LMFDB - Embedded newform 210.4.i.j.151.2

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			151.2
Root			$-1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	210.151
Dual form			210.4.i.j.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} +(0.809475 - 18.5026i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(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} +(0.809475 - 18.5026i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(21.9284 - 37.9811i) q^{11} +(6.00000 + 10.3923i) q^{12} +66.8569 q^{13} +(32.8569 - 17.1005i) q^{14} +15.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-8.07157 + 13.9804i) q^{17} +(9.00000 - 15.5885i) q^{18} +(38.7379 + 67.0960i) q^{19} -20.0000 q^{20} +(-46.8569 - 29.8569i) q^{21} +87.7137 q^{22} +(-51.1663 - 88.6227i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(66.8569 + 115.799i) q^{26} -27.0000 q^{27} +(62.4758 + 39.8092i) q^{28} +192.333 q^{29} +(15.0000 + 25.9808i) q^{30} +(151.927 - 263.146i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-65.7853 - 113.943i) q^{33} -32.2863 q^{34} +(82.1421 - 42.7513i) q^{35} +36.0000 q^{36} +(183.666 + 318.119i) q^{37} +(-77.4758 + 134.192i) q^{38} +(100.285 - 173.699i) q^{39} +(-20.0000 - 34.6410i) q^{40} -7.85685 q^{41} +(4.85685 - 111.015i) q^{42} -182.095 q^{43} +(87.7137 + 151.925i) q^{44} +(22.5000 - 38.9711i) q^{45} +(102.333 - 177.245i) q^{46} +(-134.238 - 232.507i) q^{47} -48.0000 q^{48} +(-341.690 - 29.9547i) q^{49} -50.0000 q^{50} +(24.2147 + 41.9411i) q^{51} +(-133.714 + 231.599i) q^{52} +(-194.522 + 336.922i) q^{53} +(-27.0000 - 46.7654i) q^{54} +219.284 q^{55} +(-6.47580 + 148.020i) q^{56} +232.427 q^{57} +(192.333 + 333.130i) q^{58} +(-325.926 + 564.521i) q^{59} +(-30.0000 + 51.9615i) q^{60} +(-62.4758 - 108.211i) q^{61} +607.710 q^{62} +(-147.856 + 76.9523i) q^{63} +64.0000 q^{64} +(167.142 + 289.499i) q^{65} +(131.571 - 227.887i) q^{66} +(372.951 - 645.969i) q^{67} +(-32.2863 - 55.9215i) q^{68} -306.998 q^{69} +(156.190 + 99.5231i) q^{70} -561.853 q^{71} +(36.0000 + 62.3538i) q^{72} +(203.142 - 351.852i) q^{73} +(-367.333 + 636.239i) q^{74} +(37.5000 + 64.9519i) q^{75} -309.903 q^{76} +(-684.998 - 436.477i) q^{77} +401.141 q^{78} +(463.262 + 802.393i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-7.85685 - 13.6085i) q^{82} -1104.61 q^{83} +(197.141 - 102.603i) q^{84} -80.7157 q^{85} +(-182.095 - 315.397i) q^{86} +(288.499 - 499.695i) q^{87} +(-175.427 + 303.849i) q^{88} +(-354.596 - 614.178i) q^{89} +90.0000 q^{90} +(54.1190 - 1237.02i) q^{91} +409.331 q^{92} +(-455.782 - 789.438i) q^{93} +(268.476 - 465.014i) q^{94} +(-193.690 + 335.480i) q^{95} +(-48.0000 - 83.1384i) q^{96} -48.7580 q^{97} +(-289.806 - 621.778i) q^{98} -394.712 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
$7$	0.809475	−	18.5026i	0.0437075	−	0.999044i
$7$	0.809475	−	18.5026i	0.0437075	−	0.999044i
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	21.9284	−	37.9811i	0.601061	−	1.04107i	−0.391600	−	0.920136i	$-0.628078\pi$
$11$	21.9284	−	37.9811i	0.601061	−	1.04107i	0.992661	−	0.120932i	$-0.0385884\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	66.8569			1.42637			0.713183	−	0.700978i	$-0.247253\pi$
$13$	66.8569			1.42637			0.713183	+	0.700978i	$0.247253\pi$
$14$	32.8569	−	17.1005i	0.627240	−	0.326450i
$15$	15.0000			0.258199
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−8.07157	+	13.9804i	−0.115156	+	0.199455i	−0.917842	−	0.396946i	$-0.870070\pi$
$17$	−8.07157	+	13.9804i	−0.115156	+	0.199455i	0.802686	+	0.596401i	$0.203403\pi$
$18$	9.00000	−	15.5885i	0.117851	−	0.204124i
$19$	38.7379	+	67.0960i	0.467741	+	0.810152i	0.999321	−	0.0368569i	$-0.0117346\pi$
$19$	38.7379	+	67.0960i	0.467741	+	0.810152i	−0.531579	+	0.847009i	$0.678401\pi$
$20$	−20.0000			−0.223607
$21$	−46.8569	−	29.8569i	−0.486905	−	0.310253i
$22$	87.7137			0.850028
$23$	−51.1663	−	88.6227i	−0.463866	−	0.803439i	0.535284	−	0.844672i	$-0.320205\pi$
$23$	−51.1663	−	88.6227i	−0.463866	−	0.803439i	−0.999150	+	0.0412330i	$0.986871\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	66.8569	+	115.799i	0.504296	+	0.873467i
$27$	−27.0000			−0.192450
$28$	62.4758	+	39.8092i	0.421672	+	0.268687i
$29$	192.333			1.23156			0.615781	−	0.787918i	$-0.288841\pi$
$29$	192.333			1.23156			0.615781	+	0.787918i	$0.288841\pi$
$30$	15.0000	+	25.9808i	0.0912871	+	0.158114i
$31$	151.927	−	263.146i	0.880225	−	1.52459i	0.0291339	−	0.999576i	$-0.490725\pi$
$31$	151.927	−	263.146i	0.880225	−	1.52459i	0.851091	−	0.525018i	$-0.175942\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−65.7853	−	113.943i	−0.347023	−	0.601061i
$34$	−32.2863			−0.162855
$35$	82.1421	−	42.7513i	0.396702	−	0.206465i
$36$	36.0000			0.166667
$37$	183.666	+	318.119i	0.816069	+	1.41347i	0.908558	+	0.417759i	$0.137185\pi$
$37$	183.666	+	318.119i	0.816069	+	1.41347i	−0.0924885	+	0.995714i	$0.529482\pi$
$38$	−77.4758	+	134.192i	−0.330743	+	0.572864i
$39$	100.285	−	173.699i	0.411756	−	0.713183i
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−7.85685			−0.0299277			−0.0149638	−	0.999888i	$-0.504763\pi$
$41$	−7.85685			−0.0299277			−0.0149638	+	0.999888i	$0.504763\pi$
$42$	4.85685	−	111.015i	0.0178435	−	0.407858i
$43$	−182.095			−0.645795			−0.322898	−	0.946434i	$-0.604657\pi$
$43$	−182.095			−0.645795			−0.322898	+	0.946434i	$0.604657\pi$
$44$	87.7137	+	151.925i	0.300530	+	0.520534i
$45$	22.5000	−	38.9711i	0.0745356	−	0.129099i
$46$	102.333	−	177.245i	0.328003	−	0.568117i
$47$	−134.238	−	232.507i	−0.416609	−	0.721587i	0.578987	−	0.815337i	$-0.303448\pi$
$47$	−134.238	−	232.507i	−0.416609	−	0.721587i	−0.995596	+	0.0937492i	$0.970115\pi$
$48$	−48.0000			−0.144338
$49$	−341.690	−	29.9547i	−0.996179	−	0.0873315i
$50$	−50.0000			−0.141421
$51$	24.2147	+	41.9411i	0.0664851	+	0.115156i
$52$	−133.714	+	231.599i	−0.356591	+	0.617634i
$53$	−194.522	+	336.922i	−0.504145	+	0.873204i	0.495844	+	0.868412i	$0.334859\pi$
$53$	−194.522	+	336.922i	−0.504145	+	0.873204i	−0.999989	+	0.00479259i	$0.998474\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	219.284			0.537605
$56$	−6.47580	+	148.020i	−0.0154529	+	0.353216i
$57$	232.427			0.540101
$58$	192.333	+	333.130i	0.435423	+	0.754174i
$59$	−325.926	+	564.521i	−0.719186	+	1.24567i	0.242136	+	0.970242i	$0.422152\pi$
$59$	−325.926	+	564.521i	−0.719186	+	1.24567i	−0.961323	+	0.275425i	$0.911181\pi$
$60$	−30.0000	+	51.9615i	−0.0645497	+	0.111803i
$61$	−62.4758	−	108.211i	−0.131135	−	0.227132i	0.792980	−	0.609248i	$-0.208529\pi$
$61$	−62.4758	−	108.211i	−0.131135	−	0.227132i	−0.924114	+	0.382116i	$0.875195\pi$
$62$	607.710			1.24483
$63$	−147.856	+	76.9523i	−0.295684	+	0.153890i
$64$	64.0000			0.125000
$65$	167.142	+	289.499i	0.318945	+	0.552429i
$66$	131.571	−	227.887i	0.245382	−	0.425014i
$67$	372.951	−	645.969i	0.680047	−	1.17788i	−0.294919	−	0.955522i	$-0.595293\pi$
$67$	372.951	−	645.969i	0.680047	−	1.17788i	0.974966	−	0.222354i	$-0.0713741\pi$
$68$	−32.2863	−	55.9215i	−0.0575778	−	0.0997276i
$69$	−306.998			−0.535626
$70$	156.190	+	99.5231i	0.266689	+	0.169933i
$71$	−561.853			−0.939150			−0.469575	−	0.882893i	$-0.655593\pi$
$71$	−561.853			−0.939150			−0.469575	+	0.882893i	$0.655593\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	203.142	−	351.852i	0.325698	−	0.564126i	−0.655955	−	0.754800i	$-0.727734\pi$
$73$	203.142	−	351.852i	0.325698	−	0.564126i	0.981653	+	0.190674i	$0.0610672\pi$
$74$	−367.333	+	636.239i	−0.577048	+	0.999476i
$75$	37.5000	+	64.9519i	0.0577350	+	0.100000i
$76$	−309.903			−0.467741
$77$	−684.998	−	436.477i	−1.01380	−	0.645989i
$78$	401.141			0.582311
$79$	463.262	+	802.393i	0.659760	+	1.14274i	0.980678	+	0.195631i	$0.0626755\pi$
$79$	463.262	+	802.393i	0.659760	+	1.14274i	−0.320917	+	0.947107i	$0.603991\pi$
$80$	40.0000	−	69.2820i	0.0559017	−	0.0968246i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−7.85685	−	13.6085i	−0.0105810	−	0.0183269i
$83$	−1104.61			−1.46080			−0.730402	−	0.683017i	$-0.760667\pi$
$83$	−1104.61			−1.46080			−0.730402	+	0.683017i	$0.760667\pi$
$84$	197.141	−	102.603i	0.256070	−	0.133273i
$85$	−80.7157			−0.102998
$86$	−182.095	−	315.397i	−0.228323	−	0.395467i
$87$	288.499	−	499.695i	0.355521	−	0.615781i
$88$	−175.427	+	303.849i	−0.212507	+	0.368073i
$89$	−354.596	−	614.178i	−0.422327	−	0.731491i	0.573840	−	0.818967i	$-0.305453\pi$
$89$	−354.596	−	614.178i	−0.422327	−	0.731491i	−0.996167	+	0.0874762i	$0.972120\pi$
$90$	90.0000			0.105409
$91$	54.1190	−	1237.02i	0.0623429	−	1.42500i
$92$	409.331			0.463866
$93$	−455.782	−	789.438i	−0.508198	−	0.880225i
$94$	268.476	−	465.014i	0.294587	−	0.510239i
$95$	−193.690	+	335.480i	−0.209180	+	0.362311i
$96$	−48.0000	−	83.1384i	−0.0510310	−	0.0883883i
$97$	−48.7580			−0.0510374			−0.0255187	−	0.999674i	$-0.508124\pi$
$97$	−48.7580			−0.0510374			−0.0255187	+	0.999674i	$0.508124\pi$
$98$	−289.806	−	621.778i	−0.298723	−	0.640909i
$99$	−394.712			−0.400707
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−726.590	+	1258.49i	−0.715825	+	1.23985i	0.246815	+	0.969063i	$0.420616\pi$
$101$	−726.590	+	1258.49i	−0.715825	+	1.23985i	−0.962640	+	0.270783i	$0.912717\pi$
$102$	−48.4294	+	83.8823i	−0.0470121	+	0.0814273i
$103$	−866.709	−	1501.18i	−0.829120	−	1.43608i	−0.898730	−	0.438503i	$-0.855509\pi$
$103$	−866.709	−	1501.18i	−0.829120	−	1.43608i	0.0696099	−	0.997574i	$-0.477825\pi$
$104$	−534.855			−0.504296
$105$	12.1421	−	277.538i	0.0112852	−	0.257952i
$106$	−778.089			−0.712968
$107$	822.547	+	1424.69i	0.743165	+	1.28720i	0.951047	+	0.309046i	$0.100010\pi$
$107$	822.547	+	1424.69i	0.743165	+	1.28720i	−0.207882	+	0.978154i	$0.566657\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−335.403	+	580.935i	−0.294732	+	0.510491i	−0.974923	−	0.222544i	$-0.928564\pi$
$109$	−335.403	+	580.935i	−0.294732	+	0.510491i	0.680190	+	0.733035i	$0.261897\pi$
$110$	219.284	+	379.811i	0.190072	+	0.329215i
$111$	1102.00			0.942315
$112$	−262.855	+	136.804i	−0.221763	+	0.115418i
$113$	−224.661			−0.187030			−0.0935148	−	0.995618i	$-0.529810\pi$
$113$	−224.661			−0.187030			−0.0935148	+	0.995618i	$0.529810\pi$
$114$	232.427	+	402.576i	0.190955	+	0.330743i
$115$	255.832	−	443.113i	0.207447	−	0.359309i
$116$	−384.665	+	666.260i	−0.307890	+	0.533282i
$117$	−300.856	−	521.098i	−0.237728	−	0.411756i
$118$	−1303.71			−1.01708
$119$	252.139	+	160.662i	0.194232	+	0.123763i
$120$	−120.000			−0.0912871
$121$	−296.212	−	513.054i	−0.222548	−	0.385465i
$122$	124.952	−	216.423i	0.0927261	−	0.160606i
$123$	−11.7853	+	20.4127i	−0.00863937	+	0.0149638i
$124$	607.710	+	1052.58i	0.440112	+	0.762297i
$125$	−125.000			−0.0894427
$126$	−281.141	−	179.142i	−0.198778	−	0.126660i
$127$	−1673.52			−1.16930			−0.584648	−	0.811287i	$-0.698768\pi$
$127$	−1673.52			−1.16930			−0.584648	+	0.811287i	$0.698768\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−273.142	+	473.096i	−0.186425	+	0.322898i
$130$	−334.284	+	578.997i	−0.225528	+	0.390626i
$131$	674.849	+	1168.87i	0.450090	+	0.779579i	0.998391	−	0.0567021i	$-0.0180585\pi$
$131$	674.849	+	1168.87i	0.450090	+	0.779579i	−0.548301	+	0.836281i	$0.684725\pi$
$132$	526.282			0.347023
$133$	1272.81	−	662.438i	0.829821	−	0.431885i
$134$	1491.80			0.961732
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	64.5726	−	111.843i	0.0407136	−	0.0705181i
$137$	−426.547	+	738.802i	−0.266003	+	0.460731i	−0.967826	−	0.251621i	$-0.919036\pi$
$137$	−426.547	+	738.802i	−0.266003	+	0.460731i	0.701823	+	0.712351i	$0.252370\pi$
$138$	−306.998	−	531.736i	−0.189372	−	0.328003i
$139$	2534.79			1.54675			0.773373	−	0.633951i	$-0.218568\pi$
$139$	2534.79			1.54675			0.773373	+	0.633951i	$0.218568\pi$
$140$	−16.1895	+	370.051i	−0.00977330	+	0.223393i
$141$	−805.427			−0.481058
$142$	−561.853	−	973.158i	−0.332040	−	0.575110i
$143$	1466.07	−	2539.30i	0.857333	−	1.48494i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	480.832	+	832.825i	0.275385	+	0.476982i
$146$	812.569			0.460607
$147$	−590.359	+	842.803i	−0.331238	+	0.472879i
$148$	−1469.33			−0.816069
$149$	913.609	+	1582.42i	0.502320	+	0.870044i	0.999996	+	0.00268146i	$0.000853535\pi$
$149$	913.609	+	1582.42i	0.502320	+	0.870044i	−0.497676	+	0.867363i	$0.665813\pi$
$150$	−75.0000	+	129.904i	−0.0408248	+	0.0707107i
$151$	−683.476	+	1183.81i	−0.368347	+	0.637997i	−0.989307	−	0.145846i	$-0.953410\pi$
$151$	−683.476	+	1183.81i	−0.368347	+	0.637997i	0.620960	+	0.783842i	$0.286743\pi$
$152$	−309.903	−	536.768i	−0.165372	−	0.286432i
$153$	145.288			0.0767704
$154$	71.0020	−	1622.93i	0.0371527	−	0.849216i
$155$	1519.27			0.787297
$156$	401.141	+	694.797i	0.205878	+	0.356591i
$157$	−39.4254	+	68.2867i	−0.0200413	+	0.0347126i	−0.875872	−	0.482543i	$-0.839713\pi$
$157$	−39.4254	+	68.2867i	−0.0200413	+	0.0347126i	0.855831	+	0.517256i	$0.173046\pi$
$158$	−926.524	+	1604.79i	−0.466521	+	0.808038i
$159$	583.566	+	1010.77i	0.291068	+	0.504145i
$160$	160.000			0.0790569
$161$	−1681.16	+	874.970i	−0.822946	+	0.428306i
$162$	−162.000			−0.0785674
$163$	800.194	+	1385.98i	0.384515	+	0.666000i	0.991702	−	0.128559i	$-0.0410352\pi$
$163$	800.194	+	1385.98i	0.384515	+	0.666000i	−0.607186	+	0.794559i	$0.707702\pi$
$164$	15.7137	−	27.2169i	0.00748191	−	0.0129591i
$165$	328.926	−	569.717i	0.155193	−	0.268803i
$166$	−1104.61	−	1913.24i	−0.516472	−	0.894556i
$167$	948.139			0.439337			0.219668	−	0.975575i	$-0.429503\pi$
$167$	948.139			0.439337			0.219668	+	0.975575i	$0.429503\pi$
$168$	374.855	+	238.855i	0.172147	+	0.109691i
$169$	2272.84			1.03452
$170$	−80.7157	−	139.804i	−0.0364154	−	0.0630733i
$171$	348.641	−	603.864i	0.155914	−	0.270051i
$172$	364.190	−	630.795i	0.161449	−	0.279637i
$173$	−850.421	−	1472.97i	−0.373736	−	0.647330i	0.616401	−	0.787432i	$-0.288590\pi$
$173$	−850.421	−	1472.97i	−0.373736	−	0.647330i	−0.990137	+	0.140103i	$0.955257\pi$
$174$	1154.00			0.502783
$175$	390.474	+	248.808i	0.168669	+	0.107475i
$176$	−701.710			−0.300530
$177$	977.779	+	1693.56i	0.415222	+	0.719186i
$178$	709.192	−	1228.36i	0.298630	−	0.517242i
$179$	−1680.15	+	2910.10i	−0.701564	+	1.21514i	0.266353	+	0.963875i	$0.414181\pi$
$179$	−1680.15	+	2910.10i	−0.701564	+	1.21514i	−0.967917	+	0.251269i	$0.919152\pi$
$180$	90.0000	+	155.885i	0.0372678	+	0.0645497i
$181$	1320.63			0.542331			0.271165	−	0.962533i	$-0.412591\pi$
$181$	1320.63			0.542331			0.271165	+	0.962533i	$0.412591\pi$
$182$	2196.71	−	1143.29i	0.894674	−	0.465637i
$183$	−374.855			−0.151421
$184$	409.331	+	708.981i	0.164001	+	0.284059i
$185$	−918.332	+	1590.60i	−0.364957	+	0.632124i
$186$	911.564	−	1578.88i	0.359350	−	0.622413i
$187$	353.994	+	613.135i	0.138431	+	0.239769i
$188$	1073.90			0.416609
$189$	−21.8558	+	499.569i	−0.00841152	+	0.192266i
$190$	−774.758			−0.295826
$191$	−233.480	−	404.399i	−0.0884503	−	0.153200i	0.818406	−	0.574641i	$-0.194858\pi$
$191$	−233.480	−	404.399i	−0.0884503	−	0.153200i	−0.906856	+	0.421440i	$0.861525\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	1552.75	−	2689.44i	0.579116	−	1.00306i	−0.416466	−	0.909152i	$-0.636731\pi$
$193$	1552.75	−	2689.44i	0.579116	−	1.00306i	0.995581	−	0.0939061i	$-0.0299353\pi$
$194$	−48.7580	−	84.4513i	−0.0180444	−	0.0312539i
$195$	1002.85			0.368286
$196$	787.145	−	1123.74i	0.286860	−	0.409525i
$197$	−50.2318			−0.0181668			−0.00908341	−	0.999959i	$-0.502891\pi$
$197$	−50.2318			−0.0181668			−0.00908341	+	0.999959i	$0.502891\pi$
$198$	−394.712	−	683.661i	−0.141671	−	0.245382i
$199$	−931.387	+	1613.21i	−0.331780	+	0.574660i	−0.982861	−	0.184348i	$-0.940983\pi$
$199$	−931.387	+	1613.21i	−0.331780	+	0.574660i	0.651081	+	0.759009i	$0.274316\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$	−1118.85	−	1937.91i	−0.392625	−	0.680047i
$202$	−2906.36			−1.01233
$203$	155.688	−	3558.65i	0.0538285	−	1.23038i
$204$	−193.718			−0.0664851
$205$	−19.6421	−	34.0212i	−0.00669203	−	0.0115909i
$206$	1733.42	−	3002.37i	0.586276	−	1.01546i
$207$	−460.497	+	797.604i	−0.154622	+	0.267813i
$208$	−534.855	−	926.396i	−0.178296	−	0.308817i
$209$	3397.84			1.12456
$210$	492.853	−	256.508i	0.161953	−	0.0842891i
$211$	4946.73			1.61396			0.806982	−	0.590575i	$-0.201099\pi$
$211$	4946.73			1.61396			0.806982	+	0.590575i	$0.201099\pi$
$212$	−778.089	−	1347.69i	−0.252072	−	0.436602i
$213$	−842.779	+	1459.74i	−0.271109	+	0.469575i
$214$	−1645.09	+	2849.39i	−0.525497	+	0.910188i
$215$	−455.237	−	788.493i	−0.144404	−	0.250115i
$216$	216.000			0.0680414
$217$	−4745.89	−	3024.06i	−1.48466	−	0.946020i
$218$	−1341.61			−0.416814
$219$	−609.426	−	1055.56i	−0.188042	−	0.325698i
$220$	−438.569	+	759.623i	−0.134401	+	0.232790i
$221$	−539.640	+	934.684i	−0.164254	+	0.284496i
$222$	1102.00	+	1908.72i	0.333159	+	0.577048i
$223$	6015.68			1.80646			0.903228	−	0.429161i	$-0.141191\pi$
$223$	6015.68			1.80646			0.903228	+	0.429161i	$0.141191\pi$
$224$	−499.806	−	318.474i	−0.149084	−	0.0949952i
$225$	225.000			0.0666667
$226$	−224.661	−	389.125i	−0.0661250	−	0.114532i
$227$	1528.39	−	2647.26i	0.446886	−	0.774029i	−0.551296	−	0.834310i	$-0.685866\pi$
$227$	1528.39	−	2647.26i	0.446886	−	0.774029i	0.998181	+	0.0602811i	$0.0191997\pi$
$228$	−464.855	+	805.152i	−0.135025	+	0.233871i
$229$	1005.49	+	1741.56i	0.290151	+	0.502556i	0.973845	−	0.227213i	$-0.0729612\pi$
$229$	1005.49	+	1741.56i	0.290151	+	0.502556i	−0.683695	+	0.729768i	$0.739628\pi$
$230$	1023.33			0.293375
$231$	−2161.50	+	1124.96i	−0.615654	+	0.320420i
$232$	−1538.66			−0.435423
$233$	−2028.74	−	3513.89i	−0.570418	−	0.987993i	−0.996523	−	0.0833193i	$-0.973448\pi$
$233$	−2028.74	−	3513.89i	−0.570418	−	0.987993i	0.426105	−	0.904674i	$-0.359885\pi$
$234$	601.712	−	1042.20i	0.168099	−	0.291156i
$235$	671.190	−	1162.53i	0.186313	−	0.322704i
$236$	−1303.71	−	2258.08i	−0.359593	−	0.622834i
$237$	2779.57			0.761825
$238$	−26.1350	+	597.379i	−0.00711797	+	0.162699i
$239$	5655.70			1.53070			0.765349	−	0.643615i	$-0.222566\pi$
$239$	5655.70			1.53070			0.765349	+	0.643615i	$0.222566\pi$
$240$	−120.000	−	207.846i	−0.0322749	−	0.0559017i
$241$	−3014.52	+	5221.30i	−0.805735	+	1.39557i	0.110058	+	0.993925i	$0.464896\pi$
$241$	−3014.52	+	5221.30i	−0.805735	+	1.39557i	−0.915794	+	0.401649i	$0.868437\pi$
$242$	592.423	−	1026.11i	0.157365	−	0.272565i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	499.806			0.131135
$245$	−724.516	−	1554.45i	−0.188929	−	0.405347i
$246$	−47.1411			−0.0122179
$247$	2589.89	+	4485.83i	0.667170	+	1.15557i
$248$	−1215.42	+	2105.17i	−0.311206	+	0.539025i
$249$	−1656.92	+	2869.86i	−0.421698	+	0.730402i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	2066.63			0.519700			0.259850	−	0.965649i	$-0.416327\pi$
$251$	2066.63			0.519700			0.259850	+	0.965649i	$0.416327\pi$
$252$	29.1411	−	666.092i	0.00728459	−	0.166507i
$253$	−4487.99			−1.11525
$254$	−1673.52	−	2898.62i	−0.413409	−	0.716045i
$255$	−121.074	+	209.706i	−0.0297330	+	0.0514991i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−977.543	−	1693.15i	−0.237266	−	0.410958i	0.722662	−	0.691201i	$-0.242918\pi$
$257$	−977.543	−	1693.15i	−0.237266	−	0.410958i	−0.959929	+	0.280244i	$0.909585\pi$
$258$	−1092.57			−0.263645
$259$	6034.70	−	3140.79i	1.44779	−	0.753510i
$260$	−1337.14			−0.318945
$261$	−865.497	−	1499.08i	−0.205260	−	0.355521i
$262$	−1349.70	+	2337.74i	−0.318262	+	0.551246i
$263$	−1070.91	+	1854.87i	−0.251084	+	0.434890i	−0.963825	−	0.266538i	$-0.914120\pi$
$263$	−1070.91	+	1854.87i	−0.251084	+	0.434890i	0.712741	+	0.701428i	$0.247454\pi$
$264$	526.282	+	911.548i	0.122691	+	0.212507i
$265$	−1945.22			−0.450921
$266$	2420.18	+	1542.13i	0.557860	+	0.355465i
$267$	−2127.57			−0.487661
$268$	1491.80	+	2583.88i	0.340024	+	0.588938i
$269$	−350.474	+	607.038i	−0.0794378	+	0.137590i	−0.903008	−	0.429625i	$-0.858646\pi$
$269$	−350.474	+	607.038i	−0.0794378	+	0.137590i	0.823570	+	0.567215i	$0.191979\pi$
$270$	135.000	−	233.827i	0.0304290	−	0.0527046i
$271$	−1555.86	−	2694.83i	−0.348752	−	0.604056i	0.637276	−	0.770635i	$-0.280061\pi$
$271$	−1555.86	−	2694.83i	−0.348752	−	0.604056i	−0.986028	+	0.166580i	$0.946728\pi$
$272$	258.290			0.0575778
$273$	−3132.70	−	1996.14i	−0.694504	−	0.442534i
$274$	−1706.19			−0.376185
$275$	548.211	+	949.529i	0.120212	+	0.208214i
$276$	613.996	−	1063.47i	0.133907	−	0.231933i
$277$	−3981.83	+	6896.73i	−0.863700	+	1.49597i	0.00463290	+	0.999989i	$0.498525\pi$
$277$	−3981.83	+	6896.73i	−0.863700	+	1.49597i	−0.868333	+	0.495982i	$0.834808\pi$
$278$	2534.79	+	4390.38i	0.546857	+	0.947185i
$279$	−2734.69			−0.586816
$280$	−657.137	+	342.010i	−0.140255	+	0.0729965i
$281$	−3427.21			−0.727581			−0.363790	−	0.931481i	$-0.618518\pi$
$281$	−3427.21			−0.727581			−0.363790	+	0.931481i	$0.618518\pi$
$282$	−805.427	−	1395.04i	−0.170080	−	0.294587i
$283$	−270.725	+	468.909i	−0.0568655	+	0.0984939i	−0.893057	−	0.449944i	$-0.851444\pi$
$283$	−270.725	+	468.909i	−0.0568655	+	0.0984939i	0.836191	+	0.548438i	$0.184777\pi$
$284$	1123.71	−	1946.32i	0.234788	−	0.406664i
$285$	581.069	+	1006.44i	0.120770	+	0.209180i
$286$	5864.26			1.21245
$287$	−6.35992	+	145.372i	−0.00130806	+	0.0298991i
$288$	−288.000			−0.0589256
$289$	2326.20	+	4029.10i	0.473478	+	0.820089i
$290$	−961.663	+	1665.65i	−0.194727	+	0.337277i
$291$	−73.1370	+	126.677i	−0.0147332	+	0.0255187i
$292$	812.569	+	1407.41i	0.162849	+	0.282063i
$293$	1303.65			0.259931			0.129966	−	0.991519i	$-0.458513\pi$
$293$	1303.65			0.259931			0.129966	+	0.991519i	$0.458513\pi$
$294$	−2050.14	−	179.728i	−0.406688	−	0.0356530i
$295$	−3259.26			−0.643260
$296$	−1469.33	−	2544.96i	−0.288524	−	0.499738i
$297$	−592.067	+	1025.49i	−0.115674	+	0.200354i
$298$	−1827.22	+	3164.83i	−0.355194	+	0.615214i
$299$	−3420.82	−	5925.03i	−0.661642	−	1.14600i
$300$	−300.000			−0.0577350
$301$	−147.401	+	3369.22i	−0.0282261	+	0.645178i
$302$	−2733.90			−0.520922
$303$	2179.77	+	3775.47i	0.413282	+	0.715825i
$304$	619.806	−	1073.54i	0.116935	−	0.202538i
$305$	312.379	−	541.056i	0.0586451	−	0.101576i
$306$	145.288	+	251.647i	0.0271424	+	0.0470121i
$307$	−3114.73			−0.579045			−0.289523	−	0.957171i	$-0.593497\pi$
$307$	−3114.73			−0.579045			−0.289523	+	0.957171i	$0.593497\pi$
$308$	2882.00	−	1499.95i	0.533172	−	0.277492i
$309$	−5200.25			−0.957385
$310$	1519.27	+	2631.46i	0.278352	+	0.482119i
$311$	−3466.39	+	6003.96i	−0.632028	+	1.09471i	0.355108	+	0.934825i	$0.384444\pi$
$311$	−3466.39	+	6003.96i	−0.632028	+	1.09471i	−0.987136	+	0.159880i	$0.948889\pi$
$312$	−802.282	+	1389.59i	−0.145578	+	0.252148i
$313$	−2555.24	−	4425.81i	−0.461440	−	0.799238i	0.537593	−	0.843205i	$-0.319334\pi$
$313$	−2555.24	−	4425.81i	−0.461440	−	0.799238i	−0.999033	+	0.0439664i	$0.986001\pi$
$314$	−157.701			−0.0283427
$315$	−702.853	−	447.854i	−0.125718	−	0.0801070i
$316$	−3706.10			−0.659760
$317$	−4681.09	−	8107.89i	−0.829389	−	1.43654i	−0.898518	−	0.438936i	$-0.855355\pi$
$317$	−4681.09	−	8107.89i	−0.829389	−	1.43654i	0.0691294	−	0.997608i	$-0.477978\pi$
$318$	−1167.13	+	2021.53i	−0.205816	+	0.356484i
$319$	4217.55	−	7305.01i	0.740243	−	1.28214i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$	4935.28			0.858133
$322$	−3196.66	−	2036.89i	−0.553238	−	0.352520i
$323$	−1250.70			−0.215452
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	−835.711	+	1447.49i	−0.142637	+	0.247054i
$326$	−1600.39	+	2771.95i	−0.271893	+	0.470933i
$327$	1006.21	+	1742.81i	0.170164	+	0.294732i
$328$	62.8548			0.0105810
$329$	−4410.63	+	2295.54i	−0.739107	+	0.384672i
$330$	1315.71			0.219476
$331$	−1446.55	−	2505.49i	−0.240210	−	0.416055i	0.720564	−	0.693388i	$-0.243883\pi$
$331$	−1446.55	−	2505.49i	−0.240210	−	0.416055i	−0.960774	+	0.277333i	$0.910550\pi$
$332$	2209.22	−	3826.48i	0.365201	−	0.632547i
$333$	1653.00	−	2863.07i	0.272023	−	0.471158i
$334$	948.139	+	1642.23i	0.155329	+	0.269038i
$335$	3729.51			0.608253
$336$	−38.8548	+	888.123i	−0.00630864	+	0.144200i
$337$	−3378.62			−0.546128			−0.273064	−	0.961996i	$-0.588037\pi$
$337$	−3378.62			−0.546128			−0.273064	+	0.961996i	$0.588037\pi$
$338$	2272.84	+	3936.67i	0.365758	+	0.633511i
$339$	−336.992	+	583.687i	−0.0539908	+	0.0935148i
$340$	161.431	−	279.608i	0.0257496	−	0.0445996i
$341$	−6663.06	−	11540.8i	−1.05814	−	1.83275i
$342$	1394.56			0.220495
$343$	−830.828	+	6297.88i	−0.130789	+	0.991410i
$344$	1456.76			0.228323
$345$	−767.495	−	1329.34i	−0.119770	−	0.207447i
$346$	1700.84	−	2945.95i	0.264271	−	0.457731i
$347$	316.173	−	547.628i	0.0489137	−	0.0847211i	−0.840532	−	0.541762i	$-0.817757\pi$
$347$	316.173	−	547.628i	0.0489137	−	0.0847211i	0.889446	+	0.457041i	$0.151091\pi$
$348$	1154.00	+	1998.78i	0.177761	+	0.307890i
$349$	−5549.40			−0.851154			−0.425577	−	0.904922i	$-0.639929\pi$
$349$	−5549.40			−0.851154			−0.425577	+	0.904922i	$0.639929\pi$
$350$	−40.4738	+	925.128i	−0.00618118	+	0.141286i
$351$	−1805.13			−0.274504
$352$	−701.710	−	1215.40i	−0.106254	−	0.184037i
$353$	2903.53	−	5029.06i	0.437789	−	0.758272i	−0.559730	−	0.828675i	$-0.689095\pi$
$353$	2903.53	−	5029.06i	0.437789	−	0.758272i	0.997519	+	0.0704030i	$0.0224285\pi$
$354$	−1955.56	+	3387.13i	−0.293607	+	0.508542i
$355$	−1404.63	−	2432.89i	−0.210000	−	0.363731i
$356$	2836.77			0.422327
$357$	795.620	−	414.084i	0.117951	−	0.0613884i
$358$	−6720.58			−0.992161
$359$	−3397.24	−	5884.19i	−0.499441	−	0.865057i	0.500559	−	0.865702i	$-0.333128\pi$
$359$	−3397.24	−	5884.19i	−0.499441	−	0.865057i	−1.00000		0.000645470i	$0.999795\pi$
$360$	−180.000	+	311.769i	−0.0263523	+	0.0456435i
$361$	428.250	−	741.751i	0.0624362	−	0.108143i
$362$	1320.63	+	2287.40i	0.191743	+	0.332109i
$363$	−1777.27			−0.256977
$364$	4176.94	+	2661.52i	0.601458	+	0.383246i
$365$	2031.42			0.291314
$366$	−374.855	−	649.268i	−0.0535354	−	0.0927261i
$367$	−4926.84	+	8533.54i	−0.700760	+	1.21375i	0.267440	+	0.963575i	$0.413822\pi$
$367$	−4926.84	+	8533.54i	−0.700760	+	1.21375i	−0.968200	+	0.250177i	$0.919511\pi$
$368$	−818.661	+	1417.96i	−0.115966	+	0.200860i
$369$	35.3558	+	61.2381i	0.00498794	+	0.00863937i
$370$	−3673.33			−0.516127
$371$	6076.46	+	3871.89i	0.850335	+	0.541829i
$372$	3646.26			0.508198
$373$	4772.09	+	8265.51i	0.662439	+	1.14738i	0.979973	+	0.199131i	$0.0638118\pi$
$373$	4772.09	+	8265.51i	0.662439	+	1.14738i	−0.317534	+	0.948247i	$0.602855\pi$
$374$	−707.988	+	1226.27i	−0.0978855	+	0.169543i
$375$	−187.500	+	324.760i	−0.0258199	+	0.0447214i
$376$	1073.90	+	1860.05i	0.147293	+	0.255120i
$377$	12858.8			1.75666
$378$	−887.135	+	461.714i	−0.120712	+	0.0628254i
$379$	9836.63			1.33318			0.666588	−	0.745426i	$-0.267754\pi$
$379$	9836.63			1.33318			0.666588	+	0.745426i	$0.267754\pi$
$380$	−774.758	−	1341.92i	−0.104590	−	0.181155i
$381$	−2510.28	+	4347.93i	−0.337547	+	0.584648i
$382$	466.960	−	808.798i	0.0625438	−	0.108329i
$383$	−5675.20	−	9829.73i	−0.757151	−	1.31142i	−0.944298	−	0.329092i	$-0.893257\pi$
$383$	−5675.20	−	9829.73i	−0.757151	−	1.31142i	0.187146	−	0.982332i	$-0.440076\pi$
$384$	384.000			0.0510310
$385$	177.505	−	4057.32i	0.0234974	−	0.537091i
$386$	6211.00			0.818993
$387$	819.426	+	1419.29i	0.107633	+	0.186425i
$388$	97.5160	−	168.903i	0.0127593	−	0.0220998i
$389$	−2248.55	+	3894.61i	−0.293075	+	0.507620i	−0.974535	−	0.224235i	$-0.928012\pi$
$389$	−2248.55	+	3894.61i	−0.293075	+	0.507620i	0.681460	+	0.731855i	$0.261345\pi$
$390$	1002.85	+	1736.99i	0.130209	+	0.225528i
$391$	1651.97			0.213667
$392$	2733.52	+	239.638i	0.352203	+	0.0308764i
$393$	4049.09			0.519719
$394$	−50.2318	−	87.0039i	−0.00642294	−	0.0111249i
$395$	−2316.31	+	4011.97i	−0.295054	+	0.511048i
$396$	789.423	−	1367.32i	0.100177	−	0.173511i
$397$	−5825.55	−	10090.2i	−0.736464	−	1.27559i	−0.954078	−	0.299558i	$-0.903161\pi$
$397$	−5825.55	−	10090.2i	−0.736464	−	1.27559i	0.217615	−	0.976035i	$-0.430172\pi$
$398$	−3725.55			−0.469208
$399$	188.144	−	4300.50i	0.0236065	−	0.539585i
$400$	400.000			0.0500000
$401$	2394.11	+	4146.73i	0.298146	+	0.516403i	0.975712	−	0.219059i	$-0.0702986\pi$
$401$	2394.11	+	4146.73i	0.298146	+	0.516403i	−0.677566	+	0.735462i	$0.736965\pi$
$402$	2237.70	−	3875.82i	0.277628	−	0.480866i
$403$	10157.4	−	17593.1i	1.25552	−	2.17463i
$404$	−2906.36	−	5033.96i	−0.357913	−	0.619923i
$405$	−405.000			−0.0496904
$406$	6319.45	−	3288.99i	0.772485	−	0.402043i
$407$	16110.1			1.96203
$408$	−193.718	−	335.529i	−0.0235060	−	0.0407136i
$409$	−2221.18	+	3847.20i	−0.268534	+	0.465114i	−0.968483	−	0.249078i	$-0.919872\pi$
$409$	−2221.18	+	3847.20i	−0.268534	+	0.465114i	0.699950	+	0.714192i	$0.253206\pi$
$410$	39.2843	−	68.0423i	0.00473198	−	0.00819603i
$411$	1279.64	+	2216.41i	0.153577	+	0.266003i
$412$	6933.67			0.829120
$413$	10181.3	+	6487.44i	1.21304	+	0.772944i
$414$	−1841.99			−0.218668
$415$	−2761.53	−	4783.10i	−0.326646	−	0.565767i
$416$	1069.71	−	1852.79i	0.126074	−	0.218367i
$417$	3802.18	−	6585.57i	0.446507	−	0.773373i
$418$	3397.84	+	5885.24i	0.397593	+	0.688652i
$419$	−15118.8			−1.76278			−0.881388	−	0.472393i	$-0.843390\pi$
$419$	−15118.8			−1.76278			−0.881388	+	0.472393i	$0.843390\pi$
$420$	937.137	+	597.138i	0.108875	+	0.0693747i
$421$	−3131.11			−0.362473			−0.181236	−	0.983440i	$-0.558010\pi$
$421$	−3131.11			−0.362473			−0.181236	+	0.983440i	$0.558010\pi$
$422$	4946.73	+	8567.98i	0.570623	+	0.988348i
$423$	−1208.14	+	2092.56i	−0.138870	+	0.240529i
$424$	1556.18	−	2695.38i	0.178242	−	0.308724i
$425$	−201.789	−	349.509i	−0.0230311	−	0.0398911i
$426$	−3371.12			−0.383406
$427$	−2052.76	+	1068.37i	−0.232646	+	0.121082i
$428$	−6580.38			−0.743165
$429$	−4398.20	−	7617.90i	−0.494981	−	0.857333i
$430$	910.474	−	1576.99i	0.102109	−	0.176858i
$431$	−7631.10	+	13217.4i	−0.852847	+	1.47717i	0.0257811	+	0.999668i	$0.491793\pi$
$431$	−7631.10	+	13217.4i	−0.852847	+	1.47717i	−0.878628	+	0.477507i	$0.841541\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	531.300			0.0589668			0.0294834	−	0.999565i	$-0.490614\pi$
$433$	531.300			0.0589668			0.0294834	+	0.999565i	$0.490614\pi$
$434$	491.926	−	11244.2i	0.0544083	−	1.24364i
$435$	2884.99			0.317988
$436$	−1341.61	−	2323.74i	−0.147366	−	0.255245i
$437$	3964.15	−	6866.11i	0.433938	−	0.751603i
$438$	1218.85	−	2111.11i	0.132966	−	0.230304i
$439$	−3147.10	−	5450.93i	−0.342148	−	0.592617i	0.642684	−	0.766132i	$-0.277821\pi$
$439$	−3147.10	−	5450.93i	−0.342148	−	0.592617i	−0.984831	+	0.173515i	$0.944488\pi$
$440$	−1754.27			−0.190072
$441$	1304.13	+	2798.00i	0.140819	+	0.302127i
$442$	−2158.56			−0.232290
$443$	6493.00	+	11246.2i	0.696369	+	1.20615i	0.969717	+	0.244232i	$0.0785358\pi$
$443$	6493.00	+	11246.2i	0.696369	+	1.20615i	−0.273347	+	0.961915i	$0.588131\pi$
$444$	−2204.00	+	3817.43i	−0.235579	+	0.408035i
$445$	1772.98	−	3070.89i	0.188870	−	0.327133i
$446$	6015.68	+	10419.5i	0.638679	+	1.10622i
$447$	5481.65			0.580030
$448$	51.8064	−	1184.16i	0.00546344	−	0.124881i
$449$	1775.40			0.186606			0.0933030	−	0.995638i	$-0.470257\pi$
$449$	1775.40			0.186606			0.0933030	+	0.995638i	$0.470257\pi$
$450$	225.000	+	389.711i	0.0235702	+	0.0408248i
$451$	−172.288	+	298.412i	−0.0179883	+	0.0311567i
$452$	449.322	−	778.249i	0.0467574	−	0.0809862i
$453$	2050.43	+	3551.44i	0.212666	+	0.368347i
$454$	6113.58			0.631992
$455$	5491.76	−	2858.22i	0.565841	−	0.294495i
$456$	−1859.42			−0.190955
$457$	2054.95	+	3559.27i	0.210342	+	0.364323i	0.951822	−	0.306652i	$-0.0992089\pi$
$457$	2054.95	+	3559.27i	0.210342	+	0.364323i	−0.741479	+	0.670976i	$0.765876\pi$
$458$	−2010.98	+	3483.11i	−0.205167	+	0.355361i
$459$	217.933	−	377.470i	0.0221617	−	0.0383852i
$460$	1023.33	+	1772.45i	0.103724	+	0.179655i
$461$	−3126.24			−0.315842			−0.157921	−	0.987452i	$-0.550479\pi$
$461$	−3126.24			−0.315842			−0.157921	+	0.987452i	$0.550479\pi$
$462$	−4109.99	−	2618.86i	−0.413883	−	0.263724i
$463$	11698.9			1.17428			0.587142	−	0.809484i	$-0.300253\pi$
$463$	11698.9			1.17428			0.587142	+	0.809484i	$0.300253\pi$
$464$	−1538.66	−	2665.04i	−0.153945	−	0.266641i
$465$	2278.91	−	3947.19i	0.227273	−	0.393648i
$466$	4057.49	−	7027.77i	0.403347	−	0.698617i
$467$	3247.91	+	5625.55i	0.321832	+	0.557429i	0.980866	−	0.194684i	$-0.0623682\pi$
$467$	3247.91	+	5625.55i	0.321832	+	0.557429i	−0.659034	+	0.752113i	$0.729035\pi$
$468$	2406.85			0.237728
$469$	−11650.2	−	7423.44i	−1.14703	−	0.730879i
$470$	2684.76			0.263486
$471$	118.276	+	204.860i	0.0115709	+	0.0200413i
$472$	2607.41	−	4516.17i	0.254271	−	0.440410i
$473$	−3993.05	+	6916.17i	−0.388162	+	0.672317i
$474$	2779.57	+	4814.36i	0.269346	+	0.466521i
$475$	−1936.90			−0.187097
$476$	−1060.83	+	552.112i	−0.102149	+	0.0531639i
$477$	3501.40			0.336097
$478$	5655.70	+	9795.96i	0.541184	+	0.937357i
$479$	3678.11	−	6370.67i	0.350850	−	0.607690i	−0.635549	−	0.772061i	$-0.719226\pi$
$479$	3678.11	−	6370.67i	0.350850	−	0.607690i	0.986399	+	0.164371i	$0.0525594\pi$
$480$	240.000	−	415.692i	0.0228218	−	0.0395285i
$481$	12279.4	+	21268.5i	1.16401	+	2.01613i
$482$	−12058.1			−1.13948
$483$	−248.507	+	5680.25i	−0.0234109	+	0.535114i
$484$	2369.69			0.222548
$485$	−121.895	−	211.128i	−0.0114123	−	0.0197667i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	338.264	−	585.890i	0.0314747	−	0.0545158i	−0.849859	−	0.527010i	$-0.823313\pi$
$487$	338.264	−	585.890i	0.0314747	−	0.0545158i	0.881334	+	0.472494i	$0.156646\pi$
$488$	499.806	+	865.690i	0.0463631	+	0.0803032i
$489$	4801.16			0.444000
$490$	1967.86	−	2809.34i	0.181427	−	0.259007i
$491$	−3058.37			−0.281104			−0.140552	−	0.990073i	$-0.544888\pi$
$491$	−3058.37			−0.281104			−0.140552	+	0.990073i	$0.544888\pi$
$492$	−47.1411	−	81.6508i	−0.00431968	−	0.00748191i
$493$	−1552.43	+	2688.88i	−0.141821	+	0.245641i
$494$	−5179.79	+	8971.66i	−0.471760	+	0.817113i
$495$	−986.779	−	1709.15i	−0.0896009	−	0.155193i
$496$	−4861.68			−0.440112
$497$	−454.806	+	10395.7i	−0.0410479	+	0.938253i
$498$	−6627.66			−0.596371
$499$	−8796.96	−	15236.8i	−0.789191	−	1.36692i	−0.926463	−	0.376385i	$-0.877167\pi$
$499$	−8796.96	−	15236.8i	−0.789191	−	1.36692i	0.137273	−	0.990533i	$-0.456166\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$	1422.21	−	2463.34i	0.126826	−	0.219668i
$502$	2066.63	+	3579.51i	0.183742	+	0.318250i
$503$	−10432.4			−0.924768			−0.462384	−	0.886680i	$-0.653006\pi$
$503$	−10432.4			−0.924768			−0.462384	+	0.886680i	$0.653006\pi$
$504$	1182.85	−	615.618i	0.104540	−	0.0544084i
$505$	−7265.90			−0.640254
$506$	−4487.99	−	7773.42i	−0.394299	−	0.682946i
$507$	3409.26	−	5905.01i	0.298640	−	0.517260i
$508$	3347.04	−	5797.24i	0.292324	−	0.506320i
$509$	−295.543	−	511.895i	−0.0257361	−	0.0445763i	0.852870	−	0.522123i	$-0.174860\pi$
$509$	−295.543	−	511.895i	−0.0257361	−	0.0445763i	−0.878607	+	0.477546i	$0.841526\pi$
$510$	−484.294			−0.0420489
$511$	−6345.73	−	4043.47i	−0.549352	−	0.350044i
$512$	−512.000			−0.0441942
$513$	−1045.92	−	1811.59i	−0.0900168	−	0.155914i
$514$	1955.09	−	3386.31i	0.167773	−	0.290591i
$515$	4333.54	−	7505.92i	0.370794	−	0.642233i
$516$	−1092.57	−	1892.38i	−0.0932125	−	0.161449i
$517$	−11774.5			−1.00163
$518$	11474.7	+	7311.61i	0.973300	+	0.620181i
$519$	−5102.53			−0.431553
$520$	−1337.14	−	2315.99i	−0.112764	−	0.195313i
$521$	10225.3	−	17710.7i	0.859840	−	1.48929i	−0.0122419	−	0.999925i	$-0.503897\pi$
$521$	10225.3	−	17710.7i	0.859840	−	1.48929i	0.872081	−	0.489361i	$-0.162770\pi$
$522$	1730.99	−	2998.17i	0.145141	−	0.251391i
$523$	−3751.23	−	6497.32i	−0.313632	−	0.543227i	0.665514	−	0.746386i	$-0.268213\pi$
$523$	−3751.23	−	6497.32i	−0.313632	−	0.543227i	−0.979146	+	0.203159i	$0.934879\pi$
$524$	−5398.79			−0.450090
$525$	1232.13	−	641.269i	0.102428	−	0.0533091i
$526$	−4283.64			−0.355086
$527$	2452.59	+	4248.00i	0.202726	+	0.351131i
$528$	−1052.56	+	1823.10i	−0.0867557	+	0.150265i
$529$	847.514	−	1467.94i	0.0696568	−	0.120649i
$530$	−1945.22	−	3369.22i	−0.159425	−	0.276131i
$531$	5866.67			0.479458
$532$	−250.859	+	5734.00i	−0.0204438	+	0.467294i
$533$	−525.284			−0.0426878
$534$	−2127.57	−	3685.07i	−0.172414	−	0.298630i
$535$	−4112.74	+	7123.47i	−0.332353	+	0.575653i
$536$	−2983.60	+	5167.75i	−0.240433	+	0.416442i
$537$	5040.44	+	8730.29i	0.405048	+	0.701564i
$538$	−1401.90			−0.112342
$539$	−8630.43	+	12320.9i	−0.689682	+	0.984599i
$540$	540.000			0.0430331
$541$	1155.64	+	2001.63i	0.0918392	+	0.159070i	0.908285	−	0.418352i	$-0.137392\pi$
$541$	1155.64	+	2001.63i	0.0918392	+	0.159070i	−0.816446	+	0.577422i	$0.804059\pi$
$542$	3111.72	−	5389.65i	0.246605	−	0.427132i
$543$	1980.95	−	3431.11i	0.156557	−	0.271165i
$544$	258.290	+	447.372i	0.0203568	+	0.0352590i
$545$	−3354.03			−0.263616
$546$	324.714	−	7422.14i	0.0254514	−	0.581755i
$547$	−357.963			−0.0279806			−0.0139903	−	0.999902i	$-0.504453\pi$
$547$	−357.963			−0.0279806			−0.0139903	+	0.999902i	$0.504453\pi$
$548$	−1706.19	−	2955.21i	−0.133001	−	0.230365i
$549$	−562.282	+	973.901i	−0.0437115	+	0.0757106i
$550$	−1096.42	+	1899.06i	−0.0850028	+	0.147229i
$551$	7450.56	+	12904.8i	0.576052	+	0.997751i
$552$	2455.98			0.189372
$553$	15221.3	−	7922.02i	1.17048	−	0.609183i
$554$	−15927.3			−1.22146
$555$	2754.99	+	4771.79i	0.210708	+	0.364957i
$556$	−5069.57	+	8780.76i	−0.386687	+	0.669761i
$557$	−7292.82	+	12631.5i	−0.554770	+	0.960889i	0.443152	+	0.896447i	$0.353860\pi$
$557$	−7292.82	+	12631.5i	−0.554770	+	0.960889i	−0.997921	+	0.0644425i	$0.979473\pi$
$558$	−2734.69	−	4736.63i	−0.207471	−	0.359350i
$559$	−12174.3			−0.921140
$560$	−1249.52	−	796.184i	−0.0942887	−	0.0600802i
$561$	2123.96			0.159846
$562$	−3427.21	−	5936.10i	−0.257239	−	0.445550i
$563$	−148.500	+	257.209i	−0.0111164	+	0.0192541i	−0.871530	−	0.490342i	$-0.836872\pi$
$563$	−148.500	+	257.209i	−0.0111164	+	0.0192541i	0.860414	+	0.509596i	$0.170205\pi$
$564$	1610.85	−	2790.08i	0.120265	−	0.208304i
$565$	−561.653	−	972.812i	−0.0418211	−	0.0724363i
$566$	−1082.90			−0.0804199
$567$	1265.13	+	806.137i	0.0937049	+	0.0597082i
$568$	4494.82			0.332040
$569$	3647.92	+	6318.38i	0.268767	+	0.465519i	0.968544	−	0.248843i	$-0.0800504\pi$
$569$	3647.92	+	6318.38i	0.268767	+	0.465519i	−0.699776	+	0.714362i	$0.746717\pi$
$570$	−1162.14	+	2012.88i	−0.0853975	+	0.147913i
$571$	4578.80	−	7930.72i	0.335581	−	0.581244i	−0.648015	−	0.761628i	$-0.724401\pi$
$571$	4578.80	−	7930.72i	0.335581	−	0.581244i	0.983596	+	0.180384i	$0.0577340\pi$
$572$	5864.26	+	10157.2i	0.428666	+	0.742472i
$573$	−1400.88			−0.102134
$574$	−258.151	+	134.356i	−0.0187718	+	0.00976989i
$575$	2558.32			0.185546
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−7264.87	+	12583.1i	−0.524160	+	0.907873i	0.475444	+	0.879746i	$0.342287\pi$
$577$	−7264.87	+	12583.1i	−0.524160	+	0.907873i	−0.999604	+	0.0281266i	$0.991046\pi$
$578$	−4652.40	+	8058.19i	−0.334800	+	0.579890i
$579$	−4658.25	−	8068.32i	−0.334353	−	0.579116i
$580$	−3846.65			−0.275385
$581$	−894.155	+	20438.1i	−0.0638482	+	1.45941i
$582$	−292.548			−0.0208359
$583$	8531.13	+	14776.3i	0.606043	+	1.04970i
$584$	−1625.14	+	2814.82i	−0.115152	+	0.199449i
$585$	1504.28	−	2605.49i	0.106315	−	0.184143i
$586$	1303.65	+	2257.98i	0.0918995	+	0.159175i
$587$	−9022.69			−0.634423			−0.317211	−	0.948355i	$-0.602746\pi$
$587$	−9022.69			−0.634423			−0.317211	+	0.948355i	$0.602746\pi$
$588$	−1738.84	−	3730.67i	−0.121953	−	0.261650i
$589$	23541.4			1.64687
$590$	−3259.26	−	5645.21i	−0.227427	−	0.393915i
$591$	−75.3476	+	130.506i	−0.00524431	+	0.00908341i
$592$	2938.66	−	5089.91i	0.204017	−	0.353368i
$593$	−4987.36	−	8638.36i	−0.345373	−	0.598204i	0.640048	−	0.768335i	$-0.278914\pi$
$593$	−4987.36	−	8638.36i	−0.345373	−	0.598204i	−0.985421	+	0.170131i	$0.945581\pi$
$594$	−2368.27			−0.163588
$595$	−65.3374	+	1493.45i	−0.00450180	+	0.102900i
$596$	−7308.87			−0.502320
$597$	2794.16	+	4839.63i	0.191553	+	0.331780i
$598$	6841.64	−	11850.1i	0.467852	−	0.810343i
$599$	−7611.69	+	13183.8i	−0.519208	+	0.899294i	0.480543	+	0.876971i	$0.340440\pi$
$599$	−7611.69	+	13183.8i	−0.519208	+	0.899294i	−0.999751	+	0.0223230i	$0.992894\pi$
$600$	−300.000	−	519.615i	−0.0204124	−	0.0353553i
$601$	18160.8			1.23260			0.616301	−	0.787511i	$-0.288630\pi$
$601$	18160.8			1.23260			0.616301	+	0.787511i	$0.288630\pi$
$602$	−5983.06	+	3113.91i	−0.405069	+	0.210820i
$603$	−6713.11			−0.453365
$604$	−2733.90	−	4735.26i	−0.184174	−	0.318998i
$605$	1481.06	−	2565.27i	0.0995266	−	0.172385i
$606$	−4359.54	+	7550.94i	−0.292235	+	0.506165i
$607$	−2408.39	−	4171.45i	−0.161044	−	0.278936i	0.774200	−	0.632941i	$-0.218153\pi$
$607$	−2408.39	−	4171.45i	−0.161044	−	0.278936i	−0.935243	+	0.354006i	$0.884819\pi$
$608$	2479.23			0.165372
$609$	−9012.10	−	5742.46i	−0.599653	−	0.382096i
$610$	1249.52			0.0829368
$611$	−8974.72	−	15544.7i	−0.594236	−	1.02925i
$612$	−290.577	+	503.294i	−0.0191926	+	0.0332425i
$613$	−7291.07	+	12628.5i	−0.480397	+	0.832073i	−0.999747	−	0.0224891i	$-0.992841\pi$
$613$	−7291.07	+	12628.5i	−0.480397	+	0.832073i	0.519350	+	0.854562i	$0.326174\pi$
$614$	−3114.73	−	5394.87i	−0.204723	−	0.354591i
$615$	−117.853			−0.00772729
$616$	5479.98	+	3491.81i	0.358433	+	0.228392i
$617$	1725.54			0.112590			0.0562948	−	0.998414i	$-0.482071\pi$
$617$	1725.54			0.112590			0.0562948	+	0.998414i	$0.482071\pi$
$618$	−5200.25	−	9007.10i	−0.338487	−	0.586276i
$619$	6088.92	−	10546.3i	0.395371	−	0.684802i	−0.597778	−	0.801662i	$-0.703950\pi$
$619$	6088.92	−	10546.3i	0.395371	−	0.684802i	0.993148	+	0.116860i	$0.0372829\pi$
$620$	−3038.55	+	5262.92i	−0.196824	+	0.340910i
$621$	1381.49	+	2392.81i	0.0892710	+	0.154622i
$622$	−13865.6			−0.893823
$623$	−11650.9	+	6063.77i	−0.749251	+	0.389951i
$624$	−3209.13			−0.205878
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	5110.49	−	8851.62i	0.326288	−	0.565147i
$627$	5096.77	−	8827.86i	0.324634	−	0.562282i
$628$	−157.701	−	273.147i	−0.0100207	−	0.0173563i
$629$	−5929.91			−0.375900
$630$	72.8528	−	1665.23i	0.00460718	−	0.105309i
$631$	−29011.6			−1.83032			−0.915162	−	0.403086i	$-0.867938\pi$
$631$	−29011.6			−1.83032			−0.915162	+	0.403086i	$0.867938\pi$
$632$	−3706.10	−	6419.15i	−0.233260	−	0.404019i
$633$	7420.09	−	12852.0i	0.465912	−	0.806982i
$634$	9362.18	−	16215.8i	0.586467	−	1.01579i
$635$	−4183.80	−	7246.55i	−0.261463	−	0.452867i
$636$	−4668.53			−0.291068
$637$	−22844.3	−	2002.68i	−1.42092	−	0.124567i
$638$	16870.2			1.04686
$639$	2528.34	+	4379.21i	0.156525	+	0.271109i
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	13200.7	−	22864.3i	0.813410	−	1.40887i	−0.0970536	−	0.995279i	$-0.530942\pi$
$641$	13200.7	−	22864.3i	0.813410	−	1.40887i	0.910464	−	0.413589i	$-0.135725\pi$
$642$	4935.28	+	8548.16i	0.303396	+	0.525497i
$643$	−26860.0			−1.64736			−0.823682	−	0.567052i	$-0.808084\pi$
$643$	−26860.0			−1.64736			−0.823682	+	0.567052i	$0.808084\pi$
$644$	331.343	−	7573.66i	0.0202744	−	0.463423i
$645$	−2731.42			−0.166744
$646$	−1250.70	−	2166.28i	−0.0761738	−	0.131937i
$647$	−6938.03	+	12017.0i	−0.421580	+	0.730198i	−0.996094	−	0.0882966i	$-0.971858\pi$
$647$	−6938.03	+	12017.0i	−0.421580	+	0.730198i	0.574514	+	0.818495i	$0.305191\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	14294.1	+	24758.1i	0.864550	+	1.49744i
$650$	−3342.84			−0.201719
$651$	−14975.6	+	7794.11i	−0.901596	+	0.469240i
$652$	−6401.55			−0.384515
$653$	13551.9	+	23472.5i	0.812136	+	1.40666i	0.911366	+	0.411597i	$0.135029\pi$
$653$	13551.9	+	23472.5i	0.812136	+	1.40666i	−0.0992295	+	0.995065i	$0.531638\pi$
$654$	−2012.42	+	3485.61i	−0.120324	+	0.208407i
$655$	−3374.24	+	5844.36i	−0.201286	+	0.348638i
$656$	62.8548	+	108.868i	0.00374096	+	0.00647953i
$657$	−3656.56			−0.217132
$658$	−8386.62	−	5343.91i	−0.496876	−	0.316607i
$659$	25682.0			1.51810			0.759052	−	0.651031i	$-0.225663\pi$
$659$	25682.0			1.51810			0.759052	+	0.651031i	$0.225663\pi$
$660$	1315.71	+	2278.87i	0.0775966	+	0.134401i
$661$	10233.6	−	17725.1i	0.602181	−	1.04301i	−0.390309	−	0.920684i	$-0.627632\pi$
$661$	10233.6	−	17725.1i	0.602181	−	1.04301i	0.992490	−	0.122324i	$-0.0390347\pi$
$662$	2893.09	−	5010.98i	0.169854	−	0.294195i
$663$	1618.92	+	2804.05i	0.0948321	+	0.164254i
$664$	8836.89			0.516472
$665$	6050.45	+	3855.31i	0.352822	+	0.224816i
$666$	6611.99			0.384699
$667$	−9840.95	−	17045.0i	−0.571279	−	0.989485i
$668$	−1896.28	+	3284.45i	−0.109834	+	0.190238i
$669$	9023.52	−	15629.2i	0.521479	−	0.903228i
$670$	3729.51	+	6459.69i	0.215050	+	0.372477i
$671$	−5479.98			−0.315279
$672$	−1577.13	+	820.824i	−0.0905343	+	0.0471190i
$673$	13154.0			0.753416			0.376708	−	0.926332i	$-0.377056\pi$
$673$	13154.0			0.753416			0.376708	+	0.926332i	$0.377056\pi$
$674$	−3378.62	−	5851.94i	−0.193085	−	0.334434i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	−4545.68	+	7873.34i	−0.258630	+	0.447960i
$677$	−10085.6	−	17468.8i	−0.572558	−	0.991699i	−0.996302	−	0.0859171i	$-0.972618\pi$
$677$	−10085.6	−	17468.8i	−0.572558	−	0.991699i	0.423745	−	0.905782i	$-0.360715\pi$
$678$	−1347.97			−0.0763545
$679$	−39.4684	+	902.148i	−0.00223072	+	0.0509886i
$680$	645.726			0.0364154
$681$	−4585.18	−	7941.77i	−0.258010	−	0.446886i
$682$	13326.1	−	23081.5i	0.748216	−	1.29595i
$683$	15070.9	−	26103.5i	0.844320	−	1.46241i	−0.0418895	−	0.999122i	$-0.513338\pi$
$683$	15070.9	−	26103.5i	0.844320	−	1.46241i	0.886210	−	0.463284i	$-0.153329\pi$
$684$	1394.56	+	2415.46i	0.0779569	+	0.135025i
$685$	−4265.47			−0.237920
$686$	−11739.1	+	4858.85i	−0.653353	+	0.270425i
$687$	6032.93			0.335037
$688$	1456.76	+	2523.18i	0.0807244	+	0.139819i
$689$	−13005.1	+	22525.6i	−0.719095	+	1.24551i
$690$	1534.99	−	2658.68i	0.0846899	−	0.146687i
$691$	7829.20	+	13560.6i	0.431023	+	0.746554i	0.996962	−	0.0778937i	$-0.0248195\pi$
$691$	7829.20	+	13560.6i	0.431023	+	0.746554i	−0.565939	+	0.824447i	$0.691486\pi$
$692$	6803.37			0.373736
$693$	−319.509	+	7303.18i	−0.0175139	+	0.400324i
$694$	1264.69			0.0691744
$695$	6336.96	+	10975.9i	0.345863	+	0.599052i
$696$	−2307.99	+	3997.56i	−0.125696	+	0.217711i
$697$	63.4172	−	109.842i	0.00344634	−	0.00596923i
$698$	−5549.40	−	9611.85i	−0.300928	−	0.521223i
$699$	−12172.5			−0.658662
$700$	−1642.84	+	855.025i	−0.0887052	+	0.0461670i
$701$	29322.4			1.57987			0.789937	−	0.613187i	$-0.210113\pi$
$701$	29322.4			1.57987			0.789937	+	0.613187i	$0.210113\pi$
$702$	−1805.13	−	3126.59i	−0.0970519	−	0.168099i
$703$	−14229.7	+	24646.6i	−0.763418	+	1.32228i
$704$	1403.42	−	2430.79i	0.0751326	−	0.130133i
$705$	−2013.57	−	3487.60i	−0.107568	−	0.186313i
$706$	11614.1			0.619127
$707$	22697.1	+	14462.5i	1.20737	+	0.769332i
$708$	−7822.23			−0.415222
$709$	−8843.92	−	15318.1i	−0.468463	−	0.811402i	0.530887	−	0.847443i	$-0.321859\pi$
$709$	−8843.92	−	15318.1i	−0.468463	−	0.811402i	−0.999350	+	0.0360403i	$0.988526\pi$
$710$	2809.26	−	4865.79i	0.148493	−	0.257197i
$711$	4169.36	−	7221.54i	0.219920	−	0.380913i
$712$	2836.77	+	4913.42i	0.149315	+	0.258621i
$713$	−31094.3			−1.63323
$714$	1512.83	+	963.969i	0.0792947	+	0.0505261i
$715$	14660.7			0.766822
$716$	−6720.58	−	11640.4i	−0.350782	−	0.607572i
$717$	8483.55	−	14693.9i	0.441875	−	0.765349i
$718$	6794.47	−	11768.4i	0.353158	−	0.611688i
$719$	10404.2	+	18020.7i	0.539656	+	0.934711i	0.998922	+	0.0464127i	$0.0147789\pi$
$719$	10404.2	+	18020.7i	0.539656	+	0.934711i	−0.459267	+	0.888298i	$0.651888\pi$
$720$	−720.000			−0.0372678
$721$	−28477.3	+	14821.2i	−1.47094	+	0.765560i
$722$	1713.00			0.0882982
$723$	9043.55	+	15663.9i	0.465191	+	0.805735i
$724$	−2641.27	+	4574.81i	−0.135583	+	0.234836i
$725$	−2404.16	+	4164.12i	−0.123156	+	0.213313i
$726$	−1777.27	−	3078.32i	−0.0908549	−	0.157365i
$727$	−572.373			−0.0291996			−0.0145998	−	0.999893i	$-0.504647\pi$
$727$	−572.373			−0.0291996			−0.0145998	+	0.999893i	$0.504647\pi$
$728$	−432.952	+	9896.18i	−0.0220416	+	0.503815i
$729$	729.000			0.0370370
$730$	2031.42	+	3518.52i	0.102995	+	0.178392i
$731$	1469.79	−	2545.75i	0.0743669	−	0.128807i
$732$	749.710	−	1298.54i	0.0378553	−	0.0655673i
$733$	15934.5	+	27599.4i	0.802941	+	1.39074i	0.917672	+	0.397339i	$0.130066\pi$
$733$	15934.5	+	27599.4i	0.802941	+	1.39074i	−0.114731	+	0.993397i	$0.536601\pi$
$734$	−19707.4			−0.991024
$735$	−5125.34	−	449.321i	−0.257212	−	0.0225489i
$736$	−3274.64			−0.164001
$737$	−16356.4	−	28330.2i	−0.817499	−	1.41595i
$738$	−70.7117	+	122.476i	−0.00352701	+	0.00610896i
$739$	12378.9	−	21441.0i	0.616193	−	1.06728i	−0.373981	−	0.927436i	$-0.622007\pi$
$739$	12378.9	−	21441.0i	0.616193	−	1.06728i	0.990174	−	0.139841i	$-0.0446592\pi$
$740$	−3673.33	−	6362.39i	−0.182479	−	0.316062i
$741$	15539.4			0.770382
$742$	−629.843	+	14396.6i	−0.0311621	+	0.712287i
$743$	−21112.4			−1.04245			−0.521224	−	0.853420i	$-0.674524\pi$
$743$	−21112.4			−1.04245			−0.521224	+	0.853420i	$0.674524\pi$
$744$	3646.26	+	6315.50i	0.179675	+	0.311206i
$745$	−4568.04	+	7912.08i	−0.224645	+	0.389096i
$746$	−9544.19	+	16531.0i	−0.468415	+	0.811318i
$747$	4970.75	+	8609.59i	0.243467	+	0.421698i
$748$	−2831.95			−0.138431
$749$	27026.3	−	14066.0i	1.31845	−	0.686194i
$750$	−750.000			−0.0365148
$751$	1779.94	+	3082.95i	0.0864860	+	0.149798i	0.906023	−	0.423227i	$-0.139103\pi$
$751$	1779.94	+	3082.95i	0.0864860	+	0.149798i	−0.819537	+	0.573026i	$0.805770\pi$
$752$	−2147.81	+	3720.11i	−0.104152	+	0.180397i
$753$	3099.95	−	5369.27i	0.150024	−	0.259850i
$754$	12858.8	+	22272.0i	0.621072	+	1.07573i
$755$	−6834.76			−0.329460
$756$	−1686.85	−	1074.85i	−0.0811508	−	0.0517088i
$757$	8118.48			0.389790			0.194895	−	0.980824i	$-0.437563\pi$
$757$	8118.48			0.389790			0.194895	+	0.980824i	$0.437563\pi$
$758$	9836.63	+	17037.5i	0.471349	+	0.816400i
$759$	−6731.98	+	11660.1i	−0.321944	+	0.557623i
$760$	1549.52	−	2683.84i	0.0739564	−	0.128096i
$761$	−19782.7	−	34264.7i	−0.942342	−	1.63219i	−0.760987	−	0.648768i	$-0.775285\pi$
$761$	−19782.7	−	34264.7i	−0.942342	−	1.63219i	−0.181356	−	0.983418i	$-0.558049\pi$
$762$	−10041.1			−0.477363
$763$	10477.3	+	6676.07i	0.497121	+	0.316763i
$764$	1867.84			0.0884503
$765$	363.221	+	629.117i	0.0171664	+	0.0297330i
$766$	11350.4	−	19659.5i	0.535387	−	0.927317i
$767$	−21790.4	+	37742.1i	−1.02582	+	1.77678i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	24481.4			1.14801			0.574007	−	0.818850i	$-0.305388\pi$
$769$	24481.4			1.14801			0.574007	+	0.818850i	$0.305388\pi$
$770$	7204.99	−	3749.87i	0.337208	−	0.175501i
$771$	−5865.26			−0.273972
$772$	6211.00	+	10757.8i	0.289558	+	0.501529i
$773$	15339.9	−	26569.4i	0.713761	−	1.23627i	−0.249675	−	0.968330i	$-0.580324\pi$
$773$	15339.9	−	26569.4i	0.713761	−	1.23627i	0.963436	−	0.267940i	$-0.0863428\pi$
$774$	−1638.85	+	2838.58i	−0.0761077	+	0.131822i
$775$	3798.19	+	6578.65i	0.176045	+	0.304919i
$776$	390.064			0.0180444
$777$	892.040	−	20389.8i	0.0411863	−	0.941415i
$778$	−8994.21			−0.414470
$779$	−304.358	−	527.163i	−0.0139984	−	0.0242459i
$780$	−2005.71	+	3473.98i	−0.0920715	+	0.159473i
$781$	−12320.5	+	21339.8i	−0.564486	+	0.977719i
$782$	1651.97	+	2861.30i	0.0755427	+	0.130844i
$783$	−5192.98			−0.237014
$784$	2318.45	+	4974.23i	0.105615	+	0.226596i
$785$	−394.254			−0.0179255
$786$	4049.09	+	7013.23i	0.183749	+	0.318262i
$787$	18803.3	−	32568.2i	0.851670	−	1.47514i	−0.0280294	−	0.999607i	$-0.508923\pi$
$787$	18803.3	−	32568.2i	0.851670	−	1.47514i	0.879700	−	0.475529i	$-0.157743\pi$
$788$	100.464	−	174.008i	0.00454171	−	0.00786647i
$789$	3212.73	+	5564.61i	0.144963	+	0.251084i
$790$	−9265.24			−0.417269
$791$	−181.858	+	4156.81i	−0.00817461	+	0.186851i
$792$	3157.69			0.141671
$793$	−4176.94	−	7234.66i	−0.187046	−	0.323973i
$794$	11651.1	−	20180.3i	0.520758	−	0.901980i
$795$	−2917.83	+	5053.83i	−0.130170	+	0.225460i
$796$	−3725.55	−	6452.84i	−0.165890	−	0.287330i
$797$	31156.5			1.38472			0.692358	−	0.721554i	$-0.256572\pi$
$797$	31156.5			1.38472			0.692358	+	0.721554i	$0.256572\pi$
$798$	7636.83	−	3974.63i	0.338773	−	0.176316i
$799$	4334.05			0.191899
$800$	400.000	+	692.820i	0.0176777	+	0.0306186i
$801$	−3191.36	+	5527.60i	−0.140776	+	0.243830i
$802$	−4788.23	+	8293.46i	−0.210821	+	0.365152i
$803$	−8909.17	−	15431.1i	−0.391529	−	0.678148i
$804$	8950.81			0.392625
$805$	−7991.64	−	5092.23i	−0.349899	−	0.222953i
$806$	40629.5			1.77558
$807$	1051.42	+	1821.12i	0.0458634	+	0.0794378i
$808$	5812.72	−	10067.9i	0.253083	−	0.438352i
$809$	−5231.54	+	9061.30i	−0.227356	+	0.393793i	−0.957024	−	0.290010i	$-0.906342\pi$
$809$	−5231.54	+	9061.30i	−0.227356	+	0.393793i	0.729668	+	0.683802i	$0.239675\pi$
$810$	−405.000	−	701.481i	−0.0175682	−	0.0304290i
$811$	7132.05			0.308804			0.154402	−	0.988008i	$-0.450655\pi$
$811$	7132.05			0.308804			0.154402	+	0.988008i	$0.450655\pi$
$812$	12016.1	+	7656.61i	0.519315	+	0.330905i
$813$	−9335.15			−0.402704
$814$	16110.1	+	27903.4i	0.693682	+	1.20149i
$815$	−4000.97	+	6929.88i	−0.171960	+	0.297844i
$816$	387.436	−	671.058i	0.0166213	−	0.0287889i
$817$	−7053.97	−	12217.8i	−0.302065	−	0.523192i
$818$	−8884.73			−0.379764
$819$	−9885.17	+	5144.79i	−0.421753	+	0.219504i
$820$	157.137			0.00669203
$821$	−8823.61	−	15282.9i	−0.375086	−	0.649669i	0.615254	−	0.788329i	$-0.289054\pi$
$821$	−8823.61	−	15282.9i	−0.375086	−	0.649669i	−0.990340	+	0.138661i	$0.955720\pi$
$822$	−2559.28	+	4432.81i	−0.108595	+	0.188092i
$823$	19041.3	−	32980.5i	0.806486	−	1.39687i	−0.108797	−	0.994064i	$-0.534700\pi$
$823$	19041.3	−	32980.5i	0.806486	−	1.39687i	0.915283	−	0.402811i	$-0.131967\pi$
$824$	6933.67	+	12009.5i	0.293138	+	0.507730i
$825$	3289.26			0.138809
$826$	−1055.32	+	24121.9i	−0.0444542	+	1.01611i
$827$	−17915.4			−0.753299			−0.376649	−	0.926356i	$-0.622924\pi$
$827$	−17915.4			−0.753299			−0.376649	+	0.926356i	$0.622924\pi$
$828$	−1841.99	−	3190.42i	−0.0773110	−	0.133907i
$829$	−11367.8	+	19689.6i	−0.476261	+	0.824908i	−0.999630	−	0.0271978i	$-0.991342\pi$
$829$	−11367.8	+	19689.6i	−0.476261	+	0.824908i	0.523369	+	0.852106i	$0.324675\pi$
$830$	5523.05	−	9566.21i	0.230973	−	0.400058i
$831$	11945.5	+	20690.2i	0.498657	+	0.863700i
$832$	4278.84			0.178296
$833$	3176.75	−	4535.17i	0.132134	−	0.188637i
$834$	15208.7			0.631457
$835$	2370.35	+	4105.56i	0.0982386	+	0.170154i
$836$	−6795.69	+	11770.5i	−0.281141	+	0.486950i
$837$	−4102.04	+	7104.94i	−0.169399	+	0.293408i
$838$	−15118.8	−	26186.6i	−0.623235	−	1.07948i
$839$	−16231.8			−0.667920			−0.333960	−	0.942587i	$-0.608385\pi$
$839$	−16231.8			−0.667920			−0.333960	+	0.942587i	$0.608385\pi$
$840$	−97.1370	+	2220.31i	−0.00398993	+	0.0911999i
$841$	12602.8			0.516743
$842$	−3131.11	−	5423.25i	−0.128154	−	0.221968i
$843$	−5140.81	+	8904.15i	−0.210034	+	0.363790i
$844$	−9893.45	+	17136.0i	−0.403491	+	0.698867i
$845$	5682.10	+	9841.68i	0.231325	+	0.400668i
$846$	−4832.56			−0.196391
$847$	−9732.58	+	5065.37i	−0.394823	+	0.205488i
$848$	6224.71			0.252072
$849$	812.175	+	1406.73i	0.0328313	+	0.0568655i
$850$	403.579	−	699.019i	0.0162855	−	0.0282072i
$851$	18795.1	−	32554.0i	0.757093	−	1.31132i
$852$	−3371.12	−	5838.95i	−0.135555	−	0.234788i
$853$	17115.6			0.687020			0.343510	−	0.939149i	$-0.388384\pi$
$853$	17115.6			0.687020			0.343510	+	0.939149i	$0.388384\pi$
$854$	−3903.23	−	2487.11i	−0.156400	−	0.0996572i
$855$	3486.41			0.139453
$856$	−6580.38	−	11397.6i	−0.262749	−	0.455094i
$857$	5860.50	−	10150.7i	0.233595	−	0.404598i	−0.725269	−	0.688466i	$-0.758284\pi$
$857$	5860.50	−	10150.7i	0.233595	−	0.404598i	0.958863	+	0.283868i	$0.0916178\pi$
$858$	8796.39	−	15235.8i	0.350005	−	0.606226i
$859$	−2353.90	−	4077.07i	−0.0934971	−	0.161942i	0.815483	−	0.578781i	$-0.196471\pi$
$859$	−2353.90	−	4077.07i	−0.0934971	−	0.161942i	−0.908980	+	0.416839i	$0.863138\pi$
$860$	3641.90			0.144404
$861$	368.147	+	234.581i	0.0145719	+	0.00928515i
$862$	−30524.4			−1.20611
$863$	−9057.54	−	15688.1i	−0.357268	−	0.618806i	0.630236	−	0.776404i	$-0.282958\pi$
$863$	−9057.54	−	15688.1i	−0.357268	−	0.618806i	−0.987503	+	0.157598i	$0.949625\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	4252.11	−	7364.86i	0.167140	−	0.289495i
$866$	531.300	+	920.238i	0.0208479	+	0.0361097i
$867$	13957.2			0.546726
$868$	19967.4	−	10392.1i	0.780805	−	0.406374i
$869$	40634.4			1.58622
$870$	2884.99	+	4996.95i	0.112426	+	0.194727i
$871$	24934.3	−	43187.5i	0.969996	−	1.68008i
$872$	2683.23	−	4647.48i	0.104204	−	0.180486i
$873$	219.411	+	380.031i	0.00850623	+	0.0147332i
$874$	15856.6			0.613682
$875$	−101.184	+	2312.82i	−0.00390932	+	0.0893572i
$876$	4875.41			0.188042
$877$	2228.52	+	3859.91i	0.0858059	+	0.148620i	0.905734	−	0.423846i	$-0.139320\pi$
$877$	2228.52	+	3859.91i	0.0858059	+	0.148620i	−0.819928	+	0.572466i	$0.805987\pi$
$878$	6294.20	−	10901.9i	0.241935	−	0.419044i
$879$	1955.47	−	3386.97i	0.0750356	−	0.129966i
$880$	−1754.27	−	3038.49i	−0.0672006	−	0.116395i
$881$	19498.4			0.745650			0.372825	−	0.927902i	$-0.378389\pi$
$881$	19498.4			0.745650			0.372825	+	0.927902i	$0.378389\pi$
$882$	−3542.15	+	5056.82i	−0.135227	+	0.193052i
$883$	−31592.5			−1.20405			−0.602023	−	0.798479i	$-0.705638\pi$
$883$	−31592.5			−1.20405			−0.602023	+	0.798479i	$0.705638\pi$
$884$	−2158.56	−	3738.74i	−0.0821270	−	0.142248i
$885$	−4888.90	+	8467.82i	−0.185693	+	0.321630i
$886$	−12986.0	+	22492.4i	−0.492408	+	0.852875i
$887$	−2987.24	−	5174.05i	−0.113080	−	0.195860i	0.803931	−	0.594723i	$-0.202738\pi$
$887$	−2987.24	−	5174.05i	−0.113080	−	0.195860i	−0.917011	+	0.398863i	$0.869405\pi$
$888$	−8815.98			−0.333159
$889$	−1354.67	+	30964.4i	−0.0511071	+	1.16818i
$890$	7091.92			0.267103
$891$	1776.20	+	3076.47i	0.0667845	+	0.115674i
$892$	−12031.4	+	20838.9i	−0.451614	+	0.782219i
$893$	10400.2	−	18013.7i	0.389730	−	0.675032i
$894$	5481.65	+	9494.50i	0.205071	+	0.355194i
$895$	−16801.5			−0.627498
$896$	2102.84	−	1094.43i	0.0784050	−	0.0408063i
$897$	−20524.9			−0.763999
$898$	1775.40	+	3075.08i	0.0659752	+	0.114272i
$899$	29220.6	−	50611.6i	1.08405	−	1.87763i
$900$	−450.000	+	779.423i	−0.0166667	+	0.0288675i
$901$	−3140.20	−	5438.99i	−0.116110	−	0.201109i
$902$	−689.153			−0.0254394
$903$	8532.39	+	5436.79i	0.314441	+	0.200360i
$904$	1797.29			0.0661250
$905$	3301.58	+	5718.51i	0.121269	+	0.210044i
$906$	−4100.85	+	7102.89i	−0.150377	+	0.260461i
$907$	−6566.42	+	11373.4i	−0.240391	+	0.416369i	−0.960826	−	0.277154i	$-0.910609\pi$
$907$	−6566.42	+	11373.4i	−0.240391	+	0.416369i	0.720435	+	0.693523i	$0.243942\pi$
$908$	6113.58	+	10589.0i	0.223443	+	0.387014i
$909$	13078.6			0.477217
$910$	10442.3	+	6653.80i	0.380396	+	0.242386i
$911$	13645.8			0.496273			0.248137	−	0.968725i	$-0.420182\pi$
$911$	13645.8			0.496273			0.248137	+	0.968725i	$0.420182\pi$
$912$	−1859.42	−	3220.61i	−0.0675126	−	0.116935i
$913$	−24222.4	+	41954.4i	−0.878032	+	1.52080i
$914$	−4109.89	+	7118.54i	−0.148734	+	0.257615i
$915$	−937.137	−	1623.17i	−0.0338588	−	0.0586451i
$916$	−8043.90			−0.290151
$917$	22173.4	−	11540.3i	0.798506	−	0.415586i
$918$	871.730			0.0313414
$919$	−13566.3	−	23497.5i	−0.486954	−	0.843429i	0.512934	−	0.858428i	$-0.328559\pi$
$919$	−13566.3	−	23497.5i	−0.486954	−	0.843429i	−0.999888	+	0.0149993i	$0.995225\pi$
$920$	−2046.65	+	3544.91i	−0.0733436	+	0.127035i
$921$	−4672.09	+	8092.30i	−0.167156	+	0.289523i
$922$	−3126.24	−	5414.80i	−0.111667	−	0.193413i
$923$	−37563.7			−1.33957
$924$	426.012	−	9737.57i	0.0151675	−	0.346691i
$925$	−9183.32			−0.326428
$926$	11698.9	+	20263.1i	0.415172	+	0.719099i
$927$	−7800.38	+	13510.6i	−0.276373	+	0.478693i
$928$	3077.32	−	5330.08i	0.108856	−	0.188544i
$929$	18963.6	+	32845.9i	0.669725	+	1.16000i	0.977981	+	0.208695i	$0.0669214\pi$
$929$	18963.6	+	32845.9i	0.669725	+	1.16000i	−0.308256	+	0.951304i	$0.599745\pi$
$930$	9115.64			0.321413
$931$	−11226.5	−	24086.4i	−0.395202	−	0.847905i
$932$	16229.9			0.570418
$933$	10399.2	+	18011.9i	0.364902	+	0.632028i
$934$	−6495.82	+	11251.1i	−0.227569	+	0.394162i
$935$	−1769.97	+	3065.68i	−0.0619082	+	0.107228i
$936$	2406.85	+	4168.78i	0.0840494	+	0.145578i
$937$	−21759.4			−0.758644			−0.379322	−	0.925265i	$-0.623843\pi$
$937$	−21759.4			−0.758644			−0.379322	+	0.925265i	$0.623843\pi$
$938$	1207.58	−	27602.2i	0.0420349	−	0.960813i
$939$	−15331.5			−0.532826
$940$	2684.76	+	4650.14i	0.0931565	+	0.161352i
$941$	−3393.40	+	5877.53i	−0.117557	+	0.203615i	−0.918799	−	0.394725i	$-0.870840\pi$
$941$	−3393.40	+	5877.53i	−0.117557	+	0.203615i	0.801242	+	0.598341i	$0.204173\pi$
$942$	−236.552	+	409.720i	−0.00818183	+	0.0141713i
$943$	402.006	+	696.295i	0.0138824	+	0.0240451i
$944$	10429.6			0.359593
$945$	−2217.84	+	1154.28i	−0.0763452	+	0.0397343i
$946$	−15972.2			−0.548944
$947$	−6181.61	−	10706.9i	−0.212117	−	0.367398i	0.740260	−	0.672321i	$-0.234703\pi$
$947$	−6181.61	−	10706.9i	−0.212117	−	0.367398i	−0.952377	+	0.304923i	$0.901369\pi$
$948$	−5559.15	+	9628.72i	−0.190456	+	0.329880i
$949$	13581.4	−	23523.7i	0.464565	−	0.804650i
$950$	−1936.90	−	3354.80i	−0.0661486	−	0.114573i
$951$	−28086.5			−0.957696
$952$	−2017.11	−	1285.29i	−0.0686712	−	0.0437569i
$953$	−4200.98			−0.142794			−0.0713972	−	0.997448i	$-0.522746\pi$
$953$	−4200.98			−0.142794			−0.0713972	+	0.997448i	$0.522746\pi$
$954$	3501.40	+	6064.60i	0.118828	+	0.205816i
$955$	1167.40	−	2022.00i	0.0395562	−	0.0685133i
$956$	−11311.4	+	19591.9i	−0.382675	+	0.662812i
$957$	−12652.7	−	21915.0i	−0.427380	−	0.740243i
$958$	14712.4			0.496177
$959$	13324.4	+	8490.26i	0.448664	+	0.285886i
$960$	960.000			0.0322749
$961$	−31268.4	−	54158.4i	−1.04959	−	1.81795i
$962$	−24558.7	+	42536.9i	−0.823081	+	1.42562i
$963$	7402.93	−	12822.2i	0.247722	−	0.429067i
$964$	−12058.1	−	20885.2i	−0.402868	−	0.697787i
$965$	15527.5			0.517977
$966$	−10087.0	+	5249.82i	−0.335966	+	0.174855i
$967$	33863.9			1.12615			0.563075	−	0.826405i	$-0.309618\pi$
$967$	33863.9			1.12615			0.563075	+	0.826405i	$0.309618\pi$
$968$	2369.69	+	4104.43i	0.0786827	+	0.136282i
$969$	−1876.06	+	3249.42i	−0.0621956	+	0.107726i
$970$	243.790	−	422.257i	0.00806972	−	0.0139772i
$971$	−17798.6	−	30828.1i	−0.588243	−	1.01887i	−0.994463	−	0.105091i	$-0.966487\pi$
$971$	−17798.6	−	30828.1i	−0.588243	−	1.01887i	0.406220	−	0.913775i	$-0.366847\pi$
$972$	−972.000			−0.0320750
$973$	2051.85	−	46900.0i	0.0676045	−	1.54527i
$974$	1353.05			0.0445120
$975$	2507.13	+	4342.48i	0.0823513	+	0.142637i
$976$	−999.613	+	1731.38i	−0.0327836	+	0.0567829i
$977$	8148.19	−	14113.1i	0.266821	−	0.462147i	−0.701218	−	0.712946i	$-0.747360\pi$
$977$	8148.19	−	14113.1i	0.266821	−	0.462147i	0.968039	+	0.250800i	$0.0806936\pi$
$978$	4801.16	+	8315.86i	0.156978	+	0.271893i
$979$	−31102.9			−1.01538
$980$	6833.79	+	599.094i	0.222752	+	0.0195279i
$981$	6037.26			0.196488
$982$	−3058.37	−	5297.25i	−0.0993853	−	0.172140i
$983$	−22226.4	+	38497.3i	−0.721173	+	1.24911i	0.239357	+	0.970932i	$0.423063\pi$
$983$	−22226.4	+	38497.3i	−0.721173	+	1.24911i	−0.960530	+	0.278176i	$0.910270\pi$
$984$	94.2822	−	163.302i	0.00305448	−	0.00529051i
$985$	−125.579	−	217.510i	−0.00406223	−	0.00703598i
$986$	−6209.71			−0.200565
$987$	−651.973	+	14902.5i	−0.0210259	+	0.480599i
$988$	−20719.2			−0.667170
$989$	9317.12	+	16137.7i	0.299562	+	0.518857i
$990$	1973.56	−	3418.30i	0.0633574	−	0.109738i
$991$	−11171.1	+	19348.8i	−0.358083	+	0.620218i	−0.987641	−	0.156736i	$-0.949903\pi$
$991$	−11171.1	+	19348.8i	−0.358083	+	0.620218i	0.629557	+	0.776954i	$0.283236\pi$
$992$	−4861.68	−	8420.67i	−0.155603	−	0.269513i
$993$	−8679.28			−0.277370
$994$	−18460.7	+	9607.97i	−0.589073	+	0.306586i
$995$	−9313.87			−0.296753
$996$	−6627.66	−	11479.5i	−0.210849	−	0.365201i
$997$	5350.06	−	9266.58i	0.169948	−	0.294359i	−0.768453	−	0.639906i	$-0.778973\pi$
$997$	5350.06	−	9266.58i	0.169948	−	0.294359i	0.938401	+	0.345547i	$0.112307\pi$
$998$	17593.9	−	30473.6i	0.558042	−	0.966557i
$999$	−4958.99	−	8589.22i	−0.157053	−	0.272023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.4.i.j.151.2	yes	4
3.2	odd	2		630.4.k.k.361.2		4
7.2	even	3	inner	210.4.i.j.121.2	✓	4
7.3	odd	6		1470.4.a.bj.1.1		2
7.4	even	3		1470.4.a.be.1.1		2
21.2	odd	6		630.4.k.k.541.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.i.j.121.2	✓	4	7.2	even	3	inner
210.4.i.j.151.2	yes	4	1.1	even	1	trivial
630.4.k.k.361.2		4	3.2	odd	2
630.4.k.k.541.2		4	21.2	odd	6
1470.4.a.be.1.1		2	7.4	even	3
1470.4.a.bj.1.1		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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} +(0.809475 - 18.5026i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(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} +(0.809475 - 18.5026i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(21.9284 - 37.9811i) q^{11} +(6.00000 + 10.3923i) q^{12} +66.8569 q^{13} +(32.8569 - 17.1005i) q^{14} +15.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-8.07157 + 13.9804i) q^{17} +(9.00000 - 15.5885i) q^{18} +(38.7379 + 67.0960i) q^{19} -20.0000 q^{20} +(-46.8569 - 29.8569i) q^{21} +87.7137 q^{22} +(-51.1663 - 88.6227i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(66.8569 + 115.799i) q^{26} -27.0000 q^{27} +(62.4758 + 39.8092i) q^{28} +192.333 q^{29} +(15.0000 + 25.9808i) q^{30} +(151.927 - 263.146i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-65.7853 - 113.943i) q^{33} -32.2863 q^{34} +(82.1421 - 42.7513i) q^{35} +36.0000 q^{36} +(183.666 + 318.119i) q^{37} +(-77.4758 + 134.192i) q^{38} +(100.285 - 173.699i) q^{39} +(-20.0000 - 34.6410i) q^{40} -7.85685 q^{41} +(4.85685 - 111.015i) q^{42} -182.095 q^{43} +(87.7137 + 151.925i) q^{44} +(22.5000 - 38.9711i) q^{45} +(102.333 - 177.245i) q^{46} +(-134.238 - 232.507i) q^{47} -48.0000 q^{48} +(-341.690 - 29.9547i) q^{49} -50.0000 q^{50} +(24.2147 + 41.9411i) q^{51} +(-133.714 + 231.599i) q^{52} +(-194.522 + 336.922i) q^{53} +(-27.0000 - 46.7654i) q^{54} +219.284 q^{55} +(-6.47580 + 148.020i) q^{56} +232.427 q^{57} +(192.333 + 333.130i) q^{58} +(-325.926 + 564.521i) q^{59} +(-30.0000 + 51.9615i) q^{60} +(-62.4758 - 108.211i) q^{61} +607.710 q^{62} +(-147.856 + 76.9523i) q^{63} +64.0000 q^{64} +(167.142 + 289.499i) q^{65} +(131.571 - 227.887i) q^{66} +(372.951 - 645.969i) q^{67} +(-32.2863 - 55.9215i) q^{68} -306.998 q^{69} +(156.190 + 99.5231i) q^{70} -561.853 q^{71} +(36.0000 + 62.3538i) q^{72} +(203.142 - 351.852i) q^{73} +(-367.333 + 636.239i) q^{74} +(37.5000 + 64.9519i) q^{75} -309.903 q^{76} +(-684.998 - 436.477i) q^{77} +401.141 q^{78} +(463.262 + 802.393i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-7.85685 - 13.6085i) q^{82} -1104.61 q^{83} +(197.141 - 102.603i) q^{84} -80.7157 q^{85} +(-182.095 - 315.397i) q^{86} +(288.499 - 499.695i) q^{87} +(-175.427 + 303.849i) q^{88} +(-354.596 - 614.178i) q^{89} +90.0000 q^{90} +(54.1190 - 1237.02i) q^{91} +409.331 q^{92} +(-455.782 - 789.438i) q^{93} +(268.476 - 465.014i) q^{94} +(-193.690 + 335.480i) q^{95} +(-48.0000 - 83.1384i) q^{96} -48.7580 q^{97} +(-289.806 - 621.778i) q^{98} -394.712 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more