	+	0.978182i	$0.433387\pi$
$18$	−39.0987	+	16.3915i	−0.511981	+	0.214639i
$19$	47.1006			0.568717			0.284358	−	0.958718i	$-0.408219\pi$
$19$	47.1006			0.568717			0.284358	+	0.958718i	$0.408219\pi$
$20$	−13.8361	−	23.9648i	−0.154692	−	0.267935i
$21$	168.595	+	56.8286i	1.75193	+	0.590525i
$22$	21.1162	−	36.5743i	0.204636	−	0.354439i
$23$	−56.6083	+	98.0485i	−0.513202	+	0.888892i	0.486680	+	0.873580i	$0.338208\pi$
$23$	−56.6083	+	98.0485i	−0.513202	+	0.888892i	−0.999883	+	0.0153124i	$0.995126\pi$
$24$	82.8684	−	72.9877i	0.704810	−	0.620773i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−30.6003			−0.230816
$27$	78.6910	+	116.150i	0.560892	+	0.827889i
$28$	−189.498			−1.27899
$29$	−40.6219	−	70.3593i	−0.260114	−	0.450531i	0.706158	−	0.708054i	$-0.250427\pi$
$29$	−40.6219	−	70.3593i	−0.260114	−	0.450531i	−0.966272	+	0.257524i	$0.917093\pi$
$30$	30.6139	−	26.9637i	0.186310	−	0.164096i
$31$	5.41811	−	9.38445i	0.0313910	−	0.0543708i	−0.849903	−	0.526939i	$-0.823340\pi$
$31$	5.41811	−	9.38445i	0.0313910	−	0.0543708i	0.881294	+	0.472568i	$0.156673\pi$
$32$	−93.5697	+	162.067i	−0.516904	+	0.895304i
$33$	−132.435	−	44.6399i	−0.698603	−	0.235479i
$34$	−22.8648	−	39.6029i	−0.115332	−	0.199760i
$35$	−171.199			−0.826797
$36$	−118.939	−	90.4594i	−0.550642	−	0.418794i
$37$	410.002			1.82173			0.910864	−	0.412706i	$-0.135416\pi$
$37$	410.002			1.82173			0.910864	+	0.412706i	$0.135416\pi$
$38$	−36.9789	−	64.0493i	−0.157862	−	0.273426i
$39$	19.9677	+	99.2746i	0.0819843	+	0.407606i
$40$	−53.1298	+	92.0234i	−0.210014	+	0.363755i
$41$	221.755	−	384.091i	0.844691	−	1.46305i	−0.0411978	−	0.999151i	$-0.513117\pi$
$41$	221.755	−	384.091i	0.844691	−	1.46305i	0.885889	−	0.463897i	$-0.153549\pi$
$42$	−55.0869	−	273.879i	−0.202383	−	1.00620i
$43$	−169.748	−	294.012i	−0.602007	−	1.04271i	−0.992517	−	0.122108i	$-0.961035\pi$
$43$	−169.748	−	294.012i	−0.602007	−	1.04271i	0.390510	−	0.920599i	$-0.372299\pi$
$44$	148.854			0.510015
$45$	−107.453	−	81.7240i	−0.355959	−	0.270727i
$46$	177.774			0.569811
$47$	−118.121	−	204.591i	−0.366589	−	0.634950i	0.622441	−	0.782667i	$-0.286141\pi$
$47$	−118.121	−	204.591i	−0.366589	−	0.634950i	−0.989030	+	0.147716i	$0.952808\pi$
$48$	53.6988	+	18.1003i	0.161474	+	0.0544283i
$49$	−414.681	+	718.249i	−1.20898	+	2.09402i
$50$	−19.6276	+	33.9960i	−0.0555153	+	0.0961553i
$51$	−113.561	+	100.021i	−0.311799	+	0.274622i
$52$	−53.9277	−	93.4055i	−0.143816	−	0.249096i
$53$	609.634			1.57999			0.789997	−	0.613111i	$-0.210082\pi$
$53$	609.634			1.57999			0.789997	+	0.613111i	$0.210082\pi$
$54$	96.1643	−	198.197i	0.242339	−	0.499466i
$55$	134.480			0.329696
$56$	363.830	+	630.173i	0.868194	+	1.50376i
$57$	−183.661	+	161.763i	−0.426781	+	0.375894i
$58$	−63.7849	+	110.479i	−0.144403	+	0.250113i
$59$	−7.77272	+	13.4627i	−0.0171512	+	0.0297068i	−0.874474	−	0.485073i	$-0.838793\pi$
$59$	−7.77272	+	13.4627i	−0.0171512	+	0.0297068i	0.857322	+	0.514780i	$0.172126\pi$
$60$	136.257	+	45.9283i	0.293178	+	0.0988219i
$61$	−30.5255	−	52.8717i	−0.0640719	−	0.110976i	0.832210	−	0.554461i	$-0.187075\pi$
$61$	−30.5255	−	52.8717i	−0.0640719	−	0.110976i	−0.896282	+	0.443485i	$0.853742\pi$
$62$	−17.0151			−0.0348536
$63$	−852.582	+	357.430i	−1.70500	+	0.714793i
$64$	206.603			0.403521
$65$	−48.7201	−	84.3856i	−0.0929689	−	0.161027i
$66$	43.2718	+	215.137i	0.0807029	+	0.401235i
$67$	−108.445	+	187.832i	−0.197741	+	0.342497i	−0.947796	−	0.318879i	$-0.896694\pi$
$67$	−108.445	+	187.832i	−0.197741	+	0.342497i	0.750055	+	0.661376i	$0.230027\pi$
$68$	80.5903	−	139.587i	0.143721	−	0.248932i
$69$	−116.003	−	576.740i	−0.202394	−	1.00625i
$70$	134.409	+	232.803i	0.229499	+	0.397504i
$71$	65.4315			0.109370			0.0546852	−	0.998504i	$-0.482584\pi$
$71$	65.4315			0.109370			0.0546852	+	0.998504i	$0.482584\pi$
$72$	−72.4627	+	569.208i	−0.118609	+	0.931691i
$73$	711.811			1.14125			0.570624	−	0.821211i	$-0.306701\pi$
$73$	711.811			1.14125			0.570624	+	0.821211i	$0.306701\pi$
$74$	−321.895	−	557.538i	−0.505669	−	0.875844i
$75$	123.099	+	41.4931i	0.189523	+	0.0638828i
$76$	130.338	−	225.752i	0.196721	−	0.340730i
$77$	460.457	−	797.534i	0.681479	−	1.18036i
$78$	119.321	−	105.094i	0.173211	−	0.152558i
$79$	478.876	+	829.438i	0.681997	+	1.18125i	0.974370	+	0.224949i	$0.0722217\pi$
$79$	478.876	+	829.438i	0.681997	+	1.18125i	−0.292373	+	0.956304i	$0.594445\pi$
$80$	−54.5281			−0.0762053
$81$	−705.748	−	182.650i	−0.968104	−	0.250549i
$82$	−696.404			−0.937865
$83$	261.220	+	452.446i	0.345453	+	0.598343i	0.985436	−	0.170047i	$-0.0543918\pi$
$83$	261.220	+	452.446i	0.345453	+	0.598343i	−0.639983	+	0.768389i	$0.721058\pi$
$84$	738.918	−	650.814i	0.959792	−	0.845352i
$85$	72.8080	−	126.107i	0.0929075	−	0.160920i
$86$	−266.540	+	461.660i	−0.334206	+	0.578862i
$87$	400.041	+	134.842i	0.492976	+	0.166168i
$88$	−285.796	−	495.012i	−0.346204	−	0.599642i
$89$	−1602.24			−1.90828			−0.954141	−	0.299359i	$-0.903227\pi$
$89$	−1602.24			−1.90828			−0.954141	+	0.299359i	$0.903227\pi$
$90$	−26.7697	+	210.281i	−0.0313531	+	0.246284i
$91$	−667.266			−0.768664
$92$	313.296	+	542.644i	0.355036	+	0.614941i
$93$	11.1029	+	55.2011i	0.0123798	+	0.0615494i
$94$	−185.474	+	321.251i	−0.203513	+	0.352494i
$95$	117.751	−	203.952i	0.127169	−	0.220263i
$96$	−191.745	−	953.312i	−0.203854	−	1.01351i
$97$	−400.969	−	694.499i	−0.419714	−	0.726966i	0.576197	−	0.817311i	$-0.304536\pi$
$97$	−400.969	−	694.499i	−0.419714	−	0.726966i	−0.995910	+	0.0903455i	$0.971203\pi$
$98$	1302.27			1.34234
$99$	669.719	−	280.768i	0.679892	−	0.285033i
$100$	−138.361			−0.138361
$101$	−293.065	−	507.604i	−0.288724	−	0.500084i	0.684782	−	0.728748i	$-0.259898\pi$
$101$	−293.065	−	507.604i	−0.288724	−	0.500084i	−0.973505	+	0.228664i	$0.926564\pi$
$102$	225.170	+	75.8984i	0.218580	+	0.0736770i
$103$	410.337	−	710.725i	0.392541	−	0.679901i	−0.600243	−	0.799818i	$-0.704929\pi$
$103$	410.337	−	710.725i	0.392541	−	0.679901i	0.992784	+	0.119917i	$0.0382627\pi$
$104$	−207.079	+	358.671i	−0.195248	+	0.338179i
$105$	667.563	−	587.967i	0.620452	−	0.546473i
$106$	−478.626	−	829.005i	−0.438569	−	0.759623i
$107$	−1358.33			−1.22724			−0.613621	−	0.789600i	$-0.710288\pi$
$107$	−1358.33			−1.22724			−0.613621	+	0.789600i	$0.710288\pi$
$108$	774.457	−	55.7517i	0.690020	−	0.0496732i
$109$	489.495			0.430139			0.215069	−	0.976599i	$-0.431002\pi$
$109$	489.495			0.430139			0.215069	+	0.976599i	$0.431002\pi$
$110$	−105.581	−	182.871i	−0.0915158	−	0.158510i
$111$	−1598.74	+	1408.11i	−1.36708	+	1.20407i
$112$	−186.703	+	323.379i	−0.157516	+	0.272825i
$113$	−398.832	+	690.797i	−0.332026	+	0.575086i	−0.982909	−	0.184092i	$-0.941065\pi$
$113$	−398.832	+	690.797i	−0.332026	+	0.575086i	0.650883	+	0.759178i	$0.274399\pi$
$114$	364.165	+	122.750i	0.299185	+	0.100847i
$115$	283.042	+	490.243i	0.229511	+	0.397525i
$116$	−449.640			−0.359897
$117$	−418.810	−	318.528i	−0.330932	−	0.251692i
$118$	24.4096			0.0190431
$119$	−498.586	−	863.576i	−0.384078	−	0.665243i
$120$	−108.875	−	541.300i	−0.0828240	−	0.411781i
$121$	303.803	−	526.202i	0.228251	−	0.395343i
$122$	−47.9314	+	83.0196i	−0.0355697	+	0.0616085i
$123$	454.427	+	2259.30i	0.333124	+	1.65621i
$124$	−29.9862	−	51.9377i	−0.0217165	−	0.0376141i
$125$	−125.000			−0.0894427
$126$	1155.41	+	878.756i	0.816924	+	0.621316i
$127$	1728.22			1.20752			0.603759	−	0.797167i	$-0.293669\pi$
$127$	1728.22			1.20752			0.603759	+	0.797167i	$0.293669\pi$
$128$	586.352	+	1015.59i	0.404896	+	0.701301i
$129$	1671.66	+	563.469i	1.14094	+	0.384579i
$130$	−76.5007	+	132.503i	−0.0516120	+	0.0893945i
$131$	−319.551	+	553.478i	−0.213124	+	0.369142i	−0.952691	−	0.303942i	$-0.901697\pi$
$131$	−319.551	+	553.478i	−0.213124	+	0.369142i	0.739566	+	0.673084i	$0.235031\pi$
$132$	−580.434	+	511.226i	−0.382729	+	0.337095i
$133$	−806.357	−	1396.65i	−0.525715	−	0.910564i
$134$	340.562			0.219553
$135$	699.670	−	50.3679i	0.446059	−	0.0321110i
$136$	−618.923			−0.390237
$137$	1417.97	+	2456.00i	0.884274	+	1.53161i	0.846544	+	0.532319i	$0.178679\pi$
$137$	1417.97	+	2456.00i	0.884274	+	1.53161i	0.0377300	+	0.999288i	$0.487987\pi$
$138$	−693.201	+	610.548i	−0.427603	+	0.376618i
$139$	−87.4981	+	151.551i	−0.0533920	+	0.0924777i	−0.891486	−	0.453048i	$-0.850337\pi$
$139$	−87.4981	+	151.551i	−0.0533920	+	0.0924777i	0.838094	+	0.545526i	$0.183670\pi$
$140$	−473.745	+	820.551i	−0.285991	+	0.495352i
$141$	1163.24	+	392.096i	0.694770	+	0.234187i
$142$	−51.3706	−	88.9764i	−0.0303586	−	0.0525827i
$143$	524.150			0.306515
$144$	−271.554	+	113.844i	−0.157149	+	0.0658820i
$145$	−406.219			−0.232653
$146$	−558.846	−	967.949i	−0.316784	−	0.548685i
$147$	−849.776	−	4224.88i	−0.476791	−	2.37049i
$148$	1134.57	−	1965.13i	0.630141	−	1.09144i
$149$	−511.766	+	886.405i	−0.281379	+	0.487363i	−0.971725	−	0.236117i	$-0.924125\pi$
$149$	−511.766	+	886.405i	−0.281379	+	0.487363i	0.690345	+	0.723480i	$0.257459\pi$
$150$	−40.2214	−	199.971i	−0.0218938	−	0.108851i
$151$	436.998	+	756.902i	0.235512	+	0.407920i	0.959421	−	0.281976i	$-0.0909898\pi$
$151$	436.998	+	756.902i	0.235512	+	0.407920i	−0.723909	+	0.689895i	$0.757656\pi$
$152$	−1000.98			−0.534145
$153$	99.3015	−	780.031i	0.0524709	−	0.412168i
$154$	−1446.03			−0.756650
$155$	−27.0906	−	46.9222i	−0.0140385	−	0.0243154i
$156$	531.075	+	179.010i	0.272564	+	0.0918736i
$157$	−61.7762	+	107.000i	−0.0314031	+	0.0543917i	−0.881300	−	0.472558i	$-0.843331\pi$
$157$	−61.7762	+	107.000i	−0.0314031	+	0.0543917i	0.849897	+	0.526949i	$0.176664\pi$
$158$	751.936	−	1302.39i	0.378613	−	0.655776i
$159$	−2377.17	+	2093.73i	−1.18567	+	1.04430i
$160$	467.848	+	810.337i	0.231167	+	0.400392i
$161$	3876.51			1.89759
$162$	305.711	+	1103.10i	0.148265	+	0.534988i
$163$	−1410.89			−0.677972			−0.338986	−	0.940791i	$-0.610084\pi$
$163$	−1410.89			−0.677972			−0.338986	+	0.940791i	$0.610084\pi$
$164$	−1227.29	−	2125.73i	−0.584362	−	1.01214i
$165$	−524.383	+	461.859i	−0.247413	+	0.217913i
$166$	410.170	−	710.435i	0.191779	−	0.332172i
$167$	1013.85	−	1756.04i	0.469786	−	0.813692i	−0.529618	−	0.848236i	$-0.677665\pi$
$167$	1013.85	−	1756.04i	0.469786	−	0.813692i	0.999403	+	0.0345441i	$0.0109979\pi$
$168$	−3582.97	−	1207.72i	−1.64543	−	0.554627i
$169$	908.608	+	1573.76i	0.413568	+	0.716320i
$170$	−228.648			−0.103156
$171$	160.599	−	1261.53i	0.0718206	−	0.564164i
$172$	−1878.92			−0.832944
$173$	−1351.99	−	2341.71i	−0.594160	−	1.02912i	−0.993665	−	0.112384i	$-0.964151\pi$
$173$	−1351.99	−	2341.71i	−0.594160	−	1.02912i	0.399505	−	0.916731i	$-0.369182\pi$
$174$	−130.710	−	649.858i	−0.0569487	−	0.283135i
$175$	−427.997	+	741.313i	−0.184877	+	0.320217i
$176$	146.659	−	254.020i	0.0628115	−	0.108793i
$177$	−15.9281	−	79.1905i	−0.00676399	−	0.0336289i
$178$	1257.93	+	2178.79i	0.529694	+	0.917456i
$179$	−750.694			−0.313461			−0.156730	−	0.987641i	$-0.550095\pi$
$179$	−750.694			−0.313461			−0.156730	+	0.987641i	$0.550095\pi$
$180$	−689.048	+	288.871i	−0.285325	+	0.119618i
$181$	−1134.08			−0.465722			−0.232861	−	0.972510i	$-0.574809\pi$
$181$	−1134.08			−0.465722			−0.232861	+	0.972510i	$0.574809\pi$
$182$	523.873	+	907.375i	0.213363	+	0.369556i
$183$	300.612	+	101.328i	0.121431	+	0.0409309i
$184$	1203.03	−	2083.72i	0.482005	−	0.834857i
$185$	1025.01	−	1775.36i	0.407351	−	0.705552i
$186$	66.3478	−	58.4369i	0.0261551	−	0.0230366i
$187$	391.649	+	678.355i	0.153156	+	0.265274i
$188$	−1307.46			−0.507216
$189$	2096.95	−	4321.85i	0.807040	−	1.66333i
$190$	−369.789			−0.141196
$191$	267.627	+	463.544i	0.101387	+	0.175607i	0.912256	−	0.409620i	$-0.134339\pi$
$191$	267.627	+	463.544i	0.101387	+	0.175607i	−0.810870	+	0.585227i	$0.801005\pi$
$192$	−805.615	+	709.558i	−0.302814	+	0.266708i
$193$	−1311.77	+	2272.06i	−0.489241	+	0.847391i	−0.999923	−	0.0123786i	$-0.996060\pi$
$193$	−1311.77	+	2272.06i	−0.489241	+	0.847391i	0.510682	+	0.859770i	$0.329393\pi$
$194$	−629.605	+	1090.51i	−0.233005	+	0.403577i
$195$	479.791	+	161.724i	0.176198	+	0.0593912i
$196$	2295.03	+	3975.11i	0.836382	+	1.44866i
$197$	2954.08			1.06837			0.534186	−	0.845367i	$-0.320618\pi$
$197$	2954.08			1.06837			0.534186	+	0.845367i	$0.320618\pi$
$198$	−907.599	−	690.279i	−0.325759	−	0.247758i
$199$	2639.35			0.940192			0.470096	−	0.882615i	$-0.344219\pi$
$199$	2639.35			0.940192			0.470096	+	0.882615i	$0.344219\pi$
$200$	265.649	+	460.117i	0.0939210	+	0.162676i
$201$	−222.228	−	1104.86i	−0.0779838	−	0.387717i
$202$	−460.174	+	797.044i	−0.160286	+	0.277623i
$203$	−1390.89	+	2409.09i	−0.480892	+	0.832929i
$204$	165.148	+	821.076i	0.0566797	+	0.281798i
$205$	−1108.78	−	1920.46i	−0.377757	−	0.654295i
$206$	−1288.63			−0.435841
$207$	2433.10	+	1850.50i	0.816966	+	0.621348i
$208$	−212.529			−0.0708473
$209$	633.409	+	1097.10i	0.209635	+	0.363099i
$210$	−1323.65	−	446.164i	−0.434954	−	0.146611i
$211$	995.327	−	1723.96i	0.324745	−	0.562474i	−0.656716	−	0.754138i	$-0.728055\pi$
$211$	995.327	−	1723.96i	0.324745	−	0.562474i	0.981461	+	0.191664i	$0.0613883\pi$
$212$	1686.99	−	2921.96i	0.546524	−	0.946607i
$213$	−255.140	+	224.718i	−0.0820746	+	0.0722885i
$214$	1066.43	+	1847.12i	0.340654	+	0.590029i
$215$	−1697.48			−0.538452
$216$	−1672.33	−	2468.40i	−0.526796	−	0.777562i
$217$	−371.030			−0.116070
$218$	−384.305	−	665.635i	−0.119396	−	0.206800i
$219$	−2775.59	+	2444.65i	−0.856425	+	0.754310i
$220$	372.136	−	644.558i	0.114043	−	0.197528i
$221$	283.777	−	491.516i	0.0863751	−	0.149606i
$222$	3169.99	+	1068.51i	0.958359	+	0.323035i
$223$	337.450	+	584.481i	0.101333	+	0.175515i	0.912234	−	0.409669i	$-0.134356\pi$
$223$	337.450	+	584.481i	0.101333	+	0.175515i	−0.810901	+	0.585184i	$0.801022\pi$
$224$	6407.61			1.91128
$225$	−622.508	+	260.976i	−0.184447	+	0.0773261i
$226$	1252.50			0.368650
$227$	−945.926	−	1638.39i	−0.276579	−	0.479048i	0.693954	−	0.720020i	$-0.255867\pi$
$227$	−945.926	−	1638.39i	−0.276579	−	0.479048i	−0.970532	+	0.240972i	$0.922534\pi$
$228$	267.092	+	1327.92i	0.0775815	+	0.385717i
$229$	−1704.26	+	2951.86i	−0.491792	+	0.851810i	−0.999955	−	0.00945146i	$-0.996991\pi$
$229$	−1704.26	+	2951.86i	−0.491792	+	0.851810i	0.508163	+	0.861261i	$0.330325\pi$
$230$	444.435	−	769.783i	0.127414	−	0.220687i
$231$	943.580	+	4691.25i	0.268758	+	1.33620i
$232$	863.294	+	1495.27i	0.244302	+	0.423143i
$233$	−2841.86			−0.799041			−0.399521	−	0.916724i	$-0.630823\pi$
$233$	−2841.86			−0.799041			−0.399521	+	0.916724i	$0.630823\pi$
$234$	−104.338	+	819.593i	−0.0291486	+	0.228968i
$235$	−1181.21			−0.327887
$236$	43.0177	+	74.5088i	0.0118653	+	0.0205513i
$237$	−4715.93	−	1589.60i	−1.29254	−	0.435679i
$238$	−782.884	+	1356.00i	−0.213222	+	0.369311i
$239$	−809.803	+	1402.62i	−0.219171	+	0.379615i	−0.954555	−	0.298036i	$-0.903668\pi$
$239$	−809.803	+	1402.62i	−0.219171	+	0.379615i	0.735384	+	0.677651i	$0.237002\pi$
$240$	212.624	−	187.272i	0.0571866	−	0.0503680i
$241$	−13.3504	−	23.1235i	−0.00356835	−	0.00618057i	0.864236	−	0.503087i	$-0.167803\pi$
$241$	−13.3504	−	23.1235i	−0.00356835	−	0.00618057i	−0.867804	+	0.496907i	$0.834469\pi$
$242$	−954.068			−0.253429
$243$	3379.24	−	1711.61i	0.892093	−	0.451851i
$244$	−337.883			−0.0886506
$245$	2073.41	+	3591.25i	0.540674	+	0.936475i
$246$	2715.52	−	2391.73i	0.703801	−	0.619884i
$247$	458.949	−	794.923i	0.118228	−	0.204776i
$248$	−115.145	+	199.437i	−0.0294828	+	0.0510657i
$249$	−2572.47	−	867.107i	−0.654714	−	0.220685i
$250$	98.1381	+	169.980i	0.0248272	+	0.0430019i
$251$	−427.354			−0.107467			−0.0537337	−	0.998555i	$-0.517112\pi$
$251$	−427.354			−0.107467			−0.0537337	+	0.998555i	$0.517112\pi$
$252$	−646.133	+	5075.49i	−0.161518	+	1.26875i
$253$	−3045.07			−0.756689
$254$	−1356.83	−	2350.10i	−0.335178	−	0.580546i
$255$	149.200	+	741.787i	0.0366403	+	0.182167i
$256$	1747.11	−	3026.08i	0.426540	−	0.738789i
$257$	−1920.77	+	3326.88i	−0.466204	+	0.807490i	−0.999255	−	0.0385936i	$-0.987712\pi$
$257$	−1920.77	+	3326.88i	−0.466204	+	0.807490i	0.533051	+	0.846083i	$0.321046\pi$
$258$	−546.200	−	2715.58i	−0.131802	−	0.655288i
$259$	−7019.19	−	12157.6i	−1.68398	−	2.91674i
$260$	−539.277			−0.128633
$261$	−2023.00	+	848.107i	−0.479772	+	0.201136i
$262$	1003.52			0.236633
$263$	399.437	+	691.845i	0.0936514	+	0.162209i	0.909045	−	0.416698i	$-0.136813\pi$
$263$	399.437	+	691.845i	0.0936514	+	0.162209i	−0.815394	+	0.578907i	$0.803479\pi$
$264$	2814.49	+	948.684i	0.656135	+	0.221165i
$265$	1524.08	−	2639.79i	0.353297	−	0.611929i
$266$	−1266.15	+	2193.03i	−0.291852	+	0.505502i
$267$	6247.68	−	5502.74i	1.43203	−	1.26128i
$268$	600.181	+	1039.54i	0.136798	+	0.236941i
$269$	7934.42			1.79840			0.899201	−	0.437536i	$-0.144149\pi$
$269$	7934.42			1.79840			0.899201	+	0.437536i	$0.144149\pi$
$270$	−617.806	−	911.896i	−0.139254	−	0.205542i
$271$	−2309.09			−0.517592			−0.258796	−	0.965932i	$-0.583326\pi$
$271$	−2309.09			−0.517592			−0.258796	+	0.965932i	$0.583326\pi$
$272$	−158.803	−	275.055i	−0.0354002	−	0.0613150i
$273$	2601.90	−	2291.66i	0.576828	−	0.508050i
$274$	2226.51	−	3856.43i	0.490907	−	0.850276i
$275$	336.200	−	582.315i	0.0737223	−	0.127691i
$276$	−3085.31	−	1039.97i	−0.672875	−	0.226807i
$277$	−380.651	−	659.307i	−0.0825672	−	0.143011i	0.821785	−	0.569798i	$-0.192979\pi$
$277$	−380.651	−	659.307i	−0.0825672	−	0.143011i	−0.904352	+	0.426787i	$0.859645\pi$
$278$	274.781			0.0592815
$279$	−232.877	−	177.116i	−0.0499713	−	0.0380059i
$280$	3638.30			0.776536
$281$	643.638	+	1114.81i	0.136641	+	0.236670i	0.926223	−	0.376975i	$-0.123036\pi$
$281$	643.638	+	1114.81i	0.136641	+	0.236670i	−0.789582	+	0.613645i	$0.789703\pi$
$282$	−380.079	−	1889.66i	−0.0802601	−	0.399034i
$283$	1363.25	−	2361.22i	0.286350	−	0.495972i	−0.686586	−	0.727049i	$-0.740891\pi$
$283$	1363.25	−	2361.22i	0.286350	−	0.495972i	0.972936	+	0.231076i	$0.0742248\pi$
$284$	181.064	−	313.611i	0.0378315	−	0.0655261i
$285$	241.299	+	1199.68i	0.0501521	+	0.249344i
$286$	−411.512	−	712.760i	−0.0850813	−	0.147365i
$287$	−15185.7			−3.12329
$288$	4021.74	+	3058.76i	0.822859	+	0.625830i
$289$	−4064.84			−0.827364
$290$	318.925	+	552.394i	0.0645790	+	0.111854i
$291$	3948.71	+	1331.00i	0.795454	+	0.268125i
$292$	1969.74	−	3411.69i	0.394761	−	0.683746i
$293$	48.1869	−	83.4622i	0.00960789	−	0.0166414i	−0.861181	−	0.508298i	$-0.830275\pi$
$293$	48.1869	−	83.4622i	0.00960789	−	0.0166414i	0.870789	+	0.491656i	$0.163608\pi$
$294$	−5078.00	+	4472.53i	−1.00733	+	0.887223i
$295$	38.8636	+	67.3137i	0.00767026	+	0.0132853i
$296$	−8713.33			−1.71099
$297$	−1647.19	+	3394.90i	−0.321817	+	0.663273i
$298$	1607.16			0.312417
$299$	1103.18	+	1910.77i	0.213374	+	0.369575i
$300$	539.517	−	475.188i	0.103830	−	0.0914500i
$301$	−5812.13	+	10066.9i	−1.11298	+	1.92773i
$302$	686.178	−	1188.50i	0.130745	−	0.226458i
$303$	2886.08	+	972.815i	0.547198	+	0.184445i
$304$	−256.831	−	444.844i	−0.0484547	−	0.0839261i
$305$	−305.255			−0.0573076
$306$	−1138.68	+	477.372i	−0.212726	+	0.0891814i
$307$	5258.02			0.977495			0.488747	−	0.872425i	$-0.337454\pi$
$307$	5258.02			0.977495			0.488747	+	0.872425i	$0.337454\pi$
$308$	−2548.37	−	4413.91i	−0.471451	−	0.816577i
$309$	840.874	+	4180.62i	0.154808	+	0.769668i
$310$	−42.5378	+	73.6777i	−0.00779351	+	0.0134988i
$311$	2615.66	−	4530.45i	0.476914	−	0.826039i	−0.522736	−	0.852495i	$-0.675089\pi$
$311$	2615.66	−	4530.45i	0.476914	−	0.826039i	0.999650	+	0.0264555i	$0.00842202\pi$
$312$	−424.351	−	2109.77i	−0.0770005	−	0.382828i
$313$	1996.33	+	3457.74i	0.360509	+	0.624419i	0.988045	−	0.154168i	$-0.0492698\pi$
$313$	1996.33	+	3457.74i	0.360509	+	0.624419i	−0.627536	+	0.778588i	$0.715936\pi$
$314$	194.003			0.0348670
$315$	−583.738	+	4585.36i	−0.104412	+	0.820178i
$316$	5300.63			0.943619
$317$	2366.79	+	4099.40i	0.419344	+	0.726325i	0.995874	−	0.0907509i	$-0.0289267\pi$
$317$	2366.79	+	4099.40i	0.419344	+	0.726325i	−0.576529	+	0.817076i	$0.695593\pi$
$318$	4713.47	+	1588.78i	0.831189	+	0.280170i
$319$	1092.57	−	1892.38i	0.191762	−	0.332141i
$320$	516.507	−	894.617i	0.0902301	−	0.156283i
$321$	5296.60	−	4665.07i	0.920958	−	0.811148i
$322$	−3043.47	−	5271.44i	−0.526726	−	0.912317i
$323$	1371.72			0.236299
$324$	−2828.40	+	2877.19i	−0.484979	+	0.493346i
$325$	−487.201			−0.0831539
$326$	1107.70	+	1918.59i	0.188189	+	0.325953i
$327$	−1908.71	+	1681.12i	−0.322788	+	0.284301i
$328$	−4712.72	+	8162.67i	−0.793343	+	1.37411i
$329$	−4044.43	+	7005.15i	−0.677740	+	1.17388i
$330$	1039.75	+	350.470i	0.173444	+	0.0584629i
$331$	−4684.92	−	8114.52i	−0.777965	−	1.34747i	−0.933113	−	0.359583i	$-0.882919\pi$
$331$	−4684.92	−	8114.52i	−0.777965	−	1.34747i	0.155148	−	0.987891i	$-0.450415\pi$
$332$	2891.42			0.477973
$333$	1397.99	−	10981.4i	0.230058	−	1.80714i
$334$	−3183.92			−0.521605
$335$	542.223	+	939.159i	0.0884323	+	0.153169i
$336$	−382.597	−	1902.18i	−0.0621201	−	0.308846i
$337$	−2724.41	+	4718.83i	−0.440381	+	0.762762i	−0.997718	−	0.0675246i	$-0.978490\pi$
$337$	−2724.41	+	4718.83i	−0.440381	+	0.762762i	0.557337	+	0.830287i	$0.311823\pi$
$338$	1426.71	−	2471.13i	0.229593	−	0.397667i
$339$	−817.296	−	4063.40i	−0.130942	−	0.651014i
$340$	−402.952	−	697.933i	−0.0642739	−	0.111326i
$341$	291.451			0.0462843
$342$	−1841.57	+	772.047i	−0.291172	+	0.122069i
$343$	16653.0			2.62150
$344$	3607.47	+	6248.31i	0.565411	+	0.979321i
$345$	−2787.37	−	939.542i	−0.434976	−	0.146618i
$346$	−2122.90	+	3676.98i	−0.329850	+	0.571316i
$347$	1948.77	−	3375.38i	0.301486	−	0.522189i	−0.674987	−	0.737830i	$-0.735851\pi$
$347$	1948.77	−	3375.38i	0.301486	−	0.522189i	0.976473	+	0.215641i	$0.0691840\pi$
$348$	1753.30	−	1544.25i	0.270077	−	0.237874i
$349$	3129.53	+	5420.51i	0.480000	+	0.831384i	0.999737	−	0.0229422i	$-0.00730337\pi$
$349$	3129.53	+	5420.51i	0.480000	+	0.831384i	−0.519737	+	0.854326i	$0.673970\pi$
$350$	1344.09			0.205270
$351$	2727.04	−	196.314i	0.414697	−	0.0298532i
$352$	−5033.30			−0.762147
$353$	−171.433	−	296.931i	−0.0258483	−	0.0447706i	0.852812	−	0.522218i	$-0.174895\pi$
$353$	−171.433	−	296.931i	−0.0258483	−	0.0447706i	−0.878660	+	0.477448i	$0.841562\pi$
$354$	−95.1813	+	83.8324i	−0.0142905	+	0.0125866i
$355$	163.579	−	283.327i	0.0244559	−	0.0423589i
$356$	−4433.75	+	7679.48i	−0.660080	+	1.14329i
$357$	4910.03	+	1655.03i	0.727917	+	0.245360i
$358$	589.373	+	1020.82i	0.0870093	+	0.150705i
$359$	10448.9			1.53613			0.768066	−	0.640371i	$-0.221219\pi$
$359$	10448.9			1.53613			0.768066	+	0.640371i	$0.221219\pi$
$360$	2283.58	+	1736.79i	0.334321	+	0.254269i
$361$	−4640.53			−0.676561
$362$	890.373	+	1542.17i	0.129273	+	0.223908i
$363$	622.561	+	3095.22i	0.0900164	+	0.447540i
$364$	−1846.47	+	3198.18i	−0.265883	+	0.460523i
$365$	1779.53	−	3082.23i	0.255191	−	0.442004i
$366$	−98.2222	−	488.337i	−0.0140278	−	0.0697426i
$367$	2586.87	+	4480.58i	0.367938	+	0.637288i	0.989243	−	0.146281i	$-0.0467305\pi$
$367$	2586.87	+	4480.58i	0.367938	+	0.637288i	−0.621305	+	0.783569i	$0.713397\pi$
$368$	1234.70			0.174900
$369$	−9531.32	−	7249.09i	−1.34466	−	1.02269i
$370$	−3218.95			−0.452284
$371$	−10436.9	−	18077.2i	−1.46053	−	2.52970i
$372$	295.302	+	99.5378i	0.0411577	+	0.0138731i
$373$	−1050.53	+	1819.58i	−0.145830	+	0.252585i	−0.929682	−	0.368362i	$-0.879919\pi$
$373$	−1050.53	+	1819.58i	−0.145830	+	0.252585i	0.783852	+	0.620947i	$0.213252\pi$
$374$	614.970	−	1065.16i	0.0850250	−	0.147268i
$375$	487.418	−	429.301i	0.0671204	−	0.0591173i
$376$	2510.29	+	4347.95i	0.344304	+	0.596352i
$377$	−1583.28			−0.216295
$378$	−7523.36	+	541.593i	−1.02370	+	0.0736945i
$379$	11242.6			1.52374			0.761868	−	0.647732i	$-0.224282\pi$
$379$	11242.6			1.52374			0.761868	+	0.647732i	$0.224282\pi$
$380$	−651.689	−	1128.76i	−0.0879762	−	0.152379i
$381$	−6738.92	+	5935.41i	−0.906155	+	0.798111i
$382$	420.231	−	727.862i	0.0562851	−	0.0974886i
$383$	−3397.44	+	5884.53i	−0.453266	+	0.785080i	−0.998587	−	0.0531478i	$-0.983075\pi$
$383$	−3397.44	+	5884.53i	−0.453266	+	0.785080i	0.545321	+	0.838227i	$0.316408\pi$
$384$	−5774.34	−	1946.37i	−0.767372	−	0.258659i
$385$	−2302.28	−	3987.67i	−0.304767	−	0.527871i
$386$	4119.52			0.543207
$387$	−8453.56	+	3544.01i	−1.11038	+	0.465509i
$388$	−4438.28			−0.580721
$389$	−3524.70	−	6104.96i	−0.459407	−	0.795717i	0.539522	−	0.841971i	$-0.318605\pi$
$389$	−3524.70	−	6104.96i	−0.459407	−	0.795717i	−0.998930	+	0.0462544i	$0.985272\pi$
$390$	−156.767	−	779.409i	−0.0203544	−	0.101197i
$391$	−1648.62	+	2855.49i	−0.213233	+	0.369330i
$392$	8812.77	−	15264.2i	1.13549	−	1.96673i
$393$	−654.832	−	3255.67i	−0.0840506	−	0.417879i
$394$	−2319.26	−	4017.08i	−0.296555	−	0.513648i
$395$	4788.76			0.609997
$396$	507.550	−	3986.89i	0.0644074	−	0.505931i
$397$	3011.36			0.380694			0.190347	−	0.981717i	$-0.439039\pi$
$397$	3011.36			0.380694			0.190347	+	0.981717i	$0.439039\pi$
$398$	−2072.16	−	3589.09i	−0.260975	−	0.452022i
$399$	7940.93	+	2676.66i	0.996350	+	0.335841i
$400$	−136.320	+	236.114i	−0.0170400	+	0.0295142i
$401$	2084.07	−	3609.72i	0.259535	−	0.449528i	−0.706582	−	0.707631i	$-0.749764\pi$
$401$	2084.07	−	3609.72i	0.259535	−	0.449528i	0.966118	+	0.258103i	$0.0830973\pi$
$402$	−1327.97	+	1169.63i	−0.164758	+	0.145114i
$403$	−105.588	−	182.884i	−0.0130514	−	0.0226058i
$404$	−3243.91			−0.399481
$405$	−2555.27	+	2599.35i	−0.313512	+	0.318921i
$406$	4367.96			0.533937
$407$	5513.71	+	9550.03i	0.671510	+	1.16309i
$408$	2413.39	−	2125.63i	0.292845	−	0.257928i
$409$	6302.68	−	10916.6i	0.761974	−	1.31978i	−0.179858	−	0.983693i	$-0.557564\pi$
$409$	6302.68	−	10916.6i	0.761974	−	1.31978i	0.941832	−	0.336085i	$-0.109103\pi$
$410$	−1741.01	+	3015.52i	−0.209713	+	0.363234i
$411$	−13964.1	−	4706.88i	−1.67590	−	0.564899i
$412$	−2270.99	−	3933.47i	−0.271562	−	0.470359i
$413$	532.272			0.0634175
$414$	606.156	−	4761.46i	0.0719588	−	0.565249i
$415$	2612.20			0.308983
$416$	1823.49	+	3158.37i	0.214913	+	0.372240i
$417$	−179.303	−	891.454i	−0.0210564	−	0.104687i
$418$	994.584	−	1722.67i	0.116380	−	0.201575i
$419$	2572.24	−	4455.24i	0.299909	−	0.519458i	−0.676206	−	0.736713i	$-0.736377\pi$
$419$	2572.24	−	4455.24i	0.299909	−	0.519458i	0.976115	+	0.217255i	$0.0697102\pi$
$420$	−970.812	−	4826.64i	−0.112788	−	0.560752i
$421$	1685.03	+	2918.56i	0.195068	+	0.337867i	0.946923	−	0.321461i	$-0.104174\pi$
$421$	1685.03	+	2918.56i	0.195068	+	0.337867i	−0.751855	+	0.659329i	$0.770841\pi$
$422$	−3125.74			−0.360566
$423$	−5882.49	+	2466.13i	−0.676162	+	0.283469i
$424$	−12955.9			−1.48395
$425$	−364.040	−	630.536i	−0.0415495	−	0.0719658i
$426$	505.893	+	170.522i	0.0575366	+	0.0193939i
$427$	−1045.19	+	1810.31i	−0.118454	+	0.205169i
$428$	−3758.81	+	6510.45i	−0.424507	+	0.735267i
$429$	−2043.84	+	1800.14i	−0.230017	+	0.202592i
$430$	1332.70	+	2308.30i	0.149461	+	0.258875i
$431$	14948.3			1.67061			0.835306	−	0.549785i	$-0.185290\pi$
$431$	14948.3			1.67061			0.835306	+	0.549785i	$0.185290\pi$
$432$	667.893	−	1376.54i	0.0743843	−	0.153308i
$433$	−14011.1			−1.55504			−0.777520	−	0.628858i	$-0.783523\pi$
$433$	−14011.1			−1.55504			−0.777520	+	0.628858i	$0.783523\pi$
$434$	291.297	+	504.542i	0.0322182	+	0.0558036i
$435$	1583.99	−	1395.12i	0.174589	−	0.153772i
$436$	1354.54	−	2346.13i	0.148786	−	0.257705i
$437$	−2666.29	+	4618.14i	−0.291867	+	0.505528i
$438$	5503.46	+	1855.06i	0.600378	+	0.202370i
$439$	2391.10	+	4141.50i	0.259956	+	0.450257i	0.966230	−	0.257681i	$-0.0829585\pi$
$439$	2391.10	+	4141.50i	0.259956	+	0.450257i	−0.706274	+	0.707939i	$0.749625\pi$
$440$	−2857.96			−0.309654
$441$	17823.5	+	13555.8i	1.92458	+	1.46375i
$442$	−891.178			−0.0959027
$443$	−2387.01	−	4134.42i	−0.256005	−	0.443413i	0.709163	−	0.705044i	$-0.249073\pi$
$443$	−2387.01	−	4134.42i	−0.256005	−	0.443413i	−0.965168	+	0.261631i	$0.915740\pi$
$444$	2324.99	+	11559.3i	0.248511	+	1.23554i
$445$	−4005.60	+	6937.90i	−0.426705	+	0.739074i
$446$	529.867	−	917.757i	0.0562555	−	0.0974374i
$447$	−1048.72	−	5214.01i	−0.110969	−	0.551709i
$448$	−3537.02	−	6126.30i	−0.373010	−	0.646072i
$449$	−855.812			−0.0899516			−0.0449758	−	0.998988i	$-0.514321\pi$
$449$	−855.812			−0.0899516			−0.0449758	+	0.998988i	$0.514321\pi$
$450$	843.620	+	641.619i	0.0883747	+	0.0672138i
$451$	11928.7			1.24545
$452$	2207.31	+	3823.18i	0.229697	+	0.397848i
$453$	−4303.51	−	1450.59i	−0.446350	−	0.150452i
$454$	−1485.30	+	2572.62i	−0.153543	+	0.265945i
$455$	−1668.16	+	2889.35i	−0.171879	+	0.297702i
$456$	3903.15	−	3437.76i	0.400837	−	0.353044i
$457$	6708.99	+	11620.3i	0.686725	+	1.18944i	0.972891	+	0.231263i	$0.0742857\pi$
$457$	6708.99	+	11620.3i	0.686725	+	1.18944i	−0.286166	+	0.958180i	$0.592381\pi$
$458$	5352.08			0.546040
$459$	2291.73	+	3382.65i	0.233048	+	0.343984i
$460$	3132.96			0.317554
$461$	7942.99	+	13757.7i	0.802477	+	1.38993i	0.917981	+	0.396625i	$0.129819\pi$
$461$	7942.99	+	13757.7i	0.802477	+	1.38993i	−0.115503	+	0.993307i	$0.536848\pi$
$462$	5638.55	−	4966.24i	0.567812	−	0.500109i
$463$	−3280.69	+	5682.32i	−0.329302	+	0.570367i	−0.982373	−	0.186929i	$-0.940147\pi$
$463$	−3280.69	+	5682.32i	−0.329302	+	0.570367i	0.653072	+	0.757296i	$0.273480\pi$
$464$	−443.007	+	767.311i	−0.0443235	+	0.0767705i
$465$	266.785	+	89.9257i	0.0266062	+	0.00896818i
$466$	2231.16	+	3864.48i	0.221795	+	0.384160i
$467$	−6792.37			−0.673048			−0.336524	−	0.941675i	$-0.609251\pi$
$467$	−6792.37			−0.673048			−0.336524	+	0.941675i	$0.609251\pi$
$468$	−2685.64	+	1125.91i	−0.265264	+	0.111207i
$469$	7426.25			0.731156
$470$	927.371	+	1606.25i	0.0910137	+	0.157640i
$471$	−126.593	−	629.392i	−0.0123845	−	0.0615730i
$472$	165.185	−	286.109i	0.0161086	−	0.0279009i
$473$	4565.54	−	7907.74i	0.443813	−	0.768707i
$474$	1540.89	+	7660.92i	0.149315	+	0.742358i
$475$	−588.757	−	1019.76i	−0.0568717	−	0.0985046i
$476$	−5518.79			−0.531415
$477$	2078.67	−	16328.3i	0.199530	−	1.56734i
$478$	2543.12			0.243346
$479$	−8826.24	−	15287.5i	−0.841923	−	1.45825i	−0.888267	−	0.459328i	$-0.848090\pi$
$479$	−8826.24	−	15287.5i	−0.841923	−	1.45825i	0.0463438	−	0.998926i	$-0.485243\pi$
$480$	−4607.33	−	1553.00i	−0.438114	−	0.147676i
$481$	3995.07	−	6919.66i	0.378710	−	0.655945i
$482$	−20.9629	+	36.3088i	−0.00198098	+	0.00343116i
$483$	−15115.8	+	13313.5i	−1.42401	+	1.25422i
$484$	−1681.38	−	2912.23i	−0.157906	−	0.273501i
$485$	−4009.69			−0.375403
$486$	−4980.58	−	3251.44i	−0.464863	−	0.303474i
$487$	−5318.16			−0.494844			−0.247422	−	0.968908i	$-0.579583\pi$
$487$	−5318.16			−0.494844			−0.247422	+	0.968908i	$0.579583\pi$
$488$	648.724	+	1123.62i	0.0601770	+	0.104230i
$489$	5501.54	−	4845.57i	0.508769	−	0.448107i
$490$	3255.68	−	5639.01i	0.300157	−	0.519886i
$491$	−5434.98	+	9413.66i	−0.499546	+	0.865239i	−1.00000		0.000523887i	$-0.999833\pi$
$491$	−5434.98	+	9413.66i	−0.499546	+	0.865239i	0.500454	+	0.865763i	$0.333167\pi$
$492$	12086.3	+	4073.93i	1.10750	+	0.373307i
$493$	−1183.04	−	2049.09i	−0.108076	−	0.187193i
$494$	−1441.29			−0.131269
$495$	458.537	−	3601.89i	0.0416358	−	0.327056i
$496$	−118.176			−0.0106981
$497$	−1120.18	−	1940.21i	−0.101101	−	0.175111i
$498$	840.531	+	4178.92i	0.0756328	+	0.376028i
$499$	−5185.25	+	8981.12i	−0.465178	+	0.805711i	−0.999210	−	0.0397529i	$-0.987343\pi$
$499$	−5185.25	+	8981.12i	−0.465178	+	0.805711i	0.534032	+	0.845464i	$0.320676\pi$
$500$	−345.903	+	599.121i	−0.0309385	+	0.0535870i
$501$	2077.61	+	10329.4i	0.185271	+	0.921123i
$502$	335.517	+	581.133i	0.0298304	+	0.0516678i
$503$	−12396.4			−1.09886			−0.549432	−	0.835538i	$-0.685156\pi$
$503$	−12396.4			−1.09886			−0.549432	+	0.835538i	$0.685156\pi$
$504$	18119.0	−	7596.07i	1.60136	−	0.671341i
$505$	−2930.65			−0.258242
$506$	2390.70	+	4140.82i	0.210039	+	0.363798i
$507$	−8947.89	−	3016.08i	−0.783806	−	0.264199i
$508$	4782.37	−	8283.30i	0.417684	−	0.723449i
$509$	−2780.52	+	4816.00i	−0.242130	+	0.419382i	−0.961321	−	0.275431i	$-0.911180\pi$
$509$	−2780.52	+	4816.00i	−0.242130	+	0.419382i	0.719190	+	0.694813i	$0.244513\pi$
$510$	891.574	−	785.269i	0.0774109	−	0.0681809i
$511$	−12186.1	−	21107.0i	−1.05496	−	1.82724i
$512$	3894.99			0.336203
$513$	3706.39	+	5470.72i	0.318989	+	0.470834i
$514$	6032.03			0.517629
$515$	−2051.69	−	3553.63i	−0.175550	−	0.304061i
$516$	7326.55	−	6452.98i	0.625065	−	0.550536i
$517$	3176.97	−	5502.68i	0.270258	−	0.468100i
$518$	−11021.6	+	19090.0i	−0.934868	+	1.61924i
$519$	13314.2	+	4487.85i	1.12607	+	0.379566i
$520$	1035.39	+	1793.36i	0.0873174	+	0.151238i
$521$	−2613.39			−0.219760			−0.109880	−	0.993945i	$-0.535047\pi$
$521$	−2613.39			−0.219760			−0.109880	+	0.993945i	$0.535047\pi$
$522$	2741.56	+	2085.11i	0.229875	+	0.174833i
$523$	−2927.73			−0.244781			−0.122391	−	0.992482i	$-0.539056\pi$
$523$	−2927.73			−0.244781			−0.122391	+	0.992482i	$0.539056\pi$
$524$	1768.53	+	3063.19i	0.147440	+	0.255374i
$525$	−877.063	−	4360.55i	−0.0729108	−	0.362495i
$526$	627.199	−	1086.34i	0.0519908	−	0.0900508i
$527$	157.793	−	273.305i	0.0130428	−	0.0225908i
$528$	300.537	+	1494.20i	0.0247712	+	0.123156i
$529$	−325.506	−	563.793i	−0.0267532	−	0.0463379i
$530$	−4786.26			−0.392268
$531$	334.081	+	254.087i	0.0273030	+	0.0207654i
$532$	−8925.48			−0.727384
$533$	−4321.57	−	7485.18i	−0.351197	−	0.608291i
$534$	−12387.9	−	4175.62i	−1.00389	−	0.338383i
$535$	−3395.83	+	5881.75i	−0.274420	+	0.475309i
$536$	2304.66	−	3991.78i	0.185720	−	0.321677i
$537$	2927.21	−	2578.19i	0.235230	−	0.207183i
$538$	−6229.35	−	10789.5i	−0.499194	−	0.864629i
$539$	−22306.5			−1.78258
$540$	1694.73	−	3492.88i	0.135055	−	0.278351i
$541$	−4023.02			−0.319710			−0.159855	−	0.987140i	$-0.551103\pi$
$541$	−4023.02			−0.319710			−0.159855	+	0.987140i	$0.551103\pi$
$542$	1812.88	+	3140.00i	0.143671	+	0.248846i
$543$	4422.17	−	3894.90i	0.349491	−	0.307820i
$544$	−2725.05	+	4719.92i	−0.214771	+	0.371994i
$545$	1223.74	−	2119.57i	0.0961819	−	0.166592i
$546$	−5159.06	−	1738.97i	−0.404372	−	0.136302i
$547$	−1652.77	−	2862.68i	−0.129191	−	0.223765i	0.794172	−	0.607692i	$-0.207905\pi$
$547$	−1652.77	−	2862.68i	−0.129191	−	0.223765i	−0.923363	+	0.383927i	$0.874571\pi$
$548$	15695.4			1.22349
$549$	−1520.19	+	637.312i	−0.118179	+	0.0495443i
$550$	−1055.81			−0.0818542
$551$	−1913.32	−	3313.96i	−0.147931	−	0.256224i
$552$	2465.29	+	12256.8i	0.190090	+	0.945082i
$553$	16396.6	−	28399.8i	1.26086	−	2.18387i
$554$	−597.702	+	1035.25i	−0.0458374	+	0.0793927i
$555$	2100.47	+	10443.0i	0.160649	+	0.798706i
$556$	484.253	+	838.752i	0.0369369	+	0.0639766i
$557$	6472.87			0.492396			0.246198	−	0.969220i	$-0.420819\pi$
$557$	6472.87			0.492396			0.246198	+	0.969220i	$0.420819\pi$
$558$	−58.0166	+	455.731i	−0.00440150	+	0.0345746i
$559$	−6616.10			−0.500593
$560$	933.515	+	1616.90i	0.0704432	+	0.122011i
$561$	−3856.92	−	1300.06i	−0.290266	−	0.0978404i
$562$	1010.65	−	1750.49i	0.0758569	−	0.131388i
$563$	10277.6	−	17801.4i	0.769362	−	1.33257i	−0.168547	−	0.985694i	$-0.553907\pi$
$563$	10277.6	−	17801.4i	0.769362	−	1.33257i	0.937909	−	0.346881i	$-0.112759\pi$
$564$	5098.25	−	4490.37i	0.380629	−	0.335246i
$565$	1994.16	+	3453.98i	0.148487	+	0.257186i
$566$	−4281.18			−0.317936
$567$	6666.29	+	24054.2i	0.493753	+	1.78162i
$568$	−1390.54			−0.102722
$569$	−635.311	−	1100.39i	−0.0468078	−	0.0810735i	0.841672	−	0.539989i	$-0.181571\pi$
$569$	−635.311	−	1100.39i	−0.0468078	−	0.0810735i	−0.888480	+	0.458915i	$0.848238\pi$
$570$	1441.93	−	1270.01i	0.105958	−	0.0933240i
$571$	8376.66	−	14508.8i	0.613927	−	1.06335i	−0.376645	−	0.926358i	$-0.622922\pi$
$571$	8376.66	−	14508.8i	0.613927	−	1.06335i	0.990572	−	0.136995i	$-0.0437444\pi$
$572$	1450.44	−	2512.23i	0.106024	−	0.183639i
$573$	−2635.57	−	888.376i	−0.192151	−	0.0647686i
$574$	11922.4	+	20650.1i	0.866951	+	1.50160i
$575$	2830.42			0.205281
$576$	704.455	−	5533.62i	0.0509588	−	0.400291i
$577$	−7800.01			−0.562770			−0.281385	−	0.959595i	$-0.590794\pi$
$577$	−7800.01			−0.562770			−0.281385	+	0.959595i	$0.590794\pi$
$578$	3191.32	+	5527.53i	0.229657	+	0.397777i
$579$	−2688.12	−	13364.7i	−0.192944	−	0.959271i
$580$	−1124.10	+	1947.00i	−0.0804753	+	0.139387i
$581$	8944.12	−	15491.7i	0.638665	−	1.10620i
$582$	−1290.20	−	6414.58i	−0.0918912	−	0.456861i
$583$	8198.35	+	14200.0i	0.582403	+	1.00875i
$584$	−15127.3			−1.07187
$585$	−2426.29	+	1017.18i	−0.171478	+	0.0718893i
$586$	−151.327			−0.0106677
$587$	1184.62	+	2051.83i	0.0832958	+	0.144273i	0.904664	−	0.426126i	$-0.140122\pi$
$587$	1184.62	+	2051.83i	0.0832958	+	0.144273i	−0.821368	+	0.570399i	$0.806789\pi$
$588$	−22601.2	−	7618.24i	−1.58514	−	0.534304i
$589$	255.196	−	442.013i	0.0178526	−	0.0309216i
$590$	61.0240	−	105.697i	0.00425816	−	0.00737536i
$591$	−11519.0	+	10145.5i	−0.801737	+	0.706143i
$592$	−2235.66	−	3872.28i	−0.155212	−	0.268834i
$593$	11974.3			0.829218			0.414609	−	0.910000i	$-0.363918\pi$
$593$	11974.3			0.829218			0.414609	+	0.910000i	$0.363918\pi$
$594$	5909.74	−	425.431i	0.408215	−	0.0293866i
$595$	−4985.86			−0.343530
$596$	2832.34	+	4905.76i	0.194660	+	0.337160i
$597$	−10291.7	+	9064.59i	−0.705547	+	0.621422i
$598$	1732.23	−	3000.31i	0.118455	−	0.205170i
$599$	−11099.7	+	19225.3i	−0.757134	+	1.31139i	0.187173	+	0.982327i	$0.440068\pi$
$599$	−11099.7	+	19225.3i	−0.757134	+	1.31139i	−0.944307	+	0.329067i	$0.893266\pi$
$600$	−2616.08	−	881.808i	−0.178002	−	0.0599994i
$601$	5749.47	+	9958.38i	0.390226	+	0.675891i	0.992479	−	0.122414i	$-0.0390635\pi$
$601$	5749.47	+	9958.38i	0.390226	+	0.675891i	−0.602253	+	0.798305i	$0.705730\pi$
$602$	18252.5			1.23574
$603$	4661.09	+	3545.02i	0.314783	+	0.239410i
$604$	4837.08			0.325858
$605$	−1519.01	−	2631.01i	−0.102077	−	0.176803i
$606$	−943.000	−	4688.37i	−0.0632125	−	0.314277i
$607$	7636.51	−	13226.8i	0.510636	−	0.884448i	−0.489288	−	0.872122i	$-0.662743\pi$
$607$	7636.51	−	13226.8i	0.510636	−	0.884448i	0.999924	−	0.0123257i	$-0.00392350\pi$
$608$	−4407.19	+	7633.47i	−0.293972	+	0.509175i
$609$	−2850.24	−	14170.7i	−0.189651	−	0.942900i
$610$	239.657	+	415.098i	0.0159072	+	0.0275522i
$611$	−4603.88			−0.304833
$612$	−3463.87	−	2634.47i	−0.228789	−	0.174007i
$613$	−16440.8			−1.08326			−0.541630	−	0.840617i	$-0.682192\pi$
$613$	−16440.8			−1.08326			−0.541630	+	0.840617i	$0.682192\pi$
$614$	−4128.09	−	7150.07i	−0.271329	−	0.469956i
$615$	10919.1	+	3680.52i	0.715937	+	0.241322i
$616$	−9785.58	+	16949.1i	−0.640052	+	1.10860i
$617$	−4679.57	+	8105.25i	−0.305336	+	0.528857i	−0.977336	−	0.211694i	$-0.932102\pi$
$617$	−4679.57	+	8105.25i	−0.305336	+	0.528857i	0.672000	+	0.740551i	$0.265435\pi$
$618$	5024.81	−	4425.68i	0.327067	−	0.288070i
$619$	12742.3	+	22070.3i	0.827392	+	1.43308i	0.900078	+	0.435729i	$0.143510\pi$
$619$	12742.3	+	22070.3i	0.827392	+	1.43308i	−0.0726861	+	0.997355i	$0.523157\pi$
$620$	−299.862			−0.0194238
$621$	−15842.9	+	1140.50i	−1.02376	+	0.0736982i
$622$	−8214.25			−0.529520
$623$	27430.2	+	47510.4i	1.76399	+	3.05532i
$624$	828.723	−	729.911i	0.0531658	−	0.0468266i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	3134.65	−	5429.38i	0.200137	−	0.346648i
$627$	−6237.75	−	2102.57i	−0.397307	−	0.133921i
$628$	341.897	+	592.183i	0.0217248	+	0.0376285i
$629$	11940.6			0.756919
$630$	6693.66	−	2806.20i	0.423304	−	0.177463i
$631$	−21733.8			−1.37117			−0.685585	−	0.727993i	$-0.740454\pi$
$631$	−21733.8			−1.37117			−0.685585	+	0.727993i	$0.740454\pi$
$632$	−10177.0	−	17627.1i	−0.640539	−	1.10945i
$633$	2039.65	+	10140.6i	0.128071	+	0.636737i
$634$	3716.35	−	6436.91i	0.232800	−	0.403222i
$635$	4320.55	−	7483.41i	0.270009	−	0.467669i
$636$	3457.03	+	17187.5i	0.215535	+	1.07159i
$637$	8081.32	+	13997.3i	0.502659	+	0.870631i
$638$	−3431.12			−0.212914
$639$	223.102	−	1752.51i	0.0138119	−	0.108495i
$640$	5863.52			0.362150
$641$	10162.4	+	17601.8i	0.626195	+	1.08460i	0.988308	+	0.152468i	$0.0487220\pi$
$641$	10162.4	+	17601.8i	0.626195	+	1.08460i	−0.362113	+	0.932134i	$0.617945\pi$
$642$	−10502.1	−	3539.97i	−0.645617	−	0.217619i
$643$	−3363.72	+	5826.13i	−0.206302	+	0.357325i	−0.950547	−	0.310581i	$-0.899476\pi$
$643$	−3363.72	+	5826.13i	−0.206302	+	0.357325i	0.744245	+	0.667907i	$0.232810\pi$
$644$	10727.2	−	18580.0i	0.656382	−	1.13689i
$645$	6619.05	−	5829.83i	0.404069	−	0.355891i
$646$	−1076.94	−	1865.32i	−0.0655910	−	0.113607i
$647$	6724.69			0.408616			0.204308	−	0.978907i	$-0.434506\pi$
$647$	6724.69			0.408616			0.204308	+	0.978907i	$0.434506\pi$
$648$	14998.5	+	3881.66i	0.909253	+	0.235318i
$649$	−418.110			−0.0252885
$650$	382.503	+	662.515i	0.0230816	+	0.0399784i
$651$	1446.77	−	1274.27i	0.0871021	−	0.0767166i
$652$	−3904.25	+	6762.35i	−0.234512	+	0.406187i
$653$	15398.2	−	26670.4i	0.922782	−	1.59831i	0.127693	−	0.991814i	$-0.459243\pi$
$653$	15398.2	−	26670.4i	0.922782	−	1.59831i	0.795089	−	0.606492i	$-0.207424\pi$
$654$	3784.60	+	1275.68i	0.226283	+	0.0762737i
$655$	1597.75	+	2767.39i	0.0953120	+	0.165085i
$656$	−4836.75			−0.287871
$657$	2427.07	−	19065.0i	0.144123	−	1.13211i
$658$	12701.2			0.752498
$659$	−8267.16	−	14319.1i	−0.488684	−	0.846426i	0.511231	−	0.859443i	$-0.329190\pi$
$659$	−8267.16	−	14319.1i	−0.488684	−	0.846426i	−0.999915	+	0.0130174i	$0.995856\pi$
$660$	762.591	+	3791.42i	0.0449755	+	0.223607i
$661$	−968.527	+	1677.54i	−0.0569914	+	0.0987121i	−0.893114	−	0.449831i	$-0.851484\pi$
$661$	−968.527	+	1677.54i	−0.0569914	+	0.0987121i	0.836122	+	0.548543i	$0.184817\pi$
$662$	−7356.30	+	12741.5i	−0.431889	+	0.748054i
$663$	581.523	+	2891.19i	0.0340641	+	0.169358i
$664$	−5551.42	−	9615.35i	−0.324453	−	0.561970i
$665$	−8063.57			−0.470213
$666$	−16030.6	+	6720.53i	−0.932691	+	0.391014i
$667$	9198.16			0.533964
$668$	−5611.10	−	9718.72i	−0.325000	−	0.562917i
$669$	−3323.18	−	1120.15i	−0.192050	−	0.0647346i
$670$	851.404	−	1474.68i	0.0490935	−	0.0850324i
$671$	821.013	−	1422.04i	0.0472352	−	0.0818138i
$672$	−24985.5	+	22006.3i	−1.43428	+	1.26326i
$673$	230.294	+	398.881i	0.0131905	+	0.0228465i	0.872545	−	0.488533i	$-0.162468\pi$
$673$	230.294	+	398.881i	0.0131905	+	0.0228465i	−0.859355	+	0.511380i	$0.829135\pi$
$674$	8555.80			0.488957
$675$	1531.08	−	3155.58i	0.0873054	−	0.179938i
$676$	10057.3			0.572217
$677$	−14529.8	−	25166.4i	−0.824854	−	1.42869i	−0.902031	−	0.431671i	$-0.857924\pi$
$677$	−14529.8	−	25166.4i	−0.824854	−	1.42869i	0.0771775	−	0.997017i	$-0.475409\pi$
$678$	−4883.92	+	4301.59i	−0.276646	+	0.243660i
$679$	−13729.1	+	23779.5i	−0.775956	+	1.34400i
$680$	−1547.31	+	2680.02i	−0.0872597	+	0.151138i
$681$	9315.39	+	3139.95i	0.524180	+	0.176686i
$682$	−228.820	−	396.327i	−0.0128474	−	0.0222524i
$683$	14366.9			0.804881			0.402440	−	0.915446i	$-0.368162\pi$
$683$	14366.9			0.804881			0.402440	+	0.915446i	$0.368162\pi$
$684$	−5602.08	−	4260.69i	−0.313159	−	0.238175i
$685$	14179.7			0.790918
$686$	−13074.3	−	22645.4i	−0.727667	−	1.26036i
$687$	−3492.41	−	17363.4i	−0.193950	−	0.964273i
$688$	−1851.21	+	3206.38i	−0.102582	+	0.177678i
$689$	5940.28	−	10288.9i	0.328457	−	0.568904i
$690$	910.747	+	4528.02i	0.0502486	+	0.249824i
$691$	6353.97	+	11005.4i	0.349807	+	0.605883i	0.986215	−	0.165469i	$-0.0529139\pi$
$691$	6353.97	+	11005.4i	0.349807	+	0.605883i	−0.636408	+	0.771352i	$0.719581\pi$
$692$	−14965.0			−0.822087
$693$	−19791.0	−	15052.1i	−1.08485	−	0.825085i
$694$	−6119.97			−0.334742
$695$	437.491	+	757.756i	0.0238776	+	0.0413573i
$696$	−8501.63	−	2865.66i	−0.463008	−	0.156067i
$697$	6458.22	−	11186.0i	0.350965	−	0.607889i
$698$	4914.02	−	8511.33i	0.266473	−	0.461545i
$699$	11081.4	−	9760.11i	0.599623	−	0.528128i
$700$	2368.73	+	4102.76i	0.127899	+	0.221528i
$701$	5959.06			0.321071			0.160535	−	0.987030i	$-0.448678\pi$
$701$	5959.06			0.321071			0.160535	+	0.987030i	$0.448678\pi$
$702$	−2407.97	−	3554.21i	−0.129463	−	0.191090i
$703$	19311.4			1.03605
$704$	2778.40	+	4812.32i	0.148743	+	0.257630i
$705$	4605.93	−	4056.74i	0.246056	−	0.216718i
$706$	−269.186	+	466.243i	−0.0143498	+	0.0248545i
$707$	−10034.5	+	17380.2i	−0.533785	+	0.924542i
$708$	−423.634	−	142.795i	−0.0224875	−	0.00757989i
$709$	−225.912	−	391.292i	−0.0119666	−	0.0207268i	0.859980	−	0.510328i	$-0.170476\pi$
$709$	−225.912	−	391.292i	−0.0119666	−	0.0207268i	−0.871947	+	0.489601i	$0.837143\pi$
$710$	−513.706			−0.0271536
$711$	23848.4	−	9998.00i	1.25792	−	0.527362i
$712$	34050.6			1.79228
$713$	613.421	+	1062.48i	0.0322199	+	0.0558065i
$714$	−1604.31	−	7976.23i	−0.0840892	−	0.418071i
$715$	1310.37	−	2269.64i	0.0685388	−	0.118713i
$716$	−2077.34	+	3598.05i	−0.108427	+	0.187801i
$717$	−1659.47	−	8250.48i	−0.0864352	−	0.429735i
$718$	−8203.47	−	14208.8i	−0.426394	−	0.738536i
$719$	−13488.4			−0.699627			−0.349814	−	0.936819i	$-0.613755\pi$
$719$	−13488.4			−0.699627			−0.349814	+	0.936819i	$0.613755\pi$
$720$	−185.925	+	1460.47i	−0.00962362	+	0.0755952i
$721$	−28099.7			−1.45144
$722$	3643.30	+	6310.39i	0.187797	+	0.325275i
$723$	131.473	+	44.3159i	0.00676285	+	0.00227957i
$724$	−3138.26	+	5435.62i	−0.161094	+	0.279024i
$725$	−1015.55	+	1758.98i	−0.0520228	+	0.0901061i
$726$	3720.23	−	3276.66i	0.190180	−	0.167504i
$727$	−14591.6	−	25273.3i	−0.744389	−	1.28932i	−0.950480	−	0.310787i	$-0.899407\pi$
$727$	−14591.6	−	25273.3i	−0.744389	−	1.28932i	0.206090	−	0.978533i	$-0.433926\pi$
$728$	14180.7			0.721938
$729$	−7298.46	+	18279.9i	−0.370800	+	0.928713i
$730$	−5588.46			−0.283340
$731$	−4943.60	−	8562.57i	−0.250131	−	0.433239i
$732$	1317.52	−	1160.43i	0.0665259	−	0.0585938i
$733$	−6256.24	+	10836.1i	−0.315252	+	0.546032i	−0.979491	−	0.201488i	$-0.935422\pi$
$733$	−6256.24	+	10836.1i	−0.315252	+	0.546032i	0.664239	+	0.747520i	$0.268756\pi$
$734$	4061.92	−	7035.45i	0.204262	−	0.353792i
$735$	−20418.7	−	6882.57i	−1.02470	−	0.345398i
$736$	−10593.6	−	18348.7i	−0.530553	−	0.918945i
$737$	−5833.46			−0.291558
$738$	−2374.53	+	18652.4i	−0.118439	+	0.930357i
$739$	−32248.2			−1.60524			−0.802619	−	0.596492i	$-0.796561\pi$
$739$	−32248.2			−1.60524			−0.802619	+	0.596492i	$0.796561\pi$
$740$	−5672.84	−	9825.64i	−0.281808	−	0.488105i
$741$	940.490	+	4675.89i	0.0466259	+	0.231813i
$742$	−16388.1	+	28384.9i	−0.810815	+	1.40437i
$743$	−9244.50	+	16011.9i	−0.456457	+	0.790607i	−0.998771	−	0.0495691i	$-0.984215\pi$
$743$	−9244.50	+	16011.9i	−0.456457	+	0.790607i	0.542313	+	0.840176i	$0.317549\pi$
$744$	−235.959	−	1173.13i	−0.0116272	−	0.0578078i
$745$	2558.83	+	4432.02i	0.125837	+	0.217955i
$746$	3299.12			0.161916
$747$	13008.9	−	5453.77i	0.637178	−	0.267126i
$748$	4335.12			0.211908
$749$	23254.5	+	40278.0i	1.13445	+	1.96492i
$750$	−966.454	−	325.764i	−0.0470532	−	0.0158603i
$751$	1026.10	−	1777.26i	0.0498575	−	0.0863558i	−0.840020	−	0.542556i	$-0.817457\pi$
$751$	1026.10	−	1777.26i	0.0498575	−	0.0863558i	0.889877	+	0.456200i	$0.150790\pi$
$752$	−1288.18	+	2231.19i	−0.0624668	+	0.108196i
$753$	1666.40	−	1467.71i	0.0806466	−	0.0710308i
$754$	1243.04	+	2153.01i	0.0600384	+	0.103990i
$755$	4369.98			0.210649
$756$	−14911.8	−	22010.1i	−0.717377	−	1.05886i
$757$	10118.9			0.485834			0.242917	−	0.970047i	$-0.421896\pi$
$757$	10118.9			0.485834			0.242917	+	0.970047i	$0.421896\pi$
$758$	−8826.65	−	15288.2i	−0.422953	−	0.732576i
$759$	11873.8	−	10458.0i	0.567841	−	0.500135i
$760$	−2502.44	+	4334.36i	−0.119438	+	0.206873i
$761$	−13652.0	+	23646.0i	−0.650309	+	1.12637i	0.332739	+	0.943019i	$0.392027\pi$
$761$	−13652.0	+	23646.0i	−0.650309	+	1.12637i	−0.983048	+	0.183349i	$0.941306\pi$
$762$	13362.0	+	4503.94i	0.635240	+	0.214121i
$763$	−8380.10	−	14514.8i	−0.397615	−	0.688689i
$764$	2962.34			0.140280
$765$	−3129.38	−	2380.07i	−0.147899	−	0.112486i
$766$	10669.4			0.503264
$767$	151.475	+	262.362i	0.00713096	+	0.0123512i
$768$	3580.22	+	17800.0i	0.168216	+	0.836330i
$769$	11236.9	−	19462.9i	0.526935	−	0.912679i	−0.472572	−	0.881292i	$-0.656674\pi$
$769$	11236.9	−	19462.9i	0.526935	−	0.912679i	0.999507	−	0.0313867i	$-0.00999234\pi$
$770$	−3615.06	+	6261.48i	−0.169192	+	0.293049i
$771$	−3936.10	−	19569.3i	−0.183859	−	0.914102i
$772$	7259.94	+	12574.6i	0.338460	+	0.586230i
$773$	−35405.6			−1.64741			−0.823707	−	0.567015i	$-0.808098\pi$
$773$	−35405.6			−1.64741			−0.823707	+	0.567015i	$0.808098\pi$
$774$	11456.2	+	8713.08i	0.532022	+	0.404632i
$775$	−270.906			−0.0125564
$776$	8521.35	+	14759.4i	0.394200	+	0.682774i
$777$	69124.4	+	23299.9i	3.19154	+	1.07578i
$778$	−5534.52	+	9586.07i	−0.255041	+	0.441744i
$779$	10444.8	−	18090.9i	0.480390	−	0.832060i
$780$	2102.82	−	1852.10i	0.0965297	−	0.0850201i
$781$	879.923	+	1524.07i	0.0403151	+	0.0698278i
$782$	5177.34			0.236754
$783$	4975.62	−	10254.9i	0.227093	−	0.468044i
$784$	9044.71			0.412022
$785$	308.881	+	534.998i	0.0140439	+	0.0243247i
$786$	−3913.08	+	3446.50i	−0.177576	+	0.156403i
$787$	6090.02	−	10548.2i	0.275840	−	0.477769i	−0.694507	−	0.719486i	$-0.744377\pi$
$787$	6090.02	−	10548.2i	0.275840	−	0.477769i	0.970347	+	0.241718i	$0.0777107\pi$
$788$	8174.59	−	14158.8i	0.369553	−	0.640085i
$789$	−3933.62	−	1325.91i	−0.177491	−	0.0598272i
$790$	−3759.68	−	6511.95i	−0.169321	−	0.293272i
$791$	27311.8			1.22768
$792$	−14232.8	+	5966.86i	−0.638562	+	0.267706i
$793$	−1189.76			−0.0532783
$794$	−2364.23	−	4094.97i	−0.105672	−	0.183029i
$795$	3123.19	+	15527.8i	0.139331	+	0.692721i
$796$	7303.65	−	12650.3i	0.325215	−	0.563289i
$797$	−1146.54	+	1985.86i	−0.0509567	+	0.0882596i	−0.890379	−	0.455221i	$-0.849560\pi$
$797$	−1146.54	+	1985.86i	−0.0509567	+	0.0882596i	0.839422	+	0.543480i	$0.182894\pi$
$798$	−2594.63	−	12899.9i	−0.115099	−	0.572243i
$799$	−3440.05	−	5958.35i	−0.152316	−	0.263819i
$800$	4678.48			0.206762
$801$	−5463.16	+	42914.1i	−0.240988	+	1.89300i
$802$	−6544.86			−0.288164
$803$	9572.43	+	16579.9i	0.420677	+	0.728634i
$804$	−5910.53	−	1992.27i	−0.259264	−	0.0873905i
$805$	9691.29	−	16785.8i	0.424314	−	0.734934i
$806$	−165.796	+	287.167i	−0.00724554	+	0.0125496i
$807$	−30939.0	+	27250.0i	−1.34957	+	1.18866i
$808$	6228.19	+	10787.5i	0.271172	+	0.469684i
$809$	−25264.0			−1.09794			−0.548972	−	0.835841i	$-0.684981\pi$
$809$	−25264.0			−1.09794			−0.548972	+	0.835841i	$0.684981\pi$
$810$	5540.86	+	1433.99i	0.240353	+	0.0622042i
$811$	18781.2			0.813190			0.406595	−	0.913608i	$-0.366716\pi$
$811$	18781.2			0.813190			0.406595	+	0.913608i	$0.366716\pi$
$812$	7697.78	+	13333.0i	0.332684	+	0.576225i
$813$	9003.94	−	7930.37i	0.388416	−	0.342103i
$814$	8657.68	−	14995.5i	0.372790	−	0.645692i
$815$	−3527.23	+	6109.33i	−0.151599	+	0.262577i
$816$	1563.88	+	527.139i	0.0670916	+	0.0226147i
$817$	−7995.23	−	13848.1i	−0.342372	−	0.593005i
$818$	−19793.0			−0.846023
$819$	−2275.18	+	17871.9i	−0.0970711	+	0.762510i
$820$	−12272.9			−0.522669
$821$	−15787.4	−	27344.6i	−0.671114	−	1.16240i	−0.977588	−	0.210525i	$-0.932483\pi$
$821$	−15787.4	−	27344.6i	−0.671114	−	1.16240i	0.306474	−	0.951879i	$-0.400851\pi$
$822$	4562.63	+	22684.3i	0.193601	+	0.962537i
$823$	473.129	−	819.484i	0.0200392	−	0.0347089i	−0.855832	−	0.517254i	$-0.826954\pi$
$823$	473.129	−	819.484i	0.0200392	−	0.0347089i	0.875871	+	0.482545i	$0.160288\pi$
$824$	−8720.45	+	15104.3i	−0.368679	+	0.638570i
$825$	688.950	+	3425.29i	0.0290741	+	0.144550i
$826$	−417.889	−	723.806i	−0.0176032	−	0.0304896i
$827$	35044.7			1.47355			0.736774	−	0.676139i	$-0.236348\pi$
$827$	35044.7			1.47355			0.736774	+	0.676139i	$0.236348\pi$
$828$	15602.3	−	6541.00i	0.654853	−	0.274536i
$829$	31029.2			1.29999			0.649993	−	0.759940i	$-0.274772\pi$
$829$	31029.2			1.29999			0.649993	+	0.759940i	$0.274772\pi$
$830$	−2050.85	−	3552.18i	−0.0857663	−	0.148552i
$831$	3748.62	+	1263.55i	0.156484	+	0.0527463i
$832$	2013.14	−	3486.86i	0.0838860	−	0.145295i
$833$	−12076.8	+	20917.7i	−0.502327	+	0.870055i
$834$	−1071.46	+	943.708i	−0.0444865	+	0.0391822i
$835$	−5069.26	−	8780.21i	−0.210094	−	0.363894i
$836$	7011.13			0.290054
$837$	1516.36	−	109.160i	0.0626200	−	0.00450790i
$838$	−8077.90			−0.332991
$839$	10599.9	+	18359.6i	0.436175	+	0.755477i	0.997391	−	0.0721924i	$-0.0229996\pi$
$839$	10599.9	+	18359.6i	0.436175	+	0.755477i	−0.561216	+	0.827669i	$0.689666\pi$
$840$	−14187.0	+	12495.4i	−0.582735	+	0.513253i
$841$	8894.22	−	15405.2i	0.364681	−	0.631647i
$842$	2645.86	−	4582.76i	0.108292	−	0.187568i
$843$	−6338.49	−	2136.52i	−0.258967	−	0.0872904i
$844$	−5508.58	−	9541.14i	−0.224660	−	0.389123i
$845$	9086.08			0.369906
$846$	7971.91	+	6063.08i	0.323972	+	0.246398i
$847$	−20804.3			−0.843971
$848$	−3324.22	−	5757.71i	−0.134616	−	0.233161i
$849$	2793.61	+	13889.2i	0.112929	+	0.561455i
$850$	−571.619	+	990.073i	−0.0230663	+	0.0399520i
$851$	−23209.5	+	40200.1i	−0.934915	+	1.61932i
$852$	371.040	+	1844.72i	0.0149197	+	0.0741774i
$853$	−5489.93	−	9508.84i	−0.220365	−	0.381684i	0.734554	−	0.678551i	$-0.237392\pi$
$853$	−5489.93	−	9508.84i	−0.220365	−	0.381684i	−0.954919	+	0.296867i	$0.904058\pi$
$854$	3282.32			0.131521
$855$	−5061.11	−	3849.25i	−0.202440	−	0.153967i
$856$	28867.2			1.15264
$857$	−22407.2	−	38810.4i	−0.893133	−	1.54695i	−0.836098	−	0.548580i	$-0.815169\pi$
$857$	−22407.2	−	38810.4i	−0.893133	−	1.54695i	−0.0570348	−	0.998372i	$-0.518165\pi$
$858$	4052.54	+	1365.99i	0.161249	+	0.0543523i
$859$	−18693.1	+	32377.4i	−0.742492	+	1.28603i	0.208866	+	0.977944i	$0.433023\pi$
$859$	−18693.1	+	32377.4i	−0.742492	+	1.28603i	−0.951358	+	0.308089i	$0.900311\pi$
$860$	−4697.30	+	8135.96i	−0.186252	+	0.322598i
$861$	59214.2	−	52153.9i	2.34380	−	2.06434i
$862$	−11736.0	−	20327.3i	−0.463722	−	0.803191i
$863$	−30536.3			−1.20448			−0.602241	−	0.798314i	$-0.705725\pi$
$863$	−30536.3			−1.20448			−0.602241	+	0.798314i	$0.705725\pi$
$864$	−26187.2	+	1885.16i	−1.03114	+	0.0742299i
$865$	−13519.9			−0.531433
$866$	11000.2	+	19052.9i	0.431643	+	0.747627i
$867$	15850.2	−	13960.3i	0.620877	−	0.546848i
$868$	−1026.72	+	1778.34i	−0.0401489	+	0.0695399i
$869$	−12879.8	+	22308.6i	−0.502784	+	0.870847i
$870$	−3140.74	−	1058.65i	−0.122392	−	0.0412549i
$871$	2113.37	+	3660.47i	0.0822146	+	0.142400i
$872$	−10402.7			−0.403991
$873$	−19968.5	+	8371.45i	−0.774149	+	0.324548i
$874$	8373.25			0.324061
$875$	2139.99	+	3706.57i	0.0826797	+	0.143205i
$876$	4036.44	+	20068.2i	0.155683	+	0.774021i
$877$	−17163.7	+	29728.4i	−0.660864	+	1.14465i	0.319525	+	0.947578i	$0.396477\pi$
$877$	−17163.7	+	29728.4i	−0.660864	+	1.14465i	−0.980389	+	0.197072i	$0.936857\pi$
$878$	3754.52	−	6503.02i	0.144315	−	0.249962i
$879$	98.7460	+	490.941i	0.00378910	+	0.0188385i
$880$	−733.294	−	1270.10i	−0.0280901	−	0.0486535i
$881$	−18009.6			−0.688718			−0.344359	−	0.938838i	$-0.611904\pi$
$881$	−18009.6			−0.688718			−0.344359	+	0.938838i	$0.611904\pi$
$882$	4440.37	−	34879.9i	0.169518	−	1.33159i
$883$	−29074.4			−1.10808			−0.554039	−	0.832491i	$-0.686914\pi$
$883$	−29074.4			−1.10808			−0.554039	+	0.832491i	$0.686914\pi$
$884$	−1570.55	−	2720.27i	−0.0597548	−	0.103498i
$885$	−382.725	−	129.006i	−0.0145369	−	0.00489998i
$886$	−3748.10	+	6491.90i	−0.142122	+	0.246162i
$887$	16451.3	−	28494.5i	0.622752	−	1.07864i	−0.366220	−	0.930528i	$-0.619348\pi$
$887$	16451.3	−	28494.5i	0.622752	−	1.07864i	0.988971	−	0.148109i	$-0.0473186\pi$
$888$	33976.2	−	29925.1i	1.28397	−	1.13088i
$889$	−29586.9	−	51246.1i	−1.11621	−	1.93334i
$890$	12579.3			0.473772
$891$	−5236.50	−	18895.0i	−0.196890	−	0.710444i
$892$	3735.20			0.140206
$893$	−5563.56	−	9636.36i	−0.208485	−	0.361107i
$894$	−6266.86	+	5519.64i	−0.234446	+	0.206493i
$895$	−1876.74	+	3250.60i	−0.0700920	+	0.121403i
$896$	20076.6	−	34773.7i	0.748562	−	1.29655i
$897$	−10864.1	−	3661.96i	−0.404393	−	0.136309i
$898$	671.902	+	1163.77i	0.0249684	+	0.0432466i
$899$	−880.377			−0.0326610
$900$	−471.771	+	3705.84i	−0.0174730	+	0.137253i
$901$	17754.5			0.656479
$902$	−9365.24	−	16221.1i	−0.345708	−	0.598783i
$903$	−11910.4	−	59215.5i	−0.438928	−	2.18225i
$904$	8475.93	−	14680.7i	0.311842	−	0.540127i
$905$	−2835.21	+	4910.72i	−0.104139	+	0.180373i
$906$	1406.13	+	6990.96i	0.0515625	+	0.256357i
$907$	407.908	+	706.517i	0.0149331	+	0.0258649i	0.873395	−	0.487012i	$-0.161913\pi$
$907$	407.908	+	706.517i	0.0149331	+	0.0258649i	−0.858462	+	0.512877i	$0.828580\pi$
$908$	−10470.4			−0.382677
$909$	−14594.8	+	6118.63i	−0.532542	+	0.223259i
$910$	5238.73			0.190838
$911$	−7921.41	−	13720.3i	−0.288088	−	0.498983i	0.685265	−	0.728293i	$-0.259686\pi$
$911$	−7921.41	−	13720.3i	−0.288088	−	0.498983i	−0.973353	+	0.229311i	$0.926353\pi$
$912$	2529.24	+	852.536i	0.0918329	+	0.0309543i
$913$	−7025.77	+	12169.0i	−0.254676	+	0.441112i
$914$	10534.5	−	18246.3i	0.381237	−	0.660322i
$915$	1190.29	−	1048.37i	0.0430053	−	0.0378776i
$916$	9432.11	+	16336.9i	0.340225	+	0.589286i
$917$	21882.7			0.788037
$918$	2800.61	−	5772.12i	0.100691	−	0.207526i
$919$	23848.4			0.856025			0.428013	−	0.903773i	$-0.359214\pi$
$919$	23848.4			0.856025			0.428013	+	0.903773i	$0.359214\pi$
$920$	−6015.17	−	10418.6i	−0.215559	−	0.373359i
$921$	−20502.8	+	18058.2i	−0.733540	+	0.646077i
$922$	12472.2	−	21602.4i	0.445498	−	0.771624i
$923$	637.566	−	1104.30i	0.0227364	−	0.0393807i
$924$	25096.1	+	8459.19i	0.893508	+	0.301176i
$925$	−5125.03	−	8876.81i	−0.182173	−	0.315533i
$926$	10302.7			0.365625
$927$	−17636.8	−	13413.8i	−0.624886	−	0.475260i
$928$	15203.9			0.537816
$929$	19796.0	+	34287.7i	0.699123	+	1.21092i	0.968771	+	0.247958i	$0.0797595\pi$
$929$	19796.0	+	34287.7i	0.699123	+	1.21092i	−0.269647	+	0.962959i	$0.586907\pi$
$930$	−87.1697	−	433.387i	−0.00307356	−	0.0152810i
$931$	−19531.7	+	33830.0i	−0.687569	+	1.19090i
$932$	−7864.07	+	13621.0i	−0.276391	+	0.478723i
$933$	5360.07	+	26649.0i	0.188082	+	0.935100i
$934$	5332.72	+	9236.54i	0.186822	+	0.323585i
$935$	3916.49			0.136987
$936$	8900.51	+	6769.33i	0.310814	+	0.236391i
$937$	10255.0			0.357540			0.178770	−	0.983891i	$-0.442788\pi$
$937$	10255.0			0.357540			0.178770	+	0.983891i	$0.442788\pi$
$938$	−5830.38	−	10098.5i	−0.202952	−	0.351523i
$939$	−19659.7	−	6626.71i	−0.683247	−	0.230303i
$940$	−3268.66	+	5661.49i	−0.113417	+	0.196444i
$941$	11947.2	−	20693.1i	0.413886	−	0.716871i	−0.581425	−	0.813600i	$-0.697505\pi$
$941$	11947.2	−	20693.1i	0.413886	−	0.716871i	0.995311	+	0.0967289i	$0.0308380\pi$
$942$	−756.484	+	666.286i	−0.0261652	+	0.0230454i
$943$	25106.4	+	43485.5i	0.866995	+	1.50168i
$944$	169.533			0.00584514
$945$	−13471.8	−	19884.7i	−0.463744	−	0.684496i
$946$	−14337.7			−0.492768
$947$	18128.6	+	31399.7i	0.622072	+	1.07746i	0.989099	+	0.147250i	$0.0470421\pi$
$947$	18128.6	+	31399.7i	0.622072	+	1.07746i	−0.367028	+	0.930210i	$0.619625\pi$
$948$	−20668.9	+	18204.5i	−0.708118	+	0.623686i
$949$	6935.89	−	12013.3i	0.237248	−	0.410926i
$950$	−924.472	+	1601.23i	−0.0315725	+	0.0546851i
$951$	−23307.9	−	7856.43i	−0.794754	−	0.267889i
$952$	10595.9	+	18352.6i	0.360730	+	0.624803i
$953$	−46736.7			−1.58861			−0.794307	−	0.607516i	$-0.792166\pi$
$953$	−46736.7			−1.58861			−0.794307	+	0.607516i	$0.792166\pi$
$954$	−23835.9	+	9992.78i	−0.808927	+	0.339128i
$955$	2676.27			0.0906830
$956$	4481.81	+	7762.72i	0.151623	+	0.262620i
$957$	2238.92	+	11131.4i	0.0756259	+	0.375994i
$958$	−13859.0	+	24004.6i	−0.467396	+	0.809553i
$959$	48551.0	−	84092.9i	1.63482	−	2.83160i
$960$	1058.44	+	5262.31i	0.0355844	+	0.176917i
$961$	14836.8	+	25698.1i	0.498029	+	0.862612i
$962$	−12546.2			−0.420484
$963$	−4631.51	+	36381.4i	−0.154983	+	1.21742i
$964$	−147.774			−0.00493721
$965$	6558.87	+	11360.3i	0.218795	+	0.378965i
$966$	29971.8	+	10102.6i	0.998268	+	0.336488i
$967$	−22178.5	+	38414.3i	−0.737552	+	1.27748i	0.216043	+	0.976384i	$0.430685\pi$
$967$	−22178.5	+	38414.3i	−0.737552	+	1.27748i	−0.953595	+	0.301094i	$0.902648\pi$
$968$	−6456.39	+	11182.8i	−0.214376	+	0.371310i
$969$	−5348.80	+	4711.04i	−0.177325	+	0.156182i
$970$	3148.03	+	5452.54i	0.104203	+	0.180485i
$971$	−650.540			−0.0215003			−0.0107502	−	0.999942i	$-0.503422\pi$
$971$	−650.540			−0.0215003			−0.0107502	+	0.999942i	$0.503422\pi$
$972$	1147.42	−	20933.0i	0.0378639	−	0.690769i
$973$	5991.83			0.197420
$974$	4175.31	+	7231.85i	0.137357	+	0.237909i
$975$	1899.76	−	1673.25i	0.0624011	−	0.0549607i
$976$	−332.899	+	576.598i	−0.0109179	+	0.0189103i
$977$	−25837.5	+	44751.9i	−0.846075	+	1.46544i	0.0386096	+	0.999254i	$0.487707\pi$
$977$	−25837.5	+	44751.9i	−0.846075	+	1.46544i	−0.884684	+	0.466190i	$0.845626\pi$
$978$	−10908.5	−	3676.94i	−0.356662	−	0.120220i
$979$	−21546.9	−	37320.3i	−0.703414	−	1.21835i
$980$	22950.3			0.748082
$981$	1669.03	−	13110.5i	0.0543202	−	0.426695i
$982$	17068.1			0.554649
$983$	−11759.5	−	20368.0i	−0.381556	−	0.660874i	0.609729	−	0.792610i	$-0.291278\pi$
$983$	−11759.5	−	20368.0i	−0.381556	−	0.660874i	−0.991285	+	0.131736i	$0.957945\pi$
$984$	−9657.43	−	48014.4i	−0.312874	−	1.55553i
$985$	7385.20	−	12791.5i	0.238895	−	0.413779i
$986$	−1857.62	+	3217.49i	−0.0599987	+	0.103921i
$987$	−8287.95	−	41205.7i	−0.267283	−	1.32887i
$988$	−2540.03	−	4399.46i	−0.0817905	−	0.141665i
$989$	38436.6			1.23581
$990$	−5258.00	+	2204.32i	−0.168798	+	0.0707656i
$991$	−27732.9			−0.888966			−0.444483	−	0.895787i	$-0.646613\pi$
$991$	−27732.9			−0.888966			−0.444483	+	0.895787i	$0.646613\pi$
$992$	1013.94	+	1756.20i	0.0324523	+	0.0562090i
$993$	46136.6	+	15551.3i	1.47442	+	0.496986i
$994$	−1758.92	+	3046.53i	−0.0561262	+	0.0972135i
$995$	6598.36	−	11428.7i	0.210233	−	0.364135i
$996$	−11274.6	+	9930.30i	−0.358685	+	0.315917i
$997$	17163.9	+	29728.7i	0.545221	+	0.944351i	0.998593	+	0.0530293i	$0.0168877\pi$
$997$	17163.9	+	29728.7i	0.545221	+	0.944351i	−0.453372	+	0.891322i	$0.649779\pi$
$998$	16283.9			0.516489
$999$	32263.5	+	47621.6i	1.02179	+	1.50819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.c.31.3	yes	14
3.2	odd	2		135.4.e.c.91.5		14
5.2	odd	4		225.4.k.d.49.9		28
5.3	odd	4		225.4.k.d.49.6		28
5.4	even	2		225.4.e.d.76.5		14
9.2	odd	6		135.4.e.c.46.5		14
9.4	even	3		405.4.a.m.1.5		7
9.5	odd	6		405.4.a.n.1.3		7
9.7	even	3	inner	45.4.e.c.16.3	✓	14
45.4	even	6		2025.4.a.bb.1.3		7
45.7	odd	12		225.4.k.d.124.6		28
45.14	odd	6		2025.4.a.ba.1.5		7
45.34	even	6		225.4.e.d.151.5		14
45.43	odd	12		225.4.k.d.124.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.3	✓	14	9.7	even	3	inner
45.4.e.c.31.3	yes	14	1.1	even	1	trivial
135.4.e.c.46.5		14	9.2	odd	6
135.4.e.c.91.5		14	3.2	odd	2
225.4.e.d.76.5		14	5.4	even	2
225.4.e.d.151.5		14	45.34	even	6
225.4.k.d.49.6		28	5.3	odd	4
225.4.k.d.49.9		28	5.2	odd	4
225.4.k.d.124.6		28	45.7	odd	12
225.4.k.d.124.9		28	45.43	odd	12
405.4.a.m.1.5		7	9.4	even	3
405.4.a.n.1.3		7	9.5	odd	6
2025.4.a.ba.1.5		7	45.14	odd	6
2025.4.a.bb.1.3		7	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.785104 - 1.35984i) q^{2} +(-3.89934 + 3.43441i) q^{3} +(2.76722 - 4.79297i) q^{4} +(2.50000 - 4.33013i) q^{5} +(7.73164 + 2.60611i) q^{6} +(-17.1199 - 29.6525i) q^{7} -21.2519 q^{8} +(3.40971 - 26.7838i) q^{9} +O(q^{10})\)	\(q+(-0.785104 - 1.35984i) q^{2} +(-3.89934 + 3.43441i) q^{3} +(2.76722 - 4.79297i) q^{4} +(2.50000 - 4.33013i) q^{5} +(7.73164 + 2.60611i) q^{6} +(-17.1199 - 29.6525i) q^{7} -21.2519 q^{8} +(3.40971 - 26.7838i) q^{9} -7.85104 q^{10} +(13.4480 + 23.2926i) q^{11} +(5.67066 + 28.1932i) q^{12} +(9.74401 - 16.8771i) q^{13} +(-26.8818 + 46.5607i) q^{14} +(5.12307 + 25.4707i) q^{15} +(-5.45281 - 9.44454i) q^{16} +29.1232 q^{17} +(-39.0987 + 16.3915i) q^{18} +47.1006 q^{19} +(-13.8361 - 23.9648i) q^{20} +(168.595 + 56.8286i) q^{21} +(21.1162 - 36.5743i) q^{22} +(-56.6083 + 98.0485i) q^{23} +(82.8684 - 72.9877i) q^{24} +(-12.5000 - 21.6506i) q^{25} -30.6003 q^{26} +(78.6910 + 116.150i) q^{27} -189.498 q^{28} +(-40.6219 - 70.3593i) q^{29} +(30.6139 - 26.9637i) q^{30} +(5.41811 - 9.38445i) q^{31} +(-93.5697 + 162.067i) q^{32} +(-132.435 - 44.6399i) q^{33} +(-22.8648 - 39.6029i) q^{34} -171.199 q^{35} +(-118.939 - 90.4594i) q^{36} +410.002 q^{37} +(-36.9789 - 64.0493i) q^{38} +(19.9677 + 99.2746i) q^{39} +(-53.1298 + 92.0234i) q^{40} +(221.755 - 384.091i) q^{41} +(-55.0869 - 273.879i) q^{42} +(-169.748 - 294.012i) q^{43} +148.854 q^{44} +(-107.453 - 81.7240i) q^{45} +177.774 q^{46} +(-118.121 - 204.591i) q^{47} +(53.6988 + 18.1003i) q^{48} +(-414.681 + 718.249i) q^{49} +(-19.6276 + 33.9960i) q^{50} +(-113.561 + 100.021i) q^{51} +(-53.9277 - 93.4055i) q^{52} +609.634 q^{53} +(96.1643 - 198.197i) q^{54} +134.480 q^{55} +(363.830 + 630.173i) q^{56} +(-183.661 + 161.763i) q^{57} +(-63.7849 + 110.479i) q^{58} +(-7.77272 + 13.4627i) q^{59} +(136.257 + 45.9283i) q^{60} +(-30.5255 - 52.8717i) q^{61} -17.0151 q^{62} +(-852.582 + 357.430i) q^{63} +206.603 q^{64} +(-48.7201 - 84.3856i) q^{65} +(43.2718 + 215.137i) q^{66} +(-108.445 + 187.832i) q^{67} +(80.5903 - 139.587i) q^{68} +(-116.003 - 576.740i) q^{69} +(134.409 + 232.803i) q^{70} +65.4315 q^{71} +(-72.4627 + 569.208i) q^{72} +711.811 q^{73} +(-321.895 - 557.538i) q^{74} +(123.099 + 41.4931i) q^{75} +(130.338 - 225.752i) q^{76} +(460.457 - 797.534i) q^{77} +(119.321 - 105.094i) q^{78} +(478.876 + 829.438i) q^{79} -54.5281 q^{80} +(-705.748 - 182.650i) q^{81} -696.404 q^{82} +(261.220 + 452.446i) q^{83} +(738.918 - 650.814i) q^{84} +(72.8080 - 126.107i) q^{85} +(-266.540 + 461.660i) q^{86} +(400.041 + 134.842i) q^{87} +(-285.796 - 495.012i) q^{88} -1602.24 q^{89} +(-26.7697 + 210.281i) q^{90} -667.266 q^{91} +(313.296 + 542.644i) q^{92} +(11.1029 + 55.2011i) q^{93} +(-185.474 + 321.251i) q^{94} +(117.751 - 203.952i) q^{95} +(-191.745 - 953.312i) q^{96} +(-400.969 - 694.499i) q^{97} +1302.27 q^{98} +(669.719 - 280.768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more