LMFDB - Embedded newform 114.4.e.d.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(7,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("114.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.e (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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.627014547.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 26x^{4} + 169x^{2} + 147 $ x^6 + 26x^4 + 169x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$2.99107i$ of defining polynomial
Character	$\chi$	$=$	114.7
Dual form			114.4.e.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.12716 - 12.3446i) q^{5} +(3.00000 - 5.19615i) q^{6} +13.2543 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.12716 - 12.3446i) q^{5} +(3.00000 - 5.19615i) q^{6} +13.2543 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-14.2543 + 24.6892i) q^{10} -65.9138 q^{11} -12.0000 q^{12} +(34.2629 - 59.3451i) q^{13} +(-13.2543 - 22.9571i) q^{14} +(21.3815 - 37.0338i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-49.8470 - 86.3375i) q^{17} +18.0000 q^{18} +(-80.3556 - 20.0493i) q^{19} +57.0172 q^{20} +(19.8815 + 34.4357i) q^{21} +(65.9138 + 114.166i) q^{22} +(-1.76943 + 3.06475i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-39.0927 + 67.7105i) q^{25} -137.052 q^{26} -27.0000 q^{27} +(-26.5086 + 45.9143i) q^{28} +(40.9504 - 70.9282i) q^{29} -85.5259 q^{30} -247.190 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-98.8707 - 171.249i) q^{33} +(-99.6940 + 172.675i) q^{34} +(-94.4655 - 163.619i) q^{35} +(-18.0000 - 31.1769i) q^{36} +421.065 q^{37} +(45.6293 + 159.229i) q^{38} +205.578 q^{39} +(-57.0172 - 98.7568i) q^{40} +(172.629 + 299.003i) q^{41} +(39.7629 - 68.8714i) q^{42} +(183.084 + 317.111i) q^{43} +(131.828 - 228.332i) q^{44} +128.289 q^{45} +7.07773 q^{46} +(45.4699 - 78.7562i) q^{47} +(24.0000 - 41.5692i) q^{48} -167.323 q^{49} +156.371 q^{50} +(149.541 - 259.013i) q^{51} +(137.052 + 237.381i) q^{52} +(344.246 - 596.251i) q^{53} +(27.0000 + 46.7654i) q^{54} +(469.778 + 813.680i) q^{55} +106.034 q^{56} +(-68.4439 - 238.844i) q^{57} -163.802 q^{58} +(-91.1444 - 157.867i) q^{59} +(85.5259 + 148.135i) q^{60} +(0.258685 - 0.448055i) q^{61} +(247.190 + 428.145i) q^{62} +(-59.6444 + 103.307i) q^{63} +64.0000 q^{64} -976.789 q^{65} +(-197.741 + 342.498i) q^{66} +(79.9310 - 138.445i) q^{67} +398.776 q^{68} -10.6166 q^{69} +(-188.931 + 327.238i) q^{70} +(395.942 + 685.792i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(-161.065 - 278.972i) q^{73} +(-421.065 - 729.306i) q^{74} -234.556 q^{75} +(230.164 - 238.262i) q^{76} -873.642 q^{77} +(-205.578 - 356.071i) q^{78} +(-159.185 - 275.717i) q^{79} +(-114.034 + 197.514i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(345.259 - 598.005i) q^{82} +684.160 q^{83} -159.052 q^{84} +(-710.535 + 1230.68i) q^{85} +(366.168 - 634.222i) q^{86} +245.703 q^{87} -527.311 q^{88} +(-360.203 + 623.890i) q^{89} +(-128.289 - 222.203i) q^{90} +(454.132 - 786.579i) q^{91} +(-7.07773 - 12.2590i) q^{92} +(-370.784 - 642.218i) q^{93} -181.880 q^{94} +(325.207 + 1134.85i) q^{95} -96.0000 q^{96} +(-207.696 - 359.740i) q^{97} +(167.323 + 289.812i) q^{98} +(296.612 - 513.747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9	\( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} - 20 q^{10} - 88 q^{11} - 72 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} - 48 q^{16} + 84 q^{17} + 108 q^{18} + 32 q^{19} + 80 q^{20} + 21 q^{21} + 88 q^{22} + 2 q^{23} + 72 q^{24} + 83 q^{25} - 36 q^{26} - 162 q^{27} - 28 q^{28} - 92 q^{29} - 120 q^{30} - 218 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} - 282 q^{35} - 108 q^{36} + 490 q^{37} - 74 q^{38} + 54 q^{39} - 80 q^{40} + 688 q^{41} + 42 q^{42} + 103 q^{43} + 176 q^{44} + 180 q^{45} - 8 q^{46} - 322 q^{47} + 144 q^{48} - 1508 q^{49} - 332 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} + 162 q^{54} + 248 q^{55} + 112 q^{56} + 111 q^{57} + 368 q^{58} - 252 q^{59} + 120 q^{60} + 435 q^{61} + 218 q^{62} - 63 q^{63} + 384 q^{64} - 3164 q^{65} - 264 q^{66} + 719 q^{67} - 672 q^{68} + 12 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} + 581 q^{73} - 490 q^{74} + 498 q^{75} + 20 q^{76} - 408 q^{77} - 54 q^{78} + 489 q^{79} - 160 q^{80} - 243 q^{81} + 1376 q^{82} + 4992 q^{83} - 168 q^{84} - 1632 q^{85} + 206 q^{86} - 552 q^{87} - 704 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} + 8 q^{92} - 327 q^{93} + 1288 q^{94} + 2362 q^{95} - 576 q^{96} - 974 q^{97} + 1508 q^{98} + 396 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9 - 20 * q^10 - 88 * q^11 - 72 * q^12 + 9 * q^13 - 14 * q^14 + 30 * q^15 - 48 * q^16 + 84 * q^17 + 108 * q^18 + 32 * q^19 + 80 * q^20 + 21 * q^21 + 88 * q^22 + 2 * q^23 + 72 * q^24 + 83 * q^25 - 36 * q^26 - 162 * q^27 - 28 * q^28 - 92 * q^29 - 120 * q^30 - 218 * q^31 - 96 * q^32 - 132 * q^33 + 168 * q^34 - 282 * q^35 - 108 * q^36 + 490 * q^37 - 74 * q^38 + 54 * q^39 - 80 * q^40 + 688 * q^41 + 42 * q^42 + 103 * q^43 + 176 * q^44 + 180 * q^45 - 8 * q^46 - 322 * q^47 + 144 * q^48 - 1508 * q^49 - 332 * q^50 - 252 * q^51 + 36 * q^52 + 1322 * q^53 + 162 * q^54 + 248 * q^55 + 112 * q^56 + 111 * q^57 + 368 * q^58 - 252 * q^59 + 120 * q^60 + 435 * q^61 + 218 * q^62 - 63 * q^63 + 384 * q^64 - 3164 * q^65 - 264 * q^66 + 719 * q^67 - 672 * q^68 + 12 * q^69 - 564 * q^70 + 62 * q^71 - 216 * q^72 + 581 * q^73 - 490 * q^74 + 498 * q^75 + 20 * q^76 - 408 * q^77 - 54 * q^78 + 489 * q^79 - 160 * q^80 - 243 * q^81 + 1376 * q^82 + 4992 * q^83 - 168 * q^84 - 1632 * q^85 + 206 * q^86 - 552 * q^87 - 704 * q^88 - 1584 * q^89 - 180 * q^90 + 1573 * q^91 + 8 * q^92 - 327 * q^93 + 1288 * q^94 + 2362 * q^95 - 576 * q^96 - 974 * q^97 + 1508 * q^98 + 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−7.12716	−	12.3446i	−0.637472	−	1.10413i	−0.985986	−	0.166830i	$-0.946647\pi$
$5$	−7.12716	−	12.3446i	−0.637472	−	1.10413i	0.348513	−	0.937304i	$-0.386687\pi$
$6$	3.00000	−	5.19615i	0.204124	−	0.353553i
$7$	13.2543			0.715666			0.357833	−	0.933786i	$-0.383516\pi$
$7$	13.2543			0.715666			0.357833	+	0.933786i	$0.383516\pi$
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−14.2543	+	24.6892i	−0.450761	+	0.780741i
$11$	−65.9138			−1.80671			−0.903353	−	0.428898i	$-0.858902\pi$
$11$	−65.9138			−1.80671			−0.903353	+	0.428898i	$0.858902\pi$
$12$	−12.0000			−0.288675
$13$	34.2629	−	59.3451i	0.730987	−	1.26611i	−0.225475	−	0.974249i	$-0.572393\pi$
$13$	34.2629	−	59.3451i	0.730987	−	1.26611i	0.956462	−	0.291857i	$-0.0942732\pi$
$14$	−13.2543	−	22.9571i	−0.253026	−	0.438254i
$15$	21.3815	−	37.0338i	0.368045	−	0.637472i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−49.8470	−	86.3375i	−0.711157	−	1.23176i	−0.964423	−	0.264364i	$-0.914838\pi$
$17$	−49.8470	−	86.3375i	−0.711157	−	1.23176i	0.253266	−	0.967397i	$-0.418495\pi$
$18$	18.0000			0.235702
$19$	−80.3556	−	20.0493i	−0.970255	−	0.242085i
$19$	−80.3556	−	20.0493i	−0.970255	−	0.242085i
$20$	57.0172			0.637472
$21$	19.8815	+	34.4357i	0.206595	+	0.357833i
$22$	65.9138	+	114.166i	0.638767	+	1.10638i
$23$	−1.76943	+	3.06475i	−0.0160414	+	0.0277845i	−0.873935	−	0.486043i	$-0.838440\pi$
$23$	−1.76943	+	3.06475i	−0.0160414	+	0.0277845i	0.857893	+	0.513828i	$0.171773\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	−39.0927	+	67.7105i	−0.312742	+	0.541684i
$26$	−137.052			−1.03377
$27$	−27.0000			−0.192450
$28$	−26.5086	+	45.9143i	−0.178916	+	0.309892i
$29$	40.9504	−	70.9282i	0.262217	−	0.454174i	−0.704614	−	0.709591i	$-0.748880\pi$
$29$	40.9504	−	70.9282i	0.262217	−	0.454174i	0.966831	+	0.255418i	$0.0822129\pi$
$30$	−85.5259			−0.520494
$31$	−247.190			−1.43215			−0.716074	−	0.698025i	$-0.754063\pi$
$31$	−247.190			−1.43215			−0.716074	+	0.698025i	$0.754063\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−98.8707	−	171.249i	−0.521551	−	0.903353i
$34$	−99.6940	+	172.675i	−0.502864	+	0.870986i
$35$	−94.4655	−	163.619i	−0.456217	−	0.790191i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	421.065			1.87088			0.935441	−	0.353483i	$-0.115003\pi$
$37$	421.065			1.87088			0.935441	+	0.353483i	$0.115003\pi$
$38$	45.6293	+	159.229i	0.194791	+	0.679747i
$39$	205.578			0.844071
$40$	−57.0172	−	98.7568i	−0.225380	−	0.390370i
$41$	172.629	+	299.003i	0.657565	+	1.13894i	0.981244	+	0.192769i	$0.0617468\pi$
$41$	172.629	+	299.003i	0.657565	+	1.13894i	−0.323679	+	0.946167i	$0.604920\pi$
$42$	39.7629	−	68.8714i	0.146085	−	0.253026i
$43$	183.084	+	317.111i	0.649304	+	1.12463i	0.983289	+	0.182049i	$0.0582730\pi$
$43$	183.084	+	317.111i	0.649304	+	1.12463i	−0.333986	+	0.942578i	$0.608394\pi$
$44$	131.828	−	228.332i	0.451677	−	0.782327i
$45$	128.289			0.424981
$46$	7.07773			0.0226860
$47$	45.4699	−	78.7562i	0.141116	−	0.244421i	−0.786801	−	0.617207i	$-0.788264\pi$
$47$	45.4699	−	78.7562i	0.141116	−	0.244421i	0.927917	+	0.372786i	$0.121597\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	−167.323			−0.487823
$50$	156.371			0.442283
$51$	149.541	−	259.013i	0.410587	−	0.711157i
$52$	137.052	+	237.381i	0.365493	+	0.633053i
$53$	344.246	−	596.251i	0.892185	−	1.54531i	0.0549339	−	0.998490i	$-0.482505\pi$
$53$	344.246	−	596.251i	0.892185	−	1.54531i	0.837251	−	0.546819i	$-0.184161\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	469.778	+	813.680i	1.15172	+	1.99485i
$56$	106.034			0.253026
$57$	−68.4439	−	238.844i	−0.159046	−	0.555011i
$58$	−163.802			−0.370831
$59$	−91.1444	−	157.867i	−0.201118	−	0.348347i	0.747771	−	0.663957i	$-0.231124\pi$
$59$	−91.1444	−	157.867i	−0.201118	−	0.348347i	−0.948889	+	0.315610i	$0.897791\pi$
$60$	85.5259	+	148.135i	0.184022	+	0.318736i
$61$	0.258685	−	0.448055i	0.000542971	−	0.000940453i	−0.865754	−	0.500470i	$-0.833161\pi$
$61$	0.258685	−	0.448055i	0.000542971	−	0.000940453i	0.866297	+	0.499530i	$0.166494\pi$
$62$	247.190	+	428.145i	0.506341	+	0.877008i
$63$	−59.6444	+	103.307i	−0.119278	+	0.206595i
$64$	64.0000			0.125000
$65$	−976.789			−1.86393
$66$	−197.741	+	342.498i	−0.368792	+	0.638767i
$67$	79.9310	−	138.445i	0.145748	−	0.252443i	−0.783904	−	0.620883i	$-0.786774\pi$
$67$	79.9310	−	138.445i	0.145748	−	0.252443i	0.929652	+	0.368439i	$0.120108\pi$
$68$	398.776			0.711157
$69$	−10.6166			−0.0185230
$70$	−188.931	+	327.238i	−0.322594	+	0.558749i
$71$	395.942	+	685.792i	0.661826	+	1.14632i	0.980135	+	0.198330i	$0.0635517\pi$
$71$	395.942	+	685.792i	0.661826	+	1.14632i	−0.318309	+	0.947987i	$0.603115\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−161.065	−	278.972i	−0.258235	−	0.447277i	0.707534	−	0.706679i	$-0.249808\pi$
$73$	−161.065	−	278.972i	−0.258235	−	0.447277i	−0.965769	+	0.259403i	$0.916474\pi$
$74$	−421.065	−	729.306i	−0.661457	−	1.14568i
$75$	−234.556			−0.361123
$76$	230.164	−	238.262i	0.347390	−	0.359611i
$77$	−873.642			−1.29300
$78$	−205.578	−	356.071i	−0.298424	−	0.516886i
$79$	−159.185	−	275.717i	−0.226706	−	0.392666i	0.730124	−	0.683315i	$-0.239462\pi$
$79$	−159.185	−	275.717i	−0.226706	−	0.392666i	−0.956830	+	0.290649i	$0.906129\pi$
$80$	−114.034	+	197.514i	−0.159368	+	0.276034i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	345.259	−	598.005i	0.464969	−	0.805349i
$83$	684.160			0.904774			0.452387	−	0.891822i	$-0.350573\pi$
$83$	684.160			0.904774			0.452387	+	0.891822i	$0.350573\pi$
$84$	−159.052			−0.206595
$85$	−710.535	+	1230.68i	−0.906686	+	1.57043i
$86$	366.168	−	634.222i	0.459127	−	0.795232i
$87$	245.703			0.302782
$88$	−527.311			−0.638767
$89$	−360.203	+	623.890i	−0.429005	+	0.743058i	−0.996785	−	0.0801222i	$-0.974469\pi$
$89$	−360.203	+	623.890i	−0.429005	+	0.743058i	0.567780	+	0.823180i	$0.307802\pi$
$90$	−128.289	−	222.203i	−0.150254	−	0.260247i
$91$	454.132	−	786.579i	0.523142	−	0.906109i
$92$	−7.07773	−	12.2590i	−0.00802070	−	0.0138923i
$93$	−370.784	−	642.218i	−0.413425	−	0.716074i
$94$	−181.880			−0.199569
$95$	325.207	+	1134.85i	0.351216	+	1.22561i
$96$	−96.0000			−0.102062
$97$	−207.696	−	359.740i	−0.217406	−	0.376558i	0.736608	−	0.676319i	$-0.236426\pi$
$97$	−207.696	−	359.740i	−0.217406	−	0.376558i	−0.954014	+	0.299762i	$0.903093\pi$
$98$	167.323	+	289.812i	0.172471	+	0.298729i
$99$	296.612	−	513.747i	0.301118	−	0.521551i
$100$	−156.371	−	270.842i	−0.156371	−	0.270842i
$101$	−168.670	+	292.146i	−0.166172	+	0.287818i	−0.937071	−	0.349140i	$-0.886474\pi$
$101$	−168.670	+	292.146i	−0.166172	+	0.287818i	0.770899	+	0.636957i	$0.219807\pi$
$102$	−598.164			−0.580658
$103$	−1467.05			−1.40342			−0.701711	−	0.712462i	$-0.747580\pi$
$103$	−1467.05			−1.40342			−0.701711	+	0.712462i	$0.747580\pi$
$104$	274.103	−	474.761i	0.258443	−	0.447636i
$105$	283.397	−	490.857i	0.263397	−	0.456217i
$106$	−1376.98			−1.26174
$107$	382.014			0.345146			0.172573	−	0.984997i	$-0.444792\pi$
$107$	382.014			0.345146			0.172573	+	0.984997i	$0.444792\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	66.4287	+	115.058i	0.0583736	+	0.101106i	0.893735	−	0.448594i	$-0.148075\pi$
$109$	66.4287	+	115.058i	0.0583736	+	0.101106i	−0.835362	+	0.549700i	$0.814742\pi$
$110$	939.556	−	1627.36i	0.814393	−	1.41057i
$111$	631.597	+	1093.96i	0.540077	+	0.935441i
$112$	−106.034	−	183.657i	−0.0894582	−	0.154946i
$113$	−1137.94			−0.947331			−0.473665	−	0.880705i	$-0.657069\pi$
$113$	−1137.94			−0.947331			−0.473665	+	0.880705i	$0.657069\pi$
$114$	−345.246	+	357.392i	−0.283642	+	0.293622i
$115$	50.4441			0.0409038
$116$	163.802	+	283.713i	0.131109	+	0.227087i
$117$	308.366	+	534.106i	0.243662	+	0.422035i
$118$	−182.289	+	315.733i	−0.142212	+	0.246319i
$119$	−660.688	−	1144.34i	−0.508951	−	0.881529i
$120$	171.052	−	296.270i	0.130123	−	0.225380i
$121$	3013.63			2.26419
$122$	−1.03474			−0.000767877
$123$	−517.888	+	897.008i	−0.379645	+	0.657565i
$124$	494.379	−	856.290i	0.358037	−	0.620138i
$125$	−667.310			−0.477488
$126$	238.578			0.168684
$127$	754.987	−	1307.68i	0.527514	−	0.913681i	−0.471971	−	0.881614i	$-0.656457\pi$
$127$	754.987	−	1307.68i	0.527514	−	0.913681i	0.999486	−	0.0320676i	$-0.0102092\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−549.252	+	951.333i	−0.374876	+	0.649304i
$130$	976.789	+	1691.85i	0.659001	+	1.14142i
$131$	185.472	+	321.247i	0.123701	+	0.214256i	0.921224	−	0.389032i	$-0.127190\pi$
$131$	185.472	+	321.247i	0.123701	+	0.214256i	−0.797524	+	0.603288i	$0.793857\pi$
$132$	790.966			0.521551
$133$	−1065.06	−	265.739i	−0.694378	−	0.173252i
$134$	−319.724			−0.206119
$135$	192.433	+	333.304i	0.122682	+	0.212491i
$136$	−398.776	−	690.700i	−0.251432	−	0.435493i
$137$	845.187	−	1463.91i	0.527075	−	0.912920i	−0.472428	−	0.881370i	$-0.656622\pi$
$137$	845.187	−	1463.91i	0.527075	−	0.912920i	0.999502	−	0.0315505i	$-0.0100445\pi$
$138$	10.6166	+	18.3885i	0.00654887	+	0.0113430i
$139$	1355.76	−	2348.25i	0.827296	−	1.43292i	−0.0728556	−	0.997343i	$-0.523211\pi$
$139$	1355.76	−	2348.25i	0.827296	−	1.43292i	0.900152	−	0.435576i	$-0.143455\pi$
$140$	755.724			0.456217
$141$	272.820			0.162947
$142$	791.884	−	1371.58i	0.467982	−	0.810568i
$143$	−2258.40	+	3911.67i	−1.32068	+	2.28748i
$144$	144.000			0.0833333
$145$	−1167.44			−0.668625
$146$	−322.129	+	557.944i	−0.182600	+	0.316273i
$147$	−250.985	−	434.719i	−0.140822	−	0.243911i
$148$	−842.130	+	1458.61i	−0.467720	+	0.810116i
$149$	−1299.45	−	2250.71i	−0.714464	−	1.23749i	−0.963166	−	0.268908i	$-0.913337\pi$
$149$	−1299.45	−	2250.71i	−0.714464	−	1.23749i	0.248702	−	0.968580i	$-0.419996\pi$
$150$	234.556	+	406.263i	0.127676	+	0.221142i
$151$	594.863			0.320591			0.160296	−	0.987069i	$-0.448755\pi$
$151$	594.863			0.320591			0.160296	+	0.987069i	$0.448755\pi$
$152$	−642.845	−	160.394i	−0.343037	−	0.0855900i
$153$	897.246			0.474105
$154$	873.642	+	1513.19i	0.457144	+	0.791796i
$155$	1761.76	+	3051.46i	0.912954	+	1.58128i
$156$	−411.155	+	712.142i	−0.211018	+	0.365493i
$157$	29.1274	+	50.4502i	0.0148065	+	0.0256456i	0.873334	−	0.487122i	$-0.161953\pi$
$157$	29.1274	+	50.4502i	0.0148065	+	0.0256456i	−0.858527	+	0.512768i	$0.828620\pi$
$158$	−318.371	+	551.434i	−0.160305	+	0.277657i
$159$	2065.47			1.03021
$160$	456.138			0.225380
$161$	−23.4526	+	40.6211i	−0.0114803	+	0.0198844i
$162$	−81.0000	+	140.296i	−0.0392837	+	0.0680414i
$163$	1152.53			0.553825			0.276912	−	0.960895i	$-0.410689\pi$
$163$	1152.53			0.553825			0.276912	+	0.960895i	$0.410689\pi$
$164$	−1381.03			−0.657565
$165$	−1409.33	+	2441.04i	−0.664949	+	1.15172i
$166$	−684.160	−	1185.00i	−0.319886	−	0.554059i
$167$	−629.554	+	1090.42i	−0.291715	+	0.505265i	−0.974215	−	0.225620i	$-0.927559\pi$
$167$	−629.554	+	1090.42i	−0.291715	+	0.505265i	0.682500	+	0.730885i	$0.260893\pi$
$168$	159.052	+	275.486i	0.0730423	+	0.126513i
$169$	−1249.40	−	2164.02i	−0.568683	−	0.984988i
$170$	2842.14			1.28225
$171$	517.869	−	536.088i	0.231593	−	0.239741i
$172$	−1464.67			−0.649304
$173$	637.050	+	1103.40i	0.279965	+	0.484914i	0.971376	−	0.237548i	$-0.0763437\pi$
$173$	637.050	+	1103.40i	0.279965	+	0.484914i	−0.691411	+	0.722462i	$0.743010\pi$
$174$	−245.703	−	425.569i	−0.107050	−	0.185416i
$175$	−518.147	+	897.456i	−0.223818	+	0.387665i
$176$	527.311	+	913.329i	0.225838	+	0.391163i
$177$	273.433	−	473.600i	0.116116	−	0.201118i
$178$	1440.81			0.606704
$179$	2034.50			0.849528			0.424764	−	0.905304i	$-0.360357\pi$
$179$	2034.50			0.849528			0.424764	+	0.905304i	$0.360357\pi$
$180$	−256.578	+	444.405i	−0.106245	+	0.184022i
$181$	−516.657	+	894.876i	−0.212170	+	0.367490i	−0.952393	−	0.304872i	$-0.901386\pi$
$181$	−516.657	+	894.876i	−0.212170	+	0.367490i	0.740223	+	0.672361i	$0.234720\pi$
$182$	−1816.53			−0.739835
$183$	1.55211			0.000626969
$184$	−14.1555	+	24.5180i	−0.00567149	+	0.00982331i
$185$	−3000.99	−	5197.87i	−1.19264	−	2.06570i
$186$	−741.569	+	1284.44i	−0.292336	+	0.506341i
$187$	3285.61	+	5690.84i	1.28485	+	2.22543i
$188$	181.880	+	315.025i	0.0705582	+	0.122210i
$189$	−357.866			−0.137730
$190$	1640.41	−	1698.13i	0.626359	−	0.648395i
$191$	−1135.46			−0.430154			−0.215077	−	0.976597i	$-0.569000\pi$
$191$	−1135.46			−0.430154			−0.215077	+	0.976597i	$0.569000\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	−545.536	−	944.897i	−0.203464	−	0.352410i	0.746178	−	0.665746i	$-0.231887\pi$
$193$	−545.536	−	944.897i	−0.203464	−	0.352410i	−0.949642	+	0.313336i	$0.898553\pi$
$194$	−415.392	+	719.480i	−0.153729	+	0.266266i
$195$	−1465.18	−	2537.77i	−0.538072	−	0.931967i
$196$	334.646	−	579.625i	0.121956	−	0.211233i
$197$	4138.08			1.49658			0.748289	−	0.663373i	$-0.230876\pi$
$197$	4138.08			1.49658			0.748289	+	0.663373i	$0.230876\pi$
$198$	−1186.45			−0.425845
$199$	1367.12	−	2367.91i	0.486997	−	0.843503i	−0.512892	−	0.858453i	$-0.671426\pi$
$199$	1367.12	−	2367.91i	0.486997	−	0.843503i	0.999888	+	0.0149506i	$0.00475910\pi$
$200$	−312.742	+	541.684i	−0.110571	+	0.191514i
$201$	479.586			0.168296
$202$	674.682			0.235002
$203$	542.770	−	940.104i	0.187660	−	0.325036i
$204$	598.164	+	1036.05i	0.205293	+	0.355579i
$205$	2460.71	−	4262.08i	0.838359	−	1.45208i
$206$	1467.05	+	2541.00i	0.496185	+	0.859417i
$207$	−15.9249	−	27.5827i	−0.00534713	−	0.00926150i
$208$	−1096.41			−0.365493
$209$	5296.55	+	1321.52i	1.75297	+	0.437377i
$210$	−1133.59			−0.372500
$211$	−1529.00	−	2648.31i	−0.498867	−	0.864063i	0.501132	−	0.865371i	$-0.332917\pi$
$211$	−1529.00	−	2648.31i	−0.498867	−	0.864063i	−0.999999	+	0.00130803i	$0.999584\pi$
$212$	1376.98	+	2385.00i	0.446092	+	0.772655i
$213$	−1187.83	+	2057.38i	−0.382106	+	0.661826i
$214$	−382.014	−	661.667i	−0.122028	−	0.211358i
$215$	2609.74	−	4520.20i	0.827826	−	1.43384i
$216$	−216.000			−0.0680414
$217$	−3276.33			−1.02494
$218$	132.857	−	230.116i	0.0412764	−	0.0714927i
$219$	483.194	−	836.916i	0.149092	−	0.258235i
$220$	−3758.23			−1.15172
$221$	−6831.62			−2.07939
$222$	1263.19	−	2187.92i	0.381892	−	0.661457i
$223$	−809.133	−	1401.46i	−0.242976	−	0.420846i	0.718585	−	0.695439i	$-0.244790\pi$
$223$	−809.133	−	1401.46i	−0.242976	−	0.420846i	−0.961561	+	0.274593i	$0.911457\pi$
$224$	−212.069	+	367.314i	−0.0632565	+	0.109563i
$225$	−351.834	−	609.395i	−0.104247	−	0.180561i
$226$	1137.94	+	1970.97i	0.334932	+	0.580119i
$227$	−6065.43			−1.77347			−0.886733	−	0.462282i	$-0.847031\pi$
$227$	−6065.43			−1.77347			−0.886733	+	0.462282i	$0.847031\pi$
$228$	964.268	+	240.591i	0.280088	+	0.0698840i
$229$	−1916.36			−0.552999			−0.276500	−	0.961014i	$-0.589174\pi$
$229$	−1916.36			−0.552999			−0.276500	+	0.961014i	$0.589174\pi$
$230$	−50.4441	−	87.3717i	−0.0144617	−	0.0250483i
$231$	−1310.46	−	2269.79i	−0.373256	−	0.646499i
$232$	327.603	−	567.426i	0.0927078	−	0.160575i
$233$	2004.27	+	3471.50i	0.563537	+	0.976074i	0.997184	+	0.0749917i	$0.0238930\pi$
$233$	2004.27	+	3471.50i	0.563537	+	0.976074i	−0.433647	+	0.901083i	$0.642774\pi$
$234$	616.733	−	1068.21i	0.172295	−	0.298424i
$235$	−1296.29			−0.359831
$236$	729.155			0.201118
$237$	477.556	−	827.152i	0.130889	−	0.226706i
$238$	−1321.38	+	2288.69i	−0.359883	+	0.623335i
$239$	530.292			0.143522			0.0717610	−	0.997422i	$-0.477138\pi$
$239$	530.292			0.143522			0.0717610	+	0.997422i	$0.477138\pi$
$240$	−684.207			−0.184022
$241$	−635.613	+	1100.91i	−0.169890	+	0.294258i	−0.938381	−	0.345603i	$-0.887674\pi$
$241$	−635.613	+	1100.91i	−0.169890	+	0.294258i	0.768491	+	0.639860i	$0.221008\pi$
$242$	−3013.63	−	5219.77i	−0.800511	−	1.38653i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	1.03474	+	1.79222i	0.000271485	+	0.000470226i
$245$	1192.54	+	2065.54i	0.310973	+	0.538622i
$246$	2071.55			0.536900
$247$	−3943.05	+	4081.77i	−1.01575	+	1.05148i
$248$	−1977.52			−0.506341
$249$	1026.24	+	1777.50i	0.261186	+	0.452387i
$250$	667.310	+	1155.81i	0.168818	+	0.292401i
$251$	−275.994	+	478.036i	−0.0694048	+	0.120213i	−0.898639	−	0.438688i	$-0.855443\pi$
$251$	−275.994	+	478.036i	−0.0694048	+	0.120213i	0.829235	+	0.558901i	$0.188777\pi$
$252$	−238.578	−	413.229i	−0.0596388	−	0.103297i
$253$	116.630	−	202.009i	0.0289821	−	0.0501984i
$254$	−3019.95			−0.746018
$255$	−4263.21			−1.04695
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2617.92	−	4534.37i	0.635414	−	1.10057i	−0.351014	−	0.936370i	$-0.614163\pi$
$257$	2617.92	−	4534.37i	0.635414	−	1.10057i	0.986427	−	0.164198i	$-0.0525037\pi$
$258$	2197.01			0.530154
$259$	5580.92			1.33893
$260$	1953.58	−	3383.70i	0.465984	−	0.807107i
$261$	368.554	+	638.354i	0.0874058	+	0.151391i
$262$	370.944	−	642.494i	0.0874695	−	0.151502i
$263$	907.129	+	1571.19i	0.212684	+	0.368380i	0.952554	−	0.304371i	$-0.0984461\pi$
$263$	907.129	+	1571.19i	0.212684	+	0.368380i	−0.739869	+	0.672750i	$0.765113\pi$
$264$	−790.966	−	1369.99i	−0.184396	−	0.319384i
$265$	−9813.97			−2.27497
$266$	604.785	+	2110.47i	0.139405	+	0.486472i
$267$	−2161.22			−0.495372
$268$	319.724	+	553.779i	0.0728741	+	0.126222i
$269$	−506.699	−	877.629i	−0.114848	−	0.198922i	0.802871	−	0.596153i	$-0.203305\pi$
$269$	−506.699	−	877.629i	−0.114848	−	0.198922i	−0.917719	+	0.397231i	$0.869971\pi$
$270$	384.866	−	666.608i	0.0867490	−	0.150254i
$271$	959.258	+	1661.48i	0.215021	+	0.372428i	0.953279	−	0.302091i	$-0.0976845\pi$
$271$	959.258	+	1661.48i	0.215021	+	0.372428i	−0.738258	+	0.674519i	$0.764351\pi$
$272$	−797.552	+	1381.40i	−0.177789	+	0.307940i
$273$	2724.79			0.604072
$274$	−3380.75			−0.745396
$275$	2576.75	−	4463.06i	0.565032	−	0.978664i
$276$	21.2332	−	36.7769i	0.00463075	−	0.00802070i
$277$	6283.45			1.36295			0.681473	−	0.731844i	$-0.261340\pi$
$277$	6283.45			1.36295			0.681473	+	0.731844i	$0.261340\pi$
$278$	−5423.04			−1.16997
$279$	1112.35	−	1926.65i	0.238691	−	0.413425i
$280$	−755.724	−	1308.95i	−0.161297	−	0.279375i
$281$	4028.68	−	6977.88i	0.855270	−	1.48137i	−0.0211241	−	0.999777i	$-0.506724\pi$
$281$	4028.68	−	6977.88i	0.855270	−	1.48137i	0.876394	−	0.481594i	$-0.159942\pi$
$282$	−272.820	−	472.537i	−0.0576105	−	0.0997844i
$283$	96.7083	+	167.504i	0.0203135	+	0.0351840i	0.876003	−	0.482305i	$-0.160200\pi$
$283$	96.7083	+	167.504i	0.0203135	+	0.0351840i	−0.855690	+	0.517489i	$0.826867\pi$
$284$	−3167.54			−0.661826
$285$	−2460.62	+	2547.19i	−0.511420	+	0.529412i
$286$	9033.61			1.86772
$287$	2288.08	+	3963.07i	0.470597	+	0.815097i
$288$	−144.000	−	249.415i	−0.0294628	−	0.0510310i
$289$	−2512.95	+	4352.55i	−0.511489	+	0.885926i
$290$	1167.44	+	2022.07i	0.236395	+	0.409447i
$291$	623.088	−	1079.22i	0.125519	−	0.217406i
$292$	1288.52			0.258235
$293$	−4735.47			−0.944194			−0.472097	−	0.881547i	$-0.656503\pi$
$293$	−4735.47			−0.944194			−0.472097	+	0.881547i	$0.656503\pi$
$294$	−501.970	+	869.437i	−0.0995764	+	0.172471i
$295$	−1299.20	+	2250.28i	−0.256415	+	0.444124i
$296$	3368.52			0.661457
$297$	1779.67			0.347701
$298$	−2598.90	+	4501.43i	−0.505202	+	0.875036i
$299$	121.252	+	210.014i	0.0234521	+	0.0406202i
$300$	469.112	−	812.526i	0.0902807	−	0.156371i
$301$	2426.65	+	4203.09i	0.464684	+	0.804857i
$302$	−594.863	−	1030.33i	−0.113346	−	0.196321i
$303$	−1012.02			−0.191879
$304$	365.034	+	1273.83i	0.0688689	+	0.240327i
$305$	−7.37475			−0.00138451
$306$	−897.246	−	1554.08i	−0.167621	−	0.290329i
$307$	14.3561	+	24.8655i	0.00266888	+	0.00462263i	0.867357	−	0.497687i	$-0.165817\pi$
$307$	14.3561	+	24.8655i	0.00266888	+	0.00462263i	−0.864688	+	0.502310i	$0.832484\pi$
$308$	1747.28	−	3026.39i	0.323249	−	0.559884i
$309$	−2200.57	−	3811.50i	−0.405133	−	0.701711i
$310$	3523.52	−	6102.91i	0.645556	−	1.11814i
$311$	−1165.69			−0.212540			−0.106270	−	0.994337i	$-0.533891\pi$
$311$	−1165.69			−0.212540			−0.106270	+	0.994337i	$0.533891\pi$
$312$	1644.62			0.298424
$313$	−1256.38	+	2176.11i	−0.226884	+	0.392974i	−0.956883	−	0.290474i	$-0.906187\pi$
$313$	−1256.38	+	2176.11i	−0.226884	+	0.392974i	0.729999	+	0.683448i	$0.239520\pi$
$314$	58.2549	−	100.900i	0.0104698	−	0.0181342i
$315$	1700.38			0.304145
$316$	1273.48			0.226706
$317$	863.783	−	1496.12i	0.153044	−	0.265080i	−0.779301	−	0.626649i	$-0.784426\pi$
$317$	863.783	−	1496.12i	0.153044	−	0.265080i	0.932345	+	0.361570i	$0.117759\pi$
$318$	−2065.47	−	3577.51i	−0.364233	−	0.630870i
$319$	−2699.20	+	4675.15i	−0.473750	+	0.820558i
$320$	−456.138	−	790.054i	−0.0796840	−	0.138017i
$321$	573.020	+	992.500i	0.0996351	+	0.172573i
$322$	93.8104			0.0162356
$323$	2274.48	+	7937.10i	0.391813	+	1.36728i
$324$	324.000			0.0555556
$325$	2678.86	+	4639.92i	0.457220	+	0.791928i
$326$	−1152.53	−	1996.25i	−0.195807	−	0.339147i
$327$	−199.286	+	345.174i	−0.0337020	+	0.0583736i
$328$	1381.03	+	2392.02i	0.232484	+	0.402675i
$329$	602.673	−	1043.86i	0.100992	−	0.174924i
$330$	5637.34			0.940379
$331$	−6816.13			−1.13187			−0.565934	−	0.824450i	$-0.691484\pi$
$331$	−6816.13			−1.13187			−0.565934	+	0.824450i	$0.691484\pi$
$332$	−1368.32	+	2370.00i	−0.226194	+	0.391779i
$333$	−1894.79	+	3281.88i	−0.311814	+	0.540077i
$334$	2518.22			0.412547
$335$	−2278.72			−0.371642
$336$	318.103	−	550.971i	0.0516487	−	0.0894582i
$337$	5204.19	+	9013.93i	0.841218	+	1.45703i	0.888865	+	0.458168i	$0.151494\pi$
$337$	5204.19	+	9013.93i	0.841218	+	1.45703i	−0.0476473	+	0.998864i	$0.515172\pi$
$338$	−2498.79	+	4328.04i	−0.402120	+	0.696492i
$339$	−1706.91	−	2956.45i	−0.273471	−	0.473665i
$340$	−2842.14	−	4922.73i	−0.453343	−	0.785213i
$341$	16293.2			2.58747
$342$	−1446.40	−	360.887i	−0.228691	−	0.0570600i
$343$	−6763.98			−1.06478
$344$	1464.67	+	2536.89i	0.229564	+	0.397616i
$345$	75.6661	+	131.058i	0.0118079	+	0.0204519i
$346$	1274.10	−	2206.80i	0.197965	−	0.342886i
$347$	2792.02	+	4835.92i	0.431940	+	0.748143i	0.997040	−	0.0768797i	$-0.0244957\pi$
$347$	2792.02	+	4835.92i	0.431940	+	0.748143i	−0.565100	+	0.825022i	$0.691162\pi$
$348$	−491.405	+	851.138i	−0.0756956	+	0.131109i
$349$	5505.82			0.844470			0.422235	−	0.906486i	$-0.361246\pi$
$349$	5505.82			0.844470			0.422235	+	0.906486i	$0.361246\pi$
$350$	2072.59			0.316527
$351$	−925.099	+	1602.32i	−0.140678	+	0.243662i
$352$	1054.62	−	1826.66i	0.159692	−	0.276594i
$353$	−5782.46			−0.871868			−0.435934	−	0.899979i	$-0.643582\pi$
$353$	−5782.46			−0.871868			−0.435934	+	0.899979i	$0.643582\pi$
$354$	−1093.73			−0.164213
$355$	5643.88	−	9775.49i	0.843792	−	1.46149i
$356$	−1440.81	−	2495.56i	−0.214502	−	0.371529i
$357$	1982.06	−	3433.03i	0.293843	−	0.508951i
$358$	−2034.50	−	3523.85i	−0.300353	−	0.520227i
$359$	951.820	+	1648.60i	0.139931	+	0.242367i	0.927470	−	0.373897i	$-0.121979\pi$
$359$	951.820	+	1648.60i	0.139931	+	0.242367i	−0.787539	+	0.616264i	$0.788645\pi$
$360$	1026.31			0.150254
$361$	6055.05	+	3222.14i	0.882790	+	0.469769i
$362$	2066.63			0.300054
$363$	4520.45	+	7829.65i	0.653615	+	1.13209i
$364$	1816.53	+	3146.32i	0.261571	+	0.453054i
$365$	−2295.87	+	3976.55i	−0.329236	+	0.570253i
$366$	−1.55211	−	2.68833i	−0.000221667	−	0.000383938i
$367$	6374.02	−	11040.1i	0.906597	−	1.57027i	0.0878374	−	0.996135i	$-0.472004\pi$
$367$	6374.02	−	11040.1i	0.906597	−	1.57027i	0.818759	−	0.574137i	$-0.194662\pi$
$368$	56.6218			0.00802070
$369$	−3107.33			−0.438377
$370$	−6001.99	+	10395.7i	−0.843320	+	1.46067i
$371$	4562.74	−	7902.90i	0.638506	−	1.10592i
$372$	2966.28			0.413425
$373$	−736.660			−0.102260			−0.0511298	−	0.998692i	$-0.516282\pi$
$373$	−736.660			−0.102260			−0.0511298	+	0.998692i	$0.516282\pi$
$374$	6571.21	−	11381.7i	0.908528	−	1.57362i
$375$	−1000.97	−	1733.72i	−0.137839	−	0.238744i
$376$	363.760	−	630.050i	0.0498922	−	0.0864158i
$377$	−2806.16	−	4860.42i	−0.383355	−	0.663990i
$378$	357.866	+	619.843i	0.0486949	+	0.0843420i
$379$	1543.57			0.209202			0.104601	−	0.994514i	$-0.466643\pi$
$379$	1543.57			0.209202			0.104601	+	0.994514i	$0.466643\pi$
$380$	−4581.66	−	1143.15i	−0.618511	−	0.154323i
$381$	4529.92			0.609121
$382$	1135.46	+	1966.68i	0.152082	+	0.263414i
$383$	−3282.18	−	5684.90i	−0.437889	−	0.758446i	0.559637	−	0.828738i	$-0.310940\pi$
$383$	−3282.18	−	5684.90i	−0.437889	−	0.758446i	−0.997527	+	0.0702912i	$0.977607\pi$
$384$	192.000	−	332.554i	0.0255155	−	0.0441942i
$385$	6226.59	+	10784.8i	0.824250	+	1.42764i
$386$	−1091.07	+	1889.79i	−0.143871	+	0.249192i
$387$	−3295.51			−0.432869
$388$	1661.57			0.217406
$389$	1749.13	−	3029.59i	0.227981	−	0.394875i	−0.729229	−	0.684270i	$-0.760121\pi$
$389$	1749.13	−	3029.59i	0.227981	−	0.394875i	0.957210	+	0.289395i	$0.0934542\pi$
$390$	−2930.37	+	5075.54i	−0.380474	+	0.659001i
$391$	352.803			0.0456318
$392$	−1338.59			−0.172471
$393$	−556.416	+	963.741i	−0.0714185	+	0.123701i
$394$	−4138.08	−	7167.36i	−0.529120	−	0.916463i
$395$	−2269.08	+	3930.16i	−0.289037	+	0.500627i
$396$	1186.45	+	2054.99i	0.150559	+	0.260776i
$397$	−4305.30	−	7457.00i	−0.544274	−	0.942710i	−0.998652	−	0.0519013i	$-0.983472\pi$
$397$	−4305.30	−	7457.00i	−0.544274	−	0.942710i	0.454378	−	0.890809i	$-0.349861\pi$
$398$	−5468.47			−0.688717
$399$	−907.177	−	3165.71i	−0.113824	−	0.397203i
$400$	1250.97			0.156371
$401$	−882.872	−	1529.18i	−0.109946	−	0.190433i	0.805802	−	0.592185i	$-0.201735\pi$
$401$	−882.872	−	1529.18i	−0.109946	−	0.190433i	−0.915748	+	0.401752i	$0.868401\pi$
$402$	−479.586	−	830.668i	−0.0595015	−	0.103060i
$403$	−8469.44	+	14669.5i	−1.04688	+	1.81325i
$404$	−674.682	−	1168.58i	−0.0830858	−	0.143909i
$405$	−577.300	+	999.912i	−0.0708302	+	0.122682i
$406$	−2171.08			−0.265391
$407$	−27754.0			−3.38013
$408$	1196.33	−	2072.10i	0.145164	−	0.251432i
$409$	−6697.86	+	11601.0i	−0.809751	+	1.40253i	0.103286	+	0.994652i	$0.467064\pi$
$409$	−6697.86	+	11601.0i	−0.809751	+	1.40253i	−0.913037	+	0.407877i	$0.866269\pi$
$410$	−9842.85			−1.18562
$411$	5071.12			0.608613
$412$	2934.10	−	5082.00i	0.350856	−	0.607700i
$413$	−1208.06	−	2092.41i	−0.143934	−	0.249300i
$414$	−31.8498	+	55.1654i	−0.00378099	+	0.00654887i
$415$	−4876.11	−	8445.67i	−0.576769	−	0.998992i
$416$	1096.41	+	1899.04i	0.129221	+	0.223818i
$417$	8134.57			0.955279
$418$	−3007.60	−	10495.4i	−0.351930	−	1.22810i
$419$	9117.71			1.06308			0.531539	−	0.847034i	$-0.321614\pi$
$419$	9117.71			1.06308			0.531539	+	0.847034i	$0.321614\pi$
$420$	1133.59	+	1963.43i	0.131698	+	0.228108i
$421$	−4102.23	−	7105.27i	−0.474894	−	0.822540i	0.524693	−	0.851292i	$-0.324180\pi$
$421$	−4102.23	−	7105.27i	−0.474894	−	0.822540i	−0.999587	+	0.0287514i	$0.990847\pi$
$422$	−3058.01	+	5296.62i	−0.352752	+	0.610985i
$423$	409.229	+	708.806i	0.0470388	+	0.0814736i
$424$	2753.97	−	4770.01i	0.315435	−	0.546349i
$425$	7794.61			0.889634
$426$	4751.30			0.540379
$427$	3.42869	−	5.93867i	0.000388585	−	0.000673050i
$428$	−764.027	+	1323.33i	−0.0862865	+	0.149453i
$429$	−13550.4			−1.52499
$430$	−10439.0			−1.17072
$431$	635.672	−	1101.02i	0.0710423	−	0.123049i	−0.828316	−	0.560261i	$-0.810701\pi$
$431$	635.672	−	1101.02i	0.0710423	−	0.123049i	0.899358	+	0.437212i	$0.144034\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	1983.79	−	3436.03i	0.220173	−	0.381351i	−0.734687	−	0.678406i	$-0.762671\pi$
$433$	1983.79	−	3436.03i	0.220173	−	0.381351i	0.954860	+	0.297055i	$0.0960044\pi$
$434$	3276.33	+	5674.77i	0.362370	+	0.627644i
$435$	−1751.16	−	3033.10i	−0.193015	−	0.334312i
$436$	−531.430			−0.0583736
$437$	203.630	−	210.794i	0.0222905	−	0.0230747i
$438$	−1932.78			−0.210848
$439$	−104.519	−	181.032i	−0.0113632	−	0.0196816i	0.860288	−	0.509808i	$-0.170284\pi$
$439$	−104.519	−	181.032i	−0.0113632	−	0.0196816i	−0.871651	+	0.490127i	$0.836950\pi$
$440$	3758.23	+	6509.44i	0.407196	+	0.705285i
$441$	752.955	−	1304.16i	0.0813038	−	0.140822i
$442$	6831.62	+	11832.7i	0.735174	+	1.27336i
$443$	−2867.02	+	4965.83i	−0.307486	+	0.532581i	−0.977812	−	0.209486i	$-0.932821\pi$
$443$	−2867.02	+	4965.83i	−0.307486	+	0.532581i	0.670326	+	0.742067i	$0.266154\pi$
$444$	−5052.78			−0.540077
$445$	10268.9			1.09391
$446$	−1618.27	+	2802.92i	−0.171810	+	0.297583i
$447$	3898.35	−	6752.14i	0.412496	−	0.714464i
$448$	848.276			0.0894582
$449$	9741.13			1.02386			0.511929	−	0.859028i	$-0.328931\pi$
$449$	9741.13			1.02386			0.511929	+	0.859028i	$0.328931\pi$
$450$	−703.668	+	1218.79i	−0.0737139	+	0.127676i
$451$	−11378.7	−	19708.4i	−1.18803	−	2.05772i
$452$	2275.88	−	3941.94i	0.236833	−	0.410206i
$453$	892.294	+	1545.50i	0.0925467	+	0.160296i
$454$	6065.43	+	10505.6i	0.627015	+	1.08602i
$455$	−12946.7			−1.33395
$456$	−547.551	−	1910.75i	−0.0562312	−	0.196226i
$457$	−17233.8			−1.76403			−0.882016	−	0.471220i	$-0.843814\pi$
$457$	−17233.8			−1.76403			−0.882016	+	0.471220i	$0.843814\pi$
$458$	1916.36	+	3319.24i	0.195515	+	0.338641i
$459$	1345.87	+	2331.11i	0.136862	+	0.237052i
$460$	−100.888	+	174.743i	−0.0102259	+	0.0177118i
$461$	−832.617	−	1442.14i	−0.0841190	−	0.145698i	0.820896	−	0.571077i	$-0.193474\pi$
$461$	−832.617	−	1442.14i	−0.0841190	−	0.145698i	−0.905015	+	0.425379i	$0.860141\pi$
$462$	−2620.93	+	4539.58i	−0.263932	+	0.457144i
$463$	−10694.0			−1.07342			−0.536710	−	0.843767i	$-0.680333\pi$
$463$	−10694.0			−1.07342			−0.536710	+	0.843767i	$0.680333\pi$
$464$	−1310.41			−0.131109
$465$	−5285.28	+	9154.37i	−0.527094	+	0.912954i
$466$	4008.54	−	6942.99i	0.398481	−	0.690189i
$467$	13212.7			1.30923			0.654614	−	0.755963i	$-0.272831\pi$
$467$	13212.7			1.30923			0.654614	+	0.755963i	$0.272831\pi$
$468$	−2466.93			−0.243662
$469$	1059.43	−	1834.99i	0.104307	−	0.180665i
$470$	1296.29	+	2245.23i	0.127220	+	0.220351i
$471$	−87.3823	+	151.351i	−0.00854854	+	0.0148065i
$472$	−729.155	−	1262.93i	−0.0711061	−	0.123159i
$473$	−12067.8	−	20902.0i	−1.17310	−	2.03187i
$474$	−1910.22			−0.185105
$475$	4498.86	−	4657.14i	0.434573	−	0.449862i
$476$	5285.50			0.508951
$477$	3098.21	+	5366.26i	0.297395	+	0.515103i
$478$	−530.292	−	918.493i	−0.0507427	−	0.0878889i
$479$	−2704.77	+	4684.79i	−0.258004	+	0.446876i	−0.965707	−	0.259634i	$-0.916398\pi$
$479$	−2704.77	+	4684.79i	−0.258004	+	0.446876i	0.707703	+	0.706510i	$0.249731\pi$
$480$	684.207	+	1185.08i	0.0650617	+	0.112690i
$481$	14426.9	−	24988.1i	1.36759	−	2.36874i
$482$	2542.45			0.240260
$483$	−140.716			−0.0132563
$484$	−6027.27	+	10439.5i	−0.566047	+	0.980422i
$485$	−2960.56	+	5127.85i	−0.277180	+	0.480090i
$486$	−486.000			−0.0453609
$487$	14297.0			1.33031			0.665154	−	0.746706i	$-0.268366\pi$
$487$	14297.0			1.33031			0.665154	+	0.746706i	$0.268366\pi$
$488$	2.06948	−	3.58444i	0.000191969	−	0.000332500i
$489$	1728.80	+	2994.37i	0.159875	+	0.276912i
$490$	2385.08	−	4131.08i	0.219891	−	0.380863i
$491$	−1401.21	−	2426.97i	−0.128790	−	0.223070i	0.794418	−	0.607371i	$-0.207776\pi$
$491$	−1401.21	−	2426.97i	−0.128790	−	0.223070i	−0.923208	+	0.384301i	$0.874443\pi$
$492$	−2071.55	−	3588.03i	−0.189823	−	0.328782i
$493$	−8165.02			−0.745911
$494$	11012.9	+	2747.79i	1.00302	+	0.250261i
$495$	−8456.01			−0.767817
$496$	1977.52	+	3425.16i	0.179018	+	0.310069i
$497$	5247.94	+	9089.70i	0.473646	+	0.820380i
$498$	2052.48	−	3555.00i	0.184686	−	0.319886i
$499$	−7089.13	−	12278.7i	−0.635978	−	1.10155i	−0.986307	−	0.164919i	$-0.947264\pi$
$499$	−7089.13	−	12278.7i	−0.635978	−	1.10155i	0.350329	−	0.936627i	$-0.386070\pi$
$500$	1334.62	−	2311.63i	0.119372	−	0.206758i
$501$	−3777.33			−0.336843
$502$	1103.98			0.0981533
$503$	2768.93	−	4795.92i	0.245448	−	0.425128i	−0.716810	−	0.697269i	$-0.754398\pi$
$503$	2768.93	−	4795.92i	0.245448	−	0.425128i	0.962257	+	0.272141i	$0.0877317\pi$
$504$	−477.155	+	826.457i	−0.0421710	+	0.0730423i
$505$	4808.56			0.423719
$506$	−466.520			−0.0409869
$507$	3748.19	−	6492.06i	0.328329	−	0.568683i
$508$	3019.95	+	5230.71i	0.263757	+	0.456841i
$509$	−4557.55	+	7893.90i	−0.396876	+	0.687409i	−0.993339	−	0.115232i	$-0.963239\pi$
$509$	−4557.55	+	7893.90i	−0.396876	+	0.687409i	0.596463	+	0.802641i	$0.296572\pi$
$510$	4263.21	+	7384.09i	0.370153	+	0.641124i
$511$	−2134.80	−	3697.58i	−0.184810	−	0.320101i
$512$	512.000			0.0441942
$513$	2169.60	+	541.330i	0.186726	+	0.0465893i
$514$	−10471.7			−0.898610
$515$	10455.9	+	18110.1i	0.894643	+	1.54957i
$516$	−2197.01	−	3805.33i	−0.187438	−	0.324652i
$517$	−2997.10	+	5191.13i	−0.254956	+	0.441597i
$518$	−5580.92	−	9666.44i	−0.473382	−	0.819921i
$519$	−1911.15	+	3310.21i	−0.161638	+	0.279965i
$520$	−7814.31			−0.659001
$521$	−2705.46			−0.227502			−0.113751	−	0.993509i	$-0.536287\pi$
$521$	−2705.46			−0.227502			−0.113751	+	0.993509i	$0.536287\pi$
$522$	737.108	−	1276.71i	0.0618052	−	0.107050i
$523$	11564.2	−	20029.7i	0.966856	−	1.67464i	0.262311	−	0.964983i	$-0.415515\pi$
$523$	11564.2	−	20029.7i	0.966856	−	1.67464i	0.704544	−	0.709660i	$-0.251151\pi$
$524$	−1483.78			−0.123701
$525$	−3108.88			−0.258443
$526$	1814.26	−	3142.39i	0.150390	−	0.260484i
$527$	12321.7	+	21341.7i	1.01848	+	1.76406i
$528$	−1581.93	+	2739.99i	−0.130388	+	0.225838i
$529$	6077.24	+	10526.1i	0.499485	+	0.865134i
$530$	9813.97	+	16998.3i	0.804324	+	1.39313i
$531$	1640.60			0.134079
$532$	3050.66	−	3157.99i	0.248615	−	0.257362i
$533$	23659.1			1.92269
$534$	2161.22	+	3743.34i	0.175140	+	0.303352i
$535$	−2722.67	−	4715.80i	−0.220021	−	0.381088i
$536$	639.448	−	1107.56i	0.0515298	−	0.0892522i
$537$	3051.75	+	5285.78i	0.245238	+	0.424764i
$538$	−1013.40	+	1755.26i	−0.0812095	+	0.140659i
$539$	11028.9			0.881353
$540$	−1539.47			−0.122682
$541$	4820.58	−	8349.50i	0.383093	−	0.663536i	−0.608410	−	0.793623i	$-0.708192\pi$
$541$	4820.58	−	8349.50i	0.383093	−	0.663536i	0.991503	+	0.130087i	$0.0415257\pi$
$542$	1918.52	−	3322.97i	0.152043	−	0.263346i
$543$	−3099.94			−0.244993
$544$	3190.21			0.251432
$545$	946.896	−	1640.07i	0.0744231	−	0.128905i
$546$	−2724.79	−	4719.47i	−0.213572	−	0.369917i
$547$	8688.50	−	15048.9i	0.679147	−	1.17632i	−0.296091	−	0.955160i	$-0.595683\pi$
$547$	8688.50	−	15048.9i	0.679147	−	1.17632i	0.975238	−	0.221158i	$-0.0709835\pi$
$548$	3380.75	+	5855.63i	0.263537	+	0.456460i
$549$	2.32816	+	4.03250i	0.000180990	+	0.000313484i
$550$	−10307.0			−0.799076
$551$	−4712.66	+	4878.45i	−0.364366	+	0.377185i
$552$	−84.9327			−0.00654887
$553$	−2109.89	−	3654.44i	−0.162246	−	0.281018i
$554$	−6283.45	−	10883.3i	−0.481874	−	0.834630i
$555$	9002.98	−	15593.6i	0.688568	−	1.19264i
$556$	5423.04	+	9392.99i	0.413648	+	0.716459i
$557$	−9372.14	+	16233.0i	−0.712945	+	1.23486i	0.250802	+	0.968038i	$0.419306\pi$
$557$	−9372.14	+	16233.0i	−0.712945	+	1.23486i	−0.963747	+	0.266819i	$0.914028\pi$
$558$	−4449.41			−0.337560
$559$	25092.0			1.89853
$560$	−1511.45	+	2617.91i	−0.114054	+	0.197548i
$561$	−9856.82	+	17072.5i	−0.741810	+	1.28485i
$562$	−16114.7			−1.20953
$563$	−7618.70			−0.570320			−0.285160	−	0.958480i	$-0.592047\pi$
$563$	−7618.70			−0.570320			−0.285160	+	0.958480i	$0.592047\pi$
$564$	−545.639	+	945.075i	−0.0407368	+	0.0705582i
$565$	8110.28	+	14047.4i	0.603897	+	1.04598i
$566$	193.417	−	335.007i	0.0143638	−	0.0248788i
$567$	−536.800	−	929.764i	−0.0397592	−	0.0688649i
$568$	3167.54	+	5486.33i	0.233991	+	0.405284i
$569$	−13081.6			−0.963816			−0.481908	−	0.876222i	$-0.660056\pi$
$569$	−13081.6			−0.963816			−0.481908	+	0.876222i	$0.660056\pi$
$570$	6872.48	+	1714.73i	0.505012	+	0.126004i
$571$	8643.49			0.633483			0.316741	−	0.948512i	$-0.397411\pi$
$571$	8643.49			0.633483			0.316741	+	0.948512i	$0.397411\pi$
$572$	−9033.61	−	15646.7i	−0.660339	−	1.14374i
$573$	−1703.20	−	2950.02i	−0.124175	−	0.215077i
$574$	4576.16	−	7926.15i	0.332762	−	0.576361i
$575$	−138.344	−	239.618i	−0.0100336	−	0.0173787i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	9841.26			0.710047			0.355024	−	0.934857i	$-0.384473\pi$
$577$	9841.26			0.710047			0.355024	+	0.934857i	$0.384473\pi$
$578$	10051.8			0.723355
$579$	1636.61	−	2834.69i	0.117470	−	0.203464i
$580$	2334.88	−	4044.13i	0.167156	−	0.289523i
$581$	9068.06			0.647516
$582$	−2492.35			−0.177511
$583$	−22690.6	+	39301.2i	−1.61192	+	2.79192i
$584$	−1288.52	−	2231.78i	−0.0913000	−	0.158136i
$585$	4395.55	−	7613.32i	0.310656	−	0.538072i
$586$	4735.47	+	8202.07i	0.333823	+	0.578198i
$587$	−9949.24	−	17232.6i	−0.699573	−	1.21170i	−0.968615	−	0.248567i	$-0.920040\pi$
$587$	−9949.24	−	17232.6i	−0.699573	−	1.21170i	0.269042	−	0.963128i	$-0.413293\pi$
$588$	2007.88			0.140822
$589$	19863.1	+	4955.97i	1.38955	+	0.346702i
$590$	5196.80			0.362625
$591$	6207.12	+	10751.0i	0.432025	+	0.748289i
$592$	−3368.52	−	5834.44i	−0.233860	−	0.405058i
$593$	−11097.5	+	19221.4i	−0.768497	+	1.33108i	0.169881	+	0.985465i	$0.445662\pi$
$593$	−11097.5	+	19221.4i	−0.768497	+	1.33108i	−0.938378	+	0.345611i	$0.887672\pi$
$594$	−1779.67	−	3082.48i	−0.122931	−	0.212922i
$595$	−9417.65	+	16311.8i	−0.648884	+	1.12390i
$596$	10395.6			0.714464
$597$	8202.70			0.562335
$598$	242.504	−	420.029i	0.0165831	−	0.0287228i
$599$	−9848.11	+	17057.4i	−0.671758	+	1.16352i	0.305647	+	0.952145i	$0.401127\pi$
$599$	−9848.11	+	17057.4i	−0.671758	+	1.16352i	−0.977405	+	0.211374i	$0.932206\pi$
$600$	−1876.45			−0.127676
$601$	−14626.5			−0.992724			−0.496362	−	0.868116i	$-0.665331\pi$
$601$	−14626.5			−0.992724			−0.496362	+	0.868116i	$0.665331\pi$
$602$	4853.31	−	8406.17i	0.328581	−	0.569120i
$603$	719.379	+	1246.00i	0.0485827	+	0.0841478i
$604$	−1189.73	+	2060.67i	−0.0801478	+	0.138820i
$605$	−21478.6	−	37202.1i	−1.44336	−	2.49997i
$606$	1012.02	+	1752.88i	0.0678393	+	0.117501i
$607$	−16312.0			−1.09075			−0.545375	−	0.838192i	$-0.683613\pi$
$607$	−16312.0			−1.09075			−0.545375	+	0.838192i	$0.683613\pi$
$608$	1841.31	−	1906.09i	0.122821	−	0.127142i
$609$	3256.62			0.216691
$610$	7.37475	+	12.7734i	0.000489500	+	0.000847839i
$611$	−3115.87	−	5396.84i	−0.206308	−	0.357337i
$612$	−1794.49	+	3108.15i	−0.118526	+	0.205293i
$613$	−8874.36	−	15370.8i	−0.584718	−	1.01276i	−0.994911	−	0.100762i	$-0.967872\pi$
$613$	−8874.36	−	15370.8i	−0.584718	−	1.01276i	0.410192	−	0.911999i	$-0.365462\pi$
$614$	28.7122	−	49.7309i	0.00188718	−	0.00326869i
$615$	14764.3			0.968053
$616$	−6989.14			−0.457144
$617$	−1864.90	+	3230.10i	−0.121682	+	0.210760i	−0.920431	−	0.390905i	$-0.872162\pi$
$617$	−1864.90	+	3230.10i	−0.121682	+	0.210760i	0.798749	+	0.601665i	$0.205496\pi$
$618$	−4401.14	+	7623.00i	−0.286472	+	0.496185i
$619$	−1003.67			−0.0651714			−0.0325857	−	0.999469i	$-0.510374\pi$
$619$	−1003.67			−0.0651714			−0.0325857	+	0.999469i	$0.510374\pi$
$620$	−14094.1			−0.912954
$621$	47.7747	−	82.7481i	0.00308717	−	0.00534713i
$622$	1165.69	+	2019.03i	0.0751444	+	0.130154i
$623$	−4774.24	+	8269.23i	−0.307024	+	0.531781i
$624$	−1644.62	−	2848.57i	−0.105509	−	0.182747i
$625$	9642.61	+	16701.5i	0.617127	+	1.06890i
$626$	5025.51			0.320862
$627$	4511.40	+	15743.1i	0.287349	+	1.00274i
$628$	−233.019			−0.0148065
$629$	−20988.8	−	36353.7i	−1.33049	−	2.30448i
$630$	−1700.38	−	2945.14i	−0.107531	−	0.186250i
$631$	−8423.38	+	14589.7i	−0.531426	+	0.920456i	0.467902	+	0.883781i	$0.345010\pi$
$631$	−8423.38	+	14589.7i	−0.531426	+	0.920456i	−0.999327	+	0.0366756i	$0.988323\pi$
$632$	−1273.48	−	2205.74i	−0.0801526	−	0.138828i
$633$	4587.01	−	7944.93i	0.288021	−	0.498867i
$634$	−3455.13			−0.216437
$635$	−21523.7			−1.34510
$636$	−4130.95	+	7155.01i	−0.257552	+	0.446092i
$637$	−5732.98	+	9929.82i	−0.356592	+	0.617636i
$638$	10796.8			0.669983
$639$	−7126.96			−0.441218
$640$	−912.276	+	1580.11i	−0.0563451	+	0.0975926i
$641$	80.9977	+	140.292i	0.00499098	+	0.00864463i	0.868510	−	0.495671i	$-0.165078\pi$
$641$	80.9977	+	140.292i	0.00499098	+	0.00864463i	−0.863519	+	0.504316i	$0.831745\pi$
$642$	1146.04	−	1985.00i	0.0704527	−	0.122028i
$643$	−3145.45	−	5448.09i	−0.192915	−	0.334139i	0.753300	−	0.657677i	$-0.228461\pi$
$643$	−3145.45	−	5448.09i	−0.192915	−	0.334139i	−0.946215	+	0.323538i	$0.895128\pi$
$644$	−93.8104	−	162.484i	−0.00574014	−	0.00994221i
$645$	15658.4			0.955891
$646$	11473.0	−	11876.6i	0.698759	−	0.723343i
$647$	28249.8			1.71656			0.858280	−	0.513181i	$-0.171533\pi$
$647$	28249.8			1.71656			0.858280	+	0.513181i	$0.171533\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	6007.68	+	10405.6i	0.363362	+	0.629361i
$650$	5357.72	−	9279.85i	0.323303	−	0.559978i
$651$	−4914.49	−	8512.15i	−0.295874	−	0.512469i
$652$	−2305.07	+	3992.50i	−0.138456	+	0.239813i
$653$	11423.5			0.684587			0.342293	−	0.939593i	$-0.388796\pi$
$653$	11423.5			0.684587			0.342293	+	0.939593i	$0.388796\pi$
$654$	797.145			0.0476618
$655$	2643.78	−	4579.16i	0.157711	−	0.273164i
$656$	2762.07	−	4784.04i	0.164391	−	0.284734i
$657$	2899.16			0.172157
$658$	−2410.69			−0.142824
$659$	−100.069	+	173.324i	−0.00591522	+	0.0102455i	−0.868968	−	0.494869i	$-0.835216\pi$
$659$	−100.069	+	173.324i	−0.00591522	+	0.0102455i	0.863053	+	0.505114i	$0.168550\pi$
$660$	−5637.34	−	9764.16i	−0.332474	−	0.575862i
$661$	1303.50	−	2257.73i	0.0767026	−	0.132853i	−0.825123	−	0.564953i	$-0.808894\pi$
$661$	1303.50	−	2257.73i	0.0767026	−	0.132853i	0.901825	+	0.432101i	$0.142227\pi$
$662$	6816.13	+	11805.9i	0.400176	+	0.693125i
$663$	−10247.4	−	17749.1i	−0.600267	−	1.03969i
$664$	5473.28			0.319886
$665$	4310.39	+	15041.7i	0.251353	+	0.877130i
$666$	7579.17			0.440971
$667$	144.918	+	251.005i	0.00841266	+	0.0145712i
$668$	−2518.22	−	4361.68i	−0.145857	−	0.252632i
$669$	2427.40	−	4204.38i	0.140282	−	0.242976i
$670$	2278.72	+	3946.87i	0.131395	+	0.227583i
$671$	−17.0509	+	29.5331i	−0.000980989	+	0.00169912i
$672$	−1272.41			−0.0730423
$673$	14561.2			0.834015			0.417007	−	0.908903i	$-0.363079\pi$
$673$	14561.2			0.834015			0.417007	+	0.908903i	$0.363079\pi$
$674$	10408.4	−	18027.9i	0.594831	−	1.03028i
$675$	1055.50	−	1828.18i	0.0601871	−	0.104247i
$676$	9995.18			0.568683
$677$	12684.6			0.720100			0.360050	−	0.932933i	$-0.382760\pi$
$677$	12684.6			0.720100			0.360050	+	0.932933i	$0.382760\pi$
$678$	−3413.82	+	5912.91i	−0.193373	+	0.334932i
$679$	−2752.87	−	4768.11i	−0.155590	−	0.269489i
$680$	−5684.28	+	9845.46i	−0.320562	+	0.555230i
$681$	−9098.15	−	15758.5i	−0.511956	−	0.886733i
$682$	−16293.2	−	28220.7i	−0.914809	−	1.58450i
$683$	12054.5			0.675332			0.337666	−	0.941266i	$-0.390363\pi$
$683$	12054.5			0.675332			0.337666	+	0.941266i	$0.390363\pi$
$684$	821.327	+	2866.13i	0.0459126	+	0.160218i
$685$	−24095.1			−1.34398
$686$	6763.98	+	11715.6i	0.376458	+	0.652044i
$687$	−2874.54	−	4978.86i	−0.159637	−	0.276500i
$688$	2929.35	−	5073.78i	0.162326	−	0.281157i
$689$	−23589.7	−	40858.6i	−1.30435	−	2.25920i
$690$	151.332	−	262.115i	0.00834945	−	0.0144617i
$691$	3338.42			0.183791			0.0918953	−	0.995769i	$-0.470707\pi$
$691$	3338.42			0.183791			0.0918953	+	0.995769i	$0.470707\pi$
$692$	−5096.40			−0.279965
$693$	3931.39	−	6809.37i	0.215500	−	0.373256i
$694$	5584.03	−	9671.83i	0.305428	−	0.529017i
$695$	−38650.9			−2.10951
$696$	1965.62			0.107050
$697$	17210.1	−	29808.8i	0.935264	−	1.61993i
$698$	−5505.82	−	9536.37i	−0.298565	−	0.517130i
$699$	−6012.81	+	10414.5i	−0.325358	+	0.563537i
$700$	−2072.59	−	3589.83i	−0.111909	−	0.193832i
$701$	11891.4	+	20596.5i	0.640702	+	1.10973i	0.985276	+	0.170969i	$0.0546898\pi$
$701$	11891.4	+	20596.5i	0.640702	+	1.10973i	−0.344575	+	0.938759i	$0.611977\pi$
$702$	3700.40			0.198949
$703$	−33834.9	−	8442.04i	−1.81523	−	0.452913i
$704$	−4218.49			−0.225838
$705$	−1944.43	−	3367.85i	−0.103874	−	0.179916i
$706$	5782.46	+	10015.5i	0.308252	+	0.533908i
$707$	−2235.61	+	3872.19i	−0.118923	+	0.205981i
$708$	1093.73	+	1894.40i	0.0580579	+	0.100559i
$709$	−16092.6	+	27873.1i	−0.852424	+	1.47644i	0.0265907	+	0.999646i	$0.491535\pi$
$709$	−16092.6	+	27873.1i	−0.852424	+	1.47644i	−0.879015	+	0.476795i	$0.841798\pi$
$710$	−22575.5			−1.19330
$711$	2865.34			0.151137
$712$	−2881.62	+	4991.12i	−0.151676	+	0.262711i
$713$	437.385	−	757.573i	0.0229736	−	0.0397915i
$714$	−7928.25			−0.415557
$715$	64383.9			3.36758
$716$	−4068.99	+	7047.70i	−0.212382	+	0.367856i
$717$	795.438	+	1377.74i	0.0414312	+	0.0717610i
$718$	1903.64	−	3297.20i	0.0989459	−	0.171379i
$719$	19159.7	+	33185.5i	0.993791	+	1.72130i	0.593255	+	0.805015i	$0.297843\pi$
$719$	19159.7	+	33185.5i	0.993791	+	1.72130i	0.400536	+	0.916281i	$0.368824\pi$
$720$	−1026.31	−	1777.62i	−0.0531227	−	0.0920112i
$721$	−19444.7			−1.00438
$722$	−474.139	−	13709.8i	−0.0244399	−	0.706684i
$723$	−3813.68			−0.196172
$724$	−2066.63	−	3579.50i	−0.106085	−	0.183745i
$725$	3201.72	+	5545.55i	0.164012	+	0.284078i
$726$	9040.90	−	15659.3i	0.462175	−	0.800511i
$727$	18271.6	+	31647.3i	0.932125	+	1.61449i	0.779683	+	0.626175i	$0.215380\pi$
$727$	18271.6	+	31647.3i	0.932125	+	1.61449i	0.152442	+	0.988312i	$0.451286\pi$
$728$	3633.05	−	6292.63i	0.184959	−	0.320358i
$729$	729.000			0.0370370
$730$	9183.46			0.465610
$731$	18252.4	−	31614.1i	0.923514	−	1.59957i
$732$	−3.10422	+	5.37667i	−0.000156742	+	0.000271485i
$733$	−15689.3			−0.790584			−0.395292	−	0.918555i	$-0.629357\pi$
$733$	−15689.3			−0.790584			−0.395292	+	0.918555i	$0.629357\pi$
$734$	−25496.1			−1.28212
$735$	−3577.62	+	6196.61i	−0.179541	+	0.310973i
$736$	−56.6218	−	98.0719i	−0.00283574	−	0.00491165i
$737$	−5268.56	+	9125.42i	−0.263324	+	0.456091i
$738$	3107.33	+	5382.05i	0.154990	+	0.268450i
$739$	18222.8	+	31562.9i	0.907088	+	1.57112i	0.818089	+	0.575091i	$0.195033\pi$
$739$	18222.8	+	31562.9i	0.907088	+	1.57112i	0.0889991	+	0.996032i	$0.471633\pi$
$740$	24008.0			1.19264
$741$	−16519.3	−	4121.68i	−0.818964	−	0.204337i
$742$	−18251.0			−0.902984
$743$	−839.144	−	1453.44i	−0.0414337	−	0.0717652i	0.844565	−	0.535453i	$-0.179859\pi$
$743$	−839.144	−	1453.44i	−0.0414337	−	0.0717652i	−0.885999	+	0.463688i	$0.846526\pi$
$744$	−2966.28	−	5137.74i	−0.146168	−	0.253170i
$745$	−18522.8	+	32082.4i	−0.910902	+	1.57773i
$746$	736.660	+	1275.93i	0.0361542	+	0.0626209i
$747$	−3078.72	+	5332.50i	−0.150796	+	0.261186i
$748$	−26284.9			−1.28485
$749$	5063.33			0.247009
$750$	−2001.93	+	3467.44i	−0.0974669	+	0.168818i
$751$	−4320.84	+	7483.91i	−0.209946	+	0.363637i	−0.951697	−	0.307038i	$-0.900662\pi$
$751$	−4320.84	+	7483.91i	−0.209946	+	0.363637i	0.741751	+	0.670675i	$0.233996\pi$
$752$	−1455.04			−0.0705582
$753$	−1655.97			−0.0801418
$754$	−5612.33	+	9720.83i	−0.271073	+	0.469512i
$755$	−4239.68	−	7343.34i	−0.204368	−	0.353976i
$756$	715.733	−	1239.69i	0.0344325	−	0.0596388i
$757$	−1793.40	−	3106.25i	−0.0861058	−	0.149140i	0.819756	−	0.572713i	$-0.194109\pi$
$757$	−1793.40	−	3106.25i	−0.0861058	−	0.149140i	−0.905862	+	0.423573i	$0.860776\pi$
$758$	−1543.57	−	2673.54i	−0.0739642	−	0.128110i
$759$	699.780			0.0334656
$760$	2601.66	+	9078.82i	0.124174	+	0.433320i
$761$	−11615.4			−0.553297			−0.276649	−	0.960971i	$-0.589224\pi$
$761$	−11615.4			−0.553297			−0.276649	+	0.960971i	$0.589224\pi$
$762$	−4529.92	−	7846.06i	−0.215357	−	0.373009i
$763$	880.467	+	1525.01i	0.0417760	+	0.0723581i
$764$	2270.93	−	3933.37i	0.107538	−	0.186262i
$765$	−6394.81	−	11076.1i	−0.302229	−	0.523475i
$766$	−6564.36	+	11369.8i	−0.309634	+	0.536303i
$767$	−12491.5			−0.588060
$768$	−768.000			−0.0360844
$769$	−3010.91	+	5215.06i	−0.141192	+	0.244551i	−0.927946	−	0.372716i	$-0.878427\pi$
$769$	−3010.91	+	5215.06i	−0.141192	+	0.244551i	0.786754	+	0.617267i	$0.211760\pi$
$770$	12453.2	−	21569.5i	0.582833	−	1.00950i
$771$	15707.5			0.733712
$772$	4364.29			0.203464
$773$	754.493	−	1306.82i	0.0351064	−	0.0608061i	−0.847938	−	0.530095i	$-0.822156\pi$
$773$	754.493	−	1306.82i	0.0351064	−	0.0608061i	0.883045	+	0.469289i	$0.155490\pi$
$774$	3295.51	+	5708.00i	0.153042	+	0.265077i
$775$	9663.31	−	16737.3i	0.447892	−	0.775772i
$776$	−1661.57	−	2877.92i	−0.0768645	−	0.133133i
$777$	8371.39	+	14499.7i	0.386515	+	0.669463i
$778$	−6996.54			−0.322414
$779$	−7876.95	−	27487.6i	−0.362286	−	1.26425i
$780$	11721.5			0.538072
$781$	−26098.1	−	45203.2i	−1.19573	−	2.07106i
$782$	−352.803	−	611.074i	−0.0161333	−	0.0279437i
$783$	−1105.66	+	1915.06i	−0.0504637	+	0.0874058i
$784$	1338.59	+	2318.50i	0.0609779	+	0.105617i
$785$	415.192	−	719.133i	0.0188775	−	0.0326968i
$786$	2225.67			0.101001
$787$	3255.84			0.147469			0.0737346	−	0.997278i	$-0.476508\pi$
$787$	3255.84			0.147469			0.0737346	+	0.997278i	$0.476508\pi$
$788$	−8276.16	+	14334.7i	−0.374144	+	0.648037i
$789$	−2721.39	+	4713.58i	−0.122793	+	0.212684i
$790$	9076.31			0.408760
$791$	−15082.6			−0.677972
$792$	2372.90	−	4109.98i	0.106461	−	0.184396i
$793$	−17.7266	−	30.7034i	−0.000793809	−	0.00137492i
$794$	−8610.60	+	14914.0i	−0.384860	+	0.666597i
$795$	−14721.0	−	25497.4i	−0.656728	−	1.13749i
$796$	5468.47	+	9471.66i	0.243498	+	0.421751i
$797$	31732.8			1.41033			0.705164	−	0.709044i	$-0.250873\pi$
$797$	31732.8			1.41033			0.705164	+	0.709044i	$0.250873\pi$
$798$	−4576.00	+	4736.99i	−0.202993	+	0.210135i
$799$	−9066.16			−0.401424
$800$	−1250.97	−	2166.74i	−0.0552854	−	0.0957572i
$801$	−3241.83	−	5615.01i	−0.143002	−	0.247686i
$802$	−1765.74	+	3058.36i	−0.0777439	+	0.134656i
$803$	10616.4	+	18388.1i	0.466556	+	0.808098i
$804$	−959.173	+	1661.34i	−0.0420739	+	0.0728741i
$805$	668.601			0.0292734
$806$	33877.8			1.48051
$807$	1520.10	−	2632.89i	0.0663073	−	0.114848i
$808$	−1349.36	+	2337.17i	−0.0587506	+	0.101759i
$809$	3853.96			0.167488			0.0837441	−	0.996487i	$-0.473312\pi$
$809$	3853.96			0.167488			0.0837441	+	0.996487i	$0.473312\pi$
$810$	2309.20			0.100169
$811$	−15935.9	+	27601.8i	−0.689995	+	1.19511i	0.281844	+	0.959460i	$0.409054\pi$
$811$	−15935.9	+	27601.8i	−0.689995	+	1.19511i	−0.971839	+	0.235646i	$0.924279\pi$
$812$	2171.08	+	3760.42i	0.0938299	+	0.162518i
$813$	−2877.78	+	4984.45i	−0.124143	+	0.215021i
$814$	27754.0	+	48071.3i	1.19506	+	2.06990i
$815$	−8214.29	−	14227.6i	−0.353048	−	0.611497i
$816$	−4785.31			−0.205293
$817$	−8354.00	−	29152.4i	−0.357735	−	1.24836i
$818$	26791.4			1.14516
$819$	4087.18	+	7079.21i	0.174381	+	0.302036i
$820$	9842.85	+	17048.3i	0.419179	+	0.726040i
$821$	19585.0	−	33922.2i	0.832547	−	1.44201i	−0.0634643	−	0.997984i	$-0.520215\pi$
$821$	19585.0	−	33922.2i	0.832547	−	1.44201i	0.896012	−	0.444030i	$-0.146452\pi$
$822$	−5071.12	−	8783.44i	−0.215177	−	0.372698i
$823$	9419.41	−	16314.9i	0.398955	−	0.691010i	−0.594642	−	0.803990i	$-0.702706\pi$
$823$	9419.41	−	16314.9i	0.398955	−	0.691010i	0.993597	+	0.112980i	$0.0360396\pi$
$824$	−11736.4			−0.496185
$825$	15460.5			0.652443
$826$	−2416.11	+	4184.83i	−0.101776	+	0.176282i
$827$	−443.653	+	768.430i	−0.0186546	+	0.0323107i	−0.875202	−	0.483758i	$-0.839272\pi$
$827$	−443.653	+	768.430i	−0.0186546	+	0.0323107i	0.856547	+	0.516068i	$0.172605\pi$
$828$	127.399			0.00534713
$829$	32877.0			1.37740			0.688700	−	0.725046i	$-0.258182\pi$
$829$	32877.0			1.37740			0.688700	+	0.725046i	$0.258182\pi$
$830$	−9752.22	+	16891.3i	−0.407837	+	0.706394i
$831$	9425.17	+	16324.9i	0.393448	+	0.681473i
$832$	2192.83	−	3798.09i	0.0913733	−	0.158263i
$833$	8340.56	+	14446.3i	0.346919	+	0.600881i
$834$	−8134.57	−	14089.5i	−0.337742	−	0.584987i
$835$	17947.7			0.743840
$836$	−15171.0	+	15704.7i	−0.627631	+	0.649712i
$837$	6674.12			0.275617
$838$	−9117.71	−	15792.3i	−0.375855	−	0.650999i
$839$	20756.4	+	35951.1i	0.854099	+	1.47934i	0.877478	+	0.479616i	$0.159224\pi$
$839$	20756.4	+	35951.1i	0.854099	+	1.47934i	−0.0233792	+	0.999727i	$0.507443\pi$
$840$	2267.17	−	3926.86i	0.0931249	−	0.161297i
$841$	8840.63	+	15312.4i	0.362484	+	0.627841i
$842$	−8204.45	+	14210.5i	−0.335801	+	0.581624i
$843$	24172.1			0.987581
$844$	12232.0			0.498867
$845$	−17809.3	+	30846.6i	−0.725040	+	1.25581i
$846$	818.459	−	1417.61i	0.0332615	−	0.0576105i
$847$	39943.6			1.62040
$848$	−11015.9			−0.446092
$849$	−290.125	+	502.511i	−0.0117280	+	0.0203135i
$850$	−7794.61	−	13500.7i	−0.314533	−	0.544787i
$851$	−745.045	+	1290.46i	−0.0300115	+	0.0519815i
$852$	−4751.30	−	8229.50i	−0.191053	−	0.330913i
$853$	−743.876	−	1288.43i	−0.0298591	−	0.0517175i	0.850710	−	0.525636i	$-0.176173\pi$
$853$	−743.876	−	1288.43i	−0.0298591	−	0.0517175i	−0.880569	+	0.473918i	$0.842839\pi$
$854$	−13.7148			−0.000549543
$855$	−10308.7	−	2572.10i	−0.412340	−	0.102882i
$856$	3056.11			0.122028
$857$	−10138.0	−	17559.6i	−0.404094	−	0.699911i	0.590122	−	0.807314i	$-0.299080\pi$
$857$	−10138.0	−	17559.6i	−0.404094	−	0.699911i	−0.994216	+	0.107403i	$0.965746\pi$
$858$	13550.4	+	23470.0i	0.539165	+	0.933861i
$859$	−3718.43	+	6440.51i	−0.147696	+	0.255818i	−0.930376	−	0.366608i	$-0.880519\pi$
$859$	−3718.43	+	6440.51i	−0.147696	+	0.255818i	0.782679	+	0.622425i	$0.213853\pi$
$860$	10439.0	+	18080.8i	0.413913	+	0.716919i
$861$	−6864.25	+	11889.2i	−0.271699	+	0.470597i
$862$	−2542.69			−0.100469
$863$	35570.4			1.40305			0.701524	−	0.712646i	$-0.252503\pi$
$863$	35570.4			1.40305			0.701524	+	0.712646i	$0.252503\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	9080.70	−	15728.2i	0.356940	−	0.618238i
$866$	−7935.18			−0.311372
$867$	−15077.7			−0.590617
$868$	6552.66	−	11349.5i	0.256235	−	0.443811i
$869$	10492.5	+	18173.6i	0.409591	+	0.709432i
$870$	−3502.32	+	6066.20i	−0.136482	+	0.236395i
$871$	−5477.34	−	9487.04i	−0.213080	−	0.369065i
$872$	531.430	+	920.464i	0.0206382	+	0.0357464i
$873$	3738.53			0.144937
$874$	−568.735	−	141.903i	−0.0220112	−	0.00549193i
$875$	−8844.74			−0.341722
$876$	1932.78	+	3347.66i	0.0745461	+	0.129118i
$877$	−1934.21	−	3350.15i	−0.0744740	−	0.128993i	0.826383	−	0.563108i	$-0.190394\pi$
$877$	−1934.21	−	3350.15i	−0.0744740	−	0.128993i	−0.900857	+	0.434115i	$0.857061\pi$
$878$	−209.038	+	362.065i	−0.00803496	+	0.0139170i
$879$	−7103.20	−	12303.1i	−0.272565	−	0.472097i
$880$	7516.45	−	13018.9i	0.287931	−	0.498712i
$881$	−20877.4			−0.798384			−0.399192	−	0.916867i	$-0.630709\pi$
$881$	−20877.4			−0.798384			−0.399192	+	0.916867i	$0.630709\pi$
$882$	−3011.82			−0.114981
$883$	12103.4	−	20963.7i	0.461283	−	0.798965i	−0.537742	−	0.843109i	$-0.680723\pi$
$883$	12103.4	−	20963.7i	0.461283	−	0.798965i	0.999025	+	0.0441440i	$0.0140561\pi$
$884$	13663.2	−	23665.4i	0.519847	−	0.900401i
$885$	−7795.20			−0.296082
$886$	11468.1			0.434851
$887$	13558.8	−	23484.5i	0.513256	−	0.888986i	−0.486625	−	0.873611i	$-0.661772\pi$
$887$	13558.8	−	23484.5i	0.513256	−	0.888986i	0.999882	−	0.0153754i	$-0.00489433\pi$
$888$	5052.78	+	8751.67i	0.190946	+	0.330728i
$889$	10006.8	−	17332.4i	0.377524	−	0.653890i
$890$	−10268.9	−	17786.2i	−0.386757	−	0.669883i
$891$	2669.51	+	4623.73i	0.100373	+	0.173850i
$892$	6473.07			0.242976
$893$	−5232.77	+	5416.87i	−0.196090	+	0.202988i
$894$	−15593.4			−0.583357
$895$	−14500.2	−	25115.0i	−0.541550	−	0.937993i
$896$	−848.276	−	1469.26i	−0.0316282	−	0.0547817i
$897$	−363.756	+	630.043i	−0.0135401	+	0.0234521i
$898$	−9741.13	−	16872.1i	−0.361989	−	0.626983i
$899$	−10122.5	+	17532.7i	−0.375534	+	0.650444i
$900$	2814.67			0.104247
$901$	−68638.5			−2.53793
$902$	−22757.3	+	39416.8i	−0.840062	+	1.45503i
$903$	−7279.96	+	12609.3i	−0.268286	+	0.464684i
$904$	−9103.52			−0.334932
$905$	14729.2			0.541010
$906$	1784.59	−	3091.00i	0.0654404	−	0.113346i
$907$	17797.4	+	30826.0i	0.651548	+	1.12851i	0.982747	+	0.184953i	$0.0592134\pi$
$907$	17797.4	+	30826.0i	0.651548	+	1.12851i	−0.331199	+	0.943561i	$0.607453\pi$
$908$	12130.9	−	21011.3i	0.443367	−	0.767933i
$909$	−1518.03	−	2629.31i	−0.0553906	−	0.0959393i
$910$	12946.7	+	22424.3i	0.471624	+	0.816877i
$911$	27909.5			1.01502			0.507510	−	0.861646i	$-0.330566\pi$
$911$	27909.5			1.01502			0.507510	+	0.861646i	$0.330566\pi$
$912$	−2761.97	+	2859.14i	−0.100283	+	0.103811i
$913$	−45095.6			−1.63466
$914$	17233.8	+	29849.8i	0.623679	+	1.08024i
$915$	−11.0621	−	19.1602i	−0.000399675	−	0.000692257i
$916$	3832.73	−	6638.47i	0.138250	−	0.239456i
$917$	2458.30	+	4257.91i	0.0885282	+	0.153335i
$918$	2691.74	−	4662.23i	0.0967763	−	0.167621i
$919$	−48960.0			−1.75739			−0.878696	−	0.477383i	$-0.841586\pi$
$919$	−48960.0			−1.75739			−0.878696	+	0.477383i	$0.841586\pi$
$920$	403.552			0.0144617
$921$	−43.0682	+	74.5964i	−0.00154088	+	0.00266888i
$922$	−1665.23	+	2884.27i	−0.0594811	+	0.103024i
$923$	54264.5			1.93515
$924$	10483.7			0.373256
$925$	−16460.6	+	28510.5i	−0.585102	+	1.01343i
$926$	10694.0	+	18522.6i	0.379511	+	0.657333i
$927$	6601.71	−	11434.5i	0.233904	−	0.405133i
$928$	1310.41	+	2269.70i	0.0463539	+	0.0802873i
$929$	5985.87	+	10367.8i	0.211399	+	0.366155i	0.952153	−	0.305623i	$-0.0988646\pi$
$929$	5985.87	+	10367.8i	0.211399	+	0.366155i	−0.740753	+	0.671777i	$0.765531\pi$
$930$	21141.1			0.745424
$931$	13445.4	+	3354.71i	0.473313	+	0.118095i
$932$	−16034.2			−0.563537
$933$	−1748.53	−	3028.54i	−0.0613551	−	0.106270i
$934$	−13212.7	−	22885.0i	−0.462882	−	0.801736i
$935$	46834.1	−	81119.0i	1.63812	−	2.83730i
$936$	2466.93	+	4272.85i	0.0861476	+	0.149212i
$937$	25217.1	−	43677.3i	0.879197	−	1.52281i	0.0269728	−	0.999636i	$-0.491413\pi$
$937$	25217.1	−	43677.3i	0.879197	−	1.52281i	0.852224	−	0.523177i	$-0.175253\pi$
$938$	−4237.72			−0.147512
$939$	−7538.26			−0.261983
$940$	2592.57	−	4490.46i	0.0899578	−	0.155811i
$941$	−6297.13	+	10906.9i	−0.218151	+	0.377849i	−0.954243	−	0.299033i	$-0.903336\pi$
$941$	−6297.13	+	10906.9i	−0.218151	+	0.377849i	0.736091	+	0.676882i	$0.236669\pi$
$942$	349.529			0.0120895
$943$	−1221.82			−0.0421930
$944$	−1458.31	+	2525.87i	−0.0502796	+	0.0870869i
$945$	2550.57	+	4417.72i	0.0877990	+	0.152072i
$946$	−24135.5	+	41804.0i	−0.829508	+	1.43675i
$947$	−13816.3	−	23930.5i	−0.474096	−	0.821158i	0.525464	−	0.850816i	$-0.323892\pi$
$947$	−13816.3	−	23930.5i	−0.474096	−	0.821158i	−0.999560	+	0.0296574i	$0.990558\pi$
$948$	1910.22	+	3308.61i	0.0654443	+	0.113353i
$949$	−22074.2			−0.755067
$950$	−12565.3	−	3135.12i	−0.429128	−	0.107070i
$951$	5182.70			0.176720
$952$	−5285.50	−	9154.76i	−0.179941	−	0.311667i
$953$	−16010.9	−	27731.6i	−0.544221	−	0.942619i	−0.998655	−	0.0518388i	$-0.983492\pi$
$953$	−16010.9	−	27731.6i	−0.544221	−	0.942619i	0.454434	−	0.890780i	$-0.349842\pi$
$954$	6196.42	−	10732.5i	0.210290	−	0.364233i
$955$	8092.64	+	14016.9i	0.274211	+	0.474947i
$956$	−1060.58	+	1836.99i	−0.0358805	+	0.0621468i
$957$	−16195.2			−0.547039
$958$	10819.1			0.364873
$959$	11202.4	−	19403.1i	0.377209	−	0.653345i
$960$	1368.41	−	2370.16i	0.0460056	−	0.0796840i
$961$	31311.7			1.05105
$962$	−57707.7			−1.93406
$963$	−1719.06	+	2977.50i	−0.0575244	+	0.0996351i
$964$	−2542.45	−	4403.65i	−0.0849448	−	0.147129i
$965$	−7776.24	+	13468.9i	−0.259405	+	0.449303i
$966$	140.716	+	243.727i	0.00468680	+	0.00811778i
$967$	6438.21	+	11151.3i	0.214104	+	0.370840i	0.952995	−	0.302985i	$-0.0979834\pi$
$967$	6438.21	+	11151.3i	0.214104	+	0.370840i	−0.738891	+	0.673825i	$0.764650\pi$
$968$	24109.1			0.800511
$969$	−17209.5	+	17814.9i	−0.570535	+	0.590607i
$970$	11842.3			0.391992
$971$	−1207.26	−	2091.03i	−0.0398998	−	0.0691085i	0.845386	−	0.534156i	$-0.179371\pi$
$971$	−1207.26	−	2091.03i	−0.0398998	−	0.0691085i	−0.885286	+	0.465048i	$0.846037\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	17969.7	−	31124.4i	0.592067	−	1.02549i
$974$	−14297.0	−	24763.2i	−0.470335	−	0.814644i
$975$	−8036.58	+	13919.8i	−0.263976	+	0.457220i
$976$	−8.27792			−0.000271485
$977$	−14131.4			−0.462746			−0.231373	−	0.972865i	$-0.574322\pi$
$977$	−14131.4			−0.462746			−0.231373	+	0.972865i	$0.574322\pi$
$978$	3457.60	−	5988.74i	0.113049	−	0.195807i
$979$	23742.3	−	41122.9i	0.775085	−	1.34249i
$980$	−9540.31			−0.310973
$981$	−1195.72			−0.0389157
$982$	−2802.42	+	4853.94i	−0.0910681	+	0.157735i
$983$	10134.1	+	17552.7i	0.328817	+	0.569528i	0.982277	−	0.187433i	$-0.0600168\pi$
$983$	10134.1	+	17552.7i	0.328817	+	0.569528i	−0.653460	+	0.756961i	$0.726683\pi$
$984$	−4143.10	+	7176.06i	−0.134225	+	0.232484i
$985$	−29492.7	−	51082.9i	−0.954027	−	1.65242i
$986$	8165.02	+	14142.2i	0.263719	+	0.456775i
$987$	3616.04			0.116616
$988$	−6253.57	−	21822.7i	−0.201369	−	0.702703i
$989$	−1295.82			−0.0416629
$990$	8456.01	+	14646.2i	0.271464	+	0.470190i
$991$	−7775.08	−	13466.8i	−0.249226	−	0.431673i	0.714085	−	0.700059i	$-0.246843\pi$
$991$	−7775.08	−	13466.8i	−0.249226	−	0.431673i	−0.963311	+	0.268386i	$0.913510\pi$
$992$	3955.03	−	6850.32i	0.126585	−	0.219252i
$993$	−10224.2	−	17708.8i	−0.326742	−	0.565934i
$994$	10495.9	−	18179.4i	0.334919	−	0.580096i
$995$	−38974.6			−1.24179
$996$	−8209.92			−0.261186
$997$	−6357.89	+	11012.2i	−0.201962	+	0.349809i	−0.949161	−	0.314792i	$-0.898065\pi$
$997$	−6357.89	+	11012.2i	−0.201962	+	0.349809i	0.747198	+	0.664601i	$0.231399\pi$
$998$	−14178.3	+	24557.5i	−0.449704	+	0.778910i
$999$	−11368.7			−0.360051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.e.d.7.1	✓	6
3.2	odd	2		342.4.g.h.235.3		6
19.7	even	3		2166.4.a.u.1.3		3
19.11	even	3	inner	114.4.e.d.49.1	yes	6
19.12	odd	6		2166.4.a.t.1.3		3
57.11	odd	6		342.4.g.h.163.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.d.7.1	✓	6	1.1	even	1	trivial
114.4.e.d.49.1	yes	6	19.11	even	3	inner
342.4.g.h.163.3		6	57.11	odd	6
342.4.g.h.235.3		6	3.2	odd	2
2166.4.a.t.1.3		3	19.12	odd	6
2166.4.a.u.1.3		3	19.7	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.12716 - 12.3446i) q^{5} +(3.00000 - 5.19615i) q^{6} +13.2543 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.12716 - 12.3446i) q^{5} +(3.00000 - 5.19615i) q^{6} +13.2543 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-14.2543 + 24.6892i) q^{10} -65.9138 q^{11} -12.0000 q^{12} +(34.2629 - 59.3451i) q^{13} +(-13.2543 - 22.9571i) q^{14} +(21.3815 - 37.0338i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-49.8470 - 86.3375i) q^{17} +18.0000 q^{18} +(-80.3556 - 20.0493i) q^{19} +57.0172 q^{20} +(19.8815 + 34.4357i) q^{21} +(65.9138 + 114.166i) q^{22} +(-1.76943 + 3.06475i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-39.0927 + 67.7105i) q^{25} -137.052 q^{26} -27.0000 q^{27} +(-26.5086 + 45.9143i) q^{28} +(40.9504 - 70.9282i) q^{29} -85.5259 q^{30} -247.190 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-98.8707 - 171.249i) q^{33} +(-99.6940 + 172.675i) q^{34} +(-94.4655 - 163.619i) q^{35} +(-18.0000 - 31.1769i) q^{36} +421.065 q^{37} +(45.6293 + 159.229i) q^{38} +205.578 q^{39} +(-57.0172 - 98.7568i) q^{40} +(172.629 + 299.003i) q^{41} +(39.7629 - 68.8714i) q^{42} +(183.084 + 317.111i) q^{43} +(131.828 - 228.332i) q^{44} +128.289 q^{45} +7.07773 q^{46} +(45.4699 - 78.7562i) q^{47} +(24.0000 - 41.5692i) q^{48} -167.323 q^{49} +156.371 q^{50} +(149.541 - 259.013i) q^{51} +(137.052 + 237.381i) q^{52} +(344.246 - 596.251i) q^{53} +(27.0000 + 46.7654i) q^{54} +(469.778 + 813.680i) q^{55} +106.034 q^{56} +(-68.4439 - 238.844i) q^{57} -163.802 q^{58} +(-91.1444 - 157.867i) q^{59} +(85.5259 + 148.135i) q^{60} +(0.258685 - 0.448055i) q^{61} +(247.190 + 428.145i) q^{62} +(-59.6444 + 103.307i) q^{63} +64.0000 q^{64} -976.789 q^{65} +(-197.741 + 342.498i) q^{66} +(79.9310 - 138.445i) q^{67} +398.776 q^{68} -10.6166 q^{69} +(-188.931 + 327.238i) q^{70} +(395.942 + 685.792i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(-161.065 - 278.972i) q^{73} +(-421.065 - 729.306i) q^{74} -234.556 q^{75} +(230.164 - 238.262i) q^{76} -873.642 q^{77} +(-205.578 - 356.071i) q^{78} +(-159.185 - 275.717i) q^{79} +(-114.034 + 197.514i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(345.259 - 598.005i) q^{82} +684.160 q^{83} -159.052 q^{84} +(-710.535 + 1230.68i) q^{85} +(366.168 - 634.222i) q^{86} +245.703 q^{87} -527.311 q^{88} +(-360.203 + 623.890i) q^{89} +(-128.289 - 222.203i) q^{90} +(454.132 - 786.579i) q^{91} +(-7.07773 - 12.2590i) q^{92} +(-370.784 - 642.218i) q^{93} -181.880 q^{94} +(325.207 + 1134.85i) q^{95} -96.0000 q^{96} +(-207.696 - 359.740i) q^{97} +(167.323 + 289.812i) q^{98} +(296.612 - 513.747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9	\( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} - 20 q^{10} - 88 q^{11} - 72 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} - 48 q^{16} + 84 q^{17} + 108 q^{18} + 32 q^{19} + 80 q^{20} + 21 q^{21} + 88 q^{22} + 2 q^{23} + 72 q^{24} + 83 q^{25} - 36 q^{26} - 162 q^{27} - 28 q^{28} - 92 q^{29} - 120 q^{30} - 218 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} - 282 q^{35} - 108 q^{36} + 490 q^{37} - 74 q^{38} + 54 q^{39} - 80 q^{40} + 688 q^{41} + 42 q^{42} + 103 q^{43} + 176 q^{44} + 180 q^{45} - 8 q^{46} - 322 q^{47} + 144 q^{48} - 1508 q^{49} - 332 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} + 162 q^{54} + 248 q^{55} + 112 q^{56} + 111 q^{57} + 368 q^{58} - 252 q^{59} + 120 q^{60} + 435 q^{61} + 218 q^{62} - 63 q^{63} + 384 q^{64} - 3164 q^{65} - 264 q^{66} + 719 q^{67} - 672 q^{68} + 12 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} + 581 q^{73} - 490 q^{74} + 498 q^{75} + 20 q^{76} - 408 q^{77} - 54 q^{78} + 489 q^{79} - 160 q^{80} - 243 q^{81} + 1376 q^{82} + 4992 q^{83} - 168 q^{84} - 1632 q^{85} + 206 q^{86} - 552 q^{87} - 704 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} + 8 q^{92} - 327 q^{93} + 1288 q^{94} + 2362 q^{95} - 576 q^{96} - 974 q^{97} + 1508 q^{98} + 396 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9 - 20 * q^10 - 88 * q^11 - 72 * q^12 + 9 * q^13 - 14 * q^14 + 30 * q^15 - 48 * q^16 + 84 * q^17 + 108 * q^18 + 32 * q^19 + 80 * q^20 + 21 * q^21 + 88 * q^22 + 2 * q^23 + 72 * q^24 + 83 * q^25 - 36 * q^26 - 162 * q^27 - 28 * q^28 - 92 * q^29 - 120 * q^30 - 218 * q^31 - 96 * q^32 - 132 * q^33 + 168 * q^34 - 282 * q^35 - 108 * q^36 + 490 * q^37 - 74 * q^38 + 54 * q^39 - 80 * q^40 + 688 * q^41 + 42 * q^42 + 103 * q^43 + 176 * q^44 + 180 * q^45 - 8 * q^46 - 322 * q^47 + 144 * q^48 - 1508 * q^49 - 332 * q^50 - 252 * q^51 + 36 * q^52 + 1322 * q^53 + 162 * q^54 + 248 * q^55 + 112 * q^56 + 111 * q^57 + 368 * q^58 - 252 * q^59 + 120 * q^60 + 435 * q^61 + 218 * q^62 - 63 * q^63 + 384 * q^64 - 3164 * q^65 - 264 * q^66 + 719 * q^67 - 672 * q^68 + 12 * q^69 - 564 * q^70 + 62 * q^71 - 216 * q^72 + 581 * q^73 - 490 * q^74 + 498 * q^75 + 20 * q^76 - 408 * q^77 - 54 * q^78 + 489 * q^79 - 160 * q^80 - 243 * q^81 + 1376 * q^82 + 4992 * q^83 - 168 * q^84 - 1632 * q^85 + 206 * q^86 - 552 * q^87 - 704 * q^88 - 1584 * q^89 - 180 * q^90 + 1573 * q^91 + 8 * q^92 - 327 * q^93 + 1288 * q^94 + 2362 * q^95 - 576 * q^96 - 974 * q^97 + 1508 * q^98 + 396 * q^99

Introduction

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