LMFDB - Embedded newform 210.3.v.b.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	210.193
Dual form			210.3.v.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.22909 - 4.84658i) q^{5} +2.44949 q^{6} +(6.32429 - 3.00056i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.22909 - 4.84658i) q^{5} +2.44949 q^{6} +(6.32429 - 3.00056i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(0.0950035 - 7.07043i) q^{10} +(-1.95694 + 3.38951i) q^{11} +(3.34607 + 0.896575i) q^{12} +(-8.93314 - 8.93314i) q^{13} +(9.73742 - 1.78399i) q^{14} +(-4.22897 - 7.55750i) q^{15} +(2.00000 + 3.46410i) q^{16} +(3.83238 + 14.3027i) q^{17} +(4.09808 - 1.09808i) q^{18} +(28.0079 - 16.1704i) q^{19} +(2.71773 - 9.62361i) q^{20} +(9.23562 - 7.85514i) q^{21} +(-3.91387 + 3.91387i) q^{22} +(-3.30186 + 12.3227i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-21.9787 + 11.9138i) q^{25} +(-8.93314 - 15.4726i) q^{26} +(3.67423 - 3.67423i) q^{27} +(13.9546 + 1.12716i) q^{28} +26.6068i q^{29} +(-3.01064 - 11.8716i) q^{30} +(-17.0130 + 29.4674i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-1.75454 + 6.54804i) q^{33} +20.9405i q^{34} +(-22.3156 - 26.9632i) q^{35} +6.00000 q^{36} +(-6.25026 - 1.67475i) q^{37} +(44.1783 - 11.8375i) q^{38} +(-18.9500 - 10.9408i) q^{39} +(7.23498 - 12.1513i) q^{40} -26.0073 q^{41} +(15.4913 - 7.34985i) q^{42} +(21.0534 + 21.0534i) q^{43} +(-6.77903 + 3.91387i) q^{44} +(-10.4631 - 10.7481i) q^{45} +(-9.02086 + 15.6246i) q^{46} +(-40.1094 - 10.7473i) q^{47} +(4.89898 + 4.89898i) q^{48} +(30.9932 - 37.9528i) q^{49} +(-34.3842 + 8.22975i) q^{50} +(12.8234 + 22.2108i) q^{51} +(-6.53951 - 24.4058i) q^{52} +(-43.7126 + 11.7128i) q^{53} +(6.36396 - 3.67423i) q^{54} +(18.8328 + 5.31843i) q^{55} +(18.6497 + 6.64745i) q^{56} +(39.6092 - 39.6092i) q^{57} +(-9.73878 + 36.3456i) q^{58} +(20.7971 + 12.0072i) q^{59} +(0.232710 - 17.3189i) q^{60} +(8.39818 + 14.5461i) q^{61} +(-34.0260 + 34.0260i) q^{62} +(11.9301 - 17.2821i) q^{63} +8.00000i q^{64} +(-32.3155 + 54.2748i) q^{65} +(-4.79349 + 8.30258i) q^{66} +(-15.2798 - 57.0249i) q^{67} +(-7.66477 + 28.6053i) q^{68} +22.0965i q^{69} +(-20.6144 - 45.0005i) q^{70} -132.560 q^{71} +(8.19615 + 2.19615i) q^{72} +(-8.56704 + 2.29553i) q^{73} +(-7.92501 - 4.57551i) q^{74} +(-31.4302 + 29.7849i) q^{75} +64.6815 q^{76} +(-2.20578 + 27.3082i) q^{77} +(-21.8816 - 21.8816i) q^{78} +(-90.6550 + 52.3397i) q^{79} +(14.3309 - 13.9509i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-35.5266 - 9.51932i) q^{82} +(94.1629 + 94.1629i) q^{83} +(23.8517 - 4.36988i) q^{84} +(64.6086 - 36.1532i) q^{85} +(21.0534 + 36.4656i) q^{86} +(11.9275 + 44.5141i) q^{87} +(-10.6929 + 2.86515i) q^{88} +(43.2731 - 24.9837i) q^{89} +(-10.3588 - 18.5120i) q^{90} +(-83.3002 - 29.6913i) q^{91} +(-18.0417 + 18.0417i) q^{92} +(-15.2534 + 56.9266i) q^{93} +(-50.8567 - 29.3621i) q^{94} +(-112.795 - 115.868i) q^{95} +(4.89898 + 8.48528i) q^{96} +(118.224 - 118.224i) q^{97} +(56.2293 - 40.5002i) q^{98} +11.7416i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	−1.22909	−	4.84658i	−0.245818	−	0.969316i
$5$	−1.22909	−	4.84658i	−0.245818	−	0.969316i
$6$	2.44949			0.408248
$7$	6.32429	−	3.00056i	0.903470	−	0.428652i
$7$	6.32429	−	3.00056i	0.903470	−	0.428652i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	0.0950035	−	7.07043i	0.00950035	−	0.707043i
$11$	−1.95694	+	3.38951i	−0.177903	+	0.308138i	−0.941162	−	0.337955i	$-0.890265\pi$
$11$	−1.95694	+	3.38951i	−0.177903	+	0.308138i	0.763259	+	0.646093i	$0.223598\pi$
$12$	3.34607	+	0.896575i	0.278839	+	0.0747146i
$13$	−8.93314	−	8.93314i	−0.687164	−	0.687164i	0.274440	−	0.961604i	$-0.411508\pi$
$13$	−8.93314	−	8.93314i	−0.687164	−	0.687164i	−0.961604	+	0.274440i	$0.911508\pi$
$14$	9.73742	−	1.78399i	0.695530	−	0.127428i
$15$	−4.22897	−	7.55750i	−0.281931	−	0.503833i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	3.83238	+	14.3027i	0.225434	+	0.841332i	0.982230	+	0.187681i	$0.0600971\pi$
$17$	3.83238	+	14.3027i	0.225434	+	0.841332i	−0.756796	+	0.653651i	$0.773236\pi$
$18$	4.09808	−	1.09808i	0.227671	−	0.0610042i
$19$	28.0079	−	16.1704i	1.47410	−	0.851072i	0.474526	−	0.880242i	$-0.342620\pi$
$19$	28.0079	−	16.1704i	1.47410	−	0.851072i	0.999574	+	0.0291696i	$0.00928630\pi$
$20$	2.71773	−	9.62361i	0.135887	−	0.481181i
$21$	9.23562	−	7.85514i	0.439792	−	0.374054i
$22$	−3.91387	+	3.91387i	−0.177903	+	0.177903i
$23$	−3.30186	+	12.3227i	−0.143559	+	0.535770i	0.856256	+	0.516552i	$0.172785\pi$
$23$	−3.30186	+	12.3227i	−0.143559	+	0.535770i	−0.999815	+	0.0192188i	$0.993882\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	−21.9787	+	11.9138i	−0.879147	+	0.476551i
$26$	−8.93314	−	15.4726i	−0.343582	−	0.595102i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	13.9546	+	1.12716i	0.498377	+	0.0402557i
$29$			26.6068i			0.917478i	0.888571	+	0.458739i	$0.151699\pi$
$29$			26.6068i			0.917478i	−0.888571	+	0.458739i	$0.848301\pi$
$30$	−3.01064	−	11.8716i	−0.100355	−	0.395722i
$31$	−17.0130	+	29.4674i	−0.548807	+	0.950561i	0.449550	+	0.893255i	$0.351584\pi$
$31$	−17.0130	+	29.4674i	−0.548807	+	0.950561i	−0.998357	+	0.0573060i	$0.981749\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−1.75454	+	6.54804i	−0.0531679	+	0.198425i
$34$			20.9405i			0.615898i
$35$	−22.3156	−	26.9632i	−0.637588	−	0.770377i
$36$	6.00000			0.166667
$37$	−6.25026	−	1.67475i	−0.168926	−	0.0452636i	0.173365	−	0.984858i	$-0.444536\pi$
$37$	−6.25026	−	1.67475i	−0.168926	−	0.0452636i	−0.342291	+	0.939594i	$0.611203\pi$
$38$	44.1783	−	11.8375i	1.16259	−	0.311514i
$39$	−18.9500	−	10.9408i	−0.485898	−	0.280534i
$40$	7.23498	−	12.1513i	0.180875	−	0.303783i
$41$	−26.0073			−0.634324			−0.317162	−	0.948371i	$-0.602730\pi$
$41$	−26.0073			−0.634324			−0.317162	+	0.948371i	$0.602730\pi$
$42$	15.4913	−	7.34985i	0.368840	−	0.174996i
$43$	21.0534	+	21.0534i	0.489614	+	0.489614i	0.908185	−	0.418570i	$-0.137469\pi$
$43$	21.0534	+	21.0534i	0.489614	+	0.489614i	−0.418570	+	0.908185i	$0.637469\pi$
$44$	−6.77903	+	3.91387i	−0.154069	+	0.0889516i
$45$	−10.4631	−	10.7481i	−0.232514	−	0.238848i
$46$	−9.02086	+	15.6246i	−0.196106	+	0.339665i
$47$	−40.1094	−	10.7473i	−0.853391	−	0.228666i	−0.194499	−	0.980903i	$-0.562308\pi$
$47$	−40.1094	−	10.7473i	−0.853391	−	0.228666i	−0.658892	+	0.752237i	$0.728975\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$	30.9932	−	37.9528i	0.632515	−	0.774548i
$50$	−34.3842	+	8.22975i	−0.687683	+	0.164595i
$51$	12.8234	+	22.2108i	0.251439	+	0.435506i
$52$	−6.53951	−	24.4058i	−0.125760	−	0.469342i
$53$	−43.7126	+	11.7128i	−0.824766	+	0.220995i	−0.646429	−	0.762974i	$-0.723738\pi$
$53$	−43.7126	+	11.7128i	−0.824766	+	0.220995i	−0.178337	+	0.983969i	$0.557072\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$	18.8328	+	5.31843i	0.342414	+	0.0966988i
$56$	18.6497	+	6.64745i	0.333030	+	0.118704i
$57$	39.6092	−	39.6092i	0.694897	−	0.694897i
$58$	−9.73878	+	36.3456i	−0.167910	+	0.626649i
$59$	20.7971	+	12.0072i	0.352494	+	0.203512i	0.665783	−	0.746145i	$-0.268098\pi$
$59$	20.7971	+	12.0072i	0.352494	+	0.203512i	−0.313289	+	0.949658i	$0.601431\pi$
$60$	0.232710	−	17.3189i	0.00387850	−	0.288649i
$61$	8.39818	+	14.5461i	0.137675	+	0.238460i	0.926616	−	0.376009i	$-0.122704\pi$
$61$	8.39818	+	14.5461i	0.137675	+	0.238460i	−0.788941	+	0.614469i	$0.789370\pi$
$62$	−34.0260	+	34.0260i	−0.548807	+	0.548807i
$63$	11.9301	−	17.2821i	0.189367	−	0.274319i
$64$			8.00000i			0.125000i
$65$	−32.3155	+	54.2748i	−0.497162	+	0.834997i
$66$	−4.79349	+	8.30258i	−0.0726287	+	0.125797i
$67$	−15.2798	−	57.0249i	−0.228056	−	0.851118i	−0.981157	−	0.193213i	$-0.938109\pi$
$67$	−15.2798	−	57.0249i	−0.228056	−	0.851118i	0.753100	−	0.657906i	$-0.228557\pi$
$68$	−7.66477	+	28.6053i	−0.112717	+	0.420666i
$69$			22.0965i			0.320239i
$70$	−20.6144	−	45.0005i	−0.294492	−	0.642864i
$71$	−132.560			−1.86705			−0.933524	−	0.358515i	$-0.883283\pi$
$71$	−132.560			−1.86705			−0.933524	+	0.358515i	$0.883283\pi$
$72$	8.19615	+	2.19615i	0.113835	+	0.0305021i
$73$	−8.56704	+	2.29553i	−0.117357	+	0.0314457i	−0.317019	−	0.948419i	$-0.602682\pi$
$73$	−8.56704	+	2.29553i	−0.117357	+	0.0314457i	0.199663	+	0.979865i	$0.436015\pi$
$74$	−7.92501	−	4.57551i	−0.107095	−	0.0618312i
$75$	−31.4302	+	29.7849i	−0.419070	+	0.397132i
$76$	64.6815			0.851072
$77$	−2.20578	+	27.3082i	−0.0286465	+	0.354651i
$78$	−21.8816	−	21.8816i	−0.280534	−	0.280534i
$79$	−90.6550	+	52.3397i	−1.14753	+	0.662528i	−0.948284	−	0.317422i	$-0.897183\pi$
$79$	−90.6550	+	52.3397i	−1.14753	+	0.662528i	−0.199247	+	0.979949i	$0.563850\pi$
$80$	14.3309	−	13.9509i	0.179136	−	0.174386i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	−35.5266	−	9.51932i	−0.433251	−	0.116089i
$83$	94.1629	+	94.1629i	1.13449	+	1.13449i	0.989421	+	0.145072i	$0.0463413\pi$
$83$	94.1629	+	94.1629i	1.13449	+	1.13449i	0.145072	+	0.989421i	$0.453659\pi$
$84$	23.8517	−	4.36988i	0.283949	−	0.0520223i
$85$	64.6086	−	36.1532i	0.760101	−	0.425332i
$86$	21.0534	+	36.4656i	0.244807	+	0.424019i
$87$	11.9275	+	44.5141i	0.137098	+	0.511657i
$88$	−10.6929	+	2.86515i	−0.121510	+	0.0325586i
$89$	43.2731	−	24.9837i	0.486215	−	0.280716i	−0.236788	−	0.971561i	$-0.576095\pi$
$89$	43.2731	−	24.9837i	0.486215	−	0.280716i	0.723003	+	0.690845i	$0.242761\pi$
$90$	−10.3588	−	18.5120i	−0.115098	−	0.205689i
$91$	−83.3002	−	29.6913i	−0.915386	−	0.326278i
$92$	−18.0417	+	18.0417i	−0.196106	+	0.196106i
$93$	−15.2534	+	56.9266i	−0.164016	+	0.612114i
$94$	−50.8567	−	29.3621i	−0.541028	−	0.312363i
$95$	−112.795	−	115.868i	−1.18732	−	1.21966i
$96$	4.89898	+	8.48528i	0.0510310	+	0.0883883i
$97$	118.224	−	118.224i	1.21881	−	1.21881i	0.250755	−	0.968050i	$-0.419321\pi$
$97$	118.224	−	118.224i	1.21881	−	1.21881i	0.968050	−	0.250755i	$-0.0806790\pi$
$98$	56.2293	−	40.5002i	0.573768	−	0.413268i
$99$			11.7416i			0.118602i
$100$	−49.9819	−	1.34343i	−0.499819	−	0.0134343i
$101$	−55.9197	+	96.8557i	−0.553660	+	0.958967i	0.444346	+	0.895855i	$0.353436\pi$
$101$	−55.9197	+	96.8557i	−0.553660	+	0.958967i	−0.998006	+	0.0631124i	$0.979897\pi$
$102$	9.38738	+	35.0342i	0.0920332	+	0.343473i
$103$	47.9268	−	178.865i	0.465309	−	1.73656i	−0.190556	−	0.981676i	$-0.561029\pi$
$103$	47.9268	−	178.865i	0.465309	−	1.73656i	0.655864	−	0.754879i	$-0.272304\pi$
$104$		−	35.7325i		−	0.343582i
$105$	−49.4220	−	35.1065i	−0.470686	−	0.334348i
$106$	−63.9997			−0.603771
$107$	−30.9123	−	8.28292i	−0.288900	−	0.0774105i	0.111459	−	0.993769i	$-0.464448\pi$
$107$	−30.9123	−	8.28292i	−0.288900	−	0.0774105i	−0.400358	+	0.916359i	$0.631114\pi$
$108$	10.0382	−	2.68973i	0.0929463	−	0.0249049i
$109$	151.129	+	87.2544i	1.38651	+	0.800499i	0.992920	−	0.118788i	$-0.0379010\pi$
$109$	151.129	+	87.2544i	1.38651	+	0.800499i	0.393586	+	0.919288i	$0.371234\pi$
$110$	23.7794	+	14.1584i	0.216176	+	0.128713i
$111$	−11.2077			−0.100970
$112$	23.0428	+	15.9069i	0.205740	+	0.142025i
$113$	−6.20286	−	6.20286i	−0.0548925	−	0.0548925i	0.679128	−	0.734020i	$-0.262358\pi$
$113$	−6.20286	−	6.20286i	−0.0548925	−	0.0548925i	−0.734020	+	0.679128i	$0.762358\pi$
$114$	68.6051	−	39.6092i	0.601799	−	0.347449i
$115$	63.7813	+	0.857013i	0.554620	+	0.00745229i
$116$	−26.6068	+	46.0844i	−0.229369	+	0.397279i
$117$	−36.6087	−	9.80926i	−0.312895	−	0.0838399i
$118$	24.0145	+	24.0145i	0.203512	+	0.203512i
$119$	67.1531	+	78.9548i	0.564312	+	0.663486i
$120$	6.65706	−	23.5729i	0.0554755	−	0.196441i
$121$	52.8408	+	91.5230i	0.436701	+	0.756388i
$122$	6.14790	+	22.9443i	0.0503926	+	0.188068i
$123$	−43.5110	+	11.6587i	−0.353748	+	0.0947865i
$124$	−58.9348	+	34.0260i	−0.475281	+	0.274403i
$125$	84.7548	+	91.8783i	0.678038	+	0.735027i
$126$	22.6226	−	19.2411i	0.179544	−	0.152707i
$127$	38.4037	−	38.4037i	0.302392	−	0.302392i	−0.539557	−	0.841949i	$-0.681408\pi$
$127$	38.4037	−	38.4037i	0.302392	−	0.302392i	0.841949	+	0.539557i	$0.181408\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	44.6610	+	25.7851i	0.346210	+	0.199884i
$130$	−64.0098	+	62.3124i	−0.492383	+	0.479326i
$131$	−73.5861	−	127.455i	−0.561726	−	0.972938i	−0.997346	−	0.0728073i	$-0.976804\pi$
$131$	−73.5861	−	127.455i	−0.561726	−	0.972938i	0.435620	−	0.900131i	$-0.356529\pi$
$132$	−9.58699	+	9.58699i	−0.0726287	+	0.0726287i
$133$	128.610	−	186.306i	0.966991	−	1.40079i
$134$		−	83.4903i		−	0.623062i
$135$	−22.3234	−	13.2915i	−0.165359	−	0.0984556i
$136$	−20.9405	+	36.2701i	−0.153975	+	0.266692i
$137$	−0.303261	−	1.13179i	−0.00221359	−	0.00826122i	0.964810	−	0.262947i	$-0.0846945\pi$
$137$	−0.303261	−	1.13179i	−0.00221359	−	0.00826122i	−0.967024	+	0.254686i	$0.918028\pi$
$138$	−8.08788	+	30.1844i	−0.0586078	+	0.218727i
$139$			234.615i			1.68788i	0.536439	+	0.843939i	$0.319769\pi$
$139$			234.615i			1.68788i	−0.536439	+	0.843939i	$0.680231\pi$
$140$	−11.6885	−	69.0172i	−0.0834894	−	0.492980i
$141$	−71.9222			−0.510086
$142$	−181.081	−	48.5205i	−1.27522	−	0.341694i
$143$	47.7605	−	12.7974i	0.333990	−	0.0894923i
$144$	10.3923	+	6.00000i	0.0721688	+	0.0416667i
$145$	128.952	−	32.7022i	0.889326	−	0.225532i
$146$	−12.5430			−0.0859111
$147$	34.8389	−	77.3902i	0.236999	−	0.526464i
$148$	−9.15101	−	9.15101i	−0.0618312	−	0.0618312i
$149$	224.139	−	129.407i	1.50429	−	0.868501i	0.504300	−	0.863528i	$-0.331750\pi$
$149$	224.139	−	129.407i	1.50429	−	0.868501i	0.999988	−	0.00497290i	$-0.00158293\pi$
$150$	−53.8365	+	29.1826i	−0.358910	+	0.194551i
$151$	−72.8305	+	126.146i	−0.482321	+	0.835405i	−0.999794	−	0.0202948i	$-0.993540\pi$
$151$	−72.8305	+	126.146i	−0.482321	+	0.835405i	0.517473	+	0.855700i	$0.326873\pi$
$152$	88.3565	+	23.6751i	0.581293	+	0.155757i
$153$	31.4108	+	31.4108i	0.205299	+	0.205299i
$154$	−13.0086	+	36.4963i	−0.0844717	+	0.236989i
$155$	163.727	+	46.2368i	1.05630	+	0.298302i
$156$	−21.8816	−	37.9001i	−0.140267	−	0.242949i
$157$	−2.55973	−	9.55304i	−0.0163040	−	0.0608474i	0.957295	−	0.289114i	$-0.0933608\pi$
$157$	−2.55973	−	9.55304i	−0.0163040	−	0.0608474i	−0.973599	+	0.228267i	$0.926694\pi$
$158$	−142.995	+	38.3153i	−0.905029	+	0.242502i
$159$	−67.8819	+	39.1917i	−0.426930	+	0.246488i
$160$	24.6827	−	13.8118i	0.154267	−	0.0863235i
$161$	16.0932	+	87.8399i	0.0999575	+	0.545589i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	59.3922	−	221.655i	0.364369	−	1.35985i	−0.503904	−	0.863760i	$-0.668104\pi$
$163$	59.3922	−	221.655i	0.364369	−	1.35985i	0.868274	−	0.496086i	$-0.165230\pi$
$164$	−45.0459	−	26.0073i	−0.274670	−	0.158581i
$165$	33.8921	+	0.455399i	0.205406	+	0.00275999i
$166$	94.1629	+	163.095i	0.567246	+	0.982500i
$167$	181.703	−	181.703i	1.08804	−	1.08804i	0.0923104	−	0.995730i	$-0.470575\pi$
$167$	181.703	−	181.703i	1.08804	−	1.08804i	0.995730	−	0.0923104i	$-0.0294252\pi$
$168$	34.1815	+	2.76097i	0.203461	+	0.0164343i
$169$		−	9.39820i		−	0.0556106i
$170$	101.490	−	25.7378i	0.597000	−	0.151399i
$171$	48.5111	−	84.0237i	0.283691	−	0.491367i
$172$	15.4122	+	57.5190i	0.0896057	+	0.334413i
$173$	67.1837	−	250.733i	0.388345	−	1.44932i	−0.444481	−	0.895788i	$-0.646612\pi$
$173$	67.1837	−	250.733i	0.388345	−	1.44932i	0.832826	−	0.553535i	$-0.186721\pi$
$174$			65.1732i			0.374559i
$175$	−103.251	+	141.294i	−0.590008	+	0.807397i
$176$	−15.6555			−0.0889516
$177$	40.1770	+	10.7654i	0.226988	+	0.0608214i
$178$	68.2568	−	18.2894i	0.383465	−	0.102749i
$179$	−267.294	−	154.322i	−1.49326	−	0.862135i	−0.493292	−	0.869864i	$-0.664206\pi$
$179$	−267.294	−	154.322i	−1.49326	−	0.862135i	−0.999970	+	0.00772900i	$0.997540\pi$
$180$	−7.37454	−	29.0795i	−0.0409697	−	0.161553i
$181$	172.566			0.953406			0.476703	−	0.879064i	$-0.341832\pi$
$181$	172.566			0.953406			0.476703	+	0.879064i	$0.341832\pi$
$182$	−102.922	−	71.0490i	−0.565507	−	0.390379i
$183$	20.5713	+	20.5713i	0.112411	+	0.112411i
$184$	−31.2492	+	18.0417i	−0.169832	+	0.0980528i
$185$	−0.434689	+	32.3508i	−0.00234967	+	0.174869i
$186$	−41.6732	+	72.1801i	−0.224049	+	0.388065i
$187$	−55.9787	−	14.9995i	−0.299352	−	0.0802110i
$188$	−58.7242	−	58.7242i	−0.312363	−	0.312363i
$189$	12.2121	−	34.2617i	0.0646145	−	0.181279i
$190$	−111.671	−	199.564i	−0.587740	−	1.05034i
$191$	67.6472	+	117.168i	0.354174	+	0.613447i	0.986976	−	0.160866i	$-0.0514288\pi$
$191$	67.6472	+	117.168i	0.354174	+	0.613447i	−0.632802	+	0.774313i	$0.718095\pi$
$192$	3.58630	+	13.3843i	0.0186787	+	0.0697097i
$193$	−21.2706	+	5.69944i	−0.110210	+	0.0295308i	−0.313503	−	0.949587i	$-0.601502\pi$
$193$	−21.2706	+	5.69944i	−0.110210	+	0.0295308i	0.203292	+	0.979118i	$0.434836\pi$
$194$	204.770	−	118.224i	1.05552	−	0.609403i
$195$	−29.7342	+	105.290i	−0.152483	+	0.539949i
$196$	91.6347	−	34.7430i	0.467524	−	0.177260i
$197$	61.7521	−	61.7521i	0.313462	−	0.313462i	−0.532787	−	0.846249i	$-0.678855\pi$
$197$	61.7521	−	61.7521i	0.313462	−	0.313462i	0.846249	+	0.532787i	$0.178855\pi$
$198$	−4.29773	+	16.0393i	−0.0217057	+	0.0810068i
$199$	−287.540	−	166.011i	−1.44492	−	0.834227i	−0.446751	−	0.894658i	$-0.647419\pi$
$199$	−287.540	−	166.011i	−1.44492	−	0.834227i	−0.998172	+	0.0604310i	$0.980752\pi$
$200$	−67.7849	−	20.1298i	−0.338924	−	0.100649i
$201$	−51.1272	−	88.5548i	−0.254364	−	0.440571i
$202$	−111.839	+	111.839i	−0.553660	+	0.553660i
$203$	79.8355	+	168.269i	0.393278	+	0.828913i
$204$			51.2936i			0.251439i
$205$	31.9653	+	126.046i	0.155928	+	0.614860i
$206$	130.938	−	226.792i	0.635623	−	1.10093i
$207$	9.90559	+	36.9682i	0.0478531	+	0.178590i
$208$	13.0790	−	48.8116i	0.0628799	−	0.234671i
$209$			126.578i			0.605634i
$210$	−54.6618	−	66.0461i	−0.260294	−	0.314505i
$211$	−4.76592			−0.0225873			−0.0112936	−	0.999936i	$-0.503595\pi$
$211$	−4.76592			−0.0225873			−0.0112936	+	0.999936i	$0.503595\pi$
$212$	−87.4252	−	23.4255i	−0.412383	−	0.110498i
$213$	−221.778	+	59.4252i	−1.04121	+	0.278992i
$214$	−39.1952	−	22.6294i	−0.183155	−	0.105745i
$215$	76.1605	−	127.914i	0.354235	−	0.594947i
$216$	14.6969			0.0680414
$217$	−19.1764	+	237.409i	−0.0883705	+	1.09405i
$218$	174.509	+	174.509i	0.800499	+	0.800499i
$219$	−13.3039	+	7.68100i	−0.0607483	+	0.0350731i
$220$	27.3009	+	28.0446i	0.124095	+	0.127475i
$221$	93.5323	−	162.003i	0.423223	−	0.733044i
$222$	−15.3099	−	4.10229i	−0.0689637	−	0.0184788i
$223$	−96.4999	−	96.4999i	−0.432735	−	0.432735i	0.456823	−	0.889558i	$-0.348987\pi$
$223$	−96.4999	−	96.4999i	−0.432735	−	0.432735i	−0.889558	+	0.456823i	$0.848987\pi$
$224$	25.6548	+	30.1634i	0.114530	+	0.134658i
$225$	−39.2316	+	63.9209i	−0.174363	+	0.284093i
$226$	−6.20286	−	10.7437i	−0.0274463	−	0.0475383i
$227$	−15.9499	−	59.5258i	−0.0702639	−	0.262228i	0.921854	−	0.387538i	$-0.126674\pi$
$227$	−15.9499	−	59.5258i	−0.0702639	−	0.262228i	−0.992118	+	0.125309i	$0.960008\pi$
$228$	108.214	−	28.9959i	0.474624	−	0.127175i
$229$	−390.888	+	225.680i	−1.70694	+	0.985500i	−0.768631	+	0.639693i	$0.779062\pi$
$229$	−390.888	+	225.680i	−1.70694	+	0.985500i	−0.938305	+	0.345808i	$0.887605\pi$
$230$	86.8132	+	24.5163i	0.377449	+	0.106593i
$231$	8.55157	+	46.6763i	0.0370198	+	0.202062i
$232$	−53.2137	+	53.2137i	−0.229369	+	0.229369i
$233$	−66.3620	+	247.666i	−0.284816	+	1.06295i	0.664158	+	0.747592i	$0.268790\pi$
$233$	−66.3620	+	247.666i	−0.284816	+	1.06295i	−0.948974	+	0.315354i	$0.897877\pi$
$234$	−46.4179	−	26.7994i	−0.198367	−	0.114527i
$235$	−2.78950	+	207.603i	−0.0118702	+	0.883416i
$236$	24.0145	+	41.5943i	0.101756	+	0.176247i
$237$	−128.205	+	128.205i	−0.540951	+	0.540951i
$238$	62.8334	+	132.434i	0.264006	+	0.556445i
$239$		−	7.06316i		−	0.0295529i	−0.999891	−	0.0147765i	$-0.995296\pi$
$239$		−	7.06316i		−	0.0295529i	0.999891	−	0.0147765i	$-0.00470367\pi$
$240$	17.7220	−	29.7646i	0.0738417	−	0.124019i
$241$	−45.2255	+	78.3328i	−0.187658	+	0.325033i	−0.944469	−	0.328601i	$-0.893423\pi$
$241$	−45.2255	+	78.3328i	−0.187658	+	0.325033i	0.756811	+	0.653634i	$0.226756\pi$
$242$	38.6822	+	144.364i	0.159844	+	0.596544i
$243$	4.03459	−	15.0573i	0.0166032	−	0.0619642i
$244$			33.5927i			0.137675i
$245$	−222.035	−	103.564i	−0.906265	−	0.422709i
$246$	−63.7046			−0.258962
$247$	−394.650	−	105.746i	−1.59778	−	0.428123i
$248$	−92.9608	+	24.9088i	−0.374842	+	0.100439i
$249$	199.750	+	115.326i	0.802208	+	0.463155i
$250$	82.1474	+	156.531i	0.328590	+	0.626122i
$251$	79.0027			0.314752			0.157376	−	0.987539i	$-0.449697\pi$
$251$	79.0027			0.314752			0.157376	+	0.987539i	$0.449697\pi$
$252$	37.9457	−	18.0034i	0.150578	−	0.0714420i
$253$	−35.3065	−	35.3065i	−0.139551	−	0.139551i
$254$	66.5172	−	38.4037i	0.261879	−	0.151196i
$255$	91.8853	−	89.4487i	0.360334	−	0.350779i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	278.141	+	74.5277i	1.08226	+	0.289991i	0.755522	−	0.655124i	$-0.227383\pi$
$257$	278.141	+	74.5277i	1.08226	+	0.289991i	0.326739	+	0.945115i	$0.394050\pi$
$258$	51.5701	+	51.5701i	0.199884	+	0.199884i
$259$	−44.5536	+	8.16268i	−0.172022	+	0.0315161i
$260$	−110.247	+	61.6911i	−0.424027	+	0.237274i
$261$	39.9103	+	69.1266i	0.152913	+	0.264853i
$262$	−53.8688	−	201.041i	−0.205606	−	0.767332i
$263$	−257.786	+	69.0735i	−0.980174	+	0.262637i	−0.713118	−	0.701044i	$-0.752718\pi$
$263$	−257.786	+	69.0735i	−0.980174	+	0.262637i	−0.267056	+	0.963681i	$0.586051\pi$
$264$	−16.6052	+	9.58699i	−0.0628983	+	0.0363144i
$265$	110.494	+	197.461i	0.416957	+	0.745134i
$266$	243.877	−	207.424i	0.916830	−	0.779788i
$267$	61.1974	−	61.1974i	0.229204	−	0.229204i
$268$	30.5596	−	114.050i	0.114028	−	0.425559i
$269$	−127.690	−	73.7221i	−0.474686	−	0.274060i	0.243514	−	0.969898i	$-0.421700\pi$
$269$	−127.690	−	73.7221i	−0.474686	−	0.274060i	−0.718199	+	0.695838i	$0.755033\pi$
$270$	−25.6294	−	26.3275i	−0.0949235	−	0.0975092i
$271$	−248.993	−	431.268i	−0.918793	−	1.59140i	−0.801251	−	0.598328i	$-0.795832\pi$
$271$	−248.993	−	431.268i	−0.918793	−	1.59140i	−0.117542	−	0.993068i	$-0.537501\pi$
$272$	−41.8811	+	41.8811i	−0.153975	+	0.153975i
$273$	−152.674	−	12.3321i	−0.559246	−	0.0451724i
$274$		−	1.65705i		−	0.00604763i
$275$	2.62901	−	97.8115i	0.00956003	−	0.355678i
$276$	−22.0965	+	38.2723i	−0.0800598	+	0.138668i
$277$	67.3127	+	251.215i	0.243006	+	0.906912i	0.974375	+	0.224930i	$0.0722152\pi$
$277$	67.3127	+	251.215i	0.243006	+	0.906912i	−0.731369	+	0.681982i	$0.761118\pi$
$278$	−85.8751	+	320.490i	−0.308903	+	1.15284i
$279$			102.078i			0.365871i
$280$	9.29524	−	98.5576i	0.0331973	−	0.351991i
$281$	−170.124			−0.605422			−0.302711	−	0.953082i	$-0.597892\pi$
$281$	−170.124			−0.605422			−0.302711	+	0.953082i	$0.597892\pi$
$282$	−98.2475	−	26.3253i	−0.348396	−	0.0933523i
$283$	−328.238	+	87.9512i	−1.15985	+	0.310782i	−0.786907	−	0.617072i	$-0.788319\pi$
$283$	−328.238	+	87.9512i	−1.15985	+	0.310782i	−0.372946	+	0.927853i	$0.621652\pi$
$284$	−229.601	−	132.560i	−0.808456	−	0.466762i
$285$	−240.652	−	143.286i	−0.844393	−	0.502757i
$286$	69.9263			0.244498
$287$	−164.478	+	78.0365i	−0.573092	+	0.271904i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	60.4027	−	34.8735i	0.209006	−	0.120670i
$290$	188.122	+	2.52774i	0.648696	+	0.00871636i
$291$	144.794	−	250.791i	0.497575	−	0.861826i
$292$	−17.1341	−	4.59106i	−0.0586784	−	0.0157228i
$293$	−373.925	−	373.925i	−1.27619	−	1.27619i	−0.942780	−	0.333415i	$-0.891799\pi$
$293$	−373.925	−	373.925i	−1.27619	−	1.27619i	−0.333415	−	0.942780i	$-0.608201\pi$
$294$	75.9176	−	92.9651i	0.258223	−	0.316208i
$295$	32.6324	−	115.553i	0.110618	−	0.391705i
$296$	−9.15101	−	15.8500i	−0.0309156	−	0.0535474i
$297$	5.26362	+	19.6441i	0.0177226	+	0.0661418i
$298$	353.546	−	94.7323i	1.18639	−	0.317893i
$299$	139.577	−	80.5845i	0.466811	−	0.269514i
$300$	−84.2237	+	20.1587i	−0.280746	+	0.0671956i
$301$	196.320	+	69.9758i	0.652226	+	0.232478i
$302$	−145.661	+	145.661i	−0.482321	+	0.482321i
$303$	−50.1362	+	187.111i	−0.165466	+	0.617528i
$304$	112.032	+	64.6815i	0.368525	+	0.212768i
$305$	60.1766	−	58.5809i	0.197300	−	0.192069i
$306$	31.4108	+	54.4051i	0.102650	+	0.177794i
$307$	−7.39324	+	7.39324i	−0.0240822	+	0.0240822i	−0.719045	−	0.694963i	$-0.755421\pi$
$307$	−7.39324	+	7.39324i	−0.0240822	+	0.0240822i	0.694963	+	0.719045i	$0.255421\pi$
$308$	−31.1287	+	45.0933i	−0.101067	+	0.146407i
$309$		−	320.732i		−	1.03797i
$310$	206.731	+	123.089i	0.666874	+	0.397061i
$311$	−146.398	+	253.569i	−0.470733	+	0.815334i	−0.999440	−	0.0334709i	$-0.989344\pi$
$311$	−146.398	+	253.569i	−0.470733	+	0.815334i	0.528707	+	0.848805i	$0.322677\pi$
$312$	−16.0185	−	59.7817i	−0.0513412	−	0.191608i
$313$	−89.1847	+	332.842i	−0.284935	+	1.06339i	0.663951	+	0.747776i	$0.268878\pi$
$313$	−89.1847	+	332.842i	−0.284935	+	1.06339i	−0.948887	+	0.315617i	$0.897788\pi$
$314$		−	13.9866i		−	0.0445434i
$315$	−98.4224	−	36.5791i	−0.312452	−	0.116124i
$316$	−209.359			−0.662528
$317$	123.264	+	33.0285i	0.388845	+	0.104191i	0.447944	−	0.894061i	$-0.352156\pi$
$317$	123.264	+	33.0285i	0.388845	+	0.104191i	−0.0590994	+	0.998252i	$0.518823\pi$
$318$	−107.074	+	28.6903i	−0.336709	+	0.0902210i
$319$	−90.1842	−	52.0679i	−0.282709	−	0.163222i
$320$	38.7726	−	9.83272i	0.121165	−	0.0307272i
$321$	−55.4304			−0.172680
$322$	−10.1680	+	125.882i	−0.0315775	+	0.390938i
$323$	338.616	+	338.616i	1.04835	+	1.04835i
$324$	15.5885	−	9.00000i	0.0481125	−	0.0277778i
$325$	302.766	+	89.9112i	0.931587	+	0.276650i
$326$	162.263	−	281.047i	0.497738	−	0.862107i
$327$	291.959	+	78.2302i	0.892841	+	0.239236i
$328$	−52.0146	−	52.0146i	−0.158581	−	0.158581i
$329$	−285.911	+	52.3819i	−0.869031	+	0.159215i
$330$	46.1307	+	13.0274i	0.139790	+	0.0394771i
$331$	115.234	+	199.591i	0.348139	+	0.602994i	0.985919	−	0.167225i	$-0.0534805\pi$
$331$	115.234	+	199.591i	0.348139	+	0.602994i	−0.637780	+	0.770218i	$0.720147\pi$
$332$	68.9320	+	257.258i	0.207627	+	0.774873i
$333$	−18.7508	+	5.02425i	−0.0563086	+	0.0150879i
$334$	314.718	−	181.703i	0.942271	−	0.544020i
$335$	−257.596	+	144.143i	−0.768942	+	0.430279i
$336$	45.6823	+	16.2829i	0.135959	+	0.0484609i
$337$	261.018	−	261.018i	0.774533	−	0.774533i	−0.204363	−	0.978895i	$-0.565512\pi$
$337$	261.018	−	261.018i	0.774533	−	0.774533i	0.978895	+	0.204363i	$0.0655122\pi$
$338$	3.43998	−	12.8382i	0.0101775	−	0.0379828i
$339$	−13.1582	−	7.59692i	−0.0388149	−	0.0224098i
$340$	148.059	+	1.98942i	0.435466	+	0.00585125i
$341$	−66.5867	−	115.332i	−0.195269	−	0.338216i
$342$	97.0222	−	97.0222i	0.283691	−	0.283691i
$343$	82.1303	−	333.022i	0.239447	−	0.970909i
$344$			84.2137i			0.244807i
$345$	107.092	−	27.1586i	0.310413	−	0.0787205i
$346$	183.549	−	317.917i	0.530489	−	0.918834i
$347$	−27.0336	−	100.891i	−0.0779066	−	0.290751i	0.915970	−	0.401247i	$-0.131423\pi$
$347$	−27.0336	−	100.891i	−0.0779066	−	0.290751i	−0.993877	+	0.110495i	$0.964756\pi$
$348$	−23.8550	+	89.0283i	−0.0685490	+	0.255828i
$349$		−	425.240i		−	1.21845i	−0.792996	−	0.609227i	$-0.791480\pi$
$349$		−	425.240i		−	1.21845i	0.792996	−	0.609227i	$-0.208520\pi$
$350$	−192.762	+	155.219i	−0.550747	+	0.443483i
$351$	−65.6449			−0.187022
$352$	−21.3858	−	5.73031i	−0.0607551	−	0.0162793i
$353$	−58.8597	+	15.7714i	−0.166741	+	0.0446782i	−0.341224	−	0.939982i	$-0.610841\pi$
$353$	−58.8597	+	15.7714i	−0.166741	+	0.0446782i	0.174483	+	0.984660i	$0.444175\pi$
$354$	50.9423	+	29.4116i	0.143905	+	0.0830836i
$355$	162.929	+	642.465i	0.458954	+	1.80976i
$356$	99.9350			0.280716
$357$	147.744	+	101.990i	0.413848	+	0.285686i
$358$	−308.644	−	308.644i	−0.862135	−	0.862135i
$359$	527.860	−	304.760i	1.47036	−	0.848914i	0.470916	−	0.882178i	$-0.343924\pi$
$359$	527.860	−	304.760i	1.47036	−	0.848914i	0.999447	+	0.0332639i	$0.0105902\pi$
$360$	0.570021	−	42.4226i	0.00158339	−	0.117840i
$361$	342.462	−	593.161i	0.948647	−	1.64311i
$362$	235.730	+	63.1637i	0.651188	+	0.174485i
$363$	129.433	+	129.433i	0.356565	+	0.356565i
$364$	−114.589	−	134.727i	−0.314804	−	0.370129i
$365$	21.6551	+	38.6994i	0.0593292	+	0.106026i
$366$	20.5713	+	35.6305i	0.0562056	+	0.0973510i
$367$	21.7126	+	81.0326i	0.0591625	+	0.220797i	0.989177	−	0.146724i	$-0.0468730\pi$
$367$	21.7126	+	81.0326i	0.0591625	+	0.220797i	−0.930015	+	0.367522i	$0.880206\pi$
$368$	−49.2909	+	13.2075i	−0.133943	+	0.0358898i
$369$	−67.5689	+	39.0109i	−0.183114	+	0.105721i
$370$	−12.4350	+	44.0329i	−0.0336081	+	0.119008i
$371$	−241.306	+	205.237i	−0.650421	+	0.553200i
$372$	−83.3464	+	83.3464i	−0.224049	+	0.224049i
$373$	−36.5025	+	136.229i	−0.0978620	+	0.365226i	−0.997438	−	0.0715386i	$-0.977209\pi$
$373$	−36.5025	+	136.229i	−0.0978620	+	0.365226i	0.899576	+	0.436765i	$0.143876\pi$
$374$	−70.9782	−	40.9793i	−0.189781	−	0.109570i
$375$	182.985	+	115.721i	0.487961	+	0.308589i
$376$	−58.7242	−	101.713i	−0.156181	−	0.270514i
$377$	237.683	−	237.683i	0.630458	−	0.630458i
$378$	29.2228	−	42.3324i	0.0773089	−	0.111990i
$379$			123.783i			0.326603i	0.986576	+	0.163302i	$0.0522144\pi$
$379$			123.783i			0.326603i	−0.986576	+	0.163302i	$0.947786\pi$
$380$	−79.4993	−	313.484i	−0.209209	−	0.824958i
$381$	47.0348	−	81.4666i	0.123451	−	0.213823i
$382$	49.5212	+	184.816i	0.129637	+	0.483810i
$383$	81.7732	−	305.182i	0.213507	−	0.796819i	−0.773180	−	0.634187i	$-0.781335\pi$
$383$	81.7732	−	305.182i	0.213507	−	0.796819i	0.986687	−	0.162632i	$-0.0519984\pi$
$384$			19.5959i			0.0510310i
$385$	135.062	−	22.8737i	0.350811	−	0.0594122i
$386$	−31.1423			−0.0806796
$387$	86.2785	+	23.1183i	0.222942	+	0.0597371i
$388$	322.994	−	86.5461i	0.832460	−	0.223057i
$389$	300.792	+	173.662i	0.773243	+	0.446432i	0.834030	−	0.551718i	$-0.186028\pi$
$389$	300.792	+	173.662i	0.773243	+	0.446432i	−0.0607870	+	0.998151i	$0.519361\pi$
$390$	−79.1566	+	132.946i	−0.202966	+	0.340886i
$391$	−188.902			−0.483124
$392$	137.892	−	13.9192i	0.351766	−	0.0355082i
$393$	−180.248	−	180.248i	−0.458647	−	0.458647i
$394$	106.958	−	61.7521i	0.271466	−	0.156731i
$395$	365.092	+	375.036i	0.924282	+	0.949459i
$396$	−11.7416	+	20.3371i	−0.0296505	+	0.0513563i
$397$	−365.656	−	97.9772i	−0.921047	−	0.246794i	−0.233014	−	0.972473i	$-0.574859\pi$
$397$	−365.656	−	97.9772i	−0.921047	−	0.246794i	−0.688033	+	0.725679i	$0.741526\pi$
$398$	−332.022	−	332.022i	−0.834227	−	0.834227i
$399$	131.650	−	369.349i	0.329950	−	0.925688i
$400$	−85.2278	−	52.3088i	−0.213070	−	0.130772i
$401$	−85.2179	−	147.602i	−0.212513	−	0.368084i	0.739987	−	0.672621i	$-0.234832\pi$
$401$	−85.2179	−	147.602i	−0.212513	−	0.368084i	−0.952500	+	0.304537i	$0.901498\pi$
$402$	−37.4277	−	139.682i	−0.0931037	−	0.347468i
$403$	415.216	−	111.257i	1.03031	−	0.276071i
$404$	−193.711	+	111.839i	−0.479484	+	0.276830i
$405$	−43.3063	−	12.2298i	−0.106929	−	0.0301970i
$406$	47.4665	+	259.082i	0.116913	+	0.638133i
$407$	17.9079	−	17.9079i	0.0439999	−	0.0439999i
$408$	−18.7748	+	70.0684i	−0.0460166	+	0.171736i
$409$	−230.144	−	132.873i	−0.562698	−	0.324874i	0.191530	−	0.981487i	$-0.438655\pi$
$409$	−230.144	−	132.873i	−0.562698	−	0.324874i	−0.754228	+	0.656613i	$0.771989\pi$
$410$	−2.47078	+	183.883i	−0.00602630	+	0.448494i
$411$	−1.01473	−	1.75757i	−0.00246894	−	0.00427632i
$412$	261.877	−	261.877i	0.635623	−	0.635623i
$413$	167.555	+	13.5341i	0.405703	+	0.0327702i
$414$			54.1251i			0.130737i
$415$	340.633	−	572.103i	0.820803	−	1.37856i
$416$	35.7325	−	61.8906i	0.0858955	−	0.148775i
$417$	105.175	+	392.519i	0.252218	+	0.941292i
$418$	−46.3306	+	172.908i	−0.110839	+	0.413656i
$419$			173.250i			0.413485i	0.978395	+	0.206742i	$0.0662862\pi$
$419$			173.250i			0.413485i	−0.978395	+	0.206742i	$0.933714\pi$
$420$	−50.4949	−	110.228i	−0.120226	−	0.262448i
$421$	541.087			1.28524			0.642621	−	0.766184i	$-0.277847\pi$
$421$	541.087			1.28524			0.642621	+	0.766184i	$0.277847\pi$
$422$	−6.51036	−	1.74445i	−0.0154274	−	0.00413376i
$423$	−120.328	+	32.2418i	−0.284464	+	0.0762218i
$424$	−110.851	−	63.9997i	−0.261440	−	0.150943i
$425$	−254.629	−	268.695i	−0.599127	−	0.632224i
$426$	−324.705			−0.762219
$427$	96.7590	+	66.7943i	0.226602	+	0.156427i
$428$	−45.2587	−	45.2587i	−0.105745	−	0.105745i
$429$	74.1680	−	42.8209i	0.172886	−	0.0998157i
$430$	150.857	−	146.857i	0.350830	−	0.341527i
$431$	272.438	−	471.876i	0.632106	−	1.09484i	−0.355014	−	0.934861i	$-0.615524\pi$
$431$	272.438	−	471.876i	0.632106	−	1.09484i	0.987120	−	0.159979i	$-0.0511428\pi$
$432$	20.0764	+	5.37945i	0.0464731	+	0.0124524i
$433$	−440.714	−	440.714i	−1.01782	−	1.01782i	−0.999838	−	0.0179771i	$-0.994277\pi$
$433$	−440.714	−	440.714i	−1.01782	−	1.01782i	−0.0179771	−	0.999838i	$-0.505723\pi$
$434$	−113.093	+	317.288i	−0.260583	+	0.731077i
$435$	201.081	−	112.520i	0.462256	−	0.258666i
$436$	174.509	+	302.258i	0.400250	+	0.693253i
$437$	106.785	+	398.526i	0.244359	+	0.911959i
$438$	−20.9849	+	5.62288i	−0.0479107	+	0.0128376i
$439$	−411.747	+	237.722i	−0.937920	+	0.541508i	−0.889308	−	0.457310i	$-0.848813\pi$
$439$	−411.747	+	237.722i	−0.937920	+	0.541508i	−0.0486121	+	0.998818i	$0.515480\pi$
$440$	27.0287	+	48.3025i	0.0614289	+	0.109778i
$441$	23.5935	−	145.094i	0.0535001	−	0.329012i
$442$	187.065	−	187.065i	0.423223	−	0.423223i
$443$	−121.797	+	454.552i	−0.274937	+	1.02608i	0.680947	+	0.732332i	$0.261568\pi$
$443$	−121.797	+	454.552i	−0.274937	+	1.02608i	−0.955884	+	0.293745i	$0.905098\pi$
$444$	−19.4122	−	11.2077i	−0.0437212	−	0.0252425i
$445$	−174.272	−	179.019i	−0.391623	−	0.402291i
$446$	−96.4999	−	167.143i	−0.216367	−	0.374759i
$447$	316.980	−	316.980i	0.709128	−	0.709128i
$448$	24.0045	+	50.5943i	0.0535815	+	0.112934i
$449$			728.737i			1.62302i	0.584337	+	0.811511i	$0.301355\pi$
$449$			728.737i			1.62302i	−0.584337	+	0.811511i	$0.698645\pi$
$450$	−76.9881	+	72.9578i	−0.171085	+	0.162128i
$451$	50.8946	−	88.1520i	0.112848	−	0.195459i
$452$	−4.54081	−	16.9465i	−0.0100460	−	0.0374923i
$453$	−65.2980	+	243.696i	−0.144146	+	0.537959i
$454$		−	87.1519i		−	0.191965i
$455$	−41.5178	+	440.214i	−0.0912480	+	0.967504i
$456$	158.437			0.347449
$457$	−601.427	−	161.152i	−1.31603	−	0.352630i	−0.468543	−	0.883441i	$-0.655221\pi$
$457$	−601.427	−	161.152i	−1.31603	−	0.352630i	−0.847490	+	0.530811i	$0.821887\pi$
$458$	−616.568	+	165.209i	−1.34622	+	0.360718i
$459$	66.6324	+	38.4702i	0.145169	+	0.0838131i
$460$	109.616	+	65.2657i	0.238295	+	0.141882i
$461$	−796.674			−1.72814			−0.864071	−	0.503370i	$-0.832093\pi$
$461$	−796.674			−1.72814			−0.864071	+	0.503370i	$0.832093\pi$
$462$	−5.40304	+	66.8911i	−0.0116949	+	0.144786i
$463$	215.541	+	215.541i	0.465531	+	0.465531i	0.900463	−	0.434932i	$-0.143228\pi$
$463$	215.541	+	215.541i	0.465531	+	0.465531i	−0.434932	+	0.900463i	$0.643228\pi$
$464$	−92.1688	+	53.2137i	−0.198640	+	0.114685i
$465$	294.647	+	3.95910i	0.633650	+	0.00851419i
$466$	−181.304	+	314.028i	−0.389065	+	0.673881i
$467$	276.298	+	74.0339i	0.591645	+	0.158531i	0.542205	−	0.840246i	$-0.317590\pi$
$467$	276.298	+	74.0339i	0.591645	+	0.158531i	0.0494401	+	0.998777i	$0.484256\pi$
$468$	−53.5988	−	53.5988i	−0.114527	−	0.114527i
$469$	−267.741	−	314.794i	−0.570876	−	0.671203i
$470$	−79.7984	+	282.570i	−0.169784	+	0.601212i
$471$	−8.56502	−	14.8351i	−0.0181848	−	0.0314969i
$472$	17.5798	+	65.6087i	0.0372453	+	0.139001i
$473$	−112.561	+	30.1606i	−0.237973	+	0.0637646i
$474$	−222.058	+	128.205i	−0.468478	+	0.270476i
$475$	−422.927	+	689.083i	−0.890372	+	1.45070i
$476$	37.3578	+	203.907i	0.0784828	+	0.428376i
$477$	−95.9996	+	95.9996i	−0.201257	+	0.201257i
$478$	2.58529	−	9.64845i	0.00540857	−	0.0201850i
$479$	581.667	+	335.826i	1.21434	+	0.701098i	0.963701	−	0.266984i	$-0.0860270\pi$
$479$	581.667	+	335.826i	1.21434	+	0.701098i	0.250636	+	0.968081i	$0.419360\pi$
$480$	35.1033	−	34.1725i	0.0731319	−	0.0711926i
$481$	40.8736	+	70.7952i	0.0849763	+	0.147183i
$482$	−90.4510	+	90.4510i	−0.187658	+	0.187658i
$483$	66.3019	+	139.745i	0.137271	+	0.289326i
$484$			211.363i			0.436701i
$485$	−718.291	−	427.675i	−1.48101	−	0.881804i
$486$	11.0227	−	19.0919i	0.0226805	−	0.0392837i
$487$	26.4722	+	98.7957i	0.0543578	+	0.202866i	0.987764	−	0.155955i	$-0.0498455\pi$
$487$	26.4722	+	98.7957i	0.0543578	+	0.202866i	−0.933406	+	0.358821i	$0.883179\pi$
$488$	−12.2958	+	45.8885i	−0.0251963	+	0.0940339i
$489$		−	397.460i		−	0.812802i
$490$	−265.398	−	222.741i	−0.541630	−	0.454574i
$491$	260.790			0.531140			0.265570	−	0.964092i	$-0.414440\pi$
$491$	260.790			0.531140			0.265570	+	0.964092i	$0.414440\pi$
$492$	−87.0220	−	23.3175i	−0.176874	−	0.0473933i
$493$	−380.548	+	101.968i	−0.771904	+	0.206831i
$494$	−500.397	−	288.904i	−1.01295	−	0.584826i
$495$	56.9067	−	14.4315i	0.114963	−	0.0291545i
$496$	−136.104			−0.274403
$497$	−838.350	+	397.756i	−1.68682	+	0.800314i
$498$	230.651	+	230.651i	0.463155	+	0.463155i
$499$	−82.9389	+	47.8848i	−0.166210	+	0.0959615i	−0.580798	−	0.814048i	$-0.697259\pi$
$499$	−82.9389	+	47.8848i	−0.166210	+	0.0959615i	0.414587	+	0.910009i	$0.363926\pi$
$500$	54.9213	+	243.893i	0.109843	+	0.487785i
$501$	222.540	−	385.450i	0.444191	−	0.769361i
$502$	107.920	+	28.9170i	0.214979	+	0.0576036i
$503$	−172.595	−	172.595i	−0.343132	−	0.343132i	0.514412	−	0.857543i	$-0.328010\pi$
$503$	−172.595	−	172.595i	−0.343132	−	0.343132i	−0.857543	+	0.514412i	$0.828010\pi$
$504$	58.4245	−	10.7040i	0.115922	−	0.0212380i
$505$	538.149	+	151.975i	1.06564	+	0.300940i
$506$	−35.3065	−	61.1526i	−0.0697757	−	0.120855i
$507$	−4.21310	−	15.7235i	−0.00830985	−	0.0310128i
$508$	104.921	−	28.1135i	0.206537	−	0.0553415i
$509$	−165.245	+	95.4042i	−0.324646	+	0.187435i	−0.653462	−	0.756960i	$-0.726684\pi$
$509$	−165.245	+	95.4042i	−0.324646	+	0.187435i	0.328815	+	0.944394i	$0.393351\pi$
$510$	158.258	−	88.5569i	0.310310	−	0.173641i
$511$	−47.2926	+	40.2236i	−0.0925491	+	0.0787154i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	43.4939	−	162.321i	0.0847834	−	0.316416i
$514$	352.669	+	203.613i	0.686126	+	0.396135i
$515$	−925.791	−	12.4396i	−1.79765	−	0.0241546i
$516$	51.5701	+	89.3221i	0.0999421	+	0.173105i
$517$	114.920	−	114.920i	0.222282	−	0.222282i
$518$	−63.8491	−	5.15733i	−0.123261	−	0.00995624i
$519$		−	449.602i		−	0.866285i
$520$	−173.181	+	43.9185i	−0.333040	+	0.0844587i
$521$	321.064	−	556.100i	0.616246	−	1.06737i	−0.373918	−	0.927462i	$-0.621986\pi$
$521$	321.064	−	556.100i	0.616246	−	1.06737i	0.990164	−	0.139908i	$-0.0446808\pi$
$522$	29.2163	+	109.037i	0.0559700	+	0.208883i
$523$	30.1396	−	112.482i	0.0576283	−	0.215072i	−0.931107	−	0.364746i	$-0.881156\pi$
$523$	30.1396	−	112.482i	0.0576283	−	0.215072i	0.988735	+	0.149674i	$0.0478225\pi$
$524$		−	294.344i		−	0.561726i
$525$	−109.403	+	282.677i	−0.208386	+	0.538432i
$526$	−377.424			−0.717537
$527$	−486.662	−	130.401i	−0.923458	−	0.247440i
$528$	−26.1921	+	7.01816i	−0.0496063	+	0.0132920i
$529$	317.180	+	183.124i	0.599585	+	0.346170i
$530$	78.6614	+	310.180i	0.148418	+	0.585245i
$531$	72.0434			0.135675
$532$	409.064	−	194.081i	0.768918	−	0.364814i
$533$	232.327	+	232.327i	0.435885	+	0.435885i
$534$	105.997	−	61.1974i	0.198496	−	0.114602i
$535$	−2.14987	+	159.999i	−0.00401845	+	0.299064i
$536$	83.4903	−	144.609i	0.155765	−	0.269794i
$537$	−516.372	−	138.361i	−0.961587	−	0.257656i
$538$	−147.444	−	147.444i	−0.274060	−	0.274060i
$539$	67.9899	+	179.323i	0.126141	+	0.332696i
$540$	−25.3738	−	45.3450i	−0.0469886	−	0.0839722i
$541$	211.339	+	366.049i	0.390645	+	0.676616i	0.992535	−	0.121963i	$-0.0389188\pi$
$541$	211.339	+	366.049i	0.390645	+	0.676616i	−0.601890	+	0.798579i	$0.705585\pi$
$542$	−182.275	−	680.261i	−0.336302	−	1.25509i
$543$	288.709	−	77.3594i	0.531693	−	0.142467i
$544$	−72.5401	+	41.8811i	−0.133346	+	0.0769873i
$545$	237.134	−	839.703i	0.435109	−	1.54074i
$546$	−204.043	−	72.7285i	−0.373705	−	0.133202i
$547$	−57.9153	+	57.9153i	−0.105878	+	0.105878i	−0.758061	−	0.652183i	$-0.773853\pi$
$547$	−57.9153	+	57.9153i	−0.105878	+	0.105878i	0.652183	+	0.758061i	$0.273853\pi$
$548$	0.606523	−	2.26357i	0.00110679	−	0.00413061i
$549$	43.6382	+	25.1946i	0.0794868	+	0.0458917i
$550$	39.3928	−	132.651i	0.0716232	−	0.241183i
$551$	430.243	+	745.202i	0.780840	+	1.35245i
$552$	−44.1930	+	44.1930i	−0.0800598	+	0.0800598i
$553$	−416.280	+	603.027i	−0.752766	+	1.09046i
$554$			367.804i			0.663906i
$555$	13.7752	+	54.3188i	0.0248202	+	0.0978717i
$556$	−234.615	+	406.365i	−0.421970	+	0.730873i
$557$	−6.94144	−	25.9058i	−0.0124622	−	0.0465095i	0.959415	−	0.281999i	$-0.0909974\pi$
$557$	−6.94144	−	25.9058i	−0.0124622	−	0.0465095i	−0.971877	+	0.235489i	$0.924331\pi$
$558$	−37.3632	+	139.441i	−0.0669591	+	0.249895i
$559$		−	376.146i		−	0.672891i
$560$	48.7721	−	131.230i	0.0870931	−	0.234339i
$561$	−100.378			−0.178928
$562$	−232.393	−	62.2696i	−0.413511	−	0.110800i
$563$	1003.19	−	268.804i	1.78186	−	0.477449i	0.790942	−	0.611892i	$-0.209591\pi$
$563$	1003.19	−	268.804i	1.78186	−	0.477449i	0.990921	+	0.134443i	$0.0429245\pi$
$564$	−124.573	−	71.9222i	−0.220874	−	0.127522i
$565$	−22.4388	+	37.6865i	−0.0397146	+	0.0667018i
$566$	−480.574			−0.849071
$567$	5.07222	−	62.7955i	0.00894572	−	0.110750i
$568$	−265.121	−	265.121i	−0.466762	−	0.466762i
$569$	35.1341	−	20.2847i	0.0617471	−	0.0356497i	−0.468809	−	0.883300i	$-0.655317\pi$
$569$	35.1341	−	20.2847i	0.0617471	−	0.0356497i	0.530556	+	0.847650i	$0.321983\pi$
$570$	−276.291	−	283.817i	−0.484721	−	0.497924i
$571$	−104.960	+	181.797i	−0.183819	+	0.318383i	−0.943178	−	0.332289i	$-0.892179\pi$
$571$	−104.960	+	181.797i	−0.183819	+	0.318383i	0.759359	+	0.650672i	$0.225513\pi$
$572$	95.5211	+	25.5948i	0.166995	+	0.0447462i
$573$	165.701	+	165.701i	0.289182	+	0.289182i
$574$	−253.244	+	46.3969i	−0.441191	+	0.0808308i
$575$	−74.2394	−	310.175i	−0.129112	−	0.539434i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	9.56994	+	35.7155i	0.0165857	+	0.0618986i	0.973723	−	0.227737i	$-0.0731326\pi$
$577$	9.56994	+	35.7155i	0.0165857	+	0.0618986i	−0.957137	+	0.289635i	$0.906466\pi$
$578$	95.2762	−	25.5292i	0.164838	−	0.0441681i
$579$	−33.0314	+	19.0707i	−0.0570491	+	0.0329373i
$580$	256.054	+	72.3103i	0.441472	+	0.124673i
$581$	878.055	+	312.972i	1.51128	+	0.538678i
$582$	289.589	−	289.589i	0.497575	−	0.497575i
$583$	45.8422	−	171.086i	0.0786316	−	0.293457i
$584$	−21.7252	−	12.5430i	−0.0372006	−	0.0214778i
$585$	−2.54604	+	189.483i	−0.00435220	+	0.323903i
$586$	−373.925	−	647.657i	−0.638097	−	1.10522i
$587$	452.761	−	452.761i	0.771314	−	0.771314i	−0.207022	−	0.978336i	$-0.566377\pi$
$587$	452.761	−	452.761i	0.771314	−	0.771314i	0.978336	+	0.207022i	$0.0663773\pi$
$588$	137.733	−	99.2049i	0.234240	−	0.168716i
$589$			1100.43i			1.86830i
$590$	86.8721	−	145.904i	0.147241	−	0.247295i
$591$	75.6305	−	130.996i	0.127970	−	0.221651i
$592$	−6.69901	−	25.0010i	−0.0113159	−	0.0422315i
$593$	1.05483	−	3.93666i	0.00177880	−	0.00663855i	−0.965031	−	0.262137i	$-0.915573\pi$
$593$	1.05483	−	3.93666i	0.00177880	−	0.00663855i	0.966810	+	0.255498i	$0.0822395\pi$
$594$			28.7610i			0.0484191i
$595$	300.123	−	422.505i	0.504409	−	0.710093i
$596$	517.627			0.868501
$597$	−555.484	−	148.842i	−0.930459	−	0.249316i
$598$	220.161	−	58.9920i	0.368162	−	0.0986488i
$599$	−499.784	−	288.550i	−0.834364	−	0.481720i	0.0209807	−	0.999780i	$-0.493321\pi$
$599$	−499.784	−	288.550i	−0.834364	−	0.481720i	−0.855344	+	0.518060i	$0.826654\pi$
$600$	−122.430	−	3.29072i	−0.204050	−	0.00548454i
$601$	16.8472			0.0280319			0.0140160	−	0.999902i	$-0.495538\pi$
$601$	16.8472			0.0280319			0.0140160	+	0.999902i	$0.495538\pi$
$602$	242.565	+	167.447i	0.402932	+	0.278151i
$603$	−125.235	−	125.235i	−0.207687	−	0.207687i
$604$	−252.292	+	145.661i	−0.417702	+	0.241161i
$605$	378.627	−	368.587i	0.625830	−	0.609235i
$606$	−136.975	+	237.247i	−0.226031	+	0.391497i
$607$	400.443	+	107.298i	0.659709	+	0.176768i	0.573115	−	0.819475i	$-0.305735\pi$
$607$	400.443	+	107.298i	0.659709	+	0.176768i	0.0865941	+	0.996244i	$0.472402\pi$
$608$	129.363	+	129.363i	0.212768	+	0.212768i
$609$	209.001	+	245.731i	0.343186	+	0.403499i
$610$	103.645	−	57.9968i	0.169910	−	0.0950768i
$611$	262.296	+	454.310i	0.429289	+	0.743551i
$612$	22.9943	+	85.8159i	0.0375724	+	0.140222i
$613$	958.356	−	256.791i	1.56339	−	0.418908i	0.629653	−	0.776876i	$-0.283197\pi$
$613$	958.356	−	256.791i	1.56339	−	0.418908i	0.933734	+	0.357968i	$0.116530\pi$
$614$	−12.8055	+	7.39324i	−0.0208558	+	0.0120411i
$615$	109.984	+	196.550i	0.178836	+	0.319594i
$616$	−59.0279	+	50.2048i	−0.0958245	+	0.0815012i
$617$	−435.763	+	435.763i	−0.706261	+	0.706261i	−0.965747	−	0.259486i	$-0.916447\pi$
$617$	−435.763	+	435.763i	−0.706261	+	0.706261i	0.259486	+	0.965747i	$0.416447\pi$
$618$	117.396	−	438.128i	0.189961	−	0.708946i
$619$	−339.430	−	195.970i	−0.548352	−	0.316591i	0.200105	−	0.979774i	$-0.435872\pi$
$619$	−339.430	−	195.970i	−0.548352	−	0.316591i	−0.748457	+	0.663183i	$0.769205\pi$
$620$	237.346	+	243.811i	0.382816	+	0.393244i
$621$	33.1447	+	57.4084i	0.0533732	+	0.0924451i
$622$	−292.796	+	292.796i	−0.470733	+	0.470733i
$623$	198.706	−	287.848i	0.318951	−	0.462035i
$624$		−	87.5265i		−	0.140267i
$625$	341.124	−	523.698i	0.545799	−	0.837916i
$626$	−243.657	+	422.027i	−0.389229	+	0.674164i
$627$	56.7431	+	211.768i	0.0904994	+	0.337748i
$628$	5.11946	−	19.1061i	0.00815201	−	0.0304237i
$629$		−	95.8136i		−	0.152327i
$630$	−121.059	−	85.9931i	−0.192157	−	0.136497i
$631$	−786.782			−1.24688			−0.623441	−	0.781870i	$-0.714266\pi$
$631$	−786.782			−1.24688			−0.623441	+	0.781870i	$0.714266\pi$
$632$	−285.989	−	76.6306i	−0.452515	−	0.121251i
$633$	−7.97353	+	2.13650i	−0.0125964	+	0.00337520i
$634$	156.292	+	90.2354i	0.246518	+	0.142327i
$635$	−233.328	−	138.925i	−0.367446	−	0.218780i
$636$	−156.767			−0.246488
$637$	−615.905	+	62.1711i	−0.966883	+	0.0975998i
$638$	−104.136	−	104.136i	−0.163222	−	0.163222i
$639$	−344.402	+	198.841i	−0.538970	+	0.311175i
$640$	56.5634	+	0.760028i	0.0883804	+	0.00118754i
$641$	−350.141	+	606.461i	−0.546241	+	0.946118i	0.452286	+	0.891873i	$0.350609\pi$
$641$	−350.141	+	606.461i	−0.546241	+	0.946118i	−0.998528	+	0.0542449i	$0.982725\pi$
$642$	−75.7193	−	20.2889i	−0.117943	−	0.0316027i
$643$	175.844	+	175.844i	0.273474	+	0.273474i	0.830497	−	0.557023i	$-0.188056\pi$
$643$	175.844	+	175.844i	0.273474	+	0.273474i	−0.557023	+	0.830497i	$0.688056\pi$
$644$	−59.9657	+	168.236i	−0.0931144	+	0.261236i
$645$	70.0770	−	248.146i	0.108646	−	0.384722i
$646$	338.616	+	586.500i	0.524174	+	0.907895i
$647$	−320.893	−	1197.59i	−0.495971	−	1.85099i	−0.524523	−	0.851396i	$-0.675756\pi$
$647$	−320.893	−	1197.59i	−0.495971	−	1.85099i	0.0285523	−	0.999592i	$-0.490910\pi$
$648$	24.5885	−	6.58846i	0.0379452	−	0.0101674i
$649$	−81.3973	+	46.9947i	−0.125420	+	0.0724110i
$650$	380.676	+	233.641i	0.585655	+	0.359448i
$651$	74.3448	+	405.789i	0.114201	+	0.623332i
$652$	324.525	−	324.525i	0.497738	−	0.497738i
$653$	−13.1774	+	49.1787i	−0.0201798	+	0.0753119i	−0.975281	−	0.220966i	$-0.929079\pi$
$653$	−13.1774	+	49.1787i	−0.0201798	+	0.0753119i	0.955102	+	0.296278i	$0.0957456\pi$
$654$	370.189	+	213.729i	0.566039	+	0.326802i
$655$	−527.276	+	513.294i	−0.805002	+	0.783656i
$656$	−52.0146	−	90.0919i	−0.0792905	−	0.137335i
$657$	−18.8145	+	18.8145i	−0.0286370	+	0.0286370i
$658$	−409.735	−	33.0958i	−0.622698	−	0.0502976i
$659$		−	741.347i		−	1.12496i	−0.826812	−	0.562479i	$-0.809848\pi$
$659$		−	741.347i		−	1.12496i	0.826812	−	0.562479i	$-0.190152\pi$
$660$	58.2474	+	34.6808i	0.0882536	+	0.0525467i
$661$	−337.951	+	585.348i	−0.511272	+	0.885549i	0.488642	+	0.872484i	$0.337492\pi$
$661$	−337.951	+	585.348i	−0.511272	+	0.885549i	−0.999915	+	0.0130653i	$0.995841\pi$
$662$	84.3571	+	314.825i	0.127428	+	0.475566i
$663$	83.8588	−	312.965i	0.126484	−	0.472044i
$664$			376.652i			0.567246i
$665$	−1061.02	−	394.332i	−1.59552	−	0.592980i
$666$	−27.4530			−0.0412208
$667$	−327.869	−	87.8522i	−0.491557	−	0.131712i
$668$	496.421	−	133.016i	0.743146	−	0.199125i
$669$	−204.707	−	118.188i	−0.305990	−	0.176663i
$670$	−404.642	+	102.617i	−0.603944	+	0.153160i
$671$	−65.7388			−0.0979714
$672$	56.4432	+	38.9637i	0.0839928	+	0.0579817i
$673$	212.014	+	212.014i	0.315029	+	0.315029i	0.846854	−	0.531825i	$-0.178494\pi$
$673$	212.014	+	212.014i	0.315029	+	0.315029i	−0.531825	+	0.846854i	$0.678494\pi$
$674$	452.096	−	261.018i	0.670765	−	0.387266i
$675$	−36.9808	+	124.529i	−0.0547864	+	0.184487i
$676$	9.39820	−	16.2782i	0.0139027	−	0.0240801i
$677$	815.048	+	218.391i	1.20391	+	0.322587i	0.804370	−	0.594128i	$-0.202503\pi$
$677$	815.048	+	218.391i	1.20391	+	0.322587i	0.399541	+	0.916715i	$0.369170\pi$
$678$	−15.1938	−	15.1938i	−0.0224098	−	0.0224098i
$679$	392.945	−	1102.42i	0.578711	−	1.62360i
$680$	201.524	+	56.9108i	0.296358	+	0.0836924i
$681$	−53.3694	−	92.4385i	−0.0783692	−	0.135739i
$682$	−48.7449	−	181.918i	−0.0714734	−	0.266742i
$683$	910.072	−	243.853i	1.33246	−	0.357032i	0.478830	−	0.877908i	$-0.341061\pi$
$683$	910.072	−	243.853i	1.33246	−	0.357032i	0.853633	+	0.520875i	$0.174394\pi$
$684$	168.047	−	97.0222i	0.245683	−	0.141845i
$685$	−5.11256	+	2.86085i	−0.00746359	+	0.00417642i
$686$	234.087	−	424.855i	0.341234	−	0.619322i
$687$	−552.800	+	552.800i	−0.804658	+	0.804658i
$688$	−30.8243	+	115.038i	−0.0448028	+	0.167206i
$689$	495.122	+	285.859i	0.718610	+	0.414890i
$690$	156.232	+	2.09925i	0.226423	+	0.00304238i
$691$	241.773	+	418.764i	0.349889	+	0.606026i	0.986229	−	0.165383i	$-0.0528860\pi$
$691$	241.773	+	418.764i	0.349889	+	0.606026i	−0.636340	+	0.771408i	$0.719553\pi$
$692$	367.098	−	367.098i	0.530489	−	0.530489i
$693$	35.2315	+	74.2574i	0.0508390	+	0.107153i
$694$		−	147.714i		−	0.212845i
$695$	1137.08	−	288.363i	1.63609	−	0.414911i
$696$	−65.1732	+	112.883i	−0.0936397	+	0.162189i
$697$	−99.6699	−	371.973i	−0.142998	−	0.533677i
$698$	155.649	−	580.889i	0.222993	−	0.832220i
$699$			444.103i			0.635341i
$700$	−320.131	+	141.478i	−0.457330	+	0.202111i
$701$	−1192.55			−1.70122			−0.850609	−	0.525799i	$-0.823767\pi$
$701$	−1192.55			−1.70122			−0.850609	+	0.525799i	$0.823767\pi$
$702$	−89.6726	−	24.0277i	−0.127739	−	0.0342275i
$703$	−202.138	+	54.1627i	−0.287536	+	0.0770451i
$704$	−27.1161	−	15.6555i	−0.0385172	−	0.0222379i
$705$	88.3988	+	348.577i	0.125388	+	0.494435i
$706$	−86.1765			−0.122063
$707$	−63.0305	+	780.334i	−0.0891520	+	1.10373i
$708$	58.8232	+	58.8232i	0.0830836	+	0.0830836i
$709$	1102.14	−	636.323i	1.55450	−	0.897494i	0.556738	−	0.830688i	$-0.312053\pi$
$709$	1102.14	−	636.323i	1.55450	−	0.897494i	0.997766	−	0.0668057i	$-0.0212808\pi$
$710$	−12.5937	+	937.259i	−0.0177376	+	1.32008i
$711$	−157.019	+	271.965i	−0.220843	+	0.382510i
$712$	136.514	+	36.5787i	0.191733	+	0.0513746i
$713$	−306.944	−	306.944i	−0.430496	−	0.430496i
$714$	164.491	+	193.399i	0.230379	+	0.270867i
$715$	−120.726	−	215.746i	−0.168847	−	0.301743i
$716$	−308.644	−	534.588i	−0.431068	−	0.746631i
$717$	−3.16633	−	11.8169i	−0.00441608	−	0.0164810i
$718$	832.620	−	223.100i	1.15964	−	0.310724i
$719$	492.720	−	284.472i	0.685285	−	0.395650i	−0.116558	−	0.993184i	$-0.537186\pi$
$719$	492.720	−	284.472i	0.685285	−	0.395650i	0.801843	+	0.597534i	$0.203853\pi$
$720$	16.3064	−	57.7417i	0.0226478	−	0.0801968i
$721$	−233.593	−	1275.00i	−0.323985	−	1.76838i
$722$	684.923	−	684.923i	0.948647	−	0.948647i
$723$	−40.5481	+	151.327i	−0.0560831	+	0.209305i
$724$	298.894	+	172.566i	0.412837	+	0.238351i
$725$	−316.988	−	584.783i	−0.437224	−	0.806598i
$726$	129.433	+	224.185i	0.178282	+	0.308794i
$727$	−467.794	+	467.794i	−0.643459	+	0.643459i	−0.951404	−	0.307945i	$-0.900359\pi$
$727$	−467.794	+	467.794i	−0.643459	+	0.643459i	0.307945	+	0.951404i	$0.400359\pi$
$728$	−107.218	−	225.983i	−0.147277	−	0.310416i
$729$		−	27.0000i		−	0.0370370i
$730$	15.4165	+	60.7908i	0.0211185	+	0.0832750i
$731$	−220.435	+	381.805i	−0.301553	+	0.522304i
$732$	15.0592	+	56.2017i	0.0205727	+	0.0767783i
$733$	−164.832	+	615.162i	−0.224873	+	0.839239i	0.757582	+	0.652740i	$0.226381\pi$
$733$	−164.832	+	615.162i	−0.224873	+	0.839239i	−0.982455	+	0.186499i	$0.940286\pi$
$734$			118.640i			0.161635i
$735$	−417.898	−	73.7300i	−0.568569	−	0.100313i
$736$	−72.1669			−0.0980528
$737$	223.188	+	59.8031i	0.302833	+	0.0811440i
$738$	−106.580	+	28.5580i	−0.144417	+	0.0386964i
$739$	306.153	+	176.758i	0.414280	+	0.239185i	0.692627	−	0.721296i	$-0.256453\pi$
$739$	306.153	+	176.758i	0.414280	+	0.239185i	−0.278347	+	0.960481i	$0.589787\pi$
$740$	−33.1037	+	55.5985i	−0.0447347	+	0.0751332i
$741$	−707.668			−0.955017
$742$	−404.753	+	192.035i	−0.545489	+	0.258807i
$743$	−278.067	−	278.067i	−0.374250	−	0.374250i	0.494773	−	0.869022i	$-0.335251\pi$
$743$	−278.067	−	278.067i	−0.374250	−	0.374250i	−0.869022	+	0.494773i	$0.835251\pi$
$744$	−144.360	+	83.3464i	−0.194032	+	0.112025i
$745$	−902.667	−	927.255i	−1.21163	−	1.24464i
$746$	−99.7268	+	172.732i	−0.133682	+	0.231544i
$747$	385.887	+	103.398i	0.516582	+	0.138418i
$748$	−81.9586	−	81.9586i	−0.109570	−	0.109570i
$749$	−220.352	+	40.3707i	−0.294194	+	0.0538994i
$750$	207.606	+	225.055i	0.276808	+	0.300073i
$751$	375.703	+	650.737i	0.500271	+	0.866494i	1.00000		0.000312486i	$9.94674e-5\pi$
$751$	375.703	+	650.737i	0.500271	+	0.866494i	−0.499729	+	0.866182i	$0.666567\pi$
$752$	−42.9891	−	160.438i	−0.0571664	−	0.213348i
$753$	132.174	−	35.4159i	0.175530	−	0.0470331i
$754$	411.678	−	237.683i	0.545992	−	0.315229i
$755$	700.893	+	197.934i	0.928335	+	0.262164i
$756$	55.4137	−	47.1308i	0.0732986	−	0.0623424i
$757$	−554.603	+	554.603i	−0.732632	+	0.732632i	−0.971140	−	0.238508i	$-0.923342\pi$
$757$	−554.603	+	554.603i	−0.732632	+	0.732632i	0.238508	+	0.971140i	$0.423342\pi$
$758$	−45.3076	+	169.090i	−0.0597726	+	0.223074i
$759$	−74.8964	−	43.2414i	−0.0986777	−	0.0569716i
$760$	6.14497	−	457.326i	0.00808548	−	0.601745i
$761$	127.641	+	221.080i	0.167728	+	0.290513i	0.937621	−	0.347660i	$-0.113024\pi$
$761$	127.641	+	221.080i	0.167728	+	0.290513i	−0.769893	+	0.638173i	$0.779690\pi$
$762$	94.0696	−	94.0696i	0.123451	−	0.123451i
$763$	1217.60	+	98.3498i	1.59580	+	0.128899i
$764$			270.589i			0.354174i
$765$	113.628	−	190.842i	0.148534	−	0.249466i
$766$	223.409	−	386.955i	0.291656	−	0.505163i
$767$	−78.5214	−	293.046i	−0.102375	−	0.382067i
$768$	−7.17260	+	26.7685i	−0.00933933	+	0.0348548i
$769$			274.062i			0.356387i	0.983995	+	0.178194i	$0.0570253\pi$
$769$			274.062i			0.356387i	−0.983995	+	0.178194i	$0.942975\pi$
$770$	192.871	+	18.1902i	0.250482	+	0.0236236i
$771$	498.749			0.646886
$772$	−42.5412	−	11.3989i	−0.0551052	−	0.0147654i
$773$	−172.874	+	46.3214i	−0.223640	+	0.0599242i	−0.368899	−	0.929469i	$-0.620265\pi$
$773$	−172.874	+	46.3214i	−0.223640	+	0.0599242i	0.145259	+	0.989394i	$0.453599\pi$
$774$	109.397	+	63.1603i	0.141340	+	0.0816024i
$775$	22.8558	−	850.343i	0.0294914	−	1.09722i
$776$	472.897			0.609403
$777$	−70.8804	+	33.6293i	−0.0912232	+	0.0432809i
$778$	347.324	+	347.324i	0.446432	+	0.446432i
$779$	−728.409	+	420.547i	−0.935057	+	0.539855i
$780$	−156.791	+	152.634i	−0.201014	+	0.195684i
$781$	259.412	−	449.315i	0.332154	−	0.575308i
$782$	−258.044	−	69.1428i	−0.329980	−	0.0884179i
$783$	97.7598	+	97.7598i	0.124853	+	0.124853i
$784$	193.459	+	31.4580i	0.246759	+	0.0401251i
$785$	−43.1535	+	24.1475i	−0.0549725	+	0.0307611i
$786$	−180.248	−	312.199i	−0.229324	−	0.397200i
$787$	82.6936	+	308.617i	0.105074	+	0.392143i	0.998354	−	0.0573592i	$-0.0182680\pi$
$787$	82.6936	+	308.617i	0.105074	+	0.392143i	−0.893279	+	0.449502i	$0.851601\pi$
$788$	168.710	−	45.2057i	0.214099	−	0.0573676i
$789$	−400.319	+	231.124i	−0.507375	+	0.292933i
$790$	361.451	+	645.942i	0.457533	+	0.817648i
$791$	−57.8407	−	20.6166i	−0.0731235	−	0.0260640i
$792$	−23.4832	+	23.4832i	−0.0296505	+	0.0296505i
$793$	54.9200	−	204.964i	0.0692560	−	0.258467i
$794$	−463.633	−	267.679i	−0.583920	−	0.337127i
$795$	273.378	+	280.825i	0.343872	+	0.353239i
$796$	−332.022	−	575.080i	−0.417114	−	0.722462i
$797$	360.903	−	360.903i	0.452827	−	0.452827i	−0.443464	−	0.896292i	$-0.646251\pi$
$797$	360.903	−	360.903i	0.452827	−	0.452827i	0.896292	+	0.443464i	$0.146251\pi$
$798$	315.028	−	456.354i	0.394773	−	0.571872i
$799$		−	614.858i		−	0.769535i
$800$	−97.2770	−	102.651i	−0.121596	−	0.128313i
$801$	74.9512	−	129.819i	0.0935721	−	0.162072i
$802$	−62.3838	−	232.820i	−0.0777853	−	0.290299i
$803$	8.98442	−	33.5303i	0.0111886	−	0.0417563i
$804$		−	204.509i		−	0.254364i
$805$	405.943	−	185.960i	0.504277	−	0.231006i
$806$	607.918			0.754241
$807$	−246.679	−	66.0974i	−0.305674	−	0.0819051i
$808$	−305.551	+	81.8721i	−0.378157	+	0.101327i
$809$	720.956	+	416.244i	0.891169	+	0.514517i	0.874325	−	0.485342i	$-0.161305\pi$
$809$	720.956	+	416.244i	0.891169	+	0.514517i	0.0168442	+	0.999858i	$0.494638\pi$
$810$	−54.6810	−	32.5574i	−0.0675074	−	0.0401943i
$811$	−375.130			−0.462553			−0.231276	−	0.972888i	$-0.574290\pi$
$811$	−375.130			−0.462553			−0.231276	+	0.972888i	$0.574290\pi$
$812$	−29.9902	+	371.287i	−0.0369337	+	0.457250i
$813$	−609.905	−	609.905i	−0.750191	−	0.750191i
$814$	31.0175	−	17.9079i	0.0381050	−	0.0219999i
$815$	−1147.27	−	15.4155i	−1.40769	−	0.0189147i
$816$	−51.2936	+	88.8432i	−0.0628598	+	0.108876i
$817$	930.104	+	249.221i	1.13844	+	0.305043i
$818$	−265.747	−	265.747i	−0.324874	−	0.324874i
$819$	−260.957	+	47.8100i	−0.318629	+	0.0583761i
$820$	−70.6809	+	250.284i	−0.0861962	+	0.305224i
$821$	701.328	+	1214.74i	0.854236	+	1.47958i	0.877352	+	0.479847i	$0.159308\pi$
$821$	701.328	+	1214.74i	0.854236	+	1.47958i	−0.0231161	+	0.999733i	$0.507359\pi$
$822$	−0.742836	−	2.77230i	−0.000903693	−	0.00337263i
$823$	−834.098	+	223.496i	−1.01348	+	0.271562i	−0.727085	−	0.686548i	$-0.759125\pi$
$823$	−834.098	+	223.496i	−1.01348	+	0.271562i	−0.286400	+	0.958110i	$0.592459\pi$
$824$	453.584	−	261.877i	0.550466	−	0.317812i
$825$	−39.4493	−	164.820i	−0.0478173	−	0.199782i
$826$	223.931	+	79.8174i	0.271103	+	0.0966313i
$827$	785.335	−	785.335i	0.949619	−	0.949619i	−0.0491718	−	0.998790i	$-0.515658\pi$
$827$	785.335	−	785.335i	0.949619	−	0.949619i	0.998790	+	0.0491718i	$0.0156582\pi$
$828$	−19.8112	+	73.9363i	−0.0239265	+	0.0892951i
$829$	1243.93	+	718.182i	1.50052	+	0.866324i	1.00000		0.000596877i	$0.000189992\pi$
$829$	1243.93	+	718.182i	1.50052	+	0.866324i	0.500517	+	0.865727i	$0.333143\pi$
$830$	674.718	−	656.826i	0.812913	−	0.791357i
$831$	225.233	+	390.115i	0.271038	+	0.469452i
$832$	71.4651	−	71.4651i	0.0858955	−	0.0858955i
$833$	661.604	+	297.836i	0.794243	+	0.357546i
$834$			574.687i			0.689073i
$835$	−1103.97	−	657.308i	−1.32212	−	0.787195i
$836$	−126.578	+	219.239i	−0.151409	+	0.262247i
$837$	45.7603	+	170.780i	0.0546719	+	0.204038i
$838$	−63.4140	+	236.664i	−0.0756730	+	0.282415i
$839$			702.434i			0.837228i	0.908164	+	0.418614i	$0.137484\pi$
$839$			702.434i			0.837228i	−0.908164	+	0.418614i	$0.862516\pi$
$840$	−28.6309	−	169.057i	−0.0340844	−	0.201258i
$841$	133.076			0.158235
$842$	739.138	+	198.051i	0.877836	+	0.235216i
$843$	−284.623	+	76.2644i	−0.337631	+	0.0904678i
$844$	−8.25481	−	4.76592i	−0.00978058	−	0.00564682i
$845$	−45.5491	+	11.5512i	−0.0539043	+	0.0136701i
$846$	−176.173			−0.208242
$847$	608.801	+	420.265i	0.718773	+	0.496181i
$848$	−127.999	−	127.999i	−0.150943	−	0.150943i
$849$	−509.726	+	294.290i	−0.600384	+	0.346632i
$850$	−249.481	−	460.245i	−0.293507	−	0.541465i
$851$	41.2750	−	71.4904i	0.0485018	−	0.0840075i
$852$	−443.556	−	118.850i	−0.520605	−	0.139496i
$853$	−230.504	−	230.504i	−0.270227	−	0.270227i	0.558964	−	0.829192i	$-0.311199\pi$
$853$	−230.504	−	230.504i	−0.270227	−	0.270227i	−0.829192	+	0.558964i	$0.811199\pi$
$854$	107.727	+	126.659i	0.126144	+	0.148313i
$855$	−466.852	−	131.840i	−0.546026	−	0.154199i
$856$	−45.2587	−	78.3904i	−0.0528723	−	0.0915775i
$857$	−283.900	−	1059.53i	−0.331272	−	1.23632i	−0.907855	−	0.419284i	$-0.862281\pi$
$857$	−283.900	−	1059.53i	−0.331272	−	1.23632i	0.576583	−	0.817038i	$-0.304386\pi$
$858$	116.989	−	31.3471i	0.136351	−	0.0365351i
$859$	−629.320	+	363.338i	−0.732619	+	0.422978i	−0.819380	−	0.573251i	$-0.805682\pi$
$859$	−629.320	+	363.338i	−0.732619	+	0.422978i	0.0867605	+	0.996229i	$0.472349\pi$
$860$	259.828	−	145.392i	0.302125	−	0.169061i
$861$	−240.193	+	204.291i	−0.278970	+	0.237272i
$862$	544.876	−	544.876i	0.632106	−	0.632106i
$863$	−192.455	+	718.251i	−0.223007	+	0.832272i	0.760187	+	0.649705i	$0.225107\pi$
$863$	−192.455	+	718.251i	−0.223007	+	0.832272i	−0.983193	+	0.182567i	$0.941559\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	−1297.77	−	17.4378i	−1.50031	−	0.0201593i
$866$	−440.714	−	763.339i	−0.508908	−	0.881454i
$867$	85.4223	−	85.4223i	0.0985263	−	0.0985263i
$868$	−270.623	+	392.028i	−0.311778	+	0.451645i
$869$		−	409.702i		−	0.471463i
$870$	315.867	−	80.1037i	0.363066	−	0.0920732i
$871$	−372.915	+	645.908i	−0.428146	+	0.741570i
$872$	127.749	+	476.767i	0.146502	+	0.546751i
$873$	129.819	−	484.492i	0.148705	−	0.554973i
$874$			583.482i			0.667600i
$875$	811.700	+	326.753i	0.927658	+	0.373432i
$876$	−30.7240			−0.0350731
$877$	1203.12	+	322.376i	1.37186	+	0.367589i	0.868158	−	0.496288i	$-0.165304\pi$
$877$	1203.12	+	322.376i	1.37186	+	0.367589i	0.503703	+	0.863877i	$0.331971\pi$
$878$	−649.469	+	174.025i	−0.739714	+	0.198206i
$879$	−793.215	−	457.963i	−0.902406	−	0.521004i
$880$	19.2420	+	75.8756i	0.0218659	+	0.0862222i
$881$	308.518			0.350191			0.175095	−	0.984551i	$-0.443977\pi$
$881$	308.518			0.350191			0.175095	+	0.984551i	$0.443977\pi$
$882$	85.3376	−	189.567i	0.0967546	−	0.214928i
$883$	−113.247	−	113.247i	−0.128252	−	0.128252i	0.640067	−	0.768319i	$-0.278907\pi$
$883$	−113.247	−	113.247i	−0.128252	−	0.128252i	−0.768319	+	0.640067i	$0.778907\pi$
$884$	324.005	−	187.065i	0.366522	−	0.211612i
$885$	2.79420	−	207.952i	0.00315729	−	0.234975i
$886$	−332.755	+	576.349i	−0.375570	+	0.650507i
$887$	−979.674	−	262.503i	−1.10448	−	0.295945i	−0.339892	−	0.940464i	$-0.610391\pi$
$887$	−979.674	−	262.503i	−1.10448	−	0.295945i	−0.764588	+	0.644520i	$0.777057\pi$
$888$	−22.4153	−	22.4153i	−0.0252425	−	0.0252425i
$889$	127.643	−	358.109i	0.143581	−	0.402822i
$890$	−172.535	−	308.333i	−0.193859	−	0.346442i
$891$	17.6124	+	30.5056i	0.0197670	+	0.0342375i
$892$	−70.6428	−	263.643i	−0.0791960	−	0.295563i
$893$	−1297.17	+	347.575i	−1.45260	+	0.389222i
$894$	549.026	−	316.980i	0.614123	−	0.354564i
$895$	−419.407	+	1485.14i	−0.468611	+	1.65937i
$896$	14.2720	+	77.8994i	0.0159285	+	0.0869413i
$897$	197.391	−	197.391i	0.220057	−	0.220057i
$898$	−266.736	+	995.473i	−0.297034	+	1.10854i
$899$	−784.035	−	452.663i	−0.872119	−	0.503518i
$900$	−131.872	+	71.4826i	−0.146525	+	0.0794251i
$901$	−335.047	−	580.318i	−0.371861	−	0.644083i
$902$	101.789	−	101.789i	0.112848	−	0.112848i
$903$	359.819	+	29.0639i	0.398471	+	0.0321860i
$904$		−	24.8114i		−	0.0274463i
$905$	−212.100	−	836.357i	−0.234364	−	0.924151i
$906$	−178.398	+	308.994i	−0.196907	+	0.341053i
$907$	−142.439	−	531.590i	−0.157044	−	0.586097i	−0.998922	−	0.0464285i	$-0.985216\pi$
$907$	−142.439	−	531.590i	−0.157044	−	0.586097i	0.841877	−	0.539669i	$-0.181451\pi$
$908$	31.8998	−	119.052i	0.0351319	−	0.131114i
$909$			335.518i			0.369107i
$910$	−217.844	+	586.147i	−0.239389	+	0.644118i
$911$	−1091.64			−1.19829			−0.599144	−	0.800641i	$-0.704492\pi$
$911$	−1091.64			−1.19829			−0.599144	+	0.800641i	$0.704492\pi$
$912$	216.428	+	57.9918i	0.237312	+	0.0635875i
$913$	−503.437	+	134.896i	−0.551410	+	0.147750i
$914$	−762.579	−	440.275i	−0.834331	−	0.481701i
$915$	74.4164	−	124.984i	0.0813294	−	0.136595i
$916$	−902.718			−0.985500
$917$	−847.816	−	585.262i	−0.924554	−	0.638235i
$918$	76.9404	+	76.9404i	0.0838131	+	0.0838131i
$919$	448.935	−	259.193i	0.488503	−	0.282038i	−0.235450	−	0.971886i	$-0.575656\pi$
$919$	448.935	−	259.193i	0.488503	−	0.282038i	0.723953	+	0.689849i	$0.242323\pi$
$920$	125.849	+	129.277i	0.136792	+	0.140518i
$921$	−9.05484	+	15.6834i	−0.00983153	+	0.0170287i
$922$	−1088.28	−	291.603i	−1.18034	−	0.316272i
$923$	1184.18	+	1184.18i	1.28297	+	1.28297i
$924$	−31.8645	+	89.3972i	−0.0344854	+	0.0967503i
$925$	157.325	−	37.6553i	0.170081	−	0.0407084i
$926$	215.541	+	373.327i	0.232765	+	0.403161i
$927$	−143.780	−	536.596i	−0.155103	−	0.578852i
$928$	−145.383	+	38.9551i	−0.156662	+	0.0419775i
$929$	−191.262	+	110.425i	−0.205879	+	0.118864i	−0.599395	−	0.800453i	$-0.704592\pi$
$929$	−191.262	+	110.425i	−0.205879	+	0.118864i	0.393516	+	0.919318i	$0.371259\pi$
$930$	401.047	+	113.257i	0.431233	+	0.121781i
$931$	254.344	−	1564.15i	0.273195	−	1.68008i
$932$	−362.609	+	362.609i	−0.389065	+	0.389065i
$933$	−131.257	+	489.857i	−0.140683	+	0.525035i
$934$	350.332	+	202.264i	0.375088	+	0.216557i
$935$	−3.89318	+	289.741i	−0.00416383	+	0.309884i
$936$	−53.5988	−	92.8359i	−0.0572637	−	0.0991836i
$937$	999.171	−	999.171i	1.06635	−	1.06635i	0.0687153	−	0.997636i	$-0.478110\pi$
$937$	999.171	−	999.171i	1.06635	−	1.06635i	0.997636	−	0.0687153i	$-0.0218900\pi$
$938$	−250.518	−	528.017i	−0.267077	−	0.562918i
$939$			596.836i			0.635608i
$940$	−212.434	+	356.789i	−0.225994	+	0.379563i
$941$	−252.279	+	436.960i	−0.268097	+	0.464357i	−0.968370	−	0.249517i	$-0.919728\pi$
$941$	−252.279	+	436.960i	−0.268097	+	0.464357i	0.700274	+	0.713875i	$0.253061\pi$
$942$	−6.27003	−	23.4001i	−0.00665609	−	0.0248409i
$943$	85.8725	−	320.480i	0.0910631	−	0.339852i
$944$			96.0578i			0.101756i
$945$	−181.062	−	17.0765i	−0.191600	−	0.0180703i
$946$	−164.801			−0.174208
$947$	−940.882	−	252.109i	−0.993540	−	0.266218i	−0.274803	−	0.961501i	$-0.588613\pi$
$947$	−940.882	−	252.109i	−0.993540	−	0.266218i	−0.718737	+	0.695282i	$0.755279\pi$
$948$	−350.264	+	93.8529i	−0.369477	+	0.0990010i
$949$	97.0369	+	56.0243i	0.102252	+	0.0590350i
$950$	−829.950	+	786.503i	−0.873632	+	0.827898i
$951$	221.031			0.232419
$952$	−23.6034	+	292.216i	−0.0247934	+	0.306949i
$953$	−166.543	−	166.543i	−0.174757	−	0.174757i	0.614309	−	0.789066i	$-0.289435\pi$
$953$	−166.543	−	166.543i	−0.174757	−	0.174757i	−0.789066	+	0.614309i	$0.789435\pi$
$954$	−166.276	+	95.9996i	−0.174294	+	0.100628i
$955$	484.721	−	471.868i	0.507562	−	0.494103i
$956$	7.06316	−	12.2337i	0.00738824	−	0.0127968i
$957$	−174.223	−	46.6828i	−0.182051	−	0.0487804i
$958$	671.652	+	671.652i	0.701098	+	0.701098i
$959$	−5.31391	−	6.24779i	−0.00554110	−	0.00651490i
$960$	60.4600	−	33.8318i	0.0629792	−	0.0352414i
$961$	−98.3850	−	170.408i	−0.102378	−	0.177323i
$962$	29.9216	+	111.669i	0.0311035	+	0.116080i
$963$	−92.7368	+	24.8488i	−0.0962999	+	0.0258035i
$964$	−156.666	+	90.4510i	−0.162516	+	0.0938288i
$965$	53.7662	+	96.0845i	0.0557163	+	0.0995694i
$966$	39.4200	+	215.163i	0.0408075	+	0.222736i
$967$	−75.7515	+	75.7515i	−0.0783366	+	0.0783366i	−0.745189	−	0.666853i	$-0.767641\pi$
$967$	−75.7515	+	75.7515i	−0.0783366	+	0.0783366i	0.666853	+	0.745189i	$0.267641\pi$
$968$	−77.3643	+	288.728i	−0.0799218	+	0.298272i
$969$	718.313	+	414.718i	0.741293	+	0.427986i
$970$	−824.664	−	847.127i	−0.850169	−	0.873327i
$971$	222.519	+	385.415i	0.229165	+	0.396926i	0.957561	−	0.288231i	$-0.0930670\pi$
$971$	222.519	+	385.415i	0.229165	+	0.396926i	−0.728396	+	0.685157i	$0.759734\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	703.977	+	1483.77i	0.723512	+	1.52495i
$974$			144.647i			0.148508i
$975$	546.843	+	14.6982i	0.560865	+	0.0150751i
$976$	−33.5927	+	58.1843i	−0.0344188	+	0.0596151i
$977$	471.135	+	1758.30i	0.482226	+	1.79969i	0.592238	+	0.805763i	$0.298245\pi$
$977$	471.135	+	1758.30i	0.482226	+	1.79969i	−0.110012	+	0.993930i	$0.535089\pi$
$978$	145.481	−	542.941i	0.148753	−	0.555154i
$979$			195.566i			0.199761i
$980$	−281.012	−	401.413i	−0.286747	−	0.409605i
$981$	523.527			0.533666
$982$	356.246	+	95.4557i	0.362775	+	0.0972054i
$983$	716.158	−	191.894i	0.728543	−	0.195213i	0.124563	−	0.992212i	$-0.460247\pi$
$983$	716.158	−	191.894i	0.728543	−	0.195213i	0.603980	+	0.796999i	$0.293580\pi$
$984$	−110.340	−	63.7046i	−0.112134	−	0.0647404i
$985$	−375.185	−	223.388i	−0.380899	−	0.226789i
$986$	−557.162			−0.565073
$987$	−454.857	+	215.807i	−0.460848	+	0.218650i
$988$	−577.808	−	577.808i	−0.584826	−	0.584826i
$989$	−328.951	+	189.920i	−0.332610	+	0.192032i
$990$	83.0183	+	1.11549i	0.0838568	+	0.00112676i
$991$	−135.511	+	234.713i	−0.136742	+	0.236844i	−0.926262	−	0.376881i	$-0.876996\pi$
$991$	−135.511	+	234.713i	−0.136742	+	0.236844i	0.789520	+	0.613725i	$0.210330\pi$
$992$	−185.922	−	49.8176i	−0.187421	−	0.0502193i
$993$	282.264	+	282.264i	0.284254	+	0.284254i
$994$	−1290.80	+	236.487i	−1.29859	+	0.237915i
$995$	−451.174	+	1597.63i	−0.453441	+	1.60566i
$996$	230.651	+	399.499i	0.231577	+	0.401104i
$997$	104.030	+	388.246i	0.104343	+	0.389415i	0.998270	−	0.0587989i	$-0.0187271\pi$
$997$	104.030	+	388.246i	0.104343	+	0.389415i	−0.893927	+	0.448214i	$0.852060\pi$
$998$	−130.824	+	35.0541i	−0.131086	+	0.0351244i
$999$	−29.1183	+	16.8115i	−0.0291475	+	0.0168283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.b.193.6	yes	32
5.2	odd	4	inner	210.3.v.b.67.2	yes	32
7.2	even	3	inner	210.3.v.b.163.2	yes	32
35.2	odd	12	inner	210.3.v.b.37.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.b.37.6	✓	32	35.2	odd	12	inner
210.3.v.b.67.2	yes	32	5.2	odd	4	inner
210.3.v.b.163.2	yes	32	7.2	even	3	inner
210.3.v.b.193.6	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.22909 - 4.84658i) q^{5} +2.44949 q^{6} +(6.32429 - 3.00056i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.22909 - 4.84658i) q^{5} +2.44949 q^{6} +(6.32429 - 3.00056i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(0.0950035 - 7.07043i) q^{10} +(-1.95694 + 3.38951i) q^{11} +(3.34607 + 0.896575i) q^{12} +(-8.93314 - 8.93314i) q^{13} +(9.73742 - 1.78399i) q^{14} +(-4.22897 - 7.55750i) q^{15} +(2.00000 + 3.46410i) q^{16} +(3.83238 + 14.3027i) q^{17} +(4.09808 - 1.09808i) q^{18} +(28.0079 - 16.1704i) q^{19} +(2.71773 - 9.62361i) q^{20} +(9.23562 - 7.85514i) q^{21} +(-3.91387 + 3.91387i) q^{22} +(-3.30186 + 12.3227i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-21.9787 + 11.9138i) q^{25} +(-8.93314 - 15.4726i) q^{26} +(3.67423 - 3.67423i) q^{27} +(13.9546 + 1.12716i) q^{28} +26.6068i q^{29} +(-3.01064 - 11.8716i) q^{30} +(-17.0130 + 29.4674i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-1.75454 + 6.54804i) q^{33} +20.9405i q^{34} +(-22.3156 - 26.9632i) q^{35} +6.00000 q^{36} +(-6.25026 - 1.67475i) q^{37} +(44.1783 - 11.8375i) q^{38} +(-18.9500 - 10.9408i) q^{39} +(7.23498 - 12.1513i) q^{40} -26.0073 q^{41} +(15.4913 - 7.34985i) q^{42} +(21.0534 + 21.0534i) q^{43} +(-6.77903 + 3.91387i) q^{44} +(-10.4631 - 10.7481i) q^{45} +(-9.02086 + 15.6246i) q^{46} +(-40.1094 - 10.7473i) q^{47} +(4.89898 + 4.89898i) q^{48} +(30.9932 - 37.9528i) q^{49} +(-34.3842 + 8.22975i) q^{50} +(12.8234 + 22.2108i) q^{51} +(-6.53951 - 24.4058i) q^{52} +(-43.7126 + 11.7128i) q^{53} +(6.36396 - 3.67423i) q^{54} +(18.8328 + 5.31843i) q^{55} +(18.6497 + 6.64745i) q^{56} +(39.6092 - 39.6092i) q^{57} +(-9.73878 + 36.3456i) q^{58} +(20.7971 + 12.0072i) q^{59} +(0.232710 - 17.3189i) q^{60} +(8.39818 + 14.5461i) q^{61} +(-34.0260 + 34.0260i) q^{62} +(11.9301 - 17.2821i) q^{63} +8.00000i q^{64} +(-32.3155 + 54.2748i) q^{65} +(-4.79349 + 8.30258i) q^{66} +(-15.2798 - 57.0249i) q^{67} +(-7.66477 + 28.6053i) q^{68} +22.0965i q^{69} +(-20.6144 - 45.0005i) q^{70} -132.560 q^{71} +(8.19615 + 2.19615i) q^{72} +(-8.56704 + 2.29553i) q^{73} +(-7.92501 - 4.57551i) q^{74} +(-31.4302 + 29.7849i) q^{75} +64.6815 q^{76} +(-2.20578 + 27.3082i) q^{77} +(-21.8816 - 21.8816i) q^{78} +(-90.6550 + 52.3397i) q^{79} +(14.3309 - 13.9509i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-35.5266 - 9.51932i) q^{82} +(94.1629 + 94.1629i) q^{83} +(23.8517 - 4.36988i) q^{84} +(64.6086 - 36.1532i) q^{85} +(21.0534 + 36.4656i) q^{86} +(11.9275 + 44.5141i) q^{87} +(-10.6929 + 2.86515i) q^{88} +(43.2731 - 24.9837i) q^{89} +(-10.3588 - 18.5120i) q^{90} +(-83.3002 - 29.6913i) q^{91} +(-18.0417 + 18.0417i) q^{92} +(-15.2534 + 56.9266i) q^{93} +(-50.8567 - 29.3621i) q^{94} +(-112.795 - 115.868i) q^{95} +(4.89898 + 8.48528i) q^{96} +(118.224 - 118.224i) q^{97} +(56.2293 - 40.5002i) q^{98} +11.7416i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

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