LMFDB - Embedded newform 406.2.e.b.291.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(233,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("406.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.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:	$3.24192632206$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 11x^{8} - 2x^{7} + 51x^{6} - 3x^{5} + 156x^{4} + 70x^{3} + 220x^{2} - 42x + 9 $ x^10 - 2x^9 + 11x^8 - 2x^7 + 51x^6 - 3x^5 + 156x^4 + 70x^3 + 220x^2 - 42*x + 9
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			291.1
Root			$1.47344 - 2.55208i$ of defining polynomial
Character	$\chi$	$=$	406.291
Dual form			406.2.e.b.233.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.973442 + 1.68605i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.63596 + 2.83357i) q^{5} +1.94688 q^{6} +(2.61488 - 0.402984i) q^{7} +1.00000 q^{8} +(-0.395181 - 0.684473i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.973442 + 1.68605i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.63596 + 2.83357i) q^{5} +1.94688 q^{6} +(2.61488 - 0.402984i) q^{7} +1.00000 q^{8} +(-0.395181 - 0.684473i) q^{9} +(1.63596 - 2.83357i) q^{10} +(-1.64144 + 2.84306i) q^{11} +(-0.973442 - 1.68605i) q^{12} -5.52251 q^{13} +(-1.65643 - 2.06306i) q^{14} -6.37005 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.78692 - 6.55913i) q^{17} +(-0.395181 + 0.684473i) q^{18} +(-0.363145 - 0.628985i) q^{19} -3.27192 q^{20} +(-1.86598 + 4.80111i) q^{21} +3.28288 q^{22} +(3.97803 + 6.89014i) q^{23} +(-0.973442 + 1.68605i) q^{24} +(-2.85273 + 4.94108i) q^{25} +(2.76125 + 4.78263i) q^{26} -4.30191 q^{27} +(-0.958446 + 2.46605i) q^{28} +1.00000 q^{29} +(3.18503 + 5.51663i) q^{30} +(-3.32354 + 5.75653i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.19569 - 5.53510i) q^{33} -7.57383 q^{34} +(5.41972 + 6.75017i) q^{35} +0.790361 q^{36} +(2.55973 + 4.43359i) q^{37} +(-0.363145 + 0.628985i) q^{38} +(5.37584 - 9.31124i) q^{39} +(1.63596 + 2.83357i) q^{40} -4.58090 q^{41} +(5.09087 - 0.784563i) q^{42} +0.209639 q^{43} +(-1.64144 - 2.84306i) q^{44} +(1.29300 - 2.23954i) q^{45} +(3.97803 - 6.89014i) q^{46} +(-2.84470 - 4.92717i) q^{47} +1.94688 q^{48} +(6.67521 - 2.10751i) q^{49} +5.70546 q^{50} +(7.37269 + 12.7699i) q^{51} +(2.76125 - 4.78263i) q^{52} +(2.88506 - 4.99707i) q^{53} +(2.15096 + 3.72557i) q^{54} -10.7413 q^{55} +(2.61488 - 0.402984i) q^{56} +1.41400 q^{57} +(-0.500000 - 0.866025i) q^{58} +(4.26937 - 7.39477i) q^{59} +(3.18503 - 5.51663i) q^{60} +(-0.0756237 - 0.130984i) q^{61} +6.64707 q^{62} +(-1.30918 - 1.63056i) q^{63} +1.00000 q^{64} +(-9.03460 - 15.6484i) q^{65} +(-3.19569 + 5.53510i) q^{66} +(-5.66305 + 9.80869i) q^{67} +(3.78692 + 6.55913i) q^{68} -15.4895 q^{69} +(3.13596 - 8.06870i) q^{70} -1.37636 q^{71} +(-0.395181 - 0.684473i) q^{72} +(2.89713 - 5.01797i) q^{73} +(2.55973 - 4.43359i) q^{74} +(-5.55394 - 9.61971i) q^{75} +0.726289 q^{76} +(-3.14646 + 8.09573i) q^{77} -10.7517 q^{78} +(-0.357577 - 0.619342i) q^{79} +(1.63596 - 2.83357i) q^{80} +(5.37321 - 9.30667i) q^{81} +(2.29045 + 3.96718i) q^{82} +5.49921 q^{83} +(-3.22489 - 4.01654i) q^{84} +24.7810 q^{85} +(-0.104819 - 0.181553i) q^{86} +(-0.973442 + 1.68605i) q^{87} +(-1.64144 + 2.84306i) q^{88} +(-4.50777 - 7.80768i) q^{89} -2.58600 q^{90} +(-14.4407 + 2.22548i) q^{91} -7.95605 q^{92} +(-6.47054 - 11.2073i) q^{93} +(-2.84470 + 4.92717i) q^{94} +(1.18818 - 2.05799i) q^{95} +(-0.973442 - 1.68605i) q^{96} +17.9462 q^{97} +(-5.16276 - 4.72714i) q^{98} +2.59466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + 3 q^{3} - 5 q^{4} + 7 q^{5} - 6 q^{6} - 3 q^{7} + 10 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 + 3 * q^3 - 5 * q^4 + 7 * q^5 - 6 * q^6 - 3 * q^7 + 10 * q^8 - 4 * q^9	\( 10 q - 5 q^{2} + 3 q^{3} - 5 q^{4} + 7 q^{5} - 6 q^{6} - 3 q^{7} + 10 q^{8} - 4 q^{9} + 7 q^{10} + 3 q^{12} - 16 q^{13} + 3 q^{14} + 8 q^{15} - 5 q^{16} + 16 q^{17} - 4 q^{18} + 2 q^{19} - 14 q^{20} - 5 q^{21} + 5 q^{23} + 3 q^{24} - 4 q^{25} + 8 q^{26} - 18 q^{27} + 10 q^{29} - 4 q^{30} + 5 q^{31} - 5 q^{32} + 3 q^{33} - 32 q^{34} - 14 q^{35} + 8 q^{36} + 2 q^{38} + 20 q^{39} + 7 q^{40} - 34 q^{41} + 16 q^{42} + 2 q^{43} + 14 q^{45} + 5 q^{46} - 4 q^{47} - 6 q^{48} + q^{49} + 8 q^{50} + 3 q^{51} + 8 q^{52} - 5 q^{53} + 9 q^{54} - 24 q^{55} - 3 q^{56} + 12 q^{57} - 5 q^{58} + 17 q^{59} - 4 q^{60} + 13 q^{61} - 10 q^{62} - 11 q^{63} + 10 q^{64} + 7 q^{65} + 3 q^{66} + 14 q^{67} + 16 q^{68} - 32 q^{69} + 22 q^{70} - 16 q^{71} - 4 q^{72} + 6 q^{73} + 8 q^{75} - 4 q^{76} - 35 q^{77} - 40 q^{78} - 11 q^{79} + 7 q^{80} + 19 q^{81} + 17 q^{82} - 4 q^{83} - 11 q^{84} + 78 q^{85} - q^{86} + 3 q^{87} + 9 q^{89} - 28 q^{90} - 30 q^{91} - 10 q^{92} + 3 q^{93} - 4 q^{94} + 13 q^{95} + 3 q^{96} - 24 q^{97} + 4 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 + 3 * q^3 - 5 * q^4 + 7 * q^5 - 6 * q^6 - 3 * q^7 + 10 * q^8 - 4 * q^9 + 7 * q^10 + 3 * q^12 - 16 * q^13 + 3 * q^14 + 8 * q^15 - 5 * q^16 + 16 * q^17 - 4 * q^18 + 2 * q^19 - 14 * q^20 - 5 * q^21 + 5 * q^23 + 3 * q^24 - 4 * q^25 + 8 * q^26 - 18 * q^27 + 10 * q^29 - 4 * q^30 + 5 * q^31 - 5 * q^32 + 3 * q^33 - 32 * q^34 - 14 * q^35 + 8 * q^36 + 2 * q^38 + 20 * q^39 + 7 * q^40 - 34 * q^41 + 16 * q^42 + 2 * q^43 + 14 * q^45 + 5 * q^46 - 4 * q^47 - 6 * q^48 + q^49 + 8 * q^50 + 3 * q^51 + 8 * q^52 - 5 * q^53 + 9 * q^54 - 24 * q^55 - 3 * q^56 + 12 * q^57 - 5 * q^58 + 17 * q^59 - 4 * q^60 + 13 * q^61 - 10 * q^62 - 11 * q^63 + 10 * q^64 + 7 * q^65 + 3 * q^66 + 14 * q^67 + 16 * q^68 - 32 * q^69 + 22 * q^70 - 16 * q^71 - 4 * q^72 + 6 * q^73 + 8 * q^75 - 4 * q^76 - 35 * q^77 - 40 * q^78 - 11 * q^79 + 7 * q^80 + 19 * q^81 + 17 * q^82 - 4 * q^83 - 11 * q^84 + 78 * q^85 - q^86 + 3 * q^87 + 9 * q^89 - 28 * q^90 - 30 * q^91 - 10 * q^92 + 3 * q^93 - 4 * q^94 + 13 * q^95 + 3 * q^96 - 24 * q^97 + 4 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/406\mathbb{Z}\right)^\times$.

$n$	$59$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.973442	+	1.68605i	−0.562017	+	0.973442i	0.435303	+	0.900284i	$0.356641\pi$
$3$	−0.973442	+	1.68605i	−0.562017	+	0.973442i	−0.997320	+	0.0731585i	$0.976692\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.63596	+	2.83357i	0.731624	+	1.26721i	0.956189	+	0.292750i	$0.0945705\pi$
$5$	1.63596	+	2.83357i	0.731624	+	1.26721i	−0.224565	+	0.974459i	$0.572096\pi$
$6$	1.94688			0.794812
$7$	2.61488	−	0.402984i	0.988332	−	0.152314i
$7$	2.61488	−	0.402984i	0.988332	−	0.152314i
$8$	1.00000			0.353553
$9$	−0.395181	−	0.684473i	−0.131727	−	0.228158i
$10$	1.63596	−	2.83357i	0.517336	−	0.896052i
$11$	−1.64144	+	2.84306i	−0.494912	+	0.857213i	−0.999983	−	0.00586471i	$-0.998133\pi$
$11$	−1.64144	+	2.84306i	−0.494912	+	0.857213i	0.505070	+	0.863078i	$0.331467\pi$
$12$	−0.973442	−	1.68605i	−0.281009	−	0.486721i
$13$	−5.52251			−1.53167			−0.765834	−	0.643038i	$-0.777674\pi$
$13$	−5.52251			−1.53167			−0.765834	+	0.643038i	$0.777674\pi$
$14$	−1.65643	−	2.06306i	−0.442701	−	0.551376i
$15$	−6.37005			−1.64474
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.78692	−	6.55913i	0.918462	−	1.59082i	0.116710	−	0.993166i	$-0.462765\pi$
$17$	3.78692	−	6.55913i	0.918462	−	1.59082i	0.801752	−	0.597657i	$-0.203902\pi$
$18$	−0.395181	+	0.684473i	−0.0931450	+	0.161332i
$19$	−0.363145	−	0.628985i	−0.0833111	−	0.144299i	0.821359	−	0.570411i	$-0.193216\pi$
$19$	−0.363145	−	0.628985i	−0.0833111	−	0.144299i	−0.904670	+	0.426112i	$0.859883\pi$
$20$	−3.27192			−0.731624
$21$	−1.86598	+	4.80111i	−0.407191	+	1.04769i
$22$	3.28288			0.699912
$23$	3.97803	+	6.89014i	0.829476	+	1.43669i	0.898450	+	0.439076i	$0.144694\pi$
$23$	3.97803	+	6.89014i	0.829476	+	1.43669i	−0.0689744	+	0.997618i	$0.521973\pi$
$24$	−0.973442	+	1.68605i	−0.198703	+	0.344164i
$25$	−2.85273	+	4.94108i	−0.570546	+	0.988215i
$26$	2.76125	+	4.78263i	0.541527	+	0.937951i
$27$	−4.30191			−0.827903
$28$	−0.958446	+	2.46605i	−0.181129	+	0.466039i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	3.18503	+	5.51663i	0.581504	+	1.00719i
$31$	−3.32354	+	5.75653i	−0.596925	+	1.03390i	0.396347	+	0.918101i	$0.370278\pi$
$31$	−3.32354	+	5.75653i	−0.596925	+	1.03390i	−0.993272	+	0.115803i	$0.963056\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.19569	−	5.53510i	−0.556299	−	0.963538i
$34$	−7.57383			−1.29890
$35$	5.41972	+	6.75017i	0.916100	+	1.14099i
$36$	0.790361			0.131727
$37$	2.55973	+	4.43359i	0.420817	+	0.728877i	0.996020	−	0.0891341i	$-0.0284100\pi$
$37$	2.55973	+	4.43359i	0.420817	+	0.728877i	−0.575202	+	0.818011i	$0.695077\pi$
$38$	−0.363145	+	0.628985i	−0.0589098	+	0.102035i
$39$	5.37584	−	9.31124i	0.860824	−	1.49099i
$40$	1.63596	+	2.83357i	0.258668	+	0.448026i
$41$	−4.58090			−0.715416			−0.357708	−	0.933833i	$-0.616442\pi$
$41$	−4.58090			−0.715416			−0.357708	+	0.933833i	$0.616442\pi$
$42$	5.09087	−	0.784563i	0.785539	−	0.121061i
$43$	0.209639			0.0319696			0.0159848	−	0.999872i	$-0.494912\pi$
$43$	0.209639			0.0319696			0.0159848	+	0.999872i	$0.494912\pi$
$44$	−1.64144	−	2.84306i	−0.247456	−	0.428607i
$45$	1.29300	−	2.23954i	0.192749	−	0.333851i
$46$	3.97803	−	6.89014i	0.586528	−	1.01590i
$47$	−2.84470	−	4.92717i	−0.414943	−	0.718702i	0.580480	−	0.814275i	$-0.302865\pi$
$47$	−2.84470	−	4.92717i	−0.414943	−	0.718702i	−0.995422	+	0.0955729i	$0.969532\pi$
$48$	1.94688			0.281009
$49$	6.67521	−	2.10751i	0.953601	−	0.301073i
$50$	5.70546			0.806874
$51$	7.37269	+	12.7699i	1.03238	+	1.78814i
$52$	2.76125	−	4.78263i	0.382917	−	0.663232i
$53$	2.88506	−	4.99707i	0.396293	−	0.686400i	−0.596972	−	0.802262i	$-0.703630\pi$
$53$	2.88506	−	4.99707i	0.396293	−	0.686400i	0.993265	+	0.115862i	$0.0369630\pi$
$54$	2.15096	+	3.72557i	0.292708	+	0.506985i
$55$	−10.7413			−1.44836
$56$	2.61488	−	0.402984i	0.349428	−	0.0538510i
$57$	1.41400			0.187289
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$	4.26937	−	7.39477i	0.555825	−	0.962717i	−0.442014	−	0.897008i	$-0.645736\pi$
$59$	4.26937	−	7.39477i	0.555825	−	0.962717i	0.997839	−	0.0657086i	$-0.0209308\pi$
$60$	3.18503	−	5.51663i	0.411185	−	0.712194i
$61$	−0.0756237	−	0.130984i	−0.00968262	−	0.0167708i	0.861143	−	0.508362i	$-0.169749\pi$
$61$	−0.0756237	−	0.130984i	−0.00968262	−	0.0167708i	−0.870826	+	0.491591i	$0.836415\pi$
$62$	6.64707			0.844179
$63$	−1.30918	−	1.63056i	−0.164941	−	0.205432i
$64$	1.00000			0.125000
$65$	−9.03460	−	15.6484i	−1.12060	−	1.94094i
$66$	−3.19569	+	5.53510i	−0.393363	+	0.681324i
$67$	−5.66305	+	9.80869i	−0.691852	+	1.19832i	0.279378	+	0.960181i	$0.409872\pi$
$67$	−5.66305	+	9.80869i	−0.691852	+	1.19832i	−0.971230	+	0.238142i	$0.923462\pi$
$68$	3.78692	+	6.55913i	0.459231	+	0.795412i
$69$	−15.4895			−1.86472
$70$	3.13596	−	8.06870i	0.374819	−	0.964395i
$71$	−1.37636			−0.163344			−0.0816719	−	0.996659i	$-0.526026\pi$
$71$	−1.37636			−0.163344			−0.0816719	+	0.996659i	$0.526026\pi$
$72$	−0.395181	−	0.684473i	−0.0465725	−	0.0806659i
$73$	2.89713	−	5.01797i	0.339083	−	0.587309i	−0.645178	−	0.764033i	$-0.723217\pi$
$73$	2.89713	−	5.01797i	0.339083	−	0.587309i	0.984260	+	0.176724i	$0.0565499\pi$
$74$	2.55973	−	4.43359i	0.297563	−	0.515394i
$75$	−5.55394	−	9.61971i	−0.641314	−	1.11079i
$76$	0.726289			0.0833111
$77$	−3.14646	+	8.09573i	−0.358573	+	0.922594i
$78$	−10.7517			−1.21739
$79$	−0.357577	−	0.619342i	−0.0402306	−	0.0696814i	0.845209	−	0.534436i	$-0.179476\pi$
$79$	−0.357577	−	0.619342i	−0.0402306	−	0.0696814i	−0.885440	+	0.464755i	$0.846143\pi$
$80$	1.63596	−	2.83357i	0.182906	−	0.316802i
$81$	5.37321	−	9.30667i	0.597023	−	1.03407i
$82$	2.29045	+	3.96718i	0.252938	+	0.438101i
$83$	5.49921			0.603617			0.301808	−	0.953369i	$-0.402410\pi$
$83$	5.49921			0.603617			0.301808	+	0.953369i	$0.402410\pi$
$84$	−3.22489	−	4.01654i	−0.351864	−	0.438241i
$85$	24.7810			2.68787
$86$	−0.104819	−	0.181553i	−0.0113030	−	0.0195773i
$87$	−0.973442	+	1.68605i	−0.104364	+	0.180764i
$88$	−1.64144	+	2.84306i	−0.174978	+	0.303071i
$89$	−4.50777	−	7.80768i	−0.477822	−	0.827612i	0.521855	−	0.853034i	$-0.325240\pi$
$89$	−4.50777	−	7.80768i	−0.477822	−	0.827612i	−0.999677	+	0.0254221i	$0.991907\pi$
$90$	−2.58600			−0.272588
$91$	−14.4407	+	2.22548i	−1.51380	+	0.233294i
$92$	−7.95605			−0.829476
$93$	−6.47054	−	11.2073i	−0.670964	−	1.16214i
$94$	−2.84470	+	4.92717i	−0.293409	+	0.508199i
$95$	1.18818	−	2.05799i	0.121905	−	0.211145i
$96$	−0.973442	−	1.68605i	−0.0993516	−	0.172082i
$97$	17.9462			1.82216			0.911078	−	0.412233i	$-0.135251\pi$
$97$	17.9462			1.82216			0.911078	+	0.412233i	$0.135251\pi$
$98$	−5.16276	−	4.72714i	−0.521518	−	0.477514i
$99$	2.59466			0.260773
$100$	−2.85273	−	4.94108i	−0.285273	−	0.494108i
$101$	5.49850	−	9.52368i	0.547121	−	0.947642i	−0.451349	−	0.892348i	$-0.649057\pi$
$101$	5.49850	−	9.52368i	0.547121	−	0.947642i	0.998470	−	0.0552942i	$-0.0176097\pi$
$102$	7.37269	−	12.7699i	0.730005	−	1.26441i
$103$	8.63042	+	14.9483i	0.850381	+	1.47290i	0.880865	+	0.473367i	$0.156962\pi$
$103$	8.63042	+	14.9483i	0.850381	+	1.47290i	−0.0304844	+	0.999535i	$0.509705\pi$
$104$	−5.52251			−0.541527
$105$	−16.6569	+	2.56703i	−1.62555	+	0.250516i
$106$	−5.77012			−0.560443
$107$	7.48401	+	12.9627i	0.723507	+	1.25315i	0.959586	+	0.281416i	$0.0908042\pi$
$107$	7.48401	+	12.9627i	0.723507	+	1.25315i	−0.236079	+	0.971734i	$0.575862\pi$
$108$	2.15096	−	3.72557i	0.206976	−	0.358493i
$109$	−3.05823	+	5.29701i	−0.292926	+	0.507362i	−0.974500	−	0.224387i	$-0.927962\pi$
$109$	−3.05823	+	5.29701i	−0.292926	+	0.507362i	0.681575	+	0.731749i	$0.261295\pi$
$110$	5.37066	+	9.30225i	0.512072	+	0.886935i
$111$	−9.96701			−0.946027
$112$	−1.65643	−	2.06306i	−0.156518	−	0.194941i
$113$	9.72278			0.914643			0.457321	−	0.889302i	$-0.348809\pi$
$113$	9.72278			0.914643			0.457321	+	0.889302i	$0.348809\pi$
$114$	−0.707001	−	1.22456i	−0.0662167	−	0.114691i
$115$	−13.0158	+	22.5440i	−1.21373	+	2.10224i
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$	2.18239	+	3.78001i	0.201762	+	0.349462i
$118$	−8.53874			−0.786055
$119$	7.25911	−	18.6774i	0.665442	−	1.71216i
$120$	−6.37005			−0.581504
$121$	0.111358	+	0.192877i	0.0101234	+	0.0175343i
$122$	−0.0756237	+	0.130984i	−0.00684665	+	0.0118587i
$123$	4.45924	−	7.72364i	0.402076	−	0.696417i
$124$	−3.32354	−	5.75653i	−0.298462	−	0.516952i
$125$	−2.30822			−0.206453
$126$	−0.757519	+	1.94907i	−0.0674851	+	0.173637i
$127$	−3.95078			−0.350575			−0.175287	−	0.984517i	$-0.556085\pi$
$127$	−3.95078			−0.350575			−0.175287	+	0.984517i	$0.556085\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.204071	+	0.353462i	−0.0179675	+	0.0311206i
$130$	−9.03460	+	15.6484i	−0.792387	+	1.37245i
$131$	1.63596	+	2.83357i	0.142935	+	0.247570i	0.928600	−	0.371081i	$-0.121013\pi$
$131$	1.63596	+	2.83357i	0.142935	+	0.247570i	−0.785666	+	0.618651i	$0.787680\pi$
$132$	6.39138			0.556299
$133$	−1.20305	−	1.49838i	−0.104318	−	0.129926i
$134$	11.3261			0.978426
$135$	−7.03776	−	12.1898i	−0.605714	−	1.04913i
$136$	3.78692	−	6.55913i	0.324725	−	0.562441i
$137$	5.32962	−	9.23117i	0.455340	−	0.788672i	−0.543368	−	0.839495i	$-0.682851\pi$
$137$	5.32962	−	9.23117i	0.455340	−	0.788672i	0.998708	+	0.0508227i	$0.0161844\pi$
$138$	7.74476	+	13.4143i	0.659278	+	1.14190i
$139$	−0.656434			−0.0556780			−0.0278390	−	0.999612i	$-0.508863\pi$
$139$	−0.656434			−0.0556780			−0.0278390	+	0.999612i	$0.508863\pi$
$140$	−8.55568	+	1.31853i	−0.723087	+	0.111436i
$141$	11.0766			0.932820
$142$	0.688180	+	1.19196i	0.0577508	+	0.100027i
$143$	9.06486	−	15.7008i	0.758042	−	1.31297i
$144$	−0.395181	+	0.684473i	−0.0329317	+	0.0570394i
$145$	1.63596	+	2.83357i	0.135859	+	0.235315i
$146$	−5.79425			−0.479536
$147$	−2.94456	+	13.3063i	−0.242863	+	1.09748i
$148$	−5.11946			−0.420817
$149$	−5.08548	−	8.80832i	−0.416619	−	0.721605i	0.578978	−	0.815343i	$-0.303452\pi$
$149$	−5.08548	−	8.80832i	−0.416619	−	0.721605i	−0.995597	+	0.0937379i	$0.970118\pi$
$150$	−5.55394	+	9.61971i	−0.453477	+	0.785446i
$151$	9.81950	−	17.0079i	0.799099	−	1.38408i	−0.121104	−	0.992640i	$-0.538643\pi$
$151$	9.81950	−	17.0079i	0.799099	−	1.38408i	0.920203	−	0.391441i	$-0.128023\pi$
$152$	−0.363145	−	0.628985i	−0.0294549	−	0.0510174i
$153$	−5.98606			−0.483945
$154$	8.58433	−	1.32295i	0.691745	−	0.106606i
$155$	−21.7487			−1.74690
$156$	5.37584	+	9.31124i	0.430412	+	0.745496i
$157$	0.0823397	−	0.142617i	0.00657142	−	0.0113820i	−0.862721	−	0.505680i	$-0.831242\pi$
$157$	0.0823397	−	0.142617i	0.00657142	−	0.0113820i	0.869292	+	0.494298i	$0.164575\pi$
$158$	−0.357577	+	0.619342i	−0.0284473	+	0.0492722i
$159$	5.61688	+	9.72872i	0.445447	+	0.771537i
$160$	−3.27192			−0.258668
$161$	13.1787	+	16.4138i	1.03863	+	1.29359i
$162$	−10.7464			−0.844318
$163$	−7.12907	−	12.3479i	−0.558392	−	0.967163i	−0.997631	−	0.0687930i	$-0.978085\pi$
$163$	−7.12907	−	12.3479i	−0.558392	−	0.967163i	0.439239	−	0.898370i	$-0.355248\pi$
$164$	2.29045	−	3.96718i	0.178854	−	0.309784i
$165$	10.4561	−	18.1104i	0.814003	−	1.40989i
$166$	−2.74960	−	4.76245i	−0.213411	−	0.369638i
$167$	7.63407			0.590742			0.295371	−	0.955383i	$-0.404557\pi$
$167$	7.63407			0.590742			0.295371	+	0.955383i	$0.404557\pi$
$168$	−1.86598	+	4.80111i	−0.143964	+	0.370413i
$169$	17.4981			1.34601
$170$	−12.3905	−	21.4610i	−0.950307	−	1.64598i
$171$	−0.287015	+	0.497125i	−0.0219486	+	0.0380161i
$172$	−0.104819	+	0.181553i	−0.00799241	+	0.0138433i
$173$	6.98694	+	12.1017i	0.531207	+	0.920078i	0.999337	+	0.0364179i	$0.0115947\pi$
$173$	6.98694	+	12.1017i	0.531207	+	0.920078i	−0.468130	+	0.883660i	$0.655072\pi$
$174$	1.94688			0.147593
$175$	−5.46838	+	14.0699i	−0.413371	+	1.06359i
$176$	3.28288			0.247456
$177$	8.31197	+	14.3968i	0.624766	+	1.08213i
$178$	−4.50777	+	7.80768i	−0.337871	+	0.585210i
$179$	−6.26689	+	10.8546i	−0.468409	+	0.811308i	−0.999348	−	0.0361016i	$-0.988506\pi$
$179$	−6.26689	+	10.8546i	−0.468409	+	0.811308i	0.530939	+	0.847410i	$0.321839\pi$
$180$	1.29300	+	2.23954i	0.0963745	+	0.166926i
$181$	−21.3711			−1.58850			−0.794252	−	0.607588i	$-0.792137\pi$
$181$	−21.3711			−1.58850			−0.794252	+	0.607588i	$0.792137\pi$
$182$	9.14768	+	11.3933i	0.678071	+	0.844526i
$183$	0.294461			0.0217672
$184$	3.97803	+	6.89014i	0.293264	+	0.507948i
$185$	−8.37524	+	14.5063i	−0.615760	+	1.06653i
$186$	−6.47054	+	11.2073i	−0.474443	+	0.821760i
$187$	12.4320	+	21.5328i	0.909117	+	1.57464i
$188$	5.68941			0.414943
$189$	−11.2490	+	1.73360i	−0.818244	+	0.126101i
$190$	−2.37636			−0.172399
$191$	3.31013	+	5.73331i	0.239512	+	0.414848i	0.960574	−	0.278023i	$-0.0896791\pi$
$191$	3.31013	+	5.73331i	0.239512	+	0.414848i	−0.721062	+	0.692871i	$0.756346\pi$
$192$	−0.973442	+	1.68605i	−0.0702522	+	0.121680i
$193$	2.02630	−	3.50966i	0.145857	−	0.252631i	−0.783836	−	0.620968i	$-0.786740\pi$
$193$	2.02630	−	3.50966i	0.145857	−	0.252631i	0.929692	+	0.368337i	$0.120073\pi$
$194$	−8.97308	−	15.5418i	−0.644230	−	1.11584i
$195$	35.1787			2.51920
$196$	−1.51245	+	6.83465i	−0.108032	+	0.488190i
$197$	21.1218			1.50487			0.752434	−	0.658668i	$-0.228880\pi$
$197$	21.1218			1.50487			0.752434	+	0.658668i	$0.228880\pi$
$198$	−1.29733	−	2.24704i	−0.0921972	−	0.159690i
$199$	3.61767	−	6.26600i	0.256450	−	0.444185i	−0.708838	−	0.705371i	$-0.750780\pi$
$199$	3.61767	−	6.26600i	0.256450	−	0.444185i	0.965288	+	0.261186i	$0.0841137\pi$
$200$	−2.85273	+	4.94108i	−0.201719	+	0.349387i
$201$	−11.0253	−	19.0964i	−0.777665	−	1.34696i
$202$	−10.9970			−0.773746
$203$	2.61488	−	0.402984i	0.183529	−	0.0282839i
$204$	−14.7454			−1.03238
$205$	−7.49417	−	12.9803i	−0.523416	−	0.906582i
$206$	8.63042	−	14.9483i	0.601310	−	1.04150i
$207$	3.14408	−	5.44570i	0.218528	−	0.378502i
$208$	2.76125	+	4.78263i	0.191459	+	0.331616i
$209$	2.38432			0.164927
$210$	10.5516	+	13.1418i	0.728128	+	0.906871i
$211$	6.76446			0.465684			0.232842	−	0.972515i	$-0.425197\pi$
$211$	6.76446			0.465684			0.232842	+	0.972515i	$0.425197\pi$
$212$	2.88506	+	4.99707i	0.198147	+	0.343200i
$213$	1.33981	−	2.32061i	0.0918021	−	0.159006i
$214$	7.48401	−	12.9627i	0.511596	−	0.886111i
$215$	0.342961	+	0.594026i	0.0233897	+	0.0405122i
$216$	−4.30191			−0.292708
$217$	−6.37086	+	16.3920i	−0.432482	+	1.11276i
$218$	6.11647			0.414259
$219$	5.64037	+	9.76941i	0.381141	+	0.660155i
$220$	5.37066	−	9.30225i	0.362090	−	0.627158i
$221$	−20.9133	+	36.2229i	−1.40678	+	2.43661i
$222$	4.98350	+	8.63168i	0.334471	+	0.579321i
$223$	−23.3248			−1.56195			−0.780973	−	0.624565i	$-0.785276\pi$
$223$	−23.3248			−1.56195			−0.780973	+	0.624565i	$0.785276\pi$
$224$	−0.958446	+	2.46605i	−0.0640389	+	0.164770i
$225$	4.50938			0.300625
$226$	−4.86139	−	8.42018i	−0.323375	−	0.560102i
$227$	13.4625	−	23.3177i	0.893538	−	1.54765i	0.0579339	−	0.998320i	$-0.481549\pi$
$227$	13.4625	−	23.3177i	0.893538	−	1.54765i	0.835604	−	0.549332i	$-0.185118\pi$
$228$	−0.707001	+	1.22456i	−0.0468223	+	0.0810985i
$229$	−4.93851	−	8.55374i	−0.326346	−	0.565247i	0.655438	−	0.755249i	$-0.272484\pi$
$229$	−4.93851	−	8.55374i	−0.326346	−	0.565247i	−0.981784	+	0.190002i	$0.939151\pi$
$230$	26.0316			1.71647
$231$	−10.5869	−	13.1858i	−0.696568	−	0.867563i
$232$	1.00000			0.0656532
$233$	4.22649	+	7.32050i	0.276887	+	0.479582i	0.970609	−	0.240660i	$-0.0773640\pi$
$233$	4.22649	+	7.32050i	0.276887	+	0.479582i	−0.693723	+	0.720242i	$0.744031\pi$
$234$	2.18239	−	3.78001i	0.142667	−	0.247107i
$235$	9.30764	−	16.1213i	0.607164	−	1.05164i
$236$	4.26937	+	7.39477i	0.277912	+	0.481358i
$237$	1.39232			0.0904411
$238$	−19.8047	+	3.05213i	−1.28375	+	0.197840i
$239$	10.6075			0.686141			0.343071	−	0.939310i	$-0.388533\pi$
$239$	10.6075			0.686141			0.343071	+	0.939310i	$0.388533\pi$
$240$	3.18503	+	5.51663i	0.205593	+	0.356097i
$241$	−13.6018	+	23.5590i	−0.876167	+	1.51757i	−0.0206527	+	0.999787i	$0.506574\pi$
$241$	−13.6018	+	23.5590i	−0.876167	+	1.51757i	−0.855514	+	0.517779i	$0.826759\pi$
$242$	0.111358	−	0.192877i	0.00715833	−	0.0123986i
$243$	4.00815	+	6.94231i	0.257123	+	0.445350i
$244$	0.151247			0.00968262
$245$	16.8921	+	15.4668i	1.07920	+	0.988140i
$246$	−8.91849			−0.568622
$247$	2.00547	+	3.47357i	0.127605	+	0.221018i
$248$	−3.32354	+	5.75653i	−0.211045	+	0.365540i
$249$	−5.35316	+	9.27195i	−0.339243	+	0.587586i
$250$	1.15411	+	1.99898i	0.0729923	+	0.126426i
$251$	19.4237			1.22601			0.613005	−	0.790079i	$-0.289960\pi$
$251$	19.4237			1.22601			0.613005	+	0.790079i	$0.289960\pi$
$252$	2.06670	−	0.318503i	0.130190	−	0.0200638i
$253$	−26.1187			−1.64207
$254$	1.97539	+	3.42147i	0.123947	+	0.214682i
$255$	−24.1229	+	41.7820i	−1.51063	+	2.61649i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.1942	−	22.8531i	−0.823034	−	1.42554i	−0.903413	−	0.428772i	$-0.858947\pi$
$257$	−13.1942	−	22.8531i	−0.823034	−	1.42554i	0.0803794	−	0.996764i	$-0.474387\pi$
$258$	0.408143			0.0254099
$259$	8.48006	+	10.5618i	0.526925	+	0.656277i
$260$	18.0692			1.12060
$261$	−0.395181	−	0.684473i	−0.0244611	−	0.0423678i
$262$	1.63596	−	2.83357i	0.101070	−	0.175058i
$263$	4.21342	−	7.29785i	0.259810	−	0.450005i	−0.706381	−	0.707832i	$-0.749673\pi$
$263$	4.21342	−	7.29785i	0.259810	−	0.450005i	0.966191	+	0.257827i	$0.0830066\pi$
$264$	−3.19569	−	5.53510i	−0.196681	−	0.340662i
$265$	18.8794			1.15975
$266$	−0.696109	+	1.79106i	−0.0426812	+	0.109817i
$267$	17.5522			1.07418
$268$	−5.66305	−	9.80869i	−0.345926	−	0.599161i
$269$	3.58697	−	6.21282i	0.218702	−	0.378802i	−0.735710	−	0.677297i	$-0.763151\pi$
$269$	3.58697	−	6.21282i	0.218702	−	0.378802i	0.954411	+	0.298495i	$0.0964845\pi$
$270$	−7.03776	+	12.1898i	−0.428304	+	0.741845i
$271$	−6.59928	−	11.4303i	−0.400878	−	0.694341i	0.592954	−	0.805236i	$-0.297961\pi$
$271$	−6.59928	−	11.4303i	−0.400878	−	0.694341i	−0.993832	+	0.110895i	$0.964628\pi$
$272$	−7.57383			−0.459231
$273$	10.3049	−	26.5142i	0.623682	−	1.60471i
$274$	−10.6592			−0.643948
$275$	−9.36517	−	16.2209i	−0.564741	−	0.978160i
$276$	7.74476	−	13.4143i	0.466180	−	0.807447i
$277$	−0.563078	+	0.975280i	−0.0338321	+	0.0585989i	−0.882446	−	0.470414i	$-0.844104\pi$
$277$	−0.563078	+	0.975280i	−0.0338321	+	0.0585989i	0.848614	+	0.529013i	$0.177438\pi$
$278$	0.328217	+	0.568488i	0.0196851	+	0.0340957i
$279$	5.25359			0.314524
$280$	5.41972	+	6.75017i	0.323890	+	0.403400i
$281$	−23.4326			−1.39787			−0.698935	−	0.715185i	$-0.746342\pi$
$281$	−23.4326			−1.39787			−0.698935	+	0.715185i	$0.746342\pi$
$282$	−5.53831	−	9.59264i	−0.329802	−	0.571233i
$283$	−6.79613	+	11.7712i	−0.403988	+	0.699728i	−0.994203	−	0.107518i	$-0.965710\pi$
$283$	−6.79613	+	11.7712i	−0.403988	+	0.699728i	0.590215	+	0.807246i	$0.299043\pi$
$284$	0.688180	−	1.19196i	0.0408360	−	0.0707300i
$285$	2.31325	+	4.00667i	0.137025	+	0.237334i
$286$	−18.1297			−1.07203
$287$	−11.9785	+	1.84603i	−0.707069	+	0.108968i
$288$	0.790361			0.0465725
$289$	−20.1815	−	34.9553i	−1.18715	−	2.05620i
$290$	1.63596	−	2.83357i	0.0960669	−	0.166393i
$291$	−17.4696	+	30.2582i	−1.02408	+	1.77376i
$292$	2.89713	+	5.01797i	0.169541	+	0.293654i
$293$	11.5465			0.674555			0.337278	−	0.941405i	$-0.390494\pi$
$293$	11.5465			0.674555			0.337278	+	0.941405i	$0.390494\pi$
$294$	12.9959	−	4.10308i	0.757934	−	0.239296i
$295$	27.9381			1.62662
$296$	2.55973	+	4.43359i	0.148781	+	0.257697i
$297$	7.06133	−	12.2306i	0.409740	−	0.709690i
$298$	−5.08548	+	8.80832i	−0.294594	+	0.510252i
$299$	−21.9687	−	38.0509i	−1.27048	−	2.20054i
$300$	11.1079			0.641314
$301$	0.548181	−	0.0844811i	0.0315966	−	0.00486941i
$302$	−19.6390			−1.13010
$303$	10.7049	+	18.5415i	0.614983	+	1.06518i
$304$	−0.363145	+	0.628985i	−0.0208278	+	0.0360747i
$305$	0.247435	−	0.428569i	0.0141681	−	0.0245398i
$306$	2.99303	+	5.18408i	0.171100	+	0.296354i
$307$	−13.7316			−0.783705			−0.391853	−	0.920028i	$-0.628166\pi$
$307$	−13.7316			−0.783705			−0.391853	+	0.920028i	$0.628166\pi$
$308$	−5.43787	−	6.77278i	−0.309852	−	0.385915i
$309$	−33.6049			−1.91171
$310$	10.8743	+	18.8349i	0.617621	+	1.06975i
$311$	−11.8714	+	20.5619i	−0.673166	+	1.16596i	0.303835	+	0.952725i	$0.401733\pi$
$311$	−11.8714	+	20.5619i	−0.673166	+	1.16596i	−0.977001	+	0.213233i	$0.931601\pi$
$312$	5.37584	−	9.31124i	0.304347	−	0.527145i
$313$	3.29573	+	5.70837i	0.186285	+	0.322656i	0.944009	−	0.329920i	$-0.107022\pi$
$313$	3.29573	+	5.70837i	0.186285	+	0.322656i	−0.757723	+	0.652576i	$0.773688\pi$
$314$	−0.164679			−0.00929339
$315$	2.47854	−	6.37719i	0.139650	−	0.359314i
$316$	0.715154			0.0402306
$317$	9.68786	+	16.7799i	0.544124	+	0.942451i	0.998661	+	0.0517231i	$0.0164713\pi$
$317$	9.68786	+	16.7799i	0.544124	+	0.942451i	−0.454537	+	0.890728i	$0.650195\pi$
$318$	5.61688	−	9.72872i	0.314979	−	0.545559i
$319$	−1.64144	+	2.84306i	−0.0919029	+	0.159181i
$320$	1.63596	+	2.83357i	0.0914530	+	0.158401i
$321$	−29.1410			−1.62649
$322$	7.62545	−	19.6200i	0.424950	−	1.09338i
$323$	−5.50079			−0.306072
$324$	5.37321	+	9.30667i	0.298511	+	0.517037i
$325$	15.7542	−	27.2871i	0.873888	−	1.51362i
$326$	−7.12907	+	12.3479i	−0.394843	+	0.683888i
$327$	−5.95403	−	10.3127i	−0.329258	−	0.570292i
$328$	−4.58090			−0.252938
$329$	−9.42413	−	11.7376i	−0.519569	−	0.647115i
$330$	−20.9121			−1.15117
$331$	−4.04245	−	7.00173i	−0.222193	−	0.384850i	0.733281	−	0.679926i	$-0.237988\pi$
$331$	−4.04245	−	7.00173i	−0.222193	−	0.384850i	−0.955474	+	0.295076i	$0.904655\pi$
$332$	−2.74960	+	4.76245i	−0.150904	+	0.261374i
$333$	2.02311	−	3.50413i	0.110866	−	0.192025i
$334$	−3.81704	−	6.61130i	−0.208859	−	0.361754i
$335$	−37.0581			−2.02470
$336$	5.09087	−	0.784563i	0.277730	−	0.0428014i
$337$	4.71806			0.257009			0.128505	−	0.991709i	$-0.458982\pi$
$337$	4.71806			0.257009			0.128505	+	0.991709i	$0.458982\pi$
$338$	−8.74905	−	15.1538i	−0.475886	−	0.824258i
$339$	−9.46457	+	16.3931i	−0.514045	+	0.890352i
$340$	−12.3905	+	21.4610i	−0.671969	+	1.16388i
$341$	−10.9108	−	18.8980i	−0.590851	−	1.02338i
$342$	0.574031			0.0310400
$343$	16.6056	−	8.20089i	0.896617	−	0.442806i
$344$	0.209639			0.0113030
$345$	−25.3402	−	43.8906i	−1.36427	−	2.36299i
$346$	6.98694	−	12.1017i	0.375620	−	0.650593i
$347$	7.13844	−	12.3641i	0.383212	−	0.663742i	−0.608308	−	0.793701i	$-0.708151\pi$
$347$	7.13844	−	12.3641i	0.383212	−	0.663742i	0.991519	+	0.129959i	$0.0414847\pi$
$348$	−0.973442	−	1.68605i	−0.0521820	−	0.0903819i
$349$	12.2263			0.654457			0.327228	−	0.944945i	$-0.393885\pi$
$349$	12.2263			0.654457			0.327228	+	0.944945i	$0.393885\pi$
$350$	14.9191	−	2.29921i	0.797460	−	0.122898i
$351$	23.7574			1.26807
$352$	−1.64144	−	2.84306i	−0.0874890	−	0.151535i
$353$	−15.8825	+	27.5093i	−0.845339	+	1.46417i	0.0399872	+	0.999200i	$0.487268\pi$
$353$	−15.8825	+	27.5093i	−0.845339	+	1.46417i	−0.885326	+	0.464970i	$0.846065\pi$
$354$	8.31197	−	14.3968i	0.441776	−	0.765179i
$355$	−2.25167	−	3.90001i	−0.119506	−	0.206991i
$356$	9.01553			0.477822
$357$	24.4248	+	30.4206i	1.29270	+	1.61003i
$358$	12.5338			0.662431
$359$	3.20645	+	5.55373i	0.169230	+	0.293115i	0.938149	−	0.346231i	$-0.112539\pi$
$359$	3.20645	+	5.55373i	0.169230	+	0.293115i	−0.768919	+	0.639346i	$0.779205\pi$
$360$	1.29300	−	2.23954i	0.0681471	−	0.118034i
$361$	9.23625	−	15.9977i	0.486119	−	0.841982i
$362$	10.6856	+	18.5080i	0.561621	+	0.972756i
$363$	−0.433601			−0.0227581
$364$	5.29303	−	13.6188i	0.277430	−	0.713817i
$365$	18.9583			0.992324
$366$	−0.147231	−	0.255011i	−0.00769587	−	0.0133296i
$367$	5.68961	−	9.85469i	0.296995	−	0.514411i	−0.678452	−	0.734645i	$-0.737349\pi$
$367$	5.68961	−	9.85469i	0.296995	−	0.514411i	0.975447	+	0.220234i	$0.0706821\pi$
$368$	3.97803	−	6.89014i	0.207369	−	0.359174i
$369$	1.81028	+	3.13550i	0.0942396	+	0.163228i
$370$	16.7505			0.870816
$371$	5.53035	−	14.2294i	0.287121	−	0.738752i
$372$	12.9411			0.670964
$373$	−0.679595	−	1.17709i	−0.0351881	−	0.0609476i	0.847895	−	0.530164i	$-0.177870\pi$
$373$	−0.679595	−	1.17709i	−0.0351881	−	0.0609476i	−0.883083	+	0.469217i	$0.844536\pi$
$374$	12.4320	−	21.5328i	0.642843	−	1.11344i
$375$	2.24692	−	3.89178i	0.116030	−	0.200971i
$376$	−2.84470	−	4.92717i	−0.146704	−	0.254099i
$377$	−5.52251			−0.284424
$378$	7.12584	+	8.87511i	0.366514	+	0.456486i
$379$	1.85052			0.0950550			0.0475275	−	0.998870i	$-0.484866\pi$
$379$	1.85052			0.0950550			0.0475275	+	0.998870i	$0.484866\pi$
$380$	1.18818	+	2.05799i	0.0609523	+	0.105573i
$381$	3.84585	−	6.66121i	0.197029	−	0.341264i
$382$	3.31013	−	5.73331i	0.169361	−	0.293342i
$383$	8.99158	+	15.5739i	0.459448	+	0.795788i	0.998932	−	0.0462082i	$-0.0147138\pi$
$383$	8.99158	+	15.5739i	0.459448	+	0.795788i	−0.539483	+	0.841996i	$0.681380\pi$
$384$	1.94688			0.0993516
$385$	−28.0873	+	4.32858i	−1.43146	+	0.220605i
$386$	−4.05261			−0.206272
$387$	−0.0828452	−	0.143492i	−0.00421126	−	0.00729411i
$388$	−8.97308	+	15.5418i	−0.455539	+	0.789017i
$389$	−4.53760	+	7.85936i	−0.230066	+	0.398485i	−0.957827	−	0.287345i	$-0.907227\pi$
$389$	−4.53760	+	7.85936i	−0.230066	+	0.398485i	0.727762	+	0.685830i	$0.240561\pi$
$390$	−17.5893	−	30.4656i	−0.890671	−	1.54269i
$391$	60.2578			3.04737
$392$	6.67521	−	2.10751i	0.337149	−	0.106445i
$393$	−6.37005			−0.321327
$394$	−10.5609	−	18.2920i	−0.532051	−	0.921539i
$395$	1.16996	−	2.02644i	0.0588673	−	0.101961i
$396$	−1.29733	+	2.24704i	−0.0651933	+	0.112918i
$397$	4.69586	+	8.13346i	0.235678	+	0.408207i	0.959470	−	0.281812i	$-0.0909355\pi$
$397$	4.69586	+	8.13346i	0.235678	+	0.408207i	−0.723791	+	0.690019i	$0.757602\pi$
$398$	−7.23535			−0.362675
$399$	3.69745	−	0.569820i	0.185104	−	0.0285267i
$400$	5.70546			0.285273
$401$	−9.12997	−	15.8136i	−0.455929	−	0.789692i	0.542812	−	0.839854i	$-0.317360\pi$
$401$	−9.12997	−	15.8136i	−0.455929	−	0.789692i	−0.998741	+	0.0501619i	$0.984026\pi$
$402$	−11.0253	+	19.0964i	−0.549893	+	0.952442i
$403$	18.3543	−	31.7905i	0.914291	−	1.58360i
$404$	5.49850	+	9.52368i	0.273561	+	0.473821i
$405$	35.1614			1.74718
$406$	−1.65643	−	2.06306i	−0.0822075	−	0.102388i
$407$	−16.8066			−0.833071
$408$	7.37269	+	12.7699i	0.365003	+	0.632203i
$409$	−18.6008	+	32.2174i	−0.919748	+	1.59305i	−0.119951	+	0.992780i	$0.538274\pi$
$409$	−18.6008	+	32.2174i	−0.919748	+	1.59305i	−0.799797	+	0.600270i	$0.795060\pi$
$410$	−7.49417	+	12.9803i	−0.370111	+	0.641051i
$411$	10.3762	+	17.9720i	0.511818	+	0.886495i
$412$	−17.2608			−0.850381
$413$	8.18393	−	21.0569i	0.402705	−	1.03614i
$414$	−6.28815			−0.309046
$415$	8.99649	+	15.5824i	0.441620	+	0.764908i
$416$	2.76125	−	4.78263i	0.135382	−	0.234488i
$417$	0.639001	−	1.10678i	0.0312920	−	0.0541993i
$418$	−1.19216	−	2.06488i	−0.0583104	−	0.100997i
$419$	−15.7480			−0.769339			−0.384669	−	0.923054i	$-0.625685\pi$
$419$	−15.7480			−0.769339			−0.384669	+	0.923054i	$0.625685\pi$
$420$	6.10535	−	15.7088i	0.297911	−	0.766513i
$421$	−17.7989			−0.867463			−0.433732	−	0.901042i	$-0.642803\pi$
$421$	−17.7989			−0.867463			−0.433732	+	0.901042i	$0.642803\pi$
$422$	−3.38223	−	5.85819i	−0.164644	−	0.285172i
$423$	−2.24834	+	3.89424i	−0.109318	+	0.189345i
$424$	2.88506	−	4.99707i	0.140111	−	0.242679i
$425$	21.6061	+	37.4229i	1.04805	+	1.81528i
$426$	−2.67961			−0.129828
$427$	−0.250531	−	0.312033i	−0.0121241	−	0.0151003i
$428$	−14.9680			−0.723507
$429$	17.6482	+	30.5676i	0.852065	+	1.47582i
$430$	0.342961	−	0.594026i	0.0165390	−	0.0286465i
$431$	9.21865	−	15.9672i	0.444047	−	0.769111i	−0.553939	−	0.832557i	$-0.686876\pi$
$431$	9.21865	−	15.9672i	0.444047	−	0.769111i	0.997985	+	0.0634462i	$0.0202091\pi$
$432$	2.15096	+	3.72557i	0.103488	+	0.179246i
$433$	−9.21863			−0.443019			−0.221509	−	0.975158i	$-0.571098\pi$
$433$	−9.21863			−0.443019			−0.221509	+	0.975158i	$0.571098\pi$
$434$	17.3813	−	2.67866i	0.834329	−	0.128580i
$435$	−6.37005			−0.305421
$436$	−3.05823	−	5.29701i	−0.146463	−	0.253681i
$437$	2.88920	−	5.00424i	0.138209	−	0.239385i
$438$	5.64037	−	9.76941i	0.269507	−	0.466800i
$439$	−6.60539	−	11.4409i	−0.315258	−	0.546043i	0.664234	−	0.747525i	$-0.268758\pi$
$439$	−6.60539	−	11.4409i	−0.315258	−	0.546043i	−0.979492	+	0.201481i	$0.935424\pi$
$440$	−10.7413			−0.512072
$441$	−4.08045	−	3.73615i	−0.194307	−	0.177912i
$442$	41.8266			1.98949
$443$	8.93920	+	15.4831i	0.424714	+	0.735627i	0.996394	−	0.0848505i	$-0.0270413\pi$
$443$	8.93920	+	15.4831i	0.424714	+	0.735627i	−0.571680	+	0.820477i	$0.693708\pi$
$444$	4.98350	−	8.63168i	0.236507	−	0.409642i
$445$	14.7491	−	25.5461i	0.699172	−	1.21100i
$446$	11.6624	+	20.1999i	0.552231	+	0.956492i
$447$	19.8017			0.936588
$448$	2.61488	−	0.402984i	0.123542	−	0.0190392i
$449$	−15.8464			−0.747836			−0.373918	−	0.927462i	$-0.621986\pi$
$449$	−15.8464			−0.747836			−0.373918	+	0.927462i	$0.621986\pi$
$450$	−2.25469	−	3.90523i	−0.106287	−	0.184095i
$451$	7.51927	−	13.0238i	0.354068	−	0.613265i
$452$	−4.86139	+	8.42018i	−0.228661	+	0.396052i
$453$	19.1174	+	33.1124i	0.898215	+	1.55575i
$454$	−26.9250			−1.26365
$455$	−29.9305	−	37.2779i	−1.40316	−	1.74761i
$456$	1.41400			0.0662167
$457$	−5.76090	−	9.97818i	−0.269484	−	0.466759i	0.699245	−	0.714882i	$-0.253520\pi$
$457$	−5.76090	−	9.97818i	−0.269484	−	0.466759i	−0.968729	+	0.248123i	$0.920186\pi$
$458$	−4.93851	+	8.55374i	−0.230761	+	0.399690i
$459$	−16.2910	+	28.2168i	−0.760398	+	1.31705i
$460$	−13.0158	−	22.5440i	−0.606864	−	1.05112i
$461$	−16.6699			−0.776394			−0.388197	−	0.921576i	$-0.626902\pi$
$461$	−16.6699			−0.776394			−0.388197	+	0.921576i	$0.626902\pi$
$462$	−6.12580	+	15.7614i	−0.284998	+	0.733289i
$463$	3.57103			0.165960			0.0829800	−	0.996551i	$-0.473556\pi$
$463$	3.57103			0.165960			0.0829800	+	0.996551i	$0.473556\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$	21.1711	−	36.6694i	0.981786	−	1.70050i
$466$	4.22649	−	7.32050i	0.195788	−	0.339115i
$467$	−15.0223	−	26.0194i	−0.695151	−	1.20404i	−0.970130	−	0.242586i	$-0.922004\pi$
$467$	−15.0223	−	26.0194i	−0.695151	−	1.20404i	0.274979	−	0.961450i	$-0.411329\pi$
$468$	−4.36478			−0.201762
$469$	−10.8555	+	27.9307i	−0.501259	+	1.28972i
$470$	−18.6153			−0.858659
$471$	0.160306	+	0.277658i	0.00738650	+	0.0127938i
$472$	4.26937	−	7.39477i	0.196514	−	0.340372i
$473$	−0.344109	+	0.596015i	−0.0158222	+	0.0274048i
$474$	−0.696161	−	1.20579i	−0.0319757	−	0.0553836i
$475$	4.14382			0.190131
$476$	12.5456	+	15.6253i	0.575025	+	0.716184i
$477$	−4.56048			−0.208810
$478$	−5.30374	−	9.18636i	−0.242588	−	0.420174i
$479$	3.72063	−	6.44432i	0.170000	−	0.294449i	−0.768420	−	0.639946i	$-0.778957\pi$
$479$	3.72063	−	6.44432i	0.170000	−	0.294449i	0.938420	+	0.345498i	$0.112290\pi$
$480$	3.18503	−	5.51663i	0.145376	−	0.251798i
$481$	−14.1361	−	24.4845i	−0.644553	−	1.11640i
$482$	27.2035			1.23909
$483$	−40.5032	+	6.24203i	−1.84296	+	0.284022i
$484$	−0.222715			−0.0101234
$485$	29.3592	+	50.8516i	1.33313	+	2.30905i
$486$	4.00815	−	6.94231i	0.181813	−	0.314910i
$487$	−5.63683	+	9.76328i	−0.255429	+	0.442416i	−0.965012	−	0.262206i	$-0.915550\pi$
$487$	−5.63683	+	9.76328i	−0.255429	+	0.442416i	0.709583	+	0.704622i	$0.248883\pi$
$488$	−0.0756237	−	0.130984i	−0.00342332	−	0.00592937i
$489$	27.7590			1.25530
$490$	4.94861	−	22.3624i	0.223555	−	1.01023i
$491$	−36.6241			−1.65282			−0.826411	−	0.563067i	$-0.809621\pi$
$491$	−36.6241			−1.65282			−0.826411	+	0.563067i	$0.809621\pi$
$492$	4.45924	+	7.72364i	0.201038	+	0.348208i
$493$	3.78692	−	6.55913i	0.170554	−	0.295408i
$494$	2.00547	−	3.47357i	0.0902303	−	0.156283i
$495$	4.24476	+	7.35214i	0.190788	+	0.330454i
$496$	6.64707			0.298462
$497$	−3.59902	+	0.554651i	−0.161438	+	0.0248795i
$498$	10.7063			0.479762
$499$	−8.95633	−	15.5128i	−0.400940	−	0.694449i	0.592899	−	0.805277i	$-0.297983\pi$
$499$	−8.95633	−	15.5128i	−0.400940	−	0.694449i	−0.993840	+	0.110828i	$0.964650\pi$
$500$	1.15411	−	1.99898i	0.0516134	−	0.0893970i
$501$	−7.43133	+	12.8714i	−0.332007	+	0.575054i
$502$	−9.71183	−	16.8214i	−0.433460	−	0.750775i
$503$	−15.1356			−0.674862			−0.337431	−	0.941350i	$-0.609558\pi$
$503$	−15.1356			−0.674862			−0.337431	+	0.941350i	$0.609558\pi$
$504$	−1.30918	−	1.63056i	−0.0583156	−	0.0726311i
$505$	35.9813			1.60115
$506$	13.0594	+	22.6195i	0.580560	+	1.00556i
$507$	−17.0334	+	29.5027i	−0.756480	+	1.31026i
$508$	1.97539	−	3.42147i	0.0876436	−	0.151803i
$509$	2.72723	+	4.72370i	0.120882	+	0.209375i	0.920116	−	0.391646i	$-0.128094\pi$
$509$	2.72723	+	4.72370i	0.120882	+	0.209375i	−0.799233	+	0.601021i	$0.794761\pi$
$510$	48.2457			2.13636
$511$	5.55348	−	14.2889i	0.245671	−	0.632103i
$512$	1.00000			0.0441942
$513$	1.56222	+	2.70584i	0.0689735	+	0.119466i
$514$	−13.1942	+	22.8531i	−0.581973	+	1.00801i
$515$	−28.2381	+	48.9097i	−1.24432	+	2.15522i
$516$	−0.204071	−	0.353462i	−0.00898374	−	0.0155603i
$517$	18.6776			0.821441
$518$	4.90673	−	12.6248i	0.215589	−	0.554703i
$519$	−27.2055			−1.19419
$520$	−9.03460	−	15.6484i	−0.396194	−	0.686227i
$521$	11.2685	−	19.5176i	0.493680	−	0.855080i	−0.506293	−	0.862362i	$-0.668985\pi$
$521$	11.2685	−	19.5176i	0.493680	−	0.855080i	0.999973	+	0.00728187i	$0.00231791\pi$
$522$	−0.395181	+	0.684473i	−0.0172966	+	0.0299586i
$523$	−16.7708	−	29.0479i	−0.733335	−	1.27017i	−0.955450	−	0.295154i	$-0.904629\pi$
$523$	−16.7708	−	29.0479i	−0.733335	−	1.27017i	0.222114	−	0.975021i	$-0.428704\pi$
$524$	−3.27192			−0.142935
$525$	−18.3995	−	22.9162i	−0.803019	−	1.00015i
$526$	−8.42683			−0.367427
$527$	25.1719	+	43.5990i	1.09651	+	1.89920i
$528$	−3.19569	+	5.53510i	−0.139075	+	0.240884i
$529$	−20.1494	+	34.8997i	−0.876060	+	1.51738i
$530$	−9.43968	−	16.3500i	−0.410034	−	0.710199i
$531$	−6.74869			−0.292868
$532$	1.89916	−	0.292683i	0.0823390	−	0.0126894i
$533$	25.2981			1.09578
$534$	−8.77610	−	15.2007i	−0.379779	−	0.657797i
$535$	−24.4871	+	42.4129i	−1.05867	+	1.83367i
$536$	−5.66305	+	9.80869i	−0.244607	+	0.423671i
$537$	−12.2009	−	21.1326i	−0.526508	−	0.911939i
$538$	−7.17395			−0.309291
$539$	−4.96518	+	22.4373i	−0.213865	+	0.966444i
$540$	14.0755			0.605714
$541$	12.1678	+	21.0753i	0.523135	+	0.906097i	0.999637	+	0.0269235i	$0.00857104\pi$
$541$	12.1678	+	21.0753i	0.523135	+	0.906097i	−0.476502	+	0.879173i	$0.658096\pi$
$542$	−6.59928	+	11.4303i	−0.283463	+	0.490973i
$543$	20.8036	−	36.0329i	0.892767	−	1.54632i
$544$	3.78692	+	6.55913i	0.162363	+	0.281220i
$545$	−20.0126			−0.857245
$546$	−28.1144	+	4.33276i	−1.20318	+	0.185425i
$547$	0.837618			0.0358139			0.0179070	−	0.999840i	$-0.494300\pi$
$547$	0.837618			0.0358139			0.0179070	+	0.999840i	$0.494300\pi$
$548$	5.32962	+	9.23117i	0.227670	+	0.394336i
$549$	−0.0597700	+	0.103525i	−0.00255092	+	0.00441833i
$550$	−9.36517	+	16.2209i	−0.399332	+	0.691664i
$551$	−0.363145	−	0.628985i	−0.0154705	−	0.0267957i
$552$	−15.4895			−0.659278
$553$	−1.18461	−	1.47541i	−0.0503746	−	0.0627407i
$554$	1.12616			0.0478458
$555$	−16.3056	−	28.2422i	−0.692135	−	1.19881i
$556$	0.328217	−	0.568488i	0.0139195	−	0.0241093i
$557$	15.7566	−	27.2912i	0.667627	−	1.15636i	−0.310938	−	0.950430i	$-0.600643\pi$
$557$	15.7566	−	27.2912i	0.667627	−	1.15636i	0.978566	−	0.205935i	$-0.0660234\pi$
$558$	−2.62679	−	4.54974i	−0.111201	−	0.192606i
$559$	−1.15773			−0.0489669
$560$	3.13596	−	8.06870i	0.132519	−	0.340965i
$561$	−48.4073			−2.04376
$562$	11.7163	+	20.2932i	0.494222	+	0.856017i
$563$	3.47136	−	6.01257i	0.146300	−	0.253400i	−0.783557	−	0.621320i	$-0.786597\pi$
$563$	3.47136	−	6.01257i	0.146300	−	0.253400i	0.929857	+	0.367920i	$0.119930\pi$
$564$	−5.53831	+	9.59264i	−0.233205	+	0.403923i
$565$	15.9061	+	27.5502i	0.669174	+	1.15904i
$566$	13.5923			0.571325
$567$	10.2999	−	26.5011i	0.432553	−	1.11294i
$568$	−1.37636			−0.0577508
$569$	−4.29221	−	7.43432i	−0.179939	−	0.311663i	0.761921	−	0.647670i	$-0.224257\pi$
$569$	−4.29221	−	7.43432i	−0.179939	−	0.311663i	−0.941859	+	0.336007i	$0.890923\pi$
$570$	2.31325	−	4.00667i	0.0968914	−	0.167821i
$571$	6.68561	−	11.5798i	0.279784	−	0.484600i	−0.691547	−	0.722332i	$-0.743070\pi$
$571$	6.68561	−	11.5798i	0.279784	−	0.484600i	0.971331	+	0.237731i	$0.0764038\pi$
$572$	9.06486	+	15.7008i	0.379021	+	0.656483i
$573$	−12.8889			−0.538441
$574$	7.58796	+	9.45068i	0.316715	+	0.394464i
$575$	−45.3930			−1.89302
$576$	−0.395181	−	0.684473i	−0.0164659	−	0.0285197i
$577$	−5.25900	+	9.10885i	−0.218935	+	0.379206i	−0.954483	−	0.298267i	$-0.903592\pi$
$577$	−5.25900	+	9.10885i	−0.218935	+	0.379206i	0.735548	+	0.677473i	$0.236925\pi$
$578$	−20.1815	+	34.9553i	−0.839439	+	1.45395i
$579$	3.94498	+	6.83291i	0.163948	+	0.283966i
$580$	−3.27192			−0.135859
$581$	14.3798	−	2.21609i	0.596574	−	0.0919390i
$582$	34.9391			1.44827
$583$	9.47129	+	16.4048i	0.392261	+	0.679416i
$584$	2.89713	−	5.01797i	0.119884	−	0.207645i
$585$	−7.14060	+	12.3679i	−0.295227	+	0.511349i
$586$	−5.77326	−	9.99958i	−0.238491	−	0.413079i
$587$	−0.917043			−0.0378504			−0.0189252	−	0.999821i	$-0.506024\pi$
$587$	−0.917043			−0.0378504			−0.0189252	+	0.999821i	$0.506024\pi$
$588$	−10.0513	−	9.20321i	−0.414509	−	0.379534i
$589$	4.82770			0.198922
$590$	−13.9690	−	24.1951i	−0.575096	−	0.996096i
$591$	−20.5609	+	35.6125i	−0.845761	+	1.46490i
$592$	2.55973	−	4.43359i	0.105204	−	0.182219i
$593$	−0.339844	−	0.588627i	−0.0139557	−	0.0241720i	0.858963	−	0.512037i	$-0.171109\pi$
$593$	−0.339844	−	0.588627i	−0.0139557	−	0.0241720i	−0.872919	+	0.487865i	$0.837776\pi$
$594$	−14.1227			−0.579459
$595$	64.7993	−	9.98634i	2.65651	−	0.409400i
$596$	10.1710			0.416619
$597$	7.04320	+	12.1992i	0.288259	+	0.499279i
$598$	−21.9687	+	38.0509i	−0.898366	+	1.55602i
$599$	−1.16124	+	2.01133i	−0.0474471	+	0.0821808i	−0.888774	−	0.458346i	$-0.848442\pi$
$599$	−1.16124	+	2.01133i	−0.0474471	+	0.0821808i	0.841326	+	0.540527i	$0.181775\pi$
$600$	−5.55394	−	9.61971i	−0.226739	−	0.392723i
$601$	−10.4183			−0.424971			−0.212485	−	0.977164i	$-0.568156\pi$
$601$	−10.4183			−0.424971			−0.212485	+	0.977164i	$0.568156\pi$
$602$	−0.347253	−	0.432498i	−0.0141530	−	0.0176273i
$603$	8.95171			0.364542
$604$	9.81950	+	17.0079i	0.399550	+	0.692040i
$605$	−0.364353	+	0.631078i	−0.0148131	+	0.0256570i
$606$	10.7049	−	18.5415i	0.434859	−	0.753198i
$607$	−2.47567	−	4.28799i	−0.100484	−	0.174044i	0.811400	−	0.584491i	$-0.198706\pi$
$607$	−2.47567	−	4.28799i	−0.100484	−	0.174044i	−0.911884	+	0.410447i	$0.865373\pi$
$608$	0.726289			0.0294549
$609$	−1.86598	+	4.80111i	−0.0756135	+	0.194551i
$610$	−0.494869			−0.0200367
$611$	15.7099	+	27.2103i	0.635555	+	1.10081i
$612$	2.99303	−	5.18408i	0.120986	−	0.209554i
$613$	−3.84832	+	6.66548i	−0.155432	+	0.269216i	−0.933216	−	0.359315i	$-0.883010\pi$
$613$	−3.84832	+	6.66548i	−0.155432	+	0.269216i	0.777784	+	0.628531i	$0.216344\pi$
$614$	6.86581	+	11.8919i	0.277082	+	0.479919i
$615$	29.1806			1.17667
$616$	−3.14646	+	8.09573i	−0.126775	+	0.326186i
$617$	−15.1756			−0.610947			−0.305473	−	0.952201i	$-0.598815\pi$
$617$	−15.1756			−0.610947			−0.305473	+	0.952201i	$0.598815\pi$
$618$	16.8024	+	29.1027i	0.675893	+	1.17068i
$619$	−4.29436	+	7.43805i	−0.172605	+	0.298960i	−0.939330	−	0.343015i	$-0.888552\pi$
$619$	−4.29436	+	7.43805i	−0.172605	+	0.298960i	0.766725	+	0.641976i	$0.221885\pi$
$620$	10.8743	−	18.8349i	0.436724	−	0.756429i
$621$	−17.1131	−	29.6408i	−0.686726	−	1.18944i
$622$	23.7428			0.952001
$623$	−14.9336	−	18.5996i	−0.598304	−	0.745177i
$624$	−10.7517			−0.430412
$625$	10.4875	+	18.1649i	0.419500	+	0.726595i
$626$	3.29573	−	5.70837i	0.131724	−	0.228152i
$627$	−2.32100	+	4.02008i	−0.0926917	+	0.160547i
$628$	0.0823397	+	0.142617i	0.00328571	+	0.00569102i
$629$	38.7740			1.54602
$630$	−6.76208	+	1.04212i	−0.269408	+	0.0415189i
$631$	−22.3220			−0.888625			−0.444312	−	0.895872i	$-0.646552\pi$
$631$	−22.3220			−0.888625			−0.444312	+	0.895872i	$0.646552\pi$
$632$	−0.357577	−	0.619342i	−0.0142237	−	0.0246361i
$633$	−6.58481	+	11.4052i	−0.261723	+	0.453317i
$634$	9.68786	−	16.7799i	0.384754	−	0.666413i
$635$	−6.46331	−	11.1948i	−0.256489	−	0.444251i
$636$	−11.2338			−0.445447
$637$	−36.8639	+	11.6387i	−1.46060	+	0.461144i
$638$	3.28288			0.129970
$639$	0.543911	+	0.942081i	0.0215168	+	0.0372681i
$640$	1.63596	−	2.83357i	0.0646670	−	0.112007i
$641$	18.3128	−	31.7187i	0.723312	−	1.25281i	−0.236353	−	0.971667i	$-0.575952\pi$
$641$	18.3128	−	31.7187i	0.723312	−	1.25281i	0.959665	−	0.281146i	$-0.0907144\pi$
$642$	14.5705	+	25.2369i	0.575052	+	0.996019i
$643$	−4.74242			−0.187023			−0.0935114	−	0.995618i	$-0.529809\pi$
$643$	−4.74242			−0.187023			−0.0935114	+	0.995618i	$0.529809\pi$
$644$	−20.8041	+	3.20616i	−0.819798	+	0.126340i
$645$	−1.33541			−0.0525817
$646$	2.75040	+	4.76383i	0.108213	+	0.187430i
$647$	11.8428	−	20.5123i	0.465589	−	0.806423i	−0.533639	−	0.845712i	$-0.679176\pi$
$647$	11.8428	−	20.5123i	0.465589	−	0.806423i	0.999228	+	0.0392891i	$0.0125093\pi$
$648$	5.37321	−	9.30667i	0.211079	−	0.365600i
$649$	14.0158	+	24.2761i	0.550169	+	0.952921i
$650$	−31.5085			−1.23586
$651$	−21.4361	−	26.6983i	−0.840146	−	1.04639i
$652$	14.2581			0.558392
$653$	8.26031	+	14.3073i	0.323251	+	0.559887i	0.981157	−	0.193213i	$-0.0618909\pi$
$653$	8.26031	+	14.3073i	0.323251	+	0.559887i	−0.657906	+	0.753100i	$0.728558\pi$
$654$	−5.95403	+	10.3127i	−0.232821	+	0.403258i
$655$	−5.35273	+	9.27120i	−0.209149	+	0.362256i
$656$	2.29045	+	3.96718i	0.0894271	+	0.154892i
$657$	−4.57955			−0.178665
$658$	−5.45299	+	14.0303i	−0.212580	+	0.546960i
$659$	−36.6326			−1.42700			−0.713502	−	0.700653i	$-0.752892\pi$
$659$	−36.6326			−1.42700			−0.713502	+	0.700653i	$0.752892\pi$
$660$	10.4561	+	18.1104i	0.407001	+	0.704947i
$661$	15.7696	−	27.3138i	0.613367	−	1.06238i	−0.377302	−	0.926090i	$-0.623148\pi$
$661$	15.7696	−	27.3138i	0.613367	−	1.06238i	0.990669	−	0.136292i	$-0.0435186\pi$
$662$	−4.04245	+	7.00173i	−0.157114	+	0.272130i
$663$	−40.7157	−	70.5217i	−1.58127	−	2.73884i
$664$	5.49921			0.213411
$665$	2.27761	−	5.86021i	0.0883221	−	0.227249i
$666$	−4.04623			−0.156788
$667$	3.97803	+	6.89014i	0.154030	+	0.266787i
$668$	−3.81704	+	6.61130i	−0.147686	+	0.255799i
$669$	22.7054	−	39.3269i	0.877840	−	1.52046i
$670$	18.5291	+	32.0933i	0.715840	+	1.23987i
$671$	0.496527			0.0191682
$672$	−3.22489	−	4.01654i	−0.124403	−	0.154942i
$673$	8.46574			0.326330			0.163165	−	0.986599i	$-0.447830\pi$
$673$	8.46574			0.326330			0.163165	+	0.986599i	$0.447830\pi$
$674$	−2.35903	−	4.08596i	−0.0908664	−	0.157385i
$675$	12.2722	−	21.2561i	0.472357	−	0.818147i
$676$	−8.74905	+	15.1538i	−0.336502	+	0.582838i
$677$	15.7758	+	27.3245i	0.606314	+	1.05017i	0.991842	+	0.127471i	$0.0406859\pi$
$677$	15.7758	+	27.3245i	0.606314	+	1.05017i	−0.385528	+	0.922696i	$0.625981\pi$
$678$	18.9291			0.726969
$679$	46.9271	−	7.23201i	1.80090	−	0.277539i
$680$	24.7810			0.950307
$681$	26.2099	+	45.3970i	1.00437	+	1.73962i
$682$	−10.9108	+	18.8980i	−0.417795	+	0.723642i
$683$	18.3445	−	31.7736i	0.701932	−	1.21578i	−0.265855	−	0.964013i	$-0.585654\pi$
$683$	18.3445	−	31.7736i	0.701932	−	1.21578i	0.967787	−	0.251769i	$-0.0810124\pi$
$684$	−0.287015	−	0.497125i	−0.0109743	−	0.0190081i
$685$	34.8762			1.33255
$686$	−15.4050	−	10.2804i	−0.588165	−	0.392508i
$687$	19.2294			0.733648
$688$	−0.104819	−	0.181553i	−0.00399620	−	0.00692163i
$689$	−15.9328	+	27.5964i	−0.606990	+	1.05134i
$690$	−25.3402	+	43.8906i	−0.964686	+	1.67089i
$691$	−21.2970	−	36.8875i	−0.810176	−	1.40327i	−0.912741	−	0.408540i	$-0.866038\pi$
$691$	−21.2970	−	36.8875i	−0.810176	−	1.40327i	0.102565	−	0.994726i	$-0.467295\pi$
$692$	−13.9739			−0.531207
$693$	6.78472	−	1.04561i	0.257730	−	0.0397193i
$694$	−14.2769			−0.541943
$695$	−1.07390	−	1.86005i	−0.0407353	−	0.0705557i
$696$	−0.973442	+	1.68605i	−0.0368982	+	0.0639096i
$697$	−17.3475	+	30.0467i	−0.657083	+	1.13810i
$698$	−6.11313	−	10.5882i	−0.231385	−	0.400771i
$699$	−16.4570			−0.622460
$700$	−9.45073	−	11.7707i	−0.357204	−	0.444891i
$701$	19.1484			0.723227			0.361613	−	0.932328i	$-0.382226\pi$
$701$	19.1484			0.723227			0.361613	+	0.932328i	$0.382226\pi$
$702$	−11.8787	−	20.5745i	−0.448332	−	0.776533i
$703$	1.85911	−	3.22007i	0.0701175	−	0.121447i
$704$	−1.64144	+	2.84306i	−0.0618641	+	0.107152i
$705$	18.1209	+	31.3863i	0.682473	+	1.18208i
$706$	31.7650			1.19549
$707$	10.5400	−	27.1191i	0.396399	−	1.01992i
$708$	−16.6239			−0.624766
$709$	−1.32434	−	2.29383i	−0.0497367	−	0.0861465i	0.840085	−	0.542454i	$-0.182505\pi$
$709$	−1.32434	−	2.29383i	−0.0497367	−	0.0861465i	−0.889822	+	0.456308i	$0.849172\pi$
$710$	−2.25167	+	3.90001i	−0.0845037	+	0.146365i
$711$	−0.282615	+	0.489504i	−0.0105989	+	0.0183578i
$712$	−4.50777	−	7.80768i	−0.168936	−	0.292605i
$713$	−52.8844			−1.98054
$714$	14.1327	−	36.3628i	0.528901	−	1.36084i
$715$	59.3190			2.21840
$716$	−6.26689	−	10.8546i	−0.234205	−	0.405654i
$717$	−10.3258	+	17.8848i	−0.385623	+	0.667919i
$718$	3.20645	−	5.55373i	0.119664	−	0.207263i
$719$	12.2340	+	21.1898i	0.456249	+	0.790247i	0.998759	−	0.0498023i	$-0.0158591\pi$
$719$	12.2340	+	21.1898i	0.456249	+	0.790247i	−0.542510	+	0.840050i	$0.682526\pi$
$720$	−2.58600			−0.0963745
$721$	28.5915	+	35.6102i	1.06480	+	1.32619i
$722$	−18.4725			−0.687475
$723$	−26.4811	−	45.8666i	−0.984842	−	1.70580i
$724$	10.6856	−	18.5080i	0.397126	−	0.687843i
$725$	−2.85273	+	4.94108i	−0.105948	+	0.183507i
$726$	0.216800	+	0.375509i	0.00804622	+	0.0139365i
$727$	10.3496			0.383847			0.191923	−	0.981410i	$-0.438528\pi$
$727$	10.3496			0.383847			0.191923	+	0.981410i	$0.438528\pi$
$728$	−14.4407	+	2.22548i	−0.535208	+	0.0824818i
$729$	16.6324			0.616016
$730$	−9.47916	−	16.4184i	−0.350840	−	0.607672i
$731$	0.793885	−	1.37505i	0.0293629	−	0.0508580i
$732$	−0.147231	+	0.255011i	−0.00544180	+	0.00942547i
$733$	−7.01827	−	12.1560i	−0.259226	−	0.448992i	0.706809	−	0.707404i	$-0.250134\pi$
$733$	−7.01827	−	12.1560i	−0.259226	−	0.448992i	−0.966035	+	0.258412i	$0.916801\pi$
$734$	−11.3792			−0.420015
$735$	−42.5214	+	13.4249i	−1.56843	+	0.495187i
$736$	−7.95605			−0.293264
$737$	−18.5911	−	32.2007i	−0.684812	−	1.18613i
$738$	1.81028	−	3.13550i	0.0666374	−	0.115419i
$739$	−1.76787	+	3.06204i	−0.0650322	+	0.112639i	−0.896708	−	0.442622i	$-0.854048\pi$
$739$	−1.76787	+	3.06204i	−0.0650322	+	0.112639i	0.831676	+	0.555261i	$0.187382\pi$
$740$	−8.37524	−	14.5063i	−0.307880	−	0.533264i
$741$	−7.80883			−0.286865
$742$	−15.0882	+	2.32526i	−0.553904	+	0.0853631i
$743$	1.52701			0.0560204			0.0280102	−	0.999608i	$-0.491083\pi$
$743$	1.52701			0.0560204			0.0280102	+	0.999608i	$0.491083\pi$
$744$	−6.47054	−	11.2073i	−0.237222	−	0.410880i
$745$	16.6393	−	28.8201i	0.609617	−	1.05589i
$746$	−0.679595	+	1.17709i	−0.0248818	+	0.0430965i
$747$	−2.17318	−	3.76406i	−0.0795125	−	0.137720i
$748$	−24.8640			−0.909117
$749$	24.7936	+	30.8799i	0.905937	+	1.12833i
$750$	−4.49384			−0.164092
$751$	20.1405	+	34.8844i	0.734938	+	1.27295i	0.954750	+	0.297408i	$0.0961222\pi$
$751$	20.1405	+	34.8844i	0.734938	+	1.27295i	−0.219812	+	0.975542i	$0.570544\pi$
$752$	−2.84470	+	4.92717i	−0.103736	+	0.179675i
$753$	−18.9078	+	32.7493i	−0.689039	+	1.19345i
$754$	2.76125	+	4.78263i	0.100559	+	0.174173i
$755$	64.2572			2.33856
$756$	4.12315	−	10.6087i	0.149958	−	0.385835i
$757$	1.02370			0.0372071			0.0186036	−	0.999827i	$-0.494078\pi$
$757$	1.02370			0.0372071			0.0186036	+	0.999827i	$0.494078\pi$
$758$	−0.925262	−	1.60260i	−0.0336070	−	0.0582091i
$759$	25.4251	−	44.0376i	0.922872	−	1.59846i
$760$	1.18818	−	2.05799i	0.0430998	−	0.0746511i
$761$	12.0544	+	20.8788i	0.436972	+	0.756857i	0.997454	−	0.0713091i	$-0.0227177\pi$
$761$	12.0544	+	20.8788i	0.436972	+	0.756857i	−0.560483	+	0.828166i	$0.689384\pi$
$762$	−7.69170			−0.278641
$763$	−5.86230	+	15.0835i	−0.212230	+	0.546059i
$764$	−6.62026			−0.239512
$765$	−9.79296	−	16.9619i	−0.354065	−	0.613259i
$766$	8.99158	−	15.5739i	0.324879	−	0.562707i
$767$	−23.5776	+	40.8377i	−0.851339	+	1.47456i
$768$	−0.973442	−	1.68605i	−0.0351261	−	0.0608402i
$769$	−26.1822			−0.944155			−0.472077	−	0.881557i	$-0.656496\pi$
$769$	−26.1822			−0.944155			−0.472077	+	0.881557i	$0.656496\pi$
$770$	17.7923	+	22.1600i	0.641190	+	0.798591i
$771$	51.3753			1.85024
$772$	2.02630	+	3.50966i	0.0729283	+	0.126315i
$773$	15.2518	−	26.4169i	0.548570	−	0.950151i	−0.449803	−	0.893128i	$-0.648506\pi$
$773$	15.2518	−	26.4169i	0.548570	−	0.950151i	0.998373	−	0.0570233i	$-0.0181609\pi$
$774$	−0.0828452	+	0.143492i	−0.00297781	+	0.00515772i
$775$	−18.9623	−	32.8437i	−0.681146	−	1.17978i
$776$	17.9462			0.644230
$777$	−26.0625	+	4.01654i	−0.934989	+	0.144093i
$778$	9.07521			0.325362
$779$	1.66353	+	2.88132i	0.0596021	+	0.103234i
$780$	−17.5893	+	30.4656i	−0.629799	+	1.09084i
$781$	2.25921	−	3.91307i	0.0808409	−	0.140021i
$782$	−30.1289	−	52.1848i	−1.07741	−	1.86612i
$783$	−4.30191			−0.153738
$784$	−5.16276	−	4.72714i	−0.184384	−	0.168827i
$785$	0.538818			0.0192312
$786$	3.18503	+	5.51663i	0.113606	+	0.196772i
$787$	21.3085	−	36.9073i	0.759564	−	1.31560i	−0.183509	−	0.983018i	$-0.558746\pi$
$787$	21.3085	−	36.9073i	0.759564	−	1.31560i	0.943073	−	0.332586i	$-0.107921\pi$
$788$	−10.5609	+	18.2920i	−0.376217	+	0.651627i
$789$	8.20304	+	14.2081i	0.292036	+	0.505821i
$790$	−2.33993			−0.0832509
$791$	25.4239	−	3.91812i	0.903971	−	0.139312i
$792$	2.59466			0.0921972
$793$	0.417632	+	0.723361i	0.0148306	+	0.0256873i
$794$	4.69586	−	8.13346i	0.166650	−	0.288646i
$795$	−18.3780	+	31.8316i	−0.651800	+	1.12895i
$796$	3.61767	+	6.26600i	0.128225	+	0.222092i
$797$	−26.5763			−0.941379			−0.470690	−	0.882299i	$-0.655995\pi$
$797$	−26.5763			−0.941379			−0.470690	+	0.882299i	$0.655995\pi$
$798$	−2.34220	−	2.91717i	−0.0829130	−	0.103267i
$799$	−43.0906			−1.52444
$800$	−2.85273	−	4.94108i	−0.100859	−	0.174693i
$801$	−3.56276	+	6.17089i	−0.125884	+	0.218038i
$802$	−9.12997	+	15.8136i	−0.322391	+	0.558397i
$803$	9.51091	+	16.4734i	0.335633	+	0.581333i
$804$	22.0506			0.777665
$805$	−24.9499	+	64.1950i	−0.879367	+	2.26258i
$806$	−36.7085			−1.29300
$807$	6.98342	+	12.0956i	0.245828	+	0.425787i
$808$	5.49850	−	9.52368i	0.193437	−	0.335042i
$809$	−17.2825	+	29.9342i	−0.607621	+	1.05243i	0.384010	+	0.923329i	$0.374543\pi$
$809$	−17.2825	+	29.9342i	−0.607621	+	1.05243i	−0.991631	+	0.129102i	$0.958791\pi$
$810$	−17.5807	−	30.4507i	−0.617723	−	1.06993i
$811$	51.5669			1.81076			0.905379	−	0.424605i	$-0.139587\pi$
$811$	51.5669			1.81076			0.905379	+	0.424605i	$0.139587\pi$
$812$	−0.958446	+	2.46605i	−0.0336349	+	0.0865412i
$813$	25.6961			0.901201
$814$	8.40329	+	14.5549i	0.294535	+	0.510150i
$815$	23.3258	−	40.4014i	0.817066	−	1.41520i
$816$	7.37269	−	12.7699i	0.258096	−	0.447035i
$817$	−0.0761292	−	0.131860i	−0.00266342	−	0.00461318i
$818$	37.2015			1.30072
$819$	7.22997	+	9.00480i	0.252636	+	0.314653i
$820$	14.9883			0.523416
$821$	−16.5980	−	28.7487i	−0.579276	−	1.00333i	−0.995563	−	0.0941016i	$-0.970002\pi$
$821$	−16.5980	−	28.7487i	−0.579276	−	1.00333i	0.416287	−	0.909233i	$-0.363331\pi$
$822$	10.3762	−	17.9720i	0.361910	−	0.626846i
$823$	−15.6460	+	27.0996i	−0.545384	+	0.944632i	0.453199	+	0.891409i	$0.350283\pi$
$823$	−15.6460	+	27.0996i	−0.545384	+	0.944632i	−0.998583	+	0.0532229i	$0.983051\pi$
$824$	8.63042	+	14.9483i	0.300655	+	0.520750i
$825$	36.4658			1.26958
$826$	−22.3278	+	3.44098i	−0.776883	+	0.119727i
$827$	−22.8284			−0.793821			−0.396910	−	0.917857i	$-0.629918\pi$
$827$	−22.8284			−0.793821			−0.396910	+	0.917857i	$0.629918\pi$
$828$	3.14408	+	5.44570i	0.109264	+	0.189251i
$829$	−1.82536	+	3.16162i	−0.0633975	+	0.109808i	−0.895982	−	0.444090i	$-0.853527\pi$
$829$	−1.82536	+	3.16162i	−0.0633975	+	0.109808i	0.832585	+	0.553898i	$0.186860\pi$
$830$	8.99649	−	15.5824i	0.312273	−	0.540872i
$831$	−1.09625	−	1.89876i	−0.0380284	−	0.0658672i
$832$	−5.52251			−0.191459
$833$	11.4550	−	51.7645i	0.396893	−	1.79353i
$834$	−1.27800			−0.0442536
$835$	12.4890	+	21.6317i	0.432201	+	0.748594i
$836$	−1.19216	+	2.06488i	−0.0412317	+	0.0714154i
$837$	14.2976	−	24.7641i	0.494196	−	0.855973i
$838$	7.87398	+	13.6381i	0.272002	+	0.471122i
$839$	−10.9777			−0.378991			−0.189495	−	0.981882i	$-0.560685\pi$
$839$	−10.9777			−0.378991			−0.189495	+	0.981882i	$0.560685\pi$
$840$	−16.6569	+	2.56703i	−0.574719	+	0.0885709i
$841$	1.00000			0.0344828
$842$	8.89943	+	15.4143i	0.306694	+	0.531210i
$843$	22.8103	−	39.5085i	0.785627	−	1.36075i
$844$	−3.38223	+	5.85819i	−0.116421	+	0.201647i
$845$	28.6262	+	49.5820i	0.984771	+	1.70567i
$846$	4.49669			0.154599
$847$	0.368913	+	0.459475i	0.0126760	+	0.0157877i
$848$	−5.77012			−0.198147
$849$	−13.2313	−	22.9173i	−0.454097	−	0.786518i
$850$	21.6061	−	37.4229i	0.741084	−	1.28359i
$851$	−20.3654	+	35.2738i	−0.698116	+	1.20917i
$852$	1.33981	+	2.32061i	0.0459010	+	0.0795029i
$853$	24.9620			0.854683			0.427342	−	0.904090i	$-0.359450\pi$
$853$	24.9620			0.854683			0.427342	+	0.904090i	$0.359450\pi$
$854$	−0.144962	+	0.372983i	−0.00496051	+	0.0127632i
$855$	−1.87818			−0.0642325
$856$	7.48401	+	12.9627i	0.255798	+	0.443055i
$857$	−9.45790	+	16.3816i	−0.323076	+	0.559583i	−0.981121	−	0.193395i	$-0.938050\pi$
$857$	−9.45790	+	16.3816i	−0.323076	+	0.559583i	0.658045	+	0.752978i	$0.271384\pi$
$858$	17.6482	−	30.5676i	0.602501	−	1.04356i
$859$	−24.3742	−	42.2174i	−0.831639	−	1.44044i	−0.896738	−	0.442561i	$-0.854070\pi$
$859$	−24.3742	−	42.2174i	−0.831639	−	1.44044i	0.0650996	−	0.997879i	$-0.479263\pi$
$860$	−0.685922			−0.0233897
$861$	8.54789	−	21.9934i	0.291311	−	0.749533i
$862$	−18.4373			−0.627977
$863$	−24.5864	−	42.5849i	−0.836930	−	1.44961i	−0.892449	−	0.451148i	$-0.851015\pi$
$863$	−24.5864	−	42.5849i	−0.836930	−	1.44961i	0.0555192	−	0.998458i	$-0.482319\pi$
$864$	2.15096	−	3.72557i	0.0731770	−	0.126746i
$865$	−22.8607	+	39.5959i	−0.777287	+	1.34630i
$866$	4.60931	+	7.98357i	0.156631	+	0.271293i
$867$	78.5820			2.66879
$868$	−11.0104	−	13.7133i	−0.373719	−	0.465460i
$869$	2.34776			0.0796424
$870$	3.18503	+	5.51663i	0.107983	+	0.187031i
$871$	31.2743	−	54.1686i	1.05969	−	1.83543i
$872$	−3.05823	+	5.29701i	−0.103565	+	0.179380i
$873$	−7.09198	−	12.2837i	−0.240027	−	0.415739i
$874$	−5.77839			−0.195457
$875$	−6.03572	+	0.930175i	−0.204045	+	0.0314457i
$876$	−11.2807			−0.381141
$877$	−27.9675	−	48.4412i	−0.944397	−	1.63574i	−0.756955	−	0.653467i	$-0.773314\pi$
$877$	−27.9675	−	48.4412i	−0.944397	−	1.63574i	−0.187442	−	0.982276i	$-0.560020\pi$
$878$	−6.60539	+	11.4409i	−0.222921	+	0.386111i
$879$	−11.2399	+	19.4680i	−0.379112	+	0.656641i
$880$	5.37066	+	9.30225i	0.181045	+	0.313579i
$881$	17.2684			0.581789			0.290894	−	0.956755i	$-0.406047\pi$
$881$	17.2684			0.581789			0.290894	+	0.956755i	$0.406047\pi$
$882$	−1.19538	+	5.40185i	−0.0402505	+	0.181890i
$883$	−5.45803			−0.183677			−0.0918386	−	0.995774i	$-0.529274\pi$
$883$	−5.45803			−0.183677			−0.0918386	+	0.995774i	$0.529274\pi$
$884$	−20.9133	−	36.2229i	−0.703390	−	1.21831i
$885$	−27.1961	+	47.1051i	−0.914188	+	1.58342i
$886$	8.93920	−	15.4831i	0.300318	−	0.520167i
$887$	12.4802	+	21.6164i	0.419045	+	0.725807i	0.995844	−	0.0910792i	$-0.0290316\pi$
$887$	12.4802	+	21.6164i	0.419045	+	0.725807i	−0.576799	+	0.816886i	$0.695698\pi$
$888$	−9.96701			−0.334471
$889$	−10.3308	+	1.59210i	−0.346484	+	0.0533973i
$890$	−29.4981			−0.988779
$891$	17.6396	+	30.5526i	0.590948	+	1.02355i
$892$	11.6624	−	20.1999i	0.390486	−	0.676342i
$893$	−2.06608	+	3.57855i	−0.0691386	+	0.119752i
$894$	−9.90085	−	17.1488i	−0.331134	−	0.573541i
$895$	−41.0095			−1.37080
$896$	−1.65643	−	2.06306i	−0.0553376	−	0.0689221i
$897$	85.5410			2.85613
$898$	7.92318	+	13.7233i	0.264400	+	0.457954i
$899$	−3.32354	+	5.75653i	−0.110846	+	0.191991i
$900$	−2.25469	+	3.90523i	−0.0751563	+	0.130174i
$901$	−21.8510	−	37.8470i	−0.727961	−	1.26087i
$902$	−15.0385			−0.500728
$903$	−0.391183	+	1.00650i	−0.0130178	+	0.0334942i
$904$	9.72278			0.323375
$905$	−34.9623	−	60.5565i	−1.16219	−	2.01297i
$906$	19.1174	−	33.1124i	0.635134	−	1.10008i
$907$	−3.33738	+	5.78051i	−0.110816	+	0.191939i	−0.916099	−	0.400951i	$-0.868680\pi$
$907$	−3.33738	+	5.78051i	−0.110816	+	0.191939i	0.805284	+	0.592890i	$0.202013\pi$
$908$	13.4625	+	23.3177i	0.446769	+	0.773826i
$909$	−8.69160			−0.288282
$910$	−17.3184	+	44.5595i	−0.574098	+	1.47713i
$911$	16.4305			0.544368			0.272184	−	0.962245i	$-0.412254\pi$
$911$	16.4305			0.544368			0.272184	+	0.962245i	$0.412254\pi$
$912$	−0.707001	−	1.22456i	−0.0234111	−	0.0405493i
$913$	−9.02661	+	15.6346i	−0.298737	+	0.517428i
$914$	−5.76090	+	9.97818i	−0.190554	+	0.330049i
$915$	0.481727	+	0.834375i	0.0159254	+	0.0275836i
$916$	9.87701			0.326346
$917$	5.41972	+	6.75017i	0.178975	+	0.222910i
$918$	32.5820			1.07537
$919$	4.07867	+	7.06446i	0.134543	+	0.233035i	0.925423	−	0.378936i	$-0.123710\pi$
$919$	4.07867	+	7.06446i	0.134543	+	0.233035i	−0.790880	+	0.611971i	$0.790377\pi$
$920$	−13.0158	+	22.5440i	−0.429118	+	0.743254i
$921$	13.3669	−	23.1522i	0.440456	−	0.762892i
$922$	8.33495	+	14.4366i	0.274497	+	0.475443i
$923$	7.60096			0.250189
$924$	16.7127	−	2.57563i	0.549808	−	0.0847318i
$925$	−29.2089			−0.960383
$926$	−1.78552	−	3.09260i	−0.0586757	−	0.101629i
$927$	6.82115	−	11.8146i	0.224036	−	0.388042i
$928$	−0.500000	+	0.866025i	−0.0164133	+	0.0284287i
$929$	−25.0626	−	43.4097i	−0.822277	−	1.42423i	−0.903982	−	0.427569i	$-0.859370\pi$
$929$	−25.0626	−	43.4097i	−0.822277	−	1.42423i	0.0817052	−	0.996657i	$-0.473963\pi$
$930$	−42.3422			−1.38846
$931$	−3.74966	−	3.43327i	−0.122890	−	0.112521i
$932$	−8.45298			−0.276887
$933$	−23.1123	−	40.0316i	−0.756662	−	1.31058i
$934$	−15.0223	+	26.0194i	−0.491546	+	0.851382i
$935$	−40.6765	+	70.4537i	−1.33026	+	2.30408i
$936$	2.18239	+	3.78001i	0.0713336	+	0.123553i
$937$	−38.3790			−1.25379			−0.626893	−	0.779105i	$-0.715674\pi$
$937$	−38.3790			−1.25379			−0.626893	+	0.779105i	$0.715674\pi$
$938$	29.6164	−	4.56424i	0.967010	−	0.149028i
$939$	−12.8328			−0.418783
$940$	9.30764	+	16.1213i	0.303582	+	0.525819i
$941$	−3.16566	+	5.48309i	−0.103198	+	0.178744i	−0.913000	−	0.407959i	$-0.866241\pi$
$941$	−3.16566	+	5.48309i	−0.103198	+	0.178744i	0.809803	+	0.586702i	$0.199574\pi$
$942$	0.160306	−	0.277658i	0.00522305	−	0.00904658i
$943$	−18.2229	−	31.5631i	−0.593421	−	1.02783i
$944$	−8.53874			−0.277912
$945$	−23.3152	−	29.0387i	−0.758443	−	0.944628i
$946$	0.688219			0.0223759
$947$	7.66089	+	13.2691i	0.248946	+	0.431186i	0.963234	−	0.268666i	$-0.0865827\pi$
$947$	7.66089	+	13.2691i	0.248946	+	0.431186i	−0.714288	+	0.699852i	$0.753249\pi$
$948$	−0.696161	+	1.20579i	−0.0226103	+	0.0391621i
$949$	−15.9994	+	27.7118i	−0.519363	+	0.899562i
$950$	−2.07191	−	3.58865i	−0.0672216	−	0.116431i
$951$	−37.7223			−1.22323
$952$	7.25911	−	18.6774i	0.235269	−	0.605339i
$953$	5.44368			0.176338			0.0881690	−	0.996106i	$-0.471898\pi$
$953$	5.44368			0.176338			0.0881690	+	0.996106i	$0.471898\pi$
$954$	2.28024	+	3.94949i	0.0738254	+	0.127869i
$955$	−10.8305	+	18.7589i	−0.350466	+	0.607025i
$956$	−5.30374	+	9.18636i	−0.171535	+	0.297108i
$957$	−3.19569	−	5.53510i	−0.103302	−	0.178924i
$958$	−7.44127			−0.240416
$959$	10.2163	−	26.2862i	0.329902	−	0.848825i
$960$	−6.37005			−0.205593
$961$	−6.59178	−	11.4173i	−0.212638	−	0.368300i
$962$	−14.1361	+	24.4845i	−0.455768	+	0.789413i
$963$	5.91507	−	10.2452i	0.190610	−	0.330147i
$964$	−13.6018	−	23.5590i	−0.438084	−	0.758783i
$965$	13.2598			0.426848
$966$	25.6574	+	31.9558i	0.825513	+	1.02816i
$967$	−24.9842			−0.803439			−0.401719	−	0.915763i	$-0.631587\pi$
$967$	−24.9842			−0.803439			−0.401719	+	0.915763i	$0.631587\pi$
$968$	0.111358	+	0.192877i	0.00357917	+	0.00619930i
$969$	5.35470	−	9.27462i	0.172018	−	0.297944i
$970$	29.3592	−	50.8516i	0.942667	−	1.63275i
$971$	−1.73205	−	2.99999i	−0.0555840	−	0.0962743i	0.836895	−	0.547364i	$-0.184369\pi$
$971$	−1.73205	−	2.99999i	−0.0555840	−	0.0962743i	−0.892479	+	0.451090i	$0.851035\pi$
$972$	−8.01629			−0.257123
$973$	−1.71650	+	0.264532i	−0.0550284	+	0.00848052i
$974$	11.2737			0.361232
$975$	30.6717	+	53.1249i	0.982280	+	1.70136i
$976$	−0.0756237	+	0.130984i	−0.00242065	+	0.00419270i
$977$	16.8793	−	29.2359i	0.540018	−	0.935338i	−0.458884	−	0.888496i	$-0.651751\pi$
$977$	16.8793	−	29.2359i	0.540018	−	0.935338i	0.998902	−	0.0468424i	$-0.0149159\pi$
$978$	−13.8795	−	24.0400i	−0.443817	−	0.768713i
$979$	29.5969			0.945921
$980$	−21.8407	+	6.89560i	−0.697677	+	0.220272i
$981$	4.83422			0.154345
$982$	18.3120	+	31.7174i	0.584361	+	1.01214i
$983$	27.9082	−	48.3384i	0.890133	−	1.54176i	0.0504181	−	0.998728i	$-0.483945\pi$
$983$	27.9082	−	48.3384i	0.890133	−	1.54176i	0.839715	−	0.543027i	$-0.182722\pi$
$984$	4.45924	−	7.72364i	0.142155	−	0.246220i
$985$	34.5545	+	59.8501i	1.10100	+	1.90698i
$986$	−7.57383			−0.241200
$987$	28.9641	−	4.46370i	0.921936	−	0.142081i
$988$	−4.01094			−0.127605
$989$	0.833949	+	1.44444i	0.0265180	+	0.0459306i
$990$	4.24476	−	7.35214i	0.134907	−	0.233666i
$991$	8.01370	−	13.8801i	0.254564	−	0.440917i	−0.710213	−	0.703987i	$-0.751402\pi$
$991$	8.01370	−	13.8801i	0.254564	−	0.440917i	0.964777	+	0.263070i	$0.0847349\pi$
$992$	−3.32354	−	5.75653i	−0.105522	−	0.182770i
$993$	15.7404			0.499506
$994$	2.27985	+	2.83952i	0.0723125	+	0.0900640i
$995$	23.6735			0.750500
$996$	−5.35316	−	9.27195i	−0.169621	−	0.293793i
$997$	−1.95000	+	3.37750i	−0.0617572	+	0.106967i	−0.895251	−	0.445562i	$-0.853004\pi$
$997$	−1.95000	+	3.37750i	−0.0617572	+	0.106967i	0.833494	+	0.552529i	$0.186337\pi$
$998$	−8.95633	+	15.5128i	−0.283508	+	0.491050i
$999$	−11.0117	−	19.0729i	−0.348396	−	0.603440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.e.b.291.1	yes	10
7.2	even	3	inner	406.2.e.b.233.1	✓	10
7.3	odd	6		2842.2.a.y.1.1		5
7.4	even	3		2842.2.a.w.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.b.233.1	✓	10	7.2	even	3	inner
406.2.e.b.291.1	yes	10	1.1	even	1	trivial
2842.2.a.w.1.5		5	7.4	even	3
2842.2.a.y.1.1		5	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.973442 + 1.68605i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.63596 + 2.83357i) q^{5} +1.94688 q^{6} +(2.61488 - 0.402984i) q^{7} +1.00000 q^{8} +(-0.395181 - 0.684473i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.973442 + 1.68605i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.63596 + 2.83357i) q^{5} +1.94688 q^{6} +(2.61488 - 0.402984i) q^{7} +1.00000 q^{8} +(-0.395181 - 0.684473i) q^{9} +(1.63596 - 2.83357i) q^{10} +(-1.64144 + 2.84306i) q^{11} +(-0.973442 - 1.68605i) q^{12} -5.52251 q^{13} +(-1.65643 - 2.06306i) q^{14} -6.37005 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.78692 - 6.55913i) q^{17} +(-0.395181 + 0.684473i) q^{18} +(-0.363145 - 0.628985i) q^{19} -3.27192 q^{20} +(-1.86598 + 4.80111i) q^{21} +3.28288 q^{22} +(3.97803 + 6.89014i) q^{23} +(-0.973442 + 1.68605i) q^{24} +(-2.85273 + 4.94108i) q^{25} +(2.76125 + 4.78263i) q^{26} -4.30191 q^{27} +(-0.958446 + 2.46605i) q^{28} +1.00000 q^{29} +(3.18503 + 5.51663i) q^{30} +(-3.32354 + 5.75653i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.19569 - 5.53510i) q^{33} -7.57383 q^{34} +(5.41972 + 6.75017i) q^{35} +0.790361 q^{36} +(2.55973 + 4.43359i) q^{37} +(-0.363145 + 0.628985i) q^{38} +(5.37584 - 9.31124i) q^{39} +(1.63596 + 2.83357i) q^{40} -4.58090 q^{41} +(5.09087 - 0.784563i) q^{42} +0.209639 q^{43} +(-1.64144 - 2.84306i) q^{44} +(1.29300 - 2.23954i) q^{45} +(3.97803 - 6.89014i) q^{46} +(-2.84470 - 4.92717i) q^{47} +1.94688 q^{48} +(6.67521 - 2.10751i) q^{49} +5.70546 q^{50} +(7.37269 + 12.7699i) q^{51} +(2.76125 - 4.78263i) q^{52} +(2.88506 - 4.99707i) q^{53} +(2.15096 + 3.72557i) q^{54} -10.7413 q^{55} +(2.61488 - 0.402984i) q^{56} +1.41400 q^{57} +(-0.500000 - 0.866025i) q^{58} +(4.26937 - 7.39477i) q^{59} +(3.18503 - 5.51663i) q^{60} +(-0.0756237 - 0.130984i) q^{61} +6.64707 q^{62} +(-1.30918 - 1.63056i) q^{63} +1.00000 q^{64} +(-9.03460 - 15.6484i) q^{65} +(-3.19569 + 5.53510i) q^{66} +(-5.66305 + 9.80869i) q^{67} +(3.78692 + 6.55913i) q^{68} -15.4895 q^{69} +(3.13596 - 8.06870i) q^{70} -1.37636 q^{71} +(-0.395181 - 0.684473i) q^{72} +(2.89713 - 5.01797i) q^{73} +(2.55973 - 4.43359i) q^{74} +(-5.55394 - 9.61971i) q^{75} +0.726289 q^{76} +(-3.14646 + 8.09573i) q^{77} -10.7517 q^{78} +(-0.357577 - 0.619342i) q^{79} +(1.63596 - 2.83357i) q^{80} +(5.37321 - 9.30667i) q^{81} +(2.29045 + 3.96718i) q^{82} +5.49921 q^{83} +(-3.22489 - 4.01654i) q^{84} +24.7810 q^{85} +(-0.104819 - 0.181553i) q^{86} +(-0.973442 + 1.68605i) q^{87} +(-1.64144 + 2.84306i) q^{88} +(-4.50777 - 7.80768i) q^{89} -2.58600 q^{90} +(-14.4407 + 2.22548i) q^{91} -7.95605 q^{92} +(-6.47054 - 11.2073i) q^{93} +(-2.84470 + 4.92717i) q^{94} +(1.18818 - 2.05799i) q^{95} +(-0.973442 - 1.68605i) q^{96} +17.9462 q^{97} +(-5.16276 - 4.72714i) q^{98} +2.59466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + 3 q^{3} - 5 q^{4} + 7 q^{5} - 6 q^{6} - 3 q^{7} + 10 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 + 3 * q^3 - 5 * q^4 + 7 * q^5 - 6 * q^6 - 3 * q^7 + 10 * q^8 - 4 * q^9	\( 10 q - 5 q^{2} + 3 q^{3} - 5 q^{4} + 7 q^{5} - 6 q^{6} - 3 q^{7} + 10 q^{8} - 4 q^{9} + 7 q^{10} + 3 q^{12} - 16 q^{13} + 3 q^{14} + 8 q^{15} - 5 q^{16} + 16 q^{17} - 4 q^{18} + 2 q^{19} - 14 q^{20} - 5 q^{21} + 5 q^{23} + 3 q^{24} - 4 q^{25} + 8 q^{26} - 18 q^{27} + 10 q^{29} - 4 q^{30} + 5 q^{31} - 5 q^{32} + 3 q^{33} - 32 q^{34} - 14 q^{35} + 8 q^{36} + 2 q^{38} + 20 q^{39} + 7 q^{40} - 34 q^{41} + 16 q^{42} + 2 q^{43} + 14 q^{45} + 5 q^{46} - 4 q^{47} - 6 q^{48} + q^{49} + 8 q^{50} + 3 q^{51} + 8 q^{52} - 5 q^{53} + 9 q^{54} - 24 q^{55} - 3 q^{56} + 12 q^{57} - 5 q^{58} + 17 q^{59} - 4 q^{60} + 13 q^{61} - 10 q^{62} - 11 q^{63} + 10 q^{64} + 7 q^{65} + 3 q^{66} + 14 q^{67} + 16 q^{68} - 32 q^{69} + 22 q^{70} - 16 q^{71} - 4 q^{72} + 6 q^{73} + 8 q^{75} - 4 q^{76} - 35 q^{77} - 40 q^{78} - 11 q^{79} + 7 q^{80} + 19 q^{81} + 17 q^{82} - 4 q^{83} - 11 q^{84} + 78 q^{85} - q^{86} + 3 q^{87} + 9 q^{89} - 28 q^{90} - 30 q^{91} - 10 q^{92} + 3 q^{93} - 4 q^{94} + 13 q^{95} + 3 q^{96} - 24 q^{97} + 4 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 + 3 * q^3 - 5 * q^4 + 7 * q^5 - 6 * q^6 - 3 * q^7 + 10 * q^8 - 4 * q^9 + 7 * q^10 + 3 * q^12 - 16 * q^13 + 3 * q^14 + 8 * q^15 - 5 * q^16 + 16 * q^17 - 4 * q^18 + 2 * q^19 - 14 * q^20 - 5 * q^21 + 5 * q^23 + 3 * q^24 - 4 * q^25 + 8 * q^26 - 18 * q^27 + 10 * q^29 - 4 * q^30 + 5 * q^31 - 5 * q^32 + 3 * q^33 - 32 * q^34 - 14 * q^35 + 8 * q^36 + 2 * q^38 + 20 * q^39 + 7 * q^40 - 34 * q^41 + 16 * q^42 + 2 * q^43 + 14 * q^45 + 5 * q^46 - 4 * q^47 - 6 * q^48 + q^49 + 8 * q^50 + 3 * q^51 + 8 * q^52 - 5 * q^53 + 9 * q^54 - 24 * q^55 - 3 * q^56 + 12 * q^57 - 5 * q^58 + 17 * q^59 - 4 * q^60 + 13 * q^61 - 10 * q^62 - 11 * q^63 + 10 * q^64 + 7 * q^65 + 3 * q^66 + 14 * q^67 + 16 * q^68 - 32 * q^69 + 22 * q^70 - 16 * q^71 - 4 * q^72 + 6 * q^73 + 8 * q^75 - 4 * q^76 - 35 * q^77 - 40 * q^78 - 11 * q^79 + 7 * q^80 + 19 * q^81 + 17 * q^82 - 4 * q^83 - 11 * q^84 + 78 * q^85 - q^86 + 3 * q^87 + 9 * q^89 - 28 * q^90 - 30 * q^91 - 10 * q^92 + 3 * q^93 - 4 * q^94 + 13 * q^95 + 3 * q^96 - 24 * q^97 + 4 * q^98 + 20 * q^99

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