LMFDB - Embedded newform 177.5.b.a.119.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (of order $2$, degree $1$, 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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.4
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.75

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.42214i q^{2} +(2.94091 - 8.50594i) q^{3} -39.0882 q^{4} +22.5647i q^{5} +(-63.1323 - 21.8278i) q^{6} +11.4871 q^{7} +171.364i q^{8} +(-63.7021 - 50.0304i) q^{9} +O(q^{10})$	\(q-7.42214i q^{2} +(2.94091 - 8.50594i) q^{3} -39.0882 q^{4} +22.5647i q^{5} +(-63.1323 - 21.8278i) q^{6} +11.4871 q^{7} +171.364i q^{8} +(-63.7021 - 50.0304i) q^{9} +167.478 q^{10} +181.567i q^{11} +(-114.955 + 332.482i) q^{12} -136.108 q^{13} -85.2592i q^{14} +(191.934 + 66.3606i) q^{15} +646.474 q^{16} +36.3548i q^{17} +(-371.333 + 472.806i) q^{18} +224.708 q^{19} -882.012i q^{20} +(33.7827 - 97.7090i) q^{21} +1347.62 q^{22} +719.829i q^{23} +(1457.61 + 503.965i) q^{24} +115.836 q^{25} +1010.22i q^{26} +(-612.898 + 394.712i) q^{27} -449.012 q^{28} -1088.37i q^{29} +(492.538 - 1424.56i) q^{30} -737.969 q^{31} -2056.40i q^{32} +(1544.40 + 533.972i) q^{33} +269.830 q^{34} +259.204i q^{35} +(2490.00 + 1955.60i) q^{36} -2150.01 q^{37} -1667.82i q^{38} +(-400.282 + 1157.73i) q^{39} -3866.76 q^{40} +1610.62i q^{41} +(-725.210 - 250.740i) q^{42} -2334.50 q^{43} -7097.12i q^{44} +(1128.92 - 1437.42i) q^{45} +5342.67 q^{46} +1691.84i q^{47} +(1901.22 - 5498.87i) q^{48} -2269.05 q^{49} -859.748i q^{50} +(309.232 + 106.916i) q^{51} +5320.23 q^{52} +124.583i q^{53} +(2929.61 + 4549.01i) q^{54} -4097.00 q^{55} +1968.48i q^{56} +(660.847 - 1911.36i) q^{57} -8078.04 q^{58} +453.188i q^{59} +(-7502.34 - 2593.92i) q^{60} +3339.38 q^{61} +5477.31i q^{62} +(-731.756 - 574.707i) q^{63} -4919.33 q^{64} -3071.24i q^{65} +(3963.21 - 11462.7i) q^{66} +2181.86 q^{67} -1421.04i q^{68} +(6122.82 + 2116.95i) q^{69} +1923.85 q^{70} +6712.50i q^{71} +(8573.39 - 10916.2i) q^{72} +7126.64 q^{73} +15957.7i q^{74} +(340.662 - 985.290i) q^{75} -8783.44 q^{76} +2085.69i q^{77} +(8592.84 + 2970.95i) q^{78} +7863.06 q^{79} +14587.5i q^{80} +(1554.92 + 6374.08i) q^{81} +11954.3 q^{82} -11056.4i q^{83} +(-1320.50 + 3819.27i) q^{84} -820.334 q^{85} +17327.0i q^{86} +(-9257.62 - 3200.80i) q^{87} -31114.0 q^{88} +3376.87i q^{89} +(-10668.7 - 8379.00i) q^{90} -1563.50 q^{91} -28136.8i q^{92} +(-2170.30 + 6277.12i) q^{93} +12557.1 q^{94} +5070.47i q^{95} +(-17491.6 - 6047.69i) q^{96} -14133.9 q^{97} +16841.2i q^{98} +(9083.87 - 11566.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	7.42214i		−	1.85554i	−0.373159	−	0.927768i	$-0.621725\pi$
$2$		−	7.42214i		−	1.85554i	0.373159	−	0.927768i	$-0.378275\pi$
$3$	2.94091	−	8.50594i	0.326768	−	0.945105i
$3$	2.94091	−	8.50594i	0.326768	−	0.945105i
$4$	−39.0882			−2.44301
$5$			22.5647i			0.902587i	0.892376	+	0.451293i	$0.149037\pi$
$5$			22.5647i			0.902587i	−0.892376	+	0.451293i	$0.850963\pi$
$6$	−63.1323	−	21.8278i	−1.75367	−	0.606329i
$7$	11.4871			0.234432			0.117216	−	0.993106i	$-0.462603\pi$
$7$	11.4871			0.234432			0.117216	+	0.993106i	$0.462603\pi$
$8$			171.364i			2.67756i
$9$	−63.7021	−	50.0304i	−0.786446	−	0.617659i
$10$	167.478			1.67478
$11$			181.567i			1.50055i	0.661124	+	0.750277i	$0.270080\pi$
$11$			181.567i			1.50055i	−0.661124	+	0.750277i	$0.729920\pi$
$12$	−114.955	+	332.482i	−0.798297	+	2.30890i
$13$	−136.108			−0.805375			−0.402688	−	0.915337i	$-0.631924\pi$
$13$	−136.108			−0.805375			−0.402688	+	0.915337i	$0.631924\pi$
$14$		−	85.2592i		−	0.434996i
$15$	191.934	+	66.3606i	0.853039	+	0.294936i
$16$	646.474			2.52529
$17$			36.3548i			0.125795i	0.998020	+	0.0628976i	$0.0200341\pi$
$17$			36.3548i			0.125795i	−0.998020	+	0.0628976i	$0.979966\pi$
$18$	−371.333	+	472.806i	−1.14609	+	1.45928i
$19$	224.708			0.622461			0.311231	−	0.950334i	$-0.399259\pi$
$19$	224.708			0.622461			0.311231	+	0.950334i	$0.399259\pi$
$20$		−	882.012i		−	2.20503i
$21$	33.7827	−	97.7090i	0.0766046	−	0.221562i
$22$	1347.62			2.78433
$23$			719.829i			1.36073i	0.732871	+	0.680367i	$0.238180\pi$
$23$			719.829i			1.36073i	−0.732871	+	0.680367i	$0.761820\pi$
$24$	1457.61	+	503.965i	2.53057	+	0.874939i
$25$	115.836			0.185337
$26$			1010.22i			1.49440i
$27$	−612.898	+	394.712i	−0.840738	+	0.541443i
$28$	−449.012			−0.572719
$29$		−	1088.37i		−	1.29414i	−0.762431	−	0.647069i	$-0.775994\pi$
$29$		−	1088.37i		−	1.29414i	0.762431	−	0.647069i	$-0.224006\pi$
$30$	492.538	−	1424.56i	0.547264	−	1.58284i
$31$	−737.969			−0.767917			−0.383959	−	0.923350i	$-0.625440\pi$
$31$	−737.969			−0.767917			−0.383959	+	0.923350i	$0.625440\pi$
$32$		−	2056.40i		−	2.00821i
$33$	1544.40	+	533.972i	1.41818	+	0.490332i
$34$	269.830			0.233417
$35$			259.204i			0.211595i
$36$	2490.00	+	1955.60i	1.92130	+	1.50895i
$37$	−2150.01			−1.57050			−0.785248	−	0.619181i	$-0.787465\pi$
$37$	−2150.01			−1.57050			−0.785248	+	0.619181i	$0.787465\pi$
$38$		−	1667.82i		−	1.15500i
$39$	−400.282	+	1157.73i	−0.263170	+	0.761164i
$40$	−3866.76			−2.41673
$41$			1610.62i			0.958133i	0.877779	+	0.479067i	$0.159025\pi$
$41$			1610.62i			0.958133i	−0.877779	+	0.479067i	$0.840975\pi$
$42$	−725.210	−	250.740i	−0.411117	−	0.142143i
$43$	−2334.50			−1.26257			−0.631287	−	0.775549i	$-0.717473\pi$
$43$	−2334.50			−1.26257			−0.631287	+	0.775549i	$0.717473\pi$
$44$		−	7097.12i		−	3.66587i
$45$	1128.92	−	1437.42i	0.557491	−	0.709836i
$46$	5342.67			2.52489
$47$			1691.84i			0.765885i	0.923772	+	0.382943i	$0.125089\pi$
$47$			1691.84i			0.765885i	−0.923772	+	0.382943i	$0.874911\pi$
$48$	1901.22	−	5498.87i	0.825183	−	2.38666i
$49$	−2269.05			−0.945042
$50$		−	859.748i		−	0.343899i
$51$	309.232	+	106.916i	0.118890	+	0.0411058i
$52$	5320.23			1.96754
$53$			124.583i			0.0443513i	0.999754	+	0.0221757i	$0.00705931\pi$
$53$			124.583i			0.0443513i	−0.999754	+	0.0221757i	$0.992941\pi$
$54$	2929.61	+	4549.01i	1.00467	+	1.56002i
$55$	−4097.00			−1.35438
$56$			1968.48i			0.627704i
$57$	660.847	−	1911.36i	0.203400	−	0.588291i
$58$	−8078.04			−2.40132
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−7502.34	−	2593.92i	−2.08398	−	0.720532i
$61$	3339.38			0.897442			0.448721	−	0.893672i	$-0.351880\pi$
$61$	3339.38			0.897442			0.448721	+	0.893672i	$0.351880\pi$
$62$			5477.31i			1.42490i
$63$	−731.756	−	574.707i	−0.184368	−	0.144799i
$64$	−4919.33			−1.20101
$65$		−	3071.24i		−	0.726921i
$66$	3963.21	−	11462.7i	0.909829	−	2.63148i
$67$	2181.86			0.486045			0.243023	−	0.970021i	$-0.421861\pi$
$67$	2181.86			0.486045			0.243023	+	0.970021i	$0.421861\pi$
$68$		−	1421.04i		−	0.307319i
$69$	6122.82	+	2116.95i	1.28604	+	0.444644i
$70$	1923.85			0.392622
$71$			6712.50i			1.33158i	0.746139	+	0.665791i	$0.231906\pi$
$71$			6712.50i			1.33158i	−0.746139	+	0.665791i	$0.768094\pi$
$72$	8573.39	−	10916.2i	1.65382	−	2.10575i
$73$	7126.64			1.33733			0.668666	−	0.743563i	$-0.266866\pi$
$73$	7126.64			1.33733			0.668666	+	0.743563i	$0.266866\pi$
$74$			15957.7i			2.91411i
$75$	340.662	−	985.290i	0.0605621	−	0.175163i
$76$	−8783.44			−1.52068
$77$			2085.69i			0.351777i
$78$	8592.84	+	2970.95i	1.41237	+	0.488322i
$79$	7863.06			1.25990			0.629952	−	0.776634i	$-0.283074\pi$
$79$	7863.06			1.25990			0.629952	+	0.776634i	$0.283074\pi$
$80$			14587.5i			2.27929i
$81$	1554.92	+	6374.08i	0.236994	+	0.971511i
$82$	11954.3			1.77785
$83$		−	11056.4i		−	1.60493i	−0.596696	−	0.802467i	$-0.703520\pi$
$83$		−	11056.4i		−	1.60493i	0.596696	−	0.802467i	$-0.296480\pi$
$84$	−1320.50	+	3819.27i	−0.187146	+	0.541279i
$85$	−820.334			−0.113541
$86$			17327.0i			2.34275i
$87$	−9257.62	−	3200.80i	−1.22310	−	0.422883i
$88$	−31114.0			−4.01782
$89$			3376.87i			0.426318i	0.977018	+	0.213159i	$0.0683753\pi$
$89$			3376.87i			0.426318i	−0.977018	+	0.213159i	$0.931625\pi$
$90$	−10668.7	−	8379.00i	−1.31713	−	1.03444i
$91$	−1563.50			−0.188805
$92$		−	28136.8i		−	3.32429i
$93$	−2170.30	+	6277.12i	−0.250931	+	0.725762i
$94$	12557.1			1.42113
$95$			5070.47i			0.561825i
$96$	−17491.6	−	6047.69i	−1.89797	−	0.656217i
$97$	−14133.9			−1.50217			−0.751083	−	0.660208i	$-0.770468\pi$
$97$	−14133.9			−1.50217			−0.751083	+	0.660208i	$0.770468\pi$
$98$			16841.2i			1.75356i
$99$	9083.87	−	11566.2i	0.926831	−	1.18010i
$100$	−4527.80			−0.452780
$101$		−	2748.95i		−	0.269478i	−0.990881	−	0.134739i	$-0.956980\pi$
$101$		−	2748.95i		−	0.269478i	0.990881	−	0.134739i	$-0.0430197\pi$
$102$	793.546	−	2295.16i	0.0762732	−	0.220604i
$103$	−1332.88			−0.125636			−0.0628182	−	0.998025i	$-0.520009\pi$
$103$	−1332.88			−0.125636			−0.0628182	+	0.998025i	$0.520009\pi$
$104$		−	23324.0i		−	2.15644i
$105$	2204.77	+	762.294i	0.199979	+	0.0691424i
$106$	924.672			0.0822955
$107$			13219.8i			1.15467i	0.816509	+	0.577333i	$0.195906\pi$
$107$			13219.8i			1.15467i	−0.816509	+	0.577333i	$0.804094\pi$
$108$	23957.0	−	15428.6i	2.05393	−	1.32275i
$109$	−17531.8			−1.47561			−0.737807	−	0.675012i	$-0.764138\pi$
$109$	−17531.8			−1.47561			−0.737807	+	0.675012i	$0.764138\pi$
$110$			30408.5i			2.51310i
$111$	−6322.98	+	18287.9i	−0.513187	+	1.48428i
$112$	7426.14			0.592008
$113$			120.154i			0.00940986i	0.999989	+	0.00470493i	$0.00149763\pi$
$113$			120.154i			0.00940986i	−0.999989	+	0.00470493i	$0.998502\pi$
$114$	−14186.4	−	4904.90i	−1.09159	−	0.377416i
$115$	−16242.7			−1.22818
$116$			42542.4i			3.16159i
$117$	8670.39	+	6809.56i	0.633384	+	0.497447i
$118$	3363.62			0.241570
$119$			417.613i			0.0294904i
$120$	−11371.8	+	32890.5i	−0.789708	+	2.28406i
$121$	−18325.6			−1.25166
$122$		−	24785.4i		−	1.66524i
$123$	13699.9	+	4736.69i	0.905536	+	0.313087i
$124$	28845.8			1.87603
$125$			16716.7i			1.06987i
$126$	−4265.55	+	5431.19i	−0.268679	+	0.342101i
$127$	11909.4			0.738387			0.369193	−	0.929353i	$-0.379634\pi$
$127$	11909.4			0.738387			0.369193	+	0.929353i	$0.379634\pi$
$128$			3609.50i			0.220306i
$129$	−6865.55	+	19857.1i	−0.412568	+	1.19326i
$130$	−22795.2			−1.34883
$131$		−	13105.4i		−	0.763672i	−0.924230	−	0.381836i	$-0.875292\pi$
$131$		−	13105.4i		−	0.763672i	0.924230	−	0.381836i	$-0.124708\pi$
$132$	−60367.7	−	20872.0i	−3.46463	−	1.19789i
$133$	2581.26			0.145925
$134$		−	16194.0i		−	0.901874i
$135$	−8906.54	−	13829.8i	−0.488699	−	0.758839i
$136$	−6229.89			−0.336824
$137$			31042.7i			1.65393i	0.562250	+	0.826967i	$0.309936\pi$
$137$			31042.7i			1.65393i	−0.562250	+	0.826967i	$0.690064\pi$
$138$	15712.3	−	45444.4i	0.825052	−	2.38629i
$139$	680.779			0.0352352			0.0176176	−	0.999845i	$-0.494392\pi$
$139$	680.779			0.0352352			0.0176176	+	0.999845i	$0.494392\pi$
$140$		−	10131.8i		−	0.516929i
$141$	14390.7	+	4975.55i	0.723842	+	0.250266i
$142$	49821.1			2.47080
$143$		−	24712.8i		−	1.20851i
$144$	−41181.8	−	32343.3i	−1.98600	−	1.55977i
$145$	24558.7			1.16807
$146$		−	52894.9i		−	2.48147i
$147$	−6673.05	+	19300.4i	−0.308809	+	0.893163i
$148$	84039.9			3.83674
$149$		−	15407.1i		−	0.693984i	−0.937868	−	0.346992i	$-0.887203\pi$
$149$		−	15407.1i		−	0.693984i	0.937868	−	0.346992i	$-0.112797\pi$
$150$	−7312.96	−	2528.44i	−0.325021	−	0.112375i
$151$	−38409.0			−1.68453			−0.842265	−	0.539063i	$-0.818778\pi$
$151$	−38409.0			−1.68453			−0.842265	+	0.539063i	$0.818778\pi$
$152$			38506.9i			1.66667i
$153$	1818.84	−	2315.88i	0.0776985	−	0.0989311i
$154$	15480.3			0.652735
$155$		−	16652.0i		−	0.693112i
$156$	15646.3	−	45253.6i	0.642928	−	1.85953i
$157$	2444.86			0.0991869			0.0495935	−	0.998769i	$-0.484207\pi$
$157$	2444.86			0.0991869			0.0495935	+	0.998769i	$0.484207\pi$
$158$		−	58360.8i		−	2.33780i
$159$	1059.69	+	366.387i	0.0419167	+	0.0144926i
$160$	46402.1			1.81258
$161$			8268.78i			0.318999i
$162$	47309.3	−	11540.8i	1.80267	−	0.439751i
$163$	6820.63			0.256714			0.128357	−	0.991728i	$-0.459030\pi$
$163$	6820.63			0.256714			0.128357	+	0.991728i	$0.459030\pi$
$164$		−	62956.2i		−	2.34073i
$165$	−12048.9	+	34848.9i	−0.442568	+	1.28003i
$166$	−82062.1			−2.97801
$167$		−	39521.9i		−	1.41712i	−0.705653	−	0.708558i	$-0.749346\pi$
$167$		−	39521.9i		−	1.41712i	0.705653	−	0.708558i	$-0.250654\pi$
$168$	16743.8	+	5789.12i	0.593246	+	0.205113i
$169$	−10035.5			−0.351371
$170$			6088.64i			0.210679i
$171$	−14314.4	−	11242.3i	−0.489532	−	0.384469i
$172$	91251.3			3.08448
$173$			12144.2i			0.405768i	0.979203	+	0.202884i	$0.0650314\pi$
$173$			12144.2i			0.405768i	−0.979203	+	0.202884i	$0.934969\pi$
$174$	−23756.8	+	68711.3i	−0.784673	+	2.26950i
$175$	1330.62			0.0434488
$176$			117378.i			3.78933i
$177$	3854.79	+	1332.78i	0.123042	+	0.0425415i
$178$	25063.6			0.791048
$179$			30884.1i			0.963892i	0.876201	+	0.481946i	$0.160070\pi$
$179$			30884.1i			0.963892i	−0.876201	+	0.481946i	$0.839930\pi$
$180$	−44127.4	+	56186.0i	−1.36196	+	1.73414i
$181$	11872.7			0.362405			0.181202	−	0.983446i	$-0.442001\pi$
$181$	11872.7			0.362405			0.181202	+	0.983446i	$0.442001\pi$
$182$			11604.5i			0.350335i
$183$	9820.82	−	28404.6i	0.293255	−	0.848177i
$184$	−123352.			−3.64344
$185$		−	48514.3i		−	1.41751i
$186$	46589.7	+	16108.3i	1.34668	+	0.465610i
$187$	−6600.83			−0.188762
$188$		−	66130.9i		−	1.87107i
$189$	−7040.45	+	4534.11i	−0.197095	+	0.126931i
$190$	37633.8			1.04249
$191$		−	33931.1i		−	0.930103i	−0.885284	−	0.465052i	$-0.846036\pi$
$191$		−	33931.1i		−	0.930103i	0.885284	−	0.465052i	$-0.153964\pi$
$192$	−14467.3	+	41843.5i	−0.392450	+	1.13508i
$193$	−4191.30			−0.112521			−0.0562606	−	0.998416i	$-0.517918\pi$
$193$	−4191.30			−0.112521			−0.0562606	+	0.998416i	$0.517918\pi$
$194$			104904.i			2.78732i
$195$	−26123.8	−	9032.24i	−0.687017	−	0.237534i
$196$	88692.8			2.30875
$197$			42251.1i			1.08869i	0.838860	+	0.544347i	$0.183223\pi$
$197$			42251.1i			1.08869i	−0.838860	+	0.544347i	$0.816777\pi$
$198$	−85846.0	−	67421.8i	−2.18973	−	1.71977i
$199$	−51870.1			−1.30982			−0.654909	−	0.755708i	$-0.727293\pi$
$199$	−51870.1			−1.30982			−0.654909	+	0.755708i	$0.727293\pi$
$200$			19850.0i			0.496250i
$201$	6416.64	−	18558.8i	0.158824	−	0.459364i
$202$	−20403.1			−0.500027
$203$		−	12502.3i		−	0.303387i
$204$	−12087.3	−	4179.16i	−0.290449	−	0.100422i
$205$	−36343.2			−0.864798
$206$			9892.79i			0.233123i
$207$	36013.3	−	45854.6i	0.840470	−	1.07014i
$208$	−87990.5			−2.03381
$209$			40799.7i			0.934037i
$210$	5657.86	−	16364.1i	0.128296	−	0.371069i
$211$	−79865.5			−1.79388			−0.896942	−	0.442147i	$-0.854217\pi$
$211$	−79865.5			−1.79388			−0.896942	+	0.442147i	$0.854217\pi$
$212$		−	4869.72i		−	0.108351i
$213$	57096.2	+	19740.9i	1.25848	+	0.435118i
$214$	98119.0			2.14252
$215$		−	52677.2i		−	1.13958i
$216$	−67639.2	−	105028.i	−1.44974	−	2.25112i
$217$	−8477.16			−0.180024
$218$			130123.i			2.73805i
$219$	20958.8	−	60618.8i	0.436997	−	1.26392i
$220$	160144.			3.30877
$221$		−	4948.19i		−	0.101312i
$222$	135735.	+	46930.0i	2.75414	+	0.952237i
$223$	70159.9			1.41085			0.705423	−	0.708787i	$-0.250757\pi$
$223$	70159.9			1.41085			0.705423	+	0.708787i	$0.250757\pi$
$224$		−	23622.2i		−	0.470787i
$225$	−7378.97	−	5795.30i	−0.145757	−	0.114475i
$226$	891.803			0.0174603
$227$			46725.3i			0.906776i	0.891313	+	0.453388i	$0.149785\pi$
$227$			46725.3i			0.906776i	−0.891313	+	0.453388i	$0.850215\pi$
$228$	−25831.3	+	74711.5i	−0.496909	+	1.43720i
$229$	22705.6			0.432975			0.216487	−	0.976285i	$-0.430540\pi$
$229$	22705.6			0.432975			0.216487	+	0.976285i	$0.430540\pi$
$230$			120556.i			2.27893i
$231$	17740.7	+	6133.82i	0.332466	+	0.114949i
$232$	186507.			3.46513
$233$			12368.3i			0.227823i	0.993491	+	0.113911i	$0.0363380\pi$
$233$			12368.3i			0.227823i	−0.993491	+	0.113911i	$0.963662\pi$
$234$	50541.5	−	64352.9i	0.923031	−	1.17527i
$235$	−38175.8			−0.691278
$236$		−	17714.3i		−	0.318053i
$237$	23124.5	−	66882.8i	0.411696	−	1.19074i
$238$	3099.58			0.0547204
$239$		−	41816.7i		−	0.732071i	−0.930601	−	0.366036i	$-0.880715\pi$
$239$		−	41816.7i		−	0.732071i	0.930601	−	0.366036i	$-0.119285\pi$
$240$	124080.	+	42900.4i	2.15417	+	0.744799i
$241$	−43392.7			−0.747107			−0.373554	−	0.927609i	$-0.621861\pi$
$241$	−43392.7			−0.747107			−0.373554	+	0.927609i	$0.621861\pi$
$242$			136015.i			2.32250i
$243$	58790.5	+	5519.54i	0.995622	+	0.0934738i
$244$	−130530.			−2.19246
$245$		−	51200.3i		−	0.852982i
$246$	35156.4	−	101682.i	0.580944	−	1.68025i
$247$	−30584.7			−0.501315
$248$		−	126461.i		−	2.05614i
$249$	−94045.0	−	32515.8i	−1.51683	−	0.524441i
$250$	124074.			1.98518
$251$			107367.i			1.70421i	0.523372	+	0.852104i	$0.324674\pi$
$251$			107367.i			1.70421i	−0.523372	+	0.852104i	$0.675326\pi$
$252$	28603.0	+	22464.2i	0.450412	+	0.353745i
$253$	−130697.			−2.04186
$254$		−	88393.5i		−	1.37010i
$255$	−2412.53	+	6977.72i	−0.0371015	+	0.107308i
$256$	−51919.1			−0.792222
$257$		−	121344.i		−	1.83719i	−0.395202	−	0.918594i	$-0.629326\pi$
$257$		−	121344.i		−	1.83719i	0.395202	−	0.918594i	$-0.370674\pi$
$258$	147382.	+	50957.1i	2.21414	+	0.765535i
$259$	−24697.5			−0.368174
$260$			120049.i			1.77588i
$261$	−54451.6	+	69331.5i	−0.799337	+	1.01777i
$262$	−97269.9			−1.41702
$263$		−	82089.6i		−	1.18680i	−0.804908	−	0.593399i	$-0.797786\pi$
$263$		−	82089.6i		−	1.18680i	0.804908	−	0.593399i	$-0.202214\pi$
$264$	−91503.4	+	264654.i	−1.31289	+	3.79726i
$265$	−2811.17			−0.0400309
$266$		−	19158.5i		−	0.270768i
$267$	28723.4	+	9931.05i	0.402915	+	0.139307i
$268$	−85284.8			−1.18741
$269$		−	21537.5i		−	0.297640i	−0.988864	−	0.148820i	$-0.952452\pi$
$269$		−	21537.5i		−	0.297640i	0.988864	−	0.148820i	$-0.0475475\pi$
$270$	−102647.	+	66105.6i	−1.40805	+	0.906798i
$271$	−100382.			−1.36684			−0.683421	−	0.730024i	$-0.739509\pi$
$271$	−100382.			−1.36684			−0.683421	+	0.730024i	$0.739509\pi$
$272$			23502.4i			0.317669i
$273$	−4598.10	+	13299.0i	−0.0616955	+	0.178441i
$274$	230403.			3.06893
$275$			21031.9i			0.278108i
$276$	−239330.	−	82747.7i	−3.14180	−	1.08627i
$277$	34277.3			0.446732			0.223366	−	0.974735i	$-0.428296\pi$
$277$	34277.3			0.446732			0.223366	+	0.974735i	$0.428296\pi$
$278$		−	5052.84i		−	0.0653801i
$279$	47010.2	+	36920.9i	0.603926	+	0.474311i
$280$	−44418.1			−0.566557
$281$			9887.03i			0.125214i	0.998038	+	0.0626070i	$0.0199415\pi$
$281$			9887.03i			0.125214i	−0.998038	+	0.0626070i	$0.980059\pi$
$282$	36929.2	−	106810.i	0.464378	−	1.34311i
$283$	−10379.8			−0.129603			−0.0648015	−	0.997898i	$-0.520641\pi$
$283$	−10379.8			−0.129603			−0.0648015	+	0.997898i	$0.520641\pi$
$284$		−	262379.i		−	3.25307i
$285$	43129.2	+	14911.8i	0.530984	+	0.183586i
$286$	−183422.			−2.24243
$287$			18501.5i			0.224617i
$288$	−102883.	+	130997.i	−1.24039	+	1.57935i
$289$	82199.3			0.984176
$290$		−	182278.i		−	2.16740i
$291$	−41566.4	+	120222.i	−0.490859	+	1.41970i
$292$	−278567.			−3.26712
$293$			47375.0i			0.551841i	0.961181	+	0.275920i	$0.0889826\pi$
$293$			47375.0i			0.551841i	−0.961181	+	0.275920i	$0.911017\pi$
$294$	143250.	+	49528.3i	1.65730	+	0.573006i
$295$	−10226.0			−0.117507
$296$		−	368433.i		−	4.20509i
$297$	−71666.6	−	111282.i	−0.812464	−	1.26157i
$298$	−114354.			−1.28771
$299$		−	97974.7i		−	1.09590i
$300$	−13315.8	+	38513.2i	−0.147954	+	0.427924i
$301$	−26816.7			−0.295987
$302$			285077.i			3.12571i
$303$	−23382.4	−	8084.41i	−0.254685	−	0.0880568i
$304$	145268.			1.57189
$305$			75352.1i			0.810019i
$306$	−17188.8	−	13499.7i	−0.183570	−	0.144172i
$307$	182834.			1.93990			0.969951	−	0.243302i	$-0.0782307\pi$
$307$	182834.			1.93990			0.969951	+	0.243302i	$0.0782307\pi$
$308$		−	81525.7i		−	0.859396i
$309$	−3919.87	+	11337.4i	−0.0410539	+	0.118740i
$310$	−123594.			−1.28609
$311$			87920.5i			0.909011i	0.890744	+	0.454506i	$0.150184\pi$
$311$			87920.5i			0.909011i	−0.890744	+	0.454506i	$0.849816\pi$
$312$	−198393.	−	68593.8i	−2.03806	−	0.704654i
$313$	−137873.			−1.40731			−0.703655	−	0.710542i	$-0.748450\pi$
$313$	−137873.			−1.40731			−0.703655	+	0.710542i	$0.748450\pi$
$314$		−	18146.1i		−	0.184045i
$315$	12968.1	−	16511.8i	0.130694	−	0.166408i
$316$	−307353.			−3.07796
$317$		−	121818.i		−	1.21225i	−0.795368	−	0.606126i	$-0.792723\pi$
$317$		−	121818.i		−	1.21225i	0.795368	−	0.606126i	$-0.207277\pi$
$318$	2719.37	−	7865.20i	0.0268915	−	0.0777778i
$319$	197612.			1.94193
$320$		−	111003.i		−	1.08401i
$321$	112447.	+	38878.1i	1.09128	+	0.377307i
$322$	61372.0			0.591914
$323$			8169.23i			0.0783026i
$324$	−60779.0	−	249151.i	−0.578980	−	2.37341i
$325$	−15766.2			−0.149266
$326$		−	50623.7i		−	0.476342i
$327$	−51559.3	+	149124.i	−0.482183	+	1.39461i
$328$	−276002.			−2.56546
$329$			19434.4i			0.179548i
$330$	258653.	+	89428.6i	2.37514	+	0.821200i
$331$	165646.			1.51190			0.755952	−	0.654627i	$-0.227174\pi$
$331$	165646.			1.51190			0.755952	+	0.654627i	$0.227174\pi$
$332$			432174.i			3.92087i
$333$	136960.	+	107566.i	1.23511	+	0.970031i
$334$	−293337.			−2.62951
$335$			49232.9i			0.438698i
$336$	21839.6	−	63166.4i	0.193449	−	0.559509i
$337$	142493.			1.25468			0.627340	−	0.778746i	$-0.284144\pi$
$337$	142493.			1.25468			0.627340	+	0.778746i	$0.284144\pi$
$338$			74484.9i			0.651981i
$339$	1022.03	+	353.363i	0.00889330	+	0.00307484i
$340$	32065.4			0.277382
$341$		−	133991.i		−	1.15230i
$342$	−83441.6	+	106244.i	−0.713395	+	0.908344i
$343$	−53645.5			−0.455979
$344$		−	400048.i		−	3.38061i
$345$	−47768.3	+	138159.i	−0.401330	+	1.16076i
$346$	90136.2			0.752917
$347$		−	230828.i		−	1.91703i	−0.285044	−	0.958514i	$-0.592008\pi$
$347$		−	230828.i		−	1.91703i	0.285044	−	0.958514i	$-0.407992\pi$
$348$	361863.	+	125113.i	2.98804	+	1.03311i
$349$	37673.0			0.309299			0.154650	−	0.987969i	$-0.450575\pi$
$349$	37673.0			0.309299			0.154650	+	0.987969i	$0.450575\pi$
$350$		−	9876.05i		−	0.0806208i
$351$	83420.5	−	53723.6i	0.677109	−	0.436065i
$352$	373375.			3.01342
$353$		−	109796.i		−	0.881124i	−0.897722	−	0.440562i	$-0.854779\pi$
$353$		−	109796.i		−	0.881124i	0.897722	−	0.440562i	$-0.145221\pi$
$354$	9892.10	−	28610.8i	0.0789373	−	0.228309i
$355$	−151465.			−1.20187
$356$		−	131996.i		−	1.04150i
$357$	3552.19	+	1228.16i	0.0278715	+	0.00963649i
$358$	229226.			1.78854
$359$		−	108379.i		−	0.840920i	−0.907311	−	0.420460i	$-0.861869\pi$
$359$		−	108379.i		−	0.840920i	0.907311	−	0.420460i	$-0.138131\pi$
$360$	246321.	+	193456.i	1.90063	+	1.49271i
$361$	−79827.1			−0.612542
$362$		−	88121.2i		−	0.672455i
$363$	−53893.9	+	155876.i	−0.409003	+	1.18295i
$364$	61114.2			0.461254
$365$			160810.i			1.20706i
$366$	−210823.	−	72891.5i	−1.57382	−	0.544145i
$367$	−189422.			−1.40637			−0.703185	−	0.711007i	$-0.748239\pi$
$367$	−189422.			−1.40637			−0.703185	+	0.711007i	$0.748239\pi$
$368$			465350.i			3.43625i
$369$	80580.0	−	102600.i	0.591800	−	0.753520i
$370$	−360080.			−2.63024
$371$			1431.10i			0.0103974i
$372$	84833.0	−	245361.i	0.613026	−	1.77305i
$373$	−4743.01			−0.0340907			−0.0170454	−	0.999855i	$-0.505426\pi$
$373$	−4743.01			−0.0340907			−0.0170454	+	0.999855i	$0.505426\pi$
$374$			48992.3i			0.350255i
$375$	142191.	+	49162.3i	1.01114	+	0.349599i
$376$	−289920.			−2.05070
$377$			148136.i			1.04227i
$378$	33652.8	+	52255.2i	0.235525	+	0.365718i
$379$	228656.			1.59186			0.795930	−	0.605389i	$-0.206982\pi$
$379$	228656.			1.59186			0.795930	+	0.605389i	$0.206982\pi$
$380$		−	198196.i		−	1.37255i
$381$	35024.6	−	101301.i	0.241281	−	0.697853i
$382$	−251841.			−1.72584
$383$			204491.i			1.39405i	0.717048	+	0.697023i	$0.245493\pi$
$383$			204491.i			1.39405i	−0.717048	+	0.697023i	$0.754507\pi$
$384$	30702.2	+	10615.2i	0.208212	+	0.0719889i
$385$	−47062.9			−0.317510
$386$			31108.4i			0.208787i
$387$	148713.	+	116796.i	0.992946	+	0.779840i
$388$	552467.			3.66981
$389$			129979.i			0.858964i	0.903075	+	0.429482i	$0.141304\pi$
$389$			129979.i			0.858964i	−0.903075	+	0.429482i	$0.858696\pi$
$390$	−67038.5	+	193895.i	−0.440753	+	1.27478i
$391$	−26169.2			−0.171174
$392$		−	388832.i		−	2.53040i
$393$	−111474.	−	38541.7i	−0.721750	−	0.249543i
$394$	313594.			2.02011
$395$			177427.i			1.13717i
$396$	−355072.	+	452102.i	−2.26426	+	2.88301i
$397$	173033.			1.09786			0.548930	−	0.835869i	$-0.315035\pi$
$397$	173033.			1.09786			0.548930	+	0.835869i	$0.315035\pi$
$398$			384987.i			2.43041i
$399$	7591.25	−	21956.0i	0.0476834	−	0.137914i
$400$	74884.7			0.468029
$401$			97409.5i			0.605777i	0.953026	+	0.302888i	$0.0979510\pi$
$401$			97409.5i			0.605777i	−0.953026	+	0.302888i	$0.902049\pi$
$402$	−137746.	−	47625.2i	−0.852365	−	0.294703i
$403$	100444.			0.618462
$404$			107451.i			0.658339i
$405$	−143829.	+	35086.3i	−0.876873	+	0.213908i
$406$	−92793.6			−0.562945
$407$		−	390371.i		−	2.35661i
$408$	−18321.5	+	52991.1i	−0.110063	+	0.318334i
$409$	132708.			0.793326			0.396663	−	0.917964i	$-0.370168\pi$
$409$	132708.			0.793326			0.396663	+	0.917964i	$0.370168\pi$
$410$			269744.i			1.60466i
$411$	264047.	+	91293.7i	1.56314	+	0.540452i
$412$	52099.7			0.306931
$413$			5205.83i			0.0305204i
$414$	−340339.	−	267296.i	−1.98569	−	1.55952i
$415$	249484.			1.44859
$416$			279894.i			1.61736i
$417$	2002.11	−	5790.67i	0.0115137	−	0.0333010i
$418$	302821.			1.73314
$419$			147512.i			0.840233i	0.907470	+	0.420117i	$0.138011\pi$
$419$			147512.i			0.840233i	−0.907470	+	0.420117i	$0.861989\pi$
$420$	−86180.5	−	29796.7i	−0.488552	−	0.168915i
$421$	−51683.0			−0.291598			−0.145799	−	0.989314i	$-0.546575\pi$
$421$	−51683.0			−0.291598			−0.145799	+	0.989314i	$0.546575\pi$
$422$			592773.i			3.32862i
$423$	84643.4	−	107774.i	0.473056	−	0.602327i
$424$	−21349.0			−0.118753
$425$			4211.18i			0.0233145i
$426$	146519.	−	423776.i	0.807376	−	2.33516i
$427$	38360.0			0.210389
$428$		−	516736.i		−	2.82086i
$429$	−210206.	−	72678.1i	−1.14217	−	0.394902i
$430$	−390978.			−2.11454
$431$			116826.i			0.628906i	0.949273	+	0.314453i	$0.101821\pi$
$431$			116826.i			0.628906i	−0.949273	+	0.314453i	$0.898179\pi$
$432$	−396222.	+	255171.i	−2.12311	+	1.36730i
$433$	−182862.			−0.975321			−0.487661	−	0.873033i	$-0.662150\pi$
$433$	−182862.			−0.975321			−0.487661	+	0.873033i	$0.662150\pi$
$434$			62918.6i			0.334041i
$435$	72225.0	−	208895.i	0.381688	−	1.10395i
$436$	685284.			3.60494
$437$			161752.i			0.847004i
$438$	−449921.	−	155559.i	−2.34525	−	0.810863i
$439$	−47853.4			−0.248304			−0.124152	−	0.992263i	$-0.539621\pi$
$439$	−47853.4			−0.248304			−0.124152	+	0.992263i	$0.539621\pi$
$440$		−	702077.i		−	3.62643i
$441$	144543.	+	113521.i	0.743224	+	0.583714i
$442$	−36726.2			−0.187989
$443$			314613.i			1.60313i	0.597906	+	0.801566i	$0.295999\pi$
$443$			314613.i			1.60313i	−0.597906	+	0.801566i	$0.704001\pi$
$444$	247154.	−	714839.i	1.25372	−	3.62612i
$445$	−76197.9			−0.384789
$446$		−	520737.i		−	2.61787i
$447$	−131052.	−	45311.0i	−0.655887	−	0.226771i
$448$	−56509.1			−0.281554
$449$			324728.i			1.61075i	0.592768	+	0.805374i	$0.298035\pi$
$449$			324728.i			1.61075i	−0.592768	+	0.805374i	$0.701965\pi$
$450$	−43013.5	+	54767.7i	−0.212412	+	0.270458i
$451$	−292436.			−1.43773
$452$		−	4696.62i		−	0.0229884i
$453$	−112957.	+	326705.i	−0.550450	+	1.59206i
$454$	346801.			1.68255
$455$		−	35279.8i		−	0.170413i
$456$	327537.	+	113245.i	1.57518	+	0.544615i
$457$	228122.			1.09228			0.546141	−	0.837693i	$-0.316096\pi$
$457$	228122.			1.09228			0.546141	+	0.837693i	$0.316096\pi$
$458$		−	168524.i		−	0.803400i
$459$	−14349.7	−	22281.8i	−0.0681109	−	0.105761i
$460$	634897.			3.00046
$461$		−	260465.i		−	1.22560i	−0.790238	−	0.612799i	$-0.790043\pi$
$461$		−	260465.i		−	1.22560i	0.790238	−	0.612799i	$-0.209957\pi$
$462$	45526.0	−	131674.i	0.213293	−	0.616903i
$463$	39151.0			0.182634			0.0913168	−	0.995822i	$-0.470892\pi$
$463$	39151.0			0.182634			0.0913168	+	0.995822i	$0.470892\pi$
$464$		−	703603.i		−	3.26807i
$465$	−141641.	−	48972.1i	−0.655064	−	0.226487i
$466$	91799.1			0.422733
$467$		−	383832.i		−	1.75998i	−0.474996	−	0.879988i	$-0.657550\pi$
$467$		−	383832.i		−	1.75998i	0.474996	−	0.879988i	$-0.342450\pi$
$468$	−338910.	−	266173.i	−1.54736	−	1.21527i
$469$	25063.3			0.113944
$470$			283346.i			1.28269i
$471$	7190.11	−	20795.8i	0.0324111	−	0.0937420i
$472$	−77659.9			−0.348588
$473$		−	423868.i		−	1.89456i
$474$	−496413.	−	171634.i	−2.20946	−	0.763916i
$475$	26029.2			0.115365
$476$		−	16323.7i		−	0.0720453i
$477$	6232.93	−	7936.19i	0.0273940	−	0.0348799i
$478$	−310369.			−1.35838
$479$		−	238559.i		−	1.03974i	−0.854245	−	0.519871i	$-0.825980\pi$
$479$		−	238559.i		−	1.03974i	0.854245	−	0.519871i	$-0.174020\pi$
$480$	136464.	−	394693.i	0.592293	−	1.71308i
$481$	292634.			1.26484
$482$			322067.i			1.38628i
$483$	70333.7	+	24317.7i	0.301488	+	0.104239i
$484$	716314.			3.05782
$485$		−	318926.i		−	1.35584i
$486$	40966.8	−	436351.i	0.173444	−	1.84741i
$487$	206624.			0.871210			0.435605	−	0.900138i	$-0.356534\pi$
$487$	206624.			0.871210			0.435605	+	0.900138i	$0.356534\pi$
$488$			572249.i			2.40295i
$489$	20058.9	−	58015.9i	0.0838858	−	0.242622i
$490$	−380016.			−1.58274
$491$			356108.i			1.47713i	0.674183	+	0.738564i	$0.264496\pi$
$491$			356108.i			1.47713i	−0.674183	+	0.738564i	$0.735504\pi$
$492$	−535502.	−	185149.i	−2.21223	−	0.764874i
$493$	39567.5			0.162796
$494$			227004.i			0.930207i
$495$	260988.	+	204975.i	1.06515	+	0.836545i
$496$	−477078.			−1.93921
$497$			77107.5i			0.312165i
$498$	−241337.	+	698016.i	−0.973118	+	2.81453i
$499$	−234823.			−0.943062			−0.471531	−	0.881850i	$-0.656298\pi$
$499$	−234823.			−0.943062			−0.471531	+	0.881850i	$0.656298\pi$
$500$		−	653426.i		−	2.61370i
$501$	−336171.	−	116230.i	−1.33932	−	0.463067i
$502$	796892.			3.16222
$503$		−	386137.i		−	1.52618i	−0.646294	−	0.763089i	$-0.723682\pi$
$503$		−	386137.i		−	1.52618i	0.646294	−	0.763089i	$-0.276318\pi$
$504$	98483.8	−	125396.i	0.387707	−	0.493655i
$505$	62029.2			0.243228
$506$			970052.i			3.78873i
$507$	−29513.5	+	85361.4i	−0.114817	+	0.332082i
$508$	−465518.			−1.80389
$509$			47078.4i			0.181713i	0.995864	+	0.0908565i	$0.0289605\pi$
$509$			47078.4i			0.181713i	−0.995864	+	0.0908565i	$0.971040\pi$
$510$	51789.6	+	17906.1i	0.199114	+	0.0688432i
$511$	81864.8			0.313513
$512$			443103.i			1.69030i
$513$	−137723.	+	88695.1i	−0.523327	+	0.337027i
$514$	−900635.			−3.40897
$515$		−	30075.9i		−	0.113398i
$516$	268362.	−	776178.i	1.00791	−	2.91516i
$517$	−307182.			−1.14925
$518$			183308.i			0.683160i
$519$	103298.	+	35715.1i	0.383493	+	0.132592i
$520$	526299.			1.94637
$521$			309459.i			1.14006i	0.821624	+	0.570029i	$0.193068\pi$
$521$			309459.i			1.14006i	−0.821624	+	0.570029i	$0.806932\pi$
$522$	514588.	+	404147.i	1.88851	+	1.48320i
$523$	216367.			0.791019			0.395509	−	0.918462i	$-0.370568\pi$
$523$	216367.			0.791019			0.395509	+	0.918462i	$0.370568\pi$
$524$			512265.i			1.86566i
$525$	3913.23	−	11318.2i	0.0141977	−	0.0410637i
$526$	−609281.			−2.20215
$527$		−	26828.7i		−	0.0966003i
$528$	998414.	+	345199.i	3.58132	+	1.23823i
$529$	−238312.			−0.851598
$530$			20864.9i			0.0742788i
$531$	22673.2	−	28869.0i	0.0804124	−	0.102387i
$532$	−100897.			−0.356495
$533$		−	219219.i		−	0.771657i
$534$	73709.7	−	213189.i	0.258489	−	0.747623i
$535$	−298300.			−1.04219
$536$			373891.i			1.30141i
$537$	262698.	+	90827.2i	0.910979	+	0.314969i
$538$	−159855.			−0.552282
$539$		−	411984.i		−	1.41809i
$540$	348140.	+	540583.i	1.19390	+	1.85385i
$541$	63972.1			0.218573			0.109286	−	0.994010i	$-0.465143\pi$
$541$	63972.1			0.218573			0.109286	+	0.994010i	$0.465143\pi$
$542$			745051.i			2.53622i
$543$	34916.7	−	100989.i	0.118422	−	0.342511i
$544$	74760.1			0.252623
$545$		−	395598.i		−	1.33187i
$546$	98707.2	+	34127.8i	0.331103	+	0.114478i
$547$	315353.			1.05396			0.526978	−	0.849879i	$-0.323325\pi$
$547$	315353.			1.05396			0.526978	+	0.849879i	$0.323325\pi$
$548$		−	1.21340e6i		−	4.04058i
$549$	−212726.	−	167071.i	−0.705790	−	0.554313i
$550$	156102.			0.516039
$551$		−	244566.i		−	0.805551i
$552$	−362768.	+	1.04923e6i	−1.19056	+	3.44344i
$553$	90324.2			0.295361
$554$		−	254411.i		−	0.828926i
$555$	−412660.	−	142676.i	−1.33969	−	0.463196i
$556$	−26610.4			−0.0860800
$557$		−	235733.i		−	0.759818i	−0.925024	−	0.379909i	$-0.875955\pi$
$557$		−	235733.i		−	0.759818i	0.925024	−	0.379909i	$-0.124045\pi$
$558$	274032.	−	348916.i	0.880101	−	1.12061i
$559$	317745.			1.01685
$560$			167568.i			0.534338i
$561$	−19412.4	+	56146.3i	−0.0616814	+	0.178400i
$562$	73382.9			0.232339
$563$			139368.i			0.439689i	0.975535	+	0.219845i	$0.0705550\pi$
$563$			139368.i			0.439689i	−0.975535	+	0.219845i	$0.929445\pi$
$564$	−562506.	−	194485.i	−1.76835	−	0.611403i
$565$	−2711.25			−0.00849321
$566$			77040.2i			0.240483i
$567$	17861.6	+	73220.1i	0.0555590	+	0.227753i
$568$	−1.15028e6			−3.56538
$569$			108323.i			0.334576i	0.985908	+	0.167288i	$0.0535009\pi$
$569$			108323.i			0.334576i	−0.985908	+	0.167288i	$0.946499\pi$
$570$	110677.	−	320111.i	0.340651	−	0.985259i
$571$	−136058.			−0.417305			−0.208652	−	0.977990i	$-0.566908\pi$
$571$	−136058.			−0.417305			−0.208652	+	0.977990i	$0.566908\pi$
$572$			965978.i			2.95240i
$573$	−288616.	−	99788.2i	−0.879045	−	0.303928i
$574$	137320.			0.416784
$575$			83381.7i			0.252194i
$576$	313372.	+	246116.i	0.944528	+	0.741814i
$577$	−242991.			−0.729860			−0.364930	−	0.931035i	$-0.618907\pi$
$577$	−242991.			−0.729860			−0.364930	+	0.931035i	$0.618907\pi$
$578$		−	610095.i		−	1.82617i
$579$	−12326.2	+	35651.0i	−0.0367683	+	0.106344i
$580$	−959956.			−2.85361
$581$		−	127006.i		−	0.376247i
$582$	892304.	+	308512.i	2.63431	+	0.910806i
$583$	−22620.1			−0.0665516
$584$			1.22125e6i			3.58078i
$585$	−153655.	+	195645.i	−0.448989	+	0.571684i
$586$	351624.			1.02396
$587$			199495.i			0.578969i	0.957183	+	0.289485i	$0.0934839\pi$
$587$			199495.i			0.578969i	−0.957183	+	0.289485i	$0.906516\pi$
$588$	260837.	−	754416.i	0.754424	−	2.18201i
$589$	−165828.			−0.477999
$590$			75899.0i			0.218038i
$591$	359386.	+	124257.i	1.02893	+	0.355750i
$592$	−1.38993e6			−3.96596
$593$			218091.i			0.620196i	0.950705	+	0.310098i	$0.100362\pi$
$593$			218091.i			0.620196i	−0.950705	+	0.310098i	$0.899638\pi$
$594$	−825951.	+	531920.i	−2.34089	+	1.50756i
$595$	−9423.30			−0.0266176
$596$			602236.i			1.69541i
$597$	−152545.	+	441204.i	−0.428006	+	1.23792i
$598$	−727182.			−2.03348
$599$		−	347865.i		−	0.969522i	−0.874647	−	0.484761i	$-0.838907\pi$
$599$		−	347865.i		−	0.969522i	0.874647	−	0.484761i	$-0.161093\pi$
$600$	168843.	+	58377.0i	0.469008	+	0.162158i
$601$	−63259.7			−0.175137			−0.0875685	−	0.996158i	$-0.527910\pi$
$601$	−63259.7			−0.175137			−0.0875685	+	0.996158i	$0.527910\pi$
$602$			199038.i			0.549215i
$603$	−138989.	−	109159.i	−0.382248	−	0.300210i
$604$	1.50134e6			4.11533
$605$		−	413511.i		−	1.12973i
$606$	−60003.6	+	173548.i	−0.163393	+	0.472578i
$607$	−407.887			−0.00110704			−0.000553518	−	1.00000i	$-0.500176\pi$
$607$	−407.887			−0.00110704			−0.000553518		1.00000i	$0.500176\pi$
$608$		−	462091.i		−	1.25003i
$609$	−106344.	−	36768.0i	−0.286733	−	0.0991370i
$610$	559274.			1.50302
$611$		−	230274.i		−	0.616825i
$612$	−71095.3	+	90523.4i	−0.189818	+	0.241690i
$613$	−96854.0			−0.257749			−0.128874	−	0.991661i	$-0.541136\pi$
$613$	−96854.0			−0.257749			−0.128874	+	0.991661i	$0.541136\pi$
$614$		−	1.35702e6i		−	3.59955i
$615$	−106882.	+	309133.i	−0.282588	+	0.817325i
$616$	−357411.			−0.941904
$617$			414820.i			1.08966i	0.838548	+	0.544828i	$0.183405\pi$
$617$			414820.i			1.08966i	−0.838548	+	0.544828i	$0.816595\pi$
$618$	84147.5	+	29093.8i	0.220325	+	0.0761769i
$619$	285041.			0.743919			0.371960	−	0.928249i	$-0.378686\pi$
$619$	285041.			0.743919			0.371960	+	0.928249i	$0.378686\pi$
$620$			650897.i			1.69328i
$621$	−284125.	−	441181.i	−0.736760	−	1.14402i
$622$	652558.			1.68670
$623$			38790.6i			0.0999425i
$624$	−258772.	+	748443.i	−0.664582	+	1.92216i
$625$	−304810.			−0.780313
$626$			1.02331e6i			2.61131i
$627$	347040.	+	119988.i	0.882762	+	0.305213i
$628$	−95565.0			−0.242315
$629$		−	78163.2i		−	0.197561i
$630$	−122553.	−	96250.8i	−0.308776	−	0.242506i
$631$	303230.			0.761576			0.380788	−	0.924662i	$-0.375653\pi$
$631$	303230.			0.761576			0.380788	+	0.924662i	$0.375653\pi$
$632$			1.34744e6i			3.37346i
$633$	−234877.	+	679332.i	−0.586183	+	1.69541i
$634$	−904151.			−2.24938
$635$			268733.i			0.666458i
$636$	−41421.5	−	14321.4i	−0.102403	−	0.0354055i
$637$	308836.			0.761113
$638$		−	1.46671e6i		−	3.60331i
$639$	335829.	−	427601.i	0.822463	−	1.04722i
$640$	−81447.1			−0.198845
$641$			595247.i			1.44871i	0.689428	+	0.724354i	$0.257862\pi$
$641$			595247.i			1.44871i	−0.689428	+	0.724354i	$0.742138\pi$
$642$	288559.	−	834594.i	0.700107	−	2.02491i
$643$	222035.			0.537032			0.268516	−	0.963275i	$-0.413467\pi$
$643$	222035.			0.537032			0.268516	+	0.963275i	$0.413467\pi$
$644$		−	323211.i		−	0.779318i
$645$	−448069.	−	154919.i	−1.07703	−	0.372379i
$646$	60633.2			0.145293
$647$		−	378014.i		−	0.903023i	−0.892265	−	0.451512i	$-0.850885\pi$
$647$		−	378014.i		−	0.903023i	0.892265	−	0.451512i	$-0.149115\pi$
$648$	−1.09229e6	+	266457.i	−2.60128	+	0.634566i
$649$	−82283.9			−0.195355
$650$			117019.i			0.276968i
$651$	−24930.5	+	72106.2i	−0.0588261	+	0.170142i
$652$	−266606.			−0.627155
$653$		−	525594.i		−	1.23260i	−0.787510	−	0.616302i	$-0.788630\pi$
$653$		−	525594.i		−	1.23260i	0.787510	−	0.616302i	$-0.211370\pi$
$654$	1.10682e6	+	382680.i	2.58775	+	0.894707i
$655$	295718.			0.689280
$656$			1.04123e6i			2.41956i
$657$	−453982.	−	356549.i	−1.05174	−	0.826015i
$658$	144245.			0.333157
$659$		−	322632.i		−	0.742912i	−0.928451	−	0.371456i	$-0.878859\pi$
$659$		−	322632.i		−	0.742912i	0.928451	−	0.371456i	$-0.121141\pi$
$660$	470970.	−	1.36218e6i	1.08120	−	3.12713i
$661$	74391.1			0.170262			0.0851311	−	0.996370i	$-0.472869\pi$
$661$	74391.1			0.170262			0.0851311	+	0.996370i	$0.472869\pi$
$662$		−	1.22945e6i		−	2.80539i
$663$	−42089.1	−	14552.2i	−0.0957507	−	0.0331056i
$664$	1.89466e6			4.29730
$665$			58245.3i			0.131710i
$666$	798369.	−	1.01654e6i	1.79993	−	2.29179i
$667$	783440.			1.76098
$668$			1.54484e6i			3.46203i
$669$	206334.	−	596776.i	0.461018	−	1.33340i
$670$	365413.			0.814020
$671$			606322.i			1.34666i
$672$	−200929.	−	69470.8i	−0.444943	−	0.153838i
$673$	186945.			0.412747			0.206373	−	0.978473i	$-0.433834\pi$
$673$	186945.			0.412747			0.206373	+	0.978473i	$0.433834\pi$
$674$		−	1.05760e6i		−	2.32810i
$675$	−70995.3	+	45721.7i	−0.155820	+	0.100349i
$676$	392269.			0.858403
$677$		−	286936.i		−	0.626048i	−0.949745	−	0.313024i	$-0.898658\pi$
$677$		−	286936.i		−	0.626048i	0.949745	−	0.313024i	$-0.101342\pi$
$678$	2622.71	−	7585.63i	0.00570547	−	0.0165018i
$679$	−162358.			−0.352155
$680$		−	140575.i		−	0.304013i
$681$	397442.	+	137415.i	0.856998	+	0.296305i
$682$	−994498.			−2.13814
$683$		−	749589.i		−	1.60687i	−0.595390	−	0.803437i	$-0.703002\pi$
$683$		−	749589.i		−	1.60687i	0.595390	−	0.803437i	$-0.296998\pi$
$684$	559524.	+	439439.i	1.19593	+	0.939261i
$685$	−700468.			−1.49282
$686$			398164.i			0.846086i
$687$	66775.2	−	193133.i	0.141482	−	0.409207i
$688$	−1.50919e6			−3.18836
$689$		−	16956.8i		−	0.0357195i
$690$	1.02544e6	+	354543.i	2.15383	+	0.744681i
$691$	310447.			0.650177			0.325089	−	0.945684i	$-0.394606\pi$
$691$	310447.			0.650177			0.325089	+	0.945684i	$0.394606\pi$
$692$		−	474696.i		−	0.991296i
$693$	104348.	−	132863.i	0.217278	−	0.276654i
$694$	−1.71323e6			−3.55711
$695$			15361.6i			0.0318028i
$696$	548500.	−	1.58642e6i	1.13229	−	3.27491i
$697$	−58553.8			−0.120529
$698$		−	279614.i		−	0.573916i
$699$	105204.	+	36374.0i	0.215316	+	0.0744451i
$700$	−52011.5			−0.106146
$701$			213477.i			0.434425i	0.976124	+	0.217213i	$0.0696965\pi$
$701$			213477.i			0.434425i	−0.976124	+	0.217213i	$0.930303\pi$
$702$	−398744.	−	619159.i	−0.809133	−	1.25640i
$703$	−483125.			−0.977573
$704$		−	893188.i		−	1.80218i
$705$	−112272.	+	324721.i	−0.225887	+	0.653330i
$706$	−814921.			−1.63496
$707$		−	31577.6i		−	0.0631743i
$708$	−150677.	−	52096.0i	−0.300593	−	0.103929i
$709$	136608.			0.271759			0.135879	−	0.990725i	$-0.456614\pi$
$709$	136608.			0.271759			0.135879	+	0.990725i	$0.456614\pi$
$710$			1.12420e6i			2.23011i
$711$	−500894.	−	393392.i	−0.990847	−	0.778191i
$712$	−578672.			−1.14149
$713$		−	531211.i		−	1.04493i
$714$	9115.59	−	26364.9i	0.0178809	−	0.0517165i
$715$	557636.			1.09078
$716$		−	1.20720e6i		−	2.35480i
$717$	−355690.	−	122979.i	−0.691884	−	0.239217i
$718$	−804401.			−1.56036
$719$			248297.i			0.480301i	0.970736	+	0.240151i	$0.0771968\pi$
$719$			248297.i			0.480301i	−0.970736	+	0.240151i	$0.922803\pi$
$720$	729817.	−	929253.i	1.40783	−	1.79254i
$721$	−15310.9			−0.0294531
$722$			592488.i			1.13659i
$723$	−127614.	+	369096.i	−0.244130	+	0.706094i
$724$	−464084.			−0.885359
$725$		−	126072.i		−	0.239852i
$726$	1.15694e6	+	400008.i	2.19501	+	0.758919i
$727$	−867716.			−1.64176			−0.820878	−	0.571103i	$-0.806516\pi$
$727$	−867716.			−1.64176			−0.820878	+	0.571103i	$0.806516\pi$
$728$		−	267927.i		−	0.505537i
$729$	219846.	−	483836.i	0.413679	−	0.910423i
$730$	1.19356e6			2.23974
$731$		−	84870.3i		−	0.158826i
$732$	−383878.	+	1.11028e6i	−0.716425	+	2.07210i
$733$	560656.			1.04349			0.521745	−	0.853101i	$-0.325281\pi$
$733$	560656.			1.04349			0.521745	+	0.853101i	$0.325281\pi$
$734$			1.40592e6i			2.60957i
$735$	−435507.	−	150575.i	−0.806158	−	0.278727i
$736$	1.48026e6			2.73264
$737$			396153.i			0.729337i
$738$	−761512.	−	598076.i	−1.39818	−	1.09811i
$739$	246818.			0.451947			0.225974	−	0.974133i	$-0.427444\pi$
$739$	246818.			0.451947			0.225974	+	0.974133i	$0.427444\pi$
$740$			1.89633e6i			3.46299i
$741$	−89946.8	+	260152.i	−0.163813	+	0.473795i
$742$	10621.8			0.0192927
$743$		−	78964.1i		−	0.143038i	−0.997439	−	0.0715191i	$-0.977215\pi$
$743$		−	78964.1i		−	0.143038i	0.997439	−	0.0715191i	$-0.0227847\pi$
$744$	−1.07567e6	−	371910.i	−1.94327	−	0.671881i
$745$	347657.			0.626381
$746$			35203.3i			0.0632566i
$747$	−553156.	+	704316.i	−0.991302	+	1.26219i
$748$	258014.			0.461149
$749$			151857.i			0.270690i
$750$	364890.	−	1.05536e6i	0.648693	−	1.87620i
$751$	−411768.			−0.730084			−0.365042	−	0.930991i	$-0.618945\pi$
$751$	−411768.			−0.730084			−0.365042	+	0.930991i	$0.618945\pi$
$752$			1.09373e6i			1.93408i
$753$	913256.	+	315756.i	1.61066	+	0.556880i
$754$	1.09949e6			1.93396
$755$		−	866686.i		−	1.52044i
$756$	275198.	−	177230.i	0.481506	−	0.310094i
$757$	−1.00647e6			−1.75634			−0.878171	−	0.478347i	$-0.841236\pi$
$757$	−1.00647e6			−1.75634			−0.878171	+	0.478347i	$0.841236\pi$
$758$		−	1.69712e6i		−	2.95375i
$759$	−384368.	+	1.11170e6i	−0.667212	+	1.92977i
$760$	−868895.			−1.50432
$761$			470668.i			0.812729i	0.913711	+	0.406364i	$0.133204\pi$
$761$			470668.i			0.812729i	−0.913711	+	0.406364i	$0.866796\pi$
$762$	−751870.	−	259957.i	−1.29489	−	0.447705i
$763$	−201390.			−0.345930
$764$			1.32630e6i			2.27225i
$765$	52257.0	+	41041.6i	0.0892939	+	0.0701297i
$766$	1.51776e6			2.58670
$767$		−	61682.6i		−	0.104851i
$768$	−152689.	+	441621.i	−0.258873	+	0.748733i
$769$	−485133.			−0.820367			−0.410183	−	0.912003i	$-0.634535\pi$
$769$	−485133.			−0.820367			−0.410183	+	0.912003i	$0.634535\pi$
$770$			349307.i			0.589150i
$771$	−1.03215e6	−	356863.i	−1.73634	−	0.600334i
$772$	163830.			0.274890
$773$			699399.i			1.17049i	0.810858	+	0.585243i	$0.199001\pi$
$773$			699399.i			1.17049i	−0.810858	+	0.585243i	$0.800999\pi$
$774$	866876.	−	1.10377e6i	1.44702	−	1.84245i
$775$	−85483.0			−0.142323
$776$		−	2.42203e6i		−	4.02213i
$777$	−72633.0	+	210075.i	−0.120307	+	0.347963i
$778$	964724.			1.59384
$779$			361920.i			0.596401i
$780$	1.02113e6	+	353054.i	1.67839	+	0.580299i
$781$	−1.21877e6			−1.99811
$782$			194232.i			0.317619i
$783$	429593.	+	667060.i	0.700702	+	1.08803i
$784$	−1.46688e6			−2.38650
$785$			55167.4i			0.0895248i
$786$	−286062.	+	827372.i	−0.463036	+	1.33923i
$787$	1.17448e6			1.89625			0.948126	−	0.317896i	$-0.102976\pi$
$787$	1.17448e6			1.89625			0.948126	+	0.317896i	$0.102976\pi$
$788$		−	1.65152e6i		−	2.65969i
$789$	−698250.	−	241418.i	−1.12165	−	0.387807i
$790$	1.31689e6			2.11006
$791$			1380.23i			0.00220597i
$792$	1.98203e6	+	1.55664e6i	3.15980	+	2.48164i
$793$	−454518.			−0.722778
$794$		−	1.28427e6i		−	2.03712i
$795$	−8267.40	+	23911.7i	−0.0130808	+	0.0378334i
$796$	2.02751e6			3.19990
$797$			1.17027e6i			1.84233i	0.389171	+	0.921165i	$0.372761\pi$
$797$			1.17027e6i			1.84233i	−0.389171	+	0.921165i	$0.627239\pi$
$798$	−162961.	−	56343.3i	−0.255904	−	0.0884783i
$799$	−61506.5			−0.0963446
$800$		−	238205.i		−	0.372195i
$801$	168946.	−	215114.i	0.263319	−	0.335276i
$802$	722987.			1.12404
$803$			1.29396e6i			2.00674i
$804$	−250815.	+	725428.i	−0.388008	+	1.12223i
$805$	−186582.			−0.287924
$806$		−	745508.i		−	1.14758i
$807$	−183197.	−	63339.9i	−0.281301	−	0.0972591i
$808$	471070.			0.721544
$809$		−	294046.i		−	0.449281i	−0.974442	−	0.224640i	$-0.927879\pi$
$809$		−	294046.i		−	0.449281i	0.974442	−	0.224640i	$-0.0721207\pi$
$810$	260415.	+	1.06752e6i	0.396914	+	1.62707i
$811$	574141.			0.872925			0.436462	−	0.899722i	$-0.356231\pi$
$811$	574141.			0.872925			0.436462	+	0.899722i	$0.356231\pi$
$812$			488691.i			0.741178i
$813$	−295215.	+	853846.i	−0.446640	+	1.29181i
$814$	−2.89739e6			−4.37278
$815$			153905.i			0.231707i
$816$	199910.	+	69118.5i	0.300231	+	0.103804i
$817$	−524582.			−0.785903
$818$		−	984980.i		−	1.47204i
$819$	99598.1	+	78222.4i	0.148485	+	0.116617i
$820$	1.42059e6			2.11271
$821$		−	648301.i		−	0.961812i	−0.876772	−	0.480906i	$-0.840308\pi$
$821$		−	648301.i		−	0.961812i	0.876772	−	0.480906i	$-0.159692\pi$
$822$	677595.	−	1.95980e6i	1.00283	−	2.90046i
$823$	944498.			1.39444			0.697222	−	0.716855i	$-0.254419\pi$
$823$	944498.			1.39444			0.697222	+	0.716855i	$0.254419\pi$
$824$		−	228406.i		−	0.336398i
$825$	178896.	+	61852.9i	0.262841	+	0.0908767i
$826$	38638.4			0.0566317
$827$			131880.i			0.192827i	0.995341	+	0.0964134i	$0.0307371\pi$
$827$			131880.i			0.192827i	−0.995341	+	0.0964134i	$0.969263\pi$
$828$	−1.40769e6	+	1.79237e6i	−2.05328	+	2.61437i
$829$	1.07710e6			1.56728			0.783641	−	0.621214i	$-0.213360\pi$
$829$	1.07710e6			1.56728			0.783641	+	0.621214i	$0.213360\pi$
$830$		−	1.85170e6i		−	2.68791i
$831$	100806.	−	291561.i	0.145977	−	0.422208i
$832$	669562.			0.967262
$833$		−	82490.7i		−	0.118882i
$834$	−42979.2	−	14859.9i	−0.0617911	−	0.0213641i
$835$	891799.			1.27907
$836$		−	1.59478e6i		−	2.28186i
$837$	452299.	−	291285.i	0.645617	−	0.415783i
$838$	1.09486e6			1.55908
$839$			524409.i			0.744982i	0.928036	+	0.372491i	$0.121496\pi$
$839$			524409.i			0.744982i	−0.928036	+	0.372491i	$0.878504\pi$
$840$	−130630.	+	377818.i	−0.185133	+	0.535456i
$841$	−477270.			−0.674795
$842$			383599.i			0.541069i
$843$	84098.5	+	29076.8i	0.118340	+	0.0409159i
$844$	3.12180e6			4.38248
$845$		−	226448.i		−	0.317143i
$846$	−799912.	−	628235.i	−1.11764	−	0.877772i
$847$	−210509.			−0.293429
$848$			80539.6i			0.112000i
$849$	−30526.0	+	88289.8i	−0.0423501	+	0.122488i
$850$	31256.0			0.0432608
$851$		−	1.54764e6i		−	2.13703i
$852$	−2.23178e6	−	771634.i	−3.07449	−	1.06300i
$853$	−744113.			−1.02268			−0.511342	−	0.859378i	$-0.670851\pi$
$853$	−744113.			−1.02268			−0.511342	+	0.859378i	$0.670851\pi$
$854$		−	284713.i		−	0.390384i
$855$	253678.	−	323000.i	0.347017	−	0.441845i
$856$	−2.26539e6			−3.09168
$857$			959898.i			1.30696i	0.756942	+	0.653482i	$0.226692\pi$
$857$			959898.i			1.30696i	−0.756942	+	0.653482i	$0.773308\pi$
$858$	−539427.	+	1.56018e6i	−0.732754	+	2.11933i
$859$	68736.2			0.0931536			0.0465768	−	0.998915i	$-0.485169\pi$
$859$	68736.2			0.0931536			0.0465768	+	0.998915i	$0.485169\pi$
$860$			2.05906e6i			2.78401i
$861$	157372.	+	54411.1i	0.212286	+	0.0733974i
$862$	867100.			1.16696
$863$			365918.i			0.491317i	0.969356	+	0.245659i	$0.0790042\pi$
$863$			365918.i			0.491317i	−0.969356	+	0.245659i	$0.920996\pi$
$864$	811687.	+	1.26036e6i	1.08733	+	1.68837i
$865$	−274031.			−0.366241
$866$			1.35723e6i			1.80974i
$867$	241741.	−	699183.i	0.321597	−	0.930149i
$868$	331357.			0.439801
$869$			1.42767e6i			1.89055i
$870$	−1.55045e6	−	536064.i	−2.04842	−	0.708236i
$871$	−296969.			−0.391449
$872$		−	3.00431e6i		−	3.95104i
$873$	900358.	+	707123.i	1.18137	+	0.927827i
$874$	1.20054e6			1.57165
$875$			192027.i			0.250811i
$876$	−819241.	+	2.36948e6i	−1.06759	+	3.08777i
$877$	650497.			0.845758			0.422879	−	0.906186i	$-0.361020\pi$
$877$	650497.			0.845758			0.422879	+	0.906186i	$0.361020\pi$
$878$			355175.i			0.460737i
$879$	402969.	+	139325.i	0.521547	+	0.180324i
$880$	−2.64860e6			−3.42020
$881$			425212.i			0.547840i	0.961752	+	0.273920i	$0.0883203\pi$
$881$			425212.i			0.547840i	−0.961752	+	0.273920i	$0.911680\pi$
$882$	842570.	−	1.07282e6i	1.08310	−	1.37908i
$883$	1.05224e6			1.34957			0.674783	−	0.738016i	$-0.264237\pi$
$883$	1.05224e6			1.34957			0.674783	+	0.738016i	$0.264237\pi$
$884$			193416.i			0.247507i
$885$	−30073.8	+	86982.0i	−0.0383974	+	0.111056i
$886$	2.33510e6			2.97467
$887$		−	510726.i		−	0.649144i	−0.945861	−	0.324572i	$-0.894780\pi$
$887$		−	510726.i		−	0.649144i	0.945861	−	0.324572i	$-0.105220\pi$
$888$	−3.13387e6	−	1.08353e6i	−3.97425	−	1.37409i
$889$	136805.			0.173101
$890$			565551.i			0.713990i
$891$	−1.15732e6	+	282322.i	−1.45780	+	0.355623i
$892$	−2.74242e6			−3.44671
$893$			380171.i			0.476734i
$894$	−336304.	+	972688.i	−0.420782	+	1.21702i
$895$	−696889.			−0.869996
$896$			41462.8i			0.0516467i
$897$	−833367.	−	288135.i	−1.03574	−	0.358105i
$898$	2.41018e6			2.98880
$899$			803184.i			0.993792i
$900$	288430.	+	226528.i	0.356087	+	0.279664i
$901$	−4529.19			−0.00557918
$902$			2.17050e6i			2.66776i
$903$	−78865.6	+	228102.i	−0.0967190	+	0.279739i
$904$	−20590.1			−0.0251954
$905$			267905.i			0.327102i
$906$	2.42485e6	+	838385.i	2.95412	+	1.02138i
$907$	154450.			0.187747			0.0938736	−	0.995584i	$-0.470075\pi$
$907$	154450.			0.187747			0.0938736	+	0.995584i	$0.470075\pi$
$908$		−	1.82640e6i		−	2.21526i
$909$	−137531.	+	175114.i	−0.166446	+	0.211930i
$910$	−261852.			−0.316208
$911$			942044.i			1.13510i	0.823339	+	0.567550i	$0.192109\pi$
$911$			942044.i			1.13510i	−0.823339	+	0.567550i	$0.807891\pi$
$912$	427220.	−	1.23564e6i	0.513644	−	1.48560i
$913$	2.00748e6			2.40829
$914$		−	1.69315e6i		−	2.02677i
$915$	640940.	+	221603.i	0.765553	+	0.264688i
$916$	−887521.			−1.05776
$917$		−	150543.i		−	0.179029i
$918$	−165378.	+	106505.i	−0.196243	+	0.126382i
$919$	−823235.			−0.974749			−0.487375	−	0.873193i	$-0.662045\pi$
$919$	−823235.			−0.974749			−0.487375	+	0.873193i	$0.662045\pi$
$920$		−	2.78341e6i		−	3.28852i
$921$	537697.	−	1.55517e6i	0.633897	−	1.83341i
$922$	−1.93321e6			−2.27414
$923$		−	913628.i		−	1.07242i
$924$	−693453.	−	239760.i	−0.812219	−	0.280823i
$925$	−249048.			−0.291071
$926$		−	290584.i		−	0.338883i
$927$	84907.0	+	66684.3i	0.0988062	+	0.0776004i
$928$	−2.23813e6			−2.59890
$929$			691516.i			0.801255i	0.916241	+	0.400628i	$0.131208\pi$
$929$			691516.i			0.801255i	−0.916241	+	0.400628i	$0.868792\pi$
$930$	−363478.	+	1.05128e6i	−0.420254	+	1.21549i
$931$	−509874.			−0.588252
$932$		−	483453.i		−	0.556574i
$933$	747846.	+	258566.i	0.859111	+	0.297035i
$934$	−2.84885e6			−3.26570
$935$		−	148946.i		−	0.170374i
$936$	−1.16691e6	+	1.48579e6i	−1.33194	+	1.69592i
$937$	435979.			0.496577			0.248288	−	0.968686i	$-0.420132\pi$
$937$	435979.			0.496577			0.248288	+	0.968686i	$0.420132\pi$
$938$		−	186023.i		−	0.211428i
$939$	−405471.	+	1.17274e6i	−0.459863	+	1.33006i
$940$	1.49222e6			1.68880
$941$		−	464164.i		−	0.524194i	−0.965042	−	0.262097i	$-0.915586\pi$
$941$		−	464164.i		−	0.524194i	0.965042	−	0.262097i	$-0.0844140\pi$
$942$	−154350.	−	53366.0i	−0.173942	−	0.0601399i
$943$	−1.15937e6			−1.30376
$944$			292974.i			0.328765i
$945$	−102311.	−	158865.i	−0.114567	−	0.177896i
$946$	−3.14601e6			−3.51542
$947$		−	768628.i		−	0.857070i	−0.903525	−	0.428535i	$-0.859030\pi$
$947$		−	768628.i		−	0.857070i	0.903525	−	0.428535i	$-0.140970\pi$
$948$	−903896.	+	2.61432e6i	−1.00578	+	2.90899i
$949$	−969996.			−1.07705
$950$		−	193193.i		−	0.214064i
$951$	−1.03618e6	−	358256.i	−1.14571	−	0.396125i
$952$	−71563.7			−0.0789621
$953$			307997.i			0.339126i	0.985519	+	0.169563i	$0.0542356\pi$
$953$			307997.i			0.339126i	−0.985519	+	0.169563i	$0.945764\pi$
$954$	−58903.5	−	46261.7i	−0.0647209	−	0.0508305i
$955$	765644.			0.839499
$956$			1.63454e6i			1.78846i
$957$	581159.	−	1.68088e6i	0.634558	−	1.83532i
$958$	−1.77062e6			−1.92928
$959$			356592.i			0.387734i
$960$	−944185.	−	326450.i	−1.02451	−	0.354221i
$961$	−378923.			−0.410303
$962$		−	2.17197e6i		−	2.34695i
$963$	661390.	−	842127.i	0.713190	−	0.908082i
$964$	1.69614e6			1.82519
$965$		−	94575.3i		−	0.101560i
$966$	180489.	−	522027.i	0.193418	−	0.559421i
$967$	−392915.			−0.420190			−0.210095	−	0.977681i	$-0.567377\pi$
$967$	−392915.			−0.420190			−0.210095	+	0.977681i	$0.567377\pi$
$968$		−	3.14034e6i		−	3.35140i
$969$	69487.0	+	24025.0i	0.0740042	+	0.0255868i
$970$	−2.36712e6			−2.51580
$971$		−	501915.i		−	0.532343i	−0.963926	−	0.266171i	$-0.914241\pi$
$971$		−	501915.i		−	0.532343i	0.963926	−	0.266171i	$-0.0857587\pi$
$972$	−2.29801e6	−	215749.i	−2.43231	−	0.228358i
$973$	7820.21			0.00826024
$974$		−	1.53359e6i		−	1.61656i
$975$	−46366.9	+	134106.i	−0.0487752	+	0.141072i
$976$	2.15882e6			2.26630
$977$		−	157423.i		−	0.164922i	−0.996594	−	0.0824611i	$-0.973722\pi$
$977$		−	157423.i		−	0.164922i	0.996594	−	0.0824611i	$-0.0262780\pi$
$978$	−430602.	−	148880.i	−0.450193	−	0.155653i
$979$	−613128.			−0.639713
$980$			2.00132e6i			2.08384i
$981$	1.11681e6	+	877121.i	1.16049	+	0.911426i
$982$	2.64308e6			2.74086
$983$			1.08380e6i			1.12161i	0.827947	+	0.560806i	$0.189509\pi$
$983$			1.08380e6i			1.12161i	−0.827947	+	0.560806i	$0.810491\pi$
$984$	−811696.	+	2.34766e6i	−0.838308	+	2.42462i
$985$	−953383.			−0.982641
$986$		−	293676.i		−	0.302074i
$987$	165308.	+	57154.8i	0.169691	+	0.0586704i
$988$	1.19550e6			1.22472
$989$		−	1.68044e6i		−	1.71803i
$990$	1.52135e6	−	1.93709e6i	1.55224	−	1.97642i
$991$	444964.			0.453083			0.226542	−	0.974001i	$-0.427258\pi$
$991$	444964.			0.453083			0.226542	+	0.974001i	$0.427258\pi$
$992$			1.51756e6i			1.54214i
$993$	487149.	−	1.40897e6i	0.494041	−	1.42891i
$994$	572303.			0.579233
$995$		−	1.17043e6i		−	1.18223i
$996$	3.67605e6	+	1.27098e6i	3.70563	+	1.28121i
$997$	775871.			0.780548			0.390274	−	0.920699i	$-0.372380\pi$
$997$	775871.			0.780548			0.390274	+	0.920699i	$0.372380\pi$
$998$			1.74289e6i			1.74988i
$999$	1.31774e6	−	848634.i	1.32038	−	0.850334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.4	✓	78
3.2	odd	2	inner	177.5.b.a.119.75	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.4	✓	78	1.1	even	1	trivial
177.5.b.a.119.75	yes	78	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.42214i q^{2} +(2.94091 - 8.50594i) q^{3} -39.0882 q^{4} +22.5647i q^{5} +(-63.1323 - 21.8278i) q^{6} +11.4871 q^{7} +171.364i q^{8} +(-63.7021 - 50.0304i) q^{9} +O(q^{10})\)	\(q-7.42214i q^{2} +(2.94091 - 8.50594i) q^{3} -39.0882 q^{4} +22.5647i q^{5} +(-63.1323 - 21.8278i) q^{6} +11.4871 q^{7} +171.364i q^{8} +(-63.7021 - 50.0304i) q^{9} +167.478 q^{10} +181.567i q^{11} +(-114.955 + 332.482i) q^{12} -136.108 q^{13} -85.2592i q^{14} +(191.934 + 66.3606i) q^{15} +646.474 q^{16} +36.3548i q^{17} +(-371.333 + 472.806i) q^{18} +224.708 q^{19} -882.012i q^{20} +(33.7827 - 97.7090i) q^{21} +1347.62 q^{22} +719.829i q^{23} +(1457.61 + 503.965i) q^{24} +115.836 q^{25} +1010.22i q^{26} +(-612.898 + 394.712i) q^{27} -449.012 q^{28} -1088.37i q^{29} +(492.538 - 1424.56i) q^{30} -737.969 q^{31} -2056.40i q^{32} +(1544.40 + 533.972i) q^{33} +269.830 q^{34} +259.204i q^{35} +(2490.00 + 1955.60i) q^{36} -2150.01 q^{37} -1667.82i q^{38} +(-400.282 + 1157.73i) q^{39} -3866.76 q^{40} +1610.62i q^{41} +(-725.210 - 250.740i) q^{42} -2334.50 q^{43} -7097.12i q^{44} +(1128.92 - 1437.42i) q^{45} +5342.67 q^{46} +1691.84i q^{47} +(1901.22 - 5498.87i) q^{48} -2269.05 q^{49} -859.748i q^{50} +(309.232 + 106.916i) q^{51} +5320.23 q^{52} +124.583i q^{53} +(2929.61 + 4549.01i) q^{54} -4097.00 q^{55} +1968.48i q^{56} +(660.847 - 1911.36i) q^{57} -8078.04 q^{58} +453.188i q^{59} +(-7502.34 - 2593.92i) q^{60} +3339.38 q^{61} +5477.31i q^{62} +(-731.756 - 574.707i) q^{63} -4919.33 q^{64} -3071.24i q^{65} +(3963.21 - 11462.7i) q^{66} +2181.86 q^{67} -1421.04i q^{68} +(6122.82 + 2116.95i) q^{69} +1923.85 q^{70} +6712.50i q^{71} +(8573.39 - 10916.2i) q^{72} +7126.64 q^{73} +15957.7i q^{74} +(340.662 - 985.290i) q^{75} -8783.44 q^{76} +2085.69i q^{77} +(8592.84 + 2970.95i) q^{78} +7863.06 q^{79} +14587.5i q^{80} +(1554.92 + 6374.08i) q^{81} +11954.3 q^{82} -11056.4i q^{83} +(-1320.50 + 3819.27i) q^{84} -820.334 q^{85} +17327.0i q^{86} +(-9257.62 - 3200.80i) q^{87} -31114.0 q^{88} +3376.87i q^{89} +(-10668.7 - 8379.00i) q^{90} -1563.50 q^{91} -28136.8i q^{92} +(-2170.30 + 6277.12i) q^{93} +12557.1 q^{94} +5070.47i q^{95} +(-17491.6 - 6047.69i) q^{96} -14133.9 q^{97} +16841.2i q^{98} +(9083.87 - 11566.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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