LMFDB - Embedded newform 1001.2.i.d.144.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, 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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.19
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.d.716.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.677177 + 1.17291i) q^{2} +(0.426504 - 0.738727i) q^{3} +(0.0828624 - 0.143522i) q^{4} +(-0.558163 - 0.966767i) q^{5} +1.15527 q^{6} +(-0.188015 + 2.63906i) q^{7} +2.93316 q^{8} +(1.13619 + 1.96794i) q^{9} +O(q^{10})$	\(q+(0.677177 + 1.17291i) q^{2} +(0.426504 - 0.738727i) q^{3} +(0.0828624 - 0.143522i) q^{4} +(-0.558163 - 0.966767i) q^{5} +1.15527 q^{6} +(-0.188015 + 2.63906i) q^{7} +2.93316 q^{8} +(1.13619 + 1.96794i) q^{9} +(0.755950 - 1.30934i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.0706823 - 0.122425i) q^{12} -1.00000 q^{13} +(-3.22269 + 1.56659i) q^{14} -0.952235 q^{15} +(1.82054 + 3.15327i) q^{16} +(1.70994 - 2.96171i) q^{17} +(-1.53880 + 2.66528i) q^{18} +(1.92505 + 3.33429i) q^{19} -0.185003 q^{20} +(1.86936 + 1.26446i) q^{21} -1.35435 q^{22} +(4.15310 + 7.19338i) q^{23} +(1.25100 - 2.16680i) q^{24} +(1.87691 - 3.25090i) q^{25} +(-0.677177 - 1.17291i) q^{26} +4.49738 q^{27} +(0.363184 + 0.245663i) q^{28} -8.58489 q^{29} +(-0.644832 - 1.11688i) q^{30} +(3.53953 - 6.13065i) q^{31} +(0.467499 - 0.809732i) q^{32} +(0.426504 + 0.738727i) q^{33} +4.63174 q^{34} +(2.65630 - 1.29126i) q^{35} +0.376589 q^{36} +(-1.43674 - 2.48851i) q^{37} +(-2.60720 + 4.51581i) q^{38} +(-0.426504 + 0.738727i) q^{39} +(-1.63718 - 2.83568i) q^{40} +5.55558 q^{41} +(-0.217209 + 3.04884i) q^{42} -0.468993 q^{43} +(0.0828624 + 0.143522i) q^{44} +(1.26836 - 2.19686i) q^{45} +(-5.62477 + 9.74239i) q^{46} +(2.52101 + 4.36652i) q^{47} +3.10587 q^{48} +(-6.92930 - 0.992366i) q^{49} +5.08400 q^{50} +(-1.45860 - 2.52636i) q^{51} +(-0.0828624 + 0.143522i) q^{52} +(-2.46949 + 4.27728i) q^{53} +(3.04552 + 5.27500i) q^{54} +1.11633 q^{55} +(-0.551477 + 7.74079i) q^{56} +3.28417 q^{57} +(-5.81349 - 10.0693i) q^{58} +(6.15462 - 10.6601i) q^{59} +(-0.0789045 + 0.136667i) q^{60} +(1.58576 + 2.74661i) q^{61} +9.58756 q^{62} +(-5.40713 + 2.62847i) q^{63} +8.54849 q^{64} +(0.558163 + 0.966767i) q^{65} +(-0.577637 + 1.00050i) q^{66} +(-1.79785 + 3.11396i) q^{67} +(-0.283380 - 0.490829i) q^{68} +7.08526 q^{69} +(3.31331 + 2.24118i) q^{70} +9.24998 q^{71} +(3.33262 + 5.77227i) q^{72} +(-0.479743 + 0.830939i) q^{73} +(1.94586 - 3.37032i) q^{74} +(-1.60102 - 2.77304i) q^{75} +0.638058 q^{76} +(-2.19149 - 1.48236i) q^{77} -1.15527 q^{78} +(2.42354 + 4.19769i) q^{79} +(2.03232 - 3.52008i) q^{80} +(-1.49042 + 2.58148i) q^{81} +(3.76211 + 6.51617i) q^{82} -12.0344 q^{83} +(0.336378 - 0.163517i) q^{84} -3.81771 q^{85} +(-0.317591 - 0.550084i) q^{86} +(-3.66149 + 6.34188i) q^{87} +(-1.46658 + 2.54019i) q^{88} +(-7.23169 - 12.5257i) q^{89} +3.43561 q^{90} +(0.188015 - 2.63906i) q^{91} +1.37654 q^{92} +(-3.01925 - 5.22949i) q^{93} +(-3.41434 + 5.91381i) q^{94} +(2.14899 - 3.72216i) q^{95} +(-0.398780 - 0.690708i) q^{96} +2.70558 q^{97} +(-3.52841 - 8.79942i) q^{98} -2.27238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.677177	+	1.17291i	0.478836	+	0.829369i	0.999706	−	0.0242675i	$-0.00772534\pi$
$2$	0.677177	+	1.17291i	0.478836	+	0.829369i	−0.520869	+	0.853637i	$0.674392\pi$
$3$	0.426504	−	0.738727i	0.246242	−	0.426504i	−0.716238	−	0.697856i	$-0.754137\pi$
$3$	0.426504	−	0.738727i	0.246242	−	0.426504i	0.962480	+	0.271352i	$0.0874708\pi$
$4$	0.0828624	−	0.143522i	0.0414312	−	0.0717610i
$5$	−0.558163	−	0.966767i	−0.249618	−	0.432351i	0.713802	−	0.700348i	$-0.246972\pi$
$5$	−0.558163	−	0.966767i	−0.249618	−	0.432351i	−0.963420	+	0.267997i	$0.913638\pi$
$6$	1.15527			0.471639
$7$	−0.188015	+	2.63906i	−0.0710629	+	0.997472i
$7$	−0.188015	+	2.63906i	−0.0710629	+	0.997472i
$8$	2.93316			1.03703
$9$	1.13619	+	1.96794i	0.378730	+	0.655979i
$10$	0.755950	−	1.30934i	0.239053	−	0.414051i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.0706823	−	0.122425i	−0.0204042	−	0.0353412i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−3.22269	+	1.56659i	−0.861300	+	0.418689i
$15$	−0.952235			−0.245866
$16$	1.82054	+	3.15327i	0.455136	+	0.788318i
$17$	1.70994	−	2.96171i	0.414723	−	0.718320i	−0.580677	−	0.814134i	$-0.697212\pi$
$17$	1.70994	−	2.96171i	0.414723	−	0.718320i	0.995399	+	0.0958137i	$0.0305453\pi$
$18$	−1.53880	+	2.66528i	−0.362699	+	0.628213i
$19$	1.92505	+	3.33429i	0.441638	+	0.764939i	0.997811	−	0.0661275i	$-0.0210644\pi$
$19$	1.92505	+	3.33429i	0.441638	+	0.764939i	−0.556174	+	0.831066i	$0.687731\pi$
$20$	−0.185003			−0.0413679
$21$	1.86936	+	1.26446i	0.407927	+	0.275928i
$22$	−1.35435			−0.288749
$23$	4.15310	+	7.19338i	0.865982	+	1.49992i	0.866069	+	0.499924i	$0.166639\pi$
$23$	4.15310	+	7.19338i	0.865982	+	1.49992i	−8.77213e−5		1.00000i	$0.500028\pi$
$24$	1.25100	−	2.16680i	0.255360	−	0.442297i
$25$	1.87691	−	3.25090i	0.375382	−	0.650180i
$26$	−0.677177	−	1.17291i	−0.132805	−	0.230026i
$27$	4.49738			0.865521
$28$	0.363184	+	0.245663i	0.0686353	+	0.0464260i
$29$	−8.58489			−1.59417			−0.797087	−	0.603865i	$-0.793627\pi$
$29$	−8.58489			−1.59417			−0.797087	+	0.603865i	$0.793627\pi$
$30$	−0.644832	−	1.11688i	−0.117730	−	0.203914i
$31$	3.53953	−	6.13065i	0.635719	−	1.10110i	−0.350644	−	0.936509i	$-0.614037\pi$
$31$	3.53953	−	6.13065i	0.635719	−	1.10110i	0.986362	−	0.164588i	$-0.0526294\pi$
$32$	0.467499	−	0.809732i	0.0826429	−	0.143142i
$33$	0.426504	+	0.738727i	0.0742448	+	0.128596i
$34$	4.63174			0.794337
$35$	2.65630	−	1.29126i	0.448997	−	0.218263i
$36$	0.376589			0.0627649
$37$	−1.43674	−	2.48851i	−0.236199	−	0.409109i	0.723422	−	0.690407i	$-0.242568\pi$
$37$	−1.43674	−	2.48851i	−0.236199	−	0.409109i	−0.959620	+	0.281298i	$0.909235\pi$
$38$	−2.60720	+	4.51581i	−0.422944	+	0.732561i
$39$	−0.426504	+	0.738727i	−0.0682953	+	0.118291i
$40$	−1.63718	−	2.83568i	−0.258861	−	0.448360i
$41$	5.55558			0.867636			0.433818	−	0.901000i	$-0.357166\pi$
$41$	5.55558			0.867636			0.433818	+	0.901000i	$0.357166\pi$
$42$	−0.217209	+	3.04884i	−0.0335160	+	0.470447i
$43$	−0.468993			−0.0715208			−0.0357604	−	0.999360i	$-0.511385\pi$
$43$	−0.468993			−0.0715208			−0.0357604	+	0.999360i	$0.511385\pi$
$44$	0.0828624	+	0.143522i	0.0124920	+	0.0216368i
$45$	1.26836	−	2.19686i	0.189076	−	0.327488i
$46$	−5.62477	+	9.74239i	−0.829327	+	1.43644i
$47$	2.52101	+	4.36652i	0.367727	+	0.636922i	0.989210	−	0.146506i	$-0.0468027\pi$
$47$	2.52101	+	4.36652i	0.367727	+	0.636922i	−0.621483	+	0.783428i	$0.713469\pi$
$48$	3.10587			0.448294
$49$	−6.92930	−	0.992366i	−0.989900	−	0.141767i
$50$	5.08400			0.718986
$51$	−1.45860	−	2.52636i	−0.204244	−	0.353762i
$52$	−0.0828624	+	0.143522i	−0.0114910	+	0.0199029i
$53$	−2.46949	+	4.27728i	−0.339210	+	0.587529i	−0.984284	−	0.176591i	$-0.943493\pi$
$53$	−2.46949	+	4.27728i	−0.339210	+	0.587529i	0.645074	+	0.764120i	$0.276826\pi$
$54$	3.04552	+	5.27500i	0.414443	+	0.717837i
$55$	1.11633			0.150525
$56$	−0.551477	+	7.74079i	−0.0736943	+	1.03441i
$57$	3.28417			0.434999
$58$	−5.81349	−	10.0693i	−0.763348	−	1.32216i
$59$	6.15462	−	10.6601i	0.801264	−	1.38783i	−0.117521	−	0.993070i	$-0.537495\pi$
$59$	6.15462	−	10.6601i	0.801264	−	1.38783i	0.918785	−	0.394759i	$-0.129172\pi$
$60$	−0.0789045	+	0.136667i	−0.0101865	+	0.0176436i
$61$	1.58576	+	2.74661i	0.203035	+	0.351667i	0.949505	−	0.313752i	$-0.101586\pi$
$61$	1.58576	+	2.74661i	0.203035	+	0.351667i	−0.746470	+	0.665419i	$0.768253\pi$
$62$	9.58756			1.21762
$63$	−5.40713	+	2.62847i	−0.681234	+	0.331156i
$64$	8.54849			1.06856
$65$	0.558163	+	0.966767i	0.0692316	+	0.119913i
$66$	−0.577637	+	1.00050i	−0.0711023	+	0.123153i
$67$	−1.79785	+	3.11396i	−0.219642	+	0.380431i	−0.954698	−	0.297575i	$-0.903822\pi$
$67$	−1.79785	+	3.11396i	−0.219642	+	0.380431i	0.735057	+	0.678006i	$0.237156\pi$
$68$	−0.283380	−	0.490829i	−0.0343649	−	0.0595218i
$69$	7.08526			0.852965
$70$	3.31331	+	2.24118i	0.396017	+	0.267872i
$71$	9.24998			1.09777			0.548885	−	0.835898i	$-0.315052\pi$
$71$	9.24998			1.09777			0.548885	+	0.835898i	$0.315052\pi$
$72$	3.33262	+	5.77227i	0.392753	+	0.680269i
$73$	−0.479743	+	0.830939i	−0.0561497	+	0.0972541i	−0.892734	−	0.450584i	$-0.851216\pi$
$73$	−0.479743	+	0.830939i	−0.0561497	+	0.0972541i	0.836584	+	0.547838i	$0.184549\pi$
$74$	1.94586	−	3.37032i	0.226201	−	0.391792i
$75$	−1.60102	−	2.77304i	−0.184870	−	0.320203i
$76$	0.638058			0.0731903
$77$	−2.19149	−	1.48236i	−0.249743	−	0.168930i
$78$	−1.15527			−0.130809
$79$	2.42354	+	4.19769i	0.272669	+	0.472277i	0.969544	−	0.244916i	$-0.0787603\pi$
$79$	2.42354	+	4.19769i	0.272669	+	0.472277i	−0.696875	+	0.717192i	$0.745427\pi$
$80$	2.03232	−	3.52008i	0.227220	−	0.393557i
$81$	−1.49042	+	2.58148i	−0.165602	+	0.286831i
$82$	3.76211	+	6.51617i	0.415456	+	0.719591i
$83$	−12.0344			−1.32094			−0.660471	−	0.750852i	$-0.729643\pi$
$83$	−12.0344			−1.32094			−0.660471	+	0.750852i	$0.729643\pi$
$84$	0.336378	−	0.163517i	0.0367018	−	0.0178412i
$85$	−3.81771			−0.414089
$86$	−0.317591	−	0.550084i	−0.0342467	−	0.0593171i
$87$	−3.66149	+	6.34188i	−0.392553	+	0.679921i
$88$	−1.46658	+	2.54019i	−0.156338	+	0.270785i
$89$	−7.23169	−	12.5257i	−0.766558	−	1.32772i	−0.939419	−	0.342771i	$-0.888635\pi$
$89$	−7.23169	−	12.5257i	−0.766558	−	1.32772i	0.172861	−	0.984946i	$-0.444699\pi$
$90$	3.43561			0.362145
$91$	0.188015	−	2.63906i	0.0197093	−	0.276649i
$92$	1.37654			0.143515
$93$	−3.01925	−	5.22949i	−0.313081	−	0.542273i
$94$	−3.41434	+	5.91381i	−0.352162	+	0.609963i
$95$	2.14899	−	3.72216i	0.220481	−	0.381885i
$96$	−0.398780	−	0.690708i	−0.0407003	−	0.0704951i
$97$	2.70558			0.274710			0.137355	−	0.990522i	$-0.456140\pi$
$97$	2.70558			0.274710			0.137355	+	0.990522i	$0.456140\pi$
$98$	−3.52841	−	8.79942i	−0.356424	−	0.888876i
$99$	−2.27238			−0.228383
$100$	−0.311050	−	0.538755i	−0.0311050	−	0.0538755i
$101$	−9.00083	+	15.5899i	−0.895616	+	1.55125i	−0.0625747	+	0.998040i	$0.519931\pi$
$101$	−9.00083	+	15.5899i	−0.895616	+	1.55125i	−0.833041	+	0.553211i	$0.813402\pi$
$102$	1.97546	−	3.42159i	0.195599	−	0.338788i
$103$	−4.57342	−	7.92139i	−0.450632	−	0.780518i	0.547793	−	0.836614i	$-0.315468\pi$
$103$	−4.57342	−	7.92139i	−0.450632	−	0.780518i	−0.998425	+	0.0560960i	$0.982135\pi$
$104$	−2.93316			−0.287620
$105$	0.179034	−	2.51301i	0.0174720	−	0.245244i
$106$	−6.68912			−0.649704
$107$	−6.06944	−	10.5126i	−0.586755	−	1.01629i	−0.994654	−	0.103263i	$-0.967072\pi$
$107$	−6.06944	−	10.5126i	−0.586755	−	1.01629i	0.407899	−	0.913027i	$-0.366262\pi$
$108$	0.372664	−	0.645473i	0.0358596	−	0.0621106i
$109$	−4.34171	+	7.52006i	−0.415860	+	0.720291i	−0.995518	−	0.0945685i	$-0.969853\pi$
$109$	−4.34171	+	7.52006i	−0.415860	+	0.720291i	0.579658	+	0.814860i	$0.303186\pi$
$110$	0.755950	+	1.30934i	0.0720770	+	0.124841i
$111$	−2.45110			−0.232649
$112$	−8.66397	+	4.21166i	−0.818668	+	0.397965i
$113$	−21.1752			−1.99199			−0.995997	−	0.0893871i	$-0.971509\pi$
$113$	−21.1752			−1.99199			−0.995997	+	0.0893871i	$0.971509\pi$
$114$	2.22397	+	3.85202i	0.208293	+	0.360775i
$115$	4.63622	−	8.03016i	0.432329	−	0.748816i
$116$	−0.711365	+	1.23212i	−0.0660486	+	0.114399i
$117$	−1.13619	−	1.96794i	−0.105041	−	0.181936i
$118$	16.6711			1.53470
$119$	7.49465	+	5.06950i	0.687033	+	0.464720i
$120$	−2.79306			−0.254970
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−2.14767	+	3.71988i	−0.194441	+	0.336782i
$123$	2.36948	−	4.10406i	0.213649	−	0.370050i
$124$	−0.586588	−	1.01600i	−0.0526772	−	0.0912396i
$125$	−9.77211			−0.874044
$126$	−6.74453	−	4.56211i	−0.600851	−	0.406425i
$127$	−11.1702			−0.991193			−0.495596	−	0.868553i	$-0.665050\pi$
$127$	−11.1702			−0.991193			−0.495596	+	0.868553i	$0.665050\pi$
$128$	4.85384	+	8.40710i	0.429023	+	0.743090i
$129$	−0.200027	+	0.346458i	−0.0176114	+	0.0305039i
$130$	−0.755950	+	1.30934i	−0.0663012	+	0.114837i
$131$	−7.39239	−	12.8040i	−0.645877	−	1.11869i	−0.984098	−	0.177625i	$-0.943159\pi$
$131$	−7.39239	−	12.8040i	−0.645877	−	1.11869i	0.338222	−	0.941066i	$-0.390175\pi$
$132$	0.141365			0.0123042
$133$	−9.16134	+	4.45344i	−0.794389	+	0.386162i
$134$	−4.86984			−0.420690
$135$	−2.51027	−	4.34792i	−0.216050	−	0.374209i
$136$	5.01554	−	8.68717i	0.430079	−	0.744919i
$137$	3.13826	−	5.43563i	0.268120	−	0.464397i	−0.700257	−	0.713891i	$-0.746931\pi$
$137$	3.13826	−	5.43563i	0.268120	−	0.464397i	0.968376	+	0.249494i	$0.0802644\pi$
$138$	4.79797	+	8.31033i	0.408431	+	0.707423i
$139$	−13.6296			−1.15605			−0.578023	−	0.816021i	$-0.696176\pi$
$139$	−13.6296			−1.15605			−0.578023	+	0.816021i	$0.696176\pi$
$140$	0.0347833	−	0.488235i	0.00293973	−	0.0412633i
$141$	4.30088			0.362200
$142$	6.26387	+	10.8493i	0.525653	+	0.910457i
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$	−4.13696	+	7.16543i	−0.344747	+	0.597119i
$145$	4.79177	+	8.29958i	0.397935	+	0.689243i
$146$	−1.29948			−0.107546
$147$	−3.68846	+	4.69561i	−0.304219	+	0.387287i
$148$	−0.476208			−0.0391440
$149$	6.89126	+	11.9360i	0.564554	+	0.977836i	0.997091	+	0.0762200i	$0.0242851\pi$
$149$	6.89126	+	11.9360i	0.564554	+	0.977836i	−0.432537	+	0.901616i	$0.642382\pi$
$150$	2.16834	−	3.75568i	0.177045	−	0.306650i
$151$	11.5058	−	19.9286i	0.936328	−	1.62177i	0.164078	−	0.986447i	$-0.447535\pi$
$151$	11.5058	−	19.9286i	0.936328	−	1.62177i	0.772249	−	0.635320i	$-0.219132\pi$
$152$	5.64649	+	9.78000i	0.457991	+	0.793263i
$153$	7.77128			0.628271
$154$	0.254639	−	3.57423i	0.0205194	−	0.288019i
$155$	−7.90254			−0.634747
$156$	0.0706823	+	0.122425i	0.00565912	+	0.00980187i
$157$	10.4270	−	18.0602i	0.832169	−	1.44136i	−0.0641463	−	0.997941i	$-0.520432\pi$
$157$	10.4270	−	18.0602i	0.832169	−	1.44136i	0.896315	−	0.443418i	$-0.146234\pi$
$158$	−3.28233	+	5.68515i	−0.261128	+	0.452287i
$159$	2.10649	+	3.64855i	0.167056	+	0.289349i
$160$	−1.04376			−0.0825167
$161$	−19.7646	+	9.60783i	−1.55767	+	0.757203i
$162$	−4.03710			−0.317185
$163$	−4.64000	−	8.03672i	−0.363433	−	0.629485i	0.625090	−	0.780553i	$-0.285062\pi$
$163$	−4.64000	−	8.03672i	−0.363433	−	0.629485i	−0.988523	+	0.151068i	$0.951729\pi$
$164$	0.460349	−	0.797348i	0.0359472	−	0.0622624i
$165$	0.476118	−	0.824660i	0.0370657	−	0.0641997i
$166$	−8.14939	−	14.1152i	−0.632515	−	1.09555i
$167$	3.65832			0.283089			0.141545	−	0.989932i	$-0.454793\pi$
$167$	3.65832			0.283089			0.141545	+	0.989932i	$0.454793\pi$
$168$	5.48312	+	3.70887i	0.423032	+	0.286145i
$169$	1.00000			0.0769231
$170$	−2.58527	−	4.47781i	−0.198281	−	0.343433i
$171$	−4.37445	+	7.57677i	−0.334522	+	0.579410i
$172$	−0.0388619	+	0.0673108i	−0.00296319	+	0.00513240i
$173$	−1.17579	−	2.03653i	−0.0893937	−	0.154834i	0.817861	−	0.575415i	$-0.195160\pi$
$173$	−1.17579	−	2.03653i	−0.0893937	−	0.154834i	−0.907255	+	0.420581i	$0.861826\pi$
$174$	−9.91790			−0.751874
$175$	8.22644	+	5.56449i	0.621861	+	0.420636i
$176$	−3.64109			−0.274457
$177$	−5.24994	−	9.09317i	−0.394610	−	0.683484i
$178$	9.79427	−	16.9642i	0.734112	−	1.27152i
$179$	−10.2319	+	17.7221i	−0.764766	+	1.32461i	0.175604	+	0.984461i	$0.443812\pi$
$179$	−10.2319	+	17.7221i	−0.764766	+	1.32461i	−0.940370	+	0.340153i	$0.889521\pi$
$180$	−0.210198	−	0.364074i	−0.0156673	−	0.0271365i
$181$	8.76733			0.651671			0.325835	−	0.945427i	$-0.394354\pi$
$181$	8.76733			0.651671			0.325835	+	0.945427i	$0.394354\pi$
$182$	3.22269	−	1.56659i	0.238882	−	0.116123i
$183$	2.70532			0.199983
$184$	12.1817	+	21.0993i	0.898047	+	1.55546i
$185$	−1.60387	+	2.77799i	−0.117919	+	0.204242i
$186$	4.08913	−	7.08258i	0.299830	−	0.519320i
$187$	1.70994	+	2.96171i	0.125044	+	0.216582i
$188$	0.835588			0.0609415
$189$	−0.845574	+	11.8689i	−0.0615065	+	0.863333i
$190$	5.82098			0.422298
$191$	−10.8398	−	18.7750i	−0.784339	−	1.35851i	−0.929393	−	0.369091i	$-0.879669\pi$
$191$	−10.8398	−	18.7750i	−0.784339	−	1.35851i	0.145055	−	0.989424i	$-0.453664\pi$
$192$	3.64596	−	6.31500i	0.263125	−	0.455746i
$193$	−0.866257	+	1.50040i	−0.0623546	+	0.108001i	−0.895517	−	0.445026i	$-0.853194\pi$
$193$	−0.866257	+	1.50040i	−0.0623546	+	0.108001i	0.833163	+	0.553028i	$0.186528\pi$
$194$	1.83216	+	3.17339i	0.131541	+	0.227836i
$195$	0.952235			0.0681910
$196$	−0.716605	+	0.912277i	−0.0511861	+	0.0651626i
$197$	21.8485			1.55664			0.778321	−	0.627866i	$-0.216071\pi$
$197$	21.8485			1.55664			0.778321	+	0.627866i	$0.216071\pi$
$198$	−1.53880	−	2.66528i	−0.109358	−	0.189413i
$199$	−1.69448	+	2.93493i	−0.120119	+	0.208052i	−0.919814	−	0.392354i	$-0.871661\pi$
$199$	−1.69448	+	2.93493i	−0.120119	+	0.208052i	0.799696	+	0.600406i	$0.204994\pi$
$200$	5.50527	−	9.53540i	0.389281	−	0.674255i
$201$	1.53358	+	2.65623i	0.108170	+	0.187356i
$202$	−24.3806			−1.71541
$203$	1.61409	−	22.6561i	0.113287	−	1.59014i
$204$	−0.483451			−0.0338484
$205$	−3.10092	−	5.37095i	−0.216578	−	0.375124i
$206$	6.19403	−	10.7284i	0.431558	−	0.747481i
$207$	−9.43741	+	16.3461i	−0.655946	+	1.13613i
$208$	−1.82054	−	3.15327i	−0.126232	−	0.218640i
$209$	−3.85011			−0.266317
$210$	3.06876	−	1.49176i	0.211764	−	0.102941i
$211$	12.5215			0.862018			0.431009	−	0.902348i	$-0.358158\pi$
$211$	12.5215			0.862018			0.431009	+	0.902348i	$0.358158\pi$
$212$	0.409255	+	0.708851i	0.0281078	+	0.0486841i
$213$	3.94515	−	6.83320i	0.270317	−	0.468203i
$214$	8.22017	−	14.2378i	0.561920	−	0.973273i
$215$	0.261775	+	0.453407i	0.0178529	+	0.0309221i
$216$	13.1915			0.897570
$217$	15.5137	+	10.4937i	1.05314	+	0.712358i
$218$	−11.7604			−0.796517
$219$	0.409225	+	0.708798i	0.0276528	+	0.0478961i
$220$	0.0925015	−	0.160217i	0.00623645	−	0.0108018i
$221$	−1.70994	+	2.96171i	−0.115023	+	0.199226i
$222$	−1.65983	−	2.87491i	−0.111401	−	0.192952i
$223$	7.37305			0.493736			0.246868	−	0.969049i	$-0.420599\pi$
$223$	7.37305			0.493736			0.246868	+	0.969049i	$0.420599\pi$
$224$	2.04904	+	1.38600i	0.136907	+	0.0926060i
$225$	8.53009			0.568672
$226$	−14.3394	−	24.8365i	−0.953839	−	1.65210i
$227$	−3.34908	+	5.80077i	−0.222286	+	0.385011i	−0.955502	−	0.294985i	$-0.904685\pi$
$227$	−3.34908	+	5.80077i	−0.222286	+	0.385011i	0.733216	+	0.679996i	$0.238019\pi$
$228$	0.272134	−	0.471351i	0.0180225	−	0.0312160i
$229$	−1.74398	−	3.02066i	−0.115245	−	0.199611i	0.802633	−	0.596474i	$-0.203432\pi$
$229$	−1.74398	−	3.02066i	−0.115245	−	0.199611i	−0.917878	+	0.396863i	$0.870099\pi$
$230$	12.5582			0.828060
$231$	−2.02973	+	0.986679i	−0.133547	+	0.0649187i
$232$	−25.1808			−1.65320
$233$	0.978600	+	1.69498i	0.0641102	+	0.111042i	0.896299	−	0.443450i	$-0.146246\pi$
$233$	0.978600	+	1.69498i	0.0641102	+	0.111042i	−0.832189	+	0.554492i	$0.812912\pi$
$234$	1.53880	−	2.66528i	0.100595	−	0.174235i
$235$	2.81427	−	4.87446i	0.183583	−	0.317975i
$236$	−1.01997	−	1.76665i	−0.0663947	−	0.114999i
$237$	4.13459			0.268570
$238$	−0.870836	+	12.2235i	−0.0564479	+	0.792329i
$239$	−13.0072			−0.841363			−0.420681	−	0.907208i	$-0.638209\pi$
$239$	−13.0072			−0.841363			−0.420681	+	0.907208i	$0.638209\pi$
$240$	−1.73358	−	3.00266i	−0.111902	−	0.193821i
$241$	6.98026	−	12.0902i	0.449638	−	0.778796i	−0.548724	−	0.836004i	$-0.684886\pi$
$241$	6.98026	−	12.0902i	0.449638	−	0.778796i	0.998362	+	0.0572072i	$0.0182196\pi$
$242$	0.677177	−	1.17291i	0.0435306	−	0.0753972i
$243$	8.01741	+	13.8866i	0.514317	+	0.890823i
$244$	0.525598			0.0336480
$245$	2.90829	+	7.25292i	0.185804	+	0.463372i
$246$	6.41823			0.409211
$247$	−1.92505	−	3.33429i	−0.122488	−	0.212156i
$248$	10.3820	−	17.9822i	0.659258	−	1.14187i
$249$	−5.13270	+	8.89009i	−0.325272	+	0.563387i
$250$	−6.61745	−	11.4618i	−0.418524	−	0.724905i
$251$	−17.6777			−1.11581			−0.557903	−	0.829906i	$-0.688394\pi$
$251$	−17.6777			−1.11581			−0.557903	+	0.829906i	$0.688394\pi$
$252$	−0.0708044	+	0.993843i	−0.00446026	+	0.0626062i
$253$	−8.30620			−0.522207
$254$	−7.56418	−	13.1016i	−0.474619	−	0.822064i
$255$	−1.62827	+	2.82025i	−0.101966	+	0.176611i
$256$	1.97467	−	3.42022i	0.123417	−	0.213764i
$257$	−4.54081	−	7.86492i	−0.283248	−	0.490600i	0.688935	−	0.724823i	$-0.258079\pi$
$257$	−4.54081	−	7.86492i	−0.283248	−	0.490600i	−0.972183	+	0.234223i	$0.924745\pi$
$258$	−0.541816			−0.0337320
$259$	6.83746	−	3.32378i	0.424859	−	0.206529i
$260$	0.185003			0.0114734
$261$	−9.75405	−	16.8945i	−0.603761	−	1.04574i
$262$	10.0119	−	17.3412i	0.618539	−	1.07134i
$263$	−6.12509	+	10.6090i	−0.377689	+	0.654177i	−0.990726	−	0.135878i	$-0.956615\pi$
$263$	−6.12509	+	10.6090i	−0.377689	+	0.654177i	0.613036	+	0.790055i	$0.289948\pi$
$264$	1.25100	+	2.16680i	0.0769940	+	0.133357i
$265$	5.51350			0.338692
$266$	−11.4273	−	7.72961i	−0.700653	−	0.473933i
$267$	−12.3374			−0.755035
$268$	0.297948	+	0.516061i	0.0182001	+	0.0315234i
$269$	0.691058	−	1.19695i	0.0421345	−	0.0729792i	−0.844189	−	0.536046i	$-0.819918\pi$
$269$	0.691058	−	1.19695i	0.0421345	−	0.0729792i	0.886324	+	0.463066i	$0.153251\pi$
$270$	3.39980	−	5.88862i	0.206905	−	0.358370i
$271$	12.7613	+	22.1033i	0.775196	+	1.34268i	0.934684	+	0.355479i	$0.115682\pi$
$271$	12.7613	+	22.1033i	0.775196	+	1.34268i	−0.159489	+	0.987200i	$0.550985\pi$
$272$	12.4521			0.755020
$273$	−1.86936	−	1.26446i	−0.113139	−	0.0765287i
$274$	8.50063			0.513542
$275$	1.87691	+	3.25090i	0.113182	+	0.196037i
$276$	0.587102	−	1.01689i	0.0353394	−	0.0612096i
$277$	−6.35453	+	11.0064i	−0.381807	+	0.661309i	−0.991321	−	0.131467i	$-0.958031\pi$
$277$	−6.35453	+	11.0064i	−0.381807	+	0.661309i	0.609514	+	0.792776i	$0.291365\pi$
$278$	−9.22964	−	15.9862i	−0.553557	−	0.958789i
$279$	16.0863			0.963062
$280$	7.79135	−	3.78747i	0.465622	−	0.226345i
$281$	−1.10595			−0.0659754			−0.0329877	−	0.999456i	$-0.510502\pi$
$281$	−1.10595			−0.0659754			−0.0329877	+	0.999456i	$0.510502\pi$
$282$	2.91246	+	5.04453i	0.173434	+	0.300397i
$283$	0.709791	−	1.22939i	0.0421927	−	0.0730799i	−0.844158	−	0.536095i	$-0.819899\pi$
$283$	0.709791	−	1.22939i	0.0421927	−	0.0730799i	0.886351	+	0.463015i	$0.153232\pi$
$284$	0.766476	−	1.32758i	0.0454820	−	0.0787771i
$285$	−1.83310	−	3.17503i	−0.108584	−	0.188072i
$286$	1.35435			0.0800846
$287$	−1.04453	+	14.6615i	−0.0616568	+	0.865443i
$288$	2.12467			0.125197
$289$	2.65218	+	4.59371i	0.156010	+	0.270218i
$290$	−6.48975	+	11.2406i	−0.381091	+	0.660069i
$291$	1.15394	−	1.99868i	0.0676451	−	0.117165i
$292$	0.0795053	+	0.137707i	0.00465270	+	0.00805871i
$293$	−32.1466			−1.87803			−0.939014	−	0.343880i	$-0.888259\pi$
$293$	−32.1466			−1.87803			−0.939014	+	0.343880i	$0.888259\pi$
$294$	−8.00525	−	1.14646i	−0.466875	−	0.0668626i
$295$	−13.7411			−0.800040
$296$	−4.21419	−	7.29919i	−0.244945	−	0.424257i
$297$	−2.24869	+	3.89485i	−0.130482	+	0.226002i
$298$	−9.33321	+	16.1656i	−0.540658	+	0.936447i
$299$	−4.15310	−	7.19338i	−0.240180	−	0.416004i
$300$	−0.530657			−0.0306375
$301$	0.0881776	−	1.23770i	0.00508247	−	0.0713399i
$302$	31.1658			1.79339
$303$	7.67778	+	13.2983i	0.441077	+	0.763967i
$304$	−7.00928	+	12.1404i	−0.402010	+	0.696302i
$305$	1.77022	−	3.06611i	0.101362	−	0.175565i
$306$	5.26253	+	9.11497i	0.300839	+	0.521068i
$307$	14.7953			0.844410			0.422205	−	0.906500i	$-0.361256\pi$
$307$	14.7953			0.844410			0.422205	+	0.906500i	$0.361256\pi$
$308$	−0.394343	+	0.191695i	−0.0224698	+	0.0109228i
$309$	−7.80232			−0.443859
$310$	−5.35142	−	9.26893i	−0.303940	−	0.526440i
$311$	3.33209	−	5.77136i	0.188946	−	0.327264i	−0.755953	−	0.654626i	$-0.772826\pi$
$311$	3.33209	−	5.77136i	0.188946	−	0.327264i	0.944899	+	0.327362i	$0.106160\pi$
$312$	−1.25100	+	2.16680i	−0.0708241	+	0.122671i
$313$	0.374133	+	0.648017i	0.0211472	+	0.0366281i	0.876405	−	0.481574i	$-0.159935\pi$
$313$	0.374133	+	0.648017i	0.0211472	+	0.0366281i	−0.855258	+	0.518202i	$0.826601\pi$
$314$	28.2438			1.59389
$315$	5.55918	+	3.76032i	0.313224	+	0.211870i
$316$	0.803280			0.0451880
$317$	15.0614	+	26.0871i	0.845933	+	1.46520i	0.884808	+	0.465955i	$0.154289\pi$
$317$	15.0614	+	26.0871i	0.845933	+	1.46520i	−0.0388748	+	0.999244i	$0.512377\pi$
$318$	−2.85294	+	4.94143i	−0.159985	+	0.277102i
$319$	4.29244	−	7.43473i	0.240331	−	0.416265i
$320$	−4.77145	−	8.26440i	−0.266732	−	0.461994i
$321$	−10.3546			−0.577935
$322$	−24.6532	−	16.6758i	−1.37387	−	0.929308i
$323$	13.1669			0.732628
$324$	0.246999	+	0.427815i	0.0137222	+	0.0237675i
$325$	−1.87691	+	3.25090i	−0.104112	+	0.180327i
$326$	6.28421	−	10.8846i	0.348050	−	0.602841i
$327$	3.70351	+	6.41467i	0.204805	+	0.354732i
$328$	16.2954			0.899763
$329$	−11.9975	+	5.83213i	−0.661444	+	0.321536i
$330$	1.28966			0.0709936
$331$	−16.8256	−	29.1428i	−0.924820	−	1.60184i	−0.791851	−	0.610715i	$-0.790882\pi$
$331$	−16.8256	−	29.1428i	−0.924820	−	1.60184i	−0.132969	−	0.991120i	$-0.542451\pi$
$332$	−0.997196	+	1.72719i	−0.0547282	+	0.0947921i
$333$	3.26482	−	5.65483i	0.178911	−	0.309883i
$334$	2.47733	+	4.29086i	0.135553	+	0.234786i
$335$	4.01396			0.219306
$336$	−0.583951	+	8.19660i	−0.0318571	+	0.447161i
$337$	22.7331			1.23835			0.619176	−	0.785252i	$-0.287467\pi$
$337$	22.7331			1.23835			0.619176	+	0.785252i	$0.287467\pi$
$338$	0.677177	+	1.17291i	0.0368336	+	0.0637976i
$339$	−9.03130	+	15.6427i	−0.490513	+	0.849593i
$340$	−0.316345	+	0.547926i	−0.0171562	+	0.0297154i
$341$	3.53953	+	6.13065i	0.191676	+	0.331993i
$342$	−11.8491			−0.640726
$343$	3.92173	−	18.1003i	0.211753	−	0.977323i
$344$	−1.37563			−0.0741690
$345$	−3.95473	−	6.84979i	−0.212915	−	0.368780i
$346$	1.59244	−	2.75818i	0.0856099	−	0.148281i
$347$	−4.40779	+	7.63451i	−0.236622	+	0.409842i	−0.959743	−	0.280880i	$-0.909374\pi$
$347$	−4.40779	+	7.63451i	−0.236622	+	0.409842i	0.723120	+	0.690722i	$0.242707\pi$
$348$	0.606800	+	1.05101i	0.0325279	+	0.0563399i
$349$	−2.89828			−0.155142			−0.0775708	−	0.996987i	$-0.524716\pi$
$349$	−2.89828			−0.155142			−0.0775708	+	0.996987i	$0.524716\pi$
$350$	−0.955867	+	13.4170i	−0.0510932	+	0.717168i
$351$	−4.49738			−0.240052
$352$	0.467499	+	0.809732i	0.0249178	+	0.0431588i
$353$	11.6581	−	20.1925i	0.620500	−	1.07474i	−0.368893	−	0.929472i	$-0.620263\pi$
$353$	11.6581	−	20.1925i	0.620500	−	1.07474i	0.989393	−	0.145265i	$-0.0464035\pi$
$354$	7.11028	−	12.3154i	0.377907	−	0.654555i
$355$	−5.16300	−	8.94257i	−0.274023	−	0.474622i
$356$	−2.39694			−0.127038
$357$	6.94147	−	3.37433i	0.367381	−	0.178589i
$358$	−27.7152			−1.46479
$359$	−12.8204	−	22.2055i	−0.676633	−	1.17196i	−0.975989	−	0.217821i	$-0.930105\pi$
$359$	−12.8204	−	22.2055i	−0.676633	−	1.17196i	0.299356	−	0.954141i	$-0.403228\pi$
$360$	3.72029	−	6.44374i	0.196077	−	0.339615i
$361$	2.08834	−	3.61711i	0.109913	−	0.190374i
$362$	5.93704	+	10.2832i	0.312044	+	0.540476i
$363$	−0.853008			−0.0447713
$364$	−0.363184	−	0.245663i	−0.0190360	−	0.0128763i
$365$	1.07110			0.0560639
$366$	1.83198	+	3.17309i	0.0957593	+	0.165860i
$367$	6.31702	−	10.9414i	0.329746	−	0.571137i	−0.652715	−	0.757603i	$-0.726370\pi$
$367$	6.31702	−	10.9414i	0.329746	−	0.571137i	0.982461	+	0.186466i	$0.0597036\pi$
$368$	−15.1218	+	26.1917i	−0.788278	+	1.36534i
$369$	6.31219	+	10.9330i	0.328600	+	0.569151i
$370$	−4.34442			−0.225856
$371$	−10.8237	−	7.32132i	−0.561938	−	0.380104i
$372$	−1.00073			−0.0518854
$373$	−12.5392	−	21.7185i	−0.649256	−	1.12454i	−0.983301	−	0.181987i	$-0.941747\pi$
$373$	−12.5392	−	21.7185i	−0.649256	−	1.12454i	0.334045	−	0.942557i	$-0.391586\pi$
$374$	−2.31587	+	4.01121i	−0.119751	+	0.207415i
$375$	−4.16785	+	7.21892i	−0.215227	+	0.372783i
$376$	7.39452	+	12.8077i	0.381343	+	0.660506i
$377$	8.58489			0.442144
$378$	−14.4937	+	7.04555i	−0.745473	+	0.362384i
$379$	23.3132			1.19752			0.598759	−	0.800929i	$-0.295661\pi$
$379$	23.3132			1.19752			0.598759	+	0.800929i	$0.295661\pi$
$380$	−0.356141	−	0.616854i	−0.0182696	−	0.0316439i
$381$	−4.76412	+	8.25170i	−0.244073	+	0.422748i
$382$	14.6809	−	25.4281i	0.751140	−	1.30101i
$383$	−2.24570	−	3.88967i	−0.114750	−	0.198753i	0.802930	−	0.596074i	$-0.203273\pi$
$383$	−2.24570	−	3.88967i	−0.114750	−	0.198753i	−0.917680	+	0.397321i	$0.869940\pi$
$384$	8.28073			0.422574
$385$	−0.209886	+	2.94605i	−0.0106968	+	0.150145i
$386$	−2.34644			−0.119431
$387$	−0.532865	−	0.922948i	−0.0270870	−	0.0469161i
$388$	0.224191	−	0.388310i	0.0113816	−	0.0197134i
$389$	−7.39593	+	12.8101i	−0.374989	+	0.649500i	−0.990325	−	0.138765i	$-0.955687\pi$
$389$	−7.39593	+	12.8101i	−0.374989	+	0.649500i	0.615337	+	0.788264i	$0.289020\pi$
$390$	0.644832	+	1.11688i	0.0326523	+	0.0565555i
$391$	28.4063			1.43657
$392$	−20.3247	−	2.91077i	−1.02655	−	0.147016i
$393$	−12.6115			−0.636168
$394$	14.7953	+	25.6262i	0.745377	+	1.29103i
$395$	2.70546	−	4.68599i	0.136126	−	0.235778i
$396$	−0.188295	+	0.326136i	−0.00946217	+	0.0163890i
$397$	8.91889	+	15.4480i	0.447626	+	0.775311i	0.998231	−	0.0594546i	$-0.0189362\pi$
$397$	8.91889	+	15.4480i	0.447626	+	0.775311i	−0.550605	+	0.834766i	$0.685603\pi$
$398$	−4.58986			−0.230069
$399$	−0.617473	+	8.66713i	−0.0309123	+	0.433899i
$400$	13.6680			0.683398
$401$	−8.53768	−	14.7877i	−0.426351	−	0.738462i	0.570194	−	0.821510i	$-0.306868\pi$
$401$	−8.53768	−	14.7877i	−0.426351	−	0.738462i	−0.996546	+	0.0830478i	$0.973535\pi$
$402$	−2.07701	+	3.59748i	−0.103592	+	0.179426i
$403$	−3.53953	+	6.13065i	−0.176317	+	0.305389i
$404$	1.49166	+	2.58363i	0.0742129	+	0.128541i
$405$	3.32758			0.165349
$406$	27.6664	−	13.4490i	1.37306	−	0.667462i
$407$	2.87348			0.142433
$408$	−4.27829	−	7.41022i	−0.211807	−	0.366861i
$409$	13.5492	−	23.4679i	0.669964	−	1.16041i	−0.307949	−	0.951403i	$-0.599643\pi$
$409$	13.5492	−	23.4679i	0.669964	−	1.16041i	0.977914	−	0.209010i	$-0.0670240\pi$
$410$	4.19975	−	7.27417i	0.207411	−	0.359246i
$411$	−2.67696	−	4.63663i	−0.132045	−	0.228708i
$412$	−1.51586			−0.0746810
$413$	26.9756	+	18.2467i	1.32738	+	0.897861i
$414$	−25.5632			−1.25636
$415$	6.71713	+	11.6344i	0.329731	+	0.571111i
$416$	−0.467499	+	0.809732i	−0.0229210	+	0.0397004i
$417$	−5.81307	+	10.0685i	−0.284667	+	0.493058i
$418$	−2.60720	−	4.51581i	−0.127523	−	0.220875i
$419$	−32.6971			−1.59736			−0.798679	−	0.601757i	$-0.794468\pi$
$419$	−32.6971			−1.59736			−0.798679	+	0.601757i	$0.794468\pi$
$420$	−0.345837	−	0.233929i	−0.0168751	−	0.0114146i
$421$	14.5209			0.707705			0.353852	−	0.935301i	$-0.384872\pi$
$421$	14.5209			0.707705			0.353852	+	0.935301i	$0.384872\pi$
$422$	8.47930	+	14.6866i	0.412766	+	0.714931i
$423$	−5.72869	+	9.92238i	−0.278538	+	0.482442i
$424$	−7.24339	+	12.5459i	−0.351770	+	0.609284i
$425$	−6.41882	−	11.1177i	−0.311358	−	0.539289i
$426$	10.6863			0.517751
$427$	−7.54662	+	3.66850i	−0.365206	+	0.177531i
$428$	−2.01172			−0.0972399
$429$	−0.426504	−	0.738727i	−0.0205918	−	0.0356661i
$430$	−0.354535	+	0.614073i	−0.0170972	+	0.0296132i
$431$	−3.90391	+	6.76178i	−0.188045	+	0.325703i	−0.944598	−	0.328229i	$-0.893548\pi$
$431$	−3.90391	+	6.76178i	−0.188045	+	0.325703i	0.756553	+	0.653932i	$0.226882\pi$
$432$	8.18767	+	14.1815i	0.393930	+	0.682306i
$433$	29.0179			1.39451			0.697255	−	0.716823i	$-0.254405\pi$
$433$	29.0179			1.39451			0.697255	+	0.716823i	$0.254405\pi$
$434$	−1.80260	+	25.3022i	−0.0865277	+	1.21454i
$435$	8.17483			0.391953
$436$	0.719529	+	1.24626i	0.0344592	+	0.0596851i
$437$	−15.9899	+	27.6953i	−0.764900	+	1.32485i
$438$	−0.554235	+	0.959963i	−0.0264824	+	0.0458688i
$439$	−4.41128	−	7.64057i	−0.210539	−	0.364664i	0.741344	−	0.671125i	$-0.234189\pi$
$439$	−4.41128	−	7.64057i	−0.210539	−	0.364664i	−0.951883	+	0.306461i	$0.900855\pi$
$440$	3.27436			0.156099
$441$	−5.92008	−	14.7639i	−0.281909	−	0.703045i
$442$	−4.63174			−0.220309
$443$	2.26974	+	3.93130i	0.107839	+	0.186782i	0.914894	−	0.403693i	$-0.132274\pi$
$443$	2.26974	+	3.93130i	0.107839	+	0.186782i	−0.807056	+	0.590475i	$0.798940\pi$
$444$	−0.203105	+	0.351787i	−0.00963891	+	0.0166951i
$445$	−8.07293	+	13.9827i	−0.382693	+	0.662844i
$446$	4.99286	+	8.64789i	0.236419	+	0.409490i
$447$	11.7566			0.556068
$448$	−1.60724	+	22.5600i	−0.0759351	+	1.06586i
$449$	−16.1604			−0.762658			−0.381329	−	0.924439i	$-0.624533\pi$
$449$	−16.1604			−0.762658			−0.381329	+	0.924439i	$0.624533\pi$
$450$	5.77638	+	10.0050i	0.272301	+	0.471639i
$451$	−2.77779	+	4.81128i	−0.130801	+	0.226554i
$452$	−1.75463	+	3.03910i	−0.0825307	+	0.142947i
$453$	−9.81453	−	16.9993i	−0.461127	−	0.798695i
$454$	−9.07167			−0.425755
$455$	−2.65630	+	1.29126i	−0.124529	+	0.0605352i
$456$	9.63300			0.451106
$457$	8.79744	+	15.2376i	0.411527	+	0.712786i	0.995057	−	0.0993059i	$-0.0316622\pi$
$457$	8.79744	+	15.2376i	0.411527	+	0.712786i	−0.583530	+	0.812092i	$0.698329\pi$
$458$	2.36196	−	4.09104i	0.110367	−	0.191162i
$459$	7.69027	−	13.3199i	0.358951	−	0.621722i
$460$	−0.768336	−	1.33080i	−0.0358239	−	0.0620488i
$461$	−20.1098			−0.936607			−0.468303	−	0.883568i	$-0.655135\pi$
$461$	−20.1098			−0.936607			−0.468303	+	0.883568i	$0.655135\pi$
$462$	−2.53177	−	1.71253i	−0.117789	−	0.0796741i
$463$	−7.52186			−0.349570			−0.174785	−	0.984607i	$-0.555923\pi$
$463$	−7.52186			−0.349570			−0.174785	+	0.984607i	$0.555923\pi$
$464$	−15.6292	−	27.0705i	−0.725565	−	1.25672i
$465$	−3.37047	+	5.83782i	−0.156302	+	0.270722i
$466$	−1.32537	+	2.29561i	−0.0613966	+	0.106342i
$467$	7.88230	+	13.6525i	0.364749	+	0.631764i	0.988736	−	0.149671i	$-0.0478214\pi$
$467$	7.88230	+	13.6525i	0.364749	+	0.631764i	−0.623987	+	0.781435i	$0.714488\pi$
$468$	−0.376589			−0.0174079
$469$	−7.87991	−	5.33010i	−0.363861	−	0.246121i
$470$	7.62303			0.351624
$471$	−8.89435	−	15.4055i	−0.409830	−	0.709847i
$472$	18.0525	−	31.2678i	0.830933	−	1.43922i
$473$	0.234496	−	0.406160i	0.0107822	−	0.0186752i
$474$	2.79985	+	4.84948i	0.128601	+	0.222744i
$475$	14.4526			0.663130
$476$	1.34861	−	0.655575i	0.0618134	−	0.0300482i
$477$	−11.2232			−0.513875
$478$	−8.80814	−	15.2562i	−0.402875	−	0.697800i
$479$	16.8257	−	29.1430i	0.768788	−	1.33158i	−0.169433	−	0.985542i	$-0.554194\pi$
$479$	16.8257	−	29.1430i	0.768788	−	1.33158i	0.938221	−	0.346038i	$-0.112473\pi$
$480$	−0.445169	+	0.771055i	−0.0203191	+	0.0351937i
$481$	1.43674	+	2.48851i	0.0655098	+	0.113466i
$482$	18.9075			0.861213
$483$	−1.33213	+	18.6984i	−0.0606142	+	0.850808i
$484$	−0.165725			−0.00753295
$485$	−1.51015	−	2.61566i	−0.0685725	−	0.118771i
$486$	−10.8584	+	18.8073i	−0.492547	+	0.853117i
$487$	−5.66666	+	9.81495i	−0.256781	+	0.444758i	−0.965378	−	0.260856i	$-0.915995\pi$
$487$	−5.66666	+	9.81495i	−0.256781	+	0.444758i	0.708597	+	0.705614i	$0.249329\pi$
$488$	4.65127	+	8.05624i	0.210553	+	0.364689i
$489$	−7.91592			−0.357970
$490$	−6.53756	+	8.32266i	−0.295337	+	0.375980i
$491$	−2.01433			−0.0909054			−0.0454527	−	0.998966i	$-0.514473\pi$
$491$	−2.01433			−0.0909054			−0.0454527	+	0.998966i	$0.514473\pi$
$492$	−0.392682	−	0.680144i	−0.0177035	−	0.0306633i
$493$	−14.6797	+	25.4260i	−0.661140	+	1.14513i
$494$	2.60720	−	4.51581i	0.117304	−	0.203176i
$495$	1.26836	+	2.19686i	0.0570084	+	0.0987415i
$496$	25.7755			1.15735
$497$	−1.73913	+	24.4113i	−0.0780108	+	1.09500i
$498$	−13.9030			−0.623008
$499$	−8.72181	−	15.1066i	−0.390442	−	0.676265i	0.602066	−	0.798446i	$-0.294344\pi$
$499$	−8.72181	−	15.1066i	−0.390442	−	0.676265i	−0.992508	+	0.122181i	$0.961011\pi$
$500$	−0.809741	+	1.40251i	−0.0362127	+	0.0627223i
$501$	1.56029	−	2.70250i	0.0697085	−	0.120739i
$502$	−11.9709	−	20.7343i	−0.534289	−	0.925415i
$503$	11.3619			0.506602			0.253301	−	0.967387i	$-0.418484\pi$
$503$	11.3619			0.506602			0.253301	+	0.967387i	$0.418484\pi$
$504$	−15.8600	+	7.70972i	−0.706459	+	0.343418i
$505$	20.0957			0.894247
$506$	−5.62477	−	9.74239i	−0.250052	−	0.433102i
$507$	0.426504	−	0.738727i	0.0189417	−	0.0328080i
$508$	−0.925588	+	1.60317i	−0.0410663	+	0.0711289i
$509$	−1.24319	−	2.15326i	−0.0551033	−	0.0954418i	0.837158	−	0.546961i	$-0.184215\pi$
$509$	−1.24319	−	2.15326i	−0.0551033	−	0.0954418i	−0.892261	+	0.451519i	$0.850882\pi$
$510$	−4.41051			−0.195301
$511$	−2.10270	−	1.42230i	−0.0930180	−	0.0629189i
$512$	24.7642			1.09443
$513$	8.65770	+	14.9956i	0.382247	+	0.662071i
$514$	6.14987	−	10.6519i	0.271259	−	0.469834i
$515$	−5.10542	+	8.84286i	−0.224972	+	0.389663i
$516$	0.0331495	+	0.0574166i	0.00145933	+	0.00252763i
$517$	−5.04202			−0.221748
$518$	8.52865	+	5.76891i	0.374727	+	0.253471i
$519$	−2.00592			−0.0880500
$520$	1.63718	+	2.83568i	0.0717951	+	0.124353i
$521$	−8.01071	+	13.8750i	−0.350955	+	0.607873i	−0.986417	−	0.164260i	$-0.947476\pi$
$521$	−8.01071	+	13.8750i	−0.350955	+	0.607873i	0.635462	+	0.772132i	$0.280810\pi$
$522$	13.2104	−	22.8812i	0.578205	−	1.00148i
$523$	7.92790	+	13.7315i	0.346663	+	0.600438i	0.985654	−	0.168776i	$-0.0539814\pi$
$523$	7.92790	+	13.7315i	0.346663	+	0.600438i	−0.638991	+	0.769214i	$0.720648\pi$
$524$	−2.45021			−0.107038
$525$	7.61925	−	3.70381i	0.332531	−	0.161648i
$526$	−16.5911			−0.723406
$527$	−12.1048	−	20.9661i	−0.527294	−	0.913299i
$528$	−1.55294	+	2.68977i	−0.0675829	+	0.117057i
$529$	−22.9965	+	39.8311i	−0.999848	+	1.73179i
$530$	3.73362	+	6.46682i	0.162178	+	0.280901i
$531$	27.9713			1.21385
$532$	−0.119964	+	1.68388i	−0.00520112	+	0.0730053i
$533$	−5.55558			−0.240639
$534$	−8.35459	−	14.4706i	−0.361538	−	0.626203i
$535$	−6.77548	+	11.7355i	−0.292929	+	0.507369i
$536$	−5.27337	+	9.13374i	−0.227775	+	0.394517i
$537$	8.72787	+	15.1171i	0.376635	+	0.652351i
$538$	1.87187			0.0807022
$539$	4.32406	−	5.50477i	0.186251	−	0.237107i
$540$	−0.832029			−0.0358048
$541$	4.48786	+	7.77320i	0.192948	+	0.334196i	0.946226	−	0.323506i	$-0.104862\pi$
$541$	4.48786	+	7.77320i	0.192948	+	0.334196i	−0.753278	+	0.657703i	$0.771528\pi$
$542$	−17.2834	+	29.9357i	−0.742384	+	1.28585i
$543$	3.73930	−	6.47666i	0.160469	−	0.277940i
$544$	−1.59879	−	2.76919i	−0.0685477	−	0.118728i
$545$	9.69353			0.415225
$546$	0.217209	−	3.04884i	0.00929568	−	0.130478i
$547$	1.65695			0.0708459			0.0354230	−	0.999372i	$-0.488722\pi$
$547$	1.65695			0.0708459			0.0354230	+	0.999372i	$0.488722\pi$
$548$	−0.520088	−	0.900819i	−0.0222171	−	0.0384811i
$549$	−3.60343	+	6.24133i	−0.153791	+	0.266373i
$550$	−2.54200	+	4.40287i	−0.108391	+	0.187739i
$551$	−16.5264	−	28.6245i	−0.704047	−	1.21944i
$552$	20.7822			0.884548
$553$	−11.5336	+	5.60663i	−0.490459	+	0.238418i
$554$	−17.2126			−0.731292
$555$	1.36812	+	2.36965i	0.0580733	+	0.100586i
$556$	−1.12938	+	1.95614i	−0.0478964	+	0.0829590i
$557$	−20.6115	+	35.7001i	−0.873336	+	1.51266i	−0.0148107	+	0.999890i	$0.504715\pi$
$557$	−20.6115	+	35.7001i	−0.873336	+	1.51266i	−0.858525	+	0.512772i	$0.828619\pi$
$558$	10.8933	+	18.8677i	0.461149	+	0.798734i
$559$	0.468993			0.0198363
$560$	8.90761	+	6.02525i	0.376415	+	0.254613i
$561$	2.91719			0.123164
$562$	−0.748923	−	1.29717i	−0.0315914	−	0.0547179i
$563$	−22.5348	+	39.0314i	−0.949728	+	1.64498i	−0.203731	+	0.979027i	$0.565307\pi$
$563$	−22.5348	+	39.0314i	−0.949728	+	1.64498i	−0.745997	+	0.665949i	$0.768027\pi$
$564$	0.356382	−	0.617271i	0.0150064	−	0.0259918i
$565$	11.8192	+	20.4715i	0.497238	+	0.861241i
$566$	1.92262			0.0808137
$567$	−6.53246	−	4.41866i	−0.274337	−	0.185566i
$568$	27.1317			1.13842
$569$	−5.47602	−	9.48475i	−0.229567	−	0.397621i	0.728113	−	0.685457i	$-0.240398\pi$
$569$	−5.47602	−	9.48475i	−0.229567	−	0.397621i	−0.957680	+	0.287836i	$0.907064\pi$
$570$	2.48267	−	4.30011i	0.103988	−	0.180112i
$571$	−1.80667	+	3.12924i	−0.0756067	+	0.130955i	−0.901350	−	0.433092i	$-0.857423\pi$
$571$	−1.80667	+	3.12924i	−0.0756067	+	0.130955i	0.825743	+	0.564046i	$0.190756\pi$
$572$	−0.0828624	−	0.143522i	−0.00346465	−	0.00600095i
$573$	−18.4928			−0.772549
$574$	−17.9039	+	8.70332i	−0.747295	+	0.363269i
$575$	31.1800			1.30029
$576$	9.71270	+	16.8229i	0.404696	+	0.700954i
$577$	−12.3206	+	21.3399i	−0.512913	+	0.888391i	0.486975	+	0.873416i	$0.338100\pi$
$577$	−12.3206	+	21.3399i	−0.512913	+	0.888391i	−0.999888	+	0.0149749i	$0.995233\pi$
$578$	−3.59199	+	6.22151i	−0.149407	+	0.258781i
$579$	0.738924	+	1.27985i	0.0307086	+	0.0531889i
$580$	1.58823			0.0659477
$581$	2.26264	−	31.7594i	0.0938700	−	1.31760i
$582$	3.12569			0.129564
$583$	−2.46949	−	4.27728i	−0.102276	−	0.177147i
$584$	−1.40716	+	2.43728i	−0.0582288	+	0.100855i
$585$	−1.26836	+	2.19686i	−0.0524401	+	0.0908289i
$586$	−21.7690	−	37.7050i	−0.899268	−	1.55758i
$587$	−3.76341			−0.155332			−0.0776662	−	0.996979i	$-0.524747\pi$
$587$	−3.76341			−0.155332			−0.0776662	+	0.996979i	$0.524747\pi$
$588$	0.368288	+	0.918465i	0.0151880	+	0.0378769i
$589$	27.2551			1.12303
$590$	−9.30518	−	16.1170i	−0.383088	−	0.663528i
$591$	9.31848	−	16.1401i	0.383311	−	0.663914i
$592$	5.23130	−	9.06088i	0.215005	−	0.372400i
$593$	−1.89800	−	3.28743i	−0.0779414	−	0.134998i	0.824420	−	0.565978i	$-0.191501\pi$
$593$	−1.89800	−	3.28743i	−0.0779414	−	0.134998i	−0.902362	+	0.430980i	$0.858168\pi$
$594$	−6.09105			−0.249919
$595$	0.717786	−	10.0752i	0.0294264	−	0.413042i
$596$	2.28411			0.0935606
$597$	1.44541	+	2.50352i	0.0591566	+	0.102462i
$598$	5.62477	−	9.74239i	0.230014	−	0.398396i
$599$	24.0196	−	41.6032i	0.981415	−	1.69986i	0.324518	−	0.945879i	$-0.394798\pi$
$599$	24.0196	−	41.6032i	0.981415	−	1.69986i	0.656896	−	0.753981i	$-0.271869\pi$
$600$	−4.69604	−	8.13378i	−0.191715	−	0.332060i
$601$	−17.6581			−0.720288			−0.360144	−	0.932897i	$-0.617273\pi$
$601$	−17.6581			−0.720288			−0.360144	+	0.932897i	$0.617273\pi$
$602$	1.51142	−	0.734719i	0.0616008	−	0.0299449i
$603$	−8.17077			−0.332739
$604$	−1.90680	−	3.30267i	−0.0775864	−	0.134384i
$605$	−0.558163	+	0.966767i	−0.0226926	+	0.0393047i
$606$	−10.3984	+	18.0106i	−0.422407	+	0.731631i
$607$	15.6974	+	27.1887i	0.637137	+	1.10355i	0.986058	+	0.166402i	$0.0532149\pi$
$607$	15.6974	+	27.1887i	0.637137	+	1.10355i	−0.348921	+	0.937152i	$0.613452\pi$
$608$	3.59984			0.145993
$609$	−16.0482	−	10.8553i	−0.650306	−	0.439878i
$610$	4.79501			0.194144
$611$	−2.52101	−	4.36652i	−0.101989	−	0.176650i
$612$	0.643947	−	1.11535i	0.0260300	−	0.0450853i
$613$	11.8294	−	20.4892i	0.477786	−	0.827550i	−0.521890	−	0.853013i	$-0.674773\pi$
$613$	11.8294	−	20.4892i	0.477786	−	0.827550i	0.999676	+	0.0254634i	$0.00810612\pi$
$614$	10.0190	+	17.3534i	0.404335	+	0.700328i
$615$	−5.29022			−0.213322
$616$	−6.42798	−	4.34799i	−0.258991	−	0.175185i
$617$	30.7318			1.23722			0.618608	−	0.785700i	$-0.287697\pi$
$617$	30.7318			1.23722			0.618608	+	0.785700i	$0.287697\pi$
$618$	−5.28355	−	9.15138i	−0.212536	−	0.368123i
$619$	−4.92975	+	8.53859i	−0.198144	+	0.343195i	−0.947927	−	0.318489i	$-0.896825\pi$
$619$	−4.92975	+	8.53859i	−0.198144	+	0.343195i	0.749783	+	0.661684i	$0.230158\pi$
$620$	−0.654824	+	1.13419i	−0.0262984	+	0.0455501i
$621$	18.6781	+	32.3514i	0.749525	+	1.29822i
$622$	9.02567			0.361896
$623$	34.4157	−	16.7299i	1.37883	−	0.670268i
$624$	−3.10587			−0.124335
$625$	−3.93011	−	6.80714i	−0.157204	−	0.272286i
$626$	−0.506708	+	0.877645i	−0.0202521	+	0.0350777i
$627$	−1.64209	+	2.84418i	−0.0655786	+	0.113585i
$628$	−1.72802	−	2.99302i	−0.0689555	−	0.119434i
$629$	−9.82700			−0.391828
$630$	−0.645946	+	9.06679i	−0.0257351	+	0.361229i
$631$	6.13739			0.244326			0.122163	−	0.992510i	$-0.461017\pi$
$631$	6.13739			0.244326			0.122163	+	0.992510i	$0.461017\pi$
$632$	7.10861	+	12.3125i	0.282765	+	0.489764i
$633$	5.34048	−	9.24999i	0.212265	−	0.367654i
$634$	−20.3985	+	35.3312i	−0.810128	+	1.40318i
$635$	6.23478	+	10.7990i	0.247420	+	0.428543i
$636$	0.698196			0.0276853
$637$	6.92930	+	0.992366i	0.274549	+	0.0393190i
$638$	11.6270			0.460316
$639$	10.5097	+	18.2034i	0.415758	+	0.720114i
$640$	5.41847	−	9.38507i	0.214184	−	0.370977i
$641$	0.875073	−	1.51567i	0.0345633	−	0.0598654i	−0.848226	−	0.529634i	$-0.822329\pi$
$641$	0.875073	−	1.51567i	0.0345633	−	0.0598654i	0.882790	+	0.469769i	$0.155663\pi$
$642$	−7.01187	−	12.1449i	−0.276737	−	0.479322i
$643$	−20.2414			−0.798241			−0.399121	−	0.916898i	$-0.630685\pi$
$643$	−20.2414			−0.798241			−0.399121	+	0.916898i	$0.630685\pi$
$644$	−0.258811	+	3.63279i	−0.0101986	+	0.143152i
$645$	0.446592			0.0175845
$646$	8.91635	+	15.4436i	0.350809	+	0.607619i
$647$	18.2926	−	31.6837i	0.719155	−	1.24561i	−0.242180	−	0.970231i	$-0.577862\pi$
$647$	18.2926	−	31.6837i	0.719155	−	1.24561i	0.961335	−	0.275382i	$-0.0888042\pi$
$648$	−4.37163	+	7.57188i	−0.171734	+	0.297451i
$649$	6.15462	+	10.6601i	0.241590	+	0.418446i
$650$	−5.08400			−0.199411
$651$	14.3686	−	6.98476i	0.563150	−	0.273754i
$652$	−1.53793			−0.0602299
$653$	19.3020	+	33.4321i	0.755347	+	1.30830i	0.945202	+	0.326487i	$0.105865\pi$
$653$	19.3020	+	33.4321i	0.755347	+	1.30830i	−0.189855	+	0.981812i	$0.560802\pi$
$654$	−5.01587	+	8.68774i	−0.196136	+	0.339718i
$655$	−8.25232	+	14.2934i	−0.322445	+	0.558491i
$656$	10.1142	+	17.5183i	0.394892	+	0.683974i
$657$	−2.18031			−0.0850622
$658$	−14.9650	−	10.1225i	−0.583395	−	0.394618i
$659$	4.77197			0.185889			0.0929447	−	0.995671i	$-0.470372\pi$
$659$	4.77197			0.185889			0.0929447	+	0.995671i	$0.470372\pi$
$660$	−0.0789045	−	0.136667i	−0.00307135	−	0.00531974i
$661$	−23.1702	+	40.1319i	−0.901216	+	1.56095i	−0.0752975	+	0.997161i	$0.523991\pi$
$661$	−23.1702	+	40.1319i	−0.901216	+	1.56095i	−0.825918	+	0.563790i	$0.809343\pi$
$662$	22.7879	−	39.4697i	0.885675	−	1.53403i
$663$	1.45860	+	2.52636i	0.0566472	+	0.0981158i
$664$	−35.2987			−1.36985
$665$	9.41896	+	6.37113i	0.365252	+	0.247062i
$666$	8.84345			0.342677
$667$	−35.6539	−	61.7544i	−1.38052	−	2.39114i
$668$	0.303137	−	0.525049i	0.0117287	−	0.0203148i
$669$	3.14464	−	5.44667i	0.121579	−	0.210580i
$670$	2.71816	+	4.70800i	0.105012	+	0.181886i
$671$	−3.17151			−0.122435
$672$	1.89780	−	0.922543i	0.0732091	−	0.0355879i
$673$	39.0171			1.50400			0.751999	−	0.659164i	$-0.229090\pi$
$673$	39.0171			1.50400			0.751999	+	0.659164i	$0.229090\pi$
$674$	15.3944	+	26.6638i	0.592968	+	1.02705i
$675$	8.44117	−	14.6205i	0.324901	−	0.562745i
$676$	0.0828624	−	0.143522i	0.00318702	−	0.00552008i
$677$	−16.0329	−	27.7697i	−0.616193	−	1.06728i	−0.990174	−	0.139841i	$-0.955341\pi$
$677$	−16.0329	−	27.7697i	−0.616193	−	1.06728i	0.373981	−	0.927436i	$-0.377993\pi$
$678$	−24.4632			−0.939502
$679$	−0.508689	+	7.14019i	−0.0195217	+	0.274015i
$680$	−11.1980			−0.429422
$681$	2.85679	+	4.94810i	0.109472	+	0.189612i
$682$	−4.79378	+	8.30307i	−0.183563	+	0.317941i
$683$	12.2261	−	21.1763i	0.467820	−	0.810287i	−0.531504	−	0.847056i	$-0.678373\pi$
$683$	12.2261	−	21.1763i	0.467820	−	0.810287i	0.999324	+	0.0367683i	$0.0117064\pi$
$684$	0.724955	+	1.25566i	0.0277193	+	0.0480113i
$685$	−7.00665			−0.267710
$686$	23.8856	−	7.65728i	0.911957	−	0.292356i
$687$	−2.97525			−0.113513
$688$	−0.853822	−	1.47886i	−0.0325516	−	0.0563811i
$689$	2.46949	−	4.27728i	0.0940799	−	0.162951i
$690$	5.35610	−	9.27704i	0.203903	−	0.353171i
$691$	10.1666	+	17.6091i	0.386757	+	0.669883i	0.992011	−	0.126149i	$-0.0402618\pi$
$691$	10.1666	+	17.6091i	0.386757	+	0.669883i	−0.605254	+	0.796032i	$0.706929\pi$
$692$	−0.389715			−0.0148148
$693$	0.427241	−	5.99695i	0.0162295	−	0.227805i
$694$	−11.9394			−0.453214
$695$	7.60753	+	13.1766i	0.288570	+	0.499818i
$696$	−10.7397	+	18.6017i	−0.407088	+	0.705098i
$697$	9.49974	−	16.4540i	0.359828	−	0.623241i
$698$	−1.96265	−	3.39941i	−0.0742875	−	0.128670i
$699$	1.66951			0.0631465
$700$	1.48029	−	0.719587i	0.0559497	−	0.0271978i
$701$	11.6546			0.440189			0.220095	−	0.975479i	$-0.429363\pi$
$701$	11.6546			0.440189			0.220095	+	0.975479i	$0.429363\pi$
$702$	−3.04552	−	5.27500i	−0.114946	−	0.199092i
$703$	5.53161	−	9.58103i	0.208629	−	0.361355i
$704$	−4.27424	+	7.40321i	−0.161092	+	0.279019i
$705$	−2.40059	−	4.15795i	−0.0904116	−	0.156597i
$706$	31.5785			1.18847
$707$	−39.4504	−	26.6849i	−1.48368	−	1.00359i
$708$	−1.74009			−0.0653967
$709$	−13.2565	−	22.9609i	−0.497858	−	0.862316i	0.502139	−	0.864787i	$-0.332547\pi$
$709$	−13.2565	−	22.9609i	−0.497858	−	0.862316i	−0.999997	+	0.00247128i	$0.999213\pi$
$710$	6.99253	−	12.1114i	0.262425	−	0.454533i
$711$	−5.50719	+	9.53873i	−0.206536	+	0.357730i
$712$	−21.2117	−	36.7397i	−0.794942	−	1.37688i
$713$	58.8001			2.20208
$714$	8.65838	+	5.85666i	0.324032	+	0.219180i
$715$	−1.11633			−0.0417482
$716$	1.69568	+	2.93700i	0.0633704	+	0.109761i
$717$	−5.54760	+	9.60873i	−0.207179	+	0.358845i
$718$	17.3633	−	30.0741i	0.647993	−	1.12236i
$719$	3.81392	+	6.60589i	0.142235	+	0.246358i	0.928338	−	0.371737i	$-0.121238\pi$
$719$	3.81392	+	6.60589i	0.142235	+	0.246358i	−0.786103	+	0.618096i	$0.787904\pi$
$720$	9.23639			0.344220
$721$	21.7649	−	10.5802i	0.810568	−	0.394027i
$722$	5.65670			0.210521
$723$	−5.95422	−	10.3130i	−0.221440	−	0.383545i
$724$	0.726483	−	1.25830i	0.0269995	−	0.0467645i
$725$	−16.1130	+	27.9086i	−0.598423	+	1.03650i
$726$	−0.577637	−	1.00050i	−0.0214381	−	0.0371319i
$727$	−7.84437			−0.290931			−0.145466	−	0.989363i	$-0.546468\pi$
$727$	−7.84437			−0.290931			−0.145466	+	0.989363i	$0.546468\pi$
$728$	0.551477	−	7.74079i	0.0204391	−	0.286893i
$729$	4.73533			0.175383
$730$	0.725324	+	1.25630i	0.0268454	+	0.0464977i
$731$	−0.801952	+	1.38902i	−0.0296613	+	0.0513748i
$732$	0.224170	−	0.388273i	0.00828555	−	0.0143510i
$733$	−20.0458	−	34.7203i	−0.740407	−	1.28242i	−0.952310	−	0.305132i	$-0.901299\pi$
$733$	−20.0458	−	34.7203i	−0.740407	−	1.28242i	0.211903	−	0.977291i	$-0.432034\pi$
$734$	17.1110			0.631578
$735$	6.59832	+	0.944965i	0.243383	+	0.0348556i
$736$	7.76628			0.286269
$737$	−1.79785	−	3.11396i	−0.0662245	−	0.114704i
$738$	−8.54894	+	14.8072i	−0.314691	+	0.545061i
$739$	−8.02699	+	13.9032i	−0.295278	+	0.511436i	−0.975049	−	0.221988i	$-0.928745\pi$
$739$	−8.02699	+	13.9032i	−0.295278	+	0.511436i	0.679772	+	0.733424i	$0.262079\pi$
$740$	0.265802	+	0.460382i	0.00977106	+	0.0169240i
$741$	−3.28417			−0.120647
$742$	1.25765	−	17.6530i	0.0461699	−	0.648062i
$743$	3.11202			0.114169			0.0570845	−	0.998369i	$-0.481820\pi$
$743$	3.11202			0.114169			0.0570845	+	0.998369i	$0.481820\pi$
$744$	−8.85593	−	15.3389i	−0.324674	−	0.562352i
$745$	7.69289	−	13.3245i	0.281846	−	0.488171i
$746$	16.9825	−	29.4146i	0.621775	−	1.07695i
$747$	−13.6733	−	23.6828i	−0.500280	−	0.866510i
$748$	0.566761			0.0207228
$749$	28.8845	−	14.0411i	1.05542	−	0.513051i
$750$	−11.2895			−0.412233
$751$	−1.61771	−	2.80196i	−0.0590311	−	0.102245i	0.835000	−	0.550251i	$-0.185468\pi$
$751$	−1.61771	−	2.80196i	−0.0590311	−	0.102245i	−0.894031	+	0.448006i	$0.852134\pi$
$752$	−9.17921	+	15.8989i	−0.334731	+	0.579772i
$753$	−7.53960	+	13.0590i	−0.274758	+	0.475896i
$754$	5.81349	+	10.0693i	0.211715	+	0.366701i
$755$	−25.6884			−0.934897
$756$	1.63338	+	1.10484i	0.0594053	+	0.0401827i
$757$	28.0816			1.02064			0.510321	−	0.859984i	$-0.329527\pi$
$757$	28.0816			1.02064			0.510321	+	0.859984i	$0.329527\pi$
$758$	15.7872	+	27.3442i	0.573416	+	0.993185i
$759$	−3.54263	+	6.13601i	−0.128589	+	0.222723i
$760$	6.30332	−	10.9177i	0.228645	−	0.396026i
$761$	−5.56388	−	9.63692i	−0.201691	−	0.349338i	0.747383	−	0.664394i	$-0.231310\pi$
$761$	−5.56388	−	9.63692i	−0.201691	−	0.349338i	−0.949073	+	0.315056i	$0.897977\pi$
$762$	−12.9046			−0.467485
$763$	−19.0296	−	12.8719i	−0.688918	−	0.465995i
$764$	−3.59284			−0.129984
$765$	−4.33764	−	7.51302i	−0.156828	−	0.271634i
$766$	3.04148	−	5.26800i	0.109893	−	0.190340i
$767$	−6.15462	+	10.6601i	−0.222231	+	0.384915i
$768$	−1.68441	−	2.91748i	−0.0607808	−	0.105275i
$769$	17.0347			0.614287			0.307144	−	0.951663i	$-0.400627\pi$
$769$	17.0347			0.614287			0.307144	+	0.951663i	$0.400627\pi$
$770$	−3.59757	+	1.74882i	−0.129647	+	0.0630233i
$771$	−7.74670			−0.278990
$772$	0.143560	+	0.248654i	0.00516685	+	0.00894925i
$773$	−10.8165	+	18.7348i	−0.389044	+	0.673843i	−0.992321	−	0.123688i	$-0.960528\pi$
$773$	−10.8165	+	18.7348i	−0.389044	+	0.673843i	0.603277	+	0.797531i	$0.293861\pi$
$774$	0.721687	−	1.25000i	0.0259405	−	0.0449303i
$775$	−13.2867	−	23.0133i	−0.477274	−	0.826663i
$776$	7.93589			0.284882
$777$	0.460844	−	6.46862i	0.0165327	−	0.232060i
$778$	−20.0334			−0.718233
$779$	10.6948	+	18.5239i	0.383181	+	0.663689i
$780$	0.0789045	−	0.136667i	0.00282524	−	0.00489345i
$781$	−4.62499	+	8.01072i	−0.165495	+	0.286646i
$782$	19.2361	+	33.3179i	0.687881	+	1.19145i
$783$	−38.6095			−1.37979
$784$	−9.48589	−	23.6566i	−0.338782	−	0.844879i
$785$	−23.2800			−0.830898
$786$	−8.54025	−	14.7921i	−0.304621	−	0.527618i
$787$	19.5964	−	33.9419i	0.698535	−	1.20990i	−0.270440	−	0.962737i	$-0.587169\pi$
$787$	19.5964	−	33.9419i	0.698535	−	1.20990i	0.968975	−	0.247161i	$-0.0794975\pi$
$788$	1.81042	−	3.13574i	0.0644936	−	0.111706i
$789$	5.22475	+	9.04954i	0.186006	+	0.322172i
$790$	7.32829			0.260729
$791$	3.98125	−	55.8826i	0.141557	−	1.98696i
$792$	−6.66524			−0.236839
$793$	−1.58576	−	2.74661i	−0.0563118	−	0.0975349i
$794$	−12.0793	+	20.9220i	−0.428680	+	0.742495i
$795$	2.35153	−	4.07297i	0.0834002	−	0.144453i
$796$	0.280818	+	0.486391i	0.00995333	+	0.0172397i
$797$	51.6070			1.82801			0.914006	−	0.405700i	$-0.132972\pi$
$797$	51.6070			1.82801			0.914006	+	0.405700i	$0.132972\pi$
$798$	−10.5839	+	5.14495i	−0.374665	+	0.182129i
$799$	17.2432			0.610019
$800$	−1.75490	−	3.03958i	−0.0620453	−	0.107466i
$801$	16.4331	−	28.4630i	0.580636	−	1.00569i
$802$	11.5630	−	20.0278i	0.408305	−	0.707205i
$803$	−0.479743	−	0.830939i	−0.0169298	−	0.0293232i
$804$	0.508304			0.0179265
$805$	20.3204	+	13.7451i	0.716201	+	0.484449i
$806$	−9.58756			−0.337707
$807$	−0.589478	−	1.02101i	−0.0207506	−	0.0359411i
$808$	−26.4008	+	45.7276i	−0.928779	+	1.60869i
$809$	4.07725	−	7.06201i	0.143349	−	0.248287i	−0.785407	−	0.618980i	$-0.787546\pi$
$809$	4.07725	−	7.06201i	0.143349	−	0.248287i	0.928756	+	0.370693i	$0.120880\pi$
$810$	2.25336	+	3.90294i	0.0791750	+	0.137135i
$811$	10.4275			0.366158			0.183079	−	0.983098i	$-0.441394\pi$
$811$	10.4275			0.366158			0.183079	+	0.983098i	$0.441394\pi$
$812$	−3.11789	−	2.10899i	−0.109417	−	0.0740111i
$813$	21.7710			0.763544
$814$	1.94586	+	3.37032i	0.0682023	+	0.118130i
$815$	−5.17976	+	8.97161i	−0.181439	+	0.314262i
$816$	5.31087	−	9.19870i	0.185918	−	0.322019i
$817$	−0.902836	−	1.56376i	−0.0315862	−	0.0547090i
$818$	36.7008			1.28321
$819$	5.40713	−	2.62847i	0.188940	−	0.0918462i
$820$	−1.02780			−0.0358923
$821$	25.0958	+	43.4673i	0.875851	+	1.51702i	0.855854	+	0.517218i	$0.173032\pi$
$821$	25.0958	+	43.4673i	0.875851	+	1.51702i	0.0199971	+	0.999800i	$0.493634\pi$
$822$	3.62555	−	6.27964i	0.126456	−	0.219028i
$823$	13.6842	−	23.7018i	0.477002	−	0.826192i	−0.522650	−	0.852547i	$-0.675057\pi$
$823$	13.6842	−	23.7018i	0.477002	−	0.826192i	0.999653	+	0.0263547i	$0.00838994\pi$
$824$	−13.4146	−	23.2347i	−0.467318	−	0.809419i
$825$	3.20203			0.111481
$826$	−3.13441	+	43.9960i	−0.109060	+	1.53082i
$827$	36.9654			1.28541			0.642706	−	0.766113i	$-0.277812\pi$
$827$	36.9654			1.28541			0.642706	+	0.766113i	$0.277812\pi$
$828$	1.56401	+	2.70895i	0.0543533	+	0.0941426i
$829$	−10.3071	+	17.8525i	−0.357981	+	0.620042i	−0.987623	−	0.156843i	$-0.949868\pi$
$829$	−10.3071	+	17.8525i	−0.357981	+	0.620042i	0.629642	+	0.776885i	$0.283202\pi$
$830$	−9.09737	+	15.7571i	−0.315774	+	0.546937i
$831$	5.42047	+	9.38853i	0.188034	+	0.325684i
$832$	−8.54849			−0.296366
$833$	−14.7878	+	18.8257i	−0.512368	+	0.652272i
$834$	−15.7459			−0.545236
$835$	−2.04194	−	3.53674i	−0.0706642	−	0.122394i
$836$	−0.319029	+	0.552575i	−0.0110339	+	0.0191112i
$837$	15.9186	−	27.5719i	0.550228	−	0.953023i
$838$	−22.1417	−	38.3506i	−0.764874	−	1.32480i
$839$	7.03945			0.243029			0.121514	−	0.992590i	$-0.461225\pi$
$839$	7.03945			0.243029			0.121514	+	0.992590i	$0.461225\pi$
$840$	0.525136	−	7.37105i	0.0181189	−	0.254325i
$841$	44.7003			1.54139
$842$	9.83321	+	17.0316i	0.338875	+	0.586949i
$843$	−0.471692	+	0.816994i	−0.0162459	+	0.0281388i
$844$	1.03756	−	1.79712i	0.0357145	−	0.0618593i
$845$	−0.558163	−	0.966767i	−0.0192014	−	0.0332578i
$846$	−15.5173			−0.533497
$847$	2.37950	−	1.15671i	0.0817607	−	0.0397449i
$848$	−17.9832			−0.617546
$849$	−0.605458	−	1.04868i	−0.0207793	−	0.0359907i
$850$	8.69335	−	15.0573i	0.298180	−	0.516462i
$851$	11.9339	−	20.6701i	0.409088	−	0.708561i
$852$	−0.653810	−	1.13243i	−0.0223992	−	0.0387965i
$853$	−34.0937			−1.16735			−0.583673	−	0.811989i	$-0.698385\pi$
$853$	−34.0937			−1.16735			−0.583673	+	0.811989i	$0.698385\pi$
$854$	−9.41320	−	6.36724i	−0.322113	−	0.217882i
$855$	9.76662			0.334011
$856$	−17.8026	−	30.8351i	−0.608482	−	1.05392i
$857$	−23.8901	+	41.3788i	−0.816069	+	1.41347i	0.0924885	+	0.995714i	$0.470518\pi$
$857$	−23.8901	+	41.3788i	−0.816069	+	1.41347i	−0.908558	+	0.417760i	$0.862815\pi$
$858$	0.577637	−	1.00050i	0.0197202	−	0.0341564i
$859$	−18.5620	−	32.1504i	−0.633328	−	1.09696i	−0.986867	−	0.161536i	$-0.948355\pi$
$859$	−18.5620	−	32.1504i	−0.633328	−	1.09696i	0.353539	−	0.935420i	$-0.384978\pi$
$860$	0.0867651			0.00295867
$861$	10.3854	+	7.02483i	0.353932	+	0.239405i
$862$	−10.5746			−0.360171
$863$	20.8286	+	36.0762i	0.709014	+	1.22805i	0.965223	+	0.261427i	$0.0841930\pi$
$863$	20.8286	+	36.0762i	0.709014	+	1.22805i	−0.256210	+	0.966621i	$0.582474\pi$
$864$	2.10252	−	3.64167i	0.0715292	−	0.123892i
$865$	−1.31257	+	2.27343i	−0.0446286	+	0.0772989i
$866$	19.6502	+	34.0352i	0.667742	+	1.15656i
$867$	4.52466			0.153665
$868$	2.79158	−	1.35702i	0.0947523	−	0.0460603i
$869$	−4.84707			−0.164426
$870$	5.53581	+	9.58830i	0.187681	+	0.325074i
$871$	1.79785	−	3.11396i	0.0609177	−	0.105513i
$872$	−12.7349	+	22.0575i	−0.431259	+	0.746962i
$873$	3.07405	+	5.32441i	0.104041	+	0.180204i
$874$	−43.3119			−1.46505
$875$	1.83730	−	25.7892i	0.0621122	−	0.871835i
$876$	0.135637			0.00458276
$877$	9.92361	+	17.1882i	0.335097	+	0.580404i	0.983503	−	0.180890i	$-0.0578977\pi$
$877$	9.92361	+	17.1882i	0.335097	+	0.580404i	−0.648407	+	0.761294i	$0.724564\pi$
$878$	5.97444	−	10.3480i	0.201628	−	0.349229i
$879$	−13.7107	+	23.7476i	−0.462450	+	0.800986i
$880$	2.03232	+	3.52008i	0.0685095	+	0.118662i
$881$	−46.8084			−1.57701			−0.788507	−	0.615025i	$-0.789146\pi$
$881$	−46.8084			−1.57701			−0.788507	+	0.615025i	$0.789146\pi$
$882$	13.3078	−	16.9415i	0.448095	−	0.570450i
$883$	−0.386621			−0.0130108			−0.00650542	−	0.999979i	$-0.502071\pi$
$883$	−0.386621			−0.0130108			−0.00650542	+	0.999979i	$0.502071\pi$
$884$	0.283380	+	0.490829i	0.00953111	+	0.0165084i
$885$	−5.86065	+	10.1509i	−0.197004	+	0.341220i
$886$	−3.07403	+	5.32437i	−0.103274	+	0.178876i
$887$	21.9509	+	38.0200i	0.737038	+	1.27659i	0.953823	+	0.300369i	$0.0971097\pi$
$887$	21.9509	+	38.0200i	0.737038	+	1.27659i	−0.216785	+	0.976219i	$0.569557\pi$
$888$	−7.18948			−0.241263
$889$	2.10016	−	29.4788i	0.0704370	−	0.988687i
$890$	−21.8672			−0.732990
$891$	−1.49042	−	2.58148i	−0.0499308	−	0.0864827i
$892$	0.610949	−	1.05820i	0.0204561	−	0.0354310i
$893$	−9.70616	+	16.8116i	−0.324804	+	0.562577i
$894$	7.96130	+	13.7894i	0.266266	+	0.461186i
$895$	22.8442			0.763598
$896$	−23.0995	+	11.2289i	−0.771699	+	0.375132i
$897$	−7.08526			−0.236570
$898$	−10.9435	−	18.9546i	−0.365188	−	0.632525i
$899$	−30.3865	+	52.6309i	−1.01345	+	1.75534i
$900$	0.706824	−	1.22425i	0.0235608	−	0.0408085i
$901$	8.44537	+	14.6278i	0.281356	+	0.487323i
$902$	−7.52423			−0.250529
$903$	−0.876715	−	0.593024i	−0.0291752	−	0.0197346i
$904$	−62.1102			−2.06575
$905$	−4.89360	−	8.47597i	−0.162669	−	0.281751i
$906$	13.2923	−	23.0230i	0.441609	−	0.764889i
$907$	−16.6727	+	28.8779i	−0.553607	+	0.958875i	0.444403	+	0.895827i	$0.353416\pi$
$907$	−16.6727	+	28.8779i	−0.553607	+	0.958875i	−0.998010	+	0.0630487i	$0.979918\pi$
$908$	0.555025	+	0.961332i	0.0184192	+	0.0319029i
$909$	−40.9065			−1.35678
$910$	−3.31331	−	2.24118i	−0.109835	−	0.0742943i
$911$	−24.0327			−0.796238			−0.398119	−	0.917334i	$-0.630337\pi$
$911$	−24.0327			−0.796238			−0.398119	+	0.917334i	$0.630337\pi$
$912$	5.97897	+	10.3559i	0.197984	+	0.342918i
$913$	6.01718	−	10.4221i	0.199139	−	0.344920i
$914$	−11.9149	+	20.6371i	−0.394108	+	0.682616i
$915$	−1.51001	−	2.61542i	−0.0499194	−	0.0864630i
$916$	−0.578040			−0.0190990
$917$	35.1804	−	17.1016i	1.16176	−	0.564746i
$918$	20.8307			0.687516
$919$	−18.8036	−	32.5687i	−0.620273	−	1.07434i	−0.989435	−	0.144979i	$-0.953689\pi$
$919$	−18.8036	−	32.5687i	−0.620273	−	1.07434i	0.369162	−	0.929365i	$-0.379645\pi$
$920$	13.5988	−	23.5537i	0.448338	−	0.776544i
$921$	6.31024	−	10.9297i	0.207929	−	0.360144i
$922$	−13.6179	−	23.5869i	−0.448482	−	0.776793i
$923$	−9.24998			−0.304467
$924$	−0.0265786	+	0.373070i	−0.000874373	+	0.0122731i
$925$	−10.7865			−0.354659
$926$	−5.09363	−	8.82242i	−0.167387	−	0.289923i
$927$	10.3925	−	18.0004i	0.341335	−	0.591210i
$928$	−4.01342	+	6.95146i	−0.131747	+	0.228193i
$929$	−6.61575	−	11.4588i	−0.217056	−	0.375952i	0.736851	−	0.676055i	$-0.236312\pi$
$929$	−6.61575	−	11.4588i	−0.217056	−	0.375952i	−0.953907	+	0.300104i	$0.902979\pi$
$930$	−9.12961			−0.299372
$931$	−10.0304	−	25.0147i	−0.328734	−	0.819822i
$932$	0.324357			0.0106247
$933$	−2.84230	−	4.92301i	−0.0930528	−	0.161172i
$934$	−10.6754	+	18.4904i	−0.349310	+	0.605023i
$935$	1.90886	−	3.30624i	0.0624263	−	0.108125i
$936$	−3.33262	−	5.77227i	−0.108930	−	0.188673i
$937$	−24.6180			−0.804235			−0.402118	−	0.915588i	$-0.631726\pi$
$937$	−24.6180			−0.804235			−0.402118	+	0.915588i	$0.631726\pi$
$938$	0.915602	−	12.8518i	0.0298955	−	0.419626i
$939$	0.638277			0.0208294
$940$	−0.466394	−	0.807819i	−0.0152121	−	0.0263481i
$941$	14.3623	−	24.8762i	0.468198	−	0.810942i	−0.531142	−	0.847283i	$-0.678237\pi$
$941$	14.3623	−	24.8762i	0.468198	−	0.810942i	0.999339	+	0.0363407i	$0.0115702\pi$
$942$	12.0461	−	20.8645i	0.392483	−	0.679801i
$943$	23.0729	+	39.9634i	0.751357	+	1.30139i
$944$	44.8190			1.45874
$945$	11.9464	−	5.80729i	0.388616	−	0.188911i
$946$	0.635183			0.0206516
$947$	−6.39969	−	11.0846i	−0.207962	−	0.360201i	0.743110	−	0.669169i	$-0.233350\pi$
$947$	−6.39969	−	11.0846i	−0.207962	−	0.360201i	−0.951072	+	0.308968i	$0.900016\pi$
$948$	0.342602	−	0.593404i	0.0111272	−	0.0192729i
$949$	0.479743	−	0.830939i	0.0155731	−	0.0269734i
$950$	9.78696	+	16.9515i	0.317531	+	0.549980i
$951$	25.6950			0.833218
$952$	21.9830	+	14.8696i	0.712473	+	0.481928i
$953$	−15.3510			−0.497266			−0.248633	−	0.968598i	$-0.579981\pi$
$953$	−15.3510			−0.497266			−0.248633	+	0.968598i	$0.579981\pi$
$954$	−7.60010	−	13.1638i	−0.246062	−	0.426192i
$955$	−12.1007	+	20.9591i	−0.391570	+	0.678220i
$956$	−1.07780	+	1.86681i	−0.0348587	+	0.0603770i
$957$	−3.66149	−	6.34188i	−0.118359	−	0.205004i
$958$	45.5760			1.47249
$959$	13.7549	+	9.30405i	0.444170	+	0.300443i
$960$	−8.14017			−0.262723
$961$	−9.55656	−	16.5524i	−0.308276	−	0.533950i
$962$	−1.94586	+	3.37032i	−0.0627370	+	0.108664i
$963$	13.7921	−	23.8886i	0.444443	−	0.769798i
$964$	−1.15680	−	2.00364i	−0.0372581	−	0.0645330i
$965$	1.93405			0.0622593
$966$	−22.8336	+	11.0997i	−0.734658	+	0.357127i
$967$	45.6819			1.46903			0.734515	−	0.678593i	$-0.237410\pi$
$967$	45.6819			1.46903			0.734515	+	0.678593i	$0.237410\pi$
$968$	−1.46658	−	2.54019i	−0.0471376	−	0.0816448i
$969$	5.61575	−	9.72677i	0.180404	−	0.312469i
$970$	2.04528	−	3.54253i	0.0656701	−	0.113744i
$971$	6.77175	+	11.7290i	0.217316	+	0.376402i	0.953986	−	0.299850i	$-0.0969365\pi$
$971$	6.77175	+	11.7290i	0.217316	+	0.376402i	−0.736671	+	0.676252i	$0.763603\pi$
$972$	2.65737			0.0852351
$973$	2.56256	−	35.9693i	0.0821520	−	1.15312i
$974$	−15.3493			−0.491825
$975$	1.60102	+	2.77304i	0.0512736	+	0.0888085i
$976$	−5.77387	+	10.0006i	−0.184817	+	0.320113i
$977$	6.84500	−	11.8559i	0.218991	−	0.379304i	−0.735509	−	0.677515i	$-0.763057\pi$
$977$	6.84500	−	11.8559i	0.218991	−	0.379304i	0.954500	+	0.298212i	$0.0963901\pi$
$978$	−5.36048	−	9.28462i	−0.171409	−	0.296890i
$979$	14.4634			0.462252
$980$	1.28194	+	0.183591i	0.0409501	+	0.00586459i
$981$	−19.7320			−0.629995
$982$	−1.36406	−	2.36262i	−0.0435288	−	0.0753941i
$983$	−10.8872	+	18.8571i	−0.347246	+	0.601448i	−0.985759	−	0.168163i	$-0.946217\pi$
$983$	−10.8872	+	18.8571i	−0.347246	+	0.601448i	0.638513	+	0.769611i	$0.279550\pi$
$984$	6.95006	−	12.0379i	0.221560	−	0.383753i
$985$	−12.1950	−	21.1224i	−0.388566	−	0.673016i
$986$	−39.7630			−1.26631
$987$	−0.808630	+	11.3503i	−0.0257390	+	0.361284i
$988$	−0.638058			−0.0202993
$989$	−1.94778	−	3.37365i	−0.0619357	−	0.107276i
$990$	−1.71780	+	2.97533i	−0.0545954	+	0.0945620i
$991$	3.48649	−	6.03878i	0.110752	−	0.191828i	−0.805322	−	0.592838i	$-0.798007\pi$
$991$	3.48649	−	6.03878i	0.110752	−	0.191828i	0.916074	+	0.401010i	$0.131341\pi$
$992$	−3.30945	−	5.73214i	−0.105075	−	0.181996i
$993$	−28.7048			−0.910919
$994$	−29.8098	+	14.4909i	−0.945510	+	0.459624i
$995$	3.78319			0.119935
$996$	0.850616	+	1.47331i	0.0269528	+	0.0466836i
$997$	−13.3292	+	23.0869i	−0.422140	+	0.731168i	−0.996149	−	0.0876812i	$-0.972054\pi$
$997$	−13.3292	+	23.0869i	−0.422140	+	0.731168i	0.574008	+	0.818849i	$0.305388\pi$
$998$	11.8124	−	20.4597i	0.373916	−	0.647641i
$999$	−6.46157	−	11.1918i	−0.204435	−	0.354092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.144.19	✓	50
7.2	even	3	inner	1001.2.i.d.716.19	yes	50
7.3	odd	6		7007.2.a.bi.1.7		25
7.4	even	3		7007.2.a.bh.1.7		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.19	✓	50	1.1	even	1	trivial
1001.2.i.d.716.19	yes	50	7.2	even	3	inner
7007.2.a.bh.1.7		25	7.4	even	3
7007.2.a.bi.1.7		25	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:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.677177 + 1.17291i) q^{2} +(0.426504 - 0.738727i) q^{3} +(0.0828624 - 0.143522i) q^{4} +(-0.558163 - 0.966767i) q^{5} +1.15527 q^{6} +(-0.188015 + 2.63906i) q^{7} +2.93316 q^{8} +(1.13619 + 1.96794i) q^{9} +O(q^{10})\)	\(q+(0.677177 + 1.17291i) q^{2} +(0.426504 - 0.738727i) q^{3} +(0.0828624 - 0.143522i) q^{4} +(-0.558163 - 0.966767i) q^{5} +1.15527 q^{6} +(-0.188015 + 2.63906i) q^{7} +2.93316 q^{8} +(1.13619 + 1.96794i) q^{9} +(0.755950 - 1.30934i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.0706823 - 0.122425i) q^{12} -1.00000 q^{13} +(-3.22269 + 1.56659i) q^{14} -0.952235 q^{15} +(1.82054 + 3.15327i) q^{16} +(1.70994 - 2.96171i) q^{17} +(-1.53880 + 2.66528i) q^{18} +(1.92505 + 3.33429i) q^{19} -0.185003 q^{20} +(1.86936 + 1.26446i) q^{21} -1.35435 q^{22} +(4.15310 + 7.19338i) q^{23} +(1.25100 - 2.16680i) q^{24} +(1.87691 - 3.25090i) q^{25} +(-0.677177 - 1.17291i) q^{26} +4.49738 q^{27} +(0.363184 + 0.245663i) q^{28} -8.58489 q^{29} +(-0.644832 - 1.11688i) q^{30} +(3.53953 - 6.13065i) q^{31} +(0.467499 - 0.809732i) q^{32} +(0.426504 + 0.738727i) q^{33} +4.63174 q^{34} +(2.65630 - 1.29126i) q^{35} +0.376589 q^{36} +(-1.43674 - 2.48851i) q^{37} +(-2.60720 + 4.51581i) q^{38} +(-0.426504 + 0.738727i) q^{39} +(-1.63718 - 2.83568i) q^{40} +5.55558 q^{41} +(-0.217209 + 3.04884i) q^{42} -0.468993 q^{43} +(0.0828624 + 0.143522i) q^{44} +(1.26836 - 2.19686i) q^{45} +(-5.62477 + 9.74239i) q^{46} +(2.52101 + 4.36652i) q^{47} +3.10587 q^{48} +(-6.92930 - 0.992366i) q^{49} +5.08400 q^{50} +(-1.45860 - 2.52636i) q^{51} +(-0.0828624 + 0.143522i) q^{52} +(-2.46949 + 4.27728i) q^{53} +(3.04552 + 5.27500i) q^{54} +1.11633 q^{55} +(-0.551477 + 7.74079i) q^{56} +3.28417 q^{57} +(-5.81349 - 10.0693i) q^{58} +(6.15462 - 10.6601i) q^{59} +(-0.0789045 + 0.136667i) q^{60} +(1.58576 + 2.74661i) q^{61} +9.58756 q^{62} +(-5.40713 + 2.62847i) q^{63} +8.54849 q^{64} +(0.558163 + 0.966767i) q^{65} +(-0.577637 + 1.00050i) q^{66} +(-1.79785 + 3.11396i) q^{67} +(-0.283380 - 0.490829i) q^{68} +7.08526 q^{69} +(3.31331 + 2.24118i) q^{70} +9.24998 q^{71} +(3.33262 + 5.77227i) q^{72} +(-0.479743 + 0.830939i) q^{73} +(1.94586 - 3.37032i) q^{74} +(-1.60102 - 2.77304i) q^{75} +0.638058 q^{76} +(-2.19149 - 1.48236i) q^{77} -1.15527 q^{78} +(2.42354 + 4.19769i) q^{79} +(2.03232 - 3.52008i) q^{80} +(-1.49042 + 2.58148i) q^{81} +(3.76211 + 6.51617i) q^{82} -12.0344 q^{83} +(0.336378 - 0.163517i) q^{84} -3.81771 q^{85} +(-0.317591 - 0.550084i) q^{86} +(-3.66149 + 6.34188i) q^{87} +(-1.46658 + 2.54019i) q^{88} +(-7.23169 - 12.5257i) q^{89} +3.43561 q^{90} +(0.188015 - 2.63906i) q^{91} +1.37654 q^{92} +(-3.01925 - 5.22949i) q^{93} +(-3.41434 + 5.91381i) q^{94} +(2.14899 - 3.72216i) q^{95} +(-0.398780 - 0.690708i) q^{96} +2.70558 q^{97} +(-3.52841 - 8.79942i) q^{98} -2.27238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

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