LMFDB - Embedded newform 63.4.s.a.59.13

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			59.13
Character	$\chi$	$=$	63.59
Dual form			63.4.s.a.47.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.725355 + 0.418784i) q^{2} +(0.141982 + 5.19421i) q^{3} +(-3.64924 - 6.32067i) q^{4} -21.9169 q^{5} +(-2.07226 + 3.82711i) q^{6} +(2.19637 + 18.3896i) q^{7} -12.8135i q^{8} +(-26.9597 + 1.47497i) q^{9} +O(q^{10})$	\(q+(0.725355 + 0.418784i) q^{2} +(0.141982 + 5.19421i) q^{3} +(-3.64924 - 6.32067i) q^{4} -21.9169 q^{5} +(-2.07226 + 3.82711i) q^{6} +(2.19637 + 18.3896i) q^{7} -12.8135i q^{8} +(-26.9597 + 1.47497i) q^{9} +(-15.8975 - 9.17842i) q^{10} -15.4606i q^{11} +(32.3128 - 19.8524i) q^{12} +(33.3594 + 19.2600i) q^{13} +(-6.10810 + 14.2588i) q^{14} +(-3.11180 - 113.841i) q^{15} +(-23.8278 + 41.2710i) q^{16} +(-34.8682 + 60.3936i) q^{17} +(-20.1730 - 10.2204i) q^{18} +(-55.4679 + 32.0244i) q^{19} +(79.9799 + 138.529i) q^{20} +(-95.2074 + 14.0194i) q^{21} +(6.47465 - 11.2144i) q^{22} -69.8230i q^{23} +(66.5561 - 1.81929i) q^{24} +355.349 q^{25} +(16.1316 + 27.9407i) q^{26} +(-11.4891 - 139.825i) q^{27} +(108.219 - 80.9905i) q^{28} +(-168.609 + 97.3466i) q^{29} +(45.4175 - 83.8781i) q^{30} +(68.0764 - 39.3039i) q^{31} +(-123.342 + 71.2115i) q^{32} +(80.3057 - 2.19513i) q^{33} +(-50.5837 + 29.2045i) q^{34} +(-48.1376 - 403.041i) q^{35} +(107.705 + 165.021i) q^{36} +(3.34533 + 5.79428i) q^{37} -53.6452 q^{38} +(-95.3043 + 176.010i) q^{39} +280.832i q^{40} +(9.21172 - 15.9552i) q^{41} +(-74.9303 - 29.7023i) q^{42} +(-12.2255 - 21.1752i) q^{43} +(-97.7214 + 56.4195i) q^{44} +(590.872 - 32.3267i) q^{45} +(29.2407 - 50.6465i) q^{46} +(-138.270 + 239.491i) q^{47} +(-217.754 - 117.907i) q^{48} +(-333.352 + 80.7806i) q^{49} +(257.754 + 148.814i) q^{50} +(-318.648 - 172.538i) q^{51} -281.138i q^{52} +(-95.3706 - 55.0622i) q^{53} +(50.2227 - 106.234i) q^{54} +338.848i q^{55} +(235.635 - 28.1432i) q^{56} +(-174.217 - 283.565i) q^{57} -163.069 q^{58} +(176.782 + 306.196i) q^{59} +(-708.194 + 435.101i) q^{60} +(-460.697 - 265.983i) q^{61} +65.8393 q^{62} +(-86.3376 - 492.537i) q^{63} +261.957 q^{64} +(-731.132 - 422.120i) q^{65} +(59.1694 + 32.0385i) q^{66} +(-262.021 - 453.834i) q^{67} +508.970 q^{68} +(362.676 - 9.91363i) q^{69} +(133.870 - 312.507i) q^{70} -43.3150i q^{71} +(18.8996 + 345.448i) q^{72} +(54.9811 + 31.7433i) q^{73} +5.60388i q^{74} +(50.4532 + 1845.76i) q^{75} +(404.831 + 233.729i) q^{76} +(284.314 - 33.9572i) q^{77} +(-142.840 + 87.7579i) q^{78} +(-606.173 + 1049.92i) q^{79} +(522.231 - 904.531i) q^{80} +(724.649 - 79.5295i) q^{81} +(13.3635 - 7.71543i) q^{82} +(111.327 + 192.824i) q^{83} +(436.047 + 550.615i) q^{84} +(764.202 - 1323.64i) q^{85} -20.4793i q^{86} +(-529.578 - 861.971i) q^{87} -198.105 q^{88} +(-35.2649 - 61.0806i) q^{89} +(442.129 + 223.999i) q^{90} +(-280.914 + 655.766i) q^{91} +(-441.328 + 254.801i) q^{92} +(213.818 + 348.023i) q^{93} +(-200.590 + 115.811i) q^{94} +(1215.68 - 701.874i) q^{95} +(-387.400 - 630.553i) q^{96} +(483.359 - 279.067i) q^{97} +(-275.628 - 81.0077i) q^{98} +(22.8040 + 416.813i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.725355	+	0.418784i	0.256452	+	0.148062i	0.622715	−	0.782449i	$-0.286030\pi$
$2$	0.725355	+	0.418784i	0.256452	+	0.148062i	−0.366263	+	0.930511i	$0.619363\pi$
$3$	0.141982	+	5.19421i	0.0273245	+	0.999627i
$3$	0.141982	+	5.19421i	0.0273245	+	0.999627i
$4$	−3.64924	−	6.32067i	−0.456155	−	0.790084i
$5$	−21.9169			−1.96030			−0.980152	−	0.198249i	$-0.936475\pi$
$5$	−21.9169			−1.96030			−0.980152	+	0.198249i	$0.936475\pi$
$6$	−2.07226	+	3.82711i	−0.141000	+	0.260402i
$7$	2.19637	+	18.3896i	0.118593	+	0.992943i
$7$	2.19637	+	18.3896i	0.118593	+	0.992943i
$8$		−	12.8135i		−	0.566282i
$9$	−26.9597	+	1.47497i	−0.998507	+	0.0546286i
$10$	−15.8975	−	9.17842i	−0.502723	−	0.290247i
$11$		−	15.4606i		−	0.423777i	−0.977294	−	0.211889i	$-0.932039\pi$
$11$		−	15.4606i		−	0.423777i	0.977294	−	0.211889i	$-0.0679614\pi$
$12$	32.3128	−	19.8524i	0.777325	−	0.477573i
$13$	33.3594	+	19.2600i	0.711709	+	0.410906i	0.811694	−	0.584083i	$-0.198546\pi$
$13$	33.3594	+	19.2600i	0.711709	+	0.410906i	−0.0999842	+	0.994989i	$0.531879\pi$
$14$	−6.10810	+	14.2588i	−0.116604	+	0.272201i
$15$	−3.11180	−	113.841i	−0.0535643	−	1.95957i
$16$	−23.8278	+	41.2710i	−0.372310	+	0.644860i
$17$	−34.8682	+	60.3936i	−0.497458	+	0.861623i	−0.999996	−	0.00293248i	$-0.999067\pi$
$17$	−34.8682	+	60.3936i	−0.497458	+	0.861623i	0.502537	+	0.864555i	$0.332400\pi$
$18$	−20.1730	−	10.2204i	−0.264157	−	0.133832i
$19$	−55.4679	+	32.0244i	−0.669748	+	0.386679i	−0.795981	−	0.605322i	$-0.793045\pi$
$19$	−55.4679	+	32.0244i	−0.669748	+	0.386679i	0.126233	+	0.992001i	$0.459711\pi$
$20$	79.9799	+	138.529i	0.894202	+	1.54880i
$21$	−95.2074	+	14.0194i	−0.989332	+	0.145680i
$22$	6.47465	−	11.2144i	0.0627455	−	0.108678i
$23$		−	69.8230i		−	0.633005i	−0.948592	−	0.316502i	$-0.897491\pi$
$23$		−	69.8230i		−	0.633005i	0.948592	−	0.316502i	$-0.102509\pi$
$24$	66.5561	−	1.81929i	0.566071	−	0.0154734i
$25$	355.349			2.84279
$26$	16.1316	+	27.9407i	0.121679	+	0.210755i
$27$	−11.4891	−	139.825i	−0.0818919	−	0.996641i
$28$	108.219	−	80.9905i	0.730411	−	0.546634i
$29$	−168.609	+	97.3466i	−1.07965	+	0.623338i	−0.930803	−	0.365521i	$-0.880891\pi$
$29$	−168.609	+	97.3466i	−1.07965	+	0.623338i	−0.148851	+	0.988860i	$0.547557\pi$
$30$	45.4175	−	83.8781i	0.276402	−	0.510466i
$31$	68.0764	−	39.3039i	0.394415	−	0.227716i	−0.289656	−	0.957131i	$-0.593541\pi$
$31$	68.0764	−	39.3039i	0.394415	−	0.227716i	0.684071	+	0.729415i	$0.260208\pi$
$32$	−123.342	+	71.2115i	−0.681374	+	0.393391i
$33$	80.3057	−	2.19513i	0.423619	−	0.0115795i
$34$	−50.5837	+	29.2045i	−0.255148	+	0.147310i
$35$	−48.1376	−	403.041i	−0.232478	−	1.94647i
$36$	107.705	+	165.021i	0.498635	+	0.763985i
$37$	3.34533	+	5.79428i	0.0148640	+	0.0257453i	0.873362	−	0.487072i	$-0.161935\pi$
$37$	3.34533	+	5.79428i	0.0148640	+	0.0257453i	−0.858498	+	0.512817i	$0.828602\pi$
$38$	−53.6452			−0.229010
$39$	−95.3043	+	176.010i	−0.391305	+	0.722672i
$40$			280.832i			1.11009i
$41$	9.21172	−	15.9552i	0.0350885	−	0.0607751i	−0.847948	−	0.530080i	$-0.822162\pi$
$41$	9.21172	−	15.9552i	0.0350885	−	0.0607751i	0.883036	+	0.469305i	$0.155495\pi$
$42$	−74.9303	−	29.7023i	−0.275285	−	0.109123i
$43$	−12.2255	−	21.1752i	−0.0433574	−	0.0750973i	0.843532	−	0.537078i	$-0.180472\pi$
$43$	−12.2255	−	21.1752i	−0.0433574	−	0.0750973i	−0.886890	+	0.461981i	$0.847139\pi$
$44$	−97.7214	+	56.4195i	−0.334819	+	0.193308i
$45$	590.872	−	32.3267i	1.95738	−	0.107089i
$46$	29.2407	−	50.6465i	0.0937242	−	0.162335i
$47$	−138.270	+	239.491i	−0.429124	+	0.743264i	−0.996796	−	0.0799909i	$-0.974511\pi$
$47$	−138.270	+	239.491i	−0.429124	+	0.743264i	0.567672	+	0.823255i	$0.307844\pi$
$48$	−217.754	−	117.907i	−0.654792	−	0.354550i
$49$	−333.352	+	80.7806i	−0.971871	+	0.235512i
$50$	257.754	+	148.814i	0.729038	+	0.420910i
$51$	−318.648	−	172.538i	−0.874894	−	0.473729i
$52$		−	281.138i		−	0.749747i
$53$	−95.3706	−	55.0622i	−0.247173	−	0.142705i	0.371296	−	0.928514i	$-0.378913\pi$
$53$	−95.3706	−	55.0622i	−0.247173	−	0.142705i	−0.618469	+	0.785809i	$0.712247\pi$
$54$	50.2227	−	106.234i	0.126564	−	0.267715i
$55$			338.848i			0.830732i
$56$	235.635	−	28.1432i	0.562286	−	0.0671571i
$57$	−174.217	−	283.565i	−0.404835	−	0.658932i
$58$	−163.069			−0.369172
$59$	176.782	+	306.196i	0.390086	+	0.675649i	0.992461	−	0.122565i	$-0.0391119\pi$
$59$	176.782	+	306.196i	0.390086	+	0.675649i	−0.602374	+	0.798214i	$0.705779\pi$
$60$	−708.194	+	435.101i	−1.52379	+	0.936189i
$61$	−460.697	−	265.983i	−0.966986	−	0.558290i	−0.0686701	−	0.997639i	$-0.521876\pi$
$61$	−460.697	−	265.983i	−0.966986	−	0.558290i	−0.898316	+	0.439350i	$0.855209\pi$
$62$	65.8393			0.134865
$63$	−86.3376	−	492.537i	−0.172659	−	0.984982i
$64$	261.957			0.511634
$65$	−731.132	−	422.120i	−1.39517	−	0.805500i
$66$	59.1694	+	32.0385i	0.110352	+	0.0597525i
$67$	−262.021	−	453.834i	−0.477776	−	0.827532i	0.521899	−	0.853007i	$-0.325224\pi$
$67$	−262.021	−	453.834i	−0.477776	−	0.827532i	−0.999675	+	0.0254747i	$0.991890\pi$
$68$	508.970			0.907672
$69$	362.676	−	9.91363i	0.632768	−	0.0172965i
$70$	133.870	−	312.507i	0.228580	−	0.533596i
$71$		−	43.3150i		−	0.0724020i	−0.999345	−	0.0362010i	$-0.988474\pi$
$71$		−	43.3150i		−	0.0724020i	0.999345	−	0.0362010i	$-0.0115256\pi$
$72$	18.8996	+	345.448i	0.0309352	+	0.565437i
$73$	54.9811	+	31.7433i	0.0881513	+	0.0508942i	0.543428	−	0.839456i	$-0.317126\pi$
$73$	54.9811	+	31.7433i	0.0881513	+	0.0508942i	−0.455276	+	0.890350i	$0.650460\pi$
$74$			5.60388i			0.00880322i
$75$	50.4532	+	1845.76i	0.0776778	+	2.84173i
$76$	404.831	+	233.729i	0.611018	+	0.352771i
$77$	284.314	−	33.9572i	0.420787	−	0.0502570i
$78$	−142.840	+	87.7579i	−0.207351	+	0.127393i
$79$	−606.173	+	1049.92i	−0.863289	+	1.49526i	0.00544698	+	0.999985i	$0.498266\pi$
$79$	−606.173	+	1049.92i	−0.863289	+	1.49526i	−0.868736	+	0.495275i	$0.835067\pi$
$80$	522.231	−	904.531i	0.729840	−	1.26412i
$81$	724.649	−	79.5295i	0.994031	−	0.109094i
$82$	13.3635	−	7.71543i	0.0179970	−	0.0103906i
$83$	111.327	+	192.824i	0.147226	+	0.255003i	0.930201	−	0.367050i	$-0.119632\pi$
$83$	111.327	+	192.824i	0.147226	+	0.255003i	−0.782975	+	0.622053i	$0.786299\pi$
$84$	436.047	+	550.615i	0.566388	+	0.715202i
$85$	764.202	−	1323.64i	0.975169	−	1.68904i
$86$		−	20.4793i		−	0.0256784i
$87$	−529.578	−	861.971i	−0.652607	−	1.06222i
$88$	−198.105			−0.239978
$89$	−35.2649	−	61.0806i	−0.0420008	−	0.0727475i	0.844261	−	0.535933i	$-0.180040\pi$
$89$	−35.2649	−	61.0806i	−0.0420008	−	0.0727475i	−0.886262	+	0.463185i	$0.846707\pi$
$90$	442.129	+	223.999i	0.517828	+	0.262351i
$91$	−280.914	+	655.766i	−0.323602	+	0.755417i
$92$	−441.328	+	254.801i	−0.500127	+	0.288748i
$93$	213.818	+	348.023i	0.238408	+	0.388046i
$94$	−200.590	+	115.811i	−0.220099	+	0.127074i
$95$	1215.68	−	701.874i	1.31291	−	0.758008i
$96$	−387.400	−	630.553i	−0.411863	−	0.670370i
$97$	483.359	−	279.067i	0.505955	−	0.292114i	−0.225214	−	0.974309i	$-0.572308\pi$
$97$	483.359	−	279.067i	0.505955	−	0.292114i	0.731170	+	0.682196i	$0.238975\pi$
$98$	−275.628	−	81.0077i	−0.284108	−	0.0835002i
$99$	22.8040	+	416.813i	0.0231503	+	0.423144i
$100$	−1296.75	−	2246.04i	−1.29675	−	2.24604i
$101$	734.157			0.723281			0.361641	−	0.932318i	$-0.382217\pi$
$101$	734.157			0.723281			0.361641	+	0.932318i	$0.382217\pi$
$102$	−158.876	−	258.596i	−0.154227	−	0.251027i
$103$			748.708i			0.716237i	0.933676	+	0.358119i	$0.116582\pi$
$103$			748.708i			0.716237i	−0.933676	+	0.358119i	$0.883418\pi$
$104$	246.789	−	427.451i	0.232689	−	0.403029i
$105$	2086.65	−	307.261i	1.93939	−	0.285578i
$106$	−46.1183	−	79.8793i	−0.0422586	−	0.0731940i
$107$	682.104	−	393.813i	0.616276	−	0.355807i	−0.159142	−	0.987256i	$-0.550873\pi$
$107$	682.104	−	393.813i	0.616276	−	0.355807i	0.775418	+	0.631449i	$0.217539\pi$
$108$	−841.860	+	582.874i	−0.750075	+	0.519324i
$109$	−798.482	+	1383.01i	−0.701658	+	1.21531i	0.266227	+	0.963910i	$0.414223\pi$
$109$	−798.482	+	1383.01i	−0.701658	+	1.21531i	−0.967884	+	0.251396i	$0.919110\pi$
$110$	−141.904	+	245.785i	−0.123000	+	0.213042i
$111$	−29.6218	+	18.1990i	−0.0253295	+	0.0155620i
$112$	−811.291	−	347.537i	−0.684462	−	0.293207i
$113$	1648.59	+	951.814i	1.37245	+	0.792382i	0.991235	−	0.132107i	$-0.0421743\pi$
$113$	1648.59	+	951.814i	1.37245	+	0.792382i	0.381210	+	0.924489i	$0.375508\pi$
$114$	−7.61666	−	278.644i	−0.00625759	−	0.228925i
$115$			1530.30i			1.24088i
$116$	1230.59	+	710.482i	0.984979	+	0.568678i
$117$	−927.766	−	470.040i	−0.733094	−	0.371412i
$118$			296.134i			0.231028i
$119$	−1187.19	−	508.565i	−0.914537	−	0.391765i
$120$	−1458.70	+	39.8731i	−1.10967	+	0.0303325i
$121$	1091.97			0.820413
$122$	−222.779	−	385.864i	−0.165323	−	0.286349i
$123$	84.1824	+	45.5823i	0.0617111	+	0.0334147i
$124$	−496.854	−	286.859i	−0.359829	−	0.207747i
$125$	−5048.52			−3.61243
$126$	143.641	−	393.421i	0.101560	−	0.278164i
$127$	141.535			0.0988916			0.0494458	−	0.998777i	$-0.484254\pi$
$127$	141.535			0.0988916			0.0494458	+	0.998777i	$0.484254\pi$
$128$	1176.75	+	679.395i	0.812583	+	0.469145i
$129$	108.253	−	66.5083i	0.0738845	−	0.0453933i
$130$	−353.554	−	612.373i	−0.238528	−	0.413143i
$131$	−1136.92			−0.758270			−0.379135	−	0.925341i	$-0.623778\pi$
$131$	−1136.92			−0.758270			−0.379135	+	0.925341i	$0.623778\pi$
$132$	−306.929	−	499.575i	−0.202385	−	0.329412i
$133$	−710.743	−	949.693i	−0.463378	−	0.619164i
$134$		−	438.921i		−	0.282963i
$135$	251.805	+	3064.52i	0.160533	+	1.95372i
$136$	773.853	+	446.785i	0.487922	+	0.281702i
$137$			872.712i			0.544240i	0.962263	+	0.272120i	$0.0877247\pi$
$137$			872.712i			0.544240i	−0.962263	+	0.272120i	$0.912275\pi$
$138$	267.220	+	144.692i	0.164835	+	0.0892535i
$139$	920.123	+	531.233i	0.561466	+	0.324163i	0.753734	−	0.657180i	$-0.228251\pi$
$139$	920.123	+	531.233i	0.561466	+	0.324163i	−0.192268	+	0.981343i	$0.561584\pi$
$140$	−2371.83	+	1775.06i	−1.43183	+	1.07157i
$141$	−1263.60	−	684.202i	−0.754712	−	0.408654i
$142$	18.1396	−	31.4187i	0.0107200	−	0.0185676i
$143$	297.772	−	515.756i	0.174132	−	0.301606i
$144$	581.517	−	1147.80i	0.336526	−	0.664236i
$145$	3695.39	−	2133.53i	2.11645	−	1.22193i
$146$	26.5872	+	46.0504i	0.0150710	+	0.0261038i
$147$	−466.922	−	1720.03i	−0.261980	−	0.965073i
$148$	24.4158	−	42.2895i	0.0135606	−	0.0234877i
$149$		−	2426.93i		−	1.33437i	−0.744890	−	0.667187i	$-0.767498\pi$
$149$		−	2426.93i		−	1.33437i	0.744890	−	0.667187i	$-0.232502\pi$
$150$	−736.376	+	1359.96i	−0.400832	+	0.740267i
$151$	667.648			0.359817			0.179909	−	0.983683i	$-0.442420\pi$
$151$	667.648			0.359817			0.179909	+	0.983683i	$0.442420\pi$
$152$	410.345	+	710.738i	0.218970	+	0.379266i
$153$	850.958	−	1679.62i	0.449646	−	0.887512i
$154$	220.449	+	94.4349i	0.115353	+	0.0494142i
$155$	−1492.02	+	861.418i	−0.773174	+	0.446392i
$156$	1460.29	−	39.9166i	0.749467	−	0.0204864i
$157$	−1937.34	+	1118.52i	−0.984818	+	0.568585i	−0.903721	−	0.428121i	$-0.859176\pi$
$157$	−1937.34	+	1118.52i	−0.984818	+	0.568585i	−0.0810967	+	0.996706i	$0.525842\pi$
$158$	−879.381	+	507.711i	−0.442784	+	0.255641i
$159$	272.464	−	503.193i	0.135898	−	0.250980i
$160$	2703.27	−	1560.73i	1.33570	−	0.771167i
$161$	1284.01	−	153.357i	0.628538	−	0.0750699i
$162$	558.933	+	245.784i	0.271074	+	0.119201i
$163$	−405.745	−	702.771i	−0.194972	−	0.337701i	0.751919	−	0.659255i	$-0.229128\pi$
$163$	−405.745	−	702.771i	−0.194972	−	0.337701i	−0.946891	+	0.321554i	$0.895795\pi$
$164$	−134.463			−0.0640232
$165$	−1760.05	+	48.1104i	−0.830422	+	0.0226993i
$166$			186.488i			0.0871944i
$167$	−927.945	+	1607.25i	−0.429979	+	0.744746i	−0.996871	−	0.0790465i	$-0.974812\pi$
$167$	−927.945	+	1607.25i	−0.429979	+	0.744746i	0.566892	+	0.823792i	$0.308146\pi$
$168$	179.638	+	1219.94i	0.0824962	+	0.560241i
$169$	−356.602	−	617.652i	−0.162313	−	0.281134i
$170$	1108.64	−	640.071i	0.500167	−	0.288772i
$171$	1448.16	−	945.181i	0.647624	−	0.422689i
$172$	−89.2275	+	154.547i	−0.0395554	+	0.0685120i
$173$	290.151	−	502.557i	0.127513	−	0.220859i	−0.795199	−	0.606348i	$-0.792634\pi$
$173$	290.151	−	502.557i	0.127513	−	0.220859i	0.922713	+	0.385489i	$0.125967\pi$
$174$	−23.1529	−	847.013i	−0.0100874	−	0.369034i
$175$	780.478	+	6534.71i	0.337135	+	2.82273i
$176$	638.075	+	368.393i	0.273277	+	0.157776i
$177$	−1565.35	+	961.718i	−0.664738	+	0.408402i
$178$		−	59.0735i		−	0.0248750i
$179$	−23.5912	−	13.6204i	−0.00985077	−	0.00568735i	0.495067	−	0.868855i	$-0.335144\pi$
$179$	−23.5912	−	13.6204i	−0.00985077	−	0.00568735i	−0.504917	+	0.863168i	$0.668477\pi$
$180$	−2360.56	−	3616.74i	−0.977476	−	1.49764i
$181$			2680.82i			1.10090i	0.834867	+	0.550452i	$0.185545\pi$
$181$			2680.82i			1.10090i	−0.834867	+	0.550452i	$0.814455\pi$
$182$	−478.387	+	358.021i	−0.194837	+	0.145815i
$183$	1316.16	−	2430.72i	0.531659	−	0.981880i
$184$	−894.678			−0.358459
$185$	−73.3192	−	126.993i	−0.0291380	−	0.0504685i
$186$	9.34801	+	341.983i	0.00368511	+	0.134814i
$187$	933.721	+	539.084i	0.365136	+	0.210811i
$188$	2018.33			0.782988
$189$	2546.08	−	518.387i	0.979896	−	0.199509i
$190$	1175.73			0.448930
$191$	3219.66	+	1858.87i	1.21972	+	0.704206i	0.964858	−	0.262771i	$-0.0846364\pi$
$191$	3219.66	+	1858.87i	1.21972	+	0.704206i	0.254863	+	0.966977i	$0.417970\pi$
$192$	37.1932	+	1360.66i	0.0139801	+	0.511443i
$193$	−858.493	−	1486.95i	−0.320185	−	0.554577i	0.660341	−	0.750966i	$-0.270412\pi$
$193$	−858.493	−	1486.95i	−0.320185	−	0.554577i	−0.980526	+	0.196389i	$0.937078\pi$
$194$	467.476			0.173004
$195$	2088.77	−	3857.59i	0.767077	−	1.41666i
$196$	1727.07	+	1812.22i	0.629398	+	0.660430i
$197$			2991.54i			1.08192i	0.841048	+	0.540961i	$0.181939\pi$
$197$			2991.54i			1.08192i	−0.841048	+	0.540961i	$0.818061\pi$
$198$	−158.014	+	311.887i	−0.0567148	+	0.111944i
$199$	−4369.83	−	2522.93i	−1.55663	−	0.898721i	−0.997576	−	0.0695896i	$-0.977831\pi$
$199$	−4369.83	−	2522.93i	−1.55663	−	0.898721i	−0.559054	−	0.829131i	$-0.688836\pi$
$200$		−	4553.26i		−	1.60982i
$201$	2320.11	−	1425.43i	0.814168	−	0.500209i
$202$	532.524	+	307.453i	0.185487	+	0.107091i
$203$	−2160.49	−	2886.84i	−0.746979	−	0.998111i
$204$	72.2647	+	2643.70i	0.0248017	+	0.907333i
$205$	−201.892	+	349.687i	−0.0687841	+	0.119138i
$206$	−313.547	+	543.079i	−0.106048	+	0.183680i
$207$	102.987	+	1882.41i	0.0345801	+	0.632059i
$208$	−1589.76	+	917.850i	−0.529953	+	0.305968i
$209$	495.117	+	857.567i	0.163866	+	0.283824i
$210$	1642.24	+	650.981i	0.539643	+	0.213914i
$211$	2012.27	−	3485.36i	0.656543	−	1.13717i	−0.324962	−	0.945727i	$-0.605352\pi$
$211$	2012.27	−	3485.36i	0.656543	−	1.13717i	0.981505	−	0.191438i	$-0.0613151\pi$
$212$			803.741i			0.260383i
$213$	224.987	−	6.14995i	0.0723749	−	0.00197835i
$214$	659.690			0.210726
$215$	267.944	+	464.093i	0.0849937	+	0.147213i
$216$	−1791.65	+	147.216i	−0.564380	+	0.0463739i
$217$	872.303	+	1165.57i	0.272884	+	0.364626i
$218$	−1158.36	+	668.782i	−0.359882	+	0.207778i
$219$	−157.075	+	290.090i	−0.0484665	+	0.0895091i
$220$	2141.75	−	1236.54i	0.656348	−	0.378943i
$221$	−2326.36	+	1343.13i	−0.708092	+	0.408817i
$222$	−29.1078	+	0.795651i	−0.00879993	+	0.000240543i
$223$	−3886.54	+	2243.90i	−1.16709	+	0.673822i	−0.952994	−	0.302989i	$-0.902015\pi$
$223$	−3886.54	+	2243.90i	−1.16709	+	0.673822i	−0.214101	+	0.976812i	$0.568682\pi$
$224$	−1580.45	−	2111.80i	−0.471421	−	0.629912i
$225$	−9580.09	+	524.129i	−2.83854	+	0.155298i
$226$	797.208	+	1380.81i	0.234644	+	0.406415i
$227$	−5451.53			−1.59397			−0.796984	−	0.604000i	$-0.793573\pi$
$227$	−5451.53			−1.59397			−0.796984	+	0.604000i	$0.793573\pi$
$228$	−1156.56	+	2135.97i	−0.335944	+	0.620429i
$229$		−	6015.51i		−	1.73588i	−0.496670	−	0.867940i	$-0.665444\pi$
$229$		−	6015.51i		−	1.73588i	0.496670	−	0.867940i	$-0.334556\pi$
$230$	−640.865	+	1110.01i	−0.183728	+	0.318226i
$231$	216.749	+	1471.96i	0.0617360	+	0.419256i
$232$	1247.35	+	2160.48i	0.352986	+	0.611389i
$233$	2153.30	−	1243.21i	0.605440	−	0.349551i	−0.165739	−	0.986170i	$-0.553001\pi$
$233$	2153.30	−	1243.21i	0.605440	−	0.349551i	0.771179	+	0.636619i	$0.219667\pi$
$234$	−476.114	−	729.479i	−0.133011	−	0.203793i
$235$	3030.45	−	5248.90i	0.841213	−	1.45702i
$236$	1290.24	−	2234.76i	0.355879	−	0.616401i
$237$	−5539.59	−	2999.52i	−1.51829	−	0.822110i
$238$	−648.159	−	866.068i	−0.176529	−	0.235877i
$239$	1860.18	+	1073.98i	0.503453	+	0.290669i	0.730138	−	0.683299i	$-0.239456\pi$
$239$	1860.18	+	1073.98i	0.503453	+	0.290669i	−0.226685	+	0.973968i	$0.572789\pi$
$240$	4772.47	+	2584.15i	1.28359	+	0.695026i
$241$		−	3019.11i		−	0.806961i	−0.914988	−	0.403481i	$-0.867800\pi$
$241$		−	3019.11i		−	0.806961i	0.914988	−	0.403481i	$-0.132200\pi$
$242$	792.065	+	457.299i	0.210396	+	0.121472i
$243$	515.980	+	3752.69i	0.136215	+	0.990679i
$244$			3882.55i			1.01867i
$245$	7306.03	−	1770.46i	1.90516	−	0.461675i
$246$	41.9730	+	68.3175i	0.0108785	+	0.0177064i
$247$	−2467.16			−0.635554
$248$	−503.621	−	872.297i	−0.128951	−	0.223350i
$249$	−985.763	+	605.634i	−0.250884	+	0.154139i
$250$	−3661.97	−	2114.24i	−0.926413	−	0.534865i
$251$	−4007.26			−1.00771			−0.503856	−	0.863788i	$-0.668086\pi$
$251$	−4007.26			−1.00771			−0.503856	+	0.863788i	$0.668086\pi$
$252$	−2798.10	+	2343.10i	−0.699459	+	0.585719i
$253$	−1079.51			−0.268253
$254$	102.663	+	59.2727i	0.0253609	+	0.0146421i
$255$	6983.76	+	3781.50i	1.71506	+	0.928653i
$256$	−478.787	−	829.284i	−0.116891	−	0.202462i
$257$	2856.75			0.693383			0.346692	−	0.937979i	$-0.387305\pi$
$257$	2856.75			0.693383			0.346692	+	0.937979i	$0.387305\pi$
$258$	106.374	−	2.90770i	0.0256688	−	0.000701650i
$259$	−99.2068	+	74.2456i	−0.0238008	+	0.0178123i
$260$			6161.66i			1.46973i
$261$	4402.07	−	2873.13i	1.04399	−	0.681387i
$262$	−824.672	−	476.124i	−0.194460	−	0.112271i
$263$		−	2104.93i		−	0.493520i	−0.969077	−	0.246760i	$-0.920634\pi$
$263$		−	2104.93i		−	0.493520i	0.969077	−	0.246760i	$-0.0793659\pi$
$264$	−28.1273	−	1029.00i	−0.00655726	−	0.239888i
$265$	2090.22	+	1206.79i	0.484534	+	0.279746i
$266$	−117.825	−	986.511i	−0.0271590	−	0.227394i
$267$	312.259	−	191.846i	0.0715727	−	0.0439729i
$268$	−1912.36	+	3312.30i	−0.435880	+	0.754966i
$269$	−1624.71	+	2814.07i	−0.368253	+	0.637833i	−0.989293	−	0.145946i	$-0.953377\pi$
$269$	−1624.71	+	2814.07i	−0.368253	+	0.637833i	0.621039	+	0.783779i	$0.286711\pi$
$270$	−1100.72	+	2328.32i	−0.248103	+	0.524803i
$271$	−5975.60	+	3450.02i	−1.33945	+	0.773334i	−0.986726	−	0.162392i	$-0.948079\pi$
$271$	−5975.60	+	3450.02i	−1.33945	+	0.773334i	−0.352728	+	0.935726i	$0.614746\pi$
$272$	−1661.67	−	2878.10i	−0.370417	−	0.641582i
$273$	−3446.07	−	1366.02i	−0.763978	−	0.302840i
$274$	−365.478	+	633.026i	−0.0805814	+	0.139571i
$275$		−	5493.91i		−	1.20471i
$276$	−1386.15	−	2256.18i	−0.302306	−	0.492050i
$277$	−531.341			−0.115253			−0.0576267	−	0.998338i	$-0.518353\pi$
$277$	−531.341			−0.115253			−0.0576267	+	0.998338i	$0.518353\pi$
$278$	444.944	+	770.665i	0.0959926	+	0.166264i
$279$	−1777.34	+	1160.03i	−0.381387	+	0.248922i
$280$	−5164.37	+	616.811i	−1.10225	+	0.131648i
$281$	4234.76	−	2444.94i	0.899020	−	0.519049i	0.0221380	−	0.999755i	$-0.492953\pi$
$281$	4234.76	−	2444.94i	0.899020	−	0.519049i	0.876882	+	0.480705i	$0.159619\pi$
$282$	−630.026	−	1025.46i	−0.133041	−	0.216544i
$283$	−3948.09	+	2279.43i	−0.829291	+	0.478792i	−0.853610	−	0.520913i	$-0.825592\pi$
$283$	−3948.09	+	2279.43i	−0.829291	+	0.478792i	0.0243187	+	0.999704i	$0.492258\pi$
$284$	−273.780	+	158.067i	−0.0572036	+	0.0330265i
$285$	3818.29	+	6214.86i	0.793600	+	1.29171i
$286$	431.980	−	249.404i	0.0893131	−	0.0515649i
$287$	313.641	+	134.356i	0.0645074	+	0.0276334i
$288$	3220.22	−	2101.76i	0.658866	−	0.430026i
$289$	24.9118	+	43.1484i	0.00507058	+	0.00878250i
$290$	3573.95			0.723689
$291$	1518.16	+	2471.05i	0.305829	+	0.497785i
$292$		−	463.356i		−	0.0928626i
$293$	2199.14	−	3809.02i	0.438482	−	0.759473i	−0.559091	−	0.829106i	$-0.688850\pi$
$293$	2199.14	−	3809.02i	0.438482	−	0.759473i	0.997573	+	0.0696337i	$0.0221830\pi$
$294$	381.637	−	1443.17i	0.0757059	−	0.286284i
$295$	−3874.51	−	6710.85i	−0.764687	−	1.32448i
$296$	74.2451	−	42.8654i	0.0145791	−	0.00841724i
$297$	−2161.78	+	177.629i	−0.422354	+	0.0347039i
$298$	1016.36	−	1760.38i	0.197571	−	0.342203i
$299$	1344.79	−	2329.25i	0.260105	−	0.450515i
$300$	11482.3	−	7054.51i	2.20977	−	1.35764i
$301$	362.550	−	271.330i	0.0694254	−	0.0519575i
$302$	484.282	+	279.600i	0.0922757	+	0.0532754i
$303$	104.237	+	3813.37i	0.0197633	+	0.723011i
$304$		−	3052.29i		−	0.575858i
$305$	10097.0	+	5829.52i	1.89559	+	1.09442i
$306$	1320.64	−	861.954i	0.246720	−	0.161028i
$307$		−	5046.53i		−	0.938179i	−0.883151	−	0.469089i	$-0.844582\pi$
$307$		−	5046.53i		−	0.938179i	0.883151	−	0.469089i	$-0.155418\pi$
$308$	−1252.16	−	1673.14i	−0.231651	−	0.309532i
$309$	−3888.95	+	106.303i	−0.715970	+	0.0195708i
$310$	−1442.99			−0.264376
$311$	1016.19	+	1760.10i	0.185283	+	0.320920i	0.943672	−	0.330883i	$-0.107346\pi$
$311$	1016.19	+	1760.10i	0.185283	+	0.320920i	−0.758389	+	0.651803i	$0.774013\pi$
$312$	2255.31	+	1221.18i	0.409236	+	0.221589i
$313$	7783.59	+	4493.86i	1.40561	+	0.811527i	0.994960	−	0.100269i	$-0.0319702\pi$
$313$	7783.59	+	4493.86i	1.40561	+	0.811527i	0.410645	+	0.911795i	$0.365304\pi$
$314$	−1873.68			−0.336744
$315$	1892.25	+	10794.9i	0.338464	+	1.93086i
$316$	8848.29			1.57517
$317$	−2476.58	−	1429.85i	−0.438797	−	0.253339i	0.264290	−	0.964443i	$-0.414862\pi$
$317$	−2476.58	−	1429.85i	−0.438797	−	0.253339i	−0.703087	+	0.711104i	$0.748196\pi$
$318$	408.362	−	250.890i	0.0720120	−	0.0442428i
$319$	1505.04	+	2606.80i	0.264157	+	0.457533i
$320$	−5741.26			−1.00296
$321$	2142.39	+	3487.08i	0.372513	+	0.606323i
$322$	995.590	+	426.486i	0.172304	+	0.0738110i
$323$		−	4466.54i		−	0.769427i
$324$	−3147.10	−	4290.04i	−0.539626	−	0.735604i
$325$	11854.2	+	6844.03i	2.02324	+	1.16812i
$326$		−	679.678i		−	0.115472i
$327$	−7297.02	−	3951.12i	−1.23403	−	0.668188i
$328$	−204.442	−	118.034i	−0.0344158	−	0.0198700i
$329$	−4707.83	−	2016.72i	−0.788910	−	0.337949i
$330$	−1296.81	−	702.182i	−0.216324	−	0.117133i
$331$	2938.58	−	5089.76i	0.487972	−	0.845193i	−0.511932	−	0.859026i	$-0.671070\pi$
$331$	2938.58	−	5089.76i	0.487972	−	0.845193i	0.999904	+	0.0138333i	$0.00440343\pi$
$332$	812.519	−	1407.32i	0.134316	−	0.232641i
$333$	−98.7355	−	151.278i	−0.0162483	−	0.0248948i
$334$	−1346.18	+	777.216i	−0.220538	+	0.127328i
$335$	5742.68	+	9946.62i	0.936586	+	1.62221i
$336$	1689.99	−	4263.36i	0.274395	−	0.692218i
$337$	859.112	−	1488.03i	0.138869	−	0.240528i	−0.788200	−	0.615419i	$-0.788987\pi$
$337$	859.112	−	1488.03i	0.138869	−	0.240528i	0.927069	+	0.374891i	$0.122320\pi$
$338$		−	597.356i		−	0.0961299i
$339$	−4709.85	+	8698.27i	−0.754584	+	1.39358i
$340$	−11155.0			−1.77931
$341$	−607.662	−	1052.50i	−0.0965007	−	0.167144i
$342$	1446.26	−	79.1251i	0.228669	−	0.0125105i
$343$	−2217.68	−	5952.77i	−0.349107	−	0.937083i
$344$	−271.328	+	156.651i	−0.0425263	+	0.0245526i
$345$	−7948.71	+	217.276i	−1.24042	+	0.0339064i
$346$	420.925	−	243.021i	0.0654019	−	0.0377598i
$347$	−5147.27	+	2971.78i	−0.796311	+	0.459750i	−0.842179	−	0.539197i	$-0.818728\pi$
$347$	−5147.27	+	2971.78i	−0.796311	+	0.459750i	0.0458688	+	0.998947i	$0.485394\pi$
$348$	−3515.67	+	6492.83i	−0.541551	+	1.00015i
$349$	5172.94	−	2986.60i	0.793414	−	0.458078i	−0.0477492	−	0.998859i	$-0.515205\pi$
$349$	5172.94	−	2986.60i	0.793414	−	0.458078i	0.841163	+	0.540782i	$0.181872\pi$
$350$	−2170.51	+	5066.83i	−0.331481	+	0.773810i
$351$	2309.76	−	4885.75i	0.351242	−	0.742969i
$352$	1100.97	+	1906.94i	0.166710	+	0.288751i
$353$	−463.073			−0.0698212			−0.0349106	−	0.999390i	$-0.511115\pi$
$353$	−463.073			−0.0698212			−0.0349106	+	0.999390i	$0.511115\pi$
$354$	−1538.18	+	42.0458i	−0.230942	+	0.00631273i
$355$			949.328i			0.141930i
$356$	−257.380	+	445.796i	−0.0383178	+	0.0663683i
$357$	2473.03	−	6238.75i	0.366630	−	0.924901i
$358$	−11.4080	−	19.7592i	−0.00168416	−	0.00291706i
$359$	−6957.39	+	4016.85i	−1.02283	+	0.590532i	−0.914923	−	0.403628i	$-0.867749\pi$
$359$	−6957.39	+	4016.85i	−1.02283	+	0.590532i	−0.107909	+	0.994161i	$0.534416\pi$
$360$	−414.219	−	7571.14i	−0.0606424	−	1.10843i
$361$	−1378.38	+	2387.42i	−0.200959	+	0.348071i
$362$	−1122.68	+	1944.54i	−0.163003	+	0.282329i
$363$	155.040	+	5671.92i	0.0224174	+	0.820107i
$364$	5170.01	−	617.484i	0.744456	−	0.0889147i
$365$	−1205.01	−	695.714i	−0.172803	−	0.0997681i
$366$	1972.63	−	1211.95i	0.281724	−	0.173086i
$367$			7641.16i			1.08683i	0.839465	+	0.543413i	$0.182868\pi$
$367$			7641.16i			1.08683i	−0.839465	+	0.543413i	$0.817132\pi$
$368$	2881.67	+	1663.73i	0.408199	+	0.235674i
$369$	−224.812	+	443.733i	−0.0317160	+	0.0626011i
$370$		−	122.819i		−	0.0172570i
$371$	803.101	−	1874.76i	0.112385	−	0.262352i
$372$	1419.46	−	2621.49i	0.197838	−	0.365371i
$373$	−9981.85			−1.38563			−0.692816	−	0.721115i	$-0.743630\pi$
$373$	−9981.85			−1.38563			−0.692816	+	0.721115i	$0.743630\pi$
$374$	451.519	+	782.054i	0.0624265	+	0.108126i
$375$	−716.800	−	26223.1i	−0.0987077	−	3.61108i
$376$	3068.73	+	1771.73i	0.420897	+	0.243005i
$377$	−7499.60			−1.02453
$378$	2063.91	+	690.244i	0.280836	+	0.0939215i
$379$	1375.75			0.186458			0.0932292	−	0.995645i	$-0.470281\pi$
$379$	1375.75			0.186458			0.0932292	+	0.995645i	$0.470281\pi$
$380$	−8872.63	−	5122.62i	−1.19778	−	0.691538i
$381$	20.0955	+	735.165i	0.00270216	+	0.0988547i
$382$	1556.93	+	2696.69i	0.208533	+	0.361190i
$383$	9171.81			1.22365			0.611825	−	0.790993i	$-0.290436\pi$
$383$	9171.81			1.22365			0.611825	+	0.790993i	$0.290436\pi$
$384$	−3361.84	+	6208.73i	−0.446767	+	0.825099i
$385$	−6231.27	+	744.236i	−0.824869	+	0.0985189i
$386$		−	1438.09i		−	0.189629i
$387$	360.828	+	552.844i	0.0473952	+	0.0726166i
$388$	−3527.79	−	2036.77i	−0.461588	−	0.266498i
$389$			12181.2i			1.58769i	0.608120	+	0.793845i	$0.291924\pi$
$389$			12181.2i			1.58769i	−0.608120	+	0.793845i	$0.708076\pi$
$390$	3130.60	−	1923.38i	0.406471	−	0.249728i
$391$	4216.86	+	2434.61i	0.545411	+	0.314893i
$392$	1035.08	+	4271.41i	0.133366	+	0.550354i
$393$	−161.423	−	5905.41i	−0.0207193	−	0.757987i
$394$	−1252.81	+	2169.93i	−0.160192	+	0.277460i
$395$	13285.4	−	23011.0i	1.69231	−	2.93116i
$396$	2551.32	−	1665.19i	0.323759	−	0.211310i
$397$	−7055.50	+	4073.50i	−0.891953	+	0.514970i	−0.874581	−	0.484880i	$-0.838863\pi$
$397$	−7055.50	+	4073.50i	−0.891953	+	0.514970i	−0.0173725	+	0.999849i	$0.505530\pi$
$398$	−2113.12	−	3660.03i	−0.266133	−	0.460957i
$399$	4831.99	−	3826.59i	0.606271	−	0.480123i
$400$	−8467.19	+	14665.6i	−1.05840	+	1.83320i
$401$			11486.4i			1.43043i	0.698903	+	0.715217i	$0.253672\pi$
$401$			11486.4i			1.43043i	−0.698903	+	0.715217i	$0.746328\pi$
$402$	2279.85	−	62.3190i	0.282857	−	0.00773181i
$403$	3027.98			0.374279
$404$	−2679.12	−	4640.37i	−0.329928	−	0.571453i
$405$	−15882.0	+	1743.04i	−1.94860	+	0.213857i
$406$	−358.159	−	2998.76i	−0.0437812	−	0.366567i
$407$	89.5832	−	51.7209i	0.0109103	−	0.00629904i
$408$	−2210.82	+	4082.99i	−0.268264	+	0.495437i
$409$	5198.69	−	3001.46i	0.628505	−	0.362868i	−0.151668	−	0.988432i	$-0.548464\pi$
$409$	5198.69	−	3001.46i	0.628505	−	0.362868i	0.780173	+	0.625564i	$0.215131\pi$
$410$	−292.886	+	169.098i	−0.0352796	+	0.0203687i
$411$	−4533.05	+	123.910i	−0.544036	+	0.0148711i
$412$	4732.34	−	2732.22i	0.565887	−	0.326715i
$413$	−5242.53	+	3923.47i	−0.624619	+	0.467460i
$414$	−713.619	+	1408.54i	−0.0847161	+	0.167213i
$415$	−2439.94	−	4226.10i	−0.288607	−	0.499882i
$416$	−5486.14			−0.646587
$417$	−2628.70	+	4854.74i	−0.308700	+	0.570114i
$418$			829.387i			0.0970494i
$419$	−2054.99	+	3559.35i	−0.239601	+	0.415001i	−0.960600	−	0.277935i	$-0.910350\pi$
$419$	−2054.99	+	3559.35i	−0.239601	+	0.415001i	0.720999	+	0.692936i	$0.243683\pi$
$420$	−9556.78	−	12067.7i	−1.11029	−	1.40201i
$421$	4576.65	+	7926.99i	0.529816	+	0.917668i	0.999395	+	0.0347773i	$0.0110722\pi$
$421$	4576.65	+	7926.99i	0.529816	+	0.917668i	−0.469579	+	0.882890i	$0.655594\pi$
$422$	2919.22	−	1685.41i	0.336743	−	0.194419i
$423$	3374.48	−	6660.56i	0.387879	−	0.765597i
$424$	−705.540	+	1222.03i	−0.0808115	+	0.139970i
$425$	−12390.4	+	21460.8i	−1.41417	+	2.44941i
$426$	165.771	+	89.7600i	0.0188536	+	0.0102087i
$427$	3879.46	−	9056.21i	0.439672	−	1.02637i
$428$	−4978.32	−	2874.24i	−0.562234	−	0.324606i
$429$	2721.22	+	1473.46i	0.306252	+	0.165826i
$430$			448.843i			0.0503375i
$431$	−4959.23	−	2863.21i	−0.554241	−	0.319991i	0.196590	−	0.980486i	$-0.437013\pi$
$431$	−4959.23	−	2863.21i	−0.554241	−	0.319991i	−0.750831	+	0.660495i	$0.770347\pi$
$432$	6044.48	+	2857.56i	0.673183	+	0.318251i
$433$		−	7458.28i		−	0.827764i	−0.910331	−	0.413882i	$-0.864173\pi$
$433$		−	7458.28i		−	0.827764i	0.910331	−	0.413882i	$-0.135827\pi$
$434$	144.608	+	1210.76i	0.0159940	+	0.133913i
$435$	11606.7	+	18891.7i	1.27931	+	2.08227i
$436$	11655.4			1.28026
$437$	2236.04	+	3872.94i	0.244770	+	0.423953i
$438$	−235.420	+	144.638i	−0.0256822	+	0.0157787i
$439$	12038.5	+	6950.44i	1.30881	+	0.755641i	0.981897	−	0.189415i	$-0.0606590\pi$
$439$	12038.5	+	6950.44i	1.30881	+	0.755641i	0.326911	+	0.945055i	$0.393992\pi$
$440$	4341.83			0.470429
$441$	8867.91	−	2669.50i	0.957554	−	0.288252i
$442$	−2249.92			−0.242122
$443$	12562.8	+	7253.12i	1.34735	+	0.777892i	0.987873	−	0.155262i	$-0.0496223\pi$
$443$	12562.8	+	7253.12i	1.34735	+	0.777892i	0.359476	+	0.933154i	$0.382956\pi$
$444$	223.127	+	120.817i	0.0238494	+	0.0129138i
$445$	772.896	+	1338.69i	0.0823343	+	0.142607i
$446$	−3758.83			−0.399071
$447$	12606.0	−	344.581i	1.33388	−	0.0364611i
$448$	575.354	+	4817.27i	0.0606762	+	0.508023i
$449$			2949.31i			0.309993i	0.987915	+	0.154996i	$0.0495366\pi$
$449$			2949.31i			0.309993i	−0.987915	+	0.154996i	$0.950463\pi$
$450$	−7168.46	−	3631.81i	−0.750943	−	0.380455i
$451$	−246.676	−	142.419i	−0.0257551	−	0.0148697i
$452$		−	13893.6i		−	1.44580i
$453$	94.7941	+	3467.91i	0.00983183	+	0.359683i
$454$	−3954.29	−	2283.01i	−0.408776	−	0.236007i
$455$	6156.75	−	14372.3i	0.634358	−	1.48085i
$456$	−3633.46	+	2232.33i	−0.373142	+	0.229251i
$457$	7953.13	−	13775.2i	0.814074	−	1.41002i	−0.0959168	−	0.995389i	$-0.530578\pi$
$457$	7953.13	−	13775.2i	0.814074	−	1.41002i	0.909991	−	0.414628i	$-0.136088\pi$
$458$	2519.20	−	4363.38i	0.257018	−	0.445169i
$459$	8845.13	+	4181.58i	0.899467	+	0.425227i
$460$	9672.53	−	5584.44i	0.980400	−	0.566034i
$461$	−1398.44	−	2422.16i	−0.141283	−	0.244710i	0.786697	−	0.617340i	$-0.211790\pi$
$461$	−1398.44	−	2422.16i	−0.141283	−	0.244710i	−0.927980	+	0.372629i	$0.878456\pi$
$462$	−459.215	+	1158.47i	−0.0462438	+	0.116660i
$463$	2736.29	−	4739.39i	0.274657	−	0.475719i	−0.695392	−	0.718631i	$-0.744769\pi$
$463$	2736.29	−	4739.39i	0.274657	−	0.475719i	0.970048	+	0.242911i	$0.0781024\pi$
$464$		−	9278.24i		−	0.928300i
$465$	−4686.23	−	7627.56i	−0.467352	−	0.760688i
$466$	2082.54			0.207021
$467$	−5003.44	−	8666.21i	−0.495785	−	0.858724i	0.504203	−	0.863585i	$-0.331786\pi$
$467$	−5003.44	−	8666.21i	−0.495785	−	0.858724i	−0.999988	+	0.00486046i	$0.998453\pi$
$468$	414.671	+	7579.39i	0.0409576	+	0.748627i
$469$	7770.31	−	5815.24i	0.765032	−	0.572544i
$470$	4396.31	−	2538.21i	0.431461	−	0.249104i
$471$	−6084.91	−	9904.14i	−0.595282	−	0.968914i
$472$	3923.44	−	2265.20i	0.382608	−	0.220899i
$473$	−327.381	+	189.014i	−0.0318245	+	0.0183739i
$474$	−2762.02	−	4495.61i	−0.267645	−	0.435633i
$475$	−19710.4	+	11379.8i	−1.90395	+	1.09925i
$476$	1117.89	+	9359.74i	0.107644	+	0.901267i
$477$	2652.38	+	1343.79i	0.254599	+	0.128989i
$478$	899.528	+	1558.03i	0.0860742	+	0.149085i
$479$	−11987.7			−1.14349			−0.571744	−	0.820432i	$-0.693733\pi$
$479$	−11987.7			−1.14349			−0.571744	+	0.820432i	$0.693733\pi$
$480$	8490.59	+	13819.7i	0.807376	+	1.31413i
$481$			257.725i			0.0244309i
$482$	1264.35	−	2189.92i	0.119481	−	0.206947i
$483$	978.878	+	6647.67i	0.0922163	+	0.626252i
$484$	−3984.86	−	6901.98i	−0.374235	−	0.648195i
$485$	−10593.7	+	6116.28i	−0.991826	+	0.572631i
$486$	−1197.30	+	2938.11i	−0.111750	+	0.274230i
$487$	−4178.18	+	7236.82i	−0.388771	+	0.673371i	−0.992285	−	0.123982i	$-0.960434\pi$
$487$	−4178.18	+	7236.82i	−0.388771	+	0.673371i	0.603513	+	0.797353i	$0.293767\pi$
$488$	−3408.18	+	5903.14i	−0.316150	+	0.547587i
$489$	3592.73	−	2207.31i	0.332248	−	0.204127i
$490$	6040.90	+	1775.44i	0.556939	+	0.163686i
$491$	−5884.50	−	3397.42i	−0.540863	−	0.312268i	0.204565	−	0.978853i	$-0.434422\pi$
$491$	−5884.50	−	3397.42i	−0.540863	−	0.312268i	−0.745429	+	0.666585i	$0.767755\pi$
$492$	−19.0914	−	698.430i	−0.00174940	−	0.0639993i
$493$		−	13577.2i		−	1.24034i
$494$	−1789.57	−	1033.21i	−0.162989	−	0.0941017i
$495$	−499.791	−	9135.23i	−0.0453817	−	0.829491i
$496$			3746.11i			0.339123i
$497$	796.543	−	95.1358i	0.0718910	−	0.00858636i
$498$	−968.658	+	26.4780i	−0.0871618	+	0.00238254i
$499$	−10956.2			−0.982901			−0.491451	−	0.870905i	$-0.663533\pi$
$499$	−10956.2			−0.982901			−0.491451	+	0.870905i	$0.663533\pi$
$500$	18423.3	+	31910.0i	1.64783	+	2.85412i
$501$	−8480.14	−	4591.74i	−0.756217	−	0.409469i
$502$	−2906.68	−	1678.17i	−0.258429	−	0.149204i
$503$	20300.4			1.79950			0.899752	−	0.436402i	$-0.143747\pi$
$503$	20300.4			1.79950			0.899752	+	0.436402i	$0.143747\pi$
$504$	−6311.13	+	1106.29i	−0.557778	+	0.0977737i
$505$	−16090.4			−1.41785
$506$	−783.025	−	452.080i	−0.0687939	−	0.0397182i
$507$	3157.59	−	1939.96i	0.276594	−	0.169934i
$508$	−516.497	−	894.599i	−0.0451099	−	0.0781327i
$509$	22338.8			1.94528			0.972641	−	0.232313i	$-0.0746293\pi$
$509$	22338.8			1.94528			0.972641	+	0.232313i	$0.0746293\pi$
$510$	3482.07	+	5667.61i	0.302331	+	0.492090i
$511$	−462.987	+	1080.80i	−0.0400809	+	0.0935650i
$512$		−	11672.3i		−	1.00752i
$513$	5115.08	+	7387.86i	0.440227	+	0.635832i
$514$	2072.16	+	1196.36i	0.177819	+	0.102664i
$515$		−	16409.3i		−	1.40404i
$516$	−815.417	−	441.524i	−0.0695673	−	0.0376686i
$517$	3702.68	+	2137.74i	0.314978	+	0.181853i
$518$	−103.053	+	12.3082i	−0.00874109	+	0.00104400i
$519$	2651.58	+	1435.75i	0.224261	+	0.121431i
$520$	−5408.83	+	9368.37i	−0.456140	+	0.790058i
$521$	−8830.18	+	15294.3i	−0.742528	+	1.28610i	0.208812	+	0.977956i	$0.433040\pi$
$521$	−8830.18	+	15294.3i	−0.742528	+	1.28610i	−0.951341	+	0.308141i	$0.900293\pi$
$522$	4396.28	−	240.522i	0.368621	−	0.0201673i
$523$	−2859.14	+	1650.72i	−0.239046	+	0.138014i	−0.614738	−	0.788731i	$-0.710738\pi$
$523$	−2859.14	+	1650.72i	−0.239046	+	0.138014i	0.375692	+	0.926745i	$0.377405\pi$
$524$	4148.90	+	7186.11i	0.345889	+	0.599097i
$525$	−33831.8	+	4981.78i	−2.81246	+	0.414138i
$526$	881.511	−	1526.82i	0.0730717	−	0.126564i
$527$			5481.83i			0.453116i
$528$	−1822.92	+	3366.60i	−0.150250	+	0.277486i
$529$	7291.74			0.599305
$530$	1010.77	+	1750.70i	0.0828396	+	0.143482i
$531$	−5217.62	−	7994.19i	−0.426413	−	0.653330i
$532$	−3409.02	+	7958.03i	−0.277819	+	0.648542i
$533$	614.594	−	354.836i	0.0499456	−	0.0288361i
$534$	306.840	−	8.38738i	0.0248657	−	0.000679696i
$535$	−14949.6	+	8631.14i	−1.20809	+	0.697489i
$536$	−5815.21	+	3357.41i	−0.468617	+	0.270556i
$537$	67.3976	−	124.472i	0.00541606	−	0.0100025i
$538$	−2356.98	+	1360.80i	−0.188878	+	0.109049i
$539$	1248.92	+	5153.82i	0.0998046	+	0.411857i
$540$	18450.9	−	12774.8i	1.47037	−	1.01803i
$541$	6388.13	+	11064.6i	0.507666	+	0.879303i	0.999961	+	0.00887458i	$0.00282490\pi$
$541$	6388.13	+	11064.6i	0.507666	+	0.879303i	−0.492295	+	0.870429i	$0.663842\pi$
$542$	−5779.24			−0.458007
$543$	−13924.7	+	380.629i	−1.10049	+	0.0300817i
$544$		−	9932.07i		−	0.782783i
$545$	17500.2	−	30311.3i	1.37546	−	2.38237i
$546$	−1927.56	−	2434.01i	−0.151084	−	0.190780i
$547$	−2018.12	−	3495.49i	−0.157749	−	0.273229i	0.776308	−	0.630354i	$-0.217090\pi$
$547$	−2018.12	−	3495.49i	−0.157749	−	0.273229i	−0.934057	+	0.357125i	$0.883757\pi$
$548$	5516.13	−	3184.74i	0.429995	−	0.248258i
$549$	12812.6	+	6491.31i	0.996041	+	0.504631i
$550$	2300.76	−	3985.03i	0.178372	−	0.308950i
$551$	6234.93	−	10799.2i	0.482064	−	0.834959i
$552$	−127.028	−	4647.15i	−0.00979472	−	0.358326i
$553$	−20639.0	−	8841.24i	−1.58709	−	0.679869i
$554$	−385.411	−	222.517i	−0.0295569	−	0.0170647i
$555$	649.216	−	398.866i	0.0496535	−	0.0305062i
$556$		−	7754.39i		−	0.591474i
$557$	−16380.5	−	9457.30i	−1.24608	−	0.719423i	−0.275752	−	0.961229i	$-0.588927\pi$
$557$	−16380.5	−	9457.30i	−1.24608	−	0.719423i	−0.970325	+	0.241806i	$0.922260\pi$
$558$	−1775.01	+	97.1111i	−0.134663	+	0.00736746i
$559$		−	941.854i		−	0.0712633i
$560$	17780.9	+	7616.92i	1.34175	+	0.574774i
$561$	−2667.55	+	4926.49i	−0.200756	+	0.370760i
$562$	4095.60			0.307407
$563$	−4725.13	−	8184.17i	−0.353713	−	0.612650i	0.633183	−	0.774002i	$-0.281748\pi$
$563$	−4725.13	−	8184.17i	−0.353713	−	0.612650i	−0.986897	+	0.161352i	$0.948415\pi$
$564$	286.567	+	10483.6i	0.0213947	+	0.782695i
$565$	−36131.9	−	20860.8i	−2.69041	−	1.55331i
$566$	−3818.35			−0.283564
$567$	3054.11	+	13151.3i	0.226209	+	0.974079i
$568$	−555.017			−0.0410000
$569$	877.171	+	506.435i	0.0646273	+	0.0373126i	0.531965	−	0.846766i	$-0.321454\pi$
$569$	877.171	+	506.435i	0.0646273	+	0.0373126i	−0.467338	+	0.884079i	$0.654787\pi$
$570$	166.933	+	6107.01i	0.0122668	+	0.448762i
$571$	4817.96	+	8344.96i	0.353109	+	0.611603i	0.986793	−	0.161989i	$-0.0517910\pi$
$571$	4817.96	+	8344.96i	0.353109	+	0.611603i	−0.633683	+	0.773593i	$0.718458\pi$
$572$	−4346.57			−0.317726
$573$	−9198.25	+	16987.5i	−0.670615	+	1.23851i
$574$	171.235	+	228.803i	0.0124516	+	0.0166377i
$575$		−	24811.5i		−	1.79950i
$576$	−7062.27	+	386.378i	−0.510870	+	0.0279498i
$577$	6716.95	+	3878.03i	0.484628	+	0.279800i	0.722343	−	0.691535i	$-0.243065\pi$
$577$	6716.95	+	3878.03i	0.484628	+	0.279800i	−0.237715	+	0.971335i	$0.576399\pi$
$578$			41.7305i			0.00300305i
$579$	7601.66	−	4670.32i	0.545621	−	0.335219i
$580$	−26970.7	−	15571.5i	−1.93086	−	1.11478i
$581$	−3301.44	+	2470.77i	−0.235743	+	0.176428i
$582$	66.3732	+	2428.17i	0.00472725	+	0.172940i
$583$	−851.296	+	1474.49i	−0.0604752	+	0.104746i
$584$	406.744	−	704.501i	0.0288205	−	0.0499186i
$585$	20333.7	+	10301.8i	1.43709	+	0.728081i
$586$	3190.31	−	1841.93i	0.224899	−	0.129845i
$587$	4195.04	+	7266.02i	0.294970	+	0.510904i	0.974978	−	0.222301i	$-0.0713568\pi$
$587$	4195.04	+	7266.02i	0.294970	+	0.510904i	−0.680008	+	0.733205i	$0.738024\pi$
$588$	−9167.84	+	9228.07i	−0.642985	+	0.647209i
$589$	−2517.37	+	4360.21i	−0.176106	+	0.305024i
$590$		−	6490.33i		−	0.452886i
$591$	−15538.7	+	424.746i	−1.08152	+	0.0295629i
$592$	−318.848			−0.0221361
$593$	−3762.06	−	6516.09i	−0.260522	−	0.451237i	0.705859	−	0.708353i	$-0.250561\pi$
$593$	−3762.06	−	6516.09i	−0.260522	−	0.451237i	−0.966381	+	0.257115i	$0.917228\pi$
$594$	−1642.44	−	776.474i	−0.113452	−	0.0536348i
$595$	26019.6	+	11146.1i	1.79277	+	0.767979i
$596$	−15339.8	+	8856.45i	−1.05427	+	0.608682i
$597$	12484.2	−	23056.1i	0.855851	−	1.58061i
$598$	1950.91	−	1126.36i	0.133409	−	0.0770236i
$599$	−2801.79	+	1617.62i	−0.191116	+	0.110341i	−0.592505	−	0.805567i	$-0.701861\pi$
$599$	−2801.79	+	1617.62i	−0.191116	+	0.110341i	0.401389	+	0.915908i	$0.368528\pi$
$600$	23650.6	−	646.482i	1.60922	−	0.0439876i
$601$	4501.29	−	2598.82i	0.305510	−	0.176386i	−0.339405	−	0.940640i	$-0.610226\pi$
$601$	4501.29	−	2598.82i	0.305510	−	0.176386i	0.644916	+	0.764254i	$0.276893\pi$
$602$	376.606	−	44.9803i	0.0254972	−	0.00304528i
$603$	7733.40	+	11848.8i	0.522269	+	0.800196i
$604$	−2436.41	−	4219.98i	−0.164133	−	0.284286i
$605$	−23932.5			−1.60826
$606$	−1521.37	+	2809.70i	−0.101982	+	0.188344i
$607$			12070.8i			0.807149i	0.914947	+	0.403575i	$0.132232\pi$
$607$			12070.8i			0.807149i	−0.914947	+	0.403575i	$0.867768\pi$
$608$	4561.01	−	7899.90i	0.304232	−	0.526946i
$609$	14688.1	−	11631.9i	0.977327	−	0.773973i
$610$	4882.62	+	8456.94i	0.324084	+	0.561330i
$611$	−9225.23	+	5326.19i	−0.610823	+	0.352659i
$612$	−13721.7	+	750.717i	−0.906317	+	0.0495848i
$613$	2363.66	−	4093.98i	0.155738	−	0.269746i	−0.777590	−	0.628772i	$-0.783558\pi$
$613$	2363.66	−	4093.98i	0.155738	−	0.269746i	0.933327	+	0.359026i	$0.116891\pi$
$614$	2113.41	−	3660.53i	0.138909	−	0.240597i
$615$	−1845.01	−	999.020i	−0.120973	−	0.0655030i
$616$	−435.111	−	3643.06i	−0.0284596	−	0.238284i
$617$	21673.5	+	12513.2i	1.41417	+	0.816473i	0.995778	−	0.0917932i	$-0.0292599\pi$
$617$	21673.5	+	12513.2i	1.41417	+	0.816473i	0.418394	+	0.908266i	$0.362593\pi$
$618$	−2865.39	−	1551.52i	−0.186509	−	0.100989i
$619$			10903.0i			0.707961i	0.935253	+	0.353980i	$0.115172\pi$
$619$			10903.0i			0.707961i	−0.935253	+	0.353980i	$0.884828\pi$
$620$	10889.5	+	6287.04i	0.705374	+	0.407248i
$621$	−9763.00	+	802.204i	−0.630879	+	0.0518379i
$622$			1702.26i			0.109734i
$623$	1045.79	−	782.662i	0.0672532	−	0.0503318i
$624$	−4993.23	−	8127.25i	−0.320335	−	0.521395i
$625$	66229.1			4.23866
$626$	3763.91	+	6519.28i	0.240313	+	0.416235i
$627$	−4384.09	+	2693.50i	−0.279240	+	0.171560i
$628$	14139.6	+	8163.52i	0.898459	+	0.518726i
$629$	−466.583			−0.0295769
$630$	−3148.16	+	8622.55i	−0.199089	+	0.545287i
$631$	−18322.8			−1.15598			−0.577988	−	0.816046i	$-0.696162\pi$
$631$	−18322.8			−1.15598			−0.577988	+	0.816046i	$0.696162\pi$
$632$	13453.2	+	7767.21i	0.846740	+	0.488865i
$633$	18389.4	+	9957.31i	1.15468	+	0.625225i
$634$	−1197.60	−	2074.30i	−0.0750201	−	0.129939i
$635$	−3102.01			−0.193858
$636$	−4174.80	+	114.117i	−0.260286	+	0.00711483i
$637$	−12676.2	−	3725.58i	−0.788463	−	0.231731i
$638$			2521.14i			0.156447i
$639$	63.8883	+	1167.76i	0.00395522	+	0.0722939i
$640$	−25790.6	−	14890.2i	−1.59291	−	0.919667i
$641$		−	15760.0i		−	0.971111i	−0.874206	−	0.485555i	$-0.838617\pi$
$641$		−	15760.0i		−	0.971111i	0.874206	−	0.485555i	$-0.161383\pi$
$642$	93.6642	+	3426.57i	0.00575799	+	0.210648i
$643$	−22823.4	−	13177.1i	−1.39979	−	0.808170i	−0.405421	−	0.914130i	$-0.632875\pi$
$643$	−22823.4	−	13177.1i	−1.39979	−	0.808170i	−0.994370	+	0.105961i	$0.966208\pi$
$644$	−5655.00	−	7556.20i	−0.346022	−	0.462354i
$645$	−2372.56	+	1457.65i	−0.144836	+	0.0889845i
$646$	1870.51	−	3239.82i	0.113923	−	0.197321i
$647$	1173.51	−	2032.57i	0.0713065	−	0.123507i	−0.828168	−	0.560480i	$-0.810616\pi$
$647$	1173.51	−	2032.57i	0.0713065	−	0.123507i	0.899474	+	0.436974i	$0.143950\pi$
$648$	−1019.05	−	9285.30i	−0.0617780	−	0.562903i
$649$	4733.97	−	2733.16i	0.286325	−	0.165310i
$650$	5732.34	+	9928.70i	0.345909	+	0.599132i
$651$	−5930.36	+	4696.41i	−0.357034	+	0.282745i
$652$	−2961.32	+	5129.16i	−0.177875	+	0.308088i
$653$			16913.9i			1.01362i	0.862058	+	0.506809i	$0.169175\pi$
$653$			16913.9i			1.01362i	−0.862058	+	0.506809i	$0.830825\pi$
$654$	−3638.26	−	5921.84i	−0.217534	−	0.354071i
$655$	24917.8			1.48644
$656$	438.990	+	760.354i	0.0261276	+	0.0452543i
$657$	−1529.09	−	774.695i	−0.0908000	−	0.0460026i
$658$	−2570.28	−	3434.40i	−0.152280	−	0.203476i
$659$	−12126.6	+	7001.31i	−0.716822	+	0.413858i	−0.813582	−	0.581450i	$-0.802486\pi$
$659$	−12126.6	+	7001.31i	−0.716822	+	0.413858i	0.0967597	+	0.995308i	$0.469152\pi$
$660$	6726.93	+	10949.1i	0.396735	+	0.645748i
$661$	2921.69	−	1686.84i	0.171922	−	0.0992593i	−0.411570	−	0.911378i	$-0.635019\pi$
$661$	2921.69	−	1686.84i	0.171922	−	0.0992593i	0.583492	+	0.812119i	$0.301686\pi$
$662$	4263.02	−	2461.26i	0.250282	−	0.144501i
$663$	−7306.79	−	11892.9i	−0.428012	−	0.696656i
$664$	2470.75	−	1426.49i	0.144403	−	0.0833714i
$665$	15577.2	+	20814.3i	0.908361	+	1.21375i
$666$	−8.26557	−	151.079i	−0.000480907	−	0.00879007i
$667$	6797.04	+	11772.8i	0.394576	+	0.683426i
$668$	13545.2			0.784549
$669$	−12207.1	−	19868.9i	−0.705461	−	1.14825i
$670$			9619.77i			0.554693i
$671$	−4112.26	+	7122.65i	−0.236590	+	0.409787i
$672$	10744.7	−	8509.04i	0.616795	−	0.488457i
$673$	10197.9	+	17663.3i	0.584102	+	1.01169i	0.994987	+	0.100007i	$0.0318866\pi$
$673$	10197.9	+	17663.3i	0.584102	+	1.01169i	−0.410884	+	0.911687i	$0.634780\pi$
$674$	1246.32	−	719.564i	0.0712263	−	0.0411225i
$675$	−4082.64	−	49686.6i	−0.232801	−	2.83324i
$676$	−2602.65	+	4507.92i	−0.148080	+	0.256482i
$677$	2168.44	−	3755.85i	0.123102	−	0.213219i	−0.797888	−	0.602806i	$-0.794049\pi$
$677$	2168.44	−	3755.85i	0.123102	−	0.213219i	0.920989	+	0.389588i	$0.127382\pi$
$678$	−7059.01	+	4336.92i	−0.399852	+	0.245661i
$679$	6193.56	+	8275.83i	0.350055	+	0.467742i
$680$	−16960.4	−	9792.11i	−0.956475	−	0.552221i
$681$	−774.021	−	28316.4i	−0.0435544	−	1.59337i
$682$		−	1017.92i		−	0.0571525i
$683$	25968.2	+	14992.7i	1.45483	+	0.839944i	0.998749	−	0.0499974i	$-0.0159213\pi$
$683$	25968.2	+	14992.7i	1.45483	+	0.839944i	0.456076	+	0.889941i	$0.349255\pi$
$684$	−11258.9	−	5704.16i	−0.629377	−	0.318865i
$685$		−	19127.1i		−	1.06687i
$686$	884.315	−	5246.60i	0.0492177	−	0.292006i
$687$	31245.9	−	854.096i	1.73523	−	0.0474320i
$688$	1165.23			0.0645696
$689$	−2121.00	−	3673.68i	−0.117277	−	0.203129i
$690$	−5856.63	−	3171.19i	−0.323127	−	0.174964i
$691$	−1394.23	−	804.961i	−0.0767570	−	0.0443157i	0.461130	−	0.887332i	$-0.347444\pi$
$691$	−1394.23	−	804.961i	−0.0767570	−	0.0443157i	−0.537887	+	0.843017i	$0.680777\pi$
$692$	−4235.33			−0.232663
$693$	−7614.92	+	1334.83i	−0.417413	+	0.0731689i
$694$	−4978.13			−0.272287
$695$	−20166.2	−	11643.0i	−1.10064	−	0.635457i
$696$	−11044.9	+	6785.76i	−0.601515	+	0.369560i
$697$	642.393	+	1112.66i	0.0349101	+	0.0604661i
$698$	5002.96			0.271296
$699$	6763.23	+	11008.2i	0.365964	+	0.595663i
$700$	38455.6	−	28779.9i	2.07641	−	1.55397i
$701$			9944.60i			0.535809i	0.963445	+	0.267905i	$0.0863312\pi$
$701$			9944.60i			0.535809i	−0.963445	+	0.267905i	$0.913669\pi$
$702$	3721.47	−	2576.61i	0.200082	−	0.138530i
$703$	−371.117	−	214.264i	−0.0199103	−	0.0114952i
$704$		−	4050.01i		−	0.216819i
$705$	27694.2	+	14995.6i	1.47946	+	0.801086i
$706$	−335.892	−	193.927i	−0.0179058	−	0.0103379i
$707$	1612.48	+	13500.8i	0.0857760	+	0.718177i
$708$	11791.0	+	6384.49i	0.625895	+	0.338904i
$709$	−9535.18	+	16515.4i	−0.505079	+	0.874823i	0.494904	+	0.868948i	$0.335203\pi$
$709$	−9535.18	+	16515.4i	−0.505079	+	0.874823i	−0.999983	+	0.00587486i	$0.998130\pi$
$710$	−397.563	+	688.599i	−0.0210145	+	0.0363981i
$711$	14793.6	−	29199.7i	0.780316	−	1.54019i
$712$	−782.657	+	451.867i	−0.0411957	+	0.0237843i
$713$	−2744.32	−	4753.30i	−0.144145	−	0.249667i
$714$	4406.51	−	3489.64i	0.230966	−	0.182908i
$715$	−6526.22	+	11303.8i	−0.341352	+	0.591240i
$716$			198.816i			0.0103772i
$717$	−5314.35	+	9814.67i	−0.276804	+	0.511207i
$718$	−6728.76			−0.349743
$719$	−15050.6	−	26068.3i	−0.780655	−	1.35213i	−0.931561	−	0.363586i	$-0.881552\pi$
$719$	−15050.6	−	26068.3i	−0.780655	−	1.35213i	0.150906	−	0.988548i	$-0.451781\pi$
$720$	−12745.0	+	25156.1i	−0.659693	+	1.30210i
$721$	−13768.4	+	1644.44i	−0.711183	+	0.0849406i
$722$	−1999.62	+	1154.48i	−0.103072	+	0.0595089i
$723$	15681.9	−	428.659i	0.806660	−	0.0220498i
$724$	16944.6	−	9782.95i	0.869807	−	0.502183i
$725$	−59915.1	+	34592.0i	−3.06923	+	1.77202i
$726$	−2262.85	+	4179.08i	−0.115678	+	0.213637i
$727$	11506.5	−	6643.29i	0.587005	−	0.338908i	−0.176907	−	0.984228i	$-0.556609\pi$
$727$	11506.5	−	6643.29i	0.587005	−	0.338908i	0.763912	+	0.645320i	$0.223276\pi$
$728$	8402.67	+	3599.50i	0.427780	+	0.183250i
$729$	−19419.0	+	3212.93i	−0.986587	+	0.163234i
$730$	−582.708	−	1009.28i	−0.0295438	−	0.0511714i
$731$	1705.13			0.0862741
$732$	−20166.8	+	551.253i	−1.01829	+	0.0278345i
$733$		−	7447.71i		−	0.375290i	−0.982237	−	0.187645i	$-0.939915\pi$
$733$		−	7447.71i		−	0.375290i	0.982237	−	0.187645i	$-0.0600855\pi$
$734$	−3199.99	+	5542.55i	−0.160918	+	0.278718i
$735$	10233.5	+	37697.7i	0.513560	+	1.89184i
$736$	4972.20	+	8612.10i	0.249019	+	0.431313i
$737$	−7016.55	+	4051.01i	−0.350689	+	0.202471i
$738$	−348.896	+	227.716i	−0.0174025	+	0.0113582i
$739$	−9760.23	+	16905.2i	−0.485840	+	0.841500i	−0.999868	−	0.0162741i	$-0.994820\pi$
$739$	−9760.23	+	16905.2i	−0.485840	+	0.841500i	0.514028	+	0.857774i	$0.328153\pi$
$740$	−535.119	+	926.852i	−0.0265829	+	0.0460429i
$741$	−350.293	−	12815.0i	−0.0173662	−	0.635317i
$742$	1367.65	−	1023.54i	0.0676659	−	0.0506406i
$743$	−30522.1	−	17621.9i	−1.50706	−	0.870103i	−0.999966	−	0.00821382i	$-0.997385\pi$
$743$	−30522.1	−	17621.9i	−1.50706	−	0.870103i	−0.507097	−	0.861889i	$-0.669281\pi$
$744$	4459.39	−	2739.76i	0.219744	−	0.135006i
$745$			53190.7i			2.61578i
$746$	−7240.38	−	4180.24i	−0.355347	−	0.205160i
$747$	−3285.75	−	5034.28i	−0.160936	−	0.246579i
$748$		−	7868.99i		−	0.384651i
$749$	8740.20	+	11678.6i	0.426382	+	0.569730i
$750$	10461.9	−	19321.2i	0.509351	−	0.940682i
$751$	−19406.0			−0.942922			−0.471461	−	0.881887i	$-0.656273\pi$
$751$	−19406.0			−0.942922			−0.471461	+	0.881887i	$0.656273\pi$
$752$	−6589.37	−	11413.1i	−0.319534	−	0.553449i
$753$	−568.959	−	20814.5i	−0.0275352	−	1.00734i
$754$	−5439.87	−	3140.71i	−0.262743	−	0.151695i
$755$	−14632.7			−0.705351
$756$	−12567.8	−	14201.2i	−0.604613	−	0.683193i
$757$	25155.3			1.20777			0.603886	−	0.797071i	$-0.293618\pi$
$757$	25155.3			1.20777			0.603886	+	0.797071i	$0.293618\pi$
$758$	997.909	+	576.143i	0.0478175	+	0.0276075i
$759$	−153.271	−	5607.19i	−0.00732987	−	0.268153i
$760$	−8993.47	−	15577.1i	−0.429247	−	0.743477i
$761$	−25985.8			−1.23782			−0.618912	−	0.785461i	$-0.712426\pi$
$761$	−25985.8			−1.23782			−0.618912	+	0.785461i	$0.712426\pi$
$762$	−293.299	+	541.671i	−0.0139437	+	0.0257515i
$763$	−27186.7	−	11646.1i	−1.28994	−	0.552579i
$764$		−	27133.9i		−	1.28491i
$765$	−18650.3	+	36812.0i	−0.881443	+	1.73979i
$766$	6652.82	+	3841.00i	0.313807	+	0.181176i
$767$			13619.3i			0.641154i
$768$	4239.50	−	2604.67i	0.199192	−	0.122380i
$769$	21774.7	+	12571.6i	1.02109	+	0.589525i	0.914419	−	0.404770i	$-0.132648\pi$
$769$	21774.7	+	12571.6i	1.02109	+	0.589525i	0.106668	+	0.994295i	$0.465982\pi$
$770$	−4831.55	−	2069.72i	−0.226126	−	0.0968668i
$771$	405.608	+	14838.6i	0.0189463	+	0.693124i
$772$	−6265.70	+	10852.5i	−0.292108	+	0.505946i
$773$	12751.7	−	22086.6i	0.593335	−	1.02769i	−0.400445	−	0.916321i	$-0.631144\pi$
$773$	12751.7	−	22086.6i	0.593335	−	1.02769i	0.993780	−	0.111365i	$-0.0355223\pi$
$774$	30.2065	+	552.117i	0.00140278	+	0.0256401i
$775$	24190.8	−	13966.6i	1.12124	−	0.647348i
$776$	−3575.83	−	6193.53i	−0.165419	−	0.286514i
$777$	−399.733	−	504.759i	−0.0184560	−	0.0233052i
$778$	−5101.29	+	8835.69i	−0.235077	+	0.407166i
$779$			1180.00i			0.0542719i
$780$	−32005.0	+	874.846i	−1.46918	+	0.0401596i
$781$	−669.676			−0.0306823
$782$	2039.15	+	3531.91i	0.0932478	+	0.161510i
$783$	15548.6	+	22457.3i	0.709660	+	1.02498i
$784$	4609.16	−	15682.6i	0.209965	−	0.714404i
$785$	42460.4	−	24514.5i	1.93054	−	1.11460i
$786$	2356.00	−	4351.12i	0.106916	−	0.197455i
$787$	13270.0	−	7661.44i	0.601048	−	0.347015i	−0.168406	−	0.985718i	$-0.553862\pi$
$787$	13270.0	−	7661.44i	0.601048	−	0.347015i	0.769454	+	0.638703i	$0.220529\pi$
$788$	18908.5	−	10916.9i	0.854808	−	0.493524i
$789$	10933.5	−	298.863i	0.493336	−	0.0134852i
$790$	19273.3	−	11127.4i	0.867990	−	0.501135i
$791$	−13882.5	+	32407.4i	−0.624027	+	1.45673i
$792$	5340.84	−	292.199i	0.239619	−	0.0131096i
$793$	−10245.7	−	17746.1i	−0.458809	−	0.794680i
$794$	−6823.66			−0.304991
$795$	−5971.56	+	11028.4i	−0.266402	+	0.491997i
$796$			36827.0i			1.63982i
$797$	15911.5	−	27559.5i	0.707169	−	1.22485i	−0.258734	−	0.965949i	$-0.583305\pi$
$797$	15911.5	−	27559.5i	0.707169	−	1.22485i	0.965903	−	0.258904i	$-0.0833614\pi$
$798$	5107.42	−	752.074i	0.226567	−	0.0333623i
$799$	−9642.49	−	16701.3i	−0.426942	−	0.739486i
$800$	−43829.4	+	25304.9i	−1.93700	+	1.11833i
$801$	1040.82	+	1594.70i	0.0459122	+	0.0703445i
$802$	−4810.32	+	8331.72i	−0.211793	+	0.366837i
$803$	490.771	−	850.041i	0.0215678	−	0.0373565i
$804$	−17476.3	−	9462.90i	−0.766594	−	0.415088i
$805$	−28141.6	+	3361.11i	−1.23212	+	0.147160i
$806$	2196.36	+	1268.07i	0.0959844	+	0.0554166i
$807$	−14847.6	−	8039.52i	−0.647657	−	0.350687i
$808$		−	9407.13i		−	0.409581i
$809$	33531.7	+	19359.5i	1.45724	+	0.841341i	0.998875	−	0.0474209i	$-0.0151002\pi$
$809$	33531.7	+	19359.5i	1.45724	+	0.841341i	0.458370	+	0.888762i	$0.348434\pi$
$810$	−12250.1	−	5386.81i	−0.531387	−	0.233671i
$811$			10326.3i			0.447108i	0.974692	+	0.223554i	$0.0717658\pi$
$811$			10326.3i			0.447108i	−0.974692	+	0.223554i	$0.928234\pi$
$812$	−10362.6	+	24190.5i	−0.447853	+	1.04547i
$813$	−18768.5	−	30548.7i	−0.809645	−	1.31782i
$814$	86.6394			0.00373060
$815$	8892.66	+	15402.5i	0.382204	+	0.661997i
$816$	14713.5	−	9039.70i	0.631221	−	0.387810i
$817$	1356.24	+	783.028i	0.0580771	+	0.0335308i
$818$	5027.86			0.214908
$819$	6606.12	−	18093.6i	0.281852	−	0.771967i
$820$	2947.01			0.125505
$821$	1680.92	+	970.482i	0.0714551	+	0.0412546i	0.535302	−	0.844661i	$-0.320198\pi$
$821$	1680.92	+	970.482i	0.0714551	+	0.0412546i	−0.463847	+	0.885915i	$0.653531\pi$
$822$	−3339.96	−	1808.49i	−0.141721	−	0.0767376i
$823$	−4557.71	−	7894.19i	−0.193040	−	0.334355i	0.753216	−	0.657773i	$-0.228501\pi$
$823$	−4557.71	−	7894.19i	−0.193040	−	0.334355i	−0.946256	+	0.323418i	$0.895168\pi$
$824$	9593.58			0.405592
$825$	28536.5	−	780.037i	1.20426	−	0.0329181i
$826$	−5445.77	+	650.420i	−0.229398	+	0.0273983i
$827$			33576.1i			1.41180i	0.708314	+	0.705898i	$0.249456\pi$
$827$			33576.1i			1.41180i	−0.708314	+	0.705898i	$0.750544\pi$
$828$	11522.2	−	7520.30i	0.483606	−	0.315638i
$829$	17471.9	+	10087.4i	0.731996	+	0.422618i	0.819152	−	0.573577i	$-0.194445\pi$
$829$	17471.9	+	10087.4i	0.731996	+	0.422618i	−0.0871560	+	0.996195i	$0.527778\pi$
$830$		−	4087.23i		−	0.170927i
$831$	−75.4410	−	2759.90i	−0.00314924	−	0.115210i
$832$	8738.70	+	5045.29i	0.364135	+	0.210233i
$833$	6744.76	−	22949.0i	0.280543	−	0.954544i
$834$	−3939.82	+	2420.55i	−0.163579	+	0.100500i
$835$	20337.6	−	35225.8i	0.842890	−	1.45993i
$836$	3613.60	−	6258.94i	0.149496	−	0.258935i
$837$	−6277.80	−	9067.20i	−0.259250	−	0.374442i
$838$	−2981.19	+	1721.19i	−0.122892	+	0.0709518i
$839$	16012.2	+	27734.0i	0.658883	+	1.14122i	0.980905	+	0.194487i	$0.0623043\pi$
$839$	16012.2	+	27734.0i	0.658883	+	1.14122i	−0.322022	+	0.946732i	$0.604362\pi$
$840$	−3937.10	−	26737.3i	−0.161718	−	1.09824i
$841$	6758.22	−	11705.6i	0.277101	−	0.479954i
$842$			7666.51i			0.313783i
$843$	13300.8	+	21649.1i	0.543421	+	0.884502i
$844$	−29373.0			−1.19794
$845$	7815.59	+	13537.0i	0.318183	+	0.551109i
$846$	5237.03	−	3418.09i	0.212828	−	0.138908i
$847$	2398.37	+	20080.8i	0.0972952	+	0.814623i
$848$	4544.95	−	2624.03i	0.184050	−	0.106261i
$849$	−12400.4	−	20183.6i	−0.501273	−	0.815899i
$850$	−17974.8	+	10377.8i	−0.725332	+	0.418771i
$851$	404.575	−	233.581i	0.0162969	−	0.00940900i
$852$	−859.904	−	1399.63i	−0.0345773	−	0.0562798i
$853$	−13435.9	+	7757.24i	−0.539317	+	0.311375i	−0.744802	−	0.667285i	$-0.767456\pi$
$853$	−13435.9	+	7757.24i	−0.539317	+	0.311375i	0.205485	+	0.978660i	$0.434123\pi$
$854$	6606.57	−	4944.31i	0.264722	−	0.198116i
$855$	−31739.1	+	20715.4i	−1.26954	+	0.828599i
$856$	−5046.13	−	8740.15i	−0.201487	−	0.348986i
$857$	18691.3			0.745022			0.372511	−	0.928028i	$-0.378497\pi$
$857$	18691.3			0.745022			0.372511	+	0.928028i	$0.378497\pi$
$858$	1356.79	+	2208.39i	0.0539861	+	0.0878707i
$859$			16224.1i			0.644421i	0.946668	+	0.322211i	$0.104426\pi$
$859$			16224.1i			0.644421i	−0.946668	+	0.322211i	$0.895574\pi$
$860$	1955.59	−	3387.18i	0.0775407	−	0.134304i
$861$	−653.342	+	1648.19i	−0.0258604	+	0.0652384i
$862$	−2398.13	−	4153.69i	−0.0947573	−	0.164124i
$863$	35402.0	−	20439.3i	1.39640	−	0.806214i	0.402390	−	0.915468i	$-0.368180\pi$
$863$	35402.0	−	20439.3i	1.39640	−	0.806214i	0.994014	+	0.109254i	$0.0348463\pi$
$864$	11374.2	+	16428.1i	0.447869	+	0.646870i
$865$	−6359.20	+	11014.5i	−0.249965	+	0.432951i
$866$	3123.40	−	5409.90i	0.122561	−	0.212281i
$867$	−220.585	+	135.523i	−0.00864067	+	0.00530866i
$868$	4183.93	−	9766.98i	0.163608	−	0.381927i
$869$	16232.4	+	9371.81i	0.633657	+	0.365842i
$870$	507.438	+	18563.9i	0.0197744	+	0.723419i
$871$		−	20186.2i		−	0.785283i
$872$	17721.2	+	10231.4i	0.688207	+	0.397336i
$873$	−12619.6	+	8236.51i	−0.489242	+	0.319317i
$874$			3745.67i			0.144965i
$875$	−11088.4	−	92840.1i	−0.428408	−	3.58693i
$876$	2406.77	−	65.7883i	0.0928279	−	0.00253742i
$877$	−7497.10			−0.288665			−0.144332	−	0.989529i	$-0.546103\pi$
$877$	−7497.10			−0.288665			−0.144332	+	0.989529i	$0.546103\pi$
$878$	5821.46	+	10083.1i	0.223764	+	0.387571i
$879$	20097.1	+	10882.0i	0.771170	+	0.417566i
$880$	−13984.6	−	8074.01i	−0.535705	−	0.309290i
$881$	−25989.7			−0.993887			−0.496944	−	0.867783i	$-0.665544\pi$
$881$	−25989.7			−0.993887			−0.496944	+	0.867783i	$0.665544\pi$
$882$	7550.33	+	1777.40i	0.288246	+	0.0678551i
$883$	−20005.7			−0.762454			−0.381227	−	0.924481i	$-0.624498\pi$
$883$	−20005.7			−0.762454			−0.381227	+	0.924481i	$0.624498\pi$
$884$	16978.9	+	9802.79i	0.645999	+	0.372968i
$885$	34307.5	−	21077.8i	1.30309	−	0.800592i
$886$	6074.98	+	10522.2i	0.230353	+	0.398983i
$887$	−1350.69			−0.0511292			−0.0255646	−	0.999673i	$-0.508138\pi$
$887$	−1350.69			−0.0511292			−0.0255646	+	0.999673i	$0.508138\pi$
$888$	233.194	+	379.559i	0.00881246	+	0.0143436i
$889$	310.864	+	2602.77i	0.0117278	+	0.0981937i
$890$			1294.70i			0.0487625i
$891$	−1229.57	−	11203.5i	−0.0462315	−	0.421248i
$892$	28365.9	+	16377.0i	1.06475	+	0.614735i
$893$		−	17712.1i		−	0.663732i
$894$	9288.12	+	5029.24i	0.347473	+	0.188146i
$895$	517.045	+	298.516i	0.0193105	+	0.0111489i
$896$	−9909.20	+	23132.1i	−0.369468	+	0.862486i
$897$	12289.6	+	6654.43i	0.457454	+	0.247698i
$898$	−1235.13	+	2139.30i	−0.0458983	+	0.0794982i
$899$	−7652.20	+	13254.0i	−0.283888	+	0.491708i
$900$	38272.9	+	58639.9i	1.41751	+	2.17185i
$901$	6650.81	−	3839.85i	0.245916	−	0.141980i
$902$	−119.285	−	206.608i	−0.00440329	−	0.00762672i
$903$	1460.82	+	1844.64i	0.0538351	+	0.0679798i
$904$	12196.1	−	21124.2i	0.448712	−	0.777192i
$905$		−	58755.1i		−	2.15811i
$906$	−1383.54	+	2555.16i	−0.0507341	+	0.0936970i
$907$	23250.4			0.851176			0.425588	−	0.904917i	$-0.360067\pi$
$907$	23250.4			0.851176			0.425588	+	0.904917i	$0.360067\pi$
$908$	19894.0	+	34457.3i	0.727097	+	1.25937i
$909$	−19792.6	+	1082.86i	−0.722201	+	0.0395118i
$910$	10484.7	−	7846.69i	0.381940	−	0.285841i
$911$	−30824.3	+	17796.4i	−1.12103	+	0.647225i	−0.941663	−	0.336558i	$-0.890737\pi$
$911$	−30824.3	+	17796.4i	−1.12103	+	0.647225i	−0.179364	+	0.983783i	$0.557404\pi$
$912$	15854.2	−	433.371i	0.575643	−	0.0157350i
$913$	2981.18	−	1721.18i	0.108064	−	0.0623909i
$914$	11537.7	−	6661.28i	0.417541	−	0.241068i
$915$	−28846.2	+	53273.8i	−1.04221	+	1.92478i
$916$	−38022.1	+	21952.1i	−1.37149	+	0.791830i
$917$	−2497.10	−	20907.5i	−0.0899254	−	0.752919i
$918$	4664.68	+	6737.32i	0.167709	+	0.242227i
$919$	6397.75	+	11081.2i	0.229643	+	0.397754i	0.957702	−	0.287761i	$-0.0929107\pi$
$919$	6397.75	+	11081.2i	0.229643	+	0.397754i	−0.728059	+	0.685514i	$0.759577\pi$
$920$	19608.5			0.702689
$921$	26212.8	−	716.518i	0.937828	−	0.0256352i
$922$		−	2342.57i		−	0.0836751i
$923$	834.248	−	1444.96i	0.0297504	−	0.0515292i
$924$	8512.84	−	6741.55i	0.303086	−	0.240022i
$925$	1188.76	+	2058.99i	0.0422553	+	0.0731883i
$926$	3969.56	−	2291.83i	0.140872	−	0.0813327i
$927$	−1104.32	−	20184.9i	−0.0391270	−	0.715168i
$928$	13864.4	−	24013.8i	0.490432	−	0.849453i
$929$	14950.0	−	25894.1i	0.527979	−	0.914486i	−0.471489	−	0.881872i	$-0.656283\pi$
$929$	14950.0	−	25894.1i	0.527979	−	0.914486i	0.999468	−	0.0326142i	$-0.0103833\pi$
$930$	−204.879	−	7495.20i	−0.00722392	−	0.264277i
$931$	15903.4	−	15156.1i	0.559841	−	0.533536i
$932$	−15715.8	−	9073.54i	−0.552349	−	0.318899i
$933$	−8998.05	+	5528.23i	−0.315737	+	0.193983i
$934$		−	8381.43i		−	0.293628i
$935$	−20464.2	−	11815.0i	−0.715778	−	0.413254i
$936$	−6022.87	+	11887.9i	−0.210324	+	0.415138i
$937$		−	21288.1i		−	0.742211i	−0.928591	−	0.371106i	$-0.878979\pi$
$937$		−	21288.1i		−	0.742211i	0.928591	−	0.371106i	$-0.121021\pi$
$938$	8071.56	−	964.034i	0.280966	−	0.0335574i
$939$	−22236.9	+	41067.7i	−0.772816	+	1.42726i
$940$	−44235.4			−1.53489
$941$	−13252.9	−	22954.6i	−0.459119	−	0.795218i	0.539795	−	0.841796i	$-0.318502\pi$
$941$	−13252.9	−	22954.6i	−0.459119	−	0.795218i	−0.998915	+	0.0465785i	$0.985168\pi$
$942$	−266.029	−	9732.27i	−0.00920136	−	0.336618i
$943$	−1114.04	−	643.190i	−0.0384709	−	0.0222112i
$944$	−16849.3			−0.580932
$945$	−55802.2	+	11361.4i	−1.92089	+	0.391097i
$946$	−316.623			−0.0108819
$947$	7870.79	+	4544.20i	0.270081	+	0.155931i	0.628924	−	0.777467i	$-0.283496\pi$
$947$	7870.79	+	4544.20i	0.270081	+	0.155931i	−0.358844	+	0.933398i	$0.616829\pi$
$948$	1256.30	+	45959.9i	0.0430408	+	1.57459i
$949$	1222.76	+	2117.88i	0.0418254	+	0.0724438i
$950$	−19062.7			−0.651029
$951$	7075.33	−	13066.9i	0.241255	−	0.445555i
$952$	−6516.50	+	15212.1i	−0.221850	+	0.517887i
$953$		−	21333.9i		−	0.725156i	−0.931953	−	0.362578i	$-0.881897\pi$
$953$		−	21333.9i		−	0.725156i	0.931953	−	0.362578i	$-0.118103\pi$
$954$	1361.16	+	2085.50i	0.0461940	+	0.0707762i
$955$	−70564.9	−	40740.7i	−2.39102	−	1.38046i
$956$		−	15676.8i		−	0.530360i
$957$	−13326.6	+	8187.61i	−0.450144	+	0.276560i
$958$	−8695.31	−	5020.24i	−0.293249	−	0.169307i
$959$	−16048.8	+	1916.80i	−0.540399	+	0.0645430i
$960$	−815.157	−	29821.3i	−0.0274053	−	1.00258i
$961$	−11805.9	+	20448.4i	−0.396291	+	0.686396i
$962$	−107.931	+	186.942i	−0.00361729	+	0.00626533i
$963$	−17808.4	+	11623.2i	−0.595918	+	0.388942i
$964$	−19082.8	+	11017.4i	−0.637567	+	0.368100i
$965$	18815.5	+	32589.4i	0.627660	+	1.08714i
$966$	−2073.90	+	5231.86i	−0.0690753	+	0.174257i
$967$	10750.5	−	18620.4i	0.357510	−	0.619225i	−0.630035	−	0.776567i	$-0.716959\pi$
$967$	10750.5	−	18620.4i	0.357510	−	0.619225i	0.987544	+	0.157342i	$0.0502926\pi$
$968$		−	13992.0i		−	0.464585i
$969$	23200.1	−	634.169i	0.769139	−	0.0210242i
$970$	−10245.6			−0.339141
$971$	25147.4	+	43556.5i	0.831120	+	1.43954i	0.897151	+	0.441725i	$0.145633\pi$
$971$	25147.4	+	43556.5i	0.831120	+	1.43954i	−0.0660306	+	0.997818i	$0.521033\pi$
$972$	21836.6	−	16955.8i	0.720585	−	0.559524i
$973$	−7748.21	+	18087.4i	−0.255289	+	0.595947i
$974$	−6061.33	+	3499.51i	−0.199402	+	0.115125i
$975$	−33866.3	+	62545.0i	−1.11240	+	2.05440i
$976$	21954.8	−	12675.6i	0.720037	−	0.415714i
$977$	−26633.7	+	15377.0i	−0.872148	+	0.503535i	−0.868061	−	0.496457i	$-0.834634\pi$
$977$	−26633.7	+	15377.0i	−0.872148	+	0.503535i	−0.00408625	+	0.999992i	$0.501301\pi$
$978$	3530.39	−	96.5022i	0.115429	−	0.00315521i
$979$	−944.343	+	545.217i	−0.0308287	+	0.0177990i
$980$	−37851.9	−	39718.2i	−1.23381	−	1.29464i
$981$	19486.9	−	38463.3i	0.634219	−	1.25182i
$982$	−2845.57	−	4928.67i	−0.0924702	−	0.160163i
$983$	−53202.1			−1.72623			−0.863115	−	0.505008i	$-0.831490\pi$
$983$	−53202.1			−1.72623			−0.863115	+	0.505008i	$0.831490\pi$
$984$	584.069	−	1078.67i	0.0189222	−	0.0349459i
$985$		−	65565.2i		−	2.12089i
$986$	5685.92	−	9848.30i	0.183648	−	0.318087i
$987$	9806.84	−	24739.8i	0.316267	−	0.797850i
$988$	9003.28	+	15594.1i	0.289911	+	0.502141i
$989$	−1478.51	+	853.621i	−0.0475369	+	0.0274455i
$990$	3463.16	−	6835.59i	0.111178	−	0.219444i
$991$	13889.8	−	24057.9i	0.445232	−	0.771165i	−0.552836	−	0.833290i	$-0.686454\pi$
$991$	13889.8	−	24057.9i	0.445232	−	0.771165i	0.998068	+	0.0621249i	$0.0197877\pi$
$992$	−5597.78	+	9695.63i	−0.179163	+	0.310319i
$993$	26854.5	+	14540.9i	0.858211	+	0.464695i
$994$	617.618	+	264.572i	0.0197079	+	0.00844237i
$995$	95773.0	+	55294.6i	3.05147	+	1.76177i
$996$	7425.30	+	4020.58i	0.236225	+	0.127909i
$997$		−	47174.3i		−	1.49852i	−0.662276	−	0.749260i	$-0.730410\pi$
$997$		−	47174.3i		−	1.49852i	0.662276	−	0.749260i	$-0.269590\pi$
$998$	−7947.15	−	4588.29i	−0.252067	−	0.145531i
$999$	771.750	−	534.332i	0.0244415	−	0.0169224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.59.13	yes	44
3.2	odd	2		189.4.s.a.17.10		44
7.5	odd	6		63.4.i.a.5.10	✓	44
9.2	odd	6		63.4.i.a.38.13	yes	44
9.7	even	3		189.4.i.a.143.10		44
21.5	even	6		189.4.i.a.152.13		44
63.47	even	6	inner	63.4.s.a.47.13	yes	44
63.61	odd	6		189.4.s.a.89.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.10	✓	44	7.5	odd	6
63.4.i.a.38.13	yes	44	9.2	odd	6
63.4.s.a.47.13	yes	44	63.47	even	6	inner
63.4.s.a.59.13	yes	44	1.1	even	1	trivial
189.4.i.a.143.10		44	9.7	even	3
189.4.i.a.152.13		44	21.5	even	6
189.4.s.a.17.10		44	3.2	odd	2
189.4.s.a.89.10		44	63.61	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.725355 + 0.418784i) q^{2} +(0.141982 + 5.19421i) q^{3} +(-3.64924 - 6.32067i) q^{4} -21.9169 q^{5} +(-2.07226 + 3.82711i) q^{6} +(2.19637 + 18.3896i) q^{7} -12.8135i q^{8} +(-26.9597 + 1.47497i) q^{9} +O(q^{10})\)	\(q+(0.725355 + 0.418784i) q^{2} +(0.141982 + 5.19421i) q^{3} +(-3.64924 - 6.32067i) q^{4} -21.9169 q^{5} +(-2.07226 + 3.82711i) q^{6} +(2.19637 + 18.3896i) q^{7} -12.8135i q^{8} +(-26.9597 + 1.47497i) q^{9} +(-15.8975 - 9.17842i) q^{10} -15.4606i q^{11} +(32.3128 - 19.8524i) q^{12} +(33.3594 + 19.2600i) q^{13} +(-6.10810 + 14.2588i) q^{14} +(-3.11180 - 113.841i) q^{15} +(-23.8278 + 41.2710i) q^{16} +(-34.8682 + 60.3936i) q^{17} +(-20.1730 - 10.2204i) q^{18} +(-55.4679 + 32.0244i) q^{19} +(79.9799 + 138.529i) q^{20} +(-95.2074 + 14.0194i) q^{21} +(6.47465 - 11.2144i) q^{22} -69.8230i q^{23} +(66.5561 - 1.81929i) q^{24} +355.349 q^{25} +(16.1316 + 27.9407i) q^{26} +(-11.4891 - 139.825i) q^{27} +(108.219 - 80.9905i) q^{28} +(-168.609 + 97.3466i) q^{29} +(45.4175 - 83.8781i) q^{30} +(68.0764 - 39.3039i) q^{31} +(-123.342 + 71.2115i) q^{32} +(80.3057 - 2.19513i) q^{33} +(-50.5837 + 29.2045i) q^{34} +(-48.1376 - 403.041i) q^{35} +(107.705 + 165.021i) q^{36} +(3.34533 + 5.79428i) q^{37} -53.6452 q^{38} +(-95.3043 + 176.010i) q^{39} +280.832i q^{40} +(9.21172 - 15.9552i) q^{41} +(-74.9303 - 29.7023i) q^{42} +(-12.2255 - 21.1752i) q^{43} +(-97.7214 + 56.4195i) q^{44} +(590.872 - 32.3267i) q^{45} +(29.2407 - 50.6465i) q^{46} +(-138.270 + 239.491i) q^{47} +(-217.754 - 117.907i) q^{48} +(-333.352 + 80.7806i) q^{49} +(257.754 + 148.814i) q^{50} +(-318.648 - 172.538i) q^{51} -281.138i q^{52} +(-95.3706 - 55.0622i) q^{53} +(50.2227 - 106.234i) q^{54} +338.848i q^{55} +(235.635 - 28.1432i) q^{56} +(-174.217 - 283.565i) q^{57} -163.069 q^{58} +(176.782 + 306.196i) q^{59} +(-708.194 + 435.101i) q^{60} +(-460.697 - 265.983i) q^{61} +65.8393 q^{62} +(-86.3376 - 492.537i) q^{63} +261.957 q^{64} +(-731.132 - 422.120i) q^{65} +(59.1694 + 32.0385i) q^{66} +(-262.021 - 453.834i) q^{67} +508.970 q^{68} +(362.676 - 9.91363i) q^{69} +(133.870 - 312.507i) q^{70} -43.3150i q^{71} +(18.8996 + 345.448i) q^{72} +(54.9811 + 31.7433i) q^{73} +5.60388i q^{74} +(50.4532 + 1845.76i) q^{75} +(404.831 + 233.729i) q^{76} +(284.314 - 33.9572i) q^{77} +(-142.840 + 87.7579i) q^{78} +(-606.173 + 1049.92i) q^{79} +(522.231 - 904.531i) q^{80} +(724.649 - 79.5295i) q^{81} +(13.3635 - 7.71543i) q^{82} +(111.327 + 192.824i) q^{83} +(436.047 + 550.615i) q^{84} +(764.202 - 1323.64i) q^{85} -20.4793i q^{86} +(-529.578 - 861.971i) q^{87} -198.105 q^{88} +(-35.2649 - 61.0806i) q^{89} +(442.129 + 223.999i) q^{90} +(-280.914 + 655.766i) q^{91} +(-441.328 + 254.801i) q^{92} +(213.818 + 348.023i) q^{93} +(-200.590 + 115.811i) q^{94} +(1215.68 - 701.874i) q^{95} +(-387.400 - 630.553i) q^{96} +(483.359 - 279.067i) q^{97} +(-275.628 - 81.0077i) q^{98} +(22.8040 + 416.813i) 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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