LMFDB - Embedded newform 130.4.e.d.61.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(61,130)] 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("130.61"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67024830075$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	130.61
Dual form			130.4.e.d.81.1

$q$-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} +(-2.00000 + 3.46410i) q^{3} +(-2.00000 - 3.46410i) q^{4} +5.00000 q^{5} +(4.00000 + 6.92820i) q^{6} +(-11.5000 - 19.9186i) q^{7} -8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(5.00000 - 8.66025i) q^{10} +(28.5000 - 49.3634i) q^{11} +16.0000 q^{12} +(32.5000 - 33.7750i) q^{13} -46.0000 q^{14} +(-10.0000 + 17.3205i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-24.0000 - 41.5692i) q^{17} +22.0000 q^{18} +(-2.50000 - 4.33013i) q^{19} +(-10.0000 - 17.3205i) q^{20} +92.0000 q^{21} +(-57.0000 - 98.7269i) q^{22} +(90.0000 - 155.885i) q^{23} +(16.0000 - 27.7128i) q^{24} +25.0000 q^{25} +(-26.0000 - 90.0666i) q^{26} -152.000 q^{27} +(-46.0000 + 79.6743i) q^{28} +(-60.0000 + 103.923i) q^{29} +(20.0000 + 34.6410i) q^{30} -34.0000 q^{31} +(16.0000 + 27.7128i) q^{32} +(114.000 + 197.454i) q^{33} -96.0000 q^{34} +(-57.5000 - 99.5929i) q^{35} +(22.0000 - 38.1051i) q^{36} +(-113.500 + 196.588i) q^{37} -10.0000 q^{38} +(52.0000 + 180.133i) q^{39} -40.0000 q^{40} +(-3.00000 + 5.19615i) q^{41} +(92.0000 - 159.349i) q^{42} +(107.000 + 185.329i) q^{43} -228.000 q^{44} +(27.5000 + 47.6314i) q^{45} +(-180.000 - 311.769i) q^{46} +549.000 q^{47} +(-32.0000 - 55.4256i) q^{48} +(-93.0000 + 161.081i) q^{49} +(25.0000 - 43.3013i) q^{50} +192.000 q^{51} +(-182.000 - 45.0333i) q^{52} -537.000 q^{53} +(-152.000 + 263.272i) q^{54} +(142.500 - 246.817i) q^{55} +(92.0000 + 159.349i) q^{56} +20.0000 q^{57} +(120.000 + 207.846i) q^{58} +(150.000 + 259.808i) q^{59} +80.0000 q^{60} +(161.000 + 278.860i) q^{61} +(-34.0000 + 58.8897i) q^{62} +(126.500 - 219.104i) q^{63} +64.0000 q^{64} +(162.500 - 168.875i) q^{65} +456.000 q^{66} +(386.000 - 668.572i) q^{67} +(-96.0000 + 166.277i) q^{68} +(360.000 + 623.538i) q^{69} -230.000 q^{70} +(447.000 + 774.227i) q^{71} +(-44.0000 - 76.2102i) q^{72} +272.000 q^{73} +(227.000 + 393.176i) q^{74} +(-50.0000 + 86.6025i) q^{75} +(-10.0000 + 17.3205i) q^{76} -1311.00 q^{77} +(364.000 + 90.0666i) q^{78} -454.000 q^{79} +(-40.0000 + 69.2820i) q^{80} +(155.500 - 269.334i) q^{81} +(6.00000 + 10.3923i) q^{82} -1068.00 q^{83} +(-184.000 - 318.697i) q^{84} +(-120.000 - 207.846i) q^{85} +428.000 q^{86} +(-240.000 - 415.692i) q^{87} +(-228.000 + 394.908i) q^{88} +(-340.500 + 589.763i) q^{89} +110.000 q^{90} +(-1046.50 - 258.942i) q^{91} -720.000 q^{92} +(68.0000 - 117.779i) q^{93} +(549.000 - 950.896i) q^{94} +(-12.5000 - 21.6506i) q^{95} -128.000 q^{96} +(-550.000 - 952.628i) q^{97} +(186.000 + 322.161i) q^{98} +627.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{3} - 4 q^{4} + 10 q^{5} + 8 q^{6} - 23 q^{7} - 16 q^{8} + 11 q^{9} + 10 q^{10} + 57 q^{11} + 32 q^{12} + 65 q^{13} - 92 q^{14} - 20 q^{15} - 16 q^{16} - 48 q^{17} + 44 q^{18} - 5 q^{19}+ \cdots + 1254 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^3 - 4 * q^4 + 10 * q^5 + 8 * q^6 - 23 * q^7 - 16 * q^8 + 11 * q^9 + 10 * q^10 + 57 * q^11 + 32 * q^12 + 65 * q^13 - 92 * q^14 - 20 * q^15 - 16 * q^16 - 48 * q^17 + 44 * q^18 - 5 * q^19 - 20 * q^20 + 184 * q^21 - 114 * q^22 + 180 * q^23 + 32 * q^24 + 50 * q^25 - 52 * q^26 - 304 * q^27 - 92 * q^28 - 120 * q^29 + 40 * q^30 - 68 * q^31 + 32 * q^32 + 228 * q^33 - 192 * q^34 - 115 * q^35 + 44 * q^36 - 227 * q^37 - 20 * q^38 + 104 * q^39 - 80 * q^40 - 6 * q^41 + 184 * q^42 + 214 * q^43 - 456 * q^44 + 55 * q^45 - 360 * q^46 + 1098 * q^47 - 64 * q^48 - 186 * q^49 + 50 * q^50 + 384 * q^51 - 364 * q^52 - 1074 * q^53 - 304 * q^54 + 285 * q^55 + 184 * q^56 + 40 * q^57 + 240 * q^58 + 300 * q^59 + 160 * q^60 + 322 * q^61 - 68 * q^62 + 253 * q^63 + 128 * q^64 + 325 * q^65 + 912 * q^66 + 772 * q^67 - 192 * q^68 + 720 * q^69 - 460 * q^70 + 894 * q^71 - 88 * q^72 + 544 * q^73 + 454 * q^74 - 100 * q^75 - 20 * q^76 - 2622 * q^77 + 728 * q^78 - 908 * q^79 - 80 * q^80 + 311 * q^81 + 12 * q^82 - 2136 * q^83 - 368 * q^84 - 240 * q^85 + 856 * q^86 - 480 * q^87 - 456 * q^88 - 681 * q^89 + 220 * q^90 - 2093 * q^91 - 1440 * q^92 + 136 * q^93 + 1098 * q^94 - 25 * q^95 - 256 * q^96 - 1100 * q^97 + 372 * q^98 + 1254 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−2.00000	+	3.46410i	−0.384900	+	0.666667i	−0.991755	−	0.128146i	$-0.959097\pi$
$3$	−2.00000	+	3.46410i	−0.384900	+	0.666667i	0.606855	+	0.794812i	$0.292431\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	4.00000	+	6.92820i	0.272166	+	0.471405i
$7$	−11.5000	−	19.9186i	−0.620942	−	1.07550i	−0.989311	−	0.145823i	$-0.953417\pi$
$7$	−11.5000	−	19.9186i	−0.620942	−	1.07550i	0.368369	−	0.929680i	$-0.379916\pi$
$8$	−8.00000			−0.353553
$9$	5.50000	+	9.52628i	0.203704	+	0.352825i
$10$	5.00000	−	8.66025i	0.158114	−	0.273861i
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	−0.150061	−	0.988677i	$-0.547947\pi$
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	0.931250	−	0.364381i	$-0.118720\pi$
$12$	16.0000			0.384900
$13$	32.5000	−	33.7750i	0.693375	−	0.720577i
$13$	32.5000	−	33.7750i	0.693375	−	0.720577i
$14$	−46.0000			−0.878144
$15$	−10.0000	+	17.3205i	−0.172133	+	0.298142i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−24.0000	−	41.5692i	−0.342403	−	0.593060i	0.642475	−	0.766306i	$-0.277908\pi$
$17$	−24.0000	−	41.5692i	−0.342403	−	0.593060i	−0.984878	+	0.173247i	$0.944574\pi$
$18$	22.0000			0.288081
$19$	−2.50000	−	4.33013i	−0.0301863	−	0.0522842i	0.850538	−	0.525914i	$-0.176277\pi$
$19$	−2.50000	−	4.33013i	−0.0301863	−	0.0522842i	−0.880724	+	0.473630i	$0.842943\pi$
$20$	−10.0000	−	17.3205i	−0.111803	−	0.193649i
$21$	92.0000			0.956002
$22$	−57.0000	−	98.7269i	−0.552384	−	0.956757i
$23$	90.0000	−	155.885i	0.815926	−	1.41323i	−0.0927351	−	0.995691i	$-0.529561\pi$
$23$	90.0000	−	155.885i	0.815926	−	1.41323i	0.908661	−	0.417534i	$-0.137106\pi$
$24$	16.0000	−	27.7128i	0.136083	−	0.235702i
$25$	25.0000			0.200000
$26$	−26.0000	−	90.0666i	−0.196116	−	0.679366i
$27$	−152.000			−1.08342
$28$	−46.0000	+	79.6743i	−0.310471	+	0.537751i
$29$	−60.0000	+	103.923i	−0.384197	+	0.665449i	−0.991657	−	0.128901i	$-0.958855\pi$
$29$	−60.0000	+	103.923i	−0.384197	+	0.665449i	0.607460	+	0.794350i	$0.292188\pi$
$30$	20.0000	+	34.6410i	0.121716	+	0.210819i
$31$	−34.0000			−0.196986			−0.0984932	−	0.995138i	$-0.531402\pi$
$31$	−34.0000			−0.196986			−0.0984932	+	0.995138i	$0.531402\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	114.000	+	197.454i	0.601359	+	1.04158i
$34$	−96.0000			−0.484231
$35$	−57.5000	−	99.5929i	−0.277694	−	0.480979i
$36$	22.0000	−	38.1051i	0.101852	−	0.176413i
$37$	−113.500	+	196.588i	−0.504305	+	0.873482i	0.495683	+	0.868504i	$0.334918\pi$
$37$	−113.500	+	196.588i	−0.504305	+	0.873482i	−0.999988	+	0.00497814i	$0.998415\pi$
$38$	−10.0000			−0.0426898
$39$	52.0000	+	180.133i	0.213504	+	0.739600i
$40$	−40.0000			−0.158114
$41$	−3.00000	+	5.19615i	−0.0114273	+	0.0197927i	−0.871683	−	0.490071i	$-0.836971\pi$
$41$	−3.00000	+	5.19615i	−0.0114273	+	0.0197927i	0.860255	+	0.509864i	$0.170304\pi$
$42$	92.0000	−	159.349i	0.337998	−	0.585429i
$43$	107.000	+	185.329i	0.379473	+	0.657267i	0.990986	−	0.133968i	$-0.0427719\pi$
$43$	107.000	+	185.329i	0.379473	+	0.657267i	−0.611512	+	0.791235i	$0.709439\pi$
$44$	−228.000			−0.781188
$45$	27.5000	+	47.6314i	0.0910991	+	0.157788i
$46$	−180.000	−	311.769i	−0.576947	−	0.999301i
$47$	549.000			1.70383			0.851914	−	0.523682i	$-0.175442\pi$
$47$	549.000			1.70383			0.851914	+	0.523682i	$0.175442\pi$
$48$	−32.0000	−	55.4256i	−0.0962250	−	0.166667i
$49$	−93.0000	+	161.081i	−0.271137	+	0.469623i
$50$	25.0000	−	43.3013i	0.0707107	−	0.122474i
$51$	192.000			0.527164
$52$	−182.000	−	45.0333i	−0.485363	−	0.120096i
$53$	−537.000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$53$	−537.000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$54$	−152.000	+	263.272i	−0.383048	+	0.663458i
$55$	142.500	−	246.817i	0.349358	−	0.605106i
$56$	92.0000	+	159.349i	0.219536	+	0.380248i
$57$	20.0000			0.0464748
$58$	120.000	+	207.846i	0.271668	+	0.470544i
$59$	150.000	+	259.808i	0.330989	+	0.573289i	0.982706	−	0.185173i	$-0.0592844\pi$
$59$	150.000	+	259.808i	0.330989	+	0.573289i	−0.651717	+	0.758462i	$0.725951\pi$
$60$	80.0000			0.172133
$61$	161.000	+	278.860i	0.337933	+	0.585318i	0.984044	−	0.177926i	$-0.0569388\pi$
$61$	161.000	+	278.860i	0.337933	+	0.585318i	−0.646110	+	0.763244i	$0.723605\pi$
$62$	−34.0000	+	58.8897i	−0.0696452	+	0.120629i
$63$	126.500	−	219.104i	0.252976	−	0.438168i
$64$	64.0000			0.125000
$65$	162.500	−	168.875i	0.310087	−	0.322252i
$66$	456.000			0.850450
$67$	386.000	−	668.572i	0.703842	−	1.21909i	−0.263266	−	0.964723i	$-0.584800\pi$
$67$	386.000	−	668.572i	0.703842	−	1.21909i	0.967108	−	0.254367i	$-0.0818670\pi$
$68$	−96.0000	+	166.277i	−0.171202	+	0.296530i
$69$	360.000	+	623.538i	0.628100	+	1.08790i
$70$	−230.000			−0.392718
$71$	447.000	+	774.227i	0.747171	+	1.29414i	0.949174	+	0.314753i	$0.101922\pi$
$71$	447.000	+	774.227i	0.747171	+	1.29414i	−0.202003	+	0.979385i	$0.564745\pi$
$72$	−44.0000	−	76.2102i	−0.0720201	−	0.124743i
$73$	272.000			0.436099			0.218049	−	0.975938i	$-0.430031\pi$
$73$	272.000			0.436099			0.218049	+	0.975938i	$0.430031\pi$
$74$	227.000	+	393.176i	0.356597	+	0.617645i
$75$	−50.0000	+	86.6025i	−0.0769800	+	0.133333i
$76$	−10.0000	+	17.3205i	−0.0150931	+	0.0261421i
$77$	−1311.00			−1.94029
$78$	364.000	+	90.0666i	0.528396	+	0.130744i
$79$	−454.000			−0.646570			−0.323285	−	0.946302i	$-0.604787\pi$
$79$	−454.000			−0.646570			−0.323285	+	0.946302i	$0.604787\pi$
$80$	−40.0000	+	69.2820i	−0.0559017	+	0.0968246i
$81$	155.500	−	269.334i	0.213306	−	0.369457i
$82$	6.00000	+	10.3923i	0.00808036	+	0.0139956i
$83$	−1068.00			−1.41239			−0.706194	−	0.708018i	$-0.749589\pi$
$83$	−1068.00			−1.41239			−0.706194	+	0.708018i	$0.749589\pi$
$84$	−184.000	−	318.697i	−0.239001	−	0.413961i
$85$	−120.000	−	207.846i	−0.153127	−	0.265224i
$86$	428.000			0.536656
$87$	−240.000	−	415.692i	−0.295755	−	0.512263i
$88$	−228.000	+	394.908i	−0.276192	+	0.478378i
$89$	−340.500	+	589.763i	−0.405539	+	0.702413i	−0.994384	−	0.105832i	$-0.966249\pi$
$89$	−340.500	+	589.763i	−0.405539	+	0.702413i	0.588845	+	0.808246i	$0.299583\pi$
$90$	110.000			0.128834
$91$	−1046.50	−	258.942i	−1.20553	−	0.298291i
$92$	−720.000			−0.815926
$93$	68.0000	−	117.779i	0.0758201	−	0.131324i
$94$	549.000	−	950.896i	0.602394	−	1.04338i
$95$	−12.5000	−	21.6506i	−0.0134997	−	0.0233822i
$96$	−128.000			−0.136083
$97$	−550.000	−	952.628i	−0.575712	−	0.997162i	−0.995964	−	0.0897546i	$-0.971392\pi$
$97$	−550.000	−	952.628i	−0.575712	−	0.997162i	0.420252	−	0.907407i	$-0.361942\pi$
$98$	186.000	+	322.161i	0.191723	+	0.332074i
$99$	627.000			0.636524
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−222.000	+	384.515i	−0.218711	+	0.378819i	−0.954414	−	0.298485i	$-0.903519\pi$
$101$	−222.000	+	384.515i	−0.218711	+	0.378819i	0.735703	+	0.677304i	$0.236852\pi$
$102$	192.000	−	332.554i	0.186381	−	0.322821i
$103$	−1435.00			−1.37276			−0.686382	−	0.727241i	$-0.740802\pi$
$103$	−1435.00			−1.37276			−0.686382	+	0.727241i	$0.740802\pi$
$104$	−260.000	+	270.200i	−0.245145	+	0.254762i
$105$	460.000			0.427537
$106$	−537.000	+	930.111i	−0.492057	+	0.852268i
$107$	1017.00	−	1761.50i	0.918851	−	1.59150i	0.117689	−	0.993051i	$-0.462451\pi$
$107$	1017.00	−	1761.50i	0.918851	−	1.59150i	0.801163	−	0.598447i	$-0.204215\pi$
$108$	304.000	+	526.543i	0.270856	+	0.469136i
$109$	2198.00			1.93147			0.965735	−	0.259530i	$-0.0835678\pi$
$109$	2198.00			1.93147			0.965735	+	0.259530i	$0.0835678\pi$
$110$	−285.000	−	493.634i	−0.247033	−	0.427875i
$111$	−454.000	−	786.351i	−0.388214	−	0.672407i
$112$	368.000			0.310471
$113$	468.000	+	810.600i	0.389608	+	0.674821i	0.992397	−	0.123080i	$-0.0392771\pi$
$113$	468.000	+	810.600i	0.389608	+	0.674821i	−0.602789	+	0.797901i	$0.705944\pi$
$114$	20.0000	−	34.6410i	0.0164313	−	0.0284599i
$115$	450.000	−	779.423i	0.364893	−	0.632014i
$116$	480.000			0.384197
$117$	500.500	+	123.842i	0.395481	+	0.0978561i
$118$	600.000			0.468089
$119$	−552.000	+	956.092i	−0.425225	+	0.736511i
$120$	80.0000	−	138.564i	0.0608581	−	0.105409i
$121$	−959.000	−	1661.04i	−0.720511	−	1.24796i
$122$	644.000			0.477910
$123$	−12.0000	−	20.7846i	−0.00879678	−	0.0152365i
$124$	68.0000	+	117.779i	0.0492466	+	0.0852976i
$125$	125.000			0.0894427
$126$	−253.000	−	438.209i	−0.178881	−	0.309831i
$127$	888.500	−	1538.93i	0.620800	−	1.07526i	−0.368537	−	0.929613i	$-0.620141\pi$
$127$	888.500	−	1538.93i	0.620800	−	1.07526i	0.989337	−	0.145644i	$-0.0465255\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−856.000			−0.584237
$130$	−130.000	−	450.333i	−0.0877058	−	0.303822i
$131$	−489.000			−0.326138			−0.163069	−	0.986615i	$-0.552139\pi$
$131$	−489.000			−0.326138			−0.163069	+	0.986615i	$0.552139\pi$
$132$	456.000	−	789.815i	0.300680	−	0.520792i
$133$	−57.5000	+	99.5929i	−0.0374878	+	0.0649308i
$134$	−772.000	−	1337.14i	−0.497691	−	0.862027i
$135$	−760.000			−0.484521
$136$	192.000	+	332.554i	0.121058	+	0.209678i
$137$	144.000	+	249.415i	0.0898011	+	0.155540i	0.907427	−	0.420210i	$-0.138044\pi$
$137$	144.000	+	249.415i	0.0898011	+	0.155540i	−0.817626	+	0.575750i	$0.804710\pi$
$138$	1440.00			0.888268
$139$	315.500	+	546.462i	0.192521	+	0.333455i	0.946085	−	0.323919i	$-0.105000\pi$
$139$	315.500	+	546.462i	0.192521	+	0.333455i	−0.753564	+	0.657374i	$0.771667\pi$
$140$	−230.000	+	398.372i	−0.138847	+	0.240490i
$141$	−1098.00	+	1901.79i	−0.655803	+	1.13588i
$142$	1788.00			1.05666
$143$	−741.000	−	2566.90i	−0.433325	−	1.50108i
$144$	−176.000			−0.101852
$145$	−300.000	+	519.615i	−0.171818	+	0.297598i
$146$	272.000	−	471.118i	0.154184	−	0.267055i
$147$	−372.000	−	644.323i	−0.208721	−	0.361516i
$148$	908.000			0.504305
$149$	1011.00	+	1751.10i	0.555868	+	0.962792i	0.997835	+	0.0657606i	$0.0209474\pi$
$149$	1011.00	+	1751.10i	0.555868	+	0.962792i	−0.441967	+	0.897031i	$0.645719\pi$
$150$	100.000	+	173.205i	0.0544331	+	0.0942809i
$151$	1574.00			0.848280			0.424140	−	0.905597i	$-0.360576\pi$
$151$	1574.00			0.848280			0.424140	+	0.905597i	$0.360576\pi$
$152$	20.0000	+	34.6410i	0.0106725	+	0.0184852i
$153$	264.000	−	457.261i	0.139498	−	0.241617i
$154$	−1311.00	+	2270.72i	−0.685996	+	1.18818i
$155$	−170.000			−0.0880950
$156$	520.000	−	540.400i	0.266880	−	0.277350i
$157$	1109.00			0.563744			0.281872	−	0.959452i	$-0.409045\pi$
$157$	1109.00			0.563744			0.281872	+	0.959452i	$0.409045\pi$
$158$	−454.000	+	786.351i	−0.228597	+	0.395941i
$159$	1074.00	−	1860.22i	0.535684	−	0.927832i
$160$	80.0000	+	138.564i	0.0395285	+	0.0684653i
$161$	−4140.00			−2.02657
$162$	−311.000	−	538.668i	−0.150830	−	0.261245i
$163$	62.0000	+	107.387i	0.0297927	+	0.0516025i	0.880537	−	0.473977i	$-0.157182\pi$
$163$	62.0000	+	107.387i	0.0297927	+	0.0516025i	−0.850745	+	0.525579i	$0.823849\pi$
$164$	24.0000			0.0114273
$165$	570.000	+	987.269i	0.268936	+	0.465811i
$166$	−1068.00	+	1849.83i	−0.499355	+	0.864908i
$167$	−1972.50	+	3416.47i	−0.913992	+	1.58308i	−0.105621	+	0.994406i	$0.533683\pi$
$167$	−1972.50	+	3416.47i	−0.913992	+	1.58308i	−0.808371	+	0.588674i	$0.799650\pi$
$168$	−736.000			−0.337998
$169$	−84.5000	−	2195.37i	−0.0384615	−	0.999260i
$170$	−480.000			−0.216555
$171$	27.5000	−	47.6314i	0.0122981	−	0.0213010i
$172$	428.000	−	741.318i	0.189737	−	0.328633i
$173$	1762.50	+	3052.74i	0.774569	+	1.34159i	0.935037	+	0.354551i	$0.115366\pi$
$173$	1762.50	+	3052.74i	0.774569	+	1.34159i	−0.160468	+	0.987041i	$0.551300\pi$
$174$	−960.000			−0.418261
$175$	−287.500	−	497.965i	−0.124188	−	0.215100i
$176$	456.000	+	789.815i	0.195297	+	0.338265i
$177$	−1200.00			−0.509591
$178$	681.000	+	1179.53i	0.286759	+	0.496681i
$179$	−222.000	+	384.515i	−0.0926987	+	0.160559i	−0.908646	−	0.417568i	$-0.862883\pi$
$179$	−222.000	+	384.515i	−0.0926987	+	0.160559i	0.815947	+	0.578126i	$0.196216\pi$
$180$	110.000	−	190.526i	0.0455495	−	0.0788941i
$181$	3638.00			1.49398			0.746990	−	0.664835i	$-0.231498\pi$
$181$	3638.00			1.49398			0.746990	+	0.664835i	$0.231498\pi$
$182$	−1495.00	+	1553.65i	−0.608883	+	0.632770i
$183$	−1288.00			−0.520283
$184$	−720.000	+	1247.08i	−0.288473	+	0.499651i
$185$	−567.500	+	982.939i	−0.225532	+	0.390633i
$186$	−136.000	−	235.559i	−0.0536129	−	0.0928603i
$187$	−2736.00			−1.06993
$188$	−1098.00	−	1901.79i	−0.425957	−	0.737779i
$189$	1748.00	+	3027.62i	0.672742	+	1.16522i
$190$	−50.0000			−0.0190915
$191$	−585.000	−	1013.25i	−0.221618	−	0.383854i	0.733681	−	0.679494i	$-0.237801\pi$
$191$	−585.000	−	1013.25i	−0.221618	−	0.383854i	−0.955300	+	0.295640i	$0.904467\pi$
$192$	−128.000	+	221.703i	−0.0481125	+	0.0833333i
$193$	−904.000	+	1565.77i	−0.337157	+	0.583973i	−0.983897	−	0.178737i	$-0.942799\pi$
$193$	−904.000	+	1565.77i	−0.337157	+	0.583973i	0.646740	+	0.762711i	$0.276132\pi$
$194$	−2200.00			−0.814179
$195$	260.000	+	900.666i	0.0954820	+	0.330759i
$196$	744.000			0.271137
$197$	1729.50	−	2995.58i	0.625491	−	1.08338i	−0.362954	−	0.931807i	$-0.618232\pi$
$197$	1729.50	−	2995.58i	0.625491	−	1.08338i	0.988446	−	0.151576i	$-0.0484347\pi$
$198$	627.000	−	1086.00i	0.225045	−	0.389790i
$199$	815.000	+	1411.62i	0.290321	+	0.502850i	0.973886	−	0.227040i	$-0.0729047\pi$
$199$	815.000	+	1411.62i	0.290321	+	0.502850i	−0.683565	+	0.729890i	$0.739571\pi$
$200$	−200.000			−0.0707107
$201$	1544.00	+	2674.29i	0.541818	+	0.938456i
$202$	444.000	+	769.031i	0.154652	+	0.267865i
$203$	2760.00			0.954256
$204$	−384.000	−	665.108i	−0.131791	−	0.228269i
$205$	−15.0000	+	25.9808i	−0.00511047	+	0.00885159i
$206$	−1435.00	+	2485.49i	−0.485346	+	0.840643i
$207$	1980.00			0.664829
$208$	208.000	+	720.533i	0.0693375	+	0.240192i
$209$	−285.000			−0.0943247
$210$	460.000	−	796.743i	0.151157	−	0.261812i
$211$	408.500	−	707.543i	0.133281	−	0.230850i	−0.791658	−	0.610964i	$-0.790782\pi$
$211$	408.500	−	707.543i	0.133281	−	0.230850i	0.924939	+	0.380114i	$0.124115\pi$
$212$	1074.00	+	1860.22i	0.347937	+	0.602644i
$213$	−3576.00			−1.15034
$214$	−2034.00	−	3522.99i	−0.649726	−	1.12536i
$215$	535.000	+	926.647i	0.169706	+	0.293939i
$216$	1216.00			0.383048
$217$	391.000	+	677.232i	0.122317	+	0.211859i
$218$	2198.00	−	3807.05i	0.682878	−	1.18278i
$219$	−544.000	+	942.236i	−0.167854	+	0.290732i
$220$	−1140.00			−0.349358
$221$	−2184.00	−	540.400i	−0.664759	−	0.164485i
$222$	−1816.00			−0.549018
$223$	63.5000	−	109.985i	0.0190685	−	0.0330276i	−0.856334	−	0.516423i	$-0.827263\pi$
$223$	63.5000	−	109.985i	0.0190685	−	0.0330276i	0.875402	+	0.483395i	$0.160597\pi$
$224$	368.000	−	637.395i	0.109768	−	0.190124i
$225$	137.500	+	238.157i	0.0407407	+	0.0705650i
$226$	1872.00			0.550989
$227$	2754.00	+	4770.07i	0.805240	+	1.39472i	0.916129	+	0.400883i	$0.131297\pi$
$227$	2754.00	+	4770.07i	0.805240	+	1.39472i	−0.110890	+	0.993833i	$0.535370\pi$
$228$	−40.0000	−	69.2820i	−0.0116187	−	0.0201242i
$229$	−226.000			−0.0652162			−0.0326081	−	0.999468i	$-0.510381\pi$
$229$	−226.000			−0.0652162			−0.0326081	+	0.999468i	$0.510381\pi$
$230$	−900.000	−	1558.85i	−0.258018	−	0.446901i
$231$	2622.00	−	4541.44i	0.746818	−	1.29353i
$232$	480.000	−	831.384i	0.135834	−	0.235272i
$233$	3618.00			1.01727			0.508633	−	0.860983i	$-0.330151\pi$
$233$	3618.00			1.01727			0.508633	+	0.860983i	$0.330151\pi$
$234$	715.000	−	743.050i	0.199748	−	0.207584i
$235$	2745.00			0.761975
$236$	600.000	−	1039.23i	0.165494	−	0.286645i
$237$	908.000	−	1572.70i	0.248865	−	0.431046i
$238$	1104.00	+	1912.18i	0.300679	+	0.520792i
$239$	−3150.00			−0.852538			−0.426269	−	0.904596i	$-0.640172\pi$
$239$	−3150.00			−0.852538			−0.426269	+	0.904596i	$0.640172\pi$
$240$	−160.000	−	277.128i	−0.0430331	−	0.0745356i
$241$	2208.50	+	3825.23i	0.590299	+	1.02243i	0.994192	+	0.107621i	$0.0343234\pi$
$241$	2208.50	+	3825.23i	0.590299	+	1.02243i	−0.403893	+	0.914806i	$0.632343\pi$
$242$	−3836.00			−1.01896
$243$	−1430.00	−	2476.83i	−0.377508	−	0.653864i
$244$	644.000	−	1115.44i	0.168967	−	0.292659i
$245$	−465.000	+	805.404i	−0.121256	+	0.210022i
$246$	−48.0000			−0.0124405
$247$	−227.500	−	56.2917i	−0.0586052	−	0.0145010i
$248$	272.000			0.0696452
$249$	2136.00	−	3699.66i	0.543629	−	0.941592i
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	−2242.50	−	3884.12i	−0.563926	−	0.976748i	−0.997149	−	0.0754612i	$-0.975957\pi$
$251$	−2242.50	−	3884.12i	−0.563926	−	0.976748i	0.433223	−	0.901287i	$-0.357376\pi$
$252$	−1012.00			−0.252976
$253$	−5130.00	−	8885.42i	−1.27478	−	2.20799i
$254$	−1777.00	−	3077.85i	−0.438972	−	0.760322i
$255$	960.000			0.235755
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2292.00	+	3969.86i	−0.556308	+	0.963553i	0.441493	+	0.897265i	$0.354449\pi$
$257$	−2292.00	+	3969.86i	−0.556308	+	0.963553i	−0.997801	+	0.0662882i	$0.978884\pi$
$258$	−856.000	+	1482.64i	−0.206559	+	0.357771i
$259$	5221.00			1.25258
$260$	−910.000	−	225.167i	−0.217061	−	0.0537086i
$261$	−1320.00			−0.313050
$262$	−489.000	+	846.973i	−0.115307	+	0.199718i
$263$	−2848.50	+	4933.75i	−0.667856	+	1.15676i	0.310647	+	0.950525i	$0.399454\pi$
$263$	−2848.50	+	4933.75i	−0.667856	+	1.15676i	−0.978503	+	0.206235i	$0.933879\pi$
$264$	−912.000	−	1579.63i	−0.212613	−	0.368256i
$265$	−2685.00			−0.622408
$266$	115.000	+	199.186i	0.0265079	+	0.0459130i
$267$	−1362.00	−	2359.05i	−0.312184	−	0.540718i
$268$	−3088.00			−0.703842
$269$	1998.00	+	3460.64i	0.452863	+	0.784382i	0.998563	−	0.0535989i	$-0.0170692\pi$
$269$	1998.00	+	3460.64i	0.452863	+	0.784382i	−0.545699	+	0.837981i	$0.683736\pi$
$270$	−760.000	+	1316.36i	−0.171304	+	0.296708i
$271$	1640.00	−	2840.56i	0.367612	−	0.636723i	−0.621579	−	0.783351i	$-0.713509\pi$
$271$	1640.00	−	2840.56i	0.367612	−	0.636723i	0.989192	+	0.146628i	$0.0468421\pi$
$272$	768.000			0.171202
$273$	2990.00	−	3107.30i	0.662868	−	0.688873i
$274$	576.000			0.126998
$275$	712.500	−	1234.09i	0.156238	−	0.270612i
$276$	1440.00	−	2494.15i	0.314050	−	0.543951i
$277$	2898.50	+	5020.35i	0.628715	+	1.08897i	0.987810	+	0.155665i	$0.0497520\pi$
$277$	2898.50	+	5020.35i	0.628715	+	1.08897i	−0.359095	+	0.933301i	$0.616915\pi$
$278$	1262.00			0.272265
$279$	−187.000	−	323.894i	−0.0401269	−	0.0695018i
$280$	460.000	+	796.743i	0.0981795	+	0.170052i
$281$	−1446.00			−0.306979			−0.153490	−	0.988150i	$-0.549051\pi$
$281$	−1446.00			−0.306979			−0.153490	+	0.988150i	$0.549051\pi$
$282$	2196.00	+	3803.58i	0.463723	+	0.803192i
$283$	449.000	−	777.691i	0.0943119	−	0.163353i	−0.815009	−	0.579448i	$-0.803268\pi$
$283$	449.000	−	777.691i	0.0943119	−	0.163353i	0.909321	+	0.416095i	$0.136602\pi$
$284$	1788.00	−	3096.91i	0.373585	−	0.647069i
$285$	100.000			0.0207842
$286$	−5187.00	−	1283.45i	−1.07243	−	0.265357i
$287$	138.000			0.0283829
$288$	−176.000	+	304.841i	−0.0360101	+	0.0623713i
$289$	1304.50	−	2259.46i	0.265520	−	0.459894i
$290$	600.000	+	1039.23i	0.121494	+	0.210434i
$291$	4400.00			0.886366
$292$	−544.000	−	942.236i	−0.109025	−	0.188836i
$293$	−208.500	−	361.133i	−0.0415724	−	0.0720054i	0.844491	−	0.535570i	$-0.179903\pi$
$293$	−208.500	−	361.133i	−0.0415724	−	0.0720054i	−0.886063	+	0.463565i	$0.846570\pi$
$294$	−1488.00			−0.295177
$295$	750.000	+	1299.04i	0.148023	+	0.256383i
$296$	908.000	−	1572.70i	0.178299	−	0.308822i
$297$	−4332.00	+	7503.24i	−0.846357	+	1.46593i
$298$	4044.00			0.786116
$299$	−2340.00	−	8106.00i	−0.452594	−	1.56783i
$300$	400.000			0.0769800
$301$	2461.00	−	4262.58i	0.471261	−	0.816249i
$302$	1574.00	−	2726.25i	0.299912	−	0.519463i
$303$	−888.000	−	1538.06i	−0.168364	−	0.291615i
$304$	80.0000			0.0150931
$305$	805.000	+	1394.30i	0.151128	+	0.261762i
$306$	−528.000	−	914.523i	−0.0986397	−	0.170849i
$307$	6734.00			1.25189			0.625944	−	0.779868i	$-0.284714\pi$
$307$	6734.00			1.25189			0.625944	+	0.779868i	$0.284714\pi$
$308$	2622.00	+	4541.44i	0.485072	+	0.840170i
$309$	2870.00	−	4970.99i	0.528377	−	0.915176i
$310$	−170.000	+	294.449i	−0.0311463	+	0.0539470i
$311$	−7020.00			−1.27996			−0.639980	−	0.768391i	$-0.721057\pi$
$311$	−7020.00			−1.27996			−0.639980	+	0.768391i	$0.721057\pi$
$312$	−416.000	−	1441.07i	−0.0754851	−	0.261488i
$313$	−4018.00			−0.725594			−0.362797	−	0.931868i	$-0.618178\pi$
$313$	−4018.00			−0.725594			−0.362797	+	0.931868i	$0.618178\pi$
$314$	1109.00	−	1920.84i	0.199314	−	0.345221i
$315$	632.500	−	1095.52i	0.113134	−	0.195955i
$316$	908.000	+	1572.70i	0.161642	+	0.279973i
$317$	−8625.00			−1.52816			−0.764082	−	0.645119i	$-0.776808\pi$
$317$	−8625.00			−1.52816			−0.764082	+	0.645119i	$0.776808\pi$
$318$	−2148.00	−	3720.45i	−0.378786	−	0.656076i
$319$	3420.00	+	5923.61i	0.600261	+	1.03968i
$320$	320.000			0.0559017
$321$	4068.00	+	7045.98i	0.707332	+	1.22514i
$322$	−4140.00	+	7170.69i	−0.716501	+	1.24102i
$323$	−120.000	+	207.846i	−0.0206718	+	0.0358045i
$324$	−1244.00			−0.213306
$325$	812.500	−	844.375i	0.138675	−	0.144115i
$326$	248.000			0.0421333
$327$	−4396.00	+	7614.10i	−0.743423	+	1.28765i
$328$	24.0000	−	41.5692i	0.00404018	−	0.00699779i
$329$	−6313.50	−	10935.3i	−1.05798	−	1.83247i
$330$	2280.00			0.380333
$331$	−4030.00	−	6980.16i	−0.669211	−	1.15911i	−0.978125	−	0.208017i	$-0.933299\pi$
$331$	−4030.00	−	6980.16i	−0.669211	−	1.15911i	0.308914	−	0.951090i	$-0.400034\pi$
$332$	2136.00	+	3699.66i	0.353097	+	0.611582i
$333$	−2497.00			−0.410915
$334$	3945.00	+	6832.94i	0.646290	+	1.11941i
$335$	1930.00	−	3342.86i	0.314768	−	0.545194i
$336$	−736.000	+	1274.79i	−0.119500	+	0.206981i
$337$	698.000			0.112826			0.0564132	−	0.998408i	$-0.482034\pi$
$337$	698.000			0.112826			0.0564132	+	0.998408i	$0.482034\pi$
$338$	−3887.00	−	2049.02i	−0.625518	−	0.329739i
$339$	−3744.00			−0.599841
$340$	−480.000	+	831.384i	−0.0765637	+	0.132612i
$341$	−969.000	+	1678.36i	−0.153884	+	0.266534i
$342$	−55.0000	−	95.2628i	−0.00869608	−	0.0150621i
$343$	−3611.00			−0.568442
$344$	−856.000	−	1482.64i	−0.134164	−	0.232379i
$345$	1800.00	+	3117.69i	0.280895	+	0.486524i
$346$	7050.00			1.09541
$347$	−1206.00	−	2088.85i	−0.186575	−	0.323157i	0.757531	−	0.652799i	$-0.226405\pi$
$347$	−1206.00	−	2088.85i	−0.186575	−	0.323157i	−0.944106	+	0.329642i	$0.893072\pi$
$348$	−960.000	+	1662.77i	−0.147878	+	0.256132i
$349$	1706.00	−	2954.88i	0.261662	−	0.453212i	−0.705022	−	0.709186i	$-0.749063\pi$
$349$	1706.00	−	2954.88i	0.261662	−	0.453212i	0.966684	+	0.255974i	$0.0823961\pi$
$350$	−1150.00			−0.175629
$351$	−4940.00	+	5133.80i	−0.751218	+	0.780689i
$352$	1824.00			0.276192
$353$	−414.000	+	717.069i	−0.0624221	+	0.108118i	−0.895548	−	0.444966i	$-0.853216\pi$
$353$	−414.000	+	717.069i	−0.0624221	+	0.108118i	0.833125	+	0.553084i	$0.186549\pi$
$354$	−1200.00	+	2078.46i	−0.180167	+	0.312059i
$355$	2235.00	+	3871.13i	0.334145	+	0.578756i
$356$	2724.00			0.405539
$357$	−2208.00	−	3824.37i	−0.327338	−	0.566966i
$358$	444.000	+	769.031i	0.0655478	+	0.113532i
$359$	−3354.00			−0.493085			−0.246542	−	0.969132i	$-0.579294\pi$
$359$	−3354.00			−0.493085			−0.246542	+	0.969132i	$0.579294\pi$
$360$	−220.000	−	381.051i	−0.0322084	−	0.0557866i
$361$	3417.00	−	5918.42i	0.498178	−	0.862869i
$362$	3638.00	−	6301.20i	0.528202	−	0.914872i
$363$	7672.00			1.10930
$364$	1196.00	+	4143.07i	0.172218	+	0.596581i
$365$	1360.00			0.195029
$366$	−1288.00	+	2230.88i	−0.183948	+	0.318607i
$367$	908.000	−	1572.70i	0.129148	−	0.223690i	−0.794199	−	0.607658i	$-0.792109\pi$
$367$	908.000	−	1572.70i	0.129148	−	0.223690i	0.923347	+	0.383967i	$0.125443\pi$
$368$	1440.00	+	2494.15i	0.203981	+	0.353306i
$369$	−66.0000			−0.00931117
$370$	1135.00	+	1965.88i	0.159475	+	0.276219i
$371$	6175.50	+	10696.3i	0.864194	+	1.49683i
$372$	−544.000			−0.0758201
$373$	1079.00	+	1868.88i	0.149782	+	0.259429i	0.931147	−	0.364645i	$-0.118810\pi$
$373$	1079.00	+	1868.88i	0.149782	+	0.259429i	−0.781365	+	0.624074i	$0.785476\pi$
$374$	−2736.00	+	4738.89i	−0.378276	+	0.655193i
$375$	−250.000	+	433.013i	−0.0344265	+	0.0596285i
$376$	−4392.00			−0.602394
$377$	1560.00	+	5404.00i	0.213114	+	0.738250i
$378$	6992.00			0.951401
$379$	−5744.50	+	9949.77i	−0.778562	+	1.34851i	0.154208	+	0.988038i	$0.450717\pi$
$379$	−5744.50	+	9949.77i	−0.778562	+	1.34851i	−0.932770	+	0.360471i	$0.882616\pi$
$380$	−50.0000	+	86.6025i	−0.00674986	+	0.0116911i
$381$	3554.00	+	6155.71i	0.477892	+	0.827734i
$382$	−2340.00			−0.313416
$383$	2310.00	+	4001.04i	0.308187	+	0.533795i	0.977966	−	0.208765i	$-0.0669445\pi$
$383$	2310.00	+	4001.04i	0.308187	+	0.533795i	−0.669779	+	0.742560i	$0.733611\pi$
$384$	256.000	+	443.405i	0.0340207	+	0.0589256i
$385$	−6555.00			−0.867724
$386$	1808.00	+	3131.55i	0.238406	+	0.412932i
$387$	−1177.00	+	2038.62i	−0.154600	+	0.267775i
$388$	−2200.00	+	3810.51i	−0.287856	+	0.498581i
$389$	3000.00			0.391018			0.195509	−	0.980702i	$-0.437364\pi$
$389$	3000.00			0.391018			0.195509	+	0.980702i	$0.437364\pi$
$390$	1820.00	+	450.333i	0.236306	+	0.0584705i
$391$	−8640.00			−1.11750
$392$	744.000	−	1288.65i	0.0958614	−	0.166037i
$393$	978.000	−	1693.95i	0.125531	−	0.217426i
$394$	−3459.00	−	5991.16i	−0.442289	−	0.766067i
$395$	−2270.00			−0.289155
$396$	−1254.00	−	2171.99i	−0.159131	−	0.275623i
$397$	−3689.50	−	6390.40i	−0.466425	−	0.807872i	0.532840	−	0.846216i	$-0.321125\pi$
$397$	−3689.50	−	6390.40i	−0.466425	−	0.807872i	−0.999265	+	0.0383446i	$0.987792\pi$
$398$	3260.00			0.410575
$399$	−230.000	−	398.372i	−0.0288582	−	0.0499838i
$400$	−200.000	+	346.410i	−0.0250000	+	0.0433013i
$401$	4507.50	−	7807.22i	0.561331	−	0.972254i	−0.436049	−	0.899923i	$-0.643623\pi$
$401$	4507.50	−	7807.22i	0.561331	−	0.972254i	0.997381	−	0.0723314i	$-0.0230439\pi$
$402$	6176.00			0.766246
$403$	−1105.00	+	1148.35i	−0.136586	+	0.141944i
$404$	1776.00			0.218711
$405$	777.500	−	1346.67i	0.0953933	−	0.165226i
$406$	2760.00	−	4780.46i	0.337381	−	0.584360i
$407$	6469.50	+	11205.5i	0.787915	+	1.36471i
$408$	−1536.00			−0.186381
$409$	687.500	+	1190.78i	0.0831166	+	0.143962i	0.904587	−	0.426289i	$-0.140179\pi$
$409$	687.500	+	1190.78i	0.0831166	+	0.143962i	−0.821471	+	0.570251i	$0.806846\pi$
$410$	30.0000	+	51.9615i	0.00361364	+	0.00625902i
$411$	−1152.00			−0.138258
$412$	2870.00	+	4970.99i	0.343191	+	0.594424i
$413$	3450.00	−	5975.58i	0.411049	−	0.711958i
$414$	1980.00	−	3429.46i	0.235052	−	0.407123i
$415$	−5340.00			−0.631639
$416$	1456.00	+	360.267i	0.171602	+	0.0424604i
$417$	−2524.00			−0.296405
$418$	−285.000	+	493.634i	−0.0333488	+	0.0577618i
$419$	3822.00	−	6619.90i	0.445625	−	0.771845i	−0.552470	−	0.833532i	$-0.686315\pi$
$419$	3822.00	−	6619.90i	0.445625	−	0.771845i	0.998096	+	0.0616872i	$0.0196481\pi$
$420$	−920.000	−	1593.49i	−0.106884	−	0.185129i
$421$	−12700.0			−1.47021			−0.735107	−	0.677951i	$-0.762868\pi$
$421$	−12700.0			−1.47021			−0.735107	+	0.677951i	$0.762868\pi$
$422$	−817.000	−	1415.09i	−0.0942439	−	0.163235i
$423$	3019.50	+	5229.93i	0.347076	+	0.601153i
$424$	4296.00			0.492057
$425$	−600.000	−	1039.23i	−0.0684806	−	0.118612i
$426$	−3576.00	+	6193.81i	−0.406708	+	0.704440i
$427$	3703.00	−	6413.78i	0.419674	−	0.726896i
$428$	−8136.00			−0.918851
$429$	10374.0	+	2566.90i	1.16751	+	0.288884i
$430$	2140.00			0.240000
$431$	630.000	−	1091.19i	0.0704084	−	0.121951i	−0.828672	−	0.559735i	$-0.810903\pi$
$431$	630.000	−	1091.19i	0.0704084	−	0.121951i	0.899080	+	0.437784i	$0.144236\pi$
$432$	1216.00	−	2106.17i	0.135428	−	0.234568i
$433$	−7336.00	−	12706.3i	−0.814193	−	1.41022i	−0.909906	−	0.414815i	$-0.863846\pi$
$433$	−7336.00	−	12706.3i	−0.814193	−	1.41022i	0.0957126	−	0.995409i	$-0.469487\pi$
$434$	1564.00			0.172982
$435$	−1200.00	−	2078.46i	−0.132266	−	0.229091i
$436$	−4396.00	−	7614.10i	−0.482867	−	0.836351i
$437$	−900.000			−0.0985191
$438$	1088.00	+	1884.47i	0.118691	+	0.205579i
$439$	1415.00	−	2450.85i	0.153837	−	0.266453i	−0.778798	−	0.627275i	$-0.784170\pi$
$439$	1415.00	−	2450.85i	0.153837	−	0.266453i	0.932635	+	0.360822i	$0.117504\pi$
$440$	−1140.00	+	1974.54i	−0.123517	+	0.213937i
$441$	−2046.00			−0.220926
$442$	−3120.00	+	3242.40i	−0.335754	+	0.348926i
$443$	10626.0			1.13963			0.569815	−	0.821773i	$-0.307015\pi$
$443$	10626.0			1.13963			0.569815	+	0.821773i	$0.307015\pi$
$444$	−1816.00	+	3145.40i	−0.194107	+	0.336203i
$445$	−1702.50	+	2948.82i	−0.181362	+	0.314129i
$446$	−127.000	−	219.970i	−0.0134835	−	0.0233540i
$447$	−8088.00			−0.855815
$448$	−736.000	−	1274.79i	−0.0776177	−	0.134438i
$449$	−940.500	−	1628.99i	−0.0988529	−	0.171218i	0.812357	−	0.583160i	$-0.198184\pi$
$449$	−940.500	−	1628.99i	−0.0988529	−	0.171218i	−0.911210	+	0.411942i	$0.864851\pi$
$450$	550.000			0.0576161
$451$	171.000	+	296.181i	0.0178538	+	0.0309237i
$452$	1872.00	−	3242.40i	0.194804	−	0.337411i
$453$	−3148.00	+	5452.50i	−0.326503	+	0.565520i
$454$	11016.0			1.13878
$455$	−5232.50	−	1294.71i	−0.539128	−	0.133400i
$456$	−160.000			−0.0164313
$457$	2729.00	−	4726.77i	0.279337	−	0.483827i	−0.691883	−	0.722010i	$-0.743219\pi$
$457$	2729.00	−	4726.77i	0.279337	−	0.483827i	0.971220	+	0.238183i	$0.0765518\pi$
$458$	−226.000	+	391.443i	−0.0230574	+	0.0399366i
$459$	3648.00	+	6318.52i	0.370967	+	0.642534i
$460$	−3600.00			−0.364893
$461$	8646.00	+	14975.3i	0.873502	+	1.51295i	0.858350	+	0.513064i	$0.171490\pi$
$461$	8646.00	+	14975.3i	0.873502	+	1.51295i	0.0151518	+	0.999885i	$0.495177\pi$
$462$	−5244.00	−	9082.87i	−0.528080	−	0.914661i
$463$	−9256.00			−0.929077			−0.464539	−	0.885553i	$-0.653780\pi$
$463$	−9256.00			−0.929077			−0.464539	+	0.885553i	$0.653780\pi$
$464$	−960.000	−	1662.77i	−0.0960493	−	0.166362i
$465$	340.000	−	588.897i	0.0339078	−	0.0587300i
$466$	3618.00	−	6266.56i	0.359658	−	0.622946i
$467$	9876.00			0.978601			0.489301	−	0.872115i	$-0.337252\pi$
$467$	9876.00			0.978601			0.489301	+	0.872115i	$0.337252\pi$
$468$	−572.000	−	1981.47i	−0.0564972	−	0.195712i
$469$	−17756.0			−1.74818
$470$	2745.00	−	4754.48i	0.269399	−	0.466612i
$471$	−2218.00	+	3841.69i	−0.216985	+	0.375829i
$472$	−1200.00	−	2078.46i	−0.117022	−	0.202688i
$473$	12198.0			1.18576
$474$	−1816.00	−	3145.40i	−0.175974	−	0.304796i
$475$	−62.5000	−	108.253i	−0.00603726	−	0.0104568i
$476$	4416.00			0.425225
$477$	−2953.50	−	5115.61i	−0.283504	−	0.491044i
$478$	−3150.00	+	5455.96i	−0.301418	+	0.522071i
$479$	−6540.00	+	11327.6i	−0.623842	+	1.08053i	0.364922	+	0.931038i	$0.381096\pi$
$479$	−6540.00	+	11327.6i	−0.623842	+	1.08053i	−0.988764	+	0.149488i	$0.952238\pi$
$480$	−640.000			−0.0608581
$481$	2951.00	+	10222.6i	0.279738	+	0.969041i
$482$	8834.00			0.834808
$483$	8280.00	−	14341.4i	0.780027	−	1.35105i
$484$	−3836.00	+	6644.15i	−0.360255	+	0.623981i
$485$	−2750.00	−	4763.14i	−0.257466	−	0.445944i
$486$	−5720.00			−0.533878
$487$	4311.50	+	7467.74i	0.401176	+	0.694857i	0.993868	−	0.110572i	$-0.0352682\pi$
$487$	4311.50	+	7467.74i	0.401176	+	0.694857i	−0.592692	+	0.805429i	$0.701935\pi$
$488$	−1288.00	−	2230.88i	−0.119478	−	0.206941i
$489$	−496.000			−0.0458689
$490$	930.000	+	1610.81i	0.0857411	+	0.148508i
$491$	6856.50	−	11875.8i	0.630203	−	1.09154i	−0.357307	−	0.933987i	$-0.616305\pi$
$491$	6856.50	−	11875.8i	0.630203	−	1.09154i	0.987510	−	0.157556i	$-0.0503615\pi$
$492$	−48.0000	+	83.1384i	−0.00439839	+	0.00761823i
$493$	5760.00			0.526202
$494$	−325.000	+	337.750i	−0.0296001	+	0.0307613i
$495$	3135.00			0.284662
$496$	272.000	−	471.118i	0.0246233	−	0.0426488i
$497$	10281.0	−	17807.2i	0.927899	−	1.60717i
$498$	−4272.00	−	7399.32i	−0.384403	−	0.665806i
$499$	1604.00			0.143898			0.0719488	−	0.997408i	$-0.477078\pi$
$499$	1604.00			0.143898			0.0719488	+	0.997408i	$0.477078\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$	−7890.00	−	13665.9i	−0.703591	−	1.21866i
$502$	−8970.00			−0.797511
$503$	−2698.50	−	4673.94i	−0.239205	−	0.414315i	0.721281	−	0.692642i	$-0.243553\pi$
$503$	−2698.50	−	4673.94i	−0.239205	−	0.414315i	−0.960486	+	0.278327i	$0.910220\pi$
$504$	−1012.00	+	1752.84i	−0.0894406	+	0.154916i
$505$	−1110.00	+	1922.58i	−0.0978106	+	0.169413i
$506$	−20520.0			−1.80282
$507$	7774.00	+	4098.03i	0.680977	+	0.358974i
$508$	−7108.00			−0.620800
$509$	−8277.00	+	14336.2i	−0.720769	+	1.24841i	0.239923	+	0.970792i	$0.422878\pi$
$509$	−8277.00	+	14336.2i	−0.720769	+	1.24841i	−0.960692	+	0.277617i	$0.910455\pi$
$510$	960.000	−	1662.77i	0.0833520	−	0.144370i
$511$	−3128.00	−	5417.85i	−0.270792	−	0.469025i
$512$	−512.000			−0.0441942
$513$	380.000	+	658.179i	0.0327045	+	0.0566459i
$514$	4584.00	+	7939.72i	0.393369	+	0.681335i
$515$	−7175.00			−0.613919
$516$	1712.00	+	2965.27i	0.146059	+	0.252982i
$517$	15646.5	−	27100.5i	1.33101	−	2.30538i
$518$	5221.00	−	9043.04i	0.442852	−	0.767043i
$519$	−14100.0			−1.19253
$520$	−1300.00	+	1351.00i	−0.109632	+	0.113933i
$521$	−7407.00			−0.622853			−0.311427	−	0.950270i	$-0.600807\pi$
$521$	−7407.00			−0.622853			−0.311427	+	0.950270i	$0.600807\pi$
$522$	−1320.00	+	2286.31i	−0.110680	+	0.191703i
$523$	−6061.00	+	10498.0i	−0.506748	+	0.877713i	0.493222	+	0.869904i	$0.335819\pi$
$523$	−6061.00	+	10498.0i	−0.506748	+	0.877713i	−0.999970	+	0.00780913i	$0.997514\pi$
$524$	978.000	+	1693.95i	0.0815346	+	0.141222i
$525$	2300.00			0.191200
$526$	5697.00	+	9867.49i	0.472245	+	0.817953i
$527$	816.000	+	1413.35i	0.0674488	+	0.116825i
$528$	−3648.00			−0.300680
$529$	−10116.5	−	17522.3i	−0.831470	−	1.44015i
$530$	−2685.00	+	4650.56i	−0.220055	+	0.381146i
$531$	−1650.00	+	2857.88i	−0.134847	+	0.233562i
$532$	460.000			0.0374878
$533$	78.0000	+	270.200i	0.00633875	+	0.0219581i
$534$	−5448.00			−0.441494
$535$	5085.00	−	8807.48i	0.410923	−	0.711739i
$536$	−3088.00	+	5348.57i	−0.248846	+	0.431013i
$537$	−888.000	−	1538.06i	−0.0713595	−	0.123598i
$538$	7992.00			0.640445
$539$	5301.00	+	9181.60i	0.423618	+	0.733728i
$540$	1520.00	+	2632.72i	0.121130	+	0.209804i
$541$	15590.0			1.23894			0.619470	−	0.785020i	$-0.287348\pi$
$541$	15590.0			1.23894			0.619470	+	0.785020i	$0.287348\pi$
$542$	−3280.00	−	5681.13i	−0.259941	−	0.450231i
$543$	−7276.00	+	12602.4i	−0.575033	+	0.995987i
$544$	768.000	−	1330.22i	0.0605289	−	0.104839i
$545$	10990.0			0.863780
$546$	−2392.00	−	8286.13i	−0.187487	−	0.649476i
$547$	−10618.0			−0.829969			−0.414984	−	0.909829i	$-0.636213\pi$
$547$	−10618.0			−0.829969			−0.414984	+	0.909829i	$0.636213\pi$
$548$	576.000	−	997.661i	0.0449005	−	0.0777700i
$549$	−1771.00	+	3067.46i	−0.137677	+	0.238463i
$550$	−1425.00	−	2468.17i	−0.110477	−	0.191351i
$551$	600.000			0.0463899
$552$	−2880.00	−	4988.31i	−0.222067	−	0.384631i
$553$	5221.00	+	9043.04i	0.401482	+	0.695387i
$554$	11594.0			0.889137
$555$	−2270.00	−	3931.76i	−0.173615	−	0.300709i
$556$	1262.00	−	2185.85i	0.0962603	−	0.166728i
$557$	12331.5	−	21358.8i	0.938065	−	1.62478i	0.168991	−	0.985618i	$-0.445949\pi$
$557$	12331.5	−	21358.8i	0.938065	−	1.62478i	0.769074	−	0.639159i	$-0.220718\pi$
$558$	−748.000			−0.0567480
$559$	9737.00	+	2409.28i	0.736728	+	0.182293i
$560$	1840.00			0.138847
$561$	5472.00	−	9477.78i	0.411815	−	0.713284i
$562$	−1446.00	+	2504.55i	−0.108534	+	0.187986i
$563$	7224.00	+	12512.3i	0.540773	+	0.936647i	0.998860	+	0.0477391i	$0.0152016\pi$
$563$	7224.00	+	12512.3i	0.540773	+	0.936647i	−0.458087	+	0.888908i	$0.651465\pi$
$564$	8784.00			0.655803
$565$	2340.00	+	4053.00i	0.174238	+	0.301789i
$566$	−898.000	−	1555.38i	−0.0666886	−	0.115508i
$567$	−7153.00			−0.529802
$568$	−3576.00	−	6193.81i	−0.264165	−	0.457547i
$569$	7489.50	−	12972.2i	0.551803	−	0.955752i	−0.446341	−	0.894863i	$-0.647273\pi$
$569$	7489.50	−	12972.2i	0.551803	−	0.955752i	0.998145	−	0.0608887i	$-0.0193935\pi$
$570$	100.000	−	173.205i	0.00734831	−	0.0127277i
$571$	5537.00			0.405808			0.202904	−	0.979199i	$-0.434962\pi$
$571$	5537.00			0.405808			0.202904	+	0.979199i	$0.434962\pi$
$572$	−7410.00	+	7700.70i	−0.541657	+	0.562906i
$573$	4680.00			0.341204
$574$	138.000	−	239.023i	0.0100349	−	0.0173809i
$575$	2250.00	−	3897.11i	0.163185	−	0.282645i
$576$	352.000	+	609.682i	0.0254630	+	0.0441031i
$577$	4634.00			0.334343			0.167172	−	0.985928i	$-0.446537\pi$
$577$	4634.00			0.334343			0.167172	+	0.985928i	$0.446537\pi$
$578$	−2609.00	−	4518.92i	−0.187751	−	0.325194i
$579$	−3616.00	−	6263.10i	−0.259544	−	0.449543i
$580$	2400.00			0.171818
$581$	12282.0	+	21273.0i	0.877011	+	1.51903i
$582$	4400.00	−	7621.02i	0.313378	−	0.542786i
$583$	−15304.5	+	26508.2i	−1.08722	+	1.88312i
$584$	−2176.00			−0.154184
$585$	2502.50	+	619.208i	0.176864	+	0.0437626i
$586$	−834.000			−0.0587922
$587$	−9129.00	+	15811.9i	−0.641898	+	1.11180i	0.343111	+	0.939295i	$0.388519\pi$
$587$	−9129.00	+	15811.9i	−0.641898	+	1.11180i	−0.985009	+	0.172505i	$0.944814\pi$
$588$	−1488.00	+	2577.29i	−0.104361	+	0.180758i
$589$	85.0000	+	147.224i	0.00594629	+	0.0102993i
$590$	3000.00			0.209336
$591$	6918.00	+	11982.3i	0.481503	+	0.833988i
$592$	−1816.00	−	3145.40i	−0.126076	−	0.218370i
$593$	15132.0			1.04789			0.523943	−	0.851753i	$-0.324460\pi$
$593$	15132.0			1.04789			0.523943	+	0.851753i	$0.324460\pi$
$594$	8664.00	+	15006.5i	0.598465	+	1.03657i
$595$	−2760.00	+	4780.46i	−0.190166	+	0.329378i
$596$	4044.00	−	7004.41i	0.277934	−	0.481396i
$597$	−6520.00			−0.446978
$598$	−16380.0	−	4053.00i	−1.12011	−	0.277156i
$599$	198.000			0.0135059			0.00675297	−	0.999977i	$-0.497850\pi$
$599$	198.000			0.0135059			0.00675297	+	0.999977i	$0.497850\pi$
$600$	400.000	−	692.820i	0.0272166	−	0.0471405i
$601$	−11990.5	+	20768.2i	−0.813815	+	1.40957i	0.0963610	+	0.995346i	$0.469280\pi$
$601$	−11990.5	+	20768.2i	−0.813815	+	1.40957i	−0.910176	+	0.414222i	$0.864054\pi$
$602$	−4922.00	−	8525.15i	−0.333232	−	0.577175i
$603$	8492.00			0.573501
$604$	−3148.00	−	5452.50i	−0.212070	−	0.367316i
$605$	−4795.00	−	8305.18i	−0.322222	−	0.558105i
$606$	−3552.00			−0.238103
$607$	−13199.5	−	22862.2i	−0.882621	−	1.52875i	−0.848416	−	0.529330i	$-0.822443\pi$
$607$	−13199.5	−	22862.2i	−0.882621	−	1.52875i	−0.0342055	−	0.999415i	$-0.510890\pi$
$608$	80.0000	−	138.564i	0.00533623	−	0.00924262i
$609$	−5520.00	+	9560.92i	−0.367293	+	0.636171i
$610$	3220.00			0.213728
$611$	17842.5	−	18542.5i	1.18139	−	1.22774i
$612$	−2112.00			−0.139498
$613$	−7385.50	+	12792.1i	−0.486619	+	0.842849i	−0.999882	−	0.0153826i	$-0.995103\pi$
$613$	−7385.50	+	12792.1i	−0.486619	+	0.842849i	0.513263	+	0.858232i	$0.328437\pi$
$614$	6734.00	−	11663.6i	0.442609	−	0.766622i
$615$	−60.0000	−	103.923i	−0.00393404	−	0.00681395i
$616$	10488.0			0.685996
$617$	−4413.00	−	7643.54i	−0.287943	−	0.498732i	0.685376	−	0.728190i	$-0.259638\pi$
$617$	−4413.00	−	7643.54i	−0.287943	−	0.498732i	−0.973319	+	0.229458i	$0.926305\pi$
$618$	−5740.00	−	9941.97i	−0.373619	−	0.647127i
$619$	3671.00			0.238368			0.119184	−	0.992872i	$-0.461972\pi$
$619$	3671.00			0.238368			0.119184	+	0.992872i	$0.461972\pi$
$620$	340.000	+	588.897i	0.0220238	+	0.0381463i
$621$	−13680.0	+	23694.5i	−0.883993	+	1.53112i
$622$	−7020.00	+	12159.0i	−0.452534	+	0.783812i
$623$	15663.0			1.00726
$624$	−2912.00	−	720.533i	−0.186816	−	0.0462250i
$625$	625.000			0.0400000
$626$	−4018.00	+	6959.38i	−0.256536	+	0.444334i
$627$	570.000	−	987.269i	0.0363056	−	0.0628831i
$628$	−2218.00	−	3841.69i	−0.140936	−	0.244108i
$629$	10896.0			0.690703
$630$	−1265.00	−	2191.04i	−0.0799981	−	0.138561i
$631$	−5506.00	−	9536.67i	−0.347370	−	0.601662i	0.638411	−	0.769695i	$-0.279592\pi$
$631$	−5506.00	−	9536.67i	−0.347370	−	0.601662i	−0.985781	+	0.168033i	$0.946258\pi$
$632$	3632.00			0.228597
$633$	1634.00	+	2830.17i	0.102600	+	0.177708i
$634$	−8625.00	+	14938.9i	−0.540288	+	0.935806i
$635$	4442.50	−	7694.64i	0.277630	−	0.480870i
$636$	−8592.00			−0.535684
$637$	2418.00	+	8376.20i	0.150400	+	0.521000i
$638$	13680.0			0.848897
$639$	−4917.00	+	8516.49i	−0.304403	+	0.527241i
$640$	320.000	−	554.256i	0.0197642	−	0.0342327i
$641$	−8815.50	−	15268.9i	−0.543200	−	0.940850i	−0.998718	−	0.0506235i	$-0.983879\pi$
$641$	−8815.50	−	15268.9i	−0.543200	−	0.940850i	0.455518	−	0.890227i	$-0.349454\pi$
$642$	16272.0			1.00032
$643$	4262.00	+	7382.00i	0.261395	+	0.452749i	0.966613	−	0.256241i	$-0.0824842\pi$
$643$	4262.00	+	7382.00i	0.261395	+	0.452749i	−0.705218	+	0.708991i	$0.749151\pi$
$644$	8280.00	+	14341.4i	0.506642	+	0.877530i
$645$	−4280.00			−0.261279
$646$	240.000	+	415.692i	0.0146171	+	0.0253176i
$647$	−13153.5	+	22782.5i	−0.799254	+	1.38435i	0.120848	+	0.992671i	$0.461439\pi$
$647$	−13153.5	+	22782.5i	−0.799254	+	1.38435i	−0.920102	+	0.391678i	$0.871895\pi$
$648$	−1244.00	+	2154.67i	−0.0754150	+	0.130623i
$649$	17100.0			1.03426
$650$	−650.000	−	2251.67i	−0.0392232	−	0.135873i
$651$	−3128.00			−0.188319
$652$	248.000	−	429.549i	0.0148964	−	0.0258013i
$653$	−10054.5	+	17414.9i	−0.602547	+	1.04364i	0.389887	+	0.920863i	$0.372514\pi$
$653$	−10054.5	+	17414.9i	−0.602547	+	1.04364i	−0.992434	+	0.122779i	$0.960819\pi$
$654$	8792.00	+	15228.2i	0.525680	+	0.910504i
$655$	−2445.00			−0.145854
$656$	−48.0000	−	83.1384i	−0.00285684	−	0.00494819i
$657$	1496.00	+	2591.15i	0.0888349	+	0.153867i
$658$	−25254.0			−1.49621
$659$	−1794.00	−	3107.30i	−0.106046	−	0.183677i	0.808119	−	0.589019i	$-0.200486\pi$
$659$	−1794.00	−	3107.30i	−0.106046	−	0.183677i	−0.914165	+	0.405342i	$0.867152\pi$
$660$	2280.00	−	3949.08i	0.134468	−	0.232905i
$661$	12017.0	−	20814.1i	0.707121	−	1.22477i	−0.258799	−	0.965931i	$-0.583327\pi$
$661$	12017.0	−	20814.1i	0.707121	−	1.22477i	0.965921	−	0.258839i	$-0.0833398\pi$
$662$	−16120.0			−0.946407
$663$	6240.00	−	6484.80i	0.365523	−	0.379862i
$664$	8544.00			0.499355
$665$	−287.500	+	497.965i	−0.0167651	+	0.0290380i
$666$	−2497.00	+	4324.93i	−0.145280	+	0.251633i
$667$	10800.0	+	18706.1i	0.626953	+	1.08591i
$668$	15780.0			0.913992
$669$	254.000	+	439.941i	0.0146789	+	0.0254247i
$670$	−3860.00	−	6685.72i	−0.222574	−	0.385510i
$671$	18354.0			1.05596
$672$	1472.00	+	2549.58i	0.0844995	+	0.146357i
$673$	−7540.00	+	13059.7i	−0.431866	+	0.748013i	−0.997034	−	0.0769623i	$-0.975478\pi$
$673$	−7540.00	+	13059.7i	−0.431866	+	0.748013i	0.565168	+	0.824976i	$0.308811\pi$
$674$	698.000	−	1208.97i	0.0398901	−	0.0690918i
$675$	−3800.00			−0.216685
$676$	−7436.00	+	4683.47i	−0.423077	+	0.266469i
$677$	−12546.0			−0.712233			−0.356117	−	0.934442i	$-0.615899\pi$
$677$	−12546.0			−0.712233			−0.356117	+	0.934442i	$0.615899\pi$
$678$	−3744.00	+	6484.80i	−0.212076	+	0.367326i
$679$	−12650.0	+	21910.4i	−0.714967	+	1.23836i
$680$	960.000	+	1662.77i	0.0541387	+	0.0937710i
$681$	−22032.0			−1.23975
$682$	1938.00	+	3356.71i	0.108812	+	0.188468i
$683$	219.000	+	379.319i	0.0122691	+	0.0212507i	0.872095	−	0.489337i	$-0.162761\pi$
$683$	219.000	+	379.319i	0.0122691	+	0.0212507i	−0.859826	+	0.510588i	$0.829428\pi$
$684$	−220.000			−0.0122981
$685$	720.000	+	1247.08i	0.0401603	+	0.0695596i
$686$	−3611.00	+	6254.44i	−0.200975	+	0.348098i
$687$	452.000	−	782.887i	0.0251017	−	0.0434774i
$688$	−3424.00			−0.189737
$689$	−17452.5	+	18137.2i	−0.965003	+	1.00286i
$690$	7200.00			0.397245
$691$	12576.5	−	21783.1i	0.692377	−	1.19923i	−0.278680	−	0.960384i	$-0.589897\pi$
$691$	12576.5	−	21783.1i	0.692377	−	1.19923i	0.971057	−	0.238848i	$-0.0767699\pi$
$692$	7050.00	−	12211.0i	0.387284	−	0.670796i
$693$	−7210.50	−	12489.0i	−0.395244	−	0.684583i
$694$	−4824.00			−0.263857
$695$	1577.50	+	2732.31i	0.0860978	+	0.149126i
$696$	1920.00	+	3325.54i	0.104565	+	0.181112i
$697$	288.000			0.0156510
$698$	−3412.00	−	5909.76i	−0.185023	−	0.320469i
$699$	−7236.00	+	12533.1i	−0.391546	+	0.678178i
$700$	−1150.00	+	1991.86i	−0.0620942	+	0.107550i
$701$	−35004.0			−1.88600			−0.942998	−	0.332799i	$-0.892007\pi$
$701$	−35004.0			−1.88600			−0.942998	+	0.332799i	$0.892007\pi$
$702$	3952.00	+	13690.1i	0.212477	+	0.736041i
$703$	1135.00			0.0608924
$704$	1824.00	−	3159.26i	0.0976486	−	0.169132i
$705$	−5490.00	+	9508.96i	−0.293284	+	0.507983i
$706$	828.000	+	1434.14i	0.0441391	+	0.0764511i
$707$	10212.0			0.543227
$708$	2400.00	+	4156.92i	0.127398	+	0.220659i
$709$	−11170.0	−	19347.0i	−0.591676	−	1.02481i	−0.994007	−	0.109318i	$-0.965133\pi$
$709$	−11170.0	−	19347.0i	−0.591676	−	1.02481i	0.402331	−	0.915494i	$-0.368200\pi$
$710$	8940.00			0.472552
$711$	−2497.00	−	4324.93i	−0.131709	−	0.228126i
$712$	2724.00	−	4718.11i	0.143380	−	0.248341i
$713$	−3060.00	+	5300.08i	−0.160726	+	0.278386i
$714$	−8832.00			−0.462926
$715$	−3705.00	−	12834.5i	−0.193789	−	0.671305i
$716$	1776.00			0.0926987
$717$	6300.00	−	10911.9i	0.328142	−	0.568359i
$718$	−3354.00	+	5809.30i	−0.174332	+	0.301951i
$719$	−6570.00	−	11379.6i	−0.340778	−	0.590245i	0.643799	−	0.765195i	$-0.277357\pi$
$719$	−6570.00	−	11379.6i	−0.340778	−	0.590245i	−0.984577	+	0.174949i	$0.944024\pi$
$720$	−880.000			−0.0455495
$721$	16502.5	+	28583.2i	0.852407	+	1.47641i
$722$	−6834.00	−	11836.8i	−0.352265	−	0.610140i
$723$	−17668.0			−0.908824
$724$	−7276.00	−	12602.4i	−0.373495	−	0.646912i
$725$	−1500.00	+	2598.08i	−0.0768395	+	0.133090i
$726$	7672.00	−	13288.3i	0.392196	−	0.679304i
$727$	−10327.0			−0.526833			−0.263416	−	0.964682i	$-0.584849\pi$
$727$	−10327.0			−0.526833			−0.263416	+	0.964682i	$0.584849\pi$
$728$	8372.00	+	2071.53i	0.426218	+	0.105462i
$729$	19837.0			1.00782
$730$	1360.00	−	2355.59i	0.0689532	−	0.119430i
$731$	5136.00	−	8895.81i	0.259866	−	0.450101i
$732$	2576.00	+	4461.76i	0.130071	+	0.225289i
$733$	9335.00			0.470390			0.235195	−	0.971948i	$-0.424427\pi$
$733$	9335.00			0.470390			0.235195	+	0.971948i	$0.424427\pi$
$734$	−1816.00	−	3145.40i	−0.0913212	−	0.158173i
$735$	−1860.00	−	3221.61i	−0.0933430	−	0.161675i
$736$	5760.00			0.288473
$737$	−22002.0	−	38108.6i	−1.09967	−	1.90468i
$738$	−66.0000	+	114.315i	−0.00329200	+	0.00570191i
$739$	8841.50	−	15313.9i	0.440108	−	0.762289i	−0.557589	−	0.830117i	$-0.688273\pi$
$739$	8841.50	−	15313.9i	0.440108	−	0.762289i	0.997697	+	0.0678277i	$0.0216068\pi$
$740$	4540.00			0.225532
$741$	650.000	−	675.500i	0.0322245	−	0.0334887i
$742$	24702.0			1.22215
$743$	10752.0	−	18623.0i	0.530892	−	0.919532i	−0.468458	−	0.883486i	$-0.655190\pi$
$743$	10752.0	−	18623.0i	0.530892	−	0.919532i	0.999350	−	0.0360460i	$-0.0114763\pi$
$744$	−544.000	+	942.236i	−0.0268065	+	0.0464302i
$745$	5055.00	+	8755.52i	0.248592	+	0.430574i
$746$	4316.00			0.211823
$747$	−5874.00	−	10174.1i	−0.287709	−	0.498326i
$748$	5472.00	+	9477.78i	0.267481	+	0.463291i
$749$	−46782.0			−2.28221
$750$	500.000	+	866.025i	0.0243432	+	0.0421637i
$751$	−910.000	+	1576.17i	−0.0442162	+	0.0765847i	−0.887287	−	0.461219i	$-0.847412\pi$
$751$	−910.000	+	1576.17i	−0.0442162	+	0.0765847i	0.843070	+	0.537803i	$0.180746\pi$
$752$	−4392.00	+	7607.17i	−0.212978	+	0.368889i
$753$	17940.0			0.868220
$754$	10920.0	+	2702.00i	0.527431	+	0.130505i
$755$	7870.00			0.379362
$756$	6992.00	−	12110.5i	0.336371	−	0.582612i
$757$	594.500	−	1029.70i	0.0285436	−	0.0494389i	−0.851401	−	0.524516i	$-0.824246\pi$
$757$	594.500	−	1029.70i	0.0285436	−	0.0494389i	0.879944	+	0.475077i	$0.157580\pi$
$758$	11489.0	+	19899.5i	0.550527	+	0.953540i
$759$	41040.0			1.96266
$760$	100.000	+	173.205i	0.00477287	+	0.00826685i
$761$	−4078.50	−	7064.17i	−0.194278	−	0.336499i	0.752386	−	0.658723i	$-0.228903\pi$
$761$	−4078.50	−	7064.17i	−0.194278	−	0.336499i	−0.946664	+	0.322224i	$0.895570\pi$
$762$	14216.0			0.675842
$763$	−25277.0	−	43781.0i	−1.19933	−	2.07730i
$764$	−2340.00	+	4053.00i	−0.110809	+	0.191927i
$765$	1320.00	−	2286.31i	0.0623852	−	0.108054i
$766$	9240.00			0.435842
$767$	13650.0	+	3377.50i	0.642598	+	0.159002i
$768$	1024.00			0.0481125
$769$	293.000	−	507.491i	0.0137397	−	0.0237979i	−0.859074	−	0.511852i	$-0.828960\pi$
$769$	293.000	−	507.491i	0.0137397	−	0.0237979i	0.872814	+	0.488054i	$0.162293\pi$
$770$	−6555.00	+	11353.6i	−0.306787	+	0.531370i
$771$	−9168.00	−	15879.4i	−0.428246	−	0.741743i
$772$	7232.00			0.337157
$773$	−17503.5	−	30317.0i	−0.814434	−	1.41064i	−0.909734	−	0.415192i	$-0.863714\pi$
$773$	−17503.5	−	30317.0i	−0.814434	−	1.41064i	0.0953004	−	0.995449i	$-0.469619\pi$
$774$	2354.00	+	4077.25i	0.109319	+	0.189346i
$775$	−850.000			−0.0393973
$776$	4400.00	+	7621.02i	0.203545	+	0.352550i
$777$	−10442.0	+	18086.1i	−0.482117	+	0.835051i
$778$	3000.00	−	5196.15i	0.138246	−	0.239449i
$779$	30.0000			0.00137980
$780$	2600.00	−	2702.00i	0.119352	−	0.124035i
$781$	50958.0			2.33473
$782$	−8640.00	+	14964.9i	−0.395097	+	0.684328i
$783$	9120.00	−	15796.3i	0.416248	−	0.720963i
$784$	−1488.00	−	2577.29i	−0.0677843	−	0.117406i
$785$	5545.00			0.252114
$786$	−1956.00	−	3387.89i	−0.0887636	−	0.153743i
$787$	5012.00	+	8681.04i	0.227012	+	0.393196i	0.956921	−	0.290348i	$-0.0937710\pi$
$787$	5012.00	+	8681.04i	0.227012	+	0.393196i	−0.729909	+	0.683544i	$0.760438\pi$
$788$	−13836.0			−0.625491
$789$	−11394.0	−	19735.0i	−0.514116	−	0.890474i
$790$	−2270.00	+	3931.76i	−0.102232	+	0.177070i
$791$	10764.0	−	18643.8i	0.483848	−	0.838049i
$792$	−5016.00			−0.225045
$793$	14651.0	+	3625.18i	0.656081	+	0.162338i
$794$	−14758.0			−0.659624
$795$	5370.00	−	9301.11i	0.239565	−	0.414939i
$796$	3260.00	−	5646.49i	0.145160	−	0.251425i
$797$	10443.0	+	18087.8i	0.464128	+	0.803893i	0.999162	−	0.0409374i	$-0.0130344\pi$
$797$	10443.0	+	18087.8i	0.464128	+	0.803893i	−0.535034	+	0.844831i	$0.679701\pi$
$798$	−920.000			−0.0408116
$799$	−13176.0	−	22821.5i	−0.583396	−	1.01047i
$800$	400.000	+	692.820i	0.0176777	+	0.0306186i
$801$	−7491.00			−0.330439
$802$	−9015.00	−	15614.4i	−0.396921	−	0.687487i
$803$	7752.00	−	13426.9i	0.340675	−	0.590067i
$804$	6176.00	−	10697.1i	0.270909	−	0.469228i
$805$	−20700.0			−0.906309
$806$	884.000	+	3062.27i	0.0386322	+	0.133826i
$807$	−15984.0			−0.697229
$808$	1776.00	−	3076.12i	0.0773261	−	0.133933i
$809$	−639.000	+	1106.78i	−0.0277701	+	0.0480993i	−0.879576	−	0.475758i	$-0.842174\pi$
$809$	−639.000	+	1106.78i	−0.0277701	+	0.0480993i	0.851806	+	0.523857i	$0.175507\pi$
$810$	−1555.00	−	2693.34i	−0.0674532	−	0.116832i
$811$	23471.0			1.01625			0.508125	−	0.861284i	$-0.330339\pi$
$811$	23471.0			1.01625			0.508125	+	0.861284i	$0.330339\pi$
$812$	−5520.00	−	9560.92i	−0.238564	−	0.413205i
$813$	6560.00	+	11362.3i	0.282988	+	0.490150i
$814$	25878.0			1.11428
$815$	310.000	+	536.936i	0.0133237	+	0.0230773i
$816$	−1536.00	+	2660.43i	−0.0658955	+	0.114134i
$817$	535.000	−	926.647i	0.0229098	−	0.0396809i
$818$	2750.00			0.117545
$819$	−3289.00	−	11393.4i	−0.140326	−	0.486103i
$820$	120.000			0.00511047
$821$	−18453.0	+	31961.5i	−0.784426	+	1.35867i	0.144915	+	0.989444i	$0.453709\pi$
$821$	−18453.0	+	31961.5i	−0.784426	+	1.35867i	−0.929341	+	0.369222i	$0.879624\pi$
$822$	−1152.00	+	1995.32i	−0.0488815	+	0.0846653i
$823$	4599.50	+	7966.57i	0.194810	+	0.337421i	0.946838	−	0.321710i	$-0.104258\pi$
$823$	4599.50	+	7966.57i	0.194810	+	0.337421i	−0.752028	+	0.659131i	$0.770924\pi$
$824$	11480.0			0.485346
$825$	2850.00	+	4936.34i	0.120272	+	0.208317i
$826$	−6900.00	−	11951.2i	−0.290656	−	0.503431i
$827$	4662.00			0.196026			0.0980131	−	0.995185i	$-0.468751\pi$
$827$	4662.00			0.196026			0.0980131	+	0.995185i	$0.468751\pi$
$828$	−3960.00	−	6858.92i	−0.166207	−	0.287879i
$829$	17930.0	−	31055.7i	0.751188	−	1.30110i	−0.196060	−	0.980592i	$-0.562815\pi$
$829$	17930.0	−	31055.7i	0.751188	−	1.30110i	0.947247	−	0.320503i	$-0.103852\pi$
$830$	−5340.00	+	9249.15i	−0.223318	+	0.386798i
$831$	−23188.0			−0.967970
$832$	2080.00	−	2161.60i	0.0866719	−	0.0900721i
$833$	8928.00			0.371353
$834$	−2524.00	+	4371.70i	−0.104795	+	0.181510i
$835$	−9862.50	+	17082.4i	−0.408750	+	0.707975i
$836$	570.000	+	987.269i	0.0235812	+	0.0408438i
$837$	5168.00			0.213420
$838$	−7644.00	−	13239.8i	−0.315105	−	0.545777i
$839$	−11727.0	−	20311.8i	−0.482552	−	0.835804i	0.517247	−	0.855836i	$-0.326957\pi$
$839$	−11727.0	−	20311.8i	−0.482552	−	0.835804i	−0.999799	+	0.0200315i	$0.993623\pi$
$840$	−3680.00			−0.151157
$841$	4994.50	+	8650.73i	0.204785	+	0.354698i
$842$	−12700.0	+	21997.0i	−0.519799	+	0.900319i
$843$	2892.00	−	5009.09i	0.118156	−	0.204653i
$844$	−3268.00			−0.133281
$845$	−422.500	−	10976.9i	−0.0172005	−	0.446883i
$846$	12078.0			0.490839
$847$	−22057.0	+	38203.8i	−0.894790	+	1.54982i
$848$	4296.00	−	7440.89i	0.173968	−	0.301322i
$849$	1796.00	+	3110.76i	0.0726014	+	0.125749i
$850$	−2400.00			−0.0968463
$851$	20430.0	+	35385.8i	0.822951	+	1.42539i
$852$	7152.00	+	12387.6i	0.287586	+	0.498114i
$853$	−4678.00			−0.187775			−0.0938873	−	0.995583i	$-0.529929\pi$
$853$	−4678.00			−0.187775			−0.0938873	+	0.995583i	$0.529929\pi$
$854$	−7406.00	−	12827.6i	−0.296754	−	0.513993i
$855$	137.500	−	238.157i	0.00549988	−	0.00952608i
$856$	−8136.00	+	14092.0i	−0.324863	+	0.562679i
$857$	27246.0			1.08600			0.543002	−	0.839731i	$-0.317288\pi$
$857$	27246.0			1.08600			0.543002	+	0.839731i	$0.317288\pi$
$858$	14820.0	−	15401.4i	0.589681	−	0.612815i
$859$	−5779.00			−0.229542			−0.114771	−	0.993392i	$-0.536613\pi$
$859$	−5779.00			−0.229542			−0.114771	+	0.993392i	$0.536613\pi$
$860$	2140.00	−	3706.59i	0.0848528	−	0.146969i
$861$	−276.000	+	478.046i	−0.0109246	+	0.0189219i
$862$	−1260.00	−	2182.38i	−0.0497863	−	0.0862324i
$863$	−33912.0			−1.33763			−0.668817	−	0.743427i	$-0.733199\pi$
$863$	−33912.0			−1.33763			−0.668817	+	0.743427i	$0.733199\pi$
$864$	−2432.00	−	4212.35i	−0.0957619	−	0.165865i
$865$	8812.50	+	15263.7i	0.346398	+	0.599978i
$866$	−29344.0			−1.15144
$867$	5218.00	+	9037.84i	0.204397	+	0.354027i
$868$	1564.00	−	2708.93i	0.0611585	−	0.105930i
$869$	−12939.0	+	22411.0i	−0.505093	+	0.874846i
$870$	−4800.00			−0.187052
$871$	−10036.0	−	34765.7i	−0.390421	−	1.35246i
$872$	−17584.0			−0.682878
$873$	6050.00	−	10478.9i	0.234549	−	0.406251i
$874$	−900.000	+	1558.85i	−0.0348318	+	0.0603304i
$875$	−1437.50	−	2489.82i	−0.0555387	−	0.0961959i
$876$	4352.00			0.167854
$877$	−4015.00	−	6954.18i	−0.154592	−	0.267761i	0.778319	−	0.627870i	$-0.216073\pi$
$877$	−4015.00	−	6954.18i	−0.154592	−	0.267761i	−0.932910	+	0.360109i	$0.882740\pi$
$878$	−2830.00	−	4901.70i	−0.108779	−	0.188411i
$879$	1668.00			0.0640048
$880$	2280.00	+	3949.08i	0.0873395	+	0.151276i
$881$	−1162.50	+	2013.51i	−0.0444559	+	0.0769998i	−0.887397	−	0.461006i	$-0.847489\pi$
$881$	−1162.50	+	2013.51i	−0.0444559	+	0.0769998i	0.842941	+	0.538006i	$0.180822\pi$
$882$	−2046.00	+	3543.78i	−0.0781093	+	0.135289i
$883$	−26386.0			−1.00562			−0.502808	−	0.864398i	$-0.667700\pi$
$883$	−26386.0			−1.00562			−0.502808	+	0.864398i	$0.667700\pi$
$884$	2496.00	+	8646.40i	0.0949656	+	0.328970i
$885$	−6000.00			−0.227896
$886$	10626.0	−	18404.8i	0.402920	−	0.697879i
$887$	−9340.50	+	16178.2i	−0.353578	+	0.612414i	−0.986873	−	0.161495i	$-0.948368\pi$
$887$	−9340.50	+	16178.2i	−0.353578	+	0.612414i	0.633296	+	0.773910i	$0.281702\pi$
$888$	3632.00	+	6290.81i	0.137254	+	0.237732i
$889$	−40871.0			−1.54192
$890$	3405.00	+	5897.63i	0.128243	+	0.222123i
$891$	−8863.50	−	15352.0i	−0.333264	−	0.577231i
$892$	−508.000			−0.0190685
$893$	−1372.50	−	2377.24i	−0.0514322	−	0.0890832i
$894$	−8088.00	+	14008.8i	−0.302576	+	0.524077i
$895$	−1110.00	+	1922.58i	−0.0414561	+	0.0718041i
$896$	−2944.00			−0.109768
$897$	32760.0	+	8106.00i	1.21943	+	0.301730i
$898$	−3762.00			−0.139799
$899$	2040.00	−	3533.38i	0.0756817	−	0.131084i
$900$	550.000	−	952.628i	0.0203704	−	0.0352825i
$901$	12888.0	+	22322.7i	0.476539	+	0.825390i
$902$	684.000			0.0252491
$903$	9844.00	+	17050.3i	0.362777	+	0.628349i
$904$	−3744.00	−	6484.80i	−0.137747	−	0.238585i
$905$	18190.0			0.668128
$906$	6296.00	+	10905.0i	0.230873	+	0.399883i
$907$	2897.00	−	5017.75i	0.106057	−	0.183695i	−0.808113	−	0.589028i	$-0.799511\pi$
$907$	2897.00	−	5017.75i	0.106057	−	0.183695i	0.914169	+	0.405332i	$0.132844\pi$
$908$	11016.0	−	19080.3i	0.402620	−	0.697358i
$909$	−4884.00			−0.178209
$910$	−7475.00	+	7768.25i	−0.272301	+	0.282983i
$911$	−52980.0			−1.92679			−0.963395	−	0.268086i	$-0.913609\pi$
$911$	−52980.0			−1.92679			−0.963395	+	0.268086i	$0.913609\pi$
$912$	−160.000	+	277.128i	−0.00580935	+	0.0100621i
$913$	−30438.0	+	52720.2i	−1.10334	+	1.91104i
$914$	−5458.00	−	9453.53i	−0.197521	−	0.342117i
$915$	−6440.00			−0.232677
$916$	452.000	+	782.887i	0.0163040	+	0.0282394i
$917$	5623.50	+	9740.19i	0.202513	+	0.350763i
$918$	14592.0			0.524627
$919$	15173.0	+	26280.4i	0.544626	+	0.943320i	0.998630	+	0.0523202i	$0.0166616\pi$
$919$	15173.0	+	26280.4i	0.544626	+	0.943320i	−0.454005	+	0.890999i	$0.650005\pi$
$920$	−3600.00	+	6235.38i	−0.129009	+	0.223451i
$921$	−13468.0	+	23327.3i	−0.481852	+	0.834592i
$922$	34584.0			1.23532
$923$	40677.0	+	10064.9i	1.45060	+	0.358929i
$924$	−20976.0			−0.746818
$925$	−2837.50	+	4914.69i	−0.100861	+	0.174696i
$926$	−9256.00	+	16031.9i	−0.328478	+	0.568941i
$927$	−7892.50	−	13670.2i	−0.279637	−	0.484346i
$928$	−3840.00			−0.135834
$929$	19911.0	+	34486.9i	0.703185	+	1.21795i	0.967343	+	0.253472i	$0.0815727\pi$
$929$	19911.0	+	34486.9i	0.703185	+	1.21795i	−0.264158	+	0.964479i	$0.585094\pi$
$930$	−680.000	−	1177.79i	−0.0239764	−	0.0415284i
$931$	930.000			0.0327385
$932$	−7236.00	−	12533.1i	−0.254317	−	0.440489i
$933$	14040.0	−	24318.0i	0.492657	−	0.853307i
$934$	9876.00	−	17105.7i	0.345988	−	0.599268i
$935$	−13680.0			−0.478485
$936$	−4004.00	−	990.733i	−0.139824	−	0.0345974i
$937$	23870.0			0.832229			0.416115	−	0.909312i	$-0.363391\pi$
$937$	23870.0			0.832229			0.416115	+	0.909312i	$0.363391\pi$
$938$	−17756.0	+	30754.3i	−0.618075	+	1.07054i
$939$	8036.00	−	13918.8i	0.279281	−	0.483729i
$940$	−5490.00	−	9508.96i	−0.190494	−	0.329945i
$941$	12360.0			0.428188			0.214094	−	0.976813i	$-0.431320\pi$
$941$	12360.0			0.428188			0.214094	+	0.976813i	$0.431320\pi$
$942$	4436.00	+	7683.38i	0.153432	+	0.265752i
$943$	540.000	+	935.307i	0.0186477	+	0.0322988i
$944$	−4800.00			−0.165494
$945$	8740.00	+	15138.1i	0.300859	+	0.521104i
$946$	12198.0	−	21127.6i	0.419230	−	0.726127i
$947$	−9003.00	+	15593.7i	−0.308932	+	0.535085i	−0.978129	−	0.208000i	$-0.933305\pi$
$947$	−9003.00	+	15593.7i	−0.308932	+	0.535085i	0.669197	+	0.743085i	$0.266638\pi$
$948$	−7264.00			−0.248865
$949$	8840.00	−	9186.80i	0.302380	−	0.314242i
$950$	−250.000			−0.00853797
$951$	17250.0	−	29877.9i	0.588191	−	1.01878i
$952$	4416.00	−	7648.74i	0.150340	−	0.260396i
$953$	−11691.0	−	20249.4i	−0.397386	−	0.688292i	0.596017	−	0.802972i	$-0.296749\pi$
$953$	−11691.0	−	20249.4i	−0.397386	−	0.688292i	−0.993403	+	0.114680i	$0.963416\pi$
$954$	−11814.0			−0.400935
$955$	−2925.00	−	5066.25i	−0.0991108	−	0.171665i
$956$	6300.00	+	10911.9i	0.213134	+	0.369160i
$957$	−27360.0			−0.924162
$958$	13080.0	+	22655.2i	0.441123	+	0.764047i
$959$	3312.00	−	5736.55i	0.111522	−	0.193163i
$960$	−640.000	+	1108.51i	−0.0215166	+	0.0372678i
$961$	−28635.0			−0.961196
$962$	20657.0	+	5111.28i	0.692316	+	0.171304i
$963$	22374.0			0.748694
$964$	8834.00	−	15300.9i	0.295149	−	0.511214i
$965$	−4520.00	+	7828.87i	−0.150781	+	0.261161i
$966$	−16560.0	−	28682.8i	−0.551562	−	0.955334i
$967$	38045.0			1.26520			0.632598	−	0.774480i	$-0.281989\pi$
$967$	38045.0			1.26520			0.632598	+	0.774480i	$0.281989\pi$
$968$	7672.00	+	13288.3i	0.254739	+	0.441221i
$969$	−480.000	−	831.384i	−0.0159131	−	0.0275623i
$970$	−11000.0			−0.364112
$971$	−19186.5	−	33232.0i	−0.634113	−	1.09832i	−0.986702	−	0.162538i	$-0.948032\pi$
$971$	−19186.5	−	33232.0i	−0.634113	−	1.09832i	0.352589	−	0.935778i	$-0.385301\pi$
$972$	−5720.00	+	9907.33i	−0.188754	+	0.326932i
$973$	7256.50	−	12568.6i	0.239088	−	0.414113i
$974$	17246.0			0.567349
$975$	1300.00	+	4503.33i	0.0427008	+	0.147920i
$976$	−5152.00			−0.168967
$977$	−20400.0	+	35333.8i	−0.668018	+	1.15704i	0.310439	+	0.950593i	$0.399524\pi$
$977$	−20400.0	+	35333.8i	−0.668018	+	1.15704i	−0.978458	+	0.206448i	$0.933809\pi$
$978$	−496.000	+	859.097i	−0.0162171	+	0.0280889i
$979$	19408.5	+	33616.5i	0.633604	+	1.09743i
$980$	3720.00			0.121256
$981$	12089.0	+	20938.8i	0.393448	+	0.681471i
$982$	−13713.0	−	23751.6i	−0.445621	−	0.771837i
$983$	−7233.00			−0.234687			−0.117343	−	0.993091i	$-0.537438\pi$
$983$	−7233.00			−0.234687			−0.117343	+	0.993091i	$0.537438\pi$
$984$	96.0000	+	166.277i	0.00311013	+	0.00538690i
$985$	8647.50	−	14977.9i	0.279728	−	0.484503i
$986$	5760.00	−	9976.61i	0.186040	−	0.322231i
$987$	50508.0			1.62886
$988$	260.000	+	900.666i	0.00837217	+	0.0290020i
$989$	38520.0			1.23849
$990$	3135.00	−	5429.98i	0.100643	−	0.174319i
$991$	−26689.0	+	46226.7i	−0.855504	+	1.48178i	0.0206735	+	0.999786i	$0.493419\pi$
$991$	−26689.0	+	46226.7i	−0.855504	+	1.48178i	−0.876177	+	0.481989i	$0.839914\pi$
$992$	−544.000	−	942.236i	−0.0174113	−	0.0301573i
$993$	32240.0			1.03032
$994$	−20562.0	−	35614.4i	−0.656124	−	1.13644i
$995$	4075.00	+	7058.11i	0.129835	+	0.224881i
$996$	−17088.0			−0.543629
$997$	22401.5	+	38800.5i	0.711597	+	1.23252i	0.964257	+	0.264968i	$0.0853613\pi$
$997$	22401.5	+	38800.5i	0.711597	+	1.23252i	−0.252660	+	0.967555i	$0.581305\pi$
$998$	1604.00	−	2778.21i	0.0508755	−	0.0881189i
$999$	17252.0	−	29881.3i	0.546376	−	0.946350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.e.d.61.1	✓	2
13.3	even	3	inner	130.4.e.d.81.1	yes	2
13.4	even	6		1690.4.a.l.1.1		1
13.9	even	3		1690.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.e.d.61.1	✓	2	1.1	even	1	trivial
130.4.e.d.81.1	yes	2	13.3	even	3	inner
1690.4.a.f.1.1		1	13.9	even	3
1690.4.a.l.1.1		1	13.4	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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{3} +(-2.00000 - 3.46410i) q^{4} +5.00000 q^{5} +(4.00000 + 6.92820i) q^{6} +(-11.5000 - 19.9186i) q^{7} -8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(5.00000 - 8.66025i) q^{10} +(28.5000 - 49.3634i) q^{11} +16.0000 q^{12} +(32.5000 - 33.7750i) q^{13} -46.0000 q^{14} +(-10.0000 + 17.3205i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-24.0000 - 41.5692i) q^{17} +22.0000 q^{18} +(-2.50000 - 4.33013i) q^{19} +(-10.0000 - 17.3205i) q^{20} +92.0000 q^{21} +(-57.0000 - 98.7269i) q^{22} +(90.0000 - 155.885i) q^{23} +(16.0000 - 27.7128i) q^{24} +25.0000 q^{25} +(-26.0000 - 90.0666i) q^{26} -152.000 q^{27} +(-46.0000 + 79.6743i) q^{28} +(-60.0000 + 103.923i) q^{29} +(20.0000 + 34.6410i) q^{30} -34.0000 q^{31} +(16.0000 + 27.7128i) q^{32} +(114.000 + 197.454i) q^{33} -96.0000 q^{34} +(-57.5000 - 99.5929i) q^{35} +(22.0000 - 38.1051i) q^{36} +(-113.500 + 196.588i) q^{37} -10.0000 q^{38} +(52.0000 + 180.133i) q^{39} -40.0000 q^{40} +(-3.00000 + 5.19615i) q^{41} +(92.0000 - 159.349i) q^{42} +(107.000 + 185.329i) q^{43} -228.000 q^{44} +(27.5000 + 47.6314i) q^{45} +(-180.000 - 311.769i) q^{46} +549.000 q^{47} +(-32.0000 - 55.4256i) q^{48} +(-93.0000 + 161.081i) q^{49} +(25.0000 - 43.3013i) q^{50} +192.000 q^{51} +(-182.000 - 45.0333i) q^{52} -537.000 q^{53} +(-152.000 + 263.272i) q^{54} +(142.500 - 246.817i) q^{55} +(92.0000 + 159.349i) q^{56} +20.0000 q^{57} +(120.000 + 207.846i) q^{58} +(150.000 + 259.808i) q^{59} +80.0000 q^{60} +(161.000 + 278.860i) q^{61} +(-34.0000 + 58.8897i) q^{62} +(126.500 - 219.104i) q^{63} +64.0000 q^{64} +(162.500 - 168.875i) q^{65} +456.000 q^{66} +(386.000 - 668.572i) q^{67} +(-96.0000 + 166.277i) q^{68} +(360.000 + 623.538i) q^{69} -230.000 q^{70} +(447.000 + 774.227i) q^{71} +(-44.0000 - 76.2102i) q^{72} +272.000 q^{73} +(227.000 + 393.176i) q^{74} +(-50.0000 + 86.6025i) q^{75} +(-10.0000 + 17.3205i) q^{76} -1311.00 q^{77} +(364.000 + 90.0666i) q^{78} -454.000 q^{79} +(-40.0000 + 69.2820i) q^{80} +(155.500 - 269.334i) q^{81} +(6.00000 + 10.3923i) q^{82} -1068.00 q^{83} +(-184.000 - 318.697i) q^{84} +(-120.000 - 207.846i) q^{85} +428.000 q^{86} +(-240.000 - 415.692i) q^{87} +(-228.000 + 394.908i) q^{88} +(-340.500 + 589.763i) q^{89} +110.000 q^{90} +(-1046.50 - 258.942i) q^{91} -720.000 q^{92} +(68.0000 - 117.779i) q^{93} +(549.000 - 950.896i) q^{94} +(-12.5000 - 21.6506i) q^{95} -128.000 q^{96} +(-550.000 - 952.628i) q^{97} +(186.000 + 322.161i) q^{98} +627.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{3} - 4 q^{4} + 10 q^{5} + 8 q^{6} - 23 q^{7} - 16 q^{8} + 11 q^{9} + 10 q^{10} + 57 q^{11} + 32 q^{12} + 65 q^{13} - 92 q^{14} - 20 q^{15} - 16 q^{16} - 48 q^{17} + 44 q^{18} - 5 q^{19}+ \cdots + 1254 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^3 - 4 * q^4 + 10 * q^5 + 8 * q^6 - 23 * q^7 - 16 * q^8 + 11 * q^9 + 10 * q^10 + 57 * q^11 + 32 * q^12 + 65 * q^13 - 92 * q^14 - 20 * q^15 - 16 * q^16 - 48 * q^17 + 44 * q^18 - 5 * q^19 - 20 * q^20 + 184 * q^21 - 114 * q^22 + 180 * q^23 + 32 * q^24 + 50 * q^25 - 52 * q^26 - 304 * q^27 - 92 * q^28 - 120 * q^29 + 40 * q^30 - 68 * q^31 + 32 * q^32 + 228 * q^33 - 192 * q^34 - 115 * q^35 + 44 * q^36 - 227 * q^37 - 20 * q^38 + 104 * q^39 - 80 * q^40 - 6 * q^41 + 184 * q^42 + 214 * q^43 - 456 * q^44 + 55 * q^45 - 360 * q^46 + 1098 * q^47 - 64 * q^48 - 186 * q^49 + 50 * q^50 + 384 * q^51 - 364 * q^52 - 1074 * q^53 - 304 * q^54 + 285 * q^55 + 184 * q^56 + 40 * q^57 + 240 * q^58 + 300 * q^59 + 160 * q^60 + 322 * q^61 - 68 * q^62 + 253 * q^63 + 128 * q^64 + 325 * q^65 + 912 * q^66 + 772 * q^67 - 192 * q^68 + 720 * q^69 - 460 * q^70 + 894 * q^71 - 88 * q^72 + 544 * q^73 + 454 * q^74 - 100 * q^75 - 20 * q^76 - 2622 * q^77 + 728 * q^78 - 908 * q^79 - 80 * q^80 + 311 * q^81 + 12 * q^82 - 2136 * q^83 - 368 * q^84 - 240 * q^85 + 856 * q^86 - 480 * q^87 - 456 * q^88 - 681 * q^89 + 220 * q^90 - 2093 * q^91 - 1440 * q^92 + 136 * q^93 + 1098 * q^94 - 25 * q^95 - 256 * q^96 - 1100 * q^97 + 372 * q^98 + 1254 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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