LMFDB - Embedded newform 114.4.e.e.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:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$0.0702177 - 0.121621i$ of defining polynomial
Character	$\chi$	$=$	114.7
Dual form			114.4.e.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-10.1010 - 17.4954i) q^{5} +(-3.00000 + 5.19615i) q^{6} -22.8872 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-10.1010 - 17.4954i) q^{5} +(-3.00000 + 5.19615i) q^{6} -22.8872 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(20.2020 - 34.9909i) q^{10} -57.5614 q^{11} -12.0000 q^{12} +(-13.6574 + 23.6553i) q^{13} +(-22.8872 - 39.6418i) q^{14} +(30.3030 - 52.4863i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(36.7243 + 63.6083i) q^{17} -18.0000 q^{18} +(82.8135 + 0.964044i) q^{19} +80.8079 q^{20} +(-34.3308 - 59.4627i) q^{21} +(-57.5614 - 99.6992i) q^{22} +(94.2919 - 163.318i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-141.560 + 245.189i) q^{25} -54.6296 q^{26} -27.0000 q^{27} +(45.7744 - 79.2836i) q^{28} +(3.57797 - 6.19723i) q^{29} +121.212 q^{30} -117.144 q^{31} +(16.0000 - 27.7128i) q^{32} +(-86.3420 - 149.549i) q^{33} +(-73.4486 + 127.217i) q^{34} +(231.183 + 400.422i) q^{35} +(-18.0000 - 31.1769i) q^{36} -332.600 q^{37} +(81.1437 + 144.401i) q^{38} -81.9443 q^{39} +(80.8079 + 139.963i) q^{40} +(21.3579 + 36.9930i) q^{41} +(68.6616 - 118.925i) q^{42} +(-23.6234 - 40.9170i) q^{43} +(115.123 - 199.398i) q^{44} +181.818 q^{45} +377.168 q^{46} +(253.997 - 439.936i) q^{47} +(24.0000 - 41.5692i) q^{48} +180.824 q^{49} -566.240 q^{50} +(-110.173 + 190.825i) q^{51} +(-54.6296 - 94.6212i) q^{52} +(-246.305 + 426.612i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(581.427 + 1007.06i) q^{55} +183.098 q^{56} +(121.716 + 216.602i) q^{57} +14.3119 q^{58} +(-230.020 - 398.407i) q^{59} +(121.212 + 209.945i) q^{60} +(-225.372 + 390.356i) q^{61} +(-117.144 - 202.899i) q^{62} +(102.992 - 178.388i) q^{63} +64.0000 q^{64} +551.813 q^{65} +(172.684 - 299.098i) q^{66} +(-261.232 + 452.468i) q^{67} -293.794 q^{68} +565.751 q^{69} +(-462.367 + 800.843i) q^{70} +(-465.709 - 806.632i) q^{71} +(36.0000 - 62.3538i) q^{72} +(-175.062 - 303.216i) q^{73} +(-332.600 - 576.079i) q^{74} -849.360 q^{75} +(-168.966 + 284.946i) q^{76} +1317.42 q^{77} +(-81.9443 - 141.932i) q^{78} +(-97.4340 - 168.761i) q^{79} +(-161.616 + 279.927i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-42.7158 + 73.9860i) q^{82} -286.083 q^{83} +274.646 q^{84} +(741.903 - 1285.01i) q^{85} +(47.2469 - 81.8340i) q^{86} +21.4678 q^{87} +460.491 q^{88} +(-419.845 + 727.193i) q^{89} +(181.818 + 314.918i) q^{90} +(312.579 - 541.404i) q^{91} +(377.168 + 653.273i) q^{92} +(-175.716 - 304.348i) q^{93} +1015.99 q^{94} +(-819.632 - 1458.60i) q^{95} +96.0000 q^{96} +(-302.758 - 524.392i) q^{97} +(180.824 + 313.197i) q^{98} +(259.026 - 448.646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9	\( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9} + 4 q^{10} - 104 q^{11} - 72 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} - 48 q^{16} + 48 q^{17} - 108 q^{18} + 104 q^{19} + 16 q^{20} - 51 q^{21} - 104 q^{22} + 238 q^{23} - 72 q^{24} - 229 q^{25} - 300 q^{26} - 162 q^{27} + 68 q^{28} + 8 q^{29} + 24 q^{30} + 214 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} + 294 q^{35} - 108 q^{36} + 610 q^{37} - 430 q^{38} - 450 q^{39} + 16 q^{40} - 16 q^{41} + 102 q^{42} + 331 q^{43} + 208 q^{44} + 36 q^{45} + 952 q^{46} + 766 q^{47} + 144 q^{48} + 2284 q^{49} - 916 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} - 162 q^{54} + 1400 q^{55} + 272 q^{56} - 645 q^{57} + 32 q^{58} - 936 q^{59} + 24 q^{60} + 399 q^{61} + 214 q^{62} + 153 q^{63} + 384 q^{64} + 740 q^{65} + 312 q^{66} - 61 q^{67} - 384 q^{68} + 1428 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} - 91 q^{73} + 610 q^{74} - 1374 q^{75} - 1276 q^{76} - 72 q^{77} - 450 q^{78} + 321 q^{79} - 32 q^{80} - 243 q^{81} + 32 q^{82} - 4296 q^{83} + 408 q^{84} + 1680 q^{85} - 662 q^{86} + 48 q^{87} + 832 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} + 952 q^{92} + 321 q^{93} + 3064 q^{94} - 4198 q^{95} + 576 q^{96} - 1382 q^{97} + 2284 q^{98} + 468 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9 + 4 * q^10 - 104 * q^11 - 72 * q^12 - 75 * q^13 - 34 * q^14 + 6 * q^15 - 48 * q^16 + 48 * q^17 - 108 * q^18 + 104 * q^19 + 16 * q^20 - 51 * q^21 - 104 * q^22 + 238 * q^23 - 72 * q^24 - 229 * q^25 - 300 * q^26 - 162 * q^27 + 68 * q^28 + 8 * q^29 + 24 * q^30 + 214 * q^31 + 96 * q^32 - 156 * q^33 - 96 * q^34 + 294 * q^35 - 108 * q^36 + 610 * q^37 - 430 * q^38 - 450 * q^39 + 16 * q^40 - 16 * q^41 + 102 * q^42 + 331 * q^43 + 208 * q^44 + 36 * q^45 + 952 * q^46 + 766 * q^47 + 144 * q^48 + 2284 * q^49 - 916 * q^50 - 144 * q^51 - 300 * q^52 + 118 * q^53 - 162 * q^54 + 1400 * q^55 + 272 * q^56 - 645 * q^57 + 32 * q^58 - 936 * q^59 + 24 * q^60 + 399 * q^61 + 214 * q^62 + 153 * q^63 + 384 * q^64 + 740 * q^65 + 312 * q^66 - 61 * q^67 - 384 * q^68 + 1428 * q^69 - 588 * q^70 - 974 * q^71 + 216 * q^72 - 91 * q^73 + 610 * q^74 - 1374 * q^75 - 1276 * q^76 - 72 * q^77 - 450 * q^78 + 321 * q^79 - 32 * q^80 - 243 * q^81 + 32 * q^82 - 4296 * q^83 + 408 * q^84 + 1680 * q^85 - 662 * q^86 + 48 * q^87 + 832 * q^88 - 1116 * q^89 + 36 * q^90 - 1367 * q^91 + 952 * q^92 + 321 * q^93 + 3064 * q^94 - 4198 * q^95 + 576 * q^96 - 1382 * q^97 + 2284 * q^98 + 468 * 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
$5$	−10.1010	−	17.4954i	−0.903460	−	1.56484i	−0.822971	−	0.568083i	$-0.807685\pi$
$5$	−10.1010	−	17.4954i	−0.903460	−	1.56484i	−0.0804891	−	0.996755i	$-0.525648\pi$
$6$	−3.00000	+	5.19615i	−0.204124	+	0.353553i
$7$	−22.8872			−1.23579			−0.617897	−	0.786259i	$-0.712015\pi$
$7$	−22.8872			−1.23579			−0.617897	+	0.786259i	$0.712015\pi$
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	20.2020	−	34.9909i	0.638843	−	1.10651i
$11$	−57.5614			−1.57776			−0.788882	−	0.614545i	$-0.789340\pi$
$11$	−57.5614			−1.57776			−0.788882	+	0.614545i	$0.789340\pi$
$12$	−12.0000			−0.288675
$13$	−13.6574	+	23.6553i	−0.291375	+	0.504677i	−0.974135	−	0.225966i	$-0.927446\pi$
$13$	−13.6574	+	23.6553i	−0.291375	+	0.504677i	0.682760	+	0.730643i	$0.260779\pi$
$14$	−22.8872	−	39.6418i	−0.436919	−	0.756766i
$15$	30.3030	−	52.4863i	0.521613	−	0.903460i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	36.7243	+	63.6083i	0.523938	+	0.907487i	0.999612	+	0.0278654i	$0.00887099\pi$
$17$	36.7243	+	63.6083i	0.523938	+	0.907487i	−0.475674	+	0.879622i	$0.657796\pi$
$18$	−18.0000			−0.235702
$19$	82.8135	+	0.964044i	0.999932	+	0.0116404i
$19$	82.8135	+	0.964044i	0.999932	+	0.0116404i
$20$	80.8079			0.903460
$21$	−34.3308	−	59.4627i	−0.356743	−	0.617897i
$22$	−57.5614	−	99.6992i	−0.557824	−	0.966179i
$23$	94.2919	−	163.318i	0.854836	−	1.48062i	−0.0219618	−	0.999759i	$-0.506991\pi$
$23$	94.2919	−	163.318i	0.854836	−	1.48062i	0.876797	−	0.480860i	$-0.159675\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−141.560	+	245.189i	−1.13248	+	1.96151i
$26$	−54.6296			−0.412067
$27$	−27.0000			−0.192450
$28$	45.7744	−	79.2836i	0.308948	−	0.535114i
$29$	3.57797	−	6.19723i	0.0229108	−	0.0396826i	−0.854343	−	0.519710i	$-0.826040\pi$
$29$	3.57797	−	6.19723i	0.0229108	−	0.0396826i	0.877253	+	0.480027i	$0.159373\pi$
$30$	121.212			0.737672
$31$	−117.144			−0.678698			−0.339349	−	0.940661i	$-0.610207\pi$
$31$	−117.144			−0.678698			−0.339349	+	0.940661i	$0.610207\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−86.3420	−	149.549i	−0.455461	−	0.788882i
$34$	−73.4486	+	127.217i	−0.370480	+	0.641690i
$35$	231.183	+	400.422i	1.11649	+	1.93382i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−332.600			−1.47781			−0.738906	−	0.673809i	$-0.764657\pi$
$37$	−332.600			−1.47781			−0.738906	+	0.673809i	$0.764657\pi$
$38$	81.1437	+	144.401i	0.346401	+	0.616446i
$39$	−81.9443			−0.336451
$40$	80.8079	+	139.963i	0.319421	+	0.553254i
$41$	21.3579	+	36.9930i	0.0813548	+	0.140911i	0.903832	−	0.427887i	$-0.140742\pi$
$41$	21.3579	+	36.9930i	0.0813548	+	0.140911i	−0.822477	+	0.568798i	$0.807409\pi$
$42$	68.6616	−	118.925i	0.252255	−	0.436919i
$43$	−23.6234	−	40.9170i	−0.0837800	−	0.145111i	0.821091	−	0.570798i	$-0.193366\pi$
$43$	−23.6234	−	40.9170i	−0.0837800	−	0.145111i	−0.904871	+	0.425687i	$0.860033\pi$
$44$	115.123	−	199.398i	0.394441	−	0.683192i
$45$	181.818			0.602307
$46$	377.168			1.20892
$47$	253.997	−	439.936i	0.788284	−	1.36535i	−0.138734	−	0.990330i	$-0.544303\pi$
$47$	253.997	−	439.936i	0.788284	−	1.36535i	0.927018	−	0.375017i	$-0.122363\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	180.824			0.527184
$50$	−566.240			−1.60157
$51$	−110.173	+	190.825i	−0.302496	+	0.523938i
$52$	−54.6296	−	94.6212i	−0.145688	−	0.252338i
$53$	−246.305	+	426.612i	−0.638350	+	1.10565i	0.347445	+	0.937700i	$0.387049\pi$
$53$	−246.305	+	426.612i	−0.638350	+	1.10565i	−0.985795	+	0.167954i	$0.946284\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	581.427	+	1007.06i	1.42545	+	2.46895i
$56$	183.098			0.436919
$57$	121.716	+	216.602i	0.282835	+	0.503326i
$58$	14.3119			0.0324007
$59$	−230.020	−	398.407i	−0.507561	−	0.879121i	−0.999962	−	0.00875259i	$-0.997214\pi$
$59$	−230.020	−	398.407i	−0.507561	−	0.879121i	0.492401	−	0.870369i	$-0.336119\pi$
$60$	121.212	+	209.945i	0.260806	+	0.451730i
$61$	−225.372	+	390.356i	−0.473049	+	0.819344i	−0.999524	−	0.0308459i	$-0.990180\pi$
$61$	−225.372	+	390.356i	−0.473049	+	0.819344i	0.526475	+	0.850190i	$0.323513\pi$
$62$	−117.144	−	202.899i	−0.239956	−	0.415616i
$63$	102.992	−	178.388i	0.205966	−	0.356743i
$64$	64.0000			0.125000
$65$	551.813			1.05298
$66$	172.684	−	299.098i	0.322060	−	0.557824i
$67$	−261.232	+	452.468i	−0.476337	+	0.825041i	−0.999632	−	0.0271110i	$-0.991369\pi$
$67$	−261.232	+	452.468i	−0.476337	+	0.825041i	0.523295	+	0.852152i	$0.324703\pi$
$68$	−293.794			−0.523938
$69$	565.751			0.987079
$70$	−462.367	+	800.843i	−0.789477	+	1.36742i
$71$	−465.709	−	806.632i	−0.778444	−	1.34830i	−0.932838	−	0.360296i	$-0.882676\pi$
$71$	−465.709	−	806.632i	−0.778444	−	1.34830i	0.154394	−	0.988009i	$-0.450657\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	−175.062	−	303.216i	−0.280677	−	0.486147i	0.690875	−	0.722974i	$-0.257226\pi$
$73$	−175.062	−	303.216i	−0.280677	−	0.486147i	−0.971552	+	0.236828i	$0.923892\pi$
$74$	−332.600	−	576.079i	−0.522485	−	0.904971i
$75$	−849.360			−1.30768
$76$	−168.966	+	284.946i	−0.255023	+	0.430073i
$77$	1317.42			1.94979
$78$	−81.9443	−	141.932i	−0.118953	−	0.206033i
$79$	−97.4340	−	168.761i	−0.138762	−	0.240342i	0.788266	−	0.615334i	$-0.210979\pi$
$79$	−97.4340	−	168.761i	−0.138762	−	0.240342i	−0.927028	+	0.374992i	$0.877646\pi$
$80$	−161.616	+	279.927i	−0.225865	+	0.391210i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−42.7158	+	73.9860i	−0.0575265	+	0.0996389i
$83$	−286.083			−0.378333			−0.189167	−	0.981945i	$-0.560579\pi$
$83$	−286.083			−0.378333			−0.189167	+	0.981945i	$0.560579\pi$
$84$	274.646			0.356743
$85$	741.903	−	1285.01i	0.946714	−	1.63976i
$86$	47.2469	−	81.8340i	0.0592414	−	0.102609i
$87$	21.4678			0.0264551
$88$	460.491			0.557824
$89$	−419.845	+	727.193i	−0.500039	+	0.866093i	0.499961	+	0.866048i	$0.333348\pi$
$89$	−419.845	+	727.193i	−0.500039	+	0.866093i	−1.00000		4.52935e-5i	$0.999986\pi$
$90$	181.818	+	314.918i	0.212948	+	0.368836i
$91$	312.579	−	541.404i	0.360079	−	0.623676i
$92$	377.168	+	653.273i	0.427418	+	0.740309i
$93$	−175.716	−	304.348i	−0.195923	−	0.339349i
$94$	1015.99			1.11480
$95$	−819.632	−	1458.60i	−0.885184	−	1.57525i
$96$	96.0000			0.102062
$97$	−302.758	−	524.392i	−0.316911	−	0.548906i	0.662931	−	0.748681i	$-0.269312\pi$
$97$	−302.758	−	524.392i	−0.316911	−	0.548906i	−0.979842	+	0.199774i	$0.935979\pi$
$98$	180.824	+	313.197i	0.186388	+	0.322833i
$99$	259.026	−	448.646i	0.262961	−	0.455461i
$100$	−566.240	−	980.757i	−0.566240	−	0.980757i
$101$	−23.6380	+	40.9422i	−0.0232878	+	0.0403356i	−0.877434	−	0.479697i	$-0.840747\pi$
$101$	−23.6380	+	40.9422i	−0.0232878	+	0.0403356i	0.854147	+	0.520032i	$0.174080\pi$
$102$	−440.691			−0.427794
$103$	−430.750			−0.412069			−0.206034	−	0.978545i	$-0.566056\pi$
$103$	−430.750			−0.412069			−0.206034	+	0.978545i	$0.566056\pi$
$104$	109.259	−	189.242i	0.103017	−	0.178430i
$105$	−693.550	+	1201.26i	−0.644606	+	1.11649i
$106$	−985.219			−0.902763
$107$	1055.78			0.953893			0.476946	−	0.878932i	$-0.341744\pi$
$107$	1055.78			0.953893			0.476946	+	0.878932i	$0.341744\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	141.286	+	244.714i	0.124153	+	0.215040i	0.921402	−	0.388612i	$-0.127045\pi$
$109$	141.286	+	244.714i	0.124153	+	0.215040i	−0.797248	+	0.603651i	$0.793712\pi$
$110$	−1162.85	+	2014.12i	−1.00794	+	1.74581i
$111$	−498.899	−	864.119i	−0.426607	−	0.738906i
$112$	183.098	+	317.134i	0.154474	+	0.267557i
$113$	−841.860			−0.700846			−0.350423	−	0.936592i	$-0.613962\pi$
$113$	−841.860			−0.700846			−0.350423	+	0.936592i	$0.613962\pi$
$114$	−253.450	+	427.419i	−0.208226	+	0.351153i
$115$	−3809.77			−3.08924
$116$	14.3119	+	24.7889i	0.0114554	+	0.0198413i
$117$	−122.916	−	212.898i	−0.0971251	−	0.168226i
$118$	460.041	−	796.814i	0.358900	−	0.621633i
$119$	−840.516	−	1455.82i	−0.647479	−	1.12147i
$120$	−242.424	+	419.890i	−0.184418	+	0.319421i
$121$	1982.31			1.48934
$122$	−901.489			−0.668992
$123$	−64.0738	+	110.979i	−0.0469702	+	0.0813548i
$124$	234.287	−	405.798i	0.169674	−	0.293885i
$125$	3194.34			2.28568
$126$	411.970			0.291279
$127$	477.697	−	827.395i	0.333769	−	0.578106i	−0.649478	−	0.760380i	$-0.725013\pi$
$127$	477.697	−	827.395i	0.333769	−	0.578106i	0.983248	+	0.182275i	$0.0583460\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	70.8703	−	122.751i	0.0483704	−	0.0837800i
$130$	551.813	+	955.767i	0.372286	+	0.644818i
$131$	819.554	+	1419.51i	0.546601	+	0.946741i	0.998504	+	0.0546739i	$0.0174119\pi$
$131$	819.554	+	1419.51i	0.546601	+	0.946741i	−0.451903	+	0.892067i	$0.649255\pi$
$132$	690.736			0.455461
$133$	−1895.37	−	22.0643i	−1.23571	−	0.0143851i
$134$	−1044.93			−0.673643
$135$	272.727	+	472.377i	0.173871	+	0.301153i
$136$	−293.794	−	508.867i	−0.185240	−	0.320845i
$137$	423.856	−	734.140i	0.264324	−	0.457823i	−0.703062	−	0.711129i	$-0.748184\pi$
$137$	423.856	−	734.140i	0.264324	−	0.457823i	0.967386	+	0.253305i	$0.0815177\pi$
$138$	565.751	+	979.910i	0.348985	+	0.604460i
$139$	−583.802	+	1011.17i	−0.356240	+	0.617026i	−0.987329	−	0.158684i	$-0.949275\pi$
$139$	−583.802	+	1011.17i	−0.356240	+	0.617026i	0.631089	+	0.775710i	$0.282608\pi$
$140$	−1849.47			−1.11649
$141$	1523.98			0.910231
$142$	931.419	−	1613.26i	0.550443	−	0.953396i
$143$	786.138	−	1361.63i	0.459721	−	0.796261i
$144$	144.000			0.0833333
$145$	−144.564			−0.0827959
$146$	350.123	−	606.431i	0.198469	−	0.343758i
$147$	271.236	+	469.795i	0.152185	+	0.263592i
$148$	665.199	−	1152.16i	0.369453	−	0.639911i
$149$	860.783	+	1490.92i	0.473276	+	0.819738i	0.999532	−	0.0305883i	$-0.00973807\pi$
$149$	860.783	+	1490.92i	0.473276	+	0.819738i	−0.526256	+	0.850326i	$0.676405\pi$
$150$	−849.360	−	1471.14i	−0.462333	−	0.800785i
$151$	2327.14			1.25417			0.627085	−	0.778951i	$-0.284248\pi$
$151$	2327.14			1.25417			0.627085	+	0.778951i	$0.284248\pi$
$152$	−662.508	−	7.71235i	−0.353529	−	0.00411549i
$153$	−661.037			−0.349292
$154$	1317.42	+	2281.84i	0.689355	+	1.19400i
$155$	1183.27	+	2049.48i	0.613176	+	1.06205i
$156$	163.889	−	283.863i	0.0841128	−	0.145688i
$157$	477.339	+	826.776i	0.242649	+	0.420280i	0.961468	−	0.274917i	$-0.0886505\pi$
$157$	477.339	+	826.776i	0.242649	+	0.420280i	−0.718819	+	0.695197i	$0.755317\pi$
$158$	194.868	−	337.521i	0.0981194	−	0.169948i
$159$	−1477.83			−0.737103
$160$	−646.463			−0.319421
$161$	−2158.08	+	3737.90i	−1.05640	+	1.82974i
$162$	81.0000	−	140.296i	0.0392837	−	0.0680414i
$163$	1826.52			0.877696			0.438848	−	0.898561i	$-0.355387\pi$
$163$	1826.52			0.877696			0.438848	+	0.898561i	$0.355387\pi$
$164$	−170.863			−0.0813548
$165$	−1744.28	+	3021.18i	−0.822982	+	1.42545i
$166$	−286.083	−	495.510i	−0.133761	−	0.231681i
$167$	−732.806	+	1269.26i	−0.339558	+	0.588132i	−0.984350	−	0.176227i	$-0.943611\pi$
$167$	−732.806	+	1269.26i	−0.339558	+	0.588132i	0.644791	+	0.764359i	$0.276944\pi$
$168$	274.646	+	475.702i	0.126128	+	0.218459i
$169$	725.452	+	1256.52i	0.330201	+	0.571925i
$170$	2967.61			1.33886
$171$	−380.175	+	641.129i	−0.170016	+	0.286716i
$172$	188.987			0.0837800
$173$	−2081.43	−	3605.15i	−0.914730	−	1.58436i	−0.807295	−	0.590147i	$-0.799070\pi$
$173$	−2081.43	−	3605.15i	−0.914730	−	1.58436i	−0.107435	−	0.994212i	$-0.534264\pi$
$174$	21.4678	+	37.1834i	0.00935328	+	0.0162004i
$175$	3239.91	−	5611.70i	1.39951	−	2.42402i
$176$	460.491	+	797.593i	0.197220	+	0.341596i
$177$	690.061	−	1195.22i	0.293040	−	0.507561i
$178$	−1679.38			−0.707162
$179$	−2637.74			−1.10142			−0.550710	−	0.834697i	$-0.685643\pi$
$179$	−2637.74			−1.10142			−0.550710	+	0.834697i	$0.685643\pi$
$180$	−363.636	+	629.835i	−0.150577	+	0.260806i
$181$	389.916	−	675.354i	0.160123	−	0.277341i	−0.774790	−	0.632219i	$-0.782144\pi$
$181$	389.916	−	675.354i	0.160123	−	0.277341i	0.934913	+	0.354878i	$0.115478\pi$
$182$	1250.32			0.509229
$183$	−1352.23			−0.546230
$184$	−754.335	+	1306.55i	−0.302230	+	0.523478i
$185$	3359.59	+	5818.97i	1.33514	+	2.31254i
$186$	351.431	−	608.696i	0.138539	−	0.239956i
$187$	−2113.90	−	3661.38i	−0.826650	−	1.43180i
$188$	1015.99	+	1759.75i	0.394142	+	0.682674i
$189$	617.955			0.237828
$190$	1706.73	−	2878.24i	0.651680	−	1.09900i
$191$	3961.70			1.50083			0.750415	−	0.660967i	$-0.229854\pi$
$191$	3961.70			1.50083			0.750415	+	0.660967i	$0.229854\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	182.202	+	315.584i	0.0679545	+	0.117701i	0.898001	−	0.439994i	$-0.145019\pi$
$193$	182.202	+	315.584i	0.0679545	+	0.117701i	−0.830046	+	0.557695i	$0.811686\pi$
$194$	605.516	−	1048.78i	0.224090	−	0.388135i
$195$	827.719	+	1433.65i	0.303970	+	0.526492i
$196$	−361.648	+	626.394i	−0.131796	+	0.228278i
$197$	2309.32			0.835190			0.417595	−	0.908633i	$-0.362873\pi$
$197$	2309.32			0.835190			0.417595	+	0.908633i	$0.362873\pi$
$198$	1036.10			0.371882
$199$	−1838.27	+	3183.98i	−0.654833	+	1.13420i	0.327103	+	0.944989i	$0.393928\pi$
$199$	−1838.27	+	3183.98i	−0.654833	+	1.13420i	−0.981936	+	0.189215i	$0.939406\pi$
$200$	1132.48	−	1961.51i	0.400392	−	0.693500i
$201$	−1567.39			−0.550027
$202$	−94.5519			−0.0329339
$203$	−81.8898	+	141.837i	−0.0283130	+	0.0490395i
$204$	−440.691	−	763.300i	−0.151248	−	0.261969i
$205$	431.472	−	747.332i	0.147002	−	0.254614i
$206$	−430.750	−	746.081i	−0.145688	−	0.252340i
$207$	848.627	+	1469.87i	0.284945	+	0.493540i
$208$	437.036			0.145688
$209$	−4766.86	−	55.4917i	−1.57766	−	0.0183657i
$210$	−2774.20			−0.911610
$211$	−671.302	−	1162.73i	−0.219025	−	0.379363i	0.735485	−	0.677541i	$-0.236954\pi$
$211$	−671.302	−	1162.73i	−0.219025	−	0.379363i	−0.954510	+	0.298178i	$0.903621\pi$
$212$	−985.219	−	1706.45i	−0.319175	−	0.552827i
$213$	1397.13	−	2419.90i	0.449435	−	0.778444i
$214$	1055.78	+	1828.67i	0.337252	+	0.584138i
$215$	−477.240	+	826.604i	−0.151384	+	0.262204i
$216$	216.000			0.0680414
$217$	2681.09			0.838730
$218$	−282.571	+	489.428i	−0.0877896	+	0.152056i
$219$	525.185	−	909.647i	0.162049	−	0.280677i
$220$	−4651.41			−1.42545
$221$	−2006.23			−0.610650
$222$	997.799	−	1728.24i	0.301657	−	0.522485i
$223$	1119.79	+	1939.54i	0.336264	+	0.582426i	0.983727	−	0.179671i	$-0.0575033\pi$
$223$	1119.79	+	1939.54i	0.336264	+	0.582426i	−0.647463	+	0.762097i	$0.724170\pi$
$224$	−366.195	+	634.269i	−0.109230	+	0.189191i
$225$	−1274.04	−	2206.70i	−0.377493	−	0.653838i
$226$	−841.860	−	1458.15i	−0.247786	−	0.429179i
$227$	−6233.41			−1.82258			−0.911291	−	0.411763i	$-0.864913\pi$
$227$	−6233.41			−1.82258			−0.911291	+	0.411763i	$0.864913\pi$
$228$	−993.762	−	11.5685i	−0.288656	−	0.00336028i
$229$	−2291.74			−0.661320			−0.330660	−	0.943750i	$-0.607271\pi$
$229$	−2291.74			−0.661320			−0.330660	+	0.943750i	$0.607271\pi$
$230$	−3809.77	−	6598.71i	−1.09221	−	1.89177i
$231$	1976.13	+	3422.75i	0.562856	+	0.974895i
$232$	−28.6238	+	49.5778i	−0.00810018	+	0.0140299i
$233$	−799.537	−	1384.84i	−0.224804	−	0.389372i	0.731456	−	0.681888i	$-0.238841\pi$
$233$	−799.537	−	1384.84i	−0.224804	−	0.389372i	−0.956261	+	0.292516i	$0.905508\pi$
$234$	245.833	−	425.795i	0.0686778	−	0.118953i
$235$	−10262.5			−2.84873
$236$	1840.16			0.507561
$237$	292.302	−	506.282i	0.0801142	−	0.138762i
$238$	1681.03	−	2911.63i	0.457837	−	0.792996i
$239$	−2443.37			−0.661291			−0.330646	−	0.943755i	$-0.607266\pi$
$239$	−2443.37			−0.661291			−0.330646	+	0.943755i	$0.607266\pi$
$240$	−969.695			−0.260806
$241$	498.245	−	862.986i	0.133173	−	0.230663i	−0.791725	−	0.610878i	$-0.790817\pi$
$241$	498.245	−	862.986i	0.133173	−	0.230663i	0.924898	+	0.380215i	$0.124150\pi$
$242$	1982.31	+	3433.46i	0.526561	+	0.912030i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−901.489	−	1561.43i	−0.236524	−	0.409672i
$245$	−1826.50	−	3163.60i	−0.476290	−	0.824959i
$246$	−256.295			−0.0664259
$247$	−1153.82	+	1945.81i	−0.297230	+	0.501251i
$248$	937.150			0.239956
$249$	−429.124	−	743.265i	−0.109215	−	0.189167i
$250$	3194.34	+	5532.76i	0.808111	+	1.39969i
$251$	−379.945	+	658.084i	−0.0955455	+	0.165490i	−0.909836	−	0.414968i	$-0.863793\pi$
$251$	−379.945	+	658.084i	−0.0955455	+	0.165490i	0.814291	+	0.580457i	$0.197126\pi$
$252$	411.970	+	713.552i	0.102983	+	0.178371i
$253$	−5427.57	+	9400.83i	−1.34873	+	2.33607i
$254$	1910.79			0.472021
$255$	4451.42			1.09317
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2386.60	−	4133.71i	0.579268	−	1.00332i	−0.416296	−	0.909229i	$-0.636672\pi$
$257$	2386.60	−	4133.71i	0.579268	−	1.00332i	0.995563	−	0.0940922i	$-0.0299948\pi$
$258$	283.481			0.0684061
$259$	7612.27			1.82627
$260$	−1103.63	+	1911.53i	−0.263246	+	0.455955i
$261$	32.2017	+	55.7750i	0.00763692	+	0.0132275i
$262$	−1639.11	+	2839.02i	−0.386505	+	0.669447i
$263$	−2178.22	−	3772.78i	−0.510702	−	0.884562i	−0.999923	−	0.0124018i	$-0.996052\pi$
$263$	−2178.22	−	3772.78i	−0.510702	−	0.884562i	0.489221	−	0.872160i	$-0.337281\pi$
$264$	690.736	+	1196.39i	0.161030	+	0.278912i
$265$	9951.69			2.30690
$266$	−1857.15	−	3304.94i	−0.428080	−	0.761800i
$267$	−2519.07			−0.577396
$268$	−1044.93	−	1809.87i	−0.238169	−	0.412520i
$269$	70.3573	+	121.862i	0.0159471	+	0.0276211i	0.873889	−	0.486126i	$-0.161590\pi$
$269$	70.3573	+	121.862i	0.0159471	+	0.0276211i	−0.857942	+	0.513747i	$0.828257\pi$
$270$	−545.454	+	944.753i	−0.122945	+	0.212948i
$271$	−761.530	−	1319.01i	−0.170700	−	0.295661i	0.767965	−	0.640492i	$-0.221269\pi$
$271$	−761.530	−	1319.01i	−0.170700	−	0.295661i	−0.938665	+	0.344831i	$0.887936\pi$
$272$	587.588	−	1017.73i	0.130985	−	0.226872i
$273$	1875.48			0.415784
$274$	1695.42			0.373811
$275$	8148.39	−	14113.4i	1.78679	−	3.09480i
$276$	−1131.50	+	1959.82i	−0.246770	+	0.427418i
$277$	2217.54			0.481008			0.240504	−	0.970648i	$-0.422687\pi$
$277$	2217.54			0.481008			0.240504	+	0.970648i	$0.422687\pi$
$278$	−2335.21			−0.503800
$279$	527.147	−	913.045i	0.113116	−	0.195923i
$280$	−1849.47	−	3203.37i	−0.394739	−	0.683708i
$281$	−85.2598	+	147.674i	−0.0181003	+	0.0313506i	−0.874934	−	0.484243i	$-0.839095\pi$
$281$	−85.2598	+	147.674i	−0.0181003	+	0.0313506i	0.856833	+	0.515593i	$0.172428\pi$
$282$	1523.98	+	2639.62i	0.321815	+	0.557401i
$283$	−1088.15	−	1884.73i	−0.228565	−	0.395886i	0.728818	−	0.684708i	$-0.240070\pi$
$283$	−1088.15	−	1884.73i	−0.228565	−	0.395886i	−0.957383	+	0.288821i	$0.906737\pi$
$284$	3725.68			0.778444
$285$	2560.09	−	4317.36i	0.532094	−	0.897327i
$286$	3144.55			0.650144
$287$	−488.823	−	846.667i	−0.100538	−	0.174136i
$288$	144.000	+	249.415i	0.0294628	+	0.0510310i
$289$	−240.845	+	417.157i	−0.0490221	+	0.0849087i
$290$	−144.564	−	250.393i	−0.0292728	−	0.0507019i
$291$	908.273	−	1573.18i	0.182969	−	0.316911i
$292$	1400.49			0.280677
$293$	−9879.00			−1.96975			−0.984876	−	0.173261i	$-0.944569\pi$
$293$	−9879.00			−1.96975			−0.984876	+	0.173261i	$0.944569\pi$
$294$	−542.473	+	939.590i	−0.107611	+	0.186388i
$295$	−4646.87	+	8048.61i	−0.917122	+	1.58850i
$296$	2660.80			0.522485
$297$	1554.16			0.303641
$298$	−1721.57	+	2981.84i	−0.334657	+	0.579642i
$299$	2575.56	+	4461.00i	0.498156	+	0.862831i
$300$	1698.72	−	2942.27i	0.326919	−	0.566240i
$301$	540.674	+	936.475i	0.103535	+	0.179327i
$302$	2327.14	+	4030.72i	0.443416	+	0.768019i
$303$	−141.828			−0.0268904
$304$	−649.150	−	1155.21i	−0.122471	−	0.217947i
$305$	9105.94			1.70952
$306$	−661.037	−	1144.95i	−0.123493	−	0.213897i
$307$	671.855	+	1163.69i	0.124902	+	0.216336i	0.921694	−	0.387917i	$-0.126805\pi$
$307$	671.855	+	1163.69i	0.124902	+	0.216336i	−0.796793	+	0.604252i	$0.793472\pi$
$308$	−2634.84	+	4563.67i	−0.487447	+	0.844284i
$309$	−646.125	−	1119.12i	−0.118954	−	0.206034i
$310$	−2366.53	+	4098.96i	−0.433581	+	0.750985i
$311$	88.3559			0.0161100			0.00805499	−	0.999968i	$-0.497436\pi$
$311$	88.3559			0.0161100			0.00805499	+	0.999968i	$0.497436\pi$
$312$	655.555			0.118953
$313$	946.230	−	1638.92i	0.170876	−	0.295965i	−0.767851	−	0.640629i	$-0.778674\pi$
$313$	946.230	−	1638.92i	0.170876	−	0.295965i	0.938726	+	0.344664i	$0.112007\pi$
$314$	−954.679	+	1653.55i	−0.171578	+	0.297183i
$315$	−4161.30			−0.744326
$316$	779.472			0.138762
$317$	−4189.43	+	7256.31i	−0.742277	+	1.28566i	0.209179	+	0.977877i	$0.432921\pi$
$317$	−4189.43	+	7256.31i	−0.742277	+	1.28566i	−0.951456	+	0.307784i	$0.900413\pi$
$318$	−1477.83	−	2559.67i	−0.260605	−	0.451382i
$319$	−205.953	+	356.721i	−0.0361478	+	0.0626098i
$320$	−646.463	−	1119.71i	−0.112933	−	0.195605i
$321$	1583.68	+	2743.01i	0.275365	+	0.476946i
$322$	−8632.31			−1.49398
$323$	2979.94	+	5303.03i	0.513339	+	0.913525i
$324$	324.000			0.0555556
$325$	−3866.68	−	6697.29i	−0.659953	−	1.14307i
$326$	1826.52	+	3163.63i	0.310312	+	0.537477i
$327$	−423.857	+	734.142i	−0.0716799	+	0.124153i
$328$	−170.863	−	295.944i	−0.0287633	−	0.0498194i
$329$	−5813.29	+	10068.9i	−0.974155	+	1.68729i
$330$	−6977.12			−1.16387
$331$	4833.50			0.802639			0.401319	−	0.915938i	$-0.368552\pi$
$331$	4833.50			0.802639			0.401319	+	0.915938i	$0.368552\pi$
$332$	572.166	−	991.020i	0.0945833	−	0.163823i
$333$	1496.70	−	2592.36i	0.246302	−	0.426607i
$334$	−2931.22			−0.480208
$335$	10554.8			1.72141
$336$	−549.293	+	951.403i	−0.0891857	+	0.154474i
$337$	1312.89	+	2273.99i	0.212218	+	0.367573i	0.952408	−	0.304825i	$-0.0985979\pi$
$337$	1312.89	+	2273.99i	0.212218	+	0.367573i	−0.740190	+	0.672397i	$0.765265\pi$
$338$	−1450.90	+	2513.04i	−0.233487	+	0.404412i
$339$	−1262.79	−	2187.22i	−0.202317	−	0.350423i
$340$	2967.61	+	5140.06i	0.473357	+	0.819879i
$341$	6742.95			1.07082
$342$	−1490.64	−	17.3528i	−0.235686	−	0.00274366i
$343$	3711.75			0.584302
$344$	188.987	+	327.336i	0.0296207	+	0.0513045i
$345$	−5714.65	−	9898.06i	−0.891787	−	1.54462i
$346$	4162.86	−	7210.29i	0.646812	−	1.12031i
$347$	−4020.74	−	6964.13i	−0.622031	−	1.07739i	−0.989107	−	0.147199i	$-0.952974\pi$
$347$	−4020.74	−	6964.13i	−0.622031	−	1.07739i	0.367076	−	0.930191i	$-0.380359\pi$
$348$	−42.9356	+	74.3667i	−0.00661377	+	0.0114554i
$349$	8603.95			1.31965			0.659826	−	0.751418i	$-0.270630\pi$
$349$	8603.95			1.31965			0.659826	+	0.751418i	$0.270630\pi$
$350$	12959.7			1.97921
$351$	368.749	−	638.693i	0.0560752	−	0.0971251i
$352$	−920.982	+	1595.19i	−0.139456	+	0.241545i
$353$	−10359.4			−1.56198			−0.780988	−	0.624547i	$-0.785284\pi$
$353$	−10359.4			−1.56198			−0.780988	+	0.624547i	$0.785284\pi$
$354$	2760.24			0.414422
$355$	−9408.25	+	16295.6i	−1.40659	+	2.43628i
$356$	−1679.38	−	2908.77i	−0.250020	−	0.433047i
$357$	2521.55	−	4367.45i	0.373822	−	0.647479i
$358$	−2637.74	−	4568.70i	−0.389411	−	0.674479i
$359$	1772.34	+	3069.78i	0.260558	+	0.451300i	0.966390	−	0.257079i	$-0.0827600\pi$
$359$	1772.34	+	3069.78i	0.260558	+	0.451300i	−0.705832	+	0.708379i	$0.749427\pi$
$360$	−1454.54			−0.212948
$361$	6857.14	+	159.672i	0.999729	+	0.0232791i
$362$	1559.66			0.226448
$363$	2973.46	+	5150.19i	0.429935	+	0.744669i
$364$	1250.32	+	2165.61i	0.180040	+	0.311838i
$365$	−3536.59	+	6125.56i	−0.507161	+	0.878428i
$366$	−1352.23	−	2342.14i	−0.193121	−	0.334496i
$367$	−165.126	+	286.007i	−0.0234864	+	0.0406797i	−0.877530	−	0.479522i	$-0.840810\pi$
$367$	−165.126	+	286.007i	−0.0234864	+	0.0406797i	0.854043	+	0.520202i	$0.174143\pi$
$368$	−3017.34			−0.427418
$369$	−384.443			−0.0542365
$370$	−6719.17	+	11637.9i	−0.944089	+	1.63521i
$371$	5637.23	−	9763.96i	0.788869	−	1.36636i
$372$	1405.72			0.195923
$373$	−12016.2			−1.66802			−0.834012	−	0.551747i	$-0.813961\pi$
$373$	−12016.2			−1.66802			−0.834012	+	0.551747i	$0.813961\pi$
$374$	4227.80	−	7322.76i	0.584530	−	1.01244i
$375$	4791.51	+	8299.14i	0.659820	+	1.14284i
$376$	−2031.98	+	3519.49i	−0.278700	+	0.482723i
$377$	97.7315	+	169.276i	0.0133513	+	0.0231251i
$378$	617.955	+	1070.33i	0.0840851	+	0.145640i
$379$	5463.94			0.740538			0.370269	−	0.928925i	$-0.379266\pi$
$379$	5463.94			0.740538			0.370269	+	0.928925i	$0.379266\pi$
$380$	6691.98	+	77.9024i	0.903399	+	0.0105166i
$381$	2866.18			0.385404
$382$	3961.70	+	6861.86i	0.530623	+	0.919066i
$383$	−3690.29	−	6391.77i	−0.492337	−	0.852752i	0.507624	−	0.861578i	$-0.330524\pi$
$383$	−3690.29	−	6391.77i	−0.492337	−	0.852752i	−0.999961	+	0.00882645i	$0.997190\pi$
$384$	−192.000	+	332.554i	−0.0255155	+	0.0441942i
$385$	−13307.2	−	23048.8i	−1.76156	−	3.05111i
$386$	−364.405	+	631.167i	−0.0480511	+	0.0832269i
$387$	425.222			0.0558533
$388$	2422.06			0.316911
$389$	−1017.92	+	1763.08i	−0.132675	+	0.229799i	−0.924707	−	0.380680i	$-0.875690\pi$
$389$	−1017.92	+	1763.08i	−0.132675	+	0.229799i	0.792032	+	0.610479i	$0.209023\pi$
$390$	−1655.44	+	2867.30i	−0.214939	+	0.372286i
$391$	13851.2			1.79152
$392$	−1446.59			−0.186388
$393$	−2458.66	+	4258.53i	−0.315580	+	0.546601i
$394$	2309.32	+	3999.86i	0.295284	+	0.511447i
$395$	−1968.36	+	3409.30i	−0.250731	+	0.434280i
$396$	1036.10	+	1794.59i	0.131480	+	0.227731i
$397$	−6657.13	−	11530.5i	−0.841592	−	1.45768i	−0.888548	−	0.458783i	$-0.848285\pi$
$397$	−6657.13	−	11530.5i	−0.841592	−	1.45768i	0.0469563	−	0.998897i	$-0.485048\pi$
$398$	−7353.09			−0.926074
$399$	−2785.73	−	4957.41i	−0.349526	−	0.622007i
$400$	4529.92			0.566240
$401$	−6602.17	−	11435.3i	−0.822186	−	1.42407i	−0.904051	−	0.427424i	$-0.859421\pi$
$401$	−6602.17	−	11435.3i	−0.822186	−	1.42407i	0.0818652	−	0.996643i	$-0.473912\pi$
$402$	−1567.39	−	2714.81i	−0.194464	−	0.336821i
$403$	1599.88	−	2771.07i	0.197756	−	0.342523i
$404$	−94.5519	−	163.769i	−0.0116439	−	0.0201678i
$405$	−818.180	+	1417.13i	−0.100384	+	0.173871i
$406$	−327.559			−0.0400406
$407$	19144.9			2.33164
$408$	881.383	−	1526.60i	0.106948	−	0.185240i
$409$	−1380.93	+	2391.84i	−0.166950	+	0.289166i	−0.937346	−	0.348400i	$-0.886725\pi$
$409$	−1380.93	+	2391.84i	−0.166950	+	0.289166i	0.770396	+	0.637566i	$0.220059\pi$
$410$	1725.89			0.207892
$411$	2543.13			0.305215
$412$	861.501	−	1492.16i	0.103017	−	0.178431i
$413$	5264.52	+	9118.42i	0.627240	+	1.08641i
$414$	−1697.25	+	2939.73i	−0.201487	+	0.348985i
$415$	2889.72	+	5005.14i	0.341809	+	0.592031i
$416$	437.036	+	756.969i	0.0515083	+	0.0892151i
$417$	−3502.81			−0.411351
$418$	−4670.74	−	8311.93i	−0.546539	−	0.972607i
$419$	−15182.0			−1.77015			−0.885073	−	0.465453i	$-0.845891\pi$
$419$	−15182.0			−1.77015			−0.885073	+	0.465453i	$0.845891\pi$
$420$	−2774.20	−	4805.06i	−0.322303	−	0.558245i
$421$	−7990.18	−	13839.4i	−0.924982	−	1.60212i	−0.791590	−	0.611052i	$-0.790747\pi$
$421$	−7990.18	−	13839.4i	−0.924982	−	1.60212i	−0.133391	−	0.991063i	$-0.542587\pi$
$422$	1342.60	−	2325.46i	0.154874	−	0.268250i
$423$	2285.98	+	3959.43i	0.262761	+	0.455116i
$424$	1970.44	−	3412.90i	0.225691	−	0.390908i
$425$	−20794.8			−2.37340
$426$	5588.51			0.635597
$427$	5158.14	−	8934.17i	0.584590	−	1.01254i
$428$	−2111.57	+	3657.34i	−0.238473	+	0.413048i
$429$	4716.83			0.530840
$430$	−1908.96			−0.214089
$431$	−2381.00	+	4124.01i	−0.266099	+	0.460897i	−0.967851	−	0.251524i	$-0.919068\pi$
$431$	−2381.00	+	4124.01i	−0.266099	+	0.460897i	0.701752	+	0.712421i	$0.252402\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−4987.45	+	8638.52i	−0.553537	+	0.958754i	0.444479	+	0.895789i	$0.353389\pi$
$433$	−4987.45	+	8638.52i	−0.553537	+	0.958754i	−0.998016	+	0.0629648i	$0.979944\pi$
$434$	2681.09	+	4643.79i	0.296536	+	0.513615i
$435$	−216.846	−	375.589i	−0.0239011	−	0.0413979i
$436$	−1130.29			−0.124153
$437$	7966.08	−	13434.1i	0.872013	−	1.47057i
$438$	2100.74			0.229172
$439$	4478.44	+	7756.89i	0.486890	+	0.843317i	0.999886	−	0.0150731i	$-0.00479810\pi$
$439$	4478.44	+	7756.89i	0.486890	+	0.843317i	−0.512997	+	0.858390i	$0.671465\pi$
$440$	−4651.41	−	8056.48i	−0.503971	−	0.872904i
$441$	−813.709	+	1409.39i	−0.0878641	+	0.152185i
$442$	−2006.23	−	3474.89i	−0.215897	−	0.373945i
$443$	−5684.06	+	9845.08i	−0.609612	+	1.05588i	0.381693	+	0.924289i	$0.375341\pi$
$443$	−5684.06	+	9845.08i	−0.609612	+	1.05588i	−0.991304	+	0.131589i	$0.957992\pi$
$444$	3991.19			0.426607
$445$	16963.4			1.80706
$446$	−2239.58	+	3879.07i	−0.237774	+	0.411837i
$447$	−2582.35	+	4472.76i	−0.273246	+	0.473276i
$448$	−1464.78			−0.154474
$449$	7630.20			0.801985			0.400993	−	0.916081i	$-0.368665\pi$
$449$	7630.20			0.801985			0.400993	+	0.916081i	$0.368665\pi$
$450$	2548.08	−	4413.41i	0.266928	−	0.462333i
$451$	−1229.39	−	2129.37i	−0.128359	−	0.222324i
$452$	1683.72	−	2916.29i	0.175211	−	0.303475i
$453$	3490.70	+	6046.08i	0.362048	+	0.627085i
$454$	−6233.41	−	10796.6i	−0.644380	−	1.11610i
$455$	−12629.4			−1.30127
$456$	−973.724	−	1732.81i	−0.0999974	−	0.177953i
$457$	−1500.40			−0.153579			−0.0767896	−	0.997047i	$-0.524467\pi$
$457$	−1500.40			−0.153579			−0.0767896	+	0.997047i	$0.524467\pi$
$458$	−2291.74	−	3969.40i	−0.233812	−	0.404974i
$459$	−991.556	−	1717.42i	−0.100832	−	0.174646i
$460$	7619.53	−	13197.4i	0.772310	−	1.33768i
$461$	7247.90	+	12553.7i	0.732252	+	1.26830i	0.955919	+	0.293632i	$0.0948640\pi$
$461$	7247.90	+	12553.7i	0.732252	+	1.26830i	−0.223667	+	0.974666i	$0.571803\pi$
$462$	−3952.26	+	6845.51i	−0.397999	+	0.689355i
$463$	−12265.2			−1.23113			−0.615566	−	0.788086i	$-0.711072\pi$
$463$	−12265.2			−1.23113			−0.615566	+	0.788086i	$0.711072\pi$
$464$	−114.495			−0.0114554
$465$	−3549.80	+	6148.44i	−0.354018	+	0.613176i
$466$	1599.07	−	2769.68i	0.158961	−	0.275328i
$467$	−1890.82			−0.187360			−0.0936798	−	0.995602i	$-0.529863\pi$
$467$	−1890.82			−0.187360			−0.0936798	+	0.995602i	$0.529863\pi$
$468$	983.332			0.0971251
$469$	5978.88	−	10355.7i	0.588654	−	1.01958i
$470$	−10262.5	−	17775.2i	−1.00718	−	1.74448i
$471$	−1432.02	+	2480.33i	−0.140093	+	0.242649i
$472$	1840.16	+	3187.25i	0.179450	+	0.310816i
$473$	1359.80	+	2355.24i	0.132185	+	0.228951i
$474$	1169.21			0.113299
$475$	−11959.5	+	20168.5i	−1.15524	+	1.94820i
$476$	6724.13			0.647479
$477$	−2216.74	−	3839.51i	−0.212783	−	0.368552i
$478$	−2443.37	−	4232.04i	−0.233802	−	0.404956i
$479$	5831.44	−	10100.4i	0.556254	−	0.963460i	−0.441551	−	0.897236i	$-0.645572\pi$
$479$	5831.44	−	10100.4i	0.556254	−	0.963460i	0.997805	−	0.0662235i	$-0.0210950\pi$
$480$	−969.695	−	1679.56i	−0.0922090	−	0.159711i
$481$	4542.44	−	7867.74i	0.430598	−	0.745817i
$482$	1992.98			0.188336
$483$	−12948.5			−1.21983
$484$	−3964.62	+	6866.92i	−0.372335	+	0.644902i
$485$	−6116.31	+	10593.8i	−0.572633	+	0.991830i
$486$	486.000			0.0453609
$487$	13286.6			1.23629			0.618147	−	0.786063i	$-0.287884\pi$
$487$	13286.6			1.23629			0.618147	+	0.786063i	$0.287884\pi$
$488$	1802.98	−	3122.85i	0.167248	−	0.289682i
$489$	2739.79	+	4745.45i	0.253369	+	0.438848i
$490$	3653.01	−	6327.20i	0.336788	−	0.583334i
$491$	−2018.86	−	3496.76i	−0.185559	−	0.321398i	0.758205	−	0.652016i	$-0.226076\pi$
$491$	−2018.86	−	3496.76i	−0.185559	−	0.321398i	−0.943765	+	0.330617i	$0.892743\pi$
$492$	−256.295	−	443.916i	−0.0234851	−	0.0406774i
$493$	525.594			0.0480153
$494$	−4524.06	−	52.6653i	−0.412039	−	0.00479661i
$495$	−10465.7			−0.950298
$496$	937.150	+	1623.19i	0.0848372	+	0.146942i
$497$	10658.8	+	18461.6i	0.961996	+	1.66623i
$498$	858.248	−	1486.53i	0.0772270	−	0.133761i
$499$	−1772.42	−	3069.91i	−0.159006	−	0.275407i	0.775504	−	0.631342i	$-0.217496\pi$
$499$	−1772.42	−	3069.91i	−0.159006	−	0.275407i	−0.934511	+	0.355935i	$0.884162\pi$
$500$	−6388.68	+	11065.5i	−0.571421	+	0.989730i
$501$	−4396.83			−0.392088
$502$	−1519.78			−0.135122
$503$	6479.19	−	11222.3i	0.574339	−	0.994785i	−0.421774	−	0.906701i	$-0.638592\pi$
$503$	6479.19	−	11222.3i	0.574339	−	0.994785i	0.996113	−	0.0880839i	$-0.0280743\pi$
$504$	−823.939	+	1427.10i	−0.0728198	+	0.126128i
$505$	955.068			0.0841584
$506$	−21710.3			−1.90739
$507$	−2176.35	+	3769.56i	−0.190642	+	0.330201i
$508$	1910.79	+	3309.58i	0.166885	+	0.289053i
$509$	4118.14	−	7132.83i	0.358612	−	0.621134i	−0.629117	−	0.777310i	$-0.716584\pi$
$509$	4118.14	−	7132.83i	0.358612	−	0.621134i	0.987729	+	0.156177i	$0.0499169\pi$
$510$	4451.42	+	7710.08i	0.386494	+	0.669428i
$511$	4006.67	+	6939.76i	0.346859	+	0.600777i
$512$	−512.000			−0.0441942
$513$	−2235.96	−	26.0292i	−0.192437	−	0.00224019i
$514$	9546.39			0.819209
$515$	4351.00	+	7536.16i	0.372288	+	0.644821i
$516$	283.481	+	491.004i	0.0241852	+	0.0418900i
$517$	−14620.4	+	25323.3i	−1.24373	+	2.15420i
$518$	7612.27	+	13184.8i	0.645684	+	1.11836i
$519$	6244.30	−	10815.4i	0.528120	−	0.914730i
$520$	−4414.50			−0.372286
$521$	7427.58			0.624584			0.312292	−	0.949986i	$-0.398903\pi$
$521$	7427.58			0.624584			0.312292	+	0.949986i	$0.398903\pi$
$522$	−64.4035	+	111.550i	−0.00540012	+	0.00935328i
$523$	2302.44	−	3987.95i	0.192502	−	0.333424i	−0.753577	−	0.657360i	$-0.771673\pi$
$523$	2302.44	−	3987.95i	0.192502	−	0.333424i	0.946079	+	0.323936i	$0.105006\pi$
$524$	−6556.43			−0.546601
$525$	19439.5			1.61602
$526$	4356.43	−	7545.56i	0.361121	−	0.625479i
$527$	−4302.02	−	7451.31i	−0.355596	−	0.615910i
$528$	−1381.47	+	2392.78i	−0.113865	+	0.197220i
$529$	−11698.4	−	20262.3i	−0.961488	−	1.66535i
$530$	9951.69	+	17236.8i	0.815611	+	1.41268i
$531$	4140.36			0.338374
$532$	3867.17	−	6521.62i	0.315156	−	0.531482i
$533$	−1166.77			−0.0948191
$534$	−2519.07	−	4363.16i	−0.204140	−	0.353581i
$535$	−10664.5	−	18471.4i	−0.861804	−	1.49269i
$536$	2089.86	−	3619.74i	0.168411	−	0.291696i
$537$	−3956.61	−	6853.06i	−0.317953	−	0.550710i
$538$	−140.715	+	243.725i	−0.0112763	+	0.0195311i
$539$	−10408.5			−0.831772
$540$	−2181.81			−0.173871
$541$	−4515.43	+	7820.96i	−0.358842	+	0.621533i	−0.987768	−	0.155933i	$-0.950162\pi$
$541$	−4515.43	+	7820.96i	−0.358842	+	0.621533i	0.628925	+	0.777466i	$0.283495\pi$
$542$	1523.06	−	2638.02i	0.120703	−	0.209064i
$543$	2339.50			0.184894
$544$	2350.35			0.185240
$545$	2854.25	−	4943.71i	0.224335	−	0.388560i
$546$	1875.48	+	3248.42i	0.147002	+	0.254615i
$547$	−6437.80	+	11150.6i	−0.503218	+	0.871599i	0.496775	+	0.867879i	$0.334517\pi$
$547$	−6437.80	+	11150.6i	−0.503218	+	0.871599i	−0.999993	+	0.00372003i	$0.998816\pi$
$548$	1695.42	+	2936.56i	0.132162	+	0.228912i
$549$	−2028.35	−	3513.21i	−0.157683	−	0.273115i
$550$	32593.6			2.52690
$551$	302.279	−	509.765i	0.0233711	−	0.0394132i
$552$	−4526.01			−0.348985
$553$	2229.99	+	3862.46i	0.171481	+	0.297014i
$554$	2217.54	+	3840.90i	0.170062	+	0.294556i
$555$	−10078.8	+	17456.9i	−0.770846	+	1.33514i
$556$	−2335.21	−	4044.70i	−0.178120	−	0.308513i
$557$	2445.60	−	4235.90i	0.186038	−	0.322228i	−0.757888	−	0.652385i	$-0.773768\pi$
$557$	2445.60	−	4235.90i	0.186038	−	0.322228i	0.943926	+	0.330157i	$0.107102\pi$
$558$	2108.59			0.159971
$559$	1290.54			0.0976456
$560$	3698.94	−	6406.74i	0.279122	−	0.483454i
$561$	6341.70	−	10984.1i	0.477267	−	0.826650i
$562$	−341.039			−0.0255976
$563$	2367.05			0.177192			0.0885961	−	0.996068i	$-0.471762\pi$
$563$	2367.05			0.177192			0.0885961	+	0.996068i	$0.471762\pi$
$564$	−3047.97	+	5279.24i	−0.227558	+	0.394142i
$565$	8503.62	+	14728.7i	0.633186	+	1.09671i
$566$	2176.30	−	3769.47i	0.161620	−	0.279934i
$567$	926.932	+	1605.49i	0.0686552	+	0.118914i
$568$	3725.68	+	6453.06i	0.275222	+	0.476698i
$569$	−675.013			−0.0497329			−0.0248665	−	0.999691i	$-0.507916\pi$
$569$	−675.013			−0.0497329			−0.0248665	+	0.999691i	$0.507916\pi$
$570$	10038.0	+	116.854i	0.737622	+	0.00858677i
$571$	17245.3			1.26391			0.631955	−	0.775005i	$-0.282253\pi$
$571$	17245.3			1.26391			0.631955	+	0.775005i	$0.282253\pi$
$572$	3144.55	+	5446.52i	0.229861	+	0.398130i
$573$	5942.55	+	10292.8i	0.433252	+	0.750415i
$574$	977.646	−	1693.33i	0.0710909	−	0.123133i
$575$	26695.9	+	46238.7i	1.93617	+	3.35354i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	24732.5			1.78445			0.892226	−	0.451589i	$-0.149143\pi$
$577$	24732.5			1.78445			0.892226	+	0.451589i	$0.149143\pi$
$578$	−963.382			−0.0693277
$579$	−546.607	+	946.751i	−0.0392335	+	0.0679545i
$580$	289.128	−	500.785i	0.0206990	−	0.0358517i
$581$	6547.64			0.467542
$582$	3633.09			0.258757
$583$	14177.6	−	24556.4i	1.00717	−	1.74446i
$584$	1400.49	+	2425.73i	0.0992343	+	0.171879i
$585$	−2483.16	+	4300.95i	−0.175497	+	0.303970i
$586$	−9879.00	−	17110.9i	−0.696412	−	1.20622i
$587$	−6859.27	−	11880.6i	−0.482304	−	0.835374i	0.517490	−	0.855689i	$-0.326866\pi$
$587$	−6859.27	−	11880.6i	−0.482304	−	0.835374i	−0.999794	+	0.0203148i	$0.993533\pi$
$588$	−2169.89			−0.152185
$589$	−9701.08	−	112.932i	−0.678652	−	0.00790029i
$590$	−18587.5			−1.29701
$591$	3463.98	+	5999.79i	0.241098	+	0.417595i
$592$	2660.80	+	4608.63i	0.184726	+	0.319956i
$593$	−3582.47	+	6205.02i	−0.248085	+	0.429696i	−0.962995	−	0.269521i	$-0.913135\pi$
$593$	−3582.47	+	6205.02i	−0.248085	+	0.429696i	0.714909	+	0.699217i	$0.246468\pi$
$594$	1554.16	+	2691.88i	0.107353	+	0.185941i
$595$	−16980.1	+	29410.4i	−1.16994	+	2.02640i
$596$	−6886.26			−0.473276
$597$	−11029.6			−0.756136
$598$	−5151.12	+	8922.01i	−0.352249	+	0.610114i
$599$	753.918	−	1305.82i	0.0514262	−	0.0890727i	−0.839166	−	0.543875i	$-0.816957\pi$
$599$	753.918	−	1305.82i	0.0514262	−	0.0890727i	0.890593	+	0.454802i	$0.150290\pi$
$600$	6794.88			0.462333
$601$	8574.64			0.581975			0.290987	−	0.956727i	$-0.406016\pi$
$601$	8574.64			0.581975			0.290987	+	0.956727i	$0.406016\pi$
$602$	−1081.35	+	1872.95i	−0.0732101	+	0.126804i
$603$	−2351.09	−	4072.21i	−0.158779	−	0.275014i
$604$	−4654.27	+	8061.43i	−0.313542	+	0.543071i
$605$	−20023.3	−	34681.4i	−1.34556	−	2.33057i
$606$	−141.828	−	245.653i	−0.00950720	−	0.0164670i
$607$	504.688			0.0337474			0.0168737	−	0.999858i	$-0.494629\pi$
$607$	504.688			0.0337474			0.0168737	+	0.999858i	$0.494629\pi$
$608$	1351.73	−	2279.57i	0.0901644	−	0.152054i
$609$	−491.339			−0.0326930
$610$	9105.94	+	15771.9i	0.604408	+	1.04686i
$611$	6937.88	+	12016.8i	0.459373	+	0.795657i
$612$	1322.07	−	2289.90i	0.0873230	−	0.151248i
$613$	−7472.22	−	12942.3i	−0.492333	−	0.852746i	0.507628	−	0.861576i	$-0.330522\pi$
$613$	−7472.22	−	12942.3i	−0.492333	−	0.852746i	−0.999961	+	0.00883041i	$0.997189\pi$
$614$	−1343.71	+	2327.37i	−0.0883187	+	0.152973i
$615$	2588.83			0.169743
$616$	−10539.3			−0.689355
$617$	1741.05	−	3015.59i	0.113601	−	0.196763i	−0.803618	−	0.595145i	$-0.797095\pi$
$617$	1741.05	−	3015.59i	0.113601	−	0.196763i	0.917220	+	0.398381i	$0.130428\pi$
$618$	1292.25	−	2238.24i	0.0841132	−	0.145688i
$619$	3577.83			0.232319			0.116159	−	0.993231i	$-0.462942\pi$
$619$	3577.83			0.232319			0.116159	+	0.993231i	$0.462942\pi$
$620$	−9466.14			−0.613176
$621$	−2545.88	+	4409.60i	−0.164513	+	0.284945i
$622$	88.3559	+	153.037i	0.00569574	+	0.00986531i
$623$	9609.08	−	16643.4i	0.617945	−	1.07031i
$624$	655.555	+	1135.45i	0.0420564	+	0.0728438i
$625$	−14571.0	−	25237.7i	−0.932543	−	1.61521i
$626$	3784.92			0.241655
$627$	−7006.11	−	12467.9i	−0.446247	−	0.794130i
$628$	−3818.72			−0.242649
$629$	−12214.5	−	21156.1i	−0.774282	−	1.34110i
$630$	−4161.30	−	7207.59i	−0.263159	−	0.455805i
$631$	−1824.72	+	3160.50i	−0.115120	+	0.199394i	−0.917828	−	0.396979i	$-0.870059\pi$
$631$	−1824.72	+	3160.50i	−0.115120	+	0.199394i	0.802708	+	0.596373i	$0.203392\pi$
$632$	779.472	+	1350.09i	0.0490597	+	0.0849739i
$633$	2013.91	−	3488.19i	0.126454	−	0.219025i
$634$	−16757.7			−1.04974
$635$	−19300.8			−1.20619
$636$	2955.66	−	5119.35i	0.184276	−	0.319175i
$637$	−2469.59	+	4277.45i	−0.153608	+	0.266058i
$638$	−823.811			−0.0511207
$639$	8382.77			0.518963
$640$	1292.93	−	2239.42i	0.0798553	−	0.138314i
$641$	7334.60	+	12703.9i	0.451949	+	0.782799i	0.998507	−	0.0546226i	$-0.0173956\pi$
$641$	7334.60	+	12703.9i	0.451949	+	0.782799i	−0.546558	+	0.837421i	$0.684062\pi$
$642$	−3167.35	+	5486.02i	−0.194713	+	0.337252i
$643$	−3504.05	−	6069.20i	−0.214909	−	0.372233i	0.738335	−	0.674434i	$-0.235612\pi$
$643$	−3504.05	−	6069.20i	−0.214909	−	0.372233i	−0.953244	+	0.302200i	$0.902279\pi$
$644$	−8632.31	−	14951.6i	−0.528200	−	0.914869i
$645$	−2863.44			−0.174803
$646$	−6205.17	+	10464.4i	−0.377925	+	0.637334i
$647$	9659.76			0.586962			0.293481	−	0.955965i	$-0.405186\pi$
$647$	9659.76			0.586962			0.293481	+	0.955965i	$0.405186\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	13240.3	+	22932.8i	0.800811	+	1.38705i
$650$	7733.36	−	13394.6i	0.466658	−	0.808275i
$651$	4021.64	+	6965.68i	0.242120	+	0.419365i
$652$	−3653.05	+	6327.27i	−0.219424	+	0.380054i
$653$	6799.09			0.407456			0.203728	−	0.979027i	$-0.434694\pi$
$653$	6799.09			0.407456			0.203728	+	0.979027i	$0.434694\pi$
$654$	−1695.43			−0.101371
$655$	16556.6	−	28676.9i	0.987665	−	1.71069i
$656$	341.727	−	591.888i	0.0203387	−	0.0352277i
$657$	3151.11			0.187118
$658$	−23253.2			−1.37766
$659$	9674.12	−	16756.1i	0.571851	−	0.990476i	−0.424524	−	0.905416i	$-0.639559\pi$
$659$	9674.12	−	16756.1i	0.571851	−	0.990476i	0.996376	−	0.0850593i	$-0.0271080\pi$
$660$	−6977.12	−	12084.7i	−0.411491	−	0.712723i
$661$	−2564.00	+	4440.98i	−0.150875	+	0.261322i	−0.931549	−	0.363615i	$-0.881542\pi$
$661$	−2564.00	+	4440.98i	−0.150875	+	0.261322i	0.780675	+	0.624938i	$0.214876\pi$
$662$	4833.50	+	8371.87i	0.283776	+	0.491514i
$663$	−3009.35	−	5212.34i	−0.176280	−	0.305325i
$664$	2288.66			0.133761
$665$	18759.1	+	33383.2i	1.09390	+	1.94668i
$666$	5986.79			0.348324
$667$	−674.747	−	1168.70i	−0.0391699	−	0.0678442i
$668$	−2931.22	−	5077.03i	−0.169779	−	0.294066i
$669$	−3359.38	+	5818.61i	−0.194142	+	0.336264i
$670$	10554.8	+	18281.5i	0.608609	+	1.05414i
$671$	12972.7	−	22469.4i	0.746359	−	1.29273i
$672$	−2197.17			−0.126128
$673$	−23921.1			−1.37012			−0.685061	−	0.728486i	$-0.740224\pi$
$673$	−23921.1			−1.37012			−0.685061	+	0.728486i	$0.740224\pi$
$674$	−2625.77	+	4547.98i	−0.150061	+	0.259913i
$675$	3822.12	−	6620.11i	0.217946	−	0.377493i
$676$	−5803.61			−0.330201
$677$	−766.891			−0.0435362			−0.0217681	−	0.999763i	$-0.506930\pi$
$677$	−766.891			−0.0435362			−0.0217681	+	0.999763i	$0.506930\pi$
$678$	2525.58	−	4374.44i	0.143060	−	0.247786i
$679$	6929.28	+	12001.9i	0.391637	+	0.678335i
$680$	−5935.23	+	10280.1i	−0.334714	+	0.579742i
$681$	−9350.12	−	16194.9i	−0.526134	−	0.911291i
$682$	6742.95	+	11679.1i	0.378594	+	0.655743i
$683$	−6573.45			−0.368267			−0.184133	−	0.982901i	$-0.558948\pi$
$683$	−6573.45			−0.368267			−0.184133	+	0.982901i	$0.558948\pi$
$684$	−1460.59	−	2599.22i	−0.0816475	−	0.145298i
$685$	−17125.5			−0.955226
$686$	3711.75	+	6428.94i	0.206582	+	0.357811i
$687$	−3437.60	−	5954.10i	−0.190907	−	0.330660i
$688$	−377.975	+	654.672i	−0.0209450	+	0.0362778i
$689$	−6727.76	−	11652.8i	−0.371999	−	0.644321i
$690$	11429.3	−	19796.1i	0.630588	−	1.09221i
$691$	−12816.9			−0.705613			−0.352806	−	0.935696i	$-0.614773\pi$
$691$	−12816.9			−0.705613			−0.352806	+	0.935696i	$0.614773\pi$
$692$	16651.5			0.914730
$693$	−5928.38	+	10268.3i	−0.324965	+	0.562856i
$694$	8041.49	−	13928.3i	0.439843	−	0.761830i
$695$	23587.9			1.28740
$696$	−171.743			−0.00935328
$697$	−1568.71	+	2717.08i	−0.0852498	+	0.147657i
$698$	8603.95	+	14902.5i	0.466568	+	0.808119i
$699$	2398.61	−	4154.51i	0.129791	−	0.224804i
$700$	12959.7	+	22446.8i	0.699756	+	1.21201i
$701$	15520.8	+	26882.8i	0.836251	+	1.44843i	0.893008	+	0.450041i	$0.148591\pi$
$701$	15520.8	+	26882.8i	0.836251	+	1.44843i	−0.0567573	+	0.998388i	$0.518076\pi$
$702$	1475.00			0.0793023
$703$	−27543.7	−	320.641i	−1.47771	−	0.0172023i
$704$	−3683.93			−0.197220
$705$	−15393.8	−	26662.8i	−0.822358	−	1.42437i
$706$	−10359.4	−	17943.1i	−0.552242	−	0.956511i
$707$	541.007	−	937.052i	0.0287789	−	0.0498465i
$708$	2760.24	+	4780.88i	0.146520	+	0.253780i
$709$	6820.49	−	11813.4i	0.361282	−	0.625759i	−0.626890	−	0.779108i	$-0.715673\pi$
$709$	6820.49	−	11813.4i	0.361282	−	0.625759i	0.988172	+	0.153349i	$0.0490058\pi$
$710$	−37633.0			−1.98921
$711$	1753.81			0.0925079
$712$	3358.76	−	5817.54i	0.176791	−	0.306210i
$713$	−11045.7	+	19131.7i	−0.580175	+	1.00489i
$714$	10086.2			0.528664
$715$	−31763.1			−1.66136
$716$	5275.49	−	9137.41i	0.275355	−	0.476929i
$717$	−3665.06	−	6348.07i	−0.190898	−	0.330646i
$718$	−3544.68	+	6139.56i	−0.184243	+	0.319118i
$719$	−13766.9	−	23845.0i	−0.714073	−	1.23681i	−0.963316	−	0.268370i	$-0.913515\pi$
$719$	−13766.9	−	23845.0i	−0.714073	−	1.23681i	0.249243	−	0.968441i	$-0.419818\pi$
$720$	−1454.54	−	2519.34i	−0.0752883	−	0.130403i
$721$	9858.67			0.509232
$722$	6580.58	+	12036.6i	0.339202	+	0.620437i
$723$	2989.47			0.153775
$724$	1559.66	+	2701.42i	0.0800614	+	0.138670i
$725$	1013.00	+	1754.56i	0.0518920	+	0.0898796i
$726$	−5946.93	+	10300.4i	−0.304010	+	0.526561i
$727$	−10433.6	−	18071.6i	−0.532273	−	0.921924i	−0.999290	−	0.0376757i	$-0.988005\pi$
$727$	−10433.6	−	18071.6i	−0.532273	−	0.921924i	0.467017	−	0.884248i	$-0.345329\pi$
$728$	−2500.64	+	4331.23i	−0.127307	+	0.220503i
$729$	729.000			0.0370370
$730$	−14146.4			−0.717234
$731$	1735.11	−	3005.29i	0.0877910	−	0.152059i
$732$	2704.47	−	4684.28i	0.136557	−	0.236524i
$733$	−18422.0			−0.928282			−0.464141	−	0.885761i	$-0.653637\pi$
$733$	−18422.0			−0.928282			−0.464141	+	0.885761i	$0.653637\pi$
$734$	−660.505			−0.0332148
$735$	5479.51	−	9490.79i	0.274986	−	0.476290i
$736$	−3017.34	−	5226.19i	−0.151115	−	0.261739i
$737$	15036.9	−	26044.6i	0.751548	−	1.30172i
$738$	−384.443	−	665.874i	−0.0191755	−	0.0332130i
$739$	7753.99	+	13430.3i	0.385975	+	0.668527i	0.991904	−	0.126991i	$-0.0405319\pi$
$739$	7753.99	+	13430.3i	0.385975	+	0.668527i	−0.605929	+	0.795518i	$0.707199\pi$
$740$	−26876.7			−1.33514
$741$	−6786.09	−	78.9979i	−0.336428	−	0.00391641i
$742$	22548.9			1.11563
$743$	5938.51	+	10285.8i	0.293221	+	0.507873i	0.974569	−	0.224086i	$-0.0719397\pi$
$743$	5938.51	+	10285.8i	0.293221	+	0.507873i	−0.681349	+	0.731959i	$0.738606\pi$
$744$	1405.72	+	2434.79i	0.0692693	+	0.119978i
$745$	17389.5	−	30119.5i	0.855172	−	1.48120i
$746$	−12016.2	−	20812.6i	−0.589735	−	1.02145i
$747$	1287.37	−	2229.79i	0.0630556	−	0.109215i
$748$	16911.2			0.826650
$749$	−24164.0			−1.17881
$750$	−9583.02	+	16598.3i	−0.466563	+	0.808111i
$751$	−13417.1	+	23239.1i	−0.651927	+	1.12917i	0.330727	+	0.943726i	$0.392706\pi$
$751$	−13417.1	+	23239.1i	−0.651927	+	1.12917i	−0.982655	+	0.185445i	$0.940627\pi$
$752$	−8127.92			−0.394142
$753$	−2279.67			−0.110326
$754$	−195.463	+	338.552i	−0.00944077	+	0.0163519i
$755$	−23506.4	−	40714.2i	−1.13309	−	1.96257i
$756$	−1235.91	+	2140.66i	−0.0594571	+	0.102983i
$757$	19552.5	+	33865.9i	0.938767	+	1.62599i	0.767774	+	0.640720i	$0.221364\pi$
$757$	19552.5	+	33865.9i	0.938767	+	1.62599i	0.170993	+	0.985272i	$0.445303\pi$
$758$	5463.94	+	9463.83i	0.261820	+	0.453485i
$759$	−32565.4			−1.55738
$760$	6557.05	+	11668.8i	0.312960	+	0.556935i
$761$	13627.0			0.649117			0.324559	−	0.945866i	$-0.394784\pi$
$761$	13627.0			0.649117			0.324559	+	0.945866i	$0.394784\pi$
$762$	2866.18	+	4964.37i	0.136261	+	0.236011i
$763$	−3233.63	−	5600.82i	−0.153428	−	0.265745i
$764$	−7923.40	+	13723.7i	−0.375207	+	0.649878i
$765$	6677.13	+	11565.1i	0.315571	+	0.546586i
$766$	7380.58	−	12783.5i	0.348135	−	0.602987i
$767$	12565.9			0.591563
$768$	−768.000			−0.0360844
$769$	−11583.2	+	20062.7i	−0.543173	+	0.940804i	0.455546	+	0.890212i	$0.349444\pi$
$769$	−11583.2	+	20062.7i	−0.543173	+	0.940804i	−0.998719	+	0.0505917i	$0.983889\pi$
$770$	26614.5	−	46097.6i	1.24561	−	2.15746i
$771$	14319.6			0.668881
$772$	−1457.62			−0.0679545
$773$	−16100.8	+	27887.4i	−0.749167	+	1.29760i	0.199055	+	0.979988i	$0.436213\pi$
$773$	−16100.8	+	27887.4i	−0.749167	+	1.29760i	−0.948222	+	0.317607i	$0.897121\pi$
$774$	425.222	+	736.506i	0.0197471	+	0.0342030i
$775$	16582.9	−	28722.4i	0.768612	−	1.33127i
$776$	2422.06	+	4195.14i	0.112045	+	0.194068i
$777$	11418.4	+	19777.3i	0.527199	+	0.913135i
$778$	−4071.67			−0.187630
$779$	1733.06	+	3084.11i	0.0797090	+	0.141848i
$780$	−6621.75			−0.303970
$781$	26806.9	+	46430.9i	1.22820	+	2.12731i
$782$	13851.2	+	23991.0i	0.633399	+	1.09708i
$783$	−96.6052	+	167.325i	−0.00440918	+	0.00763692i
$784$	−1446.59	−	2505.57i	−0.0658980	−	0.114139i
$785$	9643.20	−	16702.5i	0.438447	−	0.759412i
$786$	−9834.65			−0.446298
$787$	−36081.7			−1.63427			−0.817137	−	0.576443i	$-0.804440\pi$
$787$	−36081.7			−1.63427			−0.817137	+	0.576443i	$0.804440\pi$
$788$	−4618.64	+	7999.73i	−0.208797	+	0.361648i
$789$	6534.65	−	11318.3i	0.294854	−	0.510702i
$790$	−7873.44			−0.354588
$791$	19267.8			0.866100
$792$	−2072.21	+	3589.17i	−0.0929706	+	0.161030i
$793$	−6156.00	−	10662.5i	−0.275669	−	0.477473i
$794$	13314.3	−	23061.0i	0.595095	−	1.03074i
$795$	14927.5	+	25855.2i	0.665943	+	1.15345i
$796$	−7353.09	−	12735.9i	−0.327416	−	0.567102i
$797$	−39094.9			−1.73753			−0.868765	−	0.495224i	$-0.835086\pi$
$797$	−39094.9			−1.73753			−0.868765	+	0.495224i	$0.835086\pi$
$798$	5800.76	−	9782.43i	0.257324	−	0.433953i
$799$	37311.5			1.65205
$800$	4529.92	+	7846.05i	0.200196	+	0.346750i
$801$	−3778.61	−	6544.74i	−0.166680	−	0.288698i
$802$	13204.3	−	22870.6i	0.581373	−	1.00697i
$803$	10076.8	+	17453.5i	0.442842	+	0.767025i
$804$	3134.79	−	5429.61i	0.137507	−	0.238169i
$805$	87194.9			3.81766
$806$	6399.51			0.279669
$807$	−211.072	+	365.587i	−0.00920704	+	0.0159471i
$808$	189.104	−	327.538i	0.00823348	−	0.0142608i
$809$	7261.33			0.315568			0.157784	−	0.987474i	$-0.449565\pi$
$809$	7261.33			0.315568			0.157784	+	0.987474i	$0.449565\pi$
$810$	−3272.72			−0.141965
$811$	−17066.6	+	29560.3i	−0.738953	+	1.27990i	0.214014	+	0.976831i	$0.431346\pi$
$811$	−17066.6	+	29560.3i	−0.738953	+	1.27990i	−0.952967	+	0.303073i	$0.901987\pi$
$812$	−327.559	−	567.349i	−0.0141565	−	0.0245198i
$813$	2284.59	−	3957.02i	0.0985535	−	0.170700i
$814$	19144.9	+	33159.9i	0.824358	+	1.42783i
$815$	−18449.7	−	31955.8i	−0.792963	−	1.37345i
$816$	3525.53			0.151248
$817$	−1916.89	−	3411.25i	−0.0820852	−	0.146077i
$818$	−5523.72			−0.236103
$819$	2813.22	+	4872.63i	0.120026	+	0.207892i
$820$	1725.89	+	2989.33i	0.0735008	+	0.127307i
$821$	−6940.15	+	12020.7i	−0.295022	+	0.510992i	−0.974990	−	0.222249i	$-0.928660\pi$
$821$	−6940.15	+	12020.7i	−0.295022	+	0.510992i	0.679968	+	0.733242i	$0.261994\pi$
$822$	2543.13	+	4404.84i	0.107910	+	0.186906i
$823$	−6508.05	+	11272.3i	−0.275646	+	0.477432i	−0.970298	−	0.241913i	$-0.922225\pi$
$823$	−6508.05	+	11272.3i	−0.275646	+	0.477432i	0.694652	+	0.719346i	$0.255558\pi$
$824$	3446.00			0.145688
$825$	48890.3			2.06320
$826$	−10529.0	+	18236.8i	−0.443526	+	0.768209i
$827$	9932.04	−	17202.8i	0.417619	−	0.723338i	−0.578080	−	0.815980i	$-0.696198\pi$
$827$	9932.04	−	17202.8i	0.417619	−	0.723338i	0.995699	+	0.0926423i	$0.0295313\pi$
$828$	−6789.02			−0.284945
$829$	11325.6			0.474494			0.237247	−	0.971449i	$-0.423755\pi$
$829$	11325.6			0.474494			0.237247	+	0.971449i	$0.423755\pi$
$830$	−5779.44	+	10010.3i	−0.241695	+	0.418629i
$831$	3326.32	+	5761.35i	0.138855	+	0.240504i
$832$	−874.073	+	1513.94i	−0.0364219	+	0.0630846i
$833$	6640.64	+	11501.9i	0.276212	+	0.478413i
$834$	−3502.81	−	6067.04i	−0.145434	−	0.251900i
$835$	29608.3			1.22711
$836$	9725.94	−	16401.9i	0.402367	−	0.678554i
$837$	3162.88			0.130615
$838$	−15182.0	−	26296.1i	−0.625841	−	1.08399i
$839$	−2253.99	−	3904.03i	−0.0927491	−	0.160646i	0.815918	−	0.578168i	$-0.196232\pi$
$839$	−2253.99	−	3904.03i	−0.0927491	−	0.160646i	−0.908667	+	0.417522i	$0.862899\pi$
$840$	5548.40	−	9610.12i	0.227903	−	0.394739i
$841$	12168.9	+	21077.1i	0.498950	+	0.864207i
$842$	15980.4	−	27678.8i	0.654061	−	1.13287i
$843$	−511.559			−0.0209004
$844$	5370.42			0.219025
$845$	14655.6	−	25384.2i	0.596647	−	1.03342i
$846$	−4571.95	+	7918.85i	−0.185800	+	0.321815i
$847$	−45369.5			−1.84051
$848$	7881.75			0.319175
$849$	3264.46	−	5654.20i	0.131962	−	0.228565i
$850$	−20794.8	−	36017.6i	−0.839123	−	1.45340i
$851$	−31361.4	+	54319.6i	−1.26329	+	2.18808i
$852$	5588.51	+	9679.59i	0.224717	+	0.389222i
$853$	15756.2	+	27290.6i	0.632454	+	1.09544i	0.987049	+	0.160422i	$0.0512855\pi$
$853$	15756.2	+	27290.6i	0.632454	+	1.09544i	−0.354595	+	0.935020i	$0.615381\pi$
$854$	20632.6			0.826736
$855$	15057.0	+	175.280i	0.602266	+	0.00701107i
$856$	−8446.28			−0.337252
$857$	3170.25	+	5491.04i	0.126364	+	0.218869i	0.922265	−	0.386558i	$-0.126336\pi$
$857$	3170.25	+	5491.04i	0.126364	+	0.218869i	−0.795901	+	0.605426i	$0.793003\pi$
$858$	4716.83	+	8169.78i	0.187680	+	0.325072i
$859$	10103.0	−	17498.9i	0.401291	−	0.695057i	−0.592591	−	0.805504i	$-0.701895\pi$
$859$	10103.0	−	17498.9i	0.401291	−	0.695057i	0.993882	+	0.110447i	$0.0352282\pi$
$860$	−1908.96	−	3306.42i	−0.0756919	−	0.131102i
$861$	1466.47	−	2540.00i	0.0580455	−	0.100538i
$862$	−9524.00			−0.376321
$863$	−34553.8			−1.36295			−0.681474	−	0.731842i	$-0.738661\pi$
$863$	−34553.8			−1.36295			−0.681474	+	0.731842i	$0.738661\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−42049.1	+	72831.1i	−1.65284	+	2.86281i
$866$	−19949.8			−0.782820
$867$	−1445.07			−0.0566058
$868$	−5362.18	+	9287.58i	−0.209682	+	0.363181i
$869$	5608.43	+	9714.09i	0.218933	+	0.379204i
$870$	433.693	−	751.178i	0.0169006	−	0.0292728i
$871$	−7135.50	−	12359.1i	−0.277586	−	0.480793i
$872$	−1130.29	−	1957.71i	−0.0438948	−	0.0760281i
$873$	5449.64			0.211274
$874$	31234.6	+	363.606i	1.20884	+	0.0140723i
$875$	−73109.5			−2.82463
$876$	2100.74	+	3638.59i	0.0810244	+	0.140338i
$877$	−15294.1	−	26490.1i	−0.588877	−	1.01996i	−0.994380	−	0.105871i	$-0.966237\pi$
$877$	−15294.1	−	26490.1i	−0.588877	−	1.01996i	0.405503	−	0.914094i	$-0.367096\pi$
$878$	−8956.89	+	15513.8i	−0.344283	+	0.596315i
$879$	−14818.5	−	25666.4i	−0.568618	−	0.984876i
$880$	9302.83	−	16113.0i	0.356362	−	0.617236i
$881$	48445.7			1.85264			0.926321	−	0.376735i	$-0.122953\pi$
$881$	48445.7			1.85264			0.926321	+	0.376735i	$0.122953\pi$
$882$	−3254.84			−0.124259
$883$	−5135.18	+	8894.39i	−0.195711	+	0.338981i	−0.947133	−	0.320840i	$-0.896035\pi$
$883$	−5135.18	+	8894.39i	−0.195711	+	0.338981i	0.751423	+	0.659821i	$0.229368\pi$
$884$	4012.46	−	6949.79i	0.152663	−	0.264419i
$885$	−27881.2			−1.05900
$886$	−22736.2			−0.862121
$887$	−13815.2	+	23928.6i	−0.522962	+	0.905797i	0.476681	+	0.879077i	$0.341840\pi$
$887$	−13815.2	+	23928.6i	−0.522962	+	0.905797i	−0.999643	+	0.0267207i	$0.991494\pi$
$888$	3991.19	+	6912.95i	0.150829	+	0.261243i
$889$	−10933.1	+	18936.8i	−0.412470	+	0.714419i
$890$	16963.4	+	29381.5i	0.638893	+	1.10659i
$891$	2331.23	+	4037.82i	0.0876535	+	0.151820i
$892$	−8958.34			−0.336264
$893$	21458.5	−	36187.8i	0.804123	−	1.35608i
$894$	−10329.4			−0.386428
$895$	26643.8	+	46148.4i	0.995089	+	1.72354i
$896$	−1464.78	−	2537.08i	−0.0546149	−	0.0945957i
$897$	−7726.69	+	13383.0i	−0.287610	+	0.498156i
$898$	7630.20	+	13215.9i	0.283545	+	0.491114i
$899$	−419.137	+	725.966i	−0.0155495	+	0.0269325i
$900$	10192.3			0.377493
$901$	−36181.5			−1.33782
$902$	2458.78	−	4258.74i	0.0907633	−	0.157207i
$903$	−1622.02	+	2809.43i	−0.0597758	+	0.103535i
$904$	6734.88			0.247786
$905$	−15754.2			−0.578658
$906$	−6981.41	+	12092.2i	−0.256006	+	0.443416i
$907$	−20373.3	−	35287.5i	−0.745847	−	1.29184i	−0.949798	−	0.312863i	$-0.898712\pi$
$907$	−20373.3	−	35287.5i	−0.745847	−	1.29184i	0.203952	−	0.978981i	$-0.434621\pi$
$908$	12466.8	−	21593.2i	0.455645	−	0.789201i
$909$	−212.742	−	368.480i	−0.00776260	−	0.0134452i
$910$	−12629.4	−	21874.8i	−0.460068	−	0.796862i
$911$	13335.5			0.484989			0.242494	−	0.970153i	$-0.422034\pi$
$911$	13335.5			0.484989			0.242494	+	0.970153i	$0.422034\pi$
$912$	2027.60	−	3419.35i	0.0736189	−	0.124151i
$913$	16467.3			0.596921
$914$	−1500.40	−	2598.77i	−0.0542984	−	0.0940477i
$915$	13658.9	+	23657.9i	0.493497	+	0.854761i
$916$	4583.47	−	7938.81i	0.165330	−	0.286360i
$917$	−18757.3	−	32488.6i	−0.675486	−	1.16998i
$918$	1983.11	−	3434.85i	0.0712989	−	0.123493i
$919$	16604.5			0.596009			0.298005	−	0.954564i	$-0.403679\pi$
$919$	16604.5			0.596009			0.298005	+	0.954564i	$0.403679\pi$
$920$	30478.1			1.09221
$921$	−2015.56	+	3491.06i	−0.0721119	+	0.124902i
$922$	−14495.8	+	25107.4i	−0.517780	+	0.896822i
$923$	25441.5			0.907277
$924$	−15809.0			−0.562856
$925$	47082.8	−	81549.8i	1.67359	−	2.89875i
$926$	−12265.2	−	21244.0i	−0.435271	−	0.753911i
$927$	1938.38	−	3357.37i	0.0686781	−	0.118954i
$928$	−114.495	−	198.311i	−0.00405009	−	0.00701496i
$929$	8339.69	+	14444.8i	0.294528	+	0.510137i	0.974875	−	0.222753i	$-0.0715043\pi$
$929$	8339.69	+	14444.8i	0.294528	+	0.510137i	−0.680347	+	0.732890i	$0.738171\pi$
$930$	−14199.2			−0.500656
$931$	14974.7	+	174.323i	0.527149	+	0.00613662i
$932$	6396.29			0.224804
$933$	132.534	+	229.555i	0.00465055	+	0.00805499i
$934$	−1890.82	−	3275.00i	−0.0662416	−	0.114734i
$935$	−42705.0	+	73967.2i	−1.49369	+	2.58715i
$936$	983.332	+	1703.18i	0.0343389	+	0.0594767i
$937$	−3433.62	+	5947.21i	−0.119713	+	0.207350i	−0.919654	−	0.392729i	$-0.871531\pi$
$937$	−3433.62	+	5947.21i	−0.119713	+	0.207350i	0.799941	+	0.600079i	$0.204864\pi$
$938$	23915.5			0.832483
$939$	5677.38			0.197310
$940$	20525.0	−	35550.3i	0.712183	−	1.23354i
$941$	−24082.0	+	41711.2i	−0.834272	+	1.44500i	0.0603500	+	0.998177i	$0.480778\pi$
$941$	−24082.0	+	41711.2i	−0.834272	+	1.44500i	−0.894622	+	0.446824i	$0.852555\pi$
$942$	−5728.07			−0.198122
$943$	8055.52			0.278180
$944$	−3680.32	+	6374.51i	−0.126890	+	0.219780i
$945$	−6241.95	−	10811.4i	−0.214869	−	0.372163i
$946$	−2719.59	+	4710.47i	−0.0934689	+	0.161893i
$947$	22655.6	+	39240.7i	0.777412	+	1.34652i	0.933429	+	0.358762i	$0.116801\pi$
$947$	22655.6	+	39240.7i	0.777412	+	1.34652i	−0.156017	+	0.987754i	$0.549866\pi$
$948$	1169.21	+	2025.13i	0.0400571	+	0.0693809i
$949$	9563.54			0.327129
$950$	−46892.3	−	545.880i	−1.60146	−	0.0186428i
$951$	−25136.6			−0.857108
$952$	6724.13	+	11646.5i	0.228918	+	0.396498i
$953$	−3482.31	−	6031.53i	−0.118366	−	0.205016i	0.800754	−	0.598993i	$-0.204432\pi$
$953$	−3482.31	−	6031.53i	−0.118366	−	0.205016i	−0.919120	+	0.393977i	$0.871099\pi$
$954$	4433.49	−	7679.02i	0.150461	−	0.260605i
$955$	−40017.1	−	69311.6i	−1.35594	−	2.34856i
$956$	4886.74	−	8464.09i	0.165323	−	0.286347i
$957$	−1235.72			−0.0417399
$958$	23325.8			0.786661
$959$	−9700.87	+	16802.4i	−0.326650	+	0.565775i
$960$	1939.39	−	3359.12i	0.0652016	−	0.112933i
$961$	−16068.4			−0.539369
$962$	18169.8			0.608957
$963$	−4751.03	+	8229.03i	−0.158982	+	0.275365i
$964$	1992.98	+	3451.94i	0.0665867	+	0.115332i
$965$	3680.85	−	6375.42i	0.122788	−	0.212676i
$966$	−12948.5	−	22427.4i	−0.431273	−	0.746988i
$967$	−23149.7	−	40096.5i	−0.769851	−	1.33342i	−0.937644	−	0.347598i	$-0.886997\pi$
$967$	−23149.7	−	40096.5i	−0.769851	−	1.33342i	0.167793	−	0.985822i	$-0.446336\pi$
$968$	−15858.5			−0.526561
$969$	−9307.76	+	15696.7i	−0.308574	+	0.520381i
$970$	−24465.2			−0.809826
$971$	−22201.2	−	38453.5i	−0.733748	−	1.27089i	−0.955270	−	0.295734i	$-0.904436\pi$
$971$	−22201.2	−	38453.5i	−0.733748	−	1.27089i	0.221522	−	0.975155i	$-0.428897\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	13361.6	−	23142.9i	0.440239	−	0.762517i
$974$	13286.6	+	23013.1i	0.437096	+	0.757072i
$975$	11600.0	−	20091.9i	0.381024	−	0.659953i
$976$	7211.92			0.236524
$977$	36365.1			1.19081			0.595405	−	0.803426i	$-0.296992\pi$
$977$	36365.1			1.19081			0.595405	+	0.803426i	$0.296992\pi$
$978$	−5479.57	+	9490.90i	−0.179159	+	0.310312i
$979$	24166.9	−	41858.2i	0.788944	−	1.36649i
$980$	14612.0			0.476290
$981$	−2543.14			−0.0827689
$982$	4037.71	−	6993.52i	0.131210	−	0.227263i
$983$	−1841.12	−	3188.91i	−0.0597381	−	0.103469i	0.834610	−	0.550842i	$-0.185693\pi$
$983$	−1841.12	−	3188.91i	−0.0597381	−	0.103469i	−0.894348	+	0.447372i	$0.852360\pi$
$984$	512.590	−	887.832i	0.0166065	−	0.0287633i
$985$	−23326.4	−	40402.6i	−0.754561	−	1.30694i
$986$	525.594	+	910.355i	0.0169760	+	0.0294032i
$987$	−34879.7			−1.12486
$988$	−4432.84	−	7888.57i	−0.142740	−	0.254017i
$989$	−8909.99			−0.286472
$990$	−10465.7	−	18127.1i	−0.335981	−	0.581936i
$991$	2206.38	+	3821.57i	0.0707246	+	0.122499i	0.899219	−	0.437499i	$-0.144136\pi$
$991$	2206.38	+	3821.57i	0.0707246	+	0.122499i	−0.828494	+	0.559997i	$0.810802\pi$
$992$	−1874.30	+	3246.38i	−0.0599890	+	0.103904i
$993$	7250.25	+	12557.8i	0.231702	+	0.401319i
$994$	−21317.6	+	36923.1i	−0.680234	+	1.17820i
$995$	74273.5			2.36646
$996$	3432.99			0.109215
$997$	12413.0	−	21499.9i	0.394305	−	0.682956i	−0.598707	−	0.800968i	$-0.704319\pi$
$997$	12413.0	−	21499.9i	0.394305	−	0.682956i	0.993012	+	0.118012i	$0.0376520\pi$
$998$	3544.83	−	6139.83i	0.112435	−	0.194742i
$999$	8980.19			0.284405

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-10.1010 - 17.4954i) q^{5} +(-3.00000 + 5.19615i) q^{6} -22.8872 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-10.1010 - 17.4954i) q^{5} +(-3.00000 + 5.19615i) q^{6} -22.8872 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(20.2020 - 34.9909i) q^{10} -57.5614 q^{11} -12.0000 q^{12} +(-13.6574 + 23.6553i) q^{13} +(-22.8872 - 39.6418i) q^{14} +(30.3030 - 52.4863i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(36.7243 + 63.6083i) q^{17} -18.0000 q^{18} +(82.8135 + 0.964044i) q^{19} +80.8079 q^{20} +(-34.3308 - 59.4627i) q^{21} +(-57.5614 - 99.6992i) q^{22} +(94.2919 - 163.318i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-141.560 + 245.189i) q^{25} -54.6296 q^{26} -27.0000 q^{27} +(45.7744 - 79.2836i) q^{28} +(3.57797 - 6.19723i) q^{29} +121.212 q^{30} -117.144 q^{31} +(16.0000 - 27.7128i) q^{32} +(-86.3420 - 149.549i) q^{33} +(-73.4486 + 127.217i) q^{34} +(231.183 + 400.422i) q^{35} +(-18.0000 - 31.1769i) q^{36} -332.600 q^{37} +(81.1437 + 144.401i) q^{38} -81.9443 q^{39} +(80.8079 + 139.963i) q^{40} +(21.3579 + 36.9930i) q^{41} +(68.6616 - 118.925i) q^{42} +(-23.6234 - 40.9170i) q^{43} +(115.123 - 199.398i) q^{44} +181.818 q^{45} +377.168 q^{46} +(253.997 - 439.936i) q^{47} +(24.0000 - 41.5692i) q^{48} +180.824 q^{49} -566.240 q^{50} +(-110.173 + 190.825i) q^{51} +(-54.6296 - 94.6212i) q^{52} +(-246.305 + 426.612i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(581.427 + 1007.06i) q^{55} +183.098 q^{56} +(121.716 + 216.602i) q^{57} +14.3119 q^{58} +(-230.020 - 398.407i) q^{59} +(121.212 + 209.945i) q^{60} +(-225.372 + 390.356i) q^{61} +(-117.144 - 202.899i) q^{62} +(102.992 - 178.388i) q^{63} +64.0000 q^{64} +551.813 q^{65} +(172.684 - 299.098i) q^{66} +(-261.232 + 452.468i) q^{67} -293.794 q^{68} +565.751 q^{69} +(-462.367 + 800.843i) q^{70} +(-465.709 - 806.632i) q^{71} +(36.0000 - 62.3538i) q^{72} +(-175.062 - 303.216i) q^{73} +(-332.600 - 576.079i) q^{74} -849.360 q^{75} +(-168.966 + 284.946i) q^{76} +1317.42 q^{77} +(-81.9443 - 141.932i) q^{78} +(-97.4340 - 168.761i) q^{79} +(-161.616 + 279.927i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-42.7158 + 73.9860i) q^{82} -286.083 q^{83} +274.646 q^{84} +(741.903 - 1285.01i) q^{85} +(47.2469 - 81.8340i) q^{86} +21.4678 q^{87} +460.491 q^{88} +(-419.845 + 727.193i) q^{89} +(181.818 + 314.918i) q^{90} +(312.579 - 541.404i) q^{91} +(377.168 + 653.273i) q^{92} +(-175.716 - 304.348i) q^{93} +1015.99 q^{94} +(-819.632 - 1458.60i) q^{95} +96.0000 q^{96} +(-302.758 - 524.392i) q^{97} +(180.824 + 313.197i) q^{98} +(259.026 - 448.646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9	\( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9} + 4 q^{10} - 104 q^{11} - 72 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} - 48 q^{16} + 48 q^{17} - 108 q^{18} + 104 q^{19} + 16 q^{20} - 51 q^{21} - 104 q^{22} + 238 q^{23} - 72 q^{24} - 229 q^{25} - 300 q^{26} - 162 q^{27} + 68 q^{28} + 8 q^{29} + 24 q^{30} + 214 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} + 294 q^{35} - 108 q^{36} + 610 q^{37} - 430 q^{38} - 450 q^{39} + 16 q^{40} - 16 q^{41} + 102 q^{42} + 331 q^{43} + 208 q^{44} + 36 q^{45} + 952 q^{46} + 766 q^{47} + 144 q^{48} + 2284 q^{49} - 916 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} - 162 q^{54} + 1400 q^{55} + 272 q^{56} - 645 q^{57} + 32 q^{58} - 936 q^{59} + 24 q^{60} + 399 q^{61} + 214 q^{62} + 153 q^{63} + 384 q^{64} + 740 q^{65} + 312 q^{66} - 61 q^{67} - 384 q^{68} + 1428 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} - 91 q^{73} + 610 q^{74} - 1374 q^{75} - 1276 q^{76} - 72 q^{77} - 450 q^{78} + 321 q^{79} - 32 q^{80} - 243 q^{81} + 32 q^{82} - 4296 q^{83} + 408 q^{84} + 1680 q^{85} - 662 q^{86} + 48 q^{87} + 832 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} + 952 q^{92} + 321 q^{93} + 3064 q^{94} - 4198 q^{95} + 576 q^{96} - 1382 q^{97} + 2284 q^{98} + 468 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9 + 4 * q^10 - 104 * q^11 - 72 * q^12 - 75 * q^13 - 34 * q^14 + 6 * q^15 - 48 * q^16 + 48 * q^17 - 108 * q^18 + 104 * q^19 + 16 * q^20 - 51 * q^21 - 104 * q^22 + 238 * q^23 - 72 * q^24 - 229 * q^25 - 300 * q^26 - 162 * q^27 + 68 * q^28 + 8 * q^29 + 24 * q^30 + 214 * q^31 + 96 * q^32 - 156 * q^33 - 96 * q^34 + 294 * q^35 - 108 * q^36 + 610 * q^37 - 430 * q^38 - 450 * q^39 + 16 * q^40 - 16 * q^41 + 102 * q^42 + 331 * q^43 + 208 * q^44 + 36 * q^45 + 952 * q^46 + 766 * q^47 + 144 * q^48 + 2284 * q^49 - 916 * q^50 - 144 * q^51 - 300 * q^52 + 118 * q^53 - 162 * q^54 + 1400 * q^55 + 272 * q^56 - 645 * q^57 + 32 * q^58 - 936 * q^59 + 24 * q^60 + 399 * q^61 + 214 * q^62 + 153 * q^63 + 384 * q^64 + 740 * q^65 + 312 * q^66 - 61 * q^67 - 384 * q^68 + 1428 * q^69 - 588 * q^70 - 974 * q^71 + 216 * q^72 - 91 * q^73 + 610 * q^74 - 1374 * q^75 - 1276 * q^76 - 72 * q^77 - 450 * q^78 + 321 * q^79 - 32 * q^80 - 243 * q^81 + 32 * q^82 - 4296 * q^83 + 408 * q^84 + 1680 * q^85 - 662 * q^86 + 48 * q^87 + 832 * q^88 - 1116 * q^89 + 36 * q^90 - 1367 * q^91 + 952 * q^92 + 321 * q^93 + 3064 * q^94 - 4198 * q^95 + 576 * q^96 - 1382 * q^97 + 2284 * q^98 + 468 * q^99

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