LMFDB - Embedded newform 177.5.b.a.119.3

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			119.3
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.76

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.49534i q^{2} +(-6.13251 + 6.58728i) q^{3} -40.1801 q^{4} -24.9668i q^{5} +(49.3739 + 45.9653i) q^{6} -52.3496 q^{7} +181.238i q^{8} +(-5.78454 - 80.7932i) q^{9} +O(q^{10})$	\(q-7.49534i q^{2} +(-6.13251 + 6.58728i) q^{3} -40.1801 q^{4} -24.9668i q^{5} +(49.3739 + 45.9653i) q^{6} -52.3496 q^{7} +181.238i q^{8} +(-5.78454 - 80.7932i) q^{9} -187.134 q^{10} +127.308i q^{11} +(246.405 - 264.678i) q^{12} -56.9103 q^{13} +392.378i q^{14} +(164.463 + 153.109i) q^{15} +715.561 q^{16} +227.481i q^{17} +(-605.572 + 43.3571i) q^{18} -187.501 q^{19} +1003.17i q^{20} +(321.035 - 344.841i) q^{21} +954.213 q^{22} -905.445i q^{23} +(-1193.87 - 1111.45i) q^{24} +1.66106 q^{25} +426.562i q^{26} +(567.681 + 457.361i) q^{27} +2103.41 q^{28} -1371.77i q^{29} +(1147.60 - 1232.71i) q^{30} +812.896 q^{31} -2463.56i q^{32} +(-838.610 - 780.715i) q^{33} +1705.05 q^{34} +1307.00i q^{35} +(232.424 + 3246.28i) q^{36} +253.452 q^{37} +1405.38i q^{38} +(349.003 - 374.884i) q^{39} +4524.93 q^{40} +1746.31i q^{41} +(-2584.70 - 2406.26i) q^{42} +1428.74 q^{43} -5115.23i q^{44} +(-2017.14 + 144.421i) q^{45} -6786.61 q^{46} +1935.60i q^{47} +(-4388.19 + 4713.60i) q^{48} +339.479 q^{49} -12.4502i q^{50} +(-1498.48 - 1395.03i) q^{51} +2286.66 q^{52} +4446.72i q^{53} +(3428.08 - 4254.96i) q^{54} +3178.46 q^{55} -9487.75i q^{56} +(1149.85 - 1235.12i) q^{57} -10281.8 q^{58} -453.188i q^{59} +(-6608.15 - 6151.94i) q^{60} -2336.04 q^{61} -6092.93i q^{62} +(302.819 + 4229.49i) q^{63} -7016.24 q^{64} +1420.86i q^{65} +(-5851.73 + 6285.67i) q^{66} +4913.00 q^{67} -9140.23i q^{68} +(5964.42 + 5552.65i) q^{69} +9796.41 q^{70} +8307.66i q^{71} +(14642.8 - 1048.38i) q^{72} -3769.78 q^{73} -1899.71i q^{74} +(-10.1865 + 10.9419i) q^{75} +7533.80 q^{76} -6664.50i q^{77} +(-2809.88 - 2615.90i) q^{78} +2128.79 q^{79} -17865.2i q^{80} +(-6494.08 + 934.704i) q^{81} +13089.2 q^{82} +7492.96i q^{83} +(-12899.2 + 13855.8i) q^{84} +5679.47 q^{85} -10708.9i q^{86} +(9036.20 + 8412.37i) q^{87} -23073.0 q^{88} -10955.2i q^{89} +(1082.49 + 15119.2i) q^{90} +2979.23 q^{91} +36380.9i q^{92} +(-4985.09 + 5354.77i) q^{93} +14508.0 q^{94} +4681.28i q^{95} +(16228.2 + 15107.8i) q^{96} -16012.3 q^{97} -2544.51i q^{98} +(10285.6 - 736.416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	7.49534i		−	1.87384i	−0.349550	−	0.936918i	$-0.613666\pi$
$2$		−	7.49534i		−	1.87384i	0.349550	−	0.936918i	$-0.386334\pi$
$3$	−6.13251	+	6.58728i	−0.681390	+	0.731920i
$3$	−6.13251	+	6.58728i	−0.681390	+	0.731920i
$4$	−40.1801			−2.51126
$5$		−	24.9668i		−	0.998670i	−0.866409	−	0.499335i	$-0.833578\pi$
$5$		−	24.9668i		−	0.998670i	0.866409	−	0.499335i	$-0.166422\pi$
$6$	49.3739	+	45.9653i	1.37150	+	1.27681i
$7$	−52.3496			−1.06836			−0.534179	−	0.845371i	$-0.679379\pi$
$7$	−52.3496			−1.06836			−0.534179	+	0.845371i	$0.679379\pi$
$8$			181.238i			2.83185i
$9$	−5.78454	−	80.7932i	−0.0714141	−	0.997447i
$10$	−187.134			−1.87134
$11$			127.308i			1.05213i	0.850445	+	0.526064i	$0.176333\pi$
$11$			127.308i			1.05213i	−0.850445	+	0.526064i	$0.823667\pi$
$12$	246.405	−	264.678i	1.71115	−	1.83804i
$13$	−56.9103			−0.336747			−0.168374	−	0.985723i	$-0.553851\pi$
$13$	−56.9103			−0.336747			−0.168374	+	0.985723i	$0.553851\pi$
$14$			392.378i			2.00193i
$15$	164.463	+	153.109i	0.730947	+	0.680484i
$16$	715.561			2.79516
$17$			227.481i			0.787133i	0.919296	+	0.393566i	$0.128759\pi$
$17$			227.481i			0.787133i	−0.919296	+	0.393566i	$0.871241\pi$
$18$	−605.572	+	43.3571i	−1.86905	+	0.133818i
$19$	−187.501			−0.519392			−0.259696	−	0.965690i	$-0.583622\pi$
$19$	−187.501			−0.519392			−0.259696	+	0.965690i	$0.583622\pi$
$20$			1003.17i			2.50792i
$21$	321.035	−	344.841i	0.727970	−	0.781953i
$22$	954.213			1.97151
$23$		−	905.445i		−	1.71162i	−0.517294	−	0.855808i	$-0.673061\pi$
$23$		−	905.445i		−	1.71162i	0.517294	−	0.855808i	$-0.326939\pi$
$24$	−1193.87	−	1111.45i	−2.07269	−	1.92959i
$25$	1.66106			0.00265769
$26$			426.562i			0.631009i
$27$	567.681	+	457.361i	0.778712	+	0.627381i
$28$	2103.41			2.68293
$29$		−	1371.77i		−	1.63111i	−0.578678	−	0.815556i	$-0.696431\pi$
$29$		−	1371.77i		−	1.63111i	0.578678	−	0.815556i	$-0.303569\pi$
$30$	1147.60	−	1232.71i	1.27512	−	1.36967i
$31$	812.896			0.845885			0.422943	−	0.906157i	$-0.360997\pi$
$31$	812.896			0.845885			0.422943	+	0.906157i	$0.360997\pi$
$32$		−	2463.56i		−	2.40582i
$33$	−838.610	−	780.715i	−0.770074	−	0.716910i
$34$	1705.05			1.47496
$35$			1307.00i			1.06694i
$36$	232.424	+	3246.28i	0.179339	+	2.50485i
$37$	253.452			0.185136			0.0925682	−	0.995706i	$-0.470492\pi$
$37$	253.452			0.185136			0.0925682	+	0.995706i	$0.470492\pi$
$38$			1405.38i			0.973255i
$39$	349.003	−	374.884i	0.229456	−	0.246472i
$40$	4524.93			2.82808
$41$			1746.31i			1.03885i	0.854515	+	0.519427i	$0.173854\pi$
$41$			1746.31i			1.03885i	−0.854515	+	0.519427i	$0.826146\pi$
$42$	−2584.70	−	2406.26i	−1.46525	−	1.36409i
$43$	1428.74			0.772708			0.386354	−	0.922350i	$-0.373734\pi$
$43$	1428.74			0.772708			0.386354	+	0.922350i	$0.373734\pi$
$44$		−	5115.23i		−	2.64217i
$45$	−2017.14	+	144.421i	−0.996120	+	0.0713192i
$46$	−6786.61			−3.20728
$47$			1935.60i			0.876233i	0.898918	+	0.438117i	$0.144354\pi$
$47$			1935.60i			0.876233i	−0.898918	+	0.438117i	$0.855646\pi$
$48$	−4388.19	+	4713.60i	−1.90459	+	2.04583i
$49$	339.479			0.141391
$50$		−	12.4502i		−	0.00498008i
$51$	−1498.48	−	1395.03i	−0.576118	−	0.536345i
$52$	2286.66			0.845659
$53$			4446.72i			1.58303i	0.611152	+	0.791513i	$0.290706\pi$
$53$			4446.72i			1.58303i	−0.611152	+	0.791513i	$0.709294\pi$
$54$	3428.08	−	4254.96i	1.17561	−	1.45918i
$55$	3178.46			1.05073
$56$		−	9487.75i		−	3.02543i
$57$	1149.85	−	1235.12i	0.353909	−	0.380154i
$58$	−10281.8			−3.05644
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	−6608.15	−	6151.94i	−1.83560	−	1.70887i
$61$	−2336.04			−0.627798			−0.313899	−	0.949456i	$-0.601635\pi$
$61$	−2336.04			−0.627798			−0.313899	+	0.949456i	$0.601635\pi$
$62$		−	6092.93i		−	1.58505i
$63$	302.819	+	4229.49i	0.0762959	+	1.06563i
$64$	−7016.24			−1.71295
$65$			1420.86i			0.336299i
$66$	−5851.73	+	6285.67i	−1.34337	+	1.44299i
$67$	4913.00			1.09445			0.547227	−	0.836984i	$-0.315683\pi$
$67$	4913.00			1.09445			0.547227	+	0.836984i	$0.315683\pi$
$68$		−	9140.23i		−	1.97669i
$69$	5964.42	+	5552.65i	1.25277	+	1.16628i
$70$	9796.41			1.99927
$71$			8307.66i			1.64802i	0.566577	+	0.824009i	$0.308267\pi$
$71$			8307.66i			1.64802i	−0.566577	+	0.824009i	$0.691733\pi$
$72$	14642.8	−	1048.38i	2.82462	−	0.202234i
$73$	−3769.78			−0.707408			−0.353704	−	0.935357i	$-0.615078\pi$
$73$	−3769.78			−0.707408			−0.353704	+	0.935357i	$0.615078\pi$
$74$		−	1899.71i		−	0.346915i
$75$	−10.1865	+	10.9419i	−0.00181093	+	0.00194522i
$76$	7533.80			1.30433
$77$		−	6664.50i		−	1.12405i
$78$	−2809.88	−	2615.90i	−0.461848	−	0.429963i
$79$	2128.79			0.341097			0.170549	−	0.985349i	$-0.445446\pi$
$79$	2128.79			0.341097			0.170549	+	0.985349i	$0.445446\pi$
$80$		−	17865.2i		−	2.79144i
$81$	−6494.08	+	934.704i	−0.989800	+	0.142464i
$82$	13089.2			1.94664
$83$			7492.96i			1.08767i	0.839192	+	0.543835i	$0.183028\pi$
$83$			7492.96i			1.08767i	−0.839192	+	0.543835i	$0.816972\pi$
$84$	−12899.2	+	13855.8i	−1.82812	+	1.96369i
$85$	5679.47			0.786086
$86$		−	10708.9i		−	1.44793i
$87$	9036.20	+	8412.37i	1.19384	+	1.11142i
$88$	−23073.0			−2.97947
$89$		−	10955.2i		−	1.38306i	−0.722349	−	0.691529i	$-0.756937\pi$
$89$		−	10955.2i		−	1.38306i	0.722349	−	0.691529i	$-0.243063\pi$
$90$	1082.49	+	15119.2i	0.133640	+	1.86657i
$91$	2979.23			0.359767
$92$			36380.9i			4.29831i
$93$	−4985.09	+	5354.77i	−0.576378	+	0.619120i
$94$	14508.0			1.64192
$95$			4681.28i			0.518702i
$96$	16228.2	+	15107.8i	1.76087	+	1.63930i
$97$	−16012.3			−1.70181			−0.850906	−	0.525318i	$-0.823946\pi$
$97$	−16012.3			−1.70181			−0.850906	+	0.525318i	$0.823946\pi$
$98$		−	2544.51i		−	0.264943i
$99$	10285.6	−	736.416i	1.04944	−	0.0751368i
$100$	−66.7416			−0.00667416
$101$			13426.8i			1.31622i	0.752920	+	0.658112i	$0.228645\pi$
$101$			13426.8i			1.31622i	−0.752920	+	0.658112i	$0.771355\pi$
$102$	−10456.2	+	11231.6i	−1.00502	+	1.07955i
$103$	16881.8			1.59127			0.795635	−	0.605777i	$-0.207138\pi$
$103$	16881.8			1.59127			0.795635	+	0.605777i	$0.207138\pi$
$104$		−	10314.3i		−	0.953617i
$105$	−8609.57	−	8015.19i	−0.780914	−	0.727002i
$106$	33329.7			2.96633
$107$			8103.84i			0.707820i	0.935279	+	0.353910i	$0.115148\pi$
$107$			8103.84i			0.707820i	−0.935279	+	0.353910i	$0.884852\pi$
$108$	−22809.5	−	18376.8i	−1.95555	−	1.57552i
$109$	4896.71			0.412146			0.206073	−	0.978537i	$-0.433932\pi$
$109$	4896.71			0.412146			0.206073	+	0.978537i	$0.433932\pi$
$110$		−	23823.6i		−	1.96889i
$111$	−1554.30	+	1669.56i	−0.126150	+	0.135505i
$112$	−37459.3			−2.98623
$113$			11924.9i			0.933897i	0.884284	+	0.466949i	$0.154647\pi$
$113$			11924.9i			0.933897i	−0.884284	+	0.466949i	$0.845353\pi$
$114$	−9257.64	−	8618.52i	−0.712345	−	0.663167i
$115$	−22606.0			−1.70934
$116$			55117.7i			4.09614i
$117$	329.200	+	4597.96i	0.0240485	+	0.335887i
$118$	−3396.80			−0.243953
$119$		−	11908.6i		−	0.840940i
$120$	−27749.2	+	29807.0i	−1.92703	+	2.06993i
$121$	−1566.21			−0.106974
$122$			17509.4i			1.17639i
$123$	−11503.4	−	10709.3i	−0.760357	−	0.707865i
$124$	−32662.2			−2.12424
$125$		−	15645.7i		−	1.00132i
$126$	31701.5	−	2269.73i	1.99682	−	0.142966i
$127$	22268.1			1.38063			0.690313	−	0.723510i	$-0.257473\pi$
$127$	22268.1			1.38063			0.690313	+	0.723510i	$0.257473\pi$
$128$			13172.2i			0.803965i
$129$	−8761.76	+	9411.50i	−0.526516	+	0.565561i
$130$	10649.9			0.630169
$131$		−	13648.9i		−	0.795343i	−0.917528	−	0.397672i	$-0.869818\pi$
$131$		−	13648.9i		−	0.795343i	0.917528	−	0.397672i	$-0.130182\pi$
$132$	33695.5	+	31369.2i	1.93385	+	1.80035i
$133$	9815.58			0.554897
$134$		−	36824.6i		−	2.05083i
$135$	11418.8	−	14173.2i	0.626547	−	0.777677i
$136$	−41228.3			−2.22904
$137$		−	33762.7i		−	1.79885i	−0.437070	−	0.899427i	$-0.643984\pi$
$137$		−	33762.7i		−	1.79885i	0.437070	−	0.899427i	$-0.356016\pi$
$138$	41619.0	−	44705.3i	2.18541	−	2.34748i
$139$	9781.52			0.506264			0.253132	−	0.967432i	$-0.418539\pi$
$139$	9781.52			0.506264			0.253132	+	0.967432i	$0.418539\pi$
$140$		−	52515.4i		−	2.67936i
$141$	−12750.3	−	11870.1i	−0.641333	−	0.597057i
$142$	62268.7			3.08811
$143$		−	7245.10i		−	0.354301i
$144$	−4139.19	−	57812.4i	−0.199614	−	2.78802i
$145$	−34248.5			−1.62894
$146$			28255.8i			1.32557i
$147$	−2081.86	+	2236.25i	−0.0963424	+	0.103487i
$148$	−10183.7			−0.464925
$149$			43389.2i			1.95438i	0.212363	+	0.977191i	$0.431884\pi$
$149$			43389.2i			1.95438i	−0.212363	+	0.977191i	$0.568116\pi$
$150$	82.0130	+	76.3511i	0.00364502	+	0.00339338i
$151$	−15713.3			−0.689148			−0.344574	−	0.938759i	$-0.611977\pi$
$151$	−15713.3			−0.689148			−0.344574	+	0.938759i	$0.611977\pi$
$152$		−	33982.3i		−	1.47084i
$153$	18378.9	−	1315.88i	0.785123	−	0.0562124i
$154$	−49952.7			−2.10629
$155$		−	20295.4i		−	0.844760i
$156$	−14023.0	+	15062.9i	−0.576224	+	0.618955i
$157$	−14305.3			−0.580361			−0.290181	−	0.956972i	$-0.593715\pi$
$157$	−14305.3			−0.580361			−0.290181	+	0.956972i	$0.593715\pi$
$158$		−	15956.0i		−	0.639160i
$159$	−29291.8	−	27269.6i	−1.15865	−	1.07866i
$160$	−61507.1			−2.40262
$161$			47399.6i			1.82862i
$162$	7005.92	+	48675.3i	0.266953	+	1.85472i
$163$	−11045.1			−0.415713			−0.207857	−	0.978159i	$-0.566649\pi$
$163$	−11045.1			−0.415713			−0.207857	+	0.978159i	$0.566649\pi$
$164$		−	70167.0i		−	2.60883i
$165$	−19491.9	+	20937.4i	−0.715957	+	0.769050i
$166$	56162.3			2.03812
$167$			36094.9i			1.29424i	0.762390	+	0.647118i	$0.224026\pi$
$167$			36094.9i			1.29424i	−0.762390	+	0.647118i	$0.775974\pi$
$168$	62498.5	+	58183.8i	2.21437	+	2.06150i
$169$	−25322.2			−0.886601
$170$		−	42569.6i		−	1.47300i
$171$	1084.61	+	15148.8i	0.0370919	+	0.518066i
$172$	−57406.9			−1.94047
$173$			36096.8i			1.20608i	0.797711	+	0.603040i	$0.206044\pi$
$173$			36096.8i			1.20608i	−0.797711	+	0.603040i	$0.793956\pi$
$174$	63053.6	−	67729.4i	2.08263	−	2.23707i
$175$	−86.9558			−0.00283937
$176$			91096.3i			2.94087i
$177$	2985.27	+	2779.18i	0.0952879	+	0.0887095i
$178$	−82113.0			−2.59162
$179$			4409.95i			0.137635i	0.997629	+	0.0688174i	$0.0219226\pi$
$179$			4409.95i			0.137635i	−0.997629	+	0.0688174i	$0.978077\pi$
$180$	81049.1	−	5802.87i	2.50152	−	0.179101i
$181$	−43407.5			−1.32497			−0.662487	−	0.749074i	$-0.730499\pi$
$181$	−43407.5			−1.32497			−0.662487	+	0.749074i	$0.730499\pi$
$182$		−	22330.3i		−	0.674144i
$183$	14325.8	−	15388.1i	0.427776	−	0.459498i
$184$	164101.			4.84704
$185$		−	6327.87i		−	0.184890i
$186$	40135.8	+	37365.0i	1.16013	+	1.08004i
$187$	−28960.1			−0.828165
$188$		−	77772.6i		−	2.20045i
$189$	−29717.9	−	23942.7i	−0.831944	−	0.670268i
$190$	35087.8			0.971961
$191$			40966.2i			1.12295i	0.827495	+	0.561473i	$0.189765\pi$
$191$			40966.2i			1.12295i	−0.827495	+	0.561473i	$0.810235\pi$
$192$	43027.2	−	46217.9i	1.16719	−	1.25374i
$193$	37461.5			1.00571			0.502853	−	0.864372i	$-0.332284\pi$
$193$	37461.5			1.00571			0.502853	+	0.864372i	$0.332284\pi$
$194$			120018.i			3.18891i
$195$	−9359.63	−	8713.47i	−0.246144	−	0.229151i
$196$	−13640.3			−0.355069
$197$		−	60634.8i		−	1.56239i	−0.624287	−	0.781195i	$-0.714611\pi$
$197$		−	60634.8i		−	1.56239i	0.624287	−	0.781195i	$-0.285389\pi$
$198$	−5519.69	−	77093.9i	−0.140794	−	1.96648i
$199$	−37712.7			−0.952317			−0.476159	−	0.879359i	$-0.657971\pi$
$199$	−37712.7			−0.952317			−0.476159	+	0.879359i	$0.657971\pi$
$200$			301.048i			0.00752619i
$201$	−30129.1	+	32363.3i	−0.745751	+	0.801053i
$202$	100638.			2.46639
$203$			71811.4i			1.74261i
$204$	60209.3	+	56052.6i	1.44678	+	1.34690i
$205$	43599.7			1.03747
$206$		−	126535.i		−	2.98178i
$207$	−73153.7	+	5237.58i	−1.70725	+	0.122234i
$208$	−40722.7			−0.941262
$209$		−	23870.2i		−	0.546467i
$210$	−60076.6	+	64531.7i	−1.36228	+	1.46330i
$211$	44136.4			0.991362			0.495681	−	0.868505i	$-0.334919\pi$
$211$	44136.4			0.991362			0.495681	+	0.868505i	$0.334919\pi$
$212$		−	178670.i		−	3.97539i
$213$	−54724.9	−	50946.8i	−1.20622	−	1.12294i
$214$	60741.0			1.32634
$215$		−	35671.0i		−	0.771681i
$216$	−82891.3	+	102886.i	−1.77665	+	2.20520i
$217$	−42554.7			−0.903709
$218$		−	36702.5i		−	0.772293i
$219$	23118.2	−	24832.6i	0.482021	−	0.517767i
$220$	−127711.			−2.63865
$221$		−	12946.0i		−	0.265065i
$222$	12513.9	+	11650.0i	0.253914	+	0.236385i
$223$	44232.6			0.889473			0.444736	−	0.895662i	$-0.353297\pi$
$223$	44232.6			0.889473			0.444736	+	0.895662i	$0.353297\pi$
$224$			128966.i			2.57028i
$225$	−9.60847	−	134.202i	−0.000189797	−	0.00265091i
$226$	89381.4			1.74997
$227$		−	18920.9i		−	0.367190i	−0.983002	−	0.183595i	$-0.941227\pi$
$227$		−	18920.9i		−	0.367190i	0.983002	−	0.183595i	$-0.0587735\pi$
$228$	−46201.1	+	49627.2i	−0.888757	+	0.954664i
$229$	32265.4			0.615271			0.307635	−	0.951504i	$-0.400462\pi$
$229$	32265.4			0.615271			0.307635	+	0.951504i	$0.400462\pi$
$230$			169440.i			3.20302i
$231$	43900.9	+	40870.1i	0.822715	+	0.765917i
$232$	248616.			4.61906
$233$		−	22096.7i		−	0.407019i	−0.979073	−	0.203509i	$-0.934765\pi$
$233$		−	22096.7i		−	0.407019i	0.979073	−	0.203509i	$-0.0652348\pi$
$234$	34463.3	−	2467.47i	0.629397	−	0.0450629i
$235$	48325.6			0.875068
$236$			18209.1i			0.326938i
$237$	−13054.8	+	14022.9i	−0.232420	+	0.249656i
$238$	−89258.7			−1.57578
$239$		−	24979.4i		−	0.437307i	−0.975803	−	0.218654i	$-0.929834\pi$
$239$		−	24979.4i		−	0.437307i	0.975803	−	0.218654i	$-0.0701665\pi$
$240$	117683.	+	109559.i	2.04311	+	1.90206i
$241$	32935.6			0.567064			0.283532	−	0.958963i	$-0.408494\pi$
$241$	32935.6			0.567064			0.283532	+	0.958963i	$0.408494\pi$
$242$			11739.2i			0.200452i
$243$	33667.9	−	48510.4i	0.570168	−	0.821528i
$244$	93862.3			1.57656
$245$		−	8475.70i		−	0.141203i
$246$	−80269.7	+	86222.3i	−1.32642	+	1.42478i
$247$	10670.7			0.174904
$248$			147328.i			2.39542i
$249$	−49358.3	−	45950.7i	−0.796088	−	0.741128i
$250$	−117270.			−1.87632
$251$			15587.0i			0.247409i	0.992319	+	0.123705i	$0.0394776\pi$
$251$			15587.0i			0.247409i	−0.992319	+	0.123705i	$0.960522\pi$
$252$	−12167.3	−	169941.i	−0.191599	−	2.67607i
$253$	115270.			1.80084
$254$		−	166907.i		−	2.58707i
$255$	−34829.4	+	37412.3i	−0.535631	+	0.575352i
$256$	−13530.0			−0.206451
$257$			7399.34i			0.112028i	0.998430	+	0.0560140i	$0.0178392\pi$
$257$			7399.34i			0.112028i	−0.998430	+	0.0560140i	$0.982161\pi$
$258$	70542.4	+	65672.3i	1.05977	+	0.986604i
$259$	−13268.1			−0.197792
$260$		−	57090.5i		−	0.844534i
$261$	−110829.	+	7935.04i	−1.62695	+	0.116484i
$262$	−102303.			−1.49034
$263$			111995.i			1.61916i	0.587013	+	0.809578i	$0.300304\pi$
$263$			111995.i			1.61916i	−0.587013	+	0.809578i	$0.699696\pi$
$264$	141495.	−	151988.i	2.03018	−	2.18073i
$265$	111020.			1.58092
$266$		−	73571.1i		−	1.03979i
$267$	72165.0	+	67182.9i	1.01229	+	0.942403i
$268$	−197405.			−2.74846
$269$		−	21091.5i		−	0.291475i	−0.989323	−	0.145738i	$-0.953444\pi$
$269$		−	21091.5i		−	0.291475i	0.989323	−	0.145738i	$-0.0465556\pi$
$270$	−106233.	−	85587.9i	−1.45724	−	1.17405i
$271$	−71615.9			−0.975148			−0.487574	−	0.873082i	$-0.662118\pi$
$271$	−71615.9			−0.975148			−0.487574	+	0.873082i	$0.662118\pi$
$272$			162777.i			2.20016i
$273$	−18270.2	+	19625.0i	−0.245142	+	0.263321i
$274$	−253063.			−3.37076
$275$			211.465i			0.00279624i
$276$	−239651.	−	223106.i	−3.14602	−	2.92883i
$277$	90722.5			1.18238			0.591188	−	0.806534i	$-0.298659\pi$
$277$	90722.5			1.18238			0.591188	+	0.806534i	$0.298659\pi$
$278$		−	73315.8i		−	0.948655i
$279$	−4702.23	−	65676.4i	−0.0604081	−	0.843725i
$280$	−236878.			−3.02141
$281$		−	44079.6i		−	0.558246i	−0.960255	−	0.279123i	$-0.909956\pi$
$281$		−	44079.6i		−	0.558246i	0.960255	−	0.279123i	$-0.0900436\pi$
$282$	−88970.4	+	95568.1i	−1.11879	+	1.20175i
$283$	4240.96			0.0529530			0.0264765	−	0.999649i	$-0.491571\pi$
$283$	4240.96			0.0529530			0.0264765	+	0.999649i	$0.491571\pi$
$284$		−	333803.i		−	4.13860i
$285$	−30836.9	−	28708.0i	−0.379648	−	0.353438i
$286$	−54304.5			−0.663902
$287$		−	91418.7i		−	1.10987i
$288$	−199039.	+	14250.6i	−2.39968	+	0.171809i
$289$	31773.2			0.380422
$290$			256704.i			3.05237i
$291$	98195.9	−	105478.i	1.15960	−	1.24559i
$292$	151470.			1.77649
$293$			11551.5i			0.134556i	0.997734	+	0.0672778i	$0.0214314\pi$
$293$			11551.5i			0.134556i	−0.997734	+	0.0672778i	$0.978569\pi$
$294$	16761.4	+	15604.3i	0.193917	+	0.180530i
$295$	−11314.6			−0.130016
$296$			45935.2i			0.524278i
$297$	−58225.5	+	72270.1i	−0.660086	+	0.819305i
$298$	325217.			3.66219
$299$			51529.1i			0.576381i
$300$	409.294	−	439.646i	0.00454771	−	0.00488495i
$301$	−74793.8			−0.825530
$302$			117776.i			1.29135i
$303$	−88446.1	−	82340.1i	−0.963371	−	0.896863i
$304$	−134168.			−1.45178
$305$			58323.3i			0.626964i
$306$	−9862.94	−	137756.i	−0.105333	−	1.47119i
$307$	−13202.7			−0.140084			−0.0700418	−	0.997544i	$-0.522313\pi$
$307$	−13202.7			−0.140084			−0.0700418	+	0.997544i	$0.522313\pi$
$308$			267780.i			2.82278i
$309$	−103528.	+	111205.i	−1.08428	+	1.16468i
$310$	−152121.			−1.58294
$311$		−	68017.1i		−	0.703230i	−0.936145	−	0.351615i	$-0.885633\pi$
$311$		−	68017.1i		−	0.703230i	0.936145	−	0.351615i	$-0.114367\pi$
$312$	67943.3	+	63252.7i	0.697971	+	0.649785i
$313$	10627.8			0.108481			0.0542404	−	0.998528i	$-0.482726\pi$
$313$	10627.8			0.108481			0.0542404	+	0.998528i	$0.482726\pi$
$314$			107223.i			1.08750i
$315$	105597.	−	7560.40i	1.06421	−	0.0761945i
$316$	−85534.9			−0.856583
$317$			123218.i			1.22619i	0.790010	+	0.613094i	$0.210075\pi$
$317$			123218.i			1.22619i	−0.790010	+	0.613094i	$0.789925\pi$
$318$	−204395.	+	219552.i	−2.02123	+	2.17112i
$319$	174636.			1.71614
$320$			175173.i			1.71067i
$321$	−53382.3	−	49696.9i	−0.518068	−	0.482302i
$322$	355277.			3.42653
$323$		−	42652.9i		−	0.408831i
$324$	260933.	−	37556.5i	2.48564	−	0.357763i
$325$	−94.5313			−0.000894971
$326$			82786.7i			0.778978i
$327$	−30029.1	+	32256.0i	−0.280832	+	0.301658i
$328$	−316499.			−2.94187
$329$		−	101328.i		−	0.936132i
$330$	156933.	+	146099.i	1.44107	+	1.34159i
$331$	−142152.			−1.29747			−0.648734	−	0.761015i	$-0.724701\pi$
$331$	−142152.			−1.29747			−0.648734	+	0.761015i	$0.724701\pi$
$332$		−	301068.i		−	2.73142i
$333$	−1466.10	−	20477.2i	−0.0132214	−	0.184664i
$334$	270544.			2.42518
$335$		−	122662.i		−	1.09300i
$336$	229720.	−	246755.i	2.03479	−	2.18568i
$337$	−115078.			−1.01328			−0.506642	−	0.862156i	$-0.669114\pi$
$337$	−115078.			−1.01328			−0.506642	+	0.862156i	$0.669114\pi$
$338$			189799.i			1.66134i
$339$	−78552.9	−	73129.8i	−0.683538	−	0.636349i
$340$	−228202.			−1.97406
$341$			103488.i			0.889980i
$342$	113545.	−	8129.49i	0.970770	−	0.0695042i
$343$	107920.			0.917303
$344$			258942.i			2.18819i
$345$	138632.	−	148912.i	1.16473	−	1.25110i
$346$	270558.			2.26000
$347$			155553.i			1.29188i	0.763390	+	0.645938i	$0.223533\pi$
$347$			155553.i			1.29188i	−0.763390	+	0.645938i	$0.776467\pi$
$348$	−363076.	−	338010.i	−2.99805	−	2.79107i
$349$	−71293.8			−0.585330			−0.292665	−	0.956215i	$-0.594542\pi$
$349$	−71293.8			−0.585330			−0.292665	+	0.956215i	$0.594542\pi$
$350$			651.763i			0.00532052i
$351$	−32306.9	−	26028.5i	−0.262229	−	0.211269i
$352$	313630.			2.53123
$353$			64338.5i			0.516323i	0.966102	+	0.258162i	$0.0831167\pi$
$353$			64338.5i			0.516323i	−0.966102	+	0.258162i	$0.916883\pi$
$354$	20830.9	−	22375.6i	0.166227	−	0.178554i
$355$	207415.			1.64583
$356$			440182.i			3.47322i
$357$	78445.0	+	73029.4i	0.615501	+	0.573009i
$358$	33054.1			0.257905
$359$		−	38102.5i		−	0.295641i	−0.989014	−	0.147821i	$-0.952774\pi$
$359$		−	38102.5i		−	0.295641i	0.989014	−	0.147821i	$-0.0472258\pi$
$360$	−26174.7	−	365584.i	−0.201965	−	2.82086i
$361$	−95164.5			−0.730232
$362$			325354.i			2.48278i
$363$	9604.78	−	10317.0i	0.0728910	−	0.0782964i
$364$	−119706.			−0.903467
$365$			94119.2i			0.706468i
$366$	−115339.	−	107377.i	−0.861024	−	0.801582i
$367$	170699.			1.26736			0.633679	−	0.773596i	$-0.281544\pi$
$367$	170699.			1.26736			0.633679	+	0.773596i	$0.281544\pi$
$368$		−	647901.i		−	4.78424i
$369$	141090.	−	10101.6i	1.03620	−	0.0741888i
$370$	−47429.5			−0.346454
$371$		−	232784.i		−	1.69124i
$372$	200302.	−	215155.i	1.44743	−	1.55477i
$373$	63737.6			0.458118			0.229059	−	0.973412i	$-0.426435\pi$
$373$	63737.6			0.458118			0.229059	+	0.973412i	$0.426435\pi$
$374$			217066.i			1.55184i
$375$	103063.	+	95947.4i	0.732889	+	0.682293i
$376$	−350805.			−2.48136
$377$			78067.5i			0.549272i
$378$	−179458.	+	222746.i	−1.25597	+	1.55893i
$379$	−278735.			−1.94050			−0.970249	−	0.242111i	$-0.922160\pi$
$379$	−278735.			−1.94050			−0.970249	+	0.242111i	$0.922160\pi$
$380$		−	188095.i		−	1.30259i
$381$	−136560.	+	146686.i	−0.940746	+	1.01051i
$382$	307056.			2.10422
$383$			82161.9i			0.560110i	0.959984	+	0.280055i	$0.0903527\pi$
$383$			82161.9i			0.560110i	−0.959984	+	0.280055i	$0.909647\pi$
$384$	−86768.8	−	80778.5i	−0.588438	−	0.547814i
$385$	−166391.			−1.12256
$386$		−	280787.i		−	1.88453i
$387$	−8264.60	−	115432.i	−0.0551823	−	0.770736i
$388$	643378.			4.27369
$389$		−	101073.i		−	0.667939i	−0.942584	−	0.333969i	$-0.891612\pi$
$389$		−	101073.i		−	0.667939i	0.942584	−	0.333969i	$-0.108388\pi$
$390$	−65310.4	+	70153.6i	−0.429391	+	0.461234i
$391$	205972.			1.34727
$392$			61526.7i			0.400398i
$393$	89909.0	+	83702.0i	0.582128	+	0.541939i
$394$	−454478.			−2.92766
$395$		−	53148.9i		−	0.340643i
$396$	−413276.	+	29589.3i	−2.63542	+	0.188688i
$397$	60367.3			0.383019			0.191510	−	0.981491i	$-0.438662\pi$
$397$	60367.3			0.383019			0.191510	+	0.981491i	$0.438662\pi$
$398$			282670.i			1.78449i
$399$	−60194.2	+	64658.0i	−0.378102	+	0.406141i
$400$	1188.59			0.00742868
$401$		−	91315.9i		−	0.567881i	−0.958842	−	0.283941i	$-0.908358\pi$
$401$		−	91315.9i		−	0.567881i	0.958842	−	0.283941i	$-0.0916419\pi$
$402$	242574.	+	225828.i	1.50104	+	1.39741i
$403$	−46262.1			−0.284849
$404$		−	539491.i		−	3.30538i
$405$	23336.5	+	162136.i	0.142274	+	0.988484i
$406$	538251.			3.26537
$407$			32266.3i			0.194787i
$408$	252833.	−	271583.i	1.51885	−	1.63148i
$409$	23670.6			0.141502			0.0707510	−	0.997494i	$-0.477460\pi$
$409$	23670.6			0.141502			0.0707510	+	0.997494i	$0.477460\pi$
$410$		−	326795.i		−	1.94405i
$411$	222404.	+	207050.i	1.31662	+	1.22572i
$412$	−678312.			−3.99609
$413$			23724.2i			0.139088i
$414$	39257.5	+	548312.i	0.229045	+	3.19910i
$415$	187075.			1.08622
$416$			140202.i			0.810153i
$417$	−59985.3	+	64433.6i	−0.344963	+	0.370545i
$418$	−178916.			−1.02399
$419$			116387.i			0.662946i	0.943465	+	0.331473i	$0.107546\pi$
$419$			116387.i			0.662946i	−0.943465	+	0.331473i	$0.892454\pi$
$420$	345934.	+	322051.i	1.96108	+	1.82569i
$421$	321783.			1.81551			0.907755	−	0.419500i	$-0.137795\pi$
$421$	321783.			1.81551			0.907755	+	0.419500i	$0.137795\pi$
$422$		−	330818.i		−	1.85765i
$423$	156383.	−	11196.6i	0.873996	−	0.0625754i
$424$	−805916.			−4.48289
$425$			377.860i			0.00209196i
$426$	−381864.	+	410182.i	−2.10421	+	2.26025i
$427$	122291.			0.670714
$428$		−	325613.i		−	1.77752i
$429$	47725.5	+	44430.7i	0.259320	+	0.241417i
$430$	−267366.			−1.44600
$431$			300041.i			1.61520i	0.589732	+	0.807599i	$0.299233\pi$
$431$			300041.i			1.61520i	−0.589732	+	0.807599i	$0.700767\pi$
$432$	406210.	+	327270.i	2.17662	+	1.75363i
$433$	41166.3			0.219566			0.109783	−	0.993956i	$-0.464984\pi$
$433$	41166.3			0.219566			0.109783	+	0.993956i	$0.464984\pi$
$434$			318962.i			1.69340i
$435$	210030.	−	225605.i	1.10995	−	1.19226i
$436$	−196750.			−1.03500
$437$			169771.i			0.889000i
$438$	−186129.	−	173279.i	−0.970209	−	0.903229i
$439$	−132293.			−0.686450			−0.343225	−	0.939253i	$-0.611519\pi$
$439$	−132293.			−0.686450			−0.343225	+	0.939253i	$0.611519\pi$
$440$			576058.i			2.97551i
$441$	−1963.73	−	27427.6i	−0.0100973	−	0.141030i
$442$	−97034.8			−0.496687
$443$			125977.i			0.641926i	0.947092	+	0.320963i	$0.104007\pi$
$443$			125977.i			0.641926i	−0.947092	+	0.320963i	$0.895993\pi$
$444$	62451.8	−	67083.0i	0.316796	−	0.340288i
$445$	−273516.			−1.38122
$446$		−	331538.i		−	1.66673i
$447$	−285817.	−	266085.i	−1.43045	−	1.33170i
$448$	367297.			1.83004
$449$		−	129881.i		−	0.644246i	−0.946698	−	0.322123i	$-0.895604\pi$
$449$		−	129881.i		−	0.644246i	0.946698	−	0.322123i	$-0.104396\pi$
$450$	−1005.89	+	72.0188i	−0.00496737	+	0.000355648i
$451$	−222319.			−1.09301
$452$		−	479145.i		−	2.34526i
$453$	96361.8	−	103508.i	0.469579	−	0.504401i
$454$	−141819.			−0.688053
$455$		−	74381.7i		−	0.359288i
$456$	223851.	+	208397.i	1.07654	+	1.00222i
$457$	−63515.2			−0.304120			−0.152060	−	0.988371i	$-0.548591\pi$
$457$	−63515.2			−0.304120			−0.152060	+	0.988371i	$0.548591\pi$
$458$		−	241840.i		−	1.15292i
$459$	−104041.	+	129137.i	−0.493832	+	0.612950i
$460$	908313.			4.29259
$461$		−	75639.2i		−	0.355914i	−0.984038	−	0.177957i	$-0.943051\pi$
$461$		−	75639.2i		−	0.355914i	0.984038	−	0.177957i	$-0.0569488\pi$
$462$	306335.	−	329052.i	1.43520	−	1.54163i
$463$	−180512.			−0.842062			−0.421031	−	0.907046i	$-0.638332\pi$
$463$	−180512.			−0.842062			−0.421031	+	0.907046i	$0.638332\pi$
$464$		−	981581.i		−	4.55922i
$465$	133691.	+	124462.i	0.618297	+	0.575612i
$466$	−165622.			−0.762686
$467$			57521.3i			0.263752i	0.991266	+	0.131876i	$0.0421000\pi$
$467$			57521.3i			0.263752i	−0.991266	+	0.131876i	$0.957900\pi$
$468$	−13227.3	−	184747.i	−0.0603920	−	0.843500i
$469$	−257194.			−1.16927
$470$		−	362217.i		−	1.63973i
$471$	87727.6	−	94233.2i	0.395453	−	0.424778i
$472$	82135.0			0.368675
$473$			181889.i			0.812988i
$474$	105107.	+	97850.3i	0.467814	+	0.435517i
$475$	−311.450			−0.00138039
$476$			478487.i			2.11182i
$477$	359265.	−	25722.2i	1.57898	−	0.113050i
$478$	−187229.			−0.819441
$479$		−	337448.i		−	1.47074i	−0.677666	−	0.735370i	$-0.737008\pi$
$479$		−	337448.i		−	1.47074i	0.677666	−	0.735370i	$-0.262992\pi$
$480$	377193.	−	405164.i	1.63712	−	1.75853i
$481$	−14424.0			−0.0623441
$482$		−	246864.i		−	1.06258i
$483$	−312235.	−	290679.i	−1.33840	−	1.24600i
$484$	62930.4			0.268639
$485$			399776.i			1.69955i
$486$	−363602.	−	252352.i	−1.53941	−	1.06840i
$487$	−118967.			−0.501615			−0.250807	−	0.968037i	$-0.580696\pi$
$487$	−118967.			−0.501615			−0.250807	+	0.968037i	$0.580696\pi$
$488$		−	423380.i		−	1.77783i
$489$	67734.1	−	72757.1i	0.283263	−	0.304269i
$490$	−63528.3			−0.264591
$491$		−	250334.i		−	1.03838i	−0.854658	−	0.519191i	$-0.826233\pi$
$491$		−	250334.i		−	1.03838i	0.854658	−	0.519191i	$-0.173767\pi$
$492$	462210.	+	430300.i	1.90945	+	1.77763i
$493$	312051.			1.28390
$494$		−	79980.6i		−	0.327741i
$495$	−18385.9	−	256798.i	−0.0750369	−	1.04805i
$496$	581676.			2.36438
$497$		−	434902.i		−	1.76067i
$498$	−344416.	+	369957.i	−1.38875	+	1.49174i
$499$	163877.			0.658140			0.329070	−	0.944306i	$-0.393265\pi$
$499$	163877.			0.658140			0.329070	+	0.944306i	$0.393265\pi$
$500$			628646.i			2.51458i
$501$	−237767.	−	221353.i	−0.947277	−	0.881879i
$502$	116830.			0.463605
$503$			151110.i			0.597253i	0.954370	+	0.298626i	$0.0965285\pi$
$503$			151110.i			0.597253i	−0.954370	+	0.298626i	$0.903472\pi$
$504$	−766546.	+	54882.3i	−3.01771	+	0.216059i
$505$	335224.			1.31447
$506$		−	863987.i		−	3.37448i
$507$	155289.	−	166805.i	0.604122	−	0.648921i
$508$	−894736.			−3.46711
$509$			493716.i			1.90564i	0.303533	+	0.952821i	$0.401834\pi$
$509$			493716.i			1.90564i	−0.303533	+	0.952821i	$0.598166\pi$
$510$	280418.	+	261058.i	1.07812	+	1.00369i
$511$	197346.			0.755766
$512$			312166.i			1.19082i
$513$	−106441.	−	85755.5i	−0.404457	−	0.325857i
$514$	55460.6			0.209922
$515$		−	421483.i		−	1.58915i
$516$	352048.	−	378155.i	1.32222	−	1.42027i
$517$	−246416.			−0.921910
$518$			99448.9i			0.370630i
$519$	−237780.	−	221364.i	−0.882754	−	0.821811i
$520$	−257515.			−0.952349
$521$			212011.i			0.781056i	0.920591	+	0.390528i	$0.127708\pi$
$521$			212011.i			0.781056i	−0.920591	+	0.390528i	$0.872292\pi$
$522$	59475.8	+	830703.i	0.218273	+	3.04863i
$523$	59345.3			0.216962			0.108481	−	0.994099i	$-0.465401\pi$
$523$	59345.3			0.216962			0.108481	+	0.994099i	$0.465401\pi$
$524$			548414.i			1.99731i
$525$	533.257	−	572.802i	0.00193472	−	0.00207819i
$526$	839443.			3.03403
$527$			184919.i			0.665824i
$528$	−600077.	−	558649.i	−2.15248	−	2.00388i
$529$	−539989.			−1.92963
$530$		−	832134.i		−	2.96239i
$531$	−36614.5	+	2621.48i	−0.129857	+	0.00929733i
$532$	−394391.			−1.39349
$533$		−	99383.1i		−	0.349831i
$534$	503559.	−	540901.i	1.76591	−	1.89686i
$535$	202327.			0.706879
$536$			890425.i			3.09933i
$537$	−29049.6	−	27044.1i	−0.100738	−	0.0937830i
$538$	−158088.			−0.546177
$539$			43218.3i			0.148761i
$540$	−458810.	+	569479.i	−1.57342	+	1.95295i
$541$	87347.9			0.298440			0.149220	−	0.988804i	$-0.452324\pi$
$541$	87347.9			0.298440			0.149220	+	0.988804i	$0.452324\pi$
$542$			536785.i			1.82727i
$543$	266197.	−	285937.i	0.902824	−	0.969775i
$544$	560414.			1.89370
$545$		−	122255.i		−	0.411598i
$546$	147096.	+	136941.i	0.493419	+	0.459355i
$547$	224496.			0.750298			0.375149	−	0.926964i	$-0.377592\pi$
$547$	224496.			0.750298			0.375149	+	0.926964i	$0.377592\pi$
$548$			1.35659e6i			4.51739i
$549$	13512.9	+	188736.i	0.0448337	+	0.626196i
$550$	1585.00			0.00523969
$551$			257207.i			0.847187i
$552$	−1.00635e6	+	1.08098e6i	−3.30272	+	3.54764i
$553$	−111441.			−0.364414
$554$		−	679996.i		−	2.21558i
$555$	41683.4	+	38805.7i	0.135325	+	0.125982i
$556$	−393023.			−1.27136
$557$		−	28993.3i		−	0.0934518i	−0.998908	−	0.0467259i	$-0.985121\pi$
$557$		−	28993.3i		−	0.0934518i	0.998908	−	0.0467259i	$-0.0148787\pi$
$558$	−492267.	+	35244.8i	−1.58100	+	0.113195i
$559$	−81309.8			−0.260207
$560$			935238.i			2.98226i
$561$	177598.	−	190768.i	0.564303	−	0.606150i
$562$	−330392.			−1.04606
$563$		−	398832.i		−	1.25827i	−0.777297	−	0.629134i	$-0.783410\pi$
$563$		−	398832.i		−	1.25827i	0.777297	−	0.629134i	$-0.216590\pi$
$564$	512310.	+	476942.i	1.61055	+	1.49936i
$565$	297727.			0.932655
$566$		−	31787.4i		−	0.0992253i
$567$	339962.	−	48931.3i	1.05746	−	0.152202i
$568$	−1.50567e6			−4.66694
$569$			191717.i			0.592155i	0.955164	+	0.296078i	$0.0956787\pi$
$569$			191717.i			0.592155i	−0.955164	+	0.296078i	$0.904321\pi$
$570$	−215176.	+	231133.i	−0.662285	+	0.711398i
$571$	35119.6			0.107715			0.0538577	−	0.998549i	$-0.482848\pi$
$571$	35119.6			0.107715			0.0538577	+	0.998549i	$0.482848\pi$
$572$			291109.i			0.889742i
$573$	−269856.	−	251226.i	−0.821907	−	0.765165i
$574$	−685214.			−2.07971
$575$		−	1504.00i		−	0.00454895i
$576$	40585.7	+	566864.i	0.122329	+	1.70858i
$577$	−125393.			−0.376636			−0.188318	−	0.982108i	$-0.560303\pi$
$577$	−125393.			−0.376636			−0.188318	+	0.982108i	$0.560303\pi$
$578$		−	238151.i		−	0.712848i
$579$	−229733.	+	246770.i	−0.685279	+	0.736097i
$580$	1.37611e6			4.09070
$581$		−	392254.i		−	1.16202i
$582$	−790592.	−	736012.i	−2.33403	−	2.17290i
$583$	−566101.			−1.66555
$584$		−	683229.i		−	2.00327i
$585$	114796.	−	8219.05i	0.335441	−	0.0240165i
$586$	86582.2			0.252135
$587$			241835.i			0.701848i	0.936404	+	0.350924i	$0.114133\pi$
$587$			241835.i			0.701848i	−0.936404	+	0.350924i	$0.885867\pi$
$588$	83649.5	−	89852.7i	0.241941	−	0.259882i
$589$	−152418.			−0.439346
$590$			84807.0i			0.243628i
$591$	399418.	+	371844.i	1.14354	+	1.06460i
$592$	181360.			0.517486
$593$			658549.i			1.87275i	0.351007	+	0.936373i	$0.385839\pi$
$593$			658549.i			1.87275i	−0.351007	+	0.936373i	$0.614161\pi$
$594$	541689.	+	436420.i	1.53524	+	1.23689i
$595$	−297318.			−0.839822
$596$		−	1.74338e6i		−	4.90796i
$597$	231274.	−	248424.i	0.648900	−	0.697020i
$598$	386228.			1.08004
$599$			217294.i			0.605611i	0.953052	+	0.302805i	$0.0979232\pi$
$599$			217294.i			0.605611i	−0.953052	+	0.302805i	$0.902077\pi$
$600$	−1983.08	−	1846.18i	−0.00550857	−	0.00512827i
$601$	−103070.			−0.285353			−0.142677	−	0.989769i	$-0.545571\pi$
$601$	−103070.			−0.285353			−0.142677	+	0.989769i	$0.545571\pi$
$602$			560605.i			1.54691i
$603$	−28419.5	−	396937.i	−0.0781595	−	1.09166i
$604$	631361.			1.73063
$605$			39103.1i			0.106832i
$606$	−617167.	+	662934.i	−1.68057	+	1.80520i
$607$	405932.			1.10173			0.550866	−	0.834594i	$-0.314298\pi$
$607$	405932.			1.10173			0.550866	+	0.834594i	$0.314298\pi$
$608$			461919.i			1.24956i
$609$	−473042.	−	440384.i	−1.27545	−	1.18740i
$610$	437153.			1.17483
$611$		−	110155.i		−	0.295069i
$612$	−738468.	+	52872.1i	−1.97165	+	0.141164i
$613$	−71073.7			−0.189142			−0.0945710	−	0.995518i	$-0.530148\pi$
$613$	−71073.7			−0.189142			−0.0945710	+	0.995518i	$0.530148\pi$
$614$			98959.0i			0.262493i
$615$	−267376.	+	287204.i	−0.706923	+	0.759346i
$616$	1.20786e6			3.18314
$617$			442654.i			1.16277i	0.813628	+	0.581386i	$0.197489\pi$
$617$			442654.i			1.16277i	−0.813628	+	0.581386i	$0.802511\pi$
$618$	833519.	+	775975.i	2.18242	+	2.03175i
$619$	−255374.			−0.666493			−0.333246	−	0.942840i	$-0.608144\pi$
$619$	−255374.			−0.666493			−0.333246	+	0.942840i	$0.608144\pi$
$620$			815470.i			2.12141i
$621$	414115.	−	514004.i	1.07384	−	1.33286i
$622$	−509812.			−1.31774
$623$			573500.i			1.47760i
$624$	249733.	−	268252.i	0.641367	−	0.688928i
$625$	−389584.			−0.997335
$626$		−	79658.6i		−	0.203275i
$627$	157240.	+	146385.i	0.399970	+	0.372358i
$628$	574790.			1.45744
$629$			57655.5i			0.145727i
$630$	−56667.7	−	791483.i	−0.142776	−	1.99416i
$631$	200823.			0.504376			0.252188	−	0.967678i	$-0.418850\pi$
$631$	200823.			0.504376			0.252188	+	0.967678i	$0.418850\pi$
$632$			385818.i			0.965935i
$633$	−270667.	+	290739.i	−0.675505	+	0.725598i
$634$	923564.			2.29767
$635$		−	555963.i		−	1.37879i
$636$	1.17695e6	+	1.09569e6i	2.90967	+	2.70879i
$637$	−19319.9			−0.0476130
$638$		−	1.30896e6i		−	3.21576i
$639$	671202.	−	48056.0i	1.64381	−	0.117692i
$640$	328866.			0.802896
$641$		−	557807.i		−	1.35759i	−0.734328	−	0.678794i	$-0.762503\pi$
$641$		−	557807.i		−	1.35759i	0.734328	−	0.678794i	$-0.237497\pi$
$642$	−372495.	+	400118.i	−0.903755	+	0.970774i
$643$	117775.			0.284859			0.142429	−	0.989805i	$-0.454509\pi$
$643$	117775.			0.284859			0.142429	+	0.989805i	$0.454509\pi$
$644$		−	1.90452e6i		−	4.59214i
$645$	234975.	+	218753.i	0.564809	+	0.525816i
$646$	−319698.			−0.766081
$647$			179763.i			0.429430i	0.976677	+	0.214715i	$0.0688823\pi$
$647$			179763.i			0.429430i	−0.976677	+	0.214715i	$0.931118\pi$
$648$	−169404.	−	1.17698e6i	−0.403435	−	2.80296i
$649$	57694.2			0.136975
$650$			708.544i			0.00167703i
$651$	260968.	−	280320.i	0.615779	−	0.661443i
$652$	443793.			1.04396
$653$		−	369529.i		−	0.866608i	−0.901248	−	0.433304i	$-0.857348\pi$
$653$		−	369529.i		−	0.866608i	0.901248	−	0.433304i	$-0.142652\pi$
$654$	241770.	+	225078.i	0.565257	+	0.526233i
$655$	−340768.			−0.794286
$656$			1.24959e6i			2.90376i
$657$	21806.5	+	304573.i	0.0505190	+	0.705602i
$658$	−759487.			−1.75416
$659$		−	245142.i		−	0.564477i	−0.959344	−	0.282239i	$-0.908923\pi$
$659$		−	245142.i		−	0.564477i	0.959344	−	0.282239i	$-0.0910770\pi$
$660$	783188.	−	841267.i	1.79795	−	1.93128i
$661$	−440649.			−1.00853			−0.504266	−	0.863548i	$-0.668237\pi$
$661$	−440649.			−1.00853			−0.504266	+	0.863548i	$0.668237\pi$
$662$			1.06548e6i			2.43124i
$663$	85279.1	+	79391.7i	0.194006	+	0.180613i
$664$	−1.35801e6			−3.08012
$665$		−	245063.i		−	0.554160i
$666$	−153483.	+	10988.9i	−0.346029	+	0.0247746i
$667$	−1.24206e6			−2.79184
$668$		−	1.45030e6i		−	3.25016i
$669$	−271257.	+	291372.i	−0.606078	+	0.651023i
$670$	−919392.			−2.04810
$671$		−	297395.i		−	0.660525i
$672$	−849537.	−	790888.i	−1.88124	−	1.75136i
$673$	409414.			0.903925			0.451963	−	0.892037i	$-0.350724\pi$
$673$	409414.			0.903925			0.451963	+	0.892037i	$0.350724\pi$
$674$			862547.i			1.89873i
$675$	942.952	+	759.704i	0.00206958	+	0.00166739i
$676$	1.01745e6			2.22648
$677$			877372.i			1.91429i	0.289617	+	0.957143i	$0.406472\pi$
$677$			877372.i			1.91429i	−0.289617	+	0.957143i	$0.593528\pi$
$678$	−548133.	+	588781.i	−1.19241	+	1.28084i
$679$	838240.			1.81815
$680$			1.02934e6i			2.22608i
$681$	124637.	+	116033.i	0.268754	+	0.250200i
$682$	775676.			1.66768
$683$			170253.i			0.364967i	0.983209	+	0.182483i	$0.0584136\pi$
$683$			170253.i			0.364967i	−0.983209	+	0.182483i	$0.941586\pi$
$684$	−43579.6	−	608680.i	−0.0931474	−	1.30100i
$685$	−842945.			−1.79646
$686$		−	808895.i		−	1.71887i
$687$	−197868.	+	212541.i	−0.419239	+	0.450329i
$688$	1.02235e6			2.15984
$689$		−	253064.i		−	0.533079i
$690$	−1.11615e6	−	1.03909e6i	−2.34435	−	2.18251i
$691$	−582038.			−1.21898			−0.609488	−	0.792796i	$-0.708625\pi$
$691$	−582038.			−1.21898			−0.609488	+	0.792796i	$0.708625\pi$
$692$		−	1.45037e6i		−	3.02878i
$693$	−538446.	+	38551.1i	−1.12118	+	0.0802731i
$694$	1.16593e6			2.42076
$695$		−	244213.i		−	0.505591i
$696$	−1.52464e6	+	1.63771e6i	−3.14739	+	3.38078i
$697$	−397253.			−0.817715
$698$			534372.i			1.09681i
$699$	145557.	+	135508.i	0.297905	+	0.277339i
$700$	3493.89			0.00713040
$701$		−	441218.i		−	0.897877i	−0.893563	−	0.448939i	$-0.851802\pi$
$701$		−	441218.i		−	0.897877i	0.893563	−	0.448939i	$-0.148198\pi$
$702$	−195093.	+	242151.i	−0.395883	+	0.491374i
$703$	−47522.3			−0.0961584
$704$		−	893220.i		−	1.80224i
$705$	−296358.	+	318335.i	−0.596263	+	0.640480i
$706$	482239.			0.967504
$707$		−	702888.i		−	1.40620i
$708$	−119949.	−	111668.i	−0.239292	−	0.222772i
$709$	338754.			0.673895			0.336947	−	0.941523i	$-0.390606\pi$
$709$	338754.			0.673895			0.336947	+	0.941523i	$0.390606\pi$
$710$		−	1.55465e6i		−	3.08401i
$711$	−12314.1	−	171991.i	−0.0243591	−	0.340226i
$712$	1.98550e6			3.91661
$713$		−	736032.i		−	1.44783i
$714$	547380.	−	587972.i	1.07372	−	1.15335i
$715$	−180887.			−0.353830
$716$		−	177193.i		−	0.345636i
$717$	164546.	+	153187.i	0.320074	+	0.297977i
$718$	−285591.			−0.553982
$719$			380368.i			0.735777i	0.929870	+	0.367889i	$0.119919\pi$
$719$			380368.i			0.735777i	−0.929870	+	0.367889i	$0.880081\pi$
$720$	−1.44339e6	+	103342.i	−2.78432	+	0.199348i
$721$	−883754.			−1.70005
$722$			713291.i			1.36833i
$723$	−201978.	+	216956.i	−0.386392	+	0.415046i
$724$	1.74412e6			3.32735
$725$		−	2278.58i		−	0.00433500i
$726$	−77329.7	−	71991.1i	−0.146715	−	0.136586i
$727$	−698672.			−1.32192			−0.660959	−	0.750422i	$-0.729850\pi$
$727$	−698672.			−1.32192			−0.660959	+	0.750422i	$0.729850\pi$
$728$			539950.i			1.01881i
$729$	113083.	+	519270.i	0.212786	+	0.977099i
$730$	705455.			1.32380
$731$			325011.i			0.608224i
$732$	−575612.	+	618297.i	−1.07426	+	1.15392i
$733$	633385.			1.17885			0.589427	−	0.807822i	$-0.299354\pi$
$733$	633385.			1.17885			0.589427	+	0.807822i	$0.299354\pi$
$734$		−	1.27945e6i		−	2.37482i
$735$	55831.8	+	51977.4i	0.103349	+	0.0962143i
$736$	−2.23062e6			−4.11784
$737$			625462.i			1.15151i
$738$	−75715.1	−	1.05752e6i	−0.139018	−	1.94167i
$739$	809388.			1.48207			0.741034	−	0.671468i	$-0.234336\pi$
$739$	809388.			1.48207			0.741034	+	0.671468i	$0.234336\pi$
$740$			254255.i			0.464307i
$741$	−65438.3	+	70291.0i	−0.119178	+	0.128016i
$742$	−1.74479e6			−3.16910
$743$			93385.4i			0.169161i	0.996417	+	0.0845807i	$0.0269551\pi$
$743$			93385.4i			0.169161i	−0.996417	+	0.0845807i	$0.973045\pi$
$744$	−970490.	−	903490.i	−1.75325	−	1.63222i
$745$	1.08329e6			1.95178
$746$		−	477735.i		−	0.858438i
$747$	605380.	−	43343.4i	1.08489	−	0.0776750i
$748$	1.16362e6			2.07973
$749$		−	424233.i		−	0.756206i
$750$	719159.	−	772489.i	1.27850	−	1.37331i
$751$	728422.			1.29153			0.645763	−	0.763538i	$-0.276539\pi$
$751$	728422.			1.29153			0.645763	+	0.763538i	$0.276539\pi$
$752$			1.38504e6i			2.44921i
$753$	−102676.	−	95587.8i	−0.181084	−	0.168582i
$754$	585143.			1.02925
$755$			392309.i			0.688232i
$756$	1.19407e6	+	962019.i	2.08923	+	1.68322i
$757$	625905.			1.09224			0.546118	−	0.837708i	$-0.316105\pi$
$757$	625905.			1.09224			0.546118	+	0.837708i	$0.316105\pi$
$758$			2.08921e6i			3.63617i
$759$	−706894.	+	759315.i	−1.22707	+	1.31807i
$760$	−848428.			−1.46888
$761$			545569.i			0.942064i	0.882116	+	0.471032i	$0.156118\pi$
$761$			545569.i			0.942064i	−0.882116	+	0.471032i	$0.843882\pi$
$762$	1.09946e6	+	1.02356e6i	1.89353	+	1.76280i
$763$	−256341.			−0.440320
$764$		−	1.64603e6i		−	2.82001i
$765$	−32853.2	−	458863.i	−0.0561376	−	0.784079i
$766$	615832.			1.04955
$767$			25791.0i			0.0438407i
$768$	82972.7	−	89125.7i	0.140674	−	0.151106i
$769$	−577208.			−0.976066			−0.488033	−	0.872825i	$-0.662285\pi$
$769$	−577208.			−0.976066			−0.488033	+	0.872825i	$0.662285\pi$
$770$			1.24716e6i			2.10348i
$771$	−48741.5	−	45376.6i	−0.0819956	−	0.0763349i
$772$	−1.50521e6			−2.52559
$773$			1.00968e6i			1.68977i	0.534951	+	0.844883i	$0.320330\pi$
$773$			1.00968e6i			1.68977i	−0.534951	+	0.844883i	$0.679670\pi$
$774$	−865204.	+	61946.0i	−1.44423	+	0.103403i
$775$	1350.27			0.00224810
$776$		−	2.90205e6i		−	4.81927i
$777$	81366.8	−	87400.7i	0.134774	−	0.144768i
$778$	−757578.			−1.25161
$779$		−	327435.i		−	0.539572i
$780$	376071.	+	350108.i	0.618132	+	0.575458i
$781$	−1.05763e6			−1.73393
$782$		−	1.54383e6i		−	2.52456i
$783$	627392.	−	778725.i	1.02333	−	1.27017i
$784$	242918.			0.395210
$785$			357158.i			0.579590i
$786$	627375.	−	673899.i	1.01550	−	1.09081i
$787$	−153315.			−0.247534			−0.123767	−	0.992311i	$-0.539498\pi$
$787$	−153315.			−0.247534			−0.123767	+	0.992311i	$0.539498\pi$
$788$			2.43631e6i			3.92356i
$789$	−737745.	−	686813.i	−1.18509	−	1.10328i
$790$	−398369.			−0.638310
$791$		−	624265.i		−	0.997738i
$792$	133467.	+	1.86414e6i	0.212776	+	2.97186i
$793$	132945.			0.211409
$794$		−	452473.i		−	0.717715i
$795$	−680833.	+	731321.i	−1.07722	+	1.15711i
$796$	1.51530e6			2.39151
$797$		−	620724.i		−	0.977197i	−0.872509	−	0.488598i	$-0.837508\pi$
$797$		−	620724.i		−	0.977197i	0.872509	−	0.488598i	$-0.162492\pi$
$798$	484634.	+	451176.i	0.761040	+	0.708500i
$799$	−440313.			−0.689712
$800$		−	4092.12i		−	0.00639393i
$801$	−885106.	+	63370.9i	−1.37953	+	0.0987699i
$802$	−684444.			−1.06412
$803$		−	479921.i		−	0.744284i
$804$	1.21059e6	−	1.30036e6i	1.87277	−	2.01165i
$805$	1.18342e6			1.82619
$806$			346750.i			0.533761i
$807$	138935.	+	129344.i	0.213337	+	0.198609i
$808$	−2.43345e6			−3.72735
$809$			713419.i			1.09005i	0.838419	+	0.545027i	$0.183480\pi$
$809$			713419.i			1.09005i	−0.838419	+	0.545027i	$0.816520\pi$
$810$	1.21527e6	−	174915.i	1.85226	−	0.266598i
$811$	1.03006e6			1.56610			0.783050	−	0.621959i	$-0.213663\pi$
$811$	1.03006e6			1.56610			0.783050	+	0.621959i	$0.213663\pi$
$812$		−	2.88539e6i		−	4.37615i
$813$	439185.	−	471754.i	0.664457	−	0.713731i
$814$	241847.			0.364999
$815$			275760.i			0.415160i
$816$	−1.07226e6	−	998231.i	−1.61034	−	1.49917i
$817$	−267889.			−0.401339
$818$		−	177419.i		−	0.265152i
$819$	−17233.5	−	240701.i	−0.0256924	−	0.358848i
$820$	−1.75184e6			−2.60536
$821$		−	796533.i		−	1.18173i	−0.806771	−	0.590864i	$-0.798787\pi$
$821$		−	796533.i		−	1.18173i	0.806771	−	0.590864i	$-0.201213\pi$
$822$	1.55191e6	−	1.66700e6i	2.29680	−	2.46712i
$823$	−574913.			−0.848795			−0.424397	−	0.905476i	$-0.639514\pi$
$823$	−574913.			−0.848795			−0.424397	+	0.905476i	$0.639514\pi$
$824$			3.05962e6i			4.50623i
$825$	−1392.98	−	1296.81i	−0.00204662	−	0.00190533i
$826$	177821.			0.260629
$827$			342178.i			0.500312i	0.968206	+	0.250156i	$0.0804819\pi$
$827$			342178.i			0.500312i	−0.968206	+	0.250156i	$0.919518\pi$
$828$	2.93933e6	−	210447.i	4.28733	−	0.306960i
$829$	−46861.3			−0.0681876			−0.0340938	−	0.999419i	$-0.510855\pi$
$829$	−46861.3			−0.0681876			−0.0340938	+	0.999419i	$0.510855\pi$
$830$		−	1.40219e6i		−	2.03541i
$831$	−556357.	+	597614.i	−0.805659	+	0.865404i
$832$	399296.			0.576831
$833$			77225.2i			0.111293i
$834$	482952.	+	449610.i	0.694340	+	0.646404i
$835$	901173.			1.29251
$836$			959109.i			1.37232i
$837$	461466.	+	371787.i	0.658701	+	0.530692i
$838$	872363.			1.24225
$839$			531080.i			0.754460i	0.926120	+	0.377230i	$0.123123\pi$
$839$			531080.i			0.754460i	−0.926120	+	0.377230i	$0.876877\pi$
$840$	1.45266e6	−	1.56038e6i	2.05876	−	2.21143i
$841$	−1.17446e6			−1.66053
$842$		−	2.41187e6i		−	3.40197i
$843$	290365.	+	270319.i	0.408591	+	0.380383i
$844$	−1.77341e6			−2.48957
$845$			632214.i			0.885422i
$846$	−83922.0	−	1.17215e6i	−0.117256	−	1.63772i
$847$	81990.2			0.114287
$848$			3.18190e6i			4.42481i
$849$	−26007.7	+	27936.4i	−0.0360817	+	0.0387574i
$850$	2832.19			0.00391999
$851$		−	229486.i		−	0.316882i
$852$	2.19885e6	+	2.04705e6i	3.02912	+	2.82000i
$853$	545553.			0.749788			0.374894	−	0.927068i	$-0.377679\pi$
$853$	545553.			0.749788			0.374894	+	0.927068i	$0.377679\pi$
$854$		−	916610.i		−	1.25681i
$855$	378216.	−	27079.1i	0.517377	−	0.0370426i
$856$	−1.46873e6			−2.00444
$857$			1.21696e6i			1.65698i	0.560007	+	0.828488i	$0.310799\pi$
$857$			1.21696e6i			1.65698i	−0.560007	+	0.828488i	$0.689201\pi$
$858$	333023.	−	357719.i	0.452376	−	0.485923i
$859$	−57401.7			−0.0777926			−0.0388963	−	0.999243i	$-0.512384\pi$
$859$	−57401.7			−0.0777926			−0.0388963	+	0.999243i	$0.512384\pi$
$860$			1.43326e6i			1.93789i
$861$	602201.	+	560627.i	0.812335	+	0.756253i
$862$	2.24891e6			3.02661
$863$			157657.i			0.211686i	0.994383	+	0.105843i	$0.0337540\pi$
$863$			157657.i			0.211686i	−0.994383	+	0.105843i	$0.966246\pi$
$864$	1.12674e6	−	1.39852e6i	1.50937	−	1.87344i
$865$	901219.			1.20448
$866$		−	308555.i		−	0.411431i
$867$	−194850.	+	209299.i	−0.259216	+	0.278439i
$868$	1.70986e6			2.26945
$869$			271011.i			0.358878i
$870$	−1.69098e6	−	1.57424e6i	−2.23409	−	2.07986i
$871$	−279600.			−0.368554
$872$			887471.i			1.16713i
$873$	92624.1	+	1.29369e6i	0.121533	+	1.69747i
$874$	1.27249e6			1.66584
$875$			819046.i			1.06977i
$876$	−928893.	+	997777.i	−1.21048	+	1.30025i
$877$	949711.			1.23479			0.617394	−	0.786654i	$-0.288188\pi$
$877$	949711.			1.23479			0.617394	+	0.786654i	$0.288188\pi$
$878$			991583.i			1.28629i
$879$	−76092.8	−	70839.5i	−0.0984840	−	0.0916849i
$880$	2.27438e6			2.93696
$881$		−	175198.i		−	0.225724i	−0.993611	−	0.112862i	$-0.963998\pi$
$881$		−	175198.i		−	0.225724i	0.993611	−	0.112862i	$-0.0360018\pi$
$882$	−205579.	+	14718.9i	−0.264267	+	0.0189207i
$883$	−700135.			−0.897967			−0.448984	−	0.893540i	$-0.648214\pi$
$883$	−700135.			−0.897967			−0.448984	+	0.893540i	$0.648214\pi$
$884$			520173.i			0.665646i
$885$	69387.1	−	74532.6i	0.0885915	−	0.0951612i
$886$	944244.			1.20286
$887$			693550.i			0.881517i	0.897626	+	0.440758i	$0.145290\pi$
$887$			693550.i			0.881517i	−0.897626	+	0.440758i	$0.854710\pi$
$888$	−302588.	−	281698.i	−0.383730	−	0.357238i
$889$	−1.16573e6			−1.47500
$890$			2.05009e6i			2.58818i
$891$	−118995.	−	826745.i	−0.149890	−	1.04140i
$892$	−1.77727e6			−2.23370
$893$		−	362926.i		−	0.455109i
$894$	−1.99440e6	+	2.14230e6i	−2.49538	+	2.68043i
$895$	110102.			0.137452
$896$		−	689557.i		−	0.858923i
$897$	−339437.	−	316003.i	−0.421865	−	0.392741i
$898$	−973499.			−1.20721
$899$		−	1.11510e6i		−	1.37973i
$900$	386.070	+	5392.26i	0.000476629	+	0.00665712i
$901$	−1.01155e6			−1.24605
$902$			1.66635e6i			2.04811i
$903$	458674.	−	492688.i	0.562508	−	0.604222i
$904$	−2.16125e6			−2.64466
$905$			1.08374e6i			1.32321i
$906$	−775825.	−	722265.i	−0.945165	−	0.879913i
$907$	1.02333e6			1.24395			0.621974	−	0.783038i	$-0.286331\pi$
$907$	1.02333e6			1.24395			0.621974	+	0.783038i	$0.286331\pi$
$908$			760245.i			0.922109i
$909$	1.08479e6	−	77667.9i	1.31286	−	0.0939970i
$910$	−557516.			−0.673247
$911$		−	199363.i		−	0.240219i	−0.992761	−	0.120110i	$-0.961675\pi$
$911$		−	199363.i		−	0.240219i	0.992761	−	0.120110i	$-0.0383246\pi$
$912$	822788.	−	883803.i	0.989232	−	1.06259i
$913$	−953911.			−1.14437
$914$			476068.i			0.569871i
$915$	−384192.	−	357668.i	−0.458887	−	0.427207i
$916$	−1.29643e6			−1.54510
$917$			714513.i			0.849712i
$918$	967925.	+	779823.i	1.14857	+	0.925360i
$919$	174760.			0.206924			0.103462	−	0.994633i	$-0.467008\pi$
$919$	174760.			0.206924			0.103462	+	0.994633i	$0.467008\pi$
$920$		−	4.09708e6i		−	4.84059i
$921$	80965.9	−	86970.1i	0.0954516	−	0.102530i
$922$	−566941.			−0.666924
$923$		−	472791.i		−	0.554965i
$924$	−1.76394e6	−	1.64217e6i	−2.06605	−	1.92342i
$925$	420.998			0.000492036
$926$			1.35300e6i			1.57788i
$927$	−97653.4	−	1.36393e6i	−0.113639	−	1.58721i
$928$	−3.37942e6			−3.92416
$929$			947396.i			1.09774i	0.835907	+	0.548871i	$0.184942\pi$
$929$			947396.i			1.09774i	−0.835907	+	0.548871i	$0.815058\pi$
$930$	932882.	−	1.00206e6i	1.07860	−	1.15859i
$931$	−63652.6			−0.0734373
$932$			887846.i			1.02213i
$933$	448048.	+	417116.i	0.514708	+	0.479174i
$934$	431142.			0.494227
$935$			723039.i			0.827063i
$936$	−833327.	+	59663.6i	−0.951182	+	0.0681017i
$937$	−393273.			−0.447935			−0.223968	−	0.974597i	$-0.571901\pi$
$937$	−393273.			−0.447935			−0.223968	+	0.974597i	$0.571901\pi$
$938$			1.92775e6i			2.19102i
$939$	−65174.8	+	70008.0i	−0.0739178	+	0.0793993i
$940$	−1.94173e6			−2.19752
$941$		−	211502.i		−	0.238856i	−0.992843	−	0.119428i	$-0.961894\pi$
$941$		−	211502.i		−	0.238856i	0.992843	−	0.119428i	$-0.0381060\pi$
$942$	−706310.	−	657548.i	−0.795964	−	0.741013i
$943$	1.58119e6			1.77812
$944$		−	324283.i		−	0.363899i
$945$	−597770.	+	741959.i	−0.669377	+	0.830838i
$946$	1.36332e6			1.52341
$947$		−	1.54738e6i		−	1.72543i	−0.505687	−	0.862717i	$-0.668761\pi$
$947$		−	1.54738e6i		−	1.72543i	0.505687	−	0.862717i	$-0.331239\pi$
$948$	524544.	−	563443.i	0.583667	−	0.626950i
$949$	214539.			0.238218
$950$			2334.42i			0.00258662i
$951$	−811675.	−	755639.i	−0.897472	−	0.835513i
$952$	2.15829e6			2.38142
$953$		−	589681.i		−	0.649279i	−0.945838	−	0.324640i	$-0.894757\pi$
$953$		−	589681.i		−	0.649279i	0.945838	−	0.324640i	$-0.105243\pi$
$954$	−192797.	−	2.69281e6i	−0.211838	−	2.95876i
$955$	1.02279e6			1.12145
$956$			1.00368e6i			1.09819i
$957$	−1.07096e6	+	1.15038e6i	−1.16936	+	1.25608i
$958$	−2.52929e6			−2.75592
$959$			1.76746e6i			1.92182i
$960$	−1.15391e6	−	1.07425e6i	−1.25207	−	1.16564i
$961$	−262722.			−0.284478
$962$			108113.i			0.116823i
$963$	654735.	−	46877.0i	0.706013	−	0.0505484i
$964$	−1.32336e6			−1.42404
$965$		−	935293.i		−	1.00437i
$966$	−2.17874e6	+	2.34031e6i	−2.33481	+	2.50795i
$967$	−126892.			−0.135700			−0.0678501	−	0.997696i	$-0.521614\pi$
$967$	−126892.			−0.135700			−0.0678501	+	0.997696i	$0.521614\pi$
$968$		−	283856.i		−	0.302934i
$969$	280967.	+	261569.i	0.299231	+	0.278573i
$970$	2.99646e6			3.18467
$971$			76870.5i			0.0815308i	0.999169	+	0.0407654i	$0.0129796\pi$
$971$			76870.5i			0.0815308i	−0.999169	+	0.0407654i	$0.987020\pi$
$972$	−1.35278e6	+	1.94915e6i	−1.43184	+	2.06307i
$973$	−512059.			−0.540871
$974$			891702.i			0.939943i
$975$	579.715	−	622.704i	0.000609825	−	0.000655047i
$976$	−1.67158e6			−1.75480
$977$		−	1.22620e6i		−	1.28462i	−0.766447	−	0.642308i	$-0.777977\pi$
$977$		−	1.22620e6i		−	1.28462i	0.766447	−	0.642308i	$-0.222023\pi$
$978$	−545339.	−	507690.i	−0.570150	−	0.530788i
$979$	1.39468e6			1.45515
$980$			340555.i			0.354597i
$981$	−28325.2	−	395620.i	−0.0294330	−	0.411094i
$982$	−1.87634e6			−1.94576
$983$			1.20316e6i			1.24514i	0.782565	+	0.622569i	$0.213911\pi$
$983$			1.20316e6i			1.24514i	−0.782565	+	0.622569i	$0.786089\pi$
$984$	1.94093e6	−	2.08487e6i	2.00457	−	2.15322i
$985$	−1.51385e6			−1.56031
$986$		−	2.33893e6i		−	2.40582i
$987$	667475.	+	621394.i	0.685174	+	0.637871i
$988$	−428750.			−0.439229
$989$		−	1.29364e6i		−	1.32258i
$990$	−1.92479e6	+	137809.i	−1.96387	+	0.140607i
$991$	−608943.			−0.620053			−0.310027	−	0.950728i	$-0.600338\pi$
$991$	−608943.			−0.620053			−0.310027	+	0.950728i	$0.600338\pi$
$992$		−	2.00262e6i		−	2.03505i
$993$	871749.	−	936395.i	0.884083	−	0.949643i
$994$	−3.25974e6			−3.29921
$995$			941564.i			0.951051i
$996$	1.98322e6	+	1.84631e6i	1.99918	+	1.86116i
$997$	−741591.			−0.746060			−0.373030	−	0.927819i	$-0.621681\pi$
$997$	−741591.			−0.746060			−0.373030	+	0.927819i	$0.621681\pi$
$998$		−	1.22832e6i		−	1.23325i
$999$	143880.	+	115919.i	0.144168	+	0.116151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.3	✓	78
3.2	odd	2	inner	177.5.b.a.119.76	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.3	✓	78	1.1	even	1	trivial
177.5.b.a.119.76	yes	78	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-7.49534i q^{2} +(-6.13251 + 6.58728i) q^{3} -40.1801 q^{4} -24.9668i q^{5} +(49.3739 + 45.9653i) q^{6} -52.3496 q^{7} +181.238i q^{8} +(-5.78454 - 80.7932i) q^{9} +O(q^{10})\)	\(q-7.49534i q^{2} +(-6.13251 + 6.58728i) q^{3} -40.1801 q^{4} -24.9668i q^{5} +(49.3739 + 45.9653i) q^{6} -52.3496 q^{7} +181.238i q^{8} +(-5.78454 - 80.7932i) q^{9} -187.134 q^{10} +127.308i q^{11} +(246.405 - 264.678i) q^{12} -56.9103 q^{13} +392.378i q^{14} +(164.463 + 153.109i) q^{15} +715.561 q^{16} +227.481i q^{17} +(-605.572 + 43.3571i) q^{18} -187.501 q^{19} +1003.17i q^{20} +(321.035 - 344.841i) q^{21} +954.213 q^{22} -905.445i q^{23} +(-1193.87 - 1111.45i) q^{24} +1.66106 q^{25} +426.562i q^{26} +(567.681 + 457.361i) q^{27} +2103.41 q^{28} -1371.77i q^{29} +(1147.60 - 1232.71i) q^{30} +812.896 q^{31} -2463.56i q^{32} +(-838.610 - 780.715i) q^{33} +1705.05 q^{34} +1307.00i q^{35} +(232.424 + 3246.28i) q^{36} +253.452 q^{37} +1405.38i q^{38} +(349.003 - 374.884i) q^{39} +4524.93 q^{40} +1746.31i q^{41} +(-2584.70 - 2406.26i) q^{42} +1428.74 q^{43} -5115.23i q^{44} +(-2017.14 + 144.421i) q^{45} -6786.61 q^{46} +1935.60i q^{47} +(-4388.19 + 4713.60i) q^{48} +339.479 q^{49} -12.4502i q^{50} +(-1498.48 - 1395.03i) q^{51} +2286.66 q^{52} +4446.72i q^{53} +(3428.08 - 4254.96i) q^{54} +3178.46 q^{55} -9487.75i q^{56} +(1149.85 - 1235.12i) q^{57} -10281.8 q^{58} -453.188i q^{59} +(-6608.15 - 6151.94i) q^{60} -2336.04 q^{61} -6092.93i q^{62} +(302.819 + 4229.49i) q^{63} -7016.24 q^{64} +1420.86i q^{65} +(-5851.73 + 6285.67i) q^{66} +4913.00 q^{67} -9140.23i q^{68} +(5964.42 + 5552.65i) q^{69} +9796.41 q^{70} +8307.66i q^{71} +(14642.8 - 1048.38i) q^{72} -3769.78 q^{73} -1899.71i q^{74} +(-10.1865 + 10.9419i) q^{75} +7533.80 q^{76} -6664.50i q^{77} +(-2809.88 - 2615.90i) q^{78} +2128.79 q^{79} -17865.2i q^{80} +(-6494.08 + 934.704i) q^{81} +13089.2 q^{82} +7492.96i q^{83} +(-12899.2 + 13855.8i) q^{84} +5679.47 q^{85} -10708.9i q^{86} +(9036.20 + 8412.37i) q^{87} -23073.0 q^{88} -10955.2i q^{89} +(1082.49 + 15119.2i) q^{90} +2979.23 q^{91} +36380.9i q^{92} +(-4985.09 + 5354.77i) q^{93} +14508.0 q^{94} +4681.28i q^{95} +(16228.2 + 15107.8i) q^{96} -16012.3 q^{97} -2544.51i q^{98} +(10285.6 - 736.416i) 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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