LMFDB - Embedded newform 441.3.j.f.263.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(263,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 4]))

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

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

chi := DirichletCharacter("441.263");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.j (of order $6$, degree $2$, not 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.4
Character	$\chi$	$=$	441.263
Dual form			441.3.j.f.275.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46555i q^{2} +(-0.993737 + 2.83063i) q^{3} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(4.14843 + 1.45637i) q^{6} -8.57663i q^{8} +(-7.02497 - 5.62581i) q^{9} +O(q^{10})$	\(q-1.46555i q^{2} +(-0.993737 + 2.83063i) q^{3} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(4.14843 + 1.45637i) q^{6} -8.57663i q^{8} +(-7.02497 - 5.62581i) q^{9} +(-0.844669 + 1.46301i) q^{10} +(0.209014 - 0.120674i) q^{11} +(-1.84057 + 5.24282i) q^{12} +(-7.70332 - 13.3426i) q^{13} +(2.62345 - 2.25299i) q^{15} -5.16078 q^{16} +(10.9102 + 6.29901i) q^{17} +(-8.24489 + 10.2954i) q^{18} +(-13.7090 - 23.7446i) q^{19} +(-1.84896 - 1.06750i) q^{20} +(-0.176854 - 0.306320i) q^{22} +(17.6566 + 10.1940i) q^{23} +(24.2773 + 8.52292i) q^{24} +(-11.8356 - 20.4999i) q^{25} +(-19.5541 + 11.2896i) q^{26} +(22.9056 - 14.2945i) q^{27} +(16.9161 + 9.76653i) q^{29} +(-3.30186 - 3.84480i) q^{30} +2.72674 q^{31} -26.7432i q^{32} +(0.133880 + 0.711561i) q^{33} +(9.23150 - 15.9894i) q^{34} +(-13.0114 - 10.4200i) q^{36} +(-11.4455 - 19.8242i) q^{37} +(-34.7989 + 20.0911i) q^{38} +(45.4230 - 8.54630i) q^{39} +(-4.94315 + 8.56178i) q^{40} +(61.9933 - 35.7918i) q^{41} +(14.8972 - 25.8028i) q^{43} +(0.387130 - 0.223510i) q^{44} +(3.77037 + 9.66492i) q^{45} +(14.9398 - 25.8766i) q^{46} +29.9915i q^{47} +(5.12846 - 14.6083i) q^{48} +(-30.0436 + 17.3457i) q^{50} +(-28.6721 + 24.6232i) q^{51} +(-14.2679 - 24.7127i) q^{52} +(-90.5906 - 52.3025i) q^{53} +(-20.9493 - 33.5692i) q^{54} -0.278203 q^{55} +(80.8355 - 15.2091i) q^{57} +(14.3133 - 24.7914i) q^{58} -86.7123i q^{59} +(4.85908 - 4.17292i) q^{60} -17.8845 q^{61} -3.99616i q^{62} -59.8365 q^{64} +17.7593i q^{65} +(1.04283 - 0.196207i) q^{66} -18.0439 q^{67} +(20.2076 + 11.6669i) q^{68} +(-46.4016 + 39.8491i) q^{69} +74.2118i q^{71} +(-48.2505 + 60.2506i) q^{72} +(-13.0598 + 22.6203i) q^{73} +(-29.0533 + 16.7739i) q^{74} +(69.7893 - 13.1308i) q^{75} +(-25.3914 - 43.9791i) q^{76} +(-12.5250 - 66.5695i) q^{78} +22.5123 q^{79} +(5.15184 + 2.97442i) q^{80} +(17.7005 + 79.0424i) q^{81} +(-52.4546 - 90.8541i) q^{82} +(77.0996 + 44.5135i) q^{83} +(-7.26088 - 12.5762i) q^{85} +(-37.8152 - 21.8326i) q^{86} +(-44.4557 + 38.1780i) q^{87} +(-1.03498 - 1.79264i) q^{88} +(-49.7459 + 28.7208i) q^{89} +(14.1644 - 5.52565i) q^{90} +(32.7030 + 18.8811i) q^{92} +(-2.70966 + 7.71839i) q^{93} +43.9540 q^{94} +31.6047i q^{95} +(75.7001 + 26.5757i) q^{96} +(-73.9883 + 128.152i) q^{97} +(-2.14721 - 0.328140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 19 q^{3} - 24 q^{4} - 12 q^{5} + 8 q^{6} - 37 q^{9}+O(q^{10}) $ 22 * q + 19 * q^3 - 24 * q^4 - 12 * q^5 + 8 * q^6 - 37 * q^9	$ 22 q + 19 q^{3} - 24 q^{4} - 12 q^{5} + 8 q^{6} - 37 q^{9} - 25 q^{10} + 24 q^{11} - 40 q^{12} + 18 q^{13} + 53 q^{15} - 24 q^{16} + 6 q^{17} + 40 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} + 81 q^{23} - 126 q^{24} + 57 q^{25} - 3 q^{26} + 97 q^{27} - 63 q^{29} - 38 q^{30} - 58 q^{31} + 4 q^{33} + 99 q^{34} + 76 q^{36} - 20 q^{37} + 48 q^{38} - 76 q^{39} + 105 q^{40} + 51 q^{41} + 65 q^{43} - 54 q^{44} + 214 q^{45} + 75 q^{46} + 113 q^{48} + 63 q^{50} + 141 q^{51} + 46 q^{52} + 63 q^{53} - 433 q^{54} + 100 q^{55} + 224 q^{57} + 40 q^{58} - 482 q^{60} + 156 q^{61} + 106 q^{64} - 61 q^{66} + 264 q^{67} - 27 q^{68} + 297 q^{69} - 222 q^{72} - q^{73} + 342 q^{74} + 296 q^{75} - 233 q^{76} - 440 q^{78} - 280 q^{79} + 96 q^{80} - 169 q^{81} + 157 q^{82} - 255 q^{83} + 102 q^{85} + 504 q^{86} - 704 q^{87} + 408 q^{88} - 720 q^{89} - 418 q^{90} - 1239 q^{92} - 36 q^{93} + 522 q^{94} + 397 q^{96} - 178 q^{97} - 103 q^{99}+O(q^{100}) $ 22 * q + 19 * q^3 - 24 * q^4 - 12 * q^5 + 8 * q^6 - 37 * q^9 - 25 * q^10 + 24 * q^11 - 40 * q^12 + 18 * q^13 + 53 * q^15 - 24 * q^16 + 6 * q^17 + 40 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 + 81 * q^23 - 126 * q^24 + 57 * q^25 - 3 * q^26 + 97 * q^27 - 63 * q^29 - 38 * q^30 - 58 * q^31 + 4 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 48 * q^38 - 76 * q^39 + 105 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 214 * q^45 + 75 * q^46 + 113 * q^48 + 63 * q^50 + 141 * q^51 + 46 * q^52 + 63 * q^53 - 433 * q^54 + 100 * q^55 + 224 * q^57 + 40 * q^58 - 482 * q^60 + 156 * q^61 + 106 * q^64 - 61 * q^66 + 264 * q^67 - 27 * q^68 + 297 * q^69 - 222 * q^72 - q^73 + 342 * q^74 + 296 * q^75 - 233 * q^76 - 440 * q^78 - 280 * q^79 + 96 * q^80 - 169 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 504 * q^86 - 704 * q^87 + 408 * q^88 - 720 * q^89 - 418 * q^90 - 1239 * q^92 - 36 * q^93 + 522 * q^94 + 397 * q^96 - 178 * q^97 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.46555i		−	0.732774i	−0.930463	−	0.366387i	$-0.880595\pi$
$2$		−	1.46555i		−	0.732774i	0.930463	−	0.366387i	$-0.119405\pi$
$3$	−0.993737	+	2.83063i	−0.331246	+	0.943544i
$3$	−0.993737	+	2.83063i	−0.331246	+	0.943544i
$4$	1.85217			0.463043
$5$	−0.998268	−	0.576350i	−0.199654	−	0.115270i	0.396840	−	0.917888i	$-0.370107\pi$
$5$	−0.998268	−	0.576350i	−0.199654	−	0.115270i	−0.596494	+	0.802618i	$0.703440\pi$
$6$	4.14843	+	1.45637i	0.691405	+	0.242728i
$7$		0			0
$7$		0			0
$8$		−	8.57663i		−	1.07208i
$9$	−7.02497	−	5.62581i	−0.780552	−	0.625090i
$10$	−0.844669	+	1.46301i	−0.0844669	+	0.146301i
$11$	0.209014	−	0.120674i	0.0190013	−	0.0109704i	−0.490469	−	0.871458i	$-0.663175\pi$
$11$	0.209014	−	0.120674i	0.0190013	−	0.0109704i	0.509471	+	0.860488i	$0.329841\pi$
$12$	−1.84057	+	5.24282i	−0.153381	+	0.436901i
$13$	−7.70332	−	13.3426i	−0.592563	−	1.02635i	−0.993886	−	0.110413i	$-0.964783\pi$
$13$	−7.70332	−	13.3426i	−0.592563	−	1.02635i	0.401322	−	0.915937i	$-0.368551\pi$
$14$		0			0
$15$	2.62345	−	2.25299i	0.174897	−	0.150199i
$16$	−5.16078			−0.322549
$17$	10.9102	+	6.29901i	0.641777	+	0.370530i	0.785299	−	0.619117i	$-0.212509\pi$
$17$	10.9102	+	6.29901i	0.641777	+	0.370530i	−0.143522	+	0.989647i	$0.545843\pi$
$18$	−8.24489	+	10.2954i	−0.458050	+	0.571968i
$19$	−13.7090	−	23.7446i	−0.721525	−	1.24972i	−0.960389	−	0.278664i	$-0.910108\pi$
$19$	−13.7090	−	23.7446i	−0.721525	−	1.24972i	0.238864	−	0.971053i	$-0.423225\pi$
$20$	−1.84896	−	1.06750i	−0.0924482	−	0.0533750i
$21$		0			0
$22$	−0.176854	−	0.306320i	−0.00803882	−	0.0139236i
$23$	17.6566	+	10.1940i	0.767678	+	0.443219i	0.832046	−	0.554707i	$-0.187170\pi$
$23$	17.6566	+	10.1940i	0.767678	+	0.443219i	−0.0643676	+	0.997926i	$0.520503\pi$
$24$	24.2773	+	8.52292i	1.01155	+	0.355122i
$25$	−11.8356	−	20.4999i	−0.473426	−	0.819997i
$26$	−19.5541	+	11.2896i	−0.752082	+	0.434215i
$27$	22.9056	−	14.2945i	0.848355	−	0.529427i
$28$		0			0
$29$	16.9161	+	9.76653i	0.583315	+	0.336777i	0.762450	−	0.647048i	$-0.223997\pi$
$29$	16.9161	+	9.76653i	0.583315	+	0.336777i	−0.179135	+	0.983825i	$0.557330\pi$
$30$	−3.30186	−	3.84480i	−0.110062	−	0.128160i
$31$	2.72674			0.0879592			0.0439796	−	0.999032i	$-0.485996\pi$
$31$	2.72674			0.0879592			0.0439796	+	0.999032i	$0.485996\pi$
$32$		−	26.7432i		−	0.835724i
$33$	0.133880	+	0.711561i	0.00405696	+	0.0215625i
$34$	9.23150	−	15.9894i	0.271515	−	0.470277i
$35$		0			0
$36$	−13.0114	−	10.4200i	−0.361429	−	0.289444i
$37$	−11.4455	−	19.8242i	−0.309338	−	0.535789i	0.668880	−	0.743371i	$-0.266774\pi$
$37$	−11.4455	−	19.8242i	−0.309338	−	0.535789i	−0.978218	+	0.207582i	$0.933441\pi$
$38$	−34.7989	+	20.0911i	−0.915760	+	0.528714i
$39$	45.4230	−	8.54630i	1.16469	−	0.219136i
$40$	−4.94315	+	8.56178i	−0.123579	+	0.214045i
$41$	61.9933	−	35.7918i	1.51203	−	0.872972i	0.512130	−	0.858908i	$-0.328856\pi$
$41$	61.9933	−	35.7918i	1.51203	−	0.872972i	0.999901	−	0.0140641i	$-0.00447689\pi$
$42$		0			0
$43$	14.8972	−	25.8028i	0.346447	−	0.600064i	−0.639168	−	0.769067i	$-0.720721\pi$
$43$	14.8972	−	25.8028i	0.346447	−	0.600064i	0.985616	+	0.169003i	$0.0540546\pi$
$44$	0.387130	−	0.223510i	0.00879841	−	0.00507977i
$45$	3.77037	+	9.66492i	0.0837859	+	0.214776i
$46$	14.9398	−	25.8766i	0.324779	−	0.562534i
$47$			29.9915i			0.638117i	0.947735	+	0.319059i	$0.103367\pi$
$47$			29.9915i			0.638117i	−0.947735	+	0.319059i	$0.896633\pi$
$48$	5.12846	−	14.6083i	0.106843	−	0.304339i
$49$		0			0
$50$	−30.0436	+	17.3457i	−0.600872	+	0.346914i
$51$	−28.6721	+	24.6232i	−0.562198	+	0.482809i
$52$	−14.2679	−	24.7127i	−0.274382	−	0.475244i
$53$	−90.5906	−	52.3025i	−1.70926	−	0.986840i	−0.935479	−	0.353383i	$-0.885031\pi$
$53$	−90.5906	−	52.3025i	−1.70926	−	0.986840i	−0.773778	−	0.633457i	$-0.781635\pi$
$54$	−20.9493	−	33.5692i	−0.387950	−	0.621652i
$55$	−0.278203			−0.00505824
$56$		0			0
$57$	80.8355	−	15.2091i	1.41817	−	0.266827i
$58$	14.3133	−	24.7914i	0.246781	−	0.427438i
$59$		−	86.7123i		−	1.46970i	−0.678230	−	0.734850i	$-0.737253\pi$
$59$		−	86.7123i		−	1.46970i	0.678230	−	0.734850i	$-0.262747\pi$
$60$	4.85908	−	4.17292i	0.0809847	−	0.0695487i
$61$	−17.8845			−0.293188			−0.146594	−	0.989197i	$-0.546831\pi$
$61$	−17.8845			−0.293188			−0.146594	+	0.989197i	$0.546831\pi$
$62$		−	3.99616i		−	0.0644542i
$63$		0			0
$64$	−59.8365			−0.934945
$65$			17.7593i			0.273219i
$66$	1.04283	−	0.196207i	0.0158004	−	0.00297284i
$67$	−18.0439			−0.269312			−0.134656	−	0.990892i	$-0.542993\pi$
$67$	−18.0439			−0.269312			−0.134656	+	0.990892i	$0.542993\pi$
$68$	20.2076	+	11.6669i	0.297170	+	0.171571i
$69$	−46.4016	+	39.8491i	−0.672487	+	0.577524i
$70$		0			0
$71$			74.2118i			1.04524i	0.852567	+	0.522618i	$0.175045\pi$
$71$			74.2118i			1.04524i	−0.852567	+	0.522618i	$0.824955\pi$
$72$	−48.2505	+	60.2506i	−0.670146	+	0.836814i
$73$	−13.0598	+	22.6203i	−0.178902	+	0.309867i	−0.941505	−	0.337000i	$-0.890588\pi$
$73$	−13.0598	+	22.6203i	−0.178902	+	0.309867i	0.762603	+	0.646867i	$0.223921\pi$
$74$	−29.0533	+	16.7739i	−0.392612	+	0.226675i
$75$	69.7893	−	13.1308i	0.930524	−	0.175077i
$76$	−25.3914	−	43.9791i	−0.334097	−	0.578673i
$77$		0			0
$78$	−12.5250	−	66.5695i	−0.160577	−	0.853455i
$79$	22.5123			0.284966			0.142483	−	0.989797i	$-0.454491\pi$
$79$	22.5123			0.284966			0.142483	+	0.989797i	$0.454491\pi$
$80$	5.15184	+	2.97442i	0.0643980	+	0.0371802i
$81$	17.7005	+	79.0424i	0.218524	+	0.975832i
$82$	−52.4546	−	90.8541i	−0.639691	−	1.10798i
$83$	77.0996	+	44.5135i	0.928911	+	0.536307i	0.886467	−	0.462792i	$-0.153152\pi$
$83$	77.0996	+	44.5135i	0.928911	+	0.536307i	0.0424438	+	0.999099i	$0.486486\pi$
$84$		0			0
$85$	−7.26088	−	12.5762i	−0.0854221	−	0.147955i
$86$	−37.8152	−	21.8326i	−0.439711	−	0.253867i
$87$	−44.4557	+	38.1780i	−0.510985	+	0.438827i
$88$	−1.03498	−	1.79264i	−0.0117611	−	0.0203709i
$89$	−49.7459	+	28.7208i	−0.558942	+	0.322706i	−0.752721	−	0.658340i	$-0.771259\pi$
$89$	−49.7459	+	28.7208i	−0.558942	+	0.322706i	0.193779	+	0.981045i	$0.437926\pi$
$90$	14.1644	−	5.52565i	0.157382	−	0.0613961i
$91$		0			0
$92$	32.7030	+	18.8811i	0.355468	+	0.205229i
$93$	−2.70966	+	7.71839i	−0.0291361	+	0.0829934i
$94$	43.9540			0.467596
$95$			31.6047i			0.332681i
$96$	75.7001	+	26.5757i	0.788543	+	0.276830i
$97$	−73.9883	+	128.152i	−0.762766	+	1.32115i	0.178653	+	0.983912i	$0.442826\pi$
$97$	−73.9883	+	128.152i	−0.762766	+	1.32115i	−0.941419	+	0.337238i	$0.890507\pi$
$98$		0			0
$99$	−2.14721	−	0.328140i	−0.0216890	−	0.00331455i
$100$	−21.9216	−	37.9694i	−0.219216	−	0.379694i
$101$	−72.8647	+	42.0685i	−0.721433	+	0.416519i	−0.815280	−	0.579067i	$-0.803417\pi$
$101$	−72.8647	+	42.0685i	−0.721433	+	0.416519i	0.0938471	+	0.995587i	$0.470084\pi$
$102$	36.0865	+	42.0203i	0.353790	+	0.411964i
$103$	29.4838	−	51.0674i	0.286250	−	0.495800i	−0.686661	−	0.726977i	$-0.740924\pi$
$103$	29.4838	−	51.0674i	0.286250	−	0.495800i	0.972912	+	0.231178i	$0.0742578\pi$
$104$	−114.434	+	66.0686i	−1.10033	+	0.635275i
$105$		0			0
$106$	−76.6518	+	132.765i	−0.723130	+	1.25250i
$107$	76.9320	−	44.4167i	0.718990	−	0.415109i	−0.0953906	−	0.995440i	$-0.530410\pi$
$107$	76.9320	−	44.4167i	0.718990	−	0.415109i	0.814381	+	0.580331i	$0.197077\pi$
$108$	42.4251	−	26.4759i	0.392825	−	0.245148i
$109$	94.4610	−	163.611i	0.866615	−	1.50102i	0.00117990	−	0.999999i	$-0.499624\pi$
$109$	94.4610	−	163.611i	0.866615	−	1.50102i	0.865435	−	0.501021i	$-0.167042\pi$
$110$			0.407720i			0.00370654i
$111$	67.4889	−	12.6980i	0.608008	−	0.114396i
$112$		0			0
$113$	101.115	−	58.3790i	0.894827	−	0.516629i	0.0193087	−	0.999814i	$-0.493853\pi$
$113$	101.115	−	58.3790i	0.894827	−	0.516629i	0.875518	+	0.483185i	$0.160520\pi$
$114$	−22.2897	−	118.468i	−0.195524	−	1.03919i
$115$	−11.7507	−	20.3528i	−0.102180	−	0.176981i
$116$	31.3316	+	18.0893i	0.270100	+	0.155942i
$117$	−20.9470	+	137.069i	−0.179035	+	1.17153i
$118$	−127.081			−1.07696
$119$		0			0
$120$	−19.3231	−	22.5004i	−0.161026	−	0.187503i
$121$	−60.4709	+	104.739i	−0.499759	+	0.865609i
$122$			26.2106i			0.214841i
$123$	39.7085	+	211.048i	0.322834	+	1.71584i
$124$	5.05038			0.0407289
$125$			56.1034i			0.448827i
$126$		0			0
$127$	−33.5427			−0.264116			−0.132058	−	0.991242i	$-0.542159\pi$
$127$	−33.5427			−0.264116			−0.132058	+	0.991242i	$0.542159\pi$
$128$		−	19.2795i		−	0.150621i
$129$	58.2342	+	67.8098i	0.451428	+	0.525657i
$130$	26.0270			0.200208
$131$	61.9195	+	35.7493i	0.472668	+	0.272895i	0.717356	−	0.696707i	$-0.245352\pi$
$131$	61.9195	+	35.7493i	0.472668	+	0.272895i	−0.244688	+	0.969602i	$0.578685\pi$
$132$	0.247968	+	1.31793i	0.00187855	+	0.00998434i
$133$		0			0
$134$			26.4442i			0.197345i
$135$	−31.1046	+	1.06814i	−0.230404	+	0.00791213i
$136$	54.0243	−	93.5729i	0.397238	−	0.688036i
$137$	−187.723	+	108.382i	−1.37024	+	0.791108i	−0.990958	−	0.134173i	$-0.957162\pi$
$137$	−187.723	+	108.382i	−1.37024	+	0.791108i	−0.379281	+	0.925281i	$0.623829\pi$
$138$	58.4008	+	68.0038i	0.423194	+	0.492781i
$139$	−53.7032	−	93.0167i	−0.386354	−	0.669185i	0.605602	−	0.795768i	$-0.292932\pi$
$139$	−53.7032	−	93.0167i	−0.386354	−	0.669185i	−0.991956	+	0.126583i	$0.959599\pi$
$140$		0			0
$141$	−84.8950	−	29.8037i	−0.602092	−	0.211374i
$142$	108.761			0.765921
$143$	−3.22021	−	1.85919i	−0.0225189	−	0.0130013i
$144$	36.2543	+	29.0336i	0.251766	+	0.201622i
$145$	−11.2579	−	19.4992i	−0.0776406	−	0.134477i
$146$	33.1511	+	19.1398i	0.227062	+	0.131094i
$147$		0			0
$148$	−21.1990	−	36.7178i	−0.143237	−	0.248093i
$149$	136.043	+	78.5443i	0.913038	+	0.527143i	0.881408	−	0.472357i	$-0.156597\pi$
$149$	136.043	+	78.5443i	0.913038	+	0.527143i	0.0316309	+	0.999500i	$0.489930\pi$
$150$	−19.2438	−	102.280i	−0.128292	−	0.681864i
$151$	60.2412	+	104.341i	0.398948	+	0.690999i	0.993596	−	0.112987i	$-0.0360419\pi$
$151$	60.2412	+	104.341i	0.398948	+	0.690999i	−0.594648	+	0.803986i	$0.702709\pi$
$152$	−203.649	+	117.577i	−1.33980	+	0.773532i
$153$	−41.2069	−	105.629i	−0.269326	−	0.690387i
$154$		0			0
$155$	−2.72201	−	1.57156i	−0.0175614	−	0.0101391i
$156$	84.1311	−	15.8292i	0.539302	−	0.101469i
$157$	−7.75554			−0.0493984			−0.0246992	−	0.999695i	$-0.507863\pi$
$157$	−7.75554			−0.0493984			−0.0246992	+	0.999695i	$0.507863\pi$
$158$		−	32.9928i		−	0.208815i
$159$	238.073	−	204.454i	1.49731	−	1.28587i
$160$	−15.4134	+	26.6969i	−0.0963340	+	0.166855i
$161$		0			0
$162$	115.840	−	25.9409i	0.715064	−	0.160129i
$163$	129.964	+	225.104i	0.797323	+	1.38100i	0.921354	+	0.388725i	$0.127084\pi$
$163$	129.964	+	225.104i	0.797323	+	1.38100i	−0.124031	+	0.992278i	$0.539582\pi$
$164$	114.822	−	66.2926i	0.700135	−	0.404223i
$165$	0.276461	−	0.787491i	0.00167552	−	0.00477267i
$166$	65.2366	−	112.993i	0.392992	−	0.680681i
$167$	−97.3809	+	56.2229i	−0.583119	+	0.336664i	−0.762372	−	0.647139i	$-0.775965\pi$
$167$	−97.3809	+	56.2229i	−0.583119	+	0.336664i	0.179253	+	0.983803i	$0.442632\pi$
$168$		0			0
$169$	−34.1824	+	59.2057i	−0.202263	+	0.350330i
$170$	−18.4310	+	10.6412i	−0.108418	+	0.0625951i
$171$	−37.2777	+	243.929i	−0.217998	+	1.42649i
$172$	27.5922	−	47.7911i	0.160420	−	0.277855i
$173$		−	13.9867i		−	0.0808478i	−0.999183	−	0.0404239i	$-0.987129\pi$
$173$		−	13.9867i		−	0.0808478i	0.999183	−	0.0404239i	$-0.0128708\pi$
$174$	55.9517	+	65.1519i	0.321561	+	0.374436i
$175$		0			0
$176$	−1.07868	+	0.622774i	−0.00612884	+	0.00353849i
$177$	245.451	+	86.1693i	1.38673	+	0.486832i
$178$	42.0917	+	72.9049i	0.236470	+	0.409578i
$179$	44.1214	+	25.4735i	0.246488	+	0.142310i	0.618155	−	0.786056i	$-0.287880\pi$
$179$	44.1214	+	25.4735i	0.246488	+	0.142310i	−0.371667	+	0.928366i	$0.621214\pi$
$180$	6.98336	+	17.9011i	0.0387965	+	0.0994504i
$181$	239.784			1.32477			0.662387	−	0.749161i	$-0.269543\pi$
$181$	239.784			1.32477			0.662387	+	0.749161i	$0.269543\pi$
$182$		0			0
$183$	17.7725	−	50.6244i	0.0971174	−	0.276636i
$184$	87.4305	−	151.434i	0.475166	−	0.823012i
$185$			26.3865i			0.142630i
$186$	11.3117	+	3.97113i	0.0608154	+	0.0213502i
$187$	3.04052			0.0162595
$188$			55.5494i			0.295476i
$189$		0			0
$190$	46.3182			0.243780
$191$		−	183.841i		−	0.962519i	−0.876578	−	0.481259i	$-0.840180\pi$
$191$		−	183.841i		−	0.962519i	0.876578	−	0.481259i	$-0.159820\pi$
$192$	59.4618	−	169.375i	0.309697	−	0.882162i
$193$	152.797			0.791695			0.395847	−	0.918316i	$-0.370451\pi$
$193$	152.797			0.791695			0.395847	+	0.918316i	$0.370451\pi$
$194$	187.812	+	108.433i	0.968104	+	0.558935i
$195$	−50.2700	−	17.6480i	−0.257795	−	0.0905028i
$196$		0			0
$197$			386.007i			1.95943i	0.200402	+	0.979714i	$0.435775\pi$
$197$			386.007i			1.95943i	−0.200402	+	0.979714i	$0.564225\pi$
$198$	−0.480905	+	3.14684i	−0.00242882	+	0.0158931i
$199$	22.8387	−	39.5577i	0.114767	−	0.198782i	−0.802920	−	0.596087i	$-0.796721\pi$
$199$	22.8387	−	39.5577i	0.114767	−	0.198782i	0.917687	+	0.397305i	$0.130054\pi$
$200$	−175.820	+	101.510i	−0.879102	+	0.507550i
$201$	17.9309	−	51.0757i	0.0892086	−	0.254108i
$202$	61.6533	+	106.787i	0.305214	+	0.528647i
$203$		0			0
$204$	−53.1056	+	45.6065i	−0.260322	+	0.223561i
$205$	−82.5146			−0.402510
$206$	−74.8417	−	43.2099i	−0.363309	−	0.209757i
$207$	−66.6873	−	170.946i	−0.322161	−	0.825824i
$208$	39.7552	+	68.8579i	0.191131	+	0.331048i
$209$	−5.73074	−	3.30864i	−0.0274198	−	0.0158308i
$210$		0			0
$211$	−169.338	−	293.302i	−0.802550	−	1.39006i	−0.917933	−	0.396736i	$-0.870143\pi$
$211$	−169.338	−	293.302i	−0.802550	−	1.39006i	0.115383	−	0.993321i	$-0.463190\pi$
$212$	−167.789	−	96.8732i	−0.791459	−	0.456949i
$213$	−210.066	−	73.7470i	−0.986227	−	0.346230i
$214$	−65.0948	−	112.747i	−0.304181	−	0.526857i
$215$	−29.7429	+	17.1721i	−0.138339	+	0.0798700i
$216$	−122.599	−	196.453i	−0.567588	−	0.909504i
$217$		0			0
$218$	−239.780	−	138.437i	−1.09991	−	0.635032i
$219$	−51.0517	−	59.4462i	−0.233113	−	0.271444i
$220$	−0.515280			−0.00234218
$221$		−	194.093i		−	0.878251i
$222$	−18.6095	−	98.9081i	−0.0838266	−	0.445532i
$223$	−43.8681	+	75.9817i	−0.196718	+	0.340725i	−0.947462	−	0.319868i	$-0.896362\pi$
$223$	−43.8681	+	75.9817i	−0.196718	+	0.340725i	0.750745	+	0.660593i	$0.229695\pi$
$224$		0			0
$225$	−32.1837	+	210.597i	−0.143039	+	0.935985i
$226$	−85.5572	−	148.189i	−0.378572	−	0.655706i
$227$	−305.444	+	176.348i	−1.34557	+	0.776864i	−0.987618	−	0.156876i	$-0.949858\pi$
$227$	−305.444	+	176.348i	−1.34557	+	0.776864i	−0.357950	+	0.933741i	$0.616524\pi$
$228$	149.721	−	28.1699i	0.656672	−	0.123552i
$229$	−190.395	+	329.774i	−0.831421	+	1.44006i	0.0654913	+	0.997853i	$0.479139\pi$
$229$	−190.395	+	329.774i	−0.831421	+	1.44006i	−0.896912	+	0.442209i	$0.854195\pi$
$230$	−29.8280	+	17.2212i	−0.129687	+	0.0748747i
$231$		0			0
$232$	83.7640	−	145.083i	0.361052	−	0.625360i
$233$	−271.555	+	156.782i	−1.16547	+	0.672885i	−0.952609	−	0.304197i	$-0.901612\pi$
$233$	−271.555	+	156.782i	−1.16547	+	0.672885i	−0.212862	+	0.977082i	$0.568278\pi$
$234$	200.880	+	30.6989i	0.858463	+	0.131192i
$235$	17.2856	−	29.9396i	0.0735558	−	0.127402i
$236$		−	160.606i		−	0.680534i
$237$	−22.3713	+	63.7241i	−0.0943937	+	0.268878i
$238$		0			0
$239$	199.851	−	115.384i	0.836195	−	0.482777i	−0.0197741	−	0.999804i	$-0.506295\pi$
$239$	199.851	−	115.384i	0.836195	−	0.482777i	0.855969	+	0.517027i	$0.172961\pi$
$240$	−13.5391	+	11.6272i	−0.0564128	+	0.0484466i
$241$	−90.4282	−	156.626i	−0.375221	−	0.649902i	0.615139	−	0.788419i	$-0.289100\pi$
$241$	−90.4282	−	156.626i	−0.375221	−	0.649902i	−0.990360	+	0.138517i	$0.955766\pi$
$242$	153.499	+	88.6229i	0.634295	+	0.366210i
$243$	−241.330	−	28.4438i	−0.993126	−	0.117053i
$244$	−33.1251			−0.135759
$245$		0			0
$246$	309.301	−	58.1947i	1.25732	−	0.236564i
$247$	−211.209	+	365.825i	−0.855098	+	1.48107i
$248$		−	23.3862i		−	0.0942992i
$249$	−202.618	+	174.006i	−0.813727	+	0.698819i
$250$	82.2222			0.328889
$251$		−	161.864i		−	0.644878i	−0.946590	−	0.322439i	$-0.895497\pi$
$251$		−	161.864i		−	0.644878i	0.946590	−	0.322439i	$-0.104503\pi$
$252$		0			0
$253$	4.92064			0.0194492
$254$			49.1585i			0.193537i
$255$	42.8141	−	8.05544i	0.167898	−	0.0315899i
$256$	−267.601			−1.04532
$257$	−65.5360	−	37.8372i	−0.255004	−	0.147227i	0.367049	−	0.930201i	$-0.380368\pi$
$257$	−65.5360	−	37.8372i	−0.255004	−	0.147227i	−0.622053	+	0.782975i	$0.713701\pi$
$258$	99.3784	−	85.3450i	0.385188	−	0.330795i
$259$		0			0
$260$			32.8932i			0.126512i
$261$	−63.8906	−	163.777i	−0.244792	−	0.627496i
$262$	52.3922	−	90.7460i	0.199970	−	0.346359i
$263$	10.0862	−	5.82326i	0.0383505	−	0.0221417i	−0.480702	−	0.876884i	$-0.659618\pi$
$263$	10.0862	−	5.82326i	0.0383505	−	0.0221417i	0.519053	+	0.854742i	$0.326285\pi$
$264$	6.10280	−	1.14824i	0.0231167	−	0.00434939i
$265$	60.2892	+	104.424i	0.227506	+	0.394052i
$266$		0			0
$267$	−31.8637	−	169.353i	−0.119340	−	0.634282i
$268$	−33.4204			−0.124703
$269$	265.976	+	153.562i	0.988760	+	0.570861i	0.904903	−	0.425617i	$-0.139943\pi$
$269$	265.976	+	153.562i	0.988760	+	0.570861i	0.0838565	+	0.996478i	$0.473276\pi$
$270$	1.56541	+	45.5853i	0.00579780	+	0.168834i
$271$	−169.039	−	292.784i	−0.623759	−	1.08038i	−0.988779	−	0.149383i	$-0.952271\pi$
$271$	−169.039	−	292.784i	−0.623759	−	1.08038i	0.365020	−	0.931000i	$-0.381062\pi$
$272$	−56.3052	−	32.5078i	−0.207004	−	0.119514i
$273$		0			0
$274$	158.839	+	275.117i	0.579703	+	1.00408i
$275$	−4.94763	−	2.85652i	−0.0179914	−	0.0103873i
$276$	−85.9437	+	73.8074i	−0.311390	+	0.267418i
$277$	66.0110	+	114.334i	0.238307	+	0.412760i	0.960229	−	0.279215i	$-0.0900743\pi$
$277$	66.0110	+	114.334i	0.238307	+	0.412760i	−0.721922	+	0.691975i	$0.756741\pi$
$278$	−136.320	+	78.7046i	−0.490361	+	0.283110i
$279$	−19.1552	−	15.3401i	−0.0686568	−	0.0549824i
$280$		0			0
$281$	−64.2832	−	37.1139i	−0.228766	−	0.132078i	0.381237	−	0.924477i	$-0.375498\pi$
$281$	−64.2832	−	37.1139i	−0.228766	−	0.132078i	−0.610003	+	0.792399i	$0.708832\pi$
$282$	−43.6787	+	124.418i	−0.154889	+	0.441197i
$283$	11.3030			0.0399401			0.0199701	−	0.999801i	$-0.493643\pi$
$283$	11.3030			0.0399401			0.0199701	+	0.999801i	$0.493643\pi$
$284$			137.453i			0.483989i
$285$	−89.4613	−	31.4068i	−0.313899	−	0.110199i
$286$	−2.72473	+	4.71937i	−0.00952702	+	0.0165013i
$287$		0			0
$288$	−150.452	+	187.870i	−0.522403	+	0.652326i
$289$	−65.1449	−	112.834i	−0.225415	−	0.390430i
$290$	−28.5771	+	16.4990i	−0.0985416	+	0.0568930i
$291$	−289.225	−	336.783i	−0.993901	−	1.15733i
$292$	−24.1890	+	41.8966i	−0.0828391	+	0.143482i
$293$	144.131	−	83.2139i	0.491913	−	0.284006i	−0.233454	−	0.972368i	$-0.575003\pi$
$293$	144.131	−	83.2139i	0.491913	−	0.284006i	0.725368	+	0.688361i	$0.241670\pi$
$294$		0			0
$295$	−49.9767	+	86.5621i	−0.169412	+	0.293431i
$296$	−170.025	+	98.1639i	−0.574408	+	0.331635i
$297$	3.06261	−	5.75188i	0.0103118	−	0.0193666i
$298$	115.110	−	199.377i	0.386276	−	0.669050i
$299$		−	314.112i		−	1.05054i
$300$	129.262	−	24.3205i	0.430872	−	0.0810684i
$301$		0			0
$302$	152.916	−	88.2864i	0.506346	−	0.292339i
$303$	−46.6720	−	248.058i	−0.154033	−	0.818674i
$304$	70.7490	+	122.541i	0.232727	+	0.403095i
$305$	17.8535	+	10.3077i	0.0585361	+	0.0337958i
$306$	−154.805	+	60.3906i	−0.505897	+	0.197355i
$307$	382.982			1.24750			0.623749	−	0.781625i	$-0.285609\pi$
$307$	382.982			1.24750			0.623749	+	0.781625i	$0.285609\pi$
$308$		0			0
$309$	115.254	+	134.205i	0.372990	+	0.434321i
$310$	−2.30319	+	3.98924i	−0.00742964	+	0.0128685i
$311$		−	156.011i		−	0.501642i	−0.968033	−	0.250821i	$-0.919299\pi$
$311$		−	156.011i		−	0.501642i	0.968033	−	0.250821i	$-0.0807006\pi$
$312$	−73.2985	−	389.576i	−0.234931	−	1.24864i
$313$	−116.530			−0.372301			−0.186150	−	0.982521i	$-0.559601\pi$
$313$	−116.530			−0.372301			−0.186150	+	0.982521i	$0.559601\pi$
$314$			11.3661i			0.0361978i
$315$		0			0
$316$	41.6966			0.131951
$317$		−	187.863i		−	0.592626i	−0.955091	−	0.296313i	$-0.904243\pi$
$317$		−	187.863i		−	0.592626i	0.955091	−	0.296313i	$-0.0957572\pi$
$318$	−299.637	−	348.907i	−0.942254	−	1.09719i
$319$	4.71428			0.0147783
$320$	59.7329	+	34.4868i	0.186665	+	0.107771i
$321$	49.2772	+	261.905i	0.153512	+	0.815903i
$322$		0			0
$323$		−	345.412i		−	1.06939i
$324$	32.7843	+	146.400i	0.101186	+	0.451852i
$325$	−182.348	+	315.835i	−0.561069	+	0.971801i
$326$	329.900	−	190.468i	1.01196	−	0.584257i
$327$	369.254	+	429.971i	1.12922	+	1.31490i
$328$	−306.974	−	531.694i	−0.935895	−	1.62102i
$329$		0			0
$330$	−1.15411	−	0.405166i	−0.00349729	−	0.00122778i
$331$	−63.4321			−0.191638			−0.0958189	−	0.995399i	$-0.530547\pi$
$331$	−63.4321			−0.191638			−0.0958189	+	0.995399i	$0.530547\pi$
$332$	142.802	+	82.4466i	0.430125	+	0.248333i
$333$	−31.1229	+	203.655i	−0.0934620	+	0.611576i
$334$	82.3973	+	142.716i	0.246698	+	0.427294i
$335$	18.0127	+	10.3996i	0.0537692	+	0.0310437i
$336$		0			0
$337$	88.4049	+	153.122i	0.262329	+	0.454367i	0.966860	−	0.255306i	$-0.0821761\pi$
$337$	88.4049	+	153.122i	0.262329	+	0.454367i	−0.704531	+	0.709673i	$0.748843\pi$
$338$	86.7688	+	50.0960i	0.256712	+	0.148213i
$339$	64.7674	+	344.234i	0.191054	+	1.01544i
$340$	−13.4484	−	23.2933i	−0.0395541	−	0.0685097i
$341$	0.569926	−	0.329047i	0.00167134	−	0.000964948i
$342$	357.490	+	54.6323i	1.04529	+	0.159743i
$343$		0			0
$344$	−221.301	−	127.768i	−0.643316	−	0.371419i
$345$	69.2883	−	13.0366i	0.200836	−	0.0377871i
$346$	−20.4981			−0.0592431
$347$		−	243.303i		−	0.701161i	−0.936533	−	0.350580i	$-0.885984\pi$
$347$		−	243.303i		−	0.701161i	0.936533	−	0.350580i	$-0.114016\pi$
$348$	−82.3395	+	70.7122i	−0.236608	+	0.203196i
$349$	209.668	−	363.156i	0.600768	−	1.04056i	−0.391937	−	0.919992i	$-0.628195\pi$
$349$	209.668	−	363.156i	0.600768	−	1.04056i	0.992705	−	0.120568i	$-0.0384717\pi$
$350$		0			0
$351$	−367.175	−	195.504i	−1.04608	−	0.556990i
$352$	−3.22722	−	5.58970i	−0.00916823	−	0.0158798i
$353$	301.257	−	173.931i	0.853419	−	0.492722i	−0.00838407	−	0.999965i	$-0.502669\pi$
$353$	301.257	−	173.931i	0.853419	−	0.492722i	0.861803	+	0.507243i	$0.169335\pi$
$354$	126.285	−	359.720i	0.356738	−	1.01616i
$355$	42.7720	−	74.0833i	0.120484	−	0.208685i
$356$	−92.1379	+	53.1958i	−0.258814	+	0.149426i
$357$		0			0
$358$	37.3326	−	64.6620i	0.104281	−	0.180620i
$359$	392.233	−	226.456i	1.09257	−	0.630796i	0.158311	−	0.987389i	$-0.449395\pi$
$359$	392.233	−	226.456i	1.09257	−	0.630796i	0.934260	+	0.356593i	$0.116062\pi$
$360$	82.8925	−	32.3371i	0.230257	−	0.0898252i
$361$	−195.372	+	338.394i	−0.541196	+	0.937379i
$362$		−	351.415i		−	0.970760i
$363$	−236.384	−	275.254i	−0.651197	−	0.758274i
$364$		0			0
$365$	26.0744	−	15.0541i	0.0714368	−	0.0412440i
$366$	−74.1925	−	26.0464i	−0.202712	−	0.0711651i
$367$	−1.59980	−	2.77094i	−0.00435913	−	0.00755024i	0.863838	−	0.503770i	$-0.168054\pi$
$367$	−1.59980	−	2.77094i	−0.00435913	−	0.00755024i	−0.868197	+	0.496220i	$0.834721\pi$
$368$	−91.1218	−	52.6092i	−0.247613	−	0.142960i
$369$	−636.859	−	97.3260i	−1.72591	−	0.263756i
$370$	38.6706			0.104515
$371$		0			0
$372$	−5.01875	+	14.2958i	−0.0134913	+	0.0384295i
$373$	74.7215	−	129.421i	0.200326	−	0.346974i	−0.748308	−	0.663352i	$-0.769133\pi$
$373$	74.7215	−	129.421i	0.200326	−	0.346974i	0.948633	+	0.316377i	$0.102467\pi$
$374$		−	4.45602i		−	0.0119145i
$375$	−158.808	−	55.7521i	−0.423489	−	0.148672i
$376$	257.226			0.684112
$377$		−	300.939i		−	0.798247i
$378$		0			0
$379$	431.217			1.13778			0.568888	−	0.822415i	$-0.307374\pi$
$379$	431.217			1.13778			0.568888	+	0.822415i	$0.307374\pi$
$380$			58.5373i			0.154045i
$381$	33.3327	−	94.9472i	0.0874874	−	0.249205i
$382$	−269.428			−0.705308
$383$	155.685	+	89.8850i	0.406489	+	0.234687i	0.689280	−	0.724495i	$-0.257927\pi$
$383$	155.685	+	89.8850i	0.406489	+	0.234687i	−0.282791	+	0.959182i	$0.591260\pi$
$384$	54.5731	+	19.1587i	0.142117	+	0.0498925i
$385$		0			0
$386$		−	223.931i		−	0.580133i
$387$	−249.814	+	97.4547i	−0.645515	+	0.251821i
$388$	−137.039	+	237.359i	−0.353193	+	0.611749i
$389$	291.978	−	168.574i	0.750587	−	0.433352i	−0.0753189	−	0.997159i	$-0.523997\pi$
$389$	291.978	−	168.574i	0.750587	−	0.433352i	0.825906	+	0.563808i	$0.190664\pi$
$390$	−25.8640	+	73.6730i	−0.0663181	+	0.188905i
$391$	128.425	+	222.438i	0.328452	+	0.568896i
$392$		0			0
$393$	−162.725	+	139.746i	−0.414058	+	0.355588i
$394$	565.712			1.43582
$395$	−22.4733	−	12.9750i	−0.0568945	−	0.0328480i
$396$	−3.97700	−	0.607772i	−0.0100429	−	0.00153478i
$397$	266.853	+	462.203i	0.672174	+	1.16424i	0.977286	+	0.211923i	$0.0679725\pi$
$397$	266.853	+	462.203i	0.672174	+	1.16424i	−0.305113	+	0.952316i	$0.598694\pi$
$398$	−57.9737	−	33.4711i	−0.145663	−	0.0840983i
$399$		0			0
$400$	61.0811	+	105.796i	0.152703	+	0.264489i
$401$	525.012	+	303.116i	1.30926	+	0.755900i	0.981972	−	0.189025i	$-0.0605327\pi$
$401$	525.012	+	303.116i	1.30926	+	0.755900i	0.327286	+	0.944925i	$0.393866\pi$
$402$	−74.8539	−	26.2786i	−0.186204	−	0.0653697i
$403$	−21.0049	−	36.3816i	−0.0521214	−	0.0902769i
$404$	−134.958	+	77.9180i	−0.334054	+	0.192866i
$405$	27.8863	−	89.1071i	0.0688550	−	0.220018i
$406$		0			0
$407$	−4.78455	−	2.76236i	−0.0117556	−	0.00678712i
$408$	211.185	+	245.910i	0.517609	+	0.602720i
$409$	392.113			0.958711			0.479355	−	0.877621i	$-0.340870\pi$
$409$	392.113			0.958711			0.479355	+	0.877621i	$0.340870\pi$
$410$			120.929i			0.294949i
$411$	−120.242	−	639.077i	−0.292560	−	1.55493i
$412$	54.6090	−	94.5855i	0.132546	−	0.229577i
$413$		0			0
$414$	−250.529	+	97.7334i	−0.605142	+	0.236071i
$415$	−51.3107	−	88.8728i	−0.123640	−	0.214151i
$416$	−356.822	+	206.011i	−0.857745	+	0.495220i
$417$	316.663	−	59.5800i	0.759384	−	0.142878i
$418$	−4.84897	+	8.39867i	−0.0116004	+	0.0200925i
$419$	577.328	−	333.321i	1.37787	−	0.795515i	0.385969	−	0.922512i	$-0.373867\pi$
$419$	577.328	−	333.321i	1.37787	−	0.795515i	0.991903	+	0.126997i	$0.0405338\pi$
$420$		0			0
$421$	235.637	−	408.136i	0.559708	−	0.969443i	−0.437812	−	0.899067i	$-0.644246\pi$
$421$	235.637	−	408.136i	0.559708	−	0.969443i	0.997520	−	0.0703769i	$-0.0224202\pi$
$422$	−429.848	+	248.173i	−1.01860	+	0.588087i
$423$	168.727	−	210.690i	0.398881	−	0.498084i
$424$	−448.579	+	776.962i	−1.05797	+	1.83246i
$425$		−	298.211i		−	0.701674i
$426$	−108.080	+	307.862i	−0.253708	+	0.722681i
$427$		0			0
$428$	142.491	−	82.2673i	0.332923	−	0.192213i
$429$	8.46272	−	7.26769i	0.0197266	−	0.0169410i
$430$	25.1665	+	43.5896i	0.0585266	+	0.101371i
$431$	204.379	+	117.998i	0.474197	+	0.273778i	0.717995	−	0.696048i	$-0.245060\pi$
$431$	204.379	+	117.998i	0.474197	+	0.273778i	−0.243798	+	0.969826i	$0.578393\pi$
$432$	−118.211	+	73.7710i	−0.273636	+	0.170766i
$433$	−388.304			−0.896776			−0.448388	−	0.893839i	$-0.648002\pi$
$433$	−388.304			−0.896776			−0.448388	+	0.893839i	$0.648002\pi$
$434$		0			0
$435$	66.3826	−	12.4898i	0.152604	−	0.0287123i
$436$	174.958	−	303.036i	0.401280	−	0.695037i
$437$		−	558.999i		−	1.27917i
$438$	−87.1212	+	74.8187i	−0.198907	+	0.170819i
$439$	351.316			0.800264			0.400132	−	0.916458i	$-0.368964\pi$
$439$	351.316			0.800264			0.400132	+	0.916458i	$0.368964\pi$
$440$			2.38605i			0.00542283i
$441$		0			0
$442$	−284.453			−0.643559
$443$			53.1399i			0.119955i	0.998200	+	0.0599773i	$0.0191028\pi$
$443$			53.1399i			0.119955i	−0.998200	+	0.0599773i	$0.980897\pi$
$444$	125.001	−	23.5188i	0.281534	−	0.0529704i
$445$	66.2130			0.148793
$446$	111.355	+	64.2907i	0.249674	+	0.144150i
$447$	−357.521	+	307.035i	−0.799823	+	0.686878i
$448$		0			0
$449$			526.389i			1.17236i	0.810181	+	0.586179i	$0.199369\pi$
$449$			526.389i			1.17236i	−0.810181	+	0.586179i	$0.800631\pi$
$450$	308.639	+	47.1668i	0.685865	+	0.104815i
$451$	8.63832	−	14.9620i	0.0191537	−	0.0331752i
$452$	187.283	−	108.128i	0.414343	−	0.239221i
$453$	−355.215	+	66.8334i	−0.784138	+	0.147535i
$454$	258.447	+	447.643i	0.569266	+	0.985997i
$455$		0			0
$456$	−130.443	−	693.296i	−0.286060	−	1.52039i
$457$	−739.761			−1.61873			−0.809367	−	0.587303i	$-0.800190\pi$
$457$	−739.761			−1.61873			−0.809367	+	0.587303i	$0.800190\pi$
$458$	483.300	+	279.033i	1.05524	+	0.609243i
$459$	339.946	−	11.6738i	0.740624	−	0.0254332i
$460$	−21.7643	−	37.6968i	−0.0473136	−	0.0819496i
$461$	−284.624	−	164.328i	−0.617406	−	0.356460i	0.158452	−	0.987367i	$-0.449350\pi$
$461$	−284.624	−	164.328i	−0.617406	−	0.356460i	−0.775858	+	0.630907i	$0.782683\pi$
$462$		0			0
$463$	3.64605	+	6.31515i	0.00787484	+	0.0136396i	0.869936	−	0.493165i	$-0.164160\pi$
$463$	3.64605	+	6.31515i	0.00787484	+	0.0136396i	−0.862061	+	0.506804i	$0.830827\pi$
$464$	−87.3004	−	50.4029i	−0.188147	−	0.108627i
$465$	7.15346	−	6.14331i	0.0153838	−	0.0132114i
$466$	229.772	+	397.976i	0.493072	+	0.854026i
$467$	446.593	−	257.841i	0.956303	−	0.552122i	0.0612697	−	0.998121i	$-0.480485\pi$
$467$	446.593	−	257.841i	0.956303	−	0.552122i	0.895033	+	0.445999i	$0.147152\pi$
$468$	−38.7975	+	253.874i	−0.0829007	+	0.542466i
$469$		0			0
$470$	−43.8779	−	25.3329i	−0.0933572	−	0.0538998i
$471$	7.70697	−	21.9531i	0.0163630	−	0.0466095i
$472$	−743.700			−1.57563
$473$		−	7.19086i		−	0.0152027i
$474$	93.3906	+	32.7862i	0.197027	+	0.0691692i
$475$	−324.509	+	562.066i	−0.683177	+	1.18330i
$476$		0			0
$477$	342.152	+	877.070i	0.717301	+	1.83872i
$478$	−169.100	−	292.890i	−0.353767	−	0.612742i
$479$	250.854	−	144.830i	0.523703	−	0.302360i	−0.214746	−	0.976670i	$-0.568892\pi$
$479$	250.854	−	144.830i	0.523703	−	0.302360i	0.738448	+	0.674310i	$0.235559\pi$
$480$	−60.2521	−	70.1595i	−0.125525	−	0.146166i
$481$	−176.337	+	305.424i	−0.366605	+	0.634978i
$482$	−229.543	+	132.527i	−0.476231	+	0.274952i
$483$		0			0
$484$	−112.002	+	193.994i	−0.231410	+	0.400814i
$485$	147.720	−	85.2864i	0.304578	−	0.175848i
$486$	−41.6858	+	353.680i	−0.0857732	+	0.727736i
$487$	−252.275	+	436.953i	−0.518018	+	0.897234i	0.481763	+	0.876302i	$0.339997\pi$
$487$	−252.275	+	436.953i	−0.518018	+	0.897234i	−0.999781	+	0.0209323i	$0.993337\pi$
$488$			153.389i			0.314321i
$489$	−766.335	+	144.185i	−1.56715	+	0.294858i
$490$		0			0
$491$	−311.614	+	179.910i	−0.634651	+	0.366416i	−0.782551	−	0.622586i	$-0.786082\pi$
$491$	−311.614	+	179.910i	−0.634651	+	0.366416i	0.147900	+	0.989002i	$0.452749\pi$
$492$	73.5470	+	390.897i	0.149486	+	0.794506i
$493$	123.039	+	213.110i	0.249572	+	0.432271i
$494$	536.134	+	309.537i	1.08529	+	0.626594i
$495$	1.95437	+	1.56512i	0.00394822	+	0.00316186i
$496$	−14.0721			−0.0283711
$497$		0			0
$498$	255.014	+	296.946i	0.512076	+	0.596278i
$499$	323.521	−	560.354i	0.648338	−	1.12295i	−0.335181	−	0.942154i	$-0.608798\pi$
$499$	323.521	−	560.354i	0.648338	−	1.12295i	0.983520	−	0.180801i	$-0.0578691\pi$
$500$			103.913i			0.207826i
$501$	−62.3753	−	331.520i	−0.124502	−	0.661717i
$502$	−237.220			−0.472549
$503$			183.191i			0.364198i	0.983280	+	0.182099i	$0.0582891\pi$
$503$			183.191i			0.364198i	−0.983280	+	0.182099i	$0.941711\pi$
$504$		0			0
$505$	96.9847			0.192049
$506$		−	7.21143i		−	0.0142518i
$507$	−133.621	−	155.593i	−0.263553	−	0.306889i
$508$	−62.1269			−0.122297
$509$	751.000	+	433.590i	1.47544	+	0.851846i	0.999616	−	0.0276937i	$-0.00881632\pi$
$509$	751.000	+	433.590i	1.47544	+	0.851846i	0.475825	+	0.879540i	$0.342150\pi$
$510$	−11.8056	−	62.7460i	−0.0231483	−	0.123031i
$511$		0			0
$512$			315.064i			0.615359i
$513$	−653.431	−	347.921i	−1.27374	−	0.678209i
$514$	−55.4523	+	96.0462i	−0.107884	+	0.186860i
$515$	−58.8654	+	33.9860i	−0.114302	+	0.0659922i
$516$	107.860	+	125.595i	0.209031	+	0.243402i
$517$	3.61921	+	6.26865i	0.00700040	+	0.0121251i
$518$		0			0
$519$	39.5911	+	13.8991i	0.0762835	+	0.0267805i
$520$	152.315			0.292913
$521$	−60.2047	−	34.7592i	−0.115556	−	0.0667163i	0.441108	−	0.897454i	$-0.354586\pi$
$521$	−60.2047	−	34.7592i	−0.115556	−	0.0667163i	−0.556664	+	0.830738i	$0.687919\pi$
$522$	−240.022	+	93.6348i	−0.459813	+	0.179377i
$523$	356.425	+	617.347i	0.681502	+	1.18040i	0.974523	+	0.224290i	$0.0720062\pi$
$523$	356.425	+	617.347i	0.681502	+	1.18040i	−0.293021	+	0.956106i	$0.594661\pi$
$524$	114.686	+	66.2137i	0.218866	+	0.126362i
$525$		0			0
$526$	−8.53426	−	14.7818i	−0.0162248	−	0.0281022i
$527$	29.7493	+	17.1757i	0.0564502	+	0.0325915i
$528$	−0.690924	−	3.67221i	−0.00130857	−	0.00695494i
$529$	−56.6631	−	98.1434i	−0.107114	−	0.185526i
$530$	153.038	−	88.3566i	0.288751	−	0.166711i
$531$	−487.827	+	609.152i	−0.918695	+	1.14718i
$532$		0			0
$533$	−955.109	−	551.432i	−1.79195	−	1.03458i
$534$	−248.195	+	46.6978i	−0.464785	+	0.0874490i
$535$	−102.398			−0.191399
$536$			154.756i			0.288724i
$537$	−115.951	+	99.5776i	−0.215924	+	0.185433i
$538$	225.052	−	389.801i	0.418312	−	0.724537i
$539$		0			0
$540$	−57.6110	+	1.97837i	−0.106687	+	0.00366366i
$541$	180.101	+	311.944i	0.332904	+	0.576607i	0.983080	−	0.183177i	$-0.0586381\pi$
$541$	180.101	+	311.944i	0.332904	+	0.576607i	−0.650176	+	0.759784i	$0.725305\pi$
$542$	−429.088	+	247.734i	−0.791676	+	0.457074i
$543$	−238.283	+	678.741i	−0.438826	+	1.24998i
$544$	168.456	−	291.774i	0.309661	−	0.536349i
$545$	−188.595	+	108.885i	−0.346046	+	0.199790i
$546$		0			0
$547$	−47.0212	+	81.4432i	−0.0859620	+	0.148891i	−0.905801	−	0.423704i	$-0.860730\pi$
$547$	−47.0212	+	81.4432i	−0.0859620	+	0.148891i	0.819839	+	0.572595i	$0.194063\pi$
$548$	−347.695	+	200.742i	−0.634479	+	0.366317i
$549$	125.638	+	100.615i	0.228849	+	0.183269i
$550$	−4.18636	+	7.25099i	−0.00761157	+	0.0131836i
$551$		−	535.556i		−	0.971972i
$552$	341.772	+	397.970i	0.619151	+	0.720959i
$553$		0			0
$554$	167.562	−	96.7422i	0.302459	−	0.174625i
$555$	−74.6905	−	26.2212i	−0.134577	−	0.0472455i
$556$	−99.4676	−	172.283i	−0.178899	−	0.309861i
$557$	516.609	+	298.264i	0.927484	+	0.535483i	0.886015	−	0.463657i	$-0.153463\pi$
$557$	516.609	+	298.264i	0.927484	+	0.535483i	0.0414691	+	0.999140i	$0.486796\pi$
$558$	−22.4816	+	28.0729i	−0.0402897	+	0.0503099i
$559$	−459.033			−0.821168
$560$		0			0
$561$	−3.02148	+	8.60660i	−0.00538588	+	0.0153415i
$562$	−54.3922	+	94.2101i	−0.0967833	+	0.167634i
$563$		−	724.219i		−	1.28636i	−0.765716	−	0.643179i	$-0.777615\pi$
$563$		−	724.219i		−	1.28636i	0.765716	−	0.643179i	$-0.222385\pi$
$564$	−157.240	−	55.2015i	−0.278794	−	0.0978751i
$565$	−134.587			−0.238207
$566$		−	16.5652i		−	0.0292671i
$567$		0			0
$568$	636.487			1.12058
$569$			328.919i			0.578065i	0.957319	+	0.289032i	$0.0933335\pi$
$569$			328.919i			0.578065i	−0.957319	+	0.289032i	$0.906666\pi$
$570$	−46.0281	+	131.110i	−0.0807510	+	0.230017i
$571$	7.51403			0.0131594			0.00657971	−	0.999978i	$-0.497906\pi$
$571$	7.51403			0.0131594			0.00657971	+	0.999978i	$0.497906\pi$
$572$	−5.96438	−	3.44354i	−0.0104272	−	0.00602017i
$573$	520.387	+	182.690i	0.908179	+	0.318830i
$574$		0			0
$575$		−	482.612i		−	0.839325i
$576$	420.350	+	336.629i	0.729774	+	0.584425i
$577$	367.284	−	636.154i	0.636540	−	1.10252i	−0.349647	−	0.936882i	$-0.613698\pi$
$577$	367.284	−	636.154i	0.636540	−	1.10252i	0.986187	−	0.165638i	$-0.0529683\pi$
$578$	−165.364	+	95.4729i	−0.286097	+	0.165178i
$579$	−151.840	+	432.512i	−0.262245	+	0.746999i
$580$	−20.8515	−	36.1159i	−0.0359509	−	0.0622688i
$581$		0			0
$582$	−493.571	+	423.873i	−0.848061	+	0.728304i
$583$	−25.2463			−0.0433041
$584$	194.006	+	112.009i	0.332202	+	0.191797i
$585$	99.9103	−	124.758i	0.170787	−	0.213262i
$586$	−121.954	−	211.230i	−0.208112	−	0.360461i
$587$	−125.855	−	72.6624i	−0.214404	−	0.123786i	0.388953	−	0.921258i	$-0.372837\pi$
$587$	−125.855	−	72.6624i	−0.214404	−	0.123786i	−0.603356	+	0.797472i	$0.706170\pi$
$588$		0			0
$589$	−37.3807	−	64.7453i	−0.0634647	−	0.109924i
$590$	126.861	+	73.2432i	0.215019	+	0.124141i
$591$	−1092.64	−	383.590i	−1.84881	−	0.649052i
$592$	59.0677	+	102.308i	0.0997765	+	0.172818i
$593$	−248.428	+	143.430i	−0.418934	+	0.241872i	−0.694621	−	0.719376i	$-0.744428\pi$
$593$	−248.428	+	143.430i	−0.418934	+	0.241872i	0.275687	+	0.961247i	$0.411095\pi$
$594$	−8.42965	−	4.48840i	−0.0141913	−	0.00755623i
$595$		0			0
$596$	251.974	+	145.477i	0.422776	+	0.244090i
$597$	89.2778	+	103.958i	0.149544	+	0.174134i
$598$	−460.346			−0.769809
$599$		−	699.608i		−	1.16796i	−0.811768	−	0.583980i	$-0.801495\pi$
$599$		−	699.608i		−	1.16796i	0.811768	−	0.583980i	$-0.198505\pi$
$600$	−112.618	−	598.557i	−0.187697	−	0.997596i
$601$	−58.2075	+	100.818i	−0.0968511	+	0.167751i	−0.910380	−	0.413774i	$-0.864210\pi$
$601$	−58.2075	+	100.818i	−0.0968511	+	0.167751i	0.813529	+	0.581525i	$0.197544\pi$
$602$		0			0
$603$	126.758	+	101.512i	0.210212	+	0.168345i
$604$	111.577	+	193.257i	0.184730	+	0.319962i
$605$	120.732	−	69.7048i	0.199558	−	0.115215i
$606$	−363.541	+	68.4000i	−0.599903	+	0.112871i
$607$	321.155	−	556.257i	0.529086	−	0.916404i	−0.470339	−	0.882486i	$-0.655868\pi$
$607$	321.155	−	556.257i	0.529086	−	0.916404i	0.999425	−	0.0339178i	$-0.0107985\pi$
$608$	−635.007	+	366.621i	−1.04442	+	0.602996i
$609$		0			0
$610$	15.1065	−	26.1652i	0.0247647	−	0.0428937i
$611$	400.163	−	231.034i	0.654932	−	0.378125i
$612$	−76.3222	−	195.643i	−0.124709	−	0.319679i
$613$	257.842	−	446.595i	0.420623	−	0.728540i	−0.575378	−	0.817888i	$-0.695145\pi$
$613$	257.842	−	446.595i	0.420623	−	0.728540i	0.996000	+	0.0893481i	$0.0284783\pi$
$614$		−	561.278i		−	0.914133i
$615$	81.9978	−	233.569i	0.133330	−	0.379786i
$616$		0			0
$617$	352.937	−	203.768i	0.572021	−	0.330257i	−0.185935	−	0.982562i	$-0.559531\pi$
$617$	352.937	−	203.768i	0.572021	−	0.330257i	0.757956	+	0.652305i	$0.226198\pi$
$618$	196.684	−	168.910i	0.318259	−	0.273317i
$619$	−21.1760	−	36.6779i	−0.0342100	−	0.0592535i	0.848413	−	0.529334i	$-0.177558\pi$
$619$	−21.1760	−	36.6779i	−0.0342100	−	0.0592535i	−0.882624	+	0.470081i	$0.844225\pi$
$620$	−5.04163	−	2.91079i	−0.00813167	−	0.00469482i
$621$	550.154	−	18.8924i	0.885916	−	0.0304225i
$622$	−228.641			−0.367590
$623$		0			0
$624$	−234.418	+	44.1055i	−0.375670	+	0.0706820i
$625$	−263.556	+	456.492i	−0.421689	+	0.730387i
$626$			170.780i			0.272812i
$627$	15.0604	−	12.9337i	0.0240198	−	0.0206279i
$628$	−14.3646			−0.0228736
$629$		−	288.382i		−	0.458476i
$630$		0			0
$631$	−534.410			−0.846926			−0.423463	−	0.905914i	$-0.639186\pi$
$631$	−534.410			−0.846926			−0.423463	+	0.905914i	$0.639186\pi$
$632$		−	193.080i		−	0.305506i
$633$	998.508	−	187.869i	1.57742	−	0.296791i
$634$	−275.321			−0.434261
$635$	33.4847	+	19.3324i	0.0527318	+	0.0304447i
$636$	440.951	−	378.684i	0.693319	−	0.595414i
$637$		0			0
$638$		−	6.90900i		−	0.0108292i
$639$	417.501	−	521.336i	0.653367	−	0.815862i
$640$	−11.1117	+	19.2461i	−0.0173621	+	0.0300720i
$641$	−303.746	+	175.368i	−0.473862	+	0.273584i	−0.717855	−	0.696193i	$-0.754876\pi$
$641$	−303.746	+	175.368i	−0.473862	+	0.273584i	0.243993	+	0.969777i	$0.421543\pi$
$642$	383.834	−	72.2181i	0.597872	−	0.112489i
$643$	329.068	+	569.963i	0.511770	+	0.886412i	0.999907	+	0.0136450i	$0.00434346\pi$
$643$	329.068	+	569.963i	0.511770	+	0.886412i	−0.488137	+	0.872767i	$0.662323\pi$
$644$		0			0
$645$	−19.0512	−	101.256i	−0.0295367	−	0.156986i
$646$	−506.218			−0.783619
$647$	−482.718	−	278.697i	−0.746087	−	0.430753i	0.0781915	−	0.996938i	$-0.475085\pi$
$647$	−482.718	−	278.697i	−0.746087	−	0.430753i	−0.824278	+	0.566185i	$0.808419\pi$
$648$	677.917	−	151.810i	1.04617	−	0.234275i
$649$	−10.4640	−	18.1241i	−0.0161232	−	0.0279262i
$650$	462.871	+	267.239i	0.712110	+	0.411137i
$651$		0			0
$652$	240.715	+	416.930i	0.369194	+	0.639464i
$653$	158.002	+	91.2224i	0.241963	+	0.139697i	0.616079	−	0.787685i	$-0.288720\pi$
$653$	158.002	+	91.2224i	0.241963	+	0.139697i	−0.374116	+	0.927382i	$0.622054\pi$
$654$	630.143	−	541.159i	0.963521	−	0.827461i
$655$	−41.2082	−	71.3747i	−0.0629133	−	0.108969i
$656$	−319.934	+	184.714i	−0.487704	+	0.281576i
$657$	219.002	−	85.4347i	0.333337	−	0.130038i
$658$		0			0
$659$	−10.7149	−	6.18625i	−0.0162593	−	0.00938733i	0.491848	−	0.870681i	$-0.336321\pi$
$659$	−10.7149	−	6.18625i	−0.0162593	−	0.00938733i	−0.508108	+	0.861294i	$0.669655\pi$
$660$	0.512053	−	1.45857i	0.000775837	−	0.00220995i
$661$	531.258			0.803719			0.401860	−	0.915701i	$-0.368364\pi$
$661$	531.258			0.803719			0.401860	+	0.915701i	$0.368364\pi$
$662$			92.9628i			0.140427i
$663$	549.407	+	192.878i	0.828669	+	0.290917i
$664$	381.776	−	661.255i	0.574963	−	0.995866i
$665$		0			0
$666$	298.466	+	45.6120i	0.448146	+	0.0684865i
$667$	199.121	+	344.887i	0.298532	+	0.517072i
$668$	−180.366	+	104.134i	−0.270009	+	0.155890i
$669$	−171.483	−	199.680i	−0.256327	−	0.298476i
$670$	15.2411	−	26.3984i	0.0227480	−	0.0394006i
$671$	−3.73811	+	2.15820i	−0.00557096	+	0.00321639i
$672$		0			0
$673$	−29.8818	+	51.7568i	−0.0444009	+	0.0769046i	−0.887372	−	0.461055i	$-0.847471\pi$
$673$	−29.8818	+	51.7568i	−0.0444009	+	0.0769046i	0.842971	+	0.537959i	$0.180805\pi$
$674$	224.407	−	129.561i	0.332948	−	0.192228i
$675$	−564.139	−	300.378i	−0.835762	−	0.445004i
$676$	−63.3117	+	109.659i	−0.0936564	+	0.162218i
$677$			920.447i			1.35960i	0.733399	+	0.679799i	$0.237933\pi$
$677$			920.447i			1.35960i	−0.733399	+	0.679799i	$0.762067\pi$
$678$	504.491	−	94.9197i	0.744088	−	0.140000i
$679$		0			0
$680$	−107.862	+	62.2739i	−0.158620	+	0.0915793i
$681$	−195.646	−	1039.84i	−0.287292	−	1.52694i
$682$	−0.482234	−	0.835254i	−0.000707088	−	0.00122471i
$683$	−487.711	−	281.580i	−0.714071	−	0.412269i	0.0984954	−	0.995138i	$-0.468597\pi$
$683$	−487.711	−	281.580i	−0.714071	−	0.412269i	−0.812567	+	0.582868i	$0.801930\pi$
$684$	−69.0447	+	451.799i	−0.100943	+	0.660525i
$685$	249.864			0.364764
$686$		0			0
$687$	−744.267	−	866.648i	−1.08336	−	1.26150i
$688$	−76.8813	+	133.162i	−0.111746	+	0.193550i
$689$			1611.61i			2.33906i
$690$	−19.1057	−	101.545i	−0.0276894	−	0.147167i
$691$	−421.308			−0.609708			−0.304854	−	0.952399i	$-0.598608\pi$
$691$	−421.308			−0.609708			−0.304854	+	0.952399i	$0.598608\pi$
$692$		−	25.9057i		−	0.0374360i
$693$		0			0
$694$	−356.572			−0.513792
$695$			123.808i			0.178140i
$696$	327.439	+	381.280i	0.470458	+	0.547816i
$697$	901.813			1.29385
$698$	−532.222	−	307.278i	−0.762495	−	0.440227i
$699$	−173.939	−	924.472i	−0.248840	−	1.32256i
$700$		0			0
$701$			523.850i			0.747289i	0.927572	+	0.373645i	$0.121892\pi$
$701$			523.850i			0.747289i	−0.927572	+	0.373645i	$0.878108\pi$
$702$	−286.520	+	538.112i	−0.408148	+	0.766541i
$703$	−313.812	+	543.539i	−0.446390	+	0.773170i
$704$	−12.5067	+	7.22073i	−0.0177652	+	0.0102567i
$705$	67.5706	+	78.6813i	0.0958448	+	0.111605i
$706$	−254.904	−	441.506i	−0.361053	−	0.625363i
$707$		0			0
$708$	454.617	+	159.600i	0.642114	+	0.225424i
$709$	67.9357			0.0958190			0.0479095	−	0.998852i	$-0.484744\pi$
$709$	67.9357			0.0958190			0.0479095	+	0.998852i	$0.484744\pi$
$710$	−108.573	−	62.6844i	−0.152919	−	0.0882878i
$711$	−158.148	−	126.650i	−0.222431	−	0.178129i
$712$	246.328	+	426.652i	0.345966	+	0.599230i
$713$	48.1449	+	27.7964i	0.0675243	+	0.0389852i
$714$		0			0
$715$	2.14309	+	3.71194i	0.00299733	+	0.00519152i
$716$	81.7204	+	47.1813i	0.114135	+	0.0658957i
$717$	128.010	+	680.365i	0.178536	+	0.948905i
$718$	−331.882	−	574.836i	−0.462231	−	0.800607i
$719$	−766.286	+	442.415i	−1.06577	+	0.615321i	−0.927022	−	0.375008i	$-0.877640\pi$
$719$	−766.286	+	442.415i	−1.06577	+	0.615321i	−0.138745	+	0.990328i	$0.544307\pi$
$720$	−19.4580	−	49.8785i	−0.0270250	−	0.0692757i
$721$		0			0
$722$	495.932	+	286.327i	0.686887	+	0.396574i
$723$	533.214	−	100.324i	0.737502	−	0.138760i
$724$	444.121			0.613427
$725$		−	462.373i		−	0.637755i
$726$	−403.397	+	346.433i	−0.555643	+	0.477180i
$727$	228.413	−	395.623i	0.314186	−	0.544186i	−0.665078	−	0.746774i	$-0.731602\pi$
$727$	228.413	−	395.623i	0.314186	−	0.544186i	0.979264	+	0.202588i	$0.0649352\pi$
$728$		0			0
$729$	320.332	−	654.850i	0.439413	−	0.898285i
$730$	−22.0625	−	38.2133i	−0.0302225	−	0.0523470i
$731$	325.064	−	187.676i	0.444684	−	0.256738i
$732$	32.9177	−	93.7651i	0.0449695	−	0.128094i
$733$	−52.6692	+	91.2258i	−0.0718543	+	0.124455i	−0.899714	−	0.436480i	$-0.856225\pi$
$733$	−52.6692	+	91.2258i	−0.0718543	+	0.124455i	0.827860	+	0.560935i	$0.189558\pi$
$734$	−4.06094	+	2.34458i	−0.00553261	+	0.00319426i
$735$		0			0
$736$	272.621	−	472.193i	0.370409	−	0.641567i
$737$	−3.77144	+	2.17744i	−0.00511728	+	0.00295446i
$738$	−142.636	+	933.348i	−0.193273	+	1.26470i
$739$	169.442	−	293.482i	0.229285	−	0.397133i	−0.728311	−	0.685246i	$-0.759695\pi$
$739$	169.442	−	293.482i	0.229285	−	0.397133i	0.957596	+	0.288113i	$0.0930279\pi$
$740$			48.8723i			0.0660436i
$741$	−825.631	−	961.390i	−1.11421	−	1.29742i
$742$		0			0
$743$	200.529	−	115.776i	0.269891	−	0.155822i	−0.358947	−	0.933358i	$-0.616864\pi$
$743$	200.529	−	115.776i	0.269891	−	0.155822i	0.628838	+	0.777536i	$0.283531\pi$
$744$	66.1978	+	23.2398i	0.0889755	+	0.0312362i
$745$	−90.5381	−	156.817i	−0.121528	−	0.210492i
$746$	−189.673	−	109.508i	−0.254254	−	0.146793i
$747$	−291.198	−	746.454i	−0.389823	−	0.999269i
$748$	5.63156			0.00752883
$749$		0			0
$750$	−81.7073	+	232.741i	−0.108943	+	0.310321i
$751$	61.2911	−	106.159i	0.0816127	−	0.141357i	−0.822330	−	0.569011i	$-0.807326\pi$
$751$	61.2911	−	106.159i	0.0816127	−	0.141357i	0.903943	+	0.427653i	$0.140660\pi$
$752$		−	154.780i		−	0.205824i
$753$	458.179	+	160.851i	0.608471	+	0.213613i
$754$	−441.040			−0.584934
$755$		−	138.880i		−	0.183947i
$756$		0			0
$757$	162.273			0.214363			0.107181	−	0.994239i	$-0.465817\pi$
$757$	162.273			0.214363			0.107181	+	0.994239i	$0.465817\pi$
$758$		−	631.969i		−	0.833732i
$759$	−4.88982	+	13.9285i	−0.00644246	+	0.0183512i
$760$	271.062			0.356660
$761$	−301.090	−	173.834i	−0.395650	−	0.228429i	0.288955	−	0.957343i	$-0.406692\pi$
$761$	−301.090	−	173.834i	−0.395650	−	0.228429i	−0.684605	+	0.728914i	$0.740025\pi$
$762$	−139.150	−	48.8506i	−0.182611	−	0.0641084i
$763$		0			0
$764$		−	340.505i		−	0.445687i
$765$	−19.7439	+	129.196i	−0.0258091	+	0.168884i
$766$	131.731	−	228.164i	0.171972	−	0.297865i
$767$	−1156.96	+	667.973i	−1.50843	+	0.870891i
$768$	265.925	−	757.480i	0.346257	−	0.986302i
$769$	−21.9448	−	38.0094i	−0.0285367	−	0.0494271i	0.851404	−	0.524510i	$-0.175751\pi$
$769$	−21.9448	−	38.0094i	−0.0285367	−	0.0494271i	−0.879941	+	0.475083i	$0.842418\pi$
$770$		0			0
$771$	172.229	−	147.908i	0.223384	−	0.191839i
$772$	283.006			0.366588
$773$	31.3486	+	18.0991i	0.0405545	+	0.0234141i	0.520140	−	0.854081i	$-0.325880\pi$
$773$	31.3486	+	18.0991i	0.0405545	+	0.0234141i	−0.479586	+	0.877495i	$0.659213\pi$
$774$	142.824	+	366.114i	0.184528	+	0.473016i
$775$	−32.2727	−	55.8979i	−0.0416421	−	0.0721263i
$776$	1099.11	+	634.571i	1.41638	+	0.817746i
$777$		0			0
$778$	−247.053	−	427.908i	−0.317549	−	0.550010i
$779$	−1699.73	−	981.339i	−2.18194	−	1.25974i
$780$	−93.1086	−	32.6872i	−0.119370	−	0.0419067i
$781$	8.95546	+	15.5113i	0.0114667	+	0.0198608i
$782$	325.994	−	188.213i	0.416872	−	0.240681i
$783$	527.082	−	18.1001i	0.673157	−	0.0231164i
$784$		0			0
$785$	7.74211	+	4.46991i	0.00986256	+	0.00569415i
$786$	204.805	+	238.481i	0.260566	+	0.303411i
$787$	669.648			0.850887			0.425443	−	0.904985i	$-0.360118\pi$
$787$	669.648			0.850887			0.425443	+	0.904985i	$0.360118\pi$
$788$			714.951i			0.907299i
$789$	6.46050	+	34.3371i	0.00818821	+	0.0435197i
$790$	−19.0154	+	32.9357i	−0.0240702	+	0.0416908i
$791$		0			0
$792$	−2.81434	+	18.4158i	−0.00355346	+	0.0232523i
$793$	137.770	+	238.625i	0.173733	+	0.300914i
$794$	677.380	−	391.086i	0.853124	−	0.492551i
$795$	−355.497	+	66.8866i	−0.447166	+	0.0841341i
$796$	42.3011	−	73.2677i	0.0531421	−	0.0920448i
$797$	−12.4445	+	7.18485i	−0.0156142	+	0.00901487i	−0.507787	−	0.861483i	$-0.669536\pi$
$797$	−12.4445	+	7.18485i	−0.0156142	+	0.00901487i	0.492173	+	0.870498i	$0.336203\pi$
$798$		0			0
$799$	−188.917	+	327.214i	−0.236442	+	0.409529i
$800$	−548.233	+	316.523i	−0.685291	+	0.395653i
$801$	511.041	+	78.0982i	0.638004	+	0.0975009i
$802$	444.231	−	769.431i	0.553904	−	0.959390i
$803$			6.30395i			0.00785049i
$804$	33.2111	−	94.6010i	0.0413074	−	0.117663i
$805$		0			0
$806$	−53.3190	+	30.7837i	−0.0661526	+	0.0381932i
$807$	−698.987	+	600.282i	−0.866155	+	0.743844i
$808$	360.806	+	624.934i	0.446542	+	0.773433i
$809$	134.305	+	77.5408i	0.166013	+	0.0958478i	0.580705	−	0.814114i	$-0.302777\pi$
$809$	134.305	+	77.5408i	0.166013	+	0.0958478i	−0.414691	+	0.909962i	$0.636110\pi$
$810$	−130.591	−	40.8687i	−0.161223	−	0.0504552i
$811$	758.588			0.935374			0.467687	−	0.883894i	$-0.345087\pi$
$811$	758.588			0.935374			0.467687	+	0.883894i	$0.345087\pi$
$812$		0			0
$813$	996.743	−	187.537i	1.22601	−	0.230672i
$814$	−4.04837	+	7.01198i	−0.00497343	+	0.00861422i
$815$		−	299.618i		−	0.367630i
$816$	147.970	−	127.075i	0.181336	−	0.155729i
$817$	−816.903			−0.999881
$818$		−	574.660i		−	0.702518i
$819$		0			0
$820$	−152.831			−0.186379
$821$			225.364i			0.274500i	0.990536	+	0.137250i	$0.0438263\pi$
$821$			225.364i			0.274500i	−0.990536	+	0.137250i	$0.956174\pi$
$822$	−936.598	+	176.220i	−1.13941	+	0.214380i
$823$	599.694			0.728668			0.364334	−	0.931268i	$-0.381297\pi$
$823$	599.694			0.728668			0.364334	+	0.931268i	$0.381297\pi$
$824$	−437.986	−	252.871i	−0.531537	−	0.306883i
$825$	13.0024	−	11.1663i	0.0157605	−	0.0135349i
$826$		0			0
$827$			634.083i			0.766727i	0.923598	+	0.383363i	$0.125234\pi$
$827$			634.083i			0.766727i	−0.923598	+	0.383363i	$0.874766\pi$
$828$	−123.516	−	316.620i	−0.149174	−	0.382392i
$829$	376.723	−	652.503i	0.454431	−	0.787097i	−0.544225	−	0.838940i	$-0.683176\pi$
$829$	376.723	−	652.503i	0.454431	−	0.787097i	0.998655	+	0.0518425i	$0.0165094\pi$
$830$	−130.247	+	75.1983i	−0.156924	+	0.0906003i
$831$	−389.236	+	73.2346i	−0.468395	+	0.0881282i
$832$	460.940	+	798.371i	0.554014	+	0.959581i
$833$		0			0
$834$	−87.3173	−	464.085i	−0.104697	−	0.556457i
$835$	129.616			0.155229
$836$	−10.6143	−	6.12817i	−0.0126965	−	0.00733035i
$837$	62.4575	−	38.9774i	0.0746206	−	0.0465680i
$838$	−488.497	−	846.102i	−0.582932	−	1.00967i
$839$	−953.473	−	550.488i	−1.13644	−	0.656124i	−0.190893	−	0.981611i	$-0.561138\pi$
$839$	−953.473	−	550.488i	−1.13644	−	0.656124i	−0.945547	+	0.325487i	$0.894472\pi$
$840$		0			0
$841$	−229.730	−	397.904i	−0.273163	−	0.473132i
$842$	−598.142	−	345.338i	−0.710383	−	0.410140i
$843$	168.937	−	145.081i	0.200399	−	0.172101i
$844$	−313.643	−	543.246i	−0.371615	−	0.643656i
$845$	68.2465	−	39.4021i	0.0807651	−	0.0466297i
$846$	−308.776	−	247.277i	−0.364983	−	0.292289i
$847$		0			0
$848$	467.518	+	269.922i	0.551318	+	0.318304i
$849$	−11.2323	+	31.9948i	−0.0132300	+	0.0376853i
$850$	−437.043			−0.514168
$851$		−	466.704i		−	0.548418i
$852$	−389.079	−	136.592i	−0.456665	−	0.160319i
$853$	−161.623	+	279.939i	−0.189476	+	0.328181i	−0.945076	−	0.326852i	$-0.894012\pi$
$853$	−161.623	+	279.939i	−0.189476	+	0.328181i	0.755600	+	0.655033i	$0.227345\pi$
$854$		0			0
$855$	177.802	−	222.022i	0.207956	−	0.259675i
$856$	−380.946	−	659.817i	−0.445030	−	0.770815i
$857$	−1128.73	+	651.675i	−1.31708	+	0.760414i	−0.983257	−	0.182224i	$-0.941671\pi$
$857$	−1128.73	+	651.675i	−1.31708	+	0.760414i	−0.333818	+	0.942637i	$0.608337\pi$
$858$	−10.6511	−	12.4025i	−0.0124139	−	0.0144552i
$859$	−87.8268	+	152.121i	−0.102243	+	0.177090i	−0.912609	−	0.408835i	$-0.865935\pi$
$859$	−87.8268	+	152.121i	−0.102243	+	0.177090i	0.810365	+	0.585925i	$0.199269\pi$
$860$	−55.0889	+	31.8056i	−0.0640568	+	0.0369832i
$861$		0			0
$862$	172.932	−	299.527i	0.200617	−	0.347479i
$863$	289.608	−	167.205i	0.335582	−	0.193749i	−0.322734	−	0.946490i	$-0.604602\pi$
$863$	289.608	−	167.205i	0.335582	−	0.193749i	0.658317	+	0.752741i	$0.271269\pi$
$864$	−382.281	−	612.568i	−0.442455	−	0.708991i
$865$	−8.06122	+	13.9624i	−0.00931933	+	0.0161416i
$866$			569.078i			0.657134i
$867$	384.129	−	72.2736i	0.443056	−	0.0833606i
$868$		0			0
$869$	4.70539	−	2.71666i	0.00541472	−	0.00312619i
$870$	−18.3044	−	97.2868i	−0.0210396	−	0.111824i
$871$	138.998	+	240.752i	0.159585	+	0.276409i
$872$	−1403.23	−	810.157i	−1.60921	−	0.929080i
$873$	1240.72	−	484.017i	1.42122	−	0.554429i
$874$	−819.240			−0.937345
$875$		0			0
$876$	−94.5564	−	110.105i	−0.107941	−	0.125690i
$877$	−395.615	+	685.225i	−0.451100	+	0.781328i	−0.998455	−	0.0555725i	$-0.982302\pi$
$877$	−395.615	+	685.225i	−0.451100	+	0.781328i	0.547355	+	0.836901i	$0.315635\pi$
$878$		−	514.870i		−	0.586412i
$879$	92.3199	+	490.674i	0.105028	+	0.558218i
$880$	1.43574			0.00163153
$881$			307.622i			0.349174i	0.984642	+	0.174587i	$0.0558591\pi$
$881$			307.622i			0.349174i	−0.984642	+	0.174587i	$0.944141\pi$
$882$		0			0
$883$	−1744.35			−1.97548			−0.987742	−	0.156094i	$-0.950110\pi$
$883$	−1744.35			−1.97548			−0.987742	+	0.156094i	$0.950110\pi$
$884$		−	359.494i		−	0.406668i
$885$	−195.362	−	227.486i	−0.220748	−	0.257046i
$886$	77.8791			0.0878996
$887$	−152.854	−	88.2501i	−0.172327	−	0.0994928i	0.411356	−	0.911475i	$-0.365055\pi$
$887$	−152.854	−	88.2501i	−0.172327	−	0.0994928i	−0.583682	+	0.811982i	$0.698389\pi$
$888$	−108.906	−	578.827i	−0.122642	−	0.651832i
$889$		0			0
$890$		−	97.0382i		−	0.109032i
$891$	13.2380	+	14.3850i	0.0148575	+	0.0161448i
$892$	−81.2511	+	140.731i	−0.0910887	+	0.157770i
$893$	712.138	−	411.153i	0.797466	−	0.460417i
$894$	449.974	+	523.964i	0.503326	+	0.586089i
$895$	−29.3634	−	50.8588i	−0.0328082	−	0.0568255i
$896$		0			0
$897$	889.136	+	312.145i	0.991233	+	0.347988i
$898$	771.448			0.859074
$899$	46.1258	+	26.6307i	0.0513079	+	0.0296226i
$900$	−59.6098	+	390.061i	−0.0662331	+	0.433401i
$901$	−658.908	−	1141.26i	−0.731308	−	1.26666i
$902$	−21.9275	−	12.6599i	−0.0243099	−	0.0140353i
$903$		0			0
$904$	−500.696	−	867.230i	−0.553867	−	0.959325i
$905$	−239.369	−	138.200i	−0.264496	−	0.152707i
$906$	97.9475	+	520.584i	0.108110	+	0.574596i
$907$	−847.482	−	1467.88i	−0.934379	−	1.61839i	−0.775737	−	0.631056i	$-0.782622\pi$
$907$	−847.482	−	1467.88i	−0.934379	−	1.61839i	−0.158642	−	0.987336i	$-0.550711\pi$
$908$	−565.735	+	326.627i	−0.623056	+	0.359721i
$909$	748.542	+	114.393i	0.823478	+	0.125845i
$910$		0			0
$911$	893.443	+	515.830i	0.980728	+	0.566224i	0.902490	−	0.430711i	$-0.141737\pi$
$911$	893.443	+	515.830i	0.980728	+	0.566224i	0.0782381	+	0.996935i	$0.475071\pi$
$912$	−417.174	+	78.4910i	−0.457428	+	0.0860647i
$913$	21.4865			0.0235340
$914$			1084.16i			1.18617i
$915$	−46.9191	+	40.2936i	−0.0512777	+	0.0440367i
$916$	−352.645	+	610.798i	−0.384983	+	0.666811i
$917$		0			0
$918$	−17.1085	−	498.207i	−0.0186368	−	0.542710i
$919$	362.145	+	627.254i	0.394064	+	0.682539i	0.992981	−	0.118272i	$-0.0377354\pi$
$919$	362.145	+	627.254i	0.394064	+	0.682539i	−0.598917	+	0.800811i	$0.704402\pi$
$920$	−174.558	+	100.781i	−0.189737	+	0.109545i
$921$	−380.583	+	1084.08i	−0.413228	+	1.17707i
$922$	−240.830	+	417.130i	−0.261204	+	0.452419i
$923$	990.174	−	571.677i	1.07278	−	0.619369i
$924$		0			0
$925$	−270.930	+	469.264i	−0.292897	+	0.507312i
$926$	9.25515	−	5.34346i	0.00999476	−	0.00577048i
$927$	−494.418	+	192.877i	−0.533353	+	0.208066i
$928$	261.188	−	452.391i	0.281453	−	0.487490i
$929$			1463.68i			1.57555i	0.615966	+	0.787773i	$0.288766\pi$
$929$			1463.68i			1.57555i	−0.615966	+	0.787773i	$0.711234\pi$
$930$	−9.00331	−	10.4837i	−0.00968098	−	0.0112728i
$931$		0			0
$932$	−502.966	+	290.387i	−0.539663	+	0.311575i
$933$	441.609	+	155.034i	0.473322	+	0.166167i
$934$	−377.878	−	654.504i	−0.404580	−	0.700754i
$935$	−3.03525	−	1.75240i	−0.00324626	−	0.00187423i
$936$	1175.59	+	179.655i	1.25597	+	0.191939i
$937$	−282.325			−0.301308			−0.150654	−	0.988587i	$-0.548138\pi$
$937$	−282.325			−0.301308			−0.150654	+	0.988587i	$0.548138\pi$
$938$		0			0
$939$	115.800	−	329.854i	0.123323	−	0.351282i
$940$	32.0159	−	55.4532i	0.0340595	−	0.0589928i
$941$			294.458i			0.312921i	0.987684	+	0.156460i	$0.0500083\pi$
$941$			294.458i			0.312921i	−0.987684	+	0.156460i	$0.949992\pi$
$942$	−32.1733	−	11.2949i	−0.0341542	−	0.0119904i
$943$	1459.45			1.54767
$944$			447.503i			0.474050i
$945$		0			0
$946$	−10.5385			−0.0111401
$947$			882.114i			0.931482i	0.884921	+	0.465741i	$0.154212\pi$
$947$			882.114i			0.931482i	−0.884921	+	0.465741i	$0.845788\pi$
$948$	−41.4355	+	118.028i	−0.0437083	+	0.124502i
$949$	402.416			0.424042
$950$	823.734	+	475.583i	0.867089	+	0.500614i
$951$	531.770	+	186.686i	0.559169	+	0.196305i
$952$		0			0
$953$		−	347.203i		−	0.364326i	−0.983268	−	0.182163i	$-0.941690\pi$
$953$		−	347.203i		−	0.364326i	0.983268	−	0.182163i	$-0.0583099\pi$
$954$	1285.39	−	501.440i	1.34737	−	0.525619i
$955$	−105.957	+	183.523i	−0.110950	+	0.192170i
$956$	370.157	−	213.711i	0.387194	−	0.223547i
$957$	−4.68476	+	13.3444i	−0.00489525	+	0.0139440i
$958$	−212.256	−	367.638i	−0.221561	−	0.383756i
$959$		0			0
$960$	−156.978	+	134.811i	−0.163519	+	0.140428i
$961$	−953.565			−0.992263
$962$	447.614	+	258.430i	0.465295	+	0.268638i
$963$	−790.325	−	120.779i	−0.820691	−	0.125419i
$964$	−167.489	−	290.099i	−0.173743	−	0.300932i
$965$	−152.532	−	88.0647i	−0.158065	−	0.0912587i
$966$		0			0
$967$	774.207	+	1340.97i	0.800627	+	1.38673i	0.919204	+	0.393782i	$0.128834\pi$
$967$	774.207	+	1340.97i	0.800627	+	1.38673i	−0.118577	+	0.992945i	$0.537833\pi$
$968$	898.305	+	518.637i	0.928001	+	0.535782i
$969$	977.735	+	343.249i	1.00901	+	0.354230i
$970$	−124.991	−	216.491i	−0.128857	−	0.223187i
$971$	859.844	−	496.431i	0.885525	−	0.511258i	0.0130486	−	0.999915i	$-0.495846\pi$
$971$	859.844	−	496.431i	0.885525	−	0.511258i	0.872476	+	0.488657i	$0.162513\pi$
$972$	−446.984	−	52.6828i	−0.459860	−	0.0542004i
$973$		0			0
$974$	640.375	+	369.721i	0.657470	+	0.379590i
$975$	−712.808	−	830.016i	−0.731085	−	0.851299i
$976$	92.2978			0.0945675
$977$			238.021i			0.243625i	0.992553	+	0.121812i	$0.0388706\pi$
$977$			238.021i			0.243625i	−0.992553	+	0.121812i	$0.961129\pi$
$978$	211.311	+	1123.10i	0.216064	+	1.14836i
$979$	−6.93173	+	12.0061i	−0.00708042	+	0.0122636i
$980$		0			0
$981$	−1584.03	+	617.945i	−1.61471	+	0.629913i
$982$	263.667	+	456.685i	0.268500	+	0.465056i
$983$	−548.070	+	316.428i	−0.557548	+	0.321901i	−0.752161	−	0.658980i	$-0.770988\pi$
$983$	−548.070	+	316.428i	−0.557548	+	0.321901i	0.194613	+	0.980880i	$0.437655\pi$
$984$	1810.08	−	340.566i	1.83951	−	0.346103i
$985$	222.475	−	385.339i	0.225863	−	0.391207i
$986$	312.323	−	180.320i	0.316757	−	0.182880i
$987$		0			0
$988$	−391.196	+	677.571i	−0.395947	+	0.685801i
$989$	526.069	−	303.726i	0.531920	−	0.307104i
$990$	2.29375	−	2.86422i	0.00231692	−	0.00289315i
$991$	589.789	−	1021.54i	0.595145	−	1.03082i	−0.398381	−	0.917220i	$-0.630428\pi$
$991$	589.789	−	1021.54i	0.595145	−	1.03082i	0.993526	−	0.113602i	$-0.0362389\pi$
$992$		−	72.9215i		−	0.0735096i
$993$	63.0349	−	179.553i	0.0634792	−	0.180819i
$994$		0			0
$995$	−45.5982	+	26.3261i	−0.0458274	+	0.0264584i
$996$	−375.283	+	322.289i	−0.376790	+	0.323583i
$997$	−746.149	−	1292.37i	−0.748394	−	1.29626i	−0.948592	−	0.316501i	$-0.897492\pi$
$997$	−746.149	−	1292.37i	−0.748394	−	1.29626i	0.200198	−	0.979755i	$-0.435841\pi$
$998$	−821.226	−	474.135i	−0.822872	−	0.475085i
$999$	−545.544	−	290.477i	−0.546090	−	0.290767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.j.f.263.4		22
7.2	even	3		441.3.n.f.128.4		22
7.3	odd	6		441.3.r.g.344.8		22
7.4	even	3		441.3.r.f.344.8		22
7.5	odd	6		63.3.n.b.2.4	yes	22
7.6	odd	2		63.3.j.b.11.4	✓	22
9.5	odd	6		441.3.n.f.410.4		22
21.5	even	6		189.3.n.b.170.8		22
21.20	even	2		189.3.j.b.116.8		22
63.5	even	6		63.3.j.b.23.8	yes	22
63.13	odd	6		189.3.n.b.179.8		22
63.23	odd	6	inner	441.3.j.f.275.8		22
63.32	odd	6		441.3.r.f.50.8		22
63.40	odd	6		189.3.j.b.44.4		22
63.41	even	6		63.3.n.b.32.4	yes	22
63.59	even	6		441.3.r.g.50.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.4	✓	22	7.6	odd	2
63.3.j.b.23.8	yes	22	63.5	even	6
63.3.n.b.2.4	yes	22	7.5	odd	6
63.3.n.b.32.4	yes	22	63.41	even	6
189.3.j.b.44.4		22	63.40	odd	6
189.3.j.b.116.8		22	21.20	even	2
189.3.n.b.170.8		22	21.5	even	6
189.3.n.b.179.8		22	63.13	odd	6
441.3.j.f.263.4		22	1.1	even	1	trivial
441.3.j.f.275.8		22	63.23	odd	6	inner
441.3.n.f.128.4		22	7.2	even	3
441.3.n.f.410.4		22	9.5	odd	6
441.3.r.f.50.8		22	63.32	odd	6
441.3.r.f.344.8		22	7.4	even	3
441.3.r.g.50.8		22	63.59	even	6
441.3.r.g.344.8		22	7.3	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.46555i q^{2} +(-0.993737 + 2.83063i) q^{3} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(4.14843 + 1.45637i) q^{6} -8.57663i q^{8} +(-7.02497 - 5.62581i) q^{9} +O(q^{10})\)	\(q-1.46555i q^{2} +(-0.993737 + 2.83063i) q^{3} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(4.14843 + 1.45637i) q^{6} -8.57663i q^{8} +(-7.02497 - 5.62581i) q^{9} +(-0.844669 + 1.46301i) q^{10} +(0.209014 - 0.120674i) q^{11} +(-1.84057 + 5.24282i) q^{12} +(-7.70332 - 13.3426i) q^{13} +(2.62345 - 2.25299i) q^{15} -5.16078 q^{16} +(10.9102 + 6.29901i) q^{17} +(-8.24489 + 10.2954i) q^{18} +(-13.7090 - 23.7446i) q^{19} +(-1.84896 - 1.06750i) q^{20} +(-0.176854 - 0.306320i) q^{22} +(17.6566 + 10.1940i) q^{23} +(24.2773 + 8.52292i) q^{24} +(-11.8356 - 20.4999i) q^{25} +(-19.5541 + 11.2896i) q^{26} +(22.9056 - 14.2945i) q^{27} +(16.9161 + 9.76653i) q^{29} +(-3.30186 - 3.84480i) q^{30} +2.72674 q^{31} -26.7432i q^{32} +(0.133880 + 0.711561i) q^{33} +(9.23150 - 15.9894i) q^{34} +(-13.0114 - 10.4200i) q^{36} +(-11.4455 - 19.8242i) q^{37} +(-34.7989 + 20.0911i) q^{38} +(45.4230 - 8.54630i) q^{39} +(-4.94315 + 8.56178i) q^{40} +(61.9933 - 35.7918i) q^{41} +(14.8972 - 25.8028i) q^{43} +(0.387130 - 0.223510i) q^{44} +(3.77037 + 9.66492i) q^{45} +(14.9398 - 25.8766i) q^{46} +29.9915i q^{47} +(5.12846 - 14.6083i) q^{48} +(-30.0436 + 17.3457i) q^{50} +(-28.6721 + 24.6232i) q^{51} +(-14.2679 - 24.7127i) q^{52} +(-90.5906 - 52.3025i) q^{53} +(-20.9493 - 33.5692i) q^{54} -0.278203 q^{55} +(80.8355 - 15.2091i) q^{57} +(14.3133 - 24.7914i) q^{58} -86.7123i q^{59} +(4.85908 - 4.17292i) q^{60} -17.8845 q^{61} -3.99616i q^{62} -59.8365 q^{64} +17.7593i q^{65} +(1.04283 - 0.196207i) q^{66} -18.0439 q^{67} +(20.2076 + 11.6669i) q^{68} +(-46.4016 + 39.8491i) q^{69} +74.2118i q^{71} +(-48.2505 + 60.2506i) q^{72} +(-13.0598 + 22.6203i) q^{73} +(-29.0533 + 16.7739i) q^{74} +(69.7893 - 13.1308i) q^{75} +(-25.3914 - 43.9791i) q^{76} +(-12.5250 - 66.5695i) q^{78} +22.5123 q^{79} +(5.15184 + 2.97442i) q^{80} +(17.7005 + 79.0424i) q^{81} +(-52.4546 - 90.8541i) q^{82} +(77.0996 + 44.5135i) q^{83} +(-7.26088 - 12.5762i) q^{85} +(-37.8152 - 21.8326i) q^{86} +(-44.4557 + 38.1780i) q^{87} +(-1.03498 - 1.79264i) q^{88} +(-49.7459 + 28.7208i) q^{89} +(14.1644 - 5.52565i) q^{90} +(32.7030 + 18.8811i) q^{92} +(-2.70966 + 7.71839i) q^{93} +43.9540 q^{94} +31.6047i q^{95} +(75.7001 + 26.5757i) q^{96} +(-73.9883 + 128.152i) q^{97} +(-2.14721 - 0.328140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 19 q^{3} - 24 q^{4} - 12 q^{5} + 8 q^{6} - 37 q^{9}+O(q^{10}) \) 22 * q + 19 * q^3 - 24 * q^4 - 12 * q^5 + 8 * q^6 - 37 * q^9	\( 22 q + 19 q^{3} - 24 q^{4} - 12 q^{5} + 8 q^{6} - 37 q^{9} - 25 q^{10} + 24 q^{11} - 40 q^{12} + 18 q^{13} + 53 q^{15} - 24 q^{16} + 6 q^{17} + 40 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} + 81 q^{23} - 126 q^{24} + 57 q^{25} - 3 q^{26} + 97 q^{27} - 63 q^{29} - 38 q^{30} - 58 q^{31} + 4 q^{33} + 99 q^{34} + 76 q^{36} - 20 q^{37} + 48 q^{38} - 76 q^{39} + 105 q^{40} + 51 q^{41} + 65 q^{43} - 54 q^{44} + 214 q^{45} + 75 q^{46} + 113 q^{48} + 63 q^{50} + 141 q^{51} + 46 q^{52} + 63 q^{53} - 433 q^{54} + 100 q^{55} + 224 q^{57} + 40 q^{58} - 482 q^{60} + 156 q^{61} + 106 q^{64} - 61 q^{66} + 264 q^{67} - 27 q^{68} + 297 q^{69} - 222 q^{72} - q^{73} + 342 q^{74} + 296 q^{75} - 233 q^{76} - 440 q^{78} - 280 q^{79} + 96 q^{80} - 169 q^{81} + 157 q^{82} - 255 q^{83} + 102 q^{85} + 504 q^{86} - 704 q^{87} + 408 q^{88} - 720 q^{89} - 418 q^{90} - 1239 q^{92} - 36 q^{93} + 522 q^{94} + 397 q^{96} - 178 q^{97} - 103 q^{99}+O(q^{100}) \) 22 * q + 19 * q^3 - 24 * q^4 - 12 * q^5 + 8 * q^6 - 37 * q^9 - 25 * q^10 + 24 * q^11 - 40 * q^12 + 18 * q^13 + 53 * q^15 - 24 * q^16 + 6 * q^17 + 40 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 + 81 * q^23 - 126 * q^24 + 57 * q^25 - 3 * q^26 + 97 * q^27 - 63 * q^29 - 38 * q^30 - 58 * q^31 + 4 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 48 * q^38 - 76 * q^39 + 105 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 214 * q^45 + 75 * q^46 + 113 * q^48 + 63 * q^50 + 141 * q^51 + 46 * q^52 + 63 * q^53 - 433 * q^54 + 100 * q^55 + 224 * q^57 + 40 * q^58 - 482 * q^60 + 156 * q^61 + 106 * q^64 - 61 * q^66 + 264 * q^67 - 27 * q^68 + 297 * q^69 - 222 * q^72 - q^73 + 342 * q^74 + 296 * q^75 - 233 * q^76 - 440 * q^78 - 280 * q^79 + 96 * q^80 - 169 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 504 * q^86 - 704 * q^87 + 408 * q^88 - 720 * q^89 - 418 * q^90 - 1239 * q^92 - 36 * q^93 + 522 * q^94 + 397 * q^96 - 178 * q^97 - 103 * q^99

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