LMFDB - Embedded newform 45.3.k.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(7,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("45.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$45 = 3^{2} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	45.k (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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	45.13
Dual form			45.3.k.a.7.9

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.40598 + 0.644680i) q^{2} +(-0.325974 - 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(0.360208 + 4.98701i) q^{5} +(1.13830 - 7.38535i) q^{6} +(-0.0658171 - 0.0176356i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +(-2.34837 + 12.2309i) q^{10} +(4.62292 + 8.00713i) q^{11} +(2.66465 - 6.05242i) q^{12} +(-12.6403 + 3.38696i) q^{13} +(-0.146985 - 0.0848619i) q^{14} +(14.7550 - 2.69986i) q^{15} +(-9.97912 - 17.2843i) q^{16} +(13.6029 - 13.6029i) q^{17} +(-22.3959 - 0.987258i) q^{18} -5.80704i q^{19} +(-4.80889 + 9.91729i) q^{20} +(-0.0311390 + 0.202031i) q^{21} +(5.96060 + 22.2453i) q^{22} +(43.8013 - 11.7365i) q^{23} +(-8.40093 + 10.4628i) q^{24} +(-24.7405 + 3.59273i) q^{25} -32.5958 q^{26} +(8.66274 + 25.5726i) q^{27} +(-0.106208 - 0.106208i) q^{28} +(-6.37222 + 3.67900i) q^{29} +(37.2408 + 3.01646i) q^{30} +(-8.35363 + 14.4689i) q^{31} +(-8.23618 - 30.7378i) q^{32} +(22.3722 - 16.3967i) q^{33} +(41.4978 - 23.9587i) q^{34} +(0.0642412 - 0.334583i) q^{35} +(-18.9184 - 5.97368i) q^{36} +(36.0680 - 36.0680i) q^{37} +(3.74368 - 13.9716i) q^{38} +(14.2211 + 36.5923i) q^{39} +(14.6331 - 16.9116i) q^{40} +(-31.1567 + 53.9649i) q^{41} +(-0.205165 + 0.466007i) q^{42} +(-2.59980 + 9.70259i) q^{43} +20.3810i q^{44} +(-12.8614 - 43.1229i) q^{45} +112.951 q^{46} +(-44.6476 - 11.9633i) q^{47} +(-48.2931 + 35.3944i) q^{48} +(-42.4312 - 24.4977i) q^{49} +(-61.8413 - 7.30568i) q^{50} +(-45.0012 - 36.1329i) q^{51} +(-27.8636 - 7.46602i) q^{52} +(28.0258 + 28.0258i) q^{53} +(4.35625 + 67.1118i) q^{54} +(-38.2664 + 25.9388i) q^{55} +(0.152383 + 0.263935i) q^{56} +(-17.3180 + 1.89294i) q^{57} +(-17.7032 + 4.74356i) q^{58} +(-16.3509 - 9.44022i) q^{59} +(31.1433 + 11.1085i) q^{60} +(2.69547 + 4.66870i) q^{61} +(-29.4265 + 29.4265i) q^{62} +(0.612655 + 0.0270071i) q^{63} +0.568692i q^{64} +(-21.4439 - 61.8173i) q^{65} +(64.3977 - 25.0273i) q^{66} +(12.8379 + 47.9117i) q^{67} +(40.9609 - 10.9754i) q^{68} +(-49.2792 - 126.800i) q^{69} +(0.370262 - 0.763584i) q^{70} +56.4200 q^{71} +(33.9412 + 21.6430i) q^{72} +(-54.7135 - 54.7135i) q^{73} +(110.031 - 63.5264i) q^{74} +(18.7791 + 72.6109i) q^{75} +(6.40036 - 11.0857i) q^{76} +(-0.163056 - 0.608534i) q^{77} +(10.6254 + 97.2084i) q^{78} +(40.9692 - 23.6536i) q^{79} +(82.6026 - 55.9919i) q^{80} +(73.4397 - 34.1704i) q^{81} +(-109.752 + 109.752i) q^{82} +(-16.0841 + 60.0267i) q^{83} +(-0.282117 + 0.351360i) q^{84} +(72.7376 + 62.9379i) q^{85} +(-12.5101 + 21.6682i) q^{86} +(13.0488 + 17.8042i) q^{87} +(10.7032 - 39.9449i) q^{88} +59.1599i q^{89} +(-3.14373 - 112.044i) q^{90} +0.891679 q^{91} +(96.5530 + 25.8713i) q^{92} +(45.8728 + 20.1960i) q^{93} +(-99.7085 - 57.5668i) q^{94} +(28.9598 - 2.09175i) q^{95} +(-88.9828 + 34.5820i) q^{96} +(-150.251 - 40.2595i) q^{97} +(-86.2954 - 86.2954i) q^{98} +(-56.1918 - 61.3743i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100})$ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

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

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	2.40598	+	0.644680i	1.20299	+	0.322340i	0.804008	−	0.594619i	$-0.202697\pi$
$2$	2.40598	+	0.644680i	1.20299	+	0.322340i	0.398981	+	0.916959i	$0.369364\pi$
$3$	−0.325974	−	2.98224i	−0.108658	−	0.994079i
$3$	−0.325974	−	2.98224i	−0.108658	−	0.994079i
$4$	1.90902	+	1.10217i	0.477254	+	0.275543i
$5$	0.360208	+	4.98701i	0.0720417	+	0.997402i
$5$	0.360208	+	4.98701i	0.0720417	+	0.997402i
$6$	1.13830	−	7.38535i	0.189717	−	1.23089i
$7$	−0.0658171	−	0.0176356i	−0.00940244	−	0.00251938i	0.254115	−	0.967174i	$-0.418216\pi$
$7$	−0.0658171	−	0.0176356i	−0.00940244	−	0.00251938i	−0.263517	+	0.964655i	$0.584883\pi$
$8$	−3.16269	−	3.16269i	−0.395336	−	0.395336i
$9$	−8.78748	+	1.94426i	−0.976387	+	0.216029i
$10$	−2.34837	+	12.2309i	−0.234837	+	1.22309i
$11$	4.62292	+	8.00713i	0.420265	+	0.727921i	0.995965	−	0.0897404i	$-0.0286037\pi$
$11$	4.62292	+	8.00713i	0.420265	+	0.727921i	−0.575700	+	0.817661i	$0.695270\pi$
$12$	2.66465	−	6.05242i	0.222054	−	0.504368i
$13$	−12.6403	+	3.38696i	−0.972331	+	0.260535i	−0.709812	−	0.704391i	$-0.751220\pi$
$13$	−12.6403	+	3.38696i	−0.972331	+	0.260535i	−0.262519	+	0.964927i	$0.584553\pi$
$14$	−0.146985	−	0.0848619i	−0.0104989	−	0.00606156i
$15$	14.7550	−	2.69986i	0.983668	−	0.179991i
$16$	−9.97912	−	17.2843i	−0.623695	−	1.08027i
$17$	13.6029	−	13.6029i	0.800170	−	0.800170i	−0.182952	−	0.983122i	$-0.558565\pi$
$17$	13.6029	−	13.6029i	0.800170	−	0.800170i	0.983122	+	0.182952i	$0.0585652\pi$
$18$	−22.3959	−	0.987258i	−1.24422	−	0.0548477i
$19$		−	5.80704i		−	0.305634i	−0.988255	−	0.152817i	$-0.951166\pi$
$19$		−	5.80704i		−	0.305634i	0.988255	−	0.152817i	$-0.0488345\pi$
$20$	−4.80889	+	9.91729i	−0.240445	+	0.495865i
$21$	−0.0311390	+	0.202031i	−0.00148281	+	0.00962052i
$22$	5.96060	+	22.2453i	0.270936	+	1.01115i
$23$	43.8013	−	11.7365i	1.90440	−	0.510283i	0.908728	−	0.417390i	$-0.137055\pi$
$23$	43.8013	−	11.7365i	1.90440	−	0.510283i	0.995676	−	0.0928936i	$-0.0296117\pi$
$24$	−8.40093	+	10.4628i	−0.350039	+	0.435952i
$25$	−24.7405	+	3.59273i	−0.989620	+	0.143709i
$26$	−32.5958			−1.25368
$27$	8.66274	+	25.5726i	0.320842	+	0.947133i
$28$	−0.106208	−	0.106208i	−0.00379316	−	0.00379316i
$29$	−6.37222	+	3.67900i	−0.219732	+	0.126862i	−0.605826	−	0.795597i	$-0.707157\pi$
$29$	−6.37222	+	3.67900i	−0.219732	+	0.126862i	0.386094	+	0.922459i	$0.373824\pi$
$30$	37.2408	+	3.01646i	1.24136	+	0.100549i
$31$	−8.35363	+	14.4689i	−0.269472	+	0.466739i	−0.968726	−	0.248135i	$-0.920183\pi$
$31$	−8.35363	+	14.4689i	−0.269472	+	0.466739i	0.699254	+	0.714874i	$0.253516\pi$
$32$	−8.23618	−	30.7378i	−0.257381	−	0.960558i
$33$	22.3722	−	16.3967i	0.677946	−	0.496871i
$34$	41.4978	−	23.9587i	1.22052	−	0.704669i
$35$	0.0642412	−	0.334583i	0.00183546	−	0.00955951i
$36$	−18.9184	−	5.97368i	−0.525510	−	0.165936i
$37$	36.0680	−	36.0680i	0.974810	−	0.974810i	−0.0248806	−	0.999690i	$-0.507921\pi$
$37$	36.0680	−	36.0680i	0.974810	−	0.974810i	0.999690	+	0.0248806i	$0.00792055\pi$
$38$	3.74368	−	13.9716i	0.0985180	−	0.367674i
$39$	14.2211	+	36.5923i	0.364644	+	0.938265i
$40$	14.6331	−	16.9116i	0.365828	−	0.422789i
$41$	−31.1567	+	53.9649i	−0.759919	+	1.31622i	0.182973	+	0.983118i	$0.441428\pi$
$41$	−31.1567	+	53.9649i	−0.759919	+	1.31622i	−0.942892	+	0.333100i	$0.891905\pi$
$42$	−0.205165	+	0.466007i	−0.00488488	+	0.0110954i
$43$	−2.59980	+	9.70259i	−0.0604605	+	0.225642i	−0.989545	−	0.144227i	$-0.953931\pi$
$43$	−2.59980	+	9.70259i	−0.0604605	+	0.225642i	0.929084	+	0.369868i	$0.120597\pi$
$44$			20.3810i			0.463204i
$45$	−12.8614	−	43.1229i	−0.285808	−	0.958287i
$46$	112.951			2.45546
$47$	−44.6476	−	11.9633i	−0.949948	−	0.254538i	−0.249608	−	0.968347i	$-0.580302\pi$
$47$	−44.6476	−	11.9633i	−0.949948	−	0.254538i	−0.700340	+	0.713809i	$0.746968\pi$
$48$	−48.2931	+	35.3944i	−1.00611	+	0.737382i
$49$	−42.4312	−	24.4977i	−0.865943	−	0.499953i
$50$	−61.8413	−	7.30568i	−1.23683	−	0.146114i
$51$	−45.0012	−	36.1329i	−0.882377	−	0.708488i
$52$	−27.8636	−	7.46602i	−0.535838	−	0.143577i
$53$	28.0258	+	28.0258i	0.528789	+	0.528789i	0.920211	−	0.391423i	$-0.128017\pi$
$53$	28.0258	+	28.0258i	0.528789	+	0.528789i	−0.391423	+	0.920211i	$0.628017\pi$
$54$	4.35625	+	67.1118i	0.0806712	+	1.24281i
$55$	−38.2664	+	25.9388i	−0.695753	+	0.471614i
$56$	0.152383	+	0.263935i	0.00272112	+	0.00471312i
$57$	−17.3180	+	1.89294i	−0.303824	+	0.0332096i
$58$	−17.7032	+	4.74356i	−0.305228	+	0.0817855i
$59$	−16.3509	−	9.44022i	−0.277135	−	0.160004i	0.354991	−	0.934870i	$-0.384484\pi$
$59$	−16.3509	−	9.44022i	−0.277135	−	0.160004i	−0.632126	+	0.774866i	$0.717817\pi$
$60$	31.1433	+	11.1085i	0.519055	+	0.185141i
$61$	2.69547	+	4.66870i	0.0441881	+	0.0765360i	0.887274	−	0.461244i	$-0.152597\pi$
$61$	2.69547	+	4.66870i	0.0441881	+	0.0765360i	−0.843085	+	0.537780i	$0.819263\pi$
$62$	−29.4265	+	29.4265i	−0.474621	+	0.474621i
$63$	0.612655	+	0.0270071i	0.00972468	+	0.000428684i
$64$			0.568692i			0.00888582i
$65$	−21.4439	−	61.8173i	−0.329907	−	0.951035i
$66$	64.3977	−	25.0273i	0.975722	−	0.379202i
$67$	12.8379	+	47.9117i	0.191610	+	0.715100i	0.993118	+	0.117116i	$0.0373648\pi$
$67$	12.8379	+	47.9117i	0.191610	+	0.715100i	−0.801508	+	0.597984i	$0.795969\pi$
$68$	40.9609	−	10.9754i	0.602366	−	0.161403i
$69$	−49.2792	−	126.800i	−0.714191	−	1.83768i
$70$	0.370262	−	0.763584i	0.00528945	−	0.0109083i
$71$	56.4200			0.794648			0.397324	−	0.917678i	$-0.369939\pi$
$71$	56.4200			0.794648			0.397324	+	0.917678i	$0.369939\pi$
$72$	33.9412	+	21.6430i	0.471405	+	0.300597i
$73$	−54.7135	−	54.7135i	−0.749500	−	0.749500i	0.224885	−	0.974385i	$-0.427799\pi$
$73$	−54.7135	−	54.7135i	−0.749500	−	0.749500i	−0.974385	+	0.224885i	$0.927799\pi$
$74$	110.031	−	63.5264i	1.48691	−	0.858465i
$75$	18.7791	+	72.6109i	0.250388	+	0.968146i
$76$	6.40036	−	11.0857i	0.0842152	−	0.145865i
$77$	−0.163056	−	0.608534i	−0.00211761	−	0.00790303i
$78$	10.6254	+	97.2084i	0.136223	+	1.24626i
$79$	40.9692	−	23.6536i	0.518597	−	0.299412i	−0.217763	−	0.976002i	$-0.569876\pi$
$79$	40.9692	−	23.6536i	0.518597	−	0.299412i	0.736361	+	0.676589i	$0.236543\pi$
$80$	82.6026	−	55.9919i	1.03253	−	0.699899i
$81$	73.4397	−	34.1704i	0.906663	−	0.421856i
$82$	−109.752	+	109.752i	−1.33844	+	1.33844i
$83$	−16.0841	+	60.0267i	−0.193784	+	0.723213i	0.798794	+	0.601605i	$0.205472\pi$
$83$	−16.0841	+	60.0267i	−0.193784	+	0.723213i	−0.992578	+	0.121608i	$0.961195\pi$
$84$	−0.282117	+	0.351360i	−0.00335854	+	0.00418285i
$85$	72.7376	+	62.9379i	0.855737	+	0.740445i
$86$	−12.5101	+	21.6682i	−0.145467	+	0.251956i
$87$	13.0488	+	17.8042i	0.149987	+	0.204646i
$88$	10.7032	−	39.9449i	0.121627	−	0.453919i
$89$			59.1599i			0.664718i	0.943153	+	0.332359i	$0.107844\pi$
$89$			59.1599i			0.664718i	−0.943153	+	0.332359i	$0.892156\pi$
$90$	−3.14373	−	112.044i	−0.0349304	−	1.24494i
$91$	0.891679			0.00979867
$92$	96.5530	+	25.8713i	1.04949	+	0.281210i
$93$	45.8728	+	20.1960i	0.493256	+	0.217162i
$94$	−99.7085	−	57.5668i	−1.06073	−	0.612412i
$95$	28.9598	−	2.09175i	0.304840	−	0.0220184i
$96$	−88.9828	+	34.5820i	−0.926904	+	0.360229i
$97$	−150.251	−	40.2595i	−1.54898	−	0.415047i	−0.619823	−	0.784742i	$-0.712796\pi$
$97$	−150.251	−	40.2595i	−1.54898	−	0.415047i	−0.929153	+	0.369695i	$0.879462\pi$
$98$	−86.2954	−	86.2954i	−0.880566	−	0.880566i
$99$	−56.1918	−	61.3743i	−0.567594	−	0.619943i
$100$	−51.1898	−	20.4097i	−0.511898	−	0.204097i
$101$	27.6053	+	47.8137i	0.273319	+	0.473403i	0.969710	−	0.244260i	$-0.0785451\pi$
$101$	27.6053	+	47.8137i	0.273319	+	0.473403i	−0.696390	+	0.717663i	$0.745212\pi$
$102$	−84.9779	−	115.946i	−0.833116	−	1.13673i
$103$	88.3218	−	23.6658i	0.857493	−	0.229765i	0.196821	−	0.980439i	$-0.436938\pi$
$103$	88.3218	−	23.6658i	0.857493	−	0.229765i	0.660672	+	0.750675i	$0.270271\pi$
$104$	50.6892	+	29.2654i	0.487397	+	0.281399i
$105$	−1.01875	−	0.0825172i	−0.00970234	−	0.000785878i
$106$	49.3618	+	85.4971i	0.465677	+	0.806576i
$107$	−14.6336	+	14.6336i	−0.136762	+	0.136762i	−0.772174	−	0.635411i	$-0.780831\pi$
$107$	−14.6336	+	14.6336i	−0.136762	+	0.136762i	0.635411	+	0.772174i	$0.280831\pi$
$108$	−11.6480	+	58.3663i	−0.107852	+	0.540429i
$109$			112.055i			1.02803i	0.857781	+	0.514015i	$0.171843\pi$
$109$			112.055i			1.02803i	−0.857781	+	0.514015i	$0.828157\pi$
$110$	−108.790	+	37.7385i	−0.989003	+	0.343077i
$111$	−119.320	−	95.8060i	−1.07496	−	0.863117i
$112$	0.351976	+	1.31359i	0.00314264	+	0.0117285i
$113$	−35.8191	+	9.59771i	−0.316984	+	0.0849355i	−0.413803	−	0.910366i	$-0.635800\pi$
$113$	−35.8191	+	9.59771i	−0.316984	+	0.0849355i	0.0968194	+	0.995302i	$0.469133\pi$
$114$	−42.8870	−	6.61017i	−0.376202	−	0.0579840i
$115$	74.3077	+	214.210i	0.646154	+	1.86269i
$116$	−16.2196			−0.139824
$117$	104.491	−	54.3389i	0.893088	−	0.464435i
$118$	−33.2541	−	33.2541i	−0.281814	−	0.281814i
$119$	−1.13520	+	0.655407i	−0.00953948	+	0.00550762i
$120$	−55.2044	−	38.1267i	−0.460036	−	0.317723i
$121$	17.7573	−	30.7565i	0.146754	−	0.254186i
$122$	3.47543	+	12.9705i	0.0284872	+	0.106316i
$123$	171.092	+	75.3254i	1.39100	+	0.612402i
$124$	−31.8944	+	18.4143i	−0.257213	+	0.148502i
$125$	−26.8287	−	122.087i	−0.214629	−	0.976696i
$126$	1.45662	+	0.459945i	0.0115605	+	0.00365035i
$127$	151.793	−	151.793i	1.19522	−	1.19522i	0.219643	−	0.975580i	$-0.429511\pi$
$127$	151.793	−	151.793i	1.19522	−	1.19522i	0.975580	−	0.219643i	$-0.0704892\pi$
$128$	−33.3113	+	124.320i	−0.260245	+	0.971247i
$129$	29.7829	+	4.59044i	0.230875	+	0.0355848i
$130$	−11.7413	−	162.556i	−0.0903176	−	1.25043i
$131$	−0.751448	+	1.30155i	−0.00573624	+	0.00993547i	−0.868879	−	0.495024i	$-0.835159\pi$
$131$	−0.751448	+	1.30155i	−0.00573624	+	0.00993547i	0.863143	+	0.504960i	$0.168493\pi$
$132$	60.7809	−	6.64367i	0.460462	−	0.0503308i
$133$	−0.102411	+	0.382203i	−0.000770006	+	0.00287370i
$134$			123.551i			0.922021i
$135$	−124.410	+	52.4126i	−0.921558	+	0.388242i
$136$	−86.0434			−0.632672
$137$	67.4699	+	18.0785i	0.492481	+	0.131960i	0.496508	−	0.868032i	$-0.334615\pi$
$137$	67.4699	+	18.0785i	0.492481	+	0.131960i	−0.00402717	+	0.999992i	$0.501282\pi$
$138$	−36.8192	−	336.847i	−0.266805	−	2.44092i
$139$	106.332	+	61.3909i	0.764980	+	0.441661i	0.831081	−	0.556152i	$-0.187723\pi$
$139$	106.332	+	61.3909i	0.764980	+	0.441661i	−0.0661012	+	0.997813i	$0.521056\pi$
$140$	0.491405	−	0.567919i	0.00351004	−	0.00405657i
$141$	−21.1234	+	137.049i	−0.149811	+	0.971981i
$142$	135.745	+	36.3728i	0.955953	+	0.256147i
$143$	−85.5549	−	85.5549i	−0.598286	−	0.598286i
$144$	121.297	+	132.484i	0.842338	+	0.920027i
$145$	−20.6426	−	30.4531i	−0.142362	−	0.210021i
$146$	−96.3668	−	166.912i	−0.660047	−	1.14323i
$147$	−59.2264	+	134.526i	−0.402901	+	0.915140i
$148$	108.607	−	29.1013i	0.733834	−	0.196630i
$149$	23.0090	+	13.2842i	0.154423	+	0.0891560i	0.575220	−	0.817999i	$-0.304916\pi$
$149$	23.0090	+	13.2842i	0.154423	+	0.0891560i	−0.420797	+	0.907155i	$0.638250\pi$
$150$	−1.62865	+	186.807i	−0.0108577	+	1.24538i
$151$	−49.2414	−	85.2887i	−0.326102	−	0.564826i	0.655633	−	0.755080i	$-0.272402\pi$
$151$	−49.2414	−	85.2887i	−0.326102	−	0.564826i	−0.981735	+	0.190254i	$0.939069\pi$
$152$	−18.3659	+	18.3659i	−0.120828	+	0.120828i
$153$	−93.0876	+	145.983i	−0.608415	+	0.954136i
$154$		−	1.56924i		−	0.0101899i
$155$	−75.1656	−	36.4478i	−0.484940	−	0.235147i
$156$	−13.1826	+	85.5295i	−0.0845042	+	0.548266i
$157$	−44.6968	−	166.811i	−0.284693	−	1.06249i	−0.949063	−	0.315086i	$-0.897967\pi$
$157$	−44.6968	−	166.811i	−0.284693	−	1.06249i	0.664370	−	0.747404i	$-0.268700\pi$
$158$	113.820	−	30.4980i	0.720379	−	0.193025i
$159$	74.4439	−	92.7152i	0.468201	−	0.583115i
$160$	150.323	−	52.1459i	0.939520	−	0.325912i
$161$	−3.08985			−0.0191916
$162$	198.723	−	34.8680i	1.22669	−	0.215235i
$163$	−65.0824	−	65.0824i	−0.399278	−	0.399278i	0.478700	−	0.877978i	$-0.341108\pi$
$163$	−65.0824	−	65.0824i	−0.399278	−	0.399278i	−0.877978	+	0.478700i	$0.841108\pi$
$164$	−118.957	+	68.6800i	−0.725349	+	0.418780i
$165$	89.8294	+	105.664i	0.544420	+	0.640389i
$166$	−77.3960	+	134.054i	−0.466241	+	0.807553i
$167$	−51.7034	−	192.960i	−0.309601	−	1.15545i	−0.928912	−	0.370301i	$-0.879255\pi$
$167$	−51.7034	−	192.960i	−0.309601	−	1.15545i	0.619311	−	0.785146i	$-0.287412\pi$
$168$	0.737444	−	0.540478i	0.00438955	−	0.00321713i
$169$	1.94752	−	1.12440i	0.0115238	−	0.00665325i
$170$	134.430	+	198.320i	0.790767	+	1.16659i
$171$	11.2904	+	51.0293i	0.0660258	+	0.298417i
$172$	−15.6570	+	15.6570i	−0.0910290	+	0.0910290i
$173$	8.94958	−	33.4003i	0.0517317	−	0.193065i	−0.935224	−	0.354056i	$-0.884802\pi$
$173$	8.94958	−	33.4003i	0.0517317	−	0.193065i	0.986956	+	0.160991i	$0.0514689\pi$
$174$	19.9172	+	51.2489i	0.114467	+	0.294534i
$175$	1.69171	+	0.199852i	0.00966690	+	0.00114201i
$176$	92.2653	−	159.808i	0.524235	−	0.908001i
$177$	−22.8230	+	51.8397i	−0.128944	+	0.292879i
$178$	−38.1392	+	142.337i	−0.214265	+	0.799648i
$179$		−	185.962i		−	1.03890i	−0.854502	−	0.519448i	$-0.826138\pi$
$179$		−	185.962i		−	1.03890i	0.854502	−	0.519448i	$-0.173862\pi$
$180$	22.9762	−	96.4978i	0.127646	−	0.536099i
$181$	−97.7851			−0.540249			−0.270125	−	0.962825i	$-0.587065\pi$
$181$	−97.7851			−0.540249			−0.270125	+	0.962825i	$0.587065\pi$
$182$	2.14536	+	0.574847i	0.0117877	+	0.00315850i
$183$	13.0445	−	9.56041i	0.0712814	−	0.0522427i
$184$	−175.649	−	101.411i	−0.954613	−	0.551146i
$185$	192.863	+	166.879i	1.04250	+	0.902050i
$186$	97.3490	+	78.1645i	0.523382	+	0.420239i
$187$	171.805	+	46.0350i	0.918744	+	0.246177i
$188$	−72.0473	−	72.0473i	−0.383231	−	0.383231i
$189$	−0.119168	−	1.83589i	−0.000630518	−	0.00971368i
$190$	71.0251	+	13.6371i	0.373816	+	0.0717741i
$191$	−68.2090	−	118.141i	−0.357115	−	0.618542i	0.630362	−	0.776301i	$-0.282906\pi$
$191$	−68.2090	−	118.141i	−0.357115	−	0.618542i	−0.987478	+	0.157759i	$0.949573\pi$
$192$	1.69598	−	0.185379i	0.00883321	−	0.000965515i
$193$	−89.2148	+	23.9050i	−0.462253	+	0.123860i	−0.482427	−	0.875936i	$-0.660245\pi$
$193$	−89.2148	+	23.9050i	−0.462253	+	0.123860i	0.0201740	+	0.999796i	$0.493578\pi$
$194$	−335.545	−	193.727i	−1.72961	−	0.998594i
$195$	−177.364	+	84.1017i	−0.909557	+	0.431291i
$196$	−54.0013	−	93.5329i	−0.275517	−	0.477209i
$197$	−170.623	+	170.623i	−0.866107	+	0.866107i	−0.992039	−	0.125932i	$-0.959808\pi$
$197$	−170.623	+	170.623i	−0.866107	+	0.866107i	0.125932	+	0.992039i	$0.459808\pi$
$198$	−95.6294	−	183.891i	−0.482977	−	0.928742i
$199$			36.4196i			0.183013i	0.995804	+	0.0915066i	$0.0291683\pi$
$199$			36.4196i			0.183013i	−0.995804	+	0.0915066i	$0.970832\pi$
$200$	89.6092	+	66.8838i	0.448046	+	0.334419i
$201$	138.699	−	53.9036i	0.690046	−	0.268177i
$202$	35.5931	+	132.835i	0.176204	+	0.657601i
$203$	0.484283	−	0.129763i	0.00238563	−	0.000639227i
$204$	−46.0835	−	118.577i	−0.225900	−	0.581261i
$205$	−280.346	−	135.940i	−1.36754	−	0.663121i
$206$	227.757			1.10562
$207$	−362.084	+	188.296i	−1.74920	+	0.909641i
$208$	184.681	+	184.681i	0.887887	+	0.887887i
$209$	46.4977	−	26.8455i	0.222477	−	0.128447i
$210$	−2.39788	−	0.855300i	−0.0114185	−	0.00407286i
$211$	96.8033	−	167.668i	0.458784	−	0.794636i	−0.540113	−	0.841592i	$-0.681619\pi$
$211$	96.8033	−	167.668i	0.458784	−	0.794636i	0.998897	+	0.0469559i	$0.0149520\pi$
$212$	22.6125	+	84.3909i	0.106663	+	0.398070i
$213$	−18.3914	−	168.258i	−0.0863448	−	0.789943i
$214$	−44.6420	+	25.7741i	−0.208607	+	0.120440i
$215$	−49.3234	−	9.47028i	−0.229411	−	0.0440478i
$216$	53.4805	−	108.276i	0.247595	−	0.501276i
$217$	0.804980	−	0.804980i	0.00370959	−	0.00370959i
$218$	−72.2398	+	269.603i	−0.331375	+	1.23671i
$219$	−145.334	+	181.004i	−0.663623	+	0.826502i
$220$	−101.640	+	7.34140i	−0.462001	+	0.0333700i
$221$	−125.872	+	218.017i	−0.569558	+	0.986503i
$222$	−225.318	−	307.431i	−1.01495	−	1.38482i
$223$	−24.7802	+	92.4808i	−0.111122	+	0.414712i	−0.998968	−	0.0454290i	$-0.985535\pi$
$223$	−24.7802	+	92.4808i	−0.111122	+	0.414712i	0.887846	+	0.460141i	$0.152201\pi$
$224$			2.16833i			0.00968002i
$225$	210.421	−	79.6731i	0.935207	−	0.354102i
$226$	−92.3675			−0.408706
$227$	318.219	+	85.2664i	1.40184	+	0.375623i	0.879007	−	0.476810i	$-0.158207\pi$
$227$	318.219	+	85.2664i	1.40184	+	0.375623i	0.522837	+	0.852433i	$0.324874\pi$
$228$	−35.1467	−	15.4737i	−0.154152	−	0.0678672i
$229$	360.256	+	207.994i	1.57317	+	0.908269i	0.995777	+	0.0918017i	$0.0292626\pi$
$229$	360.256	+	207.994i	1.57317	+	0.908269i	0.577391	+	0.816468i	$0.304071\pi$
$230$	40.6860	+	563.289i	0.176896	+	2.44908i
$231$	−1.76164	+	0.684638i	−0.00762615	+	0.00296380i
$232$	31.7889	+	8.51781i	0.137021	+	0.0367147i
$233$	−22.0213	−	22.0213i	−0.0945121	−	0.0945121i	0.658270	−	0.752782i	$-0.271289\pi$
$233$	−22.0213	−	22.0213i	−0.0945121	−	0.0945121i	−0.752782	+	0.658270i	$0.771289\pi$
$234$	286.435	−	63.3748i	1.22408	−	0.270833i
$235$	43.5785	−	226.967i	0.185441	−	0.965817i
$236$	−20.8095	−	36.0431i	−0.0881758	−	0.152725i
$237$	−83.8955	−	114.469i	−0.353989	−	0.482993i
$238$	−3.15379	+	0.845055i	−0.0132512	+	0.00355065i
$239$	−267.552	−	154.471i	−1.11946	−	0.646323i	−0.178200	−	0.983994i	$-0.557027\pi$
$239$	−267.552	−	154.471i	−1.11946	−	0.646323i	−0.941264	+	0.337672i	$0.890361\pi$
$240$	−193.908	−	228.089i	−0.807948	−	0.950370i
$241$	−12.8569	−	22.2688i	−0.0533481	−	0.0924016i	0.838118	−	0.545489i	$-0.183656\pi$
$241$	−12.8569	−	22.2688i	−0.0533481	−	0.0924016i	−0.891466	+	0.453087i	$0.850323\pi$
$242$	62.5517	−	62.5517i	0.258478	−	0.258478i
$243$	−125.844	−	207.876i	−0.517875	−	0.855457i
$244$			11.8835i			0.0487028i
$245$	106.886	−	220.429i	0.436270	−	0.899711i
$246$	363.084	+	291.531i	1.47595	+	1.18509i
$247$	19.6682	+	73.4028i	0.0796284	+	0.297177i
$248$	72.1806	−	19.3407i	0.291051	−	0.0779868i
$249$	184.257	+	28.3995i	0.739987	+	0.114054i
$250$	14.1578	−	311.034i	0.0566311	−	1.24414i
$251$	275.877			1.09911			0.549556	−	0.835457i	$-0.314797\pi$
$251$	275.877			1.09911			0.549556	+	0.835457i	$0.314797\pi$
$252$	1.13980	+	0.726807i	0.00452302	+	0.00288416i
$253$	296.465	+	296.465i	1.17180	+	1.17180i
$254$	463.070	−	267.353i	1.82311	−	1.05257i
$255$	163.985	−	237.437i	0.643079	−	0.931125i
$256$	−159.155	+	275.665i	−0.621701	+	1.07682i
$257$	1.65593	+	6.18001i	0.00644330	+	0.0240467i	0.969073	−	0.246776i	$-0.0793711\pi$
$257$	1.65593	+	6.18001i	0.00644330	+	0.0240467i	−0.962629	+	0.270822i	$0.912704\pi$
$258$	68.6977	+	30.2449i	0.266270	+	0.117228i
$259$	−3.00997	+	1.73781i	−0.0116215	+	0.00670968i
$260$	27.1964	−	141.645i	0.104602	−	0.544789i
$261$	48.8428	−	44.7185i	0.187137	−	0.171335i
$262$	−2.64705	+	2.64705i	−0.0101032	+	0.0101032i
$263$	54.9964	−	205.249i	0.209112	−	0.780416i	−0.779045	−	0.626968i	$-0.784296\pi$
$263$	54.9964	−	205.249i	0.209112	−	0.780416i	0.988157	−	0.153448i	$-0.0490377\pi$
$264$	−122.614	−	18.8985i	−0.464447	−	0.0715852i
$265$	−129.670	+	149.860i	−0.489320	+	0.565509i
$266$	−0.492797	+	0.853549i	−0.00185262	+	0.00320883i
$267$	176.429	−	19.2846i	0.660782	−	0.0722269i
$268$	−28.2991	+	105.614i	−0.105594	+	0.394081i
$269$			349.046i			1.29757i	0.760973	+	0.648784i	$0.224722\pi$
$269$			349.046i			1.29757i	−0.760973	+	0.648784i	$0.775278\pi$
$270$	−333.118	+	45.8989i	−1.23377	+	0.169996i
$271$	−202.277			−0.746409			−0.373205	−	0.927749i	$-0.621741\pi$
$271$	−202.277			−0.746409			−0.373205	+	0.927749i	$0.621741\pi$
$272$	−370.862	−	99.3722i	−1.36346	−	0.365339i
$273$	−0.290664	−	2.65920i	−0.00106470	−	0.00974065i
$274$	150.676	+	86.9930i	0.549913	+	0.317493i
$275$	−143.141	−	181.491i	−0.520512	−	0.659969i
$276$	45.6806	−	296.377i	0.165509	−	1.07383i
$277$	−234.373	−	62.8000i	−0.846112	−	0.226715i	−0.190381	−	0.981710i	$-0.560972\pi$
$277$	−234.373	−	62.8000i	−0.846112	−	0.226715i	−0.655730	+	0.754995i	$0.727639\pi$
$278$	216.255	+	216.255i	0.777897	+	0.777897i
$279$	45.2760	−	143.387i	0.162280	−	0.513932i
$280$	−1.26136	+	0.855006i	−0.00450484	+	0.00305359i
$281$	140.160	+	242.764i	0.498789	+	0.863929i	0.999999	−	0.00139729i	$-0.000444772\pi$
$281$	140.160	+	242.764i	0.498789	+	0.863929i	−0.501210	+	0.865326i	$0.667111\pi$
$282$	−139.175	+	316.120i	−0.493530	+	1.12099i
$283$	−372.686	+	99.8610i	−1.31691	+	0.352866i	−0.847820	−	0.530283i	$-0.822086\pi$
$283$	−372.686	+	99.8610i	−1.31691	+	0.352866i	−0.469092	+	0.883149i	$0.655419\pi$
$284$	107.707	+	62.1845i	0.379249	+	0.218959i
$285$	−15.6782	−	85.6831i	−0.0550113	−	0.300642i
$286$	−150.688	−	260.999i	−0.526880	−	0.912583i
$287$	3.00235	−	3.00235i	0.0104611	−	0.0104611i
$288$	132.138	+	254.095i	0.458812	+	0.882274i
$289$		−	81.0774i		−	0.280545i
$290$	−30.0330	−	86.5774i	−0.103562	−	0.298543i
$291$	−71.0857	+	461.207i	−0.244281	+	1.58490i
$292$	−44.1453	−	164.753i	−0.151183	−	0.564222i
$293$	40.8052	−	10.9337i	0.139267	−	0.0373164i	−0.188512	−	0.982071i	$-0.560367\pi$
$293$	40.8052	−	10.9337i	0.139267	−	0.0373164i	0.327779	+	0.944754i	$0.393700\pi$
$294$	−229.223	+	285.484i	−0.779672	+	0.971032i
$295$	41.1887	−	84.9427i	0.139623	−	0.287941i
$296$	−228.143			−0.770755
$297$	−164.716	+	187.584i	−0.554598	+	0.631595i
$298$	46.7950	+	46.7950i	0.157030	+	0.157030i
$299$	−513.910	+	296.706i	−1.71876	+	0.992329i
$300$	−44.1800	+	159.313i	−0.147267	+	0.531044i
$301$	0.342223	−	0.592747i	0.00113695	−	0.00196926i
$302$	−63.4899	−	236.948i	−0.210232	−	0.784595i
$303$	133.593	−	97.9115i	0.440902	−	0.323140i
$304$	−100.371	+	57.9492i	−0.330168	+	0.190622i
$305$	−22.3119	+	15.1240i	−0.0731537	+	0.0495870i
$306$	−318.079	+	291.220i	−1.03947	+	0.951698i
$307$	−85.1111	+	85.1111i	−0.277235	+	0.277235i	−0.832004	−	0.554769i	$-0.812806\pi$
$307$	−85.1111	+	85.1111i	−0.277235	+	0.277235i	0.554769	+	0.832004i	$0.312806\pi$
$308$	0.359431	−	1.34142i	0.00116699	−	0.00435525i
$309$	−99.3675	−	255.682i	−0.321578	−	0.827450i
$310$	−157.350	−	136.150i	−0.507580	−	0.439195i
$311$	227.093	−	393.336i	0.730202	−	1.26475i	−0.226595	−	0.973989i	$-0.572759\pi$
$311$	227.093	−	393.336i	0.730202	−	1.26475i	0.956797	−	0.290758i	$-0.0939074\pi$
$312$	70.7531	−	160.707i	0.226773	−	0.515087i
$313$	76.9018	−	287.001i	0.245693	−	0.916937i	−0.727342	−	0.686276i	$-0.759244\pi$
$313$	76.9018	−	287.001i	0.245693	−	0.916937i	0.973034	−	0.230661i	$-0.0740890\pi$
$314$		−	430.158i		−	1.36993i
$315$	0.0859989	+	3.06504i	0.000273012	+	0.00973029i
$316$	104.281			0.330004
$317$	85.3965	+	22.8819i	0.269389	+	0.0721827i	0.390985	−	0.920397i	$-0.372134\pi$
$317$	85.3965	+	22.8819i	0.269389	+	0.0721827i	−0.121596	+	0.992580i	$0.538801\pi$
$318$	238.882	−	175.078i	0.751201	−	0.550561i
$319$	−58.9165	−	34.0155i	−0.184691	−	0.106632i
$320$	−2.83607	+	0.204848i	−0.00886273	+	0.000640149i
$321$	48.4109	+	38.8706i	0.150813	+	0.121092i
$322$	−7.43412	−	1.99197i	−0.0230873	−	0.00618623i
$323$	−78.9926	−	78.9926i	−0.244559	−	0.244559i
$324$	177.859	+	15.7113i	0.548948	+	0.0484917i
$325$	300.559	−	129.208i	0.924797	−	0.397564i
$326$	−114.629	−	198.544i	−0.351624	−	0.609031i
$327$	334.176	−	36.5271i	1.02194	−	0.111704i
$328$	269.213	−	72.1354i	0.820771	−	0.219925i
$329$	2.72759	+	1.57478i	0.00829055	+	0.00478655i
$330$	148.008	+	312.137i	0.448509	+	0.945869i
$331$	223.152	+	386.510i	0.674175	+	1.16770i	0.976709	+	0.214566i	$0.0688338\pi$
$331$	223.152	+	386.510i	0.674175	+	1.16770i	−0.302535	+	0.953138i	$0.597833\pi$
$332$	−96.8645	+	96.8645i	−0.291761	+	0.291761i
$333$	−246.821	+	387.072i	−0.741204	+	1.16238i
$334$		−	497.589i		−	1.48979i
$335$	−234.312	+	81.2809i	−0.699438	+	0.242630i
$336$	3.80271	−	1.47787i	0.0113176	−	0.00439843i
$337$	7.58184	+	28.2958i	0.0224980	+	0.0839638i	0.976262	−	0.216593i	$-0.0694943\pi$
$337$	7.58184	+	28.2958i	0.0224980	+	0.0839638i	−0.953764	+	0.300556i	$0.902828\pi$
$338$	5.41056	−	1.44975i	0.0160076	−	0.00428921i
$339$	40.2988	+	103.693i	0.118875	+	0.305878i
$340$	69.4890	+	200.319i	0.204379	+	0.589173i
$341$	−154.473			−0.452999
$342$	−5.73305	+	130.054i	−0.0167633	+	0.380275i
$343$	4.72156	+	4.72156i	0.0137655	+	0.0137655i
$344$	38.9086	−	22.4639i	0.113107	−	0.0653021i
$345$	614.602	−	291.430i	1.78146	−	0.844725i
$346$	43.0650	−	74.5907i	0.124465	−	0.215580i
$347$	87.3943	+	326.160i	0.251857	+	0.939942i	0.969812	+	0.243853i	$0.0784114\pi$
$347$	87.3943	+	326.160i	0.251857	+	0.939942i	−0.717956	+	0.696089i	$0.754922\pi$
$348$	5.28716	+	48.3706i	0.0151930	+	0.138996i
$349$	51.4915	−	29.7286i	0.147540	−	0.0851823i	−0.424413	−	0.905469i	$-0.639519\pi$
$349$	51.4915	−	29.7286i	0.147540	−	0.0851823i	0.571953	+	0.820287i	$0.306186\pi$
$350$	3.94137	+	1.57145i	0.0112611	+	0.00448985i
$351$	−196.113	−	293.905i	−0.558727	−	0.837336i
$352$	208.047	−	208.047i	0.591042	−	0.591042i
$353$	−137.840	+	514.426i	−0.390482	+	1.45730i	0.438860	+	0.898555i	$0.355382\pi$
$353$	−137.840	+	514.426i	−0.390482	+	1.45730i	−0.829342	+	0.558742i	$0.811284\pi$
$354$	−88.3316	+	110.012i	−0.249524	+	0.310767i
$355$	20.3230	+	281.367i	0.0572478	+	0.792583i
$356$	−65.2043	+	112.937i	−0.183158	+	0.317239i
$357$	2.32462	+	3.17178i	0.00651155	+	0.00888455i
$358$	119.886	−	447.421i	0.334878	−	1.24978i
$359$			342.196i			0.953192i	0.879122	+	0.476596i	$0.158130\pi$
$359$			342.196i			0.953192i	−0.879122	+	0.476596i	$0.841870\pi$
$360$	−95.7078	+	177.061i	−0.265855	+	0.491836i
$361$	327.278			0.906588
$362$	−235.269	−	63.0401i	−0.649914	−	0.174144i
$363$	−97.5117	−	42.9306i	−0.268627	−	0.118266i
$364$	1.70223	+	0.982783i	0.00467646	+	0.00269995i
$365$	253.148	−	292.565i	0.693557	−	0.801548i
$366$	37.5482	−	14.5926i	0.102591	−	0.0398705i
$367$	355.509	+	95.2584i	0.968690	+	0.259560i	0.708275	−	0.705937i	$-0.249474\pi$
$367$	355.509	+	95.2584i	0.968690	+	0.259560i	0.260416	+	0.965497i	$0.416140\pi$
$368$	−639.956	−	639.956i	−1.73901	−	1.73901i
$369$	168.867	−	534.793i	0.457633	−	1.44930i
$370$	356.441	+	525.843i	0.963354	+	1.42120i
$371$	−1.35032	−	2.33883i	−0.00363968	−	0.00630412i
$372$	65.3125	+	89.1142i	0.175571	+	0.239554i
$373$	−321.501	+	86.1459i	−0.861933	+	0.230954i	−0.662596	−	0.748977i	$-0.730545\pi$
$373$	−321.501	+	86.1459i	−0.861933	+	0.230954i	−0.199337	+	0.979931i	$0.563879\pi$
$374$	383.681	+	221.519i	1.02589	+	0.592296i
$375$	−355.347	+	119.807i	−0.947592	+	0.319484i
$376$	103.370	+	179.042i	0.274921	+	0.476177i
$377$	68.0862	−	68.0862i	0.180600	−	0.180600i
$378$	0.896843	−	4.49392i	0.00237260	−	0.0118887i
$379$			203.700i			0.537466i	0.963215	+	0.268733i	$0.0866049\pi$
$379$			203.700i			0.537466i	−0.963215	+	0.268733i	$0.913395\pi$
$380$	57.5901	+	27.9254i	0.151553	+	0.0734880i
$381$	−502.164	−	403.203i	−1.31802	−	1.05828i
$382$	−87.9460	−	328.219i	−0.230225	−	0.859212i
$383$	19.9865	−	5.35538i	0.0521842	−	0.0139827i	−0.232633	−	0.972565i	$-0.574734\pi$
$383$	19.9865	−	5.35538i	0.0521842	−	0.0139827i	0.284817	+	0.958582i	$0.408067\pi$
$384$	381.609	+	58.8174i	0.993774	+	0.153170i
$385$	2.97603	−	1.03236i	0.00772994	−	0.00268146i
$386$	−230.060			−0.596010
$387$	3.98132	−	90.3161i	0.0102876	−	0.233375i
$388$	−242.458	−	242.458i	−0.624892	−	0.624892i
$389$	160.439	−	92.6297i	0.412440	−	0.238123i	−0.279397	−	0.960176i	$-0.590135\pi$
$389$	160.439	−	92.6297i	0.412440	−	0.238123i	0.691838	+	0.722053i	$0.256801\pi$
$390$	−480.952	+	88.0042i	−1.23321	+	0.225652i
$391$	436.174	−	755.475i	1.11553	−	1.93216i
$392$	56.7182	+	211.675i	0.144689	+	0.539988i
$393$	4.12647	+	1.81673i	0.0104999	+	0.00462271i
$394$	−520.513	+	300.518i	−1.32110	+	0.762737i
$395$	132.718	+	195.793i	0.335995	+	0.495680i
$396$	−39.6260	−	179.098i	−0.100066	−	0.452266i
$397$	−236.474	+	236.474i	−0.595652	+	0.595652i	−0.939152	−	0.343501i	$-0.888387\pi$
$397$	−236.474	+	236.474i	−0.595652	+	0.595652i	0.343501	+	0.939152i	$0.388387\pi$
$398$	−23.4790	+	87.6248i	−0.0589925	+	0.220163i
$399$	1.17320	+	0.180825i	0.00294036	+	0.000453197i
$400$	308.986	+	391.771i	0.772466	+	0.979428i
$401$	−34.0375	+	58.9547i	−0.0848816	+	0.147019i	−0.905341	−	0.424686i	$-0.860385\pi$
$401$	−34.0375	+	58.9547i	−0.0848816	+	0.147019i	0.820459	+	0.571705i	$0.193718\pi$
$402$	368.458	−	40.2743i	0.916562	−	0.100185i
$403$	56.5868	−	211.185i	0.140414	−	0.524032i
$404$			121.703i			0.301245i
$405$	196.861	+	353.936i	0.486078	+	0.873916i
$406$	1.24883			0.00307593
$407$	455.540	+	122.062i	1.11926	+	0.299906i
$408$	28.0479	+	256.602i	0.0687449	+	0.628926i
$409$	−326.511	−	188.511i	−0.798315	−	0.460907i	0.0445668	−	0.999006i	$-0.485809\pi$
$409$	−326.511	−	188.511i	−0.798315	−	0.460907i	−0.842882	+	0.538099i	$0.819143\pi$
$410$	−586.870	−	507.802i	−1.43139	−	1.23854i
$411$	31.9210	−	207.104i	0.0776666	−	0.503904i
$412$	194.691	+	52.1674i	0.472552	+	0.126620i
$413$	0.909687	+	0.909687i	0.00220263	+	0.00220263i
$414$	−992.557	+	219.607i	−2.39748	+	0.530451i
$415$	−305.147	−	58.5894i	−0.735295	−	0.141179i
$416$	208.216	+	360.640i	0.500518	+	0.866923i
$417$	148.421	−	337.120i	0.355925	−	0.808440i
$418$	129.179	−	34.6135i	0.309041	−	0.0828074i
$419$	198.025	+	114.330i	0.472613	+	0.272863i	0.717333	−	0.696731i	$-0.245363\pi$
$419$	198.025	+	114.330i	0.472613	+	0.272863i	−0.244720	+	0.969594i	$0.578696\pi$
$420$	−1.85386	−	1.28036i	−0.00441394	−	0.00304847i
$421$	204.894	+	354.887i	0.486684	+	0.842961i	0.999883	−	0.0153086i	$-0.00487306\pi$
$421$	204.894	+	354.887i	0.486684	+	0.842961i	−0.513199	+	0.858270i	$0.671540\pi$
$422$	340.999	−	340.999i	0.808055	−	0.808055i
$423$	415.599	+	18.3205i	0.982504	+	0.0433108i
$424$		−	177.274i		−	0.418098i
$425$	−287.671	+	385.414i	−0.676873	+	0.906856i
$426$	64.2230	−	416.681i	0.150758	−	0.978125i
$427$	−0.0950727	−	0.354816i	−0.000222653	−	0.000830951i
$428$	−44.0644	+	11.8070i	−0.102954	+	0.0275865i
$429$	−227.256	+	283.034i	−0.529735	+	0.659752i
$430$	−112.566	−	54.5831i	−0.261781	−	0.126937i
$431$	46.4787			0.107839			0.0539196	−	0.998545i	$-0.482829\pi$
$431$	46.4787			0.107839			0.0539196	+	0.998545i	$0.482829\pi$
$432$	355.559	−	404.922i	0.823053	−	0.937319i
$433$	−430.638	−	430.638i	−0.994544	−	0.994544i	0.00544093	−	0.999985i	$-0.498268\pi$
$433$	−430.638	−	430.638i	−0.994544	−	0.994544i	−0.999985	+	0.00544093i	$0.998268\pi$
$434$	2.45572	−	1.41781i	0.00565834	−	0.00326684i
$435$	−84.0895	+	71.4879i	−0.193309	+	0.164340i
$436$	−123.504	+	213.916i	−0.283266	+	0.490632i
$437$	−68.1545	−	254.356i	−0.155960	−	0.582050i
$438$	−466.359	+	341.798i	−1.06475	+	0.780360i
$439$	−335.332	+	193.604i	−0.763855	+	0.441012i	−0.830678	−	0.556753i	$-0.812047\pi$
$439$	−335.332	+	193.604i	−0.763855	+	0.441012i	0.0668232	+	0.997765i	$0.478714\pi$
$440$	203.061	+	38.9885i	0.461502	+	0.0886101i
$441$	420.494	+	132.775i	0.953500	+	0.301078i
$442$	−443.397	+	443.397i	−1.00316	+	1.00316i
$443$	189.882	−	708.648i	0.428627	−	1.59966i	−0.327247	−	0.944939i	$-0.606121\pi$
$443$	189.882	−	708.648i	0.428627	−	1.59966i	0.755874	−	0.654717i	$-0.227212\pi$
$444$	−122.190	−	314.407i	−0.275203	−	0.708124i
$445$	−295.031	+	21.3099i	−0.662990	+	0.0478874i
$446$	−119.241	+	206.531i	−0.267357	+	0.463075i
$447$	32.1164	−	72.9486i	0.0718489	−	0.163196i
$448$	0.0100292	−	0.0374297i	2.23867e−5	−	8.35483e-5i
$449$		−	141.098i		−	0.314250i	−0.987579	−	0.157125i	$-0.949777\pi$
$449$		−	141.098i		−	0.314250i	0.987579	−	0.157125i	$-0.0502226\pi$
$450$	557.633	−	56.0371i	1.23918	−	0.124527i
$451$	−576.139			−1.27747
$452$	−78.9577	−	21.1566i	−0.174685	−	0.0468067i
$453$	−238.300	+	174.652i	−0.526048	+	0.385544i
$454$	710.657	+	410.298i	1.56532	+	0.903740i
$455$	0.321190	+	4.44681i	0.000705913	+	0.00977321i
$456$	60.7582	+	48.7846i	0.133242	+	0.106984i
$457$	−709.254	−	190.044i	−1.55198	−	0.415851i	−0.621865	−	0.783124i	$-0.713625\pi$
$457$	−709.254	−	190.044i	−1.55198	−	0.415851i	−0.930113	+	0.367273i	$0.880291\pi$
$458$	732.678	+	732.678i	1.59973	+	1.59973i
$459$	465.699	+	230.023i	1.01460	+	0.501139i
$460$	−94.2412	+	490.830i	−0.204872	+	1.06702i
$461$	−321.041	−	556.060i	−0.696402	−	1.20620i	−0.969706	−	0.244275i	$-0.921450\pi$
$461$	−321.041	−	556.060i	−0.696402	−	1.20620i	0.273304	−	0.961928i	$-0.411883\pi$
$462$	−4.67984	+	0.511530i	−0.0101295	+	0.00110721i
$463$	268.091	−	71.8346i	0.579029	−	0.155150i	0.0425948	−	0.999092i	$-0.486438\pi$
$463$	268.091	−	71.8346i	0.579029	−	0.155150i	0.536434	+	0.843942i	$0.319771\pi$
$464$	127.178	+	73.4265i	0.274091	+	0.158247i
$465$	−84.1940	+	236.043i	−0.181062	+	0.507619i
$466$	−38.7861	−	67.1795i	−0.0832320	−	0.144162i
$467$	−57.4439	+	57.4439i	−0.123006	+	0.123006i	−0.765930	−	0.642924i	$-0.777721\pi$
$467$	−57.4439	+	57.4439i	−0.123006	+	0.123006i	0.642924	+	0.765930i	$0.277721\pi$
$468$	259.366	+	11.4334i	0.554202	+	0.0244304i
$469$		−	3.37981i		−	0.00720642i
$470$	251.170	−	517.983i	0.534404	−	1.10209i
$471$	−482.900	+	187.673i	−1.02526	+	0.398456i
$472$	21.8565	+	81.5694i	0.0463061	+	0.172817i
$473$	−89.7086	+	24.0373i	−0.189659	+	0.0508189i
$474$	−128.055	−	329.497i	−0.270157	−	0.695140i
$475$	20.8631	+	143.669i	0.0439223	+	0.302461i
$476$	−2.88948			−0.00607034
$477$	−300.766	−	191.787i	−0.630536	−	0.402068i
$478$	−544.139	−	544.139i	−1.13837	−	1.13837i
$479$	419.328	−	242.099i	0.875423	−	0.505426i	0.00627671	−	0.999980i	$-0.498002\pi$
$479$	419.328	−	242.099i	0.875423	−	0.505426i	0.869147	+	0.494554i	$0.164669\pi$
$480$	−204.513	−	431.301i	−0.426069	−	0.898544i
$481$	−333.749	+	578.071i	−0.693866	+	1.20181i
$482$	−16.5771	−	61.8668i	−0.0343924	−	0.128354i
$483$	1.00721	+	9.21467i	0.00208532	+	0.0190780i
$484$	67.7979	−	39.1431i	0.140078	−	0.0808742i
$485$	146.653	−	763.803i	0.302378	−	1.57485i
$486$	−168.763	−	581.274i	−0.347250	−	1.19604i
$487$	−162.179	+	162.179i	−0.333017	+	0.333017i	−0.853731	−	0.520714i	$-0.825666\pi$
$487$	−162.179	+	162.179i	−0.333017	+	0.333017i	0.520714	+	0.853731i	$0.325666\pi$
$488$	6.24069	−	23.2906i	0.0127883	−	0.0477266i
$489$	−172.876	+	215.306i	−0.353530	+	0.440299i
$490$	399.272	−	461.440i	0.814840	−	0.941715i
$491$	−395.023	+	684.199i	−0.804527	+	1.39348i	0.112083	+	0.993699i	$0.464248\pi$
$491$	−395.023	+	684.199i	−0.804527	+	1.39348i	−0.916610	+	0.399783i	$0.869086\pi$
$492$	243.597	+	332.371i	0.495116	+	0.675550i
$493$	−36.6356	+	136.726i	−0.0743115	+	0.277334i
$494$			189.285i			0.383168i
$495$	285.833	−	302.336i	0.577441	−	0.610780i
$496$	333.448			0.672274
$497$	−3.71340	−	0.995002i	−0.00747163	−	0.00200202i
$498$	425.009	+	187.115i	0.853433	+	0.375733i
$499$	−422.362	−	243.851i	−0.846418	−	0.488680i	0.0130228	−	0.999915i	$-0.495855\pi$
$499$	−422.362	−	243.851i	−0.846418	−	0.488680i	−0.859441	+	0.511236i	$0.829188\pi$
$500$	83.3443	−	262.636i	0.166689	−	0.525272i
$501$	−558.597	+	217.091i	−1.11496	+	0.433316i
$502$	663.754	+	177.852i	1.32222	+	0.354288i
$503$	346.274	+	346.274i	0.688418	+	0.688418i	0.961882	−	0.273465i	$-0.0881696\pi$
$503$	346.274	+	346.274i	0.688418	+	0.688418i	−0.273465	+	0.961882i	$0.588170\pi$
$504$	−1.85222	−	2.02305i	−0.00367504	−	0.00401399i
$505$	−228.504	+	154.891i	−0.452483	+	0.306714i
$506$	522.164	+	904.415i	1.03194	+	1.78738i
$507$	−3.98806	−	5.44143i	−0.00786600	−	0.0107326i
$508$	457.078	−	122.474i	0.899760	−	0.241090i
$509$	362.182	+	209.106i	0.711557	+	0.410818i	0.811637	−	0.584162i	$-0.198577\pi$
$509$	362.182	+	209.106i	0.711557	+	0.410818i	−0.100080	+	0.994979i	$0.531910\pi$
$510$	547.615	−	465.550i	1.07376	−	0.912843i
$511$	2.63618	+	4.56599i	0.00515886	+	0.00893540i
$512$	−196.607	+	196.607i	−0.383998	+	0.383998i
$513$	148.501	−	50.3049i	0.289476	−	0.0980603i
$514$			15.9365i			0.0310049i
$515$	149.836	+	431.937i	0.290943	+	0.838712i
$516$	51.7966	+	41.5891i	0.100381	+	0.0805990i
$517$	−110.610	−	412.804i	−0.213947	−	0.798460i
$518$	−8.36225	+	2.24066i	−0.0161433	+	0.00432559i
$519$	−102.525	−	15.8022i	−0.197543	−	0.0304473i
$520$	−127.688	+	263.329i	−0.245554	+	0.506403i
$521$	−17.3149			−0.0332341			−0.0166170	−	0.999862i	$-0.505290\pi$
$521$	−17.3149			−0.0332341			−0.0166170	+	0.999862i	$0.505290\pi$
$522$	146.344	−	76.1036i	0.280352	−	0.145792i
$523$	577.571	+	577.571i	1.10434	+	1.10434i	0.993880	+	0.110462i	$0.0352329\pi$
$523$	577.571	+	577.571i	1.10434	+	1.10434i	0.110462	+	0.993880i	$0.464767\pi$
$524$	−2.86905	+	1.65645i	−0.00547529	+	0.00316116i
$525$	0.0445528	−	5.11022i	8.48625e−5	−	0.00973375i
$526$	264.640	−	458.370i	0.503118	−	0.871427i
$527$	83.1855	+	310.453i	0.157847	+	0.589094i
$528$	−506.662	−	223.064i	−0.959587	−	0.422469i
$529$	1322.68	−	763.649i	2.50034	−	1.44357i
$530$	−408.594	+	276.964i	−0.770932	+	0.522574i
$531$	162.038	+	51.1652i	0.305156	+	0.0963564i
$532$	−0.616757	+	0.616757i	−0.00115932	+	0.00115932i
$533$	211.053	−	787.659i	0.395971	−	1.47778i
$534$	436.916	+	67.3418i	0.818195	+	0.126108i
$535$	−78.2488	−	67.7066i	−0.146260	−	0.126554i
$536$	110.927	−	192.132i	0.206954	−	0.358455i
$537$	−554.584	+	60.6189i	−1.03274	+	0.112884i
$538$	−225.023	+	839.797i	−0.418258	+	1.56096i
$539$		−	453.003i		−	0.840451i
$540$	−295.269	−	37.0648i	−0.546794	−	0.0686386i
$541$	846.162			1.56407			0.782035	−	0.623234i	$-0.214182\pi$
$541$	846.162			1.56407			0.782035	+	0.623234i	$0.214182\pi$
$542$	−486.674	−	130.404i	−0.897922	−	0.240598i
$543$	31.8754	+	291.618i	0.0587024	+	0.537050i
$544$	−530.160	−	306.088i	−0.974558	−	0.562661i
$545$	−558.821	+	40.3633i	−1.02536	+	0.0740611i
$546$	1.01500	−	6.58536i	0.00185897	−	0.0120611i
$547$	66.0385	+	17.6950i	0.120728	+	0.0323491i	0.318677	−	0.947863i	$-0.396761\pi$
$547$	66.0385	+	17.6950i	0.120728	+	0.0323491i	−0.197949	+	0.980212i	$0.563428\pi$
$548$	108.876	+	108.876i	0.198678	+	0.198678i
$549$	−32.7636	−	35.7854i	−0.0596787	−	0.0651828i
$550$	−227.389	−	528.944i	−0.413435	−	0.961717i
$551$	21.3641	+	37.0038i	0.0387734	+	0.0671575i
$552$	−245.174	+	556.884i	−0.444156	+	1.00885i
$553$	−3.11362	+	0.834291i	−0.00563041	+	0.00150866i
$554$	−523.410	−	302.191i	−0.944784	−	0.545471i
$555$	434.805	−	629.562i	0.783433	−	1.13435i
$556$	135.327	+	234.392i	0.243393	+	0.421569i
$557$	367.003	−	367.003i	0.658893	−	0.658893i	−0.296225	−	0.955118i	$-0.595728\pi$
$557$	367.003	−	367.003i	0.658893	−	0.658893i	0.955118	+	0.296225i	$0.0957279\pi$
$558$	201.372	−	315.797i	0.360881	−	0.565945i
$559$		−	131.449i		−	0.235151i
$560$	−6.42411	+	2.22848i	−0.0114716	+	0.00397942i
$561$	81.2835	−	527.370i	0.144890	−	0.940053i
$562$	180.716	+	674.443i	0.321560	+	1.20008i
$563$	−303.953	+	81.4441i	−0.539882	+	0.144661i	−0.518448	−	0.855109i	$-0.673490\pi$
$563$	−303.953	+	81.4441i	−0.539882	+	0.144661i	−0.0214341	+	0.999770i	$0.506823\pi$
$564$	−191.377	+	238.348i	−0.339320	+	0.422603i
$565$	−60.7662	−	175.173i	−0.107551	−	0.310041i
$566$	−961.053			−1.69797
$567$	−5.43620	+	0.953838i	−0.00958765	+	0.00168225i
$568$	−178.439	−	178.439i	−0.314153	−	0.314153i
$569$	−882.789	+	509.679i	−1.55148	+	0.895745i	−0.553453	+	0.832880i	$0.686690\pi$
$569$	−882.789	+	509.679i	−1.55148	+	0.895745i	−0.998022	+	0.0628645i	$0.979976\pi$
$570$	17.5167	−	216.259i	0.0307311	−	0.379402i
$571$	443.096	−	767.465i	0.776000	−	1.34407i	−0.158231	−	0.987402i	$-0.550579\pi$
$571$	443.096	−	767.465i	0.776000	−	1.34407i	0.934231	−	0.356669i	$-0.116088\pi$
$572$	−69.0296	−	257.622i	−0.120681	−	0.450388i
$573$	−330.092	+	241.927i	−0.576076	+	0.422210i
$574$	9.15913	−	5.28803i	0.0159567	−	0.00921259i
$575$	−1041.50	+	447.733i	−1.81130	+	0.778667i
$576$	−1.10569	−	4.99737i	−0.00191960	−	0.00867600i
$577$	194.509	−	194.509i	0.337105	−	0.337105i	−0.518172	−	0.855277i	$-0.673387\pi$
$577$	194.509	−	194.509i	0.337105	−	0.337105i	0.855277	+	0.518172i	$0.173387\pi$
$578$	52.2689	−	195.070i	0.0904307	−	0.337492i
$579$	100.372	+	258.267i	0.173354	+	0.446058i
$580$	−5.84243	−	80.8871i	−0.0100732	−	0.139461i
$581$	2.11722	−	3.66713i	0.00364409	−	0.00631175i
$582$	−468.361	+	1063.83i	−0.804745	+	1.82788i
$583$	−94.8452	+	353.967i	−0.162685	+	0.607147i
$584$			346.084i			0.592609i
$585$	308.627	+	501.526i	0.527568	+	0.857309i
$586$	105.225			0.179565
$587$	−775.720	−	207.853i	−1.32150	−	0.354095i	−0.471960	−	0.881620i	$-0.656453\pi$
$587$	−775.720	−	207.853i	−1.32150	−	0.354095i	−0.849539	+	0.527526i	$0.823120\pi$
$588$	−261.334	+	191.534i	−0.444446	+	0.325738i
$589$	84.0216	+	48.5099i	0.142651	+	0.0823598i
$590$	153.860	−	177.817i	0.260780	−	0.301384i
$591$	564.457	+	453.220i	0.955089	+	0.766870i
$592$	−983.338	−	263.485i	−1.66104	−	0.445075i
$593$	572.308	+	572.308i	0.965106	+	0.965106i	0.999411	−	0.0343049i	$-0.0109217\pi$
$593$	572.308	+	572.308i	0.965106	+	0.965106i	−0.0343049	+	0.999411i	$0.510922\pi$
$594$	−517.234	+	345.133i	−0.870764	+	0.581032i
$595$	−3.67743	−	5.42516i	−0.00618055	−	0.00911791i
$596$	29.2830	+	50.7197i	0.0491326	+	0.0851001i
$597$	108.612	−	11.8718i	0.181930	−	0.0198858i
$598$	−1427.74	+	382.561i	−2.38752	+	0.639734i
$599$	263.198	+	151.957i	0.439396	+	0.253685i	0.703341	−	0.710852i	$-0.251691\pi$
$599$	263.198	+	151.957i	0.439396	+	0.253685i	−0.263945	+	0.964538i	$0.585024\pi$
$600$	170.253	−	289.038i	0.283755	−	0.481730i
$601$	−52.0948	−	90.2308i	−0.0866801	−	0.150134i	0.819426	−	0.573185i	$-0.194292\pi$
$601$	−52.0948	−	90.2308i	−0.0866801	−	0.150134i	−0.906106	+	0.423051i	$0.860959\pi$
$602$	1.20551	−	1.20551i	0.00200251	−	0.00200251i
$603$	−205.966	−	396.063i	−0.341568	−	0.656821i
$604$		−	217.090i		−	0.359420i
$605$	159.779	+	77.4770i	0.264098	+	0.128061i
$606$	384.544	−	149.448i	0.634561	−	0.246614i
$607$	75.9472	+	283.439i	0.125119	+	0.466950i	0.999844	−	0.0176696i	$-0.00562469\pi$
$607$	75.9472	+	283.439i	0.125119	+	0.466950i	−0.874725	+	0.484620i	$0.838958\pi$
$608$	−178.496	+	47.8279i	−0.293579	+	0.0786642i
$609$	−0.544848	−	1.40195i	−0.000894660	−	0.00230205i
$610$	−63.4321	+	22.0041i	−0.103987	+	0.0360723i
$611$	604.878			0.989980
$612$	−338.604	+	176.085i	−0.553274	+	0.287721i
$613$	610.767	+	610.767i	0.996357	+	0.996357i	0.999993	−	0.00363596i	$-0.00115736\pi$
$613$	610.767	+	610.767i	0.996357	+	0.996357i	−0.00363596	+	0.999993i	$0.501157\pi$
$614$	−259.645	+	149.906i	−0.422874	+	0.244147i
$615$	−314.019	+	880.372i	−0.510601	+	1.43150i
$616$	−1.40891	+	2.44030i	−0.00228719	+	0.00396152i
$617$	−260.666	−	972.818i	−0.422473	−	1.57669i	−0.769381	−	0.638791i	$-0.779435\pi$
$617$	−260.666	−	972.818i	−0.422473	−	1.57669i	0.346908	−	0.937899i	$-0.387232\pi$
$618$	−74.2429	−	679.226i	−0.120134	−	1.09907i
$619$	189.444	−	109.376i	0.306049	−	0.176697i	−0.339108	−	0.940747i	$-0.610125\pi$
$619$	189.444	−	109.376i	0.306049	−	0.176697i	0.645157	+	0.764050i	$0.276792\pi$
$620$	−103.321	−	152.425i	−0.166646	−	0.245847i
$621$	679.572	+	1018.44i	1.09432	+	1.64000i
$622$	799.956	−	799.956i	1.28610	−	1.28610i
$623$	1.04332	−	3.89373i	0.00167467	−	0.00624997i
$624$	490.560	−	610.962i	0.786154	−	0.979106i
$625$	599.185	−	177.772i	0.958695	−	0.284435i
$626$	370.048	−	640.942i	0.591131	−	1.02387i
$627$	−95.2166	−	129.916i	−0.151861	−	0.207203i
$628$	98.5271	−	367.708i	0.156890	−	0.585523i
$629$		−	981.257i		−	1.56003i
$630$	−1.76906	+	7.42986i	−0.00280803	+	0.0117934i
$631$	−427.714			−0.677835			−0.338917	−	0.940816i	$-0.610061\pi$
$631$	−427.714			−0.677835			−0.338917	+	0.940816i	$0.610061\pi$
$632$	−204.382	−	54.7639i	−0.323389	−	0.0866517i
$633$	−531.582	−	234.035i	−0.839782	−	0.369724i
$634$	190.711	+	110.107i	0.300805	+	0.173670i
$635$	811.672	+	702.317i	1.27822	+	1.10601i
$636$	244.303	−	94.9450i	0.384124	−	0.149285i
$637$	619.316	+	165.945i	0.972239	+	0.260511i
$638$	−119.823	−	119.823i	−0.187810	−	0.187810i
$639$	−495.790	+	109.695i	−0.775884	+	0.171667i
$640$	−631.982	−	121.343i	−0.987472	−	0.189598i
$641$	−256.912	−	444.984i	−0.400798	−	0.694203i	0.593024	−	0.805185i	$-0.297934\pi$
$641$	−256.912	−	444.984i	−0.400798	−	0.694203i	−0.993822	+	0.110982i	$0.964600\pi$
$642$	91.4165	+	124.731i	0.142393	+	0.194286i
$643$	187.988	−	50.3713i	0.292361	−	0.0783379i	−0.109657	−	0.993969i	$-0.534975\pi$
$643$	187.988	−	50.3713i	0.292361	−	0.0783379i	0.402019	+	0.915632i	$0.368309\pi$
$644$	−5.89858	−	3.40555i	−0.00915929	−	0.00528812i
$645$	−12.1645	+	150.181i	−0.0188597	+	0.232839i
$646$	−139.129	−	240.979i	−0.215371	−	0.373033i
$647$	−139.726	+	139.726i	−0.215960	+	0.215960i	−0.806794	−	0.590833i	$-0.798799\pi$
$647$	−139.726	+	139.726i	−0.215960	+	0.215960i	0.590833	+	0.806794i	$0.298799\pi$
$648$	−340.337	−	124.197i	−0.525211	−	0.191661i
$649$		−	174.565i		−	0.268976i
$650$	806.436	−	117.108i	1.24067	−	0.180166i
$651$	−2.66304	−	2.13824i	−0.00409070	−	0.00328455i
$652$	−52.5114	−	195.975i	−0.0805390	−	0.300576i
$653$	622.466	−	166.789i	0.953240	−	0.255420i	0.251503	−	0.967856i	$-0.419075\pi$
$653$	622.466	−	166.789i	0.953240	−	0.255420i	0.701737	+	0.712437i	$0.252408\pi$
$654$	827.568	+	127.553i	1.26539	+	0.195035i
$655$	−6.76150	−	3.27865i	−0.0103229	−	0.00500557i
$656$	1243.66			1.89583
$657$	587.172	+	374.417i	0.893716	+	0.569888i
$658$	5.54730	+	5.54730i	0.00843054	+	0.00843054i
$659$	−210.200	+	121.359i	−0.318968	+	0.184156i	−0.650932	−	0.759136i	$-0.725622\pi$
$659$	−210.200	+	121.359i	−0.318968	+	0.184156i	0.331965	+	0.943292i	$0.392289\pi$
$660$	55.0258	+	300.722i	0.0833725	+	0.455639i
$661$	−331.364	+	573.939i	−0.501307	+	0.868288i	0.498692	+	0.866779i	$0.333814\pi$
$661$	−331.364	+	573.939i	−0.501307	+	0.868288i	−0.999999	+	0.00150927i	$0.999520\pi$
$662$	287.723	+	1073.80i	0.434627	+	1.62205i
$663$	691.210	+	304.313i	1.04255	+	0.458994i
$664$	240.715	−	138.977i	0.362522	−	0.209302i
$665$	−1.94294	−	0.373051i	−0.00292171	−	0.000560979i
$666$	−843.384	+	772.167i	−1.26634	+	1.15941i
$667$	−235.933	+	235.933i	−0.353722	+	0.353722i
$668$	113.972	−	425.349i	0.170617	−	0.636750i
$669$	283.877	+	43.7540i	0.424331	+	0.0654021i
$670$	−616.149	+	44.5041i	−0.919625	+	0.0664240i
$671$	−24.9219	+	43.1660i	−0.0371414	+	0.0643308i
$672$	6.46646	−	0.706817i	0.00962271	−	0.00105181i
$673$	125.305	−	467.643i	0.186188	−	0.694864i	−0.808185	−	0.588929i	$-0.799550\pi$
$673$	125.305	−	467.643i	0.186188	−	0.694864i	0.994373	−	0.105935i	$-0.0337835\pi$
$674$			72.9670i			0.108260i
$675$	−306.196	−	601.556i	−0.453624	−	0.891193i
$676$	4.95712			0.00733302
$677$	425.004	+	113.880i	0.627776	+	0.168212i	0.558660	−	0.829397i	$-0.311316\pi$
$677$	425.004	+	113.880i	0.627776	+	0.168212i	0.0691156	+	0.997609i	$0.477982\pi$
$678$	30.1094	+	275.462i	0.0444091	+	0.406286i
$679$	9.17906	+	5.29953i	0.0135185	+	0.00780490i
$680$	−30.9936	−	429.099i	−0.0455788	−	0.631028i
$681$	150.554	−	976.798i	0.221077	−	1.43436i
$682$	−371.658	−	99.5854i	−0.544953	−	0.146020i
$683$	−336.034	−	336.034i	−0.491998	−	0.491998i	0.416938	−	0.908935i	$-0.363103\pi$
$683$	−336.034	−	336.034i	−0.491998	−	0.491998i	−0.908935	+	0.416938i	$0.863103\pi$
$684$	−34.6894	+	109.860i	−0.0507155	+	0.160614i
$685$	−65.8544	+	342.985i	−0.0961379	+	0.500708i
$686$	8.31607	+	14.4039i	0.0121226	+	0.0209969i
$687$	502.853	−	1142.17i	0.731954	−	1.66254i
$688$	193.647	−	51.8875i	0.281463	−	0.0754179i
$689$	−449.177	−	259.332i	−0.651926	−	0.376389i
$690$	1666.60	−	304.953i	2.41536	−	0.441960i
$691$	−465.054	−	805.496i	−0.673015	−	1.16570i	−0.977045	−	0.213034i	$-0.931665\pi$
$691$	−465.054	−	805.496i	−0.673015	−	1.16570i	0.304029	−	0.952663i	$-0.401668\pi$
$692$	53.8977	−	53.8977i	0.0778869	−	0.0778869i
$693$	2.61600	+	5.03045i	0.00377489	+	0.00725895i
$694$			841.075i			1.21192i
$695$	−267.855	+	552.393i	−0.385403	+	0.794810i
$696$	15.0398	−	97.5786i	0.0216089	−	0.140199i
$697$	310.258	+	1157.90i	0.445134	+	1.66126i
$698$	143.053	−	38.3309i	0.204947	−	0.0549153i
$699$	−58.4944	+	72.8512i	−0.0836830	+	0.104222i
$700$	3.00923	+	2.24607i	0.00429889	+	0.00320867i
$701$	−1057.58			−1.50868			−0.754338	−	0.656486i	$-0.772042\pi$
$701$	−1057.58			−1.50868			−0.754338	+	0.656486i	$0.772042\pi$
$702$	−282.369	−	833.559i	−0.402235	−	1.18741i
$703$	−209.448	−	209.448i	−0.297935	−	0.297935i
$704$	−4.55359	+	2.62902i	−0.00646817	+	0.00373440i
$705$	−691.075	−	55.9762i	−0.980248	−	0.0793989i
$706$	−663.280	+	1148.83i	−0.939490	+	1.62724i
$707$	−0.973672	−	3.63379i	−0.00137719	−	0.00513974i
$708$	−100.706	+	73.8079i	−0.142240	+	0.104248i
$709$	−450.749	+	260.240i	−0.635754	+	0.367053i	−0.782977	−	0.622051i	$-0.786300\pi$
$709$	−450.749	+	260.240i	−0.635754	+	0.367053i	0.147223	+	0.989103i	$0.452966\pi$
$710$	−132.495	+	690.065i	−0.186613	+	0.971922i
$711$	−314.027	+	287.510i	−0.441670	+	0.404374i
$712$	187.104	−	187.104i	0.262787	−	0.262787i
$713$	−196.085	+	731.800i	−0.275014	+	1.02637i
$714$	3.54821	+	9.12988i	0.00496948	+	0.0127870i
$715$	395.845	−	457.481i	0.553630	−	0.639833i
$716$	204.962	−	355.005i	0.286260	−	0.495817i
$717$	−373.455	+	848.257i	−0.520857	+	1.18306i
$718$	−220.607	+	823.316i	−0.307252	+	1.14668i
$719$		−	1211.89i		−	1.68553i	−0.538285	−	0.842763i	$-0.680928\pi$
$719$		−	1211.89i		−	1.68553i	0.538285	−	0.842763i	$-0.319072\pi$
$720$	−617.006	+	652.629i	−0.856953	+	0.906430i
$721$	−6.23044			−0.00864139
$722$	787.424	+	210.990i	1.09062	+	0.292230i
$723$	−62.2198	+	45.6013i	−0.0860578	+	0.0630724i
$724$	−186.673	−	107.776i	−0.257836	−	0.148862i
$725$	144.434	−	113.914i	0.199220	−	0.157123i
$726$	−206.934	−	166.154i	−0.285034	−	0.228862i
$727$	−201.292	−	53.9360i	−0.276880	−	0.0741899i	0.117707	−	0.993048i	$-0.462446\pi$
$727$	−201.292	−	53.9360i	−0.276880	−	0.0741899i	−0.394587	+	0.918859i	$0.629112\pi$
$728$	−2.82010	−	2.82010i	−0.00387377	−	0.00387377i
$729$	−578.914	+	443.057i	−0.794120	+	0.607761i
$730$	797.680	−	540.705i	1.09271	−	0.740692i
$731$	96.6185	+	167.348i	0.132173	+	0.228930i
$732$	35.4394	−	3.87371i	0.0484145	−	0.00529195i
$733$	707.621	−	189.606i	0.965376	−	0.258672i	0.258502	−	0.966011i	$-0.416771\pi$
$733$	707.621	−	189.606i	0.965376	−	0.258672i	0.706874	+	0.707339i	$0.250105\pi$
$734$	793.936	+	458.379i	1.08166	+	0.624495i
$735$	−692.214	−	246.905i	−0.941788	−	0.335926i
$736$	−721.511	−	1249.69i	−0.980313	−	1.69795i
$737$	−324.286	+	324.286i	−0.440009	+	0.440009i
$738$	751.059	−	1177.83i	1.01770	−	1.59598i
$739$			1243.93i			1.68326i	0.540056	+	0.841629i	$0.318403\pi$
$739$			1243.93i			1.68326i	−0.540056	+	0.841629i	$0.681597\pi$
$740$	184.250	+	531.144i	0.248986	+	0.717762i
$741$	212.493	−	82.5827i	0.286766	−	0.111448i
$742$	−1.74105	−	6.49769i	−0.00234643	−	0.00875700i
$743$	−1239.64	+	332.161i	−1.66843	+	0.447054i	−0.964687	−	0.263400i	$-0.915156\pi$
$743$	−1239.64	+	332.161i	−1.66843	+	0.447054i	−0.703743	+	0.710455i	$0.748489\pi$
$744$	−81.2077	−	208.955i	−0.109150	−	0.280854i
$745$	−57.9606	+	119.531i	−0.0777995	+	0.160444i
$746$	−829.060			−1.11134
$747$	24.6311	−	558.755i	0.0329733	−	0.747999i
$748$	277.240	+	277.240i	0.370642	+	0.370642i
$749$	1.22121	−	0.705066i	0.00163045	−	0.000941343i
$750$	−932.194	+	59.1673i	−1.24292	+	0.0788897i
$751$	−470.274	+	814.539i	−0.626198	+	1.08461i	0.362110	+	0.932135i	$0.382056\pi$
$751$	−470.274	+	814.539i	−0.626198	+	1.08461i	−0.988308	+	0.152471i	$0.951277\pi$
$752$	238.766	+	891.087i	0.317508	+	1.18496i
$753$	−89.9287	−	822.731i	−0.119427	−	1.09260i
$754$	207.708	−	119.920i	0.275474	−	0.159045i
$755$	407.598	−	276.289i	0.539865	−	0.365946i
$756$	1.79597	−	3.63608i	0.00237562	−	0.00480963i
$757$	872.169	−	872.169i	1.15214	−	1.15214i	0.166015	−	0.986123i	$-0.446910\pi$
$757$	872.169	−	872.169i	1.15214	−	1.15214i	0.986123	−	0.166015i	$-0.0530901\pi$
$758$	−131.321	+	490.097i	−0.173247	+	0.646566i
$759$	787.490	−	980.770i	1.03754	−	1.29219i
$760$	−98.2063	−	84.9752i	−0.129219	−	0.111809i
$761$	−229.806	+	398.036i	−0.301979	+	0.523043i	−0.976584	−	0.215136i	$-0.930981\pi$
$761$	−229.806	+	398.036i	−0.301979	+	0.523043i	0.674605	+	0.738179i	$0.264314\pi$
$762$	−948.260	−	1293.83i	−1.24444	−	1.69794i
$763$	1.97617	−	7.37515i	0.00259000	−	0.00966599i
$764$		−	300.712i		−	0.393602i
$765$	−761.548	−	411.644i	−0.995488	−	0.538097i
$766$	51.5397			0.0672842
$767$	238.655	+	63.9473i	0.311153	+	0.0833733i
$768$	873.980	+	384.779i	1.13799	+	0.501015i
$769$	−775.372	−	447.661i	−1.00829	−	0.582134i	−0.0975969	−	0.995226i	$-0.531116\pi$
$769$	−775.372	−	447.661i	−1.00829	−	0.582134i	−0.910689	+	0.413092i	$0.864449\pi$
$770$	7.82580	−	0.565253i	0.0101634	−	0.000734094i
$771$	17.8905	−	6.95289i	0.0232042	−	0.00901802i
$772$	−196.660	−	52.6949i	−0.254741	−	0.0682576i
$773$	94.0446	+	94.0446i	0.121662	+	0.121662i	0.765316	−	0.643654i	$-0.222583\pi$
$773$	94.0446	+	94.0446i	0.121662	+	0.121662i	−0.643654	+	0.765316i	$0.722583\pi$
$774$	67.8039	−	214.732i	0.0876020	−	0.277431i
$775$	154.690	−	387.981i	0.199600	−	0.500620i
$776$	347.868	+	602.524i	0.448283	+	0.776449i
$777$	6.16372	+	8.40996i	0.00793272	+	0.0108236i
$778$	445.730	−	119.433i	0.572918	−	0.153513i
$779$	313.377	+	180.928i	0.402281	+	0.232257i
$780$	−431.285	−	34.9335i	−0.552929	−	0.0447866i
$781$	260.825	+	451.762i	0.333963	+	0.578441i
$782$	1536.46	−	1536.46i	1.96479	−	1.96479i
$783$	−149.283	−	131.084i	−0.190655	−	0.167412i
$784$			977.861i			1.24727i
$785$	815.787	−	282.990i	1.03922	−	0.360497i
$786$	8.75699	+	7.03126i	0.0111412	+	0.00894562i
$787$	−241.144	−	899.963i	−0.306410	−	1.14354i	−0.931725	−	0.363164i	$-0.881696\pi$
$787$	−241.144	−	899.963i	−0.306410	−	1.14354i	0.625315	−	0.780372i	$-0.284970\pi$
$788$	−513.778	+	137.666i	−0.652003	+	0.174704i
$789$	−630.030	−	97.1064i	−0.798517	−	0.123075i
$790$	193.093	+	556.635i	0.244421	+	0.704602i
$791$	2.52677			0.00319440
$792$	−16.3908	+	371.825i	−0.0206955	+	0.469476i
$793$	−49.8843	−	49.8843i	−0.0629058	−	0.0629058i
$794$	−721.400	+	416.501i	−0.908565	+	0.524560i
$795$	489.187	+	337.855i	0.615330	+	0.424975i
$796$	−40.1407	+	69.5257i	−0.0504280	+	0.0873438i
$797$	−43.8496	−	163.649i	−0.0550183	−	0.205331i	0.932945	−	0.360019i	$-0.117230\pi$
$797$	−43.8496	−	163.649i	−0.0550183	−	0.205331i	−0.987963	+	0.154687i	$0.950563\pi$
$798$	2.70612	+	1.19140i	0.00339113	+	0.00149298i
$799$	−770.071	+	444.601i	−0.963793	+	0.556446i
$800$	314.200	+	730.879i	0.392750	+	0.913599i
$801$	−115.022	−	519.866i	−0.143598	−	0.649022i
$802$	−119.900	+	119.900i	−0.149502	+	0.149502i
$803$	185.162	−	691.034i	0.230588	−	0.860565i
$804$	324.190	+	49.9674i	0.403222	+	0.0621485i
$805$	−1.11299	−	15.4091i	−0.00138260	−	0.0191418i
$806$	272.293	−	471.626i	0.337833	−	0.585144i
$807$	1040.94	−	113.780i	1.28989	−	0.140991i
$808$	63.9130	−	238.527i	0.0791003	−	0.295206i
$809$			1540.82i			1.90459i	0.305175	+	0.952296i	$0.401285\pi$
$809$			1540.82i			1.90459i	−0.305175	+	0.952296i	$0.598715\pi$
$810$	245.469	+	978.474i	0.303048	+	1.20799i
$811$	−895.419			−1.10409			−0.552046	−	0.833813i	$-0.686153\pi$
$811$	−895.419			−1.10409			−0.552046	+	0.833813i	$0.686153\pi$
$812$	1.06752	+	0.286042i	0.00131469	+	0.000352269i
$813$	65.9370	+	603.238i	0.0811033	+	0.741990i
$814$	1017.33	+	587.355i	1.24979	+	0.721566i
$815$	301.123	−	348.010i	0.369476	−	0.427006i
$816$	−175.460	+	1138.39i	−0.215025	+	1.39509i
$817$	56.3434	+	15.0972i	0.0689637	+	0.0184788i
$818$	−664.048	−	664.048i	−0.811795	−	0.811795i
$819$	−7.83561	+	1.73366i	−0.00956729	+	0.00211680i
$820$	−385.357	−	568.501i	−0.469947	−	0.693294i
$821$	−322.268	−	558.185i	−0.392531	−	0.679884i	0.600251	−	0.799811i	$-0.295067\pi$
$821$	−322.268	−	558.185i	−0.392531	−	0.679884i	−0.992783	+	0.119927i	$0.961734\pi$
$822$	210.317	−	477.710i	0.255860	−	0.581156i
$823$	211.257	−	56.6061i	0.256691	−	0.0687802i	−0.128179	−	0.991751i	$-0.540913\pi$
$823$	211.257	−	56.6061i	0.256691	−	0.0687802i	0.384870	+	0.922971i	$0.374246\pi$
$824$	−354.182	−	204.487i	−0.429832	−	0.248164i
$825$	−494.590	+	486.041i	−0.599504	+	0.589141i
$826$	1.60223	+	2.77514i	0.00193975	+	0.00335974i
$827$	−982.768	+	982.768i	−1.18835	+	1.18835i	−0.210831	+	0.977522i	$0.567617\pi$
$827$	−982.768	+	982.768i	−1.18835	+	1.18835i	−0.977522	+	0.210831i	$0.932383\pi$
$828$	−898.759	−	39.6191i	−1.08546	−	0.0478492i
$829$			763.031i			0.920424i	0.887809	+	0.460212i	$0.152227\pi$
$829$			763.031i			0.920424i	−0.887809	+	0.460212i	$0.847773\pi$
$830$	−696.406	−	337.687i	−0.839044	−	0.406852i
$831$	−110.885	+	719.427i	−0.133436	+	0.865736i
$832$	−1.92614	−	7.18844i	−0.00231507	−	0.00863996i
$833$	−910.427	+	243.948i	−1.09295	+	0.292855i
$834$	574.431	−	715.418i	0.688766	−	0.857816i
$835$	943.667	−	327.351i	1.13014	−	0.392037i
$836$	118.353			0.141571
$837$	−442.373	−	88.2834i	−0.528522	−	0.105476i
$838$	402.737	+	402.737i	0.480593	+	0.480593i
$839$	946.477	−	546.449i	1.12810	−	0.651309i	0.184644	−	0.982805i	$-0.440887\pi$
$839$	946.477	−	546.449i	1.12810	−	0.651309i	0.943457	+	0.331496i	$0.107553\pi$
$840$	2.96100	+	3.48295i	0.00352500	+	0.00414637i
$841$	−393.430	+	681.440i	−0.467812	+	0.810274i
$842$	264.182	+	985.940i	0.313755	+	1.17095i
$843$	678.291	−	497.125i	0.804616	−	0.589709i
$844$	369.598	−	213.388i	0.437913	−	0.252829i
$845$	6.30890	+	9.30726i	0.00746615	+	0.0110145i
$846$	988.112	+	312.007i	1.16798	+	0.368803i
$847$	−1.71114	+	1.71114i	−0.00202024	+	0.00202024i
$848$	204.735	−	764.080i	0.241432	−	0.901038i
$849$	419.295	+	1078.89i	0.493870	+	1.27077i
$850$	−940.598	+	741.842i	−1.10659	+	0.872755i
$851$	1156.51	−	2003.14i	1.35900	−	2.35386i
$852$	150.339	−	341.478i	0.176455	−	0.400795i
$853$	425.510	−	1588.02i	0.498839	−	1.86169i	−0.00853057	−	0.999964i	$-0.502715\pi$
$853$	425.510	−	1588.02i	0.498839	−	1.86169i	0.507369	−	0.861729i	$-0.330618\pi$
$854$		−	0.914971i		−	0.00107140i
$855$	−250.417	+	74.6866i	−0.292885	+	0.0873527i
$856$	92.5628			0.108134
$857$	−318.230	−	85.2695i	−0.371330	−	0.0994977i	0.0683276	−	0.997663i	$-0.478234\pi$
$857$	−318.230	−	85.2695i	−0.371330	−	0.0994977i	−0.439658	+	0.898165i	$0.644900\pi$
$858$	−729.240	+	534.465i	−0.849930	+	0.622920i
$859$	−1361.73	−	786.197i	−1.58525	−	0.915247i	−0.994074	−	0.108707i	$-0.965329\pi$
$859$	−1361.73	−	786.197i	−1.58525	−	0.915247i	−0.591180	−	0.806540i	$-0.701338\pi$
$860$	−83.7213	−	72.4417i	−0.0973503	−	0.0842346i
$861$	−9.93239	−	7.97502i	−0.0115359	−	0.00926251i
$862$	111.827	+	29.9639i	0.129729	+	0.0347609i
$863$	458.505	+	458.505i	0.531292	+	0.531292i	0.920957	−	0.389665i	$-0.127409\pi$
$863$	458.505	+	458.505i	0.531292	+	0.531292i	−0.389665	+	0.920957i	$0.627409\pi$
$864$	714.698	−	476.895i	0.827197	−	0.551961i
$865$	169.791	+	32.6006i	0.196290	+	0.0376885i
$866$	−758.481	−	1313.73i	−0.875844	−	1.51701i
$867$	−241.792	+	26.4291i	−0.278883	+	0.0304834i
$868$	2.42395	−	0.649494i	0.00279256	−	0.000748265i
$869$	378.794	+	218.697i	0.435897	+	0.251665i
$870$	−248.404	+	117.788i	−0.285522	+	0.135388i
$871$	−324.550	−	562.137i	−0.372618	−	0.645393i
$872$	354.396	−	354.396i	0.406418	−	0.406418i
$873$	1398.60	+	61.6532i	1.60206	+	0.0706222i
$874$		−	655.913i		−	0.750472i
$875$	−0.387295	+	8.50854i	−0.000442622	+	0.00972405i
$876$	−476.941	+	185.357i	−0.544454	+	0.211595i
$877$	279.129	+	1041.72i	0.318277	+	1.18783i	0.920900	+	0.389800i	$0.127456\pi$
$877$	279.129	+	1041.72i	0.318277	+	1.18783i	−0.602623	+	0.798026i	$0.705878\pi$
$878$	−931.615	+	249.625i	−1.06106	+	0.284311i
$879$	−45.9083	−	118.127i	−0.0522279	−	0.134387i
$880$	830.199	+	402.564i	0.943408	+	0.457459i
$881$	1585.15			1.79927			0.899633	−	0.436647i	$-0.143834\pi$
$881$	1585.15			1.79927			0.899633	+	0.436647i	$0.143834\pi$
$882$	926.101	+	590.539i	1.05000	+	0.669545i
$883$	−1004.45	−	1004.45i	−1.13755	−	1.13755i	−0.988889	−	0.148657i	$-0.952505\pi$
$883$	−1004.45	−	1004.45i	−1.13755	−	1.13755i	−0.148657	−	0.988889i	$-0.547495\pi$
$884$	−480.584	+	277.466i	−0.543648	+	0.313875i
$885$	−266.746	−	95.1454i	−0.301408	−	0.107509i
$886$	913.702	−	1582.58i	1.03127	−	1.78621i
$887$	81.0299	+	302.408i	0.0913528	+	0.340933i	0.996441	−	0.0842901i	$-0.0268622\pi$
$887$	81.0299	+	302.408i	0.0913528	+	0.340933i	−0.905088	+	0.425223i	$0.860196\pi$
$888$	74.3688	+	680.378i	0.0837487	+	0.766191i
$889$	−12.6676	+	7.31362i	−0.0142492	+	0.00822680i
$890$	−723.576	−	138.929i	−0.813006	−	0.156100i
$891$	613.112	+	430.074i	0.688117	+	0.482687i
$892$	−149.235	+	149.235i	−0.167304	+	0.167304i
$893$	−69.4713	+	259.270i	−0.0777954	+	0.290336i
$894$	124.300	−	154.808i	0.139038	−	0.173163i
$895$	927.395	−	66.9852i	1.03620	−	0.0748438i
$896$	4.38491	−	7.59489i	0.00489387	−	0.00847644i
$897$	1052.37	+	1435.88i	1.17321	+	1.60076i
$898$	90.9632	−	339.479i	0.101295	−	0.378039i
$899$		−	122.932i		−	0.136743i
$900$	489.511	+	79.8233i	0.543902	+	0.0886926i
$901$	762.464			0.846242
$902$	−1386.18	−	371.425i	−1.53678	−	0.411779i
$903$	−1.87927	−	0.827369i	−0.00208114	−	0.000916245i
$904$	143.639	+	82.9302i	0.158893	+	0.0917370i
$905$	−35.2230	−	487.655i	−0.0389205	−	0.538845i
$906$	−685.938	+	266.581i	−0.757106	+	0.294239i
$907$	−357.992	−	95.9237i	−0.394699	−	0.105759i	0.0560100	−	0.998430i	$-0.482162\pi$
$907$	−357.992	−	95.9237i	−0.394699	−	0.105759i	−0.450709	+	0.892671i	$0.648829\pi$
$908$	513.506	+	513.506i	0.565536	+	0.565536i
$909$	−335.543	−	366.490i	−0.369134	−	0.403180i
$910$	−2.09399	+	10.9060i	−0.00230109	+	0.0119846i
$911$	490.084	+	848.851i	0.537963	+	0.931779i	0.999014	+	0.0444052i	$0.0141393\pi$
$911$	490.084	+	848.851i	0.537963	+	0.931779i	−0.461051	+	0.887374i	$0.652527\pi$
$912$	205.537	+	280.440i	0.225369	+	0.307500i
$913$	−554.997	+	148.711i	−0.607883	+	0.162882i
$914$	−1583.93	−	914.484i	−1.73297	−	1.00053i
$915$	52.3766	+	61.6093i	0.0572422	+	0.0673326i
$916$	458.489	+	794.127i	0.500534	+	0.866951i
$917$	0.0724117	−	0.0724117i	7.89659e−5	−	7.89659e-5i
$918$	972.172	+	853.657i	1.05901	+	0.929909i
$919$		−	1321.17i		−	1.43762i	−0.695205	−	0.718811i	$-0.744687\pi$
$919$		−	1321.17i		−	1.43762i	0.695205	−	0.718811i	$-0.255313\pi$
$920$	442.467	−	912.491i	0.480942	−	0.991838i
$921$	281.565	+	226.077i	0.305717	+	0.245470i
$922$	−413.938	−	1544.84i	−0.448956	−	1.67553i
$923$	−713.166	+	191.092i	−0.772661	+	0.207034i
$924$	−4.11759	−	0.634643i	−0.00445626	−	0.000686843i
$925$	−762.757	+	1021.92i	−0.824602	+	1.10478i
$926$	691.330			0.746577
$927$	−730.114	+	379.683i	−0.787609	+	0.409583i
$928$	165.567	+	165.567i	0.178413	+	0.178413i
$929$	672.297	−	388.151i	0.723678	−	0.417816i	−0.0924267	−	0.995719i	$-0.529462\pi$
$929$	672.297	−	388.151i	0.723678	−	0.417816i	0.816105	+	0.577904i	$0.196129\pi$
$930$	−354.741	+	513.636i	−0.381442	+	0.552297i
$931$	−142.259	+	246.400i	−0.152802	+	0.264662i
$932$	−17.7678	−	66.3103i	−0.0190642	−	0.0711484i
$933$	−1247.05	−	549.027i	−1.33660	−	0.588454i
$934$	−175.242	+	101.176i	−0.187625	+	0.108325i
$935$	−167.691	+	873.376i	−0.179349	+	0.934092i
$936$	−502.331	−	158.616i	−0.536678	−	0.169462i
$937$	295.586	−	295.586i	0.315459	−	0.315459i	−0.531561	−	0.847020i	$-0.678394\pi$
$937$	295.586	−	295.586i	0.315459	−	0.315459i	0.847020	+	0.531561i	$0.178394\pi$
$938$	2.17890	−	8.13175i	0.00232292	−	0.00866925i
$939$	−880.974	−	135.784i	−0.938205	−	0.144605i
$940$	333.349	−	385.253i	0.354626	−	0.409843i
$941$	−48.8020	+	84.5275i	−0.0518618	+	0.0898273i	−0.890791	−	0.454413i	$-0.849849\pi$
$941$	−48.8020	+	84.5275i	−0.0518618	+	0.0898273i	0.838929	+	0.544241i	$0.183182\pi$
$942$	−1282.83	+	140.220i	−1.36182	+	0.148854i
$943$	−731.341	+	2729.40i	−0.775548	+	2.89438i
$944$			376.820i			0.399174i
$945$	9.11265	−	1.25559i	0.00964301	−	0.00132867i
$946$	−231.333			−0.244538
$947$	−177.098	−	47.4532i	−0.187009	−	0.0501090i	0.164099	−	0.986444i	$-0.447528\pi$
$947$	−177.098	−	47.4532i	−0.187009	−	0.0501090i	−0.351108	+	0.936335i	$0.614195\pi$
$948$	−33.9929	−	310.991i	−0.0358575	−	0.328050i
$949$	876.908	+	506.283i	0.924034	+	0.533491i
$950$	−42.4244	+	359.115i	−0.0446573	+	0.378016i
$951$	40.4023	−	262.131i	0.0424840	−	0.275638i
$952$	5.66313	+	1.51743i	0.00594866	+	0.00159394i
$953$	−16.8810	−	16.8810i	−0.0177135	−	0.0177135i	0.698195	−	0.715908i	$-0.253987\pi$
$953$	−16.8810	−	16.8810i	−0.0177135	−	0.0177135i	−0.715908	+	0.698195i	$0.753987\pi$
$954$	−599.995	−	655.332i	−0.628925	−	0.686931i
$955$	564.603	−	382.714i	0.591207	−	0.400748i
$956$	−340.507	−	589.776i	−0.356179	−	0.616920i
$957$	−82.2369	+	186.791i	−0.0859320	+	0.195184i
$958$	1164.97	−	312.153i	1.21604	−	0.325838i
$959$	−4.12185	−	2.37975i	−0.00429807	−	0.00248149i
$960$	1.53539	+	8.39107i	0.00159937	+	0.00874070i
$961$	340.934	+	590.514i	0.354770	+	0.614479i
$962$	−1175.66	+	1175.66i	−1.22210	+	1.22210i
$963$	100.141	−	157.044i	0.103988	−	0.163078i
$964$		−	56.6819i		−	0.0587987i
$965$	−151.351	−	436.304i	−0.156840	−	0.452129i
$966$	−3.51719	+	22.8196i	−0.00364098	+	0.0236228i
$967$	−311.140	−	1161.19i	−0.321758	−	1.20082i	−0.917531	−	0.397665i	$-0.869821\pi$
$967$	−311.140	−	1161.19i	−0.321758	−	1.20082i	0.595772	−	0.803153i	$-0.296846\pi$
$968$	−153.434	+	41.1125i	−0.158506	+	0.0424716i
$969$	−209.825	+	261.324i	−0.216538	+	0.269684i
$970$	845.253	−	1743.15i	0.871395	−	1.79706i
$971$	−608.975			−0.627163			−0.313582	−	0.949561i	$-0.601529\pi$
$971$	−608.975			−0.627163			−0.313582	+	0.949561i	$0.601529\pi$
$972$	−11.1225	−	535.540i	−0.0114429	−	0.550967i
$973$	−5.91580	−	5.91580i	−0.00607996	−	0.00607996i
$974$	−494.753	+	285.646i	−0.507960	+	0.293271i
$975$	−483.304	−	854.220i	−0.495696	−	0.876123i
$976$	53.7969	−	93.1790i	0.0551198	−	0.0954702i
$977$	−22.8425	−	85.2493i	−0.0233802	−	0.0872562i	0.953250	−	0.302183i	$-0.0977154\pi$
$977$	−22.8425	−	85.2493i	−0.0233802	−	0.0872562i	−0.976630	+	0.214927i	$0.931049\pi$
$978$	−554.739	+	406.572i	−0.567218	+	0.415718i
$979$	−473.701	+	273.491i	−0.483862	+	0.279358i
$980$	446.998	−	302.996i	0.456120	−	0.309180i
$981$	−217.865	−	984.684i	−0.222085	−	1.00376i
$982$	−1391.51	+	1391.51i	−1.41701	+	1.41701i
$983$	−369.494	+	1378.97i	−0.375884	+	1.40282i	0.476166	+	0.879356i	$0.342026\pi$
$983$	−369.494	+	1378.97i	−0.375884	+	1.40282i	−0.852049	+	0.523461i	$0.824640\pi$
$984$	−302.881	−	779.343i	−0.307806	−	0.792015i
$985$	−912.359	−	789.439i	−0.926253	−	0.801461i
$986$	−176.289	+	305.341i	−0.178792	+	0.309676i
$987$	3.80723	−	8.64766i	0.00385738	−	0.00876156i
$988$	−43.3555	+	161.805i	−0.0438821	+	0.163770i
$989$			455.499i			0.460565i
$990$	882.619	−	543.143i	0.891534	−	0.548630i
$991$	14.7275			0.0148613			0.00743063	−	0.999972i	$-0.497635\pi$
$991$	14.7275			0.0148613			0.00743063	+	0.999972i	$0.497635\pi$
$992$	513.545	+	137.604i	0.517687	+	0.138714i
$993$	1079.92	−	791.484i	1.08754	−	0.797063i
$994$	−8.29290	−	4.78791i	−0.00834296	−	0.00481681i
$995$	−181.625	+	13.1187i	−0.182538	+	0.0131846i
$996$	320.448	+	257.298i	0.321735	+	0.258331i
$997$	222.758	+	59.6878i	0.223428	+	0.0598674i	0.368796	−	0.929510i	$-0.379770\pi$
$997$	222.758	+	59.6878i	0.223428	+	0.0598674i	−0.145368	+	0.989378i	$0.546437\pi$
$998$	−858.989	−	858.989i	−0.860710	−	0.860710i
$999$	1234.80	+	609.903i	1.23603	+	0.610514i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.13.9	yes	40
3.2	odd	2		135.3.l.a.118.2		40
5.2	odd	4	inner	45.3.k.a.22.2	yes	40
5.3	odd	4		225.3.o.b.157.9		40
5.4	even	2		225.3.o.b.193.2		40
9.2	odd	6		135.3.l.a.73.9		40
9.4	even	3		405.3.g.h.163.2		20
9.5	odd	6		405.3.g.g.163.9		20
9.7	even	3	inner	45.3.k.a.43.2	yes	40
15.2	even	4		135.3.l.a.37.9		40
45.2	even	12		135.3.l.a.127.2		40
45.7	odd	12	inner	45.3.k.a.7.9	✓	40
45.22	odd	12		405.3.g.h.82.2		20
45.32	even	12		405.3.g.g.82.9		20
45.34	even	6		225.3.o.b.43.9		40
45.43	odd	12		225.3.o.b.7.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	45.7	odd	12	inner
45.3.k.a.13.9	yes	40	1.1	even	1	trivial
45.3.k.a.22.2	yes	40	5.2	odd	4	inner
45.3.k.a.43.2	yes	40	9.7	even	3	inner
135.3.l.a.37.9		40	15.2	even	4
135.3.l.a.73.9		40	9.2	odd	6
135.3.l.a.118.2		40	3.2	odd	2
135.3.l.a.127.2		40	45.2	even	12
225.3.o.b.7.2		40	45.43	odd	12
225.3.o.b.43.9		40	45.34	even	6
225.3.o.b.157.9		40	5.3	odd	4
225.3.o.b.193.2		40	5.4	even	2
405.3.g.g.82.9		20	45.32	even	12
405.3.g.g.163.9		20	9.5	odd	6
405.3.g.h.82.2		20	45.22	odd	12
405.3.g.h.163.2		20	9.4	even	3

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

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	45.3.k.a.13.9

Level	$45$
Weight	$3$
Character	45.13
Analytic conductor	$1.226$
Analytic rank	$0$
Dimension	$40$
Inner twists	$4$