LMFDB - Embedded newform 210.3.v.b.193.8

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			193.8
Character	$\chi$	$=$	210.193
Dual form			210.3.v.b.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.73071 - 1.61876i) q^{5} +2.44949 q^{6} +(-4.13228 - 5.65016i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.73071 - 1.61876i) q^{5} +2.44949 q^{6} +(-4.13228 - 5.65016i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(7.05478 - 0.479709i) q^{10} +(2.47138 - 4.28056i) q^{11} +(3.34607 + 0.896575i) q^{12} +(7.82868 + 7.82868i) q^{13} +(-3.57669 - 9.23078i) q^{14} +(7.18896 - 4.82896i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-0.914015 - 3.41115i) q^{17} +(4.09808 - 1.09808i) q^{18} +(-26.8487 + 15.5011i) q^{19} +(9.81259 + 1.92693i) q^{20} +(-9.44633 - 7.60045i) q^{21} +(4.94276 - 4.94276i) q^{22} +(-4.61097 + 17.2084i) q^{23} +(4.24264 + 2.44949i) q^{24} +(19.7592 - 15.3158i) q^{25} +(7.82868 + 13.5597i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-1.50715 - 13.9186i) q^{28} +24.0299i q^{29} +(11.5878 - 3.96514i) q^{30} +(7.79698 - 13.5048i) q^{31} +(1.46410 + 5.46410i) q^{32} +(2.21578 - 8.26940i) q^{33} -4.99427i q^{34} +(-28.6949 - 20.0401i) q^{35} +6.00000 q^{36} +(33.2900 + 8.92003i) q^{37} +(-42.3498 + 11.3476i) q^{38} +(16.6071 + 9.58813i) q^{39} +(12.6989 + 6.22390i) q^{40} -19.3822 q^{41} +(-10.1220 - 13.8400i) q^{42} +(-11.5955 - 11.5955i) q^{43} +(8.56111 - 4.94276i) q^{44} +(9.86260 - 11.3017i) q^{45} +(-12.5974 + 21.8194i) q^{46} +(-30.3558 - 8.13382i) q^{47} +(4.89898 + 4.89898i) q^{48} +(-14.8486 + 46.6960i) q^{49} +(32.5976 - 13.6894i) q^{50} +(-3.05835 - 5.29722i) q^{51} +(5.73099 + 21.3883i) q^{52} +(-100.477 + 26.9228i) q^{53} +(6.36396 - 3.67423i) q^{54} +(4.76218 - 24.2506i) q^{55} +(3.03577 - 19.5649i) q^{56} +(-37.9698 + 37.9698i) q^{57} +(-8.79557 + 32.8255i) q^{58} +(-13.5357 - 7.81482i) q^{59} +(17.2806 - 1.17504i) q^{60} +(-44.1937 - 76.5457i) q^{61} +(15.5940 - 15.5940i) q^{62} +(-19.2112 - 8.48113i) q^{63} +8.00000i q^{64} +(49.7079 + 24.3624i) q^{65} +(6.05362 - 10.4852i) q^{66} +(20.2731 + 75.6604i) q^{67} +(1.82803 - 6.82230i) q^{68} +30.8572i q^{69} +(-31.8627 - 37.8783i) q^{70} -59.7196 q^{71} +(8.19615 + 2.19615i) q^{72} +(102.892 - 27.5699i) q^{73} +(42.2100 + 24.3700i) q^{74} +(26.1920 - 34.4816i) q^{75} -62.0044 q^{76} +(-34.3982 + 3.72475i) q^{77} +(19.1763 + 19.1763i) q^{78} +(23.6823 - 13.6730i) q^{79} +(15.0690 + 13.1501i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-26.4765 - 7.09436i) q^{82} +(-48.9951 - 48.9951i) q^{83} +(-8.76107 - 22.6107i) q^{84} +(-9.84577 - 14.6576i) q^{85} +(-11.5955 - 20.0839i) q^{86} +(10.7723 + 40.2029i) q^{87} +(13.5039 - 3.61835i) q^{88} +(-98.6980 + 56.9833i) q^{89} +(17.6093 - 11.8285i) q^{90} +(11.8830 - 76.5835i) q^{91} +(-25.1948 + 25.1948i) q^{92} +(6.99058 - 26.0892i) q^{93} +(-38.4896 - 22.2220i) q^{94} +(-101.921 + 116.793i) q^{95} +(4.89898 + 8.48528i) q^{96} +(99.3285 - 99.3285i) q^{97} +(-37.3755 + 58.3530i) q^{98} -14.8283i 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
$5$	4.73071	−	1.61876i	0.946142	−	0.323752i
$5$	4.73071	−	1.61876i	0.946142	−	0.323752i
$6$	2.44949			0.408248
$7$	−4.13228	−	5.65016i	−0.590325	−	0.807166i
$7$	−4.13228	−	5.65016i	−0.590325	−	0.807166i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	7.05478	−	0.479709i	0.705478	−	0.0479709i
$11$	2.47138	−	4.28056i	0.224671	−	0.389141i	−0.731550	−	0.681788i	$-0.761203\pi$
$11$	2.47138	−	4.28056i	0.224671	−	0.389141i	0.956221	+	0.292647i	$0.0945360\pi$
$12$	3.34607	+	0.896575i	0.278839	+	0.0747146i
$13$	7.82868	+	7.82868i	0.602206	+	0.602206i	0.940897	−	0.338692i	$-0.109984\pi$
$13$	7.82868	+	7.82868i	0.602206	+	0.602206i	−0.338692	+	0.940897i	$0.609984\pi$
$14$	−3.57669	−	9.23078i	−0.255478	−	0.659341i
$15$	7.18896	−	4.82896i	0.479264	−	0.321931i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−0.914015	−	3.41115i	−0.0537656	−	0.200656i	0.933819	−	0.357747i	$-0.116455\pi$
$17$	−0.914015	−	3.41115i	−0.0537656	−	0.200656i	−0.987584	+	0.157091i	$0.949788\pi$
$18$	4.09808	−	1.09808i	0.227671	−	0.0610042i
$19$	−26.8487	+	15.5011i	−1.41309	+	0.815848i	−0.995678	−	0.0928696i	$-0.970396\pi$
$19$	−26.8487	+	15.5011i	−1.41309	+	0.815848i	−0.417412	+	0.908718i	$0.637063\pi$
$20$	9.81259	+	1.92693i	0.490630	+	0.0963467i
$21$	−9.44633	−	7.60045i	−0.449825	−	0.361926i
$22$	4.94276	−	4.94276i	0.224671	−	0.224671i
$23$	−4.61097	+	17.2084i	−0.200477	+	0.748191i	0.790304	+	0.612715i	$0.209923\pi$
$23$	−4.61097	+	17.2084i	−0.200477	+	0.748191i	−0.990781	+	0.135475i	$0.956744\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	19.7592	−	15.3158i	0.790369	−	0.612631i
$26$	7.82868	+	13.5597i	0.301103	+	0.521526i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−1.50715	−	13.9186i	−0.0538269	−	0.497094i
$29$			24.0299i			0.828619i	0.910136	+	0.414309i	$0.135977\pi$
$29$			24.0299i			0.828619i	−0.910136	+	0.414309i	$0.864023\pi$
$30$	11.5878	−	3.96514i	0.386261	−	0.132171i
$31$	7.79698	−	13.5048i	0.251515	−	0.435638i	−0.712428	−	0.701745i	$-0.752404\pi$
$31$	7.79698	−	13.5048i	0.251515	−	0.435638i	0.963943	+	0.266108i	$0.0857377\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	2.21578	−	8.26940i	0.0671448	−	0.250588i
$34$		−	4.99427i		−	0.146890i
$35$	−28.6949	−	20.0401i	−0.819853	−	0.572574i
$36$	6.00000			0.166667
$37$	33.2900	+	8.92003i	0.899730	+	0.241082i	0.678900	−	0.734231i	$-0.262457\pi$
$37$	33.2900	+	8.92003i	0.899730	+	0.241082i	0.220830	+	0.975312i	$0.429124\pi$
$38$	−42.3498	+	11.3476i	−1.11447	+	0.298621i
$39$	16.6071	+	9.58813i	0.425824	+	0.245850i
$40$	12.6989	+	6.22390i	0.317474	+	0.155597i
$41$	−19.3822			−0.472736			−0.236368	−	0.971664i	$-0.575957\pi$
$41$	−19.3822			−0.472736			−0.236368	+	0.971664i	$0.575957\pi$
$42$	−10.1220	−	13.8400i	−0.240999	−	0.329524i
$43$	−11.5955	−	11.5955i	−0.269662	−	0.269662i	0.559302	−	0.828964i	$-0.311069\pi$
$43$	−11.5955	−	11.5955i	−0.269662	−	0.269662i	−0.828964	+	0.559302i	$0.811069\pi$
$44$	8.56111	−	4.94276i	0.194571	−	0.112335i
$45$	9.86260	−	11.3017i	0.219169	−	0.251150i
$46$	−12.5974	+	21.8194i	−0.273857	+	0.474334i
$47$	−30.3558	−	8.13382i	−0.645869	−	0.173060i	−0.0790084	−	0.996874i	$-0.525175\pi$
$47$	−30.3558	−	8.13382i	−0.645869	−	0.173060i	−0.566860	+	0.823814i	$0.691842\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$	−14.8486	+	46.6960i	−0.303033	+	0.952980i
$50$	32.5976	−	13.6894i	0.651951	−	0.273787i
$51$	−3.05835	−	5.29722i	−0.0599677	−	0.103867i
$52$	5.73099	+	21.3883i	0.110211	+	0.411314i
$53$	−100.477	+	26.9228i	−1.89580	+	0.507977i	−0.898128	+	0.439735i	$0.855072\pi$
$53$	−100.477	+	26.9228i	−1.89580	+	0.507977i	−0.997669	+	0.0682425i	$0.978261\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$	4.76218	−	24.2506i	0.0865852	−	0.440921i
$56$	3.03577	−	19.5649i	0.0542101	−	0.349373i
$57$	−37.9698	+	37.9698i	−0.666137	+	0.666137i
$58$	−8.79557	+	32.8255i	−0.151648	+	0.565957i
$59$	−13.5357	−	7.81482i	−0.229418	−	0.132455i	0.380885	−	0.924622i	$-0.375619\pi$
$59$	−13.5357	−	7.81482i	−0.229418	−	0.132455i	−0.610304	+	0.792168i	$0.708953\pi$
$60$	17.2806	−	1.17504i	0.288010	−	0.0195840i
$61$	−44.1937	−	76.5457i	−0.724486	−	1.25485i	−0.959185	−	0.282779i	$-0.908744\pi$
$61$	−44.1937	−	76.5457i	−0.724486	−	1.25485i	0.234699	−	0.972068i	$-0.424590\pi$
$62$	15.5940	−	15.5940i	0.251515	−	0.251515i
$63$	−19.2112	−	8.48113i	−0.304940	−	0.134621i
$64$			8.00000i			0.125000i
$65$	49.7079	+	24.3624i	0.764738	+	0.374807i
$66$	6.05362	−	10.4852i	0.0917215	−	0.158866i
$67$	20.2731	+	75.6604i	0.302584	+	1.12926i	0.935005	+	0.354634i	$0.115395\pi$
$67$	20.2731	+	75.6604i	0.302584	+	1.12926i	−0.632421	+	0.774625i	$0.717939\pi$
$68$	1.82803	−	6.82230i	0.0268828	−	0.100328i
$69$			30.8572i			0.447206i
$70$	−31.8627	−	37.8783i	−0.455182	−	0.541119i
$71$	−59.7196			−0.841121			−0.420560	−	0.907265i	$-0.638167\pi$
$71$	−59.7196			−0.841121			−0.420560	+	0.907265i	$0.638167\pi$
$72$	8.19615	+	2.19615i	0.113835	+	0.0305021i
$73$	102.892	−	27.5699i	1.40948	−	0.377670i	0.527743	−	0.849404i	$-0.323038\pi$
$73$	102.892	−	27.5699i	1.40948	−	0.377670i	0.881741	+	0.471734i	$0.156372\pi$
$74$	42.2100	+	24.3700i	0.570406	+	0.329324i
$75$	26.1920	−	34.4816i	0.349226	−	0.459755i
$76$	−62.0044			−0.815848
$77$	−34.3982	+	3.72475i	−0.446730	+	0.0483733i
$78$	19.1763	+	19.1763i	0.245850	+	0.245850i
$79$	23.6823	−	13.6730i	0.299776	−	0.173076i	−0.342566	−	0.939494i	$-0.611296\pi$
$79$	23.6823	−	13.6730i	0.299776	−	0.173076i	0.642342	+	0.766418i	$0.277963\pi$
$80$	15.0690	+	13.1501i	0.188362	+	0.164377i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	−26.4765	−	7.09436i	−0.322884	−	0.0865166i
$83$	−48.9951	−	48.9951i	−0.590302	−	0.590302i	0.347411	−	0.937713i	$-0.387061\pi$
$83$	−48.9951	−	48.9951i	−0.590302	−	0.590302i	−0.937713	+	0.347411i	$0.887061\pi$
$84$	−8.76107	−	22.6107i	−0.104298	−	0.269175i
$85$	−9.84577	−	14.6576i	−0.115833	−	0.172442i
$86$	−11.5955	−	20.0839i	−0.134831	−	0.233534i
$87$	10.7723	+	40.2029i	0.123820	+	0.462102i
$88$	13.5039	−	3.61835i	0.153453	−	0.0411176i
$89$	−98.6980	+	56.9833i	−1.10897	+	0.640262i	−0.938561	−	0.345112i	$-0.887841\pi$
$89$	−98.6980	+	56.9833i	−1.10897	+	0.640262i	−0.170405	+	0.985374i	$0.554508\pi$
$90$	17.6093	−	11.8285i	0.195659	−	0.131428i
$91$	11.8830	−	76.5835i	0.130583	−	0.841577i
$92$	−25.1948	+	25.1948i	−0.273857	+	0.273857i
$93$	6.99058	−	26.0892i	0.0751675	−	0.280529i
$94$	−38.4896	−	22.2220i	−0.409464	−	0.236404i
$95$	−101.921	+	116.793i	−1.07285	+	1.22940i
$96$	4.89898	+	8.48528i	0.0510310	+	0.0883883i
$97$	99.3285	−	99.3285i	1.02400	−	1.02400i	0.0243000	−	0.999705i	$-0.492264\pi$
$97$	99.3285	−	99.3285i	1.02400	−	1.02400i	0.999705	−	0.0243000i	$-0.00773568\pi$
$98$	−37.3755	+	58.3530i	−0.381383	+	0.595439i
$99$		−	14.8283i		−	0.149781i
$100$	49.5398	−	6.76847i	0.495398	−	0.0676847i
$101$	39.4954	−	68.4080i	0.391043	−	0.677307i	−0.601544	−	0.798839i	$-0.705448\pi$
$101$	39.4954	−	68.4080i	0.391043	−	0.677307i	0.992587	+	0.121533i	$0.0387810\pi$
$102$	−2.23887	−	8.35558i	−0.0219497	−	0.0819174i
$103$	−23.4941	+	87.6811i	−0.228098	+	0.851272i	0.753042	+	0.657972i	$0.228586\pi$
$103$	−23.4941	+	87.6811i	−0.228098	+	0.851272i	−0.981140	+	0.193300i	$0.938081\pi$
$104$			31.3147i			0.301103i
$105$	−56.9912	−	20.6642i	−0.542773	−	0.196802i
$106$	−147.109			−1.38782
$107$	76.5792	+	20.5193i	0.715694	+	0.191770i	0.598250	−	0.801310i	$-0.295863\pi$
$107$	76.5792	+	20.5193i	0.715694	+	0.191770i	0.117444	+	0.993079i	$0.462530\pi$
$108$	10.0382	−	2.68973i	0.0929463	−	0.0249049i
$109$	−37.6062	−	21.7120i	−0.345011	−	0.199192i	0.317475	−	0.948267i	$-0.397165\pi$
$109$	−37.6062	−	21.7120i	−0.345011	−	0.199192i	−0.662486	+	0.749074i	$0.730499\pi$
$110$	15.3816	−	31.3839i	0.139833	−	0.285308i
$111$	59.6940			0.537784
$112$	11.3082	−	25.6149i	0.100966	−	0.228705i
$113$	129.101	+	129.101i	1.14249	+	1.14249i	0.987994	+	0.154493i	$0.0493745\pi$
$113$	129.101	+	129.101i	1.14249	+	1.14249i	0.154493	+	0.987994i	$0.450625\pi$
$114$	−65.7656	+	37.9698i	−0.576892	+	0.333068i
$115$	6.04309	+	88.8720i	0.0525486	+	0.772800i
$116$	−24.0299	+	41.6211i	−0.207155	+	0.358802i
$117$	32.0825	+	8.59648i	0.274209	+	0.0734742i
$118$	−15.6296	−	15.6296i	−0.132455	−	0.132455i
$119$	−15.4966	+	19.2601i	−0.130223	+	0.161850i
$120$	24.0358	+	4.72000i	0.200299	+	0.0393334i
$121$	48.2846	+	83.6313i	0.399046	+	0.691168i
$122$	−32.3520	−	120.739i	−0.265180	−	0.989666i
$123$	−32.4270	+	8.68879i	−0.263634	+	0.0706405i
$124$	27.0095	−	15.5940i	0.217819	−	0.125758i
$125$	68.6826	−	104.440i	0.549461	−	0.835520i
$126$	−23.1387	−	18.6172i	−0.183640	−	0.147756i
$127$	152.616	−	152.616i	1.20170	−	1.20170i	0.228056	−	0.973648i	$-0.426763\pi$
$127$	152.616	−	152.616i	1.20170	−	1.20170i	0.973648	−	0.228056i	$-0.0732370\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	−24.5977	−	14.2015i	−0.190680	−	0.110089i
$130$	58.9850	+	51.4741i	0.453731	+	0.395954i
$131$	−97.2153	−	168.382i	−0.742102	−	1.28536i	−0.951537	−	0.307535i	$-0.900496\pi$
$131$	−97.2153	−	168.382i	−0.742102	−	1.28536i	0.209435	−	0.977823i	$-0.432838\pi$
$132$	12.1072	−	12.1072i	0.0917215	−	0.0917215i
$133$	198.530	+	87.6446i	1.49271	+	0.658982i
$134$			110.774i			0.826675i
$135$	11.4340	−	23.3294i	0.0846965	−	0.172811i
$136$	4.99427	−	8.65033i	0.0367226	−	0.0636054i
$137$	48.1776	+	179.801i	0.351661	+	1.31242i	0.884634	+	0.466285i	$0.154408\pi$
$137$	48.1776	+	179.801i	0.351661	+	1.31242i	−0.532973	+	0.846132i	$0.678925\pi$
$138$	−11.2945	+	42.1518i	−0.0818445	+	0.305448i
$139$		−	202.296i		−	1.45537i	−0.685913	−	0.727683i	$-0.740597\pi$
$139$		−	202.296i		−	1.45537i	0.685913	−	0.727683i	$-0.259403\pi$
$140$	−29.6608	−	63.4053i	−0.211863	−	0.452895i
$141$	−54.4326			−0.386047
$142$	−81.5785	−	21.8589i	−0.574496	−	0.153936i
$143$	52.8587	−	14.1634i	0.369641	−	0.0990451i
$144$	10.3923	+	6.00000i	0.0721688	+	0.0416667i
$145$	38.8987	+	113.679i	0.268267	+	0.783991i
$146$	150.645			1.03181
$147$	−3.90893	+	84.7804i	−0.0265913	+	0.576738i
$148$	48.7399	+	48.7399i	0.329324	+	0.329324i
$149$	89.3747	−	51.6005i	0.599830	−	0.346312i	−0.169144	−	0.985591i	$-0.554100\pi$
$149$	89.3747	−	51.6005i	0.599830	−	0.346312i	0.768975	+	0.639279i	$0.220767\pi$
$150$	48.4000	−	37.5158i	0.322667	−	0.250106i
$151$	37.3443	−	64.6822i	0.247313	−	0.428359i	−0.715466	−	0.698647i	$-0.753786\pi$
$151$	37.3443	−	64.6822i	0.247313	−	0.428359i	0.962779	+	0.270288i	$0.0871190\pi$
$152$	−84.6996	−	22.6952i	−0.557234	−	0.149311i
$153$	−7.49140	−	7.49140i	−0.0489634	−	0.0489634i
$154$	−48.3522	−	7.50253i	−0.313975	−	0.0487177i
$155$	15.0243	−	76.5086i	0.0969307	−	0.493604i
$156$	19.1763	+	33.2143i	0.122925	+	0.212912i
$157$	52.2685	+	195.069i	0.332920	+	1.24248i	0.906106	+	0.423050i	$0.139041\pi$
$157$	52.2685	+	195.069i	0.332920	+	1.24248i	−0.573186	+	0.819425i	$0.694293\pi$
$158$	37.3553	−	10.0093i	0.236426	−	0.0633502i
$159$	−156.033	+	90.0854i	−0.981336	+	0.566575i
$160$	15.7713	+	23.4790i	0.0985707	+	0.146744i
$161$	116.284	−	45.0571i	0.722261	−	0.279858i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−42.8461	+	159.904i	−0.262859	+	0.981004i	0.700688	+	0.713467i	$0.252876\pi$
$163$	−42.8461	+	159.904i	−0.262859	+	0.981004i	−0.963548	+	0.267537i	$0.913790\pi$
$164$	−33.5709	−	19.3822i	−0.204701	−	0.118184i
$165$	−2.90397	−	42.7069i	−0.0175998	−	0.258830i
$166$	−48.9951	−	84.8619i	−0.295151	−	0.511216i
$167$	129.993	−	129.993i	0.778403	−	0.778403i	−0.201156	−	0.979559i	$-0.564470\pi$
$167$	129.993	−	129.993i	0.778403	−	0.778403i	0.979559	+	0.201156i	$0.0644698\pi$
$168$	−3.69175	−	34.0936i	−0.0219747	−	0.202938i
$169$		−	46.4237i		−	0.274696i
$170$	−8.08453	−	23.6264i	−0.0475560	−	0.138979i
$171$	−46.5033	+	80.5461i	−0.271949	+	0.471030i
$172$	−8.48846	−	31.6794i	−0.0493515	−	0.184182i
$173$	7.65408	−	28.5654i	0.0442432	−	0.165118i	−0.940270	−	0.340431i	$-0.889427\pi$
$173$	7.65408	−	28.5654i	0.0442432	−	0.165118i	0.984513	+	0.175313i	$0.0560937\pi$
$174$			58.8611i			0.338282i
$175$	−168.187	−	48.3538i	−0.961069	−	0.276307i
$176$	19.7710			0.112335
$177$	−26.1489	−	7.00658i	−0.147734	−	0.0395852i
$178$	−155.681	+	41.7147i	−0.874614	+	0.234352i
$179$	187.148	+	108.050i	1.04552	+	0.603629i	0.921391	−	0.388637i	$-0.127054\pi$
$179$	187.148	+	108.050i	1.04552	+	0.603629i	0.124126	+	0.992266i	$0.460387\pi$
$180$	28.3843	−	9.71257i	0.157690	−	0.0539587i
$181$	138.273			0.763937			0.381968	−	0.924175i	$-0.375246\pi$
$181$	138.273			0.763937			0.381968	+	0.924175i	$0.375246\pi$
$182$	44.2640	−	100.266i	0.243209	−	0.550910i
$183$	−108.252	−	108.252i	−0.591540	−	0.591540i
$184$	−43.6387	+	25.1948i	−0.237167	+	0.136928i
$185$	171.925	−	11.6905i	0.929323	−	0.0631918i
$186$	19.0986	−	33.0798i	0.102681	−	0.177848i
$187$	−16.8605	−	4.51775i	−0.0901631	−	0.0241591i
$188$	−44.4440	−	44.4440i	−0.236404	−	0.236404i
$189$	−35.9430	−	5.57706i	−0.190174	−	0.0295083i
$190$	−181.976	+	122.236i	−0.957767	+	0.643350i
$191$	−76.7883	−	133.001i	−0.402033	−	0.696342i	0.591938	−	0.805983i	$-0.298363\pi$
$191$	−76.7883	−	133.001i	−0.402033	−	0.696342i	−0.993971	+	0.109642i	$0.965030\pi$
$192$	3.58630	+	13.3843i	0.0186787	+	0.0697097i
$193$	300.636	−	80.5552i	1.55770	−	0.417385i	0.625766	−	0.780011i	$-0.284787\pi$
$193$	300.636	−	80.5552i	1.55770	−	0.417385i	0.931935	+	0.362627i	$0.118120\pi$
$194$	172.042	−	99.3285i	0.886814	−	0.512002i
$195$	94.0844	+	18.4757i	0.482484	+	0.0947471i
$196$	−72.4146	+	66.0313i	−0.369462	+	0.336894i
$197$	67.5608	−	67.5608i	0.342948	−	0.342948i	−0.514526	−	0.857475i	$-0.672032\pi$
$197$	67.5608	−	67.5608i	0.342948	−	0.342948i	0.857475	+	0.514526i	$0.172032\pi$
$198$	5.42753	−	20.2558i	0.0274118	−	0.102302i
$199$	−279.894	−	161.597i	−1.40650	−	0.812044i	−0.411453	−	0.911431i	$-0.634979\pi$
$199$	−279.894	−	161.597i	−1.40650	−	0.812044i	−0.995049	+	0.0993866i	$0.968312\pi$
$200$	70.1500	+	8.88690i	0.350750	+	0.0444345i
$201$	67.8352	+	117.494i	0.337489	+	0.584548i
$202$	78.9907	−	78.9907i	0.391043	−	0.391043i
$203$	135.773	−	99.2983i	0.668833	−	0.489154i
$204$		−	12.2334i		−	0.0599677i
$205$	−91.6914	+	31.3751i	−0.447275	+	0.153049i
$206$	−64.1870	+	111.175i	−0.311587	+	0.539685i
$207$	13.8329	+	51.6252i	0.0668257	+	0.249397i
$208$	−11.4620	+	42.7767i	−0.0551057	+	0.205657i
$209$			153.237i			0.733189i
$210$	−70.2877	−	49.0880i	−0.334704	−	0.233752i
$211$	−327.292			−1.55115			−0.775575	−	0.631256i	$-0.782540\pi$
$211$	−327.292			−1.55115			−0.775575	+	0.631256i	$0.782540\pi$
$212$	−200.954	−	53.8456i	−0.947898	−	0.253989i
$213$	−99.9128	+	26.7716i	−0.469074	+	0.125688i
$214$	97.0986	+	56.0599i	0.453732	+	0.261962i
$215$	−73.6250	−	36.0845i	−0.342442	−	0.167835i
$216$	14.6969			0.0680414
$217$	−108.523	+	11.7512i	−0.500108	+	0.0541532i
$218$	−43.4239	−	43.4239i	−0.199192	−	0.199192i
$219$	159.783	−	92.2507i	0.729603	−	0.421236i
$220$	32.4990	−	37.2412i	0.147723	−	0.169278i
$221$	19.5493	−	33.8603i	0.0884582	−	0.153214i
$222$	81.5435	+	21.8495i	0.367313	+	0.0984213i
$223$	87.5407	+	87.5407i	0.392559	+	0.392559i	0.875599	−	0.483040i	$-0.160467\pi$
$223$	87.5407	+	87.5407i	0.392559	+	0.392559i	−0.483040	+	0.875599i	$0.660467\pi$
$224$	24.8230	−	30.8516i	0.110817	−	0.137730i
$225$	28.3623	−	69.4304i	0.126055	−	0.308580i
$226$	129.101	+	223.610i	0.571244	+	0.989423i
$227$	75.3933	+	281.372i	0.332129	+	1.23952i	0.906948	+	0.421242i	$0.138406\pi$
$227$	75.3933	+	281.372i	0.332129	+	1.23952i	−0.574819	+	0.818280i	$0.694928\pi$
$228$	−103.735	+	27.7958i	−0.454980	+	0.121912i
$229$	−56.5510	+	32.6497i	−0.246948	+	0.142575i	−0.618366	−	0.785890i	$-0.712205\pi$
$229$	−56.5510	+	32.6497i	−0.246948	+	0.142575i	0.371418	+	0.928466i	$0.378872\pi$
$230$	−24.2744	+	123.613i	−0.105541	+	0.537449i
$231$	−55.8796	+	21.6519i	−0.241903	+	0.0937313i
$232$	−48.0599	+	48.0599i	−0.207155	+	0.207155i
$233$	42.6828	−	159.294i	0.183188	−	0.683667i	−0.811823	−	0.583903i	$-0.801525\pi$
$233$	42.6828	−	159.294i	0.183188	−	0.683667i	0.995011	−	0.0997635i	$-0.0318086\pi$
$234$	40.6790	+	23.4860i	0.173842	+	0.100368i
$235$	−156.771	+	10.6601i	−0.667112	+	0.0453621i
$236$	−15.6296	−	27.0713i	−0.0662273	−	0.114709i
$237$	33.4919	−	33.4919i	0.141316	−	0.141316i
$238$	−28.2184	+	20.6377i	−0.118565	+	0.0867130i
$239$		−	84.6324i		−	0.354110i	−0.984201	−	0.177055i	$-0.943343\pi$
$239$		−	84.6324i		−	0.354110i	0.984201	−	0.177055i	$-0.0566571\pi$
$240$	31.1059	+	15.2454i	0.129608	+	0.0635224i
$241$	−220.268	+	381.516i	−0.913976	+	1.58305i	−0.105583	+	0.994410i	$0.533671\pi$
$241$	−220.268	+	381.516i	−0.913976	+	1.58305i	−0.808393	+	0.588643i	$0.799662\pi$
$242$	35.3468	+	131.916i	0.146061	+	0.545107i
$243$	4.03459	−	15.0573i	0.0166032	−	0.0619642i
$244$		−	176.775i		−	0.724486i
$245$	5.34531	+	244.942i	0.0218176	+	0.999762i
$246$	−47.4764			−0.192994
$247$	−331.543	−	88.8367i	−1.34228	−	0.359663i
$248$	42.6035	−	11.4156i	0.171788	−	0.0460305i
$249$	−103.934	−	60.0064i	−0.417406	−	0.240990i
$250$	132.050	−	117.528i	0.528199	−	0.470112i
$251$	−78.4347			−0.312489			−0.156244	−	0.987718i	$-0.549939\pi$
$251$	−78.4347			−0.312489			−0.156244	+	0.987718i	$0.549939\pi$
$252$	−24.7937	−	33.9010i	−0.0983875	−	0.134528i
$253$	62.2660	+	62.2660i	0.246111	+	0.246111i
$254$	264.339	−	152.616i	1.04071	−	0.600852i
$255$	−23.0431	−	20.1089i	−0.0903652	−	0.0788583i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−384.537	−	103.036i	−1.49625	−	0.400920i	−0.584409	−	0.811459i	$-0.698674\pi$
$257$	−384.537	−	103.036i	−1.49625	−	0.400920i	−0.911843	+	0.410540i	$0.865340\pi$
$258$	−28.4029	−	28.4029i	−0.110089	−	0.110089i
$259$	−87.1639	−	224.954i	−0.336540	−	0.868548i
$260$	61.7343	+	91.9049i	0.237439	+	0.353480i
$261$	36.0449	+	62.4316i	0.138103	+	0.239202i
$262$	−71.1666	−	265.597i	−0.271628	−	1.01373i
$263$	−391.508	+	104.904i	−1.48862	+	0.398876i	−0.909272	−	0.416201i	$-0.863361\pi$
$263$	−391.508	+	104.904i	−1.48862	+	0.398876i	−0.579352	+	0.815077i	$0.696694\pi$
$264$	20.9704	−	12.1072i	0.0794332	−	0.0458608i
$265$	−431.747	+	290.012i	−1.62923	+	1.09439i
$266$	239.117	+	192.392i	0.898936	+	0.723277i
$267$	−139.580	+	139.580i	−0.522772	+	0.522772i
$268$	−40.5463	+	151.321i	−0.151292	+	0.564630i
$269$	113.642	+	65.6115i	0.422463	+	0.243909i	0.696130	−	0.717915i	$-0.254904\pi$
$269$	113.642	+	65.6115i	0.422463	+	0.243909i	−0.273668	+	0.961824i	$0.588237\pi$
$270$	24.1583	−	27.6835i	0.0894753	−	0.102531i
$271$	31.0750	+	53.8235i	0.114668	+	0.198611i	0.917647	−	0.397397i	$-0.130086\pi$
$271$	31.0750	+	53.8235i	0.114668	+	0.198611i	−0.802979	+	0.596007i	$0.796753\pi$
$272$	9.98854	−	9.98854i	0.0367226	−	0.0367226i
$273$	−14.4508	−	133.454i	−0.0529332	−	0.488841i
$274$			263.247i			0.960756i
$275$	−16.7275	−	122.432i	−0.0608272	−	0.445206i
$276$	−30.8572	+	53.4463i	−0.111802	+	0.193646i
$277$	−23.2422	−	86.7411i	−0.0839068	−	0.313145i	0.911198	−	0.411968i	$-0.135159\pi$
$277$	−23.2422	−	86.7411i	−0.0839068	−	0.313145i	−0.995105	+	0.0988239i	$0.968492\pi$
$278$	74.0454	−	276.341i	0.266351	−	0.994034i
$279$		−	46.7819i		−	0.167677i
$280$	−17.3095	−	97.4699i	−0.0618197	−	0.348107i
$281$	−3.27031			−0.0116381			−0.00581906	−	0.999983i	$-0.501852\pi$
$281$	−3.27031			−0.0116381			−0.00581906	+	0.999983i	$0.501852\pi$
$282$	−74.3563	−	19.9237i	−0.263675	−	0.0706514i
$283$	−197.270	+	52.8584i	−0.697068	+	0.186779i	−0.589917	−	0.807464i	$-0.700840\pi$
$283$	−197.270	+	52.8584i	−0.697068	+	0.186779i	−0.107151	+	0.994243i	$0.534173\pi$
$284$	−103.437	−	59.7196i	−0.364216	−	0.210280i
$285$	−118.160	+	241.088i	−0.414597	+	0.845923i
$286$	77.3905			0.270596
$287$	80.0924	+	109.512i	0.279068	+	0.381576i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	239.481	−	138.264i	0.828653	−	0.478423i
$290$	11.5274	+	169.526i	0.0397495	+	0.584572i
$291$	121.652	−	210.707i	0.418048	−	0.724081i
$292$	205.785	+	55.1398i	0.704742	+	0.188835i
$293$	−269.541	−	269.541i	−0.919935	−	0.919935i	0.0770891	−	0.997024i	$-0.475437\pi$
$293$	−269.541	−	269.541i	−0.919935	−	0.919935i	−0.997024	+	0.0770891i	$0.975437\pi$
$294$	−36.3715	+	114.381i	−0.123713	+	0.389053i
$295$	−76.6837	−	15.0586i	−0.259945	−	0.0510463i
$296$	48.7399	+	84.4201i	0.164662	+	0.285203i
$297$	−6.64734	−	24.8082i	−0.0223816	−	0.0835293i
$298$	140.975	−	37.7742i	0.473071	−	0.126759i
$299$	−170.817	+	98.6211i	−0.571293	+	0.329836i
$300$	79.8474	−	33.5319i	0.266158	−	0.111773i
$301$	−17.6005	+	113.432i	−0.0584736	+	0.376850i
$302$	74.6886	−	74.6886i	0.247313	−	0.247313i
$303$	35.4106	−	132.154i	0.116867	−	0.436152i
$304$	−107.395	−	62.0044i	−0.353272	−	0.203962i
$305$	−332.976	−	290.576i	−1.09173	−	0.952709i
$306$	−7.49140	−	12.9755i	−0.0244817	−	0.0424036i
$307$	167.472	−	167.472i	0.545511	−	0.545511i	−0.379628	−	0.925139i	$-0.623948\pi$
$307$	167.472	−	167.472i	0.545511	−	0.545511i	0.925139	+	0.379628i	$0.123948\pi$
$308$	−63.3042	−	27.9468i	−0.205533	−	0.0907363i
$309$			157.225i			0.508820i
$310$	48.5276	−	99.0134i	0.156541	−	0.319398i
$311$	275.366	−	476.948i	0.885422	−	1.53360i	0.0401933	−	0.999192i	$-0.487203\pi$
$311$	275.366	−	476.948i	0.885422	−	1.53360i	0.845229	−	0.534404i	$-0.179464\pi$
$312$	14.0380	+	52.3905i	0.0449936	+	0.167918i
$313$	73.4448	−	274.100i	0.234648	−	0.875718i	−0.743659	−	0.668559i	$-0.766912\pi$
$313$	73.4448	−	274.100i	0.234648	−	0.875718i	0.978307	−	0.207159i	$-0.0664218\pi$
$314$			285.600i			0.909555i
$315$	−104.612	−	9.02342i	−0.332100	−	0.0286458i
$316$	54.6920			0.173076
$317$	−364.326	−	97.6208i	−1.14929	−	0.307952i	−0.366611	−	0.930374i	$-0.619482\pi$
$317$	−364.326	−	97.6208i	−1.14929	−	0.307952i	−0.782682	+	0.622422i	$0.786149\pi$
$318$	−246.118	+	65.9471i	−0.773956	+	0.207381i
$319$	102.861	+	59.3871i	0.322450	+	0.186167i
$320$	12.9501	+	37.8457i	0.0404690	+	0.118268i
$321$	137.318			0.427782
$322$	175.339	−	18.9862i	0.544531	−	0.0589634i
$323$	77.4167	+	77.4167i	0.239680	+	0.239680i
$324$	15.5885	−	9.00000i	0.0481125	−	0.0277778i
$325$	274.591	+	34.7863i	0.844895	+	0.107035i
$326$	−117.058	+	202.750i	−0.359072	+	0.621932i
$327$	−72.6497	−	19.4664i	−0.222170	−	0.0595303i
$328$	−38.7643	−	38.7643i	−0.118184	−	0.118184i
$329$	79.4813	+	205.126i	0.241584	+	0.623485i
$330$	11.6649	−	59.4017i	0.0353482	−	0.180005i
$331$	203.687	+	352.797i	0.615369	+	1.06585i	0.990320	+	0.138806i	$0.0443264\pi$
$331$	203.687	+	352.797i	0.615369	+	1.06585i	−0.374950	+	0.927045i	$0.622340\pi$
$332$	−35.8669	−	133.857i	−0.108033	−	0.403184i
$333$	99.8700	−	26.7601i	0.299910	−	0.0803606i
$334$	225.155	−	129.993i	0.674117	−	0.389202i
$335$	218.382	+	325.110i	0.651888	+	0.970477i
$336$	7.43608	−	47.9239i	0.0221312	−	0.142631i
$337$	−51.7090	+	51.7090i	−0.153439	+	0.153439i	−0.779652	−	0.626213i	$-0.784604\pi$
$337$	−51.7090	+	51.7090i	−0.153439	+	0.153439i	0.626213	+	0.779652i	$0.284604\pi$
$338$	16.9922	−	63.4159i	0.0502729	−	0.187621i
$339$	273.865	+	158.116i	0.807860	+	0.466418i
$340$	−2.39579	−	35.2335i	−0.00704645	−	0.103628i
$341$	−38.5386	−	66.7508i	−0.113016	−	0.195750i
$342$	−93.0067	+	93.0067i	−0.271949	+	0.271949i
$343$	325.198	−	109.064i	0.948101	−	0.317971i
$344$		−	46.3818i		−	0.134831i
$345$	49.9505	+	145.977i	0.144784	+	0.423121i
$346$	20.9113	−	36.2195i	0.0604374	−	0.104681i
$347$	124.666	+	465.261i	0.359269	+	1.34081i	0.875027	+	0.484075i	$0.160844\pi$
$347$	124.666	+	465.261i	0.359269	+	1.34081i	−0.515758	+	0.856734i	$0.672490\pi$
$348$	−21.5447	+	80.4058i	−0.0619099	+	0.231051i
$349$			165.950i			0.475501i	0.971326	+	0.237750i	$0.0764100\pi$
$349$			165.950i			0.475501i	−0.971326	+	0.237750i	$0.923590\pi$
$350$	−212.049	−	127.613i	−0.605855	−	0.364609i
$351$	57.5288			0.163900
$352$	27.0077	+	7.23670i	0.0767265	+	0.0205588i
$353$	−60.9899	+	16.3422i	−0.172776	+	0.0462951i	−0.344170	−	0.938907i	$-0.611840\pi$
$353$	−60.9899	+	16.3422i	−0.172776	+	0.0462951i	0.171394	+	0.985203i	$0.445173\pi$
$354$	−33.1555	−	19.1423i	−0.0936596	−	0.0540744i
$355$	−282.516	+	96.6717i	−0.795820	+	0.272315i
$356$	−227.933			−0.640262
$357$	−17.2922	+	39.1698i	−0.0484375	+	0.109719i
$358$	216.099	+	216.099i	0.603629	+	0.603629i
$359$	140.408	−	81.0646i	0.391109	−	0.225807i	−0.291532	−	0.956561i	$-0.594165\pi$
$359$	140.408	−	81.0646i	0.391109	−	0.225807i	0.682640	+	0.730754i	$0.260832\pi$
$360$	42.3287	−	2.87825i	0.117580	−	0.00799514i
$361$	300.069	−	519.734i	0.831215	−	1.43971i
$362$	188.884	+	50.6113i	0.521778	+	0.139810i
$363$	118.273	+	118.273i	0.325820	+	0.325820i
$364$	97.1655	−	120.764i	0.266938	−	0.331768i
$365$	442.125	−	296.983i	1.21130	−	0.813653i
$366$	−108.252	−	187.498i	−0.295770	−	0.512289i
$367$	−4.98370	−	18.5994i	−0.0135796	−	0.0506796i	0.958804	−	0.284070i	$-0.0916847\pi$
$367$	−4.98370	−	18.5994i	−0.0135796	−	0.0506796i	−0.972383	+	0.233390i	$0.925018\pi$
$368$	−68.8336	+	18.4439i	−0.187048	+	0.0501193i
$369$	−50.3563	+	29.0732i	−0.136467	+	0.0787893i
$370$	239.133	+	46.9593i	0.646304	+	0.126917i
$371$	567.318	+	456.460i	1.52916	+	1.23035i
$372$	38.1972	−	38.1972i	0.102681	−	0.102681i
$373$	87.5772	−	326.843i	0.234791	−	0.876253i	−0.743451	−	0.668790i	$-0.766813\pi$
$373$	87.5772	−	326.843i	0.234791	−	0.876253i	0.978243	−	0.207463i	$-0.0665208\pi$
$374$	−21.3782	−	12.3427i	−0.0571611	−	0.0330020i
$375$	68.0891	−	205.521i	0.181571	−	0.548056i
$376$	−44.4440	−	76.9793i	−0.118202	−	0.204732i
$377$	−188.123	+	188.123i	−0.498999	+	0.498999i
$378$	−47.0577	−	20.7744i	−0.124491	−	0.0549588i
$379$		−	531.207i		−	1.40160i	−0.713357	−	0.700801i	$-0.752826\pi$
$379$		−	531.207i		−	1.40160i	0.713357	−	0.700801i	$-0.247174\pi$
$380$	−293.325	+	100.370i	−0.771908	+	0.264133i
$381$	186.916	−	323.748i	0.490594	−	0.849733i
$382$	−56.2129	−	209.790i	−0.147154	−	0.549187i
$383$	25.8421	−	96.4442i	0.0674730	−	0.251813i	−0.923948	−	0.382517i	$-0.875057\pi$
$383$	25.8421	−	96.4442i	0.0674730	−	0.251813i	0.991421	+	0.130705i	$0.0417240\pi$
$384$			19.5959i			0.0510310i
$385$	−156.699	+	73.3032i	−0.407009	+	0.190398i
$386$	440.162			1.14032
$387$	−47.5191	−	12.7327i	−0.122788	−	0.0329010i
$388$	271.370	−	72.7135i	0.699408	−	0.187406i
$389$	−528.011	−	304.848i	−1.35736	−	0.783670i	−0.368089	−	0.929791i	$-0.619988\pi$
$389$	−528.011	−	304.848i	−1.35736	−	0.783670i	−0.989267	+	0.146121i	$0.953321\pi$
$390$	121.759	+	59.6755i	0.312203	+	0.153014i
$391$	62.9149			0.160908
$392$	−123.089	+	63.6949i	−0.314003	+	0.162487i
$393$	−238.128	−	238.128i	−0.605924	−	0.605924i
$394$	117.019	−	67.5608i	0.297002	−	0.171474i
$395$	89.9009	−	103.019i	0.227597	−	0.260808i
$396$	14.8283	−	25.6833i	0.0374451	−	0.0648569i
$397$	649.017	+	173.904i	1.63480	+	0.438044i	0.955302	−	0.295631i	$-0.0955298\pi$
$397$	649.017	+	173.904i	1.63480	+	0.438044i	0.679501	+	0.733675i	$0.262196\pi$
$398$	−323.194	−	323.194i	−0.812044	−	0.812044i
$399$	371.437	+	57.6337i	0.930920	+	0.144445i
$400$	92.5739	+	37.8164i	0.231435	+	0.0945410i
$401$	304.095	+	526.709i	0.758343	+	1.31349i	0.943695	+	0.330816i	$0.107324\pi$
$401$	304.095	+	526.709i	0.758343	+	1.31349i	−0.185353	+	0.982672i	$0.559343\pi$
$402$	49.6588	+	185.329i	0.123529	+	0.461018i
$403$	166.764	−	44.6844i	0.413808	−	0.110879i
$404$	136.816	−	78.9907i	0.338653	−	0.195522i
$405$	8.67120	−	44.1567i	0.0214104	−	0.109029i
$406$	221.815	−	85.9477i	0.546343	−	0.211694i
$407$	120.455	−	120.455i	0.295958	−	0.295958i
$408$	4.47774	−	16.7112i	0.0109749	−	0.0409587i
$409$	322.212	+	186.029i	0.787804	+	0.454839i	0.839189	−	0.543840i	$-0.183030\pi$
$409$	322.212	+	186.029i	0.787804	+	0.454839i	−0.0513849	+	0.998679i	$0.516364\pi$
$410$	−136.737	+	9.29779i	−0.333504	+	0.0226775i
$411$	161.205	+	279.216i	0.392227	+	0.679357i
$412$	−128.374	+	128.374i	−0.311587	+	0.311587i
$413$	11.7781	+	108.772i	0.0285185	+	0.263370i
$414$			75.5845i			0.182571i
$415$	−311.093	−	152.470i	−0.749621	−	0.367398i
$416$	−31.3147	+	54.2387i	−0.0752757	+	0.130381i
$417$	−90.6868	−	338.448i	−0.217474	−	0.811625i
$418$	−56.0885	+	209.325i	−0.134183	+	0.500777i
$419$			338.166i			0.807079i	0.914962	+	0.403540i	$0.132220\pi$
$419$			338.166i			0.807079i	−0.914962	+	0.403540i	$0.867780\pi$
$420$	−78.0474	−	92.7826i	−0.185827	−	0.220911i
$421$	13.7324			0.0326186			0.0163093	−	0.999867i	$-0.494808\pi$
$421$	13.7324			0.0326186			0.0163093	+	0.999867i	$0.494808\pi$
$422$	−447.090	−	119.797i	−1.05945	−	0.283880i
$423$	−91.0675	+	24.4015i	−0.215290	+	0.0576867i
$424$	−254.800	−	147.109i	−0.600943	−	0.346955i
$425$	−70.3046	−	53.4028i	−0.165423	−	0.125654i
$426$	−146.282			−0.343386
$427$	−249.875	+	566.009i	−0.585187	+	1.32555i
$428$	112.120	+	112.120i	0.261962	+	0.261962i
$429$	82.0851	−	47.3918i	0.191340	−	0.110470i
$430$	−87.3658	−	76.2409i	−0.203176	−	0.177304i
$431$	−54.4290	+	94.2738i	−0.126285	+	0.218733i	−0.922235	−	0.386631i	$-0.873639\pi$
$431$	−54.4290	+	94.2738i	−0.126285	+	0.218733i	0.795949	+	0.605363i	$0.206972\pi$
$432$	20.0764	+	5.37945i	0.0464731	+	0.0124524i
$433$	−449.174	−	449.174i	−1.03735	−	1.03735i	−0.999275	−	0.0380787i	$-0.987876\pi$
$433$	−449.174	−	449.174i	−1.03735	−	1.03735i	−0.0380787	−	0.999275i	$-0.512124\pi$
$434$	−152.547	−	23.6698i	−0.351491	−	0.0545387i
$435$	116.040	+	172.750i	0.266758	+	0.397127i
$436$	−43.4239	−	75.2125i	−0.0995962	−	0.172506i
$437$	−142.950	−	533.498i	−0.327118	−	1.22082i
$438$	252.034	−	67.5322i	0.575419	−	0.154183i
$439$	−97.0976	+	56.0593i	−0.221179	+	0.127698i	−0.606496	−	0.795086i	$-0.707425\pi$
$439$	−97.0976	+	56.0593i	−0.221179	+	0.127698i	0.385317	+	0.922784i	$0.374092\pi$
$440$	58.0256	−	38.9769i	0.131876	−	0.0885839i
$441$	31.4663	+	143.593i	0.0713521	+	0.325607i
$442$	39.0985	−	39.0985i	0.0884582	−	0.0884582i
$443$	−164.566	+	614.169i	−0.371481	+	1.38639i	0.486938	+	0.873437i	$0.338114\pi$
$443$	−164.566	+	614.169i	−0.371481	+	1.38639i	−0.858419	+	0.512950i	$0.828553\pi$
$444$	103.393	+	59.6940i	0.232867	+	0.134446i
$445$	−374.669	+	429.340i	−0.841953	+	0.964809i
$446$	87.5407	+	151.625i	0.196279	+	0.339966i
$447$	126.395	−	126.395i	0.282763	−	0.282763i
$448$	45.2013	−	33.0582i	0.100896	−	0.0737906i
$449$		−	199.822i		−	0.445038i	−0.974928	−	0.222519i	$-0.928572\pi$
$449$		−	199.822i		−	0.445038i	0.974928	−	0.222519i	$-0.0714279\pi$
$450$	64.1569	−	84.4624i	0.142571	−	0.187694i
$451$	−47.9007	+	82.9664i	−0.106210	+	0.183961i
$452$	94.5085	+	352.711i	0.209090	+	0.780333i
$453$	33.4820	−	124.956i	0.0739116	−	0.275842i
$454$			411.957i			0.907393i
$455$	−67.7553	−	381.530i	−0.148913	−	0.838528i
$456$	−151.879			−0.333068
$457$	−409.459	−	109.714i	−0.895971	−	0.240075i	−0.218686	−	0.975795i	$-0.570177\pi$
$457$	−409.459	−	109.714i	−0.895971	−	0.240075i	−0.677285	+	0.735720i	$0.736844\pi$
$458$	−89.2008	+	23.9013i	−0.194761	+	0.0521862i
$459$	−15.8917	−	9.17506i	−0.0346224	−	0.0199892i
$460$	−78.4050	+	159.974i	−0.170446	+	0.347769i
$461$	−768.361			−1.66673			−0.833364	−	0.552725i	$-0.813588\pi$
$461$	−768.361			−1.66673			−0.833364	+	0.552725i	$0.813588\pi$
$462$	−84.2581	+	9.12373i	−0.182377	+	0.0197483i
$463$	−2.18079	−	2.18079i	−0.00471013	−	0.00471013i	0.704748	−	0.709458i	$-0.251060\pi$
$463$	−2.18079	−	2.18079i	−0.00471013	−	0.00471013i	−0.709458	+	0.704748i	$0.751060\pi$
$464$	−83.2422	+	48.0599i	−0.179401	+	0.103577i
$465$	−9.16177	−	134.737i	−0.0197027	−	0.289756i
$466$	116.612	−	201.977i	0.250239	−	0.433427i
$467$	831.079	+	222.687i	1.77961	+	0.476846i	0.990513	−	0.137419i	$-0.0438808\pi$
$467$	831.079	+	222.687i	1.77961	+	0.476846i	0.789100	+	0.614265i	$0.210547\pi$
$468$	46.9721	+	46.9721i	0.100368	+	0.100368i
$469$	343.719	−	427.196i	0.732876	−	0.910866i
$470$	−218.055	−	42.8203i	−0.463948	−	0.0911071i
$471$	174.894	+	302.925i	0.371324	+	0.643153i
$472$	−11.4417	−	42.7010i	−0.0242409	−	0.0904682i
$473$	−78.2918	+	20.9782i	−0.165522	+	0.0443514i
$474$	58.0096	−	33.4919i	0.122383	−	0.0706579i
$475$	−293.098	+	717.499i	−0.617049	+	1.51052i
$476$	−46.1010	+	17.8630i	−0.0968508	+	0.0375272i
$477$	−220.663	+	220.663i	−0.462606	+	0.462606i
$478$	30.9776	−	115.610i	0.0648067	−	0.241862i
$479$	−440.106	−	254.095i	−0.918801	−	0.530470i	−0.0355485	−	0.999368i	$-0.511318\pi$
$479$	−440.106	−	254.095i	−0.918801	−	0.530470i	−0.883252	+	0.468898i	$0.844651\pi$
$480$	36.9113	+	32.2111i	0.0768985	+	0.0671065i
$481$	190.785	+	330.449i	0.396642	+	0.687003i
$482$	−440.537	+	440.537i	−0.913976	+	0.913976i
$483$	174.348	−	127.511i	0.360970	−	0.263997i
$484$			193.138i			0.399046i
$485$	309.105	−	630.683i	0.637330	−	1.30038i
$486$	11.0227	−	19.0919i	0.0226805	−	0.0392837i
$487$	−196.648	−	733.901i	−0.403795	−	1.50698i	−0.806268	−	0.591551i	$-0.798516\pi$
$487$	−196.648	−	733.901i	−0.403795	−	1.50698i	0.402473	−	0.915432i	$-0.368151\pi$
$488$	64.7040	−	241.479i	0.132590	−	0.494833i
$489$			286.731i			0.586363i
$490$	−82.3530	+	336.553i	−0.168067	+	0.686843i
$491$	−160.570			−0.327027			−0.163514	−	0.986541i	$-0.552283\pi$
$491$	−160.570			−0.327027			−0.163514	+	0.986541i	$0.552283\pi$
$492$	−64.8540	−	17.3776i	−0.131817	−	0.0353203i
$493$	81.9697	−	21.9637i	0.166267	−	0.0445512i
$494$	−420.380	−	242.706i	−0.850971	−	0.491308i
$495$	−24.0034	−	70.1483i	−0.0484918	−	0.141714i
$496$	62.3758			0.125758
$497$	246.778	+	337.425i	0.496535	+	0.678924i
$498$	−120.013	−	120.013i	−0.240990	−	0.240990i
$499$	53.3534	−	30.8036i	0.106921	−	0.0617307i	−0.445586	−	0.895239i	$-0.647005\pi$
$499$	53.3534	−	30.8036i	0.106921	−	0.0617307i	0.552507	+	0.833508i	$0.313671\pi$
$500$	223.402	−	112.213i	0.446803	−	0.224425i
$501$	159.209	−	275.758i	0.317782	−	0.550414i
$502$	−107.144	−	28.7091i	−0.213434	−	0.0571894i
$503$	10.2453	+	10.2453i	0.0203684	+	0.0203684i	0.717218	−	0.696849i	$-0.245415\pi$
$503$	10.2453	+	10.2453i	0.0203684	+	0.0203684i	−0.696849	+	0.717218i	$0.745415\pi$
$504$	−21.4602	−	55.3847i	−0.0425797	−	0.109890i
$505$	76.1049	−	387.552i	0.150703	−	0.767429i
$506$	62.2660	+	107.848i	0.123055	+	0.213138i
$507$	−20.8112	−	77.6683i	−0.0410476	−	0.153192i
$508$	416.956	−	111.723i	0.820779	−	0.219927i
$509$	−447.613	+	258.430i	−0.879398	+	0.507720i	−0.870460	−	0.492240i	$-0.836178\pi$
$509$	−447.613	+	258.430i	−0.879398	+	0.507720i	−0.00893787	+	0.999960i	$0.502845\pi$
$510$	−24.1171	−	35.9036i	−0.0472885	−	0.0703992i
$511$	−580.954	−	467.432i	−1.13690	−	0.914739i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−41.6937	+	155.603i	−0.0812744	+	0.303320i
$514$	−487.573	−	281.500i	−0.948586	−	0.547666i
$515$	30.7910	+	452.825i	0.0597884	+	0.879272i
$516$	−28.4029	−	49.1953i	−0.0550445	−	0.0953398i
$517$	−109.838	+	109.838i	−0.212453	+	0.212453i
$518$	−36.7293	−	339.197i	−0.0709059	−	0.654820i
$519$		−	51.2221i		−	0.0986938i
$520$	50.6910	+	148.141i	0.0974827	+	0.284886i
$521$	−319.243	+	552.945i	−0.612751	+	1.06132i	0.378024	+	0.925796i	$0.376604\pi$
$521$	−319.243	+	552.945i	−0.612751	+	1.06132i	−0.990775	+	0.135520i	$0.956730\pi$
$522$	26.3867	+	98.4765i	0.0505492	+	0.188652i
$523$	−178.051	+	664.497i	−0.340442	+	1.27055i	0.557405	+	0.830241i	$0.311797\pi$
$523$	−178.051	+	664.497i	−0.340442	+	1.27055i	−0.897847	+	0.440307i	$0.854870\pi$
$524$		−	388.861i		−	0.742102i
$525$	−303.059	−	5.50120i	−0.577255	−	0.0104785i
$526$	−573.208			−1.08975
$527$	−53.1933	−	14.2531i	−0.100936	−	0.0270457i
$528$	33.0776	−	8.86311i	0.0626470	−	0.0167862i
$529$	183.260	+	105.805i	0.346427	+	0.200010i
$530$	−695.929	+	238.134i	−1.31307	+	0.449310i
$531$	−46.8889			−0.0883031
$532$	256.219	+	350.335i	0.481615	+	0.658524i
$533$	−151.737	−	151.737i	−0.284684	−	0.284684i
$534$	−241.760	+	139.580i	−0.452734	+	0.261386i
$535$	395.490	−	26.8924i	0.739234	−	0.0502662i
$536$	−110.774	+	191.867i	−0.206669	+	0.357961i
$537$	361.541	+	96.8747i	0.673261	+	0.180400i
$538$	131.223	+	131.223i	0.243909	+	0.243909i
$539$	163.188	+	178.964i	0.302761	+	0.332029i
$540$	43.1338	−	28.9738i	0.0798773	−	0.0536551i
$541$	63.2590	+	109.568i	0.116930	+	0.202528i	0.918550	−	0.395306i	$-0.129361\pi$
$541$	63.2590	+	109.568i	0.116930	+	0.202528i	−0.801620	+	0.597834i	$0.796028\pi$
$542$	22.7485	+	84.8985i	0.0419714	+	0.156639i
$543$	231.334	−	61.9859i	0.426030	−	0.114154i
$544$	17.3007	−	9.98854i	0.0318027	−	0.0183613i
$545$	−213.051	−	41.8375i	−0.390919	−	0.0767661i
$546$	29.1073	−	187.591i	0.0533101	−	0.343572i
$547$	425.173	−	425.173i	0.777281	−	0.777281i	−0.202087	−	0.979368i	$-0.564772\pi$
$547$	425.173	−	425.173i	0.777281	−	0.777281i	0.979368	+	0.202087i	$0.0647723\pi$
$548$	−96.3552	+	359.602i	−0.175831	+	0.656209i
$549$	−229.637	−	132.581i	−0.418282	−	0.241495i
$550$	21.9629	−	173.367i	0.0399326	−	0.315213i
$551$	−372.491	−	645.173i	−0.676027	−	1.17091i
$552$	−61.7145	+	61.7145i	−0.111802	+	0.111802i
$553$	−175.116	−	77.3083i	−0.316666	−	0.139798i
$554$		−	126.998i		−	0.229238i
$555$	282.395	−	96.6303i	0.508820	−	0.174109i
$556$	202.296	−	350.387i	0.363842	−	0.630192i
$557$	3.95376	+	14.7556i	0.00709831	+	0.0264912i	0.969384	−	0.245549i	$-0.0789683\pi$
$557$	3.95376	+	14.7556i	0.00709831	+	0.0264912i	−0.962286	+	0.272040i	$0.912302\pi$
$558$	17.1234	−	63.9052i	0.0306870	−	0.114526i
$559$		−	181.554i		−	0.324784i
$560$	12.0312	−	139.482i	0.0214843	−	0.249075i
$561$	−30.2334			−0.0538920
$562$	−4.46733	−	1.19702i	−0.00794899	−	0.00212992i
$563$	229.658	−	61.5366i	0.407918	−	0.109301i	−0.0490246	−	0.998798i	$-0.515611\pi$
$563$	229.658	−	61.5366i	0.407918	−	0.109301i	0.456942	+	0.889496i	$0.348945\pi$
$564$	−94.2800	−	54.4326i	−0.167163	−	0.0965117i
$565$	819.723	+	401.756i	1.45084	+	0.711072i
$566$	−288.824			−0.510290
$567$	−62.6339	+	6.78219i	−0.110465	+	0.0119615i
$568$	−119.439	−	119.439i	−0.210280	−	0.210280i
$569$	−179.993	+	103.919i	−0.316331	+	0.182634i	−0.649756	−	0.760143i	$-0.725129\pi$
$569$	−179.993	+	103.919i	−0.316331	+	0.182634i	0.333425	+	0.942777i	$0.391796\pi$
$570$	−249.654	+	286.083i	−0.437990	+	0.501900i
$571$	−214.885	+	372.192i	−0.376331	+	0.651824i	−0.990525	−	0.137331i	$-0.956148\pi$
$571$	−214.885	+	372.192i	−0.376331	+	0.651824i	0.614194	+	0.789155i	$0.289481\pi$
$572$	105.717	+	28.3269i	0.184821	+	0.0495226i
$573$	−188.092	−	188.092i	−0.328259	−	0.328259i
$574$	69.3240	+	178.912i	0.120774	+	0.311694i
$575$	172.451	+	410.645i	0.299914	+	0.714165i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−95.6927	−	357.130i	−0.165845	−	0.618943i	−0.997931	−	0.0642958i	$-0.979520\pi$
$577$	−95.6927	−	357.130i	−0.165845	−	0.618943i	0.832086	−	0.554647i	$-0.187147\pi$
$578$	377.745	−	101.217i	0.653538	−	0.175115i
$579$	466.862	−	269.543i	0.806325	−	0.465532i
$580$	−46.3041	+	235.796i	−0.0798347	+	0.406545i
$581$	−74.3688	+	479.291i	−0.128001	+	0.824941i
$582$	243.304	−	243.304i	0.418048	−	0.418048i
$583$	−133.073	+	496.635i	−0.228255	+	0.851861i
$584$	260.924	+	150.645i	0.446788	+	0.257953i
$585$	165.689	−	11.2664i	0.283229	−	0.0192589i
$586$	−269.541	−	466.859i	−0.459968	−	0.796687i
$587$	425.963	−	425.963i	0.725661	−	0.725661i	−0.244091	−	0.969752i	$-0.578490\pi$
$587$	425.963	−	425.963i	0.725661	−	0.725661i	0.969752	+	0.244091i	$0.0784897\pi$
$588$	−91.5509	+	142.935i	−0.155699	+	0.243087i
$589$			483.447i			0.820794i
$590$	−99.2400	−	48.6387i	−0.168203	−	0.0824384i
$591$	82.7447	−	143.318i	0.140008	−	0.242501i
$592$	35.6801	+	133.160i	0.0602705	+	0.224932i
$593$	49.0753	−	183.152i	0.0827577	−	0.308856i	−0.912122	−	0.409918i	$-0.865557\pi$
$593$	49.0753	−	183.152i	0.0827577	−	0.308856i	0.994880	+	0.101062i	$0.0322240\pi$
$594$		−	36.3217i		−	0.0611477i
$595$	−42.1322	+	116.199i	−0.0708105	+	0.195293i
$596$	206.402			0.346312
$597$	−540.714	−	144.884i	−0.905718	−	0.242686i
$598$	−269.438	+	72.1956i	−0.450565	+	0.120729i
$599$	238.166	+	137.505i	0.397605	+	0.229557i	0.685450	−	0.728120i	$-0.259605\pi$
$599$	238.166	+	137.505i	0.397605	+	0.229557i	−0.287845	+	0.957677i	$0.592939\pi$
$600$	121.347	−	16.5793i	0.202245	−	0.0276322i
$601$	−1029.92			−1.71368			−0.856842	−	0.515580i	$-0.827577\pi$
$601$	−1029.92			−1.71368			−0.856842	+	0.515580i	$0.827577\pi$
$602$	−65.5617	+	148.508i	−0.108906	+	0.246692i
$603$	166.162	+	166.162i	0.275558	+	0.275558i
$604$	129.364	−	74.6886i	0.214179	−	0.123657i
$605$	363.799	+	317.474i	0.601321	+	0.524751i
$606$	96.7435	−	167.565i	0.159643	−	0.276509i
$607$	−25.4962	−	6.83168i	−0.0420036	−	0.0112548i	0.237756	−	0.971325i	$-0.423588\pi$
$607$	−25.4962	−	6.83168i	−0.0420036	−	0.0112548i	−0.279760	+	0.960070i	$0.590255\pi$
$608$	−124.009	−	124.009i	−0.203962	−	0.203962i
$609$	182.638	−	226.995i	0.299899	−	0.372734i
$610$	−348.496	−	518.812i	−0.571305	−	0.850512i
$611$	−173.969	−	301.323i	−0.284728	−	0.493164i
$612$	−5.48409	−	20.4669i	−0.00896093	−	0.0334426i
$613$	33.5012	−	8.97661i	0.0546511	−	0.0146437i	−0.231390	−	0.972861i	$-0.574327\pi$
$613$	33.5012	−	8.97661i	0.0546511	−	0.0146437i	0.286041	+	0.958217i	$0.407661\pi$
$614$	290.070	−	167.472i	0.472427	−	0.272756i
$615$	−139.338	+	93.5957i	−0.226565	+	0.152188i
$616$	−76.2460	−	61.3470i	−0.123776	−	0.0995893i
$617$	349.027	−	349.027i	0.565684	−	0.565684i	−0.365232	−	0.930916i	$-0.619011\pi$
$617$	349.027	−	349.027i	0.565684	−	0.565684i	0.930916	+	0.365232i	$0.119011\pi$
$618$	−57.5485	+	214.774i	−0.0931205	+	0.347530i
$619$	942.217	+	543.989i	1.52216	+	0.878820i	0.999657	+	0.0261820i	$0.00833493\pi$
$619$	942.217	+	543.989i	1.52216	+	0.878820i	0.522503	+	0.852638i	$0.324998\pi$
$620$	102.531	−	117.492i	0.165373	−	0.189504i
$621$	46.2859	+	80.1695i	0.0745344	+	0.129097i
$622$	550.733	−	550.733i	0.885422	−	0.885422i
$623$	729.812	+	322.189i	1.17145	+	0.517157i
$624$			76.7050i			0.122925i
$625$	155.854	−	605.256i	0.249367	−	0.968409i
$626$	200.655	−	347.544i	0.320535	−	0.555183i
$627$	68.6940	+	256.370i	0.109560	+	0.408883i
$628$	−104.537	+	390.137i	−0.166460	+	0.621238i
$629$		−	121.710i		−	0.193498i
$630$	−139.599	−	50.6167i	−0.221586	−	0.0803440i
$631$	573.080			0.908209			0.454104	−	0.890949i	$-0.349959\pi$
$631$	573.080			0.908209			0.454104	+	0.890949i	$0.349959\pi$
$632$	74.7106	+	20.0187i	0.118213	+	0.0316751i
$633$	−547.571	+	146.721i	−0.865041	+	0.231787i
$634$	−461.947	−	266.705i	−0.728623	−	0.420671i
$635$	474.934	−	969.033i	0.747928	−	1.52604i
$636$	−360.342			−0.566575
$637$	−481.813	+	249.323i	−0.756378	+	0.391402i
$638$	118.774	+	118.774i	0.186167	+	0.186167i
$639$	−155.156	+	89.5794i	−0.242811	+	0.140187i
$640$	3.83767	+	56.4382i	0.00599636	+	0.0881847i
$641$	515.594	−	893.035i	0.804359	−	1.39319i	−0.112364	−	0.993667i	$-0.535842\pi$
$641$	515.594	−	893.035i	0.804359	−	1.39319i	0.916723	−	0.399523i	$-0.130824\pi$
$642$	187.580	+	50.2619i	0.292181	+	0.0782896i
$643$	413.439	+	413.439i	0.642985	+	0.642985i	0.951288	−	0.308303i	$-0.0997612\pi$
$643$	413.439	+	413.439i	0.642985	+	0.642985i	−0.308303	+	0.951288i	$0.599761\pi$
$644$	246.467	+	38.2428i	0.382712	+	0.0593833i
$645$	−139.353	−	27.3653i	−0.216052	−	0.0424268i
$646$	77.4167	+	134.090i	0.119840	+	0.207569i
$647$	−196.283	−	732.536i	−0.303373	−	1.13220i	−0.934337	−	0.356392i	$-0.884007\pi$
$647$	−196.283	−	732.536i	−0.303373	−	1.13220i	0.630963	−	0.775813i	$-0.282660\pi$
$648$	24.5885	−	6.58846i	0.0379452	−	0.0101674i
$649$	−66.9036	+	38.6268i	−0.103087	+	0.0595174i
$650$	362.365	+	148.026i	0.557485	+	0.227733i
$651$	−176.295	+	68.3099i	−0.270807	+	0.104931i
$652$	−234.115	+	234.115i	−0.359072	+	0.359072i
$653$	−190.326	+	710.307i	−0.291464	+	1.08776i	0.652521	+	0.757771i	$0.273712\pi$
$653$	−190.326	+	710.307i	−0.291464	+	1.08776i	−0.943985	+	0.329988i	$0.892955\pi$
$654$	−92.1161	−	53.1832i	−0.140850	−	0.0813199i
$655$	−732.468	−	639.198i	−1.11827	−	0.975874i
$656$	−38.7643	−	67.1418i	−0.0590920	−	0.102350i
$657$	225.967	−	225.967i	0.343938	−	0.343938i
$658$	33.4919	+	309.300i	0.0508996	+	0.470061i
$659$			913.700i			1.38650i	0.720700	+	0.693248i	$0.243821\pi$
$659$			913.700i			1.38650i	−0.720700	+	0.693248i	$0.756179\pi$
$660$	37.6771	−	76.8746i	0.0570865	−	0.116477i
$661$	−27.1929	+	47.0994i	−0.0411390	+	0.0712548i	−0.885862	−	0.463949i	$-0.846432\pi$
$661$	−27.1929	+	47.0994i	−0.0411390	+	0.0712548i	0.844723	+	0.535204i	$0.179765\pi$
$662$	149.109	+	556.484i	0.225241	+	0.840610i
$663$	17.5274	−	65.4131i	0.0264365	−	0.0986623i
$664$		−	195.980i		−	0.295151i
$665$	1081.06	+	93.2487i	1.62566	+	0.140224i
$666$	146.220			0.219549
$667$	−413.517	−	110.801i	−0.619965	−	0.166119i
$668$	355.148	−	95.1617i	0.531659	−	0.142458i
$669$	185.702	+	107.215i	0.277581	+	0.160262i
$670$	179.317	+	524.042i	0.267638	+	0.782152i
$671$	−436.877			−0.651084
$672$	27.6993	−	62.7435i	0.0412191	−	0.0933684i
$673$	−93.9180	−	93.9180i	−0.139551	−	0.139551i	0.633880	−	0.773431i	$-0.281461\pi$
$673$	−93.9180	−	93.9180i	−0.139551	−	0.139551i	−0.773431	+	0.633880i	$0.781461\pi$
$674$	−89.5626	+	51.7090i	−0.132882	+	0.0767196i
$675$	16.3263	−	128.874i	0.0241871	−	0.190924i
$676$	46.4237	−	80.4081i	0.0686741	−	0.118947i
$677$	−227.229	−	60.8859i	−0.335642	−	0.0899349i	0.0870620	−	0.996203i	$-0.472252\pi$
$677$	−227.229	−	60.8859i	−0.335642	−	0.0899349i	−0.422704	+	0.906268i	$0.638919\pi$
$678$	316.232	+	316.232i	0.466418	+	0.466418i
$679$	−971.674	−	150.769i	−1.43104	−	0.222046i
$680$	9.62362	−	49.0067i	0.0141524	−	0.0720687i
$681$	252.271	+	436.946i	0.370442	+	0.641624i
$682$	−28.2122	−	105.289i	−0.0413669	−	0.154383i
$683$	−523.038	+	140.148i	−0.765795	+	0.205194i	−0.620513	−	0.784196i	$-0.713076\pi$
$683$	−523.038	+	140.148i	−0.765795	+	0.205194i	−0.145282	+	0.989390i	$0.546409\pi$
$684$	−161.092	+	93.0067i	−0.235515	+	0.135975i
$685$	518.969	+	772.599i	0.757619	+	1.12788i
$686$	484.150	−	29.9532i	0.705757	−	0.0436636i
$687$	−79.9752	+	79.9752i	−0.116412	+	0.116412i
$688$	16.9769	−	63.3587i	0.0246758	−	0.0920912i
$689$	−997.373	−	575.834i	−1.44757	−	0.835753i
$690$	14.8025	+	217.691i	0.0214529	+	0.315494i
$691$	−245.831	−	425.792i	−0.355761	−	0.616196i	0.631487	−	0.775387i	$-0.282445\pi$
$691$	−245.831	−	425.792i	−0.355761	−	0.616196i	−0.987248	+	0.159190i	$0.949112\pi$
$692$	41.8227	−	41.8227i	0.0604374	−	0.0604374i
$693$	−83.7821	+	61.2745i	−0.120898	+	0.0884192i
$694$			681.189i			0.981540i
$695$	−327.469	−	957.003i	−0.471178	−	1.37698i
$696$	−58.8611	+	101.950i	−0.0845705	+	0.146480i
$697$	17.7156	+	66.1155i	0.0254169	+	0.0948572i
$698$	−60.7418	+	226.692i	−0.0870226	+	0.324773i
$699$		−	285.639i		−	0.408639i
$700$	−242.955	−	251.938i	−0.347078	−	0.359912i
$701$	−372.833			−0.531858			−0.265929	−	0.963993i	$-0.585679\pi$
$701$	−372.833			−0.531858			−0.265929	+	0.963993i	$0.585679\pi$
$702$	78.5858	+	21.0570i	0.111946	+	0.0299957i
$703$	−1032.06	+	276.541i	−1.46809	+	0.393372i
$704$	34.2444	+	19.7710i	0.0486427	+	0.0280839i
$705$	−257.505	+	88.1133i	−0.365255	+	0.124983i
$706$	−89.2954			−0.126481
$707$	−549.722	+	59.5255i	−0.777541	+	0.0841945i
$708$	−38.2847	−	38.2847i	−0.0540744	−	0.0540744i
$709$	−471.040	+	271.955i	−0.664372	+	0.383575i	−0.793941	−	0.607995i	$-0.791974\pi$
$709$	−471.040	+	271.955i	−0.664372	+	0.383575i	0.129569	+	0.991570i	$0.458641\pi$
$710$	−421.308	+	28.6480i	−0.593392	+	0.0403493i
$711$	41.0190	−	71.0470i	0.0576920	−	0.0999254i
$712$	−311.363	−	83.4294i	−0.437307	−	0.117176i
$713$	196.444	+	196.444i	0.275517	+	0.275517i
$714$	−37.9587	+	47.1775i	−0.0531634	+	0.0660749i
$715$	227.132	−	152.569i	0.317667	−	0.213383i
$716$	216.099	+	374.295i	0.301815	+	0.522758i
$717$	−37.9396	−	141.593i	−0.0529144	−	0.197479i
$718$	221.473	−	59.3434i	0.308458	−	0.0826510i
$719$	479.506	−	276.843i	0.666906	−	0.385039i	−0.127997	−	0.991775i	$-0.540855\pi$
$719$	479.506	−	276.843i	0.666906	−	0.385039i	0.794903	+	0.606736i	$0.207521\pi$
$720$	58.8755	+	11.5616i	0.0817716	+	0.0160578i
$721$	592.496	−	229.577i	0.821770	−	0.318415i
$722$	600.138	−	600.138i	0.831215	−	0.831215i
$723$	−197.487	+	737.032i	−0.273150	+	1.01941i
$724$	239.495	+	138.273i	0.330794	+	0.190984i
$725$	368.037	+	474.813i	0.507638	+	0.654915i
$726$	118.273	+	204.854i	0.162910	+	0.282168i
$727$	544.208	−	544.208i	0.748566	−	0.748566i	−0.225644	−	0.974210i	$-0.572449\pi$
$727$	544.208	−	544.208i	0.748566	−	0.748566i	0.974210	+	0.225644i	$0.0724485\pi$
$728$	176.933	−	129.401i	0.243040	−	0.177749i
$729$		−	27.0000i		−	0.0370370i
$730$	712.657	−	243.858i	0.976242	−	0.334052i
$731$	−28.9554	+	50.1522i	−0.0396107	+	0.0686077i
$732$	−79.2459	−	295.750i	−0.108259	−	0.404030i
$733$	7.94468	−	29.6500i	0.0108386	−	0.0404501i	−0.960295	−	0.278987i	$-0.910001\pi$
$733$	7.94468	−	29.6500i	0.0108386	−	0.0404501i	0.971133	+	0.238537i	$0.0766679\pi$
$734$		−	27.2314i		−	0.0371001i
$735$	118.747	+	407.399i	0.161561	+	0.554285i
$736$	−100.779			−0.136928
$737$	373.971	+	100.205i	0.507423	+	0.135964i
$738$	−79.4296	+	21.2831i	−0.107628	+	0.0288389i
$739$	−70.2506	−	40.5592i	−0.0950616	−	0.0548839i	0.451716	−	0.892162i	$-0.350812\pi$
$739$	−70.2506	−	40.5592i	−0.0950616	−	0.0548839i	−0.546777	+	0.837278i	$0.684146\pi$
$740$	309.473	+	151.676i	0.418207	+	0.204968i
$741$	−594.507			−0.802303
$742$	607.894	+	831.188i	0.819265	+	1.12020i
$743$	824.672	+	824.672i	1.10992	+	1.10992i	0.993160	+	0.116761i	$0.0372513\pi$
$743$	824.672	+	824.672i	1.10992	+	1.10992i	0.116761	+	0.993160i	$0.462749\pi$
$744$	66.1596	−	38.1972i	0.0889242	−	0.0513404i
$745$	339.277	−	388.783i	0.455405	−	0.521857i
$746$	239.265	−	414.420i	0.320731	−	0.555522i
$747$	−200.785	−	53.8003i	−0.268789	−	0.0720218i
$748$	−24.6855	−	24.6855i	−0.0330020	−	0.0330020i
$749$	−200.509	−	517.477i	−0.267702	−	0.690890i
$750$	168.237	−	255.825i	0.224316	−	0.341099i
$751$	91.6006	+	158.657i	0.121972	+	0.211261i	0.920545	−	0.390636i	$-0.127745\pi$
$751$	91.6006	+	158.657i	0.121972	+	0.211261i	−0.798574	+	0.601897i	$0.794412\pi$
$752$	−32.5353	−	121.423i	−0.0432650	−	0.161467i
$753$	−131.224	+	35.1613i	−0.174268	+	0.0466950i
$754$	−325.838	+	188.123i	−0.432146	+	0.249500i
$755$	71.9600	−	366.444i	0.0953112	−	0.485357i
$756$	−56.6780	−	45.6027i	−0.0749709	−	0.0603210i
$757$	298.331	−	298.331i	0.394096	−	0.394096i	−0.482048	−	0.876145i	$-0.660107\pi$
$757$	298.331	−	298.331i	0.394096	−	0.394096i	0.876145	+	0.482048i	$0.160107\pi$
$758$	194.435	−	725.642i	0.256511	−	0.957312i
$759$	132.086	+	76.2600i	0.174027	+	0.100474i
$760$	−437.427	+	29.7441i	−0.575562	+	0.0391369i
$761$	16.0986	+	27.8836i	0.0211546	+	0.0366408i	0.876409	−	0.481568i	$-0.159932\pi$
$761$	16.0986	+	27.8836i	0.0211546	+	0.0366408i	−0.855254	+	0.518208i	$0.826599\pi$
$762$	373.832	−	373.832i	0.490594	−	0.490594i
$763$	32.7232	+	302.201i	0.0428876	+	0.396069i
$764$		−	307.153i		−	0.402033i
$765$	−47.5664	−	23.3129i	−0.0621784	−	0.0304743i
$766$	70.6020	−	122.286i	0.0921698	−	0.159643i
$767$	−44.7867	−	167.146i	−0.0583920	−	0.217922i
$768$	−7.17260	+	26.7685i	−0.00933933	+	0.0348548i
$769$			210.008i			0.273092i	0.990634	+	0.136546i	$0.0436002\pi$
$769$			210.008i			0.273092i	−0.990634	+	0.136546i	$0.956400\pi$
$770$	−240.885	+	42.7784i	−0.312838	+	0.0555563i
$771$	−689.532			−0.894335
$772$	601.272	+	161.110i	0.778850	+	0.208692i
$773$	339.317	−	90.9196i	0.438961	−	0.117619i	−0.0325686	−	0.999470i	$-0.510369\pi$
$773$	339.317	−	90.9196i	0.438961	−	0.117619i	0.471529	+	0.881850i	$0.343702\pi$
$774$	−60.2518	−	34.7864i	−0.0778446	−	0.0449436i
$775$	−52.7737	−	386.261i	−0.0680950	−	0.498401i
$776$	397.314			0.512002
$777$	−246.672	−	337.281i	−0.317467	−	0.434081i
$778$	−609.695	−	609.695i	−0.783670	−	0.783670i
$779$	520.386	−	300.445i	0.668018	−	0.385680i
$780$	144.483	+	126.085i	0.185235	+	0.161648i
$781$	−147.590	+	255.633i	−0.188975	+	0.327315i
$782$	85.9433	+	23.0284i	0.109902	+	0.0294481i
$783$	88.2916	+	88.2916i	0.112761	+	0.112761i
$784$	−191.457	+	41.9550i	−0.244205	+	0.0535140i
$785$	563.037	+	838.203i	0.717244	+	1.06777i
$786$	−238.128	−	412.450i	−0.302962	−	0.524745i
$787$	190.980	+	712.746i	0.242668	+	0.905649i	0.974541	+	0.224209i	$0.0719797\pi$
$787$	190.980	+	712.746i	0.242668	+	0.905649i	−0.731873	+	0.681441i	$0.761354\pi$
$788$	184.579	−	49.4579i	0.234238	−	0.0627639i
$789$	−607.979	+	351.017i	−0.770569	+	0.444888i
$790$	160.514	−	107.821i	0.203183	−	0.136482i
$791$	195.960	−	1262.92i	0.247737	−	1.59662i
$792$	29.6566	−	29.6566i	0.0374451	−	0.0374451i
$793$	253.273	−	945.229i	0.319386	−	1.19197i
$794$	822.920	+	475.113i	1.03642	+	0.598379i
$795$	−592.318	+	678.747i	−0.745054	+	0.853770i
$796$	−323.194	−	559.788i	−0.406022	−	0.703251i
$797$	−34.9409	+	34.9409i	−0.0438406	+	0.0438406i	−0.728687	−	0.684847i	$-0.759869\pi$
$797$	−34.9409	+	34.9409i	−0.0438406	+	0.0438406i	0.684847	+	0.728687i	$0.259869\pi$
$798$	486.297	+	214.685i	0.609395	+	0.269028i
$799$			110.983i			0.138902i
$800$	112.616	+	85.5426i	0.140771	+	0.106928i
$801$	−170.950	+	296.094i	−0.213421	+	0.369655i
$802$	222.613	+	830.804i	0.277573	+	1.03592i
$803$	136.271	−	508.572i	0.169703	−	0.633340i
$804$			271.341i			0.337489i
$805$	477.169	−	401.388i	0.592757	−	0.498618i
$806$	244.160			0.302928
$807$	219.540	+	58.8257i	0.272045	+	0.0728943i
$808$	215.807	−	57.8252i	0.267087	−	0.0715659i
$809$	226.253	+	130.627i	0.279670	+	0.161468i	0.633274	−	0.773928i	$-0.281711\pi$
$809$	226.253	+	130.627i	0.279670	+	0.161468i	−0.353604	+	0.935395i	$0.615044\pi$
$810$	28.0075	−	57.1452i	0.0345772	−	0.0705497i
$811$	1476.16			1.82018			0.910089	−	0.414413i	$-0.136013\pi$
$811$	1476.16			1.82018			0.910089	+	0.414413i	$0.136013\pi$
$812$	334.464	−	36.2168i	0.411902	−	0.0446019i
$813$	76.1179	+	76.1179i	0.0936260	+	0.0936260i
$814$	208.634	−	120.455i	0.256307	−	0.147979i
$815$	56.1535	+	825.815i	0.0689001	+	1.01327i
$816$	12.2334	−	21.1889i	0.0149919	−	0.0259668i
$817$	491.065	+	131.581i	0.601059	+	0.161053i
$818$	372.058	+	372.058i	0.454839	+	0.454839i
$819$	−84.0023	−	216.794i	−0.102567	−	0.264706i
$820$	−190.189	−	37.3481i	−0.231938	−	0.0455465i
$821$	−644.418	−	1116.16i	−0.784918	−	1.35952i	−0.929048	−	0.369959i	$-0.879372\pi$
$821$	−644.418	−	1116.16i	−0.784918	−	1.35952i	0.144130	−	0.989559i	$-0.453962\pi$
$822$	118.011	+	440.421i	0.143565	+	0.535792i
$823$	−124.816	+	33.4443i	−0.151660	+	0.0406371i	−0.333850	−	0.942626i	$-0.608348\pi$
$823$	−124.816	+	33.4443i	−0.151660	+	0.0406371i	0.182190	+	0.983263i	$0.441681\pi$
$824$	−222.350	+	128.374i	−0.269843	+	0.155794i
$825$	−82.8702	−	197.333i	−0.100449	−	0.239192i
$826$	−23.7240	+	152.896i	−0.0287215	+	0.185104i
$827$	−830.887	+	830.887i	−1.00470	+	1.00470i	−0.00471131	+	0.999989i	$0.501500\pi$
$827$	−830.887	+	830.887i	−1.00470	+	1.00470i	−0.999989	+	0.00471131i	$0.998500\pi$
$828$	−27.6658	+	103.250i	−0.0334129	+	0.124698i
$829$	371.475	+	214.471i	0.448100	+	0.258711i	0.707027	−	0.707186i	$-0.250036\pi$
$829$	371.475	+	214.471i	0.448100	+	0.258711i	−0.258928	+	0.965897i	$0.583369\pi$
$830$	−369.153	−	322.146i	−0.444762	−	0.388127i
$831$	−77.7699	−	134.701i	−0.0935859	−	0.162096i
$832$	−62.6294	+	62.6294i	−0.0752757	+	0.0752757i
$833$	172.859	+	7.96992i	0.207514	+	0.00956773i
$834$		−	495.522i		−	0.594151i
$835$	404.533	−	825.389i	0.484470	−	0.988490i
$836$	−153.237	+	265.413i	−0.183297	+	0.317480i
$837$	−20.9717	−	78.2676i	−0.0250558	−	0.0935097i
$838$	−123.777	+	461.944i	−0.147706	+	0.551245i
$839$			1335.08i			1.59127i	0.605775	+	0.795636i	$0.292863\pi$
$839$			1335.08i			1.59127i	−0.605775	+	0.795636i	$0.707137\pi$
$840$	−72.6539	−	155.311i	−0.0864928	−	0.184894i
$841$	263.562			0.313391
$842$	18.7588	+	5.02642i	0.0222789	+	0.00596962i
$843$	−5.47134	+	1.46604i	−0.00649032	+	0.00173908i
$844$	−566.887	−	327.292i	−0.671667	−	0.387787i
$845$	−75.1488	−	219.617i	−0.0889335	−	0.259902i
$846$	−133.332			−0.157603
$847$	273.005	−	618.403i	0.322320	−	0.730110i
$848$	−294.218	−	294.218i	−0.346955	−	0.346955i
$849$	−306.344	+	176.868i	−0.360829	+	0.208325i
$850$	−76.4911	−	98.6829i	−0.0899895	−	0.116098i
$851$	−306.999	+	531.737i	−0.360750	+	0.624838i
$852$	−199.826	−	53.5431i	−0.234537	−	0.0628440i
$853$	−650.928	−	650.928i	−0.763104	−	0.763104i	0.213778	−	0.976882i	$-0.431423\pi$
$853$	−650.928	−	650.928i	−0.763104	−	0.763104i	−0.976882	+	0.213778i	$0.931423\pi$
$854$	−548.509	+	681.722i	−0.642282	+	0.798269i
$855$	−89.6088	+	456.318i	−0.104806	+	0.533705i
$856$	112.120	+	194.197i	0.130981	+	0.226866i
$857$	−181.493	−	677.342i	−0.211777	−	0.790364i	−0.987276	−	0.159015i	$-0.949168\pi$
$857$	−181.493	−	677.342i	−0.211777	−	0.790364i	0.775499	−	0.631349i	$-0.217499\pi$
$858$	129.477	−	34.6932i	0.150905	−	0.0404350i
$859$	267.011	−	154.159i	0.310839	−	0.179463i	−0.336463	−	0.941697i	$-0.609231\pi$
$859$	267.011	−	154.159i	0.310839	−	0.179463i	0.647302	+	0.762234i	$0.275897\pi$
$860$	−91.4378	−	136.125i	−0.106323	−	0.158285i
$861$	183.090	+	147.313i	0.212648	+	0.171095i
$862$	−108.858	+	108.858i	−0.126285	+	0.126285i
$863$	−325.107	+	1213.32i	−0.376717	+	1.40593i	0.474102	+	0.880470i	$0.342773\pi$
$863$	−325.107	+	1213.32i	−0.376717	+	1.40593i	−0.850819	+	0.525458i	$0.823894\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	−10.0313	−	147.525i	−0.0115969	−	0.170549i
$866$	−449.174	−	777.992i	−0.518677	−	0.898374i
$867$	338.677	−	338.677i	0.390631	−	0.390631i
$868$	−199.719	−	88.1696i	−0.230091	−	0.101578i
$869$		−	135.165i		−	0.155540i
$870$	95.2820	+	278.455i	0.109520	+	0.320063i
$871$	−433.609	+	751.032i	−0.497829	+	0.862265i
$872$	−31.7885	−	118.636i	−0.0364547	−	0.136051i
$873$	109.070	−	407.056i	0.124937	−	0.466272i
$874$		−	781.096i		−	0.893702i
$875$	−873.918	+	43.5071i	−0.998763	+	0.0497224i
$876$	369.003			0.421236
$877$	−1315.76	−	352.556i	−1.50029	−	0.402002i	−0.587094	−	0.809518i	$-0.699728\pi$
$877$	−1315.76	−	352.556i	−1.50029	−	0.402002i	−0.913198	+	0.407516i	$0.866395\pi$
$878$	−153.157	+	41.0383i	−0.174438	+	0.0467406i
$879$	−571.783	−	330.119i	−0.650492	−	0.375562i
$880$	93.5310	−	32.0046i	0.106285	−	0.0363688i
$881$	−717.855			−0.814818			−0.407409	−	0.913246i	$-0.633568\pi$
$881$	−717.855			−0.814818			−0.407409	+	0.913246i	$0.633568\pi$
$882$	−9.57488	+	207.669i	−0.0108559	+	0.235452i
$883$	−385.364	−	385.364i	−0.436426	−	0.436426i	0.454381	−	0.890807i	$-0.349860\pi$
$883$	−385.364	−	385.364i	−0.436426	−	0.436426i	−0.890807	+	0.454381i	$0.849860\pi$
$884$	67.7206	−	39.0985i	0.0766070	−	0.0442291i
$885$	−135.045	+	9.18274i	−0.152593	+	0.0103760i
$886$	−449.603	+	778.735i	−0.507453	+	0.878934i
$887$	−160.446	−	42.9913i	−0.180886	−	0.0484682i	0.167239	−	0.985916i	$-0.446515\pi$
$887$	−160.446	−	42.9913i	−0.180886	−	0.0484682i	−0.348125	+	0.937448i	$0.613181\pi$
$888$	119.388	+	119.388i	0.134446	+	0.134446i
$889$	−1492.96	−	231.654i	−1.67937	−	0.260578i
$890$	−668.957	+	449.351i	−0.751637	+	0.504889i
$891$	−22.2424	−	38.5250i	−0.0249634	−	0.0432379i
$892$	64.0842	+	239.166i	0.0718433	+	0.268123i
$893$	941.098	−	252.166i	1.05386	−	0.282381i
$894$	218.922	−	126.395i	0.244880	−	0.141381i
$895$	1060.25	+	208.205i	1.18463	+	0.232631i
$896$	73.8462	−	28.6135i	0.0824177	−	0.0319347i
$897$	−241.571	+	241.571i	−0.269310	+	0.269310i
$898$	73.1399	−	272.962i	0.0814476	−	0.303966i
$899$	324.519	+	187.361i	0.360977	+	0.208410i
$900$	118.555	−	91.8947i	0.131728	−	0.102105i
$901$	183.675	+	318.135i	0.203857	+	0.353091i
$902$	−95.8014	+	95.8014i	−0.106210	+	0.106210i
$903$	21.4038	+	197.665i	0.0237030	+	0.218898i
$904$			516.404i			0.571244i
$905$	654.127	−	223.830i	0.722792	−	0.247326i
$906$	91.4745	−	158.438i	0.100965	−	0.174877i
$907$	376.838	+	1406.38i	0.415478	+	1.55058i	0.783877	+	0.620916i	$0.213239\pi$
$907$	376.838	+	1406.38i	0.415478	+	1.55058i	−0.368400	+	0.929668i	$0.620094\pi$
$908$	−150.787	+	562.743i	−0.166064	+	0.619761i
$909$		−	236.972i		−	0.260695i
$910$	47.0943	−	545.980i	0.0517519	−	0.599978i
$911$	−1585.71			−1.74062			−0.870311	−	0.492502i	$-0.836082\pi$
$911$	−1585.71			−1.74062			−0.870311	+	0.492502i	$0.836082\pi$
$912$	−207.471	−	55.5917i	−0.227490	−	0.0609558i
$913$	−330.811	+	88.6406i	−0.362335	+	0.0970872i
$914$	−519.173	−	299.745i	−0.568023	−	0.327948i
$915$	−687.342	−	336.874i	−0.751194	−	0.368169i
$916$	−130.599			−0.142575
$917$	−549.664	+	1245.08i	−0.599415	+	1.35778i
$918$	−18.3501	−	18.3501i	−0.0199892	−	0.0199892i
$919$	255.071	−	147.266i	0.277553	−	0.160245i	−0.354762	−	0.934957i	$-0.615438\pi$
$919$	255.071	−	147.266i	0.277553	−	0.160245i	0.632315	+	0.774711i	$0.282105\pi$
$920$	−165.658	+	189.830i	−0.180063	+	0.206337i
$921$	205.110	−	355.262i	0.222704	−	0.385735i
$922$	−1049.60	−	281.240i	−1.13840	−	0.305032i
$923$	−467.525	−	467.525i	−0.506528	−	0.506528i
$924$	−118.438	−	18.3774i	−0.128180	−	0.0198889i
$925$	794.402	−	333.609i	0.858813	−	0.360659i
$926$	−2.18079	−	3.77724i	−0.00235507	−	0.00407909i
$927$	70.4822	+	263.043i	0.0760326	+	0.283757i
$928$	−131.302	+	35.1823i	−0.141489	+	0.0379119i
$929$	−910.483	+	525.668i	−0.980068	+	0.565842i	−0.902291	−	0.431128i	$-0.858116\pi$
$929$	−910.483	+	525.668i	−0.980068	+	0.565842i	−0.0777771	+	0.996971i	$0.524782\pi$
$930$	36.8018	−	187.407i	0.0395718	−	0.201513i
$931$	−325.175	−	1483.90i	−0.349275	−	1.59388i
$932$	233.223	−	233.223i	0.250239	−	0.250239i
$933$	246.887	−	921.394i	0.264616	−	0.987560i
$934$	1053.77	+	608.392i	1.12823	+	0.651383i
$935$	−87.0753	+	5.92092i	−0.0931286	+	0.00633253i
$936$	46.9721	+	81.3580i	0.0501838	+	0.0869209i
$937$	−839.139	+	839.139i	−0.895559	+	0.895559i	−0.995040	−	0.0994803i	$-0.968282\pi$
$937$	−839.139	+	839.139i	−0.895559	+	0.895559i	0.0994803	+	0.995040i	$0.468282\pi$
$938$	625.893	−	457.751i	0.667264	−	0.488007i
$939$		−	491.502i		−	0.523431i
$940$	−282.196	−	138.307i	−0.300208	−	0.147136i
$941$	−244.702	+	423.836i	−0.260045	+	0.450411i	−0.966254	−	0.257593i	$-0.917071\pi$
$941$	−244.702	+	423.836i	−0.260045	+	0.450411i	0.706209	+	0.708004i	$0.250404\pi$
$942$	128.031	+	477.819i	0.135914	+	0.507239i
$943$	89.3707	−	333.536i	0.0947727	−	0.353697i
$944$		−	62.5186i		−	0.0662273i
$945$	−179.064	+	31.7996i	−0.189485	+	0.0336504i
$946$	−114.627			−0.121170
$947$	895.495	+	239.947i	0.945612	+	0.253376i	0.698499	−	0.715611i	$-0.253852\pi$
$947$	895.495	+	239.947i	0.945612	+	0.253376i	0.247113	+	0.968987i	$0.420518\pi$
$948$	91.5015	−	24.5177i	0.0965205	−	0.0258626i
$949$	1021.35	+	589.675i	1.07623	+	0.621364i
$950$	−663.002	+	872.840i	−0.697897	+	0.918779i
$951$	−653.291			−0.686952
$952$	−69.5134	+	7.52712i	−0.0730183	+	0.00790664i
$953$	−1057.61	−	1057.61i	−1.10977	−	1.10977i	−0.993181	−	0.116587i	$-0.962805\pi$
$953$	−1057.61	−	1057.61i	−1.10977	−	1.10977i	−0.116587	−	0.993181i	$-0.537195\pi$
$954$	−382.200	+	220.663i	−0.400629	+	0.231303i
$955$	−578.560	−	504.888i	−0.605822	−	0.528679i
$956$	84.6324	−	146.588i	0.0885276	−	0.153334i
$957$	198.713	+	53.2450i	0.207642	+	0.0556374i
$958$	−508.190	−	508.190i	−0.530470	−	0.530470i
$959$	816.822	−	1015.20i	0.851744	−	1.05860i
$960$	38.6317	+	57.5117i	0.0402413	+	0.0599080i
$961$	358.914	+	621.658i	0.373480	+	0.646886i
$962$	139.664	+	521.233i	0.145181	+	0.541822i
$963$	229.738	−	61.5580i	0.238565	−	0.0639232i
$964$	−763.032	+	440.537i	−0.791527	+	0.456988i
$965$	1291.82	−	867.741i	1.33868	−	0.899214i
$966$	284.836	−	110.367i	0.294862	−	0.114251i
$967$	−607.869	+	607.869i	−0.628613	+	0.628613i	−0.947719	−	0.319106i	$-0.896617\pi$
$967$	−607.869	+	607.869i	−0.628613	+	0.628613i	0.319106	+	0.947719i	$0.396617\pi$
$968$	−70.6935	+	263.832i	−0.0730305	+	0.272553i
$969$	164.226	+	94.8157i	0.169480	+	0.0978490i
$970$	653.091	−	748.389i	0.673290	−	0.771535i
$971$	328.192	+	568.446i	0.337994	+	0.585423i	0.984055	−	0.177863i	$-0.0569183\pi$
$971$	328.192	+	568.446i	0.337994	+	0.585423i	−0.646061	+	0.763286i	$0.723585\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−1143.00	+	835.943i	−1.17472	+	0.859139i
$974$		−	1074.51i		−	1.10319i
$975$	474.994	−	64.8970i	0.487173	−	0.0665610i
$976$	176.775	−	306.183i	0.181122	−	0.313712i
$977$	204.802	+	764.332i	0.209624	+	0.782326i	0.987990	+	0.154516i	$0.0493818\pi$
$977$	204.802	+	764.332i	0.209624	+	0.782326i	−0.778367	+	0.627810i	$0.783952\pi$
$978$	−104.951	+	391.682i	−0.107312	+	0.400493i
$979$			563.310i			0.575393i
$980$	−235.683	+	429.597i	−0.240493	+	0.438364i
$981$	−130.272			−0.132795
$982$	−219.343	−	58.7728i	−0.223364	−	0.0598501i
$983$	−596.854	+	159.927i	−0.607176	+	0.162692i	−0.549291	−	0.835631i	$-0.685102\pi$
$983$	−596.854	+	159.927i	−0.607176	+	0.162692i	−0.0578848	+	0.998323i	$0.518436\pi$
$984$	−82.2316	−	47.4764i	−0.0835687	−	0.0482484i
$985$	210.246	−	428.975i	0.213447	−	0.435508i
$986$	120.012			0.121716
$987$	224.930	+	307.553i	0.227893	+	0.311604i
$988$	−485.413	−	485.413i	−0.491308	−	0.491308i
$989$	253.005	−	146.073i	0.255819	−	0.147697i
$990$	−7.11325	−	104.610i	−0.00718510	−	0.105667i
$991$	−241.741	+	418.708i	−0.243937	+	0.422511i	−0.961832	−	0.273640i	$-0.911772\pi$
$991$	−241.741	+	418.708i	−0.243937	+	0.422511i	0.717895	+	0.696151i	$0.245106\pi$
$992$	85.2070	+	22.8311i	0.0858941	+	0.0230153i
$993$	498.930	+	498.930i	0.502447	+	0.502447i
$994$	213.599	+	551.258i	0.214888	+	0.554586i
$995$	−1585.68	−	311.386i	−1.59365	−	0.312951i
$996$	−120.013	−	207.868i	−0.120495	−	0.208703i
$997$	42.1697	+	157.380i	0.0422966	+	0.157853i	0.983844	−	0.179027i	$-0.0572950\pi$
$997$	42.1697	+	157.380i	0.0422966	+	0.157853i	−0.941548	+	0.336880i	$0.890628\pi$
$998$	84.1570	−	22.5498i	0.0843257	−	0.0225950i
$999$	155.090	−	89.5410i	0.155245	−	0.0896306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.b.193.8	yes	32
5.2	odd	4	inner	210.3.v.b.67.1	yes	32
7.2	even	3	inner	210.3.v.b.163.1	yes	32
35.2	odd	12	inner	210.3.v.b.37.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.b.37.8	✓	32	35.2	odd	12	inner
210.3.v.b.67.1	yes	32	5.2	odd	4	inner
210.3.v.b.163.1	yes	32	7.2	even	3	inner
210.3.v.b.193.8	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)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.73071 - 1.61876i) q^{5} +2.44949 q^{6} +(-4.13228 - 5.65016i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(4.73071 - 1.61876i) q^{5} +2.44949 q^{6} +(-4.13228 - 5.65016i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(7.05478 - 0.479709i) q^{10} +(2.47138 - 4.28056i) q^{11} +(3.34607 + 0.896575i) q^{12} +(7.82868 + 7.82868i) q^{13} +(-3.57669 - 9.23078i) q^{14} +(7.18896 - 4.82896i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-0.914015 - 3.41115i) q^{17} +(4.09808 - 1.09808i) q^{18} +(-26.8487 + 15.5011i) q^{19} +(9.81259 + 1.92693i) q^{20} +(-9.44633 - 7.60045i) q^{21} +(4.94276 - 4.94276i) q^{22} +(-4.61097 + 17.2084i) q^{23} +(4.24264 + 2.44949i) q^{24} +(19.7592 - 15.3158i) q^{25} +(7.82868 + 13.5597i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-1.50715 - 13.9186i) q^{28} +24.0299i q^{29} +(11.5878 - 3.96514i) q^{30} +(7.79698 - 13.5048i) q^{31} +(1.46410 + 5.46410i) q^{32} +(2.21578 - 8.26940i) q^{33} -4.99427i q^{34} +(-28.6949 - 20.0401i) q^{35} +6.00000 q^{36} +(33.2900 + 8.92003i) q^{37} +(-42.3498 + 11.3476i) q^{38} +(16.6071 + 9.58813i) q^{39} +(12.6989 + 6.22390i) q^{40} -19.3822 q^{41} +(-10.1220 - 13.8400i) q^{42} +(-11.5955 - 11.5955i) q^{43} +(8.56111 - 4.94276i) q^{44} +(9.86260 - 11.3017i) q^{45} +(-12.5974 + 21.8194i) q^{46} +(-30.3558 - 8.13382i) q^{47} +(4.89898 + 4.89898i) q^{48} +(-14.8486 + 46.6960i) q^{49} +(32.5976 - 13.6894i) q^{50} +(-3.05835 - 5.29722i) q^{51} +(5.73099 + 21.3883i) q^{52} +(-100.477 + 26.9228i) q^{53} +(6.36396 - 3.67423i) q^{54} +(4.76218 - 24.2506i) q^{55} +(3.03577 - 19.5649i) q^{56} +(-37.9698 + 37.9698i) q^{57} +(-8.79557 + 32.8255i) q^{58} +(-13.5357 - 7.81482i) q^{59} +(17.2806 - 1.17504i) q^{60} +(-44.1937 - 76.5457i) q^{61} +(15.5940 - 15.5940i) q^{62} +(-19.2112 - 8.48113i) q^{63} +8.00000i q^{64} +(49.7079 + 24.3624i) q^{65} +(6.05362 - 10.4852i) q^{66} +(20.2731 + 75.6604i) q^{67} +(1.82803 - 6.82230i) q^{68} +30.8572i q^{69} +(-31.8627 - 37.8783i) q^{70} -59.7196 q^{71} +(8.19615 + 2.19615i) q^{72} +(102.892 - 27.5699i) q^{73} +(42.2100 + 24.3700i) q^{74} +(26.1920 - 34.4816i) q^{75} -62.0044 q^{76} +(-34.3982 + 3.72475i) q^{77} +(19.1763 + 19.1763i) q^{78} +(23.6823 - 13.6730i) q^{79} +(15.0690 + 13.1501i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-26.4765 - 7.09436i) q^{82} +(-48.9951 - 48.9951i) q^{83} +(-8.76107 - 22.6107i) q^{84} +(-9.84577 - 14.6576i) q^{85} +(-11.5955 - 20.0839i) q^{86} +(10.7723 + 40.2029i) q^{87} +(13.5039 - 3.61835i) q^{88} +(-98.6980 + 56.9833i) q^{89} +(17.6093 - 11.8285i) q^{90} +(11.8830 - 76.5835i) q^{91} +(-25.1948 + 25.1948i) q^{92} +(6.99058 - 26.0892i) q^{93} +(-38.4896 - 22.2220i) q^{94} +(-101.921 + 116.793i) q^{95} +(4.89898 + 8.48528i) q^{96} +(99.3285 - 99.3285i) q^{97} +(-37.3755 + 58.3530i) q^{98} -14.8283i 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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