LMFDB - Embedded newform 70.3.l.c.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,3,Mod(23,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 4]))

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

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

chi := DirichletCharacter("70.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.l (of order $12$, degree $4$, 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:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 $ x^16 - 2x^15 + 2x^14 - 8x^13 - 722x^12 + 1354x^11 - 1232x^10 + 9306x^9 + 505731x^8 - 1157418x^7 + 1256080x^6 - 9824090x^5 + 5294974x^4 + 30978760x^3 + 12152450x^2 + 35619250*x + 52200625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.1
Root			$1.35330 + 5.05060i$ of defining polynomial
Character	$\chi$	$=$	70.53
Dual form			70.3.l.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(-5.05060 + 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.84634 - 1.23005i) q^{5} +7.39459 q^{6} +(1.26709 - 6.88437i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(-5.05060 + 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.84634 - 1.23005i) q^{5} +7.39459 q^{6} +(1.26709 - 6.88437i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +(-7.07045 - 0.0936064i) q^{10} +(5.56894 - 9.64568i) q^{11} +(-10.1012 - 2.70661i) q^{12} +(9.62415 + 9.62415i) q^{13} +(-4.25073 + 8.94043i) q^{14} +(-22.8123 + 12.7710i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-2.29193 - 8.55361i) q^{17} +(-25.0529 + 6.71290i) q^{18} +(-5.79257 + 3.34434i) q^{19} +(9.62415 + 2.71583i) q^{20} +(2.91708 + 36.4849i) q^{21} +(-11.1379 + 11.1379i) q^{22} +(7.37457 - 27.5223i) q^{23} +(12.8078 + 7.39459i) q^{24} +(21.9740 - 11.9224i) q^{25} +(-9.62415 - 16.6695i) q^{26} +(-34.5327 + 34.5327i) q^{27} +(9.07903 - 10.6570i) q^{28} -29.0733i q^{29} +(35.8367 - 9.09570i) q^{30} +(-11.9038 + 20.6179i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-15.0729 + 56.2529i) q^{33} +12.5233i q^{34} +(-2.32736 - 34.9225i) q^{35} +36.6800 q^{36} +(-14.9820 - 4.01442i) q^{37} +(9.13690 - 2.44823i) q^{38} +(-61.6321 - 35.5833i) q^{39} +(-12.1528 - 7.23258i) q^{40} -9.18256 q^{41} +(9.36960 - 50.9071i) q^{42} +(55.1244 + 55.1244i) q^{43} +(19.2914 - 11.1379i) q^{44} +(65.6943 - 63.9776i) q^{45} +(-20.1477 + 34.8968i) q^{46} +(8.55361 + 2.29193i) q^{47} +(-14.7892 - 14.7892i) q^{48} +(-45.7890 - 17.4462i) q^{49} +(-34.3809 + 8.24334i) q^{50} +(23.1513 + 40.0992i) q^{51} +(7.04537 + 26.2937i) q^{52} +(13.8047 - 3.69897i) q^{53} +(59.8123 - 34.5327i) q^{54} +(15.1243 - 53.5963i) q^{55} +(-16.3029 + 11.2346i) q^{56} +(24.7300 - 24.7300i) q^{57} +(-10.6416 + 39.7149i) q^{58} +(67.7986 + 39.1435i) q^{59} +(-52.2831 - 0.692181i) q^{60} +(-10.7196 - 18.5670i) q^{61} +(23.8075 - 23.8075i) q^{62} +(-43.0045 - 120.963i) q^{63} +8.00000i q^{64} +(58.4800 + 34.8037i) q^{65} +(41.1800 - 71.3259i) q^{66} +(13.7678 + 51.3823i) q^{67} +(4.58386 - 17.1072i) q^{68} +148.984i q^{69} +(-9.60330 + 48.5569i) q^{70} -101.186 q^{71} +(-50.1058 - 13.4258i) q^{72} +(-101.181 + 27.1115i) q^{73} +(18.9964 + 10.9676i) q^{74} +(-94.8470 + 89.9530i) q^{75} -13.3774 q^{76} +(-59.3481 - 50.5605i) q^{77} +(71.1666 + 71.1666i) q^{78} +(-11.7992 + 6.81228i) q^{79} +(13.9537 + 14.3281i) q^{80} +(45.1475 - 78.1978i) q^{81} +(12.5436 + 3.36105i) q^{82} +(28.4835 + 28.4835i) q^{83} +(-31.4324 + 66.1108i) q^{84} +(-21.6288 - 38.6345i) q^{85} +(-55.1244 - 95.4783i) q^{86} +(39.3451 + 146.838i) q^{87} +(-30.4292 + 8.15349i) q^{88} +(-6.56157 + 3.78833i) q^{89} +(-113.158 + 63.3492i) q^{90} +(78.4508 - 54.0615i) q^{91} +(40.2954 - 40.2954i) q^{92} +(32.2188 - 120.242i) q^{93} +(-10.8455 - 6.26167i) q^{94} +(-23.9590 + 23.3329i) q^{95} +(14.7892 + 25.6156i) q^{96} +(74.4232 - 74.4232i) q^{97} +(56.1632 + 40.5919i) q^{98} -204.268i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8	$ 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8} - 6 q^{10} + 40 q^{11} + 4 q^{12} + 16 q^{13} - 20 q^{15} + 32 q^{16} + 46 q^{17} - 52 q^{18} + 16 q^{20} - 20 q^{21} - 80 q^{22} + 54 q^{23} - 26 q^{25} - 16 q^{26} - 52 q^{27} - 36 q^{28} - 22 q^{30} - 208 q^{31} + 32 q^{32} - 22 q^{33} + 50 q^{35} + 208 q^{36} - 38 q^{37} + 36 q^{38} - 4 q^{40} - 72 q^{41} + 184 q^{42} + 144 q^{43} + 254 q^{45} + 108 q^{46} + 46 q^{47} + 16 q^{48} - 60 q^{50} - 136 q^{51} - 16 q^{52} + 30 q^{53} - 192 q^{55} - 48 q^{56} - 492 q^{57} + 132 q^{58} - 64 q^{60} - 120 q^{61} + 416 q^{62} - 292 q^{63} + 230 q^{65} - 44 q^{66} - 74 q^{67} - 92 q^{68} - 162 q^{70} + 16 q^{71} - 104 q^{72} - 54 q^{73} + 300 q^{75} - 144 q^{76} + 570 q^{77} + 168 q^{78} + 8 q^{80} + 244 q^{81} + 36 q^{82} + 64 q^{83} + 544 q^{85} - 144 q^{86} - 236 q^{87} - 80 q^{88} - 1048 q^{90} + 336 q^{91} - 216 q^{92} + 142 q^{93} - 396 q^{95} - 16 q^{96} + 136 q^{97} - 268 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8 - 6 * q^10 + 40 * q^11 + 4 * q^12 + 16 * q^13 - 20 * q^15 + 32 * q^16 + 46 * q^17 - 52 * q^18 + 16 * q^20 - 20 * q^21 - 80 * q^22 + 54 * q^23 - 26 * q^25 - 16 * q^26 - 52 * q^27 - 36 * q^28 - 22 * q^30 - 208 * q^31 + 32 * q^32 - 22 * q^33 + 50 * q^35 + 208 * q^36 - 38 * q^37 + 36 * q^38 - 4 * q^40 - 72 * q^41 + 184 * q^42 + 144 * q^43 + 254 * q^45 + 108 * q^46 + 46 * q^47 + 16 * q^48 - 60 * q^50 - 136 * q^51 - 16 * q^52 + 30 * q^53 - 192 * q^55 - 48 * q^56 - 492 * q^57 + 132 * q^58 - 64 * q^60 - 120 * q^61 + 416 * q^62 - 292 * q^63 + 230 * q^65 - 44 * q^66 - 74 * q^67 - 92 * q^68 - 162 * q^70 + 16 * q^71 - 104 * q^72 - 54 * q^73 + 300 * q^75 - 144 * q^76 + 570 * q^77 + 168 * q^78 + 8 * q^80 + 244 * q^81 + 36 * q^82 + 64 * q^83 + 544 * q^85 - 144 * q^86 - 236 * q^87 - 80 * q^88 - 1048 * q^90 + 336 * q^91 - 216 * q^92 + 142 * q^93 - 396 * q^95 - 16 * q^96 + 136 * q^97 - 268 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	−5.05060	+	1.35330i	−1.68353	+	0.451101i	−0.968708	−	0.248202i	$-0.920160\pi$
$3$	−5.05060	+	1.35330i	−1.68353	+	0.451101i	−0.714825	+	0.699304i	$0.753494\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	4.84634	−	1.23005i	0.969267	−	0.246009i
$5$	4.84634	−	1.23005i	0.969267	−	0.246009i
$6$	7.39459			1.23243
$7$	1.26709	−	6.88437i	0.181013	−	0.983481i
$7$	1.26709	−	6.88437i	0.181013	−	0.983481i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	15.8829	−	9.16999i	1.76477	−	1.01889i
$10$	−7.07045	−	0.0936064i	−0.707045	−	0.00936064i
$11$	5.56894	−	9.64568i	0.506267	−	0.876880i	−0.493707	−	0.869629i	$-0.664358\pi$
$11$	5.56894	−	9.64568i	0.506267	−	0.876880i	0.999974	−	0.00725183i	$-0.00230835\pi$
$12$	−10.1012	−	2.70661i	−0.841767	−	0.225551i
$13$	9.62415	+	9.62415i	0.740319	+	0.740319i	0.972639	−	0.232320i	$-0.0746317\pi$
$13$	9.62415	+	9.62415i	0.740319	+	0.740319i	−0.232320	+	0.972639i	$0.574632\pi$
$14$	−4.25073	+	8.94043i	−0.303623	+	0.638602i
$15$	−22.8123	+	12.7710i	−1.52082	+	0.851403i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−2.29193	−	8.55361i	−0.134820	−	0.503153i	−0.999999	−	0.00169021i	$-0.999462\pi$
$17$	−2.29193	−	8.55361i	−0.134820	−	0.503153i	0.865179	−	0.501463i	$-0.167205\pi$
$18$	−25.0529	+	6.71290i	−1.39183	+	0.372939i
$19$	−5.79257	+	3.34434i	−0.304872	+	0.176018i	−0.644629	−	0.764495i	$-0.722988\pi$
$19$	−5.79257	+	3.34434i	−0.304872	+	0.176018i	0.339758	+	0.940513i	$0.389655\pi$
$20$	9.62415	+	2.71583i	0.481207	+	0.135792i
$21$	2.91708	+	36.4849i	0.138909	+	1.73738i
$22$	−11.1379	+	11.1379i	−0.506267	+	0.506267i
$23$	7.37457	−	27.5223i	0.320633	−	1.19662i	−0.597996	−	0.801499i	$-0.704036\pi$
$23$	7.37457	−	27.5223i	0.320633	−	1.19662i	0.918629	−	0.395121i	$-0.129297\pi$
$24$	12.8078	+	7.39459i	0.533659	+	0.308108i
$25$	21.9740	−	11.9224i	0.878959	−	0.476898i
$26$	−9.62415	−	16.6695i	−0.370160	−	0.641135i
$27$	−34.5327	+	34.5327i	−1.27899	+	1.27899i
$28$	9.07903	−	10.6570i	0.324251	−	0.380607i
$29$		−	29.0733i		−	1.00253i	−0.865294	−	0.501265i	$-0.832868\pi$
$29$		−	29.0733i		−	1.00253i	0.865294	−	0.501265i	$-0.167132\pi$
$30$	35.8367	−	9.09570i	1.19456	−	0.303190i
$31$	−11.9038	+	20.6179i	−0.383992	+	0.665094i	−0.991629	−	0.129121i	$-0.958784\pi$
$31$	−11.9038	+	20.6179i	−0.383992	+	0.665094i	0.607637	+	0.794215i	$0.292118\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	−15.0729	+	56.2529i	−0.456756	+	1.70463i
$34$			12.5233i			0.368334i
$35$	−2.32736	−	34.9225i	−0.0664960	−	0.997787i
$36$	36.6800			1.01889
$37$	−14.9820	−	4.01442i	−0.404919	−	0.108498i	0.0506104	−	0.998718i	$-0.483883\pi$
$37$	−14.9820	−	4.01442i	−0.404919	−	0.108498i	−0.455529	+	0.890221i	$0.650550\pi$
$38$	9.13690	−	2.44823i	0.240445	−	0.0644270i
$39$	−61.6321	−	35.5833i	−1.58031	−	0.912393i
$40$	−12.1528	−	7.23258i	−0.303819	−	0.180814i
$41$	−9.18256			−0.223965			−0.111982	−	0.993710i	$-0.535720\pi$
$41$	−9.18256			−0.223965			−0.111982	+	0.993710i	$0.535720\pi$
$42$	9.36960	−	50.9071i	0.223086	−	1.21207i
$43$	55.1244	+	55.1244i	1.28196	+	1.28196i	0.939549	+	0.342414i	$0.111244\pi$
$43$	55.1244	+	55.1244i	1.28196	+	1.28196i	0.342414	+	0.939549i	$0.388756\pi$
$44$	19.2914	−	11.1379i	0.438440	−	0.253134i
$45$	65.6943	−	63.9776i	1.45987	−	1.42172i
$46$	−20.1477	+	34.8968i	−0.437993	+	0.758627i
$47$	8.55361	+	2.29193i	0.181992	+	0.0487645i	0.348664	−	0.937248i	$-0.386636\pi$
$47$	8.55361	+	2.29193i	0.181992	+	0.0487645i	−0.166672	+	0.986012i	$0.553302\pi$
$48$	−14.7892	−	14.7892i	−0.308108	−	0.308108i
$49$	−45.7890	−	17.4462i	−0.934469	−	0.356045i
$50$	−34.3809	+	8.24334i	−0.687618	+	0.164867i
$51$	23.1513	+	40.0992i	0.453946	+	0.786258i
$52$	7.04537	+	26.2937i	0.135488	+	0.505647i
$53$	13.8047	−	3.69897i	0.260467	−	0.0697918i	−0.126223	−	0.992002i	$-0.540285\pi$
$53$	13.8047	−	3.69897i	0.260467	−	0.0697918i	0.386689	+	0.922210i	$0.373619\pi$
$54$	59.8123	−	34.5327i	1.10764	−	0.639494i
$55$	15.1243	−	53.5963i	0.274987	−	0.974478i
$56$	−16.3029	+	11.2346i	−0.291123	+	0.200617i
$57$	24.7300	−	24.7300i	0.433860	−	0.433860i
$58$	−10.6416	+	39.7149i	−0.183476	+	0.684740i
$59$	67.7986	+	39.1435i	1.14913	+	0.663450i	0.948675	−	0.316253i	$-0.102425\pi$
$59$	67.7986	+	39.1435i	1.14913	+	0.663450i	0.200454	+	0.979703i	$0.435758\pi$
$60$	−52.2831	−	0.692181i	−0.871384	−	0.0115363i
$61$	−10.7196	−	18.5670i	−0.175732	−	0.304376i	0.764682	−	0.644407i	$-0.222896\pi$
$61$	−10.7196	−	18.5670i	−0.175732	−	0.304376i	−0.940414	+	0.340031i	$0.889562\pi$
$62$	23.8075	−	23.8075i	0.383992	−	0.383992i
$63$	−43.0045	−	120.963i	−0.682612	−	1.92004i
$64$			8.00000i			0.125000i
$65$	58.4800	+	34.8037i	0.899693	+	0.535442i
$66$	41.1800	−	71.3259i	0.623940	−	1.08070i
$67$	13.7678	+	51.3823i	0.205490	+	0.766900i	0.989300	+	0.145898i	$0.0466072\pi$
$67$	13.7678	+	51.3823i	0.205490	+	0.766900i	−0.783809	+	0.621001i	$0.786726\pi$
$68$	4.58386	−	17.1072i	0.0674098	−	0.251577i
$69$			148.984i			2.15919i
$70$	−9.60330	+	48.5569i	−0.137190	+	0.693671i
$71$	−101.186			−1.42516			−0.712579	−	0.701591i	$-0.752473\pi$
$71$	−101.186			−1.42516			−0.712579	+	0.701591i	$0.752473\pi$
$72$	−50.1058	−	13.4258i	−0.695913	−	0.186469i
$73$	−101.181	+	27.1115i	−1.38605	+	0.371390i	−0.873314	−	0.487157i	$-0.838034\pi$
$73$	−101.181	+	27.1115i	−1.38605	+	0.371390i	−0.512734	+	0.858548i	$0.671367\pi$
$74$	18.9964	+	10.9676i	0.256708	+	0.148211i
$75$	−94.8470	+	89.9530i	−1.26463	+	1.19937i
$76$	−13.3774			−0.176018
$77$	−59.3481	−	50.5605i	−0.770754	−	0.656630i
$78$	71.1666	+	71.1666i	0.912393	+	0.912393i
$79$	−11.7992	+	6.81228i	−0.149357	+	0.0862314i	−0.572816	−	0.819684i	$-0.694149\pi$
$79$	−11.7992	+	6.81228i	−0.149357	+	0.0862314i	0.423459	+	0.905915i	$0.360816\pi$
$80$	13.9537	+	14.3281i	0.174421	+	0.179101i
$81$	45.1475	−	78.1978i	0.557377	−	0.965406i
$82$	12.5436	+	3.36105i	0.152971	+	0.0409884i
$83$	28.4835	+	28.4835i	0.343175	+	0.343175i	0.857560	−	0.514385i	$-0.171980\pi$
$83$	28.4835	+	28.4835i	0.343175	+	0.343175i	−0.514385	+	0.857560i	$0.671980\pi$
$84$	−31.4324	+	66.1108i	−0.374195	+	0.787034i
$85$	−21.6288	−	38.6345i	−0.254457	−	0.454523i
$86$	−55.1244	−	95.4783i	−0.640981	−	1.11021i
$87$	39.3451	+	146.838i	0.452242	+	1.68779i
$88$	−30.4292	+	8.15349i	−0.345787	+	0.0926533i
$89$	−6.56157	+	3.78833i	−0.0737256	+	0.0425655i	−0.536410	−	0.843958i	$-0.680220\pi$
$89$	−6.56157	+	3.78833i	−0.0737256	+	0.0425655i	0.462684	+	0.886523i	$0.346886\pi$
$90$	−113.158	+	63.3492i	−1.25731	+	0.703880i
$91$	78.4508	−	54.0615i	0.862097	−	0.594083i
$92$	40.2954	−	40.2954i	0.437993	−	0.437993i
$93$	32.2188	−	120.242i	0.346439	−	1.29293i
$94$	−10.8455	−	6.26167i	−0.115378	−	0.0666136i
$95$	−23.9590	+	23.3329i	−0.252200	+	0.245610i
$96$	14.7892	+	25.6156i	0.154054	+	0.266829i
$97$	74.4232	−	74.4232i	0.767249	−	0.767249i	−0.210372	−	0.977621i	$-0.567468\pi$
$97$	74.4232	−	74.4232i	0.767249	−	0.767249i	0.977621	+	0.210372i	$0.0674676\pi$
$98$	56.1632	+	40.5919i	0.573093	+	0.414203i
$99$		−	204.268i		−	2.06332i
$100$	49.9825	+	1.32368i	0.499825	+	0.0132368i
$101$	−62.1520	+	107.650i	−0.615366	+	1.06585i	0.374954	+	0.927044i	$0.377659\pi$
$101$	−62.1520	+	107.650i	−0.615366	+	1.06585i	−0.990320	+	0.138802i	$0.955675\pi$
$102$	−16.9479	−	63.2504i	−0.166156	−	0.620102i
$103$	26.8210	−	100.098i	0.260398	−	0.971820i	−0.704609	−	0.709596i	$-0.748877\pi$
$103$	26.8210	−	100.098i	0.260398	−	0.971820i	0.965007	−	0.262224i	$-0.0844560\pi$
$104$		−	38.4966i		−	0.370160i
$105$	59.0154	+	173.230i	0.562051	+	1.64981i
$106$	−20.2115			−0.190675
$107$	−86.7110	−	23.2341i	−0.810383	−	0.217142i	−0.170245	−	0.985402i	$-0.554456\pi$
$107$	−86.7110	−	23.2341i	−0.810383	−	0.217142i	−0.640138	+	0.768260i	$0.721123\pi$
$108$	−94.3450	+	25.2797i	−0.873565	+	0.234071i
$109$	145.926	+	84.2503i	1.33877	+	0.772938i	0.986625	−	0.163008i	$-0.0521196\pi$
$109$	145.926	+	84.2503i	1.33877	+	0.772938i	0.352143	+	0.935946i	$0.385453\pi$
$110$	−40.2778	+	67.6780i	−0.366162	+	0.615255i
$111$	81.1008			0.730638
$112$	26.3823	−	9.37941i	0.235556	−	0.0837447i
$113$	22.2552	+	22.2552i	0.196949	+	0.196949i	0.798691	−	0.601742i	$-0.205526\pi$
$113$	22.2552	+	22.2552i	0.196949	+	0.196949i	−0.601742	+	0.798691i	$0.705526\pi$
$114$	−42.8336	+	24.7300i	−0.375734	+	0.216930i
$115$	1.88595	−	142.453i	0.0163996	−	1.23872i
$116$	29.0733	−	50.3565i	0.250632	−	0.434108i
$117$	241.113	+	64.6059i	2.06079	+	0.552188i
$118$	−78.2871	−	78.2871i	−0.663450	−	0.663450i
$119$	−61.7902	+	4.94032i	−0.519246	+	0.0415153i
$120$	71.1666	+	20.0825i	0.593055	+	0.167354i
$121$	−1.52615	−	2.64336i	−0.0126128	−	0.0218460i
$122$	7.84732	+	29.2866i	0.0643223	+	0.240054i
$123$	46.3775	−	12.4268i	0.377052	−	0.101031i
$124$	−41.2358	+	23.8075i	−0.332547	+	0.191996i
$125$	91.8281	−	84.8092i	0.734625	−	0.678474i
$126$	14.4698	+	180.979i	0.114840	+	1.43634i
$127$	−80.5418	+	80.5418i	−0.634187	+	0.634187i	−0.949115	−	0.314928i	$-0.898020\pi$
$127$	−80.5418	+	80.5418i	−0.634187	+	0.634187i	0.314928	+	0.949115i	$0.398020\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$	−353.011	−	203.811i	−2.73652	−	1.57993i
$130$	−67.1462	−	68.9479i	−0.516509	−	0.530369i
$131$	−38.6646	−	66.9690i	−0.295149	−	0.511214i	0.679870	−	0.733332i	$-0.262036\pi$
$131$	−38.6646	−	66.9690i	−0.295149	−	0.511214i	−0.975020	+	0.222119i	$0.928703\pi$
$132$	−82.3600	+	82.3600i	−0.623940	+	0.623940i
$133$	15.6840	+	44.1157i	0.117925	+	0.331697i
$134$		−	75.2289i		−	0.561409i
$135$	−124.880	+	209.834i	−0.925038	+	1.55432i
$136$	−12.5233	+	21.6911i	−0.0920834	+	0.159493i
$137$	16.6880	+	62.2804i	0.121810	+	0.454602i	0.999706	−	0.0242501i	$-0.00771980\pi$
$137$	16.6880	+	62.2804i	0.121810	+	0.454602i	−0.877896	+	0.478852i	$0.841053\pi$
$138$	54.5319	−	203.516i	0.395159	−	1.47475i
$139$			51.4750i			0.370324i	0.982708	+	0.185162i	$0.0592810\pi$
$139$			51.4750i			0.370324i	−0.982708	+	0.185162i	$0.940719\pi$
$140$	30.8914	−	62.8150i	0.220653	−	0.448678i
$141$	−46.3025			−0.328387
$142$	138.223	+	37.0368i	0.973402	+	0.260822i
$143$	146.428	−	39.2352i	1.02397	−	0.274372i
$144$	63.5316	+	36.6800i	0.441191	+	0.254722i
$145$	−35.7616	−	140.899i	−0.246632	−	0.971719i
$146$	148.140			1.01466
$147$	254.872	+	26.1473i	1.73382	+	0.177873i
$148$	−21.9352	−	21.9352i	−0.148211	−	0.148211i
$149$	47.3177	−	27.3189i	0.317568	−	0.183348i	−0.332740	−	0.943019i	$-0.607973\pi$
$149$	47.3177	−	27.3189i	0.317568	−	0.183348i	0.650308	+	0.759670i	$0.274640\pi$
$150$	162.488	−	88.1616i	1.08326	−	0.587744i
$151$	62.2354	−	107.795i	0.412155	−	0.713874i	−0.582970	−	0.812494i	$-0.698109\pi$
$151$	62.2354	−	107.795i	0.412155	−	0.713874i	0.995125	+	0.0986200i	$0.0314428\pi$
$152$	18.2738	+	4.89645i	0.120222	+	0.0322135i
$153$	−114.839	−	114.839i	−0.750582	−	0.750582i
$154$	62.5645	+	90.7899i	0.406263	+	0.589545i
$155$	−32.3286	+	114.564i	−0.208572	+	0.739120i
$156$	−71.1666	−	123.264i	−0.456196	−	0.790155i
$157$	−20.6950	−	77.2347i	−0.131815	−	0.491941i	0.868176	−	0.496257i	$-0.165293\pi$
$157$	−20.6950	−	77.2347i	−0.131815	−	0.491941i	−0.999991	+	0.00431635i	$0.998626\pi$
$158$	18.6115	−	4.98693i	0.117794	−	0.0315629i
$159$	−64.7163	+	37.3640i	−0.407021	+	0.234994i
$160$	−13.8166	−	24.6800i	−0.0863540	−	0.154250i
$161$	−180.129	−	85.6424i	−1.11881	−	0.531940i
$162$	−90.2951	+	90.2951i	−0.557377	+	0.557377i
$163$	−48.8390	+	182.269i	−0.299626	+	1.11822i	0.637848	+	0.770162i	$0.279825\pi$
$163$	−48.8390	+	182.269i	−0.299626	+	1.11822i	−0.937474	+	0.348056i	$0.886842\pi$
$164$	−15.9047	−	9.18256i	−0.0969797	−	0.0559912i
$165$	−3.85471	+	291.161i	−0.0233619	+	1.76461i
$166$	−28.4835	−	49.3349i	−0.171587	−	0.297198i
$167$	116.548	−	116.548i	0.697892	−	0.697892i	−0.266064	−	0.963955i	$-0.585723\pi$
$167$	116.548	−	116.548i	0.697892	−	0.697892i	0.963955	+	0.266064i	$0.0857231\pi$
$168$	67.1357	−	78.8040i	0.399617	−	0.469072i
$169$			16.2485i			0.0961450i
$170$	15.4043	+	60.6924i	0.0906136	+	0.357014i
$171$	−61.3351	+	106.236i	−0.358685	+	0.621260i
$172$	40.3539	+	150.603i	0.234615	+	0.875597i
$173$	−82.3855	+	307.467i	−0.476217	+	1.77727i	0.140500	+	0.990081i	$0.455129\pi$
$173$	−82.3855	+	307.467i	−0.476217	+	1.77727i	−0.616717	+	0.787185i	$0.711538\pi$
$174$		−	214.985i		−	1.23555i
$175$	−54.2355	−	166.384i	−0.309917	−	0.950763i
$176$	44.5515			0.253134
$177$	−395.397	−	105.946i	−2.23388	−	0.598566i
$178$	10.3499	−	2.77325i	0.0581455	−	0.0155800i
$179$	57.5525	+	33.2280i	0.321522	+	0.185631i	0.652071	−	0.758158i	$-0.273900\pi$
$179$	57.5525	+	33.2280i	0.321522	+	0.185631i	−0.330549	+	0.943789i	$0.607234\pi$
$180$	177.763	−	45.1181i	0.987575	−	0.250656i
$181$	−71.5932			−0.395543			−0.197771	−	0.980248i	$-0.563370\pi$
$181$	−71.5932			−0.395543			−0.197771	+	0.980248i	$0.563370\pi$
$182$	−126.954	+	45.1344i	−0.697548	+	0.247991i
$183$	79.2673	+	79.2673i	0.433155	+	0.433155i
$184$	−69.7937	+	40.2954i	−0.379313	+	0.218997i
$185$	−77.5457	−	1.02664i	−0.419166	−	0.00554938i
$186$	−88.0234	+	152.461i	−0.473244	+	0.819683i
$187$	−95.2690	−	25.5273i	−0.509460	−	0.136509i
$188$	12.5233	+	12.5233i	0.0666136	+	0.0666136i
$189$	193.980	+	281.491i	1.02635	+	1.48937i
$190$	41.2691	−	23.1038i	0.217206	−	0.121599i
$191$	166.665	+	288.672i	0.872590	+	1.51137i	0.859308	+	0.511458i	$0.170894\pi$
$191$	166.665	+	288.672i	0.872590	+	1.51137i	0.0132816	+	0.999912i	$0.495772\pi$
$192$	−10.8264	−	40.4048i	−0.0563877	−	0.210442i
$193$	−95.9658	+	25.7140i	−0.497232	+	0.133233i	−0.498715	−	0.866766i	$-0.666195\pi$
$193$	−95.9658	+	25.7140i	−0.497232	+	0.133233i	0.00148294	+	0.999999i	$0.499528\pi$
$194$	−128.905	+	74.4232i	−0.664457	+	0.383625i
$195$	−342.459	−	96.6383i	−1.75620	−	0.495581i
$196$	−61.8626	−	76.0067i	−0.315626	−	0.387789i
$197$	−131.527	+	131.527i	−0.667651	+	0.667651i	−0.957172	−	0.289521i	$-0.906504\pi$
$197$	−131.527	+	131.527i	−0.667651	+	0.667651i	0.289521	+	0.957172i	$0.406504\pi$
$198$	−74.7674	+	279.036i	−0.377613	+	1.40927i
$199$	211.873	+	122.325i	1.06469	+	0.614697i	0.926725	−	0.375741i	$-0.122612\pi$
$199$	211.873	+	122.325i	1.06469	+	0.614697i	0.137961	+	0.990438i	$0.455945\pi$
$200$	−67.7928	−	20.1030i	−0.338964	−	0.100515i
$201$	−139.072	−	240.879i	−0.691899	−	1.19840i
$202$	124.304	−	124.304i	0.615366	−	0.615366i
$203$	−200.152	−	36.8385i	−0.985968	−	0.181470i
$204$			92.6050i			0.453946i
$205$	−44.5018	+	11.2950i	−0.217082	+	0.0550975i
$206$	−73.2765	+	126.919i	−0.355711	+	0.616109i
$207$	−135.249	−	504.758i	−0.653379	−	2.43844i
$208$	−14.0907	+	52.5873i	−0.0677439	+	0.252824i
$209$			74.4977i			0.356448i
$210$	−17.2099	−	258.238i	−0.0819518	−	1.22970i
$211$	203.685			0.965329			0.482665	−	0.875805i	$-0.339669\pi$
$211$	203.685			0.965329			0.482665	+	0.875805i	$0.339669\pi$
$212$	27.6095	+	7.39793i	0.130233	+	0.0348959i
$213$	511.051	−	136.936i	2.39930	−	0.642891i
$214$	109.945	+	63.4769i	0.513762	+	0.296621i
$215$	334.957	+	199.346i	1.55794	+	0.927190i
$216$	138.131			0.639494
$217$	126.858	+	108.075i	0.584600	+	0.498039i
$218$	−168.501	−	168.501i	−0.772938	−	0.772938i
$219$	474.337	−	273.859i	2.16592	−	1.25050i
$220$	79.7924	−	77.7072i	0.362693	−	0.353215i
$221$	60.2633	−	104.379i	0.272685	−	0.472303i
$222$	−110.786	−	29.6850i	−0.499035	−	0.133716i
$223$	−194.661	−	194.661i	−0.872921	−	0.872921i	0.119869	−	0.992790i	$-0.461753\pi$
$223$	−194.661	−	194.661i	−0.872921	−	0.872921i	−0.992790	+	0.119869i	$0.961753\pi$
$224$	−39.4720	+	3.15591i	−0.176214	+	0.0140889i
$225$	239.681	−	390.864i	1.06525	−	1.73717i
$226$	−22.2552	−	38.5472i	−0.0984744	−	0.170563i
$227$	−59.0356	−	220.324i	−0.260069	−	0.970589i	−0.965200	−	0.261513i	$-0.915779\pi$
$227$	−59.0356	−	220.324i	−0.260069	−	0.970589i	0.705132	−	0.709077i	$-0.250888\pi$
$228$	67.5637	−	18.1036i	0.296332	−	0.0794019i
$229$	161.759	−	93.3917i	0.706372	−	0.407824i	−0.103344	−	0.994646i	$-0.532954\pi$
$229$	161.759	−	93.3917i	0.706372	−	0.407824i	0.809716	+	0.586821i	$0.199621\pi$
$230$	−54.7178	+	193.904i	−0.237903	+	0.843063i
$231$	368.167	+	175.045i	1.59380	+	0.757771i
$232$	−58.1467	+	58.1467i	−0.250632	+	0.250632i
$233$	−87.0627	+	324.922i	−0.373660	+	1.39452i	0.481634	+	0.876373i	$0.340044\pi$
$233$	−87.0627	+	324.922i	−0.373660	+	1.39452i	−0.855293	+	0.518144i	$0.826623\pi$
$234$	−305.719	−	176.507i	−1.30649	−	0.754302i
$235$	44.2728	+	0.586133i	0.188395	+	0.00249418i
$236$	78.2871	+	135.597i	0.331725	+	0.574564i
$237$	50.3740	−	50.3740i	0.212549	−	0.212549i
$238$	86.2153	+	15.8682i	0.362249	+	0.0666731i
$239$			83.6738i			0.350099i	0.984560	+	0.175050i	$0.0560086\pi$
$239$			83.6738i			0.350099i	−0.984560	+	0.175050i	$0.943991\pi$
$240$	−89.8647	−	53.4820i	−0.374436	−	0.222841i
$241$	−57.1739	+	99.0280i	−0.237236	+	0.410905i	−0.959920	−	0.280274i	$-0.909575\pi$
$241$	−57.1739	+	99.0280i	−0.237236	+	0.410905i	0.722684	+	0.691178i	$0.242908\pi$
$242$	1.11722	+	4.16951i	0.00461660	+	0.0172294i
$243$	−8.43820	+	31.4918i	−0.0347251	+	0.129596i
$244$		−	42.8786i		−	0.175732i
$245$	−243.368	−	28.2275i	−0.993341	−	0.115214i
$246$	−67.9013			−0.276022
$247$	−87.9349	−	23.5621i	−0.356012	−	0.0953931i
$248$	65.0433	−	17.4283i	0.262272	−	0.0702754i
$249$	−182.406	−	105.312i	−0.732553	−	0.422940i
$250$	−156.482	+	82.2402i	−0.625927	+	0.328961i
$251$	−2.86375			−0.0114094			−0.00570468	−	0.999984i	$-0.501816\pi$
$251$	−2.86375			−0.0114094			−0.00570468	+	0.999984i	$0.501816\pi$
$252$	46.4768	−	252.518i	0.184432	−	1.00206i
$253$	−224.403	−	224.403i	−0.886967	−	0.886967i
$254$	139.502	−	80.5418i	0.549222	−	0.317094i
$255$	161.523	+	165.857i	0.633422	+	0.650419i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−82.9396	−	22.2236i	−0.322722	−	0.0864731i	0.0938211	−	0.995589i	$-0.470092\pi$
$257$	−82.9396	−	22.2236i	−0.322722	−	0.0864731i	−0.416543	+	0.909116i	$0.636759\pi$
$258$	407.622	+	407.622i	1.57993	+	1.57993i
$259$	−46.6202	+	98.0550i	−0.180001	+	0.378591i
$260$	66.4867	+	118.762i	0.255718	+	0.456776i
$261$	−266.602	−	461.769i	−1.02146	−	1.76923i
$262$	28.3044	+	105.634i	0.108032	+	0.403182i
$263$	244.691	−	65.5647i	0.930384	−	0.249296i	0.238365	−	0.971176i	$-0.423388\pi$
$263$	244.691	−	65.5647i	0.930384	−	0.249296i	0.692018	+	0.721880i	$0.256722\pi$
$264$	142.652	−	82.3600i	0.540348	−	0.311970i
$265$	62.3525	−	34.9069i	0.235292	−	0.131724i
$266$	−5.27722	−	66.0039i	−0.0198392	−	0.248135i
$267$	28.0131	−	28.0131i	0.104918	−	0.104918i
$268$	−27.5357	+	102.765i	−0.102745	+	0.383450i
$269$	−435.001	−	251.148i	−1.61710	−	0.933636i	−0.987664	−	0.156587i	$-0.949951\pi$
$269$	−435.001	−	251.148i	−1.61710	−	0.933636i	−0.629441	−	0.777049i	$-0.716716\pi$
$270$	247.394	−	240.929i	0.916274	−	0.892330i
$271$	99.2563	+	171.917i	0.366259	+	0.634380i	0.988977	−	0.148066i	$-0.0473049\pi$
$271$	99.2563	+	171.917i	0.366259	+	0.634380i	−0.622718	+	0.782446i	$0.713972\pi$
$272$	25.0467	−	25.0467i	0.0920834	−	0.0920834i
$273$	−323.062	+	379.211i	−1.18338	+	1.38905i
$274$		−	91.1849i		−	0.332792i
$275$	7.37148	−	278.349i	0.0268054	−	1.01218i
$276$	−148.984	+	258.048i	−0.539797	+	0.934956i
$277$	98.4162	+	367.294i	0.355293	+	1.32597i	0.880115	+	0.474760i	$0.157465\pi$
$277$	98.4162	+	367.294i	0.355293	+	1.32597i	−0.524822	+	0.851212i	$0.675868\pi$
$278$	18.8412	−	70.3162i	0.0677740	−	0.252936i
$279$			436.629i			1.56498i
$280$	−65.1903	+	74.4998i	−0.232823	+	0.266071i
$281$	135.599			0.482558			0.241279	−	0.970456i	$-0.422433\pi$
$281$	135.599			0.482558			0.241279	+	0.970456i	$0.422433\pi$
$282$	63.2504	+	16.9479i	0.224292	+	0.0600989i
$283$	−340.827	+	91.3244i	−1.20434	+	0.322701i	−0.804538	−	0.593902i	$-0.797587\pi$
$283$	−340.827	+	91.3244i	−1.20434	+	0.322701i	−0.399799	+	0.916603i	$0.630920\pi$
$284$	−175.260	−	101.186i	−0.617112	−	0.356290i
$285$	89.4309	−	150.269i	0.313793	−	0.527260i
$286$	−214.385			−0.749599
$287$	−11.6351	+	63.2161i	−0.0405405	+	0.220265i
$288$	−73.3599	−	73.3599i	−0.254722	−	0.254722i
$289$	182.370	−	105.291i	0.631039	−	0.364330i
$290$	−2.72145	+	205.562i	−0.00938431	+	0.708833i
$291$	−275.164	+	476.599i	−0.945582	+	1.63780i
$292$	−202.363	−	54.2230i	−0.693024	−	0.185695i
$293$	73.2341	+	73.2341i	0.249946	+	0.249946i	0.820948	−	0.571003i	$-0.193445\pi$
$293$	73.2341	+	73.2341i	0.249946	+	0.249946i	−0.571003	+	0.820948i	$0.693445\pi$
$294$	−338.591	−	129.007i	−1.15167	−	0.438801i
$295$	376.723	+	106.307i	1.27703	+	0.360364i
$296$	21.9352	+	37.9928i	0.0741053	+	0.128354i
$297$	140.781	+	525.402i	0.474010	+	1.76903i
$298$	−74.6366	+	19.9988i	−0.250458	+	0.0671101i
$299$	335.852	−	193.904i	1.12325	−	0.648510i
$300$	−254.233	+	60.9561i	−0.847443	+	0.203187i
$301$	449.344	−	309.649i	1.49284	−	1.02873i
$302$	−124.471	+	124.471i	−0.412155	+	0.412155i
$303$	168.221	−	627.810i	0.555185	−	2.07198i
$304$	−23.1703	−	13.3774i	−0.0762180	−	0.0440045i
$305$	−74.7892	−	76.7961i	−0.245211	−	0.251790i
$306$	114.839	+	198.907i	0.375291	+	0.650023i
$307$	−394.192	+	394.192i	−1.28401	+	1.28401i	−0.345652	+	0.938363i	$0.612342\pi$
$307$	−394.192	+	394.192i	−1.28401	+	1.28401i	−0.938363	+	0.345652i	$0.887658\pi$
$308$	−52.2333	−	146.922i	−0.169589	−	0.477018i
$309$			541.849i			1.75356i
$310$	86.0949	−	144.664i	0.277725	−	0.466657i
$311$	−117.796	+	204.029i	−0.378766	+	0.656041i	−0.990883	−	0.134726i	$-0.956985\pi$
$311$	−117.796	+	204.029i	−0.378766	+	0.656041i	0.612117	+	0.790767i	$0.290318\pi$
$312$	52.0976	+	194.431i	0.166979	+	0.623176i
$313$	94.8023	−	353.807i	0.302883	−	1.13037i	−0.631870	−	0.775075i	$-0.717712\pi$
$313$	94.8023	−	353.807i	0.302883	−	1.13037i	0.934752	−	0.355300i	$-0.115621\pi$
$314$			113.079i			0.360126i
$315$	−357.205	−	533.329i	−1.13398	−	1.69311i
$316$	−27.2491			−0.0862314
$317$	19.9576	+	5.34762i	0.0629577	+	0.0168695i	0.290160	−	0.956978i	$-0.406291\pi$
$317$	19.9576	+	5.34762i	0.0629577	+	0.0168695i	−0.227203	+	0.973847i	$0.572958\pi$
$318$	102.080	−	27.3523i	0.321007	−	0.0860136i
$319$	−280.432	−	161.908i	−0.879098	−	0.507548i
$320$	9.84038	+	38.7707i	0.0307512	+	0.121158i
$321$	469.385			1.46226
$322$	214.714	+	182.922i	0.666813	+	0.568079i
$323$	41.8823	+	41.8823i	0.129667	+	0.129667i
$324$	156.396	−	90.2951i	0.482703	−	0.278689i
$325$	326.224	+	96.7373i	1.00377	+	0.297653i
$326$	133.431	−	231.108i	0.409296	−	0.708922i
$327$	−851.029	−	228.032i	−2.60253	−	0.697347i
$328$	18.3651	+	18.3651i	0.0559912	+	0.0559912i
$329$	26.6167	−	55.9821i	0.0809017	−	0.170158i
$330$	111.838	−	396.323i	0.338903	−	1.20098i
$331$	−70.6868	−	122.433i	−0.213555	−	0.369889i	0.739269	−	0.673410i	$-0.235171\pi$
$331$	−70.6868	−	122.433i	−0.213555	−	0.369889i	−0.952825	+	0.303521i	$0.901838\pi$
$332$	20.8514	+	77.8184i	0.0628054	+	0.234393i
$333$	−274.770	+	73.6243i	−0.825134	+	0.221094i
$334$	−201.867	+	116.548i	−0.604392	+	0.348946i
$335$	129.926	+	232.081i	0.387839	+	0.692778i
$336$	−120.553	+	83.0749i	−0.358790	+	0.247247i
$337$	226.963	−	226.963i	0.673482	−	0.673482i	−0.285035	−	0.958517i	$-0.592005\pi$
$337$	226.963	−	226.963i	0.673482	−	0.673482i	0.958517	+	0.285035i	$0.0920052\pi$
$338$	5.94737	−	22.1959i	0.0175958	−	0.0656683i
$339$	−142.520	−	82.2841i	−0.420414	−	0.242726i
$340$	1.17227	−	88.5457i	0.00344784	−	0.260428i
$341$	132.583	+	229.640i	0.388805	+	0.673430i
$342$	122.670	−	122.670i	0.358685	−	0.358685i
$343$	−178.125	+	293.122i	−0.519314	+	0.854584i
$344$		−	220.498i		−	0.640981i
$345$	183.257	+	722.027i	0.531181	+	2.09283i
$346$	225.081	−	389.852i	0.650524	−	1.12674i
$347$	−149.887	−	559.385i	−0.431950	−	1.61206i	−0.748261	−	0.663404i	$-0.769111\pi$
$347$	−149.887	−	559.385i	−0.431950	−	1.61206i	0.316311	−	0.948656i	$-0.397556\pi$
$348$	−78.6902	+	293.676i	−0.226121	+	0.843896i
$349$		−	46.5465i		−	0.133371i	−0.997774	−	0.0666856i	$-0.978758\pi$
$349$		−	46.5465i		−	0.133371i	0.997774	−	0.0666856i	$-0.0212424\pi$
$350$	13.1865	+	247.136i	0.0376757	+	0.706102i
$351$	−664.695			−1.89372
$352$	−60.8585	−	16.3070i	−0.172893	−	0.0463267i
$353$	513.383	−	137.561i	1.45434	−	0.389690i	0.556811	−	0.830639i	$-0.312025\pi$
$353$	513.383	−	137.561i	1.45434	−	0.389690i	0.897532	+	0.440949i	$0.145358\pi$
$354$	501.343	+	289.450i	1.41622	+	0.817657i
$355$	−490.383	+	124.464i	−1.38136	+	0.350603i
$356$	−15.1533			−0.0425655
$357$	305.392	−	108.573i	0.855439	−	0.304125i
$358$	−66.4559	−	66.4559i	−0.185631	−	0.185631i
$359$	61.5713	−	35.5482i	0.171508	−	0.0990201i	−0.411789	−	0.911279i	$-0.635096\pi$
$359$	61.5713	−	35.5482i	0.171508	−	0.0990201i	0.583297	+	0.812259i	$0.301763\pi$
$360$	−259.344	−	3.43348i	−0.720399	−	0.00953744i
$361$	−158.131	+	273.891i	−0.438035	+	0.758700i
$362$	97.7982	+	26.2049i	0.270161	+	0.0723893i
$363$	11.2852	+	11.2852i	0.0310888	+	0.0310888i
$364$	189.942	−	15.1865i	0.521820	−	0.0417211i
$365$	−457.011	+	255.850i	−1.25209	+	0.700958i
$366$	−79.2673	−	137.295i	−0.216577	−	0.375123i
$367$	−36.5132	−	136.269i	−0.0994911	−	0.371306i	0.898171	−	0.439646i	$-0.144896\pi$
$367$	−36.5132	−	136.269i	−0.0994911	−	0.371306i	−0.997662	+	0.0683405i	$0.978230\pi$
$368$	110.089	−	29.4983i	0.299155	−	0.0801584i
$369$	−145.846	+	84.2040i	−0.395246	+	0.228195i
$370$	105.554	+	29.7861i	0.285280	+	0.0805030i
$371$	−7.97322	−	99.7237i	−0.0214912	−	0.268797i
$372$	176.047	−	176.047i	0.473244	−	0.473244i
$373$	−78.3283	+	292.325i	−0.209995	+	0.783714i	0.777873	+	0.628421i	$0.216299\pi$
$373$	−78.3283	+	292.325i	−0.209995	+	0.783714i	−0.987869	+	0.155292i	$0.950368\pi$
$374$	120.796	+	69.7417i	0.322985	+	0.186475i
$375$	−349.014	+	552.609i	−0.930704	+	1.47362i
$376$	−12.5233	−	21.6911i	−0.0333068	−	0.0576890i
$377$	279.806	−	279.806i	0.742192	−	0.742192i
$378$	−161.948	−	455.526i	−0.428434	−	1.20510i
$379$		−	329.976i		−	0.870649i	−0.900274	−	0.435325i	$-0.856634\pi$
$379$		−	329.976i		−	0.870649i	0.900274	−	0.435325i	$-0.143366\pi$
$380$	−64.8312	+	16.4548i	−0.170608	+	0.0433021i
$381$	297.787	−	515.782i	0.781593	−	1.35376i
$382$	−122.007	−	455.336i	−0.319390	−	1.19198i
$383$	46.0298	−	171.786i	0.120182	−	0.448527i	−0.879440	−	0.476010i	$-0.842083\pi$
$383$	46.0298	−	171.786i	0.120182	−	0.448527i	0.999622	+	0.0274833i	$0.00874931\pi$
$384$			59.1567i			0.154054i
$385$	−349.813	−	172.032i	−0.908604	−	0.446838i
$386$	140.504			0.363999
$387$	1381.03	+	370.045i	3.56854	+	0.956188i
$388$	203.328	−	54.4815i	0.524041	−	0.140416i
$389$	−207.304	−	119.687i	−0.532914	−	0.307678i	0.209288	−	0.977854i	$-0.432885\pi$
$389$	−207.304	−	119.687i	−0.532914	−	0.307678i	−0.742202	+	0.670176i	$0.766219\pi$
$390$	432.436	+	257.359i	1.10881	+	0.659895i
$391$	−252.317			−0.645311
$392$	56.6856	+	126.470i	0.144606	+	0.322628i
$393$	285.909	+	285.909i	0.727503	+	0.727503i
$394$	227.812	−	131.527i	0.578202	−	0.333825i
$395$	−48.8035	+	47.5282i	−0.123553	+	0.120325i
$396$	204.268	−	353.803i	0.515829	−	0.893443i
$397$	594.046	+	159.174i	1.49634	+	0.400942i	0.911871	−	0.410476i	$-0.134638\pi$
$397$	594.046	+	159.174i	1.49634	+	0.400942i	0.584466	+	0.811419i	$0.301304\pi$
$398$	−244.649	−	244.649i	−0.614697	−	0.614697i
$399$	−138.915	−	201.586i	−0.348159	−	0.505227i
$400$	85.2485	+	52.2752i	0.213121	+	0.130688i
$401$	−243.686	−	422.077i	−0.607697	−	1.05256i	−0.991619	−	0.129197i	$-0.958760\pi$
$401$	−243.686	−	422.077i	−0.607697	−	1.05256i	0.383922	−	0.923366i	$-0.374573\pi$
$402$	101.808	+	379.951i	0.253253	+	0.945151i
$403$	−312.993	+	83.8663i	−0.776659	+	0.208105i
$404$	−215.301	+	124.304i	−0.532923	+	0.307683i
$405$	122.613	−	434.507i	0.302749	−	1.07286i
$406$	259.928	+	123.583i	0.640217	+	0.304391i
$407$	−122.156	+	122.156i	−0.300137	+	0.300137i
$408$	33.8958	−	126.501i	0.0830779	−	0.310051i
$409$	197.730	+	114.159i	0.483447	+	0.279119i	0.721852	−	0.692047i	$-0.243291\pi$
$409$	197.730	+	114.159i	0.483447	+	0.279119i	−0.238405	+	0.971166i	$0.576624\pi$
$410$	64.9248	+	0.859547i	0.158353	+	0.00209646i
$411$	−168.569	−	291.970i	−0.410143	−	0.710388i
$412$	146.553	−	146.553i	0.355711	−	0.355711i
$413$	355.385	−	417.152i	0.860497	−	1.01005i
$414$			739.017i			1.78506i
$415$	173.077	+	103.005i	0.417053	+	0.248204i
$416$	38.4966	−	66.6781i	0.0925399	−	0.160284i
$417$	−69.6614	−	259.980i	−0.167054	−	0.623453i
$418$	27.2680	−	101.766i	0.0652345	−	0.243459i
$419$			312.625i			0.746121i	0.927807	+	0.373061i	$0.121692\pi$
$419$			312.625i			0.746121i	−0.927807	+	0.373061i	$0.878308\pi$
$420$	−71.0125	+	359.059i	−0.169077	+	0.854902i
$421$	479.690			1.13941			0.569703	−	0.821851i	$-0.307058\pi$
$421$	479.690			1.13941			0.569703	+	0.821851i	$0.307058\pi$
$422$	−278.238	−	74.5537i	−0.659332	−	0.176668i
$423$	156.873	−	42.0340i	0.370858	−	0.0993711i
$424$	−35.0074	−	20.2115i	−0.0825646	−	0.0476687i
$425$	−152.343	−	160.631i	−0.358454	−	0.377956i
$426$	−748.231			−1.75641
$427$	−141.404	+	50.2719i	−0.331158	+	0.117733i
$428$	−126.954	−	126.954i	−0.296621	−	0.296621i
$429$	−686.451	+	396.323i	−1.60012	+	0.923829i
$430$	−384.594	−	394.914i	−0.894405	−	0.918405i
$431$	268.836	−	465.638i	0.623750	−	1.08037i	−0.365031	−	0.930995i	$-0.618942\pi$
$431$	268.836	−	465.638i	0.623750	−	1.08037i	0.988781	−	0.149371i	$-0.0477250\pi$
$432$	−188.690	−	50.5593i	−0.436782	−	0.117036i
$433$	13.8191	+	13.8191i	0.0319148	+	0.0319148i	0.722884	−	0.690969i	$-0.242816\pi$
$433$	13.8191	+	13.8191i	0.0319148	+	0.0319148i	−0.690969	+	0.722884i	$0.742816\pi$
$434$	−133.733	−	194.066i	−0.308142	−	0.447156i
$435$	371.297	+	663.229i	0.853556	+	1.52466i
$436$	168.501	+	291.851i	0.386469	+	0.669384i
$437$	49.3261	+	184.088i	0.112874	+	0.421253i
$438$	−748.196	+	200.478i	−1.70821	+	0.457713i
$439$	160.490	−	92.6588i	0.365580	−	0.211068i	−0.305945	−	0.952049i	$-0.598973\pi$
$439$	160.490	−	92.6588i	0.365580	−	0.211068i	0.671526	+	0.740981i	$0.265639\pi$
$440$	−137.441	+	76.9440i	−0.312366	+	0.174873i
$441$	−887.243	+	142.788i	−2.01189	+	0.323783i
$442$	−120.527	+	120.527i	−0.272685	+	0.272685i
$443$	44.0219	−	164.292i	0.0993722	−	0.370862i	−0.898274	−	0.439436i	$-0.855178\pi$
$443$	44.0219	−	164.292i	0.0993722	−	0.370862i	0.997646	+	0.0685740i	$0.0218449\pi$
$444$	140.471	+	81.1008i	0.316375	+	0.182659i
$445$	−27.1398	+	26.4306i	−0.0609883	+	0.0593945i
$446$	194.661	+	337.163i	0.436460	+	0.755972i
$447$	−202.012	+	202.012i	−0.451928	+	0.451928i
$448$	55.0749	+	10.1367i	0.122935	+	0.0226266i
$449$			136.021i			0.302943i	0.988462	+	0.151472i	$0.0484012\pi$
$449$			136.021i			0.302943i	−0.988462	+	0.151472i	$0.951599\pi$
$450$	−470.477	+	446.201i	−1.04550	+	0.991557i
$451$	−51.1371	+	88.5721i	−0.113386	+	0.196391i
$452$	16.2919	+	60.8024i	0.0360441	+	0.134518i
$453$	−168.447	+	628.652i	−0.371847	+	1.38775i
$454$			322.576i			0.710520i
$455$	313.701	−	358.499i	0.689452	−	0.787909i
$456$	−98.9201			−0.216930
$457$	−744.760	−	199.558i	−1.62967	−	0.436669i	−0.675850	−	0.737040i	$-0.736223\pi$
$457$	−744.760	−	199.558i	−1.62967	−	0.436669i	−0.953823	+	0.300370i	$0.902890\pi$
$458$	−255.151	+	68.3675i	−0.557098	+	0.149274i
$459$	374.525	+	216.232i	0.815959	+	0.471094i
$460$	145.720	−	244.850i	0.316782	−	0.532283i
$461$	−174.788			−0.379149			−0.189574	−	0.981866i	$-0.560711\pi$
$461$	−174.788			−0.379149			−0.189574	+	0.981866i	$0.560711\pi$
$462$	−438.855	−	373.874i	−0.949902	−	0.809252i
$463$	−219.730	−	219.730i	−0.474578	−	0.474578i	0.428814	−	0.903393i	$-0.358931\pi$
$463$	−219.730	−	219.730i	−0.474578	−	0.474578i	−0.903393	+	0.428814i	$0.858931\pi$
$464$	100.713	−	58.1467i	0.217054	−	0.125316i
$465$	8.23955	−	622.365i	0.0177195	−	1.33842i
$466$	237.860	−	411.985i	0.510429	−	0.884088i
$467$	749.905	+	200.936i	1.60579	+	0.430270i	0.946785	−	0.321867i	$-0.104310\pi$
$467$	749.905	+	200.936i	1.60579	+	0.430270i	0.659006	+	0.752137i	$0.270977\pi$
$468$	353.013	+	353.013i	0.754302	+	0.754302i
$469$	371.179	−	29.6770i	0.791427	−	0.0632771i
$470$	−60.2633	−	17.0057i	−0.128220	−	0.0361822i
$471$	209.044	+	362.075i	0.443830	+	0.768737i
$472$	−57.3101	−	213.884i	−0.121420	−	0.453145i
$473$	838.697	−	224.728i	1.77314	−	0.475112i
$474$	−87.2503	+	50.3740i	−0.184072	+	0.106274i
$475$	−87.4129	+	142.550i	−0.184027	+	0.300105i
$476$	−111.964	−	53.2333i	−0.235219	−	0.111835i
$477$	185.339	−	185.339i	0.388552	−	0.388552i
$478$	30.6267	−	114.300i	0.0640726	−	0.239122i
$479$	−78.4044	−	45.2668i	−0.163684	−	0.0945028i	0.415921	−	0.909401i	$-0.363459\pi$
$479$	−78.4044	−	45.2668i	−0.163684	−	0.0945028i	−0.579604	+	0.814898i	$0.696793\pi$
$480$	103.182	+	105.950i	0.214962	+	0.220730i
$481$	−105.554	−	182.824i	−0.219446	−	0.380092i
$482$	114.348	−	114.348i	0.237236	−	0.237236i
$483$	1025.66	+	188.776i	2.12352	+	0.390840i
$484$		−	6.10459i		−	0.0126128i
$485$	269.136	−	452.224i	0.554919	−	0.932420i
$486$	23.0536	−	39.9300i	0.0474354	−	0.0821605i
$487$	236.419	+	882.327i	0.485460	+	1.81176i	0.577982	+	0.816050i	$0.303841\pi$
$487$	236.419	+	882.327i	0.485460	+	1.81176i	−0.0925219	+	0.995711i	$0.529493\pi$
$488$	−15.6946	+	58.5732i	−0.0321611	+	0.120027i
$489$		−	986.664i		−	2.01772i
$490$	322.115	+	127.639i	0.657379	+	0.260487i
$491$	−885.439			−1.80334			−0.901669	−	0.432427i	$-0.857657\pi$
$491$	−885.439			−1.80334			−0.901669	+	0.432427i	$0.857657\pi$
$492$	92.7549	+	24.8536i	0.188526	+	0.0505154i
$493$	−248.682	+	66.6341i	−0.504426	+	0.135161i
$494$	111.497	+	64.3728i	0.225702	+	0.130309i
$495$	−251.260	−	989.954i	−0.507596	−	1.99991i
$496$	−95.2301			−0.191996
$497$	−128.212	+	696.603i	−0.257972	+	1.40162i
$498$	210.624	+	210.624i	0.422940	+	0.422940i
$499$	−559.499	+	323.027i	−1.12124	+	0.647348i	−0.941717	−	0.336406i	$-0.890789\pi$
$499$	−559.499	+	323.027i	−1.12124	+	0.647348i	−0.179522	+	0.983754i	$0.557455\pi$
$500$	243.860	−	55.0658i	0.487720	−	0.110132i
$501$	−430.912	+	746.362i	−0.860104	+	1.48974i
$502$	3.91195	+	1.04821i	0.00779274	+	0.00208806i
$503$	−498.400	−	498.400i	−0.990855	−	0.990855i	0.00910371	−	0.999959i	$-0.497102\pi$
$503$	−498.400	−	498.400i	−0.990855	−	0.990855i	−0.999959	+	0.00910371i	$0.997102\pi$
$504$	−155.917	+	327.935i	−0.309358	+	0.650664i
$505$	−168.794	+	598.160i	−0.334246	+	1.18448i
$506$	224.403	+	388.677i	0.443483	+	0.768136i
$507$	−21.9892	−	82.0647i	−0.0433711	−	0.161863i
$508$	−220.044	+	58.9607i	−0.433158	+	0.116064i
$509$	−256.295	+	147.972i	−0.503526	+	0.290711i	−0.730169	−	0.683267i	$-0.760558\pi$
$509$	−256.295	+	147.972i	−0.503526	+	0.290711i	0.226642	+	0.973978i	$0.427225\pi$
$510$	−159.936	−	285.686i	−0.313600	−	0.560169i
$511$	58.4396	+	730.923i	0.114363	+	1.43038i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	84.5438	−	315.522i	0.164803	−	0.615052i
$514$	105.163	+	60.7160i	0.204598	+	0.118124i
$515$	6.85914	−	518.097i	0.0133187	−	1.00601i
$516$	−407.622	−	706.023i	−0.789966	−	1.36826i
$517$	69.7417	−	69.7417i	0.134897	−	0.134897i
$518$	99.5750	−	116.881i	0.192230	−	0.225640i
$519$		−	1664.38i		−	3.20691i
$520$	−47.3526	−	186.567i	−0.0910628	−	0.358784i
$521$	−343.065	+	594.206i	−0.658474	+	1.14051i	0.322537	+	0.946557i	$0.395464\pi$
$521$	−343.065	+	594.206i	−0.658474	+	1.14051i	−0.981011	+	0.193953i	$0.937869\pi$
$522$	195.166	+	728.371i	0.373882	+	1.39535i
$523$	−119.269	+	445.117i	−0.228047	+	0.851085i	0.753113	+	0.657891i	$0.228551\pi$
$523$	−119.269	+	445.117i	−0.228047	+	0.851085i	−0.981161	+	0.193194i	$0.938115\pi$
$524$		−	154.658i		−	0.295149i
$525$	499.090	+	766.940i	0.950647	+	1.46084i
$526$	−358.252			−0.681088
$527$	203.640	+	54.5652i	0.386414	+	0.103539i
$528$	−225.012	+	60.2917i	−0.426159	+	0.114189i
$529$	−244.964	−	141.430i	−0.463069	−	0.267353i
$530$	−97.9519	+	24.8611i	−0.184815	+	0.0469078i
$531$	1435.78			2.70392
$532$	−16.9503	+	92.0946i	−0.0318614	+	0.173110i
$533$	−88.3744	−	88.3744i	−0.165806	−	0.165806i
$534$	−48.5202	+	28.0131i	−0.0908617	+	0.0524590i
$535$	−448.810	−	5.94184i	−0.838897	−	0.0111062i
$536$	75.2289	−	130.300i	0.140352	−	0.243097i
$537$	−335.642	−	89.9350i	−0.625032	−	0.167477i
$538$	502.296	+	502.296i	0.933636	+	0.933636i
$539$	−423.276	+	344.509i	−0.785300	+	0.639164i
$540$	−426.133	+	238.563i	−0.789134	+	0.441783i
$541$	−78.6223	−	136.178i	−0.145328	−	0.251715i	0.784167	−	0.620549i	$-0.213090\pi$
$541$	−78.6223	−	136.178i	−0.145328	−	0.251715i	−0.929495	+	0.368834i	$0.879757\pi$
$542$	−72.6607	−	271.173i	−0.134060	−	0.500320i
$543$	361.589	−	96.8874i	0.665909	−	0.178430i
$544$	−43.3821	+	25.0467i	−0.0797466	+	0.0460417i
$545$	810.837	+	228.810i	1.48777	+	0.419834i
$546$	580.112	−	399.763i	1.06248	−	0.732166i
$547$	−13.1899	+	13.1899i	−0.0241132	+	0.0241132i	−0.719061	−	0.694947i	$-0.755428\pi$
$547$	−13.1899	+	13.1899i	−0.0241132	+	0.0241132i	0.694947	+	0.719061i	$0.255428\pi$
$548$	−33.3760	+	124.561i	−0.0609051	+	0.227301i
$549$	−340.518	−	196.598i	−0.620251	−	0.358102i
$550$	−111.953	+	377.534i	−0.203550	+	0.686426i
$551$	97.2311	+	168.409i	0.176463	+	0.305643i
$552$	297.968	−	297.968i	0.539797	−	0.539797i
$553$	31.9476	+	89.8618i	0.0577714	+	0.162499i
$554$		−	537.756i		−	0.970679i
$555$	393.042	−	99.7578i	0.708183	−	0.179744i
$556$	−51.4750	+	89.1574i	−0.0925810	+	0.160355i
$557$	−145.580	−	543.313i	−0.261365	−	0.975427i	−0.964438	−	0.264309i	$-0.914856\pi$
$557$	−145.580	−	543.313i	−0.261365	−	0.975427i	0.703073	−	0.711117i	$-0.251811\pi$
$558$	159.817	−	596.447i	0.286411	−	1.06890i
$559$			1061.05i			1.89812i
$560$	116.320	−	77.9073i	0.207715	−	0.139120i
$561$	515.712			0.919272
$562$	−185.231	−	49.6326i	−0.329593	−	0.0883143i
$563$	−810.309	+	217.122i	−1.43927	+	0.385651i	−0.892278	−	0.451486i	$-0.850894\pi$
$563$	−810.309	+	217.122i	−1.43927	+	0.385651i	−0.546992	+	0.837138i	$0.684227\pi$
$564$	−80.1983	−	46.3025i	−0.142196	−	0.0820967i
$565$	135.231	+	80.4813i	0.239347	+	0.142445i
$566$	499.006			0.881636
$567$	−481.137	−	409.896i	−0.848566	−	0.722920i
$568$	202.373	+	202.373i	0.356290	+	0.356290i
$569$	−271.713	+	156.874i	−0.477527	+	0.275701i	−0.719385	−	0.694611i	$-0.755576\pi$
$569$	−271.713	+	156.874i	−0.477527	+	0.275701i	0.241858	+	0.970312i	$0.422243\pi$
$570$	−177.167	+	172.537i	−0.310820	+	0.302697i
$571$	340.272	−	589.368i	0.595923	−	1.03217i	−0.397493	−	0.917605i	$-0.630120\pi$
$571$	340.272	−	589.368i	0.595923	−	1.03217i	0.993416	−	0.114564i	$-0.0365470\pi$
$572$	292.856	+	78.4704i	0.511985	+	0.137186i
$573$	−1232.42	−	1232.42i	−2.15081	−	2.15081i
$574$	39.0326	−	82.0961i	0.0680010	−	0.143025i
$575$	−166.084	−	692.696i	−0.288842	−	1.20469i
$576$	73.3599	+	127.063i	0.127361	+	0.220596i
$577$	213.851	+	798.104i	0.370626	+	1.38320i	0.859631	+	0.510915i	$0.170693\pi$
$577$	213.851	+	798.104i	0.370626	+	1.38320i	−0.489005	+	0.872281i	$0.662640\pi$
$578$	−287.662	+	77.0787i	−0.497684	+	0.133354i
$579$	449.886	−	259.742i	0.777005	−	0.448604i
$580$	78.9583	−	279.806i	0.136135	−	0.482425i
$581$	232.182	−	160.000i	0.399625	−	0.275387i
$582$	550.329	−	550.329i	0.945582	−	0.945582i
$583$	41.1986	−	153.755i	0.0706666	−	0.263731i
$584$	256.586	+	148.140i	0.439360	+	0.253664i
$585$	1247.98	+	16.5222i	2.13330	+	0.0282430i
$586$	−73.2341	−	126.845i	−0.124973	−	0.216459i
$587$	−345.401	+	345.401i	−0.588417	+	0.588417i	−0.937202	−	0.348786i	$-0.886594\pi$
$587$	−345.401	+	345.401i	−0.588417	+	0.588417i	0.348786	+	0.937202i	$0.386594\pi$
$588$	415.303	+	300.160i	0.706298	+	0.510477i
$589$		−	159.241i		−	0.270358i
$590$	−475.702	−	283.109i	−0.806275	−	0.479845i
$591$	486.295	−	842.287i	0.822834	−	1.42519i
$592$	−16.0577	−	59.9280i	−0.0271244	−	0.101230i
$593$	−46.7804	+	174.587i	−0.0788876	+	0.294413i	−0.994087	−	0.108589i	$-0.965367\pi$
$593$	−46.7804	+	174.587i	−0.0788876	+	0.294413i	0.915199	+	0.403002i	$0.132033\pi$
$594$		−	769.241i		−	1.29502i
$595$	−293.379	+	99.9474i	−0.493075	+	0.167979i
$596$	109.276			0.183348
$597$	−1235.63	−	331.085i	−2.06972	−	0.554581i
$598$	−529.757	+	141.948i	−0.885881	+	0.237371i
$599$	267.890	+	154.666i	0.447229	+	0.258208i	0.706659	−	0.707554i	$-0.250201\pi$
$599$	267.890	+	154.666i	0.447229	+	0.258208i	−0.259430	+	0.965762i	$0.583535\pi$
$600$	369.600	+	9.78806i	0.616000	+	0.0163134i
$601$	−583.911			−0.971566			−0.485783	−	0.874079i	$-0.661465\pi$
$601$	−583.911			−0.971566			−0.485783	+	0.874079i	$0.661465\pi$
$602$	−727.155	+	258.517i	−1.20790	+	0.429430i
$603$	689.848	+	689.848i	1.14403	+	1.14403i
$604$	215.590	−	124.471i	0.356937	−	0.206078i
$605$	−10.6477	−	10.9334i	−0.0175995	−	0.0180717i
$606$	−459.589	+	796.031i	−0.758397	+	1.31358i
$607$	162.955	+	43.6636i	0.268459	+	0.0719335i	0.390537	−	0.920587i	$-0.372289\pi$
$607$	162.955	+	43.6636i	0.268459	+	0.0719335i	−0.122078	+	0.992520i	$0.538956\pi$
$608$	26.7547	+	26.7547i	0.0440045	+	0.0440045i
$609$	1060.74	−	84.8094i	1.74177	−	0.139260i
$610$	74.0547	+	132.280i	0.121401	+	0.216853i
$611$	60.2633	+	104.379i	0.0986306	+	0.170833i
$612$	−84.0680	−	313.746i	−0.137366	−	0.512657i
$613$	365.798	−	98.0152i	0.596734	−	0.159894i	0.0522047	−	0.998636i	$-0.483375\pi$
$613$	365.798	−	98.0152i	0.596734	−	0.159894i	0.544529	+	0.838742i	$0.316709\pi$
$614$	682.761	−	394.192i	1.11199	−	0.642007i
$615$	209.475	−	117.271i	0.340610	−	0.190684i
$616$	17.5751	+	219.817i	0.0285310	+	0.356846i
$617$	788.089	−	788.089i	1.27729	−	1.27729i	0.335114	−	0.942178i	$-0.391225\pi$
$617$	788.089	−	788.089i	1.27729	−	1.27729i	0.942178	−	0.335114i	$-0.108775\pi$
$618$	198.331	−	740.180i	0.320923	−	1.19770i
$619$	506.750	+	292.572i	0.818660	+	0.472653i	0.849954	−	0.526857i	$-0.176630\pi$
$619$	506.750	+	292.572i	0.818660	+	0.472653i	−0.0312944	+	0.999510i	$0.509963\pi$
$620$	−170.558	+	166.101i	−0.275094	+	0.267905i
$621$	695.754	+	1205.08i	1.12038	+	1.94055i
$622$	235.592	−	235.592i	0.378766	−	0.378766i
$623$	17.7661	+	49.9724i	0.0285171	+	0.0802126i
$624$		−	284.667i		−	0.456196i
$625$	340.710	−	523.967i	0.545137	−	0.838347i
$626$	−259.005	+	448.609i	−0.413746	+	0.716629i
$627$	−100.818	−	376.258i	−0.160794	−	0.600092i
$628$	41.3900	−	154.469i	0.0659076	−	0.245970i
$629$			137.351i			0.218364i
$630$	292.739	+	859.287i	0.464664	+	1.36395i
$631$	592.443			0.938895			0.469448	−	0.882960i	$-0.344453\pi$
$631$	592.443			0.938895			0.469448	+	0.882960i	$0.344453\pi$
$632$	37.2230	+	9.97387i	0.0588971	+	0.0157814i
$633$	−1028.73	+	275.647i	−1.62516	+	0.435461i
$634$	−25.3052	−	14.6100i	−0.0399136	−	0.0230441i
$635$	−291.262	+	489.403i	−0.458681	+	0.770713i
$636$	−149.456			−0.234994
$637$	−272.775	−	608.585i	−0.428218	−	0.955392i
$638$	323.815	+	323.815i	0.507548	+	0.507548i
$639$	−1607.13	+	927.877i	−2.51507	+	1.45208i
$640$	0.748851	−	56.5636i	0.00117008	−	0.0883806i
$641$	−190.823	+	330.516i	−0.297696	+	0.515625i	−0.975609	−	0.219518i	$-0.929552\pi$
$641$	−190.823	+	330.516i	−0.297696	+	0.515625i	0.677912	+	0.735143i	$0.262885\pi$
$642$	−641.192	−	171.807i	−0.998742	−	0.267612i
$643$	34.6664	+	34.6664i	0.0539135	+	0.0539135i	0.733550	−	0.679636i	$-0.237862\pi$
$643$	34.6664	+	34.6664i	0.0539135	+	0.0539135i	−0.679636	+	0.733550i	$0.737862\pi$
$644$	−226.350	−	328.466i	−0.351476	−	0.510040i
$645$	−1961.51	−	553.517i	−3.04110	−	0.858166i
$646$	−41.8823	−	72.5423i	−0.0648333	−	0.112295i
$647$	−180.656	−	674.219i	−0.279222	−	1.04207i	−0.952959	−	0.303098i	$-0.901979\pi$
$647$	−180.656	−	674.219i	−0.279222	−	1.04207i	0.673738	−	0.738971i	$-0.264688\pi$
$648$	−246.691	+	66.1006i	−0.380696	+	0.102007i
$649$	755.133	−	435.976i	1.16353	−	0.671766i
$650$	−410.222	−	251.552i	−0.631111	−	0.387003i
$651$	−786.967	−	374.164i	−1.20886	−	0.574752i
$652$	−266.861	+	266.861i	−0.409296	+	0.409296i
$653$	−288.387	+	1076.27i	−0.441634	+	1.64820i	0.283041	+	0.959108i	$0.408657\pi$
$653$	−288.387	+	1076.27i	−0.441634	+	1.64820i	−0.724675	+	0.689091i	$0.758010\pi$
$654$	1079.06	+	622.996i	1.64994	+	0.952594i
$655$	−269.757	−	276.995i	−0.411842	−	0.422893i
$656$	−18.3651	−	31.8093i	−0.0279956	−	0.0484898i
$657$	−1358.44	+	1358.44i	−2.06764	+	2.06764i
$658$	−56.8499	+	66.7305i	−0.0863980	+	0.101414i
$659$			894.905i			1.35797i	0.734150	+	0.678987i	$0.237581\pi$
$659$			894.905i			1.35797i	−0.734150	+	0.678987i	$0.762419\pi$
$660$	−297.838	+	500.451i	−0.451269	+	0.758259i
$661$	505.683	−	875.868i	0.765026	−	1.32506i	−0.175206	−	0.984532i	$-0.556059\pi$
$661$	505.683	−	875.868i	0.765026	−	1.32506i	0.940233	−	0.340533i	$-0.110607\pi$
$662$	51.7464	+	193.120i	0.0781667	+	0.291722i
$663$	−163.109	+	608.731i	−0.246017	+	0.918147i
$664$		−	113.934i		−	0.171587i
$665$	130.274	+	194.508i	0.195901	+	0.292493i
$666$	402.291			0.604040
$667$	−800.165	−	214.403i	−1.19965	−	0.321444i
$668$	318.415	−	85.3190i	0.476669	−	0.127723i
$669$	1246.59	+	719.720i	1.86337	+	1.07582i
$670$	−92.5351	−	364.584i	−0.138112	−	0.544156i
$671$	−238.788			−0.355869
$672$	195.086	−	69.3569i	0.290307	−	0.103210i
$673$	331.906	+	331.906i	0.493174	+	0.493174i	0.909305	−	0.416131i	$-0.136614\pi$
$673$	331.906	+	331.906i	0.493174	+	0.493174i	−0.416131	+	0.909305i	$0.636614\pi$
$674$	−393.112	+	226.963i	−0.583253	+	0.336741i
$675$	−347.106	+	1170.53i	−0.514231	+	1.73412i
$676$	−16.2485	+	28.1432i	−0.0240363	+	0.0416320i
$677$	−272.549	−	73.0294i	−0.402584	−	0.107872i	0.0518447	−	0.998655i	$-0.483490\pi$
$677$	−272.549	−	73.0294i	−0.402584	−	0.107872i	−0.454429	+	0.890783i	$0.650157\pi$
$678$	164.568	+	164.568i	0.242726	+	0.242726i
$679$	−418.055	−	606.657i	−0.615693	−	0.893456i
$680$	−34.0113	+	120.527i	−0.0500166	+	0.177245i
$681$	596.330	+	1032.87i	0.875668	+	1.51670i
$682$	−97.0572	−	362.222i	−0.142313	−	0.531118i
$683$	413.854	−	110.892i	0.605935	−	0.162360i	0.0572092	−	0.998362i	$-0.481780\pi$
$683$	413.854	−	110.892i	0.605935	−	0.162360i	0.548726	+	0.836002i	$0.315113\pi$
$684$	−212.471	+	122.670i	−0.310630	+	0.179342i
$685$	157.484	+	281.305i	0.229903	+	0.410664i
$686$	350.613	−	335.214i	0.511098	−	0.488650i
$687$	−690.594	+	690.594i	−1.00523	+	1.00523i
$688$	−80.7077	+	301.205i	−0.117308	+	0.437798i
$689$	168.458	+	97.2594i	0.244497	+	0.141160i
$690$	13.9459	−	1053.38i	0.0202114	−	1.52664i
$691$	23.9800	+	41.5345i	0.0347033	+	0.0601079i	0.882855	−	0.469645i	$-0.155618\pi$
$691$	23.9800	+	41.5345i	0.0347033	+	0.0601079i	−0.848152	+	0.529753i	$0.822285\pi$
$692$	−450.163	+	450.163i	−0.650524	+	0.650524i
$693$	−1406.26	−	258.826i	−2.02923	−	0.373487i
$694$			818.996i			1.18011i
$695$	63.3168	+	249.465i	0.0911032	+	0.358943i
$696$	214.985	−	372.366i	0.308887	−	0.535008i
$697$	21.0458	+	78.5440i	0.0301948	+	0.112689i
$698$	−17.0372	+	63.5837i	−0.0244086	+	0.0910942i
$699$		−	1758.87i		−	2.51627i
$700$	72.4449	−	342.420i	0.103493	−	0.489172i
$701$	−952.278			−1.35846			−0.679228	−	0.733927i	$-0.737685\pi$
$701$	−952.278			−1.35846			−0.679228	+	0.733927i	$0.737685\pi$
$702$	907.990	+	243.295i	1.29343	+	0.346575i
$703$	100.210	−	26.8511i	0.142546	−	0.0381951i
$704$	77.1655	+	44.5515i	0.109610	+	0.0632834i
$705$	−224.398	+	56.9543i	−0.318294	+	0.0807862i
$706$	−751.645			−1.06465
$707$	662.353	+	564.280i	0.936850	+	0.798133i
$708$	−578.901	−	578.901i	−0.817657	−	0.817657i
$709$	619.824	−	357.856i	0.874224	−	0.504733i	0.00547406	−	0.999985i	$-0.498258\pi$
$709$	619.824	−	357.856i	0.874224	−	0.504733i	0.868749	+	0.495252i	$0.164924\pi$
$710$	715.432	+	9.47168i	1.00765	+	0.0133404i
$711$	−124.937	+	216.397i	−0.175720	+	0.304356i
$712$	20.6998	+	5.54650i	0.0290728	+	0.00779002i
$713$	479.667	+	479.667i	0.672744	+	0.672744i
$714$	−456.913	+	36.5317i	−0.639935	+	0.0511648i
$715$	661.377	−	370.260i	0.925003	−	0.517846i
$716$	66.4559	+	115.105i	0.0928155	+	0.160761i
$717$	−113.236	−	422.603i	−0.157930	−	0.589404i
$718$	−97.1195	+	26.0231i	−0.135264	+	0.0362439i
$719$	66.9619	−	38.6605i	0.0931320	−	0.0537698i	−0.452711	−	0.891657i	$-0.649543\pi$
$719$	66.9619	−	38.6605i	0.0931320	−	0.0537698i	0.545843	+	0.837888i	$0.316210\pi$
$720$	353.013	+	99.6166i	0.490296	+	0.138356i
$721$	−655.123	−	311.478i	−0.908631	−	0.432009i
$722$	316.262	−	316.262i	0.438035	−	0.438035i
$723$	154.747	−	577.524i	0.214035	−	0.798789i
$724$	−124.003	−	71.5932i	−0.171275	−	0.0988857i
$725$	−346.626	−	638.857i	−0.478104	−	0.881182i
$726$	−11.2852	−	19.5466i	−0.0155444	−	0.0269237i
$727$	760.852	−	760.852i	1.04656	−	1.04656i	0.0477025	−	0.998862i	$-0.484810\pi$
$727$	760.852	−	760.852i	1.04656	−	1.04656i	0.998862	−	0.0477025i	$-0.0151899\pi$
$728$	−265.025	−	48.7786i	−0.364045	−	0.0670036i
$729$			642.184i			0.880911i
$730$	717.936	−	182.219i	0.983474	−	0.249615i
$731$	345.171	−	597.854i	0.472190	−	0.817857i
$732$	58.0277	+	216.562i	0.0792728	+	0.295850i
$733$	280.505	−	1046.86i	0.382681	−	1.42818i	−0.459110	−	0.888379i	$-0.651832\pi$
$733$	280.505	−	1046.86i	0.382681	−	1.42818i	0.841791	−	0.539804i	$-0.181502\pi$
$734$			199.512i			0.271815i
$735$	1267.36	−	186.786i	1.72430	−	0.254130i
$736$	−161.182			−0.218997
$737$	572.289	+	153.344i	0.776512	+	0.208066i
$738$	230.050	−	61.6416i	0.311720	−	0.0835252i
$739$	−1026.64	−	592.730i	−1.38923	−	0.802070i	−0.395999	−	0.918251i	$-0.629602\pi$
$739$	−1026.64	−	592.730i	−1.38923	−	0.802070i	−0.993228	+	0.116181i	$0.962935\pi$
$740$	−133.287	−	79.3239i	−0.180117	−	0.107195i
$741$	476.011			0.642390
$742$	−25.6098	+	139.144i	−0.0345145	+	0.187525i
$743$	65.8954	+	65.8954i	0.0886883	+	0.0886883i	0.750059	−	0.661371i	$-0.230025\pi$
$743$	65.8954	+	65.8954i	0.0886883	+	0.0886883i	−0.661371	+	0.750059i	$0.730025\pi$
$744$	−304.922	+	176.047i	−0.409841	+	0.236622i
$745$	195.714	−	190.600i	0.262703	−	0.255838i
$746$	213.997	−	370.653i	0.286859	−	0.496855i
$747$	713.594	+	191.207i	0.955280	+	0.255967i
$748$	−139.483	−	139.483i	−0.186475	−	0.186475i
$749$	−269.823	+	567.510i	−0.360244	+	0.757691i
$750$	679.031	−	627.130i	0.905375	−	0.836173i
$751$	−146.301	−	253.400i	−0.194808	−	0.337417i	0.752030	−	0.659129i	$-0.229075\pi$
$751$	−146.301	−	253.400i	−0.194808	−	0.337417i	−0.946837	+	0.321712i	$0.895742\pi$
$752$	9.16773	+	34.2144i	0.0121911	+	0.0454979i
$753$	14.4637	−	3.87552i	0.0192080	−	0.00514678i
$754$	−484.639	+	279.806i	−0.642757	+	0.371096i
$755$	169.021	−	598.963i	0.223869	−	0.793329i
$756$	54.4910	+	681.537i	0.0720781	+	0.901504i
$757$	742.193	−	742.193i	0.980440	−	0.980440i	−0.0193719	−	0.999812i	$-0.506167\pi$
$757$	742.193	−	742.193i	0.980440	−	0.980440i	0.999812	+	0.0193719i	$0.00616667\pi$
$758$	−120.780	+	450.756i	−0.159340	+	0.594665i
$759$	1437.05	+	829.683i	1.89335	+	1.09313i
$760$	94.5839	+	1.25221i	0.124453	+	0.00164764i
$761$	−308.160	−	533.749i	−0.404941	−	0.701378i	0.589374	−	0.807860i	$-0.299375\pi$
$761$	−308.160	−	533.749i	−0.404941	−	0.701378i	−0.994315	+	0.106482i	$0.966041\pi$
$762$	−595.574	+	595.574i	−0.781593	+	0.781593i
$763$	764.910	−	897.854i	1.00250	−	1.17674i
$764$			666.659i			0.872590i
$765$	−697.806	−	415.291i	−0.912164	−	0.542864i
$766$	−125.756	+	217.816i	−0.164172	+	0.284354i
$767$	275.781	+	1029.23i	0.359558	+	1.34189i
$768$	21.6529	−	80.8096i	0.0281938	−	0.105221i
$769$		−	743.180i		−	0.966424i	−0.875503	−	0.483212i	$-0.839470\pi$
$769$		−	743.180i		−	0.966424i	0.875503	−	0.483212i	$-0.160530\pi$
$770$	414.885	+	363.041i	0.538811	+	0.471482i
$771$	448.970			0.582321
$772$	−191.932	−	51.4279i	−0.248616	−	0.0666165i
$773$	320.715	−	85.9354i	0.414897	−	0.111171i	−0.0453311	−	0.998972i	$-0.514434\pi$
$773$	320.715	−	85.9354i	0.414897	−	0.111171i	0.460228	+	0.887801i	$0.347768\pi$
$774$	−1751.07	−	1010.98i	−2.26236	−	1.30618i
$775$	−15.7567	+	594.979i	−0.0203313	+	0.767715i
$776$	−297.693			−0.383625
$777$	102.762	−	558.328i	0.132255	−	0.718568i
$778$	239.373	+	239.373i	0.307678	+	0.307678i
$779$	53.1906	−	30.7096i	0.0682806	−	0.0394218i
$780$	−496.518	−	509.842i	−0.636562	−	0.653643i
$781$	−563.500	+	976.011i	−0.721511	+	1.24969i
$782$	344.671	+	92.3543i	0.440756	+	0.118100i
$783$	1003.98	+	1003.98i	1.28222	+	1.28222i
$784$	−31.1425	−	193.510i	−0.0397226	−	0.246824i
$785$	−195.297	−	348.850i	−0.248786	−	0.444395i
$786$	−285.909	−	495.208i	−0.363752	−	0.630036i
$787$	−182.282	−	680.286i	−0.231616	−	0.864404i	−0.979645	−	0.200738i	$-0.935666\pi$
$787$	−182.282	−	680.286i	−0.231616	−	0.864404i	0.748029	−	0.663667i	$-0.231001\pi$
$788$	−359.339	+	96.2846i	−0.456014	+	0.122189i
$789$	−1147.11	+	662.282i	−1.45387	+	0.839395i
$790$	84.0634	−	47.0614i	0.106409	−	0.0595714i
$791$	181.412	−	125.014i	0.229346	−	0.158045i
$792$	−408.537	+	408.537i	−0.515829	+	0.515829i
$793$	75.5238	−	281.859i	0.0952381	−	0.355433i
$794$	−753.220	−	434.872i	−0.948640	−	0.547697i
$795$	−267.678	+	260.683i	−0.336701	+	0.327903i
$796$	244.649	+	423.745i	0.307348	+	0.532343i
$797$	559.866	−	559.866i	0.702467	−	0.702467i	−0.262472	−	0.964940i	$-0.584538\pi$
$797$	559.866	−	559.866i	0.702467	−	0.702467i	0.964940	+	0.262472i	$0.0845379\pi$
$798$	115.976	+	326.218i	0.145334	+	0.408794i
$799$		−	78.4171i		−	0.0981441i
$800$	−97.3176	−	102.612i	−0.121647	−	0.128265i
$801$	−69.4778	+	120.339i	−0.0867389	+	0.150236i
$802$	178.391	+	665.764i	0.222433	+	0.830130i
$803$	−301.965	+	1126.95i	−0.376046	+	1.40342i
$804$		−	556.287i		−	0.691899i
$805$	−978.311	−	193.484i	−1.21529	−	0.240353i
$806$	458.254			0.568554
$807$	2536.90	+	679.759i	3.14361	+	0.842329i
$808$	339.605	−	90.9969i	0.420303	−	0.112620i
$809$	−772.252	−	445.860i	−0.954576	−	0.551125i	−0.0600765	−	0.998194i	$-0.519134\pi$
$809$	−772.252	−	445.860i	−0.954576	−	0.551125i	−0.894499	+	0.447069i	$0.852468\pi$
$810$	−326.533	+	548.668i	−0.403127	+	0.677368i
$811$	−725.006			−0.893965			−0.446982	−	0.894543i	$-0.647501\pi$
$811$	−725.006			−0.893965			−0.446982	+	0.894543i	$0.647501\pi$
$812$	−309.834	−	263.958i	−0.381569	−	0.325071i
$813$	−733.960	−	733.960i	−0.902780	−	0.902780i
$814$	211.580	−	122.156i	0.259926	−	0.150068i
$815$	−12.4899	+	943.414i	−0.0153251	+	1.15756i
$816$	−92.6050	+	160.397i	−0.113487	+	0.196564i
$817$	−503.666	−	134.957i	−0.616483	−	0.165186i
$818$	−228.319	−	228.319i	−0.279119	−	0.279119i
$819$	750.282	−	1578.05i	0.916095	−	1.92680i
$820$	−88.3744	−	24.9383i	−0.107774	−	0.0304126i
$821$	377.073	+	653.109i	0.459285	+	0.795504i	0.998923	−	0.0463923i	$-0.0147724\pi$
$821$	377.073	+	653.109i	0.459285	+	0.795504i	−0.539639	+	0.841897i	$0.681439\pi$
$822$	123.401	+	460.538i	0.150123	+	0.560266i
$823$	1012.22	−	271.224i	1.22992	−	0.329556i	0.415371	−	0.909652i	$-0.363652\pi$
$823$	1012.22	−	271.224i	1.22992	−	0.329556i	0.814548	+	0.580096i	$0.196985\pi$
$824$	−253.837	+	146.553i	−0.308055	+	0.177855i
$825$	339.461	+	1415.81i	0.411468	+	1.71613i
$826$	−638.154	+	439.760i	−0.772583	+	0.532397i
$827$	−29.7436	+	29.7436i	−0.0359656	+	0.0359656i	−0.724861	−	0.688895i	$-0.758096\pi$
$827$	−29.7436	+	29.7436i	−0.0359656	+	0.0359656i	0.688895	+	0.724861i	$0.258096\pi$
$828$	270.499	−	1009.52i	0.326690	−	1.21922i
$829$	159.407	+	92.0338i	0.192289	+	0.111018i	0.593053	−	0.805163i	$-0.297922\pi$
$829$	159.407	+	92.0338i	0.192289	+	0.111018i	−0.400765	+	0.916181i	$0.631256\pi$
$830$	−198.725	−	204.058i	−0.239428	−	0.245852i
$831$	−994.122	−	1721.87i	−1.19630	−	2.07205i
$832$	−76.9932	+	76.9932i	−0.0925399	+	0.0925399i
$833$	−44.2827	+	431.646i	−0.0531605	+	0.518183i
$834$			380.637i			0.456399i
$835$	421.471	−	708.190i	0.504756	−	0.848132i
$836$	−74.4977	+	129.034i	−0.0891120	+	0.154347i
$837$	−300.923	−	1123.06i	−0.359526	−	1.34177i
$838$	114.429	−	427.054i	0.136550	−	0.509610i
$839$			230.146i			0.274310i	0.990550	+	0.137155i	$0.0437958\pi$
$839$			230.146i			0.274310i	−0.990550	+	0.137155i	$0.956204\pi$
$840$	228.429	−	464.491i	0.271940	−	0.552965i
$841$	−4.25956			−0.00506488
$842$	−655.269	−	175.579i	−0.778229	−	0.208526i
$843$	−684.855	+	183.506i	−0.812403	+	0.217683i
$844$	352.792	+	203.685i	0.418000	+	0.241332i
$845$	19.9864	+	78.7458i	0.0236526	+	0.0931902i
$846$	−229.678			−0.271487
$847$	−20.1317	+	7.15718i	−0.0237682	+	0.00845004i
$848$	40.4230	+	40.4230i	0.0476687	+	0.0476687i
$849$	1597.79	−	922.486i	1.88197	−	1.08656i
$850$	149.309	+	275.188i	0.175658	+	0.323750i
$851$	−220.972	+	382.734i	−0.259661	+	0.449746i
$852$	1022.10	+	273.872i	1.19965	+	0.321446i
$853$	1144.00	+	1144.00i	1.34115	+	1.34115i	0.894912	+	0.446242i	$0.147238\pi$
$853$	1144.00	+	1144.00i	1.34115	+	1.34115i	0.446242	+	0.894912i	$0.352762\pi$
$854$	211.563	−	16.9151i	0.247732	−	0.0198069i
$855$	−166.576	+	590.298i	−0.194826	+	0.690407i
$856$	126.954	+	219.890i	0.148310	+	0.256881i
$857$	−92.2922	−	344.439i	−0.107692	−	0.401913i	0.890944	−	0.454112i	$-0.150043\pi$
$857$	−92.2922	−	344.439i	−0.107692	−	0.401913i	−0.998637	+	0.0521995i	$0.983377\pi$
$858$	1082.77	−	290.128i	1.26197	−	0.338145i
$859$	−1316.32	+	759.978i	−1.53239	+	0.884724i	−0.533136	+	0.846029i	$0.678987\pi$
$859$	−1316.32	+	759.978i	−1.53239	+	0.884724i	−0.999251	+	0.0386951i	$0.987680\pi$
$860$	380.817	+	680.234i	0.442810	+	0.790970i
$861$	−26.7863	−	335.025i	−0.0311107	−	0.389112i
$862$	−537.672	+	537.672i	−0.623750	+	0.623750i
$863$	−58.7013	+	219.076i	−0.0680200	+	0.253854i	−0.991560	−	0.129648i	$-0.958615\pi$
$863$	−58.7013	+	219.076i	−0.0680200	+	0.253854i	0.923540	+	0.383502i	$0.125282\pi$
$864$	239.249	+	138.131i	0.276909	+	0.159873i
$865$	−21.0691	+	1591.43i	−0.0243573	+	1.83980i
$866$	−13.8191	−	23.9354i	−0.0159574	−	0.0276391i
$867$	−778.587	+	778.587i	−0.898024	+	0.898024i
$868$	111.650	+	314.049i	0.128629	+	0.361807i
$869$			151.749i			0.174624i
$870$	−264.442	−	1041.89i	−0.303957	−	1.19758i
$871$	−362.007	+	627.014i	−0.415622	+	0.719879i
$872$	−123.351	−	460.352i	−0.141458	−	0.527927i
$873$	499.595	−	1864.51i	0.572274	−	2.13576i
$874$		−	269.523i		−	0.308379i
$875$	−467.503	−	739.639i	−0.534290	−	0.845301i
$876$	1095.43			1.25050
$877$	942.868	+	252.641i	1.07511	+	0.288074i	0.752590	−	0.658490i	$-0.228804\pi$
$877$	942.868	+	252.641i	1.07511	+	0.288074i	0.322517	+	0.946564i	$0.395471\pi$
$878$	−253.149	+	67.8310i	−0.288324	+	0.0772562i
$879$	−468.984	−	270.768i	−0.533543	−	0.308041i
$880$	215.912	−	54.8005i	0.245354	−	0.0622733i
$881$	495.620			0.562566			0.281283	−	0.959625i	$-0.409240\pi$
$881$	495.620			0.562566			0.281283	+	0.959625i	$0.409240\pi$
$882$	1264.26	+	129.701i	1.43340	+	0.147053i
$883$	−918.390	−	918.390i	−1.04008	−	1.04008i	−0.999163	−	0.0409167i	$-0.986972\pi$
$883$	−918.390	−	918.390i	−1.04008	−	1.04008i	−0.0409167	−	0.999163i	$-0.513028\pi$
$884$	208.758	−	120.527i	0.236152	−	0.136342i
$885$	−2046.54	−	27.0944i	−2.31248	−	0.0306152i
$886$	−120.270	+	208.314i	−0.135745	+	0.235117i
$887$	−137.822	−	36.9292i	−0.155379	−	0.0416338i	0.180291	−	0.983613i	$-0.442296\pi$
$887$	−137.822	−	36.9292i	−0.155379	−	0.0416338i	−0.335670	+	0.941980i	$0.608963\pi$
$888$	−162.202	−	162.202i	−0.182659	−	0.182659i
$889$	452.426	+	656.533i	0.508915	+	0.738507i
$890$	46.7479	−	26.1710i	0.0525257	−	0.0294056i
$891$	−502.848	−	870.958i	−0.564363	−	0.977506i
$892$	−142.502	−	531.825i	−0.159756	−	0.596216i
$893$	−57.2123	+	15.3300i	−0.0640675	+	0.0171668i
$894$	349.895	−	202.012i	0.391381	−	0.225964i
$895$	319.791	+	90.2415i	0.357308	+	0.100829i
$896$	−71.5235	−	34.0058i	−0.0798253	−	0.0379529i
$897$	−1433.84	+	1433.84i	−1.59849	+	1.59849i
$898$	49.7873	−	185.809i	0.0554424	−	0.206914i
$899$	599.432	+	346.082i	0.666776	+	0.384963i
$900$	806.004	−	437.315i	0.895560	−	0.485906i
$901$	−63.2790	−	109.602i	−0.0702319	−	0.121645i
$902$	102.274	−	102.274i	0.113386	−	0.113386i
$903$	−1850.41	+	2172.01i	−2.04918	+	2.40533i
$904$		−	89.0208i		−	0.0984744i
$905$	−346.965	+	88.0631i	−0.383387	+	0.0973072i
$906$	460.205	−	797.099i	0.507953	−	0.879801i
$907$	−22.8874	−	85.4170i	−0.0252342	−	0.0941753i	0.952160	−	0.305599i	$-0.0988567\pi$
$907$	−22.8874	−	85.4170i	−0.0252342	−	0.0941753i	−0.977395	+	0.211424i	$0.932190\pi$
$908$	118.071	−	440.647i	0.130034	−	0.485295i
$909$			2279.73i			2.50796i
$910$	−559.743	+	374.896i	−0.615102	+	0.411973i
$911$	−19.6420			−0.0215609			−0.0107805	−	0.999942i	$-0.503432\pi$
$911$	−19.6420			−0.0215609			−0.0107805	+	0.999942i	$0.503432\pi$
$912$	135.127	+	36.2073i	0.148166	+	0.0397009i
$913$	433.366	−	116.120i	0.474662	−	0.127185i
$914$	944.318	+	545.202i	1.03317	+	0.596501i
$915$	481.659	+	286.654i	0.526403	+	0.313283i
$916$	373.567			0.407824
$917$	−510.031	+	181.325i	−0.556195	+	0.197738i
$918$	−432.465	−	432.465i	−0.471094	−	0.471094i
$919$	−730.678	+	421.857i	−0.795080	+	0.459039i	−0.841748	−	0.539871i	$-0.818473\pi$
$919$	−730.678	+	421.857i	−0.795080	+	0.459039i	0.0466681	+	0.998910i	$0.485140\pi$
$920$	−288.678	+	281.135i	−0.313781	+	0.305581i
$921$	1457.45	−	2524.37i	1.58246	−	2.74090i
$922$	238.764	+	63.9767i	0.258963	+	0.0693890i
$923$	−973.832	−	973.832i	−1.05507	−	1.05507i
$924$	462.639	+	671.354i	0.500692	+	0.726574i
$925$	−377.076	+	90.4095i	−0.407649	+	0.0977400i
$926$	219.730	+	380.583i	0.237289	+	0.410997i
$927$	−491.897	−	1835.79i	−0.530634	−	1.98035i
$928$	−158.860	+	42.5663i	−0.171185	+	0.0458689i
$929$	−325.901	+	188.159i	−0.350808	+	0.202539i	−0.665041	−	0.746807i	$-0.731586\pi$
$929$	−325.901	+	188.159i	−0.350808	+	0.202539i	0.314233	+	0.949346i	$0.398253\pi$
$930$	−239.057	+	847.150i	−0.257050	+	0.910914i
$931$	323.582	−	52.0756i	0.347564	−	0.0559351i
$932$	−475.719	+	475.719i	−0.510429	+	0.510429i
$933$	318.828	−	1189.88i	0.341723	−	1.27533i
$934$	−950.841	−	548.968i	−1.01803	−	0.587760i
$935$	−493.105	−	6.52827i	−0.527385	−	0.00698211i
$936$	−353.013	−	611.437i	−0.377151	−	0.653245i
$937$	333.039	−	333.039i	0.355431	−	0.355431i	−0.506694	−	0.862126i	$-0.669133\pi$
$937$	333.039	−	333.039i	0.355431	−	0.355431i	0.862126	+	0.506694i	$0.169133\pi$
$938$	−517.903	−	95.3216i	−0.552135	−	0.101622i
$939$			1915.23i			2.03965i
$940$	76.0967	+	45.2881i	0.0809539	+	0.0481788i
$941$	−462.718	+	801.452i	−0.491730	+	0.851702i	−0.999955	−	0.00952274i	$-0.996969\pi$
$941$	−462.718	+	801.452i	−0.491730	+	0.851702i	0.508224	+	0.861225i	$0.330302\pi$
$942$	−153.031	−	571.119i	−0.162453	−	0.606284i
$943$	−67.7175	+	252.725i	−0.0718107	+	0.268001i
$944$			313.148i			0.331725i
$945$	1286.34	+	1125.60i	1.36120	+	1.19111i
$946$	−1227.94			−1.29803
$947$	−872.417	−	233.763i	−0.921243	−	0.246846i	−0.233126	−	0.972446i	$-0.574896\pi$
$947$	−872.417	−	233.763i	−0.921243	−	0.246846i	−0.688116	+	0.725600i	$0.741562\pi$
$948$	137.624	−	36.8763i	0.145173	−	0.0388991i
$949$	−1234.71	−	712.861i	−1.30107	−	0.751170i
$950$	171.585	−	162.732i	0.180616	−	0.171296i
$951$	−108.035			−0.113601
$952$	133.461	+	113.700i	0.140190	+	0.119433i
$953$	−336.361	−	336.361i	−0.352950	−	0.352950i	0.508256	−	0.861206i	$-0.330290\pi$
$953$	−336.361	−	336.361i	−0.352950	−	0.352950i	−0.861206	+	0.508256i	$0.830290\pi$
$954$	−321.017	+	185.339i	−0.336496	+	0.194276i
$955$	1162.79	+	1193.99i	1.21758	+	1.25026i
$956$	−83.6738	+	144.927i	−0.0875249	+	0.151598i
$957$	1635.46	+	438.221i	1.70895	+	0.457911i
$958$	90.5336	+	90.5336i	0.0945028	+	0.0945028i
$959$	449.906	−	35.9714i	0.469141	−	0.0375093i
$960$	−102.168	−	182.498i	−0.106425	−	0.190102i
$961$	197.101	+	341.389i	0.205100	+	0.355244i
$962$	77.2707	+	288.378i	0.0803229	+	0.299769i
$963$	−1590.28	+	426.114i	−1.65138	+	0.442486i
$964$	−198.056	+	114.348i	−0.205452	+	0.118618i
$965$	−433.453	+	242.661i	−0.449174	+	0.251462i
$966$	−1331.98	−	633.290i	−1.37886	−	0.655580i
$967$	95.1413	−	95.1413i	0.0983881	−	0.0983881i	−0.656199	−	0.754588i	$-0.727837\pi$
$967$	95.1413	−	95.1413i	0.0983881	−	0.0983881i	0.754588	+	0.656199i	$0.227837\pi$
$968$	−2.23443	+	8.33902i	−0.00230830	+	0.00861469i
$969$	−268.210	−	154.851i	−0.276791	−	0.159805i
$970$	−533.172	+	519.239i	−0.549661	+	0.535297i
$971$	−541.576	−	938.036i	−0.557750	−	0.966052i	−0.997684	−	0.0680216i	$-0.978331\pi$
$971$	−541.576	−	938.036i	−0.557750	−	0.966052i	0.439934	−	0.898030i	$-0.355002\pi$
$972$	−46.1072	+	46.1072i	−0.0474354	+	0.0474354i
$973$	354.373	+	65.2234i	0.364207	+	0.0670333i
$974$		−	1291.82i		−	1.32630i
$975$	−1778.54	−	47.1009i	−1.82415	−	0.0483086i
$976$	42.8786	−	74.2678i	0.0439329	−	0.0760941i
$977$	492.348	+	1837.47i	0.503939	+	1.88072i	0.472722	+	0.881212i	$0.343271\pi$
$977$	492.348	+	1837.47i	0.503939	+	1.88072i	0.0312166	+	0.999513i	$0.490062\pi$
$978$	−361.144	+	1347.81i	−0.369268	+	1.37813i
$979$			84.3878i			0.0861980i
$980$	−393.299	−	292.260i	−0.401326	−	0.298224i
$981$	3090.30			3.15015
$982$	1209.53	+	324.093i	1.23170	+	0.330034i
$983$	916.515	−	245.579i	0.932365	−	0.249826i	0.239502	−	0.970896i	$-0.423016\pi$
$983$	916.515	−	245.579i	0.932365	−	0.249826i	0.692863	+	0.721069i	$0.256349\pi$
$984$	−117.609	−	67.9013i	−0.119521	−	0.0690054i
$985$	−475.640	+	799.210i	−0.482884	+	0.811380i
$986$	364.096			0.369265
$987$	−58.6694	+	318.763i	−0.0594421	+	0.322962i
$988$	−128.746	−	128.746i	−0.130309	−	0.130309i
$989$	1923.67	−	1110.63i	1.94506	−	1.12298i
$990$	−19.1208	+	1444.27i	−0.0193140	+	1.45886i
$991$	898.430	−	1556.13i	0.906590	−	1.57026i	0.0878205	−	0.996136i	$-0.472010\pi$
$991$	898.430	−	1556.13i	0.906590	−	1.57026i	0.818769	−	0.574123i	$-0.194657\pi$
$992$	130.087	+	34.8566i	0.131136	+	0.0351377i
$993$	522.700	+	522.700i	0.526385	+	0.526385i
$994$	430.115	−	904.649i	0.432712	−	0.910110i
$995$	1177.27	+	332.213i	1.18319	+	0.333883i
$996$	−210.624	−	364.811i	−0.211470	−	0.366277i
$997$	−126.473	−	472.003i	−0.126853	−	0.473423i	0.873046	−	0.487639i	$-0.162142\pi$
$997$	−126.473	−	472.003i	−0.126853	−	0.473423i	−0.999899	+	0.0142155i	$0.995475\pi$
$998$	882.525	−	236.472i	0.884294	−	0.236946i
$999$	655.997	−	378.740i	0.656654	−	0.379119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.l.c.53.1	yes	16
5.2	odd	4	inner	70.3.l.c.67.4	yes	16
5.3	odd	4		350.3.p.e.207.1		16
5.4	even	2		350.3.p.e.193.4		16
7.2	even	3	inner	70.3.l.c.23.4	✓	16
7.3	odd	6		490.3.f.p.393.1		8
7.4	even	3		490.3.f.o.393.4		8
35.2	odd	12	inner	70.3.l.c.37.1	yes	16
35.9	even	6		350.3.p.e.93.1		16
35.17	even	12		490.3.f.p.197.1		8
35.23	odd	12		350.3.p.e.107.4		16
35.32	odd	12		490.3.f.o.197.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.4	✓	16	7.2	even	3	inner
70.3.l.c.37.1	yes	16	35.2	odd	12	inner
70.3.l.c.53.1	yes	16	1.1	even	1	trivial
70.3.l.c.67.4	yes	16	5.2	odd	4	inner
350.3.p.e.93.1		16	35.9	even	6
350.3.p.e.107.4		16	35.23	odd	12
350.3.p.e.193.4		16	5.4	even	2
350.3.p.e.207.1		16	5.3	odd	4
490.3.f.o.197.4		8	35.32	odd	12
490.3.f.o.393.4		8	7.4	even	3
490.3.f.p.197.1		8	35.17	even	12
490.3.f.p.393.1		8	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-5.05060 + 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.84634 - 1.23005i) q^{5} +7.39459 q^{6} +(1.26709 - 6.88437i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-5.05060 + 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.84634 - 1.23005i) q^{5} +7.39459 q^{6} +(1.26709 - 6.88437i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +(-7.07045 - 0.0936064i) q^{10} +(5.56894 - 9.64568i) q^{11} +(-10.1012 - 2.70661i) q^{12} +(9.62415 + 9.62415i) q^{13} +(-4.25073 + 8.94043i) q^{14} +(-22.8123 + 12.7710i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-2.29193 - 8.55361i) q^{17} +(-25.0529 + 6.71290i) q^{18} +(-5.79257 + 3.34434i) q^{19} +(9.62415 + 2.71583i) q^{20} +(2.91708 + 36.4849i) q^{21} +(-11.1379 + 11.1379i) q^{22} +(7.37457 - 27.5223i) q^{23} +(12.8078 + 7.39459i) q^{24} +(21.9740 - 11.9224i) q^{25} +(-9.62415 - 16.6695i) q^{26} +(-34.5327 + 34.5327i) q^{27} +(9.07903 - 10.6570i) q^{28} -29.0733i q^{29} +(35.8367 - 9.09570i) q^{30} +(-11.9038 + 20.6179i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-15.0729 + 56.2529i) q^{33} +12.5233i q^{34} +(-2.32736 - 34.9225i) q^{35} +36.6800 q^{36} +(-14.9820 - 4.01442i) q^{37} +(9.13690 - 2.44823i) q^{38} +(-61.6321 - 35.5833i) q^{39} +(-12.1528 - 7.23258i) q^{40} -9.18256 q^{41} +(9.36960 - 50.9071i) q^{42} +(55.1244 + 55.1244i) q^{43} +(19.2914 - 11.1379i) q^{44} +(65.6943 - 63.9776i) q^{45} +(-20.1477 + 34.8968i) q^{46} +(8.55361 + 2.29193i) q^{47} +(-14.7892 - 14.7892i) q^{48} +(-45.7890 - 17.4462i) q^{49} +(-34.3809 + 8.24334i) q^{50} +(23.1513 + 40.0992i) q^{51} +(7.04537 + 26.2937i) q^{52} +(13.8047 - 3.69897i) q^{53} +(59.8123 - 34.5327i) q^{54} +(15.1243 - 53.5963i) q^{55} +(-16.3029 + 11.2346i) q^{56} +(24.7300 - 24.7300i) q^{57} +(-10.6416 + 39.7149i) q^{58} +(67.7986 + 39.1435i) q^{59} +(-52.2831 - 0.692181i) q^{60} +(-10.7196 - 18.5670i) q^{61} +(23.8075 - 23.8075i) q^{62} +(-43.0045 - 120.963i) q^{63} +8.00000i q^{64} +(58.4800 + 34.8037i) q^{65} +(41.1800 - 71.3259i) q^{66} +(13.7678 + 51.3823i) q^{67} +(4.58386 - 17.1072i) q^{68} +148.984i q^{69} +(-9.60330 + 48.5569i) q^{70} -101.186 q^{71} +(-50.1058 - 13.4258i) q^{72} +(-101.181 + 27.1115i) q^{73} +(18.9964 + 10.9676i) q^{74} +(-94.8470 + 89.9530i) q^{75} -13.3774 q^{76} +(-59.3481 - 50.5605i) q^{77} +(71.1666 + 71.1666i) q^{78} +(-11.7992 + 6.81228i) q^{79} +(13.9537 + 14.3281i) q^{80} +(45.1475 - 78.1978i) q^{81} +(12.5436 + 3.36105i) q^{82} +(28.4835 + 28.4835i) q^{83} +(-31.4324 + 66.1108i) q^{84} +(-21.6288 - 38.6345i) q^{85} +(-55.1244 - 95.4783i) q^{86} +(39.3451 + 146.838i) q^{87} +(-30.4292 + 8.15349i) q^{88} +(-6.56157 + 3.78833i) q^{89} +(-113.158 + 63.3492i) q^{90} +(78.4508 - 54.0615i) q^{91} +(40.2954 - 40.2954i) q^{92} +(32.2188 - 120.242i) q^{93} +(-10.8455 - 6.26167i) q^{94} +(-23.9590 + 23.3329i) q^{95} +(14.7892 + 25.6156i) q^{96} +(74.4232 - 74.4232i) q^{97} +(56.1632 + 40.5919i) q^{98} -204.268i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8	\( 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8} - 6 q^{10} + 40 q^{11} + 4 q^{12} + 16 q^{13} - 20 q^{15} + 32 q^{16} + 46 q^{17} - 52 q^{18} + 16 q^{20} - 20 q^{21} - 80 q^{22} + 54 q^{23} - 26 q^{25} - 16 q^{26} - 52 q^{27} - 36 q^{28} - 22 q^{30} - 208 q^{31} + 32 q^{32} - 22 q^{33} + 50 q^{35} + 208 q^{36} - 38 q^{37} + 36 q^{38} - 4 q^{40} - 72 q^{41} + 184 q^{42} + 144 q^{43} + 254 q^{45} + 108 q^{46} + 46 q^{47} + 16 q^{48} - 60 q^{50} - 136 q^{51} - 16 q^{52} + 30 q^{53} - 192 q^{55} - 48 q^{56} - 492 q^{57} + 132 q^{58} - 64 q^{60} - 120 q^{61} + 416 q^{62} - 292 q^{63} + 230 q^{65} - 44 q^{66} - 74 q^{67} - 92 q^{68} - 162 q^{70} + 16 q^{71} - 104 q^{72} - 54 q^{73} + 300 q^{75} - 144 q^{76} + 570 q^{77} + 168 q^{78} + 8 q^{80} + 244 q^{81} + 36 q^{82} + 64 q^{83} + 544 q^{85} - 144 q^{86} - 236 q^{87} - 80 q^{88} - 1048 q^{90} + 336 q^{91} - 216 q^{92} + 142 q^{93} - 396 q^{95} - 16 q^{96} + 136 q^{97} - 268 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8 - 6 * q^10 + 40 * q^11 + 4 * q^12 + 16 * q^13 - 20 * q^15 + 32 * q^16 + 46 * q^17 - 52 * q^18 + 16 * q^20 - 20 * q^21 - 80 * q^22 + 54 * q^23 - 26 * q^25 - 16 * q^26 - 52 * q^27 - 36 * q^28 - 22 * q^30 - 208 * q^31 + 32 * q^32 - 22 * q^33 + 50 * q^35 + 208 * q^36 - 38 * q^37 + 36 * q^38 - 4 * q^40 - 72 * q^41 + 184 * q^42 + 144 * q^43 + 254 * q^45 + 108 * q^46 + 46 * q^47 + 16 * q^48 - 60 * q^50 - 136 * q^51 - 16 * q^52 + 30 * q^53 - 192 * q^55 - 48 * q^56 - 492 * q^57 + 132 * q^58 - 64 * q^60 - 120 * q^61 + 416 * q^62 - 292 * q^63 + 230 * q^65 - 44 * q^66 - 74 * q^67 - 92 * q^68 - 162 * q^70 + 16 * q^71 - 104 * q^72 - 54 * q^73 + 300 * q^75 - 144 * q^76 + 570 * q^77 + 168 * q^78 + 8 * q^80 + 244 * q^81 + 36 * q^82 + 64 * q^83 + 544 * q^85 - 144 * q^86 - 236 * q^87 - 80 * q^88 - 1048 * q^90 + 336 * q^91 - 216 * q^92 + 142 * q^93 - 396 * q^95 - 16 * q^96 + 136 * q^97 - 268 * q^98

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