LMFDB - Embedded newform 29.4.d.a.20.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [29,4,Mod(7,29)] 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("29.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	29.d (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.71105539017$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			20.5
Character	$\chi$	$=$	29.20
Dual form			29.4.d.a.16.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.61147 - 1.25762i) q^{2} +(2.77920 + 3.48501i) q^{3} +(0.250272 - 0.313832i) q^{4} +(2.95793 - 1.42446i) q^{5} +(11.6406 + 5.60583i) q^{6} +(-21.6928 - 27.2019i) q^{7} +(-4.90095 + 21.4725i) q^{8} +(1.58675 - 6.95200i) q^{9} +(5.93312 - 7.43990i) q^{10} +(1.53896 + 6.74263i) q^{11} +1.78926 q^{12} +(11.6798 + 51.1726i) q^{13} +(-90.8598 - 43.7558i) q^{14} +(13.1849 + 6.34953i) q^{15} +(14.9201 + 65.3690i) q^{16} -43.9870 q^{17} +(-4.59922 - 20.1505i) q^{18} +(45.2440 - 56.7342i) q^{19} +(0.293246 - 1.28480i) q^{20} +(34.5102 - 151.199i) q^{21} +(12.4986 + 15.6728i) q^{22} +(59.5779 + 28.6912i) q^{23} +(-88.4524 + 42.5964i) q^{24} +(-71.2160 + 89.3020i) q^{25} +(94.8573 + 118.947i) q^{26} +(137.071 - 66.0100i) q^{27} -13.9659 q^{28} +(139.258 - 70.6841i) q^{29} +42.4174 q^{30} +(57.8278 - 27.8484i) q^{31} +(11.3155 + 14.1892i) q^{32} +(-19.2210 + 24.1024i) q^{33} +(-114.871 + 55.3189i) q^{34} +(-102.914 - 49.5607i) q^{35} +(-1.78464 - 2.23786i) q^{36} +(-26.6876 + 116.926i) q^{37} +(46.8035 - 205.060i) q^{38} +(-145.876 + 182.923i) q^{39} +(16.0901 + 70.4953i) q^{40} -377.848 q^{41} +(-100.028 - 438.253i) q^{42} +(-97.3776 - 46.8946i) q^{43} +(2.50121 + 1.20452i) q^{44} +(-5.20938 - 22.8238i) q^{45} +191.669 q^{46} +(-53.1388 - 232.816i) q^{47} +(-186.346 + 233.670i) q^{48} +(-193.042 + 845.771i) q^{49} +(-73.6707 + 322.773i) q^{50} +(-122.249 - 153.295i) q^{51} +(18.9827 + 9.14160i) q^{52} +(490.223 - 236.079i) q^{53} +(274.943 - 344.767i) q^{54} +(14.1568 + 17.7520i) q^{55} +(690.407 - 332.483i) q^{56} +323.461 q^{57} +(274.775 - 359.723i) q^{58} -350.082 q^{59} +(5.29251 - 2.54874i) q^{60} +(486.799 + 610.427i) q^{61} +(115.993 - 145.451i) q^{62} +(-223.529 + 107.646i) q^{63} +(-435.886 - 209.912i) q^{64} +(107.442 + 134.728i) q^{65} +(-19.8836 + 87.1156i) q^{66} +(-67.0468 + 293.751i) q^{67} +(-11.0087 + 13.8045i) q^{68} +(65.5899 + 287.368i) q^{69} -331.086 q^{70} +(-221.101 - 968.707i) q^{71} +(141.500 + 68.1428i) q^{72} +(-357.239 - 172.037i) q^{73} +(77.3545 + 338.912i) q^{74} -509.141 q^{75} +(-6.48166 - 28.3980i) q^{76} +(150.028 - 188.129i) q^{77} +(-150.905 + 661.156i) q^{78} +(299.148 - 1310.65i) q^{79} +(137.248 + 172.104i) q^{80} +(437.529 + 210.703i) q^{81} +(-986.739 + 475.189i) q^{82} +(-483.787 + 606.649i) q^{83} +(-38.8141 - 48.6713i) q^{84} +(-130.110 + 62.6579i) q^{85} -313.275 q^{86} +(633.360 + 288.869i) q^{87} -152.323 q^{88} +(-75.4909 + 36.3545i) q^{89} +(-42.3078 - 53.0523i) q^{90} +(1138.63 - 1427.79i) q^{91} +(23.9149 - 11.5168i) q^{92} +(257.767 + 124.134i) q^{93} +(-431.565 - 541.165i) q^{94} +(53.0128 - 232.264i) q^{95} +(-18.0014 + 78.8693i) q^{96} +(-88.3025 + 110.728i) q^{97} +(559.535 + 2451.48i) q^{98} +49.3167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 5 q^{2} - 5 q^{3} - 23 q^{4} - 7 q^{5} - 11 q^{6} - 31 q^{7} + 38 q^{8} - 72 q^{9} + 31 q^{10} - 63 q^{11} + 136 q^{12} + 173 q^{13} + 129 q^{14} - 229 q^{15} - 451 q^{16} - 140 q^{17} + 846 q^{18}+ \cdots - 17404 q^{99}+O(q^{100}) $ 42 * q - 5 * q^2 - 5 * q^3 - 23 * q^4 - 7 * q^5 - 11 * q^6 - 31 * q^7 + 38 * q^8 - 72 * q^9 + 31 * q^10 - 63 * q^11 + 136 * q^12 + 173 * q^13 + 129 * q^14 - 229 * q^15 - 451 * q^16 - 140 * q^17 + 846 * q^18 - q^19 - 395 * q^20 - 961 * q^21 - 396 * q^22 + 57 * q^23 - 83 * q^24 + 1028 * q^25 + 141 * q^26 - 35 * q^27 + 356 * q^28 + 472 * q^29 + 2174 * q^30 + 175 * q^31 + 1356 * q^32 - 173 * q^33 - 1469 * q^34 + 477 * q^35 - 712 * q^36 - 417 * q^37 - 2834 * q^38 - 2273 * q^39 + 507 * q^40 + 1104 * q^41 + 2866 * q^42 - 573 * q^43 - 1644 * q^44 - 81 * q^45 - 5984 * q^46 - 223 * q^47 - 2442 * q^48 + 1400 * q^49 - 1234 * q^50 + 92 * q^51 + 2394 * q^52 - 791 * q^53 + 4228 * q^54 + 1505 * q^55 + 4167 * q^56 + 1718 * q^57 + 3635 * q^58 + 6172 * q^59 - 848 * q^60 + 2591 * q^61 + 1333 * q^62 - 1797 * q^63 + 2426 * q^64 - 3483 * q^65 + 679 * q^66 - 2611 * q^67 - 2796 * q^68 + 3665 * q^69 - 13558 * q^70 - 2169 * q^71 - 12175 * q^72 - 1309 * q^73 + 44 * q^74 - 7468 * q^75 + 1679 * q^76 - 1697 * q^77 + 6185 * q^78 + 933 * q^79 + 4604 * q^80 + 2562 * q^81 - 7016 * q^82 + 2553 * q^83 + 5579 * q^84 + 5294 * q^85 + 6824 * q^86 - 3909 * q^87 + 16298 * q^88 - 2543 * q^89 + 16038 * q^90 + 2781 * q^91 - 290 * q^92 + 6515 * q^93 - 3230 * q^94 + 1737 * q^95 - 15242 * q^96 - 5527 * q^97 - 786 * q^98 - 17404 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	2.61147	−	1.25762i	0.923296	−	0.444636i	0.0890490	−	0.996027i	$-0.471617\pi$
$2$	2.61147	−	1.25762i	0.923296	−	0.444636i	0.834247	+	0.551392i	$0.185903\pi$
$3$	2.77920	+	3.48501i	0.534857	+	0.670690i	0.973689	−	0.227879i	$-0.0731792\pi$
$3$	2.77920	+	3.48501i	0.534857	+	0.670690i	−0.438832	+	0.898569i	$0.644608\pi$
$4$	0.250272	−	0.313832i	0.0312840	−	0.0392290i
$5$	2.95793	−	1.42446i	0.264565	−	0.127408i	−0.296899	−	0.954909i	$-0.595952\pi$
$5$	2.95793	−	1.42446i	0.264565	−	0.127408i	0.561464	+	0.827501i	$0.310238\pi$
$6$	11.6406	+	5.60583i	0.792044	+	0.381428i
$7$	−21.6928	−	27.2019i	−1.17130	−	1.46877i	−0.853872	−	0.520483i	$-0.825752\pi$
$7$	−21.6928	−	27.2019i	−1.17130	−	1.46877i	−0.317429	−	0.948282i	$-0.602820\pi$
$8$	−4.90095	+	21.4725i	−0.216593	+	0.948957i
$9$	1.58675	−	6.95200i	0.0587684	−	0.257481i
$10$	5.93312	−	7.43990i	0.187622	−	0.235270i
$11$	1.53896	+	6.74263i	0.0421831	+	0.184816i	0.991630	−	0.129111i	$-0.0412123\pi$
$11$	1.53896	+	6.74263i	0.0421831	+	0.184816i	−0.949447	+	0.313927i	$0.898355\pi$
$12$	1.78926			0.0430430
$13$	11.6798	+	51.1726i	0.249185	+	1.09175i	0.932370	+	0.361504i	$0.117737\pi$
$13$	11.6798	+	51.1726i	0.249185	+	1.09175i	−0.683186	+	0.730245i	$0.739406\pi$
$14$	−90.8598	−	43.7558i	−1.73452	−	0.835302i
$15$	13.1849	+	6.34953i	0.226956	+	0.109296i
$16$	14.9201	+	65.3690i	0.233126	+	1.02139i
$17$	−43.9870			−0.627554			−0.313777	−	0.949497i	$-0.601594\pi$
$17$	−43.9870			−0.627554			−0.313777	+	0.949497i	$0.601594\pi$
$18$	−4.59922	−	20.1505i	−0.0602248	−	0.263862i
$19$	45.2440	−	56.7342i	0.546299	−	0.685038i	−0.429660	−	0.902991i	$-0.641367\pi$
$19$	45.2440	−	56.7342i	0.546299	−	0.685038i	0.975959	+	0.217953i	$0.0699380\pi$
$20$	0.293246	−	1.28480i	0.00327859	−	0.0143645i
$21$	34.5102	−	151.199i	0.358607	−	1.57116i
$22$	12.4986	+	15.6728i	0.121123	+	0.151884i
$23$	59.5779	+	28.6912i	0.540124	+	0.260110i	0.683995	−	0.729486i	$-0.260241\pi$
$23$	59.5779	+	28.6912i	0.540124	+	0.260110i	−0.143871	+	0.989596i	$0.545955\pi$
$24$	−88.4524	+	42.5964i	−0.752303	+	0.362290i
$25$	−71.2160	+	89.3020i	−0.569728	+	0.714416i
$26$	94.8573	+	118.947i	0.715502	+	0.897211i
$27$	137.071	−	66.0100i	0.977014	−	0.470505i
$28$	−13.9659			−0.0942612
$29$	139.258	−	70.6841i	0.891708	−	0.452611i
$29$	139.258	−	70.6841i	0.891708	−	0.452611i
$30$	42.4174			0.258144
$31$	57.8278	−	27.8484i	0.335038	−	0.161346i	−0.258799	−	0.965931i	$-0.583327\pi$
$31$	57.8278	−	27.8484i	0.335038	−	0.161346i	0.593837	+	0.804585i	$0.297612\pi$
$32$	11.3155	+	14.1892i	0.0625100	+	0.0783850i
$33$	−19.2210	+	24.1024i	−0.101393	+	0.127142i
$34$	−114.871	+	55.3189i	−0.579418	+	0.279033i
$35$	−102.914	−	49.5607i	−0.497018	−	0.239351i
$36$	−1.78464	−	2.23786i	−0.00826221	−	0.0103605i
$37$	−26.6876	+	116.926i	−0.118579	+	0.519528i	0.880395	+	0.474241i	$0.157277\pi$
$37$	−26.6876	+	116.926i	−0.118579	+	0.519528i	−0.998974	+	0.0452869i	$0.985580\pi$
$38$	46.8035	−	205.060i	0.199803	−	0.875396i
$39$	−145.876	+	182.923i	−0.598947	+	0.751055i
$40$	16.0901	+	70.4953i	0.0636016	+	0.278657i
$41$	−377.848			−1.43927			−0.719633	−	0.694355i	$-0.755690\pi$
$41$	−377.848			−1.43927			−0.719633	+	0.694355i	$0.755690\pi$
$42$	−100.028	−	438.253i	−0.367493	−	1.61009i
$43$	−97.3776	−	46.8946i	−0.345347	−	0.166311i	0.253167	−	0.967423i	$-0.418528\pi$
$43$	−97.3776	−	46.8946i	−0.345347	−	0.166311i	−0.598514	+	0.801112i	$0.704242\pi$
$44$	2.50121	+	1.20452i	0.00856981	+	0.00412700i
$45$	−5.20938	−	22.8238i	−0.0172571	−	0.0756082i
$46$	191.669			0.614349
$47$	−53.1388	−	232.816i	−0.164917	−	0.722548i	−0.987978	−	0.154595i	$-0.950593\pi$
$47$	−53.1388	−	232.816i	−0.164917	−	0.722548i	0.823061	−	0.567953i	$-0.192264\pi$
$48$	−186.346	+	233.670i	−0.560348	+	0.702654i
$49$	−193.042	+	845.771i	−0.562804	+	2.46580i
$50$	−73.6707	+	322.773i	−0.208372	+	0.912939i
$51$	−122.249	−	153.295i	−0.335652	−	0.420894i
$52$	18.9827	+	9.14160i	0.0506237	+	0.0243791i
$53$	490.223	−	236.079i	1.27052	−	0.611848i	0.327580	−	0.944824i	$-0.393767\pi$
$53$	490.223	−	236.079i	1.27052	−	0.611848i	0.942935	+	0.332976i	$0.108053\pi$
$54$	274.943	−	344.767i	0.692869	−	0.868831i
$55$	14.1568	+	17.7520i	0.0347073	+	0.0435215i
$56$	690.407	−	332.483i	1.64749	−	0.793390i
$57$	323.461			0.751640
$58$	274.775	−	359.723i	0.622063	−	0.814379i
$59$	−350.082			−0.772488			−0.386244	−	0.922397i	$-0.626228\pi$
$59$	−350.082			−0.772488			−0.386244	+	0.922397i	$0.626228\pi$
$60$	5.29251	−	2.54874i	0.0113877	−	0.00548401i
$61$	486.799	+	610.427i	1.02177	+	1.28126i	0.959051	+	0.283233i	$0.0914071\pi$
$61$	486.799	+	610.427i	1.02177	+	1.28126i	0.0627232	+	0.998031i	$0.480021\pi$
$62$	115.993	−	145.451i	0.237599	−	0.297940i
$63$	−223.529	+	107.646i	−0.447015	+	0.215271i
$64$	−435.886	−	209.912i	−0.851339	−	0.409983i
$65$	107.442	+	134.728i	0.205023	+	0.257091i
$66$	−19.8836	+	87.1156i	−0.0370833	+	0.162473i
$67$	−67.0468	+	293.751i	−0.122255	+	0.535633i	0.876294	+	0.481777i	$0.160008\pi$
$67$	−67.0468	+	293.751i	−0.122255	+	0.535633i	−0.998549	+	0.0538564i	$0.982849\pi$
$68$	−11.0087	+	13.8045i	−0.0196324	+	0.0246183i
$69$	65.5899	+	287.368i	0.114436	+	0.501378i
$70$	−331.086			−0.565319
$71$	−221.101	−	968.707i	−0.369576	−	1.61922i	−0.727944	−	0.685636i	$-0.759524\pi$
$71$	−221.101	−	968.707i	−0.369576	−	1.61922i	0.358369	−	0.933580i	$-0.383333\pi$
$72$	141.500	+	68.1428i	0.231610	+	0.111538i
$73$	−357.239	−	172.037i	−0.572763	−	0.275828i	0.125000	−	0.992157i	$-0.460107\pi$
$73$	−357.239	−	172.037i	−0.572763	−	0.275828i	−0.697763	+	0.716329i	$0.745821\pi$
$74$	77.3545	+	338.912i	0.121517	+	0.532402i
$75$	−509.141			−0.783875
$76$	−6.48166	−	28.3980i	−0.00978286	−	0.0428615i
$77$	150.028	−	188.129i	0.222043	−	0.278433i
$78$	−150.905	+	661.156i	−0.219059	+	0.959759i
$79$	299.148	−	1310.65i	0.426035	−	1.86658i	−0.0688544	−	0.997627i	$-0.521934\pi$
$79$	299.148	−	1310.65i	0.426035	−	1.86658i	0.494890	−	0.868956i	$-0.335208\pi$
$80$	137.248	+	172.104i	0.191810	+	0.240523i
$81$	437.529	+	210.703i	0.600177	+	0.289030i
$82$	−986.739	+	475.189i	−1.32887	+	0.639949i
$83$	−483.787	+	606.649i	−0.639789	+	0.802270i	−0.990977	−	0.134035i	$-0.957207\pi$
$83$	−483.787	+	606.649i	−0.639789	+	0.802270i	0.351188	+	0.936305i	$0.385778\pi$
$84$	−38.8141	−	48.6713i	−0.0504163	−	0.0632200i
$85$	−130.110	+	62.6579i	−0.166029	+	0.0799553i
$86$	−313.275			−0.392805
$87$	633.360	+	288.869i	0.780498	+	0.355977i
$88$	−152.323			−0.184519
$89$	−75.4909	+	36.3545i	−0.0899104	+	0.0432986i	−0.478298	−	0.878197i	$-0.658746\pi$
$89$	−75.4909	+	36.3545i	−0.0899104	+	0.0432986i	0.388388	+	0.921496i	$0.373032\pi$
$90$	−42.3078	−	53.0523i	−0.0495515	−	0.0621356i
$91$	1138.63	−	1427.79i	1.31165	−	1.64476i
$92$	23.9149	−	11.5168i	0.0271011	−	0.0130512i
$93$	257.767	+	124.134i	0.287410	+	0.138410i
$94$	−431.565	−	541.165i	−0.473538	−	0.593797i
$95$	53.0128	−	232.264i	0.0572526	−	0.250840i
$96$	−18.0014	+	78.8693i	−0.0191381	+	0.0838496i
$97$	−88.3025	+	110.728i	−0.0924305	+	0.115904i	−0.825896	−	0.563823i	$-0.809330\pi$
$97$	−88.3025	+	110.728i	−0.0924305	+	0.115904i	0.733465	+	0.679727i	$0.237902\pi$
$98$	559.535	+	2451.48i	0.576750	+	2.52691i
$99$	49.3167			0.0500658
$100$	10.2024	+	44.6997i	0.0102024	+	0.0446997i
$101$	−1230.49	−	592.575i	−1.21226	−	0.583796i	−0.285117	−	0.958493i	$-0.592033\pi$
$101$	−1230.49	−	592.575i	−1.21226	−	0.583796i	−0.927148	+	0.374697i	$0.877747\pi$
$102$	−512.036	−	246.584i	−0.497050	−	0.239367i
$103$	356.645	+	1562.57i	0.341178	+	1.49480i	0.796592	+	0.604518i	$0.206634\pi$
$103$	356.645	+	1562.57i	0.341178	+	1.49480i	−0.455414	+	0.890280i	$0.650509\pi$
$104$	−1156.04			−1.09000
$105$	−113.299	−	496.395i	−0.105303	−	0.461364i
$106$	983.307	−	1233.03i	0.901012	−	1.12983i
$107$	179.956	−	788.437i	0.162588	−	0.712346i	−0.826244	−	0.563313i	$-0.809527\pi$
$107$	179.956	−	788.437i	0.162588	−	0.712346i	0.988832	−	0.149033i	$-0.0476162\pi$
$108$	13.5891	−	59.5378i	0.0121075	−	0.0530465i
$109$	464.162	+	582.041i	0.407878	+	0.511462i	0.942764	−	0.333462i	$-0.108217\pi$
$109$	464.162	+	582.041i	0.407878	+	0.511462i	−0.534886	+	0.844924i	$0.679645\pi$
$110$	59.2954	+	28.5552i	0.0513963	+	0.0247512i
$111$	−481.658	+	231.954i	−0.411865	+	0.198344i
$112$	1454.50	−	1823.89i	1.22712	−	1.53876i
$113$	23.5974	+	29.5902i	0.0196448	+	0.0246337i	0.791557	−	0.611096i	$-0.209271\pi$
$113$	23.5974	+	29.5902i	0.0196448	+	0.0246337i	−0.771912	+	0.635729i	$0.780699\pi$
$114$	844.710	−	406.791i	0.693986	−	0.334206i
$115$	217.097			0.176038
$116$	12.6695	−	61.3938i	0.0101408	−	0.0491403i
$117$	374.285			0.295749
$118$	−914.230	+	440.270i	−0.713234	+	0.343476i
$119$	954.201	+	1196.53i	0.735054	+	0.921729i
$120$	−200.959	+	251.994i	−0.152875	+	0.191699i
$121$	1156.09	−	556.746i	0.868591	−	0.418291i
$122$	2038.95	+	981.905i	1.51310	+	0.728668i
$123$	−1050.11	−	1316.80i	−0.769802	−	0.965301i
$124$	5.73299	−	25.1179i	0.00415192	−	0.0181907i
$125$	−174.763	+	765.686i	−0.125050	+	0.547881i
$126$	−448.362	+	562.228i	−0.317010	+	0.397518i
$127$	26.2362	+	114.948i	0.0183314	+	0.0803151i	0.983266	−	0.182175i	$-0.0583136\pi$
$127$	26.2362	+	114.948i	0.0183314	+	0.0803151i	−0.964935	+	0.262490i	$0.915456\pi$
$128$	−1547.48			−1.06859
$129$	−107.204	−	469.691i	−0.0731688	−	0.320573i
$130$	450.017	+	216.717i	0.303609	+	0.146210i
$131$	−270.094	−	130.070i	−0.180139	−	0.0867505i	0.341641	−	0.939831i	$-0.389017\pi$
$131$	−270.094	−	130.070i	−0.180139	−	0.0867505i	−0.521780	+	0.853080i	$0.674732\pi$
$132$	2.75361	+	12.0643i	0.00181569	+	0.00795504i
$133$	−2524.75			−1.64604
$134$	194.336	+	851.444i	0.125284	+	0.548907i
$135$	311.418	−	390.506i	0.198538	−	0.248959i
$136$	215.578	−	944.509i	0.135924	−	0.595522i
$137$	−500.408	+	2192.43i	−0.312064	+	1.36724i	0.539056	+	0.842270i	$0.318781\pi$
$137$	−500.408	+	2192.43i	−0.312064	+	1.36724i	−0.851120	+	0.524971i	$0.824076\pi$
$138$	532.686	+	667.967i	0.328589	+	0.412037i
$139$	487.852	+	234.937i	0.297691	+	0.143360i	0.576767	−	0.816909i	$-0.304314\pi$
$139$	487.852	+	234.937i	0.297691	+	0.143360i	−0.279076	+	0.960269i	$0.590028\pi$
$140$	−41.3102	+	19.8940i	−0.0249382	+	0.0120096i
$141$	663.683	−	832.232i	0.396398	−	0.497068i
$142$	−1795.66	−	2251.69i	−1.06119	−	1.33069i
$143$	−327.064	+	157.505i	−0.191262	+	0.0921068i
$144$	478.120			0.276690
$145$	311.228	−	407.447i	0.178249	−	0.233356i
$146$	−1149.28			−0.651473
$147$	−3484.02	+	1677.81i	−1.95481	+	0.941387i
$148$	30.0159	+	37.6388i	0.0166709	+	0.0209046i
$149$	1312.03	−	1645.23i	0.721380	−	0.904582i	−0.277035	−	0.960860i	$-0.589352\pi$
$149$	1312.03	−	1645.23i	0.721380	−	0.904582i	0.998415	+	0.0562782i	$0.0179234\pi$
$150$	−1329.61	+	640.306i	−0.723748	+	0.348539i
$151$	−1621.93	−	781.082i	−0.874113	−	0.420951i	−0.0576421	−	0.998337i	$-0.518358\pi$
$151$	−1621.93	−	781.082i	−0.874113	−	0.420951i	−0.816471	+	0.577387i	$0.804073\pi$
$152$	996.484	+	1249.55i	0.531747	+	0.666789i
$153$	−69.7963	+	305.797i	−0.0368804	+	0.161583i
$154$	155.199	−	679.973i	0.0812099	−	0.355804i
$155$	131.381	−	164.747i	0.0680827	−	0.0853730i
$156$	20.8983	+	91.5613i	0.0107256	+	0.0469921i
$157$	369.755			0.187960			0.0939799	−	0.995574i	$-0.470041\pi$
$157$	369.755			0.187960			0.0939799	+	0.995574i	$0.470041\pi$
$158$	−867.086	−	3798.95i	−0.436593	−	1.91284i
$159$	2185.16	+	1052.32i	1.08990	+	0.524870i
$160$	53.6825	+	25.8521i	0.0265249	+	0.0127737i
$161$	−511.956	−	2243.03i	−0.250607	−	1.09798i
$162$	1407.58			0.682654
$163$	309.590	+	1356.40i	0.148767	+	0.651789i	0.993229	+	0.116174i	$0.0370630\pi$
$163$	309.590	+	1356.40i	0.148767	+	0.651789i	−0.844462	+	0.535615i	$0.820080\pi$
$164$	−94.5648	+	118.581i	−0.0450260	+	0.0564609i
$165$	−22.5215	+	98.6729i	−0.0106260	+	0.0465556i
$166$	−500.462	+	2192.67i	−0.233996	+	1.02521i
$167$	1252.80	+	1570.97i	0.580508	+	0.727934i	0.982199	−	0.187841i	$-0.0601490\pi$
$167$	1252.80	+	1570.97i	0.580508	+	0.727934i	−0.401691	+	0.915775i	$0.631578\pi$
$168$	3077.48	+	1482.04i	1.41329	+	0.680605i
$169$	−502.792	+	242.132i	−0.228854	+	0.110210i
$170$	−260.980	+	327.259i	−0.117743	+	0.147645i
$171$	−322.625	−	404.559i	−0.144279	−	0.180920i
$172$	−39.0879	+	18.8237i	−0.0173281	+	0.00834475i
$173$	−1303.20			−0.572720			−0.286360	−	0.958122i	$-0.592445\pi$
$173$	−1303.20			−0.572720			−0.286360	+	0.958122i	$0.592445\pi$
$174$	2017.29	−	42.1517i	0.878911	−	0.0183650i
$175$	3974.06			1.71663
$176$	−417.798	+	201.201i	−0.178936	+	0.0861710i
$177$	−972.947	−	1220.04i	−0.413171	−	0.518099i
$178$	−151.423	+	189.878i	−0.0637618	+	0.0799547i
$179$	1940.62	−	934.552i	0.810327	−	0.390233i	0.0176269	−	0.999845i	$-0.494389\pi$
$179$	1940.62	−	934.552i	0.810327	−	0.390233i	0.792700	+	0.609612i	$0.208675\pi$
$180$	−8.46659	−	4.07730i	−0.00350590	−	0.00168835i
$181$	2208.88	+	2769.85i	0.907099	+	1.13747i	0.990022	+	0.140911i	$0.0450031\pi$
$181$	2208.88	+	2769.85i	0.907099	+	1.13747i	−0.0829229	+	0.996556i	$0.526426\pi$
$182$	1177.87	−	5160.60i	0.479724	−	2.10181i
$183$	−774.429	+	3393.00i	−0.312828	+	1.37059i
$184$	−908.059	+	1138.67i	−0.363821	+	0.456217i
$185$	87.6169	+	383.875i	0.0348201	+	0.152557i
$186$	829.264			0.326907
$187$	−67.6943	−	296.588i	−0.0264722	−	0.115982i
$188$	−86.3643	−	41.5909i	−0.0335041	−	0.0161347i
$189$	−4769.06	−	2296.66i	−1.83544	−	0.883901i
$190$	−153.659	−	673.222i	−0.0586714	−	0.257056i
$191$	2097.93			0.794768			0.397384	−	0.917652i	$-0.369918\pi$
$191$	2097.93			0.794768			0.397384	+	0.917652i	$0.369918\pi$
$192$	−479.871	−	2102.45i	−0.180373	−	0.790267i
$193$	202.557	−	253.999i	0.0755460	−	0.0947317i	−0.742622	−	0.669710i	$-0.766418\pi$
$193$	202.557	−	253.999i	0.0755460	−	0.0947317i	0.818168	+	0.574979i	$0.194990\pi$
$194$	−91.3462	+	400.214i	−0.0338055	+	0.148112i
$195$	−170.925	+	748.870i	−0.0627701	+	0.275014i
$196$	217.117	+	272.256i	0.0791241	+	0.0992185i
$197$	1329.70	+	640.352i	0.480901	+	0.231590i	0.658597	−	0.752496i	$-0.271150\pi$
$197$	1329.70	+	640.352i	0.480901	+	0.231590i	−0.177696	+	0.984085i	$0.556864\pi$
$198$	128.789	−	62.0217i	0.0462255	−	0.0222611i
$199$	915.640	−	1148.18i	0.326171	−	0.409005i	−0.591527	−	0.806286i	$-0.701475\pi$
$199$	915.640	−	1148.18i	0.326171	−	0.409005i	0.917697	+	0.397280i	$0.130046\pi$
$200$	−1568.51	−	1966.85i	−0.554551	−	0.695385i
$201$	−1210.06	+	582.735i	−0.424633	+	0.204492i
$202$	−3958.64			−1.37886
$203$	−4943.64	−	2254.74i	−1.70924	−	0.779566i
$204$	−78.7043			−0.0270118
$205$	−1117.65	+	538.230i	−0.380780	+	0.183374i
$206$	2896.48	+	3632.07i	0.979648	+	1.22844i
$207$	293.996	−	368.660i	0.0987158	−	0.123786i
$208$	−3170.84	+	1527.00i	−1.05701	+	0.509030i
$209$	452.167	+	217.752i	0.149651	+	0.0720680i
$210$	−920.153	−	1153.84i	−0.302365	−	0.379153i
$211$	−1304.55	+	5715.63i	−0.425636	+	1.86483i	0.0719323	+	0.997410i	$0.477083\pi$
$211$	−1304.55	+	5715.63i	−0.425636	+	1.86483i	−0.497569	+	0.867425i	$0.665774\pi$
$212$	48.6002	−	212.932i	0.0157447	−	0.0689821i
$213$	2761.47	−	3462.77i	0.888322	−	1.11392i
$214$	−521.604	−	2285.30i	−0.166617	−	0.729999i
$215$	−354.836			−0.112556
$216$	745.619	+	3266.77i	0.234875	+	1.02905i
$217$	−2011.98	−	968.916i	−0.629409	−	0.303107i
$218$	1944.13	+	936.245i	0.604006	+	0.290874i
$219$	−393.288	−	1723.11i	−0.121351	−	0.531675i
$220$	9.11420			0.00279309
$221$	−513.760	−	2250.93i	−0.156377	−	0.685131i
$222$	−966.127	+	1211.49i	−0.292082	+	0.366259i
$223$	−450.591	+	1974.17i	−0.135309	+	0.592826i	0.861121	+	0.508400i	$0.169763\pi$
$223$	−450.591	+	1974.17i	−0.135309	+	0.592826i	−0.996430	+	0.0844260i	$0.973094\pi$
$224$	140.508	−	615.607i	0.0419112	−	0.183625i
$225$	507.825	+	636.793i	0.150467	+	0.188679i
$226$	98.8373	+	47.5975i	0.0290910	+	0.0140095i
$227$	−3980.32	+	1916.82i	−1.16380	+	0.560458i	−0.913152	−	0.407620i	$-0.866359\pi$
$227$	−3980.32	+	1916.82i	−1.16380	+	0.560458i	−0.250651	+	0.968078i	$0.580644\pi$
$228$	80.9534	−	101.512i	0.0235143	−	0.0294860i
$229$	110.826	+	138.971i	0.0319807	+	0.0401026i	0.797565	−	0.603233i	$-0.206121\pi$
$229$	110.826	+	138.971i	0.0319807	+	0.0401026i	−0.765584	+	0.643336i	$0.777550\pi$
$230$	566.943	−	273.025i	0.162535	−	0.0782729i
$231$	1072.59			0.305503
$232$	835.267	+	3336.63i	0.236370	+	0.944226i
$233$	3219.30			0.905164			0.452582	−	0.891723i	$-0.350503\pi$
$233$	3219.30			0.905164			0.452582	+	0.891723i	$0.350503\pi$
$234$	977.436	−	470.708i	0.273064	−	0.131501i
$235$	−488.819	−	612.960i	−0.135690	−	0.170149i
$236$	−87.6158	+	109.867i	−0.0241665	+	0.0303039i
$237$	5399.03	−	2600.03i	1.47977	−	0.712618i
$238$	3996.65	+	1924.69i	1.08851	+	0.524197i
$239$	−1746.28	−	2189.77i	−0.472625	−	0.592653i	0.487186	−	0.873298i	$-0.338023\pi$
$239$	−1746.28	−	2189.77i	−0.472625	−	0.592653i	−0.959812	+	0.280645i	$0.909452\pi$
$240$	−218.343	+	956.622i	−0.0587249	+	0.257290i
$241$	1084.47	−	4751.35i	0.289861	−	1.26997i	−0.594854	−	0.803834i	$-0.702790\pi$
$241$	1084.47	−	4751.35i	0.289861	−	1.26997i	0.884715	−	0.466132i	$-0.154353\pi$
$242$	2318.94	−	2907.86i	0.615979	−	0.772413i
$243$	−432.373	−	1894.35i	−0.114143	−	0.500093i
$244$	313.404			0.0822279
$245$	633.766	+	2776.71i	0.165265	+	0.724072i
$246$	−4398.38	−	2118.15i	−1.13996	−	0.548977i
$247$	3431.68	+	1652.61i	0.884018	+	0.425721i
$248$	314.562	+	1378.19i	0.0805433	+	0.352883i
$249$	−3458.72			−0.880270
$250$	506.553	+	2219.36i	0.128149	+	0.561458i
$251$	1630.96	−	2045.16i	0.410142	−	0.514301i	−0.533261	−	0.845951i	$-0.679034\pi$
$251$	1630.96	−	2045.16i	0.410142	−	0.514301i	0.943403	+	0.331649i	$0.107605\pi$
$252$	−22.1604	+	97.0911i	−0.00553958	+	0.0242705i
$253$	−101.766	+	445.867i	−0.0252885	+	0.110796i
$254$	213.076	+	267.189i	0.0526362	+	0.0660038i
$255$	−579.966	−	279.297i	−0.142427	−	0.0685892i
$256$	−554.126	+	266.853i	−0.135285	+	0.0651496i
$257$	−3622.04	+	4541.90i	−0.879131	+	1.10240i	0.114909	+	0.993376i	$0.463343\pi$
$257$	−3622.04	+	4541.90i	−0.879131	+	1.10240i	−0.994040	+	0.109019i	$0.965229\pi$
$258$	−870.653	−	1091.76i	−0.210095	−	0.263451i
$259$	3759.54	−	1810.50i	0.901955	−	0.434359i
$260$	69.1715			0.0164994
$261$	−270.429	−	1080.28i	−0.0641346	−	0.256197i
$262$	−868.923			−0.204894
$263$	2455.64	−	1182.57i	0.575745	−	0.277264i	−0.123268	−	0.992373i	$-0.539337\pi$
$263$	2455.64	−	1182.57i	0.575745	−	0.277264i	0.699013	+	0.715109i	$0.253623\pi$
$264$	−423.337	−	530.848i	−0.0986916	−	0.123755i
$265$	1113.76	−	1396.61i	0.258180	−	0.323747i
$266$	−6593.31	+	3175.17i	−1.51978	+	0.731888i
$267$	−336.500	−	162.050i	−0.0771291	−	0.0371434i
$268$	75.4085	+	94.5593i	0.0171877	+	0.0215527i
$269$	−348.217	+	1525.64i	−0.0789263	+	0.345799i	−0.998937	−	0.0460944i	$-0.985322\pi$
$269$	−348.217	+	1525.64i	−0.0789263	+	0.345799i	0.920011	+	0.391893i	$0.128180\pi$
$270$	322.153	−	1411.44i	0.0726133	−	0.318139i
$271$	−2696.37	+	3381.14i	−0.604400	+	0.757894i	−0.986057	−	0.166410i	$-0.946782\pi$
$271$	−2696.37	+	3381.14i	−0.604400	+	0.757894i	0.381656	+	0.924304i	$0.375354\pi$
$272$	−656.288	−	2875.39i	−0.146299	−	0.640978i
$273$	8140.33			1.80467
$274$	1450.44	+	6354.80i	0.319797	+	1.40112i
$275$	−711.729	−	342.751i	−0.156069	−	0.0751587i
$276$	106.601	+	51.3361i	0.0232485	+	0.0111959i
$277$	−234.002	−	1025.23i	−0.0507575	−	0.222383i	0.943188	−	0.332261i	$-0.107811\pi$
$277$	−234.002	−	1025.23i	−0.0507575	−	0.222383i	−0.993945	+	0.109877i	$0.964954\pi$
$278$	1569.47			0.338600
$279$	−101.844	−	446.207i	−0.0218539	−	0.0957480i
$280$	1568.57	−	1966.92i	0.334785	−	0.419807i
$281$	1077.52	−	4720.94i	0.228753	−	1.00223i	−0.721904	−	0.691993i	$-0.756733\pi$
$281$	1077.52	−	4720.94i	0.228753	−	1.00223i	0.950658	−	0.310241i	$-0.100410\pi$
$282$	686.559	−	3008.01i	0.144979	−	0.635194i
$283$	−3082.70	−	3865.59i	−0.647518	−	0.811962i	0.344402	−	0.938822i	$-0.388082\pi$
$283$	−3082.70	−	3865.59i	−0.647518	−	0.811962i	−0.991921	+	0.126860i	$0.959510\pi$
$284$	−359.346	−	173.052i	−0.0750820	−	0.0361576i
$285$	956.775	−	460.759i	0.198858	−	0.0957649i
$286$	−656.036	+	822.643i	−0.135637	+	0.170084i
$287$	8196.57	+	10278.2i	1.68581	+	2.11394i
$288$	116.598	−	56.1507i	0.0238563	−	0.0114886i
$289$	−2978.14			−0.606176
$290$	300.351	−	1455.44i	0.0608180	−	0.294712i
$291$	−631.297			−0.127173
$292$	−143.398	+	69.0568i	−0.0287388	+	0.0138399i
$293$	−4243.95	−	5321.74i	−0.846191	−	1.06109i	−0.997362	−	0.0725824i	$-0.976876\pi$
$293$	−4243.95	−	5321.74i	−0.846191	−	1.06109i	0.151171	−	0.988508i	$-0.451695\pi$
$294$	−6988.37	+	8763.14i	−1.38629	+	1.73836i
$295$	−1035.52	+	498.679i	−0.204373	+	0.0984210i
$296$	−2379.89	−	1146.10i	−0.467326	−	0.225052i
$297$	656.029	+	822.634i	0.128171	+	0.160721i
$298$	1357.25	−	5946.51i	0.263837	−	1.15595i
$299$	−772.346	+	3383.87i	−0.149384	+	0.654496i
$300$	−127.424	+	159.785i	−0.0245228	+	0.0307506i
$301$	836.770	+	3666.13i	0.160235	+	0.702034i
$302$	−5217.94			−0.994234
$303$	−1354.66	−	5935.16i	−0.256843	−	1.12530i
$304$	4383.70	+	2111.08i	0.827048	+	0.398285i
$305$	2309.45	+	1112.17i	0.433569	+	0.208796i
$306$	202.306	+	886.359i	0.0377943	+	0.165588i
$307$	1047.99			0.194828			0.0974139	−	0.995244i	$-0.468943\pi$
$307$	1047.99			0.194828			0.0974139	+	0.995244i	$0.468943\pi$
$308$	−21.4930	−	94.1671i	−0.00397623	−	0.0174210i
$309$	−4454.36	+	5585.59i	−0.820064	+	1.02833i
$310$	135.910	−	595.461i	0.0249006	−	0.109096i
$311$	554.936	−	2431.33i	0.101182	−	0.443306i	−0.898806	−	0.438347i	$-0.855564\pi$
$311$	554.936	−	2431.33i	0.101182	−	0.443306i	0.999988	−	0.00495952i	$-0.00157867\pi$
$312$	−3212.88	−	4028.82i	−0.582992	−	0.731049i
$313$	−3144.49	−	1514.31i	−0.567850	−	0.273462i	0.127851	−	0.991793i	$-0.459192\pi$
$313$	−3144.49	−	1514.31i	−0.567850	−	0.273462i	−0.695701	+	0.718331i	$0.744906\pi$
$314$	965.606	−	465.012i	0.173542	−	0.0835736i
$315$	−507.845	+	636.817i	−0.0908375	+	0.113907i
$316$	−336.456	−	421.902i	−0.0598960	−	0.0751072i
$317$	−5347.29	+	2575.12i	−0.947424	+	0.456256i	−0.842782	−	0.538254i	$-0.819084\pi$
$317$	−5347.29	+	2575.12i	−0.947424	+	0.456256i	−0.104642	+	0.994510i	$0.533370\pi$
$318$	7029.92			1.23968
$319$	690.910	+	830.184i	0.121265	+	0.145710i
$320$	−1588.33			−0.277470
$321$	3247.84	−	1564.08i	0.564725	−	0.271957i
$322$	−4157.83	−	5213.76i	−0.719587	−	0.902334i
$323$	−1990.15	+	2495.57i	−0.342832	+	0.429898i
$324$	175.627	−	84.5774i	0.0301143	−	0.0145023i
$325$	−5401.61	−	2601.28i	−0.921930	−	0.443978i
$326$	2514.32	+	3152.86i	0.427164	+	0.535647i
$327$	−738.417	+	3235.22i	−0.124876	+	0.547119i
$328$	1851.81	−	8113.32i	0.311735	−	1.36580i
$329$	−5180.32	+	6495.91i	−0.868086	+	1.08855i
$330$	65.2788	+	286.005i	0.0108893	+	0.0477093i
$331$	−7078.74			−1.17548			−0.587739	−	0.809051i	$-0.699982\pi$
$331$	−7078.74			−1.17548			−0.587739	+	0.809051i	$0.699982\pi$
$332$	69.3073	+	303.655i	0.0114570	+	0.0501965i
$333$	770.523	+	371.064i	0.126800	+	0.0610637i
$334$	5247.34	+	2526.99i	0.859646	+	0.413984i
$335$	220.118	+	964.402i	0.0358996	+	0.157286i
$336$	10398.6			1.68837
$337$	−490.824	−	2150.44i	−0.0793379	−	0.347602i	0.919642	−	0.392757i	$-0.128479\pi$
$337$	−490.824	−	2150.44i	−0.0793379	−	0.347602i	−0.998980	+	0.0451555i	$0.985622\pi$
$338$	−1008.52	+	1264.64i	−0.162297	+	0.203513i
$339$	−37.5402	+	164.474i	−0.00601446	+	0.0263511i
$340$	−12.8990	+	56.5143i	−0.00205749	+	0.00901447i
$341$	276.766	+	347.054i	0.0439523	+	0.0551144i
$342$	−1351.31	−	650.756i	−0.213656	−	0.102891i
$343$	16442.2	−	7918.13i	2.58832	−	1.24647i
$344$	1484.18	−	1861.11i	0.232622	−	0.291698i
$345$	603.356	+	756.584i	0.0941553	+	0.118067i
$346$	−3403.28	+	1638.93i	−0.528790	+	0.254652i
$347$	6318.41			0.977493			0.488746	−	0.872426i	$-0.337454\pi$
$347$	6318.41			0.977493			0.488746	+	0.872426i	$0.337454\pi$
$348$	249.169	−	126.472i	0.0383818	−	0.0194817i
$349$	−4618.78			−0.708417			−0.354208	−	0.935167i	$-0.615250\pi$
$349$	−4618.78			−0.708417			−0.354208	+	0.935167i	$0.615250\pi$
$350$	10378.2	−	4997.85i	1.58496	−	0.763276i
$351$	4978.88	+	6243.31i	0.757130	+	0.949411i
$352$	−78.2585	+	98.1330i	−0.0118500	+	0.0148594i
$353$	6377.82	−	3071.39i	0.961634	−	0.463099i	0.113884	−	0.993494i	$-0.463671\pi$
$353$	6377.82	−	3071.39i	0.961634	−	0.463099i	0.847750	+	0.530395i	$0.177957\pi$
$354$	−4075.17	−	1962.50i	−0.611844	−	0.294649i
$355$	−2033.89	−	2550.42i	−0.304078	−	0.381302i
$356$	−7.48410	+	32.7900i	−0.00111420	+	0.00488164i
$357$	−1518.00	+	6650.79i	−0.225045	+	0.985987i
$358$	3892.56	−	4881.12i	0.574660	−	0.720601i
$359$	−2374.43	−	10403.0i	−0.349074	−	1.52939i	−0.779289	−	0.626665i	$-0.784420\pi$
$359$	−2374.43	−	10403.0i	−0.349074	−	1.52939i	0.430215	−	0.902726i	$-0.358438\pi$
$360$	515.614			0.0754867
$361$	354.523	+	1553.27i	0.0516873	+	0.226457i
$362$	9251.86	+	4455.46i	1.34328	+	0.646889i
$363$	5153.28	+	2481.69i	0.745116	+	0.358829i
$364$	−163.120	−	714.673i	−0.0234884	−	0.102910i
$365$	−1301.75			−0.186676
$366$	2244.70	+	9834.66i	0.320580	+	1.40455i
$367$	−5675.51	+	7116.87i	−0.807246	+	1.01225i	0.192276	+	0.981341i	$0.438413\pi$
$367$	−5675.51	+	7116.87i	−0.807246	+	1.01225i	−0.999522	+	0.0309138i	$0.990158\pi$
$368$	−986.611	+	4322.63i	−0.139757	+	0.612317i
$369$	−599.549	+	2626.80i	−0.0845834	+	0.370584i
$370$	711.577	+	892.290i	0.0999815	+	0.125373i
$371$	−17056.1	−	8213.79i	−2.38682	−	1.14943i
$372$	103.469	−	49.8281i	0.0144210	−	0.00694480i
$373$	−2275.79	+	2853.75i	−0.315914	+	0.396144i	−0.914282	−	0.405077i	$-0.867245\pi$
$373$	−2275.79	+	2853.75i	−0.315914	+	0.396144i	0.598368	+	0.801221i	$0.295816\pi$
$374$	−549.777	−	689.399i	−0.0760115	−	0.0953154i
$375$	−3154.12	+	1518.95i	−0.434342	+	0.209168i
$376$	5259.57			0.721387
$377$	5243.60	+	6300.61i	0.716337	+	0.860738i
$378$	−15342.6			−2.08767
$379$	2071.98	−	997.812i	0.280819	−	0.135235i	−0.288173	−	0.957578i	$-0.593048\pi$
$379$	2071.98	−	997.812i	0.280819	−	0.135235i	0.568992	+	0.822343i	$0.307334\pi$
$380$	−59.6242	−	74.7664i	−0.00804910	−	0.0100933i
$381$	−327.680	+	410.898i	−0.0440618	+	0.0552518i
$382$	5478.68	−	2638.39i	0.733806	−	0.353382i
$383$	−912.037	−	439.214i	−0.121679	−	0.0585973i	0.372054	−	0.928211i	$-0.378654\pi$
$383$	−912.037	−	439.214i	−0.121679	−	0.0585973i	−0.493733	+	0.869614i	$0.664368\pi$
$384$	−4300.76	−	5392.99i	−0.571543	−	0.716692i
$385$	175.789	−	770.183i	0.0232703	−	0.101954i
$386$	209.539	−	918.051i	0.0276302	−	0.121056i
$387$	−480.525	+	602.559i	−0.0631174	+	0.0791467i
$388$	12.6502	+	55.4242i	0.00165520	+	0.00725190i
$389$	7379.62			0.961855			0.480928	−	0.876760i	$-0.340300\pi$
$389$	7379.62			0.961855			0.480928	+	0.876760i	$0.340300\pi$
$390$	495.428	+	2170.61i	0.0643256	+	0.281829i
$391$	−2620.65	−	1262.04i	−0.338957	−	0.163233i
$392$	−17214.7	−	8290.16i	−2.21804	−	1.06815i
$393$	−297.349	−	1302.77i	−0.0381661	−	0.167217i
$394$	4277.81			0.546987
$395$	−982.119	−	4302.95i	−0.125103	−	0.548113i
$396$	12.3426	−	15.4771i	0.00156626	−	0.00196403i
$397$	−1778.03	+	7790.07i	−0.224778	+	0.984817i	0.729049	+	0.684462i	$0.239963\pi$
$397$	−1778.03	+	7790.07i	−0.224778	+	0.984817i	−0.953827	+	0.300356i	$0.902895\pi$
$398$	947.201	−	4149.96i	0.119294	−	0.522660i
$399$	−7016.78	−	8798.76i	−0.880396	−	1.10398i
$400$	−6900.13	−	3322.93i	−0.862516	−	0.415366i
$401$	6977.09	−	3359.99i	0.868876	−	0.418429i	0.0543268	−	0.998523i	$-0.482699\pi$
$401$	6977.09	−	3359.99i	0.868876	−	0.418429i	0.814549	+	0.580095i	$0.196984\pi$
$402$	−2427.19	+	3043.60i	−0.301137	+	0.377614i
$403$	2100.49	+	2633.94i	0.259635	+	0.325572i
$404$	−493.927	+	237.863i	−0.0608263	+	0.0292924i
$405$	1594.32			0.195611
$406$	−15745.8	+	329.011i	−1.92475	+	0.0402181i
$407$	−829.460			−0.101019
$408$	3890.75	−	1873.69i	0.472110	−	0.227356i
$409$	−4412.34	−	5532.89i	−0.533438	−	0.668910i	0.439964	−	0.898015i	$-0.354991\pi$
$409$	−4412.34	−	5532.89i	−0.533438	−	0.668910i	−0.973402	+	0.229106i	$0.926420\pi$
$410$	−2241.82	+	2811.15i	−0.270038	+	0.338617i
$411$	−9031.37	+	4349.28i	−1.08390	+	0.521981i
$412$	579.641	+	279.140i	0.0693128	+	0.0333793i
$413$	7594.25	+	9522.89i	0.904815	+	1.13460i
$414$	304.130	−	1332.48i	0.0361043	−	0.158183i
$415$	−566.857	+	2483.56i	−0.0670504	+	0.293767i
$416$	−593.936	+	744.772i	−0.0700003	+	0.0877776i
$417$	537.081	+	2353.10i	0.0630718	+	0.276336i
$418$	1454.67			0.170216
$419$	685.066	+	3001.47i	0.0798751	+	0.349956i	0.999035	−	0.0439298i	$-0.0139878\pi$
$419$	685.066	+	3001.47i	0.0798751	+	0.349956i	−0.919160	+	0.393885i	$0.871131\pi$
$420$	−184.140	−	88.6771i	−0.0213931	−	0.0103024i
$421$	8789.12	+	4232.61i	1.01747	+	0.489988i	0.866832	−	0.498601i	$-0.166153\pi$
$421$	8789.12	+	4232.61i	1.01747	+	0.489988i	0.150639	+	0.988589i	$0.451867\pi$
$422$	3781.27	+	16566.8i	0.436184	+	1.91105i
$423$	−1702.86			−0.195735
$424$	2666.64	+	11683.3i	0.305432	+	1.33819i
$425$	3132.58	−	3928.13i	0.357535	−	0.448334i
$426$	2856.65	−	12515.8i	0.324895	−	1.42346i
$427$	6044.74	−	26483.7i	0.685071	−	3.00149i
$428$	−202.398	−	253.800i	−0.0228582	−	0.0286632i
$429$	−1457.88	−	702.079i	−0.164073	−	0.0790133i
$430$	−926.644	+	446.248i	−0.103923	+	0.0500465i
$431$	−956.430	+	1199.32i	−0.106890	+	0.134036i	−0.832399	−	0.554177i	$-0.813033\pi$
$431$	−956.430	+	1199.32i	−0.106890	+	0.134036i	0.725509	+	0.688213i	$0.241604\pi$
$432$	6360.12	+	7975.34i	0.708337	+	0.888226i
$433$	−1218.37	+	586.738i	−0.135222	+	0.0651197i	−0.500272	−	0.865869i	$-0.666766\pi$
$433$	−1218.37	+	586.738i	−0.135222	+	0.0651197i	0.365049	+	0.930988i	$0.381052\pi$
$434$	−6472.75			−0.715903
$435$	2284.92	−	47.7438i	0.251847	−	0.00526239i
$436$	298.830			0.0328242
$437$	4323.32	−	2082.00i	0.473255	−	0.227907i
$438$	−3194.08	−	4005.24i	−0.348445	−	0.436936i
$439$	9009.46	−	11297.5i	0.979495	−	1.22825i	0.00589552	−	0.999983i	$-0.498123\pi$
$439$	9009.46	−	11297.5i	0.979495	−	1.22825i	0.973599	−	0.228265i	$-0.0733052\pi$
$440$	−450.562	+	216.979i	−0.0488175	+	0.0235092i
$441$	5573.49	+	2684.05i	0.601824	+	0.289823i
$442$	−4172.49	−	5232.13i	−0.449016	−	0.563048i
$443$	−1782.22	+	7808.40i	−0.191141	+	0.837445i	0.784859	+	0.619675i	$0.212735\pi$
$443$	−1782.22	+	7808.40i	−0.191141	+	0.837445i	−0.976000	+	0.217770i	$0.930122\pi$
$444$	−47.7511	+	209.211i	−0.00510398	+	0.0223620i
$445$	−171.511	+	215.068i	−0.0182706	+	0.0229106i
$446$	1306.05	+	5722.16i	0.138662	+	0.607516i
$447$	9380.03			0.992529
$448$	3745.59	+	16410.5i	0.395005	+	1.73063i
$449$	9098.86	+	4381.78i	0.956352	+	0.460555i	0.845909	−	0.533328i	$-0.179059\pi$
$449$	9098.86	+	4381.78i	0.956352	+	0.460555i	0.110443	+	0.993882i	$0.464773\pi$
$450$	2127.02	+	1024.32i	0.222819	+	0.107304i
$451$	−581.493	−	2547.69i	−0.0607127	−	0.266000i
$452$	15.1921			0.00158092
$453$	−1785.60	−	7823.23i	−0.185198	−	0.811407i
$454$	−7983.87	+	10011.5i	−0.825334	+	1.03494i
$455$	1334.14	−	5845.24i	0.137462	−	0.602262i
$456$	−1585.27	+	6945.50i	−0.162800	+	0.713274i
$457$	−612.044	−	767.479i	−0.0626482	−	0.0785584i	0.749520	−	0.661982i	$-0.230284\pi$
$457$	−612.044	−	767.479i	−0.0626482	−	0.0785584i	−0.812168	+	0.583423i	$0.801713\pi$
$458$	464.192	+	223.543i	0.0473587	+	0.0228067i
$459$	−6029.35	+	2903.58i	−0.613129	+	0.295267i
$460$	54.3334	−	68.1319i	0.00550719	−	0.00690580i
$461$	−6570.01	−	8238.53i	−0.663765	−	0.832335i	0.329982	−	0.943987i	$-0.392957\pi$
$461$	−6570.01	−	8238.53i	−0.663765	−	0.832335i	−0.993747	+	0.111652i	$0.964386\pi$
$462$	2801.04	−	1348.91i	0.282070	−	0.135838i
$463$	−4266.69			−0.428271			−0.214136	−	0.976804i	$-0.568693\pi$
$463$	−4266.69			−0.428271			−0.214136	+	0.976804i	$0.568693\pi$
$464$	6698.29	+	8048.54i	0.670173	+	0.805267i
$465$	939.280			0.0936733
$466$	8407.12	−	4048.65i	0.835734	−	0.402468i
$467$	−9180.55	−	11512.0i	−0.909689	−	1.14071i	−0.989591	−	0.143912i	$-0.954032\pi$
$467$	−9180.55	−	11512.0i	−0.909689	−	1.14071i	0.0799011	−	0.996803i	$-0.474540\pi$
$468$	93.6732	−	117.462i	0.00925223	−	0.0116019i
$469$	9445.03	−	4548.49i	0.929917	−	0.447824i
$470$	−2047.41	−	985.981i	−0.200936	−	0.0967657i
$471$	1027.62	+	1288.60i	0.100532	+	0.126063i
$472$	1715.73	−	7517.12i	0.167316	−	0.733058i
$473$	166.332	−	728.750i	0.0161691	−	0.0708414i
$474$	10829.6	−	13579.8i	1.04941	−	1.31591i
$475$	1844.38	+	8080.76i	0.178160	+	0.780570i
$476$	614.319			0.0591539
$477$	−863.360	−	3782.63i	−0.0828732	−	0.363091i
$478$	−7314.26	−	3522.36i	−0.699888	−	0.337048i
$479$	8184.15	+	3941.28i	0.780675	+	0.375953i	0.781387	−	0.624047i	$-0.214512\pi$
$479$	8184.15	+	3941.28i	0.780675	+	0.375953i	−0.000712465		1.00000i	$0.500227\pi$
$480$	59.0996	+	258.932i	0.00561982	+	0.0246220i
$481$	−6295.12			−0.596742
$482$	−3143.34	−	13771.9i	−0.297044	−	1.30144i
$483$	6394.13	−	8017.99i	0.602367	−	0.755344i
$484$	114.614	−	502.157i	0.0107639	−	0.0471598i
$485$	−103.465	+	453.309i	−0.00968679	+	0.0424406i
$486$	−3511.50	−	4403.28i	−0.327747	−	0.410981i
$487$	−704.693	−	339.362i	−0.0655702	−	0.0315769i	0.400811	−	0.916161i	$-0.368728\pi$
$487$	−704.693	−	339.362i	−0.0655702	−	0.0315769i	−0.466381	+	0.884584i	$0.654443\pi$
$488$	−15493.1	+	7461.10i	−1.43717	+	0.692107i
$489$	−3866.66	+	4848.64i	−0.357579	+	0.448390i
$490$	5147.11	+	6454.28i	0.474536	+	0.595050i
$491$	−2909.19	+	1400.99i	−0.267393	+	0.128770i	−0.562777	−	0.826609i	$-0.690267\pi$
$491$	−2909.19	+	1400.99i	−0.267393	+	0.128770i	0.295384	+	0.955379i	$0.404553\pi$
$492$	−676.068			−0.0619502
$493$	−6125.53	+	3109.18i	−0.559595	+	0.284038i
$494$	11040.1			1.00550
$495$	145.875	−	70.2499i	0.0132457	−	0.00637878i
$496$	2683.22	+	3364.65i	0.242903	+	0.304591i
$497$	−21554.4	+	27028.3i	−1.94536	+	2.43941i
$498$	−9032.35	+	4349.75i	−0.812749	+	0.391400i
$499$	5969.83	+	2874.92i	0.535564	+	0.257914i	0.682058	−	0.731298i	$-0.261085\pi$
$499$	5969.83	+	2874.92i	0.535564	+	0.257914i	−0.146495	+	0.989211i	$0.546799\pi$
$500$	196.558	+	246.476i	0.0175807	+	0.0220455i
$501$	−1993.03	+	8732.06i	−0.177729	+	0.778682i
$502$	1687.18	−	7392.03i	0.150005	−	0.657216i
$503$	−7812.89	+	9797.05i	−0.692564	+	0.868447i	−0.996444	−	0.0842629i	$-0.973146\pi$
$503$	−7812.89	+	9797.05i	−0.692564	+	0.868447i	0.303880	+	0.952710i	$0.401718\pi$
$504$	−1215.92	−	5327.27i	−0.107463	−	0.470825i
$505$	−4483.82			−0.395104
$506$	294.971	+	1292.35i	0.0259152	+	0.113542i
$507$	−2241.19	−	1079.30i	−0.196321	−	0.0945433i
$508$	42.6406	+	20.5346i	0.00372416	+	0.00179346i
$509$	−4254.82	−	18641.6i	−0.370514	−	1.62333i	−0.725338	−	0.688393i	$-0.758316\pi$
$509$	−4254.82	−	18641.6i	−0.370514	−	1.62333i	0.354824	−	0.934933i	$-0.384541\pi$
$510$	−1865.82			−0.161999
$511$	3069.77	+	13449.6i	0.265751	+	1.16433i
$512$	6607.23	−	8285.21i	0.570315	−	0.715152i
$513$	2456.63	−	10763.2i	0.211428	−	0.926328i
$514$	−3746.89	+	16416.2i	−0.321533	+	1.40873i
$515$	3280.75	+	4113.93i	0.280713	+	0.352003i
$516$	−174.234	−	83.9067i	−0.0148648	−	0.00715850i
$517$	1488.02	−	716.591i	0.126582	−	0.0609587i
$518$	7541.02	−	9456.14i	0.639640	−	0.802083i
$519$	−3621.86	−	4541.66i	−0.306323	−	0.384117i
$520$	−3419.50	+	1646.74i	−0.288375	+	0.138874i
$521$	7261.51			0.610619			0.305310	−	0.952253i	$-0.401240\pi$
$521$	7261.51			0.610619			0.305310	+	0.952253i	$0.401240\pi$
$522$	−2064.80	−	2481.02i	−0.173130	−	0.208029i
$523$	1886.78			0.157750			0.0788749	−	0.996885i	$-0.474867\pi$
$523$	1886.78			0.157750			0.0788749	+	0.996885i	$0.474867\pi$
$524$	−108.417	+	52.2110i	−0.00903861	+	0.00435277i
$525$	11044.7	+	13849.6i	0.918153	+	1.15133i
$526$	4925.60	−	6176.51i	0.408301	−	0.511994i
$527$	−2543.67	+	1224.97i	−0.210254	+	0.101253i
$528$	−1862.33	−	896.851i	−0.153499	−	0.0739213i
$529$	−4859.66	−	6093.82i	−0.399413	−	0.500848i
$530$	1152.15	−	5047.90i	0.0944268	−	0.413711i
$531$	−555.492	+	2433.77i	−0.0453979	+	0.198901i
$532$	−631.874	+	792.345i	−0.0514948	+	0.0645724i
$533$	−4413.19	−	19335.5i	−0.358643	−	1.57132i
$534$	−1082.56			−0.0877283
$535$	−590.804	−	2588.48i	−0.0477433	−	0.209177i
$536$	−5978.97	−	2879.32i	−0.481814	−	0.232029i
$537$	8650.28	+	4165.76i	0.695135	+	0.334759i
$538$	1009.31	+	4422.09i	0.0808821	+	0.354368i
$539$	−5999.81			−0.479462
$540$	−44.6138	−	195.466i	−0.00355532	−	0.0155769i
$541$	−1438.11	+	1803.33i	−0.114287	+	0.143311i	−0.835684	−	0.549210i	$-0.814929\pi$
$541$	−1438.11	+	1803.33i	−0.114287	+	0.143311i	0.721398	+	0.692521i	$0.243500\pi$
$542$	−2789.31	+	12220.8i	−0.221053	+	0.968498i
$543$	−3514.02	+	15395.9i	−0.277719	+	1.21676i
$544$	−497.736	−	624.141i	−0.0392284	−	0.0491908i
$545$	2202.06	+	1060.45i	0.173075	+	0.0833484i
$546$	21258.3	−	10237.4i	1.66624	−	0.802421i
$547$	193.072	−	242.105i	0.0150917	−	0.0189244i	−0.774228	−	0.632906i	$-0.781862\pi$
$547$	193.072	−	242.105i	0.0150917	−	0.0189244i	0.789320	+	0.613982i	$0.210433\pi$
$548$	562.816	+	705.749i	0.0438728	+	0.0550148i
$549$	5016.11	−	2415.63i	0.389950	−	0.187790i
$550$	−2289.71			−0.177516
$551$	2290.38	−	11098.7i	0.177084	−	0.858115i
$552$	−6491.95			−0.500572
$553$	−42141.6	+	20294.3i	−3.24059	+	1.56058i
$554$	−1900.44	−	2383.08i	−0.145744	−	0.182757i
$555$	−1094.30	+	1372.21i	−0.0836945	+	0.104950i
$556$	195.827	−	94.3051i	0.0149369	−	0.00719321i
$557$	11087.5	+	5339.46i	0.843433	+	0.406176i	0.805136	−	0.593090i	$-0.202092\pi$
$557$	11087.5	+	5339.46i	0.843433	+	0.406176i	0.0382972	+	0.999266i	$0.487807\pi$
$558$	−827.121	−	1037.18i	−0.0627506	−	0.0786867i
$559$	1262.37	−	5530.79i	0.0955141	−	0.418475i
$560$	1704.26	−	7466.83i	0.128603	−	0.563449i
$561$	845.476	−	1060.19i	0.0636292	−	0.0797885i
$562$	−3123.22	−	13683.7i	−0.234422	−	1.02707i
$563$	2558.68			0.191537			0.0957685	−	0.995404i	$-0.469469\pi$
$563$	2558.68			0.191537			0.0957685	+	0.995404i	$0.469469\pi$
$564$	−95.0793	−	416.569i	−0.00709851	−	0.0311006i
$565$	111.950	+	53.9121i	0.00833586	+	0.00401434i
$566$	−12911.8	−	6218.01i	−0.958878	−	0.461771i
$567$	−3759.71	−	16472.4i	−0.278471	−	1.22006i
$568$	21884.1			1.61662
$569$	−1914.09	−	8386.18i	−0.141024	−	0.617868i	−0.995198	−	0.0978805i	$-0.968794\pi$
$569$	−1914.09	−	8386.18i	−0.141024	−	0.617868i	0.854174	−	0.519988i	$-0.174063\pi$
$570$	1919.13	−	2406.52i	0.141024	−	0.176839i
$571$	−1750.71	+	7670.34i	−0.128310	+	0.562161i	0.869375	+	0.494153i	$0.164522\pi$
$571$	−1750.71	+	7670.34i	−0.128310	+	0.562161i	−0.997685	+	0.0680084i	$0.978336\pi$
$572$	−32.4248	+	142.062i	−0.00237019	+	0.0103845i
$573$	5830.56	+	7311.29i	0.425087	+	0.533043i
$574$	34331.2	+	16533.0i	2.49644	+	1.20222i
$575$	−6805.08	+	3277.16i	−0.493551	+	0.237681i
$576$	−2150.95	+	2697.20i	−0.155595	+	0.195110i
$577$	−610.093	−	765.032i	−0.0440182	−	0.0551971i	0.759335	−	0.650700i	$-0.225524\pi$
$577$	−610.093	−	765.032i	−0.0440182	−	0.0551971i	−0.803353	+	0.595503i	$0.796953\pi$
$578$	−7777.35	+	3745.37i	−0.559680	+	0.269528i
$579$	1448.13			0.103942
$580$	−49.9778	−	199.646i	−0.00357796	−	0.0142928i
$581$	26996.7			1.92773
$582$	−1648.62	+	793.932i	−0.117418	+	0.0565456i
$583$	2346.23	+	2942.08i	0.166674	+	0.209002i
$584$	5444.88	−	6827.66i	0.385806	−	0.483785i
$585$	1107.11	−	533.156i	0.0782450	−	0.0376808i
$586$	−17775.7	−	8560.32i	−1.25308	−	0.603453i
$587$	11197.0	+	14040.6i	0.787311	+	0.987256i	0.999949	+	0.0101253i	$0.00322303\pi$
$587$	11197.0	+	14040.6i	0.787311	+	0.987256i	−0.212638	+	0.977131i	$0.568206\pi$
$588$	−345.402	+	1513.31i	−0.0242247	+	0.106136i
$589$	1036.40	−	4540.78i	0.0725030	−	0.317657i
$590$	−2077.08	+	2604.57i	−0.144936	+	0.181743i
$591$	1463.88	+	6413.69i	0.101889	+	0.446403i
$592$	−8041.52			−0.558285
$593$	−389.222	−	1705.29i	−0.0269535	−	0.118091i	0.959661	−	0.281158i	$-0.0907185\pi$
$593$	−389.222	−	1705.29i	−0.0269535	−	0.118091i	−0.986615	+	0.163067i	$0.947861\pi$
$594$	2747.76	+	1323.25i	0.189802	+	0.0914036i
$595$	4526.87	+	2180.03i	0.311905	+	0.150206i
$596$	−187.961	−	823.512i	−0.0129181	−	0.0565979i
$597$	6546.15			0.448770
$598$	2238.66	+	9808.20i	0.153086	+	0.670714i
$599$	−11804.0	+	14801.7i	−0.805173	+	1.00965i	0.194414	+	0.980919i	$0.437719\pi$
$599$	−11804.0	+	14801.7i	−0.805173	+	1.00965i	−0.999587	+	0.0287350i	$0.990852\pi$
$600$	2495.28	−	10932.5i	0.169782	−	0.743864i
$601$	−3412.01	+	14949.0i	−0.231579	+	1.01461i	0.716752	+	0.697328i	$0.245628\pi$
$601$	−3412.01	+	14949.0i	−0.231579	+	1.01461i	−0.948331	+	0.317284i	$0.897229\pi$
$602$	6795.80	+	8521.67i	0.460093	+	0.576939i
$603$	1935.77	+	932.219i	0.130731	+	0.0629567i
$604$	−651.053	+	313.531i	−0.0438592	+	0.0211215i
$605$	2626.58	−	3293.63i	0.176505	−	0.221331i
$606$	−11001.8	−	13795.9i	−0.737491	−	0.924784i
$607$	7746.38	−	3730.46i	0.517983	−	0.249448i	−0.156579	−	0.987665i	$-0.550047\pi$
$607$	7746.38	−	3730.46i	0.517983	−	0.249448i	0.674562	+	0.738218i	$0.264332\pi$
$608$	1316.97			0.0878459
$609$	−5881.56	−	23495.0i	−0.391351	−	1.56332i
$610$	7429.75			0.493151
$611$	11293.2	−	5438.51i	0.747746	−	0.360096i
$612$	78.5008	+	98.4369i	0.00518498	+	0.00650176i
$613$	8865.04	−	11116.4i	0.584104	−	0.732443i	−0.398703	−	0.917080i	$-0.630540\pi$
$613$	8865.04	−	11116.4i	0.584104	−	0.732443i	0.982807	+	0.184637i	$0.0591110\pi$
$614$	2736.81	−	1317.98i	0.179884	−	0.0866274i
$615$	−4981.90	−	2399.16i	−0.326650	−	0.157306i
$616$	3304.32	+	4143.48i	0.216128	+	0.271016i
$617$	3861.89	−	16920.1i	0.251984	−	1.10401i	−0.677609	−	0.735423i	$-0.736984\pi$
$617$	3861.89	−	16920.1i	0.251984	−	1.10401i	0.929592	−	0.368590i	$-0.120159\pi$
$618$	−4607.90	+	20188.5i	−0.299930	+	1.31408i
$619$	−846.828	+	1061.89i	−0.0549869	+	0.0689514i	−0.808564	−	0.588408i	$-0.799755\pi$
$619$	−846.828	+	1061.89i	−0.0549869	+	0.0689514i	0.753578	+	0.657359i	$0.228326\pi$
$620$	−18.8217	−	82.4633i	−0.00121919	−	0.00534162i
$621$	10060.3			0.650092
$622$	−1608.49	−	7047.26i	−0.103689	−	0.454292i
$623$	2626.52	+	1264.87i	0.168908	+	0.0813416i
$624$	−14134.0	−	6806.58i	−0.906751	−	0.436668i
$625$	−2603.33	−	11405.9i	−0.166613	−	0.729980i
$626$	−10116.2			−0.645885
$627$	497.794	+	2180.98i	0.0317065	+	0.138915i
$628$	92.5395	−	116.041i	0.00588014	−	0.00737346i
$629$	1173.91	−	5143.22i	0.0744146	−	0.326031i
$630$	−525.349	+	2301.71i	−0.0332229	+	0.145559i
$631$	10574.1	+	13259.5i	0.667113	+	0.836534i	0.994097	−	0.108496i	$-0.0346036\pi$
$631$	10574.1	+	13259.5i	0.667113	+	0.836534i	−0.326984	+	0.945030i	$0.606032\pi$
$632$	26676.8	+	12846.9i	1.67903	+	0.808579i
$633$	−23544.6	+	11338.5i	−1.47838	+	0.711950i
$634$	−10725.8	+	13449.7i	−0.671885	+	0.842518i
$635$	241.345	+	302.637i	0.0150826	+	0.0189130i
$636$	877.137	−	422.407i	0.0546867	−	0.0263357i
$637$	−45535.0			−2.83228
$638$	2848.35	+	1299.10i	0.176751	+	0.0806144i
$639$	−7085.28			−0.438637
$640$	−4577.35	+	2204.33i	−0.282712	+	0.136147i
$641$	−291.052	−	364.968i	−0.0179343	−	0.0224889i	0.772783	−	0.634670i	$-0.218864\pi$
$641$	−291.052	−	364.968i	−0.0179343	−	0.0224889i	−0.790718	+	0.612181i	$0.790292\pi$
$642$	6514.63	−	8169.09i	0.400486	−	0.502194i
$643$	3641.11	−	1753.47i	0.223315	−	0.107543i	−0.318882	−	0.947795i	$-0.603307\pi$
$643$	3641.11	−	1753.47i	0.223315	−	0.107543i	0.542196	+	0.840252i	$0.317593\pi$
$644$	−832.061	−	400.700i	−0.0509127	−	0.0245183i
$645$	−986.159	−	1236.60i	−0.0602015	−	0.0754903i
$646$	−2058.75	+	9019.96i	−0.125387	+	0.549358i
$647$	−33.5023	+	146.783i	−0.00203572	+	0.00891907i	−0.975936	−	0.218059i	$-0.930027\pi$
$647$	−33.5023	+	146.783i	−0.00203572	+	0.00891907i	0.973900	+	0.226978i	$0.0728846\pi$
$648$	−6668.62	+	8362.18i	−0.404272	+	0.506941i
$649$	−538.763	−	2360.47i	−0.0325859	−	0.142768i
$650$	−17377.6			−1.04862
$651$	−2215.00	−	9704.56i	−0.133353	−	0.584258i
$652$	503.164	+	242.311i	0.0302230	+	0.0145546i
$653$	−19685.7	−	9480.16i	−1.17973	−	0.568127i	−0.261897	−	0.965096i	$-0.584348\pi$
$653$	−19685.7	−	9480.16i	−1.17973	−	0.568127i	−0.917832	+	0.396969i	$0.870062\pi$
$654$	2140.31	+	9377.33i	0.127971	+	0.560677i
$655$	−984.200			−0.0587113
$656$	−5637.51	−	24699.5i	−0.335530	−	1.47005i
$657$	−1762.85	+	2210.55i	−0.104681	+	0.131266i
$658$	−5358.88	+	23478.8i	−0.317494	+	1.39103i
$659$	636.163	−	2787.21i	0.0376045	−	0.164756i	−0.952639	−	0.304103i	$-0.901643\pi$
$659$	636.163	−	2787.21i	0.0376045	−	0.164756i	0.990244	+	0.139347i	$0.0445004\pi$
$660$	25.3302	+	31.7631i	0.00149390	+	0.00187330i
$661$	−6491.40	−	3126.09i	−0.381976	−	0.183950i	0.233035	−	0.972468i	$-0.425134\pi$
$661$	−6491.40	−	3126.09i	−0.381976	−	0.183950i	−0.615011	+	0.788518i	$0.710849\pi$
$662$	−18486.0	+	8902.37i	−1.08531	+	0.522659i
$663$	6416.67	−	8046.24i	0.375871	−	0.471328i
$664$	−10655.2	−	13361.2i	−0.622746	−	0.780899i
$665$	−7468.03	+	3596.41i	−0.435485	+	0.209719i
$666$	2478.86			0.144225
$667$	10324.7	−	215.737i	0.599362	−	0.0125238i
$668$	806.561			0.0467167
$669$	−8132.28	+	3916.30i	−0.469973	+	0.226327i
$670$	1787.68	+	2241.69i	0.103081	+	0.129259i
$671$	−3366.72	+	4221.73i	−0.193697	+	0.242888i
$672$	2535.90	−	1221.22i	0.145572	−	0.0701037i
$673$	14869.6	+	7160.83i	0.851682	+	0.410148i	0.808202	−	0.588906i	$-0.200441\pi$
$673$	14869.6	+	7160.83i	0.851682	+	0.410148i	0.0434802	+	0.999054i	$0.486155\pi$
$674$	−3986.21	−	4998.55i	−0.227809	−	0.285663i
$675$	−3866.83	+	16941.7i	−0.220496	+	0.966054i
$676$	−49.8464	+	218.391i	−0.00283605	+	0.0124255i
$677$	21013.0	−	26349.4i	1.19290	−	1.49585i	0.368706	−	0.929546i	$-0.379801\pi$
$677$	21013.0	−	26349.4i	1.19290	−	1.49585i	0.824196	−	0.566305i	$-0.191628\pi$
$678$	108.811	+	476.732i	0.00616350	+	0.0270041i
$679$	4927.54			0.278500
$680$	−707.754	−	3100.87i	−0.0399134	−	0.174872i
$681$	−17742.2	−	8544.21i	−0.998361	−	0.480785i
$682$	1159.23	+	558.256i	0.0650868	+	0.0313441i
$683$	2776.59	+	12165.0i	0.155554	+	0.681525i	0.991213	+	0.132277i	$0.0422287\pi$
$683$	2776.59	+	12165.0i	0.155554	+	0.681525i	−0.835659	+	0.549248i	$0.814914\pi$
$684$	−207.708			−0.0116110
$685$	1642.87	+	7197.87i	0.0916361	+	0.401484i
$686$	32980.3	−	41356.0i	1.83556	−	2.30172i
$687$	−176.309	+	772.458i	−0.00979126	+	0.0428983i
$688$	1612.57	−	7065.15i	0.0893587	−	0.391506i
$689$	17806.5	+	22328.6i	0.984577	+	1.23462i
$690$	2527.14	+	1217.01i	0.139430	+	0.0671460i
$691$	11123.5	−	5356.81i	0.612386	−	0.294910i	−0.101866	−	0.994798i	$-0.532481\pi$
$691$	11123.5	−	5356.81i	0.612386	−	0.294910i	0.714252	+	0.699889i	$0.246767\pi$
$692$	−326.155	+	408.986i	−0.0179170	+	0.0224672i
$693$	−1069.82	−	1341.51i	−0.0586421	−	0.0735349i
$694$	16500.4	−	7946.16i	0.902515	−	0.434628i
$695$	1777.69			0.0970240
$696$	−9306.80	+	12184.1i	−0.506858	+	0.663557i
$697$	16620.4			0.903216
$698$	−12061.8	+	5808.67i	−0.654078	+	0.314987i
$699$	8947.07	+	11219.3i	0.484134	+	0.607084i
$700$	994.597	−	1247.19i	0.0537032	−	0.0673417i
$701$	−5189.60	+	2499.18i	−0.279613	+	0.134654i	−0.568435	−	0.822728i	$-0.692451\pi$
$701$	−5189.60	+	2499.18i	−0.279613	+	0.134654i	0.288822	+	0.957383i	$0.406736\pi$
$702$	20853.9	+	10042.7i	1.12120	+	0.539940i
$703$	5426.25	+	6804.30i	0.291116	+	0.365048i
$704$	744.545	−	3262.06i	0.0398595	−	0.174636i
$705$	777.643	−	3407.08i	0.0415429	−	0.182011i
$706$	12792.9	−	16041.7i	0.681962	−	0.855154i
$707$	10573.7	+	46326.4i	0.562468	+	2.46433i
$708$	−626.388			−0.0332501
$709$	−3185.95	−	13958.6i	−0.168760	−	0.739386i	−0.986495	−	0.163791i	$-0.947628\pi$
$709$	−3185.95	−	13958.6i	−0.168760	−	0.739386i	0.817735	−	0.575595i	$-0.195230\pi$
$710$	−8518.91	−	4102.49i	−0.450294	−	0.216850i
$711$	−8636.99	−	4159.35i	−0.455573	−	0.219392i
$712$	−410.644	−	1799.15i	−0.0216145	−	0.0946993i
$713$	4244.26			0.222930
$714$	4399.95	+	19277.4i	0.230622	+	1.01042i
$715$	−743.070	+	931.781i	−0.0388661	+	0.0487365i
$716$	192.391	−	842.920i	0.0100419	−	0.0439964i
$717$	2778.09	−	12171.6i	0.144699	−	0.633970i
$718$	−19283.8	−	24181.1i	−1.00232	−	1.25687i
$719$	−24012.4	−	11563.8i	−1.24550	−	0.599800i	−0.309196	−	0.950998i	$-0.600060\pi$
$719$	−24012.4	−	11563.8i	−1.24550	−	0.599800i	−0.936301	+	0.351199i	$0.885774\pi$
$720$	1414.24	−	681.064i	0.0732025	−	0.0352525i
$721$	34768.1	−	43597.8i	1.79588	−	2.25197i
$722$	2879.25	+	3610.46i	0.148414	+	0.186105i
$723$	19572.4	−	9425.59i	1.00679	−	0.484843i
$724$	1422.09			0.0729994
$725$	−3605.15	+	17469.8i	−0.184678	+	0.894916i
$726$	16578.7			0.847511
$727$	−10251.7	+	4936.95i	−0.522990	+	0.251859i	−0.676702	−	0.736257i	$-0.736591\pi$
$727$	−10251.7	+	4936.95i	−0.522990	+	0.251859i	0.153712	+	0.988116i	$0.450877\pi$
$728$	25077.8	+	31446.6i	1.27671	+	1.60095i
$729$	13575.2	−	17022.8i	0.689693	−	0.864847i
$730$	−3399.49	+	1637.11i	−0.172357	+	0.0830028i
$731$	4283.35	+	2062.75i	0.216724	+	0.104369i
$732$	871.011	+	1092.21i	0.0439802	+	0.0551494i
$733$	−1591.99	+	6974.97i	−0.0802204	+	0.351469i	−0.999069	−	0.0431418i	$-0.986263\pi$
$733$	−1591.99	+	6974.97i	−0.0802204	+	0.351469i	0.918849	+	0.394610i	$0.129120\pi$
$734$	−5871.14	+	25723.2i	−0.295242	+	1.29354i
$735$	−7915.50	+	9925.72i	−0.397235	+	0.498116i
$736$	267.049	+	1170.02i	0.0133744	+	0.0585971i
$737$	−2083.84			−0.104151
$738$	1737.80	+	7613.81i	0.0866794	+	0.379767i
$739$	−6896.02	−	3320.95i	−0.343267	−	0.165309i	0.254305	−	0.967124i	$-0.418153\pi$
$739$	−6896.02	−	3320.95i	−0.343267	−	0.165309i	−0.597572	+	0.801816i	$0.703868\pi$
$740$	142.400	+	68.5763i	0.00707396	+	0.00340664i
$741$	3777.97	+	16552.4i	0.187297	+	0.820602i
$742$	−54871.4			−2.71482
$743$	−5525.99	−	24211.0i	−0.272852	−	1.19544i	−0.906630	−	0.421928i	$-0.861354\pi$
$743$	−5525.99	−	24211.0i	−0.272852	−	1.19544i	0.633777	−	0.773515i	$-0.281503\pi$
$744$	−3928.76	+	4926.51i	−0.193596	+	0.242762i
$745$	1537.32	−	6735.42i	0.0756012	−	0.331230i
$746$	−2354.23	+	10314.6i	−0.115542	+	0.506225i
$747$	3449.78	+	4325.88i	0.168970	+	0.211882i
$748$	−110.021	−	52.9832i	−0.00537802	−	0.00258992i
$749$	−25350.7	+	12208.3i	−1.23671	+	0.595568i
$750$	−6326.66	+	7933.37i	−0.308022	+	0.386248i
$751$	−18978.1	−	23797.7i	−0.922130	−	1.15631i	−0.987368	−	0.158444i	$-0.949352\pi$
$751$	−18978.1	−	23797.7i	−0.922130	−	1.15631i	0.0652383	−	0.997870i	$-0.479219\pi$
$752$	14426.1	−	6947.26i	0.699558	−	0.336889i
$753$	11660.2			0.564304
$754$	21617.3	+	9859.44i	1.04411	+	0.476206i
$755$	−5910.19			−0.284892
$756$	−1914.33	+	921.891i	−0.0920945	+	0.0443504i
$757$	−14819.4	−	18583.0i	−0.711521	−	0.892220i	0.286304	−	0.958139i	$-0.407573\pi$
$757$	−14819.4	−	18583.0i	−0.711521	−	0.892220i	−0.997825	+	0.0659194i	$0.979002\pi$
$758$	4156.05	−	5211.52i	0.199148	−	0.249724i
$759$	−1836.68	+	884.497i	−0.0878355	+	0.0422994i
$760$	4727.47	+	2276.63i	0.225636	+	0.108661i
$761$	−17170.3	−	21530.9i	−0.817901	−	1.02561i	−0.999110	−	0.0421705i	$-0.986573\pi$
$761$	−17170.3	−	21530.9i	−0.817901	−	1.02561i	0.181210	−	0.983444i	$-0.441999\pi$
$762$	−338.975	+	1485.15i	−0.0161152	+	0.0706052i
$763$	5763.65	−	25252.2i	0.273471	−	1.19815i
$764$	525.053	−	658.396i	0.0248636	−	0.0311779i
$765$	229.145	+	1003.95i	0.0108297	+	0.0474482i
$766$	−2934.12			−0.138400
$767$	−4088.89	−	17914.6i	−0.192492	−	0.843363i
$768$	−2470.01	−	1189.49i	−0.116053	−	0.0558882i
$769$	26256.6	+	12644.5i	1.23126	+	0.592942i	0.932425	−	0.361363i	$-0.117689\pi$
$769$	26256.6	+	12644.5i	1.23126	+	0.592942i	0.298833	+	0.954306i	$0.403403\pi$
$770$	−509.528	−	2232.39i	−0.0238469	−	0.104480i
$771$	−25894.9			−1.20957
$772$	−29.0184	−	127.138i	−0.00135284	−	0.00592718i
$773$	−10172.1	+	12755.4i	−0.473305	+	0.593506i	−0.959977	−	0.280079i	$-0.909639\pi$
$773$	−10172.1	+	12755.4i	−0.473305	+	0.593506i	0.486672	+	0.873585i	$0.338211\pi$
$774$	−497.088	+	2177.88i	−0.0230846	+	0.101140i
$775$	−1631.34	+	7147.39i	−0.0756124	+	0.331280i
$776$	−1944.83	−	2438.74i	−0.0899683	−	0.112817i
$777$	16758.1	+	8070.28i	0.773737	+	0.372612i
$778$	19271.7	−	9280.76i	0.888077	−	0.427675i
$779$	−17095.3	+	21436.9i	−0.786270	+	0.985951i
$780$	192.241	+	241.063i	0.00882480	+	0.0110659i
$781$	6191.37	−	2981.61i	0.283668	−	0.136607i
$782$	−8430.94			−0.385537
$783$	14422.4	−	18881.2i	0.658256	−	0.861760i
$784$	−58167.4			−2.64975
$785$	1093.71	−	526.703i	0.0497276	−	0.0239476i
$786$	−2414.91	−	3028.20i	−0.109589	−	0.137420i
$787$	9430.32	−	11825.2i	0.427134	−	0.535609i	−0.520968	−	0.853576i	$-0.674429\pi$
$787$	9430.32	−	11825.2i	0.427134	−	0.535609i	0.948102	+	0.317967i	$0.103000\pi$
$788$	533.751	−	257.041i	0.0241296	−	0.0116202i
$789$	10946.0	+	5271.30i	0.493900	+	0.237850i
$790$	−7976.25	−	10001.9i	−0.359218	−	0.450445i
$791$	293.017	−	1283.79i	0.0131713	−	0.0577071i
$792$	−241.699	+	1058.95i	−0.0108439	+	0.0475103i
$793$	−25551.4	+	32040.5i	−1.14421	+	1.43479i
$794$	5153.66	+	22579.7i	0.230348	+	1.00922i
$795$	7962.55			0.355224
$796$	−131.175	−	574.713i	−0.00584090	−	0.0255907i
$797$	16489.0	+	7940.69i	0.732836	+	0.352915i	0.762799	−	0.646636i	$-0.223825\pi$
$797$	16489.0	+	7940.69i	0.732836	+	0.352915i	−0.0299627	+	0.999551i	$0.509539\pi$
$798$	−29389.6	−	14153.3i	−1.30374	−	0.627846i
$799$	2337.42	+	10240.9i	0.103494	+	0.453438i
$800$	−2072.97			−0.0916132
$801$	132.951	+	582.498i	0.00586468	+	0.0256948i
$802$	13994.9	−	17549.1i	0.616181	−	0.772666i
$803$	610.207	−	2673.49i	0.0268166	−	0.117491i
$804$	−119.964	+	525.598i	−0.00526221	+	0.0230552i
$805$	−4709.44	−	5905.45i	−0.206194	−	0.258559i
$806$	8797.87	+	4236.83i	0.384481	+	0.185156i
$807$	−6284.62	+	3026.51i	−0.274138	+	0.132018i
$808$	18754.6	−	23517.6i	0.816566	−	1.02394i
$809$	15519.1	+	19460.3i	0.674440	+	0.845721i	0.994829	−	0.101565i	$-0.0323851\pi$
$809$	15519.1	+	19460.3i	0.674440	+	0.845721i	−0.320389	+	0.947286i	$0.603814\pi$
$810$	4163.53	−	2005.05i	0.180607	−	0.0869756i
$811$	19933.7			0.863093			0.431546	−	0.902091i	$-0.357968\pi$
$811$	19933.7			0.863093			0.431546	+	0.902091i	$0.357968\pi$
$812$	−1944.87	+	987.170i	−0.0840534	+	0.0426636i
$813$	−19277.0			−0.831580
$814$	−2166.11	+	1043.15i	−0.0932706	+	0.0449168i
$815$	2847.89	+	3571.14i	0.122402	+	0.153487i
$816$	8196.79	−	10278.4i	0.351648	−	0.440953i
$817$	−7066.28	+	3402.94i	−0.302592	+	0.145721i
$818$	−18481.0	−	8899.97i	−0.789942	−	0.380416i
$819$	−8119.29	−	10181.3i	−0.346411	−	0.434386i
$820$	−110.802	+	485.457i	−0.00471877	+	0.0206743i
$821$	−8656.87	+	37928.2i	−0.367998	+	1.61231i	0.364272	+	0.931293i	$0.381318\pi$
$821$	−8656.87	+	37928.2i	−0.367998	+	1.61231i	−0.732271	+	0.681014i	$0.761539\pi$
$822$	−18115.4	+	22716.1i	−0.768672	+	0.963885i
$823$	9007.50	+	39464.4i	0.381509	+	1.67150i	0.692758	+	0.721170i	$0.256395\pi$
$823$	9007.50	+	39464.4i	0.381509	+	1.67150i	−0.311249	+	0.950328i	$0.600747\pi$
$824$	−35300.0			−1.49240
$825$	−783.549	−	3432.95i	−0.0330663	−	0.144873i
$826$	31808.4	+	15318.1i	1.33990	+	0.645260i
$827$	1187.62	+	571.926i	0.0499364	+	0.0240481i	0.458685	−	0.888599i	$-0.348321\pi$
$827$	1187.62	+	571.926i	0.0499364	+	0.0240481i	−0.408749	+	0.912647i	$0.634035\pi$
$828$	−42.1179	−	184.531i	−0.00176775	−	0.00774503i
$829$	15446.1			0.647125			0.323563	−	0.946207i	$-0.395119\pi$
$829$	15446.1			0.647125			0.323563	+	0.946207i	$0.395119\pi$
$830$	1643.05	+	7198.65i	0.0687120	+	0.301047i
$831$	2922.60	−	3664.82i	0.122002	−	0.152986i
$832$	5650.66	−	24757.2i	0.235458	−	1.03161i
$833$	8491.32	−	37202.9i	0.353190	−	1.54742i
$834$	4361.88	+	5469.63i	0.181103	+	0.227096i
$835$	5943.49	+	2862.23i	0.246327	+	0.118625i
$836$	181.502	−	87.4069i	0.00750884	−	0.00361606i
$837$	6088.25	−	7634.43i	0.251423	−	0.315274i
$838$	5563.74	+	6976.71i	0.229351	+	0.287597i
$839$	−29137.0	+	14031.6i	−1.19895	+	0.577385i	−0.923377	−	0.383894i	$-0.874583\pi$
$839$	−29137.0	+	14031.6i	−1.19895	+	0.577385i	−0.275576	+	0.961279i	$0.588868\pi$
$840$	11214.1			0.460622
$841$	14396.5	−	19686.6i	0.590287	−	0.807194i
$842$	28275.6			1.15729
$843$	19447.2	−	9365.26i	0.794539	−	0.382630i
$844$	1467.25	+	1839.87i	0.0598399	+	0.0750368i
$845$	−1142.32	+	1432.42i	−0.0465052	+	0.0583157i
$846$	−4446.97	+	2141.55i	−0.180721	+	0.0870306i
$847$	−40223.5	−	19370.6i	−1.63175	−	0.785811i
$848$	22746.4	+	28523.1i	0.921126	+	1.15506i
$849$	4904.15	−	21486.5i	0.198245	−	0.868568i
$850$	3240.55	−	14197.8i	0.130765	−	0.572918i
$851$	−4944.74	+	6200.51i	−0.199182	+	0.249766i
$852$	−395.608	−	1733.27i	−0.0159076	−	0.0696959i
$853$	−6726.56			−0.270003			−0.135002	−	0.990845i	$-0.543104\pi$
$853$	−6726.56			−0.270003			−0.135002	+	0.990845i	$0.543104\pi$
$854$	−17520.8	−	76763.6i	−0.702048	−	3.07587i
$855$	−1530.58	−	737.089i	−0.0612220	−	0.0294830i
$856$	16047.7	+	7728.17i	0.640771	+	0.308579i
$857$	3926.11	+	17201.4i	0.156492	+	0.685634i	0.990913	+	0.134507i	$0.0429450\pi$
$857$	3926.11	+	17201.4i	0.156492	+	0.685634i	−0.834421	+	0.551127i	$0.814198\pi$
$858$	−4690.17			−0.186620
$859$	2465.64	+	10802.7i	0.0979355	+	0.429083i	0.999997	−	0.00252452i	$-0.000803579\pi$
$859$	2465.64	+	10802.7i	0.0979355	+	0.429083i	−0.902061	+	0.431608i	$0.857946\pi$
$860$	−88.8056	+	111.359i	−0.00352121	+	0.00441546i
$861$	−13039.6	+	57130.2i	−0.516130	+	2.26132i
$862$	−989.397	+	4334.83i	−0.0390940	+	0.171282i
$863$	−3069.58	−	3849.14i	−0.121077	−	0.151826i	0.717599	−	0.696457i	$-0.245241\pi$
$863$	−3069.58	−	3849.14i	−0.121077	−	0.151826i	−0.838676	+	0.544631i	$0.816670\pi$
$864$	2487.66	+	1197.99i	0.0979537	+	0.0471720i
$865$	−3854.78	+	1856.36i	−0.151522	+	0.0729691i
$866$	−2443.86	+	3064.50i	−0.0958957	+	0.120249i
$867$	−8276.86	−	10378.9i	−0.324218	−	0.406556i
$868$	−807.618	+	388.929i	−0.0315811	+	0.0152086i
$869$	9297.63			0.362947
$870$	5906.96	−	2998.24i	0.230189	−	0.116839i
$871$	−15815.1			−0.615241
$872$	−14772.7	+	7114.15i	−0.573700	+	0.276279i
$873$	629.666	+	789.576i	0.0244112	+	0.0306106i
$874$	8671.87	−	10874.2i	0.335618	−	0.420852i
$875$	24619.2	−	11856.0i	0.951179	−	0.458064i
$876$	−639.195	−	307.820i	−0.0246534	−	0.0118725i
$877$	−745.327	−	934.610i	−0.0286977	−	0.0359858i	0.767276	−	0.641318i	$-0.221612\pi$
$877$	−745.327	−	934.610i	−0.0286977	−	0.0359858i	−0.795973	+	0.605332i	$0.793040\pi$
$878$	9320.01	−	40833.6i	0.358240	−	1.56955i
$879$	6751.52	−	29580.4i	0.259071	−	1.13506i
$880$	−949.214	+	1190.28i	−0.0363614	+	0.0455957i
$881$	208.525	+	913.607i	0.00797433	+	0.0349378i	0.978759	−	0.205016i	$-0.0657247\pi$
$881$	208.525	+	913.607i	0.00797433	+	0.0349378i	−0.970784	+	0.239954i	$0.922868\pi$
$882$	17930.5			0.684527
$883$	4035.16	+	17679.2i	0.153787	+	0.673784i	0.991764	+	0.128079i	$0.0408811\pi$
$883$	4035.16	+	17679.2i	0.153787	+	0.673784i	−0.837977	+	0.545705i	$0.816262\pi$
$884$	−834.993	−	402.112i	−0.0317691	−	0.0152992i
$885$	−4615.81	−	2222.86i	−0.175321	−	0.0844299i
$886$	5165.78	+	22632.8i	0.195878	+	0.858197i
$887$	26591.9			1.00662			0.503309	−	0.864106i	$-0.332116\pi$
$887$	26591.9			1.00662			0.503309	+	0.864106i	$0.332116\pi$
$888$	−2620.05	−	11479.2i	−0.0990124	−	0.433802i
$889$	2557.68	−	3207.23i	0.0964924	−	0.120998i
$890$	−177.423	+	777.341i	−0.00668229	+	0.0292770i
$891$	−747.352	+	3274.36i	−0.0281002	+	0.123115i
$892$	506.786	+	635.490i	0.0190229	+	0.0238540i
$893$	−15612.9	−	7518.75i	−0.585066	−	0.281753i
$894$	24495.7	−	11796.5i	0.916397	−	0.441314i
$895$	4408.97	−	5528.68i	0.164666	−	0.206484i
$896$	33569.2	+	42094.5i	1.25164	+	1.56951i
$897$	−13939.3	+	6712.82i	−0.518863	+	0.249871i
$898$	29272.1			1.08777
$899$	6084.53	−	7965.61i	0.225729	−	0.295515i
$900$	326.940			0.0121089
$901$	−21563.4	+	10384.4i	−0.797317	+	0.383967i
$902$	−4722.58	−	5921.92i	−0.174329	−	0.218601i
$903$	−10450.9	+	13105.1i	−0.385144	+	0.482956i
$904$	−751.024	+	361.674i	−0.0276313	+	0.0133065i
$905$	10479.3	+	5046.55i	0.384909	+	0.185363i
$906$	−14501.7	−	18184.6i	−0.531773	−	0.666823i
$907$	−78.4075	+	343.526i	−0.00287043	+	0.0125762i	−0.976343	−	0.216228i	$-0.930624\pi$
$907$	−78.4075	+	343.526i	−0.00287043	+	0.0125762i	0.973472	+	0.228804i	$0.0734816\pi$
$908$	−394.605	+	1728.88i	−0.0144223	+	0.0631881i
$909$	−6072.06	+	7614.13i	−0.221560	+	0.277827i
$910$	−3867.02	−	16942.5i	−0.140869	−	0.617186i
$911$	−51218.5			−1.86273			−0.931363	−	0.364091i	$-0.881380\pi$
$911$	−51218.5			−1.86273			−0.931363	+	0.364091i	$0.881380\pi$
$912$	4826.06	+	21144.3i	0.175227	+	0.767718i
$913$	−4834.94	−	2328.39i	−0.175261	−	0.0844012i
$914$	−2563.54	−	1234.53i	−0.0927727	−	0.0446770i
$915$	2542.49	+	11139.4i	0.0918604	+	0.402466i
$916$	71.3503			0.00257367
$917$	2320.93	+	10168.7i	0.0835812	+	0.366193i
$918$	−12093.9	+	15165.3i	−0.434813	+	0.545238i
$919$	−9849.42	+	43153.1i	−0.353539	+	1.54896i	0.415403	+	0.909638i	$0.363641\pi$
$919$	−9849.42	+	43153.1i	−0.353539	+	1.54896i	−0.768942	+	0.639319i	$0.779216\pi$
$920$	−1063.98	+	4661.61i	−0.0381287	+	0.167053i
$921$	2912.58	+	3652.26i	0.104205	+	0.130669i
$922$	−27518.3	−	13252.1i	−0.982937	−	0.473358i
$923$	46988.9	−	22628.6i	1.67569	−	0.806968i
$924$	268.440	−	336.613i	0.00955737	−	0.0119846i
$925$	−8541.14	−	10710.3i	−0.303601	−	0.380704i
$926$	−11142.3	+	5365.87i	−0.395421	+	0.190425i
$927$	11428.9			0.404933
$928$	2578.73	+	1176.13i	0.0912186	+	0.0416039i
$929$	−15097.5			−0.533189			−0.266595	−	0.963809i	$-0.585898\pi$
$929$	−15097.5			−0.533189			−0.266595	+	0.963809i	$0.585898\pi$
$930$	2452.91	−	1181.26i	0.0864881	−	0.0416505i
$931$	39250.1	+	49218.1i	1.38171	+	1.73261i
$932$	805.701	−	1010.32i	0.0283172	−	0.0355086i
$933$	10015.5	−	4823.21i	0.351439	−	0.169244i
$934$	−38452.5	−	18517.8i	−1.34711	−	0.648736i
$935$	−622.714	−	780.859i	−0.0217807	−	0.0273121i
$936$	−1834.35	+	8036.82i	−0.0640573	+	0.280653i
$937$	−9998.25	+	43805.2i	−0.348590	+	1.52727i	0.431795	+	0.901972i	$0.357880\pi$
$937$	−9998.25	+	43805.2i	−0.348590	+	1.52727i	−0.780385	+	0.625300i	$0.784977\pi$
$938$	18945.2	−	23756.5i	0.659470	−	0.826949i
$939$	−3461.80	−	15167.1i	−0.120310	−	0.527115i
$940$	−314.704			−0.0109197
$941$	−4199.51	−	18399.2i	−0.145484	−	0.637405i	−0.994107	−	0.108407i	$-0.965425\pi$
$941$	−4199.51	−	18399.2i	−0.145484	−	0.637405i	0.848623	−	0.528998i	$-0.177432\pi$
$942$	4304.18	+	2072.78i	0.148872	+	0.0716932i
$943$	−22511.4	−	10840.9i	−0.777382	−	0.374368i
$944$	−5223.24	−	22884.5i	−0.180087	−	0.789012i
$945$	−17378.0			−0.598209
$946$	−482.118	−	2112.30i	−0.0165698	−	0.0725969i
$947$	7888.10	−	9891.36i	0.270674	−	0.339415i	−0.627853	−	0.778332i	$-0.716066\pi$
$947$	7888.10	−	9891.36i	0.270674	−	0.339415i	0.898528	+	0.438917i	$0.144638\pi$
$948$	535.254	−	2345.10i	0.0183378	−	0.0803432i
$949$	4631.12	−	20290.2i	0.158411	−	0.694045i
$950$	14979.1	+	18783.2i	0.511564	+	0.641480i
$951$	−23835.5	−	11478.6i	−0.812743	−	0.391396i
$952$	−30368.9	+	14624.9i	−1.03389	+	0.497895i
$953$	−17322.9	+	21722.2i	−0.588817	+	0.738353i	−0.983588	−	0.180426i	$-0.942252\pi$
$953$	−17322.9	+	21722.2i	−0.588817	+	0.738353i	0.394772	+	0.918779i	$0.370824\pi$
$954$	−7011.75	−	8792.45i	−0.237960	−	0.298392i
$955$	6205.52	−	2988.42i	0.210268	−	0.101260i
$956$	−1124.26			−0.0380348
$957$	−973.022	+	4715.07i	−0.0328666	+	0.159265i
$958$	26329.3			0.887956
$959$	70493.5	−	33947.9i	2.37368	−	1.14310i
$960$	−4414.29	−	5535.34i	−0.148407	−	0.186096i
$961$	−16005.9	+	20070.7i	−0.537272	+	0.673718i
$962$	−16439.5	+	7916.87i	−0.550969	+	0.265333i
$963$	−5195.67	−	2502.10i	−0.173861	−	0.0837270i
$964$	−1219.71	−	1529.47i	−0.0407514	−	0.0511006i
$965$	237.338	−	1039.85i	0.00791729	−	0.0346879i
$966$	6614.53	−	28980.2i	0.220310	−	0.965240i
$967$	1636.96	−	2052.68i	0.0544375	−	0.0682624i	−0.753867	−	0.657027i	$-0.771814\pi$
$967$	1636.96	−	2052.68i	0.0544375	−	0.0682624i	0.808305	+	0.588764i	$0.200385\pi$
$968$	6288.74	+	27552.8i	0.208810	+	0.914855i
$969$	−14228.1			−0.471694
$970$	299.894	+	1313.92i	0.00992684	+	0.0434923i
$971$	−53018.3	−	25532.2i	−1.75225	−	0.843840i	−0.977312	−	0.211805i	$-0.932066\pi$
$971$	−53018.3	−	25532.2i	−1.75225	−	0.843840i	−0.774940	−	0.632035i	$-0.782220\pi$
$972$	−702.717	−	338.411i	−0.0231890	−	0.0111672i
$973$	−4192.13	−	18366.9i	−0.138123	−	0.605156i
$974$	−2267.08			−0.0745809
$975$	−5946.68	−	26054.1i	−0.195329	−	0.855794i
$976$	−32639.9	+	40929.2i	−1.07047	+	1.34233i
$977$	8822.19	−	38652.6i	0.288892	−	1.26572i	−0.597157	−	0.802124i	$-0.703703\pi$
$977$	8822.19	−	38652.6i	0.288892	−	1.26572i	0.886049	−	0.463592i	$-0.153440\pi$
$978$	−3999.94	+	17524.9i	−0.130781	+	0.572989i
$979$	−361.303	−	453.060i	−0.0117950	−	0.0147904i
$980$	1030.03	+	496.038i	0.0335747	+	0.0161687i
$981$	4782.85	−	2303.30i	0.155662	−	0.0749631i
$982$	−5835.36	+	7317.31i	−0.189627	+	0.237785i
$983$	820.824	+	1029.28i	0.0266330	+	0.0333967i	0.794970	−	0.606649i	$-0.207487\pi$
$983$	820.824	+	1029.28i	0.0266330	+	0.0333967i	−0.768337	+	0.640046i	$0.778915\pi$
$984$	33421.5	−	16095.0i	1.08276	−	0.521431i
$985$	4845.33			0.156736
$986$	−12086.5	+	15823.1i	−0.390378	+	0.511067i
$987$	−37035.4			−1.19438
$988$	1377.50	−	663.367i	0.0443563	−	0.0213608i
$989$	−4456.09	−	5587.76i	−0.143271	−	0.179657i
$990$	292.602	−	366.912i	0.00939344	−	0.0117790i
$991$	7566.61	−	3643.89i	0.242544	−	0.116803i	−0.308663	−	0.951171i	$-0.599882\pi$
$991$	7566.61	−	3643.89i	0.242544	−	0.116803i	0.551207	+	0.834368i	$0.314167\pi$
$992$	1049.50	+	505.411i	0.0335903	+	0.0161762i
$993$	−19673.2	−	24669.5i	−0.628712	−	0.788381i
$994$	−22297.3	+	97691.0i	−0.711498	+	3.11727i
$995$	1072.86	−	4700.52i	0.0341830	−	0.149765i
$996$	−865.621	+	1085.45i	−0.0275384	+	0.0345321i
$997$	−4939.78	−	21642.6i	−0.156915	−	0.687490i	−0.990775	−	0.135515i	$-0.956731\pi$
$997$	−4939.78	−	21642.6i	−0.156915	−	0.687490i	0.833860	−	0.551976i	$-0.186126\pi$
$998$	19205.6			0.609161
$999$	4060.19	+	17788.8i	0.128587	+	0.563378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.4.d.a.20.5	yes	42
29.4	even	14		841.4.a.i.1.15		21
29.16	even	7	inner	29.4.d.a.16.5	✓	42
29.25	even	7		841.4.a.h.1.7		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.16.5	✓	42	29.16	even	7	inner
29.4.d.a.20.5	yes	42	1.1	even	1	trivial
841.4.a.h.1.7		21	29.25	even	7
841.4.a.i.1.15		21	29.4	even	14

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.61147 - 1.25762i) q^{2} +(2.77920 + 3.48501i) q^{3} +(0.250272 - 0.313832i) q^{4} +(2.95793 - 1.42446i) q^{5} +(11.6406 + 5.60583i) q^{6} +(-21.6928 - 27.2019i) q^{7} +(-4.90095 + 21.4725i) q^{8} +(1.58675 - 6.95200i) q^{9} +(5.93312 - 7.43990i) q^{10} +(1.53896 + 6.74263i) q^{11} +1.78926 q^{12} +(11.6798 + 51.1726i) q^{13} +(-90.8598 - 43.7558i) q^{14} +(13.1849 + 6.34953i) q^{15} +(14.9201 + 65.3690i) q^{16} -43.9870 q^{17} +(-4.59922 - 20.1505i) q^{18} +(45.2440 - 56.7342i) q^{19} +(0.293246 - 1.28480i) q^{20} +(34.5102 - 151.199i) q^{21} +(12.4986 + 15.6728i) q^{22} +(59.5779 + 28.6912i) q^{23} +(-88.4524 + 42.5964i) q^{24} +(-71.2160 + 89.3020i) q^{25} +(94.8573 + 118.947i) q^{26} +(137.071 - 66.0100i) q^{27} -13.9659 q^{28} +(139.258 - 70.6841i) q^{29} +42.4174 q^{30} +(57.8278 - 27.8484i) q^{31} +(11.3155 + 14.1892i) q^{32} +(-19.2210 + 24.1024i) q^{33} +(-114.871 + 55.3189i) q^{34} +(-102.914 - 49.5607i) q^{35} +(-1.78464 - 2.23786i) q^{36} +(-26.6876 + 116.926i) q^{37} +(46.8035 - 205.060i) q^{38} +(-145.876 + 182.923i) q^{39} +(16.0901 + 70.4953i) q^{40} -377.848 q^{41} +(-100.028 - 438.253i) q^{42} +(-97.3776 - 46.8946i) q^{43} +(2.50121 + 1.20452i) q^{44} +(-5.20938 - 22.8238i) q^{45} +191.669 q^{46} +(-53.1388 - 232.816i) q^{47} +(-186.346 + 233.670i) q^{48} +(-193.042 + 845.771i) q^{49} +(-73.6707 + 322.773i) q^{50} +(-122.249 - 153.295i) q^{51} +(18.9827 + 9.14160i) q^{52} +(490.223 - 236.079i) q^{53} +(274.943 - 344.767i) q^{54} +(14.1568 + 17.7520i) q^{55} +(690.407 - 332.483i) q^{56} +323.461 q^{57} +(274.775 - 359.723i) q^{58} -350.082 q^{59} +(5.29251 - 2.54874i) q^{60} +(486.799 + 610.427i) q^{61} +(115.993 - 145.451i) q^{62} +(-223.529 + 107.646i) q^{63} +(-435.886 - 209.912i) q^{64} +(107.442 + 134.728i) q^{65} +(-19.8836 + 87.1156i) q^{66} +(-67.0468 + 293.751i) q^{67} +(-11.0087 + 13.8045i) q^{68} +(65.5899 + 287.368i) q^{69} -331.086 q^{70} +(-221.101 - 968.707i) q^{71} +(141.500 + 68.1428i) q^{72} +(-357.239 - 172.037i) q^{73} +(77.3545 + 338.912i) q^{74} -509.141 q^{75} +(-6.48166 - 28.3980i) q^{76} +(150.028 - 188.129i) q^{77} +(-150.905 + 661.156i) q^{78} +(299.148 - 1310.65i) q^{79} +(137.248 + 172.104i) q^{80} +(437.529 + 210.703i) q^{81} +(-986.739 + 475.189i) q^{82} +(-483.787 + 606.649i) q^{83} +(-38.8141 - 48.6713i) q^{84} +(-130.110 + 62.6579i) q^{85} -313.275 q^{86} +(633.360 + 288.869i) q^{87} -152.323 q^{88} +(-75.4909 + 36.3545i) q^{89} +(-42.3078 - 53.0523i) q^{90} +(1138.63 - 1427.79i) q^{91} +(23.9149 - 11.5168i) q^{92} +(257.767 + 124.134i) q^{93} +(-431.565 - 541.165i) q^{94} +(53.0128 - 232.264i) q^{95} +(-18.0014 + 78.8693i) q^{96} +(-88.3025 + 110.728i) q^{97} +(559.535 + 2451.48i) q^{98} +49.3167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 5 q^{2} - 5 q^{3} - 23 q^{4} - 7 q^{5} - 11 q^{6} - 31 q^{7} + 38 q^{8} - 72 q^{9} + 31 q^{10} - 63 q^{11} + 136 q^{12} + 173 q^{13} + 129 q^{14} - 229 q^{15} - 451 q^{16} - 140 q^{17} + 846 q^{18}+ \cdots - 17404 q^{99}+O(q^{100}) \) 42 * q - 5 * q^2 - 5 * q^3 - 23 * q^4 - 7 * q^5 - 11 * q^6 - 31 * q^7 + 38 * q^8 - 72 * q^9 + 31 * q^10 - 63 * q^11 + 136 * q^12 + 173 * q^13 + 129 * q^14 - 229 * q^15 - 451 * q^16 - 140 * q^17 + 846 * q^18 - q^19 - 395 * q^20 - 961 * q^21 - 396 * q^22 + 57 * q^23 - 83 * q^24 + 1028 * q^25 + 141 * q^26 - 35 * q^27 + 356 * q^28 + 472 * q^29 + 2174 * q^30 + 175 * q^31 + 1356 * q^32 - 173 * q^33 - 1469 * q^34 + 477 * q^35 - 712 * q^36 - 417 * q^37 - 2834 * q^38 - 2273 * q^39 + 507 * q^40 + 1104 * q^41 + 2866 * q^42 - 573 * q^43 - 1644 * q^44 - 81 * q^45 - 5984 * q^46 - 223 * q^47 - 2442 * q^48 + 1400 * q^49 - 1234 * q^50 + 92 * q^51 + 2394 * q^52 - 791 * q^53 + 4228 * q^54 + 1505 * q^55 + 4167 * q^56 + 1718 * q^57 + 3635 * q^58 + 6172 * q^59 - 848 * q^60 + 2591 * q^61 + 1333 * q^62 - 1797 * q^63 + 2426 * q^64 - 3483 * q^65 + 679 * q^66 - 2611 * q^67 - 2796 * q^68 + 3665 * q^69 - 13558 * q^70 - 2169 * q^71 - 12175 * q^72 - 1309 * q^73 + 44 * q^74 - 7468 * q^75 + 1679 * q^76 - 1697 * q^77 + 6185 * q^78 + 933 * q^79 + 4604 * q^80 + 2562 * q^81 - 7016 * q^82 + 2553 * q^83 + 5579 * q^84 + 5294 * q^85 + 6824 * q^86 - 3909 * q^87 + 16298 * q^88 - 2543 * q^89 + 16038 * q^90 + 2781 * q^91 - 290 * q^92 + 6515 * q^93 - 3230 * q^94 + 1737 * q^95 - 15242 * q^96 - 5527 * q^97 - 786 * q^98 - 17404 * q^99

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