LMFDB - Embedded newform 177.5.b.a.119.14

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			119.14
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.65

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.57893i q^{2} +(-6.24762 + 6.47821i) q^{3} -15.1244 q^{4} +38.3444i q^{5} +(36.1415 + 34.8550i) q^{6} +12.9947 q^{7} -4.88479i q^{8} +(-2.93443 - 80.9468i) q^{9} +O(q^{10})$	\(q-5.57893i q^{2} +(-6.24762 + 6.47821i) q^{3} -15.1244 q^{4} +38.3444i q^{5} +(36.1415 + 34.8550i) q^{6} +12.9947 q^{7} -4.88479i q^{8} +(-2.93443 - 80.9468i) q^{9} +213.920 q^{10} +6.78867i q^{11} +(94.4917 - 97.9792i) q^{12} +101.844 q^{13} -72.4966i q^{14} +(-248.403 - 239.561i) q^{15} -269.243 q^{16} +232.064i q^{17} +(-451.596 + 16.3710i) q^{18} -576.777 q^{19} -579.936i q^{20} +(-81.1861 + 84.1825i) q^{21} +37.8735 q^{22} -40.2549i q^{23} +(31.6447 + 30.5183i) q^{24} -845.289 q^{25} -568.182i q^{26} +(542.724 + 486.715i) q^{27} -196.538 q^{28} -784.639i q^{29} +(-1336.49 + 1385.82i) q^{30} -1041.73 q^{31} +1423.93i q^{32} +(-43.9784 - 42.4130i) q^{33} +1294.67 q^{34} +498.274i q^{35} +(44.3815 + 1224.27i) q^{36} -2432.59 q^{37} +3217.79i q^{38} +(-636.285 + 659.769i) q^{39} +187.304 q^{40} -2586.07i q^{41} +(469.648 + 452.931i) q^{42} +1128.10 q^{43} -102.675i q^{44} +(3103.85 - 112.519i) q^{45} -224.579 q^{46} +2146.95i q^{47} +(1682.13 - 1744.21i) q^{48} -2232.14 q^{49} +4715.81i q^{50} +(-1503.36 - 1449.85i) q^{51} -1540.34 q^{52} -2753.90i q^{53} +(2715.35 - 3027.82i) q^{54} -260.307 q^{55} -63.4765i q^{56} +(3603.48 - 3736.48i) q^{57} -4377.44 q^{58} +453.188i q^{59} +(3756.95 + 3623.22i) q^{60} +1249.49 q^{61} +5811.74i q^{62} +(-38.1320 - 1051.88i) q^{63} +3636.11 q^{64} +3905.16i q^{65} +(-236.619 + 245.352i) q^{66} -7317.61 q^{67} -3509.84i q^{68} +(260.780 + 251.497i) q^{69} +2779.83 q^{70} +4746.24i q^{71} +(-395.408 + 14.3341i) q^{72} -2510.30 q^{73} +13571.2i q^{74} +(5281.05 - 5475.96i) q^{75} +8723.41 q^{76} +88.2168i q^{77} +(3680.80 + 3549.79i) q^{78} -3075.09 q^{79} -10323.9i q^{80} +(-6543.78 + 475.065i) q^{81} -14427.5 q^{82} -5431.72i q^{83} +(1227.89 - 1273.21i) q^{84} -8898.35 q^{85} -6293.57i q^{86} +(5083.05 + 4902.13i) q^{87} +33.1612 q^{88} +10693.2i q^{89} +(-627.733 - 17316.2i) q^{90} +1323.44 q^{91} +608.832i q^{92} +(6508.34 - 6748.55i) q^{93} +11977.7 q^{94} -22116.1i q^{95} +(-9224.51 - 8896.17i) q^{96} +12979.5 q^{97} +12452.9i q^{98} +(549.521 - 19.9208i) 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 $

$2$		−	5.57893i		−	1.39473i	−0.716715	−	0.697366i	$-0.754355\pi$
$2$		−	5.57893i		−	1.39473i	0.716715	−	0.697366i	$-0.245645\pi$
$3$	−6.24762	+	6.47821i	−0.694180	+	0.719801i
$3$	−6.24762	+	6.47821i	−0.694180	+	0.719801i
$4$	−15.1244			−0.945276
$5$			38.3444i			1.53377i	0.641782	+	0.766887i	$0.278195\pi$
$5$			38.3444i			1.53377i	−0.641782	+	0.766887i	$0.721805\pi$
$6$	36.1415	+	34.8550i	1.00393	+	0.968195i
$7$	12.9947			0.265198			0.132599	−	0.991170i	$-0.457668\pi$
$7$	12.9947			0.265198			0.132599	+	0.991170i	$0.457668\pi$
$8$		−	4.88479i		−	0.0763248i
$9$	−2.93443	−	80.9468i	−0.0362275	−	0.999344i
$10$	213.920			2.13920
$11$			6.78867i			0.0561047i	0.999606	+	0.0280523i	$0.00893051\pi$
$11$			6.78867i			0.0561047i	−0.999606	+	0.0280523i	$0.991069\pi$
$12$	94.4917	−	97.9792i	0.656192	−	0.680411i
$13$	101.844			0.602630			0.301315	−	0.953525i	$-0.402575\pi$
$13$	101.844			0.602630			0.301315	+	0.953525i	$0.402575\pi$
$14$		−	72.4966i		−	0.369880i
$15$	−248.403	−	239.561i	−1.10401	−	1.06472i
$16$	−269.243			−1.05173
$17$			232.064i			0.802990i	0.915861	+	0.401495i	$0.131509\pi$
$17$			232.064i			0.802990i	−0.915861	+	0.401495i	$0.868491\pi$
$18$	−451.596	+	16.3710i	−1.39382	+	0.0505276i
$19$	−576.777			−1.59772			−0.798860	−	0.601518i	$-0.794563\pi$
$19$	−576.777			−1.59772			−0.798860	+	0.601518i	$0.794563\pi$
$20$		−	579.936i		−	1.44984i
$21$	−81.1861	+	84.1825i	−0.184095	+	0.190890i
$22$	37.8735			0.0782510
$23$		−	40.2549i		−	0.0760962i	−0.999276	−	0.0380481i	$-0.987886\pi$
$23$		−	40.2549i		−	0.0760962i	0.999276	−	0.0380481i	$-0.0121140\pi$
$24$	31.6447	+	30.5183i	0.0549387	+	0.0529832i
$25$	−845.289			−1.35246
$26$		−	568.182i		−	0.840506i
$27$	542.724	+	486.715i	0.744477	+	0.667648i
$28$	−196.538			−0.250686
$29$		−	784.639i		−	0.932983i	−0.884526	−	0.466491i	$-0.845518\pi$
$29$		−	784.639i		−	0.932983i	0.884526	−	0.466491i	$-0.154482\pi$
$30$	−1336.49	+	1385.82i	−1.48499	+	1.53980i
$31$	−1041.73			−1.08401			−0.542003	−	0.840376i	$-0.682334\pi$
$31$	−1041.73			−1.08401			−0.542003	+	0.840376i	$0.682334\pi$
$32$			1423.93i			1.39055i
$33$	−43.9784	−	42.4130i	−0.0403842	−	0.0389468i
$34$	1294.67			1.11996
$35$			498.274i			0.406754i
$36$	44.3815	+	1224.27i	0.0342450	+	0.944656i
$37$	−2432.59			−1.77691			−0.888455	−	0.458963i	$-0.848221\pi$
$37$	−2432.59			−1.77691			−0.888455	+	0.458963i	$0.848221\pi$
$38$			3217.79i			2.22839i
$39$	−636.285	+	659.769i	−0.418334	+	0.433773i
$40$	187.304			0.117065
$41$		−	2586.07i		−	1.53841i	−0.639000	−	0.769206i	$-0.720652\pi$
$41$		−	2586.07i		−	1.53841i	0.639000	−	0.769206i	$-0.279348\pi$
$42$	469.648	+	452.931i	0.266240	+	0.256764i
$43$	1128.10			0.610112			0.305056	−	0.952334i	$-0.401325\pi$
$43$	1128.10			0.610112			0.305056	+	0.952334i	$0.401325\pi$
$44$		−	102.675i		−	0.0530344i
$45$	3103.85	−	112.519i	1.53277	−	0.0555648i
$46$	−224.579			−0.106134
$47$			2146.95i			0.971909i	0.873984	+	0.485954i	$0.161528\pi$
$47$			2146.95i			0.971909i	−0.873984	+	0.485954i	$0.838472\pi$
$48$	1682.13	−	1744.21i	0.730090	−	0.757036i
$49$	−2232.14			−0.929670
$50$			4715.81i			1.88632i
$51$	−1503.36	−	1449.85i	−0.577993	−	0.557420i
$52$	−1540.34			−0.569651
$53$		−	2753.90i		−	0.980384i	−0.871614	−	0.490192i	$-0.836927\pi$
$53$		−	2753.90i		−	0.980384i	0.871614	−	0.490192i	$-0.163073\pi$
$54$	2715.35	−	3027.82i	0.931190	−	1.03835i
$55$	−260.307			−0.0860519
$56$		−	63.4765i		−	0.0202412i
$57$	3603.48	−	3736.48i	1.10911	−	1.15004i
$58$	−4377.44			−1.30126
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	3756.95	+	3623.22i	1.04360	+	1.00645i
$61$	1249.49			0.335794			0.167897	−	0.985805i	$-0.446302\pi$
$61$	1249.49			0.335794			0.167897	+	0.985805i	$0.446302\pi$
$62$			5811.74i			1.51190i
$63$	−38.1320	−	1051.88i	−0.00960747	−	0.265024i
$64$	3636.11			0.887722
$65$			3905.16i			0.924297i
$66$	−236.619	+	245.352i	−0.0543203	+	0.0563252i
$67$	−7317.61			−1.63012			−0.815060	−	0.579376i	$-0.803296\pi$
$67$	−7317.61			−1.63012			−0.815060	+	0.579376i	$0.803296\pi$
$68$		−	3509.84i		−	0.759047i
$69$	260.780	+	251.497i	0.0547741	+	0.0528245i
$70$	2779.83			0.567313
$71$			4746.24i			0.941528i	0.882259	+	0.470764i	$0.156022\pi$
$71$			4746.24i			0.941528i	−0.882259	+	0.470764i	$0.843978\pi$
$72$	−395.408	+	14.3341i	−0.0762747	+	0.00276506i
$73$	−2510.30			−0.471064			−0.235532	−	0.971867i	$-0.575683\pi$
$73$	−2510.30			−0.471064			−0.235532	+	0.971867i	$0.575683\pi$
$74$			13571.2i			2.47831i
$75$	5281.05	−	5475.96i	0.938853	−	0.973504i
$76$	8723.41			1.51029
$77$			88.2168i			0.0148789i
$78$	3680.80	+	3549.79i	0.604998	+	0.583463i
$79$	−3075.09			−0.492724			−0.246362	−	0.969178i	$-0.579235\pi$
$79$	−3075.09			−0.492724			−0.246362	+	0.969178i	$0.579235\pi$
$80$		−	10323.9i		−	1.61311i
$81$	−6543.78	+	475.065i	−0.997375	+	0.0724074i
$82$	−14427.5			−2.14567
$83$		−	5431.72i		−	0.788463i	−0.919011	−	0.394231i	$-0.871011\pi$
$83$		−	5431.72i		−	0.788463i	0.919011	−	0.394231i	$-0.128989\pi$
$84$	1227.89	−	1273.21i	0.174021	−	0.180444i
$85$	−8898.35			−1.23161
$86$		−	6293.57i		−	0.850943i
$87$	5083.05	+	4902.13i	0.671562	+	0.647658i
$88$	33.1612			0.00428218
$89$			10693.2i			1.34998i	0.737828	+	0.674989i	$0.235851\pi$
$89$			10693.2i			1.34998i	−0.737828	+	0.674989i	$0.764149\pi$
$90$	−627.733	−	17316.2i	−0.0774980	−	2.13780i
$91$	1323.44			0.159816
$92$			608.832i			0.0719319i
$93$	6508.34	−	6748.55i	0.752496	−	0.780269i
$94$	11977.7			1.35555
$95$		−	22116.1i		−	2.45054i
$96$	−9224.51	−	8896.17i	−1.00092	−	0.965296i
$97$	12979.5			1.37948			0.689740	−	0.724057i	$-0.257725\pi$
$97$	12979.5			1.37948			0.689740	+	0.724057i	$0.257725\pi$
$98$			12452.9i			1.29664i
$99$	549.521	−	19.9208i	0.0560679	−	0.00203253i
$100$	12784.5			1.27845
$101$		−	10719.9i		−	1.05087i	−0.850835	−	0.525434i	$-0.823903\pi$
$101$		−	10719.9i		−	1.05087i	0.850835	−	0.525434i	$-0.176097\pi$
$102$	−8088.60	+	8387.14i	−0.777451	+	0.806145i
$103$	−6184.26			−0.582926			−0.291463	−	0.956582i	$-0.594142\pi$
$103$	−6184.26			−0.582926			−0.291463	+	0.956582i	$0.594142\pi$
$104$		−	497.488i		−	0.0459956i
$105$	−3227.92	−	3113.03i	−0.292782	−	0.282361i
$106$	−15363.8			−1.36737
$107$		−	8100.09i		−	0.707493i	−0.935341	−	0.353747i	$-0.884908\pi$
$107$		−	8100.09i		−	0.707493i	0.935341	−	0.353747i	$-0.115092\pi$
$108$	−8208.38	−	7361.29i	−0.703737	−	0.631112i
$109$	163.281			0.0137430			0.00687151	−	0.999976i	$-0.497813\pi$
$109$	163.281			0.0137430			0.00687151	+	0.999976i	$0.497813\pi$
$110$			1452.23i			0.120019i
$111$	15197.9	−	15758.8i	1.23350	−	1.27902i
$112$	−3498.73			−0.278917
$113$			4303.61i			0.337036i	0.985699	+	0.168518i	$0.0538981\pi$
$113$			4303.61i			0.337036i	−0.985699	+	0.168518i	$0.946102\pi$
$114$	−20845.5	−	20103.6i	−1.60400	−	1.54690i
$115$	1543.55			0.116714
$116$			11867.2i			0.881927i
$117$	−298.855	−	8243.98i	−0.0218318	−	0.602234i
$118$	2528.30			0.181579
$119$			3015.61i			0.212952i
$120$	−1170.21	+	1213.40i	−0.0812643	+	0.0842636i
$121$	14594.9			0.996852
$122$		−	6970.80i		−	0.468342i
$123$	16753.1	+	16156.8i	1.10735	+	1.06794i
$124$	15755.6			1.02469
$125$		−	8446.85i		−	0.540598i
$126$	−5868.37	+	212.736i	−0.369638	+	0.0133998i
$127$	−9886.33			−0.612954			−0.306477	−	0.951878i	$-0.599150\pi$
$127$	−9886.33			−0.612954			−0.306477	+	0.951878i	$0.599150\pi$
$128$			2497.27i			0.152421i
$129$	−7047.93	+	7308.06i	−0.423528	+	0.439160i
$130$	21786.6			1.28915
$131$			4937.30i			0.287705i	0.989599	+	0.143852i	$0.0459491\pi$
$131$			4937.30i			0.287705i	−0.989599	+	0.143852i	$0.954051\pi$
$132$	665.148	+	641.473i	0.0381743	+	0.0368155i
$133$	−7495.05			−0.423712
$134$			40824.4i			2.27358i
$135$	−18662.8	+	20810.4i	−1.02402	+	1.14186i
$136$	1133.58			0.0612881
$137$		−	6806.81i		−	0.362662i	−0.983422	−	0.181331i	$-0.941959\pi$
$137$		−	6806.81i		−	0.362662i	0.983422	−	0.181331i	$-0.0580406\pi$
$138$	1403.09	−	1454.87i	0.0736760	−	0.0763952i
$139$	12888.9			0.667095			0.333548	−	0.942733i	$-0.391754\pi$
$139$	12888.9			0.667095			0.333548	+	0.942733i	$0.391754\pi$
$140$		−	7536.11i		−	0.384495i
$141$	−13908.4	−	13413.3i	−0.699581	−	0.674680i
$142$	26478.9			1.31318
$143$			691.388i			0.0338103i
$144$	790.073	+	21794.3i	0.0381015	+	1.05104i
$145$	30086.5			1.43098
$146$			14004.8i			0.657007i
$147$	13945.6	−	14460.3i	0.645358	−	0.669177i
$148$	36791.5			1.67967
$149$			26852.8i			1.20953i	0.796404	+	0.604765i	$0.206733\pi$
$149$			26852.8i			1.20953i	−0.796404	+	0.604765i	$0.793267\pi$
$150$	−30550.0	−	29462.6i	−1.35778	−	1.30945i
$151$	30292.0			1.32854			0.664269	−	0.747494i	$-0.268743\pi$
$151$	30292.0			1.32854			0.664269	+	0.747494i	$0.268743\pi$
$152$			2817.43i			0.121946i
$153$	18784.9	−	680.975i	0.802463	−	0.0290903i
$154$	492.155			0.0207520
$155$		−	39944.5i		−	1.66262i
$156$	9623.45	−	9978.63i	0.395441	−	0.410036i
$157$	11799.5			0.478703			0.239351	−	0.970933i	$-0.423065\pi$
$157$	11799.5			0.478703			0.239351	+	0.970933i	$0.423065\pi$
$158$			17155.7i			0.687218i
$159$	17840.3	+	17205.3i	0.705682	+	0.680564i
$160$	−54599.6			−2.13280
$161$		−	523.101i		−	0.0201806i
$162$	2650.35	+	36507.3i	0.100989	+	1.39107i
$163$	−17056.7			−0.641978			−0.320989	−	0.947083i	$-0.604015\pi$
$163$	−17056.7			−0.641978			−0.320989	+	0.947083i	$0.604015\pi$
$164$			39112.8i			1.45423i
$165$	1626.30	−	1686.32i	0.0597356	−	0.0619403i
$166$	−30303.2			−1.09969
$167$			31563.1i			1.13174i	0.824494	+	0.565870i	$0.191460\pi$
$167$			31563.1i			1.13174i	−0.824494	+	0.565870i	$0.808540\pi$
$168$	411.214	+	396.577i	0.0145697	+	0.0140511i
$169$	−18188.7			−0.636838
$170$			49643.2i			1.71776i
$171$	1692.51	+	46688.2i	0.0578814	+	1.59667i
$172$	−17061.8			−0.576725
$173$		−	48967.2i		−	1.63611i	−0.575139	−	0.818055i	$-0.695052\pi$
$173$		−	48967.2i		−	1.63611i	0.575139	−	0.818055i	$-0.304948\pi$
$174$	27348.6	−	28358.0i	0.903309	−	0.936649i
$175$	−10984.3			−0.358671
$176$		−	1827.80i		−	0.0590069i
$177$	−2935.84	−	2831.35i	−0.0937101	−	0.0903746i
$178$	59656.4			1.88286
$179$			55542.2i			1.73347i	0.498766	+	0.866737i	$0.333787\pi$
$179$			55542.2i			1.73347i	−0.498766	+	0.866737i	$0.666213\pi$
$180$	−46944.0	+	1701.78i	−1.44889	+	0.0525241i
$181$	−29763.3			−0.908499			−0.454249	−	0.890875i	$-0.650093\pi$
$181$	−29763.3			−0.908499			−0.454249	+	0.890875i	$0.650093\pi$
$182$		−	7383.37i		−	0.222901i
$183$	−7806.33	+	8094.45i	−0.233101	+	0.241705i
$184$	−196.637			−0.00580803
$185$		−	93276.1i		−	2.72538i
$186$	−37649.7	−	36309.5i	−1.08827	−	1.04953i
$187$	−1575.41			−0.0450515
$188$		−	32471.3i		−	0.918722i
$189$	7052.54	+	6324.73i	0.197434	+	0.177059i
$190$	−123384.			−3.41785
$191$			12576.4i			0.344739i	0.985032	+	0.172369i	$0.0551423\pi$
$191$			12576.4i			0.344739i	−0.985032	+	0.172369i	$0.944858\pi$
$192$	−22717.0	+	23555.5i	−0.616239	+	0.638983i
$193$	16944.0			0.454886			0.227443	−	0.973791i	$-0.426963\pi$
$193$	16944.0			0.454886			0.227443	+	0.973791i	$0.426963\pi$
$194$		−	72411.8i		−	1.92400i
$195$	−25298.4	−	24397.9i	−0.665310	−	0.641629i
$196$	33759.8			0.878795
$197$			37753.7i			0.972808i	0.873734	+	0.486404i	$0.161692\pi$
$197$			37753.7i			0.972808i	−0.873734	+	0.486404i	$0.838308\pi$
$198$	−111.137	−	3065.74i	−0.00283484	−	0.0781996i
$199$	−41087.8			−1.03754			−0.518772	−	0.854913i	$-0.673611\pi$
$199$	−41087.8			−1.03754			−0.518772	+	0.854913i	$0.673611\pi$
$200$			4129.06i			0.103227i
$201$	45717.7	−	47405.0i	1.13160	−	1.17336i
$202$	−59805.5			−1.46568
$203$		−	10196.2i		−	0.247425i
$204$	22737.5	+	21928.1i	0.546363	+	0.526916i
$205$	99161.3			2.35958
$206$			34501.5i			0.813025i
$207$	−3258.51	+	118.125i	−0.0760462	+	0.00275677i
$208$	−27420.8			−0.633803
$209$		−	3915.54i		−	0.0896395i
$210$	−17367.4	+	18008.4i	−0.393818	+	0.408353i
$211$	−16254.8			−0.365104			−0.182552	−	0.983196i	$-0.558436\pi$
$211$	−16254.8			−0.365104			−0.182552	+	0.983196i	$0.558436\pi$
$212$			41651.1i			0.926734i
$213$	−30747.1	−	29652.7i	−0.677713	−	0.653590i
$214$	−45189.8			−0.986763
$215$			43256.2i			0.935775i
$216$	2377.50	−	2651.09i	0.0509581	−	0.0568221i
$217$	−13537.0			−0.287477
$218$		−	910.931i		−	0.0191678i
$219$	15683.4	−	16262.2i	0.327003	−	0.339072i
$220$	3936.99			0.0813428
$221$			23634.4i			0.483905i
$222$	−87917.4	−	84788.0i	−1.78389	−	1.72040i
$223$	82199.1			1.65294			0.826471	−	0.562980i	$-0.190345\pi$
$223$	82199.1			1.65294			0.826471	+	0.562980i	$0.190345\pi$
$224$			18503.5i			0.368773i
$225$	2480.44	+	68423.5i	0.0489963	+	1.35157i
$226$	24009.5			0.470074
$227$			29189.5i			0.566468i	0.959051	+	0.283234i	$0.0914073\pi$
$227$			29189.5i			0.566468i	−0.959051	+	0.283234i	$0.908593\pi$
$228$	−54500.6	+	56512.1i	−1.04841	+	1.08711i
$229$	−28329.3			−0.540212			−0.270106	−	0.962831i	$-0.587059\pi$
$229$	−28329.3			−0.540212			−0.270106	+	0.962831i	$0.587059\pi$
$230$		−	8611.34i		−	0.162785i
$231$	−571.487	−	551.145i	−0.0107098	−	0.0103286i
$232$	−3832.79			−0.0712098
$233$		−	12095.0i		−	0.222790i	−0.993776	−	0.111395i	$-0.964468\pi$
$233$		−	12095.0i		−	0.222790i	0.993776	−	0.111395i	$-0.0355319\pi$
$234$	−45992.6	+	1667.29i	−0.839955	+	0.0304494i
$235$	−82323.3			−1.49069
$236$		−	6854.20i		−	0.123064i
$237$	19212.0	−	19921.1i	0.342039	−	0.354663i
$238$	16823.9			0.297010
$239$			96293.0i			1.68577i	0.538091	+	0.842886i	$0.319145\pi$
$239$			96293.0i			1.68577i	−0.538091	+	0.842886i	$0.680855\pi$
$240$	66880.6	+	64500.0i	1.16112	+	1.11979i
$241$	61200.7			1.05371			0.526856	−	0.849954i	$-0.323371\pi$
$241$	61200.7			1.05371			0.526856	+	0.849954i	$0.323371\pi$
$242$		−	81424.0i		−	1.39034i
$243$	37805.5	−	45360.0i	0.640239	−	0.768176i
$244$	−18897.8			−0.317418
$245$		−	85589.9i		−	1.42590i
$246$	90137.6	−	93464.4i	1.48948	−	1.54446i
$247$	−58741.5			−0.962833
$248$			5088.63i			0.0827366i
$249$	35187.8	+	33935.3i	0.567536	+	0.547335i
$250$	−47124.3			−0.753990
$251$		−	101001.i		−	1.60317i	−0.597879	−	0.801586i	$-0.703990\pi$
$251$		−	101001.i		−	1.60317i	0.597879	−	0.801586i	$-0.296010\pi$
$252$	576.725	+	15909.1i	0.00908171	+	0.250521i
$253$	273.277			0.00426935
$254$			55155.1i			0.854906i
$255$	55593.5	−	57645.4i	0.854956	−	0.886511i
$256$	72109.8			1.10031
$257$			36299.1i			0.549578i	0.961505	+	0.274789i	$0.0886080\pi$
$257$			36299.1i			0.549578i	−0.961505	+	0.274789i	$0.911392\pi$
$258$	40771.1	+	39319.9i	0.612510	+	0.590708i
$259$	−31610.8			−0.471234
$260$		−	59063.2i		−	0.873717i
$261$	−63514.0	+	2302.46i	−0.932370	+	0.0337996i
$262$	27544.9			0.401271
$263$			734.663i			0.0106213i	0.999986	+	0.00531064i	$0.00169044\pi$
$263$			734.663i			0.0106213i	−0.999986	+	0.00531064i	$0.998310\pi$
$264$	−207.179	+	214.825i	−0.00297261	+	0.00308232i
$265$	105597.			1.50369
$266$			41814.3i			0.590965i
$267$	−69272.6	−	66806.9i	−0.971715	−	0.937128i
$268$	110675.			1.54091
$269$			51411.5i			0.710487i	0.934774	+	0.355243i	$0.115602\pi$
$269$			51411.5i			0.710487i	−0.934774	+	0.355243i	$0.884398\pi$
$270$	116100.	+	104118.i	1.59259	+	1.42823i
$271$	−17169.8			−0.233791			−0.116895	−	0.993144i	$-0.537294\pi$
$271$	−17169.8			−0.233791			−0.116895	+	0.993144i	$0.537294\pi$
$272$		−	62481.6i		−	0.844528i
$273$	−8268.35	+	8573.52i	−0.110941	+	0.115036i
$274$	−37974.7			−0.505816
$275$		−	5738.39i		−	0.0758795i
$276$	−3944.14	−	3803.75i	−0.0517767	−	0.0499337i
$277$	23472.2			0.305911			0.152955	−	0.988233i	$-0.451121\pi$
$277$	23472.2			0.305911			0.152955	+	0.988233i	$0.451121\pi$
$278$		−	71906.5i		−	0.930419i
$279$	3056.88	+	84324.8i	0.0392708	+	1.08330i
$280$	2433.96			0.0310455
$281$			11914.9i			0.150896i	0.997150	+	0.0754479i	$0.0240387\pi$
$281$			11914.9i			0.150896i	−0.997150	+	0.0754479i	$0.975961\pi$
$282$	−74831.9	+	77593.8i	−0.940997	+	0.975728i
$283$	−44053.2			−0.550053			−0.275027	−	0.961437i	$-0.588687\pi$
$283$	−44053.2			−0.550053			−0.275027	+	0.961437i	$0.588687\pi$
$284$		−	71784.1i		−	0.890004i
$285$	143273.	+	138173.i	1.76390	+	1.70112i
$286$	3857.20			0.0471564
$287$		−	33605.3i		−	0.407985i
$288$	115262.	−	4178.41i	1.38964	−	0.0503763i
$289$	29667.2			0.355207
$290$		−	167850.i		−	1.99584i
$291$	−81091.1	+	84084.1i	−0.957607	+	0.992951i
$292$	37966.8			0.445285
$293$			82313.8i			0.958820i	0.877591	+	0.479410i	$0.159149\pi$
$293$			82313.8i			0.958820i	−0.877591	+	0.479410i	$0.840851\pi$
$294$	−80672.7	−	77801.2i	−0.933323	−	0.900102i
$295$	−17377.2			−0.199680
$296$			11882.7i			0.135622i
$297$	−3304.15	+	3684.37i	−0.0374582	+	0.0417687i
$298$	149810.			1.68697
$299$		−	4099.73i		−	0.0458578i
$300$	−79872.8	+	82820.8i	−0.887475	+	0.920231i
$301$	14659.3			0.161801
$302$		−	168997.i		−	1.85295i
$303$	69445.7	+	66973.9i	0.756415	+	0.729491i
$304$	155293.			1.68037
$305$			47910.8i			0.515031i
$306$	−3799.11	−	104799.i	−0.0405732	−	1.11922i
$307$	−37488.0			−0.397755			−0.198878	−	0.980024i	$-0.563730\pi$
$307$	−37488.0			−0.397755			−0.198878	+	0.980024i	$0.563730\pi$
$308$		−	1334.23i		−	0.0140646i
$309$	38636.9	−	40062.9i	0.404656	−	0.419591i
$310$	−222847.			−2.31891
$311$		−	11774.6i		−	0.121738i	−0.998146	−	0.0608688i	$-0.980613\pi$
$311$		−	11774.6i		−	0.121738i	0.998146	−	0.0608688i	$-0.0193871\pi$
$312$	3222.83	+	3108.12i	0.0331077	+	0.0319292i
$313$	−114514.			−1.16888			−0.584442	−	0.811435i	$-0.698687\pi$
$313$	−114514.			−1.16888			−0.584442	+	0.811435i	$0.698687\pi$
$314$		−	65828.8i		−	0.667662i
$315$	40333.7	−	1462.15i	0.406487	−	0.0147357i
$316$	46509.0			0.465760
$317$		−	113216.i		−	1.12665i	−0.826235	−	0.563325i	$-0.809522\pi$
$317$		−	113216.i		−	1.12665i	0.826235	−	0.563325i	$-0.190478\pi$
$318$	95987.3	−	99530.0i	0.949204	−	0.984237i
$319$	5326.65			0.0523447
$320$			139424.i			1.36156i
$321$	52474.1	+	50606.3i	0.509254	+	0.491128i
$322$	−2918.34			−0.0281465
$323$		−	133849.i		−	1.28295i
$324$	98970.9	−	7185.08i	0.942795	−	0.0684450i
$325$	−86088.0			−0.815034
$326$			95158.2i			0.895388i
$327$	−1020.12	+	1057.77i	−0.00954013	+	0.00989224i
$328$	−12632.4			−0.117419
$329$			27899.0i			0.257749i
$330$	−9407.88	−	9073.01i	−0.0863901	−	0.0833151i
$331$	−188979.			−1.72487			−0.862437	−	0.506164i	$-0.831063\pi$
$331$	−188979.			−1.72487			−0.862437	+	0.506164i	$0.831063\pi$
$332$			82151.6i			0.745315i
$333$	7138.26	+	196911.i	0.0643730	+	1.77574i
$334$	176088.			1.57847
$335$		−	280589.i		−	2.50024i
$336$	21858.8	−	22665.5i	0.193619	−	0.200765i
$337$	−137175.			−1.20786			−0.603929	−	0.797038i	$-0.706399\pi$
$337$	−137175.			−1.20786			−0.603929	+	0.797038i	$0.706399\pi$
$338$			101474.i			0.888218i
$339$	−27879.7	−	26887.3i	−0.242599	−	0.233964i
$340$	134582.			1.16421
$341$		−	7071.96i		−	0.0608179i
$342$	260470.	−	9442.38i	2.22693	−	0.0807290i
$343$	−60206.3			−0.511745
$344$		−	5510.52i		−	0.0465667i
$345$	−9643.50	+	9999.43i	−0.0810208	+	0.0840111i
$346$	−273184.			−2.28194
$347$		−	123162.i		−	1.02286i	−0.859325	−	0.511431i	$-0.829116\pi$
$347$		−	123162.i		−	1.02286i	0.859325	−	0.511431i	$-0.170884\pi$
$348$	−76878.2	−	74141.8i	−0.634812	−	0.612216i
$349$	177581.			1.45796			0.728979	−	0.684536i	$-0.239995\pi$
$349$	177581.			1.45796			0.728979	+	0.684536i	$0.239995\pi$
$350$			61280.6i			0.500250i
$351$	55273.4	+	49569.2i	0.448644	+	0.402344i
$352$	−9666.58			−0.0780167
$353$		−	134012.i		−	1.07546i	−0.843117	−	0.537731i	$-0.819282\pi$
$353$		−	134012.i		−	1.07546i	0.843117	−	0.537731i	$-0.180718\pi$
$354$	−15795.9	+	16378.9i	−0.126048	+	0.130700i
$355$	−181992.			−1.44409
$356$		−	161728.i		−	1.27610i
$357$	−19535.7	−	18840.4i	−0.153283	−	0.147827i
$358$	309866.			2.41773
$359$			214315.i			1.66289i	0.555606	+	0.831446i	$0.312486\pi$
$359$			214315.i			1.66289i	−0.555606	+	0.831446i	$0.687514\pi$
$360$	−549.630	−	15161.7i	−0.00424097	−	0.116988i
$361$	202350.			1.55271
$362$			166047.i			1.26711i
$363$	−91183.5	+	94548.9i	−0.691995	+	0.717535i
$364$	−20016.2			−0.151071
$365$		−	96255.7i		−	0.722505i
$366$	45158.3	+	43550.9i	0.337113	+	0.325114i
$367$	−160738.			−1.19340			−0.596700	−	0.802465i	$-0.703522\pi$
$367$	−160738.			−1.19340			−0.596700	+	0.802465i	$0.703522\pi$
$368$			10838.3i			0.0800326i
$369$	−209334.	+	7588.64i	−1.53740	+	0.0557328i
$370$	−520381.			−3.80117
$371$		−	35786.2i		−	0.259996i
$372$	−98434.9	+	102068.i	−0.711317	+	0.737570i
$373$	165801.			1.19171			0.595854	−	0.803093i	$-0.296814\pi$
$373$	165801.			1.19171			0.595854	+	0.803093i	$0.296814\pi$
$374$			8789.08i			0.0628348i
$375$	54720.5	+	52772.7i	0.389123	+	0.375273i
$376$	10487.4			0.0741808
$377$		−	79911.0i		−	0.562243i
$378$	35285.2	−	39345.6i	0.246950	−	0.275368i
$379$	−200893.			−1.39858			−0.699289	−	0.714839i	$-0.746500\pi$
$379$	−200893.			−1.39858			−0.699289	+	0.714839i	$0.746500\pi$
$380$			334494.i			2.31644i
$381$	61766.1	−	64045.7i	0.425500	−	0.441205i
$382$	70162.9			0.480818
$383$			106868.i			0.728538i	0.931294	+	0.364269i	$0.118681\pi$
$383$			106868.i			0.728538i	−0.931294	+	0.364269i	$0.881319\pi$
$384$	−16177.8	−	15602.0i	−0.109713	−	0.105808i
$385$	−3382.62			−0.0228208
$386$		−	94529.6i		−	0.634444i
$387$	−3310.32	−	91315.9i	−0.0221028	−	0.609712i
$388$	−196308.			−1.30399
$389$		−	232911.i		−	1.53918i	−0.638536	−	0.769592i	$-0.720459\pi$
$389$		−	232911.i		−	1.53918i	0.638536	−	0.769592i	$-0.279541\pi$
$390$	−136114.	+	141138.i	−0.894900	+	0.927929i
$391$	9341.72			0.0611045
$392$			10903.5i			0.0709569i
$393$	−31984.9	−	30846.4i	−0.207090	−	0.199719i
$394$	210625.			1.35681
$395$		−	117912.i		−	0.755727i
$396$	−8311.19	+	301.291i	−0.0529996	+	0.00192130i
$397$	−212073.			−1.34557			−0.672783	−	0.739840i	$-0.734901\pi$
$397$	−212073.			−1.34557			−0.672783	+	0.739840i	$0.734901\pi$
$398$			229226.i			1.44710i
$399$	46826.2	−	48554.5i	0.294133	−	0.304989i
$400$	227588.			1.42242
$401$			11049.0i			0.0687121i	0.999410	+	0.0343560i	$0.0109380\pi$
$401$			11049.0i			0.0687121i	−0.999410	+	0.0343560i	$0.989062\pi$
$402$	−264469.	−	255056.i	−1.63653	−	1.57827i
$403$	−106094.			−0.653254
$404$			162132.i			0.993360i
$405$	−18216.1	−	250917.i	−0.111057	−	1.52975i
$406$	−56883.6			−0.345092
$407$		−	16514.1i		−	0.0996930i
$408$	−7082.21	+	7343.60i	−0.0425450	+	0.0441152i
$409$	261486.			1.56315			0.781577	−	0.623809i	$-0.214416\pi$
$409$	261486.			1.56315			0.781577	+	0.623809i	$0.214416\pi$
$410$		−	553213.i		−	3.29098i
$411$	44095.9	+	42526.4i	0.261045	+	0.251753i
$412$	93533.4			0.551026
$413$			5889.05i			0.0345259i
$414$	659.011	+	18179.0i	0.00384496	+	0.106064i
$415$	208276.			1.20932
$416$			145019.i			0.837989i
$417$	−80525.3	+	83497.3i	−0.463084	+	0.480176i
$418$	−21844.5			−0.125023
$419$		−	199009.i		−	1.13356i	−0.823870	−	0.566779i	$-0.808189\pi$
$419$		−	199009.i		−	1.13356i	0.823870	−	0.566779i	$-0.191811\pi$
$420$	48820.5	+	47082.7i	0.276760	+	0.266909i
$421$	137054.			0.773262			0.386631	−	0.922235i	$-0.373639\pi$
$421$	137054.			0.773262			0.386631	+	0.922235i	$0.373639\pi$
$422$			90684.2i			0.509222i
$423$	173788.	−	6300.06i	0.971271	−	0.0352098i
$424$	−13452.2			−0.0748277
$425$		−	196161.i		−	1.08601i
$426$	−165430.	+	171536.i	−0.911583	+	0.945227i
$427$	16236.7			0.0890519
$428$			122509.i			0.668776i
$429$	−4478.96	−	4319.53i	−0.0243367	−	0.0234705i
$430$	241323.			1.30515
$431$			170227.i			0.916377i	0.888855	+	0.458188i	$0.151501\pi$
$431$			170227.i			0.916377i	−0.888855	+	0.458188i	$0.848499\pi$
$432$	−146124.	−	131045.i	−0.782988	−	0.702185i
$433$	265080.			1.41384			0.706921	−	0.707293i	$-0.250084\pi$
$433$	265080.			1.41384			0.706921	+	0.707293i	$0.250084\pi$
$434$			75521.9i			0.400953i
$435$	−187969.	+	194906.i	−0.993361	+	1.03002i
$436$	−2469.53			−0.0129909
$437$			23218.1i			0.121580i
$438$	−90725.8	−	87496.5i	−0.472915	−	0.456081i
$439$	−291195.			−1.51097			−0.755484	−	0.655167i	$-0.772598\pi$
$439$	−291195.			−1.51097			−0.755484	+	0.655167i	$0.772598\pi$
$440$			1271.55i			0.00656790i
$441$	6550.04	+	180684.i	0.0336796	+	0.929060i
$442$	131855.			0.674918
$443$			207205.i			1.05583i	0.849299	+	0.527913i	$0.177025\pi$
$443$			207205.i			1.05583i	−0.849299	+	0.527913i	$0.822975\pi$
$444$	−229860.	+	238343.i	−1.16599	+	1.20903i
$445$	−410023.			−2.07056
$446$		−	458583.i		−	2.30541i
$447$	−173958.	−	167766.i	−0.870621	−	0.839632i
$448$	47250.2			0.235422
$449$		−	77382.6i		−	0.383840i	−0.981411	−	0.191920i	$-0.938529\pi$
$449$		−	77382.6i		−	0.383840i	0.981411	−	0.191920i	$-0.0614715\pi$
$450$	381730.	−	13838.2i	1.88508	−	0.0683367i
$451$	17556.0			0.0863122
$452$		−	65089.6i		−	0.318592i
$453$	−189253.	+	196238.i	−0.922244	+	0.956283i
$454$	162846.			0.790071
$455$			50746.4i			0.245122i
$456$	−18251.9	−	17602.3i	−0.0877766	−	0.0846523i
$457$	−117220.			−0.561268			−0.280634	−	0.959815i	$-0.590545\pi$
$457$	−117220.			−0.561268			−0.280634	+	0.959815i	$0.590545\pi$
$458$			158047.i			0.753451i
$459$	−112949.	+	125947.i	−0.536115	+	0.597808i
$460$	−23345.3			−0.110327
$461$			295320.i			1.38960i	0.719202	+	0.694802i	$0.244508\pi$
$461$			295320.i			1.38960i	−0.719202	+	0.694802i	$0.755492\pi$
$462$	−3074.80	+	3188.29i	−0.0144057	+	0.0149373i
$463$	54174.8			0.252718			0.126359	−	0.991985i	$-0.459671\pi$
$463$	54174.8			0.252718			0.126359	+	0.991985i	$0.459671\pi$
$464$			211258.i			0.981245i
$465$	258769.	+	249558.i	1.19676	+	1.15416i
$466$	−67477.4			−0.310732
$467$			335342.i			1.53764i	0.639467	+	0.768819i	$0.279155\pi$
$467$			335342.i			1.53764i	−0.639467	+	0.768819i	$0.720845\pi$
$468$	4520.01	+	124685.i	0.0206370	+	0.569277i
$469$	−95090.3			−0.432305
$470$			459275.i			2.07911i
$471$	−73719.1	+	76440.0i	−0.332306	+	0.344571i
$472$	2213.73			0.00993665
$473$			7658.28i			0.0342302i
$474$	−111138.	−	107182.i	−0.494660	−	0.477053i
$475$	487543.			2.16086
$476$		−	45609.3i		−	0.201298i
$477$	−222919.	+	8081.12i	−0.979741	+	0.0355169i
$478$	537212.			2.35120
$479$			352835.i			1.53780i	0.639367	+	0.768902i	$0.279197\pi$
$479$			352835.i			1.53780i	−0.639367	+	0.768902i	$0.720803\pi$
$480$	341118.	−	353708.i	1.48055	−	1.53519i
$481$	−247746.			−1.07082
$482$		−	341434.i		−	1.46965i
$483$	3388.76	+	3268.14i	0.0145260	+	0.0140090i
$484$	−220740.			−0.942301
$485$			497691.i			2.11581i
$486$	−253060.	−	210914.i	−1.07140	−	0.892962i
$487$	207837.			0.876324			0.438162	−	0.898896i	$-0.355630\pi$
$487$	207837.			0.876324			0.438162	+	0.898896i	$0.355630\pi$
$488$		−	6103.49i		−	0.0256294i
$489$	106564.	−	110497.i	0.445649	−	0.462097i
$490$	−477500.			−1.98875
$491$			12389.1i			0.0513899i	0.999670	+	0.0256950i	$0.00817986\pi$
$491$			12389.1i			0.0513899i	−0.999670	+	0.0256950i	$0.991820\pi$
$492$	−253381.	−	244362.i	−1.04675	−	1.00949i
$493$	182086.			0.749176
$494$			327714.i			1.34289i
$495$	763.852	+	21071.0i	0.00311745	+	0.0859954i
$496$	280478.			1.14008
$497$			61676.1i			0.249692i
$498$	189323.	−	196310.i	0.763386	−	0.791561i
$499$	−50253.7			−0.201821			−0.100911	−	0.994895i	$-0.532176\pi$
$499$	−50253.7			−0.201821			−0.100911	+	0.994895i	$0.532176\pi$
$500$			127754.i			0.511015i
$501$	−204472.	−	197194.i	−0.814628	−	0.785632i
$502$	−563480.			−2.23600
$503$			362596.i			1.43314i	0.697517	+	0.716568i	$0.254288\pi$
$503$			362596.i			1.43314i	−0.697517	+	0.716568i	$0.745712\pi$
$504$	−5138.22	+	186.267i	−0.0202279	+	0.000733289i
$505$	411047.			1.61179
$506$		−	1524.59i		−	0.00595460i
$507$	113636.	−	117830.i	0.442080	−	0.458397i
$508$	149525.			0.579411
$509$			169930.i			0.655896i	0.944696	+	0.327948i	$0.106357\pi$
$509$			169930.i			0.655896i	−0.944696	+	0.327948i	$0.893643\pi$
$510$	−321599.	−	310152.i	−1.23644	−	1.19243i
$511$	−32620.6			−0.124925
$512$		−	362339.i		−	1.38221i
$513$	−313030.	−	280726.i	−1.18947	−	1.06671i
$514$	202510.			0.766514
$515$		−	237131.i		−	0.894077i
$516$	106596.	−	110530.i	0.400351	−	0.415127i
$517$	−14574.9			−0.0545286
$518$			176355.i			0.657245i
$519$	317220.	+	305928.i	1.17767	+	1.13576i
$520$	19075.9			0.0705469
$521$			68945.7i			0.253999i	0.991903	+	0.126999i	$0.0405346\pi$
$521$			68945.7i			0.253999i	−0.991903	+	0.126999i	$0.959465\pi$
$522$	12845.3	+	354340.i	0.0471414	+	1.30041i
$523$	−408744.			−1.49434			−0.747168	−	0.664636i	$-0.768587\pi$
$523$	−408744.			−1.49434			−0.747168	+	0.664636i	$0.768587\pi$
$524$		−	74673.9i		−	0.271961i
$525$	68625.7	−	71158.6i	0.248982	−	0.258172i
$526$	4098.63			0.0148138
$527$		−	241748.i		−	0.870447i
$528$	11840.9	+	11419.4i	0.0424733	+	0.0409615i
$529$	278221.			0.994209
$530$		−	589115.i		−	2.09724i
$531$	36684.1	−	1329.85i	0.130103	−	0.00471642i
$532$	113358.			0.400525
$533$		−	263377.i		−	0.927093i
$534$	−372711.	+	386467.i	−1.30704	+	1.35528i
$535$	310593.			1.08513
$536$			35745.0i			0.124419i
$537$	−359814.	−	347007.i	−1.24776	−	1.20334i
$538$	286821.			0.990938
$539$		−	15153.2i		−	0.0521588i
$540$	282264.	−	314745.i	0.967983	−	1.07937i
$541$	−362238.			−1.23766			−0.618828	−	0.785527i	$-0.712392\pi$
$541$	−362238.			−1.23766			−0.618828	+	0.785527i	$0.712392\pi$
$542$			95789.1i			0.326075i
$543$	185950.	−	192813.i	0.630662	−	0.653939i
$544$	−330443.			−1.11660
$545$			6260.89i			0.0210787i
$546$	47831.0	+	46128.5i	0.160444	+	0.154733i
$547$	179531.			0.600020			0.300010	−	0.953936i	$-0.403010\pi$
$547$	179531.			0.600020			0.300010	+	0.953936i	$0.403010\pi$
$548$			102949.i			0.342816i
$549$	−3666.53	−	101142.i	−0.0121650	−	0.335573i
$550$	−32014.0			−0.105832
$551$			452561.i			1.49064i
$552$	1228.51	−	1273.85i	0.00403182	−	0.00418063i
$553$	−39959.9			−0.130670
$554$		−	130950.i		−	0.426663i
$555$	604262.	+	582754.i	1.96173	+	1.89190i
$556$	−194938.			−0.630589
$557$		−	423794.i		−	1.36598i	−0.730427	−	0.682991i	$-0.760679\pi$
$557$		−	423794.i		−	1.36598i	0.730427	−	0.682991i	$-0.239321\pi$
$558$	470442.	−	17054.1i	1.51091	−	0.0547723i
$559$	114890.			0.367672
$560$		−	134157.i		−	0.427795i
$561$	9842.54	−	10205.8i	0.0312739	−	0.0324281i
$562$	66472.3			0.210459
$563$		−	554411.i		−	1.74910i	−0.484933	−	0.874552i	$-0.661156\pi$
$563$		−	554411.i		−	1.74910i	0.484933	−	0.874552i	$-0.338844\pi$
$564$	210356.	+	202869.i	0.661297	+	0.637759i
$565$	−165019.			−0.516937
$566$			245770.i			0.767177i
$567$	−85034.6	+	6173.34i	−0.264502	+	0.0192023i
$568$	23184.4			0.0718620
$569$		−	490601.i		−	1.51532i	−0.652651	−	0.757659i	$-0.726343\pi$
$569$		−	490601.i		−	1.51532i	0.652651	−	0.757659i	$-0.273657\pi$
$570$	770858.	−	799309.i	2.37260	−	2.46017i
$571$	−540936.			−1.65910			−0.829552	−	0.558429i	$-0.811404\pi$
$571$	−540936.			−1.65910			−0.829552	+	0.558429i	$0.811404\pi$
$572$		−	10456.8i		−	0.0319601i
$573$	−81472.7	−	78572.7i	−0.248143	−	0.239311i
$574$	−187481.			−0.569029
$575$			34027.0i			0.102917i
$576$	−10669.9	−	294331.i	−0.0321599	−	0.887139i
$577$	−469761.			−1.41100			−0.705498	−	0.708712i	$-0.749277\pi$
$577$	−469761.			−1.41100			−0.705498	+	0.708712i	$0.749277\pi$
$578$		−	165511.i		−	0.495418i
$579$	−105860.	+	109767.i	−0.315773	+	0.327427i
$580$	−455040.			−1.35268
$581$		−	70583.7i		−	0.209099i
$582$	469099.	+	452402.i	1.38490	+	1.33561i
$583$	18695.3			0.0550042
$584$			12262.3i			0.0359539i
$585$	316110.	−	11459.4i	0.923691	−	0.0334850i
$586$	459222.			1.33730
$587$		−	215040.i		−	0.624083i	−0.950068	−	0.312041i	$-0.898987\pi$
$587$		−	215040.i		−	0.624083i	0.950068	−	0.312041i	$-0.101013\pi$
$588$	−210918.	+	218703.i	−0.610042	+	0.632558i
$589$	600846.			1.73194
$590$			96946.0i			0.278501i
$591$	−244576.	−	235871.i	−0.700228	−	0.675304i
$592$	654957.			1.86883
$593$		−	573291.i		−	1.63029i	−0.579254	−	0.815147i	$-0.696656\pi$
$593$		−	573291.i		−	1.63029i	0.579254	−	0.815147i	$-0.303344\pi$
$594$	20554.8	+	18433.6i	0.0582561	+	0.0522441i
$595$	−115632.			−0.326620
$596$		−	406133.i		−	1.14334i
$597$	256701.	−	266175.i	0.720243	−	0.746825i
$598$	−22872.1			−0.0639593
$599$			178694.i			0.498032i	0.968499	+	0.249016i	$0.0801071\pi$
$599$			178694.i			0.498032i	−0.968499	+	0.249016i	$0.919893\pi$
$600$	−26748.9	−	25796.8i	−0.0743026	−	0.0716578i
$601$	668298.			1.85021			0.925106	−	0.379709i	$-0.123976\pi$
$601$	668298.			1.85021			0.925106	+	0.379709i	$0.123976\pi$
$602$		−	81783.2i		−	0.225669i
$603$	21473.0	+	592337.i	0.0590552	+	1.62905i
$604$	−458149.			−1.25583
$605$			559633.i			1.52895i
$606$	373642.	−	387433.i	1.01744	−	1.05500i
$607$	109937.			0.298379			0.149189	−	0.988809i	$-0.452334\pi$
$607$	109937.			0.298379			0.149189	+	0.988809i	$0.452334\pi$
$608$		−	821288.i		−	2.22172i
$609$	66052.8	+	63701.7i	0.178097	+	0.171758i
$610$	267291.			0.718331
$611$			218654.i			0.585701i
$612$	−284110.	+	10299.4i	−0.758549	+	0.0274984i
$613$	−205618.			−0.547193			−0.273597	−	0.961845i	$-0.588213\pi$
$613$	−205618.			−0.547193			−0.273597	+	0.961845i	$0.588213\pi$
$614$			209143.i			0.554762i
$615$	−619522.	+	642388.i	−1.63797	+	1.69843i
$616$	430.921			0.00113563
$617$			83595.6i			0.219590i	0.993954	+	0.109795i	$0.0350195\pi$
$617$			83595.6i			0.219590i	−0.993954	+	0.109795i	$0.964981\pi$
$618$	−223508.	−	215553.i	−0.585216	−	0.564386i
$619$	280975.			0.733308			0.366654	−	0.930357i	$-0.380503\pi$
$619$	280975.			0.733308			0.366654	+	0.930357i	$0.380503\pi$
$620$			604137.i			1.57164i
$621$	19592.7	−	21847.3i	0.0508055	−	0.0566519i
$622$	−65689.5			−0.169791
$623$			138955.i			0.358012i
$624$	171315.	−	177638.i	0.439973	−	0.456212i
$625$	−204417.			−0.523307
$626$			638868.i			1.63028i
$627$	25365.7	+	24462.8i	0.0645226	+	0.0622260i
$628$	−178461.			−0.452507
$629$		−	564517.i		−	1.42684i
$630$	−8157.22	−	225019.i	−0.0205523	−	0.566941i
$631$	−494877.			−1.24291			−0.621454	−	0.783451i	$-0.713458\pi$
$631$	−494877.			−1.24291			−0.621454	+	0.783451i	$0.713458\pi$
$632$			15021.2i			0.0376071i
$633$	101554.	−	105302.i	0.253448	−	0.262802i
$634$	−631623.			−1.57137
$635$		−	379085.i		−	0.940133i
$636$	−269825.	−	260221.i	−0.667064	−	0.643321i
$637$	−227331.			−0.560246
$638$		−	29717.0i		−	0.0730068i
$639$	384193.	−	13927.5i	0.940910	−	0.0341092i
$640$	−95756.1			−0.233780
$641$		−	389193.i		−	0.947217i	−0.880736	−	0.473608i	$-0.842951\pi$
$641$		−	389193.i		−	0.947217i	0.880736	−	0.473608i	$-0.157049\pi$
$642$	282329.	−	292749.i	0.684991	−	0.710273i
$643$	−527339.			−1.27546			−0.637732	−	0.770259i	$-0.720127\pi$
$643$	−527339.			−1.27546			−0.637732	+	0.770259i	$0.720127\pi$
$644$			7911.60i			0.0190762i
$645$	−280223.	−	270248.i	−0.673572	−	0.649596i
$646$	−746735.			−1.78937
$647$			36056.0i			0.0861328i	0.999072	+	0.0430664i	$0.0137127\pi$
$647$			36056.0i			0.0861328i	−0.999072	+	0.0430664i	$0.986287\pi$
$648$	2320.59	+	31965.0i	0.00552649	+	0.0761245i
$649$	−3076.54			−0.00730421
$650$			480278.i			1.13675i
$651$	84574.0	−	87695.5i	0.199561	−	0.206926i
$652$	257973.			0.606847
$653$			329386.i			0.772464i	0.922402	+	0.386232i	$0.126224\pi$
$653$			329386.i			0.772464i	−0.922402	+	0.386232i	$0.873776\pi$
$654$	5901.20	+	5691.15i	0.0137970	+	0.0133059i
$655$	−189318.			−0.441274
$656$			696281.i			1.61799i
$657$	7366.29	+	203201.i	0.0170655	+	0.470754i
$658$	155646.			0.359490
$659$		−	34206.6i		−	0.0787660i	−0.999224	−	0.0393830i	$-0.987461\pi$
$659$		−	34206.6i		−	0.0787660i	0.999224	−	0.0393830i	$-0.0125392\pi$
$660$	−24596.9	+	25504.7i	−0.0564666	+	0.0585507i
$661$	16004.0			0.0366290			0.0183145	−	0.999832i	$-0.494170\pi$
$661$	16004.0			0.0366290			0.0183145	+	0.999832i	$0.494170\pi$
$662$			1.05430e6i			2.40574i
$663$	−153109.	−	147659.i	−0.348316	−	0.335918i
$664$	−26532.8			−0.0601793
$665$		−	287393.i		−	0.649879i
$666$	1.09855e6	−	39823.8i	2.47669	−	0.0897831i
$667$	−31585.5			−0.0709964
$668$		−	477374.i		−	1.06981i
$669$	−513549.	+	532503.i	−1.14744	+	1.18979i
$670$	−1.56539e6			−3.48716
$671$			8482.36i			0.0188396i
$672$	−119870.	−	115603.i	−0.265443	−	0.255995i
$673$	599163.			1.32286			0.661432	−	0.750005i	$-0.269949\pi$
$673$	599163.			1.32286			0.661432	+	0.750005i	$0.269949\pi$
$674$			765290.i			1.68464i
$675$	−458759.	−	411415.i	−1.00688	−	0.902969i
$676$	275094.			0.601988
$677$			349265.i			0.762040i	0.924567	+	0.381020i	$0.124427\pi$
$677$			349265.i			0.762040i	−0.924567	+	0.381020i	$0.875573\pi$
$678$	−150002.	+	155539.i	−0.326316	+	0.338360i
$679$	168665.			0.365836
$680$			43466.6i			0.0940021i
$681$	−189096.	−	182365.i	−0.407744	−	0.393231i
$682$	−39454.0			−0.0848246
$683$		−	202624.i		−	0.434360i	−0.976132	−	0.217180i	$-0.930314\pi$
$683$		−	202624.i		−	0.434360i	0.976132	−	0.217180i	$-0.0696858\pi$
$684$	−25598.2	−	706133.i	−0.0547139	−	1.50929i
$685$	261003.			0.556242
$686$			335887.i			0.713747i
$687$	176991.	−	183523.i	0.375005	−	0.388845i
$688$	−303732.			−0.641673
$689$		−	280469.i		−	0.590809i
$690$	55786.1	+	53800.4i	0.117173	+	0.113002i
$691$	498749.			1.04454			0.522271	−	0.852779i	$-0.325085\pi$
$691$	498749.			1.04454			0.522271	+	0.852779i	$0.325085\pi$
$692$			740600.i			1.54658i
$693$	7140.87	−	258.866i	0.0148691	−	0.000539024i
$694$	−687110.			−1.42662
$695$			494218.i			1.02317i
$696$	23945.9	−	24829.6i	0.0494324	−	0.0512569i
$697$	600135.			1.23533
$698$		−	990710.i		−	2.03346i
$699$	78354.2	+	75565.3i	0.160364	+	0.154656i
$700$	166131.			0.339043
$701$			295314.i			0.600963i	0.953788	+	0.300482i	$0.0971474\pi$
$701$			295314.i			0.600963i	−0.953788	+	0.300482i	$0.902853\pi$
$702$	276543.	−	308366.i	0.561162	−	0.625738i
$703$	1.40306e6			2.83900
$704$			24684.3i			0.0498054i
$705$	514325.	−	533307.i	1.03481	−	1.07300i
$706$	−747644.			−1.49998
$707$		−	139302.i		−	0.278688i
$708$	44403.0	+	42822.5i	0.0885820	+	0.0854289i
$709$	288827.			0.574574			0.287287	−	0.957845i	$-0.407247\pi$
$709$	288827.			0.574574			0.287287	+	0.957845i	$0.407247\pi$
$710$			1.01532e6i			2.01412i
$711$	9023.63	+	248919.i	0.0178502	+	0.492401i
$712$	52233.9			0.103037
$713$			41934.7i			0.0824888i
$714$	−105109.	+	108988.i	−0.206179	+	0.213788i
$715$	−26510.8			−0.0518574
$716$		−	840044.i		−	1.63861i
$717$	−623807.	−	601603.i	−1.21342	−	1.17023i
$718$	1.19565e6			2.31929
$719$		−	701167.i		−	1.35632i	−0.734912	−	0.678162i	$-0.762777\pi$
$719$		−	701167.i		−	1.35632i	0.734912	−	0.678162i	$-0.237223\pi$
$720$	−835690.	+	30294.8i	−1.61206	+	0.0584391i
$721$	−80362.7			−0.154591
$722$		−	1.12890e6i		−	2.16561i
$723$	−382359.	+	396471.i	−0.731466	+	0.758463i
$724$	450153.			0.858783
$725$			663247.i			1.26182i
$726$	527482.	+	508706.i	1.00077	+	0.965148i
$727$	742674.			1.40517			0.702586	−	0.711599i	$-0.252029\pi$
$727$	742674.			1.40517			0.702586	+	0.711599i	$0.252029\pi$
$728$		−	6464.72i		−	0.0121980i
$729$	57657.2	+	528304.i	0.108492	+	0.994097i
$730$	−537004.			−1.00770
$731$			261791.i			0.489914i
$732$	118066.	−	122424.i	0.220345	−	0.228478i
$733$	628469.			1.16970			0.584852	−	0.811140i	$-0.301153\pi$
$733$	628469.			1.16970			0.584852	+	0.811140i	$0.301153\pi$
$734$			896744.i			1.66447i
$735$	554469.	+	534733.i	1.02637	+	0.989834i
$736$	57320.1			0.105816
$737$		−	49676.8i		−	0.0914574i
$738$	42336.5	+	1.16786e6i	0.0777324	+	2.14426i
$739$	317437.			0.581257			0.290628	−	0.956836i	$-0.406136\pi$
$739$	317437.			0.581257			0.290628	+	0.956836i	$0.406136\pi$
$740$			1.41075e6i			2.57624i
$741$	366994.	−	380540.i	0.668379	−	0.693048i
$742$	−199648.			−0.362625
$743$		−	854010.i		−	1.54698i	−0.633807	−	0.773492i	$-0.718509\pi$
$743$		−	854010.i		−	1.54698i	0.633807	−	0.773492i	$-0.281491\pi$
$744$	−32965.2	−	31791.9i	−0.0595539	−	0.0574341i
$745$	−1.02965e6			−1.85515
$746$		−	924992.i		−	1.66211i
$747$	−439681.	+	15939.0i	−0.787945	+	0.0285640i
$748$	23827.1			0.0425861
$749$		−	105258.i		−	0.187626i
$750$	294415.	−	305281.i	0.523405	−	0.542723i
$751$	−364327.			−0.645969			−0.322985	−	0.946404i	$-0.604686\pi$
$751$	−364327.			−0.645969			−0.322985	+	0.946404i	$0.604686\pi$
$752$		−	578049.i		−	1.02218i
$753$	654309.	+	631019.i	1.15397	+	1.11289i
$754$	−445818.			−0.784178
$755$			1.16153e6i			2.03768i
$756$	−106666.	−	95657.9i	−0.186630	−	0.167370i
$757$	−952412.			−1.66201			−0.831004	−	0.556266i	$-0.812234\pi$
$757$	−952412.			−1.66201			−0.831004	+	0.556266i	$0.812234\pi$
$758$			1.12077e6i			1.95064i
$759$	−1707.33	+	1770.35i	−0.00296370	+	0.00307309i
$760$	−108033.			−0.187037
$761$			814752.i			1.40688i	0.710756	+	0.703439i	$0.248353\pi$
$761$			814752.i			1.40688i	−0.710756	+	0.703439i	$0.751647\pi$
$762$	−357306.	−	344588.i	−0.615362	−	0.593459i
$763$	2121.79			0.00364462
$764$		−	190211.i		−	0.325873i
$765$	26111.5	+	720293.i	0.0446180	+	1.23080i
$766$	596211.			1.01611
$767$			46154.6i			0.0784557i
$768$	−450515.	+	467143.i	−0.763812	+	0.792003i
$769$	841756.			1.42342			0.711711	−	0.702473i	$-0.247921\pi$
$769$	841756.			1.42342			0.711711	+	0.702473i	$0.247921\pi$
$770$			18871.4i			0.0318289i
$771$	−235153.	−	226783.i	−0.395587	−	0.381506i
$772$	−256269.			−0.429993
$773$		−	972648.i		−	1.62778i	−0.581017	−	0.813892i	$-0.697345\pi$
$773$		−	972648.i		−	1.62778i	0.581017	−	0.813892i	$-0.302655\pi$
$774$	−509445.	+	18468.0i	−0.850384	+	0.0308275i
$775$	880564.			1.46608
$776$		−	63402.2i		−	0.105289i
$777$	197493.	−	204782.i	0.327121	−	0.339195i
$778$	−1.29939e6			−2.14675
$779$			1.49159e6i			2.45795i
$780$	382624.	+	369005.i	0.628902	+	0.606517i
$781$	−32220.7			−0.0528241
$782$		−	52116.7i		−	0.0852244i
$783$	381896.	−	425842.i	0.622904	−	0.694584i
$784$	600987.			0.977761
$785$			452446.i			0.734222i
$786$	−172090.	+	178441.i	−0.278555	+	0.288835i
$787$	994252.			1.60527			0.802633	−	0.596473i	$-0.203432\pi$
$787$	994252.			1.60527			0.802633	+	0.596473i	$0.203432\pi$
$788$		−	571003.i		−	0.919572i
$789$	−4759.30	−	4589.90i	−0.00764520	−	0.00737308i
$790$	−657824.			−1.05404
$791$			55924.2i			0.0893813i
$792$	−97.3092	−	2684.30i	−0.000155133	−	0.00427937i
$793$	127253.			0.202359
$794$			1.18314e6i			1.87670i
$795$	−659727.	+	684076.i	−1.04383	+	1.08236i
$796$	621429.			0.980766
$797$		−	1.16190e6i		−	1.82917i	−0.404395	−	0.914584i	$-0.632518\pi$
$797$		−	1.16190e6i		−	1.82917i	0.404395	−	0.914584i	$-0.367482\pi$
$798$	−270882.	−	261240.i	−0.425377	−	0.410236i
$799$	−498229.			−0.780433
$800$		−	1.20363e6i		−	1.88067i
$801$	865578.	−	31378.3i	1.34909	−	0.0489063i
$802$	61641.4			0.0958349
$803$		−	17041.6i		−	0.0264289i
$804$	−691453.	+	716974.i	−1.06967	+	1.10915i
$805$	20058.0			0.0309525
$806$			591893.i			0.911115i
$807$	−333055.	−	321200.i	−0.511409	−	0.493206i
$808$	−52364.4			−0.0802073
$809$			205268.i			0.313634i	0.987628	+	0.156817i	$0.0501234\pi$
$809$			205268.i			0.313634i	−0.987628	+	0.156817i	$0.949877\pi$
$810$	−1.39985e6	+	101626.i	−2.13359	+	0.154894i
$811$	−38421.9			−0.0584167			−0.0292084	−	0.999573i	$-0.509299\pi$
$811$	−38421.9			−0.0584167			−0.0292084	+	0.999573i	$0.509299\pi$
$812$			154211.i			0.233885i
$813$	107270.	−	111230.i	0.162293	−	0.168283i
$814$	−92130.7			−0.139045
$815$		−	654029.i		−	0.984650i
$816$	404769.	+	390361.i	0.607892	+	0.586255i
$817$	−650660.			−0.974788
$818$		−	1.45881e6i		−	2.18018i
$819$	−3883.53	−	107128.i	−0.00578974	−	0.159711i
$820$	−1.49976e6			−2.23045
$821$		−	916219.i		−	1.35929i	−0.733540	−	0.679646i	$-0.762133\pi$
$821$		−	916219.i		−	1.35929i	0.733540	−	0.679646i	$-0.237867\pi$
$822$	237251.	−	246008.i	0.351128	−	0.364087i
$823$	−188909.			−0.278903			−0.139452	−	0.990229i	$-0.544534\pi$
$823$	−188909.			−0.278903			−0.139452	+	0.990229i	$0.544534\pi$
$824$			30208.8i			0.0444917i
$825$	37174.5	+	35851.3i	0.0546182	+	0.0526741i
$826$	32854.5			0.0481543
$827$		−	981063.i		−	1.43445i	−0.696841	−	0.717226i	$-0.745412\pi$
$827$		−	981063.i		−	1.43445i	0.696841	−	0.717226i	$-0.254588\pi$
$828$	49283.0	−	1786.57i	0.0718847	−	0.00260591i
$829$	−190338.			−0.276959			−0.138479	−	0.990365i	$-0.544221\pi$
$829$	−190338.			−0.276959			−0.138479	+	0.990365i	$0.544221\pi$
$830$		−	1.16196e6i		−	1.68668i
$831$	−146646.	+	152058.i	−0.212357	+	0.220195i
$832$	370317.			0.534967
$833$		−	517999.i		−	0.746516i
$834$	465825.	+	449245.i	0.669716	+	0.645878i
$835$	−1.21027e6			−1.73583
$836$			59220.4i			0.0847341i
$837$	−565372.	−	507026.i	−0.807018	−	0.723735i
$838$	−1.11025e6			−1.58101
$839$		−	333477.i		−	0.473742i	−0.971541	−	0.236871i	$-0.923878\pi$
$839$		−	333477.i		−	0.473742i	0.971541	−	0.236871i	$-0.0761218\pi$
$840$	−15206.5	+	15767.7i	−0.0215511	+	0.0223466i
$841$	91623.4			0.129543
$842$		−	764613.i		−	1.07849i
$843$	−77187.2	−	74439.7i	−0.108615	−	0.104749i
$844$	245844.			0.345124
$845$		−	697435.i		−	0.976765i
$846$	−35147.5	−	969553.i	−0.0491082	−	1.35466i
$847$	189657.			0.264364
$848$			741467.i			1.03110i
$849$	275228.	−	285386.i	0.381836	−	0.395929i
$850$	−1.09437e6			−1.51470
$851$			97923.7i			0.135216i
$852$	465033.	+	448480.i	0.640626	+	0.617823i
$853$	−866917.			−1.19146			−0.595730	−	0.803185i	$-0.703137\pi$
$853$	−866917.			−1.19146			−0.595730	+	0.803185i	$0.703137\pi$
$854$		−	90583.6i		−	0.124203i
$855$	−1.79023e6	+	64898.1i	−2.44893	+	0.0887769i
$856$	−39567.2			−0.0539993
$857$			1.35844e6i			1.84960i	0.380455	+	0.924800i	$0.375768\pi$
$857$			1.35844e6i			1.84960i	−0.380455	+	0.924800i	$0.624232\pi$
$858$	−24098.3	+	24987.8i	−0.0327350	+	0.0339432i
$859$	−394658.			−0.534853			−0.267427	−	0.963578i	$-0.586173\pi$
$859$	−394658.			−0.534853			−0.267427	+	0.963578i	$0.586173\pi$
$860$		−	654225.i		−	0.884566i
$861$	217702.	+	209953.i	0.293668	+	0.283215i
$862$	949684.			1.27810
$863$		−	1.08545e6i		−	1.45744i	−0.684813	−	0.728719i	$-0.740116\pi$
$863$		−	1.08545e6i		−	1.45744i	0.684813	−	0.728719i	$-0.259884\pi$
$864$	−693048.	+	772800.i	−0.928401	+	1.03524i
$865$	1.87761e6			2.50942
$866$		−	1.47886e6i		−	1.97193i
$867$	−185350.	+	192191.i	−0.246578	+	0.255678i
$868$	204739.			0.271745
$869$		−	20875.8i		−	0.0276441i
$870$	1.08737e6	+	1.04866e6i	1.43661	+	1.38547i
$871$	−745258.			−0.982359
$872$		−	797.592i		−	0.00104893i
$873$	−38087.5	−	1.05065e6i	−0.0499751	−	1.37857i
$874$	129532.			0.169572
$875$		−	109764.i		−	0.143366i
$876$	−237202.	+	245957.i	−0.309108	+	0.320517i
$877$	1.31088e6			1.70437			0.852187	−	0.523238i	$-0.175276\pi$
$877$	1.31088e6			1.70437			0.852187	+	0.523238i	$0.175276\pi$
$878$			1.62456e6i			2.10739i
$879$	−533246.	−	514265.i	−0.690160	−	0.665594i
$880$	70085.8			0.0905033
$881$			671754.i			0.865483i	0.901518	+	0.432741i	$0.142454\pi$
$881$			671754.i			0.865483i	−0.901518	+	0.432741i	$0.857546\pi$
$882$	1.00803e6	−	36542.2i	1.29579	−	0.0469740i
$883$	−1.18159e6			−1.51546			−0.757732	−	0.652566i	$-0.773693\pi$
$883$	−1.18159e6			−1.51546			−0.757732	+	0.652566i	$0.773693\pi$
$884$		−	357457.i		−	0.457424i
$885$	108566.	−	112573.i	0.138614	−	0.143730i
$886$	1.15598e6			1.47259
$887$		−	1.41190e6i		−	1.79455i	−0.441472	−	0.897275i	$-0.645544\pi$
$887$		−	1.41190e6i		−	1.79455i	0.441472	−	0.897275i	$-0.354456\pi$
$888$	−76978.6	−	74238.6i	−0.0976212	−	0.0941464i
$889$	−128470.			−0.162554
$890$			2.28749e6i			2.88788i
$891$	−3225.06	−	44423.5i	−0.00406240	−	0.0559574i
$892$	−1.24321e6			−1.56249
$893$		−	1.23831e6i		−	1.55284i
$894$	−935955.	+	970499.i	−1.17106	+	1.21428i
$895$	−2.12973e6			−2.65876
$896$			32451.3i			0.0404218i
$897$	26558.9	+	25613.6i	0.0330085	+	0.0318336i
$898$	−431712.			−0.535354
$899$			817382.i			1.01136i
$900$	−37515.2	−	1.03487e6i	−0.0463151	−	1.27761i
$901$	639081.			0.787239
$902$		−	97943.6i		−	0.120382i
$903$	−91585.9	+	94966.1i	−0.112319	+	0.116464i
$904$	21022.2			0.0257242
$905$		−	1.14126e6i		−	1.39343i
$906$	1.09480e6	+	1.05583e6i	1.33376	+	1.28628i
$907$	871792.			1.05974			0.529869	−	0.848080i	$-0.322241\pi$
$907$	871792.			1.05974			0.529869	+	0.848080i	$0.322241\pi$
$908$		−	441475.i		−	0.535469i
$909$	−867741.	+	31456.7i	−1.05018	+	0.0380703i
$910$	283111.			0.341880
$911$			534453.i			0.643980i	0.946743	+	0.321990i	$0.104352\pi$
$911$			534453.i			0.643980i	−0.946743	+	0.321990i	$0.895648\pi$
$912$	−970211.	+	1.00602e6i	−1.16648	+	1.20953i
$913$	36874.1			0.0442365
$914$			653963.i			0.782819i
$915$	−310376.	−	299329.i	−0.370720	−	0.357525i
$916$	428464.			0.510650
$917$			64158.9i			0.0762989i
$918$	702647.	+	630135.i	0.833781	+	0.747736i
$919$	669335.			0.792524			0.396262	−	0.918138i	$-0.370307\pi$
$919$	669335.			0.792524			0.396262	+	0.918138i	$0.370307\pi$
$920$		−	7539.91i		−	0.00890821i
$921$	234211.	−	242855.i	0.276114	−	0.286305i
$922$	1.64757e6			1.93812
$923$			483378.i			0.567392i
$924$	8643.41	+	8335.76i	0.0101237	+	0.00976340i
$925$	2.05624e6			2.40321
$926$		−	302237.i		−	0.352473i
$927$	18147.3	+	500596.i	0.0211179	+	0.582543i
$928$	1.11727e6			1.29736
$929$			941965.i			1.09145i	0.837965	+	0.545724i	$0.183745\pi$
$929$			941965.i			1.09145i	−0.837965	+	0.545724i	$0.816255\pi$
$930$	1.39227e6	−	1.44365e6i	1.60974	−	1.66915i
$931$	1.28744e6			1.48535
$932$			182931.i			0.210598i
$933$	76278.2	+	73563.1i	0.0876268	+	0.0845078i
$934$	1.87085e6			2.14459
$935$		−	60407.9i		−	0.0690988i
$936$	−40270.1	+	1459.84i	−0.0459654	+	0.00166631i
$937$	−1.37284e6			−1.56365			−0.781827	−	0.623496i	$-0.785712\pi$
$937$	−1.37284e6			−1.56365			−0.781827	+	0.623496i	$0.785712\pi$
$938$			530502.i			0.602950i
$939$	715443.	−	741849.i	0.811416	−	0.841364i
$940$	1.24509e6			1.40911
$941$			86138.0i			0.0972782i	0.998816	+	0.0486391i	$0.0154884\pi$
$941$			86138.0i			0.0972782i	−0.998816	+	0.0486391i	$0.984512\pi$
$942$	426453.	+	411274.i	0.480584	+	0.463478i
$943$	−104102.			−0.117067
$944$		−	122017.i		−	0.136923i
$945$	−242518.	+	270425.i	−0.271569	+	0.302819i
$946$	42725.0			0.0477419
$947$			931042.i			1.03817i	0.854722	+	0.519086i	$0.173728\pi$
$947$			931042.i			1.03817i	−0.854722	+	0.519086i	$0.826272\pi$
$948$	−290570.	+	301295.i	−0.323322	+	0.335255i
$949$	−255660.			−0.283877
$950$		−	2.71997e6i		−	3.01381i
$951$	733437.	+	707331.i	0.810964	+	0.782098i
$952$	14730.6			0.0162535
$953$		−	1.15486e6i		−	1.27158i	−0.771860	−	0.635792i	$-0.780674\pi$
$953$		−	1.15486e6i		−	1.27158i	0.771860	−	0.635792i	$-0.219326\pi$
$954$	45084.0	+	1.24365e6i	0.0495365	+	1.36648i
$955$	−482235.			−0.528751
$956$		−	1.45638e6i		−	1.59352i
$957$	−33278.9	+	34507.2i	−0.0363367	+	0.0376778i
$958$	1.96844e6			2.14482
$959$		−	88452.5i		−	0.0961774i
$960$	−903220.	−	871070.i	−0.980056	−	0.945171i
$961$	161681.			0.175071
$962$			1.38216e6i			1.49350i
$963$	−655676.	+	23769.1i	−0.707029	+	0.0256307i
$964$	−925625.			−0.996049
$965$			649708.i			0.697692i
$966$	18232.7	−	18905.6i	0.0195387	−	0.0202599i
$967$	−314233.			−0.336046			−0.168023	−	0.985783i	$-0.553738\pi$
$967$	−314233.			−0.336046			−0.168023	+	0.985783i	$0.553738\pi$
$968$		−	71293.1i		−	0.0760846i
$969$	867103.	+	836239.i	0.923471	+	0.890600i
$970$	2.77658e6			2.95099
$971$		−	1.28501e6i		−	1.36292i	−0.731857	−	0.681459i	$-0.761346\pi$
$971$		−	1.28501e6i		−	1.36292i	0.731857	−	0.681459i	$-0.238654\pi$
$972$	−571786.	+	686044.i	−0.605203	+	0.726138i
$973$	167488.			0.176913
$974$		−	1.15951e6i		−	1.22224i
$975$	537845.	−	557696.i	0.565781	−	0.586662i
$976$	−336415.			−0.353164
$977$			437783.i			0.458638i	0.973351	+	0.229319i	$0.0736499\pi$
$977$			437783.i			0.458638i	−0.973351	+	0.229319i	$0.926350\pi$
$978$	−616455.	−	594513.i	−0.644501	−	0.621560i
$979$	−72592.4			−0.0757401
$980$			1.29450e6i			1.34787i
$981$	−479.135	−	13217.1i	−0.000497875	−	0.0137340i
$982$	69118.1			0.0716752
$983$		−	472878.i		−	0.489375i	−0.969602	−	0.244687i	$-0.921315\pi$
$983$		−	472878.i		−	0.489375i	0.969602	−	0.244687i	$-0.0786854\pi$
$984$	78922.6	−	81835.5i	0.0815100	−	0.0845184i
$985$	−1.44764e6			−1.49207
$986$		−	1.01585e6i		−	1.04490i
$987$	−180735.	−	174302.i	−0.185528	−	0.178924i
$988$	888431.			0.910143
$989$		−	45411.5i		−	0.0464272i
$990$	117554.	−	4261.47i	0.119941	−	0.00434800i
$991$	−1.05616e6			−1.07543			−0.537714	−	0.843127i	$-0.680712\pi$
$991$	−1.05616e6			−1.07543			−0.537714	+	0.843127i	$0.680712\pi$
$992$		−	1.48335e6i		−	1.50737i
$993$	1.18067e6	−	1.22425e6i	1.19737	−	1.24157i
$994$	344086.			0.348253
$995$		−	1.57548e6i		−	1.59136i
$996$	−532196.	−	513252.i	−0.536479	−	0.517383i
$997$	−453205.			−0.455937			−0.227968	−	0.973669i	$-0.573208\pi$
$997$	−453205.			−0.455937			−0.227968	+	0.973669i	$0.573208\pi$
$998$			280362.i			0.281487i
$999$	−1.32022e6	−	1.18398e6i	−1.32287	−	1.18635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.14	✓	78
3.2	odd	2	inner	177.5.b.a.119.65	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.14	✓	78	1.1	even	1	trivial
177.5.b.a.119.65	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)

\(f(q)\)	\(=\)	\(q-5.57893i q^{2} +(-6.24762 + 6.47821i) q^{3} -15.1244 q^{4} +38.3444i q^{5} +(36.1415 + 34.8550i) q^{6} +12.9947 q^{7} -4.88479i q^{8} +(-2.93443 - 80.9468i) q^{9} +O(q^{10})\)	\(q-5.57893i q^{2} +(-6.24762 + 6.47821i) q^{3} -15.1244 q^{4} +38.3444i q^{5} +(36.1415 + 34.8550i) q^{6} +12.9947 q^{7} -4.88479i q^{8} +(-2.93443 - 80.9468i) q^{9} +213.920 q^{10} +6.78867i q^{11} +(94.4917 - 97.9792i) q^{12} +101.844 q^{13} -72.4966i q^{14} +(-248.403 - 239.561i) q^{15} -269.243 q^{16} +232.064i q^{17} +(-451.596 + 16.3710i) q^{18} -576.777 q^{19} -579.936i q^{20} +(-81.1861 + 84.1825i) q^{21} +37.8735 q^{22} -40.2549i q^{23} +(31.6447 + 30.5183i) q^{24} -845.289 q^{25} -568.182i q^{26} +(542.724 + 486.715i) q^{27} -196.538 q^{28} -784.639i q^{29} +(-1336.49 + 1385.82i) q^{30} -1041.73 q^{31} +1423.93i q^{32} +(-43.9784 - 42.4130i) q^{33} +1294.67 q^{34} +498.274i q^{35} +(44.3815 + 1224.27i) q^{36} -2432.59 q^{37} +3217.79i q^{38} +(-636.285 + 659.769i) q^{39} +187.304 q^{40} -2586.07i q^{41} +(469.648 + 452.931i) q^{42} +1128.10 q^{43} -102.675i q^{44} +(3103.85 - 112.519i) q^{45} -224.579 q^{46} +2146.95i q^{47} +(1682.13 - 1744.21i) q^{48} -2232.14 q^{49} +4715.81i q^{50} +(-1503.36 - 1449.85i) q^{51} -1540.34 q^{52} -2753.90i q^{53} +(2715.35 - 3027.82i) q^{54} -260.307 q^{55} -63.4765i q^{56} +(3603.48 - 3736.48i) q^{57} -4377.44 q^{58} +453.188i q^{59} +(3756.95 + 3623.22i) q^{60} +1249.49 q^{61} +5811.74i q^{62} +(-38.1320 - 1051.88i) q^{63} +3636.11 q^{64} +3905.16i q^{65} +(-236.619 + 245.352i) q^{66} -7317.61 q^{67} -3509.84i q^{68} +(260.780 + 251.497i) q^{69} +2779.83 q^{70} +4746.24i q^{71} +(-395.408 + 14.3341i) q^{72} -2510.30 q^{73} +13571.2i q^{74} +(5281.05 - 5475.96i) q^{75} +8723.41 q^{76} +88.2168i q^{77} +(3680.80 + 3549.79i) q^{78} -3075.09 q^{79} -10323.9i q^{80} +(-6543.78 + 475.065i) q^{81} -14427.5 q^{82} -5431.72i q^{83} +(1227.89 - 1273.21i) q^{84} -8898.35 q^{85} -6293.57i q^{86} +(5083.05 + 4902.13i) q^{87} +33.1612 q^{88} +10693.2i q^{89} +(-627.733 - 17316.2i) q^{90} +1323.44 q^{91} +608.832i q^{92} +(6508.34 - 6748.55i) q^{93} +11977.7 q^{94} -22116.1i q^{95} +(-9224.51 - 8896.17i) q^{96} +12979.5 q^{97} +12452.9i q^{98} +(549.521 - 19.9208i) 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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