LMFDB - Embedded newform 130.4.n.a.29.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(9,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.9"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.n (of order $6$, degree $2$, 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:	$7.67024830075$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.15
Character	$\chi$	$=$	130.29
Dual form			130.4.n.a.9.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-3.43924 + 1.98565i) q^{3} +(2.00000 - 3.46410i) q^{4} +(2.28471 - 10.9444i) q^{5} +(-3.97130 + 6.87849i) q^{6} +(-5.96841 - 3.44587i) q^{7} -8.00000i q^{8} +(-5.61440 + 9.72443i) q^{9} +(-6.98717 - 21.2410i) q^{10} +(-11.9927 - 20.7720i) q^{11} +15.8852i q^{12} +(-12.7059 - 45.1172i) q^{13} -13.7835 q^{14} +(13.8741 + 42.1771i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-98.9190 - 57.1109i) q^{17} +22.4576i q^{18} +(29.6596 - 51.3719i) q^{19} +(-33.3431 - 29.8033i) q^{20} +27.3691 q^{21} +(-41.5441 - 23.9855i) q^{22} +(97.2861 - 56.1682i) q^{23} +(15.8852 + 27.5139i) q^{24} +(-114.560 - 50.0096i) q^{25} +(-67.1245 - 65.4393i) q^{26} -151.818i q^{27} +(-23.8737 + 13.7835i) q^{28} +(129.631 + 224.528i) q^{29} +(66.2077 + 59.1789i) q^{30} +72.9962 q^{31} +(-27.7128 - 16.0000i) q^{32} +(82.4919 + 47.6267i) q^{33} -228.444 q^{34} +(-51.3491 + 57.4480i) q^{35} +(22.4576 + 38.8977i) q^{36} +(-228.988 + 132.206i) q^{37} -118.638i q^{38} +(133.286 + 129.939i) q^{39} +(-87.5553 - 18.2777i) q^{40} +(97.3724 + 168.654i) q^{41} +(47.4047 - 27.3691i) q^{42} +(363.409 + 209.814i) q^{43} -95.9419 q^{44} +(93.6008 + 83.6638i) q^{45} +(112.336 - 194.572i) q^{46} +462.569i q^{47} +(55.0279 + 31.7704i) q^{48} +(-147.752 - 255.914i) q^{49} +(-248.434 + 27.9410i) q^{50} +453.609 q^{51} +(-181.702 - 46.2197i) q^{52} -268.393i q^{53} +(-151.818 - 262.956i) q^{54} +(-254.738 + 83.7954i) q^{55} +(-27.5669 + 47.7473i) q^{56} +235.574i q^{57} +(449.057 + 259.263i) q^{58} +(230.636 - 399.474i) q^{59} +(173.854 + 36.2931i) q^{60} +(362.734 - 628.274i) q^{61} +(126.433 - 72.9962i) q^{62} +(67.0182 - 38.6930i) q^{63} -64.0000 q^{64} +(-522.810 + 35.9791i) q^{65} +190.507 q^{66} +(472.888 - 273.022i) q^{67} +(-395.676 + 228.444i) q^{68} +(-223.060 + 386.352i) q^{69} +(-31.4912 + 150.852i) q^{70} +(207.638 - 359.640i) q^{71} +(77.7954 + 44.9152i) q^{72} +250.888i q^{73} +(-264.413 + 457.976i) q^{74} +(493.302 - 55.4809i) q^{75} +(-118.638 - 205.488i) q^{76} +165.302i q^{77} +(360.797 + 91.7761i) q^{78} -579.349 q^{79} +(-169.928 + 55.8974i) q^{80} +(149.868 + 259.579i) q^{81} +(337.308 + 194.745i) q^{82} +461.064i q^{83} +(54.7382 - 94.8094i) q^{84} +(-851.047 + 952.128i) q^{85} +839.257 q^{86} +(-891.669 - 514.805i) q^{87} +(-166.176 + 95.9419i) q^{88} +(-51.7716 - 89.6710i) q^{89} +(245.785 + 51.3092i) q^{90} +(-79.6335 + 313.061i) q^{91} -449.345i q^{92} +(-251.052 + 144.945i) q^{93} +(462.569 + 801.194i) q^{94} +(-494.471 - 441.976i) q^{95} +127.081 q^{96} +(1035.45 + 597.815i) q^{97} +(-511.828 - 295.504i) q^{98} +269.328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) $ 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−3.43924	+	1.98565i	−0.661883	+	0.382138i	−0.792994	−	0.609229i	$-0.791479\pi$
$3$	−3.43924	+	1.98565i	−0.661883	+	0.382138i	0.131111	+	0.991368i	$0.458145\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	2.28471	−	10.9444i	0.204351	−	0.978898i
$5$	2.28471	−	10.9444i	0.204351	−	0.978898i
$6$	−3.97130	+	6.87849i	−0.270213	+	0.468022i
$7$	−5.96841	−	3.44587i	−0.322264	−	0.186059i	0.330137	−	0.943933i	$-0.392905\pi$
$7$	−5.96841	−	3.44587i	−0.322264	−	0.186059i	−0.652401	+	0.757874i	$0.726238\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−5.61440	+	9.72443i	−0.207941	+	0.360164i
$10$	−6.98717	−	21.2410i	−0.220954	−	0.671699i
$11$	−11.9927	−	20.7720i	−0.328722	−	0.569364i	0.653536	−	0.756895i	$-0.273285\pi$
$11$	−11.9927	−	20.7720i	−0.328722	−	0.569364i	−0.982259	+	0.187531i	$0.939951\pi$
$12$			15.8852i			0.382138i
$13$	−12.7059	−	45.1172i	−0.271076	−	0.962558i
$13$	−12.7059	−	45.1172i	−0.271076	−	0.962558i
$14$	−13.7835			−0.263128
$15$	13.8741	+	42.1771i	0.238818	+	0.726006i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−98.9190	−	57.1109i	−1.41126	−	0.814790i	−0.415751	−	0.909478i	$-0.636481\pi$
$17$	−98.9190	−	57.1109i	−1.41126	−	0.814790i	−0.995507	+	0.0946883i	$0.969815\pi$
$18$			22.4576i			0.294073i
$19$	29.6596	−	51.3719i	0.358125	−	0.620290i	−0.629523	−	0.776982i	$-0.716750\pi$
$19$	29.6596	−	51.3719i	0.358125	−	0.620290i	0.987648	+	0.156692i	$0.0500829\pi$
$20$	−33.3431	−	29.8033i	−0.372787	−	0.333211i
$21$	27.3691			0.284401
$22$	−41.5441	−	23.9855i	−0.402601	−	0.232442i
$23$	97.2861	−	56.1682i	0.881981	−	0.509212i	0.0106697	−	0.999943i	$-0.496604\pi$
$23$	97.2861	−	56.1682i	0.881981	−	0.509212i	0.871311	+	0.490731i	$0.163270\pi$
$24$	15.8852	+	27.5139i	0.135106	+	0.234011i
$25$	−114.560	−	50.0096i	−0.916481	−	0.400077i
$26$	−67.1245	−	65.4393i	−0.506315	−	0.493604i
$27$		−	151.818i		−	1.08212i
$28$	−23.8737	+	13.7835i	−0.161132	+	0.0930296i
$29$	129.631	+	224.528i	0.830068	+	1.43772i	0.897984	+	0.440028i	$0.145032\pi$
$29$	129.631	+	224.528i	0.830068	+	1.43772i	−0.0679162	+	0.997691i	$0.521635\pi$
$30$	66.2077	+	59.1789i	0.402927	+	0.360151i
$31$	72.9962			0.422920			0.211460	−	0.977387i	$-0.432178\pi$
$31$	72.9962			0.422920			0.211460	+	0.977387i	$0.432178\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	82.4919	+	47.6267i	0.435152	+	0.251235i
$34$	−228.444			−1.15229
$35$	−51.3491	+	57.4480i	−0.247988	+	0.277442i
$36$	22.4576	+	38.8977i	0.103970	+	0.180082i
$37$	−228.988	+	132.206i	−1.01744	+	0.587421i	−0.913362	−	0.407148i	$-0.866523\pi$
$37$	−228.988	+	132.206i	−1.01744	+	0.587421i	−0.104081	+	0.994569i	$0.533190\pi$
$38$		−	118.638i		−	0.506465i
$39$	133.286	+	129.939i	0.547251	+	0.533512i
$40$	−87.5553	−	18.2777i	−0.346093	−	0.0722489i
$41$	97.3724	+	168.654i	0.370903	+	0.642422i	0.989705	−	0.143125i	$-0.0457150\pi$
$41$	97.3724	+	168.654i	0.370903	+	0.642422i	−0.618802	+	0.785547i	$0.712382\pi$
$42$	47.4047	−	27.3691i	0.174160	−	0.100551i
$43$	363.409	+	209.814i	1.28882	+	0.744102i	0.978444	−	0.206511i	$-0.0662110\pi$
$43$	363.409	+	209.814i	1.28882	+	0.744102i	0.310378	+	0.950613i	$0.399544\pi$
$44$	−95.9419			−0.328722
$45$	93.6008	+	83.6638i	0.310071	+	0.277153i
$46$	112.336	−	194.572i	0.360067	−	0.623655i
$47$			462.569i			1.43559i	0.696255	+	0.717794i	$0.254848\pi$
$47$			462.569i			1.43559i	−0.696255	+	0.717794i	$0.745152\pi$
$48$	55.0279	+	31.7704i	0.165471	+	0.0955345i
$49$	−147.752	−	255.914i	−0.430764	−	0.746105i
$50$	−248.434	+	27.9410i	−0.702677	+	0.0790289i
$51$	453.609			1.24545
$52$	−181.702	−	46.2197i	−0.484569	−	0.123260i
$53$		−	268.393i		−	0.695598i	−0.937569	−	0.347799i	$-0.886929\pi$
$53$		−	268.393i		−	0.695598i	0.937569	−	0.347799i	$-0.113071\pi$
$54$	−151.818	−	262.956i	−0.382589	−	0.662663i
$55$	−254.738	+	83.7954i	−0.624524	+	0.205436i
$56$	−27.5669	+	47.7473i	−0.0657819	+	0.113938i
$57$			235.574i			0.547413i
$58$	449.057	+	259.263i	1.01662	+	0.586946i
$59$	230.636	−	399.474i	0.508920	−	0.881476i	−0.491026	−	0.871145i	$-0.663378\pi$
$59$	230.636	−	399.474i	0.508920	−	0.881476i	0.999947	−	0.0103311i	$-0.00328854\pi$
$60$	173.854	+	36.2931i	0.374074	+	0.0780903i
$61$	362.734	−	628.274i	0.761367	−	1.31873i	−0.180779	−	0.983524i	$-0.557862\pi$
$61$	362.734	−	628.274i	0.761367	−	1.31873i	0.942146	−	0.335202i	$-0.108805\pi$
$62$	126.433	−	72.9962i	0.258984	−	0.149525i
$63$	67.0182	−	38.6930i	0.134024	−	0.0773786i
$64$	−64.0000			−0.125000
$65$	−522.810	+	35.9791i	−0.997640	+	0.0686563i
$66$	190.507			0.355300
$67$	472.888	−	273.022i	0.862276	−	0.497835i	−0.00249808	−	0.999997i	$-0.500795\pi$
$67$	472.888	−	273.022i	0.862276	−	0.497835i	0.864774	+	0.502162i	$0.167462\pi$
$68$	−395.676	+	228.444i	−0.705629	+	0.407395i
$69$	−223.060	+	386.352i	−0.389179	+	0.674077i
$70$	−31.4912	+	150.852i	−0.0537703	+	0.257575i
$71$	207.638	−	359.640i	0.347072	−	0.601147i	−0.638656	−	0.769493i	$-0.720509\pi$
$71$	207.638	−	359.640i	0.347072	−	0.601147i	0.985728	+	0.168346i	$0.0538426\pi$
$72$	77.7954	+	44.9152i	0.127337	+	0.0735182i
$73$			250.888i			0.402249i	0.979566	+	0.201125i	$0.0644596\pi$
$73$			250.888i			0.402249i	−0.979566	+	0.201125i	$0.935540\pi$
$74$	−264.413	+	457.976i	−0.415369	+	0.719441i
$75$	493.302	−	55.4809i	0.759488	−	0.0854184i
$76$	−118.638	−	205.488i	−0.179062	−	0.310145i
$77$			165.302i			0.244647i
$78$	360.797	+	91.7761i	0.523746	+	0.133226i
$79$	−579.349			−0.825086			−0.412543	−	0.910938i	$-0.635359\pi$
$79$	−579.349			−0.825086			−0.412543	+	0.910938i	$0.635359\pi$
$80$	−169.928	+	55.8974i	−0.237481	+	0.0781190i
$81$	149.868	+	259.579i	0.205580	+	0.356076i
$82$	337.308	+	194.745i	0.454261	+	0.262268i
$83$			461.064i			0.609739i	0.952394	+	0.304869i	$0.0986128\pi$
$83$			461.064i			0.609739i	−0.952394	+	0.304869i	$0.901387\pi$
$84$	54.7382	−	94.8094i	0.0711004	−	0.123149i
$85$	−851.047	+	952.128i	−1.08599	+	1.21497i
$86$	839.257			1.05232
$87$	−891.669	−	514.805i	−1.09881	−	0.634401i
$88$	−166.176	+	95.9419i	−0.201301	+	0.116221i
$89$	−51.7716	−	89.6710i	−0.0616604	−	0.106799i	0.833547	−	0.552448i	$-0.186306\pi$
$89$	−51.7716	−	89.6710i	−0.0616604	−	0.106799i	−0.895208	+	0.445649i	$0.852973\pi$
$90$	245.785	+	51.3092i	0.287867	+	0.0600940i
$91$	−79.6335	+	313.061i	−0.0917347	+	0.360634i
$92$		−	449.345i		−	0.509212i
$93$	−251.052	+	144.945i	−0.279923	+	0.161614i
$94$	462.569	+	801.194i	0.507557	+	0.879115i
$95$	−494.471	−	441.976i	−0.534018	−	0.477324i
$96$	127.081			0.135106
$97$	1035.45	+	597.815i	1.08385	+	0.625762i	0.931933	−	0.362630i	$-0.118121\pi$
$97$	1035.45	+	597.815i	1.08385	+	0.625762i	0.151919	+	0.988393i	$0.451455\pi$
$98$	−511.828	−	295.504i	−0.527576	−	0.304596i
$99$	269.328			0.273419
$100$	−402.359	+	296.829i	−0.402359	+	0.296829i
$101$	7.72749	+	13.3844i	0.00761301	+	0.0131861i	0.869807	−	0.493392i	$-0.164243\pi$
$101$	7.72749	+	13.3844i	0.00761301	+	0.0131861i	−0.862194	+	0.506579i	$0.830910\pi$
$102$	785.674	−	453.609i	0.762679	−	0.440333i
$103$		−	1690.22i		−	1.61692i	−0.588551	−	0.808460i	$-0.700302\pi$
$103$		−	1690.22i		−	1.61692i	0.588551	−	0.808460i	$-0.299698\pi$
$104$	−360.937	+	101.647i	−0.340316	+	0.0958399i
$105$	62.5305	−	299.539i	0.0581177	−	0.278400i
$106$	−268.393	−	464.871i	−0.245931	−	0.425965i
$107$	−514.432	+	297.008i	−0.464785	+	0.268344i	−0.714054	−	0.700090i	$-0.753143\pi$
$107$	−514.432	+	297.008i	−0.464785	+	0.268344i	0.249269	+	0.968434i	$0.419810\pi$
$108$	−525.913	−	303.636i	−0.468574	−	0.270531i
$109$	−1053.50			−0.925749			−0.462875	−	0.886424i	$-0.653182\pi$
$109$	−1053.50			−0.925749			−0.462875	+	0.886424i	$0.653182\pi$
$110$	−357.423	+	399.875i	−0.309809	+	0.346606i
$111$	525.030	−	909.379i	0.448952	−	0.777608i
$112$			110.268i			0.0930296i
$113$	−495.109	−	285.851i	−0.412176	−	0.237970i	0.279548	−	0.960132i	$-0.409815\pi$
$113$	−495.109	−	285.851i	−0.412176	−	0.237970i	−0.691724	+	0.722162i	$0.743149\pi$
$114$	235.574	+	408.026i	0.193540	+	0.335220i
$115$	−392.457	−	1193.07i	−0.318233	−	0.967427i
$116$	1037.05			0.830068
$117$	510.075	+	129.748i	0.403047	+	0.102523i
$118$		−	922.545i		−	0.719722i
$119$	393.593	+	681.723i	0.303199	+	0.525155i
$120$	337.417	−	110.993i	0.256682	−	0.0844349i
$121$	377.848	−	654.452i	0.283883	−	0.491700i
$122$		−	1450.94i		−	1.07674i
$123$	−669.775	−	386.695i	−0.490988	−	0.283472i
$124$	145.992	−	252.866i	0.105730	−	0.183130i
$125$	−809.063	+	1139.54i	−0.578918	+	0.815386i
$126$	77.3859	−	134.036i	0.0547150	−	0.0947691i
$127$	−568.622	+	328.294i	−0.397299	+	0.229381i	−0.685318	−	0.728244i	$-0.740337\pi$
$127$	−568.622	+	328.294i	−0.397299	+	0.229381i	0.288019	+	0.957625i	$0.407003\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−1666.47			−1.13740
$130$	−869.555	+	585.128i	−0.586654	+	0.394762i
$131$	−315.833			−0.210644			−0.105322	−	0.994438i	$-0.533587\pi$
$131$	−315.833			−0.210644			−0.105322	+	0.994438i	$0.533587\pi$
$132$	329.968	−	190.507i	0.217576	−	0.125617i
$133$	−354.041	+	204.406i	−0.230822	+	0.133265i
$134$	546.044	−	945.776i	0.352023	−	0.609721i
$135$	−1661.56	−	346.860i	−1.05929	−	0.221133i
$136$	−456.887	+	791.352i	−0.288072	+	0.498955i
$137$	−1773.52	−	1023.94i	−1.10600	−	0.638549i	−0.168209	−	0.985751i	$-0.553798\pi$
$137$	−1773.52	−	1023.94i	−1.10600	−	0.638549i	−0.937790	+	0.347203i	$0.887132\pi$
$138$			892.242i			0.550382i
$139$	1172.62	−	2031.04i	0.715545	−	1.23936i	−0.247205	−	0.968963i	$-0.579512\pi$
$139$	1172.62	−	2031.04i	0.715545	−	1.23936i	0.962749	−	0.270396i	$-0.0871547\pi$
$140$	96.3074	+	292.774i	0.0581390	+	0.176742i
$141$	−918.500	−	1590.89i	−0.548593	−	0.950192i
$142$		−	830.553i		−	0.490834i
$143$	−784.797	+	805.007i	−0.458937	+	0.470755i
$144$	179.661			0.103970
$145$	2753.50	−	905.758i	1.57701	−	0.518752i
$146$	250.888	+	434.550i	0.142217	+	0.246326i
$147$	1016.31	+	586.767i	0.570230	+	0.329223i
$148$			1057.65i			0.587421i
$149$	−412.442	+	714.371i	−0.226769	+	0.392776i	−0.956849	−	0.290586i	$-0.906150\pi$
$149$	−412.442	+	714.371i	−0.226769	+	0.392776i	0.730080	+	0.683362i	$0.239483\pi$
$150$	798.943	−	589.398i	0.434890	−	0.320827i
$151$	3296.44			1.77656			0.888279	−	0.459305i	$-0.151902\pi$
$151$	3296.44			1.77656			0.888279	+	0.459305i	$0.151902\pi$
$152$	−410.975	−	237.277i	−0.219306	−	0.126616i
$153$	1110.74	−	641.287i	0.586916	−	0.338856i
$154$	165.302	+	286.311i	0.0864959	+	0.149815i
$155$	166.775	−	798.900i	0.0864240	−	0.413995i
$156$	716.695	−	201.836i	0.367830	−	0.103589i
$157$			1816.35i			0.923313i	0.887059	+	0.461657i	$0.152745\pi$
$157$			1816.35i			0.923313i	−0.887059	+	0.461657i	$0.847255\pi$
$158$	−1003.46	+	579.349i	−0.505260	+	0.291712i
$159$	532.935	+	923.071i	0.265814	+	0.460404i
$160$	−238.426	+	266.745i	−0.117808	+	0.131800i
$161$	−774.192			−0.378974
$162$	519.158	+	299.736i	0.251784	+	0.145367i
$163$	−401.801	−	231.980i	−0.193077	−	0.111473i	0.400345	−	0.916364i	$-0.368890\pi$
$163$	−401.801	−	231.980i	−0.193077	−	0.111473i	−0.593422	+	0.804891i	$0.702223\pi$
$164$	778.979			0.370903
$165$	709.717	−	794.012i	0.334857	−	0.374629i
$166$	461.064	+	798.586i	0.215575	+	0.373387i
$167$	10.4854	−	6.05378i	0.00485861	−	0.00280512i	−0.497569	−	0.867425i	$-0.665774\pi$
$167$	10.4854	−	6.05378i	0.00485861	−	0.00280512i	0.502427	+	0.864619i	$0.332440\pi$
$168$		−	218.953i		−	0.100551i
$169$	−1874.12	+	1146.51i	−0.853035	+	0.521853i
$170$	−521.928	+	2500.18i	−0.235471	+	1.12797i
$171$	333.041	+	576.845i	0.148938	+	0.257967i
$172$	1453.64	−	839.257i	0.644411	−	0.372051i
$173$	−412.577	−	238.201i	−0.181316	−	0.104683i	0.406595	−	0.913609i	$-0.366716\pi$
$173$	−412.577	−	238.201i	−0.181316	−	0.104683i	−0.587911	+	0.808926i	$0.700049\pi$
$174$	−2059.22			−0.897179
$175$	511.416	+	693.237i	0.220911	+	0.299450i
$176$	−191.884	+	332.353i	−0.0821806	+	0.142341i
$177$			1831.85i			0.777911i
$178$	−179.342	−	103.543i	−0.0755182	−	0.0436005i
$179$	1194.92	+	2069.66i	0.498952	+	0.864210i	0.999999	−	0.00120978i	$-0.000385084\pi$
$179$	1194.92	+	2069.66i	0.498952	+	0.864210i	−0.501047	+	0.865420i	$0.667052\pi$
$180$	477.022	−	156.915i	0.197528	−	0.0649765i
$181$	−793.462			−0.325843			−0.162921	−	0.986639i	$-0.552092\pi$
$181$	−793.462			−0.325843			−0.162921	+	0.986639i	$0.552092\pi$
$182$	175.132	+	621.871i	0.0713276	+	0.253276i
$183$			2881.05i			1.16379i
$184$	−449.345	−	778.289i	−0.180034	−	0.311827i
$185$	923.748	+	2808.19i	0.367110	+	1.11601i
$186$	−289.890	+	502.103i	−0.114278	+	0.197936i
$187$			2739.67i			1.07136i
$188$	1602.39	+	925.139i	0.621628	+	0.358897i
$189$	−523.144	+	906.112i	−0.201339	+	0.348730i
$190$	−1298.43	−	271.054i	−0.495777	−	0.103497i
$191$	1191.69	−	2064.07i	0.451454	−	0.781941i	−0.547023	−	0.837118i	$-0.684239\pi$
$191$	1191.69	−	2064.07i	0.451454	−	0.781941i	0.998477	+	0.0551768i	$0.0175723\pi$
$192$	220.112	−	127.081i	0.0827353	−	0.0477673i
$193$	3025.08	−	1746.53i	1.12824	−	0.651388i	0.184746	−	0.982786i	$-0.440854\pi$
$193$	3025.08	−	1746.53i	1.12824	−	0.651388i	0.943491	+	0.331398i	$0.107520\pi$
$194$	2391.26			0.884962
$195$	1726.63	−	1161.86i	0.634085	−	0.426679i
$196$	−1182.02			−0.430764
$197$	−1879.15	+	1084.93i	−0.679612	+	0.392374i	−0.799709	−	0.600388i	$-0.795013\pi$
$197$	−1879.15	+	1084.93i	−0.679612	+	0.392374i	0.120097	+	0.992762i	$0.461680\pi$
$198$	466.490	−	269.328i	0.167434	−	0.0966683i
$199$	1593.23	−	2759.55i	0.567542	−	0.983012i	−0.429266	−	0.903178i	$-0.641228\pi$
$199$	1593.23	−	2759.55i	0.567542	−	0.983012i	0.996808	−	0.0798336i	$-0.0254389\pi$
$200$	−400.077	+	916.481i	−0.141449	+	0.324025i
$201$	−1084.25	+	1877.98i	−0.380484	+	0.659017i
$202$	26.7688	+	15.4550i	0.00932399	+	0.00538321i
$203$		−	1786.77i		−	0.617767i
$204$	907.218	−	1571.35i	0.311362	−	0.539296i
$205$	2068.29	−	680.358i	0.704660	−	0.231796i
$206$	−1690.22	−	2927.55i	−0.571667	−	0.990157i
$207$			1261.40i			0.423544i
$208$	−523.515	+	536.996i	−0.174515	+	0.179009i
$209$	−1422.80			−0.470895
$210$	−191.233	−	581.347i	−0.0628396	−	0.191032i
$211$	809.096	+	1401.40i	0.263983	+	0.457233i	0.967297	−	0.253647i	$-0.0816303\pi$
$211$	809.096	+	1401.40i	0.263983	+	0.457233i	−0.703313	+	0.710880i	$0.748297\pi$
$212$	−929.742	−	536.787i	−0.301203	−	0.173899i
$213$			1649.19i			0.530518i
$214$	−594.015	+	1028.86i	−0.189748	+	0.328653i
$215$	3126.58	−	3497.93i	0.991772	−	1.10957i
$216$	−1214.54			−0.382589
$217$	−435.672	−	251.535i	−0.136292	−	0.0786881i
$218$	−1824.71	+	1053.50i	−0.566903	+	0.327302i
$219$	−498.175	−	862.864i	−0.153715	−	0.266242i
$220$	−219.200	+	1050.03i	−0.0671747	+	0.321786i
$221$	−1319.83	+	5188.59i	−0.401724	+	1.57929i
$222$		−	2100.12i		−	0.634914i
$223$	−1059.25	+	611.560i	−0.318084	+	0.183646i	−0.650538	−	0.759473i	$-0.725457\pi$
$223$	−1059.25	+	611.560i	−0.318084	+	0.183646i	0.332454	+	0.943119i	$0.392123\pi$
$224$	110.268	+	190.989i	0.0328909	+	0.0569688i
$225$	1129.50	−	833.258i	0.334667	−	0.246891i
$226$	−1143.40			−0.336541
$227$	−3962.57	−	2287.79i	−1.15861	−	0.668925i	−0.207642	−	0.978205i	$-0.566579\pi$
$227$	−3962.57	−	2287.79i	−1.15861	−	0.668925i	−0.950971	+	0.309279i	$0.899912\pi$
$228$	816.052	+	471.148i	0.237037	+	0.136853i
$229$	5646.91			1.62951			0.814756	−	0.579805i	$-0.196871\pi$
$229$	5646.91			1.62951			0.814756	+	0.579805i	$0.196871\pi$
$230$	−1872.82	−	1674.00i	−0.536914	−	0.479913i
$231$	−328.231	−	568.512i	−0.0934891	−	0.161928i
$232$	1796.23	−	1037.05i	0.508311	−	0.293473i
$233$		−	1636.34i		−	0.460085i	−0.973181	−	0.230043i	$-0.926113\pi$
$233$		−	1636.34i		−	0.460085i	0.973181	−	0.230043i	$-0.0738866\pi$
$234$	1013.22	−	285.345i	0.283062	−	0.0797161i
$235$	5062.55	+	1056.84i	1.40529	+	0.293364i
$236$	−922.545	−	1597.90i	−0.254460	−	0.440738i
$237$	1992.52	−	1150.38i	0.546110	−	0.315297i
$238$	1363.45	+	787.186i	0.371341	+	0.214394i
$239$	−4352.59			−1.17801			−0.589007	−	0.808128i	$-0.700481\pi$
$239$	−4352.59			−1.17801			−0.589007	+	0.808128i	$0.700481\pi$
$240$	473.431	−	529.662i	0.127333	−	0.142456i
$241$	2790.16	−	4832.70i	0.745768	−	1.29171i	−0.204068	−	0.978957i	$-0.565416\pi$
$241$	2790.16	−	4832.70i	0.745768	−	1.29171i	0.949835	−	0.312751i	$-0.101250\pi$
$242$		−	1511.39i		−	0.401471i
$243$	2519.04	+	1454.37i	0.665007	+	0.383942i
$244$	−1450.94	−	2513.10i	−0.380683	−	0.659363i
$245$	−3138.40	+	1032.37i	−0.818387	+	0.269207i
$246$	−1546.78			−0.400890
$247$	−2694.61	−	685.429i	−0.694145	−	0.176570i
$248$		−	583.970i		−	0.149525i
$249$	−915.511	−	1585.71i	−0.233005	−	0.403576i
$250$	−261.802	+	2782.80i	−0.0662313	+	0.703998i
$251$	−3620.58	+	6271.03i	−0.910474	+	1.57699i	−0.0970784	+	0.995277i	$0.530950\pi$
$251$	−3620.58	+	6271.03i	−0.910474	+	1.57699i	−0.813396	+	0.581711i	$0.802384\pi$
$252$		−	309.544i		−	0.0773786i
$253$	−2333.45	−	1347.22i	−0.579854	−	0.334779i
$254$	−656.588	+	1137.24i	−0.162197	+	0.280933i
$255$	1036.37	−	4964.48i	0.254509	−	1.21917i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	380.160	−	219.485i	0.0922713	−	0.0532729i	−0.453154	−	0.891432i	$-0.649701\pi$
$257$	380.160	−	219.485i	0.0922713	−	0.0532729i	0.545426	+	0.838159i	$0.316368\pi$
$258$	−2886.41	+	1666.47i	−0.696512	+	0.402131i
$259$	1822.26			0.437180
$260$	−920.985	+	1883.03i	−0.219681	+	0.449155i
$261$	−2911.21			−0.690420
$262$	−547.038	+	315.833i	−0.128993	+	0.0744741i
$263$	2575.04	−	1486.70i	0.603741	−	0.348570i	−0.166771	−	0.985996i	$-0.553334\pi$
$263$	2575.04	−	1486.70i	0.603741	−	0.348570i	0.770512	+	0.637426i	$0.220001\pi$
$264$	381.014	−	659.935i	0.0888249	−	0.153849i
$265$	−2937.41	−	613.202i	−0.680919	−	0.142146i
$266$	−408.812	+	708.082i	−0.0942325	+	0.163215i
$267$	356.110	+	205.600i	0.0816239	+	0.0471256i
$268$		−	2184.18i		−	0.497835i
$269$	1245.48	−	2157.24i	0.282298	−	0.488955i	−0.689652	−	0.724141i	$-0.742237\pi$
$269$	1245.48	−	2157.24i	0.282298	−	0.488955i	0.971950	+	0.235186i	$0.0755698\pi$
$270$	−3224.76	+	1060.78i	−0.726862	+	0.239100i
$271$	1006.23	+	1742.84i	0.225550	+	0.390664i	0.956484	−	0.291784i	$-0.0942488\pi$
$271$	1006.23	+	1742.84i	0.225550	+	0.390664i	−0.730934	+	0.682448i	$0.760915\pi$
$272$			1827.55i			0.407395i
$273$	−347.750	−	1234.82i	−0.0770944	−	0.273753i
$274$	−4095.76			−0.903044
$275$	335.089	+	2979.40i	0.0734786	+	0.653326i
$276$	892.242	+	1545.41i	0.194589	+	0.337039i
$277$	971.396	+	560.836i	0.210706	+	0.121651i	0.601639	−	0.798768i	$-0.294514\pi$
$277$	971.396	+	560.836i	0.210706	+	0.121651i	−0.390933	+	0.920419i	$0.627848\pi$
$278$		−	4690.50i		−	1.01193i
$279$	−409.830	+	709.846i	−0.0879422	+	0.152320i
$280$	459.584	+	410.793i	0.0980906	+	0.0876770i
$281$	−4902.02			−1.04068			−0.520338	−	0.853960i	$-0.674194\pi$
$281$	−4902.02			−1.04068			−0.520338	+	0.853960i	$0.674194\pi$
$282$	−3181.78	−	1837.00i	−0.671887	−	0.387914i
$283$	7345.90	−	4241.16i	1.54300	−	0.890851i	0.544351	−	0.838858i	$-0.316776\pi$
$283$	7345.90	−	4241.16i	1.54300	−	0.890851i	0.998647	−	0.0519931i	$-0.0165574\pi$
$284$	−830.553	−	1438.56i	−0.173536	−	0.300573i
$285$	2578.22	+	538.218i	0.535861	+	0.111864i
$286$	−554.301	+	2179.11i	−0.114603	+	0.450536i
$287$		−	1342.13i		−	0.276040i
$288$	311.182	−	179.661i	0.0636686	−	0.0367591i
$289$	4066.82	+	7043.93i	0.827766	+	1.43373i
$290$	3863.44	−	4322.32i	0.782308	−	0.875225i
$291$	−4748.20			−0.956511
$292$	869.101	+	501.776i	0.174179	+	0.100562i
$293$	−939.569	−	542.460i	−0.187339	−	0.108160i	0.403397	−	0.915025i	$-0.367829\pi$
$293$	−939.569	−	542.460i	−0.187339	−	0.108160i	−0.590736	+	0.806865i	$0.701163\pi$
$294$	2347.07			0.465591
$295$	−3845.07	−	3436.86i	−0.758876	−	0.678311i
$296$	1057.65	+	1831.90i	0.207685	+	0.359720i
$297$	−3153.57	+	1820.71i	−0.616123	+	0.355719i
$298$			1649.77i			0.320700i
$299$	−3770.26	−	3675.61i	−0.729230	−	0.710922i
$300$	794.412	−	1819.81i	0.152885	−	0.350223i
$301$	−1445.98	−	2504.52i	−0.276894	−	0.479595i
$302$	5709.59	−	3296.44i	1.08791	−	0.628108i
$303$	−53.1534	−	30.6881i	−0.0100778	−	0.00581844i
$304$	−949.106			−0.179062
$305$	−6047.35	−	5405.34i	−1.13531	−	1.01478i
$306$	1282.57	−	2221.48i	0.239608	−	0.415012i
$307$		−	1429.56i		−	0.265763i	−0.991132	−	0.132882i	$-0.957577\pi$
$307$		−	1429.56i		−	0.265763i	0.991132	−	0.132882i	$-0.0424230\pi$
$308$	572.621	+	330.603i	0.105935	+	0.0611619i
$309$	3356.19	+	5813.09i	0.617887	+	1.07021i
$310$	−510.037	−	1550.51i	−0.0934457	−	0.284075i
$311$	3320.22			0.605377			0.302688	−	0.953090i	$-0.402116\pi$
$311$	3320.22			0.605377			0.302688	+	0.953090i	$0.402116\pi$
$312$	1039.52	−	1066.28i	0.188625	−	0.193482i
$313$		−	2147.56i		−	0.387819i	−0.981019	−	0.193910i	$-0.937883\pi$
$313$		−	2147.56i		−	0.387819i	0.981019	−	0.193910i	$-0.0621168\pi$
$314$	1816.35	+	3146.00i	0.326441	+	0.565412i
$315$	−270.354	−	821.876i	−0.0483579	−	0.147008i
$316$	−1158.70	+	2006.92i	−0.206272	+	0.357273i
$317$			4555.21i			0.807086i	0.914961	+	0.403543i	$0.132221\pi$
$317$			4555.21i			0.807086i	−0.914961	+	0.403543i	$0.867779\pi$
$318$	1846.14	+	1065.87i	0.325555	+	0.187959i
$319$	3109.27	−	5385.42i	0.545724	−	0.945221i
$320$	−146.222	+	700.442i	−0.0255439	+	0.122362i
$321$	1179.51	−	2042.96i	0.205089	−	0.355225i
$322$	−1340.94	+	774.192i	−0.232073	+	0.133988i
$323$	−5867.79	+	3387.77i	−1.01081	+	0.583593i
$324$	1198.95			0.205580
$325$	−800.700	+	5804.05i	−0.136661	+	0.990618i
$326$	−927.919			−0.157646
$327$	3623.23	−	2091.87i	0.612737	−	0.353764i
$328$	1349.23	−	778.979i	0.227131	−	0.131134i
$329$	1593.95	−	2760.81i	0.267105	−	0.462639i
$330$	435.253	−	2084.99i	0.0726058	−	0.347802i
$331$	−5381.83	+	9321.61i	−0.893693	+	1.54792i	−0.0582782	+	0.998300i	$0.518561\pi$
$331$	−5381.83	+	9321.61i	−0.893693	+	1.54792i	−0.835414	+	0.549621i	$0.814772\pi$
$332$	1597.17	+	922.128i	0.264025	+	0.152435i
$333$		−	2969.04i		−	0.488595i
$334$	12.1076	−	20.9709i	0.00198352	−	0.00343556i
$335$	−1907.65	−	5799.26i	−0.311123	−	0.945813i
$336$	−218.953	−	379.238i	−0.0355502	−	0.0615747i
$337$			3767.92i			0.609055i	0.952504	+	0.304527i	$0.0984985\pi$
$337$			3767.92i			0.609055i	−0.952504	+	0.304527i	$0.901501\pi$
$338$	−2099.56	+	3859.93i	−0.337873	+	0.621162i
$339$	2270.40			0.363750
$340$	1596.18	+	4852.37i	0.254602	+	0.773990i
$341$	−875.425	−	1516.28i	−0.139023	−	0.240795i
$342$	1153.69	+	666.083i	0.182410	+	0.105315i
$343$			4400.40i			0.692709i
$344$	1678.51	−	2907.27i	0.263080	−	0.455668i
$345$	3718.77	+	3323.97i	0.580324	+	0.518714i
$346$	−952.805			−0.148044
$347$	7436.03	+	4293.19i	1.15039	+	0.664181i	0.948983	−	0.315326i	$-0.102114\pi$
$347$	7436.03	+	4293.19i	1.15039	+	0.664181i	0.201411	+	0.979507i	$0.435447\pi$
$348$	−3566.67	+	2059.22i	−0.549407	+	0.317201i
$349$	−2468.56	−	4275.67i	−0.378622	−	0.655792i	0.612240	−	0.790672i	$-0.290269\pi$
$349$	−2468.56	−	4275.67i	−0.378622	−	0.655792i	−0.990862	+	0.134880i	$0.956935\pi$
$350$	1579.04	+	689.306i	0.241152	+	0.105271i
$351$	−6849.60	+	1928.99i	−1.04161	+	0.293338i
$352$			767.535i			0.116221i
$353$	−4127.30	+	2382.90i	−0.622306	+	0.359289i	−0.777766	−	0.628554i	$-0.783647\pi$
$353$	−4127.30	+	2382.90i	−0.622306	+	0.359289i	0.155460	+	0.987842i	$0.450314\pi$
$354$	1831.85	+	3172.86i	0.275033	+	0.476372i
$355$	−3461.65	−	3094.15i	−0.517537	−	0.462593i
$356$	−414.172			−0.0616604
$357$	−2707.33	−	1563.08i	−0.401364	−	0.231727i
$358$	4139.32	+	2389.84i	0.611089	+	0.352812i
$359$	−655.678			−0.0963938			−0.0481969	−	0.998838i	$-0.515347\pi$
$359$	−655.678			−0.0963938			−0.0481969	+	0.998838i	$0.515347\pi$
$360$	669.311	−	748.807i	0.0979882	−	0.109627i
$361$	1670.12	+	2892.73i	0.243493	+	0.421743i
$362$	−1374.32	+	793.462i	−0.199537	+	0.115203i
$363$			3001.10i			0.433930i
$364$	925.208	+	901.980i	0.133225	+	0.129881i
$365$	2745.82	+	573.206i	0.393761	+	0.0822000i
$366$	2881.05	+	4990.13i	0.411462	+	0.712673i
$367$	−2947.00	+	1701.45i	−0.419161	+	0.242003i	−0.694718	−	0.719282i	$-0.744471\pi$
$367$	−2947.00	+	1701.45i	−0.419161	+	0.242003i	0.275557	+	0.961285i	$0.411138\pi$
$368$	−1556.58	−	898.691i	−0.220495	−	0.127303i
$369$	−2186.75			−0.308503
$370$	4408.17	+	3940.18i	0.619378	+	0.553622i
$371$	−924.848	+	1601.88i	−0.129422	+	0.224166i
$372$			1159.56i			0.161614i
$373$	5613.28	+	3240.83i	0.779208	+	0.449876i	0.836150	−	0.548502i	$-0.184802\pi$
$373$	5613.28	+	3240.83i	0.779208	+	0.449876i	−0.0569415	+	0.998378i	$0.518135\pi$
$374$	2739.67	+	4745.24i	0.378783	+	0.656071i
$375$	519.847	−	5525.66i	0.0715861	−	0.760916i
$376$	3700.56			0.507557
$377$	8483.00	−	8701.45i	1.15888	−	1.18872i
$378$			2092.58i			0.284737i
$379$	448.254	+	776.398i	0.0607526	+	0.105227i	0.894802	−	0.446463i	$-0.147317\pi$
$379$	448.254	+	776.398i	0.0607526	+	0.105227i	−0.834049	+	0.551690i	$0.813983\pi$
$380$	−2519.99	+	828.946i	−0.340192	+	0.111905i
$381$	1303.75	−	2258.16i	0.175310	−	0.303646i
$382$		−	4766.76i		−	0.638452i
$383$	10228.4	+	5905.37i	1.36461	+	0.787860i	0.990234	−	0.139416i	$-0.0445225\pi$
$383$	10228.4	+	5905.37i	1.36461	+	0.787860i	0.374379	+	0.927276i	$0.377856\pi$
$384$	254.163	−	440.223i	0.0337766	−	0.0585027i
$385$	1809.13	+	377.666i	0.239485	+	0.0499939i
$386$	3493.06	−	6050.15i	0.460601	−	0.797784i
$387$	−4080.65	+	2355.96i	−0.535998	+	0.309458i
$388$	4141.79	−	2391.26i	0.541926	−	0.312881i
$389$	−2545.71			−0.331806			−0.165903	−	0.986142i	$-0.553054\pi$
$389$	−2545.71			−0.331806			−0.165903	+	0.986142i	$0.553054\pi$
$390$	1828.75	−	3739.03i	0.237442	−	0.485469i
$391$	−12831.3			−1.65960
$392$	−2047.31	+	1182.02i	−0.263788	+	0.152298i
$393$	1086.23	−	627.133i	0.139422	−	0.0804953i
$394$	−2169.85	+	3758.29i	−0.277451	+	0.480558i
$395$	−1323.64	+	6340.63i	−0.168607	+	0.807675i
$396$	538.657	−	932.981i	0.0683548	−	0.118394i
$397$	−5095.24	−	2941.74i	−0.644138	−	0.371893i	0.142069	−	0.989857i	$-0.454624\pi$
$397$	−5095.24	−	2941.74i	−0.644138	−	0.371893i	−0.786207	+	0.617964i	$0.787958\pi$
$398$		−	6372.91i		−	0.802626i
$399$	811.756	−	1406.00i	0.101851	−	0.176411i
$400$	223.528	+	1987.47i	0.0279410	+	0.248434i
$401$	−5166.22	−	8948.15i	−0.643363	−	1.11434i	−0.984677	−	0.174388i	$-0.944205\pi$
$401$	−5166.22	−	8948.15i	−0.643363	−	1.11434i	0.341314	−	0.939949i	$-0.389128\pi$
$402$			4337.01i			0.538085i
$403$	−927.484	−	3293.38i	−0.114643	−	0.407085i
$404$	61.8199			0.00761301
$405$	3183.35	−	1047.15i	0.390572	−	0.128478i
$406$	−1786.77	−	3094.78i	−0.218414	−	0.378304i
$407$	5492.39	+	3171.03i	0.668913	+	0.386197i
$408$		−	3628.87i		−	0.440333i
$409$	7632.89	−	13220.6i	0.922792	−	1.59832i	0.127719	−	0.991810i	$-0.459234\pi$
$409$	7632.89	−	13220.6i	0.922792	−	1.59832i	0.795074	−	0.606513i	$-0.207432\pi$
$410$	2902.02	−	3246.70i	0.349562	−	0.391081i
$411$	8132.75			0.976055
$412$	−5855.11	−	3380.45i	−0.700147	−	0.404230i
$413$	−2753.07	+	1589.48i	−0.328013	+	0.189379i
$414$	1261.40	+	2184.81i	0.149745	+	0.259366i
$415$	5046.07	+	1053.40i	0.596872	+	0.124601i
$416$	−369.758	+	1453.62i	−0.0435790	+	0.171321i
$417$			9313.68i			1.09375i
$418$	−2464.36	+	1422.80i	−0.288363	+	0.166486i
$419$	5507.19	+	9538.73i	0.642109	+	1.11217i	0.984961	+	0.172776i	$0.0552738\pi$
$419$	5507.19	+	9538.73i	0.642109	+	1.11217i	−0.342852	+	0.939389i	$0.611393\pi$
$420$	−912.572	−	815.690i	−0.106021	−	0.0947657i
$421$	9994.51			1.15701			0.578507	−	0.815677i	$-0.303636\pi$
$421$	9994.51			1.15701			0.578507	+	0.815677i	$0.303636\pi$
$422$	2802.79	+	1618.19i	0.323312	+	0.186664i
$423$	−4498.22	−	2597.05i	−0.517048	−	0.298518i
$424$	−2147.15			−0.245931
$425$	8476.08	+	11489.5i	0.967413	+	1.31135i
$426$	1649.19	+	2856.47i	0.187566	+	0.324875i
$427$	−4329.90	+	2499.87i	−0.490722	+	0.283319i
$428$			2376.06i			0.268344i
$429$	1100.65	−	4326.94i	0.123869	−	0.486962i
$430$	1917.46	−	9185.18i	0.215042	−	1.03011i
$431$	−5221.03	−	9043.09i	−0.583499	−	1.01065i	−0.995061	−	0.0992686i	$-0.968350\pi$
$431$	−5221.03	−	9043.09i	−0.583499	−	1.01065i	0.411561	−	0.911382i	$-0.364984\pi$
$432$	−2103.65	+	1214.54i	−0.234287	+	0.135266i
$433$	−11381.3	−	6571.00i	−1.26317	−	0.729289i	−0.289480	−	0.957184i	$-0.593482\pi$
$433$	−11381.3	−	6571.00i	−1.26317	−	0.729289i	−0.973686	+	0.227895i	$0.926816\pi$
$434$	−1006.14			−0.111282
$435$	−7671.44	+	8582.60i	−0.845558	+	0.945987i
$436$	−2106.99	+	3649.42i	−0.231437	+	0.400861i
$437$		−	6663.69i		−	0.729446i
$438$	−1725.73	−	996.350i	−0.188261	−	0.108693i
$439$	−8055.48	−	13952.5i	−0.875779	−	1.51689i	−0.855930	−	0.517092i	$-0.827015\pi$
$439$	−8055.48	−	13952.5i	−0.875779	−	1.51689i	−0.0198493	−	0.999803i	$-0.506319\pi$
$440$	670.363	+	2037.90i	0.0726325	+	0.220803i
$441$	3318.16			0.358294
$442$	2902.59	+	10306.7i	0.312358	+	1.10914i
$443$			5798.58i			0.621893i	0.950427	+	0.310947i	$0.100646\pi$
$443$			5798.58i			0.621893i	−0.950427	+	0.310947i	$0.899354\pi$
$444$	−2100.12	−	3637.52i	−0.224476	−	0.388804i
$445$	−1099.68	+	361.737i	−0.117146	+	0.0385348i
$446$	−1223.12	+	2118.51i	−0.129857	+	0.224920i
$447$		−	3275.86i		−	0.346629i
$448$	381.979	+	220.535i	0.0402830	+	0.0232574i
$449$	−3335.44	+	5777.15i	−0.350577	+	0.607217i	−0.986351	−	0.164658i	$-0.947348\pi$
$449$	−3335.44	+	5777.15i	−0.350577	+	0.607217i	0.635774	+	0.771876i	$0.280681\pi$
$450$	1123.10	−	2572.75i	0.117652	−	0.269512i
$451$	2335.52	−	4045.25i	0.243848	−	0.422357i
$452$	−1980.44	+	1143.40i	−0.206088	+	0.118985i
$453$	−11337.2	+	6545.56i	−1.17587	+	0.678890i
$454$	−9151.17			−0.946003
$455$	3244.33	+	1586.80i	0.334278	+	0.163495i
$456$	1884.59			0.193540
$457$	3971.67	−	2293.04i	0.406535	−	0.234713i	−0.282765	−	0.959189i	$-0.591252\pi$
$457$	3971.67	−	2293.04i	0.406535	−	0.234713i	0.689300	+	0.724476i	$0.257918\pi$
$458$	9780.73	−	5646.91i	0.997868	−	0.576119i
$459$	−8670.46	+	15017.7i	−0.881705	+	1.52716i
$460$	−4917.82	−	1026.62i	−0.498466	−	0.104058i
$461$	−784.031	+	1357.98i	−0.0792103	+	0.137196i	−0.902909	−	0.429831i	$-0.858573\pi$
$461$	−784.031	+	1357.98i	−0.0792103	+	0.137196i	0.823699	+	0.567027i	$0.191907\pi$
$462$	−1137.02	−	656.461i	−0.114500	−	0.0661068i
$463$			13553.6i			1.36046i	0.733001	+	0.680228i	$0.238119\pi$
$463$			13553.6i			1.36046i	−0.733001	+	0.680228i	$0.761881\pi$
$464$	2074.10	−	3592.45i	0.207517	−	0.359430i
$465$	1012.75	+	3078.77i	0.101001	+	0.307042i
$466$	−1636.34	−	2834.22i	−0.162665	−	0.281744i
$467$		−	8932.36i		−	0.885097i	−0.896745	−	0.442549i	$-0.854074\pi$
$467$		−	8932.36i		−	0.885097i	0.896745	−	0.442549i	$-0.145926\pi$
$468$	1469.61	−	1507.46i	0.145155	−	0.148893i
$469$	−3763.19			−0.370507
$470$	9825.43	−	3232.05i	0.964284	−	0.317199i
$471$	−3606.62	−	6246.86i	−0.352833	−	0.611125i
$472$	−3195.79	−	1845.09i	−0.311649	−	0.179930i
$473$		−	10065.0i		−	0.978412i
$474$	2300.76	−	3985.04i	0.222949	−	0.386158i
$475$	−5966.89	+	4401.91i	−0.576379	+	0.425207i
$476$	3148.75			0.303199
$477$	2609.97	+	1506.87i	0.250529	+	0.144643i
$478$	−7538.90	+	4352.59i	−0.721384	+	0.416491i
$479$	7084.18	+	12270.2i	0.675751	+	1.17043i	0.976249	+	0.216652i	$0.0695137\pi$
$479$	7084.18	+	12270.2i	0.675751	+	1.17043i	−0.300498	+	0.953782i	$0.597153\pi$
$480$	290.345	−	1390.83i	0.0276091	−	0.132255i
$481$	8874.28	+	8651.49i	0.841231	+	0.820112i
$482$		−	11160.6i		−	1.05467i
$483$	2662.63	−	1537.27i	0.250837	−	0.144821i
$484$	−1511.39	−	2617.81i	−0.141942	−	0.245850i
$485$	8908.43	−	9966.52i	0.834044	−	0.933106i
$486$	5817.48			0.542976
$487$	−12744.8	−	7358.19i	−1.18587	−	0.684664i	−0.228507	−	0.973542i	$-0.573384\pi$
$487$	−12744.8	−	7358.19i	−1.18587	−	0.684664i	−0.957366	+	0.288879i	$0.906718\pi$
$488$	−5026.20	−	2901.88i	−0.466240	−	0.269184i
$489$	1842.52			0.170392
$490$	−4403.50	+	4926.51i	−0.405979	+	0.454198i
$491$	7015.92	+	12151.9i	0.644856	+	1.11692i	0.984335	+	0.176309i	$0.0564159\pi$
$491$	7015.92	+	12151.9i	0.644856	+	1.11692i	−0.339479	+	0.940614i	$0.610251\pi$
$492$	−2679.10	+	1546.78i	−0.245494	+	0.141736i
$493$		−	29613.5i		−	2.70532i
$494$	−5352.62	+	1507.41i	−0.487502	+	0.137291i
$495$	615.337	−	2947.64i	0.0558735	−	0.267650i
$496$	−583.970	−	1011.47i	−0.0528649	−	0.0915648i
$497$	−2478.54	+	1430.99i	−0.223698	+	0.129152i
$498$	−3171.42	−	1831.02i	−0.285371	−	0.164759i
$499$	−7831.85			−0.702609			−0.351305	−	0.936261i	$-0.614262\pi$
$499$	−7831.85			−0.702609			−0.351305	+	0.936261i	$0.614262\pi$
$500$	2329.34	+	5081.75i	0.208343	+	0.454525i
$501$	−24.0413	+	41.6408i	−0.00214389	+	0.00371332i
$502$			14482.3i			1.28760i
$503$	10156.8	+	5864.02i	0.900334	+	0.519808i	0.877309	−	0.479927i	$-0.159337\pi$
$503$	10156.8	+	5864.02i	0.900334	+	0.519808i	0.0230258	+	0.999735i	$0.492670\pi$
$504$	−309.544	−	536.145i	−0.0273575	−	0.0473845i
$505$	164.139	−	53.9933i	0.0144636	−	0.00475776i
$506$	−5388.88			−0.473449
$507$	4168.98	−	7664.47i	0.365190	−	0.671383i
$508$			2626.35i			0.229381i
$509$	235.362	+	407.659i	0.0204956	+	0.0354994i	0.876091	−	0.482145i	$-0.160142\pi$
$509$	235.362	+	407.659i	0.0204956	+	0.0354994i	−0.855596	+	0.517645i	$0.826809\pi$
$510$	−3169.44	−	9635.10i	−0.275187	−	0.836567i
$511$	864.526	−	1497.40i	0.0748422	−	0.129631i
$512$			512.000i			0.0441942i
$513$	−7799.17	−	4502.85i	−0.671232	−	0.387536i
$514$	438.971	−	760.320i	0.0376696	−	0.0652457i
$515$	−18498.5	−	3861.67i	−1.58280	−	0.330419i
$516$	−3332.94	+	5772.82i	−0.284350	+	0.492508i
$517$	9608.51	−	5547.47i	0.817373	−	0.471910i
$518$	3156.25	−	1822.26i	0.267717	−	0.154567i
$519$	1891.94			0.160013
$520$	287.833	+	4182.48i	0.0242737	+	0.352719i
$521$	22825.5			1.91939			0.959695	−	0.281045i	$-0.0906811\pi$
$521$	22825.5			1.91939			0.959695	+	0.281045i	$0.0906811\pi$
$522$	−5042.37	+	2911.21i	−0.422794	+	0.244100i
$523$	−13983.0	+	8073.10i	−1.16909	+	0.674975i	−0.953466	−	0.301501i	$-0.902512\pi$
$523$	−13983.0	+	8073.10i	−1.16909	+	0.674975i	−0.215625	+	0.976476i	$0.569179\pi$
$524$	−631.665	+	1094.08i	−0.0526611	+	0.0912117i
$525$	−3135.41	−	1368.72i	−0.260649	−	0.113782i
$526$	2973.40	−	5150.08i	0.246476	−	0.426909i
$527$	−7220.71	−	4168.88i	−0.596849	−	0.344591i
$528$		−	1524.06i		−	0.125617i
$529$	226.225	−	391.833i	0.0185933	−	0.0322046i
$530$	−5700.94	+	1875.31i	−0.467232	+	0.153695i
$531$	2589.77	+	4485.61i	0.211651	+	0.366590i
$532$			1635.25i			0.133265i
$533$	6371.98	−	6536.07i	0.517826	−	0.531161i
$534$	822.401			0.0666456
$535$	2075.24	+	6308.73i	0.167702	+	0.509814i
$536$	−2184.18	−	3783.10i	−0.176011	−	0.304860i
$537$	−8219.23	−	4745.38i	−0.660495	−	0.381337i
$538$		−	4981.92i		−	0.399230i
$539$	−3543.90	+	6138.22i	−0.283204	+	0.490523i
$540$	−4524.67	+	5062.08i	−0.360576	+	0.403403i
$541$	1367.53			0.108678			0.0543391	−	0.998523i	$-0.482695\pi$
$541$	1367.53			0.108678			0.0543391	+	0.998523i	$0.482695\pi$
$542$	3485.68	+	2012.46i	0.276241	+	0.159488i
$543$	2728.91	−	1575.54i	0.215670	−	0.124517i
$544$	1827.55	+	3165.41i	0.144036	+	0.249478i
$545$	−2406.94	+	11529.9i	−0.189178	+	0.906214i
$546$	−1837.14	−	1791.02i	−0.143997	−	0.140382i
$547$		−	8855.84i		−	0.692228i	−0.938193	−	0.346114i	$-0.887501\pi$
$547$		−	8855.84i		−	0.692228i	0.938193	−	0.346114i	$-0.112499\pi$
$548$	−7094.07	+	4095.76i	−0.552999	+	0.319274i
$549$	4073.07	+	7054.77i	0.316639	+	0.548434i
$550$	3559.79	+	4825.39i	0.275982	+	0.374100i
$551$	15379.3			1.18907
$552$	3090.82	+	1784.48i	0.238322	+	0.137595i
$553$	3457.79	+	1996.36i	0.265896	+	0.153515i
$554$	2243.34			0.172041
$555$	−8753.07	−	7823.81i	−0.669455	−	0.598383i
$556$	−4690.50	−	8124.18i	−0.357772	−	0.619680i
$557$	21005.4	−	12127.5i	1.59790	−	0.922547i	0.606007	−	0.795459i	$-0.292770\pi$
$557$	21005.4	−	12127.5i	1.59790	−	0.922547i	0.991892	−	0.127088i	$-0.0405629\pi$
$558$			1639.32i			0.124369i
$559$	4848.78	−	19061.9i	0.366872	−	1.44227i
$560$	1206.81	+	251.930i	0.0910665	+	0.0190107i
$561$	−5440.01	−	9422.38i	−0.409407	−	0.709114i
$562$	−8490.55	+	4902.02i	−0.637282	+	0.367935i
$563$	61.8937	+	35.7343i	0.00463323	+	0.00267500i	0.502315	−	0.864685i	$-0.332482\pi$
$563$	61.8937	+	35.7343i	0.00463323	+	0.00267500i	−0.497682	+	0.867360i	$0.665815\pi$
$564$	−7348.00			−0.548593
$565$	−4259.65	+	4765.59i	−0.317177	+	0.354849i
$566$	8482.32	−	14691.8i	0.629927	−	1.09106i
$567$		−	2065.70i		−	0.153001i
$568$	−2877.12	−	1661.11i	−0.212537	−	0.122709i
$569$	−2358.97	−	4085.85i	−0.173802	−	0.301033i	0.765944	−	0.642907i	$-0.222272\pi$
$569$	−2358.97	−	4085.85i	−0.173802	−	0.301033i	−0.939746	+	0.341874i	$0.888938\pi$
$570$	5003.82	−	1646.00i	0.367696	−	0.120953i
$571$	494.721			0.0362582			0.0181291	−	0.999836i	$-0.494229\pi$
$571$	494.721			0.0362582			0.0181291	+	0.999836i	$0.494229\pi$
$572$	1219.03	+	4328.63i	0.0891088	+	0.316414i
$573$			9465.11i			0.690071i
$574$	−1342.13	−	2324.64i	−0.0975947	−	0.169039i
$575$	−13954.1	+	1569.39i	−1.01204	+	0.113823i
$576$	359.322	−	622.363i	0.0259926	−	0.0450205i
$577$			20572.0i			1.48427i	0.670249	+	0.742136i	$0.266187\pi$
$577$			20572.0i			1.48427i	−0.670249	+	0.742136i	$0.733813\pi$
$578$	14087.9	+	8133.63i	1.01380	+	0.585319i
$579$	−6935.98	+	12013.5i	−0.497840	+	0.862285i
$580$	2369.36	−	11349.9i	0.169625	−	0.812551i
$581$	1588.76	−	2751.82i	0.113448	−	0.196497i
$582$	−8224.13	+	4748.20i	−0.585741	+	0.338178i
$583$	−5575.08	+	3218.77i	−0.396048	+	0.228659i
$584$	2007.10			0.142217
$585$	2585.39	−	5286.03i	0.182723	−	0.373591i
$586$	−2169.84			−0.152961
$587$	14004.9	−	8085.72i	0.984742	−	0.568541i	0.0810434	−	0.996711i	$-0.474175\pi$
$587$	14004.9	−	8085.72i	0.984742	−	0.568541i	0.903698	+	0.428170i	$0.140841\pi$
$588$	4065.24	−	2347.07i	0.285115	−	0.164611i
$589$	2165.04	−	3749.95i	0.151458	−	0.262333i
$590$	−10096.7	−	2107.75i	−0.704534	−	0.147076i
$591$	4308.56	−	7462.65i	0.299882	−	0.519412i
$592$	3663.81	+	2115.30i	0.254361	+	0.146855i
$593$			20840.9i			1.44322i	0.692297	+	0.721612i	$0.256599\pi$
$593$			20840.9i			1.44322i	−0.692297	+	0.721612i	$0.743401\pi$
$594$	−3641.43	+	6307.13i	−0.251531	+	0.435665i
$595$	8360.31	−	2750.10i	0.576032	−	0.189484i
$596$	1649.77	+	2857.48i	0.113385	+	0.196388i
$597$			12654.4i			0.867518i
$598$	−10205.9	−	2596.08i	−0.697909	−	0.177528i
$599$	−22275.6			−1.51946			−0.759729	−	0.650239i	$-0.774669\pi$
$599$	−22275.6			−1.51946			−0.759729	+	0.650239i	$0.774669\pi$
$600$	−443.847	−	3946.42i	−0.0302000	−	0.268520i
$601$	1599.33	+	2770.13i	0.108549	+	0.188013i	0.915183	−	0.403039i	$-0.132046\pi$
$601$	1599.33	+	2770.13i	0.108549	+	0.188013i	−0.806633	+	0.591052i	$0.798713\pi$
$602$	−5009.04	−	2891.97i	−0.339125	−	0.195794i
$603$			6131.42i			0.414081i
$604$	6592.87	−	11419.2i	0.444139	−	0.769272i
$605$	−6299.32	−	5630.56i	−0.423312	−	0.378372i
$606$	−122.753			−0.00822852
$607$	4196.73	+	2422.98i	0.280626	+	0.162019i	0.633707	−	0.773573i	$-0.281533\pi$
$607$	4196.73	+	2422.98i	0.280626	+	0.162019i	−0.353081	+	0.935593i	$0.614866\pi$
$608$	−1643.90	+	949.106i	−0.109653	+	0.0633081i
$609$	3547.90	+	6145.14i	0.236072	+	0.408889i
$610$	−15879.7	−	3314.97i	−1.05401	−	0.220032i
$611$	20869.8	−	5877.37i	1.38184	−	0.389154i
$612$		−	5130.30i		−	0.338856i
$613$	−8079.49	+	4664.70i	−0.532345	+	0.307350i	−0.741971	−	0.670432i	$-0.766109\pi$
$613$	−8079.49	+	4664.70i	−0.532345	+	0.307350i	0.209626	+	0.977782i	$0.432775\pi$
$614$	−1429.56	−	2476.07i	−0.0939615	−	0.162746i
$615$	−5762.39	+	6446.80i	−0.377824	+	0.422700i
$616$	1322.41			0.0864959
$617$	7667.13	+	4426.62i	0.500271	+	0.288832i	0.728825	−	0.684700i	$-0.240067\pi$
$617$	7667.13	+	4426.62i	0.500271	+	0.288832i	−0.228554	+	0.973531i	$0.573400\pi$
$618$	11626.2	+	6712.38i	0.756754	+	0.436912i
$619$	−294.794			−0.0191418			−0.00957091	−	0.999954i	$-0.503047\pi$
$619$	−294.794			−0.0191418			−0.00957091	+	0.999954i	$0.503047\pi$
$620$	−2433.92	−	2175.53i	−0.157659	−	0.140921i
$621$	−8527.33	−	14769.8i	−0.551031	−	0.954413i
$622$	5750.78	−	3320.22i	0.370716	−	0.214033i
$623$			713.591i			0.0458899i
$624$	734.209	−	2886.38i	0.0471024	−	0.185172i
$625$	10623.1	+	11458.2i	0.679877	+	0.733327i
$626$	−2147.56	−	3719.69i	−0.137115	−	0.237490i
$627$	4893.35	−	2825.18i	0.311677	−	0.179947i
$628$	6292.01	+	3632.69i	0.399806	+	0.230828i
$629$	30201.7			1.91450
$630$	−1290.14	−	1153.18i	−0.0815882	−	0.0729265i
$631$	4102.02	−	7104.91i	0.258794	−	0.448244i	−0.707125	−	0.707088i	$-0.750008\pi$
$631$	4102.02	−	7104.91i	0.258794	−	0.448244i	0.965919	+	0.258844i	$0.0833416\pi$
$632$			4634.79i			0.291712i
$633$	−5565.36	−	3213.16i	−0.349452	−	0.201756i
$634$	4555.21	+	7889.86i	0.285348	+	0.494237i
$635$	2293.85	+	6973.28i	0.143352	+	0.435790i
$636$	4263.48			0.265814
$637$	−9668.79	+	9917.78i	−0.601399	+	0.616886i
$638$		−	12437.1i		−	0.771770i
$639$	2331.53	+	4038.33i	0.144341	+	0.250006i
$640$	447.179	+	1359.42i	0.0276192	+	0.0839624i
$641$	3953.73	−	6848.07i	0.243624	−	0.421969i	−0.718120	−	0.695920i	$-0.754997\pi$
$641$	3953.73	−	6848.07i	0.243624	−	0.421969i	0.961744	+	0.273950i	$0.0883303\pi$
$642$		−	4718.02i		−	0.290040i
$643$	18172.0	+	10491.6i	1.11452	+	0.643466i	0.939995	−	0.341187i	$-0.110829\pi$
$643$	18172.0	+	10491.6i	1.11452	+	0.643466i	0.174521	+	0.984653i	$0.444162\pi$
$644$	−1548.38	+	2681.88i	−0.0947436	+	0.164101i
$645$	−3807.40	+	18238.5i	−0.232428	+	1.11340i
$646$	−6775.54	+	11735.6i	−0.412663	+	0.714753i
$647$	11461.9	−	6617.51i	0.696464	−	0.402104i	−0.109565	−	0.993980i	$-0.534946\pi$
$647$	11461.9	−	6617.51i	0.696464	−	0.402104i	0.806029	+	0.591876i	$0.201612\pi$
$648$	2076.63	−	1198.95i	0.125892	−	0.0726837i
$649$	−11063.8			−0.669174
$650$	4417.20	+	10853.6i	0.266549	+	0.654944i
$651$	1997.84			0.120279
$652$	−1607.20	+	927.919i	−0.0965383	+	0.0557364i
$653$	16537.5	−	9547.92i	0.991060	−	0.572189i	0.0854687	−	0.996341i	$-0.472761\pi$
$653$	16537.5	−	9547.92i	0.991060	−	0.572189i	0.905591	+	0.424152i	$0.139428\pi$
$654$	4183.75	−	7246.46i	0.250149	−	0.433271i
$655$	−721.587	+	3456.60i	−0.0430454	+	0.206199i
$656$	1557.96	−	2698.46i	0.0927257	−	0.160606i
$657$	−2439.74	−	1408.59i	−0.144876	−	0.0836441i
$658$		−	6375.81i		−	0.377743i
$659$	−11156.2	+	19323.1i	−0.659459	+	1.14222i	0.321296	+	0.946979i	$0.395881\pi$
$659$	−11156.2	+	19323.1i	−0.659459	+	1.14222i	−0.980756	+	0.195239i	$0.937452\pi$
$660$	−1331.10	−	4046.55i	−0.0785048	−	0.238654i
$661$	7816.77	+	13539.1i	0.459966	+	0.796684i	0.998959	−	0.0456264i	$-0.0145284\pi$
$661$	7816.77	+	13539.1i	0.459966	+	0.796684i	−0.538993	+	0.842310i	$0.681195\pi$
$662$			21527.3i			1.26387i
$663$	−5763.52	−	20465.5i	−0.337612	−	1.19882i
$664$	3688.51			0.215575
$665$	1428.22	+	4341.78i	0.0832841	+	0.253183i
$666$	−2969.04	−	5142.52i	−0.172744	−	0.299202i
$667$	25222.7	+	14562.3i	1.46421	+	0.845361i
$668$		−	48.4302i		−	0.00280512i
$669$	2428.69	−	4206.61i	0.140356	−	0.243104i
$670$	−9103.41	−	8136.95i	−0.524918	−	0.469191i
$671$	−17400.7			−1.00111
$672$	−758.475	−	437.906i	−0.0435399	−	0.0251378i
$673$	6540.40	−	3776.10i	0.374612	−	0.216282i	−0.300860	−	0.953668i	$-0.597274\pi$
$673$	6540.40	−	3776.10i	0.374612	−	0.216282i	0.675471	+	0.737386i	$0.263940\pi$
$674$	3767.92	+	6526.22i	0.215333	+	0.372968i
$675$	−7592.36	+	17392.3i	−0.432933	+	0.991747i
$676$	223.392	+	8785.16i	0.0127101	+	0.499838i
$677$		−	8262.62i		−	0.469067i	−0.972108	−	0.234533i	$-0.924644\pi$
$677$		−	8262.62i		−	0.469067i	0.972108	−	0.234533i	$-0.0753562\pi$
$678$	3932.45	−	2270.40i	0.222750	−	0.128605i
$679$	−4119.98	−	7136.02i	−0.232858	−	0.403322i
$680$	7617.03	+	6808.37i	0.429558	+	0.383955i
$681$	18171.0			1.02249
$682$	−3032.56	−	1750.85i	−0.170268	−	0.0983042i
$683$	23323.0	+	13465.6i	1.30663	+	0.754385i	0.981533	−	0.191294i	$-0.0612684\pi$
$683$	23323.0	+	13465.6i	1.30663	+	0.754385i	0.325101	+	0.945679i	$0.394602\pi$
$684$	2664.33			0.148938
$685$	−15258.4	+	17070.7i	−0.851086	+	0.952172i
$686$	4400.40	+	7621.71i	0.244910	+	0.424196i
$687$	−19421.1	+	11212.8i	−1.07855	+	0.622698i
$688$		−	6714.06i		−	0.372051i
$689$	−12109.2	+	3410.19i	−0.669553	+	0.188560i
$690$	9765.06	+	2038.52i	0.538767	+	0.112471i
$691$	6383.47	+	11056.5i	0.351430	+	0.608695i	0.986500	−	0.163759i	$-0.0523620\pi$
$691$	6383.47	+	11056.5i	0.351430	+	0.608695i	−0.635070	+	0.772455i	$0.719029\pi$
$692$	−1650.31	+	952.805i	−0.0906579	+	0.0523414i
$693$	−1607.46	−	928.069i	−0.0881132	−	0.0508722i
$694$	17172.8			0.939293
$695$	−19549.5	−	17474.0i	−1.06698	−	0.953709i
$696$	−4118.44	+	7133.35i	−0.224295	+	0.388490i
$697$		−	22244.1i		−	1.20883i
$698$	−8551.34	−	4937.12i	−0.463715	−	0.267726i
$699$	3249.19	+	5627.76i	0.175816	+	0.304523i
$700$	3424.28	−	385.123i	0.184894	−	0.0207947i
$701$	−25843.0			−1.39241			−0.696204	−	0.717844i	$-0.745129\pi$
$701$	−25843.0			−1.39241			−0.696204	+	0.717844i	$0.745129\pi$
$702$	−9934.86	+	10190.7i	−0.534141	+	0.547896i
$703$			15684.7i			0.841480i
$704$	767.535	+	1329.41i	0.0410903	+	0.0711705i
$705$	−19509.8	+	6417.72i	−1.04225	+	0.342844i
$706$	−4765.80	+	8254.60i	−0.254055	+	0.440037i
$707$		−	106.512i		−	0.00566588i
$708$	6345.72	+	3663.70i	0.336846	+	0.194478i
$709$	−9502.09	+	16458.1i	−0.503327	+	0.871787i	0.496666	+	0.867942i	$0.334557\pi$
$709$	−9502.09	+	16458.1i	−0.503327	+	0.871787i	−0.999993	+	0.00384554i	$0.998776\pi$
$710$	−9089.91	−	1897.57i	−0.480476	−	0.100302i
$711$	3252.70	−	5633.83i	0.171569	−	0.297166i
$712$	−717.368	+	414.172i	−0.0377591	+	0.0218002i
$713$	7101.52	−	4100.06i	0.373007	−	0.215356i
$714$	−6252.30			−0.327712
$715$	7017.29	+	10428.3i	0.367037	+	0.545452i
$716$	9559.35			0.498952
$717$	14969.6	−	8642.71i	0.779708	−	0.450164i
$718$	−1135.67	+	655.678i	−0.0590289	+	0.0340804i
$719$	8269.21	−	14322.7i	0.428914	−	0.742901i	−0.567863	−	0.823123i	$-0.692230\pi$
$719$	8269.21	−	14322.7i	0.428914	−	0.742901i	0.996777	+	0.0802219i	$0.0255629\pi$
$720$	410.473	−	1966.28i	0.0212464	−	0.101776i
$721$	−5824.29	+	10088.0i	−0.300843	+	0.521075i
$722$	5785.47	+	3340.24i	0.298217	+	0.172176i
$723$			22161.1i			1.13995i
$724$	−1586.92	+	2748.63i	−0.0814607	+	0.141094i
$725$	−3622.03	−	32204.8i	−0.185543	−	1.64973i
$726$	3001.10	+	5198.05i	0.153417	+	0.265727i
$727$		−	29114.4i		−	1.48527i	−0.669694	−	0.742637i	$-0.733575\pi$
$727$		−	29114.4i		−	1.48527i	0.669694	−	0.742637i	$-0.266425\pi$
$728$	2504.49	+	637.068i	0.127503	+	0.0324331i
$729$	−19644.4			−0.998037
$730$	5329.10	−	1753.00i	0.270190	−	0.0888785i
$731$	−23965.4	−	41509.3i	−1.21257	−	2.10024i
$732$	9980.26	+	5762.10i	0.503936	+	0.290947i
$733$		−	9711.06i		−	0.489340i	−0.969606	−	0.244670i	$-0.921320\pi$
$733$		−	9711.06i		−	0.489340i	0.969606	−	0.244670i	$-0.0786796\pi$
$734$	−3402.90	+	5894.00i	−0.171122	+	0.296392i
$735$	8743.79	−	9782.32i	0.438802	−	0.490920i
$736$	−3594.76			−0.180034
$737$	−11342.4	−	6548.56i	−0.566899	−	0.327299i
$738$	−3787.56	+	2186.75i	−0.188919	+	0.109072i
$739$	2049.07	+	3549.10i	0.101998	+	0.176665i	0.912508	−	0.409060i	$-0.134143\pi$
$739$	2049.07	+	3549.10i	0.101998	+	0.176665i	−0.810510	+	0.585725i	$0.800810\pi$
$740$	11575.4	+	2416.43i	0.575025	+	0.120040i
$741$	10628.4	−	2993.18i	0.526916	−	0.148391i
$742$			3699.39i			0.183031i
$743$	−27677.1	+	15979.4i	−1.36659	+	0.789000i	−0.990491	−	0.137580i	$-0.956068\pi$
$743$	−27677.1	+	15979.4i	−1.36659	+	0.789000i	−0.376097	+	0.926580i	$0.622734\pi$
$744$	1159.56	+	2008.41i	0.0571391	+	0.0989678i
$745$	6876.06	+	6146.07i	0.338147	+	0.302248i
$746$	12963.3			0.636221
$747$	−4483.58	−	2588.60i	−0.219606	−	0.126790i
$748$	9490.48	+	5479.33i	0.463912	+	0.267840i
$749$	4093.79			0.199712
$750$	−4625.25	−	10090.6i	−0.225187	−	0.491274i
$751$	−3109.40	−	5385.64i	−0.151083	−	0.261684i	0.780543	−	0.625103i	$-0.214943\pi$
$751$	−3109.40	−	5385.64i	−0.151083	−	0.261684i	−0.931626	+	0.363419i	$0.881610\pi$
$752$	6409.55	−	3700.56i	0.310814	−	0.179449i
$753$		−	28756.8i		−	1.39171i
$754$	5991.53	−	23554.3i	0.289388	−	1.13766i
$755$	7531.41	−	36077.5i	0.363041	−	1.73907i
$756$	2092.58	+	3624.45i	0.100670	+	0.174365i
$757$	−28827.6	+	16643.6i	−1.38409	+	0.799104i	−0.992641	−	0.121096i	$-0.961359\pi$
$757$	−28827.6	+	16643.6i	−1.38409	+	0.799104i	−0.391448	+	0.920200i	$0.628026\pi$
$758$	1552.80	+	896.508i	0.0744065	+	0.0429586i
$759$	10700.4			0.511727
$760$	−3535.81	+	3955.77i	−0.168760	+	0.188804i
$761$	−12721.5	+	22034.3i	−0.605986	+	1.04960i	0.385909	+	0.922537i	$0.373888\pi$
$761$	−12721.5	+	22034.3i	−0.605986	+	1.04960i	−0.991895	+	0.127062i	$0.959445\pi$
$762$		−	5215.01i		−	0.247926i
$763$	6287.70	+	3630.21i	0.298336	+	0.172244i
$764$	−4766.76	−	8256.27i	−0.225727	−	0.390970i
$765$	−4480.79	−	13621.6i	−0.211769	−	0.643777i
$766$	23621.5			1.11420
$767$	−20953.6	−	5329.98i	−0.986428	−	0.250918i
$768$		−	1016.65i		−	0.0477673i
$769$	−14958.3	−	25908.6i	−0.701446	−	1.21494i	−0.967959	−	0.251109i	$-0.919205\pi$
$769$	−14958.3	−	25908.6i	−0.701446	−	1.21494i	0.266513	−	0.963831i	$-0.414128\pi$
$770$	3511.17	−	1154.99i	0.164329	−	0.0540558i
$771$	−871.642	+	1509.73i	−0.0407152	+	0.0705208i
$772$		−	13972.2i		−	0.651388i
$773$	−27859.3	−	16084.6i	−1.29629	−	0.748412i	−0.316527	−	0.948583i	$-0.602517\pi$
$773$	−27859.3	−	16084.6i	−1.29629	−	0.748412i	−0.979761	+	0.200171i	$0.935850\pi$
$774$	−4711.93	+	8161.30i	−0.218820	+	0.379008i
$775$	−8362.46	−	3650.51i	−0.387598	−	0.169200i
$776$	4782.52	−	8283.57i	0.221240	−	0.383200i
$777$	−6267.20	+	3618.37i	−0.289362	+	0.167063i
$778$	−4409.30	+	2545.71i	−0.203189	+	0.117311i
$779$	11552.1			0.531318
$780$	−571.535	−	8304.94i	−0.0262362	−	0.381236i
$781$	−9960.61			−0.456362
$782$	−22224.4	+	12831.3i	−1.01630	+	0.586758i
$783$	34087.4	−	19680.4i	1.55579	−	0.898237i
$784$	−2364.03	+	4094.62i	−0.107691	+	0.186526i
$785$	19878.8	+	4149.83i	0.903829	+	0.188680i
$786$	1254.27	−	2172.45i	0.0569188	−	0.0985862i
$787$	1596.19	+	921.561i	0.0722974	+	0.0417409i	0.535713	−	0.844400i	$-0.320043\pi$
$787$	1596.19	+	921.561i	0.0722974	+	0.0417409i	−0.463416	+	0.886141i	$0.653376\pi$
$788$			8679.40i			0.392374i
$789$	−5904.13	+	10226.3i	−0.266404	+	0.461425i
$790$	4048.01	+	12305.9i	0.182306	+	0.554209i
$791$	1970.01	+	3412.16i	0.0885531	+	0.153378i
$792$		−	2154.63i		−	0.0966683i
$793$	−32954.8	−	8382.74i	−1.47574	−	0.375385i
$794$	−11766.9			−0.525936
$795$	11320.1	−	3723.71i	0.505008	−	0.166121i
$796$	−6372.91	−	11038.2i	−0.283771	−	0.491506i
$797$	−4019.17	−	2320.47i	−0.178628	−	0.103131i	0.408020	−	0.912973i	$-0.366219\pi$
$797$	−4019.17	−	2320.47i	−0.178628	−	0.103131i	−0.586648	+	0.809842i	$0.699553\pi$
$798$		−	3247.02i		−	0.144039i
$799$	26417.8	−	45756.9i	1.16970	−	2.02599i
$800$	2374.63	+	3218.87i	0.104945	+	0.142255i
$801$	1162.67			0.0512868
$802$	−17896.3	−	10332.4i	−0.787956	−	0.454926i
$803$	5211.45	−	3008.83i	0.229026	−	0.132228i
$804$	4337.01	+	7511.91i	0.190242	+	0.329508i
$805$	−1768.81	+	8473.07i	−0.0774437	+	0.370977i
$806$	−4899.83	−	4776.82i	−0.214131	−	0.208755i
$807$			9892.34i			0.431508i
$808$	107.075	−	61.8199i	0.00466200	−	0.00269160i
$809$	−17485.7	−	30286.1i	−0.759907	−	1.31620i	−0.942898	−	0.333083i	$-0.891911\pi$
$809$	−17485.7	−	30286.1i	−0.759907	−	1.31620i	0.182991	−	0.983115i	$-0.441422\pi$
$810$	4466.56	−	4997.07i	0.193752	−	0.216764i
$811$	−206.069			−0.00892239			−0.00446119	−	0.999990i	$-0.501420\pi$
$811$	−206.069			−0.00892239			−0.00446119	+	0.999990i	$0.501420\pi$
$812$	−6189.56	−	3573.54i	−0.267501	−	0.154442i
$813$	−6921.33	−	3996.03i	−0.298575	−	0.172382i
$814$	12684.1			0.546165
$815$	−3456.88	+	3867.47i	−0.148576	+	0.166223i
$816$	−3628.87	−	6285.39i	−0.155681	−	0.269648i
$817$	21557.1	−	12446.0i	0.923119	−	0.532963i
$818$		−	30531.6i		−	1.30503i
$819$	−2597.24	−	2532.04i	−0.110812	−	0.108030i
$820$	1779.74	−	8525.47i	0.0757943	−	0.363076i
$821$	2178.89	+	3773.95i	0.0926235	+	0.160429i	0.908614	−	0.417636i	$-0.137141\pi$
$821$	2178.89	+	3773.95i	0.0926235	+	0.160429i	−0.815991	+	0.578065i	$0.803808\pi$
$822$	14086.3	−	8132.75i	0.597709	−	0.345088i
$823$	−7434.75	−	4292.46i	−0.314896	−	0.181805i	0.334219	−	0.942495i	$-0.391527\pi$
$823$	−7434.75	−	4292.46i	−0.314896	−	0.181805i	−0.649115	+	0.760690i	$0.724861\pi$
$824$	−13521.8			−0.571667
$825$	−7068.49	−	9581.52i	−0.298295	−	0.404346i
$826$	−3178.97	+	5506.13i	−0.133911	+	0.231941i
$827$		−	2544.35i		−	0.106984i	−0.998568	−	0.0534919i	$-0.982965\pi$
$827$		−	2544.35i		−	0.106984i	0.998568	−	0.0534919i	$-0.0170351\pi$
$828$	4369.63	+	2522.81i	0.183400	+	0.105886i
$829$	−4053.39	−	7020.67i	−0.169819	−	0.294135i	0.768537	−	0.639805i	$-0.220985\pi$
$829$	−4053.39	−	7020.67i	−0.169819	−	0.294135i	−0.938356	+	0.345670i	$0.887652\pi$
$830$	9793.45	−	3221.53i	0.409561	−	0.134724i
$831$	−4454.49			−0.185950
$832$	813.179	+	2887.50i	0.0338845	+	0.120320i
$833$			33753.0i			1.40393i
$834$	9313.68	+	16131.8i	0.386698	+	0.669781i
$835$	−42.2988	−	128.588i	−0.00175307	−	0.00532931i
$836$	−2845.60	+	4928.72i	−0.117724	+	0.203903i
$837$		−	11082.1i		−	0.457652i
$838$	19077.5	+	11014.4i	0.786420	+	0.454040i
$839$	−11719.5	+	20298.8i	−0.482244	+	0.835272i	−0.999792	−	0.0203824i	$-0.993512\pi$
$839$	−11719.5	+	20298.8i	−0.482244	+	0.835272i	0.517548	+	0.855654i	$0.326845\pi$
$840$	−2396.31	−	500.244i	−0.0984292	−	0.0205477i
$841$	−21414.1	+	37090.4i	−0.878025	+	1.52078i
$842$	17311.0	−	9994.51i	0.708523	−	0.409066i
$843$	16859.3	−	9733.69i	0.688806	−	0.397682i
$844$	6472.77			0.263983
$845$	8266.06	+	23130.6i	0.336522	+	0.941676i
$846$	−10388.2			−0.422168
$847$	−4510.31	+	2604.03i	−0.182971	+	0.105638i
$848$	−3718.97	+	2147.15i	−0.150601	+	0.0869497i
$849$	−16842.9	+	29172.8i	−0.680856	+	1.17928i
$850$	26170.6	+	11424.4i	1.05605	+	0.461004i
$851$	−14851.6	+	25723.7i	−0.598243	+	1.03619i
$852$	5712.95	+	3298.37i	0.229721	+	0.132630i
$853$		−	24689.2i		−	0.991024i	−0.868601	−	0.495512i	$-0.834980\pi$
$853$		−	24689.2i		−	0.991024i	0.868601	−	0.495512i	$-0.165020\pi$
$854$	−4999.74	+	8659.80i	−0.200337	+	0.346993i
$855$	7074.13	−	2327.02i	0.282959	−	0.0930788i
$856$	2376.06	+	4115.46i	0.0948739	+	0.164326i
$857$			18992.4i			0.757022i	0.925597	+	0.378511i	$0.123564\pi$
$857$			18992.4i			0.757022i	−0.925597	+	0.378511i	$0.876436\pi$
$858$	−2420.57	−	8595.13i	−0.0963133	−	0.341997i
$859$	24561.9			0.975601			0.487801	−	0.872955i	$-0.337799\pi$
$859$	24561.9			0.975601			0.487801	+	0.872955i	$0.337799\pi$
$860$	−5864.04	−	17826.7i	−0.232514	−	0.706842i
$861$	2665.00	+	4615.91i	0.105485	+	0.182706i
$862$	−18086.2	−	10442.1i	−0.714638	−	0.412596i
$863$			29205.2i			1.15198i	0.817458	+	0.575988i	$0.195383\pi$
$863$			29205.2i			1.15198i	−0.817458	+	0.575988i	$0.804617\pi$
$864$	−2429.09	+	4207.30i	−0.0956472	+	0.165666i
$865$	−3549.59	+	3971.19i	−0.139526	+	0.156098i
$866$	−26284.0			−1.03137
$867$	−27973.5	−	16150.5i	−1.09577	−	0.632642i
$868$	−1742.69	+	1006.14i	−0.0681459	+	0.0393441i
$869$	6947.98	+	12034.2i	0.271224	+	0.469774i
$870$	−4704.72	+	22536.9i	−0.183339	+	0.878246i
$871$	−18326.5	−	17866.4i	−0.712937	−	0.695039i
$872$			8427.97i			0.327302i
$873$	−11626.8	+	6712.75i	−0.450754	+	0.260243i
$874$	−6663.69	−	11541.9i	−0.257898	−	0.446692i
$875$	8755.51	−	4013.30i	0.338275	−	0.155056i
$876$	−3985.40			−0.153715
$877$	12772.8	+	7374.39i	0.491798	+	0.283940i	0.725320	−	0.688412i	$-0.241692\pi$
$877$	12772.8	+	7374.39i	0.491798	+	0.283940i	−0.233522	+	0.972352i	$0.575025\pi$
$878$	−27905.0	−	16111.0i	−1.07261	−	0.619270i
$879$	4308.54			0.165328
$880$	3199.00	+	2859.39i	0.122544	+	0.109534i
$881$	1775.50	+	3075.25i	0.0678978	+	0.117602i	0.897976	−	0.440045i	$-0.145037\pi$
$881$	1775.50	+	3075.25i	0.0678978	+	0.117602i	−0.830078	+	0.557647i	$0.811704\pi$
$882$	5747.22	−	3318.16i	0.219409	−	0.126676i
$883$		−	626.491i		−	0.0238767i	−0.999929	−	0.0119383i	$-0.996200\pi$
$883$		−	626.491i		−	0.0238767i	0.999929	−	0.0119383i	$-0.00380018\pi$
$884$	15334.2	+	14949.2i	0.583421	+	0.568774i
$885$	20048.5	+	4185.25i	0.761496	+	0.158967i
$886$	5798.58	+	10043.4i	0.219872	+	0.380830i
$887$	−31665.8	+	18282.3i	−1.19869	+	0.692062i	−0.960262	−	0.279100i	$-0.909964\pi$
$887$	−31665.8	+	18282.3i	−1.19869	+	0.692062i	−0.238424	+	0.971161i	$0.576631\pi$
$888$	−7275.03	−	4200.24i	−0.274926	−	0.158728i
$889$	4525.03			0.170714
$890$	−1542.96	+	1726.23i	−0.0581126	+	0.0650148i
$891$	3594.66	−	6226.13i	0.135158	−	0.234100i
$892$			4892.48i			0.183646i
$893$	23763.1	+	13719.6i	0.890482	+	0.514120i
$894$	−3275.86	−	5673.96i	−0.122552	−	0.212266i
$895$	25381.2	−	8349.10i	0.947935	−	0.311821i
$896$	882.142			0.0328909
$897$	20265.3	+	5154.90i	0.754335	+	0.191881i
$898$			13341.8i			0.495791i
$899$	9462.61	+	16389.7i	0.351052	+	0.608040i
$900$	−627.487	−	5579.23i	−0.0232403	−	0.206638i
$901$	−15328.2	+	26549.2i	−0.566766	+	0.981668i
$902$		−	9342.10i		−	0.344853i
$903$	9946.18	+	5742.43i	0.366543	+	0.211624i
$904$	−2286.81	+	3960.87i	−0.0841351	+	0.145726i
$905$	−1812.83	+	8683.97i	−0.0665863	+	0.318967i
$906$	−13091.1	+	22674.5i	−0.480048	+	0.831467i
$907$	8340.22	−	4815.23i	0.305328	−	0.176281i	−0.339506	−	0.940604i	$-0.610260\pi$
$907$	8340.22	−	4815.23i	0.305328	−	0.176281i	0.644834	+	0.764323i	$0.276927\pi$
$908$	−15850.3	+	9151.17i	−0.579306	+	0.334463i
$909$	−173.541			−0.00633222
$910$	7206.14	−	495.917i	0.262507	−	0.0180654i
$911$	47165.1			1.71531			0.857655	−	0.514225i	$-0.171920\pi$
$911$	47165.1			1.71531			0.857655	+	0.514225i	$0.171920\pi$
$912$	3264.21	−	1884.59i	0.118518	−	0.0684266i
$913$	9577.23	−	5529.42i	0.347163	−	0.200435i
$914$	4586.09	−	7943.33i	0.165967	−	0.287464i
$915$	31531.4	+	6582.37i	1.13923	+	0.237821i
$916$	11293.8	−	19561.5i	0.407378	−	0.705599i
$917$	1885.02	+	1088.32i	0.0678832	+	0.0391924i
$918$			34681.8i			1.24692i
$919$	22771.8	−	39441.9i	0.817380	−	1.41574i	−0.0902260	−	0.995921i	$-0.528759\pi$
$919$	22771.8	−	39441.9i	0.817380	−	1.41574i	0.907606	−	0.419823i	$-0.137908\pi$
$920$	−9544.54	+	3139.65i	−0.342037	+	0.112512i
$921$	2838.60	+	4916.61i	0.101558	+	0.175904i
$922$			3136.12i			0.112020i
$923$	−18864.2	−	4798.49i	−0.672721	−	0.171121i
$924$	−2625.85			−0.0934891
$925$	32844.5	−	3693.97i	1.16748	−	0.131305i
$926$	13553.6	+	23475.6i	0.480994	+	0.833105i
$927$	16436.5	+	9489.60i	0.582356	+	0.336224i
$928$		−	8296.42i		−	0.293473i
$929$	7341.93	−	12716.6i	0.259291	−	0.449104i	−0.706761	−	0.707452i	$-0.749845\pi$
$929$	7341.93	−	12716.6i	0.259291	−	0.449104i	0.966052	+	0.258347i	$0.0831779\pi$
$930$	4832.91	+	4319.83i	0.170406	+	0.152315i
$931$	−17529.0			−0.617069
$932$	−5668.43	−	3272.67i	−0.199223	−	0.115021i
$933$	−11419.0	+	6592.78i	−0.400689	+	0.231338i
$934$	−8932.36	−	15471.3i	−0.312929	−	0.542009i
$935$	29984.0	+	6259.35i	1.04875	+	0.218933i
$936$	1037.98	−	4080.60i	0.0362474	−	0.142498i
$937$			22857.5i			0.796929i	0.917184	+	0.398465i	$0.130457\pi$
$937$			22857.5i			0.796929i	−0.917184	+	0.398465i	$0.869543\pi$
$938$	−6518.03	+	3763.19i	−0.226888	+	0.130994i
$939$	4264.30	+	7385.99i	0.148200	+	0.256691i
$940$	13786.1	−	15423.5i	0.478354	−	0.535170i
$941$	−45781.3			−1.58600			−0.793001	−	0.609220i	$-0.791483\pi$
$941$	−45781.3			−1.58600			−0.793001	+	0.609220i	$0.791483\pi$
$942$	−12493.7	−	7213.25i	−0.432131	−	0.249491i
$943$	18946.0	+	10938.5i	0.654258	+	0.377736i
$944$	−7380.36			−0.254460
$945$	8721.63	+	7795.71i	0.300227	+	0.268354i
$946$	−10065.0	−	17433.1i	−0.345921	−	0.599153i
$947$	2741.70	−	1582.92i	0.0940795	−	0.0543168i	−0.452222	−	0.891905i	$-0.649369\pi$
$947$	2741.70	−	1582.92i	0.0940795	−	0.0543168i	0.546302	+	0.837589i	$0.316035\pi$
$948$		−	9203.06i		−	0.315297i
$949$	11319.4	−	3187.76i	0.387188	−	0.109040i
$950$	−5933.06	+	13591.2i	−0.202625	+	0.464166i
$951$	−9045.05	−	15666.5i	−0.308418	−	0.534196i
$952$	5453.79	−	3148.75i	0.185670	−	0.107197i
$953$	−7969.60	−	4601.25i	−0.270893	−	0.156400i	0.358401	−	0.933568i	$-0.383322\pi$
$953$	−7969.60	−	4601.25i	−0.270893	−	0.156400i	−0.629293	+	0.777168i	$0.716656\pi$
$954$	6027.48			0.204556
$955$	−19867.3	−	17758.1i	−0.673185	−	0.601717i
$956$	−8705.18	+	15077.8i	−0.294504	+	0.510095i
$957$			24695.7i			0.834168i
$958$	24540.3	+	14168.4i	0.827622	+	0.477828i
$959$	7056.73	+	12222.6i	0.237616	+	0.411563i
$960$	−887.940	−	2699.34i	−0.0298522	−	0.0907507i
$961$	−24462.6			−0.821139
$962$	24022.2	+	6110.54i	0.805100	+	0.204794i
$963$		−	6670.08i		−	0.223199i
$964$	−11160.6	−	19330.8i	−0.372884	−	0.645854i
$965$	−12203.3	−	37098.0i	−0.407086	−	1.23754i
$966$	3074.55	−	5325.27i	0.102404	−	0.177368i
$967$		−	526.712i		−	0.0175159i	−0.999962	−	0.00875797i	$-0.997212\pi$
$967$		−	526.712i		−	0.0175159i	0.999962	−	0.00875797i	$-0.00278778\pi$
$968$	−5235.62	−	3022.79i	−0.173842	−	0.100368i
$969$	13453.8	−	23302.7i	0.446026	−	0.772541i
$970$	5463.34	−	26170.9i	0.180843	−	0.866287i
$971$	−15262.3	+	26435.1i	−0.504419	+	0.873680i	0.495568	+	0.868569i	$0.334960\pi$
$971$	−15262.3	+	26435.1i	−0.504419	+	0.873680i	−0.999987	+	0.00511057i	$0.998373\pi$
$972$	10076.2	−	5817.48i	0.332504	−	0.191971i
$973$	−13997.4	+	8081.41i	−0.461189	+	0.266267i
$974$	−29432.7			−0.968261
$975$	−8771.00	−	21551.5i	−0.288099	−	0.707896i
$976$	−11607.5			−0.380683
$977$	26913.9	−	15538.8i	0.881323	−	0.508832i	0.0102283	−	0.999948i	$-0.496744\pi$
$977$	26913.9	−	15538.8i	0.881323	−	0.508832i	0.871094	+	0.491116i	$0.163411\pi$
$978$	3191.34	−	1842.52i	0.104343	−	0.0602427i
$979$	−1241.77	+	2150.80i	−0.0405383	+	0.0702144i
$980$	−2700.57	+	12936.5i	−0.0880270	+	0.421674i
$981$	5914.75	−	10244.7i	0.192501	−	0.333422i
$982$	24303.9	+	14031.8i	0.789784	+	0.455982i
$983$			7429.44i			0.241060i	0.992710	+	0.120530i	$0.0384595\pi$
$983$			7429.44i			0.241060i	−0.992710	+	0.120530i	$0.961541\pi$
$984$	−3093.56	+	5358.20i	−0.100223	+	0.173591i
$985$	7580.56	+	23044.9i	0.245215	+	0.745453i
$986$	−29613.5	−	51292.1i	−0.956476	−	1.65667i
$987$			12660.1i			0.408284i
$988$	−7763.61	+	7963.53i	−0.249993	+	0.256431i
$989$	47139.5			1.51562
$990$	−1881.84	−	5720.80i	−0.0604130	−	0.183655i
$991$	3786.83	+	6558.98i	0.121385	+	0.210245i	0.920314	−	0.391180i	$-0.127933\pi$
$991$	3786.83	+	6558.98i	0.121385	+	0.210245i	−0.798929	+	0.601425i	$0.794600\pi$
$992$	−2022.93	−	1167.94i	−0.0647461	−	0.0373812i
$993$		−	42745.7i		−	1.36606i
$994$	−2861.97	+	4957.08i	−0.0913243	+	0.158178i
$995$	−26561.6	−	23741.7i	−0.846290	−	0.756445i
$996$	−7324.08			−0.233005
$997$	52943.0	+	30566.7i	1.68177	+	0.970969i	0.960487	+	0.278326i	$0.0897795\pi$
$997$	52943.0	+	30566.7i	1.68177	+	0.970969i	0.721281	+	0.692643i	$0.243554\pi$
$998$	−13565.2	+	7831.85i	−0.430258	+	0.248410i
$999$	20071.3	+	34764.5i	0.635663	+	1.10100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.n.a.29.15	yes	44
5.4	even	2	inner	130.4.n.a.29.8	yes	44
13.9	even	3	inner	130.4.n.a.9.8	✓	44
65.9	even	6	inner	130.4.n.a.9.15	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.n.a.9.8	✓	44	13.9	even	3	inner
130.4.n.a.9.15	yes	44	65.9	even	6	inner
130.4.n.a.29.8	yes	44	5.4	even	2	inner
130.4.n.a.29.15	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-3.43924 + 1.98565i) q^{3} +(2.00000 - 3.46410i) q^{4} +(2.28471 - 10.9444i) q^{5} +(-3.97130 + 6.87849i) q^{6} +(-5.96841 - 3.44587i) q^{7} -8.00000i q^{8} +(-5.61440 + 9.72443i) q^{9} +(-6.98717 - 21.2410i) q^{10} +(-11.9927 - 20.7720i) q^{11} +15.8852i q^{12} +(-12.7059 - 45.1172i) q^{13} -13.7835 q^{14} +(13.8741 + 42.1771i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-98.9190 - 57.1109i) q^{17} +22.4576i q^{18} +(29.6596 - 51.3719i) q^{19} +(-33.3431 - 29.8033i) q^{20} +27.3691 q^{21} +(-41.5441 - 23.9855i) q^{22} +(97.2861 - 56.1682i) q^{23} +(15.8852 + 27.5139i) q^{24} +(-114.560 - 50.0096i) q^{25} +(-67.1245 - 65.4393i) q^{26} -151.818i q^{27} +(-23.8737 + 13.7835i) q^{28} +(129.631 + 224.528i) q^{29} +(66.2077 + 59.1789i) q^{30} +72.9962 q^{31} +(-27.7128 - 16.0000i) q^{32} +(82.4919 + 47.6267i) q^{33} -228.444 q^{34} +(-51.3491 + 57.4480i) q^{35} +(22.4576 + 38.8977i) q^{36} +(-228.988 + 132.206i) q^{37} -118.638i q^{38} +(133.286 + 129.939i) q^{39} +(-87.5553 - 18.2777i) q^{40} +(97.3724 + 168.654i) q^{41} +(47.4047 - 27.3691i) q^{42} +(363.409 + 209.814i) q^{43} -95.9419 q^{44} +(93.6008 + 83.6638i) q^{45} +(112.336 - 194.572i) q^{46} +462.569i q^{47} +(55.0279 + 31.7704i) q^{48} +(-147.752 - 255.914i) q^{49} +(-248.434 + 27.9410i) q^{50} +453.609 q^{51} +(-181.702 - 46.2197i) q^{52} -268.393i q^{53} +(-151.818 - 262.956i) q^{54} +(-254.738 + 83.7954i) q^{55} +(-27.5669 + 47.7473i) q^{56} +235.574i q^{57} +(449.057 + 259.263i) q^{58} +(230.636 - 399.474i) q^{59} +(173.854 + 36.2931i) q^{60} +(362.734 - 628.274i) q^{61} +(126.433 - 72.9962i) q^{62} +(67.0182 - 38.6930i) q^{63} -64.0000 q^{64} +(-522.810 + 35.9791i) q^{65} +190.507 q^{66} +(472.888 - 273.022i) q^{67} +(-395.676 + 228.444i) q^{68} +(-223.060 + 386.352i) q^{69} +(-31.4912 + 150.852i) q^{70} +(207.638 - 359.640i) q^{71} +(77.7954 + 44.9152i) q^{72} +250.888i q^{73} +(-264.413 + 457.976i) q^{74} +(493.302 - 55.4809i) q^{75} +(-118.638 - 205.488i) q^{76} +165.302i q^{77} +(360.797 + 91.7761i) q^{78} -579.349 q^{79} +(-169.928 + 55.8974i) q^{80} +(149.868 + 259.579i) q^{81} +(337.308 + 194.745i) q^{82} +461.064i q^{83} +(54.7382 - 94.8094i) q^{84} +(-851.047 + 952.128i) q^{85} +839.257 q^{86} +(-891.669 - 514.805i) q^{87} +(-166.176 + 95.9419i) q^{88} +(-51.7716 - 89.6710i) q^{89} +(245.785 + 51.3092i) q^{90} +(-79.6335 + 313.061i) q^{91} -449.345i q^{92} +(-251.052 + 144.945i) q^{93} +(462.569 + 801.194i) q^{94} +(-494.471 - 441.976i) q^{95} +127.081 q^{96} +(1035.45 + 597.815i) q^{97} +(-511.828 - 295.504i) q^{98} +269.328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) \) 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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