LMFDB - Embedded newform 177.5.b.a.119.68

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			119.68
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.25305i q^{2} +(-4.60229 + 7.73427i) q^{3} -23.1007 q^{4} +36.4421i q^{5} +(-48.3628 - 28.7783i) q^{6} +14.4138 q^{7} -44.4009i q^{8} +(-38.6379 - 71.1907i) q^{9} +O(q^{10})$	\(q+6.25305i q^{2} +(-4.60229 + 7.73427i) q^{3} -23.1007 q^{4} +36.4421i q^{5} +(-48.3628 - 28.7783i) q^{6} +14.4138 q^{7} -44.4009i q^{8} +(-38.6379 - 71.1907i) q^{9} -227.875 q^{10} -167.318i q^{11} +(106.316 - 178.667i) q^{12} -78.8759 q^{13} +90.1305i q^{14} +(-281.853 - 167.717i) q^{15} -91.9695 q^{16} +272.347i q^{17} +(445.159 - 241.605i) q^{18} -177.403 q^{19} -841.838i q^{20} +(-66.3366 + 111.481i) q^{21} +1046.25 q^{22} +272.413i q^{23} +(343.409 + 204.346i) q^{24} -703.030 q^{25} -493.215i q^{26} +(728.431 + 28.8035i) q^{27} -332.969 q^{28} -340.721i q^{29} +(1048.74 - 1762.44i) q^{30} +165.290 q^{31} -1285.51i q^{32} +(1294.08 + 770.044i) q^{33} -1703.00 q^{34} +525.271i q^{35} +(892.562 + 1644.55i) q^{36} +2330.09 q^{37} -1109.31i q^{38} +(363.009 - 610.048i) q^{39} +1618.06 q^{40} +1950.10i q^{41} +(-697.094 - 414.806i) q^{42} -2852.52 q^{43} +3865.15i q^{44} +(2594.34 - 1408.05i) q^{45} -1703.41 q^{46} +455.409i q^{47} +(423.270 - 711.317i) q^{48} -2193.24 q^{49} -4396.09i q^{50} +(-2106.41 - 1253.42i) q^{51} +1822.09 q^{52} +4275.25i q^{53} +(-180.110 + 4554.92i) q^{54} +6097.42 q^{55} -639.988i q^{56} +(816.458 - 1372.08i) q^{57} +2130.55 q^{58} -453.188i q^{59} +(6511.01 + 3874.38i) q^{60} -492.928 q^{61} +1033.56i q^{62} +(-556.921 - 1026.13i) q^{63} +6566.82 q^{64} -2874.41i q^{65} +(-4815.13 + 8091.96i) q^{66} -3713.44 q^{67} -6291.41i q^{68} +(-2106.91 - 1253.72i) q^{69} -3284.55 q^{70} -7643.39i q^{71} +(-3160.93 + 1715.56i) q^{72} -2044.92 q^{73} +14570.2i q^{74} +(3235.55 - 5437.43i) q^{75} +4098.12 q^{76} -2411.69i q^{77} +(3814.66 + 2269.92i) q^{78} -9053.34 q^{79} -3351.57i q^{80} +(-3575.22 + 5501.32i) q^{81} -12194.1 q^{82} -3263.38i q^{83} +(1532.42 - 2575.28i) q^{84} -9924.93 q^{85} -17837.0i q^{86} +(2635.23 + 1568.10i) q^{87} -7429.06 q^{88} -6547.57i q^{89} +(8804.61 + 16222.6i) q^{90} -1136.90 q^{91} -6292.92i q^{92} +(-760.710 + 1278.40i) q^{93} -2847.70 q^{94} -6464.93i q^{95} +(9942.45 + 5916.26i) q^{96} +11735.6 q^{97} -13714.5i q^{98} +(-11911.5 + 6464.81i) 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 $

$2$			6.25305i			1.56326i	0.623740	+	0.781632i	$0.285612\pi$
$2$			6.25305i			1.56326i	−0.623740	+	0.781632i	$0.714388\pi$
$3$	−4.60229	+	7.73427i	−0.511365	+	0.859364i
$3$	−4.60229	+	7.73427i	−0.511365	+	0.859364i
$4$	−23.1007			−1.44379
$5$			36.4421i			1.45769i	0.684681	+	0.728843i	$0.259942\pi$
$5$			36.4421i			1.45769i	−0.684681	+	0.728843i	$0.740058\pi$
$6$	−48.3628	−	28.7783i	−1.34341	−	0.799398i
$7$	14.4138			0.294160			0.147080	−	0.989125i	$-0.453013\pi$
$7$	14.4138			0.294160			0.147080	+	0.989125i	$0.453013\pi$
$8$		−	44.4009i		−	0.693764i
$9$	−38.6379	−	71.1907i	−0.477012	−	0.878897i
$10$	−227.875			−2.27875
$11$		−	167.318i		−	1.38279i	−0.722476	−	0.691396i	$-0.756996\pi$
$11$		−	167.318i		−	1.38279i	0.722476	−	0.691396i	$-0.243004\pi$
$12$	106.316	−	178.667i	0.738305	−	1.24074i
$13$	−78.8759			−0.466721			−0.233361	−	0.972390i	$-0.574972\pi$
$13$	−78.8759			−0.466721			−0.233361	+	0.972390i	$0.574972\pi$
$14$			90.1305i			0.459850i
$15$	−281.853	−	167.717i	−1.25268	−	0.745410i
$16$	−91.9695			−0.359256
$17$			272.347i			0.942379i	0.882032	+	0.471189i	$0.156175\pi$
$17$			272.347i			0.942379i	−0.882032	+	0.471189i	$0.843825\pi$
$18$	445.159	−	241.605i	1.37395	−	0.745695i
$19$	−177.403			−0.491420			−0.245710	−	0.969343i	$-0.579021\pi$
$19$	−177.403			−0.491420			−0.245710	+	0.969343i	$0.579021\pi$
$20$		−	841.838i		−	2.10460i
$21$	−66.3366	+	111.481i	−0.150423	+	0.252790i
$22$	1046.25			2.16167
$23$			272.413i			0.514958i	0.966284	+	0.257479i	$0.0828918\pi$
$23$			272.413i			0.514958i	−0.966284	+	0.257479i	$0.917108\pi$
$24$	343.409	+	204.346i	0.596196	+	0.354767i
$25$	−703.030			−1.12485
$26$		−	493.215i		−	0.729608i
$27$	728.431	+	28.8035i	0.999219	+	0.0395109i
$28$	−332.969			−0.424706
$29$		−	340.721i		−	0.405138i	−0.979268	−	0.202569i	$-0.935071\pi$
$29$		−	340.721i		−	0.405138i	0.979268	−	0.202569i	$-0.0649290\pi$
$30$	1048.74	−	1762.44i	1.16527	−	1.95827i
$31$	165.290			0.171998			0.0859988	−	0.996295i	$-0.472592\pi$
$31$	165.290			0.171998			0.0859988	+	0.996295i	$0.472592\pi$
$32$		−	1285.51i		−	1.25538i
$33$	1294.08	+	770.044i	1.18832	+	0.707111i
$34$	−1703.00			−1.47319
$35$			525.271i			0.428793i
$36$	892.562	+	1644.55i	0.688706	+	1.26894i
$37$	2330.09			1.70204			0.851018	−	0.525136i	$-0.175986\pi$
$37$	2330.09			1.70204			0.851018	+	0.525136i	$0.175986\pi$
$38$		−	1109.31i		−	0.768219i
$39$	363.009	−	610.048i	0.238665	−	0.401083i
$40$	1618.06			1.01129
$41$			1950.10i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$41$			1950.10i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$42$	−697.094	−	414.806i	−0.395178	−	0.235151i
$43$	−2852.52			−1.54274			−0.771369	−	0.636388i	$-0.780428\pi$
$43$	−2852.52			−1.54274			−0.771369	+	0.636388i	$0.780428\pi$
$44$			3865.15i			1.99646i
$45$	2594.34	−	1408.05i	1.28116	−	0.695333i
$46$	−1703.41			−0.805015
$47$			455.409i			0.206161i	0.994673	+	0.103080i	$0.0328699\pi$
$47$			455.409i			0.206161i	−0.994673	+	0.103080i	$0.967130\pi$
$48$	423.270	−	711.317i	0.183711	−	0.308731i
$49$	−2193.24			−0.913470
$50$		−	4396.09i		−	1.75843i
$51$	−2106.41	−	1253.42i	−0.809846	−	0.481900i
$52$	1822.09			0.673848
$53$			4275.25i			1.52198i	0.648761	+	0.760992i	$0.275287\pi$
$53$			4275.25i			1.52198i	−0.648761	+	0.760992i	$0.724713\pi$
$54$	−180.110	+	4554.92i	−0.0617660	+	1.56204i
$55$	6097.42			2.01568
$56$		−	639.988i		−	0.204078i
$57$	816.458	−	1372.08i	0.251295	−	0.422308i
$58$	2130.55			0.633337
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	6511.01	+	3874.38i	1.80861	+	1.07622i
$61$	−492.928			−0.132472			−0.0662359	−	0.997804i	$-0.521099\pi$
$61$	−492.928			−0.132472			−0.0662359	+	0.997804i	$0.521099\pi$
$62$			1033.56i			0.268877i
$63$	−556.921	−	1026.13i	−0.140318	−	0.258536i
$64$	6566.82			1.60323
$65$		−	2874.41i		−	0.680333i
$66$	−4815.13	+	8091.96i	−1.10540	+	1.85766i
$67$	−3713.44			−0.827231			−0.413616	−	0.910452i	$-0.635734\pi$
$67$	−3713.44			−0.827231			−0.413616	+	0.910452i	$0.635734\pi$
$68$		−	6291.41i		−	1.36060i
$69$	−2106.91	−	1253.72i	−0.442536	−	0.263332i
$70$	−3284.55			−0.670316
$71$		−	7643.39i		−	1.51624i	−0.652112	−	0.758122i	$-0.726117\pi$
$71$		−	7643.39i		−	1.51624i	0.652112	−	0.758122i	$-0.273883\pi$
$72$	−3160.93	+	1715.56i	−0.609747	+	0.330934i
$73$	−2044.92			−0.383735			−0.191867	−	0.981421i	$-0.561454\pi$
$73$	−2044.92			−0.383735			−0.191867	+	0.981421i	$0.561454\pi$
$74$			14570.2i			2.66073i
$75$	3235.55	−	5437.43i	0.575208	−	0.966654i
$76$	4098.12			0.709509
$77$		−	2411.69i		−	0.406762i
$78$	3814.66	+	2269.92i	0.626999	+	0.373096i
$79$	−9053.34			−1.45062			−0.725312	−	0.688421i	$-0.758304\pi$
$79$	−9053.34			−1.45062			−0.725312	+	0.688421i	$0.758304\pi$
$80$		−	3351.57i		−	0.523682i
$81$	−3575.22	+	5501.32i	−0.544920	+	0.838488i
$82$	−12194.1			−1.81352
$83$		−	3263.38i		−	0.473709i	−0.971545	−	0.236854i	$-0.923884\pi$
$83$		−	3263.38i		−	0.473709i	0.971545	−	0.236854i	$-0.0761164\pi$
$84$	1532.42	−	2575.28i	0.217180	−	0.364977i
$85$	−9924.93			−1.37369
$86$		−	17837.0i		−	2.41171i
$87$	2635.23	+	1568.10i	0.348161	+	0.207173i
$88$	−7429.06			−0.959331
$89$		−	6547.57i		−	0.826609i	−0.910593	−	0.413304i	$-0.864375\pi$
$89$		−	6547.57i		−	0.826609i	0.910593	−	0.413304i	$-0.135625\pi$
$90$	8804.61	+	16222.6i	1.08699	+	2.00278i
$91$	−1136.90			−0.137291
$92$		−	6292.92i		−	0.743492i
$93$	−760.710	+	1278.40i	−0.0879535	+	0.147808i
$94$	−2847.70			−0.322283
$95$		−	6464.93i		−	0.716336i
$96$	9942.45	+	5916.26i	1.07882	+	0.641955i
$97$	11735.6			1.24728			0.623639	−	0.781713i	$-0.285654\pi$
$97$	11735.6			1.24728			0.623639	+	0.781713i	$0.285654\pi$
$98$		−	13714.5i		−	1.42799i
$99$	−11911.5	+	6464.81i	−1.21533	+	0.659607i
$100$	16240.5			1.62405
$101$		−	15311.1i		−	1.50095i	−0.660902	−	0.750473i	$-0.729826\pi$
$101$		−	15311.1i		−	1.50095i	0.660902	−	0.750473i	$-0.270174\pi$
$102$	7837.71	−	13171.5i	0.753336	−	1.26600i
$103$	5975.99			0.563294			0.281647	−	0.959518i	$-0.409119\pi$
$103$	5975.99			0.563294			0.281647	+	0.959518i	$0.409119\pi$
$104$			3502.16i			0.323795i
$105$	−4062.59	−	2417.45i	−0.368489	−	0.219270i
$106$	−26733.4			−2.37926
$107$			2861.36i			0.249923i	0.992162	+	0.124961i	$0.0398807\pi$
$107$			2861.36i			0.249923i	−0.992162	+	0.124961i	$0.960119\pi$
$108$	−16827.2	−	665.379i	−1.44266	−	0.0570456i
$109$	−10296.8			−0.866663			−0.433331	−	0.901235i	$-0.642662\pi$
$109$	−10296.8			−0.866663			−0.433331	+	0.901235i	$0.642662\pi$
$110$			38127.5i			3.15103i
$111$	−10723.7	+	18021.5i	−0.870362	+	1.46267i
$112$	−1325.63			−0.105679
$113$			4167.98i			0.326414i	0.986592	+	0.163207i	$0.0521838\pi$
$113$			4167.98i			0.326414i	−0.986592	+	0.163207i	$0.947816\pi$
$114$	8579.69	+	5105.35i	0.660179	+	0.392840i
$115$	−9927.31			−0.750647
$116$			7870.89i			0.584935i
$117$	3047.60	+	5615.23i	0.222631	+	0.410200i
$118$	2833.81			0.203520
$119$			3925.57i			0.277210i
$120$	−7446.80	+	12514.6i	−0.517139	+	0.869066i
$121$	−13354.2			−0.912112
$122$		−	3082.30i		−	0.207088i
$123$	−15082.6	−	8974.92i	−0.996933	−	0.593226i
$124$	−3818.30			−0.248329
$125$		−	2843.59i		−	0.181990i
$126$	6416.45	−	3482.46i	0.404160	−	0.219354i
$127$	−5496.44			−0.340780			−0.170390	−	0.985377i	$-0.554503\pi$
$127$	−5496.44			−0.340780			−0.170390	+	0.985377i	$0.554503\pi$
$128$			20494.6i			1.25089i
$129$	13128.1	−	22062.2i	0.788902	−	1.32577i
$130$	17973.8			1.06354
$131$			11680.7i			0.680653i	0.940307	+	0.340327i	$0.110538\pi$
$131$			11680.7i			0.680653i	−0.940307	+	0.340327i	$0.889462\pi$
$132$	−29894.1	−	17788.5i	−1.71569	−	1.02092i
$133$	−2557.05			−0.144556
$134$		−	23220.3i		−	1.29318i
$135$	−1049.66	+	26545.6i	−0.0575945	+	1.45655i
$136$	12092.5			0.653789
$137$			17084.5i			0.910250i	0.890428	+	0.455125i	$0.150405\pi$
$137$			17084.5i			0.910250i	−0.890428	+	0.455125i	$0.849595\pi$
$138$	7839.59	−	13174.6i	0.411657	−	0.691801i
$139$	16865.0			0.872887			0.436443	−	0.899732i	$-0.356238\pi$
$139$	16865.0			0.872887			0.436443	+	0.899732i	$0.356238\pi$
$140$		−	12134.1i		−	0.619088i
$141$	−3522.26	−	2095.92i	−0.177167	−	0.105423i
$142$	47794.5			2.37029
$143$			13197.3i			0.645378i
$144$	3553.51	+	6547.37i	0.171369	+	0.315749i
$145$	12416.6			0.590564
$146$		−	12787.0i		−	0.599878i
$147$	10093.9	−	16963.1i	0.467117	−	0.785003i
$148$	−53826.6			−2.45739
$149$			43570.1i			1.96253i	0.192662	+	0.981265i	$0.438288\pi$
$149$			43570.1i			1.96253i	−0.192662	+	0.981265i	$0.561712\pi$
$150$	34000.5	+	20232.0i	1.51113	+	0.899202i
$151$	11807.7			0.517860			0.258930	−	0.965896i	$-0.416630\pi$
$151$	11807.7			0.517860			0.258930	+	0.965896i	$0.416630\pi$
$152$			7876.84i			0.340930i
$153$	19388.6	−	10522.9i	0.828254	−	0.449525i
$154$	15080.4			0.635876
$155$			6023.51i			0.250718i
$156$	−8385.76	+	14092.5i	−0.344583	+	0.579081i
$157$	−39145.2			−1.58810			−0.794052	−	0.607850i	$-0.792032\pi$
$157$	−39145.2			−1.58810			−0.794052	+	0.607850i	$0.792032\pi$
$158$		−	56611.0i		−	2.26771i
$159$	−33066.0	−	19675.9i	−1.30794	−	0.778289i
$160$	46846.6			1.82994
$161$			3926.51i			0.151480i
$162$	−34400.0	−	22356.0i	−1.31078	−	0.851853i
$163$	42110.0			1.58493			0.792465	−	0.609917i	$-0.208797\pi$
$163$	42110.0			1.58493			0.792465	+	0.609917i	$0.208797\pi$
$164$		−	45048.6i		−	1.67492i
$165$	−28062.1	+	47159.1i	−1.03075	+	1.73220i
$166$	20406.1			0.740532
$167$		−	51642.8i		−	1.85173i	−0.377860	−	0.925863i	$-0.623340\pi$
$167$		−	51642.8i		−	1.85173i	0.377860	−	0.925863i	$-0.376660\pi$
$168$	4949.84	+	2945.41i	0.175377	+	0.104358i
$169$	−22339.6			−0.782171
$170$		−	62061.1i		−	2.14744i
$171$	6854.47	+	12629.4i	0.234413	+	0.431908i
$172$	65895.2			2.22739
$173$			13701.7i			0.457807i	0.973449	+	0.228903i	$0.0735140\pi$
$173$			13701.7i			0.457807i	−0.973449	+	0.228903i	$0.926486\pi$
$174$	−9805.38	+	16478.2i	−0.323867	+	0.544267i
$175$	−10133.4			−0.330885
$176$			15388.1i			0.496776i
$177$	3505.08	+	2085.70i	0.111880	+	0.0665741i
$178$	40942.3			1.29221
$179$			20812.2i			0.649549i	0.945791	+	0.324774i	$0.105288\pi$
$179$			20812.2i			0.649549i	−0.945791	+	0.324774i	$0.894712\pi$
$180$	−59931.0	+	32526.9i	−1.84972	+	1.00392i
$181$	−32800.3			−1.00120			−0.500600	−	0.865679i	$-0.666887\pi$
$181$	−32800.3			−1.00120			−0.500600	+	0.865679i	$0.666887\pi$
$182$		−	7109.12i		−	0.214622i
$183$	2268.60	−	3812.44i	0.0677415	−	0.113842i
$184$	12095.4			0.357259
$185$			84913.4i			2.48104i
$186$	−7993.87	−	4756.76i	−0.231063	−	0.137495i
$187$	45568.6			1.30311
$188$		−	10520.3i		−	0.297653i
$189$	10499.5	+	415.168i	0.293930	+	0.0116225i
$190$	40425.6			1.11982
$191$		−	1293.80i		−	0.0354651i	−0.999843	−	0.0177326i	$-0.994355\pi$
$191$		−	1293.80i		−	0.0354651i	0.999843	−	0.0177326i	$-0.00564475\pi$
$192$	−30222.4	+	50789.6i	−0.819835	+	1.37776i
$193$	−55244.0			−1.48310			−0.741550	−	0.670898i	$-0.765909\pi$
$193$	−55244.0			−1.48310			−0.741550	+	0.670898i	$0.765909\pi$
$194$			73383.6i			1.94982i
$195$	22231.4	+	13228.8i	0.584653	+	0.347898i
$196$	50665.4			1.31886
$197$		−	56388.7i		−	1.45298i	−0.687177	−	0.726490i	$-0.741150\pi$
$197$		−	56388.7i		−	1.45298i	0.687177	−	0.726490i	$-0.258850\pi$
$198$	−40424.8	−	74483.0i	−1.03114	−	1.89988i
$199$	9051.91			0.228578			0.114289	−	0.993448i	$-0.463541\pi$
$199$	9051.91			0.228578			0.114289	+	0.993448i	$0.463541\pi$
$200$			31215.2i			0.780380i
$201$	17090.3	−	28720.8i	0.423017	−	0.710892i
$202$	95741.4			2.34637
$203$		−	4911.10i		−	0.119175i
$204$	48659.5	+	28954.9i	1.16925	+	0.695763i
$205$	−71065.8			−1.69104
$206$			37368.2i			0.880577i
$207$	19393.2	−	10525.5i	0.452595	−	0.245641i
$208$	7254.18			0.167672
$209$			29682.6i			0.679531i
$210$	15116.4	−	25403.6i	0.342776	−	0.576045i
$211$	−4619.34			−0.103756			−0.0518782	−	0.998653i	$-0.516521\pi$
$211$	−4619.34			−0.103756			−0.0518782	+	0.998653i	$0.516521\pi$
$212$		−	98761.2i		−	2.19743i
$213$	59116.1	+	35177.1i	1.30301	+	0.775355i
$214$	−17892.3			−0.390695
$215$		−	103952.i		−	2.24883i
$216$	1278.90	−	32343.0i	0.0274113	−	0.693223i
$217$	2382.46			0.0505948
$218$		−	64386.6i		−	1.35482i
$219$	9411.31	−	15816.0i	0.196228	−	0.329768i
$220$	−140854.			−2.91022
$221$		−	21481.6i		−	0.439828i
$222$	−112690.	−	67056.1i	−2.28654	−	1.36061i
$223$	−8847.56			−0.177916			−0.0889578	−	0.996035i	$-0.528354\pi$
$223$	−8847.56			−0.177916			−0.0889578	+	0.996035i	$0.528354\pi$
$224$		−	18529.1i		−	0.369281i
$225$	27163.6	+	50049.2i	0.536566	+	0.988626i
$226$	−26062.6			−0.510271
$227$			46243.0i			0.897417i	0.893678	+	0.448709i	$0.148116\pi$
$227$			46243.0i			0.897417i	−0.893678	+	0.448709i	$0.851884\pi$
$228$	−18860.7	+	31696.0i	−0.362818	+	0.609726i
$229$	68889.8			1.31366			0.656832	−	0.754037i	$-0.271896\pi$
$229$	68889.8			1.31366			0.656832	+	0.754037i	$0.271896\pi$
$230$		−	62076.0i		−	1.17346i
$231$	18652.7	+	11099.3i	0.349556	+	0.208004i
$232$	−15128.3			−0.281070
$233$		−	44615.8i		−	0.821820i	−0.911676	−	0.410910i	$-0.865211\pi$
$233$		−	44615.8i		−	0.821820i	0.911676	−	0.410910i	$-0.134789\pi$
$234$	−35112.3	+	19056.8i	−0.641250	+	0.348031i
$235$	−16596.1			−0.300518
$236$			10468.9i			0.187966i
$237$	41666.1	−	70021.0i	0.741798	−	1.24661i
$238$	−24546.8			−0.433352
$239$		−	2705.84i		−	0.0473703i	−0.999719	−	0.0236852i	$-0.992460\pi$
$239$		−	2705.84i		−	0.0473703i	0.999719	−	0.0236852i	$-0.00753992\pi$
$240$	25921.9	+	15424.9i	0.450034	+	0.267793i
$241$	−70711.2			−1.21746			−0.608729	−	0.793378i	$-0.708320\pi$
$241$	−70711.2			−1.21746			−0.608729	+	0.793378i	$0.708320\pi$
$242$		−	83504.7i		−	1.42587i
$243$	−26094.5	−	52970.4i	−0.441913	−	0.897058i
$244$	11387.0			0.191262
$245$		−	79926.4i		−	1.33155i
$246$	56120.6	−	94312.3i	0.927368	−	1.55847i
$247$	13992.8			0.229356
$248$		−	7339.01i		−	0.119326i
$249$	25239.9	+	15019.0i	0.407088	+	0.242238i
$250$	17781.1			0.284498
$251$			110496.i			1.75388i	0.480603	+	0.876938i	$0.340418\pi$
$251$			110496.i			1.75388i	−0.480603	+	0.876938i	$0.659582\pi$
$252$	12865.3	+	23704.3i	0.202590	+	0.373273i
$253$	45579.5			0.712079
$254$		−	34369.5i		−	0.532728i
$255$	45677.3	−	76762.1i	0.702458	−	1.18050i
$256$	−23084.7			−0.352244
$257$			99487.8i			1.50627i	0.657864	+	0.753136i	$0.271460\pi$
$257$			99487.8i			1.50627i	−0.657864	+	0.753136i	$0.728540\pi$
$258$	137956.	+	82090.8i	2.07253	+	1.23326i
$259$	33585.5			0.500671
$260$			66400.7i			0.982259i
$261$	−24256.2	+	13164.8i	−0.356075	+	0.193255i
$262$	−73040.0			−1.06404
$263$			130318.i			1.88405i	0.335536	+	0.942027i	$0.391082\pi$
$263$			130318.i			1.88405i	−0.335536	+	0.942027i	$0.608918\pi$
$264$	34190.7	−	57458.4i	0.490569	−	0.824414i
$265$	−155799.			−2.21857
$266$		−	15989.4i		−	0.225979i
$267$	50640.7	+	30133.8i	0.710358	+	0.422699i
$268$	85783.0			1.19435
$269$			5034.64i			0.0695768i	0.999395	+	0.0347884i	$0.0110757\pi$
$269$			5034.64i			0.0695768i	−0.999395	+	0.0347884i	$0.988924\pi$
$270$	−165991.	−	6563.58i	−2.27697	−	0.0900354i
$271$	−78323.1			−1.06648			−0.533238	−	0.845965i	$-0.679025\pi$
$271$	−78323.1			−1.06648			−0.533238	+	0.845965i	$0.679025\pi$
$272$		−	25047.7i		−	0.338555i
$273$	5232.36	−	8793.13i	0.0702057	−	0.117983i
$274$	−106830.			−1.42296
$275$			117629.i			1.55543i
$276$	48671.2	+	28961.8i	0.638930	+	0.380196i
$277$	−89690.5			−1.16893			−0.584463	−	0.811421i	$-0.698695\pi$
$277$	−89690.5			−1.16893			−0.584463	+	0.811421i	$0.698695\pi$
$278$			105458.i			1.36455i
$279$	−6386.45	−	11767.1i	−0.0820448	−	0.151168i
$280$	23322.5			0.297481
$281$			7922.50i			0.100334i	0.998741	+	0.0501672i	$0.0159754\pi$
$281$			7922.50i			0.100334i	−0.998741	+	0.0501672i	$0.984025\pi$
$282$	13105.9	−	22024.9i	0.164805	−	0.276959i
$283$	61789.8			0.771514			0.385757	−	0.922600i	$-0.373940\pi$
$283$	61789.8			0.771514			0.385757	+	0.922600i	$0.373940\pi$
$284$			176567.i			2.18914i
$285$	50001.6	+	29753.5i	0.615593	+	0.366309i
$286$	−82523.6			−1.00890
$287$			28108.4i			0.341250i
$288$	−91516.0	+	49669.3i	−1.10335	+	0.598829i
$289$	9347.88			0.111923
$290$			77641.7i			0.923207i
$291$	−54010.8	+	90766.6i	−0.637814	+	1.07187i
$292$	47239.1			0.554033
$293$			122115.i			1.42244i	0.702970	+	0.711220i	$0.251857\pi$
$293$			122115.i			1.42244i	−0.702970	+	0.711220i	$0.748143\pi$
$294$	106071.	+	63117.8i	1.22717	+	0.730226i
$295$	16515.1			0.189775
$296$		−	103458.i		−	1.18081i
$297$	4819.33	−	121879.i	0.0546353	−	1.38171i
$298$	−272446.			−3.06795
$299$		−	21486.8i		−	0.240342i
$300$	−74743.3	+	125608.i	−0.830481	+	1.39565i
$301$	−41115.8			−0.453812
$302$			73834.4i			0.809552i
$303$	118421.	+	70466.2i	1.28986	+	0.767531i
$304$	16315.6			0.176546
$305$		−	17963.4i		−	0.193102i
$306$	65800.5	+	121238.i	0.702727	+	1.29478i
$307$	28408.8			0.301423			0.150712	−	0.988578i	$-0.451844\pi$
$307$	28408.8			0.301423			0.150712	+	0.988578i	$0.451844\pi$
$308$			55711.7i			0.587280i
$309$	−27503.2	+	46219.9i	−0.288049	+	0.484074i
$310$	−37665.3			−0.391939
$311$			86931.4i			0.898786i	0.893334	+	0.449393i	$0.148360\pi$
$311$			86931.4i			0.898786i	−0.893334	+	0.449393i	$0.851640\pi$
$312$	−27086.7	−	16117.9i	−0.278257	−	0.165577i
$313$	−76544.3			−0.781311			−0.390656	−	0.920537i	$-0.627752\pi$
$313$	−76544.3			−0.781311			−0.390656	+	0.920537i	$0.627752\pi$
$314$		−	244777.i		−	2.48262i
$315$	37394.4	−	20295.4i	0.376865	−	0.204539i
$316$	209138.			2.09440
$317$		−	99325.7i		−	0.988424i	−0.869341	−	0.494212i	$-0.835457\pi$
$317$		−	99325.7i		−	0.988424i	0.869341	−	0.494212i	$-0.164543\pi$
$318$	123035.	−	206763.i	1.21667	−	2.04465i
$319$	−57008.7			−0.560221
$320$			239309.i			2.33700i
$321$	−22130.6	−	13168.8i	−0.214774	−	0.127802i
$322$	−24552.7			−0.236803
$323$		−	48315.2i		−	0.463104i
$324$	82590.0	−	127084.i	0.786751	−	1.21060i
$325$	55452.1			0.524991
$326$			263316.i			2.47766i
$327$	47388.9	−	79638.4i	0.443181	−	0.744779i
$328$	86586.2			0.804824
$329$			6564.19i			0.0606442i
$330$	−294888.	−	175474.i	−2.70788	−	1.61133i
$331$	−60947.0			−0.556283			−0.278142	−	0.960540i	$-0.589718\pi$
$331$	−60947.0			−0.556283			−0.278142	+	0.960540i	$0.589718\pi$
$332$			75386.3i			0.683937i
$333$	−90029.8	−	165881.i	−0.811891	−	1.49592i
$334$	322925.			2.89474
$335$		−	135326.i		−	1.20584i
$336$	6100.95	−	10252.8i	0.0540404	−	0.0908165i
$337$	11894.5			0.104733			0.0523667	−	0.998628i	$-0.483324\pi$
$337$	11894.5			0.104733			0.0523667	+	0.998628i	$0.483324\pi$
$338$		−	139691.i		−	1.22274i
$339$	−32236.3	−	19182.2i	−0.280508	−	0.166917i
$340$	229273.			1.98333
$341$		−	27655.9i		−	0.237837i
$342$	−78972.4	+	42861.4i	−0.675185	+	0.366449i
$343$	−66220.7			−0.562866
$344$			126655.i			1.07030i
$345$	45688.3	−	76780.5i	0.383855	−	0.645079i
$346$	−85677.5			−0.715673
$347$			127509.i			1.05897i	0.848320	+	0.529484i	$0.177615\pi$
$347$			127509.i			1.05897i	−0.848320	+	0.529484i	$0.822385\pi$
$348$	−60875.6	−	36224.1i	−0.502672	−	0.299115i
$349$	103272.			0.847871			0.423936	−	0.905692i	$-0.360648\pi$
$349$	103272.			0.847871			0.423936	+	0.905692i	$0.360648\pi$
$350$		−	63364.5i		−	0.517261i
$351$	−57455.6	−	2271.90i	−0.466357	−	0.0184406i
$352$	−215088.			−1.73592
$353$			50118.6i			0.402207i	0.979570	+	0.201103i	$0.0644527\pi$
$353$			50118.6i			0.402207i	−0.979570	+	0.201103i	$0.935547\pi$
$354$	−13042.0	+	21917.4i	−0.104073	+	0.174897i
$355$	278542.			2.21021
$356$			151253.i			1.19345i
$357$	−30361.4	−	18066.6i	−0.238224	−	0.141756i
$358$	−130140.			−1.01542
$359$		−	177386.i		−	1.37636i	−0.725541	−	0.688179i	$-0.758410\pi$
$359$		−	177386.i		−	1.37636i	0.725541	−	0.688179i	$-0.241590\pi$
$360$	−62518.7	−	115191.i	−0.482397	−	0.888820i
$361$	−98849.3			−0.758506
$362$		−	205102.i		−	1.56514i
$363$	61460.0	−	103285.i	0.466422	−	0.783836i
$364$	26263.3			0.198219
$365$		−	74521.3i		−	0.559365i
$366$	23839.4	+	14185.6i	0.177964	+	0.105898i
$367$	236899.			1.75886			0.879428	−	0.476031i	$-0.157925\pi$
$367$	236899.			1.75886			0.879428	+	0.476031i	$0.157925\pi$
$368$		−	25053.7i		−	0.185002i
$369$	138829.	−	75347.8i	1.01959	−	0.553373i
$370$	−530968.			−3.87851
$371$			61622.8i			0.447707i
$372$	17572.9	−	29531.8i	0.126987	−	0.213405i
$373$	−255567.			−1.83691			−0.918454	−	0.395527i	$-0.870562\pi$
$373$	−255567.			−1.83691			−0.918454	+	0.395527i	$0.870562\pi$
$374$			284943.i			2.03711i
$375$	21993.1	+	13087.0i	0.156395	+	0.0930631i
$376$	20220.6			0.143027
$377$			26874.7i			0.189086i
$378$	−2596.07	+	65653.8i	−0.0181691	+	0.459490i
$379$	31719.6			0.220826			0.110413	−	0.993886i	$-0.464783\pi$
$379$	31719.6			0.220826			0.110413	+	0.993886i	$0.464783\pi$
$380$			149344.i			1.03424i
$381$	25296.2	−	42510.9i	0.174263	−	0.292854i
$382$	8090.23			0.0554414
$383$			23091.9i			0.157421i	0.996898	+	0.0787105i	$0.0250803\pi$
$383$			23091.9i			0.157421i	−0.996898	+	0.0787105i	$0.974920\pi$
$384$	−158511.	−	94322.0i	−1.07497	−	0.639662i
$385$	87887.2			0.592931
$386$		−	345444.i		−	2.31848i
$387$	110216.	+	203073.i	0.735904	+	1.35591i
$388$	−271101.			−1.80081
$389$			227541.i			1.50370i	0.659336	+	0.751848i	$0.270837\pi$
$389$			227541.i			1.50370i	−0.659336	+	0.751848i	$0.729163\pi$
$390$	−82720.6	+	139014.i	−0.543857	+	0.913967i
$391$	−74190.9			−0.485285
$392$			97381.9i			0.633733i
$393$	−90341.6	−	53757.9i	−0.584929	−	0.348062i
$394$	352602.			2.27139
$395$		−	329923.i		−	2.11455i
$396$	275163.	−	149342.i	1.75469	−	0.952336i
$397$	67250.0			0.426689			0.213344	−	0.976977i	$-0.431564\pi$
$397$	67250.0			0.426689			0.213344	+	0.976977i	$0.431564\pi$
$398$			56602.1i			0.357327i
$399$	11768.3	−	19776.9i	0.0739210	−	0.124226i
$400$	64657.4			0.404108
$401$		−	273508.i		−	1.70091i	−0.526048	−	0.850455i	$-0.676327\pi$
$401$		−	273508.i		−	1.70091i	0.526048	−	0.850455i	$-0.323673\pi$
$402$	179592.	+	106867.i	1.11131	+	0.661287i
$403$	−13037.4			−0.0802749
$404$			353698.i			2.16705i
$405$	−200480.	−	130289.i	−1.22225	−	0.794322i
$406$	30709.4			0.186303
$407$		−	389865.i		−	2.35356i
$408$	−55653.0	+	93526.5i	−0.334325	+	0.561842i
$409$	−124970.			−0.747069			−0.373534	−	0.927616i	$-0.621854\pi$
$409$	−124970.			−0.747069			−0.373534	+	0.927616i	$0.621854\pi$
$410$		−	444378.i		−	2.64354i
$411$	−132136.	−	78627.7i	−0.782236	−	0.465470i
$412$	−138049.			−0.813280
$413$		−	6532.17i		−	0.0382964i
$414$	65816.3	+	121267.i	0.384001	+	0.707525i
$415$	118925.			0.690519
$416$			101395.i			0.585911i
$417$	−77617.8	+	130439.i	−0.446364	+	0.750127i
$418$	−185607.			−1.06229
$419$		−	55609.2i		−	0.316751i	−0.987379	−	0.158376i	$-0.949374\pi$
$419$		−	55609.2i		−	0.316751i	0.987379	−	0.158376i	$-0.0506257\pi$
$420$	93848.6	+	55844.7i	0.532022	+	0.316580i
$421$	117171.			0.661086			0.330543	−	0.943791i	$-0.392768\pi$
$421$	117171.			0.661086			0.330543	+	0.943791i	$0.392768\pi$
$422$		−	28885.0i		−	0.162199i
$423$	32420.9	−	17596.1i	0.181194	−	0.0983410i
$424$	189825.			1.05590
$425$		−	191468.i		−	1.06003i
$426$	−219964.	+	369656.i	−1.21208	+	2.03694i
$427$	−7104.98			−0.0389679
$428$		−	66099.5i		−	0.360836i
$429$	−102072.	−	60737.9i	−0.554614	−	0.330024i
$430$	650018.			3.51551
$431$			214459.i			1.15449i	0.816572	+	0.577244i	$0.195872\pi$
$431$			214459.i			1.15449i	−0.816572	+	0.577244i	$0.804128\pi$
$432$	−66993.4	−	2649.04i	−0.358975	−	0.0141945i
$433$	−267726.			−1.42795			−0.713977	−	0.700169i	$-0.753108\pi$
$433$	−267726.			−1.42795			−0.713977	+	0.700169i	$0.753108\pi$
$434$			14897.6i			0.0790930i
$435$	−57144.8	+	96033.4i	−0.301994	+	0.507509i
$436$	237864.			1.25128
$437$		−	48326.7i		−	0.253061i
$438$	98898.2	+	58849.5i	0.515514	+	0.306757i
$439$	89658.4			0.465224			0.232612	−	0.972570i	$-0.425273\pi$
$439$	89658.4			0.465224			0.232612	+	0.972570i	$0.425273\pi$
$440$		−	270731.i		−	1.39840i
$441$	84742.3	+	156138.i	0.435736	+	0.802846i
$442$	134326.			0.687567
$443$			202713.i			1.03294i	0.856307	+	0.516468i	$0.172753\pi$
$443$			202713.i			1.03294i	−0.856307	+	0.516468i	$0.827247\pi$
$444$	247725.	−	416310.i	1.25662	−	2.11179i
$445$	238607.			1.20494
$446$		−	55324.3i		−	0.278129i
$447$	−336983.	−	200522.i	−1.68653	−	1.00357i
$448$	94653.1			0.471605
$449$		−	344509.i		−	1.70886i	−0.519563	−	0.854432i	$-0.673905\pi$
$449$		−	344509.i		−	1.70886i	0.519563	−	0.854432i	$-0.326095\pi$
$450$	−312960.	+	169856.i	−1.54548	+	0.838793i
$451$	326286.			1.60415
$452$		−	96283.1i		−	0.471274i
$453$	−54342.6	+	91324.2i	−0.264816	+	0.445030i
$454$	−289160.			−1.40290
$455$		−	41431.2i		−	0.200127i
$456$	−60921.6	−	36251.5i	−0.292983	−	0.174340i
$457$	−53061.8			−0.254068			−0.127034	−	0.991898i	$-0.540546\pi$
$457$	−53061.8			−0.254068			−0.127034	+	0.991898i	$0.540546\pi$
$458$			430772.i			2.05360i
$459$	−7844.55	+	198386.i	−0.0372342	+	0.941643i
$460$	229328.			1.08378
$461$		−	49500.4i		−	0.232920i	−0.993195	−	0.116460i	$-0.962845\pi$
$461$		−	49500.4i		−	0.232920i	0.993195	−	0.116460i	$-0.0371547\pi$
$462$	−69404.5	+	116636.i	−0.325165	+	0.546449i
$463$	−333434.			−1.55542			−0.777711	−	0.628622i	$-0.783619\pi$
$463$	−333434.			−1.55542			−0.777711	+	0.628622i	$0.783619\pi$
$464$			31336.0i			0.145548i
$465$	−46587.5	−	27721.9i	−0.215458	−	0.128209i
$466$	278985.			1.28472
$467$			69025.7i			0.316502i	0.987399	+	0.158251i	$0.0505856\pi$
$467$			69025.7i			0.316502i	−0.987399	+	0.158251i	$0.949414\pi$
$468$	−70401.7	−	129716.i	−0.321434	−	0.592243i
$469$	−53524.9			−0.243338
$470$		−	103776.i		−	0.469788i
$471$	180157.	−	302759.i	0.812100	−	1.36476i
$472$	−20121.9			−0.0903204
$473$			477278.i			2.13328i
$474$	437845.	+	260540.i	1.94878	+	1.15963i
$475$	124719.			0.552773
$476$		−	90683.4i		−	0.400234i
$477$	304358.	−	165187.i	1.33767	−	0.726004i
$478$	16919.8			0.0740523
$479$		−	179644.i		−	0.782965i	−0.920186	−	0.391482i	$-0.871962\pi$
$479$		−	179644.i		−	0.782965i	0.920186	−	0.391482i	$-0.128038\pi$
$480$	−215601.	+	362324.i	−0.935769	+	1.57259i
$481$	−183788.			−0.794377
$482$		−	442161.i		−	1.90321i
$483$	−30368.7	−	18070.9i	−0.130176	−	0.0774616i
$484$	308492.			1.31690
$485$			427672.i			1.81814i
$486$	331227.	−	163170.i	1.40234	−	0.690826i
$487$	−174642.			−0.736361			−0.368180	−	0.929754i	$-0.620019\pi$
$487$	−174642.			−0.736361			−0.368180	+	0.929754i	$0.620019\pi$
$488$			21886.5i			0.0919043i
$489$	−193802.	+	325690.i	−0.810478	+	1.36203i
$490$	499784.			2.08157
$491$			13092.0i			0.0543055i	0.999631	+	0.0271528i	$0.00864405\pi$
$491$			13092.0i			0.0543055i	−0.999631	+	0.0271528i	$0.991356\pi$
$492$	348418.	+	207327.i	1.43936	+	0.856495i
$493$	92794.5			0.381793
$494$			87497.7i			0.358544i
$495$	−235592.	−	434079.i	−0.961500	−	1.77157i
$496$	−15201.6			−0.0617911
$497$		−	110171.i		−	0.446019i
$498$	−93914.7	+	157826.i	−0.378682	+	0.636386i
$499$	410282.			1.64771			0.823856	−	0.566800i	$-0.191819\pi$
$499$	410282.			1.64771			0.823856	+	0.566800i	$0.191819\pi$
$500$			65688.8i			0.262755i
$501$	399419.	+	237675.i	1.59131	+	0.946908i
$502$	−690937.			−2.74177
$503$			179300.i			0.708670i	0.935119	+	0.354335i	$0.115293\pi$
$503$			179300.i			0.708670i	−0.935119	+	0.354335i	$0.884707\pi$
$504$	−45561.2	+	24727.8i	−0.179363	+	0.0973474i
$505$	557971.			2.18791
$506$			285011.i			1.11317i
$507$	102813.	−	172781.i	0.399975	−	0.672170i
$508$	126971.			0.492015
$509$		−	3989.98i		−	0.0154005i	−0.999970	−	0.00770025i	$-0.997549\pi$
$509$		−	3989.98i		−	0.0154005i	0.999970	−	0.00770025i	$-0.00245109\pi$
$510$	479997.	+	285623.i	1.84543	+	1.09813i
$511$	−29475.2			−0.112879
$512$			183564.i			0.700240i
$513$	−129226.	−	5109.81i	−0.491036	−	0.0194165i
$514$	−622103.			−2.35470
$515$			217778.i			0.821106i
$516$	−303269.	+	509651.i	−1.13901	+	1.91414i
$517$	76198.0			0.285077
$518$			210012.i			0.782681i
$519$	−105973.	−	63059.1i	−0.393423	−	0.234106i
$520$	−127626.			−0.471991
$521$			495584.i			1.82575i	0.408238	+	0.912876i	$0.366143\pi$
$521$			495584.i			1.82575i	−0.408238	+	0.912876i	$0.633857\pi$
$522$	−82319.9	−	151675.i	−0.302109	−	0.556638i
$523$	311871.			1.14018			0.570088	−	0.821584i	$-0.306909\pi$
$523$	311871.			1.14018			0.570088	+	0.821584i	$0.306909\pi$
$524$		−	269832.i		−	0.982722i
$525$	46636.6	−	78374.2i	0.169203	−	0.284351i
$526$	−814886.			−2.94527
$527$			45016.2i			0.162087i
$528$	−119016.	−	70820.6i	−0.426911	−	0.254034i
$529$	205632.			0.734818
$530$		−	974222.i		−	3.46822i
$531$	−32262.7	+	17510.2i	−0.114423	+	0.0621016i
$532$	59069.7			0.208709
$533$		−	153816.i		−	0.541435i
$534$	−188428.	+	316659.i	−0.660790	+	1.11048i
$535$	−104274.			−0.364309
$536$			164880.i			0.573903i
$537$	−160967.	−	95783.7i	−0.558199	−	0.332157i
$538$	−31481.9			−0.108767
$539$			366968.i			1.26314i
$540$	24247.9	−	613221.i	0.0831545	−	2.10295i
$541$	72663.1			0.248267			0.124134	−	0.992266i	$-0.460385\pi$
$541$	72663.1			0.248267			0.124134	+	0.992266i	$0.460385\pi$
$542$		−	489758.i		−	1.66718i
$543$	150957.	−	253687.i	0.511979	−	0.860395i
$544$	350104.			1.18304
$545$		−	375238.i		−	1.26332i
$546$	54983.9	+	32718.2i	0.184438	+	0.109750i
$547$	198926.			0.664840			0.332420	−	0.943131i	$-0.392135\pi$
$547$	198926.			0.664840			0.332420	+	0.943131i	$0.392135\pi$
$548$		−	394663.i		−	1.31421i
$549$	19045.7	+	35091.9i	0.0631906	+	0.116429i
$550$	−735543.			−2.43155
$551$			60444.8i			0.199093i
$552$	−55666.4	+	93548.9i	−0.182690	+	0.307016i
$553$	−130493.			−0.426715
$554$		−	560839.i		−	1.82734i
$555$	−656744.	−	390796.i	−2.13211	−	1.26871i
$556$	−389594.			−1.26027
$557$			589282.i			1.89939i	0.313183	+	0.949693i	$0.398605\pi$
$557$			589282.i			1.89939i	−0.313183	+	0.949693i	$0.601395\pi$
$558$	73580.2	−	39934.8i	0.236316	−	0.128258i
$559$	224995.			0.720028
$560$		−	48309.0i		−	0.154046i
$561$	−209720.	+	352440.i	−0.666366	+	1.11985i
$562$	−49539.8			−0.156849
$563$			407823.i			1.28663i	0.765600	+	0.643317i	$0.222442\pi$
$563$			407823.i			1.28663i	−0.765600	+	0.643317i	$0.777558\pi$
$564$	81366.5	+	48417.2i	0.255792	+	0.152209i
$565$	−151890.			−0.475809
$566$			386375.i			1.20608i
$567$	−51532.7	+	79295.1i	−0.160294	+	0.246650i
$568$	−339374.			−1.05192
$569$			272243.i			0.840877i	0.907321	+	0.420439i	$0.138124\pi$
$569$			272243.i			0.840877i	−0.907321	+	0.420439i	$0.861876\pi$
$570$	−186050.	+	312662.i	−0.572638	+	0.962334i
$571$	−382479.			−1.17310			−0.586551	−	0.809913i	$-0.699515\pi$
$571$	−382479.			−1.17310			−0.586551	+	0.809913i	$0.699515\pi$
$572$		−	304867.i		−	0.931792i
$573$	10006.6	+	5954.46i	0.0304775	+	0.0181356i
$574$	−175763.			−0.533464
$575$		−	191514.i		−	0.579250i
$576$	−253728.	−	467496.i	−0.764758	−	1.40907i
$577$	−229401.			−0.689038			−0.344519	−	0.938779i	$-0.611958\pi$
$577$	−229401.			−0.689038			−0.344519	+	0.938779i	$0.611958\pi$
$578$			58452.8i			0.174964i
$579$	254249.	−	427272.i	0.758406	−	1.27452i
$580$	−286832.			−0.852652
$581$		−	47037.8i		−	0.139346i
$582$	−567568.	−	337732.i	−1.67561	−	0.997072i
$583$	715326.			2.10459
$584$			90796.4i			0.266221i
$585$	−204631.	+	111061.i	−0.597943	+	0.324527i
$586$	−763592.			−2.22365
$587$		−	452777.i		−	1.31404i	−0.753873	−	0.657020i	$-0.771817\pi$
$587$		−	452777.i		−	1.31404i	0.753873	−	0.657020i	$-0.228183\pi$
$588$	−233176.	+	391860.i	−0.674419	+	1.13338i
$589$	−29322.8			−0.0845230
$590$			103270.i			0.296668i
$591$	436126.	+	259517.i	1.24864	+	0.743004i
$592$	−214297.			−0.611467
$593$			414618.i			1.17907i	0.807744	+	0.589534i	$0.200688\pi$
$593$			414618.i			1.17907i	−0.807744	+	0.589534i	$0.799312\pi$
$594$	762118.	+	30135.5i	2.15998	+	0.0854094i
$595$	−143056.			−0.404085
$596$		−	1.00650e6i		−	2.83349i
$597$	−41659.5	+	70009.9i	−0.116887	+	0.196431i
$598$	134358.			0.375718
$599$		−	194294.i		−	0.541508i	−0.962649	−	0.270754i	$-0.912727\pi$
$599$		−	194294.i		−	0.541508i	0.962649	−	0.270754i	$-0.0872730\pi$
$600$	−241427.	−	143661.i	−0.670630	−	0.399059i
$601$	394812.			1.09305			0.546526	−	0.837442i	$-0.315950\pi$
$601$	394812.			1.09305			0.546526	+	0.837442i	$0.315950\pi$
$602$		−	257099.i		−	0.709427i
$603$	143480.	+	264362.i	0.394599	+	0.727051i
$604$	−272767.			−0.747683
$605$		−	486657.i		−	1.32957i
$606$	−440629.	+	740490.i	−1.19985	+	2.01639i
$607$	−356291.			−0.967002			−0.483501	−	0.875344i	$-0.660635\pi$
$607$	−356291.			−0.967002			−0.483501	+	0.875344i	$0.660635\pi$
$608$			228052.i			0.616917i
$609$	37983.8	+	22602.3i	0.102415	+	0.0609421i
$610$	112326.			0.301870
$611$		−	35920.8i		−	0.0962196i
$612$	−447890.	+	243087.i	−1.19583	+	0.649021i
$613$	39079.2			0.103998			0.0519989	−	0.998647i	$-0.483441\pi$
$613$	39079.2			0.103998			0.0519989	+	0.998647i	$0.483441\pi$
$614$			177642.i			0.471204i
$615$	327065.	−	549642.i	0.864737	−	1.45322i
$616$	−107081.			−0.282197
$617$			128439.i			0.337385i	0.985669	+	0.168692i	$0.0539544\pi$
$617$			128439.i			0.337385i	−0.985669	+	0.168692i	$0.946046\pi$
$618$	−289016.	−	171979.i	−0.756736	−	0.450296i
$619$	185094.			0.483070			0.241535	−	0.970392i	$-0.422349\pi$
$619$	185094.			0.483070			0.241535	+	0.970392i	$0.422349\pi$
$620$		−	139147.i		−	0.361985i
$621$	−7846.43	+	198434.i	−0.0203465	+	0.514556i
$622$	−543587.			−1.40504
$623$		−	94375.6i		−	0.243155i
$624$	−33385.8	+	56105.8i	−0.0857418	+	0.144092i
$625$	−335767.			−0.859565
$626$		−	478635.i		−	1.22140i
$627$	−229573.	−	136608.i	−0.583965	−	0.347489i
$628$	904280.			2.29289
$629$			634594.i			1.60396i
$630$	126908.	+	233829.i	0.319749	+	0.589139i
$631$	231418.			0.581218			0.290609	−	0.956842i	$-0.406142\pi$
$631$	231418.			0.581218			0.290609	+	0.956842i	$0.406142\pi$
$632$			401977.i			1.00639i
$633$	21259.5	−	35727.2i	0.0530574	−	0.0891645i
$634$	621089.			1.54517
$635$		−	200302.i		−	0.496750i
$636$	763846.	+	454527.i	1.88839	+	1.12369i
$637$	172994.			0.426336
$638$		−	356478.i		−	0.875773i
$639$	−544138.	+	295325.i	−1.33262	+	0.723266i
$640$	−746867.			−1.82341
$641$		−	248945.i		−	0.605880i	−0.953010	−	0.302940i	$-0.902032\pi$
$641$		−	248945.i		−	0.605880i	0.953010	−	0.302940i	$-0.0979682\pi$
$642$	82345.3	−	138384.i	0.199788	−	0.335749i
$643$	−90943.6			−0.219963			−0.109982	−	0.993934i	$-0.535079\pi$
$643$	−90943.6			−0.219963			−0.109982	+	0.993934i	$0.535079\pi$
$644$		−	90705.1i		−	0.218706i
$645$	803993.	+	478417.i	1.93256	+	1.14997i
$646$	302117.			0.723953
$647$		−	836160.i		−	1.99747i	−0.0502618	−	0.998736i	$-0.516006\pi$
$647$		−	836160.i		−	1.99747i	0.0502618	−	0.998736i	$-0.483994\pi$
$648$	244264.	+	158743.i	0.581713	+	0.378046i
$649$	−75826.3			−0.180024
$650$			346745.i			0.820698i
$651$	−10964.8	+	18426.6i	−0.0258724	+	0.0434793i
$652$	−972770.			−2.28831
$653$			827823.i			1.94138i	0.240327	+	0.970692i	$0.422745\pi$
$653$			827823.i			1.94138i	−0.240327	+	0.970692i	$0.577255\pi$
$654$	497983.	+	296325.i	1.16429	+	0.692809i
$655$	−425669.			−0.992179
$656$		−	179350.i		−	0.416767i
$657$	79011.6	+	145579.i	0.183046	+	0.337263i
$658$	−41046.3			−0.0948029
$659$			655544.i			1.50949i	0.656016	+	0.754747i	$0.272240\pi$
$659$			655544.i			1.50949i	−0.656016	+	0.754747i	$0.727760\pi$
$660$	648253.	−	1.08941e6i	1.48818	−	2.50093i
$661$	370337.			0.847607			0.423803	−	0.905754i	$-0.360695\pi$
$661$	370337.			0.847607			0.423803	+	0.905754i	$0.360695\pi$
$662$		−	381105.i		−	0.869617i
$663$	166145.	+	98864.7i	0.377972	+	0.224913i
$664$	−144897.			−0.328642
$665$		−	93184.5i		−	0.210717i
$666$	1.03726e6	−	562961.i	2.33851	−	1.26920i
$667$	92816.8			0.208629
$668$			1.19298e6i			2.67351i
$669$	40719.0	−	68429.5i	0.0909798	−	0.152894i
$670$	846199.			1.88505
$671$			82475.6i			0.183181i
$672$	143309.	+	85276.1i	0.317347	+	0.188838i
$673$	585474.			1.29264			0.646320	−	0.763067i	$-0.276307\pi$
$673$	585474.			1.29264			0.646320	+	0.763067i	$0.276307\pi$
$674$			74376.7i			0.163726i
$675$	−512109.	−	20249.7i	−1.12397	−	0.0444438i
$676$	516060.			1.12929
$677$			714650.i			1.55925i	0.626246	+	0.779626i	$0.284591\pi$
$677$			714650.i			1.55925i	−0.626246	+	0.779626i	$0.715409\pi$
$678$	119948.	−	201575.i	0.260935	−	0.438508i
$679$	169156.			0.366899
$680$			440676.i			0.953019i
$681$	−357656.	−	212824.i	−0.771208	−	0.458908i
$682$	172934.			0.371801
$683$		−	643561.i		−	1.37959i	−0.724007	−	0.689793i	$-0.757702\pi$
$683$		−	643561.i		−	1.37959i	0.724007	−	0.689793i	$-0.242298\pi$
$684$	−158343.	−	291748.i	−0.338444	−	0.623585i
$685$	−622595.			−1.32686
$686$		−	414081.i		−	0.879908i
$687$	−317051.	+	532813.i	−0.671761	+	1.12891i
$688$	262345.			0.554238
$689$		−	337214.i		−	0.710342i
$690$	480113.	+	285691.i	1.00843	+	0.600066i
$691$	30031.3			0.0628952			0.0314476	−	0.999505i	$-0.489988\pi$
$691$	30031.3			0.0628952			0.0314476	+	0.999505i	$0.489988\pi$
$692$		−	316519.i		−	0.660978i
$693$	−171690.	+	93182.8i	−0.357502	+	0.194030i
$694$	−797323.			−1.65545
$695$			614599.i			1.27239i
$696$	69624.9	−	117007.i	0.143730	−	0.241542i
$697$	−531105.			−1.09324
$698$			645763.i			1.32545i
$699$	345071.	+	205335.i	0.706242	+	0.420250i
$700$	234088.			0.477730
$701$			143951.i			0.292940i	0.989215	+	0.146470i	$0.0467912\pi$
$701$			143951.i			0.292940i	−0.989215	+	0.146470i	$0.953209\pi$
$702$	14206.3	−	359273.i	0.0288275	−	0.729038i
$703$	−413364.			−0.836415
$704$		−	1.09875e6i		−	2.21693i
$705$	76379.9	−	128359.i	0.153674	−	0.258254i
$706$	−313394.			−0.628755
$707$		−	220692.i		−	0.441518i
$708$	−80969.6	−	48181.1i	−0.161531	−	0.0961191i
$709$	939736.			1.86945			0.934724	−	0.355375i	$-0.115647\pi$
$709$	939736.			1.86945			0.934724	+	0.355375i	$0.115647\pi$
$710$			1.74174e6i			3.45514i
$711$	349802.	+	644513.i	0.691964	+	1.27495i
$712$	−290718.			−0.573472
$713$			45027.0i			0.0885715i
$714$	112971.	−	189852.i	0.221601	−	0.372407i
$715$	−480939.			−0.940758
$716$		−	480776.i		−	0.937814i
$717$	20927.7	+	12453.0i	0.0407083	+	0.0242235i
$718$	1.10921e6			2.15161
$719$		−	402190.i		−	0.777988i	−0.921240	−	0.388994i	$-0.872823\pi$
$719$		−	402190.i		−	0.777988i	0.921240	−	0.388994i	$-0.127177\pi$
$720$	−238600.	+	129498.i	−0.460263	+	0.249803i
$721$	86136.9			0.165699
$722$		−	618110.i		−	1.18575i
$723$	325433.	−	546900.i	0.622566	−	1.04624i
$724$	757710.			1.44553
$725$			239537.i			0.455719i
$726$	645848.	+	384313.i	1.22534	+	0.729141i
$727$	−422494.			−0.799377			−0.399689	−	0.916651i	$-0.630882\pi$
$727$	−422494.			−0.799377			−0.399689	+	0.916651i	$0.630882\pi$
$728$			50479.6i			0.0952474i
$729$	529782.	+	41962.6i	0.996878	+	0.0789601i
$730$	465986.			0.874434
$731$		−	776877.i		−	1.45384i
$732$	−52406.1	+	88069.9i	−0.0978047	+	0.164364i
$733$	−471600.			−0.877741			−0.438870	−	0.898550i	$-0.644621\pi$
$733$	−471600.			−0.877741			−0.438870	+	0.898550i	$0.644621\pi$
$734$			1.48134e6i			2.74956i
$735$	618173.	+	367844.i	1.14429	+	0.680909i
$736$	350188.			0.646466
$737$			621325.i			1.14389i
$738$	471154.	+	868104.i	0.865068	+	1.59389i
$739$	637081.			1.16656			0.583278	−	0.812272i	$-0.301770\pi$
$739$	637081.			1.16656			0.583278	+	0.812272i	$0.301770\pi$
$740$		−	1.96156e6i		−	3.58210i
$741$	−64398.8	+	108224.i	−0.117285	+	0.197100i
$742$	−385331.			−0.699884
$743$		−	324714.i		−	0.588198i	−0.955775	−	0.294099i	$-0.904980\pi$
$743$		−	324714.i		−	0.588198i	0.955775	−	0.294099i	$-0.0950196\pi$
$744$	56761.9	+	33776.2i	0.102544	+	0.0610190i
$745$	−1.58779e6			−2.86075
$746$		−	1.59808e6i		−	2.87157i
$747$	−232322.	+	126090.i	−0.416341	+	0.225965i
$748$	−1.05266e6			−1.88142
$749$			41243.3i			0.0735173i
$750$	−81833.7	+	137524.i	−0.145482	+	0.244487i
$751$	−284150.			−0.503812			−0.251906	−	0.967752i	$-0.581057\pi$
$751$	−284150.			−0.503812			−0.251906	+	0.967752i	$0.581057\pi$
$752$		−	41883.8i		−	0.0740645i
$753$	−854606.	−	508534.i	−1.50722	−	0.896871i
$754$	−168049.			−0.295592
$755$			430299.i			0.754878i
$756$	−242545.	−	9590.67i	−0.424374	−	0.0167805i
$757$	343716.			0.599802			0.299901	−	0.953970i	$-0.403046\pi$
$757$	343716.			0.599802			0.299901	+	0.953970i	$0.403046\pi$
$758$			198344.i			0.345209i
$759$	−209770.	+	352524.i	−0.364133	+	0.611935i
$760$	−287049.			−0.496968
$761$		−	218313.i		−	0.376974i	−0.982076	−	0.188487i	$-0.939642\pi$
$761$		−	218313.i		−	0.376974i	0.982076	−	0.188487i	$-0.0603583\pi$
$762$	265823.	+	158178.i	0.457807	+	0.272419i
$763$	−148417.			−0.254938
$764$			29887.7i			0.0512043i
$765$	383479.	+	706562.i	0.655267	+	1.20733i
$766$	−144395.			−0.246090
$767$			35745.6i			0.0607619i
$768$	106242.	−	178543.i	0.180125	−	0.302706i
$769$	−1.07369e6			−1.81562			−0.907810	−	0.419382i	$-0.862247\pi$
$769$	−1.07369e6			−1.81562			−0.907810	+	0.419382i	$0.862247\pi$
$770$			549563.i			0.926907i
$771$	−769466.	−	457871.i	−1.29444	−	0.770255i
$772$	1.27617e6			2.14129
$773$		−	310794.i		−	0.520132i	−0.965591	−	0.260066i	$-0.916256\pi$
$773$		−	310794.i		−	0.520132i	0.965591	−	0.260066i	$-0.0837443\pi$
$774$	−1.26983e6	+	689184.i	−2.11964	+	1.15041i
$775$	−116204.			−0.193471
$776$		−	521073.i		−	0.865317i
$777$	−154570.	+	259760.i	−0.256026	+	0.430259i
$778$	−1.42283e6			−2.35067
$779$		−	345953.i		−	0.570088i
$780$	−513561.	−	305595.i	−0.844118	−	0.502293i
$781$	−1.27887e6			−2.09665
$782$		−	463920.i		−	0.758629i
$783$	9813.94	−	248192.i	0.0160074	−	0.404822i
$784$	201711.			0.328169
$785$		−	1.42653e6i		−	2.31496i
$786$	336151.	−	564911.i	0.544113	−	0.914398i
$787$	346788.			0.559906			0.279953	−	0.960014i	$-0.409681\pi$
$787$	346788.			0.559906			0.279953	+	0.960014i	$0.409681\pi$
$788$			1.30262e6i			2.09780i
$789$	−1.00792e6	−	599761.i	−1.61909	−	0.963440i
$790$	2.06303e6			3.30560
$791$			60076.6i			0.0960179i
$792$	287044.	+	528880.i	0.457612	+	0.843153i
$793$	38880.1			0.0618274
$794$			420518.i			0.667027i
$795$	717033.	−	1.20499e6i	1.13450	−	1.90656i
$796$	−209105.			−0.330019
$797$		−	537349.i		−	0.845941i	−0.906144	−	0.422970i	$-0.860987\pi$
$797$		−	537349.i		−	0.845941i	0.906144	−	0.422970i	$-0.139013\pi$
$798$	123666.	+	73587.7i	0.194198	+	0.115558i
$799$	−124029.			−0.194281
$800$			903749.i			1.41211i
$801$	−466126.	+	252985.i	−0.726504	+	0.394302i
$802$	1.71026e6			2.65897
$803$			342152.i			0.530625i
$804$	−394798.	+	663469.i	−0.610749	+	1.02638i
$805$	−143091.			−0.220810
$806$		−	81523.3i		−	0.125491i
$807$	−38939.3	−	23170.9i	−0.0597917	−	0.0355791i
$808$	−679829.			−1.04130
$809$		−	693266.i		−	1.05926i	−0.848229	−	0.529630i	$-0.822331\pi$
$809$		−	693266.i		−	1.05926i	0.848229	−	0.529630i	$-0.177669\pi$
$810$	814702.	−	1.25361e6i	1.24173	−	1.91070i
$811$	1.25756e6			1.91199			0.955995	−	0.293385i	$-0.0947816\pi$
$811$	1.25756e6			1.91199			0.955995	+	0.293385i	$0.0947816\pi$
$812$			113450.i			0.172065i
$813$	360465.	−	605772.i	0.545359	−	0.916491i
$814$	2.43785e6			3.67924
$815$			1.53458e6i			2.31033i
$816$	193725.	+	115277.i	0.290942	+	0.173125i
$817$	506045.			0.758132
$818$		−	781447.i		−	1.16787i
$819$	43927.6	+	80937.0i	0.0654893	+	0.120664i
$820$	1.64167e6			2.44151
$821$			944389.i			1.40109i	0.713611	+	0.700543i	$0.247059\pi$
$821$			944389.i			1.40109i	−0.713611	+	0.700543i	$0.752941\pi$
$822$	491663.	−	826254.i	0.727652	−	1.22284i
$823$	−239119.			−0.353032			−0.176516	−	0.984298i	$-0.556483\pi$
$823$	−239119.			−0.353032			−0.176516	+	0.984298i	$0.556483\pi$
$824$		−	265339.i		−	0.390793i
$825$	−909778.	−	541364.i	−1.33668	−	0.795393i
$826$	40846.0			0.0598673
$827$		−	312328.i		−	0.456667i	−0.973583	−	0.228334i	$-0.926672\pi$
$827$		−	312328.i		−	0.456667i	0.973583	−	0.228334i	$-0.0733277\pi$
$828$	−447997.	+	243145.i	−0.653453	+	0.354654i
$829$	361674.			0.526269			0.263135	−	0.964759i	$-0.415244\pi$
$829$	361674.			0.526269			0.263135	+	0.964759i	$0.415244\pi$
$830$			743642.i			1.07946i
$831$	412781.	−	693690.i	0.597748	−	1.00453i
$832$	−517964.			−0.748260
$833$		−	597324.i		−	0.860835i
$834$	−815641.	−	485348.i	−1.17265	−	0.697784i
$835$	1.88197e6			2.69923
$836$		−	685688.i		−	0.981102i
$837$	120402.	+	4760.91i	0.171863	+	0.00679578i
$838$	347727.			0.495166
$839$		−	763857.i		−	1.08515i	−0.840008	−	0.542573i	$-0.817450\pi$
$839$		−	763857.i		−	1.08515i	0.840008	−	0.542573i	$-0.182550\pi$
$840$	−107337.	+	180383.i	−0.152122	+	0.255645i
$841$	591190.			0.835863
$842$			732679.i			1.03345i
$843$	−61274.8	−	36461.6i	−0.0862237	−	0.0513075i
$844$	106710.			0.149803
$845$		−	814103.i		−	1.14016i
$846$	110029.	+	202729.i	0.153733	+	0.283254i
$847$	−192486.			−0.268307
$848$		−	393193.i		−	0.546782i
$849$	−284374.	+	477899.i	−0.394525	+	0.663011i
$850$	1.19726e6			1.65711
$851$			634746.i			0.876477i
$852$	−1.36562e6	−	812614.i	−1.88127	−	1.11945i
$853$	558102.			0.767036			0.383518	−	0.923533i	$-0.374712\pi$
$853$	558102.			0.767036			0.383518	+	0.923533i	$0.374712\pi$
$854$		−	44427.8i		−	0.0609171i
$855$	−460243.	+	249792.i	−0.629586	+	0.341701i
$856$	127047.			0.173387
$857$		−	979716.i		−	1.33395i	−0.745082	−	0.666973i	$-0.767590\pi$
$857$		−	979716.i		−	1.33395i	0.745082	−	0.666973i	$-0.232410\pi$
$858$	379797.	−	638260.i	0.515914	−	0.867008i
$859$	−1.20323e6			−1.63065			−0.815326	−	0.579002i	$-0.803442\pi$
$859$	−1.20323e6			−1.63065			−0.815326	+	0.579002i	$0.803442\pi$
$860$			2.40136e6i			3.24684i
$861$	−217398.	−	129363.i	−0.293258	−	0.174503i
$862$	−1.34102e6			−1.80477
$863$		−	4984.90i		−	0.00669321i	−0.999994	−	0.00334660i	$-0.998935\pi$
$863$		−	4984.90i		−	0.00669321i	0.999994	−	0.00334660i	$-0.00106526\pi$
$864$	37027.0	−	936401.i	0.0496011	−	1.25440i
$865$	−499319.			−0.667339
$866$		−	1.67410e6i		−	2.23227i
$867$	−43021.6	+	72299.0i	−0.0572333	+	0.0961821i
$868$	−55036.4			−0.0730484
$869$			1.51478e6i			2.00591i
$870$	−600502.	−	357329.i	−0.793370	−	0.472096i
$871$	292901.			0.386086
$872$			457188.i			0.601260i
$873$	−453441.	−	835468.i	−0.594966	−	1.09623i
$874$	302190.			0.395600
$875$		−	40987.0i		−	0.0535341i
$876$	−217408.	+	365360.i	−0.283313	+	0.476116i
$877$	22131.4			0.0287746			0.0143873	−	0.999896i	$-0.495420\pi$
$877$	22131.4			0.0287746			0.0143873	+	0.999896i	$0.495420\pi$
$878$			560639.i			0.727267i
$879$	−944471.	−	562008.i	−1.22239	−	0.727386i
$880$	−560777.			−0.724143
$881$			1.07659e6i			1.38707i	0.720423	+	0.693535i	$0.243948\pi$
$881$			1.07659e6i			1.38707i	−0.720423	+	0.693535i	$0.756052\pi$
$882$	−976341.	+	529898.i	−1.25506	+	0.681170i
$883$	−992221.			−1.27259			−0.636293	−	0.771448i	$-0.719533\pi$
$883$	−992221.			−1.27259			−0.636293	+	0.771448i	$0.719533\pi$
$884$			496241.i			0.635020i
$885$	−76007.3	+	127733.i	−0.0970441	+	0.163085i
$886$	−1.26757e6			−1.61475
$887$			336820.i			0.428106i	0.976822	+	0.214053i	$0.0686665\pi$
$887$			336820.i			0.428106i	−0.976822	+	0.214053i	$0.931334\pi$
$888$	800173.	+	476144.i	1.01475	+	0.603826i
$889$	−79224.8			−0.100244
$890$			1.49203e6i			1.88363i
$891$	920468.	+	598198.i	1.15945	+	0.753511i
$892$	204385.			0.256873
$893$		−	80790.8i		−	0.101312i
$894$	1.25388e6	−	2.10717e6i	1.56884	−	2.63649i
$895$	−758441.			−0.946838
$896$			295406.i			0.367962i
$897$	166185.	+	98888.4i	0.206541	+	0.122902i
$898$	2.15423e6			2.67141
$899$		−	56317.7i		−	0.0696827i
$900$	−627498.	−	1.15617e6i	−0.774689	−	1.42737i
$901$	−1.16435e6			−1.43429
$902$			2.04029e6i			2.50771i
$903$	189227.	−	318001.i	0.232063	−	0.389989i
$904$	185062.			0.226454
$905$		−	1.19531e6i		−	1.45944i
$906$	−571055.	−	339807.i	−0.695700	−	0.413977i
$907$	1.47051e6			1.78753			0.893763	−	0.448540i	$-0.148056\pi$
$907$	1.47051e6			1.78753			0.893763	+	0.448540i	$0.148056\pi$
$908$		−	1.06825e6i		−	1.29568i
$909$	−1.09001e6	+	591591.i	−1.31918	+	0.715968i
$910$	259072.			0.312851
$911$			1.10724e6i			1.33416i	0.744988	+	0.667078i	$0.232455\pi$
$911$			1.10724e6i			1.33416i	−0.744988	+	0.667078i	$0.767545\pi$
$912$	−75089.2	+	126190.i	−0.0902792	+	0.151717i
$913$	−546021.			−0.655040
$914$		−	331798.i		−	0.397175i
$915$	138933.	+	82672.5i	0.165945	+	0.0987458i
$916$	−1.59140e6			−1.89666
$917$			168364.i			0.200221i
$918$	−1.24052e6	−	49052.4i	−1.47204	−	0.0582069i
$919$	116150.			0.137527			0.0687634	−	0.997633i	$-0.478095\pi$
$919$	116150.			0.137527			0.0687634	+	0.997633i	$0.478095\pi$
$920$			440782.i			0.520772i
$921$	−130746.	+	219722.i	−0.154137	+	0.259032i
$922$	309529.			0.364116
$923$			602879.i			0.707664i
$924$	−430889.	−	256401.i	−0.504687	−	0.300314i
$925$	−1.63812e6			−1.91453
$926$		−	2.08498e6i		−	2.43153i
$927$	−230900.	−	425434.i	−0.268698	−	0.495077i
$928$	−437999.			−0.508600
$929$			513080.i			0.594502i	0.954799	+	0.297251i	$0.0960698\pi$
$929$			513080.i			0.594502i	−0.954799	+	0.297251i	$0.903930\pi$
$930$	173347.	−	291314.i	0.200424	−	0.336818i
$931$	389087.			0.448897
$932$			1.03066e6i			1.18654i
$933$	−672351.	−	400083.i	−0.772384	−	0.459608i
$934$	−431621.			−0.494777
$935$			1.66062e6i			1.89953i
$936$	249321.	−	135316.i	0.284582	−	0.154454i
$937$	972195.			1.10732			0.553662	−	0.832742i	$-0.313230\pi$
$937$	972195.			1.10732			0.553662	+	0.832742i	$0.313230\pi$
$938$		−	334694.i		−	0.380402i
$939$	352279.	−	592014.i	0.399535	−	0.671430i
$940$	383381.			0.433885
$941$			52737.5i			0.0595580i	0.999557	+	0.0297790i	$0.00948035\pi$
$941$			52737.5i			0.0595580i	−0.999557	+	0.0297790i	$0.990520\pi$
$942$	1.89317e6	+	1.12653e6i	2.13348	+	1.26953i
$943$	−531232.			−0.597394
$944$			41679.4i			0.0467711i
$945$	−15129.6	+	382624.i	−0.0169420	+	0.428458i
$946$	−2.98444e6			−3.33489
$947$			412170.i			0.459596i	0.973238	+	0.229798i	$0.0738065\pi$
$947$			412170.i			0.459596i	−0.973238	+	0.229798i	$0.926193\pi$
$948$	−962514.	+	1.61753e6i	−1.07100	+	1.79985i
$949$	161295.			0.179097
$950$			779877.i			0.864130i
$951$	768212.	+	457125.i	0.849416	+	0.505446i
$952$	174299.			0.192318
$953$			434292.i			0.478185i	0.970997	+	0.239092i	$0.0768499\pi$
$953$			434292.i			0.478185i	−0.970997	+	0.239092i	$0.923150\pi$
$954$	1.03292e6	+	1.90317e6i	1.13494	+	2.09113i
$955$	47149.0			0.0516970
$956$			62506.7i			0.0683929i
$957$	262370.	−	440921.i	0.286478	−	0.481434i
$958$	1.12332e6			1.22398
$959$			246253.i			0.267759i
$960$	−1.85088e6	−	1.10137e6i	−2.00833	−	1.19506i
$961$	−896200.			−0.970417
$962$		−	1.14923e6i		−	1.24182i
$963$	203702.	−	110557.i	0.219656	−	0.119216i
$964$	1.63348e6			1.75776
$965$		−	2.01321e6i		−	2.16189i
$966$	112999.	−	189897.i	0.121093	−	0.203500i
$967$	270489.			0.289265			0.144633	−	0.989485i	$-0.453800\pi$
$967$	270489.			0.289265			0.144633	+	0.989485i	$0.453800\pi$
$968$			592940.i			0.632791i
$969$	373683.	+	222360.i	0.397975	+	0.236815i
$970$	−2.67425e6			−2.84223
$971$		−	76446.1i		−	0.0810806i	−0.999178	−	0.0405403i	$-0.987092\pi$
$971$		−	76446.1i		−	0.0810806i	0.999178	−	0.0405403i	$-0.0129079\pi$
$972$	602801.	+	1.22365e6i	0.638031	+	1.29517i
$973$	243090.			0.256768
$974$		−	1.09205e6i		−	1.15113i
$975$	−255207.	+	428882.i	−0.268462	+	0.451158i
$976$	45334.3			0.0475913
$977$			756574.i			0.792615i	0.918118	+	0.396307i	$0.129709\pi$
$977$			756574.i			0.792615i	−0.918118	+	0.396307i	$0.870291\pi$
$978$	−2.03656e6	−	1.21186e6i	−2.12921	−	1.26699i
$979$	−1.09552e6			−1.14303
$980$			1.84635e6i			1.92248i
$981$	397848.	+	733038.i	0.413408	+	0.761707i
$982$	−81865.2			−0.0848938
$983$			492108.i			0.509276i	0.967036	+	0.254638i	$0.0819563\pi$
$983$			492108.i			0.509276i	−0.967036	+	0.254638i	$0.918044\pi$
$984$	−398495.	+	669681.i	−0.411559	+	0.691637i
$985$	2.05493e6			2.11799
$986$			580249.i			0.596844i
$987$	−50769.3	−	30210.3i	−0.0521155	−	0.0310113i
$988$	−323243.			−0.331143
$989$		−	777063.i		−	0.794445i
$990$	2.71432e6	−	1.47317e6i	2.76943	−	1.50308i
$991$	1.24264e6			1.26532			0.632658	−	0.774431i	$-0.281964\pi$
$991$	1.24264e6			1.26532			0.632658	+	0.774431i	$0.281964\pi$
$992$		−	212481.i		−	0.215922i
$993$	280495.	−	471380.i	0.284464	−	0.478050i
$994$	688903.			0.697245
$995$			329871.i			0.333195i
$996$	−583058.	−	346949.i	−0.587751	−	0.349742i
$997$	407750.			0.410207			0.205104	−	0.978740i	$-0.434247\pi$
$997$	407750.			0.410207			0.205104	+	0.978740i	$0.434247\pi$
$998$			2.56551e6i			2.57581i
$999$	1.69731e6	+	67114.6i	1.70071	+	0.0672490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.68	yes	78
3.2	odd	2	inner	177.5.b.a.119.11	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.11	✓	78	3.2	odd	2	inner
177.5.b.a.119.68	yes	78	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+6.25305i q^{2} +(-4.60229 + 7.73427i) q^{3} -23.1007 q^{4} +36.4421i q^{5} +(-48.3628 - 28.7783i) q^{6} +14.4138 q^{7} -44.4009i q^{8} +(-38.6379 - 71.1907i) q^{9} +O(q^{10})\)	\(q+6.25305i q^{2} +(-4.60229 + 7.73427i) q^{3} -23.1007 q^{4} +36.4421i q^{5} +(-48.3628 - 28.7783i) q^{6} +14.4138 q^{7} -44.4009i q^{8} +(-38.6379 - 71.1907i) q^{9} -227.875 q^{10} -167.318i q^{11} +(106.316 - 178.667i) q^{12} -78.8759 q^{13} +90.1305i q^{14} +(-281.853 - 167.717i) q^{15} -91.9695 q^{16} +272.347i q^{17} +(445.159 - 241.605i) q^{18} -177.403 q^{19} -841.838i q^{20} +(-66.3366 + 111.481i) q^{21} +1046.25 q^{22} +272.413i q^{23} +(343.409 + 204.346i) q^{24} -703.030 q^{25} -493.215i q^{26} +(728.431 + 28.8035i) q^{27} -332.969 q^{28} -340.721i q^{29} +(1048.74 - 1762.44i) q^{30} +165.290 q^{31} -1285.51i q^{32} +(1294.08 + 770.044i) q^{33} -1703.00 q^{34} +525.271i q^{35} +(892.562 + 1644.55i) q^{36} +2330.09 q^{37} -1109.31i q^{38} +(363.009 - 610.048i) q^{39} +1618.06 q^{40} +1950.10i q^{41} +(-697.094 - 414.806i) q^{42} -2852.52 q^{43} +3865.15i q^{44} +(2594.34 - 1408.05i) q^{45} -1703.41 q^{46} +455.409i q^{47} +(423.270 - 711.317i) q^{48} -2193.24 q^{49} -4396.09i q^{50} +(-2106.41 - 1253.42i) q^{51} +1822.09 q^{52} +4275.25i q^{53} +(-180.110 + 4554.92i) q^{54} +6097.42 q^{55} -639.988i q^{56} +(816.458 - 1372.08i) q^{57} +2130.55 q^{58} -453.188i q^{59} +(6511.01 + 3874.38i) q^{60} -492.928 q^{61} +1033.56i q^{62} +(-556.921 - 1026.13i) q^{63} +6566.82 q^{64} -2874.41i q^{65} +(-4815.13 + 8091.96i) q^{66} -3713.44 q^{67} -6291.41i q^{68} +(-2106.91 - 1253.72i) q^{69} -3284.55 q^{70} -7643.39i q^{71} +(-3160.93 + 1715.56i) q^{72} -2044.92 q^{73} +14570.2i q^{74} +(3235.55 - 5437.43i) q^{75} +4098.12 q^{76} -2411.69i q^{77} +(3814.66 + 2269.92i) q^{78} -9053.34 q^{79} -3351.57i q^{80} +(-3575.22 + 5501.32i) q^{81} -12194.1 q^{82} -3263.38i q^{83} +(1532.42 - 2575.28i) q^{84} -9924.93 q^{85} -17837.0i q^{86} +(2635.23 + 1568.10i) q^{87} -7429.06 q^{88} -6547.57i q^{89} +(8804.61 + 16222.6i) q^{90} -1136.90 q^{91} -6292.92i q^{92} +(-760.710 + 1278.40i) q^{93} -2847.70 q^{94} -6464.93i q^{95} +(9942.45 + 5916.26i) q^{96} +11735.6 q^{97} -13714.5i q^{98} +(-11911.5 + 6464.81i) 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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