LMFDB - Embedded newform 72.3.j.a.29.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (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:	$1.96185790339$
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			29.21
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96814 - 0.355563i) q^{2} +(2.21491 + 2.02340i) q^{3} +(3.74715 - 1.39960i) q^{4} +(-4.28090 - 7.41474i) q^{5} +(5.07871 + 3.19480i) q^{6} +(-3.75800 + 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +(0.811683 + 8.96332i) q^{9} +O(q^{10})$	\(q+(1.96814 - 0.355563i) q^{2} +(2.21491 + 2.02340i) q^{3} +(3.74715 - 1.39960i) q^{4} +(-4.28090 - 7.41474i) q^{5} +(5.07871 + 3.19480i) q^{6} +(-3.75800 + 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +(0.811683 + 8.96332i) q^{9} +(-11.0618 - 13.0711i) q^{10} +(-4.74705 + 8.22213i) q^{11} +(11.1316 + 4.48201i) q^{12} +(-9.54725 + 5.51211i) q^{13} +(-5.08189 + 14.1469i) q^{14} +(5.52118 - 25.0850i) q^{15} +(12.0823 - 10.4890i) q^{16} -11.3516i q^{17} +(4.78453 + 17.3525i) q^{18} -18.3798i q^{19} +(-26.4188 - 21.7926i) q^{20} +(-21.4941 + 6.81302i) q^{21} +(-6.41937 + 17.8702i) q^{22} +(22.8408 - 13.1871i) q^{23} +(23.5021 + 4.86324i) q^{24} +(-24.1522 + 41.8329i) q^{25} +(-16.8304 + 14.2433i) q^{26} +(-16.3386 + 21.4953i) q^{27} +(-4.97174 + 29.6500i) q^{28} +(3.48316 - 6.03301i) q^{29} +(1.94715 - 51.3339i) q^{30} +(6.42393 + 11.1266i) q^{31} +(20.0501 - 24.9398i) q^{32} +(-27.1510 + 8.60611i) q^{33} +(-4.03621 - 22.3415i) q^{34} +64.3505 q^{35} +(15.5865 + 32.4509i) q^{36} +5.89614i q^{37} +(-6.53519 - 36.1741i) q^{38} +(-32.2996 - 7.10909i) q^{39} +(-59.7446 - 33.4973i) q^{40} +(32.7049 - 18.8822i) q^{41} +(-39.8808 + 21.0515i) q^{42} +(21.1756 + 12.2257i) q^{43} +(-6.28023 + 37.4535i) q^{44} +(62.9860 - 44.3895i) q^{45} +(40.2650 - 34.0754i) q^{46} +(-15.8834 - 9.17030i) q^{47} +(47.9846 + 1.21506i) q^{48} +(-3.74509 - 6.48669i) q^{49} +(-32.6607 + 90.9207i) q^{50} +(22.9688 - 25.1428i) q^{51} +(-28.0603 + 34.0170i) q^{52} -58.4847 q^{53} +(-24.5137 + 48.1153i) q^{54} +81.2866 q^{55} +(0.757376 + 60.1232i) q^{56} +(37.1898 - 40.7097i) q^{57} +(4.71023 - 13.1123i) q^{58} +(-13.1643 - 22.8013i) q^{59} +(-14.4202 - 101.725i) q^{60} +(56.0654 + 32.3694i) q^{61} +(16.5994 + 19.6145i) q^{62} +(-61.3930 - 28.4009i) q^{63} +(30.5937 - 56.2141i) q^{64} +(81.7417 + 47.1936i) q^{65} +(-50.3769 + 26.5919i) q^{66} +(28.4707 - 16.4376i) q^{67} +(-15.8876 - 42.5361i) q^{68} +(77.2732 + 17.0077i) q^{69} +(126.651 - 22.8807i) q^{70} +84.5841i q^{71} +(42.2148 + 58.3259i) q^{72} -94.1083 q^{73} +(2.09645 + 11.6044i) q^{74} +(-138.140 + 43.7866i) q^{75} +(-25.7243 - 68.8719i) q^{76} +(-35.6788 - 61.7975i) q^{77} +(-66.0978 - 2.50715i) q^{78} +(-12.3221 + 21.3425i) q^{79} +(-129.496 - 44.6844i) q^{80} +(-79.6823 + 14.5508i) q^{81} +(57.6540 - 48.7914i) q^{82} +(-57.7838 + 100.085i) q^{83} +(-71.0060 + 55.6124i) q^{84} +(-84.1691 + 48.5950i) q^{85} +(46.0236 + 16.5327i) q^{86} +(19.9221 - 6.31476i) q^{87} +(0.956706 + 75.9467i) q^{88} -131.872i q^{89} +(108.182 - 109.760i) q^{90} -82.8580i q^{91} +(67.1311 - 81.3820i) q^{92} +(-8.28509 + 37.6426i) q^{93} +(-34.5214 - 12.4009i) q^{94} +(-136.282 + 78.6822i) q^{95} +(94.8725 - 14.6702i) q^{96} +(94.1484 - 163.070i) q^{97} +(-9.67730 - 11.4351i) q^{98} +(-77.5507 - 35.8756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.96814	−	0.355563i	0.984070	−	0.177782i
$2$	1.96814	−	0.355563i	0.984070	−	0.177782i
$3$	2.21491	+	2.02340i	0.738304	+	0.674468i
$3$	2.21491	+	2.02340i	0.738304	+	0.674468i
$4$	3.74715	−	1.39960i	0.936787	−	0.349899i
$5$	−4.28090	−	7.41474i	−0.856180	−	1.48295i	−0.875546	−	0.483135i	$-0.839498\pi$
$5$	−4.28090	−	7.41474i	−0.856180	−	1.48295i	0.0193654	−	0.999812i	$-0.493835\pi$
$6$	5.07871	+	3.19480i	0.846451	+	0.532466i
$7$	−3.75800	+	6.50904i	−0.536857	+	0.929863i	0.462214	+	0.886768i	$0.347055\pi$
$7$	−3.75800	+	6.50904i	−0.536857	+	0.929863i	−0.999071	+	0.0430950i	$0.986278\pi$
$8$	6.87727	−	4.08695i	0.859659	−	0.510869i
$9$	0.811683	+	8.96332i	0.0901870	+	0.995925i
$10$	−11.0618	−	13.0711i	−1.10618	−	1.30711i
$11$	−4.74705	+	8.22213i	−0.431550	+	0.747466i	−0.997007	−	0.0773115i	$-0.975366\pi$
$11$	−4.74705	+	8.22213i	−0.431550	+	0.747466i	0.565457	+	0.824778i	$0.308700\pi$
$12$	11.1316	+	4.48201i	0.927630	+	0.373501i
$13$	−9.54725	+	5.51211i	−0.734404	+	0.424008i	−0.820031	−	0.572319i	$-0.806044\pi$
$13$	−9.54725	+	5.51211i	−0.734404	+	0.424008i	0.0856271	+	0.996327i	$0.472711\pi$
$14$	−5.08189	+	14.1469i	−0.362992	+	1.01049i
$15$	5.52118	−	25.0850i	0.368078	−	1.67233i
$16$	12.0823	−	10.4890i	0.755141	−	0.655562i
$17$		−	11.3516i		−	0.667740i	−0.942619	−	0.333870i	$-0.891645\pi$
$17$		−	11.3516i		−	0.667740i	0.942619	−	0.333870i	$-0.108355\pi$
$18$	4.78453	+	17.3525i	0.265807	+	0.964026i
$19$		−	18.3798i		−	0.967359i	−0.875245	−	0.483680i	$-0.839300\pi$
$19$		−	18.3798i		−	0.967359i	0.875245	−	0.483680i	$-0.160700\pi$
$20$	−26.4188	−	21.7926i	−1.32094	−	1.08963i
$21$	−21.4941	+	6.81302i	−1.02353	+	0.324430i
$22$	−6.41937	+	17.8702i	−0.291789	+	0.812281i
$23$	22.8408	−	13.1871i	0.993077	−	0.573353i	0.0868842	−	0.996218i	$-0.472309\pi$
$23$	22.8408	−	13.1871i	0.993077	−	0.573353i	0.906193	+	0.422865i	$0.138976\pi$
$24$	23.5021	+	4.86324i	0.979254	+	0.202635i
$25$	−24.1522	+	41.8329i	−0.966090	+	1.67332i
$26$	−16.8304	+	14.2433i	−0.647324	+	0.547817i
$27$	−16.3386	+	21.4953i	−0.605134	+	0.796124i
$28$	−4.97174	+	29.6500i	−0.177562	+	1.05893i
$29$	3.48316	−	6.03301i	0.120109	−	0.208035i	−0.799701	−	0.600398i	$-0.795009\pi$
$29$	3.48316	−	6.03301i	0.120109	−	0.208035i	0.919810	+	0.392363i	$0.128342\pi$
$30$	1.94715	−	51.3339i	0.0649049	−	1.71113i
$31$	6.42393	+	11.1266i	0.207224	+	0.358922i	0.950839	−	0.309686i	$-0.100224\pi$
$31$	6.42393	+	11.1266i	0.207224	+	0.358922i	−0.743615	+	0.668608i	$0.766891\pi$
$32$	20.0501	−	24.9398i	0.626565	−	0.779369i
$33$	−27.1510	+	8.60611i	−0.822757	+	0.260791i
$34$	−4.03621	−	22.3415i	−0.118712	−	0.657103i
$35$	64.3505			1.83859
$36$	15.5865	+	32.4509i	0.432959	+	0.901413i
$37$			5.89614i			0.159355i	0.996821	+	0.0796776i	$0.0253891\pi$
$37$			5.89614i			0.159355i	−0.996821	+	0.0796776i	$0.974611\pi$
$38$	−6.53519	−	36.1741i	−0.171979	−	0.951949i
$39$	−32.2996	−	7.10909i	−0.828194	−	0.182284i
$40$	−59.7446	−	33.4973i	−1.49361	−	0.837433i
$41$	32.7049	−	18.8822i	0.797681	−	0.460541i	−0.0449789	−	0.998988i	$-0.514322\pi$
$41$	32.7049	−	18.8822i	0.797681	−	0.460541i	0.842659	+	0.538447i	$0.180989\pi$
$42$	−39.8808	+	21.0515i	−0.949544	+	0.501226i
$43$	21.1756	+	12.2257i	0.492456	+	0.284320i	0.725593	−	0.688124i	$-0.241566\pi$
$43$	21.1756	+	12.2257i	0.492456	+	0.284320i	−0.233137	+	0.972444i	$0.574899\pi$
$44$	−6.28023	+	37.4535i	−0.142733	+	0.851216i
$45$	62.9860	−	44.3895i	1.39969	−	0.986434i
$46$	40.2650	−	34.0754i	0.875325	−	0.740770i
$47$	−15.8834	−	9.17030i	−0.337945	−	0.195113i	0.321418	−	0.946937i	$-0.395841\pi$
$47$	−15.8834	−	9.17030i	−0.337945	−	0.195113i	−0.659363	+	0.751825i	$0.729174\pi$
$48$	47.9846	+	1.21506i	0.999680	+	0.0253137i
$49$	−3.74509	−	6.48669i	−0.0764305	−	0.132382i
$50$	−32.6607	+	90.9207i	−0.653215	+	1.81841i
$51$	22.9688	−	25.1428i	0.450369	−	0.492996i
$52$	−28.0603	+	34.0170i	−0.539620	+	0.654173i
$53$	−58.4847			−1.10348			−0.551742	−	0.834015i	$-0.686037\pi$
$53$	−58.4847			−1.10348			−0.551742	+	0.834015i	$0.686037\pi$
$54$	−24.5137	+	48.1153i	−0.453958	+	0.891023i
$55$	81.2866			1.47794
$56$	0.757376	+	60.1232i	0.0135246	+	1.07363i
$57$	37.1898	−	40.7097i	0.652452	−	0.714206i
$58$	4.71023	−	13.1123i	0.0812109	−	0.226074i
$59$	−13.1643	−	22.8013i	−0.223124	−	0.386462i	0.732631	−	0.680626i	$-0.238292\pi$
$59$	−13.1643	−	22.8013i	−0.223124	−	0.386462i	−0.955755	+	0.294164i	$0.904959\pi$
$60$	−14.4202	−	101.725i	−0.240337	−	1.69541i
$61$	56.0654	+	32.3694i	0.919104	+	0.530645i	0.883349	−	0.468715i	$-0.155283\pi$
$61$	56.0654	+	32.3694i	0.919104	+	0.530645i	0.0357552	+	0.999361i	$0.488616\pi$
$62$	16.5994	+	19.6145i	0.267732	+	0.316364i
$63$	−61.3930	−	28.4009i	−0.974491	−	0.450807i
$64$	30.5937	−	56.2141i	0.478026	−	0.878346i
$65$	81.7417	+	47.1936i	1.25756	+	0.726055i
$66$	−50.3769	+	26.5919i	−0.763286	+	0.402908i
$67$	28.4707	−	16.4376i	0.424936	−	0.245337i	−0.272251	−	0.962226i	$-0.587768\pi$
$67$	28.4707	−	16.4376i	0.424936	−	0.245337i	0.697187	+	0.716889i	$0.254435\pi$
$68$	−15.8876	−	42.5361i	−0.233642	−	0.625531i
$69$	77.2732	+	17.0077i	1.11990	+	0.246489i
$70$	126.651	−	22.8807i	1.80930	−	0.326867i
$71$			84.5841i			1.19132i	0.803235	+	0.595662i	$0.203110\pi$
$71$			84.5841i			1.19132i	−0.803235	+	0.595662i	$0.796890\pi$
$72$	42.2148	+	58.3259i	0.586317	+	0.810082i
$73$	−94.1083			−1.28915			−0.644577	−	0.764539i	$-0.722967\pi$
$73$	−94.1083			−1.28915			−0.644577	+	0.764539i	$0.722967\pi$
$74$	2.09645	+	11.6044i	0.0283304	+	0.156817i
$75$	−138.140	+	43.7866i	−1.84187	+	0.583821i
$76$	−25.7243	−	68.8719i	−0.338478	−	0.906210i
$77$	−35.6788	−	61.7975i	−0.463361	−	0.802565i
$78$	−66.0978	−	2.50715i	−0.847407	−	0.0321430i
$79$	−12.3221	+	21.3425i	−0.155976	+	0.270158i	−0.933414	−	0.358802i	$-0.883185\pi$
$79$	−12.3221	+	21.3425i	−0.155976	+	0.270158i	0.777438	+	0.628959i	$0.216519\pi$
$80$	−129.496	−	44.6844i	−1.61870	−	0.558555i
$81$	−79.6823	+	14.5508i	−0.983733	+	0.179639i
$82$	57.6540	−	48.7914i	0.703098	−	0.595018i
$83$	−57.7838	+	100.085i	−0.696191	+	1.20584i	0.273587	+	0.961847i	$0.411790\pi$
$83$	−57.7838	+	100.085i	−0.696191	+	1.20584i	−0.969778	+	0.243991i	$0.921543\pi$
$84$	−71.0060	+	55.6124i	−0.845309	+	0.662053i
$85$	−84.1691	+	48.5950i	−0.990224	+	0.571706i
$86$	46.0236	+	16.5327i	0.535158	+	0.192241i
$87$	19.9221	−	6.31476i	0.228990	−	0.0725835i
$88$	0.956706	+	75.9467i	0.0108717	+	0.863031i
$89$		−	131.872i		−	1.48171i	−0.671664	−	0.740856i	$-0.734420\pi$
$89$		−	131.872i		−	1.48171i	0.671664	−	0.740856i	$-0.265580\pi$
$90$	108.182	−	109.760i	1.20202	−	1.21956i
$91$		−	82.8580i		−	0.910527i
$92$	67.1311	−	81.3820i	0.729686	−	0.884587i
$93$	−8.28509	+	37.6426i	−0.0890870	+	0.404759i
$94$	−34.5214	−	12.4009i	−0.367249	−	0.131924i
$95$	−136.282	+	78.6822i	−1.43454	+	0.828234i
$96$	94.8725	−	14.6702i	0.988255	−	0.152814i
$97$	94.1484	−	163.070i	0.970603	−	1.68113i	0.276859	−	0.960910i	$-0.410706\pi$
$97$	94.1484	−	163.070i	0.970603	−	1.68113i	0.693743	−	0.720223i	$-0.255960\pi$
$98$	−9.67730	−	11.4351i	−0.0987480	−	0.116685i
$99$	−77.5507	−	35.8756i	−0.783340	−	0.362379i
$100$	−31.9529	+	190.558i	−0.319529	+	1.90558i
$101$	−28.3361	+	49.0795i	−0.280555	+	0.485936i	−0.971522	−	0.236951i	$-0.923852\pi$
$101$	−28.3361	+	49.0795i	−0.280555	+	0.485936i	0.690966	+	0.722887i	$0.257185\pi$
$102$	36.2660	−	57.6514i	0.355549	−	0.565210i
$103$	−5.46478	−	9.46528i	−0.0530561	−	0.0918959i	0.838278	−	0.545244i	$-0.183563\pi$
$103$	−5.46478	−	9.46528i	−0.0530561	−	0.0918959i	−0.891334	+	0.453348i	$0.850230\pi$
$104$	−43.1313	+	76.9274i	−0.414724	+	0.739687i
$105$	142.531	+	130.207i	1.35744	+	1.24007i
$106$	−115.106	+	20.7950i	−1.08591	+	0.196179i
$107$	57.2955			0.535472			0.267736	−	0.963492i	$-0.413724\pi$
$107$	57.2955			0.535472			0.267736	+	0.963492i	$0.413724\pi$
$108$	−31.1384	+	103.414i	−0.288318	+	0.957535i
$109$			49.9283i			0.458058i	0.973420	+	0.229029i	$0.0735551\pi$
$109$			49.9283i			0.458058i	−0.973420	+	0.229029i	$0.926445\pi$
$110$	159.983	−	28.9025i	1.45439	−	0.262750i
$111$	−11.9303	+	13.0594i	−0.107480	+	0.117653i
$112$	22.8682	+	118.062i	0.204181	+	1.05412i
$113$	−44.6255	+	25.7646i	−0.394916	+	0.228005i	−0.684288	−	0.729212i	$-0.739887\pi$
$113$	−44.6255	+	25.7646i	−0.394916	+	0.228005i	0.289372	+	0.957217i	$0.406554\pi$
$114$	58.7198	−	93.3457i	0.515086	−	0.818822i
$115$	−195.558	−	112.906i	−1.70051	−	0.981787i
$116$	4.60814	−	27.4816i	0.0397254	−	0.236911i
$117$	−57.1562	−	81.1010i	−0.488514	−	0.693171i
$118$	−34.0165	−	40.1953i	−0.288275	−	0.340638i
$119$	73.8880	+	42.6592i	0.620907	+	0.358481i
$120$	−64.5505	−	195.081i	−0.537921	−	1.62568i
$121$	15.4311	+	26.7274i	0.127530	+	0.220888i
$122$	121.854	+	43.7726i	0.998802	+	0.358792i
$123$	110.645	+	24.3528i	0.899551	+	0.197990i
$124$	39.6441	+	32.7020i	0.319711	+	0.263726i
$125$	199.528			1.59623
$126$	−130.928	−	34.0678i	−1.03911	−	0.270379i
$127$	18.7898			0.147951			0.0739756	−	0.997260i	$-0.476431\pi$
$127$	18.7898			0.147951			0.0739756	+	0.997260i	$0.476431\pi$
$128$	40.2249	−	121.515i	0.314257	−	0.949338i
$129$	22.1645	+	69.9257i	0.171818	+	0.542060i
$130$	177.659	+	63.8192i	1.36661	+	0.490917i
$131$	18.9279	+	32.7842i	0.144488	+	0.250261i	0.929182	−	0.369623i	$-0.120513\pi$
$131$	18.9279	+	32.7842i	0.144488	+	0.250261i	−0.784694	+	0.619884i	$0.787180\pi$
$132$	−89.6937	+	70.2488i	−0.679498	+	0.532188i
$133$	119.635	+	69.0713i	0.899512	+	0.519333i
$134$	50.1898	−	42.4746i	0.374551	−	0.316975i
$135$	229.326	+	29.1270i	1.69871	+	0.215756i
$136$	−46.3934	−	78.0679i	−0.341128	−	0.574029i
$137$	−224.690	−	129.725i	−1.64007	−	0.946896i	−0.980806	−	0.194987i	$-0.937534\pi$
$137$	−224.690	−	129.725i	−1.64007	−	0.946896i	−0.659266	−	0.751909i	$-0.729133\pi$
$138$	158.132	+	5.99810i	1.14588	+	0.0434645i
$139$	80.7028	−	46.5938i	0.580595	−	0.335207i	−0.180775	−	0.983525i	$-0.557860\pi$
$139$	80.7028	−	46.5938i	0.580595	−	0.335207i	0.761370	+	0.648318i	$0.224527\pi$
$140$	241.131	−	90.0647i	1.72236	−	0.643319i
$141$	−16.6252	−	52.4500i	−0.117909	−	0.371986i
$142$	30.0750	+	166.473i	0.211796	+	1.17235i
$143$		−	104.665i		−	0.731923i
$144$	103.823	+	99.7835i	0.720995	+	0.692941i
$145$	−59.6443			−0.411340
$146$	−185.218	+	33.4614i	−1.26862	+	0.229188i
$147$	4.83013	−	21.9453i	0.0328581	−	0.149288i
$148$	8.25222	+	22.0937i	0.0557583	+	0.149282i
$149$	−90.5257	−	156.795i	−0.607555	−	1.05232i	−0.991642	−	0.129020i	$-0.958817\pi$
$149$	−90.5257	−	156.795i	−0.607555	−	1.05232i	0.384087	−	0.923297i	$-0.374516\pi$
$150$	−256.310	+	135.296i	−1.70873	+	0.901970i
$151$	−25.1778	+	43.6092i	−0.166740	+	0.288803i	−0.937272	−	0.348599i	$-0.886658\pi$
$151$	−25.1778	+	43.6092i	−0.166740	+	0.288803i	0.770532	+	0.637402i	$0.219991\pi$
$152$	−75.1174	−	126.403i	−0.494194	−	0.831599i
$153$	101.748	−	9.21389i	0.665019	−	0.0602215i
$154$	−92.1938	−	108.940i	−0.598661	−	0.707403i
$155$	55.0004	−	95.2635i	0.354842	−	0.614604i
$156$	−130.981	+	18.5675i	−0.839623	+	0.119023i
$157$	−84.5771	+	48.8306i	−0.538707	+	0.311023i	−0.744555	−	0.667561i	$-0.767338\pi$
$157$	−84.5771	+	48.8306i	−0.538707	+	0.311023i	0.205847	+	0.978584i	$0.434005\pi$
$158$	−16.6630	+	46.3862i	−0.105462	+	0.293584i
$159$	−129.539	−	118.338i	−0.814708	−	0.744265i
$160$	−270.755	−	41.9012i	−1.69222	−	0.261882i
$161$			198.229i			1.23123i
$162$	−151.652	+	56.9700i	−0.936125	+	0.351667i
$163$			275.467i			1.68998i	0.534782	+	0.844990i	$0.320394\pi$
$163$			275.467i			1.68998i	−0.534782	+	0.844990i	$0.679606\pi$
$164$	96.1227	−	116.528i	0.586114	−	0.710537i
$165$	180.043	+	164.475i	1.09117	+	0.996821i
$166$	−78.1403	+	217.526i	−0.470725	+	1.31040i
$167$	−81.5588	+	47.0880i	−0.488376	+	0.281964i	−0.723900	−	0.689904i	$-0.757653\pi$
$167$	−81.5588	+	47.0880i	−0.488376	+	0.281964i	0.235525	+	0.971868i	$0.424319\pi$
$168$	−119.976	+	134.700i	−0.714142	+	0.801787i
$169$	−23.7333	+	41.1073i	−0.140434	+	0.243238i
$170$	−148.378	+	125.569i	−0.872811	+	0.738643i
$171$	164.744	−	14.9186i	0.963417	−	0.0872432i
$172$	96.4592	+	16.1744i	0.560810	+	0.0940370i
$173$	−88.1674	+	152.710i	−0.509638	+	0.882720i	0.490299	+	0.871554i	$0.336887\pi$
$173$	−88.1674	+	152.710i	−0.509638	+	0.882720i	−0.999938	+	0.0111654i	$0.996446\pi$
$174$	36.9642	−	19.5119i	0.212438	−	0.112137i
$175$	−181.528	−	314.416i	−1.03730	−	1.79666i
$176$	28.8868	+	149.134i	0.164130	+	0.847350i
$177$	16.9783	−	77.1395i	0.0959227	−	0.435816i
$178$	−46.8890	−	259.543i	−0.263421	−	1.45811i
$179$	21.4052			0.119582			0.0597911	−	0.998211i	$-0.480957\pi$
$179$	21.4052			0.119582			0.0597911	+	0.998211i	$0.480957\pi$
$180$	173.890	−	254.489i	0.966058	−	1.41383i
$181$		−	319.291i		−	1.76404i	−0.471215	−	0.882019i	$-0.656184\pi$
$181$		−	319.291i		−	1.76404i	0.471215	−	0.882019i	$-0.343816\pi$
$182$	−29.4613	−	163.076i	−0.161875	−	0.896022i
$183$	58.6837	+	185.138i	0.320676	+	1.01168i
$184$	103.187	−	184.040i	0.560799	−	1.00022i
$185$	43.7184	−	25.2408i	0.236315	−	0.136437i
$186$	−2.92189	+	77.0318i	−0.0157091	+	0.414149i
$187$	93.3342	+	53.8865i	0.499113	+	0.288163i
$188$	−72.3523	−	12.1321i	−0.384852	−	0.0645324i
$189$	−78.5137	−	187.128i	−0.415416	−	0.990096i
$190$	−240.245	+	203.314i	−1.26445	+	1.07008i
$191$	−168.265	−	97.1480i	−0.880970	−	0.508628i	−0.00999168	−	0.999950i	$-0.503181\pi$
$191$	−168.265	−	97.1480i	−0.880970	−	0.508628i	−0.870978	+	0.491322i	$0.836514\pi$
$192$	181.506	−	62.6061i	0.945344	−	0.326073i
$193$	20.4962	+	35.5005i	0.106198	+	0.183940i	0.914227	−	0.405202i	$-0.132799\pi$
$193$	20.4962	+	35.5005i	0.106198	+	0.183940i	−0.808029	+	0.589143i	$0.799466\pi$
$194$	127.316	−	354.420i	0.656266	−	1.82691i
$195$	85.5591	+	269.926i	0.438765	+	1.38424i
$196$	−23.1122	−	19.0650i	−0.117919	−	0.0972704i
$197$	14.2759			0.0724666			0.0362333	−	0.999343i	$-0.488464\pi$
$197$	14.2759			0.0724666			0.0362333	+	0.999343i	$0.488464\pi$
$198$	−165.387	−	43.0340i	−0.835286	−	0.217343i
$199$	298.873			1.50188			0.750938	−	0.660373i	$-0.229602\pi$
$199$	298.873			1.50188			0.750938	+	0.660373i	$0.229602\pi$
$200$	4.86757	+	386.405i	0.0243379	+	1.93203i
$201$	96.3201	+	21.1999i	0.479204	+	0.105472i
$202$	−38.3185	+	106.671i	−0.189695	+	0.528072i
$203$	26.1794	+	45.3441i	0.128963	+	0.223370i
$204$	50.8779	−	126.361i	0.249401	−	0.619416i
$205$	−280.013	−	161.666i	−1.36592	−	0.788613i
$206$	−14.1210	−	16.6859i	−0.0685484	−	0.0809996i
$207$	136.740	+	194.025i	0.660579	+	0.937321i
$208$	−57.5359	+	166.740i	−0.276615	+	0.801634i
$209$	151.121	+	87.2499i	0.723068	+	0.417464i
$210$	326.817	+	205.587i	1.55627	+	0.978985i
$211$	202.413	−	116.863i	0.959305	−	0.553855i	0.0633463	−	0.997992i	$-0.479823\pi$
$211$	202.413	−	116.863i	0.959305	−	0.553855i	0.895959	+	0.444136i	$0.146489\pi$
$212$	−219.151	+	81.8550i	−1.03373	+	0.386108i
$213$	−171.148	+	187.346i	−0.803510	+	0.879561i
$214$	112.766	−	20.3722i	0.526942	−	0.0951971i
$215$		−	209.349i		−	0.973715i
$216$	−24.5146	+	214.604i	−0.113493	+	0.993539i
$217$	−96.5645			−0.444998
$218$	17.7527	+	98.2659i	0.0814343	+	0.450761i
$219$	−208.442	−	190.419i	−0.951788	−	0.869493i
$220$	304.593	−	113.768i	1.38451	−	0.517129i
$221$	62.5712	+	108.376i	0.283128	+	0.490391i
$222$	−18.8370	+	29.9448i	−0.0848513	+	0.134886i
$223$	−1.38344	+	2.39619i	−0.00620377	+	0.0107452i	−0.869111	−	0.494618i	$-0.835308\pi$
$223$	−1.38344	+	2.39619i	−0.00620377	+	0.0107452i	0.862907	+	0.505363i	$0.168641\pi$
$224$	86.9862	+	224.231i	0.388331	+	1.00103i
$225$	−394.566	−	182.529i	−1.75363	−	0.811241i
$226$	−78.6684	+	66.5755i	−0.348090	+	0.294582i
$227$	24.5897	−	42.5906i	0.108325	−	0.187624i	−0.806767	−	0.590870i	$-0.798785\pi$
$227$	24.5897	−	42.5906i	0.108325	−	0.187624i	0.915092	+	0.403246i	$0.132118\pi$
$228$	82.3785	−	204.596i	0.361309	−	0.897351i
$229$	227.507	−	131.351i	0.993481	−	0.573587i	0.0871681	−	0.996194i	$-0.472218\pi$
$229$	227.507	−	131.351i	0.993481	−	0.573587i	0.906313	+	0.422607i	$0.138885\pi$
$230$	−425.031	−	152.681i	−1.84796	−	0.663829i
$231$	46.0158	−	209.069i	0.199202	−	0.905059i
$232$	−0.701986	−	55.7262i	−0.00302580	−	0.240199i
$233$			320.513i			1.37559i	0.725903	+	0.687797i	$0.241422\pi$
$233$			320.513i			1.37559i	−0.725903	+	0.687797i	$0.758578\pi$
$234$	−141.328	−	139.296i	−0.603965	−	0.595280i
$235$			157.029i			0.668207i
$236$	−81.2412	−	67.0150i	−0.344242	−	0.283962i
$237$	−70.4767	+	22.3392i	−0.297370	+	0.0942582i
$238$	160.590	+	57.6875i	0.674748	+	0.242384i
$239$	317.949	−	183.568i	1.33033	−	0.768066i	0.344979	−	0.938610i	$-0.387886\pi$
$239$	317.949	−	183.568i	1.33033	−	0.768066i	0.985350	+	0.170545i	$0.0545527\pi$
$240$	−196.408	−	360.995i	−0.818367	−	1.50415i
$241$	53.3543	−	92.4123i	0.221387	−	0.383454i	−0.733842	−	0.679320i	$-0.762275\pi$
$241$	53.3543	−	92.4123i	0.221387	−	0.383454i	0.955229	+	0.295866i	$0.0956082\pi$
$242$	39.8738	+	47.1166i	0.164768	+	0.194697i
$243$	−205.932	−	129.001i	−0.847455	−	0.530868i
$244$	255.389	+	42.8239i	1.04668	+	0.175508i
$245$	−32.0648	+	55.5378i	−0.130877	+	0.226685i
$246$	226.423	+	8.58847i	0.920420	+	0.0349125i
$247$	101.312	+	175.477i	0.410168	+	0.710432i
$248$	89.6529	+	50.2662i	0.361504	+	0.202686i
$249$	−330.498	+	104.759i	−1.32730	+	0.420717i
$250$	392.700	−	70.9449i	1.57080	−	0.283780i
$251$	−255.233			−1.01686			−0.508432	−	0.861102i	$-0.669775\pi$
$251$	−255.233			−1.01686			−0.508432	+	0.861102i	$0.669775\pi$
$252$	−269.798	−	20.4969i	−1.07063	−	0.0813370i
$253$			250.400i			0.989722i
$254$	36.9809	−	6.68096i	0.145594	−	0.0263030i
$255$	−284.754	−	62.6741i	−1.11668	−	0.245781i
$256$	35.9619	−	253.462i	0.140476	−	0.990084i
$257$	−138.828	+	80.1521i	−0.540185	+	0.311876i	−0.745154	−	0.666893i	$-0.767624\pi$
$257$	−138.828	+	80.1521i	−0.540185	+	0.311876i	0.204969	+	0.978768i	$0.434291\pi$
$258$	68.4859	+	129.743i	0.265449	+	0.502879i
$259$	−38.3783	−	22.1577i	−0.148179	−	0.0855509i
$260$	372.350	+	62.4360i	1.43212	+	0.240139i
$261$	56.9031	+	26.3238i	0.218019	+	0.100858i
$262$	48.9097	+	57.7937i	0.186678	+	0.220587i
$263$	350.611	+	202.425i	1.33312	+	0.769678i	0.985777	−	0.168060i	$-0.0537501\pi$
$263$	350.611	+	202.425i	1.33312	+	0.769678i	0.347345	+	0.937738i	$0.387083\pi$
$264$	−151.552	+	170.151i	−0.574060	+	0.644512i
$265$	250.367	+	433.649i	0.944782	+	1.63641i
$266$	260.018	+	93.4042i	0.977510	+	0.351144i
$267$	266.831	−	292.086i	0.999367	−	1.09395i
$268$	83.6781	−	101.442i	0.312232	−	0.378514i
$269$	18.9169			0.0703230			0.0351615	−	0.999382i	$-0.488805\pi$
$269$	18.9169			0.0703230			0.0351615	+	0.999382i	$0.488805\pi$
$270$	461.703	−	24.2139i	1.71001	−	0.0896813i
$271$	−502.339			−1.85365			−0.926824	−	0.375495i	$-0.877473\pi$
$271$	−502.339			−1.85365			−0.926824	+	0.375495i	$0.877473\pi$
$272$	−119.067	−	137.153i	−0.437745	−	0.504238i
$273$	167.655	−	183.523i	0.614121	−	0.672246i
$274$	−488.347	−	175.425i	−1.78229	−	0.640237i
$275$	−229.304	−	397.166i	−0.833831	−	1.44424i
$276$	313.358	−	44.4208i	1.13536	−	0.160945i
$277$	164.430	+	94.9335i	0.593609	+	0.342720i	0.766523	−	0.642217i	$-0.221985\pi$
$277$	164.430	+	94.9335i	0.593609	+	0.342720i	−0.172914	+	0.984937i	$0.555318\pi$
$278$	142.267	−	120.398i	0.511753	−	0.433086i
$279$	−94.5169	+	66.6110i	−0.338770	+	0.238749i
$280$	442.556	−	262.997i	1.58056	−	0.939276i
$281$	53.6619	+	30.9817i	0.190968	+	0.110255i	0.592436	−	0.805618i	$-0.298166\pi$
$281$	53.6619	+	30.9817i	0.190968	+	0.110255i	−0.401468	+	0.915873i	$0.631500\pi$
$282$	−51.3700	−	97.3176i	−0.182163	−	0.345098i
$283$	−455.790	+	263.151i	−1.61057	+	0.929861i	−0.621327	+	0.783551i	$0.713406\pi$
$283$	−455.790	+	263.151i	−1.61057	+	0.929861i	−0.989239	+	0.146310i	$0.953260\pi$
$284$	118.384	+	316.949i	0.416844	+	1.11602i
$285$	−461.058	−	101.478i	−1.61775	−	0.356064i
$286$	−37.2150	−	205.995i	−0.130122	−	0.720263i
$287$			283.837i			0.988979i
$288$	239.818	+	159.472i	0.832701	+	0.553723i
$289$	160.141			0.554123
$290$	−117.388	+	21.2073i	−0.404787	+	0.0731287i
$291$	538.487	−	170.685i	1.85047	−	0.586548i
$292$	−352.638	+	131.714i	−1.20766	+	0.451074i
$293$	127.500	+	220.837i	0.435154	+	0.753709i	0.997308	−	0.0733236i	$-0.0233606\pi$
$293$	127.500	+	220.837i	0.435154	+	0.753709i	−0.562154	+	0.827032i	$0.690027\pi$
$294$	1.70344	−	44.9088i	0.00579400	−	0.152751i
$295$	−112.710	+	195.220i	−0.382069	+	0.661762i
$296$	24.0972	+	40.5494i	0.0814096	+	0.136991i
$297$	−99.1773	−	236.378i	−0.333930	−	0.795884i
$298$	−233.918	−	276.407i	−0.784959	−	0.927541i
$299$	−145.378	+	251.802i	−0.486213	+	0.842146i
$300$	−456.347	+	357.415i	−1.52116	+	1.19138i
$301$	−159.156	+	91.8886i	−0.528757	+	0.305278i
$302$	−34.0476	+	94.7814i	−0.112740	+	0.313846i
$303$	−162.070	+	51.3716i	−0.534883	+	0.169543i
$304$	−192.786	−	222.070i	−0.634164	−	0.730493i
$305$		−	554.280i		−	1.81731i
$306$	196.978	−	54.3121i	0.643719	−	0.177490i
$307$			365.110i			1.18928i	0.803990	+	0.594642i	$0.202706\pi$
$307$			365.110i			1.18928i	−0.803990	+	0.594642i	$0.797294\pi$
$308$	−220.185	−	181.628i	−0.714887	−	0.589703i
$309$	7.04805	−	32.0222i	0.0228092	−	0.103632i
$310$	74.3763	−	207.048i	0.239924	−	0.667897i
$311$	359.227	−	207.400i	1.15507	−	0.666881i	0.204953	−	0.978772i	$-0.434296\pi$
$311$	359.227	−	207.400i	1.15507	−	0.666881i	0.950118	+	0.311891i	$0.100962\pi$
$312$	−251.187	+	83.1155i	−0.805087	+	0.266396i
$313$	266.359	−	461.348i	0.850988	−	1.47396i	−0.0293289	−	0.999570i	$-0.509337\pi$
$313$	266.359	−	461.348i	0.850988	−	1.47396i	0.880317	−	0.474385i	$-0.157330\pi$
$314$	−149.097	+	126.178i	−0.474832	+	0.401841i
$315$	52.2322	+	576.794i	0.165816	+	1.83109i
$316$	−16.3018	+	97.2193i	−0.0515881	+	0.307656i
$317$	298.687	−	517.342i	0.942231	−	1.63199i	0.181029	−	0.983478i	$-0.442057\pi$
$317$	298.687	−	517.342i	0.942231	−	1.63199i	0.761202	−	0.648514i	$-0.224609\pi$
$318$	−297.027	−	186.847i	−0.934046	−	0.587569i
$319$	33.0695	+	57.2780i	0.103666	+	0.179555i
$320$	−547.782	+	13.8031i	−1.71182	+	0.0431346i
$321$	126.905	+	115.932i	0.395341	+	0.361159i
$322$	70.4828	+	390.142i	0.218891	+	1.21162i
$323$	−208.640			−0.645945
$324$	−278.216	+	166.047i	−0.858693	+	0.512491i
$325$		−	532.519i		−	1.63852i
$326$	97.9459	+	542.157i	0.300447	+	1.66306i
$327$	−101.025	+	110.587i	−0.308945	+	0.338186i
$328$	147.750	−	263.521i	0.450457	−	0.803418i
$329$	119.380	−	68.9239i	0.362856	−	0.209495i
$330$	412.831	+	259.694i	1.25100	+	0.786952i
$331$	−182.783	−	105.530i	−0.552215	−	0.318821i	0.197800	−	0.980242i	$-0.436620\pi$
$331$	−182.783	−	105.530i	−0.552215	−	0.318821i	−0.750015	+	0.661421i	$0.769954\pi$
$332$	−76.4467	+	455.906i	−0.230261	+	1.37321i
$333$	−52.8490	+	4.78580i	−0.158706	+	0.0143718i
$334$	−143.776	+	121.675i	−0.430468	+	0.364297i
$335$	−243.761	−	140.735i	−0.727644	−	0.420106i
$336$	−188.235	+	307.768i	−0.560223	+	0.915975i
$337$	155.181	+	268.782i	0.460479	+	0.797573i	0.998985	−	0.0450488i	$-0.0143443\pi$
$337$	155.181	+	268.782i	0.460479	+	0.797573i	−0.538506	+	0.842622i	$0.681011\pi$
$338$	−32.0942	+	89.3436i	−0.0949533	+	0.264330i
$339$	−150.974	−	33.2291i	−0.445350	−	0.0980211i
$340$	−247.381	+	299.896i	−0.727590	+	0.882046i
$341$	−121.979			−0.357709
$342$	318.935	−	87.9389i	0.932559	−	0.257131i
$343$	−311.988			−0.909585
$344$	195.596	−	2.46394i	0.568594	−	0.00716261i
$345$	−204.691	−	645.769i	−0.593307	−	1.87179i
$346$	−119.228	+	331.905i	−0.344588	+	0.959262i
$347$	−14.0423	−	24.3220i	−0.0404678	−	0.0700923i	0.845082	−	0.534637i	$-0.179551\pi$
$347$	−14.0423	−	24.3220i	−0.0404678	−	0.0700923i	−0.885550	+	0.464544i	$0.846218\pi$
$348$	65.8130	−	51.5453i	0.189118	−	0.148119i
$349$	429.084	+	247.732i	1.22947	+	0.709833i	0.966918	−	0.255086i	$-0.0821037\pi$
$349$	429.084	+	247.732i	1.22947	+	0.709833i	0.262549	+	0.964919i	$0.415437\pi$
$350$	−469.067	−	554.270i	−1.34019	−	1.58363i
$351$	37.5041	−	295.282i	0.106849	−	0.841258i
$352$	109.880	+	283.245i	0.312158	+	0.804673i
$353$	−96.6875	−	55.8225i	−0.273902	−	0.158137i	0.356757	−	0.934197i	$-0.383882\pi$
$353$	−96.6875	−	55.8225i	−0.273902	−	0.158137i	−0.630660	+	0.776060i	$0.717216\pi$
$354$	5.98772	−	157.858i	0.0169145	−	0.445927i
$355$	627.169	−	362.096i	1.76667	−	1.01999i
$356$	−184.568	−	494.146i	−0.518450	−	1.38805i
$357$	77.3386	+	243.992i	0.216635	+	0.683450i
$358$	42.1284	−	7.61090i	0.117677	−	0.0212595i
$359$		−	64.1895i		−	0.178801i	−0.995996	−	0.0894004i	$-0.971505\pi$
$359$		−	64.1895i		−	0.178801i	0.995996	−	0.0894004i	$-0.0284951\pi$
$360$	251.754	−	562.699i	0.699316	−	1.56305i
$361$	23.1821			0.0642163
$362$	−113.528	−	628.409i	−0.313613	−	1.73594i
$363$	−19.9018	+	90.4222i	−0.0548259	+	0.249097i
$364$	−115.968	−	310.481i	−0.318593	−	0.852970i
$365$	402.868	+	697.788i	1.10375	+	1.91175i
$366$	181.326	+	343.512i	0.495426	+	0.938557i
$367$	−315.787	+	546.960i	−0.860456	+	1.49035i	0.0110327	+	0.999939i	$0.496488\pi$
$367$	−315.787	+	546.960i	−0.860456	+	1.49035i	−0.871489	+	0.490415i	$0.836845\pi$
$368$	137.648	−	398.907i	0.374044	−	1.08399i
$369$	195.793	+	277.818i	0.530605	+	0.752895i
$370$	77.0692	−	65.2221i	0.208295	−	0.176276i
$371$	219.785	−	380.679i	0.592413	−	1.02609i
$372$	21.6390	+	152.648i	0.0581693	+	0.410345i
$373$	326.479	−	188.493i	0.875279	−	0.505342i	0.00617981	−	0.999981i	$-0.498033\pi$
$373$	326.479	−	188.493i	0.875279	−	0.505342i	0.869099	+	0.494639i	$0.164700\pi$
$374$	202.855	+	72.8700i	0.542393	+	0.194840i
$375$	441.938	+	403.726i	1.17850	+	1.07660i
$376$	−146.713	+	1.84815i	−0.390194	+	0.00491530i
$377$			76.7983i			0.203709i
$378$	−221.062	−	340.378i	−0.584820	−	0.900470i
$379$		−	385.660i		−	1.01757i	−0.860893	−	0.508786i	$-0.830095\pi$
$379$		−	385.660i		−	1.01757i	0.860893	−	0.508786i	$-0.169905\pi$
$380$	−400.544	+	485.573i	−1.05406	+	1.27782i
$381$	41.6178	+	38.0193i	0.109233	+	0.0997882i
$382$	−365.712	−	131.372i	−0.957361	−	0.343905i
$383$	−92.9952	+	53.6908i	−0.242807	+	0.140185i	−0.616466	−	0.787381i	$-0.711436\pi$
$383$	−92.9952	+	53.6908i	−0.242807	+	0.140185i	0.373659	+	0.927566i	$0.378103\pi$
$384$	334.969	−	187.754i	0.872315	−	0.488944i
$385$	−305.475	+	529.098i	−0.793441	+	1.37428i
$386$	52.9620	+	62.5822i	0.137207	+	0.162130i
$387$	−92.3954	+	199.727i	−0.238748	+	0.516091i
$388$	124.556	−	742.817i	0.321021	−	1.91448i
$389$	23.1238	−	40.0515i	0.0594441	−	0.102960i	−0.834772	−	0.550596i	$-0.814401\pi$
$389$	23.1238	−	40.0515i	0.0594441	−	0.102960i	0.894216	+	0.447636i	$0.147734\pi$
$390$	264.368	+	500.831i	0.677867	+	1.28418i
$391$	−149.695	−	259.279i	−0.382851	−	0.663117i
$392$	−52.2668	−	29.3047i	−0.133334	−	0.0747570i
$393$	−24.4118	+	110.913i	−0.0621166	+	0.282221i
$394$	28.0970	−	5.07599i	0.0713122	−	0.0128832i
$395$	210.998			0.534173
$396$	−340.805	−	25.8914i	−0.860620	−	0.0653824i
$397$		−	301.305i		−	0.758955i	−0.925201	−	0.379477i	$-0.876104\pi$
$397$		−	301.305i		−	0.758955i	0.925201	−	0.379477i	$-0.123896\pi$
$398$	588.225	−	106.268i	1.47795	−	0.267006i
$399$	125.222	+	395.057i	0.313840	+	0.990118i
$400$	146.972	+	758.769i	0.367429	+	1.89692i
$401$	−188.370	+	108.755i	−0.469751	+	0.271211i	−0.716135	−	0.697962i	$-0.754091\pi$
$401$	−188.370	+	108.755i	−0.469751	+	0.271211i	0.246385	+	0.969172i	$0.420757\pi$
$402$	197.109	+	7.47655i	0.490322	+	0.0185984i
$403$	−122.662	−	70.8188i	−0.304372	−	0.175729i
$404$	−37.4880	+	223.567i	−0.0927920	+	0.553384i
$405$	449.002	+	528.533i	1.10865	+	1.30502i
$406$	67.6475	+	79.9351i	0.166619	+	0.196884i
$407$	−48.4788	−	27.9893i	−0.119113	−	0.0687697i
$408$	55.2055	−	266.786i	0.135308	−	0.653888i
$409$	−328.133	−	568.344i	−0.802282	−	1.38959i	−0.918110	−	0.396325i	$-0.870285\pi$
$409$	−328.133	−	568.344i	−0.802282	−	1.38959i	0.115828	−	0.993269i	$-0.463048\pi$
$410$	−608.587	−	218.618i	−1.48436	−	0.533215i
$411$	−235.183	−	741.967i	−0.572222	−	1.80527i
$412$	−33.7249	−	27.8193i	−0.0818566	−	0.0675226i
$413$	197.886			0.479142
$414$	338.112	+	333.249i	0.816695	+	0.804950i
$415$	989.468			2.38426
$416$	−53.9521	+	348.625i	−0.129693	+	0.838041i
$417$	273.028	+	60.0930i	0.654742	+	0.144108i
$418$	328.451	+	117.987i	0.785767	+	0.282265i
$419$	193.367	+	334.922i	0.461497	+	0.799336i	0.999036	−	0.0439028i	$-0.0139792\pi$
$419$	193.367	+	334.922i	0.461497	+	0.799336i	−0.537539	+	0.843239i	$0.680646\pi$
$420$	716.321	+	288.419i	1.70553	+	0.686713i
$421$	−280.678	−	162.049i	−0.666693	−	0.384916i	0.128129	−	0.991757i	$-0.459103\pi$
$421$	−280.678	−	162.049i	−0.666693	−	0.384916i	−0.794823	+	0.606842i	$0.792436\pi$
$422$	356.826	−	301.974i	0.845558	−	0.715579i
$423$	69.3040	−	149.812i	0.163839	−	0.354165i
$424$	−402.215	+	239.024i	−0.948620	+	0.563736i
$425$	474.870	+	274.166i	1.11734	+	0.645097i
$426$	−270.229	+	429.578i	−0.634340	+	1.00840i
$427$	−421.387	+	243.288i	−0.986855	+	0.569761i
$428$	214.695	−	80.1906i	0.501624	−	0.187361i
$429$	211.779	−	231.824i	0.493658	−	0.540382i
$430$	−74.4367	−	412.028i	−0.173109	−	0.958204i
$431$		−	417.635i		−	0.968991i	−0.874794	−	0.484495i	$-0.839003\pi$
$431$		−	417.635i		−	0.968991i	0.874794	−	0.484495i	$-0.160997\pi$
$432$	28.0573	+	431.088i	0.0649475	+	0.997889i
$433$	−420.782			−0.971784			−0.485892	−	0.874019i	$-0.661505\pi$
$433$	−420.782			−0.971784			−0.485892	+	0.874019i	$0.661505\pi$
$434$	−190.052	+	34.3348i	−0.437909	+	0.0791124i
$435$	−132.107	−	120.684i	−0.303694	−	0.277435i
$436$	69.8795	+	187.089i	0.160274	+	0.429103i
$437$	−242.377	−	419.809i	−0.554638	−	0.960662i
$438$	−477.948	−	300.657i	−1.09121	−	0.686431i
$439$	93.9396	−	162.708i	0.213985	−	0.370634i	−0.738973	−	0.673735i	$-0.764689\pi$
$439$	93.9396	−	162.708i	0.213985	−	0.370634i	0.952958	+	0.303102i	$0.0980222\pi$
$440$	559.030	−	332.214i	1.27052	−	0.755032i
$441$	55.1025	−	38.8336i	0.124949	−	0.0880581i
$442$	161.684	+	191.052i	0.365800	+	0.432244i
$443$	112.177	−	194.296i	0.253220	−	0.438591i	−0.711190	−	0.703000i	$-0.751844\pi$
$443$	112.177	−	194.296i	0.253220	−	0.438591i	0.964411	+	0.264409i	$0.0851769\pi$
$444$	−26.4266	+	65.6333i	−0.0595193	+	0.147823i
$445$	−977.799	+	564.533i	−2.19730	+	1.26861i
$446$	−1.87081	+	5.20794i	−0.00419464	+	0.0116770i
$447$	116.753	−	530.458i	0.261193	−	1.18671i
$448$	250.929	+	410.388i	0.560110	+	0.916045i
$449$		−	207.466i		−	0.462063i	−0.972946	−	0.231032i	$-0.925790\pi$
$449$		−	207.466i		−	0.462063i	0.972946	−	0.231032i	$-0.0742101\pi$
$450$	−841.461	−	218.950i	−1.86991	−	0.486556i
$451$			358.539i			0.794986i
$452$	−131.159	+	159.001i	−0.290174	+	0.351773i
$453$	−144.006	+	45.6458i	−0.317893	+	0.100763i
$454$	33.2523	−	92.5675i	0.0732430	−	0.203893i
$455$	−614.370	+	354.707i	−1.35026	+	0.779575i
$456$	89.3856	−	431.965i	0.196021	−	0.947291i
$457$	29.9392	−	51.8562i	0.0655124	−	0.113471i	−0.831409	−	0.555661i	$-0.812465\pi$
$457$	29.9392	−	51.8562i	0.0655124	−	0.113471i	0.896921	+	0.442190i	$0.145798\pi$
$458$	401.062	−	339.411i	0.875682	−	0.741072i
$459$	244.006	+	185.469i	0.531604	+	0.404072i
$460$	−890.808	−	149.371i	−1.93654	−	0.324721i
$461$	90.0395	−	155.953i	0.195313	−	0.338293i	−0.751690	−	0.659517i	$-0.770761\pi$
$461$	90.0395	−	155.953i	0.195313	−	0.338293i	0.947003	+	0.321224i	$0.104094\pi$
$462$	16.2283	−	427.838i	0.0351262	−	0.926056i
$463$	−199.548	−	345.627i	−0.430989	−	0.746496i	0.565969	−	0.824426i	$-0.308502\pi$
$463$	−199.548	−	345.627i	−0.430989	−	0.746496i	−0.996959	+	0.0779307i	$0.975169\pi$
$464$	−21.1958	−	109.427i	−0.0456806	−	0.235835i
$465$	314.578	−	99.7125i	0.676511	−	0.214435i
$466$	113.963	+	630.815i	0.244555	+	1.35368i
$467$	−284.941			−0.610153			−0.305077	−	0.952328i	$-0.598682\pi$
$467$	−284.941			−0.610153			−0.305077	+	0.952328i	$0.598682\pi$
$468$	−327.681	−	223.902i	−0.700174	−	0.478423i
$469$			247.090i			0.526844i
$470$	55.8336	+	309.054i	0.118795	+	0.657562i
$471$	−286.135	−	62.9779i	−0.607505	−	0.133711i
$472$	−183.722	−	103.008i	−0.389242	−	0.218238i
$473$	−201.043	+	116.072i	−0.425038	+	0.245396i
$474$	−130.765	+	69.0256i	−0.275876	+	0.145624i
$475$	768.881	+	443.914i	1.61870	+	0.934555i
$476$	336.575	+	56.4372i	0.707090	+	0.118566i
$477$	−47.4710	−	524.217i	−0.0995200	−	1.09899i
$478$	560.497	−	474.338i	1.17259	−	0.992338i
$479$	−243.933	−	140.835i	−0.509255	−	0.294018i	0.223272	−	0.974756i	$-0.428326\pi$
$479$	−243.933	−	140.835i	−0.509255	−	0.294018i	−0.732527	+	0.680738i	$0.761659\pi$
$480$	−514.915	−	640.653i	−1.07274	−	1.33469i
$481$	−32.5002	−	56.2920i	−0.0675680	−	0.117031i
$482$	72.1503	−	200.851i	0.149689	−	0.416704i
$483$	−401.096	+	439.059i	−0.830428	+	0.909026i
$484$	95.2302	+	78.5543i	0.196757	+	0.162302i
$485$	−1612.16			−3.32404
$486$	−451.170	−	180.670i	−0.928333	−	0.371749i
$487$	490.070			1.00630			0.503152	−	0.864198i	$-0.332174\pi$
$487$	490.070			1.00630			0.503152	+	0.864198i	$0.332174\pi$
$488$	517.869	−	6.52362i	1.06121	−	0.0133681i
$489$	−557.380	+	610.135i	−1.13984	+	1.24772i
$490$	−43.3607	+	120.707i	−0.0884913	+	0.246341i
$491$	167.001	+	289.254i	0.340124	+	0.589113i	0.984456	−	0.175634i	$-0.0561975\pi$
$491$	167.001	+	289.254i	0.340124	+	0.589113i	−0.644331	+	0.764747i	$0.722864\pi$
$492$	448.687	−	63.6045i	0.911965	−	0.129278i
$493$	−68.4843	−	39.5394i	−0.138913	−	0.0802016i
$494$	261.789	+	309.340i	0.529936	+	0.626195i
$495$	65.9789	+	728.598i	0.133291	+	1.47191i
$496$	194.322	+	67.0536i	0.391779	+	0.135189i
$497$	−550.561	−	317.867i	−1.10777	−	0.639571i
$498$	−613.217	+	323.692i	−1.23136	+	0.649985i
$499$	−413.436	+	238.697i	−0.828528	+	0.478351i	−0.853348	−	0.521341i	$-0.825432\pi$
$499$	−413.436	+	238.697i	−0.828528	+	0.478351i	0.0248203	+	0.999692i	$0.492099\pi$
$500$	747.662	−	279.259i	1.49532	−	0.558518i
$501$	−275.924	−	60.7304i	−0.550746	−	0.121218i
$502$	−502.334	+	90.7515i	−1.00067	+	0.180780i
$503$			413.724i			0.822512i	0.911520	+	0.411256i	$0.134910\pi$
$503$			413.724i			0.822512i	−0.911520	+	0.411256i	$0.865090\pi$
$504$	−538.289	+	55.5896i	−1.06803	+	0.110297i
$505$	485.216			0.960823
$506$	89.0329	+	492.821i	0.175954	+	0.973955i
$507$	−135.744	+	43.0271i	−0.267739	+	0.0848660i
$508$	70.4082	−	26.2981i	0.138599	−	0.0517680i
$509$	75.5535	+	130.862i	0.148435	+	0.257097i	0.930649	−	0.365912i	$-0.119243\pi$
$509$	75.5535	+	130.862i	0.148435	+	0.257097i	−0.782214	+	0.623010i	$0.785910\pi$
$510$	−582.721	−	22.1032i	−1.14259	−	0.0433396i
$511$	353.659	−	612.555i	0.692091	−	1.19874i
$512$	−19.3435	−	511.634i	−0.0377802	−	0.999286i
$513$	395.081	+	300.301i	0.770138	+	0.585381i
$514$	−244.733	+	207.113i	−0.476134	+	0.402943i
$515$	−46.7884	+	81.0399i	−0.0908512	+	0.157359i
$516$	180.922	+	231.001i	0.350623	+	0.447676i
$517$	150.799	−	87.0637i	0.291680	−	0.168402i
$518$	−83.4122	−	29.9635i	−0.161027	−	0.0578447i
$519$	−504.278	+	159.842i	−0.971634	+	0.307981i
$520$	755.038	−	9.51126i	1.45200	−	0.0182909i
$521$			1031.73i			1.98029i	0.140063	+	0.990143i	$0.455269\pi$
$521$			1031.73i			1.98029i	−0.140063	+	0.990143i	$0.544731\pi$
$522$	121.353	+	31.5763i	0.232477	+	0.0604910i
$523$		−	700.814i		−	1.33999i	−0.742366	−	0.669994i	$-0.766296\pi$
$523$		−	700.814i		−	1.33999i	0.742366	−	0.669994i	$-0.233704\pi$
$524$	116.810	+	96.3557i	0.222921	+	0.183885i
$525$	234.121	−	1063.71i	0.445945	−	2.02611i
$526$	762.026	+	273.737i	1.44872	+	0.520412i
$527$	126.304	−	72.9218i	0.239667	−	0.138372i
$528$	−237.776	+	388.768i	−0.450333	+	0.736302i
$529$	83.3004	−	144.280i	0.157468	−	0.272742i
$530$	646.947	+	764.460i	1.22066	+	1.44238i
$531$	193.690	−	136.503i	0.364764	−	0.257068i
$532$	544.962	+	91.3798i	1.02437	+	0.171767i
$533$	−208.161	+	360.546i	−0.390547	+	0.676447i
$534$	421.306	−	669.741i	0.788962	−	1.25420i
$535$	−245.276	−	424.831i	−0.458461	−	0.794077i
$536$	128.621	−	229.404i	0.239965	−	0.427993i
$537$	47.4107	+	43.3113i	0.0882880	+	0.0806543i
$538$	37.2311	−	6.72615i	0.0692028	−	0.0125021i
$539$	71.1126			0.131934
$540$	900.086	−	211.821i	1.66683	−	0.392261i
$541$			431.063i			0.796790i	0.917214	+	0.398395i	$0.130433\pi$
$541$			431.063i			0.796790i	−0.917214	+	0.398395i	$0.869567\pi$
$542$	−988.673	+	178.613i	−1.82412	+	0.329545i
$543$	646.054	−	707.201i	1.18979	−	1.30240i
$544$	−283.107	−	227.600i	−0.520416	−	0.418383i
$545$	370.205	−	213.738i	0.679276	−	0.392180i
$546$	264.714	−	420.811i	0.484825	−	0.770717i
$547$	−625.543	−	361.158i	−1.14359	−	0.660252i	−0.196272	−	0.980549i	$-0.562884\pi$
$547$	−625.543	−	361.158i	−1.14359	−	0.660252i	−0.947317	+	0.320298i	$0.896217\pi$
$548$	−1023.51	−	171.623i	−1.86772	−	0.313180i
$549$	−244.630	+	528.806i	−0.445592	+	0.963216i
$550$	−592.519	−	700.145i	−1.07731	−	1.27299i
$551$	−110.886	−	64.0199i	−0.201244	−	0.116189i
$552$	600.938	−	198.845i	1.08866	−	0.360226i
$553$	−92.6127	−	160.410i	−0.167473	−	0.290072i
$554$	357.375	+	128.377i	0.645082	+	0.231728i
$555$	147.905	+	32.5537i	0.266495	+	0.0586552i
$556$	237.193	−	287.545i	0.426606	−	0.517167i
$557$	907.654			1.62954			0.814770	−	0.579784i	$-0.196863\pi$
$557$	907.654			1.62954			0.814770	+	0.579784i	$0.196863\pi$
$558$	−162.338	+	164.707i	−0.290928	+	0.295173i
$559$	−269.558			−0.482215
$560$	777.499	−	674.972i	1.38839	−	1.20531i
$561$	97.6930	+	308.207i	0.174141	+	0.549388i
$562$	116.630	+	41.8962i	0.207527	+	0.0745484i
$563$	521.945	+	904.036i	0.927079	+	1.60575i	0.788183	+	0.615441i	$0.211022\pi$
$563$	521.945	+	904.036i	0.927079	+	1.60575i	0.138896	+	0.990307i	$0.455645\pi$
$564$	−135.706	−	173.269i	−0.240613	−	0.307215i
$565$	382.075	+	220.591i	0.676239	+	0.390427i
$566$	−803.492	+	679.979i	−1.41960	+	1.20138i
$567$	204.735	−	573.337i	0.361084	−	1.01118i
$568$	345.691	+	581.707i	0.608611	+	1.02413i
$569$	−493.155	−	284.723i	−0.866705	−	0.500392i	−0.000453262	−	1.00000i	$-0.500144\pi$
$569$	−493.155	−	284.723i	−0.866705	−	0.500392i	−0.866252	+	0.499607i	$0.833478\pi$
$570$	−943.508	−	35.7882i	−1.65528	−	0.0627863i
$571$	850.255	−	490.895i	1.48906	−	0.859711i	0.489141	−	0.872205i	$-0.337310\pi$
$571$	850.255	−	490.895i	1.48906	−	0.859711i	0.999922	+	0.0124934i	$0.00397689\pi$
$572$	−146.489	−	392.195i	−0.256099	−	0.685656i
$573$	−176.123	−	555.643i	−0.307371	−	0.969708i
$574$	100.922	+	558.631i	0.175822	+	0.973224i
$575$			1273.99i			2.21564i
$576$	528.698	+	228.593i	0.917878	+	0.396863i
$577$	−461.080			−0.799099			−0.399550	−	0.916712i	$-0.630834\pi$
$577$	−461.080			−0.799099			−0.399550	+	0.916712i	$0.630834\pi$
$578$	315.181	−	56.9404i	0.545296	−	0.0985129i
$579$	−26.4344	+	120.102i	−0.0456553	+	0.207431i
$580$	−223.496	+	83.4779i	−0.385338	+	0.143927i
$581$	−434.303	−	752.235i	−0.747510	−	1.29472i
$582$	999.128	−	527.399i	1.71671	−	0.906184i
$583$	277.630	−	480.869i	0.476209	−	0.824818i
$584$	−647.208	+	384.616i	−1.10823	+	0.658589i
$585$	−356.663	+	770.984i	−0.609681	+	1.31792i
$586$	329.459	+	389.303i	0.562218	+	0.664340i
$587$	94.0800	−	162.951i	0.160273	−	0.277600i	−0.774694	−	0.632337i	$-0.782096\pi$
$587$	94.0800	−	162.951i	0.160273	−	0.277600i	0.934966	+	0.354736i	$0.115429\pi$
$588$	−12.6153	−	88.9926i	−0.0214546	−	0.151348i
$589$	204.504	−	118.071i	0.347206	−	0.200460i
$590$	−152.416	+	424.296i	−0.258333	+	0.719145i
$591$	31.6199	+	28.8859i	0.0535024	+	0.0488764i
$592$	61.8446	+	71.2387i	0.104467	+	0.120336i
$593$		−	127.877i		−	0.215644i	−0.994170	−	0.107822i	$-0.965612\pi$
$593$		−	127.877i		−	0.215644i	0.994170	−	0.107822i	$-0.0343877\pi$
$594$	−279.242	−	429.960i	−0.470104	−	0.723839i
$595$		−	730.480i		−	1.22770i
$596$	−558.663	−	460.835i	−0.937355	−	0.773214i
$597$	661.979	+	604.741i	1.10884	+	1.01297i
$598$	−196.592	+	547.272i	−0.328750	+	0.915170i
$599$	−21.9156	+	12.6530i	−0.0365869	+	0.0211235i	−0.518182	−	0.855270i	$-0.673391\pi$
$599$	−21.9156	+	12.6530i	−0.0365869	+	0.0211235i	0.481595	+	0.876394i	$0.340058\pi$
$600$	−771.072	+	865.703i	−1.28512	+	1.44284i
$601$	125.146	−	216.760i	0.208230	−	0.360665i	−0.742927	−	0.669372i	$-0.766563\pi$
$601$	125.146	−	216.760i	0.208230	−	0.360665i	0.951157	+	0.308708i	$0.0998964\pi$
$602$	−280.569	+	237.440i	−0.466061	+	0.394418i
$603$	170.445	+	241.850i	0.282661	+	0.401079i
$604$	−33.3097	+	198.649i	−0.0551484	+	0.328889i
$605$	132.118	−	228.835i	0.218377	−	0.378239i
$606$	−300.710	+	158.732i	−0.496221	+	0.261935i
$607$	564.183	+	977.193i	0.929461	+	1.60987i	0.784225	+	0.620477i	$0.213061\pi$
$607$	564.183	+	977.193i	0.929461	+	1.60987i	0.145236	+	0.989397i	$0.453606\pi$
$608$	−458.389	−	368.517i	−0.753930	−	0.606113i
$609$	−33.7642	+	153.405i	−0.0554420	+	0.251896i
$610$	−197.082	−	1090.90i	−0.323085	−	1.78836i
$611$	202.191			0.330918
$612$	368.369	−	176.932i	0.601910	−	0.289104i
$613$			4.96469i			0.00809901i	0.999992	+	0.00404951i	$0.00128900\pi$
$613$			4.96469i			0.00809901i	−0.999992	+	0.00404951i	$0.998711\pi$
$614$	129.820	+	718.588i	0.211433	+	1.17034i
$615$	−293.090	−	924.654i	−0.476569	−	1.50350i
$616$	−497.936	−	279.180i	−0.808337	−	0.453215i
$617$	196.879	−	113.668i	0.319090	−	0.184227i	−0.331897	−	0.943316i	$-0.607689\pi$
$617$	196.879	−	113.668i	0.319090	−	0.184227i	0.650987	+	0.759089i	$0.274355\pi$
$618$	2.48563	−	65.5303i	0.00402205	−	0.106036i
$619$	261.088	+	150.739i	0.421790	+	0.243521i	0.695843	−	0.718194i	$-0.255031\pi$
$619$	261.088	+	150.739i	0.421790	+	0.243521i	−0.274053	+	0.961715i	$0.588364\pi$
$620$	72.7643	−	433.945i	0.117362	−	0.699912i
$621$	−89.7245	+	706.429i	−0.144484	+	1.13757i
$622$	633.266	−	535.920i	1.01811	−	0.861608i
$623$	858.363	+	495.576i	1.37779	+	0.795467i
$624$	−464.819	+	252.896i	−0.744902	+	0.405282i
$625$	−250.355	−	433.628i	−0.400568	−	0.693805i
$626$	360.194	−	1002.70i	0.575390	−	1.60177i
$627$	158.179	+	499.030i	0.252279	+	0.795901i
$628$	−248.580	+	301.349i	−0.395828	+	0.479856i
$629$	66.9306			0.106408
$630$	307.887	+	1116.64i	0.488710	+	1.77244i
$631$	−894.608			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$631$	−894.608			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$632$	2.48335	+	197.138i	0.00392936	+	0.311927i
$633$	684.790	+	150.721i	1.08182	+	0.238107i
$634$	403.911	−	1124.40i	0.637083	−	1.77351i
$635$	−80.4373	−	139.321i	−0.126673	−	0.219404i
$636$	−651.026	−	262.129i	−1.02363	−	0.412152i
$637$	71.5107	+	41.2867i	0.112262	+	0.0648143i
$638$	85.4513	+	100.973i	0.133936	+	0.158265i
$639$	−758.154	+	68.6554i	−1.18647	+	0.107442i
$640$	−1073.20	+	221.937i	−1.67688	+	0.346777i
$641$	112.447	+	64.9216i	0.175425	+	0.101282i	0.585141	−	0.810931i	$-0.301039\pi$
$641$	112.447	+	64.9216i	0.175425	+	0.101282i	−0.409716	+	0.912213i	$0.634372\pi$
$642$	290.987	+	183.048i	0.453251	+	0.285121i
$643$	166.070	−	95.8808i	0.258274	−	0.149115i	−0.365273	−	0.930901i	$-0.619024\pi$
$643$	166.070	−	95.8808i	0.258274	−	0.149115i	0.623547	+	0.781786i	$0.285691\pi$
$644$	277.440	+	742.793i	0.430808	+	1.15340i
$645$	423.597	−	463.689i	0.656739	−	0.718898i
$646$	−410.633	+	74.1848i	−0.635655	+	0.114837i
$647$		−	940.799i		−	1.45409i	−0.686588	−	0.727047i	$-0.740892\pi$
$647$		−	940.799i		−	1.45409i	0.686588	−	0.727047i	$-0.259108\pi$
$648$	−488.529	+	425.727i	−0.753902	+	0.656986i
$649$	249.966			0.385156
$650$	−189.344	−	1048.07i	−0.291299	−	1.61242i
$651$	−213.882	−	195.389i	−0.328544	−	0.300136i
$652$	385.542	+	1032.22i	0.591323	+	1.58315i
$653$	−353.929	−	613.023i	−0.542004	−	0.938779i	−0.998789	−	0.0492016i	$-0.984332\pi$
$653$	−353.929	−	613.023i	−0.542004	−	0.938779i	0.456785	−	0.889577i	$-0.349001\pi$
$654$	−159.511	+	253.571i	−0.243900	+	0.387724i
$655$	162.057	−	280.692i	0.247416	−	0.428537i
$656$	197.094	−	571.181i	0.300448	−	0.870703i
$657$	−76.3861	−	843.523i	−0.116265	−	1.28390i
$658$	210.449	−	178.099i	0.319832	−	0.270667i
$659$	−284.270	+	492.370i	−0.431365	+	0.747147i	−0.996991	−	0.0775154i	$-0.975301\pi$
$659$	−284.270	+	492.370i	−0.431365	+	0.747147i	0.565626	+	0.824662i	$0.308635\pi$
$660$	904.846	+	364.327i	1.37098	+	0.552011i
$661$	394.236	−	227.612i	0.596424	−	0.344346i	−0.171209	−	0.985235i	$-0.554767\pi$
$661$	394.236	−	227.612i	0.596424	−	0.344346i	0.767634	+	0.640889i	$0.221434\pi$
$662$	−397.265	−	142.707i	−0.600098	−	0.215569i
$663$	−80.6995	+	366.651i	−0.121719	+	0.553018i
$664$	11.6456	+	924.468i	0.0175385	+	1.39227i
$665$		−	1182.75i		−	1.77857i
$666$	−102.313	+	28.2103i	−0.153623	+	0.0423578i
$667$		−	183.731i		−	0.275459i
$668$	−239.709	+	290.595i	−0.358845	+	0.435023i
$669$	−7.91266	+	2.50809i	−0.0118276	+	0.00374902i
$670$	−529.796	−	190.315i	−0.790740	−	0.284052i
$671$	−532.290	+	307.318i	−0.793279	+	0.458000i
$672$	−261.042	+	672.659i	−0.388455	+	1.00098i
$673$	−301.556	+	522.311i	−0.448078	+	0.776093i	−0.998261	−	0.0589506i	$-0.981225\pi$
$673$	−301.556	+	522.311i	−0.448078	+	0.776093i	0.550183	+	0.835044i	$0.314558\pi$
$674$	400.988	+	473.824i	0.594937	+	0.703003i
$675$	−504.599	−	1202.65i	−0.747554	−	1.78171i
$676$	−31.3986	+	187.252i	−0.0464477	+	0.277000i
$677$	−150.521	+	260.711i	−0.222336	+	0.385097i	−0.955517	−	0.294937i	$-0.904701\pi$
$677$	−150.521	+	260.711i	−0.222336	+	0.385097i	0.733181	+	0.680033i	$0.238035\pi$
$678$	−308.953	−	11.7189i	−0.455682	−	0.0172845i
$679$	707.619	+	1225.63i	1.04215	+	1.80506i
$680$	−380.248	+	678.196i	−0.559188	+	0.997347i
$681$	140.642	−	44.5796i	0.206523	−	0.0654620i
$682$	−240.071	+	43.3712i	−0.352011	+	0.0635941i
$683$	244.466			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$683$	244.466			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$684$	596.442	−	286.478i	0.871991	−	0.418827i
$685$			2221.36i			3.24286i
$686$	−614.035	+	110.931i	−0.895095	+	0.161707i
$687$	769.685	+	169.407i	1.12036	+	0.246589i
$688$	384.085	−	74.3962i	0.558263	−	0.108134i
$689$	558.368	−	322.374i	0.810404	−	0.467887i
$690$	−632.472	−	1198.18i	−0.916626	−	1.73650i
$691$	−37.7206	−	21.7780i	−0.0545884	−	0.0315166i	0.472457	−	0.881353i	$-0.343367\pi$
$691$	−37.7206	−	21.7780i	−0.0545884	−	0.0315166i	−0.527046	+	0.849837i	$0.676700\pi$
$692$	−116.643	+	695.628i	−0.168560	+	1.00524i
$693$	524.951	−	369.960i	0.757505	−	0.533853i
$694$	−36.2853	−	42.8762i	−0.0522843	−	0.0617813i
$695$	−690.961	−	398.927i	−0.994189	−	0.573995i
$696$	111.202	−	124.849i	0.159772	−	0.179381i
$697$	−214.343	−	371.253i	−0.307522	−	0.532644i
$698$	932.582	+	335.004i	1.33608	+	0.479949i
$699$	−648.528	+	709.909i	−0.927794	+	1.01561i
$700$	−1120.27	−	924.097i	−1.60038	−	1.32014i
$701$	505.146			0.720607			0.360304	−	0.932835i	$-0.382673\pi$
$701$	505.146			0.720607			0.360304	+	0.932835i	$0.382673\pi$
$702$	−31.1780	−	594.491i	−0.0444131	−	0.846853i
$703$	108.370			0.154154
$704$	316.970	+	518.396i	0.450242	+	0.736358i
$705$	−317.732	+	347.805i	−0.450684	+	0.493340i
$706$	−210.143	−	75.4880i	−0.297653	−	0.106924i
$707$	−212.974	−	368.881i	−0.301236	−	0.521756i
$708$	−44.3439	−	312.816i	−0.0626326	−	0.441831i
$709$	−940.019	−	542.720i	−1.32584	−	0.765473i	−0.341185	−	0.939996i	$-0.610828\pi$
$709$	−940.019	−	542.720i	−1.32584	−	0.765473i	−0.984653	+	0.174524i	$0.944161\pi$
$710$	1105.61	−	935.654i	1.55719	−	1.31782i
$711$	−201.301	−	93.1234i	−0.283124	−	0.130975i
$712$	−538.956	−	906.922i	−0.756961	−	1.27377i
$713$	293.455	+	169.426i	0.411578	+	0.237625i
$714$	238.968	+	452.711i	0.334689	+	0.634049i
$715$	−776.063	+	448.060i	−1.08540	+	0.626658i
$716$	80.2085	−	29.9586i	0.112023	−	0.0418417i
$717$	1075.66	+	236.751i	1.50022	+	0.330197i
$718$	−22.8234	−	126.334i	−0.0317875	−	0.175952i
$719$		−	508.844i		−	0.707710i	−0.935300	−	0.353855i	$-0.884871\pi$
$719$		−	508.844i		−	0.707710i	0.935300	−	0.353855i	$-0.115129\pi$
$720$	295.411	−	1196.99i	0.410293	−	1.66248i
$721$	82.1465			0.113934
$722$	45.6256	−	8.24270i	0.0631934	−	0.0114165i
$723$	305.162	−	96.7281i	0.422078	−	0.133787i
$724$	−446.878	−	1196.43i	−0.617235	−	1.65253i
$725$	168.252	+	291.421i	0.232072	+	0.401961i
$726$	−7.01875	+	185.040i	−0.00966770	+	0.254876i
$727$	−197.956	+	342.870i	−0.272292	+	0.471623i	−0.969448	−	0.245296i	$-0.921115\pi$
$727$	−197.956	+	342.870i	−0.272292	+	0.471623i	0.697156	+	0.716919i	$0.254448\pi$
$728$	−338.636	−	569.837i	−0.465160	−	0.782743i
$729$	−195.100	−	702.408i	−0.267627	−	0.963523i
$730$	1041.01	+	1230.10i	1.42604	+	1.68507i
$731$	138.782	−	240.377i	0.189852	−	0.328833i
$732$	479.015	+	611.607i	0.654393	+	0.835528i
$733$	−210.592	+	121.586i	−0.287302	+	0.165874i	−0.636724	−	0.771091i	$-0.719711\pi$
$733$	−210.592	+	121.586i	−0.287302	+	0.165874i	0.349422	+	0.936965i	$0.386378\pi$
$734$	−427.035	+	1188.78i	−0.581792	+	1.61959i
$735$	−183.396	+	58.1315i	−0.249518	+	0.0790905i
$736$	129.075	−	834.047i	0.175373	−	1.13322i
$737$			312.120i			0.423501i
$738$	484.130	+	477.168i	0.656003	+	0.646570i
$739$			315.637i			0.427113i	0.976931	+	0.213557i	$0.0685048\pi$
$739$			315.637i			0.427113i	−0.976931	+	0.213557i	$0.931495\pi$
$740$	128.492	−	155.769i	0.173638	−	0.210499i
$741$	−130.664	+	593.660i	−0.176335	+	0.801161i
$742$	297.213	−	827.378i	0.400556	−	1.11506i
$743$	−855.729	+	494.055i	−1.15172	+	0.664947i	−0.949306	−	0.314353i	$-0.898212\pi$
$743$	−855.729	+	494.055i	−1.15172	+	0.664947i	−0.202415	+	0.979300i	$0.564879\pi$
$744$	96.8646	+	292.739i	0.130194	+	0.393466i
$745$	−775.064	+	1342.45i	−1.04035	+	1.80195i
$746$	575.535	−	487.064i	0.771495	−	0.652901i
$747$	−943.992	−	436.698i	−1.26371	−	0.584603i
$748$	425.157	+	71.2906i	0.568391	+	0.0953083i
$749$	−215.316	+	372.939i	−0.287472	+	0.497916i
$750$	1013.35	+	637.453i	1.35113	+	0.849937i
$751$	374.852	+	649.262i	0.499137	+	0.864530i	1.00000		0.000996439i	$-0.000317176\pi$
$751$	374.852	+	649.262i	0.499137	+	0.864530i	−0.500863	+	0.865527i	$0.666984\pi$
$752$	−288.095	+	55.8032i	−0.383105	+	0.0742064i
$753$	−565.319	−	516.439i	−0.750756	−	0.685842i
$754$	27.3066	+	151.150i	0.0362157	+	0.200464i
$755$	431.135			0.571040
$756$	−556.106	−	591.310i	−0.735591	−	0.782156i
$757$		−	731.923i		−	0.966873i	−0.875379	−	0.483436i	$-0.839388\pi$
$757$		−	731.923i		−	0.966873i	0.875379	−	0.483436i	$-0.160612\pi$
$758$	−137.126	−	759.032i	−0.180906	−	1.00136i
$759$	−506.659	+	554.613i	−0.667535	+	0.730716i
$760$	−615.675	+	1098.09i	−0.810099	+	1.44486i
$761$	777.865	−	449.101i	1.02216	−	0.590146i	0.107433	−	0.994212i	$-0.465737\pi$
$761$	777.865	−	449.101i	1.02216	−	0.590146i	0.914729	+	0.404067i	$0.132404\pi$
$762$	95.4279	+	60.0296i	0.125233	+	0.0787790i
$763$	−324.986	−	187.630i	−0.425931	−	0.245912i
$764$	−766.483	−	128.525i	−1.00325	−	0.168226i
$765$	−503.892	−	714.991i	−0.658682	−	0.934628i
$766$	−163.937	+	138.737i	−0.214017	+	0.181118i
$767$	251.366	+	145.126i	0.327726	+	0.189213i
$768$	592.507	−	488.630i	0.771494	−	0.636237i
$769$	275.386	+	476.983i	0.358109	+	0.620264i	0.987645	−	0.156708i	$-0.0500882\pi$
$769$	275.386	+	476.983i	0.358109	+	0.620264i	−0.629536	+	0.776972i	$0.716755\pi$
$770$	−413.089	+	1149.95i	−0.536480	+	1.49345i
$771$	−469.671	−	103.374i	−0.609171	−	0.134078i
$772$	126.489	+	104.339i	0.163845	+	0.135154i
$773$	−328.803			−0.425360			−0.212680	−	0.977122i	$-0.568219\pi$
$773$	−328.803			−0.425360			−0.212680	+	0.977122i	$0.568219\pi$
$774$	−110.831	+	425.943i	−0.143193	+	0.550315i
$775$	−620.609			−0.800786
$776$	−18.9744	−	1506.26i	−0.0244515	−	1.94105i
$777$	−40.1706	−	126.732i	−0.0516996	−	0.163104i
$778$	31.2700	−	87.0490i	0.0401927	−	0.111888i
$779$	−347.051	−	601.110i	−0.445509	−	0.771644i
$780$	698.391	+	891.705i	0.895373	+	1.14321i
$781$	−695.461	−	401.525i	−0.890475	−	0.514116i
$782$	−386.810	−	457.071i	−0.494642	−	0.584490i
$783$	72.7717	+	173.443i	0.0929396	+	0.221511i
$784$	−113.288	−	39.0916i	−0.144500	−	0.0498618i
$785$	724.132	+	418.078i	0.922461	+	0.532583i
$786$	−8.60928	+	226.972i	−0.0109533	+	0.288769i
$787$	−347.183	+	200.446i	−0.441147	+	0.254696i	−0.704084	−	0.710117i	$-0.748642\pi$
$787$	−347.183	+	200.446i	−0.441147	+	0.254696i	0.262937	+	0.964813i	$0.415309\pi$
$788$	53.4940	−	19.9805i	0.0678858	−	0.0253560i
$789$	366.985	+	1157.78i	0.465127	+	1.46740i
$790$	415.274	−	75.0233i	0.525664	−	0.0949662i
$791$		−	387.293i		−	0.489624i
$792$	−679.959	+	70.2199i	−0.858534	+	0.0886615i
$793$	−713.694			−0.899992
$794$	−107.133	−	593.011i	−0.134928	−	0.746865i
$795$	−322.904	+	1467.09i	−0.406169	+	1.84539i
$796$	1119.92	−	418.302i	1.40694	−	0.525505i
$797$	129.797	+	224.815i	0.162857	+	0.282077i	0.935892	−	0.352286i	$-0.114596\pi$
$797$	129.797	+	224.815i	0.162857	+	0.282077i	−0.773035	+	0.634363i	$0.781262\pi$
$798$	386.922	+	733.003i	0.484865	+	0.918550i
$799$	−104.097	+	180.302i	−0.130285	+	0.225660i
$800$	559.051	+	1441.11i	0.698814	+	1.80138i
$801$	1182.01	−	107.039i	1.47567	−	0.133631i
$802$	−332.069	+	281.023i	−0.414051	+	0.350403i
$803$	446.736	−	773.770i	0.556334	−	0.963599i
$804$	390.597	−	55.3699i	0.485817	−	0.0688681i
$805$	1469.81	−	848.598i	1.82586	−	1.05416i
$806$	−266.596	−	95.7673i	−0.330764	−	0.118818i
$807$	41.8993	+	38.2765i	0.0519198	+	0.0474306i
$808$	5.71077	+	453.341i	0.00706778	+	0.561066i
$809$		−	934.520i		−	1.15515i	−0.816336	−	0.577577i	$-0.803998\pi$
$809$		−	934.520i		−	1.15515i	0.816336	−	0.577577i	$-0.196002\pi$
$810$	1071.63	+	880.579i	1.32300	+	1.08713i
$811$			235.144i			0.289943i	0.989436	+	0.144972i	$0.0463091\pi$
$811$			235.144i			0.289943i	−0.989436	+	0.144972i	$0.953691\pi$
$812$	161.562	+	133.270i	0.198968	+	0.164126i
$813$	−1112.64	−	1016.43i	−1.36856	−	1.25023i
$814$	−105.365	−	37.8495i	−0.129441	−	0.0464982i
$815$	2042.51	−	1179.25i	2.50615	−	1.44693i
$816$	13.7928	−	544.702i	0.0169030	−	0.667526i
$817$	224.707	−	389.204i	0.275039	−	0.476382i
$818$	−847.895	−	1001.91i	−1.03655	−	1.22483i
$819$	742.683	−	67.2544i	0.906817	−	0.0821177i
$820$	−1275.52	−	213.880i	−1.55551	−	0.260829i
$821$	55.7034	−	96.4812i	0.0678483	−	0.117517i	−0.830106	−	0.557606i	$-0.811720\pi$
$821$	55.7034	−	96.4812i	0.0678483	−	0.117517i	0.897954	+	0.440089i	$0.145053\pi$
$822$	−726.690	−	1376.67i	−0.884051	−	1.67478i
$823$	−244.582	−	423.628i	−0.297183	−	0.514736i	0.678307	−	0.734778i	$-0.262714\pi$
$823$	−244.582	−	423.628i	−0.297183	−	0.514736i	−0.975490	+	0.220042i	$0.929380\pi$
$824$	−76.2669	−	42.7610i	−0.0925569	−	0.0518944i
$825$	295.738	−	1343.66i	0.358470	−	1.62868i
$826$	389.467	−	70.3609i	0.471510	−	0.0851827i
$827$	−595.430			−0.719988			−0.359994	−	0.932955i	$-0.617221\pi$
$827$	−595.430			−0.719988			−0.359994	+	0.932955i	$0.617221\pi$
$828$	783.942	+	535.662i	0.946790	+	0.646934i
$829$		−	952.457i		−	1.14892i	−0.818532	−	0.574461i	$-0.805212\pi$
$829$		−	952.457i		−	1.14892i	0.818532	−	0.574461i	$-0.194788\pi$
$830$	1947.41	−	351.818i	2.34628	−	0.423878i
$831$	172.109	+	542.977i	0.207110	+	0.653402i
$832$	17.7729	+	705.326i	0.0213617	+	0.847748i
$833$	−73.6343	+	42.5128i	−0.0883965	+	0.0510357i
$834$	558.723	+	21.1929i	0.669932	+	0.0254112i
$835$	698.290	+	403.158i	0.836276	+	0.482824i
$836$	688.389	+	115.430i	0.823431	+	0.138074i
$837$	−344.128	−	43.7081i	−0.411144	−	0.0522200i
$838$	499.660	+	590.419i	0.596253	+	0.704557i
$839$	719.566	+	415.442i	0.857647	+	0.495163i	0.863224	−	0.504821i	$-0.168442\pi$
$839$	719.566	+	415.442i	0.857647	+	0.495163i	−0.00557635	+	0.999984i	$0.501775\pi$
$840$	1512.37	+	312.952i	1.80044	+	0.372562i
$841$	396.235	+	686.299i	0.471148	+	0.816052i
$842$	−610.032	−	219.137i	−0.724504	−	0.260258i
$843$	56.1680	+	177.202i	0.0666287	+	0.210204i
$844$	594.912	−	721.202i	0.704872	−	0.854505i
$845$	406.400			0.480946
$846$	83.1325	−	319.492i	0.0982654	−	0.377650i
$847$	−231.960			−0.273861
$848$	−706.627	+	613.446i	−0.833287	+	0.723403i
$849$	−1542.00	−	339.391i	−1.81625	−	0.399754i
$850$	1032.09	+	370.751i	1.21423	+	0.436178i
$851$	77.7532	+	134.672i	0.0913668	+	0.158252i
$852$	−379.106	+	941.553i	−0.444961	+	1.10511i
$853$	463.386	+	267.536i	0.543243	+	0.313641i	0.746392	−	0.665506i	$-0.231784\pi$
$853$	463.386	+	267.536i	0.543243	+	0.313641i	−0.203149	+	0.979148i	$0.565118\pi$
$854$	−742.845	+	628.655i	−0.869841	+	0.736129i
$855$	−815.872	−	1157.67i	−0.954236	−	1.35400i
$856$	394.037	−	234.164i	0.460323	−	0.273556i
$857$	91.7985	+	52.9999i	0.107116	+	0.0618435i	0.552601	−	0.833446i	$-0.313635\pi$
$857$	91.7985	+	52.9999i	0.107116	+	0.0618435i	−0.445485	+	0.895289i	$0.646969\pi$
$858$	334.383	−	531.563i	0.389724	−	0.619537i
$859$	340.158	−	196.391i	0.395993	−	0.228627i	−0.288760	−	0.957401i	$-0.593243\pi$
$859$	340.158	−	196.391i	0.395993	−	0.228627i	0.684754	+	0.728774i	$0.259910\pi$
$860$	−293.004	−	784.461i	−0.340702	−	0.912164i
$861$	−574.316	+	628.674i	−0.667034	+	0.730167i
$862$	−148.496	−	821.964i	−0.172269	−	0.953555i
$863$			989.382i			1.14644i	0.819400	+	0.573222i	$0.194307\pi$
$863$			989.382i			1.14644i	−0.819400	+	0.573222i	$0.805693\pi$
$864$	208.500	+	838.465i	0.241319	+	0.970446i
$865$	1509.74			1.74537
$866$	−828.159	+	149.615i	−0.956303	+	0.172765i
$867$	354.700	+	324.031i	0.409111	+	0.373738i
$868$	−361.842	+	135.151i	−0.416868	+	0.155704i
$869$	−116.987	−	202.627i	−0.134623	−	0.233173i
$870$	−302.916	−	190.551i	−0.348179	−	0.219025i
$871$	−181.212	+	313.868i	−0.208050	+	0.360353i
$872$	204.055	+	343.370i	0.234008	+	0.393773i
$873$	1538.07	+	711.522i	1.76182	+	0.815031i
$874$	−626.301	−	740.063i	−0.716591	−	0.846754i
$875$	−749.827	+	1298.74i	−0.856945	+	1.48427i
$876$	−1047.57	−	421.794i	−1.19586	−	0.481500i
$877$	−501.720	+	289.668i	−0.572087	+	0.330294i	−0.757982	−	0.652275i	$-0.773815\pi$
$877$	−501.720	+	289.668i	−0.572087	+	0.330294i	0.185896	+	0.982569i	$0.440481\pi$
$878$	127.033	−	353.634i	0.144685	−	0.402772i
$879$	−164.440	+	747.118i	−0.187076	+	0.849964i
$880$	982.125	−	852.614i	1.11605	−	0.968880i
$881$			1186.52i			1.34679i	0.739284	+	0.673394i	$0.235164\pi$
$881$			1186.52i			1.34679i	−0.739284	+	0.673394i	$0.764836\pi$
$882$	94.6416	−	96.0225i	0.107303	−	0.108869i
$883$		−	883.300i		−	1.00034i	−0.865927	−	0.500170i	$-0.833271\pi$
$883$		−	883.300i		−	1.00034i	0.865927	−	0.500170i	$-0.166729\pi$
$884$	386.147	+	318.528i	0.436818	+	0.360326i
$885$	−644.652	+	204.337i	−0.728420	+	0.230889i
$886$	151.695	−	422.287i	0.171213	−	0.476622i
$887$	−659.656	+	380.853i	−0.743694	+	0.429372i	−0.823411	−	0.567446i	$-0.807932\pi$
$887$	−659.656	+	380.853i	−0.743694	+	0.429372i	0.0797171	+	0.996818i	$0.474598\pi$
$888$	−28.6744	+	138.572i	−0.0322910	+	0.156049i
$889$	−70.6120	+	122.304i	−0.0794286	+	0.137574i
$890$	−1723.72	+	1458.75i	−1.93676	+	1.63904i
$891$	258.618	−	724.231i	0.290256	−	0.812830i
$892$	−1.83026	+	10.9151i	−0.00205186	+	0.0122367i
$893$	−168.548	+	291.934i	−0.188744	+	0.326914i
$894$	41.1752	−	1085.53i	0.0460572	−	1.21424i
$895$	−91.6336	−	158.714i	−0.102384	−	0.177334i
$896$	639.783	+	718.480i	0.714043	+	0.801875i
$897$	−831.495	+	263.561i	−0.926973	+	0.293825i
$898$	−73.7674	−	408.323i	−0.0821464	−	0.454703i
$899$	89.5023			0.0995577
$900$	−1733.96	−	131.732i	−1.92663	−	0.146368i
$901$			663.894i			0.736841i
$902$	127.483	+	705.654i	0.141334	+	0.782322i
$903$	−538.444	−	118.511i	−0.596283	−	0.131241i
$904$	−201.603	+	359.572i	−0.223012	+	0.397757i
$905$	−2367.46	+	1366.85i	−2.61597	+	1.51033i
$906$	−267.193	+	141.041i	−0.294915	+	0.155674i
$907$	−335.644	−	193.784i	−0.370060	−	0.213654i	0.303425	−	0.952855i	$-0.401870\pi$
$907$	−335.644	−	193.784i	−0.370060	−	0.213654i	−0.673485	+	0.739201i	$0.735203\pi$
$908$	32.5316	−	194.009i	0.0358278	−	0.213666i
$909$	−462.915	−	214.148i	−0.509258	−	0.235587i
$910$	−1083.05	+	916.560i	−1.19016	+	1.00721i
$911$	−748.017	−	431.868i	−0.821094	−	0.474059i	0.0296996	−	0.999559i	$-0.490545\pi$
$911$	−748.017	−	431.868i	−0.821094	−	0.474059i	−0.850794	+	0.525500i	$0.823878\pi$
$912$	22.3326	−	881.949i	0.0244875	−	0.967049i
$913$	−548.605	−	950.212i	−0.600882	−	1.04076i
$914$	40.4863	−	112.705i	0.0442958	−	0.123310i
$915$	1121.53	−	1227.68i	1.22572	−	1.34173i
$916$	668.664	−	810.611i	0.729983	−	0.884947i
$917$	−284.525			−0.310278
$918$	546.185	+	278.269i	0.594972	+	0.303126i
$919$	−7.98109			−0.00868453			−0.00434227	−	0.999991i	$-0.501382\pi$
$919$	−7.98109			−0.00868453			−0.00434227	+	0.999991i	$0.501382\pi$
$920$	−1806.35	+	22.7546i	−1.96342	+	0.0247333i
$921$	−738.765	+	808.688i	−0.802134	+	0.878054i
$922$	121.759	−	338.952i	0.132060	−	0.367627i
$923$	−466.237	−	807.546i	−0.505132	−	0.874914i
$924$	−120.184	−	847.815i	−0.130069	−	0.917548i
$925$	−246.653	−	142.405i	−0.266652	−	0.153951i
$926$	−515.631	−	609.291i	−0.556837	−	0.657982i
$927$	80.4047	−	56.6654i	0.0867365	−	0.0611277i
$928$	−80.6246	−	207.832i	−0.0868799	−	0.223957i
$929$	−402.056	−	232.127i	−0.432783	−	0.249867i	0.267748	−	0.963489i	$-0.413720\pi$
$929$	−402.056	−	232.127i	−0.432783	−	0.249867i	−0.700532	+	0.713621i	$0.747054\pi$
$930$	583.679	−	308.100i	0.627612	−	0.331291i
$931$	−119.224	+	68.8342i	−0.128060	+	0.0739357i
$932$	448.590	+	1201.01i	0.481319	+	1.28864i
$933$	1215.31	+	267.488i	1.30258	+	0.286697i
$934$	−560.805	+	101.315i	−0.600433	+	0.108474i
$935$		−	922.732i		−	0.986879i
$936$	−724.534	−	324.159i	−0.774075	−	0.346324i
$937$	312.292			0.333289			0.166645	−	0.986017i	$-0.446707\pi$
$937$	312.292			0.333289			0.166645	+	0.986017i	$0.446707\pi$
$938$	87.8560	+	486.307i	0.0936631	+	0.518451i
$939$	1523.46	−	482.893i	1.62242	−	0.514264i
$940$	219.777	+	588.409i	0.233805	+	0.625967i
$941$	466.897	+	808.689i	0.496171	+	0.859393i	0.999990	−	0.00441583i	$-0.00140561\pi$
$941$	466.897	+	808.689i	0.496171	+	0.859393i	−0.503819	+	0.863809i	$0.668072\pi$
$942$	−585.546	−	22.2103i	−0.621599	−	0.0235779i
$943$	498.003	−	862.567i	0.528105	−	0.914705i
$944$	−398.217	−	137.410i	−0.421840	−	0.145562i
$945$	−1051.40	+	1383.24i	−1.11259	+	1.46374i
$946$	−354.410	+	299.930i	−0.374641	+	0.317051i
$947$	−697.096	+	1207.40i	−0.736109	+	1.27498i	0.218126	+	0.975921i	$0.430006\pi$
$947$	−697.096	+	1207.40i	−0.736109	+	1.27498i	−0.954235	+	0.299058i	$0.903328\pi$
$948$	−232.821	+	182.347i	−0.245592	+	0.192349i
$949$	898.475	−	518.735i	0.946760	−	0.546612i
$950$	1671.11	+	600.299i	1.75906	+	0.631893i
$951$	1708.36	−	541.502i	1.79638	−	0.569403i
$952$	682.494	−	8.59742i	0.716905	−	0.00903090i
$953$		−	1110.04i		−	1.16478i	−0.812909	−	0.582390i	$-0.802118\pi$
$953$		−	1110.04i		−	1.16478i	0.812909	−	0.582390i	$-0.197882\pi$
$954$	−279.822	−	1014.85i	−0.293315	−	1.06379i
$955$			1663.52i			1.74191i
$956$	934.480	−	1132.86i	0.977490	−	1.18500i
$957$	−42.6504	+	193.779i	−0.0445668	+	0.202486i
$958$	−530.170	−	190.449i	−0.553413	−	0.198799i
$959$	1688.77	−	975.011i	1.76097	−	1.01670i
$960$	−1241.22	−	1077.81i	−1.29294	−	1.12272i
$961$	397.966	−	689.298i	0.414117	−	0.717271i
$962$	−83.9803	−	99.2346i	−0.0872976	−	0.103154i
$963$	46.5058	+	513.558i	0.0482926	+	0.533290i
$964$	70.5865	−	420.957i	0.0732225	−	0.436678i
$965$	175.484	−	303.948i	0.181849	−	0.314972i
$966$	−633.301	+	1006.75i	−0.655591	+	1.04218i
$967$	−826.703	−	1431.89i	−0.854915	−	1.48076i	−0.876723	−	0.480995i	$-0.840276\pi$
$967$	−826.703	−	1431.89i	−0.854915	−	1.48076i	0.0218081	−	0.999762i	$-0.493058\pi$
$968$	215.357	+	120.746i	0.222477	+	0.124737i
$969$	−462.120	−	422.163i	−0.476904	−	0.435669i
$970$	−3172.96	+	573.225i	−3.27109	+	0.590954i
$971$	677.141			0.697365			0.348683	−	0.937241i	$-0.386629\pi$
$971$	677.141			0.697365			0.348683	+	0.937241i	$0.386629\pi$
$972$	−952.205	−	195.164i	−0.979635	−	0.200786i
$973$			700.397i			0.719832i
$974$	964.527	−	174.251i	0.990274	−	0.178902i
$975$	1077.50	−	1179.48i	1.10513	−	1.20973i
$976$	1016.92	−	196.974i	1.04192	−	0.201818i
$977$	−816.419	+	471.360i	−0.835639	+	0.482456i	−0.855779	−	0.517341i	$-0.826922\pi$
$977$	−816.419	+	471.360i	−0.835639	+	0.482456i	0.0201405	+	0.999797i	$0.493589\pi$
$978$	−880.061	+	1399.02i	−0.899857	+	1.43049i
$979$	1084.27	+	626.005i	1.10753	+	0.639433i
$980$	−42.4209	+	252.986i	−0.0432867	+	0.258149i
$981$	−447.524	+	40.5260i	−0.456191	+	0.0413109i
$982$	431.530	+	509.914i	0.439440	+	0.519260i
$983$	1071.25	+	618.485i	1.08977	+	0.629181i	0.933516	−	0.358536i	$-0.116724\pi$
$983$	1071.25	+	618.485i	1.08977	+	0.629181i	0.156257	+	0.987716i	$0.450057\pi$
$984$	860.463	−	284.719i	0.874454	−	0.289349i
$985$	−61.1138	−	105.852i	−0.0620445	−	0.107464i
$986$	−148.845	−	53.4686i	−0.150959	−	0.0542278i
$987$	403.877	+	88.8927i	0.409196	+	0.0900636i
$988$	625.226	+	515.743i	0.632820	+	0.522007i
$989$	644.889			0.652062
$990$	388.918	+	1410.52i	0.392847	+	1.42477i
$991$	−123.871			−0.124996			−0.0624979	−	0.998045i	$-0.519907\pi$
$991$	−123.871			−0.124996			−0.0624979	+	0.998045i	$0.519907\pi$
$992$	406.295	+	62.8770i	0.409572	+	0.0633840i
$993$	−191.319	−	603.583i	−0.192668	−	0.607838i
$994$	−1196.60	−	429.847i	−1.20383	−	0.432441i
$995$	−1279.45	−	2216.07i	−1.28588	−	2.22720i
$996$	−1091.80	+	855.109i	−1.09619	+	0.858544i
$997$	591.638	+	341.582i	0.593418	+	0.342610i	0.766448	−	0.642307i	$-0.222022\pi$
$997$	591.638	+	341.582i	0.593418	+	0.342610i	−0.173030	+	0.984917i	$0.555356\pi$
$998$	−728.827	+	616.792i	−0.730288	+	0.618028i
$999$	−126.740	−	96.3348i	−0.126867	−	0.0964312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.21	yes	44
3.2	odd	2		216.3.j.a.197.2		44
4.3	odd	2		288.3.n.a.209.5		44
8.3	odd	2		288.3.n.a.209.18		44
8.5	even	2	inner	72.3.j.a.29.14	yes	44
9.2	odd	6		648.3.h.a.485.32		44
9.4	even	3		216.3.j.a.125.9		44
9.5	odd	6	inner	72.3.j.a.5.14	✓	44
9.7	even	3		648.3.h.a.485.13		44
12.11	even	2		864.3.n.a.305.22		44
24.5	odd	2		216.3.j.a.197.9		44
24.11	even	2		864.3.n.a.305.1		44
36.7	odd	6		2592.3.h.a.1457.43		44
36.11	even	6		2592.3.h.a.1457.2		44
36.23	even	6		288.3.n.a.113.18		44
36.31	odd	6		864.3.n.a.17.1		44
72.5	odd	6	inner	72.3.j.a.5.21	yes	44
72.11	even	6		2592.3.h.a.1457.44		44
72.13	even	6		216.3.j.a.125.2		44
72.29	odd	6		648.3.h.a.485.14		44
72.43	odd	6		2592.3.h.a.1457.1		44
72.59	even	6		288.3.n.a.113.5		44
72.61	even	6		648.3.h.a.485.31		44
72.67	odd	6		864.3.n.a.17.22		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.14	✓	44	9.5	odd	6	inner
72.3.j.a.5.21	yes	44	72.5	odd	6	inner
72.3.j.a.29.14	yes	44	8.5	even	2	inner
72.3.j.a.29.21	yes	44	1.1	even	1	trivial
216.3.j.a.125.2		44	72.13	even	6
216.3.j.a.125.9		44	9.4	even	3
216.3.j.a.197.2		44	3.2	odd	2
216.3.j.a.197.9		44	24.5	odd	2
288.3.n.a.113.5		44	72.59	even	6
288.3.n.a.113.18		44	36.23	even	6
288.3.n.a.209.5		44	4.3	odd	2
288.3.n.a.209.18		44	8.3	odd	2
648.3.h.a.485.13		44	9.7	even	3
648.3.h.a.485.14		44	72.29	odd	6
648.3.h.a.485.31		44	72.61	even	6
648.3.h.a.485.32		44	9.2	odd	6
864.3.n.a.17.1		44	36.31	odd	6
864.3.n.a.17.22		44	72.67	odd	6
864.3.n.a.305.1		44	24.11	even	2
864.3.n.a.305.22		44	12.11	even	2
2592.3.h.a.1457.1		44	72.43	odd	6
2592.3.h.a.1457.2		44	36.11	even	6
2592.3.h.a.1457.43		44	36.7	odd	6
2592.3.h.a.1457.44		44	72.11	even	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.96814 - 0.355563i) q^{2} +(2.21491 + 2.02340i) q^{3} +(3.74715 - 1.39960i) q^{4} +(-4.28090 - 7.41474i) q^{5} +(5.07871 + 3.19480i) q^{6} +(-3.75800 + 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +(0.811683 + 8.96332i) q^{9} +O(q^{10})\)	\(q+(1.96814 - 0.355563i) q^{2} +(2.21491 + 2.02340i) q^{3} +(3.74715 - 1.39960i) q^{4} +(-4.28090 - 7.41474i) q^{5} +(5.07871 + 3.19480i) q^{6} +(-3.75800 + 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +(0.811683 + 8.96332i) q^{9} +(-11.0618 - 13.0711i) q^{10} +(-4.74705 + 8.22213i) q^{11} +(11.1316 + 4.48201i) q^{12} +(-9.54725 + 5.51211i) q^{13} +(-5.08189 + 14.1469i) q^{14} +(5.52118 - 25.0850i) q^{15} +(12.0823 - 10.4890i) q^{16} -11.3516i q^{17} +(4.78453 + 17.3525i) q^{18} -18.3798i q^{19} +(-26.4188 - 21.7926i) q^{20} +(-21.4941 + 6.81302i) q^{21} +(-6.41937 + 17.8702i) q^{22} +(22.8408 - 13.1871i) q^{23} +(23.5021 + 4.86324i) q^{24} +(-24.1522 + 41.8329i) q^{25} +(-16.8304 + 14.2433i) q^{26} +(-16.3386 + 21.4953i) q^{27} +(-4.97174 + 29.6500i) q^{28} +(3.48316 - 6.03301i) q^{29} +(1.94715 - 51.3339i) q^{30} +(6.42393 + 11.1266i) q^{31} +(20.0501 - 24.9398i) q^{32} +(-27.1510 + 8.60611i) q^{33} +(-4.03621 - 22.3415i) q^{34} +64.3505 q^{35} +(15.5865 + 32.4509i) q^{36} +5.89614i q^{37} +(-6.53519 - 36.1741i) q^{38} +(-32.2996 - 7.10909i) q^{39} +(-59.7446 - 33.4973i) q^{40} +(32.7049 - 18.8822i) q^{41} +(-39.8808 + 21.0515i) q^{42} +(21.1756 + 12.2257i) q^{43} +(-6.28023 + 37.4535i) q^{44} +(62.9860 - 44.3895i) q^{45} +(40.2650 - 34.0754i) q^{46} +(-15.8834 - 9.17030i) q^{47} +(47.9846 + 1.21506i) q^{48} +(-3.74509 - 6.48669i) q^{49} +(-32.6607 + 90.9207i) q^{50} +(22.9688 - 25.1428i) q^{51} +(-28.0603 + 34.0170i) q^{52} -58.4847 q^{53} +(-24.5137 + 48.1153i) q^{54} +81.2866 q^{55} +(0.757376 + 60.1232i) q^{56} +(37.1898 - 40.7097i) q^{57} +(4.71023 - 13.1123i) q^{58} +(-13.1643 - 22.8013i) q^{59} +(-14.4202 - 101.725i) q^{60} +(56.0654 + 32.3694i) q^{61} +(16.5994 + 19.6145i) q^{62} +(-61.3930 - 28.4009i) q^{63} +(30.5937 - 56.2141i) q^{64} +(81.7417 + 47.1936i) q^{65} +(-50.3769 + 26.5919i) q^{66} +(28.4707 - 16.4376i) q^{67} +(-15.8876 - 42.5361i) q^{68} +(77.2732 + 17.0077i) q^{69} +(126.651 - 22.8807i) q^{70} +84.5841i q^{71} +(42.2148 + 58.3259i) q^{72} -94.1083 q^{73} +(2.09645 + 11.6044i) q^{74} +(-138.140 + 43.7866i) q^{75} +(-25.7243 - 68.8719i) q^{76} +(-35.6788 - 61.7975i) q^{77} +(-66.0978 - 2.50715i) q^{78} +(-12.3221 + 21.3425i) q^{79} +(-129.496 - 44.6844i) q^{80} +(-79.6823 + 14.5508i) q^{81} +(57.6540 - 48.7914i) q^{82} +(-57.7838 + 100.085i) q^{83} +(-71.0060 + 55.6124i) q^{84} +(-84.1691 + 48.5950i) q^{85} +(46.0236 + 16.5327i) q^{86} +(19.9221 - 6.31476i) q^{87} +(0.956706 + 75.9467i) q^{88} -131.872i q^{89} +(108.182 - 109.760i) q^{90} -82.8580i q^{91} +(67.1311 - 81.3820i) q^{92} +(-8.28509 + 37.6426i) q^{93} +(-34.5214 - 12.4009i) q^{94} +(-136.282 + 78.6822i) q^{95} +(94.8725 - 14.6702i) q^{96} +(94.1484 - 163.070i) q^{97} +(-9.67730 - 11.4351i) q^{98} +(-77.5507 - 35.8756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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