LMFDB - Embedded newform 120.4.v.a.43.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(43,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("120.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$120 = 2^{3} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	120.v (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.16
Character	$\chi$	$=$	120.43
Dual form			120.4.v.a.67.16

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.541804 + 2.77605i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-7.41290 - 3.00815i) q^{4} +(9.61270 + 5.70930i) q^{5} +(7.03823 - 4.73955i) q^{6} +(7.34859 + 7.34859i) q^{7} +(12.3671 - 18.9487i) q^{8} +9.00000i q^{9} +(-21.0575 + 23.5920i) q^{10} +14.6783 q^{11} +(9.34388 + 22.1064i) q^{12} +(-33.1544 + 33.1544i) q^{13} +(-24.3816 + 16.4186i) q^{14} +(-8.28036 - 32.5029i) q^{15} +(45.9021 + 44.5982i) q^{16} +(-92.1341 + 92.1341i) q^{17} +(-24.9844 - 4.87624i) q^{18} +118.923i q^{19} +(-54.0835 - 71.2389i) q^{20} -31.1774i q^{21} +(-7.95276 + 40.7477i) q^{22} +(54.6543 - 54.6543i) q^{23} +(-66.4309 + 13.9617i) q^{24} +(59.8079 + 109.763i) q^{25} +(-74.0749 - 110.001i) q^{26} +(19.0919 - 19.0919i) q^{27} +(-32.3687 - 76.5800i) q^{28} -48.5611 q^{29} +(94.7159 - 5.37651i) q^{30} -223.074i q^{31} +(-148.677 + 103.263i) q^{32} +(-31.1374 - 31.1374i) q^{33} +(-205.850 - 305.687i) q^{34} +(28.6845 + 112.595i) q^{35} +(27.0733 - 66.7161i) q^{36} +(239.614 + 239.614i) q^{37} +(-330.136 - 64.4330i) q^{38} +140.662 q^{39} +(227.065 - 111.541i) q^{40} -1.44144 q^{41} +(86.5501 + 16.8921i) q^{42} +(301.529 + 301.529i) q^{43} +(-108.809 - 44.1545i) q^{44} +(-51.3837 + 86.5143i) q^{45} +(122.111 + 181.335i) q^{46} +(34.2470 + 34.2470i) q^{47} +(-2.76592 - 191.980i) q^{48} -234.996i q^{49} +(-337.113 + 106.559i) q^{50} +390.892 q^{51} +(345.503 - 146.037i) q^{52} +(-75.1151 + 75.1151i) q^{53} +(42.6559 + 63.3441i) q^{54} +(141.098 + 83.8027i) q^{55} +(230.127 - 48.3657i) q^{56} +(252.274 - 252.274i) q^{57} +(26.3106 - 134.808i) q^{58} -237.059i q^{59} +(-36.3920 + 265.849i) q^{60} +109.300i q^{61} +(619.265 + 120.862i) q^{62} +(-66.1373 + 66.1373i) q^{63} +(-206.109 - 468.682i) q^{64} +(-507.991 + 129.415i) q^{65} +(103.309 - 69.5685i) q^{66} +(-297.916 + 297.916i) q^{67} +(960.134 - 405.827i) q^{68} -231.878 q^{69} +(-328.111 + 18.6251i) q^{70} -1136.64i q^{71} +(170.539 + 111.304i) q^{72} +(-152.188 - 152.188i) q^{73} +(-795.002 + 535.355i) q^{74} +(105.972 - 359.715i) q^{75} +(357.738 - 881.564i) q^{76} +(107.865 + 107.865i) q^{77} +(-76.2112 + 390.485i) q^{78} +688.560 q^{79} +(186.618 + 690.778i) q^{80} -81.0000 q^{81} +(0.780980 - 4.00152i) q^{82} +(-169.952 - 169.952i) q^{83} +(-93.7864 + 231.115i) q^{84} +(-1411.68 + 359.636i) q^{85} +(-1000.43 + 673.690i) q^{86} +(103.014 + 103.014i) q^{87} +(181.528 - 278.135i) q^{88} -892.041i q^{89} +(-212.328 - 189.517i) q^{90} -487.276 q^{91} +(-569.555 + 240.738i) q^{92} +(-473.212 + 473.212i) q^{93} +(-113.627 + 76.5162i) q^{94} +(-678.967 + 1143.17i) q^{95} +(534.445 + 96.3373i) q^{96} +(-1081.23 + 1081.23i) q^{97} +(652.361 + 127.322i) q^{98} +132.105i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 12 q^{6} + 84 q^{8} - 72 q^{10} + 24 q^{12} - 20 q^{16} - 104 q^{17} + 380 q^{20} + 44 q^{22} - 88 q^{25} - 368 q^{26} - 1068 q^{28} + 408 q^{30} + 340 q^{32} + 912 q^{35} - 108 q^{36} - 40 q^{38}+ \cdots + 7576 q^{98}+O(q^{100})$ 72 * q + 12 * q^6 + 84 * q^8 - 72 * q^10 + 24 * q^12 - 20 * q^16 - 104 * q^17 + 380 * q^20 + 44 * q^22 - 88 * q^25 - 368 * q^26 - 1068 * q^28 + 408 * q^30 + 340 * q^32 + 912 * q^35 - 108 * q^36 - 40 * q^38 - 952 * q^40 - 660 * q^42 + 864 * q^43 - 2256 * q^46 + 528 * q^48 - 344 * q^50 - 1488 * q^51 + 2544 * q^52 + 2144 * q^56 + 1004 * q^58 + 420 * q^60 + 2608 * q^62 - 1048 * q^65 + 1368 * q^66 + 3696 * q^67 - 1464 * q^68 + 204 * q^70 - 756 * q^72 + 1480 * q^73 - 4016 * q^76 - 72 * q^78 - 1684 * q^80 - 5832 * q^81 - 6712 * q^82 - 5360 * q^83 - 8416 * q^86 - 404 * q^88 + 108 * q^90 + 3392 * q^91 + 8432 * q^92 + 3828 * q^96 - 328 * q^97 + 7576 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$ .

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.541804	+	2.77605i	−0.191557	+	0.981482i
$2$	−0.541804	+	2.77605i	−0.191557	+	0.981482i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$	−7.41290	−	3.00815i	−0.926612	−	0.376019i
$5$	9.61270	+	5.70930i	0.859786	+	0.510655i
$5$	9.61270	+	5.70930i	0.859786	+	0.510655i
$6$	7.03823	−	4.73955i	0.478891	−	0.322485i
$7$	7.34859	+	7.34859i	0.396787	+	0.396787i	0.877098	−	0.480311i	$-0.159476\pi$
$7$	7.34859	+	7.34859i	0.396787	+	0.396787i	−0.480311	+	0.877098i	$0.659476\pi$
$8$	12.3671	−	18.9487i	0.546554	−	0.837424i
$9$			9.00000i			0.333333i
$10$	−21.0575	+	23.5920i	−0.665896	+	0.746044i
$11$	14.6783			0.402334			0.201167	−	0.979557i	$-0.435527\pi$
$11$	14.6783			0.402334			0.201167	+	0.979557i	$0.435527\pi$
$12$	9.34388	+	22.1064i	0.224779	+	0.531797i
$13$	−33.1544	+	33.1544i	−0.707336	+	0.707336i	−0.965974	−	0.258639i	$-0.916726\pi$
$13$	−33.1544	+	33.1544i	−0.707336	+	0.707336i	0.258639	+	0.965974i	$0.416726\pi$
$14$	−24.3816	+	16.4186i	−0.465446	+	0.313432i
$15$	−8.28036	−	32.5029i	−0.142532	−	0.559480i
$16$	45.9021	+	44.5982i	0.717220	+	0.696847i
$17$	−92.1341	+	92.1341i	−1.31446	+	1.31446i	−0.396366	+	0.918092i	$0.629729\pi$
$17$	−92.1341	+	92.1341i	−1.31446	+	1.31446i	−0.918092	+	0.396366i	$0.870271\pi$
$18$	−24.9844	−	4.87624i	−0.327161	−	0.0638522i
$19$			118.923i			1.43594i	0.696075	+	0.717969i	$0.254928\pi$
$19$			118.923i			1.43594i	−0.696075	+	0.717969i	$0.745072\pi$
$20$	−54.0835	−	71.2389i	−0.604672	−	0.796475i
$21$		−	31.1774i		−	0.323975i
$22$	−7.95276	+	40.7477i	−0.0770697	+	0.394883i
$23$	54.6543	−	54.6543i	0.495487	−	0.495487i	−0.414543	−	0.910030i	$-0.636058\pi$
$23$	54.6543	−	54.6543i	0.495487	−	0.495487i	0.910030	+	0.414543i	$0.136058\pi$
$24$	−66.4309	+	13.9617i	−0.565007	+	0.118747i
$25$	59.8079	+	109.763i	0.478463	+	0.878108i
$26$	−74.0749	−	110.001i	−0.558742	−	0.829732i
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$	−32.3687	−	76.5800i	−0.218468	−	0.516867i
$29$	−48.5611			−0.310951			−0.155475	−	0.987840i	$-0.549691\pi$
$29$	−48.5611			−0.310951			−0.155475	+	0.987840i	$0.549691\pi$
$30$	94.7159	−	5.37651i	0.576422	−	0.0327204i
$31$		−	223.074i		−	1.29243i	−0.763156	−	0.646214i	$-0.776351\pi$
$31$		−	223.074i		−	1.29243i	0.763156	−	0.646214i	$-0.223649\pi$
$32$	−148.677	+	103.263i	−0.821331	+	0.570452i
$33$	−31.1374	−	31.1374i	−0.164252	−	0.164252i
$34$	−205.850	−	305.687i	−1.03832	−	1.54191i
$35$	28.6845	+	112.595i	0.138530	+	0.543773i
$36$	27.0733	−	66.7161i	0.125340	−	0.308871i
$37$	239.614	+	239.614i	1.06465	+	1.06465i	0.997760	+	0.0668946i	$0.0213091\pi$
$37$	239.614	+	239.614i	1.06465	+	1.06465i	0.0668946	+	0.997760i	$0.478691\pi$
$38$	−330.136	−	64.4330i	−1.40935	−	0.275063i
$39$	140.662			0.577537
$40$	227.065	−	111.541i	0.897554	−	0.440904i
$41$	−1.44144			−0.00549062			−0.00274531	−	0.999996i	$-0.500874\pi$
$41$	−1.44144			−0.00549062			−0.00274531	+	0.999996i	$0.500874\pi$
$42$	86.5501	+	16.8921i	0.317975	+	0.0620596i
$43$	301.529	+	301.529i	1.06937	+	1.06937i	0.997408	+	0.0719593i	$0.0229252\pi$
$43$	301.529	+	301.529i	1.06937	+	1.06937i	0.0719593	+	0.997408i	$0.477075\pi$
$44$	−108.809	−	44.1545i	−0.372807	−	0.151285i
$45$	−51.3837	+	86.5143i	−0.170218	+	0.286595i
$46$	122.111	+	181.335i	0.391398	+	0.581225i
$47$	34.2470	+	34.2470i	0.106286	+	0.106286i	0.758250	−	0.651964i	$-0.226055\pi$
$47$	34.2470	+	34.2470i	0.106286	+	0.106286i	−0.651964	+	0.758250i	$0.726055\pi$
$48$	−2.76592	−	191.980i	−0.00831722	−	0.577290i
$49$		−	234.996i		−	0.685121i
$50$	−337.113	+	106.559i	−0.953499	+	0.301395i
$51$	390.892			1.07325
$52$	345.503	−	146.037i	0.921397	−	0.389454i
$53$	−75.1151	+	75.1151i	−0.194676	+	0.194676i	−0.797713	−	0.603037i	$-0.793957\pi$
$53$	−75.1151	+	75.1151i	−0.194676	+	0.194676i	0.603037	+	0.797713i	$0.293957\pi$
$54$	42.6559	+	63.3441i	0.107495	+	0.159630i
$55$	141.098	+	83.8027i	0.345921	+	0.205454i
$56$	230.127	−	48.3657i	0.549144	−	0.115413i
$57$	252.274	−	252.274i	0.586219	−	0.586219i
$58$	26.3106	−	134.808i	0.0595647	−	0.305192i
$59$		−	237.059i		−	0.523091i	−0.965191	−	0.261546i	$-0.915768\pi$
$59$		−	237.059i		−	0.523091i	0.965191	−	0.261546i	$-0.0842322\pi$
$60$	−36.3920	+	265.849i	−0.0783031	+	0.572016i
$61$			109.300i			0.229417i	0.993399	+	0.114709i	$0.0365935\pi$
$61$			109.300i			0.229417i	−0.993399	+	0.114709i	$0.963407\pi$
$62$	619.265	+	120.862i	1.26850	+	0.247573i
$63$	−66.1373	+	66.1373i	−0.132262	+	0.132262i
$64$	−206.109	−	468.682i	−0.402557	−	0.915395i
$65$	−507.991	+	129.415i	−0.969361	+	0.246953i
$66$	103.309	−	69.5685i	0.192674	−	0.129747i
$67$	−297.916	+	297.916i	−0.543227	+	0.543227i	−0.924473	−	0.381246i	$-0.875495\pi$
$67$	−297.916	+	297.916i	−0.543227	+	0.543227i	0.381246	+	0.924473i	$0.375495\pi$
$68$	960.134	−	405.827i	1.71225	−	0.723732i
$69$	−231.878			−0.404563
$70$	−328.111	+	18.6251i	−0.560239	+	0.0318018i
$71$		−	1136.64i		−	1.89991i	−0.312382	−	0.949957i	$-0.601127\pi$
$71$		−	1136.64i		−	1.89991i	0.312382	−	0.949957i	$-0.398873\pi$
$72$	170.539	+	111.304i	0.279141	+	0.182185i
$73$	−152.188	−	152.188i	−0.244003	−	0.244003i	0.574501	−	0.818504i	$-0.305196\pi$
$73$	−152.188	−	152.188i	−0.244003	−	0.244003i	−0.818504	+	0.574501i	$0.805196\pi$
$74$	−795.002	+	535.355i	−1.24888	+	0.840997i
$75$	105.972	−	359.715i	0.163154	−	0.553818i
$76$	357.738	−	881.564i	0.539939	−	1.33056i
$77$	107.865	+	107.865i	0.159641	+	0.159641i
$78$	−76.2112	+	390.485i	−0.110631	+	0.566842i
$79$	688.560			0.980621			0.490310	−	0.871548i	$-0.336883\pi$
$79$	688.560			0.980621			0.490310	+	0.871548i	$0.336883\pi$
$80$	186.618	+	690.778i	0.260807	+	0.965391i
$81$	−81.0000			−0.111111
$82$	0.780980	−	4.00152i	0.00105177	−	0.00538895i
$83$	−169.952	−	169.952i	−0.224755	−	0.224755i	0.585742	−	0.810497i	$-0.300803\pi$
$83$	−169.952	−	169.952i	−0.224755	−	0.224755i	−0.810497	+	0.585742i	$0.800803\pi$
$84$	−93.7864	+	231.115i	−0.121821	+	0.300199i
$85$	−1411.68	+	359.636i	−1.80139	+	0.458918i
$86$	−1000.43	+	673.690i	−1.25441	+	0.844719i
$87$	103.014	+	103.014i	0.126945	+	0.126945i
$88$	181.528	−	278.135i	0.219897	−	0.336924i
$89$		−	892.041i		−	1.06243i	−0.847237	−	0.531214i	$-0.821736\pi$
$89$		−	892.041i		−	1.06243i	0.847237	−	0.531214i	$-0.178264\pi$
$90$	−212.328	−	189.517i	−0.248681	−	0.221965i
$91$	−487.276			−0.561323
$92$	−569.555	+	240.738i	−0.645437	+	0.272812i
$93$	−473.212	+	473.212i	−0.527632	+	0.527632i
$94$	−113.627	+	76.5162i	−0.124677	+	0.0839579i
$95$	−678.967	+	1143.17i	−0.733269	+	1.23460i
$96$	534.445	+	96.3373i	0.568193	+	0.102421i
$97$	−1081.23	+	1081.23i	−1.13177	+	1.13177i	−0.141891	+	0.989882i	$0.545318\pi$
$97$	−1081.23	+	1081.23i	−1.13177	+	1.13177i	−0.989882	+	0.141891i	$0.954682\pi$
$98$	652.361	+	127.322i	0.672433	+	0.131239i
$99$			132.105i			0.134111i
$100$	−113.165	−	993.576i	−0.113165	−	0.993576i
$101$		−	404.610i		−	0.398616i	−0.979937	−	0.199308i	$-0.936131\pi$
$101$		−	404.610i		−	0.398616i	0.979937	−	0.199308i	$-0.0638694\pi$
$102$	−211.787	+	1085.13i	−0.205588	+	1.05338i
$103$	843.889	−	843.889i	0.807290	−	0.807290i	−0.176933	−	0.984223i	$-0.556618\pi$
$103$	843.889	−	843.889i	0.807290	−	0.807290i	0.984223	+	0.176933i	$0.0566176\pi$
$104$	218.210	+	1038.26i	0.205742	+	0.978937i
$105$	178.001	−	299.699i	0.165439	−	0.278549i
$106$	−167.825	−	249.221i	−0.153780	−	0.228363i
$107$	584.343	−	584.343i	0.527949	−	0.527949i	−0.392011	−	0.919960i	$-0.628221\pi$
$107$	584.343	−	584.343i	0.527949	−	0.527949i	0.919960	+	0.392011i	$0.128221\pi$
$108$	−198.957	+	84.0949i	−0.177266	+	0.0749263i
$109$	1427.79			1.25465			0.627327	−	0.778756i	$-0.284149\pi$
$109$	1427.79			1.25465			0.627327	+	0.778756i	$0.284149\pi$
$110$	−309.088	+	346.290i	−0.267912	+	0.300159i
$111$		−	1016.59i		−	0.869287i
$112$	9.58160	+	665.050i	0.00808372	+	0.561083i
$113$	538.966	+	538.966i	0.448687	+	0.448687i	0.894918	−	0.446231i	$-0.147234\pi$
$113$	538.966	+	538.966i	0.448687	+	0.448687i	−0.446231	+	0.894918i	$0.647234\pi$
$114$	563.642	+	837.008i	0.463069	+	0.687657i
$115$	837.412	−	213.337i	0.679036	−	0.172990i
$116$	359.978	+	146.079i	0.288131	+	0.116923i
$117$	−298.389	−	298.389i	−0.235779	−	0.235779i
$118$	658.086	+	128.439i	0.513405	+	0.100202i
$119$	−1354.11			−1.04312
$120$	−718.292	−	245.064i	−0.546423	−	0.186426i
$121$	−1115.55			−0.838128
$122$	−303.423	−	59.2193i	−0.225169	−	0.0439464i
$123$	3.05776	+	3.05776i	0.00224154	+	0.00224154i
$124$	−671.040	+	1653.63i	−0.485977	+	1.19758i
$125$	−51.7573	+	1396.58i	−0.0370345	+	0.999314i
$126$	−147.767	−	219.434i	−0.104477	−	0.155149i
$127$	−325.122	−	325.122i	−0.227165	−	0.227165i	0.584342	−	0.811507i	$-0.301353\pi$
$127$	−325.122	−	325.122i	−0.227165	−	0.227165i	−0.811507	+	0.584342i	$0.801353\pi$
$128$	1412.76	−	318.235i	0.975556	−	0.219752i
$129$		−	1279.28i		−	0.873134i
$130$	−84.0301	−	1480.32i	−0.0566917	−	0.998716i
$131$	−559.021			−0.372839			−0.186419	−	0.982470i	$-0.559688\pi$
$131$	−559.021			−0.372839			−0.186419	+	0.982470i	$0.559688\pi$
$132$	137.152	+	324.484i	0.0904361	+	0.213960i
$133$	−873.917	+	873.917i	−0.569761	+	0.569761i
$134$	−665.617	−	988.441i	−0.429109	−	0.637226i
$135$	292.526	−	74.5233i	0.186493	−	0.0475107i
$136$	606.392	+	2885.26i	0.382336	+	1.81918i
$137$	1335.61	−	1335.61i	0.832914	−	0.832914i	−0.155001	−	0.987914i	$-0.549538\pi$
$137$	1335.61	−	1335.61i	0.832914	−	0.832914i	0.987914	+	0.155001i	$0.0495380\pi$
$138$	125.633	−	643.706i	0.0774968	−	0.397072i
$139$			2066.81i			1.26118i	0.776116	+	0.630590i	$0.217187\pi$
$139$			2066.81i			1.26118i	−0.776116	+	0.630590i	$0.782813\pi$
$140$	126.068	−	920.943i	0.0761047	−	0.555956i
$141$		−	145.298i		−	0.0867821i
$142$	3155.36	+	615.834i	1.86473	+	0.363941i
$143$	−486.649	+	486.649i	−0.284585	+	0.284585i
$144$	−401.384	+	413.119i	−0.232282	+	0.239073i
$145$	−466.803	−	277.250i	−0.267351	−	0.158789i
$146$	504.936	−	340.024i	0.286225	−	0.192744i
$147$	−498.503	+	498.503i	−0.279699	+	0.279699i
$148$	−1055.44	−	2497.02i	−0.586192	−	1.38685i
$149$	1984.93			1.09135			0.545677	−	0.837996i	$-0.316273\pi$
$149$	1984.93			1.09135			0.545677	+	0.837996i	$0.316273\pi$
$150$	941.171	+	489.078i	0.512309	+	0.266220i
$151$			1683.07i			0.907060i	0.891241	+	0.453530i	$0.149836\pi$
$151$			1683.07i			0.907060i	−0.891241	+	0.453530i	$0.850164\pi$
$152$	2253.44	+	1470.73i	1.20249	+	0.784818i
$153$	−829.207	−	829.207i	−0.438153	−	0.438153i
$154$	−357.879	+	240.996i	−0.187265	+	0.126104i
$155$	1273.60	−	2144.34i	0.659985	−	1.11121i
$156$	−1042.71	−	423.132i	−0.535153	−	0.217165i
$157$	−1106.71	−	1106.71i	−0.562579	−	0.562579i	0.367460	−	0.930039i	$-0.380227\pi$
$157$	−1106.71	−	1106.71i	−0.562579	−	0.562579i	−0.930039	+	0.367460i	$0.880227\pi$
$158$	−373.065	+	1911.48i	−0.187844	+	0.962461i
$159$	318.686			0.158953
$160$	−2018.74	+	143.796i	−0.997473	+	0.0710502i
$161$	803.264			0.393205
$162$	43.8861	−	224.860i	0.0212841	−	0.109054i
$163$	−743.159	−	743.159i	−0.357109	−	0.357109i	0.505637	−	0.862746i	$-0.331257\pi$
$163$	−743.159	−	743.159i	−0.357109	−	0.357109i	−0.862746	+	0.505637i	$0.831257\pi$
$164$	10.6853	+	4.33608i	0.00508768	+	0.00206458i
$165$	−121.542	−	477.086i	−0.0573454	−	0.225098i
$166$	563.875	−	379.714i	0.263646	−	0.177539i
$167$	−1496.20	−	1496.20i	−0.693288	−	0.693288i	0.269666	−	0.962954i	$-0.413087\pi$
$167$	−1496.20	−	1496.20i	−0.693288	−	0.693288i	−0.962954	+	0.269666i	$0.913087\pi$
$168$	−590.773	−	385.575i	−0.271304	−	0.177070i
$169$		−	1.42200i		−	0.000647246i
$170$	−233.515	−	4113.74i	−0.105352	−	1.85594i
$171$	−1070.31			−0.478646
$172$	−1328.16	−	3142.25i	−0.588786	−	1.39299i
$173$	2683.29	−	2683.29i	1.17923	−	1.17923i	0.199291	−	0.979940i	$-0.436136\pi$
$173$	2683.29	−	2683.29i	1.17923	−	1.17923i	0.979940	−	0.199291i	$-0.0638639\pi$
$174$	−341.784	+	230.158i	−0.148911	+	0.100277i
$175$	−367.103	+	1246.11i	−0.158574	+	0.538269i
$176$	673.764	+	654.625i	0.288562	+	0.280365i
$177$	−502.877	+	502.877i	−0.213551	+	0.213551i
$178$	2476.35	+	483.312i	1.04275	+	0.203515i
$179$		−	3005.96i		−	1.25517i	−0.778546	−	0.627587i	$-0.784043\pi$
$179$		−	3005.96i		−	1.25517i	0.778546	−	0.627587i	$-0.215957\pi$
$180$	641.150	−	486.752i	0.265492	−	0.201557i
$181$		−	609.852i		−	0.250442i	−0.992129	−	0.125221i	$-0.960036\pi$
$181$		−	609.852i		−	0.250442i	0.992129	−	0.125221i	$-0.0399639\pi$
$182$	264.008	−	1352.70i	0.107525	−	0.550928i
$183$	231.861	−	231.861i	0.0936592	−	0.0936592i
$184$	−359.714	−	1711.54i	−0.144122	−	0.685743i
$185$	935.307	+	3671.36i	0.371704	+	1.45905i
$186$	−1057.27	−	1570.05i	−0.416790	−	0.618932i
$187$	−1352.37	+	1352.37i	−0.528851	+	0.528851i
$188$	−150.849	−	356.890i	−0.0585203	−	0.138451i
$189$	280.597			0.107992
$190$	−2805.63	−	2504.22i	−1.07127	−	0.956185i
$191$			1609.74i			0.609827i	0.952380	+	0.304913i	$0.0986275\pi$
$191$			1609.74i			0.609827i	−0.952380	+	0.304913i	$0.901372\pi$
$192$	−557.001	+	1431.45i	−0.209365	+	0.538052i
$193$	2524.02	+	2524.02i	0.941363	+	0.941363i	0.998374	−	0.0570103i	$-0.0181568\pi$
$193$	2524.02	+	2524.02i	0.941363	+	0.941363i	−0.0570103	+	0.998374i	$0.518157\pi$
$194$	−2415.73	−	3587.35i	−0.894016	−	1.32761i
$195$	1352.14	+	803.081i	0.496558	+	0.294922i
$196$	−706.904	+	1742.00i	−0.257618	+	0.634841i
$197$	528.156	+	528.156i	0.191013	+	0.191013i	0.796134	−	0.605121i	$-0.206875\pi$
$197$	528.156	+	528.156i	0.191013	+	0.191013i	−0.605121	+	0.796134i	$0.706875\pi$
$198$	−366.729	−	71.5748i	−0.131628	−	0.0256899i
$199$	3932.63			1.40089			0.700443	−	0.713708i	$-0.252986\pi$
$199$	3932.63			1.40089			0.700443	+	0.713708i	$0.252986\pi$
$200$	2819.53	+	224.173i	0.996854	+	0.0792572i
$201$	1263.95			0.443543
$202$	1123.22	+	219.220i	0.391234	+	0.0763576i
$203$	−356.856	−	356.856i	−0.123381	−	0.123381i
$204$	−2897.64	−	1175.86i	−0.994487	−	0.403562i
$205$	−13.8562	−	8.22963i	−0.00472076	−	0.00280381i
$206$	1885.45	+	2799.90i	0.637698	+	0.946982i
$207$	491.888	+	491.888i	0.165162	+	0.165162i
$208$	−3000.48	+	43.2289i	−1.00022	+	0.0144105i
$209$			1745.59i			0.577726i
$210$	735.538	+	656.518i	0.241700	+	0.215734i
$211$	279.778			0.0912829			0.0456415	−	0.998958i	$-0.485467\pi$
$211$	279.778			0.0912829			0.0456415	+	0.998958i	$0.485467\pi$
$212$	782.777	−	330.863i	0.253591	−	0.107188i
$213$	−2411.17	+	2411.17i	−0.775636	+	0.775636i
$214$	1305.56	+	1938.76i	0.417040	+	0.619304i
$215$	1176.99	+	4620.03i	0.373349	+	1.46550i
$216$	−125.656	−	597.878i	−0.0395823	−	0.188336i
$217$	1639.28	−	1639.28i	0.512819	−	0.512819i
$218$	−773.582	+	3963.61i	−0.240338	+	1.23142i
$219$			645.677i			0.199228i
$220$	−793.853	−	1045.66i	−0.243280	−	0.320449i
$221$		−	6109.29i		−	1.85953i
$222$	2822.12	+	550.795i	0.853189	+	0.166518i
$223$	−751.879	+	751.879i	−0.225783	+	0.225783i	−0.810928	−	0.585146i	$-0.801037\pi$
$223$	−751.879	+	751.879i	−0.225783	+	0.225783i	0.585146	+	0.810928i	$0.301037\pi$
$224$	−1851.40	−	333.728i	−0.552241	−	0.0995452i
$225$	−987.871	+	538.271i	−0.292703	+	0.159488i
$226$	−1788.21	+	1204.18i	−0.526327	+	0.354429i
$227$	−2729.51	+	2729.51i	−0.798079	+	0.798079i	−0.982792	−	0.184713i	$-0.940864\pi$
$227$	−2729.51	+	2729.51i	−0.798079	+	0.798079i	0.184713	+	0.982792i	$0.440864\pi$
$228$	−2628.96	+	1111.20i	−0.763627	+	0.322768i
$229$	3140.94			0.906373			0.453187	−	0.891416i	$-0.350287\pi$
$229$	3140.94			0.906373			0.453187	+	0.891416i	$0.350287\pi$
$230$	138.522	+	2440.28i	0.0397124	+	0.699598i
$231$		−	457.631i		−	0.130346i
$232$	−600.560	+	920.171i	−0.169951	+	0.260397i
$233$	4230.86	+	4230.86i	1.18958	+	1.18958i	0.977182	+	0.212402i	$0.0681286\pi$
$233$	4230.86	+	4230.86i	1.18958	+	1.18958i	0.212402	+	0.977182i	$0.431871\pi$
$234$	990.011	−	666.674i	0.276577	−	0.186247i
$235$	133.680	+	524.732i	0.0371077	+	0.145659i
$236$	−713.108	+	1757.29i	−0.196692	+	0.484703i
$237$	−1460.66	−	1460.66i	−0.400337	−	0.400337i
$238$	733.663	−	3759.08i	0.199817	−	1.02380i
$239$	−4829.56			−1.30710			−0.653552	−	0.756881i	$-0.726722\pi$
$239$	−4829.56			−1.30710			−0.653552	+	0.756881i	$0.726722\pi$
$240$	1069.48	−	1861.24i	0.287645	−	0.500593i
$241$	1407.79			0.376281			0.188141	−	0.982142i	$-0.439754\pi$
$241$	1407.79			0.376281			0.188141	+	0.982142i	$0.439754\pi$
$242$	604.408	−	3096.82i	0.160549	−	0.822607i
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$	328.791	−	810.231i	0.0862652	−	0.212581i
$245$	1341.66	−	2258.95i	0.349860	−	0.589057i
$246$	−10.1452	+	6.83179i	−0.00262941	+	0.00177065i
$247$	−3942.82	−	3942.82i	−1.01569	−	1.01569i
$248$	−4226.97	−	2758.78i	−1.08231	−	0.706382i
$249$			721.045i			0.183511i
$250$	−3848.94	−	900.356i	−0.973714	−	0.227774i
$251$	−893.910			−0.224793			−0.112397	−	0.993663i	$-0.535853\pi$
$251$	−893.910			−0.224793			−0.112397	+	0.993663i	$0.535853\pi$
$252$	689.220	−	291.318i	0.172289	−	0.0728227i
$253$	802.231	−	802.231i	0.199351	−	0.199351i
$254$	1078.71	−	726.402i	0.266473	−	0.179443i
$255$	3757.52	+	2231.72i	0.922766	+	0.548061i
$256$	118.001	+	4094.30i	0.0288087	+	0.999585i
$257$	−975.692	+	975.692i	−0.236817	+	0.236817i	−0.815531	−	0.578714i	$-0.803555\pi$
$257$	−975.692	+	975.692i	−0.236817	+	0.236817i	0.578714	+	0.815531i	$0.303555\pi$
$258$	3551.34	+	693.119i	0.856965	+	0.167255i
$259$			3521.64i			0.844882i
$260$	4154.98	+	568.774i	0.991081	+	0.135669i
$261$		−	437.050i		−	0.103650i
$262$	302.880	−	1551.87i	0.0714197	−	0.365934i
$263$	−3067.51	+	3067.51i	−0.719204	+	0.719204i	−0.968442	−	0.249238i	$-0.919820\pi$
$263$	−3067.51	+	3067.51i	−0.719204	+	0.719204i	0.249238	+	0.968442i	$0.419820\pi$
$264$	−975.093	+	204.934i	−0.227321	+	0.0477759i
$265$	−1150.91	+	293.204i	−0.266792	+	0.0679675i
$266$	−1952.54	−	2899.53i	−0.450068	−	0.668351i
$267$	−1892.30	+	1892.30i	−0.433735	+	0.433735i
$268$	3104.60	−	1312.24i	0.707624	−	0.299097i
$269$	6962.20			1.57804			0.789021	−	0.614367i	$-0.210588\pi$
$269$	6962.20			1.57804			0.789021	+	0.614367i	$0.210588\pi$
$270$	48.3886	+	852.443i	0.0109068	+	0.192141i
$271$			3058.92i			0.685669i	0.939396	+	0.342835i	$0.111387\pi$
$271$			3058.92i			0.685669i	−0.939396	+	0.342835i	$0.888613\pi$
$272$	−8338.16	+	120.131i	−1.85873	+	0.0267794i
$273$	1033.67	+	1033.67i	0.229159	+	0.229159i
$274$	2984.09	+	4431.37i	0.657939	+	0.977040i
$275$	877.877	+	1611.14i	0.192502	+	0.353292i
$276$	1718.89	+	697.525i	0.374873	+	0.152123i
$277$	−5084.37	−	5084.37i	−1.10285	−	1.10285i	−0.994065	−	0.108788i	$-0.965303\pi$
$277$	−5084.37	−	5084.37i	−1.10285	−	1.10285i	−0.108788	−	0.994065i	$-0.534697\pi$
$278$	−5737.55	−	1119.80i	−1.23783	−	0.241588i
$279$	2007.67			0.430810
$280$	2488.28	+	848.941i	0.531083	+	0.181193i
$281$	−6551.57			−1.39087			−0.695434	−	0.718590i	$-0.744788\pi$
$281$	−6551.57			−1.39087			−0.695434	+	0.718590i	$0.744788\pi$
$282$	403.354	+	78.7229i	0.0851750	+	0.0166237i
$283$	−5196.89	−	5196.89i	−1.09160	−	1.09160i	−0.995358	−	0.0962430i	$-0.969317\pi$
$283$	−5196.89	−	5196.89i	−1.09160	−	1.09160i	−0.0962430	−	0.995358i	$-0.530683\pi$
$284$	−3419.17	+	8425.76i	−0.714403	+	1.76048i
$285$	3865.34	−	984.726i	0.803379	−	0.204667i
$286$	−1087.29	−	1614.63i	−0.224801	−	0.333829i
$287$	−10.5926	−	10.5926i	−0.00217861	−	0.00217861i
$288$	−929.366	−	1338.09i	−0.190151	−	0.273777i
$289$		−	12064.4i		−	2.45560i
$290$	1022.57	−	1145.65i	0.207061	−	0.231983i
$291$	4587.26			0.924089
$292$	670.348	+	1585.95i	0.134346	+	0.317846i
$293$	−5584.74	+	5584.74i	−1.11353	+	1.11353i	−0.120859	+	0.992670i	$0.538565\pi$
$293$	−5584.74	+	5584.74i	−1.11353	+	1.11353i	−0.992670	+	0.120859i	$0.961435\pi$
$294$	−1113.78	−	1653.96i	−0.220941	−	0.328098i
$295$	1353.44	−	2278.77i	0.267119	−	0.449747i
$296$	7503.70	−	1577.05i	1.47346	−	0.309676i
$297$	280.236	−	280.236i	0.0547507	−	0.0547507i
$298$	−1075.44	+	5510.26i	−0.209056	+	1.07114i
$299$			3624.05i			0.700951i
$300$	−1867.64	+	2347.75i	−0.359427	+	0.451825i
$301$			4431.63i			0.848621i
$302$	−4672.28	−	911.893i	−0.890263	−	0.173753i
$303$	−858.308	+	858.308i	−0.162734	+	0.162734i
$304$	−5303.75	+	5458.81i	−1.00063	+	1.02988i
$305$	−624.027	+	1050.67i	−0.117153	+	0.197250i
$306$	2751.19	−	1852.65i	0.513970	−	0.346108i
$307$	1811.67	−	1811.67i	0.336800	−	0.336800i	−0.518362	−	0.855161i	$-0.673458\pi$
$307$	1811.67	−	1811.67i	0.336800	−	0.336800i	0.855161	+	0.518362i	$0.173458\pi$
$308$	−475.117	−	1124.06i	−0.0878971	−	0.207953i
$309$	−3580.32			−0.659149
$310$	5262.76	+	4697.38i	0.964209	+	0.860623i
$311$		−	3672.46i		−	0.669601i	−0.942289	−	0.334801i	$-0.891331\pi$
$311$		−	3672.46i		−	0.669601i	0.942289	−	0.334801i	$-0.108669\pi$
$312$	1739.58	−	2665.37i	0.315655	−	0.483643i
$313$	974.139	+	974.139i	0.175916	+	0.175916i	0.789573	−	0.613657i	$-0.210302\pi$
$313$	974.139	+	974.139i	0.175916	+	0.175916i	−0.613657	+	0.789573i	$0.710302\pi$
$314$	3671.89	−	2472.66i	0.659927	−	0.444395i
$315$	−1013.36	+	258.160i	−0.181258	+	0.0461768i
$316$	−5104.22	−	2071.29i	−0.908655	−	0.368732i
$317$	6777.25	+	6777.25i	1.20078	+	1.20078i	0.973928	+	0.226855i	$0.0728444\pi$
$317$	6777.25	+	6777.25i	1.20078	+	1.20078i	0.226855	+	0.973928i	$0.427156\pi$
$318$	−172.665	+	884.689i	−0.0304484	+	0.156009i
$319$	−712.794			−0.125106
$320$	694.580	−	5682.04i	0.121338	−	0.992611i
$321$	−2479.16			−0.431069
$322$	−435.212	+	2229.90i	−0.0753211	+	0.385924i
$323$	−10956.9	−	10956.9i	−1.88748	−	1.88748i
$324$	600.445	+	243.660i	0.102957	+	0.0417799i
$325$	−5622.03	−	1656.25i	−0.959551	−	0.282683i
$326$	2465.69	−	1660.40i	0.418902	−	0.282089i
$327$	−3028.80	−	3028.80i	−0.512211	−	0.512211i
$328$	−17.8265	+	27.3135i	−0.00300092	+	0.00459798i
$329$			503.335i			0.0843457i
$330$	1390.27	−	78.9180i	0.231914	−	0.0131645i
$331$	8878.68			1.47437			0.737185	−	0.675691i	$-0.236155\pi$
$331$	8878.68			1.47437			0.737185	+	0.675691i	$0.236155\pi$
$332$	748.595	+	1771.08i	0.123748	+	0.292772i
$333$	−2156.52	+	2156.52i	−0.354885	+	0.354885i
$334$	4964.16	−	3342.87i	0.813253	−	0.547645i
$335$	−4564.67	+	1162.88i	−0.744461	+	0.189657i
$336$	1390.46	−	1431.11i	0.225761	−	0.232361i
$337$	5997.91	−	5997.91i	0.969517	−	0.969517i	−0.0300319	−	0.999549i	$-0.509561\pi$
$337$	5997.91	−	5997.91i	0.969517	−	0.969517i	0.999549	+	0.0300319i	$0.00956090\pi$
$338$	3.94754	+	0.770445i	0.000635260	+	0.000123984i
$339$		−	2286.64i		−	0.366352i
$340$	11546.5	+	1580.59i	1.84175	+	0.252117i
$341$		−	3274.35i		−	0.519988i
$342$	579.897	−	2971.23i	0.0916878	−	0.469782i
$343$	4247.46	−	4247.46i	0.668633	−	0.668633i
$344$	9442.64	−	1984.55i	1.47998	−	0.311046i
$345$	−2228.98	−	1323.86i	−0.347838	−	0.206592i
$346$	5995.13	+	8902.77i	0.931504	+	1.38328i
$347$	2605.13	−	2605.13i	0.403029	−	0.403029i	−0.476270	−	0.879299i	$-0.658012\pi$
$347$	2605.13	−	2605.13i	0.403029	−	0.403029i	0.879299	+	0.476270i	$0.158012\pi$
$348$	−453.749	−	1073.51i	−0.0698951	−	0.165363i
$349$	3306.01			0.507068			0.253534	−	0.967327i	$-0.418407\pi$
$349$	3306.01			0.507068			0.253534	+	0.967327i	$0.418407\pi$
$350$	−3260.37	−	1694.24i	−0.497925	−	0.258746i
$351$			1265.96i			0.192512i
$352$	−2182.32	+	1515.72i	−0.330449	+	0.229512i
$353$	−2627.08	−	2627.08i	−0.396105	−	0.396105i	0.480751	−	0.876857i	$-0.340364\pi$
$353$	−2627.08	−	2627.08i	−0.396105	−	0.396105i	−0.876857	+	0.480751i	$0.840364\pi$
$354$	−1123.55	−	1668.47i	−0.168689	−	0.250504i
$355$	6489.39	−	10926.1i	0.970200	−	1.63352i
$356$	−2683.39	+	6612.61i	−0.399493	+	0.984459i
$357$	2872.51	+	2872.51i	0.425852	+	0.425852i
$358$	8344.70	+	1628.64i	1.23193	+	0.240437i
$359$	1656.98			0.243599			0.121799	−	0.992555i	$-0.461134\pi$
$359$	1656.98			0.243599			0.121799	+	0.992555i	$0.461134\pi$
$360$	1003.87	+	2043.59i	0.146968	+	0.299185i
$361$	−7283.69			−1.06192
$362$	1692.98	+	330.420i	0.245804	+	0.0479738i
$363$	2366.43	+	2366.43i	0.342164	+	0.342164i
$364$	3612.12	+	1465.80i	0.520128	+	0.211068i
$365$	−594.049	−	2331.82i	−0.0851889	−	0.334392i
$366$	518.034	+	769.280i	0.0739838	+	0.109866i
$367$	−2930.84	−	2930.84i	−0.416863	−	0.416863i	0.467258	−	0.884121i	$-0.345242\pi$
$367$	−2930.84	−	2930.84i	−0.416863	−	0.416863i	−0.884121	+	0.467258i	$0.845242\pi$
$368$	4946.23	−	71.2620i	0.700652	−	0.0100945i
$369$		−	12.9730i		−	0.00183021i
$370$	−10698.6	+	607.303i	−1.50323	+	0.0853302i
$371$	−1103.98			−0.154490
$372$	4931.36	−	2084.38i	0.687310	−	0.290511i
$373$	−9879.71	+	9879.71i	−1.37145	+	1.37145i	−0.513159	+	0.858294i	$0.671525\pi$
$373$	−9879.71	+	9879.71i	−1.37145	+	1.37145i	−0.858294	+	0.513159i	$0.828475\pi$
$374$	−3021.53	−	4486.97i	−0.417753	−	0.620363i
$375$	3072.40	−	2852.81i	0.423087	−	0.392849i
$376$	1072.47	−	225.401i	0.147097	−	0.0309153i
$377$	1610.01	−	1610.01i	0.219946	−	0.219946i
$378$	−152.029	+	778.951i	−0.0206865	+	0.105992i
$379$		−	7361.60i		−	0.997731i	−0.866679	−	0.498865i	$-0.833750\pi$
$379$		−	7361.60i		−	0.997731i	0.866679	−	0.498865i	$-0.166250\pi$
$380$	8471.94	−	6431.77i	1.14369	−	0.868271i
$381$			1379.38i			0.185479i
$382$	−4468.73	−	872.165i	−0.598534	−	0.116816i
$383$	9278.86	−	9278.86i	1.23793	−	1.23793i	0.277086	−	0.960845i	$-0.410631\pi$
$383$	9278.86	−	9278.86i	1.23793	−	1.23793i	0.960845	−	0.277086i	$-0.0893688\pi$
$384$	−3671.99	−	2321.83i	−0.487982	−	0.308555i
$385$	421.039	+	1652.70i	0.0557355	+	0.218778i
$386$	−8374.34	+	5639.28i	−1.10426	+	0.743606i
$387$	−2713.76	+	2713.76i	−0.356456	+	0.356456i
$388$	11267.5	−	4762.53i	1.47428	−	0.623147i
$389$	−11323.2			−1.47586			−0.737929	−	0.674878i	$-0.764196\pi$
$389$	−11323.2			−1.47586			−0.737929	+	0.674878i	$0.764196\pi$
$390$	−2961.99	+	3318.50i	−0.384580	+	0.430868i
$391$			10071.0i			1.30259i
$392$	−4452.88	−	2906.23i	−0.573736	−	0.374456i
$393$	1185.86	+	1185.86i	0.152211	+	0.152211i
$394$	−1752.34	+	1180.03i	−0.224066	+	0.150886i
$395$	6618.92	+	3931.19i	0.843124	+	0.500759i
$396$	397.390	−	979.278i	0.0504283	−	0.124269i
$397$	1717.16	+	1717.16i	0.217082	+	0.217082i	0.807268	−	0.590186i	$-0.200945\pi$
$397$	1717.16	+	1717.16i	0.217082	+	0.217082i	−0.590186	+	0.807268i	$0.700945\pi$
$398$	−2130.71	+	10917.2i	−0.268349	+	1.37494i
$399$	3707.72			0.465208
$400$	−2149.95	+	7705.69i	−0.268744	+	0.963212i
$401$	870.753			0.108437			0.0542186	−	0.998529i	$-0.482733\pi$
$401$	870.753			0.108437			0.0542186	+	0.998529i	$0.482733\pi$
$402$	−684.813	+	3508.79i	−0.0849636	+	0.435329i
$403$	7395.88	+	7395.88i	0.914181	+	0.914181i
$404$	−1217.13	+	2999.33i	−0.149887	+	0.369363i
$405$	−778.628	−	462.453i	−0.0955317	−	0.0567394i
$406$	1183.99	−	797.303i	0.144731	−	0.0974618i
$407$	3517.12	+	3517.12i	0.428346	+	0.428346i
$408$	4834.20	−	7406.91i	0.586590	−	0.898766i
$409$		−	2784.26i		−	0.336608i	−0.985735	−	0.168304i	$-0.946171\pi$
$409$		−	2784.26i		−	0.336608i	0.985735	−	0.168304i	$-0.0538290\pi$
$410$	30.3532	−	34.0065i	0.00365619	−	0.00409625i
$411$	−5666.53			−0.680071
$412$	−8794.21	+	3717.12i	−1.05160	+	0.444488i
$413$	1742.05	−	1742.05i	0.207556	−	0.207556i
$414$	−1632.01	+	1099.00i	−0.193742	+	0.130466i
$415$	−663.390	−	2604.00i	−0.0784688	−	0.308013i
$416$	1505.67	−	8352.90i	0.177455	−	0.984458i
$417$	4384.36	−	4384.36i	0.514875	−	0.514875i
$418$	−4845.83	−	945.766i	−0.567028	−	0.110667i
$419$			12239.6i			1.42707i	0.700621	+	0.713534i	$0.252907\pi$
$419$			12239.6i			1.42707i	−0.700621	+	0.713534i	$0.747093\pi$
$420$	−2221.05	+	1686.19i	−0.258038	+	0.195899i
$421$			6094.88i			0.705573i	0.935704	+	0.352786i	$0.114766\pi$
$421$			6094.88i			0.705573i	−0.935704	+	0.352786i	$0.885234\pi$
$422$	−151.585	+	776.677i	−0.0174859	+	0.0895925i
$423$	−308.223	+	308.223i	−0.0354286	+	0.0354286i
$424$	494.379	+	2352.29i	0.0566254	+	0.269428i
$425$	−15623.3	−	4602.61i	−1.78316	−	0.525317i
$426$	−5387.14	−	7999.90i	−0.612694	−	0.909851i
$427$	−803.203	+	803.203i	−0.0910298	+	0.0910298i
$428$	−6089.46	+	2573.88i	−0.687723	+	0.290685i
$429$	2064.68			0.232363
$430$	−13463.1	+	764.229i	−1.50988	+	0.0857079i
$431$		−	6769.78i		−	0.756586i	−0.925686	−	0.378293i	$-0.876511\pi$
$431$		−	6769.78i		−	0.756586i	0.925686	−	0.378293i	$-0.123489\pi$
$432$	1727.82	−	24.8933i	0.192430	−	0.00277241i
$433$	6363.34	+	6363.34i	0.706241	+	0.706241i	0.965743	−	0.259501i	$-0.0835582\pi$
$433$	6363.34	+	6363.34i	0.706241	+	0.706241i	−0.259501	+	0.965743i	$0.583558\pi$
$434$	3662.56	+	5438.89i	0.405088	+	0.601556i
$435$	402.103	+	1578.37i	0.0443204	+	0.173971i
$436$	−10584.1	−	4295.00i	−1.16258	−	0.471774i
$437$	6499.65	+	6499.65i	0.711489	+	0.711489i
$438$	−1792.43	−	349.831i	−0.195538	−	0.0381634i
$439$	−9188.12			−0.998918			−0.499459	−	0.866337i	$-0.666468\pi$
$439$	−9188.12			−0.998918			−0.499459	+	0.866337i	$0.666468\pi$
$440$	3332.93	−	1637.23i	0.361116	−	0.177391i
$441$	2114.97			0.228374
$442$	16959.7	+	3310.04i	1.82509	+	0.356205i
$443$	1938.58	+	1938.58i	0.207911	+	0.207911i	0.803379	−	0.595468i	$-0.203033\pi$
$443$	1938.58	+	1938.58i	0.207911	+	0.207911i	−0.595468	+	0.803379i	$0.703033\pi$
$444$	−3058.07	+	7535.91i	−0.326868	+	0.805492i
$445$	5092.93	−	8574.92i	0.542535	−	0.913461i
$446$	−1679.88	−	2494.62i	−0.178351	−	0.264852i
$447$	−4210.67	−	4210.67i	−0.445543	−	0.445543i
$448$	1929.54	−	4958.77i	0.203487	−	0.522946i
$449$			2790.73i			0.293325i	0.989187	+	0.146662i	$0.0468531\pi$
$449$			2790.73i			0.293325i	−0.989187	+	0.146662i	$0.953147\pi$
$450$	−959.034	−	3034.02i	−0.100465	−	0.317833i
$451$	−21.1579			−0.00220906
$452$	−2374.01	−	5616.59i	−0.247044	−	0.584474i
$453$	3570.33	−	3570.33i	0.370306	−	0.370306i
$454$	−6098.39	−	9056.11i	−0.630422	−	0.936177i
$455$	−4684.03	−	2782.00i	−0.482617	−	0.286642i
$456$	−1660.37	−	7900.17i	−0.170513	−	0.811314i
$457$	−6649.37	+	6649.37i	−0.680622	+	0.680622i	−0.960140	−	0.279518i	$-0.909825\pi$
$457$	−6649.37	+	6649.37i	−0.680622	+	0.680622i	0.279518	+	0.960140i	$0.409825\pi$
$458$	−1701.78	+	8719.42i	−0.173622	+	0.889589i
$459$			3518.03i			0.357750i
$460$	−6849.40	−	937.613i	−0.694250	−	0.0950357i
$461$			999.150i			0.100944i	0.998725	+	0.0504718i	$0.0160725\pi$
$461$			999.150i			0.100944i	−0.998725	+	0.0504718i	$0.983927\pi$
$462$	1270.41	+	247.947i	0.127932	+	0.0249687i
$463$	12732.8	−	12732.8i	1.27807	−	1.27807i	0.336318	−	0.941748i	$-0.390818\pi$
$463$	12732.8	−	12732.8i	1.27807	−	1.27807i	0.941748	−	0.336318i	$-0.109182\pi$
$464$	−2229.06	−	2165.74i	−0.223020	−	0.216685i
$465$	−7250.55	+	1847.13i	−0.723088	+	0.184212i
$466$	−14037.4	+	9452.79i	−1.39543	+	0.939682i
$467$	−5607.94	+	5607.94i	−0.555685	+	0.555685i	−0.928076	−	0.372391i	$-0.878538\pi$
$467$	−5607.94	+	5607.94i	−0.555685	+	0.555685i	0.372391	+	0.928076i	$0.378538\pi$
$468$	1314.33	+	3109.53i	0.129818	+	0.307132i
$469$	−4378.53			−0.431091
$470$	−1529.11	+	86.7994i	−0.150069	+	0.00851864i
$471$			4695.36i			0.459344i
$472$	−4491.96	−	2931.73i	−0.438049	−	0.285898i
$473$	4425.93	+	4425.93i	0.430242	+	0.430242i
$474$	4846.24	−	3263.46i	0.469610	−	0.316236i
$475$	−13053.4	+	7112.53i	−1.26091	+	0.687043i
$476$	10037.9	+	4073.37i	0.966567	+	0.392232i
$477$	−676.036	−	676.036i	−0.0648921	−	0.0648921i
$478$	2616.67	−	13407.1i	0.250385	−	1.28290i
$479$	−4422.72			−0.421877			−0.210939	−	0.977499i	$-0.567652\pi$
$479$	−4422.72			−0.421877			−0.210939	+	0.977499i	$0.567652\pi$
$480$	4587.44	+	3977.36i	0.436223	+	0.378210i
$481$	−15888.5			−1.50614
$482$	−762.747	+	3908.10i	−0.0720792	+	0.369313i
$483$	−1703.98	−	1703.98i	−0.160525	−	0.160525i
$484$	8269.44	+	3355.73i	0.776619	+	0.315152i
$485$	−16566.6	+	4220.46i	−1.55103	+	0.395137i
$486$	−570.097	+	383.903i	−0.0532101	+	0.0358317i
$487$	6483.55	+	6483.55i	0.603281	+	0.603281i	0.941182	−	0.337901i	$-0.109717\pi$
$487$	6483.55	+	6483.55i	0.603281	+	0.603281i	−0.337901	+	0.941182i	$0.609717\pi$
$488$	2071.10	+	1351.73i	0.192120	+	0.125389i
$489$			3152.96i			0.291578i
$490$	5544.03	+	4948.43i	0.511130	+	0.456219i
$491$	13907.7			1.27830			0.639148	−	0.769083i	$-0.279287\pi$
$491$	13907.7			1.27830			0.639148	+	0.769083i	$0.279287\pi$
$492$	−13.4687	−	31.8651i	−0.00123418	−	0.00291990i
$493$	4474.13	−	4474.13i	0.408732	−	0.408732i
$494$	13081.7	−	8809.22i	1.19144	−	0.802319i
$495$	−754.224	+	1269.88i	−0.0684846	+	0.115307i
$496$	9948.71	−	10239.6i	0.900625	−	0.926956i
$497$	8352.67	−	8352.67i	0.753860	−	0.753860i
$498$	−2001.66	−	390.665i	−0.180113	−	0.0351528i
$499$			21380.3i			1.91807i	0.283292	+	0.959034i	$0.408574\pi$
$499$			21380.3i			1.91807i	−0.283292	+	0.959034i	$0.591426\pi$
$500$	4584.80	−	10197.0i	0.410077	−	0.912051i
$501$			6347.82i			0.566067i
$502$	484.324	−	2481.54i	0.0430606	−	0.220630i
$503$	5565.49	−	5565.49i	0.493346	−	0.493346i	−0.416013	−	0.909359i	$-0.636573\pi$
$503$	5565.49	−	5565.49i	0.493346	−	0.493346i	0.909359	+	0.416013i	$0.136573\pi$
$504$	435.291	+	2071.15i	0.0384711	+	0.183048i
$505$	2310.04	−	3889.40i	0.203555	−	0.342724i
$506$	1792.38	+	2661.69i	0.157472	+	0.233847i
$507$	−3.01652	+	3.01652i	−0.000264237	+	0.000264237i
$508$	1432.08	+	3388.11i	0.125075	+	0.295912i
$509$	−4699.25			−0.409215			−0.204608	−	0.978844i	$-0.565592\pi$
$509$	−4699.25			−0.409215			−0.204608	+	0.978844i	$0.565592\pi$
$510$	−8231.20	+	9221.92i	−0.714674	+	0.800693i
$511$		−	2236.73i		−	0.193634i
$512$	−11429.9	−	1890.73i	−0.986593	−	0.163202i
$513$	2270.46	+	2270.46i	0.195406	+	0.195406i
$514$	−2179.93	−	3237.20i	−0.187068	−	0.277795i
$515$	12930.1	−	3294.04i	1.10634	−	0.281850i
$516$	−3848.27	+	9483.17i	−0.328315	+	0.809057i
$517$	502.687	+	502.687i	0.0427624	+	0.0427624i
$518$	−9776.26	−	1908.04i	−0.829236	−	0.161843i
$519$	−11384.2			−0.962838
$520$	−3830.13	+	11226.3i	−0.323005	+	0.946739i
$521$	11283.3			0.948808			0.474404	−	0.880307i	$-0.342664\pi$
$521$	11283.3			0.948808			0.474404	+	0.880307i	$0.342664\pi$
$522$	1213.27	+	236.795i	0.101731	+	0.0198549i
$523$	−9323.40	−	9323.40i	−0.779510	−	0.779510i	0.200237	−	0.979747i	$-0.435829\pi$
$523$	−9323.40	−	9323.40i	−0.779510	−	0.779510i	−0.979747	+	0.200237i	$0.935829\pi$
$524$	4143.96	+	1681.62i	0.345477	+	0.140194i
$525$	3422.14	−	1864.66i	0.284485	−	0.155010i
$526$	−6853.56	−	10177.5i	−0.568117	−	0.843653i
$527$	20552.7	+	20552.7i	1.69884	+	1.69884i
$528$	−40.5990	−	2817.94i	−0.00334630	−	0.232263i
$529$			6192.82i			0.508985i
$530$	−190.380	−	3353.85i	−0.0156030	−	0.274871i
$531$	2133.53			0.174364
$532$	9107.13	−	3849.38i	0.742188	−	0.313707i
$533$	47.7901	−	47.7901i	0.00388371	−	0.00388371i
$534$	−4227.87	−	6278.39i	−0.342618	−	0.508787i
$535$	8953.29	−	2280.92i	0.723523	−	0.184323i
$536$	1960.77	+	9329.49i	0.158008	+	0.751814i
$537$	−6376.61	+	6376.61i	−0.512423	+	0.512423i
$538$	−3772.15	+	19327.4i	−0.302284	+	1.54882i
$539$		−	3449.34i		−	0.275647i
$540$	−2392.64	−	327.528i	−0.190672	−	0.0261010i
$541$		−	12770.8i		−	1.01490i	−0.861681	−	0.507450i	$-0.830588\pi$
$541$		−	12770.8i		−	1.01490i	0.861681	−	0.507450i	$-0.169412\pi$
$542$	−8491.72	−	1657.34i	−0.672972	−	0.131345i
$543$	−1293.69	+	1293.69i	−0.102242	+	0.102242i
$544$	4184.16	−	23212.2i	0.329769	−	1.82944i
$545$	13724.9	+	8151.67i	1.07873	+	0.640696i
$546$	−3429.56	+	2309.47i	−0.268812	+	0.181018i
$547$	−1235.92	+	1235.92i	−0.0966074	+	0.0966074i	−0.753759	−	0.657151i	$-0.771761\pi$
$547$	−1235.92	+	1235.92i	−0.0966074	+	0.0966074i	0.657151	+	0.753759i	$0.271761\pi$
$548$	−13918.5	+	5883.04i	−1.08498	+	0.458597i
$549$	−983.702			−0.0764725
$550$	−4948.24	+	1564.11i	−0.383625	+	0.121261i
$551$		−	5775.03i		−	0.446506i
$552$	−2867.67	+	4393.80i	−0.221116	+	0.338791i
$553$	5059.95	+	5059.95i	0.389097	+	0.389097i
$554$	16869.2	−	11359.7i	1.29369	−	0.871171i
$555$	5804.04	−	9772.21i	0.443906	−	0.747400i
$556$	6217.26	−	15321.0i	0.474228	−	1.16863i
$557$	15771.8	+	15771.8i	1.19977	+	1.19977i	0.974234	+	0.225541i	$0.0724150\pi$
$557$	15771.8	+	15771.8i	1.19977	+	1.19977i	0.225541	+	0.974234i	$0.427585\pi$
$558$	−1087.76	+	5573.38i	−0.0825245	+	0.422832i
$559$	−19994.0			−1.51280
$560$	−3704.86	+	6447.62i	−0.279570	+	0.486539i
$561$	5737.62			0.431805
$562$	3549.67	−	18187.5i	0.266430	−	1.36511i
$563$	2631.39	+	2631.39i	0.196980	+	0.196980i	0.798704	−	0.601724i	$-0.205519\pi$
$563$	2631.39	+	2631.39i	0.196980	+	0.196980i	−0.601724	+	0.798704i	$0.705519\pi$
$564$	−437.077	+	1077.08i	−0.0326317	+	0.0804133i
$565$	2103.80	+	8258.03i	0.156650	+	0.614899i
$566$	17242.5	−	11611.1i	1.28049	−	0.862283i
$567$	−595.236	−	595.236i	−0.0440874	−	0.0440874i
$568$	−21537.8	−	14056.9i	−1.59103	−	1.03841i
$569$		−	4552.16i		−	0.335389i	−0.985839	−	0.167695i	$-0.946368\pi$
$569$		−	4552.16i		−	0.335389i	0.985839	−	0.167695i	$-0.0536323\pi$
$570$	639.391	+	11263.9i	0.0469845	+	0.827707i
$571$	14577.1			1.06836			0.534181	−	0.845370i	$-0.320620\pi$
$571$	14577.1			1.06836			0.534181	+	0.845370i	$0.320620\pi$
$572$	5071.39	−	2143.57i	0.370709	−	0.156691i
$573$	3414.78	−	3414.78i	0.248961	−	0.248961i
$574$	35.1446	−	23.6664i	0.00255559	−	0.00172094i
$575$	9267.80	+	2730.29i	0.672163	+	0.198019i
$576$	4218.14	−	1854.98i	0.305132	−	0.134186i
$577$	−9151.08	+	9151.08i	−0.660251	+	0.660251i	−0.955439	−	0.295188i	$-0.904618\pi$
$577$	−9151.08	+	9151.08i	−0.660251	+	0.660251i	0.295188	+	0.955439i	$0.404618\pi$
$578$	33491.3	+	6536.53i	2.41013	+	0.470387i
$579$		−	10708.5i		−	0.768620i
$580$	2626.35	+	3459.44i	0.188023	+	0.247664i
$581$		−	2497.81i		−	0.178359i
$582$	−2485.40	+	12734.5i	−0.177015	+	0.906977i
$583$	−1102.56	+	1102.56i	−0.0783249	+	0.0783249i
$584$	−4765.88	+	1001.64i	−0.337695	+	0.0709730i
$585$	−1164.73	−	4571.92i	−0.0823175	−	0.323120i
$586$	−12477.7	−	18529.3i	−0.879604	−	1.30621i
$587$	−464.175	+	464.175i	−0.0326380	+	0.0326380i	−0.723237	−	0.690599i	$-0.757347\pi$
$587$	−464.175	+	464.175i	−0.0326380	+	0.0326380i	0.690599	+	0.723237i	$0.257347\pi$
$588$	5194.92	−	2195.78i	0.364345	−	0.154001i
$589$	26528.7			1.85585
$590$	5592.68	+	4991.86i	0.390249	+	0.348325i
$591$		−	2240.78i		−	0.155961i
$592$	312.425	+	21685.1i	0.0216902	+	1.50549i
$593$	−15527.4	−	15527.4i	−1.07527	−	1.07527i	−0.996927	−	0.0783396i	$-0.975038\pi$
$593$	−15527.4	−	15527.4i	−1.07527	−	1.07527i	−0.0783396	−	0.996927i	$-0.524962\pi$
$594$	626.116	+	929.783i	0.0432489	+	0.0642246i
$595$	−13016.7	−	7731.03i	−0.896859	−	0.532674i
$596$	−14714.1	−	5970.96i	−1.01126	−	0.410370i
$597$	−8342.36	−	8342.36i	−0.571910	−	0.571910i
$598$	−10060.6	−	1963.53i	−0.687971	−	0.134272i
$599$	−3076.08			−0.209825			−0.104913	−	0.994481i	$-0.533456\pi$
$599$	−3076.08			−0.209825			−0.104913	+	0.994481i	$0.533456\pi$
$600$	−5505.58	−	6456.67i	−0.374607	−	0.439321i
$601$	19519.6			1.32483			0.662414	−	0.749138i	$-0.269532\pi$
$601$	19519.6			1.32483			0.662414	+	0.749138i	$0.269532\pi$
$602$	−12302.4	−	2401.08i	−0.832906	−	0.162559i
$603$	−2681.24	−	2681.24i	−0.181076	−	0.181076i
$604$	5062.92	−	12476.4i	0.341072	−	0.840493i
$605$	−10723.4	−	6368.99i	−0.720610	−	0.427994i
$606$	−1917.67	−	2847.74i	−0.128548	−	0.190894i
$607$	−4254.78	−	4254.78i	−0.284508	−	0.284508i	0.550396	−	0.834904i	$-0.314477\pi$
$607$	−4254.78	−	4254.78i	−0.284508	−	0.284508i	−0.834904	+	0.550396i	$0.814477\pi$
$608$	−12280.3	−	17681.1i	−0.819134	−	1.17938i
$609$			1514.01i			0.100740i
$610$	−2578.61	−	2301.59i	−0.171156	−	0.152768i
$611$	−2270.87			−0.150360
$612$	3652.45	+	8641.20i	0.241244	+	0.570752i
$613$	−429.223	+	429.223i	−0.0282809	+	0.0282809i	−0.721106	−	0.692825i	$-0.756366\pi$
$613$	−429.223	+	429.223i	−0.0282809	+	0.0282809i	0.692825	+	0.721106i	$0.256366\pi$
$614$	4047.72	+	6010.86i	0.266047	+	0.395079i
$615$	11.9357	+	46.8510i	0.000782590	+	0.00307189i
$616$	3377.88	−	709.926i	0.220939	−	0.0464346i
$617$	18647.2	−	18647.2i	1.21671	−	1.21671i	0.247927	−	0.968779i	$-0.420251\pi$
$617$	18647.2	−	18647.2i	1.21671	−	1.21671i	0.968779	−	0.247927i	$-0.0797493\pi$
$618$	1939.83	−	9939.14i	0.126264	−	0.646943i
$619$			10986.2i			0.713363i	0.934226	+	0.356682i	$0.116092\pi$
$619$			10986.2i			0.713363i	−0.934226	+	0.356682i	$0.883908\pi$
$620$	−15891.5	+	12064.6i	−1.02939	+	0.781496i
$621$		−	2086.91i		−	0.134854i
$622$	10194.9	+	1989.75i	0.657201	+	0.128267i
$623$	6555.25	−	6555.25i	0.421558	−	0.421558i
$624$	6456.68	+	6273.27i	0.414221	+	0.402455i
$625$	−8471.04	+	13129.4i	−0.542146	+	0.840284i
$626$	−3232.05	+	2176.46i	−0.206356	+	0.138960i
$627$	3702.95	−	3702.95i	0.235856	−	0.235856i
$628$	4874.77	+	11533.1i	0.309752	+	0.732833i
$629$	−44153.1			−2.79889
$630$	−167.626	−	2953.00i	−0.0106006	−	0.186746i
$631$			20059.0i			1.26551i	0.774352	+	0.632756i	$0.218076\pi$
$631$			20059.0i			1.26551i	−0.774352	+	0.632756i	$0.781924\pi$
$632$	8515.50	−	13047.3i	0.535962	−	0.821195i
$633$	−593.498	−	593.498i	−0.0372661	−	0.0372661i
$634$	−22485.9	+	15142.0i	−1.40857	+	0.948529i
$635$	−1269.08	−	4981.52i	−0.0793102	−	0.311316i
$636$	−2362.39	−	958.656i	−0.147287	−	0.0597691i
$637$	7791.15	+	7791.15i	0.484610	+	0.484610i
$638$	386.195	−	1978.75i	0.0239649	−	0.122789i
$639$	10229.7			0.633304
$640$	15397.3	+	5006.74i	0.950986	+	0.309232i
$641$	−14998.3			−0.924177			−0.462088	−	0.886834i	$-0.652900\pi$
$641$	−14998.3			−0.924177			−0.462088	+	0.886834i	$0.652900\pi$
$642$	1343.22	−	6882.26i	0.0825741	−	0.423086i
$643$	−17699.6	−	17699.6i	−1.08554	−	1.08554i	−0.995982	−	0.0895585i	$-0.971454\pi$
$643$	−17699.6	−	17699.6i	−1.08554	−	1.08554i	−0.0895585	−	0.995982i	$-0.528546\pi$
$644$	−5954.51	−	2416.34i	−0.364349	−	0.147853i
$645$	7303.79	−	12297.3i	0.445870	−	0.750708i
$646$	36353.3	−	24480.3i	2.21409	−	1.49097i
$647$	−13445.2	−	13445.2i	−0.816981	−	0.816981i	0.168689	−	0.985669i	$-0.446047\pi$
$647$	−13445.2	−	13445.2i	−0.816981	−	0.816981i	−0.985669	+	0.168689i	$0.946047\pi$
$648$	−1001.74	+	1534.85i	−0.0607282	+	0.0930471i
$649$		−	3479.61i		−	0.210457i
$650$	7643.86	−	14709.7i	0.461256	−	0.887632i
$651$	−6954.88			−0.418715
$652$	3273.43	+	7744.50i	0.196622	+	0.465181i
$653$	18334.0	−	18334.0i	1.09872	−	1.09872i	0.104158	−	0.994561i	$-0.466785\pi$
$653$	18334.0	−	18334.0i	1.09872	−	1.09872i	0.994561	−	0.104158i	$-0.0332147\pi$
$654$	10049.1	−	6767.08i	0.600843	−	0.404608i
$655$	−5373.70	−	3191.62i	−0.320561	−	0.190392i
$656$	−66.1652	−	64.2858i	−0.00393798	−	0.00382612i
$657$	1369.69	−	1369.69i	0.0813343	−	0.0813343i
$658$	−1397.28	−	272.709i	−0.0827837	−	0.0161570i
$659$		−	10800.5i		−	0.638432i	−0.947682	−	0.319216i	$-0.896580\pi$
$659$		−	10800.5i		−	0.638432i	0.947682	−	0.319216i	$-0.103420\pi$
$660$	−534.172	+	3902.21i	−0.0315040	+	0.230141i
$661$			2752.68i			0.161977i	0.996715	+	0.0809886i	$0.0258077\pi$
$661$			2752.68i			0.161977i	−0.996715	+	0.0809886i	$0.974192\pi$
$662$	−4810.51	+	24647.7i	−0.282425	+	1.44707i
$663$	−12959.8	+	12959.8i	−0.759149	+	0.759149i
$664$	−5322.19	+	1118.56i	−0.311056	+	0.0653743i
$665$	−13390.1	+	3411.25i	−0.780824	+	0.198921i
$666$	−4818.20	−	7155.02i	−0.280332	−	0.416294i
$667$	−2654.07	+	2654.07i	−0.154072	+	0.154072i
$668$	6590.36	+	15591.9i	0.381720	+	0.903098i
$669$	3189.95			0.184351
$670$	−755.071	−	13301.8i	−0.0435387	−	0.767004i
$671$			1604.34i			0.0923023i
$672$	3219.47	+	4635.36i	0.184812	+	0.266091i
$673$	4429.24	+	4429.24i	0.253692	+	0.253692i	0.822482	−	0.568791i	$-0.192589\pi$
$673$	4429.24	+	4429.24i	0.253692	+	0.253692i	−0.568791	+	0.822482i	$0.692589\pi$
$674$	13400.8	+	19900.2i	0.765846	+	1.13728i
$675$	3237.44	+	953.746i	0.184606	+	0.0543848i
$676$	−4.27759	+	10.5411i	−0.000243377	+	0.000599746i
$677$	−2914.41	−	2914.41i	−0.165451	−	0.165451i	0.619526	−	0.784976i	$-0.287325\pi$
$677$	−2914.41	−	2914.41i	−0.165451	−	0.165451i	−0.784976	+	0.619526i	$0.787325\pi$
$678$	6347.82	+	1238.91i	0.359567	+	0.0701771i
$679$	−15891.0			−0.898146
$680$	−10643.7	+	31197.2i	−0.600247	+	1.75935i
$681$	11580.3			0.651629
$682$	9089.75	+	1774.05i	0.510358	+	0.0996071i
$683$	9037.46	+	9037.46i	0.506309	+	0.506309i	0.913391	−	0.407083i	$-0.133454\pi$
$683$	9037.46	+	9037.46i	0.506309	+	0.506309i	−0.407083	+	0.913391i	$0.633454\pi$
$684$	7934.08	+	3219.64i	0.443519	+	0.179980i
$685$	20464.3	−	5213.43i	1.14146	−	0.290796i
$686$	9489.87	+	14092.4i	0.528170	+	0.784333i
$687$	−6662.95	−	6662.95i	−0.370025	−	0.370025i
$688$	393.155	+	27288.5i	0.0217862	+	1.51216i
$689$		−	4980.78i		−	0.275403i
$690$	4882.78	−	5470.47i	0.269397	−	0.301822i
$691$	−6376.92			−0.351070			−0.175535	−	0.984473i	$-0.556166\pi$
$691$	−6376.92			−0.351070			−0.175535	+	0.984473i	$0.556166\pi$
$692$	−27962.7	+	11819.2i	−1.53610	+	0.649277i
$693$	−970.783	+	970.783i	−0.0532136	+	0.0532136i
$694$	5820.51	+	8643.45i	0.318362	+	0.472768i
$695$	−11800.0	+	19867.6i	−0.644028	+	1.08435i
$696$	3225.96	−	677.998i	0.175689	−	0.0369245i
$697$	132.806	−	132.806i	0.00721720	−	0.00721720i
$698$	−1791.21	+	9177.64i	−0.0971322	+	0.497677i
$699$		−	17950.0i		−	0.971291i
$700$	6469.79	−	8132.99i	0.349336	−	0.439140i
$701$		−	4700.98i		−	0.253286i	−0.991948	−	0.126643i	$-0.959580\pi$
$701$		−	4700.98i		−	0.253286i	0.991948	−	0.126643i	$-0.0404203\pi$
$702$	−3514.36	−	685.901i	−0.188947	−	0.0368770i
$703$	−28495.6	+	28495.6i	−1.52878	+	1.52878i
$704$	−3025.33	−	6879.45i	−0.161962	−	0.368294i
$705$	829.548	−	1396.70i	0.0443157	−	0.0746140i
$706$	8716.26	−	5869.53i	0.464647	−	0.312894i
$707$	2973.32	−	2973.32i	0.158166	−	0.158166i
$708$	5240.51	−	2215.05i	0.278178	−	0.117580i
$709$	−8874.16			−0.470065			−0.235032	−	0.971988i	$-0.575520\pi$
$709$	−8874.16			−0.470065			−0.235032	+	0.971988i	$0.575520\pi$
$710$	26815.5	+	23934.7i	1.41742	+	1.26514i
$711$			6197.04i			0.326874i
$712$	−16903.1	−	11032.0i	−0.889703	−	0.580675i
$713$	−12192.0	−	12192.0i	−0.640382	−	0.640382i
$714$	−9530.55	+	6417.88i	−0.499540	+	0.336391i
$715$	−7456.43	+	1899.59i	−0.390007	+	0.0993573i
$716$	−9042.39	+	22282.9i	−0.471969	+	1.16306i
$717$	10245.0	+	10245.0i	0.533623	+	0.533623i
$718$	−897.757	+	4599.85i	−0.0466629	+	0.239087i
$719$	4437.50			0.230168			0.115084	−	0.993356i	$-0.463286\pi$
$719$	4437.50			0.230168			0.115084	+	0.993356i	$0.463286\pi$
$720$	−6217.00	+	1679.56i	−0.321797	+	0.0869357i
$721$	12402.8			0.640644
$722$	3946.33	−	20219.9i	0.203417	−	1.04225i
$723$	−2986.37	−	2986.37i	−0.153616	−	0.153616i
$724$	−1834.53	+	4520.77i	−0.0941708	+	0.232062i
$725$	−2904.34	−	5330.23i	−0.148778	−	0.273048i
$726$	−7851.48	+	5287.19i	−0.401372	+	0.270284i
$727$	27346.2	+	27346.2i	1.39507	+	1.39507i	0.813495	+	0.581572i	$0.197562\pi$
$727$	27346.2	+	27346.2i	1.39507	+	1.39507i	0.581572	+	0.813495i	$0.302438\pi$
$728$	−6026.19	+	9233.26i	−0.306793	+	0.470065i
$729$		−	729.000i		−	0.0370370i
$730$	6795.10	−	385.721i	0.344518	−	0.0195564i
$731$	−55562.2			−2.81128
$732$	−2416.23	+	1021.29i	−0.122003	+	0.0515682i
$733$	−2012.97	+	2012.97i	−0.101433	+	0.101433i	−0.756002	−	0.654569i	$-0.772850\pi$
$733$	−2012.97	+	2012.97i	−0.101433	+	0.101433i	0.654569	+	0.756002i	$0.272850\pi$
$734$	9724.10	−	6548.21i	0.488996	−	0.329290i
$735$	−7638.05	+	1945.85i	−0.383311	+	0.0976516i
$736$	−2482.06	+	13769.6i	−0.124307	+	0.689610i
$737$	−4372.90	+	4372.90i	−0.218559	+	0.218559i
$738$	36.0137	+	7.02882i	0.00179632	+	0.000350589i
$739$			12881.8i			0.641226i	0.947210	+	0.320613i	$0.103889\pi$
$739$			12881.8i			0.641226i	−0.947210	+	0.320613i	$0.896111\pi$
$740$	4110.65	−	30028.9i	0.204204	−	1.49174i
$741$			16728.0i			0.829307i
$742$	598.141	−	3064.70i	0.0295936	−	0.151629i
$743$	11345.9	−	11345.9i	0.560218	−	0.560218i	−0.369151	−	0.929369i	$-0.620351\pi$
$743$	11345.9	−	11345.9i	0.560218	−	0.560218i	0.929369	+	0.369151i	$0.120351\pi$
$744$	3114.50	+	14819.0i	0.153472	+	0.730231i
$745$	19080.5	+	11332.6i	0.938331	+	0.557305i
$746$	−22073.7	−	32779.4i	−1.08334	−	1.60877i
$747$	1529.57	−	1529.57i	0.0749182	−	0.0749182i
$748$	14093.1	−	5956.85i	0.688898	−	0.291182i
$749$	8588.19			0.418966
$750$	6254.90	+	10074.8i	0.304529	+	0.490505i
$751$		−	13096.1i		−	0.636328i	−0.948036	−	0.318164i	$-0.896934\pi$
$751$		−	13096.1i		−	0.636328i	0.948036	−	0.318164i	$-0.103066\pi$
$752$	44.6536	+	3099.36i	0.00216536	+	0.150295i
$753$	1896.27	+	1896.27i	0.0917715	+	0.0917715i
$754$	3597.16	+	5341.78i	0.173741	+	0.258006i
$755$	−9609.13	+	16178.8i	−0.463195	+	0.779877i
$756$	−2080.04	−	844.078i	−0.100066	−	0.0406069i
$757$	−20639.3	−	20639.3i	−0.990947	−	0.990947i	0.00901282	−	0.999959i	$-0.497131\pi$
$757$	−20639.3	−	20639.3i	−0.990947	−	0.990947i	−0.999959	+	0.00901282i	$0.997131\pi$
$758$	20436.2	+	3988.55i	0.979254	+	0.191122i
$759$	−3403.58			−0.162770
$760$	13264.8	+	27003.3i	0.633111	+	1.28883i
$761$	7106.51			0.338516			0.169258	−	0.985572i	$-0.445863\pi$
$761$	7106.51			0.338516			0.169258	+	0.985572i	$0.445863\pi$
$762$	−3829.22	−	747.352i	−0.182044	−	0.0355298i
$763$	10492.2	+	10492.2i	0.497830	+	0.497830i
$764$	4842.35	−	11932.9i	0.229306	−	0.565073i
$765$	−3236.73	−	12705.1i	−0.152973	−	0.600463i
$766$	20731.3	+	30785.9i	0.977873	+	1.45214i
$767$	7859.52	+	7859.52i	0.370001	+	0.370001i
$768$	8435.00	−	8935.64i	0.396318	−	0.419840i
$769$		−	19288.3i		−	0.904490i	−0.891894	−	0.452245i	$-0.850623\pi$
$769$		−	19288.3i		−	0.904490i	0.891894	−	0.452245i	$-0.149377\pi$
$770$	−4816.11	+	273.384i	−0.225403	+	0.0127949i
$771$	4139.51			0.193360
$772$	−11117.7	−	26303.0i	−0.518308	−	1.22625i
$773$	−4702.86	+	4702.86i	−0.218823	+	0.218823i	−0.808002	−	0.589179i	$-0.799451\pi$
$773$	−4702.86	+	4702.86i	−0.218823	+	0.218823i	0.589179	+	0.808002i	$0.299451\pi$
$774$	−6063.21	−	9003.87i	−0.281573	−	0.418136i
$775$	24485.4	−	13341.6i	1.13489	−	0.618379i
$776$	7116.24	+	33859.6i	0.329199	+	1.56635i
$777$	7470.54	−	7470.54i	0.344921	−	0.344921i
$778$	6134.96	−	31433.8i	0.282711	−	1.44853i
$779$		−	171.421i		−	0.00788419i
$780$	−7607.49	−	10020.6i	−0.349221	−	0.459994i
$781$		−	16683.9i		−	0.764399i
$782$	−27957.7	−	5456.53i	−1.27847	−	0.249521i
$783$	−927.123	+	927.123i	−0.0423150	+	0.0423150i
$784$	10480.4	−	10786.8i	0.477424	−	0.491382i
$785$	−4319.92	−	16957.0i	−0.196414	−	0.770981i
$786$	−3934.52	+	2649.51i	−0.178549	+	0.120235i
$787$	21154.4	−	21154.4i	0.958160	−	0.958160i	−0.0409987	−	0.999159i	$-0.513054\pi$
$787$	21154.4	−	21154.4i	0.958160	−	0.958160i	0.999159	+	0.0409987i	$0.0130540\pi$
$788$	−2326.39	−	5503.94i	−0.105170	−	0.248819i
$789$	13014.3			0.587227
$790$	−14499.3	+	16244.5i	−0.652992	+	0.731587i
$791$			7921.28i			0.356066i
$792$	2503.22	+	1633.75i	0.112308	+	0.0732991i
$793$	−3623.78	−	3623.78i	−0.162275	−	0.162275i
$794$	−5697.27	+	3836.55i	−0.254646	+	0.171478i
$795$	3063.43	+	1819.47i	0.136665	+	0.0811699i
$796$	−29152.2	−	11829.9i	−1.29808	−	0.526760i
$797$	−21211.0	−	21211.0i	−0.942701	−	0.942701i	0.0557444	−	0.998445i	$-0.482247\pi$
$797$	−21211.0	−	21211.0i	−0.942701	−	0.942701i	−0.998445	+	0.0557444i	$0.982247\pi$
$798$	−2008.86	+	10292.8i	−0.0891137	+	0.456593i
$799$	−6310.63			−0.279417
$800$	−20226.5	−	10143.3i	−0.893895	−	0.448276i
$801$	8028.37			0.354143
$802$	−471.778	+	2417.25i	−0.0207719	+	0.106429i
$803$	−2233.85	−	2233.85i	−0.0981706	−	0.0981706i
$804$	−9369.53	−	3802.15i	−0.410992	−	0.166780i
$805$	7721.53	+	4586.07i	0.338072	+	0.200792i
$806$	−24538.4	+	16524.2i	−1.07237	+	0.722134i
$807$	−14769.1	−	14769.1i	−0.644233	−	0.644233i
$808$	−7666.85	−	5003.86i	−0.333811	−	0.217865i
$809$			16729.8i			0.727055i	0.931583	+	0.363528i	$0.118428\pi$
$809$			16729.8i			0.727055i	−0.931583	+	0.363528i	$0.881572\pi$
$810$	1705.66	−	1910.95i	0.0739885	−	0.0828938i
$811$	−6512.48			−0.281978			−0.140989	−	0.990011i	$-0.545028\pi$
$811$	−6512.48			−0.281978			−0.140989	+	0.990011i	$0.545028\pi$
$812$	1571.86	+	3718.81i	0.0679328	+	0.160720i
$813$	6488.96	−	6488.96i	0.279923	−	0.279923i
$814$	−11669.3	+	7858.10i	−0.502467	+	0.338361i
$815$	−2900.85	−	11386.7i	−0.124678	−	0.489396i
$816$	17942.7	+	17433.1i	0.769757	+	0.747892i
$817$	−35858.8	+	35858.8i	−1.53554	+	1.53554i
$818$	7729.24	+	1508.52i	0.330375	+	0.0644795i
$819$		−	4385.48i		−	0.187108i
$820$	77.9583	+	102.687i	0.00332003	+	0.00437314i
$821$			27113.4i			1.15258i	0.817247	+	0.576288i	$0.195499\pi$
$821$			27113.4i			1.15258i	−0.817247	+	0.576288i	$0.804501\pi$
$822$	3070.15	−	15730.6i	0.130272	−	0.667477i
$823$	−23856.8	+	23856.8i	−1.01045	+	1.01045i	−0.0105007	+	0.999945i	$0.503343\pi$
$823$	−23856.8	+	23856.8i	−1.01045	+	1.01045i	−0.999945	+	0.0105007i	$0.996657\pi$
$824$	−5554.16	−	26427.1i	−0.234816	−	1.11727i
$825$	1555.49	−	5280.00i	0.0656425	−	0.222820i
$826$	3892.16	+	5779.86i	0.163953	+	0.243471i
$827$	8465.67	−	8465.67i	0.355962	−	0.355962i	−0.506360	−	0.862322i	$-0.669009\pi$
$827$	8465.67	−	8465.67i	0.355962	−	0.355962i	0.862322	+	0.506360i	$0.169009\pi$
$828$	−2166.64	−	5125.99i	−0.0909373	−	0.215146i
$829$	11597.4			0.485879			0.242939	−	0.970041i	$-0.421888\pi$
$829$	11597.4			0.485879			0.242939	+	0.970041i	$0.421888\pi$
$830$	7588.26	−	430.745i	0.317340	−	0.0180137i
$831$			21571.2i			0.900476i
$832$	22372.3	+	8705.43i	0.932234	+	0.362748i
$833$	21651.2	+	21651.2i	0.900563	+	0.900563i
$834$	9795.73	+	14546.7i	0.406713	+	0.603968i
$835$	−5840.25	−	22924.7i	−0.242048	−	0.950110i
$836$	5250.99	−	12939.9i	0.217236	−	0.535328i
$837$	−4258.91	−	4258.91i	−0.175877	−	0.175877i
$838$	−33977.6	−	6631.44i	−1.40064	−	0.273364i
$839$	30878.0			1.27059			0.635296	−	0.772269i	$-0.280878\pi$
$839$	30878.0			1.27059			0.635296	+	0.772269i	$0.280878\pi$
$840$	−3477.56	−	7079.31i	−0.142842	−	0.290785i
$841$	−22030.8			−0.903310
$842$	−16919.7	−	3302.23i	−0.692507	−	0.135157i
$843$	13898.0	+	13898.0i	0.567820	+	0.567820i
$844$	−2073.96	−	841.614i	−0.0845839	−	0.0343241i
$845$	8.11861	−	13.6692i	0.000330519	−	0.000556493i
$846$	−688.646	−	1022.64i	−0.0279860	−	0.0415592i
$847$	−8197.71	−	8197.71i	−0.332558	−	0.332558i
$848$	−6797.93	+	97.9402i	−0.275285	+	0.00396613i
$849$			22048.5i			0.891288i
$850$	21241.9	−	40877.3i	0.857164	−	1.64951i
$851$	26191.8			1.05505
$852$	25126.9	−	10620.6i	1.01037	−	0.427060i
$853$	3059.94	−	3059.94i	0.122826	−	0.122826i	−0.643022	−	0.765848i	$-0.722320\pi$
$853$	3059.94	−	3059.94i	0.122826	−	0.122826i	0.765848	+	0.643022i	$0.222320\pi$
$854$	−1794.55	−	2664.91i	−0.0719067	−	0.106781i
$855$	−10288.5	−	6110.70i	−0.411533	−	0.244423i
$856$	−3845.93	−	18299.2i	−0.153564	−	0.730670i
$857$	−2550.99	+	2550.99i	−0.101680	+	0.101680i	−0.756117	−	0.654436i	$-0.772906\pi$
$857$	−2550.99	+	2550.99i	−0.101680	+	0.101680i	0.654436	+	0.756117i	$0.272906\pi$
$858$	−1118.65	+	5731.65i	−0.0445106	+	0.228060i
$859$		−	2523.56i		−	0.100236i	−0.998743	−	0.0501180i	$-0.984040\pi$
$859$		−	2523.56i		−	0.100236i	0.998743	−	0.0501180i	$-0.0159597\pi$
$860$	5172.84	−	37788.4i	0.205107	−	1.49834i
$861$			44.9405i			0.00177882i
$862$	18793.2	+	3667.89i	0.742576	+	0.144929i
$863$	−1590.61	+	1590.61i	−0.0627406	+	0.0627406i	−0.737781	−	0.675040i	$-0.764126\pi$
$863$	−1590.61	+	1590.61i	−0.0627406	+	0.0627406i	0.675040	+	0.737781i	$0.264126\pi$
$864$	−867.035	+	4810.00i	−0.0341402	+	0.189398i
$865$	41113.4	−	10474.0i	1.61607	−	0.411706i
$866$	−21112.6	+	14217.3i	−0.828448	+	0.557878i
$867$	−25592.4	+	25592.4i	−1.00250	+	1.00250i
$868$	−17083.0	+	7220.62i	−0.668013	+	0.282355i
$869$	10106.9			0.394537
$870$	−4599.51	+	261.089i	−0.179239	+	0.0101744i
$871$		−	19754.4i		−	0.768488i
$872$	17657.6	−	27054.8i	0.685737	−	1.05068i
$873$	−9731.05	−	9731.05i	−0.377258	−	0.377258i
$874$	−21564.9	+	14521.8i	−0.834603	+	0.562022i
$875$	−10643.3	+	9882.58i	−0.411209	+	0.381820i
$876$	1942.29	−	4786.34i	0.0749133	−	0.184607i
$877$	−3618.35	−	3618.35i	−0.139319	−	0.139319i	0.634008	−	0.773327i	$-0.281409\pi$
$877$	−3618.35	−	3618.35i	−0.139319	−	0.139319i	−0.773327	+	0.634008i	$0.781409\pi$
$878$	4978.16	−	25506.7i	0.191349	−	0.980420i
$879$	23694.0			0.909192
$880$	2739.24	+	10139.4i	0.104931	+	0.388409i
$881$	5690.57			0.217617			0.108808	−	0.994063i	$-0.465297\pi$
$881$	5690.57			0.217617			0.108808	+	0.994063i	$0.465297\pi$
$882$	−1145.90	+	5871.25i	−0.0437465	+	0.224144i
$883$	−708.579	−	708.579i	−0.0270052	−	0.0270052i	0.693475	−	0.720480i	$-0.256079\pi$
$883$	−708.579	−	708.579i	−0.0270052	−	0.0270052i	−0.720480	+	0.693475i	$0.756079\pi$
$884$	−18377.7	+	45287.6i	−0.699217	+	1.72306i
$885$	−7705.08	+	1962.93i	−0.292659	+	0.0745573i
$886$	−6431.93	+	4331.26i	−0.243888	+	0.164234i
$887$	−1023.06	−	1023.06i	−0.0387272	−	0.0387272i	0.687478	−	0.726205i	$-0.258718\pi$
$887$	−1023.06	−	1023.06i	−0.0387272	−	0.0387272i	−0.726205	+	0.687478i	$0.758718\pi$
$888$	−19263.2	−	12572.3i	−0.727961	−	0.475112i
$889$		−	4778.38i		−	0.180272i
$890$	21045.0	+	18784.1i	0.792619	+	0.707467i
$891$	−1188.94			−0.0447037
$892$	7835.36	−	3311.84i	0.294111	−	0.124314i
$893$	−4072.76	+	4072.76i	−0.152620	+	0.152620i
$894$	13970.4	−	9407.67i	0.522639	−	0.351946i
$895$	17161.9	−	28895.4i	0.640961	−	1.07918i
$896$	12720.3	+	8043.18i	0.474282	+	0.299893i
$897$	7687.78	−	7687.78i	0.286162	−	0.286162i
$898$	−7747.22	−	1512.03i	−0.287893	−	0.0561884i
$899$			10832.7i			0.401882i
$900$	8942.19	−	1018.48i	0.331192	−	0.0377215i
$901$		−	13841.3i		−	0.511788i
$902$	11.4634	−	58.7354i	0.000423161	−	0.00216815i
$903$	9400.91	−	9400.91i	0.346448	−	0.346448i
$904$	16878.2	−	3547.27i	0.620973	−	0.130509i
$905$	3481.83	−	5862.32i	0.127889	−	0.215326i
$906$	7976.98	+	11845.8i	0.292514	+	0.434383i
$907$	23540.0	−	23540.0i	0.861777	−	0.861777i	−0.129768	−	0.991544i	$-0.541423\pi$
$907$	23540.0	−	23540.0i	0.861777	−	0.861777i	0.991544	+	0.129768i	$0.0414232\pi$
$908$	28444.3	−	12022.8i	1.03960	−	0.439417i
$909$	3641.49			0.132872
$910$	10260.8	−	11495.8i	0.373783	−	0.418772i
$911$		−	13976.5i		−	0.508299i	−0.967165	−	0.254150i	$-0.918204\pi$
$911$		−	13976.5i		−	0.508299i	0.967165	−	0.254150i	$-0.0817956\pi$
$912$	22830.9	−	328.932i	0.828953	−	0.0119430i
$913$	−2494.60	−	2494.60i	−0.0904264	−	0.0904264i
$914$	−14856.3	−	22061.6i	−0.537641	−	0.798396i
$915$	3552.57	−	905.045i	0.128354	−	0.0326993i
$916$	−23283.5	−	9448.43i	−0.839856	−	0.340813i
$917$	−4108.02	−	4108.02i	−0.147937	−	0.147937i
$918$	−9766.21	−	1906.08i	−0.351125	−	0.0685295i
$919$	46454.3			1.66745			0.833725	−	0.552179i	$-0.186204\pi$
$919$	46454.3			1.66745			0.833725	+	0.552179i	$0.186204\pi$
$920$	6313.89	−	18506.3i	0.226264	−	0.663189i
$921$	−7686.27			−0.274996
$922$	−2773.69	−	541.343i	−0.0990744	−	0.0193364i
$923$	37684.4	+	37684.4i	1.34388	+	1.34388i
$924$	−1376.62	+	3392.37i	−0.0490126	+	0.120780i
$925$	−11970.0	+	40631.6i	−0.425484	+	1.44428i
$926$	28448.3	+	42245.7i	1.00958	+	1.49922i
$927$	7595.00	+	7595.00i	0.269097	+	0.269097i
$928$	7219.91	−	5014.56i	0.255393	−	0.177383i
$929$			10084.2i			0.356136i	0.984018	+	0.178068i	$0.0569848\pi$
$929$			10084.2i			0.356136i	−0.984018	+	0.178068i	$0.943015\pi$
$930$	−1199.36	−	21128.7i	−0.0422888	−	0.744985i
$931$	27946.5			0.983790
$932$	−18635.9	−	44090.0i	−0.654977	−	1.54959i
$933$	−7790.46	+	7790.46i	−0.273364	+	0.273364i
$934$	−12529.5	−	18606.3i	−0.438949	−	0.651839i
$935$	−20721.0	+	5278.84i	−0.724759	+	0.184638i
$936$	−9344.31	+	1963.89i	−0.326312	+	0.0685808i
$937$	7151.31	−	7151.31i	0.249331	−	0.249331i	−0.571365	−	0.820696i	$-0.693586\pi$
$937$	7151.31	−	7151.31i	0.249331	−	0.249331i	0.820696	+	0.571365i	$0.193586\pi$
$938$	2372.30	−	12155.0i	0.0825783	−	0.423108i
$939$		−	4132.92i		−	0.143634i
$940$	587.519	−	4291.92i	0.0203859	−	0.148922i
$941$			43569.7i			1.50939i	0.656078	+	0.754693i	$0.272214\pi$
$941$			43569.7i			1.50939i	−0.656078	+	0.754693i	$0.727786\pi$
$942$	−13034.6	−	2543.97i	−0.450837	−	0.0879904i
$943$	−78.7810	+	78.7810i	−0.00272053	+	0.00272053i
$944$	10572.4	−	10881.5i	0.364515	−	0.375172i
$945$	2697.29	+	1602.01i	0.0928497	+	0.0551465i
$946$	−14684.6	+	9888.62i	−0.504691	+	0.339859i
$947$	2107.97	−	2107.97i	0.0723334	−	0.0723334i	−0.670015	−	0.742348i	$-0.733712\pi$
$947$	2107.97	−	2107.97i	0.0723334	−	0.0723334i	0.742348	+	0.670015i	$0.233712\pi$
$948$	6433.82	+	15221.6i	0.220423	+	0.521491i
$949$	10091.4			0.345184
$950$	−12672.4	−	40090.5i	−0.432785	−	1.36917i
$951$		−	28753.4i		−	0.980436i
$952$	−16746.4	+	25658.7i	−0.570121	+	0.873533i
$953$	−21555.5	−	21555.5i	−0.732686	−	0.732686i	0.238465	−	0.971151i	$-0.423356\pi$
$953$	−21555.5	−	21555.5i	−0.732686	−	0.732686i	−0.971151	+	0.238465i	$0.923356\pi$
$954$	2242.99	−	1510.43i	0.0761209	−	0.0512599i
$955$	−9190.50	+	15474.0i	−0.311411	+	0.524320i
$956$	35801.0	+	14528.0i	1.21118	+	0.491496i
$957$	1512.06	+	1512.06i	0.0510743	+	0.0510743i
$958$	2396.25	−	12277.7i	0.0808134	−	0.414065i
$959$	19629.8			0.660978
$960$	−13526.8	+	10580.0i	−0.454768	+	0.355696i
$961$	−19971.1			−0.670372
$962$	8608.43	−	44107.1i	0.288510	−	1.47824i
$963$	5259.08	+	5259.08i	0.175983	+	0.175983i
$964$	−10435.8	−	4234.84i	−0.348667	−	0.141489i
$965$	9852.27	+	38673.1i	0.328659	+	1.29008i
$966$	5653.56	−	3807.11i	0.188302	−	0.126803i
$967$	−22286.6	−	22286.6i	−0.741148	−	0.741148i	0.231651	−	0.972799i	$-0.425587\pi$
$967$	−22286.6	−	22286.6i	−0.741148	−	0.741148i	−0.972799	+	0.231651i	$0.925587\pi$
$968$	−13796.1	+	21138.2i	−0.458082	+	0.701868i
$969$			46486.0i			1.54112i
$970$	−2740.38	−	48276.3i	−0.0907097	−	1.59800i
$971$	−20147.8			−0.665885			−0.332943	−	0.942947i	$-0.608042\pi$
$971$	−20147.8			−0.665885			−0.332943	+	0.942947i	$0.608042\pi$
$972$	−756.854	−	1790.62i	−0.0249754	−	0.0590885i
$973$	−15188.1	+	15188.1i	−0.500420	+	0.500420i
$974$	−21511.5	+	14485.8i	−0.707671	+	0.476546i
$975$	8412.69	+	15439.5i	0.276330	+	0.507140i
$976$	−4874.59	+	5017.11i	−0.159869	+	0.164543i
$977$	−1942.69	+	1942.69i	−0.0636153	+	0.0636153i	−0.738199	−	0.674583i	$-0.764323\pi$
$977$	−1942.69	+	1942.69i	−0.0636153	+	0.0636153i	0.674583	+	0.738199i	$0.264323\pi$
$978$	−8752.77	−	1708.29i	−0.286179	−	0.0558537i
$979$		−	13093.6i		−	0.427451i
$980$	−16740.9	+	12709.4i	−0.545681	+	0.414273i
$981$			12850.1i			0.418218i
$982$	−7535.22	+	38608.3i	−0.244866	+	1.25462i
$983$	−14653.9	+	14653.9i	−0.475469	+	0.475469i	−0.903679	−	0.428210i	$-0.859144\pi$
$983$	−14653.9	+	14653.9i	−0.475469	+	0.475469i	0.428210	+	0.903679i	$0.359144\pi$
$984$	95.7564	−	20.1251i	0.00310224	−	0.000651995i
$985$	2061.60	+	8092.40i	0.0666885	+	0.261772i
$986$	9996.31	+	14844.5i	0.322867	+	0.479458i
$987$	1067.73	−	1067.73i	0.0344340	−	0.0344340i
$988$	17367.1	+	41088.3i	0.559232	+	1.32307i
$989$	32959.7			1.05971
$990$	−3116.61	−	2781.79i	−0.100053	−	0.0893042i
$991$			14584.4i			0.467496i	0.972297	+	0.233748i	$0.0750990\pi$
$991$			14584.4i			0.467496i	−0.972297	+	0.233748i	$0.924901\pi$
$992$	23035.3	+	33165.9i	0.737269	+	1.06151i
$993$	−18834.5	−	18834.5i	−0.601909	−	0.601909i
$994$	18661.9	+	27712.9i	0.595493	+	0.884307i
$995$	37803.1	+	22452.5i	1.20446	+	0.715370i
$996$	2169.01	−	5345.03i	0.0690037	−	0.170044i
$997$	−6099.19	−	6099.19i	−0.193744	−	0.193744i	0.603567	−	0.797312i	$-0.293745\pi$
$997$	−6099.19	−	6099.19i	−0.193744	−	0.193744i	−0.797312	+	0.603567i	$0.793745\pi$
$998$	−59352.9	−	11584.0i	−1.88255	−	0.367419i
$999$	9149.35			0.289762

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.v.a.43.16	yes	72
4.3	odd	2		480.4.bh.a.463.20		72
5.2	odd	4	inner	120.4.v.a.67.2	yes	72
8.3	odd	2	inner	120.4.v.a.43.2	✓	72
8.5	even	2		480.4.bh.a.463.19		72
20.7	even	4		480.4.bh.a.367.19		72
40.27	even	4	inner	120.4.v.a.67.16	yes	72
40.37	odd	4		480.4.bh.a.367.20		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.v.a.43.2	✓	72	8.3	odd	2	inner
120.4.v.a.43.16	yes	72	1.1	even	1	trivial
120.4.v.a.67.2	yes	72	5.2	odd	4	inner
120.4.v.a.67.16	yes	72	40.27	even	4	inner
480.4.bh.a.367.19		72	20.7	even	4
480.4.bh.a.367.20		72	40.37	odd	4
480.4.bh.a.463.19		72	8.5	even	2
480.4.bh.a.463.20		72	4.3	odd	2

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	120.4.v.a.43.16

Level	$120$
Weight	$4$
Character	120.43
Analytic conductor	$7.080$
Analytic rank	$0$
Dimension	$72$
Inner twists	$4$