LMFDB - Embedded newform 210.4.i.j.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,4,Mod(121,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("210.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	210.i (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:	$12.3904011012$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	210.151
Dual form			210.4.i.j.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} +(-10.8095 + 15.0385i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} +(-10.8095 + 15.0385i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(-12.9284 + 22.3927i) q^{11} +(6.00000 + 10.3923i) q^{12} -2.85685 q^{13} +(-36.8569 - 3.68410i) q^{14} +15.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-42.9284 + 74.3542i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-7.73790 - 13.4024i) q^{19} -20.0000 q^{20} +(22.8569 + 50.6415i) q^{21} -51.7137 q^{22} +(30.1663 + 52.2496i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-2.85685 - 4.94821i) q^{26} -27.0000 q^{27} +(-30.4758 - 67.5220i) q^{28} +29.6673 q^{29} +(15.0000 + 25.9808i) q^{30} +(-126.927 + 219.845i) q^{31} +(16.0000 - 27.7128i) q^{32} +(38.7853 + 67.1781i) q^{33} -171.714 q^{34} +(-92.1421 - 9.21025i) q^{35} +36.0000 q^{36} +(102.334 + 177.247i) q^{37} +(15.4758 - 26.8049i) q^{38} +(-4.28528 + 7.42231i) q^{39} +(-20.0000 - 34.6410i) q^{40} +61.8569 q^{41} +(-64.8569 + 90.2308i) q^{42} -65.9052 q^{43} +(-51.7137 - 89.5708i) q^{44} +(22.5000 - 38.9711i) q^{45} +(-60.3327 + 104.499i) q^{46} +(-87.7621 - 152.008i) q^{47} -48.0000 q^{48} +(-109.310 - 325.116i) q^{49} -50.0000 q^{50} +(128.785 + 223.063i) q^{51} +(5.71370 - 9.89642i) q^{52} +(200.522 - 347.315i) q^{53} +(-27.0000 - 46.7654i) q^{54} -129.284 q^{55} +(86.4758 - 120.308i) q^{56} -46.4274 q^{57} +(29.6673 + 51.3854i) q^{58} +(196.926 - 341.086i) q^{59} +(-30.0000 + 51.9615i) q^{60} +(30.4758 + 52.7856i) q^{61} -507.710 q^{62} +(165.856 + 16.5785i) q^{63} +64.0000 q^{64} +(-7.14213 - 12.3705i) q^{65} +(-77.5706 + 134.356i) q^{66} +(-56.9506 + 98.6413i) q^{67} +(-171.714 - 297.417i) q^{68} +180.998 q^{69} +(-76.1895 - 168.805i) q^{70} +483.853 q^{71} +(36.0000 + 62.3538i) q^{72} +(28.8579 - 49.9833i) q^{73} +(-204.667 + 354.494i) q^{74} +(37.5000 + 64.9519i) q^{75} +61.9032 q^{76} +(-197.002 - 436.477i) q^{77} -17.1411 q^{78} +(509.738 + 882.892i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(61.8569 + 107.139i) q^{82} +870.611 q^{83} +(-221.141 - 22.1046i) q^{84} -429.284 q^{85} +(-65.9052 - 114.151i) q^{86} +(44.5010 - 77.0780i) q^{87} +(103.427 - 179.142i) q^{88} +(-482.404 - 835.549i) q^{89} +90.0000 q^{90} +(30.8810 - 42.9626i) q^{91} -241.331 q^{92} +(380.782 + 659.534i) q^{93} +(175.524 - 304.017i) q^{94} +(38.6895 - 67.0122i) q^{95} +(-48.0000 - 83.1384i) q^{96} +880.758 q^{97} +(453.806 - 514.447i) q^{98} +232.712 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 24 q^{6} - 20 q^{7} - 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 24 * q^6 - 20 * q^7 - 32 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 24 q^{6} - 20 q^{7} - 32 q^{8} - 18 q^{9} - 20 q^{10} + 18 q^{11} + 24 q^{12} + 128 q^{13} - 8 q^{14} + 60 q^{15} - 32 q^{16} - 102 q^{17} + 36 q^{18} + 62 q^{19} - 80 q^{20} - 48 q^{21} + 72 q^{22} - 42 q^{23} - 48 q^{24} - 50 q^{25} + 128 q^{26} - 108 q^{27} + 64 q^{28} + 444 q^{29} + 60 q^{30} + 50 q^{31} + 64 q^{32} - 54 q^{33} - 408 q^{34} - 20 q^{35} + 144 q^{36} + 572 q^{37} - 124 q^{38} + 192 q^{39} - 80 q^{40} + 108 q^{41} - 120 q^{42} - 496 q^{43} + 72 q^{44} + 90 q^{45} + 84 q^{46} - 444 q^{47} - 192 q^{48} - 902 q^{49} - 200 q^{50} + 306 q^{51} - 256 q^{52} + 12 q^{53} - 108 q^{54} + 180 q^{55} + 160 q^{56} + 372 q^{57} + 444 q^{58} - 258 q^{59} - 120 q^{60} - 64 q^{61} + 200 q^{62} + 36 q^{63} + 256 q^{64} + 320 q^{65} + 108 q^{66} + 632 q^{67} - 408 q^{68} - 252 q^{69} + 160 q^{70} - 156 q^{71} + 144 q^{72} + 464 q^{73} - 1144 q^{74} + 150 q^{75} - 496 q^{76} - 1764 q^{77} + 768 q^{78} + 1946 q^{79} + 160 q^{80} - 162 q^{81} + 108 q^{82} - 468 q^{83} - 48 q^{84} - 1020 q^{85} - 496 q^{86} + 666 q^{87} - 144 q^{88} - 1674 q^{89} + 360 q^{90} + 170 q^{91} + 336 q^{92} - 150 q^{93} + 888 q^{94} - 310 q^{95} - 192 q^{96} + 1664 q^{97} + 328 q^{98} - 324 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 24 * q^6 - 20 * q^7 - 32 * q^8 - 18 * q^9 - 20 * q^10 + 18 * q^11 + 24 * q^12 + 128 * q^13 - 8 * q^14 + 60 * q^15 - 32 * q^16 - 102 * q^17 + 36 * q^18 + 62 * q^19 - 80 * q^20 - 48 * q^21 + 72 * q^22 - 42 * q^23 - 48 * q^24 - 50 * q^25 + 128 * q^26 - 108 * q^27 + 64 * q^28 + 444 * q^29 + 60 * q^30 + 50 * q^31 + 64 * q^32 - 54 * q^33 - 408 * q^34 - 20 * q^35 + 144 * q^36 + 572 * q^37 - 124 * q^38 + 192 * q^39 - 80 * q^40 + 108 * q^41 - 120 * q^42 - 496 * q^43 + 72 * q^44 + 90 * q^45 + 84 * q^46 - 444 * q^47 - 192 * q^48 - 902 * q^49 - 200 * q^50 + 306 * q^51 - 256 * q^52 + 12 * q^53 - 108 * q^54 + 180 * q^55 + 160 * q^56 + 372 * q^57 + 444 * q^58 - 258 * q^59 - 120 * q^60 - 64 * q^61 + 200 * q^62 + 36 * q^63 + 256 * q^64 + 320 * q^65 + 108 * q^66 + 632 * q^67 - 408 * q^68 - 252 * q^69 + 160 * q^70 - 156 * q^71 + 144 * q^72 + 464 * q^73 - 1144 * q^74 + 150 * q^75 - 496 * q^76 - 1764 * q^77 + 768 * q^78 + 1946 * q^79 + 160 * q^80 - 162 * q^81 + 108 * q^82 - 468 * q^83 - 48 * q^84 - 1020 * q^85 - 496 * q^86 + 666 * q^87 - 144 * q^88 - 1674 * q^89 + 360 * q^90 + 170 * q^91 + 336 * q^92 - 150 * q^93 + 888 * q^94 - 310 * q^95 - 192 * q^96 + 1664 * q^97 + 328 * q^98 - 324 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	6.00000			0.408248
$7$	−10.8095	+	15.0385i	−0.583657	+	0.812000i
$7$	−10.8095	+	15.0385i	−0.583657	+	0.812000i
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	−12.9284	+	22.3927i	−0.354370	+	0.613786i	−0.987010	−	0.160660i	$-0.948638\pi$
$11$	−12.9284	+	22.3927i	−0.354370	+	0.613786i	0.632640	+	0.774446i	$0.281971\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	−2.85685			−0.0609498			−0.0304749	−	0.999536i	$-0.509702\pi$
$13$	−2.85685			−0.0609498			−0.0304749	+	0.999536i	$0.509702\pi$
$14$	−36.8569	−	3.68410i	−0.703601	−	0.0703298i
$15$	15.0000			0.258199
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−42.9284	+	74.3542i	−0.612451	+	1.06080i	0.378375	+	0.925653i	$0.376483\pi$
$17$	−42.9284	+	74.3542i	−0.612451	+	1.06080i	−0.990826	+	0.135144i	$0.956850\pi$
$18$	9.00000	−	15.5885i	0.117851	−	0.204124i
$19$	−7.73790	−	13.4024i	−0.0934314	−	0.161828i	0.815521	−	0.578727i	$-0.196450\pi$
$19$	−7.73790	−	13.4024i	−0.0934314	−	0.161828i	−0.908953	+	0.416899i	$0.863117\pi$
$20$	−20.0000			−0.223607
$21$	22.8569	+	50.6415i	0.237513	+	0.526233i
$22$	−51.7137			−0.501154
$23$	30.1663	+	52.2496i	0.273483	+	0.473687i	0.969751	−	0.244095i	$-0.0784909\pi$
$23$	30.1663	+	52.2496i	0.273483	+	0.473687i	−0.696268	+	0.717782i	$0.745158\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−2.85685	−	4.94821i	−0.0215490	−	0.0373240i
$27$	−27.0000			−0.192450
$28$	−30.4758	−	67.5220i	−0.205692	−	0.455731i
$29$	29.6673			0.189969			0.0949843	−	0.995479i	$-0.469720\pi$
$29$	29.6673			0.189969			0.0949843	+	0.995479i	$0.469720\pi$
$30$	15.0000	+	25.9808i	0.0912871	+	0.158114i
$31$	−126.927	+	219.845i	−0.735382	+	1.27372i	0.219174	+	0.975686i	$0.429664\pi$
$31$	−126.927	+	219.845i	−0.735382	+	1.27372i	−0.954556	+	0.298033i	$0.903670\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	38.7853	+	67.1781i	0.204595	+	0.354370i
$34$	−171.714			−0.866137
$35$	−92.1421	−	9.21025i	−0.444996	−	0.0444805i
$36$	36.0000			0.166667
$37$	102.334	+	177.247i	0.454691	+	0.787547i	0.998670	−	0.0515511i	$-0.0164165\pi$
$37$	102.334	+	177.247i	0.454691	+	0.787547i	−0.543980	+	0.839098i	$0.683083\pi$
$38$	15.4758	−	26.8049i	0.0660660	−	0.114430i
$39$	−4.28528	+	7.42231i	−0.0175947	+	0.0304749i
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	61.8569			0.235620			0.117810	−	0.993036i	$-0.462413\pi$
$41$	61.8569			0.235620			0.117810	+	0.993036i	$0.462413\pi$
$42$	−64.8569	+	90.2308i	−0.238277	+	0.331498i
$43$	−65.9052			−0.233732			−0.116866	−	0.993148i	$-0.537285\pi$
$43$	−65.9052			−0.233732			−0.116866	+	0.993148i	$0.537285\pi$
$44$	−51.7137	−	89.5708i	−0.177185	−	0.306893i
$45$	22.5000	−	38.9711i	0.0745356	−	0.129099i
$46$	−60.3327	+	104.499i	−0.193382	+	0.334947i
$47$	−87.7621	−	152.008i	−0.272371	−	0.471760i	0.697098	−	0.716976i	$-0.254474\pi$
$47$	−87.7621	−	152.008i	−0.272371	−	0.471760i	−0.969468	+	0.245216i	$0.921141\pi$
$48$	−48.0000			−0.144338
$49$	−109.310	−	325.116i	−0.318690	−	0.947859i
$50$	−50.0000			−0.141421
$51$	128.785	+	223.063i	0.353599	+	0.612451i
$52$	5.71370	−	9.89642i	0.0152375	−	0.0263920i
$53$	200.522	−	347.315i	0.519695	−	0.900138i	−0.480043	−	0.877245i	$-0.659379\pi$
$53$	200.522	−	347.315i	0.519695	−	0.900138i	0.999738	−	0.0228932i	$-0.00728775\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	−129.284			−0.316958
$56$	86.4758	−	120.308i	0.206354	−	0.287086i
$57$	−46.4274			−0.107885
$58$	29.6673	+	51.3854i	0.0671640	+	0.116332i
$59$	196.926	−	341.086i	0.434536	−	0.752639i	−0.562722	−	0.826647i	$-0.690246\pi$
$59$	196.926	−	341.086i	0.434536	−	0.752639i	0.997258	+	0.0740079i	$0.0235790\pi$
$60$	−30.0000	+	51.9615i	−0.0645497	+	0.111803i
$61$	30.4758	+	52.7856i	0.0639676	+	0.110795i	0.896236	−	0.443578i	$-0.146291\pi$
$61$	30.4758	+	52.7856i	0.0639676	+	0.110795i	−0.832268	+	0.554374i	$0.812958\pi$
$62$	−507.710			−1.03999
$63$	165.856	+	16.5785i	0.331680	+	0.0331538i
$64$	64.0000			0.125000
$65$	−7.14213	−	12.3705i	−0.0136288	−	0.0236058i
$66$	−77.5706	+	134.356i	−0.144671	+	0.250577i
$67$	−56.9506	+	98.6413i	−0.103845	+	0.179865i	−0.913266	−	0.407364i	$-0.866448\pi$
$67$	−56.9506	+	98.6413i	−0.103845	+	0.179865i	0.809421	+	0.587229i	$0.199781\pi$
$68$	−171.714	−	297.417i	−0.306226	−	0.530398i
$69$	180.998			0.315791
$70$	−76.1895	−	168.805i	−0.130091	−	0.288230i
$71$	483.853			0.808771			0.404386	−	0.914589i	$-0.367485\pi$
$71$	483.853			0.808771			0.404386	+	0.914589i	$0.367485\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	28.8579	−	49.9833i	0.0462679	−	0.0801384i	−0.841964	−	0.539534i	$-0.818601\pi$
$73$	28.8579	−	49.9833i	0.0462679	−	0.0801384i	0.888232	+	0.459395i	$0.151934\pi$
$74$	−204.667	+	354.494i	−0.321515	+	0.556880i
$75$	37.5000	+	64.9519i	0.0577350	+	0.100000i
$76$	61.9032			0.0934314
$77$	−197.002	−	436.477i	−0.291565	−	0.645989i
$78$	−17.1411			−0.0248827
$79$	509.738	+	882.892i	0.725949	+	1.25738i	0.958582	+	0.284816i	$0.0919326\pi$
$79$	509.738	+	882.892i	0.725949	+	1.25738i	−0.232633	+	0.972565i	$0.574734\pi$
$80$	40.0000	−	69.2820i	0.0559017	−	0.0968246i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	61.8569	+	107.139i	0.0833042	+	0.144287i
$83$	870.611			1.15135			0.575674	−	0.817679i	$-0.304740\pi$
$83$	870.611			1.15135			0.575674	+	0.817679i	$0.304740\pi$
$84$	−221.141	−	22.1046i	−0.287244	−	0.0287120i
$85$	−429.284			−0.547793
$86$	−65.9052	−	114.151i	−0.0826366	−	0.143131i
$87$	44.5010	−	77.0780i	0.0548392	−	0.0949843i
$88$	103.427	−	179.142i	0.125289	−	0.217006i
$89$	−482.404	−	835.549i	−0.574548	−	0.995146i	−0.996091	−	0.0883374i	$-0.971845\pi$
$89$	−482.404	−	835.549i	−0.574548	−	0.995146i	0.421543	−	0.906808i	$-0.361489\pi$
$90$	90.0000			0.105409
$91$	30.8810	−	42.9626i	0.0355738	−	0.0494913i
$92$	−241.331			−0.273483
$93$	380.782	+	659.534i	0.424573	+	0.735382i
$94$	175.524	−	304.017i	0.192595	−	0.333584i
$95$	38.6895	−	67.0122i	0.0417838	−	0.0723716i
$96$	−48.0000	−	83.1384i	−0.0510310	−	0.0883883i
$97$	880.758			0.921932			0.460966	−	0.887418i	$-0.347503\pi$
$97$	880.758			0.921932			0.460966	+	0.887418i	$0.347503\pi$
$98$	453.806	−	514.447i	0.467769	−	0.530275i
$99$	232.712			0.236246
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	609.590	−	1055.84i	0.600559	−	1.04020i	−0.392178	−	0.919889i	$-0.628278\pi$
$101$	609.590	−	1055.84i	0.600559	−	1.04020i	0.992737	−	0.120309i	$-0.0383885\pi$
$102$	−257.571	+	446.125i	−0.250032	+	0.433068i
$103$	492.709	+	853.396i	0.471340	+	0.816385i	0.999462	−	0.0327834i	$-0.0104371\pi$
$103$	492.709	+	853.396i	0.471340	+	0.816385i	−0.528122	+	0.849168i	$0.677104\pi$
$104$	22.8548			0.0215490
$105$	−162.142	+	225.577i	−0.150700	+	0.209658i
$106$	802.089			0.734960
$107$	764.453	+	1324.07i	0.690677	+	1.19629i	0.971616	+	0.236562i	$0.0760206\pi$
$107$	764.453	+	1324.07i	0.690677	+	1.19629i	−0.280940	+	0.959725i	$0.590646\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	36.4032	−	63.0522i	0.0319889	−	0.0554065i	−0.849588	−	0.527447i	$-0.823149\pi$
$109$	36.4032	−	63.0522i	0.0319889	−	0.0554065i	0.881577	+	0.472041i	$0.156483\pi$
$110$	−129.284	−	223.927i	−0.112062	−	0.194096i
$111$	614.002			0.525031
$112$	294.855	+	29.4728i	0.248760	+	0.0248653i
$113$	1076.66			0.896317			0.448158	−	0.893954i	$-0.352080\pi$
$113$	1076.66			0.896317			0.448158	+	0.893954i	$0.352080\pi$
$114$	−46.4274	−	80.4146i	−0.0381432	−	0.0660660i
$115$	−150.832	+	261.248i	−0.122305	+	0.211839i
$116$	−59.3347	+	102.771i	−0.0474921	+	0.0822588i
$117$	12.8558	+	22.2669i	0.0101583	+	0.0175947i
$118$	787.706			0.614527
$119$	−654.139	−	1449.31i	−0.503906	−	1.11645i
$120$	−120.000			−0.0912871
$121$	331.212	+	573.675i	0.248844	+	0.431011i
$122$	−60.9516	+	105.571i	−0.0452320	+	0.0783440i
$123$	92.7853	−	160.709i	0.0680176	−	0.117810i
$124$	−507.710	−	879.379i	−0.367691	−	0.636859i
$125$	−125.000			−0.0894427
$126$	137.141	+	303.849i	0.0969643	+	0.214834i
$127$	−302.482			−0.211346			−0.105673	−	0.994401i	$-0.533700\pi$
$127$	−302.482			−0.211346			−0.105673	+	0.994401i	$0.533700\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−98.8579	+	171.227i	−0.0674725	+	0.116866i
$130$	14.2843	−	24.7410i	0.00963701	−	0.0166918i
$131$	−1346.85	−	2332.81i	−0.898280	−	1.55587i	−0.829692	−	0.558222i	$-0.811484\pi$
$131$	−1346.85	−	2332.81i	−0.898280	−	1.55587i	−0.0685886	−	0.997645i	$-0.521850\pi$
$132$	−310.282			−0.204595
$133$	285.195	+	28.5072i	0.185936	+	0.0185856i
$134$	−227.802			−0.146859
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	343.427	−	594.834i	0.216534	−	0.375048i
$137$	−368.453	+	638.179i	−0.229774	+	0.397980i	−0.957741	−	0.287632i	$-0.907132\pi$
$137$	−368.453	+	638.179i	−0.229774	+	0.397980i	0.727967	+	0.685612i	$0.240465\pi$
$138$	180.998	+	313.498i	0.111649	+	0.193382i
$139$	−3088.79			−1.88480			−0.942401	−	0.334486i	$-0.891437\pi$
$139$	−3088.79			−1.88480			−0.942401	+	0.334486i	$0.891437\pi$
$140$	216.190	−	300.769i	0.130510	−	0.181569i
$141$	−526.573			−0.314506
$142$	483.853	+	838.058i	0.285944	+	0.495269i
$143$	36.9346	−	63.9726i	0.0215988	−	0.0374102i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	74.1684	+	128.463i	0.0424783	+	0.0735745i
$146$	115.431			0.0654327
$147$	−1008.64	−	203.677i	−0.565927	−	0.114279i
$148$	−818.669			−0.454691
$149$	−1549.61	−	2684.00i	−0.852006	−	1.47572i	−0.879395	−	0.476093i	$-0.842053\pi$
$149$	−1549.61	−	2684.00i	−0.852006	−	1.47572i	0.0273891	−	0.999625i	$-0.491281\pi$
$150$	−75.0000	+	129.904i	−0.0408248	+	0.0707107i
$151$	−590.524	+	1022.82i	−0.318253	+	0.551230i	−0.980124	−	0.198388i	$-0.936429\pi$
$151$	−590.524	+	1022.82i	−0.318253	+	0.551230i	0.661871	+	0.749618i	$0.269763\pi$
$152$	61.9032	+	107.219i	0.0330330	+	0.0572148i
$153$	772.712			0.408301
$154$	558.998	−	777.694i	0.292502	−	0.406938i
$155$	−1269.27			−0.657745
$156$	−17.1411	−	29.6893i	−0.00879735	−	0.0152375i
$157$	727.425	−	1259.94i	0.369776	−	0.640471i	−0.619754	−	0.784796i	$-0.712768\pi$
$157$	727.425	−	1259.94i	0.369776	−	0.640471i	0.989530	+	0.144325i	$0.0461010\pi$
$158$	−1019.48	+	1765.78i	−0.513324	+	0.889103i
$159$	−601.566	−	1041.94i	−0.300046	−	0.519695i
$160$	160.000			0.0790569
$161$	−1111.84	−	111.136i	−0.544254	−	0.0544020i
$162$	−162.000			−0.0785674
$163$	1543.81	+	2673.95i	0.741842	+	1.28491i	0.951656	+	0.307167i	$0.0993809\pi$
$163$	1543.81	+	2673.95i	0.741842	+	1.28491i	−0.209814	+	0.977741i	$0.567286\pi$
$164$	−123.714	+	214.278i	−0.0589050	+	0.102026i
$165$	−193.926	+	335.890i	−0.0914979	+	0.158479i
$166$	870.611	+	1507.94i	0.407063	+	0.705054i
$167$	41.8609			0.0193970			0.00969850	−	0.999953i	$-0.496913\pi$
$167$	41.8609			0.0193970			0.00969850	+	0.999953i	$0.496913\pi$
$168$	−182.855	−	405.132i	−0.0839735	−	0.186051i
$169$	−2188.84			−0.996285
$170$	−429.284	−	743.542i	−0.193674	−	0.335453i
$171$	−69.6411	+	120.622i	−0.0311438	+	0.0539426i
$172$	131.810	−	228.302i	0.0584329	−	0.101209i
$173$	892.421	+	1545.72i	0.392194	+	0.679300i	0.992739	−	0.120291i	$-0.0383829\pi$
$173$	892.421	+	1545.72i	0.392194	+	0.679300i	−0.600545	+	0.799591i	$0.705050\pi$
$174$	178.004			0.0775543
$175$	−190.474	−	422.013i	−0.0822769	−	0.182292i
$176$	413.710			0.177185
$177$	−590.779	−	1023.26i	−0.250880	−	0.434536i
$178$	964.808	−	1671.10i	0.406267	−	0.703674i
$179$	−2237.85	+	3876.08i	−0.934442	+	1.61850i	−0.158816	+	0.987308i	$0.550768\pi$
$179$	−2237.85	+	3876.08i	−0.934442	+	1.61850i	−0.775626	+	0.631193i	$0.782566\pi$
$180$	90.0000	+	155.885i	0.0372678	+	0.0645497i
$181$	4713.37			1.93559			0.967795	−	0.251740i	$-0.0810027\pi$
$181$	4713.37			1.93559			0.967795	+	0.251740i	$0.0810027\pi$
$182$	105.294	+	10.5249i	0.0428843	+	0.00428659i
$183$	182.855			0.0738635
$184$	−241.331	−	417.997i	−0.0966909	−	0.167474i
$185$	−511.668	+	886.236i	−0.203344	+	0.352202i
$186$	−761.564	+	1319.07i	−0.300218	+	0.519993i
$187$	−1109.99	−	1922.57i	−0.434068	−	0.751829i
$188$	702.097			0.272371
$189$	291.856	−	406.038i	0.112325	−	0.156270i
$190$	154.758			0.0590912
$191$	−1116.52	−	1933.87i	−0.422977	−	0.732617i	0.573252	−	0.819379i	$-0.305681\pi$
$191$	−1116.52	−	1933.87i	−0.422977	−	0.732617i	−0.996229	+	0.0867617i	$0.972348\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	−1572.75	+	2724.08i	−0.586575	+	1.01598i	0.408102	+	0.912936i	$0.366191\pi$
$193$	−1572.75	+	2724.08i	−0.586575	+	1.01598i	−0.994677	+	0.103041i	$0.967143\pi$
$194$	880.758	+	1525.52i	0.325952	+	0.564566i
$195$	−42.8528			−0.0157372
$196$	1344.85	+	271.569i	0.490107	+	0.0989682i
$197$	1460.23			0.528108			0.264054	−	0.964508i	$-0.414940\pi$
$197$	1460.23			0.528108			0.264054	+	0.964508i	$0.414940\pi$
$198$	232.712	+	403.068i	0.0835257	+	0.144671i
$199$	−2418.61	+	4189.16i	−0.861562	+	1.49227i	0.00885807	+	0.999961i	$0.497180\pi$
$199$	−2418.61	+	4189.16i	−0.861562	+	1.49227i	−0.870420	+	0.492309i	$0.836153\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$	170.852	+	295.924i	0.0599550	+	0.103845i
$202$	2438.36			0.849318
$203$	−320.688	+	446.151i	−0.110876	+	0.154255i
$204$	−1030.28			−0.353599
$205$	154.642	+	267.848i	0.0526862	+	0.0912552i
$206$	−985.417	+	1706.79i	−0.333288	+	0.577271i
$207$	271.497	−	470.246i	0.0911611	−	0.157896i
$208$	22.8548	+	39.5857i	0.00761873	+	0.0131960i
$209$	400.155			0.132437
$210$	−552.853	−	55.2615i	−0.181669	−	0.0181591i
$211$	−3790.73			−1.23680			−0.618399	−	0.785864i	$-0.712218\pi$
$211$	−3790.73			−1.23680			−0.618399	+	0.785864i	$0.712218\pi$
$212$	802.089	+	1389.26i	0.259848	+	0.450069i
$213$	725.779	−	1257.09i	0.233472	−	0.404386i
$214$	−1528.91	+	2648.14i	−0.488382	+	0.845903i
$215$	−164.763	−	285.378i	−0.0522640	−	0.0905238i
$216$	216.000			0.0680414
$217$	−1934.11	−	4285.20i	−0.605049	−	1.34054i
$218$	145.613			0.0452392
$219$	−86.5736	−	149.950i	−0.0267128	−	0.0462679i
$220$	258.569	−	447.854i	0.0792395	−	0.137247i
$221$	122.640	−	212.419i	0.0373288	−	0.0646554i
$222$	614.002	+	1063.48i	0.185627	+	0.321515i
$223$	−1931.68			−0.580067			−0.290033	−	0.957017i	$-0.593666\pi$
$223$	−1931.68			−0.580067			−0.290033	+	0.957017i	$0.593666\pi$
$224$	243.806	+	540.176i	0.0727232	+	0.161125i
$225$	225.000			0.0666667
$226$	1076.66	+	1864.83i	0.316896	+	0.548880i
$227$	−1039.39	+	1800.28i	−0.303907	+	0.526383i	−0.977017	−	0.213159i	$-0.931625\pi$
$227$	−1039.39	+	1800.28i	−0.303907	+	0.526383i	0.673110	+	0.739542i	$0.264958\pi$
$228$	92.8548	−	160.829i	0.0269713	−	0.0467157i
$229$	−1922.49	−	3329.85i	−0.554767	−	0.960884i	−0.997922	−	0.0644390i	$-0.979474\pi$
$229$	−1922.49	−	3329.85i	−0.554767	−	0.960884i	0.443155	−	0.896445i	$-0.353859\pi$
$230$	−603.327			−0.172966
$231$	−1429.50	−	142.889i	−0.407162	−	0.0406987i
$232$	−237.339			−0.0671640
$233$	2316.74	+	4012.72i	0.651395	+	1.12825i	0.982785	+	0.184755i	$0.0591490\pi$
$233$	2316.74	+	4012.72i	0.651395	+	1.12825i	−0.331390	+	0.943494i	$0.607518\pi$
$234$	−25.7117	+	44.5339i	−0.00718301	+	0.0124413i
$235$	438.810	−	760.042i	0.121808	−	0.210977i
$236$	787.706	+	1364.35i	0.217268	+	0.376319i
$237$	3058.43			0.838254
$238$	1856.13	−	2582.31i	0.505527	−	0.703304i
$239$	2588.30			0.700515			0.350258	−	0.936653i	$-0.386094\pi$
$239$	2588.30			0.700515			0.350258	+	0.936653i	$0.386094\pi$
$240$	−120.000	−	207.846i	−0.0322749	−	0.0559017i
$241$	−1643.48	+	2846.59i	−0.439278	+	0.760852i	−0.997634	−	0.0687498i	$-0.978099\pi$
$241$	−1643.48	+	2846.59i	−0.439278	+	0.760852i	0.558356	+	0.829601i	$0.311432\pi$
$242$	−662.423	+	1147.35i	−0.175959	+	0.304771i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−243.806			−0.0639676
$245$	1134.52	−	1286.12i	0.295843	−	0.335376i
$246$	371.141			0.0961914
$247$	22.1060	+	38.2888i	0.00569463	+	0.00986338i
$248$	1015.42	−	1758.76i	0.259997	−	0.450328i
$249$	1305.92	−	2261.91i	0.332366	−	0.575674i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	4971.37			1.25016			0.625080	−	0.780561i	$-0.285066\pi$
$251$	4971.37			1.25016			0.625080	+	0.780561i	$0.285066\pi$
$252$	−389.141	+	541.385i	−0.0972761	+	0.135333i
$253$	−1560.01			−0.387657
$254$	−302.482	−	523.914i	−0.0747221	−	0.129422i
$255$	−643.926	+	1115.31i	−0.158134	+	0.273897i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	56.5433	+	97.9358i	0.0137240	+	0.0237707i	0.872806	−	0.488068i	$-0.162298\pi$
$257$	56.5433	+	97.9358i	0.0137240	+	0.0237707i	−0.859082	+	0.511838i	$0.828965\pi$
$258$	−395.431			−0.0954205
$259$	−3771.70	−	377.008i	−0.904872	−	0.0904483i
$260$	57.1370			0.0136288
$261$	−133.503	−	231.234i	−0.0316614	−	0.0548392i
$262$	2693.70	−	4665.62i	0.635180	−	1.10016i
$263$	−2163.09	+	3746.58i	−0.507155	+	0.878419i	0.492810	+	0.870137i	$0.335970\pi$
$263$	−2163.09	+	3746.58i	−0.507155	+	0.878419i	−0.999966	+	0.00828221i	$0.997364\pi$
$264$	−310.282	−	537.425i	−0.0723354	−	0.125289i
$265$	2005.22			0.464829
$266$	235.819	+	522.479i	0.0543570	+	0.120433i
$267$	−2894.43			−0.663431
$268$	−227.802	−	394.565i	−0.0519225	−	0.0899325i
$269$	230.474	−	399.192i	0.0522388	−	0.0904802i	−0.838724	−	0.544557i	$-0.816698\pi$
$269$	230.474	−	399.192i	0.0522388	−	0.0904802i	0.890962	+	0.454077i	$0.150031\pi$
$270$	135.000	−	233.827i	0.0304290	−	0.0527046i
$271$	−1974.14	−	3419.31i	−0.442511	−	0.766452i	0.555364	−	0.831607i	$-0.312579\pi$
$271$	−1974.14	−	3419.31i	−0.442511	−	0.766452i	−0.997875	+	0.0651556i	$0.979246\pi$
$272$	1373.71			0.306226
$273$	−65.2986	−	144.675i	−0.0144764	−	0.0320738i
$274$	−1473.81			−0.324949
$275$	−323.211	−	559.817i	−0.0708739	−	0.122757i
$276$	−361.996	+	626.995i	−0.0789478	+	0.136742i
$277$	3163.83	−	5479.91i	0.686267	−	1.18865i	−0.286770	−	0.957999i	$-0.592582\pi$
$277$	3163.83	−	5479.91i	0.686267	−	1.18865i	0.973037	−	0.230650i	$-0.0740852\pi$
$278$	−3088.79	−	5349.93i	−0.666378	−	1.15420i
$279$	2284.69			0.490254
$280$	737.137	+	73.6820i	0.157330	+	0.0157262i
$281$	3451.21			0.732676			0.366338	−	0.930482i	$-0.380611\pi$
$281$	3451.21			0.732676			0.366338	+	0.930482i	$0.380611\pi$
$282$	−526.573	−	912.050i	−0.111195	−	0.192595i
$283$	−2815.28	+	4876.20i	−0.591345	+	1.02424i	0.402706	+	0.915329i	$0.368070\pi$
$283$	−2815.28	+	4876.20i	−0.591345	+	1.02424i	−0.994052	+	0.108911i	$0.965264\pi$
$284$	−967.706	+	1676.12i	−0.202193	+	0.350208i
$285$	−116.069	−	201.037i	−0.0241239	−	0.0417838i
$286$	147.738			0.0305453
$287$	−668.640	+	930.232i	−0.137521	+	0.191323i
$288$	−288.000			−0.0589256
$289$	−1229.20	−	2129.04i	−0.250193	−	0.433347i
$290$	−148.337	+	256.927i	−0.0300367	+	0.0520250i
$291$	1321.14	−	2288.28i	0.266139	−	0.460966i
$292$	115.431	+	199.933i	0.0231340	+	0.0400692i
$293$	7624.35			1.52020			0.760102	−	0.649804i	$-0.225149\pi$
$293$	7624.35			1.52020			0.760102	+	0.649804i	$0.225149\pi$
$294$	−655.863	−	1950.69i	−0.130104	−	0.386962i
$295$	1969.26			0.388661
$296$	−818.669	−	1417.98i	−0.160757	−	0.278440i
$297$	349.067	−	604.603i	0.0681985	−	0.118123i
$298$	3099.22	−	5368.00i	0.602459	−	1.04349i
$299$	−86.1807	−	149.269i	−0.0166688	−	0.0288711i
$300$	−300.000			−0.0577350
$301$	712.401	−	991.113i	0.136419	−	0.189790i
$302$	−2362.10			−0.450077
$303$	−1828.77	−	3167.52i	−0.346733	−	0.600559i
$304$	−123.806	+	214.439i	−0.0233578	+	0.0404570i
$305$	−152.379	+	263.928i	−0.0286072	+	0.0495491i
$306$	772.712	+	1338.38i	0.144356	+	0.250032i
$307$	5134.73			0.954574			0.477287	−	0.878747i	$-0.341620\pi$
$307$	5134.73			0.954574			0.477287	+	0.878747i	$0.341620\pi$
$308$	1906.00	+	190.518i	0.352613	+	0.0352461i
$309$	2956.25			0.544257
$310$	−1269.27	−	2198.45i	−0.232548	−	0.402785i
$311$	565.388	−	979.280i	0.103087	−	0.178553i	−0.809868	−	0.586613i	$-0.800461\pi$
$311$	565.388	−	979.280i	0.103087	−	0.178553i	0.912955	+	0.408060i	$0.133795\pi$
$312$	34.2822	−	59.3785i	0.00622066	−	0.0107745i
$313$	−3728.76	−	6458.40i	−0.673360	−	1.16629i	−0.976945	−	0.213490i	$-0.931517\pi$
$313$	−3728.76	−	6458.40i	−0.673360	−	1.16629i	0.303585	−	0.952804i	$-0.401816\pi$
$314$	2909.70			0.522943
$315$	342.853	+	759.623i	0.0613256	+	0.135873i
$316$	−4077.90			−0.725949
$317$	1930.09	+	3343.02i	0.341971	+	0.592311i	0.984799	−	0.173700i	$-0.0555723\pi$
$317$	1930.09	+	3343.02i	0.341971	+	0.592311i	−0.642828	+	0.766011i	$0.722239\pi$
$318$	1203.13	−	2083.89i	0.212165	−	0.367480i
$319$	−383.552	+	664.332i	−0.0673191	+	0.116600i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$	4586.72			0.797525
$322$	−919.343	−	2036.89i	−0.159109	−	0.352520i
$323$	1328.70			0.228889
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	35.7106	−	61.8526i	0.00609498	−	0.0105568i
$326$	−3087.61	+	5347.90i	−0.524562	+	0.908567i
$327$	−109.210	−	189.157i	−0.0184688	−	0.0319889i
$328$	−494.855			−0.0833042
$329$	3234.63	+	323.324i	0.542040	+	0.0541807i
$330$	−775.706			−0.129398
$331$	−1144.45	−	1982.25i	−0.190045	−	0.329167i	0.755220	−	0.655471i	$-0.227530\pi$
$331$	−1144.45	−	1982.25i	−0.190045	−	0.329167i	−0.945265	+	0.326304i	$0.894197\pi$
$332$	−1741.22	+	3015.88i	−0.287837	+	0.498549i
$333$	921.003	−	1595.22i	0.151564	−	0.262516i
$334$	41.8609	+	72.5053i	0.00685787	+	0.0118782i
$335$	−569.506			−0.0928819
$336$	518.855	−	721.846i	0.0842436	−	0.117202i
$337$	8170.62			1.32072			0.660359	−	0.750950i	$-0.270404\pi$
$337$	8170.62			1.32072			0.660359	+	0.750950i	$0.270404\pi$
$338$	−2188.84	−	3791.18i	−0.352240	−	0.610098i
$339$	1614.99	−	2797.25i	0.258744	−	0.448158i
$340$	858.569	−	1487.08i	0.136948	−	0.237201i
$341$	−3281.94	−	5684.49i	−0.521194	−	0.902735i
$342$	−278.564			−0.0440440
$343$	6070.83	+	1870.47i	0.955667	+	0.294448i
$344$	527.242			0.0826366
$345$	452.495	+	783.744i	0.0706131	+	0.122305i
$346$	−1784.84	+	3091.44i	−0.277323	+	0.480337i
$347$	−3820.17	+	6616.73i	−0.591002	+	1.02365i	0.403096	+	0.915158i	$0.367934\pi$
$347$	−3820.17	+	6616.73i	−0.591002	+	1.02365i	−0.994098	+	0.108487i	$0.965399\pi$
$348$	178.004	+	308.312i	0.0274196	+	0.0474921i
$349$	585.403			0.0897877			0.0448938	−	0.998992i	$-0.485705\pi$
$349$	585.403			0.0897877			0.0448938	+	0.998992i	$0.485705\pi$
$350$	540.474	−	751.923i	0.0825415	−	0.114834i
$351$	77.1350			0.0117298
$352$	413.710	+	716.566i	0.0626443	+	0.108503i
$353$	−1058.53	+	1833.43i	−0.159603	+	0.276441i	−0.934726	−	0.355370i	$-0.884355\pi$
$353$	−1058.53	+	1833.43i	−0.159603	+	0.276441i	0.775122	+	0.631811i	$0.217688\pi$
$354$	1181.56	−	2046.52i	0.177399	−	0.307263i
$355$	1209.63	+	2095.14i	0.180847	+	0.313236i
$356$	3859.23			0.574548
$357$	−4746.62	−	474.458i	−0.703691	−	0.0703389i
$358$	−8951.42			−1.32150
$359$	2656.24	+	4600.74i	0.390504	+	0.676372i	0.992516	−	0.122115i	$-0.0389676\pi$
$359$	2656.24	+	4600.74i	0.390504	+	0.676372i	−0.602012	+	0.798487i	$0.705634\pi$
$360$	−180.000	+	311.769i	−0.0263523	+	0.0456435i
$361$	3309.75	−	5732.65i	0.482541	−	0.835786i
$362$	4713.37	+	8163.79i	0.684334	+	1.18530i
$363$	1987.27			0.287341
$364$	87.0648	+	192.900i	0.0125369	+	0.0277767i
$365$	288.579			0.0413833
$366$	182.855	+	316.714i	0.0261147	+	0.0452320i
$367$	−709.161	+	1228.30i	−0.100866	+	0.174705i	−0.912042	−	0.410097i	$-0.865495\pi$
$367$	−709.161	+	1228.30i	−0.100866	+	0.174705i	0.811176	+	0.584803i	$0.198828\pi$
$368$	482.661	−	835.994i	0.0683708	−	0.118422i
$369$	−278.356	−	482.126i	−0.0392700	−	0.0680176i
$370$	−2046.67			−0.287572
$371$	3055.54	+	6769.83i	0.427589	+	0.947364i
$372$	−3046.26			−0.424573
$373$	4411.91	+	7641.65i	0.612439	+	1.06078i	0.990828	+	0.135129i	$0.0431449\pi$
$373$	4411.91	+	7641.65i	0.612439	+	1.06078i	−0.378389	+	0.925647i	$0.623522\pi$
$374$	2219.99	−	3845.13i	0.306933	−	0.531623i
$375$	−187.500	+	324.760i	−0.0258199	+	0.0447214i
$376$	702.097	+	1216.07i	0.0962975	+	0.166792i
$377$	−84.7552			−0.0115786
$378$	995.135	+	99.4707i	0.135408	+	0.0135350i
$379$	12253.4			1.66072			0.830361	−	0.557226i	$-0.188134\pi$
$379$	12253.4			1.66072			0.830361	+	0.557226i	$0.188134\pi$
$380$	154.758	+	268.049i	0.0208919	+	0.0361858i
$381$	−453.723	+	785.871i	−0.0610103	+	0.105673i
$382$	2233.04	−	3867.74i	0.299090	−	0.518039i
$383$	−6906.80	−	11962.9i	−0.921465	−	1.59602i	−0.797149	−	0.603782i	$-0.793660\pi$
$383$	−6906.80	−	11962.9i	−0.921465	−	1.59602i	−0.124316	−	0.992243i	$-0.539674\pi$
$384$	384.000			0.0510310
$385$	1397.49	−	1944.24i	0.184995	−	0.257370i
$386$	−6291.00			−0.829542
$387$	296.574	+	513.681i	0.0389553	+	0.0674725i
$388$	−1761.52	+	3051.04i	−0.230483	+	0.399208i
$389$	−3166.45	+	5484.45i	−0.412713	+	0.714840i	−0.995185	−	0.0980107i	$-0.968752\pi$
$389$	−3166.45	+	5484.45i	−0.412713	+	0.714840i	0.582472	+	0.812850i	$0.302085\pi$
$390$	−42.8528	−	74.2231i	−0.00556393	−	0.00963701i
$391$	−5179.97			−0.669981
$392$	874.484	+	2600.93i	0.112674	+	0.335119i
$393$	−8081.09			−1.03724
$394$	1460.23	+	2529.20i	0.186714	+	0.323399i
$395$	−2548.69	+	4414.46i	−0.324654	+	0.562318i
$396$	−465.423	+	806.137i	−0.0590616	+	0.102298i
$397$	−980.449	−	1698.19i	−0.123948	−	0.214684i	0.797373	−	0.603486i	$-0.206222\pi$
$397$	−980.449	−	1698.19i	−0.123948	−	0.214684i	−0.921321	+	0.388802i	$0.872889\pi$
$398$	−9674.45			−1.21843
$399$	501.856	−	698.197i	0.0629680	−	0.0876029i
$400$	400.000			0.0500000
$401$	−4368.11	−	7565.80i	−0.543973	−	0.942189i	−0.998671	−	0.0515432i	$-0.983586\pi$
$401$	−4368.11	−	7565.80i	−0.543973	−	0.942189i	0.454698	−	0.890646i	$-0.349747\pi$
$402$	−341.703	+	591.848i	−0.0423946	+	0.0734296i
$403$	362.613	−	628.063i	0.0448214	−	0.0776329i
$404$	2438.36	+	4223.36i	0.300279	+	0.520099i
$405$	−405.000			−0.0496904
$406$	−1093.45	−	109.298i	−0.133662	−	0.0133605i
$407$	−5292.05			−0.644514
$408$	−1030.28	−	1784.50i	−0.125016	−	0.216534i
$409$	−5799.82	+	10045.6i	−0.701180	+	1.21448i	0.266873	+	0.963732i	$0.414010\pi$
$409$	−5799.82	+	10045.6i	−0.701180	+	1.21448i	−0.968053	+	0.250747i	$0.919324\pi$
$410$	−309.284	+	535.696i	−0.0372548	+	0.0645272i
$411$	1105.36	+	1914.54i	0.132660	+	0.229774i
$412$	−3941.67			−0.471340
$413$	3000.74	+	6648.44i	0.357523	+	0.792126i
$414$	1085.99			0.128921
$415$	2176.53	+	3769.86i	0.257449	+	0.445915i
$416$	−45.7096	+	79.1714i	−0.00538725	+	0.00933100i
$417$	−4633.18	+	8024.90i	−0.544095	+	0.942401i
$418$	400.155	+	693.090i	0.0468235	+	0.0811008i
$419$	−7729.17			−0.901181			−0.450591	−	0.892731i	$-0.648787\pi$
$419$	−7729.17			−0.901181			−0.450591	+	0.892731i	$0.648787\pi$
$420$	−457.137	−	1012.83i	−0.0531095	−	0.117669i
$421$	−7406.89			−0.857457			−0.428729	−	0.903433i	$-0.641038\pi$
$421$	−7406.89			−0.857457			−0.428729	+	0.903433i	$0.641038\pi$
$422$	−3790.73	−	6565.73i	−0.437274	−	0.757381i
$423$	−789.859	+	1368.08i	−0.0907902	+	0.157253i
$424$	−1604.18	+	2778.52i	−0.183740	+	0.318247i
$425$	−1073.21	−	1858.86i	−0.122490	−	0.212159i
$426$	2903.12			0.330179
$427$	−1123.24	−	112.276i	−0.127301	−	0.0127246i
$428$	−6115.62			−0.690677
$429$	−110.804	−	191.918i	−0.0124701	−	0.0215988i
$430$	329.526	−	570.756i	0.0369562	−	0.0640100i
$431$	3035.10	−	5256.94i	0.339201	−	0.587513i	−0.645082	−	0.764113i	$-0.723177\pi$
$431$	3035.10	−	5256.94i	0.339201	−	0.587513i	0.984283	+	0.176601i	$0.0565101\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−7439.30			−0.825658			−0.412829	−	0.910809i	$-0.635459\pi$
$433$	−7439.30			−0.825658			−0.412829	+	0.910809i	$0.635459\pi$
$434$	5488.07	−	7635.17i	0.606995	−	0.844470i
$435$	445.010			0.0490497
$436$	145.613	+	252.209i	0.0159945	+	0.0277032i
$437$	466.848	−	808.604i	0.0511038	−	0.0885144i
$438$	173.147	−	299.900i	0.0188888	−	0.0327164i
$439$	7519.10	+	13023.5i	0.817465	+	1.41589i	0.907545	+	0.419956i	$0.137954\pi$
$439$	7519.10	+	13023.5i	0.817465	+	1.41589i	−0.0900800	+	0.995935i	$0.528712\pi$
$440$	1034.27			0.112062
$441$	−2042.13	+	2315.01i	−0.220508	+	0.249974i
$442$	490.560			0.0527909
$443$	6005.00	+	10401.0i	0.644032	+	1.11550i	0.984524	+	0.175249i	$0.0560731\pi$
$443$	6005.00	+	10401.0i	0.644032	+	1.11550i	−0.340492	+	0.940247i	$0.610594\pi$
$444$	−1228.00	+	2126.97i	−0.131258	+	0.227345i
$445$	2412.02	−	4177.74i	0.256946	−	0.445043i
$446$	−1931.68	−	3345.77i	−0.205085	−	0.355217i
$447$	−9297.65			−0.983812
$448$	−691.806	+	962.461i	−0.0729571	+	0.101500i
$449$	16740.6			1.75955			0.879775	−	0.475390i	$-0.157693\pi$
$449$	16740.6			1.75955			0.879775	+	0.475390i	$0.157693\pi$
$450$	225.000	+	389.711i	0.0235702	+	0.0408248i
$451$	−799.712	+	1385.14i	−0.0834966	+	0.144620i
$452$	−2153.32	+	3729.66i	−0.224079	+	0.388116i
$453$	1771.57	+	3068.45i	0.183743	+	0.318253i
$454$	−4157.58			−0.429790
$455$	263.236	+	26.3123i	0.0271224	+	0.00271108i
$456$	371.419			0.0381432
$457$	649.054	+	1124.19i	0.0664364	+	0.115071i	0.897330	−	0.441360i	$-0.145504\pi$
$457$	649.054	+	1124.19i	0.0664364	+	0.115071i	−0.830894	+	0.556431i	$0.812170\pi$
$458$	3844.98	−	6659.69i	0.392279	−	0.679448i
$459$	1159.07	−	2007.56i	0.117866	−	0.204150i
$460$	−603.327	−	1044.99i	−0.0611527	−	0.105920i
$461$	−2591.76			−0.261845			−0.130922	−	0.991393i	$-0.541794\pi$
$461$	−2591.76			−0.261845			−0.130922	+	0.991393i	$0.541794\pi$
$462$	−1182.01	−	2618.86i	−0.119031	−	0.263724i
$463$	−4590.88			−0.460813			−0.230407	−	0.973094i	$-0.574006\pi$
$463$	−4590.88			−0.460813			−0.230407	+	0.973094i	$0.574006\pi$
$464$	−237.339	−	411.083i	−0.0237461	−	0.0411294i
$465$	−1903.91	+	3297.67i	−0.189875	+	0.328873i
$466$	−4633.49	+	8025.44i	−0.460605	+	0.797792i
$467$	−6697.91	−	11601.1i	−0.663688	−	1.14954i	−0.979639	−	0.200766i	$-0.935657\pi$
$467$	−6697.91	−	11601.1i	−0.663688	−	1.14954i	0.315951	−	0.948775i	$-0.397676\pi$
$468$	−102.847			−0.0101583
$469$	−867.807	−	1922.71i	−0.0854405	−	0.189302i
$470$	1755.24			0.172262
$471$	−2182.28	−	3779.81i	−0.213490	−	0.369776i
$472$	−1575.41	+	2728.69i	−0.153632	+	0.266098i
$473$	852.051	−	1475.80i	0.0828274	−	0.143461i
$474$	3058.43	+	5297.35i	0.296368	+	0.513324i
$475$	386.895			0.0373725
$476$	6328.83	+	632.611i	0.609414	+	0.0609153i
$477$	−3609.40			−0.346463
$478$	2588.30	+	4483.06i	0.247670	+	0.428976i
$479$	6977.89	−	12086.1i	0.665612	−	1.15287i	−0.313507	−	0.949586i	$-0.601504\pi$
$479$	6977.89	−	12086.1i	0.665612	−	1.15287i	0.979119	−	0.203287i	$-0.0651626\pi$
$480$	240.000	−	415.692i	0.0228218	−	0.0395285i
$481$	−292.352	−	506.368i	−0.0277133	−	0.0480009i
$482$	−6573.93			−0.621233
$483$	−1956.49	+	2721.93i	−0.184314	+	0.256423i
$484$	−2649.69			−0.248844
$485$	2201.90	+	3813.79i	0.206150	+	0.357063i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	6391.74	−	11070.8i	0.594738	−	1.03012i	−0.398846	−	0.917018i	$-0.630589\pi$
$487$	6391.74	−	11070.8i	0.594738	−	1.03012i	0.993584	−	0.113098i	$-0.0360774\pi$
$488$	−243.806	−	422.285i	−0.0226160	−	0.0391720i
$489$	9262.84			0.856605
$490$	3362.14	+	678.922i	0.309971	+	0.0625930i
$491$	334.367			0.0307327			0.0153664	−	0.999882i	$-0.495109\pi$
$491$	334.367			0.0307327			0.0153664	+	0.999882i	$0.495109\pi$
$492$	371.141	+	642.835i	0.0340088	+	0.0589050i
$493$	−1273.57	+	2205.89i	−0.116347	+	0.201518i
$494$	−44.2120	+	76.5775i	−0.00402671	+	0.00697446i
$495$	581.779	+	1007.67i	0.0528263	+	0.0914979i
$496$	4061.68			0.367691
$497$	−5230.19	+	7276.40i	−0.472045	+	0.656723i
$498$	5223.66			0.470036
$499$	5749.96	+	9959.23i	0.515839	+	0.893459i	0.999831	+	0.0183870i	$0.00585308\pi$
$499$	5749.96	+	9959.23i	0.515839	+	0.893459i	−0.483992	+	0.875072i	$0.660814\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$	62.7914	−	108.758i	0.00559943	−	0.00969850i
$502$	4971.37	+	8610.66i	0.441998	+	0.765563i
$503$	−18751.6			−1.66221			−0.831105	−	0.556115i	$-0.812291\pi$
$503$	−18751.6			−1.66221			−0.831105	+	0.556115i	$0.812291\pi$
$504$	−1326.85	−	132.628i	−0.117267	−	0.0117216i
$505$	6095.90			0.537156
$506$	−1560.01	−	2702.02i	−0.137057	−	0.237390i
$507$	−3283.26	+	5686.77i	−0.287603	+	0.498143i
$508$	604.964	−	1047.83i	0.0528365	−	0.0915155i
$509$	−4780.46	−	8280.00i	−0.416287	−	0.721030i	0.579276	−	0.815132i	$-0.303335\pi$
$509$	−4780.46	−	8280.00i	−0.416287	−	0.721030i	−0.995563	+	0.0941016i	$0.970002\pi$
$510$	−2575.71			−0.223636
$511$	439.733	+	974.271i	0.0380678	+	0.0843429i
$512$	−512.000			−0.0441942
$513$	208.923	+	361.866i	0.0179809	+	0.0311438i
$514$	−113.087	+	195.872i	−0.00970435	+	0.0168084i
$515$	−2463.54	+	4266.98i	−0.210790	+	0.365098i
$516$	−395.431	−	684.907i	−0.0337362	−	0.0584329i
$517$	4538.50			0.386080
$518$	−3118.70	−	6909.78i	−0.264533	−	0.586097i
$519$	5354.53			0.452866
$520$	57.1370	+	98.9642i	0.00481851	+	0.00834590i
$521$	2068.75	−	3583.18i	0.173961	−	0.301309i	−0.765840	−	0.643031i	$-0.777677\pi$
$521$	2068.75	−	3583.18i	0.173961	−	0.301309i	0.939801	+	0.341722i	$0.111010\pi$
$522$	267.006	−	462.468i	0.0223880	−	0.0387772i
$523$	−1020.77	−	1768.03i	−0.0853447	−	0.147821i	0.820193	−	0.572086i	$-0.193866\pi$
$523$	−1020.77	−	1768.03i	−0.0853447	−	0.147821i	−0.905538	+	0.424265i	$0.860532\pi$
$524$	10774.8			0.898280
$525$	−1382.13	−	138.154i	−0.114897	−	0.0114848i
$526$	−8652.36			−0.717226
$527$	−10897.6	−	18875.2i	−0.900771	−	1.56018i
$528$	620.564	−	1074.85i	0.0511489	−	0.0885924i
$529$	4263.49	−	7384.57i	0.350414	−	0.606935i
$530$	2005.22	+	3473.15i	0.164342	+	0.284649i
$531$	−3544.67			−0.289691
$532$	−669.141	+	930.929i	−0.0545319	+	0.0758663i
$533$	−176.716			−0.0143610
$534$	−2894.43	−	5013.29i	−0.234558	−	0.406267i
$535$	−3822.26	+	6620.35i	−0.308880	+	0.534996i
$536$	455.605	−	789.130i	0.0367148	−	0.0635919i
$537$	6713.56	+	11628.2i	0.539500	+	0.934442i
$538$	921.895			0.0738768
$539$	8693.43	+	1755.48i	0.694717	+	0.140285i
$540$	540.000			0.0430331
$541$	−9812.64	−	16996.0i	−0.779812	−	1.35067i	−0.932050	−	0.362331i	$-0.881981\pi$
$541$	−9812.64	−	16996.0i	−0.779812	−	1.35067i	0.152237	−	0.988344i	$-0.451352\pi$
$542$	3948.28	−	6838.63i	0.312903	−	0.541963i
$543$	7070.05	−	12245.7i	0.558757	−	0.967795i
$544$	1373.71	+	2379.33i	0.108267	+	0.187524i
$545$	364.032			0.0286118
$546$	185.286	−	257.776i	0.0145229	−	0.0202047i
$547$	8425.96			0.658626			0.329313	−	0.944221i	$-0.393183\pi$
$547$	8425.96			0.658626			0.329313	+	0.944221i	$0.393183\pi$
$548$	−1473.81	−	2552.71i	−0.114887	−	0.198990i
$549$	274.282	−	475.071i	0.0213225	−	0.0369317i
$550$	646.421	−	1119.63i	0.0501154	−	0.0868025i
$551$	−229.563	−	397.615i	−0.0177490	−	0.0307422i
$552$	−1447.98			−0.111649
$553$	−18787.3	−	1877.93i	−1.44470	−	0.144408i
$554$	12655.3			0.970528
$555$	1535.01	+	2658.71i	0.117401	+	0.203344i
$556$	6177.57	−	10699.9i	0.471200	−	0.816143i
$557$	−9477.18	+	16415.0i	−0.720935	+	1.24870i	0.239690	+	0.970850i	$0.422954\pi$
$557$	−9477.18	+	16415.0i	−0.720935	+	1.24870i	−0.960625	+	0.277847i	$0.910379\pi$
$558$	2284.69	+	3957.20i	0.173331	+	0.300218i
$559$	188.281			0.0142459
$560$	609.516	+	1350.44i	0.0459942	+	0.101905i
$561$	−6659.96			−0.501219
$562$	3451.21	+	5977.67i	0.259040	+	0.448670i
$563$	5614.50	−	9724.60i	0.420289	−	0.727963i	−0.575678	−	0.817676i	$-0.695262\pi$
$563$	5614.50	−	9724.60i	0.420289	−	0.727963i	0.995968	+	0.0897137i	$0.0285952\pi$
$564$	1053.15	−	1824.10i	0.0786266	−	0.136185i
$565$	2691.65	+	4662.08i	0.200422	+	0.347142i
$566$	−11261.1			−0.836289
$567$	−617.135	−	1367.32i	−0.0457094	−	0.101274i
$568$	−3870.82			−0.285944
$569$	−10352.9	−	17931.8i	−0.762771	−	1.32116i	−0.941417	−	0.337245i	$-0.890505\pi$
$569$	−10352.9	−	17931.8i	−0.762771	−	1.32116i	0.178646	−	0.983913i	$-0.442828\pi$
$570$	232.137	−	402.073i	0.0170582	−	0.0295456i
$571$	−2903.80	+	5029.53i	−0.212820	+	0.368615i	−0.952596	−	0.304238i	$-0.901598\pi$
$571$	−2903.80	+	5029.53i	−0.212820	+	0.368615i	0.739776	+	0.672853i	$0.234932\pi$
$572$	147.738	+	255.890i	0.0107994	+	0.0187051i
$573$	−6699.12			−0.488411
$574$	−2279.85	−	227.887i	−0.165782	−	0.0165711i
$575$	−1508.32			−0.109393
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	11708.9	−	20280.4i	0.844795	−	1.46323i	−0.0410040	−	0.999159i	$-0.513056\pi$
$577$	11708.9	−	20280.4i	0.844795	−	1.46323i	0.885799	−	0.464069i	$-0.153611\pi$
$578$	2458.40	−	4258.07i	0.176913	−	0.306423i
$579$	4718.25	+	8172.24i	0.338659	+	0.586575i
$580$	−593.347			−0.0424783
$581$	−9410.85	+	13092.6i	−0.671993	+	0.934896i
$582$	5284.55			0.376377
$583$	5184.87	+	8980.46i	0.368328	+	0.637963i
$584$	−230.863	+	399.866i	−0.0163582	+	0.0283332i
$585$	−64.2791	+	111.335i	−0.00454293	+	0.00786859i
$586$	7624.35	+	13205.8i	0.537473	+	0.930931i
$587$	−2539.31			−0.178550			−0.0892748	−	0.996007i	$-0.528455\pi$
$587$	−2539.31			−0.178550			−0.0892748	+	0.996007i	$0.528455\pi$
$588$	2722.84	−	3086.68i	0.190966	−	0.216484i
$589$	3928.61			0.274831
$590$	1969.26	+	3410.86i	0.137412	+	0.238005i
$591$	2190.35	−	3793.79i	0.152452	−	0.264054i
$592$	1637.34	−	2835.95i	0.113673	−	0.196887i
$593$	−5161.64	−	8940.23i	−0.357442	−	0.619108i	0.630091	−	0.776522i	$-0.283018\pi$
$593$	−5161.64	−	8940.23i	−0.357442	−	0.619108i	−0.987533	+	0.157414i	$0.949684\pi$
$594$	1396.27			0.0964472
$595$	4640.34	−	6455.77i	0.319723	−	0.444808i
$596$	12396.9			0.852006
$597$	7255.84	+	12567.5i	0.497423	+	0.861562i
$598$	172.361	−	298.539i	0.0117866	−	0.0204150i
$599$	8445.69	−	14628.4i	0.576096	−	0.997828i	−0.419825	−	0.907605i	$-0.637909\pi$
$599$	8445.69	−	14628.4i	0.576096	−	0.997828i	0.995922	−	0.0902232i	$-0.0287580\pi$
$600$	−300.000	−	519.615i	−0.0204124	−	0.0353553i
$601$	11561.2			0.784679			0.392339	−	0.919821i	$-0.371666\pi$
$601$	11561.2			0.784679			0.392339	+	0.919821i	$0.371666\pi$
$602$	2429.06	+	242.802i	0.164454	+	0.0164383i
$603$	1025.11			0.0692301
$604$	−2362.10	−	4091.27i	−0.159126	−	0.275615i
$605$	−1656.06	+	2868.38i	−0.111287	+	0.192754i
$606$	3657.54	−	6335.04i	0.245177	−	0.424659i
$607$	−4139.61	−	7170.02i	−0.276807	−	0.479443i	0.693783	−	0.720184i	$-0.255943\pi$
$607$	−4139.61	−	7170.02i	−0.276807	−	0.479443i	−0.970589	+	0.240741i	$0.922609\pi$
$608$	−495.226			−0.0330330
$609$	678.102	+	1502.40i	0.0451200	+	0.0999677i
$610$	−609.516			−0.0404567
$611$	250.723	+	434.265i	0.0166009	+	0.0287537i
$612$	−1545.42	+	2676.75i	−0.102075	+	0.176799i
$613$	9719.07	−	16833.9i	0.640375	−	1.10916i	−0.344975	−	0.938612i	$-0.612112\pi$
$613$	9719.07	−	16833.9i	0.640375	−	1.10916i	0.985349	−	0.170549i	$-0.0545542\pi$
$614$	5134.73	+	8893.61i	0.337493	+	0.584555i
$615$	927.853			0.0608368
$616$	1576.02	+	3491.81i	0.103084	+	0.228392i
$617$	6698.46			0.437066			0.218533	−	0.975830i	$-0.429873\pi$
$617$	6698.46			0.437066			0.218533	+	0.975830i	$0.429873\pi$
$618$	2956.25	+	5120.38i	0.192424	+	0.333288i
$619$	−7179.92	+	12436.0i	−0.466212	+	0.807503i	−0.999255	−	0.0385848i	$-0.987715\pi$
$619$	−7179.92	+	12436.0i	−0.466212	+	0.807503i	0.533043	+	0.846088i	$0.321048\pi$
$620$	2538.55	−	4396.89i	0.164436	−	0.284812i
$621$	−814.491	−	1410.74i	−0.0526319	−	0.0911611i
$622$	2261.55			0.145788
$623$	17779.9	+	1777.23i	1.14340	+	0.114291i
$624$	137.129			0.00879735
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	7457.51	−	12916.8i	0.476138	−	0.824695i
$627$	600.233	−	1039.63i	0.0382313	−	0.0662185i
$628$	2909.70	+	5039.75i	0.184888	+	0.320236i
$629$	−17572.1			−1.11390
$630$	−972.853	+	1353.46i	−0.0615228	+	0.0855924i
$631$	14675.6			0.925876			0.462938	−	0.886391i	$-0.346795\pi$
$631$	14675.6			0.925876			0.462938	+	0.886391i	$0.346795\pi$
$632$	−4077.90	−	7063.14i	−0.256662	−	0.444551i
$633$	−5686.09	+	9848.59i	−0.357033	+	0.618399i
$634$	−3860.18	+	6686.03i	−0.241810	+	0.418827i
$635$	−756.205	−	1309.79i	−0.0472584	−	0.0818539i
$636$	4812.53			0.300046
$637$	312.284	+	928.807i	0.0194241	+	0.0577718i
$638$	−1534.21			−0.0952036
$639$	−2177.34	−	3771.26i	−0.134795	−	0.233472i
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	−9351.69	+	16197.6i	−0.576240	+	0.998076i	0.419666	+	0.907679i	$0.362147\pi$
$641$	−9351.69	+	16197.6i	−0.576240	+	0.998076i	−0.995906	+	0.0903977i	$0.971186\pi$
$642$	4586.72	+	7944.42i	0.281968	+	0.488382i
$643$	−25396.0			−1.55757			−0.778787	−	0.627288i	$-0.784165\pi$
$643$	−25396.0			−1.55757			−0.778787	+	0.627288i	$0.784165\pi$
$644$	2608.66	−	3629.24i	0.159620	−	0.222068i
$645$	−988.579			−0.0603492
$646$	1328.70	+	2301.38i	0.0809244	+	0.140165i
$647$	13337.0	−	23100.4i	0.810406	−	1.40366i	−0.102174	−	0.994767i	$-0.532580\pi$
$647$	13337.0	−	23100.4i	0.810406	−	1.40366i	0.912580	−	0.408898i	$-0.134087\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	5091.90	+	8819.42i	0.307973	+	0.533425i
$650$	142.843			0.00861961
$651$	−14034.4	−	1402.84i	−0.844935	−	0.0844572i
$652$	−12350.5			−0.741842
$653$	7475.14	+	12947.3i	0.447971	+	0.775908i	0.998254	−	0.0590699i	$-0.0188135\pi$
$653$	7475.14	+	12947.3i	0.447971	+	0.775908i	−0.550283	+	0.834978i	$0.685480\pi$
$654$	218.419	−	378.313i	0.0130594	−	0.0226196i
$655$	6734.24	−	11664.1i	0.401723	−	0.695805i
$656$	−494.855	−	857.114i	−0.0294525	−	0.0510132i
$657$	−519.442			−0.0308453
$658$	2674.62	+	5925.88i	0.158461	+	0.351086i
$659$	10438.0			0.617004			0.308502	−	0.951224i	$-0.400172\pi$
$659$	10438.0			0.617004			0.308502	+	0.951224i	$0.400172\pi$
$660$	−775.706	−	1343.56i	−0.0457489	−	0.0792395i
$661$	3471.39	−	6012.62i	0.204268	−	0.353803i	−0.745631	−	0.666359i	$-0.767852\pi$
$661$	3471.39	−	6012.62i	0.204268	−	0.353803i	0.949899	+	0.312556i	$0.101185\pi$
$662$	2288.91	−	3964.50i	0.134382	−	0.232757i
$663$	−367.920	−	637.257i	−0.0215518	−	0.0373288i
$664$	−6964.89			−0.407063
$665$	589.547	+	1306.20i	0.0343784	+	0.0761686i
$666$	3684.01			0.214343
$667$	894.955	+	1550.11i	0.0519532	+	0.0899856i
$668$	−83.7219	+	145.011i	−0.00484925	+	0.00839914i
$669$	−2897.52	+	5018.65i	−0.167451	+	0.290033i
$670$	−569.506	−	986.413i	−0.0328387	−	0.0568783i
$671$	−1576.02			−0.0906728
$672$	1769.13	+	176.837i	0.101556	+	0.0101512i
$673$	−14290.0			−0.818482			−0.409241	−	0.912426i	$-0.634206\pi$
$673$	−14290.0			−0.818482			−0.409241	+	0.912426i	$0.634206\pi$
$674$	8170.62	+	14151.9i	0.466944	+	0.808771i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	4377.68	−	7582.36i	0.249071	−	0.431404i
$677$	−2103.39	−	3643.18i	−0.119409	−	0.206822i	0.800125	−	0.599834i	$-0.204767\pi$
$677$	−2103.39	−	3643.18i	−0.119409	−	0.206822i	−0.919534	+	0.393011i	$0.871433\pi$
$678$	6459.97			0.365920
$679$	−9520.53	+	13245.2i	−0.538092	+	0.748609i
$680$	3434.27			0.193674
$681$	3118.18	+	5400.85i	0.175461	+	0.303907i
$682$	6563.89	−	11369.0i	0.368540	−	0.638330i
$683$	12898.1	−	22340.2i	0.722596	−	1.25157i	−0.237360	−	0.971422i	$-0.576282\pi$
$683$	12898.1	−	22340.2i	0.722596	−	1.25157i	0.959956	−	0.280151i	$-0.0903847\pi$
$684$	−278.564	−	482.488i	−0.0155719	−	0.0269713i
$685$	−3684.53			−0.205516
$686$	2831.08	+	12385.5i	0.157567	+	0.689328i
$687$	−11534.9			−0.640589
$688$	527.242	+	913.210i	0.0292164	+	0.0506044i
$689$	−572.862	+	992.226i	−0.0316753	+	0.0548633i
$690$	−904.990	+	1567.49i	−0.0499310	+	0.0864830i
$691$	15799.8	+	27366.1i	0.869830	+	1.50659i	0.862170	+	0.506620i	$0.169105\pi$
$691$	15799.8	+	27366.1i	0.869830	+	1.50659i	0.00766055	+	0.999971i	$0.497562\pi$
$692$	−7139.37			−0.392194
$693$	−2515.49	+	3499.62i	−0.137887	+	0.191832i
$694$	−15280.7			−0.835803
$695$	−7721.96	−	13374.8i	−0.421454	−	0.729980i
$696$	−356.008	+	616.624i	−0.0193886	+	0.0335820i
$697$	−2655.42	+	4599.32i	−0.144306	+	0.249945i
$698$	585.403	+	1013.95i	0.0317447	+	0.0549835i
$699$	13900.5			0.752166
$700$	1842.84	+	184.205i	0.0995041	+	0.00994614i
$701$	3551.58			0.191357			0.0956787	−	0.995412i	$-0.469498\pi$
$701$	3551.58			0.191357			0.0956787	+	0.995412i	$0.469498\pi$
$702$	77.1350	+	133.602i	0.00414711	+	0.00718301i
$703$	1583.70	−	2743.04i	0.0849647	−	0.147163i
$704$	−827.419	+	1433.13i	−0.0442962	+	0.0767233i
$705$	−1316.43	−	2280.13i	−0.0703258	−	0.121808i
$706$	−4234.12			−0.225713
$707$	9288.87	+	20580.4i	0.494121	+	1.09477i
$708$	4726.23			0.250880
$709$	−13352.1	−	23126.5i	−0.707261	−	1.22501i	−0.965870	−	0.259029i	$-0.916597\pi$
$709$	−13352.1	−	23126.5i	−0.707261	−	1.22501i	0.258609	−	0.965982i	$-0.416736\pi$
$710$	−2419.26	+	4190.29i	−0.127878	+	0.221491i
$711$	4587.64	−	7946.03i	0.241983	−	0.419127i
$712$	3859.23	+	6684.39i	0.203133	+	0.351837i
$713$	−15315.7			−0.804458
$714$	−3924.83	−	8695.84i	−0.205719	−	0.455790i
$715$	369.346			0.0193185
$716$	−8951.42	−	15504.3i	−0.467221	−	0.809251i
$717$	3882.45	−	6724.60i	0.202221	−	0.350258i
$718$	−5312.47	+	9201.47i	−0.276128	+	0.478267i
$719$	−1656.24	−	2868.68i	−0.0859070	−	0.148795i	0.819870	−	0.572549i	$-0.194045\pi$
$719$	−1656.24	−	2868.68i	−0.0859070	−	0.148795i	−0.905777	+	0.423754i	$0.860712\pi$
$720$	−720.000			−0.0372678
$721$	−18159.7	−	1815.19i	−0.938006	−	0.0937602i
$722$	13239.0			0.682416
$723$	4930.45	+	8539.78i	0.253617	+	0.439278i
$724$	−9426.73	+	16327.6i	−0.483897	+	0.838135i
$725$	−370.842	+	642.317i	−0.0189969	+	0.0329035i
$726$	1987.27	+	3442.05i	0.101590	+	0.175959i
$727$	1356.37			0.0691954			0.0345977	−	0.999401i	$-0.488985\pi$
$727$	1356.37			0.0691954			0.0345977	+	0.999401i	$0.488985\pi$
$728$	−247.048	+	343.701i	−0.0125772	+	0.0174978i
$729$	729.000			0.0370370
$730$	288.579	+	499.833i	0.0146312	+	0.0253420i
$731$	2829.21	−	4900.33i	0.143149	−	0.247942i
$732$	−365.710	+	633.428i	−0.0184659	+	0.0319838i
$733$	−924.548	−	1601.36i	−0.0465880	−	0.0806927i	0.841791	−	0.539803i	$-0.181501\pi$
$733$	−924.548	−	1601.36i	−0.0465880	−	0.0806927i	−0.888379	+	0.459111i	$0.848168\pi$
$734$	−2836.64			−0.142646
$735$	−1639.66	−	4876.74i	−0.0822853	−	0.244736i
$736$	1930.64			0.0966909
$737$	−1472.56	−	2550.55i	−0.0735991	−	0.127477i
$738$	556.712	−	964.253i	0.0277681	−	0.0480957i
$739$	3990.06	−	6910.98i	0.198615	−	0.344012i	−0.749464	−	0.662045i	$-0.769689\pi$
$739$	3990.06	−	6910.98i	0.198615	−	0.344012i	0.948080	+	0.318033i	$0.103022\pi$
$740$	−2046.67	−	3544.94i	−0.101672	−	0.176101i
$741$	132.636			0.00657559
$742$	−8670.16	+	12062.2i	−0.428964	+	0.596788i
$743$	9538.40			0.470969			0.235484	−	0.971878i	$-0.424332\pi$
$743$	9538.40			0.470969			0.235484	+	0.971878i	$0.424332\pi$
$744$	−3046.26	−	5276.27i	−0.150109	−	0.259997i
$745$	7748.04	−	13420.0i	0.381029	−	0.659961i
$746$	−8823.81	+	15283.3i	−0.433060	+	0.750082i
$747$	−3917.75	−	6785.74i	−0.191891	−	0.332366i
$748$	8879.95			0.434068
$749$	−28175.3	−	2816.32i	−1.37450	−	0.137391i
$750$	−750.000			−0.0365148
$751$	−6608.94	−	11447.0i	−0.321123	−	0.556202i	0.659597	−	0.751620i	$-0.270727\pi$
$751$	−6608.94	−	11447.0i	−0.321123	−	0.556202i	−0.980720	+	0.195418i	$0.937394\pi$
$752$	−1404.19	+	2432.13i	−0.0680926	+	0.117940i
$753$	7457.05	−	12916.0i	0.360890	−	0.625080i
$754$	−84.7552	−	146.800i	−0.00409364	−	0.00709038i
$755$	−5905.24			−0.284654
$756$	822.847	+	1823.10i	0.0395855	+	0.0877055i
$757$	31077.5			1.49212			0.746058	−	0.665881i	$-0.231944\pi$
$757$	31077.5			1.49212			0.746058	+	0.665881i	$0.231944\pi$
$758$	12253.4	+	21223.5i	0.587154	+	1.01698i
$759$	−2340.02	+	4053.03i	−0.111907	+	0.193828i
$760$	−309.516	+	536.097i	−0.0147728	+	0.0255872i
$761$	9903.71	+	17153.7i	0.471760	+	0.817112i	0.999478	−	0.0323077i	$-0.0102856\pi$
$761$	9903.71	+	17153.7i	0.471760	+	0.817112i	−0.527718	+	0.849419i	$0.676952\pi$
$762$	−1814.89			−0.0862816
$763$	554.708	+	1229.01i	0.0263195	+	0.0583134i
$764$	8932.16			0.422977
$765$	1931.78	+	3345.94i	0.0912989	+	0.158134i
$766$	13813.6	−	23925.9i	0.651574	−	1.12856i
$767$	−562.589	+	974.433i	−0.0264849	+	0.0458732i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	−32451.4			−1.52175			−0.760877	−	0.648896i	$-0.775231\pi$
$769$	−32451.4			−1.52175			−0.760877	+	0.648896i	$0.775231\pi$
$770$	4765.01	+	476.296i	0.223012	+	0.0222916i
$771$	339.260			0.0158471
$772$	−6291.00	−	10896.3i	−0.293287	−	0.507989i
$773$	2129.13	−	3687.76i	0.0990678	−	0.171590i	−0.812231	−	0.583336i	$-0.801747\pi$
$773$	2129.13	−	3687.76i	0.0990678	−	0.171590i	0.911299	+	0.411745i	$0.135081\pi$
$774$	−593.147	+	1027.36i	−0.0275455	+	0.0477103i
$775$	−3173.19	−	5496.12i	−0.147076	−	0.254744i
$776$	−7046.06			−0.325952
$777$	−6637.04	+	9233.64i	−0.306438	+	0.426326i
$778$	−12665.8			−0.583664
$779$	−478.642	−	829.032i	−0.0220143	−	0.0381299i
$780$	85.7055	−	148.446i	0.00393429	−	0.00681440i
$781$	−6255.45	+	10834.8i	−0.286604	+	0.496413i
$782$	−5179.97	−	8971.97i	−0.236874	−	0.410278i
$783$	−801.018			−0.0365595
$784$	−3630.45	+	4115.58i	−0.165381	+	0.187481i
$785$	7274.25			0.330738
$786$	−8081.09	−	13996.9i	−0.366721	−	0.635180i
$787$	−4597.28	+	7962.73i	−0.208228	+	0.360661i	−0.951156	−	0.308709i	$-0.900103\pi$
$787$	−4597.28	+	7962.73i	−0.208228	+	0.360661i	0.742928	+	0.669371i	$0.233436\pi$
$788$	−2920.46	+	5058.39i	−0.132027	+	0.228677i
$789$	6489.27	+	11239.7i	0.292806	+	0.507155i
$790$	−10194.8			−0.459131
$791$	−11638.1	+	16191.3i	−0.523141	+	0.727809i
$792$	−1861.69			−0.0835257
$793$	−87.0648	−	150.801i	−0.00389882	−	0.00675295i
$794$	1960.90	−	3396.37i	0.0876444	−	0.151805i
$795$	3007.83	−	5209.72i	0.134185	−	0.232415i
$796$	−9674.45	−	16756.6i	−0.430781	−	0.746135i
$797$	15145.5			0.673128			0.336564	−	0.941661i	$-0.390735\pi$
$797$	15145.5			0.673128			0.336564	+	0.941661i	$0.390735\pi$
$798$	1711.17	+	171.043i	0.0759081	+	0.00758755i
$799$	15070.0			0.667255
$800$	400.000	+	692.820i	0.0176777	+	0.0306186i
$801$	−4341.64	+	7519.94i	−0.191516	+	0.331715i
$802$	8736.23	−	15131.6i	0.384647	−	0.666228i
$803$	746.174	+	1292.41i	0.0327919	+	0.0567972i
$804$	−1366.81			−0.0599550
$805$	−2298.36	−	5092.23i	−0.100629	−	0.222953i
$806$	1450.45			0.0633870
$807$	−691.421	−	1197.58i	−0.0301601	−	0.0522388i
$808$	−4876.72	+	8446.72i	−0.212330	+	0.367766i
$809$	−20754.5	+	35947.8i	−0.901963	+	1.56225i	−0.0770197	+	0.997030i	$0.524540\pi$
$809$	−20754.5	+	35947.8i	−0.901963	+	1.56225i	−0.824943	+	0.565216i	$0.808793\pi$
$810$	−405.000	−	701.481i	−0.0175682	−	0.0304290i
$811$	17868.0			0.773648			0.386824	−	0.922154i	$-0.373572\pi$
$811$	17868.0			0.773648			0.386824	+	0.922154i	$0.373572\pi$
$812$	−904.136	−	2003.20i	−0.0390751	−	0.0865746i
$813$	−11844.8			−0.510968
$814$	−5292.05	−	9166.10i	−0.227870	−	0.394683i
$815$	−7719.03	+	13369.8i	−0.331762	+	0.574628i
$816$	2060.56	−	3569.00i	0.0883997	−	0.153113i
$817$	509.968	+	883.291i	0.0218379	+	0.0378243i
$818$	−23199.3			−0.991618
$819$	−473.825	−	47.3622i	−0.0202159	−	0.00202072i
$820$	−1237.14			−0.0526862
$821$	11172.6	+	19351.5i	0.474941	+	0.822622i	0.999588	−	0.0286977i	$-0.00913602\pi$
$821$	11172.6	+	19351.5i	0.474941	+	0.822622i	−0.524647	+	0.851320i	$0.675803\pi$
$822$	−2210.72	+	3829.07i	−0.0938048	+	0.162475i
$823$	11070.7	−	19175.0i	0.468895	−	0.812149i	−0.530473	−	0.847702i	$-0.677986\pi$
$823$	11070.7	−	19175.0i	0.468895	−	0.812149i	0.999368	+	0.0355523i	$0.0113190\pi$
$824$	−3941.67	−	6827.17i	−0.166644	−	0.288636i
$825$	−1939.26			−0.0818382
$826$	−8514.68	+	11845.9i	−0.358673	+	0.498996i
$827$	−1044.64			−0.0439248			−0.0219624	−	0.999759i	$-0.506991\pi$
$827$	−1044.64			−0.0439248			−0.0219624	+	0.999759i	$0.506991\pi$
$828$	1085.99	+	1880.99i	0.0455805	+	0.0789478i
$829$	−6325.19	+	10955.5i	−0.264997	+	0.458989i	−0.967563	−	0.252630i	$-0.918704\pi$
$829$	−6325.19	+	10955.5i	−0.264997	+	0.458989i	0.702566	+	0.711619i	$0.252038\pi$
$830$	−4353.05	+	7539.71i	−0.182044	+	0.315310i
$831$	−9491.48	−	16439.7i	−0.396216	−	0.686267i
$832$	−182.838			−0.00761873
$833$	28866.2	+	5829.01i	1.20067	+	0.242453i
$834$	−18532.7			−0.769467
$835$	104.652	+	181.263i	0.00433730	+	0.00751242i
$836$	−800.311	+	1386.18i	−0.0331092	+	0.0573469i
$837$	3427.04	−	5935.81i	0.141524	−	0.245127i
$838$	−7729.17	−	13387.3i	−0.318616	−	0.551858i
$839$	−33358.2			−1.37265			−0.686324	−	0.727296i	$-0.740777\pi$
$839$	−33358.2			−1.37265			−0.686324	+	0.727296i	$0.740777\pi$
$840$	1297.14	−	1804.62i	0.0532803	−	0.0741252i
$841$	−23508.8			−0.963912
$842$	−7406.89	−	12829.1i	−0.303157	−	0.525083i
$843$	5176.81	−	8966.50i	0.211505	−	0.366338i
$844$	7581.45	−	13131.5i	0.309199	−	0.535549i
$845$	−5472.10	−	9477.95i	−0.222776	−	0.385860i
$846$	−3159.44			−0.128397
$847$	−12207.4	−	1220.22i	−0.495221	−	0.0495008i
$848$	−6416.71			−0.259848
$849$	8445.83	+	14628.6i	0.341413	+	0.591345i
$850$	2146.42	−	3717.71i	0.0866137	−	0.150019i
$851$	−6174.06	+	10693.8i	−0.248700	+	0.430762i
$852$	2903.12	+	5028.35i	0.116736	+	0.202193i
$853$	−4007.63			−0.160866			−0.0804329	−	0.996760i	$-0.525630\pi$
$853$	−4007.63			−0.160866			−0.0804329	+	0.996760i	$0.525630\pi$
$854$	−928.774	−	2057.79i	−0.0372155	−	0.0824544i
$855$	−696.411			−0.0278559
$856$	−6115.62	−	10592.6i	−0.244191	−	0.422951i
$857$	−17923.5	+	31044.4i	−0.714416	+	1.23741i	0.248768	+	0.968563i	$0.419974\pi$
$857$	−17923.5	+	31044.4i	−0.714416	+	1.23741i	−0.963184	+	0.268842i	$0.913359\pi$
$858$	221.607	−	383.835i	0.00881766	−	0.0152726i
$859$	21557.9	+	37339.4i	0.856282	+	1.48312i	0.875451	+	0.483307i	$0.160565\pi$
$859$	21557.9	+	37339.4i	0.856282	+	1.48312i	−0.0191690	+	0.999816i	$0.506102\pi$
$860$	1318.10			0.0522640
$861$	1413.85	+	3132.53i	0.0559628	+	0.123991i
$862$	12140.4			0.479702
$863$	10485.5	+	18161.5i	0.413594	+	0.716366i	0.995280	−	0.0970475i	$-0.0309399\pi$
$863$	10485.5	+	18161.5i	0.413594	+	0.716366i	−0.581686	+	0.813414i	$0.697607\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−4462.11	+	7728.59i	−0.175394	+	0.303792i
$866$	−7439.30	−	12885.2i	−0.291914	−	0.505610i
$867$	−7375.20			−0.288898
$868$	18712.6	+	1870.45i	0.731735	+	0.0731421i
$869$	−26360.4			−1.02902
$870$	445.010	+	770.780i	0.0173417	+	0.0300367i
$871$	162.699	−	281.803i	0.00632934	−	0.0109627i
$872$	−291.226	+	504.418i	−0.0113098	+	0.0195891i
$873$	−3963.41	−	6864.83i	−0.153655	−	0.266139i
$874$	1867.39			0.0722717
$875$	1351.18	−	1879.81i	0.0522039	−	0.0726275i
$876$	692.589			0.0267128
$877$	1345.48	+	2330.44i	0.0518057	+	0.0897302i	0.890765	−	0.454464i	$-0.150169\pi$
$877$	1345.48	+	2330.44i	0.0518057	+	0.0897302i	−0.838960	+	0.544194i	$0.816836\pi$
$878$	−15038.2	+	26046.9i	−0.578035	+	1.00119i
$879$	11436.5	−	19808.7i	0.438845	−	0.760102i
$880$	1034.27	+	1791.42i	0.0396197	+	0.0686234i
$881$	47941.6			1.83336			0.916682	−	0.399618i	$-0.130857\pi$
$881$	47941.6			1.83336			0.916682	+	0.399618i	$0.130857\pi$
$882$	−6051.85	−	1222.06i	−0.231039	−	0.0466541i
$883$	27408.5			1.04459			0.522293	−	0.852766i	$-0.325077\pi$
$883$	27408.5			1.04459			0.522293	+	0.852766i	$0.325077\pi$
$884$	490.560	+	849.675i	0.0186644	+	0.0323277i
$885$	2953.90	−	5116.30i	0.112197	−	0.194330i
$886$	−12010.0	+	20801.9i	−0.455400	+	0.788775i
$887$	2090.24	+	3620.40i	0.0791245	+	0.137048i	0.902872	−	0.429909i	$-0.141454\pi$
$887$	2090.24	+	3620.40i	0.0791245	+	0.137048i	−0.823748	+	0.566956i	$0.808121\pi$
$888$	−4912.02			−0.185627
$889$	3269.67	−	4548.86i	0.123353	−	0.171613i
$890$	9648.08			0.363376
$891$	−1047.20	−	1813.81i	−0.0393744	−	0.0681985i
$892$	3863.36	−	6691.54i	0.145017	−	0.251176i
$893$	−1358.19	+	2352.45i	−0.0508959	+	0.0881543i
$894$	−9297.65	−	16104.0i	−0.347830	−	0.602459i
$895$	−22378.5			−0.835790
$896$	−2358.84	−	235.782i	−0.0879501	−	0.00879123i
$897$	−517.084			−0.0192474
$898$	16740.6	+	28995.6i	0.622095	+	1.07750i
$899$	−3765.60	+	6522.21i	−0.139699	+	0.241966i
$900$	−450.000	+	779.423i	−0.0166667	+	0.0288675i
$901$	17216.2	+	29819.3i	0.636576	+	1.10258i
$902$	−3198.85			−0.118082
$903$	−1506.39	−	3337.54i	−0.0555143	−	0.122997i
$904$	−8613.29			−0.316896
$905$	11783.4	+	20409.5i	0.432811	+	0.749651i
$906$	−3543.15	+	6136.91i	−0.129926	+	0.225039i
$907$	−15617.6	+	27050.4i	−0.571746	+	0.990292i	0.424641	+	0.905362i	$0.360400\pi$
$907$	−15617.6	+	27050.4i	−0.571746	+	0.990292i	−0.996387	+	0.0849307i	$0.972933\pi$
$908$	−4157.58	−	7201.13i	−0.151954	−	0.263192i
$909$	−10972.6			−0.400373
$910$	217.662	+	482.251i	0.00792904	+	0.0175675i
$911$	42112.2			1.53155			0.765774	−	0.643110i	$-0.222356\pi$
$911$	42112.2			1.53155			0.765774	+	0.643110i	$0.222356\pi$
$912$	371.419	+	643.317i	0.0134857	+	0.0233578i
$913$	−11255.6	+	19495.3i	−0.408003	+	0.706682i
$914$	−1298.11	+	2248.39i	−0.0469776	+	0.0813677i
$915$	457.137	+	791.785i	0.0165164	+	0.0286072i
$916$	15379.9			0.554767
$917$	49640.6	+	4961.93i	1.78765	+	0.178688i
$918$	4636.27			0.166688
$919$	−20932.7	−	36256.5i	−0.751367	−	1.30141i	−0.947160	−	0.320761i	$-0.896061\pi$
$919$	−20932.7	−	36256.5i	−0.751367	−	1.30141i	0.195793	−	0.980645i	$-0.437272\pi$
$920$	1206.65	−	2089.98i	0.0432415	−	0.0748965i
$921$	7702.09	−	13340.4i	0.275562	−	0.477287i
$922$	−2591.76	−	4489.07i	−0.0925761	−	0.160347i
$923$	−1382.29			−0.0492945
$924$	3353.99	−	4666.17i	0.119414	−	0.166132i
$925$	−5116.68			−0.181876
$926$	−4590.88	−	7951.64i	−0.162922	−	0.282189i
$927$	4434.38	−	7680.57i	0.157113	−	0.272128i
$928$	474.678	−	822.166i	0.0167910	−	0.0290829i
$929$	−19878.6	−	34430.7i	−0.702040	−	1.21597i	−0.967749	−	0.251915i	$-0.918940\pi$
$929$	−19878.6	−	34430.7i	−0.702040	−	1.21597i	0.265710	−	0.964053i	$-0.414394\pi$
$930$	−7615.64			−0.268523
$931$	−3511.51	+	3980.74i	−0.123614	+	0.140133i
$932$	−18533.9			−0.651395
$933$	−1696.16	−	2937.84i	−0.0595176	−	0.103087i
$934$	13395.8	−	23202.2i	0.469298	−	0.812849i
$935$	5549.97	−	9612.83i	0.194121	−	0.336228i
$936$	−102.847	−	178.136i	−0.00359150	−	0.00622066i
$937$	45235.4			1.57714			0.788568	−	0.614947i	$-0.210823\pi$
$937$	45235.4			1.57714			0.788568	+	0.614947i	$0.210823\pi$
$938$	2462.42	−	3425.80i	0.0857153	−	0.119250i
$939$	−22372.5			−0.777530
$940$	1755.24	+	3040.17i	0.0609039	+	0.105489i
$941$	−1313.60	+	2275.23i	−0.0455072	+	0.0788208i	−0.887882	−	0.460072i	$-0.847824\pi$
$941$	−1313.60	+	2275.23i	−0.0455072	+	0.0788208i	0.842375	+	0.538892i	$0.181157\pi$
$942$	4364.55	−	7559.63i	0.150961	−	0.261471i
$943$	1865.99	+	3232.00i	0.0644381	+	0.111610i
$944$	−6301.64			−0.217268
$945$	2487.84	+	248.677i	0.0856395	+	0.00856027i
$946$	3408.20			0.117136
$947$	−8749.39	−	15154.4i	−0.300229	−	0.520012i	0.675958	−	0.736940i	$-0.263730\pi$
$947$	−8749.39	−	15154.4i	−0.300229	−	0.520012i	−0.976188	+	0.216927i	$0.930397\pi$
$948$	−6116.85	+	10594.7i	−0.209564	+	0.362975i
$949$	−82.4426	+	142.795i	−0.00282002	+	0.00488442i
$950$	386.895	+	670.122i	0.0132132	+	0.0228859i
$951$	11580.5			0.394874
$952$	5233.11	+	11594.5i	0.178158	+	0.394725i
$953$	12205.0			0.414856			0.207428	−	0.978250i	$-0.433491\pi$
$953$	12205.0			0.414856			0.207428	+	0.978250i	$0.433491\pi$
$954$	−3609.40	−	6251.66i	−0.122493	−	0.212165i
$955$	5582.60	−	9669.35i	0.189161	−	0.327636i
$956$	−5176.60	+	8966.13i	−0.175129	+	0.303332i
$957$	1150.66	+	1993.00i	0.0388667	+	0.0673191i
$958$	27911.6			0.941317
$959$	−5614.44	−	12439.3i	−0.189051	−	0.418860i
$960$	960.000			0.0322749
$961$	−17325.6	−	30008.9i	−0.581573	−	1.00731i
$962$	584.704	−	1012.74i	0.0195963	−	0.0339417i
$963$	6880.07	−	11916.6i	0.230226	−	0.398762i
$964$	−6573.93	−	11386.4i	−0.219639	−	0.380426i
$965$	−15727.5			−0.524648
$966$	−6671.01	−	666.815i	−0.222191	−	0.0222095i
$967$	−1759.85			−0.0585243			−0.0292621	−	0.999572i	$-0.509316\pi$
$967$	−1759.85			−0.0585243			−0.0292621	+	0.999572i	$0.509316\pi$
$968$	−2649.69	−	4589.40i	−0.0879797	−	0.152385i
$969$	1993.06	−	3452.07i	0.0660745	−	0.114444i
$970$	−4403.79	+	7627.59i	−0.145770	+	0.252482i
$971$	24122.6	+	41781.5i	0.797251	+	1.38088i	0.921400	+	0.388615i	$0.127047\pi$
$971$	24122.6	+	41781.5i	0.797251	+	1.38088i	−0.124149	+	0.992264i	$0.539620\pi$
$972$	−972.000			−0.0320750
$973$	33388.2	−	46450.6i	1.10008	−	1.53046i
$974$	25566.9			0.841086
$975$	−107.132	−	185.558i	−0.00351894	−	0.00609498i
$976$	487.613	−	844.570i	0.0159919	−	0.0276988i
$977$	−9129.19	+	15812.2i	−0.298944	+	0.517787i	−0.975895	−	0.218242i	$-0.929968\pi$
$977$	−9129.19	+	15812.2i	−0.298944	+	0.517787i	0.676950	+	0.736029i	$0.263301\pi$
$978$	9262.84	+	16043.7i	0.302856	+	0.524562i
$979$	24946.9			0.814409
$980$	2186.21	+	6502.31i	0.0712611	+	0.211948i
$981$	−655.258			−0.0213260
$982$	334.367	+	579.140i	0.0108657	+	0.0188199i
$983$	8087.42	−	14007.8i	0.262410	−	0.454507i	−0.704472	−	0.709732i	$-0.748816\pi$
$983$	8087.42	−	14007.8i	0.262410	−	0.454507i	0.966882	+	0.255225i	$0.0821495\pi$
$984$	−742.282	+	1285.67i	−0.0240479	+	0.0416521i
$985$	3650.58	+	6322.99i	0.118088	+	0.204535i
$986$	−5094.29			−0.164539
$987$	5691.97	−	7918.84i	0.183564	−	0.255379i
$988$	−176.848			−0.00569463
$989$	−1988.12	−	3443.52i	−0.0639217	−	0.110716i
$990$	−1163.56	+	2015.34i	−0.0373538	+	0.0646988i
$991$	13554.1	−	23476.3i	0.434469	−	0.752523i	−0.562783	−	0.826605i	$-0.690269\pi$
$991$	13554.1	−	23476.3i	0.434469	−	0.752523i	0.997252	+	0.0740820i	$0.0236026\pi$
$992$	4061.68	+	7035.03i	0.129998	+	0.225164i
$993$	−6866.72			−0.219445
$994$	−17833.3	−	1782.56i	−0.569052	−	0.0568807i
$995$	−24186.1			−0.770605
$996$	5223.66	+	9047.65i	0.166183	+	0.287837i
$997$	−13368.1	+	23154.2i	−0.424645	+	0.735506i	−0.996387	−	0.0849269i	$-0.972934\pi$
$997$	−13368.1	+	23154.2i	−0.424645	+	0.735506i	0.571742	+	0.820433i	$0.306268\pi$
$998$	−11499.9	+	19918.5i	−0.364753	+	0.631771i
$999$	−2763.01	−	4785.67i	−0.0875052	−	0.151564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.4.i.j.151.1	yes	4
3.2	odd	2		630.4.k.k.361.1		4
7.2	even	3	inner	210.4.i.j.121.1	✓	4
7.3	odd	6		1470.4.a.bj.1.2		2
7.4	even	3		1470.4.a.be.1.2		2
21.2	odd	6		630.4.k.k.541.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.i.j.121.1	✓	4	7.2	even	3	inner
210.4.i.j.151.1	yes	4	1.1	even	1	trivial
630.4.k.k.361.1		4	3.2	odd	2
630.4.k.k.541.1		4	21.2	odd	6
1470.4.a.be.1.2		2	7.4	even	3
1470.4.a.bj.1.2		2	7.3	odd	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	210.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} +(-10.8095 + 15.0385i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} +(-10.8095 + 15.0385i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(-12.9284 + 22.3927i) q^{11} +(6.00000 + 10.3923i) q^{12} -2.85685 q^{13} +(-36.8569 - 3.68410i) q^{14} +15.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-42.9284 + 74.3542i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-7.73790 - 13.4024i) q^{19} -20.0000 q^{20} +(22.8569 + 50.6415i) q^{21} -51.7137 q^{22} +(30.1663 + 52.2496i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-2.85685 - 4.94821i) q^{26} -27.0000 q^{27} +(-30.4758 - 67.5220i) q^{28} +29.6673 q^{29} +(15.0000 + 25.9808i) q^{30} +(-126.927 + 219.845i) q^{31} +(16.0000 - 27.7128i) q^{32} +(38.7853 + 67.1781i) q^{33} -171.714 q^{34} +(-92.1421 - 9.21025i) q^{35} +36.0000 q^{36} +(102.334 + 177.247i) q^{37} +(15.4758 - 26.8049i) q^{38} +(-4.28528 + 7.42231i) q^{39} +(-20.0000 - 34.6410i) q^{40} +61.8569 q^{41} +(-64.8569 + 90.2308i) q^{42} -65.9052 q^{43} +(-51.7137 - 89.5708i) q^{44} +(22.5000 - 38.9711i) q^{45} +(-60.3327 + 104.499i) q^{46} +(-87.7621 - 152.008i) q^{47} -48.0000 q^{48} +(-109.310 - 325.116i) q^{49} -50.0000 q^{50} +(128.785 + 223.063i) q^{51} +(5.71370 - 9.89642i) q^{52} +(200.522 - 347.315i) q^{53} +(-27.0000 - 46.7654i) q^{54} -129.284 q^{55} +(86.4758 - 120.308i) q^{56} -46.4274 q^{57} +(29.6673 + 51.3854i) q^{58} +(196.926 - 341.086i) q^{59} +(-30.0000 + 51.9615i) q^{60} +(30.4758 + 52.7856i) q^{61} -507.710 q^{62} +(165.856 + 16.5785i) q^{63} +64.0000 q^{64} +(-7.14213 - 12.3705i) q^{65} +(-77.5706 + 134.356i) q^{66} +(-56.9506 + 98.6413i) q^{67} +(-171.714 - 297.417i) q^{68} +180.998 q^{69} +(-76.1895 - 168.805i) q^{70} +483.853 q^{71} +(36.0000 + 62.3538i) q^{72} +(28.8579 - 49.9833i) q^{73} +(-204.667 + 354.494i) q^{74} +(37.5000 + 64.9519i) q^{75} +61.9032 q^{76} +(-197.002 - 436.477i) q^{77} -17.1411 q^{78} +(509.738 + 882.892i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(61.8569 + 107.139i) q^{82} +870.611 q^{83} +(-221.141 - 22.1046i) q^{84} -429.284 q^{85} +(-65.9052 - 114.151i) q^{86} +(44.5010 - 77.0780i) q^{87} +(103.427 - 179.142i) q^{88} +(-482.404 - 835.549i) q^{89} +90.0000 q^{90} +(30.8810 - 42.9626i) q^{91} -241.331 q^{92} +(380.782 + 659.534i) q^{93} +(175.524 - 304.017i) q^{94} +(38.6895 - 67.0122i) q^{95} +(-48.0000 - 83.1384i) q^{96} +880.758 q^{97} +(453.806 - 514.447i) q^{98} +232.712 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 24 q^{6} - 20 q^{7} - 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 24 * q^6 - 20 * q^7 - 32 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 24 q^{6} - 20 q^{7} - 32 q^{8} - 18 q^{9} - 20 q^{10} + 18 q^{11} + 24 q^{12} + 128 q^{13} - 8 q^{14} + 60 q^{15} - 32 q^{16} - 102 q^{17} + 36 q^{18} + 62 q^{19} - 80 q^{20} - 48 q^{21} + 72 q^{22} - 42 q^{23} - 48 q^{24} - 50 q^{25} + 128 q^{26} - 108 q^{27} + 64 q^{28} + 444 q^{29} + 60 q^{30} + 50 q^{31} + 64 q^{32} - 54 q^{33} - 408 q^{34} - 20 q^{35} + 144 q^{36} + 572 q^{37} - 124 q^{38} + 192 q^{39} - 80 q^{40} + 108 q^{41} - 120 q^{42} - 496 q^{43} + 72 q^{44} + 90 q^{45} + 84 q^{46} - 444 q^{47} - 192 q^{48} - 902 q^{49} - 200 q^{50} + 306 q^{51} - 256 q^{52} + 12 q^{53} - 108 q^{54} + 180 q^{55} + 160 q^{56} + 372 q^{57} + 444 q^{58} - 258 q^{59} - 120 q^{60} - 64 q^{61} + 200 q^{62} + 36 q^{63} + 256 q^{64} + 320 q^{65} + 108 q^{66} + 632 q^{67} - 408 q^{68} - 252 q^{69} + 160 q^{70} - 156 q^{71} + 144 q^{72} + 464 q^{73} - 1144 q^{74} + 150 q^{75} - 496 q^{76} - 1764 q^{77} + 768 q^{78} + 1946 q^{79} + 160 q^{80} - 162 q^{81} + 108 q^{82} - 468 q^{83} - 48 q^{84} - 1020 q^{85} - 496 q^{86} + 666 q^{87} - 144 q^{88} - 1674 q^{89} + 360 q^{90} + 170 q^{91} + 336 q^{92} - 150 q^{93} + 888 q^{94} - 310 q^{95} - 192 q^{96} + 1664 q^{97} + 328 q^{98} - 324 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 24 * q^6 - 20 * q^7 - 32 * q^8 - 18 * q^9 - 20 * q^10 + 18 * q^11 + 24 * q^12 + 128 * q^13 - 8 * q^14 + 60 * q^15 - 32 * q^16 - 102 * q^17 + 36 * q^18 + 62 * q^19 - 80 * q^20 - 48 * q^21 + 72 * q^22 - 42 * q^23 - 48 * q^24 - 50 * q^25 + 128 * q^26 - 108 * q^27 + 64 * q^28 + 444 * q^29 + 60 * q^30 + 50 * q^31 + 64 * q^32 - 54 * q^33 - 408 * q^34 - 20 * q^35 + 144 * q^36 + 572 * q^37 - 124 * q^38 + 192 * q^39 - 80 * q^40 + 108 * q^41 - 120 * q^42 - 496 * q^43 + 72 * q^44 + 90 * q^45 + 84 * q^46 - 444 * q^47 - 192 * q^48 - 902 * q^49 - 200 * q^50 + 306 * q^51 - 256 * q^52 + 12 * q^53 - 108 * q^54 + 180 * q^55 + 160 * q^56 + 372 * q^57 + 444 * q^58 - 258 * q^59 - 120 * q^60 - 64 * q^61 + 200 * q^62 + 36 * q^63 + 256 * q^64 + 320 * q^65 + 108 * q^66 + 632 * q^67 - 408 * q^68 - 252 * q^69 + 160 * q^70 - 156 * q^71 + 144 * q^72 + 464 * q^73 - 1144 * q^74 + 150 * q^75 - 496 * q^76 - 1764 * q^77 + 768 * q^78 + 1946 * q^79 + 160 * q^80 - 162 * q^81 + 108 * q^82 - 468 * q^83 - 48 * q^84 - 1020 * q^85 - 496 * q^86 + 666 * q^87 - 144 * q^88 - 1674 * q^89 + 360 * q^90 + 170 * q^91 + 336 * q^92 - 150 * q^93 + 888 * q^94 - 310 * q^95 - 192 * q^96 + 1664 * q^97 + 328 * q^98 - 324 * q^99

Introduction

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