LMFDB - Embedded newform 670.2.e.g.171.3

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:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.3
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.g.431.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +2.08613 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.04307 + 1.80664i) q^{6} +(1.21903 - 2.11143i) q^{7} -1.00000 q^{8} +1.35194 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +2.08613 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.04307 + 1.80664i) q^{6} +(1.21903 - 2.11143i) q^{7} -1.00000 q^{8} +1.35194 q^{9} +(0.500000 + 0.866025i) q^{10} +(1.67597 - 2.90286i) q^{11} +(-1.04307 + 1.80664i) q^{12} +(1.21903 + 2.11143i) q^{13} +2.43807 q^{14} +2.08613 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.367095 - 0.635828i) q^{17} +(0.675970 + 1.17081i) q^{18} +(0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.54307 - 4.40472i) q^{21} +3.35194 q^{22} +(2.21903 + 3.84348i) q^{23} -2.08613 q^{24} +1.00000 q^{25} +(-1.21903 + 2.11143i) q^{26} -3.43807 q^{27} +(1.21903 + 2.11143i) q^{28} +(0.895004 - 1.55019i) q^{29} +(1.04307 + 1.80664i) q^{30} +(-5.08613 + 8.80944i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.49629 - 6.05575i) q^{33} +(0.367095 - 0.635828i) q^{34} +(1.21903 - 2.11143i) q^{35} +(-0.675970 + 1.17081i) q^{36} +(-5.82032 - 10.0811i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(2.54307 + 4.40472i) q^{39} -1.00000 q^{40} +(-1.32403 + 2.29329i) q^{41} +5.08613 q^{42} -2.08613 q^{43} +(1.67597 + 2.90286i) q^{44} +1.35194 q^{45} +(-2.21903 + 3.84348i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(-1.04307 - 1.80664i) q^{48} +(0.527909 + 0.914365i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.765809 - 1.32642i) q^{51} -2.43807 q^{52} +2.26581 q^{53} +(-1.71903 - 2.97746i) q^{54} +(1.67597 - 2.90286i) q^{55} +(-1.21903 + 2.11143i) q^{56} +(1.04307 + 1.80664i) q^{57} +1.79001 q^{58} -10.6965 q^{59} +(-1.04307 + 1.80664i) q^{60} +(1.64806 + 2.85453i) q^{61} -10.1723 q^{62} +(1.64806 - 2.85453i) q^{63} +1.00000 q^{64} +(1.21903 + 2.11143i) q^{65} +6.99258 q^{66} +(-4.02791 - 7.12572i) q^{67} +0.734191 q^{68} +(4.62920 + 8.01800i) q^{69} +2.43807 q^{70} +(2.45693 - 4.25554i) q^{71} -1.35194 q^{72} +(-1.36710 - 2.36788i) q^{73} +(5.82032 - 10.0811i) q^{74} +2.08613 q^{75} -1.00000 q^{76} +(-4.08613 - 7.07739i) q^{77} +(-2.54307 + 4.40472i) q^{78} +(7.52420 - 13.0323i) q^{79} +(-0.500000 - 0.866025i) q^{80} -11.2281 q^{81} -2.64806 q^{82} +(6.84823 + 11.8615i) q^{83} +(2.54307 + 4.40472i) q^{84} +(-0.367095 - 0.635828i) q^{85} +(-1.04307 - 1.80664i) q^{86} +(1.86710 - 3.23390i) q^{87} +(-1.67597 + 2.90286i) q^{88} -4.46838 q^{89} +(0.675970 + 1.17081i) q^{90} +5.94418 q^{91} -4.43807 q^{92} +(-10.6103 + 18.3776i) q^{93} -6.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(1.04307 - 1.80664i) q^{96} +(0.453226 + 0.785010i) q^{97} +(-0.527909 + 0.914365i) q^{98} +(2.26581 - 3.92450i) 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} + 4 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 + 4 * q^9	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9} + 3 q^{10} + 8 q^{11} + q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 3 q^{20} + 8 q^{21} + 16 q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 2 q^{27} - 2 q^{28} - 6 q^{29} - q^{30} - 16 q^{31} + 3 q^{32} - 6 q^{33} - 3 q^{34} - 2 q^{35} - 2 q^{36} - 10 q^{37} - 3 q^{38} + 8 q^{39} - 6 q^{40} - 10 q^{41} + 16 q^{42} + 2 q^{43} + 8 q^{44} + 4 q^{45} - 4 q^{46} - 18 q^{47} + q^{48} - 3 q^{49} + 3 q^{50} - 15 q^{51} + 4 q^{52} + 24 q^{53} - q^{54} + 8 q^{55} + 2 q^{56} - q^{57} - 12 q^{58} - 2 q^{59} + q^{60} + 14 q^{61} - 32 q^{62} + 14 q^{63} + 6 q^{64} - 2 q^{65} - 12 q^{66} - 18 q^{67} - 6 q^{68} + 6 q^{69} - 4 q^{70} + 22 q^{71} - 4 q^{72} - 3 q^{73} + 10 q^{74} - 2 q^{75} - 6 q^{76} - 10 q^{77} - 8 q^{78} + 12 q^{79} - 3 q^{80} - 26 q^{81} - 20 q^{82} + 10 q^{83} + 8 q^{84} + 3 q^{85} + q^{86} + 6 q^{87} - 8 q^{88} - 6 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} - 16 q^{93} - 36 q^{94} + 3 q^{95} - q^{96} - 17 q^{97} + 3 q^{98} + 24 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9 + 3 * q^10 + 8 * q^11 + q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 3 * q^20 + 8 * q^21 + 16 * q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 2 * q^27 - 2 * q^28 - 6 * q^29 - q^30 - 16 * q^31 + 3 * q^32 - 6 * q^33 - 3 * q^34 - 2 * q^35 - 2 * q^36 - 10 * q^37 - 3 * q^38 + 8 * q^39 - 6 * q^40 - 10 * q^41 + 16 * q^42 + 2 * q^43 + 8 * q^44 + 4 * q^45 - 4 * q^46 - 18 * q^47 + q^48 - 3 * q^49 + 3 * q^50 - 15 * q^51 + 4 * q^52 + 24 * q^53 - q^54 + 8 * q^55 + 2 * q^56 - q^57 - 12 * q^58 - 2 * q^59 + q^60 + 14 * q^61 - 32 * q^62 + 14 * q^63 + 6 * q^64 - 2 * q^65 - 12 * q^66 - 18 * q^67 - 6 * q^68 + 6 * q^69 - 4 * q^70 + 22 * q^71 - 4 * q^72 - 3 * q^73 + 10 * q^74 - 2 * q^75 - 6 * q^76 - 10 * q^77 - 8 * q^78 + 12 * q^79 - 3 * q^80 - 26 * q^81 - 20 * q^82 + 10 * q^83 + 8 * q^84 + 3 * q^85 + q^86 + 6 * q^87 - 8 * q^88 - 6 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 - 16 * q^93 - 36 * q^94 + 3 * q^95 - q^96 - 17 * q^97 + 3 * 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
$3$	2.08613			1.20443			0.602214	−	0.798335i	$-0.294285\pi$
$3$	2.08613			1.20443			0.602214	+	0.798335i	$0.294285\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.04307	+	1.80664i	0.425830	+	0.737558i
$7$	1.21903	−	2.11143i	0.460752	−	0.798046i	−0.538247	−	0.842787i	$-0.680913\pi$
$7$	1.21903	−	2.11143i	0.460752	−	0.798046i	0.998999	+	0.0447417i	$0.0142465\pi$
$8$	−1.00000			−0.353553
$9$	1.35194			0.450646
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.67597	−	2.90286i	0.505324	−	0.875247i	−0.494657	−	0.869088i	$-0.664706\pi$
$11$	1.67597	−	2.90286i	0.505324	−	0.875247i	0.999981	−	0.00615840i	$-0.00196029\pi$
$12$	−1.04307	+	1.80664i	−0.301107	+	0.521533i
$13$	1.21903	+	2.11143i	0.338099	+	0.585605i	0.984075	−	0.177753i	$-0.0568827\pi$
$13$	1.21903	+	2.11143i	0.338099	+	0.585605i	−0.645976	+	0.763358i	$0.723549\pi$
$14$	2.43807			0.651601
$15$	2.08613			0.538637
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.367095	−	0.635828i	−0.0890337	−	0.154211i	0.818069	−	0.575120i	$-0.195045\pi$
$17$	−0.367095	−	0.635828i	−0.0890337	−	0.154211i	−0.907103	+	0.420909i	$0.861711\pi$
$18$	0.675970	+	1.17081i	0.159328	+	0.275963i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	2.54307	−	4.40472i	0.554942	−	0.961188i
$22$	3.35194			0.714636
$23$	2.21903	+	3.84348i	0.462701	+	0.801421i	0.999094	−	0.0425467i	$-0.0135471\pi$
$23$	2.21903	+	3.84348i	0.462701	+	0.801421i	−0.536394	+	0.843968i	$0.680214\pi$
$24$	−2.08613			−0.425830
$25$	1.00000			0.200000
$26$	−1.21903	+	2.11143i	−0.239072	+	0.414085i
$27$	−3.43807			−0.661657
$28$	1.21903	+	2.11143i	0.230376	+	0.399023i
$29$	0.895004	−	1.55019i	0.166198	−	0.287864i	−0.770882	−	0.636978i	$-0.780184\pi$
$29$	0.895004	−	1.55019i	0.166198	−	0.287864i	0.937080	+	0.349114i	$0.113518\pi$
$30$	1.04307	+	1.80664i	0.190437	+	0.329846i
$31$	−5.08613	+	8.80944i	−0.913496	+	1.58222i	−0.104407	+	0.994535i	$0.533295\pi$
$31$	−5.08613	+	8.80944i	−0.913496	+	1.58222i	−0.809089	+	0.587687i	$0.800039\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.49629	−	6.05575i	0.608626	−	1.05417i
$34$	0.367095	−	0.635828i	0.0629564	−	0.109044i
$35$	1.21903	−	2.11143i	0.206054	−	0.356897i
$36$	−0.675970	+	1.17081i	−0.112662	+	0.195136i
$37$	−5.82032	−	10.0811i	−0.956855	−	1.65732i	−0.730065	−	0.683378i	$-0.760510\pi$
$37$	−5.82032	−	10.0811i	−0.956855	−	1.65732i	−0.226790	−	0.973944i	$-0.572823\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	2.54307	+	4.40472i	0.407216	+	0.705319i
$40$	−1.00000			−0.158114
$41$	−1.32403	+	2.29329i	−0.206779	+	0.358151i	−0.950698	−	0.310118i	$-0.899631\pi$
$41$	−1.32403	+	2.29329i	−0.206779	+	0.358151i	0.743919	+	0.668270i	$0.232965\pi$
$42$	5.08613			0.784807
$43$	−2.08613			−0.318132			−0.159066	−	0.987268i	$-0.550848\pi$
$43$	−2.08613			−0.318132			−0.159066	+	0.987268i	$0.550848\pi$
$44$	1.67597	+	2.90286i	0.252662	+	0.437623i
$45$	1.35194			0.201535
$46$	−2.21903	+	3.84348i	−0.327179	+	0.566690i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	−1.04307	−	1.80664i	−0.150553	−	0.260766i
$49$	0.527909	+	0.914365i	0.0754155	+	0.130624i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.765809	−	1.32642i	−0.107235	−	0.185736i
$52$	−2.43807			−0.338099
$53$	2.26581			0.311233			0.155616	−	0.987818i	$-0.450264\pi$
$53$	2.26581			0.311233			0.155616	+	0.987818i	$0.450264\pi$
$54$	−1.71903	−	2.97746i	−0.233931	−	0.405180i
$55$	1.67597	−	2.90286i	0.225988	−	0.391422i
$56$	−1.21903	+	2.11143i	−0.162900	+	0.282152i
$57$	1.04307	+	1.80664i	0.138157	+	0.239296i
$58$	1.79001			0.235040
$59$	−10.6965			−1.39256			−0.696280	−	0.717770i	$-0.745163\pi$
$59$	−10.6965			−1.39256			−0.696280	+	0.717770i	$0.745163\pi$
$60$	−1.04307	+	1.80664i	−0.134659	+	0.233236i
$61$	1.64806	+	2.85453i	0.211013	+	0.365484i	0.952032	−	0.305999i	$-0.0989906\pi$
$61$	1.64806	+	2.85453i	0.211013	+	0.365484i	−0.741019	+	0.671484i	$0.765657\pi$
$62$	−10.1723			−1.29188
$63$	1.64806	−	2.85453i	0.207636	−	0.359636i
$64$	1.00000			0.125000
$65$	1.21903	+	2.11143i	0.151203	+	0.261891i
$66$	6.99258			0.860727
$67$	−4.02791	−	7.12572i	−0.492087	−	0.870546i
$67$	−4.02791	−	7.12572i	−0.492087	−	0.870546i
$68$	0.734191			0.0890337
$69$	4.62920	+	8.01800i	0.557290	+	0.965254i
$70$	2.43807			0.291405
$71$	2.45693	−	4.25554i	0.291585	−	0.505039i	−0.682600	−	0.730792i	$-0.739151\pi$
$71$	2.45693	−	4.25554i	0.291585	−	0.505039i	0.974185	+	0.225753i	$0.0724842\pi$
$72$	−1.35194			−0.159328
$73$	−1.36710	−	2.36788i	−0.160006	−	0.277139i	0.774864	−	0.632128i	$-0.217818\pi$
$73$	−1.36710	−	2.36788i	−0.160006	−	0.277139i	−0.934871	+	0.354988i	$0.884485\pi$
$74$	5.82032	−	10.0811i	0.676599	−	1.17190i
$75$	2.08613			0.240886
$76$	−1.00000			−0.114708
$77$	−4.08613	−	7.07739i	−0.465658	−	0.806543i
$78$	−2.54307	+	4.40472i	−0.287945	+	0.498736i
$79$	7.52420	−	13.0323i	0.846539	−	1.46625i	−0.0377397	−	0.999288i	$-0.512016\pi$
$79$	7.52420	−	13.0323i	0.846539	−	1.46625i	0.884278	−	0.466960i	$-0.154651\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−11.2281			−1.24756
$82$	−2.64806			−0.292429
$83$	6.84823	+	11.8615i	0.751691	+	1.30197i	0.947003	+	0.321226i	$0.104095\pi$
$83$	6.84823	+	11.8615i	0.751691	+	1.30197i	−0.195312	+	0.980741i	$0.562572\pi$
$84$	2.54307	+	4.40472i	0.277471	+	0.480594i
$85$	−0.367095	−	0.635828i	−0.0398171	−	0.0689652i
$86$	−1.04307	−	1.80664i	−0.112477	−	0.194815i
$87$	1.86710	−	3.23390i	0.200174	−	0.346711i
$88$	−1.67597	+	2.90286i	−0.178659	+	0.309446i
$89$	−4.46838			−0.473648			−0.236824	−	0.971553i	$-0.576106\pi$
$89$	−4.46838			−0.473648			−0.236824	+	0.971553i	$0.576106\pi$
$90$	0.675970	+	1.17081i	0.0712535	+	0.123415i
$91$	5.94418			0.623120
$92$	−4.43807			−0.462701
$93$	−10.6103	+	18.3776i	−1.10024	+	1.90567i
$94$	−6.00000			−0.618853
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	1.04307	−	1.80664i	0.106457	−	0.184390i
$97$	0.453226	+	0.785010i	0.0460181	+	0.0797057i	0.888117	−	0.459617i	$-0.152013\pi$
$97$	0.453226	+	0.785010i	0.0460181	+	0.0797057i	−0.842099	+	0.539323i	$0.818680\pi$
$98$	−0.527909	+	0.914365i	−0.0533268	+	0.0923648i
$99$	2.26581	−	3.92450i	0.227722	−	0.394427i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.895004	−	1.55019i	0.0890563	−	0.154250i	−0.818056	−	0.575138i	$-0.804948\pi$
$101$	0.895004	−	1.55019i	0.0890563	−	0.154250i	0.907112	+	0.420888i	$0.138282\pi$
$102$	0.765809	−	1.32642i	0.0758264	−	0.131335i
$103$	−1.38225	+	2.39413i	−0.136197	+	0.235901i	−0.926054	−	0.377391i	$-0.876821\pi$
$103$	−1.38225	+	2.39413i	−0.136197	+	0.235901i	0.789857	+	0.613291i	$0.210155\pi$
$104$	−1.21903	−	2.11143i	−0.119536	−	0.207043i
$105$	2.54307	−	4.40472i	0.248178	−	0.429856i
$106$	1.13290	+	1.96225i	0.110037	+	0.190590i
$107$	−3.58002			−0.346093			−0.173047	−	0.984914i	$-0.555361\pi$
$107$	−3.58002			−0.346093			−0.173047	+	0.984914i	$0.555361\pi$
$108$	1.71903	−	2.97746i	0.165414	−	0.286506i
$109$	9.08613			0.870293			0.435147	−	0.900360i	$-0.356696\pi$
$109$	9.08613			0.870293			0.435147	+	0.900360i	$0.356696\pi$
$110$	3.35194			0.319595
$111$	−12.1419	−	21.0305i	−1.15246	−	1.99612i
$112$	−2.43807			−0.230376
$113$	−3.60500	+	6.24404i	−0.339129	+	0.587389i	−0.984269	−	0.176675i	$-0.943466\pi$
$113$	−3.60500	+	6.24404i	−0.339129	+	0.587389i	0.645140	+	0.764065i	$0.276799\pi$
$114$	−1.04307	+	1.80664i	−0.0976920	+	0.169208i
$115$	2.21903	+	3.84348i	0.206926	+	0.358406i
$116$	0.895004	+	1.55019i	0.0830991	+	0.143932i
$117$	1.64806	+	2.85453i	0.152363	+	0.263901i
$118$	−5.34823	−	9.26341i	−0.492344	−	0.852766i
$119$	−1.79001			−0.164090
$120$	−2.08613			−0.190437
$121$	−0.117748	−	0.203946i	−0.0107044	−	0.0185405i
$122$	−1.64806	+	2.85453i	−0.149208	+	0.258437i
$123$	−2.76210	+	4.78410i	−0.249050	+	0.431368i
$124$	−5.08613	−	8.80944i	−0.456748	−	0.791111i
$125$	1.00000			0.0894427
$126$	3.29612			0.293642
$127$	0.561931	−	0.973292i	0.0498633	−	0.0863657i	−0.840016	−	0.542561i	$-0.817455\pi$
$127$	0.561931	−	0.973292i	0.0498633	−	0.0863657i	0.889880	+	0.456195i	$0.150788\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.35194			−0.383167
$130$	−1.21903	+	2.11143i	−0.106916	+	0.185185i
$131$	−5.52420			−0.482652			−0.241326	−	0.970444i	$-0.577582\pi$
$131$	−5.52420			−0.482652			−0.241326	+	0.970444i	$0.577582\pi$
$132$	3.49629	+	6.05575i	0.304313	+	0.527086i
$133$	2.43807			0.211407
$134$	4.15710	−	7.05113i	0.359119	−	0.609125i
$135$	−3.43807			−0.295902
$136$	0.367095	+	0.635828i	0.0314782	+	0.0545218i
$137$	16.6029			1.41848			0.709241	−	0.704966i	$-0.249038\pi$
$137$	16.6029			1.41848			0.709241	+	0.704966i	$0.249038\pi$
$138$	−4.62920	+	8.01800i	−0.394063	+	0.682538i
$139$	−14.2207			−1.20618			−0.603090	−	0.797673i	$-0.706064\pi$
$139$	−14.2207			−1.20618			−0.603090	+	0.797673i	$0.706064\pi$
$140$	1.21903	+	2.11143i	0.103027	+	0.178448i
$141$	−6.25839	+	10.8399i	−0.527052	+	0.912880i
$142$	4.91387			0.412363
$143$	8.17226			0.683399
$144$	−0.675970	−	1.17081i	−0.0563308	−	0.0975678i
$145$	0.895004	−	1.55019i	0.0743261	−	0.128737i
$146$	1.36710	−	2.36788i	0.113142	−	0.195967i
$147$	1.10129	+	1.90748i	0.0908326	+	0.157327i
$148$	11.6406			0.956855
$149$	−8.17226			−0.669498			−0.334749	−	0.942307i	$-0.608651\pi$
$149$	−8.17226			−0.669498			−0.334749	+	0.942307i	$0.608651\pi$
$150$	1.04307	+	1.80664i	0.0851659	+	0.147512i
$151$	−9.33307	−	16.1654i	−0.759515	−	1.31552i	−0.943098	−	0.332514i	$-0.892103\pi$
$151$	−9.33307	−	16.1654i	−0.759515	−	1.31552i	0.183584	−	0.983004i	$-0.441230\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	−0.496291	−	0.859601i	−0.0401227	−	0.0694946i
$154$	4.08613	−	7.07739i	0.329270	−	0.570312i
$155$	−5.08613	+	8.80944i	−0.408528	+	0.707591i
$156$	−5.08613			−0.407216
$157$	−0.601286	−	1.04146i	−0.0479879	−	0.0831175i	0.841034	−	0.540983i	$-0.181948\pi$
$157$	−0.601286	−	1.04146i	−0.0479879	−	0.0831175i	−0.889022	+	0.457865i	$0.848614\pi$
$158$	15.0484			1.19719
$159$	4.72677			0.374857
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	10.8203			0.852761
$162$	−5.61404	−	9.72380i	−0.441081	−	0.763974i
$163$	3.77485	−	6.53824i	0.295669	−	0.512114i	−0.679471	−	0.733702i	$-0.737791\pi$
$163$	3.77485	−	6.53824i	0.295669	−	0.512114i	0.975140	+	0.221588i	$0.0711240\pi$
$164$	−1.32403	−	2.29329i	−0.103389	−	0.179076i
$165$	3.49629	−	6.05575i	0.272186	−	0.471440i
$166$	−6.84823	+	11.8615i	−0.531526	+	0.920630i
$167$	−1.17968	+	2.04326i	−0.0912863	+	0.158112i	−0.908053	−	0.418856i	$-0.862431\pi$
$167$	−1.17968	+	2.04326i	−0.0912863	+	0.158112i	0.816766	+	0.576969i	$0.195765\pi$
$168$	−2.54307	+	4.40472i	−0.196202	+	0.339831i
$169$	3.52791	−	6.11052i	0.271378	−	0.470040i
$170$	0.367095	−	0.635828i	0.0281549	−	0.0487658i
$171$	0.675970	+	1.17081i	0.0516927	+	0.0895344i
$172$	1.04307	−	1.80664i	0.0795330	−	0.137755i
$173$	2.18872	+	3.79098i	0.166405	+	0.288223i	0.937153	−	0.348917i	$-0.113451\pi$
$173$	2.18872	+	3.79098i	0.166405	+	0.288223i	−0.770748	+	0.637140i	$0.780117\pi$
$174$	3.73419			0.283088
$175$	1.21903	−	2.11143i	0.0921504	−	0.159609i
$176$	−3.35194			−0.252662
$177$	−22.3142			−1.67724
$178$	−2.23419	−	3.86973i	−0.167460	−	0.290049i
$179$	17.5652			1.31288			0.656442	−	0.754377i	$-0.272061\pi$
$179$	17.5652			1.31288			0.656442	+	0.754377i	$0.272061\pi$
$180$	−0.675970	+	1.17081i	−0.0503838	+	0.0872673i
$181$	11.0673	−	19.1691i	0.822623	−	1.42483i	−0.0810989	−	0.996706i	$-0.525843\pi$
$181$	11.0673	−	19.1691i	0.822623	−	1.42483i	0.903722	−	0.428119i	$-0.140824\pi$
$182$	2.97209	+	5.14781i	0.220306	+	0.381581i
$183$	3.43807	+	5.95491i	0.254149	+	0.440200i
$184$	−2.21903	−	3.84348i	−0.163589	−	0.283345i
$185$	−5.82032	−	10.0811i	−0.427919	−	0.741177i
$186$	−21.2207			−1.55597
$187$	−2.46096			−0.179963
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	−4.19113	+	7.25924i	−0.304860	+	0.528032i
$190$	−0.500000	+	0.866025i	−0.0362738	+	0.0628281i
$191$	−9.44952	−	16.3670i	−0.683743	−	1.18428i	−0.973830	−	0.227277i	$-0.927018\pi$
$191$	−9.44952	−	16.3670i	−0.683743	−	1.18428i	0.290087	−	0.957000i	$-0.406316\pi$
$192$	2.08613			0.150553
$193$	−9.52420			−0.685567			−0.342783	−	0.939414i	$-0.611370\pi$
$193$	−9.52420			−0.685567			−0.342783	+	0.939414i	$0.611370\pi$
$194$	−0.453226	+	0.785010i	−0.0325397	+	0.0563604i
$195$	2.54307	+	4.40472i	0.182113	+	0.315428i
$196$	−1.05582			−0.0754155
$197$	−5.04840	+	8.74408i	−0.359684	+	0.622990i	−0.987908	−	0.155042i	$-0.950449\pi$
$197$	−5.04840	+	8.74408i	−0.359684	+	0.622990i	0.628224	+	0.778032i	$0.283782\pi$
$198$	4.53162			0.322048
$199$	−1.19113	−	2.06309i	−0.0844367	−	0.146249i	0.820714	−	0.571339i	$-0.193576\pi$
$199$	−1.19113	−	2.06309i	−0.0844367	−	0.146249i	−0.905151	+	0.425090i	$0.860242\pi$
$200$	−1.00000			−0.0707107
$201$	−8.40274	−	14.8652i	−0.592684	−	1.04851i
$202$	1.79001			0.125945
$203$	−2.18208	−	3.77948i	−0.153152	−	0.265267i
$204$	1.53162			0.107235
$205$	−1.32403	+	2.29329i	−0.0924743	+	0.160170i
$206$	−2.76450			−0.192612
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	1.21903	−	2.11143i	0.0845248	−	0.146401i
$209$	3.35194			0.231858
$210$	5.08613			0.350976
$211$	0.623861	+	1.08056i	0.0429484	+	0.0743888i	0.886701	−	0.462344i	$-0.152992\pi$
$211$	0.623861	+	1.08056i	0.0429484	+	0.0743888i	−0.843752	+	0.536733i	$0.819658\pi$
$212$	−1.13290	+	1.96225i	−0.0778082	+	0.134768i
$213$	5.12549	−	8.87760i	0.351193	−	0.608283i
$214$	−1.79001	−	3.10039i	−0.122362	−	0.211938i
$215$	−2.08613			−0.142273
$216$	3.43807			0.233931
$217$	12.4003	+	21.4780i	0.841790	+	1.45802i
$218$	4.54307	+	7.86882i	0.307695	+	0.532944i
$219$	−2.85194	−	4.93970i	−0.192716	−	0.333794i
$220$	1.67597	+	2.90286i	0.112994	+	0.195711i
$221$	0.895004	−	1.55019i	0.0602045	−	0.104277i
$222$	12.1419	−	21.0305i	0.814914	−	1.41147i
$223$	8.67095			0.580650			0.290325	−	0.956928i	$-0.406237\pi$
$223$	8.67095			0.580650			0.290325	+	0.956928i	$0.406237\pi$
$224$	−1.21903	−	2.11143i	−0.0814502	−	0.141076i
$225$	1.35194			0.0901293
$226$	−7.20999			−0.479601
$227$	−3.33678	+	5.77948i	−0.221470	+	0.383597i	−0.955255	−	0.295785i	$-0.904419\pi$
$227$	−3.33678	+	5.77948i	−0.221470	+	0.383597i	0.733785	+	0.679382i	$0.237752\pi$
$228$	−2.08613			−0.138157
$229$	5.03031	+	8.71276i	0.332412	+	0.575755i	0.982984	−	0.183689i	$-0.0588041\pi$
$229$	5.03031	+	8.71276i	0.332412	+	0.575755i	−0.650572	+	0.759445i	$0.725471\pi$
$230$	−2.21903	+	3.84348i	−0.146319	+	0.253432i
$231$	−8.52420	−	14.7643i	−0.560851	−	0.971423i
$232$	−0.895004	+	1.55019i	−0.0587599	+	0.101775i
$233$	−3.97743	+	6.88910i	−0.260570	+	0.451320i	−0.966393	−	0.257067i	$-0.917244\pi$
$233$	−3.97743	+	6.88910i	−0.260570	+	0.451320i	0.705824	+	0.708388i	$0.250577\pi$
$234$	−1.64806	+	2.85453i	−0.107737	+	0.186606i
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$	5.34823	−	9.26341i	0.348140	−	0.602996i
$237$	15.6965	−	27.1871i	1.01959	−	1.76599i
$238$	−0.895004	−	1.55019i	−0.0580145	−	0.100484i
$239$	−9.22808	+	15.9835i	−0.596915	+	1.03389i	0.396359	+	0.918096i	$0.370274\pi$
$239$	−9.22808	+	15.9835i	−0.596915	+	1.03389i	−0.993274	+	0.115791i	$0.963060\pi$
$240$	−1.04307	−	1.80664i	−0.0673296	−	0.116618i
$241$	−15.7523			−1.01469			−0.507347	−	0.861742i	$-0.669374\pi$
$241$	−15.7523			−1.01469			−0.507347	+	0.861742i	$0.669374\pi$
$242$	0.117748	−	0.203946i	0.00756914	−	0.0131101i
$243$	−13.1090			−0.840944
$244$	−3.29612			−0.211013
$245$	0.527909	+	0.914365i	0.0337269	+	0.0584166i
$246$	−5.52420			−0.352210
$247$	−1.21903	+	2.11143i	−0.0775653	+	0.134347i
$248$	5.08613	−	8.80944i	0.322970	−	0.559400i
$249$	14.2863	+	24.7446i	0.905357	+	1.56813i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−14.2547	−	24.6898i	−0.899748	−	1.55841i	−0.827817	−	0.560999i	$-0.810417\pi$
$251$	−14.2547	−	24.6898i	−0.899748	−	1.55841i	−0.0719309	−	0.997410i	$-0.522916\pi$
$252$	1.64806	+	2.85453i	0.103818	+	0.179818i
$253$	14.8761			0.935255
$254$	1.12386			0.0705173
$255$	−0.765809	−	1.32642i	−0.0479568	−	0.0830636i
$256$	−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	$0.226587\pi$
$258$	−2.17597	−	3.76889i	−0.135470	−	0.234641i
$259$	−28.3807			−1.76349
$260$	−2.43807			−0.151203
$261$	1.20999	−	2.09577i	0.0748966	−	0.129725i
$262$	−2.76210	−	4.78410i	−0.170643	−	0.295563i
$263$	28.7071			1.77016			0.885079	−	0.465441i	$-0.154104\pi$
$263$	28.7071			1.77016			0.885079	+	0.465441i	$0.154104\pi$
$264$	−3.49629	+	6.05575i	−0.215182	+	0.372706i
$265$	2.26581			0.139188
$266$	1.21903	+	2.11143i	0.0747438	+	0.129460i
$267$	−9.32163			−0.570474
$268$	8.18501	+	0.0745909i	0.499979	+	0.00455637i
$269$	−0.382252			−0.0233063			−0.0116532	−	0.999932i	$-0.503709\pi$
$269$	−0.382252			−0.0233063			−0.0116532	+	0.999932i	$0.503709\pi$
$270$	−1.71903	−	2.97746i	−0.104617	−	0.181202i
$271$	−23.8506			−1.44882			−0.724411	−	0.689368i	$-0.757888\pi$
$271$	−23.8506			−1.44882			−0.724411	+	0.689368i	$0.757888\pi$
$272$	−0.367095	+	0.635828i	−0.0222584	+	0.0385527i
$273$	12.4003			0.750503
$274$	8.30146	+	14.3785i	0.501509	+	0.868640i
$275$	1.67597	−	2.90286i	0.101065	−	0.175049i
$276$	−9.25839			−0.557290
$277$	4.68904			0.281737			0.140869	−	0.990028i	$-0.455010\pi$
$277$	4.68904			0.281737			0.140869	+	0.990028i	$0.455010\pi$
$278$	−7.11033	−	12.3155i	−0.426449	−	0.738632i
$279$	−6.87614	+	11.9098i	−0.411664	+	0.713022i
$280$	−1.21903	+	2.11143i	−0.0728513	+	0.126182i
$281$	10.4065	+	18.0245i	0.620797	+	1.07525i	0.989338	+	0.145640i	$0.0465242\pi$
$281$	10.4065	+	18.0245i	0.620797	+	1.07525i	−0.368541	+	0.929612i	$0.620143\pi$
$282$	−12.5168			−0.745363
$283$	2.25839			0.134247			0.0671237	−	0.997745i	$-0.478618\pi$
$283$	2.25839			0.134247			0.0671237	+	0.997745i	$0.478618\pi$
$284$	2.45693	+	4.25554i	0.145792	+	0.252520i
$285$	1.04307	+	1.80664i	0.0617858	+	0.107016i
$286$	4.08613	+	7.07739i	0.241618	+	0.418495i
$287$	3.22808	+	5.59120i	0.190547	+	0.330038i
$288$	0.675970	−	1.17081i	0.0398319	−	0.0689909i
$289$	8.23048	−	14.2556i	0.484146	−	0.838565i
$290$	1.79001			0.105113
$291$	0.945488	+	1.63763i	0.0554255	+	0.0959997i
$292$	2.73419			0.160006
$293$	13.8310			0.808015			0.404008	−	0.914756i	$-0.367617\pi$
$293$	13.8310			0.808015			0.404008	+	0.914756i	$0.367617\pi$
$294$	−1.10129	+	1.90748i	−0.0642283	+	0.111247i
$295$	−10.6965			−0.622772
$296$	5.82032	+	10.0811i	0.338299	+	0.585952i
$297$	−5.76210	+	9.98025i	−0.334351	+	0.579113i
$298$	−4.08613	−	7.07739i	−0.236703	−	0.409982i
$299$	−5.41016	+	9.37067i	−0.312878	+	0.541920i
$300$	−1.04307	+	1.80664i	−0.0602214	+	0.104307i
$301$	−2.54307	+	4.40472i	−0.146580	+	0.253884i
$302$	9.33307	−	16.1654i	0.537058	−	0.930212i
$303$	1.86710	−	3.23390i	0.107262	−	0.185783i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	1.64806	+	2.85453i	0.0943677	+	0.163450i
$306$	0.496291	−	0.859601i	0.0283711	−	0.0491401i
$307$	5.01516	+	8.68651i	0.286230	+	0.495765i	0.972907	−	0.231198i	$-0.0742645\pi$
$307$	5.01516	+	8.68651i	0.286230	+	0.495765i	−0.686677	+	0.726963i	$0.740931\pi$
$308$	8.17226			0.465658
$309$	−2.88356	+	4.99447i	−0.164040	+	0.284125i
$310$	−10.1723			−0.577746
$311$	31.6029			1.79204			0.896018	−	0.444017i	$-0.146447\pi$
$311$	31.6029			1.79204			0.896018	+	0.444017i	$0.146447\pi$
$312$	−2.54307	−	4.40472i	−0.143973	−	0.249368i
$313$	−13.5497			−0.765875			−0.382937	−	0.923774i	$-0.625087\pi$
$313$	−13.5497			−0.765875			−0.382937	+	0.923774i	$0.625087\pi$
$314$	0.601286	−	1.04146i	0.0339326	−	0.0587729i
$315$	1.64806	−	2.85453i	0.0928577	−	0.160834i
$316$	7.52420	+	13.0323i	0.423269	+	0.733124i
$317$	15.8687	+	27.4854i	0.891276	+	1.54374i	0.838347	+	0.545137i	$0.183522\pi$
$317$	15.8687	+	27.4854i	0.891276	+	1.54374i	0.0529293	+	0.998598i	$0.483144\pi$
$318$	2.36339	+	4.09351i	0.132532	+	0.229552i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	1.00000			0.0559017
$321$	−7.46838			−0.416844
$322$	5.41016	+	9.37067i	0.301496	+	0.522207i
$323$	0.367095	−	0.635828i	0.0204257	−	0.0353784i
$324$	5.61404	−	9.72380i	0.311891	−	0.540211i
$325$	1.21903	+	2.11143i	0.0676199	+	0.117121i
$326$	7.54970			0.418139
$327$	18.9549			1.04821
$328$	1.32403	−	2.29329i	0.0731073	−	0.126626i
$329$	7.31421	+	12.6686i	0.403245	+	0.698441i
$330$	6.99258			0.384929
$331$	−16.9307	+	29.3247i	−0.930593	+	1.61183i	−0.148282	+	0.988945i	$0.547374\pi$
$331$	−16.9307	+	29.3247i	−0.930593	+	1.61183i	−0.782310	+	0.622889i	$0.785959\pi$
$332$	−13.6965			−0.751691
$333$	−7.86872	−	13.6290i	−0.431203	−	0.746866i
$334$	−2.35936			−0.129098
$335$	−4.02791	−	7.12572i	−0.220068	−	0.389320i
$336$	−5.08613			−0.277471
$337$	10.2863	+	17.8164i	0.560330	+	0.970521i	0.997467	+	0.0711258i	$0.0226592\pi$
$337$	10.2863	+	17.8164i	0.560330	+	0.970521i	−0.437137	+	0.899395i	$0.644007\pi$
$338$	7.05582			0.383786
$339$	−7.52049	+	13.0259i	−0.408457	+	0.707468i
$340$	0.734191			0.0398171
$341$	17.0484	+	29.5287i	0.923223	+	1.59907i
$342$	−0.675970	+	1.17081i	−0.0365522	+	0.0633104i
$343$	19.6406			1.06050
$344$	2.08613			0.112477
$345$	4.62920	+	8.01800i	0.249227	+	0.431675i
$346$	−2.18872	+	3.79098i	−0.117666	+	0.203804i
$347$	−14.0636	+	24.3588i	−0.754971	+	1.30765i	0.190417	+	0.981703i	$0.439016\pi$
$347$	−14.0636	+	24.3588i	−0.754971	+	1.30765i	−0.945389	+	0.325945i	$0.894317\pi$
$348$	1.86710	+	3.23390i	0.100087	+	0.173355i
$349$	23.7145			1.26941			0.634705	−	0.772754i	$-0.281122\pi$
$349$	23.7145			1.26941			0.634705	+	0.772754i	$0.281122\pi$
$350$	2.43807			0.130320
$351$	−4.19113	−	7.25924i	−0.223706	−	0.387470i
$352$	−1.67597	−	2.90286i	−0.0893295	−	0.154723i
$353$	11.0181	+	19.0839i	0.586434	+	1.01573i	0.994695	+	0.102868i	$0.0328018\pi$
$353$	11.0181	+	19.0839i	0.586434	+	1.01573i	−0.408261	+	0.912865i	$0.633865\pi$
$354$	−11.1571	−	19.3247i	−0.592993	−	1.02709i
$355$	2.45693	−	4.25554i	0.130401	−	0.225860i
$356$	2.23419	−	3.86973i	0.118412	−	0.205095i
$357$	−3.73419			−0.197634
$358$	8.78259	+	15.2119i	0.464174	+	0.803973i
$359$	7.98516			0.421441			0.210720	−	0.977546i	$-0.432419\pi$
$359$	7.98516			0.421441			0.210720	+	0.977546i	$0.432419\pi$
$360$	−1.35194			−0.0712535
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	22.1345			1.16337
$363$	−0.245638	−	0.425458i	−0.0128927	−	0.0223307i
$364$	−2.97209	+	5.14781i	−0.155780	+	0.269819i
$365$	−1.36710	−	2.36788i	−0.0715570	−	0.123940i
$366$	−3.43807	+	5.95491i	−0.179711	+	0.311268i
$367$	5.27485	−	9.13631i	0.275345	−	0.476912i	−0.694877	−	0.719129i	$-0.744541\pi$
$367$	5.27485	−	9.13631i	0.275345	−	0.476912i	0.970222	+	0.242217i	$0.0778746\pi$
$368$	2.21903	−	3.84348i	0.115675	−	0.200355i
$369$	−1.79001	+	3.10039i	−0.0931841	+	0.161400i
$370$	5.82032	−	10.0811i	0.302584	−	0.524091i
$371$	2.76210	−	4.78410i	0.143401	−	0.248378i
$372$	−10.6103	−	18.3776i	−0.550120	−	0.952836i
$373$	13.8458	−	23.9817i	0.716910	−	1.24172i	−0.245309	−	0.969445i	$-0.578889\pi$
$373$	13.8458	−	23.9817i	0.716910	−	1.24172i	0.962218	−	0.272279i	$-0.0877774\pi$
$374$	−1.23048	−	2.13126i	−0.0636267	−	0.110205i
$375$	2.08613			0.107727
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	4.36417			0.224766
$378$	−8.38225			−0.431137
$379$	−9.41016	−	16.2989i	−0.483367	−	0.837217i	0.516450	−	0.856317i	$-0.327253\pi$
$379$	−9.41016	−	16.2989i	−0.483367	−	0.837217i	−0.999818	+	0.0191003i	$0.993920\pi$
$380$	−1.00000			−0.0512989
$381$	1.17226	−	2.03041i	0.0600567	−	0.104021i
$382$	9.44952	−	16.3670i	0.483479	−	0.837411i
$383$	19.3445	+	33.5057i	0.988459	+	1.71206i	0.625423	+	0.780286i	$0.284926\pi$
$383$	19.3445	+	33.5057i	0.988459	+	1.71206i	0.363035	+	0.931775i	$0.381740\pi$
$384$	1.04307	+	1.80664i	0.0532287	+	0.0921948i
$385$	−4.08613	−	7.07739i	−0.208248	−	0.360697i
$386$	−4.76210	−	8.24820i	−0.242384	−	0.419822i
$387$	−2.82032			−0.143365
$388$	−0.906451			−0.0460181
$389$	10.3142	+	17.8647i	0.522951	+	0.905778i	0.999643	+	0.0267076i	$0.00850231\pi$
$389$	10.3142	+	17.8647i	0.522951	+	0.905778i	−0.476692	+	0.879070i	$0.658164\pi$
$390$	−2.54307	+	4.40472i	−0.128773	+	0.223042i
$391$	1.62920	−	2.82185i	0.0823919	−	0.142707i
$392$	−0.527909	−	0.914365i	−0.0266634	−	0.0461824i
$393$	−11.5242			−0.581319
$394$	−10.0968			−0.508669
$395$	7.52420	−	13.0323i	0.378584	−	0.655726i
$396$	2.26581	+	3.92450i	0.113861	+	0.197213i
$397$	18.8942			0.948274			0.474137	−	0.880451i	$-0.342760\pi$
$397$	18.8942			0.948274			0.474137	+	0.880451i	$0.342760\pi$
$398$	1.19113	−	2.06309i	0.0597057	−	0.103413i
$399$	5.08613			0.254625
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	26.1526			1.30600			0.653000	−	0.757358i	$-0.273510\pi$
$401$	26.1526			1.30600			0.653000	+	0.757358i	$0.273510\pi$
$402$	8.67226	−	14.7096i	0.432533	−	0.733647i
$403$	−24.8007			−1.23541
$404$	0.895004	+	1.55019i	0.0445281	+	0.0771250i
$405$	−11.2281			−0.557928
$406$	2.18208	−	3.77948i	0.108295	−	0.187572i
$407$	−39.0187			−1.93409
$408$	0.765809	+	1.32642i	0.0379132	+	0.0656676i
$409$	−9.49389	+	16.4439i	−0.469442	+	0.813098i	−0.999390	−	0.0349324i	$-0.988878\pi$
$409$	−9.49389	+	16.4439i	−0.469442	+	0.813098i	0.529947	+	0.848031i	$0.322212\pi$
$410$	−2.64806			−0.130778
$411$	34.6358			1.70846
$412$	−1.38225	−	2.39413i	−0.0680987	−	0.117950i
$413$	−13.0394	+	22.5848i	−0.641625	+	1.11133i
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	6.84823	+	11.8615i	0.336166	+	0.582257i
$416$	2.43807			0.119536
$417$	−29.6661			−1.45276
$418$	1.67597	+	2.90286i	0.0819744	+	0.141984i
$419$	−12.2268	−	21.1774i	−0.597317	−	1.03458i	−0.993215	−	0.116289i	$-0.962900\pi$
$419$	−12.2268	−	21.1774i	−0.597317	−	1.03458i	0.395898	−	0.918294i	$-0.370433\pi$
$420$	2.54307	+	4.40472i	0.124089	+	0.214928i
$421$	−6.96969	−	12.0719i	−0.339682	−	0.588346i	0.644691	−	0.764443i	$-0.276986\pi$
$421$	−6.96969	−	12.0719i	−0.339682	−	0.588346i	−0.984373	+	0.176097i	$0.943653\pi$
$422$	−0.623861	+	1.08056i	−0.0303691	+	0.0526008i
$423$	−4.05582	+	7.02488i	−0.197201	+	0.341561i
$424$	−2.26581			−0.110037
$425$	−0.367095	−	0.635828i	−0.0178067	−	0.0308422i
$426$	10.2510			0.496661
$427$	8.03617			0.388898
$428$	1.79001	−	3.10039i	0.0865233	−	0.149863i
$429$	17.0484			0.823104
$430$	−1.04307	−	1.80664i	−0.0503011	−	0.0871240i
$431$	−4.75306	+	8.23254i	−0.228947	+	0.396547i	−0.957496	−	0.288446i	$-0.906861\pi$
$431$	−4.75306	+	8.23254i	−0.228947	+	0.396547i	0.728550	+	0.684993i	$0.240195\pi$
$432$	1.71903	+	2.97746i	0.0827071	+	0.143253i
$433$	−5.35968	+	9.28323i	−0.257570	+	0.446124i	−0.965590	−	0.260068i	$-0.916255\pi$
$433$	−5.35968	+	9.28323i	−0.257570	+	0.446124i	0.708021	+	0.706192i	$0.249588\pi$
$434$	−12.4003	+	21.4780i	−0.595235	+	1.03098i
$435$	1.86710	−	3.23390i	0.0895204	−	0.155054i
$436$	−4.54307	+	7.86882i	−0.217573	+	0.376848i
$437$	−2.21903	+	3.84348i	−0.106151	+	0.183859i
$438$	2.85194	−	4.93970i	0.136271	−	0.236028i
$439$	−19.7711	−	34.2446i	−0.943625	−	1.63441i	−0.758481	−	0.651695i	$-0.774058\pi$
$439$	−19.7711	−	34.2446i	−0.943625	−	1.63441i	−0.185144	−	0.982711i	$-0.559275\pi$
$440$	−1.67597	+	2.90286i	−0.0798987	+	0.138389i
$441$	0.713701	+	1.23617i	0.0339857	+	0.0588650i
$442$	1.79001			0.0851420
$443$	−9.25306	+	16.0268i	−0.439626	+	0.761455i	−0.997660	−	0.0683632i	$-0.978222\pi$
$443$	−9.25306	+	16.0268i	−0.439626	+	0.761455i	0.558035	+	0.829818i	$0.311556\pi$
$444$	24.2839			1.15246
$445$	−4.46838			−0.211822
$446$	4.33548	+	7.50927i	0.205291	+	0.355574i
$447$	−17.0484			−0.806362
$448$	1.21903	−	2.11143i	0.0575940	−	0.0997557i
$449$	−10.7900	+	18.6888i	−0.509212	+	0.881981i	0.490731	+	0.871311i	$0.336730\pi$
$449$	−10.7900	+	18.6888i	−0.509212	+	0.881981i	−0.999943	+	0.0106700i	$0.996604\pi$
$450$	0.675970	+	1.17081i	0.0318655	+	0.0551927i
$451$	4.43807	+	7.68696i	0.208981	+	0.361965i
$452$	−3.60500	−	6.24404i	−0.169565	−	0.293695i
$453$	−19.4700	−	33.7230i	−0.914781	−	1.58445i
$454$	−6.67357			−0.313206
$455$	5.94418			0.278668
$456$	−1.04307	−	1.80664i	−0.0488460	−	0.0846038i
$457$	−7.38759	+	12.7957i	−0.345577	+	0.598556i	−0.985458	−	0.169917i	$-0.945650\pi$
$457$	−7.38759	+	12.7957i	−0.345577	+	0.598556i	0.639882	+	0.768473i	$0.278983\pi$
$458$	−5.03031	+	8.71276i	−0.235051	+	0.407120i
$459$	1.26210	+	2.18602i	0.0589098	+	0.102035i
$460$	−4.43807			−0.206926
$461$	17.1223			0.797465			0.398733	−	0.917067i	$-0.369450\pi$
$461$	17.1223			0.797465			0.398733	+	0.917067i	$0.369450\pi$
$462$	8.52420	−	14.7643i	0.396582	−	0.686900i
$463$	3.54547	+	6.14093i	0.164772	+	0.285393i	0.936574	−	0.350469i	$-0.113978\pi$
$463$	3.54547	+	6.14093i	0.164772	+	0.285393i	−0.771802	+	0.635863i	$0.780645\pi$
$464$	−1.79001			−0.0830991
$465$	−10.6103	+	18.3776i	−0.492042	+	0.852242i
$466$	−7.95485			−0.368501
$467$	4.82032	+	8.34904i	0.223058	+	0.386348i	0.955735	−	0.294229i	$-0.0950628\pi$
$467$	4.82032	+	8.34904i	0.223058	+	0.386348i	−0.732677	+	0.680576i	$0.761729\pi$
$468$	−3.29612			−0.152363
$469$	−19.9556	−	0.181858i	−0.921465	−	0.00839742i
$470$	−6.00000			−0.276759
$471$	−1.25436	−	2.17262i	−0.0577979	−	0.100109i
$472$	10.6965			0.492344
$473$	−3.49629	+	6.05575i	−0.160760	+	0.278444i
$474$	31.3929			1.44192
$475$	0.500000	+	0.866025i	0.0229416	+	0.0397360i
$476$	0.895004	−	1.55019i	0.0410225	−	0.0710530i
$477$	3.06324			0.140256
$478$	−18.4562			−0.844165
$479$	−9.67759	−	16.7621i	−0.442181	−	0.765879i	0.555670	−	0.831403i	$-0.312462\pi$
$479$	−9.67759	−	16.7621i	−0.442181	−	0.765879i	−0.997851	+	0.0655234i	$0.979128\pi$
$480$	1.04307	−	1.80664i	0.0476092	−	0.0824615i
$481$	14.1903	−	24.5784i	0.647024	−	1.12068i
$482$	−7.87614	−	13.6419i	−0.358748	−	0.621370i
$483$	22.5726			1.02709
$484$	0.235496			0.0107044
$485$	0.453226	+	0.785010i	0.0205799	+	0.0356455i
$486$	−6.55451	−	11.3527i	−0.297319	−	0.514971i
$487$	−15.7358	−	27.2552i	−0.713058	−	1.23505i	−0.963704	−	0.266974i	$-0.913976\pi$
$487$	−15.7358	−	27.2552i	−0.713058	−	1.23505i	0.250646	−	0.968079i	$-0.419357\pi$
$488$	−1.64806	−	2.85453i	−0.0746042	−	0.129218i
$489$	7.87483	−	13.6396i	0.356112	−	0.616805i
$490$	−0.527909	+	0.914365i	−0.0238485	+	0.0413068i
$491$	5.11164			0.230685			0.115342	−	0.993326i	$-0.463203\pi$
$491$	5.11164			0.230685			0.115342	+	0.993326i	$0.463203\pi$
$492$	−2.76210	−	4.78410i	−0.124525	−	0.215684i
$493$	−1.31421			−0.0591890
$494$	−2.43807			−0.109694
$495$	2.26581	−	3.92450i	0.101841	−	0.176393i
$496$	10.1723			0.456748
$497$	−5.99018	−	10.3753i	−0.268696	−	0.465395i
$498$	−14.2863	+	24.7446i	−0.640184	+	1.10883i
$499$	−16.3310	−	28.2861i	−0.731075	−	1.26626i	−0.956424	−	0.291982i	$-0.905685\pi$
$499$	−16.3310	−	28.2861i	−0.731075	−	1.26626i	0.225348	−	0.974278i	$-0.427648\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−2.46096	+	4.26251i	−0.109948	+	0.190435i
$502$	14.2547	−	24.6898i	0.636218	−	1.10196i
$503$	−0.750653	+	1.30017i	−0.0334699	+	0.0579717i	−0.882275	−	0.470734i	$-0.843989\pi$
$503$	−0.750653	+	1.30017i	−0.0334699	+	0.0579717i	0.848805	+	0.528706i	$0.177322\pi$
$504$	−1.64806	+	2.85453i	−0.0734105	+	0.127151i
$505$	0.895004	−	1.55019i	0.0398272	−	0.0689827i
$506$	7.43807	+	12.8831i	0.330663	+	0.572724i
$507$	7.35968	−	12.7473i	0.326855	−	0.566129i
$508$	0.561931	+	0.973292i	0.0249316	+	0.0431829i
$509$	12.8384			0.569052			0.284526	−	0.958668i	$-0.408164\pi$
$509$	12.8384			0.569052			0.284526	+	0.958668i	$0.408164\pi$
$510$	0.765809	−	1.32642i	0.0339106	−	0.0587349i
$511$	−6.66615			−0.294893
$512$	−1.00000			−0.0441942
$513$	−1.71903	−	2.97746i	−0.0758972	−	0.131458i
$514$	−6.00000			−0.264649
$515$	−1.38225	+	2.39413i	−0.0609093	+	0.105498i
$516$	2.17597	−	3.76889i	0.0957917	−	0.165916i
$517$	10.0558	+	17.4172i	0.442254	+	0.766007i
$518$	−14.1903	−	24.5784i	−0.623488	−	1.07991i
$519$	4.56596	+	7.90847i	0.200423	+	0.347143i
$520$	−1.21903	−	2.11143i	−0.0534582	−	0.0925923i
$521$	5.23289			0.229257			0.114628	−	0.993408i	$-0.463432\pi$
$521$	5.23289			0.229257			0.114628	+	0.993408i	$0.463432\pi$
$522$	2.41998			0.105920
$523$	2.38759	+	4.13542i	0.104402	+	0.180829i	0.913494	−	0.406853i	$-0.133374\pi$
$523$	2.38759	+	4.13542i	0.104402	+	0.180829i	−0.809092	+	0.587682i	$0.800041\pi$
$524$	2.76210	−	4.78410i	0.120663	−	0.208994i
$525$	2.54307	−	4.40472i	0.110988	−	0.192238i
$526$	14.3536	+	24.8611i	0.625845	+	1.08400i
$527$	7.46838			0.325328
$528$	−6.99258			−0.304313
$529$	1.65177	−	2.86095i	0.0718161	−	0.124389i
$530$	1.13290	+	1.96225i	0.0492102	+	0.0852346i
$531$	−14.4610			−0.627552
$532$	−1.21903	+	2.11143i	−0.0528519	+	0.0915421i
$533$	−6.45616			−0.279647
$534$	−4.66081	−	8.07277i	−0.201693	−	0.349343i
$535$	−3.58002			−0.154778
$536$	4.02791	+	7.12572i	0.173979	+	0.307784i
$537$	36.6433			1.58127
$538$	−0.191126	−	0.331040i	−0.00824002	−	0.0142721i
$539$	3.53904			0.152437
$540$	1.71903	−	2.97746i	0.0739755	−	0.128129i
$541$	9.33385			0.401294			0.200647	−	0.979664i	$-0.435696\pi$
$541$	9.33385			0.401294			0.200647	+	0.979664i	$0.435696\pi$
$542$	−11.9253	−	20.6553i	−0.512236	−	0.887219i
$543$	23.0878	−	39.9892i	0.990790	−	1.71610i
$544$	−0.734191			−0.0314782
$545$	9.08613			0.389207
$546$	6.20017	+	10.7390i	0.265343	+	0.459587i
$547$	8.99258	−	15.5756i	0.384495	−	0.665965i	−0.607204	−	0.794546i	$-0.707709\pi$
$547$	8.99258	−	15.5756i	0.384495	−	0.665965i	0.991699	+	0.128581i	$0.0410423\pi$
$548$	−8.30146	+	14.3785i	−0.354621	+	0.614221i
$549$	2.22808	+	3.85914i	0.0950921	+	0.164704i
$550$	3.35194			0.142927
$551$	1.79001			0.0762569
$552$	−4.62920	−	8.01800i	−0.197032	−	0.341269i
$553$	−18.3445	−	31.7736i	−0.780088	−	1.35115i
$554$	2.34452	+	4.06083i	0.0996091	+	0.172528i
$555$	−12.1419	−	21.0305i	−0.515397	−	0.892694i
$556$	7.11033	−	12.3155i	0.301545	−	0.522292i
$557$	8.52420	−	14.7643i	0.361182	−	0.625585i	−0.626974	−	0.779040i	$-0.715707\pi$
$557$	8.52420	−	14.7643i	0.361182	−	0.625585i	0.988156	+	0.153455i	$0.0490400\pi$
$558$	−13.7523			−0.582180
$559$	−2.54307	−	4.40472i	−0.107560	−	0.186300i
$560$	−2.43807			−0.103027
$561$	−5.13389			−0.216753
$562$	−10.4065	+	18.0245i	−0.438970	+	0.760318i
$563$	−18.2994			−0.771227			−0.385613	−	0.922661i	$-0.626010\pi$
$563$	−18.2994			−0.771227			−0.385613	+	0.922661i	$0.626010\pi$
$564$	−6.25839	−	10.8399i	−0.263526	−	0.456440i
$565$	−3.60500	+	6.24404i	−0.151663	+	0.262689i
$566$	1.12920	+	1.95582i	0.0474636	+	0.0822094i
$567$	−13.6874	+	23.7073i	−0.574817	+	0.995613i
$568$	−2.45693	+	4.25554i	−0.103091	+	0.178558i
$569$	7.99629	−	13.8500i	0.335222	−	0.580621i	−0.648305	−	0.761380i	$-0.724522\pi$
$569$	7.99629	−	13.8500i	0.335222	−	0.580621i	0.983527	+	0.180759i	$0.0578554\pi$
$570$	−1.04307	+	1.80664i	−0.0436892	+	0.0756719i
$571$	−6.90776	+	11.9646i	−0.289081	+	0.500702i	−0.973591	−	0.228301i	$-0.926683\pi$
$571$	−6.90776	+	11.9646i	−0.289081	+	0.500702i	0.684510	+	0.729004i	$0.260016\pi$
$572$	−4.08613	+	7.07739i	−0.170850	+	0.295920i
$573$	−19.7129	−	34.1438i	−0.823519	−	1.42638i
$574$	−3.22808	+	5.59120i	−0.134737	+	0.233372i
$575$	2.21903	+	3.84348i	0.0925401	+	0.160284i
$576$	1.35194			0.0563308
$577$	−4.19243	+	7.26150i	−0.174533	+	0.302300i	−0.940000	−	0.341175i	$-0.889175\pi$
$577$	−4.19243	+	7.26150i	−0.174533	+	0.302300i	0.765466	+	0.643476i	$0.222508\pi$
$578$	16.4610			0.684686
$579$	−19.8687			−0.825716
$580$	0.895004	+	1.55019i	0.0371630	+	0.0643683i
$581$	33.3929			1.38537
$582$	−0.945488	+	1.63763i	−0.0391917	+	0.0678821i
$583$	3.79743	−	6.57734i	0.157273	−	0.272405i
$584$	1.36710	+	2.36788i	0.0565708	+	0.0979835i
$585$	1.64806	+	2.85453i	0.0681389	+	0.118020i
$586$	6.91549	+	11.9780i	0.285676	+	0.494806i
$587$	−14.4253	−	24.9854i	−0.595397	−	1.03126i	−0.993491	−	0.113913i	$-0.963662\pi$
$587$	−14.4253	−	24.9854i	−0.595397	−	1.03126i	0.398094	−	0.917345i	$-0.369672\pi$
$588$	−2.20257			−0.0908326
$589$	−10.1723			−0.419141
$590$	−5.34823	−	9.26341i	−0.220183	−	0.381368i
$591$	−10.5316	+	18.2413i	−0.433213	+	0.750347i
$592$	−5.82032	+	10.0811i	−0.239214	+	0.414330i
$593$	−19.7953	−	34.2865i	−0.812897	−	1.40798i	−0.910828	−	0.412786i	$-0.864556\pi$
$593$	−19.7953	−	34.2865i	−0.812897	−	1.40798i	0.0979307	−	0.995193i	$-0.468778\pi$
$594$	−11.5242			−0.472844
$595$	−1.79001			−0.0733832
$596$	4.08613	−	7.07739i	0.167374	−	0.289901i
$597$	−2.48484	−	4.30388i	−0.101698	−	0.176146i
$598$	−10.8203			−0.442476
$599$	18.9926	−	32.8961i	0.776016	−	1.34410i	−0.158206	−	0.987406i	$-0.550571\pi$
$599$	18.9926	−	32.8961i	0.776016	−	1.34410i	0.934222	−	0.356693i	$-0.116096\pi$
$600$	−2.08613			−0.0851659
$601$	9.77888	+	16.9375i	0.398889	+	0.690896i	0.993589	−	0.113052i	$-0.0360626\pi$
$601$	9.77888	+	16.9375i	0.398889	+	0.690896i	−0.594700	+	0.803948i	$0.702729\pi$
$602$	−5.08613			−0.207295
$603$	−5.44549	−	9.63355i	−0.221757	−	0.392308i
$604$	18.6661			0.759515
$605$	−0.117748	−	0.203946i	−0.00478715	−	0.00829158i
$606$	3.73419			0.151691
$607$	−10.5636	+	18.2966i	−0.428761	+	0.742637i	−0.996763	−	0.0803905i	$-0.974383\pi$
$607$	−10.5636	+	18.2966i	−0.428761	+	0.742637i	0.568002	+	0.823027i	$0.307717\pi$
$608$	1.00000			0.0405554
$609$	−4.55211	−	7.88448i	−0.184461	−	0.319495i
$610$	−1.64806	+	2.85453i	−0.0667280	+	0.115576i
$611$	−14.6284			−0.591802
$612$	0.992582			0.0401227
$613$	−0.0483992	−	0.0838299i	−0.00195483	−	0.00338586i	0.865046	−	0.501692i	$-0.167289\pi$
$613$	−0.0483992	−	0.0838299i	−0.00195483	−	0.00338586i	−0.867001	+	0.498306i	$0.833956\pi$
$614$	−5.01516	+	8.68651i	−0.202395	+	0.350559i
$615$	−2.76210	+	4.78410i	−0.111379	+	0.192913i
$616$	4.08613	+	7.07739i	0.164635	+	0.285156i
$617$	14.2329			0.572994			0.286497	−	0.958081i	$-0.407509\pi$
$617$	14.2329			0.572994			0.286497	+	0.958081i	$0.407509\pi$
$618$	−5.76711			−0.231987
$619$	10.6369	+	18.4237i	0.427534	+	0.740511i	0.996653	−	0.0817438i	$-0.0260489\pi$
$619$	10.6369	+	18.4237i	0.427534	+	0.740511i	−0.569119	+	0.822255i	$0.692716\pi$
$620$	−5.08613	−	8.80944i	−0.204264	−	0.353795i
$621$	−7.62920	−	13.2142i	−0.306149	−	0.530266i
$622$	15.8015	+	27.3689i	0.633581	+	1.09739i
$623$	−5.44711	+	9.43468i	−0.218234	+	0.377992i
$624$	2.54307	−	4.40472i	0.101804	−	0.176330i
$625$	1.00000			0.0400000
$626$	−6.77485	−	11.7344i	−0.270778	−	0.469000i
$627$	6.99258			0.279257
$628$	1.20257			0.0479879
$629$	−4.27323	+	7.40145i	−0.170385	+	0.295115i
$630$	3.29612			0.131321
$631$	−3.20257	−	5.54702i	−0.127492	−	0.220823i	0.795212	−	0.606331i	$-0.207360\pi$
$631$	−3.20257	−	5.54702i	−0.127492	−	0.220823i	−0.922704	+	0.385508i	$0.874026\pi$
$632$	−7.52420	+	13.0323i	−0.299297	+	0.518397i
$633$	1.30146	+	2.25419i	0.0517282	+	0.0895959i
$634$	−15.8687	+	27.4854i	−0.630227	+	1.09159i
$635$	0.561931	−	0.973292i	0.0222995	−	0.0386239i
$636$	−2.36339	+	4.09351i	−0.0937144	+	0.162318i
$637$	−1.28708	+	2.22929i	−0.0509959	+	0.0883275i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	3.32163	−	5.75323i	0.131402	−	0.227594i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	10.9865	−	19.0291i	0.433939	−	0.751605i	−0.563269	−	0.826274i	$-0.690457\pi$
$641$	10.9865	−	19.0291i	0.433939	−	0.751605i	0.997208	+	0.0746685i	$0.0237899\pi$
$642$	−3.73419	−	6.46781i	−0.147377	−	0.255264i
$643$	11.3823			0.448872			0.224436	−	0.974489i	$-0.427946\pi$
$643$	11.3823			0.448872			0.224436	+	0.974489i	$0.427946\pi$
$644$	−5.41016	+	9.37067i	−0.213190	+	0.369256i
$645$	−4.35194			−0.171357
$646$	0.734191			0.0288864
$647$	9.61033	+	16.6456i	0.377821	+	0.654405i	0.990745	−	0.135737i	$-0.0433401\pi$
$647$	9.61033	+	16.6456i	0.377821	+	0.654405i	−0.612924	+	0.790142i	$0.710007\pi$
$648$	11.2281			0.441081
$649$	−17.9269	+	31.0504i	−0.703694	+	1.21883i
$650$	−1.21903	+	2.11143i	−0.0478145	+	0.0828171i
$651$	25.8687	+	44.8059i	1.01388	+	1.75608i
$652$	3.77485	+	6.53824i	0.147835	+	0.256057i
$653$	−14.7991	−	25.6327i	−0.579132	−	1.00309i	−0.995579	−	0.0939257i	$-0.970058\pi$
$653$	−14.7991	−	25.6327i	−0.579132	−	1.00309i	0.416448	−	0.909160i	$-0.363275\pi$
$654$	9.47743	+	16.4154i	0.370597	+	0.641892i
$655$	−5.52420			−0.215848
$656$	2.64806			0.103389
$657$	−1.84823	−	3.20123i	−0.0721063	−	0.124892i
$658$	−7.31421	+	12.6686i	−0.285138	+	0.493873i
$659$	−0.940473	+	1.62895i	−0.0366356	+	0.0634548i	−0.883762	−	0.467937i	$-0.844997\pi$
$659$	−0.940473	+	1.62895i	−0.0366356	+	0.0634548i	0.847126	+	0.531392i	$0.178331\pi$
$660$	3.49629	+	6.05575i	0.136093	+	0.235720i
$661$	−5.02551			−0.195469			−0.0977347	−	0.995212i	$-0.531160\pi$
$661$	−5.02551			−0.195469			−0.0977347	+	0.995212i	$0.531160\pi$
$662$	−33.8613			−1.31606
$663$	1.86710	−	3.23390i	0.0725120	−	0.125594i
$664$	−6.84823	−	11.8615i	−0.265763	−	0.460315i
$665$	2.43807			0.0945443
$666$	7.86872	−	13.6290i	0.304907	−	0.528114i
$667$	7.94418			0.307600
$668$	−1.17968	−	2.04326i	−0.0456431	−	0.0790562i
$669$	18.0887			0.699351
$670$	4.15710	−	7.05113i	0.160603	−	0.272409i
$671$	11.0484			0.426519
$672$	−2.54307	−	4.40472i	−0.0981009	−	0.169916i
$673$	−30.0617			−1.15879			−0.579396	−	0.815046i	$-0.696712\pi$
$673$	−30.0617			−1.15879			−0.579396	+	0.815046i	$0.696712\pi$
$674$	−10.2863	+	17.8164i	−0.396213	+	0.686262i
$675$	−3.43807			−0.132331
$676$	3.52791	+	6.11052i	0.135689	+	0.235020i
$677$	24.6103	−	42.6263i	0.945852	−	1.63826i	0.191815	−	0.981431i	$-0.438563\pi$
$677$	24.6103	−	42.6263i	0.945852	−	1.63826i	0.754037	−	0.656832i	$-0.228104\pi$
$678$	−15.0410			−0.577645
$679$	2.20999			0.0848117
$680$	0.367095	+	0.635828i	0.0140775	+	0.0243829i
$681$	−6.96096	+	12.0567i	−0.266745	+	0.462015i
$682$	−17.0484	+	29.5287i	−0.652817	+	1.13071i
$683$	4.23582	+	7.33665i	0.162079	+	0.280729i	0.935614	−	0.353024i	$-0.114847\pi$
$683$	4.23582	+	7.33665i	0.162079	+	0.280729i	−0.773535	+	0.633753i	$0.781513\pi$
$684$	−1.35194			−0.0516927
$685$	16.6029			0.634365
$686$	9.82032	+	17.0093i	0.374942	+	0.649418i
$687$	10.4939	+	18.1759i	0.400367	+	0.693456i
$688$	1.04307	+	1.80664i	0.0397665	+	0.0688776i
$689$	2.76210	+	4.78410i	0.105228	+	0.182260i
$690$	−4.62920	+	8.01800i	−0.176230	+	0.305240i
$691$	16.0386	−	27.7796i	0.610136	−	1.05679i	−0.381081	−	0.924542i	$-0.624448\pi$
$691$	16.0386	−	27.7796i	0.610136	−	1.05679i	0.991217	−	0.132245i	$-0.0422186\pi$
$692$	−4.37744			−0.166405
$693$	−5.52420	−	9.56819i	−0.209847	−	0.363466i
$694$	−28.1271			−1.06769
$695$	−14.2207			−0.539420
$696$	−1.86710	+	3.23390i	−0.0707721	+	0.122581i
$697$	1.94418			0.0736412
$698$	11.8573	+	20.5374i	0.448804	+	0.777352i
$699$	−8.29743	+	14.3716i	−0.313838	+	0.543583i
$700$	1.21903	+	2.11143i	0.0460752	+	0.0798046i
$701$	−14.6587	+	25.3897i	−0.553653	+	0.958954i	0.444354	+	0.895851i	$0.353433\pi$
$701$	−14.6587	+	25.3897i	−0.553653	+	0.958954i	−0.998007	+	0.0631033i	$0.979900\pi$
$702$	4.19113	−	7.25924i	0.158184	−	0.273982i
$703$	5.82032	−	10.0811i	0.219518	−	0.380216i
$704$	1.67597	−	2.90286i	0.0631655	−	0.109406i
$705$	−6.25839	+	10.8399i	−0.235705	+	0.408252i
$706$	−11.0181	+	19.0839i	−0.414671	+	0.718232i
$707$	−2.18208	−	3.77948i	−0.0820657	−	0.142142i
$708$	11.1571	−	19.3247i	0.419310	−	0.726266i
$709$	−11.9549	−	20.7064i	−0.448974	−	0.777645i	0.549346	−	0.835595i	$-0.314877\pi$
$709$	−11.9549	−	20.7064i	−0.448974	−	0.777645i	−0.998320	+	0.0579497i	$0.981544\pi$
$710$	4.91387			0.184414
$711$	10.1723	−	17.6189i	0.381490	−	0.660759i
$712$	4.46838			0.167460
$713$	−45.1452			−1.69070
$714$	−1.86710	−	3.23390i	−0.0698743	−	0.121026i
$715$	8.17226			0.305625
$716$	−8.78259	+	15.2119i	−0.328221	+	0.568495i
$717$	−19.2510	+	33.3437i	−0.718941	+	1.24524i
$718$	3.99258	+	6.91535i	0.149002	+	0.258079i
$719$	−7.92454	−	13.7257i	−0.295535	−	0.511882i	0.679574	−	0.733607i	$-0.262165\pi$
$719$	−7.92454	−	13.7257i	−0.295535	−	0.511882i	−0.975109	+	0.221725i	$0.928831\pi$
$720$	−0.675970	−	1.17081i	−0.0251919	−	0.0436337i
$721$	3.37003	+	5.83706i	0.125506	+	0.217383i
$722$	18.0000			0.669891
$723$	−32.8613			−1.22212
$724$	11.0673	+	19.1691i	0.411312	+	0.712413i
$725$	0.895004	−	1.55019i	0.0332396	−	0.0575727i
$726$	0.245638	−	0.425458i	0.00911648	−	0.0157902i
$727$	−14.6029	−	25.2930i	−0.541592	−	0.938065i	−0.998813	−	0.0487117i	$-0.984488\pi$
$727$	−14.6029	−	25.2930i	−0.541592	−	0.938065i	0.457221	−	0.889353i	$-0.348845\pi$
$728$	−5.94418			−0.220306
$729$	6.33710			0.234707
$730$	1.36710	−	2.36788i	0.0505985	−	0.0876391i
$731$	0.765809	+	1.32642i	0.0283245	+	0.0490594i
$732$	−6.87614			−0.254149
$733$	7.23550	−	12.5322i	0.267249	−	0.462889i	−0.700901	−	0.713258i	$-0.747219\pi$
$733$	7.23550	−	12.5322i	0.267249	−	0.462889i	0.968150	+	0.250369i	$0.0805520\pi$
$734$	10.5497			0.389397
$735$	1.10129	+	1.90748i	0.0406216	+	0.0703586i
$736$	4.43807			0.163589
$737$	−27.4357	−	0.250024i	−1.01061	−	0.00920976i
$738$	−3.58002			−0.131782
$739$	−20.3360	−	35.2230i	−0.748072	−	1.29570i	−0.948746	−	0.316041i	$-0.897646\pi$
$739$	−20.3360	−	35.2230i	−0.748072	−	1.29570i	0.200674	−	0.979658i	$-0.435687\pi$
$740$	11.6406			0.427919
$741$	−2.54307	+	4.40472i	−0.0934218	+	0.161811i
$742$	5.52420			0.202800
$743$	19.0697	+	33.0296i	0.699598	+	1.21174i	0.968606	+	0.248602i	$0.0799710\pi$
$743$	19.0697	+	33.0296i	0.699598	+	1.21174i	−0.269008	+	0.963138i	$0.586696\pi$
$744$	10.6103	−	18.3776i	0.388994	−	0.673757i
$745$	−8.17226			−0.299408
$746$	27.6917			1.01386
$747$	9.25839	+	16.0360i	0.338747	+	0.586727i
$748$	1.23048	−	2.13126i	0.0449909	−	0.0779265i
$749$	−4.36417	+	7.55896i	−0.159463	+	0.276198i
$750$	1.04307	+	1.80664i	0.0380874	+	0.0659692i
$751$	18.1574			0.662574			0.331287	−	0.943530i	$-0.392517\pi$
$751$	18.1574			0.662574			0.331287	+	0.943530i	$0.392517\pi$
$752$	6.00000			0.218797
$753$	−29.7371	−	51.5062i	−1.08368	−	1.87699i
$754$	2.18208	+	3.77948i	0.0794668	+	0.137640i
$755$	−9.33307	−	16.1654i	−0.339665	−	0.588318i
$756$	−4.19113	−	7.25924i	−0.152430	−	0.264016i
$757$	−9.29612	+	16.1014i	−0.337873	+	0.585214i	−0.984032	−	0.177989i	$-0.943041\pi$
$757$	−9.29612	+	16.1014i	−0.337873	+	0.585214i	0.646159	+	0.763203i	$0.276374\pi$
$758$	9.41016	−	16.2989i	0.341792	−	0.592002i
$759$	31.0336			1.12645
$760$	−0.500000	−	0.866025i	−0.0181369	−	0.0314140i
$761$	−37.9655			−1.37625			−0.688124	−	0.725593i	$-0.741566\pi$
$761$	−37.9655			−1.37625			−0.688124	+	0.725593i	$0.741566\pi$
$762$	2.34452			0.0849330
$763$	11.0763	−	19.1847i	0.400989	−	0.694534i
$764$	18.8990			0.683743
$765$	−0.496291	−	0.859601i	−0.0179434	−	0.0310789i
$766$	−19.3445	+	33.5057i	−0.698946	+	1.21061i
$767$	−13.0394	−	22.5848i	−0.470824	−	0.815491i
$768$	−1.04307	+	1.80664i	−0.0376384	+	0.0651916i
$769$	4.85434	−	8.40797i	0.175052	−	0.303199i	−0.765127	−	0.643879i	$-0.777324\pi$
$769$	4.85434	−	8.40797i	0.175052	−	0.303199i	0.940179	+	0.340680i	$0.110657\pi$
$770$	4.08613	−	7.07739i	0.147254	−	0.255051i
$771$	−6.25839	+	10.8399i	−0.225390	+	0.390388i
$772$	4.76210	−	8.24820i	0.171392	−	0.296859i
$773$	13.8506	−	23.9900i	0.498173	−	0.862860i	−0.501825	−	0.864969i	$-0.667338\pi$
$773$	13.8506	−	23.9900i	0.498173	−	0.862860i	0.999998	+	0.00210873i	$0.000671231\pi$
$774$	−1.41016	−	2.44247i	−0.0506872	−	0.0877928i
$775$	−5.08613	+	8.80944i	−0.182699	+	0.316444i
$776$	−0.453226	−	0.785010i	−0.0162699	−	0.0281802i
$777$	−59.2058			−2.12400
$778$	−10.3142	+	17.8647i	−0.369782	+	0.640482i
$779$	−2.64806			−0.0948766
$780$	−5.08613			−0.182113
$781$	−8.23550	−	14.2643i	−0.294689	−	0.510417i
$782$	3.25839			0.116520
$783$	−3.07709	+	5.32967i	−0.109966	+	0.190467i
$784$	0.527909	−	0.914365i	0.0188539	−	0.0326559i
$785$	−0.601286	−	1.04146i	−0.0214608	−	0.0371713i
$786$	−5.76210	−	9.98025i	−0.205527	−	0.355984i
$787$	16.6284	+	28.8013i	0.592739	+	1.02665i	0.993862	+	0.110630i	$0.0352868\pi$
$787$	16.6284	+	28.8013i	0.592739	+	1.02665i	−0.401123	+	0.916024i	$0.631380\pi$
$788$	−5.04840	−	8.74408i	−0.179842	−	0.311495i
$789$	59.8868			2.13203
$790$	15.0484			0.535398
$791$	8.78923	+	15.2234i	0.312509	+	0.541282i
$792$	−2.26581	+	3.92450i	−0.0805120	+	0.139451i
$793$	−4.01809	+	6.95953i	−0.142686	+	0.247140i
$794$	9.44711	+	16.3629i	0.335265	+	0.580697i
$795$	4.72677			0.167641
$796$	2.38225			0.0844367
$797$	1.57839	−	2.73386i	0.0559095	−	0.0968381i	−0.836716	−	0.547637i	$-0.815527\pi$
$797$	1.57839	−	2.73386i	0.0559095	−	0.0968381i	0.892626	+	0.450799i	$0.148861\pi$
$798$	2.54307	+	4.40472i	0.0900235	+	0.155925i
$799$	4.40515			0.155843
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−6.04098			−0.213448
$802$	13.0763	+	22.6488i	0.461740	+	0.799758i
$803$	−9.16484			−0.323420
$804$	17.0750	+	0.155606i	0.602189	+	0.00548781i
$805$	10.8203			0.381366
$806$	−12.4003	−	21.4780i	−0.436783	−	0.756531i
$807$	−0.797427			−0.0280708
$808$	−0.895004	+	1.55019i	−0.0314861	+	0.0545356i
$809$	22.3035			0.784151			0.392075	−	0.919933i	$-0.371757\pi$
$809$	22.3035			0.784151			0.392075	+	0.919933i	$0.371757\pi$
$810$	−5.61404	−	9.72380i	−0.197257	−	0.341660i
$811$	5.52660	−	9.57236i	0.194065	−	0.336131i	−0.752528	−	0.658560i	$-0.771166\pi$
$811$	5.52660	−	9.57236i	0.194065	−	0.336131i	0.946594	+	0.322429i	$0.104499\pi$
$812$	4.36417			0.153152
$813$	−49.7555			−1.74500
$814$	−19.5094	−	33.7912i	−0.683803	−	1.18438i
$815$	3.77485	−	6.53824i	0.132227	−	0.229024i
$816$	−0.765809	+	1.32642i	−0.0268087	+	0.0464340i
$817$	−1.04307	−	1.80664i	−0.0364922	−	0.0632064i
$818$	−18.9878			−0.663892
$819$	8.03617			0.280807
$820$	−1.32403	−	2.29329i	−0.0462371	−	0.0800851i
$821$	−13.0968	−	22.6843i	−0.457081	−	0.791688i	0.541724	−	0.840557i	$-0.317772\pi$
$821$	−13.0968	−	22.6843i	−0.457081	−	0.791688i	−0.998805	+	0.0488683i	$0.984439\pi$
$822$	17.3179	+	29.9955i	0.604032	+	1.04621i
$823$	−15.8761	−	27.4983i	−0.553407	−	0.958530i	−0.998026	−	0.0628095i	$-0.979994\pi$
$823$	−15.8761	−	27.4983i	−0.553407	−	0.958530i	0.444618	−	0.895720i	$-0.353339\pi$
$824$	1.38225	−	2.39413i	0.0481530	−	0.0834035i
$825$	3.49629	−	6.05575i	0.121725	−	0.210834i
$826$	−26.0787			−0.907394
$827$	−22.6661	−	39.2589i	−0.788179	−	1.36517i	−0.927081	−	0.374860i	$-0.877691\pi$
$827$	−22.6661	−	39.2589i	−0.788179	−	1.36517i	0.138902	−	0.990306i	$-0.455643\pi$
$828$	−6.00000			−0.208514
$829$	9.67682			0.336090			0.168045	−	0.985779i	$-0.446255\pi$
$829$	9.67682			0.336090			0.168045	+	0.985779i	$0.446255\pi$
$830$	−6.84823	+	11.8615i	−0.237706	+	0.411718i
$831$	9.78195			0.339332
$832$	1.21903	+	2.11143i	0.0422624	+	0.0732007i
$833$	0.387586	−	0.671318i	0.0134291	−	0.0232598i
$834$	−14.8331	−	25.6916i	−0.513627	−	0.889629i
$835$	−1.17968	+	2.04326i	−0.0408245	+	0.0707101i
$836$	−1.67597	+	2.90286i	−0.0579646	+	0.100398i
$837$	17.4865	−	30.2875i	0.604421	−	1.04689i
$838$	12.2268	−	21.1774i	0.422367	−	0.731561i
$839$	−13.3142	+	23.0609i	−0.459658	+	0.796150i	−0.998943	−	0.0459730i	$-0.985361\pi$
$839$	−13.3142	+	23.0609i	−0.459658	+	0.796150i	0.539285	+	0.842123i	$0.318694\pi$
$840$	−2.54307	+	4.40472i	−0.0877441	+	0.151977i
$841$	12.8979	+	22.3399i	0.444756	+	0.770341i
$842$	6.96969	−	12.0719i	0.240191	−	0.416024i
$843$	21.7092	+	37.6015i	0.747705	+	1.29506i
$844$	−1.24772			−0.0429484
$845$	3.52791	−	6.11052i	0.121364	−	0.210208i
$846$	−8.11164			−0.278884
$847$	−0.574157			−0.0197283
$848$	−1.13290	−	1.96225i	−0.0389041	−	0.0673839i
$849$	4.71130			0.161691
$850$	0.367095	−	0.635828i	0.0125913	−	0.0218087i
$851$	25.8310	−	44.7406i	0.885475	−	1.53369i
$852$	5.12549	+	8.87760i	0.175596	+	0.304142i
$853$	9.56193	+	16.5617i	0.327394	+	0.567064i	0.981994	−	0.188912i	$-0.0604961\pi$
$853$	9.56193	+	16.5617i	0.327394	+	0.567064i	−0.654600	+	0.755976i	$0.727163\pi$
$854$	4.01809	+	6.95953i	0.137496	+	0.238150i
$855$	0.675970	+	1.17081i	0.0231177	+	0.0400410i
$856$	3.58002			0.122362
$857$	−7.59485			−0.259435			−0.129718	−	0.991551i	$-0.541407\pi$
$857$	−7.59485			−0.259435			−0.129718	+	0.991551i	$0.541407\pi$
$858$	8.52420	+	14.7643i	0.291011	+	0.504046i
$859$	−12.2547	+	21.2257i	−0.418124	+	0.724213i	−0.995751	−	0.0920886i	$-0.970646\pi$
$859$	−12.2547	+	21.2257i	−0.418124	+	0.724213i	0.577626	+	0.816301i	$0.303979\pi$
$860$	1.04307	−	1.80664i	0.0355682	−	0.0616060i
$861$	6.73419	+	11.6640i	0.229501	+	0.397507i
$862$	−9.50611			−0.323779
$863$	−6.39553			−0.217706			−0.108853	−	0.994058i	$-0.534718\pi$
$863$	−6.39553			−0.217706			−0.108853	+	0.994058i	$0.534718\pi$
$864$	−1.71903	+	2.97746i	−0.0584827	+	0.101295i
$865$	2.18872	+	3.79098i	0.0744188	+	0.128897i
$866$	−10.7194			−0.364258
$867$	17.1699	−	29.7391i	0.583119	−	1.00999i
$868$	−24.8007			−0.841790
$869$	−25.2207	−	43.6835i	−0.855552	−	1.48186i
$870$	3.73419			0.126601
$871$	10.1353	−	17.1912i	0.343422	−	0.582500i
$872$	−9.08613			−0.307695
$873$	0.612734	+	1.06129i	0.0207379	+	0.0359191i
$874$	−4.43807			−0.150120
$875$	1.21903	−	2.11143i	0.0412109	−	0.0713794i
$876$	5.70388			0.192716
$877$	26.3052	+	45.5619i	0.888262	+	1.53852i	0.841928	+	0.539589i	$0.181421\pi$
$877$	26.3052	+	45.5619i	0.888262	+	1.53852i	0.0463340	+	0.998926i	$0.485246\pi$
$878$	19.7711	−	34.2446i	0.667244	−	1.15570i
$879$	28.8532			0.973196
$880$	−3.35194			−0.112994
$881$	1.55211	+	2.68833i	0.0522919	+	0.0905722i	0.890986	−	0.454030i	$-0.150014\pi$
$881$	1.55211	+	2.68833i	0.0522919	+	0.0905722i	−0.838695	+	0.544602i	$0.816681\pi$
$882$	−0.713701	+	1.23617i	−0.0240315	+	0.0416239i
$883$	−13.2584	+	22.9642i	−0.446180	+	0.772807i	−0.998134	−	0.0610680i	$-0.980549\pi$
$883$	−13.2584	+	22.9642i	−0.446180	+	0.772807i	0.551953	+	0.833875i	$0.313883\pi$
$884$	0.895004	+	1.55019i	0.0301023	+	0.0521386i
$885$	−22.3142			−0.750084
$886$	−18.5061			−0.621725
$887$	0.750653	+	1.30017i	0.0252045	+	0.0436554i	0.878353	−	0.478013i	$-0.158643\pi$
$887$	0.750653	+	1.30017i	0.0252045	+	0.0436554i	−0.853148	+	0.521669i	$0.825310\pi$
$888$	12.1419	+	21.0305i	0.407457	+	0.705736i
$889$	−1.37003	−	2.37295i	−0.0459492	−	0.0795863i
$890$	−2.23419	−	3.86973i	−0.0748903	−	0.129714i
$891$	−18.8179	+	32.5936i	−0.630424	+	1.09193i
$892$	−4.33548	+	7.50927i	−0.145163	+	0.251429i
$893$	−6.00000			−0.200782
$894$	−8.52420	−	14.7643i	−0.285092	−	0.493794i
$895$	17.5652			0.587139
$896$	2.43807			0.0814502
$897$	−11.2863	+	19.5484i	−0.376839	+	0.652704i
$898$	−21.5800			−0.720135
$899$	9.10422	+	15.7690i	0.303643	+	0.525924i
$900$	−0.675970	+	1.17081i	−0.0225323	+	0.0390271i
$901$	−0.831768	−	1.44066i	−0.0277102	−	0.0479955i
$902$	−4.43807	+	7.68696i	−0.147772	+	0.255948i
$903$	−5.30516	+	9.18882i	−0.176545	+	0.305785i
$904$	3.60500	−	6.24404i	0.119900	−	0.207674i
$905$	11.0673	−	19.1691i	0.367888	−	0.637201i
$906$	19.4700	−	33.7230i	0.646848	−	1.12037i
$907$	22.0787	−	38.2415i	0.733112	−	1.26979i	−0.222435	−	0.974947i	$-0.571401\pi$
$907$	22.0787	−	38.2415i	0.733112	−	1.26979i	0.955547	−	0.294839i	$-0.0952660\pi$
$908$	−3.33678	−	5.77948i	−0.110735	−	0.191799i
$909$	1.20999	−	2.09577i	0.0401329	−	0.0695122i
$910$	2.97209	+	5.14781i	0.0985239	+	0.170648i
$911$	8.75489			0.290062			0.145031	−	0.989427i	$-0.453672\pi$
$911$	8.75489			0.290062			0.145031	+	0.989427i	$0.453672\pi$
$912$	1.04307	−	1.80664i	0.0345393	−	0.0598239i
$913$	45.9097			1.51939
$914$	−14.7752			−0.488719
$915$	3.43807	+	5.95491i	0.113659	+	0.196863i
$916$	−10.0606			−0.332412
$917$	−6.73419	+	11.6640i	−0.222383	+	0.385178i
$918$	−1.26210	+	2.18602i	−0.0416555	+	0.0721494i
$919$	5.57338	+	9.65337i	0.183849	+	0.318435i	0.943188	−	0.332260i	$-0.107811\pi$
$919$	5.57338	+	9.65337i	0.183849	+	0.318435i	−0.759339	+	0.650695i	$0.774478\pi$
$920$	−2.21903	−	3.84348i	−0.0731594	−	0.126716i
$921$	10.4623	+	18.1212i	0.344743	+	0.597113i
$922$	8.56115	+	14.8283i	0.281947	+	0.488346i
$923$	11.9804			0.394338
$924$	17.0484			0.560851
$925$	−5.82032	−	10.0811i	−0.191371	−	0.331464i
$926$	−3.54547	+	6.14093i	−0.116511	+	0.201804i
$927$	−1.86872	+	3.23672i	−0.0613768	+	0.106308i
$928$	−0.895004	−	1.55019i	−0.0293800	−	0.0508876i
$929$	−18.7013			−0.613569			−0.306784	−	0.951779i	$-0.599253\pi$
$929$	−18.7013			−0.613569			−0.306784	+	0.951779i	$0.599253\pi$
$930$	−21.2207			−0.695853
$931$	−0.527909	+	0.914365i	−0.0173015	+	0.0299671i
$932$	−3.97743	−	6.88910i	−0.130285	−	0.225660i
$933$	65.9278			2.15838
$934$	−4.82032	+	8.34904i	−0.157726	+	0.273189i
$935$	−2.46096			−0.0804821
$936$	−1.64806	−	2.85453i	−0.0538686	−	0.0933031i
$937$	0.0148368			0.000484698			0.000242349	−	1.00000i	$-0.499923\pi$
$937$	0.0148368			0.000484698			0.000242349		1.00000i	$0.499923\pi$
$938$	−9.82032	−	17.3730i	−0.320645	−	0.567249i
$939$	−28.2664			−0.922441
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−24.1952			−0.788739			−0.394370	−	0.918952i	$-0.629037\pi$
$941$	−24.1952			−0.788739			−0.394370	+	0.918952i	$0.629037\pi$
$942$	1.25436	−	2.17262i	0.0408693	−	0.0707877i
$943$	−11.7523			−0.382707
$944$	5.34823	+	9.26341i	0.174070	+	0.301498i
$945$	−4.19113	+	7.25924i	−0.136337	+	0.236143i
$946$	−6.99258			−0.227348
$947$	50.0368			1.62598			0.812989	−	0.582279i	$-0.197839\pi$
$947$	50.0368			1.62598			0.812989	+	0.582279i	$0.197839\pi$
$948$	15.6965	+	27.1871i	0.509797	+	0.882995i
$949$	3.33307	−	5.77305i	0.108196	−	0.187401i
$950$	−0.500000	+	0.866025i	−0.0162221	+	0.0280976i
$951$	33.1042	+	57.3382i	1.07348	+	1.85932i
$952$	1.79001			0.0580145
$953$	−44.1223			−1.42926			−0.714631	−	0.699502i	$-0.753405\pi$
$953$	−44.1223			−1.42926			−0.714631	+	0.699502i	$0.753405\pi$
$954$	1.53162	+	2.65284i	0.0495880	+	0.0858889i
$955$	−9.44952	−	16.3670i	−0.305779	−	0.529625i
$956$	−9.22808	−	15.9835i	−0.298457	−	0.516943i
$957$	−6.25839	−	10.8399i	−0.202305	−	0.350403i
$958$	9.67759	−	16.7621i	0.312669	−	0.541558i
$959$	20.2395	−	35.0559i	0.653568	−	1.13201i
$960$	2.08613			0.0673296
$961$	−36.2374	−	62.7651i	−1.16895	−	2.02468i
$962$	28.3807			0.915030
$963$	−4.83997			−0.155966
$964$	7.87614	−	13.6419i	0.253673	−	0.439375i
$965$	−9.52420			−0.306595
$966$	11.2863	+	19.5484i	0.363131	+	0.628961i
$967$	−29.5423	+	51.1687i	−0.950016	+	1.64548i	−0.204633	+	0.978839i	$0.565600\pi$
$967$	−29.5423	+	51.1687i	−0.950016	+	1.64548i	−0.745382	+	0.666637i	$0.767733\pi$
$968$	0.117748	+	0.203946i	0.00378457	+	0.00655507i
$969$	0.765809	−	1.32642i	0.0246013	−	0.0426108i
$970$	−0.453226	+	0.785010i	−0.0145522	+	0.0252051i
$971$	10.2826	−	17.8100i	0.329984	−	0.571549i	−0.652524	−	0.757768i	$-0.726290\pi$
$971$	10.2826	−	17.8100i	0.329984	−	0.571549i	0.982508	+	0.186219i	$0.0596233\pi$
$972$	6.55451	−	11.3527i	0.210236	−	0.364140i
$973$	−17.3355	+	30.0259i	−0.555750	+	0.962587i
$974$	15.7358	−	27.2552i	0.504208	−	0.873314i
$975$	2.54307	+	4.40472i	0.0814433	+	0.141064i
$976$	1.64806	−	2.85453i	0.0527531	−	0.0913711i
$977$	−12.9016	−	22.3463i	−0.412760	−	0.714922i	0.582430	−	0.812881i	$-0.302102\pi$
$977$	−12.9016	−	22.3463i	−0.412760	−	0.714922i	−0.995190	+	0.0979591i	$0.968769\pi$
$978$	15.7497			0.503619
$979$	−7.48887	+	12.9711i	−0.239345	+	0.414558i
$980$	−1.05582			−0.0337269
$981$	12.2839			0.392195
$982$	2.55582	+	4.42681i	0.0815594	+	0.141265i
$983$	47.5046			1.51516			0.757580	−	0.652742i	$-0.226382\pi$
$983$	47.5046			1.51516			0.757580	+	0.652742i	$0.226382\pi$
$984$	2.76210	−	4.78410i	0.0880525	−	0.152511i
$985$	−5.04840	+	8.74408i	−0.160855	+	0.278610i
$986$	−0.657104	−	1.13814i	−0.0209265	−	0.0362457i
$987$	15.2584	+	26.4283i	0.485680	+	0.841222i
$988$	−1.21903	−	2.11143i	−0.0387827	−	0.0671735i
$989$	−4.62920	−	8.01800i	−0.147200	−	0.254958i
$990$	4.53162			0.144024
$991$	58.5152			1.85880			0.929399	−	0.369077i	$-0.120326\pi$
$991$	58.5152			1.85880			0.929399	+	0.369077i	$0.120326\pi$
$992$	5.08613	+	8.80944i	0.161485	+	0.279700i
$993$	−35.3195	+	61.1752i	−1.12083	+	1.94134i
$994$	5.99018	−	10.3753i	0.189997	−	0.329084i
$995$	−1.19113	−	2.06309i	−0.0377612	−	0.0654044i
$996$	−28.5726			−0.905357
$997$	54.2117			1.71690			0.858451	−	0.512896i	$-0.171427\pi$
$997$	54.2117			1.71690			0.858451	+	0.512896i	$0.171427\pi$
$998$	16.3310	−	28.2861i	0.516948	−	0.895381i
$999$	20.0107	+	34.6595i	0.633110	+	1.09658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.g.171.3	✓	6
67.29	even	3	inner	670.2.e.g.431.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.g.171.3	✓	6	1.1	even	1	trivial
670.2.e.g.431.3	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +2.08613 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.04307 + 1.80664i) q^{6} +(1.21903 - 2.11143i) q^{7} -1.00000 q^{8} +1.35194 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +2.08613 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.04307 + 1.80664i) q^{6} +(1.21903 - 2.11143i) q^{7} -1.00000 q^{8} +1.35194 q^{9} +(0.500000 + 0.866025i) q^{10} +(1.67597 - 2.90286i) q^{11} +(-1.04307 + 1.80664i) q^{12} +(1.21903 + 2.11143i) q^{13} +2.43807 q^{14} +2.08613 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.367095 - 0.635828i) q^{17} +(0.675970 + 1.17081i) q^{18} +(0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.54307 - 4.40472i) q^{21} +3.35194 q^{22} +(2.21903 + 3.84348i) q^{23} -2.08613 q^{24} +1.00000 q^{25} +(-1.21903 + 2.11143i) q^{26} -3.43807 q^{27} +(1.21903 + 2.11143i) q^{28} +(0.895004 - 1.55019i) q^{29} +(1.04307 + 1.80664i) q^{30} +(-5.08613 + 8.80944i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.49629 - 6.05575i) q^{33} +(0.367095 - 0.635828i) q^{34} +(1.21903 - 2.11143i) q^{35} +(-0.675970 + 1.17081i) q^{36} +(-5.82032 - 10.0811i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(2.54307 + 4.40472i) q^{39} -1.00000 q^{40} +(-1.32403 + 2.29329i) q^{41} +5.08613 q^{42} -2.08613 q^{43} +(1.67597 + 2.90286i) q^{44} +1.35194 q^{45} +(-2.21903 + 3.84348i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(-1.04307 - 1.80664i) q^{48} +(0.527909 + 0.914365i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.765809 - 1.32642i) q^{51} -2.43807 q^{52} +2.26581 q^{53} +(-1.71903 - 2.97746i) q^{54} +(1.67597 - 2.90286i) q^{55} +(-1.21903 + 2.11143i) q^{56} +(1.04307 + 1.80664i) q^{57} +1.79001 q^{58} -10.6965 q^{59} +(-1.04307 + 1.80664i) q^{60} +(1.64806 + 2.85453i) q^{61} -10.1723 q^{62} +(1.64806 - 2.85453i) q^{63} +1.00000 q^{64} +(1.21903 + 2.11143i) q^{65} +6.99258 q^{66} +(-4.02791 - 7.12572i) q^{67} +0.734191 q^{68} +(4.62920 + 8.01800i) q^{69} +2.43807 q^{70} +(2.45693 - 4.25554i) q^{71} -1.35194 q^{72} +(-1.36710 - 2.36788i) q^{73} +(5.82032 - 10.0811i) q^{74} +2.08613 q^{75} -1.00000 q^{76} +(-4.08613 - 7.07739i) q^{77} +(-2.54307 + 4.40472i) q^{78} +(7.52420 - 13.0323i) q^{79} +(-0.500000 - 0.866025i) q^{80} -11.2281 q^{81} -2.64806 q^{82} +(6.84823 + 11.8615i) q^{83} +(2.54307 + 4.40472i) q^{84} +(-0.367095 - 0.635828i) q^{85} +(-1.04307 - 1.80664i) q^{86} +(1.86710 - 3.23390i) q^{87} +(-1.67597 + 2.90286i) q^{88} -4.46838 q^{89} +(0.675970 + 1.17081i) q^{90} +5.94418 q^{91} -4.43807 q^{92} +(-10.6103 + 18.3776i) q^{93} -6.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(1.04307 - 1.80664i) q^{96} +(0.453226 + 0.785010i) q^{97} +(-0.527909 + 0.914365i) q^{98} +(2.26581 - 3.92450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9} + 3 q^{10} + 8 q^{11} + q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 3 q^{20} + 8 q^{21} + 16 q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 2 q^{27} - 2 q^{28} - 6 q^{29} - q^{30} - 16 q^{31} + 3 q^{32} - 6 q^{33} - 3 q^{34} - 2 q^{35} - 2 q^{36} - 10 q^{37} - 3 q^{38} + 8 q^{39} - 6 q^{40} - 10 q^{41} + 16 q^{42} + 2 q^{43} + 8 q^{44} + 4 q^{45} - 4 q^{46} - 18 q^{47} + q^{48} - 3 q^{49} + 3 q^{50} - 15 q^{51} + 4 q^{52} + 24 q^{53} - q^{54} + 8 q^{55} + 2 q^{56} - q^{57} - 12 q^{58} - 2 q^{59} + q^{60} + 14 q^{61} - 32 q^{62} + 14 q^{63} + 6 q^{64} - 2 q^{65} - 12 q^{66} - 18 q^{67} - 6 q^{68} + 6 q^{69} - 4 q^{70} + 22 q^{71} - 4 q^{72} - 3 q^{73} + 10 q^{74} - 2 q^{75} - 6 q^{76} - 10 q^{77} - 8 q^{78} + 12 q^{79} - 3 q^{80} - 26 q^{81} - 20 q^{82} + 10 q^{83} + 8 q^{84} + 3 q^{85} + q^{86} + 6 q^{87} - 8 q^{88} - 6 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} - 16 q^{93} - 36 q^{94} + 3 q^{95} - q^{96} - 17 q^{97} + 3 q^{98} + 24 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9 + 3 * q^10 + 8 * q^11 + q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 3 * q^20 + 8 * q^21 + 16 * q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 2 * q^27 - 2 * q^28 - 6 * q^29 - q^30 - 16 * q^31 + 3 * q^32 - 6 * q^33 - 3 * q^34 - 2 * q^35 - 2 * q^36 - 10 * q^37 - 3 * q^38 + 8 * q^39 - 6 * q^40 - 10 * q^41 + 16 * q^42 + 2 * q^43 + 8 * q^44 + 4 * q^45 - 4 * q^46 - 18 * q^47 + q^48 - 3 * q^49 + 3 * q^50 - 15 * q^51 + 4 * q^52 + 24 * q^53 - q^54 + 8 * q^55 + 2 * q^56 - q^57 - 12 * q^58 - 2 * q^59 + q^60 + 14 * q^61 - 32 * q^62 + 14 * q^63 + 6 * q^64 - 2 * q^65 - 12 * q^66 - 18 * q^67 - 6 * q^68 + 6 * q^69 - 4 * q^70 + 22 * q^71 - 4 * q^72 - 3 * q^73 + 10 * q^74 - 2 * q^75 - 6 * q^76 - 10 * q^77 - 8 * q^78 + 12 * q^79 - 3 * q^80 - 26 * q^81 - 20 * q^82 + 10 * q^83 + 8 * q^84 + 3 * q^85 + q^86 + 6 * q^87 - 8 * q^88 - 6 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 - 16 * q^93 - 36 * q^94 + 3 * q^95 - q^96 - 17 * q^97 + 3 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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