LMFDB - Embedded newform 1407.2.i.h.604.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1407,2,Mod(403,1407)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1407, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1407.403");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1407 = 3 \cdot 7 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1407.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:	$11.2349515644$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			604.11
Character	$\chi$	$=$	1407.604
Dual form			1407.2.i.h.403.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.308565 - 0.534450i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.809576 + 1.40223i) q^{4} +(1.42238 - 2.46364i) q^{5} -0.617129 q^{6} +(2.64135 - 0.152582i) q^{7} +2.23348 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.308565 - 0.534450i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.809576 + 1.40223i) q^{4} +(1.42238 - 2.46364i) q^{5} -0.617129 q^{6} +(2.64135 - 0.152582i) q^{7} +2.23348 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.877793 - 1.52038i) q^{10} +(-1.03150 - 1.78661i) q^{11} +(0.809576 - 1.40223i) q^{12} +1.55898 q^{13} +(0.733479 - 1.45875i) q^{14} -2.84476 q^{15} +(-0.929977 + 1.61077i) q^{16} +(-2.27834 - 3.94620i) q^{17} +(0.308565 + 0.534450i) q^{18} +(1.90292 - 3.29595i) q^{19} +4.60610 q^{20} +(-1.45281 - 2.21118i) q^{21} -1.27313 q^{22} +(0.518661 - 0.898347i) q^{23} +(-1.11674 - 1.93425i) q^{24} +(-1.54634 - 2.67834i) q^{25} +(0.481046 - 0.833197i) q^{26} +1.00000 q^{27} +(2.35233 + 3.58024i) q^{28} -7.02499 q^{29} +(-0.877793 + 1.52038i) q^{30} +(4.16560 + 7.21504i) q^{31} +(2.80740 + 4.86256i) q^{32} +(-1.03150 + 1.78661i) q^{33} -2.81206 q^{34} +(3.38110 - 6.72435i) q^{35} -1.61915 q^{36} +(-0.136948 + 0.237201i) q^{37} +(-1.17435 - 2.03403i) q^{38} +(-0.779491 - 1.35012i) q^{39} +(3.17687 - 5.50249i) q^{40} +3.05700 q^{41} +(-1.63005 + 0.0941630i) q^{42} +3.65301 q^{43} +(1.67015 - 2.89278i) q^{44} +(1.42238 + 2.46364i) q^{45} +(-0.320081 - 0.554396i) q^{46} +(1.06512 - 1.84485i) q^{47} +1.85995 q^{48} +(6.95344 - 0.806046i) q^{49} -1.90858 q^{50} +(-2.27834 + 3.94620i) q^{51} +(1.26211 + 2.18604i) q^{52} +(-0.167473 - 0.290072i) q^{53} +(0.308565 - 0.534450i) q^{54} -5.86873 q^{55} +(5.89941 - 0.340790i) q^{56} -3.80584 q^{57} +(-2.16766 + 3.75450i) q^{58} +(-1.50586 - 2.60823i) q^{59} +(-2.30305 - 3.98900i) q^{60} +(-5.17804 + 8.96862i) q^{61} +5.14143 q^{62} +(-1.18853 + 2.36377i) q^{63} -0.254851 q^{64} +(2.21747 - 3.84076i) q^{65} +(0.636567 + 1.10257i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(3.68898 - 6.38950i) q^{68} -1.03732 q^{69} +(-2.55054 - 3.88192i) q^{70} -11.8039 q^{71} +(-1.11674 + 1.93425i) q^{72} +(-5.09533 - 8.82537i) q^{73} +(0.0845147 + 0.146384i) q^{74} +(-1.54634 + 2.67834i) q^{75} +6.16222 q^{76} +(-2.99715 - 4.56166i) q^{77} -0.962093 q^{78} +(-1.10476 + 1.91351i) q^{79} +(2.64557 + 4.58225i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.943282 - 1.63381i) q^{82} +0.316159 q^{83} +(1.92442 - 3.82729i) q^{84} -12.9627 q^{85} +(1.12719 - 1.95235i) q^{86} +(3.51249 + 6.08382i) q^{87} +(-2.30383 - 3.99035i) q^{88} +(-0.294446 + 0.509995i) q^{89} +1.75559 q^{90} +(4.11781 - 0.237873i) q^{91} +1.67958 q^{92} +(4.16560 - 7.21504i) q^{93} +(-0.657320 - 1.13851i) q^{94} +(-5.41335 - 9.37620i) q^{95} +(2.80740 - 4.86256i) q^{96} +14.8208 q^{97} +(1.71479 - 3.96498i) q^{98} +2.06299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 5 q^{2} - 19 q^{3} - 13 q^{4} - 2 q^{5} - 10 q^{6} + 2 q^{7} - 30 q^{8} - 19 q^{9}+O(q^{10}) $ 38 * q + 5 * q^2 - 19 * q^3 - 13 * q^4 - 2 * q^5 - 10 * q^6 + 2 * q^7 - 30 * q^8 - 19 * q^9	\( 38 q + 5 q^{2} - 19 q^{3} - 13 q^{4} - 2 q^{5} - 10 q^{6} + 2 q^{7} - 30 q^{8} - 19 q^{9} + 9 q^{10} + 12 q^{11} - 13 q^{12} - 44 q^{13} - q^{14} + 4 q^{15} - 5 q^{16} + 2 q^{17} + 5 q^{18} + 14 q^{19} + 54 q^{20} - q^{21} - 18 q^{22} + 14 q^{23} + 15 q^{24} - 11 q^{25} + q^{26} + 38 q^{27} - 6 q^{28} - 52 q^{29} + 9 q^{30} + 13 q^{31} + 10 q^{32} + 12 q^{33} - 2 q^{34} + 12 q^{35} + 26 q^{36} + 16 q^{37} + 8 q^{38} + 22 q^{39} + 24 q^{40} + 28 q^{41} + 2 q^{42} - 54 q^{43} + 25 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + 10 q^{48} - 4 q^{49} - 104 q^{50} + 2 q^{51} + 59 q^{52} + 8 q^{53} + 5 q^{54} - 58 q^{55} + 18 q^{56} - 28 q^{57} + 28 q^{58} - 12 q^{59} - 27 q^{60} + 19 q^{61} + 12 q^{62} - q^{63} - 30 q^{64} + 19 q^{65} + 9 q^{66} - 19 q^{67} - 9 q^{68} - 28 q^{69} + 50 q^{70} - 120 q^{71} + 15 q^{72} + 50 q^{73} - 32 q^{74} - 11 q^{75} - 26 q^{76} + 45 q^{77} - 2 q^{78} + 56 q^{79} - 18 q^{80} - 19 q^{81} - 36 q^{82} + 36 q^{83} - 76 q^{85} + 17 q^{86} + 26 q^{87} - 63 q^{88} + 2 q^{89} - 18 q^{90} + 18 q^{91} - 98 q^{92} + 13 q^{93} + 50 q^{94} + 87 q^{95} + 10 q^{96} - 18 q^{97} + 41 q^{98} - 24 q^{99}+O(q^{100}) \) 38 * q + 5 * q^2 - 19 * q^3 - 13 * q^4 - 2 * q^5 - 10 * q^6 + 2 * q^7 - 30 * q^8 - 19 * q^9 + 9 * q^10 + 12 * q^11 - 13 * q^12 - 44 * q^13 - q^14 + 4 * q^15 - 5 * q^16 + 2 * q^17 + 5 * q^18 + 14 * q^19 + 54 * q^20 - q^21 - 18 * q^22 + 14 * q^23 + 15 * q^24 - 11 * q^25 + q^26 + 38 * q^27 - 6 * q^28 - 52 * q^29 + 9 * q^30 + 13 * q^31 + 10 * q^32 + 12 * q^33 - 2 * q^34 + 12 * q^35 + 26 * q^36 + 16 * q^37 + 8 * q^38 + 22 * q^39 + 24 * q^40 + 28 * q^41 + 2 * q^42 - 54 * q^43 + 25 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + 10 * q^48 - 4 * q^49 - 104 * q^50 + 2 * q^51 + 59 * q^52 + 8 * q^53 + 5 * q^54 - 58 * q^55 + 18 * q^56 - 28 * q^57 + 28 * q^58 - 12 * q^59 - 27 * q^60 + 19 * q^61 + 12 * q^62 - q^63 - 30 * q^64 + 19 * q^65 + 9 * q^66 - 19 * q^67 - 9 * q^68 - 28 * q^69 + 50 * q^70 - 120 * q^71 + 15 * q^72 + 50 * q^73 - 32 * q^74 - 11 * q^75 - 26 * q^76 + 45 * q^77 - 2 * q^78 + 56 * q^79 - 18 * q^80 - 19 * q^81 - 36 * q^82 + 36 * q^83 - 76 * q^85 + 17 * q^86 + 26 * q^87 - 63 * q^88 + 2 * q^89 - 18 * q^90 + 18 * q^91 - 98 * q^92 + 13 * q^93 + 50 * q^94 + 87 * q^95 + 10 * q^96 - 18 * q^97 + 41 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1407\mathbb{Z}\right)^\times$.

$n$	$337$	$470$	$1207$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.308565	−	0.534450i	0.218188	−	0.377913i	−0.736066	−	0.676910i	$-0.763319\pi$
$2$	0.308565	−	0.534450i	0.218188	−	0.377913i	0.954254	+	0.298997i	$0.0966520\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.809576	+	1.40223i	0.404788	+	0.701113i
$5$	1.42238	−	2.46364i	0.636108	−	1.10177i	−0.350171	−	0.936686i	$-0.613876\pi$
$5$	1.42238	−	2.46364i	0.636108	−	1.10177i	0.986279	−	0.165086i	$-0.0527902\pi$
$6$	−0.617129			−0.251942
$7$	2.64135	−	0.152582i	0.998336	−	0.0576707i
$7$	2.64135	−	0.152582i	0.998336	−	0.0576707i
$8$	2.23348			0.789656
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.877793	−	1.52038i	−0.277583	−	0.480787i
$11$	−1.03150	−	1.78661i	−0.311008	−	0.538682i	0.667573	−	0.744545i	$-0.267333\pi$
$11$	−1.03150	−	1.78661i	−0.311008	−	0.538682i	−0.978581	+	0.205863i	$0.934000\pi$
$12$	0.809576	−	1.40223i	0.233704	−	0.404788i
$13$	1.55898			0.432384			0.216192	−	0.976351i	$-0.430636\pi$
$13$	1.55898			0.432384			0.216192	+	0.976351i	$0.430636\pi$
$14$	0.733479	−	1.45875i	0.196031	−	0.389867i
$15$	−2.84476			−0.734515
$16$	−0.929977	+	1.61077i	−0.232494	+	0.402692i
$17$	−2.27834	−	3.94620i	−0.552579	−	0.957094i	−0.998088	−	0.0618167i	$-0.980311\pi$
$17$	−2.27834	−	3.94620i	−0.552579	−	0.957094i	0.445509	−	0.895278i	$-0.353023\pi$
$18$	0.308565	+	0.534450i	0.0727294	+	0.125971i
$19$	1.90292	−	3.29595i	0.436559	−	0.756143i	−0.560862	−	0.827909i	$-0.689530\pi$
$19$	1.90292	−	3.29595i	0.436559	−	0.756143i	0.997421	+	0.0717664i	$0.0228636\pi$
$20$	4.60610			1.02996
$21$	−1.45281	−	2.21118i	−0.317030	−	0.482520i
$22$	−1.27313			−0.271433
$23$	0.518661	−	0.898347i	0.108148	−	0.187318i	−0.806872	−	0.590727i	$-0.798841\pi$
$23$	0.518661	−	0.898347i	0.108148	−	0.187318i	0.915020	+	0.403408i	$0.132175\pi$
$24$	−1.11674	−	1.93425i	−0.227954	−	0.394828i
$25$	−1.54634	−	2.67834i	−0.309268	−	0.535667i
$26$	0.481046	−	0.833197i	0.0943410	−	0.163403i
$27$	1.00000			0.192450
$28$	2.35233	+	3.58024i	0.444548	+	0.676602i
$29$	−7.02499			−1.30451			−0.652254	−	0.758001i	$-0.726176\pi$
$29$	−7.02499			−1.30451			−0.652254	+	0.758001i	$0.726176\pi$
$30$	−0.877793	+	1.52038i	−0.160262	+	0.277583i
$31$	4.16560	+	7.21504i	0.748165	+	1.29586i	0.948702	+	0.316173i	$0.102398\pi$
$31$	4.16560	+	7.21504i	0.748165	+	1.29586i	−0.200537	+	0.979686i	$0.564269\pi$
$32$	2.80740	+	4.86256i	0.496283	+	0.859587i
$33$	−1.03150	+	1.78661i	−0.179561	+	0.311008i
$34$	−2.81206			−0.482264
$35$	3.38110	−	6.72435i	0.571510	−	1.13662i
$36$	−1.61915			−0.269859
$37$	−0.136948	+	0.237201i	−0.0225141	+	0.0389956i	−0.877063	−	0.480375i	$-0.840500\pi$
$37$	−0.136948	+	0.237201i	−0.0225141	+	0.0389956i	0.854549	+	0.519371i	$0.173834\pi$
$38$	−1.17435	−	2.03403i	−0.190504	−	0.329963i
$39$	−0.779491	−	1.35012i	−0.124818	−	0.216192i
$40$	3.17687	−	5.50249i	0.502307	−	0.870021i
$41$	3.05700			0.477423			0.238712	−	0.971090i	$-0.423275\pi$
$41$	3.05700			0.477423			0.238712	+	0.971090i	$0.423275\pi$
$42$	−1.63005	+	0.0941630i	−0.251523	+	0.0145297i
$43$	3.65301			0.557078			0.278539	−	0.960425i	$-0.410150\pi$
$43$	3.65301			0.557078			0.278539	+	0.960425i	$0.410150\pi$
$44$	1.67015	−	2.89278i	0.251785	−	0.436104i
$45$	1.42238	+	2.46364i	0.212036	+	0.367257i
$46$	−0.320081	−	0.554396i	−0.0471933	−	0.0817412i
$47$	1.06512	−	1.84485i	0.155364	−	0.269099i	−0.777827	−	0.628478i	$-0.783678\pi$
$47$	1.06512	−	1.84485i	0.155364	−	0.269099i	0.933192	+	0.359379i	$0.117011\pi$
$48$	1.85995			0.268461
$49$	6.95344	−	0.806046i	0.993348	−	0.115149i
$50$	−1.90858			−0.269914
$51$	−2.27834	+	3.94620i	−0.319031	+	0.552579i
$52$	1.26211	+	2.18604i	0.175024	+	0.303150i
$53$	−0.167473	−	0.290072i	−0.0230042	−	0.0398445i	0.854294	−	0.519790i	$-0.173990\pi$
$53$	−0.167473	−	0.290072i	−0.0230042	−	0.0398445i	−0.877298	+	0.479945i	$0.840656\pi$
$54$	0.308565	−	0.534450i	0.0419903	−	0.0727294i
$55$	−5.86873			−0.791339
$56$	5.89941	−	0.340790i	0.788342	−	0.0455400i
$57$	−3.80584			−0.504095
$58$	−2.16766	+	3.75450i	−0.284628	+	0.492990i
$59$	−1.50586	−	2.60823i	−0.196047	−	0.339563i	0.751196	−	0.660079i	$-0.229477\pi$
$59$	−1.50586	−	2.60823i	−0.196047	−	0.339563i	−0.947243	+	0.320516i	$0.896144\pi$
$60$	−2.30305	−	3.98900i	−0.297323	−	0.514978i
$61$	−5.17804	+	8.96862i	−0.662980	+	1.14831i	0.316849	+	0.948476i	$0.397375\pi$
$61$	−5.17804	+	8.96862i	−0.662980	+	1.14831i	−0.979829	+	0.199839i	$0.935958\pi$
$62$	5.14143			0.652963
$63$	−1.18853	+	2.36377i	−0.149741	+	0.297806i
$64$	−0.254851			−0.0318564
$65$	2.21747	−	3.84076i	0.275043	−	0.476388i
$66$	0.636567	+	1.10257i	0.0783560	+	0.135717i
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i
$68$	3.68898	−	6.38950i	0.447354	−	0.774840i
$69$	−1.03732			−0.124879
$70$	−2.55054	−	3.88192i	−0.304848	−	0.463979i
$71$	−11.8039			−1.40087			−0.700433	−	0.713718i	$-0.747010\pi$
$71$	−11.8039			−1.40087			−0.700433	+	0.713718i	$0.747010\pi$
$72$	−1.11674	+	1.93425i	−0.131609	+	0.227954i
$73$	−5.09533	−	8.82537i	−0.596363	−	1.03293i	−0.993353	−	0.115108i	$-0.963278\pi$
$73$	−5.09533	−	8.82537i	−0.596363	−	1.03293i	0.396990	−	0.917823i	$-0.370055\pi$
$74$	0.0845147	+	0.146384i	0.00982464	+	0.0170168i
$75$	−1.54634	+	2.67834i	−0.178556	+	0.309268i
$76$	6.16222			0.706856
$77$	−2.99715	−	4.56166i	−0.341557	−	0.519849i
$78$	−0.962093			−0.108936
$79$	−1.10476	+	1.91351i	−0.124296	+	0.215286i	−0.921457	−	0.388480i	$-0.873000\pi$
$79$	−1.10476	+	1.91351i	−0.124296	+	0.215286i	0.797162	+	0.603766i	$0.206334\pi$
$80$	2.64557	+	4.58225i	0.295783	+	0.512311i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.943282	−	1.63381i	0.104168	−	0.180424i
$83$	0.316159			0.0347029			0.0173515	−	0.999849i	$-0.494477\pi$
$83$	0.316159			0.0347029			0.0173515	+	0.999849i	$0.494477\pi$
$84$	1.92442	−	3.82729i	0.209971	−	0.417592i
$85$	−12.9627			−1.40600
$86$	1.12719	−	1.95235i	0.121548	−	0.210527i
$87$	3.51249	+	6.08382i	0.376579	+	0.652254i
$88$	−2.30383	−	3.99035i	−0.245589	−	0.425373i
$89$	−0.294446	+	0.509995i	−0.0312112	+	0.0540594i	−0.881209	−	0.472727i	$-0.843270\pi$
$89$	−0.294446	+	0.509995i	−0.0312112	+	0.0540594i	0.849998	+	0.526786i	$0.176603\pi$
$90$	1.75559			0.185055
$91$	4.11781	−	0.237873i	0.431664	−	0.0249359i
$92$	1.67958			0.175108
$93$	4.16560	−	7.21504i	0.431953	−	0.748165i
$94$	−0.657320	−	1.13851i	−0.0677973	−	0.117428i
$95$	−5.41335	−	9.37620i	−0.555398	−	0.961978i
$96$	2.80740	−	4.86256i	0.286529	−	0.496283i
$97$	14.8208			1.50483			0.752414	−	0.658690i	$-0.228889\pi$
$97$	14.8208			1.50483			0.752414	+	0.658690i	$0.228889\pi$
$98$	1.71479	−	3.96498i	0.173220	−	0.400523i
$99$	2.06299			0.207339
$100$	2.50376	−	4.33663i	0.250376	−	0.433663i
$101$	1.50938	+	2.61432i	0.150189	+	0.260134i	0.931297	−	0.364261i	$-0.118679\pi$
$101$	1.50938	+	2.61432i	0.150189	+	0.260134i	−0.781108	+	0.624396i	$0.785345\pi$
$102$	1.40603	+	2.43532i	0.139218	+	0.241132i
$103$	2.86267	−	4.95829i	0.282067	−	0.488554i	−0.689827	−	0.723975i	$-0.742313\pi$
$103$	2.86267	−	4.95829i	0.282067	−	0.488554i	0.971894	+	0.235420i	$0.0756466\pi$
$104$	3.48196			0.341434
$105$	−7.51401	+	0.434060i	−0.733292	+	0.0423600i
$106$	−0.206705			−0.0200770
$107$	5.95923	−	10.3217i	0.576100	−	0.997835i	−0.419821	−	0.907607i	$-0.637907\pi$
$107$	5.95923	−	10.3217i	0.576100	−	0.997835i	0.995921	−	0.0902280i	$-0.0287596\pi$
$108$	0.809576	+	1.40223i	0.0779015	+	0.134929i
$109$	2.68750	+	4.65489i	0.257416	+	0.445858i	0.965549	−	0.260221i	$-0.0837955\pi$
$109$	2.68750	+	4.65489i	0.257416	+	0.445858i	−0.708133	+	0.706079i	$0.750462\pi$
$110$	−1.81088	+	3.13654i	−0.172661	+	0.299057i
$111$	0.273896			0.0259971
$112$	−2.21062	+	4.39650i	−0.208884	+	0.415430i
$113$	8.05239			0.757506			0.378753	−	0.925498i	$-0.376353\pi$
$113$	8.05239			0.757506			0.378753	+	0.925498i	$0.376353\pi$
$114$	−1.17435	+	2.03403i	−0.109988	+	0.190504i
$115$	−1.47547	−	2.55558i	−0.137588	−	0.238309i
$116$	−5.68726	−	9.85062i	−0.528049	−	0.914608i
$117$	−0.779491	+	1.35012i	−0.0720639	+	0.124818i
$118$	−1.85862			−0.171100
$119$	−6.62001	−	10.0757i	−0.606855	−	0.923634i
$120$	−6.35373			−0.580014
$121$	3.37203	−	5.84052i	0.306548	−	0.530957i
$122$	3.19552	+	5.53480i	0.289309	+	0.501097i
$123$	−1.52850	−	2.64744i	−0.137820	−	0.238712i
$124$	−6.74475	+	11.6822i	−0.605696	+	1.04910i
$125$	5.42588			0.485306
$126$	0.896574	+	1.36459i	0.0798732	+	0.121567i
$127$	−15.7914			−1.40126			−0.700628	−	0.713527i	$-0.747097\pi$
$127$	−15.7914			−1.40126			−0.700628	+	0.713527i	$0.747097\pi$
$128$	−5.69344	+	9.86133i	−0.503234	+	0.871626i
$129$	−1.82650	−	3.16360i	−0.160815	−	0.278539i
$130$	−1.36846	−	2.37025i	−0.120022	−	0.207885i
$131$	−4.77228	+	8.26583i	−0.416956	+	0.722189i	−0.995632	−	0.0933689i	$-0.970236\pi$
$131$	−4.77228	+	8.26583i	−0.416956	+	0.722189i	0.578676	+	0.815558i	$0.303570\pi$
$132$	−3.34030			−0.290736
$133$	4.52336	−	8.99610i	0.392225	−	0.780061i
$134$	−0.617129			−0.0533118
$135$	1.42238	−	2.46364i	0.122419	−	0.212036i
$136$	−5.08864	−	8.81378i	−0.436347	−	0.755775i
$137$	−0.0970618	−	0.168116i	−0.00829255	−	0.0143631i	0.861849	−	0.507164i	$-0.169306\pi$
$137$	−0.0970618	−	0.168116i	−0.00829255	−	0.0143631i	−0.870142	+	0.492801i	$0.835973\pi$
$138$	−0.320081	+	0.554396i	−0.0272471	+	0.0471933i
$139$	3.37742			0.286469			0.143235	−	0.989689i	$-0.454250\pi$
$139$	3.37742			0.286469			0.143235	+	0.989689i	$0.454250\pi$
$140$	12.1663	−	0.702809i	1.02824	−	0.0593982i
$141$	−2.13025			−0.179399
$142$	−3.64227	+	6.30859i	−0.305652	+	0.529405i
$143$	−1.60808	−	2.78528i	−0.134475	−	0.232917i
$144$	−0.929977	−	1.61077i	−0.0774981	−	0.134231i
$145$	−9.99221	+	17.3070i	−0.829808	+	1.43727i
$146$	−6.28895			−0.520478
$147$	−4.17477	−	5.61883i	−0.344330	−	0.463433i
$148$	−0.443480			−0.0364538
$149$	−5.81887	+	10.0786i	−0.476701	+	0.825670i	−0.999644	−	0.0266981i	$-0.991501\pi$
$149$	−5.81887	+	10.0786i	−0.476701	+	0.825670i	0.522943	+	0.852368i	$0.324834\pi$
$150$	0.954291	+	1.65288i	0.0779175	+	0.134957i
$151$	−11.6282	−	20.1407i	−0.946291	−	1.63902i	−0.753145	−	0.657855i	$-0.771464\pi$
$151$	−11.6282	−	20.1407i	−0.946291	−	1.63902i	−0.193147	−	0.981170i	$-0.561869\pi$
$152$	4.25014	−	7.36145i	0.344732	−	0.597093i
$153$	4.55668			0.368386
$154$	−3.36279	+	0.194258i	−0.270981	+	0.0156537i
$155$	23.7003			1.90366
$156$	1.26211	−	2.18604i	0.101050	−	0.175024i
$157$	7.86359	+	13.6201i	0.627583	+	1.08701i	0.988035	+	0.154228i	$0.0492890\pi$
$157$	7.86359	+	13.6201i	0.627583	+	1.08701i	−0.360452	+	0.932778i	$0.617378\pi$
$158$	0.681782	+	1.18088i	0.0542396	+	0.0939458i
$159$	−0.167473	+	0.290072i	−0.0132815	+	0.0230042i
$160$	15.9728			1.26276
$161$	1.23289	−	2.45198i	0.0971655	−	0.193243i
$162$	−0.617129			−0.0484863
$163$	−0.892199	+	1.54533i	−0.0698824	+	0.121040i	−0.898849	−	0.438258i	$-0.855596\pi$
$163$	−0.892199	+	1.54533i	−0.0698824	+	0.121040i	0.828967	+	0.559298i	$0.188929\pi$
$164$	2.47487	+	4.28661i	0.193255	+	0.334728i
$165$	2.93436	+	5.08247i	0.228440	+	0.395670i
$166$	0.0975554	−	0.168971i	0.00757176	−	0.0131147i
$167$	−5.45150			−0.421850			−0.210925	−	0.977502i	$-0.567648\pi$
$167$	−5.45150			−0.421850			−0.210925	+	0.977502i	$0.567648\pi$
$168$	−3.24484	−	4.93864i	−0.250345	−	0.381025i
$169$	−10.5696			−0.813044
$170$	−3.99982	+	6.92790i	−0.306772	+	0.531345i
$171$	1.90292	+	3.29595i	0.145520	+	0.252048i
$172$	2.95739	+	5.12234i	0.225499	+	0.390575i
$173$	−1.19514	+	2.07004i	−0.0908649	+	0.157383i	−0.907875	−	0.419240i	$-0.862296\pi$
$173$	−1.19514	+	2.07004i	−0.0908649	+	0.157383i	0.817010	+	0.576623i	$0.195630\pi$
$174$	4.33533			0.328660
$175$	−4.49309	−	6.83848i	−0.339645	−	0.516940i
$176$	3.83708			0.289230
$177$	−1.50586	+	2.60823i	−0.113188	+	0.196047i
$178$	0.181711	+	0.314733i	0.0136198	+	0.0235902i
$179$	8.99490	+	15.5796i	0.672310	+	1.16448i	0.977247	+	0.212103i	$0.0680313\pi$
$179$	8.99490	+	15.5796i	0.672310	+	1.16448i	−0.304937	+	0.952373i	$0.598635\pi$
$180$	−2.30305	+	3.98900i	−0.171659	+	0.297323i
$181$	−2.01510			−0.149781			−0.0748905	−	0.997192i	$-0.523861\pi$
$181$	−2.01510			−0.149781			−0.0748905	+	0.997192i	$0.523861\pi$
$182$	1.14348	−	2.27416i	0.0847604	−	0.168572i
$183$	10.3561			0.765543
$184$	1.15842	−	2.00644i	0.0853999	−	0.147917i
$185$	0.389585	+	0.674781i	0.0286429	+	0.0496109i
$186$	−2.57072	−	4.45261i	−0.188494	−	0.326481i
$187$	−4.70020	+	8.14099i	−0.343713	+	0.595328i
$188$	3.44920			0.251559
$189$	2.64135	−	0.152582i	0.192130	−	0.0110987i
$190$	−6.68147			−0.484725
$191$	−2.40898	+	4.17248i	−0.174308	+	0.301910i	−0.939922	−	0.341391i	$-0.889102\pi$
$191$	−2.40898	+	4.17248i	−0.174308	+	0.301910i	0.765614	+	0.643301i	$0.222435\pi$
$192$	0.127426	+	0.220708i	0.00919615	+	0.0159282i
$193$	5.57557	+	9.65717i	0.401338	+	0.695138i	0.993888	−	0.110396i	$-0.0352118\pi$
$193$	5.57557	+	9.65717i	0.401338	+	0.695138i	−0.592549	+	0.805534i	$0.701879\pi$
$194$	4.57319	−	7.92099i	0.328336	−	0.568694i
$195$	−4.43493			−0.317592
$196$	6.75959	+	9.09774i	0.482828	+	0.649838i
$197$	23.1221			1.64738			0.823690	−	0.567040i	$-0.191912\pi$
$197$	23.1221			1.64738			0.823690	+	0.567040i	$0.191912\pi$
$198$	0.636567	−	1.10257i	0.0452388	−	0.0783560i
$199$	3.17575	+	5.50057i	0.225123	+	0.389925i	0.956356	−	0.292203i	$-0.0943882\pi$
$199$	3.17575	+	5.50057i	0.225123	+	0.389925i	−0.731233	+	0.682128i	$0.761055\pi$
$200$	−3.45372	−	5.98202i	−0.244215	−	0.422993i
$201$	−0.500000	+	0.866025i	−0.0352673	+	0.0610847i
$202$	1.86296			0.131078
$203$	−18.5554	+	1.07189i	−1.30234	+	0.0752318i
$204$	−7.37796			−0.516560
$205$	4.34822	−	7.53134i	0.303693	−	0.526012i
$206$	−1.76664	−	3.05990i	−0.123087	−	0.213194i
$207$	0.518661	+	0.898347i	0.0360494	+	0.0624394i
$208$	−1.44982	+	2.51116i	−0.100527	+	0.174117i
$209$	−7.85142			−0.543094
$210$	−2.08657	+	4.14979i	−0.143987	+	0.286363i
$211$	−10.3526			−0.712705			−0.356352	−	0.934352i	$-0.615980\pi$
$211$	−10.3526			−0.712705			−0.356352	+	0.934352i	$0.615980\pi$
$212$	0.271165	−	0.469671i	0.0186237	−	0.0322571i
$213$	5.90195	+	10.2225i	0.404395	+	0.700433i
$214$	−3.67761	−	6.36981i	−0.251397	−	0.435432i
$215$	5.19597	−	8.99969i	0.354362	−	0.613773i
$216$	2.23348			0.151969
$217$	12.1037	+	18.4218i	0.821653	+	1.25056i
$218$	3.31707			0.224661
$219$	−5.09533	+	8.82537i	−0.344311	+	0.596363i
$220$	−4.75118	−	8.22929i	−0.320325	−	0.554818i
$221$	−3.55189	−	6.15205i	−0.238926	−	0.413832i
$222$	0.0845147	−	0.146384i	0.00567226	−	0.00982464i
$223$	−26.4977			−1.77442			−0.887209	−	0.461368i	$-0.847359\pi$
$223$	−26.4977			−1.77442			−0.887209	+	0.461368i	$0.847359\pi$
$224$	8.15726	+	12.4154i	0.545030	+	0.829536i
$225$	3.09268			0.206178
$226$	2.48468	−	4.30360i	0.165279	−	0.286271i
$227$	3.82104	+	6.61823i	0.253611	+	0.439268i	0.964517	−	0.264019i	$-0.0850483\pi$
$227$	3.82104	+	6.61823i	0.253611	+	0.439268i	−0.710906	+	0.703287i	$0.751715\pi$
$228$	−3.08111	−	5.33664i	−0.204052	−	0.353428i
$229$	5.22354	−	9.04744i	0.345181	−	0.597872i	−0.640205	−	0.768204i	$-0.721151\pi$
$229$	5.22354	−	9.04744i	0.345181	−	0.597872i	0.985387	+	0.170332i	$0.0544841\pi$
$230$	−1.82111			−0.120080
$231$	−2.45194	+	4.87643i	−0.161326	+	0.320846i
$232$	−15.6902			−1.03011
$233$	−13.9105	+	24.0937i	−0.911308	+	1.57843i	−0.0990887	+	0.995079i	$0.531593\pi$
$233$	−13.9105	+	24.0937i	−0.911308	+	1.57843i	−0.812219	+	0.583353i	$0.801741\pi$
$234$	0.481046	+	0.833197i	0.0314470	+	0.0544678i
$235$	−3.03003	−	5.24816i	−0.197657	−	0.342352i
$236$	2.43822	−	4.22312i	0.158715	−	0.274902i
$237$	2.20953			0.143524
$238$	−7.42763	+	0.429071i	−0.481462	+	0.0278125i
$239$	−21.8250			−1.41174			−0.705872	−	0.708339i	$-0.749445\pi$
$239$	−21.8250			−1.41174			−0.705872	+	0.708339i	$0.749445\pi$
$240$	2.64557	−	4.58225i	0.170770	−	0.295783i
$241$	−2.10841	−	3.65187i	−0.135814	−	0.235237i	0.790094	−	0.612986i	$-0.210032\pi$
$241$	−2.10841	−	3.65187i	−0.135814	−	0.235237i	−0.925908	+	0.377748i	$0.876698\pi$
$242$	−2.08098	−	3.60436i	−0.133770	−	0.231697i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−16.7681			−1.07346
$245$	7.90464	−	18.2773i	0.505009	−	1.16769i
$246$	−1.88656			−0.120283
$247$	2.96661	−	5.13832i	0.188761	−	0.326944i
$248$	9.30381	+	16.1147i	0.590793	+	1.02328i
$249$	−0.158079	−	0.273801i	−0.0100179	−	0.0173515i
$250$	1.67423	−	2.89986i	0.105888	−	0.183403i
$251$	14.6105			0.922209			0.461105	−	0.887346i	$-0.347453\pi$
$251$	14.6105			0.922209			0.461105	+	0.887346i	$0.347453\pi$
$252$	−4.27674	+	0.247054i	−0.269409	+	0.0155629i
$253$	−2.13999			−0.134540
$254$	−4.87265	+	8.43968i	−0.305737	+	0.529553i
$255$	6.48134	+	11.2260i	0.405877	+	0.703000i
$256$	3.25874	+	5.64430i	0.203671	+	0.352769i
$257$	−12.8919	+	22.3295i	−0.804177	+	1.39287i	0.112669	+	0.993633i	$0.464060\pi$
$257$	−12.8919	+	22.3295i	−0.804177	+	1.39287i	−0.916845	+	0.399242i	$0.869273\pi$
$258$	−2.25438			−0.140351
$259$	−0.325535	+	0.647427i	−0.0202278	+	0.0402291i
$260$	7.18083			0.445336
$261$	3.51249	−	6.08382i	0.217418	−	0.376579i
$262$	2.94511	+	5.10108i	0.181950	+	0.315146i
$263$	14.0586	+	24.3503i	0.866892	+	1.50150i	0.865156	+	0.501503i	$0.167219\pi$
$263$	14.0586	+	24.3503i	0.866892	+	1.50150i	0.00173642	+	0.999998i	$0.499447\pi$
$264$	−2.30383	+	3.99035i	−0.141791	+	0.245589i
$265$	−0.952844			−0.0585327
$266$	−3.41221	−	5.19339i	−0.209216	−	0.318427i
$267$	0.588892			0.0360396
$268$	0.809576	−	1.40223i	0.0494527	−	0.0856546i
$269$	9.00772	+	15.6018i	0.549211	+	0.951261i	0.998329	+	0.0577884i	$0.0184049\pi$
$269$	9.00772	+	15.6018i	0.549211	+	0.951261i	−0.449118	+	0.893472i	$0.648262\pi$
$270$	−0.877793	−	1.52038i	−0.0534208	−	0.0925275i
$271$	−8.56761	+	14.8395i	−0.520445	+	0.901438i	0.479272	+	0.877666i	$0.340901\pi$
$271$	−8.56761	+	14.8395i	−0.520445	+	0.901438i	−0.999717	+	0.0237715i	$0.992433\pi$
$272$	8.47522			0.513886
$273$	−2.26491	−	3.44719i	−0.137079	−	0.208634i
$274$	−0.119799			−0.00723734
$275$	−3.19009	+	5.52539i	−0.192370	+	0.333194i
$276$	−0.839790	−	1.45456i	−0.0505494	−	0.0875542i
$277$	6.47572	+	11.2163i	0.389088	+	0.673920i	0.992327	−	0.123640i	$-0.0394568\pi$
$277$	6.47572	+	11.2163i	0.389088	+	0.673920i	−0.603239	+	0.797560i	$0.706123\pi$
$278$	1.04215	−	1.80506i	0.0625042	−	0.108260i
$279$	−8.33121			−0.498776
$280$	7.55163	−	15.0187i	0.451296	−	0.897541i
$281$	23.9189			1.42688			0.713442	−	0.700714i	$-0.247135\pi$
$281$	23.9189			1.42688			0.713442	+	0.700714i	$0.247135\pi$
$282$	−0.657320	+	1.13851i	−0.0391428	+	0.0677973i
$283$	4.79723	+	8.30905i	0.285166	+	0.493922i	0.972649	−	0.232278i	$-0.0746180\pi$
$283$	4.79723	+	8.30905i	0.285166	+	0.493922i	−0.687484	+	0.726200i	$0.741285\pi$
$284$	−9.55616	−	16.5518i	−0.567054	−	0.982166i
$285$	−5.41335	+	9.37620i	−0.320659	+	0.555398i
$286$	−1.98479			−0.117363
$287$	8.07460	−	0.466444i	0.476629	−	0.0275333i
$288$	−5.61480			−0.330855
$289$	−1.88167	+	3.25914i	−0.110686	+	0.191714i
$290$	6.16649	+	10.6807i	0.362109	+	0.627191i
$291$	−7.41042	−	12.8352i	−0.434407	−	0.752414i
$292$	8.25011	−	14.2896i	0.482801	−	0.836236i
$293$	2.99420			0.174923			0.0874616	−	0.996168i	$-0.472124\pi$
$293$	2.99420			0.174923			0.0874616	+	0.996168i	$0.472124\pi$
$294$	−4.29117	+	0.497434i	−0.250266	+	0.0290110i
$295$	−8.56765			−0.498828
$296$	−0.305872	+	0.529785i	−0.0177784	+	0.0307931i
$297$	−1.03150	−	1.78661i	−0.0598535	−	0.103669i
$298$	3.59100	+	6.21979i	0.208021	+	0.360303i
$299$	0.808582	−	1.40051i	0.0467615	−	0.0809933i
$300$	−5.00751			−0.289109
$301$	9.64886	−	0.557384i	0.556151	−	0.0321271i
$302$	−14.3522			−0.825878
$303$	1.50938	−	2.61432i	0.0867115	−	0.150189i
$304$	3.53934	+	6.13032i	0.202995	+	0.351598i
$305$	14.7303	+	25.5136i	0.843454	+	1.46090i
$306$	1.40603	−	2.43532i	0.0803774	−	0.139218i
$307$	−14.7911			−0.844173			−0.422087	−	0.906555i	$-0.638702\pi$
$307$	−14.7911			−0.844173			−0.422087	+	0.906555i	$0.638702\pi$
$308$	3.97006	−	7.89569i	0.226215	−	0.449898i
$309$	−5.72534			−0.325703
$310$	7.31308	−	12.6666i	0.415355	−	0.719416i
$311$	−7.08733	−	12.2756i	−0.401886	−	0.696086i	0.592068	−	0.805888i	$-0.298312\pi$
$311$	−7.08733	−	12.2756i	−0.401886	−	0.696086i	−0.993953	+	0.109802i	$0.964978\pi$
$312$	−1.74098	−	3.01547i	−0.0985636	−	0.170717i
$313$	1.45836	−	2.52596i	0.0824315	−	0.142775i	−0.821862	−	0.569686i	$-0.807065\pi$
$313$	1.45836	−	2.52596i	0.0824315	−	0.142775i	0.904294	+	0.426911i	$0.140398\pi$
$314$	9.70571			0.547725
$315$	4.13291	+	6.29029i	0.232863	+	0.354418i
$316$	−3.57756			−0.201253
$317$	−4.04005	+	6.99757i	−0.226912	+	0.393023i	−0.956891	−	0.290446i	$-0.906196\pi$
$317$	−4.04005	+	6.99757i	−0.226912	+	0.393023i	0.729980	+	0.683469i	$0.239530\pi$
$318$	0.103353	+	0.179012i	0.00579573	+	0.0100385i
$319$	7.24626	+	12.5509i	0.405712	+	0.702715i
$320$	−0.362496	+	0.627861i	−0.0202641	+	0.0350985i
$321$	−11.9185			−0.665223
$322$	−0.930036	−	1.41551i	−0.0518289	−	0.0788835i
$323$	−17.3420			−0.964933
$324$	0.809576	−	1.40223i	0.0449764	−	0.0779015i
$325$	−2.41071	−	4.17548i	−0.133722	−	0.231614i
$326$	0.550602	+	0.953670i	0.0304950	+	0.0528189i
$327$	2.68750	−	4.65489i	0.148619	−	0.257416i
$328$	6.82776			0.377000
$329$	2.53187	−	5.03541i	0.139587	−	0.277611i
$330$	3.62176			0.199372
$331$	8.05017	−	13.9433i	0.442478	−	0.766394i	−0.555395	−	0.831587i	$-0.687433\pi$
$331$	8.05017	−	13.9433i	0.442478	−	0.766394i	0.997873	+	0.0651929i	$0.0207663\pi$
$332$	0.255954	+	0.443326i	0.0140473	+	0.0243307i
$333$	−0.136948	−	0.237201i	−0.00750471	−	0.0129985i
$334$	−1.68214	+	2.91355i	−0.0920427	+	0.159423i
$335$	−2.84476			−0.155426
$336$	4.91279	−	0.283796i	0.268014	−	0.0154823i
$337$	−0.519191			−0.0282821			−0.0141411	−	0.999900i	$-0.504501\pi$
$337$	−0.519191			−0.0282821			−0.0141411	+	0.999900i	$0.504501\pi$
$338$	−3.26140	+	5.64891i	−0.177397	+	0.307260i
$339$	−4.02620	−	6.97358i	−0.218673	−	0.378753i
$340$	−10.4943	−	18.1766i	−0.569132	−	0.985765i
$341$	8.59362	−	14.8846i	0.465371	−	0.806045i
$342$	2.34869			0.127003
$343$	18.2435	−	3.19002i	0.985054	−	0.172245i
$344$	8.15893			0.439900
$345$	−1.47547	+	2.55558i	−0.0794365	+	0.137588i
$346$	0.737556	+	1.27748i	0.0396513	+	0.0686780i
$347$	12.0150	+	20.8105i	0.644997	+	1.11717i	0.984302	+	0.176492i	$0.0564748\pi$
$347$	12.0150	+	20.8105i	0.644997	+	1.11717i	−0.339305	+	0.940676i	$0.610192\pi$
$348$	−5.68726	+	9.85062i	−0.304869	+	0.528049i
$349$	16.5153			0.884042			0.442021	−	0.897005i	$-0.354262\pi$
$349$	16.5153			0.884042			0.442021	+	0.897005i	$0.354262\pi$
$350$	−5.04123	+	0.291216i	−0.269465	+	0.0155661i
$351$	1.55898			0.0832123
$352$	5.79165	−	10.0314i	0.308696	−	0.534677i
$353$	−5.02697	−	8.70697i	−0.267559	−	0.463425i	0.700672	−	0.713483i	$-0.252884\pi$
$353$	−5.02697	−	8.70697i	−0.267559	−	0.463425i	−0.968231	+	0.250058i	$0.919550\pi$
$354$	0.929312	+	1.60962i	0.0493924	+	0.0855501i
$355$	−16.7897	+	29.0805i	−0.891103	+	1.54344i
$356$	−0.953505			−0.0505357
$357$	−5.41577	+	10.7709i	−0.286633	+	0.570058i
$358$	11.1020			0.586761
$359$	8.03093	−	13.9100i	0.423856	−	0.734141i	−0.572456	−	0.819935i	$-0.694009\pi$
$359$	8.03093	−	13.9100i	0.423856	−	0.734141i	0.996313	+	0.0857943i	$0.0273428\pi$
$360$	3.17687	+	5.50249i	0.167436	+	0.290007i
$361$	2.25781	+	3.91064i	0.118832	+	0.205823i
$362$	−0.621788	+	1.07697i	−0.0326805	+	0.0566042i
$363$	−6.74406			−0.353971
$364$	3.66723	+	5.58153i	0.192215	+	0.292552i
$365$	−28.9900			−1.51741
$366$	3.19552	−	5.53480i	0.167032	−	0.289309i
$367$	14.9561	+	25.9048i	0.780704	+	1.35222i	0.931532	+	0.363660i	$0.118473\pi$
$367$	14.9561	+	25.9048i	0.780704	+	1.35222i	−0.150827	+	0.988560i	$0.548194\pi$
$368$	0.964685	+	1.67088i	0.0502877	+	0.0871009i
$369$	−1.52850	+	2.64744i	−0.0795705	+	0.137820i
$370$	0.480849			0.0249981
$371$	−0.486615	−	0.740628i	−0.0252638	−	0.0384515i
$372$	13.4895			0.699398
$373$	−9.60115	+	16.6297i	−0.497129	+	0.861052i	−0.999995	−	0.00331215i	$-0.998946\pi$
$373$	−9.60115	+	16.6297i	−0.497129	+	0.861052i	0.502866	+	0.864365i	$0.332279\pi$
$374$	2.90063	+	5.02404i	0.149988	+	0.259787i
$375$	−2.71294	−	4.69895i	−0.140096	−	0.242653i
$376$	2.37894	−	4.12044i	0.122684	−	0.212496i
$377$	−10.9518			−0.564048
$378$	0.733479	−	1.45875i	0.0377261	−	0.0750299i
$379$	11.2353			0.577119			0.288560	−	0.957462i	$-0.406824\pi$
$379$	11.2353			0.577119			0.288560	+	0.957462i	$0.406824\pi$
$380$	8.76503	−	15.1815i	0.449637	−	0.778794i
$381$	7.89568	+	13.6757i	0.404508	+	0.700628i
$382$	1.48665	+	2.57496i	0.0760638	+	0.131746i
$383$	14.9118	−	25.8280i	0.761958	−	1.31975i	−0.179882	−	0.983688i	$-0.557572\pi$
$383$	14.9118	−	25.8280i	0.761958	−	1.31975i	0.941840	−	0.336062i	$-0.109095\pi$
$384$	11.3869			0.581084
$385$	−15.5014	+	0.895464i	−0.790022	+	0.0456371i
$386$	6.88169			0.350269
$387$	−1.82650	+	3.16360i	−0.0928464	+	0.160815i
$388$	11.9986	+	20.7822i	0.609136	+	1.05505i
$389$	−1.93826	−	3.35717i	−0.0982739	−	0.170215i	0.812696	−	0.582687i	$-0.197999\pi$
$389$	−1.93826	−	3.35717i	−0.0982739	−	0.170215i	−0.910970	+	0.412472i	$0.864665\pi$
$390$	−1.36846	+	2.37025i	−0.0692948	+	0.120022i
$391$	−4.72674			−0.239042
$392$	15.5304	−	1.80029i	0.784403	−	0.0909284i
$393$	9.54456			0.481459
$394$	7.13466	−	12.3576i	0.359439	−	0.622566i
$395$	3.14279	+	5.44347i	0.158131	+	0.273891i
$396$	1.67015	+	2.89278i	0.0839282	+	0.145368i
$397$	12.6614	−	21.9301i	0.635456	−	1.10064i	−0.350963	−	0.936390i	$-0.614146\pi$
$397$	12.6614	−	21.9301i	0.635456	−	1.10064i	0.986418	−	0.164252i	$-0.0525211\pi$
$398$	3.91970			0.196477
$399$	−10.0525	+	0.580703i	−0.503256	+	0.0290715i
$400$	5.75224			0.287612
$401$	1.01633	−	1.76034i	0.0507531	−	0.0879070i	−0.839533	−	0.543309i	$-0.817171\pi$
$401$	1.01633	−	1.76034i	0.0507531	−	0.0879070i	0.890286	+	0.455402i	$0.150505\pi$
$402$	0.308565	+	0.534450i	0.0153898	+	0.0266559i
$403$	6.49410	+	11.2481i	0.323494	+	0.560308i
$404$	−2.44391	+	4.23298i	−0.121589	+	0.210598i
$405$	−2.84476			−0.141357
$406$	−5.15268	+	10.2477i	−0.255723	+	0.508585i
$407$	0.565046			0.0280083
$408$	−5.08864	+	8.81378i	−0.251925	+	0.436347i
$409$	11.9510	+	20.6997i	0.590937	+	1.02353i	0.994106	+	0.108408i	$0.0345753\pi$
$409$	11.9510	+	20.6997i	0.590937	+	1.02353i	−0.403169	+	0.915126i	$0.632091\pi$
$410$	−2.68341	−	4.64781i	−0.132524	−	0.229539i
$411$	−0.0970618	+	0.168116i	−0.00478771	+	0.00829255i
$412$	9.27019			0.456709
$413$	−4.37548	−	6.65948i	−0.215303	−	0.327691i
$414$	0.640161			0.0314622
$415$	0.449698	−	0.778900i	0.0220748	−	0.0382347i
$416$	4.37668	+	7.58064i	0.214585	+	0.371671i
$417$	−1.68871	−	2.92493i	−0.0826965	−	0.143235i
$418$	−2.42267	+	4.19619i	−0.118497	+	0.205242i
$419$	27.1393			1.32584			0.662920	−	0.748690i	$-0.269317\pi$
$419$	27.1393			1.32584			0.662920	+	0.748690i	$0.269317\pi$
$420$	−6.69181	−	10.1849i	−0.326527	−	0.496974i
$421$	−22.1696			−1.08048			−0.540240	−	0.841511i	$-0.681666\pi$
$421$	−22.1696			−1.08048			−0.540240	+	0.841511i	$0.681666\pi$
$422$	−3.19446	+	5.53296i	−0.155504	+	0.269340i
$423$	1.06512	+	1.84485i	0.0517881	+	0.0896997i
$424$	−0.374049	−	0.647872i	−0.0181654	−	0.0314634i
$425$	−7.04617	+	12.2043i	−0.341789	+	0.591997i
$426$	7.28454			0.352937
$427$	−12.3085	+	24.4793i	−0.595652	+	1.18464i
$428$	19.2978			0.932794
$429$	−1.60808	+	2.78528i	−0.0776391	+	0.134475i
$430$	−3.20659	−	5.55397i	−0.154635	−	0.267836i
$431$	1.68178	+	2.91292i	0.0810083	+	0.140311i	0.903683	−	0.428201i	$-0.140853\pi$
$431$	1.68178	+	2.91292i	0.0810083	+	0.140311i	−0.822675	+	0.568512i	$0.807519\pi$
$432$	−0.929977	+	1.61077i	−0.0447436	+	0.0774981i
$433$	−39.7039			−1.90805			−0.954023	−	0.299732i	$-0.903103\pi$
$433$	−39.7039			−1.90805			−0.954023	+	0.299732i	$0.903103\pi$
$434$	13.5803	−	0.784491i	0.651876	−	0.0376568i
$435$	19.9844			0.958180
$436$	−4.35148	+	7.53698i	−0.208398	+	0.360956i
$437$	−1.97394	−	3.41896i	−0.0944262	−	0.163551i
$438$	3.14448	+	5.44639i	0.150249	+	0.260239i
$439$	−17.9963	+	31.1705i	−0.858916	+	1.48769i	0.0140485	+	0.999901i	$0.495528\pi$
$439$	−17.9963	+	31.1705i	−0.858916	+	1.48769i	−0.872964	+	0.487784i	$0.837805\pi$
$440$	−13.1077			−0.624886
$441$	−2.77866	+	6.42488i	−0.132317	+	0.305946i
$442$	−4.38395			−0.208523
$443$	4.37628	−	7.57995i	0.207924	−	0.360134i	−0.743137	−	0.669140i	$-0.766663\pi$
$443$	4.37628	−	7.57995i	0.207924	−	0.360134i	0.951060	+	0.309005i	$0.0999961\pi$
$444$	0.221740	+	0.384065i	0.0105233	+	0.0182269i
$445$	0.837629	+	1.45082i	0.0397074	+	0.0687753i
$446$	−8.17625	+	14.1617i	−0.387157	+	0.670575i
$447$	11.6377			0.550446
$448$	−0.673151	+	0.0388858i	−0.0318034	+	0.00183718i
$449$	−15.4927			−0.731144			−0.365572	−	0.930783i	$-0.619127\pi$
$449$	−15.4927			−0.731144			−0.365572	+	0.930783i	$0.619127\pi$
$450$	0.954291	−	1.65288i	0.0449857	−	0.0779175i
$451$	−3.15329	−	5.46165i	−0.148482	−	0.257179i
$452$	6.51902	+	11.2913i	0.306629	+	0.531097i
$453$	−11.6282	+	20.1407i	−0.546342	+	0.946291i
$454$	4.71615			0.221340
$455$	5.27107	−	10.4831i	0.247111	−	0.491457i
$456$	−8.50027			−0.398062
$457$	9.14711	−	15.8433i	0.427884	−	0.741116i	−0.568801	−	0.822475i	$-0.692593\pi$
$457$	9.14711	−	15.8433i	0.427884	−	0.741116i	0.996685	+	0.0813588i	$0.0259260\pi$
$458$	−3.22360	−	5.58344i	−0.150629	−	0.260897i
$459$	−2.27834	−	3.94620i	−0.106344	−	0.184193i
$460$	2.38900	−	4.13788i	0.111388	−	0.192930i
$461$	3.65072			0.170031			0.0850155	−	0.996380i	$-0.472906\pi$
$461$	3.65072			0.170031			0.0850155	+	0.996380i	$0.472906\pi$
$462$	1.84963	+	2.81513i	0.0860524	+	0.130972i
$463$	−27.0476			−1.25701			−0.628503	−	0.777807i	$-0.716332\pi$
$463$	−27.0476			−1.25701			−0.628503	+	0.777807i	$0.716332\pi$
$464$	6.53308	−	11.3156i	0.303291	−	0.525315i
$465$	−11.8502	−	20.5251i	−0.549538	−	0.951828i
$466$	8.58458	+	14.8689i	0.397673	+	0.688790i
$467$	11.0837	−	19.1976i	0.512895	−	0.888360i	−0.486993	−	0.873406i	$-0.661906\pi$
$467$	11.0837	−	19.1976i	0.512895	−	0.888360i	0.999888	−	0.0149541i	$-0.00476022\pi$
$468$	−2.52423			−0.116682
$469$	−1.45281	−	2.21118i	−0.0670847	−	0.102103i
$470$	−3.73984			−0.172506
$471$	7.86359	−	13.6201i	0.362335	−	0.627583i
$472$	−3.36332	−	5.82544i	−0.154809	−	0.268138i
$473$	−3.76807	−	6.52648i	−0.173256	−	0.300088i
$474$	0.681782	−	1.18088i	0.0313153	−	0.0542396i
$475$	−11.7702			−0.540055
$476$	8.76895	−	17.4398i	0.401924	−	0.799350i
$477$	0.334947			0.0153361
$478$	−6.73444	+	11.6644i	−0.308026	+	0.533517i
$479$	−6.55297	−	11.3501i	−0.299413	−	0.518598i	0.676589	−	0.736361i	$-0.263457\pi$
$479$	−6.55297	−	11.3501i	−0.299413	−	0.518598i	−0.976002	+	0.217763i	$0.930124\pi$
$480$	−7.98639	−	13.8328i	−0.364527	−	0.631380i
$481$	−0.213500	+	0.369792i	−0.00973474	+	0.0168611i
$482$	−2.60232			−0.118532
$483$	−2.73993	+	0.158277i	−0.124671	+	0.00720185i
$484$	10.9196			0.496348
$485$	21.0809	−	36.5132i	0.957234	−	1.65798i
$486$	0.308565	+	0.534450i	0.0139968	+	0.0242431i
$487$	−3.65055	−	6.32293i	−0.165422	−	0.286519i	0.771383	−	0.636371i	$-0.219565\pi$
$487$	−3.65055	−	6.32293i	−0.165422	−	0.286519i	−0.936805	+	0.349852i	$0.886232\pi$
$488$	−11.5651	+	20.0313i	−0.523526	+	0.906773i
$489$	1.78440			0.0806932
$490$	−7.32918	−	9.86434i	−0.331099	−	0.445626i
$491$	−39.3005			−1.77361			−0.886804	−	0.462145i	$-0.847080\pi$
$491$	−39.3005			−1.77361			−0.886804	+	0.462145i	$0.847080\pi$
$492$	2.47487	−	4.28661i	0.111576	−	0.193255i
$493$	16.0053	+	27.7220i	0.720843	+	1.24854i
$494$	−1.83078	−	3.17101i	−0.0823709	−	0.142671i
$495$	2.93436	−	5.08247i	0.131890	−	0.228440i
$496$	−15.4957			−0.695776
$497$	−31.1782	+	1.80107i	−1.39853	+	0.0807889i
$498$	−0.195111			−0.00874312
$499$	19.8985	−	34.4652i	0.890780	−	1.54288i	0.0518381	−	0.998656i	$-0.483492\pi$
$499$	19.8985	−	34.4652i	0.890780	−	1.54288i	0.838942	−	0.544221i	$-0.183175\pi$
$500$	4.39266	+	7.60831i	0.196446	+	0.340254i
$501$	2.72575	+	4.72114i	0.121778	+	0.210925i
$502$	4.50830	−	7.80860i	0.201215	−	0.348515i
$503$	−40.8741			−1.82249			−0.911244	−	0.411867i	$-0.864877\pi$
$503$	−40.8741			−1.82249			−0.911244	+	0.411867i	$0.864877\pi$
$504$	−2.65457	+	5.27943i	−0.118244	+	0.235165i
$505$	8.58764			0.382145
$506$	−0.660325	+	1.14372i	−0.0293550	+	0.0508444i
$507$	5.28479	+	9.15352i	0.234706	+	0.406522i
$508$	−12.7843	−	22.1431i	−0.567212	−	0.982439i
$509$	−12.1338	+	21.0164i	−0.537822	+	0.931535i	0.461199	+	0.887297i	$0.347419\pi$
$509$	−12.1338	+	21.0164i	−0.537822	+	0.931535i	−0.999021	+	0.0442384i	$0.985914\pi$
$510$	7.99965			0.354230
$511$	−14.8051	−	22.5334i	−0.654941	−	0.996820i
$512$	−18.7516			−0.828713
$513$	1.90292	−	3.29595i	0.0840159	−	0.145520i
$514$	7.95599	+	13.7802i	0.350924	+	0.607818i
$515$	−8.14361	−	14.1051i	−0.358850	−	0.621547i
$516$	2.95739	−	5.12234i	0.130192	−	0.225499i
$517$	−4.39469			−0.193278
$518$	0.245568	+	0.373755i	0.0107897	+	0.0164219i
$519$	2.39028			0.104922
$520$	4.95268	−	8.57829i	0.217189	−	0.376183i
$521$	−8.01230	−	13.8777i	−0.351025	−	0.607994i	0.635404	−	0.772180i	$-0.280834\pi$
$521$	−8.01230	−	13.8777i	−0.351025	−	0.607994i	−0.986429	+	0.164186i	$0.947500\pi$
$522$	−2.16766	−	3.75450i	−0.0948760	−	0.164330i
$523$	−4.60462	+	7.97543i	−0.201346	+	0.348741i	−0.948962	−	0.315390i	$-0.897865\pi$
$523$	−4.60462	+	7.97543i	−0.201346	+	0.348741i	0.747617	+	0.664131i	$0.231198\pi$
$524$	−15.4541			−0.675115
$525$	−3.67575	+	7.31036i	−0.160423	+	0.319050i
$526$	17.3520			0.756582
$527$	18.9813	−	32.8766i	0.826840	−	1.43213i
$528$	−1.91854	−	3.32300i	−0.0834936	−	0.144615i
$529$	10.9620	+	18.9867i	0.476608	+	0.825509i
$530$	−0.294014	+	0.509247i	−0.0127711	+	0.0221203i
$531$	3.01173			0.130698
$532$	16.2766	−	0.940246i	0.705679	−	0.0407648i
$533$	4.76581			0.206430
$534$	0.181711	−	0.314733i	0.00786341	−	0.0136198i
$535$	−16.9526	−	29.3628i	−0.732924	−	1.26946i
$536$	−1.11674	−	1.93425i	−0.0482359	−	0.0835471i
$537$	8.99490	−	15.5796i	0.388159	−	0.672310i
$538$	11.1179			0.479325
$539$	−8.61254	−	11.5916i	−0.370968	−	0.499286i
$540$	4.60610			0.198215
$541$	16.8017	−	29.1014i	0.722362	−	1.25117i	−0.237688	−	0.971341i	$-0.576390\pi$
$541$	16.8017	−	29.1014i	0.722362	−	1.25117i	0.960051	−	0.279827i	$-0.0902770\pi$
$542$	5.28732	+	9.15792i	0.227110	+	0.393366i
$543$	1.00755	+	1.74513i	0.0432381	+	0.0748905i
$544$	12.7924	−	22.1571i	0.548471	−	0.949979i
$545$	15.2906			0.654978
$546$	−2.54122	+	0.146798i	−0.108754	+	0.00628239i
$547$	−2.17059			−0.0928079			−0.0464039	−	0.998923i	$-0.514776\pi$
$547$	−2.17059			−0.0928079			−0.0464039	+	0.998923i	$0.514776\pi$
$548$	0.157158	−	0.272205i	0.00671345	−	0.0116280i
$549$	−5.17804	−	8.96862i	−0.220993	−	0.382772i
$550$	1.96870	+	3.40988i	0.0839455	+	0.145398i
$551$	−13.3680	+	23.1540i	−0.569495	+	0.986394i
$552$	−2.31684			−0.0986113
$553$	−2.62610	+	5.22280i	−0.111673	+	0.222096i
$554$	7.99271			0.339578
$555$	0.389585	−	0.674781i	0.0165370	−	0.0286429i
$556$	2.73428	+	4.73591i	0.115959	+	0.200847i
$557$	3.50015	+	6.06244i	0.148306	+	0.256874i	0.930602	−	0.366034i	$-0.119285\pi$
$557$	3.50015	+	6.06244i	0.148306	+	0.256874i	−0.782295	+	0.622908i	$0.785951\pi$
$558$	−2.57072	+	4.45261i	−0.108827	+	0.188494i
$559$	5.69497			0.240872
$560$	7.68703	+	11.6997i	0.324836	+	0.494401i
$561$	9.40040			0.396885
$562$	7.38054	−	12.7835i	0.311329	−	0.539238i
$563$	−8.69930	−	15.0676i	−0.366632	−	0.635025i	0.622405	−	0.782695i	$-0.286156\pi$
$563$	−8.69930	−	15.0676i	−0.366632	−	0.635025i	−0.989037	+	0.147671i	$0.952822\pi$
$564$	−1.72460	−	2.98709i	−0.0726187	−	0.125779i
$565$	11.4536	−	19.8382i	0.481856	−	0.834598i
$566$	5.92102			0.248879
$567$	−1.45281	−	2.21118i	−0.0610125	−	0.0928610i
$568$	−26.3638			−1.10620
$569$	−9.52820	+	16.5033i	−0.399443	+	0.691856i	−0.993657	−	0.112451i	$-0.964130\pi$
$569$	−9.52820	+	16.5033i	−0.399443	+	0.691856i	0.594214	+	0.804307i	$0.297463\pi$
$570$	3.34074	+	5.78633i	0.139928	+	0.242363i
$571$	−6.98166	−	12.0926i	−0.292174	−	0.506059i	0.682150	−	0.731212i	$-0.261045\pi$
$571$	−6.98166	−	12.0926i	−0.292174	−	0.506059i	−0.974323	+	0.225153i	$0.927712\pi$
$572$	2.60373	−	4.50980i	0.108868	−	0.188564i
$573$	4.81796			0.201273
$574$	2.24225	−	4.45940i	0.0935895	−	0.186132i
$575$	−3.20810			−0.133787
$576$	0.127426	−	0.220708i	0.00530940	−	0.00919615i
$577$	1.47633	+	2.55708i	0.0614604	+	0.106453i	0.895118	−	0.445829i	$-0.147091\pi$
$577$	1.47633	+	2.55708i	0.0614604	+	0.106453i	−0.833658	+	0.552281i	$0.813758\pi$
$578$	1.16123	+	2.01131i	0.0483008	+	0.0836595i
$579$	5.57557	−	9.65717i	0.231713	−	0.401338i
$580$	−32.3578			−1.34359
$581$	0.835085	−	0.0482402i	0.0346452	−	0.00200134i
$582$	−9.14637			−0.379129
$583$	−0.345496	+	0.598417i	−0.0143090	+	0.0247839i
$584$	−11.3803	−	19.7113i	−0.470922	−	0.815660i
$585$	2.21747	+	3.84076i	0.0916809	+	0.158796i
$586$	0.923905	−	1.60025i	0.0381662	−	0.0661057i
$587$	25.8110			1.06534			0.532668	−	0.846325i	$-0.321190\pi$
$587$	25.8110			1.06534			0.532668	+	0.846325i	$0.321190\pi$
$588$	4.49908	−	10.4028i	0.185539	−	0.429006i
$589$	31.7072			1.30647
$590$	−2.64367	+	4.57897i	−0.108838	+	0.188513i
$591$	−11.5610	−	20.0243i	−0.475558	−	0.823690i
$592$	−0.254717	−	0.441183i	−0.0104688	−	0.0181325i
$593$	−4.60276	+	7.97221i	−0.189013	+	0.327379i	−0.944921	−	0.327298i	$-0.893862\pi$
$593$	−4.60276	+	7.97221i	−0.189013	+	0.327379i	0.755909	+	0.654677i	$0.227195\pi$
$594$	−1.27313			−0.0522373
$595$	−34.2389	+	1.97787i	−1.40366	+	0.0810849i
$596$	−18.8433			−0.771850
$597$	3.17575	−	5.50057i	0.129975	−	0.225123i
$598$	−0.499000	−	0.864293i	−0.0204056	−	0.0353436i
$599$	−19.2891	−	33.4097i	−0.788132	−	1.36508i	−0.927110	−	0.374789i	$-0.877715\pi$
$599$	−19.2891	−	33.4097i	−0.788132	−	1.36508i	0.138978	−	0.990295i	$-0.455618\pi$
$600$	−3.45372	+	5.98202i	−0.140998	+	0.244215i
$601$	−14.2078			−0.579549			−0.289774	−	0.957095i	$-0.593580\pi$
$601$	−14.2078			−0.579549			−0.289774	+	0.957095i	$0.593580\pi$
$602$	2.67940	−	5.32882i	0.109204	−	0.217187i
$603$	1.00000			0.0407231
$604$	18.8279	−	32.6108i	0.766095	−	1.32691i
$605$	−9.59262	−	16.6149i	−0.389995	−	0.675492i
$606$	−0.931481	−	1.61337i	−0.0378388	−	0.0655388i
$607$	4.77074	−	8.26317i	0.193639	−	0.335392i	−0.752815	−	0.658232i	$-0.771304\pi$
$607$	4.77074	−	8.26317i	0.193639	−	0.335392i	0.946453	+	0.322841i	$0.104638\pi$
$608$	21.3690			0.866628
$609$	10.2060	+	15.5335i	0.413568	+	0.629451i
$610$	18.1810			0.736127
$611$	1.66051	−	2.87609i	0.0671770	−	0.116354i
$612$	3.68898	+	6.38950i	0.149118	+	0.258280i
$613$	6.03622	+	10.4550i	0.243801	+	0.422275i	0.961794	−	0.273775i	$-0.0882724\pi$
$613$	6.03622	+	10.4550i	0.243801	+	0.422275i	−0.717993	+	0.696050i	$0.754939\pi$
$614$	−4.56401	+	7.90510i	−0.184189	+	0.319024i
$615$	−8.69644			−0.350674
$616$	−6.69408	−	10.1884i	−0.269712	−	0.410502i
$617$	−35.6791			−1.43639			−0.718194	−	0.695843i	$-0.755031\pi$
$617$	−35.6791			−1.43639			−0.718194	+	0.695843i	$0.755031\pi$
$618$	−1.76664	+	3.05990i	−0.0710645	+	0.123087i
$619$	7.28314	+	12.6148i	0.292734	+	0.507031i	0.974455	−	0.224582i	$-0.0721015\pi$
$619$	7.28314	+	12.6148i	0.292734	+	0.507031i	−0.681721	+	0.731612i	$0.738768\pi$
$620$	19.1872	+	33.2332i	0.770577	+	1.33468i
$621$	0.518661	−	0.898347i	0.0208131	−	0.0360494i
$622$	−8.74760			−0.350747
$623$	−0.699918	+	1.39200i	−0.0280416	+	0.0557694i
$624$	2.89963			0.116078
$625$	15.4494	−	26.7591i	0.617975	−	1.07036i
$626$	−0.899997	−	1.55884i	−0.0359711	−	0.0623038i
$627$	3.92571	+	6.79953i	0.156778	+	0.271547i
$628$	−12.7323	+	22.0531i	−0.508076	+	0.880013i
$629$	1.24806			0.0497633
$630$	4.63711	−	0.267871i	0.184747	−	0.0106723i
$631$	−47.3559			−1.88521			−0.942604	−	0.333913i	$-0.891631\pi$
$631$	−47.3559			−1.88521			−0.942604	+	0.333913i	$0.891631\pi$
$632$	−2.46747	+	4.27378i	−0.0981507	+	0.170002i
$633$	5.17632	+	8.96565i	0.205740	+	0.356352i
$634$	2.49323	+	4.31840i	0.0990189	+	0.171506i
$635$	−22.4613	+	38.9042i	−0.891351	+	1.54386i
$636$	−0.542329			−0.0215048
$637$	10.8403	−	1.25661i	0.429507	−	0.0497887i
$638$	8.94375			0.354087
$639$	5.90195	−	10.2225i	0.233478	−	0.404395i
$640$	16.1965	+	28.0531i	0.640222	+	1.10890i
$641$	10.2264	+	17.7126i	0.403918	+	0.699606i	0.994195	−	0.107594i	$-0.0343148\pi$
$641$	10.2264	+	17.7126i	0.403918	+	0.699606i	−0.590277	+	0.807201i	$0.700981\pi$
$642$	−3.67761	+	6.36981i	−0.145144	+	0.251397i
$643$	−25.6683			−1.01226			−0.506129	−	0.862458i	$-0.668924\pi$
$643$	−25.6683			−1.01226			−0.506129	+	0.862458i	$0.668924\pi$
$644$	4.43636	−	0.256274i	0.174817	−	0.0100986i
$645$	−10.3919			−0.409182
$646$	−5.35112	+	9.26841i	−0.210537	+	0.364661i
$647$	13.1032	+	22.6953i	0.515138	+	0.892245i	0.999846	+	0.0175690i	$0.00559268\pi$
$647$	13.1032	+	22.6953i	0.515138	+	0.892245i	−0.484708	+	0.874676i	$0.661074\pi$
$648$	−1.11674	−	1.93425i	−0.0438698	−	0.0759847i
$649$	−3.10659	+	5.38076i	−0.121944	+	0.211213i
$650$	−2.97544			−0.116706
$651$	9.90192	−	19.6930i	0.388087	−	0.771831i
$652$	−2.88921			−0.113150
$653$	−16.7637	+	29.0356i	−0.656014	+	1.13625i	0.325624	+	0.945499i	$0.394426\pi$
$653$	−16.7637	+	29.0356i	−0.656014	+	1.13625i	−0.981638	+	0.190751i	$0.938908\pi$
$654$	−1.65854	−	2.87267i	−0.0648539	−	0.112330i
$655$	13.5760	+	23.5143i	0.530458	+	0.918781i
$656$	−2.84294	+	4.92412i	−0.110998	+	0.192255i
$657$	10.1907			0.397576
$658$	−1.90993	−	2.90691i	−0.0744567	−	0.113323i
$659$	−31.3103			−1.21968			−0.609838	−	0.792526i	$-0.708765\pi$
$659$	−31.3103			−1.21968			−0.609838	+	0.792526i	$0.708765\pi$
$660$	−4.75118	+	8.22929i	−0.184939	+	0.320325i
$661$	8.93129	+	15.4694i	0.347387	+	0.601692i	0.985784	−	0.168015i	$-0.0537357\pi$
$661$	8.93129	+	15.4694i	0.347387	+	0.601692i	−0.638398	+	0.769707i	$0.720402\pi$
$662$	−4.96800	−	8.60483i	−0.193087	−	0.334436i
$663$	−3.55189	+	6.15205i	−0.137944	+	0.238926i
$664$	0.706135			0.0274034
$665$	−15.7292	−	23.9398i	−0.609952	−	0.928346i
$666$	−0.169029			−0.00654976
$667$	−3.64359	+	6.31088i	−0.141080	+	0.244358i
$668$	−4.41340	−	7.64424i	−0.170760	−	0.295765i
$669$	13.2489	+	22.9477i	0.512230	+	0.887209i
$670$	−0.877793	+	1.52038i	−0.0339121	+	0.0587375i
$671$	21.3645			0.824768
$672$	6.67338	−	13.2721i	0.257431	−	0.511981i
$673$	8.41534			0.324388			0.162194	−	0.986759i	$-0.448143\pi$
$673$	8.41534			0.324388			0.162194	+	0.986759i	$0.448143\pi$
$674$	−0.160204	+	0.277482i	−0.00617083	+	0.0106882i
$675$	−1.54634	−	2.67834i	−0.0595186	−	0.103089i
$676$	−8.55687	−	14.8209i	−0.329111	−	0.570036i
$677$	14.9784	−	25.9433i	0.575665	−	0.997081i	−0.420304	−	0.907383i	$-0.638076\pi$
$677$	14.9784	−	25.9433i	0.575665	−	0.997081i	0.995969	−	0.0896980i	$-0.0285902\pi$
$678$	−4.96937			−0.190847
$679$	39.1470	−	2.26140i	1.50232	−	0.0867845i
$680$	−28.9519			−1.11026
$681$	3.82104	−	6.61823i	0.146423	−	0.253611i
$682$	−5.30337	−	9.18571i	−0.203077	−	0.351739i
$683$	7.94117	+	13.7545i	0.303861	+	0.526302i	0.977007	−	0.213207i	$-0.0683910\pi$
$683$	7.94117	+	13.7545i	0.303861	+	0.526302i	−0.673146	+	0.739509i	$0.735058\pi$
$684$	−3.08111	+	5.33664i	−0.117809	+	0.204052i
$685$	−0.552236			−0.0210998
$686$	3.92438	−	10.7345i	0.149834	−	0.409846i
$687$	−10.4471			−0.398581
$688$	−3.39721	+	5.88415i	−0.129518	+	0.224331i
$689$	−0.261088	−	0.452217i	−0.00994665	−	0.0172281i
$690$	0.910554	+	1.57713i	0.0346642	+	0.0600401i
$691$	−16.8777	+	29.2330i	−0.642058	+	1.11208i	0.342915	+	0.939367i	$0.388586\pi$
$691$	−16.8777	+	29.2330i	−0.642058	+	1.11208i	−0.984973	+	0.172710i	$0.944748\pi$
$692$	−3.87023			−0.147124
$693$	5.44909	−	0.314776i	0.206994	−	0.0119574i
$694$	14.8296			0.562923
$695$	4.80398	−	8.32074i	0.182225	−	0.315624i
$696$	7.84510	+	13.5881i	0.297368	+	0.515056i
$697$	−6.96489	−	12.0635i	−0.263814	−	0.456939i
$698$	5.09603	−	8.82658i	0.192888	−	0.334091i
$699$	27.8210			1.05229
$700$	5.95160	−	11.8366i	0.224949	−	0.447381i
$701$	10.9425			0.413293			0.206646	−	0.978416i	$-0.433745\pi$
$701$	10.9425			0.413293			0.206646	+	0.978416i	$0.433745\pi$
$702$	0.481046	−	0.833197i	0.0181559	−	0.0314470i
$703$	0.521202	+	0.902749i	0.0196575	+	0.0340478i
$704$	0.262878	+	0.455318i	0.00990760	+	0.0171605i
$705$	−3.03003	+	5.24816i	−0.114117	+	0.197657i
$706$	−6.20458			−0.233513
$707$	4.38569	+	6.67502i	0.164941	+	0.251040i
$708$	−4.87644			−0.183268
$709$	0.649043	−	1.12417i	0.0243753	−	0.0422193i	−0.853580	−	0.520961i	$-0.825574\pi$
$709$	0.649043	−	1.12417i	0.0243753	−	0.0422193i	0.877956	+	0.478742i	$0.158907\pi$
$710$	10.3614	+	17.9465i	0.388856	+	0.673518i
$711$	−1.10476	−	1.91351i	−0.0414318	−	0.0717621i
$712$	−0.657640	+	1.13907i	−0.0246461	+	0.0426883i
$713$	8.64214			0.323651
$714$	4.08540	+	6.21798i	0.152892	+	0.232702i
$715$	−9.14924			−0.342162
$716$	−14.5641	+	25.2258i	−0.544286	+	0.942731i
$717$	10.9125	+	18.9010i	0.407536	+	0.705872i
$718$	−4.95612	−	8.58426i	−0.184961	−	0.320362i
$719$	1.55598	−	2.69504i	0.0580284	−	0.100508i	−0.835552	−	0.549412i	$-0.814852\pi$
$719$	1.55598	−	2.69504i	0.0580284	−	0.100508i	0.893580	+	0.448903i	$0.148185\pi$
$720$	−5.29113			−0.197189
$721$	6.80476	−	13.5334i	0.253422	−	0.504008i
$722$	2.78672			0.103711
$723$	−2.10841	+	3.65187i	−0.0784125	+	0.135814i
$724$	−1.63137	−	2.82562i	−0.0606296	−	0.105013i
$725$	10.8630	+	18.8153i	0.403442	+	0.698782i
$726$	−2.08098	+	3.60436i	−0.0772323	+	0.133770i
$727$	25.4217			0.942839			0.471419	−	0.881909i	$-0.343742\pi$
$727$	25.4217			0.942839			0.471419	+	0.881909i	$0.343742\pi$
$728$	9.19707	−	0.531285i	0.340866	−	0.0196907i
$729$	1.00000			0.0370370
$730$	−8.94529	+	15.4937i	−0.331080	+	0.573448i
$731$	−8.32279	−	14.4155i	−0.307830	−	0.533177i
$732$	8.38403	+	14.5216i	0.309883	+	0.536732i
$733$	20.8535	−	36.1194i	0.770243	−	1.33410i	−0.167187	−	0.985925i	$-0.553468\pi$
$733$	20.8535	−	36.1194i	0.770243	−	1.33410i	0.937430	−	0.348175i	$-0.113198\pi$
$734$	18.4598			0.681362
$735$	−19.7809	+	2.29301i	−0.729629	+	0.0845789i
$736$	5.82435			0.214689
$737$	−1.03150	+	1.78661i	−0.0379957	+	0.0658105i
$738$	0.943282	+	1.63381i	0.0347227	+	0.0601415i
$739$	−17.6889	−	30.6381i	−0.650697	−	1.12704i	−0.982954	−	0.183851i	$-0.941144\pi$
$739$	−17.6889	−	30.6381i	−0.650697	−	1.12704i	0.332257	−	0.943189i	$-0.392190\pi$
$740$	−0.630797	+	1.09257i	−0.0231886	+	0.0401638i
$741$	−5.93323			−0.217963
$742$	−0.545981	+	0.0315396i	−0.0200436	+	0.00115785i
$743$	−40.7098			−1.49350			−0.746748	−	0.665107i	$-0.768386\pi$
$743$	−40.7098			−1.49350			−0.746748	+	0.665107i	$0.768386\pi$
$744$	9.30381	−	16.1147i	0.341094	−	0.590793i
$745$	16.5533	+	28.6712i	0.606466	+	1.05043i
$746$	5.92515	+	10.2627i	0.216935	+	0.375743i
$747$	−0.158079	+	0.273801i	−0.00578382	+	0.0100179i
$748$	−15.2207			−0.556523
$749$	14.1655	−	28.1724i	0.517596	−	1.02940i
$750$	−3.34847			−0.122269
$751$	19.5516	−	33.8644i	0.713449	−	1.23573i	−0.250106	−	0.968218i	$-0.580466\pi$
$751$	19.5516	−	33.8644i	0.713449	−	1.23573i	0.963555	−	0.267511i	$-0.0862011\pi$
$752$	1.98108	+	3.43134i	0.0722427	+	0.125128i
$753$	−7.30527	−	12.6531i	−0.266219	−	0.461105i
$754$	−3.37935	+	5.85320i	−0.123069	+	0.213161i
$755$	−66.1591			−2.40778
$756$	2.35233	+	3.58024i	0.0855533	+	0.130212i
$757$	−29.3464			−1.06661			−0.533307	−	0.845922i	$-0.679051\pi$
$757$	−29.3464			−1.06661			−0.533307	+	0.845922i	$0.679051\pi$
$758$	3.46682	−	6.00471i	0.125921	−	0.218101i
$759$	1.06999	+	1.85328i	0.0388383	+	0.0672699i
$760$	−12.0906	−	20.9416i	−0.438573	−	0.759631i
$761$	9.15368	−	15.8546i	0.331821	−	0.574730i	−0.651048	−	0.759036i	$-0.725670\pi$
$761$	9.15368	−	15.8546i	0.331821	−	0.574730i	0.982869	+	0.184306i	$0.0590037\pi$
$762$	9.74531			0.353035
$763$	7.80889	+	11.8851i	0.282701	+	0.430271i
$764$	−7.80101			−0.282231
$765$	6.48134	−	11.2260i	0.234333	−	0.405877i
$766$	−9.20252	−	15.9392i	−0.332500	−	0.575908i
$767$	−2.34761	−	4.06618i	−0.0847674	−	0.146821i
$768$	3.25874	−	5.64430i	0.117590	−	0.203671i
$769$	45.0127			1.62320			0.811600	−	0.584213i	$-0.198597\pi$
$769$	45.0127			1.62320			0.811600	+	0.584213i	$0.198597\pi$
$770$	−4.30459	+	8.56100i	−0.155127	+	0.308517i
$771$	25.7839			0.928583
$772$	−9.02769	+	15.6364i	−0.324914	+	0.562767i
$773$	−11.6359	−	20.1540i	−0.418516	−	0.724891i	0.577275	−	0.816550i	$-0.304116\pi$
$773$	−11.6359	−	20.1540i	−0.418516	−	0.724891i	−0.995790	+	0.0916595i	$0.970783\pi$
$774$	1.12719	+	1.95235i	0.0405160	+	0.0701757i
$775$	12.8829	−	22.3138i	0.462766	−	0.801535i
$776$	33.1021			1.18830
$777$	0.723455	−	0.0417917i	0.0259538	−	0.00149927i
$778$	−2.39232			−0.0857688
$779$	5.81722	−	10.0757i	0.208424	−	0.361000i
$780$	−3.59041	−	6.21878i	−0.128557	−	0.222668i
$781$	12.1757	+	21.0889i	0.435681	+	0.754621i
$782$	−1.45851	+	2.52621i	−0.0521560	+	0.0903369i
$783$	−7.02499			−0.251053
$784$	−5.16819	+	11.9500i	−0.184578	+	0.426785i
$785$	44.7401			1.59684
$786$	2.94511	−	5.10108i	0.105049	−	0.181950i
$787$	−9.07923	−	15.7257i	−0.323640	−	0.560560i	0.657597	−	0.753370i	$-0.271573\pi$
$787$	−9.07923	−	15.7257i	−0.323640	−	0.560560i	−0.981236	+	0.192810i	$0.938240\pi$
$788$	18.7191	+	32.4224i	0.666840	+	1.15500i
$789$	14.0586	−	24.3503i	0.500501	−	0.866892i
$790$	3.87901			0.138009
$791$	21.2692	−	1.22865i	0.756245	−	0.0436859i
$792$	4.60766			0.163726
$793$	−8.07246	+	13.9819i	−0.286662	+	0.496512i
$794$	−7.81370	−	13.5337i	−0.277298	−	0.480294i
$795$	0.476422	+	0.825187i	0.0168969	+	0.0292664i
$796$	−5.14203	+	8.90625i	−0.182254	+	0.315674i
$797$	29.0419			1.02872			0.514359	−	0.857575i	$-0.328030\pi$
$797$	29.0419			1.02872			0.514359	+	0.857575i	$0.328030\pi$
$798$	−2.79150	+	5.55176i	−0.0988180	+	0.196530i
$799$	−9.70687			−0.343404
$800$	8.68238	−	15.0383i	0.306969	−	0.531685i
$801$	−0.294446	−	0.509995i	−0.0104037	−	0.0180198i
$802$	−0.627207	−	1.08635i	−0.0221475	−	0.0383605i
$803$	−10.5116	+	18.2067i	−0.370948	+	0.642500i
$804$	−1.61915			−0.0571031
$805$	−4.28716	−	6.52506i	−0.151102	−	0.229978i
$806$	8.01540			0.282330
$807$	9.00772	−	15.6018i	0.317087	−	0.549211i
$808$	3.37117	+	5.83904i	0.118597	+	0.205417i
$809$	4.13243	+	7.15759i	0.145289	+	0.251647i	0.929481	−	0.368871i	$-0.120256\pi$
$809$	4.13243	+	7.15759i	0.145289	+	0.251647i	−0.784192	+	0.620518i	$0.786922\pi$
$810$	−0.877793	+	1.52038i	−0.0308425	+	0.0534208i
$811$	−0.331801			−0.0116511			−0.00582555	−	0.999983i	$-0.501854\pi$
$811$	−0.331801			−0.0116511			−0.00582555	+	0.999983i	$0.501854\pi$
$812$	−16.5251	−	25.1512i	−0.579916	−	0.882632i
$813$	17.1352			0.600959
$814$	0.174353	−	0.301989i	0.00611108	−	0.0105847i
$815$	2.53809	+	4.39611i	0.0889055	+	0.153989i
$816$	−4.23761	−	7.33975i	−0.148346	−	0.256943i
$817$	6.95137	−	12.0401i	0.243198	−	0.421231i
$818$	14.7506			0.515742
$819$	−1.85290	+	3.68507i	−0.0647456	+	0.128767i
$820$	14.0809			0.491725
$821$	−11.5496	+	20.0045i	−0.403084	+	0.698162i	−0.994096	−	0.108501i	$-0.965395\pi$
$821$	−11.5496	+	20.0045i	−0.403084	+	0.698162i	0.591012	+	0.806662i	$0.298728\pi$
$822$	0.0598997	+	0.103749i	0.00208924	+	0.00361867i
$823$	−26.1039	−	45.2133i	−0.909926	−	1.57604i	−0.814165	−	0.580634i	$-0.802805\pi$
$823$	−26.1039	−	45.2133i	−0.909926	−	1.57604i	−0.0957609	−	0.995404i	$-0.530528\pi$
$824$	6.39372	−	11.0743i	0.222736	−	0.385790i
$825$	6.38018			0.222129
$826$	−4.90927	+	0.283593i	−0.170815	+	0.00986746i
$827$	−35.5433			−1.23596			−0.617981	−	0.786193i	$-0.712049\pi$
$827$	−35.5433			−1.23596			−0.617981	+	0.786193i	$0.712049\pi$
$828$	−0.839790	+	1.45456i	−0.0291847	+	0.0505494i
$829$	7.16214	+	12.4052i	0.248751	+	0.430850i	0.963180	−	0.268859i	$-0.0866464\pi$
$829$	7.16214	+	12.4052i	0.248751	+	0.430850i	−0.714428	+	0.699709i	$0.753313\pi$
$830$	−0.277522	−	0.480682i	−0.00963293	−	0.0166847i
$831$	6.47572	−	11.2163i	0.224640	−	0.389088i
$832$	−0.397308			−0.0137742
$833$	−19.0231	−	25.6032i	−0.659112	−	0.887099i
$834$	−2.08431			−0.0721736
$835$	−7.75412	+	13.4305i	−0.268342	+	0.464783i
$836$	−6.35632	−	11.0095i	−0.219838	−	0.380770i
$837$	4.16560	+	7.21504i	0.143984	+	0.249388i
$838$	8.37422	−	14.5046i	0.289283	−	0.501052i
$839$	−18.1720			−0.627367			−0.313684	−	0.949528i	$-0.601563\pi$
$839$	−18.1720			−0.627367			−0.313684	+	0.949528i	$0.601563\pi$
$840$	−16.7824	+	0.969467i	−0.579049	+	0.0334498i
$841$	20.3505			0.701740
$842$	−6.84075	+	11.8485i	−0.235748	+	0.408327i
$843$	−11.9595	−	20.7144i	−0.411906	−	0.713442i
$844$	−8.38124	−	14.5167i	−0.288494	−	0.499687i
$845$	−15.0340	+	26.0396i	−0.517184	+	0.895790i
$846$	1.31464			0.0451982
$847$	8.01554	−	15.9414i	0.275417	−	0.547752i
$848$	0.622985			0.0213934
$849$	4.79723	−	8.30905i	0.164641	−	0.285166i
$850$	4.34840	+	7.53165i	0.149149	+	0.258333i
$851$	0.142059	+	0.246054i	0.00486973	+	0.00843462i
$852$	−9.55616	+	16.5518i	−0.327389	+	0.567054i
$853$	23.2578			0.796331			0.398165	−	0.917314i	$-0.369647\pi$
$853$	23.2578			0.796331			0.398165	+	0.917314i	$0.369647\pi$
$854$	9.28499	+	14.1318i	0.317726	+	0.483579i
$855$	10.8267			0.370265
$856$	13.3098	−	23.0533i	0.454921	−	0.787946i
$857$	−7.62942	−	13.2145i	−0.260616	−	0.451400i	0.705790	−	0.708421i	$-0.250592\pi$
$857$	−7.62942	−	13.2145i	−0.260616	−	0.451400i	−0.966406	+	0.257021i	$0.917259\pi$
$858$	0.992396	+	1.71888i	0.0338798	+	0.0586816i
$859$	16.7581	−	29.0259i	0.571780	−	0.990352i	−0.424603	−	0.905379i	$-0.639586\pi$
$859$	16.7581	−	29.0259i	0.571780	−	0.990352i	0.996383	−	0.0849724i	$-0.0270802\pi$
$860$	16.8261			0.573766
$861$	−4.44125	−	6.75959i	−0.151358	−	0.230366i
$862$	2.07575			0.0707002
$863$	2.58893	−	4.48416i	0.0881283	−	0.152643i	−0.818592	−	0.574376i	$-0.805245\pi$
$863$	2.58893	−	4.48416i	0.0881283	−	0.152643i	0.906720	+	0.421733i	$0.138578\pi$
$864$	2.80740	+	4.86256i	0.0955097	+	0.165428i
$865$	3.39989	+	5.88879i	0.115600	+	0.200225i
$866$	−12.2512	+	21.2197i	−0.416313	+	0.721076i
$867$	3.76333			0.127809
$868$	−16.0327	+	31.8860i	−0.544186	+	1.08228i
$869$	4.55824			0.154628
$870$	6.16649	−	10.6807i	0.209064	−	0.362109i
$871$	−0.779491	−	1.35012i	−0.0264120	−	0.0457470i
$872$	6.00250	+	10.3966i	0.203270	+	0.352074i
$873$	−7.41042	+	12.8352i	−0.250805	+	0.434407i
$874$	−2.43635			−0.0824107
$875$	14.3316	−	0.827893i	0.484498	−	0.0279879i
$876$	−16.5002			−0.557491
$877$	−3.71234	+	6.42997i	−0.125357	+	0.217125i	−0.921872	−	0.387494i	$-0.873341\pi$
$877$	−3.71234	+	6.42997i	−0.125357	+	0.217125i	0.796515	+	0.604618i	$0.206674\pi$
$878$	11.1060	+	19.2362i	0.374810	+	0.649191i
$879$	−1.49710	−	2.59306i	−0.0504960	−	0.0874616i
$880$	5.45779	−	9.45316i	0.183982	−	0.318666i
$881$	20.3727			0.686375			0.343187	−	0.939267i	$-0.388493\pi$
$881$	20.3727			0.686375			0.343187	+	0.939267i	$0.388493\pi$
$882$	2.57638	+	3.46754i	0.0867511	+	0.116758i
$883$	46.1247			1.55222			0.776110	−	0.630598i	$-0.217190\pi$
$883$	46.1247			1.55222			0.776110	+	0.630598i	$0.217190\pi$
$884$	5.75105	−	9.96111i	0.193429	−	0.335028i
$885$	4.28382	+	7.41980i	0.143999	+	0.249414i
$886$	−2.70073	−	4.67781i	−0.0907329	−	0.157154i
$887$	−18.8157	+	32.5898i	−0.631771	+	1.09426i	0.355419	+	0.934707i	$0.384338\pi$
$887$	−18.8157	+	32.5898i	−0.631771	+	1.09426i	−0.987190	+	0.159552i	$0.948995\pi$
$888$	0.611743			0.0205288
$889$	−41.7105	+	2.40948i	−1.39892	+	0.0808114i
$890$	1.03385			0.0346548
$891$	−1.03150	+	1.78661i	−0.0345565	+	0.0598535i
$892$	−21.4519	−	37.1558i	−0.718263	−	1.24407i
$893$	−4.05369	−	7.02120i	−0.135652	−	0.234955i
$894$	3.59100	−	6.21979i	0.120101	−	0.208021i
$895$	51.1767			1.71065
$896$	−13.5337	+	26.9159i	−0.452129	+	0.899197i
$897$	−1.61716			−0.0539956
$898$	−4.78049	+	8.28005i	−0.159527	+	0.276309i
$899$	−29.2633	−	50.6856i	−0.975987	−	1.69046i
$900$	2.50376	+	4.33663i	0.0834586	+	0.144554i
$901$	−0.763122	+	1.32177i	−0.0254233	+	0.0440344i
$902$	−3.89197			−0.129588
$903$	−5.30714	−	8.07747i	−0.176611	−	0.268801i
$904$	17.9849			0.598169
$905$	−2.86624	+	4.96447i	−0.0952770	+	0.165025i
$906$	7.17612	+	12.4294i	0.238411	+	0.412939i
$907$	27.2897	+	47.2672i	0.906141	+	1.56948i	0.819378	+	0.573253i	$0.194319\pi$
$907$	27.2897	+	47.2672i	0.906141	+	1.56948i	0.0867626	+	0.996229i	$0.472348\pi$
$908$	−6.18684	+	10.7159i	−0.205317	+	0.355620i
$909$	−3.01875			−0.100126
$910$	−3.97625	−	6.05185i	−0.131811	−	0.200617i
$911$	10.1328			0.335715			0.167857	−	0.985811i	$-0.446315\pi$
$911$	10.1328			0.335715			0.167857	+	0.985811i	$0.446315\pi$
$912$	3.53934	−	6.13032i	0.117199	−	0.202995i
$913$	−0.326117	−	0.564851i	−0.0107929	−	0.0186938i
$914$	−5.64495	−	9.77734i	−0.186718	−	0.323406i
$915$	14.7303	−	25.5136i	0.486968	−	0.843454i
$916$	16.9154			0.558901
$917$	−11.3440	+	22.5611i	−0.374613	+	0.745033i
$918$	−2.81206			−0.0928118
$919$	12.9100	−	22.3609i	0.425863	−	0.737617i	−0.570637	−	0.821202i	$-0.693304\pi$
$919$	12.9100	−	22.3609i	0.425863	−	0.737617i	0.996501	+	0.0835855i	$0.0266372\pi$
$920$	−3.29543	−	5.70786i	−0.108647	−	0.188182i
$921$	7.39556	+	12.8095i	0.243692	+	0.422087i
$922$	1.12648	−	1.95113i	0.0370987	−	0.0642569i
$923$	−18.4021			−0.605712
$924$	−8.82289	+	0.509670i	−0.290252	+	0.0167669i
$925$	0.847073			0.0278516
$926$	−8.34592	+	14.4556i	−0.274264	+	0.475039i
$927$	2.86267	+	4.95829i	0.0940223	+	0.162851i
$928$	−19.7220	−	34.1594i	−0.647405	−	1.12134i
$929$	19.3929	−	33.5895i	0.636260	−	1.10203i	−0.349987	−	0.936755i	$-0.613814\pi$
$929$	19.3929	−	33.5895i	0.636260	−	1.10203i	0.986247	−	0.165280i	$-0.0528528\pi$
$930$	−14.6262			−0.479611
$931$	10.5751	−	24.4520i	0.346586	−	0.801383i
$932$	−45.0464			−1.47555
$933$	−7.08733	+	12.2756i	−0.232029	+	0.401886i
$934$	−6.84011	−	11.8474i	−0.223815	−	0.387659i
$935$	13.3710	+	23.1592i	0.437277	+	0.757386i
$936$	−1.74098	+	3.01547i	−0.0569057	+	0.0985636i
$937$	36.1165			1.17987			0.589937	−	0.807450i	$-0.299153\pi$
$937$	36.1165			1.17987			0.589937	+	0.807450i	$0.299153\pi$
$938$	−1.63005	+	0.0941630i	−0.0532231	+	0.00307453i
$939$	−2.91672			−0.0951836
$940$	4.90607	−	8.49757i	0.160018	−	0.277160i
$941$	−19.4299	−	33.6535i	−0.633396	−	1.09707i	−0.986853	−	0.161622i	$-0.948327\pi$
$941$	−19.4299	−	33.6535i	−0.633396	−	1.09707i	0.353457	−	0.935451i	$-0.385006\pi$
$942$	−4.85285	−	8.40539i	−0.158114	−	0.273862i
$943$	1.58555	−	2.74625i	0.0516325	−	0.0894301i
$944$	5.60167			0.182319
$945$	3.38110	−	6.72435i	0.109987	−	0.218743i
$946$	−4.65077			−0.151210
$947$	−1.03285	+	1.78895i	−0.0335631	+	0.0581329i	−0.882319	−	0.470652i	$-0.844019\pi$
$947$	−1.03285	+	1.78895i	−0.0335631	+	0.0581329i	0.848756	+	0.528785i	$0.177352\pi$
$948$	1.78878	+	3.09826i	0.0580968	+	0.100627i
$949$	−7.94352	−	13.7586i	−0.257858	−	0.446623i
$950$	−3.63187	+	6.29059i	−0.117834	+	0.204094i
$951$	8.08010			0.262015
$952$	−14.7857	−	22.5038i	−0.479207	−	0.729353i
$953$	13.0912			0.424066			0.212033	−	0.977263i	$-0.431992\pi$
$953$	13.0912			0.424066			0.212033	+	0.977263i	$0.431992\pi$
$954$	0.103353	−	0.179012i	0.00334617	−	0.00579573i
$955$	6.85298	+	11.8697i	0.221757	+	0.384095i
$956$	−17.6690	−	30.6037i	−0.571457	−	0.989793i
$957$	7.24626	−	12.5509i	0.234238	−	0.405712i
$958$	−8.08806			−0.261313
$959$	−0.282025	−	0.429243i	−0.00910708	−	0.0138610i
$960$	0.724991			0.0233990
$961$	−19.2045	+	33.2632i	−0.619501	+	1.07301i
$962$	0.131757	+	0.228210i	0.00424801	+	0.00735777i
$963$	5.95923	+	10.3217i	0.192033	+	0.332612i
$964$	3.41383	−	5.91293i	0.109952	−	0.190443i
$965$	31.7223			1.02118
$966$	−0.760854	+	1.51319i	−0.0244801	+	0.0486861i
$967$	−26.1824			−0.841968			−0.420984	−	0.907068i	$-0.638315\pi$
$967$	−26.1824			−0.841968			−0.420984	+	0.907068i	$0.638315\pi$
$968$	7.53137	−	13.0447i	0.242067	−	0.419273i
$969$	8.67099	+	15.0186i	0.278552	+	0.482467i
$970$	−13.0096	−	22.5333i	−0.417714	−	0.723502i
$971$	16.8477	−	29.1810i	0.540667	−	0.936463i	−0.458199	−	0.888850i	$-0.651505\pi$
$971$	16.8477	−	29.1810i	0.540667	−	0.936463i	0.998866	−	0.0476132i	$-0.0151615\pi$
$972$	−1.61915			−0.0519343
$973$	8.92094	−	0.515334i	0.285992	−	0.0165209i
$974$	−4.50572			−0.144373
$975$	−2.41071	+	4.17548i	−0.0772046	+	0.133722i
$976$	−9.63091	−	16.6812i	−0.308278	−	0.533953i
$977$	−2.20140	−	3.81294i	−0.0704290	−	0.121987i	0.828660	−	0.559752i	$-0.189103\pi$
$977$	−2.20140	−	3.81294i	−0.0704290	−	0.121987i	−0.899089	+	0.437765i	$0.855770\pi$
$978$	0.550602	−	0.953670i	0.0176063	−	0.0304950i
$979$	1.21488			0.0388277
$980$	32.0282	−	3.71273i	1.02310	−	0.118599i
$981$	−5.37501			−0.171611
$982$	−12.1268	+	21.0042i	−0.386980	+	0.670270i
$983$	−31.0720	−	53.8183i	−0.991044	−	1.71654i	−0.611169	−	0.791500i	$-0.709301\pi$
$983$	−31.0720	−	53.8183i	−0.991044	−	1.71654i	−0.379874	−	0.925038i	$-0.624033\pi$
$984$	−3.41388	−	5.91302i	−0.108831	−	0.188500i
$985$	32.8884	−	56.9644i	1.04791	−	1.81504i
$986$	19.7547			0.629118
$987$	−5.62673	+	0.325038i	−0.179101	+	0.0103461i
$988$	9.60679			0.305633
$989$	1.89467	−	3.28167i	0.0602471	−	0.104351i
$990$	−1.81088	−	3.13654i	−0.0575536	−	0.0996858i
$991$	9.64745	+	16.7099i	0.306461	+	0.530807i	0.977586	−	0.210538i	$-0.0675217\pi$
$991$	9.64745	+	16.7099i	0.306461	+	0.530807i	−0.671124	+	0.741345i	$0.734188\pi$
$992$	−23.3890	+	40.5110i	−0.742603	+	1.28623i
$993$	−16.1003			−0.510929
$994$	−8.65792	+	17.2189i	−0.274613	+	0.546152i
$995$	18.0685			0.572811
$996$	0.255954	−	0.443326i	0.00811022	−	0.0140473i
$997$	−11.6920	−	20.2512i	−0.370290	−	0.641361i	0.619320	−	0.785139i	$-0.287408\pi$
$997$	−11.6920	−	20.2512i	−0.370290	−	0.641361i	−0.989610	+	0.143777i	$0.954075\pi$
$998$	−12.2800	−	21.2695i	−0.388715	−	0.673275i
$999$	−0.136948	+	0.237201i	−0.00433285	+	0.00750471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1407.2.i.h.604.11	yes	38
7.2	even	3		9849.2.a.bn.1.9		19
7.4	even	3	inner	1407.2.i.h.403.11	✓	38
7.5	odd	6		9849.2.a.bm.1.9		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1407.2.i.h.403.11	✓	38	7.4	even	3	inner
1407.2.i.h.604.11	yes	38	1.1	even	1	trivial
9849.2.a.bm.1.9		19	7.5	odd	6
9849.2.a.bn.1.9		19	7.2	even	3

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:	\( N \)	\(=\)	\( 1407 = 3 \cdot 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1407.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.308565 - 0.534450i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.809576 + 1.40223i) q^{4} +(1.42238 - 2.46364i) q^{5} -0.617129 q^{6} +(2.64135 - 0.152582i) q^{7} +2.23348 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.308565 - 0.534450i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.809576 + 1.40223i) q^{4} +(1.42238 - 2.46364i) q^{5} -0.617129 q^{6} +(2.64135 - 0.152582i) q^{7} +2.23348 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.877793 - 1.52038i) q^{10} +(-1.03150 - 1.78661i) q^{11} +(0.809576 - 1.40223i) q^{12} +1.55898 q^{13} +(0.733479 - 1.45875i) q^{14} -2.84476 q^{15} +(-0.929977 + 1.61077i) q^{16} +(-2.27834 - 3.94620i) q^{17} +(0.308565 + 0.534450i) q^{18} +(1.90292 - 3.29595i) q^{19} +4.60610 q^{20} +(-1.45281 - 2.21118i) q^{21} -1.27313 q^{22} +(0.518661 - 0.898347i) q^{23} +(-1.11674 - 1.93425i) q^{24} +(-1.54634 - 2.67834i) q^{25} +(0.481046 - 0.833197i) q^{26} +1.00000 q^{27} +(2.35233 + 3.58024i) q^{28} -7.02499 q^{29} +(-0.877793 + 1.52038i) q^{30} +(4.16560 + 7.21504i) q^{31} +(2.80740 + 4.86256i) q^{32} +(-1.03150 + 1.78661i) q^{33} -2.81206 q^{34} +(3.38110 - 6.72435i) q^{35} -1.61915 q^{36} +(-0.136948 + 0.237201i) q^{37} +(-1.17435 - 2.03403i) q^{38} +(-0.779491 - 1.35012i) q^{39} +(3.17687 - 5.50249i) q^{40} +3.05700 q^{41} +(-1.63005 + 0.0941630i) q^{42} +3.65301 q^{43} +(1.67015 - 2.89278i) q^{44} +(1.42238 + 2.46364i) q^{45} +(-0.320081 - 0.554396i) q^{46} +(1.06512 - 1.84485i) q^{47} +1.85995 q^{48} +(6.95344 - 0.806046i) q^{49} -1.90858 q^{50} +(-2.27834 + 3.94620i) q^{51} +(1.26211 + 2.18604i) q^{52} +(-0.167473 - 0.290072i) q^{53} +(0.308565 - 0.534450i) q^{54} -5.86873 q^{55} +(5.89941 - 0.340790i) q^{56} -3.80584 q^{57} +(-2.16766 + 3.75450i) q^{58} +(-1.50586 - 2.60823i) q^{59} +(-2.30305 - 3.98900i) q^{60} +(-5.17804 + 8.96862i) q^{61} +5.14143 q^{62} +(-1.18853 + 2.36377i) q^{63} -0.254851 q^{64} +(2.21747 - 3.84076i) q^{65} +(0.636567 + 1.10257i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(3.68898 - 6.38950i) q^{68} -1.03732 q^{69} +(-2.55054 - 3.88192i) q^{70} -11.8039 q^{71} +(-1.11674 + 1.93425i) q^{72} +(-5.09533 - 8.82537i) q^{73} +(0.0845147 + 0.146384i) q^{74} +(-1.54634 + 2.67834i) q^{75} +6.16222 q^{76} +(-2.99715 - 4.56166i) q^{77} -0.962093 q^{78} +(-1.10476 + 1.91351i) q^{79} +(2.64557 + 4.58225i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.943282 - 1.63381i) q^{82} +0.316159 q^{83} +(1.92442 - 3.82729i) q^{84} -12.9627 q^{85} +(1.12719 - 1.95235i) q^{86} +(3.51249 + 6.08382i) q^{87} +(-2.30383 - 3.99035i) q^{88} +(-0.294446 + 0.509995i) q^{89} +1.75559 q^{90} +(4.11781 - 0.237873i) q^{91} +1.67958 q^{92} +(4.16560 - 7.21504i) q^{93} +(-0.657320 - 1.13851i) q^{94} +(-5.41335 - 9.37620i) q^{95} +(2.80740 - 4.86256i) q^{96} +14.8208 q^{97} +(1.71479 - 3.96498i) q^{98} +2.06299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 5 q^{2} - 19 q^{3} - 13 q^{4} - 2 q^{5} - 10 q^{6} + 2 q^{7} - 30 q^{8} - 19 q^{9}+O(q^{10}) \) 38 * q + 5 * q^2 - 19 * q^3 - 13 * q^4 - 2 * q^5 - 10 * q^6 + 2 * q^7 - 30 * q^8 - 19 * q^9	\( 38 q + 5 q^{2} - 19 q^{3} - 13 q^{4} - 2 q^{5} - 10 q^{6} + 2 q^{7} - 30 q^{8} - 19 q^{9} + 9 q^{10} + 12 q^{11} - 13 q^{12} - 44 q^{13} - q^{14} + 4 q^{15} - 5 q^{16} + 2 q^{17} + 5 q^{18} + 14 q^{19} + 54 q^{20} - q^{21} - 18 q^{22} + 14 q^{23} + 15 q^{24} - 11 q^{25} + q^{26} + 38 q^{27} - 6 q^{28} - 52 q^{29} + 9 q^{30} + 13 q^{31} + 10 q^{32} + 12 q^{33} - 2 q^{34} + 12 q^{35} + 26 q^{36} + 16 q^{37} + 8 q^{38} + 22 q^{39} + 24 q^{40} + 28 q^{41} + 2 q^{42} - 54 q^{43} + 25 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + 10 q^{48} - 4 q^{49} - 104 q^{50} + 2 q^{51} + 59 q^{52} + 8 q^{53} + 5 q^{54} - 58 q^{55} + 18 q^{56} - 28 q^{57} + 28 q^{58} - 12 q^{59} - 27 q^{60} + 19 q^{61} + 12 q^{62} - q^{63} - 30 q^{64} + 19 q^{65} + 9 q^{66} - 19 q^{67} - 9 q^{68} - 28 q^{69} + 50 q^{70} - 120 q^{71} + 15 q^{72} + 50 q^{73} - 32 q^{74} - 11 q^{75} - 26 q^{76} + 45 q^{77} - 2 q^{78} + 56 q^{79} - 18 q^{80} - 19 q^{81} - 36 q^{82} + 36 q^{83} - 76 q^{85} + 17 q^{86} + 26 q^{87} - 63 q^{88} + 2 q^{89} - 18 q^{90} + 18 q^{91} - 98 q^{92} + 13 q^{93} + 50 q^{94} + 87 q^{95} + 10 q^{96} - 18 q^{97} + 41 q^{98} - 24 q^{99}+O(q^{100}) \) 38 * q + 5 * q^2 - 19 * q^3 - 13 * q^4 - 2 * q^5 - 10 * q^6 + 2 * q^7 - 30 * q^8 - 19 * q^9 + 9 * q^10 + 12 * q^11 - 13 * q^12 - 44 * q^13 - q^14 + 4 * q^15 - 5 * q^16 + 2 * q^17 + 5 * q^18 + 14 * q^19 + 54 * q^20 - q^21 - 18 * q^22 + 14 * q^23 + 15 * q^24 - 11 * q^25 + q^26 + 38 * q^27 - 6 * q^28 - 52 * q^29 + 9 * q^30 + 13 * q^31 + 10 * q^32 + 12 * q^33 - 2 * q^34 + 12 * q^35 + 26 * q^36 + 16 * q^37 + 8 * q^38 + 22 * q^39 + 24 * q^40 + 28 * q^41 + 2 * q^42 - 54 * q^43 + 25 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + 10 * q^48 - 4 * q^49 - 104 * q^50 + 2 * q^51 + 59 * q^52 + 8 * q^53 + 5 * q^54 - 58 * q^55 + 18 * q^56 - 28 * q^57 + 28 * q^58 - 12 * q^59 - 27 * q^60 + 19 * q^61 + 12 * q^62 - q^63 - 30 * q^64 + 19 * q^65 + 9 * q^66 - 19 * q^67 - 9 * q^68 - 28 * q^69 + 50 * q^70 - 120 * q^71 + 15 * q^72 + 50 * q^73 - 32 * q^74 - 11 * q^75 - 26 * q^76 + 45 * q^77 - 2 * q^78 + 56 * q^79 - 18 * q^80 - 19 * q^81 - 36 * q^82 + 36 * q^83 - 76 * q^85 + 17 * q^86 + 26 * q^87 - 63 * q^88 + 2 * q^89 - 18 * q^90 + 18 * q^91 - 98 * q^92 + 13 * q^93 + 50 * q^94 + 87 * q^95 + 10 * q^96 - 18 * q^97 + 41 * q^98 - 24 * q^99

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