LMFDB - Embedded newform 19.4.c.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,4,Mod(7,19)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("19.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	19.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.12103629011$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 55x^{2} + 3025 $ x^4 + 55*x^2 + 3025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$3.70810 + 6.42262i$ of defining polynomial
Character	$\chi$	$=$	19.11
Dual form			19.4.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-3.70810 + 6.42262i) q^{3} +(3.50000 + 6.06218i) q^{4} +(7.20810 - 12.4848i) q^{5} +(-3.70810 - 6.42262i) q^{6} +0.416198 q^{7} -15.0000 q^{8} +(-14.0000 - 24.2487i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-3.70810 + 6.42262i) q^{3} +(3.50000 + 6.06218i) q^{4} +(7.20810 - 12.4848i) q^{5} +(-3.70810 - 6.42262i) q^{6} +0.416198 q^{7} -15.0000 q^{8} +(-14.0000 - 24.2487i) q^{9} +(7.20810 + 12.4848i) q^{10} +65.9134 q^{11} -51.9134 q^{12} +(-22.6648 - 39.2566i) q^{13} +(-0.208099 + 0.360438i) q^{14} +(53.4567 + 92.5897i) q^{15} +(-20.5000 + 35.5070i) q^{16} +(-1.66479 + 2.88351i) q^{17} +28.0000 q^{18} +(-82.3729 + 8.58525i) q^{19} +100.913 q^{20} +(-1.54331 + 2.67308i) q^{21} +(-32.9567 + 57.0827i) q^{22} +(-54.4567 - 94.3218i) q^{23} +(55.6215 - 96.3392i) q^{24} +(-41.4134 - 71.7301i) q^{25} +45.3296 q^{26} +7.41620 q^{27} +(1.45669 + 2.52307i) q^{28} +(-29.5433 - 51.1705i) q^{29} -106.913 q^{30} +184.913 q^{31} +(-80.5000 - 139.430i) q^{32} +(-244.413 + 423.336i) q^{33} +(-1.66479 - 2.88351i) q^{34} +(3.00000 - 5.19615i) q^{35} +(98.0000 - 169.741i) q^{36} +142.913 q^{37} +(33.7514 - 75.6296i) q^{38} +336.173 q^{39} +(-108.121 + 187.272i) q^{40} +(87.5754 - 151.685i) q^{41} +(-1.54331 - 2.67308i) q^{42} +(-222.740 + 385.797i) q^{43} +(230.697 + 399.579i) q^{44} -403.654 q^{45} +108.913 q^{46} +(-87.1215 - 150.899i) q^{47} +(-152.032 - 263.327i) q^{48} -342.827 q^{49} +82.8268 q^{50} +(-12.3464 - 21.3847i) q^{51} +(158.654 - 274.796i) q^{52} +(117.173 + 202.950i) q^{53} +(-3.70810 + 6.42262i) q^{54} +(475.110 - 822.915i) q^{55} -6.24298 q^{56} +(250.307 - 560.884i) q^{57} +59.0866 q^{58} +(-76.2053 + 131.991i) q^{59} +(-374.197 + 648.128i) q^{60} +(-28.9651 - 50.1691i) q^{61} +(-92.4567 + 160.140i) q^{62} +(-5.82678 - 10.0923i) q^{63} -167.000 q^{64} -653.480 q^{65} +(-244.413 - 423.336i) q^{66} +(418.610 + 725.054i) q^{67} -23.3071 q^{68} +807.723 q^{69} +(3.00000 + 5.19615i) q^{70} +(-263.740 + 456.811i) q^{71} +(210.000 + 363.731i) q^{72} +(-109.749 + 190.090i) q^{73} +(-71.4567 + 123.767i) q^{74} +614.260 q^{75} +(-340.350 - 469.311i) q^{76} +27.4331 q^{77} +(-168.087 + 291.135i) q^{78} +(245.654 - 425.484i) q^{79} +(295.532 + 511.877i) q^{80} +(350.500 - 607.084i) q^{81} +(87.5754 + 151.685i) q^{82} -692.433 q^{83} -21.6063 q^{84} +(24.0000 + 41.5692i) q^{85} +(-222.740 - 385.797i) q^{86} +438.198 q^{87} -988.701 q^{88} +(-413.642 - 716.450i) q^{89} +(201.827 - 349.574i) q^{90} +(-9.43305 - 16.3385i) q^{91} +(381.197 - 660.252i) q^{92} +(-685.677 + 1187.63i) q^{93} +174.243 q^{94} +(-486.567 + 1090.29i) q^{95} +1194.01 q^{96} +(366.402 - 634.627i) q^{97} +(171.413 - 296.897i) q^{98} +(-922.787 - 1598.31i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 14 q^{4} + 14 q^{5} - 28 q^{7} - 60 q^{8} - 56 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 14 * q^4 + 14 * q^5 - 28 * q^7 - 60 * q^8 - 56 * q^9	\( 4 q - 2 q^{2} + 14 q^{4} + 14 q^{5} - 28 q^{7} - 60 q^{8} - 56 q^{9} + 14 q^{10} + 56 q^{11} + 28 q^{13} + 14 q^{14} + 110 q^{15} - 82 q^{16} + 112 q^{17} + 112 q^{18} - 196 q^{19} + 196 q^{20} - 110 q^{21} - 28 q^{22} - 114 q^{23} + 42 q^{25} - 56 q^{26} - 98 q^{28} - 222 q^{29} - 220 q^{30} + 532 q^{31} - 322 q^{32} - 770 q^{33} + 112 q^{34} + 12 q^{35} + 392 q^{36} + 364 q^{37} + 224 q^{38} + 1760 q^{39} - 210 q^{40} - 154 q^{41} - 110 q^{42} - 268 q^{43} + 196 q^{44} - 784 q^{45} + 228 q^{46} - 126 q^{47} - 956 q^{49} - 84 q^{50} - 880 q^{51} - 196 q^{52} + 884 q^{53} + 966 q^{55} + 420 q^{56} - 660 q^{57} + 444 q^{58} - 112 q^{59} - 770 q^{60} - 546 q^{61} - 266 q^{62} + 392 q^{63} - 668 q^{64} - 1368 q^{65} - 770 q^{66} + 740 q^{67} + 1568 q^{68} + 1540 q^{69} + 12 q^{70} - 432 q^{71} + 840 q^{72} - 350 q^{73} - 182 q^{74} + 3080 q^{75} + 196 q^{76} + 1148 q^{77} - 880 q^{78} + 152 q^{79} + 574 q^{80} + 1402 q^{81} - 154 q^{82} - 3808 q^{83} - 1540 q^{84} + 96 q^{85} - 268 q^{86} - 1540 q^{87} - 840 q^{88} - 112 q^{89} + 392 q^{90} - 1076 q^{91} + 798 q^{92} - 770 q^{93} + 252 q^{94} - 908 q^{95} + 546 q^{97} + 478 q^{98} - 784 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 14 * q^4 + 14 * q^5 - 28 * q^7 - 60 * q^8 - 56 * q^9 + 14 * q^10 + 56 * q^11 + 28 * q^13 + 14 * q^14 + 110 * q^15 - 82 * q^16 + 112 * q^17 + 112 * q^18 - 196 * q^19 + 196 * q^20 - 110 * q^21 - 28 * q^22 - 114 * q^23 + 42 * q^25 - 56 * q^26 - 98 * q^28 - 222 * q^29 - 220 * q^30 + 532 * q^31 - 322 * q^32 - 770 * q^33 + 112 * q^34 + 12 * q^35 + 392 * q^36 + 364 * q^37 + 224 * q^38 + 1760 * q^39 - 210 * q^40 - 154 * q^41 - 110 * q^42 - 268 * q^43 + 196 * q^44 - 784 * q^45 + 228 * q^46 - 126 * q^47 - 956 * q^49 - 84 * q^50 - 880 * q^51 - 196 * q^52 + 884 * q^53 + 966 * q^55 + 420 * q^56 - 660 * q^57 + 444 * q^58 - 112 * q^59 - 770 * q^60 - 546 * q^61 - 266 * q^62 + 392 * q^63 - 668 * q^64 - 1368 * q^65 - 770 * q^66 + 740 * q^67 + 1568 * q^68 + 1540 * q^69 + 12 * q^70 - 432 * q^71 + 840 * q^72 - 350 * q^73 - 182 * q^74 + 3080 * q^75 + 196 * q^76 + 1148 * q^77 - 880 * q^78 + 152 * q^79 + 574 * q^80 + 1402 * q^81 - 154 * q^82 - 3808 * q^83 - 1540 * q^84 + 96 * q^85 - 268 * q^86 - 1540 * q^87 - 840 * q^88 - 112 * q^89 + 392 * q^90 - 1076 * q^91 + 798 * q^92 - 770 * q^93 + 252 * q^94 - 908 * q^95 + 546 * q^97 + 478 * q^98 - 784 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	−0.940775	−	0.339032i	$-0.889900\pi$
$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	0.763998	+	0.645219i	$0.223234\pi$
$3$	−3.70810	+	6.42262i	−0.713624	+	1.23603i	0.249864	+	0.968281i	$0.419614\pi$
$3$	−3.70810	+	6.42262i	−0.713624	+	1.23603i	−0.963488	+	0.267752i	$0.913719\pi$
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	7.20810	−	12.4848i	0.644712	−	1.11667i	−0.339656	−	0.940550i	$-0.610311\pi$
$5$	7.20810	−	12.4848i	0.644712	−	1.11667i	0.984368	−	0.176124i	$-0.0563560\pi$
$6$	−3.70810	−	6.42262i	−0.252304	−	0.437004i
$7$	0.416198			0.0224726			0.0112363	−	0.999937i	$-0.496423\pi$
$7$	0.416198			0.0224726			0.0112363	+	0.999937i	$0.496423\pi$
$8$	−15.0000			−0.662913
$9$	−14.0000	−	24.2487i	−0.518519	−	0.898100i
$10$	7.20810	+	12.4848i	0.227940	+	0.394804i
$11$	65.9134			1.80669			0.903347	−	0.428910i	$-0.141102\pi$
$11$	65.9134			1.80669			0.903347	+	0.428910i	$0.141102\pi$
$12$	−51.9134			−1.24884
$13$	−22.6648	−	39.2566i	−0.483545	−	0.837524i	0.516277	−	0.856422i	$-0.327318\pi$
$13$	−22.6648	−	39.2566i	−0.483545	−	0.837524i	−0.999821	+	0.0188977i	$0.993984\pi$
$14$	−0.208099	+	0.360438i	−0.00397263	+	0.00688080i
$15$	53.4567	+	92.5897i	0.920164	+	1.59377i
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	−1.66479	+	2.88351i	−0.0237513	+	0.0411384i	−0.877657	−	0.479290i	$-0.840894\pi$
$17$	−1.66479	+	2.88351i	−0.0237513	+	0.0411384i	0.853905	+	0.520428i	$0.174228\pi$
$18$	28.0000			0.366648
$19$	−82.3729	+	8.58525i	−0.994613	+	0.103663i
$19$	−82.3729	+	8.58525i	−0.994613	+	0.103663i
$20$	100.913			1.12825
$21$	−1.54331	+	2.67308i	−0.0160370	+	0.0277769i
$22$	−32.9567	+	57.0827i	−0.319381	+	0.553185i
$23$	−54.4567	−	94.3218i	−0.493696	−	0.855106i	0.506278	−	0.862370i	$-0.331021\pi$
$23$	−54.4567	−	94.3218i	−0.493696	−	0.855106i	−0.999974	+	0.00726411i	$0.997688\pi$
$24$	55.6215	−	96.3392i	0.473070	−	0.819382i
$25$	−41.4134	−	71.7301i	−0.331307	−	0.573841i
$26$	45.3296			0.341918
$27$	7.41620			0.0528610
$28$	1.45669	+	2.52307i	0.00983177	+	0.0170291i
$29$	−29.5433	−	51.1705i	−0.189174	−	0.327659i	0.755801	−	0.654801i	$-0.227248\pi$
$29$	−29.5433	−	51.1705i	−0.189174	−	0.327659i	−0.944975	+	0.327142i	$0.893914\pi$
$30$	−106.913			−0.650654
$31$	184.913			1.07134			0.535668	−	0.844429i	$-0.320060\pi$
$31$	184.913			1.07134			0.535668	+	0.844429i	$0.320060\pi$
$32$	−80.5000	−	139.430i	−0.444704	−	0.770250i
$33$	−244.413	+	423.336i	−1.28930	+	2.23313i
$34$	−1.66479	−	2.88351i	−0.00839735	−	0.0145446i
$35$	3.00000	−	5.19615i	0.0144884	−	0.0250946i
$36$	98.0000	−	169.741i	0.453704	−	0.785838i
$37$	142.913			0.634995			0.317498	−	0.948259i	$-0.397157\pi$
$37$	142.913			0.634995			0.317498	+	0.948259i	$0.397157\pi$
$38$	33.7514	−	75.6296i	0.144084	−	0.322862i
$39$	336.173			1.38028
$40$	−108.121	+	187.272i	−0.427388	+	0.740257i
$41$	87.5754	−	151.685i	0.333585	−	0.577786i	−0.649627	−	0.760253i	$-0.725075\pi$
$41$	87.5754	−	151.685i	0.333585	−	0.577786i	0.983212	+	0.182467i	$0.0584083\pi$
$42$	−1.54331	−	2.67308i	−0.00566993	−	0.00982061i
$43$	−222.740	+	385.797i	−0.789943	+	1.36822i	0.136058	+	0.990701i	$0.456557\pi$
$43$	−222.740	+	385.797i	−0.789943	+	1.36822i	−0.926001	+	0.377521i	$0.876777\pi$
$44$	230.697	+	399.579i	0.790429	+	1.36906i
$45$	−403.654			−1.33718
$46$	108.913			0.349096
$47$	−87.1215	−	150.899i	−0.270382	−	0.468316i	0.698577	−	0.715535i	$-0.253817\pi$
$47$	−87.1215	−	150.899i	−0.270382	−	0.468316i	−0.968960	+	0.247218i	$0.920483\pi$
$48$	−152.032	−	263.327i	−0.457165	−	0.791834i
$49$	−342.827			−0.999495
$50$	82.8268			0.234270
$51$	−12.3464	−	21.3847i	−0.0338990	−	0.0587147i
$52$	158.654	−	274.796i	0.423102	−	0.732834i
$53$	117.173	+	202.950i	0.303679	+	0.525987i	0.976966	−	0.213394i	$-0.0684517\pi$
$53$	117.173	+	202.950i	0.303679	+	0.525987i	−0.673287	+	0.739381i	$0.735118\pi$
$54$	−3.70810	+	6.42262i	−0.00934460	+	0.0161853i
$55$	475.110	−	822.915i	1.16480	−	2.01749i
$56$	−6.24298			−0.0148974
$57$	250.307	−	560.884i	0.581649	−	1.30335i
$58$	59.0866			0.133766
$59$	−76.2053	+	131.991i	−0.168154	+	0.291251i	−0.937771	−	0.347255i	$-0.887114\pi$
$59$	−76.2053	+	131.991i	−0.168154	+	0.291251i	0.769617	+	0.638506i	$0.220447\pi$
$60$	−374.197	+	648.128i	−0.805143	+	1.39455i
$61$	−28.9651	−	50.1691i	−0.0607968	−	0.105303i	0.834025	−	0.551727i	$-0.186031\pi$
$61$	−28.9651	−	50.1691i	−0.0607968	−	0.105303i	−0.894822	+	0.446424i	$0.852697\pi$
$62$	−92.4567	+	160.140i	−0.189387	+	0.328028i
$63$	−5.82678	−	10.0923i	−0.0116525	−	0.0201827i
$64$	−167.000			−0.326172
$65$	−653.480			−1.24699
$66$	−244.413	−	423.336i	−0.455836	−	0.789532i
$67$	418.610	+	725.054i	0.763304	+	1.32208i	0.941138	+	0.338021i	$0.109758\pi$
$67$	418.610	+	725.054i	0.763304	+	1.32208i	−0.177834	+	0.984060i	$0.556909\pi$
$68$	−23.3071			−0.0415647
$69$	807.723			1.40925
$70$	3.00000	+	5.19615i	0.00512241	+	0.00887227i
$71$	−263.740	+	456.811i	−0.440848	+	0.763571i	−0.997753	−	0.0670055i	$-0.978656\pi$
$71$	−263.740	+	456.811i	−0.440848	+	0.763571i	0.556905	+	0.830576i	$0.311989\pi$
$72$	210.000	+	363.731i	0.343732	+	0.595362i
$73$	−109.749	+	190.090i	−0.175960	+	0.304772i	−0.940493	−	0.339813i	$-0.889636\pi$
$73$	−109.749	+	190.090i	−0.175960	+	0.304772i	0.764533	+	0.644585i	$0.222970\pi$
$74$	−71.4567	+	123.767i	−0.112252	+	0.194427i
$75$	614.260			0.945715
$76$	−340.350	−	469.311i	−0.513696	−	0.708337i
$77$	27.4331			0.0406011
$78$	−168.087	+	291.135i	−0.244001	+	0.422622i
$79$	245.654	−	425.484i	0.349850	−	0.605959i	−0.636372	−	0.771382i	$-0.719566\pi$
$79$	245.654	−	425.484i	0.349850	−	0.605959i	0.986223	+	0.165423i	$0.0528991\pi$
$80$	295.532	+	511.877i	0.413019	+	0.715369i
$81$	350.500	−	607.084i	0.480796	−	0.832762i
$82$	87.5754	+	151.685i	0.117940	+	0.204278i
$83$	−692.433			−0.915716			−0.457858	−	0.889025i	$-0.651383\pi$
$83$	−692.433			−0.915716			−0.457858	+	0.889025i	$0.651383\pi$
$84$	−21.6063			−0.0280647
$85$	24.0000	+	41.5692i	0.0306255	+	0.0530449i
$86$	−222.740	−	385.797i	−0.279287	−	0.483739i
$87$	438.198			0.539997
$88$	−988.701			−1.19768
$89$	−413.642	−	716.450i	−0.492652	−	0.853298i	0.507313	−	0.861762i	$-0.330639\pi$
$89$	−413.642	−	716.450i	−0.492652	−	0.853298i	−0.999964	+	0.00846444i	$0.997306\pi$
$90$	201.827	−	349.574i	0.236382	−	0.409426i
$91$	−9.43305	−	16.3385i	−0.0108665	−	0.0188214i
$92$	381.197	−	660.252i	0.431984	−	0.748218i
$93$	−685.677	+	1187.63i	−0.764531	+	1.32421i
$94$	174.243			0.191189
$95$	−486.567	+	1090.29i	−0.525481	+	1.17749i
$96$	1194.01			1.26941
$97$	366.402	−	634.627i	0.383531	−	0.664295i	−0.608033	−	0.793912i	$-0.708041\pi$
$97$	366.402	−	634.627i	0.383531	−	0.664295i	0.991564	+	0.129616i	$0.0413746\pi$
$98$	171.413	−	296.897i	0.176687	−	0.306032i
$99$	−922.787	−	1598.31i	−0.936804	−	1.62259i
$100$	289.894	−	502.111i	0.289894	−	0.502111i
$101$	−114.099	−	197.625i	−0.112409	−	0.194698i	0.804332	−	0.594180i	$-0.202523\pi$
$101$	−114.099	−	197.625i	−0.112409	−	0.194698i	−0.916741	+	0.399482i	$0.869190\pi$
$102$	24.6929			0.0239702
$103$	775.827			0.742179			0.371090	−	0.928597i	$-0.378984\pi$
$103$	775.827			0.742179			0.371090	+	0.928597i	$0.378984\pi$
$104$	339.972	+	588.849i	0.320548	+	0.555205i
$105$	22.2486	+	38.5357i	0.0206785	+	0.0358162i
$106$	−234.346			−0.214733
$107$	−589.134			−0.532278			−0.266139	−	0.963935i	$-0.585748\pi$
$107$	−589.134			−0.532278			−0.266139	+	0.963935i	$0.585748\pi$
$108$	25.9567	+	44.9583i	0.0231267	+	0.0400566i
$109$	−789.134	+	1366.82i	−0.693443	+	1.20108i	0.277259	+	0.960795i	$0.410574\pi$
$109$	−789.134	+	1366.82i	−0.693443	+	1.20108i	−0.970703	+	0.240284i	$0.922759\pi$
$110$	475.110	+	822.915i	0.411818	+	0.713290i
$111$	−529.937	+	917.878i	−0.453148	+	0.784875i
$112$	−8.53207	+	14.7780i	−0.00719826	+	0.0124677i
$113$	1129.27			0.940111			0.470056	−	0.882637i	$-0.344234\pi$
$113$	1129.27			0.940111			0.470056	+	0.882637i	$0.344234\pi$
$114$	360.587	+	497.215i	0.296246	+	0.408495i
$115$	−1570.12			−1.27317
$116$	206.803	−	358.194i	0.165527	−	0.286702i
$117$	−634.614	+	1099.18i	−0.501454	+	0.868544i
$118$	−76.2053	−	131.991i	−0.0594514	−	0.102973i
$119$	−0.692885	+	1.20011i	−0.000533753	+	0.000924488i
$120$	−801.850	−	1388.85i	−0.609988	−	1.05653i
$121$	3013.57			2.26414
$122$	57.9302			0.0429898
$123$	649.476	+	1124.93i	0.476108	+	0.824644i
$124$	647.197	+	1120.98i	0.468710	+	0.811829i
$125$	607.978			0.435033
$126$	11.6536			0.00823954
$127$	−163.221	−	282.706i	−0.114043	−	0.197528i	0.803354	−	0.595502i	$-0.203047\pi$
$127$	−163.221	−	282.706i	−0.114043	−	0.197528i	−0.917397	+	0.397974i	$0.869714\pi$
$128$	727.500	−	1260.07i	0.502363	−	0.870119i
$129$	−1651.89	−	2861.15i	−1.12744	−	1.95279i
$130$	326.740	−	565.931i	0.220439	−	0.381811i
$131$	−125.812	+	217.912i	−0.0839100	+	0.145336i	−0.904926	−	0.425568i	$-0.860074\pi$
$131$	−125.812	+	217.912i	−0.0839100	+	0.145336i	0.821016	+	0.570905i	$0.193407\pi$
$132$	−3421.79			−2.25628
$133$	−34.2835	+	3.57317i	−0.0223515	+	0.00232957i
$134$	−837.221			−0.539738
$135$	53.4567	−	92.5897i	0.0340801	−	0.0590285i
$136$	24.9719	−	43.2526i	0.0157450	−	0.0272712i
$137$	983.941	+	1704.24i	0.613604	+	1.06279i	0.990628	+	0.136590i	$0.0436142\pi$
$137$	983.941	+	1704.24i	0.613604	+	1.06279i	−0.377024	+	0.926204i	$0.623052\pi$
$138$	−403.862	+	699.509i	−0.249123	+	0.431494i
$139$	466.236	+	807.544i	0.284501	+	0.492770i	0.972488	−	0.232953i	$-0.0748389\pi$
$139$	466.236	+	807.544i	0.284501	+	0.492770i	−0.687987	+	0.725723i	$0.741506\pi$
$140$	42.0000			0.0253546
$141$	1292.22			0.771806
$142$	−263.740	−	456.811i	−0.155863	−	0.269963i
$143$	−1493.91	−	2587.53i	−0.873618	−	1.51315i
$144$	1148.00			0.664352
$145$	−851.804			−0.487852
$146$	−109.749	−	190.090i	−0.0622114	−	0.107753i
$147$	1271.24	−	2201.84i	0.713264	−	1.23541i
$148$	500.197	+	866.366i	0.277810	+	0.481182i
$149$	232.370	−	402.477i	0.127762	−	0.221290i	−0.795047	−	0.606547i	$-0.792554\pi$
$149$	232.370	−	402.477i	0.127762	−	0.221290i	0.922809	+	0.385258i	$0.125887\pi$
$150$	−307.130	+	531.965i	−0.167180	+	0.289565i
$151$	−1917.35			−1.03333			−0.516663	−	0.856189i	$-0.672826\pi$
$151$	−1917.35			−1.03333			−0.516663	+	0.856189i	$0.672826\pi$
$152$	1235.59	−	128.779i	0.659341	−	0.0687193i
$153$	93.2285			0.0492619
$154$	−13.7165	+	23.7577i	−0.00717733	+	0.0124315i
$155$	1332.87	−	2308.61i	0.690703	−	1.19633i
$156$	1176.61	+	2037.94i	0.603871	+	1.04594i
$157$	−320.106	+	554.440i	−0.162721	+	0.281841i	−0.935844	−	0.352415i	$-0.885360\pi$
$157$	−320.106	+	554.440i	−0.162721	+	0.281841i	0.773123	+	0.634257i	$0.218694\pi$
$158$	245.654	+	425.484i	0.123691	+	0.214239i
$159$	−1737.96			−0.866850
$160$	−2321.01			−1.14682
$161$	−22.6648	−	39.2566i	−0.0110946	−	0.0192165i
$162$	350.500	+	607.084i	0.169987	+	0.294426i
$163$	−708.969			−0.340679			−0.170340	−	0.985385i	$-0.554486\pi$
$163$	−708.969			−0.340679			−0.170340	+	0.985385i	$0.554486\pi$
$164$	1226.06			0.583773
$165$	3523.51	+	6102.90i	1.66245	+	2.87946i
$166$	346.217	−	599.665i	0.161877	−	0.280380i
$167$	−712.335	−	1233.80i	−0.330073	−	0.571703i	0.652453	−	0.757829i	$-0.273740\pi$
$167$	−712.335	−	1233.80i	−0.330073	−	0.571703i	−0.982526	+	0.186126i	$0.940407\pi$
$168$	23.1496	−	40.0962i	0.0106311	−	0.0184136i
$169$	71.1142	−	123.173i	0.0323688	−	0.0560644i
$170$	−48.0000			−0.0216555
$171$	1361.40	+	1877.24i	0.608824	+	0.839511i
$172$	−3118.36			−1.38240
$173$	85.7041	−	148.444i	0.0376645	−	0.0652369i	−0.846579	−	0.532264i	$-0.821342\pi$
$173$	85.7041	−	148.444i	0.0376645	−	0.0652369i	0.884243	+	0.467027i	$0.154675\pi$
$174$	−219.099	+	379.491i	−0.0954589	+	0.165340i
$175$	−17.2362	−	29.8540i	−0.00744533	−	0.0128957i
$176$	−1351.22	+	2340.39i	−0.578707	+	1.00235i
$177$	−565.154	−	978.875i	−0.239997	−	0.415688i
$178$	827.285			0.348357
$179$	440.433			0.183908			0.0919539	−	0.995763i	$-0.470689\pi$
$179$	440.433			0.183908			0.0919539	+	0.995763i	$0.470689\pi$
$180$	−1412.79	−	2447.02i	−0.585016	−	1.01328i
$181$	225.004	+	389.719i	0.0924003	+	0.160042i	0.908521	−	0.417840i	$-0.137213\pi$
$181$	225.004	+	389.719i	0.0924003	+	0.160042i	−0.816120	+	0.577882i	$0.803879\pi$
$182$	18.8661			0.00768378
$183$	429.622			0.173544
$184$	816.850	+	1414.83i	0.327277	+	0.566861i
$185$	1030.13	−	1784.24i	0.409389	−	0.709082i
$186$	−685.677	−	1187.63i	−0.270303	−	0.468178i
$187$	−109.732	+	190.062i	−0.0429113	+	0.0743246i
$188$	609.850	−	1056.29i	0.236585	−	0.409777i
$189$	3.08661			0.00118793
$190$	−700.937	−	966.525i	−0.267639	−	0.369048i
$191$	−2890.96			−1.09520			−0.547598	−	0.836741i	$-0.684458\pi$
$191$	−2890.96			−1.09520			−0.547598	+	0.836741i	$0.684458\pi$
$192$	619.253	−	1072.58i	0.232764	−	0.403159i
$193$	1785.48	−	3092.54i	0.665915	−	1.15340i	−0.313121	−	0.949713i	$-0.601374\pi$
$193$	1785.48	−	3092.54i	0.665915	−	1.15340i	0.979036	−	0.203686i	$-0.0652922\pi$
$194$	366.402	+	634.627i	0.135599	+	0.234864i
$195$	2423.17	−	4197.05i	0.889881	−	1.54132i
$196$	−1199.89	−	2078.28i	−0.437279	−	0.757390i
$197$	2644.14			0.956281			0.478140	−	0.878283i	$-0.341311\pi$
$197$	2644.14			0.956281			0.478140	+	0.878283i	$0.341311\pi$
$198$	1845.57			0.662421
$199$	2181.50	+	3778.47i	0.777097	+	1.34597i	0.933608	+	0.358296i	$0.116642\pi$
$199$	2181.50	+	3778.47i	0.777097	+	1.34597i	−0.156511	+	0.987676i	$0.550025\pi$
$200$	621.201	+	1075.95i	0.219628	+	0.380406i
$201$	−6208.99			−2.17885
$202$	228.198			0.0794849
$203$	−12.2959	−	21.2971i	−0.00425124	−	0.00736336i
$204$	86.4251	−	149.693i	0.0296616	−	0.0513754i
$205$	−1262.50	−	2186.72i	−0.430132	−	0.745011i
$206$	−387.913	+	671.886i	−0.131200	+	0.227245i
$207$	−1524.79	+	2641.01i	−0.511981	+	0.886777i
$208$	1858.51			0.619542
$209$	−5429.48	+	565.883i	−1.79696	+	0.187287i
$210$	−44.4972			−0.0146219
$211$	−1285.49	+	2226.53i	−0.419415	+	0.726449i	−0.995881	−	0.0906727i	$-0.971098\pi$
$211$	−1285.49	+	2226.53i	−0.419415	+	0.726449i	0.576465	+	0.817122i	$0.304432\pi$
$212$	−820.213	+	1420.65i	−0.265719	+	0.460239i
$213$	−1955.95	−	3387.80i	−0.629199	−	1.08981i
$214$	294.567	−	510.205i	0.0940943	−	0.162976i
$215$	3211.07	+	5561.73i	1.01857	+	1.76422i
$216$	−111.243			−0.0350422
$217$	76.9607			0.0240757
$218$	−789.134	−	1366.82i	−0.245169	−	0.424646i
$219$	−813.917	−	1409.75i	−0.251139	−	0.434985i
$220$	6651.54			2.03840
$221$	150.929			0.0459392
$222$	−529.937	−	917.878i	−0.160212	−	0.277495i
$223$	−503.831	+	872.661i	−0.151296	+	0.262053i	−0.931704	−	0.363218i	$-0.881678\pi$
$223$	−503.831	+	872.661i	−0.151296	+	0.262053i	0.780408	+	0.625271i	$0.215011\pi$
$224$	−33.5040	−	58.0306i	−0.00999365	−	0.0173095i
$225$	−1159.57	+	2008.44i	−0.343578	+	0.595094i
$226$	−564.634	+	977.975i	−0.166190	+	0.287849i
$227$	1268.86			0.371000			0.185500	−	0.982644i	$-0.440609\pi$
$227$	1268.86			0.371000			0.185500	+	0.982644i	$0.440609\pi$
$228$	4276.26	−	445.689i	1.24211	−	0.129458i
$229$	5310.46			1.53242			0.766212	−	0.642588i	$-0.222139\pi$
$229$	5310.46			1.53242			0.766212	+	0.642588i	$0.222139\pi$
$230$	785.059	−	1359.76i	0.225066	−	0.389826i
$231$	−101.724	+	176.192i	−0.0289739	+	0.0501843i
$232$	443.150	+	767.558i	0.125406	+	0.217210i
$233$	−801.413	+	1388.09i	−0.225332	+	0.390286i	−0.956419	−	0.291998i	$-0.905680\pi$
$233$	−801.413	+	1388.09i	−0.225332	+	0.390286i	0.731087	+	0.682284i	$0.239013\pi$
$234$	−634.614	−	1099.18i	−0.177291	−	0.307077i
$235$	−2511.92			−0.697275
$236$	−1066.87			−0.294269
$237$	1821.82	+	3155.48i	0.499323	+	0.864853i
$238$	−0.692885	−	1.20011i	−0.000188710	−	0.000326856i
$239$	1301.76			0.352318			0.176159	−	0.984362i	$-0.443633\pi$
$239$	1301.76			0.352318			0.176159	+	0.984362i	$0.443633\pi$
$240$	−4383.45			−1.17896
$241$	−3312.57	−	5737.53i	−0.885399	−	1.53356i	−0.845256	−	0.534362i	$-0.820552\pi$
$241$	−3312.57	−	5737.53i	−0.885399	−	1.53356i	−0.0401434	−	0.999194i	$-0.512781\pi$
$242$	−1506.79	+	2609.83i	−0.400248	+	0.693250i
$243$	2699.50	+	4675.66i	0.712645	+	1.23434i
$244$	202.756	−	351.183i	0.0531972	−	0.0921402i
$245$	−2471.13	+	4280.12i	−0.644386	+	1.11611i
$246$	−1298.95			−0.336659
$247$	2203.99	+	3039.09i	0.567760	+	0.782887i
$248$	−2773.70			−0.710202
$249$	2567.61	−	4447.23i	0.653477	−	1.13185i
$250$	−303.989	+	526.524i	−0.0769038	+	0.133201i
$251$	−1302.15	−	2255.39i	−0.327454	−	0.567167i	0.654552	−	0.756017i	$-0.272857\pi$
$251$	−1302.15	−	2255.39i	−0.327454	−	0.567167i	−0.982006	+	0.188850i	$0.939524\pi$
$252$	40.7875	−	70.6459i	0.0101959	−	0.0176598i
$253$	−3589.43	−	6217.07i	−0.891957	−	1.54492i
$254$	326.441			0.0806407
$255$	−355.978			−0.0874203
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$	−468.905	−	812.167i	−0.113811	−	0.197127i	0.803493	−	0.595315i	$-0.202973\pi$
$257$	−468.905	−	812.167i	−0.113811	−	0.197127i	−0.917304	+	0.398188i	$0.869639\pi$
$258$	3303.77			0.797224
$259$	59.4803			0.0142700
$260$	−2287.18	−	3961.51i	−0.545558	−	0.944933i
$261$	−827.213	+	1432.77i	−0.196181	+	0.339795i
$262$	−125.812	−	217.912i	−0.0296667	−	0.0513842i
$263$	3963.82	−	6865.54i	0.929352	−	1.60968i	0.144944	−	0.989440i	$-0.453700\pi$
$263$	3963.82	−	6865.54i	0.929352	−	1.60968i	0.784408	−	0.620245i	$-0.212967\pi$
$264$	3666.20	−	6350.05i	0.854693	−	1.48037i
$265$	3378.38			0.783142
$266$	14.0473	−	31.4769i	0.00323795	−	0.00725555i
$267$	6135.31			1.40627
$268$	−2930.27	+	5075.38i	−0.667891	+	1.15682i
$269$	−4135.22	+	7162.41i	−0.937281	+	1.62342i	−0.166767	+	0.985996i	$0.553333\pi$
$269$	−4135.22	+	7162.41i	−0.937281	+	1.62342i	−0.770515	+	0.637422i	$0.780001\pi$
$270$	53.4567	+	92.5897i	0.0120492	+	0.0208697i
$271$	941.761	−	1631.18i	0.211099	−	0.365635i	−0.740960	−	0.671550i	$-0.765629\pi$
$271$	941.761	−	1631.18i	0.211099	−	0.365635i	0.952059	+	0.305915i	$0.0989624\pi$
$272$	−68.2566	−	118.224i	−0.0152157	−	0.0263543i
$273$	139.915			0.0310184
$274$	−1967.88			−0.433884
$275$	−2729.70	−	4727.97i	−0.598571	−	1.03675i
$276$	2827.03	+	4896.56i	0.616548	+	1.06789i
$277$	−4156.22			−0.901527			−0.450764	−	0.892643i	$-0.648848\pi$
$277$	−4156.22			−0.901527			−0.450764	+	0.892643i	$0.648848\pi$
$278$	−932.471			−0.201172
$279$	−2588.79	−	4483.91i	−0.555508	−	0.962168i
$280$	−45.0000	+	77.9423i	−0.00960452	+	0.0166355i
$281$	2975.03	+	5152.90i	0.631585	+	1.09394i	0.987228	+	0.159315i	$0.0509285\pi$
$281$	2975.03	+	5152.90i	0.631585	+	1.09394i	−0.355643	+	0.934622i	$0.615738\pi$
$282$	−646.110	+	1119.10i	−0.136437	+	0.236316i
$283$	823.354	−	1426.09i	0.172945	−	0.299549i	−0.766504	−	0.642240i	$-0.778005\pi$
$283$	823.354	−	1426.09i	0.172945	−	0.299549i	0.939448	+	0.342691i	$0.111339\pi$
$284$	−3692.36			−0.771484
$285$	−5198.29	−	7167.94i	−1.08042	−	1.48980i
$286$	2987.83			0.617741
$287$	36.4487	−	63.1311i	0.00749652	−	0.0129844i
$288$	−2254.00	+	3904.04i	−0.461174	+	0.798777i
$289$	2450.96	+	4245.18i	0.498872	+	0.864071i
$290$	425.902	−	737.684i	0.0862408	−	0.149373i
$291$	2717.31	+	4706.52i	0.547394	+	0.948114i
$292$	−1536.48			−0.307931
$293$	7119.83			1.41961			0.709804	−	0.704400i	$-0.248784\pi$
$293$	7119.83			1.41961			0.709804	+	0.704400i	$0.248784\pi$
$294$	1271.24	+	2201.84i	0.252177	+	0.436783i
$295$	1098.59	+	1902.81i	0.216822	+	0.375546i
$296$	−2143.70			−0.420946
$297$	488.827			0.0955037
$298$	232.370	+	402.477i	0.0451706	+	0.0782378i
$299$	−2468.50	+	4275.57i	−0.477448	+	0.826965i
$300$	2149.91	+	3723.75i	0.413750	+	0.716636i
$301$	−92.7041	+	160.568i	−0.0177521	+	0.0307475i
$302$	958.677	−	1660.48i	0.182668	−	0.316390i
$303$	1692.36			0.320870
$304$	1383.81	−	3100.82i	0.261075	−	0.585013i
$305$	−835.134			−0.156786
$306$	−46.6142	+	80.7382i	−0.00870836	+	0.0150833i
$307$	2582.54	−	4473.10i	0.480109	−	0.831573i	−0.519631	−	0.854391i	$-0.673930\pi$
$307$	2582.54	−	4473.10i	0.480109	−	0.831573i	0.999740	+	0.0228177i	$0.00726372\pi$
$308$	96.0157	+	166.304i	0.0177630	+	0.0307664i
$309$	−2876.84	+	4982.84i	−0.529637	+	0.917358i
$310$	1332.87	+	2308.61i	0.244201	+	0.422968i
$311$	−828.756			−0.151108			−0.0755538	−	0.997142i	$-0.524072\pi$
$311$	−828.756			−0.151108			−0.0755538	+	0.997142i	$0.524072\pi$
$312$	−5042.60			−0.915003
$313$	−1731.28	−	2998.67i	−0.312645	−	0.541517i	0.666289	−	0.745694i	$-0.267882\pi$
$313$	−1731.28	−	2998.67i	−0.312645	−	0.541517i	−0.978934	+	0.204176i	$0.934548\pi$
$314$	−320.106	−	554.440i	−0.0575306	−	0.0996460i
$315$	−168.000			−0.0300499
$316$	3439.15			0.612238
$317$	2253.11	+	3902.50i	0.399203	+	0.691440i	0.993628	−	0.112712i	$-0.0359536\pi$
$317$	2253.11	+	3902.50i	0.399203	+	0.691440i	−0.594425	+	0.804151i	$0.702620\pi$
$318$	868.980	−	1505.12i	0.153239	−	0.265418i
$319$	−1947.30	−	3372.82i	−0.341780	−	0.591980i
$320$	−1203.75	+	2084.96i	−0.210287	+	0.364228i
$321$	2184.57	−	3783.78i	0.379846	−	0.657913i
$322$	45.3296			0.00784509
$323$	112.378	−	251.816i	0.0193588	−	0.0433789i
$324$	4907.00			0.841392
$325$	−1877.25	+	3251.50i	−0.320404	+	0.554955i
$326$	354.484	−	613.985i	0.0602241	−	0.104311i
$327$	−5852.37	−	10136.6i	−0.989716	−	1.71424i
$328$	−1313.63	+	2275.27i	−0.221138	+	0.383021i
$329$	−36.2598	−	62.8039i	−0.00607620	−	0.0105243i
$330$	−7047.02			−1.17553
$331$	−5665.99			−0.940879			−0.470440	−	0.882432i	$-0.655905\pi$
$331$	−5665.99			−0.940879			−0.470440	+	0.882432i	$0.655905\pi$
$332$	−2423.52	−	4197.65i	−0.400626	−	0.693904i
$333$	−2000.79	−	3465.47i	−0.329257	−	0.570289i
$334$	1424.67			0.233397
$335$	12069.5			1.96845
$336$	−63.2755	−	109.596i	−0.0102737	−	0.0177946i
$337$	−3414.85	+	5914.70i	−0.551985	+	0.956066i	0.446146	+	0.894960i	$0.352796\pi$
$337$	−3414.85	+	5914.70i	−0.551985	+	0.956066i	−0.998131	+	0.0611061i	$0.980537\pi$
$338$	71.1142	+	123.173i	0.0114441	+	0.0198218i
$339$	−4187.44	+	7252.85i	−0.670886	+	1.16201i
$340$	−168.000	+	290.985i	−0.0267973	+	0.0464143i
$341$	12188.3			1.93558
$342$	−2306.44	+	240.387i	−0.364673	+	0.0380077i
$343$	−285.440			−0.0449339
$344$	3341.10	−	5786.96i	0.523663	−	0.907011i
$345$	5822.15	−	10084.3i	0.908562	−	1.57368i
$346$	85.7041	+	148.444i	0.0133164	+	0.0230647i
$347$	2043.22	−	3538.95i	0.316097	−	0.547496i	−0.663573	−	0.748111i	$-0.730961\pi$
$347$	2043.22	−	3538.95i	0.316097	−	0.547496i	0.979670	+	0.200616i	$0.0642942\pi$
$348$	1533.69	+	2656.43i	0.236249	+	0.409195i
$349$	−10392.4			−1.59396			−0.796979	−	0.604007i	$-0.793570\pi$
$349$	−10392.4			−1.59396			−0.796979	+	0.604007i	$0.793570\pi$
$350$	34.4724			0.00526465
$351$	−168.087	−	291.135i	−0.0255607	−	0.0442724i
$352$	−5306.03	−	9190.31i	−0.803444	−	1.39161i
$353$	−7054.66			−1.06369			−0.531843	−	0.846843i	$-0.678501\pi$
$353$	−7054.66			−1.06369			−0.531843	+	0.846843i	$0.678501\pi$
$354$	1130.31			0.169704
$355$	3802.13	+	6585.48i	0.568440	+	0.984567i
$356$	2895.50	−	5015.15i	0.431070	−	0.746636i
$357$	−5.13857	−	8.90027i	−0.000761798	−	0.00131947i
$358$	−220.217	+	381.426i	−0.0325106	+	0.0563101i
$359$	5591.28	−	9684.37i	0.821995	−	1.42374i	−0.0821991	−	0.996616i	$-0.526194\pi$
$359$	5591.28	−	9684.37i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$360$	6054.80			0.886434
$361$	6711.59	−	1414.38i	0.978508	−	0.206208i
$362$	−450.009			−0.0653369
$363$	−11174.6	+	19355.0i	−1.61575	+	2.79856i
$364$	66.0314	−	114.370i	0.00950820	−	0.0164687i
$365$	1582.16	+	2740.38i	0.226887	+	0.392981i
$366$	−214.811	+	372.064i	−0.0306786	+	0.0531368i
$367$	3164.89	+	5481.74i	0.450152	+	0.779686i	0.998395	−	0.0566331i	$-0.0180365\pi$
$367$	3164.89	+	5481.74i	0.450152	+	0.779686i	−0.548243	+	0.836319i	$0.684703\pi$
$368$	4465.45			0.632548
$369$	−4904.22			−0.691880
$370$	1030.13	+	1784.24i	0.144741	+	0.250698i
$371$	48.7673	+	84.4675i	0.00682446	+	0.0118203i
$372$	−9599.48			−1.33793
$373$	−914.614			−0.126962			−0.0634811	−	0.997983i	$-0.520220\pi$
$373$	−914.614			−0.126962			−0.0634811	+	0.997983i	$0.520220\pi$
$374$	−109.732	−	190.062i	−0.0151714	−	0.0262777i
$375$	−2254.44	+	3904.81i	−0.310450	+	0.537716i
$376$	1306.82	+	2263.48i	0.179240	+	0.310453i
$377$	−1339.19	+	2319.54i	−0.182948	+	0.316876i
$378$	−1.54331	+	2.67308i	−0.000209998	+	0.000363726i
$379$	−5052.39			−0.684760			−0.342380	−	0.939562i	$-0.611233\pi$
$379$	−5052.39			−0.684760			−0.342380	+	0.939562i	$0.611233\pi$
$380$	−8312.53	+	866.366i	−1.12217	+	0.116957i
$381$	2420.95			0.325536
$382$	1445.48	−	2503.65i	0.193605	−	0.335334i
$383$	−7129.12	+	12348.0i	−0.951126	+	1.64740i	−0.208130	+	0.978101i	$0.566738\pi$
$383$	−7129.12	+	12348.0i	−0.951126	+	1.64740i	−0.742995	+	0.669297i	$0.766596\pi$
$384$	5395.28	+	9344.91i	0.716997	+	1.24188i
$385$	197.740	−	342.496i	0.0261760	−	0.0453382i
$386$	1785.48	+	3092.54i	0.235437	+	0.407788i
$387$	12473.4			1.63840
$388$	5129.63			0.671179
$389$	−2888.08	−	5002.30i	−0.376430	−	0.651996i	0.614110	−	0.789221i	$-0.289515\pi$
$389$	−2888.08	−	5002.30i	−0.376430	−	0.651996i	−0.990540	+	0.137224i	$0.956182\pi$
$390$	2423.17	+	4197.05i	0.314620	+	0.544939i
$391$	362.637			0.0469036
$392$	5142.40			0.662578
$393$	−933.044	−	1616.08i	−0.119760	−	0.207431i
$394$	−1322.07	+	2289.89i	−0.169048	+	0.292800i
$395$	−3541.39	−	6133.87i	−0.451106	−	0.781338i
$396$	6459.51	−	11188.2i	0.819704	−	1.41977i
$397$	−306.917	+	531.596i	−0.0388003	+	0.0672041i	−0.884773	−	0.466021i	$-0.845687\pi$
$397$	−306.917	+	531.596i	−0.0388003	+	0.0672041i	0.845973	+	0.533226i	$0.179020\pi$
$398$	−4363.00			−0.549491
$399$	104.177	−	233.439i	0.0130712	−	0.0292897i
$400$	3395.90			0.424487
$401$	5005.59	−	8669.94i	0.623360	−	1.07969i	−0.365495	−	0.930813i	$-0.619100\pi$
$401$	5005.59	−	8669.94i	0.623360	−	1.07969i	0.988856	−	0.148878i	$-0.0475663\pi$
$402$	3104.50	−	5377.15i	0.385170	−	0.667134i
$403$	−4191.02	−	7259.07i	−0.518039	−	0.897270i
$404$	798.693	−	1383.38i	0.0983576	−	0.170360i
$405$	−5052.88	−	8751.84i	−0.619949	−	1.07378i
$406$	24.5918			0.00300608
$407$	9419.91			1.14724
$408$	185.197	+	320.770i	0.0224721	+	0.0389227i
$409$	3740.85	+	6479.34i	0.452257	+	0.783332i	0.998526	−	0.0542776i	$-0.0172856\pi$
$409$	3740.85	+	6479.34i	0.452257	+	0.783332i	−0.546269	+	0.837610i	$0.683952\pi$
$410$	2525.01			0.304149
$411$	−14594.2			−1.75153
$412$	2715.39	+	4703.20i	0.324704	+	0.562403i
$413$	−31.7165	+	54.9346i	−0.00377886	+	0.00654517i
$414$	−1524.79	−	2641.01i	−0.181013	−	0.313523i
$415$	−4991.13	+	8644.88i	−0.590373	+	1.02256i
$416$	−3649.03	+	6320.31i	−0.430069	+	0.744901i
$417$	−6915.39			−0.812106
$418$	2224.67	−	4985.01i	0.260316	−	0.583312i
$419$	−10791.7			−1.25825			−0.629125	−	0.777304i	$-0.716587\pi$
$419$	−10791.7			−1.25825			−0.629125	+	0.777304i	$0.716587\pi$
$420$	−155.740	+	269.750i	−0.0180937	+	0.0313392i
$421$	2972.97	−	5149.33i	0.344165	−	0.596112i	−0.641036	−	0.767510i	$-0.721495\pi$
$421$	2972.97	−	5149.33i	0.344165	−	0.596112i	0.985202	+	0.171399i	$0.0548286\pi$
$422$	−1285.49	−	2226.53i	−0.148286	−	0.256838i
$423$	−2439.40	+	4225.17i	−0.280397	+	0.485661i
$424$	−1757.60	−	3044.25i	−0.201313	−	0.348684i
$425$	275.779			0.0314759
$426$	3911.90			0.444911
$427$	−12.0552	−	20.8803i	−0.00136626	−	0.00236644i
$428$	−2061.97	−	3571.43i	−0.232872	−	0.403345i
$429$	22158.3			2.49374
$430$	−6422.13			−0.720239
$431$	−7741.76	−	13409.1i	−0.865214	−	1.49859i	−0.866834	−	0.498596i	$-0.833849\pi$
$431$	−7741.76	−	13409.1i	−0.865214	−	1.49859i	0.00162037	−	0.999999i	$-0.499484\pi$
$432$	−152.032	+	263.327i	−0.0169321	+	0.0293272i
$433$	5495.74	+	9518.91i	0.609951	+	1.05647i	0.991248	+	0.132013i	$0.0421441\pi$
$433$	5495.74	+	9518.91i	0.609951	+	1.05647i	−0.381297	+	0.924452i	$0.624523\pi$
$434$	−38.4803	+	66.6499i	−0.00425603	+	0.00737165i
$435$	3158.57	−	5470.81i	0.348143	−	0.603001i
$436$	−11047.9			−1.21353
$437$	5295.53	+	7302.03i	0.579679	+	0.799322i
$438$	1627.83			0.177582
$439$	7091.38	−	12282.6i	0.770964	−	1.33535i	−0.166071	−	0.986114i	$-0.553108\pi$
$439$	7091.38	−	12282.6i	0.770964	−	1.33535i	0.937035	−	0.349235i	$-0.113559\pi$
$440$	−7126.65	+	12343.7i	−0.772159	+	1.33742i
$441$	4799.57	+	8313.11i	0.518257	+	0.897647i
$442$	−75.4644	+	130.708i	−0.00812099	+	0.0140660i
$443$	−4532.34	−	7850.25i	−0.486091	−	0.841934i	0.513782	−	0.857921i	$-0.328244\pi$
$443$	−4532.34	−	7850.25i	−0.486091	−	0.841934i	−0.999872	+	0.0159875i	$0.994911\pi$
$444$	−7419.12			−0.793009
$445$	−11926.3			−1.27047
$446$	−503.831	−	872.661i	−0.0534913	−	0.0926496i
$447$	1723.30	+	2984.85i	0.182348	+	0.315835i
$448$	−69.5051			−0.00732993
$449$	7195.06			0.756249			0.378125	−	0.925755i	$-0.376569\pi$
$449$	7195.06			0.756249			0.378125	+	0.925755i	$0.376569\pi$
$450$	−1159.57	−	2008.44i	−0.121473	−	0.210398i
$451$	5772.39	−	9998.07i	0.602686	−	1.04388i
$452$	3952.44	+	6845.82i	0.411299	+	0.712390i
$453$	7109.74	−	12314.4i	0.737406	−	1.27722i
$454$	−634.429	+	1098.86i	−0.0655842	+	0.113595i
$455$	−271.978			−0.0280231
$456$	−3754.61	+	8413.27i	−0.385582	+	0.864007i
$457$	8519.82			0.872080			0.436040	−	0.899927i	$-0.356381\pi$
$457$	8519.82			0.872080			0.436040	+	0.899927i	$0.356381\pi$
$458$	−2655.23	+	4598.99i	−0.270897	+	0.469207i
$459$	−12.3464	+	21.3847i	−0.00125552	+	0.00217462i
$460$	−5495.41	−	9518.33i	−0.557010	−	0.964770i
$461$	−5518.91	+	9559.03i	−0.557573	+	0.965745i	0.440125	+	0.897936i	$0.354934\pi$
$461$	−5518.91	+	9559.03i	−0.557573	+	0.965745i	−0.997698	+	0.0678087i	$0.978399\pi$
$462$	−101.724	−	176.192i	−0.0102438	−	0.0177428i
$463$	10524.2			1.05637			0.528187	−	0.849128i	$-0.322872\pi$
$463$	10524.2			1.05637			0.528187	+	0.849128i	$0.322872\pi$
$464$	2422.55			0.242380
$465$	9884.86	+	17121.1i	0.985805	+	1.70746i
$466$	−801.413	−	1388.09i	−0.0796669	−	0.137987i
$467$	8366.46			0.829023			0.414512	−	0.910044i	$-0.363952\pi$
$467$	8366.46			0.829023			0.414512	+	0.910044i	$0.363952\pi$
$468$	−8884.60			−0.877544
$469$	174.225	+	301.766i	0.0171534	+	0.0297106i
$470$	1255.96	−	2175.39i	0.123262	−	0.213496i
$471$	−2373.97	−	4111.83i	−0.232243	−	0.402258i
$472$	1143.08	−	1979.87i	0.111471	−	0.193074i
$473$	−14681.6	+	25429.2i	−1.42719	+	2.47196i
$474$	−3643.63			−0.353075
$475$	4027.16	+	5553.07i	0.389008	+	0.536405i
$476$	−9.70039			−0.000934068
$477$	3280.85	−	5682.60i	0.314926	−	0.545468i
$478$	−650.882	+	1127.36i	−0.0622817	+	0.107875i
$479$	6313.55	+	10935.4i	0.602241	+	1.04311i	0.992481	+	0.122399i	$0.0390586\pi$
$479$	6313.55	+	10935.4i	0.602241	+	1.04311i	−0.390240	+	0.920713i	$0.627608\pi$
$480$	8606.53	−	14906.9i	0.818401	−	1.41751i
$481$	−3239.10	−	5610.29i	−0.307049	−	0.531824i
$482$	6625.13			0.626072
$483$	336.173			0.0316696
$484$	10547.5	+	18268.8i	0.990563	+	1.71571i
$485$	−5282.13	−	9148.91i	−0.494534	−	0.856558i
$486$	−5398.99			−0.503916
$487$	−13305.1			−1.23801			−0.619006	−	0.785386i	$-0.712464\pi$
$487$	−13305.1			−1.23801			−0.619006	+	0.785386i	$0.712464\pi$
$488$	434.477	+	752.536i	0.0403030	+	0.0698068i
$489$	2628.93	−	4553.43i	0.243117	−	0.421091i
$490$	−2471.13	−	4280.12i	−0.227825	−	0.394604i
$491$	−2355.35	+	4079.59i	−0.216488	+	0.374968i	−0.953732	−	0.300658i	$-0.902794\pi$
$491$	−2355.35	+	4079.59i	−0.216488	+	0.374968i	0.737244	+	0.675627i	$0.236127\pi$
$492$	−4546.33	+	7874.48i	−0.416595	+	0.721563i
$493$	196.734			0.0179725
$494$	−3733.93	+	389.166i	−0.340076	+	0.0354441i
$495$	−26606.2			−2.41588
$496$	−3790.72	+	6565.73i	−0.343162	+	0.594375i
$497$	−109.768	+	190.124i	−0.00990700	+	0.0171594i
$498$	2567.61	+	4447.23i	0.231039	+	0.400171i
$499$	8316.55	−	14404.7i	0.746092	−	1.29227i	−0.203591	−	0.979056i	$-0.565261\pi$
$499$	8316.55	−	14404.7i	0.746092	−	1.29227i	0.949683	−	0.313213i	$-0.101405\pi$
$500$	2127.92	+	3685.67i	0.190327	+	0.329656i
$501$	10565.6			0.942191
$502$	2604.30			0.231545
$503$	−10636.3	−	18422.6i	−0.942841	−	1.63305i	−0.760018	−	0.649903i	$-0.774810\pi$
$503$	−10636.3	−	18422.6i	−0.942841	−	1.63305i	−0.182823	−	0.983146i	$-0.558524\pi$
$504$	87.4017	+	151.384i	0.00772456	+	0.0133793i
$505$	−3289.75			−0.289885
$506$	7178.85			0.630709
$507$	527.397	+	913.479i	0.0461983	+	0.0800178i
$508$	1142.54	−	1978.94i	0.0997877	−	0.172837i
$509$	−6197.37	−	10734.2i	−0.539673	−	0.934741i	−0.998921	−	0.0464329i	$-0.985215\pi$
$509$	−6197.37	−	10734.2i	−0.539673	−	0.934741i	0.459249	−	0.888308i	$-0.348119\pi$
$510$	177.989	−	308.286i	0.0154539	−	0.0267669i
$511$	−45.6772	+	79.1152i	−0.00395429	+	0.00684902i
$512$	11521.0			0.994455
$513$	−610.894	+	63.6699i	−0.0525763	+	0.00547972i
$514$	937.810			0.0804767
$515$	5592.24	−	9686.04i	0.478492	−	0.828772i
$516$	11563.2	−	20028.0i	0.986514	−	1.70869i
$517$	−5742.47	−	9946.25i	−0.488498	−	0.846104i
$518$	−29.7402	+	51.5115i	−0.00252260	+	0.00436928i
$519$	635.599	+	1100.89i	0.0537566	+	0.0931092i
$520$	9802.21			0.826644
$521$	1260.78			0.106019			0.0530094	−	0.998594i	$-0.483119\pi$
$521$	1260.78			0.106019			0.0530094	+	0.998594i	$0.483119\pi$
$522$	−827.213	−	1432.77i	−0.0693604	−	0.120136i
$523$	11916.0	+	20639.1i	0.996272	+	1.72559i	0.572849	+	0.819661i	$0.305838\pi$
$523$	11916.0	+	20639.1i	0.996272	+	1.72559i	0.423423	+	0.905932i	$0.360828\pi$
$524$	−1761.36			−0.146842
$525$	255.654			0.0212527
$526$	3963.82	+	6865.54i	0.328576	+	0.569109i
$527$	−307.843	+	533.199i	−0.0254456	+	0.0440731i
$528$	−10020.9	−	17356.8i	−0.825958	−	1.43060i
$529$	152.437	−	264.028i	0.0125287	−	0.0217004i
$530$	−1689.19	+	2925.77i	−0.138441	+	0.239787i
$531$	4267.50			0.348764
$532$	−141.653	−	195.326i	−0.0115441	−	0.0159182i
$533$	−7939.51			−0.645213
$534$	−3067.65	+	5313.33i	−0.248596	+	0.430581i
$535$	−4246.54	+	7355.22i	−0.343166	+	0.594381i
$536$	−6279.15	−	10875.8i	−0.506004	−	0.876425i
$537$	−1633.17	+	2828.73i	−0.131241	+	0.227316i
$538$	−4135.22	−	7162.41i	−0.331379	−	0.573965i
$539$	−22596.9			−1.80578
$540$	748.394			0.0596403
$541$	−2608.91	−	4518.77i	−0.207331	−	0.359107i	0.743542	−	0.668689i	$-0.233144\pi$
$541$	−2608.91	−	4518.77i	−0.207331	−	0.359107i	−0.950873	+	0.309582i	$0.899811\pi$
$542$	941.761	+	1631.18i	0.0746348	+	0.129271i
$543$	−3337.36			−0.263756
$544$	536.064			0.0422492
$545$	11376.3	+	19704.3i	0.894142	+	1.54870i
$546$	−69.9574	+	121.170i	−0.00548333	+	0.00949741i
$547$	−4890.58	−	8470.74i	−0.382278	−	0.662125i	0.609109	−	0.793086i	$-0.291527\pi$
$547$	−4890.58	−	8470.74i	−0.382278	−	0.662125i	−0.991388	+	0.130961i	$0.958194\pi$
$548$	−6887.59	+	11929.7i	−0.536904	+	0.929944i
$549$	−811.023	+	1404.73i	−0.0630485	+	0.109203i
$550$	5459.39			0.423253
$551$	2872.88	+	3961.43i	0.222121	+	0.306284i
$552$	−12115.8			−0.934212
$553$	102.241	−	177.086i	0.00786205	−	0.0136175i
$554$	2078.11	−	3599.39i	0.159369	−	0.276035i
$555$	7639.68	+	13232.3i	0.584300	+	1.01204i
$556$	−3263.65	+	5652.81i	−0.248938	+	0.431173i
$557$	9769.78	+	16921.8i	0.743194	+	1.28725i	0.951034	+	0.309086i	$0.100023\pi$
$557$	9769.78	+	16921.8i	0.743194	+	1.28725i	−0.207840	+	0.978163i	$0.566643\pi$
$558$	5177.57			0.392803
$559$	20193.4			1.52789
$560$	123.000	+	213.042i	0.00928160	+	0.0160762i
$561$	−813.796	−	1409.54i	−0.0612451	−	0.106080i
$562$	−5950.06			−0.446598
$563$	6348.35			0.475224			0.237612	−	0.971360i	$-0.423635\pi$
$563$	6348.35			0.475224			0.237612	+	0.971360i	$0.423635\pi$
$564$	4522.77	+	7833.67i	0.337665	+	0.584853i
$565$	8139.87	−	14098.7i	0.606101	−	1.04980i
$566$	823.354	+	1426.09i	0.0611451	+	0.105906i
$567$	145.878	−	252.667i	0.0108047	−	0.0187143i
$568$	3956.10	−	6852.17i	0.292244	−	0.506181i
$569$	−21005.9			−1.54765			−0.773824	−	0.633401i	$-0.781658\pi$
$569$	−21005.9			−1.54765			−0.773824	+	0.633401i	$0.781658\pi$
$570$	8806.77	−	917.878i	0.647149	−	0.0674485i
$571$	−896.764			−0.0657240			−0.0328620	−	0.999460i	$-0.510462\pi$
$571$	−896.764			−0.0657240			−0.0328620	+	0.999460i	$0.510462\pi$
$572$	10457.4	−	18112.7i	0.764415	−	1.32401i
$573$	10720.0	−	18567.5i	0.781559	−	1.35370i
$574$	36.4487	+	63.1311i	0.00265042	+	0.00459066i
$575$	−4510.47	+	7812.37i	−0.327130	+	0.566606i
$576$	2338.00	+	4049.53i	0.169126	+	0.292935i
$577$	−21971.7			−1.58526			−0.792630	−	0.609702i	$-0.791289\pi$
$577$	−21971.7			−1.58526			−0.792630	+	0.609702i	$0.791289\pi$
$578$	−4901.91			−0.352756
$579$	13241.5	+	22934.9i	0.950427	+	1.64619i
$580$	−2981.32	−	5163.79i	−0.213435	−	0.369680i
$581$	−288.190			−0.0205785
$582$	−5434.62			−0.387066
$583$	7723.28	+	13377.1i	0.548655	+	0.950298i
$584$	1646.23	−	2851.35i	0.116646	−	0.202037i
$585$	9148.72	+	15846.1i	0.646587	+	1.11992i
$586$	−3559.91	+	6165.95i	−0.250953	+	0.434664i
$587$	1168.92	−	2024.63i	0.0821915	−	0.142360i	−0.822000	−	0.569488i	$-0.807141\pi$
$587$	1168.92	−	2024.63i	0.0821915	−	0.142360i	0.904191	+	0.427128i	$0.140475\pi$
$588$	17797.3			1.24821
$589$	−15231.9	+	1587.53i	−1.06556	+	0.111058i
$590$	−2197.18			−0.153316
$591$	−9804.74	+	16982.3i	−0.682425	+	1.18199i
$592$	−2929.72	+	5074.43i	−0.203397	+	0.352294i
$593$	4055.21	+	7023.83i	0.280822	+	0.486398i	0.971587	−	0.236681i	$-0.0760595\pi$
$593$	4055.21	+	7023.83i	0.280822	+	0.486398i	−0.690765	+	0.723079i	$0.742726\pi$
$594$	−244.413	+	423.336i	−0.0168828	+	0.0292419i
$595$	9.98876	+	17.3010i	0.000688234	+	0.00119206i
$596$	3253.18			0.223583
$597$	−32356.9			−2.21822
$598$	−2468.50	−	4275.57i	−0.168803	−	0.292376i
$599$	−9744.33	−	16877.7i	−0.664679	−	1.15126i	−0.979372	−	0.202064i	$-0.935235\pi$
$599$	−9744.33	−	16877.7i	−0.664679	−	1.15126i	0.314694	−	0.949193i	$-0.398098\pi$
$600$	−9213.90			−0.626926
$601$	−3084.73			−0.209366			−0.104683	−	0.994506i	$-0.533383\pi$
$601$	−3084.73			−0.209366			−0.104683	+	0.994506i	$0.533383\pi$
$602$	−92.7041	−	160.568i	−0.00627631	−	0.0108709i
$603$	11721.1	−	20301.5i	0.791575	−	1.37105i
$604$	−6710.74	−	11623.3i	−0.452080	−	0.783025i
$605$	21722.1	−	37623.9i	1.45972	−	2.52831i
$606$	−846.181	+	1465.63i	−0.0567224	+	0.0982460i
$607$	−13705.6			−0.916463			−0.458231	−	0.888833i	$-0.651517\pi$
$607$	−13705.6			−0.916463			−0.458231	+	0.888833i	$0.651517\pi$
$608$	7828.06	+	10794.1i	0.522154	+	0.720001i
$609$	182.377			0.0121351
$610$	417.567	−	723.247i	0.0277161	−	0.0480056i
$611$	−3949.18	+	6840.18i	−0.261484	+	0.452904i
$612$	326.300	+	565.168i	0.0215521	+	0.0373293i
$613$	−2932.32	+	5078.93i	−0.193206	+	0.334643i	−0.946311	−	0.323258i	$-0.895222\pi$
$613$	−2932.32	+	5078.93i	−0.193206	+	0.334643i	0.753105	+	0.657901i	$0.228555\pi$
$614$	2582.54	+	4473.10i	0.169744	+	0.294006i
$615$	18726.0			1.22781
$616$	−411.496			−0.0269150
$617$	−6835.55	−	11839.5i	−0.446011	−	0.772514i	0.552111	−	0.833771i	$-0.313822\pi$
$617$	−6835.55	−	11839.5i	−0.446011	−	0.772514i	−0.998122	+	0.0612569i	$0.980489\pi$
$618$	−2876.84	−	4982.84i	−0.187255	−	0.324335i
$619$	1574.30			0.102224			0.0511118	−	0.998693i	$-0.483724\pi$
$619$	1574.30			0.102224			0.0511118	+	0.998693i	$0.483724\pi$
$620$	18660.2			1.20873
$621$	−403.862	−	699.509i	−0.0260973	−	0.0452018i
$622$	414.378	−	717.724i	0.0267123	−	0.0462670i
$623$	−172.157	−	298.185i	−0.0110712	−	0.0191758i
$624$	−6891.55	+	11936.5i	−0.442120	+	0.765774i
$625$	9559.04	−	16556.7i	0.611778	−	1.05963i
$626$	3462.57			0.221074
$627$	16498.6	−	36969.8i	1.05086	−	2.35475i
$628$	−4481.48			−0.284762
$629$	−237.921	+	412.092i	−0.0150819	+	0.0261227i
$630$	84.0000	−	145.492i	0.00531213	−	0.00920087i
$631$	11752.8	+	20356.5i	0.741479	+	1.28428i	0.951822	+	0.306652i	$0.0992087\pi$
$631$	11752.8	+	20356.5i	0.741479	+	1.28428i	−0.210343	+	0.977628i	$0.567458\pi$
$632$	−3684.80	+	6382.27i	−0.231920	+	0.401698i
$633$	−9533.44	−	16512.4i	−0.598610	−	1.03682i
$634$	−4506.22			−0.282279
$635$	−4706.04			−0.294100
$636$	−6082.86	−	10535.8i	−0.379247	−	0.656875i
$637$	7770.10	+	13458.2i	0.483301	+	0.837101i
$638$	3894.60			0.241675
$639$	14769.4			0.914351
$640$	−10487.8	−	18165.4i	−0.647759	−	1.12195i
$641$	−4781.18	+	8281.26i	−0.294611	+	0.510281i	−0.974894	−	0.222668i	$-0.928523\pi$
$641$	−4781.18	+	8281.26i	−0.294611	+	0.510281i	0.680284	+	0.732949i	$0.261857\pi$
$642$	2184.57	+	3783.78i	0.134296	+	0.232607i
$643$	−4145.36	+	7179.98i	−0.254241	+	0.440359i	−0.964689	−	0.263391i	$-0.915159\pi$
$643$	−4145.36	+	7179.98i	−0.254241	+	0.440359i	0.710448	+	0.703750i	$0.248492\pi$
$644$	158.654	−	274.796i	0.00970780	−	0.0168144i
$645$	−47627.8			−2.90751
$646$	161.890	+	223.230i	0.00985984	+	0.0135958i
$647$	13673.8			0.830870			0.415435	−	0.909623i	$-0.363629\pi$
$647$	13673.8			0.830870			0.415435	+	0.909623i	$0.363629\pi$
$648$	−5257.50	+	9106.26i	−0.318725	+	0.552049i
$649$	−5022.95	+	8700.00i	−0.303803	+	0.526202i
$650$	−1877.25	−	3251.50i	−0.113280	−	0.196206i
$651$	−285.378	+	494.289i	−0.0171810	+	0.0297584i
$652$	−2481.39	−	4297.89i	−0.149047	−	0.258157i
$653$	941.670			0.0564325			0.0282162	−	0.999602i	$-0.491017\pi$
$653$	941.670			0.0564325			0.0282162	+	0.999602i	$0.491017\pi$
$654$	11704.7			0.699835
$655$	1813.72	+	3141.46i	0.108196	+	0.187400i
$656$	3590.59	+	6219.08i	0.213703	+	0.370144i
$657$	6145.92			0.364955
$658$	72.5197			0.00429652
$659$	−8316.68	−	14404.9i	−0.491611	−	0.851495i	0.508342	−	0.861155i	$-0.330259\pi$
$659$	−8316.68	−	14404.9i	−0.491611	−	0.851495i	−0.999953	+	0.00965969i	$0.996925\pi$
$660$	−24664.6	+	42720.3i	−1.45465	+	2.51952i
$661$	9385.58	+	16256.3i	0.552279	+	0.956576i	0.998110	+	0.0614585i	$0.0195752\pi$
$661$	9385.58	+	16256.3i	0.552279	+	0.956576i	−0.445830	+	0.895118i	$0.647091\pi$
$662$	2833.00	−	4906.89i	0.166326	−	0.288084i
$663$	−559.659	+	969.358i	−0.0327833	+	0.0567824i
$664$	10386.5			0.607039
$665$	−202.508	+	453.778i	−0.0118089	+	0.0264613i
$666$	4001.57			0.232820
$667$	−3217.66	+	5573.15i	−0.186789	+	0.323528i
$668$	4986.35	−	8636.61i	0.288814	−	0.500240i
$669$	−3736.51	−	6471.83i	−0.215937	−	0.374014i
$670$	−6034.77	+	10452.5i	−0.347975	+	0.602711i
$671$	−1909.19	−	3306.81i	−0.109841	−	0.190251i
$672$	496.944			0.0285268
$673$	29366.8			1.68203			0.841017	−	0.541009i	$-0.181958\pi$
$673$	29366.8			1.68203			0.841017	+	0.541009i	$0.181958\pi$
$674$	−3414.85	−	5914.70i	−0.195156	−	0.338020i
$675$	−307.130	−	531.965i	−0.0175132	−	0.0303338i
$676$	995.599			0.0566454
$677$	−5330.95			−0.302636			−0.151318	−	0.988485i	$-0.548352\pi$
$677$	−5330.95			−0.302636			−0.151318	+	0.988485i	$0.548352\pi$
$678$	−4187.44	−	7252.85i	−0.237194	−	0.410832i
$679$	152.496	−	264.131i	0.00861894	−	0.0149284i
$680$	−360.000	−	623.538i	−0.0203020	−	0.0351641i
$681$	−4705.05	+	8149.39i	−0.264755	+	0.458569i
$682$	−6094.13	+	10555.3i	−0.342165	+	0.592647i
$683$	27122.2			1.51947			0.759737	−	0.650230i	$-0.225328\pi$
$683$	27122.2			1.51947			0.759737	+	0.650230i	$0.225328\pi$
$684$	−6615.28	+	14823.4i	−0.369797	+	0.828636i
$685$	28369.4			1.58239
$686$	142.720	−	247.198i	0.00794326	−	0.0137581i
$687$	−19691.7	+	34107.0i	−1.09357	+	1.89413i
$688$	−9132.35	−	15817.7i	−0.506057	−	0.876517i
$689$	5311.41	−	9199.64i	0.293685	−	0.508677i
$690$	5822.15	+	10084.3i	0.321225	+	0.556379i
$691$	13894.6			0.764945			0.382473	−	0.923967i	$-0.375073\pi$
$691$	13894.6			0.764945			0.382473	+	0.923967i	$0.375073\pi$
$692$	1199.86			0.0659129
$693$	−384.063	−	665.216i	−0.0210524	−	0.0364639i
$694$	2043.22	+	3538.95i	0.111757	+	0.193569i
$695$	13442.7			0.733684
$696$	−6572.97			−0.357971
$697$	291.590	+	505.049i	0.0158461	+	0.0274463i
$698$	5196.19	−	9000.06i	0.281775	−	0.488048i
$699$	−5943.44	−	10294.3i	−0.321605	−	0.557035i
$700$	120.653	−	208.978i	0.00651467	−	0.0112837i
$701$	8057.12	−	13955.3i	0.434113	−	0.751906i	−0.563110	−	0.826382i	$-0.690395\pi$
$701$	8057.12	−	13955.3i	0.434113	−	0.751906i	0.997223	+	0.0744764i	$0.0237286\pi$
$702$	336.173			0.0180741
$703$	−11772.2	+	1226.95i	−0.631574	+	0.0658253i
$704$	−11007.5			−0.589293
$705$	9314.45	−	16133.1i	0.497592	−	0.861855i
$706$	3527.33	−	6109.51i	0.188035	−	0.325686i
$707$	−47.4878	−	82.2513i	−0.00252612	−	0.00437536i
$708$	3956.07	−	6852.12i	0.209998	−	0.363727i
$709$	−790.511	−	1369.21i	−0.0418735	−	0.0725270i	0.844329	−	0.535825i	$-0.179999\pi$
$709$	−790.511	−	1369.21i	−0.0418735	−	0.0725270i	−0.886203	+	0.463298i	$0.846666\pi$
$710$	−7604.26			−0.401948
$711$	−13756.6			−0.725616
$712$	6204.63	+	10746.7i	0.326585	+	0.565662i
$713$	−10069.8	−	17441.4i	−0.528914	−	0.916107i
$714$	10.2771			0.000538673
$715$	−43073.1			−2.25293
$716$	1541.52	+	2669.98i	0.0804597	+	0.139360i
$717$	−4827.07	+	8360.73i	−0.251423	+	0.435477i
$718$	5591.28	+	9684.37i	0.290619	+	0.503367i
$719$	−8113.04	+	14052.2i	−0.420814	+	0.728872i	−0.996019	−	0.0891376i	$-0.971589\pi$
$719$	−8113.04	+	14052.2i	−0.420814	+	0.728872i	0.575205	+	0.818009i	$0.304922\pi$
$720$	8274.90	−	14332.5i	0.428316	−	0.741864i
$721$	322.898			0.0166787
$722$	−2130.90	+	6519.60i	−0.109839	+	0.336059i
$723$	49133.3			2.52737
$724$	−1575.03	+	2728.03i	−0.0808502	+	0.140037i
$725$	−2446.98	+	4238.29i	−0.125350	+	0.217112i
$726$	−11174.6	−	19355.0i	−0.571253	−	0.989439i
$727$	11537.6	−	19983.7i	0.588590	−	1.01947i	−0.405827	−	0.913950i	$-0.633016\pi$
$727$	11537.6	−	19983.7i	0.588590	−	1.01947i	0.994417	−	0.105518i	$-0.0336502\pi$
$728$	141.496	+	245.078i	0.00720355	+	0.0124769i
$729$	−21113.0			−1.07265
$730$	−3164.32			−0.160434
$731$	−741.633	−	1284.55i	−0.0375243	−	0.0649940i
$732$	1503.68	+	2604.45i	0.0759256	+	0.131507i
$733$	−19437.2			−0.979439			−0.489719	−	0.871880i	$-0.662901\pi$
$733$	−19437.2			−0.979439			−0.489719	+	0.871880i	$0.662901\pi$
$734$	−6329.77			−0.318305
$735$	−18326.4	−	31742.2i	−0.919699	−	1.59297i
$736$	−8767.53	+	15185.8i	−0.439097	+	0.760538i
$737$	27592.0	+	47790.8i	1.37906	+	2.38860i
$738$	2452.11	−	4247.18i	0.122308	−	0.211844i
$739$	3891.52	−	6740.30i	0.193710	−	0.335516i	−0.752767	−	0.658287i	$-0.771281\pi$
$739$	3891.52	−	6740.30i	0.193710	−	0.335516i	0.946477	+	0.322772i	$0.104615\pi$
$740$	14421.9			0.716431
$741$	−27691.6	+	2886.13i	−1.37284	+	0.143083i
$742$	−97.5346			−0.00482562
$743$	2786.72	−	4826.75i	0.137598	−	0.238326i	−0.788989	−	0.614407i	$-0.789395\pi$
$743$	2786.72	−	4826.75i	0.137598	−	0.238326i	0.926587	+	0.376081i	$0.122729\pi$
$744$	10285.2	−	17814.4i	0.506817	−	0.877834i
$745$	−3349.89	−	5802.19i	−0.164739	−	0.285336i
$746$	457.307	−	792.079i	0.0224440	−	0.0388741i
$747$	9694.06	+	16790.6i	0.474816	+	0.822405i
$748$	−1536.25			−0.0750948
$749$	−245.197			−0.0119617
$750$	−2254.44	−	3904.81i	−0.109761	−	0.190111i
$751$	−14862.4	−	25742.5i	−0.722155	−	1.25081i	−0.960134	−	0.279539i	$-0.909818\pi$
$751$	−14862.4	−	25742.5i	−0.722155	−	1.25081i	0.237979	−	0.971270i	$-0.423515\pi$
$752$	7143.96			0.346428
$753$	19314.0			0.934716
$754$	−1339.19	−	2319.54i	−0.0646821	−	0.112033i
$755$	−13820.5	+	23937.8i	−0.666197	+	1.15389i
$756$	10.8031	+	18.7116i	0.000519717	+	0.000900177i
$757$	6077.39	−	10526.4i	0.291792	−	0.505399i	−0.682441	−	0.730940i	$-0.739082\pi$
$757$	6077.39	−	10526.4i	0.291792	−	0.505399i	0.974234	+	0.225541i	$0.0724151\pi$
$758$	2526.20	−	4375.50i	0.121050	−	0.209664i
$759$	53239.8			2.54609
$760$	7298.50	−	16354.4i	0.348348	−	0.780573i
$761$	−25318.1			−1.20602			−0.603010	−	0.797734i	$-0.706032\pi$
$761$	−25318.1			−1.20602			−0.603010	+	0.797734i	$0.706032\pi$
$762$	−1210.48	+	2096.61i	−0.0575471	+	0.0996745i
$763$	−328.436	+	568.868i	−0.0155835	+	0.0269914i
$764$	−10118.4	−	17525.5i	−0.479149	−	0.829910i
$765$	672.000	−	1163.94i	0.0317598	−	0.0550095i
$766$	−7129.12	−	12348.0i	−0.336274	−	0.582443i
$767$	6908.71			0.325240
$768$	−882.528			−0.0414655
$769$	−1024.54	−	1774.55i	−0.0480440	−	0.0832147i	0.841003	−	0.541030i	$-0.181965\pi$
$769$	−1024.54	−	1774.55i	−0.0480440	−	0.0832147i	−0.889047	+	0.457815i	$0.848632\pi$
$770$	197.740	+	342.496i	0.00925462	+	0.0160295i
$771$	6954.98			0.324874
$772$	24996.7			1.16535
$773$	−14837.6	−	25699.4i	−0.690389	−	1.19579i	−0.971710	−	0.236175i	$-0.924106\pi$
$773$	−14837.6	−	25699.4i	−0.690389	−	1.19579i	0.281322	−	0.959614i	$-0.409227\pi$
$774$	−6236.72	+	10802.3i	−0.289631	+	0.501656i
$775$	−7657.89	−	13263.9i	−0.354941	−	0.614776i
$776$	−5496.03	+	9519.41i	−0.254248	+	0.440370i
$777$	−220.559	+	382.019i	−0.0101834	+	0.0176382i
$778$	5776.16			0.266176
$779$	−5911.58	+	13246.6i	−0.271893	+	0.609253i
$780$	33924.4			1.55729
$781$	−17384.0	+	30110.0i	−0.796477	+	1.37954i
$782$	−181.318	+	314.053i	−0.00829147	+	0.0143613i
$783$	−219.099	−	379.491i	−0.00999995	−	0.0173204i
$784$	7027.95	−	12172.8i	0.320151	−	0.554517i
$785$	4614.71	+	7992.91i	0.209817	+	0.363413i
$786$	1866.09			0.0846834
$787$	−42499.6			−1.92496			−0.962482	−	0.271345i	$-0.912532\pi$
$787$	−42499.6			−1.92496			−0.962482	+	0.271345i	$0.912532\pi$
$788$	9254.50	+	16029.3i	0.418373	+	0.724643i
$789$	29396.5	+	50916.2i	1.32642	+	2.29742i
$790$	7082.78			0.318980
$791$	470.000			0.0211268
$792$	13841.8	+	23974.7i	0.621019	+	1.07564i
$793$	−1312.98	+	2274.14i	−0.0587959	+	0.101838i
$794$	−306.917	−	531.596i	−0.0137180	−	0.0237602i
$795$	−12527.4	+	21698.1i	−0.558869	+	0.967989i
$796$	−15270.5	+	26449.3i	−0.679960	+	1.17773i
$797$	−10398.1			−0.462131			−0.231065	−	0.972938i	$-0.574221\pi$
$797$	−10398.1			−0.462131			−0.231065	+	0.972938i	$0.574221\pi$
$798$	150.076	+	206.940i	0.00665742	+	0.00917994i
$799$	580.157			0.0256877
$800$	−6667.56	+	11548.5i	−0.294667	+	0.510378i
$801$	−11582.0	+	20060.6i	−0.510898	+	0.884901i
$802$	5005.59	+	8669.94i	0.220391	+	0.381729i
$803$	−7233.90	+	12529.5i	−0.317906	+	0.550630i
$804$	−21731.5	−	37640.0i	−0.953246	−	1.65107i
$805$	−653.480			−0.0286114
$806$	8382.05			0.366309
$807$	−30667.6	−	53117.8i	−1.33773	−	2.31702i
$808$	1711.49	+	2964.38i	0.0745171	+	0.129067i
$809$	−298.449			−0.0129702			−0.00648512	−	0.999979i	$-0.502064\pi$
$809$	−298.449			−0.0129702			−0.00648512	+	0.999979i	$0.502064\pi$
$810$	10105.8			0.438370
$811$	3927.51	+	6802.64i	0.170054	+	0.294541i	0.938438	−	0.345447i	$-0.112273\pi$
$811$	3927.51	+	6802.64i	0.170054	+	0.294541i	−0.768385	+	0.639988i	$0.778939\pi$
$812$	86.0712	−	149.080i	0.00371983	−	0.00644294i
$813$	6984.28	+	12097.1i	0.301291	+	0.521851i
$814$	−4709.95	+	8157.88i	−0.202806	+	0.351270i
$815$	−5110.32	+	8851.33i	−0.219640	+	0.380428i
$816$	1012.41			0.0434331
$817$	15035.6	−	33691.5i	0.643854	−	1.44274i
$818$	−7481.70			−0.319794
$819$	−264.125	+	457.479i	−0.0112690	+	0.0195184i
$820$	8837.53	−	15307.0i	0.376366	−	0.651884i
$821$	9327.00	+	16154.8i	0.396485	+	0.686733i	0.993290	−	0.115654i	$-0.0368964\pi$
$821$	9327.00	+	16154.8i	0.396485	+	0.686733i	−0.596804	+	0.802387i	$0.703563\pi$
$822$	7297.10	−	12639.0i	0.309630	−	0.536294i
$823$	19245.0	+	33333.3i	0.815113	+	1.41182i	0.909247	+	0.416258i	$0.136659\pi$
$823$	19245.0	+	33333.3i	0.815113	+	1.41182i	−0.0941338	+	0.995560i	$0.530008\pi$
$824$	−11637.4			−0.492000
$825$	40487.9			1.70862
$826$	−31.7165	−	54.9346i	−0.00133603	−	0.00231407i
$827$	−7939.76	−	13752.1i	−0.333848	−	0.578242i	0.649415	−	0.760434i	$-0.275014\pi$
$827$	−7939.76	−	13752.1i	−0.333848	−	0.578242i	−0.983263	+	0.182192i	$0.941681\pi$
$828$	−21347.0			−0.895967
$829$	42150.6			1.76592			0.882961	−	0.469446i	$-0.155546\pi$
$829$	42150.6			1.76592			0.882961	+	0.469446i	$0.155546\pi$
$830$	−4991.13	−	8644.88i	−0.208728	−	0.361528i
$831$	15411.7	−	26693.8i	0.643352	−	1.11432i
$832$	3785.02	+	6555.85i	0.157719	+	0.273177i
$833$	570.736	−	988.544i	0.0237393	−	0.0411177i
$834$	3457.70	−	5988.91i	0.143561	−	0.248656i
$835$	−20538.3			−0.851208
$836$	−22433.6	−	30933.9i	−0.928091	−	1.27975i
$837$	1371.35			0.0566320
$838$	5395.83	−	9345.85i	0.222429	−	0.385259i
$839$	−3371.43	+	5839.49i	−0.138730	+	0.240288i	−0.927016	−	0.375021i	$-0.877635\pi$
$839$	−3371.43	+	5839.49i	−0.138730	+	0.240288i	0.788286	+	0.615309i	$0.210969\pi$
$840$	−333.729	−	578.035i	−0.0137080	−	0.0237430i
$841$	10448.9	−	18098.0i	0.428426	−	0.742056i
$842$	2972.97	+	5149.33i	0.121681	+	0.210757i
$843$	−44126.8			−1.80286
$844$	−17996.8			−0.733977
$845$	−1025.20	−	1775.69i	−0.0417371	−	0.0722908i
$846$	−2439.40	−	4225.17i	−0.0991352	−	0.171707i
$847$	1254.25			0.0508812
$848$	−9608.20			−0.389089
$849$	6106.15	+	10576.2i	0.246835	+	0.427530i
$850$	−137.890	+	238.832i	−0.00556420	+	0.00963748i
$851$	−7782.59	−	13479.8i	−0.313494	−	0.542988i
$852$	13691.6	−	23714.6i	0.550549	−	0.953579i
$853$	14559.6	−	25218.0i	0.584422	−	1.01225i	−0.410525	−	0.911849i	$-0.634655\pi$
$853$	14559.6	−	25218.0i	0.584422	−	1.01225i	0.994947	−	0.100400i	$-0.0320121\pi$
$854$	24.1105			0.000966093
$855$	33250.1	−	3465.47i	1.32998	−	0.138616i
$856$	8837.01			0.352854
$857$	788.496	−	1365.72i	0.0314288	−	0.0544364i	−0.849883	−	0.526971i	$-0.823328\pi$
$857$	788.496	−	1365.72i	0.0314288	−	0.0544364i	0.881312	+	0.472535i	$0.156661\pi$
$858$	−11079.2	+	19189.7i	−0.440835	+	0.763548i
$859$	9000.91	+	15590.0i	0.357517	+	0.619237i	0.987545	−	0.157335i	$-0.0502901\pi$
$859$	9000.91	+	15590.0i	0.357517	+	0.619237i	−0.630028	+	0.776572i	$0.716957\pi$
$860$	−22477.5	+	38932.1i	−0.891250	+	1.54369i
$861$	270.311	+	468.193i	0.0106994	+	0.0185319i
$862$	15483.5			0.611799
$863$	−23042.8			−0.908906			−0.454453	−	0.890771i	$-0.650165\pi$
$863$	−23042.8			−0.908906			−0.454453	+	0.890771i	$0.650165\pi$
$864$	−597.004	−	1034.04i	−0.0235075	−	0.0407162i
$865$	−1235.53	−	2140.00i	−0.0485655	−	0.0841180i
$866$	−10991.5			−0.431300
$867$	−36353.6			−1.42403
$868$	269.362	+	466.549i	0.0105331	+	0.0182439i
$869$	16191.9	−	28045.1i	0.632073	−	1.09478i
$870$	3158.57	+	5470.81i	0.123087	+	0.213193i
$871$	18975.4	−	32866.4i	0.738184	−	1.27857i
$872$	11837.0	−	20502.3i	0.459692	−	0.796210i
$873$	−20518.5			−0.795472
$874$	−8971.51	+	935.048i	−0.347215	+	0.0361882i
$875$	253.039			0.00977633
$876$	5697.42	−	9868.22i	0.219747	−	0.380612i
$877$	7637.95	−	13229.3i	0.294088	−	0.509376i	−0.680684	−	0.732577i	$-0.738317\pi$
$877$	7637.95	−	13229.3i	0.294088	−	0.509376i	0.974772	+	0.223201i	$0.0716507\pi$
$878$	7091.38	+	12282.6i	0.272577	+	0.472117i
$879$	−26401.0	+	45727.9i	−1.01307	+	1.75468i
$880$	19479.5	+	33739.5i	0.746198	+	1.29245i
$881$	−18730.1			−0.716270			−0.358135	−	0.933670i	$-0.616587\pi$
$881$	−18730.1			−0.716270			−0.358135	+	0.933670i	$0.616587\pi$
$882$	−9599.15			−0.366463
$883$	6040.26	+	10462.0i	0.230205	+	0.398726i	0.957868	−	0.287208i	$-0.0927271\pi$
$883$	6040.26	+	10462.0i	0.230205	+	0.398726i	−0.727664	+	0.685934i	$0.759394\pi$
$884$	528.251	+	914.958i	0.0200984	+	0.0348115i
$885$	−16294.7			−0.618917
$886$	9064.69			0.343718
$887$	9924.03	+	17188.9i	0.375667	+	0.650674i	0.990427	−	0.138041i	$-0.0440805\pi$
$887$	9924.03	+	17188.9i	0.375667	+	0.650674i	−0.614760	+	0.788714i	$0.710747\pi$
$888$	7949.06	−	13768.2i	0.300397	−	0.520303i
$889$	−67.9321	−	117.662i	−0.00256285	−	0.00443898i
$890$	5963.15	−	10328.5i	0.224590	−	0.389002i
$891$	23102.6	−	40015.0i	0.868651	−	1.50455i
$892$	−7053.64			−0.264768
$893$	8471.95	+	11682.0i	0.317473	+	0.437765i
$894$	−3446.61			−0.128939
$895$	3174.69	−	5498.72i	0.118568	−	0.205365i
$896$	302.784	−	524.438i	0.0112894	−	0.0195538i
$897$	−18306.9	−	31708.5i	−0.681437	−	1.18028i
$898$	−3597.53	+	6231.11i	−0.133687	+	0.231553i
$899$	−5462.95	−	9462.11i	−0.202669	−	0.351033i
$900$	−16234.0			−0.601261
$901$	−780.277			−0.0288511
$902$	5772.39	+	9998.07i	0.213082	+	0.369068i
$903$	−687.512	−	1190.81i	−0.0253366	−	0.0438843i
$904$	−16939.0			−0.623212
$905$	6487.42			0.238286
$906$	7109.74	+	12314.4i	0.260712	+	0.451567i
$907$	−15976.8	+	27672.6i	−0.584895	+	1.01307i	0.409993	+	0.912089i	$0.365531\pi$
$907$	−15976.8	+	27672.6i	−0.584895	+	1.01307i	−0.994888	+	0.100980i	$0.967802\pi$
$908$	4441.00	+	7692.04i	0.162313	+	0.281134i
$909$	−3194.77	+	5533.51i	−0.116572	+	0.201909i
$910$	135.989	−	235.539i	0.00495383	−	0.00858028i
$911$	37262.5			1.35517			0.677585	−	0.735444i	$-0.263026\pi$
$911$	37262.5			1.35517			0.677585	+	0.735444i	$0.263026\pi$
$912$	14784.1	+	20385.8i	0.536786	+	0.740177i
$913$	−45640.6			−1.65442
$914$	−4259.91	+	7378.38i	−0.154163	+	0.267019i
$915$	3096.76	−	5363.74i	0.111886	−	0.193792i
$916$	18586.6	+	32192.9i	0.670435	+	1.16123i
$917$	−52.3626	+	90.6947i	−0.00188568	+	0.00326609i
$918$	−12.3464	−	21.3847i	−0.000443893	−	0.000768844i
$919$	21349.4			0.766325			0.383163	−	0.923681i	$-0.374835\pi$
$919$	21349.4			0.766325			0.383163	+	0.923681i	$0.374835\pi$
$920$	23551.8			0.843998
$921$	19152.7	+	33173.4i	0.685235	+	1.18686i
$922$	−5518.91	−	9559.03i	−0.197132	−	0.341442i
$923$	23910.5			0.852679
$924$	−1424.14			−0.0507044
$925$	−5918.53	−	10251.2i	−0.210378	−	0.364386i
$926$	−5262.10	+	9114.23i	−0.186742	+	0.323447i
$927$	−10861.6	−	18812.8i	−0.384834	−	0.666552i
$928$	−4756.47	+	8238.45i	−0.168253	+	0.291423i
$929$	−6443.91	+	11161.2i	−0.227576	+	0.394173i	−0.957089	−	0.289794i	$-0.906413\pi$
$929$	−6443.91	+	11161.2i	−0.227576	+	0.394173i	0.729513	+	0.683967i	$0.239747\pi$
$930$	−19769.7			−0.697069
$931$	28239.6	−	2943.25i	0.994110	−	0.103610i
$932$	−11219.8			−0.394331
$933$	3073.11	−	5322.78i	0.107834	−	0.186774i
$934$	−4183.23	+	7245.57i	−0.146552	+	0.253835i
$935$	1581.92	+	2739.97i	0.0553309	+	0.0958359i
$936$	9519.21	−	16487.8i	0.332420	−	0.575769i
$937$	−3581.76	−	6203.78i	−0.124878	−	0.216295i	0.796807	−	0.604234i	$-0.206521\pi$
$937$	−3581.76	−	6203.78i	−0.124878	−	0.216295i	−0.921685	+	0.387938i	$0.873187\pi$
$938$	−348.450			−0.0121293
$939$	25679.1			0.892445
$940$	−8791.72	−	15227.7i	−0.305058	−	0.528376i
$941$	27824.9	+	48194.2i	0.963939	+	1.66959i	0.712438	+	0.701735i	$0.247591\pi$
$941$	27824.9	+	48194.2i	0.963939	+	1.66959i	0.251501	+	0.967857i	$0.419076\pi$
$942$	4747.94			0.164221
$943$	−19076.3			−0.658758
$944$	−3124.42	−	5411.65i	−0.107724	−	0.186583i
$945$	22.2486	−	38.5357i	0.000765870	−	0.00132653i
$946$	−14681.6	−	25429.2i	−0.504586	−	0.873969i
$947$	−14281.7	+	24736.6i	−0.490066	+	0.848819i	−0.999935	−	0.0114331i	$-0.996361\pi$
$947$	−14281.7	+	24736.6i	−0.490066	+	0.848819i	0.509869	+	0.860252i	$0.329694\pi$
$948$	−12752.7	+	22088.3i	−0.436908	+	0.756747i
$949$	9949.72			0.340339
$950$	−6822.68	+	711.088i	−0.233007	+	0.0242850i
$951$	−33419.0			−1.13952
$952$	10.3933	−	18.0017i	0.000353832	−	0.000612855i
$953$	24971.8	−	43252.4i	0.848809	−	1.47018i	−0.0334634	−	0.999440i	$-0.510654\pi$
$953$	24971.8	−	43252.4i	0.848809	−	1.47018i	0.882272	−	0.470740i	$-0.156013\pi$
$954$	3280.85	+	5682.60i	0.111343	+	0.192852i
$955$	−20838.3	+	36093.0i	−0.706086	+	1.22298i
$956$	4556.17	+	7891.53i	0.154139	+	0.266977i
$957$	28883.1			0.975610
$958$	−12627.1			−0.425849
$959$	409.515	+	709.300i	0.0137893	+	0.0238837i
$960$	−8927.27	−	15462.5i	−0.300132	−	0.519843i
$961$	4401.96			0.147761
$962$	6478.21			0.217116
$963$	8247.87	+	14285.7i	0.275996	+	0.478039i
$964$	23188.0	−	40162.7i	0.774724	−	1.34186i
$965$	−25739.8	−	44582.7i	−0.858647	−	1.48722i
$966$	−168.087	+	291.135i	−0.00559845	+	0.00969679i
$967$	−18013.0	+	31199.4i	−0.599026	+	1.03754i	0.393939	+	0.919137i	$0.371112\pi$
$967$	−18013.0	+	31199.4i	−0.599026	+	1.03754i	−0.992965	+	0.118407i	$0.962221\pi$
$968$	−45203.6			−1.50093
$969$	1200.60	+	1655.52i	0.0398029	+	0.0548844i
$970$	10564.3			0.349688
$971$	−437.731	+	758.172i	−0.0144670	+	0.0250576i	−0.873168	−	0.487419i	$-0.837938\pi$
$971$	−437.731	+	758.172i	−0.0144670	+	0.0250576i	0.858701	+	0.512476i	$0.171272\pi$
$972$	−18896.5	+	32729.7i	−0.623564	+	1.08005i
$973$	194.047	+	336.099i	0.00639347	+	0.0110738i
$974$	6652.55	−	11522.6i	0.218852	−	0.379062i
$975$	−13922.1	−	24113.7i	−0.457296	−	0.792059i
$976$	2375.14			0.0778959
$977$	5586.26			0.182928			0.0914638	−	0.995808i	$-0.470845\pi$
$977$	5586.26			0.182928			0.0914638	+	0.995808i	$0.470845\pi$
$978$	2628.93	+	4553.43i	0.0859548	+	0.148878i
$979$	−27264.6	−	47223.6i	−0.890071	−	1.54165i
$980$	−34595.8			−1.12768
$981$	44191.5			1.43825
$982$	−2355.35	−	4079.59i	−0.0765401	−	0.132571i
$983$	−2785.74	+	4825.05i	−0.0903880	+	0.156557i	−0.907674	−	0.419675i	$-0.862144\pi$
$983$	−2785.74	+	4825.05i	−0.0903880	+	0.156557i	0.817286	+	0.576232i	$0.195477\pi$
$984$	−9742.15	−	16873.9i	−0.315618	−	0.546667i
$985$	19059.2	−	33011.6i	0.616526	−	1.06785i
$986$	−98.3670	+	170.377i	−0.00317712	+	0.00550294i
$987$	537.820			0.0173445
$988$	−10709.6	+	23997.8i	−0.344855	+	0.772745i
$989$	48518.8			1.55997
$990$	13303.1	−	23041.6i	0.427071	−	0.739708i
$991$	3647.50	−	6317.65i	0.116919	−	0.202509i	−0.801626	−	0.597825i	$-0.796032\pi$
$991$	3647.50	−	6317.65i	0.116919	−	0.202509i	0.918545	+	0.395316i	$0.129365\pi$
$992$	−14885.5	−	25782.5i	−0.476427	−	0.825196i
$993$	21010.1	−	36390.5i	0.671434	−	1.16296i
$994$	−109.768	−	190.124i	−0.00350265	−	0.00606677i
$995$	62897.9			2.00402
$996$	35946.5			1.14358
$997$	4690.97	+	8124.99i	0.149011	+	0.258095i	0.930862	−	0.365370i	$-0.119058\pi$
$997$	4690.97	+	8124.99i	0.149011	+	0.258095i	−0.781851	+	0.623465i	$0.785724\pi$
$998$	8316.55	+	14404.7i	0.263783	+	0.456886i
$999$	1059.87			0.0335665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.4.c.a.11.1	yes	4
3.2	odd	2		171.4.f.e.163.1		4
4.3	odd	2		304.4.i.c.49.2		4
19.7	even	3	inner	19.4.c.a.7.1	✓	4
19.8	odd	6		361.4.a.d.1.1		2
19.11	even	3		361.4.a.g.1.2		2
57.26	odd	6		171.4.f.e.64.1		4
76.7	odd	6		304.4.i.c.273.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.c.a.7.1	✓	4	19.7	even	3	inner
19.4.c.a.11.1	yes	4	1.1	even	1	trivial
171.4.f.e.64.1		4	57.26	odd	6
171.4.f.e.163.1		4	3.2	odd	2
304.4.i.c.49.2		4	4.3	odd	2
304.4.i.c.273.2		4	76.7	odd	6
361.4.a.d.1.1		2	19.8	odd	6
361.4.a.g.1.2		2	19.11	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-3.70810 + 6.42262i) q^{3} +(3.50000 + 6.06218i) q^{4} +(7.20810 - 12.4848i) q^{5} +(-3.70810 - 6.42262i) q^{6} +0.416198 q^{7} -15.0000 q^{8} +(-14.0000 - 24.2487i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-3.70810 + 6.42262i) q^{3} +(3.50000 + 6.06218i) q^{4} +(7.20810 - 12.4848i) q^{5} +(-3.70810 - 6.42262i) q^{6} +0.416198 q^{7} -15.0000 q^{8} +(-14.0000 - 24.2487i) q^{9} +(7.20810 + 12.4848i) q^{10} +65.9134 q^{11} -51.9134 q^{12} +(-22.6648 - 39.2566i) q^{13} +(-0.208099 + 0.360438i) q^{14} +(53.4567 + 92.5897i) q^{15} +(-20.5000 + 35.5070i) q^{16} +(-1.66479 + 2.88351i) q^{17} +28.0000 q^{18} +(-82.3729 + 8.58525i) q^{19} +100.913 q^{20} +(-1.54331 + 2.67308i) q^{21} +(-32.9567 + 57.0827i) q^{22} +(-54.4567 - 94.3218i) q^{23} +(55.6215 - 96.3392i) q^{24} +(-41.4134 - 71.7301i) q^{25} +45.3296 q^{26} +7.41620 q^{27} +(1.45669 + 2.52307i) q^{28} +(-29.5433 - 51.1705i) q^{29} -106.913 q^{30} +184.913 q^{31} +(-80.5000 - 139.430i) q^{32} +(-244.413 + 423.336i) q^{33} +(-1.66479 - 2.88351i) q^{34} +(3.00000 - 5.19615i) q^{35} +(98.0000 - 169.741i) q^{36} +142.913 q^{37} +(33.7514 - 75.6296i) q^{38} +336.173 q^{39} +(-108.121 + 187.272i) q^{40} +(87.5754 - 151.685i) q^{41} +(-1.54331 - 2.67308i) q^{42} +(-222.740 + 385.797i) q^{43} +(230.697 + 399.579i) q^{44} -403.654 q^{45} +108.913 q^{46} +(-87.1215 - 150.899i) q^{47} +(-152.032 - 263.327i) q^{48} -342.827 q^{49} +82.8268 q^{50} +(-12.3464 - 21.3847i) q^{51} +(158.654 - 274.796i) q^{52} +(117.173 + 202.950i) q^{53} +(-3.70810 + 6.42262i) q^{54} +(475.110 - 822.915i) q^{55} -6.24298 q^{56} +(250.307 - 560.884i) q^{57} +59.0866 q^{58} +(-76.2053 + 131.991i) q^{59} +(-374.197 + 648.128i) q^{60} +(-28.9651 - 50.1691i) q^{61} +(-92.4567 + 160.140i) q^{62} +(-5.82678 - 10.0923i) q^{63} -167.000 q^{64} -653.480 q^{65} +(-244.413 - 423.336i) q^{66} +(418.610 + 725.054i) q^{67} -23.3071 q^{68} +807.723 q^{69} +(3.00000 + 5.19615i) q^{70} +(-263.740 + 456.811i) q^{71} +(210.000 + 363.731i) q^{72} +(-109.749 + 190.090i) q^{73} +(-71.4567 + 123.767i) q^{74} +614.260 q^{75} +(-340.350 - 469.311i) q^{76} +27.4331 q^{77} +(-168.087 + 291.135i) q^{78} +(245.654 - 425.484i) q^{79} +(295.532 + 511.877i) q^{80} +(350.500 - 607.084i) q^{81} +(87.5754 + 151.685i) q^{82} -692.433 q^{83} -21.6063 q^{84} +(24.0000 + 41.5692i) q^{85} +(-222.740 - 385.797i) q^{86} +438.198 q^{87} -988.701 q^{88} +(-413.642 - 716.450i) q^{89} +(201.827 - 349.574i) q^{90} +(-9.43305 - 16.3385i) q^{91} +(381.197 - 660.252i) q^{92} +(-685.677 + 1187.63i) q^{93} +174.243 q^{94} +(-486.567 + 1090.29i) q^{95} +1194.01 q^{96} +(366.402 - 634.627i) q^{97} +(171.413 - 296.897i) q^{98} +(-922.787 - 1598.31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 14 q^{4} + 14 q^{5} - 28 q^{7} - 60 q^{8} - 56 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 14 * q^4 + 14 * q^5 - 28 * q^7 - 60 * q^8 - 56 * q^9	\( 4 q - 2 q^{2} + 14 q^{4} + 14 q^{5} - 28 q^{7} - 60 q^{8} - 56 q^{9} + 14 q^{10} + 56 q^{11} + 28 q^{13} + 14 q^{14} + 110 q^{15} - 82 q^{16} + 112 q^{17} + 112 q^{18} - 196 q^{19} + 196 q^{20} - 110 q^{21} - 28 q^{22} - 114 q^{23} + 42 q^{25} - 56 q^{26} - 98 q^{28} - 222 q^{29} - 220 q^{30} + 532 q^{31} - 322 q^{32} - 770 q^{33} + 112 q^{34} + 12 q^{35} + 392 q^{36} + 364 q^{37} + 224 q^{38} + 1760 q^{39} - 210 q^{40} - 154 q^{41} - 110 q^{42} - 268 q^{43} + 196 q^{44} - 784 q^{45} + 228 q^{46} - 126 q^{47} - 956 q^{49} - 84 q^{50} - 880 q^{51} - 196 q^{52} + 884 q^{53} + 966 q^{55} + 420 q^{56} - 660 q^{57} + 444 q^{58} - 112 q^{59} - 770 q^{60} - 546 q^{61} - 266 q^{62} + 392 q^{63} - 668 q^{64} - 1368 q^{65} - 770 q^{66} + 740 q^{67} + 1568 q^{68} + 1540 q^{69} + 12 q^{70} - 432 q^{71} + 840 q^{72} - 350 q^{73} - 182 q^{74} + 3080 q^{75} + 196 q^{76} + 1148 q^{77} - 880 q^{78} + 152 q^{79} + 574 q^{80} + 1402 q^{81} - 154 q^{82} - 3808 q^{83} - 1540 q^{84} + 96 q^{85} - 268 q^{86} - 1540 q^{87} - 840 q^{88} - 112 q^{89} + 392 q^{90} - 1076 q^{91} + 798 q^{92} - 770 q^{93} + 252 q^{94} - 908 q^{95} + 546 q^{97} + 478 q^{98} - 784 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 14 * q^4 + 14 * q^5 - 28 * q^7 - 60 * q^8 - 56 * q^9 + 14 * q^10 + 56 * q^11 + 28 * q^13 + 14 * q^14 + 110 * q^15 - 82 * q^16 + 112 * q^17 + 112 * q^18 - 196 * q^19 + 196 * q^20 - 110 * q^21 - 28 * q^22 - 114 * q^23 + 42 * q^25 - 56 * q^26 - 98 * q^28 - 222 * q^29 - 220 * q^30 + 532 * q^31 - 322 * q^32 - 770 * q^33 + 112 * q^34 + 12 * q^35 + 392 * q^36 + 364 * q^37 + 224 * q^38 + 1760 * q^39 - 210 * q^40 - 154 * q^41 - 110 * q^42 - 268 * q^43 + 196 * q^44 - 784 * q^45 + 228 * q^46 - 126 * q^47 - 956 * q^49 - 84 * q^50 - 880 * q^51 - 196 * q^52 + 884 * q^53 + 966 * q^55 + 420 * q^56 - 660 * q^57 + 444 * q^58 - 112 * q^59 - 770 * q^60 - 546 * q^61 - 266 * q^62 + 392 * q^63 - 668 * q^64 - 1368 * q^65 - 770 * q^66 + 740 * q^67 + 1568 * q^68 + 1540 * q^69 + 12 * q^70 - 432 * q^71 + 840 * q^72 - 350 * q^73 - 182 * q^74 + 3080 * q^75 + 196 * q^76 + 1148 * q^77 - 880 * q^78 + 152 * q^79 + 574 * q^80 + 1402 * q^81 - 154 * q^82 - 3808 * q^83 - 1540 * q^84 + 96 * q^85 - 268 * q^86 - 1540 * q^87 - 840 * q^88 - 112 * q^89 + 392 * q^90 - 1076 * q^91 + 798 * q^92 - 770 * q^93 + 252 * q^94 - 908 * q^95 + 546 * q^97 + 478 * q^98 - 784 * q^99

Introduction

L-functions

Modular forms

Varieties

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