LMFDB - Embedded newform 114.4.e.e.49.1

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			49.1
Root			$0.0702177 + 0.121621i$ of defining polynomial
Character	$\chi$	$=$	114.49
Dual form			114.4.e.e.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-10.1010 + 17.4954i) q^{5} +(-3.00000 - 5.19615i) q^{6} -22.8872 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	1.50000	−	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	−0.0804891	+	0.996755i	$0.525648\pi$
$5$	−10.1010	+	17.4954i	−0.903460	+	1.56484i	−0.822971	+	0.568083i	$0.807685\pi$
$6$	−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	0.682760	−	0.730643i	$-0.260779\pi$
$13$	−13.6574	−	23.6553i	−0.291375	−	0.504677i	−0.974135	+	0.225966i	$0.927446\pi$
$14$	−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	−0.475674	−	0.879622i	$-0.657796\pi$
$17$	36.7243	−	63.6083i	0.523938	−	0.907487i	0.999612	−	0.0278654i	$-0.00887099\pi$
$18$	−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	0.876797	+	0.480860i	$0.159675\pi$
$23$	94.2919	+	163.318i	0.854836	+	1.48062i	−0.0219618	+	0.999759i	$0.506991\pi$
$24$	−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	0.877253	−	0.480027i	$-0.159373\pi$
$29$	3.57797	+	6.19723i	0.0229108	+	0.0396826i	−0.854343	+	0.519710i	$0.826040\pi$
$30$	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	−0.822477	−	0.568798i	$-0.807409\pi$
$41$	21.3579	−	36.9930i	0.0813548	−	0.140911i	0.903832	+	0.427887i	$0.140742\pi$
$42$	68.6616	+	118.925i	0.252255	+	0.436919i
$43$	−23.6234	+	40.9170i	−0.0837800	+	0.145111i	−0.904871	−	0.425687i	$-0.860033\pi$
$43$	−23.6234	+	40.9170i	−0.0837800	+	0.145111i	0.821091	+	0.570798i	$0.193366\pi$
$44$	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	0.927018	+	0.375017i	$0.122363\pi$
$47$	253.997	+	439.936i	0.788284	+	1.36535i	−0.138734	+	0.990330i	$0.544303\pi$
$48$	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	−0.985795	−	0.167954i	$-0.946284\pi$
$53$	−246.305	−	426.612i	−0.638350	−	1.10565i	0.347445	−	0.937700i	$-0.387049\pi$
$54$	−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	0.492401	+	0.870369i	$0.336119\pi$
$59$	−230.020	+	398.407i	−0.507561	+	0.879121i	−0.999962	+	0.00875259i	$0.997214\pi$
$60$	121.212	−	209.945i	0.260806	−	0.451730i
$61$	−225.372	−	390.356i	−0.473049	−	0.819344i	0.526475	−	0.850190i	$-0.323513\pi$
$61$	−225.372	−	390.356i	−0.473049	−	0.819344i	−0.999524	+	0.0308459i	$0.990180\pi$
$62$	−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	0.523295	−	0.852152i	$-0.324703\pi$
$67$	−261.232	−	452.468i	−0.476337	−	0.825041i	−0.999632	+	0.0271110i	$0.991369\pi$
$68$	−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	0.154394	+	0.988009i	$0.450657\pi$
$71$	−465.709	+	806.632i	−0.778444	+	1.34830i	−0.932838	+	0.360296i	$0.882676\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	−175.062	+	303.216i	−0.280677	+	0.486147i	−0.971552	−	0.236828i	$-0.923892\pi$
$73$	−175.062	+	303.216i	−0.280677	+	0.486147i	0.690875	+	0.722974i	$0.257226\pi$
$74$	−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	−0.927028	−	0.374992i	$-0.877646\pi$
$79$	−97.4340	+	168.761i	−0.138762	+	0.240342i	0.788266	+	0.615334i	$0.210979\pi$
$80$	−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	−1.00000		4.52935e-5i	$-0.999986\pi$
$89$	−419.845	−	727.193i	−0.500039	−	0.866093i	0.499961	−	0.866048i	$-0.333348\pi$
$90$	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	−0.979842	−	0.199774i	$-0.935979\pi$
$97$	−302.758	+	524.392i	−0.316911	+	0.548906i	0.662931	+	0.748681i	$0.269312\pi$
$98$	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	0.854147	−	0.520032i	$-0.174080\pi$
$101$	−23.6380	−	40.9422i	−0.0232878	−	0.0403356i	−0.877434	+	0.479697i	$0.840747\pi$
$102$	−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	−0.797248	−	0.603651i	$-0.793712\pi$
$109$	141.286	−	244.714i	0.124153	−	0.215040i	0.921402	+	0.388612i	$0.127045\pi$
$110$	−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	0.983248	−	0.182275i	$-0.0583460\pi$
$127$	477.697	+	827.395i	0.333769	+	0.578106i	−0.649478	+	0.760380i	$0.725013\pi$
$128$	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	−0.451903	−	0.892067i	$-0.649255\pi$
$131$	819.554	−	1419.51i	0.546601	−	0.946741i	0.998504	−	0.0546739i	$-0.0174119\pi$
$132$	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	0.967386	−	0.253305i	$-0.0815177\pi$
$137$	423.856	+	734.140i	0.264324	+	0.457823i	−0.703062	+	0.711129i	$0.748184\pi$
$138$	565.751	−	979.910i	0.348985	−	0.604460i
$139$	−583.802	−	1011.17i	−0.356240	−	0.617026i	0.631089	−	0.775710i	$-0.282608\pi$
$139$	−583.802	−	1011.17i	−0.356240	−	0.617026i	−0.987329	+	0.158684i	$0.949275\pi$
$140$	−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	−0.526256	−	0.850326i	$-0.676405\pi$
$149$	860.783	−	1490.92i	0.473276	−	0.819738i	0.999532	+	0.0305883i	$0.00973807\pi$
$150$	−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	−0.718819	−	0.695197i	$-0.755317\pi$
$157$	477.339	−	826.776i	0.242649	−	0.420280i	0.961468	+	0.274917i	$0.0886505\pi$
$158$	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	0.644791	−	0.764359i	$-0.276944\pi$
$167$	−732.806	−	1269.26i	−0.339558	−	0.588132i	−0.984350	+	0.176227i	$0.943611\pi$
$168$	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	−0.107435	+	0.994212i	$0.534264\pi$
$173$	−2081.43	+	3605.15i	−0.914730	+	1.58436i	−0.807295	+	0.590147i	$0.799070\pi$
$174$	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	0.934913	−	0.354878i	$-0.115478\pi$
$181$	389.916	+	675.354i	0.160123	+	0.277341i	−0.774790	+	0.632219i	$0.782144\pi$
$182$	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	−0.830046	−	0.557695i	$-0.811686\pi$
$193$	182.202	−	315.584i	0.0679545	−	0.117701i	0.898001	+	0.439994i	$0.145019\pi$
$194$	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	−0.981936	−	0.189215i	$-0.939406\pi$
$199$	−1838.27	−	3183.98i	−0.654833	−	1.13420i	0.327103	−	0.944989i	$-0.393928\pi$
$200$	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	−0.954510	−	0.298178i	$-0.903621\pi$
$211$	−671.302	+	1162.73i	−0.219025	+	0.379363i	0.735485	+	0.677541i	$0.236954\pi$
$212$	−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	−0.647463	−	0.762097i	$-0.724170\pi$
$223$	1119.79	−	1939.54i	0.336264	−	0.582426i	0.983727	+	0.179671i	$0.0575033\pi$
$224$	−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	−0.956261	−	0.292516i	$-0.905508\pi$
$233$	−799.537	+	1384.84i	−0.224804	+	0.389372i	0.731456	+	0.681888i	$0.238841\pi$
$234$	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	0.924898	−	0.380215i	$-0.124150\pi$
$241$	498.245	+	862.986i	0.133173	+	0.230663i	−0.791725	+	0.610878i	$0.790817\pi$
$242$	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	0.814291	−	0.580457i	$-0.197126\pi$
$251$	−379.945	−	658.084i	−0.0955455	−	0.165490i	−0.909836	+	0.414968i	$0.863793\pi$
$252$	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	0.995563	+	0.0940922i	$0.0299948\pi$
$257$	2386.60	+	4133.71i	0.579268	+	1.00332i	−0.416296	+	0.909229i	$0.636672\pi$
$258$	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	0.489221	+	0.872160i	$0.337281\pi$
$263$	−2178.22	+	3772.78i	−0.510702	+	0.884562i	−0.999923	+	0.0124018i	$0.996052\pi$
$264$	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	−0.857942	−	0.513747i	$-0.828257\pi$
$269$	70.3573	−	121.862i	0.0159471	−	0.0276211i	0.873889	+	0.486126i	$0.161590\pi$
$270$	−545.454	−	944.753i	−0.122945	−	0.212948i
$271$	−761.530	+	1319.01i	−0.170700	+	0.295661i	−0.938665	−	0.344831i	$-0.887936\pi$
$271$	−761.530	+	1319.01i	−0.170700	+	0.295661i	0.767965	+	0.640492i	$0.221269\pi$
$272$	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	0.856833	−	0.515593i	$-0.172428\pi$
$281$	−85.2598	−	147.674i	−0.0181003	−	0.0313506i	−0.874934	+	0.484243i	$0.839095\pi$
$282$	1523.98	−	2639.62i	0.321815	−	0.557401i
$283$	−1088.15	+	1884.73i	−0.228565	+	0.395886i	−0.957383	−	0.288821i	$-0.906737\pi$
$283$	−1088.15	+	1884.73i	−0.228565	+	0.395886i	0.728818	+	0.684708i	$0.240070\pi$
$284$	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	−0.796793	−	0.604252i	$-0.793472\pi$
$307$	671.855	−	1163.69i	0.124902	−	0.216336i	0.921694	+	0.387917i	$0.126805\pi$
$308$	−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	0.938726	−	0.344664i	$-0.112007\pi$
$313$	946.230	+	1638.92i	0.170876	+	0.295965i	−0.767851	+	0.640629i	$0.778674\pi$
$314$	−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	−0.951456	−	0.307784i	$-0.900413\pi$
$317$	−4189.43	−	7256.31i	−0.742277	−	1.28566i	0.209179	−	0.977877i	$-0.432921\pi$
$318$	−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	−0.740190	−	0.672397i	$-0.765265\pi$
$337$	1312.89	−	2273.99i	0.212218	−	0.367573i	0.952408	+	0.304825i	$0.0985979\pi$
$338$	−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	0.367076	+	0.930191i	$0.380359\pi$
$347$	−4020.74	+	6964.13i	−0.622031	+	1.07739i	−0.989107	+	0.147199i	$0.952974\pi$
$348$	−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	−0.705832	−	0.708379i	$-0.749427\pi$
$359$	1772.34	−	3069.78i	0.260558	−	0.451300i	0.966390	+	0.257079i	$0.0827600\pi$
$360$	−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	0.854043	−	0.520202i	$-0.174143\pi$
$367$	−165.126	−	286.007i	−0.0234864	−	0.0406797i	−0.877530	+	0.479522i	$0.840810\pi$
$368$	−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	−0.999961	−	0.00882645i	$-0.997190\pi$
$383$	−3690.29	+	6391.77i	−0.492337	+	0.852752i	0.507624	+	0.861578i	$0.330524\pi$
$384$	−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	0.792032	−	0.610479i	$-0.209023\pi$
$389$	−1017.92	−	1763.08i	−0.132675	−	0.229799i	−0.924707	+	0.380680i	$0.875690\pi$
$390$	−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	0.0469563	+	0.998897i	$0.485048\pi$
$397$	−6657.13	+	11530.5i	−0.841592	+	1.45768i	−0.888548	+	0.458783i	$0.848285\pi$
$398$	−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	0.0818652	+	0.996643i	$0.473912\pi$
$401$	−6602.17	+	11435.3i	−0.822186	+	1.42407i	−0.904051	+	0.427424i	$0.859421\pi$
$402$	−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	0.770396	−	0.637566i	$-0.220059\pi$
$409$	−1380.93	−	2391.84i	−0.166950	−	0.289166i	−0.937346	+	0.348400i	$0.886725\pi$
$410$	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	−0.133391	+	0.991063i	$0.542587\pi$
$421$	−7990.18	+	13839.4i	−0.924982	+	1.60212i	−0.791590	+	0.611052i	$0.790747\pi$
$422$	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	0.701752	−	0.712421i	$-0.252402\pi$
$431$	−2381.00	−	4124.01i	−0.266099	−	0.460897i	−0.967851	+	0.251524i	$0.919068\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	−4987.45	−	8638.52i	−0.553537	−	0.958754i	−0.998016	−	0.0629648i	$-0.979944\pi$
$433$	−4987.45	−	8638.52i	−0.553537	−	0.958754i	0.444479	−	0.895789i	$-0.353389\pi$
$434$	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	−0.512997	−	0.858390i	$-0.671465\pi$
$439$	4478.44	−	7756.89i	0.486890	−	0.843317i	0.999886	+	0.0150731i	$0.00479810\pi$
$440$	−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	−0.991304	−	0.131589i	$-0.957992\pi$
$443$	−5684.06	−	9845.08i	−0.609612	−	1.05588i	0.381693	−	0.924289i	$-0.375341\pi$
$444$	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	−0.223667	−	0.974666i	$-0.571803\pi$
$461$	7247.90	−	12553.7i	0.732252	−	1.26830i	0.955919	−	0.293632i	$-0.0948640\pi$
$462$	−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	0.997805	+	0.0662235i	$0.0210950\pi$
$479$	5831.44	+	10100.4i	0.556254	+	0.963460i	−0.441551	+	0.897236i	$0.645572\pi$
$480$	−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	−0.943765	−	0.330617i	$-0.892743\pi$
$491$	−2018.86	+	3496.76i	−0.185559	+	0.321398i	0.758205	+	0.652016i	$0.226076\pi$
$492$	−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	−0.934511	−	0.355935i	$-0.884162\pi$
$499$	−1772.42	+	3069.91i	−0.159006	+	0.275407i	0.775504	+	0.631342i	$0.217496\pi$
$500$	−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	0.996113	+	0.0880839i	$0.0280743\pi$
$503$	6479.19	+	11222.3i	0.574339	+	0.994785i	−0.421774	+	0.906701i	$0.638592\pi$
$504$	−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	0.987729	−	0.156177i	$-0.0499169\pi$
$509$	4118.14	+	7132.83i	0.358612	+	0.621134i	−0.629117	+	0.777310i	$0.716584\pi$
$510$	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	0.946079	−	0.323936i	$-0.105006\pi$
$523$	2302.44	+	3987.95i	0.192502	+	0.333424i	−0.753577	+	0.657360i	$0.771673\pi$
$524$	−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	0.628925	−	0.777466i	$-0.283495\pi$
$541$	−4515.43	−	7820.96i	−0.358842	−	0.621533i	−0.987768	+	0.155933i	$0.950162\pi$
$542$	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	−0.999993	−	0.00372003i	$-0.998816\pi$
$547$	−6437.80	−	11150.6i	−0.503218	−	0.871599i	0.496775	−	0.867879i	$-0.334517\pi$
$548$	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	0.943926	−	0.330157i	$-0.107102\pi$
$557$	2445.60	+	4235.90i	0.186038	+	0.322228i	−0.757888	+	0.652385i	$0.773768\pi$
$558$	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	−0.999794	−	0.0203148i	$-0.993533\pi$
$587$	−6859.27	+	11880.6i	−0.482304	+	0.835374i	0.517490	+	0.855689i	$0.326866\pi$
$588$	−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	0.714909	−	0.699217i	$-0.246468\pi$
$593$	−3582.47	−	6205.02i	−0.248085	−	0.429696i	−0.962995	+	0.269521i	$0.913135\pi$
$594$	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	0.890593	−	0.454802i	$-0.150290\pi$
$599$	753.918	+	1305.82i	0.0514262	+	0.0890727i	−0.839166	+	0.543875i	$0.816957\pi$
$600$	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	−0.999961	−	0.00883041i	$-0.997189\pi$
$613$	−7472.22	+	12942.3i	−0.492333	+	0.852746i	0.507628	+	0.861576i	$0.330522\pi$
$614$	−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	0.917220	−	0.398381i	$-0.130428\pi$
$617$	1741.05	+	3015.59i	0.113601	+	0.196763i	−0.803618	+	0.595145i	$0.797095\pi$
$618$	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	0.802708	−	0.596373i	$-0.203392\pi$
$631$	−1824.72	−	3160.50i	−0.115120	−	0.199394i	−0.917828	+	0.396979i	$0.870059\pi$
$632$	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	−0.546558	−	0.837421i	$-0.684062\pi$
$641$	7334.60	−	12703.9i	0.451949	−	0.782799i	0.998507	+	0.0546226i	$0.0173956\pi$
$642$	−3167.35	−	5486.02i	−0.194713	−	0.337252i
$643$	−3504.05	+	6069.20i	−0.214909	+	0.372233i	−0.953244	−	0.302200i	$-0.902279\pi$
$643$	−3504.05	+	6069.20i	−0.214909	+	0.372233i	0.738335	+	0.674434i	$0.235612\pi$
$644$	−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	0.996376	+	0.0850593i	$0.0271080\pi$
$659$	9674.12	+	16756.1i	0.571851	+	0.990476i	−0.424524	+	0.905416i	$0.639559\pi$
$660$	−6977.12	+	12084.7i	−0.411491	+	0.712723i
$661$	−2564.00	−	4440.98i	−0.150875	−	0.261322i	0.780675	−	0.624938i	$-0.214876\pi$
$661$	−2564.00	−	4440.98i	−0.150875	−	0.261322i	−0.931549	+	0.363615i	$0.881542\pi$
$662$	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	−0.0567573	−	0.998388i	$-0.518076\pi$
$701$	15520.8	−	26882.8i	0.836251	−	1.44843i	0.893008	−	0.450041i	$-0.148591\pi$
$702$	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	0.988172	−	0.153349i	$-0.0490058\pi$
$709$	6820.49	+	11813.4i	0.361282	+	0.625759i	−0.626890	+	0.779108i	$0.715673\pi$
$710$	−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	0.249243	+	0.968441i	$0.419818\pi$
$719$	−13766.9	+	23845.0i	−0.714073	+	1.23681i	−0.963316	+	0.268370i	$0.913515\pi$
$720$	−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	0.467017	+	0.884248i	$0.345329\pi$
$727$	−10433.6	+	18071.6i	−0.532273	+	0.921924i	−0.999290	+	0.0376757i	$0.988005\pi$
$728$	−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	−0.605929	−	0.795518i	$-0.707199\pi$
$739$	7753.99	−	13430.3i	0.385975	−	0.668527i	0.991904	+	0.126991i	$0.0405319\pi$
$740$	−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	−0.681349	−	0.731959i	$-0.738606\pi$
$743$	5938.51	−	10285.8i	0.293221	−	0.507873i	0.974569	+	0.224086i	$0.0719397\pi$
$744$	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	−0.982655	−	0.185445i	$-0.940627\pi$
$751$	−13417.1	−	23239.1i	−0.651927	−	1.12917i	0.330727	−	0.943726i	$-0.392706\pi$
$752$	−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	0.170993	−	0.985272i	$-0.445303\pi$
$757$	19552.5	−	33865.9i	0.938767	−	1.62599i	0.767774	−	0.640720i	$-0.221364\pi$
$758$	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	−0.998719	−	0.0505917i	$-0.983889\pi$
$769$	−11583.2	−	20062.7i	−0.543173	−	0.940804i	0.455546	−	0.890212i	$-0.349444\pi$
$770$	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	−0.948222	−	0.317607i	$-0.897121\pi$
$773$	−16100.8	−	27887.4i	−0.749167	−	1.29760i	0.199055	−	0.979988i	$-0.436213\pi$
$774$	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	−0.952967	−	0.303073i	$-0.901987\pi$
$811$	−17066.6	−	29560.3i	−0.738953	−	1.27990i	0.214014	−	0.976831i	$-0.431346\pi$
$812$	−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	0.679968	−	0.733242i	$-0.261994\pi$
$821$	−6940.15	−	12020.7i	−0.295022	−	0.510992i	−0.974990	+	0.222249i	$0.928660\pi$
$822$	2543.13	−	4404.84i	0.107910	−	0.186906i
$823$	−6508.05	−	11272.3i	−0.275646	−	0.477432i	0.694652	−	0.719346i	$-0.255558\pi$
$823$	−6508.05	−	11272.3i	−0.275646	−	0.477432i	−0.970298	+	0.241913i	$0.922225\pi$
$824$	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	0.995699	−	0.0926423i	$-0.0295313\pi$
$827$	9932.04	+	17202.8i	0.417619	+	0.723338i	−0.578080	+	0.815980i	$0.696198\pi$
$828$	−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	−0.908667	−	0.417522i	$-0.862899\pi$
$839$	−2253.99	+	3904.03i	−0.0927491	+	0.160646i	0.815918	+	0.578168i	$0.196232\pi$
$840$	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	−0.354595	−	0.935020i	$-0.615381\pi$
$853$	15756.2	−	27290.6i	0.632454	−	1.09544i	0.987049	−	0.160422i	$-0.0512855\pi$
$854$	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	−0.795901	−	0.605426i	$-0.793003\pi$
$857$	3170.25	−	5491.04i	0.126364	−	0.218869i	0.922265	+	0.386558i	$0.126336\pi$
$858$	4716.83	−	8169.78i	0.187680	−	0.325072i
$859$	10103.0	+	17498.9i	0.401291	+	0.695057i	0.993882	−	0.110447i	$-0.0352282\pi$
$859$	10103.0	+	17498.9i	0.401291	+	0.695057i	−0.592591	+	0.805504i	$0.701895\pi$
$860$	−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	0.405503	+	0.914094i	$0.367096\pi$
$877$	−15294.1	+	26490.1i	−0.588877	+	1.01996i	−0.994380	+	0.105871i	$0.966237\pi$
$878$	−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	0.751423	−	0.659821i	$-0.229368\pi$
$883$	−5135.18	−	8894.39i	−0.195711	−	0.338981i	−0.947133	+	0.320840i	$0.896035\pi$
$884$	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	−0.999643	−	0.0267207i	$-0.991494\pi$
$887$	−13815.2	−	23928.6i	−0.522962	−	0.905797i	0.476681	−	0.879077i	$-0.341840\pi$
$888$	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	0.203952	+	0.978981i	$0.434621\pi$
$907$	−20373.3	+	35287.5i	−0.745847	+	1.29184i	−0.949798	+	0.312863i	$0.898712\pi$
$908$	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	−0.680347	−	0.732890i	$-0.738171\pi$
$929$	8339.69	−	14444.8i	0.294528	−	0.510137i	0.974875	+	0.222753i	$0.0715043\pi$
$930$	−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	0.799941	−	0.600079i	$-0.204864\pi$
$937$	−3433.62	−	5947.21i	−0.119713	−	0.207350i	−0.919654	+	0.392729i	$0.871531\pi$
$938$	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	−0.894622	−	0.446824i	$-0.852555\pi$
$941$	−24082.0	−	41711.2i	−0.834272	−	1.44500i	0.0603500	−	0.998177i	$-0.480778\pi$
$942$	−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	−0.156017	−	0.987754i	$-0.549866\pi$
$947$	22655.6	−	39240.7i	0.777412	−	1.34652i	0.933429	−	0.358762i	$-0.116801\pi$
$948$	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	−0.919120	−	0.393977i	$-0.871099\pi$
$953$	−3482.31	+	6031.53i	−0.118366	+	0.205016i	0.800754	+	0.598993i	$0.204432\pi$
$954$	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	0.167793	+	0.985822i	$0.446336\pi$
$967$	−23149.7	+	40096.5i	−0.769851	+	1.33342i	−0.937644	+	0.347598i	$0.886997\pi$
$968$	−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	0.221522	+	0.975155i	$0.428897\pi$
$971$	−22201.2	+	38453.5i	−0.733748	+	1.27089i	−0.955270	+	0.295734i	$0.904436\pi$
$972$	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	−0.894348	−	0.447372i	$-0.852360\pi$
$983$	−1841.12	+	3188.91i	−0.0597381	+	0.103469i	0.834610	+	0.550842i	$0.185693\pi$
$984$	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	−0.828494	−	0.559997i	$-0.810802\pi$
$991$	2206.38	−	3821.57i	0.0707246	−	0.122499i	0.899219	+	0.437499i	$0.144136\pi$
$992$	−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	0.993012	−	0.118012i	$-0.0376520\pi$
$997$	12413.0	+	21499.9i	0.394305	+	0.682956i	−0.598707	+	0.800968i	$0.704319\pi$
$998$	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.49.1	yes	6
3.2	odd	2		342.4.g.g.163.3		6
19.7	even	3	inner	114.4.e.e.7.1	✓	6
19.8	odd	6		2166.4.a.w.1.3		3
19.11	even	3		2166.4.a.s.1.3		3
57.26	odd	6		342.4.g.g.235.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.e.7.1	✓	6	19.7	even	3	inner
114.4.e.e.49.1	yes	6	1.1	even	1	trivial
342.4.g.g.163.3		6	3.2	odd	2
342.4.g.g.235.3		6	57.26	odd	6
2166.4.a.s.1.3		3	19.11	even	3
2166.4.a.w.1.3		3	19.8	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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