LMFDB - Embedded newform 63.4.s.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(47,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33849 + 2.50483i) q^{2} +(-5.18070 + 0.400483i) q^{3} +(8.54831 - 14.8061i) q^{4} +18.5684 q^{5} +(21.4732 - 14.7142i) q^{6} +(-17.9322 - 4.62983i) q^{7} +45.5709i q^{8} +(26.6792 - 4.14956i) q^{9} +O(q^{10})$	\(q+(-4.33849 + 2.50483i) q^{2} +(-5.18070 + 0.400483i) q^{3} +(8.54831 - 14.8061i) q^{4} +18.5684 q^{5} +(21.4732 - 14.7142i) q^{6} +(-17.9322 - 4.62983i) q^{7} +45.5709i q^{8} +(26.6792 - 4.14956i) q^{9} +(-80.5586 + 46.5105i) q^{10} +35.1341i q^{11} +(-38.3566 + 80.1294i) q^{12} +(3.94292 - 2.27645i) q^{13} +(89.3956 - 24.8307i) q^{14} +(-96.1970 + 7.43631i) q^{15} +(-45.7606 - 79.2597i) q^{16} +(20.7867 + 36.0037i) q^{17} +(-105.354 + 84.8296i) q^{18} +(64.8837 + 37.4606i) q^{19} +(158.728 - 274.925i) q^{20} +(94.7556 + 16.8042i) q^{21} +(-88.0048 - 152.429i) q^{22} +152.700i q^{23} +(-18.2504 - 236.089i) q^{24} +219.784 q^{25} +(-11.4042 + 19.7527i) q^{26} +(-136.555 + 32.1822i) q^{27} +(-221.840 + 225.929i) q^{28} +(42.5645 + 24.5746i) q^{29} +(398.723 - 273.219i) q^{30} +(87.6525 + 50.6062i) q^{31} +(81.3395 + 46.9614i) q^{32} +(-14.0706 - 182.019i) q^{33} +(-180.366 - 104.134i) q^{34} +(-332.972 - 85.9684i) q^{35} +(166.623 - 430.487i) q^{36} +(2.86552 - 4.96323i) q^{37} -375.330 q^{38} +(-19.5154 + 13.3727i) q^{39} +846.176i q^{40} +(-6.35071 - 10.9998i) q^{41} +(-453.187 + 164.442i) q^{42} +(69.1907 - 119.842i) q^{43} +(520.199 + 300.337i) q^{44} +(495.390 - 77.0506i) q^{45} +(-382.486 - 662.486i) q^{46} +(269.089 + 466.076i) q^{47} +(268.814 + 392.294i) q^{48} +(300.129 + 166.046i) q^{49} +(-953.530 + 550.521i) q^{50} +(-122.109 - 178.199i) q^{51} -77.8390i q^{52} +(105.466 - 60.8907i) q^{53} +(511.832 - 481.669i) q^{54} +652.382i q^{55} +(210.985 - 817.187i) q^{56} +(-351.145 - 168.087i) q^{57} -246.220 q^{58} +(156.280 - 270.684i) q^{59} +(-712.219 + 1487.87i) q^{60} +(-436.557 + 252.047i) q^{61} -507.039 q^{62} +(-497.630 - 49.1094i) q^{63} +261.650 q^{64} +(73.2136 - 42.2699i) q^{65} +(516.971 + 754.442i) q^{66} +(327.373 - 567.026i) q^{67} +710.766 q^{68} +(-61.1537 - 791.091i) q^{69} +(1659.93 - 461.065i) q^{70} -891.951i q^{71} +(189.099 + 1215.80i) q^{72} +(-315.436 + 182.117i) q^{73} +28.7105i q^{74} +(-1138.63 + 88.0198i) q^{75} +(1109.29 - 640.450i) q^{76} +(162.665 - 630.032i) q^{77} +(51.1711 - 106.900i) q^{78} +(-242.587 - 420.173i) q^{79} +(-849.700 - 1471.72i) q^{80} +(694.562 - 221.414i) q^{81} +(55.1049 + 31.8149i) q^{82} +(-248.712 + 430.783i) q^{83} +(1058.80 - 1259.31i) q^{84} +(385.976 + 668.530i) q^{85} +693.243i q^{86} +(-230.355 - 110.267i) q^{87} -1601.09 q^{88} +(-685.285 + 1186.95i) q^{89} +(-1956.24 + 1575.15i) q^{90} +(-81.2449 + 22.5667i) q^{91} +(2260.89 + 1305.32i) q^{92} +(-474.368 - 227.072i) q^{93} +(-2334.88 - 1348.04i) q^{94} +(1204.78 + 695.583i) q^{95} +(-440.203 - 210.718i) q^{96} +(-205.065 - 118.394i) q^{97} +(-1718.02 + 31.3824i) q^{98} +(145.791 + 937.350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.33849	+	2.50483i	−1.53389	+	0.885590i	−0.534709	+	0.845036i	$0.679579\pi$
$2$	−4.33849	+	2.50483i	−1.53389	+	0.885590i	−0.999177	+	0.0405535i	$0.987088\pi$
$3$	−5.18070	+	0.400483i	−0.997025	+	0.0770730i
$3$	−5.18070	+	0.400483i	−0.997025	+	0.0770730i
$4$	8.54831	−	14.8061i	1.06854	−	1.85076i
$5$	18.5684			1.66080			0.830402	−	0.557164i	$-0.188111\pi$
$5$	18.5684			1.66080			0.830402	+	0.557164i	$0.188111\pi$
$6$	21.4732	−	14.7142i	1.46107	−	1.00118i
$7$	−17.9322	−	4.62983i	−0.968249	−	0.249987i
$7$	−17.9322	−	4.62983i	−0.968249	−	0.249987i
$8$			45.5709i			2.01397i
$9$	26.6792	−	4.14956i	0.988120	−	0.153687i
$10$	−80.5586	+	46.5105i	−2.54749	+	1.47079i
$11$			35.1341i			0.963029i	0.876438	+	0.481515i	$0.159913\pi$
$11$			35.1341i			0.963029i	−0.876438	+	0.481515i	$0.840087\pi$
$12$	−38.3566	+	80.1294i	−0.922716	+	1.92761i
$13$	3.94292	−	2.27645i	0.0841207	−	0.0485671i	−0.457350	−	0.889287i	$-0.651201\pi$
$13$	3.94292	−	2.27645i	0.0841207	−	0.0485671i	0.541470	+	0.840720i	$0.317868\pi$
$14$	89.3956	−	24.8307i	1.70657	−	0.474019i
$15$	−96.1970	+	7.43631i	−1.65586	+	0.128003i
$16$	−45.7606	−	79.2597i	−0.715010	−	1.23843i
$17$	20.7867	+	36.0037i	0.296560	+	0.513658i	0.975347	−	0.220678i	$-0.0708271\pi$
$17$	20.7867	+	36.0037i	0.296560	+	0.513658i	−0.678786	+	0.734336i	$0.737494\pi$
$18$	−105.354	+	84.8296i	−1.37956	+	1.11081i
$19$	64.8837	+	37.4606i	0.783439	+	0.452319i	0.837648	−	0.546211i	$-0.183930\pi$
$19$	64.8837	+	37.4606i	0.783439	+	0.452319i	−0.0542084	+	0.998530i	$0.517264\pi$
$20$	158.728	−	274.925i	1.77463	−	3.07376i
$21$	94.7556	+	16.8042i	0.984636	+	0.174618i
$22$	−88.0048	−	152.429i	−0.852849	−	1.47718i
$23$			152.700i			1.38435i	0.721728	+	0.692176i	$0.243348\pi$
$23$			152.700i			1.38435i	−0.721728	+	0.692176i	$0.756652\pi$
$24$	−18.2504	−	236.089i	−0.155222	−	2.00798i
$25$	219.784			1.75827
$26$	−11.4042	+	19.7527i	−0.0860211	+	0.148993i
$27$	−136.555	+	32.1822i	−0.973335	+	0.229388i
$28$	−221.840	+	225.929i	−1.49728	+	1.52488i
$29$	42.5645	+	24.5746i	0.272552	+	0.157358i	0.630047	−	0.776557i	$-0.283036\pi$
$29$	42.5645	+	24.5746i	0.272552	+	0.157358i	−0.357495	+	0.933915i	$0.616369\pi$
$30$	398.723	−	273.219i	2.42655	−	1.66276i
$31$	87.6525	+	50.6062i	0.507834	+	0.293198i	0.731943	−	0.681366i	$-0.238614\pi$
$31$	87.6525	+	50.6062i	0.507834	+	0.293198i	−0.224109	+	0.974564i	$0.571947\pi$
$32$	81.3395	+	46.9614i	0.449342	+	0.259428i
$33$	−14.0706	−	182.019i	−0.0742236	−	0.960165i
$34$	−180.366	−	104.134i	−0.909780	−	0.525262i
$35$	−332.972	−	85.9684i	−1.60807	−	0.415180i
$36$	166.623	−	430.487i	0.771404	−	1.99300i
$37$	2.86552	−	4.96323i	0.0127321	−	0.0220527i	−0.859589	−	0.510986i	$-0.829280\pi$
$37$	2.86552	−	4.96323i	0.0127321	−	0.0220527i	0.872321	+	0.488933i	$0.162614\pi$
$38$	−375.330			−1.60228
$39$	−19.5154	+	13.3727i	−0.0801273	+	0.0549061i
$40$			846.176i			3.34481i
$41$	−6.35071	−	10.9998i	−0.0241906	−	0.0418993i	0.853677	−	0.520803i	$-0.174368\pi$
$41$	−6.35071	−	10.9998i	−0.0241906	−	0.0418993i	−0.877867	+	0.478904i	$0.841034\pi$
$42$	−453.187	+	164.442i	−1.66496	+	0.604140i
$43$	69.1907	−	119.842i	0.245383	−	0.425016i	−0.716856	−	0.697221i	$-0.754420\pi$
$43$	69.1907	−	119.842i	0.245383	−	0.425016i	0.962239	+	0.272205i	$0.0877528\pi$
$44$	520.199	+	300.337i	1.78234	+	1.02903i
$45$	495.390	−	77.0506i	1.64107	−	0.255245i
$46$	−382.486	−	662.486i	−1.22597	−	2.12344i
$47$	269.089	+	466.076i	0.835121	+	1.44647i	0.893932	+	0.448203i	$0.147936\pi$
$47$	269.089	+	466.076i	0.835121	+	1.44647i	−0.0588112	+	0.998269i	$0.518731\pi$
$48$	268.814	+	392.294i	0.808333	+	1.17964i
$49$	300.129	+	166.046i	0.875013	+	0.484100i
$50$	−953.530	+	550.521i	−2.69699	+	1.55711i
$51$	−122.109	−	178.199i	−0.335267	−	0.489273i
$52$		−	77.8390i		−	0.207583i
$53$	105.466	−	60.8907i	0.273337	−	0.157811i	−0.357066	−	0.934079i	$-0.616223\pi$
$53$	105.466	−	60.8907i	0.273337	−	0.157811i	0.630403	+	0.776268i	$0.282890\pi$
$54$	511.832	−	481.669i	1.28984	−	1.21383i
$55$			652.382i			1.59940i
$56$	210.985	−	817.187i	0.503466	−	1.95002i
$57$	−351.145	−	168.087i	−0.815971	−	0.390591i
$58$	−246.220			−0.557419
$59$	156.280	−	270.684i	0.344845	−	0.597290i	−0.640480	−	0.767975i	$-0.721265\pi$
$59$	156.280	−	270.684i	0.344845	−	0.597290i	0.985326	+	0.170685i	$0.0545980\pi$
$60$	−712.219	+	1487.87i	−1.53245	+	3.20139i
$61$	−436.557	+	252.047i	−0.916319	+	0.529037i	−0.882459	−	0.470390i	$-0.844113\pi$
$61$	−436.557	+	252.047i	−0.916319	+	0.529037i	−0.0338600	+	0.999427i	$0.510780\pi$
$62$	−507.039			−1.03861
$63$	−497.630	−	49.1094i	−0.995166	−	0.0982095i
$64$	261.650			0.511034
$65$	73.2136	−	42.2699i	0.139708	−	0.0806605i
$66$	516.971	+	754.442i	0.964163	+	1.40705i
$67$	327.373	−	567.026i	0.596939	−	1.03393i	−0.396331	−	0.918108i	$-0.629717\pi$
$67$	327.373	−	567.026i	0.596939	−	1.03393i	0.993270	−	0.115821i	$-0.0369500\pi$
$68$	710.766			1.26754
$69$	−61.1537	−	791.091i	−0.106696	−	1.38023i
$70$	1659.93	−	461.065i	2.83428	−	0.787254i
$71$		−	891.951i		−	1.49092i	−0.666552	−	0.745459i	$-0.732230\pi$
$71$		−	891.951i		−	1.49092i	0.666552	−	0.745459i	$-0.267770\pi$
$72$	189.099	+	1215.80i	0.309521	+	1.99004i
$73$	−315.436	+	182.117i	−0.505740	+	0.291989i	−0.731081	−	0.682291i	$-0.760984\pi$
$73$	−315.436	+	182.117i	−0.505740	+	0.291989i	0.225341	+	0.974280i	$0.427650\pi$
$74$			28.7105i			0.0451018i
$75$	−1138.63	+	88.0198i	−1.75304	+	0.135515i
$76$	1109.29	−	640.450i	1.67427	−	0.966640i
$77$	162.665	−	630.032i	0.240745	−	0.932452i
$78$	51.1711	−	106.900i	0.0742819	−	0.155180i
$79$	−242.587	−	420.173i	−0.345483	−	0.598394i	0.639958	−	0.768410i	$-0.278952\pi$
$79$	−242.587	−	420.173i	−0.345483	−	0.598394i	−0.985441	+	0.170016i	$0.945618\pi$
$80$	−849.700	−	1471.72i	−1.18749	−	2.05680i
$81$	694.562	−	221.414i	0.952760	−	0.303723i
$82$	55.1049	+	31.8149i	0.0742113	+	0.0428459i
$83$	−248.712	+	430.783i	−0.328912	+	0.569693i	−0.982296	−	0.187334i	$-0.940015\pi$
$83$	−248.712	+	430.783i	−0.328912	+	0.569693i	0.653384	+	0.757027i	$0.273349\pi$
$84$	1058.80	−	1259.31i	1.37530	−	1.63574i
$85$	385.976	+	668.530i	0.492529	+	0.853085i
$86$			693.243i			0.869236i
$87$	−230.355	−	110.267i	−0.283870	−	0.135884i
$88$	−1601.09			−1.93951
$89$	−685.285	+	1186.95i	−0.816181	+	1.41367i	0.0922965	+	0.995732i	$0.470579\pi$
$89$	−685.285	+	1186.95i	−0.816181	+	1.41367i	−0.908477	+	0.417935i	$0.862754\pi$
$90$	−1956.24	+	1575.15i	−2.29118	+	1.84483i
$91$	−81.2449	+	22.5667i	−0.0935910	+	0.0259960i
$92$	2260.89	+	1305.32i	2.56211	+	1.47923i
$93$	−474.368	−	227.072i	−0.528921	−	0.253186i
$94$	−2334.88	−	1348.04i	−2.56196	−	1.47915i
$95$	1204.78	+	695.583i	1.30114	+	0.751213i
$96$	−440.203	−	210.718i	−0.468000	−	0.224024i
$97$	−205.065	−	118.394i	−0.214652	−	0.123929i	0.388820	−	0.921314i	$-0.372883\pi$
$97$	−205.065	−	118.394i	−0.214652	−	0.123929i	−0.603471	+	0.797385i	$0.706216\pi$
$98$	−1718.02	+	31.3824i	−1.77088	+	0.0323480i
$99$	145.791	+	937.350i	0.148006	+	0.951588i
$100$	1878.78	−	3254.15i	1.87878	−	3.25415i
$101$	−354.109			−0.348863			−0.174431	−	0.984669i	$-0.555809\pi$
$101$	−354.109			−0.348863			−0.174431	+	0.984669i	$0.555809\pi$
$102$	976.125	+	467.255i	0.947557	+	0.453580i
$103$		−	1257.38i		−	1.20285i	−0.798929	−	0.601426i	$-0.794600\pi$
$103$		−	1257.38i		−	1.20285i	0.798929	−	0.601426i	$-0.205400\pi$
$104$	103.740	+	179.682i	0.0978126	+	0.169416i
$105$	1759.46	+	312.026i	1.63529	+	0.290006i
$106$	−305.041	+	528.347i	−0.279512	+	0.484128i
$107$	−182.056	−	105.110i	−0.164487	−	0.0949663i	0.415497	−	0.909595i	$-0.363608\pi$
$107$	−182.056	−	105.110i	−0.164487	−	0.0949663i	−0.579984	+	0.814628i	$0.696941\pi$
$108$	−690.822	+	2296.95i	−0.615504	+	2.04652i
$109$	78.9687	+	136.778i	0.0693929	+	0.120192i	0.898634	−	0.438699i	$-0.144560\pi$
$109$	78.9687	+	136.778i	0.0693929	+	0.120192i	−0.829241	+	0.558891i	$0.811227\pi$
$110$	−1634.10	−	2830.35i	−1.41642	−	2.45330i
$111$	−12.8577	+	26.8606i	−0.0109946	+	0.0229684i
$112$	453.631	+	1633.17i	0.382715	+	1.37786i
$113$	−385.384	+	222.502i	−0.320831	+	0.185232i	−0.651763	−	0.758423i	$-0.725970\pi$
$113$	−385.384	+	222.502i	−0.320831	+	0.185232i	0.330932	+	0.943655i	$0.392637\pi$
$114$	1944.47	−	150.313i	1.59751	−	0.123492i
$115$			2835.39i			2.29914i
$116$	727.708	−	420.142i	0.582465	−	0.336287i
$117$	95.7478	−	77.0952i	0.0756572	−	0.0609184i
$118$			1565.81i			1.22157i
$119$	−206.062	−	741.865i	−0.158736	−	0.571485i
$120$	−338.879	−	4383.78i	−0.257794	−	3.33486i
$121$	96.5964			0.0725743
$122$	1262.67	−	2187.00i	0.937019	−	1.62296i
$123$	37.3063	+	54.4430i	0.0273479	+	0.0399103i
$124$	1498.56	−	865.194i	1.08528	−	0.626587i
$125$	1759.99			1.25934
$126$	2281.97	−	1033.42i	1.61344	−	0.730666i
$127$	2066.68			1.44400			0.722002	−	0.691891i	$-0.243222\pi$
$127$	2066.68			1.44400			0.722002	+	0.691891i	$0.243222\pi$
$128$	−1785.88	+	1031.08i	−1.23321	+	0.711994i
$129$	−310.461	+	648.574i	−0.211896	+	0.442665i
$130$	−211.757	+	366.775i	−0.142864	+	0.247448i
$131$	−163.509			−0.109052			−0.0545260	−	0.998512i	$-0.517365\pi$
$131$	−163.509			−0.109052			−0.0545260	+	0.998512i	$0.517365\pi$
$132$	−2815.27	−	1347.62i	−1.85635	−	0.888603i
$133$	−990.073	−	972.153i	−0.645491	−	0.633807i
$134$			3280.05i			2.11457i
$135$	−2535.61	+	597.571i	−1.61652	+	0.380968i
$136$	−1640.72	+	947.270i	−1.03449	+	0.597263i
$137$		−	2624.69i		−	1.63680i	−0.574646	−	0.818402i	$-0.694860\pi$
$137$		−	2624.69i		−	1.63680i	0.574646	−	0.818402i	$-0.305140\pi$
$138$	2246.86	+	3278.96i	1.38598	+	2.02263i
$139$	−1161.11	+	670.366i	−0.708518	+	0.409063i	−0.810512	−	0.585722i	$-0.800811\pi$
$139$	−1161.11	+	670.366i	−0.708518	+	0.409063i	0.101994	+	0.994785i	$0.467478\pi$
$140$	−4119.20	+	4195.13i	−2.48669	+	2.53253i
$141$	−1580.72	−	2306.83i	−0.944121	−	1.37780i
$142$	2234.18	+	3869.72i	1.32034	+	2.28690i
$143$	79.9809	+	138.531i	0.0467716	+	0.0810107i
$144$	−1549.75	−	1924.70i	−0.896847	−	1.11383i
$145$	790.352	+	456.310i	0.452656	+	0.261341i
$146$	912.343	−	1580.22i	0.517165	−	0.895756i
$147$	−1621.38	−	740.039i	−0.909721	−	0.415220i
$148$	−48.9907	−	84.8544i	−0.0272095	−	0.0471283i
$149$			745.154i			0.409701i	0.978793	+	0.204850i	$0.0656708\pi$
$149$			745.154i			0.409701i	−0.978793	+	0.204850i	$0.934329\pi$
$150$	4719.48	−	3233.95i	2.56896	−	1.76034i
$151$	−3412.14			−1.83891			−0.919457	−	0.393190i	$-0.871371\pi$
$151$	−3412.14			−1.83891			−0.919457	+	0.393190i	$0.871371\pi$
$152$	−1707.11	+	2956.81i	−0.910955	+	1.57782i
$153$	703.974	+	874.295i	0.371980	+	0.461977i
$154$	872.402	+	3140.83i	0.456495	+	1.64348i
$155$	1627.56	+	939.674i	0.843413	+	0.486945i
$156$	31.1732	+	403.260i	0.0159991	+	0.206966i
$157$	2006.44	+	1158.42i	1.01994	+	0.588865i	0.914088	−	0.405516i	$-0.132908\pi$
$157$	2006.44	+	1158.42i	1.01994	+	0.588865i	0.105857	+	0.994381i	$0.466242\pi$
$158$	2104.92	+	1215.28i	1.05986	+	0.611912i
$159$	−522.001	+	357.694i	−0.260361	+	0.178408i
$160$	1510.34	+	871.996i	0.746269	+	0.430858i
$161$	706.974	−	2738.25i	0.346071	−	1.34040i
$162$	−2458.74	+	2700.36i	−1.19245	+	1.30963i
$163$	730.165	−	1264.68i	0.350865	−	0.607716i	−0.635536	−	0.772071i	$-0.719221\pi$
$163$	730.165	−	1264.68i	0.350865	−	0.607716i	0.986401	+	0.164355i	$0.0525544\pi$
$164$	−217.151			−0.103394
$165$	−261.268	−	3379.79i	−0.123271	−	1.59465i
$166$		−	2491.93i		−	1.16513i
$167$	−1047.84	−	1814.91i	−0.485534	−	0.840969i	0.514328	−	0.857594i	$-0.328041\pi$
$167$	−1047.84	−	1814.91i	−0.485534	−	0.840969i	−0.999862	+	0.0166244i	$0.994708\pi$
$168$	−765.781	+	4318.09i	−0.351674	+	1.98302i
$169$	−1088.14	+	1884.71i	−0.495282	+	0.857854i
$170$	−3349.10	−	1933.60i	−1.51097	−	0.872357i
$171$	1886.49	+	730.182i	0.843647	+	0.326540i
$172$	−1182.93	−	2048.89i	−0.524403	−	0.908293i
$173$	1387.37	+	2402.99i	0.609708	+	1.05604i	0.991288	+	0.131709i	$0.0420465\pi$
$173$	1387.37	+	2402.99i	0.609708	+	1.05604i	−0.381581	+	0.924336i	$0.624620\pi$
$174$	1275.59	−	98.6071i	0.555761	−	0.0429620i
$175$	−3941.22	−	1017.56i	−1.70245	−	0.439546i
$176$	2784.72	−	1607.76i	1.19265	−	0.688576i
$177$	−701.233	+	1464.92i	−0.297785	+	0.622091i
$178$		−	6866.08i		−	2.89120i
$179$	63.6106	−	36.7256i	0.0265614	−	0.0153352i	−0.486661	−	0.873591i	$-0.661785\pi$
$179$	63.6106	−	36.7256i	0.0265614	−	0.0153352i	0.513222	+	0.858256i	$0.328452\pi$
$180$	3093.92	−	7993.44i	1.28115	−	3.30998i
$181$		−	2260.38i		−	0.928247i	−0.885771	−	0.464123i	$-0.846369\pi$
$181$		−	2260.38i		−	0.928247i	0.885771	−	0.464123i	$-0.153631\pi$
$182$	295.954	−	301.410i	0.120536	−	0.122758i
$183$	2160.73	−	1480.61i	0.872819	−	0.598087i
$184$	−6958.66			−2.78804
$185$	53.2080	−	92.1590i	0.0211456	−	0.0366252i
$186$	2626.81	−	203.060i	1.03552	−	0.0800490i
$187$	−1264.96	+	730.323i	−0.494667	+	0.285596i
$188$	9201.02			3.56943
$189$	2597.74	+	55.1286i	0.999775	+	0.0212170i
$190$	−6969.25			−2.66107
$191$	3258.23	−	1881.14i	1.23433	−	0.712641i	0.266401	−	0.963862i	$-0.414165\pi$
$191$	3258.23	−	1881.14i	1.23433	−	0.712641i	0.967930	+	0.251221i	$0.0808321\pi$
$192$	−1355.53	+	104.786i	−0.509514	+	0.0393870i
$193$	70.9018	−	122.805i	0.0264436	−	0.0458017i	−0.852501	−	0.522726i	$-0.824915\pi$
$193$	70.9018	−	122.805i	0.0264436	−	0.0458017i	0.878944	+	0.476924i	$0.158248\pi$
$194$	1186.23			0.439002
$195$	−362.369	+	248.308i	−0.133076	+	0.0911883i
$196$	5024.10	−	3024.33i	1.83094	−	1.10216i
$197$		−	3470.68i		−	1.25521i	−0.778533	−	0.627603i	$-0.784036\pi$
$197$		−	3470.68i		−	1.25521i	0.778533	−	0.627603i	$-0.215964\pi$
$198$	−2980.41	−	3701.50i	−1.06974	−	1.32856i
$199$	−58.1115	+	33.5507i	−0.0207006	+	0.0119515i	−0.510315	−	0.859988i	$-0.670471\pi$
$199$	−58.1115	+	33.5507i	−0.0207006	+	0.0119515i	0.489614	+	0.871939i	$0.337138\pi$
$200$			10015.8i			3.54110i
$201$	−1468.93	+	3068.70i	−0.515476	+	1.07686i
$202$	1536.30	−	886.980i	0.535116	−	0.308949i
$203$	−649.499	−	637.743i	−0.224561	−	0.220497i
$204$	−3682.26	+	284.650i	−1.26377	+	0.0976934i
$205$	−117.922	−	204.247i	−0.0401759	−	0.0695866i
$206$	3149.53	+	5455.14i	1.06523	+	1.84504i
$207$	633.637	+	4073.91i	0.212758	+	1.36791i
$208$	−360.861	−	208.343i	−0.120294	−	0.0694520i
$209$	−1316.15	+	2279.63i	−0.435596	+	0.754475i
$210$	−8414.95	+	3053.41i	−2.76517	+	1.00336i
$211$	−820.718	−	1421.53i	−0.267775	−	0.463800i	0.700512	−	0.713641i	$-0.252955\pi$
$211$	−820.718	−	1421.53i	−0.267775	−	0.463800i	−0.968287	+	0.249841i	$0.919622\pi$
$212$		−	2082.05i		−	0.674508i
$213$	357.211	+	4620.93i	0.114909	+	1.48648i
$214$	1053.13			0.336405
$215$	1284.76	−	2225.27i	0.407534	−	0.705869i
$216$	−1466.57	−	6222.94i	−0.461979	−	1.96026i
$217$	−1337.51	−	1313.30i	−0.418414	−	0.410841i
$218$	−685.209	−	395.606i	−0.212882	−	0.122907i
$219$	1561.24	−	1069.82i	0.481731	−	0.330099i
$220$	9659.24	+	5576.76i	2.96012	+	1.70902i
$221$	163.921	+	94.6398i	0.0498937	+	0.0288062i
$222$	−11.4981	−	148.741i	−0.00347613	−	0.0449676i
$223$	2975.62	+	1717.98i	0.893554	+	0.515894i	0.875103	−	0.483936i	$-0.160793\pi$
$223$	2975.62	+	1717.98i	0.893554	+	0.515894i	0.0184507	+	0.999830i	$0.494127\pi$
$224$	−1241.18	−	1218.71i	−0.370221	−	0.363520i
$225$	5863.67	−	912.008i	1.73738	−	0.270225i
$226$	1114.66	−	1930.64i	0.328079	−	0.568249i
$227$	−3886.11			−1.13626			−0.568129	−	0.822940i	$-0.692332\pi$
$227$	−3886.11			−1.13626			−0.568129	+	0.822940i	$0.692332\pi$
$228$	−5490.42	+	3762.23i	−1.59479	+	1.09281i
$229$		−	2280.90i		−	0.658193i	−0.944296	−	0.329097i	$-0.893256\pi$
$229$		−	2280.90i		−	0.658193i	0.944296	−	0.329097i	$-0.106744\pi$
$230$	−7102.15	−	12301.3i	−2.03609	−	3.52662i
$231$	−590.400	+	3329.15i	−0.168162	+	0.948234i
$232$	−1119.89	+	1939.70i	−0.316914	+	0.548912i
$233$	691.417	+	399.190i	0.194404	+	0.112239i	0.594043	−	0.804433i	$-0.297531\pi$
$233$	691.417	+	399.190i	0.194404	+	0.112239i	−0.399638	+	0.916673i	$0.630864\pi$
$234$	−222.290	+	574.308i	−0.0621008	+	0.160443i
$235$	4996.54	+	8654.27i	1.38697	+	2.40231i
$236$	−2671.85	−	4627.79i	−0.736961	−	1.27645i
$237$	1425.04	+	2079.64i	0.390575	+	0.569987i
$238$	2752.24	+	2702.42i	0.749585	+	0.736017i
$239$	−4557.37	+	2631.20i	−1.23344	+	0.712127i	−0.967745	−	0.251931i	$-0.918934\pi$
$239$	−4557.37	+	2631.20i	−1.23344	+	0.712127i	−0.265694	+	0.964057i	$0.585601\pi$
$240$	4991.44	+	7284.26i	1.34248	+	1.95915i
$241$		−	3951.47i		−	1.05617i	−0.849192	−	0.528084i	$-0.822910\pi$
$241$		−	3951.47i		−	1.05617i	0.849192	−	0.528084i	$-0.177090\pi$
$242$	−419.082	+	241.957i	−0.111321	+	0.0642710i
$243$	−3509.64	+	1425.24i	−0.926517	+	0.376252i
$244$			8618.28i			2.26118i
$245$	5572.91	+	3083.21i	1.45323	+	0.803996i
$246$	−298.223	−	142.754i	−0.0772928	−	0.0369988i
$247$	341.109			0.0878713
$248$	−2306.17	+	3994.40i	−0.590491	+	1.02276i
$249$	1115.98	−	2331.36i	0.284026	−	0.593349i
$250$	−7635.67	+	4408.46i	−1.93169	+	1.11526i
$251$	−5548.60			−1.39532			−0.697658	−	0.716431i	$-0.745775\pi$
$251$	−5548.60			−1.39532			−0.697658	+	0.716431i	$0.745775\pi$
$252$	−4981.01	+	6948.15i	−1.24514	+	1.73687i
$253$	−5364.97			−1.33317
$254$	−8966.27	+	5176.68i	−2.21494	+	1.27879i
$255$	−2267.36	−	3308.87i	−0.556814	−	0.812587i
$256$	4118.74	−	7133.87i	1.00555	−	1.74167i
$257$	2783.15			0.675518			0.337759	−	0.941233i	$-0.390331\pi$
$257$	2783.15			0.675518			0.337759	+	0.941233i	$0.390331\pi$
$258$	−277.632	−	3591.48i	−0.0669946	−	0.866650i
$259$	−74.3641	+	75.7348i	−0.0178408	+	0.0181696i
$260$		−	1445.34i		−	0.344755i
$261$	1237.56	+	479.007i	0.293498	+	0.113601i
$262$	709.379	−	409.560i	0.167273	−	0.0965753i
$263$		−	5999.20i		−	1.40657i	−0.710910	−	0.703283i	$-0.751717\pi$
$263$		−	5999.20i		−	1.40657i	0.710910	−	0.703283i	$-0.248283\pi$
$264$	8294.76	−	641.210i	1.93374	−	0.149484i
$265$	1958.33	−	1130.64i	0.453959	−	0.262093i
$266$	6730.49	+	1737.71i	1.55140	+	0.400549i
$267$	3074.90	−	6423.66i	0.704797	−	1.47237i
$268$	−5596.96	−	9694.23i	−1.27571	−	2.20959i
$269$	1352.02	+	2341.76i	0.306445	+	0.530779i	0.977582	−	0.210555i	$-0.0675269\pi$
$269$	1352.02	+	2341.76i	0.306445	+	0.530779i	−0.671137	+	0.741334i	$0.734194\pi$
$270$	9503.88	−	8943.80i	2.14218	−	2.01594i
$271$	1538.06	+	887.999i	0.344762	+	0.199048i	0.662376	−	0.749172i	$-0.269548\pi$
$271$	1538.06	+	887.999i	0.344762	+	0.199048i	−0.317614	+	0.948220i	$0.602882\pi$
$272$	1902.43	−	3295.10i	0.424087	−	0.734541i
$273$	411.868	−	149.448i	0.0913090	−	0.0331320i
$274$	6574.38	+	11387.2i	1.44954	+	2.51067i
$275$			7721.91i			1.69327i
$276$	−12235.7	−	5857.04i	−2.66850	−	1.27736i
$277$	−873.158			−0.189397			−0.0946985	−	0.995506i	$-0.530189\pi$
$277$	−873.158			−0.189397			−0.0946985	+	0.995506i	$0.530189\pi$
$278$	3358.30	−	5816.75i	0.724524	−	1.25491i
$279$	2548.49	+	986.415i	0.546862	+	0.211667i
$280$	3917.65	−	15173.8i	0.836159	−	3.23861i
$281$	1562.82	+	902.296i	0.331780	+	0.191553i	0.656631	−	0.754212i	$-0.271981\pi$
$281$	1562.82	+	902.296i	0.331780	+	0.191553i	−0.324851	+	0.945765i	$0.605314\pi$
$282$	12636.2	+	6048.72i	2.66834	+	1.27729i
$283$	5223.93	+	3016.04i	1.09728	+	0.633515i	0.935505	−	0.353313i	$-0.114945\pi$
$283$	5223.93	+	3016.04i	1.09728	+	0.633515i	0.161775	+	0.986828i	$0.448278\pi$
$284$	−13206.3	−	7624.67i	−2.75933	−	1.59310i
$285$	−6520.19	−	3121.11i	−1.35517	−	0.648696i
$286$	−693.992	−	400.676i	−0.143485	−	0.0828409i
$287$	62.9554	+	226.653i	0.0129482	+	0.0466163i
$288$	2364.94	+	915.370i	0.483874	+	0.187287i
$289$	1592.32	−	2757.98i	0.324104	−	0.561364i
$290$	−4571.91			−0.925765
$291$	1109.80	+	531.241i	0.223565	+	0.107017i
$292$			6227.17i			1.24801i
$293$	4576.92	+	7927.46i	0.912583	+	1.58064i	0.810402	+	0.585874i	$0.199249\pi$
$293$	4576.92	+	7927.46i	0.912583	+	1.58064i	0.102180	+	0.994766i	$0.467418\pi$
$294$	8887.99	−	850.622i	1.76312	−	0.168739i
$295$	2901.86	−	5026.17i	0.572721	−	0.991982i
$296$	226.179	+	130.584i	0.0444134	+	0.0256421i
$297$	−1130.69	−	4797.74i	−0.220907	−	0.937350i
$298$	−1866.48	−	3232.84i	−0.362827	−	0.628434i
$299$	347.613	+	602.083i	0.0672340	+	0.116453i
$300$	−8430.17	+	17611.2i	−1.62239	+	3.38927i
$301$	−1795.59	+	1828.69i	−0.343841	+	0.350179i
$302$	14803.5	−	8546.82i	2.82069	−	1.62852i
$303$	1834.53	−	141.814i	0.347825	−	0.0268879i
$304$		−	6856.89i		−	1.29365i
$305$	−8106.16	+	4680.09i	−1.52183	+	0.878627i
$306$	−5244.14	−	2029.78i	−0.979697	−	0.379199i
$307$			3205.89i			0.595993i	0.954567	+	0.297997i	$0.0963184\pi$
$307$			3205.89i			0.595993i	−0.954567	+	0.297997i	$0.903682\pi$
$308$	−7937.81	−	7794.14i	−1.46850	−	1.44192i
$309$	503.561	+	6514.12i	0.0927073	+	1.19927i
$310$	−9414.88			−1.72493
$311$	−2.43583	+	4.21898i	−0.000444126	+	0.000769249i	−0.866247	−	0.499615i	$-0.833475\pi$
$311$	−2.43583	+	4.21898i	−0.000444126	+	0.000769249i	0.865803	+	0.500385i	$0.166808\pi$
$312$	−609.403	−	889.334i	−0.110579	−	0.161374i
$313$	1663.20	−	960.246i	0.300349	−	0.173407i	−0.342250	−	0.939609i	$-0.611189\pi$
$313$	1663.20	−	960.246i	0.300349	−	0.173407i	0.642600	+	0.766202i	$0.277856\pi$
$314$	−11606.5			−2.08597
$315$	−9240.17	−	911.881i	−1.65278	−	0.163107i
$316$	−8294.83			−1.47665
$317$	−8798.23	+	5079.66i	−1.55886	+	0.900007i	−0.561491	+	0.827483i	$0.689772\pi$
$317$	−8798.23	+	5079.66i	−1.55886	+	0.900007i	−0.997367	+	0.0725240i	$0.976895\pi$
$318$	1368.73	−	2859.37i	0.241367	−	0.504231i
$319$	−863.406	+	1495.46i	−0.151541	+	0.262476i
$320$	4858.41			0.848729
$321$	985.274	+	471.634i	0.171317	+	0.0820064i
$322$	3791.64	+	13650.7i	0.656210	+	2.36250i
$323$			3114.74i			0.536559i
$324$	2659.05	−	12176.5i	0.455941	−	2.08787i
$325$	866.591	−	500.327i	0.147907	−	0.0853943i
$326$			7315.75i			1.24289i
$327$	−463.890	−	676.978i	−0.0784501	−	0.114486i
$328$	501.268	−	289.407i	0.0843839	−	0.0487191i
$329$	−2667.51	−	9603.62i	−0.447005	−	1.60931i
$330$	9599.31	+	14008.8i	1.60129	+	2.33684i
$331$	5754.15	+	9966.49i	0.955519	+	1.65501i	0.733175	+	0.680040i	$0.238038\pi$
$331$	5754.15	+	9966.49i	0.955519	+	1.65501i	0.222344	+	0.974968i	$0.428629\pi$
$332$	4252.14	+	7364.92i	0.702911	+	1.21748i
$333$	55.8547	−	144.306i	0.00919164	−	0.0237475i
$334$	9092.06	+	5249.30i	1.48951	+	0.859967i
$335$	6078.77	−	10528.7i	0.991400	−	1.71715i
$336$	−3004.18	−	8279.27i	−0.487772	−	1.34426i
$337$	−4193.55	−	7263.44i	−0.677855	−	1.17408i	−0.975625	−	0.219442i	$-0.929576\pi$
$337$	−4193.55	−	7263.44i	−0.677855	−	1.17408i	0.297770	−	0.954638i	$-0.403757\pi$
$338$		−	10902.4i		−	1.75447i
$339$	1907.45	−	1307.05i	0.305600	−	0.209408i
$340$	13197.8			2.10514
$341$	−1778.00	+	3079.59i	−0.282358	+	0.489059i
$342$	−10013.5	+	1557.45i	−1.58324	+	0.246250i
$343$	−4613.22	−	4367.13i	−0.726211	−	0.687471i
$344$	5461.30	+	3153.08i	0.855969	+	0.494194i
$345$	−1135.52	−	14689.3i	−0.177202	−	2.29230i
$346$	−12038.1	−	6950.22i	−1.87044	−	1.07990i
$347$	−10783.9	−	6226.07i	−1.66832	−	0.963207i	−0.968542	−	0.248849i	$-0.919948\pi$
$347$	−10783.9	−	6226.07i	−1.66832	−	0.963207i	−0.699781	−	0.714358i	$-0.746719\pi$
$348$	−3601.77	+	2468.06i	−0.554814	+	0.380179i
$349$	1881.46	+	1086.26i	0.288574	+	0.166608i	0.637298	−	0.770617i	$-0.280052\pi$
$349$	1881.46	+	1086.26i	0.288574	+	0.166608i	−0.348725	+	0.937225i	$0.613385\pi$
$350$	19647.7	−	5457.38i	3.00062	−	0.833455i
$351$	−465.165	+	437.752i	−0.0707370	+	0.0665684i
$352$	−1649.95	+	2857.79i	−0.249836	+	0.432729i
$353$	−966.144			−0.145673			−0.0728366	−	0.997344i	$-0.523205\pi$
$353$	−966.144			−0.145673			−0.0728366	+	0.997344i	$0.523205\pi$
$354$	−627.082	−	8112.00i	−0.0941498	−	1.21793i
$355$		−	16562.1i		−	2.47612i
$356$	11716.1	+	20292.8i	1.74424	+	3.02111i
$357$	1364.65	+	3760.86i	0.202310	+	0.557551i
$358$	−183.983	+	318.667i	−0.0271614	+	0.0470449i
$359$	1011.40	+	583.931i	0.148689	+	0.0858459i	0.572499	−	0.819905i	$-0.305974\pi$
$359$	1011.40	+	583.931i	0.148689	+	0.0858459i	−0.423809	+	0.905751i	$0.639307\pi$
$360$	3511.26	+	22575.3i	0.514055	+	3.30507i
$361$	−622.901	−	1078.90i	−0.0908152	−	0.157296i
$362$	5661.86	+	9806.63i	0.822046	+	1.42383i
$363$	−500.436	+	38.6852i	−0.0723584	+	0.00559352i
$364$	−360.382	+	1395.83i	−0.0518932	+	0.200992i
$365$	−5857.13	+	3381.62i	−0.839935	+	0.484937i
$366$	−5665.63	+	11835.9i	−0.809145	+	1.69036i
$367$		−	8702.02i		−	1.23772i	−0.785503	−	0.618858i	$-0.787596\pi$
$367$		−	8702.02i		−	1.23772i	0.785503	−	0.618858i	$-0.212404\pi$
$368$	12102.9	−	6987.64i	1.71443	−	0.989826i
$369$	−215.076	−	267.112i	−0.0303426	−	0.0376838i
$370$			533.107i			0.0749052i
$371$	−2173.15	+	603.617i	−0.304109	+	0.0844697i
$372$	−7417.09	+	5082.46i	−1.03376	+	0.708369i
$373$	8449.87			1.17297			0.586485	−	0.809960i	$-0.300511\pi$
$373$	8449.87			1.17297			0.586485	+	0.809960i	$0.300511\pi$
$374$	3658.66	−	6336.99i	0.505842	−	0.876145i
$375$	−9117.95	+	704.844i	−1.25560	+	0.0970614i
$376$	−21239.5	+	12262.6i	−2.91315	+	1.68191i
$377$	223.771			0.0305697
$378$	−11408.3	+	6267.70i	−1.55233	+	0.852846i
$379$	10435.1			1.41428			0.707142	−	0.707072i	$-0.249984\pi$
$379$	10435.1			1.41428			0.707142	+	0.707072i	$0.249984\pi$
$380$	20597.7	−	11892.1i	2.78064	−	1.60540i
$381$	−10706.9	+	827.671i	−1.43971	+	0.111294i
$382$	−9423.85	+	16322.6i	−1.26222	+	2.18622i
$383$	1729.70			0.230767			0.115383	−	0.993321i	$-0.463190\pi$
$383$	1729.70			0.230767			0.115383	+	0.993321i	$0.463190\pi$
$384$	8839.17	−	6056.92i	1.17467	−	0.804924i
$385$	3020.42	−	11698.7i	0.399831	−	1.54862i
$386$			710.386i			0.0936728i
$387$	1348.66	−	3484.40i	0.177148	−	0.457679i
$388$	−3505.92	+	2024.14i	−0.458727	+	0.264846i
$389$			8787.45i			1.14535i	0.819782	+	0.572675i	$0.194094\pi$
$389$			8787.45i			1.14535i	−0.819782	+	0.572675i	$0.805906\pi$
$390$	950.164	−	1984.95i	0.123368	−	0.257723i
$391$	−5497.76	+	3174.13i	−0.711083	+	0.410544i
$392$	−7566.87	+	13677.2i	−0.974961	+	1.76225i
$393$	847.088	−	65.4824i	0.108728	−	0.00840496i
$394$	8693.45	+	15057.5i	1.11160	+	1.92534i
$395$	−4504.44	−	7801.92i	−0.573780	−	0.993816i
$396$	15124.8	+	5854.16i	1.91931	+	0.742885i
$397$	−10427.7	−	6020.42i	−1.31826	−	0.761099i	−0.334814	−	0.942284i	$-0.608673\pi$
$397$	−10427.7	−	6020.42i	−1.31826	−	0.761099i	−0.983449	+	0.181185i	$0.942007\pi$
$398$	168.077	−	291.118i	0.0211682	−	0.0366644i
$399$	5518.60	+	4639.92i	0.692420	+	0.582172i
$400$	−10057.5	−	17420.0i	−1.25718	−	2.17750i
$401$			5182.09i			0.645339i	0.946512	+	0.322670i	$0.104580\pi$
$401$			5182.09i			0.645339i	−0.946512	+	0.322670i	$0.895420\pi$
$402$	−1313.60	−	16992.9i	−0.162977	−	2.10828i
$403$	460.809			0.0569592
$404$	−3027.03	+	5242.97i	−0.372773	+	0.645662i
$405$	12896.9	−	4111.30i	1.58235	−	0.504425i
$406$	4415.28	+	1139.96i	0.539721	+	0.139348i
$407$	174.378	+	100.677i	0.0212374	+	0.0122614i
$408$	8120.70	−	5564.60i	0.985379	−	0.675217i
$409$	−3497.73	−	2019.41i	−0.422864	−	0.244141i	0.273438	−	0.961890i	$-0.411839\pi$
$409$	−3497.73	−	2019.41i	−0.422864	−	0.244141i	−0.696302	+	0.717749i	$0.745173\pi$
$410$	1023.21	+	590.750i	0.123250	+	0.0711587i
$411$	1051.14	+	13597.7i	0.126153	+	1.63194i
$412$	−18616.9	−	10748.5i	−2.22619	−	1.28529i
$413$	−4055.66	+	4130.42i	−0.483211	+	0.492118i
$414$	−12953.5	−	16087.5i	−1.53775	−	1.90980i
$415$	−4618.18	+	7998.93i	−0.546259	+	0.946149i
$416$	427.620			0.0503986
$417$	5746.88	−	3937.97i	0.674882	−	0.462454i
$418$		−	13186.9i		−	1.54304i
$419$	−1365.90	−	2365.81i	−0.159257	−	0.275841i	0.775344	−	0.631539i	$-0.217577\pi$
$419$	−1365.90	−	2365.81i	−0.159257	−	0.275841i	−0.934601	+	0.355698i	$0.884243\pi$
$420$	19660.3	−	23383.4i	2.28410	−	2.71665i
$421$	−4199.36	+	7273.51i	−0.486139	+	0.842017i	−0.999873	−	0.0159323i	$-0.994928\pi$
$421$	−4199.36	+	7273.51i	−0.486139	+	0.842017i	0.513734	+	0.857949i	$0.328262\pi$
$422$	7121.35	+	4111.51i	0.821473	+	0.474278i
$423$	9113.10	+	11317.9i	1.04750	+	1.30094i
$424$	2774.84	+	4806.17i	0.317826	+	0.550491i
$425$	4568.60	+	7913.04i	0.521434	+	0.903150i
$426$	−13124.4	−	19153.1i	−1.49267	−	2.17833i
$427$	8995.38	−	2498.57i	1.01948	−	0.283171i
$428$	−3112.55	+	1797.03i	−0.351520	+	0.202950i
$429$	−469.836	−	685.656i	−0.0528762	−	0.0771649i
$430$			12872.4i			1.44363i
$431$	9243.99	−	5337.02i	1.03310	−	0.596463i	0.115231	−	0.993339i	$-0.463239\pi$
$431$	9243.99	−	5337.02i	1.03310	−	0.596463i	0.917872	+	0.396876i	$0.129906\pi$
$432$	8799.60	+	9350.65i	0.980026	+	1.04140i
$433$		−	4332.16i		−	0.480809i	−0.970673	−	0.240404i	$-0.922720\pi$
$433$		−	4332.16i		−	0.480809i	0.970673	−	0.240404i	$-0.0772801\pi$
$434$	9092.33	+	2347.50i	1.00564	+	0.259640i
$435$	−4277.32	−	2047.48i	−0.471452	−	0.225676i
$436$	2700.19			0.296596
$437$	−5720.23	+	9907.73i	−0.626169	+	1.08456i
$438$	−4093.72	+	8552.04i	−0.446588	+	0.932951i
$439$	−2459.01	+	1419.71i	−0.267339	+	0.154348i	−0.627678	−	0.778473i	$-0.715995\pi$
$439$	−2459.01	+	1419.71i	−0.267339	+	0.154348i	0.360339	+	0.932822i	$0.382661\pi$
$440$	−29729.6			−3.22115
$441$	8696.24	+	3184.58i	0.939017	+	0.343870i
$442$	−948.225			−0.102042
$443$	−1669.39	+	963.823i	−0.179041	+	0.103369i	−0.586842	−	0.809701i	$-0.699629\pi$
$443$	−1669.39	+	963.823i	−0.179041	+	0.103369i	0.407801	+	0.913071i	$0.366296\pi$
$444$	287.789	+	419.985i	0.0307609	+	0.0448910i
$445$	−12724.6	+	22039.7i	−1.35552	+	2.34782i
$446$	−17212.9			−1.82748
$447$	−298.422	−	3860.42i	−0.0315769	−	0.408482i
$448$	−4691.96	−	1211.39i	−0.494809	−	0.127752i
$449$		−	13226.6i		−	1.39020i	−0.718913	−	0.695100i	$-0.755360\pi$
$449$		−	13226.6i		−	1.39020i	0.718913	−	0.695100i	$-0.244640\pi$
$450$	−23155.0	+	18644.2i	−2.42564	+	1.95310i
$451$	386.466	−	223.126i	0.0403503	−	0.0232963i
$452$			7608.05i			0.791709i
$453$	17677.3	−	1366.50i	1.83344	−	0.141731i
$454$	16859.8	−	9734.04i	1.74289	−	1.00626i
$455$	−1508.58	+	419.027i	−0.155436	+	0.0431742i
$456$	7659.89	−	16002.0i	0.786638	−	1.64334i
$457$	−4106.85	−	7113.26i	−0.420372	−	0.728106i	0.575604	−	0.817729i	$-0.304767\pi$
$457$	−4106.85	−	7113.26i	−0.420372	−	0.728106i	−0.995976	+	0.0896228i	$0.971434\pi$
$458$	5713.26	+	9895.66i	0.582889	+	1.00959i
$459$	−3997.21	−	4247.53i	−0.406479	−	0.431934i
$460$	41981.0	+	24237.7i	4.25516	+	2.45672i
$461$	5491.41	−	9511.40i	0.554795	−	0.960933i	−0.443125	−	0.896460i	$-0.646130\pi$
$461$	5491.41	−	9511.40i	0.554795	−	0.960933i	0.997919	−	0.0644727i	$-0.0205365\pi$
$462$	−5777.50	−	15922.3i	−0.581804	−	1.60341i
$463$	6093.85	+	10554.9i	0.611675	+	1.05945i	0.990958	+	0.134171i	$0.0428371\pi$
$463$	6093.85	+	10554.9i	0.611675	+	1.05945i	−0.379284	+	0.925280i	$0.623830\pi$
$464$		−	4498.20i		−	0.450051i
$465$	−8808.23	−	4216.35i	−0.878435	−	0.420492i
$466$	−3999.60			−0.397593
$467$	3008.23	−	5210.40i	0.298082	−	0.516292i	−0.677615	−	0.735416i	$-0.736987\pi$
$467$	3008.23	−	5210.40i	0.298082	−	0.516292i	0.975697	+	0.219124i	$0.0703199\pi$
$468$	−322.998	−	2076.69i	−0.0319030	−	0.205117i
$469$	−8495.75	+	8652.36i	−0.836455	+	0.851874i
$470$	−43354.9	−	25030.9i	−4.25492	−	2.45658i
$471$	−10858.7	−	5197.87i	−1.06230	−	0.508504i
$472$	12335.3	+	7121.80i	1.20292	+	0.694507i
$473$	4210.53	+	2430.95i	0.409303	+	0.236311i
$474$	−11391.6	−	5452.99i	−1.10387	−	0.528405i
$475$	14260.4	+	8233.25i	1.37750	+	0.795300i
$476$	−12745.6	−	3290.72i	−1.22730	−	0.316870i
$477$	2561.08	−	2062.15i	0.245836	−	0.197945i
$478$	13181.4	−	22830.9i	1.26130	−	2.18464i
$479$	10557.6			1.00708			0.503539	−	0.863972i	$-0.332031\pi$
$479$	10557.6			1.00708			0.503539	+	0.863972i	$0.332031\pi$
$480$	−8173.84	−	3912.68i	−0.777257	−	0.372060i
$481$		−	26.0928i		−	0.00247345i
$482$	9897.75	+	17143.4i	0.935332	+	1.62004i
$483$	−2566.00	+	14469.2i	−0.241733	+	1.36308i
$484$	825.735	−	1430.22i	0.0775484	−	0.134318i
$485$	−3807.73	−	2198.39i	−0.356495	−	0.205822i
$486$	11656.6	−	14974.4i	1.08797	−	1.39764i
$487$	−1762.23	−	3052.27i	−0.163972	−	0.284008i	0.772318	−	0.635236i	$-0.219097\pi$
$487$	−1762.23	−	3052.27i	−0.163972	−	0.284008i	−0.936290	+	0.351229i	$0.885764\pi$
$488$	−11486.0	−	19894.3i	−1.06546	−	1.84544i
$489$	−3276.28	+	6844.36i	−0.302983	+	0.632950i
$490$	−31900.9	+	582.720i	−2.94109	+	0.0537237i
$491$	10853.9	−	6266.52i	0.997619	−	0.575976i	0.0900762	−	0.995935i	$-0.471289\pi$
$491$	10853.9	−	6266.52i	0.997619	−	0.575976i	0.907543	+	0.419959i	$0.137956\pi$
$492$	1124.99	−	86.9654i	0.103087	−	0.00796891i
$493$			2043.30i			0.186665i
$494$	−1479.89	+	854.418i	−0.134785	+	0.0778179i
$495$	2707.10	+	17405.1i	0.245808	+	1.58040i
$496$		−	9263.09i		−	0.838558i
$497$	−4129.58	+	15994.7i	−0.372710	+	1.44358i
$498$	997.974	+	12909.9i	0.0897998	+	1.16166i
$499$	9548.65			0.856626			0.428313	−	0.903630i	$-0.359108\pi$
$499$	9548.65			0.856626			0.428313	+	0.903630i	$0.359108\pi$
$500$	15044.9	−	26058.5i	1.34566	−	2.33075i
$501$	6155.37	+	8982.85i	0.548905	+	0.801046i
$502$	24072.5	−	13898.3i	2.14026	−	1.23568i
$503$	21478.4			1.90393			0.951963	−	0.306214i	$-0.0990624\pi$
$503$	21478.4			1.90393			0.951963	+	0.306214i	$0.0990624\pi$
$504$	2237.96	−	22677.4i	0.197791	−	2.00423i
$505$	−6575.22			−0.579393
$506$	23275.8	−	13438.3i	2.04493	−	1.18064i
$507$	4882.51	−	10199.9i	0.427692	−	0.893476i
$508$	17666.6	−	30599.5i	1.54297	−	2.67251i
$509$	−16323.8			−1.42149			−0.710745	−	0.703450i	$-0.751642\pi$
$509$	−16323.8			−1.42149			−0.710745	+	0.703450i	$0.751642\pi$
$510$	18125.1	+	8676.16i	1.57371	+	0.753307i
$511$	6499.64	−	1805.35i	0.562675	−	0.156290i
$512$			24769.7i			2.13804i
$513$	−10065.8	−	3027.34i	−0.866305	−	0.260547i
$514$	−12074.7	+	6971.31i	−1.03617	+	0.598232i
$515$		−	23347.5i		−	1.99770i
$516$	6948.93	+	10140.9i	0.592848	+	0.865174i
$517$	−16375.2	+	9454.20i	−1.39299	+	0.804246i
$518$	132.925	−	514.844i	0.0112749	−	0.0436697i
$519$	−8149.87	−	11893.5i	−0.689287	−	1.00591i
$520$	1926.28	+	3336.41i	0.162448	+	0.281368i
$521$	−7116.33	−	12325.8i	−0.598411	−	1.03648i	−0.993056	−	0.117644i	$-0.962466\pi$
$521$	−7116.33	−	12325.8i	−0.598411	−	1.03648i	0.394645	−	0.918834i	$-0.370868\pi$
$522$	−6568.97	+	1021.71i	−0.550797	+	0.0856684i
$523$	−4121.11	−	2379.33i	−0.344558	−	0.198931i	0.317728	−	0.948182i	$-0.397080\pi$
$523$	−4121.11	−	2379.33i	−0.344558	−	0.198931i	−0.662286	+	0.749251i	$0.730413\pi$
$524$	−1397.72	+	2420.92i	−0.116526	+	0.201829i
$525$	20825.8	+	3693.29i	1.73126	+	0.307026i
$526$	15027.0	+	26027.5i	1.24564	+	2.15751i
$527$			4207.75i			0.347804i
$528$	−13782.9	+	9444.54i	−1.13603	+	0.778448i
$529$	−11150.2			−0.916432
$530$	−5664.12	+	9810.54i	−0.464214	+	0.804043i
$531$	3046.20	−	7870.14i	0.248953	−	0.643192i
$532$	−22857.2	+	6348.86i	−1.86276	+	0.517402i
$533$	−50.0807	−	28.9141i	−0.00406986	−	0.00234974i
$534$	2749.75	+	35571.1i	0.222834	+	2.88260i
$535$	−3380.49	−	1951.73i	−0.273180	−	0.157721i
$536$	25839.9	+	14918.7i	2.08230	+	1.20222i
$537$	−314.839	+	215.739i	−0.0253004	+	0.0173368i
$538$	−11731.4	−	6773.13i	−0.940105	−	0.542770i
$539$	−5833.88	+	10544.8i	−0.466202	+	0.842663i
$540$	−12827.4	+	42650.6i	−1.02223	+	3.39887i
$541$	5255.73	−	9103.19i	0.417674	−	0.723432i	−0.578031	−	0.816014i	$-0.696179\pi$
$541$	5255.73	−	9103.19i	0.417674	−	0.723432i	0.995705	+	0.0925827i	$0.0295122\pi$
$542$	−8897.13			−0.705101
$543$	905.244	+	11710.3i	0.0715428	+	0.925486i
$544$			3904.70i			0.307744i
$545$	1466.32	+	2539.74i	0.115248	+	0.199616i
$546$	−1412.54	+	1680.04i	−0.110716	+	0.131683i
$547$	11334.1	−	19631.2i	0.885943	−	1.53450i	0.0413133	−	0.999146i	$-0.486846\pi$
$547$	11334.1	−	19631.2i	0.885943	−	1.53450i	0.844629	−	0.535351i	$-0.179821\pi$
$548$	−38861.4	−	22436.6i	−3.02934	−	1.74899i
$549$	−10601.1	+	8535.93i	−0.824126	+	0.663578i
$550$	−19342.0	−	33501.4i	−1.49954	−	2.59728i
$551$	1841.16	+	3188.98i	0.142352	+	0.246561i
$552$	36050.7	−	2786.83i	2.77975	−	0.214883i
$553$	2404.79	+	8657.77i	0.184923	+	0.665761i
$554$	3788.18	−	2187.11i	0.290513	−	0.167728i
$555$	−238.747	+	498.757i	−0.0182599	+	0.0381460i
$556$			22922.0i			1.74840i
$557$	10244.9	−	5914.91i	0.779338	−	0.449951i	−0.0568577	−	0.998382i	$-0.518108\pi$
$557$	10244.9	−	5914.91i	0.779338	−	0.449951i	0.836196	+	0.548431i	$0.184775\pi$
$558$	−13527.4	+	2103.99i	−1.02627	+	0.159622i
$559$		−	630.036i		−	0.0476703i
$560$	8423.18	+	30325.2i	0.635615	+	2.28835i
$561$	6260.87	−	4290.18i	0.471184	−	0.322872i
$562$	−9040.38			−0.678551
$563$	2833.63	−	4907.99i	0.212119	−	0.367401i	−0.740258	−	0.672323i	$-0.765297\pi$
$563$	2833.63	−	4907.99i	0.212119	−	0.367401i	0.952378	+	0.304921i	$0.0986302\pi$
$564$	−47667.7	+	3684.85i	−3.55882	+	0.275107i
$565$	−7155.95	+	4131.49i	−0.532838	+	0.307634i
$566$	−30218.6			−2.24414
$567$	−13480.2	+	754.745i	−0.998436	+	0.0559018i
$568$	40647.0			3.00266
$569$	3471.92	−	2004.52i	0.255801	−	0.147687i	−0.366617	−	0.930372i	$-0.619484\pi$
$569$	3471.92	−	2004.52i	0.255801	−	0.147687i	0.622417	+	0.782685i	$0.286151\pi$
$570$	36105.6	−	2791.07i	2.65315	−	0.205096i
$571$	3248.70	−	5626.91i	0.238097	−	0.412397i	−0.722071	−	0.691819i	$-0.756810\pi$
$571$	3248.70	−	5626.91i	0.238097	−	0.412397i	0.960168	+	0.279422i	$0.0901429\pi$
$572$	2734.80			0.199909
$573$	−16126.5	+	11050.5i	−1.17573	+	0.805655i
$574$	−840.857	−	825.638i	−0.0611441	−	0.0600374i
$575$			33561.0i			2.43407i
$576$	6980.61	−	1085.73i	0.504963	−	0.0785396i
$577$	13721.3	−	7922.02i	0.989995	−	0.571574i	0.0847219	−	0.996405i	$-0.473000\pi$
$577$	13721.3	−	7922.02i	0.989995	−	0.571574i	0.905273	+	0.424831i	$0.139666\pi$
$578$			15954.0i			1.14809i
$579$	−318.139	+	664.613i	−0.0228349	+	0.0477036i
$580$	13512.3	−	7801.36i	0.967361	−	0.558506i
$581$	6454.42	−	6573.39i	0.460885	−	0.469381i
$582$	−6145.50	+	475.065i	−0.437696	+	0.0338352i
$583$	2139.34	+	3705.44i	0.151977	+	0.263231i
$584$	−8299.23	−	14374.7i	−0.588056	−	1.01854i
$585$	1777.88	−	1431.53i	0.125652	−	0.101174i
$586$	−39713.8	−	22928.8i	−2.79960	−	1.61635i
$587$	−3651.54	+	6324.65i	−0.256755	+	0.444713i	−0.965371	−	0.260882i	$-0.915987\pi$
$587$	−3651.54	+	6324.65i	−0.256755	+	0.444713i	0.708616	+	0.705595i	$0.249320\pi$
$588$	−24817.1	+	17680.2i	−1.74055	+	1.24000i
$589$	3791.48	+	6567.04i	0.265238	+	0.459406i
$590$			29074.6i			2.02878i
$591$	1389.95	+	17980.5i	0.0967425	+	1.25147i
$592$	−524.512			−0.0364144
$593$	2546.38	−	4410.47i	0.176336	−	0.305424i	−0.764287	−	0.644877i	$-0.776909\pi$
$593$	2546.38	−	4410.47i	0.176336	−	0.305424i	0.940623	+	0.339453i	$0.110242\pi$
$594$	16923.0	+	17982.7i	1.16895	+	1.24216i
$595$	−3826.23	−	13775.2i	−0.263630	−	0.949125i
$596$	11032.8	+	6369.81i	0.758259	+	0.437781i
$597$	287.621	−	197.089i	0.0197179	−	0.0135114i
$598$	−3016.23	−	1741.42i	−0.206259	−	0.119084i
$599$	1617.80	+	934.036i	0.110353	+	0.0637123i	0.554161	−	0.832410i	$-0.313039\pi$
$599$	1617.80	+	934.036i	0.110353	+	0.0637123i	−0.443808	+	0.896122i	$0.646373\pi$
$600$	−4011.14	−	51888.6i	−0.272923	−	3.53057i
$601$	−17969.3	−	10374.6i	−1.21960	−	0.704139i	−0.254771	−	0.967001i	$-0.582000\pi$
$601$	−17969.3	−	10374.6i	−1.21960	−	0.704139i	−0.964833	+	0.262863i	$0.915333\pi$
$602$	3209.60	−	12431.4i	0.217298	−	0.841637i
$603$	6381.14	−	16486.3i	0.430945	−	1.11339i
$604$	−29168.0	+	50520.5i	−1.96495	+	3.40339i
$605$	1793.64			0.120532
$606$	−7603.86	+	5210.44i	−0.509712	+	0.349273i
$607$			3452.62i			0.230869i	0.993315	+	0.115434i	$0.0368260\pi$
$607$			3452.62i			0.230869i	−0.993315	+	0.115434i	$0.963174\pi$
$608$	3518.41	+	6094.06i	0.234688	+	0.406491i
$609$	3620.26	+	3043.84i	0.240887	+	0.202533i
$610$	23445.6	−	40609.0i	1.55621	−	2.69543i
$611$	2121.99	+	1225.13i	0.140502	+	0.0811188i
$612$	18962.7	−	2949.37i	1.25249	−	0.194806i
$613$	8024.21	+	13898.3i	0.528703	+	0.915740i	0.999440	+	0.0334664i	$0.0106547\pi$
$613$	8024.21	+	13898.3i	0.528703	+	0.915740i	−0.470737	+	0.882273i	$0.656012\pi$
$614$	−8030.20	−	13908.7i	−0.527806	−	0.914186i
$615$	692.717	+	1010.92i	0.0454196	+	0.0662832i
$616$	28711.1	+	7412.78i	1.87793	+	0.484853i
$617$	640.877	−	370.011i	0.0418164	−	0.0241427i	−0.478946	−	0.877844i	$-0.658981\pi$
$617$	640.877	−	370.011i	0.0418164	−	0.0241427i	0.520762	+	0.853702i	$0.325648\pi$
$618$	−18501.4	−	27000.1i	−1.20427	−	1.75745i
$619$			9135.21i			0.593174i	0.955006	+	0.296587i	$0.0958485\pi$
$619$			9135.21i			0.593174i	−0.955006	+	0.296587i	$0.904151\pi$
$620$	27825.8	−	16065.2i	1.80244	−	1.04064i
$621$	−4914.22	−	20851.9i	−0.317553	−	1.34744i
$622$		−	24.4053i		−	0.00157325i
$623$	17784.1	−	18111.9i	1.14366	−	1.16475i
$624$	1952.95	+	934.844i	0.125289	+	0.0599739i
$625$	5207.04			0.333250
$626$	−4810.50	+	8332.03i	−0.307135	+	0.531973i
$627$	5905.59	−	12337.2i	0.376151	−	0.785804i
$628$	34303.3	−	19805.0i	2.17970	−	1.25845i
$629$	238.259			0.0151034
$630$	42372.4	−	19188.8i	2.67962	−	1.21349i
$631$	−11586.8			−0.731004			−0.365502	−	0.930811i	$-0.619103\pi$
$631$	−11586.8			−0.731004			−0.365502	+	0.930811i	$0.619103\pi$
$632$	19147.6	−	11054.9i	1.20515	−	0.695791i
$633$	4821.19	+	7035.81i	0.302725	+	0.441782i
$634$	25447.3	−	44076.1i	1.59407	−	2.76102i
$635$	38374.9			2.39821
$636$	833.826	+	10786.5i	0.0519864	+	0.672502i
$637$	1561.38	−	28.5211i	0.0971181	−	0.00177401i
$638$		−	8650.73i		−	0.536811i
$639$	−3701.21	−	23796.6i	−0.229135	−	1.47320i
$640$	−33160.9	+	19145.4i	−2.04812	+	1.18248i
$641$			2669.76i			0.164507i	0.996611	+	0.0822536i	$0.0262118\pi$
$641$			2669.76i			0.164507i	−0.996611	+	0.0822536i	$0.973788\pi$
$642$	−5455.96	+	421.762i	−0.335404	+	0.0259277i
$643$	−23669.3	+	13665.5i	−1.45167	+	0.838124i	−0.998577	−	0.0533376i	$-0.983014\pi$
$643$	−23669.3	+	13665.5i	−1.45167	+	0.838124i	−0.453097	+	0.891461i	$0.649681\pi$
$644$	−34499.3	−	33874.9i	−2.11097	−	2.07276i
$645$	−5764.76	+	12043.0i	−0.351918	+	0.735180i
$646$	−7801.88	−	13513.2i	−0.475171	−	0.823021i
$647$	−7270.33	−	12592.6i	−0.441771	−	0.765170i	0.556050	−	0.831149i	$-0.312316\pi$
$647$	−7270.33	−	12592.6i	−0.441771	−	0.765170i	−0.997821	+	0.0659787i	$0.978983\pi$
$648$	10090.0	+	31651.8i	0.611688	+	1.91883i
$649$	9510.25	+	5490.74i	0.575208	+	0.332096i
$650$	−2506.46	+	4341.32i	−0.151249	+	0.261970i
$651$	7455.17	+	6268.15i	0.448834	+	0.377370i
$652$	−12483.4	−	21621.8i	−0.749825	−	1.29873i
$653$		−	3829.95i		−	0.229521i	−0.993393	−	0.114761i	$-0.963390\pi$
$653$		−	3829.95i		−	0.229521i	0.993393	−	0.114761i	$-0.0366101\pi$
$654$	3708.29	+	1775.10i	0.221721	+	0.106134i
$655$	−3036.09			−0.181114
$656$	−581.225	+	1006.71i	−0.0345930	+	0.0599169i
$657$	−7659.88	+	6167.66i	−0.454856	+	0.366246i
$658$	35628.4	+	34983.5i	2.11085	+	2.07264i
$659$	−21012.5	−	12131.6i	−1.24208	−	0.717116i	−0.272564	−	0.962138i	$-0.587872\pi$
$659$	−21012.5	−	12131.6i	−1.24208	−	0.717116i	−0.969518	+	0.245021i	$0.921205\pi$
$660$	−52275.0	−	25023.2i	−3.08303	−	1.47580i
$661$	11858.1	+	6846.29i	0.697772	+	0.402859i	0.806517	−	0.591211i	$-0.201350\pi$
$661$	11858.1	+	6846.29i	0.697772	+	0.402859i	−0.108745	+	0.994070i	$0.534683\pi$
$662$	−49928.6	−	28826.3i	−2.93132	−	1.69240i
$663$	−887.126	−	424.653i	−0.0519655	−	0.0248750i
$664$	−19631.1	−	11334.0i	−1.14734	−	0.662419i
$665$	−18384.0	−	18051.3i	−1.07203	−	1.05263i
$666$	119.136	+	765.975i	0.00693158	+	0.0445659i
$667$	−3752.54	+	6499.58i	−0.217839	+	0.377309i
$668$	−35829.0			−2.07525
$669$	−16103.8	−	7708.63i	−0.930658	−	0.445490i
$670$			60905.1i			3.51189i
$671$	−8855.42	−	15338.0i	−0.509478	−	0.882442i
$672$	6918.23	+	5816.70i	0.397137	+	0.333905i
$673$	−9187.98	+	15914.0i	−0.526256	+	0.911503i	0.473276	+	0.880914i	$0.343071\pi$
$673$	−9187.98	+	15914.0i	−0.526256	+	0.911503i	−0.999532	+	0.0305886i	$0.990262\pi$
$674$	36387.3	+	21008.2i	2.07951	+	1.20060i
$675$	−30012.6	+	7073.14i	−1.71139	+	0.403326i
$676$	18603.4	+	32222.1i	1.05846	+	1.83330i
$677$	−1417.84	−	2455.77i	−0.0804904	−	0.139413i	0.822970	−	0.568084i	$-0.192315\pi$
$677$	−1417.84	−	2455.77i	−0.0804904	−	0.139413i	−0.903461	+	0.428671i	$0.858982\pi$
$678$	−5001.50	+	10448.5i	−0.283306	+	0.591845i
$679$	3129.13	+	3072.49i	0.176856	+	0.173655i
$680$	−30465.5	+	17589.3i	−1.71808	+	0.991937i
$681$	20132.8	−	1556.32i	1.13288	−	0.0875747i
$682$		−	17814.3i		−	1.00021i
$683$	14759.6	−	8521.44i	0.826880	−	0.477399i	−0.0259033	−	0.999664i	$-0.508246\pi$
$683$	14759.6	−	8521.44i	0.826880	−	0.477399i	0.852783	+	0.522265i	$0.174913\pi$
$684$	26937.5	−	21689.8i	1.50582	−	1.21247i
$685$		−	48736.1i		−	2.71841i
$686$	30953.3	+	7391.40i	1.72274	+	0.411378i
$687$	913.463	+	11816.7i	0.0507289	+	0.656236i
$688$	−12664.8			−0.701806
$689$	277.229	−	480.175i	0.0153289	−	0.0265504i
$690$	41720.5	+	60884.9i	2.30185	+	3.35920i
$691$	−4224.31	+	2438.91i	−0.232562	+	0.134270i	−0.611753	−	0.791048i	$-0.709536\pi$
$691$	−4224.31	+	2438.91i	−0.232562	+	0.134270i	0.379191	+	0.925318i	$0.376202\pi$
$692$	47438.5			2.60598
$693$	1725.41	−	17483.8i	0.0945787	−	0.958374i
$694$	62380.8			3.41202
$695$	−21559.9	+	12447.6i	−1.17671	+	0.679374i
$696$	5024.97	−	10497.5i	0.273665	−	0.571704i
$697$	264.021	−	457.298i	0.0143479	−	0.0248514i
$698$	−10883.6			−0.590186
$699$	−3741.89	−	1791.18i	−0.202477	−	0.0969223i
$700$	−48756.9	+	49655.6i	−2.63262	+	2.68115i
$701$			18496.2i			0.996564i	0.867015	+	0.498282i	$0.166036\pi$
$701$			18496.2i			0.996564i	−0.867015	+	0.498282i	$0.833964\pi$
$702$	921.619	−	3064.34i	0.0495502	−	0.164752i
$703$	371.851	−	214.688i	0.0199497	−	0.0115180i
$704$			9192.82i			0.492141i
$705$	−29351.5	−	42834.1i	−1.56800	−	2.28826i
$706$	4191.60	−	2420.02i	0.223446	−	0.129007i
$707$	6349.96	+	1639.46i	0.337786	+	0.0872112i
$708$	15695.4	+	22905.1i	0.833149	+	1.21586i
$709$	5252.92	+	9098.33i	0.278248	+	0.481939i	0.970949	−	0.239285i	$-0.0769130\pi$
$709$	5252.92	+	9098.33i	0.278248	+	0.481939i	−0.692702	+	0.721224i	$0.743580\pi$
$710$	41485.1	+	71854.3i	2.19283	+	3.79809i
$711$	−8215.56	−	10203.3i	−0.433344	−	0.538188i
$712$	−54090.3	−	31229.0i	−2.84708	−	1.64376i
$713$	−7727.56	+	13384.5i	−0.405890	+	0.703021i
$714$	−15340.8	−	12898.2i	−0.804082	−	0.676055i
$715$	1485.11	+	2572.29i	0.0776785	+	0.134543i
$716$		−	1255.77i		−	0.0655450i
$717$	22556.6	−	15456.6i	1.17488	−	0.805073i
$718$	−5850.58			−0.304097
$719$	−519.987	+	900.644i	−0.0269711	+	0.0467154i	−0.879196	−	0.476460i	$-0.841920\pi$
$719$	−519.987	+	900.644i	−0.0269711	+	0.0467154i	0.852225	+	0.523176i	$0.175253\pi$
$720$	−28776.3	−	35738.6i	−1.48949	−	1.84986i
$721$	−5821.47	+	22547.7i	−0.300697	+	1.16466i
$722$	5404.90	+	3120.52i	0.278600	+	0.160850i
$723$	1582.50	+	20471.4i	0.0814021	+	1.05303i
$724$	−33467.4	−	19322.4i	−1.71796	−	0.991867i
$725$	9354.99	+	5401.11i	0.479221	+	0.276679i
$726$	2074.24	−	1421.34i	0.106036	−	0.0726597i
$727$	28717.4	+	16580.0i	1.46502	+	0.845829i	0.999236	−	0.0390696i	$-0.0124394\pi$
$727$	28717.4	+	16580.0i	1.46502	+	0.845829i	0.465783	+	0.884899i	$0.345773\pi$
$728$	−1028.38	−	3702.40i	−0.0523550	−	0.188489i
$729$	17611.6	−	8789.29i	0.894763	−	0.446542i
$730$	16940.7	−	29342.2i	0.858910	−	1.48768i
$731$	5753.00			0.291084
$732$	−3451.48	−	44648.7i	−0.174276	−	2.25446i
$733$		−	10650.5i		−	0.536677i	−0.963325	−	0.268339i	$-0.913525\pi$
$733$		−	10650.5i		−	0.536677i	0.963325	−	0.268339i	$-0.0864746\pi$
$734$	21797.0	+	37753.6i	1.09611	+	1.89851i
$735$	−30106.3	−	13741.3i	−1.51087	−	0.689600i
$736$	−7171.00	+	12420.5i	−0.359139	+	0.622047i
$737$	19921.9	+	11501.9i	0.995704	+	0.574870i
$738$	1602.17	+	620.134i	0.0799145	+	0.0309315i
$739$	701.510	+	1215.05i	0.0349194	+	0.0604822i	0.882957	−	0.469454i	$-0.155549\pi$
$739$	701.510	+	1215.05i	0.0349194	+	0.0604822i	−0.848038	+	0.529936i	$0.822216\pi$
$740$	−909.677	−	1575.61i	−0.0451897	−	0.0782709i
$741$	−1767.18	+	136.608i	−0.0876099	+	0.00677251i
$742$	7916.22	−	8062.15i	0.391663	−	0.398882i
$743$	−27959.9	+	16142.6i	−1.38055	+	0.797060i	−0.992224	−	0.124463i	$-0.960279\pi$
$743$	−27959.9	+	16142.6i	−1.38055	+	0.797060i	−0.388324	+	0.921523i	$0.626946\pi$
$744$	10347.9	−	21617.4i	0.509907	−	1.06523i
$745$			13836.3i			0.680433i
$746$	−36659.6	+	21165.5i	−1.79920	+	1.03877i
$747$	−4847.90	+	12525.0i	−0.237450	+	0.613475i
$748$			24972.1i			1.22068i
$749$	2778.03	+	2727.75i	0.135524	+	0.133071i
$750$	37792.6	−	25896.8i	1.83999	−	1.26083i
$751$	−33807.6			−1.64269			−0.821344	−	0.570433i	$-0.806775\pi$
$751$	−33807.6			−1.64269			−0.821344	+	0.570433i	$0.806775\pi$
$752$	24627.4	−	42655.9i	1.19424	−	2.06848i
$753$	28745.6	−	2222.12i	1.39117	−	0.107541i
$754$	−970.827	+	560.507i	−0.0468905	+	0.0270723i
$755$	−63357.9			−3.05408
$756$	23022.5	−	37991.1i	1.10757	−	1.82767i
$757$	−32096.2			−1.54102			−0.770512	−	0.637426i	$-0.779999\pi$
$757$	−32096.2			−1.54102			−0.770512	+	0.637426i	$0.779999\pi$
$758$	−45272.4	+	26138.0i	−2.16935	+	1.25247i
$759$	27794.3	−	2148.58i	1.32921	−	0.102752i
$760$	−31698.3	+	54903.1i	−1.51292	+	2.62045i
$761$	2884.25			0.137390			0.0686951	−	0.997638i	$-0.478116\pi$
$761$	2884.25			0.137390			0.0686951	+	0.997638i	$0.478116\pi$
$762$	44378.4	−	30409.7i	2.10979	−	1.44570i
$763$	−782.826	−	2818.34i	−0.0371431	−	0.133723i
$764$		−	64322.2i		−	3.04594i
$765$	13071.6	+	16234.2i	0.617786	+	0.767254i
$766$	−7504.29	+	4332.60i	−0.353970	+	0.204365i
$767$		−	1423.05i		−	0.0669926i
$768$	−18481.0	+	38607.9i	−0.868326	+	1.81399i
$769$	15050.9	−	8689.61i	0.705784	−	0.407484i	−0.103714	−	0.994607i	$-0.533073\pi$
$769$	15050.9	−	8689.61i	0.705784	−	0.407484i	0.809498	+	0.587123i	$0.199739\pi$
$770$	16199.1	+	58320.1i	0.758148	+	2.72950i
$771$	−14418.7	+	1114.60i	−0.673509	+	0.0520642i
$772$	−1212.18	−	2099.56i	−0.0565121	−	0.0978818i
$773$	−7817.05	−	13539.5i	−0.363726	−	0.629991i	0.624845	−	0.780749i	$-0.285162\pi$
$773$	−7817.05	−	13539.5i	−0.363726	−	0.629991i	−0.988571	+	0.150758i	$0.951829\pi$
$774$	2876.65	+	18495.2i	0.133591	+	0.858909i
$775$	19264.6	+	11122.4i	0.892911	+	0.515522i
$776$	5395.34	−	9345.00i	0.249589	−	0.432301i
$777$	354.927	−	422.141i	0.0163873	−	0.0194906i
$778$	−22011.0	−	38124.2i	−1.01431	−	1.75684i
$779$		−	951.607i		−	0.0437675i
$780$	578.836	+	7487.89i	0.0265713	+	0.343730i
$781$	31337.9			1.43580
$782$	15901.3	−	27541.9i	0.727147	−	1.25946i
$783$	−6603.26	−	1985.97i	−0.301381	−	0.0906421i
$784$	−573.325	−	31386.6i	−0.0261172	−	1.42978i
$785$	37256.3	+	21509.9i	1.69393	+	0.977990i
$786$	−3511.06	+	2405.90i	−0.159332	+	0.109180i
$787$	22839.4	+	13186.3i	1.03448	+	0.597258i	0.918265	−	0.395966i	$-0.129590\pi$
$787$	22839.4	+	13186.3i	1.03448	+	0.597258i	0.116216	+	0.993224i	$0.462924\pi$
$788$	−51387.2	−	29668.4i	−2.32309	−	1.34124i
$789$	2402.58	+	31080.1i	0.108408	+	1.40238i
$790$	39084.9	+	22565.7i	1.76023	+	1.01627i
$791$	7940.94	−	2205.69i	0.356950	−	0.0991469i
$792$	−42715.9	+	6643.82i	−1.91647	+	0.298078i
$793$	−1147.54	+	1987.60i	−0.0513876	+	0.0890059i
$794$	60320.5			2.69609
$795$	−9692.70	+	6641.78i	−0.432408	+	0.296302i
$796$			1147.21i			0.0510825i
$797$	−4401.10	−	7622.92i	−0.195602	−	0.338793i	0.751496	−	0.659738i	$-0.229333\pi$
$797$	−4401.10	−	7622.92i	−0.195602	−	0.338793i	−0.947098	+	0.320945i	$0.895999\pi$
$798$	−35564.6	−	6307.11i	−1.57766	−	0.279786i
$799$	−11187.0	+	19376.4i	−0.495327	+	0.857932i
$800$	17877.1	+	10321.4i	0.790065	+	0.456144i
$801$	−13357.6	+	34510.5i	−0.589221	+	1.52231i
$802$	−12980.2	−	22482.4i	−0.571506	−	0.989877i
$803$	−6398.52	−	11082.6i	−0.281194	−	0.487042i
$804$	32878.5	+	47981.3i	1.44221	+	2.10469i
$805$	13127.4	−	50844.8i	0.574756	−	2.22614i
$806$	−1999.21	+	1154.25i	−0.0873689	+	0.0504424i
$807$	−7942.22	−	11590.5i	−0.346443	−	0.505582i
$808$		−	16137.0i		−	0.702598i
$809$	29529.8	−	17049.0i	1.28333	−	0.740930i	0.305873	−	0.952072i	$-0.401052\pi$
$809$	29529.8	−	17049.0i	1.28333	−	0.740930i	0.977455	+	0.211142i	$0.0677183\pi$
$810$	−45654.9	+	50141.3i	−1.98043	+	2.17504i
$811$			22436.9i			0.971475i	0.874105	+	0.485737i	$0.161449\pi$
$811$			22436.9i			0.971475i	−0.874105	+	0.485737i	$0.838551\pi$
$812$	−14994.6	+	4164.92i	−0.648039	+	0.180000i
$813$	−8323.85	−	3984.49i	−0.359078	−	0.171884i
$814$	−1008.72			−0.0434343
$815$	13558.0	−	23483.1i	0.582718	−	1.00930i
$816$	−8536.27	+	17832.8i	−0.366212	+	0.765041i
$817$	8978.70	−	5183.86i	0.384486	−	0.221983i
$818$	20233.1			0.864835
$819$	−2073.91	+	939.193i	−0.0884838	+	0.0400709i
$820$	−4032.14			−0.171718
$821$	17597.0	−	10159.6i	0.748038	−	0.431880i	−0.0769464	−	0.997035i	$-0.524517\pi$
$821$	17597.0	−	10159.6i	0.748038	−	0.431880i	0.824985	+	0.565155i	$0.191184\pi$
$822$	−38620.3	−	56360.5i	−1.63873	−	2.39148i
$823$	5250.28	−	9093.75i	0.222373	−	0.385162i	−0.733155	−	0.680062i	$-0.761953\pi$
$823$	5250.28	−	9093.75i	0.222373	−	0.385162i	0.955528	+	0.294900i	$0.0952863\pi$
$824$	57300.0			2.42250
$825$	−3092.49	−	40004.9i	−0.130505	−	1.68823i
$826$	7249.45	−	28078.5i	0.305376	−	1.18278i
$827$			12440.4i			0.523089i	0.965191	+	0.261545i	$0.0842319\pi$
$827$			12440.4i			0.523089i	−0.965191	+	0.261545i	$0.915768\pi$
$828$	65735.3	+	25443.4i	2.75901	+	1.06790i
$829$	25751.9	−	14867.9i	1.07889	−	0.622899i	0.148295	−	0.988943i	$-0.452622\pi$
$829$	25751.9	−	14867.9i	1.07889	−	0.622899i	0.930597	+	0.366045i	$0.119288\pi$
$830$		−	46271.0i		−	1.93505i
$831$	4523.57	−	349.685i	0.188834	−	0.0145974i
$832$	1031.66	−	595.631i	0.0429886	−	0.0248195i
$833$	260.432	+	14257.3i	0.0108325	+	0.593022i
$834$	−15068.8	+	31479.8i	−0.625649	+	1.30702i
$835$	−19456.6	−	33699.9i	−0.806377	−	1.39669i
$836$	22501.6	+	38974.0i	0.930903	+	1.61237i
$837$	−13598.0	−	4089.69i	−0.561549	−	0.168889i
$838$	11851.9	+	6842.70i	0.488565	+	0.282073i
$839$	−10779.3	+	18670.3i	−0.443556	+	0.768261i	−0.997950	−	0.0639928i	$-0.979617\pi$
$839$	−10779.3	+	18670.3i	−0.443556	+	0.768261i	0.554395	+	0.832254i	$0.312950\pi$
$840$	−14219.3	+	80179.9i	−0.584063	+	3.29342i
$841$	−10986.7	−	19029.5i	−0.450477	−	0.780249i
$842$		−	42074.7i		−	1.72208i
$843$	−8457.87	−	4048.64i	−0.345557	−	0.165412i
$844$	−28063.0			−1.14451
$845$	−20204.9	+	34995.9i	−0.822568	+	1.42473i
$846$	−67886.5	−	26276.0i	−2.75885	−	1.06783i
$847$	−1732.19	−	447.225i	−0.0702700	−	0.0181426i
$848$	−9652.36	−	5572.80i	−0.390877	−	0.225673i
$849$	−28271.5	−	13533.1i	−1.14284	−	0.547060i
$850$	−39641.6	−	22887.1i	−1.59964	−	0.923553i
$851$	757.884	+	437.565i	0.0305287	+	0.0176258i
$852$	71471.5	+	34212.2i	2.87391	+	1.37569i
$853$	12410.8	+	7165.35i	0.498167	+	0.287617i	0.727956	−	0.685624i	$-0.240470\pi$
$853$	12410.8	+	7165.35i	0.498167	+	0.287617i	−0.229789	+	0.973240i	$0.573804\pi$
$854$	−32767.8	+	33371.9i	−1.31299	+	1.33719i
$855$	35029.1	+	13558.3i	1.40113	+	0.542320i
$856$	4789.97	−	8296.47i	0.191259	−	0.331270i
$857$	−28895.0			−1.15173			−0.575866	−	0.817544i	$-0.695335\pi$
$857$	−28895.0			−1.15173			−0.575866	+	0.817544i	$0.695335\pi$
$858$	3755.82	+	1797.85i	0.149443	+	0.0715357i
$859$			16933.5i			0.672600i	0.941755	+	0.336300i	$0.109176\pi$
$859$			16933.5i			0.672600i	−0.941755	+	0.336300i	$0.890824\pi$
$860$	−21965.0	−	38044.5i	−0.870931	−	1.50850i
$861$	−416.923	−	1149.01i	−0.0165026	−	0.0454797i
$862$	−26736.6	+	46309.2i	−1.05644	+	1.82981i
$863$	659.862	+	380.971i	0.0260278	+	0.0150271i	0.512957	−	0.858414i	$-0.328550\pi$
$863$	659.862	+	380.971i	0.0260278	+	0.0150271i	−0.486930	+	0.873441i	$0.661883\pi$
$864$	−12618.7	−	3795.14i	−0.496869	−	0.149436i
$865$	25761.1	+	44619.5i	1.01261	+	1.75388i
$866$	10851.3	+	18795.0i	0.425799	+	0.737506i
$867$	−7144.81	+	14926.0i	−0.279874	+	0.584674i
$868$	−30878.2	+	8576.78i	−1.20746	+	0.335386i
$869$	14762.4	−	8523.07i	0.576271	−	0.332710i
$870$	23685.7	−	1830.97i	0.923011	−	0.0713515i
$871$		−	2980.99i		−	0.115967i
$872$	−6233.08	+	3598.67i	−0.242063	+	0.139755i
$873$	−5962.27	−	2307.74i	−0.231148	−	0.0894676i
$874$		−	57312.7i		−	2.21812i
$875$	−31560.5	−	8148.43i	−1.21936	−	0.314820i
$876$	−2493.88	−	32261.1i	−0.0961875	−	1.24429i
$877$	9506.85			0.366047			0.183024	−	0.983109i	$-0.441412\pi$
$877$	9506.85			0.366047			0.183024	+	0.983109i	$0.441412\pi$
$878$	7112.24	−	12318.8i	0.273379	−	0.473506i
$879$	−26886.5	−	39236.8i	−1.03169	−	1.50560i
$880$	51707.7	−	29853.4i	1.98076	−	1.14359i
$881$	35524.5			1.35851			0.679257	−	0.733901i	$-0.262302\pi$
$881$	35524.5			1.35851			0.679257	+	0.733901i	$0.262302\pi$
$882$	−45705.3	+	7966.31i	−1.74487	+	0.304126i
$883$	−20779.3			−0.791934			−0.395967	−	0.918265i	$-0.629591\pi$
$883$	−20779.3			−0.791934			−0.395967	+	0.918265i	$0.629591\pi$
$884$	2802.49	−	1618.02i	0.106627	−	0.0615610i
$885$	−13020.8	+	27201.2i	−0.494562	+	1.03317i
$886$	4828.42	−	8363.07i	0.183086	−	0.317114i
$887$	15097.7			0.571512			0.285756	−	0.958302i	$-0.407755\pi$
$887$	15097.7			0.571512			0.285756	+	0.958302i	$0.407755\pi$
$888$	−1224.06	−	585.937i	−0.0462576	−	0.0221427i
$889$	−37060.2	−	9568.39i	−1.39816	−	0.360983i
$890$		−	127492.i		−	4.80173i
$891$	7779.18	+	24402.8i	0.292494	+	0.917536i
$892$	50873.1	−	29371.6i	1.90959	−	1.10250i
$893$			40321.0i			1.51096i
$894$	10964.4	+	16000.9i	0.410183	+	0.598601i
$895$	1181.15	−	681.935i	0.0441132	−	0.0254688i
$896$	36798.5	−	10221.2i	1.37204	−	0.381101i
$897$	−2042.00	−	2980.00i	−0.0760094	−	0.110924i
$898$	33130.2	+	57383.2i	1.23115	+	2.13241i
$899$	2487.25	+	4308.05i	0.0922743	+	0.159824i
$900$	36621.2	−	94614.2i	1.35634	−	3.50423i
$901$	4384.58	+	2531.44i	0.162122	+	0.0936010i
$902$	−1117.79	+	1936.06i	−0.0412619	+	0.0714676i
$903$	8570.05	−	10193.0i	0.315829	−	0.375638i
$904$	−10139.6	−	17562.3i	−0.373051	−	0.646143i
$905$		−	41971.6i		−	1.54164i
$906$	−73269.7	+	50207.0i	−2.68678	+	1.84108i
$907$	668.119			0.0244592			0.0122296	−	0.999925i	$-0.496107\pi$
$907$	668.119			0.0244592			0.0122296	+	0.999925i	$0.496107\pi$
$908$	−33219.7	+	57538.2i	−1.21413	+	2.10294i
$909$	−9447.34	+	1469.40i	−0.344718	+	0.0536158i
$910$	5495.39	−	5596.68i	0.200187	−	0.203877i
$911$	11058.3	+	6384.54i	0.402173	+	0.232195i	0.687421	−	0.726259i	$-0.258743\pi$
$911$	11058.3	+	6384.54i	0.402173	+	0.232195i	−0.285248	+	0.958454i	$0.592076\pi$
$912$	2746.07	+	35523.5i	0.0997055	+	1.28980i
$913$	−15135.1	−	8738.28i	−0.548631	−	0.316752i
$914$	35635.0	+	20573.9i	1.28961	+	0.744555i
$915$	40121.2	−	27492.5i	1.44958	−	0.993305i
$916$	−33771.3	−	19497.9i	−1.21816	−	0.703305i
$917$	2932.07	+	757.017i	0.105589	+	0.0272616i
$918$	27981.2	+	8415.51i	1.00601	+	0.302563i
$919$	−12511.9	+	21671.3i	−0.449108	+	0.777878i	−0.998328	−	0.0577998i	$-0.981591\pi$
$919$	−12511.9	+	21671.3i	−0.449108	+	0.777878i	0.549220	+	0.835678i	$0.314925\pi$
$920$	−129211.			−4.63039
$921$	−1283.91	−	16608.8i	−0.0459350	−	0.594221i
$922$			55020.1i			1.96528i
$923$	−2030.48	−	3516.89i	−0.0724096	−	0.125417i
$924$	44244.8	+	37200.1i	1.57527	+	1.32445i
$925$	629.796	−	1090.84i	0.0223866	−	0.0387747i
$926$	−52876.2	−	30528.1i	−1.87648	−	1.08339i
$927$	−5217.59	−	33546.0i	−0.184863	−	1.18856i
$928$	2308.11	+	3997.77i	0.0816461	+	0.141415i
$929$	−6089.03	−	10546.5i	−0.215042	−	0.372464i	0.738243	−	0.674535i	$-0.235656\pi$
$929$	−6089.03	−	10546.5i	−0.215042	−	0.372464i	−0.953286	+	0.302070i	$0.902322\pi$
$930$	48775.6	−	3770.50i	1.71980	−	0.132946i
$931$	13253.3	+	22016.7i	0.466552	+	0.775048i
$932$	11820.9	−	6824.79i	0.415457	−	0.239864i
$933$	10.9297	−	22.8328i	0.000383517	−	0.000801191i
$934$			30140.3i			1.05591i
$935$	−23488.2	+	13560.9i	−0.821546	+	0.474320i
$936$	3513.30	+	4363.31i	0.122688	+	0.152371i
$937$		−	31836.0i		−	1.10996i	−0.831863	−	0.554982i	$-0.812725\pi$
$937$		−	31836.0i		−	1.10996i	0.831863	−	0.554982i	$-0.187275\pi$
$938$	15186.1	−	58818.5i	0.528616	−	2.04743i
$939$	−8231.95	+	5640.83i	−0.286091	+	0.196040i
$940$	170848.			5.92813
$941$	−22435.3	+	38859.0i	−0.777226	+	1.34619i	0.156310	+	0.987708i	$0.450040\pi$
$941$	−22435.3	+	38859.0i	−0.777226	+	1.34619i	−0.933535	+	0.358486i	$0.883293\pi$
$942$	60130.0	−	4648.23i	2.07977	−	0.160772i
$943$	1679.66	−	969.752i	0.0580035	−	0.0334883i
$944$	−28605.8			−0.986272
$945$	48235.7	+	1023.65i	1.66043	+	0.0352373i
$946$	−24356.4			−0.837100
$947$	10108.1	−	5835.91i	0.346852	−	0.200255i	−0.316446	−	0.948611i	$-0.602490\pi$
$947$	10108.1	−	5835.91i	0.346852	−	0.200255i	0.663298	+	0.748355i	$0.269156\pi$
$948$	42973.0	−	3321.94i	1.47225	−	0.113810i
$949$	−829.160	+	1436.15i	−0.0283621	+	0.0491246i
$950$	−82491.5			−2.81724
$951$	43546.6	−	29839.7i	1.48485	−	1.01748i
$952$	33807.4	−	9390.40i	1.15095	−	0.319690i
$953$		−	4481.70i		−	0.152336i	−0.997095	−	0.0761682i	$-0.975731\pi$
$953$		−	4481.70i		−	0.152336i	0.997095	−	0.0761682i	$-0.0242686\pi$
$954$	−5945.86	+	15361.7i	−0.201786	+	0.521334i
$955$	60500.0	−	34929.7i	2.04998	−	1.18356i
$956$			89969.2i			3.04374i
$957$	3874.14	−	8093.32i	0.130860	−	0.273375i
$958$	−45804.2	+	26445.0i	−1.54474	+	0.891859i
$959$	−12151.9	+	47066.5i	−0.409180	+	1.58483i
$960$	−25169.9	+	1945.71i	−0.846204	+	0.0654141i
$961$	−9773.53	−	16928.2i	−0.328070	−	0.568234i
$962$	65.3580	+	113.203i	0.00219046	+	0.00379399i
$963$	−5293.29	−	2048.81i	−0.177127	−	0.0685586i
$964$	−58505.9	−	33778.4i	−1.95472	−	1.12856i
$965$	1316.53	−	2280.30i	0.0439177	−	0.0760677i
$966$	−25110.2	−	69201.6i	−0.836343	−	2.30489i
$967$	10438.9	+	18080.8i	0.347149	+	0.601280i	0.985742	−	0.168265i	$-0.0538164\pi$
$967$	10438.9	+	18080.8i	0.347149	+	0.601280i	−0.638593	+	0.769545i	$0.720483\pi$
$968$			4401.98i			0.146162i
$969$	−1247.40	−	16136.5i	−0.0413542	−	0.534963i
$970$	22026.3			0.729096
$971$	−9951.75	+	17236.9i	−0.328905	+	0.569680i	−0.982295	−	0.187341i	$-0.940013\pi$
$971$	−9951.75	+	17236.9i	−0.328905	+	0.569680i	0.653390	+	0.757022i	$0.273346\pi$
$972$	−8899.26	+	64147.5i	−0.293666	+	2.11680i
$973$	23924.9	−	6645.43i	0.788282	−	0.218954i
$974$	15290.8	+	8828.17i	0.503029	+	0.290424i
$975$	−4289.17	+	2939.10i	−0.140886	+	0.0965399i
$976$	39954.3	+	23067.6i	1.31035	+	0.756533i
$977$	−2735.30	−	1579.22i	−0.0895700	−	0.0517133i	0.454546	−	0.890723i	$-0.349802\pi$
$977$	−2735.30	−	1579.22i	−0.0895700	−	0.0517133i	−0.544116	+	0.839010i	$0.683135\pi$
$978$	−2929.83	−	37900.7i	−0.0957932	−	1.23919i
$979$	−41702.3	−	24076.9i	−1.36140	−	0.786006i
$980$	93289.2	−	56156.9i	3.04083	−	1.83048i
$981$	2674.39	+	3321.44i	0.0870405	+	0.108099i
$982$	−31393.1	+	54374.4i	−1.02016	+	1.76696i
$983$	−2682.61			−0.0870417			−0.0435208	−	0.999053i	$-0.513857\pi$
$983$	−2682.61			−0.0870417			−0.0435208	+	0.999053i	$0.513857\pi$
$984$	−2481.02	+	1700.08i	−0.0803780	+	0.0550779i
$985$		−	64444.8i		−	2.08465i
$986$	−5118.12	−	8864.84i	−0.165308	−	0.286323i
$987$	17665.7	+	48685.1i	0.569711	+	1.57008i
$988$	2915.90	−	5050.49i	0.0938939	−	0.162629i
$989$	18299.8	+	10565.4i	0.588373	+	0.339697i
$990$	−55341.4	−	68730.8i	−1.77663	−	2.20647i
$991$	−186.928	−	323.769i	−0.00599189	−	0.0103783i	0.863014	−	0.505180i	$-0.168574\pi$
$991$	−186.928	−	323.769i	−0.00599189	−	0.0103783i	−0.869006	+	0.494802i	$0.835241\pi$
$992$	4753.08	+	8232.57i	0.152127	+	0.263492i
$993$	−33801.9	−	49328.9i	−1.08023	−	1.57644i
$994$	−22147.7	−	79736.5i	−0.706724	−	2.54436i
$995$	−1079.04	+	622.981i	−0.0343796	+	0.0198491i
$996$	−24978.6	−	36452.5i	−0.794655	−	1.15968i
$997$			48421.0i			1.53812i	0.639176	+	0.769061i	$0.279276\pi$
$997$			48421.0i			1.53812i	−0.639176	+	0.769061i	$0.720724\pi$
$998$	−41426.7	+	23917.7i	−1.31397	+	0.758619i
$999$	−231.574	+	769.973i	−0.00733401	+	0.0243853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.47.2	yes	44
3.2	odd	2		189.4.s.a.89.21		44
7.3	odd	6		63.4.i.a.38.2	yes	44
9.4	even	3		189.4.i.a.152.2		44
9.5	odd	6		63.4.i.a.5.21	✓	44
21.17	even	6		189.4.i.a.143.21		44
63.31	odd	6		189.4.s.a.17.21		44
63.59	even	6	inner	63.4.s.a.59.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.21	✓	44	9.5	odd	6
63.4.i.a.38.2	yes	44	7.3	odd	6
63.4.s.a.47.2	yes	44	1.1	even	1	trivial
63.4.s.a.59.2	yes	44	63.59	even	6	inner
189.4.i.a.143.21		44	21.17	even	6
189.4.i.a.152.2		44	9.4	even	3
189.4.s.a.17.21		44	63.31	odd	6
189.4.s.a.89.21		44	3.2	odd	2

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.33849 + 2.50483i) q^{2} +(-5.18070 + 0.400483i) q^{3} +(8.54831 - 14.8061i) q^{4} +18.5684 q^{5} +(21.4732 - 14.7142i) q^{6} +(-17.9322 - 4.62983i) q^{7} +45.5709i q^{8} +(26.6792 - 4.14956i) q^{9} +O(q^{10})\)	\(q+(-4.33849 + 2.50483i) q^{2} +(-5.18070 + 0.400483i) q^{3} +(8.54831 - 14.8061i) q^{4} +18.5684 q^{5} +(21.4732 - 14.7142i) q^{6} +(-17.9322 - 4.62983i) q^{7} +45.5709i q^{8} +(26.6792 - 4.14956i) q^{9} +(-80.5586 + 46.5105i) q^{10} +35.1341i q^{11} +(-38.3566 + 80.1294i) q^{12} +(3.94292 - 2.27645i) q^{13} +(89.3956 - 24.8307i) q^{14} +(-96.1970 + 7.43631i) q^{15} +(-45.7606 - 79.2597i) q^{16} +(20.7867 + 36.0037i) q^{17} +(-105.354 + 84.8296i) q^{18} +(64.8837 + 37.4606i) q^{19} +(158.728 - 274.925i) q^{20} +(94.7556 + 16.8042i) q^{21} +(-88.0048 - 152.429i) q^{22} +152.700i q^{23} +(-18.2504 - 236.089i) q^{24} +219.784 q^{25} +(-11.4042 + 19.7527i) q^{26} +(-136.555 + 32.1822i) q^{27} +(-221.840 + 225.929i) q^{28} +(42.5645 + 24.5746i) q^{29} +(398.723 - 273.219i) q^{30} +(87.6525 + 50.6062i) q^{31} +(81.3395 + 46.9614i) q^{32} +(-14.0706 - 182.019i) q^{33} +(-180.366 - 104.134i) q^{34} +(-332.972 - 85.9684i) q^{35} +(166.623 - 430.487i) q^{36} +(2.86552 - 4.96323i) q^{37} -375.330 q^{38} +(-19.5154 + 13.3727i) q^{39} +846.176i q^{40} +(-6.35071 - 10.9998i) q^{41} +(-453.187 + 164.442i) q^{42} +(69.1907 - 119.842i) q^{43} +(520.199 + 300.337i) q^{44} +(495.390 - 77.0506i) q^{45} +(-382.486 - 662.486i) q^{46} +(269.089 + 466.076i) q^{47} +(268.814 + 392.294i) q^{48} +(300.129 + 166.046i) q^{49} +(-953.530 + 550.521i) q^{50} +(-122.109 - 178.199i) q^{51} -77.8390i q^{52} +(105.466 - 60.8907i) q^{53} +(511.832 - 481.669i) q^{54} +652.382i q^{55} +(210.985 - 817.187i) q^{56} +(-351.145 - 168.087i) q^{57} -246.220 q^{58} +(156.280 - 270.684i) q^{59} +(-712.219 + 1487.87i) q^{60} +(-436.557 + 252.047i) q^{61} -507.039 q^{62} +(-497.630 - 49.1094i) q^{63} +261.650 q^{64} +(73.2136 - 42.2699i) q^{65} +(516.971 + 754.442i) q^{66} +(327.373 - 567.026i) q^{67} +710.766 q^{68} +(-61.1537 - 791.091i) q^{69} +(1659.93 - 461.065i) q^{70} -891.951i q^{71} +(189.099 + 1215.80i) q^{72} +(-315.436 + 182.117i) q^{73} +28.7105i q^{74} +(-1138.63 + 88.0198i) q^{75} +(1109.29 - 640.450i) q^{76} +(162.665 - 630.032i) q^{77} +(51.1711 - 106.900i) q^{78} +(-242.587 - 420.173i) q^{79} +(-849.700 - 1471.72i) q^{80} +(694.562 - 221.414i) q^{81} +(55.1049 + 31.8149i) q^{82} +(-248.712 + 430.783i) q^{83} +(1058.80 - 1259.31i) q^{84} +(385.976 + 668.530i) q^{85} +693.243i q^{86} +(-230.355 - 110.267i) q^{87} -1601.09 q^{88} +(-685.285 + 1186.95i) q^{89} +(-1956.24 + 1575.15i) q^{90} +(-81.2449 + 22.5667i) q^{91} +(2260.89 + 1305.32i) q^{92} +(-474.368 - 227.072i) q^{93} +(-2334.88 - 1348.04i) q^{94} +(1204.78 + 695.583i) q^{95} +(-440.203 - 210.718i) q^{96} +(-205.065 - 118.394i) q^{97} +(-1718.02 + 31.3824i) q^{98} +(145.791 + 937.350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Introduction

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