LMFDB - Embedded newform 29.4.d.a.16.5

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			16.5
Character	$\chi$	$=$	29.16
Dual form			29.4.d.a.20.5

$q$-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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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	0.834247	−	0.551392i	$-0.185903\pi$
$2$	2.61147	+	1.25762i	0.923296	+	0.444636i	0.0890490	+	0.996027i	$0.471617\pi$
$3$	2.77920	−	3.48501i	0.534857	−	0.670690i	−0.438832	−	0.898569i	$-0.644608\pi$
$3$	2.77920	−	3.48501i	0.534857	−	0.670690i	0.973689	+	0.227879i	$0.0731792\pi$
$4$	0.250272	+	0.313832i	0.0312840	+	0.0392290i
$5$	2.95793	+	1.42446i	0.264565	+	0.127408i	0.561464	−	0.827501i	$-0.310238\pi$
$5$	2.95793	+	1.42446i	0.264565	+	0.127408i	−0.296899	+	0.954909i	$0.595952\pi$
$6$	11.6406	−	5.60583i	0.792044	−	0.381428i
$7$	−21.6928	+	27.2019i	−1.17130	+	1.46877i	−0.317429	+	0.948282i	$0.602820\pi$
$7$	−21.6928	+	27.2019i	−1.17130	+	1.46877i	−0.853872	+	0.520483i	$0.825752\pi$
$8$	−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	−0.949447	−	0.313927i	$-0.898355\pi$
$11$	1.53896	−	6.74263i	0.0421831	−	0.184816i	0.991630	+	0.129111i	$0.0412123\pi$
$12$	1.78926			0.0430430
$13$	11.6798	−	51.1726i	0.249185	−	1.09175i	−0.683186	−	0.730245i	$-0.739406\pi$
$13$	11.6798	−	51.1726i	0.249185	−	1.09175i	0.932370	−	0.361504i	$-0.117737\pi$
$14$	−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	0.975959	−	0.217953i	$-0.0699380\pi$
$19$	45.2440	+	56.7342i	0.546299	+	0.685038i	−0.429660	+	0.902991i	$0.641367\pi$
$20$	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	−0.143871	−	0.989596i	$-0.545955\pi$
$23$	59.5779	−	28.6912i	0.540124	−	0.260110i	0.683995	+	0.729486i	$0.260241\pi$
$24$	−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	0.593837	−	0.804585i	$-0.297612\pi$
$31$	57.8278	+	27.8484i	0.335038	+	0.161346i	−0.258799	+	0.965931i	$0.583327\pi$
$32$	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	−0.998974	−	0.0452869i	$-0.985580\pi$
$37$	−26.6876	−	116.926i	−0.118579	−	0.519528i	0.880395	−	0.474241i	$-0.157277\pi$
$38$	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	−0.598514	−	0.801112i	$-0.704242\pi$
$43$	−97.3776	+	46.8946i	−0.345347	+	0.166311i	0.253167	+	0.967423i	$0.418528\pi$
$44$	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	0.823061	+	0.567953i	$0.192264\pi$
$47$	−53.1388	+	232.816i	−0.164917	+	0.722548i	−0.987978	+	0.154595i	$0.950593\pi$
$48$	−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	0.942935	−	0.332976i	$-0.108053\pi$
$53$	490.223	+	236.079i	1.27052	+	0.611848i	0.327580	+	0.944824i	$0.393767\pi$
$54$	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	0.0627232	−	0.998031i	$-0.480021\pi$
$61$	486.799	−	610.427i	1.02177	−	1.28126i	0.959051	−	0.283233i	$-0.0914071\pi$
$62$	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	−0.998549	−	0.0538564i	$-0.982849\pi$
$67$	−67.0468	−	293.751i	−0.122255	−	0.535633i	0.876294	−	0.481777i	$-0.160008\pi$
$68$	−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	0.358369	+	0.933580i	$0.383333\pi$
$71$	−221.101	+	968.707i	−0.369576	+	1.61922i	−0.727944	+	0.685636i	$0.759524\pi$
$72$	141.500	−	68.1428i	0.231610	−	0.111538i
$73$	−357.239	+	172.037i	−0.572763	+	0.275828i	−0.697763	−	0.716329i	$-0.745821\pi$
$73$	−357.239	+	172.037i	−0.572763	+	0.275828i	0.125000	+	0.992157i	$0.460107\pi$
$74$	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	0.494890	+	0.868956i	$0.335208\pi$
$79$	299.148	+	1310.65i	0.426035	+	1.86658i	−0.0688544	+	0.997627i	$0.521934\pi$
$80$	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	0.351188	−	0.936305i	$-0.385778\pi$
$83$	−483.787	−	606.649i	−0.639789	−	0.802270i	−0.990977	+	0.134035i	$0.957207\pi$
$84$	−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	0.388388	−	0.921496i	$-0.373032\pi$
$89$	−75.4909	−	36.3545i	−0.0899104	−	0.0432986i	−0.478298	+	0.878197i	$0.658746\pi$
$90$	−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	0.733465	−	0.679727i	$-0.237902\pi$
$97$	−88.3025	−	110.728i	−0.0924305	−	0.115904i	−0.825896	+	0.563823i	$0.809330\pi$
$98$	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	−0.927148	−	0.374697i	$-0.877747\pi$
$101$	−1230.49	+	592.575i	−1.21226	+	0.583796i	−0.285117	+	0.958493i	$0.592033\pi$
$102$	−512.036	+	246.584i	−0.497050	+	0.239367i
$103$	356.645	−	1562.57i	0.341178	−	1.49480i	−0.455414	−	0.890280i	$-0.650509\pi$
$103$	356.645	−	1562.57i	0.341178	−	1.49480i	0.796592	−	0.604518i	$-0.206634\pi$
$104$	−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	0.988832	+	0.149033i	$0.0476162\pi$
$107$	179.956	+	788.437i	0.162588	+	0.712346i	−0.826244	+	0.563313i	$0.809527\pi$
$108$	13.5891	+	59.5378i	0.0121075	+	0.0530465i
$109$	464.162	−	582.041i	0.407878	−	0.511462i	−0.534886	−	0.844924i	$-0.679645\pi$
$109$	464.162	−	582.041i	0.407878	−	0.511462i	0.942764	+	0.333462i	$0.108217\pi$
$110$	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	−0.771912	−	0.635729i	$-0.780699\pi$
$113$	23.5974	−	29.5902i	0.0196448	−	0.0246337i	0.791557	+	0.611096i	$0.209271\pi$
$114$	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	−0.964935	−	0.262490i	$-0.915456\pi$
$127$	26.2362	−	114.948i	0.0183314	−	0.0803151i	0.983266	+	0.182175i	$0.0583136\pi$
$128$	−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	−0.521780	−	0.853080i	$-0.674732\pi$
$131$	−270.094	+	130.070i	−0.180139	+	0.0867505i	0.341641	+	0.939831i	$0.389017\pi$
$132$	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	−0.851120	−	0.524971i	$-0.824076\pi$
$137$	−500.408	−	2192.43i	−0.312064	−	1.36724i	0.539056	−	0.842270i	$-0.318781\pi$
$138$	532.686	−	667.967i	0.328589	−	0.412037i
$139$	487.852	−	234.937i	0.297691	−	0.143360i	−0.279076	−	0.960269i	$-0.590028\pi$
$139$	487.852	−	234.937i	0.297691	−	0.143360i	0.576767	+	0.816909i	$0.304314\pi$
$140$	−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	0.998415	−	0.0562782i	$-0.0179234\pi$
$149$	1312.03	+	1645.23i	0.721380	+	0.904582i	−0.277035	+	0.960860i	$0.589352\pi$
$150$	−1329.61	−	640.306i	−0.723748	−	0.348539i
$151$	−1621.93	+	781.082i	−0.874113	+	0.420951i	−0.816471	−	0.577387i	$-0.804073\pi$
$151$	−1621.93	+	781.082i	−0.874113	+	0.420951i	−0.0576421	+	0.998337i	$0.518358\pi$
$152$	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	−0.844462	−	0.535615i	$-0.820080\pi$
$163$	309.590	−	1356.40i	0.148767	−	0.651789i	0.993229	−	0.116174i	$-0.0370630\pi$
$164$	−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	−0.401691	−	0.915775i	$-0.631578\pi$
$167$	1252.80	−	1570.97i	0.580508	−	0.727934i	0.982199	+	0.187841i	$0.0601490\pi$
$168$	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	0.792700	−	0.609612i	$-0.208675\pi$
$179$	1940.62	+	934.552i	0.810327	+	0.390233i	0.0176269	+	0.999845i	$0.494389\pi$
$180$	−8.46659	+	4.07730i	−0.00350590	+	0.00168835i
$181$	2208.88	−	2769.85i	0.907099	−	1.13747i	−0.0829229	−	0.996556i	$-0.526426\pi$
$181$	2208.88	−	2769.85i	0.907099	−	1.13747i	0.990022	−	0.140911i	$-0.0450031\pi$
$182$	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	0.818168	−	0.574979i	$-0.194990\pi$
$193$	202.557	+	253.999i	0.0755460	+	0.0947317i	−0.742622	+	0.669710i	$0.766418\pi$
$194$	−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	−0.177696	−	0.984085i	$-0.556864\pi$
$197$	1329.70	−	640.352i	0.480901	−	0.231590i	0.658597	+	0.752496i	$0.271150\pi$
$198$	128.789	+	62.0217i	0.0462255	+	0.0222611i
$199$	915.640	+	1148.18i	0.326171	+	0.409005i	0.917697	−	0.397280i	$-0.130046\pi$
$199$	915.640	+	1148.18i	0.326171	+	0.409005i	−0.591527	+	0.806286i	$0.701475\pi$
$200$	−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	−0.497569	−	0.867425i	$-0.665774\pi$
$211$	−1304.55	−	5715.63i	−0.425636	−	1.86483i	0.0719323	−	0.997410i	$-0.477083\pi$
$212$	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	−0.996430	−	0.0844260i	$-0.973094\pi$
$223$	−450.591	−	1974.17i	−0.135309	−	0.592826i	0.861121	−	0.508400i	$-0.169763\pi$
$224$	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	−0.250651	−	0.968078i	$-0.580644\pi$
$227$	−3980.32	−	1916.82i	−1.16380	−	0.560458i	−0.913152	+	0.407620i	$0.866359\pi$
$228$	80.9534	+	101.512i	0.0235143	+	0.0294860i
$229$	110.826	−	138.971i	0.0319807	−	0.0401026i	−0.765584	−	0.643336i	$-0.777550\pi$
$229$	110.826	−	138.971i	0.0319807	−	0.0401026i	0.797565	+	0.603233i	$0.206121\pi$
$230$	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	−0.959812	−	0.280645i	$-0.909452\pi$
$239$	−1746.28	+	2189.77i	−0.472625	+	0.592653i	0.487186	+	0.873298i	$0.338023\pi$
$240$	−218.343	−	956.622i	−0.0587249	−	0.257290i
$241$	1084.47	+	4751.35i	0.289861	+	1.26997i	0.884715	+	0.466132i	$0.154353\pi$
$241$	1084.47	+	4751.35i	0.289861	+	1.26997i	−0.594854	+	0.803834i	$0.702790\pi$
$242$	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	0.943403	−	0.331649i	$-0.107605\pi$
$251$	1630.96	+	2045.16i	0.410142	+	0.514301i	−0.533261	+	0.845951i	$0.679034\pi$
$252$	−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	−0.994040	−	0.109019i	$-0.965229\pi$
$257$	−3622.04	−	4541.90i	−0.879131	−	1.10240i	0.114909	−	0.993376i	$-0.463343\pi$
$258$	−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	0.699013	−	0.715109i	$-0.253623\pi$
$263$	2455.64	+	1182.57i	0.575745	+	0.277264i	−0.123268	+	0.992373i	$0.539337\pi$
$264$	−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	0.920011	−	0.391893i	$-0.128180\pi$
$269$	−348.217	−	1525.64i	−0.0789263	−	0.345799i	−0.998937	+	0.0460944i	$0.985322\pi$
$270$	322.153	+	1411.44i	0.0726133	+	0.318139i
$271$	−2696.37	−	3381.14i	−0.604400	−	0.757894i	0.381656	−	0.924304i	$-0.375354\pi$
$271$	−2696.37	−	3381.14i	−0.604400	−	0.757894i	−0.986057	+	0.166410i	$0.946782\pi$
$272$	−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	−0.993945	−	0.109877i	$-0.964954\pi$
$277$	−234.002	+	1025.23i	−0.0507575	+	0.222383i	0.943188	+	0.332261i	$0.107811\pi$
$278$	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	0.950658	+	0.310241i	$0.100410\pi$
$281$	1077.52	+	4720.94i	0.228753	+	1.00223i	−0.721904	+	0.691993i	$0.756733\pi$
$282$	686.559	+	3008.01i	0.144979	+	0.635194i
$283$	−3082.70	+	3865.59i	−0.647518	+	0.811962i	−0.991921	−	0.126860i	$-0.959510\pi$
$283$	−3082.70	+	3865.59i	−0.647518	+	0.811962i	0.344402	+	0.938822i	$0.388082\pi$
$284$	−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	0.151171	+	0.988508i	$0.451695\pi$
$293$	−4243.95	+	5321.74i	−0.846191	+	1.06109i	−0.997362	+	0.0725824i	$0.976876\pi$
$294$	−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	0.999988	+	0.00495952i	$0.00157867\pi$
$311$	554.936	+	2431.33i	0.101182	+	0.443306i	−0.898806	+	0.438347i	$0.855564\pi$
$312$	−3212.88	+	4028.82i	−0.582992	+	0.731049i
$313$	−3144.49	+	1514.31i	−0.567850	+	0.273462i	−0.695701	−	0.718331i	$-0.744906\pi$
$313$	−3144.49	+	1514.31i	−0.567850	+	0.273462i	0.127851	+	0.991793i	$0.459192\pi$
$314$	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	−0.104642	−	0.994510i	$-0.533370\pi$
$317$	−5347.29	−	2575.12i	−0.947424	−	0.456256i	−0.842782	+	0.538254i	$0.819084\pi$
$318$	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	−0.998980	−	0.0451555i	$-0.985622\pi$
$337$	−490.824	+	2150.44i	−0.0793379	+	0.347602i	0.919642	+	0.392757i	$0.128479\pi$
$338$	−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	0.847750	−	0.530395i	$-0.177957\pi$
$353$	6377.82	+	3071.39i	0.961634	+	0.463099i	0.113884	+	0.993494i	$0.463671\pi$
$354$	−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	0.430215	+	0.902726i	$0.358438\pi$
$359$	−2374.43	+	10403.0i	−0.349074	+	1.52939i	−0.779289	+	0.626665i	$0.784420\pi$
$360$	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	−0.999522	−	0.0309138i	$-0.990158\pi$
$367$	−5675.51	−	7116.87i	−0.807246	−	1.01225i	0.192276	−	0.981341i	$-0.438413\pi$
$368$	−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	0.598368	−	0.801221i	$-0.295816\pi$
$373$	−2275.79	−	2853.75i	−0.315914	−	0.396144i	−0.914282	+	0.405077i	$0.867245\pi$
$374$	−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	0.568992	−	0.822343i	$-0.307334\pi$
$379$	2071.98	+	997.812i	0.280819	+	0.135235i	−0.288173	+	0.957578i	$0.593048\pi$
$380$	−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	−0.493733	−	0.869614i	$-0.664368\pi$
$383$	−912.037	+	439.214i	−0.121679	+	0.0585973i	0.372054	+	0.928211i	$0.378654\pi$
$384$	−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	−0.953827	−	0.300356i	$-0.902895\pi$
$397$	−1778.03	−	7790.07i	−0.224778	−	0.984817i	0.729049	−	0.684462i	$-0.239963\pi$
$398$	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	0.814549	−	0.580095i	$-0.196984\pi$
$401$	6977.09	+	3359.99i	0.868876	+	0.418429i	0.0543268	+	0.998523i	$0.482699\pi$
$402$	−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	−0.973402	−	0.229106i	$-0.926420\pi$
$409$	−4412.34	+	5532.89i	−0.533438	+	0.668910i	0.439964	+	0.898015i	$0.354991\pi$
$410$	−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	−0.919160	−	0.393885i	$-0.871131\pi$
$419$	685.066	−	3001.47i	0.0798751	−	0.349956i	0.999035	+	0.0439298i	$0.0139878\pi$
$420$	−184.140	+	88.6771i	−0.0213931	+	0.0103024i
$421$	8789.12	−	4232.61i	1.01747	−	0.489988i	0.150639	−	0.988589i	$-0.451867\pi$
$421$	8789.12	−	4232.61i	1.01747	−	0.489988i	0.866832	+	0.498601i	$0.166153\pi$
$422$	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	0.725509	−	0.688213i	$-0.241604\pi$
$431$	−956.430	−	1199.32i	−0.106890	−	0.134036i	−0.832399	+	0.554177i	$0.813033\pi$
$432$	6360.12	−	7975.34i	0.708337	−	0.888226i
$433$	−1218.37	−	586.738i	−0.135222	−	0.0651197i	0.365049	−	0.930988i	$-0.381052\pi$
$433$	−1218.37	−	586.738i	−0.135222	−	0.0651197i	−0.500272	+	0.865869i	$0.666766\pi$
$434$	−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	0.973599	+	0.228265i	$0.0733052\pi$
$439$	9009.46	+	11297.5i	0.979495	+	1.22825i	0.00589552	+	0.999983i	$0.498123\pi$
$440$	−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	−0.976000	−	0.217770i	$-0.930122\pi$
$443$	−1782.22	−	7808.40i	−0.191141	−	0.837445i	0.784859	−	0.619675i	$-0.212735\pi$
$444$	−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	0.110443	−	0.993882i	$-0.464773\pi$
$449$	9098.86	−	4381.78i	0.956352	−	0.460555i	0.845909	+	0.533328i	$0.179059\pi$
$450$	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	−0.812168	−	0.583423i	$-0.801713\pi$
$457$	−612.044	+	767.479i	−0.0626482	+	0.0785584i	0.749520	+	0.661982i	$0.230284\pi$
$458$	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	−0.993747	−	0.111652i	$-0.964386\pi$
$461$	−6570.01	+	8238.53i	−0.663765	+	0.832335i	0.329982	+	0.943987i	$0.392957\pi$
$462$	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	0.0799011	+	0.996803i	$0.474540\pi$
$467$	−9180.55	+	11512.0i	−0.909689	+	1.14071i	−0.989591	+	0.143912i	$0.954032\pi$
$468$	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	−0.000712465	−	1.00000i	$-0.500227\pi$
$479$	8184.15	−	3941.28i	0.780675	−	0.375953i	0.781387	+	0.624047i	$0.214512\pi$
$480$	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	−0.466381	−	0.884584i	$-0.654443\pi$
$487$	−704.693	+	339.362i	−0.0655702	+	0.0315769i	0.400811	+	0.916161i	$0.368728\pi$
$488$	−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	0.295384	−	0.955379i	$-0.404553\pi$
$491$	−2909.19	−	1400.99i	−0.267393	−	0.128770i	−0.562777	+	0.826609i	$0.690267\pi$
$492$	−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	−0.146495	−	0.989211i	$-0.546799\pi$
$499$	5969.83	−	2874.92i	0.535564	−	0.257914i	0.682058	+	0.731298i	$0.261085\pi$
$500$	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	0.303880	−	0.952710i	$-0.401718\pi$
$503$	−7812.89	−	9797.05i	−0.692564	−	0.868447i	−0.996444	+	0.0842629i	$0.973146\pi$
$504$	−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	0.354824	+	0.934933i	$0.384541\pi$
$509$	−4254.82	+	18641.6i	−0.370514	+	1.62333i	−0.725338	+	0.688393i	$0.758316\pi$
$510$	−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	0.721398	−	0.692521i	$-0.243500\pi$
$541$	−1438.11	−	1803.33i	−0.114287	−	0.143311i	−0.835684	+	0.549210i	$0.814929\pi$
$542$	−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	0.789320	−	0.613982i	$-0.210433\pi$
$547$	193.072	+	242.105i	0.0150917	+	0.0189244i	−0.774228	+	0.632906i	$0.781862\pi$
$548$	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	0.0382972	−	0.999266i	$-0.487807\pi$
$557$	11087.5	−	5339.46i	0.843433	−	0.406176i	0.805136	+	0.593090i	$0.202092\pi$
$558$	−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	0.854174	+	0.519988i	$0.174063\pi$
$569$	−1914.09	+	8386.18i	−0.141024	+	0.617868i	−0.995198	+	0.0978805i	$0.968794\pi$
$570$	1919.13	+	2406.52i	0.141024	+	0.176839i
$571$	−1750.71	−	7670.34i	−0.128310	−	0.562161i	−0.997685	−	0.0680084i	$-0.978336\pi$
$571$	−1750.71	−	7670.34i	−0.128310	−	0.562161i	0.869375	−	0.494153i	$-0.164522\pi$
$572$	−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	−0.803353	−	0.595503i	$-0.796953\pi$
$577$	−610.093	+	765.032i	−0.0440182	+	0.0551971i	0.759335	+	0.650700i	$0.225524\pi$
$578$	−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	−0.212638	−	0.977131i	$-0.568206\pi$
$587$	11197.0	−	14040.6i	0.787311	−	0.987256i	0.999949	−	0.0101253i	$-0.00322303\pi$
$588$	−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	−0.986615	−	0.163067i	$-0.947861\pi$
$593$	−389.222	+	1705.29i	−0.0269535	+	0.118091i	0.959661	+	0.281158i	$0.0907185\pi$
$594$	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	−0.999587	−	0.0287350i	$-0.990852\pi$
$599$	−11804.0	−	14801.7i	−0.805173	−	1.00965i	0.194414	−	0.980919i	$-0.437719\pi$
$600$	2495.28	+	10932.5i	0.169782	+	0.743864i
$601$	−3412.01	−	14949.0i	−0.231579	−	1.01461i	−0.948331	−	0.317284i	$-0.897229\pi$
$601$	−3412.01	−	14949.0i	−0.231579	−	1.01461i	0.716752	−	0.697328i	$-0.245628\pi$
$602$	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	0.674562	−	0.738218i	$-0.264332\pi$
$607$	7746.38	+	3730.46i	0.517983	+	0.249448i	−0.156579	+	0.987665i	$0.550047\pi$
$608$	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	0.982807	−	0.184637i	$-0.0591110\pi$
$613$	8865.04	+	11116.4i	0.584104	+	0.732443i	−0.398703	+	0.917080i	$0.630540\pi$
$614$	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	0.929592	+	0.368590i	$0.120159\pi$
$617$	3861.89	+	16920.1i	0.251984	+	1.10401i	−0.677609	+	0.735423i	$0.736984\pi$
$618$	−4607.90	−	20188.5i	−0.299930	−	1.31408i
$619$	−846.828	−	1061.89i	−0.0549869	−	0.0689514i	0.753578	−	0.657359i	$-0.228326\pi$
$619$	−846.828	−	1061.89i	−0.0549869	−	0.0689514i	−0.808564	+	0.588408i	$0.799755\pi$
$620$	−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	−0.326984	−	0.945030i	$-0.606032\pi$
$631$	10574.1	−	13259.5i	0.667113	−	0.836534i	0.994097	+	0.108496i	$0.0346036\pi$
$632$	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	−0.790718	−	0.612181i	$-0.790292\pi$
$641$	−291.052	+	364.968i	−0.0179343	+	0.0224889i	0.772783	+	0.634670i	$0.218864\pi$
$642$	6514.63	+	8169.09i	0.400486	+	0.502194i
$643$	3641.11	+	1753.47i	0.223315	+	0.107543i	0.542196	−	0.840252i	$-0.317593\pi$
$643$	3641.11	+	1753.47i	0.223315	+	0.107543i	−0.318882	+	0.947795i	$0.603307\pi$
$644$	−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	0.973900	−	0.226978i	$-0.0728846\pi$
$647$	−33.5023	−	146.783i	−0.00203572	−	0.00891907i	−0.975936	+	0.218059i	$0.930027\pi$
$648$	−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	−0.917832	−	0.396969i	$-0.870062\pi$
$653$	−19685.7	+	9480.16i	−1.17973	+	0.568127i	−0.261897	+	0.965096i	$0.584348\pi$
$654$	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	0.990244	−	0.139347i	$-0.0445004\pi$
$659$	636.163	+	2787.21i	0.0376045	+	0.164756i	−0.952639	+	0.304103i	$0.901643\pi$
$660$	25.3302	−	31.7631i	0.00149390	−	0.00187330i
$661$	−6491.40	+	3126.09i	−0.381976	+	0.183950i	−0.615011	−	0.788518i	$-0.710849\pi$
$661$	−6491.40	+	3126.09i	−0.381976	+	0.183950i	0.233035	+	0.972468i	$0.425134\pi$
$662$	−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	0.0434802	−	0.999054i	$-0.486155\pi$
$673$	14869.6	−	7160.83i	0.851682	−	0.410148i	0.808202	+	0.588906i	$0.200441\pi$
$674$	−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	0.824196	+	0.566305i	$0.191628\pi$
$677$	21013.0	+	26349.4i	1.19290	+	1.49585i	0.368706	+	0.929546i	$0.379801\pi$
$678$	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	−0.835659	−	0.549248i	$-0.814914\pi$
$683$	2776.59	−	12165.0i	0.155554	−	0.681525i	0.991213	−	0.132277i	$-0.0422287\pi$
$684$	−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	0.714252	−	0.699889i	$-0.246767\pi$
$691$	11123.5	+	5356.81i	0.612386	+	0.294910i	−0.101866	+	0.994798i	$0.532481\pi$
$692$	−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	0.288822	−	0.957383i	$-0.406736\pi$
$701$	−5189.60	−	2499.18i	−0.279613	−	0.134654i	−0.568435	+	0.822728i	$0.692451\pi$
$702$	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	0.817735	+	0.575595i	$0.195230\pi$
$709$	−3185.95	+	13958.6i	−0.168760	+	0.739386i	−0.986495	+	0.163791i	$0.947628\pi$
$710$	−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	−0.936301	−	0.351199i	$-0.885774\pi$
$719$	−24012.4	+	11563.8i	−1.24550	+	0.599800i	−0.309196	+	0.950998i	$0.600060\pi$
$720$	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	0.153712	−	0.988116i	$-0.450877\pi$
$727$	−10251.7	−	4936.95i	−0.522990	−	0.251859i	−0.676702	+	0.736257i	$0.736591\pi$
$728$	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	0.918849	−	0.394610i	$-0.129120\pi$
$733$	−1591.99	−	6974.97i	−0.0802204	−	0.351469i	−0.999069	+	0.0431418i	$0.986263\pi$
$734$	−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	−0.597572	−	0.801816i	$-0.703868\pi$
$739$	−6896.02	+	3320.95i	−0.343267	+	0.165309i	0.254305	+	0.967124i	$0.418153\pi$
$740$	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	0.633777	+	0.773515i	$0.281503\pi$
$743$	−5525.99	+	24211.0i	−0.272852	+	1.19544i	−0.906630	+	0.421928i	$0.861354\pi$
$744$	−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	0.0652383	+	0.997870i	$0.479219\pi$
$751$	−18978.1	+	23797.7i	−0.922130	+	1.15631i	−0.987368	+	0.158444i	$0.949352\pi$
$752$	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	−0.997825	−	0.0659194i	$-0.979002\pi$
$757$	−14819.4	+	18583.0i	−0.711521	+	0.892220i	0.286304	+	0.958139i	$0.407573\pi$
$758$	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	0.181210	+	0.983444i	$0.441999\pi$
$761$	−17170.3	+	21530.9i	−0.817901	+	1.02561i	−0.999110	+	0.0421705i	$0.986573\pi$
$762$	−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	0.298833	−	0.954306i	$-0.403403\pi$
$769$	26256.6	−	12644.5i	1.23126	−	0.592942i	0.932425	+	0.361363i	$0.117689\pi$
$770$	−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	0.486672	−	0.873585i	$-0.338211\pi$
$773$	−10172.1	−	12755.4i	−0.473305	−	0.593506i	−0.959977	+	0.280079i	$0.909639\pi$
$774$	−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	0.948102	−	0.317967i	$-0.103000\pi$
$787$	9430.32	+	11825.2i	0.427134	+	0.535609i	−0.520968	+	0.853576i	$0.674429\pi$
$788$	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	−0.0299627	−	0.999551i	$-0.509539\pi$
$797$	16489.0	−	7940.69i	0.732836	−	0.352915i	0.762799	+	0.646636i	$0.223825\pi$
$798$	−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	−0.320389	−	0.947286i	$-0.603814\pi$
$809$	15519.1	−	19460.3i	0.674440	−	0.845721i	0.994829	+	0.101565i	$0.0323851\pi$
$810$	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	−0.732271	−	0.681014i	$-0.761539\pi$
$821$	−8656.87	−	37928.2i	−0.367998	−	1.61231i	0.364272	−	0.931293i	$-0.381318\pi$
$822$	−18115.4	−	22716.1i	−0.768672	−	0.963885i
$823$	9007.50	−	39464.4i	0.381509	−	1.67150i	−0.311249	−	0.950328i	$-0.600747\pi$
$823$	9007.50	−	39464.4i	0.381509	−	1.67150i	0.692758	−	0.721170i	$-0.256395\pi$
$824$	−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	−0.408749	−	0.912647i	$-0.634035\pi$
$827$	1187.62	−	571.926i	0.0499364	−	0.0240481i	0.458685	+	0.888599i	$0.348321\pi$
$828$	−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	−0.275576	−	0.961279i	$-0.588868\pi$
$839$	−29137.0	−	14031.6i	−1.19895	−	0.577385i	−0.923377	+	0.383894i	$0.874583\pi$
$840$	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	−0.834421	−	0.551127i	$-0.814198\pi$
$857$	3926.11	−	17201.4i	0.156492	−	0.685634i	0.990913	−	0.134507i	$-0.0429450\pi$
$858$	−4690.17			−0.186620
$859$	2465.64	−	10802.7i	0.0979355	−	0.429083i	−0.902061	−	0.431608i	$-0.857946\pi$
$859$	2465.64	−	10802.7i	0.0979355	−	0.429083i	0.999997	+	0.00252452i	$0.000803579\pi$
$860$	−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	−0.838676	−	0.544631i	$-0.816670\pi$
$863$	−3069.58	+	3849.14i	−0.121077	+	0.151826i	0.717599	+	0.696457i	$0.245241\pi$
$864$	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	−0.795973	−	0.605332i	$-0.793040\pi$
$877$	−745.327	+	934.610i	−0.0286977	+	0.0359858i	0.767276	+	0.641318i	$0.221612\pi$
$878$	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	−0.970784	−	0.239954i	$-0.922868\pi$
$881$	208.525	−	913.607i	0.00797433	−	0.0349378i	0.978759	+	0.205016i	$0.0657247\pi$
$882$	17930.5			0.684527
$883$	4035.16	−	17679.2i	0.153787	−	0.673784i	−0.837977	−	0.545705i	$-0.816262\pi$
$883$	4035.16	−	17679.2i	0.153787	−	0.673784i	0.991764	−	0.128079i	$-0.0408811\pi$
$884$	−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	0.973472	−	0.228804i	$-0.0734816\pi$
$907$	−78.4075	−	343.526i	−0.00287043	−	0.0125762i	−0.976343	+	0.216228i	$0.930624\pi$
$908$	−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	−0.768942	−	0.639319i	$-0.779216\pi$
$919$	−9849.42	−	43153.1i	−0.353539	−	1.54896i	0.415403	−	0.909638i	$-0.363641\pi$
$920$	−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	−0.780385	−	0.625300i	$-0.784977\pi$
$937$	−9998.25	−	43805.2i	−0.348590	−	1.52727i	0.431795	−	0.901972i	$-0.357880\pi$
$938$	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	0.848623	+	0.528998i	$0.177432\pi$
$941$	−4199.51	+	18399.2i	−0.145484	+	0.637405i	−0.994107	+	0.108407i	$0.965425\pi$
$942$	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	0.898528	−	0.438917i	$-0.144638\pi$
$947$	7888.10	+	9891.36i	0.270674	+	0.339415i	−0.627853	+	0.778332i	$0.716066\pi$
$948$	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	0.394772	−	0.918779i	$-0.370824\pi$
$953$	−17322.9	−	21722.2i	−0.588817	−	0.738353i	−0.983588	+	0.180426i	$0.942252\pi$
$954$	−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	0.808305	−	0.588764i	$-0.200385\pi$
$967$	1636.96	+	2052.68i	0.0544375	+	0.0682624i	−0.753867	+	0.657027i	$0.771814\pi$
$968$	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	−0.774940	+	0.632035i	$0.782220\pi$
$971$	−53018.3	+	25532.2i	−1.75225	+	0.843840i	−0.977312	+	0.211805i	$0.932066\pi$
$972$	−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	0.886049	+	0.463592i	$0.153440\pi$
$977$	8822.19	+	38652.6i	0.288892	+	1.26572i	−0.597157	+	0.802124i	$0.703703\pi$
$978$	−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	−0.768337	−	0.640046i	$-0.778915\pi$
$983$	820.824	−	1029.28i	0.0266330	−	0.0333967i	0.794970	+	0.606649i	$0.207487\pi$
$984$	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	0.551207	−	0.834368i	$-0.314167\pi$
$991$	7566.61	+	3643.89i	0.242544	+	0.116803i	−0.308663	+	0.951171i	$0.599882\pi$
$992$	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	0.833860	+	0.551976i	$0.186126\pi$
$997$	−4939.78	+	21642.6i	−0.156915	+	0.687490i	−0.990775	+	0.135515i	$0.956731\pi$
$998$	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.16.5	✓	42
29.7	even	7		841.4.a.h.1.7		21
29.20	even	7	inner	29.4.d.a.20.5	yes	42
29.22	even	14		841.4.a.i.1.15		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.16.5	✓	42	1.1	even	1	trivial
29.4.d.a.20.5	yes	42	29.20	even	7	inner
841.4.a.h.1.7		21	29.7	even	7
841.4.a.i.1.15		21	29.22	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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