LMFDB - Embedded newform 670.2.h.c.439.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(29,670)]

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([3, 4]))

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.h (of order $6$, 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:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.16
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -2.35660i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.42939 + 1.71955i) q^{5} +(-1.17830 - 2.04088i) q^{6} +(-3.13521 - 1.81012i) q^{7} -1.00000i q^{8} -2.55358 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -2.35660i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.42939 + 1.71955i) q^{5} +(-1.17830 - 2.04088i) q^{6} +(-3.13521 - 1.81012i) q^{7} -1.00000i q^{8} -2.55358 q^{9} +(-0.378110 + 2.20387i) q^{10} +(2.18096 - 3.77753i) q^{11} +(-2.04088 - 1.17830i) q^{12} +(-1.99296 + 1.15064i) q^{13} -3.62023 q^{14} +(4.05230 + 3.36850i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.39427 + 1.38233i) q^{17} +(-2.21146 + 1.27679i) q^{18} +(0.148470 + 0.257157i) q^{19} +(0.774481 + 2.09766i) q^{20} +(-4.26573 + 7.38846i) q^{21} -4.36192i q^{22} +(-5.34196 + 3.08418i) q^{23} -2.35660 q^{24} +(-0.913707 - 4.91581i) q^{25} +(-1.15064 + 1.99296i) q^{26} -1.05204i q^{27} +(-3.13521 + 1.81012i) q^{28} +(-2.50042 + 4.33086i) q^{29} +(5.19364 + 0.891055i) q^{30} +(2.16411 - 3.74834i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-8.90214 - 5.13965i) q^{33} +(-1.38233 + 2.39427i) q^{34} +(7.59402 - 2.80380i) q^{35} +(-1.27679 + 2.21146i) q^{36} +(-2.22059 + 1.28206i) q^{37} +(0.257157 + 0.148470i) q^{38} +(2.71159 + 4.69662i) q^{39} +(1.71955 + 1.42939i) q^{40} +(2.97392 - 5.15099i) q^{41} +8.53145i q^{42} -7.21723i q^{43} +(-2.18096 - 3.77753i) q^{44} +(3.65005 - 4.39101i) q^{45} +(-3.08418 + 5.34196i) q^{46} +(10.1904 + 5.88345i) q^{47} +(-2.04088 + 1.17830i) q^{48} +(3.05305 + 5.28803i) q^{49} +(-3.24920 - 3.80036i) q^{50} +(3.25761 + 5.64234i) q^{51} +2.30127i q^{52} -13.4249i q^{53} +(-0.526020 - 0.911093i) q^{54} +(3.37822 + 9.14982i) q^{55} +(-1.81012 + 3.13521i) q^{56} +(0.606018 - 0.349885i) q^{57} +5.00085i q^{58} -4.01470 q^{59} +(4.94335 - 1.82514i) q^{60} +(3.45542 + 5.98496i) q^{61} -4.32821i q^{62} +(8.00602 + 4.62228i) q^{63} -1.00000 q^{64} +(0.870134 - 5.07170i) q^{65} -10.2793 q^{66} +(-2.67905 - 7.73451i) q^{67} +2.76466i q^{68} +(7.26820 + 12.5889i) q^{69} +(5.17471 - 6.22517i) q^{70} +(2.20664 - 3.82201i) q^{71} +2.55358i q^{72} +(10.2075 - 5.89328i) q^{73} +(-1.28206 + 2.22059i) q^{74} +(-11.5846 + 2.15324i) q^{75} +0.296940 q^{76} +(-13.6755 + 7.89558i) q^{77} +(4.69662 + 2.71159i) q^{78} +(3.66003 - 6.33935i) q^{79} +(2.20387 + 0.378110i) q^{80} -10.1400 q^{81} -5.94785i q^{82} +(3.51537 - 2.02960i) q^{83} +(4.26573 + 7.38846i) q^{84} +(1.04535 - 6.09295i) q^{85} +(-3.60861 - 6.25030i) q^{86} +(10.2061 + 5.89250i) q^{87} +(-3.77753 - 2.18096i) q^{88} +6.67819 q^{89} +(0.965534 - 5.62775i) q^{90} +8.33114 q^{91} +6.16837i q^{92} +(-8.83336 - 5.09994i) q^{93} +11.7669 q^{94} +(-0.654416 - 0.112276i) q^{95} +(-1.17830 + 2.04088i) q^{96} +(-10.8099 + 6.24108i) q^{97} +(5.28803 + 3.05305i) q^{98} +(-5.56925 + 9.64622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * 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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		−	2.35660i		−	1.36059i	−0.732941	−	0.680293i	$-0.761853\pi$
$3$		−	2.35660i		−	1.36059i	0.732941	−	0.680293i	$-0.238147\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.42939	+	1.71955i	−0.639241	+	0.769006i
$5$	−1.42939	+	1.71955i	−0.639241	+	0.769006i
$6$	−1.17830	−	2.04088i	−0.481040	−	0.833185i
$7$	−3.13521	−	1.81012i	−1.18500	−	0.684160i	−0.227834	−	0.973700i	$-0.573164\pi$
$7$	−3.13521	−	1.81012i	−1.18500	−	0.684160i	−0.957166	+	0.289540i	$0.906498\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.55358			−0.851193
$10$	−0.378110	+	2.20387i	−0.119569	+	0.696924i
$11$	2.18096	−	3.77753i	0.657584	−	1.13897i	−0.323655	−	0.946175i	$-0.604912\pi$
$11$	2.18096	−	3.77753i	0.657584	−	1.13897i	0.981239	−	0.192794i	$-0.0617548\pi$
$12$	−2.04088	−	1.17830i	−0.589151	−	0.340146i
$13$	−1.99296	+	1.15064i	−0.552748	+	0.319129i	−0.750230	−	0.661177i	$-0.770057\pi$
$13$	−1.99296	+	1.15064i	−0.552748	+	0.319129i	0.197482	+	0.980307i	$0.436724\pi$
$14$	−3.62023			−0.967548
$15$	4.05230	+	3.36850i	1.04630	+	0.869742i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.39427	+	1.38233i	−0.580695	+	0.335265i	−0.761410	−	0.648271i	$-0.775492\pi$
$17$	−2.39427	+	1.38233i	−0.580695	+	0.335265i	0.180714	+	0.983536i	$0.442159\pi$
$18$	−2.21146	+	1.27679i	−0.521247	+	0.300942i
$19$	0.148470	+	0.257157i	0.0340613	+	0.0589959i	0.882554	−	0.470212i	$-0.155823\pi$
$19$	0.148470	+	0.257157i	0.0340613	+	0.0589959i	−0.848492	+	0.529208i	$0.822489\pi$
$20$	0.774481	+	2.09766i	0.173179	+	0.469051i
$21$	−4.26573	+	7.38846i	−0.930858	+	1.61229i
$22$		−	4.36192i		−	0.929964i
$23$	−5.34196	+	3.08418i	−1.11388	+	0.643097i	−0.939831	−	0.341641i	$-0.889017\pi$
$23$	−5.34196	+	3.08418i	−1.11388	+	0.643097i	−0.174046	+	0.984738i	$0.555684\pi$
$24$	−2.35660			−0.481040
$25$	−0.913707	−	4.91581i	−0.182741	−	0.983161i
$26$	−1.15064	+	1.99296i	−0.225658	+	0.390852i
$27$		−	1.05204i		−	0.202465i
$28$	−3.13521	+	1.81012i	−0.592500	+	0.342080i
$29$	−2.50042	+	4.33086i	−0.464317	+	0.804220i	−0.999170	−	0.0407244i	$-0.987033\pi$
$29$	−2.50042	+	4.33086i	−0.464317	+	0.804220i	0.534854	+	0.844945i	$0.320367\pi$
$30$	5.19364	+	0.891055i	0.948225	+	0.162684i
$31$	2.16411	−	3.74834i	0.388685	−	0.673222i	−0.603588	−	0.797296i	$-0.706263\pi$
$31$	2.16411	−	3.74834i	0.388685	−	0.673222i	0.992273	+	0.124074i	$0.0395961\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−8.90214	−	5.13965i	−1.54966	−	0.894699i
$34$	−1.38233	+	2.39427i	−0.237068	+	0.410613i
$35$	7.59402	−	2.80380i	1.28362	−	0.473929i
$36$	−1.27679	+	2.21146i	−0.212798	+	0.368577i
$37$	−2.22059	+	1.28206i	−0.365063	+	0.210769i	−0.671299	−	0.741186i	$-0.734263\pi$
$37$	−2.22059	+	1.28206i	−0.365063	+	0.210769i	0.306237	+	0.951955i	$0.400930\pi$
$38$	0.257157	+	0.148470i	0.0417164	+	0.0240850i
$39$	2.71159	+	4.69662i	0.434202	+	0.752061i
$40$	1.71955	+	1.42939i	0.271885	+	0.226006i
$41$	2.97392	−	5.15099i	0.464449	−	0.804449i	−0.534728	−	0.845024i	$-0.679586\pi$
$41$	2.97392	−	5.15099i	0.464449	−	0.804449i	0.999176	+	0.0405755i	$0.0129191\pi$
$42$			8.53145i			1.31643i
$43$		−	7.21723i		−	1.10062i	−0.834961	−	0.550308i	$-0.814510\pi$
$43$		−	7.21723i		−	1.10062i	0.834961	−	0.550308i	$-0.185490\pi$
$44$	−2.18096	−	3.77753i	−0.328792	−	0.569484i
$45$	3.65005	−	4.39101i	0.544117	−	0.654573i
$46$	−3.08418	+	5.34196i	−0.454738	+	0.787630i
$47$	10.1904	+	5.88345i	1.48643	+	0.858190i	0.999880	−	0.0154642i	$-0.00492259\pi$
$47$	10.1904	+	5.88345i	1.48643	+	0.858190i	0.486548	+	0.873654i	$0.338256\pi$
$48$	−2.04088	+	1.17830i	−0.294575	+	0.170073i
$49$	3.05305	+	5.28803i	0.436150	+	0.755433i
$50$	−3.24920	−	3.80036i	−0.459506	−	0.537452i
$51$	3.25761	+	5.64234i	0.456156	+	0.790085i
$52$			2.30127i			0.319129i
$53$		−	13.4249i		−	1.84405i	−0.387130	−	0.922025i	$-0.626534\pi$
$53$		−	13.4249i		−	1.84405i	0.387130	−	0.922025i	$-0.373466\pi$
$54$	−0.526020	−	0.911093i	−0.0715822	−	0.123984i
$55$	3.37822	+	9.14982i	0.455519	+	1.23376i
$56$	−1.81012	+	3.13521i	−0.241887	+	0.418961i
$57$	0.606018	−	0.349885i	0.0802690	−	0.0463433i
$58$			5.00085i			0.656643i
$59$	−4.01470			−0.522670			−0.261335	−	0.965248i	$-0.584163\pi$
$59$	−4.01470			−0.522670			−0.261335	+	0.965248i	$0.584163\pi$
$60$	4.94335	−	1.82514i	0.638184	−	0.235625i
$61$	3.45542	+	5.98496i	0.442421	+	0.766295i	0.997869	−	0.0652563i	$-0.0207865\pi$
$61$	3.45542	+	5.98496i	0.442421	+	0.766295i	−0.555448	+	0.831551i	$0.687453\pi$
$62$		−	4.32821i		−	0.549684i
$63$	8.00602	+	4.62228i	1.00866	+	0.582352i
$64$	−1.00000			−0.125000
$65$	0.870134	−	5.07170i	0.107927	−	0.629067i
$66$	−10.2793			−1.26530
$67$	−2.67905	−	7.73451i	−0.327298	−	0.944921i
$67$	−2.67905	−	7.73451i	−0.327298	−	0.944921i
$68$			2.76466i			0.335265i
$69$	7.26820	+	12.5889i	0.874988	+	1.51552i
$70$	5.17471	−	6.22517i	0.618497	−	0.744051i
$71$	2.20664	−	3.82201i	0.261880	−	0.453589i	−0.704862	−	0.709345i	$-0.748991\pi$
$71$	2.20664	−	3.82201i	0.261880	−	0.453589i	0.966741	+	0.255756i	$0.0823243\pi$
$72$			2.55358i			0.300942i
$73$	10.2075	−	5.89328i	1.19469	−	0.689756i	0.235325	−	0.971917i	$-0.424384\pi$
$73$	10.2075	−	5.89328i	1.19469	−	0.689756i	0.959367	+	0.282161i	$0.0910511\pi$
$74$	−1.28206	+	2.22059i	−0.149036	+	0.258138i
$75$	−11.5846	+	2.15324i	−1.33767	+	0.248635i
$76$	0.296940			0.0340613
$77$	−13.6755	+	7.89558i	−1.55847	+	0.899785i
$78$	4.69662	+	2.71159i	0.531787	+	0.307027i
$79$	3.66003	−	6.33935i	0.411785	−	0.713233i	−0.583300	−	0.812257i	$-0.698239\pi$
$79$	3.66003	−	6.33935i	0.411785	−	0.713233i	0.995085	+	0.0990240i	$0.0315721\pi$
$80$	2.20387	+	0.378110i	0.246400	+	0.0422740i
$81$	−10.1400			−1.12666
$82$		−	5.94785i		−	0.656830i
$83$	3.51537	−	2.02960i	0.385862	−	0.222778i	−0.294504	−	0.955650i	$-0.595154\pi$
$83$	3.51537	−	2.02960i	0.385862	−	0.222778i	0.680366	+	0.732873i	$0.261821\pi$
$84$	4.26573	+	7.38846i	0.465429	+	0.806147i
$85$	1.04535	−	6.09295i	0.113384	−	0.660873i
$86$	−3.60861	−	6.25030i	−0.389127	−	0.673987i
$87$	10.2061	+	5.89250i	1.09421	+	0.631743i
$88$	−3.77753	−	2.18096i	−0.402686	−	0.232491i
$89$	6.67819			0.707887			0.353943	−	0.935267i	$-0.384841\pi$
$89$	6.67819			0.707887			0.353943	+	0.935267i	$0.384841\pi$
$90$	0.965534	−	5.62775i	0.101776	−	0.593217i
$91$	8.33114			0.873341
$92$			6.16837i			0.643097i
$93$	−8.83336	−	5.09994i	−0.915976	−	0.528839i
$94$	11.7669			1.21366
$95$	−0.654416	−	0.112276i	−0.0671416	−	0.0115193i
$96$	−1.17830	+	2.04088i	−0.120260	+	0.208296i
$97$	−10.8099	+	6.24108i	−1.09758	+	0.633686i	−0.935583	−	0.353106i	$-0.885126\pi$
$97$	−10.8099	+	6.24108i	−1.09758	+	0.633686i	−0.161993	+	0.986792i	$0.551792\pi$
$98$	5.28803	+	3.05305i	0.534172	+	0.308404i
$99$	−5.56925	+	9.64622i	−0.559731	+	0.969482i
$100$	−4.71407	−	1.66661i	−0.471407	−	0.166661i
$101$	6.54276	−	11.3324i	0.651029	−	1.12762i	−0.331844	−	0.943334i	$-0.607671\pi$
$101$	6.54276	−	11.3324i	0.651029	−	1.12762i	0.982874	−	0.184281i	$-0.0589958\pi$
$102$	5.64234	+	3.25761i	0.558675	+	0.322551i
$103$	−7.51125	−	4.33662i	−0.740105	−	0.427300i	0.0820023	−	0.996632i	$-0.473869\pi$
$103$	−7.51125	−	4.33662i	−0.740105	−	0.427300i	−0.822108	+	0.569332i	$0.807202\pi$
$104$	1.15064	+	1.99296i	0.112829	+	0.195426i
$105$	−6.60745	−	17.8961i	−0.644821	−	1.74648i
$106$	−6.71244	−	11.6263i	−0.651970	−	1.12925i
$107$			6.70299i			0.648002i	0.946057	+	0.324001i	$0.105028\pi$
$107$			6.70299i			0.648002i	−0.946057	+	0.324001i	$0.894972\pi$
$108$	−0.911093	−	0.526020i	−0.0876699	−	0.0506163i
$109$	−14.2687			−1.36669			−0.683347	−	0.730094i	$-0.739476\pi$
$109$	−14.2687			−1.36669			−0.683347	+	0.730094i	$0.739476\pi$
$110$	7.50054	+	6.23487i	0.715148	+	0.594471i
$111$	3.02130	+	5.23305i	0.286769	+	0.496699i
$112$			3.62023i			0.342080i
$113$	4.32863	+	2.49913i	0.407203	+	0.235099i	0.689587	−	0.724203i	$-0.257792\pi$
$113$	4.32863	+	2.49913i	0.407203	+	0.235099i	−0.282384	+	0.959301i	$0.591125\pi$
$114$	0.349885	−	0.606018i	0.0327697	−	0.0567588i
$115$	2.33232	−	13.5943i	0.217490	−	1.26767i
$116$	2.50042	+	4.33086i	0.232158	+	0.402110i
$117$	5.08918	−	2.93824i	0.470495	−	0.271640i
$118$	−3.47684	+	2.00735i	−0.320069	+	0.184792i
$119$	10.0087			0.917498
$120$	3.36850	−	4.05230i	0.307500	−	0.369922i
$121$	−4.01316	−	6.95100i	−0.364833	−	0.631909i
$122$	5.98496	+	3.45542i	0.541852	+	0.312839i
$123$	−12.1388	−	7.00836i	−1.09452	−	0.631922i
$124$	−2.16411	−	3.74834i	−0.194343	−	0.336611i
$125$	9.75901	+	5.45542i	0.872873	+	0.487948i
$126$	9.24455			0.823570
$127$	−1.46341	−	0.844897i	−0.129856	−	0.0749725i	0.433665	−	0.901074i	$-0.357220\pi$
$127$	−1.46341	−	0.844897i	−0.129856	−	0.0749725i	−0.563521	+	0.826102i	$0.690554\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−17.0081			−1.49748
$130$	−1.78229	−	4.82729i	−0.156317	−	0.423381i
$131$	8.95455			0.782363			0.391181	−	0.920314i	$-0.372066\pi$
$131$	8.95455			0.782363			0.391181	+	0.920314i	$0.372066\pi$
$132$	−8.90214	+	5.13965i	−0.774832	+	0.447350i
$133$		−	1.07499i		−	0.0932136i
$134$	−6.18738	−	5.35876i	−0.534508	−	0.462926i
$135$	1.80903	+	1.50377i	0.155697	+	0.129424i
$136$	1.38233	+	2.39427i	0.118534	+	0.205307i
$137$		−	9.57003i		−	0.817623i	−0.912619	−	0.408811i	$-0.865943\pi$
$137$		−	9.57003i		−	0.817623i	0.912619	−	0.408811i	$-0.134057\pi$
$138$	12.5889	+	7.26820i	1.07164	+	0.618710i
$139$	5.71407			0.484661			0.242330	−	0.970194i	$-0.422088\pi$
$139$	5.71407			0.484661			0.242330	+	0.970194i	$0.422088\pi$
$140$	1.36885	−	7.97852i	0.115689	−	0.674308i
$141$	13.8650	−	24.0148i	1.16764	−	2.02241i
$142$		−	4.41328i		−	0.370354i
$143$			10.0380i			0.839417i
$144$	1.27679	+	2.21146i	0.106399	+	0.184289i
$145$	−3.87306	−	10.4901i	−0.321640	−	0.871153i
$146$	5.89328	−	10.2075i	0.487731	−	0.844775i
$147$	12.4618	−	7.19482i	1.02783	−	0.593419i
$148$			2.56412i			0.210769i
$149$	9.44322			0.773619			0.386810	−	0.922160i	$-0.373577\pi$
$149$	9.44322			0.773619			0.386810	+	0.922160i	$0.373577\pi$
$150$	−8.95594	+	7.65707i	−0.731249	+	0.625197i
$151$	−5.64886	−	9.78411i	−0.459697	−	0.796219i	0.539247	−	0.842147i	$-0.318709\pi$
$151$	−5.64886	−	9.78411i	−0.459697	−	0.796219i	−0.998945	+	0.0459282i	$0.985375\pi$
$152$	0.257157	−	0.148470i	0.0208582	−	0.0120425i
$153$	6.11395	−	3.52989i	0.494283	−	0.285375i
$154$	−7.89558	+	13.6755i	−0.636244	+	1.10201i
$155$	3.35212	+	9.07912i	0.269249	+	0.729253i
$156$	5.42319			0.434202
$157$	0.0567985	−	0.0327926i	0.00453301	−	0.00261714i	−0.497732	−	0.867331i	$-0.665834\pi$
$157$	0.0567985	−	0.0327926i	0.00453301	−	0.00261714i	0.502265	+	0.864714i	$0.332500\pi$
$158$		−	7.32005i		−	0.582352i
$159$	−31.6371			−2.50899
$160$	2.09766	−	0.774481i	0.165835	−	0.0612281i
$161$	22.3309			1.75992
$162$	−8.78147	+	5.06999i	−0.689938	+	0.398336i
$163$	13.1175	+	7.57338i	1.02744	+	0.593193i	0.916250	−	0.400607i	$-0.131201\pi$
$163$	13.1175	+	7.57338i	1.02744	+	0.593193i	0.111190	+	0.993799i	$0.464534\pi$
$164$	−2.97392	−	5.15099i	−0.232224	−	0.402224i
$165$	21.5625	−	7.96113i	1.67864	−	0.619773i
$166$	2.02960	−	3.51537i	0.157527	−	0.272846i
$167$	−10.4461	−	6.03108i	−0.808346	−	0.466699i	0.0380349	−	0.999276i	$-0.487890\pi$
$167$	−10.4461	−	6.03108i	−0.808346	−	0.466699i	−0.846381	+	0.532577i	$0.821224\pi$
$168$	7.38846	+	4.26573i	0.570032	+	0.329108i
$169$	−3.85207	+	6.67199i	−0.296313	+	0.513230i
$170$	−2.14118	−	5.79932i	−0.164221	−	0.444788i
$171$	−0.379129	−	0.656671i	−0.0289927	−	0.0502169i
$172$	−6.25030	−	3.60861i	−0.476581	−	0.275154i
$173$	−9.29593	+	5.36701i	−0.706756	+	0.408046i	−0.809859	−	0.586625i	$-0.800456\pi$
$173$	−9.29593	+	5.36701i	−0.706756	+	0.408046i	0.103103	+	0.994671i	$0.467123\pi$
$174$	11.7850			0.893419
$175$	−6.03352	+	17.0660i	−0.456091	+	1.29007i
$176$	−4.36192			−0.328792
$177$			9.46106i			0.711137i
$178$	5.78348	−	3.33909i	0.433490	−	0.250276i
$179$	−18.6072			−1.39077			−0.695385	−	0.718638i	$-0.744766\pi$
$179$	−18.6072			−1.39077			−0.695385	+	0.718638i	$0.744766\pi$
$180$	−1.97770	−	5.35654i	−0.147409	−	0.399253i
$181$	−2.97052	+	5.14509i	−0.220797	+	0.382432i	−0.955050	−	0.296444i	$-0.904199\pi$
$181$	−2.97052	+	5.14509i	−0.220797	+	0.382432i	0.734253	+	0.678876i	$0.237533\pi$
$182$	7.21498	−	4.16557i	0.534810	−	0.308773i
$183$	14.1042	−	8.14304i	1.04261	−	0.601951i
$184$	3.08418	+	5.34196i	0.227369	+	0.393815i
$185$	0.969518	−	5.65097i	0.0712804	−	0.415468i
$186$	−10.1999			−0.747892
$187$			12.0592i			0.881858i
$188$	10.1904	−	5.88345i	0.743214	−	0.429095i
$189$	−1.90431	+	3.29837i	−0.138518	+	0.239921i
$190$	−0.622879	+	0.229974i	−0.0451884	+	0.0166841i
$191$	−3.15293	−	5.46104i	−0.228138	−	0.395147i	0.729118	−	0.684388i	$-0.239930\pi$
$191$	−3.15293	−	5.46104i	−0.228138	−	0.395147i	−0.957256	+	0.289241i	$0.906597\pi$
$192$			2.35660i			0.170073i
$193$			18.4742i			1.32980i	0.746931	+	0.664902i	$0.231527\pi$
$193$			18.4742i			1.32980i	−0.746931	+	0.664902i	$0.768473\pi$
$194$	−6.24108	+	10.8099i	−0.448084	+	0.776104i
$195$	−11.9520	−	2.05056i	−0.855899	−	0.146844i
$196$	6.10609			0.436150
$197$	17.4206	+	10.0578i	1.24117	+	0.716588i	0.969332	−	0.245755i	$-0.0790359\pi$
$197$	17.4206	+	10.0578i	1.24117	+	0.716588i	0.271836	+	0.962344i	$0.412369\pi$
$198$			11.1385i			0.791579i
$199$	10.1887	+	17.6473i	0.722255	+	1.25098i	0.960094	+	0.279678i	$0.0902279\pi$
$199$	10.1887	+	17.6473i	0.722255	+	1.25098i	−0.237838	+	0.971305i	$0.576439\pi$
$200$	−4.91581	+	0.913707i	−0.347600	+	0.0646088i
$201$	−18.2272	+	6.31345i	−1.28565	+	0.445317i
$202$		−	13.0855i		−	0.920694i
$203$	15.6787	−	9.05212i	1.10043	−	0.635334i
$204$	6.51521			0.456156
$205$	4.60649	+	12.4766i	0.321731	+	0.871401i
$206$	−8.67324			−0.604293
$207$	13.6411	−	7.87571i	0.948124	−	0.547399i
$208$	1.99296	+	1.15064i	0.138187	+	0.0797823i
$209$	1.29523			0.0895927
$210$	−14.6703	−	12.1947i	−1.01234	−	0.841518i
$211$	−5.76238	−	9.98074i	−0.396699	−	0.687102i	0.596618	−	0.802526i	$-0.296511\pi$
$211$	−5.76238	−	9.98074i	−0.396699	−	0.687102i	−0.993316	+	0.115423i	$0.963178\pi$
$212$	−11.6263	−	6.71244i	−0.798497	−	0.461013i
$213$	−9.00696	−	5.20017i	−0.617147	−	0.356310i
$214$	3.35149	+	5.80496i	0.229103	+	0.396819i
$215$	12.4104	+	10.3162i	0.846381	+	0.703560i
$216$	−1.05204			−0.0715822
$217$	−13.5699	+	7.83457i	−0.921183	+	0.531845i
$218$	−12.3571	+	7.13435i	−0.836926	+	0.483199i
$219$	−13.8881	−	24.0549i	−0.938472	−	1.62548i
$220$	9.61309	+	1.64929i	0.648114	+	0.111195i
$221$	3.18112	−	5.50986i	0.213985	−	0.370633i
$222$	5.23305	+	3.02130i	0.351219	+	0.202777i
$223$			19.4355i			1.30150i	0.759293	+	0.650748i	$0.225545\pi$
$223$			19.4355i			1.30150i	−0.759293	+	0.650748i	$0.774455\pi$
$224$	1.81012	+	3.13521i	0.120944	+	0.209480i
$225$	2.33322	+	12.5529i	0.155548	+	0.836859i
$226$	4.99827			0.332480
$227$	17.4079	+	10.0505i	1.15540	+	0.667072i	0.950198	−	0.311647i	$-0.100881\pi$
$227$	17.4079	+	10.0505i	1.15540	+	0.667072i	0.205204	+	0.978719i	$0.434214\pi$
$228$		−	0.699769i		−	0.0463433i
$229$	2.54824	+	4.41368i	0.168392	+	0.291664i	0.937855	−	0.347028i	$-0.112809\pi$
$229$	2.54824	+	4.41368i	0.168392	+	0.291664i	−0.769462	+	0.638692i	$0.779476\pi$
$230$	−4.77728	−	12.9391i	−0.315005	−	0.853182i
$231$	18.6068	+	32.2278i	1.22423	+	2.12044i
$232$	4.33086	+	2.50042i	0.284335	+	0.164161i
$233$	25.2357	+	14.5698i	1.65325	+	0.954502i	0.975725	+	0.218999i	$0.0702792\pi$
$233$	25.2357	+	14.5698i	1.65325	+	0.954502i	0.677521	+	0.735503i	$0.263054\pi$
$234$	2.93824	−	5.08918i	0.192079	−	0.332690i
$235$	−24.6830	+	9.11324i	−1.61014	+	0.594482i
$236$	−2.00735	+	3.47684i	−0.130667	+	0.226323i
$237$	−14.9393	−	8.62523i	−0.970414	−	0.560269i
$238$	8.66781	−	5.00436i	0.561851	−	0.324385i
$239$	−3.84674	+	6.66274i	−0.248825	+	0.430977i	−0.963200	−	0.268786i	$-0.913378\pi$
$239$	−3.84674	+	6.66274i	−0.248825	+	0.430977i	0.714375	+	0.699763i	$0.246711\pi$
$240$	0.891055	−	5.19364i	0.0575174	−	0.335248i
$241$	0.0338067			0.00217768			0.00108884	−	0.999999i	$-0.499653\pi$
$241$	0.0338067			0.00217768			0.00108884	+	0.999999i	$0.499653\pi$
$242$	−6.95100	−	4.01316i	−0.446827	−	0.257976i
$243$			20.7398i			1.33046i
$244$	6.91083			0.442421
$245$	−13.4570	−	2.30878i	−0.859738	−	0.147502i
$246$	−14.0167			−0.893673
$247$	−0.591789	−	0.341670i	−0.0376546	−	0.0217399i
$248$	−3.74834	−	2.16411i	−0.238020	−	0.137421i
$249$	−4.78296	−	8.28433i	−0.303108	−	0.524998i
$250$	11.1793	−	0.154974i	0.707039	−	0.00980139i
$251$	7.92288	+	13.7228i	0.500087	+	0.866177i	1.00000		0.000101034i	$3.21602e-5\pi$
$251$	7.92288	+	13.7228i	0.500087	+	0.866177i	−0.499912	+	0.866076i	$0.666635\pi$
$252$	8.00602	−	4.62228i	0.504332	−	0.291176i
$253$			26.9059i			1.69156i
$254$	−1.68979			−0.106027
$255$	−14.3587	−	2.46347i	−0.899174	−	0.154268i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.8002	−	7.96758i	−0.860836	−	0.497004i	0.00345623	−	0.999994i	$-0.498900\pi$
$257$	−13.8002	−	7.96758i	−0.860836	−	0.497004i	−0.864292	+	0.502990i	$0.832233\pi$
$258$	−14.7295	+	8.50407i	−0.917017	+	0.529440i
$259$	9.28270			0.576799
$260$	−3.95715	−	3.28941i	−0.245412	−	0.204000i
$261$	6.38502	−	11.0592i	0.395223	−	0.684547i
$262$	7.75487	−	4.47728i	0.479098	−	0.276607i
$263$		−	25.7273i		−	1.58641i	−0.608954	−	0.793206i	$-0.708410\pi$
$263$		−	25.7273i		−	1.58641i	0.608954	−	0.793206i	$-0.291590\pi$
$264$	−5.13965	+	8.90214i	−0.316324	+	0.547889i
$265$	23.0848	+	19.1894i	1.41809	+	1.17879i
$266$	−0.537496	−	0.930970i	−0.0329560	−	0.0570814i
$267$		−	15.7378i		−	0.963140i
$268$	−8.03781	−	1.54713i	−0.490987	−	0.0945062i
$269$	30.1981			1.84121			0.920606	−	0.390492i	$-0.127695\pi$
$269$	30.1981			1.84121			0.920606	+	0.390492i	$0.127695\pi$
$270$	2.31856	+	0.397787i	0.141103	+	0.0242085i
$271$	−17.1236			−1.04019			−0.520093	−	0.854110i	$-0.674103\pi$
$271$	−17.1236			−1.04019			−0.520093	+	0.854110i	$0.674103\pi$
$272$	2.39427	+	1.38233i	0.145174	+	0.0838161i
$273$		−	19.6332i		−	1.18826i
$274$	−4.78501	−	8.28789i	−0.289073	−	0.500690i
$275$	−20.5624	−	7.26961i	−1.23996	−	0.438374i
$276$	14.5364			0.874988
$277$		−	31.4189i		−	1.88778i	−0.330258	−	0.943891i	$-0.607136\pi$
$277$		−	31.4189i		−	1.88778i	0.330258	−	0.943891i	$-0.392864\pi$
$278$	4.94853	−	2.85703i	0.296793	−	0.171353i
$279$	−5.52622	+	9.57169i	−0.330846	+	0.573042i
$280$	−2.80380	−	7.59402i	−0.167559	−	0.453830i
$281$	−14.6156	−	25.3149i	−0.871891	−	1.51016i	−0.860038	−	0.510229i	$-0.829560\pi$
$281$	−14.6156	−	25.3149i	−0.871891	−	1.51016i	−0.0118524	−	0.999930i	$-0.503773\pi$
$282$		−	27.7299i		−	1.65129i
$283$		−	24.1111i		−	1.43326i	−0.697454	−	0.716629i	$-0.745684\pi$
$283$		−	24.1111i		−	1.43326i	0.697454	−	0.716629i	$-0.254316\pi$
$284$	−2.20664	−	3.82201i	−0.130940	−	0.226795i
$285$	−0.264590	+	1.54220i	−0.0156729	+	0.0913519i
$286$	5.01898	+	8.69313i	0.296779	+	0.514036i
$287$	−18.6478	+	10.7663i	−1.10074	+	0.635515i
$288$	2.21146	+	1.27679i	0.130312	+	0.0752355i
$289$	−4.67832	+	8.10309i	−0.275195	+	0.476652i
$290$	−8.59921	−	7.14814i	−0.504963	−	0.419753i
$291$	14.7078	+	25.4746i	0.862184	+	1.49335i
$292$		−	11.7866i		−	0.689756i
$293$		−	28.4975i		−	1.66484i	−0.554144	−	0.832421i	$-0.686954\pi$
$293$		−	28.4975i		−	1.66484i	0.554144	−	0.832421i	$-0.313046\pi$
$294$	7.19482	−	12.4618i	0.419610	−	0.726787i
$295$	5.73856	−	6.90349i	0.334112	−	0.401936i
$296$	1.28206	+	2.22059i	0.0745181	+	0.129069i
$297$	−3.97411	−	2.29445i	−0.230601	−	0.133138i
$298$	8.17807	−	4.72161i	0.473743	−	0.273516i
$299$	7.09755	−	12.2933i	0.410462	−	0.710941i
$300$	−3.92754	+	11.1092i	−0.226756	+	0.641389i
$301$	−13.0640	+	22.6276i	−0.752998	+	1.30423i
$302$	−9.78411	−	5.64886i	−0.563012	−	0.325055i
$303$	−26.7060	−	15.4187i	−1.53422	−	0.885781i
$304$	0.148470	−	0.257157i	0.00851533	−	0.0147490i
$305$	−15.2306	−	2.61306i	−0.872099	−	0.149623i
$306$	3.52989	−	6.11395i	0.201790	−	0.349511i
$307$	−13.0925	+	7.55896i	−0.747229	+	0.431413i	−0.824692	−	0.565583i	$-0.808651\pi$
$307$	−13.0925	+	7.55896i	−0.747229	+	0.431413i	0.0774630	+	0.996995i	$0.475318\pi$
$308$			15.7912i			0.899785i
$309$	−10.2197	+	17.7010i	−0.581378	+	1.00698i
$310$	7.44258	+	6.18669i	0.422710	+	0.351380i
$311$	−15.3795			−0.872094			−0.436047	−	0.899924i	$-0.643622\pi$
$311$	−15.3795			−0.872094			−0.436047	+	0.899924i	$0.643622\pi$
$312$	4.69662	−	2.71159i	0.265894	−	0.153514i
$313$			17.9854i			1.01660i	0.861181	+	0.508298i	$0.169725\pi$
$313$			17.9854i			1.01660i	−0.861181	+	0.508298i	$0.830275\pi$
$314$	0.0327926	−	0.0567985i	0.00185060	−	0.00320533i
$315$	−19.3919	+	7.15973i	−1.09261	+	0.403405i
$316$	−3.66003	−	6.33935i	−0.205893	−	0.356616i
$317$	17.6467	−	10.1883i	0.991138	−	0.572234i	0.0855240	−	0.996336i	$-0.472744\pi$
$317$	17.6467	−	10.1883i	0.991138	−	0.572234i	0.905614	+	0.424102i	$0.139410\pi$
$318$	−27.3986	+	15.8186i	−1.53643	+	0.887061i
$319$	10.9066	+	18.8909i	0.610655	+	1.05768i
$320$	1.42939	−	1.71955i	0.0799052	−	0.0961258i
$321$	15.7963			0.881662
$322$	19.3392	−	11.1655i	1.07773	−	0.622227i
$323$	−0.710953	−	0.410469i	−0.0395585	−	0.0228391i
$324$	−5.06999	+	8.78147i	−0.281666	+	0.487860i
$325$	7.47729	+	8.74566i	0.414765	+	0.485122i
$326$	15.1468			0.838901
$327$			33.6257i			1.85950i
$328$	−5.15099	−	2.97392i	−0.284416	−	0.164207i
$329$	−21.2995	−	36.8918i	−1.17428	−	2.03391i
$330$	14.6931	−	17.6758i	0.808829	−	0.973020i
$331$	−5.27017	+	9.12820i	−0.289675	+	0.501731i	−0.973732	−	0.227697i	$-0.926880\pi$
$331$	−5.27017	+	9.12820i	−0.289675	+	0.501731i	0.684057	+	0.729428i	$0.260214\pi$
$332$		−	4.05920i		−	0.222778i
$333$	5.67045	−	3.27384i	0.310739	−	0.179405i
$334$	−12.0622			−0.660012
$335$	17.1293	+	6.44885i	0.935873	+	0.352339i
$336$	8.53145			0.465429
$337$	−11.3968	+	6.57997i	−0.620826	+	0.358434i	−0.777190	−	0.629265i	$-0.783356\pi$
$337$	−11.3968	+	6.57997i	−0.620826	+	0.358434i	0.156365	+	0.987699i	$0.450022\pi$
$338$			7.70414i			0.419050i
$339$	5.88947	−	10.2009i	0.319872	−	0.554034i
$340$	−4.75398	−	3.95177i	−0.257821	−	0.214315i
$341$	−9.43966	−	16.3500i	−0.511186	−	0.885400i
$342$	−0.656671	−	0.379129i	−0.0355087	−	0.0205010i
$343$			3.23615i			0.174736i
$344$	−7.21723			−0.389127
$345$	−32.0363	−	5.49636i	−1.72478	−	0.295914i
$346$	−5.36701	+	9.29593i	−0.288532	+	0.499752i
$347$	13.2302	+	7.63846i	0.710234	+	0.410054i	0.811148	−	0.584841i	$-0.198843\pi$
$347$	13.2302	+	7.63846i	0.710234	+	0.410054i	−0.100914	+	0.994895i	$0.532177\pi$
$348$	10.2061	−	5.89250i	0.547105	−	0.315871i
$349$	−14.6206			−0.782621			−0.391310	−	0.920259i	$-0.627978\pi$
$349$	−14.6206			−0.782621			−0.391310	+	0.920259i	$0.627978\pi$
$350$	3.30783	+	17.7964i	0.176811	+	0.951256i
$351$	1.21051	+	2.09667i	0.0646125	+	0.111912i
$352$	−3.77753	+	2.18096i	−0.201343	+	0.116246i
$353$	28.0698	−	16.2061i	1.49401	−	0.862565i	0.494030	−	0.869445i	$-0.335523\pi$
$353$	28.0698	−	16.2061i	1.49401	−	0.862565i	0.999976	+	0.00688018i	$0.00219005\pi$
$354$	4.73053	+	8.19352i	0.251425	+	0.435481i
$355$	3.41800	+	9.25756i	0.181409	+	0.491340i
$356$	3.33909	−	5.78348i	0.176972	−	0.306524i
$357$		−	23.5866i		−	1.24833i
$358$	−16.1143	+	9.30361i	−0.851669	+	0.491711i
$359$	8.49839			0.448528			0.224264	−	0.974528i	$-0.428002\pi$
$359$	8.49839			0.448528			0.224264	+	0.974528i	$0.428002\pi$
$360$	−4.39101	−	3.65005i	−0.231426	−	0.192375i
$361$	9.45591	−	16.3781i	0.497680	−	0.862006i
$362$			5.94104i			0.312254i
$363$	−16.3808	+	9.45743i	−0.859767	+	0.496387i
$364$	4.16557	−	7.21498i	0.218335	−	0.378168i
$365$	−4.45662	+	25.9760i	−0.233270	+	1.35965i
$366$	8.14304	−	14.1042i	0.425644	−	0.737237i
$367$	23.1231	+	13.3501i	1.20702	+	0.696872i	0.962107	−	0.272674i	$-0.0879080\pi$
$367$	23.1231	+	13.3501i	1.20702	+	0.696872i	0.244911	+	0.969546i	$0.421241\pi$
$368$	5.34196	+	3.08418i	0.278469	+	0.160774i
$369$	−7.59415	+	13.1534i	−0.395335	+	0.684741i
$370$	−1.98586	−	5.37865i	−0.103240	−	0.279623i
$371$	−24.3006	+	42.0899i	−1.26163	+	2.18520i
$372$	−8.83336	+	5.09994i	−0.457988	+	0.264420i
$373$	−0.0159394	−	0.00920259i	−0.000825309	−	0.000476492i	0.499587	−	0.866264i	$-0.333485\pi$
$373$	−0.0159394	−	0.00920259i	−0.000825309	−	0.000476492i	−0.500413	+	0.865787i	$0.666818\pi$
$374$	6.02961	+	10.4436i	0.311784	+	0.540026i
$375$	12.8563	−	22.9981i	0.663895	−	1.18762i
$376$	5.88345	−	10.1904i	0.303416	−	0.525532i
$377$		−	11.5083i		−	0.592708i
$378$			3.80863i			0.195895i
$379$	−12.2709	−	21.2538i	−0.630314	−	1.09174i	−0.987487	−	0.157697i	$-0.949593\pi$
$379$	−12.2709	−	21.2538i	−0.630314	−	1.09174i	0.357174	−	0.934038i	$-0.383740\pi$
$380$	−0.424442	+	0.510603i	−0.0217734	+	0.0261934i
$381$	−1.99109	+	3.44867i	−0.102007	+	0.176680i
$382$	−5.46104	−	3.15293i	−0.279411	−	0.161318i
$383$	8.87314	−	5.12291i	0.453396	−	0.261769i	−0.255867	−	0.966712i	$-0.582361\pi$
$383$	8.87314	−	5.12291i	0.453396	−	0.261769i	0.709264	+	0.704943i	$0.249028\pi$
$384$	1.17830	+	2.04088i	0.0601299	+	0.104148i
$385$	5.97080	−	34.8016i	0.304300	−	1.77366i
$386$	9.23712	+	15.9992i	0.470157	+	0.814335i
$387$			18.4298i			0.936837i
$388$			12.4822i			0.633686i
$389$	6.96107	+	12.0569i	0.352940	+	0.611311i	0.986763	−	0.162168i	$-0.0518485\pi$
$389$	6.96107	+	12.0569i	0.352940	+	0.611311i	−0.633823	+	0.773478i	$0.718515\pi$
$390$	−11.3760	+	4.20015i	−0.576046	+	0.212683i
$391$	8.52673	−	14.7687i	0.431215	−	0.746887i
$392$	5.28803	−	3.05305i	0.267086	−	0.154202i
$393$		−	21.1023i		−	1.06447i
$394$	20.1156			1.01341
$395$	5.66924	+	15.3550i	0.285251	+	0.772593i
$396$	5.56925	+	9.64622i	0.279865	+	0.484741i
$397$			17.0274i			0.854581i	0.904114	+	0.427290i	$0.140532\pi$
$397$			17.0274i			0.854581i	−0.904114	+	0.427290i	$0.859468\pi$
$398$	17.6473	+	10.1887i	0.884579	+	0.510712i
$399$	−2.53333			−0.126825
$400$	−3.80036	+	3.24920i	−0.190018	+	0.162460i
$401$	−36.0639			−1.80095			−0.900473	−	0.434913i	$-0.856779\pi$
$401$	−36.0639			−1.80095			−0.900473	+	0.434913i	$0.856779\pi$
$402$	−12.6285	+	14.5812i	−0.629851	+	0.727244i
$403$			9.96040i			0.496163i
$404$	−6.54276	−	11.3324i	−0.325515	−	0.563808i
$405$	14.4939	−	17.4362i	0.720210	−	0.866411i
$406$	9.05212	−	15.6787i	0.449249	−	0.778122i
$407$			11.1845i			0.554393i
$408$	5.64234	−	3.25761i	0.279337	−	0.161275i
$409$	−1.91641	+	3.31932i	−0.0947603	+	0.164130i	−0.909509	−	0.415685i	$-0.863542\pi$
$409$	−1.91641	+	3.31932i	−0.0947603	+	0.164130i	0.814748	+	0.579815i	$0.196875\pi$
$410$	10.2276	+	8.50177i	0.505106	+	0.419873i
$411$	−22.5528			−1.11245
$412$	−7.51125	+	4.33662i	−0.370053	+	0.213650i
$413$	12.5870	+	7.26708i	0.619364	+	0.357590i
$414$	7.87571	−	13.6411i	0.387070	−	0.670425i
$415$	−1.53482	+	8.94594i	−0.0753416	+	0.439139i
$416$	2.30127			0.112829
$417$		−	13.4658i		−	0.659422i
$418$	1.12170	−	0.647613i	0.0548641	−	0.0316758i
$419$	−3.73805	−	6.47449i	−0.182616	−	0.316300i	0.760155	−	0.649742i	$-0.225123\pi$
$419$	−3.73805	−	6.47449i	−0.182616	−	0.316300i	−0.942770	+	0.333442i	$0.891790\pi$
$420$	−18.8022	−	3.22583i	−0.917453	−	0.157404i
$421$	8.93743	+	15.4801i	0.435583	+	0.754453i	0.997343	−	0.0728478i	$-0.0232087\pi$
$421$	8.93743	+	15.4801i	0.435583	+	0.754453i	−0.561760	+	0.827301i	$0.689875\pi$
$422$	−9.98074	−	5.76238i	−0.485855	−	0.280508i
$423$	−26.0221	−	15.0239i	−1.26524	−	0.730485i
$424$	−13.4249			−0.651970
$425$	8.98293	+	10.5067i	0.435736	+	0.509650i
$426$	−10.4003			−0.503898
$427$		−	25.0188i		−	1.21075i
$428$	5.80496	+	3.35149i	0.280593	+	0.162001i
$429$	23.6555			1.14210
$430$	15.9058	+	2.72891i	0.767046	+	0.131600i
$431$	−3.35567	+	5.81219i	−0.161637	+	0.279963i	−0.935456	−	0.353443i	$-0.885011\pi$
$431$	−3.35567	+	5.81219i	−0.161637	+	0.279963i	0.773819	+	0.633407i	$0.218344\pi$
$432$	−0.911093	+	0.526020i	−0.0438350	+	0.0253081i
$433$	−16.3478	−	9.43841i	−0.785626	−	0.453581i	0.0527947	−	0.998605i	$-0.483187\pi$
$433$	−16.3478	−	9.43841i	−0.785626	−	0.453581i	−0.838420	+	0.545024i	$0.816520\pi$
$434$	−7.83457	+	13.5699i	−0.376072	+	0.651375i
$435$	−24.7209	+	9.12726i	−1.18528	+	0.437619i
$436$	−7.13435	+	12.3571i	−0.341673	+	0.591796i
$437$	−1.58624	−	0.915817i	−0.0758802	−	0.0438095i
$438$	−24.0549	−	13.8881i	−1.14939	−	0.663600i
$439$	3.97263	+	6.88080i	0.189603	+	0.328403i	0.945118	−	0.326729i	$-0.105946\pi$
$439$	3.97263	+	6.88080i	0.189603	+	0.328403i	−0.755515	+	0.655132i	$0.772613\pi$
$440$	9.14982	−	3.37822i	0.436201	−	0.161050i
$441$	−7.79619	−	13.5034i	−0.371247	−	0.643019i
$442$		−	6.36224i		−	0.302621i
$443$	30.9743	+	17.8830i	1.47163	+	0.849647i	0.999492	−	0.0318762i	$-0.0101482\pi$
$443$	30.9743	+	17.8830i	1.47163	+	0.849647i	0.472140	+	0.881523i	$0.343482\pi$
$444$	6.04261			0.286769
$445$	−9.54571	+	11.4835i	−0.452510	+	0.544369i
$446$	9.71775	+	16.8316i	0.460149	+	0.797001i
$447$		−	22.2539i		−	1.05257i
$448$	3.13521	+	1.81012i	0.148125	+	0.0855200i
$449$	−11.9990	+	20.7829i	−0.566268	+	0.980805i	0.430662	+	0.902513i	$0.358280\pi$
$449$	−11.9990	+	20.7829i	−0.566268	+	0.980805i	−0.996930	+	0.0782921i	$0.975053\pi$
$450$	8.29708	+	9.70451i	0.391128	+	0.457475i
$451$	−12.9720	−	22.4682i	−0.610828	−	1.05799i
$452$	4.32863	−	2.49913i	0.203601	−	0.117549i
$453$	−23.0573	+	13.3121i	−1.08332	+	0.625458i
$454$	20.1009			0.943382
$455$	−11.9084	+	14.3258i	−0.558276	+	0.671605i
$456$	−0.349885	−	0.606018i	−0.0163848	−	0.0283794i
$457$	−9.96976	−	5.75605i	−0.466366	−	0.269256i	0.248351	−	0.968670i	$-0.420111\pi$
$457$	−9.96976	−	5.75605i	−0.466366	−	0.269256i	−0.714717	+	0.699414i	$0.753445\pi$
$458$	4.41368	+	2.54824i	0.206238	+	0.119071i
$459$	1.45427	+	2.51886i	0.0678793	+	0.117570i
$460$	−10.6068	−	8.81699i	−0.494546	−	0.411094i
$461$	−35.2534			−1.64192			−0.820958	−	0.570989i	$-0.806560\pi$
$461$	−35.2534			−1.64192			−0.820958	+	0.570989i	$0.806560\pi$
$462$	32.2278	+	18.6068i	1.49937	+	0.865664i
$463$	−31.0580	+	17.9313i	−1.44339	+	0.833340i	−0.998074	−	0.0620351i	$-0.980241\pi$
$463$	−31.0580	+	17.9313i	−1.44339	+	0.833340i	−0.445313	+	0.895375i	$0.646908\pi$
$464$	5.00085			0.232158
$465$	21.3959	−	7.89961i	0.992211	−	0.366336i
$466$	29.1397			1.34987
$467$	16.0891	−	9.28907i	0.744516	−	0.429847i	−0.0791928	−	0.996859i	$-0.525234\pi$
$467$	16.0891	−	9.28907i	0.744516	−	0.429847i	0.823709	+	0.567013i	$0.191901\pi$
$468$		−	5.87648i		−	0.271640i
$469$	−5.60099	+	29.0988i	−0.258629	+	1.34366i
$470$	−16.8195	+	20.2338i	−0.775824	+	0.933315i
$471$	−0.0772792	−	0.133852i	−0.00356084	−	0.00616755i
$472$			4.01470i			0.184792i
$473$	−27.2633	−	15.7405i	−1.25357	−	0.723748i
$474$	−17.2505			−0.792340
$475$	1.12848	−	0.964815i	0.0517781	−	0.0442688i
$476$	5.00436	−	8.66781i	0.229375	−	0.397288i
$477$			34.2815i			1.56964i
$478$			7.69347i			0.351891i
$479$	−7.25262	−	12.5619i	−0.331381	−	0.573968i	0.651402	−	0.758733i	$-0.274181\pi$
$479$	−7.25262	−	12.5619i	−0.331381	−	0.573968i	−0.982783	+	0.184765i	$0.940848\pi$
$480$	−1.82514	−	4.94335i	−0.0833060	−	0.225632i
$481$	2.95037	−	5.11018i	0.134525	−	0.233004i
$482$	0.0292774	−	0.0169033i	0.00133355	−	0.000769925i
$483$		−	52.6252i		−	2.39453i
$484$	−8.02633			−0.364833
$485$	4.71963	−	27.5090i	0.214308	−	1.24912i
$486$	10.3699	+	17.9612i	0.470388	+	0.814735i
$487$	−20.5701	+	11.8761i	−0.932118	+	0.538159i	−0.887481	−	0.460845i	$-0.847547\pi$
$487$	−20.5701	+	11.8761i	−0.932118	+	0.538159i	−0.0446373	+	0.999003i	$0.514213\pi$
$488$	5.98496	−	3.45542i	0.270926	−	0.156419i
$489$	17.8474	−	30.9127i	0.807089	−	1.39792i
$490$	−12.8085	+	4.72905i	−0.578630	+	0.213637i
$491$	−12.3006			−0.555117			−0.277558	−	0.960709i	$-0.589525\pi$
$491$	−12.3006			−0.555117			−0.277558	+	0.960709i	$0.589525\pi$
$492$	−12.1388	+	7.00836i	−0.547261	+	0.315961i
$493$		−	13.8256i		−	0.622676i
$494$	−0.683339			−0.0307449
$495$	−8.62655	−	23.3648i	−0.387735	−	1.05017i
$496$	−4.32821			−0.194343
$497$	−13.8366	+	7.98855i	−0.620655	+	0.358335i
$498$	−8.28433	−	4.78296i	−0.371230	−	0.214330i
$499$	−3.50853	−	6.07694i	−0.157063	−	0.272041i	0.776745	−	0.629815i	$-0.216869\pi$
$499$	−3.50853	−	6.07694i	−0.157063	−	0.272041i	−0.933808	+	0.357774i	$0.883536\pi$
$500$	9.60404	−	5.72384i	0.429506	−	0.255978i
$501$	−14.2129	+	24.6174i	−0.634984	+	1.09982i
$502$	13.7228	+	7.92288i	0.612480	+	0.353615i
$503$	−13.3738	−	7.72139i	−0.596310	−	0.344280i	0.171278	−	0.985223i	$-0.445210\pi$
$503$	−13.3738	−	7.72139i	−0.596310	−	0.344280i	−0.767589	+	0.640943i	$0.778544\pi$
$504$	4.62228	−	8.00602i	0.205892	−	0.356616i
$505$	10.1345	+	27.4490i	0.450979	+	1.22146i
$506$	13.4530	+	23.3012i	0.598057	+	1.03587i
$507$	15.7232	+	9.07781i	0.698293	+	0.403160i
$508$	−1.46341	+	0.844897i	−0.0649281	+	0.0374863i
$509$	30.8211			1.36612			0.683061	−	0.730362i	$-0.260648\pi$
$509$	30.8211			1.36612			0.683061	+	0.730362i	$0.260648\pi$
$510$	−13.6667	+	5.04591i	−0.605172	+	0.223436i
$511$	−42.6701			−1.88761
$512$			1.00000i			0.0441942i
$513$	0.270540	−	0.156196i	0.0119446	−	0.00689623i
$514$	−15.9352			−0.702870
$515$	18.1935	−	6.71726i	0.801702	−	0.295998i
$516$	−8.50407	+	14.7295i	−0.374371	+	0.648429i
$517$	44.4499	−	25.6631i	1.95490	−	1.12866i
$518$	8.03906	−	4.64135i	0.353216	−	0.203929i
$519$	12.6479	+	21.9068i	0.555181	+	0.961602i
$520$	−5.07170	−	0.870134i	−0.222409	−	0.0381579i
$521$	28.8068			1.26205			0.631024	−	0.775763i	$-0.282635\pi$
$521$	28.8068			1.26205			0.631024	+	0.775763i	$0.282635\pi$
$522$		−	12.7700i		−	0.558930i
$523$	23.0708	−	13.3200i	1.00882	−	0.582441i	0.0979720	−	0.995189i	$-0.468764\pi$
$523$	23.0708	−	13.3200i	1.00882	−	0.582441i	0.910845	+	0.412748i	$0.135431\pi$
$524$	4.47728	−	7.75487i	0.195591	−	0.338773i
$525$	40.2178	+	14.2186i	1.75525	+	0.620551i
$526$	−12.8636	−	22.2805i	−0.560881	−	0.971475i
$527$			11.9660i			0.521249i
$528$			10.2793i			0.447350i
$529$	7.52439	−	13.0326i	0.327147	−	0.566636i
$530$	29.5867	+	5.07609i	1.28516	+	0.220491i
$531$	10.2519			0.444893
$532$	−0.930970	−	0.537496i	−0.0403627	−	0.0233034i
$533$			13.6876i			0.592876i
$534$	−7.86892	−	13.6294i	−0.340521	−	0.589800i
$535$	−11.5261	−	9.58116i	−0.498318	−	0.414230i
$536$	−7.73451	+	2.67905i	−0.334080	+	0.115717i
$537$			43.8498i			1.89226i
$538$	26.1524	−	15.0991i	1.12751	−	0.650967i
$539$	26.6343			1.14722
$540$	2.20682	−	0.814784i	0.0949665	−	0.0350627i
$541$	22.9470			0.986569			0.493285	−	0.869868i	$-0.335796\pi$
$541$	22.9470			0.986569			0.493285	+	0.869868i	$0.335796\pi$
$542$	−14.8295	+	8.56181i	−0.636981	+	0.367761i
$543$	12.1249	+	7.00034i	0.520331	+	0.300413i
$544$	2.76466			0.118534
$545$	20.3955	−	24.5357i	0.873647	−	1.05100i
$546$	−9.81660	−	17.0029i	−0.420112	−	0.727655i
$547$	13.6421	+	7.87627i	0.583294	+	0.336765i	0.762442	−	0.647057i	$-0.224000\pi$
$547$	13.6421	+	7.87627i	0.583294	+	0.336765i	−0.179147	+	0.983822i	$0.557334\pi$
$548$	−8.28789	−	4.78501i	−0.354041	−	0.204406i
$549$	−8.82367	−	15.2831i	−0.376585	−	0.652265i
$550$	−21.4423	+	3.98551i	−0.914304	+	0.169943i
$551$	−1.48495			−0.0632610
$552$	12.5889	−	7.26820i	0.535819	−	0.309355i
$553$	−22.9499	+	13.2502i	−0.975931	+	0.563454i
$554$	−15.7095	−	27.2096i	−0.667431	−	1.15603i
$555$	−13.3171	−	2.28477i	−0.565280	−	0.0969831i
$556$	2.85703	−	4.94853i	0.121165	−	0.209864i
$557$	−29.2251	−	16.8731i	−1.23831	−	0.714936i	−0.269558	−	0.962984i	$-0.586878\pi$
$557$	−29.2251	−	16.8731i	−1.23831	−	0.714936i	−0.968748	+	0.248048i	$0.920211\pi$
$558$			11.0524i			0.467887i
$559$	8.30440	+	14.3836i	0.351239	+	0.608364i
$560$	−6.22517	−	5.17471i	−0.263062	−	0.218672i
$561$	28.4188			1.19984
$562$	−25.3149	−	14.6156i	−1.06784	−	0.616520i
$563$			31.5697i			1.33051i	0.746618	+	0.665253i	$0.231676\pi$
$563$			31.5697i			1.33051i	−0.746618	+	0.665253i	$0.768324\pi$
$564$	−13.8650	−	24.0148i	−0.583820	−	1.01121i
$565$	−10.4847	+	3.87106i	−0.441093	+	0.162857i
$566$	−12.0556	−	20.8809i	−0.506733	−	0.877688i
$567$	31.7910	+	18.3545i	1.33510	+	0.770818i
$568$	−3.82201	−	2.20664i	−0.160368	−	0.0925885i
$569$	0.886398	−	1.53529i	0.0371597	−	0.0643625i	−0.846847	−	0.531836i	$-0.821502\pi$
$569$	0.886398	−	1.53529i	0.0371597	−	0.0643625i	0.884007	+	0.467473i	$0.154836\pi$
$570$	0.541958	+	1.46788i	0.0227001	+	0.0614826i
$571$	15.6564	−	27.1177i	0.655200	−	1.13484i	−0.326644	−	0.945147i	$-0.605918\pi$
$571$	15.6564	−	27.1177i	0.655200	−	1.13484i	0.981844	−	0.189692i	$-0.0607488\pi$
$572$	8.69313	+	5.01898i	0.363478	+	0.209854i
$573$	−12.8695	+	7.43021i	−0.537631	+	0.310402i
$574$	−10.7663	+	18.6478i	−0.449377	+	0.778343i
$575$	20.0422	+	23.4420i	0.835819	+	0.977600i
$576$	2.55358			0.106399
$577$	1.35698	+	0.783453i	0.0564918	+	0.0326156i	0.527980	−	0.849257i	$-0.322950\pi$
$577$	1.35698	+	0.783453i	0.0564918	+	0.0326156i	−0.471488	+	0.881872i	$0.656283\pi$
$578$			9.35664i			0.389185i
$579$	43.5364			1.80931
$580$	−11.0212	−	1.89087i	−0.457631	−	0.0785141i
$581$	−14.6953			−0.609662
$582$	25.4746	+	14.7078i	1.05596	+	0.609656i
$583$	−50.7129	−	29.2791i	−2.10032	−	1.21262i
$584$	−5.89328	−	10.2075i	−0.243866	−	0.422388i
$585$	−2.22196	+	12.9510i	−0.0918666	+	0.535457i
$586$	−14.2488	−	24.6796i	−0.588611	−	1.01950i
$587$	19.0327	−	10.9886i	0.785565	−	0.453546i	−0.0528338	−	0.998603i	$-0.516825\pi$
$587$	19.0327	−	10.9886i	0.785565	−	0.453546i	0.838399	+	0.545057i	$0.183492\pi$
$588$		−	14.3896i		−	0.593419i
$589$	1.28522			0.0529565
$590$	1.51800	−	8.84788i	0.0624951	−	0.364261i
$591$	23.7022	−	41.0535i	0.974980	−	1.68871i
$592$	2.22059	+	1.28206i	0.0912657	+	0.0526923i
$593$	−21.6217	+	12.4833i	−0.887897	+	0.512628i	−0.873254	−	0.487265i	$-0.837995\pi$
$593$	−21.6217	+	12.4833i	−0.887897	+	0.512628i	−0.0146433	+	0.999893i	$0.504661\pi$
$594$	−4.58891			−0.188285
$595$	−14.3063	+	17.2105i	−0.586503	+	0.705562i
$596$	4.72161	−	8.17807i	0.193405	−	0.334987i
$597$	41.5877	−	24.0106i	1.70207	−	0.982690i
$598$		−	14.1951i		−	0.580481i
$599$	1.51438	−	2.62298i	0.0618758	−	0.107172i	−0.833428	−	0.552628i	$-0.813625\pi$
$599$	1.51438	−	2.62298i	0.0618758	−	0.107172i	0.895304	+	0.445456i	$0.146958\pi$
$600$	2.15324	+	11.5846i	0.0879058	+	0.472939i
$601$	−2.88294	−	4.99339i	−0.117597	−	0.203685i	0.801218	−	0.598373i	$-0.204186\pi$
$601$	−2.88294	−	4.99339i	−0.117597	−	0.203685i	−0.918815	+	0.394688i	$0.870853\pi$
$602$			26.1281i			1.06490i
$603$	6.84116	+	19.7507i	0.278593	+	0.804310i
$604$	−11.2977			−0.459697
$605$	17.6890	+	3.03484i	0.719159	+	0.123384i
$606$	−30.8374			−1.25268
$607$	−4.50637	−	2.60175i	−0.182908	−	0.105602i	0.405750	−	0.913984i	$-0.367010\pi$
$607$	−4.50637	−	2.60175i	−0.182908	−	0.105602i	−0.588658	+	0.808382i	$0.700344\pi$
$608$		−	0.296940i		−	0.0120425i
$609$	−21.3322	−	36.9485i	−0.864426	−	1.49723i
$610$	−14.4966	+	5.35231i	−0.586949	+	0.216709i
$611$	−27.0789			−1.09549
$612$		−	7.05978i		−	0.285375i
$613$	24.0236	−	13.8700i	0.970304	−	0.560205i	0.0709751	−	0.997478i	$-0.477389\pi$
$613$	24.0236	−	13.8700i	0.970304	−	0.560205i	0.899329	+	0.437273i	$0.144056\pi$
$614$	−7.55896	+	13.0925i	−0.305055	+	0.528371i
$615$	29.4023	−	10.8557i	1.18562	−	0.437743i
$616$	7.89558	+	13.6755i	0.318122	+	0.551004i
$617$			5.55886i			0.223791i	0.993720	+	0.111896i	$0.0356922\pi$
$617$			5.55886i			0.223791i	−0.993720	+	0.111896i	$0.964308\pi$
$618$			20.4394i			0.822193i
$619$	−13.1274	−	22.7373i	−0.527635	−	0.913890i	−0.999481	−	0.0322092i	$-0.989746\pi$
$619$	−13.1274	−	22.7373i	−0.527635	−	0.913890i	0.471847	−	0.881681i	$-0.343588\pi$
$620$	9.53881	+	1.63654i	0.383088	+	0.0657251i
$621$	3.24468	+	5.61996i	0.130205	+	0.225521i
$622$	−13.3191	+	7.68977i	−0.534046	+	0.308332i
$623$	−20.9376	−	12.0883i	−0.838845	−	0.484308i
$624$	2.71159	−	4.69662i	0.108551	−	0.188015i
$625$	−23.3303	+	8.98321i	−0.933211	+	0.359328i
$626$	8.99271	+	15.5758i	0.359421	+	0.622535i
$627$		−	3.05234i		−	0.121899i
$628$		−	0.0655853i		−	0.00261714i
$629$	3.54446	−	6.13918i	0.141327	−	0.244785i
$630$	−13.2140	+	15.8965i	−0.526460	+	0.633331i
$631$	5.42819	+	9.40190i	0.216093	+	0.374284i	0.953610	−	0.301045i	$-0.0973353\pi$
$631$	5.42819	+	9.40190i	0.216093	+	0.374284i	−0.737517	+	0.675328i	$0.764002\pi$
$632$	−6.33935	−	3.66003i	−0.252166	−	0.145588i
$633$	−23.5206	+	13.5796i	−0.934861	+	0.539742i
$634$	10.1883	−	17.6467i	0.404631	−	0.700841i
$635$	3.54462	−	1.30871i	0.140664	−	0.0519347i
$636$	−15.8186	+	27.3986i	−0.627247	+	1.08642i
$637$	−12.1692	−	7.02589i	−0.482161	−	0.278376i
$638$	18.8909	+	10.9066i	0.747896	+	0.431798i
$639$	−5.63482	+	9.75980i	−0.222910	+	0.386092i
$640$	0.378110	−	2.20387i	0.0149461	−	0.0871155i
$641$	−3.54137	+	6.13383i	−0.139876	+	0.242272i	−0.927449	−	0.373949i	$-0.878004\pi$
$641$	−3.54137	+	6.13383i	−0.139876	+	0.242272i	0.787574	+	0.616220i	$0.211337\pi$
$642$	13.6800	−	7.89814i	0.539906	−	0.311715i
$643$			17.7241i			0.698970i	0.936942	+	0.349485i	$0.113643\pi$
$643$			17.7241i			0.698970i	−0.936942	+	0.349485i	$0.886357\pi$
$644$	11.1655	−	19.3392i	0.439981	−	0.762070i
$645$	24.3112	−	29.2464i	0.957253	−	1.15157i
$646$	−0.820938			−0.0322994
$647$	22.0366	−	12.7229i	0.866349	−	0.500187i	0.000216077	−	1.00000i	$-0.499931\pi$
$647$	22.0366	−	12.7229i	0.866349	−	0.500187i	0.866133	+	0.499813i	$0.166598\pi$
$648$			10.1400i			0.398336i
$649$	−8.75590	+	15.1657i	−0.343699	+	0.595305i
$650$	10.8483	+	3.83532i	0.425507	+	0.150434i
$651$	18.4630	+	31.9788i	0.723621	+	1.25335i
$652$	13.1175	−	7.57338i	0.513720	−	0.296596i
$653$	32.6054	−	18.8248i	1.27595	−	0.736669i	0.299848	−	0.953987i	$-0.403064\pi$
$653$	32.6054	−	18.8248i	1.27595	−	0.736669i	0.976101	+	0.217318i	$0.0697307\pi$
$654$	16.8128	+	29.1207i	0.657434	+	1.13871i
$655$	−12.7995	+	15.3978i	−0.500119	+	0.601642i
$656$	−5.94785			−0.232224
$657$	−26.0655	+	15.0489i	−1.01691	+	0.587115i
$658$	−36.8918	−	21.2995i	−1.43819	−	0.830340i
$659$	13.6749	−	23.6857i	0.532700	−	0.922663i	−0.466571	−	0.884484i	$-0.654511\pi$
$659$	13.6749	−	23.6857i	0.532700	−	0.922663i	0.999271	−	0.0381791i	$-0.0121557\pi$
$660$	3.88671	−	22.6542i	0.151290	−	0.881815i
$661$	20.0103			0.778309			0.389154	−	0.921173i	$-0.372767\pi$
$661$	20.0103			0.778309			0.389154	+	0.921173i	$0.372767\pi$
$662$			10.5403i			0.409662i
$663$	−12.9846	−	7.49664i	−0.504278	−	0.291145i
$664$	−2.02960	−	3.51537i	−0.0787637	−	0.136423i
$665$	1.84850	+	1.53658i	0.0716818	+	0.0595860i
$666$	3.27384	−	5.67045i	0.126859	−	0.219726i
$667$		−	30.8471i		−	1.19440i
$668$	−10.4461	+	6.03108i	−0.404173	+	0.233349i
$669$	45.8017			1.77080
$670$	18.0588	−	2.97977i	0.697673	−	0.115119i
$671$	30.1445			1.16371
$672$	7.38846	−	4.26573i	0.285016	−	0.164554i
$673$			7.48717i			0.288609i	0.989533	+	0.144305i	$0.0460945\pi$
$673$			7.48717i			0.288609i	−0.989533	+	0.144305i	$0.953906\pi$
$674$	−6.57997	+	11.3968i	−0.253451	+	0.438990i
$675$	−5.17162	+	0.961256i	−0.199056	+	0.0369987i
$676$	3.85207	+	6.67199i	0.148157	+	0.256615i
$677$	0.280183	+	0.161764i	0.0107683	+	0.00621709i	0.505374	−	0.862900i	$-0.331354\pi$
$677$	0.280183	+	0.161764i	0.0107683	+	0.00621709i	−0.494606	+	0.869117i	$0.664688\pi$
$678$		−	11.7789i		−	0.452367i
$679$	45.1884			1.73417
$680$	−6.09295	−	1.04535i	−0.233654	−	0.0400872i
$681$	23.6849	−	41.0235i	0.907608	−	1.57202i
$682$	−16.3500	−	9.43966i	−0.626072	−	0.361463i
$683$	41.2096	−	23.7924i	1.57684	−	0.910389i	0.581543	−	0.813515i	$-0.302449\pi$
$683$	41.2096	−	23.7924i	1.57684	−	0.910389i	0.995297	−	0.0968735i	$-0.0308842\pi$
$684$	−0.758259			−0.0289927
$685$	16.4561	+	13.6793i	0.628757	+	0.522658i
$686$	1.61807	+	2.80259i	0.0617783	+	0.107003i
$687$	10.4013	−	6.00518i	0.396834	−	0.229112i
$688$	−6.25030	+	3.60861i	−0.238291	+	0.137577i
$689$	15.4472	+	26.7553i	0.588490	+	1.01929i
$690$	−30.4924	+	11.2582i	−1.16083	+	0.428591i
$691$	23.4422	−	40.6031i	0.891784	−	1.54462i	0.0540491	−	0.998538i	$-0.482787\pi$
$691$	23.4422	−	40.6031i	0.891784	−	1.54462i	0.837735	−	0.546077i	$-0.183879\pi$
$692$			10.7340i			0.408046i
$693$	34.9216	−	20.1620i	1.32656	−	0.765890i
$694$	15.2769			0.579904
$695$	−8.16761	+	9.82563i	−0.309815	+	0.372707i
$696$	5.89250	−	10.2061i	0.223355	−	0.386862i
$697$			16.4438i			0.622853i
$698$	−12.6618	+	7.31028i	−0.479255	+	0.276698i
$699$	34.3353	−	59.4706i	1.29868	−	2.24938i
$700$	11.7628	+	13.7582i	0.444594	+	0.520011i
$701$	−4.52750	+	7.84186i	−0.171001	+	0.296183i	−0.938770	−	0.344544i	$-0.888034\pi$
$701$	−4.52750	+	7.84186i	−0.171001	+	0.296183i	0.767769	+	0.640727i	$0.221367\pi$
$702$	2.09667	+	1.21051i	0.0791338	+	0.0456879i
$703$	−0.659381	−	0.380694i	−0.0248690	−	0.0143581i
$704$	−2.18096	+	3.77753i	−0.0821980	+	0.142371i
$705$	21.4763	+	58.1680i	0.808844	+	2.19073i
$706$	16.2061	−	28.0698i	0.609925	−	1.05642i
$707$	−41.0259	+	23.6863i	−1.54294	+	0.890816i
$708$	8.19352	+	4.73053i	0.307931	+	0.177784i
$709$	−16.7909	−	29.0828i	−0.630597	−	1.09223i	−0.987430	−	0.158058i	$-0.949477\pi$
$709$	−16.7909	−	29.0828i	−0.630597	−	1.09223i	0.356833	−	0.934168i	$-0.383857\pi$
$710$	7.58885	+	6.30828i	0.284805	+	0.236746i
$711$	−9.34617	+	16.1880i	−0.350509	+	0.607099i
$712$		−	6.67819i		−	0.250276i
$713$			26.6980i			0.999849i
$714$	−11.7933	−	20.4266i	−0.441353	−	0.764446i
$715$	−17.2608	−	14.3481i	−0.645517	−	0.536590i
$716$	−9.30361	+	16.1143i	−0.347692	+	0.602221i
$717$	15.7014	+	9.06523i	0.586381	+	0.338547i
$718$	7.35982	−	4.24920i	0.274666	−	0.158579i
$719$	−10.1168	−	17.5229i	−0.377294	−	0.653492i	0.613374	−	0.789793i	$-0.289812\pi$
$719$	−10.1168	−	17.5229i	−0.377294	−	0.653492i	−0.990668	+	0.136301i	$0.956479\pi$
$720$	−5.62775	−	0.965534i	−0.209734	−	0.0359833i
$721$	15.6996	+	27.1925i	0.584683	+	1.01270i
$722$		−	18.9118i		−	0.703825i
$723$		−	0.0796689i		−	0.00296292i
$724$	2.97052	+	5.14509i	0.110399	+	0.191216i
$725$	23.5743	+	8.33446i	0.875528	+	0.309534i
$726$	−9.45743	+	16.3808i	−0.350998	+	0.607947i
$727$	−21.3506	+	12.3268i	−0.791849	+	0.457174i	−0.840613	−	0.541636i	$-0.817805\pi$
$727$	−21.3506	+	12.3268i	−0.791849	+	0.457174i	0.0487641	+	0.998810i	$0.484472\pi$
$728$		−	8.33114i		−	0.308773i
$729$	18.4555			0.683537
$730$	9.12846	+	24.7242i	0.337860	+	0.915084i
$731$	9.97660	+	17.2800i	0.368998	+	0.639123i
$732$		−	16.2861i		−	0.601951i
$733$	−17.0685	−	9.85450i	−0.630439	−	0.363984i	0.150483	−	0.988613i	$-0.451917\pi$
$733$	−17.0685	−	9.85450i	−0.630439	−	0.363984i	−0.780922	+	0.624628i	$0.785250\pi$
$734$	26.7003			0.985525
$735$	−5.44087	+	31.7129i	−0.200689	+	1.16975i
$736$	6.16837			0.227369
$737$	−35.0603	−	6.74847i	−1.29146	−	0.248583i
$738$			15.1883i			0.559089i
$739$	−11.6701	−	20.2131i	−0.429290	−	0.743552i	0.567520	−	0.823359i	$-0.307903\pi$
$739$	−11.6701	−	20.2131i	−0.429290	−	0.743552i	−0.996810	+	0.0798074i	$0.974569\pi$
$740$	−4.40913	−	3.66511i	−0.162083	−	0.134732i
$741$	−0.805180	+	1.39461i	−0.0295790	+	0.0512324i
$742$			48.6012i			1.78421i
$743$	12.2466	−	7.07057i	0.449284	−	0.259394i	−0.258244	−	0.966080i	$-0.583144\pi$
$743$	12.2466	−	7.07057i	0.449284	−	0.259394i	0.707528	+	0.706686i	$0.249810\pi$
$744$	−5.09994	+	8.83336i	−0.186973	+	0.323847i
$745$	−13.4980	+	16.2381i	−0.494529	+	0.594918i
$746$	−0.0184052			−0.000673862
$747$	−8.97677	+	5.18274i	−0.328443	+	0.189627i
$748$	10.4436	+	6.02961i	0.381856	+	0.220465i
$749$	12.1332	−	21.0153i	0.443337	−	0.767882i
$750$	−0.365211	−	26.3451i	−0.0133356	−	0.961987i
$751$	−28.5182			−1.04064			−0.520322	−	0.853970i	$-0.674188\pi$
$751$	−28.5182			−1.04064			−0.520322	+	0.853970i	$0.674188\pi$
$752$		−	11.7669i		−	0.429095i
$753$	32.3392	−	18.6711i	1.17851	−	0.680412i
$754$	−5.75415	−	9.96649i	−0.209554	−	0.362958i
$755$	24.8987	+	4.27178i	0.906155	+	0.155466i
$756$	1.90431	+	3.29837i	0.0692592	+	0.119961i
$757$	−43.7939	−	25.2844i	−1.59172	−	0.918978i	−0.993013	−	0.118008i	$-0.962349\pi$
$757$	−43.7939	−	25.2844i	−1.59172	−	0.918978i	−0.598705	−	0.800970i	$-0.704318\pi$
$758$	−21.2538	−	12.2709i	−0.771973	−	0.445699i
$759$	63.4066			2.30151
$760$	−0.112276	+	0.654416i	−0.00407267	+	0.0237382i
$761$	−14.4789			−0.524859			−0.262429	−	0.964951i	$-0.584524\pi$
$761$	−14.4789			−0.524859			−0.262429	+	0.964951i	$0.584524\pi$
$762$			3.98218i			0.144259i
$763$	44.7354	+	25.8280i	1.61953	+	0.935037i
$764$	−6.30587			−0.228138
$765$	−2.66937	+	15.5588i	−0.0965114	+	0.562530i
$766$	5.12291	−	8.87314i	0.185098	−	0.320600i
$767$	8.00115	−	4.61946i	0.288905	−	0.166799i
$768$	2.04088	+	1.17830i	0.0736438	+	0.0425183i
$769$	−1.60779	+	2.78478i	−0.0579785	+	0.100422i	−0.893558	−	0.448948i	$-0.851799\pi$
$769$	−1.60779	+	2.78478i	−0.0579785	+	0.100422i	0.835579	+	0.549370i	$0.185132\pi$
$770$	−12.2300	−	33.1245i	−0.440737	−	1.19372i
$771$	−18.7764	+	32.5217i	−0.676216	+	1.17124i
$772$	15.9992	+	9.23712i	0.575822	+	0.332451i
$773$	1.59464	+	0.920665i	0.0573551	+	0.0331140i	0.528403	−	0.848993i	$-0.322791\pi$
$773$	1.59464	+	0.920665i	0.0573551	+	0.0331140i	−0.471048	+	0.882107i	$0.656124\pi$
$774$	9.21488	+	15.9606i	0.331222	+	0.573693i
$775$	−20.4035	−	7.21344i	−0.732915	−	0.259114i
$776$	6.24108	+	10.8099i	0.224042	+	0.388052i
$777$		−	21.8756i		−	0.784784i
$778$	12.0569	+	6.96107i	0.432262	+	0.249567i
$779$	1.76615			0.0632790
$780$	−7.75183	+	9.32544i	−0.277560	+	0.333904i
$781$	−9.62518	−	16.6713i	−0.344416	−	0.596546i
$782$		−	17.0535i		−	0.609830i
$783$	4.55623	+	2.63054i	0.162827	+	0.0940079i
$784$	3.05305	−	5.28803i	0.109037	−	0.188858i
$785$	−0.0247985	+	0.144541i	−0.000885095	+	0.00515890i
$786$	−10.5512	−	18.2752i	−0.376348	−	0.651853i
$787$	29.2453	−	16.8848i	1.04248	−	0.601878i	0.121947	−	0.992537i	$-0.461086\pi$
$787$	29.2453	−	16.8848i	1.04248	−	0.601878i	0.920535	+	0.390659i	$0.127753\pi$
$788$	17.4206	−	10.0578i	0.620584	−	0.358294i
$789$	−60.6290			−2.15845
$790$	12.5872	+	10.4632i	0.447833	+	0.372264i
$791$	−9.04745	−	15.6706i	−0.321690	−	0.557184i
$792$	9.64622	+	5.56925i	0.342764	+	0.197895i
$793$	−13.7730	−	7.95185i	−0.489094	−	0.282379i
$794$	8.51370	+	14.7462i	0.302140	+	0.523322i
$795$	45.2217	−	54.4016i	1.60385	−	1.92943i
$796$	20.3773			0.722255
$797$	17.1935	+	9.92668i	0.609026	+	0.351621i	0.772584	−	0.634913i	$-0.218964\pi$
$797$	17.1935	+	9.92668i	0.609026	+	0.351621i	−0.163558	+	0.986534i	$0.552297\pi$
$798$	−2.19393	+	1.26666i	−0.0776641	+	0.0448394i
$799$	−32.5315			−1.15088
$800$	−1.66661	+	4.71407i	−0.0589235	+	0.166667i
$801$	−17.0533			−0.602548
$802$	−31.2323	+	18.0319i	−1.10285	+	0.636730i
$803$		−	51.4120i		−	1.81429i
$804$	−3.64598	+	18.9419i	−0.128584	+	0.668030i
$805$	−31.9196	+	38.3992i	−1.12502	+	1.35339i
$806$	4.98020	+	8.62596i	0.175420	+	0.303836i
$807$		−	71.1650i		−	2.50513i
$808$	−11.3324	−	6.54276i	−0.398672	−	0.230174i
$809$	−11.6646			−0.410105			−0.205052	−	0.978751i	$-0.565736\pi$
$809$	−11.6646			−0.410105			−0.205052	+	0.978751i	$0.565736\pi$
$810$	3.83403	−	22.3472i	0.134714	−	0.785199i
$811$	1.77453	−	3.07357i	0.0623121	−	0.107928i	−0.833186	−	0.552992i	$-0.813486\pi$
$811$	1.77453	−	3.07357i	0.0623121	−	0.107928i	0.895499	+	0.445064i	$0.146819\pi$
$812$		−	18.1042i		−	0.635334i
$813$			40.3536i			1.41526i
$814$	5.59223	+	9.68603i	0.196008	+	0.339495i
$815$	−31.7727	+	11.7309i	−1.11295	+	0.410914i
$816$	3.25761	−	5.64234i	0.114039	−	0.197521i
$817$	1.85596	−	1.07154i	0.0649319	−	0.0374885i
$818$			3.83282i			0.134011i
$819$	−21.2742			−0.743382
$820$	13.1083	+	2.24894i	0.457761	+	0.0785364i
$821$	22.4163	+	38.8262i	0.782336	+	1.35505i	0.930578	+	0.366094i	$0.119305\pi$
$821$	22.4163	+	38.8262i	0.782336	+	1.35505i	−0.148242	+	0.988951i	$0.547361\pi$
$822$	−19.5313	+	11.2764i	−0.681231	+	0.393309i
$823$	25.4979	−	14.7212i	0.888802	−	0.513150i	0.0152514	−	0.999884i	$-0.495145\pi$
$823$	25.4979	−	14.7212i	0.888802	−	0.513150i	0.873550	+	0.486734i	$0.161812\pi$
$824$	−4.33662	+	7.51125i	−0.151073	+	0.261667i
$825$	−17.1316	+	48.4573i	−0.596445	+	1.68707i
$826$	14.5342			0.505708
$827$	10.9326	−	6.31194i	0.380164	−	0.219488i	−0.297726	−	0.954651i	$-0.596228\pi$
$827$	10.9326	−	6.31194i	0.380164	−	0.219488i	0.677890	+	0.735164i	$0.262895\pi$
$828$		−	15.7514i		−	0.547399i
$829$	−4.36915			−0.151747			−0.0758734	−	0.997117i	$-0.524175\pi$
$829$	−4.36915			−0.151747			−0.0758734	+	0.997117i	$0.524175\pi$
$830$	3.14377	+	8.51482i	0.109122	+	0.295554i
$831$	−74.0420			−2.56849
$832$	1.99296	−	1.15064i	0.0690935	−	0.0398911i
$833$	−14.6196	−	8.44064i	−0.506540	−	0.292451i
$834$	−6.73289	−	11.6617i	−0.233141	−	0.403812i
$835$	25.3023	−	9.34191i	0.875623	−	0.323290i
$836$	0.647613	−	1.12170i	0.0223982	−	0.0387948i
$837$	−3.94340	−	2.27673i	−0.136304	−	0.0786951i
$838$	−6.47449	−	3.73805i	−0.223658	−	0.129129i
$839$	13.6174	−	23.5861i	0.470126	−	0.814282i	−0.529290	−	0.848441i	$-0.677542\pi$
$839$	13.6174	−	23.5861i	0.470126	−	0.814282i	0.999416	+	0.0341586i	$0.0108751\pi$
$840$	−17.8961	+	6.60745i	−0.617474	+	0.227979i
$841$	1.99577	+	3.45678i	0.0688197	+	0.119199i
$842$	15.4801	+	8.93743i	0.533479	+	0.308004i
$843$	−59.6571	+	34.4431i	−2.05470	+	1.18628i
$844$	−11.5248			−0.396699
$845$	−5.96671	−	16.1607i	−0.205261	−	0.555944i
$846$	−30.0477			−1.03306
$847$			29.0572i			0.998417i
$848$	−11.6263	+	6.71244i	−0.399249	+	0.230506i
$849$	−56.8204			−1.95007
$850$	13.0328	+	4.60761i	0.447021	+	0.158040i
$851$	7.90821	−	13.6974i	0.271090	−	0.469542i
$852$	−9.00696	+	5.20017i	−0.308573	+	0.178155i
$853$	−9.43101	+	5.44500i	−0.322912	+	0.186433i	−0.652690	−	0.757625i	$-0.726359\pi$
$853$	−9.43101	+	5.44500i	−0.322912	+	0.186433i	0.329778	+	0.944058i	$0.393026\pi$
$854$	−12.5094	−	21.6669i	−0.428063	−	0.741427i
$855$	1.67110	+	0.286705i	0.0571505	+	0.00980511i
$856$	6.70299			0.229103
$857$			11.8154i			0.403607i	0.979426	+	0.201804i	$0.0646803\pi$
$857$			11.8154i			0.403607i	−0.979426	+	0.201804i	$0.935320\pi$
$858$	20.4863	−	11.8277i	0.699389	−	0.403793i
$859$	19.8938	−	34.4570i	0.678767	−	1.17566i	−0.296586	−	0.955006i	$-0.595848\pi$
$859$	19.8938	−	34.4570i	0.678767	−	1.17566i	0.975353	−	0.220652i	$-0.0708186\pi$
$860$	15.1393	−	5.58960i	0.516246	−	0.190604i
$861$	25.3719	+	43.9454i	0.864672	+	1.49766i
$862$			6.71134i			0.228589i
$863$		−	8.93665i		−	0.304207i	−0.988365	−	0.152104i	$-0.951395\pi$
$863$		−	8.93665i		−	0.304207i	0.988365	−	0.152104i	$-0.0486047\pi$
$864$	−0.526020	+	0.911093i	−0.0178956	+	0.0309960i
$865$	4.05864	−	23.6563i	0.137998	−	0.804340i
$866$	−18.8768			−0.641461
$867$	19.0958	+	11.0249i	0.648526	+	0.374427i
$868$			15.6691i			0.531845i
$869$	−15.9647	−	27.6517i	−0.541567	−	0.938021i
$870$	−16.8453	+	20.2649i	−0.571110	+	0.687045i
$871$	14.2388	+	12.3320i	0.482465	+	0.417853i
$872$			14.2687i			0.483199i
$873$	27.6039	−	15.9371i	0.934249	−	0.539389i
$874$	−1.83163			−0.0619559
$875$	−20.7217	−	34.7689i	−0.700520	−	1.17540i
$876$	−27.7762			−0.938472
$877$	−18.5330	+	10.7001i	−0.625816	+	0.361315i	−0.779130	−	0.626862i	$-0.784339\pi$
$877$	−18.5330	+	10.7001i	−0.625816	+	0.361315i	0.153314	+	0.988178i	$0.451006\pi$
$878$	6.88080	+	3.97263i	0.232216	+	0.134070i
$879$	−67.1573			−2.26516
$880$	6.23487	−	7.50054i	0.210177	−	0.252843i
$881$	10.4183	+	18.0450i	0.351001	+	0.607951i	0.986425	−	0.164212i	$-0.0525082\pi$
$881$	10.4183	+	18.0450i	0.351001	+	0.607951i	−0.635424	+	0.772163i	$0.719175\pi$
$882$	−13.5034	−	7.79619i	−0.454683	−	0.262512i
$883$	−0.606212	−	0.349997i	−0.0204007	−	0.0117783i	0.489765	−	0.871854i	$-0.337083\pi$
$883$	−0.606212	−	0.349997i	−0.0204007	−	0.0117783i	−0.510166	+	0.860076i	$0.670416\pi$
$884$	−3.18112	−	5.50986i	−0.106993	−	0.185317i
$885$	−16.2688	−	13.5235i	−0.546869	−	0.454588i
$886$	35.7660			1.20158
$887$	−43.9942	+	25.4001i	−1.47718	+	0.852851i	−0.999668	−	0.0257735i	$-0.991795\pi$
$887$	−43.9942	+	25.4001i	−1.47718	+	0.852851i	−0.477513	+	0.878624i	$0.658462\pi$
$888$	5.23305	−	3.02130i	0.175610	−	0.101388i
$889$	3.05873	+	5.29787i	0.102586	+	0.177685i
$890$	−2.52509	+	14.7178i	−0.0846412	+	0.493343i
$891$	−22.1149	+	38.3041i	−0.740876	+	1.28323i
$892$	16.8316	+	9.71775i	0.563565	+	0.325374i
$893$			3.49406i			0.116924i
$894$	−11.1270	−	19.2725i	−0.372141	−	0.644568i
$895$	26.5969	−	31.9961i	0.889037	−	1.06951i
$896$	3.62023			0.120944
$897$	−28.9705	−	16.7261i	−0.967296	−	0.558468i
$898$			23.9980i			0.800824i
$899$	10.8224	+	18.7449i	0.360946	+	0.625177i
$900$	12.0377	+	4.25582i	0.401258	+	0.141861i
$901$	18.5576	+	32.1428i	0.618245	+	1.07083i
$902$	−22.4682	−	12.9720i	−0.748109	−	0.431921i
$903$	53.3242	+	30.7867i	1.77452	+	1.02452i
$904$	2.49913	−	4.32863i	0.0831199	−	0.143968i
$905$	−4.60123	−	12.4623i	−0.152950	−	0.414261i
$906$	−13.3121	+	23.0573i	−0.442265	+	0.766026i
$907$	7.32980	+	4.23186i	0.243382	+	0.140517i	0.616730	−	0.787175i	$-0.288457\pi$
$907$	7.32980	+	4.23186i	0.243382	+	0.140517i	−0.373348	+	0.927691i	$0.621790\pi$
$908$	17.4079	−	10.0505i	0.577701	−	0.333536i
$909$	−16.7075	+	28.9382i	−0.554151	+	0.959818i
$910$	−3.15009	+	18.3607i	−0.104424	+	0.608653i
$911$	54.3446			1.80052			0.900259	−	0.435355i	$-0.143377\pi$
$911$	54.3446			1.80052			0.900259	+	0.435355i	$0.143377\pi$
$912$	−0.606018	−	0.349885i	−0.0200673	−	0.0115858i
$913$		−	17.7059i		−	0.585980i
$914$	−11.5121			−0.380786
$915$	−6.15793	+	35.8924i	−0.203575	+	1.18657i
$916$	5.09647			0.168392
$917$	−28.0744	−	16.2088i	−0.927100	−	0.535261i
$918$	2.51886	+	1.45427i	0.0831349	+	0.0479979i
$919$	−25.4738	−	44.1219i	−0.840303	−	1.45545i	−0.889638	−	0.456666i	$-0.849043\pi$
$919$	−25.4738	−	44.1219i	−0.840303	−	1.45545i	0.0493348	−	0.998782i	$-0.484290\pi$
$920$	−13.5943	−	2.33232i	−0.448190	−	0.0768944i
$921$	17.8135	+	30.8538i	0.586974	+	1.01667i
$922$	−30.5304	+	17.6267i	−1.00546	+	0.580505i
$923$			10.1562i			0.334294i
$924$	37.2135			1.22423
$925$	8.33132	+	9.74456i	0.273932	+	0.320399i
$926$	−17.9313	+	31.0580i	−0.589260	+	1.02063i
$927$	19.1806	+	11.0739i	0.629972	+	0.363715i
$928$	4.33086	−	2.50042i	0.142167	−	0.0820804i
$929$	19.8991			0.652870			0.326435	−	0.945220i	$-0.394153\pi$
$929$	19.8991			0.652870			0.326435	+	0.945220i	$0.394153\pi$
$930$	14.5796	−	17.5392i	0.478083	−	0.575133i
$931$	−0.906571	+	1.57023i	−0.0297117	+	0.0514621i
$932$	25.2357	−	14.5698i	0.826623	−	0.477251i
$933$			36.2435i			1.18656i
$934$	9.28907	−	16.0891i	0.303948	−	0.526453i
$935$	−20.7364	−	17.2373i	−0.678154	−	0.563720i
$936$	−2.93824	−	5.08918i	−0.0960394	−	0.166345i
$937$		−	28.3063i		−	0.924728i	−0.886690	−	0.462364i	$-0.847001\pi$
$937$		−	28.3063i		−	0.924728i	0.886690	−	0.462364i	$-0.152999\pi$
$938$	9.69878	+	28.0008i	0.316676	+	0.914257i
$939$	42.3845			1.38317
$940$	−4.44919	+	25.9327i	−0.145116	+	0.845831i
$941$	−0.0649602			−0.00211764			−0.00105882	−	0.999999i	$-0.500337\pi$
$941$	−0.0649602			−0.00211764			−0.00105882	+	0.999999i	$0.500337\pi$
$942$	−0.133852	−	0.0772792i	−0.00436112	−	0.00251789i
$943$			36.6885i			1.19474i
$944$	2.00735	+	3.47684i	0.0653337	+	0.113161i
$945$	−2.94971	−	7.98921i	−0.0959541	−	0.259889i
$946$	−31.4810			−1.02353
$947$		−	30.9102i		−	1.00445i	−0.864738	−	0.502223i	$-0.832516\pi$
$947$		−	30.9102i		−	1.00445i	0.864738	−	0.502223i	$-0.167484\pi$
$948$	−14.9393	+	8.62523i	−0.485207	+	0.280134i
$949$	−13.5620	+	23.4901i	−0.440242	+	0.762522i
$950$	0.494882	−	1.39979i	0.0160561	−	0.0454153i
$951$	−24.0099	−	41.5863i	−0.778573	−	1.34853i
$952$		−	10.0087i		−	0.324385i
$953$		−	6.78025i		−	0.219634i	−0.993952	−	0.109817i	$-0.964974\pi$
$953$		−	6.78025i		−	0.219634i	0.993952	−	0.109817i	$-0.0350265\pi$
$954$	17.1407	+	29.6886i	0.554952	+	0.961206i
$955$	13.8973	+	2.38431i	0.449706	+	0.0771545i
$956$	3.84674	+	6.66274i	0.124412	+	0.215489i
$957$	44.5182	−	25.7026i	1.43907	−	0.830848i
$958$	−12.5619	−	7.25262i	−0.405857	−	0.234321i
$959$	−17.3229	+	30.0041i	−0.559385	+	0.968883i
$960$	−4.05230	−	3.36850i	−0.130787	−	0.108718i
$961$	6.13328	+	10.6232i	0.197848	+	0.342683i
$962$		−	5.90073i		−	0.190247i
$963$		−	17.1166i		−	0.551575i
$964$	0.0169033	−	0.0292774i	0.000544420	−	0.000942962i
$965$	−31.7674	−	26.4068i	−1.02263	−	0.850066i
$966$	−26.3126	−	45.5747i	−0.846593	−	1.46634i
$967$	20.8111	+	12.0153i	0.669239	+	0.386386i	0.795788	−	0.605575i	$-0.207057\pi$
$967$	20.8111	+	12.0153i	0.669239	+	0.386386i	−0.126549	+	0.991960i	$0.540390\pi$
$968$	−6.95100	+	4.01316i	−0.223414	+	0.128988i
$969$	−0.967312	+	1.67543i	−0.0310746	+	0.0538227i
$970$	−9.66720	−	26.1834i	−0.310395	−	0.840697i
$971$	−27.7549	+	48.0729i	−0.890697	+	1.54273i	−0.0516556	+	0.998665i	$0.516450\pi$
$971$	−27.7549	+	48.0729i	−0.890697	+	1.54273i	−0.839041	+	0.544068i	$0.816884\pi$
$972$	17.9612	+	10.3699i	0.576105	+	0.332614i
$973$	−17.9148	−	10.3431i	−0.574323	−	0.331586i
$974$	−11.8761	+	20.5701i	−0.380536	+	0.659107i
$975$	20.6101	−	17.6210i	0.660050	−	0.564323i
$976$	3.45542	−	5.98496i	0.110605	−	0.191574i
$977$	−34.7120	+	20.0410i	−1.11054	+	0.641168i	−0.938968	−	0.344005i	$-0.888216\pi$
$977$	−34.7120	+	20.0410i	−1.11054	+	0.641168i	−0.171567	+	0.985172i	$0.554883\pi$
$978$		−	35.6949i		−	1.14140i
$979$	14.5649	−	25.2271i	0.465495	−	0.806261i
$980$	−8.72797	+	10.4997i	−0.278805	+	0.335402i
$981$	36.4362			1.16332
$982$	−10.6526	+	6.15028i	−0.339938	+	0.196263i
$983$			20.1351i			0.642209i	0.947044	+	0.321105i	$0.104054\pi$
$983$			20.1351i			0.642209i	−0.947044	+	0.321105i	$0.895946\pi$
$984$	−7.00836	+	12.1388i	−0.223418	+	0.386972i
$985$	−42.1957	+	15.5791i	−1.34447	+	0.496393i
$986$	−6.91282	−	11.9734i	−0.220149	−	0.381310i
$987$	−86.9393	+	50.1944i	−2.76731	+	1.59771i
$988$	−0.591789	+	0.341670i	−0.0188273	+	0.0108700i
$989$	22.2593	+	38.5542i	0.707803	+	1.22595i
$990$	−19.1532	−	15.9212i	−0.608729	−	0.506010i
$991$	−11.8153			−0.375325			−0.187662	−	0.982234i	$-0.560091\pi$
$991$	−11.8153			−0.375325			−0.187662	+	0.982234i	$0.560091\pi$
$992$	−3.74834	+	2.16411i	−0.119010	+	0.0687105i
$993$	21.5115	+	12.4197i	0.682648	+	0.394127i
$994$	−7.98855	+	13.8366i	−0.253381	+	0.438869i
$995$	−44.9090	−	7.70488i	−1.42371	−	0.244261i
$996$	−9.56592			−0.303108
$997$			13.7836i			0.436532i	0.975889	+	0.218266i	$0.0700400\pi$
$997$			13.7836i			0.436532i	−0.975889	+	0.218266i	$0.929960\pi$
$998$	−6.07694	−	3.50853i	−0.192362	−	0.111060i
$999$	1.34878	+	2.33615i	0.0426734	+	0.0739125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.16	yes	52
5.4	even	2	inner	670.2.h.c.439.11	yes	52
67.29	even	3	inner	670.2.h.c.29.3	✓	52
335.29	even	6	inner	670.2.h.c.29.24	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.3	✓	52	67.29	even	3	inner
670.2.h.c.29.24	yes	52	335.29	even	6	inner
670.2.h.c.439.11	yes	52	5.4	even	2	inner
670.2.h.c.439.16	yes	52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -2.35660i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.42939 + 1.71955i) q^{5} +(-1.17830 - 2.04088i) q^{6} +(-3.13521 - 1.81012i) q^{7} -1.00000i q^{8} -2.55358 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -2.35660i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.42939 + 1.71955i) q^{5} +(-1.17830 - 2.04088i) q^{6} +(-3.13521 - 1.81012i) q^{7} -1.00000i q^{8} -2.55358 q^{9} +(-0.378110 + 2.20387i) q^{10} +(2.18096 - 3.77753i) q^{11} +(-2.04088 - 1.17830i) q^{12} +(-1.99296 + 1.15064i) q^{13} -3.62023 q^{14} +(4.05230 + 3.36850i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.39427 + 1.38233i) q^{17} +(-2.21146 + 1.27679i) q^{18} +(0.148470 + 0.257157i) q^{19} +(0.774481 + 2.09766i) q^{20} +(-4.26573 + 7.38846i) q^{21} -4.36192i q^{22} +(-5.34196 + 3.08418i) q^{23} -2.35660 q^{24} +(-0.913707 - 4.91581i) q^{25} +(-1.15064 + 1.99296i) q^{26} -1.05204i q^{27} +(-3.13521 + 1.81012i) q^{28} +(-2.50042 + 4.33086i) q^{29} +(5.19364 + 0.891055i) q^{30} +(2.16411 - 3.74834i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-8.90214 - 5.13965i) q^{33} +(-1.38233 + 2.39427i) q^{34} +(7.59402 - 2.80380i) q^{35} +(-1.27679 + 2.21146i) q^{36} +(-2.22059 + 1.28206i) q^{37} +(0.257157 + 0.148470i) q^{38} +(2.71159 + 4.69662i) q^{39} +(1.71955 + 1.42939i) q^{40} +(2.97392 - 5.15099i) q^{41} +8.53145i q^{42} -7.21723i q^{43} +(-2.18096 - 3.77753i) q^{44} +(3.65005 - 4.39101i) q^{45} +(-3.08418 + 5.34196i) q^{46} +(10.1904 + 5.88345i) q^{47} +(-2.04088 + 1.17830i) q^{48} +(3.05305 + 5.28803i) q^{49} +(-3.24920 - 3.80036i) q^{50} +(3.25761 + 5.64234i) q^{51} +2.30127i q^{52} -13.4249i q^{53} +(-0.526020 - 0.911093i) q^{54} +(3.37822 + 9.14982i) q^{55} +(-1.81012 + 3.13521i) q^{56} +(0.606018 - 0.349885i) q^{57} +5.00085i q^{58} -4.01470 q^{59} +(4.94335 - 1.82514i) q^{60} +(3.45542 + 5.98496i) q^{61} -4.32821i q^{62} +(8.00602 + 4.62228i) q^{63} -1.00000 q^{64} +(0.870134 - 5.07170i) q^{65} -10.2793 q^{66} +(-2.67905 - 7.73451i) q^{67} +2.76466i q^{68} +(7.26820 + 12.5889i) q^{69} +(5.17471 - 6.22517i) q^{70} +(2.20664 - 3.82201i) q^{71} +2.55358i q^{72} +(10.2075 - 5.89328i) q^{73} +(-1.28206 + 2.22059i) q^{74} +(-11.5846 + 2.15324i) q^{75} +0.296940 q^{76} +(-13.6755 + 7.89558i) q^{77} +(4.69662 + 2.71159i) q^{78} +(3.66003 - 6.33935i) q^{79} +(2.20387 + 0.378110i) q^{80} -10.1400 q^{81} -5.94785i q^{82} +(3.51537 - 2.02960i) q^{83} +(4.26573 + 7.38846i) q^{84} +(1.04535 - 6.09295i) q^{85} +(-3.60861 - 6.25030i) q^{86} +(10.2061 + 5.89250i) q^{87} +(-3.77753 - 2.18096i) q^{88} +6.67819 q^{89} +(0.965534 - 5.62775i) q^{90} +8.33114 q^{91} +6.16837i q^{92} +(-8.83336 - 5.09994i) q^{93} +11.7669 q^{94} +(-0.654416 - 0.112276i) q^{95} +(-1.17830 + 2.04088i) q^{96} +(-10.8099 + 6.24108i) q^{97} +(5.28803 + 3.05305i) q^{98} +(-5.56925 + 9.64622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

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