LMFDB - Embedded newform 143.2.e.b.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.e (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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$-1.25351 + 2.17114i$ of defining polynomial
Character	$\chi$	$=$	143.100
Dual form			143.2.e.b.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25351 + 2.17114i) q^{2} +(-1.14257 + 1.97899i) q^{3} +(-2.14257 - 3.71104i) q^{4} -1.22188 q^{5} +(-2.86445 - 4.96137i) q^{6} +(-0.389062 - 0.673875i) q^{7} +5.72889 q^{8} +(-1.11094 - 1.92420i) q^{9} +O(q^{10})$	\(q+(-1.25351 + 2.17114i) q^{2} +(-1.14257 + 1.97899i) q^{3} +(-2.14257 - 3.71104i) q^{4} -1.22188 q^{5} +(-2.86445 - 4.96137i) q^{6} +(-0.389062 - 0.673875i) q^{7} +5.72889 q^{8} +(-1.11094 - 1.92420i) q^{9} +(1.53163 - 2.65287i) q^{10} +(-0.500000 + 0.866025i) q^{11} +9.79216 q^{12} +(-2.50000 + 2.59808i) q^{13} +1.95077 q^{14} +(1.39608 - 2.41808i) q^{15} +(-2.89608 + 5.01616i) q^{16} +(2.14257 + 3.71104i) q^{17} +5.57028 q^{18} +(-4.14959 - 7.18730i) q^{19} +(2.61796 + 4.53443i) q^{20} +1.77812 q^{21} +(-1.25351 - 2.17114i) q^{22} +(1.36445 - 2.36329i) q^{23} +(-6.54567 + 11.3374i) q^{24} -3.50702 q^{25} +(-2.50702 - 8.68457i) q^{26} -1.77812 q^{27} +(-1.66719 + 2.88765i) q^{28} +(-3.68122 + 6.37607i) q^{29} +(3.50000 + 6.06218i) q^{30} -1.44375 q^{31} +(-1.53163 - 2.65287i) q^{32} +(-1.14257 - 1.97899i) q^{33} -10.7429 q^{34} +(0.475385 + 0.823392i) q^{35} +(-4.76053 + 8.24548i) q^{36} +(0.396081 - 0.686032i) q^{37} +20.8062 q^{38} +(-2.28514 - 7.91597i) q^{39} -7.00000 q^{40} +(-4.87147 + 8.43763i) q^{41} +(-2.22889 + 3.86056i) q^{42} +(4.83983 + 8.38284i) q^{43} +4.28514 q^{44} +(1.35743 + 2.35114i) q^{45} +(3.42070 + 5.92482i) q^{46} -3.38049 q^{47} +(-6.61796 - 11.4626i) q^{48} +(3.19726 - 5.53782i) q^{49} +(4.39608 - 7.61423i) q^{50} -9.79216 q^{51} +(14.9980 + 3.71104i) q^{52} +1.79216 q^{53} +(2.22889 - 3.86056i) q^{54} +(0.610938 - 1.05818i) q^{55} +(-2.22889 - 3.86056i) q^{56} +18.9648 q^{57} +(-9.22889 - 15.9849i) q^{58} +(-2.60392 - 4.51012i) q^{59} -11.9648 q^{60} +(7.26053 + 12.5756i) q^{61} +(1.80976 - 3.13459i) q^{62} +(-0.864447 + 1.49727i) q^{63} -3.90466 q^{64} +(3.05469 - 3.17453i) q^{65} +5.72889 q^{66} +(-3.03163 + 5.25094i) q^{67} +(9.18122 - 15.9023i) q^{68} +(3.11796 + 5.40046i) q^{69} -2.38360 q^{70} +(3.25351 + 5.63524i) q^{71} +(-6.36445 - 11.0235i) q^{72} -2.00000 q^{73} +(0.992981 + 1.71989i) q^{74} +(4.00702 - 6.94036i) q^{75} +(-17.7816 + 30.7986i) q^{76} +0.778124 q^{77} +(20.0511 + 4.96137i) q^{78} +13.5843 q^{79} +(3.53865 - 6.12912i) q^{80} +(5.36445 - 9.29150i) q^{81} +(-12.2129 - 21.1533i) q^{82} -13.3624 q^{83} +(-3.80976 - 6.59869i) q^{84} +(-2.61796 - 4.53443i) q^{85} -24.2671 q^{86} +(-8.41212 - 14.5702i) q^{87} +(-2.86445 + 4.96137i) q^{88} +(2.38906 - 4.13798i) q^{89} -6.80620 q^{90} +(2.72343 + 0.673875i) q^{91} -11.6937 q^{92} +(1.64959 - 2.85717i) q^{93} +(4.23747 - 7.33951i) q^{94} +(5.07028 + 8.78199i) q^{95} +7.00000 q^{96} +(2.07028 + 3.58584i) q^{97} +(8.01559 + 13.8834i) q^{98} +2.22188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9	\( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 3 q^{11} + 30 q^{12} - 15 q^{13} - 16 q^{14} - 6 q^{15} - 3 q^{16} + 7 q^{17} + 10 q^{18} - 2 q^{19} - 4 q^{20} + 16 q^{21} + q^{22} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 21 q^{30} + 2 q^{31} - 6 q^{32} - q^{33} - 8 q^{34} - 11 q^{35} - 3 q^{36} - 12 q^{37} + 62 q^{38} - 2 q^{39} - 42 q^{40} - q^{41} + 9 q^{42} + 4 q^{43} + 14 q^{44} + 14 q^{45} + 20 q^{46} - 16 q^{47} - 20 q^{48} + 12 q^{50} - 30 q^{51} + 49 q^{52} - 18 q^{53} - 9 q^{54} + q^{55} + 9 q^{56} + 52 q^{57} - 33 q^{58} - 30 q^{59} - 10 q^{60} + 18 q^{61} + 13 q^{62} + 6 q^{63} - 16 q^{64} + 5 q^{65} + 12 q^{66} - 15 q^{67} + 29 q^{68} - q^{69} - 58 q^{70} + 11 q^{71} - 27 q^{72} - 12 q^{73} + 23 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{77} + 42 q^{78} + 24 q^{79} + q^{80} + 21 q^{81} - 44 q^{82} - 28 q^{83} - 25 q^{84} + 4 q^{85} - 86 q^{86} - 43 q^{87} - 6 q^{88} + 17 q^{89} + 22 q^{90} + 35 q^{91} + 14 q^{92} - 13 q^{93} + 10 q^{94} + 7 q^{95} + 42 q^{96} - 11 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 3 * q^11 + 30 * q^12 - 15 * q^13 - 16 * q^14 - 6 * q^15 - 3 * q^16 + 7 * q^17 + 10 * q^18 - 2 * q^19 - 4 * q^20 + 16 * q^21 + q^22 - 3 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 21 * q^30 + 2 * q^31 - 6 * q^32 - q^33 - 8 * q^34 - 11 * q^35 - 3 * q^36 - 12 * q^37 + 62 * q^38 - 2 * q^39 - 42 * q^40 - q^41 + 9 * q^42 + 4 * q^43 + 14 * q^44 + 14 * q^45 + 20 * q^46 - 16 * q^47 - 20 * q^48 + 12 * q^50 - 30 * q^51 + 49 * q^52 - 18 * q^53 - 9 * q^54 + q^55 + 9 * q^56 + 52 * q^57 - 33 * q^58 - 30 * q^59 - 10 * q^60 + 18 * q^61 + 13 * q^62 + 6 * q^63 - 16 * q^64 + 5 * q^65 + 12 * q^66 - 15 * q^67 + 29 * q^68 - q^69 - 58 * q^70 + 11 * q^71 - 27 * q^72 - 12 * q^73 + 23 * q^74 + 7 * q^75 - 30 * q^76 + 10 * q^77 + 42 * q^78 + 24 * q^79 + q^80 + 21 * q^81 - 44 * q^82 - 28 * q^83 - 25 * q^84 + 4 * q^85 - 86 * q^86 - 43 * q^87 - 6 * q^88 + 17 * q^89 + 22 * q^90 + 35 * q^91 + 14 * q^92 - 13 * q^93 + 10 * q^94 + 7 * q^95 + 42 * q^96 - 11 * q^97 + 38 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.25351	+	2.17114i	−0.886365	+	1.53523i	−0.0422238	+	0.999108i	$0.513444\pi$
$2$	−1.25351	+	2.17114i	−0.886365	+	1.53523i	−0.844141	+	0.536121i	$0.819889\pi$
$3$	−1.14257	+	1.97899i	−0.659664	+	1.14257i	0.321039	+	0.947066i	$0.395968\pi$
$3$	−1.14257	+	1.97899i	−0.659664	+	1.14257i	−0.980703	+	0.195505i	$0.937365\pi$
$4$	−2.14257	−	3.71104i	−1.07129	−	1.85552i
$5$	−1.22188			−0.546440			−0.273220	−	0.961952i	$-0.588089\pi$
$5$	−1.22188			−0.546440			−0.273220	+	0.961952i	$0.588089\pi$
$6$	−2.86445	−	4.96137i	−1.16941	−	2.02547i
$7$	−0.389062	−	0.673875i	−0.147052	−	0.254701i	0.783085	−	0.621915i	$-0.213645\pi$
$7$	−0.389062	−	0.673875i	−0.147052	−	0.254701i	−0.930136	+	0.367214i	$0.880312\pi$
$8$	5.72889			2.02547
$9$	−1.11094	−	1.92420i	−0.370313	−	0.641400i
$10$	1.53163	−	2.65287i	0.484345	−	0.838910i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	9.79216			2.82675
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	1.95077			0.521365
$15$	1.39608	−	2.41808i	0.360466	−	0.624346i
$16$	−2.89608	+	5.01616i	−0.724020	+	1.25404i
$17$	2.14257	+	3.71104i	0.519650	+	0.900060i	0.999739	+	0.0228403i	$0.00727093\pi$
$17$	2.14257	+	3.71104i	0.519650	+	0.900060i	−0.480089	+	0.877220i	$0.659396\pi$
$18$	5.57028			1.31293
$19$	−4.14959	−	7.18730i	−0.951981	−	1.64888i	−0.741130	−	0.671362i	$-0.765710\pi$
$19$	−4.14959	−	7.18730i	−0.951981	−	1.64888i	−0.210851	−	0.977518i	$-0.567624\pi$
$20$	2.61796	+	4.53443i	0.585393	+	1.01393i
$21$	1.77812			0.388018
$22$	−1.25351	−	2.17114i	−0.267249	−	0.462889i
$23$	1.36445	−	2.36329i	0.284507	−	0.492780i	−0.687983	−	0.725727i	$-0.741503\pi$
$23$	1.36445	−	2.36329i	0.284507	−	0.492780i	0.972489	+	0.232947i	$0.0748368\pi$
$24$	−6.54567	+	11.3374i	−1.33613	+	2.31424i
$25$	−3.50702			−0.701404
$26$	−2.50702	−	8.68457i	−0.491667	−	1.70318i
$27$	−1.77812			−0.342200
$28$	−1.66719	+	2.88765i	−0.315068	+	0.545715i
$29$	−3.68122	+	6.37607i	−0.683586	+	1.18401i	0.290293	+	0.956938i	$0.406247\pi$
$29$	−3.68122	+	6.37607i	−0.683586	+	1.18401i	−0.973879	+	0.227068i	$0.927086\pi$
$30$	3.50000	+	6.06218i	0.639010	+	1.10680i
$31$	−1.44375			−0.259306			−0.129653	−	0.991559i	$-0.541386\pi$
$31$	−1.44375			−0.259306			−0.129653	+	0.991559i	$0.541386\pi$
$32$	−1.53163	−	2.65287i	−0.270757	−	0.468965i
$33$	−1.14257	−	1.97899i	−0.198896	−	0.344498i
$34$	−10.7429			−1.84240
$35$	0.475385	+	0.823392i	0.0803548	+	0.139179i
$36$	−4.76053	+	8.24548i	−0.793421	+	1.37425i
$37$	0.396081	−	0.686032i	0.0651152	−	0.112783i	−0.831630	−	0.555330i	$-0.812592\pi$
$37$	0.396081	−	0.686032i	0.0651152	−	0.112783i	0.896745	+	0.442547i	$0.145925\pi$
$38$	20.8062			3.37521
$39$	−2.28514	−	7.91597i	−0.365916	−	1.26757i
$40$	−7.00000			−1.10680
$41$	−4.87147	+	8.43763i	−0.760795	+	1.31774i	0.181646	+	0.983364i	$0.441857\pi$
$41$	−4.87147	+	8.43763i	−0.760795	+	1.31774i	−0.942441	+	0.334372i	$0.891476\pi$
$42$	−2.22889	+	3.86056i	−0.343926	+	0.595697i
$43$	4.83983	+	8.38284i	0.738068	+	1.27837i	0.953364	+	0.301822i	$0.0975948\pi$
$43$	4.83983	+	8.38284i	0.738068	+	1.27837i	−0.215297	+	0.976549i	$0.569072\pi$
$44$	4.28514			0.646010
$45$	1.35743	+	2.35114i	0.202354	+	0.350487i
$46$	3.42070	+	5.92482i	0.504354	+	0.873567i
$47$	−3.38049			−0.493095			−0.246547	−	0.969131i	$-0.579296\pi$
$47$	−3.38049			−0.493095			−0.246547	+	0.969131i	$0.579296\pi$
$48$	−6.61796	−	11.4626i	−0.955220	−	1.65449i
$49$	3.19726	−	5.53782i	0.456752	−	0.791117i
$50$	4.39608	−	7.61423i	0.621700	−	1.07682i
$51$	−9.79216			−1.37118
$52$	14.9980	+	3.71104i	2.07985	+	0.514629i
$53$	1.79216			0.246172			0.123086	−	0.992396i	$-0.460721\pi$
$53$	1.79216			0.246172			0.123086	+	0.992396i	$0.460721\pi$
$54$	2.22889	−	3.86056i	0.303314	−	0.525356i
$55$	0.610938	−	1.05818i	0.0823789	−	0.142684i
$56$	−2.22889	−	3.86056i	−0.297849	−	0.515889i
$57$	18.9648			2.51195
$58$	−9.22889	−	15.9849i	−1.21181	−	2.09892i
$59$	−2.60392	−	4.51012i	−0.339001	−	0.587168i	0.645244	−	0.763977i	$-0.276756\pi$
$59$	−2.60392	−	4.51012i	−0.339001	−	0.587168i	−0.984245	+	0.176809i	$0.943422\pi$
$60$	−11.9648			−1.54465
$61$	7.26053	+	12.5756i	0.929615	+	1.61014i	0.783965	+	0.620805i	$0.213194\pi$
$61$	7.26053	+	12.5756i	0.929615	+	1.61014i	0.145650	+	0.989336i	$0.453473\pi$
$62$	1.80976	−	3.13459i	0.229839	−	0.398093i
$63$	−0.864447	+	1.49727i	−0.108910	+	0.188638i
$64$	−3.90466			−0.488082
$65$	3.05469	−	3.17453i	0.378888	−	0.393752i
$66$	5.72889			0.705178
$67$	−3.03163	+	5.25094i	−0.370373	+	0.641505i	−0.989623	−	0.143689i	$-0.954103\pi$
$67$	−3.03163	+	5.25094i	−0.370373	+	0.641505i	0.619250	+	0.785194i	$0.287437\pi$
$68$	9.18122	−	15.9023i	1.11339	−	1.92844i
$69$	3.11796	+	5.40046i	0.375358	+	0.650139i
$70$	−2.38360			−0.284895
$71$	3.25351	+	5.63524i	0.386121	+	0.668780i	0.991924	−	0.126834i	$-0.0404815\pi$
$71$	3.25351	+	5.63524i	0.386121	+	0.668780i	−0.605803	+	0.795614i	$0.707148\pi$
$72$	−6.36445	−	11.0235i	−0.750057	−	1.29914i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	0.992981	+	1.71989i	0.115432	+	0.199934i
$75$	4.00702	−	6.94036i	0.462691	−	0.801404i
$76$	−17.7816	+	30.7986i	−2.03969	+	3.53284i
$77$	0.778124			0.0886754
$78$	20.0511	+	4.96137i	2.27034	+	0.561764i
$79$	13.5843			1.52836			0.764178	−	0.645006i	$-0.223145\pi$
$79$	13.5843			1.52836			0.764178	+	0.645006i	$0.223145\pi$
$80$	3.53865	−	6.12912i	0.395633	−	0.685257i
$81$	5.36445	−	9.29150i	0.596050	−	1.03239i
$82$	−12.2129	−	21.1533i	−1.34868	−	2.33599i
$83$	−13.3624			−1.46672			−0.733360	−	0.679841i	$-0.762049\pi$
$83$	−13.3624			−1.46672			−0.733360	+	0.679841i	$0.762049\pi$
$84$	−3.80976	−	6.59869i	−0.415679	−	0.719976i
$85$	−2.61796	−	4.53443i	−0.283957	−	0.491828i
$86$	−24.2671			−2.61679
$87$	−8.41212	−	14.5702i	−0.901874	−	1.56209i
$88$	−2.86445	+	4.96137i	−0.305351	+	0.528884i
$89$	2.38906	−	4.13798i	0.253240	−	0.438625i	−0.711176	−	0.703014i	$-0.751837\pi$
$89$	2.38906	−	4.13798i	0.253240	−	0.438625i	0.964416	+	0.264389i	$0.0851704\pi$
$90$	−6.80620			−0.717436
$91$	2.72343	+	0.673875i	0.285493	+	0.0706413i
$92$	−11.6937			−1.21915
$93$	1.64959	−	2.85717i	0.171055	−	0.296275i
$94$	4.23747	−	7.33951i	0.437062	−	0.757013i
$95$	5.07028	+	8.78199i	0.520200	+	0.901013i
$96$	7.00000			0.714435
$97$	2.07028	+	3.58584i	0.210206	+	0.364087i	0.951779	−	0.306785i	$-0.0992533\pi$
$97$	2.07028	+	3.58584i	0.210206	+	0.364087i	−0.741573	+	0.670872i	$0.765920\pi$
$98$	8.01559	+	13.8834i	0.809697	+	1.40244i
$99$	2.22188			0.223307
$100$	7.51404	+	13.0147i	0.751404	+	1.30147i
$101$	−2.41212	+	4.17791i	−0.240015	+	0.415718i	−0.960718	−	0.277526i	$-0.910486\pi$
$101$	−2.41212	+	4.17791i	−0.240015	+	0.415718i	0.720703	+	0.693244i	$0.243819\pi$
$102$	12.2746	−	21.2602i	1.21536	−	2.10507i
$103$	9.76008			0.961690			0.480845	−	0.876806i	$-0.340330\pi$
$103$	9.76008			0.961690			0.480845	+	0.876806i	$0.340330\pi$
$104$	−14.3222	+	14.8841i	−1.40441	+	1.45951i
$105$	−2.17265			−0.212029
$106$	−2.24649	+	3.89104i	−0.218198	+	0.377931i
$107$	−1.18122	+	2.04594i	−0.114193	+	0.197788i	−0.917457	−	0.397835i	$-0.869762\pi$
$107$	−1.18122	+	2.04594i	−0.114193	+	0.197788i	0.803264	+	0.595623i	$0.203095\pi$
$108$	3.80976	+	6.59869i	0.366594	+	0.634959i
$109$	−2.86946			−0.274845			−0.137422	−	0.990513i	$-0.543882\pi$
$109$	−2.86946			−0.274845			−0.137422	+	0.990513i	$0.543882\pi$
$110$	1.53163	+	2.65287i	0.146035	+	0.252941i
$111$	0.905101	+	1.56768i	0.0859083	+	0.148798i
$112$	4.50702			0.425873
$113$	2.80118	+	4.85179i	0.263513	+	0.456418i	0.967173	−	0.254119i	$-0.0817855\pi$
$113$	2.80118	+	4.85179i	0.263513	+	0.456418i	−0.703660	+	0.710537i	$0.748452\pi$
$114$	−23.7726	+	41.1753i	−2.22650	+	3.85642i
$115$	−1.66719	+	2.88765i	−0.155466	+	0.269275i
$116$	31.5491			2.92926
$117$	7.77657	+	1.92420i	0.718944	+	0.177892i
$118$	13.0561			1.20192
$119$	1.66719	−	2.88765i	0.152831	−	0.264710i
$120$	7.99800	−	13.8529i	0.730114	−	1.26459i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−36.4046			−3.29591
$123$	−11.1320	−	19.2812i	−1.00374	−	1.73853i
$124$	3.09334	+	5.35783i	0.277790	+	0.481147i
$125$	10.3945			0.929714
$126$	−2.16719	−	3.75368i	−0.193068	−	0.334404i
$127$	−3.61796	+	6.26648i	−0.321042	+	0.556061i	−0.980703	−	0.195502i	$-0.937366\pi$
$127$	−3.61796	+	6.26648i	−0.321042	+	0.556061i	0.659662	+	0.751563i	$0.270700\pi$
$128$	7.95779	−	13.7833i	0.703376	−	1.21828i
$129$	−22.1194			−1.94751
$130$	3.06327	+	10.6115i	0.268666	+	0.930687i
$131$	−10.3484			−0.904145			−0.452072	−	0.891981i	$-0.649315\pi$
$131$	−10.3484			−0.904145			−0.452072	+	0.891981i	$0.649315\pi$
$132$	−4.89608	+	8.48026i	−0.426149	+	0.738112i
$133$	−3.22889	+	5.59261i	−0.279981	+	0.484941i
$134$	−7.60036	−	13.1642i	−0.656571	−	1.13721i
$135$	2.17265			0.186992
$136$	12.2746	+	21.2602i	1.05254	+	1.82304i
$137$	2.46837	+	4.27534i	0.210887	+	0.365267i	0.951992	−	0.306122i	$-0.0990315\pi$
$137$	2.46837	+	4.27534i	0.210887	+	0.365267i	−0.741106	+	0.671389i	$0.765698\pi$
$138$	−15.6336			−1.33082
$139$	−8.23591	−	14.2650i	−0.698561	−	1.20994i	−0.968965	−	0.247196i	$-0.920491\pi$
$139$	−8.23591	−	14.2650i	−0.698561	−	1.20994i	0.270404	−	0.962747i	$-0.412843\pi$
$140$	2.03709	−	3.52835i	0.172166	−	0.298200i
$141$	3.86245	−	6.68995i	0.325277	−	0.563396i
$142$	−16.3132			−1.36897
$143$	−1.00000	−	3.46410i	−0.0836242	−	0.289683i
$144$	12.8695			1.07246
$145$	4.49800	−	7.79076i	0.373538	−	0.646988i
$146$	2.50702	−	4.34228i	0.207482	−	0.359370i
$147$	7.30620	+	12.6547i	0.602605	+	1.04374i
$148$	−3.39452			−0.279028
$149$	0.952328	+	1.64948i	0.0780178	+	0.135131i	0.902395	−	0.430911i	$-0.141808\pi$
$149$	0.952328	+	1.64948i	0.0780178	+	0.135131i	−0.824377	+	0.566041i	$0.808474\pi$
$150$	10.0457	+	17.3996i	0.820226	+	1.42067i
$151$	18.4086			1.49807			0.749034	−	0.662532i	$-0.230518\pi$
$151$	18.4086			1.49807			0.749034	+	0.662532i	$0.230518\pi$
$152$	−23.7726	−	41.1753i	−1.92821	−	3.33976i
$153$	4.76053	−	8.24548i	0.384866	−	0.666607i
$154$	−0.975385	+	1.68942i	−0.0785988	+	0.136137i
$155$	1.76409			0.141695
$156$	−24.4804	+	25.4408i	−1.96000	+	2.03689i
$157$	−12.1054			−0.966114			−0.483057	−	0.875589i	$-0.660474\pi$
$157$	−12.1054			−0.966114			−0.483057	+	0.875589i	$0.660474\pi$
$158$	−17.0281	+	29.4935i	−1.35468	+	2.34638i
$159$	−2.04767	+	3.54667i	−0.162391	+	0.281269i
$160$	1.87147	+	3.24147i	0.147952	+	0.256261i
$161$	−2.12342			−0.167349
$162$	13.4488	+	23.2940i	1.05664	+	1.83015i
$163$	−0.959347	−	1.66164i	−0.0751418	−	0.130149i	0.826006	−	0.563661i	$-0.190608\pi$
$163$	−0.959347	−	1.66164i	−0.0751418	−	0.130149i	−0.901148	+	0.433512i	$0.857274\pi$
$164$	41.7499			3.26012
$165$	1.39608	+	2.41808i	0.108685	+	0.188247i
$166$	16.7500	−	29.0118i	1.30005	−	2.25175i
$167$	3.53008	−	6.11427i	0.273165	−	0.473136i	−0.696505	−	0.717552i	$-0.745263\pi$
$167$	3.53008	−	6.11427i	0.273165	−	0.473136i	0.969671	+	0.244415i	$0.0785960\pi$
$168$	10.1867			0.785920
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	13.1265			1.00676
$171$	−9.21987	+	15.9693i	−0.705061	+	1.22120i
$172$	20.7394	−	35.9216i	1.58136	−	2.73900i
$173$	−0.823794	−	1.42685i	−0.0626319	−	0.108482i	0.833009	−	0.553259i	$-0.186616\pi$
$173$	−0.823794	−	1.42685i	−0.0626319	−	0.108482i	−0.895641	+	0.444778i	$0.853283\pi$
$174$	42.1787			3.19756
$175$	1.36445	+	2.36329i	0.103143	+	0.178648i
$176$	−2.89608	−	5.01616i	−0.218300	−	0.378107i
$177$	11.9007			0.894508
$178$	5.98942	+	10.3740i	0.448926	+	0.777563i
$179$	−3.66719	+	6.35175i	−0.274098	+	0.474752i	−0.969907	−	0.243475i	$-0.921713\pi$
$179$	−3.66719	+	6.35175i	−0.274098	+	0.474752i	0.695809	+	0.718227i	$0.255046\pi$
$180$	5.81678	−	10.0750i	0.433557	−	0.750943i
$181$	11.7750			0.875230			0.437615	−	0.899163i	$-0.355823\pi$
$181$	11.7750			0.875230			0.437615	+	0.899163i	$0.355823\pi$
$182$	−4.87693	+	5.06825i	−0.361502	+	0.375684i
$183$	−33.1827			−2.45293
$184$	7.81678	−	13.5391i	0.576260	−	0.998112i
$185$	−0.483961	+	0.838246i	−0.0355815	+	0.0616291i
$186$	4.13555	+	7.16299i	0.303233	+	0.525216i
$187$	−4.28514			−0.313361
$188$	7.24293	+	12.5451i	0.528245	+	0.914947i
$189$	0.691800	+	1.19823i	0.0503211	+	0.0871586i
$190$	−25.4226			−1.84435
$191$	−7.37147	−	12.7678i	−0.533381	−	0.923842i	−0.999240	−	0.0389834i	$-0.987588\pi$
$191$	−7.37147	−	12.7678i	−0.533381	−	0.923842i	0.465859	−	0.884859i	$-0.345745\pi$
$192$	4.46135	−	7.72728i	0.321970	−	0.557669i
$193$	4.45077	−	7.70896i	0.320374	−	0.554903i	−0.660192	−	0.751097i	$-0.729525\pi$
$193$	4.45077	−	7.70896i	0.320374	−	0.554903i	0.980565	+	0.196194i	$0.0628583\pi$
$194$	−10.3805			−0.745275
$195$	2.79216	+	9.67233i	0.199951	+	0.692650i
$196$	−27.4014			−1.95725
$197$	3.05625	−	5.29358i	0.217749	−	0.377152i	−0.736371	−	0.676578i	$-0.763462\pi$
$197$	3.05625	−	5.29358i	0.217749	−	0.377152i	0.954119	+	0.299427i	$0.0967954\pi$
$198$	−2.78514	+	4.82401i	−0.197931	+	0.342827i
$199$	−4.67265	−	8.09326i	−0.331235	−	0.573716i	0.651519	−	0.758632i	$-0.274132\pi$
$199$	−4.67265	−	8.09326i	−0.331235	−	0.573716i	−0.982754	+	0.184916i	$0.940799\pi$
$200$	−20.0913			−1.42067
$201$	−6.92771	−	11.9992i	−0.488643	−	0.846355i
$202$	−6.04723	−	10.4741i	−0.425481	−	0.736956i
$203$	5.72889			0.402090
$204$	20.9804	+	36.3391i	1.46892	+	2.54425i
$205$	5.95233	−	10.3097i	0.415729	−	0.720063i
$206$	−12.2344	+	21.1905i	−0.852408	+	1.47641i
$207$	−6.06327			−0.421426
$208$	−5.79216	−	20.0646i	−0.401614	−	1.39123i
$209$	8.29918			0.574066
$210$	2.72343	−	4.71713i	0.187935	−	0.325513i
$211$	2.59334	−	4.49180i	0.178533	−	0.309228i	−0.762845	−	0.646581i	$-0.776198\pi$
$211$	2.59334	−	4.49180i	0.178533	−	0.309228i	0.941378	+	0.337353i	$0.109532\pi$
$212$	−3.83983	−	6.65079i	−0.263721	−	0.456778i
$213$	−14.8695			−1.01884
$214$	−2.96135	−	5.12921i	−0.202434	−	0.350625i
$215$	−5.91368	−	10.2428i	−0.403309	−	0.698552i
$216$	−10.1867			−0.693116
$217$	0.561709	+	0.972909i	0.0381313	+	0.0660453i
$218$	3.59690	−	6.23001i	0.243613	−	0.421950i
$219$	2.28514	−	3.95798i	0.154416	−	0.267456i
$220$	−5.23591			−0.353005
$221$	−14.9980	−	3.71104i	−1.00887	−	0.249632i
$222$	−4.53821			−0.304585
$223$	−8.41714	+	14.5789i	−0.563653	+	0.976276i	0.433520	+	0.901144i	$0.357271\pi$
$223$	−8.41714	+	14.5789i	−0.563653	+	0.976276i	−0.997174	+	0.0751322i	$0.976062\pi$
$224$	−1.19180	+	2.06426i	−0.0796305	+	0.137924i
$225$	3.89608	+	6.74821i	0.259739	+	0.449881i
$226$	−14.0452			−0.934275
$227$	8.80820	+	15.2562i	0.584621	+	1.01259i	0.994923	+	0.100643i	$0.0320900\pi$
$227$	8.80820	+	15.2562i	0.584621	+	1.01259i	−0.410302	+	0.911950i	$0.634577\pi$
$228$	−40.6335	−	70.3792i	−2.69102	−	4.66098i
$229$	26.8554			1.77466			0.887328	−	0.461138i	$-0.152559\pi$
$229$	26.8554			1.77466			0.887328	+	0.461138i	$0.152559\pi$
$230$	−4.17967	−	7.23939i	−0.275599	−	0.477351i
$231$	−0.889062	+	1.53990i	−0.0584960	+	0.101318i
$232$	−21.0893	+	36.5278i	−1.38458	+	2.39817i
$233$	−27.1406			−1.77804			−0.889019	−	0.457870i	$-0.848612\pi$
$233$	−27.1406			−1.77804			−0.889019	+	0.457870i	$0.848612\pi$
$234$	−13.9257	+	14.4720i	−0.910352	+	0.946066i
$235$	4.13054			0.269446
$236$	−11.1582	+	19.3265i	−0.726335	+	1.25805i
$237$	−15.5211	+	26.8833i	−1.00820	+	1.74626i
$238$	4.17967	+	7.23939i	0.270927	+	0.469260i
$239$	0.746047			0.0482577			0.0241289	−	0.999709i	$-0.492319\pi$
$239$	0.746047			0.0482577			0.0241289	+	0.999709i	$0.492319\pi$
$240$	8.08632	+	14.0059i	0.521970	+	0.904078i
$241$	−8.08632	−	14.0059i	−0.520886	−	0.902201i	−0.999705	−	0.0242873i	$-0.992268\pi$
$241$	−8.08632	−	14.0059i	−0.520886	−	0.902201i	0.478819	−	0.877914i	$-0.341065\pi$
$242$	2.50702			0.161157
$243$	9.59134	+	16.6127i	0.615285	+	1.06570i
$244$	31.1124	−	53.8883i	1.99177	−	3.44984i
$245$	−3.90666	+	6.76653i	−0.249587	+	0.432298i
$246$	55.8162			3.55871
$247$	29.0471	+	7.18730i	1.84822	+	0.457317i
$248$	−8.27111			−0.525216
$249$	15.2675	−	26.4442i	0.967541	−	1.67583i
$250$	−13.0296	+	22.5680i	−0.824066	+	1.42732i
$251$	5.51404	+	9.55059i	0.348043	+	0.602828i	0.985902	−	0.167325i	$-0.0535130\pi$
$251$	5.51404	+	9.55059i	0.348043	+	0.602828i	−0.637859	+	0.770153i	$0.720180\pi$
$252$	7.40856			0.466695
$253$	1.36445	+	2.36329i	0.0857821	+	0.148579i
$254$	−9.07028	−	15.7102i	−0.569120	−	0.985745i
$255$	11.9648			0.749265
$256$	16.0457	+	27.7919i	1.00285	+	1.73699i
$257$	−9.42616	+	16.3266i	−0.587987	+	1.01842i	0.406508	+	0.913647i	$0.366746\pi$
$257$	−9.42616	+	16.3266i	−0.587987	+	1.01842i	−0.994496	+	0.104777i	$0.966587\pi$
$258$	27.7269	−	48.0244i	1.72620	−	2.98987i
$259$	−0.616399			−0.0383012
$260$	−18.3257	−	4.53443i	−1.13651	−	0.281214i
$261$	16.3584			1.01256
$262$	12.9718	−	22.4679i	0.801402	−	1.38807i
$263$	7.77612	−	13.4686i	0.479496	−	0.830512i	−0.520227	−	0.854028i	$-0.674153\pi$
$263$	7.77612	−	13.4686i	0.479496	−	0.830512i	0.999723	+	0.0235160i	$0.00748607\pi$
$264$	−6.54567	−	11.3374i	−0.402858	−	0.697771i
$265$	−2.18980			−0.134518
$266$	−8.09490	−	14.0208i	−0.496330	−	0.859669i
$267$	5.45935	+	9.45587i	0.334107	+	0.578690i
$268$	25.9820			1.58710
$269$	2.61094	+	4.52228i	0.159192	+	0.275728i	0.934577	−	0.355760i	$-0.115778\pi$
$269$	2.61094	+	4.52228i	0.159192	+	0.275728i	−0.775386	+	0.631488i	$0.782445\pi$
$270$	−2.72343	+	4.71713i	−0.165743	+	0.287075i
$271$	−12.9684	+	22.4619i	−0.787772	+	1.36446i	0.139557	+	0.990214i	$0.455432\pi$
$271$	−12.9684	+	22.4619i	−0.787772	+	1.36446i	−0.927329	+	0.374247i	$0.877901\pi$
$272$	−24.8202			−1.50495
$273$	−4.44531	+	4.61970i	−0.269042	+	0.279597i
$274$	−12.3765			−0.747691
$275$	1.75351	−	3.03717i	0.105741	−	0.183148i
$276$	13.3609	−	23.1417i	0.804231	−	1.39297i
$277$	8.88706	+	15.3928i	0.533972	+	0.924866i	0.999212	+	0.0396819i	$0.0126345\pi$
$277$	8.88706	+	15.3928i	0.533972	+	0.924866i	−0.465241	+	0.885184i	$0.654032\pi$
$278$	41.2952			2.47672
$279$	1.60392	+	2.77807i	0.0960241	+	0.166319i
$280$	2.72343	+	4.71713i	0.162756	+	0.281902i
$281$	7.41168			0.442143			0.221072	−	0.975258i	$-0.429045\pi$
$281$	7.41168			0.442143			0.221072	+	0.975258i	$0.429045\pi$
$282$	9.68322	+	16.7718i	0.576628	+	0.998748i
$283$	−4.65861	+	8.06895i	−0.276926	+	0.479649i	−0.970619	−	0.240621i	$-0.922649\pi$
$283$	−4.65861	+	8.06895i	−0.276926	+	0.479649i	0.693694	+	0.720270i	$0.255982\pi$
$284$	13.9418	−	24.1478i	0.827291	−	1.43291i
$285$	−23.1726			−1.37263
$286$	8.77457	+	2.17114i	0.518851	+	0.128382i
$287$	7.58121			0.447505
$288$	−3.40310	+	5.89434i	−0.200530	+	0.347327i
$289$	−0.681223	+	1.17991i	−0.0400719	+	0.0694066i
$290$	11.2766	+	19.5316i	0.662183	+	1.14693i
$291$	−9.46179			−0.554660
$292$	4.28514	+	7.42208i	0.250769	+	0.434345i
$293$	14.3765	+	24.9008i	0.839883	+	1.45472i	0.889992	+	0.455976i	$0.150710\pi$
$293$	14.3765	+	24.9008i	0.839883	+	1.45472i	−0.0501087	+	0.998744i	$0.515957\pi$
$294$	−36.6336			−2.13651
$295$	3.18167	+	5.51081i	0.185244	+	0.320852i
$296$	2.26910	−	3.93020i	0.131889	−	0.228438i
$297$	0.889062	−	1.53990i	0.0515886	−	0.0893541i
$298$	−4.77501			−0.276609
$299$	2.72889	+	9.45317i	0.157816	+	0.546691i
$300$	−34.3413			−1.98270
$301$	3.76599	−	6.52288i	0.217068	−	0.375973i
$302$	−23.0753	+	39.9676i	−1.32783	+	2.29988i
$303$	−5.51204	−	9.54713i	−0.316658	−	0.548468i
$304$	48.0702			2.75701
$305$	−8.87147	−	15.3658i	−0.507979	−	0.879845i
$306$	11.9347	+	20.6716i	0.682263	+	1.18171i
$307$	−0.792161			−0.0452110			−0.0226055	−	0.999744i	$-0.507196\pi$
$307$	−0.792161			−0.0452110			−0.0226055	+	0.999744i	$0.507196\pi$
$308$	−1.66719	−	2.88765i	−0.0949967	−	0.164539i
$309$	−11.1516	+	19.3151i	−0.634392	+	1.09880i
$310$	−2.21130	+	3.83008i	−0.125593	+	0.217534i
$311$	25.8022			1.46311			0.731554	−	0.681783i	$-0.238795\pi$
$311$	25.8022			1.46311			0.731554	+	0.681783i	$0.238795\pi$
$312$	−13.0913	−	45.3497i	−0.741151	−	2.56742i
$313$	−26.2780			−1.48532			−0.742661	−	0.669668i	$-0.766437\pi$
$313$	−26.2780			−1.48532			−0.742661	+	0.669668i	$0.766437\pi$
$314$	15.1742	−	26.2825i	0.856330	−	1.48321i
$315$	1.05625	−	1.82947i	0.0595128	−	0.103079i
$316$	−29.1054	−	50.4120i	−1.63731	−	2.83590i
$317$	10.9788			0.616633			0.308317	−	0.951284i	$-0.400234\pi$
$317$	10.9788			0.616633			0.308317	+	0.951284i	$0.400234\pi$
$318$	−5.13355	−	8.89157i	−0.287875	−	0.498615i
$319$	−3.68122	−	6.37607i	−0.206109	−	0.356991i
$320$	4.77101			0.266707
$321$	−2.69926	−	4.67526i	−0.150658	−	0.260948i
$322$	2.66172	−	4.61024i	0.148332	−	0.256919i
$323$	17.7816	−	30.7986i	0.989394	−	1.71368i
$324$	−45.9748			−2.55416
$325$	8.76755	−	9.11150i	0.486336	−	0.505415i
$326$	4.81020			0.266412
$327$	3.27857	−	5.67865i	0.181305	−	0.314030i
$328$	−27.9081	+	48.3383i	−1.54097	+	2.66903i
$329$	1.31522	+	2.27803i	0.0725103	+	0.125592i
$330$	−7.00000			−0.385337
$331$	−5.02807	−	8.70888i	−0.276368	−	0.478683i	0.694111	−	0.719868i	$-0.255798\pi$
$331$	−5.02807	−	8.70888i	−0.276368	−	0.478683i	−0.970479	+	0.241184i	$0.922464\pi$
$332$	28.6300	+	49.5886i	1.57127	+	2.72153i
$333$	−1.76008			−0.0964520
$334$	8.84997	+	15.3286i	0.484249	+	0.838743i
$335$	3.70428	−	6.41600i	0.202386	−	0.350544i
$336$	−5.14959	+	8.91935i	−0.280933	+	0.486591i
$337$	19.7398			1.07530			0.537648	−	0.843169i	$-0.319313\pi$
$337$	19.7398			1.07530			0.537648	+	0.843169i	$0.319313\pi$
$338$	28.8307	+	15.1980i	1.56818	+	0.826662i
$339$	−12.8022			−0.695320
$340$	−11.2183	+	19.4307i	−0.608399	+	1.05378i
$341$	0.721876	−	1.25033i	0.0390918	−	0.0677090i
$342$	−23.1144	−	40.0353i	−1.24988	−	2.16486i
$343$	−10.4226			−0.562767
$344$	27.7269	+	48.0244i	1.49493	+	2.58930i
$345$	−3.80976	−	6.59869i	−0.205110	−	0.355262i
$346$	4.13054			0.222059
$347$	−9.15661	−	15.8597i	−0.491553	−	0.851394i	0.508400	−	0.861121i	$-0.330237\pi$
$347$	−9.15661	−	15.8597i	−0.491553	−	0.851394i	−0.999953	+	0.00972702i	$0.996904\pi$
$348$	−36.0471	+	62.4355i	−1.93233	+	3.34689i
$349$	−8.68824	+	15.0485i	−0.465071	+	0.805526i	−0.999205	−	0.0398735i	$-0.987305\pi$
$349$	−8.68824	+	15.0485i	−0.465071	+	0.805526i	0.534134	+	0.845400i	$0.320638\pi$
$350$	−6.84139			−0.365688
$351$	4.44531	−	4.61970i	0.237273	−	0.246581i
$352$	3.06327			0.163273
$353$	−16.8835	+	29.2431i	−0.898618	+	1.55645i	−0.0693563	+	0.997592i	$0.522095\pi$
$353$	−16.8835	+	29.2431i	−0.898618	+	1.55645i	−0.829262	+	0.558860i	$0.811239\pi$
$354$	−14.9176	+	25.8380i	−0.792860	+	1.37327i
$355$	−3.97539	−	6.88557i	−0.210992	−	0.365448i
$356$	−20.4749			−1.08517
$357$	3.80976	+	6.59869i	0.201634	+	0.349240i
$358$	−9.19370	−	15.9240i	−0.485902	−	0.841607i
$359$	−4.72889			−0.249582			−0.124791	−	0.992183i	$-0.539826\pi$
$359$	−4.72889			−0.249582			−0.124791	+	0.992183i	$0.539826\pi$
$360$	7.77657	+	13.4694i	0.409861	+	0.709900i
$361$	−24.9382	+	43.1942i	−1.31254	+	2.27338i
$362$	−14.7601	+	25.5652i	−0.775773	+	1.34368i
$363$	2.28514			0.119939
$364$	−3.33437	−	11.5506i	−0.174769	−	0.605416i
$365$	2.44375			0.127912
$366$	41.5948	−	72.0443i	2.17420	−	3.76582i
$367$	−3.21330	+	5.56560i	−0.167733	+	0.290522i	−0.937622	−	0.347655i	$-0.886978\pi$
$367$	−3.21330	+	5.56560i	−0.167733	+	0.290522i	0.769890	+	0.638177i	$0.220311\pi$
$368$	7.90310	+	13.6886i	0.411978	+	0.713566i
$369$	21.6476			1.12693
$370$	−1.21330	−	2.10150i	−0.0630765	−	0.109252i
$371$	−0.697262	−	1.20769i	−0.0362000	−	0.0627003i
$372$	−14.1375			−0.732993
$373$	2.20584	+	3.82062i	0.114214	+	0.197824i	0.917465	−	0.397816i	$-0.130232\pi$
$373$	2.20584	+	3.82062i	0.114214	+	0.197824i	−0.803251	+	0.595640i	$0.796898\pi$
$374$	5.37147	−	9.30365i	0.277752	−	0.481080i
$375$	−11.8765	+	20.5707i	−0.613299	+	1.06226i
$376$	−19.3664			−0.998748
$377$	−7.36245	−	25.5043i	−0.379185	−	1.31354i
$378$	−3.46871			−0.178411
$379$	−9.75351	+	16.8936i	−0.501004	+	0.867765i	0.498995	+	0.866605i	$0.333703\pi$
$379$	−9.75351	+	16.8936i	−0.501004	+	0.867765i	−0.999999	+	0.00115985i	$0.999631\pi$
$380$	21.7269	−	37.6321i	1.11457	−	1.93049i
$381$	−8.26755	−	14.3198i	−0.423559	−	0.733626i
$382$	36.9608			1.89108
$383$	−13.8152	−	23.9287i	−0.705925	−	1.22270i	−0.966357	−	0.257205i	$-0.917198\pi$
$383$	−13.8152	−	23.9287i	−0.705925	−	1.22270i	0.260432	−	0.965492i	$-0.416135\pi$
$384$	18.1847	+	31.4968i	0.927983	+	1.60731i
$385$	−0.950771			−0.0484558
$386$	11.1582	+	19.3265i	0.567936	+	0.983693i
$387$	10.7535	−	18.6256i	0.546632	−	0.946794i
$388$	8.87147	−	15.3658i	0.450380	−	0.780082i
$389$	−28.9960			−1.47016			−0.735078	−	0.677983i	$-0.762854\pi$
$389$	−28.9960			−1.47016			−0.735078	+	0.677983i	$0.762854\pi$
$390$	−24.5000	−	6.06218i	−1.24061	−	0.306970i
$391$	11.6937			0.591376
$392$	18.3168	−	31.7256i	0.925137	−	1.60238i
$393$	11.8238	−	20.4794i	0.596432	−	1.03305i
$394$	7.66207	+	13.2711i	0.386010	+	0.668588i
$395$	−16.5984			−0.835154
$396$	−4.76053	−	8.24548i	−0.239226	−	0.414351i
$397$	−17.3293	−	30.0152i	−0.869730	−	1.50642i	−0.862272	−	0.506445i	$-0.830959\pi$
$397$	−17.3293	−	30.0152i	−0.869730	−	1.50642i	−0.00745819	−	0.999972i	$-0.502374\pi$
$398$	23.4288			1.17438
$399$	−7.37848	−	12.7799i	−0.369386	−	0.639796i
$400$	10.1566	−	17.5918i	0.507830	−	0.879588i
$401$	7.29372	−	12.6331i	0.364231	−	0.630866i	−0.624422	−	0.781088i	$-0.714665\pi$
$401$	7.29372	−	12.6331i	0.364231	−	0.630866i	0.988652	+	0.150221i	$0.0479986\pi$
$402$	34.7358			1.73246
$403$	3.60938	−	3.75098i	0.179796	−	0.186850i
$404$	20.6725			1.02850
$405$	−6.55469	+	11.3531i	−0.325705	+	0.564138i
$406$	−7.18122	+	12.4382i	−0.356398	+	0.617300i
$407$	0.396081	+	0.686032i	0.0196330	+	0.0340053i
$408$	−56.0983			−2.77728
$409$	−8.30074	−	14.3773i	−0.410445	−	0.710912i	0.584493	−	0.811398i	$-0.301293\pi$
$409$	−8.30074	−	14.3773i	−0.410445	−	0.710912i	−0.994938	+	0.100487i	$0.967960\pi$
$410$	14.9226	+	25.8467i	0.736975	+	1.27648i
$411$	−11.2811			−0.556458
$412$	−20.9117	−	36.2201i	−1.03024	−	1.78444i
$413$	−2.02617	+	3.50943i	−0.0997014	+	0.172688i
$414$	7.60036	−	13.1642i	0.373537	−	0.646986i
$415$	16.3273			0.801473
$416$	10.7214	+	2.65287i	0.525661	+	0.130067i
$417$	37.6405			1.84326
$418$	−10.4031	+	18.0187i	−0.508832	+	0.881323i
$419$	11.1476	−	19.3082i	0.544595	−	0.943267i	−0.454037	−	0.890983i	$-0.650017\pi$
$419$	11.1476	−	19.3082i	0.544595	−	0.943267i	0.998632	−	0.0522839i	$-0.0166501\pi$
$420$	4.65505	+	8.06279i	0.227143	+	0.393424i
$421$	−3.45779			−0.168522			−0.0842612	−	0.996444i	$-0.526853\pi$
$421$	−3.45779			−0.168522			−0.0842612	+	0.996444i	$0.526853\pi$
$422$	6.50156	+	11.2610i	0.316491	+	0.548178i
$423$	3.75551	+	6.50474i	0.182599	+	0.316271i
$424$	10.2671			0.498615
$425$	−7.51404	−	13.0147i	−0.364484	−	0.631305i
$426$	18.6390	−	32.2837i	0.903063	−	1.56415i
$427$	5.64959	−	9.78538i	0.273403	−	0.473548i
$428$	10.1234			0.489334
$429$	7.99800	+	1.97899i	0.386147	+	0.0955466i
$430$	29.6514			1.42992
$431$	−12.9402	+	22.4131i	−0.623307	+	1.07960i	0.365558	+	0.930788i	$0.380878\pi$
$431$	−12.9402	+	22.4131i	−0.623307	+	1.07960i	−0.988866	+	0.148811i	$0.952455\pi$
$432$	5.14959	−	8.91935i	0.247760	−	0.429132i
$433$	−7.19024	−	12.4539i	−0.345541	−	0.598495i	0.639911	−	0.768449i	$-0.278971\pi$
$433$	−7.19024	−	12.4539i	−0.345541	−	0.598495i	−0.985452	+	0.169955i	$0.945638\pi$
$434$	−2.81643			−0.135193
$435$	10.2786	+	17.8030i	0.492820	+	0.853589i
$436$	6.14803	+	10.6487i	0.294437	+	0.509980i
$437$	−22.6476			−1.08338
$438$	5.72889	+	9.92274i	0.273737	+	0.474127i
$439$	−2.28314	+	3.95452i	−0.108968	+	0.188739i	−0.915353	−	0.402653i	$-0.868088\pi$
$439$	−2.28314	+	3.95452i	−0.108968	+	0.188739i	0.806384	+	0.591392i	$0.201421\pi$
$440$	3.50000	−	6.06218i	0.166856	−	0.289003i
$441$	−14.2078			−0.676564
$442$	26.8573	−	27.9110i	1.27747	−	1.32759i
$443$	18.1718			0.863366			0.431683	−	0.902025i	$-0.357920\pi$
$443$	18.1718			0.863366			0.431683	+	0.902025i	$0.357920\pi$
$444$	3.87848	−	6.71773i	0.184065	−	0.318809i
$445$	−2.91914	+	5.05609i	−0.138380	+	0.239682i
$446$	−21.1019	−	36.5496i	−0.999205	−	1.73067i
$447$	−4.35241			−0.205862
$448$	1.51915	+	2.63125i	0.0717732	+	0.124315i
$449$	6.31477	+	10.9375i	0.298013	+	0.516173i	0.975681	−	0.219194i	$-0.0703429\pi$
$449$	6.31477	+	10.9375i	0.298013	+	0.516173i	−0.677669	+	0.735367i	$0.737010\pi$
$450$	−19.5351			−0.920893
$451$	−4.87147	−	8.43763i	−0.229388	−	0.397312i
$452$	12.0035	−	20.7906i	0.564595	−	0.977908i
$453$	−21.0331	+	36.4304i	−0.988221	+	1.71165i
$454$	−44.1646			−2.07275
$455$	−3.32770	−	0.823392i	−0.156005	−	0.0386012i
$456$	108.647			5.08788
$457$	12.8941	−	22.3332i	0.603160	−	1.04470i	−0.389180	−	0.921162i	$-0.627242\pi$
$457$	12.8941	−	22.3332i	0.603160	−	1.04470i	0.992339	−	0.123541i	$-0.0394251\pi$
$458$	−33.6635	+	58.3069i	−1.57299	+	2.72450i
$459$	−3.80976	−	6.59869i	−0.177824	−	0.308001i
$460$	14.2883			0.666193
$461$	6.31678	+	10.9410i	0.294202	+	0.509572i	0.974799	−	0.223086i	$-0.0716130\pi$
$461$	6.31678	+	10.9410i	0.294202	+	0.509572i	−0.680597	+	0.732658i	$0.738280\pi$
$462$	−2.22889	−	3.86056i	−0.103698	−	0.179609i
$463$	−3.47494			−0.161494			−0.0807471	−	0.996735i	$-0.525731\pi$
$463$	−3.47494			−0.161494			−0.0807471	+	0.996735i	$0.525731\pi$
$464$	−21.3222	−	36.9312i	−0.989860	−	1.71449i
$465$	−2.01559	+	3.49111i	−0.0934710	+	0.161896i
$466$	34.0210	−	58.9260i	1.57599	−	2.72970i
$467$	−18.7258			−0.866526			−0.433263	−	0.901268i	$-0.642638\pi$
$467$	−18.7258			−0.866526			−0.433263	+	0.901268i	$0.642638\pi$
$468$	−9.52106	−	32.9819i	−0.440111	−	1.52459i
$469$	4.71797			0.217856
$470$	−5.17766	+	8.96798i	−0.238828	+	0.413662i
$471$	13.8313	−	23.9564i	0.637311	−	1.10385i
$472$	−14.9176	−	25.8380i	−0.686637	−	1.18929i
$473$	−9.67967			−0.445072
$474$	−38.9116	−	67.3968i	−1.78727	−	3.09564i
$475$	14.5527	+	25.2060i	0.667723	+	1.15653i
$476$	−14.2883			−0.654901
$477$	−1.99098	−	3.44848i	−0.0911607	−	0.157895i
$478$	−0.935176	+	1.61977i	−0.0427740	+	0.0740867i
$479$	−4.64257	+	8.04117i	−0.212124	+	0.367410i	−0.952379	−	0.304916i	$-0.901372\pi$
$479$	−4.64257	+	8.04117i	−0.212124	+	0.367410i	0.740255	+	0.672327i	$0.234705\pi$
$480$	−8.55313			−0.390395
$481$	0.792161	+	2.74413i	0.0361194	+	0.125121i
$482$	40.5451			1.84678
$483$	2.42616	−	4.20223i	0.110394	−	0.191208i
$484$	−2.14257	+	3.71104i	−0.0973896	+	0.168684i
$485$	−2.52963	−	4.38145i	−0.114865	−	0.198951i
$486$	−48.0913			−2.18147
$487$	19.9648	+	34.5801i	0.904692	+	1.56697i	0.821330	+	0.570453i	$0.193232\pi$
$487$	19.9648	+	34.5801i	0.904692	+	1.56697i	0.0833614	+	0.996519i	$0.473434\pi$
$488$	41.5948	+	72.0443i	1.88291	+	3.26129i
$489$	4.38449			0.198273
$490$	−9.79406	−	16.9638i	−0.442451	−	0.766347i
$491$	20.5913	−	35.6652i	0.929274	−	1.60955i	0.144735	−	0.989470i	$-0.453767\pi$
$491$	20.5913	−	35.6652i	0.929274	−	1.60955i	0.784539	−	0.620080i	$-0.212900\pi$
$492$	−47.7022	+	82.6226i	−2.15058	+	3.72491i
$493$	−31.5491			−1.42090
$494$	−52.0155	+	54.0561i	−2.34029	+	2.43210i
$495$	−2.71486			−0.122024
$496$	4.18122	−	7.24209i	0.187742	−	0.325179i
$497$	2.53163	−	4.38492i	0.113559	−	0.196690i
$498$	38.2760	+	66.2960i	1.71519	+	2.97080i
$499$	19.3132			0.864578			0.432289	−	0.901735i	$-0.357706\pi$
$499$	19.3132			0.864578			0.432289	+	0.901735i	$0.357706\pi$
$500$	−22.2710	−	38.5745i	−0.995990	−	1.72510i
$501$	8.06673	+	13.9720i	0.360395	+	0.624222i
$502$	−27.6476			−1.23397
$503$	−9.84485	−	17.0518i	−0.438960	−	0.760301i	0.558649	−	0.829404i	$-0.311320\pi$
$503$	−9.84485	−	17.0518i	−0.438960	−	0.760301i	−0.997610	+	0.0691026i	$0.977986\pi$
$504$	−4.95233	+	8.57768i	−0.220594	+	0.382080i
$505$	2.94731	−	5.10489i	0.131154	−	0.227165i
$506$	−6.84139			−0.304137
$507$	26.2791	+	13.8529i	1.16710	+	0.615231i
$508$	31.0069			1.37571
$509$	−6.73747	+	11.6696i	−0.298633	+	0.517248i	−0.975823	−	0.218560i	$-0.929864\pi$
$509$	−6.73747	+	11.6696i	−0.298633	+	0.517248i	0.677190	+	0.735808i	$0.263197\pi$
$510$	−14.9980	+	25.9773i	−0.664123	+	1.15029i
$511$	0.778124	+	1.34775i	0.0344222	+	0.0596210i
$512$	−48.6224			−2.14883
$513$	7.37848	+	12.7799i	0.325768	+	0.564247i
$514$	−23.6315	−	40.9310i	−1.04234	−	1.80539i
$515$	−11.9256			−0.525505
$516$	47.3924	+	82.0861i	2.08634	+	3.61364i
$517$	1.69024	−	2.92759i	0.0743368	−	0.128755i
$518$	0.772662	−	1.33829i	0.0339488	−	0.0588011i
$519$	3.76497			0.165264
$520$	17.5000	−	18.1865i	0.767426	−	0.797532i
$521$	19.4266			0.851095			0.425547	−	0.904936i	$-0.360082\pi$
$521$	19.4266			0.851095			0.425547	+	0.904936i	$0.360082\pi$
$522$	−20.5055	+	35.5165i	−0.897500	+	1.55452i
$523$	−5.46135	+	9.45933i	−0.238808	+	0.413628i	−0.960373	−	0.278720i	$-0.910090\pi$
$523$	−5.46135	+	9.45933i	−0.238808	+	0.413628i	0.721564	+	0.692347i	$0.243423\pi$
$524$	22.1722	+	38.4034i	0.968597	+	1.67766i
$525$	−6.23591			−0.272158
$526$	19.4949	+	33.7661i	0.850017	+	1.47227i
$527$	−3.09334	−	5.35783i	−0.134748	−	0.233391i
$528$	13.2359			0.576019
$529$	7.77657	+	13.4694i	0.338112	+	0.585626i
$530$	2.74493	−	4.75436i	0.119232	−	0.206516i
$531$	−5.78559	+	10.0209i	−0.251073	+	0.434871i
$532$	27.6725			1.19976
$533$	−9.74293	−	33.7505i	−0.422013	−	1.46190i
$534$	−27.3734			−1.18456
$535$	1.44331	−	2.49988i	0.0623997	−	0.108079i
$536$	−17.3679	+	30.0821i	−0.750179	+	1.29935i
$537$	−8.38004	−	14.5147i	−0.361626	−	0.626354i
$538$	−13.0913			−0.564408
$539$	3.19726	+	5.53782i	0.137716	+	0.238531i
$540$	−4.65505	−	8.06279i	−0.200322	−	0.346967i
$541$	−16.9820			−0.730111			−0.365056	−	0.930986i	$-0.618950\pi$
$541$	−16.9820			−0.730111			−0.365056	+	0.930986i	$0.618950\pi$
$542$	−32.5119	−	56.3123i	−1.39651	−	2.41882i
$543$	−13.4538	+	23.3026i	−0.577357	+	1.00001i
$544$	6.56327	−	11.3679i	0.281398	−	0.487395i
$545$	3.50613			0.150186
$546$	−4.45779	−	15.4422i	−0.190776	−	0.660867i
$547$	1.13345			0.0484629			0.0242315	−	0.999706i	$-0.492286\pi$
$547$	1.13345			0.0484629			0.0242315	+	0.999706i	$0.492286\pi$
$548$	10.5773	−	18.3204i	0.451840	−	0.782610i
$549$	16.1320	−	27.9414i	0.688497	−	1.19251i
$550$	4.39608	+	7.61423i	0.187450	+	0.324672i
$551$	61.1023			2.60304
$552$	17.8624	+	30.9387i	0.760276	+	1.31684i
$553$	−5.28514	−	9.15414i	−0.224747	−	0.389273i
$554$	−44.5601			−1.89318
$555$	−1.10592	−	1.91551i	−0.0469437	−	0.0813089i
$556$	−35.2921	+	61.1276i	−1.49672	+	2.59239i
$557$	10.1336	−	17.5518i	0.429372	−	0.743695i	−0.567445	−	0.823411i	$-0.692068\pi$
$557$	10.1336	−	17.5518i	0.429372	−	0.743695i	0.996818	+	0.0797164i	$0.0254015\pi$
$558$	−8.04211			−0.340450
$559$	−33.8788	−	8.38284i	−1.43292	−	0.354556i
$560$	−5.50702			−0.232714
$561$	4.89608	−	8.48026i	0.206713	−	0.358037i
$562$	−9.29060	+	16.0918i	−0.391900	+	0.678792i
$563$	−0.156609	−	0.271254i	−0.00660026	−	0.0114320i	0.862706	−	0.505705i	$-0.168768\pi$
$563$	−0.156609	−	0.271254i	−0.00660026	−	0.0114320i	−0.869307	+	0.494273i	$0.835434\pi$
$564$	−33.1023			−1.39386
$565$	−3.42270	−	5.92828i	−0.143994	−	0.249405i
$566$	−11.6792	−	20.2290i	−0.490914	−	0.850289i
$567$	−8.34841			−0.350600
$568$	18.6390	+	32.2837i	0.782076	+	1.35459i
$569$	5.54211	−	9.59922i	0.232337	−	0.402420i	−0.726158	−	0.687528i	$-0.758696\pi$
$569$	5.54211	−	9.59922i	0.232337	−	0.402420i	0.958496	+	0.285108i	$0.0920293\pi$
$570$	29.0471	−	50.3111i	1.21665	−	2.10730i
$571$	41.7037			1.74525			0.872624	−	0.488393i	$-0.162417\pi$
$571$	41.7037			1.74525			0.872624	+	0.488393i	$0.162417\pi$
$572$	−10.7129	+	11.1331i	−0.447927	+	0.465499i
$573$	33.6897			1.40741
$574$	−9.50311	+	16.4599i	−0.396652	+	0.687022i
$575$	−4.78514	+	8.28811i	−0.199554	+	0.345638i
$576$	4.33783	+	7.51334i	0.180743	+	0.313056i
$577$	19.1867			0.798752			0.399376	−	0.916787i	$-0.369227\pi$
$577$	19.1867			0.798752			0.399376	+	0.916787i	$0.369227\pi$
$578$	−1.70784	−	2.95806i	−0.0710367	−	0.123039i
$579$	10.1706	+	17.6161i	0.422678	+	0.732099i
$580$	−38.5491			−1.60067
$581$	5.19882	+	9.00462i	0.215683	+	0.373575i
$582$	11.8604	−	20.5429i	0.491631	−	0.851530i
$583$	−0.896081	+	1.55206i	−0.0371119	+	0.0642796i
$584$	−11.4578			−0.474127
$585$	−9.50200	−	2.35114i	−0.392859	−	0.0972075i
$586$	−72.0842			−2.97777
$587$	6.29216	−	10.8983i	0.259705	−	0.449823i	−0.706458	−	0.707755i	$-0.749708\pi$
$587$	6.29216	−	10.8983i	0.259705	−	0.449823i	0.966163	+	0.257933i	$0.0830412\pi$
$588$	31.3081	−	54.2272i	1.29112	−	2.23629i
$589$	5.99098	+	10.3767i	0.246854	+	0.427564i
$590$	−15.9530			−0.656775
$591$	6.98396	+	12.0966i	0.287282	+	0.497587i
$592$	2.29416	+	3.97361i	0.0942895	+	0.163314i
$593$	−13.7117			−0.563074			−0.281537	−	0.959550i	$-0.590844\pi$
$593$	−13.7117			−0.563074			−0.281537	+	0.959550i	$0.590844\pi$
$594$	2.22889	+	3.86056i	0.0914527	+	0.158401i
$595$	−2.03709	+	3.52835i	−0.0835127	+	0.144648i
$596$	4.08086	−	7.06826i	0.167159	−	0.289527i
$597$	21.3553			0.874015
$598$	−23.9449	−	5.92482i	−0.979178	−	0.242284i
$599$	−15.3905			−0.628840			−0.314420	−	0.949284i	$-0.601810\pi$
$599$	−15.3905			−0.628840			−0.314420	+	0.949284i	$0.601810\pi$
$600$	22.9558	−	39.7606i	0.937166	−	1.62322i
$601$	8.10738	−	14.0424i	0.330707	−	0.572801i	−0.651944	−	0.758267i	$-0.726046\pi$
$601$	8.10738	−	14.0424i	0.330707	−	0.572801i	0.982651	+	0.185466i	$0.0593795\pi$
$602$	9.44141	+	16.3530i	0.384803	+	0.666498i
$603$	13.4718			0.548615
$604$	−39.4417	−	68.3149i	−1.60486	−	2.77970i
$605$	0.610938	+	1.05818i	0.0248382	+	0.0430210i
$606$	27.6376			1.12270
$607$	−1.34139	−	2.32336i	−0.0544453	−	0.0943021i	0.837518	−	0.546409i	$-0.184006\pi$
$607$	−1.34139	−	2.32336i	−0.0544453	−	0.0943021i	−0.891964	+	0.452107i	$0.850672\pi$
$608$	−12.7113	+	22.0166i	−0.515511	+	0.892892i
$609$	−6.54567	+	11.3374i	−0.265244	+	0.459416i
$610$	44.4819			1.80102
$611$	8.45122	−	8.78276i	0.341900	−	0.355312i
$612$	−40.7991			−1.64921
$613$	18.0457	−	31.2560i	0.728858	−	1.26242i	−0.228509	−	0.973542i	$-0.573385\pi$
$613$	18.0457	−	31.2560i	0.728858	−	1.26242i	0.957366	−	0.288877i	$-0.0932818\pi$
$614$	0.992981	−	1.71989i	0.0400735	−	0.0694093i
$615$	13.6019	+	23.5592i	0.548482	+	0.949999i
$616$	4.45779			0.179609
$617$	9.58588	+	16.6032i	0.385913	+	0.668421i	0.991895	−	0.127057i	$-0.0405532\pi$
$617$	9.58588	+	16.6032i	0.385913	+	0.668421i	−0.605982	+	0.795478i	$0.707220\pi$
$618$	−27.9572	−	48.4234i	−1.12461	−	1.94787i
$619$	6.38049			0.256453			0.128227	−	0.991745i	$-0.459071\pi$
$619$	6.38049			0.256453			0.128227	+	0.991745i	$0.459071\pi$
$620$	−3.77968	−	6.54660i	−0.151796	−	0.262918i
$621$	−2.42616	+	4.20223i	−0.0973583	+	0.168630i
$622$	−32.3433	+	56.0202i	−1.29685	+	2.24621i
$623$	−3.71797			−0.148957
$624$	46.3257	+	11.4626i	1.85451	+	0.458873i
$625$	4.83427			0.193371
$626$	32.9397	−	57.0533i	1.31654	−	2.28031i
$627$	−9.48240	+	16.4240i	−0.378691	+	0.655912i
$628$	25.9366	+	44.9236i	1.03498	+	1.79265i
$629$	3.39452			0.135349
$630$	2.64803	+	4.58653i	0.105500	+	0.182732i
$631$	10.4503	+	18.1005i	0.416021	+	0.720569i	0.995535	−	0.0943928i	$-0.0300910\pi$
$631$	10.4503	+	18.1005i	0.416021	+	0.720569i	−0.579514	+	0.814962i	$0.696758\pi$
$632$	77.8232			3.09564
$633$	5.92616	+	10.2644i	0.235544	+	0.407973i
$634$	−13.7621	+	23.8366i	−0.546562	+	0.946674i
$635$	4.42070	−	7.65687i	0.175430	−	0.303854i
$636$	17.5491			0.695868
$637$	6.39452	+	22.1513i	0.253360	+	0.877666i
$638$	18.4578			0.730751
$639$	7.22889	−	12.5208i	0.285971	−	0.495316i
$640$	−9.72343	+	16.8415i	−0.384352	+	0.665718i
$641$	−9.55425	−	16.5484i	−0.377370	−	0.653624i	0.613309	−	0.789843i	$-0.289838\pi$
$641$	−9.55425	−	16.5484i	−0.377370	−	0.653624i	−0.990679	+	0.136219i	$0.956505\pi$
$642$	13.5342			0.534152
$643$	1.75351	+	3.03717i	0.0691517	+	0.119774i	0.898528	−	0.438916i	$-0.144637\pi$
$643$	1.75351	+	3.03717i	0.0691517	+	0.119774i	−0.829376	+	0.558690i	$0.811304\pi$
$644$	4.54957	+	7.88009i	0.179278	+	0.310519i
$645$	27.0272			1.06419
$646$	44.5788	+	77.2127i	1.75393	+	3.03789i
$647$	−10.4171	+	18.0430i	−0.409540	+	0.709344i	−0.994838	−	0.101474i	$-0.967644\pi$
$647$	−10.4171	+	18.0430i	−0.409540	+	0.709344i	0.585298	+	0.810818i	$0.300977\pi$
$648$	30.7324	−	53.2300i	1.20728	−	2.09107i
$649$	5.20784			0.204426
$650$	8.79216	+	30.4569i	0.344857	+	1.19462i
$651$	−2.56717			−0.100615
$652$	−4.11094	+	7.12035i	−0.160997	+	0.278855i
$653$	6.33783	−	10.9774i	0.248019	−	0.429581i	−0.714957	−	0.699168i	$-0.753554\pi$
$653$	6.33783	−	10.9774i	0.248019	−	0.429581i	0.962976	+	0.269587i	$0.0868873\pi$
$654$	8.21943	+	14.2365i	0.321405	+	0.556690i
$655$	12.6445			0.494060
$656$	−28.2163	−	48.8721i	−1.10166	−	1.90813i
$657$	2.22188	+	3.84840i	0.0866836	+	0.150140i
$658$	−6.59455			−0.257082
$659$	−2.18980	−	3.79284i	−0.0853025	−	0.147748i	0.820218	−	0.572052i	$-0.193852\pi$
$659$	−2.18980	−	3.79284i	−0.0853025	−	0.147748i	−0.905520	+	0.424303i	$0.860519\pi$
$660$	5.98240	−	10.3618i	0.232865	−	0.403334i
$661$	0.561265	−	0.972140i	0.0218307	−	0.0378118i	−0.854904	−	0.518787i	$-0.826384\pi$
$661$	0.561265	−	0.972140i	0.0218307	−	0.0378118i	0.876734	+	0.480975i	$0.159717\pi$
$662$	25.2110			0.979852
$663$	24.4804	−	25.4408i	0.950740	−	0.988038i
$664$	−76.5520			−2.97080
$665$	3.94531	−	6.83348i	0.152993	−	0.264991i
$666$	2.20628	−	3.82139i	0.0854917	−	0.148076i
$667$	10.0457	+	17.3996i	0.388970	+	0.673716i
$668$	−30.2538			−1.17055
$669$	−19.2344	−	33.3149i	−0.743643	−	1.28803i
$670$	9.28670	+	16.0850i	0.358777	+	0.621419i
$671$	−14.5211			−0.560579
$672$	−2.72343	−	4.71713i	−0.105059	−	0.181967i
$673$	−9.02461	+	15.6311i	−0.347873	+	0.602534i	−0.985871	−	0.167504i	$-0.946429\pi$
$673$	−9.02461	+	15.6311i	−0.347873	+	0.602534i	0.637998	+	0.770038i	$0.279763\pi$
$674$	−24.7440	+	42.8579i	−0.953105	+	1.65083i
$675$	6.23591			0.240020
$676$	−47.1366	+	29.6883i	−1.81294	+	1.14186i
$677$	−26.7037			−1.02631			−0.513154	−	0.858297i	$-0.671523\pi$
$677$	−26.7037			−1.02631			−0.513154	+	0.858297i	$0.671523\pi$
$678$	16.0477	−	27.7954i	0.616307	−	1.06748i
$679$	1.61094	−	2.79023i	0.0618221	−	0.107079i
$680$	−14.9980	−	25.9773i	−0.575147	−	0.996184i
$681$	−40.2560			−1.54261
$682$	1.80976	+	3.13459i	0.0692992	+	0.120030i
$683$	−15.4894	−	26.8285i	−0.592686	−	1.02656i	−0.993869	−	0.110565i	$-0.964734\pi$
$683$	−15.4894	−	26.8285i	−0.592686	−	1.02656i	0.401183	−	0.915998i	$-0.368599\pi$
$684$	79.0170			3.02129
$685$	−3.01604	−	5.22393i	−0.115237	−	0.199596i
$686$	13.0648	−	22.6289i	0.498817	−	0.863977i
$687$	−30.6842	+	53.1467i	−1.17068	+	2.02767i
$688$	−56.0662			−2.13750
$689$	−4.48040	+	4.65617i	−0.170690	+	0.177386i
$690$	19.1023			0.727211
$691$	1.16563	−	2.01893i	0.0443426	−	0.0768036i	−0.843002	−	0.537910i	$-0.819214\pi$
$691$	1.16563	−	2.01893i	0.0443426	−	0.0768036i	0.887345	+	0.461106i	$0.152547\pi$
$692$	−3.53008	+	6.11427i	−0.134193	+	0.232430i
$693$	−0.864447	−	1.49727i	−0.0328376	−	0.0568765i
$694$	45.9116			1.74278
$695$	10.0633	+	17.4301i	0.381721	+	0.661161i
$696$	−48.1921	−	83.4712i	−1.82672	−	3.16397i
$697$	−41.7499			−1.58139
$698$	−21.7816	−	37.7268i	−0.824445	−	1.42798i
$699$	31.0100	−	53.7110i	1.17291	−	2.03153i
$700$	5.84685	−	10.1270i	0.220990	−	0.382766i
$701$	−22.5834			−0.852965			−0.426482	−	0.904496i	$-0.640247\pi$
$701$	−22.5834			−0.852965			−0.426482	+	0.904496i	$0.640247\pi$
$702$	4.45779	+	15.4422i	0.168248	+	0.582830i
$703$	−6.57429			−0.247954
$704$	1.95233	−	3.38153i	0.0735811	−	0.127446i
$705$	−4.71943	+	8.17429i	−0.177744	+	0.307862i
$706$	−42.3273	−	73.3130i	−1.59301	−	2.75917i
$707$	3.75385			0.141178
$708$	−25.4980	−	44.1638i	−0.958273	−	1.65978i
$709$	7.86089	+	13.6155i	0.295222	+	0.511339i	0.975036	−	0.222045i	$-0.0712731\pi$
$709$	7.86089	+	13.6155i	0.295222	+	0.511339i	−0.679815	+	0.733384i	$0.737940\pi$
$710$	19.9327			0.748062
$711$	−15.0913	−	26.1390i	−0.565970	−	0.980288i
$712$	13.6867	−	23.7060i	0.512930	−	0.888421i
$713$	−1.96992	+	3.41201i	−0.0737742	+	0.127781i
$714$	−19.1023			−0.714884
$715$	1.22188	+	4.23270i	0.0456956	+	0.158294i
$716$	31.4288			1.17455
$717$	−0.852411	+	1.47642i	−0.0318339	+	0.0551379i
$718$	5.92771	−	10.2671i	0.221220	−	0.383165i
$719$	14.9151	+	25.8338i	0.556241	+	0.963437i	0.997806	+	0.0662079i	$0.0210901\pi$
$719$	14.9151	+	25.8338i	0.556241	+	0.963437i	−0.441565	+	0.897229i	$0.645577\pi$
$720$	−15.7249			−0.586032
$721$	−3.79728	−	6.57708i	−0.141418	−	0.244943i
$722$	−62.5205	−	108.289i	−2.32677	−	4.03009i
$723$	36.9568			1.37444
$724$	−25.2288	−	43.6976i	−0.937621	−	1.62401i
$725$	12.9101	−	22.3610i	0.479470	−	0.830466i
$726$	−2.86445	+	4.96137i	−0.106310	+	0.184134i
$727$	−36.6053			−1.35761			−0.678807	−	0.734316i	$-0.737503\pi$
$727$	−36.6053			−1.35761			−0.678807	+	0.734316i	$0.737503\pi$
$728$	15.6023	+	3.86056i	0.578258	+	0.143082i
$729$	−11.6485			−0.431425
$730$	−3.06327	+	5.30573i	−0.113377	+	0.196374i
$731$	−20.7394	+	35.9216i	−0.767073	+	1.32861i
$732$	71.0963	+	123.142i	2.62779	+	4.55147i
$733$	29.8695			1.10325			0.551627	−	0.834091i	$-0.314007\pi$
$733$	29.8695			1.10325			0.551627	+	0.834091i	$0.314007\pi$
$734$	−8.05580	−	13.9531i	−0.297345	−	0.515017i
$735$	−8.92727	−	15.4625i	−0.329287	−	0.570342i
$736$	−8.35933			−0.308129
$737$	−3.03163	−	5.25094i	−0.111672	−	0.193421i
$738$	−27.1355	+	47.0000i	−0.998870	+	1.73009i
$739$	−15.1284	+	26.2032i	−0.556508	+	0.963901i	0.441276	+	0.897371i	$0.354526\pi$
$739$	−15.1284	+	26.2032i	−0.556508	+	0.963901i	−0.997784	+	0.0665295i	$0.978807\pi$
$740$	4.14769			0.152472
$741$	−47.4120	+	49.2720i	−1.74172	+	1.81005i
$742$	3.49610			0.128346
$743$	−19.6210	+	33.9845i	−0.719824	+	1.24677i	0.241246	+	0.970464i	$0.422444\pi$
$743$	−19.6210	+	33.9845i	−0.719824	+	1.24677i	−0.961069	+	0.276307i	$0.910889\pi$
$744$	9.45033	−	16.3684i	0.346466	−	0.600096i
$745$	−1.16363	−	2.01546i	−0.0426320	−	0.0738408i
$746$	−11.0602			−0.404941
$747$	14.8449	+	25.7120i	0.543145	+	0.940754i
$748$	9.18122	+	15.9023i	0.335699	+	0.581447i
$749$	1.83828			0.0671691
$750$	−29.7746	−	51.5711i	−1.08721	−	1.88311i
$751$	−3.41168	+	5.90919i	−0.124494	+	0.215630i	−0.921535	−	0.388295i	$-0.873064\pi$
$751$	−3.41168	+	5.90919i	−0.124494	+	0.215630i	0.797041	+	0.603925i	$0.206397\pi$
$752$	9.79016	−	16.9571i	0.357010	−	0.618360i
$753$	−25.2007			−0.918365
$754$	64.6023	+	15.9849i	2.35268	+	0.582136i
$755$	−22.4930			−0.818603
$756$	2.96446	−	5.13460i	0.107816	−	0.186744i
$757$	0.376483	−	0.652088i	0.0136835	−	0.0237006i	−0.859103	−	0.511803i	$-0.828978\pi$
$757$	0.376483	−	0.652088i	0.0136835	−	0.0237006i	0.872786	+	0.488103i	$0.162311\pi$
$758$	−24.4522	−	42.3525i	−0.888145	−	1.53831i
$759$	−6.23591			−0.226349
$760$	29.0471	+	50.3111i	1.05365	+	1.82498i
$761$	−17.4874	−	30.2891i	−0.633919	−	1.09798i	−0.986743	−	0.162290i	$-0.948112\pi$
$761$	−17.4874	−	30.2891i	−0.633919	−	1.09798i	0.352825	−	0.935689i	$-0.385221\pi$
$762$	41.4538			1.50171
$763$	1.11640	+	1.93366i	0.0404164	+	0.0700032i
$764$	−31.5878	+	54.7116i	−1.14281	+	1.97940i
$765$	−5.81678	+	10.0750i	−0.210306	+	0.364261i
$766$	69.2700			2.50283
$767$	18.2274	+	4.51012i	0.658155	+	0.162851i
$768$	−73.3333			−2.64619
$769$	−7.73245	+	13.3930i	−0.278839	+	0.482964i	−0.971097	−	0.238687i	$-0.923283\pi$
$769$	−7.73245	+	13.3930i	−0.278839	+	0.482964i	0.692257	+	0.721651i	$0.256616\pi$
$770$	1.19180	−	2.06426i	0.0429495	−	0.0743907i
$771$	−21.5401	−	37.3086i	−0.775748	−	1.34364i
$772$	−38.1444			−1.37285
$773$	18.0683	+	31.2952i	0.649871	+	1.12561i	0.983153	+	0.182783i	$0.0585104\pi$
$773$	18.0683	+	31.2952i	0.649871	+	1.12561i	−0.333282	+	0.942827i	$0.608156\pi$
$774$	26.9592	+	46.6948i	0.969030	+	1.67841i
$775$	5.06327			0.181878
$776$	11.8604	+	20.5429i	0.425765	+	0.737447i
$777$	0.704280	−	1.21985i	0.0252659	−	0.0437618i
$778$	36.3468	−	62.9544i	1.30309	−	2.25703i
$779$	80.8583			2.89705
$780$	29.9120	−	31.0855i	1.07102	−	1.11304i
$781$	−6.50702			−0.232839
$782$	−14.6582	+	25.3887i	−0.524175	+	0.907898i
$783$	6.54567	−	11.3374i	0.233923	−	0.405167i
$784$	18.5191	+	32.0759i	0.661395	+	1.14557i
$785$	14.7913			0.527923
$786$	29.6425	+	51.3423i	1.05731	+	1.83132i
$787$	11.4749	+	19.8752i	0.409037	+	0.708474i	0.994782	−	0.102022i	$-0.0325312\pi$
$787$	11.4749	+	19.8752i	0.409037	+	0.708474i	−0.585745	+	0.810496i	$0.699198\pi$
$788$	−26.1929			−0.933084
$789$	17.7695	+	30.7778i	0.632613	+	1.09572i
$790$	20.8062	−	36.0374i	0.740251	−	1.28215i
$791$	2.17967	−	3.77529i	0.0775000	−	0.134234i
$792$	12.7289			0.452302
$793$	−50.8237	−	12.5756i	−1.80480	−	0.446573i
$794$	86.8895			3.08359
$795$	2.50200	−	4.33359i	0.0887368	−	0.153697i
$796$	−20.0230	+	34.6808i	−0.709695	+	1.22923i
$797$	−21.7249	−	37.6286i	−0.769535	−	1.33287i	−0.937815	−	0.347135i	$-0.887155\pi$
$797$	−21.7249	−	37.6286i	−0.769535	−	1.33287i	0.168280	−	0.985739i	$-0.446179\pi$
$798$	36.9960			1.30964
$799$	−7.24293	−	12.5451i	−0.256237	−	0.443815i
$800$	5.37147	+	9.30365i	0.189910	+	0.328934i
$801$	−10.6164			−0.375112
$802$	18.2855	+	31.6714i	0.645683	+	1.11836i
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$	−29.6862	+	51.4181i	−1.04695	+	1.81338i
$805$	2.59455			0.0914460
$806$	3.61951	+	12.5384i	0.127492	+	0.441645i
$807$	−11.9327			−0.420052
$808$	−13.8188	+	23.9348i	−0.486143	+	0.842024i
$809$	21.5547	−	37.3338i	0.757823	−	1.31259i	−0.186136	−	0.982524i	$-0.559597\pi$
$809$	21.5547	−	37.3338i	0.757823	−	1.31259i	0.943959	−	0.330063i	$-0.107070\pi$
$810$	−16.4327	−	28.4623i	−0.577387	−	1.00006i
$811$	−17.9428			−0.630056			−0.315028	−	0.949082i	$-0.602014\pi$
$811$	−17.9428			−0.630056			−0.315028	+	0.949082i	$0.602014\pi$
$812$	−12.2746	−	21.2602i	−0.430753	−	0.746086i
$813$	−29.6346	−	51.3286i	−1.03933	−	1.80017i
$814$	−1.98596			−0.0696080
$815$	1.17220	+	2.03032i	0.0410605	+	0.0711188i
$816$	28.3589	−	49.1190i	0.992760	−	1.71951i
$817$	40.1666	−	69.5707i	1.40525	−	2.43397i
$818$	41.6202			1.45522
$819$	−1.72889	−	5.98907i	−0.0604125	−	0.209275i
$820$	−51.0131			−1.78146
$821$	−7.83237	+	13.5661i	−0.273352	+	0.473459i	−0.969718	−	0.244228i	$-0.921466\pi$
$821$	−7.83237	+	13.5661i	−0.273352	+	0.473459i	0.696366	+	0.717687i	$0.254799\pi$
$822$	14.1410	−	24.4930i	0.493225	−	0.854290i
$823$	−1.84885	−	3.20231i	−0.0644470	−	0.111625i	0.832002	−	0.554773i	$-0.187195\pi$
$823$	−1.84885	−	3.20231i	−0.0644470	−	0.111625i	−0.896449	+	0.443148i	$0.853862\pi$
$824$	55.9145			1.94787
$825$	4.00702	+	6.94036i	0.139506	+	0.241632i
$826$	−5.07965	−	8.79821i	−0.176744	−	0.306129i
$827$	−42.3201			−1.47162			−0.735808	−	0.677191i	$-0.763197\pi$
$827$	−42.3201			−1.47162			−0.735808	+	0.677191i	$0.763197\pi$
$828$	12.9910	+	22.5010i	0.451468	+	0.781965i
$829$	−3.57730	+	6.19607i	−0.124245	+	0.215198i	−0.921438	−	0.388527i	$-0.872984\pi$
$829$	−3.57730	+	6.19607i	−0.124245	+	0.215198i	0.797193	+	0.603725i	$0.206318\pi$
$830$	−20.4664	+	35.4488i	−0.710398	+	1.23045i
$831$	−40.6164			−1.40897
$832$	9.76164	−	10.1446i	0.338424	−	0.351701i
$833$	27.4014			0.949404
$834$	−47.1827	+	81.7228i	−1.63380	+	2.82983i
$835$	−4.31332	+	7.47088i	−0.149268	+	0.258541i
$836$	−17.7816	−	30.7986i	−0.614989	−	1.06519i
$837$	2.56717			0.0887344
$838$	27.9472	+	48.4060i	0.965420	+	1.67216i
$839$	−1.38004	−	2.39030i	−0.0476443	−	0.0825224i	0.841220	−	0.540693i	$-0.181838\pi$
$839$	−1.38004	−	2.39030i	−0.0476443	−	0.0825224i	−0.888864	+	0.458171i	$0.848505\pi$
$840$	−12.4469			−0.429458
$841$	−12.6028	−	21.8287i	−0.434580	−	0.752714i
$842$	4.33437	−	7.50735i	0.149372	−	0.258720i
$843$	−8.46837	+	14.6676i	−0.291666	+	0.505180i
$844$	−22.2257			−0.765040
$845$	0.610938	+	15.8726i	0.0210169	+	0.546035i
$846$	−18.8303			−0.647398
$847$	−0.389062	+	0.673875i	−0.0133683	+	0.0231546i
$848$	−5.19024	+	8.98976i	−0.178234	+	0.308710i
$849$	−10.6456	−	18.4387i	−0.365356	−	0.632814i
$850$	37.6757			1.29226
$851$	−1.08086	−	1.87211i	−0.0370515	−	0.0641750i
$852$	31.8589	+	55.1812i	1.09147	+	1.89048i
$853$	46.1615			1.58054			0.790270	−	0.612758i	$-0.209940\pi$
$853$	46.1615			1.58054			0.790270	+	0.612758i	$0.209940\pi$
$854$	14.1636	+	24.5321i	0.484669	+	0.839472i
$855$	11.2655	−	19.5125i	0.385274	−	0.667313i
$856$	−6.76710	+	11.7210i	−0.231295	+	0.400614i
$857$	26.2680			0.897297			0.448649	−	0.893708i	$-0.351905\pi$
$857$	26.2680			0.897297			0.448649	+	0.893708i	$0.351905\pi$
$858$	−14.3222	+	14.8841i	−0.488953	+	0.508135i
$859$	−32.0381			−1.09313			−0.546563	−	0.837418i	$-0.684064\pi$
$859$	−32.0381			−1.09313			−0.546563	+	0.837418i	$0.684064\pi$
$860$	−25.3409	+	43.8918i	−0.864119	+	1.49670i
$861$	−8.66207	+	15.0031i	−0.295203	+	0.511306i
$862$	−32.4413	−	56.1900i	−1.10496	−	1.91384i
$863$	−24.2078			−0.824044			−0.412022	−	0.911174i	$-0.635177\pi$
$863$	−24.2078			−0.824044			−0.412022	+	0.911174i	$0.635177\pi$
$864$	2.72343	+	4.71713i	0.0926531	+	0.160480i
$865$	1.00657	+	1.74344i	0.0342246	+	0.0592787i
$866$	36.0521			1.22510
$867$	−1.55669	−	2.69627i	−0.0528680	−	0.0915701i
$868$	2.40700	−	4.16905i	0.0816990	−	0.141507i
$869$	−6.79216	+	11.7644i	−0.230408	+	0.399079i
$870$	−51.5371			−1.74727
$871$	−6.06327	−	21.0038i	−0.205446	−	0.711686i
$872$	−16.4389			−0.556690
$873$	4.59992	−	7.96729i	0.155684	−	0.269652i
$874$	28.3890	−	49.1711i	0.960271	−	1.66324i
$875$	−4.04411	−	7.00461i	−0.136716	−	0.236799i
$876$	−19.5843			−0.661693
$877$	−0.528173	−	0.914823i	−0.0178351	−	0.0308914i	0.856970	−	0.515366i	$-0.172344\pi$
$877$	−0.528173	−	0.914823i	−0.0178351	−	0.0308914i	−0.874805	+	0.484475i	$0.839011\pi$
$878$	−5.72388	−	9.91405i	−0.193172	−	0.334583i
$879$	−65.7046			−2.21616
$880$	3.53865	+	6.12912i	0.119288	+	0.206613i
$881$	12.0828	−	20.9280i	0.407079	−	0.705081i	−0.587482	−	0.809237i	$-0.699881\pi$
$881$	12.0828	−	20.9280i	0.407079	−	0.705081i	0.994561	+	0.104156i	$0.0332141\pi$
$882$	17.8097	−	30.8472i	0.599682	−	1.03868i
$883$	5.84831			0.196811			0.0984057	−	0.995146i	$-0.468626\pi$
$883$	5.84831			0.196811			0.0984057	+	0.995146i	$0.468626\pi$
$884$	18.3624	+	63.6094i	0.617596	+	2.13941i
$885$	−14.5411			−0.488795
$886$	−22.7785	+	39.4535i	−0.765258	+	1.32547i
$887$	4.33783	−	7.51334i	0.145650	−	0.252273i	−0.783965	−	0.620805i	$-0.786806\pi$
$887$	4.33783	−	7.51334i	0.145650	−	0.252273i	0.929615	+	0.368531i	$0.120139\pi$
$888$	5.18523	+	8.98107i	0.174005	+	0.301385i
$889$	5.63044			0.188839
$890$	−7.31833	−	12.6757i	−0.245311	−	0.424891i
$891$	5.36445	+	9.29150i	0.179716	+	0.311277i
$892$	72.1373			2.41533
$893$	14.0276	+	24.2966i	0.469417	+	0.813054i
$894$	5.45579	−	9.44970i	0.182469	−	0.316045i
$895$	4.48085	−	7.76105i	0.149778	−	0.259423i
$896$	−12.3843			−0.413730
$897$	−21.8257	−	5.40046i	−0.728739	−	0.180316i
$898$	−31.6625			−1.05659
$899$	5.31477	−	9.20546i	0.177258	−	0.307019i
$900$	16.6953	−	28.9170i	0.556509	−	0.963901i
$901$	3.83983	+	6.65079i	0.127923	+	0.221570i
$902$	24.4257			0.813287
$903$	8.60582	+	14.9057i	0.286384	+	0.496031i
$904$	16.0477	+	27.7954i	0.533738	+	0.924461i
$905$	−14.3876			−0.478260
$906$	−52.7304	−	91.3317i	−1.75185	−	3.03429i
$907$	7.79762	−	13.5059i	0.258916	−	0.448455i	−0.707036	−	0.707178i	$-0.749968\pi$
$907$	7.79762	−	13.5059i	0.258916	−	0.448455i	0.965952	+	0.258722i	$0.0833014\pi$
$908$	37.7444	−	65.3752i	1.25259	−	2.16955i
$909$	10.7189			0.355522
$910$	5.95900	−	6.19278i	0.197539	−	0.205289i
$911$	24.5672			0.813947			0.406973	−	0.913440i	$-0.366584\pi$
$911$	24.5672			0.813947			0.406973	+	0.913440i	$0.366584\pi$
$912$	−54.9236	+	95.1305i	−1.81870	+	3.15009i
$913$	6.68122	−	11.5722i	0.221116	−	0.382985i
$914$	32.3257	+	55.9897i	1.06924	+	1.85198i
$915$	40.5451			1.34038
$916$	−57.5397	−	99.6616i	−1.90116	−	3.29291i
$917$	4.02617	+	6.97353i	0.132956	+	0.230286i
$918$	19.1023			0.630469
$919$	−8.64057	−	14.9659i	−0.285026	−	0.493680i	0.687589	−	0.726100i	$-0.258669\pi$
$919$	−8.64057	−	14.9659i	−0.285026	−	0.493680i	−0.972616	+	0.232420i	$0.925336\pi$
$920$	−9.55113	+	16.5430i	−0.314891	+	0.545408i
$921$	0.905101	−	1.56768i	0.0298241	−	0.0516568i
$922$	−31.6725			−1.04308
$923$	−22.7746	−	5.63524i	−0.749634	−	0.185486i
$924$	7.61951			0.250664
$925$	−1.38906	+	2.40593i	−0.0456721	+	0.0791064i
$926$	4.35587	−	7.54459i	0.143143	−	0.247931i
$927$	−10.8428	−	18.7804i	−0.356126	−	0.616828i
$928$	22.5531			0.740343
$929$	24.1284	+	41.7917i	0.791628	+	1.37114i	0.924958	+	0.380069i	$0.124100\pi$
$929$	24.1284	+	41.7917i	0.791628	+	1.37114i	−0.133330	+	0.991072i	$0.542567\pi$
$930$	−5.05313	−	8.75228i	−0.165699	−	0.286999i
$931$	−53.0693			−1.73928
$932$	58.1506	+	100.720i	1.90479	+	3.29919i
$933$	−29.4808	+	51.0623i	−0.965160	+	1.67171i
$934$	23.4729	−	40.6563i	0.768058	−	1.33032i
$935$	5.23591			0.171233
$936$	44.5511	+	11.0235i	1.45620	+	0.360316i
$937$	−17.7209			−0.578916			−0.289458	−	0.957191i	$-0.593475\pi$
$937$	−17.7209			−0.578916			−0.289458	+	0.957191i	$0.593475\pi$
$938$	−5.91402	+	10.2434i	−0.193100	+	0.334458i
$939$	30.0245	−	52.0040i	0.979813	−	1.69709i
$940$	−8.84997	−	15.3286i	−0.288654	−	0.499964i
$941$	7.96392			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$941$	7.96392			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$942$	34.6752	+	60.0592i	1.12978	+	1.95684i
$943$	13.2937	+	23.0254i	0.432903	+	0.749810i
$944$	30.1646			0.981775
$945$	−0.845294	−	1.46409i	−0.0274974	−	0.0476269i
$946$	12.1336	−	21.0159i	0.394496	−	0.683287i
$947$	−7.78158	+	13.4781i	−0.252867	+	0.437979i	−0.964314	−	0.264761i	$-0.914707\pi$
$947$	−7.78158	+	13.4781i	−0.252867	+	0.437979i	0.711447	+	0.702740i	$0.248040\pi$
$948$	133.020			4.32028
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$	−72.9677			−2.36739
$951$	−12.5441	+	21.7270i	−0.406771	+	0.704548i
$952$	9.55113	−	16.5430i	0.309554	−	0.536163i
$953$	15.9242	+	27.5814i	0.515834	+	0.893451i	0.999831	+	0.0183810i	$0.00585120\pi$
$953$	15.9242	+	27.5814i	0.515834	+	0.893451i	−0.483997	+	0.875070i	$0.660815\pi$
$954$	9.98285			0.323207
$955$	9.00702	+	15.6006i	0.291460	+	0.504824i
$956$	−1.59846	−	2.76861i	−0.0516978	−	0.0895433i
$957$	16.8242			0.543850
$958$	−11.6390	−	20.1594i	−0.376039	−	0.651319i
$959$	1.92070	−	3.32674i	0.0620225	−	0.107426i
$960$	−5.45122	+	9.44178i	−0.175937	+	0.304732i
$961$	−28.9156			−0.932761
$962$	−6.95087	−	1.71989i	−0.224105	−	0.0554516i
$963$	5.24906			0.169149
$964$	−34.6510	+	60.0174i	−1.11604	+	1.93303i
$965$	−5.43829	+	9.41940i	−0.175065	+	0.303221i
$966$	6.08242	+	10.5351i	0.195699	+	0.338960i
$967$	−46.1023			−1.48255			−0.741274	−	0.671202i	$-0.765778\pi$
$967$	−46.1023			−1.48255			−0.741274	+	0.671202i	$0.765778\pi$
$968$	−2.86445	−	4.96137i	−0.0920668	−	0.159464i
$969$	40.6335	+	70.3792i	1.30533	+	2.26091i
$970$	12.6837			0.407248
$971$	7.39408	+	12.8069i	0.237287	+	0.410994i	0.959935	−	0.280223i	$-0.0904084\pi$
$971$	7.39408	+	12.8069i	0.237287	+	0.410994i	−0.722648	+	0.691217i	$0.757075\pi$
$972$	41.1003	−	71.1877i	1.31829	−	2.28335i
$973$	−6.40856	+	11.1000i	−0.205449	+	0.355848i
$974$	−100.104			−3.20755
$975$	8.01404	+	27.7614i	0.256655	+	0.889078i
$976$	−84.1083			−2.69224
$977$	−0.679666	+	1.17722i	−0.0217444	+	0.0376625i	−0.876693	−	0.481051i	$-0.840255\pi$
$977$	−0.679666	+	1.17722i	−0.0217444	+	0.0376625i	0.854948	+	0.518713i	$0.173589\pi$
$978$	−5.49600	+	9.51935i	−0.175743	+	0.304395i
$979$	2.38906	+	4.13798i	0.0763548	+	0.132250i
$980$	33.4812			1.06952
$981$	3.18780	+	5.52143i	0.101779	+	0.176286i
$982$	51.6229	+	89.4134i	1.64735	+	2.85330i
$983$	27.4709			0.876187			0.438093	−	0.898929i	$-0.355654\pi$
$983$	27.4709			0.876187			0.438093	+	0.898929i	$0.355654\pi$
$984$	−63.7740	−	110.460i	−2.03304	−	3.52133i
$985$	−3.73436	+	6.46809i	−0.118986	+	0.206091i
$986$	39.5471	−	68.4976i	1.25944	−	2.18141i
$987$	−6.01092			−0.191330
$988$	−35.5632	−	123.194i	−1.13142	−	3.91934i
$989$	26.4148			0.839941
$990$	3.40310	−	5.89434i	0.108158	−	0.187334i
$991$	−0.0867676	+	0.150286i	−0.00275626	+	0.00477399i	−0.867400	−	0.497611i	$-0.834211\pi$
$991$	−0.0867676	+	0.150286i	−0.00275626	+	0.00477399i	0.864644	+	0.502385i	$0.167544\pi$
$992$	2.21130	+	3.83008i	0.0702088	+	0.121605i
$993$	22.9797			0.729240
$994$	6.34685	+	10.9931i	0.201310	+	0.348679i
$995$	5.70940	+	9.88896i	0.181000	+	0.313501i
$996$	−130.847			−4.14605
$997$	−22.0948	−	38.2693i	−0.699749	−	1.21200i	−0.968553	−	0.248807i	$-0.919962\pi$
$997$	−22.0948	−	38.2693i	−0.699749	−	1.21200i	0.268804	−	0.963195i	$-0.413372\pi$
$998$	−24.2093	+	41.9317i	−0.766332	+	1.32733i
$999$	−0.704280	+	1.21985i	−0.0222824	+	0.0385943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.b.100.1	✓	6
13.3	even	3	inner	143.2.e.b.133.1	yes	6
13.4	even	6		1859.2.a.g.1.1		3
13.9	even	3		1859.2.a.f.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.b.100.1	✓	6	1.1	even	1	trivial
143.2.e.b.133.1	yes	6	13.3	even	3	inner
1859.2.a.f.1.3		3	13.9	even	3
1859.2.a.g.1.1		3	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25351 + 2.17114i) q^{2} +(-1.14257 + 1.97899i) q^{3} +(-2.14257 - 3.71104i) q^{4} -1.22188 q^{5} +(-2.86445 - 4.96137i) q^{6} +(-0.389062 - 0.673875i) q^{7} +5.72889 q^{8} +(-1.11094 - 1.92420i) q^{9} +O(q^{10})\)	\(q+(-1.25351 + 2.17114i) q^{2} +(-1.14257 + 1.97899i) q^{3} +(-2.14257 - 3.71104i) q^{4} -1.22188 q^{5} +(-2.86445 - 4.96137i) q^{6} +(-0.389062 - 0.673875i) q^{7} +5.72889 q^{8} +(-1.11094 - 1.92420i) q^{9} +(1.53163 - 2.65287i) q^{10} +(-0.500000 + 0.866025i) q^{11} +9.79216 q^{12} +(-2.50000 + 2.59808i) q^{13} +1.95077 q^{14} +(1.39608 - 2.41808i) q^{15} +(-2.89608 + 5.01616i) q^{16} +(2.14257 + 3.71104i) q^{17} +5.57028 q^{18} +(-4.14959 - 7.18730i) q^{19} +(2.61796 + 4.53443i) q^{20} +1.77812 q^{21} +(-1.25351 - 2.17114i) q^{22} +(1.36445 - 2.36329i) q^{23} +(-6.54567 + 11.3374i) q^{24} -3.50702 q^{25} +(-2.50702 - 8.68457i) q^{26} -1.77812 q^{27} +(-1.66719 + 2.88765i) q^{28} +(-3.68122 + 6.37607i) q^{29} +(3.50000 + 6.06218i) q^{30} -1.44375 q^{31} +(-1.53163 - 2.65287i) q^{32} +(-1.14257 - 1.97899i) q^{33} -10.7429 q^{34} +(0.475385 + 0.823392i) q^{35} +(-4.76053 + 8.24548i) q^{36} +(0.396081 - 0.686032i) q^{37} +20.8062 q^{38} +(-2.28514 - 7.91597i) q^{39} -7.00000 q^{40} +(-4.87147 + 8.43763i) q^{41} +(-2.22889 + 3.86056i) q^{42} +(4.83983 + 8.38284i) q^{43} +4.28514 q^{44} +(1.35743 + 2.35114i) q^{45} +(3.42070 + 5.92482i) q^{46} -3.38049 q^{47} +(-6.61796 - 11.4626i) q^{48} +(3.19726 - 5.53782i) q^{49} +(4.39608 - 7.61423i) q^{50} -9.79216 q^{51} +(14.9980 + 3.71104i) q^{52} +1.79216 q^{53} +(2.22889 - 3.86056i) q^{54} +(0.610938 - 1.05818i) q^{55} +(-2.22889 - 3.86056i) q^{56} +18.9648 q^{57} +(-9.22889 - 15.9849i) q^{58} +(-2.60392 - 4.51012i) q^{59} -11.9648 q^{60} +(7.26053 + 12.5756i) q^{61} +(1.80976 - 3.13459i) q^{62} +(-0.864447 + 1.49727i) q^{63} -3.90466 q^{64} +(3.05469 - 3.17453i) q^{65} +5.72889 q^{66} +(-3.03163 + 5.25094i) q^{67} +(9.18122 - 15.9023i) q^{68} +(3.11796 + 5.40046i) q^{69} -2.38360 q^{70} +(3.25351 + 5.63524i) q^{71} +(-6.36445 - 11.0235i) q^{72} -2.00000 q^{73} +(0.992981 + 1.71989i) q^{74} +(4.00702 - 6.94036i) q^{75} +(-17.7816 + 30.7986i) q^{76} +0.778124 q^{77} +(20.0511 + 4.96137i) q^{78} +13.5843 q^{79} +(3.53865 - 6.12912i) q^{80} +(5.36445 - 9.29150i) q^{81} +(-12.2129 - 21.1533i) q^{82} -13.3624 q^{83} +(-3.80976 - 6.59869i) q^{84} +(-2.61796 - 4.53443i) q^{85} -24.2671 q^{86} +(-8.41212 - 14.5702i) q^{87} +(-2.86445 + 4.96137i) q^{88} +(2.38906 - 4.13798i) q^{89} -6.80620 q^{90} +(2.72343 + 0.673875i) q^{91} -11.6937 q^{92} +(1.64959 - 2.85717i) q^{93} +(4.23747 - 7.33951i) q^{94} +(5.07028 + 8.78199i) q^{95} +7.00000 q^{96} +(2.07028 + 3.58584i) q^{97} +(8.01559 + 13.8834i) q^{98} +2.22188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9	\( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 3 q^{11} + 30 q^{12} - 15 q^{13} - 16 q^{14} - 6 q^{15} - 3 q^{16} + 7 q^{17} + 10 q^{18} - 2 q^{19} - 4 q^{20} + 16 q^{21} + q^{22} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 21 q^{30} + 2 q^{31} - 6 q^{32} - q^{33} - 8 q^{34} - 11 q^{35} - 3 q^{36} - 12 q^{37} + 62 q^{38} - 2 q^{39} - 42 q^{40} - q^{41} + 9 q^{42} + 4 q^{43} + 14 q^{44} + 14 q^{45} + 20 q^{46} - 16 q^{47} - 20 q^{48} + 12 q^{50} - 30 q^{51} + 49 q^{52} - 18 q^{53} - 9 q^{54} + q^{55} + 9 q^{56} + 52 q^{57} - 33 q^{58} - 30 q^{59} - 10 q^{60} + 18 q^{61} + 13 q^{62} + 6 q^{63} - 16 q^{64} + 5 q^{65} + 12 q^{66} - 15 q^{67} + 29 q^{68} - q^{69} - 58 q^{70} + 11 q^{71} - 27 q^{72} - 12 q^{73} + 23 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{77} + 42 q^{78} + 24 q^{79} + q^{80} + 21 q^{81} - 44 q^{82} - 28 q^{83} - 25 q^{84} + 4 q^{85} - 86 q^{86} - 43 q^{87} - 6 q^{88} + 17 q^{89} + 22 q^{90} + 35 q^{91} + 14 q^{92} - 13 q^{93} + 10 q^{94} + 7 q^{95} + 42 q^{96} - 11 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 6 * q + q^2 - q^3 - 7 * q^4 - 2 * q^5 - 6 * q^6 - 5 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 3 * q^11 + 30 * q^12 - 15 * q^13 - 16 * q^14 - 6 * q^15 - 3 * q^16 + 7 * q^17 + 10 * q^18 - 2 * q^19 - 4 * q^20 + 16 * q^21 + q^22 - 3 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 21 * q^30 + 2 * q^31 - 6 * q^32 - q^33 - 8 * q^34 - 11 * q^35 - 3 * q^36 - 12 * q^37 + 62 * q^38 - 2 * q^39 - 42 * q^40 - q^41 + 9 * q^42 + 4 * q^43 + 14 * q^44 + 14 * q^45 + 20 * q^46 - 16 * q^47 - 20 * q^48 + 12 * q^50 - 30 * q^51 + 49 * q^52 - 18 * q^53 - 9 * q^54 + q^55 + 9 * q^56 + 52 * q^57 - 33 * q^58 - 30 * q^59 - 10 * q^60 + 18 * q^61 + 13 * q^62 + 6 * q^63 - 16 * q^64 + 5 * q^65 + 12 * q^66 - 15 * q^67 + 29 * q^68 - q^69 - 58 * q^70 + 11 * q^71 - 27 * q^72 - 12 * q^73 + 23 * q^74 + 7 * q^75 - 30 * q^76 + 10 * q^77 + 42 * q^78 + 24 * q^79 + q^80 + 21 * q^81 - 44 * q^82 - 28 * q^83 - 25 * q^84 + 4 * q^85 - 86 * q^86 - 43 * q^87 - 6 * q^88 + 17 * q^89 + 22 * q^90 + 35 * q^91 + 14 * q^92 - 13 * q^93 + 10 * q^94 + 7 * q^95 + 42 * q^96 - 11 * q^97 + 38 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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