LMFDB - Embedded newform 74.4.c.b.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 84 x^{8} - 140 x^{7} + 6309 x^{6} - 5214 x^{5} + 67648 x^{4} + 164178 x^{3} + 511389 x^{2} + \cdots + 443556 $ x^10 + 84x^8 - 140x^7 + 6309x^6 - 5214x^5 + 67648x^4 + 164178x^3 + 511389x^2 + 497502x + 443556
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			47.4
Root			$2.13869 + 3.70432i$ of defining polynomial
Character	$\chi$	$=$	74.47
Dual form			74.4.c.b.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(1.63869 + 2.83829i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-9.76482 - 16.9132i) q^{5} -6.55476 q^{6} +(-7.16860 - 12.4164i) q^{7} +8.00000 q^{8} +(8.12939 - 14.0805i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(1.63869 + 2.83829i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-9.76482 - 16.9132i) q^{5} -6.55476 q^{6} +(-7.16860 - 12.4164i) q^{7} +8.00000 q^{8} +(8.12939 - 14.0805i) q^{9} +39.0593 q^{10} -40.4367 q^{11} +(6.55476 - 11.3532i) q^{12} +(29.3756 + 50.8801i) q^{13} +28.6744 q^{14} +(32.0030 - 55.4309i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(43.7292 - 75.7411i) q^{17} +(16.2588 + 28.1610i) q^{18} +(-55.4904 - 96.1122i) q^{19} +(-39.0593 + 67.6527i) q^{20} +(23.4942 - 40.6932i) q^{21} +(40.4367 - 70.0384i) q^{22} -124.640 q^{23} +(13.1095 + 22.7064i) q^{24} +(-128.203 + 222.055i) q^{25} -117.503 q^{26} +141.775 q^{27} +(-28.6744 + 49.6655i) q^{28} +169.593 q^{29} +(64.0061 + 110.862i) q^{30} -121.827 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-66.2632 - 114.771i) q^{33} +(87.4583 + 151.482i) q^{34} +(-140.000 + 242.487i) q^{35} -65.0351 q^{36} +(24.0088 + 223.778i) q^{37} +221.962 q^{38} +(-96.2751 + 166.753i) q^{39} +(-78.1186 - 135.305i) q^{40} +(-120.562 - 208.819i) q^{41} +(46.9884 + 81.3864i) q^{42} +222.885 q^{43} +(80.8734 + 140.077i) q^{44} -317.528 q^{45} +(124.640 - 215.882i) q^{46} -242.748 q^{47} -52.4381 q^{48} +(68.7224 - 119.031i) q^{49} +(-256.407 - 444.110i) q^{50} +286.634 q^{51} +(117.503 - 203.520i) q^{52} +(255.140 - 441.915i) q^{53} +(-141.775 + 245.562i) q^{54} +(394.857 + 683.912i) q^{55} +(-57.3488 - 99.3310i) q^{56} +(181.863 - 314.996i) q^{57} +(-169.593 + 293.744i) q^{58} +(138.167 - 239.312i) q^{59} -256.024 q^{60} +(185.389 + 321.103i) q^{61} +(121.827 - 211.010i) q^{62} -233.105 q^{63} +64.0000 q^{64} +(573.696 - 993.670i) q^{65} +265.053 q^{66} +(55.8336 + 96.7066i) q^{67} -349.833 q^{68} +(-204.246 - 353.764i) q^{69} +(-280.000 - 484.975i) q^{70} +(304.129 + 526.767i) q^{71} +(65.0351 - 112.644i) q^{72} -64.7080 q^{73} +(-411.604 - 182.193i) q^{74} -840.343 q^{75} +(-221.962 + 384.449i) q^{76} +(289.874 + 502.077i) q^{77} +(-192.550 - 333.507i) q^{78} +(444.196 + 769.369i) q^{79} +312.474 q^{80} +(12.8325 + 22.2265i) q^{81} +482.247 q^{82} +(643.348 - 1114.31i) q^{83} -187.954 q^{84} -1708.03 q^{85} +(-222.885 + 386.048i) q^{86} +(277.911 + 481.356i) q^{87} -323.493 q^{88} +(-201.644 + 349.257i) q^{89} +(317.528 - 549.975i) q^{90} +(421.164 - 729.478i) q^{91} +(249.279 + 431.765i) q^{92} +(-199.636 - 345.780i) q^{93} +(242.748 - 420.452i) q^{94} +(-1083.71 + 1877.04i) q^{95} +(52.4381 - 90.8254i) q^{96} +1827.81 q^{97} +(137.445 + 238.061i) q^{98} +(-328.726 + 569.369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9	\( 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9} + 4 q^{10} - 80 q^{11} - 20 q^{12} + 73 q^{13} + 4 q^{14} + 113 q^{15} - 80 q^{16} + 69 q^{17} - 76 q^{18} + 33 q^{19} - 4 q^{20} - 109 q^{21} + 80 q^{22} - 524 q^{23} - 40 q^{24} + 132 q^{25} - 292 q^{26} + 898 q^{27} - 4 q^{28} + 296 q^{29} + 226 q^{30} - 784 q^{31} - 160 q^{32} + 124 q^{33} + 138 q^{34} - 263 q^{35} + 304 q^{36} + 24 q^{37} - 132 q^{38} + 679 q^{39} - 8 q^{40} + 345 q^{41} - 218 q^{42} - 492 q^{43} + 160 q^{44} - 1816 q^{45} + 524 q^{46} - 32 q^{47} + 160 q^{48} + 150 q^{49} + 264 q^{50} + 342 q^{51} + 292 q^{52} - 19 q^{53} - 898 q^{54} + 340 q^{55} - 8 q^{56} + 207 q^{57} - 296 q^{58} - 105 q^{59} - 904 q^{60} + 219 q^{61} + 784 q^{62} - 304 q^{63} + 640 q^{64} + 1191 q^{65} - 496 q^{66} + 773 q^{67} - 552 q^{68} + 604 q^{69} - 526 q^{70} + 555 q^{71} - 304 q^{72} + 348 q^{73} + 102 q^{74} - 2952 q^{75} + 132 q^{76} + 884 q^{77} + 1358 q^{78} - 727 q^{79} + 32 q^{80} - 2609 q^{81} - 1380 q^{82} + 2229 q^{83} + 872 q^{84} - 3042 q^{85} + 492 q^{86} + 2660 q^{87} - 640 q^{88} + 901 q^{89} + 1816 q^{90} - 1405 q^{91} + 1048 q^{92} + 3236 q^{93} + 32 q^{94} - 3337 q^{95} - 160 q^{96} - 4596 q^{97} + 300 q^{98} + 6784 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9 + 4 * q^10 - 80 * q^11 - 20 * q^12 + 73 * q^13 + 4 * q^14 + 113 * q^15 - 80 * q^16 + 69 * q^17 - 76 * q^18 + 33 * q^19 - 4 * q^20 - 109 * q^21 + 80 * q^22 - 524 * q^23 - 40 * q^24 + 132 * q^25 - 292 * q^26 + 898 * q^27 - 4 * q^28 + 296 * q^29 + 226 * q^30 - 784 * q^31 - 160 * q^32 + 124 * q^33 + 138 * q^34 - 263 * q^35 + 304 * q^36 + 24 * q^37 - 132 * q^38 + 679 * q^39 - 8 * q^40 + 345 * q^41 - 218 * q^42 - 492 * q^43 + 160 * q^44 - 1816 * q^45 + 524 * q^46 - 32 * q^47 + 160 * q^48 + 150 * q^49 + 264 * q^50 + 342 * q^51 + 292 * q^52 - 19 * q^53 - 898 * q^54 + 340 * q^55 - 8 * q^56 + 207 * q^57 - 296 * q^58 - 105 * q^59 - 904 * q^60 + 219 * q^61 + 784 * q^62 - 304 * q^63 + 640 * q^64 + 1191 * q^65 - 496 * q^66 + 773 * q^67 - 552 * q^68 + 604 * q^69 - 526 * q^70 + 555 * q^71 - 304 * q^72 + 348 * q^73 + 102 * q^74 - 2952 * q^75 + 132 * q^76 + 884 * q^77 + 1358 * q^78 - 727 * q^79 + 32 * q^80 - 2609 * q^81 - 1380 * q^82 + 2229 * q^83 + 872 * q^84 - 3042 * q^85 + 492 * q^86 + 2660 * q^87 - 640 * q^88 + 901 * q^89 + 1816 * q^90 - 1405 * q^91 + 1048 * q^92 + 3236 * q^93 + 32 * q^94 - 3337 * q^95 - 160 * q^96 - 4596 * q^97 + 300 * q^98 + 6784 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	1.63869	+	2.83829i	0.315366	+	0.546230i	0.979515	−	0.201370i	$-0.0645394\pi$
$3$	1.63869	+	2.83829i	0.315366	+	0.546230i	−0.664149	+	0.747600i	$0.731206\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−9.76482	−	16.9132i	−0.873392	−	1.51276i	−0.858466	−	0.512871i	$-0.828582\pi$
$5$	−9.76482	−	16.9132i	−0.873392	−	1.51276i	−0.0149266	−	0.999889i	$-0.504751\pi$
$6$	−6.55476			−0.445995
$7$	−7.16860	−	12.4164i	−0.387068	−	0.670421i	0.604986	−	0.796236i	$-0.293179\pi$
$7$	−7.16860	−	12.4164i	−0.387068	−	0.670421i	−0.992054	+	0.125815i	$0.959845\pi$
$8$	8.00000			0.353553
$9$	8.12939	−	14.0805i	0.301089	−	0.521501i
$10$	39.0593			1.23516
$11$	−40.4367			−1.10837			−0.554187	−	0.832392i	$-0.686971\pi$
$11$	−40.4367			−1.10837			−0.554187	+	0.832392i	$0.686971\pi$
$12$	6.55476	−	11.3532i	0.157683	−	0.273115i
$13$	29.3756	+	50.8801i	0.626718	+	1.08551i	0.988206	+	0.153131i	$0.0489355\pi$
$13$	29.3756	+	50.8801i	0.626718	+	1.08551i	−0.361488	+	0.932377i	$0.617731\pi$
$14$	28.6744			0.547397
$15$	32.0030	−	55.4309i	0.550876	−	0.954146i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	43.7292	−	75.7411i	0.623875	−	1.08058i	−0.364882	−	0.931054i	$-0.618891\pi$
$17$	43.7292	−	75.7411i	0.623875	−	1.08058i	0.988757	−	0.149530i	$-0.0477760\pi$
$18$	16.2588	+	28.1610i	0.212902	+	0.368757i
$19$	−55.4904	−	96.1122i	−0.670020	−	1.16051i	−0.977898	−	0.209083i	$-0.932952\pi$
$19$	−55.4904	−	96.1122i	−0.670020	−	1.16051i	0.307878	−	0.951426i	$-0.400381\pi$
$20$	−39.0593	+	67.6527i	−0.436696	+	0.756380i
$21$	23.4942	−	40.6932i	0.244136	−	0.422856i
$22$	40.4367	−	70.0384i	0.391869	−	0.678738i
$23$	−124.640			−1.12996			−0.564982	−	0.825103i	$-0.691117\pi$
$23$	−124.640			−1.12996			−0.564982	+	0.825103i	$0.691117\pi$
$24$	13.1095	+	22.7064i	0.111499	+	0.193121i
$25$	−128.203	+	222.055i	−1.02563	+	1.77644i
$26$	−117.503			−0.886313
$27$	141.775			1.01054
$28$	−28.6744	+	49.6655i	−0.193534	+	0.335211i
$29$	169.593			1.08595			0.542977	−	0.839747i	$-0.317297\pi$
$29$	169.593			1.08595			0.542977	+	0.839747i	$0.317297\pi$
$30$	64.0061	+	110.862i	0.389528	+	0.674683i
$31$	−121.827			−0.705830			−0.352915	−	0.935655i	$-0.614810\pi$
$31$	−121.827			−0.705830			−0.352915	+	0.935655i	$0.614810\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−66.2632	−	114.771i	−0.349544	−	0.605427i
$34$	87.4583	+	151.482i	0.441146	+	0.764088i
$35$	−140.000	+	242.487i	−0.676124	+	1.17108i
$36$	−65.0351			−0.301089
$37$	24.0088	+	223.778i	0.106676	+	0.994294i
$37$	24.0088	+	223.778i	0.106676	+	0.994294i
$38$	221.962			0.947551
$39$	−96.2751	+	166.753i	−0.395291	+	0.684664i
$40$	−78.1186	−	135.305i	−0.308791	−	0.534841i
$41$	−120.562	−	208.819i	−0.459234	−	0.795416i	0.539687	−	0.841866i	$-0.318543\pi$
$41$	−120.562	−	208.819i	−0.459234	−	0.795416i	−0.998921	+	0.0464495i	$0.985209\pi$
$42$	46.9884	+	81.3864i	0.172630	+	0.299005i
$43$	222.885			0.790457			0.395229	−	0.918583i	$-0.370665\pi$
$43$	222.885			0.790457			0.395229	+	0.918583i	$0.370665\pi$
$44$	80.8734	+	140.077i	0.277094	+	0.479940i
$45$	−317.528			−1.05187
$46$	124.640	−	215.882i	0.399503	−	0.691959i
$47$	−242.748			−0.753371			−0.376686	−	0.926341i	$-0.622936\pi$
$47$	−242.748			−0.753371			−0.376686	+	0.926341i	$0.622936\pi$
$48$	−52.4381			−0.157683
$49$	68.7224	−	119.031i	0.200357	−	0.347028i
$50$	−256.407	−	444.110i	−0.725228	−	1.25613i
$51$	286.634			0.786996
$52$	117.503	−	203.520i	0.313359	−	0.542754i
$53$	255.140	−	441.915i	0.661247	−	1.14531i	−0.319041	−	0.947741i	$-0.603361\pi$
$53$	255.140	−	441.915i	0.661247	−	1.14531i	0.980288	−	0.197573i	$-0.0633059\pi$
$54$	−141.775	+	245.562i	−0.357281	+	0.618830i
$55$	394.857	+	683.912i	0.968045	+	1.67670i
$56$	−57.3488	−	99.3310i	−0.136849	−	0.237030i
$57$	181.863	−	314.996i	0.422603	−	0.731970i
$58$	−169.593	+	293.744i	−0.383943	+	0.665009i
$59$	138.167	−	239.312i	0.304878	−	0.528065i	−0.672356	−	0.740228i	$-0.734718\pi$
$59$	138.167	−	239.312i	0.304878	−	0.528065i	0.977234	+	0.212163i	$0.0680509\pi$
$60$	−256.024			−0.550876
$61$	185.389	+	321.103i	0.389125	+	0.673984i	0.992332	−	0.123601i	$-0.0394442\pi$
$61$	185.389	+	321.103i	0.389125	+	0.673984i	−0.603207	+	0.797584i	$0.706111\pi$
$62$	121.827	−	211.010i	0.249549	−	0.432231i
$63$	−233.105			−0.466167
$64$	64.0000			0.125000
$65$	573.696	−	993.670i	1.09474	−	1.89615i
$66$	265.053			0.494329
$67$	55.8336	+	96.7066i	0.101808	+	0.176337i	0.912430	−	0.409233i	$-0.134204\pi$
$67$	55.8336	+	96.7066i	0.101808	+	0.176337i	−0.810621	+	0.585571i	$0.800871\pi$
$68$	−349.833			−0.623875
$69$	−204.246	−	353.764i	−0.356352	−	0.617220i
$70$	−280.000	−	484.975i	−0.478092	−	0.828080i
$71$	304.129	+	526.767i	0.508359	+	0.880504i	0.999953	+	0.00967951i	$0.00308113\pi$
$71$	304.129	+	526.767i	0.508359	+	0.880504i	−0.491594	+	0.870825i	$0.663586\pi$
$72$	65.0351	−	112.644i	0.106451	−	0.184378i
$73$	−64.7080			−0.103747			−0.0518733	−	0.998654i	$-0.516519\pi$
$73$	−64.7080			−0.103747			−0.0518733	+	0.998654i	$0.516519\pi$
$74$	−411.604	−	182.193i	−0.646594	−	0.286210i
$75$	−840.343			−1.29379
$76$	−221.962	+	384.449i	−0.335010	+	0.580254i
$77$	289.874	+	502.077i	0.429016	+	0.743078i
$78$	−192.550	−	333.507i	−0.279513	−	0.484131i
$79$	444.196	+	769.369i	0.632606	+	1.09571i	0.987017	+	0.160616i	$0.0513482\pi$
$79$	444.196	+	769.369i	0.632606	+	1.09571i	−0.354411	+	0.935090i	$0.615318\pi$
$80$	312.474			0.436696
$81$	12.8325	+	22.2265i	0.0176029	+	0.0304890i
$82$	482.247			0.649455
$83$	643.348	−	1114.31i	0.850802	−	1.47363i	−0.0296830	−	0.999559i	$-0.509450\pi$
$83$	643.348	−	1114.31i	0.850802	−	1.47363i	0.880485	−	0.474073i	$-0.157217\pi$
$84$	−187.954			−0.244136
$85$	−1708.03			−2.17955
$86$	−222.885	+	386.048i	−0.279469	+	0.484054i
$87$	277.911	+	481.356i	0.342473	+	0.593181i
$88$	−323.493			−0.391869
$89$	−201.644	+	349.257i	−0.240160	+	0.415969i	−0.960760	−	0.277382i	$-0.910533\pi$
$89$	−201.644	+	349.257i	−0.240160	+	0.415969i	0.720600	+	0.693351i	$0.243866\pi$
$90$	317.528	−	549.975i	0.371893	−	0.644138i
$91$	421.164	−	729.478i	0.485165	−	0.840330i
$92$	249.279	+	431.765i	0.282491	+	0.489289i
$93$	−199.636	−	345.780i	−0.222595	−	0.385546i
$94$	242.748	−	420.452i	0.266357	−	0.461344i
$95$	−1083.71	+	1877.04i	−1.17038	+	2.02716i
$96$	52.4381	−	90.8254i	0.0557494	−	0.0965607i
$97$	1827.81			1.91326			0.956631	−	0.291303i	$-0.0940886\pi$
$97$	1827.81			1.91326			0.956631	+	0.291303i	$0.0940886\pi$
$98$	137.445	+	238.061i	0.141674	+	0.245386i
$99$	−328.726	+	569.369i	−0.333719	+	0.578018i
$100$	1025.63			1.02563
$101$	−375.420			−0.369858			−0.184929	−	0.982752i	$-0.559206\pi$
$101$	−375.420			−0.369858			−0.184929	+	0.982752i	$0.559206\pi$
$102$	−286.634	+	496.465i	−0.278245	+	0.481935i
$103$	−396.336			−0.379147			−0.189573	−	0.981867i	$-0.560711\pi$
$103$	−396.336			−0.379147			−0.189573	+	0.981867i	$0.560711\pi$
$104$	235.005	+	407.041i	0.221578	+	0.383785i
$105$	−917.668			−0.852907
$106$	510.279	+	883.829i	0.467572	+	0.809859i
$107$	−740.214	−	1282.09i	−0.668778	−	1.15836i	−0.978246	−	0.207447i	$-0.933484\pi$
$107$	−740.214	−	1282.09i	−0.668778	−	1.15836i	0.309469	−	0.950910i	$-0.399849\pi$
$108$	−283.551	−	491.125i	−0.252636	−	0.437579i
$109$	326.247	−	565.076i	0.286686	−	0.496555i	−0.686331	−	0.727290i	$-0.740780\pi$
$109$	326.247	−	565.076i	0.286686	−	0.496555i	0.973017	+	0.230735i	$0.0741130\pi$
$110$	−1579.43			−1.36902
$111$	−595.805	+	434.847i	−0.509471	+	0.371836i
$112$	229.395			0.193534
$113$	417.178	−	722.574i	0.347299	−	0.601540i	−0.638469	−	0.769647i	$-0.720432\pi$
$113$	417.178	−	722.574i	0.347299	−	0.601540i	0.985769	+	0.168107i	$0.0537655\pi$
$114$	363.726	+	629.993i	0.298825	+	0.517581i
$115$	1217.08	+	2108.05i	0.986902	+	1.70936i
$116$	−339.187	−	587.488i	−0.271489	−	0.470232i
$117$	955.224			0.754790
$118$	276.334	+	478.625i	0.215582	+	0.373398i
$119$	−1253.91			−0.965928
$120$	256.024	−	443.447i	0.194764	−	0.337342i
$121$	304.125			0.228493
$122$	−741.555			−0.550305
$123$	395.127	−	684.380i	0.289654	−	0.501695i
$124$	243.654	+	422.020i	0.176458	+	0.305633i
$125$	2566.33			1.83632
$126$	233.105	−	403.750i	0.164815	−	0.285468i
$127$	234.631	−	406.392i	0.163938	−	0.283949i	−0.772340	−	0.635210i	$-0.780914\pi$
$127$	234.631	−	406.392i	0.163938	−	0.283949i	0.936278	+	0.351261i	$0.114247\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	365.240	+	632.614i	0.249283	+	0.431771i
$130$	1147.39	+	1987.34i	0.774099	+	1.34078i
$131$	−803.797	+	1392.22i	−0.536092	+	0.928539i	0.463017	+	0.886349i	$0.346767\pi$
$131$	−803.797	+	1392.22i	−0.536092	+	0.928539i	−0.999110	+	0.0421899i	$0.986567\pi$
$132$	−265.053	+	459.085i	−0.174772	+	0.302714i
$133$	−795.577	+	1377.98i	−0.518687	+	0.898391i
$134$	−223.334			−0.143979
$135$	−1384.41	−	2397.87i	−0.882602	−	1.52871i
$136$	349.833	−	605.929i	0.220573	−	0.382044i
$137$	−2083.19			−1.29911			−0.649557	−	0.760313i	$-0.725046\pi$
$137$	−2083.19			−1.29911			−0.649557	+	0.760313i	$0.725046\pi$
$138$	816.984			0.503958
$139$	−15.9174	+	27.5698i	−0.00971293	+	0.0168233i	−0.870841	−	0.491565i	$-0.836425\pi$
$139$	−15.9174	+	27.5698i	−0.00971293	+	0.0168233i	0.861128	+	0.508388i	$0.169758\pi$
$140$	1120.00			0.676124
$141$	−397.789	−	688.990i	−0.237588	−	0.411514i
$142$	−1216.52			−0.718929
$143$	−1187.85	−	2057.42i	−0.694638	−	1.20315i
$144$	130.070	+	225.288i	0.0752721	+	0.130375i
$145$	−1656.05	−	2868.36i	−0.948464	−	1.64279i
$146$	64.7080	−	112.077i	0.0366799	−	0.0635315i
$147$	450.459			0.252743
$148$	727.172	−	530.725i	0.403873	−	0.294766i
$149$	−836.896			−0.460142			−0.230071	−	0.973174i	$-0.573896\pi$
$149$	−836.896			−0.460142			−0.230071	+	0.973174i	$0.573896\pi$
$150$	840.343	−	1455.52i	0.457425	−	0.792283i
$151$	−848.341	−	1469.37i	−0.457199	−	0.791892i	0.541613	−	0.840628i	$-0.317814\pi$
$151$	−848.341	−	1469.37i	−0.457199	−	0.791892i	−0.998812	+	0.0487364i	$0.984481\pi$
$152$	−443.923	−	768.898i	−0.236888	−	0.410302i
$153$	−710.983	−	1231.46i	−0.375683	−	0.650703i
$154$	−1159.50			−0.606720
$155$	1189.62	+	2060.48i	0.616467	+	1.06775i
$156$	770.201			0.395291
$157$	1406.86	−	2436.75i	0.715157	−	1.23869i	−0.247741	−	0.968826i	$-0.579688\pi$
$157$	1406.86	−	2436.75i	0.715157	−	1.23869i	0.962899	−	0.269863i	$-0.0869783\pi$
$158$	−1776.78			−0.894641
$159$	1672.38			0.834140
$160$	−312.474	+	541.221i	−0.154395	+	0.267421i
$161$	893.492	+	1547.57i	0.437373	+	0.757552i
$162$	−51.3299			−0.0248942
$163$	1042.63	−	1805.89i	0.501012	−	0.867779i	−0.498987	−	0.866610i	$-0.666294\pi$
$163$	1042.63	−	1805.89i	0.501012	−	0.867779i	0.999999	−	0.00116944i	$-0.000372245\pi$
$164$	−482.247	+	835.277i	−0.229617	+	0.397708i
$165$	−1294.10	+	2241.44i	−0.610577	+	1.05755i
$166$	1286.70	+	2228.62i	0.601608	+	1.04202i
$167$	911.200	+	1578.24i	0.422220	+	0.731307i	0.996156	−	0.0875933i	$-0.0279176\pi$
$167$	911.200	+	1578.24i	0.422220	+	0.731307i	−0.573936	+	0.818900i	$0.694584\pi$
$168$	187.954	−	325.546i	0.0863152	−	0.149502i
$169$	−627.355	+	1086.61i	−0.285551	+	0.494589i
$170$	1708.03	−	2958.39i	0.770588	−	1.33470i
$171$	−1804.41			−0.806941
$172$	−445.770	−	772.097i	−0.197614	−	0.342278i
$173$	1202.26	−	2082.38i	0.528360	−	0.915147i	−0.471093	−	0.882084i	$-0.656140\pi$
$173$	1202.26	−	2082.38i	0.528360	−	0.915147i	0.999453	−	0.0330633i	$-0.0105263\pi$
$174$	−1111.64			−0.484330
$175$	3676.16			1.58795
$176$	323.493	−	560.307i	0.138547	−	0.239970i
$177$	905.652			0.384593
$178$	−403.288	−	698.515i	−0.169819	−	0.294134i
$179$	1980.59			0.827019			0.413509	−	0.910500i	$-0.364303\pi$
$179$	1980.59			0.827019			0.413509	+	0.910500i	$0.364303\pi$
$180$	635.056	+	1099.95i	0.262968	+	0.455475i
$181$	584.421	+	1012.25i	0.239998	+	0.415689i	0.960713	−	0.277542i	$-0.0895199\pi$
$181$	584.421	+	1012.25i	0.239998	+	0.415689i	−0.720715	+	0.693231i	$0.756187\pi$
$182$	842.328	+	1458.96i	0.343063	+	0.594203i
$183$	−607.590	+	1052.38i	−0.245433	+	0.425103i
$184$	−997.118			−0.399503
$185$	3550.35	−	2591.22i	1.41096	−	1.02978i
$186$	798.545			0.314797
$187$	−1768.26	+	3062.72i	−0.691487	+	1.19769i
$188$	485.496	+	840.904i	0.188343	+	0.326219i
$189$	−1016.33	−	1760.34i	−0.391149	−	0.677491i
$190$	−2167.42	−	3754.08i	−0.827584	−	1.43342i
$191$	1907.58			0.722659			0.361329	−	0.932438i	$-0.382323\pi$
$191$	1907.58			0.722659			0.361329	+	0.932438i	$0.382323\pi$
$192$	104.876	+	181.651i	0.0394208	+	0.0682787i
$193$	−4944.00			−1.84392			−0.921960	−	0.387285i	$-0.873413\pi$
$193$	−4944.00			−1.84392			−0.921960	+	0.387285i	$0.873413\pi$
$194$	−1827.81	+	3165.87i	−0.676440	+	1.17163i
$195$	3760.44			1.38098
$196$	−549.779			−0.200357
$197$	−1041.70	+	1804.27i	−0.376741	+	0.652534i	−0.990586	−	0.136892i	$-0.956289\pi$
$197$	−1041.70	+	1804.27i	−0.376741	+	0.652534i	0.613845	+	0.789426i	$0.289622\pi$
$198$	−657.451	−	1138.74i	−0.235975	−	0.408720i
$199$	−699.778			−0.249276			−0.124638	−	0.992202i	$-0.539777\pi$
$199$	−699.778			−0.249276			−0.124638	+	0.992202i	$0.539777\pi$
$200$	−1025.63	+	1776.44i	−0.362614	+	0.628066i
$201$	−182.988	+	316.944i	−0.0642137	+	0.111221i
$202$	375.420	−	650.247i	0.130765	−	0.226491i
$203$	−1215.75	−	2105.73i	−0.420338	−	0.728047i
$204$	−573.268	−	992.930i	−0.196749	−	0.340779i
$205$	−2354.53	+	4078.16i	−0.802183	+	1.38942i
$206$	396.336	−	686.474i	0.134049	−	0.232179i
$207$	−1013.25	+	1754.99i	−0.340219	+	0.589277i
$208$	−940.020			−0.313359
$209$	2243.85	+	3886.46i	0.742633	+	1.28628i
$210$	917.668	−	1589.45i	0.301548	−	0.522296i
$211$	−1986.19			−0.648032			−0.324016	−	0.946052i	$-0.605033\pi$
$211$	−1986.19			−0.648032			−0.324016	+	0.946052i	$0.605033\pi$
$212$	−2041.12			−0.661247
$213$	−996.747	+	1726.42i	−0.320638	+	0.555362i
$214$	2960.86			0.945794
$215$	−2176.43	−	3769.69i	−0.690379	−	1.19577i
$216$	1134.20			0.357281
$217$	873.327	+	1512.65i	0.273204	+	0.473204i
$218$	652.494	+	1130.15i	0.202718	+	0.351117i
$219$	−106.036	−	183.660i	−0.0327181	−	0.0566695i
$220$	1579.43	−	2735.65i	0.484023	−	0.838352i
$221$	5138.29			1.56398
$222$	−157.372	−	1466.81i	−0.0475771	−	0.443450i
$223$	−6485.56			−1.94756			−0.973778	−	0.227500i	$-0.926945\pi$
$223$	−6485.56			−1.94756			−0.973778	+	0.227500i	$0.926945\pi$
$224$	−229.395	+	397.324i	−0.0684246	+	0.118515i
$225$	2084.43	+	3610.34i	0.617610	+	1.06973i
$226$	834.356	+	1445.15i	0.245578	+	0.425353i
$227$	326.504	+	565.522i	0.0954663	+	0.165353i	0.909803	−	0.415040i	$-0.136232\pi$
$227$	326.504	+	565.522i	0.0954663	+	0.165353i	−0.814337	+	0.580393i	$0.802899\pi$
$228$	−1454.91			−0.422603
$229$	−915.324	−	1585.39i	−0.264132	−	0.457491i	0.703204	−	0.710989i	$-0.251752\pi$
$229$	−915.324	−	1585.39i	−0.264132	−	0.457491i	−0.967336	+	0.253498i	$0.918419\pi$
$230$	−4868.34			−1.39569
$231$	−950.028	+	1645.50i	−0.270594	+	0.468683i
$232$	1356.75			0.383943
$233$	−1770.50			−0.497809			−0.248904	−	0.968528i	$-0.580071\pi$
$233$	−1770.50			−0.497809			−0.248904	+	0.968528i	$0.580071\pi$
$234$	−955.224	+	1654.50i	−0.266859	+	0.462213i
$235$	2370.39	+	4105.64i	0.657988	+	1.13967i
$236$	−1105.34			−0.304878
$237$	−1455.80	+	2521.52i	−0.399005	+	0.691097i
$238$	1253.91	−	2171.83i	0.341507	−	0.591508i
$239$	−362.719	+	628.248i	−0.0981689	+	0.170034i	−0.910927	−	0.412568i	$-0.864632\pi$
$239$	−362.719	+	628.248i	−0.0981689	+	0.170034i	0.812758	+	0.582602i	$0.197965\pi$
$240$	512.048	+	886.894i	0.137719	+	0.238537i
$241$	2196.19	+	3803.91i	0.587008	+	1.01673i	0.994622	+	0.103573i	$0.0330276\pi$
$241$	2196.19	+	3803.91i	0.587008	+	1.01673i	−0.407614	+	0.913154i	$0.633639\pi$
$242$	−304.125	+	526.760i	−0.0807846	+	0.139923i
$243$	1871.91	−	3242.25i	0.494170	−	0.855927i
$244$	741.555	−	1284.41i	0.194562	−	0.336992i
$245$	−2684.25			−0.699960
$246$	790.254	+	1368.76i	0.204816	+	0.354752i
$247$	3260.13	−	5646.72i	0.839827	−	1.45462i
$248$	−974.614			−0.249549
$249$	4216.99			1.07326
$250$	−2566.33	+	4445.02i	−0.649236	+	1.12451i
$251$	2148.42			0.540266			0.270133	−	0.962823i	$-0.412932\pi$
$251$	2148.42			0.540266			0.270133	+	0.962823i	$0.412932\pi$
$252$	466.211	+	807.501i	0.116542	+	0.201856i
$253$	5040.02			1.25242
$254$	469.262	+	812.785i	0.115922	+	0.200782i
$255$	−2798.93	−	4847.89i	−0.687356	−	1.19054i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−435.037	+	753.506i	−0.105591	+	0.182889i	−0.913979	−	0.405760i	$-0.867007\pi$
$257$	−435.037	+	753.506i	−0.105591	+	0.182889i	0.808389	+	0.588649i	$0.200340\pi$
$258$	−1460.96			−0.352540
$259$	2606.40	−	1902.28i	0.625305	−	0.456377i
$260$	−4589.56			−1.09474
$261$	1378.69	−	2387.96i	0.326968	−	0.566326i
$262$	−1607.59	−	2784.44i	−0.379075	−	0.656576i
$263$	−1049.43	−	1817.66i	−0.246048	−	0.426167i	0.716378	−	0.697712i	$-0.245799\pi$
$263$	−1049.43	−	1817.66i	−0.246048	−	0.426167i	−0.962426	+	0.271545i	$0.912465\pi$
$264$	−530.105	−	918.169i	−0.123582	−	0.214051i
$265$	−9965.57			−2.31011
$266$	−1591.15	−	2755.96i	−0.366767	−	0.635259i
$267$	−1321.73			−0.302953
$268$	223.334	−	386.826i	0.0509041	−	0.0881686i
$269$	5485.74			1.24339			0.621695	−	0.783260i	$-0.286444\pi$
$269$	5485.74			1.24339			0.621695	+	0.783260i	$0.286444\pi$
$270$	5537.65			1.24819
$271$	3048.66	−	5280.43i	0.683369	−	1.18363i	−0.290578	−	0.956851i	$-0.593847\pi$
$271$	3048.66	−	5280.43i	0.683369	−	1.18363i	0.973946	−	0.226778i	$-0.0728192\pi$
$272$	699.667	+	1211.86i	0.155969	+	0.270146i
$273$	2760.63			0.612018
$274$	2083.19	−	3608.19i	0.459306	−	0.795542i
$275$	5184.12	−	8979.16i	1.13678	−	1.96896i
$276$	−816.984	+	1415.06i	−0.178176	+	0.308610i
$277$	229.957	+	398.297i	0.0498800	+	0.0863948i	0.889887	−	0.456180i	$-0.150783\pi$
$277$	229.957	+	398.297i	0.0498800	+	0.0863948i	−0.840007	+	0.542575i	$0.817449\pi$
$278$	−31.8348	−	55.1395i	−0.00686808	−	0.0118959i
$279$	−990.377	+	1715.38i	−0.212517	+	0.368091i
$280$	−1120.00	+	1939.90i	−0.239046	+	0.414040i
$281$	−1367.74	+	2369.00i	−0.290365	+	0.502927i	−0.973896	−	0.226994i	$-0.927110\pi$
$281$	−1367.74	+	2369.00i	−0.290365	+	0.502927i	0.683531	+	0.729922i	$0.260443\pi$
$282$	1591.16			0.336000
$283$	806.341	+	1396.62i	0.169371	+	0.293359i	0.938199	−	0.346097i	$-0.112493\pi$
$283$	806.341	+	1396.62i	0.169371	+	0.293359i	−0.768828	+	0.639456i	$0.779160\pi$
$284$	1216.52	−	2107.07i	0.254180	−	0.440252i
$285$	−7103.45			−1.47639
$286$	4751.41			0.982367
$287$	−1728.52	+	2993.88i	−0.355509	+	0.615760i
$288$	−520.281			−0.106451
$289$	−1367.98	−	2369.41i	−0.278441	−	0.482273i
$290$	6624.19			1.34133
$291$	2995.22	+	5187.87i	0.603378	+	1.04508i
$292$	129.416	+	224.155i	0.0259366	+	0.0449236i
$293$	−71.6884	−	124.168i	−0.0142938	−	0.0247576i	0.858790	−	0.512328i	$-0.171217\pi$
$293$	−71.6884	−	124.168i	−0.0142938	−	0.0247576i	−0.873084	+	0.487570i	$0.837883\pi$
$294$	−450.459	+	780.217i	−0.0893581	+	0.154773i
$295$	−5396.71			−1.06511
$296$	192.071	+	1790.22i	0.0377158	+	0.351536i
$297$	−5732.93			−1.12006
$298$	836.896	−	1449.55i	0.162685	−	0.281778i
$299$	−3661.37	−	6341.68i	−0.708169	−	1.22658i
$300$	1680.69	+	2911.03i	0.323448	+	0.560229i
$301$	−1597.77	−	2767.43i	−0.305961	−	0.529939i
$302$	3393.36			0.646577
$303$	−615.197	−	1065.55i	−0.116641	−	0.202028i
$304$	1775.69			0.335010
$305$	3620.58	−	6271.02i	0.679717	−	1.17730i
$306$	2843.93			0.531296
$307$	9023.26			1.67747			0.838737	−	0.544537i	$-0.183294\pi$
$307$	9023.26			1.67747			0.838737	+	0.544537i	$0.183294\pi$
$308$	1159.50	−	2008.31i	0.214508	−	0.371539i
$309$	−649.472	−	1124.92i	−0.119570	−	0.207101i
$310$	−4758.47			−0.871815
$311$	−3418.00	+	5920.14i	−0.623205	+	1.07942i	0.365680	+	0.930741i	$0.380837\pi$
$311$	−3418.00	+	5920.14i	−0.623205	+	1.07942i	−0.988885	+	0.148682i	$0.952497\pi$
$312$	−770.201	+	1334.03i	−0.139757	+	0.242065i
$313$	3652.69	−	6326.64i	0.659623	−	1.14250i	−0.321090	−	0.947049i	$-0.604049\pi$
$313$	3652.69	−	6326.64i	0.659623	−	1.14250i	0.980713	−	0.195452i	$-0.0626175\pi$
$314$	2813.72	+	4873.51i	0.505693	+	0.875885i
$315$	2276.23	+	3942.55i	0.407147	+	0.705199i
$316$	1776.78	−	3077.48i	0.316303	−	0.547853i
$317$	−3370.39	+	5837.69i	−0.597161	+	1.03431i	0.396077	+	0.918217i	$0.370371\pi$
$317$	−3370.39	+	5837.69i	−0.597161	+	1.03431i	−0.993238	+	0.116096i	$0.962962\pi$
$318$	−1672.38	+	2896.64i	−0.294913	+	0.510804i
$319$	−6857.79			−1.20364
$320$	−624.949	−	1082.44i	−0.109174	−	0.189095i
$321$	2425.96	−	4201.89i	0.421819	−	0.730613i
$322$	−3573.97			−0.618539
$323$	−9706.20			−1.67204
$324$	51.3299	−	88.9060i	0.00880143	−	0.0152445i
$325$	−15064.2			−2.57112
$326$	2085.26	+	3611.77i	0.354269	+	0.613612i
$327$	2138.47			0.361644
$328$	−964.494	−	1670.55i	−0.162364	−	0.281222i
$329$	1740.16	+	3014.05i	0.291606	+	0.505076i
$330$	−2588.19	−	4482.88i	−0.431743	−	0.747801i
$331$	157.812	−	273.339i	0.0262059	−	0.0453900i	−0.852625	−	0.522523i	$-0.824991\pi$
$331$	157.812	−	273.339i	0.0262059	−	0.0453900i	0.878831	+	0.477133i	$0.158324\pi$
$332$	−5146.78			−0.850802
$333$	3346.09	+	1481.12i	0.550644	+	0.243739i
$334$	−3644.80			−0.597109
$335$	1090.41	−	1888.64i	0.177837	−	0.308023i
$336$	375.908	+	651.091i	0.0610340	+	0.105714i
$337$	−1236.33	−	2141.39i	−0.199844	−	0.346140i	0.748634	−	0.662984i	$-0.230710\pi$
$337$	−1236.33	−	2141.39i	−0.199844	−	0.346140i	−0.948478	+	0.316844i	$0.897377\pi$
$338$	−1254.71	−	2173.22i	−0.201915	−	0.349727i
$339$	2734.50			0.438106
$340$	3416.06	+	5916.79i	0.544888	+	0.943773i
$341$	4926.27			0.782324
$342$	1804.41	−	3125.34i	0.285297	−	0.494149i
$343$	−6888.23			−1.08434
$344$	1783.08			0.279469
$345$	−3988.85	+	6908.89i	−0.622471	+	1.07815i
$346$	2404.53	+	4164.76i	0.373607	+	0.647107i
$347$	11277.1			1.74463			0.872314	−	0.488946i	$-0.162618\pi$
$347$	11277.1			1.74463			0.872314	+	0.488946i	$0.162618\pi$
$348$	1111.64	−	1925.42i	0.171237	−	0.296590i
$349$	−636.556	+	1102.55i	−0.0976334	+	0.169106i	−0.910705	−	0.413058i	$-0.864461\pi$
$349$	−636.556	+	1102.55i	−0.0976334	+	0.169106i	0.813071	+	0.582164i	$0.197794\pi$
$350$	−3676.16	+	6367.29i	−0.561425	+	0.972417i
$351$	4164.74	+	7213.55i	0.633326	+	1.09695i
$352$	646.987	+	1120.61i	0.0979674	+	0.169684i
$353$	−1108.53	+	1920.03i	−0.167142	+	0.289499i	−0.937414	−	0.348217i	$-0.886787\pi$
$353$	−1108.53	+	1920.03i	−0.167142	+	0.289499i	0.770272	+	0.637716i	$0.220121\pi$
$354$	−905.652	+	1568.64i	−0.135974	+	0.235514i
$355$	5939.54	−	10287.6i	0.887994	−	1.53805i
$356$	1613.15			0.240160
$357$	−2054.77	−	3558.96i	−0.304621	−	0.527619i
$358$	−1980.59	+	3430.48i	−0.292395	+	0.506443i
$359$	11858.5			1.74336			0.871680	−	0.490076i	$-0.163031\pi$
$359$	11858.5			1.74336			0.871680	+	0.490076i	$0.163031\pi$
$360$	−2540.23			−0.371893
$361$	−2728.88	+	4726.55i	−0.397853	+	0.689102i
$362$	−2337.68			−0.339409
$363$	498.366	+	863.196i	0.0720591	+	0.124810i
$364$	−3369.31			−0.485165
$365$	631.862	+	1094.42i	0.0906114	+	0.156944i
$366$	−1215.18	−	2104.75i	−0.173548	−	0.300593i
$367$	−744.563	−	1289.62i	−0.105901	−	0.183427i	0.808205	−	0.588902i	$-0.200439\pi$
$367$	−744.563	−	1289.62i	−0.105901	−	0.183427i	−0.914106	+	0.405475i	$0.867106\pi$
$368$	997.118	−	1727.06i	0.141246	−	0.244644i
$369$	−3920.38			−0.553080
$370$	937.767	+	8740.61i	0.131763	+	1.22812i
$371$	−7315.97			−1.02379
$372$	−798.545	+	1383.12i	−0.111297	+	0.192773i
$373$	4540.62	+	7864.59i	0.630307	+	1.09172i	0.987489	+	0.157689i	$0.0504043\pi$
$373$	4540.62	+	7864.59i	0.630307	+	1.09172i	−0.357182	+	0.934035i	$0.616262\pi$
$374$	−3536.52	−	6125.44i	−0.488955	−	0.846895i
$375$	4205.42	+	7284.00i	0.579112	+	1.00305i
$376$	−1941.98			−0.266357
$377$	4981.91	+	8628.92i	0.680587	+	1.17881i
$378$	4065.33			0.553169
$379$	−6322.24	+	10950.4i	−0.856864	+	1.48413i	0.0180411	+	0.999837i	$0.494257\pi$
$379$	−6322.24	+	10950.4i	−0.856864	+	1.48413i	−0.874905	+	0.484295i	$0.839076\pi$
$380$	8669.67			1.17038
$381$	1537.95			0.206802
$382$	−1907.58	+	3304.03i	−0.255498	+	0.442536i
$383$	5567.73	+	9643.59i	0.742814	+	1.28659i	0.951209	+	0.308547i	$0.0998426\pi$
$383$	5567.73	+	9643.59i	0.742814	+	1.28659i	−0.208395	+	0.978045i	$0.566824\pi$
$384$	−419.505			−0.0557494
$385$	5661.14	−	9805.39i	0.749399	−	1.29800i
$386$	4944.00	−	8563.25i	0.651924	−	1.12917i
$387$	1811.92	−	3138.34i	0.237998	−	0.412224i
$388$	−3655.63	−	6331.73i	−0.478315	−	0.828467i
$389$	−6167.97	−	10683.2i	−0.803929	−	1.39245i	−0.917012	−	0.398860i	$-0.869406\pi$
$389$	−6167.97	−	10683.2i	−0.803929	−	1.39245i	0.113083	−	0.993586i	$-0.463927\pi$
$390$	−3760.44	+	6513.27i	−0.488249	+	0.845672i
$391$	−5450.39	+	9440.35i	−0.704957	+	1.22102i
$392$	549.779	−	952.245i	0.0708368	−	0.122693i
$393$	−5268.70			−0.676261
$394$	−2083.40	−	3608.55i	−0.266396	−	0.461411i
$395$	8674.98	−	15025.5i	1.10503	−	1.91396i
$396$	2629.80			0.333719
$397$	11963.0			1.51235			0.756176	−	0.654368i	$-0.227065\pi$
$397$	11963.0			1.51235			0.756176	+	0.654368i	$0.227065\pi$
$398$	699.778	−	1212.05i	0.0881325	−	0.152650i
$399$	−5214.82			−0.654304
$400$	−2051.26	−	3552.88i	−0.256407	−	0.444110i
$401$	−9154.59			−1.14005			−0.570023	−	0.821629i	$-0.693066\pi$
$401$	−9154.59			−1.14005			−0.570023	+	0.821629i	$0.693066\pi$
$402$	−365.976	−	633.888i	−0.0454060	−	0.0786455i
$403$	−3578.74	−	6198.56i	−0.442356	−	0.766184i
$404$	750.840	+	1300.49i	0.0924646	+	0.160153i
$405$	250.614	−	434.076i	0.0307484	−	0.0532578i
$406$	4862.98			0.594448
$407$	−970.837	−	9048.84i	−0.118237	−	1.10205i
$408$	2293.07			0.278245
$409$	3939.82	−	6823.98i	0.476312	−	0.824997i	−0.523319	−	0.852137i	$-0.675306\pi$
$409$	3939.82	−	6823.98i	0.476312	−	0.824997i	0.999632	+	0.0271393i	$0.00863978\pi$
$410$	−4709.06	−	8156.33i	−0.567229	−	0.982469i
$411$	−3413.70	−	5912.70i	−0.409697	−	0.709615i
$412$	792.672	+	1372.95i	0.0947867	+	0.164175i
$413$	−3961.86			−0.472035
$414$	−2026.49	−	3509.98i	−0.240571	−	0.416682i
$415$	−25128.7			−2.97234
$416$	940.020	−	1628.16i	0.110789	−	0.191892i
$417$	−104.335			−0.0122525
$418$	−8975.39			−1.05024
$419$	−5922.24	+	10257.6i	−0.690502	+	1.19598i	0.281172	+	0.959657i	$0.409277\pi$
$419$	−5922.24	+	10257.6i	−0.690502	+	1.19598i	−0.971674	+	0.236327i	$0.924056\pi$
$420$	1835.34	+	3178.89i	0.213227	+	0.369319i
$421$	8301.07			0.960972			0.480486	−	0.877002i	$-0.340460\pi$
$421$	8301.07			0.960972			0.480486	+	0.877002i	$0.340460\pi$
$422$	1986.19	−	3440.18i	0.229114	−	0.396837i
$423$	−1973.39	+	3418.02i	−0.226831	+	0.392884i
$424$	2041.12	−	3535.32i	0.233786	−	0.404930i
$425$	11212.5	+	19420.6i	1.27973	+	2.21655i
$426$	−1993.49	−	3452.83i	−0.226726	−	0.392700i
$427$	2657.96	−	4603.72i	0.301235	−	0.521755i
$428$	−2960.86	+	5128.35i	−0.334389	+	0.579178i
$429$	3893.04	−	6742.95i	0.438130	−	0.758864i
$430$	8705.73			0.976344
$431$	4475.64	+	7752.04i	0.500195	+	0.866364i	1.00000		0.000225567i	$7.18003e-5\pi$
$431$	4475.64	+	7752.04i	0.500195	+	0.866364i	−0.499805	+	0.866138i	$0.666595\pi$
$432$	−1134.20	+	1964.50i	−0.126318	+	0.218789i
$433$	13402.0			1.48743			0.743717	−	0.668495i	$-0.233061\pi$
$433$	13402.0			1.48743			0.743717	+	0.668495i	$0.233061\pi$
$434$	−3493.31			−0.386369
$435$	5427.50	−	9400.70i	0.598227	−	1.03616i
$436$	−2609.97			−0.286686
$437$	6916.31	+	11979.4i	0.757099	+	1.31133i
$438$	424.145			0.0462704
$439$	1800.71	+	3118.92i	0.195770	+	0.339084i	0.947153	−	0.320783i	$-0.103946\pi$
$439$	1800.71	+	3118.92i	0.195770	+	0.339084i	−0.751383	+	0.659867i	$0.770613\pi$
$440$	3158.86	+	5471.30i	0.342256	+	0.592804i
$441$	−1117.34	−	1935.29i	−0.120650	−	0.208972i
$442$	−5138.29	+	8899.77i	−0.552949	+	0.957735i
$443$	−8635.66			−0.926168			−0.463084	−	0.886314i	$-0.653257\pi$
$443$	−8635.66			−0.926168			−0.463084	+	0.886314i	$0.653257\pi$
$444$	2697.96	+	1194.23i	0.288378	+	0.127648i
$445$	7876.07			0.839014
$446$	6485.56	−	11233.3i	0.688565	−	1.19263i
$447$	−1371.41	−	2375.36i	−0.145113	−	0.251344i
$448$	−458.790	−	794.648i	−0.0483835	−	0.0838027i
$449$	1749.13	+	3029.57i	0.183845	+	0.318429i	0.943187	−	0.332263i	$-0.107812\pi$
$449$	1749.13	+	3029.57i	0.183845	+	0.318429i	−0.759342	+	0.650692i	$0.774479\pi$
$450$	−8337.73			−0.873432
$451$	4875.12	+	8443.95i	0.509003	+	0.881619i
$452$	−3337.43			−0.347299
$453$	2780.34	−	4815.68i	0.288370	−	0.499471i
$454$	−1306.02			−0.135010
$455$	−16450.4			−1.69496
$456$	1454.91	−	2519.97i	0.149413	−	0.258790i
$457$	−2840.03	−	4919.07i	−0.290702	−	0.503511i	0.683274	−	0.730162i	$-0.260556\pi$
$457$	−2840.03	−	4919.07i	−0.290702	−	0.503511i	−0.973976	+	0.226651i	$0.927222\pi$
$458$	3661.30			0.373540
$459$	6199.72	−	10738.2i	0.630454	−	1.09198i
$460$	4868.34	−	8432.21i	0.493451	−	0.854682i
$461$	−1791.48	+	3102.94i	−0.180993	+	0.313489i	−0.942219	−	0.334998i	$-0.891264\pi$
$461$	−1791.48	+	3102.94i	−0.180993	+	0.313489i	0.761226	+	0.648487i	$0.224598\pi$
$462$	−1900.06	−	3290.99i	−0.191339	−	0.331409i
$463$	−5659.51	−	9802.56i	−0.568077	−	0.983938i	−0.996756	−	0.0804816i	$-0.974354\pi$
$463$	−5659.51	−	9802.56i	−0.568077	−	0.983938i	0.428679	−	0.903457i	$-0.358979\pi$
$464$	−1356.75	+	2349.95i	−0.135744	+	0.235116i
$465$	−3898.83	+	6752.96i	−0.388825	+	0.673465i
$466$	1770.50	−	3066.60i	0.176002	−	0.304844i
$467$	9315.84			0.923095			0.461548	−	0.887115i	$-0.347294\pi$
$467$	9315.84			0.923095			0.461548	+	0.887115i	$0.347294\pi$
$468$	−1910.45	−	3308.99i	−0.188698	−	0.326834i
$469$	800.497	−	1386.50i	0.0788135	−	0.136509i
$470$	−9481.57			−0.930536
$471$	9221.63			0.902145
$472$	1105.34	−	1914.50i	0.107791	−	0.186699i
$473$	−9012.73			−0.876123
$474$	−2911.60	−	5043.03i	−0.282139	−	0.488679i
$475$	28456.3			2.74876
$476$	2507.81	+	4343.66i	0.241482	+	0.418259i
$477$	−4148.26	−	7184.99i	−0.398188	−	0.689682i
$478$	−725.439	−	1256.50i	−0.0694159	−	0.120232i
$479$	97.7274	−	169.269i	0.00932208	−	0.0161463i	−0.861327	−	0.508051i	$-0.830366\pi$
$479$	97.7274	−	169.269i	0.00932208	−	0.0161463i	0.870649	+	0.491905i	$0.163699\pi$
$480$	−2048.19			−0.194764
$481$	−10680.6	+	7795.19i	−1.01246	+	0.738940i
$482$	−8784.75			−0.830155
$483$	−2928.31	+	5071.99i	−0.275865	+	0.477813i
$484$	−608.250	−	1053.52i	−0.0571234	−	0.0989406i
$485$	−17848.3	−	30914.1i	−1.67103	−	2.89431i
$486$	3743.82	+	6484.49i	0.349431	+	0.605232i
$487$	−4852.49			−0.451514			−0.225757	−	0.974184i	$-0.572485\pi$
$487$	−4852.49			−0.451514			−0.225757	+	0.974184i	$0.572485\pi$
$488$	1483.11	+	2568.82i	0.137576	+	0.238289i
$489$	6834.18			0.632009
$490$	2684.25	−	4649.25i	0.247473	−	0.428636i
$491$	−18733.9			−1.72190			−0.860948	−	0.508693i	$-0.830129\pi$
$491$	−18733.9			−1.72190			−0.860948	+	0.508693i	$0.830129\pi$
$492$	−3161.01			−0.289654
$493$	7416.17	−	12845.2i	0.677500	−	1.17346i
$494$	6520.27	+	11293.4i	0.593847	+	1.02857i
$495$	12839.8			1.16587
$496$	974.614	−	1688.08i	0.0882288	−	0.152817i
$497$	4360.36	−	7552.37i	0.393539	−	0.681630i
$498$	−4216.99	+	7304.04i	−0.379454	+	0.657233i
$499$	2921.86	+	5060.82i	0.262126	+	0.454015i	0.966807	−	0.255510i	$-0.0822432\pi$
$499$	2921.86	+	5060.82i	0.262126	+	0.454015i	−0.704681	+	0.709524i	$0.748910\pi$
$500$	−5132.66	−	8890.03i	−0.459079	−	0.795149i
$501$	−2986.35	+	5172.51i	−0.266308	+	0.461259i
$502$	−2148.42	+	3721.17i	−0.191013	+	0.330844i
$503$	−9419.11	+	16314.4i	−0.834945	+	1.44617i	0.0591307	+	0.998250i	$0.481167\pi$
$503$	−9419.11	+	16314.4i	−0.834945	+	1.44617i	−0.894075	+	0.447916i	$0.852166\pi$
$504$	−1864.84			−0.164815
$505$	3665.91	+	6349.54i	0.323031	+	0.559507i
$506$	−5040.02	+	8729.56i	−0.442799	+	0.766950i
$507$	−4112.16			−0.360212
$508$	−1877.05			−0.163938
$509$	2361.49	−	4090.22i	0.205641	−	0.356180i	−0.744696	−	0.667404i	$-0.767405\pi$
$509$	2361.49	−	4090.22i	0.205641	−	0.356180i	0.950337	+	0.311224i	$0.100739\pi$
$510$	11195.7			0.972069
$511$	463.865	+	803.439i	0.0401569	+	0.0695539i
$512$	512.000			0.0441942
$513$	−7867.18	−	13626.4i	−0.677085	−	1.17275i
$514$	−870.074	−	1507.01i	−0.0746640	−	0.129322i
$515$	3870.15	+	6703.29i	0.331144	+	0.573558i
$516$	1460.96	−	2530.45i	0.124642	−	0.215886i
$517$	9815.92			0.835017
$518$	688.438	+	6416.70i	0.0583943	+	0.544273i
$519$	7880.54			0.666508
$520$	4589.56	−	7949.36i	0.387049	−	0.670389i
$521$	5163.09	+	8942.74i	0.434164	+	0.751993i	0.997227	−	0.0744204i	$-0.0237107\pi$
$521$	5163.09	+	8942.74i	0.434164	+	0.751993i	−0.563063	+	0.826414i	$0.690377\pi$
$522$	2757.38	+	4775.92i	0.231202	+	0.400453i
$523$	2228.10	+	3859.18i	0.186287	+	0.322658i	0.944009	−	0.329919i	$-0.107021\pi$
$523$	2228.10	+	3859.18i	0.186287	+	0.322658i	−0.757723	+	0.652577i	$0.773688\pi$
$524$	6430.38			0.536092
$525$	6024.08	+	10434.0i	0.500786	+	0.867386i
$526$	4197.71			0.347964
$527$	−5327.38	+	9227.30i	−0.440350	+	0.762708i
$528$	2120.42			0.174772
$529$	3368.06			0.276820
$530$	9965.57	−	17260.9i	0.816748	−	1.41465i
$531$	−2246.43	−	3890.93i	−0.183591	−	0.317989i
$532$	6364.62			0.518687
$533$	7083.16	−	12268.4i	0.575620	−	0.997004i
$534$	1321.73	−	2289.30i	0.107110	−	0.185520i
$535$	−14456.1	+	25038.7i	−1.16821	+	2.02340i
$536$	446.668	+	773.652i	0.0359947	+	0.0623446i
$537$	3245.58	+	5621.50i	0.260814	+	0.451742i
$538$	−5485.74	+	9501.59i	−0.439604	+	0.761417i
$539$	−2778.90	+	4813.20i	−0.222070	+	0.384637i
$540$	−5537.65	+	9591.49i	−0.441301	+	0.764355i
$541$	−16418.6			−1.30479			−0.652394	−	0.757880i	$-0.726235\pi$
$541$	−16418.6			−1.30479			−0.652394	+	0.757880i	$0.726235\pi$
$542$	6097.32	+	10560.9i	0.483215	+	0.836952i
$543$	−1915.37	+	3317.52i	−0.151374	+	0.262188i
$544$	−2798.67			−0.220573
$545$	−12743.0			−1.00156
$546$	−2760.63	+	4781.55i	−0.216381	+	0.374783i
$547$	4313.47			0.337168			0.168584	−	0.985687i	$-0.446081\pi$
$547$	4313.47			0.337168			0.168584	+	0.985687i	$0.446081\pi$
$548$	4166.37	+	7216.37i	0.324779	+	0.562533i
$549$	6028.39			0.468644
$550$	10368.2	+	17958.3i	0.803825	+	1.39226i
$551$	−9410.80	−	16300.0i	−0.727611	−	1.26026i
$552$	−1633.97	−	2830.11i	−0.125990	−	0.218220i
$553$	6368.52	−	11030.6i	0.489723	−	0.848226i
$554$	−919.828			−0.0705410
$555$	13172.6	+	5830.74i	1.00747	+	0.445948i
$556$	127.339			0.00971293
$557$	−5045.77	+	8739.53i	−0.383835	+	0.664822i	−0.991607	−	0.129290i	$-0.958730\pi$
$557$	−5045.77	+	8739.53i	−0.383835	+	0.664822i	0.607772	+	0.794112i	$0.292064\pi$
$558$	−1980.75	−	3430.77i	−0.150272	−	0.260280i
$559$	6547.39	+	11340.4i	0.495394	+	0.858047i
$560$	−2240.00	−	3879.80i	−0.169031	−	0.292770i
$561$	−11590.5			−0.872286
$562$	−2735.48	−	4738.00i	−0.205319	−	0.355623i
$563$	−4130.68			−0.309214			−0.154607	−	0.987976i	$-0.549411\pi$
$563$	−4130.68			−0.309214			−0.154607	+	0.987976i	$0.549411\pi$
$564$	−1591.16	+	2755.96i	−0.118794	+	0.205757i
$565$	−16294.7			−1.21331
$566$	−3225.37			−0.239527
$567$	183.982	−	318.666i	0.0136270	−	0.0236027i
$568$	2433.03	+	4214.14i	0.179732	+	0.311305i
$569$	−19461.5			−1.43386			−0.716930	−	0.697145i	$-0.754453\pi$
$569$	−19461.5			−1.43386			−0.716930	+	0.697145i	$0.754453\pi$
$570$	7103.45	−	12303.5i	0.521984	−	0.904102i
$571$	−6245.22	+	10817.0i	−0.457714	+	0.792783i	−0.998840	−	0.0481582i	$-0.984665\pi$
$571$	−6245.22	+	10817.0i	−0.457714	+	0.792783i	0.541126	+	0.840941i	$0.317998\pi$
$572$	−4751.41	+	8229.69i	−0.347319	+	0.601574i
$573$	3125.94	+	5414.28i	0.227902	+	0.394738i
$574$	−3457.04	−	5987.76i	−0.251383	−	0.435408i
$575$	15979.2	−	27676.9i	1.15892	−	2.00731i
$576$	520.281	−	901.153i	0.0376361	−	0.0651876i
$577$	13409.4	−	23225.7i	0.967486	−	1.67573i	0.264704	−	0.964330i	$-0.414726\pi$
$577$	13409.4	−	23225.7i	0.967486	−	1.67573i	0.702782	−	0.711405i	$-0.251941\pi$
$578$	5471.91			0.393774
$579$	−8101.68	−	14032.5i	−0.581510	−	1.00720i
$580$	−6624.19	+	11473.4i	−0.474232	+	0.821394i
$581$	−18447.6			−1.31727
$582$	−11980.9			−0.853305
$583$	−10317.0	+	17869.6i	−0.732909	+	1.26944i
$584$	−517.664			−0.0366799
$585$	−9327.59	−	16155.9i	−0.659228	−	1.14182i
$586$	286.754			0.0202145
$587$	8343.21	+	14450.9i	0.586646	+	1.01610i	0.994668	+	0.103128i	$0.0328852\pi$
$587$	8343.21	+	14450.9i	0.586646	+	1.01610i	−0.408022	+	0.912972i	$0.633781\pi$
$588$	−900.917	−	1560.43i	−0.0631857	−	0.109441i
$589$	6760.22	+	11709.0i	0.472920	+	0.819122i
$590$	5396.71	−	9347.37i	0.376574	−	0.652246i
$591$	−6828.08			−0.475245
$592$	−3292.83	−	1457.55i	−0.228605	−	0.101191i
$593$	8424.55			0.583398			0.291699	−	0.956510i	$-0.405780\pi$
$593$	8424.55			0.583398			0.291699	+	0.956510i	$0.405780\pi$
$594$	5732.93	−	9929.72i	0.396002	−	0.685895i
$595$	12244.2	+	21207.5i	0.843634	+	1.46122i
$596$	1673.79	+	2899.09i	0.115036	+	0.199247i
$597$	−1146.72	−	1986.18i	−0.0786133	−	0.136162i
$598$	14645.5			1.00150
$599$	−3201.65	−	5545.42i	−0.218391	−	0.378264i	0.735926	−	0.677062i	$-0.236747\pi$
$599$	−3201.65	−	5545.42i	−0.218391	−	0.378264i	−0.954316	+	0.298799i	$0.903414\pi$
$600$	−6722.74			−0.457425
$601$	4467.65	−	7738.20i	0.303227	−	0.525204i	−0.673638	−	0.739061i	$-0.735269\pi$
$601$	4467.65	−	7738.20i	0.303227	−	0.525204i	0.976865	+	0.213857i	$0.0686027\pi$
$602$	6391.10			0.432694
$603$	1815.57			0.122613
$604$	−3393.36	+	5877.48i	−0.228599	+	0.395946i
$605$	−2969.72	−	5143.71i	−0.199564	−	0.345656i
$606$	2460.79			0.164955
$607$	2781.58	−	4817.83i	0.185998	−	0.322158i	−0.757914	−	0.652354i	$-0.773782\pi$
$607$	2781.58	−	4817.83i	0.185998	−	0.322158i	0.943912	+	0.330196i	$0.107115\pi$
$608$	−1775.69	+	3075.59i	−0.118444	+	0.205151i
$609$	3984.46	−	6901.29i	0.265121	−	0.459203i
$610$	7241.16	+	12542.0i	0.480632	+	0.832480i
$611$	−7130.88	−	12351.0i	−0.472151	−	0.817790i
$612$	−2843.93	+	4925.83i	−0.187842	+	0.325351i
$613$	−8527.92	+	14770.8i	−0.561892	+	0.973225i	0.435440	+	0.900218i	$0.356593\pi$
$613$	−8527.92	+	14770.8i	−0.561892	+	0.973225i	−0.997331	+	0.0730068i	$0.976741\pi$
$614$	−9023.26	+	15628.7i	−0.593077	+	1.02724i
$615$	−15433.4			−1.01192
$616$	2318.99	+	4016.62i	0.151680	+	0.262718i
$617$	14075.3	−	24379.1i	0.918395	−	1.59071i	0.116542	−	0.993186i	$-0.462819\pi$
$617$	14075.3	−	24379.1i	0.918395	−	1.59071i	0.801853	−	0.597521i	$-0.203847\pi$
$618$	2597.89			0.169098
$619$	9297.70			0.603726			0.301863	−	0.953351i	$-0.402392\pi$
$619$	9297.70			0.603726			0.301863	+	0.953351i	$0.402392\pi$
$620$	4758.47	−	8241.91i	0.308233	−	0.533876i
$621$	−17670.9			−1.14188
$622$	−6835.99	−	11840.3i	−0.440673	−	0.763267i
$623$	5782.02			0.371832
$624$	−1540.40	−	2668.05i	−0.0988228	−	0.171166i
$625$	−9034.33	−	15647.9i	−0.578197	−	1.00147i
$626$	7305.38	+	12653.3i	0.466424	+	0.807870i
$627$	−7353.94	+	12737.4i	−0.468402	+	0.811297i
$628$	−11254.9			−0.715157
$629$	17999.1	+	7967.17i	1.14097	+	0.505043i
$630$	−9104.93			−0.575792
$631$	10438.0	−	18079.2i	0.658527	−	1.14060i	−0.322470	−	0.946580i	$-0.604513\pi$
$631$	10438.0	−	18079.2i	0.658527	−	1.14060i	0.980997	−	0.194023i	$-0.0621536\pi$
$632$	3553.56	+	6154.95i	0.223660	+	0.387391i
$633$	−3254.74	−	5637.38i	−0.204367	−	0.353975i
$634$	−6740.78	−	11675.4i	−0.422256	−	0.731370i
$635$	−9164.51			−0.572728
$636$	−3344.76	−	5793.29i	−0.208535	−	0.361193i
$637$	8075.05			0.502269
$638$	6857.79	−	11878.0i	0.425552	−	0.737078i
$639$	9889.54			0.612245
$640$	2499.79			0.154395
$641$	−4128.47	+	7150.72i	−0.254391	+	0.440619i	−0.964730	−	0.263241i	$-0.915208\pi$
$641$	−4128.47	+	7150.72i	−0.254391	+	0.440619i	0.710339	+	0.703860i	$0.248542\pi$
$642$	4851.93	+	8403.78i	0.298271	+	0.516621i
$643$	18513.8			1.13548			0.567740	−	0.823208i	$-0.307818\pi$
$643$	18513.8			1.13548			0.567740	+	0.823208i	$0.307818\pi$
$644$	3573.97	−	6190.30i	0.218687	−	0.378776i
$645$	7133.00	−	12354.7i	0.435444	−	0.754212i
$646$	9706.20	−	16811.6i	0.591154	−	1.02391i
$647$	−6941.93	−	12023.8i	−0.421817	−	0.730609i	0.574300	−	0.818645i	$-0.305274\pi$
$647$	−6941.93	−	12023.8i	−0.421817	−	0.730609i	−0.996117	+	0.0880362i	$0.971941\pi$
$648$	102.660	+	177.812i	0.00622355	+	0.0107795i
$649$	−5587.02	+	9677.00i	−0.337919	+	0.585293i
$650$	15064.2	−	26092.0i	0.909027	−	1.57448i
$651$	−2862.23	+	4957.52i	−0.172319	+	0.298465i
$652$	−8341.03			−0.501012
$653$	15016.1	+	26008.6i	0.899885	+	1.55865i	0.827640	+	0.561259i	$0.189683\pi$
$653$	15016.1	+	26008.6i	0.899885	+	1.55865i	0.0722448	+	0.997387i	$0.476984\pi$
$654$	−2138.47	+	3703.94i	−0.127861	+	0.221461i
$655$	31395.7			1.87288
$656$	3857.98			0.229617
$657$	−526.036	+	911.122i	−0.0312369	+	0.0541039i
$658$	−6960.65			−0.412393
$659$	−11871.7	−	20562.4i	−0.701755	−	1.21547i	−0.967850	−	0.251528i	$-0.919067\pi$
$659$	−11871.7	−	20562.4i	−0.701755	−	1.21547i	0.266096	−	0.963947i	$-0.414266\pi$
$660$	10352.8			0.610577
$661$	−7496.15	−	12983.7i	−0.441099	−	0.764006i	0.556672	−	0.830732i	$-0.312078\pi$
$661$	−7496.15	−	12983.7i	−0.441099	−	0.764006i	−0.997771	+	0.0667260i	$0.978745\pi$
$662$	315.625	+	546.679i	0.0185304	+	0.0320956i
$663$	8420.06	+	14584.0i	0.493225	+	0.854290i
$664$	5146.78	−	8914.49i	0.300804	−	0.521008i
$665$	31074.7			1.81207
$666$	−5911.46	+	4314.47i	−0.343941	+	0.251024i
$667$	−21138.1			−1.22709
$668$	3644.80	−	6312.98i	0.211110	−	0.365653i
$669$	−10627.8	−	18407.9i	−0.614193	−	1.06381i
$670$	2180.82	+	3777.29i	0.125750	+	0.217805i
$671$	−7496.51	−	12984.3i	−0.431296	−	0.747026i
$672$	−1503.63			−0.0863152
$673$	6961.84	+	12058.3i	0.398751	+	0.690656i	0.993572	−	0.113202i	$-0.0361106\pi$
$673$	6961.84	+	12058.3i	0.398751	+	0.690656i	−0.594821	+	0.803858i	$0.702777\pi$
$674$	4945.34			0.282622
$675$	−18176.1	+	31481.9i	−1.03644	+	1.79517i
$676$	5018.84			0.285551
$677$	−15195.9			−0.862666			−0.431333	−	0.902193i	$-0.641957\pi$
$677$	−15195.9			−0.862666			−0.431333	+	0.902193i	$0.641957\pi$
$678$	−2734.50	+	4736.30i	−0.154894	+	0.268284i
$679$	−13102.9	−	22694.8i	−0.740562	−	1.28269i
$680$	−13664.2			−0.770588
$681$	−1070.08	+	1853.43i	−0.0602137	+	0.104293i
$682$	−4926.27	+	8532.55i	−0.276593	+	0.479074i
$683$	11281.3	−	19539.8i	0.632016	−	1.09468i	−0.355123	−	0.934820i	$-0.615561\pi$
$683$	11281.3	−	19539.8i	0.632016	−	1.09468i	0.987139	−	0.159865i	$-0.0511057\pi$
$684$	3608.83	+	6250.67i	0.201735	+	0.349416i
$685$	20342.0	+	35233.3i	1.13464	+	1.96525i
$686$	6888.23	−	11930.8i	0.383373	−	0.664022i
$687$	2999.86	−	5195.92i	0.166597	−	0.288554i
$688$	−1783.08	+	3088.39i	−0.0988072	+	0.171139i
$689$	29979.5			1.65766
$690$	−7977.70	−	13817.8i	−0.440153	−	0.762368i
$691$	4942.77	−	8561.12i	0.272115	−	0.471317i	−0.697288	−	0.716791i	$-0.745610\pi$
$691$	4942.77	−	8561.12i	0.272115	−	0.471317i	0.969403	+	0.245474i	$0.0789435\pi$
$692$	−9618.10			−0.528360
$693$	9426.01			0.516687
$694$	−11277.1	+	19532.5i	−0.616819	+	1.06836i
$695$	621.723			0.0339328
$696$	2223.29	+	3850.85i	0.121083	+	0.209721i
$697$	−21088.3			−1.14602
$698$	−1273.11	−	2205.09i	−0.0690372	−	0.119576i
$699$	−2901.30	−	5025.21i	−0.156992	−	0.271918i
$700$	−7352.32	−	12734.6i	−0.396988	−	0.687603i
$701$	10548.0	−	18269.7i	0.568322	−	0.984363i	−0.428410	−	0.903585i	$-0.640926\pi$
$701$	10548.0	−	18269.7i	0.568322	−	0.984363i	0.996732	−	0.0807787i	$-0.0257407\pi$
$702$	−16659.0			−0.895659
$703$	20175.5	−	14725.1i	1.08241	−	0.789995i
$704$	−2587.95			−0.138547
$705$	−7768.67	+	13455.7i	−0.415014	+	0.718826i
$706$	−2217.06	−	3840.06i	−0.118187	−	0.204706i
$707$	2691.24	+	4661.36i	0.143160	+	0.247961i
$708$	−1811.30	−	3137.27i	−0.0961483	−	0.166534i
$709$	−12083.4			−0.640059			−0.320029	−	0.947408i	$-0.603693\pi$
$709$	−12083.4			−0.640059			−0.320029	+	0.947408i	$0.603693\pi$
$710$	11879.1	+	20575.2i	0.627907	+	1.08757i
$711$	14444.2			0.761882
$712$	−1613.15	+	2794.06i	−0.0849093	+	0.147067i
$713$	15184.5			0.797563
$714$	8219.06			0.430799
$715$	−23198.3	+	40180.7i	−1.21338	+	2.10164i
$716$	−3961.18	−	6860.97i	−0.206755	−	0.358110i
$717$	−2377.54			−0.123837
$718$	−11858.5	+	20539.5i	−0.616371	+	1.06759i
$719$	−12499.8	+	21650.4i	−0.648352	+	1.12298i	0.335164	+	0.942160i	$0.391208\pi$
$719$	−12499.8	+	21650.4i	−0.648352	+	1.12298i	−0.983516	+	0.180819i	$0.942125\pi$
$720$	2540.23	−	4399.80i	0.131484	−	0.227737i
$721$	2841.17	+	4921.06i	0.146756	+	0.254188i
$722$	−5457.75	−	9453.10i	−0.281325	−	0.487269i
$723$	−7197.74	+	12466.9i	−0.370245	+	0.641283i
$724$	2337.68	−	4048.99i	0.119999	−	0.207844i
$725$	−21742.4	+	37659.0i	−1.11379	+	1.92913i
$726$	−1993.47			−0.101907
$727$	−8380.51	−	14515.5i	−0.427532	−	0.740508i	0.569121	−	0.822254i	$-0.307284\pi$
$727$	−8380.51	−	14515.5i	−0.427532	−	0.740508i	−0.996653	+	0.0817460i	$0.973950\pi$
$728$	3369.31	−	5835.82i	0.171532	−	0.297102i
$729$	12962.9			0.658583
$730$	−2527.45			−0.128144
$731$	9746.58	−	16881.6i	0.493147	−	0.854155i
$732$	4860.72			0.245433
$733$	−943.797	−	1634.71i	−0.0475579	−	0.0823727i	0.841267	−	0.540621i	$-0.181811\pi$
$733$	−943.797	−	1634.71i	−0.0475579	−	0.0823727i	−0.888824	+	0.458248i	$0.848477\pi$
$734$	2978.25			0.149767
$735$	−4398.65	−	7618.68i	−0.220744	−	0.382339i
$736$	1994.24	+	3454.12i	0.0998757	+	0.172990i
$737$	−2257.72	−	3910.49i	−0.112842	−	0.195448i
$738$	3920.38	−	6790.29i	0.195543	−	0.338691i
$739$	19993.7			0.995236			0.497618	−	0.867396i	$-0.334208\pi$
$739$	19993.7			0.995236			0.497618	+	0.867396i	$0.334208\pi$
$740$	−16076.9	−	7116.35i	−0.798649	−	0.353516i
$741$	21369.4			1.05941
$742$	7315.97	−	12671.6i	0.361965	−	0.626941i
$743$	−18059.9	−	31280.6i	−0.891726	−	1.54451i	−0.837805	−	0.545969i	$-0.816161\pi$
$743$	−18059.9	−	31280.6i	−0.891726	−	1.54451i	−0.0539209	−	0.998545i	$-0.517172\pi$
$744$	−1597.09	−	2766.24i	−0.0786992	−	0.136311i
$745$	8172.14	+	14154.6i	0.401885	+	0.696085i
$746$	−18162.5			−0.891389
$747$	−10460.1	−	18117.3i	−0.512334	−	0.887388i
$748$	14146.1			0.691487
$749$	−10612.6	+	18381.6i	−0.517725	+	0.896726i
$750$	−16821.7			−0.818988
$751$	23374.7			1.13576			0.567879	−	0.823112i	$-0.307764\pi$
$751$	23374.7			1.13576			0.567879	+	0.823112i	$0.307764\pi$
$752$	1941.98	−	3363.62i	0.0941714	−	0.163110i
$753$	3520.59	+	6097.84i	0.170382	+	0.295110i
$754$	−19927.6			−0.962496
$755$	−16567.8	+	28696.3i	−0.798628	+	1.38326i
$756$	−4065.33	+	7041.35i	−0.195575	+	0.338745i
$757$	3087.94	−	5348.47i	0.148260	−	0.256794i	−0.782324	−	0.622871i	$-0.785966\pi$
$757$	3087.94	−	5348.47i	0.148260	−	0.256794i	0.930585	+	0.366077i	$0.119299\pi$
$758$	−12644.5	−	21900.9i	−0.605894	−	1.04944i
$759$	8259.02	+	14305.1i	0.394972	+	0.684111i
$760$	−8669.67	+	15016.3i	−0.413792	+	0.716709i
$761$	−11647.3	+	20173.8i	−0.554816	+	0.960970i	0.443101	+	0.896472i	$0.353878\pi$
$761$	−11647.3	+	20173.8i	−0.554816	+	0.960970i	−0.997918	+	0.0644988i	$0.979455\pi$
$762$	−1537.95	+	2663.80i	−0.0731155	+	0.126640i
$763$	−9354.93			−0.443868
$764$	−3815.16	−	6608.06i	−0.180665	−	0.312920i
$765$	−13885.2	+	24049.9i	−0.656238	+	1.13664i
$766$	−22270.9			−1.05050
$767$	16235.0			0.764291
$768$	419.505	−	726.603i	0.0197104	−	0.0341394i
$769$	−14698.7			−0.689269			−0.344635	−	0.938737i	$-0.611997\pi$
$769$	−14698.7			−0.689269			−0.344635	+	0.938737i	$0.611997\pi$
$770$	11322.3	+	19610.8i	0.529905	+	0.917822i
$771$	−2851.56			−0.133199
$772$	9887.99	+	17126.5i	0.460980	+	0.798441i
$773$	12907.4	+	22356.2i	0.600576	+	1.04023i	0.992734	+	0.120330i	$0.0383954\pi$
$773$	12907.4	+	22356.2i	0.600576	+	1.04023i	−0.392158	+	0.919898i	$0.628271\pi$
$774$	3623.84	+	6276.68i	0.168290	+	0.291486i
$775$	15618.6	−	27052.2i	0.723919	−	1.25386i
$776$	14622.5			0.676440
$777$	9670.31	+	4280.49i	0.446487	+	0.197634i
$778$	24671.9			1.13693
$779$	−13380.1	+	23174.9i	−0.615392	+	1.06589i
$780$	−7520.87	−	13026.5i	−0.345244	−	0.597980i
$781$	−12298.0	−	21300.7i	−0.563452	−	0.975928i
$782$	−10900.8	−	18880.7i	−0.498480	−	0.863392i
$783$	24044.2			1.09741
$784$	1099.56	+	1904.49i	0.0500892	+	0.0867570i
$785$	−54951.0			−2.49845
$786$	5268.70	−	9125.65i	0.239094	−	0.414124i
$787$	15468.0			0.700601			0.350301	−	0.936637i	$-0.386079\pi$
$787$	15468.0			0.700601			0.350301	+	0.936637i	$0.386079\pi$
$788$	8333.58			0.376741
$789$	3439.38	−	5957.17i	0.155190	−	0.268797i
$790$	17350.0	+	30051.0i	0.781372	+	1.35338i
$791$	−11962.3			−0.537714
$792$	−2629.80	+	4554.95i	−0.117987	+	0.204360i
$793$	−10891.8	+	18865.2i	−0.487743	+	0.844795i
$794$	−11963.0	+	20720.5i	−0.534697	+	0.926123i
$795$	−16330.5	−	28285.2i	−0.728531	−	1.26185i
$796$	1399.56	+	2424.10i	0.0623191	+	0.107940i
$797$	1742.17	−	3017.53i	0.0774291	−	0.134111i	−0.824711	−	0.565554i	$-0.808662\pi$
$797$	1742.17	−	3017.53i	0.0774291	−	0.134111i	0.902140	+	0.431443i	$0.141996\pi$
$798$	5214.82	−	9032.33i	0.231332	−	0.400678i
$799$	−10615.2	+	18386.0i	−0.470010	+	0.814080i
$800$	8205.02			0.362614
$801$	3278.48	+	5678.50i	0.144619	+	0.250487i
$802$	9154.59	−	15856.2i	0.403067	−	0.698133i
$803$	2616.58			0.114990
$804$	1463.90			0.0642137
$805$	17449.6	−	30223.6i	0.763996	−	1.32328i
$806$	14315.0			0.625586
$807$	8989.43	+	15570.2i	0.392123	+	0.679176i
$808$	−3003.36			−0.130765
$809$	9625.33	+	16671.6i	0.418305	+	0.724525i	0.995769	−	0.0918908i	$-0.0292911\pi$
$809$	9625.33	+	16671.6i	0.418305	+	0.724525i	−0.577464	+	0.816416i	$0.695958\pi$
$810$	501.228	+	868.152i	0.0217424	+	0.0376589i
$811$	−4946.47	−	8567.54i	−0.214173	−	0.370958i	0.738844	−	0.673877i	$-0.235372\pi$
$811$	−4946.47	−	8567.54i	−0.214173	−	0.370958i	−0.953016	+	0.302919i	$0.902039\pi$
$812$	−4862.98	+	8422.94i	−0.210169	+	0.364024i
$813$	19983.2			0.862045
$814$	16643.9	+	7367.30i	0.716668	+	0.317228i
$815$	−40724.4			−1.75032
$816$	−2293.07	+	3971.72i	−0.0983745	+	0.170390i
$817$	−12368.0	−	21422.0i	−0.529622	−	0.917332i
$818$	7879.65	+	13648.0i	0.336804	+	0.583361i
$819$	−6847.62	−	11860.4i	−0.292155	−	0.506028i
$820$	18836.2			0.802183
$821$	15029.5	+	26031.8i	0.638894	+	1.10660i	0.985676	+	0.168652i	$0.0539413\pi$
$821$	15029.5	+	26031.8i	0.638894	+	1.10660i	−0.346781	+	0.937946i	$0.612725\pi$
$822$	13654.8			0.579398
$823$	4654.26	−	8061.41i	0.197129	−	0.341438i	−0.750467	−	0.660908i	$-0.770172\pi$
$823$	4654.26	−	8061.41i	0.197129	−	0.341438i	0.947596	+	0.319470i	$0.103505\pi$
$824$	−3170.69			−0.134049
$825$	33980.7			1.43401
$826$	3961.86	−	6862.14i	0.166889	−	0.289061i
$827$	7985.05	+	13830.5i	0.335753	+	0.581541i	0.983629	−	0.180205i	$-0.0576760\pi$
$827$	7985.05	+	13830.5i	0.335753	+	0.581541i	−0.647876	+	0.761745i	$0.724343\pi$
$828$	8105.96			0.340219
$829$	−19184.4	+	33228.4i	−0.803742	+	1.39212i	0.113394	+	0.993550i	$0.463828\pi$
$829$	−19184.4	+	33228.4i	−0.803742	+	1.39212i	−0.917137	+	0.398573i	$0.869506\pi$
$830$	25128.7	−	43524.2i	1.05088	−	1.82018i
$831$	−753.656	+	1305.37i	−0.0314609	+	0.0544920i
$832$	1880.04	+	3256.33i	0.0783397	+	0.135688i
$833$	−6010.34	−	10410.2i	−0.249995	−	0.433004i
$834$	104.335	−	180.713i	0.00433192	−	0.00750310i
$835$	17795.4	−	30822.6i	0.737528	−	1.27744i
$836$	8975.39	−	15545.8i	0.371316	−	0.643139i
$837$	−17272.0			−0.713273
$838$	−11844.5	−	20515.2i	−0.488258	−	0.845688i
$839$	4242.95	−	7349.01i	0.174592	−	0.302403i	−0.765428	−	0.643522i	$-0.777473\pi$
$839$	4242.95	−	7349.01i	0.174592	−	0.302403i	0.940020	+	0.341119i	$0.110806\pi$
$840$	−7341.34			−0.301548
$841$	4372.88			0.179297
$842$	−8301.07	+	14377.9i	−0.339755	+	0.588473i
$843$	−8965.22			−0.366285
$844$	3972.37	+	6880.35i	0.162008	+	0.280606i
$845$	24504.0			0.997591
$846$	−3946.79	−	6836.04i	−0.160394	−	0.277811i
$847$	−2180.15	−	3776.13i	−0.0884425	−	0.153187i
$848$	4082.23	+	7070.63i	0.165312	+	0.286328i
$849$	−2642.69	+	4577.27i	−0.106828	+	0.185031i
$850$	−44849.8			−1.80981
$851$	−2992.45	−	27891.6i	−0.120540	−	1.12352i
$852$	7973.98			0.320638
$853$	8605.48	−	14905.1i	0.345423	−	0.598291i	−0.640007	−	0.768369i	$-0.721069\pi$
$853$	8605.48	−	14905.1i	0.345423	−	0.598291i	0.985431	+	0.170078i	$0.0544020\pi$
$854$	5315.91	+	9207.43i	0.213006	+	0.368937i
$855$	17619.8	+	30518.3i	0.704776	+	1.22071i
$856$	−5921.71	−	10256.7i	−0.236449	−	0.409541i
$857$	23152.2			0.922828			0.461414	−	0.887185i	$-0.347342\pi$
$857$	23152.2			0.922828			0.461414	+	0.887185i	$0.347342\pi$
$858$	7786.09	+	13485.9i	0.309805	+	0.536598i
$859$	39889.3			1.58441			0.792203	−	0.610258i	$-0.208934\pi$
$859$	39889.3			1.58441			0.792203	+	0.610258i	$0.208934\pi$
$860$	−8705.73	+	15078.8i	−0.345190	+	0.597886i
$861$	−11330.0			−0.448462
$862$	−17902.6			−0.707383
$863$	1837.49	−	3182.63i	0.0724785	−	0.125536i	−0.827508	−	0.561453i	$-0.810242\pi$
$863$	1837.49	−	3182.63i	0.0724785	−	0.125536i	0.899987	+	0.435917i	$0.143576\pi$
$864$	−2268.41	−	3929.00i	−0.0893204	−	0.154707i
$865$	−46959.5			−1.84586
$866$	−13402.0	+	23212.9i	−0.525887	+	0.910863i
$867$	4483.38	−	7765.45i	0.175621	−	0.304185i
$868$	3493.31	−	6050.59i	0.136602	−	0.236602i
$869$	−17961.8	−	31110.7i	−0.701165	−	1.21445i
$870$	10855.0	+	18801.4i	0.423010	+	0.732675i
$871$	−3280.29	+	5681.63i	−0.127610	+	0.221027i
$872$	2609.97	−	4520.61i	0.101359	−	0.175559i
$873$	14859.0	−	25736.6i	0.576061	−	0.997767i
$874$	−27665.3			−1.07070
$875$	−18397.0	−	31864.5i	−0.710780	−	1.23111i
$876$	−424.145	+	734.641i	−0.0163591	+	0.0283347i
$877$	11582.9			0.445984			0.222992	−	0.974820i	$-0.428418\pi$
$877$	11582.9			0.445984			0.222992	+	0.974820i	$0.428418\pi$
$878$	−7202.83			−0.276861
$879$	234.950	−	406.945i	0.00901555	−	0.0156154i
$880$	−12635.4			−0.484023
$881$	−20799.8	−	36026.3i	−0.795419	−	1.37771i	−0.922573	−	0.385822i	$-0.873918\pi$
$881$	−20799.8	−	36026.3i	−0.795419	−	1.37771i	0.127154	−	0.991883i	$-0.459416\pi$
$882$	4469.37			0.170625
$883$	−1612.79	−	2793.43i	−0.0614662	−	0.106463i	0.833655	−	0.552286i	$-0.186244\pi$
$883$	−1612.79	−	2793.43i	−0.0614662	−	0.106463i	−0.895121	+	0.445823i	$0.852911\pi$
$884$	−10276.6	−	17799.5i	−0.390994	−	0.677221i
$885$	−8843.53	−	15317.4i	−0.335901	−	0.581797i
$886$	8635.66	−	14957.4i	0.327450	−	0.567160i
$887$	11869.6			0.449315			0.224657	−	0.974438i	$-0.427874\pi$
$887$	11869.6			0.449315			0.224657	+	0.974438i	$0.427874\pi$
$888$	−4766.44	+	3478.77i	−0.180125	+	0.131464i
$889$	−6727.90			−0.253820
$890$	−7876.07	+	13641.7i	−0.296636	+	0.513789i
$891$	−518.903	−	898.766i	−0.0195106	−	0.0337933i
$892$	12971.1	+	22466.6i	0.486889	+	0.843317i
$893$	13470.2	+	23331.1i	0.504774	+	0.874294i
$894$	5485.65			0.205221
$895$	−19340.1	−	33498.1i	−0.722312	−	1.25108i
$896$	1835.16			0.0684246
$897$	11999.7	−	20784.1i	0.446665	−	0.773646i
$898$	−6996.50			−0.259996
$899$	−20661.0			−0.766499
$900$	8337.73	−	14441.4i	0.308805	−	0.534866i
$901$	−22314.1	−	38649.1i	−0.825072	−	1.42907i
$902$	−19500.5			−0.719839
$903$	5236.51	−	9069.91i	0.192979	−	0.334250i
$904$	3337.43	−	5780.59i	0.122789	−	0.212676i
$905$	11413.5	−	19768.8i	0.419225	−	0.726119i
$906$	5560.67	+	9631.37i	0.203908	+	0.353180i
$907$	−3787.34	−	6559.87i	−0.138651	−	0.240151i	0.788335	−	0.615246i	$-0.210943\pi$
$907$	−3787.34	−	6559.87i	−0.138651	−	0.240151i	−0.926986	+	0.375095i	$0.877610\pi$
$908$	1306.02	−	2262.09i	0.0477332	−	0.0826763i
$909$	−3051.94	+	5286.11i	−0.111360	+	0.192881i
$910$	16450.4	−	28492.9i	0.599258	−	1.03794i
$911$	18746.2			0.681765			0.340883	−	0.940106i	$-0.389274\pi$
$911$	18746.2			0.681765			0.340883	+	0.940106i	$0.389274\pi$
$912$	2909.81	+	5039.94i	0.105651	+	0.182992i
$913$	−26014.8	+	45059.0i	−0.943007	+	1.63334i
$914$	11360.1			0.411115
$915$	23732.0			0.857439
$916$	−3661.30	+	6341.55i	−0.132066	+	0.228745i
$917$	23048.4			0.830017
$918$	12399.4	+	21476.5i	0.445798	+	0.772145i
$919$	5586.86			0.200537			0.100269	−	0.994960i	$-0.468030\pi$
$919$	5586.86			0.200537			0.100269	+	0.994960i	$0.468030\pi$
$920$	9736.68	+	16864.4i	0.348923	+	0.604352i
$921$	14786.3	+	25610.7i	0.529018	+	0.916287i
$922$	−3582.96	−	6205.88i	−0.127981	−	0.221670i
$923$	−17868.0	+	30948.2i	−0.637196	+	1.10366i
$924$	7600.23			0.270594
$925$	−52769.0	−	23357.8i	−1.87571	−	0.830271i
$926$	22638.0			0.803382
$927$	−3221.97	+	5580.61i	−0.114157	+	0.197725i
$928$	−2713.49	−	4699.91i	−0.0959857	−	0.166252i
$929$	−7054.69	−	12219.1i	−0.249146	−	0.431534i	0.714143	−	0.700000i	$-0.246817\pi$
$929$	−7054.69	−	12219.1i	−0.249146	−	0.431534i	−0.963289	+	0.268466i	$0.913483\pi$
$930$	−7797.65	−	13505.9i	−0.274941	−	0.476212i
$931$	−15253.7			−0.536972
$932$	3541.00	+	6133.20i	0.124452	+	0.215558i
$933$	−22404.1			−0.786151
$934$	−9315.84	+	16135.5i	−0.326363	+	0.565278i
$935$	69067.0			2.41576
$936$	7641.79			0.266859
$937$	−6461.09	+	11190.9i	−0.225266	+	0.390173i	−0.956399	−	0.292062i	$-0.905659\pi$
$937$	−6461.09	+	11190.9i	−0.225266	+	0.390173i	0.731133	+	0.682235i	$0.238992\pi$
$938$	1600.99	+	2773.00i	0.0557295	+	0.0965264i
$939$	23942.5			0.832091
$940$	9481.57	−	16422.6i	0.328994	−	0.569835i
$941$	−10770.7	+	18655.4i	−0.373129	+	0.646278i	−0.990045	−	0.140751i	$-0.955048\pi$
$941$	−10770.7	+	18655.4i	−0.373129	+	0.646278i	0.616916	+	0.787029i	$0.288382\pi$
$942$	−9221.63	+	15972.3i	−0.318957	+	0.552449i
$943$	15026.8	+	26027.2i	0.518918	+	0.898792i
$944$	2210.67	+	3829.00i	0.0762196	+	0.132016i
$945$	−19848.6	+	34378.8i	−0.683254	+	1.18343i
$946$	9012.73	−	15610.5i	0.309756	−	0.536513i
$947$	5494.60	−	9516.93i	0.188543	−	0.326567i	−0.756221	−	0.654316i	$-0.772957\pi$
$947$	5494.60	−	9516.93i	0.188543	−	0.326567i	0.944765	+	0.327749i	$0.106290\pi$
$948$	11646.4			0.399005
$949$	−1900.84	−	3292.35i	−0.0650198	−	0.112618i
$950$	−28456.3	+	49287.7i	−0.971835	+	1.68327i
$951$	−22092.1			−0.753297
$952$	−10031.3			−0.341507
$953$	14247.3	−	24677.1i	0.484278	−	0.838794i	−0.515559	−	0.856854i	$-0.672416\pi$
$953$	14247.3	−	24677.1i	0.484278	−	0.838794i	0.999837	+	0.0180601i	$0.00574901\pi$
$954$	16593.0			0.563123
$955$	−18627.2	−	32263.3i	−0.631164	−	1.09321i
$956$	2901.75			0.0981689
$957$	−11237.8	−	19464.4i	−0.379588	−	0.657466i
$958$	195.455	+	338.538i	0.00659171	+	0.0114172i
$959$	14933.5	+	25865.6i	0.502846	+	0.870954i
$960$	2048.19	−	3547.58i	0.0688596	−	0.119268i
$961$	−14949.2			−0.501804
$962$	−2821.10	−	26294.5i	−0.0945486	−	0.881256i
$963$	−24070.0			−0.805445
$964$	8784.75	−	15215.6i	0.293504	−	0.508364i
$965$	48277.2	+	83618.6i	1.61047	+	2.78941i
$966$	−5856.63	−	10144.0i	−0.195066	−	0.337864i
$967$	5715.49	+	9899.52i	0.190070	+	0.329211i	0.945273	−	0.326280i	$-0.105795\pi$
$967$	5715.49	+	9899.52i	0.190070	+	0.329211i	−0.755203	+	0.655491i	$0.772462\pi$
$968$	2433.00			0.0807846
$969$	−15905.5	−	27549.1i	−0.527303	−	0.913316i
$970$	71393.1			2.36319
$971$	−12674.7	+	21953.3i	−0.418899	+	0.725555i	−0.995829	−	0.0912388i	$-0.970917\pi$
$971$	−12674.7	+	21953.3i	−0.418899	+	0.725555i	0.576930	+	0.816794i	$0.304251\pi$
$972$	−14975.3			−0.494170
$973$	456.422			0.0150383
$974$	4852.49	−	8404.75i	0.159634	−	0.276495i
$975$	−24685.6	−	42756.7i	−0.810843	−	1.40442i
$976$	−5932.44			−0.194562
$977$	−8911.05	+	15434.4i	−0.291801	+	0.505415i	−0.974236	−	0.225532i	$-0.927588\pi$
$977$	−8911.05	+	15434.4i	−0.291801	+	0.505415i	0.682434	+	0.730947i	$0.260921\pi$
$978$	−6834.18	+	11837.2i	−0.223449	+	0.387025i
$979$	8153.81	−	14122.8i	0.266187	−	0.461049i
$980$	5368.49	+	9298.50i	0.174990	+	0.303092i
$981$	−5304.38	−	9187.45i	−0.172636	−	0.299014i
$982$	18733.9	−	32448.1i	0.608782	−	1.05444i
$983$	16682.4	−	28894.8i	0.541289	−	0.937540i	−0.457542	−	0.889188i	$-0.651270\pi$
$983$	16682.4	−	28894.8i	0.541289	−	0.937540i	0.998830	−	0.0483514i	$-0.0153967\pi$
$984$	3161.01	−	5475.04i	0.102408	−	0.177376i
$985$	40688.0			1.31617
$986$	14832.3	+	25690.4i	0.479065	+	0.829765i
$987$	−5703.18	+	9878.19i	−0.183925	+	0.318568i
$988$	−26081.1			−0.839827
$989$	−27780.3			−0.893189
$990$	−12839.8	+	22239.2i	−0.412197	+	0.713946i
$991$	13204.3			0.423256			0.211628	−	0.977350i	$-0.432123\pi$
$991$	13204.3			0.423256			0.211628	+	0.977350i	$0.432123\pi$
$992$	1949.23	+	3376.16i	0.0623872	+	0.108058i
$993$	1034.42			0.0330578
$994$	8720.72	+	15104.7i	0.278274	+	0.481985i
$995$	6833.21	+	11835.5i	0.217716	+	0.377095i
$996$	−8433.98	−	14608.1i	−0.268314	−	0.464734i
$997$	−21877.7	+	37893.3i	−0.694959	+	1.20370i	0.275235	+	0.961377i	$0.411244\pi$
$997$	−21877.7	+	37893.3i	−0.694959	+	1.20370i	−0.970194	+	0.242328i	$0.922089\pi$
$998$	−11687.5			−0.370701
$999$	3403.86	+	31726.2i	0.107801	+	1.00478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.c.b.47.4	✓	10
3.2	odd	2		666.4.f.d.343.5		10
37.26	even	3	inner	74.4.c.b.63.4	yes	10
111.26	odd	6		666.4.f.d.433.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.c.b.47.4	✓	10	1.1	even	1	trivial
74.4.c.b.63.4	yes	10	37.26	even	3	inner
666.4.f.d.343.5		10	3.2	odd	2
666.4.f.d.433.5		10	111.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.63869 + 2.83829i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-9.76482 - 16.9132i) q^{5} -6.55476 q^{6} +(-7.16860 - 12.4164i) q^{7} +8.00000 q^{8} +(8.12939 - 14.0805i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.63869 + 2.83829i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-9.76482 - 16.9132i) q^{5} -6.55476 q^{6} +(-7.16860 - 12.4164i) q^{7} +8.00000 q^{8} +(8.12939 - 14.0805i) q^{9} +39.0593 q^{10} -40.4367 q^{11} +(6.55476 - 11.3532i) q^{12} +(29.3756 + 50.8801i) q^{13} +28.6744 q^{14} +(32.0030 - 55.4309i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(43.7292 - 75.7411i) q^{17} +(16.2588 + 28.1610i) q^{18} +(-55.4904 - 96.1122i) q^{19} +(-39.0593 + 67.6527i) q^{20} +(23.4942 - 40.6932i) q^{21} +(40.4367 - 70.0384i) q^{22} -124.640 q^{23} +(13.1095 + 22.7064i) q^{24} +(-128.203 + 222.055i) q^{25} -117.503 q^{26} +141.775 q^{27} +(-28.6744 + 49.6655i) q^{28} +169.593 q^{29} +(64.0061 + 110.862i) q^{30} -121.827 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-66.2632 - 114.771i) q^{33} +(87.4583 + 151.482i) q^{34} +(-140.000 + 242.487i) q^{35} -65.0351 q^{36} +(24.0088 + 223.778i) q^{37} +221.962 q^{38} +(-96.2751 + 166.753i) q^{39} +(-78.1186 - 135.305i) q^{40} +(-120.562 - 208.819i) q^{41} +(46.9884 + 81.3864i) q^{42} +222.885 q^{43} +(80.8734 + 140.077i) q^{44} -317.528 q^{45} +(124.640 - 215.882i) q^{46} -242.748 q^{47} -52.4381 q^{48} +(68.7224 - 119.031i) q^{49} +(-256.407 - 444.110i) q^{50} +286.634 q^{51} +(117.503 - 203.520i) q^{52} +(255.140 - 441.915i) q^{53} +(-141.775 + 245.562i) q^{54} +(394.857 + 683.912i) q^{55} +(-57.3488 - 99.3310i) q^{56} +(181.863 - 314.996i) q^{57} +(-169.593 + 293.744i) q^{58} +(138.167 - 239.312i) q^{59} -256.024 q^{60} +(185.389 + 321.103i) q^{61} +(121.827 - 211.010i) q^{62} -233.105 q^{63} +64.0000 q^{64} +(573.696 - 993.670i) q^{65} +265.053 q^{66} +(55.8336 + 96.7066i) q^{67} -349.833 q^{68} +(-204.246 - 353.764i) q^{69} +(-280.000 - 484.975i) q^{70} +(304.129 + 526.767i) q^{71} +(65.0351 - 112.644i) q^{72} -64.7080 q^{73} +(-411.604 - 182.193i) q^{74} -840.343 q^{75} +(-221.962 + 384.449i) q^{76} +(289.874 + 502.077i) q^{77} +(-192.550 - 333.507i) q^{78} +(444.196 + 769.369i) q^{79} +312.474 q^{80} +(12.8325 + 22.2265i) q^{81} +482.247 q^{82} +(643.348 - 1114.31i) q^{83} -187.954 q^{84} -1708.03 q^{85} +(-222.885 + 386.048i) q^{86} +(277.911 + 481.356i) q^{87} -323.493 q^{88} +(-201.644 + 349.257i) q^{89} +(317.528 - 549.975i) q^{90} +(421.164 - 729.478i) q^{91} +(249.279 + 431.765i) q^{92} +(-199.636 - 345.780i) q^{93} +(242.748 - 420.452i) q^{94} +(-1083.71 + 1877.04i) q^{95} +(52.4381 - 90.8254i) q^{96} +1827.81 q^{97} +(137.445 + 238.061i) q^{98} +(-328.726 + 569.369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9	\( 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9} + 4 q^{10} - 80 q^{11} - 20 q^{12} + 73 q^{13} + 4 q^{14} + 113 q^{15} - 80 q^{16} + 69 q^{17} - 76 q^{18} + 33 q^{19} - 4 q^{20} - 109 q^{21} + 80 q^{22} - 524 q^{23} - 40 q^{24} + 132 q^{25} - 292 q^{26} + 898 q^{27} - 4 q^{28} + 296 q^{29} + 226 q^{30} - 784 q^{31} - 160 q^{32} + 124 q^{33} + 138 q^{34} - 263 q^{35} + 304 q^{36} + 24 q^{37} - 132 q^{38} + 679 q^{39} - 8 q^{40} + 345 q^{41} - 218 q^{42} - 492 q^{43} + 160 q^{44} - 1816 q^{45} + 524 q^{46} - 32 q^{47} + 160 q^{48} + 150 q^{49} + 264 q^{50} + 342 q^{51} + 292 q^{52} - 19 q^{53} - 898 q^{54} + 340 q^{55} - 8 q^{56} + 207 q^{57} - 296 q^{58} - 105 q^{59} - 904 q^{60} + 219 q^{61} + 784 q^{62} - 304 q^{63} + 640 q^{64} + 1191 q^{65} - 496 q^{66} + 773 q^{67} - 552 q^{68} + 604 q^{69} - 526 q^{70} + 555 q^{71} - 304 q^{72} + 348 q^{73} + 102 q^{74} - 2952 q^{75} + 132 q^{76} + 884 q^{77} + 1358 q^{78} - 727 q^{79} + 32 q^{80} - 2609 q^{81} - 1380 q^{82} + 2229 q^{83} + 872 q^{84} - 3042 q^{85} + 492 q^{86} + 2660 q^{87} - 640 q^{88} + 901 q^{89} + 1816 q^{90} - 1405 q^{91} + 1048 q^{92} + 3236 q^{93} + 32 q^{94} - 3337 q^{95} - 160 q^{96} - 4596 q^{97} + 300 q^{98} + 6784 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9 + 4 * q^10 - 80 * q^11 - 20 * q^12 + 73 * q^13 + 4 * q^14 + 113 * q^15 - 80 * q^16 + 69 * q^17 - 76 * q^18 + 33 * q^19 - 4 * q^20 - 109 * q^21 + 80 * q^22 - 524 * q^23 - 40 * q^24 + 132 * q^25 - 292 * q^26 + 898 * q^27 - 4 * q^28 + 296 * q^29 + 226 * q^30 - 784 * q^31 - 160 * q^32 + 124 * q^33 + 138 * q^34 - 263 * q^35 + 304 * q^36 + 24 * q^37 - 132 * q^38 + 679 * q^39 - 8 * q^40 + 345 * q^41 - 218 * q^42 - 492 * q^43 + 160 * q^44 - 1816 * q^45 + 524 * q^46 - 32 * q^47 + 160 * q^48 + 150 * q^49 + 264 * q^50 + 342 * q^51 + 292 * q^52 - 19 * q^53 - 898 * q^54 + 340 * q^55 - 8 * q^56 + 207 * q^57 - 296 * q^58 - 105 * q^59 - 904 * q^60 + 219 * q^61 + 784 * q^62 - 304 * q^63 + 640 * q^64 + 1191 * q^65 - 496 * q^66 + 773 * q^67 - 552 * q^68 + 604 * q^69 - 526 * q^70 + 555 * q^71 - 304 * q^72 + 348 * q^73 + 102 * q^74 - 2952 * q^75 + 132 * q^76 + 884 * q^77 + 1358 * q^78 - 727 * q^79 + 32 * q^80 - 2609 * q^81 - 1380 * q^82 + 2229 * q^83 + 872 * q^84 - 3042 * q^85 + 492 * q^86 + 2660 * q^87 - 640 * q^88 + 901 * q^89 + 1816 * q^90 - 1405 * q^91 + 1048 * q^92 + 3236 * q^93 + 32 * q^94 - 3337 * q^95 - 160 * q^96 - 4596 * q^97 + 300 * q^98 + 6784 * q^99

Introduction

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