LMFDB - Embedded newform 177.5.b.a.119.48

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			119.48
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.78994i q^{2} +(-1.93435 + 8.78967i) q^{3} +12.7961 q^{4} +45.3568i q^{5} +(-15.7330 - 3.46237i) q^{6} +40.8012 q^{7} +51.5434i q^{8} +(-73.5166 - 34.0046i) q^{9} +O(q^{10})$	\(q+1.78994i q^{2} +(-1.93435 + 8.78967i) q^{3} +12.7961 q^{4} +45.3568i q^{5} +(-15.7330 - 3.46237i) q^{6} +40.8012 q^{7} +51.5434i q^{8} +(-73.5166 - 34.0046i) q^{9} -81.1862 q^{10} +171.958i q^{11} +(-24.7521 + 112.474i) q^{12} +174.496 q^{13} +73.0318i q^{14} +(-398.672 - 87.7359i) q^{15} +112.478 q^{16} -69.0862i q^{17} +(60.8662 - 131.590i) q^{18} +655.597 q^{19} +580.391i q^{20} +(-78.9238 + 358.629i) q^{21} -307.795 q^{22} -991.745i q^{23} +(-453.049 - 99.7029i) q^{24} -1432.24 q^{25} +312.338i q^{26} +(441.096 - 580.410i) q^{27} +522.097 q^{28} -284.975i q^{29} +(157.042 - 713.599i) q^{30} +62.5423 q^{31} +1026.02i q^{32} +(-1511.45 - 332.627i) q^{33} +123.660 q^{34} +1850.61i q^{35} +(-940.726 - 435.126i) q^{36} +238.232 q^{37} +1173.48i q^{38} +(-337.536 + 1533.76i) q^{39} -2337.84 q^{40} -1121.34i q^{41} +(-641.926 - 141.269i) q^{42} -1657.46 q^{43} +2200.39i q^{44} +(1542.34 - 3334.48i) q^{45} +1775.17 q^{46} -1735.39i q^{47} +(-217.572 + 988.644i) q^{48} -736.261 q^{49} -2563.63i q^{50} +(607.245 + 133.637i) q^{51} +2232.87 q^{52} -4594.16i q^{53} +(1038.90 + 789.536i) q^{54} -7799.47 q^{55} +2103.03i q^{56} +(-1268.15 + 5762.48i) q^{57} +510.088 q^{58} +453.188i q^{59} +(-5101.44 - 1122.68i) q^{60} -3935.21 q^{61} +111.947i q^{62} +(-2999.57 - 1387.43i) q^{63} -36.8751 q^{64} +7914.59i q^{65} +(595.383 - 2705.42i) q^{66} +5122.41 q^{67} -884.034i q^{68} +(8717.11 + 1918.38i) q^{69} -3312.49 q^{70} -4704.20i q^{71} +(1752.71 - 3789.29i) q^{72} +7916.13 q^{73} +426.422i q^{74} +(2770.46 - 12588.9i) q^{75} +8389.09 q^{76} +7016.10i q^{77} +(-2745.35 - 604.171i) q^{78} -274.480 q^{79} +5101.65i q^{80} +(4248.38 + 4999.80i) q^{81} +2007.13 q^{82} +4807.12i q^{83} +(-1009.92 + 4589.06i) q^{84} +3133.53 q^{85} -2966.75i q^{86} +(2504.83 + 551.240i) q^{87} -8863.30 q^{88} -5001.80i q^{89} +(5968.53 + 2760.70i) q^{90} +7119.65 q^{91} -12690.5i q^{92} +(-120.979 + 549.727i) q^{93} +3106.25 q^{94} +29735.8i q^{95} +(-9018.41 - 1984.69i) q^{96} -5744.78 q^{97} -1317.86i q^{98} +(5847.36 - 12641.8i) 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 $

$2$			1.78994i			0.447486i	0.974648	+	0.223743i	$0.0718276\pi$
$2$			1.78994i			0.447486i	−0.974648	+	0.223743i	$0.928172\pi$
$3$	−1.93435	+	8.78967i	−0.214928	+	0.976630i
$3$	−1.93435	+	8.78967i	−0.214928	+	0.976630i
$4$	12.7961			0.799757
$5$			45.3568i			1.81427i	0.420836	+	0.907137i	$0.361737\pi$
$5$			45.3568i			1.81427i	−0.420836	+	0.907137i	$0.638263\pi$
$6$	−15.7330	−	3.46237i	−0.437028	−	0.0961770i
$7$	40.8012			0.832678			0.416339	−	0.909209i	$-0.363313\pi$
$7$	40.8012			0.832678			0.416339	+	0.909209i	$0.363313\pi$
$8$			51.5434i			0.805365i
$9$	−73.5166	−	34.0046i	−0.907612	−	0.419810i
$10$	−81.1862			−0.811862
$11$			171.958i			1.42114i	0.703626	+	0.710571i	$0.251563\pi$
$11$			171.958i			1.42114i	−0.703626	+	0.710571i	$0.748437\pi$
$12$	−24.7521	+	112.474i	−0.171890	+	0.781066i
$13$	174.496			1.03252			0.516261	−	0.856432i	$-0.327324\pi$
$13$	174.496			1.03252			0.516261	+	0.856432i	$0.327324\pi$
$14$			73.0318i			0.372611i
$15$	−398.672	−	87.7359i	−1.77187	−	0.389938i
$16$	112.478			0.439367
$17$		−	69.0862i		−	0.239052i	−0.992831	−	0.119526i	$-0.961862\pi$
$17$		−	69.0862i		−	0.239052i	0.992831	−	0.119526i	$-0.0381376\pi$
$18$	60.8662	−	131.590i	0.187859	−	0.406143i
$19$	655.597			1.81606			0.908029	−	0.418907i	$-0.137587\pi$
$19$	655.597			1.81606			0.908029	+	0.418907i	$0.137587\pi$
$20$			580.391i			1.45098i
$21$	−78.9238	+	358.629i	−0.178965	+	0.813218i
$22$	−307.795			−0.635940
$23$		−	991.745i		−	1.87475i	−0.348316	−	0.937377i	$-0.613247\pi$
$23$		−	991.745i		−	1.87475i	0.348316	−	0.937377i	$-0.386753\pi$
$24$	−453.049	−	99.7029i	−0.786544	−	0.173095i
$25$	−1432.24			−2.29159
$26$			312.338i			0.462038i
$27$	441.096	−	580.410i	0.605069	−	0.796173i
$28$	522.097			0.665940
$29$		−	284.975i		−	0.338852i	−0.985543	−	0.169426i	$-0.945809\pi$
$29$		−	284.975i		−	0.338852i	0.985543	−	0.169426i	$-0.0541914\pi$
$30$	157.042	−	713.599i	0.174491	−	0.792888i
$31$	62.5423			0.0650805			0.0325402	−	0.999470i	$-0.489640\pi$
$31$	62.5423			0.0650805			0.0325402	+	0.999470i	$0.489640\pi$
$32$			1026.02i			1.00198i
$33$	−1511.45	−	332.627i	−1.38793	−	0.305442i
$34$	123.660			0.106973
$35$			1850.61i			1.51071i
$36$	−940.726	−	435.126i	−0.725869	−	0.335745i
$37$	238.232			0.174019			0.0870095	−	0.996207i	$-0.472269\pi$
$37$	238.232			0.174019			0.0870095	+	0.996207i	$0.472269\pi$
$38$			1173.48i			0.812660i
$39$	−337.536	+	1533.76i	−0.221917	+	1.00839i
$40$	−2337.84			−1.46115
$41$		−	1121.34i		−	0.667066i	−0.942739	−	0.333533i	$-0.891759\pi$
$41$		−	1121.34i		−	0.667066i	0.942739	−	0.333533i	$-0.108241\pi$
$42$	−641.926	−	141.269i	−0.363903	−	0.0800845i
$43$	−1657.46			−0.896407			−0.448204	−	0.893931i	$-0.647936\pi$
$43$	−1657.46			−0.896407			−0.448204	+	0.893931i	$0.647936\pi$
$44$			2200.39i			1.13657i
$45$	1542.34	−	3334.48i	0.761649	−	1.64666i
$46$	1775.17			0.838926
$47$		−	1735.39i		−	0.785601i	−0.919624	−	0.392800i	$-0.871506\pi$
$47$		−	1735.39i		−	0.785601i	0.919624	−	0.392800i	$-0.128494\pi$
$48$	−217.572	+	988.644i	−0.0944321	+	0.429099i
$49$	−736.261			−0.306648
$50$		−	2563.63i		−	1.02545i
$51$	607.245	+	133.637i	0.233466	+	0.0513790i
$52$	2232.87			0.825766
$53$		−	4594.16i		−	1.63552i	−0.575563	−	0.817758i	$-0.695217\pi$
$53$		−	4594.16i		−	1.63552i	0.575563	−	0.817758i	$-0.304783\pi$
$54$	1038.90	+	789.536i	0.356276	+	0.270760i
$55$	−7799.47			−2.57834
$56$			2103.03i			0.670610i
$57$	−1268.15	+	5762.48i	−0.390321	+	1.77362i
$58$	510.088			0.151631
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−5101.44	−	1122.68i	−1.41707	−	0.311855i
$61$	−3935.21			−1.05757			−0.528784	−	0.848756i	$-0.677352\pi$
$61$	−3935.21			−1.05757			−0.528784	+	0.848756i	$0.677352\pi$
$62$			111.947i			0.0291226i
$63$	−2999.57	−	1387.43i	−0.755749	−	0.349566i
$64$	−36.8751			−0.00900271
$65$			7914.59i			1.87328i
$66$	595.383	−	2705.42i	0.136681	−	0.621078i
$67$	5122.41			1.14110			0.570552	−	0.821262i	$-0.306729\pi$
$67$	5122.41			1.14110			0.570552	+	0.821262i	$0.306729\pi$
$68$		−	884.034i		−	0.191184i
$69$	8717.11	+	1918.38i	1.83094	+	0.402936i
$70$	−3312.49			−0.676019
$71$		−	4704.20i		−	0.933187i	−0.884472	−	0.466594i	$-0.845481\pi$
$71$		−	4704.20i		−	0.933187i	0.884472	−	0.466594i	$-0.154519\pi$
$72$	1752.71	−	3789.29i	0.338100	−	0.730959i
$73$	7916.13			1.48548			0.742741	−	0.669579i	$-0.233526\pi$
$73$	7916.13			1.48548			0.742741	+	0.669579i	$0.233526\pi$
$74$			426.422i			0.0778710i
$75$	2770.46	−	12588.9i	0.492526	−	2.23803i
$76$	8389.09			1.45240
$77$			7016.10i			1.18335i
$78$	−2745.35	−	604.171i	−0.451241	−	0.0993048i
$79$	−274.480			−0.0439802			−0.0219901	−	0.999758i	$-0.507000\pi$
$79$	−274.480			−0.0439802			−0.0219901	+	0.999758i	$0.507000\pi$
$80$			5101.65i			0.797132i
$81$	4248.38	+	4999.80i	0.647520	+	0.762048i
$82$	2007.13			0.298502
$83$			4807.12i			0.697796i	0.937161	+	0.348898i	$0.113444\pi$
$83$			4807.12i			0.697796i	−0.937161	+	0.348898i	$0.886556\pi$
$84$	−1009.92	+	4589.06i	−0.143129	+	0.650377i
$85$	3133.53			0.433707
$86$		−	2966.75i		−	0.401129i
$87$	2504.83	+	551.240i	0.330933	+	0.0728287i
$88$	−8863.30			−1.14454
$89$		−	5001.80i		−	0.631460i	−0.948849	−	0.315730i	$-0.897751\pi$
$89$		−	5001.80i		−	0.631460i	0.948849	−	0.315730i	$-0.102249\pi$
$90$	5968.53	+	2760.70i	0.736855	+	0.340827i
$91$	7119.65			0.859758
$92$		−	12690.5i		−	1.49935i
$93$	−120.979	+	549.727i	−0.0139876	+	0.0635595i
$94$	3106.25			0.351545
$95$			29735.8i			3.29483i
$96$	−9018.41	−	1984.69i	−0.978560	−	0.215352i
$97$	−5744.78			−0.610562			−0.305281	−	0.952262i	$-0.598750\pi$
$97$	−5744.78			−0.610562			−0.305281	+	0.952262i	$0.598750\pi$
$98$		−	1317.86i		−	0.137220i
$99$	5847.36	−	12641.8i	0.596608	−	1.28984i
$100$	−18327.1			−1.83271
$101$		−	12759.6i		−	1.25082i	−0.780295	−	0.625411i	$-0.784931\pi$
$101$		−	12759.6i		−	1.25082i	0.780295	−	0.625411i	$-0.215069\pi$
$102$	−239.202	+	1086.93i	−0.0229914	+	0.104473i
$103$	10149.9			0.956729			0.478364	−	0.878161i	$-0.341230\pi$
$103$	10149.9			0.956729			0.478364	+	0.878161i	$0.341230\pi$
$104$			8994.12i			0.831557i
$105$	−16266.3	−	3579.73i	−1.47540	−	0.324692i
$106$	8223.29			0.731870
$107$			10618.4i			0.927449i	0.885979	+	0.463725i	$0.153487\pi$
$107$			10618.4i			0.927449i	−0.885979	+	0.463725i	$0.846513\pi$
$108$	5644.31	−	7426.99i	0.483908	−	0.636744i
$109$	3232.01			0.272032			0.136016	−	0.990707i	$-0.456570\pi$
$109$	3232.01			0.272032			0.136016	+	0.990707i	$0.456570\pi$
$110$		−	13960.6i		−	1.15377i
$111$	−460.824	+	2093.98i	−0.0374015	+	0.169952i
$112$	4589.24			0.365851
$113$			21891.3i			1.71441i	0.514978	+	0.857203i	$0.327800\pi$
$113$			21891.3i			1.71441i	−0.514978	+	0.857203i	$0.672200\pi$
$114$	−10314.5	−	2269.92i	−0.793668	−	0.174663i
$115$	44982.4			3.40132
$116$		−	3646.56i		−	0.270999i
$117$	−12828.4	−	5933.66i	−0.937129	−	0.433462i
$118$	−811.180			−0.0582577
$119$		−	2818.80i		−	0.199054i
$120$	4522.21	−	20548.9i	0.314042	−	1.42701i
$121$	−14928.6			−1.01964
$122$		−	7043.81i		−	0.473247i
$123$	9856.18	+	2169.06i	0.651476	+	0.143371i
$124$	800.298			0.0520485
$125$		−	36614.0i		−	2.34330i
$126$	2483.42	−	5369.05i	0.156426	−	0.338187i
$127$	−13689.5			−0.848749			−0.424375	−	0.905487i	$-0.639506\pi$
$127$	−13689.5			−0.848749			−0.424375	+	0.905487i	$0.639506\pi$
$128$			16350.4i			0.997947i
$129$	3206.10	−	14568.5i	0.192663	−	0.875458i
$130$	−14166.7			−0.838264
$131$		−	23701.2i		−	1.38111i	−0.723280	−	0.690555i	$-0.757366\pi$
$131$		−	23701.2i		−	1.38111i	0.723280	−	0.690555i	$-0.242634\pi$
$132$	−19340.7	−	4256.33i	−1.11001	−	0.244280i
$133$	26749.2			1.51219
$134$			9168.83i			0.510628i
$135$	26325.6	+	20006.7i	1.44448	+	1.09776i
$136$	3560.93			0.192525
$137$			4651.39i			0.247823i	0.992293	+	0.123912i	$0.0395439\pi$
$137$			4651.39i			0.247823i	−0.992293	+	0.123912i	$0.960456\pi$
$138$	−3433.79	+	15603.1i	−0.180308	+	0.819320i
$139$	10259.9			0.531024			0.265512	−	0.964108i	$-0.414459\pi$
$139$	10259.9			0.531024			0.265512	+	0.964108i	$0.414459\pi$
$140$			23680.7i			1.20820i
$141$	15253.5	+	3356.85i	0.767241	+	0.168847i
$142$	8420.24			0.417588
$143$			30006.0i			1.46736i
$144$	−8269.00	−	3824.77i	−0.398775	−	0.184450i
$145$	12925.5			0.614770
$146$			14169.4i			0.664732i
$147$	1424.18	−	6471.49i	0.0659070	−	0.299481i
$148$	3048.44			0.139173
$149$			9779.91i			0.440517i	0.975442	+	0.220258i	$0.0706900\pi$
$149$			9779.91i			0.440517i	−0.975442	+	0.220258i	$0.929310\pi$
$150$	22533.5	+	4958.96i	1.00149	+	0.220398i
$151$	−3378.97			−0.148194			−0.0740969	−	0.997251i	$-0.523607\pi$
$151$	−3378.97			−0.148194			−0.0740969	+	0.997251i	$0.523607\pi$
$152$			33791.7i			1.46259i
$153$	−2349.25	+	5078.98i	−0.100357	+	0.216967i
$154$	−12558.4			−0.529533
$155$			2836.72i			0.118074i
$156$	−4319.15	+	19626.2i	−0.177480	+	0.806468i
$157$	−10591.5			−0.429692			−0.214846	−	0.976648i	$-0.568925\pi$
$157$	−10591.5			−0.429692			−0.214846	+	0.976648i	$0.568925\pi$
$158$		−	491.304i		−	0.0196805i
$159$	40381.2	+	8886.71i	1.59729	+	0.351517i
$160$	−46537.2			−1.81786
$161$		−	40464.4i		−	1.56107i
$162$	−8949.36	+	7604.35i	−0.341006	+	0.289756i
$163$	−29808.8			−1.12194			−0.560970	−	0.827836i	$-0.689572\pi$
$163$	−29808.8			−1.12194			−0.560970	+	0.827836i	$0.689572\pi$
$164$		−	14348.7i		−	0.533490i
$165$	15086.9	−	68554.8i	0.554156	−	2.51808i
$166$	−8604.47			−0.312254
$167$			31109.7i			1.11548i	0.830015	+	0.557742i	$0.188332\pi$
$167$			31109.7i			1.11548i	−0.830015	+	0.557742i	$0.811668\pi$
$168$	−18485.0	−	4068.00i	−0.654938	−	0.144133i
$169$	1887.89			0.0661002
$170$			5608.84i			0.194078i
$171$	−48197.2	−	22293.3i	−1.64828	−	0.762398i
$172$	−21209.0			−0.716908
$173$			28012.0i			0.935948i	0.883742	+	0.467974i	$0.155016\pi$
$173$			28012.0i			0.935948i	−0.883742	+	0.467974i	$0.844984\pi$
$174$	−986.688	+	4483.51i	−0.0325898	+	0.148088i
$175$	−58437.3			−1.90816
$176$			19341.5i			0.624403i
$177$	−3983.37	−	876.623i	−0.127146	−	0.0279812i
$178$	8952.93			0.282569
$179$		−	9398.89i		−	0.293340i	−0.989186	−	0.146670i	$-0.953145\pi$
$179$		−	9398.89i		−	0.293340i	0.989186	−	0.146670i	$-0.0468555\pi$
$180$	19735.9	−	42668.4i	0.609134	−	1.31692i
$181$	−10734.8			−0.327671			−0.163835	−	0.986488i	$-0.552387\pi$
$181$	−10734.8			−0.327671			−0.163835	+	0.986488i	$0.552387\pi$
$182$			12743.8i			0.384729i
$183$	7612.07	−	34589.2i	0.227301	−	1.03285i
$184$	51117.9			1.50986
$185$			10805.4i			0.315718i
$186$	−983.979	−	216.545i	−0.0284420	−	0.00625925i
$187$	11879.9			0.339727
$188$		−	22206.3i		−	0.628289i
$189$	17997.2	−	23681.4i	0.503828	−	0.662955i
$190$	−53225.4			−1.47439
$191$		−	13071.6i		−	0.358313i	−0.983821	−	0.179156i	$-0.942663\pi$
$191$		−	13071.6i		−	0.358313i	0.983821	−	0.179156i	$-0.0573368\pi$
$192$	71.3293	−	324.120i	0.00193493	−	0.00879231i
$193$	−26926.9			−0.722888			−0.361444	−	0.932394i	$-0.617716\pi$
$193$	−26926.9			−0.722888			−0.361444	+	0.932394i	$0.617716\pi$
$194$		−	10282.8i		−	0.273218i
$195$	−69566.7	−	15309.6i	−1.82950	−	0.402619i
$196$	−9421.27			−0.245243
$197$		−	16603.7i		−	0.427832i	−0.976852	−	0.213916i	$-0.931378\pi$
$197$		−	16603.7i		−	0.427832i	0.976852	−	0.213916i	$-0.0686219\pi$
$198$	22628.0	+	10466.4i	0.577187	+	0.266974i
$199$	−70795.4			−1.78772			−0.893858	−	0.448349i	$-0.852012\pi$
$199$	−70795.4			−1.78772			−0.893858	+	0.448349i	$0.852012\pi$
$200$		−	73822.7i		−	1.84557i
$201$	−9908.53	+	45024.3i	−0.245255	+	1.11444i
$202$	22839.0			0.559725
$203$		−	11627.3i		−	0.282155i
$204$	7770.37	+	1710.03i	0.186716	+	0.0410907i
$205$	50860.3			1.21024
$206$			18167.8i			0.428122i
$207$	−33723.9	+	72909.7i	−0.787040	+	1.70155i
$208$	19627.0			0.453656
$209$			112735.i			2.58087i
$210$	6407.52	−	29115.7i	0.145295	−	0.660221i
$211$	−2740.61			−0.0615577			−0.0307789	−	0.999526i	$-0.509799\pi$
$211$	−2740.61			−0.0615577			−0.0307789	+	0.999526i	$0.509799\pi$
$212$		−	58787.4i		−	1.30801i
$213$	41348.3	+	9099.55i	0.911378	+	0.200568i
$214$	−19006.3			−0.415020
$215$		−	75177.0i		−	1.62633i
$216$	29916.3	+	22735.6i	0.641210	+	0.487302i
$217$	2551.80			0.0541911
$218$			5785.11i			0.121730i
$219$	−15312.6	+	69580.2i	−0.319271	+	1.45077i
$220$	−99802.9			−2.06204
$221$		−	12055.3i		−	0.246827i
$222$	−3748.10	−	824.848i	−0.0760511	−	0.0167366i
$223$	−20547.3			−0.413185			−0.206593	−	0.978427i	$-0.566237\pi$
$223$	−20547.3			−0.413185			−0.206593	+	0.978427i	$0.566237\pi$
$224$			41863.0i			0.834323i
$225$	105294.	+	48702.8i	2.07987	+	0.962031i
$226$	−39184.1			−0.767172
$227$		−	3357.12i		−	0.0651501i	−0.999469	−	0.0325751i	$-0.989629\pi$
$227$		−	3357.12i		−	0.0651501i	0.999469	−	0.0325751i	$-0.0103708\pi$
$228$	−16227.4	+	73737.3i	−0.312162	+	1.41846i
$229$	35090.0			0.669133			0.334567	−	0.942372i	$-0.391410\pi$
$229$	35090.0			0.669133			0.334567	+	0.942372i	$0.391410\pi$
$230$			80516.0i			1.52204i
$231$	−61669.2	−	13571.6i	−1.15570	−	0.254335i
$232$	14688.6			0.272900
$233$			16941.4i			0.312060i	0.987752	+	0.156030i	$0.0498697\pi$
$233$			16941.4i			0.312060i	−0.987752	+	0.156030i	$0.950130\pi$
$234$	10620.9	−	22962.0i	0.193968	−	0.419352i
$235$	78711.9			1.42529
$236$			5799.04i			0.104119i
$237$	530.941	−	2412.59i	0.00945256	−	0.0429524i
$238$	5045.49			0.0890737
$239$		−	98857.4i		−	1.73067i	−0.501197	−	0.865333i	$-0.667107\pi$
$239$		−	98857.4i		−	1.73067i	0.501197	−	0.865333i	$-0.332893\pi$
$240$	−44841.8	−	9868.36i	−0.778503	−	0.171326i
$241$	−30200.0			−0.519963			−0.259982	−	0.965614i	$-0.583717\pi$
$241$	−30200.0			−0.519963			−0.259982	+	0.965614i	$0.583717\pi$
$242$		−	26721.3i		−	0.456275i
$243$	−52164.4	+	27670.5i	−0.883409	+	0.468602i
$244$	−50355.4			−0.845798
$245$		−	33394.5i		−	0.556343i
$246$	−3882.49	+	17642.0i	−0.0641564	+	0.291526i
$247$	114399.			1.87512
$248$			3223.64i			0.0524136i
$249$	−42253.0	−	9298.64i	−0.681489	−	0.149976i
$250$	65537.0			1.04859
$251$			71408.9i			1.13346i	0.823905	+	0.566728i	$0.191791\pi$
$251$			71408.9i			1.13346i	−0.823905	+	0.566728i	$0.808209\pi$
$252$	−38382.8	−	17753.7i	−0.604415	−	0.279568i
$253$	170539.			2.66429
$254$		−	24503.4i		−	0.379803i
$255$	−6061.34	+	27542.7i	−0.0932155	+	0.423571i
$256$	−29856.2			−0.455570
$257$		−	105862.i		−	1.60279i	−0.598139	−	0.801393i	$-0.704093\pi$
$257$		−	105862.i		−	1.60279i	0.598139	−	0.801393i	$-0.295907\pi$
$258$	26076.8	+	5738.74i	0.391755	+	0.0862138i
$259$	9720.15			0.144902
$260$			101276.i			1.49816i
$261$	−9690.44	+	20950.4i	−0.142253	+	0.307546i
$262$	42423.8			0.618027
$263$			25146.4i			0.363550i	0.983340	+	0.181775i	$0.0581843\pi$
$263$			25146.4i			0.363550i	−0.983340	+	0.181775i	$0.941816\pi$
$264$	17144.7	−	77905.5i	0.245993	−	1.11779i
$265$	208377.			2.96727
$266$			47879.4i			0.676684i
$267$	43964.1	+	9675.22i	0.616703	+	0.135718i
$268$	65546.9			0.912605
$269$			29526.3i			0.408042i	0.978967	+	0.204021i	$0.0654010\pi$
$269$			29526.3i			0.408042i	−0.978967	+	0.204021i	$0.934599\pi$
$270$	−35810.9	+	47121.2i	−0.491233	+	0.646382i
$271$	−116864.			−1.59126			−0.795629	−	0.605785i	$-0.792859\pi$
$271$	−116864.			−1.59126			−0.795629	+	0.605785i	$0.792859\pi$
$272$		−	7770.67i		−	0.105032i
$273$	−13771.9	+	62579.4i	−0.184786	+	0.839665i
$274$	−8325.73			−0.110897
$275$		−	246286.i		−	3.25667i
$276$	111545.	+	24547.8i	1.46431	+	0.322251i
$277$	−7629.65			−0.0994364			−0.0497182	−	0.998763i	$-0.515832\pi$
$277$	−7629.65			−0.0994364			−0.0497182	+	0.998763i	$0.515832\pi$
$278$			18364.7i			0.237626i
$279$	−4597.90	−	2126.73i	−0.0590678	−	0.0273214i
$280$	−95386.9			−1.21667
$281$			10278.0i			0.130166i	0.997880	+	0.0650830i	$0.0207312\pi$
$281$			10278.0i			0.130166i	−0.997880	+	0.0650830i	$0.979269\pi$
$282$	−6008.57	+	27302.9i	−0.0755567	+	0.343329i
$283$	−138146.			−1.72491			−0.862455	−	0.506134i	$-0.831074\pi$
$283$	−138146.			−1.72491			−0.862455	+	0.506134i	$0.831074\pi$
$284$		−	60195.4i		−	0.746322i
$285$	−261368.	−	57519.4i	−3.21783	−	0.708149i
$286$	−53709.0			−0.656622
$287$		−	45751.9i		−	0.555451i
$288$	34889.5	−	75429.7i	0.420639	−	0.909405i
$289$	78748.1			0.942854
$290$			23136.0i			0.275101i
$291$	11112.4	−	50494.7i	0.131227	−	0.596293i
$292$	101296.			1.18802
$293$			68877.7i			0.802312i	0.916010	+	0.401156i	$0.131392\pi$
$293$			68877.7i			0.802312i	−0.916010	+	0.401156i	$0.868608\pi$
$294$	11583.6	+	2549.21i	0.134014	+	0.0294924i
$295$	−20555.2			−0.236198
$296$			12279.3i			0.140149i
$297$	99806.2	+	75850.0i	1.13147	+	0.859889i
$298$	−17505.5			−0.197125
$299$		−	173056.i		−	1.93572i
$300$	35451.1	−	161089.i	0.393901	−	1.78988i
$301$	−67626.3			−0.746419
$302$		−	6048.16i		−	0.0663146i
$303$	112153.	+	24681.6i	1.22159	+	0.268836i
$304$	73740.2			0.797916
$305$		−	178489.i		−	1.91872i
$306$	−9091.08	−	4205.01i	−0.0970896	−	0.0449081i
$307$	122823.			1.30317			0.651587	−	0.758574i	$-0.274104\pi$
$307$	122823.			1.30317			0.651587	+	0.758574i	$0.274104\pi$
$308$			89778.7i			0.946394i
$309$	−19633.5	+	89214.6i	−0.205627	+	0.934370i
$310$	−5077.57			−0.0528363
$311$			18766.8i			0.194030i	0.995283	+	0.0970151i	$0.0309295\pi$
$311$			18766.8i			0.194030i	−0.995283	+	0.0970151i	$0.969070\pi$
$312$	−79055.3	−	17397.8i	−0.812123	−	0.178725i
$313$	131641.			1.34370			0.671850	−	0.740687i	$-0.265500\pi$
$313$	131641.			1.34370			0.671850	+	0.740687i	$0.265500\pi$
$314$		−	18958.1i		−	0.192281i
$315$	62929.3	−	136051.i	0.634209	−	1.37113i
$316$	−3512.28			−0.0351735
$317$			63563.8i			0.632545i	0.948668	+	0.316272i	$0.102431\pi$
$317$			63563.8i			0.632545i	−0.948668	+	0.316272i	$0.897569\pi$
$318$	−15906.7	+	72280.0i	−0.157299	+	0.714766i
$319$	49003.7			0.481557
$320$		−	1672.54i		−	0.0163334i
$321$	−93332.0	−	20539.6i	−0.905775	−	0.199334i
$322$	72429.0			0.698555
$323$		−	45292.7i		−	0.434133i
$324$	54362.7	+	63978.0i	0.517858	+	0.609453i
$325$	−249921.			−2.36611
$326$		−	53356.1i		−	0.502052i
$327$	−6251.83	+	28408.3i	−0.0584671	+	0.265674i
$328$	57797.5			0.537231
$329$		−	70806.1i		−	0.654152i
$330$	122709.	+	27004.7i	1.12681	+	0.247977i
$331$	−87893.3			−0.802232			−0.401116	−	0.916027i	$-0.631377\pi$
$331$	−87893.3			−0.802232			−0.401116	+	0.916027i	$0.631377\pi$
$332$			61512.4i			0.558067i
$333$	−17514.0	−	8100.97i	−0.157942	−	0.0730548i
$334$	−55684.6			−0.499163
$335$			232337.i			2.07027i
$336$	−8877.19	+	40337.9i	−0.0786315	+	0.357301i
$337$	152457.			1.34242			0.671208	−	0.741269i	$-0.265776\pi$
$337$	152457.			1.34242			0.671208	+	0.741269i	$0.265776\pi$
$338$			3379.21i			0.0295789i
$339$	−192417.	−	42345.3i	−1.67434	−	0.368473i
$340$	40097.0			0.346860
$341$			10754.7i			0.0924885i
$342$	39903.7	−	86270.3i	0.341162	−	0.737580i
$343$	−128004.			−1.08802
$344$		−	85430.9i		−	0.721935i
$345$	−87011.7	+	395381.i	−0.731037	+	3.32183i
$346$	−50139.8			−0.418823
$347$			62821.1i			0.521731i	0.965375	+	0.260865i	$0.0840079\pi$
$347$			62821.1i			0.521731i	−0.965375	+	0.260865i	$0.915992\pi$
$348$	32052.1	+	7053.73i	0.264666	+	0.0582452i
$349$	−33029.8			−0.271179			−0.135589	−	0.990765i	$-0.543293\pi$
$349$	−33029.8			−0.271179			−0.135589	+	0.990765i	$0.543293\pi$
$350$		−	104599.i		−	0.853872i
$351$	76969.5	−	101279.i	0.624747	−	0.822065i
$352$	−176433.			−1.42395
$353$		−	129177.i		−	1.03666i	−0.855182	−	0.518328i	$-0.826555\pi$
$353$		−	129177.i		−	1.03666i	0.855182	−	0.518328i	$-0.173445\pi$
$354$	1569.10	−	7130.00i	0.0125212	−	0.0568962i
$355$	213367.			1.69306
$356$		−	64003.5i		−	0.505014i
$357$	24776.3	+	5452.54i	0.194402	+	0.0427821i
$358$	16823.5			0.131265
$359$			63051.8i			0.489225i	0.969621	+	0.244613i	$0.0786608\pi$
$359$			63051.8i			0.489225i	−0.969621	+	0.244613i	$0.921339\pi$
$360$	171870.	+	79497.4i	1.32616	+	0.613406i
$361$	299486.			2.29807
$362$		−	19214.7i		−	0.146628i
$363$	28877.1	−	131217.i	0.219149	−	0.995813i
$364$	91103.8			0.687597
$365$			359051.i			2.69507i
$366$	61912.7	+	13625.2i	0.462187	+	0.101714i
$367$	−146213.			−1.08556			−0.542780	−	0.839875i	$-0.682628\pi$
$367$	−146213.			−1.08556			−0.542780	+	0.839875i	$0.682628\pi$
$368$		−	111549.i		−	0.823705i
$369$	−38130.6	+	82436.9i	−0.280040	+	0.605437i
$370$	−19341.1			−0.141279
$371$		−	187447.i		−	1.36186i
$372$	−1548.06	+	7034.36i	−0.0111867	+	0.0508322i
$373$	−46328.9			−0.332992			−0.166496	−	0.986042i	$-0.553245\pi$
$373$	−46328.9			−0.332992			−0.166496	+	0.986042i	$0.553245\pi$
$374$			21264.4i			0.152023i
$375$	321825.	+	70824.3i	2.28853	+	0.503639i
$376$	89448.0			0.632696
$377$		−	49727.0i		−	0.349872i
$378$	42388.4	+	32214.0i	0.296663	+	0.225456i
$379$	−247411.			−1.72242			−0.861212	−	0.508245i	$-0.830294\pi$
$379$	−247411.			−1.72242			−0.861212	+	0.508245i	$0.830294\pi$
$380$			380502.i			2.63506i
$381$	26480.2	−	120326.i	0.182420	−	0.828914i
$382$	23397.4			0.160340
$383$		−	121821.i		−	0.830468i	−0.909715	−	0.415234i	$-0.863700\pi$
$383$		−	121821.i		−	0.830468i	0.909715	−	0.415234i	$-0.136300\pi$
$384$	−143714.	−	31627.3i	−0.974625	−	0.214486i
$385$	−318228.			−2.14693
$386$		−	48197.5i		−	0.323482i
$387$	121851.	+	56361.1i	0.813590	+	0.376320i
$388$	−73510.8			−0.488301
$389$		−	43592.3i		−	0.288079i	−0.989572	−	0.144039i	$-0.953991\pi$
$389$		−	43592.3i		−	0.288079i	0.989572	−	0.144039i	$-0.0460092\pi$
$390$	27403.3	−	124520.i	0.180166	−	0.818674i
$391$	−68515.9			−0.448165
$392$		−	37949.4i		−	0.246963i
$393$	208326.	+	45846.4i	1.34883	+	0.296839i
$394$	29719.7			0.191449
$395$		−	12449.6i		−	0.0797921i
$396$	74823.4	−	161765.i	0.477142	−	1.03156i
$397$	−84322.8			−0.535013			−0.267506	−	0.963556i	$-0.586200\pi$
$397$	−84322.8			−0.535013			−0.267506	+	0.963556i	$0.586200\pi$
$398$		−	126720.i		−	0.799978i
$399$	−51742.2	+	235116.i	−0.325012	+	1.47685i
$400$	−161096.			−1.00685
$401$			5259.56i			0.0327085i	0.999866	+	0.0163543i	$0.00520595\pi$
$401$			5259.56i			0.0327085i	−0.999866	+	0.0163543i	$0.994794\pi$
$402$	−80591.0	−	17735.7i	−0.498694	−	0.109748i
$403$	10913.4			0.0671970
$404$		−	163274.i		−	1.00035i
$405$	−226775.	+	192693.i	−1.38256	+	1.17478i
$406$	20812.2			0.126260
$407$			40965.9i			0.247305i
$408$	−6888.09	+	31299.4i	−0.0413788	+	0.188025i
$409$	−54270.1			−0.324424			−0.162212	−	0.986756i	$-0.551863\pi$
$409$	−54270.1			−0.324424			−0.162212	+	0.986756i	$0.551863\pi$
$410$			91037.1i			0.541565i
$411$	−40884.2	−	8997.42i	−0.242032	−	0.0532640i
$412$	129880.			0.765150
$413$			18490.6i			0.108405i
$414$	−130504.	−	60363.8i	−0.761419	−	0.352189i
$415$	−218036.			−1.26599
$416$			179037.i			1.03456i
$417$	−19846.2	+	90181.2i	−0.114132	+	0.518614i
$418$	−201790.			−1.15490
$419$			73943.3i			0.421183i	0.977574	+	0.210591i	$0.0675390\pi$
$419$			73943.3i			0.421183i	−0.977574	+	0.210591i	$0.932461\pi$
$420$	−208145.	−	45806.6i	−1.17996	−	0.259675i
$421$	90926.0			0.513008			0.256504	−	0.966543i	$-0.417429\pi$
$421$	90926.0			0.513008			0.256504	+	0.966543i	$0.417429\pi$
$422$		−	4905.54i		−	0.0275462i
$423$	−59011.3	+	127580.i	−0.329803	+	0.713021i
$424$	236799.			1.31719
$425$			98948.2i			0.547810i
$426$	−16287.7	+	74011.1i	−0.0897512	+	0.407829i
$427$	−160562.			−0.880614
$428$			135874.i			0.741734i
$429$	−263743.	−	58042.1i	−1.43307	−	0.315376i
$430$	134563.			0.727759
$431$		−	111657.i		−	0.601079i	−0.953769	−	0.300540i	$-0.902833\pi$
$431$		−	111657.i		−	0.601079i	0.953769	−	0.300540i	$-0.0971667\pi$
$432$	49613.5	−	65283.3i	0.265848	−	0.349812i
$433$	−68492.5			−0.365315			−0.182657	−	0.983177i	$-0.558470\pi$
$433$	−68492.5			−0.365315			−0.182657	+	0.983177i	$0.558470\pi$
$434$			4567.58i			0.0242497i
$435$	−25002.5	+	113611.i	−0.132131	+	0.600403i
$436$	41357.1			0.217559
$437$		−	650185.i		−	3.40466i
$438$	−124545.	−	27408.6i	−0.649197	−	0.142869i
$439$	−350075.			−1.81649			−0.908244	−	0.418441i	$-0.862577\pi$
$439$	−350075.			−1.81649			−0.908244	+	0.418441i	$0.862577\pi$
$440$		−	402011.i		−	2.07650i
$441$	54127.4	+	25036.2i	0.278317	+	0.128734i
$442$	21578.2			0.110451
$443$			81503.4i			0.415306i	0.978203	+	0.207653i	$0.0665825\pi$
$443$			81503.4i			0.415306i	−0.978203	+	0.207653i	$0.933417\pi$
$444$	−5896.75	+	26794.8i	−0.0299121	+	0.135920i
$445$	226866.			1.14564
$446$		−	36778.5i		−	0.184895i
$447$	−85962.2	−	18917.8i	−0.430222	−	0.0946792i
$448$	−1504.55			−0.00749635
$449$			239830.i			1.18963i	0.803863	+	0.594814i	$0.202774\pi$
$449$			239830.i			1.18963i	−0.803863	+	0.594814i	$0.797226\pi$
$450$	−87175.3	+	188470.i	−0.430495	+	0.930714i
$451$	192823.			0.947994
$452$			280123.i			1.37111i
$453$	6536.10	−	29700.0i	0.0318509	−	0.144731i
$454$	6009.05			0.0291537
$455$			322925.i			1.55984i
$456$	−297018.	−	65364.9i	−1.42841	−	0.314351i
$457$	188974.			0.904837			0.452419	−	0.891806i	$-0.350561\pi$
$457$	188974.			0.904837			0.452419	+	0.891806i	$0.350561\pi$
$458$			62809.1i			0.299428i
$459$	−40098.3	−	30473.6i	−0.190327	−	0.144643i
$460$	575600.			2.72023
$461$			73529.7i			0.345988i	0.984923	+	0.172994i	$0.0553441\pi$
$461$			73529.7i			0.345988i	−0.984923	+	0.172994i	$0.944656\pi$
$462$	24292.3	−	110384.i	0.113811	−	0.517158i
$463$	108786.			0.507471			0.253736	−	0.967274i	$-0.418341\pi$
$463$	108786.			0.507471			0.253736	+	0.967274i	$0.418341\pi$
$464$		−	32053.4i		−	0.148880i
$465$	−24933.9	−	5487.21i	−0.115314	−	0.0253773i
$466$	−30324.2			−0.139643
$467$			267885.i			1.22833i	0.789177	+	0.614165i	$0.210507\pi$
$467$			267885.i			1.22833i	−0.789177	+	0.614165i	$0.789493\pi$
$468$	−164153.	−	75927.8i	−0.749475	−	0.346664i
$469$	209001.			0.950172
$470$			140890.i			0.637799i
$471$	20487.6	−	93095.6i	0.0923526	−	0.419650i
$472$	−23358.8			−0.104850
$473$		−	285013.i		−	1.27392i
$474$	4318.40	+	950.354i	0.0192206	+	0.00422989i
$475$	−938974.			−4.16166
$476$		−	36069.7i		−	0.159195i
$477$	−156223.	+	337747.i	−0.686605	+	1.48441i
$478$	176949.			0.774448
$479$			251819.i			1.09753i	0.835976	+	0.548766i	$0.184902\pi$
$479$			251819.i			1.09753i	−0.835976	+	0.548766i	$0.815098\pi$
$480$	90019.1	−	409046.i	0.390708	−	1.77538i
$481$	41570.5			0.179678
$482$		−	54056.2i		−	0.232676i
$483$	355669.	+	78272.2i	1.52458	+	0.335516i
$484$	−191028.			−0.815465
$485$		−	260565.i		−	1.10773i
$486$	−49528.6	−	93371.4i	−0.209693	−	0.395313i
$487$	−453861.			−1.91366			−0.956830	−	0.290648i	$-0.906129\pi$
$487$	−453861.			−1.91366			−0.956830	+	0.290648i	$0.906129\pi$
$488$		−	202834.i		−	0.851729i
$489$	57660.6	−	262010.i	0.241136	−	1.09572i
$490$	59774.2			0.248955
$491$		−	366635.i		−	1.52080i	−0.649456	−	0.760399i	$-0.725003\pi$
$491$		−	366635.i		−	1.52080i	0.649456	−	0.760399i	$-0.274997\pi$
$492$	126121.	+	27755.5i	0.521022	+	0.114662i
$493$	−19687.8			−0.0810034
$494$			204768.i			0.839089i
$495$	573391.	+	265218.i	2.34013	+	1.08241i
$496$	7034.64			0.0285942
$497$		−	191937.i		−	0.777044i
$498$	16644.0	−	75630.4i	0.0671120	−	0.304956i
$499$	−63482.8			−0.254950			−0.127475	−	0.991842i	$-0.540687\pi$
$499$	−63482.8			−0.254950			−0.127475	+	0.991842i	$0.540687\pi$
$500$		−	468517.i		−	1.87407i
$501$	−273444.	−	60177.0i	−1.08941	−	0.239748i
$502$	−127818.			−0.507205
$503$			51144.9i			0.202147i	0.994879	+	0.101073i	$0.0322277\pi$
$503$			51144.9i			0.202147i	−0.994879	+	0.101073i	$0.967772\pi$
$504$	71512.7	−	154608.i	0.281528	−	0.608654i
$505$	578737.			2.26934
$506$			305254.i			1.19223i
$507$	−3651.83	+	16593.9i	−0.0142068	+	0.0645554i
$508$	−175172.			−0.678793
$509$			106497.i			0.411055i	0.978651	+	0.205528i	$0.0658910\pi$
$509$			106497.i			0.411055i	−0.978651	+	0.205528i	$0.934109\pi$
$510$	−49299.9	−	10849.5i	−0.189542	−	0.0417126i
$511$	322988.			1.23693
$512$			208165.i			0.794086i
$513$	289181.	−	380515.i	1.09884	−	1.44590i
$514$	189488.			0.717223
$515$			460369.i			1.73577i
$516$	41025.6	−	186420.i	0.154083	−	0.700154i
$517$	298415.			1.11645
$518$			17398.5i			0.0648414i
$519$	−246216.	−	54184.9i	−0.914075	−	0.201161i
$520$	−407945.			−1.50867
$521$		−	240526.i		−	0.886109i	−0.896495	−	0.443054i	$-0.853895\pi$
$521$		−	240526.i		−	0.886109i	0.896495	−	0.443054i	$-0.146105\pi$
$522$	−37499.9	−	17345.3i	−0.137623	−	0.0636563i
$523$	73388.2			0.268301			0.134151	−	0.990961i	$-0.457169\pi$
$523$	73388.2			0.268301			0.134151	+	0.990961i	$0.457169\pi$
$524$		−	303283.i		−	1.10455i
$525$	113038.	−	513644.i	0.410115	−	1.86356i
$526$	−45010.6			−0.162684
$527$		−	4320.81i		−	0.0155577i
$528$	−170005.	−	37413.2i	−0.609810	−	0.134201i
$529$	−703717.			−2.51470
$530$			372982.i			1.32781i
$531$	15410.4	−	33316.8i	0.0546545	−	0.118161i
$532$	342285.			1.20938
$533$		−	195669.i		−	0.688759i
$534$	−17318.1	+	78693.3i	−0.0607320	+	0.275966i
$535$	−481616.			−1.68265
$536$			264027.i			0.919005i
$537$	82613.2	+	18180.7i	0.286484	+	0.0630468i
$538$	−52850.4			−0.182593
$539$		−	126606.i		−	0.435789i
$540$	336865.	+	256008.i	1.15523	+	0.877942i
$541$	403303.			1.37796			0.688981	−	0.724779i	$-0.258058\pi$
$541$	403303.			1.37796			0.688981	+	0.724779i	$0.258058\pi$
$542$		−	209179.i		−	0.712065i
$543$	20764.9	−	94355.5i	0.0704255	−	0.320013i
$544$	70884.0			0.239525
$545$			146594.i			0.493540i
$546$	−112014.	−	24650.9i	−0.375738	−	0.0826889i
$547$	−151591.			−0.506639			−0.253319	−	0.967383i	$-0.581522\pi$
$547$	−151591.			−0.506639			−0.253319	+	0.967383i	$0.581522\pi$
$548$			59519.7i			0.198198i
$549$	289303.	+	133815.i	0.959862	+	0.443977i
$550$	440837.			1.45731
$551$		−	186828.i		−	0.615375i
$552$	−98879.8	+	449309.i	−0.324511	+	1.47458i
$553$	−11199.1			−0.0366213
$554$		−	13656.6i		−	0.0444963i
$555$	−94976.3	−	20901.5i	−0.308340	−	0.0678565i
$556$	131287.			0.424690
$557$			314210.i			1.01277i	0.862308	+	0.506384i	$0.169018\pi$
$557$			314210.i			1.01277i	−0.862308	+	0.506384i	$0.830982\pi$
$558$	3806.72	−	8229.98i	0.0122259	−	0.0264320i
$559$	−289220.			−0.925560
$560$			208153.i			0.663754i
$561$	−22979.9	+	104421.i	−0.0730168	+	0.331788i
$562$	−18397.1			−0.0582474
$563$			259495.i			0.818677i	0.912383	+	0.409338i	$0.134240\pi$
$563$			259495.i			0.818677i	−0.912383	+	0.409338i	$0.865760\pi$
$564$	195186.	+	42954.6i	0.613606	+	0.135037i
$565$	−992918.			−3.11040
$566$		−	247274.i		−	0.771872i
$567$	173339.	+	203998.i	0.539176	+	0.634541i
$568$	242470.			0.751556
$569$		−	143266.i		−	0.442507i	−0.975216	−	0.221253i	$-0.928985\pi$
$569$		−	143266.i		−	0.442507i	0.975216	−	0.221253i	$-0.0710148\pi$
$570$	102956.	−	467834.i	0.316887	−	1.43993i
$571$	−45505.3			−0.139569			−0.0697846	−	0.997562i	$-0.522231\pi$
$571$	−45505.3			−0.139569			−0.0697846	+	0.997562i	$0.522231\pi$
$572$			383960.i			1.17353i
$573$	114895.	+	25285.1i	0.349939	+	0.0770114i
$574$	81893.3			0.248556
$575$			1.42042e6i			4.29617i
$576$	2710.93	+	1253.92i	0.00817097	+	0.00377942i
$577$	113688.			0.341478			0.170739	−	0.985316i	$-0.445385\pi$
$577$	113688.			0.341478			0.170739	+	0.985316i	$0.445385\pi$
$578$			140955.i			0.421914i
$579$	52085.9	−	236678.i	0.155369	−	0.705994i
$580$	165397.			0.491667
$581$			196136.i			0.581039i
$582$	90382.6	+	19890.6i	0.266833	+	0.0587220i
$583$	790003.			2.32430
$584$			408024.i			1.19636i
$585$	269132.	−	581854.i	0.786419	−	1.70021i
$586$	−123287.			−0.359023
$587$			113685.i			0.329934i	0.986299	+	0.164967i	$0.0527517\pi$
$587$			113685.i			0.329934i	−0.986299	+	0.164967i	$0.947248\pi$
$588$	18224.0	−	82809.8i	0.0527096	−	0.239512i
$589$	41002.6			0.118190
$590$		−	36792.6i		−	0.105695i
$591$	145941.	+	32117.4i	0.417834	+	0.0919530i
$592$	26795.8			0.0764582
$593$			383559.i			1.09074i	0.838194	+	0.545372i	$0.183612\pi$
$593$			383559.i			1.09074i	−0.838194	+	0.545372i	$0.816388\pi$
$594$	−135767.	+	178647.i	−0.384788	+	0.506318i
$595$	127852.			0.361138
$596$			125145.i			0.352306i
$597$	136943.	−	622268.i	0.384230	−	1.74594i
$598$	309760.			0.866209
$599$		−	416756.i		−	1.16152i	−0.814073	−	0.580762i	$-0.802755\pi$
$599$		−	416756.i		−	1.16152i	0.814073	−	0.580762i	$-0.197245\pi$
$600$	648877.	+	142799.i	1.80244	+	0.396663i
$601$	−267977.			−0.741906			−0.370953	−	0.928652i	$-0.620969\pi$
$601$	−267977.			−0.741906			−0.370953	+	0.928652i	$0.620969\pi$
$602$		−	121047.i		−	0.334012i
$603$	−376582.	−	174185.i	−1.03568	−	0.479046i
$604$	−43237.6			−0.118519
$605$		−	677113.i		−	1.84991i
$606$	−44178.7	+	200748.i	−0.120300	+	0.546645i
$607$	44388.9			0.120475			0.0602375	−	0.998184i	$-0.480814\pi$
$607$	44388.9			0.120475			0.0602375	+	0.998184i	$0.480814\pi$
$608$			672658.i			1.81965i
$609$	102200.	+	22491.3i	0.275561	+	0.0606428i
$610$	319485.			0.858599
$611$		−	302819.i		−	0.811149i
$612$	−30061.2	+	64991.2i	−0.0802608	+	0.173521i
$613$	645348.			1.71741			0.858704	−	0.512472i	$-0.171270\pi$
$613$	645348.			1.71741			0.858704	+	0.512472i	$0.171270\pi$
$614$			219846.i			0.583151i
$615$	−98381.6	+	447045.i	−0.260114	+	1.18196i
$616$	−361633.			−0.953031
$617$		−	8629.84i		−	0.0226690i	−0.999936	−	0.0113345i	$-0.996392\pi$
$617$		−	8629.84i		−	0.0226690i	0.999936	−	0.0113345i	$-0.00360796\pi$
$618$	−159689.	−	35142.9i	−0.418117	−	0.0920153i
$619$	−56618.8			−0.147768			−0.0738839	−	0.997267i	$-0.523539\pi$
$619$	−56618.8			−0.147768			−0.0738839	+	0.997267i	$0.523539\pi$
$620$			36299.0i			0.0944303i
$621$	−575619.	−	437454.i	−1.49263	−	1.13436i
$622$	−33591.5			−0.0868257
$623$		−	204079.i		−	0.525803i
$624$	−37965.4	+	172515.i	−0.0975032	+	0.443054i
$625$	765544.			1.95979
$626$			235630.i			0.601286i
$627$	−990905.	−	218069.i	−2.52056	−	0.554701i
$628$	−135530.			−0.343649
$629$		−	16458.5i		−	0.0415997i
$630$	243523.	+	112640.i	0.613563	+	0.283799i
$631$	316683.			0.795364			0.397682	−	0.917523i	$-0.369815\pi$
$631$	316683.			0.795364			0.397682	+	0.917523i	$0.369815\pi$
$632$		−	14147.6i		−	0.0354201i
$633$	5301.30	−	24089.1i	0.0132305	−	0.0601191i
$634$	−113776.			−0.283055
$635$		−	620911.i		−	1.53986i
$636$	516722.	+	113715.i	1.27745	+	0.281128i
$637$	−128475.			−0.316620
$638$			87713.8i			0.215490i
$639$	−159964.	+	345836.i	−0.391761	+	0.846972i
$640$	−741601.			−1.81055
$641$		−	393620.i		−	0.957990i	−0.877818	−	0.478995i	$-0.841001\pi$
$641$		−	393620.i		−	0.957990i	0.877818	−	0.478995i	$-0.158999\pi$
$642$	36764.8	−	167059.i	0.0891993	−	0.405321i
$643$	560933.			1.35672			0.678359	−	0.734731i	$-0.262692\pi$
$643$	560933.			1.35672			0.678359	+	0.734731i	$0.262692\pi$
$644$		−	517787.i		−	1.24847i
$645$	660781.	+	145419.i	1.58832	+	0.349543i
$646$	81071.3			0.194268
$647$		−	735617.i		−	1.75729i	−0.477477	−	0.878644i	$-0.658449\pi$
$647$		−	735617.i		−	1.75729i	0.477477	−	0.878644i	$-0.341551\pi$
$648$	−257707.	+	218976.i	−0.613727	+	0.521490i
$649$	−77929.3			−0.185017
$650$		−	447344.i		−	1.05880i
$651$	−4936.08	+	22429.5i	−0.0116472	+	0.0529246i
$652$	−381437.			−0.897278
$653$		−	445122.i		−	1.04389i	−0.852980	−	0.521943i	$-0.825207\pi$
$653$		−	445122.i		−	1.04389i	0.852980	−	0.521943i	$-0.174793\pi$
$654$	−50849.2	−	11190.4i	−0.118885	−	0.0261632i
$655$	1.07501e6			2.50571
$656$		−	126126.i		−	0.293087i
$657$	−581967.	−	269185.i	−1.34824	−	0.623619i
$658$	126739.			0.292724
$659$		−	428301.i		−	0.986230i	−0.869964	−	0.493115i	$-0.835858\pi$
$659$		−	428301.i		−	0.986230i	0.869964	−	0.493115i	$-0.164142\pi$
$660$	193054.	−	877235.i	0.443190	−	2.01385i
$661$	342234.			0.783287			0.391643	−	0.920117i	$-0.371907\pi$
$661$	342234.			0.783287			0.391643	+	0.920117i	$0.371907\pi$
$662$		−	157324.i		−	0.358987i
$663$	105962.	+	23319.1i	0.241058	+	0.0530499i
$664$	−247775.			−0.561981
$665$			1.21326e6i			2.74353i
$666$	14500.3	−	31349.1i	0.0326910	−	0.0706767i
$667$	−282622.			−0.635264
$668$			398083.i			0.892115i
$669$	39745.6	−	180604.i	0.0888049	−	0.403529i
$670$	−415869.			−0.926418
$671$		−	676692.i		−	1.50295i
$672$	−367962.	−	80977.6i	−0.814825	−	0.179319i
$673$	498087.			1.09970			0.549852	−	0.835262i	$-0.314684\pi$
$673$	498087.			1.09970			0.549852	+	0.835262i	$0.314684\pi$
$674$			272889.i			0.600712i
$675$	−631756.	+	831288.i	−1.38657	+	1.82450i
$676$	24157.6			0.0528640
$677$		−	84308.8i		−	0.183948i	−0.995761	−	0.0919741i	$-0.970682\pi$
$677$		−	84308.8i		−	0.183948i	0.995761	−	0.0919741i	$-0.0293177\pi$
$678$	75795.7	−	344415.i	0.164887	−	0.749244i
$679$	−234394.			−0.508402
$680$			161513.i			0.349292i
$681$	29508.0	+	6493.84i	0.0636276	+	0.0140026i
$682$	−19250.2			−0.0413873
$683$			458027.i			0.981860i	0.871199	+	0.490930i	$0.163343\pi$
$683$			458027.i			0.981860i	−0.871199	+	0.490930i	$0.836657\pi$
$684$	−616737.	−	285267.i	−1.31822	−	0.609733i
$685$	−210973.			−0.449619
$686$		−	229120.i		−	0.486872i
$687$	−67876.3	+	308430.i	−0.143815	+	0.653496i
$688$	−186427.			−0.393852
$689$		−	801663.i		−	1.68870i
$690$	−707709.	−	155746.i	−1.48647	−	0.327129i
$691$	486757.			1.01943			0.509714	−	0.860344i	$-0.329751\pi$
$691$	486757.			1.01943			0.509714	+	0.860344i	$0.329751\pi$
$692$			358444.i			0.748530i
$693$	238579.	−	515800.i	0.496783	−	1.07403i
$694$	−112446.			−0.233467
$695$			465357.i			0.963422i
$696$	−28412.8	+	129108.i	−0.0586537	+	0.266522i
$697$	−77468.9			−0.159464
$698$		−	59121.5i		−	0.121349i
$699$	−148910.	−	32770.7i	−0.304768	−	0.0670704i
$700$	−747769.			−1.52606
$701$			507900.i			1.03357i	0.856114	+	0.516787i	$0.172872\pi$
$701$			507900.i			1.03357i	−0.856114	+	0.516787i	$0.827128\pi$
$702$	181284.	+	137771.i	0.367862	+	0.279565i
$703$	156184.			0.316028
$704$		−	6340.97i		−	0.0127941i
$705$	−152256.	+	691852.i	−0.306335	+	1.39199i
$706$	231219.			0.463889
$707$		−	520609.i		−	1.04153i
$708$	−50971.6	−	11217.4i	−0.101686	−	0.0223781i
$709$	−37670.8			−0.0749397			−0.0374698	−	0.999298i	$-0.511930\pi$
$709$	−37670.8			−0.0749397			−0.0374698	+	0.999298i	$0.511930\pi$
$710$			381916.i			0.757619i
$711$	20178.9	+	9333.59i	0.0399170	+	0.0184633i
$712$	257809.			0.508556
$713$		−	62026.0i		−	0.122010i
$714$	−9759.74	+	44348.2i	−0.0191444	+	0.0869920i
$715$	−1.36098e6			−2.66219
$716$		−	120269.i		−	0.234600i
$717$	868924.	+	191225.i	1.69022	+	0.371968i
$718$	−112859.			−0.218921
$719$		−	402267.i		−	0.778138i	−0.921209	−	0.389069i	$-0.872797\pi$
$719$		−	402267.i		−	0.778138i	0.921209	−	0.389069i	$-0.127203\pi$
$720$	173479.	−	375056.i	0.334644	−	0.723487i
$721$	414130.			0.796647
$722$			536063.i			1.02835i
$723$	58417.3	−	265448.i	0.111754	−	0.507812i
$724$	−137364.			−0.262057
$725$			408153.i			0.776510i
$726$	234871.	+	51688.3i	0.445612	+	0.0980661i
$727$	−121439.			−0.229767			−0.114883	−	0.993379i	$-0.536649\pi$
$727$	−121439.			−0.229767			−0.114883	+	0.993379i	$0.536649\pi$
$728$			366971.i			0.692419i
$729$	−142310.	−	512033.i	−0.267782	−	0.963480i
$730$	−642680.			−1.20601
$731$			114507.i			0.214288i
$732$	97404.9	−	442607.i	0.181785	−	0.826031i
$733$	−538270.			−1.00183			−0.500913	−	0.865498i	$-0.667002\pi$
$733$	−538270.			−1.00183			−0.500913	+	0.865498i	$0.667002\pi$
$734$		−	261713.i		−	0.485773i
$735$	293526.	+	64596.5i	0.543341	+	0.119573i
$736$	1.01755e6			1.87846
$737$			880840.i			1.62167i
$738$	−147557.	−	68251.6i	−0.270924	−	0.125314i
$739$	645517.			1.18200			0.591001	−	0.806671i	$-0.298733\pi$
$739$	645517.			1.18200			0.591001	+	0.806671i	$0.298733\pi$
$740$			138268.i			0.252498i
$741$	−221288.	+	1.00553e6i	−0.403015	+	1.83130i
$742$	335520.			0.609412
$743$			873177.i			1.58170i	0.612009	+	0.790851i	$0.290362\pi$
$743$			873177.i			1.58170i	−0.612009	+	0.790851i	$0.709638\pi$
$744$	−28334.8	−	6235.65i	−0.0511887	−	0.0112651i
$745$	−443586.			−0.799218
$746$		−	82926.0i		−	0.149009i
$747$	163464.	−	353403.i	0.292941	−	0.633328i
$748$	152017.			0.271699
$749$			433242.i			0.772267i
$750$	−126771.	+	576048.i	−0.225371	+	1.02409i
$751$	473294.			0.839172			0.419586	−	0.907716i	$-0.362175\pi$
$751$	473294.			0.839172			0.419586	+	0.907716i	$0.362175\pi$
$752$		−	195193.i		−	0.345167i
$753$	−627660.	−	138130.i	−1.10697	−	0.243611i
$754$	89008.4			0.156563
$755$		−	153259.i		−	0.268864i
$756$	230295.	−	303030.i	0.402940	−	0.530203i
$757$	−837058.			−1.46071			−0.730355	−	0.683068i	$-0.760645\pi$
$757$	−837058.			−1.46071			−0.730355	+	0.683068i	$0.760645\pi$
$758$		−	442851.i		−	0.770760i
$759$	−329881.	+	1.49898e6i	−0.572629	+	2.60203i
$760$	−1.53268e6			−2.65354
$761$			199518.i			0.344518i	0.985052	+	0.172259i	$0.0551067\pi$
$761$			199518.i			0.344518i	−0.985052	+	0.172259i	$0.944893\pi$
$762$	215377.	+	47398.1i	0.370927	+	0.0816302i
$763$	131870.			0.226515
$764$		−	167266.i		−	0.286563i
$765$	−230366.	−	106554.i	−0.393637	−	0.182074i
$766$	218052.			0.371623
$767$			79079.5i			0.134423i
$768$	57752.3	−	262426.i	0.0979145	−	0.444923i
$769$	291527.			0.492977			0.246488	−	0.969146i	$-0.420723\pi$
$769$	291527.			0.492977			0.246488	+	0.969146i	$0.420723\pi$
$770$		−	569610.i		−	0.960719i
$771$	930495.	+	204775.i	1.56533	+	0.344483i
$772$	−344559.			−0.578134
$773$		−	978430.i		−	1.63746i	−0.574179	−	0.818730i	$-0.694679\pi$
$773$		−	978430.i		−	1.63746i	0.574179	−	0.818730i	$-0.305321\pi$
$774$	−100883.	+	218106.i	−0.168398	+	0.364070i
$775$	−89575.8			−0.149138
$776$		−	296105.i		−	0.491726i
$777$	−18802.2	+	85436.9i	−0.0311434	+	0.141515i
$778$	78027.8			0.128911
$779$		−	735145.i		−	1.21143i
$780$	−890182.	−	195903.i	−1.46315	−	0.321997i
$781$	808924.			1.32619
$782$		−	122639.i		−	0.200547i
$783$	−165402.	−	125701.i	−0.269785	−	0.205029i
$784$	−82813.1			−0.134731
$785$		−	480396.i		−	0.779579i
$786$	−82062.5	+	372891.i	−0.132831	+	0.603584i
$787$	−284731.			−0.459711			−0.229856	−	0.973225i	$-0.573825\pi$
$787$	−284731.			−0.459711			−0.229856	+	0.973225i	$0.573825\pi$
$788$		−	212463.i		−	0.342162i
$789$	−221029.	−	48641.9i	−0.355054	−	0.0781370i
$790$	22284.0			0.0357058
$791$			893190.i			1.42755i
$792$	651600.	+	301393.i	1.03880	+	0.480488i
$793$	−686679.			−1.09196
$794$		−	150933.i		−	0.239410i
$795$	−403073.	+	1.83156e6i	−0.637749	+	2.89793i
$796$	−905905.			−1.42974
$797$			881852.i			1.38829i	0.719837	+	0.694143i	$0.244216\pi$
$797$			881852.i			1.38829i	−0.719837	+	0.694143i	$0.755784\pi$
$798$	−420845.	−	92615.5i	−0.660870	−	0.145438i
$799$	−119892.			−0.187800
$800$		−	1.46951e6i		−	2.29612i
$801$	−170084.	+	367715.i	−0.265093	+	0.573121i
$802$	−9414.32			−0.0146366
$803$			1.36124e6i			2.11108i
$804$	−126791.	+	576136.i	−0.196144	+	0.891277i
$805$	1.83534e6			2.83220
$806$			19534.4i			0.0300697i
$807$	−259526.	−	57114.2i	−0.398506	−	0.0876994i
$808$	657675.			1.00737
$809$			501045.i			0.765561i	0.923839	+	0.382781i	$0.125034\pi$
$809$			501045.i			0.765561i	−0.923839	+	0.382781i	$0.874966\pi$
$810$	−344910.	−	405915.i	−0.525697	−	0.618678i
$811$	−634000.			−0.963935			−0.481968	−	0.876189i	$-0.660078\pi$
$811$	−634000.			−0.963935			−0.481968	+	0.876189i	$0.660078\pi$
$812$		−	148784.i		−	0.225655i
$813$	226055.	−	1.02719e6i	0.342005	−	1.55407i
$814$	−73326.6			−0.110666
$815$		−	1.35203e6i		−	2.03550i
$816$	68301.6	+	15031.2i	0.102577	+	0.0225742i
$817$	−1.08662e6			−1.62793
$818$		−	97140.3i		−	0.145175i
$819$	−523413.	−	242101.i	−0.780327	−	0.360934i
$820$	650814.			0.967897
$821$		−	560596.i		−	0.831694i	−0.909435	−	0.415847i	$-0.863485\pi$
$821$		−	560596.i		−	0.831694i	0.909435	−	0.415847i	$-0.136515\pi$
$822$	16104.9	−	73180.4i	0.0238349	−	0.108306i
$823$	−260955.			−0.385270			−0.192635	−	0.981270i	$-0.561703\pi$
$823$	−260955.			−0.385270			−0.192635	+	0.981270i	$0.561703\pi$
$824$			523162.i			0.770516i
$825$	2.16477e6	+	476403.i	3.18056	+	0.699949i
$826$	−33097.1			−0.0485099
$827$			740.688i			0.00108299i	1.00000		0.000541495i	$0.000172363\pi$
$827$			740.688i			0.00108299i	−1.00000		0.000541495i	$0.999828\pi$
$828$	−431534.	+	932960.i	−0.629440	+	1.36083i
$829$	87825.2			0.127794			0.0638969	−	0.997957i	$-0.479647\pi$
$829$	87825.2			0.127794			0.0638969	+	0.997957i	$0.479647\pi$
$830$		−	390271.i		−	0.566514i
$831$	14758.4	−	67062.1i	0.0213716	−	0.0971125i
$832$	−6434.56			−0.00929549
$833$			50865.4i			0.0733049i
$834$	−161419.	−	35523.6i	−0.232072	−	0.0510723i
$835$	−1.41104e6			−2.02379
$836$			1.44257e6i			2.06407i
$837$	27587.2	−	36300.2i	0.0393782	−	0.0518153i
$838$	−132354.			−0.188473
$839$			990377.i			1.40694i	0.710723	+	0.703471i	$0.248368\pi$
$839$			990377.i			1.40694i	−0.710723	+	0.703471i	$0.751632\pi$
$840$	184512.	−	838420.i	0.261496	−	1.18824i
$841$	626070.			0.885179
$842$			162752.i			0.229564i
$843$	−90340.5	−	19881.3i	−0.127124	−	0.0279763i
$844$	−35069.2			−0.0492312
$845$			85628.6i			0.119924i
$846$	−228361.	−	105627.i	−0.319067	−	0.147582i
$847$	−609104.			−0.849033
$848$		−	516742.i		−	0.718592i
$849$	267223.	−	1.21426e6i	0.370731	−	1.68460i
$850$	−177112.			−0.245137
$851$		−	236265.i		−	0.326243i
$852$	529098.	+	116439.i	0.728881	+	0.160405i
$853$	1.40272e6			1.92784			0.963922	−	0.266186i	$-0.0857637\pi$
$853$	1.40272e6			1.92784			0.963922	+	0.266186i	$0.0857637\pi$
$854$		−	287396.i		−	0.394062i
$855$	1.01115e6	−	2.18608e6i	1.38320	−	2.99042i
$856$	−547307.			−0.746936
$857$			164407.i			0.223851i	0.993717	+	0.111925i	$0.0357018\pi$
$857$			164407.i			0.223851i	−0.993717	+	0.111925i	$0.964298\pi$
$858$	103892.	−	472085.i	0.141126	−	0.641277i
$859$	−572775.			−0.776242			−0.388121	−	0.921608i	$-0.626876\pi$
$859$	−572775.			−0.776242			−0.388121	+	0.921608i	$0.626876\pi$
$860$		−	961973.i		−	1.30067i
$861$	402144.	+	88500.2i	0.542470	+	0.119382i
$862$	199860.			0.268974
$863$		−	944594.i		−	1.26830i	−0.773208	−	0.634152i	$-0.781349\pi$
$863$		−	944594.i		−	1.26830i	0.773208	−	0.634152i	$-0.218651\pi$
$864$	595514.	+	452574.i	0.797746	+	0.606265i
$865$	−1.27054e6			−1.69807
$866$		−	122598.i		−	0.163473i
$867$	−152326.	+	692170.i	−0.202645	+	0.920819i
$868$	32653.1			0.0433397
$869$		−	47199.1i		−	0.0625021i
$870$	−203358.	−	44753.1i	−0.268672	−	0.0591268i
$871$	893841.			1.17821
$872$			166589.i			0.219085i
$873$	422337.	+	195349.i	0.554154	+	0.256320i
$874$	1.16379e6			1.52354
$875$		−	1.49390e6i		−	1.95121i
$876$	−195941.	+	890355.i	−0.255339	+	1.16026i
$877$	1.52879e6			1.98768			0.993842	−	0.110803i	$-0.0353423\pi$
$877$	1.52879e6			1.98768			0.993842	+	0.110803i	$0.0353423\pi$
$878$		−	626615.i		−	0.812852i
$879$	−605412.	−	133234.i	−0.783562	−	0.172439i
$880$	−877269.			−1.13284
$881$			142497.i			0.183592i	0.995778	+	0.0917960i	$0.0292608\pi$
$881$			142497.i			0.183592i	−0.995778	+	0.0917960i	$0.970739\pi$
$882$	−44813.4	+	96884.9i	−0.0576064	+	0.124543i
$883$	502457.			0.644432			0.322216	−	0.946666i	$-0.395572\pi$
$883$	502457.			0.644432			0.322216	+	0.946666i	$0.395572\pi$
$884$		−	154260.i		−	0.197401i
$885$	39760.8	−	180673.i	0.0507655	−	0.230678i
$886$	−145886.			−0.185844
$887$			170765.i			0.217045i	0.994094	+	0.108523i	$0.0346120\pi$
$887$			170765.i			0.217045i	−0.994094	+	0.108523i	$0.965388\pi$
$888$	−107931.	−	23752.4i	−0.136874	−	0.0301219i
$889$	−558547.			−0.706735
$890$			406077.i			0.512658i
$891$	−859756.	+	730543.i	−1.08298	+	0.920217i
$892$	−262925.			−0.330448
$893$		−	1.13772e6i		−	1.42670i
$894$	33861.7	−	153867.i	0.0423676	−	0.192518i
$895$	426304.			0.532198
$896$			667115.i			0.830969i
$897$	1.52110e6	+	334750.i	1.89049	+	0.416040i
$898$	−429282.			−0.532341
$899$		−	17823.0i		−	0.0220527i
$900$	1.34735e6	+	623206.i	1.66339	+	0.769391i
$901$	−317393.			−0.390974
$902$			345142.i			0.424214i
$903$	130813.	−	594413.i	0.160426	−	0.728975i
$904$	−1.12835e6			−1.38072
$905$		−	486897.i		−	0.594484i
$906$	53161.3	+	11699.2i	0.0647648	+	0.0142528i
$907$	968039.			1.17673			0.588367	−	0.808594i	$-0.299771\pi$
$907$	968039.			1.17673			0.588367	+	0.808594i	$0.299771\pi$
$908$		−	42958.1i		−	0.0521042i
$909$	−433886.	+	938046.i	−0.525107	+	1.13526i
$910$	−578017.			−0.698004
$911$		−	147929.i		−	0.178245i	−0.996021	−	0.0891224i	$-0.971594\pi$
$911$		−	147929.i		−	0.178245i	0.996021	−	0.0891224i	$-0.0284062\pi$
$912$	−142639.	+	648152.i	−0.171494	+	0.779269i
$913$	−826623.			−0.991667
$914$			338253.i			0.404902i
$915$	1.56886e6	+	345260.i	1.87388	+	0.412386i
$916$	449016.			0.535144
$917$		−	967039.i		−	1.15002i
$918$	54546.0	−	71773.7i	0.0647258	−	0.0851686i
$919$	−455817.			−0.539709			−0.269855	−	0.962901i	$-0.586976\pi$
$919$	−455817.			−0.539709			−0.269855	+	0.962901i	$0.586976\pi$
$920$			2.31855e6i			2.73930i
$921$	−237582.	+	1.07957e6i	−0.280088	+	1.27272i
$922$	−131614.			−0.154825
$923$		−	820864.i		−	0.963535i
$924$	−789125.	−	173663.i	−0.924277	−	0.203406i
$925$	−341206.			−0.398780
$926$			194721.i			0.227086i
$927$	−746189.	−	345144.i	−0.868339	−	0.401644i
$928$	292391.			0.339522
$929$			785053.i			0.909636i	0.890584	+	0.454818i	$0.150296\pi$
$929$			785053.i			0.909636i	−0.890584	+	0.454818i	$0.849704\pi$
$930$	9821.79	−	44630.2i	0.0113560	−	0.0516016i
$931$	−482690.			−0.556890
$932$			216785.i			0.249572i
$933$	−164954.	−	36301.5i	−0.189496	−	0.0417024i
$934$	−479500.			−0.549660
$935$			538836.i			0.616358i
$936$	305841.	−	661217.i	0.349095	−	0.754731i
$937$	670849.			0.764092			0.382046	−	0.924143i	$-0.375220\pi$
$937$	670849.			0.764092			0.382046	+	0.924143i	$0.375220\pi$
$938$			374099.i			0.425188i
$939$	−254639.	+	1.15708e6i	−0.288798	+	1.31230i
$940$	1.00721e6			1.13989
$941$		−	319594.i		−	0.360927i	−0.983582	−	0.180463i	$-0.942240\pi$
$941$		−	319594.i		−	0.360927i	0.983582	−	0.180463i	$-0.0577597\pi$
$942$	166636.	+	36671.6i	0.187787	+	0.0413265i
$943$	−1.11208e6			−1.25058
$944$			50973.6i			0.0572007i
$945$	1.07411e6	+	816298.i	1.20278	+	0.914082i
$946$	510157.			0.570062
$947$			1.31880e6i			1.47055i	0.677771	+	0.735273i	$0.262946\pi$
$947$			1.31880e6i			1.47055i	−0.677771	+	0.735273i	$0.737054\pi$
$948$	6793.97	−	30871.8i	0.00755975	−	0.0343514i
$949$	1.38133e6			1.53379
$950$		−	1.68071e6i		−	1.86228i
$951$	−558705.	−	122954.i	−0.617762	−	0.135951i
$952$	145290.			0.160311
$953$			1.05540e6i			1.16207i	0.813878	+	0.581036i	$0.197353\pi$
$953$			1.05540e6i			1.16207i	−0.813878	+	0.581036i	$0.802647\pi$
$954$	−604548.	−	279629.i	−0.664254	−	0.307246i
$955$	592887.			0.650078
$956$		−	1.26499e6i		−	1.38411i
$957$	−94790.2	+	430726.i	−0.103500	+	0.470303i
$958$	−450741.			−0.491130
$959$			189783.i			0.206357i
$960$	14701.1	+	3235.27i	0.0159517	+	0.00351049i
$961$	−919609.			−0.995765
$962$			74408.9i			0.0804034i
$963$	361073.	−	780626.i	0.389352	−	0.841764i
$964$	−386442.			−0.415844
$965$		−	1.22132e6i		−	1.31152i
$966$	−140103.	+	636627.i	−0.150139	+	0.682230i
$967$	1.40376e6			1.50121			0.750603	−	0.660753i	$-0.229763\pi$
$967$	1.40376e6			1.50121			0.750603	+	0.660753i	$0.229763\pi$
$968$		−	769469.i		−	0.821184i
$969$	398108.	+	87611.8i	0.423987	+	0.0933072i
$970$	466396.			0.495692
$971$		−	706684.i		−	0.749527i	−0.927121	−	0.374763i	$-0.877724\pi$
$971$		−	706684.i		−	0.749527i	0.927121	−	0.374763i	$-0.122276\pi$
$972$	−667502.	+	354074.i	−0.706512	+	0.374768i
$973$	418617.			0.442172
$974$		−	812385.i		−	0.856336i
$975$	483434.	−	2.19672e6i	0.508543	−	2.31082i
$976$	−442625.			−0.464661
$977$			840725.i			0.880775i	0.897808	+	0.440388i	$0.145159\pi$
$977$			840725.i			0.880775i	−0.897808	+	0.440388i	$0.854841\pi$
$978$	468982.	+	103209.i	0.490319	+	0.107905i
$979$	860099.			0.897394
$980$		−	427319.i		−	0.444939i
$981$	−237606.	−	109903.i	−0.246899	−	0.114202i
$982$	656257.			0.680535
$983$			1.02979e6i			1.06571i	0.846206	+	0.532856i	$0.178881\pi$
$983$			1.02979e6i			1.06571i	−0.846206	+	0.532856i	$0.821119\pi$
$984$	−111801.	+	508021.i	−0.115466	+	0.524676i
$985$	753093.			0.776205
$986$		−	35240.0i		−	0.0362479i
$987$	622362.	+	136964.i	0.638865	+	0.140595i
$988$	1.46386e6			1.49964
$989$			1.64377e6i			1.68054i
$990$	−474725.	+	1.02634e6i	−0.484363	+	1.04718i
$991$	497291.			0.506365			0.253182	−	0.967419i	$-0.418523\pi$
$991$	497291.			0.506365			0.253182	+	0.967419i	$0.418523\pi$
$992$			64169.9i			0.0652091i
$993$	170016.	−	772553.i	0.172422	−	0.783483i
$994$	343556.			0.347716
$995$		−	3.21106e6i		−	3.24341i
$996$	−540674.	−	118986.i	−0.545025	−	0.119944i
$997$	−400346.			−0.402759			−0.201380	−	0.979513i	$-0.564542\pi$
$997$	−400346.			−0.402759			−0.201380	+	0.979513i	$0.564542\pi$
$998$		−	113631.i		−	0.114086i
$999$	105083.	−	138272.i	0.105294	−	0.138549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.48	yes	78
3.2	odd	2	inner	177.5.b.a.119.31	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.31	✓	78	3.2	odd	2	inner
177.5.b.a.119.48	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)

\(f(q)\)	\(=\)	\(q+1.78994i q^{2} +(-1.93435 + 8.78967i) q^{3} +12.7961 q^{4} +45.3568i q^{5} +(-15.7330 - 3.46237i) q^{6} +40.8012 q^{7} +51.5434i q^{8} +(-73.5166 - 34.0046i) q^{9} +O(q^{10})\)	\(q+1.78994i q^{2} +(-1.93435 + 8.78967i) q^{3} +12.7961 q^{4} +45.3568i q^{5} +(-15.7330 - 3.46237i) q^{6} +40.8012 q^{7} +51.5434i q^{8} +(-73.5166 - 34.0046i) q^{9} -81.1862 q^{10} +171.958i q^{11} +(-24.7521 + 112.474i) q^{12} +174.496 q^{13} +73.0318i q^{14} +(-398.672 - 87.7359i) q^{15} +112.478 q^{16} -69.0862i q^{17} +(60.8662 - 131.590i) q^{18} +655.597 q^{19} +580.391i q^{20} +(-78.9238 + 358.629i) q^{21} -307.795 q^{22} -991.745i q^{23} +(-453.049 - 99.7029i) q^{24} -1432.24 q^{25} +312.338i q^{26} +(441.096 - 580.410i) q^{27} +522.097 q^{28} -284.975i q^{29} +(157.042 - 713.599i) q^{30} +62.5423 q^{31} +1026.02i q^{32} +(-1511.45 - 332.627i) q^{33} +123.660 q^{34} +1850.61i q^{35} +(-940.726 - 435.126i) q^{36} +238.232 q^{37} +1173.48i q^{38} +(-337.536 + 1533.76i) q^{39} -2337.84 q^{40} -1121.34i q^{41} +(-641.926 - 141.269i) q^{42} -1657.46 q^{43} +2200.39i q^{44} +(1542.34 - 3334.48i) q^{45} +1775.17 q^{46} -1735.39i q^{47} +(-217.572 + 988.644i) q^{48} -736.261 q^{49} -2563.63i q^{50} +(607.245 + 133.637i) q^{51} +2232.87 q^{52} -4594.16i q^{53} +(1038.90 + 789.536i) q^{54} -7799.47 q^{55} +2103.03i q^{56} +(-1268.15 + 5762.48i) q^{57} +510.088 q^{58} +453.188i q^{59} +(-5101.44 - 1122.68i) q^{60} -3935.21 q^{61} +111.947i q^{62} +(-2999.57 - 1387.43i) q^{63} -36.8751 q^{64} +7914.59i q^{65} +(595.383 - 2705.42i) q^{66} +5122.41 q^{67} -884.034i q^{68} +(8717.11 + 1918.38i) q^{69} -3312.49 q^{70} -4704.20i q^{71} +(1752.71 - 3789.29i) q^{72} +7916.13 q^{73} +426.422i q^{74} +(2770.46 - 12588.9i) q^{75} +8389.09 q^{76} +7016.10i q^{77} +(-2745.35 - 604.171i) q^{78} -274.480 q^{79} +5101.65i q^{80} +(4248.38 + 4999.80i) q^{81} +2007.13 q^{82} +4807.12i q^{83} +(-1009.92 + 4589.06i) q^{84} +3133.53 q^{85} -2966.75i q^{86} +(2504.83 + 551.240i) q^{87} -8863.30 q^{88} -5001.80i q^{89} +(5968.53 + 2760.70i) q^{90} +7119.65 q^{91} -12690.5i q^{92} +(-120.979 + 549.727i) q^{93} +3106.25 q^{94} +29735.8i q^{95} +(-9018.41 - 1984.69i) q^{96} -5744.78 q^{97} -1317.86i q^{98} +(5847.36 - 12641.8i) 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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