LMFDB - Embedded newform 670.2.e.h.171.1

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			171.1
Root			$-0.906803 + 1.57063i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.h.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -2.10278 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.05139 - 1.82106i) q^{6} +(1.55139 - 2.68708i) q^{7} -1.00000 q^{8} +1.42166 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -2.10278 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.05139 - 1.82106i) q^{6} +(1.55139 - 2.68708i) q^{7} -1.00000 q^{8} +1.42166 q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(1.05139 - 1.82106i) q^{12} +(-1.81361 - 3.14126i) q^{13} +3.10278 q^{14} -2.10278 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.26222 - 3.91828i) q^{17} +(0.710831 + 1.23120i) q^{18} +(-3.52444 - 6.10451i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.26222 + 5.65033i) q^{21} -4.00000 q^{22} +(2.55139 + 4.41913i) q^{23} +2.10278 q^{24} +1.00000 q^{25} +(1.81361 - 3.14126i) q^{26} +3.31889 q^{27} +(1.55139 + 2.68708i) q^{28} +(4.62721 - 8.01457i) q^{29} +(-1.05139 - 1.82106i) q^{30} +(-0.864994 + 1.49821i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.20555 - 7.28423i) q^{33} +(2.26222 - 3.91828i) q^{34} +(1.55139 - 2.68708i) q^{35} +(-0.710831 + 1.23120i) q^{36} +(-4.41638 - 7.64940i) q^{37} +(3.52444 - 6.10451i) q^{38} +(3.81361 + 6.60536i) q^{39} -1.00000 q^{40} +(0.789169 - 1.36688i) q^{41} -6.52444 q^{42} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +1.42166 q^{45} +(-2.55139 + 4.41913i) q^{46} +(3.44861 - 5.97317i) q^{47} +(1.05139 + 1.82106i) q^{48} +(-1.31361 - 2.27523i) q^{49} +(0.500000 + 0.866025i) q^{50} +(4.75694 + 8.23926i) q^{51} +3.62721 q^{52} +13.8816 q^{53} +(1.65944 + 2.87424i) q^{54} +(-2.00000 + 3.46410i) q^{55} +(-1.55139 + 2.68708i) q^{56} +(7.41110 + 12.8364i) q^{57} +9.25443 q^{58} -4.20555 q^{59} +(1.05139 - 1.82106i) q^{60} +(-5.94333 - 10.2942i) q^{61} -1.72999 q^{62} +(2.20555 - 3.82012i) q^{63} +1.00000 q^{64} +(-1.81361 - 3.14126i) q^{65} +8.41110 q^{66} +(7.59498 - 3.05225i) q^{67} +4.52444 q^{68} +(-5.36499 - 9.29244i) q^{69} +3.10278 q^{70} +(-7.96777 + 13.8006i) q^{71} -1.42166 q^{72} +(2.84056 + 4.91999i) q^{73} +(4.41638 - 7.64940i) q^{74} -2.10278 q^{75} +7.04888 q^{76} +(6.20555 + 10.7483i) q^{77} +(-3.81361 + 6.60536i) q^{78} +(-6.44082 + 11.1558i) q^{79} +(-0.500000 - 0.866025i) q^{80} -11.2439 q^{81} +1.57834 q^{82} +(-8.25694 - 14.3014i) q^{83} +(-3.26222 - 5.65033i) q^{84} +(-2.26222 - 3.91828i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-9.72999 + 16.8528i) q^{87} +(2.00000 - 3.46410i) q^{88} -12.0489 q^{89} +(0.710831 + 1.23120i) q^{90} -11.2544 q^{91} -5.10278 q^{92} +(1.81889 - 3.15041i) q^{93} +6.89722 q^{94} +(-3.52444 - 6.10451i) q^{95} +(-1.05139 + 1.82106i) q^{96} +(-0.421663 - 0.730342i) q^{97} +(1.31361 - 2.27523i) q^{98} +(-2.84333 + 4.92478i) 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 $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

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

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
$3$	−2.10278			−1.21404			−0.607019	−	0.794687i	$-0.707635\pi$
$3$	−2.10278			−1.21404			−0.607019	+	0.794687i	$0.707635\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.05139	−	1.82106i	−0.429227	−	0.743443i
$7$	1.55139	−	2.68708i	0.586369	−	1.01562i	−0.408334	−	0.912833i	$-0.633890\pi$
$7$	1.55139	−	2.68708i	0.586369	−	1.01562i	0.994703	−	0.102789i	$-0.0327766\pi$
$8$	−1.00000			−0.353553
$9$	1.42166			0.473888
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	1.05139	−	1.82106i	0.303509	−	0.525694i
$13$	−1.81361	−	3.14126i	−0.503004	−	0.871228i	−0.999994	−	0.00347213i	$-0.998895\pi$
$13$	−1.81361	−	3.14126i	−0.503004	−	0.871228i	0.496990	−	0.867756i	$-0.334439\pi$
$14$	3.10278			0.829252
$15$	−2.10278			−0.542934
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.26222	−	3.91828i	−0.548669	−	0.950322i	−0.998366	−	0.0571411i	$-0.981802\pi$
$17$	−2.26222	−	3.91828i	−0.548669	−	0.950322i	0.449697	−	0.893181i	$-0.351532\pi$
$18$	0.710831	+	1.23120i	0.167545	+	0.290196i
$19$	−3.52444	−	6.10451i	−0.808562	−	1.40047i	−0.913860	−	0.406029i	$-0.866913\pi$
$19$	−3.52444	−	6.10451i	−0.808562	−	1.40047i	0.105299	−	0.994441i	$-0.466420\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−3.26222	+	5.65033i	−0.711875	+	1.23300i
$22$	−4.00000			−0.852803
$23$	2.55139	+	4.41913i	0.532001	+	0.921453i	0.999302	+	0.0373546i	$0.0118931\pi$
$23$	2.55139	+	4.41913i	0.532001	+	0.921453i	−0.467301	+	0.884098i	$0.654774\pi$
$24$	2.10278			0.429227
$25$	1.00000			0.200000
$26$	1.81361	−	3.14126i	0.355677	−	0.616051i
$27$	3.31889			0.638720
$28$	1.55139	+	2.68708i	0.293185	+	0.507811i
$29$	4.62721	−	8.01457i	0.859252	−	1.48827i	−0.0133917	−	0.999910i	$-0.504263\pi$
$29$	4.62721	−	8.01457i	0.859252	−	1.48827i	0.872644	−	0.488358i	$-0.162404\pi$
$30$	−1.05139	−	1.82106i	−0.191956	−	0.332478i
$31$	−0.864994	+	1.49821i	−0.155358	+	0.269087i	−0.933189	−	0.359386i	$-0.882986\pi$
$31$	−0.864994	+	1.49821i	−0.155358	+	0.269087i	0.777832	+	0.628473i	$0.216320\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.20555	−	7.28423i	0.732092	−	1.26802i
$34$	2.26222	−	3.91828i	0.387967	−	0.671979i
$35$	1.55139	−	2.68708i	0.262232	−	0.454200i
$36$	−0.710831	+	1.23120i	−0.118472	+	0.205199i
$37$	−4.41638	−	7.64940i	−0.726049	−	1.25755i	−0.958541	−	0.284955i	$-0.908021\pi$
$37$	−4.41638	−	7.64940i	−0.726049	−	1.25755i	0.232492	−	0.972598i	$-0.425312\pi$
$38$	3.52444	−	6.10451i	0.571739	−	0.990282i
$39$	3.81361	+	6.60536i	0.610666	+	1.05770i
$40$	−1.00000			−0.158114
$41$	0.789169	−	1.36688i	0.123247	−	0.213471i	−0.797799	−	0.602923i	$-0.794002\pi$
$41$	0.789169	−	1.36688i	0.123247	−	0.213471i	0.921047	+	0.389453i	$0.127336\pi$
$42$	−6.52444			−1.00674
$43$	−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
$45$	1.42166			0.211929
$46$	−2.55139	+	4.41913i	−0.376182	+	0.651566i
$47$	3.44861	−	5.97317i	0.503032	−	0.871277i	−0.496962	−	0.867772i	$-0.665551\pi$
$47$	3.44861	−	5.97317i	0.503032	−	0.871277i	0.999994	−	0.00350440i	$-0.00111549\pi$
$48$	1.05139	+	1.82106i	0.151755	+	0.262847i
$49$	−1.31361	−	2.27523i	−0.187658	−	0.325033i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	4.75694	+	8.23926i	0.666105	+	1.15373i
$52$	3.62721			0.503004
$53$	13.8816			1.90679			0.953395	−	0.301725i	$-0.0975626\pi$
$53$	13.8816			1.90679			0.953395	+	0.301725i	$0.0975626\pi$
$54$	1.65944	+	2.87424i	0.225822	+	0.391135i
$55$	−2.00000	+	3.46410i	−0.269680	+	0.467099i
$56$	−1.55139	+	2.68708i	−0.207313	+	0.359076i
$57$	7.41110	+	12.8364i	0.981624	+	1.70022i
$58$	9.25443			1.21517
$59$	−4.20555			−0.547516			−0.273758	−	0.961799i	$-0.588267\pi$
$59$	−4.20555			−0.547516			−0.273758	+	0.961799i	$0.588267\pi$
$60$	1.05139	−	1.82106i	0.135734	−	0.235097i
$61$	−5.94333	−	10.2942i	−0.760966	−	1.31803i	−0.942353	−	0.334619i	$-0.891392\pi$
$61$	−5.94333	−	10.2942i	−0.760966	−	1.31803i	0.181388	−	0.983412i	$-0.441941\pi$
$62$	−1.72999			−0.219709
$63$	2.20555	−	3.82012i	0.277873	−	0.481290i
$64$	1.00000			0.125000
$65$	−1.81361	−	3.14126i	−0.224950	−	0.389625i
$66$	8.41110			1.03533
$67$	7.59498	−	3.05225i	0.927875	−	0.372892i
$67$	7.59498	−	3.05225i	0.927875	−	0.372892i
$68$	4.52444			0.548669
$69$	−5.36499	−	9.29244i	−0.645869	−	1.11868i
$70$	3.10278			0.370853
$71$	−7.96777	+	13.8006i	−0.945600	+	1.63783i	−0.191055	+	0.981579i	$0.561191\pi$
$71$	−7.96777	+	13.8006i	−0.945600	+	1.63783i	−0.754545	+	0.656248i	$0.772142\pi$
$72$	−1.42166			−0.167545
$73$	2.84056	+	4.91999i	0.332462	+	0.575841i	0.982994	−	0.183638i	$-0.0587874\pi$
$73$	2.84056	+	4.91999i	0.332462	+	0.575841i	−0.650532	+	0.759479i	$0.725454\pi$
$74$	4.41638	−	7.64940i	0.513394	−	0.889224i
$75$	−2.10278			−0.242808
$76$	7.04888			0.808562
$77$	6.20555	+	10.7483i	0.707188	+	1.22489i
$78$	−3.81361	+	6.60536i	−0.431806	+	0.747910i
$79$	−6.44082	+	11.1558i	−0.724649	+	1.25513i	0.234470	+	0.972123i	$0.424665\pi$
$79$	−6.44082	+	11.1558i	−0.724649	+	1.25513i	−0.959118	+	0.283005i	$0.908669\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−11.2439			−1.24932
$82$	1.57834			0.174298
$83$	−8.25694	−	14.3014i	−0.906317	−	1.56979i	−0.819140	−	0.573594i	$-0.805549\pi$
$83$	−8.25694	−	14.3014i	−0.906317	−	1.56979i	−0.0871766	−	0.996193i	$-0.527784\pi$
$84$	−3.26222	−	5.65033i	−0.355937	−	0.616501i
$85$	−2.26222	−	3.91828i	−0.245372	−	0.424997i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	−9.72999	+	16.8528i	−1.04316	+	1.80681i
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	−12.0489			−1.27718			−0.638589	−	0.769548i	$-0.720482\pi$
$89$	−12.0489			−1.27718			−0.638589	+	0.769548i	$0.720482\pi$
$90$	0.710831	+	1.23120i	0.0749282	+	0.129779i
$91$	−11.2544			−1.17978
$92$	−5.10278			−0.532001
$93$	1.81889	−	3.15041i	0.188610	−	0.326682i
$94$	6.89722			0.711394
$95$	−3.52444	−	6.10451i	−0.361600	−	0.626309i
$96$	−1.05139	+	1.82106i	−0.107307	+	0.185861i
$97$	−0.421663	−	0.730342i	−0.0428134	−	0.0741550i	0.843825	−	0.536619i	$-0.180299\pi$
$97$	−0.421663	−	0.730342i	−0.0428134	−	0.0741550i	−0.886638	+	0.462464i	$0.846965\pi$
$98$	1.31361	−	2.27523i	0.132694	−	0.229833i
$99$	−2.84333	+	4.92478i	−0.285765	+	0.494959i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−0.683882	+	1.18452i	−0.0680488	+	0.117864i	−0.898042	−	0.439909i	$-0.855011\pi$
$101$	−0.683882	+	1.18452i	−0.0680488	+	0.117864i	0.829994	+	0.557773i	$0.188344\pi$
$102$	−4.75694	+	8.23926i	−0.471007	+	0.815808i
$103$	0.0269496	−	0.0466780i	0.00265542	−	0.00459932i	−0.864695	−	0.502298i	$-0.832488\pi$
$103$	0.0269496	−	0.0466780i	0.00265542	−	0.00459932i	0.867350	+	0.497699i	$0.165821\pi$
$104$	1.81361	+	3.14126i	0.177839	+	0.308026i
$105$	−3.26222	+	5.65033i	−0.318360	+	0.551416i
$106$	6.94082	+	12.0219i	0.674152	+	1.16767i
$107$	−2.47556			−0.239322			−0.119661	−	0.992815i	$-0.538181\pi$
$107$	−2.47556			−0.239322			−0.119661	+	0.992815i	$0.538181\pi$
$108$	−1.65944	+	2.87424i	−0.159680	+	0.276574i
$109$	−2.52444			−0.241797			−0.120899	−	0.992665i	$-0.538578\pi$
$109$	−2.52444			−0.241797			−0.120899	+	0.992665i	$0.538578\pi$
$110$	−4.00000			−0.381385
$111$	9.28666	+	16.0850i	0.881450	+	1.52672i
$112$	−3.10278			−0.293185
$113$	2.20555	−	3.82012i	0.207481	−	0.359367i	−0.743440	−	0.668803i	$-0.766807\pi$
$113$	2.20555	−	3.82012i	0.207481	−	0.359367i	0.950920	+	0.309436i	$0.100140\pi$
$114$	−7.41110	+	12.8364i	−0.694113	+	1.20224i
$115$	2.55139	+	4.41913i	0.237918	+	0.412086i
$116$	4.62721	+	8.01457i	0.429626	+	0.744134i
$117$	−2.57834	−	4.46581i	−0.238367	−	0.412864i
$118$	−2.10278	−	3.64211i	−0.193576	−	0.335284i
$119$	−14.0383			−1.28689
$120$	2.10278			0.191956
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	5.94333	−	10.2942i	0.538084	−	0.931989i
$123$	−1.65944	+	2.87424i	−0.149627	+	0.259162i
$124$	−0.864994	−	1.49821i	−0.0776788	−	0.134544i
$125$	1.00000			0.0894427
$126$	4.41110			0.392972
$127$	4.68111	−	8.10792i	0.415382	−	0.719462i	−0.580087	−	0.814555i	$-0.696981\pi$
$127$	4.68111	−	8.10792i	0.415382	−	0.719462i	0.995468	+	0.0950927i	$0.0303147\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.41110			0.740556
$130$	1.81361	−	3.14126i	0.159064	−	0.275507i
$131$	−5.20053			−0.454372			−0.227186	−	0.973851i	$-0.572953\pi$
$131$	−5.20053			−0.454372			−0.227186	+	0.973851i	$0.572953\pi$
$132$	4.20555	+	7.28423i	0.366046	+	0.634011i
$133$	−21.8711			−1.89646
$134$	6.44082	+	5.05132i	0.556402	+	0.436368i
$135$	3.31889			0.285644
$136$	2.26222	+	3.91828i	0.193984	+	0.335990i
$137$	−1.27001			−0.108504			−0.0542522	−	0.998527i	$-0.517278\pi$
$137$	−1.27001			−0.108504			−0.0542522	+	0.998527i	$0.517278\pi$
$138$	5.36499	−	9.29244i	0.456699	−	0.791025i
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	1.55139	+	2.68708i	0.131116	+	0.227100i
$141$	−7.25166	+	12.5602i	−0.610700	+	1.05776i
$142$	−15.9355			−1.33728
$143$	14.5089			1.21329
$144$	−0.710831	−	1.23120i	−0.0592360	−	0.102600i
$145$	4.62721	−	8.01457i	0.384269	−	0.665574i
$146$	−2.84056	+	4.91999i	−0.235086	+	0.407181i
$147$	2.76222	+	4.78430i	0.227824	+	0.394603i
$148$	8.83276			0.726049
$149$	9.57331			0.784276			0.392138	−	0.919906i	$-0.371735\pi$
$149$	9.57331			0.784276			0.392138	+	0.919906i	$0.371735\pi$
$150$	−1.05139	−	1.82106i	−0.0858454	−	0.148689i
$151$	10.6489	+	18.4444i	0.866594	+	1.50098i	0.865456	+	0.500985i	$0.167029\pi$
$151$	10.6489	+	18.4444i	0.866594	+	1.50098i	0.00113764	+	0.999999i	$0.499638\pi$
$152$	3.52444	+	6.10451i	0.285870	+	0.495141i
$153$	−3.21611	−	5.57047i	−0.260007	−	0.450346i
$154$	−6.20555	+	10.7483i	−0.500057	+	0.866125i
$155$	−0.864994	+	1.49821i	−0.0694780	+	0.120339i
$156$	−7.62721			−0.610666
$157$	2.42166	+	4.19444i	0.193270	+	0.334753i	0.946332	−	0.323196i	$-0.104757\pi$
$157$	2.42166	+	4.19444i	0.193270	+	0.334753i	−0.753062	+	0.657949i	$0.771424\pi$
$158$	−12.8816			−1.02481
$159$	−29.1900			−2.31491
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	15.8328			1.24780
$162$	−5.62193	−	9.73747i	−0.441701	−	0.765048i
$163$	−7.44333	+	12.8922i	−0.583007	+	1.00980i	0.412114	+	0.911132i	$0.364791\pi$
$163$	−7.44333	+	12.8922i	−0.583007	+	1.00980i	−0.995121	+	0.0986649i	$0.968543\pi$
$164$	0.789169	+	1.36688i	0.0616237	+	0.106735i
$165$	4.20555	−	7.28423i	0.327402	−	0.567076i
$166$	8.25694	−	14.3014i	0.640863	−	1.11001i
$167$	−9.90859	+	17.1622i	−0.766750	+	1.32805i	0.172567	+	0.984998i	$0.444794\pi$
$167$	−9.90859	+	17.1622i	−0.766750	+	1.32805i	−0.939317	+	0.343051i	$0.888539\pi$
$168$	3.26222	−	5.65033i	0.251686	−	0.435932i
$169$	−0.0783371	+	0.135684i	−0.00602593	+	0.0104372i
$170$	2.26222	−	3.91828i	0.173504	−	0.300518i
$171$	−5.01056	−	8.67855i	−0.383167	−	0.663665i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	6.07834	+	10.5280i	0.462127	+	0.800428i	0.999067	−	0.0431927i	$-0.0137529\pi$
$173$	6.07834	+	10.5280i	0.462127	+	0.800428i	−0.536939	+	0.843621i	$0.680420\pi$
$174$	−19.4600			−1.47526
$175$	1.55139	−	2.68708i	0.117274	−	0.203124i
$176$	4.00000			0.301511
$177$	8.84333			0.664705
$178$	−6.02444	−	10.4346i	−0.451551	−	0.782109i
$179$	18.6705			1.39550			0.697751	−	0.716340i	$-0.254184\pi$
$179$	18.6705			1.39550			0.697751	+	0.716340i	$0.254184\pi$
$180$	−0.710831	+	1.23120i	−0.0529822	+	0.0917679i
$181$	−4.36499	+	7.56039i	−0.324447	+	0.561959i	−0.981400	−	0.191972i	$-0.938512\pi$
$181$	−4.36499	+	7.56039i	−0.324447	+	0.561959i	0.656953	+	0.753932i	$0.271845\pi$
$182$	−5.62721	−	9.74662i	−0.417117	−	0.722467i
$183$	12.4975	+	21.6463i	0.923841	+	1.60014i
$184$	−2.55139	−	4.41913i	−0.188091	−	0.325783i
$185$	−4.41638	−	7.64940i	−0.324699	−	0.562395i
$186$	3.63778			0.266735
$187$	18.0978			1.32344
$188$	3.44861	+	5.97317i	0.251516	+	0.435638i
$189$	5.14888	−	8.91812i	0.374526	−	0.648698i
$190$	3.52444	−	6.10451i	0.255690	−	0.442867i
$191$	−10.8842	−	18.8519i	−0.787549	−	1.36408i	−0.927464	−	0.373912i	$-0.878016\pi$
$191$	−10.8842	−	18.8519i	−0.787549	−	1.36408i	0.139915	−	0.990164i	$-0.455317\pi$
$192$	−2.10278			−0.151755
$193$	−0.524438			−0.0377499			−0.0188749	−	0.999822i	$-0.506008\pi$
$193$	−0.524438			−0.0377499			−0.0188749	+	0.999822i	$0.506008\pi$
$194$	0.421663	−	0.730342i	0.0302736	−	0.0524355i
$195$	3.81361	+	6.60536i	0.273098	+	0.473020i
$196$	2.62721			0.187658
$197$	−1.08362	+	1.87688i	−0.0772046	+	0.133722i	−0.902043	−	0.431646i	$-0.857933\pi$
$197$	−1.08362	+	1.87688i	−0.0772046	+	0.133722i	0.824838	+	0.565369i	$0.191266\pi$
$198$	−5.68665			−0.404133
$199$	−2.42417	−	4.19879i	−0.171845	−	0.297645i	0.767220	−	0.641384i	$-0.221640\pi$
$199$	−2.42417	−	4.19879i	−0.171845	−	0.297645i	−0.939065	+	0.343740i	$0.888306\pi$
$200$	−1.00000			−0.0707107
$201$	−15.9705	+	6.41820i	−1.12647	+	0.452705i
$202$	−1.36776			−0.0962355
$203$	−14.3572	−	24.8674i	−1.00768	−	1.74535i
$204$	−9.51388			−0.666105
$205$	0.789169	−	1.36688i	0.0551179	−	0.0954670i
$206$	0.0538991			0.00375533
$207$	3.62721	+	6.28252i	0.252109	+	0.436665i
$208$	−1.81361	+	3.14126i	−0.125751	+	0.217807i
$209$	28.1955			1.95032
$210$	−6.52444			−0.450229
$211$	−10.5514	−	18.2755i	−0.726387	−	1.25814i	−0.958400	−	0.285427i	$-0.907864\pi$
$211$	−10.5514	−	18.2755i	−0.726387	−	1.25814i	0.232013	−	0.972713i	$-0.425469\pi$
$212$	−6.94082	+	12.0219i	−0.476697	+	0.825664i
$213$	16.7544	−	29.0195i	1.14799	−	1.98838i
$214$	−1.23778	−	2.14390i	−0.0846130	−	0.146554i
$215$	−4.00000			−0.272798
$216$	−3.31889			−0.225822
$217$	2.68388	+	4.64862i	0.182194	+	0.315569i
$218$	−1.26222	−	2.18623i	−0.0854883	−	0.148070i
$219$	−5.97305	−	10.3456i	−0.403621	−	0.699093i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	−8.20555	+	14.2124i	−0.551965	+	0.956031i
$222$	−9.28666	+	16.0850i	−0.623280	+	1.07955i
$223$	−15.4600			−1.03528			−0.517638	−	0.855600i	$-0.673189\pi$
$223$	−15.4600			−1.03528			−0.517638	+	0.855600i	$0.673189\pi$
$224$	−1.55139	−	2.68708i	−0.103656	−	0.179538i
$225$	1.42166			0.0947775
$226$	4.41110			0.293422
$227$	9.17332	−	15.8887i	0.608855	−	1.05457i	−0.382575	−	0.923924i	$-0.624963\pi$
$227$	9.17332	−	15.8887i	0.608855	−	1.05457i	0.991430	−	0.130643i	$-0.0417040\pi$
$228$	−14.8222			−0.981624
$229$	3.99723	+	6.92341i	0.264144	+	0.457512i	0.967339	−	0.253486i	$-0.0815771\pi$
$229$	3.99723	+	6.92341i	0.264144	+	0.457512i	−0.703195	+	0.710997i	$0.748244\pi$
$230$	−2.55139	+	4.41913i	−0.168234	+	0.291389i
$231$	−13.0489	−	22.6013i	−0.858553	−	1.48706i
$232$	−4.62721	+	8.01457i	−0.303791	+	0.526182i
$233$	9.19776	−	15.9310i	0.602565	−	1.04367i	−0.389866	−	0.920872i	$-0.627479\pi$
$233$	9.19776	−	15.9310i	0.602565	−	1.04367i	0.992431	−	0.122802i	$-0.0391880\pi$
$234$	2.57834	−	4.46581i	0.168551	−	0.291939i
$235$	3.44861	−	5.97317i	0.224963	−	0.389647i
$236$	2.10278	−	3.64211i	0.136879	−	0.237081i
$237$	13.5436	−	23.4582i	0.879751	−	1.52377i
$238$	−7.01916	−	12.1575i	−0.454984	−	0.788056i
$239$	−11.2544	+	19.4932i	−0.727988	+	1.26091i	0.229744	+	0.973251i	$0.426211\pi$
$239$	−11.2544	+	19.4932i	−0.727988	+	1.26091i	−0.957732	+	0.287662i	$0.907122\pi$
$240$	1.05139	+	1.82106i	0.0678668	+	0.117549i
$241$	18.8328			1.21312			0.606562	−	0.795036i	$-0.292548\pi$
$241$	18.8328			1.21312			0.606562	+	0.795036i	$0.292548\pi$
$242$	2.50000	−	4.33013i	0.160706	−	0.278351i
$243$	13.6867			0.877999
$244$	11.8867			0.760966
$245$	−1.31361	−	2.27523i	−0.0839232	−	0.145359i
$246$	−3.31889			−0.211605
$247$	−12.7839	+	22.1423i	−0.813419	+	1.40888i
$248$	0.864994	−	1.49821i	0.0549272	−	0.0951367i
$249$	17.3625	+	30.0727i	1.10030	+	1.90578i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−4.75694	−	8.23926i	−0.300255	−	0.520057i	0.675938	−	0.736958i	$-0.263739\pi$
$251$	−4.75694	−	8.23926i	−0.300255	−	0.520057i	−0.976194	+	0.216901i	$0.930405\pi$
$252$	2.20555	+	3.82012i	0.138937	+	0.240645i
$253$	−20.4111			−1.28323
$254$	9.36222			0.587438
$255$	4.75694	+	8.23926i	0.297891	+	0.515962i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	4.20555	+	7.28423i	0.261826	+	0.453496i
$259$	−27.4061			−1.70293
$260$	3.62721			0.224950
$261$	6.57834	−	11.3940i	0.407189	−	0.705272i
$262$	−2.60026	−	4.50379i	−0.160645	−	0.278245i
$263$	22.3033			1.37528			0.687640	−	0.726052i	$-0.258647\pi$
$263$	22.3033			1.37528			0.687640	+	0.726052i	$0.258647\pi$
$264$	−4.20555	+	7.28423i	−0.258834	+	0.448313i
$265$	13.8816			0.852742
$266$	−10.9355	−	18.9409i	−0.670501	−	1.16134i
$267$	25.3361			1.55054
$268$	−1.15416	+	8.10357i	−0.0705017	+	0.495005i
$269$	30.1744			1.83976			0.919882	−	0.392195i	$-0.128284\pi$
$269$	30.1744			1.83976			0.919882	+	0.392195i	$0.128284\pi$
$270$	1.65944	+	2.87424i	0.100991	+	0.174921i
$271$	10.2700			0.623859			0.311929	−	0.950105i	$-0.399025\pi$
$271$	10.2700			0.623859			0.311929	+	0.950105i	$0.399025\pi$
$272$	−2.26222	+	3.91828i	−0.137167	+	0.237581i
$273$	23.6655			1.43230
$274$	−0.635006	−	1.09986i	−0.0383621	−	0.0664451i
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$	10.7300			0.645869
$277$	−29.8122			−1.79124			−0.895619	−	0.444821i	$-0.853267\pi$
$277$	−29.8122			−1.79124			−0.895619	+	0.444821i	$0.853267\pi$
$278$	4.00000	+	6.92820i	0.239904	+	0.415526i
$279$	−1.22973	+	2.12995i	−0.0736220	+	0.127517i
$280$	−1.55139	+	2.68708i	−0.0927131	+	0.160584i
$281$	−12.0436	−	20.8601i	−0.718461	−	1.24441i	−0.961610	−	0.274421i	$-0.911514\pi$
$281$	−12.0436	−	20.8601i	−0.718461	−	1.24441i	0.243149	−	0.969989i	$-0.421820\pi$
$282$	−14.5033			−0.863660
$283$	4.47054			0.265746			0.132873	−	0.991133i	$-0.457580\pi$
$283$	4.47054			0.265746			0.132873	+	0.991133i	$0.457580\pi$
$284$	−7.96777	−	13.8006i	−0.472800	−	0.818914i
$285$	7.41110	+	12.8364i	0.438996	+	0.760363i
$286$	7.25443	+	12.5650i	0.428963	+	0.742986i
$287$	−2.44861	−	4.24112i	−0.144537	−	0.250345i
$288$	0.710831	−	1.23120i	0.0418861	−	0.0725489i
$289$	−1.73527	+	3.00557i	−0.102075	+	0.176799i
$290$	9.25443			0.543439
$291$	0.886662	+	1.53574i	0.0519771	+	0.0900269i
$292$	−5.68111			−0.332462
$293$	6.72496			0.392877			0.196438	−	0.980516i	$-0.437062\pi$
$293$	6.72496			0.392877			0.196438	+	0.980516i	$0.437062\pi$
$294$	−2.76222	+	4.78430i	−0.161096	+	0.279026i
$295$	−4.20555			−0.244857
$296$	4.41638	+	7.64940i	0.256697	+	0.444612i
$297$	−6.63778	+	11.4970i	−0.385163	+	0.667122i
$298$	4.78666	+	8.29073i	0.277284	+	0.480269i
$299$	9.25443	−	16.0291i	0.535197	−	0.926989i
$300$	1.05139	−	1.82106i	0.0607019	−	0.105139i
$301$	−6.20555	+	10.7483i	−0.357682	+	0.619523i
$302$	−10.6489	+	18.4444i	−0.612774	+	1.06136i
$303$	1.43805	−	2.49078i	0.0826138	−	0.143091i
$304$	−3.52444	+	6.10451i	−0.202140	+	0.350117i
$305$	−5.94333	−	10.2942i	−0.340314	−	0.589441i
$306$	3.21611	−	5.57047i	0.183853	−	0.318443i
$307$	−0.894713	−	1.54969i	−0.0510640	−	0.0884454i	0.839364	−	0.543570i	$-0.182928\pi$
$307$	−0.894713	−	1.54969i	−0.0510640	−	0.0884454i	−0.890428	+	0.455125i	$0.849595\pi$
$308$	−12.4111			−0.707188
$309$	−0.0566689	+	0.0981534i	−0.00322378	+	0.00558375i
$310$	−1.72999			−0.0982567
$311$	12.8383			0.727993			0.363997	−	0.931400i	$-0.381412\pi$
$311$	12.8383			0.727993			0.363997	+	0.931400i	$0.381412\pi$
$312$	−3.81361	−	6.60536i	−0.215903	−	0.373955i
$313$	−4.50885			−0.254855			−0.127428	−	0.991848i	$-0.540672\pi$
$313$	−4.50885			−0.254855			−0.127428	+	0.991848i	$0.540672\pi$
$314$	−2.42166	+	4.19444i	−0.136662	+	0.236706i
$315$	2.20555	−	3.82012i	0.124269	−	0.215240i
$316$	−6.44082	−	11.1558i	−0.362324	−	0.627564i
$317$	4.39722	+	7.61622i	0.246973	+	0.427769i	0.962684	−	0.270627i	$-0.0872308\pi$
$317$	4.39722	+	7.61622i	0.246973	+	0.427769i	−0.715712	+	0.698396i	$0.753898\pi$
$318$	−14.5950	−	25.2793i	−0.818446	−	1.41759i
$319$	18.5089	+	32.0583i	1.03630	+	1.79492i
$320$	1.00000			0.0559017
$321$	5.20555			0.290545
$322$	7.91638	+	13.7116i	0.441163	+	0.764116i
$323$	−15.9461	+	27.6195i	−0.887265	+	1.53679i
$324$	5.62193	−	9.73747i	0.312330	−	0.540971i
$325$	−1.81361	−	3.14126i	−0.100601	−	0.174246i
$326$	−14.8867			−0.824496
$327$	5.30833			0.293551
$328$	−0.789169	+	1.36688i	−0.0435745	+	0.0754733i
$329$	−10.7003	−	18.5334i	−0.589925	−	1.02178i
$330$	8.41110			0.463016
$331$	−5.35720	+	9.27894i	−0.294458	+	0.510017i	−0.974859	−	0.222824i	$-0.928473\pi$
$331$	−5.35720	+	9.27894i	−0.294458	+	0.510017i	0.680400	+	0.732841i	$0.261806\pi$
$332$	16.5139			0.906317
$333$	−6.27861	−	10.8749i	−0.344065	−	0.595939i
$334$	−19.8172			−1.08435
$335$	7.59498	−	3.05225i	0.414958	−	0.166762i
$336$	6.52444			0.355937
$337$	−7.99723	−	13.8516i	−0.435637	−	0.754545i	0.561710	−	0.827334i	$-0.310143\pi$
$337$	−7.99723	−	13.8516i	−0.435637	−	0.754545i	−0.997347	+	0.0727886i	$0.976810\pi$
$338$	−0.156674			−0.00852195
$339$	−4.63778	+	8.03286i	−0.251889	+	0.436285i
$340$	4.52444			0.245372
$341$	−3.45998	−	5.99285i	−0.187368	−	0.324531i
$342$	5.01056	−	8.67855i	0.270940	−	0.469282i
$343$	13.5678			0.732591
$344$	4.00000			0.215666
$345$	−5.36499	−	9.29244i	−0.288842	−	0.500288i
$346$	−6.07834	+	10.5280i	−0.326773	+	0.565988i
$347$	1.94610	−	3.37075i	0.104472	−	0.180951i	−0.809050	−	0.587739i	$-0.800018\pi$
$347$	1.94610	−	3.37075i	0.104472	−	0.180951i	0.913522	+	0.406788i	$0.133351\pi$
$348$	−9.72999	−	16.8528i	−0.521582	−	0.903407i
$349$	4.94108			0.264490			0.132245	−	0.991217i	$-0.457781\pi$
$349$	4.94108			0.264490			0.132245	+	0.991217i	$0.457781\pi$
$350$	3.10278			0.165850
$351$	−6.01916	−	10.4255i	−0.321279	−	0.556471i
$352$	2.00000	+	3.46410i	0.106600	+	0.184637i
$353$	10.4139	+	18.0374i	0.554274	+	0.960031i	0.997960	+	0.0638487i	$0.0203375\pi$
$353$	10.4139	+	18.0374i	0.554274	+	0.960031i	−0.443685	+	0.896183i	$0.646329\pi$
$354$	4.42166	+	7.65854i	0.235009	+	0.407047i
$355$	−7.96777	+	13.8006i	−0.422885	+	0.732459i
$356$	6.02444	−	10.4346i	0.319295	−	0.553034i
$357$	29.5194			1.56233
$358$	9.33527	+	16.1692i	0.493385	+	0.854567i
$359$	24.3466			1.28497			0.642483	−	0.766300i	$-0.277904\pi$
$359$	24.3466			1.28497			0.642483	+	0.766300i	$0.277904\pi$
$360$	−1.42166			−0.0749282
$361$	−15.3433	+	26.5754i	−0.807543	+	1.39871i
$362$	−8.72999			−0.458838
$363$	5.25694	+	9.10528i	0.275918	+	0.477903i
$364$	5.62721	−	9.74662i	0.294946	−	0.510862i
$365$	2.84056	+	4.91999i	0.148682	+	0.257524i
$366$	−12.4975	+	21.6463i	−0.653254	+	1.13147i
$367$	15.3842	−	26.6461i	0.803046	−	1.39092i	−0.114556	−	0.993417i	$-0.536545\pi$
$367$	15.3842	−	26.6461i	0.803046	−	1.39092i	0.917602	−	0.397500i	$-0.130122\pi$
$368$	2.55139	−	4.41913i	0.133000	−	0.230363i
$369$	1.12193	−	1.94324i	0.0584054	−	0.101161i
$370$	4.41638	−	7.64940i	0.229597	−	0.397673i
$371$	21.5358	−	37.3011i	1.11808	−	1.93658i
$372$	1.81889	+	3.15041i	0.0943049	+	0.163341i
$373$	8.12721	−	14.0767i	0.420811	−	0.728866i	−0.575208	−	0.818007i	$-0.695079\pi$
$373$	8.12721	−	14.0767i	0.420811	−	0.728866i	0.996019	+	0.0891410i	$0.0284122\pi$
$374$	9.04888	+	15.6731i	0.467906	+	0.810437i
$375$	−2.10278			−0.108587
$376$	−3.44861	+	5.97317i	−0.177849	+	0.308043i
$377$	−33.5678			−1.72883
$378$	10.2978			0.529660
$379$	0.470539	+	0.814997i	0.0241700	+	0.0418636i	0.877857	−	0.478922i	$-0.158972\pi$
$379$	0.470539	+	0.814997i	0.0241700	+	0.0418636i	−0.853687	+	0.520786i	$0.825639\pi$
$380$	7.04888			0.361600
$381$	−9.84333	+	17.0491i	−0.504289	+	0.873454i
$382$	10.8842	−	18.8519i	0.556882	−	0.964547i
$383$	−6.77886	−	11.7413i	−0.346384	−	0.599954i	0.639220	−	0.769024i	$-0.279257\pi$
$383$	−6.77886	−	11.7413i	−0.346384	−	0.599954i	−0.985604	+	0.169069i	$0.945924\pi$
$384$	−1.05139	−	1.82106i	−0.0536534	−	0.0929304i
$385$	6.20555	+	10.7483i	0.316264	+	0.547786i
$386$	−0.262219	−	0.454177i	−0.0133466	−	0.0231170i
$387$	−5.68665			−0.289069
$388$	0.843326			0.0428134
$389$	−16.7222	−	28.9637i	−0.847849	−	1.46852i	−0.883124	−	0.469140i	$-0.844564\pi$
$389$	−16.7222	−	28.9637i	−0.847849	−	1.46852i	0.0352750	−	0.999378i	$-0.488769\pi$
$390$	−3.81361	+	6.60536i	−0.193109	+	0.334475i
$391$	11.5436	−	19.9941i	0.583785	−	1.01114i
$392$	1.31361	+	2.27523i	0.0663471	+	0.114917i
$393$	10.9355			0.551625
$394$	−2.16724			−0.109184
$395$	−6.44082	+	11.1558i	−0.324073	+	0.561311i
$396$	−2.84333	−	4.92478i	−0.142882	−	0.247480i
$397$	−29.0383			−1.45739			−0.728696	−	0.684838i	$-0.759873\pi$
$397$	−29.0383			−1.45739			−0.728696	+	0.684838i	$0.759873\pi$
$398$	2.42417	−	4.19879i	0.121513	−	0.210466i
$399$	45.9900			2.30238
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−2.57834			−0.128756			−0.0643780	−	0.997926i	$-0.520506\pi$
$401$	−2.57834			−0.128756			−0.0643780	+	0.997926i	$0.520506\pi$
$402$	−13.5436	−	10.6218i	−0.675493	−	0.529767i
$403$	6.27504			0.312582
$404$	−0.683882	−	1.18452i	−0.0340244	−	0.0589320i
$405$	−11.2439			−0.558712
$406$	14.3572	−	24.8674i	0.712536	−	1.23415i
$407$	35.3311			1.75130
$408$	−4.75694	−	8.23926i	−0.235504	−	0.407904i
$409$	−8.04359	+	13.9319i	−0.397730	+	0.688889i	−0.993445	−	0.114307i	$-0.963535\pi$
$409$	−8.04359	+	13.9319i	−0.397730	+	0.688889i	0.595715	+	0.803196i	$0.296869\pi$
$410$	1.57834			0.0779485
$411$	2.67055			0.131728
$412$	0.0269496	+	0.0466780i	0.00132771	+	0.00229966i
$413$	−6.52444	+	11.3007i	−0.321047	+	0.556069i
$414$	−3.62721	+	6.28252i	−0.178268	+	0.308769i
$415$	−8.25694	−	14.3014i	−0.405317	−	0.702030i
$416$	−3.62721			−0.177839
$417$	−16.8222			−0.823787
$418$	14.0978	+	24.4180i	0.689544	+	1.19432i
$419$	8.98944	+	15.5702i	0.439163	+	0.760652i	0.997625	−	0.0688777i	$-0.0219418\pi$
$419$	8.98944	+	15.5702i	0.439163	+	0.760652i	−0.558462	+	0.829530i	$0.688608\pi$
$420$	−3.26222	−	5.65033i	−0.159180	−	0.275708i
$421$	18.2544	+	31.6176i	0.889666	+	1.54095i	0.840270	+	0.542168i	$0.182396\pi$
$421$	18.2544	+	31.6176i	0.889666	+	1.54095i	0.0493961	+	0.998779i	$0.484270\pi$
$422$	10.5514	−	18.2755i	0.513634	−	0.889639i
$423$	4.90276	−	8.49184i	0.238381	−	0.412887i
$424$	−13.8816			−0.674152
$425$	−2.26222	−	3.91828i	−0.109734	−	0.190064i
$426$	33.5089			1.62351
$427$	−36.8816			−1.78483
$428$	1.23778	−	2.14390i	0.0598304	−	0.103629i
$429$	−30.5089			−1.47298
$430$	−2.00000	−	3.46410i	−0.0964486	−	0.167054i
$431$	1.47305	−	2.55140i	0.0709543	−	0.122897i	−0.828365	−	0.560188i	$-0.810729\pi$
$431$	1.47305	−	2.55140i	0.0709543	−	0.122897i	0.899320	+	0.437292i	$0.144062\pi$
$432$	−1.65944	−	2.87424i	−0.0798400	−	0.138287i
$433$	−3.26222	+	5.65033i	−0.156772	+	0.271537i	−0.933703	−	0.358049i	$-0.883442\pi$
$433$	−3.26222	+	5.65033i	−0.156772	+	0.271537i	0.776931	+	0.629586i	$0.216776\pi$
$434$	−2.68388	+	4.64862i	−0.128830	+	0.223141i
$435$	−9.72999	+	16.8528i	−0.466517	+	0.808032i
$436$	1.26222	−	2.18623i	0.0604493	−	0.104701i
$437$	17.9844	−	31.1499i	0.860311	−	1.49010i
$438$	5.97305	−	10.3456i	0.285403	−	0.494333i
$439$	−0.453894	−	0.786167i	−0.0216632	−	0.0375217i	0.854991	−	0.518644i	$-0.173563\pi$
$439$	−0.453894	−	0.786167i	−0.0216632	−	0.0375217i	−0.876654	+	0.481122i	$0.840229\pi$
$440$	2.00000	−	3.46410i	0.0953463	−	0.165145i
$441$	−1.86751	−	3.23461i	−0.0889288	−	0.154029i
$442$	−16.4111			−0.780596
$443$	−8.99749	+	15.5841i	−0.427484	+	0.740423i	−0.996649	−	0.0817999i	$-0.973933\pi$
$443$	−8.99749	+	15.5841i	−0.427484	+	0.740423i	0.569165	+	0.822223i	$0.307266\pi$
$444$	−18.5733			−0.881450
$445$	−12.0489			−0.571171
$446$	−7.72999	−	13.3887i	−0.366026	−	0.633975i
$447$	−20.1305			−0.952141
$448$	1.55139	−	2.68708i	0.0732962	−	0.126953i
$449$	6.02444	−	10.4346i	0.284311	−	0.492441i	−0.688131	−	0.725586i	$-0.741569\pi$
$449$	6.02444	−	10.4346i	0.284311	−	0.492441i	0.972442	+	0.233146i	$0.0749019\pi$
$450$	0.710831	+	1.23120i	0.0335089	+	0.0580391i
$451$	3.15667	+	5.46752i	0.148642	+	0.257455i
$452$	2.20555	+	3.82012i	0.103740	+	0.179684i
$453$	−22.3922	−	38.7844i	−1.05208	−	1.82225i
$454$	18.3466			0.861050
$455$	−11.2544			−0.527616
$456$	−7.41110	−	12.8364i	−0.347057	−	0.601120i
$457$	0.262219	−	0.454177i	0.0122661	−	0.0212455i	−0.859827	−	0.510585i	$-0.829429\pi$
$457$	0.262219	−	0.454177i	0.0122661	−	0.0212455i	0.872093	+	0.489340i	$0.162762\pi$
$458$	−3.99723	+	6.92341i	−0.186778	+	0.323510i
$459$	−7.50805	−	13.0043i	−0.350446	−	0.606990i
$460$	−5.10278			−0.237918
$461$	4.63224			0.215745			0.107872	−	0.994165i	$-0.465596\pi$
$461$	4.63224			0.215745			0.107872	+	0.994165i	$0.465596\pi$
$462$	13.0489	−	22.6013i	0.607089	−	1.05151i
$463$	−8.28138	−	14.3438i	−0.384868	−	0.666611i	0.606883	−	0.794791i	$-0.292420\pi$
$463$	−8.28138	−	14.3438i	−0.384868	−	0.666611i	−0.991751	+	0.128180i	$0.959086\pi$
$464$	−9.25443			−0.429626
$465$	1.81889	−	3.15041i	0.0843489	−	0.146097i
$466$	18.3955			0.852156
$467$	1.99749	+	3.45975i	0.0924327	+	0.160098i	0.908534	−	0.417810i	$-0.137202\pi$
$467$	1.99749	+	3.45975i	0.0924327	+	0.160098i	−0.816102	+	0.577909i	$0.803869\pi$
$468$	5.15667			0.238367
$469$	3.58111	−	25.1436i	0.165360	−	1.16102i
$470$	6.89722			0.318145
$471$	−5.09221	−	8.81997i	−0.234637	−	0.406403i
$472$	4.20555			0.193576
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$	27.0872			1.24416
$475$	−3.52444	−	6.10451i	−0.161712	−	0.280094i
$476$	7.01916	−	12.1575i	0.321723	−	0.557240i
$477$	19.7350			0.903604
$478$	−22.5089			−1.02953
$479$	18.1517	+	31.4396i	0.829370	+	1.43651i	0.898533	+	0.438906i	$0.144634\pi$
$479$	18.1517	+	31.4396i	0.829370	+	1.43651i	−0.0691630	+	0.997605i	$0.522033\pi$
$480$	−1.05139	+	1.82106i	−0.0479891	+	0.0831195i
$481$	−16.0192	+	27.7460i	−0.730411	+	1.26511i
$482$	9.41638	+	16.3097i	0.428904	+	0.742884i
$483$	−33.2927			−1.51487
$484$	5.00000			0.227273
$485$	−0.421663	−	0.730342i	−0.0191467	−	0.0331631i
$486$	6.84333	+	11.8530i	0.310420	+	0.537662i
$487$	2.39974	+	4.15647i	0.108742	+	0.188347i	0.915261	−	0.402861i	$-0.131984\pi$
$487$	2.39974	+	4.15647i	0.108742	+	0.188347i	−0.806519	+	0.591209i	$0.798651\pi$
$488$	5.94333	+	10.2942i	0.269042	+	0.465994i
$489$	15.6517	−	27.1095i	0.707792	−	1.22593i
$490$	1.31361	−	2.27523i	0.0593427	−	0.102785i
$491$	10.2494			0.462549			0.231275	−	0.972889i	$-0.425710\pi$
$491$	10.2494			0.462549			0.231275	+	0.972889i	$0.425710\pi$
$492$	−1.65944	−	2.87424i	−0.0748135	−	0.129581i
$493$	−41.8711			−1.88578
$494$	−25.5678			−1.15035
$495$	−2.84333	+	4.92478i	−0.127798	+	0.221353i
$496$	1.72999			0.0776788
$497$	24.7222	+	42.8201i	1.10894	+	1.92074i
$498$	−17.3625	+	30.0727i	−0.778031	+	1.34759i
$499$	−0.745574	−	1.29137i	−0.0333765	−	0.0578098i	0.848855	−	0.528626i	$-0.177293\pi$
$499$	−0.745574	−	1.29137i	−0.0333765	−	0.0578098i	−0.882231	+	0.470817i	$0.843959\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	20.8355	−	36.0882i	0.930863	−	1.61230i
$502$	4.75694	−	8.23926i	0.212313	−	0.367736i
$503$	16.4111	−	28.4249i	0.731735	−	1.26740i	−0.224406	−	0.974496i	$-0.572044\pi$
$503$	16.4111	−	28.4249i	0.731735	−	1.26740i	0.956141	−	0.292906i	$-0.0946224\pi$
$504$	−2.20555	+	3.82012i	−0.0982430	+	0.170162i
$505$	−0.683882	+	1.18452i	−0.0304323	+	0.0527104i
$506$	−10.2056	−	17.6765i	−0.453692	−	0.785818i
$507$	0.164725	−	0.285313i	0.00731571	−	0.0126712i
$508$	4.68111	+	8.10792i	0.207691	+	0.359731i
$509$	−10.8277			−0.479931			−0.239966	−	0.970781i	$-0.577136\pi$
$509$	−10.8277			−0.479931			−0.239966	+	0.970781i	$0.577136\pi$
$510$	−4.75694	+	8.23926i	−0.210641	+	0.364840i
$511$	17.6272			0.779782
$512$	−1.00000			−0.0441942
$513$	−11.6972	−	20.2602i	−0.516445	−	0.894508i
$514$	−6.00000			−0.264649
$515$	0.0269496	−	0.0466780i	0.00118754	−	0.00205688i
$516$	−4.20555	+	7.28423i	−0.185139	+	0.320670i
$517$	13.7944	+	23.8927i	0.606679	+	1.05080i
$518$	−13.7030	−	23.7344i	−0.602077	−	1.04283i
$519$	−12.7814	−	22.1380i	−0.561040	−	0.971750i
$520$	1.81361	+	3.14126i	0.0795319	+	0.137753i
$521$	34.4705			1.51018			0.755091	−	0.655620i	$-0.227593\pi$
$521$	34.4705			1.51018			0.755091	+	0.655620i	$0.227593\pi$
$522$	13.1567			0.575852
$523$	−12.7517	−	22.0865i	−0.557591	−	0.965776i	−0.997697	−	0.0678301i	$-0.978392\pi$
$523$	−12.7517	−	22.0865i	−0.557591	−	0.965776i	0.440106	−	0.897946i	$-0.354941\pi$
$524$	2.60026	−	4.50379i	0.113593	−	0.196749i
$525$	−3.26222	+	5.65033i	−0.142375	+	0.246601i
$526$	11.1517	+	19.3152i	0.486235	+	0.842184i
$527$	7.82722			0.340959
$528$	−8.41110			−0.366046
$529$	−1.51916	+	2.63126i	−0.0660503	+	0.114402i
$530$	6.94082	+	12.0219i	0.301490	+	0.522196i
$531$	−5.97887			−0.259461
$532$	10.9355	−	18.9409i	0.474116	−	0.821192i
$533$	−5.72496			−0.247976
$534$	12.6680	+	21.9417i	0.548200	+	0.949510i
$535$	−2.47556			−0.107028
$536$	−7.59498	+	3.05225i	−0.328053	+	0.131837i
$537$	−39.2600			−1.69419
$538$	15.0872	+	26.1318i	0.650455	+	1.12662i
$539$	10.5089			0.452648
$540$	−1.65944	+	2.87424i	−0.0714111	+	0.123688i
$541$	23.5678			1.01326			0.506629	−	0.862164i	$-0.330891\pi$
$541$	23.5678			1.01326			0.506629	+	0.862164i	$0.330891\pi$
$542$	5.13501	+	8.89409i	0.220567	+	0.382034i
$543$	9.17860	−	15.8978i	0.393891	−	0.682240i
$544$	−4.52444			−0.193984
$545$	−2.52444			−0.108135
$546$	11.8328	+	20.4949i	0.506396	+	0.877103i
$547$	16.5461	−	28.6587i	0.707460	−	1.22536i	−0.258336	−	0.966055i	$-0.583174\pi$
$547$	16.5461	−	28.6587i	0.707460	−	1.22536i	0.965796	−	0.259302i	$-0.0834926\pi$
$548$	0.635006	−	1.09986i	0.0271261	−	0.0469838i
$549$	−8.44941	−	14.6348i	−0.360612	−	0.624599i
$550$	−4.00000			−0.170561
$551$	−65.2333			−2.77903
$552$	5.36499	+	9.29244i	0.228349	+	0.395513i
$553$	19.9844	+	34.6140i	0.849824	+	1.47194i
$554$	−14.9061	−	25.8181i	−0.633299	−	1.09691i
$555$	9.28666	+	16.0850i	0.394197	+	0.682769i
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	8.84307	−	15.3166i	0.374693	−	0.648987i	−0.615588	−	0.788068i	$-0.711082\pi$
$557$	8.84307	−	15.3166i	0.374693	−	0.648987i	0.990281	+	0.139081i	$0.0444148\pi$
$558$	−2.45946			−0.104117
$559$	7.25443	+	12.5650i	0.306830	+	0.531444i
$560$	−3.10278			−0.131116
$561$	−38.0555			−1.60670
$562$	12.0436	−	20.8601i	0.508028	−	0.879931i
$563$	8.57331			0.361322			0.180661	−	0.983545i	$-0.442176\pi$
$563$	8.57331			0.361322			0.180661	+	0.983545i	$0.442176\pi$
$564$	−7.25166	−	12.5602i	−0.305350	−	0.528881i
$565$	2.20555	−	3.82012i	0.0927882	−	0.160714i
$566$	2.23527	+	3.87160i	0.0939554	+	0.162735i
$567$	−17.4436	+	30.2132i	−0.732562	+	1.26883i
$568$	7.96777	−	13.8006i	0.334320	−	0.579060i
$569$	−3.94584	+	6.83440i	−0.165418	+	0.286513i	−0.936804	−	0.349855i	$-0.886231\pi$
$569$	−3.94584	+	6.83440i	−0.165418	+	0.286513i	0.771385	+	0.636368i	$0.219564\pi$
$570$	−7.41110	+	12.8364i	−0.310417	+	0.537658i
$571$	−19.3955	+	33.5940i	−0.811677	+	1.40587i	0.100013	+	0.994986i	$0.468112\pi$
$571$	−19.3955	+	33.5940i	−0.811677	+	1.40587i	−0.911690	+	0.410880i	$0.865222\pi$
$572$	−7.25443	+	12.5650i	−0.303323	+	0.525370i
$573$	22.8869	+	39.6413i	0.956115	+	1.65604i
$574$	2.44861	−	4.24112i	0.102203	−	0.177021i
$575$	2.55139	+	4.41913i	0.106400	+	0.184291i
$576$	1.42166			0.0592360
$577$	16.9383	−	29.3380i	0.705151	−	1.22136i	−0.261486	−	0.965207i	$-0.584213\pi$
$577$	16.9383	−	29.3380i	0.705151	−	1.22136i	0.966637	−	0.256150i	$-0.0824541\pi$
$578$	−3.47054			−0.144355
$579$	1.10278			0.0458298
$580$	4.62721	+	8.01457i	0.192135	+	0.332787i
$581$	−51.2388			−2.12575
$582$	−0.886662	+	1.53574i	−0.0367533	+	0.0636586i
$583$	−27.7633	+	48.0874i	−1.14984	+	1.99158i
$584$	−2.84056	−	4.91999i	−0.117543	−	0.203591i
$585$	−2.57834	−	4.46581i	−0.106601	−	0.184639i
$586$	3.36248	+	5.82399i	0.138903	+	0.240587i
$587$	2.94861	+	5.10715i	0.121702	+	0.210795i	0.920439	−	0.390886i	$-0.127831\pi$
$587$	2.94861	+	5.10715i	0.121702	+	0.210795i	−0.798737	+	0.601681i	$0.794498\pi$
$588$	−5.52444			−0.227824
$589$	12.1945			0.502464
$590$	−2.10278	−	3.64211i	−0.0865699	−	0.149943i
$591$	2.27861	−	3.94666i	0.0937293	−	0.162344i
$592$	−4.41638	+	7.64940i	−0.181512	+	0.314388i
$593$	10.3033	+	17.8458i	0.423106	+	0.732841i	0.996241	−	0.0866197i	$-0.0276065\pi$
$593$	10.3033	+	17.8458i	0.423106	+	0.732841i	−0.573136	+	0.819461i	$0.694273\pi$
$594$	−13.2756			−0.544702
$595$	−14.0383			−0.575515
$596$	−4.78666	+	8.29073i	−0.196069	+	0.339602i
$597$	5.09749	+	8.82912i	0.208627	+	0.361352i
$598$	18.5089			0.756883
$599$	7.51388	−	13.0144i	0.307009	−	0.531755i	−0.670698	−	0.741731i	$-0.734005\pi$
$599$	7.51388	−	13.0144i	0.307009	−	0.531755i	0.977707	+	0.209976i	$0.0673386\pi$
$600$	2.10278			0.0858454
$601$	−0.505281	−	0.875173i	−0.0206109	−	0.0356991i	0.855536	−	0.517743i	$-0.173228\pi$
$601$	−0.505281	−	0.875173i	−0.0206109	−	0.0356991i	−0.876147	+	0.482044i	$0.839894\pi$
$602$	−12.4111			−0.505839
$603$	10.7975	−	4.33927i	0.439708	−	0.176709i
$604$	−21.2978			−0.866594
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$	2.87610			0.116834
$607$	16.2005	−	28.0601i	0.657559	−	1.13893i	−0.323687	−	0.946164i	$-0.604922\pi$
$607$	16.2005	−	28.0601i	0.657559	−	1.13893i	0.981246	−	0.192761i	$-0.0617443\pi$
$608$	−7.04888			−0.285870
$609$	30.1900	+	52.2906i	1.22336	+	2.11892i
$610$	5.94333	−	10.2942i	0.240638	−	0.416798i
$611$	−25.0177			−1.01211
$612$	6.43223			0.260007
$613$	2.28389	+	3.95581i	0.0922453	+	0.159774i	0.908456	−	0.417981i	$-0.137262\pi$
$613$	2.28389	+	3.95581i	0.0922453	+	0.159774i	−0.816210	+	0.577755i	$0.803929\pi$
$614$	0.894713	−	1.54969i	0.0361077	−	0.0625404i
$615$	−1.65944	+	2.87424i	−0.0669152	+	0.115901i
$616$	−6.20555	−	10.7483i	−0.250029	−	0.433062i
$617$	−4.65336			−0.187337			−0.0936686	−	0.995603i	$-0.529859\pi$
$617$	−4.65336			−0.187337			−0.0936686	+	0.995603i	$0.529859\pi$
$618$	−0.113338			−0.00455911
$619$	−3.81638	−	6.61016i	−0.153393	−	0.265685i	0.779080	−	0.626925i	$-0.215687\pi$
$619$	−3.81638	−	6.61016i	−0.153393	−	0.265685i	−0.932473	+	0.361240i	$0.882353\pi$
$620$	−0.864994	−	1.49821i	−0.0347390	−	0.0601697i
$621$	8.46777	+	14.6666i	0.339800	+	0.588551i
$622$	6.41915	+	11.1183i	0.257385	+	0.445803i
$623$	−18.6925	+	32.3763i	−0.748898	+	1.29713i
$624$	3.81361	−	6.60536i	0.152666	−	0.264426i
$625$	1.00000			0.0400000
$626$	−2.25443	−	3.90478i	−0.0901050	−	0.156066i
$627$	−59.2888			−2.36777
$628$	−4.84333			−0.193270
$629$	−19.9816	+	34.6092i	−0.796720	+	1.37996i
$630$	4.41110			0.175742
$631$	2.84333	+	4.92478i	0.113191	+	0.196053i	0.917055	−	0.398760i	$-0.130559\pi$
$631$	2.84333	+	4.92478i	0.113191	+	0.196053i	−0.803864	+	0.594813i	$0.797226\pi$
$632$	6.44082	−	11.1558i	0.256202	−	0.443755i
$633$	22.1872	+	38.4293i	0.881862	+	1.52743i
$634$	−4.39722	+	7.61622i	−0.174636	+	0.302479i
$635$	4.68111	−	8.10792i	0.185764	−	0.321753i
$636$	14.5950	−	25.2793i	0.578729	−	1.00239i
$637$	−4.76473	+	8.25276i	−0.188785	+	0.326986i
$638$	−18.5089	+	32.0583i	−0.732772	+	1.26920i
$639$	−11.3275	+	19.6198i	−0.448108	+	0.776146i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−4.65139	+	8.05645i	−0.183719	+	0.318211i	−0.943144	−	0.332384i	$-0.892147\pi$
$641$	−4.65139	+	8.05645i	−0.183719	+	0.318211i	0.759425	+	0.650595i	$0.225480\pi$
$642$	2.60278	+	4.50814i	0.102723	+	0.177922i
$643$	−3.89722			−0.153692			−0.0768458	−	0.997043i	$-0.524485\pi$
$643$	−3.89722			−0.153692			−0.0768458	+	0.997043i	$0.524485\pi$
$644$	−7.91638	+	13.7116i	−0.311949	+	0.540312i
$645$	8.41110			0.331187
$646$	−31.8922			−1.25478
$647$	−17.7300	−	30.7092i	−0.697038	−	1.20730i	−0.969489	−	0.245135i	$-0.921168\pi$
$647$	−17.7300	−	30.7092i	−0.697038	−	1.20730i	0.272451	−	0.962170i	$-0.412166\pi$
$648$	11.2439			0.441701
$649$	8.41110	−	14.5685i	0.330165	−	0.571862i
$650$	1.81361	−	3.14126i	0.0711355	−	0.123210i
$651$	−5.64360	−	9.77500i	−0.221190	−	0.383113i
$652$	−7.44333	−	12.8922i	−0.291503	−	0.504899i
$653$	−11.3569	−	19.6708i	−0.444432	−	0.769778i	0.553581	−	0.832795i	$-0.313261\pi$
$653$	−11.3569	−	19.6708i	−0.444432	−	0.769778i	−0.998012	+	0.0630174i	$0.979928\pi$
$654$	2.65416	+	4.59714i	0.103786	+	0.179763i
$655$	−5.20053			−0.203201
$656$	−1.57834			−0.0616237
$657$	4.03831	+	6.99456i	0.157550	+	0.272884i
$658$	10.7003	−	18.5334i	0.417140	−	0.722508i
$659$	4.16724	−	7.21787i	0.162333	−	0.281168i	−0.773372	−	0.633952i	$-0.781432\pi$
$659$	4.16724	−	7.21787i	0.162333	−	0.281168i	0.935705	+	0.352784i	$0.114765\pi$
$660$	4.20555	+	7.28423i	0.163701	+	0.283538i
$661$	−3.99446			−0.155367			−0.0776833	−	0.996978i	$-0.524752\pi$
$661$	−3.99446			−0.155367			−0.0776833	+	0.996978i	$0.524752\pi$
$662$	−10.7144			−0.416427
$663$	17.2544	−	29.8855i	0.670106	−	1.16066i
$664$	8.25694	+	14.3014i	0.320431	+	0.555003i
$665$	−21.8711			−0.848124
$666$	6.27861	−	10.8749i	0.243291	−	0.421392i
$667$	47.2233			1.82849
$668$	−9.90859	−	17.1622i	−0.383375	−	0.664025i
$669$	32.5089			1.25686
$670$	6.44082	+	5.05132i	0.248831	+	0.195150i
$671$	47.5466			1.83552
$672$	3.26222	+	5.65033i	0.125843	+	0.217966i
$673$	−12.8433			−0.495074			−0.247537	−	0.968878i	$-0.579621\pi$
$673$	−12.8433			−0.495074			−0.247537	+	0.968878i	$0.579621\pi$
$674$	7.99723	−	13.8516i	0.308042	−	0.533544i
$675$	3.31889			0.127744
$676$	−0.0783371	−	0.135684i	−0.00301297	−	0.00521861i
$677$	−7.44610	+	12.8970i	−0.286177	+	0.495673i	−0.972894	−	0.231252i	$-0.925718\pi$
$677$	−7.44610	+	12.8970i	−0.286177	+	0.495673i	0.686717	+	0.726925i	$0.259051\pi$
$678$	−9.27555			−0.356225
$679$	−2.61665			−0.100418
$680$	2.26222	+	3.91828i	0.0867521	+	0.150259i
$681$	−19.2894	+	33.4103i	−0.739172	+	1.28028i
$682$	3.45998	−	5.99285i	0.132489	−	0.229478i
$683$	9.25694	+	16.0335i	0.354207	+	0.613504i	0.986982	−	0.160831i	$-0.0514175\pi$
$683$	9.25694	+	16.0335i	0.354207	+	0.613504i	−0.632775	+	0.774336i	$0.718084\pi$
$684$	10.0211			0.383167
$685$	−1.27001			−0.0485247
$686$	6.78389	+	11.7500i	0.259010	+	0.448619i
$687$	−8.40528	−	14.5584i	−0.320681	−	0.555436i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−25.1758	−	43.6058i	−0.959123	−	1.66125i
$690$	5.36499	−	9.29244i	0.204242	−	0.353757i
$691$	−5.52444	+	9.56861i	−0.210160	+	0.364007i	−0.951764	−	0.306830i	$-0.900732\pi$
$691$	−5.52444	+	9.56861i	−0.210160	+	0.364007i	0.741605	+	0.670837i	$0.234065\pi$
$692$	−12.1567			−0.462127
$693$	8.82220	+	15.2805i	0.335128	+	0.580458i
$694$	3.89220			0.147746
$695$	8.00000			0.303457
$696$	9.72999	−	16.8528i	0.368814	−	0.638805i
$697$	−7.14109			−0.270488
$698$	2.47054	+	4.27910i	0.0935113	+	0.161966i
$699$	−19.3408	+	33.4993i	−0.731537	+	1.26706i
$700$	1.55139	+	2.68708i	0.0586369	+	0.101562i
$701$	−2.10780	+	3.65081i	−0.0796104	+	0.137889i	−0.903082	−	0.429468i	$-0.858701\pi$
$701$	−2.10780	+	3.65081i	−0.0796104	+	0.137889i	0.823471	+	0.567358i	$0.192034\pi$
$702$	6.01916	−	10.4255i	0.227178	−	0.393485i
$703$	−31.1305	+	53.9197i	−1.17411	+	2.03362i
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$	−7.25166	+	12.5602i	−0.273113	+	0.473046i
$706$	−10.4139	+	18.0374i	−0.391931	+	0.678845i
$707$	2.12193	+	3.67529i	0.0798035	+	0.138224i
$708$	−4.42166	+	7.65854i	−0.166176	+	0.287826i
$709$	17.3622	+	30.0723i	0.652052	+	1.12939i	0.982624	+	0.185606i	$0.0594250\pi$
$709$	17.3622	+	30.0723i	0.652052	+	1.12939i	−0.330572	+	0.943781i	$0.607242\pi$
$710$	−15.9355			−0.598050
$711$	−9.15667	+	15.8598i	−0.343402	+	0.594790i
$712$	12.0489			0.451551
$713$	−8.82774			−0.330601
$714$	14.7597	+	25.5646i	0.552368	+	0.956730i
$715$	14.5089			0.542600
$716$	−9.33527	+	16.1692i	−0.348876	+	0.604270i
$717$	23.6655	−	40.9899i	0.883805	−	1.53080i
$718$	12.1733	+	21.0848i	0.454304	+	0.786878i
$719$	−6.12998	−	10.6174i	−0.228610	−	0.395964i	0.728787	−	0.684741i	$-0.240085\pi$
$719$	−6.12998	−	10.6174i	−0.228610	−	0.395964i	−0.957396	+	0.288777i	$0.906751\pi$
$720$	−0.710831	−	1.23120i	−0.0264911	−	0.0458840i
$721$	−0.0836184	−	0.144831i	−0.00311411	−	0.00539380i
$722$	−30.6867			−1.14204
$723$	−39.6011			−1.47278
$724$	−4.36499	−	7.56039i	−0.162224	−	0.280980i
$725$	4.62721	−	8.01457i	0.171850	−	0.297654i
$726$	−5.25694	+	9.10528i	−0.195103	+	0.337929i
$727$	0.367764	+	0.636986i	0.0136396	+	0.0236245i	0.872765	−	0.488141i	$-0.162325\pi$
$727$	0.367764	+	0.636986i	0.0136396	+	0.0236245i	−0.859125	+	0.511766i	$0.828992\pi$
$728$	11.2544			0.417117
$729$	4.95164			0.183394
$730$	−2.84056	+	4.91999i	−0.105134	+	0.182097i
$731$	9.04888	+	15.6731i	0.334685	+	0.579691i
$732$	−24.9950			−0.923841
$733$	7.34835	−	12.7277i	0.271417	−	0.470109i	−0.697808	−	0.716285i	$-0.745841\pi$
$733$	7.34835	−	12.7277i	0.271417	−	0.470109i	0.969225	+	0.246176i	$0.0791743\pi$
$734$	30.7683			1.13568
$735$	2.76222	+	4.78430i	0.101886	+	0.176472i
$736$	5.10278			0.188091
$737$	−4.61665	+	32.4143i	−0.170056	+	1.19400i
$738$	2.24386			0.0825977
$739$	−12.3083	−	21.3186i	−0.452769	−	0.784219i	0.545788	−	0.837923i	$-0.316230\pi$
$739$	−12.3083	−	21.3186i	−0.452769	−	0.784219i	−0.998557	+	0.0537044i	$0.982897\pi$
$740$	8.83276			0.324699
$741$	26.8816	−	46.5604i	0.987522	−	1.71044i
$742$	43.0716			1.58121
$743$	20.0978	+	34.8103i	0.737315	+	1.27707i	0.953700	+	0.300759i	$0.0972400\pi$
$743$	20.0978	+	34.8103i	0.737315	+	1.27707i	−0.216385	+	0.976308i	$0.569427\pi$
$744$	−1.81889	+	3.15041i	−0.0666837	+	0.115499i
$745$	9.57331			0.350739
$746$	16.2544			0.595117
$747$	−11.7386	−	20.3318i	−0.429492	−	0.743902i
$748$	−9.04888	+	15.6731i	−0.330860	+	0.573066i
$749$	−3.84056	+	6.65204i	−0.140331	+	0.243060i
$750$	−1.05139	−	1.82106i	−0.0383912	−	0.0664956i
$751$	25.7783			0.940665			0.470333	−	0.882489i	$-0.344134\pi$
$751$	25.7783			0.940665			0.470333	+	0.882489i	$0.344134\pi$
$752$	−6.89722			−0.251516
$753$	10.0028	+	17.3253i	0.364521	+	0.631369i
$754$	−16.7839	−	29.0705i	−0.611233	−	1.05869i
$755$	10.6489	+	18.4444i	0.387552	+	0.671261i
$756$	5.14888	+	8.91812i	0.187263	+	0.324349i
$757$	10.0925	−	17.4807i	0.366817	−	0.635346i	−0.622249	−	0.782819i	$-0.713781\pi$
$757$	10.0925	−	17.4807i	0.366817	−	0.635346i	0.989066	+	0.147474i	$0.0471142\pi$
$758$	−0.470539	+	0.814997i	−0.0170907	+	0.0296020i
$759$	42.9200			1.55790
$760$	3.52444	+	6.10451i	0.127845	+	0.221434i
$761$	15.5400			0.563325			0.281663	−	0.959513i	$-0.409114\pi$
$761$	15.5400			0.563325			0.281663	+	0.959513i	$0.409114\pi$
$762$	−19.6867			−0.713172
$763$	−3.91638	+	6.78337i	−0.141783	+	0.245575i
$764$	21.7683			0.787549
$765$	−3.21611	−	5.57047i	−0.116279	−	0.201401i
$766$	6.77886	−	11.7413i	0.244930	−	0.424232i
$767$	7.62721	+	13.2107i	0.275403	+	0.477011i
$768$	1.05139	−	1.82106i	0.0379387	−	0.0657117i
$769$	25.3275	−	43.8685i	0.913332	−	1.58194i	0.104008	−	0.994576i	$-0.466833\pi$
$769$	25.3275	−	43.8685i	0.913332	−	1.58194i	0.809325	−	0.587362i	$-0.199833\pi$
$770$	−6.20555	+	10.7483i	−0.223633	+	0.387343i
$771$	6.30833	−	10.9263i	0.227189	−	0.393503i
$772$	0.262219	−	0.454177i	0.00943747	−	0.0163462i
$773$	−16.9252	+	29.3154i	−0.608758	+	1.05440i	0.382687	+	0.923878i	$0.374999\pi$
$773$	−16.9252	+	29.3154i	−0.608758	+	1.05440i	−0.991445	+	0.130522i	$0.958335\pi$
$774$	−2.84333	−	4.92478i	−0.102201	−	0.177018i
$775$	−0.864994	+	1.49821i	−0.0310715	+	0.0538174i
$776$	0.421663	+	0.730342i	0.0151368	+	0.0262177i
$777$	57.6288			2.06742
$778$	16.7222	−	28.9637i	0.599520	−	1.03840i
$779$	−11.1255			−0.398612
$780$	−7.62721			−0.273098
$781$	−31.8711	−	55.2023i	−1.14044	−	1.97529i
$782$	23.0872			0.825596
$783$	15.3572	−	26.5995i	0.548822	−	0.950587i
$784$	−1.31361	+	2.27523i	−0.0469145	+	0.0812583i
$785$	2.42166	+	4.19444i	0.0864329	+	0.149706i
$786$	5.46777	+	9.47045i	0.195029	+	0.337800i
$787$	1.71334	+	2.96760i	0.0610741	+	0.105783i	0.894946	−	0.446175i	$-0.147214\pi$
$787$	1.71334	+	2.96760i	0.0610741	+	0.105783i	−0.833872	+	0.551958i	$0.813881\pi$
$788$	−1.08362	−	1.87688i	−0.0386023	−	0.0668612i
$789$	−46.8988			−1.66964
$790$	−12.8816			−0.458308
$791$	−6.84333	−	11.8530i	−0.243321	−	0.421444i
$792$	2.84333	−	4.92478i	0.101033	−	0.174995i
$793$	−21.5577	+	37.3391i	−0.765537	+	1.32595i
$794$	−14.5192	−	25.1479i	−0.515266	−	0.892466i
$795$	−29.1900			−1.03526
$796$	4.84835			0.171845
$797$	9.47028	−	16.4030i	0.335455	−	0.581024i	−0.648117	−	0.761540i	$-0.724443\pi$
$797$	9.47028	−	16.4030i	0.335455	−	0.581024i	0.983572	+	0.180516i	$0.0577768\pi$
$798$	22.9950	+	39.8285i	0.814013	+	1.40991i
$799$	−31.2061			−1.10399
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−17.1294			−0.605239
$802$	−1.28917	−	2.23291i	−0.0455221	−	0.0788466i
$803$	−22.7244			−0.801928
$804$	2.42694	−	17.0400i	0.0855917	−	0.600954i
$805$	15.8328			0.558032
$806$	3.13752	+	5.43434i	0.110514	+	0.191416i
$807$	−63.4499			−2.23354
$808$	0.683882	−	1.18452i	0.0240589	−	0.0416712i
$809$	−36.7527			−1.29216			−0.646078	−	0.763271i	$-0.723592\pi$
$809$	−36.7527			−1.29216			−0.646078	+	0.763271i	$0.723592\pi$
$810$	−5.62193	−	9.73747i	−0.197535	−	0.342140i
$811$	9.27635	−	16.0671i	0.325737	−	0.564193i	−0.655924	−	0.754827i	$-0.727721\pi$
$811$	9.27635	−	16.0671i	0.325737	−	0.564193i	0.981661	+	0.190634i	$0.0610543\pi$
$812$	28.7144			1.00768
$813$	−21.5955			−0.757388
$814$	17.6655	+	30.5976i	0.619176	+	1.07244i
$815$	−7.44333	+	12.8922i	−0.260729	+	0.451595i
$816$	4.75694	−	8.23926i	0.166526	−	0.288432i
$817$	14.0978	+	24.4180i	0.493218	+	0.854278i
$818$	−16.0872			−0.562475
$819$	−16.0000			−0.559085
$820$	0.789169	+	1.36688i	0.0275590	+	0.0477335i
$821$	27.8199	+	48.1856i	0.970923	+	1.68169i	0.692782	+	0.721148i	$0.256385\pi$
$821$	27.8199	+	48.1856i	0.970923	+	1.68169i	0.278141	+	0.960540i	$0.410282\pi$
$822$	1.33527	+	2.31276i	0.0465731	+	0.0806669i
$823$	−17.7683	−	30.7756i	−0.619364	−	1.07277i	−0.989602	−	0.143833i	$-0.954057\pi$
$823$	−17.7683	−	30.7756i	−0.619364	−	1.07277i	0.370238	−	0.928937i	$-0.379276\pi$
$824$	−0.0269496	+	0.0466780i	−0.000938833	+	0.00162611i
$825$	4.20555	−	7.28423i	0.146418	−	0.253604i
$826$	−13.0489			−0.454028
$827$	7.10278	+	12.3024i	0.246988	+	0.427795i	0.962689	−	0.270612i	$-0.0872259\pi$
$827$	7.10278	+	12.3024i	0.246988	+	0.427795i	−0.715701	+	0.698407i	$0.753893\pi$
$828$	−7.25443			−0.252109
$829$	−16.6111			−0.576928			−0.288464	−	0.957491i	$-0.593145\pi$
$829$	−16.6111			−0.576928			−0.288464	+	0.957491i	$0.593145\pi$
$830$	8.25694	−	14.3014i	0.286602	−	0.496410i
$831$	62.6883			2.17463
$832$	−1.81361	−	3.14126i	−0.0628755	−	0.108904i
$833$	−5.94333	+	10.2942i	−0.205924	+	0.356671i
$834$	−8.41110	−	14.5685i	−0.291253	−	0.504464i
$835$	−9.90859	+	17.1622i	−0.342901	+	0.593922i
$836$	−14.0978	+	24.4180i	−0.487581	+	0.844515i
$837$	−2.87082	+	4.97240i	−0.0992300	+	0.171871i
$838$	−8.98944	+	15.5702i	−0.310535	+	0.537862i
$839$	10.8353	−	18.7672i	0.374075	−	0.647917i	−0.616113	−	0.787658i	$-0.711294\pi$
$839$	10.8353	−	18.7672i	0.374075	−	0.647917i	0.990188	+	0.139741i	$0.0446268\pi$
$840$	3.26222	−	5.65033i	0.112557	−	0.194955i
$841$	−28.3222	−	49.0555i	−0.976628	−	1.69157i
$842$	−18.2544	+	31.6176i	−0.629089	+	1.08961i
$843$	25.3250	+	43.8641i	0.872238	+	1.51076i
$844$	21.1028			0.726387
$845$	−0.0783371	+	0.135684i	−0.00269488	+	0.00466767i
$846$	9.80553			0.337121
$847$	−15.5139			−0.533063
$848$	−6.94082	−	12.0219i	−0.238349	−	0.412832i
$849$	−9.40054			−0.322626
$850$	2.26222	−	3.91828i	0.0775935	−	0.134396i
$851$	22.5358	−	39.0332i	0.772517	−	1.33804i
$852$	16.7544	+	29.0195i	0.573997	+	0.994192i
$853$	3.04359	+	5.27166i	0.104211	+	0.180498i	0.913415	−	0.407029i	$-0.133435\pi$
$853$	3.04359	+	5.27166i	0.104211	+	0.180498i	−0.809205	+	0.587527i	$0.800102\pi$
$854$	−18.4408	−	31.9404i	−0.631032	−	1.09298i
$855$	−5.01056	−	8.67855i	−0.171358	−	0.296800i
$856$	2.47556			0.0846130
$857$	50.7089			1.73218			0.866091	−	0.499887i	$-0.166625\pi$
$857$	50.7089			1.73218			0.866091	+	0.499887i	$0.166625\pi$
$858$	−15.2544	−	26.4214i	−0.520778	−	0.902013i
$859$	−8.51388	+	14.7465i	−0.290490	+	0.503143i	−0.973926	−	0.226868i	$-0.927152\pi$
$859$	−8.51388	+	14.7465i	−0.290490	+	0.503143i	0.683436	+	0.730011i	$0.260485\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$	5.14888	+	8.91812i	0.175473	+	0.303929i
$862$	2.94610			0.100345
$863$	−35.3083			−1.20191			−0.600955	−	0.799283i	$-0.705213\pi$
$863$	−35.3083			−1.20191			−0.600955	+	0.799283i	$0.705213\pi$
$864$	1.65944	−	2.87424i	0.0564554	−	0.0977837i
$865$	6.07834	+	10.5280i	0.206670	+	0.357962i
$866$	−6.52444			−0.221709
$867$	3.64888	−	6.32005i	0.123923	−	0.214640i
$868$	−5.36776			−0.182194
$869$	−25.7633	−	44.6233i	−0.873959	−	1.51374i
$870$	−19.4600			−0.659755
$871$	−23.3622	−	18.3222i	−0.791599	−	0.620825i
$872$	2.52444			0.0854883
$873$	−0.599463	−	1.03830i	−0.0202887	−	0.0351411i
$874$	35.9688			1.21666
$875$	1.55139	−	2.68708i	0.0524465	−	0.0908400i
$876$	11.9461			0.403621
$877$	−23.3713	−	40.4803i	−0.789194	−	1.36692i	−0.926461	−	0.376390i	$-0.877165\pi$
$877$	−23.3713	−	40.4803i	−0.789194	−	1.36692i	0.137267	−	0.990534i	$-0.456168\pi$
$878$	0.453894	−	0.786167i	0.0153182	−	0.0265319i
$879$	−14.1411			−0.476967
$880$	4.00000			0.134840
$881$	12.8622	+	22.2780i	0.433339	+	0.750566i	0.997158	−	0.0753325i	$-0.0240018\pi$
$881$	12.8622	+	22.2780i	0.433339	+	0.750566i	−0.563819	+	0.825898i	$0.690668\pi$
$882$	1.86751	−	3.23461i	0.0628822	−	0.108915i
$883$	−2.63778	+	4.56876i	−0.0887682	+	0.153751i	−0.906991	−	0.421151i	$-0.861626\pi$
$883$	−2.63778	+	4.56876i	−0.0887682	+	0.153751i	0.818222	+	0.574902i	$0.194960\pi$
$884$	−8.20555	−	14.2124i	−0.275983	−	0.478016i
$885$	8.84333			0.297265
$886$	−17.9950			−0.604553
$887$	−9.07080	−	15.7111i	−0.304568	−	0.527527i	0.672597	−	0.740009i	$-0.265179\pi$
$887$	−9.07080	−	15.7111i	−0.304568	−	0.527527i	−0.977165	+	0.212482i	$0.931845\pi$
$888$	−9.28666	−	16.0850i	−0.311640	−	0.539776i
$889$	−14.5244	−	25.1571i	−0.487134	−	0.843741i
$890$	−6.02444	−	10.4346i	−0.201940	−	0.349770i
$891$	22.4877	−	38.9499i	0.753367	−	1.30487i
$892$	7.72999	−	13.3887i	0.258819	−	0.448288i
$893$	−48.6177			−1.62693
$894$	−10.0653	−	17.4335i	−0.336633	−	0.583065i
$895$	18.6705			0.624088
$896$	3.10278			0.103656
$897$	−19.4600	+	33.7057i	−0.649750	+	1.12540i
$898$	12.0489			0.402076
$899$	8.00502	+	13.8651i	0.266982	+	0.462427i
$900$	−0.710831	+	1.23120i	−0.0236944	+	0.0410399i
$901$	−31.4033	−	54.3921i	−1.04620	−	1.81206i
$902$	−3.15667	+	5.46752i	−0.105106	+	0.182049i
$903$	13.0489	−	22.6013i	0.434239	−	0.752125i
$904$	−2.20555	+	3.82012i	−0.0733555	+	0.127055i
$905$	−4.36499	+	7.56039i	−0.145097	+	0.251316i
$906$	22.3922	−	38.7844i	0.743931	−	1.28853i
$907$	−19.4867	+	33.7519i	−0.647044	+	1.12071i	0.336781	+	0.941583i	$0.390662\pi$
$907$	−19.4867	+	33.7519i	−0.647044	+	1.12071i	−0.983825	+	0.179130i	$0.942672\pi$
$908$	9.17332	+	15.8887i	0.304427	+	0.527284i
$909$	−0.972250	+	1.68399i	−0.0322475	+	0.0558543i
$910$	−5.62721	−	9.74662i	−0.186540	−	0.323097i
$911$	7.25945			0.240516			0.120258	−	0.992743i	$-0.461628\pi$
$911$	7.25945			0.240516			0.120258	+	0.992743i	$0.461628\pi$
$912$	7.41110	−	12.8364i	0.245406	−	0.425056i
$913$	66.0555			2.18612
$914$	0.524438			0.0173469
$915$	12.4975	+	21.6463i	0.413154	+	0.715604i
$916$	−7.99446			−0.264144
$917$	−8.06803	+	13.9742i	−0.266430	+	0.461470i
$918$	7.50805	−	13.0043i	0.247803	−	0.429207i
$919$	24.6786	+	42.7446i	0.814072	+	1.41001i	0.909992	+	0.414625i	$0.136087\pi$
$919$	24.6786	+	42.7446i	0.814072	+	1.41001i	−0.0959205	+	0.995389i	$0.530579\pi$
$920$	−2.55139	−	4.41913i	−0.0841168	−	0.145694i
$921$	1.88138	+	3.25865i	0.0619936	+	0.107376i
$922$	2.31612	+	4.01163i	0.0762773	+	0.132116i
$923$	57.8016			1.90256
$924$	26.0978			0.858553
$925$	−4.41638	−	7.64940i	−0.145210	−	0.251511i
$926$	8.28138	−	14.3438i	0.272143	−	0.471365i
$927$	0.0383132	−	0.0663604i	0.00125837	−	0.00217956i
$928$	−4.62721	−	8.01457i	−0.151896	−	0.263091i
$929$	32.5572			1.06817			0.534084	−	0.845432i	$-0.320657\pi$
$929$	32.5572			1.06817			0.534084	+	0.845432i	$0.320657\pi$
$930$	3.63778			0.119287
$931$	−9.25945	+	16.0378i	−0.303466	+	0.525619i
$932$	9.19776	+	15.9310i	0.301283	+	0.521837i
$933$	−26.9961			−0.883811
$934$	−1.99749	+	3.45975i	−0.0653598	+	0.113207i
$935$	18.0978			0.591860
$936$	2.57834	+	4.46581i	0.0842756	+	0.145970i
$937$	28.1900			0.920926			0.460463	−	0.887679i	$-0.347683\pi$
$937$	28.1900			0.920926			0.460463	+	0.887679i	$0.347683\pi$
$938$	23.5655	−	9.47045i	0.769442	−	0.309221i
$939$	9.48110			0.309404
$940$	3.44861	+	5.97317i	0.112481	+	0.194823i
$941$	18.1744			0.592468			0.296234	−	0.955115i	$-0.404269\pi$
$941$	18.1744			0.592468			0.296234	+	0.955115i	$0.404269\pi$
$942$	5.09221	−	8.81997i	0.165913	−	0.287370i
$943$	8.05390			0.262271
$944$	2.10278	+	3.64211i	0.0684395	+	0.118541i
$945$	5.14888	−	8.91812i	0.167493	−	0.290107i
$946$	16.0000			0.520205
$947$	−27.0278			−0.878284			−0.439142	−	0.898418i	$-0.644717\pi$
$947$	−27.0278			−0.878284			−0.439142	+	0.898418i	$0.644717\pi$
$948$	13.5436	+	23.4582i	0.439876	+	0.761887i
$949$	10.3033	−	17.8458i	0.334459	−	0.579301i
$950$	3.52444	−	6.10451i	0.114348	−	0.198056i
$951$	−9.24637	−	16.0152i	−0.299834	−	0.519328i
$952$	14.0383			0.454984
$953$	−36.8433			−1.19347			−0.596736	−	0.802437i	$-0.703536\pi$
$953$	−36.8433			−1.19347			−0.596736	+	0.802437i	$0.703536\pi$
$954$	9.86751	+	17.0910i	0.319472	+	0.553342i
$955$	−10.8842	−	18.8519i	−0.352203	−	0.610033i
$956$	−11.2544	−	19.4932i	−0.363994	−	0.630456i
$957$	−38.9200	−	67.4113i	−1.25810	−	2.17910i
$958$	−18.1517	+	31.4396i	−0.586453	+	1.01577i
$959$	−1.97028	+	3.41263i	−0.0636237	+	0.110199i
$960$	−2.10278			−0.0678668
$961$	14.0036	+	24.2549i	0.451728	+	0.782416i
$962$	−32.0383			−1.03296
$963$	−3.51941			−0.113412
$964$	−9.41638	+	16.3097i	−0.303281	+	0.525298i
$965$	−0.524438			−0.0168823
$966$	−16.6464	−	28.8324i	−0.535588	−	0.927666i
$967$	14.5847	−	25.2614i	0.469012	−	0.812352i	−0.530361	−	0.847772i	$-0.677944\pi$
$967$	14.5847	−	25.2614i	0.469012	−	0.812352i	0.999373	+	0.0354200i	$0.0112769\pi$
$968$	2.50000	+	4.33013i	0.0803530	+	0.139176i
$969$	33.5311	−	58.0775i	1.07717	−	1.86572i
$970$	0.421663	−	0.730342i	0.0135388	−	0.0234499i
$971$	18.3416	−	31.7686i	0.588610	−	1.01950i	−0.405804	−	0.913960i	$-0.633009\pi$
$971$	18.3416	−	31.7686i	0.588610	−	1.01950i	0.994415	−	0.105543i	$-0.0336581\pi$
$972$	−6.84333	+	11.8530i	−0.219500	+	0.380185i
$973$	12.4111	−	21.4967i	0.397882	−	0.689151i
$974$	−2.39974	+	4.15647i	−0.0768925	+	0.133182i
$975$	3.81361	+	6.60536i	0.122133	+	0.211541i
$976$	−5.94333	+	10.2942i	−0.190241	+	0.329508i
$977$	10.0567	+	17.4187i	0.321741	+	0.557272i	0.980847	−	0.194778i	$-0.0623985\pi$
$977$	10.0567	+	17.4187i	0.321741	+	0.557272i	−0.659106	+	0.752050i	$0.729065\pi$
$978$	31.3033			1.00097
$979$	24.0978	−	41.7385i	0.770167	−	1.33397i
$980$	2.62721			0.0839232
$981$	−3.58890			−0.114585
$982$	5.12470	+	8.87624i	0.163536	+	0.283252i
$983$	−14.5728			−0.464800			−0.232400	−	0.972620i	$-0.574658\pi$
$983$	−14.5728			−0.464800			−0.232400	+	0.972620i	$0.574658\pi$
$984$	1.65944	−	2.87424i	0.0529011	−	0.0916275i
$985$	−1.08362	+	1.87688i	−0.0345270	+	0.0598024i
$986$	−20.9355	−	36.2614i	−0.666723	−	1.15480i
$987$	22.5003	+	38.9716i	0.716191	+	1.24048i
$988$	−12.7839	−	22.1423i	−0.406710	−	0.704442i
$989$	−10.2056	−	17.6765i	−0.324518	−	0.562081i
$990$	−5.68665			−0.180734
$991$	−12.6428			−0.401612			−0.200806	−	0.979631i	$-0.564356\pi$
$991$	−12.6428			−0.401612			−0.200806	+	0.979631i	$0.564356\pi$
$992$	0.864994	+	1.49821i	0.0274636	+	0.0475683i
$993$	11.2650	−	19.5115i	0.357484	−	0.619180i
$994$	−24.7222	+	42.8201i	−0.784140	+	1.35817i
$995$	−2.42417	−	4.19879i	−0.0768515	−	0.133111i
$996$	−34.7250			−1.10030
$997$	−14.5678			−0.461366			−0.230683	−	0.973029i	$-0.574096\pi$
$997$	−14.5678			−0.461366			−0.230683	+	0.973029i	$0.574096\pi$
$998$	0.745574	−	1.29137i	0.0236007	−	0.0408777i
$999$	−14.6575	−	25.3875i	−0.463742	−	0.803225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.h.171.1	✓	6
67.29	even	3	inner	670.2.e.h.431.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.h.171.1	✓	6	1.1	even	1	trivial
670.2.e.h.431.1	yes	6	67.29	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -2.10278 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.05139 - 1.82106i) q^{6} +(1.55139 - 2.68708i) q^{7} -1.00000 q^{8} +1.42166 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -2.10278 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.05139 - 1.82106i) q^{6} +(1.55139 - 2.68708i) q^{7} -1.00000 q^{8} +1.42166 q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(1.05139 - 1.82106i) q^{12} +(-1.81361 - 3.14126i) q^{13} +3.10278 q^{14} -2.10278 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.26222 - 3.91828i) q^{17} +(0.710831 + 1.23120i) q^{18} +(-3.52444 - 6.10451i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.26222 + 5.65033i) q^{21} -4.00000 q^{22} +(2.55139 + 4.41913i) q^{23} +2.10278 q^{24} +1.00000 q^{25} +(1.81361 - 3.14126i) q^{26} +3.31889 q^{27} +(1.55139 + 2.68708i) q^{28} +(4.62721 - 8.01457i) q^{29} +(-1.05139 - 1.82106i) q^{30} +(-0.864994 + 1.49821i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.20555 - 7.28423i) q^{33} +(2.26222 - 3.91828i) q^{34} +(1.55139 - 2.68708i) q^{35} +(-0.710831 + 1.23120i) q^{36} +(-4.41638 - 7.64940i) q^{37} +(3.52444 - 6.10451i) q^{38} +(3.81361 + 6.60536i) q^{39} -1.00000 q^{40} +(0.789169 - 1.36688i) q^{41} -6.52444 q^{42} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +1.42166 q^{45} +(-2.55139 + 4.41913i) q^{46} +(3.44861 - 5.97317i) q^{47} +(1.05139 + 1.82106i) q^{48} +(-1.31361 - 2.27523i) q^{49} +(0.500000 + 0.866025i) q^{50} +(4.75694 + 8.23926i) q^{51} +3.62721 q^{52} +13.8816 q^{53} +(1.65944 + 2.87424i) q^{54} +(-2.00000 + 3.46410i) q^{55} +(-1.55139 + 2.68708i) q^{56} +(7.41110 + 12.8364i) q^{57} +9.25443 q^{58} -4.20555 q^{59} +(1.05139 - 1.82106i) q^{60} +(-5.94333 - 10.2942i) q^{61} -1.72999 q^{62} +(2.20555 - 3.82012i) q^{63} +1.00000 q^{64} +(-1.81361 - 3.14126i) q^{65} +8.41110 q^{66} +(7.59498 - 3.05225i) q^{67} +4.52444 q^{68} +(-5.36499 - 9.29244i) q^{69} +3.10278 q^{70} +(-7.96777 + 13.8006i) q^{71} -1.42166 q^{72} +(2.84056 + 4.91999i) q^{73} +(4.41638 - 7.64940i) q^{74} -2.10278 q^{75} +7.04888 q^{76} +(6.20555 + 10.7483i) q^{77} +(-3.81361 + 6.60536i) q^{78} +(-6.44082 + 11.1558i) q^{79} +(-0.500000 - 0.866025i) q^{80} -11.2439 q^{81} +1.57834 q^{82} +(-8.25694 - 14.3014i) q^{83} +(-3.26222 - 5.65033i) q^{84} +(-2.26222 - 3.91828i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-9.72999 + 16.8528i) q^{87} +(2.00000 - 3.46410i) q^{88} -12.0489 q^{89} +(0.710831 + 1.23120i) q^{90} -11.2544 q^{91} -5.10278 q^{92} +(1.81889 - 3.15041i) q^{93} +6.89722 q^{94} +(-3.52444 - 6.10451i) q^{95} +(-1.05139 + 1.82106i) q^{96} +(-0.421663 - 0.730342i) q^{97} +(1.31361 - 2.27523i) q^{98} +(-2.84333 + 4.92478i) 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

Fields

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Database

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