LMFDB - Embedded newform 14.4.c.a.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,4,Mod(9,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.9"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.826026740080$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	14.9
Dual form			14.4.c.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 + 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} -10.0000 q^{6} +(-14.0000 - 12.1244i) q^{7} +8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(9.00000 + 15.5885i) q^{10} +(28.5000 + 49.3634i) q^{11} +(10.0000 - 17.3205i) q^{12} -70.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-25.5000 - 44.1673i) q^{17} +(2.00000 + 3.46410i) q^{18} +(-2.50000 + 4.33013i) q^{19} -36.0000 q^{20} +(17.5000 - 90.9327i) q^{21} -114.000 q^{22} +(-34.5000 + 59.7558i) q^{23} +(20.0000 + 34.6410i) q^{24} +(22.0000 + 38.1051i) q^{25} +(70.0000 - 121.244i) q^{26} +145.000 q^{27} +(-14.0000 + 72.7461i) q^{28} +114.000 q^{29} +(-45.0000 + 77.9423i) q^{30} +(-11.5000 - 19.9186i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-142.500 + 246.817i) q^{33} +102.000 q^{34} +(-157.500 + 54.5596i) q^{35} -8.00000 q^{36} +(126.500 - 219.104i) q^{37} +(-5.00000 - 8.66025i) q^{38} +(-175.000 - 303.109i) q^{39} +(36.0000 - 62.3538i) q^{40} -42.0000 q^{41} +(140.000 + 121.244i) q^{42} -124.000 q^{43} +(114.000 - 197.454i) q^{44} +(-9.00000 - 15.5885i) q^{45} +(-69.0000 - 119.512i) q^{46} +(-100.500 + 174.071i) q^{47} -80.0000 q^{48} +(49.0000 + 339.482i) q^{49} -88.0000 q^{50} +(127.500 - 220.836i) q^{51} +(140.000 + 242.487i) q^{52} +(196.500 + 340.348i) q^{53} +(-145.000 + 251.147i) q^{54} +513.000 q^{55} +(-112.000 - 96.9948i) q^{56} -25.0000 q^{57} +(-114.000 + 197.454i) q^{58} +(-109.500 - 189.660i) q^{59} +(-90.0000 - 155.885i) q^{60} +(354.500 - 614.012i) q^{61} +46.0000 q^{62} +(-35.0000 + 12.1244i) q^{63} +64.0000 q^{64} +(-315.000 + 545.596i) q^{65} +(-285.000 - 493.634i) q^{66} +(-209.500 - 362.865i) q^{67} +(-102.000 + 176.669i) q^{68} -345.000 q^{69} +(63.0000 - 327.358i) q^{70} -96.0000 q^{71} +(8.00000 - 13.8564i) q^{72} +(156.500 + 271.066i) q^{73} +(253.000 + 438.209i) q^{74} +(-110.000 + 190.526i) q^{75} +20.0000 q^{76} +(199.500 - 1036.63i) q^{77} +700.000 q^{78} +(-230.500 + 399.238i) q^{79} +(72.0000 + 124.708i) q^{80} +(335.500 + 581.103i) q^{81} +(42.0000 - 72.7461i) q^{82} -588.000 q^{83} +(-350.000 + 121.244i) q^{84} -459.000 q^{85} +(124.000 - 214.774i) q^{86} +(285.000 + 493.634i) q^{87} +(228.000 + 394.908i) q^{88} +(508.500 - 880.748i) q^{89} +36.0000 q^{90} +(980.000 + 848.705i) q^{91} +276.000 q^{92} +(57.5000 - 99.5929i) q^{93} +(-201.000 - 348.142i) q^{94} +(22.5000 + 38.9711i) q^{95} +(80.0000 - 138.564i) q^{96} -1834.00 q^{97} +(-637.000 - 254.611i) q^{98} +114.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 5 q^{3} - 4 q^{4} + 9 q^{5} - 20 q^{6} - 28 q^{7} + 16 q^{8} + 2 q^{9} + 18 q^{10} + 57 q^{11} + 20 q^{12} - 140 q^{13} + 70 q^{14} + 90 q^{15} - 16 q^{16} - 51 q^{17} + 4 q^{18} - 5 q^{19}+ \cdots + 228 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 5 * q^3 - 4 * q^4 + 9 * q^5 - 20 * q^6 - 28 * q^7 + 16 * q^8 + 2 * q^9 + 18 * q^10 + 57 * q^11 + 20 * q^12 - 140 * q^13 + 70 * q^14 + 90 * q^15 - 16 * q^16 - 51 * q^17 + 4 * q^18 - 5 * q^19 - 72 * q^20 + 35 * q^21 - 228 * q^22 - 69 * q^23 + 40 * q^24 + 44 * q^25 + 140 * q^26 + 290 * q^27 - 28 * q^28 + 228 * q^29 - 90 * q^30 - 23 * q^31 - 32 * q^32 - 285 * q^33 + 204 * q^34 - 315 * q^35 - 16 * q^36 + 253 * q^37 - 10 * q^38 - 350 * q^39 + 72 * q^40 - 84 * q^41 + 280 * q^42 - 248 * q^43 + 228 * q^44 - 18 * q^45 - 138 * q^46 - 201 * q^47 - 160 * q^48 + 98 * q^49 - 176 * q^50 + 255 * q^51 + 280 * q^52 + 393 * q^53 - 290 * q^54 + 1026 * q^55 - 224 * q^56 - 50 * q^57 - 228 * q^58 - 219 * q^59 - 180 * q^60 + 709 * q^61 + 92 * q^62 - 70 * q^63 + 128 * q^64 - 630 * q^65 - 570 * q^66 - 419 * q^67 - 204 * q^68 - 690 * q^69 + 126 * q^70 - 192 * q^71 + 16 * q^72 + 313 * q^73 + 506 * q^74 - 220 * q^75 + 40 * q^76 + 399 * q^77 + 1400 * q^78 - 461 * q^79 + 144 * q^80 + 671 * q^81 + 84 * q^82 - 1176 * q^83 - 700 * q^84 - 918 * q^85 + 248 * q^86 + 570 * q^87 + 456 * q^88 + 1017 * q^89 + 72 * q^90 + 1960 * q^91 + 552 * q^92 + 115 * q^93 - 402 * q^94 + 45 * q^95 + 160 * q^96 - 3668 * q^97 - 1274 * q^98 + 228 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	2.50000	+	4.33013i	0.481125	+	0.833333i	0.999765	−	0.0216593i	$-0.00689490\pi$
$3$	2.50000	+	4.33013i	0.481125	+	0.833333i	−0.518640	+	0.854993i	$0.673562\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	4.50000	−	7.79423i	0.402492	−	0.697137i	−0.591534	−	0.806280i	$-0.701477\pi$
$5$	4.50000	−	7.79423i	0.402492	−	0.697137i	0.994026	+	0.109143i	$0.0348107\pi$
$6$	−10.0000			−0.680414
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$8$	8.00000			0.353553
$9$	1.00000	−	1.73205i	0.0370370	−	0.0641500i
$10$	9.00000	+	15.5885i	0.284605	+	0.492950i
$11$	28.5000	+	49.3634i	0.781188	+	1.35306i	0.931250	+	0.364381i	$0.118720\pi$
$11$	28.5000	+	49.3634i	0.781188	+	1.35306i	−0.150061	+	0.988677i	$0.547947\pi$
$12$	10.0000	−	17.3205i	0.240563	−	0.416667i
$13$	−70.0000			−1.49342			−0.746712	−	0.665148i	$-0.768369\pi$
$13$	−70.0000			−1.49342			−0.746712	+	0.665148i	$0.768369\pi$
$14$	35.0000	−	12.1244i	0.668153	−	0.231455i
$15$	45.0000			0.774597
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−25.5000	−	44.1673i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−25.5000	−	44.1673i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	2.00000	+	3.46410i	0.0261891	+	0.0453609i
$19$	−2.50000	+	4.33013i	−0.0301863	+	0.0522842i	−0.880724	−	0.473630i	$-0.842943\pi$
$19$	−2.50000	+	4.33013i	−0.0301863	+	0.0522842i	0.850538	+	0.525914i	$0.176277\pi$
$20$	−36.0000			−0.402492
$21$	17.5000	−	90.9327i	0.181848	−	0.944911i
$22$	−114.000			−1.10477
$23$	−34.5000	+	59.7558i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−34.5000	+	59.7558i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	20.0000	+	34.6410i	0.170103	+	0.294628i
$25$	22.0000	+	38.1051i	0.176000	+	0.304841i
$26$	70.0000	−	121.244i	0.528005	−	0.914531i
$27$	145.000			1.03353
$28$	−14.0000	+	72.7461i	−0.0944911	+	0.490990i
$29$	114.000			0.729975			0.364987	−	0.931012i	$-0.381073\pi$
$29$	114.000			0.729975			0.364987	+	0.931012i	$0.381073\pi$
$30$	−45.0000	+	77.9423i	−0.273861	+	0.474342i
$31$	−11.5000	−	19.9186i	−0.0666278	−	0.115403i	0.830787	−	0.556590i	$-0.187891\pi$
$31$	−11.5000	−	19.9186i	−0.0666278	−	0.115403i	−0.897415	+	0.441188i	$0.854557\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−142.500	+	246.817i	−0.751699	+	1.30198i
$34$	102.000			0.514496
$35$	−157.500	+	54.5596i	−0.760639	+	0.263493i
$36$	−8.00000			−0.0370370
$37$	126.500	−	219.104i	0.562067	−	0.973528i	−0.435249	−	0.900310i	$-0.643340\pi$
$37$	126.500	−	219.104i	0.562067	−	0.973528i	0.997316	−	0.0732182i	$-0.0233270\pi$
$38$	−5.00000	−	8.66025i	−0.0213449	−	0.0369705i
$39$	−175.000	−	303.109i	−0.718524	−	1.24452i
$40$	36.0000	−	62.3538i	0.142302	−	0.246475i
$41$	−42.0000			−0.159983			−0.0799914	−	0.996796i	$-0.525489\pi$
$41$	−42.0000			−0.159983			−0.0799914	+	0.996796i	$0.525489\pi$
$42$	140.000	+	121.244i	0.514344	+	0.445435i
$43$	−124.000			−0.439763			−0.219882	−	0.975527i	$-0.570567\pi$
$43$	−124.000			−0.439763			−0.219882	+	0.975527i	$0.570567\pi$
$44$	114.000	−	197.454i	0.390594	−	0.676529i
$45$	−9.00000	−	15.5885i	−0.0298142	−	0.0516398i
$46$	−69.0000	−	119.512i	−0.221163	−	0.383065i
$47$	−100.500	+	174.071i	−0.311903	+	0.540231i	−0.978774	−	0.204941i	$-0.934300\pi$
$47$	−100.500	+	174.071i	−0.311903	+	0.540231i	0.666871	+	0.745173i	$0.267633\pi$
$48$	−80.0000			−0.240563
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$	−88.0000			−0.248902
$51$	127.500	−	220.836i	0.350070	−	0.606339i
$52$	140.000	+	242.487i	0.373356	+	0.646671i
$53$	196.500	+	340.348i	0.509271	+	0.882083i	0.999942	+	0.0107383i	$0.00341816\pi$
$53$	196.500	+	340.348i	0.509271	+	0.882083i	−0.490672	+	0.871345i	$0.663249\pi$
$54$	−145.000	+	251.147i	−0.365407	+	0.632904i
$55$	513.000			1.25769
$56$	−112.000	−	96.9948i	−0.267261	−	0.231455i
$57$	−25.0000			−0.0580935
$58$	−114.000	+	197.454i	−0.258085	+	0.447016i
$59$	−109.500	−	189.660i	−0.241622	−	0.418501i	0.719555	−	0.694436i	$-0.244346\pi$
$59$	−109.500	−	189.660i	−0.241622	−	0.418501i	−0.961176	+	0.275935i	$0.911013\pi$
$60$	−90.0000	−	155.885i	−0.193649	−	0.335410i
$61$	354.500	−	614.012i	0.744083	−	1.28879i	−0.206539	−	0.978438i	$-0.566220\pi$
$61$	354.500	−	614.012i	0.744083	−	1.28879i	0.950622	−	0.310351i	$-0.100447\pi$
$62$	46.0000			0.0942259
$63$	−35.0000	+	12.1244i	−0.0699934	+	0.0242464i
$64$	64.0000			0.125000
$65$	−315.000	+	545.596i	−0.601091	+	1.04112i
$66$	−285.000	−	493.634i	−0.531531	−	0.920639i
$67$	−209.500	−	362.865i	−0.382007	−	0.661656i	0.609342	−	0.792908i	$-0.291434\pi$
$67$	−209.500	−	362.865i	−0.382007	−	0.661656i	−0.991349	+	0.131251i	$0.958100\pi$
$68$	−102.000	+	176.669i	−0.181902	+	0.315063i
$69$	−345.000			−0.601929
$70$	63.0000	−	327.358i	0.107571	−	0.558953i
$71$	−96.0000			−0.160466			−0.0802331	−	0.996776i	$-0.525566\pi$
$71$	−96.0000			−0.160466			−0.0802331	+	0.996776i	$0.525566\pi$
$72$	8.00000	−	13.8564i	0.0130946	−	0.0226805i
$73$	156.500	+	271.066i	0.250917	+	0.434601i	0.963779	−	0.266704i	$-0.0859346\pi$
$73$	156.500	+	271.066i	0.250917	+	0.434601i	−0.712862	+	0.701305i	$0.752601\pi$
$74$	253.000	+	438.209i	0.397441	+	0.688388i
$75$	−110.000	+	190.526i	−0.169356	+	0.293333i
$76$	20.0000			0.0301863
$77$	199.500	−	1036.63i	0.295261	−	1.53422i
$78$	700.000			1.01615
$79$	−230.500	+	399.238i	−0.328269	+	0.568579i	−0.982169	−	0.188003i	$-0.939799\pi$
$79$	−230.500	+	399.238i	−0.328269	+	0.568579i	0.653899	+	0.756582i	$0.273132\pi$
$80$	72.0000	+	124.708i	0.100623	+	0.174284i
$81$	335.500	+	581.103i	0.460219	+	0.797124i
$82$	42.0000	−	72.7461i	0.0565625	−	0.0979691i
$83$	−588.000			−0.777607			−0.388804	−	0.921321i	$-0.627112\pi$
$83$	−588.000			−0.777607			−0.388804	+	0.921321i	$0.627112\pi$
$84$	−350.000	+	121.244i	−0.454621	+	0.157485i
$85$	−459.000			−0.585712
$86$	124.000	−	214.774i	0.155480	−	0.269299i
$87$	285.000	+	493.634i	0.351209	+	0.608312i
$88$	228.000	+	394.908i	0.276192	+	0.478378i
$89$	508.500	−	880.748i	0.605628	−	1.04898i	−0.386324	−	0.922363i	$-0.626255\pi$
$89$	508.500	−	880.748i	0.605628	−	1.04898i	0.991952	−	0.126615i	$-0.0404114\pi$
$90$	36.0000			0.0421637
$91$	980.000	+	848.705i	1.12892	+	0.977675i
$92$	276.000			0.312772
$93$	57.5000	−	99.5929i	0.0641126	−	0.111046i
$94$	−201.000	−	348.142i	−0.220549	−	0.382001i
$95$	22.5000	+	38.9711i	0.0242995	+	0.0420879i
$96$	80.0000	−	138.564i	0.0850517	−	0.147314i
$97$	−1834.00			−1.91974			−0.959868	−	0.280451i	$-0.909516\pi$
$97$	−1834.00			−1.91974			−0.959868	+	0.280451i	$0.909516\pi$
$98$	−637.000	−	254.611i	−0.656599	−	0.262445i
$99$	114.000			0.115732
$100$	88.0000	−	152.420i	0.0880000	−	0.152420i
$101$	142.500	+	246.817i	0.140389	+	0.243161i	0.927643	−	0.373468i	$-0.121831\pi$
$101$	142.500	+	246.817i	0.140389	+	0.243161i	−0.787254	+	0.616629i	$0.788498\pi$
$102$	255.000	+	441.673i	0.247537	+	0.428746i
$103$	249.500	−	432.147i	0.238679	−	0.413405i	−0.721656	−	0.692252i	$-0.756619\pi$
$103$	249.500	−	432.147i	0.238679	−	0.413405i	0.960336	+	0.278847i	$0.0899522\pi$
$104$	−560.000			−0.528005
$105$	−630.000	−	545.596i	−0.585540	−	0.507093i
$106$	−786.000			−0.720218
$107$	553.500	−	958.690i	0.500083	−	0.866169i	−0.499917	−	0.866073i	$-0.666636\pi$
$107$	553.500	−	958.690i	0.500083	−	0.866169i	1.00000		9.56665e-5i	$-3.04516e-5\pi$
$108$	−290.000	−	502.295i	−0.258382	−	0.447531i
$109$	−461.500	−	799.341i	−0.405538	−	0.702413i	0.588846	−	0.808246i	$-0.299583\pi$
$109$	−461.500	−	799.341i	−0.405538	−	0.702413i	−0.994384	+	0.105832i	$0.966249\pi$
$110$	−513.000	+	888.542i	−0.444660	+	0.770174i
$111$	1265.00			1.08170
$112$	280.000	−	96.9948i	0.236228	−	0.0818317i
$113$	1542.00			1.28371			0.641855	−	0.766826i	$-0.278165\pi$
$113$	1542.00			1.28371			0.641855	+	0.766826i	$0.278165\pi$
$114$	25.0000	−	43.3013i	0.0205392	−	0.0355749i
$115$	310.500	+	537.802i	0.251776	+	0.436089i
$116$	−228.000	−	394.908i	−0.182494	−	0.316088i
$117$	−70.0000	+	121.244i	−0.0553120	+	0.0958032i
$118$	438.000			0.341705
$119$	−178.500	+	927.513i	−0.137505	+	0.714496i
$120$	360.000			0.273861
$121$	−959.000	+	1661.04i	−0.720511	+	1.24796i
$122$	709.000	+	1228.02i	0.526146	+	0.911312i
$123$	−105.000	−	181.865i	−0.0769718	−	0.133319i
$124$	−46.0000	+	79.6743i	−0.0333139	+	0.0577013i
$125$	1521.00			1.08834
$126$	14.0000	−	72.7461i	0.00989856	−	0.0514344i
$127$	−2056.00			−1.43654			−0.718270	−	0.695765i	$-0.755066\pi$
$127$	−2056.00			−1.43654			−0.718270	+	0.695765i	$0.755066\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−310.000	−	536.936i	−0.211581	−	0.366469i
$130$	−630.000	−	1091.19i	−0.425036	−	0.736184i
$131$	−1024.50	+	1774.49i	−0.683290	+	1.18349i	0.290681	+	0.956820i	$0.406118\pi$
$131$	−1024.50	+	1774.49i	−0.683290	+	1.18349i	−0.973971	+	0.226673i	$0.927215\pi$
$132$	1140.00			0.751699
$133$	87.5000	−	30.3109i	0.0570467	−	0.0197616i
$134$	838.000			0.540240
$135$	652.500	−	1130.16i	0.415987	−	0.720511i
$136$	−204.000	−	353.338i	−0.128624	−	0.222783i
$137$	70.5000	+	122.110i	0.0439651	+	0.0761498i	0.887171	−	0.461442i	$-0.152668\pi$
$137$	70.5000	+	122.110i	0.0439651	+	0.0761498i	−0.843205	+	0.537591i	$0.819334\pi$
$138$	345.000	−	597.558i	0.212814	−	0.368605i
$139$	1484.00			0.905548			0.452774	−	0.891625i	$-0.350434\pi$
$139$	1484.00			0.905548			0.452774	+	0.891625i	$0.350434\pi$
$140$	504.000	+	436.477i	0.304256	+	0.263493i
$141$	−1005.00			−0.600257
$142$	96.0000	−	166.277i	0.0567334	−	0.0982651i
$143$	−1995.00	−	3455.44i	−1.16665	−	2.02069i
$144$	16.0000	+	27.7128i	0.00925926	+	0.0160375i
$145$	513.000	−	888.542i	0.293809	−	0.508892i
$146$	−626.000			−0.354850
$147$	−1347.50	+	1060.88i	−0.756054	+	0.595238i
$148$	−1012.00			−0.562067
$149$	28.5000	−	49.3634i	0.0156699	−	0.0271410i	−0.858084	−	0.513509i	$-0.828345\pi$
$149$	28.5000	−	49.3634i	0.0156699	−	0.0271410i	0.873754	+	0.486368i	$0.161679\pi$
$150$	−220.000	−	381.051i	−0.119753	−	0.207418i
$151$	−419.500	−	726.595i	−0.226082	−	0.391586i	0.730561	−	0.682847i	$-0.239258\pi$
$151$	−419.500	−	726.595i	−0.226082	−	0.391586i	−0.956644	+	0.291261i	$0.905925\pi$
$152$	−20.0000	+	34.6410i	−0.0106725	+	0.0184852i
$153$	−102.000			−0.0538968
$154$	1596.00	+	1382.18i	0.835126	+	0.723240i
$155$	−207.000			−0.107269
$156$	−700.000	+	1212.44i	−0.359262	+	0.622260i
$157$	1416.50	+	2453.45i	0.720057	+	1.24718i	0.960976	+	0.276631i	$0.0892179\pi$
$157$	1416.50	+	2453.45i	0.720057	+	1.24718i	−0.240919	+	0.970545i	$0.577449\pi$
$158$	−461.000	−	798.475i	−0.232121	−	0.402046i
$159$	−982.500	+	1701.74i	−0.490046	+	0.848785i
$160$	−288.000			−0.142302
$161$	1207.50	−	418.290i	0.591083	−	0.204757i
$162$	−1342.00			−0.650849
$163$	1155.50	−	2001.38i	0.555250	−	0.961721i	−0.442634	−	0.896702i	$-0.645956\pi$
$163$	1155.50	−	2001.38i	0.555250	−	0.961721i	0.997884	−	0.0650188i	$-0.0207107\pi$
$164$	84.0000	+	145.492i	0.0399957	+	0.0692746i
$165$	1282.50	+	2221.36i	0.605106	+	1.04807i
$166$	588.000	−	1018.45i	0.274926	−	0.476185i
$167$	1260.00			0.583843			0.291921	−	0.956442i	$-0.405705\pi$
$167$	1260.00			0.583843			0.291921	+	0.956442i	$0.405705\pi$
$168$	140.000	−	727.461i	0.0642931	−	0.334077i
$169$	2703.00			1.23031
$170$	459.000	−	795.011i	0.207081	−	0.358674i
$171$	5.00000	+	8.66025i	0.00223602	+	0.00387290i
$172$	248.000	+	429.549i	0.109941	+	0.190423i
$173$	−1633.50	+	2829.30i	−0.717877	+	1.24340i	0.243962	+	0.969785i	$0.421553\pi$
$173$	−1633.50	+	2829.30i	−0.717877	+	1.24340i	−0.961839	+	0.273615i	$0.911781\pi$
$174$	−1140.00			−0.496685
$175$	154.000	−	800.207i	0.0665217	−	0.345657i
$176$	−912.000			−0.390594
$177$	547.500	−	948.298i	0.232501	−	0.402703i
$178$	1017.00	+	1761.50i	0.428244	+	0.741740i
$179$	−643.500	−	1114.57i	−0.268701	−	0.465403i	0.699826	−	0.714314i	$-0.253261\pi$
$179$	−643.500	−	1114.57i	−0.268701	−	0.465403i	−0.968527	+	0.248910i	$0.919928\pi$
$180$	−36.0000	+	62.3538i	−0.0149071	+	0.0258199i
$181$	−2674.00			−1.09810			−0.549052	−	0.835788i	$-0.685011\pi$
$181$	−2674.00			−1.09810			−0.549052	+	0.835788i	$0.685011\pi$
$182$	−2450.00	+	848.705i	−0.997836	+	0.345660i
$183$	3545.00			1.43199
$184$	−276.000	+	478.046i	−0.110581	+	0.191533i
$185$	−1138.50	−	1971.94i	−0.452455	−	0.783675i
$186$	115.000	+	199.186i	0.0453345	+	0.0785216i
$187$	1453.50	−	2517.54i	0.568398	−	0.984494i
$188$	804.000			0.311903
$189$	−2030.00	−	1758.03i	−0.781274	−	0.676603i
$190$	−90.0000			−0.0343647
$191$	−2092.50	+	3624.32i	−0.792712	+	1.37302i	0.131570	+	0.991307i	$0.457998\pi$
$191$	−2092.50	+	3624.32i	−0.792712	+	1.37302i	−0.924282	+	0.381711i	$0.875335\pi$
$192$	160.000	+	277.128i	0.0601407	+	0.104167i
$193$	42.5000	+	73.6122i	0.0158509	+	0.0274545i	0.873842	−	0.486210i	$-0.161621\pi$
$193$	42.5000	+	73.6122i	0.0158509	+	0.0274545i	−0.857991	+	0.513664i	$0.828288\pi$
$194$	1834.00	−	3176.58i	0.678730	−	1.17559i
$195$	−3150.00			−1.15680
$196$	1078.00	−	848.705i	0.392857	−	0.309295i
$197$	−390.000			−0.141047			−0.0705237	−	0.997510i	$-0.522467\pi$
$197$	−390.000			−0.141047			−0.0705237	+	0.997510i	$0.522467\pi$
$198$	−114.000	+	197.454i	−0.0409173	+	0.0708709i
$199$	1416.50	+	2453.45i	0.504588	+	0.873972i	0.999986	+	0.00530596i	$0.00168895\pi$
$199$	1416.50	+	2453.45i	0.504588	+	0.873972i	−0.495398	+	0.868666i	$0.664978\pi$
$200$	176.000	+	304.841i	0.0622254	+	0.107778i
$201$	1047.50	−	1814.32i	0.367587	−	0.636679i
$202$	−570.000			−0.198540
$203$	−1596.00	−	1382.18i	−0.551809	−	0.477881i
$204$	−1020.00			−0.350070
$205$	−189.000	+	327.358i	−0.0643919	+	0.111530i
$206$	499.000	+	864.293i	0.168772	+	0.292321i
$207$	69.0000	+	119.512i	0.0231683	+	0.0401286i
$208$	560.000	−	969.948i	0.186678	−	0.323336i
$209$	−285.000			−0.0943247
$210$	1575.00	−	545.596i	0.517549	−	0.179284i
$211$	−124.000			−0.0404574			−0.0202287	−	0.999795i	$-0.506439\pi$
$211$	−124.000			−0.0404574			−0.0202287	+	0.999795i	$0.506439\pi$
$212$	786.000	−	1361.39i	0.254635	−	0.441041i
$213$	−240.000	−	415.692i	−0.0772044	−	0.133722i
$214$	1107.00	+	1917.38i	0.353612	+	0.612474i
$215$	−558.000	+	966.484i	−0.177001	+	0.306575i
$216$	1160.00			0.365407
$217$	−80.5000	+	418.290i	−0.0251829	+	0.130854i
$218$	1846.00			0.573518
$219$	−782.500	+	1355.33i	−0.241445	+	0.418195i
$220$	−1026.00	−	1777.08i	−0.314422	−	0.544595i
$221$	1785.00	+	3091.71i	0.543313	+	0.941045i
$222$	−1265.00	+	2191.04i	−0.382438	+	0.662402i
$223$	56.0000			0.0168163			0.00840816	−	0.999965i	$-0.497324\pi$
$223$	56.0000			0.0168163			0.00840816	+	0.999965i	$0.497324\pi$
$224$	−112.000	+	581.969i	−0.0334077	+	0.173591i
$225$	88.0000			0.0260741
$226$	−1542.00	+	2670.82i	−0.453860	+	0.786108i
$227$	1528.50	+	2647.44i	0.446917	+	0.774083i	0.998184	−	0.0602465i	$-0.0191887\pi$
$227$	1528.50	+	2647.44i	0.446917	+	0.774083i	−0.551267	+	0.834329i	$0.685855\pi$
$228$	50.0000	+	86.6025i	0.0145234	+	0.0251552i
$229$	480.500	−	832.250i	0.138656	−	0.240160i	−0.788332	−	0.615250i	$-0.789055\pi$
$229$	480.500	−	832.250i	0.138656	−	0.240160i	0.926988	+	0.375090i	$0.122388\pi$
$230$	−1242.00			−0.356065
$231$	4987.50	−	1727.72i	1.42058	−	0.492102i
$232$	912.000			0.258085
$233$	1414.50	−	2449.99i	0.397712	−	0.688858i	−0.595731	−	0.803184i	$-0.703138\pi$
$233$	1414.50	−	2449.99i	0.397712	−	0.688858i	0.993443	+	0.114326i	$0.0364709\pi$
$234$	−140.000	−	242.487i	−0.0391115	−	0.0677431i
$235$	904.500	+	1566.64i	0.251077	+	0.434878i
$236$	−438.000	+	758.638i	−0.120811	+	0.209251i
$237$	−2305.00			−0.631755
$238$	−1428.00	−	1236.68i	−0.388922	−	0.336817i
$239$	−3540.00			−0.958090			−0.479045	−	0.877790i	$-0.659017\pi$
$239$	−3540.00			−0.958090			−0.479045	+	0.877790i	$0.659017\pi$
$240$	−360.000	+	623.538i	−0.0968246	+	0.167705i
$241$	−2615.50	−	4530.18i	−0.699084	−	1.21085i	−0.968785	−	0.247904i	$-0.920258\pi$
$241$	−2615.50	−	4530.18i	−0.699084	−	1.21085i	0.269701	−	0.962944i	$-0.413075\pi$
$242$	−1918.00	−	3322.07i	−0.509478	−	0.882442i
$243$	280.000	−	484.974i	0.0739177	−	0.128029i
$244$	−2836.00			−0.744083
$245$	2866.50	+	1145.75i	0.747486	+	0.298773i
$246$	420.000			0.108855
$247$	175.000	−	303.109i	0.0450809	−	0.0780824i
$248$	−92.0000	−	159.349i	−0.0235565	−	0.0408010i
$249$	−1470.00	−	2546.11i	−0.374126	−	0.648006i
$250$	−1521.00	+	2634.45i	−0.384786	+	0.666469i
$251$	5040.00			1.26742			0.633709	−	0.773571i	$-0.281532\pi$
$251$	5040.00			1.26742			0.633709	+	0.773571i	$0.281532\pi$
$252$	112.000	+	96.9948i	0.0279974	+	0.0242464i
$253$	−3933.00			−0.977334
$254$	2056.00	−	3561.10i	0.507893	−	0.879697i
$255$	−1147.50	−	1987.53i	−0.281801	−	0.488094i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	718.500	−	1244.48i	0.174392	−	0.302056i	−0.765559	−	0.643366i	$-0.777537\pi$
$257$	718.500	−	1244.48i	0.174392	−	0.302056i	0.939951	+	0.341310i	$0.110871\pi$
$258$	1240.00			0.299221
$259$	−4427.50	+	1533.73i	−1.06221	+	0.367959i
$260$	2520.00			0.601091
$261$	114.000	−	197.454i	0.0270361	−	0.0468279i
$262$	−2049.00	−	3548.97i	−0.483159	−	0.836856i
$263$	1162.50	+	2013.51i	0.272558	+	0.472085i	0.969516	−	0.245027i	$-0.0787969\pi$
$263$	1162.50	+	2013.51i	0.272558	+	0.472085i	−0.696958	+	0.717112i	$0.745464\pi$
$264$	−1140.00	+	1974.54i	−0.265766	+	0.460320i
$265$	3537.00			0.819910
$266$	−35.0000	+	181.865i	−0.00806762	+	0.0419206i
$267$	5085.00			1.16553
$268$	−838.000	+	1451.46i	−0.191004	+	0.330828i
$269$	1192.50	+	2065.47i	0.270290	+	0.468156i	0.968936	−	0.247311i	$-0.0795471\pi$
$269$	1192.50	+	2065.47i	0.270290	+	0.468156i	−0.698646	+	0.715467i	$0.746214\pi$
$270$	1305.00	+	2260.33i	0.294147	+	0.509478i
$271$	165.500	−	286.654i	0.0370975	−	0.0642547i	−0.846881	−	0.531783i	$-0.821522\pi$
$271$	165.500	−	286.654i	0.0370975	−	0.0642547i	0.883978	+	0.467528i	$0.154855\pi$
$272$	816.000			0.181902
$273$	−1225.00	+	6365.29i	−0.271576	+	1.41115i
$274$	−282.000			−0.0621761
$275$	−1254.00	+	2171.99i	−0.274978	+	0.476276i
$276$	690.000	+	1195.12i	0.150482	+	0.260643i
$277$	−2435.50	−	4218.41i	−0.528285	−	0.915017i	−0.999456	−	0.0329750i	$-0.989502\pi$
$277$	−2435.50	−	4218.41i	−0.528285	−	0.915017i	0.471171	−	0.882042i	$-0.343831\pi$
$278$	−1484.00	+	2570.36i	−0.320160	+	0.554533i
$279$	−46.0000			−0.00987078
$280$	−1260.00	+	436.477i	−0.268926	+	0.0931589i
$281$	−7026.00			−1.49159			−0.745794	−	0.666177i	$-0.767930\pi$
$281$	−7026.00			−1.49159			−0.745794	+	0.666177i	$0.767930\pi$
$282$	1005.00	−	1740.71i	0.212223	−	0.367581i
$283$	2676.50	+	4635.83i	0.562196	+	0.973752i	0.997305	+	0.0733738i	$0.0233766\pi$
$283$	2676.50	+	4635.83i	0.562196	+	0.973752i	−0.435109	+	0.900378i	$0.643290\pi$
$284$	192.000	+	332.554i	0.0401166	+	0.0694839i
$285$	−112.500	+	194.856i	−0.0233822	+	0.0404991i
$286$	7980.00			1.64989
$287$	588.000	+	509.223i	0.120936	+	0.104733i
$288$	−64.0000			−0.0130946
$289$	1156.00	−	2002.25i	0.235294	−	0.407541i
$290$	1026.00	+	1777.08i	0.207754	+	0.359841i
$291$	−4585.00	−	7941.45i	−0.923634	−	1.59978i
$292$	626.000	−	1084.26i	0.125458	−	0.217300i
$293$	4158.00			0.829054			0.414527	−	0.910037i	$-0.363947\pi$
$293$	4158.00			0.829054			0.414527	+	0.910037i	$0.363947\pi$
$294$	−490.000	−	3394.82i	−0.0972020	−	0.673435i
$295$	−1971.00			−0.389004
$296$	1012.00	−	1752.84i	0.198721	−	0.344194i
$297$	4132.50	+	7157.70i	0.807380	+	1.39842i
$298$	57.0000	+	98.7269i	0.0110803	+	0.0191916i
$299$	2415.00	−	4182.90i	0.467101	−	0.809042i
$300$	880.000			0.169356
$301$	1736.00	+	1503.42i	0.332430	+	0.287893i
$302$	1678.00			0.319729
$303$	−712.500	+	1234.09i	−0.135089	+	0.233982i
$304$	−40.0000	−	69.2820i	−0.00754657	−	0.0130710i
$305$	−3190.50	−	5526.11i	−0.598975	−	1.03746i
$306$	102.000	−	176.669i	0.0190554	−	0.0330049i
$307$	−9604.00			−1.78544			−0.892719	−	0.450615i	$-0.851205\pi$
$307$	−9604.00			−1.78544			−0.892719	+	0.450615i	$0.851205\pi$
$308$	−3990.00	+	1382.18i	−0.738154	+	0.255704i
$309$	2495.00			0.459338
$310$	207.000	−	358.535i	0.0379252	−	0.0656884i
$311$	−5065.50	−	8773.70i	−0.923595	−	1.59971i	−0.793805	−	0.608173i	$-0.791903\pi$
$311$	−5065.50	−	8773.70i	−0.923595	−	1.59971i	−0.129791	−	0.991541i	$-0.541430\pi$
$312$	−1400.00	−	2424.87i	−0.254037	−	0.440004i
$313$	−5399.50	+	9352.21i	−0.975073	+	1.68888i	−0.295378	+	0.955380i	$0.595446\pi$
$313$	−5399.50	+	9352.21i	−0.975073	+	1.68888i	−0.679695	+	0.733495i	$0.737888\pi$
$314$	−5666.00			−1.01831
$315$	−63.0000	+	327.358i	−0.0112687	+	0.0585540i
$316$	1844.00			0.328269
$317$	−265.500	+	459.859i	−0.0470409	+	0.0814772i	−0.888587	−	0.458708i	$-0.848312\pi$
$317$	−265.500	+	459.859i	−0.0470409	+	0.0814772i	0.841546	+	0.540185i	$0.181646\pi$
$318$	−1965.00	−	3403.48i	−0.346515	−	0.600181i
$319$	3249.00	+	5627.43i	0.570248	+	0.987698i
$320$	288.000	−	498.831i	0.0503115	−	0.0871421i
$321$	5535.00			0.962410
$322$	−483.000	+	2509.74i	−0.0835917	+	0.434355i
$323$	255.000			0.0439275
$324$	1342.00	−	2324.41i	0.230110	−	0.398562i
$325$	−1540.00	−	2667.36i	−0.262843	−	0.455257i
$326$	2311.00	+	4002.77i	0.392621	+	0.680040i
$327$	2307.50	−	3996.71i	0.390229	−	0.675897i
$328$	−336.000			−0.0565625
$329$	3517.50	−	1218.50i	0.589441	−	0.204188i
$330$	−5130.00			−0.855749
$331$	3507.50	−	6075.17i	0.582446	−	1.00883i	−0.412743	−	0.910848i	$-0.635429\pi$
$331$	3507.50	−	6075.17i	0.582446	−	1.00883i	0.995189	−	0.0979784i	$-0.0312376\pi$
$332$	1176.00	+	2036.89i	0.194402	+	0.336714i
$333$	−253.000	−	438.209i	−0.0416346	−	0.0721132i
$334$	−1260.00	+	2182.38i	−0.206420	+	0.357529i
$335$	−3771.00			−0.615020
$336$	1120.00	+	969.948i	0.181848	+	0.157485i
$337$	8990.00			1.45316			0.726582	−	0.687079i	$-0.241108\pi$
$337$	8990.00			1.45316			0.726582	+	0.687079i	$0.241108\pi$
$338$	−2703.00	+	4681.73i	−0.434982	+	0.753410i
$339$	3855.00	+	6677.06i	0.617625	+	1.06976i
$340$	918.000	+	1590.02i	0.146428	+	0.253621i
$341$	655.500	−	1135.36i	0.104098	−	0.180303i
$342$	−20.0000			−0.00316221
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	−992.000			−0.155480
$345$	−1552.50	+	2689.01i	−0.242272	+	0.419627i
$346$	−3267.00	−	5658.61i	−0.507616	−	0.879216i
$347$	4354.50	+	7542.22i	0.673665	+	1.16682i	0.976857	+	0.213893i	$0.0686143\pi$
$347$	4354.50	+	7542.22i	0.673665	+	1.16682i	−0.303192	+	0.952929i	$0.598052\pi$
$348$	1140.00	−	1974.54i	0.175605	−	0.304156i
$349$	6482.00			0.994193			0.497097	−	0.867695i	$-0.334399\pi$
$349$	6482.00			0.994193			0.497097	+	0.867695i	$0.334399\pi$
$350$	1232.00	+	1066.94i	0.188152	+	0.162944i
$351$	−10150.0			−1.54350
$352$	912.000	−	1579.63i	0.138096	−	0.239189i
$353$	1066.50	+	1847.23i	0.160805	+	0.278522i	0.935158	−	0.354232i	$-0.115258\pi$
$353$	1066.50	+	1847.23i	0.160805	+	0.278522i	−0.774353	+	0.632754i	$0.781924\pi$
$354$	1095.00	+	1896.60i	0.164403	+	0.284754i
$355$	−432.000	+	748.246i	−0.0645864	+	0.111867i
$356$	−4068.00			−0.605628
$357$	−4462.50	+	1545.86i	−0.661570	+	0.229175i
$358$	2574.00			0.380000
$359$	−1924.50	+	3333.33i	−0.282928	+	0.490046i	−0.972105	−	0.234548i	$-0.924639\pi$
$359$	−1924.50	+	3333.33i	−0.282928	+	0.490046i	0.689176	+	0.724594i	$0.257972\pi$
$360$	−72.0000	−	124.708i	−0.0105409	−	0.0182574i
$361$	3417.00	+	5918.42i	0.498178	+	0.862869i
$362$	2674.00	−	4631.50i	0.388238	−	0.672449i
$363$	−9590.00			−1.38662
$364$	980.000	−	5092.23i	0.141115	−	0.733256i
$365$	2817.00			0.403969
$366$	−3545.00	+	6140.12i	−0.506284	+	0.876910i
$367$	−3245.50	−	5621.37i	−0.461618	−	0.799545i	0.537424	−	0.843312i	$-0.319397\pi$
$367$	−3245.50	−	5621.37i	−0.461618	−	0.799545i	−0.999042	+	0.0437668i	$0.986064\pi$
$368$	−552.000	−	956.092i	−0.0781929	−	0.135434i
$369$	−42.0000	+	72.7461i	−0.00592529	+	0.0102629i
$370$	4554.00			0.639868
$371$	1375.50	−	7147.31i	0.192486	−	1.00019i
$372$	−460.000			−0.0641126
$373$	−461.500	+	799.341i	−0.0640632	+	0.110961i	−0.896278	−	0.443493i	$-0.853739\pi$
$373$	−461.500	+	799.341i	−0.0640632	+	0.110961i	0.832215	+	0.554453i	$0.187073\pi$
$374$	2907.00	+	5035.07i	0.401918	+	0.696143i
$375$	3802.50	+	6586.12i	0.523627	+	0.906949i
$376$	−804.000	+	1392.57i	−0.110274	+	0.191001i
$377$	−7980.00			−1.09016
$378$	5075.00	−	1758.03i	0.690555	−	0.239215i
$379$	6344.00			0.859814			0.429907	−	0.902873i	$-0.358546\pi$
$379$	6344.00			0.859814			0.429907	+	0.902873i	$0.358546\pi$
$380$	90.0000	−	155.885i	0.0121497	−	0.0210440i
$381$	−5140.00	−	8902.74i	−0.691155	−	1.19712i
$382$	−4185.00	−	7248.63i	−0.560532	−	0.970870i
$383$	2503.50	−	4336.19i	0.334002	−	0.578509i	−0.649290	−	0.760541i	$-0.724934\pi$
$383$	2503.50	−	4336.19i	0.334002	−	0.578509i	0.983293	+	0.182032i	$0.0582673\pi$
$384$	−640.000			−0.0850517
$385$	−7182.00	−	6219.79i	−0.950724	−	0.823351i
$386$	−170.000			−0.0224165
$387$	−124.000	+	214.774i	−0.0162875	+	0.0282108i
$388$	3668.00	+	6353.16i	0.479934	+	0.831270i
$389$	−6145.50	−	10644.3i	−0.801001	−	1.38737i	−0.918958	−	0.394355i	$-0.870968\pi$
$389$	−6145.50	−	10644.3i	−0.801001	−	1.38737i	0.117958	−	0.993019i	$-0.462365\pi$
$390$	3150.00	−	5455.96i	0.408991	−	0.708393i
$391$	3519.00			0.455150
$392$	392.000	+	2715.86i	0.0505076	+	0.349927i
$393$	−10245.0			−1.31499
$394$	390.000	−	675.500i	0.0498678	−	0.0863736i
$395$	2074.50	+	3593.14i	0.264252	+	0.457697i
$396$	−228.000	−	394.908i	−0.0289329	−	0.0501133i
$397$	−443.500	+	768.165i	−0.0560671	+	0.0971110i	−0.892697	−	0.450658i	$-0.851189\pi$
$397$	−443.500	+	768.165i	−0.0560671	+	0.0971110i	0.836630	+	0.547769i	$0.184523\pi$
$398$	−5666.00			−0.713595
$399$	350.000	+	303.109i	0.0439146	+	0.0380311i
$400$	−704.000			−0.0880000
$401$	−5977.50	+	10353.3i	−0.744394	+	1.28933i	0.206083	+	0.978535i	$0.433928\pi$
$401$	−5977.50	+	10353.3i	−0.744394	+	1.28933i	−0.950477	+	0.310794i	$0.899405\pi$
$402$	2095.00	+	3628.65i	0.259923	+	0.450200i
$403$	805.000	+	1394.30i	0.0995035	+	0.172345i
$404$	570.000	−	987.269i	0.0701945	−	0.121580i
$405$	6039.00			0.740939
$406$	3990.00	−	1382.18i	0.487735	−	0.168956i
$407$	14421.0			1.75632
$408$	1020.00	−	1766.69i	0.123768	−	0.214373i
$409$	1710.50	+	2962.67i	0.206794	+	0.358178i	0.950703	−	0.310103i	$-0.100364\pi$
$409$	1710.50	+	2962.67i	0.206794	+	0.358178i	−0.743909	+	0.668281i	$0.767030\pi$
$410$	−378.000	−	654.715i	−0.0455319	−	0.0788636i
$411$	−352.500	+	610.548i	−0.0423055	+	0.0732752i
$412$	−1996.00			−0.238679
$413$	−766.500	+	3982.85i	−0.0913245	+	0.474536i
$414$	−276.000			−0.0327649
$415$	−2646.00	+	4583.01i	−0.312981	+	0.542099i
$416$	1120.00	+	1939.90i	0.132001	+	0.228633i
$417$	3710.00	+	6425.91i	0.435682	+	0.754624i
$418$	285.000	−	493.634i	0.0333488	−	0.0577618i
$419$	−5460.00			−0.636607			−0.318304	−	0.947989i	$-0.603113\pi$
$419$	−5460.00			−0.636607			−0.318304	+	0.947989i	$0.603113\pi$
$420$	−630.000	+	3273.58i	−0.0731925	+	0.380319i
$421$	7730.00			0.894863			0.447431	−	0.894318i	$-0.352339\pi$
$421$	7730.00			0.894863			0.447431	+	0.894318i	$0.352339\pi$
$422$	124.000	−	214.774i	0.0143039	−	0.0247750i
$423$	201.000	+	348.142i	0.0231039	+	0.0400171i
$424$	1572.00	+	2722.78i	0.180054	+	0.311863i
$425$	1122.00	−	1943.36i	0.128059	−	0.221804i
$426$	960.000			0.109183
$427$	−12407.5	+	4298.08i	−1.40619	+	0.487117i
$428$	−4428.00			−0.500083
$429$	9975.00	−	17277.2i	1.12260	−	1.94441i
$430$	−1116.00	−	1932.97i	−0.125159	−	0.216781i
$431$	5656.50	+	9797.35i	0.632167	+	1.09495i	0.987108	+	0.160057i	$0.0511677\pi$
$431$	5656.50	+	9797.35i	0.632167	+	1.09495i	−0.354941	+	0.934889i	$0.615499\pi$
$432$	−1160.00	+	2009.18i	−0.129191	+	0.223765i
$433$	4214.00			0.467695			0.233847	−	0.972273i	$-0.424868\pi$
$433$	4214.00			0.467695			0.233847	+	0.972273i	$0.424868\pi$
$434$	−644.000	−	557.720i	−0.0712281	−	0.0616853i
$435$	5130.00			0.565436
$436$	−1846.00	+	3197.37i	−0.202769	+	0.351207i
$437$	−172.500	−	298.779i	−0.0188828	−	0.0327060i
$438$	−1565.00	−	2710.66i	−0.170727	−	0.295708i
$439$	−8276.50	+	14335.3i	−0.899808	+	1.55851i	−0.0720696	+	0.997400i	$0.522960\pi$
$439$	−8276.50	+	14335.3i	−0.899808	+	1.55851i	−0.827739	+	0.561114i	$0.810373\pi$
$440$	4104.00			0.444660
$441$	637.000	+	254.611i	0.0687831	+	0.0274929i
$442$	−7140.00			−0.768360
$443$	8197.50	−	14198.5i	0.879176	−	1.52278i	0.0269294	−	0.999637i	$-0.491427\pi$
$443$	8197.50	−	14198.5i	0.879176	−	1.52278i	0.852247	−	0.523140i	$-0.175240\pi$
$444$	−2530.00	−	4382.09i	−0.270425	−	0.468389i
$445$	−4576.50	−	7926.73i	−0.487521	−	0.844411i
$446$	−56.0000	+	96.9948i	−0.00594546	+	0.0102978i
$447$	285.000			0.0301567
$448$	−896.000	−	775.959i	−0.0944911	−	0.0818317i
$449$	−15090.0			−1.58606			−0.793030	−	0.609182i	$-0.791498\pi$
$449$	−15090.0			−1.58606			−0.793030	+	0.609182i	$0.791498\pi$
$450$	−88.0000	+	152.420i	−0.00921858	+	0.0159670i
$451$	−1197.00	−	2073.26i	−0.124977	−	0.216466i
$452$	−3084.00	−	5341.64i	−0.320927	−	0.555862i
$453$	2097.50	−	3632.98i	0.217548	−	0.376804i
$454$	−6114.00			−0.632036
$455$	11025.0	−	3819.17i	1.13596	−	0.393507i
$456$	−200.000			−0.0205392
$457$	7392.50	−	12804.2i	0.756688	−	1.31062i	−0.187842	−	0.982199i	$-0.560149\pi$
$457$	7392.50	−	12804.2i	0.756688	−	1.31062i	0.944531	−	0.328423i	$-0.106517\pi$
$458$	961.000	+	1664.50i	0.0980449	+	0.169819i
$459$	−3697.50	−	6404.26i	−0.376001	−	0.651253i
$460$	1242.00	−	2151.21i	0.125888	−	0.218045i
$461$	2898.00			0.292784			0.146392	−	0.989227i	$-0.453234\pi$
$461$	2898.00			0.292784			0.146392	+	0.989227i	$0.453234\pi$
$462$	−1995.00	+	10366.3i	−0.200900	+	1.04391i
$463$	464.000			0.0465743			0.0232872	−	0.999729i	$-0.492587\pi$
$463$	464.000			0.0465743			0.0232872	+	0.999729i	$0.492587\pi$
$464$	−912.000	+	1579.63i	−0.0912468	+	0.158044i
$465$	−517.500	−	896.336i	−0.0516097	−	0.0893905i
$466$	2829.00	+	4899.97i	0.281225	+	0.487096i
$467$	−2116.50	+	3665.89i	−0.209721	+	0.363248i	−0.951627	−	0.307256i	$-0.900589\pi$
$467$	−2116.50	+	3665.89i	−0.209721	+	0.363248i	0.741905	+	0.670505i	$0.233922\pi$
$468$	560.000			0.0553120
$469$	−1466.50	+	7620.16i	−0.144385	+	0.750248i
$470$	−3618.00			−0.355076
$471$	−7082.50	+	12267.2i	−0.692876	+	1.20010i
$472$	−876.000	−	1517.28i	−0.0854262	−	0.147963i
$473$	−3534.00	−	6121.07i	−0.343538	−	0.595025i
$474$	2305.00	−	3992.38i	0.223359	−	0.386869i
$475$	−220.000			−0.0212511
$476$	3570.00	−	1236.68i	0.343762	−	0.119083i
$477$	786.000			0.0754475
$478$	3540.00	−	6131.46i	0.338736	−	0.586708i
$479$	−1369.50	−	2372.04i	−0.130635	−	0.226266i	0.793287	−	0.608848i	$-0.208368\pi$
$479$	−1369.50	−	2372.04i	−0.130635	−	0.226266i	−0.923921	+	0.382582i	$0.875035\pi$
$480$	−720.000	−	1247.08i	−0.0684653	−	0.118585i
$481$	−8855.00	+	15337.3i	−0.839404	+	1.45389i
$482$	10462.0			0.988654
$483$	4830.00	+	4182.90i	0.455016	+	0.394055i
$484$	7672.00			0.720511
$485$	−8253.00	+	14294.6i	−0.772679	+	1.33832i
$486$	560.000	+	969.948i	0.0522677	+	0.0905304i
$487$	−8525.50	−	14766.6i	−0.793280	−	1.37400i	−0.923926	−	0.382572i	$-0.875038\pi$
$487$	−8525.50	−	14766.6i	−0.793280	−	1.37400i	0.130646	−	0.991429i	$-0.458295\pi$
$488$	2836.00	−	4912.10i	0.263073	−	0.455656i
$489$	11555.0			1.06858
$490$	−4851.00	+	3819.17i	−0.447236	+	0.352107i
$491$	−4296.00			−0.394859			−0.197429	−	0.980317i	$-0.563259\pi$
$491$	−4296.00			−0.394859			−0.197429	+	0.980317i	$0.563259\pi$
$492$	−420.000	+	727.461i	−0.0384859	+	0.0666595i
$493$	−2907.00	−	5035.07i	−0.265567	−	0.459976i
$494$	350.000	+	606.218i	0.0318770	+	0.0552126i
$495$	513.000	−	888.542i	0.0465811	−	0.0806808i
$496$	368.000			0.0333139
$497$	1344.00	+	1163.94i	0.121301	+	0.105050i
$498$	5880.00			0.529095
$499$	−1700.50	+	2945.35i	−0.152555	+	0.264233i	−0.932166	−	0.362031i	$-0.882083\pi$
$499$	−1700.50	+	2945.35i	−0.152555	+	0.264233i	0.779611	+	0.626264i	$0.215417\pi$
$500$	−3042.00	−	5268.90i	−0.272085	−	0.471265i
$501$	3150.00	+	5455.96i	0.280901	+	0.486536i
$502$	−5040.00	+	8729.54i	−0.448100	+	0.776132i
$503$	16800.0			1.48921			0.744607	−	0.667503i	$-0.232637\pi$
$503$	16800.0			1.48921			0.744607	+	0.667503i	$0.232637\pi$
$504$	−280.000	+	96.9948i	−0.0247464	+	0.00857241i
$505$	2565.00			0.226022
$506$	3933.00	−	6812.16i	0.345540	−	0.598493i
$507$	6757.50	+	11704.3i	0.591935	+	1.02526i
$508$	4112.00	+	7122.19i	0.359135	+	0.622040i
$509$	−919.500	+	1592.62i	−0.0800710	+	0.138687i	−0.903280	−	0.429051i	$-0.858848\pi$
$509$	−919.500	+	1592.62i	−0.0800710	+	0.138687i	0.823209	+	0.567738i	$0.192181\pi$
$510$	4590.00			0.398527
$511$	1095.50	−	5692.38i	0.0948377	−	0.492791i
$512$	512.000			0.0441942
$513$	−362.500	+	627.868i	−0.0311984	+	0.0540372i
$514$	1437.00	+	2488.96i	0.123314	+	0.213586i
$515$	−2245.50	−	3889.32i	−0.192133	−	0.332784i
$516$	−1240.00	+	2147.74i	−0.105791	+	0.183235i
$517$	−11457.0			−0.974620
$518$	1771.00	−	9202.39i	0.150219	−	0.780559i
$519$	−16335.0			−1.38155
$520$	−2520.00	+	4364.77i	−0.212518	+	0.368092i
$521$	−151.500	−	262.406i	−0.0127396	−	0.0220656i	0.859585	−	0.510992i	$-0.170722\pi$
$521$	−151.500	−	262.406i	−0.0127396	−	0.0220656i	−0.872325	+	0.488927i	$0.837389\pi$
$522$	228.000	+	394.908i	0.0191174	+	0.0331123i
$523$	10833.5	−	18764.2i	0.905767	−	1.56883i	0.0858815	−	0.996305i	$-0.472629\pi$
$523$	10833.5	−	18764.2i	0.905767	−	1.56883i	0.819885	−	0.572528i	$-0.194037\pi$
$524$	8196.00			0.683290
$525$	3850.00	−	1333.68i	0.320053	−	0.110870i
$526$	−4650.00			−0.385456
$527$	−586.500	+	1015.85i	−0.0484788	+	0.0839678i
$528$	−2280.00	−	3949.08i	−0.187925	−	0.325495i
$529$	3703.00	+	6413.78i	0.304348	+	0.527146i
$530$	−3537.00	+	6126.26i	−0.289882	+	0.502090i
$531$	−438.000			−0.0357958
$532$	−280.000	−	242.487i	−0.0228187	−	0.0197616i
$533$	2940.00			0.238922
$534$	−5085.00	+	8807.48i	−0.412078	+	0.713739i
$535$	−4981.50	−	8628.21i	−0.402559	−	0.697253i
$536$	−1676.00	−	2902.92i	−0.135060	−	0.233931i
$537$	3217.50	−	5572.87i	0.258557	−	0.447835i
$538$	−4770.00			−0.382248
$539$	−15361.5	+	12094.0i	−1.22758	+	0.966470i
$540$	−5220.00			−0.415987
$541$	−2519.50	+	4363.90i	−0.200225	+	0.346800i	−0.948601	−	0.316475i	$-0.897501\pi$
$541$	−2519.50	+	4363.90i	−0.200225	+	0.346800i	0.748376	+	0.663275i	$0.230834\pi$
$542$	331.000	+	573.309i	0.0262319	+	0.0454349i
$543$	−6685.00	−	11578.8i	−0.528326	−	0.915087i
$544$	−816.000	+	1413.35i	−0.0643120	+	0.111392i
$545$	−8307.00			−0.652904
$546$	−9800.00	−	8487.05i	−0.768134	−	0.665224i
$547$	−2392.00			−0.186974			−0.0934868	−	0.995621i	$-0.529801\pi$
$547$	−2392.00			−0.186974			−0.0934868	+	0.995621i	$0.529801\pi$
$548$	282.000	−	488.438i	0.0219826	−	0.0380749i
$549$	−709.000	−	1228.02i	−0.0551173	−	0.0954659i
$550$	−2508.00	−	4343.98i	−0.194439	−	0.336778i
$551$	−285.000	+	493.634i	−0.0220352	+	0.0381661i
$552$	−2760.00			−0.212814
$553$	8067.50	−	2794.66i	0.620371	−	0.214903i
$554$	9742.00			0.747108
$555$	5692.50	−	9859.70i	0.435375	−	0.754092i
$556$	−2968.00	−	5140.73i	−0.226387	−	0.392114i
$557$	11074.5	+	19181.6i	0.842445	+	1.45916i	0.887822	+	0.460187i	$0.152218\pi$
$557$	11074.5	+	19181.6i	0.842445	+	1.45916i	−0.0453775	+	0.998970i	$0.514449\pi$
$558$	46.0000	−	79.6743i	0.00348985	−	0.00604459i
$559$	8680.00			0.656753
$560$	504.000	−	2618.86i	0.0380319	−	0.197620i
$561$	14535.0			1.09388
$562$	7026.00	−	12169.4i	0.527356	−	0.913407i
$563$	4174.50	+	7230.45i	0.312494	+	0.541256i	0.978902	−	0.204332i	$-0.0655022\pi$
$563$	4174.50	+	7230.45i	0.312494	+	0.541256i	−0.666408	+	0.745588i	$0.732169\pi$
$564$	2010.00	+	3481.42i	0.150064	+	0.259919i
$565$	6939.00	−	12018.7i	0.516683	−	0.894921i
$566$	−10706.0			−0.795065
$567$	2348.50	−	12203.2i	0.173947	−	0.903853i
$568$	−768.000			−0.0567334
$569$	7672.50	−	13289.2i	0.565286	−	0.979105i	−0.431737	−	0.902000i	$-0.642099\pi$
$569$	7672.50	−	13289.2i	0.565286	−	0.979105i	0.997023	−	0.0771050i	$-0.0245677\pi$
$570$	−225.000	−	389.711i	−0.0165337	−	0.0286372i
$571$	5796.50	+	10039.8i	0.424827	+	0.735821i	0.996404	−	0.0847268i	$-0.0270017\pi$
$571$	5796.50	+	10039.8i	0.424827	+	0.735821i	−0.571578	+	0.820548i	$0.693668\pi$
$572$	−7980.00	+	13821.8i	−0.583323	+	1.01034i
$573$	−20925.0			−1.52557
$574$	−1470.00	+	509.223i	−0.106893	+	0.0370288i
$575$	−3036.00			−0.220191
$576$	64.0000	−	110.851i	0.00462963	−	0.00801875i
$577$	7296.50	+	12637.9i	0.526442	+	0.911825i	0.999525	+	0.0308071i	$0.00980776\pi$
$577$	7296.50	+	12637.9i	0.526442	+	0.911825i	−0.473083	+	0.881018i	$0.656859\pi$
$578$	2312.00	+	4004.50i	0.166378	+	0.288175i
$579$	−212.500	+	368.061i	−0.0152525	+	0.0264181i
$580$	−4104.00			−0.293809
$581$	8232.00	+	7129.12i	0.587816	+	0.509063i
$582$	18340.0			1.30622
$583$	−11200.5	+	19399.8i	−0.795673	+	1.37815i
$584$	1252.00	+	2168.53i	0.0887125	+	0.153655i
$585$	630.000	+	1091.19i	0.0445253	+	0.0771201i
$586$	−4158.00	+	7201.87i	−0.293115	+	0.507690i
$587$	−15372.0			−1.08087			−0.540435	−	0.841386i	$-0.681740\pi$
$587$	−15372.0			−1.08087			−0.540435	+	0.841386i	$0.681740\pi$
$588$	6370.00	+	2546.11i	0.446759	+	0.178571i
$589$	115.000			0.00804498
$590$	1971.00	−	3413.87i	0.137534	−	0.238215i
$591$	−975.000	−	1688.75i	−0.0678615	−	0.117540i
$592$	2024.00	+	3505.67i	0.140517	+	0.243382i
$593$	7186.50	−	12447.4i	0.497663	−	0.861978i	−0.502333	−	0.864674i	$-0.667525\pi$
$593$	7186.50	−	12447.4i	0.497663	−	0.861978i	0.999996	+	0.00269639i	$0.000858288\pi$
$594$	−16530.0			−1.14181
$595$	6426.00	+	5565.08i	0.442757	+	0.383439i
$596$	−228.000			−0.0156699
$597$	−7082.50	+	12267.2i	−0.485540	+	0.840980i
$598$	4830.00	+	8365.81i	0.330290	+	0.572079i
$599$	−1273.50	−	2205.77i	−0.0868678	−	0.150459i	0.819318	−	0.573340i	$-0.194352\pi$
$599$	−1273.50	−	2205.77i	−0.0868678	−	0.150459i	−0.906186	+	0.422880i	$0.861019\pi$
$600$	−880.000	+	1524.20i	−0.0598764	+	0.103709i
$601$	−7042.00			−0.477952			−0.238976	−	0.971025i	$-0.576812\pi$
$601$	−7042.00			−0.477952			−0.238976	+	0.971025i	$0.576812\pi$
$602$	−4340.00	+	1503.42i	−0.293829	+	0.101785i
$603$	−838.000			−0.0565937
$604$	−1678.00	+	2906.38i	−0.113041	+	0.195793i
$605$	8631.00	+	14949.3i	0.580000	+	1.00459i
$606$	−1425.00	−	2468.17i	−0.0955226	−	0.165450i
$607$	11295.5	−	19564.4i	0.755305	−	1.30823i	−0.189917	−	0.981800i	$-0.560822\pi$
$607$	11295.5	−	19564.4i	0.755305	−	1.30823i	0.945223	−	0.326427i	$-0.105845\pi$
$608$	160.000			0.0106725
$609$	1995.00	−	10366.3i	0.132745	−	0.689761i
$610$	12762.0			0.847079
$611$	7035.00	−	12185.0i	0.465803	−	0.806794i
$612$	204.000	+	353.338i	0.0134742	+	0.0233380i
$613$	4242.50	+	7348.23i	0.279532	+	0.484163i	0.971268	−	0.237987i	$-0.0764874\pi$
$613$	4242.50	+	7348.23i	0.279532	+	0.484163i	−0.691737	+	0.722150i	$0.743154\pi$
$614$	9604.00	−	16634.6i	0.631247	−	1.09335i
$615$	−1890.00			−0.123922
$616$	1596.00	−	8293.06i	0.104391	−	0.542430i
$617$	−18282.0			−1.19288			−0.596439	−	0.802658i	$-0.703418\pi$
$617$	−18282.0			−1.19288			−0.596439	+	0.802658i	$0.703418\pi$
$618$	−2495.00	+	4321.47i	−0.162401	+	0.281286i
$619$	−1145.50	−	1984.06i	−0.0743805	−	0.128831i	0.826436	−	0.563030i	$-0.190365\pi$
$619$	−1145.50	−	1984.06i	−0.0743805	−	0.128831i	−0.900817	+	0.434200i	$0.857031\pi$
$620$	414.000	+	717.069i	0.0268172	+	0.0464487i
$621$	−5002.50	+	8664.58i	−0.323258	+	0.559900i
$622$	20262.0			1.30616
$623$	−17797.5	+	6165.23i	−1.14453	+	0.396477i
$624$	5600.00			0.359262
$625$	4094.50	−	7091.88i	0.262048	−	0.453880i
$626$	−10799.0	−	18704.4i	−0.689481	−	1.19422i
$627$	−712.500	−	1234.09i	−0.0453820	−	0.0786039i
$628$	5666.00	−	9813.80i	0.360029	−	0.623588i
$629$	−12903.0			−0.817927
$630$	−504.000	−	436.477i	−0.0318728	−	0.0276026i
$631$	−6928.00			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$631$	−6928.00			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$632$	−1844.00	+	3193.90i	−0.116061	+	0.201023i
$633$	−310.000	−	536.936i	−0.0194651	−	0.0337145i
$634$	−531.000	−	919.719i	−0.0332629	−	0.0576131i
$635$	−9252.00	+	16024.9i	−0.578196	+	1.00146i
$636$	7860.00			0.490046
$637$	−3430.00	−	23763.7i	−0.213346	−	1.47811i
$638$	−12996.0			−0.806452
$639$	−96.0000	+	166.277i	−0.00594319	+	0.0102939i
$640$	576.000	+	997.661i	0.0355756	+	0.0616188i
$641$	−12487.5	−	21629.0i	−0.769464	−	1.33275i	−0.937854	−	0.347031i	$-0.887190\pi$
$641$	−12487.5	−	21629.0i	−0.769464	−	1.33275i	0.168390	−	0.985721i	$-0.446143\pi$
$642$	−5535.00	+	9586.90i	−0.340263	+	0.589353i
$643$	9548.00			0.585593			0.292797	−	0.956175i	$-0.405414\pi$
$643$	9548.00			0.585593			0.292797	+	0.956175i	$0.405414\pi$
$644$	−3864.00	−	3346.32i	−0.236433	−	0.204757i
$645$	−5580.00			−0.340639
$646$	−255.000	+	441.673i	−0.0155307	+	0.0269000i
$647$	−5065.50	−	8773.70i	−0.307798	−	0.533122i	0.670082	−	0.742287i	$-0.266259\pi$
$647$	−5065.50	−	8773.70i	−0.307798	−	0.533122i	−0.977880	+	0.209165i	$0.932925\pi$
$648$	2684.00	+	4648.82i	0.162712	+	0.281826i
$649$	6241.50	−	10810.6i	0.377504	−	0.653857i
$650$	6160.00			0.371716
$651$	−2012.50	+	697.150i	−0.121161	+	0.0419716i
$652$	−9244.00			−0.555250
$653$	−8329.50	+	14427.1i	−0.499171	+	0.864589i	−1.00000		0.000957229i	$-0.999695\pi$
$653$	−8329.50	+	14427.1i	−0.499171	+	0.864589i	0.500829	+	0.865546i	$0.333029\pi$
$654$	4615.00	+	7993.41i	0.275934	+	0.477932i
$655$	9220.50	+	15970.4i	0.550038	+	0.952693i
$656$	336.000	−	581.969i	0.0199979	−	0.0346373i
$657$	626.000			0.0371729
$658$	−1407.00	+	7310.99i	−0.0833595	+	0.433149i
$659$	29556.0			1.74710			0.873550	−	0.486735i	$-0.161812\pi$
$659$	29556.0			1.74710			0.873550	+	0.486735i	$0.161812\pi$
$660$	5130.00	−	8885.42i	0.302553	−	0.524037i
$661$	−95.5000	−	165.411i	−0.00561955	−	0.00973334i	0.863202	−	0.504859i	$-0.168455\pi$
$661$	−95.5000	−	165.411i	−0.00561955	−	0.00973334i	−0.868822	+	0.495125i	$0.835122\pi$
$662$	7015.00	+	12150.3i	0.411852	+	0.713348i
$663$	−8925.00	+	15458.6i	−0.522803	+	0.905521i
$664$	−4704.00			−0.274926
$665$	157.500	−	818.394i	0.00918434	−	0.0477232i
$666$	1012.00			0.0588802
$667$	−3933.00	+	6812.16i	−0.228315	+	0.395454i
$668$	−2520.00	−	4364.77i	−0.145961	−	0.252811i
$669$	140.000	+	242.487i	0.00809075	+	0.0140136i
$670$	3771.00	−	6531.56i	0.217442	−	0.376621i
$671$	40413.0			2.32508
$672$	−2800.00	+	969.948i	−0.160733	+	0.0556794i
$673$	2606.00			0.149263			0.0746314	−	0.997211i	$-0.476222\pi$
$673$	2606.00			0.149263			0.0746314	+	0.997211i	$0.476222\pi$
$674$	−8990.00	+	15571.1i	−0.513771	+	0.889878i
$675$	3190.00	+	5525.24i	0.181901	+	0.315062i
$676$	−5406.00	−	9363.47i	−0.307579	−	0.532742i
$677$	2104.50	−	3645.10i	0.119472	−	0.206931i	−0.800087	−	0.599885i	$-0.795213\pi$
$677$	2104.50	−	3645.10i	0.119472	−	0.206931i	0.919559	+	0.392953i	$0.128547\pi$
$678$	−15420.0			−0.873454
$679$	25676.0	+	22236.1i	1.45118	+	1.25676i
$680$	−3672.00			−0.207081
$681$	−7642.50	+	13237.2i	−0.430046	+	0.744861i
$682$	1311.00	+	2270.72i	0.0736082	+	0.127493i
$683$	−12151.5	−	21047.0i	−0.680768	−	1.17912i	−0.974747	−	0.223312i	$-0.928313\pi$
$683$	−12151.5	−	21047.0i	−0.680768	−	1.17912i	0.293979	−	0.955812i	$-0.405020\pi$
$684$	20.0000	−	34.6410i	0.00111801	−	0.00193645i
$685$	1269.00			0.0707825
$686$	5831.00	+	11287.8i	0.324532	+	0.628235i
$687$	4805.00			0.266845
$688$	992.000	−	1718.19i	0.0549704	−	0.0952116i
$689$	−13755.0	−	23824.4i	−0.760557	−	1.31732i
$690$	−3105.00	−	5378.02i	−0.171312	−	0.296721i
$691$	−7520.50	+	13025.9i	−0.414028	+	0.717117i	−0.995326	−	0.0965734i	$-0.969212\pi$
$691$	−7520.50	+	13025.9i	−0.414028	+	0.717117i	0.581298	+	0.813691i	$0.302545\pi$
$692$	13068.0			0.717877
$693$	−1596.00	−	1382.18i	−0.0874849	−	0.0757641i
$694$	−17418.0			−0.952706
$695$	6678.00	−	11566.6i	0.364476	−	0.631291i
$696$	2280.00	+	3949.08i	0.124171	+	0.215071i
$697$	1071.00	+	1855.03i	0.0582023	+	0.100809i
$698$	−6482.00	+	11227.2i	−0.351500	+	0.608817i
$699$	14145.0			0.765398
$700$	−3080.00	+	1066.94i	−0.166304	+	0.0576095i
$701$	24726.0			1.33222			0.666111	−	0.745852i	$-0.267958\pi$
$701$	24726.0			1.33222			0.666111	+	0.745852i	$0.267958\pi$
$702$	10150.0	−	17580.3i	0.545708	−	0.945194i
$703$	632.500	+	1095.52i	0.0339334	+	0.0587744i
$704$	1824.00	+	3159.26i	0.0976486	+	0.169132i
$705$	−4522.50	+	7833.20i	−0.241599	+	0.418462i
$706$	−4266.00			−0.227412
$707$	997.500	−	5183.16i	0.0530620	−	0.275718i
$708$	−4380.00			−0.232501
$709$	2478.50	−	4292.89i	0.131286	−	0.227395i	−0.792886	−	0.609370i	$-0.791423\pi$
$709$	2478.50	−	4292.89i	0.131286	−	0.227395i	0.924173	+	0.381975i	$0.124756\pi$
$710$	−864.000	−	1496.49i	−0.0456695	−	0.0791019i
$711$	461.000	+	798.475i	0.0243162	+	0.0421170i
$712$	4068.00	−	7045.98i	0.214122	−	0.370870i
$713$	1587.00			0.0833571
$714$	1785.00	−	9275.13i	0.0935601	−	0.486153i
$715$	−35910.0			−1.87826
$716$	−2574.00	+	4458.30i	−0.134350	+	0.232702i
$717$	−8850.00	−	15328.6i	−0.460961	−	0.798409i
$718$	−3849.00	−	6666.66i	−0.200060	−	0.346515i
$719$	−13834.5	+	23962.1i	−0.717580	+	1.24288i	0.244376	+	0.969680i	$0.421417\pi$
$719$	−13834.5	+	23962.1i	−0.717580	+	1.24288i	−0.961956	+	0.273204i	$0.911917\pi$
$720$	288.000			0.0149071
$721$	−8732.50	+	3025.03i	−0.451061	+	0.156252i
$722$	−13668.0			−0.704529
$723$	13077.5	−	22650.9i	0.672694	−	1.16514i
$724$	5348.00	+	9263.01i	0.274526	+	0.475493i
$725$	2508.00	+	4343.98i	0.128476	+	0.222526i
$726$	9590.00	−	16610.4i	0.490246	−	0.849130i
$727$	−13888.0			−0.708497			−0.354249	−	0.935151i	$-0.615263\pi$
$727$	−13888.0			−0.708497			−0.354249	+	0.935151i	$0.615263\pi$
$728$	7840.00	+	6789.64i	0.399134	+	0.345660i
$729$	20917.0			1.06269
$730$	−2817.00	+	4879.19i	−0.142824	+	0.247379i
$731$	3162.00	+	5476.74i	0.159987	+	0.277106i
$732$	−7090.00	−	12280.2i	−0.357997	−	0.620069i
$733$	−7121.50	+	12334.8i	−0.358852	+	0.621550i	−0.987769	−	0.155922i	$-0.950165\pi$
$733$	−7121.50	+	12334.8i	−0.358852	+	0.621550i	0.628917	+	0.777472i	$0.283498\pi$
$734$	12982.0			0.652826
$735$	2205.00	+	15276.7i	0.110657	+	0.766652i
$736$	2208.00			0.110581
$737$	11941.5	−	20683.3i	0.596840	−	1.03376i
$738$	−84.0000	−	145.492i	−0.00418981	−	0.00725697i
$739$	−18479.5	−	32007.4i	−0.919864	−	1.59325i	−0.799620	−	0.600507i	$-0.794966\pi$
$739$	−18479.5	−	32007.4i	−0.919864	−	1.59325i	−0.120244	−	0.992744i	$-0.538368\pi$
$740$	−4554.00	+	7887.76i	−0.226228	+	0.391838i
$741$	1750.00			0.0867582
$742$	11004.0	+	9529.74i	0.544433	+	0.471493i
$743$	−12528.0			−0.618584			−0.309292	−	0.950967i	$-0.600092\pi$
$743$	−12528.0			−0.618584			−0.309292	+	0.950967i	$0.600092\pi$
$744$	460.000	−	796.743i	0.0226672	−	0.0392608i
$745$	−256.500	−	444.271i	−0.0126140	−	0.0218481i
$746$	−923.000	−	1598.68i	−0.0452995	−	0.0784610i
$747$	−588.000	+	1018.45i	−0.0288003	+	0.0498835i
$748$	−11628.0			−0.568398
$749$	−19372.5	+	6710.83i	−0.945068	+	0.327381i
$750$	−15210.0			−0.740521
$751$	8883.50	−	15386.7i	0.431643	−	0.747627i	−0.565372	−	0.824836i	$-0.691268\pi$
$751$	8883.50	−	15386.7i	0.431643	−	0.747627i	0.997015	+	0.0772090i	$0.0246009\pi$
$752$	−1608.00	−	2785.14i	−0.0779757	−	0.135058i
$753$	12600.0	+	21823.8i	0.609787	+	1.05618i
$754$	7980.00	−	13821.8i	0.385430	−	0.667585i
$755$	−7551.00			−0.363985
$756$	−2030.00	+	10548.2i	−0.0976592	+	0.507452i
$757$	−28726.0			−1.37921			−0.689606	−	0.724184i	$-0.742216\pi$
$757$	−28726.0			−1.37921			−0.689606	+	0.724184i	$0.742216\pi$
$758$	−6344.00	+	10988.1i	−0.303990	+	0.526526i
$759$	−9832.50	−	17030.4i	−0.470220	−	0.814445i
$760$	180.000	+	311.769i	0.00859117	+	0.0148803i
$761$	13234.5	−	22922.8i	0.630421	−	1.09192i	−0.357045	−	0.934087i	$-0.616216\pi$
$761$	13234.5	−	22922.8i	0.630421	−	1.09192i	0.987466	−	0.157834i	$-0.0504510\pi$
$762$	20560.0			0.977441
$763$	−3230.50	+	16786.2i	−0.153279	+	0.796462i
$764$	16740.0			0.792712
$765$	−459.000	+	795.011i	−0.0216930	+	0.0375735i
$766$	5007.00	+	8672.38i	0.236175	+	0.409068i
$767$	7665.00	+	13276.2i	0.360844	+	0.625000i
$768$	640.000	−	1108.51i	0.0300703	−	0.0520833i
$769$	5054.00			0.236999			0.118499	−	0.992954i	$-0.462192\pi$
$769$	5054.00			0.236999			0.118499	+	0.992954i	$0.462192\pi$
$770$	17955.0	−	6219.79i	0.840329	−	0.291098i
$771$	7185.00			0.335618
$772$	170.000	−	294.449i	0.00792543	−	0.0137273i
$773$	17782.5	+	30800.2i	0.827415	+	1.43313i	0.900059	+	0.435767i	$0.143523\pi$
$773$	17782.5	+	30800.2i	0.827415	+	1.43313i	−0.0726439	+	0.997358i	$0.523144\pi$
$774$	−248.000	−	429.549i	−0.0115170	−	0.0199481i
$775$	506.000	−	876.418i	0.0234530	−	0.0406217i
$776$	−14672.0			−0.678730
$777$	−17710.0	−	15337.3i	−0.817687	−	0.708138i
$778$	24582.0			1.13279
$779$	105.000	−	181.865i	0.00482929	−	0.00836457i
$780$	6300.00	+	10911.9i	0.289200	+	0.500910i
$781$	−2736.00	−	4738.89i	−0.125354	−	0.217120i
$782$	−3519.00	+	6095.09i	−0.160920	+	0.278721i
$783$	16530.0			0.754450
$784$	−5096.00	−	2036.89i	−0.232143	−	0.0927884i
$785$	25497.0			1.15927
$786$	10245.0	−	17744.9i	0.464920	−	0.805265i
$787$	4314.50	+	7472.93i	0.195420	+	0.338477i	0.947038	−	0.321121i	$-0.104060\pi$
$787$	4314.50	+	7472.93i	0.195420	+	0.338477i	−0.751618	+	0.659598i	$0.770726\pi$
$788$	780.000	+	1351.00i	0.0352619	+	0.0610753i
$789$	−5812.50	+	10067.5i	−0.262269	+	0.454264i
$790$	−8298.00			−0.373708
$791$	−21588.0	−	18695.8i	−0.970393	−	0.840385i
$792$	912.000			0.0409173
$793$	−24815.0	+	42980.8i	−1.11123	+	1.92471i
$794$	−887.000	−	1536.33i	−0.0396454	−	0.0686679i
$795$	8842.50	+	15315.7i	0.394479	+	0.683258i
$796$	5666.00	−	9813.80i	0.252294	−	0.436986i
$797$	20706.0			0.920256			0.460128	−	0.887853i	$-0.347803\pi$
$797$	20706.0			0.920256			0.460128	+	0.887853i	$0.347803\pi$
$798$	−875.000	+	303.109i	−0.0388154	+	0.0134460i
$799$	10251.0			0.453885
$800$	704.000	−	1219.36i	0.0311127	−	0.0538888i
$801$	−1017.00	−	1761.50i	−0.0448613	−	0.0777021i
$802$	−11955.0	−	20706.7i	−0.526366	−	0.911693i
$803$	−8920.50	+	15450.8i	−0.392027	+	0.679011i
$804$	−8380.00			−0.367587
$805$	2173.50	−	11293.8i	0.0951625	−	0.494479i
$806$	−3220.00			−0.140719
$807$	−5962.50	+	10327.4i	−0.260087	+	0.450483i
$808$	1140.00	+	1974.54i	0.0496350	+	0.0859703i
$809$	8092.50	+	14016.6i	0.351690	+	0.609145i	0.986546	−	0.163486i	$-0.0522738\pi$
$809$	8092.50	+	14016.6i	0.351690	+	0.609145i	−0.634856	+	0.772631i	$0.718940\pi$
$810$	−6039.00	+	10459.9i	−0.261962	+	0.453731i
$811$	−11788.0			−0.510398			−0.255199	−	0.966889i	$-0.582141\pi$
$811$	−11788.0			−0.510398			−0.255199	+	0.966889i	$0.582141\pi$
$812$	−1596.00	+	8293.06i	−0.0689761	+	0.358411i
$813$	1655.00			0.0713941
$814$	−14421.0	+	24977.9i	−0.620953	+	1.07552i
$815$	−10399.5	−	18012.5i	−0.446968	−	0.774171i
$816$	2040.00	+	3533.38i	0.0875175	+	0.151585i
$817$	310.000	−	536.936i	0.0132748	−	0.0229927i
$818$	−6842.00			−0.292451
$819$	2450.00	−	848.705i	0.104530	−	0.0362102i
$820$	1512.00			0.0643919
$821$	14896.5	−	25801.5i	0.633242	−	1.09681i	−0.353643	−	0.935380i	$-0.615057\pi$
$821$	14896.5	−	25801.5i	0.633242	−	1.09681i	0.986885	−	0.161426i	$-0.0516094\pi$
$822$	−705.000	−	1221.10i	−0.0299145	−	0.0518134i
$823$	−15161.5	−	26260.5i	−0.642159	−	1.11225i	−0.984950	−	0.172840i	$-0.944706\pi$
$823$	−15161.5	−	26260.5i	−0.642159	−	1.11225i	0.342791	−	0.939412i	$-0.388628\pi$
$824$	1996.00	−	3457.17i	0.0843859	−	0.146161i
$825$	−12540.0			−0.529196
$826$	−6132.00	−	5310.47i	−0.258305	−	0.223698i
$827$	21156.0			0.889560			0.444780	−	0.895640i	$-0.353282\pi$
$827$	21156.0			0.889560			0.444780	+	0.895640i	$0.353282\pi$
$828$	276.000	−	478.046i	0.0115841	−	0.0200643i
$829$	2634.50	+	4563.09i	0.110374	+	0.191173i	0.915921	−	0.401358i	$-0.131462\pi$
$829$	2634.50	+	4563.09i	0.110374	+	0.191173i	−0.805547	+	0.592532i	$0.798129\pi$
$830$	−5292.00	−	9166.01i	−0.221311	−	0.383322i
$831$	12177.5	−	21092.0i	0.508343	−	0.880475i
$832$	−4480.00			−0.186678
$833$	13744.5	−	10821.0i	0.571691	−	0.450090i
$834$	−14840.0			−0.616148
$835$	5670.00	−	9820.73i	0.234992	−	0.407018i
$836$	570.000	+	987.269i	0.0235812	+	0.0408438i
$837$	−1667.50	−	2888.19i	−0.0688617	−	0.119272i
$838$	5460.00	−	9457.00i	0.225075	−	0.389841i
$839$	−39816.0			−1.63838			−0.819190	−	0.573522i	$-0.805577\pi$
$839$	−39816.0			−1.63838			−0.819190	+	0.573522i	$0.805577\pi$
$840$	−5040.00	−	4364.77i	−0.207020	−	0.179284i
$841$	−11393.0			−0.467137
$842$	−7730.00	+	13388.8i	−0.316382	+	0.547989i
$843$	−17565.0	−	30423.5i	−0.717640	−	1.24299i
$844$	248.000	+	429.549i	0.0101144	+	0.0175186i
$845$	12163.5	−	21067.8i	0.495192	−	0.857697i
$846$	−804.000			−0.0326739
$847$	33565.0	−	11627.3i	1.36164	−	0.471685i
$848$	−6288.00			−0.254635
$849$	−13382.5	+	23179.2i	−0.540973	+	0.936993i
$850$	2244.00	+	3886.72i	0.0905513	+	0.156839i
$851$	8728.50	+	15118.2i	0.351597	+	0.608984i
$852$	−960.000	+	1662.77i	−0.0386022	+	0.0668609i
$853$	14546.0			0.583875			0.291938	−	0.956437i	$-0.405700\pi$
$853$	14546.0			0.583875			0.291938	+	0.956437i	$0.405700\pi$
$854$	4963.00	−	25788.5i	0.198865	−	1.03333i
$855$	90.0000			0.00359992
$856$	4428.00	−	7669.52i	0.176806	−	0.306237i
$857$	15724.5	+	27235.6i	0.626766	+	1.08559i	0.988196	+	0.153192i	$0.0489552\pi$
$857$	15724.5	+	27235.6i	0.626766	+	1.08559i	−0.361430	+	0.932399i	$0.617711\pi$
$858$	19950.0	+	34554.4i	0.793802	+	1.37490i
$859$	12261.5	−	21237.5i	0.487028	−	0.843557i	−0.512861	−	0.858472i	$-0.671414\pi$
$859$	12261.5	−	21237.5i	0.487028	−	0.843557i	0.999889	+	0.0149147i	$0.00474766\pi$
$860$	4464.00			0.177001
$861$	−735.000	+	3819.17i	−0.0290926	+	0.151170i
$862$	−22626.0			−0.894019
$863$	4081.50	−	7069.37i	0.160992	−	0.278846i	−0.774233	−	0.632901i	$-0.781864\pi$
$863$	4081.50	−	7069.37i	0.160992	−	0.278846i	0.935225	+	0.354055i	$0.115197\pi$
$864$	−2320.00	−	4018.36i	−0.0913519	−	0.158226i
$865$	14701.5	+	25463.7i	0.577880	+	1.00092i
$866$	−4214.00	+	7298.86i	−0.165355	+	0.286403i
$867$	11560.0			0.452824
$868$	1610.00	−	557.720i	0.0629573	−	0.0218091i
$869$	−26277.0			−1.02576
$870$	−5130.00	+	8885.42i	−0.199912	+	0.346257i
$871$	14665.0	+	25400.5i	0.570499	+	0.988133i
$872$	−3692.00	−	6394.73i	−0.143379	−	0.248341i
$873$	−1834.00	+	3176.58i	−0.0711014	+	0.123151i
$874$	690.000			0.0267043
$875$	−21294.0	−	18441.1i	−0.822707	−	0.712485i
$876$	6260.00			0.241445
$877$	−2183.50	+	3781.93i	−0.0840725	+	0.145618i	−0.904996	−	0.425421i	$-0.860126\pi$
$877$	−2183.50	+	3781.93i	−0.0840725	+	0.145618i	0.820923	+	0.571039i	$0.193459\pi$
$878$	−16553.0	−	28670.6i	−0.636260	−	1.10204i
$879$	10395.0	+	18004.7i	0.398879	+	0.690879i
$880$	−4104.00	+	7108.34i	−0.157211	+	0.272298i
$881$	−50190.0			−1.91935			−0.959673	−	0.281118i	$-0.909295\pi$
$881$	−50190.0			−1.91935			−0.959673	+	0.281118i	$0.909295\pi$
$882$	−1078.00	+	848.705i	−0.0411544	+	0.0324007i
$883$	12308.0			0.469079			0.234540	−	0.972107i	$-0.424642\pi$
$883$	12308.0			0.469079			0.234540	+	0.972107i	$0.424642\pi$
$884$	7140.00	−	12366.8i	0.271656	−	0.470523i
$885$	−4927.50	−	8534.68i	−0.187159	−	0.324170i
$886$	16395.0	+	28397.0i	0.621671	+	1.07677i
$887$	−15808.5	+	27381.1i	−0.598419	+	1.03649i	0.394636	+	0.918838i	$0.370871\pi$
$887$	−15808.5	+	27381.1i	−0.598419	+	1.03649i	−0.993055	+	0.117654i	$0.962463\pi$
$888$	10120.0			0.382438
$889$	28784.0	+	24927.7i	1.08592	+	0.940436i
$890$	18306.0			0.689459
$891$	−19123.5	+	33122.9i	−0.719036	+	1.24541i
$892$	−112.000	−	193.990i	−0.00420408	−	0.00728168i
$893$	−502.500	−	870.356i	−0.0188304	−	0.0326152i
$894$	−285.000	+	493.634i	−0.0106620	+	0.0184671i
$895$	−11583.0			−0.432600
$896$	2240.00	−	775.959i	0.0835191	−	0.0289319i
$897$	24150.0			0.898935
$898$	15090.0	−	26136.6i	0.560757	−	0.971260i
$899$	−1311.00	−	2270.72i	−0.0486366	−	0.0842411i
$900$	−176.000	−	304.841i	−0.00651852	−	0.0112904i
$901$	10021.5	−	17357.7i	0.370549	−	0.641810i
$902$	4788.00			0.176744
$903$	−2170.00	+	11275.7i	−0.0799702	+	0.415537i
$904$	12336.0			0.453860
$905$	−12033.0	+	20841.8i	−0.441978	+	0.765529i
$906$	4195.00	+	7265.95i	0.153830	+	0.266441i
$907$	6762.50	+	11713.0i	0.247569	+	0.428802i	0.962851	−	0.270034i	$-0.0870350\pi$
$907$	6762.50	+	11713.0i	0.247569	+	0.428802i	−0.715282	+	0.698836i	$0.753702\pi$
$908$	6114.00	−	10589.8i	0.223458	−	0.387041i
$909$	570.000			0.0207984
$910$	−4410.00	+	22915.0i	−0.160648	+	0.834754i
$911$	−19248.0			−0.700016			−0.350008	−	0.936747i	$-0.613821\pi$
$911$	−19248.0			−0.700016			−0.350008	+	0.936747i	$0.613821\pi$
$912$	200.000	−	346.410i	0.00726169	−	0.0125776i
$913$	−16758.0	−	29025.7i	−0.607458	−	1.05215i
$914$	14785.0	+	25608.4i	0.535059	+	0.926750i
$915$	15952.5	−	27630.5i	0.576364	−	0.998292i
$916$	−3844.00			−0.138656
$917$	35857.5	−	12421.4i	1.29130	−	0.447318i
$918$	14790.0			0.531746
$919$	4347.50	−	7530.09i	0.156051	−	0.270288i	−0.777390	−	0.629019i	$-0.783457\pi$
$919$	4347.50	−	7530.09i	0.156051	−	0.270288i	0.933441	+	0.358730i	$0.116790\pi$
$920$	2484.00	+	4302.41i	0.0890164	+	0.154181i
$921$	−24010.0	−	41586.5i	−0.859019	−	1.48786i
$922$	−2898.00	+	5019.48i	−0.103515	+	0.179293i
$923$	6720.00			0.239644
$924$	−15960.0	−	13821.8i	−0.568231	−	0.492102i
$925$	11132.0			0.395695
$926$	−464.000	+	803.672i	−0.0164665	+	0.0285208i
$927$	−499.000	−	864.293i	−0.0176799	−	0.0306226i
$928$	−1824.00	−	3159.26i	−0.0645213	−	0.111754i
$929$	−9739.50	+	16869.3i	−0.343964	+	0.595763i	−0.985165	−	0.171610i	$-0.945103\pi$
$929$	−9739.50	+	16869.3i	−0.343964	+	0.595763i	0.641201	+	0.767373i	$0.278437\pi$
$930$	2070.00			0.0729871
$931$	−1592.50	−	636.529i	−0.0560602	−	0.0224075i
$932$	−11316.0			−0.397712
$933$	25327.5	−	43868.5i	0.888730	−	1.53933i
$934$	−4233.00	−	7331.77i	−0.148295	−	0.256855i
$935$	−13081.5	−	22657.8i	−0.457552	−	0.792503i
$936$	−560.000	+	969.948i	−0.0195557	+	0.0338715i
$937$	−12502.0			−0.435883			−0.217942	−	0.975962i	$-0.569934\pi$
$937$	−12502.0			−0.435883			−0.217942	+	0.975962i	$0.569934\pi$
$938$	−11732.0	−	10160.2i	−0.408383	−	0.353670i
$939$	−53995.0			−1.87653
$940$	3618.00	−	6266.56i	0.125538	−	0.217439i
$941$	7996.50	+	13850.3i	0.277023	+	0.479818i	0.970643	−	0.240523i	$-0.0773189\pi$
$941$	7996.50	+	13850.3i	0.277023	+	0.479818i	−0.693621	+	0.720340i	$0.743986\pi$
$942$	−14165.0	−	24534.5i	−0.489937	−	0.848596i
$943$	1449.00	−	2509.74i	0.0500381	−	0.0866685i
$944$	3504.00			0.120811
$945$	−22837.5	+	7911.14i	−0.786142	+	0.272327i
$946$	14136.0			0.485836
$947$	−22000.5	+	38106.0i	−0.754932	+	1.30758i	0.190477	+	0.981692i	$0.438997\pi$
$947$	−22000.5	+	38106.0i	−0.754932	+	1.30758i	−0.945408	+	0.325888i	$0.894337\pi$
$948$	4610.00	+	7984.75i	0.157939	+	0.273558i
$949$	−10955.0	−	18974.6i	−0.374725	−	0.649043i
$950$	220.000	−	381.051i	0.00751341	−	0.0130136i
$951$	−2655.00			−0.0905303
$952$	−1428.00	+	7420.11i	−0.0486153	+	0.252612i
$953$	−4002.00			−0.136031			−0.0680155	−	0.997684i	$-0.521667\pi$
$953$	−4002.00			−0.136031			−0.0680155	+	0.997684i	$0.521667\pi$
$954$	−786.000	+	1361.39i	−0.0266747	+	0.0462020i
$955$	18832.5	+	32618.8i	0.638121	+	1.10526i
$956$	7080.00	+	12262.9i	0.239523	+	0.414865i
$957$	−16245.0	+	28137.2i	−0.548721	+	0.950413i
$958$	5478.00			0.184745
$959$	493.500	−	2564.30i	0.0166173	−	0.0863458i
$960$	2880.00			0.0968246
$961$	14631.0	−	25341.6i	0.491121	−	0.850647i
$962$	−17710.0	−	30674.6i	−0.593548	−	1.02806i
$963$	−1107.00	−	1917.38i	−0.0370432	−	0.0641607i
$964$	−10462.0	+	18120.7i	−0.349542	+	0.605424i
$965$	765.000			0.0255194
$966$	−12075.0	+	4182.90i	−0.402181	+	0.139320i
$967$	10544.0			0.350643			0.175322	−	0.984511i	$-0.443903\pi$
$967$	10544.0			0.350643			0.175322	+	0.984511i	$0.443903\pi$
$968$	−7672.00	+	13288.3i	−0.254739	+	0.441221i
$969$	637.500	+	1104.18i	0.0211346	+	0.0366062i
$970$	−16506.0	−	28589.2i	−0.546367	−	0.946335i
$971$	3091.50	−	5354.64i	0.102174	−	0.176971i	−0.810406	−	0.585869i	$-0.800753\pi$
$971$	3091.50	−	5354.64i	0.102174	−	0.176971i	0.912580	+	0.408898i	$0.134087\pi$
$972$	−2240.00			−0.0739177
$973$	−20776.0	−	17992.5i	−0.684530	−	0.592821i
$974$	34102.0			1.12187
$975$	7700.00	−	13336.8i	0.252920	−	0.438071i
$976$	5672.00	+	9824.19i	0.186021	+	0.322197i
$977$	−1861.50	−	3224.21i	−0.0609567	−	0.105580i	0.833937	−	0.551860i	$-0.186082\pi$
$977$	−1861.50	−	3224.21i	−0.0609567	−	0.105580i	−0.894893	+	0.446280i	$0.852748\pi$
$978$	−11555.0	+	20013.8i	−0.377800	+	0.654368i
$979$	57969.0			1.89244
$980$	−1764.00	−	12221.4i	−0.0574989	−	0.398364i
$981$	−1846.00			−0.0600798
$982$	4296.00	−	7440.89i	0.139604	−	0.241801i
$983$	22948.5	+	39748.0i	0.744602	+	1.28969i	0.950381	+	0.311089i	$0.100694\pi$
$983$	22948.5	+	39748.0i	0.744602	+	1.28969i	−0.205779	+	0.978599i	$0.565973\pi$
$984$	−840.000	−	1454.92i	−0.0272136	−	0.0471354i
$985$	−1755.00	+	3039.75i	−0.0567705	+	0.0983294i
$986$	11628.0			0.375569
$987$	14070.0	+	12185.0i	0.453752	+	0.392961i
$988$	−1400.00			−0.0450809
$989$	4278.00	−	7409.71i	0.137545	−	0.238236i
$990$	1026.00	+	1777.08i	0.0329378	+	0.0570499i
$991$	−3233.50	−	5600.59i	−0.103648	−	0.179524i	0.809537	−	0.587069i	$-0.199718\pi$
$991$	−3233.50	−	5600.59i	−0.103648	−	0.179524i	−0.913185	+	0.407545i	$0.866385\pi$
$992$	−368.000	+	637.395i	−0.0117782	+	0.0204005i
$993$	35075.0			1.12092
$994$	−3360.00	+	1163.94i	−0.107216	+	0.0371407i
$995$	25497.0			0.812371
$996$	−5880.00	+	10184.5i	−0.187063	+	0.324003i
$997$	−11519.5	−	19952.4i	−0.365924	−	0.633799i	0.623000	−	0.782222i	$-0.285914\pi$
$997$	−11519.5	−	19952.4i	−0.365924	−	0.633799i	−0.988924	+	0.148423i	$0.952580\pi$
$998$	−3401.00	−	5890.70i	−0.107873	−	0.186841i
$999$	18342.5	−	31770.1i	0.580912	−	1.00617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.4.c.a.9.1	✓	2
3.2	odd	2		126.4.g.d.37.1		2
4.3	odd	2		112.4.i.a.65.1		2
5.2	odd	4		350.4.j.b.149.1		4
5.3	odd	4		350.4.j.b.149.2		4
5.4	even	2		350.4.e.e.51.1		2
7.2	even	3		98.4.a.d.1.1		1
7.3	odd	6		98.4.c.a.67.1		2
7.4	even	3	inner	14.4.c.a.11.1	yes	2
7.5	odd	6		98.4.a.f.1.1		1
7.6	odd	2		98.4.c.a.79.1		2
8.3	odd	2		448.4.i.e.65.1		2
8.5	even	2		448.4.i.b.65.1		2
21.2	odd	6		882.4.a.f.1.1		1
21.5	even	6		882.4.a.c.1.1		1
21.11	odd	6		126.4.g.d.109.1		2
21.17	even	6		882.4.g.u.361.1		2
21.20	even	2		882.4.g.u.667.1		2
28.11	odd	6		112.4.i.a.81.1		2
28.19	even	6		784.4.a.c.1.1		1
28.23	odd	6		784.4.a.p.1.1		1
35.4	even	6		350.4.e.e.151.1		2
35.9	even	6		2450.4.a.q.1.1		1
35.18	odd	12		350.4.j.b.249.1		4
35.19	odd	6		2450.4.a.d.1.1		1
35.32	odd	12		350.4.j.b.249.2		4
56.11	odd	6		448.4.i.e.193.1		2
56.53	even	6		448.4.i.b.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	1.1	even	1	trivial
14.4.c.a.11.1	yes	2	7.4	even	3	inner
98.4.a.d.1.1		1	7.2	even	3
98.4.a.f.1.1		1	7.5	odd	6
98.4.c.a.67.1		2	7.3	odd	6
98.4.c.a.79.1		2	7.6	odd	2
112.4.i.a.65.1		2	4.3	odd	2
112.4.i.a.81.1		2	28.11	odd	6
126.4.g.d.37.1		2	3.2	odd	2
126.4.g.d.109.1		2	21.11	odd	6
350.4.e.e.51.1		2	5.4	even	2
350.4.e.e.151.1		2	35.4	even	6
350.4.j.b.149.1		4	5.2	odd	4
350.4.j.b.149.2		4	5.3	odd	4
350.4.j.b.249.1		4	35.18	odd	12
350.4.j.b.249.2		4	35.32	odd	12
448.4.i.b.65.1		2	8.5	even	2
448.4.i.b.193.1		2	56.53	even	6
448.4.i.e.65.1		2	8.3	odd	2
448.4.i.e.193.1		2	56.11	odd	6
784.4.a.c.1.1		1	28.19	even	6
784.4.a.p.1.1		1	28.23	odd	6
882.4.a.c.1.1		1	21.5	even	6
882.4.a.f.1.1		1	21.2	odd	6
882.4.g.u.361.1		2	21.17	even	6
882.4.g.u.667.1		2	21.20	even	2
2450.4.a.d.1.1		1	35.19	odd	6
2450.4.a.q.1.1		1	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 + 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} -10.0000 q^{6} +(-14.0000 - 12.1244i) q^{7} +8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(9.00000 + 15.5885i) q^{10} +(28.5000 + 49.3634i) q^{11} +(10.0000 - 17.3205i) q^{12} -70.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-25.5000 - 44.1673i) q^{17} +(2.00000 + 3.46410i) q^{18} +(-2.50000 + 4.33013i) q^{19} -36.0000 q^{20} +(17.5000 - 90.9327i) q^{21} -114.000 q^{22} +(-34.5000 + 59.7558i) q^{23} +(20.0000 + 34.6410i) q^{24} +(22.0000 + 38.1051i) q^{25} +(70.0000 - 121.244i) q^{26} +145.000 q^{27} +(-14.0000 + 72.7461i) q^{28} +114.000 q^{29} +(-45.0000 + 77.9423i) q^{30} +(-11.5000 - 19.9186i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-142.500 + 246.817i) q^{33} +102.000 q^{34} +(-157.500 + 54.5596i) q^{35} -8.00000 q^{36} +(126.500 - 219.104i) q^{37} +(-5.00000 - 8.66025i) q^{38} +(-175.000 - 303.109i) q^{39} +(36.0000 - 62.3538i) q^{40} -42.0000 q^{41} +(140.000 + 121.244i) q^{42} -124.000 q^{43} +(114.000 - 197.454i) q^{44} +(-9.00000 - 15.5885i) q^{45} +(-69.0000 - 119.512i) q^{46} +(-100.500 + 174.071i) q^{47} -80.0000 q^{48} +(49.0000 + 339.482i) q^{49} -88.0000 q^{50} +(127.500 - 220.836i) q^{51} +(140.000 + 242.487i) q^{52} +(196.500 + 340.348i) q^{53} +(-145.000 + 251.147i) q^{54} +513.000 q^{55} +(-112.000 - 96.9948i) q^{56} -25.0000 q^{57} +(-114.000 + 197.454i) q^{58} +(-109.500 - 189.660i) q^{59} +(-90.0000 - 155.885i) q^{60} +(354.500 - 614.012i) q^{61} +46.0000 q^{62} +(-35.0000 + 12.1244i) q^{63} +64.0000 q^{64} +(-315.000 + 545.596i) q^{65} +(-285.000 - 493.634i) q^{66} +(-209.500 - 362.865i) q^{67} +(-102.000 + 176.669i) q^{68} -345.000 q^{69} +(63.0000 - 327.358i) q^{70} -96.0000 q^{71} +(8.00000 - 13.8564i) q^{72} +(156.500 + 271.066i) q^{73} +(253.000 + 438.209i) q^{74} +(-110.000 + 190.526i) q^{75} +20.0000 q^{76} +(199.500 - 1036.63i) q^{77} +700.000 q^{78} +(-230.500 + 399.238i) q^{79} +(72.0000 + 124.708i) q^{80} +(335.500 + 581.103i) q^{81} +(42.0000 - 72.7461i) q^{82} -588.000 q^{83} +(-350.000 + 121.244i) q^{84} -459.000 q^{85} +(124.000 - 214.774i) q^{86} +(285.000 + 493.634i) q^{87} +(228.000 + 394.908i) q^{88} +(508.500 - 880.748i) q^{89} +36.0000 q^{90} +(980.000 + 848.705i) q^{91} +276.000 q^{92} +(57.5000 - 99.5929i) q^{93} +(-201.000 - 348.142i) q^{94} +(22.5000 + 38.9711i) q^{95} +(80.0000 - 138.564i) q^{96} -1834.00 q^{97} +(-637.000 - 254.611i) q^{98} +114.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 5 q^{3} - 4 q^{4} + 9 q^{5} - 20 q^{6} - 28 q^{7} + 16 q^{8} + 2 q^{9} + 18 q^{10} + 57 q^{11} + 20 q^{12} - 140 q^{13} + 70 q^{14} + 90 q^{15} - 16 q^{16} - 51 q^{17} + 4 q^{18} - 5 q^{19}+ \cdots + 228 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 5 * q^3 - 4 * q^4 + 9 * q^5 - 20 * q^6 - 28 * q^7 + 16 * q^8 + 2 * q^9 + 18 * q^10 + 57 * q^11 + 20 * q^12 - 140 * q^13 + 70 * q^14 + 90 * q^15 - 16 * q^16 - 51 * q^17 + 4 * q^18 - 5 * q^19 - 72 * q^20 + 35 * q^21 - 228 * q^22 - 69 * q^23 + 40 * q^24 + 44 * q^25 + 140 * q^26 + 290 * q^27 - 28 * q^28 + 228 * q^29 - 90 * q^30 - 23 * q^31 - 32 * q^32 - 285 * q^33 + 204 * q^34 - 315 * q^35 - 16 * q^36 + 253 * q^37 - 10 * q^38 - 350 * q^39 + 72 * q^40 - 84 * q^41 + 280 * q^42 - 248 * q^43 + 228 * q^44 - 18 * q^45 - 138 * q^46 - 201 * q^47 - 160 * q^48 + 98 * q^49 - 176 * q^50 + 255 * q^51 + 280 * q^52 + 393 * q^53 - 290 * q^54 + 1026 * q^55 - 224 * q^56 - 50 * q^57 - 228 * q^58 - 219 * q^59 - 180 * q^60 + 709 * q^61 + 92 * q^62 - 70 * q^63 + 128 * q^64 - 630 * q^65 - 570 * q^66 - 419 * q^67 - 204 * q^68 - 690 * q^69 + 126 * q^70 - 192 * q^71 + 16 * q^72 + 313 * q^73 + 506 * q^74 - 220 * q^75 + 40 * q^76 + 399 * q^77 + 1400 * q^78 - 461 * q^79 + 144 * q^80 + 671 * q^81 + 84 * q^82 - 1176 * q^83 - 700 * q^84 - 918 * q^85 + 248 * q^86 + 570 * q^87 + 456 * q^88 + 1017 * q^89 + 72 * q^90 + 1960 * q^91 + 552 * q^92 + 115 * q^93 - 402 * q^94 + 45 * q^95 + 160 * q^96 - 3668 * q^97 - 1274 * q^98 + 228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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