LMFDB - Embedded newform 670.2.e.h.431.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			431.2
Root			$1.17146 + 2.02903i$ of defining polynomial
Character	$\chi$	$=$	670.431
Dual form			670.2.e.h.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} -0.146365 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.0731827 + 0.126756i) q^{6} +(0.573183 + 0.992782i) q^{7} -1.00000 q^{8} -2.97858 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} -0.146365 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.0731827 + 0.126756i) q^{6} +(0.573183 + 0.992782i) q^{7} -1.00000 q^{8} -2.97858 q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.0731827 + 0.126756i) q^{12} +(2.34292 - 4.05806i) q^{13} +1.14637 q^{14} -0.146365 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.916106 - 1.58674i) q^{17} +(-1.48929 + 2.57952i) q^{18} +(2.83221 - 4.90553i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.0838942 - 0.145309i) q^{21} -4.00000 q^{22} +(1.57318 - 2.72483i) q^{23} +0.146365 q^{24} +1.00000 q^{25} +(-2.34292 - 4.05806i) q^{26} +0.875057 q^{27} +(0.573183 - 0.992782i) q^{28} +(-3.68585 - 6.38407i) q^{29} +(-0.0731827 + 0.126756i) q^{30} +(4.26974 + 7.39541i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.292731 + 0.507025i) q^{33} +(-0.916106 - 1.58674i) q^{34} +(0.573183 + 0.992782i) q^{35} +(1.48929 + 2.57952i) q^{36} +(1.69656 - 2.93852i) q^{37} +(-2.83221 - 4.90553i) q^{38} +(-0.342923 + 0.593960i) q^{39} -1.00000 q^{40} +(2.98929 + 5.17760i) q^{41} -0.167788 q^{42} -4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} -2.97858 q^{45} +(-1.57318 - 2.72483i) q^{46} +(4.42682 + 7.66747i) q^{47} +(0.0731827 - 0.126756i) q^{48} +(2.84292 - 4.92409i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.134086 + 0.232244i) q^{51} -4.68585 q^{52} -11.0575 q^{53} +(0.437529 - 0.757822i) q^{54} +(-2.00000 - 3.46410i) q^{55} +(-0.573183 - 0.992782i) q^{56} +(-0.414538 + 0.718001i) q^{57} -7.37169 q^{58} -0.292731 q^{59} +(0.0731827 + 0.126756i) q^{60} +(-5.20884 + 9.02197i) q^{61} +8.53948 q^{62} +(-1.70727 - 2.95708i) q^{63} +1.00000 q^{64} +(2.34292 - 4.05806i) q^{65} +0.585462 q^{66} +(-7.80922 - 2.45277i) q^{67} -1.83221 q^{68} +(-0.230260 + 0.398821i) q^{69} +1.14637 q^{70} +(-0.876625 - 1.51836i) q^{71} +2.97858 q^{72} +(4.06247 - 7.03641i) q^{73} +(-1.69656 - 2.93852i) q^{74} -0.146365 q^{75} -5.66442 q^{76} +(2.29273 - 3.97113i) q^{77} +(0.342923 + 0.593960i) q^{78} +(6.02877 + 10.4421i) q^{79} +(-0.500000 + 0.866025i) q^{80} +8.80765 q^{81} +5.97858 q^{82} +(-3.36591 + 5.82993i) q^{83} +(-0.0838942 + 0.145309i) q^{84} +(0.916106 - 1.58674i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(0.539481 + 0.934408i) q^{87} +(2.00000 + 3.46410i) q^{88} +0.664423 q^{89} +(-1.48929 + 2.57952i) q^{90} +5.37169 q^{91} -3.14637 q^{92} +(-0.624943 - 1.08243i) q^{93} +8.85363 q^{94} +(2.83221 - 4.90553i) q^{95} +(-0.0731827 - 0.126756i) q^{96} +(3.97858 - 6.89110i) q^{97} +(-2.84292 - 4.92409i) q^{98} +(5.95715 + 10.3181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 2 q^{3} - 3 q^{4} + 6 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 + 6 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q + 3 q^{2} + 2 q^{3} - 3 q^{4} + 6 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} - 12 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} + 2 q^{15} - 3 q^{16} - 8 q^{17} + 6 q^{18} - 10 q^{19} - 3 q^{20} - 14 q^{21} - 24 q^{22} + 8 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 38 q^{27} + 2 q^{28} + 2 q^{29} + q^{30} + 15 q^{31} + 3 q^{32} - 4 q^{33} + 8 q^{34} + 2 q^{35} - 6 q^{36} + q^{37} + 10 q^{38} + 10 q^{39} - 6 q^{40} + 3 q^{41} - 28 q^{42} - 24 q^{43} - 12 q^{44} + 12 q^{45} - 8 q^{46} + 28 q^{47} - q^{48} + 5 q^{49} + 3 q^{50} - 8 q^{51} - 4 q^{52} + 6 q^{53} + 19 q^{54} - 12 q^{55} - 2 q^{56} - 14 q^{57} + 4 q^{58} + 4 q^{59} - q^{60} - 12 q^{61} + 30 q^{62} - 16 q^{63} + 6 q^{64} + 2 q^{65} - 8 q^{66} - 15 q^{67} + 16 q^{68} - 12 q^{69} + 4 q^{70} - 13 q^{71} - 12 q^{72} + 8 q^{73} - q^{74} + 2 q^{75} + 20 q^{76} + 8 q^{77} - 10 q^{78} - 3 q^{80} + 46 q^{81} + 6 q^{82} - 13 q^{83} - 14 q^{84} - 8 q^{85} - 12 q^{86} - 18 q^{87} + 12 q^{88} - 50 q^{89} + 6 q^{90} - 16 q^{91} - 16 q^{92} + 29 q^{93} + 56 q^{94} - 10 q^{95} + q^{96} - 6 q^{97} - 5 q^{98} - 24 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 + 6 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 - 12 * q^11 - q^12 + 2 * q^13 + 4 * q^14 + 2 * q^15 - 3 * q^16 - 8 * q^17 + 6 * q^18 - 10 * q^19 - 3 * q^20 - 14 * q^21 - 24 * q^22 + 8 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 38 * q^27 + 2 * q^28 + 2 * q^29 + q^30 + 15 * q^31 + 3 * q^32 - 4 * q^33 + 8 * q^34 + 2 * q^35 - 6 * q^36 + q^37 + 10 * q^38 + 10 * q^39 - 6 * q^40 + 3 * q^41 - 28 * q^42 - 24 * q^43 - 12 * q^44 + 12 * q^45 - 8 * q^46 + 28 * q^47 - q^48 + 5 * q^49 + 3 * q^50 - 8 * q^51 - 4 * q^52 + 6 * q^53 + 19 * q^54 - 12 * q^55 - 2 * q^56 - 14 * q^57 + 4 * q^58 + 4 * q^59 - q^60 - 12 * q^61 + 30 * q^62 - 16 * q^63 + 6 * q^64 + 2 * q^65 - 8 * q^66 - 15 * q^67 + 16 * q^68 - 12 * q^69 + 4 * q^70 - 13 * q^71 - 12 * q^72 + 8 * q^73 - q^74 + 2 * q^75 + 20 * q^76 + 8 * q^77 - 10 * q^78 - 3 * q^80 + 46 * q^81 + 6 * q^82 - 13 * q^83 - 14 * q^84 - 8 * q^85 - 12 * q^86 - 18 * q^87 + 12 * q^88 - 50 * q^89 + 6 * q^90 - 16 * q^91 - 16 * q^92 + 29 * q^93 + 56 * q^94 - 10 * q^95 + q^96 - 6 * q^97 - 5 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.146365			−0.0845042			−0.0422521	−	0.999107i	$-0.513453\pi$
$3$	−0.146365			−0.0845042			−0.0422521	+	0.999107i	$0.513453\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.0731827	+	0.126756i	−0.0298767	+	0.0517480i
$7$	0.573183	+	0.992782i	0.216643	+	0.375236i	0.953779	−	0.300507i	$-0.0971560\pi$
$7$	0.573183	+	0.992782i	0.216643	+	0.375236i	−0.737137	+	0.675744i	$0.763823\pi$
$8$	−1.00000			−0.353553
$9$	−2.97858			−0.992859
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$	0.0731827	+	0.126756i	0.0211260	+	0.0365914i
$13$	2.34292	−	4.05806i	0.649810	−	1.12550i	−0.333358	−	0.942800i	$-0.608182\pi$
$13$	2.34292	−	4.05806i	0.649810	−	1.12550i	0.983168	−	0.182704i	$-0.0584849\pi$
$14$	1.14637			0.306379
$15$	−0.146365			−0.0377914
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.916106	−	1.58674i	0.222188	−	0.384841i	−0.733284	−	0.679923i	$-0.762013\pi$
$17$	0.916106	−	1.58674i	0.222188	−	0.384841i	0.955472	+	0.295081i	$0.0953467\pi$
$18$	−1.48929	+	2.57952i	−0.351029	+	0.608000i
$19$	2.83221	−	4.90553i	0.649754	−	1.12541i	−0.333428	−	0.942776i	$-0.608205\pi$
$19$	2.83221	−	4.90553i	0.649754	−	1.12541i	0.983182	−	0.182631i	$-0.0584614\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−0.0838942	−	0.145309i	−0.0183072	−	0.0317090i
$22$	−4.00000			−0.852803
$23$	1.57318	−	2.72483i	0.328031	−	0.568167i	−0.654090	−	0.756417i	$-0.726948\pi$
$23$	1.57318	−	2.72483i	0.328031	−	0.568167i	0.982121	+	0.188250i	$0.0602815\pi$
$24$	0.146365			0.0298767
$25$	1.00000			0.200000
$26$	−2.34292	−	4.05806i	−0.459485	−	0.795851i
$27$	0.875057			0.168405
$28$	0.573183	−	0.992782i	0.108321	−	0.187618i
$29$	−3.68585	−	6.38407i	−0.684444	−	1.18549i	−0.973611	−	0.228214i	$-0.926711\pi$
$29$	−3.68585	−	6.38407i	−0.684444	−	1.18549i	0.289167	−	0.957279i	$-0.406622\pi$
$30$	−0.0731827	+	0.126756i	−0.0133613	+	0.0231424i
$31$	4.26974	+	7.39541i	0.766868	+	1.32825i	0.939253	+	0.343225i	$0.111519\pi$
$31$	4.26974	+	7.39541i	0.766868	+	1.32825i	−0.172385	+	0.985030i	$0.555147\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.292731	+	0.507025i	0.0509579	+	0.0882617i
$34$	−0.916106	−	1.58674i	−0.157111	−	0.272124i
$35$	0.573183	+	0.992782i	0.0968856	+	0.167811i
$36$	1.48929	+	2.57952i	0.248215	+	0.429921i
$37$	1.69656	−	2.93852i	0.278912	−	0.483090i	−0.692202	−	0.721703i	$-0.743359\pi$
$37$	1.69656	−	2.93852i	0.278912	−	0.483090i	0.971115	+	0.238613i	$0.0766928\pi$
$38$	−2.83221	−	4.90553i	−0.459445	−	0.795783i
$39$	−0.342923	+	0.593960i	−0.0549116	+	0.0951098i
$40$	−1.00000			−0.158114
$41$	2.98929	+	5.17760i	0.466848	+	0.808605i	0.999283	−	0.0378661i	$-0.0120560\pi$
$41$	2.98929	+	5.17760i	0.466848	+	0.808605i	−0.532434	+	0.846471i	$0.678723\pi$
$42$	−0.167788			−0.0258903
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$	−2.97858			−0.444020
$46$	−1.57318	−	2.72483i	−0.231953	−	0.401755i
$47$	4.42682	+	7.66747i	0.645718	+	1.11842i	0.984135	+	0.177420i	$0.0567750\pi$
$47$	4.42682	+	7.66747i	0.645718	+	1.11842i	−0.338418	+	0.940996i	$0.609892\pi$
$48$	0.0731827	−	0.126756i	0.0105630	−	0.0182957i
$49$	2.84292	−	4.92409i	0.406132	−	0.703441i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.134086	+	0.232244i	−0.0187758	+	0.0325207i
$52$	−4.68585			−0.649810
$53$	−11.0575			−1.51887			−0.759435	−	0.650583i	$-0.774524\pi$
$53$	−11.0575			−1.51887			−0.759435	+	0.650583i	$0.774524\pi$
$54$	0.437529	−	0.757822i	0.0595401	−	0.103126i
$55$	−2.00000	−	3.46410i	−0.269680	−	0.467099i
$56$	−0.573183	−	0.992782i	−0.0765948	−	0.132666i
$57$	−0.414538	+	0.718001i	−0.0549069	+	0.0951015i
$58$	−7.37169			−0.967951
$59$	−0.292731			−0.0381103			−0.0190552	−	0.999818i	$-0.506066\pi$
$59$	−0.292731			−0.0381103			−0.0190552	+	0.999818i	$0.506066\pi$
$60$	0.0731827	+	0.126756i	0.00944785	+	0.0163642i
$61$	−5.20884	+	9.02197i	−0.666923	+	1.15514i	0.311837	+	0.950136i	$0.399056\pi$
$61$	−5.20884	+	9.02197i	−0.666923	+	1.15514i	−0.978760	+	0.205009i	$0.934278\pi$
$62$	8.53948			1.08452
$63$	−1.70727	−	2.95708i	−0.215096	−	0.372557i
$64$	1.00000			0.125000
$65$	2.34292	−	4.05806i	0.290604	−	0.503341i
$66$	0.585462			0.0720654
$67$	−7.80922	−	2.45277i	−0.954048	−	0.299653i
$67$	−7.80922	−	2.45277i	−0.954048	−	0.299653i
$68$	−1.83221			−0.222188
$69$	−0.230260	+	0.398821i	−0.0277200	+	0.0480125i
$70$	1.14637			0.137017
$71$	−0.876625	−	1.51836i	−0.104036	−	0.180196i	0.809308	−	0.587385i	$-0.199842\pi$
$71$	−0.876625	−	1.51836i	−0.104036	−	0.180196i	−0.913344	+	0.407189i	$0.866509\pi$
$72$	2.97858			0.351029
$73$	4.06247	−	7.03641i	0.475476	−	0.823549i	−0.524129	−	0.851639i	$-0.675609\pi$
$73$	4.06247	−	7.03641i	0.475476	−	0.823549i	0.999605	+	0.0280897i	$0.00894241\pi$
$74$	−1.69656	−	2.93852i	−0.197221	−	0.341596i
$75$	−0.146365			−0.0169008
$76$	−5.66442			−0.649754
$77$	2.29273	−	3.97113i	0.261281	−	0.452552i
$78$	0.342923	+	0.593960i	0.0388284	+	0.0672527i
$79$	6.02877	+	10.4421i	0.678290	+	1.17483i	0.975496	+	0.220019i	$0.0706118\pi$
$79$	6.02877	+	10.4421i	0.678290	+	1.17483i	−0.297206	+	0.954813i	$0.596055\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	8.80765			0.978628
$82$	5.97858			0.660223
$83$	−3.36591	+	5.82993i	−0.369457	+	0.639918i	−0.989481	−	0.144665i	$-0.953790\pi$
$83$	−3.36591	+	5.82993i	−0.369457	+	0.639918i	0.620024	+	0.784583i	$0.287123\pi$
$84$	−0.0838942	+	0.145309i	−0.00915360	+	0.0158545i
$85$	0.916106	−	1.58674i	0.0993656	−	0.172106i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	0.539481	+	0.934408i	0.0578384	+	0.100179i
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	0.664423			0.0704287			0.0352144	−	0.999380i	$-0.488789\pi$
$89$	0.664423			0.0704287			0.0352144	+	0.999380i	$0.488789\pi$
$90$	−1.48929	+	2.57952i	−0.156985	+	0.271906i
$91$	5.37169			0.563106
$92$	−3.14637			−0.328031
$93$	−0.624943	−	1.08243i	−0.0648035	−	0.112243i
$94$	8.85363			0.913183
$95$	2.83221	−	4.90553i	0.290579	−	0.503297i
$96$	−0.0731827	−	0.126756i	−0.00746918	−	0.0129370i
$97$	3.97858	−	6.89110i	0.403963	−	0.699685i	−0.590237	−	0.807230i	$-0.700966\pi$
$97$	3.97858	−	6.89110i	0.403963	−	0.699685i	0.994200	+	0.107545i	$0.0342990\pi$
$98$	−2.84292	−	4.92409i	−0.287179	−	0.497408i
$99$	5.95715	+	10.3181i	0.598717	+	1.03701i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	6.89468	+	11.9419i	0.686047	+	1.18827i	0.973107	+	0.230355i	$0.0739887\pi$
$101$	6.89468	+	11.9419i	0.686047	+	1.18827i	−0.287060	+	0.957913i	$0.592678\pi$
$102$	0.134086	+	0.232244i	0.0132765	+	0.0229956i
$103$	5.40539	+	9.36242i	0.532609	+	0.922506i	0.999275	+	0.0380726i	$0.0121218\pi$
$103$	5.40539	+	9.36242i	0.532609	+	0.922506i	−0.466666	+	0.884434i	$0.654545\pi$
$104$	−2.34292	+	4.05806i	−0.229743	+	0.397926i
$105$	−0.0838942	−	0.145309i	−0.00818723	−	0.0141807i
$106$	−5.52877	+	9.57611i	−0.537002	+	0.930114i
$107$	−8.83221			−0.853842			−0.426921	−	0.904289i	$-0.640402\pi$
$107$	−8.83221			−0.853842			−0.426921	+	0.904289i	$0.640402\pi$
$108$	−0.437529	−	0.757822i	−0.0421012	−	0.0729214i
$109$	3.83221			0.367059			0.183530	−	0.983014i	$-0.441248\pi$
$109$	3.83221			0.367059			0.183530	+	0.983014i	$0.441248\pi$
$110$	−4.00000			−0.381385
$111$	−0.248317	+	0.430098i	−0.0235693	+	0.0408231i
$112$	−1.14637			−0.108321
$113$	−1.70727	−	2.95708i	−0.160606	−	0.278178i	0.774480	−	0.632598i	$-0.218012\pi$
$113$	−1.70727	−	2.95708i	−0.160606	−	0.278178i	−0.935086	+	0.354420i	$0.884678\pi$
$114$	0.414538	+	0.718001i	0.0388250	+	0.0672470i
$115$	1.57318	−	2.72483i	0.146700	−	0.254092i
$116$	−3.68585	+	6.38407i	−0.342222	+	0.592746i
$117$	−6.97858	+	12.0873i	−0.645170	+	1.11747i
$118$	−0.146365	+	0.253512i	−0.0134740	+	0.0233377i
$119$	2.10038			0.192542
$120$	0.146365			0.0133613
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	5.20884	+	9.02197i	0.471586	+	0.816811i
$123$	−0.437529	−	0.757822i	−0.0394506	−	0.0683305i
$124$	4.26974	−	7.39541i	0.383434	−	0.664127i
$125$	1.00000			0.0894427
$126$	−3.41454			−0.304191
$127$	7.12494	+	12.3408i	0.632236	+	1.09507i	0.987093	+	0.160145i	$0.0511962\pi$
$127$	7.12494	+	12.3408i	0.632236	+	1.09507i	−0.354857	+	0.934921i	$0.615470\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.585462			0.0515471
$130$	−2.34292	−	4.05806i	−0.205488	−	0.355916i
$131$	22.1825			1.93809			0.969046	−	0.246879i	$-0.0794052\pi$
$131$	22.1825			1.93809			0.969046	+	0.246879i	$0.0794052\pi$
$132$	0.292731	−	0.507025i	0.0254790	−	0.0441309i
$133$	6.49350			0.563058
$134$	−6.02877	+	5.53660i	−0.520806	+	0.478289i
$135$	0.875057			0.0753129
$136$	−0.916106	+	1.58674i	−0.0785554	+	0.136062i
$137$	−11.5395			−0.985884			−0.492942	−	0.870062i	$-0.664079\pi$
$137$	−11.5395			−0.985884			−0.492942	+	0.870062i	$0.664079\pi$
$138$	0.230260	+	0.398821i	0.0196010	+	0.0339499i
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	0.573183	−	0.992782i	0.0484428	−	0.0839054i
$141$	−0.647933	−	1.12225i	−0.0545658	−	0.0945108i
$142$	−1.75325			−0.147129
$143$	−18.7434			−1.56740
$144$	1.48929	−	2.57952i	0.124107	−	0.214960i
$145$	−3.68585	−	6.38407i	−0.306093	−	0.530168i
$146$	−4.06247	−	7.03641i	−0.336213	−	0.582337i
$147$	−0.416106	+	0.720716i	−0.0343198	+	0.0594437i
$148$	−3.39312			−0.278912
$149$	−9.49663			−0.777995			−0.388997	−	0.921239i	$-0.627178\pi$
$149$	−9.49663			−0.777995			−0.388997	+	0.921239i	$0.627178\pi$
$150$	−0.0731827	+	0.126756i	−0.00597535	+	0.0103496i
$151$	6.00157	−	10.3950i	0.488401	−	0.845935i	−0.511510	−	0.859277i	$-0.670914\pi$
$151$	6.00157	−	10.3950i	0.488401	−	0.845935i	0.999911	+	0.0133424i	$0.00424714\pi$
$152$	−2.83221	+	4.90553i	−0.229723	+	0.397891i
$153$	−2.72869	+	4.72623i	−0.220602	+	0.382093i
$154$	−2.29273	−	3.97113i	−0.184754	−	0.320002i
$155$	4.26974	+	7.39541i	0.342954	+	0.594013i
$156$	0.685846			0.0549116
$157$	−1.97858	+	3.42700i	−0.157908	+	0.273504i	−0.934114	−	0.356975i	$-0.883808\pi$
$157$	−1.97858	+	3.42700i	−0.157908	+	0.273504i	0.776206	+	0.630479i	$0.217141\pi$
$158$	12.0575			0.959246
$159$	1.61844			0.128351
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	3.60688			0.284262
$162$	4.40383	−	7.62765i	0.345997	−	0.599285i
$163$	−6.70884	−	11.6200i	−0.525477	−	0.910152i	−0.999560	−	0.0296721i	$-0.990554\pi$
$163$	−6.70884	−	11.6200i	−0.525477	−	0.910152i	0.474083	−	0.880480i	$-0.342780\pi$
$164$	2.98929	−	5.17760i	0.233424	−	0.404303i
$165$	0.292731	+	0.507025i	0.0227891	+	0.0394718i
$166$	3.36591	+	5.82993i	0.261246	+	0.452491i
$167$	9.65214	+	16.7180i	0.746905	+	1.29368i	0.949299	+	0.314374i	$0.101795\pi$
$167$	9.65214	+	16.7180i	0.746905	+	1.29368i	−0.202394	+	0.979304i	$0.564872\pi$
$168$	0.0838942	+	0.145309i	0.00647258	+	0.0112108i
$169$	−4.47858	−	7.75712i	−0.344506	−	0.596702i
$170$	−0.916106	−	1.58674i	−0.0702621	−	0.121698i
$171$	−8.43596	+	14.6115i	−0.645114	+	1.11737i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	10.4786	−	18.1494i	0.796671	−	1.37988i	−0.125101	−	0.992144i	$-0.539925\pi$
$173$	10.4786	−	18.1494i	0.796671	−	1.37988i	0.921772	−	0.387731i	$-0.126741\pi$
$174$	1.07896			0.0817958
$175$	0.573183	+	0.992782i	0.0433285	+	0.0750472i
$176$	4.00000			0.301511
$177$	0.0428457			0.00322048
$178$	0.332212	−	0.575407i	0.0249003	−	0.0431286i
$179$	17.6890			1.32214			0.661068	−	0.750326i	$-0.270103\pi$
$179$	17.6890			1.32214			0.661068	+	0.750326i	$0.270103\pi$
$180$	1.48929	+	2.57952i	0.111005	+	0.192266i
$181$	0.769740	+	1.33323i	0.0572143	+	0.0990982i	0.893214	−	0.449632i	$-0.148445\pi$
$181$	0.769740	+	1.33323i	0.0572143	+	0.0990982i	−0.836000	+	0.548730i	$0.815111\pi$
$182$	2.68585	−	4.65202i	0.199088	−	0.344831i
$183$	0.762394	−	1.32051i	0.0563578	−	0.0976145i
$184$	−1.57318	+	2.72483i	−0.115977	+	0.200877i
$185$	1.69656	−	2.93852i	0.124733	−	0.216045i
$186$	−1.24989			−0.0916460
$187$	−7.32885			−0.535938
$188$	4.42682	−	7.66747i	0.322859	−	0.559208i
$189$	0.501568	+	0.868741i	0.0364837	+	0.0631916i
$190$	−2.83221	−	4.90553i	−0.205470	−	0.355885i
$191$	2.31993	−	4.01824i	0.167864	−	0.290750i	−0.769804	−	0.638280i	$-0.779646\pi$
$191$	2.31993	−	4.01824i	0.167864	−	0.290750i	0.937669	+	0.347530i	$0.112980\pi$
$192$	−0.146365			−0.0105630
$193$	5.83221			0.419812			0.209906	−	0.977722i	$-0.432684\pi$
$193$	5.83221			0.419812			0.209906	+	0.977722i	$0.432684\pi$
$194$	−3.97858	−	6.89110i	−0.285645	−	0.494752i
$195$	−0.342923	+	0.593960i	−0.0245572	+	0.0425344i
$196$	−5.68585			−0.406132
$197$	−7.19656	−	12.4648i	−0.512733	−	0.888080i	−0.999891	−	0.0147663i	$-0.995300\pi$
$197$	−7.19656	−	12.4648i	−0.512733	−	0.888080i	0.487157	−	0.873314i	$-0.338034\pi$
$198$	11.9143			0.846713
$199$	−9.75903	+	16.9031i	−0.691799	+	1.19823i	0.279449	+	0.960161i	$0.409848\pi$
$199$	−9.75903	+	16.9031i	−0.691799	+	1.19823i	−0.971248	+	0.238071i	$0.923485\pi$
$200$	−1.00000			−0.0707107
$201$	1.14300	+	0.359000i	0.0806210	+	0.0253219i
$202$	13.7894			0.970216
$203$	4.22533	−	7.31848i	0.296560	−	0.513657i
$204$	0.268173			0.0187758
$205$	2.98929	+	5.17760i	0.208781	+	0.361619i
$206$	10.8108			0.753223
$207$	−4.68585	+	8.11612i	−0.325689	+	0.564110i
$208$	2.34292	+	4.05806i	0.162452	+	0.281376i
$209$	−22.6577			−1.56727
$210$	−0.167788			−0.0115785
$211$	−9.57318	+	16.5812i	−0.659045	+	1.14150i	0.321818	+	0.946802i	$0.395706\pi$
$211$	−9.57318	+	16.5812i	−0.659045	+	1.14150i	−0.980863	+	0.194698i	$0.937627\pi$
$212$	5.52877	+	9.57611i	0.379717	+	0.657690i
$213$	0.128308	+	0.222235i	0.00879150	+	0.0152273i
$214$	−4.41611	+	7.64892i	−0.301879	+	0.522869i
$215$	−4.00000			−0.272798
$216$	−0.875057			−0.0595401
$217$	−4.89468	+	8.47784i	−0.332273	+	0.575513i
$218$	1.91611	−	3.31879i	0.129775	−	0.224777i
$219$	−0.594606	+	1.02989i	−0.0401797	+	0.0695933i
$220$	−2.00000	+	3.46410i	−0.134840	+	0.233550i
$221$	−4.29273	−	7.43523i	−0.288760	−	0.500148i
$222$	0.248317	+	0.430098i	0.0166660	+	0.0288663i
$223$	5.07896			0.340112			0.170056	−	0.985434i	$-0.445605\pi$
$223$	5.07896			0.340112			0.170056	+	0.985434i	$0.445605\pi$
$224$	−0.573183	+	0.992782i	−0.0382974	+	0.0663330i
$225$	−2.97858			−0.198572
$226$	−3.41454			−0.227132
$227$	−1.83064	−	3.17077i	−0.121504	−	0.210451i	0.798857	−	0.601521i	$-0.205438\pi$
$227$	−1.83064	−	3.17077i	−0.121504	−	0.210451i	−0.920361	+	0.391070i	$0.872105\pi$
$228$	0.829076			0.0549069
$229$	14.0196	−	24.2827i	0.926443	−	1.60465i	0.137219	−	0.990541i	$-0.456184\pi$
$229$	14.0196	−	24.2827i	0.926443	−	1.60465i	0.789224	−	0.614106i	$-0.210483\pi$
$230$	−1.57318	−	2.72483i	−0.103733	−	0.179670i
$231$	−0.335577	+	0.581236i	−0.0220793	+	0.0382425i
$232$	3.68585	+	6.38407i	0.241988	+	0.419135i
$233$	−8.16286	−	14.1385i	−0.534766	−	0.926243i	−0.999175	−	0.0406214i	$-0.987066\pi$
$233$	−8.16286	−	14.1385i	−0.534766	−	0.926243i	0.464408	−	0.885621i	$-0.346267\pi$
$234$	6.97858	+	12.0873i	0.456204	+	0.790168i
$235$	4.42682	+	7.66747i	0.288774	+	0.500171i
$236$	0.146365	+	0.253512i	0.00952758	+	0.0165023i
$237$	−0.882404	−	1.52837i	−0.0573183	−	0.0992782i
$238$	1.05019	−	1.81899i	0.0680738	−	0.117907i
$239$	5.37169	+	9.30404i	0.347466	+	0.601829i	0.985799	−	0.167932i	$-0.0537089\pi$
$239$	5.37169	+	9.30404i	0.347466	+	0.601829i	−0.638333	+	0.769761i	$0.720376\pi$
$240$	0.0731827	−	0.126756i	0.00472393	−	0.00818208i
$241$	6.60688			0.425587			0.212793	−	0.977097i	$-0.431744\pi$
$241$	6.60688			0.425587			0.212793	+	0.977097i	$0.431744\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$	−3.91431			−0.251103
$244$	10.4177			0.666923
$245$	2.84292	−	4.92409i	0.181628	−	0.314588i
$246$	−0.875057			−0.0557916
$247$	−13.2713	−	22.9866i	−0.844433	−	1.46260i
$248$	−4.26974	−	7.39541i	−0.271129	−	0.469609i
$249$	0.492654	−	0.853301i	0.0312207	−	0.0540758i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	0.134086	−	0.232244i	0.00846345	−	0.0146591i	−0.861763	−	0.507312i	$-0.830639\pi$
$251$	0.134086	−	0.232244i	0.00846345	−	0.0146591i	0.870226	+	0.492653i	$0.163973\pi$
$252$	−1.70727	+	2.95708i	−0.107548	+	0.186278i
$253$	−12.5855			−0.791241
$254$	14.2499			0.894117
$255$	−0.134086	+	0.232244i	−0.00839681	+	0.0145437i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	0.292731	−	0.507025i	0.0182246	−	0.0315660i
$259$	3.88975			0.241697
$260$	−4.68585			−0.290604
$261$	10.9786	+	19.0155i	0.679557	+	1.17703i
$262$	11.0912	−	19.2106i	0.685219	−	1.18683i
$263$	−7.03612			−0.433865			−0.216933	−	0.976187i	$-0.569605\pi$
$263$	−7.03612			−0.433865			−0.216933	+	0.976187i	$0.569605\pi$
$264$	−0.292731	−	0.507025i	−0.0180163	−	0.0312052i
$265$	−11.0575			−0.679259
$266$	3.24675	−	5.62354i	0.199071	−	0.344801i
$267$	−0.0972486			−0.00595152
$268$	1.78045	+	7.98937i	0.108758	+	0.488028i
$269$	−27.5296			−1.67851			−0.839255	−	0.543738i	$-0.817009\pi$
$269$	−27.5296			−1.67851			−0.839255	+	0.543738i	$0.817009\pi$
$270$	0.437529	−	0.757822i	0.0266271	−	0.0461196i
$271$	20.5395			1.24768			0.623842	−	0.781550i	$-0.285571\pi$
$271$	20.5395			1.24768			0.623842	+	0.781550i	$0.285571\pi$
$272$	0.916106	+	1.58674i	0.0555471	+	0.0962104i
$273$	−0.786230			−0.0475848
$274$	−5.76974	+	9.99348i	−0.348563	+	0.603728i
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	0.460519			0.0277200
$277$	32.7795			1.96953			0.984765	−	0.173892i	$-0.0556345\pi$
$277$	32.7795			1.96953			0.984765	+	0.173892i	$0.0556345\pi$
$278$	4.00000	−	6.92820i	0.239904	−	0.415526i
$279$	−12.7178	−	22.0278i	−0.761392	−	1.31877i
$280$	−0.573183	−	0.992782i	−0.0342542	−	0.0593301i
$281$	2.38240	−	4.12644i	0.142122	−	0.246163i	−0.786173	−	0.618006i	$-0.787941\pi$
$281$	2.38240	−	4.12644i	0.142122	−	0.246163i	0.928296	+	0.371843i	$0.121274\pi$
$282$	−1.29587			−0.0771677
$283$	−12.6430			−0.751548			−0.375774	−	0.926711i	$-0.622623\pi$
$283$	−12.6430			−0.751548			−0.375774	+	0.926711i	$0.622623\pi$
$284$	−0.876625	+	1.51836i	−0.0520181	+	0.0900980i
$285$	−0.414538	+	0.718001i	−0.0245551	+	0.0425307i
$286$	−9.37169	+	16.2322i	−0.554160	+	0.959833i
$287$	−3.42682	+	5.93542i	−0.202279	+	0.350357i
$288$	−1.48929	−	2.57952i	−0.0877572	−	0.152000i
$289$	6.82150	+	11.8152i	0.401265	+	0.695011i
$290$	−7.37169			−0.432881
$291$	−0.582326	+	1.00862i	−0.0341366	+	0.0591263i
$292$	−8.12494			−0.475476
$293$	−27.0147			−1.57822			−0.789108	−	0.614255i	$-0.789457\pi$
$293$	−27.0147			−1.57822			−0.789108	+	0.614255i	$0.789457\pi$
$294$	0.416106	+	0.720716i	0.0242678	+	0.0420330i
$295$	−0.292731			−0.0170435
$296$	−1.69656	+	2.93852i	−0.0986104	+	0.170798i
$297$	−1.75011	−	3.03129i	−0.101552	−	0.175893i
$298$	−4.74832	+	8.22433i	−0.275063	+	0.476422i
$299$	−7.37169	−	12.7681i	−0.426316	−	0.738401i
$300$	0.0731827	+	0.126756i	0.00422521	+	0.00731827i
$301$	−2.29273	−	3.97113i	−0.132151	−	0.228892i
$302$	−6.00157	−	10.3950i	−0.345351	−	0.598166i
$303$	−1.00914	−	1.74789i	−0.0579738	−	0.100414i
$304$	2.83221	+	4.90553i	0.162438	+	0.281352i
$305$	−5.20884	+	9.02197i	−0.298257	+	0.516596i
$306$	2.72869	+	4.72623i	0.155989	+	0.270181i
$307$	8.88397	−	15.3875i	0.507035	−	0.878210i	−0.492932	−	0.870068i	$-0.664075\pi$
$307$	8.88397	−	15.3875i	0.507035	−	0.878210i	0.999967	−	0.00814250i	$-0.00259187\pi$
$308$	−4.58546			−0.261281
$309$	−0.791163	−	1.37033i	−0.0450077	−	0.0779556i
$310$	8.53948			0.485010
$311$	−19.4324			−1.10191			−0.550954	−	0.834535i	$-0.685736\pi$
$311$	−19.4324			−1.10191			−0.550954	+	0.834535i	$0.685736\pi$
$312$	0.342923	−	0.593960i	0.0194142	−	0.0336264i
$313$	28.7434			1.62467			0.812336	−	0.583190i	$-0.198196\pi$
$313$	28.7434			1.62467			0.812336	+	0.583190i	$0.198196\pi$
$314$	1.97858	+	3.42700i	0.111658	+	0.193397i
$315$	−1.70727	−	2.95708i	−0.0961937	−	0.166612i
$316$	6.02877	−	10.4421i	0.339145	−	0.587416i
$317$	6.35363	−	11.0048i	0.356856	−	0.618092i	−0.630578	−	0.776126i	$-0.717182\pi$
$317$	6.35363	−	11.0048i	0.356856	−	0.618092i	0.987434	+	0.158034i	$0.0505155\pi$
$318$	0.809221	−	1.40161i	0.0453789	−	0.0785985i
$319$	−14.7434	+	25.5363i	−0.825471	+	1.42976i
$320$	1.00000			0.0559017
$321$	1.29273			0.0721532
$322$	1.80344	−	3.12365i	0.100502	−	0.174074i
$323$	−5.18921	−	8.98798i	−0.288735	−	0.500104i
$324$	−4.40383	−	7.62765i	−0.244657	−	0.423758i
$325$	2.34292	−	4.05806i	0.129962	−	0.225101i
$326$	−13.4177			−0.743136
$327$	−0.560904			−0.0310180
$328$	−2.98929	−	5.17760i	−0.165056	−	0.285885i
$329$	−5.07475	+	8.78973i	−0.279780	+	0.484593i
$330$	0.585462			0.0322286
$331$	13.2253	+	22.9069i	0.726930	+	1.25908i	0.958175	+	0.286184i	$0.0923867\pi$
$331$	13.2253	+	22.9069i	0.726930	+	1.25908i	−0.231245	+	0.972896i	$0.574280\pi$
$332$	6.73183			0.369457
$333$	−5.05333	+	8.75262i	−0.276921	+	0.479641i
$334$	19.3043			1.05628
$335$	−7.80922	−	2.45277i	−0.426663	−	0.134009i
$336$	0.167788			0.00915360
$337$	−18.0196	+	31.2109i	−0.981592	+	1.70017i	−0.325392	+	0.945579i	$0.605496\pi$
$337$	−18.0196	+	31.2109i	−0.981592	+	1.70017i	−0.656200	+	0.754587i	$0.727837\pi$
$338$	−8.95715			−0.487205
$339$	0.249885	+	0.432814i	0.0135719	+	0.0235072i
$340$	−1.83221			−0.0993656
$341$	17.0790	−	29.5816i	0.924878	−	1.60194i
$342$	8.43596	+	14.6115i	0.456165	+	0.790100i
$343$	14.5426			0.785227
$344$	4.00000			0.215666
$345$	−0.230260	+	0.398821i	−0.0123968	+	0.0214718i
$346$	−10.4786	−	18.1494i	−0.563332	−	0.975719i
$347$	−8.81079	−	15.2607i	−0.472988	−	0.819239i	0.526534	−	0.850154i	$-0.323491\pi$
$347$	−8.81079	−	15.2607i	−0.472988	−	0.819239i	−0.999522	+	0.0309149i	$0.990158\pi$
$348$	0.539481	−	0.934408i	0.0289192	−	0.0500895i
$349$	−29.2860			−1.56764			−0.783822	−	0.620986i	$-0.786732\pi$
$349$	−29.2860			−1.56764			−0.783822	+	0.620986i	$0.786732\pi$
$350$	1.14637			0.0612758
$351$	2.05019	−	3.55104i	0.109431	−	0.189540i
$352$	2.00000	−	3.46410i	0.106600	−	0.184637i
$353$	−7.43416	+	12.8763i	−0.395681	+	0.685339i	−0.993188	−	0.116525i	$-0.962825\pi$
$353$	−7.43416	+	12.8763i	−0.395681	+	0.685339i	0.597507	+	0.801864i	$0.296158\pi$
$354$	0.0214229	−	0.0371055i	0.00113861	−	0.00197213i
$355$	−0.876625	−	1.51836i	−0.0465264	−	0.0805861i
$356$	−0.332212	−	0.575407i	−0.0176072	−	0.0304965i
$357$	−0.307424			−0.0162706
$358$	8.84449	−	15.3191i	0.467446	−	0.809640i
$359$	2.33871			0.123433			0.0617163	−	0.998094i	$-0.480343\pi$
$359$	2.33871			0.123433			0.0617163	+	0.998094i	$0.480343\pi$
$360$	2.97858			0.156985
$361$	−6.54285	−	11.3325i	−0.344360	−	0.596450i
$362$	1.53948			0.0809133
$363$	0.365914	−	0.633781i	0.0192055	−	0.0332649i
$364$	−2.68585	−	4.65202i	−0.140777	−	0.243832i
$365$	4.06247	−	7.03641i	0.212639	−	0.368302i
$366$	−0.762394	−	1.32051i	−0.0398510	−	0.0690239i
$367$	2.18007	+	3.77599i	0.113799	+	0.197105i	0.917299	−	0.398199i	$-0.130365\pi$
$367$	2.18007	+	3.77599i	0.113799	+	0.197105i	−0.803500	+	0.595304i	$0.797031\pi$
$368$	1.57318	+	2.72483i	0.0820078	+	0.142042i
$369$	−8.90383	−	15.4219i	−0.463515	−	0.802831i
$370$	−1.69656	−	2.93852i	−0.0881998	−	0.152767i
$371$	−6.33799	−	10.9777i	−0.329052	−	0.569935i
$372$	−0.624943	+	1.08243i	−0.0324018	+	0.0561215i
$373$	−0.185846	−	0.321895i	−0.00962275	−	0.0166671i	0.861174	−	0.508310i	$-0.169730\pi$
$373$	−0.185846	−	0.321895i	−0.00962275	−	0.0166671i	−0.870797	+	0.491643i	$0.836396\pi$
$374$	−3.66442	+	6.34697i	−0.189483	+	0.328194i
$375$	−0.146365			−0.00755828
$376$	−4.42682	−	7.66747i	−0.228296	−	0.395420i
$377$	−34.5426			−1.77904
$378$	1.00314			0.0515957
$379$	−16.6430	+	28.8265i	−0.854894	+	1.48072i	0.0218503	+	0.999761i	$0.493044\pi$
$379$	−16.6430	+	28.8265i	−0.854894	+	1.48072i	−0.876744	+	0.480958i	$0.840289\pi$
$380$	−5.66442			−0.290579
$381$	−1.04285	−	1.80626i	−0.0534266	−	0.0925376i
$382$	−2.31993	−	4.01824i	−0.118698	−	0.205591i
$383$	16.2039	−	28.0660i	0.827981	−	1.43410i	−0.0716389	−	0.997431i	$-0.522823\pi$
$383$	16.2039	−	28.0660i	0.827981	−	1.43410i	0.899620	−	0.436674i	$-0.143844\pi$
$384$	−0.0731827	+	0.126756i	−0.00373459	+	0.00646850i
$385$	2.29273	−	3.97113i	0.116848	−	0.202387i
$386$	2.91611	−	5.05084i	0.148426	−	0.257081i
$387$	11.9143			0.605638
$388$	−7.95715			−0.403963
$389$	6.99507	−	12.1158i	0.354664	−	0.614296i	−0.632396	−	0.774645i	$-0.717929\pi$
$389$	6.99507	−	12.1158i	0.354664	−	0.614296i	0.987060	+	0.160349i	$0.0512619\pi$
$390$	0.342923	+	0.593960i	0.0173646	+	0.0300763i
$391$	−2.88240	−	4.99247i	−0.145769	−	0.252480i
$392$	−2.84292	+	4.92409i	−0.143589	+	0.248704i
$393$	−3.24675			−0.163777
$394$	−14.3931			−0.725115
$395$	6.02877	+	10.4421i	0.303340	+	0.525401i
$396$	5.95715	−	10.3181i	0.299358	−	0.518504i
$397$	−12.8996			−0.647413			−0.323707	−	0.946158i	$-0.604929\pi$
$397$	−12.8996			−0.647413			−0.323707	+	0.946158i	$0.604929\pi$
$398$	9.75903	+	16.9031i	0.489176	+	0.847278i
$399$	−0.950424			−0.0475807
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−6.97858			−0.348494			−0.174247	−	0.984702i	$-0.555749\pi$
$401$	−6.97858			−0.348494			−0.174247	+	0.984702i	$0.555749\pi$
$402$	0.882404	−	0.810367i	0.0440103	−	0.0404174i
$403$	40.0147			1.99327
$404$	6.89468	−	11.9419i	0.343023	−	0.594134i
$405$	8.80765			0.437656
$406$	−4.22533	−	7.31848i	−0.209699	−	0.363210i
$407$	−13.5725			−0.672762
$408$	0.134086	−	0.232244i	0.00663826	−	0.0114978i
$409$	6.38240	+	11.0546i	0.315590	+	0.546617i	0.979563	−	0.201139i	$-0.0644644\pi$
$409$	6.38240	+	11.0546i	0.315590	+	0.546617i	−0.663973	+	0.747756i	$0.731131\pi$
$410$	5.97858			0.295261
$411$	1.68898			0.0833113
$412$	5.40539	−	9.36242i	0.266305	−	0.461253i
$413$	−0.167788	−	0.290618i	−0.00825632	−	0.0143004i
$414$	4.68585	+	8.11612i	0.230297	+	0.398886i
$415$	−3.36591	+	5.82993i	−0.165226	+	0.286180i
$416$	4.68585			0.229743
$417$	−1.17092			−0.0573404
$418$	−11.3288	+	19.6221i	−0.554112	+	0.959750i
$419$	5.56404	−	9.63720i	0.271821	−	0.470808i	−0.697507	−	0.716578i	$-0.745707\pi$
$419$	5.56404	−	9.63720i	0.271821	−	0.470808i	0.969328	+	0.245770i	$0.0790408\pi$
$420$	−0.0838942	+	0.145309i	−0.00409362	+	0.00709035i
$421$	1.62831	−	2.82031i	0.0793589	−	0.137454i	−0.823615	−	0.567150i	$-0.808046\pi$
$421$	1.62831	−	2.82031i	0.0793589	−	0.137454i	0.902973	+	0.429696i	$0.141379\pi$
$422$	9.57318	+	16.5812i	0.466015	+	0.807162i
$423$	−13.1856	−	22.8382i	−0.641107	−	1.11043i
$424$	11.0575			0.537002
$425$	0.916106	−	1.58674i	0.0444377	−	0.0769683i
$426$	0.256615			0.0124331
$427$	−11.9425			−0.577936
$428$	4.41611	+	7.64892i	0.213461	+	0.369724i
$429$	2.74338			0.132452
$430$	−2.00000	+	3.46410i	−0.0964486	+	0.167054i
$431$	−3.90539	−	6.76434i	−0.188116	−	0.325827i	0.756506	−	0.653987i	$-0.226905\pi$
$431$	−3.90539	−	6.76434i	−0.188116	−	0.325827i	−0.944622	+	0.328160i	$0.893571\pi$
$432$	−0.437529	+	0.757822i	−0.0210506	+	0.0364607i
$433$	−0.0838942	−	0.145309i	−0.00403170	−	0.00698310i	0.864003	−	0.503487i	$-0.167950\pi$
$433$	−0.0838942	−	0.145309i	−0.00403170	−	0.00698310i	−0.868034	+	0.496504i	$0.834617\pi$
$434$	4.89468	+	8.47784i	0.234952	+	0.406949i
$435$	0.539481	+	0.934408i	0.0258661	+	0.0448014i
$436$	−1.91611	−	3.31879i	−0.0917648	−	0.158941i
$437$	−8.91117	−	15.4346i	−0.426279	−	0.738337i
$438$	0.594606	+	1.02989i	0.0284114	+	0.0492099i
$439$	−3.14480	+	5.44695i	−0.150093	+	0.259969i	−0.931261	−	0.364352i	$-0.881291\pi$
$439$	−3.14480	+	5.44695i	−0.150093	+	0.259969i	0.781168	+	0.624320i	$0.214624\pi$
$440$	2.00000	+	3.46410i	0.0953463	+	0.165145i
$441$	−8.46787	+	14.6668i	−0.403232	+	0.698418i
$442$	−8.58546			−0.408369
$443$	2.73761	+	4.74167i	0.130068	+	0.225284i	0.923702	−	0.383111i	$-0.125147\pi$
$443$	2.73761	+	4.74167i	0.130068	+	0.225284i	−0.793635	+	0.608394i	$0.791814\pi$
$444$	0.496635			0.0235693
$445$	0.664423			0.0314967
$446$	2.53948	−	4.39851i	0.120248	−	0.208275i
$447$	1.38998			0.0657438
$448$	0.573183	+	0.992782i	0.0270803	+	0.0469045i
$449$	−0.332212	−	0.575407i	−0.0156780	−	0.0271552i	0.858080	−	0.513516i	$-0.171657\pi$
$449$	−0.332212	−	0.575407i	−0.0156780	−	0.0271552i	−0.873758	+	0.486361i	$0.838324\pi$
$450$	−1.48929	+	2.57952i	−0.0702057	+	0.121600i
$451$	11.9572	−	20.7104i	0.563040	−	0.975215i
$452$	−1.70727	+	2.95708i	−0.0803032	+	0.139089i
$453$	−0.878422	+	1.52147i	−0.0412719	+	0.0714850i
$454$	−3.66129			−0.171833
$455$	5.37169			0.251829
$456$	0.414538	−	0.718001i	0.0194125	−	0.0336235i
$457$	−2.91611	−	5.05084i	−0.136410	−	0.236268i	0.789725	−	0.613461i	$-0.210223\pi$
$457$	−2.91611	−	5.05084i	−0.136410	−	0.236268i	−0.926135	+	0.377192i	$0.876890\pi$
$458$	−14.0196	−	24.2827i	−0.655094	−	1.13466i
$459$	0.801645	−	1.38849i	0.0374176	−	0.0648092i
$460$	−3.14637			−0.146700
$461$	19.7894			0.921683			0.460841	−	0.887483i	$-0.347548\pi$
$461$	19.7894			0.921683			0.460841	+	0.887483i	$0.347548\pi$
$462$	0.335577	+	0.581236i	0.0156124	+	0.0270415i
$463$	2.96630	−	5.13778i	0.137856	−	0.238773i	−0.788829	−	0.614613i	$-0.789312\pi$
$463$	2.96630	−	5.13778i	0.137856	−	0.238773i	0.926685	+	0.375840i	$0.122646\pi$
$464$	7.37169			0.342222
$465$	−0.624943	−	1.08243i	−0.0289810	−	0.0501966i
$466$	−16.3257			−0.756274
$467$	−9.73761	+	16.8660i	−0.450603	+	0.780467i	−0.998424	−	0.0561289i	$-0.982124\pi$
$467$	−9.73761	+	16.8660i	−0.450603	+	0.780467i	0.547821	+	0.836596i	$0.315458\pi$
$468$	13.9572			0.645170
$469$	−2.04105	−	9.15874i	−0.0942469	−	0.422911i
$470$	8.85363			0.408388
$471$	0.289595	−	0.501594i	0.0133439	−	0.0231122i
$472$	0.292731			0.0134740
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$	−1.76481			−0.0810603
$475$	2.83221	−	4.90553i	0.129951	−	0.225081i
$476$	−1.05019	−	1.81899i	−0.0481355	−	0.0833731i
$477$	32.9357			1.50802
$478$	10.7434			0.491391
$479$	3.48194	−	6.03090i	0.159094	−	0.275559i	−0.775448	−	0.631411i	$-0.782476\pi$
$479$	3.48194	−	6.03090i	0.159094	−	0.275559i	0.934542	+	0.355852i	$0.115809\pi$
$480$	−0.0731827	−	0.126756i	−0.00334032	−	0.00578560i
$481$	−7.94981	−	13.7695i	−0.362480	−	0.627834i
$482$	3.30344	−	5.72173i	0.150468	−	0.260618i
$483$	−0.527923			−0.0240213
$484$	5.00000			0.227273
$485$	3.97858	−	6.89110i	0.180658	−	0.312909i
$486$	−1.95715	+	3.38989i	−0.0887783	+	0.153769i
$487$	16.0912	−	27.8708i	0.729164	−	1.26295i	−0.228073	−	0.973644i	$-0.573243\pi$
$487$	16.0912	−	27.8708i	0.729164	−	1.26295i	0.957237	−	0.289305i	$-0.0934241\pi$
$488$	5.20884	−	9.02197i	0.235793	−	0.408405i
$489$	0.981942	+	1.70077i	0.0444050	+	0.0769116i
$490$	−2.84292	−	4.92409i	−0.128430	−	0.222448i
$491$	−29.8469			−1.34697			−0.673486	−	0.739200i	$-0.735204\pi$
$491$	−29.8469			−1.34697			−0.673486	+	0.739200i	$0.735204\pi$
$492$	−0.437529	+	0.757822i	−0.0197253	+	0.0341653i
$493$	−13.5065			−0.608302
$494$	−26.5426			−1.19421
$495$	5.95715	+	10.3181i	0.267754	+	0.463764i
$496$	−8.53948			−0.383434
$497$	1.00493	−	1.74059i	0.0450774	−	0.0780763i
$498$	−0.492654	−	0.853301i	−0.0220763	−	0.0382373i
$499$	−17.3717	+	30.0887i	−0.777664	+	1.34695i	0.155621	+	0.987817i	$0.450262\pi$
$499$	−17.3717	+	30.0887i	−0.777664	+	1.34695i	−0.933285	+	0.359136i	$0.883071\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−1.41274	−	2.44694i	−0.0631166	−	0.109321i
$502$	−0.134086	−	0.232244i	−0.00598456	−	0.0103656i
$503$	8.58546	+	14.8705i	0.382807	+	0.663041i	0.991462	−	0.130394i	$-0.0416242\pi$
$503$	8.58546	+	14.8705i	0.382807	+	0.663041i	−0.608655	+	0.793435i	$0.708291\pi$
$504$	1.70727	+	2.95708i	0.0760478	+	0.131719i
$505$	6.89468	+	11.9419i	0.306809	+	0.531409i
$506$	−6.29273	+	10.8993i	−0.279746	+	0.484534i
$507$	0.655509	+	1.13538i	0.0291122	+	0.0504238i
$508$	7.12494	−	12.3408i	0.316118	−	0.547533i
$509$	24.8683			1.10227			0.551135	−	0.834416i	$-0.314195\pi$
$509$	24.8683			1.10227			0.551135	+	0.834416i	$0.314195\pi$
$510$	0.134086	+	0.232244i	0.00593744	+	0.0102839i
$511$	9.31415			0.412034
$512$	−1.00000			−0.0441942
$513$	2.47835	−	4.29262i	0.109422	−	0.189524i
$514$	−6.00000			−0.264649
$515$	5.40539	+	9.36242i	0.238190	+	0.412557i
$516$	−0.292731	−	0.507025i	−0.0128868	−	0.0223205i
$517$	17.7073	−	30.6699i	0.778765	−	1.34886i
$518$	1.94488	−	3.36862i	0.0854529	−	0.148009i
$519$	−1.53370	+	2.65645i	−0.0673220	+	0.116605i
$520$	−2.34292	+	4.05806i	−0.102744	+	0.177958i
$521$	17.3570			0.760424			0.380212	−	0.924899i	$-0.375851\pi$
$521$	17.3570			0.760424			0.380212	+	0.924899i	$0.375851\pi$
$522$	21.9572			0.961039
$523$	−6.14793	+	10.6485i	−0.268830	+	0.465628i	−0.968560	−	0.248780i	$-0.919970\pi$
$523$	−6.14793	+	10.6485i	−0.268830	+	0.465628i	0.699730	+	0.714408i	$0.253304\pi$
$524$	−11.0912	−	19.2106i	−0.484523	−	0.839219i
$525$	−0.0838942	−	0.145309i	−0.00366144	−	0.00634180i
$526$	−3.51806	+	6.09345i	−0.153395	+	0.265687i
$527$	15.6461			0.681556
$528$	−0.585462			−0.0254790
$529$	6.55019	+	11.3453i	0.284791	+	0.493272i
$530$	−5.52877	+	9.57611i	−0.240154	+	0.415960i
$531$	0.871922			0.0378382
$532$	−3.24675	−	5.62354i	−0.140764	−	0.243811i
$533$	28.0147			1.21345
$534$	−0.0486243	+	0.0842198i	−0.00210418	+	0.00364455i
$535$	−8.83221			−0.381850
$536$	7.80922	+	2.45277i	0.337307	+	0.105943i
$537$	−2.58906			−0.111726
$538$	−13.7648	+	23.8413i	−0.593443	+	1.02787i
$539$	−22.7434			−0.979627
$540$	−0.437529	−	0.757822i	−0.0188282	−	0.0326115i
$541$	24.5426			1.05517			0.527585	−	0.849502i	$-0.323098\pi$
$541$	24.5426			1.05517			0.527585	+	0.849502i	$0.323098\pi$
$542$	10.2697	−	17.7877i	0.441123	−	0.764048i
$543$	−0.112663	−	0.195139i	−0.00483485	−	0.00837421i
$544$	1.83221			0.0785554
$545$	3.83221			0.164154
$546$	−0.393115	+	0.680895i	−0.0168238	+	0.0291396i
$547$	13.8552	+	23.9979i	0.592406	+	1.02608i	0.993907	+	0.110218i	$0.0351550\pi$
$547$	13.8552	+	23.9979i	0.592406	+	1.02608i	−0.401502	+	0.915858i	$0.631512\pi$
$548$	5.76974	+	9.99348i	0.246471	+	0.426900i
$549$	15.5149	−	26.8726i	0.662161	−	1.14690i
$550$	−4.00000			−0.170561
$551$	−41.7564			−1.77888
$552$	0.230260	−	0.398821i	0.00980050	−	0.0169750i
$553$	−6.91117	+	11.9705i	−0.293893	+	0.509038i
$554$	16.3898	−	28.3879i	0.696334	−	1.20609i
$555$	−0.248317	+	0.430098i	−0.0105405	+	0.0182567i
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	21.8001	+	37.7588i	0.923699	+	1.59989i	0.793640	+	0.608387i	$0.208183\pi$
$557$	21.8001	+	37.7588i	0.923699	+	1.59989i	0.130059	+	0.991506i	$0.458483\pi$
$558$	−25.4355			−1.07677
$559$	−9.37169	+	16.2322i	−0.396380	+	0.686551i
$560$	−1.14637			−0.0484428
$561$	1.07269			0.0452890
$562$	−2.38240	−	4.12644i	−0.100496	−	0.174064i
$563$	−10.4966			−0.442380			−0.221190	−	0.975231i	$-0.570994\pi$
$563$	−10.4966			−0.442380			−0.221190	+	0.975231i	$0.570994\pi$
$564$	−0.647933	+	1.12225i	−0.0272829	+	0.0472554i
$565$	−1.70727	−	2.95708i	−0.0718253	−	0.124405i
$566$	−6.32150	+	10.9492i	−0.265712	+	0.460228i
$567$	5.04839	+	8.74408i	0.212013	+	0.367217i
$568$	0.876625	+	1.51836i	0.0367824	+	0.0637089i
$569$	−14.9464	−	25.8880i	−0.626587	−	1.08528i	−0.988232	−	0.152965i	$-0.951118\pi$
$569$	−14.9464	−	25.8880i	−0.626587	−	1.08528i	0.361644	−	0.932316i	$-0.382216\pi$
$570$	0.414538	+	0.718001i	0.0173631	+	0.0300738i
$571$	15.3257	+	26.5449i	0.641361	+	1.11087i	0.985129	+	0.171815i	$0.0549632\pi$
$571$	15.3257	+	26.5449i	0.641361	+	1.11087i	−0.343768	+	0.939055i	$0.611703\pi$
$572$	9.37169	+	16.2322i	0.391850	+	0.678704i
$573$	−0.339558	+	0.588132i	−0.0141852	+	0.0245696i
$574$	3.42682	+	5.93542i	0.143033	+	0.247740i
$575$	1.57318	−	2.72483i	0.0656063	−	0.113633i
$576$	−2.97858			−0.124107
$577$	−7.26638	−	12.5857i	−0.302503	−	0.523951i	0.674199	−	0.738550i	$-0.264489\pi$
$577$	−7.26638	−	12.5857i	−0.302503	−	0.523951i	−0.976702	+	0.214599i	$0.931156\pi$
$578$	13.6430			0.567474
$579$	−0.853635			−0.0354758
$580$	−3.68585	+	6.38407i	−0.153046	+	0.265084i
$581$	−7.71713			−0.320161
$582$	0.582326	+	1.00862i	0.0241382	+	0.0418086i
$583$	22.1151	+	38.3044i	0.915913	+	1.58641i
$584$	−4.06247	+	7.03641i	−0.168106	+	0.291169i
$585$	−6.97858	+	12.0873i	−0.288529	+	0.499746i
$586$	−13.5073	+	23.3954i	−0.557983	+	0.966455i
$587$	3.92682	−	6.80145i	0.162077	−	0.280726i	−0.773536	−	0.633752i	$-0.781514\pi$
$587$	3.92682	−	6.80145i	0.162077	−	0.280726i	0.935613	+	0.353026i	$0.114847\pi$
$588$	0.832212			0.0343198
$589$	48.3712			1.99310
$590$	−0.146365	+	0.253512i	−0.00602577	+	0.0104369i
$591$	1.05333	+	1.82442i	0.0433281	+	0.0750465i
$592$	1.69656	+	2.93852i	0.0697281	+	0.120773i
$593$	−19.0361	+	32.9715i	−0.781720	+	1.35398i	0.149220	+	0.988804i	$0.452324\pi$
$593$	−19.0361	+	32.9715i	−0.781720	+	1.35398i	−0.930939	+	0.365174i	$0.881010\pi$
$594$	−3.50023			−0.143616
$595$	2.10038			0.0861074
$596$	4.74832	+	8.22433i	0.194499	+	0.336882i
$597$	1.42839	−	2.47404i	0.0584599	−	0.101256i
$598$	−14.7434			−0.602902
$599$	−2.26817	−	3.92859i	−0.0926750	−	0.160518i	0.815961	−	0.578107i	$-0.196208\pi$
$599$	−2.26817	−	3.92859i	−0.0926750	−	0.160518i	−0.908636	+	0.417589i	$0.862875\pi$
$600$	0.146365			0.00597535
$601$	−2.21798	+	3.84165i	−0.0904733	+	0.156704i	−0.907710	−	0.419597i	$-0.862171\pi$
$601$	−2.21798	+	3.84165i	−0.0904733	+	0.156704i	0.817237	+	0.576302i	$0.195505\pi$
$602$	−4.58546			−0.186889
$603$	23.2604	+	7.30576i	0.947235	+	0.297513i
$604$	−12.0031			−0.488401
$605$	−2.50000	+	4.33013i	−0.101639	+	0.176045i
$606$	−2.01829			−0.0819873
$607$	−11.1825	−	19.3686i	−0.453883	−	0.786148i	0.544740	−	0.838605i	$-0.316628\pi$
$607$	−11.1825	−	19.3686i	−0.453883	−	0.786148i	−0.998623	+	0.0524565i	$0.983295\pi$
$608$	5.66442			0.229723
$609$	−0.618442	+	1.07117i	−0.0250605	+	0.0434061i
$610$	5.20884	+	9.02197i	0.210900	+	0.365289i
$611$	41.4868			1.67838
$612$	5.45738			0.220602
$613$	2.77131	−	4.80005i	0.111932	−	0.193872i	−0.804617	−	0.593794i	$-0.797629\pi$
$613$	2.77131	−	4.80005i	0.111932	−	0.193872i	0.916549	+	0.399922i	$0.130963\pi$
$614$	−8.88397	−	15.3875i	−0.358528	−	0.620989i
$615$	−0.437529	−	0.757822i	−0.0176429	−	0.0305583i
$616$	−2.29273	+	3.97113i	−0.0923768	+	0.160001i
$617$	−26.6613			−1.07334			−0.536672	−	0.843791i	$-0.680319\pi$
$617$	−26.6613			−1.07334			−0.536672	+	0.843791i	$0.680319\pi$
$618$	−1.58233			−0.0636505
$619$	10.3625	−	17.9485i	0.416506	−	0.721410i	−0.579079	−	0.815271i	$-0.696588\pi$
$619$	10.3625	−	17.9485i	0.416506	−	0.721410i	0.995585	+	0.0938617i	$0.0299212\pi$
$620$	4.26974	−	7.39541i	0.171477	−	0.297007i
$621$	1.37663	−	2.38438i	0.0552421	−	0.0956821i
$622$	−9.71618	+	16.8289i	−0.389583	+	0.674778i
$623$	0.380836	+	0.659627i	0.0152579	+	0.0264274i
$624$	−0.342923	−	0.593960i	−0.0137279	−	0.0237774i
$625$	1.00000			0.0400000
$626$	14.3717	−	24.8925i	0.574408	−	0.994904i
$627$	3.31630			0.132440
$628$	3.95715			0.157908
$629$	−3.10845	−	5.38400i	−0.123942	−	0.214674i
$630$	−3.41454			−0.136038
$631$	−5.95715	+	10.3181i	−0.237151	+	0.410757i	−0.959896	−	0.280358i	$-0.909547\pi$
$631$	−5.95715	+	10.3181i	−0.237151	+	0.410757i	0.722745	+	0.691115i	$0.242880\pi$
$632$	−6.02877	−	10.4421i	−0.239812	−	0.415366i
$633$	1.40118	−	2.42692i	0.0556920	−	0.0964615i
$634$	−6.35363	−	11.0048i	−0.252335	−	0.437057i
$635$	7.12494	+	12.3408i	0.282745	+	0.489728i
$636$	−0.809221	−	1.40161i	−0.0320877	−	0.0555775i
$637$	−13.3215	−	23.0735i	−0.527817	−	0.914206i
$638$	14.7434	+	25.5363i	0.583696	+	1.01099i
$639$	2.61110	+	4.52255i	0.103293	+	0.178909i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−11.7392	−	20.3328i	−0.463669	−	0.803099i	0.535471	−	0.844554i	$-0.320134\pi$
$641$	−11.7392	−	20.3328i	−0.463669	−	0.803099i	−0.999140	+	0.0414546i	$0.986801\pi$
$642$	0.646365	−	1.11954i	0.0255100	−	0.0441846i
$643$	−5.85363			−0.230845			−0.115422	−	0.993316i	$-0.536822\pi$
$643$	−5.85363			−0.230845			−0.115422	+	0.993316i	$0.536822\pi$
$644$	−1.80344	−	3.12365i	−0.0710656	−	0.123089i
$645$	0.585462			0.0230525
$646$	−10.3784			−0.408334
$647$	−7.46052	+	12.9220i	−0.293303	+	0.508016i	−0.974589	−	0.224002i	$-0.928088\pi$
$647$	−7.46052	+	12.9220i	−0.293303	+	0.508016i	0.681285	+	0.732018i	$0.261421\pi$
$648$	−8.80765			−0.345997
$649$	0.585462	+	1.01405i	0.0229814	+	0.0398049i
$650$	−2.34292	−	4.05806i	−0.0918970	−	0.159170i
$651$	0.716413	−	1.24086i	0.0280784	−	0.0486333i
$652$	−6.70884	+	11.6200i	−0.262738	+	0.455076i
$653$	−14.5319	+	25.1700i	−0.568677	+	0.984978i	0.428020	+	0.903769i	$0.359211\pi$
$653$	−14.5319	+	25.1700i	−0.568677	+	0.984978i	−0.996697	+	0.0812087i	$0.974122\pi$
$654$	−0.280452	+	0.485757i	−0.0109665	+	0.0189946i
$655$	22.1825			0.866741
$656$	−5.97858			−0.233424
$657$	−12.1004	+	20.9585i	−0.472081	+	0.817668i
$658$	5.07475	+	8.78973i	0.197834	+	0.342659i
$659$	16.3931	+	28.3937i	0.638585	+	1.10606i	0.985743	+	0.168255i	$0.0538133\pi$
$659$	16.3931	+	28.3937i	0.638585	+	1.10606i	−0.347158	+	0.937807i	$0.612853\pi$
$660$	0.292731	−	0.507025i	0.0113945	−	0.0197359i
$661$	−24.0393			−0.935019			−0.467509	−	0.883988i	$-0.654849\pi$
$661$	−24.0393			−0.935019			−0.467509	+	0.883988i	$0.654849\pi$
$662$	26.4507			1.02803
$663$	0.628308	+	1.08826i	0.0244014	+	0.0422645i
$664$	3.36591	−	5.82993i	0.130623	−	0.226245i
$665$	6.49350			0.251807
$666$	5.05333	+	8.75262i	0.195812	+	0.339157i
$667$	−23.1940			−0.898077
$668$	9.65214	−	16.7180i	0.373453	−	0.646839i
$669$	−0.743385			−0.0287409
$670$	−6.02877	+	5.53660i	−0.232912	+	0.213898i
$671$	41.6707			1.60868
$672$	0.0838942	−	0.145309i	0.00323629	−	0.00560542i
$673$	−4.04285			−0.155840			−0.0779201	−	0.996960i	$-0.524828\pi$
$673$	−4.04285			−0.155840			−0.0779201	+	0.996960i	$0.524828\pi$
$674$	18.0196	+	31.2109i	0.694090	+	1.20220i
$675$	0.875057			0.0336810
$676$	−4.47858	+	7.75712i	−0.172253	+	0.298351i
$677$	3.31079	+	5.73445i	0.127244	+	0.220393i	0.922608	−	0.385739i	$-0.126054\pi$
$677$	3.31079	+	5.73445i	0.127244	+	0.220393i	−0.795364	+	0.606132i	$0.792720\pi$
$678$	0.499771			0.0191936
$679$	9.12181			0.350063
$680$	−0.916106	+	1.58674i	−0.0351311	+	0.0608488i
$681$	0.267943	+	0.464091i	0.0102676	+	0.0177840i
$682$	−17.0790	−	29.5816i	−0.653987	−	1.13274i
$683$	4.36591	−	7.56198i	0.167057	−	0.289351i	−0.770327	−	0.637649i	$-0.779907\pi$
$683$	4.36591	−	7.56198i	0.167057	−	0.289351i	0.937384	+	0.348298i	$0.113240\pi$
$684$	16.8719			0.645114
$685$	−11.5395			−0.440901
$686$	7.27131	−	12.5943i	0.277620	−	0.480852i
$687$	−2.05199	+	3.55415i	−0.0782883	+	0.135599i
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−25.9070	+	44.8722i	−0.986977	+	1.70949i
$690$	0.230260	+	0.398821i	0.00876584	+	0.0151829i
$691$	0.832212	+	1.44143i	0.0316588	+	0.0548347i	0.881421	−	0.472332i	$-0.156588\pi$
$691$	0.832212	+	1.44143i	0.0316588	+	0.0548347i	−0.849762	+	0.527167i	$0.823254\pi$
$692$	−20.9572			−0.796671
$693$	−6.82908	+	11.8283i	−0.259415	+	0.449320i
$694$	−17.6216			−0.668906
$695$	8.00000			0.303457
$696$	−0.539481	−	0.934408i	−0.0204490	−	0.0354186i
$697$	10.9540			0.414913
$698$	−14.6430	+	25.3624i	−0.554246	+	0.959982i
$699$	1.19476	+	2.06939i	0.0451900	+	0.0782714i
$700$	0.573183	−	0.992782i	0.0216643	−	0.0375236i
$701$	−23.6216	−	40.9138i	−0.892175	−	1.54529i	−0.837263	−	0.546801i	$-0.815846\pi$
$701$	−23.6216	−	40.9138i	−0.892175	−	1.54529i	−0.0549118	−	0.998491i	$-0.517488\pi$
$702$	−2.05019	−	3.55104i	−0.0773795	−	0.134025i
$703$	−9.61002	−	16.6450i	−0.362449	−	0.627780i
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$	−0.647933	−	1.12225i	−0.0244026	−	0.0422665i
$706$	7.43416	+	12.8763i	0.279788	+	0.484608i
$707$	−7.90383	+	13.6898i	−0.297254	+	0.514859i
$708$	−0.0214229	−	0.0371055i	−0.000805120	−	0.00139451i
$709$	22.2499	−	38.5379i	0.835612	−	1.44732i	−0.0579192	−	0.998321i	$-0.518447\pi$
$709$	22.2499	−	38.5379i	0.835612	−	1.44732i	0.893531	−	0.449001i	$-0.148220\pi$
$710$	−1.75325			−0.0657983
$711$	−17.9572	−	31.1027i	−0.673446	−	1.16644i
$712$	−0.664423			−0.0249003
$713$	26.8683			1.00623
$714$	−0.153712	+	0.266237i	−0.00575252	+	0.00996366i
$715$	−18.7434			−0.700963
$716$	−8.84449	−	15.3191i	−0.330534	−	0.572502i
$717$	−0.786230	−	1.36179i	−0.0293623	−	0.0508570i
$718$	1.16936	−	2.02538i	0.0436400	−	0.0755867i
$719$	12.2055	−	21.1405i	0.455187	−	0.788408i	−0.543512	−	0.839402i	$-0.682906\pi$
$719$	12.2055	−	21.1405i	0.455187	−	0.788408i	0.998699	+	0.0509941i	$0.0162390\pi$
$720$	1.48929	−	2.57952i	0.0555025	−	0.0961332i
$721$	−6.19656	+	10.7328i	−0.230772	+	0.399709i
$722$	−13.0857			−0.486999
$723$	−0.967020			−0.0359639
$724$	0.769740	−	1.33323i	0.0286072	−	0.0495491i
$725$	−3.68585	−	6.38407i	−0.136889	−	0.237099i
$726$	−0.365914	−	0.633781i	−0.0135803	−	0.0235218i
$727$	−14.7894	+	25.6159i	−0.548507	+	0.950042i	0.449870	+	0.893094i	$0.351470\pi$
$727$	−14.7894	+	25.6159i	−0.548507	+	0.950042i	−0.998377	+	0.0569483i	$0.981863\pi$
$728$	−5.37169			−0.199088
$729$	−25.8500			−0.957409
$730$	−4.06247	−	7.03641i	−0.150359	−	0.260429i
$731$	−3.66442	+	6.34697i	−0.135534	+	0.234751i
$732$	−1.52479			−0.0563578
$733$	22.0181	+	38.1364i	0.813256	+	1.40860i	0.910574	+	0.413347i	$0.135640\pi$
$733$	22.0181	+	38.1364i	0.813256	+	1.40860i	−0.0973183	+	0.995253i	$0.531026\pi$
$734$	4.36014			0.160936
$735$	−0.416106	+	0.720716i	−0.0153483	+	0.0265840i
$736$	3.14637			0.115977
$737$	7.12181	+	31.9575i	0.262335	+	1.17717i
$738$	−17.8077			−0.655509
$739$	−6.43910	+	11.1528i	−0.236866	+	0.410264i	−0.959813	−	0.280639i	$-0.909454\pi$
$739$	−6.43910	+	11.1528i	−0.236866	+	0.410264i	0.722947	+	0.690903i	$0.242787\pi$
$740$	−3.39312			−0.124733
$741$	1.94246	+	3.36444i	0.0713581	+	0.123596i
$742$	−12.6760			−0.465350
$743$	−5.32885	+	9.22983i	−0.195496	+	0.338610i	−0.947063	−	0.321047i	$-0.895965\pi$
$743$	−5.32885	+	9.22983i	−0.195496	+	0.338610i	0.751567	+	0.659657i	$0.229298\pi$
$744$	0.624943	+	1.08243i	0.0229115	+	0.0396839i
$745$	−9.49663			−0.347930
$746$	−0.371692			−0.0136086
$747$	10.0256	−	17.3649i	0.366819	−	0.635349i
$748$	3.66442	+	6.34697i	0.133985	+	0.232068i
$749$	−5.06247	−	8.76846i	−0.184979	−	0.320392i
$750$	−0.0731827	+	0.126756i	−0.00267226	+	0.00462848i
$751$	46.3106			1.68990			0.844948	−	0.534848i	$-0.179631\pi$
$751$	46.3106			1.68990			0.844948	+	0.534848i	$0.179631\pi$
$752$	−8.85363			−0.322859
$753$	−0.0196256	+	0.0339925i	−0.000715197	+	0.00123876i
$754$	−17.2713	+	29.9148i	−0.628984	+	1.08943i
$755$	6.00157	−	10.3950i	0.218419	−	0.378314i
$756$	0.501568	−	0.868741i	0.0182418	−	0.0315958i
$757$	−17.0468	−	29.5260i	−0.619577	−	1.07314i	−0.989563	−	0.144102i	$-0.953971\pi$
$757$	−17.0468	−	29.5260i	−0.619577	−	1.07314i	0.369985	−	0.929038i	$-0.379363\pi$
$758$	16.6430	+	28.8265i	0.604501	+	1.04703i
$759$	1.84208			0.0668632
$760$	−2.83221	+	4.90553i	−0.102735	+	0.177942i
$761$	36.0790			1.30786			0.653931	−	0.756554i	$-0.273119\pi$
$761$	36.0790			1.30786			0.653931	+	0.756554i	$0.273119\pi$
$762$	−2.08569			−0.0755566
$763$	2.19656	+	3.80455i	0.0795207	+	0.137734i
$764$	−4.63986			−0.167864
$765$	−2.72869	+	4.72623i	−0.0986561	+	0.170877i
$766$	−16.2039	−	28.0660i	−0.585471	−	1.01407i
$767$	−0.685846	+	1.18792i	−0.0247645	+	0.0428933i
$768$	0.0731827	+	0.126756i	0.00264075	+	0.00457392i
$769$	11.3889	+	19.7262i	0.410694	+	0.711344i	0.994966	−	0.100215i	$-0.0319530\pi$
$769$	11.3889	+	19.7262i	0.410694	+	0.711344i	−0.584271	+	0.811558i	$0.698620\pi$
$770$	−2.29273	−	3.97113i	−0.0826243	−	0.143109i
$771$	0.439096	+	0.760537i	0.0158137	+	0.0273901i
$772$	−2.91611	−	5.05084i	−0.104953	−	0.181784i
$773$	22.4399	+	38.8671i	0.807109	+	1.39795i	0.914858	+	0.403775i	$0.132302\pi$
$773$	22.4399	+	38.8671i	0.807109	+	1.39795i	−0.107750	+	0.994178i	$0.534364\pi$
$774$	5.95715	−	10.3181i	0.214125	−	0.370876i
$775$	4.26974	+	7.39541i	0.153374	+	0.265651i
$776$	−3.97858	+	6.89110i	−0.142823	+	0.247376i
$777$	−0.569325			−0.0204244
$778$	−6.99507	−	12.1158i	−0.250785	−	0.434373i
$779$	33.8652			1.21335
$780$	0.685846			0.0245572
$781$	−3.50650	+	6.07344i	−0.125472	+	0.217325i
$782$	−5.76481			−0.206149
$783$	−3.22533	−	5.58643i	−0.115264	−	0.199643i
$784$	2.84292	+	4.92409i	0.101533	+	0.175860i
$785$	−1.97858	+	3.42700i	−0.0706184	+	0.122315i
$786$	−1.62337	+	2.81177i	−0.0579039	+	0.100292i
$787$	11.2483	−	19.4827i	0.400959	−	0.694482i	−0.592883	−	0.805289i	$-0.702010\pi$
$787$	11.2483	−	19.4827i	0.400959	−	0.694482i	0.993842	+	0.110807i	$0.0353436\pi$
$788$	−7.19656	+	12.4648i	−0.256367	+	0.444040i
$789$	1.02984			0.0366634
$790$	12.0575			0.428988
$791$	1.95715	−	3.38989i	0.0695884	−	0.120531i
$792$	−5.95715	−	10.3181i	−0.211678	−	0.366638i
$793$	24.4078	+	42.2756i	0.866747	+	1.50125i
$794$	−6.44981	+	11.1714i	−0.228895	+	0.396458i
$795$	1.61844			0.0574002
$796$	19.5181			0.691799
$797$	14.1142	+	24.4466i	0.499952	+	0.865942i	1.00000		5.57483e-5i	$-1.77452e-5\pi$
$797$	14.1142	+	24.4466i	0.499952	+	0.865942i	−0.500048	+	0.865998i	$0.666684\pi$
$798$	−0.475212	+	0.823092i	−0.0168223	+	0.0291371i
$799$	16.2217			0.573884
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−1.97904			−0.0699258
$802$	−3.48929	+	6.04363i	−0.123211	+	0.213408i
$803$	−32.4998			−1.14689
$804$	−0.260597	−	1.16937i	−0.00919054	−	0.0412404i
$805$	3.60688			0.127126
$806$	20.0073	−	34.6537i	0.704729	−	1.22063i
$807$	4.02939			0.141841
$808$	−6.89468	−	11.9419i	−0.242554	−	0.420116i
$809$	16.5510			0.581904			0.290952	−	0.956738i	$-0.406028\pi$
$809$	16.5510			0.581904			0.290952	+	0.956738i	$0.406028\pi$
$810$	4.40383	−	7.62765i	0.154735	−	0.268008i
$811$	−25.4415	−	44.0660i	−0.893372	−	1.54737i	−0.835806	−	0.549024i	$-0.814999\pi$
$811$	−25.4415	−	44.0660i	−0.893372	−	1.54737i	−0.0575659	−	0.998342i	$-0.518334\pi$
$812$	−8.45065			−0.296560
$813$	−3.00627			−0.105435
$814$	−6.78623	+	11.7541i	−0.237857	+	0.411981i
$815$	−6.70884	−	11.6200i	−0.235000	−	0.407032i
$816$	−0.134086	−	0.232244i	−0.00469396	−	0.00813017i
$817$	−11.3288	+	19.6221i	−0.396346	+	0.686492i
$818$	12.7648			0.446311
$819$	−16.0000			−0.559085
$820$	2.98929	−	5.17760i	0.104390	−	0.180810i
$821$	−21.3239	+	36.9341i	−0.744210	+	1.28901i	0.206353	+	0.978478i	$0.433840\pi$
$821$	−21.3239	+	36.9341i	−0.744210	+	1.28901i	−0.950563	+	0.310532i	$0.899493\pi$
$822$	0.844491	−	1.46270i	0.0294550	−	0.0510176i
$823$	8.63986	−	14.9647i	0.301167	−	0.521636i	−0.675234	−	0.737604i	$-0.735957\pi$
$823$	8.63986	−	14.9647i	0.301167	−	0.521636i	0.976401	+	0.215968i	$0.0692906\pi$
$824$	−5.40539	−	9.36242i	−0.188306	−	0.326155i
$825$	0.292731	+	0.507025i	0.0101916	+	0.0176523i
$826$	−0.335577			−0.0116762
$827$	5.14637	−	8.91377i	0.178957	−	0.309962i	−0.762567	−	0.646909i	$-0.776061\pi$
$827$	5.14637	−	8.91377i	0.178957	−	0.309962i	0.941523	+	0.336947i	$0.109394\pi$
$828$	9.37169			0.325689
$829$	−24.9174			−0.865419			−0.432709	−	0.901534i	$-0.642442\pi$
$829$	−24.9174			−0.865419			−0.432709	+	0.901534i	$0.642442\pi$
$830$	3.36591	+	5.82993i	0.116833	+	0.202360i
$831$	−4.79779			−0.166433
$832$	2.34292	−	4.05806i	0.0812262	−	0.140688i
$833$	−5.20884	−	9.02197i	−0.180475	−	0.312593i
$834$	−0.585462	+	1.01405i	−0.0202729	+	0.0351137i
$835$	9.65214	+	16.7180i	0.334026	+	0.578550i
$836$	11.3288	+	19.6221i	0.391816	+	0.678646i
$837$	3.73627	+	6.47141i	0.129144	+	0.223684i
$838$	−5.56404	−	9.63720i	−0.192207	−	0.332911i
$839$	10.3445	+	17.9172i	0.357131	+	0.618570i	0.987480	−	0.157742i	$-0.0504215\pi$
$839$	10.3445	+	17.9172i	0.357131	+	0.618570i	−0.630349	+	0.776312i	$0.717088\pi$
$840$	0.0838942	+	0.145309i	0.00289462	+	0.00501364i
$841$	−12.6709	+	21.9467i	−0.436928	+	0.756782i
$842$	−1.62831	−	2.82031i	−0.0561152	−	0.0971944i
$843$	−0.348702	+	0.603969i	−0.0120099	+	0.0208018i
$844$	19.1464			0.659045
$845$	−4.47858	−	7.75712i	−0.154068	−	0.266853i
$846$	−26.3712			−0.906662
$847$	−5.73183			−0.196948
$848$	5.52877	−	9.57611i	0.189859	−	0.328845i
$849$	1.85050			0.0635090
$850$	−0.916106	−	1.58674i	−0.0314222	−	0.0544248i
$851$	−5.33799	−	9.24567i	−0.182984	−	0.316937i
$852$	0.128308	−	0.222235i	0.00439575	−	0.00761366i
$853$	−11.3824	+	19.7149i	−0.389726	+	0.675025i	−0.992413	−	0.122953i	$-0.960764\pi$
$853$	−11.3824	+	19.7149i	−0.389726	+	0.675025i	0.602686	+	0.797978i	$0.294097\pi$
$854$	−5.97123	+	10.3425i	−0.204331	+	0.353912i
$855$	−8.43596	+	14.6115i	−0.288504	+	0.499703i
$856$	8.83221			0.301879
$857$	33.5886			1.14736			0.573682	−	0.819078i	$-0.305514\pi$
$857$	33.5886			1.14736			0.573682	+	0.819078i	$0.305514\pi$
$858$	1.37169	−	2.37584i	0.0468288	−	0.0811099i
$859$	1.26817	+	2.19654i	0.0432695	+	0.0749450i	0.886849	−	0.462059i	$-0.152889\pi$
$859$	1.26817	+	2.19654i	0.0432695	+	0.0749450i	−0.843580	+	0.537004i	$0.819556\pi$
$860$	2.00000	+	3.46410i	0.0681994	+	0.118125i
$861$	0.501568	−	0.868741i	0.0170934	−	0.0296066i
$862$	−7.81079			−0.266037
$863$	−29.4391			−1.00212			−0.501059	−	0.865413i	$-0.667056\pi$
$863$	−29.4391			−1.00212			−0.501059	+	0.865413i	$0.667056\pi$
$864$	0.437529	+	0.757822i	0.0148850	+	0.0257816i
$865$	10.4786	−	18.1494i	0.356282	−	0.617099i
$866$	−0.167788			−0.00570168
$867$	−0.998432	−	1.72934i	−0.0339085	−	0.0587313i
$868$	9.78937			0.332273
$869$	24.1151	−	41.7685i	0.818048	−	1.41690i
$870$	1.07896			0.0365802
$871$	−28.2499	+	25.9437i	−0.957211	+	0.879067i
$872$	−3.83221			−0.129775
$873$	−11.8505	+	20.5257i	−0.401079	+	0.694689i
$874$	−17.8223			−0.602850
$875$	0.573183	+	0.992782i	0.0193771	+	0.0335621i
$876$	1.18921			0.0401797
$877$	26.7507	−	46.3336i	0.903308	−	1.56458i	0.0801355	−	0.996784i	$-0.474465\pi$
$877$	26.7507	−	46.3336i	0.903308	−	1.56458i	0.823172	−	0.567791i	$-0.192202\pi$
$878$	3.14480	+	5.44695i	0.106132	+	0.183826i
$879$	3.95402			0.133366
$880$	4.00000			0.134840
$881$	17.7499	−	30.7437i	0.598009	−	1.03578i	−0.395106	−	0.918636i	$-0.629292\pi$
$881$	17.7499	−	30.7437i	0.598009	−	1.03578i	0.993115	−	0.117146i	$-0.0373746\pi$
$882$	8.46787	+	14.6668i	0.285128	+	0.493856i
$883$	2.24989	+	3.89692i	0.0757147	+	0.131142i	0.901397	−	0.432994i	$-0.142543\pi$
$883$	2.24989	+	3.89692i	0.0757147	+	0.131142i	−0.825682	+	0.564136i	$0.809210\pi$
$884$	−4.29273	+	7.43523i	−0.144380	+	0.250074i
$885$	0.0428457			0.00144024
$886$	5.47521			0.183943
$887$	21.7342	−	37.6448i	0.729764	−	1.26399i	−0.227218	−	0.973844i	$-0.572963\pi$
$887$	21.7342	−	37.6448i	0.729764	−	1.26399i	0.956983	−	0.290145i	$-0.0937036\pi$
$888$	0.248317	−	0.430098i	0.00833299	−	0.0144332i
$889$	−8.16779	+	14.1470i	−0.273939	+	0.474476i
$890$	0.332212	−	0.575407i	0.0111358	−	0.0192877i
$891$	−17.6153	−	30.5106i	−0.590135	−	1.02214i
$892$	−2.53948	−	4.39851i	−0.0850281	−	0.147273i
$893$	50.1507			1.67823
$894$	0.694990	−	1.20376i	0.0232439	−	0.0402597i
$895$	17.6890			0.591277
$896$	1.14637			0.0382974
$897$	1.07896	+	1.86882i	0.0360255	+	0.0623979i
$898$	−0.664423			−0.0221721
$899$	31.4752	−	54.5167i	1.04976	−	1.81823i
$900$	1.48929	+	2.57952i	0.0496430	+	0.0859841i
$901$	−10.1299	+	17.5455i	−0.337475	+	0.584524i
$902$	−11.9572	−	20.7104i	−0.398130	−	0.689581i
$903$	0.335577	+	0.581236i	0.0111673	+	0.0193423i
$904$	1.70727	+	2.95708i	0.0567829	+	0.0983509i
$905$	0.769740	+	1.33323i	0.0255870	+	0.0443180i
$906$	0.878422	+	1.52147i	0.0291836	+	0.0505475i
$907$	−26.0837	−	45.1782i	−0.866094	−	1.50012i	−0.865957	−	0.500119i	$-0.833290\pi$
$907$	−26.0837	−	45.1782i	−0.866094	−	1.50012i	−0.000136951	−	1.00000i	$-0.500044\pi$
$908$	−1.83064	+	3.17077i	−0.0607521	+	0.105226i
$909$	−20.5363	−	35.5700i	−0.681148	−	1.17978i
$910$	2.68585	−	4.65202i	0.0890349	−	0.154213i
$911$	14.1035			0.467270			0.233635	−	0.972324i	$-0.424938\pi$
$911$	14.1035			0.467270			0.233635	+	0.972324i	$0.424938\pi$
$912$	−0.414538	−	0.718001i	−0.0137267	−	0.0237754i
$913$	26.9273			0.891164
$914$	−5.83221			−0.192912
$915$	0.762394	−	1.32051i	0.0252040	−	0.0436546i
$916$	−28.0393			−0.926443
$917$	12.7146	+	22.0224i	0.419874	+	0.727242i
$918$	−0.801645	−	1.38849i	−0.0264582	−	0.0458270i
$919$	15.3873	−	26.6516i	0.507581	−	0.879157i	−0.492380	−	0.870380i	$-0.663873\pi$
$919$	15.3873	−	26.6516i	0.507581	−	0.879157i	0.999961	−	0.00877648i	$-0.00279368\pi$
$920$	−1.57318	+	2.72483i	−0.0518663	+	0.0898351i
$921$	−1.30031	+	2.25220i	−0.0428466	+	0.0742124i
$922$	9.89468	−	17.1381i	0.325864	−	0.564413i
$923$	−8.21546			−0.270415
$924$	0.671153			0.0220793
$925$	1.69656	−	2.93852i	0.0557825	−	0.0966181i
$926$	−2.96630	−	5.13778i	−0.0974786	−	0.168838i
$927$	−16.1004	−	27.8867i	−0.528806	−	0.915919i
$928$	3.68585	−	6.38407i	0.120994	−	0.209567i
$929$	30.1067			0.987767			0.493884	−	0.869528i	$-0.335577\pi$
$929$	30.1067			0.987767			0.493884	+	0.869528i	$0.335577\pi$
$930$	−1.24989			−0.0409854
$931$	−16.1035	−	27.8921i	−0.527772	−	0.914127i
$932$	−8.16286	+	14.1385i	−0.267383	+	0.463121i
$933$	2.84423			0.0931158
$934$	9.73761	+	16.8660i	0.318624	+	0.551873i
$935$	−7.32885			−0.239679
$936$	6.97858	−	12.0873i	0.228102	−	0.395084i
$937$	−2.61844			−0.0855408			−0.0427704	−	0.999085i	$-0.513618\pi$
$937$	−2.61844			−0.0855408			−0.0427704	+	0.999085i	$0.513618\pi$
$938$	−8.95222	−	2.81177i	−0.292300	−	0.0918075i
$939$	−4.20704			−0.137292
$940$	4.42682	−	7.66747i	0.144387	−	0.250085i
$941$	−39.5296			−1.28863			−0.644314	−	0.764761i	$-0.722857\pi$
$941$	−39.5296			−1.28863			−0.644314	+	0.764761i	$0.722857\pi$
$942$	−0.289595	−	0.501594i	−0.00943553	−	0.0163428i
$943$	18.8108			0.612564
$944$	0.146365	−	0.253512i	0.00476379	−	0.00825113i
$945$	0.501568	+	0.868741i	0.0163160	+	0.0282601i
$946$	16.0000			0.520205
$947$	−7.46365			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$947$	−7.46365			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$948$	−0.882404	+	1.52837i	−0.0286591	+	0.0496391i
$949$	−19.0361	−	32.9715i	−0.617938	−	1.07030i
$950$	−2.83221	−	4.90553i	−0.0918891	−	0.159157i
$951$	−0.929953	+	1.61073i	−0.0301558	+	0.0522314i
$952$	−2.10038			−0.0680738
$953$	−28.0428			−0.908397			−0.454198	−	0.890901i	$-0.650074\pi$
$953$	−28.0428			−0.908397			−0.454198	+	0.890901i	$0.650074\pi$
$954$	16.4679	−	28.5232i	0.533167	−	0.923472i
$955$	2.31993	−	4.01824i	0.0750713	−	0.130027i
$956$	5.37169	−	9.30404i	0.173733	−	0.300914i
$957$	2.15792	−	3.73763i	0.0697557	−	0.120820i
$958$	−3.48194	−	6.03090i	−0.112496	−	0.194850i
$959$	−6.61423	−	11.4562i	−0.213585	−	0.369939i
$960$	−0.146365			−0.00472393
$961$	−20.9614	+	36.3061i	−0.676173	+	1.17117i
$962$	−15.8996			−0.512624
$963$	26.3074			0.847745
$964$	−3.30344	−	5.72173i	−0.106397	−	0.184285i
$965$	5.83221			0.187746
$966$	−0.263962	+	0.457195i	−0.00849283	+	0.0147100i
$967$	−26.0024	−	45.0375i	−0.836181	−	1.44831i	−0.893065	−	0.449928i	$-0.851450\pi$
$967$	−26.0024	−	45.0375i	−0.836181	−	1.44831i	0.0568838	−	0.998381i	$-0.481884\pi$
$968$	2.50000	−	4.33013i	0.0803530	−	0.139176i
$969$	0.759521	+	1.31553i	0.0243993	+	0.0422609i
$970$	−3.97858	−	6.89110i	−0.127744	−	0.221260i
$971$	−27.1365	−	47.0018i	−0.870852	−	1.50836i	−0.861117	−	0.508407i	$-0.830235\pi$
$971$	−27.1365	−	47.0018i	−0.870852	−	1.50836i	−0.00973471	−	0.999953i	$-0.503099\pi$
$972$	1.95715	+	3.38989i	0.0627758	+	0.108731i
$973$	4.58546	+	7.94225i	0.147003	+	0.254617i
$974$	−16.0912	−	27.8708i	−0.515597	−	0.893040i
$975$	−0.342923	+	0.593960i	−0.0109823	+	0.0190220i
$976$	−5.20884	−	9.02197i	−0.166731	−	0.288786i
$977$	10.7912	−	18.6908i	0.345240	−	0.597973i	−0.640157	−	0.768244i	$-0.721131\pi$
$977$	10.7912	−	18.6908i	0.345240	−	0.597973i	0.985397	+	0.170271i	$0.0544642\pi$
$978$	1.96388			0.0627981
$979$	−1.32885	−	2.30163i	−0.0424701	−	0.0735604i
$980$	−5.68585			−0.181628
$981$	−11.4145			−0.364438
$982$	−14.9235	+	25.8482i	−0.476226	+	0.824848i
$983$	−39.0178			−1.24448			−0.622238	−	0.782828i	$-0.713776\pi$
$983$	−39.0178			−1.24448			−0.622238	+	0.782828i	$0.713776\pi$
$984$	0.437529	+	0.757822i	0.0139479	+	0.0241585i
$985$	−7.19656	−	12.4648i	−0.229301	−	0.397162i
$986$	−6.75325	+	11.6970i	−0.215067	+	0.372507i
$987$	0.742768	−	1.28651i	0.0236426	−	0.0409501i
$988$	−13.2713	+	22.9866i	−0.422217	+	0.731301i
$989$	−6.29273	+	10.8993i	−0.200097	+	0.346579i
$990$	11.9143			0.378662
$991$	−31.2253			−0.991905			−0.495953	−	0.868350i	$-0.665181\pi$
$991$	−31.2253			−0.991905			−0.495953	+	0.868350i	$0.665181\pi$
$992$	−4.26974	+	7.39541i	−0.135564	+	0.234804i
$993$	−1.93573	−	3.35279i	−0.0614286	−	0.106397i
$994$	−1.00493	−	1.74059i	−0.0318745	−	0.0552083i
$995$	−9.75903	+	16.9031i	−0.309382	+	0.535865i
$996$	−0.985307			−0.0312207
$997$	−15.5426			−0.492240			−0.246120	−	0.969239i	$-0.579156\pi$
$997$	−15.5426			−0.492240			−0.246120	+	0.969239i	$0.579156\pi$
$998$	17.3717	+	30.0887i	0.549891	+	0.952440i
$999$	1.48459	−	2.57138i	0.0469702	−	0.0813548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.h.431.2	yes	6
67.37	even	3	inner	670.2.e.h.171.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.h.171.2	✓	6	67.37	even	3	inner
670.2.e.h.431.2	yes	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -0.146365 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.0731827 + 0.126756i) q^{6} +(0.573183 + 0.992782i) q^{7} -1.00000 q^{8} -2.97858 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} -0.146365 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.0731827 + 0.126756i) q^{6} +(0.573183 + 0.992782i) q^{7} -1.00000 q^{8} -2.97858 q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.0731827 + 0.126756i) q^{12} +(2.34292 - 4.05806i) q^{13} +1.14637 q^{14} -0.146365 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.916106 - 1.58674i) q^{17} +(-1.48929 + 2.57952i) q^{18} +(2.83221 - 4.90553i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.0838942 - 0.145309i) q^{21} -4.00000 q^{22} +(1.57318 - 2.72483i) q^{23} +0.146365 q^{24} +1.00000 q^{25} +(-2.34292 - 4.05806i) q^{26} +0.875057 q^{27} +(0.573183 - 0.992782i) q^{28} +(-3.68585 - 6.38407i) q^{29} +(-0.0731827 + 0.126756i) q^{30} +(4.26974 + 7.39541i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.292731 + 0.507025i) q^{33} +(-0.916106 - 1.58674i) q^{34} +(0.573183 + 0.992782i) q^{35} +(1.48929 + 2.57952i) q^{36} +(1.69656 - 2.93852i) q^{37} +(-2.83221 - 4.90553i) q^{38} +(-0.342923 + 0.593960i) q^{39} -1.00000 q^{40} +(2.98929 + 5.17760i) q^{41} -0.167788 q^{42} -4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} -2.97858 q^{45} +(-1.57318 - 2.72483i) q^{46} +(4.42682 + 7.66747i) q^{47} +(0.0731827 - 0.126756i) q^{48} +(2.84292 - 4.92409i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.134086 + 0.232244i) q^{51} -4.68585 q^{52} -11.0575 q^{53} +(0.437529 - 0.757822i) q^{54} +(-2.00000 - 3.46410i) q^{55} +(-0.573183 - 0.992782i) q^{56} +(-0.414538 + 0.718001i) q^{57} -7.37169 q^{58} -0.292731 q^{59} +(0.0731827 + 0.126756i) q^{60} +(-5.20884 + 9.02197i) q^{61} +8.53948 q^{62} +(-1.70727 - 2.95708i) q^{63} +1.00000 q^{64} +(2.34292 - 4.05806i) q^{65} +0.585462 q^{66} +(-7.80922 - 2.45277i) q^{67} -1.83221 q^{68} +(-0.230260 + 0.398821i) q^{69} +1.14637 q^{70} +(-0.876625 - 1.51836i) q^{71} +2.97858 q^{72} +(4.06247 - 7.03641i) q^{73} +(-1.69656 - 2.93852i) q^{74} -0.146365 q^{75} -5.66442 q^{76} +(2.29273 - 3.97113i) q^{77} +(0.342923 + 0.593960i) q^{78} +(6.02877 + 10.4421i) q^{79} +(-0.500000 + 0.866025i) q^{80} +8.80765 q^{81} +5.97858 q^{82} +(-3.36591 + 5.82993i) q^{83} +(-0.0838942 + 0.145309i) q^{84} +(0.916106 - 1.58674i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(0.539481 + 0.934408i) q^{87} +(2.00000 + 3.46410i) q^{88} +0.664423 q^{89} +(-1.48929 + 2.57952i) q^{90} +5.37169 q^{91} -3.14637 q^{92} +(-0.624943 - 1.08243i) q^{93} +8.85363 q^{94} +(2.83221 - 4.90553i) q^{95} +(-0.0731827 - 0.126756i) q^{96} +(3.97858 - 6.89110i) q^{97} +(-2.84292 - 4.92409i) q^{98} +(5.95715 + 10.3181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 2 q^{3} - 3 q^{4} + 6 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 + 6 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q + 3 q^{2} + 2 q^{3} - 3 q^{4} + 6 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} - 12 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} + 2 q^{15} - 3 q^{16} - 8 q^{17} + 6 q^{18} - 10 q^{19} - 3 q^{20} - 14 q^{21} - 24 q^{22} + 8 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 38 q^{27} + 2 q^{28} + 2 q^{29} + q^{30} + 15 q^{31} + 3 q^{32} - 4 q^{33} + 8 q^{34} + 2 q^{35} - 6 q^{36} + q^{37} + 10 q^{38} + 10 q^{39} - 6 q^{40} + 3 q^{41} - 28 q^{42} - 24 q^{43} - 12 q^{44} + 12 q^{45} - 8 q^{46} + 28 q^{47} - q^{48} + 5 q^{49} + 3 q^{50} - 8 q^{51} - 4 q^{52} + 6 q^{53} + 19 q^{54} - 12 q^{55} - 2 q^{56} - 14 q^{57} + 4 q^{58} + 4 q^{59} - q^{60} - 12 q^{61} + 30 q^{62} - 16 q^{63} + 6 q^{64} + 2 q^{65} - 8 q^{66} - 15 q^{67} + 16 q^{68} - 12 q^{69} + 4 q^{70} - 13 q^{71} - 12 q^{72} + 8 q^{73} - q^{74} + 2 q^{75} + 20 q^{76} + 8 q^{77} - 10 q^{78} - 3 q^{80} + 46 q^{81} + 6 q^{82} - 13 q^{83} - 14 q^{84} - 8 q^{85} - 12 q^{86} - 18 q^{87} + 12 q^{88} - 50 q^{89} + 6 q^{90} - 16 q^{91} - 16 q^{92} + 29 q^{93} + 56 q^{94} - 10 q^{95} + q^{96} - 6 q^{97} - 5 q^{98} - 24 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 + 6 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 - 12 * q^11 - q^12 + 2 * q^13 + 4 * q^14 + 2 * q^15 - 3 * q^16 - 8 * q^17 + 6 * q^18 - 10 * q^19 - 3 * q^20 - 14 * q^21 - 24 * q^22 + 8 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 38 * q^27 + 2 * q^28 + 2 * q^29 + q^30 + 15 * q^31 + 3 * q^32 - 4 * q^33 + 8 * q^34 + 2 * q^35 - 6 * q^36 + q^37 + 10 * q^38 + 10 * q^39 - 6 * q^40 + 3 * q^41 - 28 * q^42 - 24 * q^43 - 12 * q^44 + 12 * q^45 - 8 * q^46 + 28 * q^47 - q^48 + 5 * q^49 + 3 * q^50 - 8 * q^51 - 4 * q^52 + 6 * q^53 + 19 * q^54 - 12 * q^55 - 2 * q^56 - 14 * q^57 + 4 * q^58 + 4 * q^59 - q^60 - 12 * q^61 + 30 * q^62 - 16 * q^63 + 6 * q^64 + 2 * q^65 - 8 * q^66 - 15 * q^67 + 16 * q^68 - 12 * q^69 + 4 * q^70 - 13 * q^71 - 12 * q^72 + 8 * q^73 - q^74 + 2 * q^75 + 20 * q^76 + 8 * q^77 - 10 * q^78 - 3 * q^80 + 46 * q^81 + 6 * q^82 - 13 * q^83 - 14 * q^84 - 8 * q^85 - 12 * q^86 - 18 * q^87 + 12 * q^88 - 50 * q^89 + 6 * q^90 - 16 * q^91 - 16 * q^92 + 29 * q^93 + 56 * q^94 - 10 * q^95 + q^96 - 6 * q^97 - 5 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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