LMFDB - Embedded newform 87.5.d.c.86.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,5,Mod(86,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.86"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	87.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.99318678829$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			86.20
Character	$\chi$	$=$	87.86
Dual form			87.5.d.c.86.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.36205 q^{2} +(-1.79151 + 8.81989i) q^{3} -14.1448 q^{4} -35.6756i q^{5} +(-2.44013 + 12.0132i) q^{6} +75.8945 q^{7} -41.0588 q^{8} +(-74.5810 - 31.6018i) q^{9} -48.5920i q^{10} +182.873 q^{11} +(25.3405 - 124.756i) q^{12} -13.7616 q^{13} +103.372 q^{14} +(314.655 + 63.9130i) q^{15} +170.393 q^{16} +243.546 q^{17} +(-101.583 - 43.0433i) q^{18} -193.045i q^{19} +504.624i q^{20} +(-135.965 + 669.381i) q^{21} +249.083 q^{22} -143.864i q^{23} +(73.5571 - 362.135i) q^{24} -647.746 q^{25} -18.7440 q^{26} +(412.336 - 601.182i) q^{27} -1073.51 q^{28} +(127.631 - 831.259i) q^{29} +(428.576 + 87.0528i) q^{30} -1004.52i q^{31} +889.025 q^{32} +(-327.618 + 1612.92i) q^{33} +331.723 q^{34} -2707.58i q^{35} +(1054.93 + 447.001i) q^{36} +314.802i q^{37} -262.938i q^{38} +(24.6539 - 121.376i) q^{39} +1464.80i q^{40} -2741.44 q^{41} +(-185.192 + 911.733i) q^{42} +1422.67i q^{43} -2586.70 q^{44} +(-1127.41 + 2660.72i) q^{45} -195.951i q^{46} +1966.47 q^{47} +(-305.259 + 1502.85i) q^{48} +3358.98 q^{49} -882.264 q^{50} +(-436.315 + 2148.05i) q^{51} +194.655 q^{52} -2903.41i q^{53} +(561.624 - 818.842i) q^{54} -6524.09i q^{55} -3116.14 q^{56} +(1702.64 + 345.842i) q^{57} +(173.840 - 1132.22i) q^{58} +4802.46i q^{59} +(-4450.73 - 904.037i) q^{60} +5904.75i q^{61} -1368.21i q^{62} +(-5660.29 - 2398.40i) q^{63} -1515.38 q^{64} +490.952i q^{65} +(-446.233 + 2196.88i) q^{66} +134.327 q^{67} -3444.92 q^{68} +(1268.87 + 257.734i) q^{69} -3687.87i q^{70} -6138.08i q^{71} +(3062.21 + 1297.53i) q^{72} +3852.80i q^{73} +428.777i q^{74} +(1160.44 - 5713.05i) q^{75} +2730.59i q^{76} +13879.0 q^{77} +(33.5800 - 165.320i) q^{78} +11276.2i q^{79} -6078.85i q^{80} +(4563.66 + 4713.78i) q^{81} -3733.99 q^{82} -265.544i q^{83} +(1923.20 - 9468.27i) q^{84} -8688.65i q^{85} +1937.76i q^{86} +(7102.96 + 2614.90i) q^{87} -7508.55 q^{88} -1093.81 q^{89} +(-1535.59 + 3624.04i) q^{90} -1044.43 q^{91} +2034.94i q^{92} +(8859.74 + 1799.60i) q^{93} +2678.43 q^{94} -6887.01 q^{95} +(-1592.69 + 7841.11i) q^{96} -11224.8i q^{97} +4575.10 q^{98} +(-13638.8 - 5779.10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 188 q^{4} - 36 q^{6} - 84 q^{7} - 452 q^{9} - 224 q^{13} - 52 q^{16} - 4216 q^{22} - 832 q^{24} - 7684 q^{25} - 396 q^{28} + 3384 q^{30} - 3308 q^{33} + 9124 q^{34} - 3680 q^{36} + 19764 q^{42} + 44 q^{45}+ \cdots + 13884 q^{96}+O(q^{100}) $ 32 * q + 188 * q^4 - 36 * q^6 - 84 * q^7 - 452 * q^9 - 224 * q^13 - 52 * q^16 - 4216 * q^22 - 832 * q^24 - 7684 * q^25 - 396 * q^28 + 3384 * q^30 - 3308 * q^33 + 9124 * q^34 - 3680 * q^36 + 19764 * q^42 + 44 * q^45 + 4796 * q^49 - 7052 * q^51 + 34048 * q^52 + 3008 * q^54 + 7976 * q^57 + 5936 * q^58 - 22848 * q^63 - 14668 * q^64 - 1872 * q^67 + 15192 * q^78 - 41088 * q^81 - 27028 * q^82 - 35572 * q^87 - 60032 * q^88 - 34272 * q^91 + 38000 * q^93 + 59636 * q^94 + 13884 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.36205			0.340513			0.170257	−	0.985400i	$-0.445540\pi$
$2$	1.36205			0.340513			0.170257	+	0.985400i	$0.445540\pi$
$3$	−1.79151	+	8.81989i	−0.199056	+	0.979988i
$3$	−1.79151	+	8.81989i	−0.199056	+	0.979988i
$4$	−14.1448			−0.884051
$5$		−	35.6756i		−	1.42702i	−0.700644	−	0.713511i	$-0.747104\pi$
$5$		−	35.6756i		−	1.42702i	0.700644	−	0.713511i	$-0.252896\pi$
$6$	−2.44013	+	12.0132i	−0.0677813	+	0.333699i
$7$	75.8945			1.54887			0.774434	−	0.632655i	$-0.218035\pi$
$7$	75.8945			1.54887			0.774434	+	0.632655i	$0.218035\pi$
$8$	−41.0588			−0.641544
$9$	−74.5810	−	31.6018i	−0.920753	−	0.390145i
$10$		−	48.5920i		−	0.485920i
$11$	182.873			1.51135			0.755673	−	0.654949i	$-0.227310\pi$
$11$	182.873			1.51135			0.755673	+	0.654949i	$0.227310\pi$
$12$	25.3405	−	124.756i	0.175976	−	0.866359i
$13$	−13.7616			−0.0814295			−0.0407147	−	0.999171i	$-0.512963\pi$
$13$	−13.7616			−0.0814295			−0.0407147	+	0.999171i	$0.512963\pi$
$14$	103.372			0.527410
$15$	314.655	+	63.9130i	1.39847	+	0.284058i
$16$	170.393			0.665596
$17$	243.546			0.842721			0.421360	−	0.906893i	$-0.361553\pi$
$17$	243.546			0.842721			0.421360	+	0.906893i	$0.361553\pi$
$18$	−101.583	−	43.0433i	−0.313529	−	0.132850i
$19$		−	193.045i		−	0.534752i	−0.963592	−	0.267376i	$-0.913843\pi$
$19$		−	193.045i		−	0.534752i	0.963592	−	0.267376i	$-0.0861566\pi$
$20$			504.624i			1.26156i
$21$	−135.965	+	669.381i	−0.308312	+	1.51787i
$22$	249.083			0.514633
$23$		−	143.864i		−	0.271956i	−0.990712	−	0.135978i	$-0.956582\pi$
$23$		−	143.864i		−	0.271956i	0.990712	−	0.135978i	$-0.0434176\pi$
$24$	73.5571	−	362.135i	0.127703	−	0.628706i
$25$	−647.746			−1.03639
$26$	−18.7440			−0.0277278
$27$	412.336	−	601.182i	0.565619	−	0.824666i
$28$	−1073.51			−1.36928
$29$	127.631	−	831.259i	0.151761	−	0.988417i
$29$	127.631	−	831.259i	0.151761	−	0.988417i
$30$	428.576	+	87.0528i	0.476196	+	0.0967254i
$31$		−	1004.52i		−	1.04528i	−0.852552	−	0.522642i	$-0.824947\pi$
$31$		−	1004.52i		−	1.04528i	0.852552	−	0.522642i	$-0.175053\pi$
$32$	889.025			0.868189
$33$	−327.618	+	1612.92i	−0.300843	+	1.48110i
$34$	331.723			0.286958
$35$		−	2707.58i		−	2.21027i
$36$	1054.93	+	447.001i	0.813993	+	0.344908i
$37$			314.802i			0.229951i	0.993368	+	0.114975i	$0.0366789\pi$
$37$			314.802i			0.229951i	−0.993368	+	0.114975i	$0.963321\pi$
$38$		−	262.938i		−	0.182090i
$39$	24.6539	−	121.376i	0.0162090	−	0.0797999i
$40$			1464.80i			0.915498i
$41$	−2741.44			−1.63084			−0.815420	−	0.578870i	$-0.803494\pi$
$41$	−2741.44			−1.63084			−0.815420	+	0.578870i	$0.803494\pi$
$42$	−185.192	+	911.733i	−0.104984	+	0.516855i
$43$			1422.67i			0.769429i	0.923036	+	0.384715i	$0.125700\pi$
$43$			1422.67i			0.769429i	−0.923036	+	0.384715i	$0.874300\pi$
$44$	−2586.70			−1.33611
$45$	−1127.41	+	2660.72i	−0.556746	+	1.31394i
$46$		−	195.951i		−	0.0926045i
$47$	1966.47			0.890208			0.445104	−	0.895479i	$-0.353167\pi$
$47$	1966.47			0.890208			0.445104	+	0.895479i	$0.353167\pi$
$48$	−305.259	+	1502.85i	−0.132491	+	0.652277i
$49$	3358.98			1.39899
$50$	−882.264			−0.352906
$51$	−436.315	+	2148.05i	−0.167749	+	0.825857i
$52$	194.655			0.0719878
$53$		−	2903.41i		−	1.03361i	−0.856103	−	0.516805i	$-0.827121\pi$
$53$		−	2903.41i		−	1.03361i	0.856103	−	0.516805i	$-0.172879\pi$
$54$	561.624	−	818.842i	0.192601	−	0.280810i
$55$		−	6524.09i		−	2.15672i
$56$	−3116.14			−0.993667
$57$	1702.64	+	345.842i	0.524051	+	0.106446i
$58$	173.840	−	1132.22i	0.0516767	−	0.336569i
$59$			4802.46i			1.37962i	0.723989	+	0.689811i	$0.242306\pi$
$59$			4802.46i			1.37962i	−0.723989	+	0.689811i	$0.757694\pi$
$60$	−4450.73	−	904.037i	−1.23631	−	0.251121i
$61$			5904.75i			1.58687i	0.608653	+	0.793436i	$0.291710\pi$
$61$			5904.75i			1.58687i	−0.608653	+	0.793436i	$0.708290\pi$
$62$		−	1368.21i		−	0.355933i
$63$	−5660.29	−	2398.40i	−1.42612	−	0.604283i
$64$	−1515.38			−0.369967
$65$			490.952i			0.116202i
$66$	−446.233	+	2196.88i	−0.102441	+	0.504334i
$67$	134.327			0.0299236			0.0149618	−	0.999888i	$-0.495237\pi$
$67$	134.327			0.0299236			0.0149618	+	0.999888i	$0.495237\pi$
$68$	−3444.92			−0.745008
$69$	1268.87	+	257.734i	0.266513	+	0.0541344i
$70$		−	3687.87i		−	0.752626i
$71$		−	6138.08i		−	1.21763i	−0.793312	−	0.608816i	$-0.791645\pi$
$71$		−	6138.08i		−	1.21763i	0.793312	−	0.608816i	$-0.208355\pi$
$72$	3062.21	+	1297.53i	0.590704	+	0.250295i
$73$			3852.80i			0.722988i	0.932374	+	0.361494i	$0.117733\pi$
$73$			3852.80i			0.722988i	−0.932374	+	0.361494i	$0.882267\pi$
$74$			428.777i			0.0783012i
$75$	1160.44	−	5713.05i	0.206300	−	1.01565i
$76$			2730.59i			0.472748i
$77$	13879.0			2.34087
$78$	33.5800	−	165.320i	0.00551939	−	0.0271729i
$79$			11276.2i			1.80680i	0.428799	+	0.903400i	$0.358937\pi$
$79$			11276.2i			1.80680i	−0.428799	+	0.903400i	$0.641063\pi$
$80$		−	6078.85i		−	0.949821i
$81$	4563.66	+	4713.78i	0.695573	+	0.718455i
$82$	−3733.99			−0.555323
$83$		−	265.544i		−	0.0385462i	−0.999814	−	0.0192731i	$-0.993865\pi$
$83$		−	265.544i		−	0.0385462i	0.999814	−	0.0192731i	$-0.00613519\pi$
$84$	1923.20	−	9468.27i	0.272563	−	1.34188i
$85$		−	8688.65i		−	1.20258i
$86$			1937.76i			0.262001i
$87$	7102.96	+	2614.90i	0.938428	+	0.345475i
$88$	−7508.55			−0.969595
$89$	−1093.81			−0.138090			−0.0690449	−	0.997614i	$-0.521995\pi$
$89$	−1093.81			−0.138090			−0.0690449	+	0.997614i	$0.521995\pi$
$90$	−1535.59	+	3624.04i	−0.189579	+	0.447413i
$91$	−1044.43			−0.126123
$92$			2034.94i			0.240423i
$93$	8859.74	+	1799.60i	1.02437	+	0.208070i
$94$	2678.43			0.303128
$95$	−6887.01			−0.763103
$96$	−1592.69	+	7841.11i	−0.172818	+	0.850815i
$97$		−	11224.8i		−	1.19299i	−0.802617	−	0.596495i	$-0.796560\pi$
$97$		−	11224.8i		−	1.19299i	0.802617	−	0.596495i	$-0.203440\pi$
$98$	4575.10			0.476375
$99$	−13638.8	−	5779.10i	−1.39158	−	0.589644i
$100$	9162.24			0.916224
$101$	4676.67			0.458452			0.229226	−	0.973373i	$-0.426381\pi$
$101$	4676.67			0.458452			0.229226	+	0.973373i	$0.426381\pi$
$102$	−594.284	+	2925.76i	−0.0571207	+	0.281215i
$103$	5318.66			0.501334			0.250667	−	0.968073i	$-0.419350\pi$
$103$	5318.66			0.501334			0.250667	+	0.968073i	$0.419350\pi$
$104$	565.035			0.0522406
$105$	23880.6	+	4850.64i	2.16604	+	0.439968i
$106$		−	3954.60i		−	0.351958i
$107$		−	8311.79i		−	0.725984i	−0.931792	−	0.362992i	$-0.881755\pi$
$107$		−	8311.79i		−	0.725984i	0.931792	−	0.362992i	$-0.118245\pi$
$108$	−5832.42	+	8503.60i	−0.500036	+	0.729047i
$109$	−19661.6			−1.65488			−0.827438	−	0.561557i	$-0.810202\pi$
$109$	−19661.6			−1.65488			−0.827438	+	0.561557i	$0.810202\pi$
$110$		−	8886.16i		−	0.734393i
$111$	−2776.52	−	563.970i	−0.225349	−	0.0457731i
$112$	12931.9			1.03092
$113$	14929.8			1.16922			0.584612	−	0.811313i	$-0.301247\pi$
$113$	14929.8			1.16922			0.584612	+	0.811313i	$0.301247\pi$
$114$	2319.09	+	471.055i	0.178446	+	0.0362462i
$115$	−5132.45			−0.388087
$116$	−1805.32	+	11758.0i	−0.134164	+	0.873811i
$117$	1026.35	+	434.890i	0.0749765	+	0.0317693i
$118$			6541.21i			0.469780i
$119$	18483.8			1.30526
$120$	−12919.4	−	2624.19i	−0.897177	−	0.182236i
$121$	18801.5			1.28417
$122$			8042.59i			0.540351i
$123$	4911.31	−	24179.2i	0.324629	−	1.59820i
$124$			14208.7i			0.924084i
$125$			811.465i			0.0519338i
$126$	−7709.61	−	3266.75i	−0.485614	−	0.205766i
$127$			2951.73i			0.183007i	0.995805	+	0.0915037i	$0.0291673\pi$
$127$			2951.73i			0.183007i	−0.995805	+	0.0915037i	$0.970833\pi$
$128$	−16288.4			−0.994167
$129$	−12547.8	−	2548.73i	−0.754032	−	0.153160i
$130$			668.703i			0.0395682i
$131$	−24361.2			−1.41957			−0.709784	−	0.704420i	$-0.751207\pi$
$131$	−24361.2			−1.41957			−0.709784	+	0.704420i	$0.751207\pi$
$132$	4634.09	−	22814.4i	0.265960	−	1.30937i
$133$		−	14651.1i		−	0.828260i
$134$	182.960			0.0101894
$135$	−21447.5	−	14710.3i	−1.17682	−	0.807151i
$136$	−9999.73			−0.540643
$137$	−19427.0			−1.03506			−0.517529	−	0.855665i	$-0.673148\pi$
$137$	−19427.0			−1.03506			−0.517529	+	0.855665i	$0.673148\pi$
$138$	1728.27	+	351.047i	0.0907513	+	0.0184335i
$139$	8092.40			0.418839			0.209420	−	0.977826i	$-0.432843\pi$
$139$	8092.40			0.418839			0.209420	+	0.977826i	$0.432843\pi$
$140$			38298.2i			1.95399i
$141$	−3522.94	+	17344.0i	−0.177201	+	0.872393i
$142$		−	8360.39i		−	0.414620i
$143$	−2516.62			−0.123068
$144$	−12708.1	−	5384.71i	−0.612850	−	0.259679i
$145$	−29655.6	−	4553.31i	−1.41049	−	0.216566i
$146$			5247.72i			0.246187i
$147$	−6017.62	+	29625.8i	−0.278478	+	1.37099i
$148$		−	4452.82i		−	0.203288i
$149$			4899.80i			0.220702i	0.993893	+	0.110351i	$0.0351975\pi$
$149$			4899.80i			0.220702i	−0.993893	+	0.110351i	$0.964803\pi$
$150$	1580.58	−	7781.47i	0.0702480	−	0.345843i
$151$	19041.4			0.835112			0.417556	−	0.908651i	$-0.362887\pi$
$151$	19041.4			0.835112			0.417556	+	0.908651i	$0.362887\pi$
$152$			7926.22i			0.343067i
$153$	−18163.9	−	7696.50i	−0.775938	−	0.328784i
$154$	18904.0			0.797099
$155$	−35836.7			−1.49164
$156$	−348.725	+	1716.84i	−0.0143296	+	0.0705472i
$157$			27695.6i			1.12360i	0.827274	+	0.561799i	$0.189891\pi$
$157$			27695.6i			1.12360i	−0.827274	+	0.561799i	$0.810109\pi$
$158$			15358.8i			0.615239i
$159$	25607.7	+	5201.47i	1.01292	+	0.205746i
$160$		−	31716.5i		−	1.23892i
$161$		−	10918.5i		−	0.421223i
$162$	6215.94	+	6420.42i	0.236852	+	0.244643i
$163$			41717.9i			1.57017i	0.619386	+	0.785086i	$0.287381\pi$
$163$			41717.9i			1.57017i	−0.619386	+	0.785086i	$0.712619\pi$
$164$	38777.2			1.44175
$165$	57541.8	+	11687.9i	2.11356	+	0.429309i
$166$		−	361.686i		−	0.0131255i
$167$			34720.9i			1.24497i	0.782633	+	0.622484i	$0.213876\pi$
$167$			34720.9i			1.24497i	−0.782633	+	0.622484i	$0.786124\pi$
$168$	5582.58	−	27484.0i	0.197796	−	0.973782i
$169$	−28371.6			−0.993369
$170$		−	11834.4i		−	0.409495i
$171$	−6100.58	+	14397.5i	−0.208631	+	0.492375i
$172$		−	20123.5i		−	0.680214i
$173$		−	29747.3i		−	0.993928i	−0.867771	−	0.496964i	$-0.834448\pi$
$173$		−	29747.3i		−	0.993928i	0.867771	−	0.496964i	$-0.165552\pi$
$174$	9674.61	+	3561.63i	0.319547	+	0.117639i
$175$	−49160.3			−1.60524
$176$	31160.2			1.00595
$177$	−42357.2	−	8603.64i	−1.35201	−	0.274622i
$178$	−1489.83			−0.0470214
$179$			44986.2i			1.40402i	0.712167	+	0.702010i	$0.247714\pi$
$179$			44986.2i			1.40402i	−0.712167	+	0.702010i	$0.752286\pi$
$180$	15947.0	−	37635.4i	0.492192	−	1.16159i
$181$	16257.7			0.496253			0.248127	−	0.968728i	$-0.420185\pi$
$181$	16257.7			0.496253			0.248127	+	0.968728i	$0.420185\pi$
$182$	−1422.57			−0.0429467
$183$	−52079.3	−	10578.4i	−1.55512	−	0.315877i
$184$			5906.91i			0.174472i
$185$	11230.7			0.328145
$186$	12067.4	+	2451.15i	0.348810	+	0.0708506i
$187$	44538.0			1.27364
$188$	−27815.3			−0.786989
$189$	31294.1	−	45626.4i	0.876069	−	1.27730i
$190$	−9380.47			−0.259847
$191$	−10450.1			−0.286452			−0.143226	−	0.989690i	$-0.545748\pi$
$191$	−10450.1			−0.286452			−0.143226	+	0.989690i	$0.545748\pi$
$192$	2714.82	−	13365.5i	0.0736441	−	0.362563i
$193$		−	53264.0i		−	1.42995i	−0.699152	−	0.714973i	$-0.746439\pi$
$193$		−	53264.0i		−	1.42995i	0.699152	−	0.714973i	$-0.253561\pi$
$194$		−	15288.8i		−	0.406229i
$195$	−4330.15	−	879.543i	−0.113876	−	0.0231307i
$196$	−47512.1			−1.23678
$197$			24417.2i			0.629163i	0.949230	+	0.314581i	$0.101864\pi$
$197$			24417.2i			0.629163i	−0.949230	+	0.314581i	$0.898136\pi$
$198$	−18576.8	−	7871.45i	−0.473850	−	0.200782i
$199$	56691.7			1.43157			0.715787	−	0.698319i	$-0.246068\pi$
$199$	56691.7			1.43157			0.715787	+	0.698319i	$0.246068\pi$
$200$	26595.7			0.664892
$201$	−240.647	+	1184.75i	−0.00595647	+	0.0293247i
$202$	6369.87			0.156109
$203$	9686.49	−	63088.0i	0.235058	−	1.53093i
$204$	6171.59	−	30383.8i	0.148298	−	0.730099i
$205$			97802.5i			2.32725i
$206$	7244.29			0.170711
$207$	−4546.37	+	10729.6i	−0.106102	+	0.250404i
$208$	−2344.87			−0.0541992
$209$		−	35302.8i		−	0.808195i
$210$	32526.6	+	6606.83i	0.737564	+	0.149815i
$211$		−	38887.0i		−	0.873453i	−0.899594	−	0.436726i	$-0.856138\pi$
$211$		−	38887.0i		−	0.873453i	0.899594	−	0.436726i	$-0.143862\pi$
$212$			41068.2i			0.913763i
$213$	54137.2	+	10996.4i	1.19326	+	0.242377i
$214$		−	11321.1i		−	0.247207i
$215$	50754.7			1.09799
$216$	−16930.1	+	24683.8i	−0.362870	+	0.529060i
$217$		−	76237.4i		−	1.61901i
$218$	−26780.1			−0.563507
$219$	−33981.3	−	6902.32i	−0.708520	−	0.143915i
$220$			92282.0i			1.90665i
$221$	−3351.58			−0.0686223
$222$	−3781.77	−	768.157i	−0.0767343	−	0.0155863i
$223$	−2744.25			−0.0551841			−0.0275921	−	0.999619i	$-0.508784\pi$
$223$	−2744.25			−0.0551841			−0.0275921	+	0.999619i	$0.508784\pi$
$224$	67472.1			1.34471
$225$	48309.5	+	20469.9i	0.954262	+	0.404344i
$226$	20335.2			0.398137
$227$		−	4950.36i		−	0.0960694i	−0.998846	−	0.0480347i	$-0.984704\pi$
$227$		−	4950.36i		−	0.0960694i	0.998846	−	0.0480347i	$-0.0152958\pi$
$228$	−24083.5	−	4891.87i	−0.463287	−	0.0941034i
$229$			55790.9i			1.06388i	0.846782	+	0.531940i	$0.178537\pi$
$229$			55790.9i			1.06388i	−0.846782	+	0.531940i	$0.821463\pi$
$230$	−6990.66			−0.132149
$231$	−24864.4	+	122412.i	−0.465965	+	2.29403i
$232$	−5240.38	+	34130.5i	−0.0973614	+	0.634113i
$233$			102717.i			1.89204i	0.324106	+	0.946021i	$0.394936\pi$
$233$			102717.i			1.89204i	−0.324106	+	0.946021i	$0.605064\pi$
$234$	1397.95	+	592.344i	0.0255305	+	0.0108179i
$235$		−	70154.9i		−	1.27035i
$236$		−	67930.0i		−	1.21966i
$237$	−99455.2	−	20201.4i	−1.77064	−	0.359655i
$238$	25176.0			0.444459
$239$		−	36491.8i		−	0.638852i	−0.947611	−	0.319426i	$-0.896510\pi$
$239$		−	36491.8i		−	0.638852i	0.947611	−	0.319426i	$-0.103490\pi$
$240$	53614.8	+	10890.3i	0.930813	+	0.189068i
$241$	28426.5			0.489428			0.244714	−	0.969595i	$-0.421306\pi$
$241$	28426.5			0.489428			0.244714	+	0.969595i	$0.421306\pi$
$242$	25608.6			0.437276
$243$	−49750.9	+	31806.2i	−0.842536	+	0.538641i
$244$		−	83521.6i		−	1.40288i
$245$		−	119833.i		−	1.99639i
$246$	6689.46	−	32933.4i	0.110540	−	0.544210i
$247$			2656.61i			0.0435446i
$248$			41244.3i			0.670596i
$249$	2342.07	+	475.724i	0.0377748	+	0.00767285i
$250$			1105.26i			0.0176841i
$251$	−100292.			−1.59191			−0.795953	−	0.605359i	$-0.793030\pi$
$251$	−100292.			−1.59191			−0.795953	+	0.605359i	$0.793030\pi$
$252$	80063.7	+	33924.9i	1.26077	+	0.534217i
$253$		−	26308.9i		−	0.411019i
$254$			4020.41i			0.0623164i
$255$	76633.0	+	15565.8i	1.17852	+	0.239381i
$256$	2060.42			0.0314395
$257$		−	59922.5i		−	0.907243i	−0.891194	−	0.453621i	$-0.850132\pi$
$257$		−	59922.5i		−	0.907243i	0.891194	−	0.453621i	$-0.149868\pi$
$258$	−17090.8	−	3471.50i	−0.256758	−	0.0521529i
$259$			23891.8i			0.356163i
$260$		−	6944.43i		−	0.102728i
$261$	−35788.1	+	57962.8i	−0.525361	+	0.850880i
$262$	−33181.2			−0.483382
$263$	24022.7			0.347304			0.173652	−	0.984807i	$-0.444443\pi$
$263$	24022.7			0.347304			0.173652	+	0.984807i	$0.444443\pi$
$264$	13451.6	−	66224.6i	0.193004	−	0.950192i
$265$	−103581.			−1.47498
$266$		−	19955.6i		−	0.282034i
$267$	1959.57	−	9647.29i	0.0274876	−	0.135326i
$268$	−1900.03			−0.0264540
$269$	1092.97			0.0151045			0.00755224	−	0.999971i	$-0.497596\pi$
$269$	1092.97			0.0151045			0.00755224	+	0.999971i	$0.497596\pi$
$270$	−29212.6	−	20036.3i	−0.400722	−	0.274846i
$271$			51618.0i			0.702849i	0.936216	+	0.351425i	$0.114303\pi$
$271$			51618.0i			0.702849i	−0.936216	+	0.351425i	$0.885697\pi$
$272$	41498.5			0.560912
$273$	1871.10	−	9211.75i	0.0251057	−	0.123600i
$274$	−26460.6			−0.352451
$275$	−118455.			−1.56635
$276$	−17947.9	−	3645.60i	−0.235611	−	0.0478576i
$277$	83749.6			1.09150			0.545750	−	0.837948i	$-0.316245\pi$
$277$	83749.6			1.09150			0.545750	+	0.837948i	$0.316245\pi$
$278$	11022.3			0.142620
$279$	−31744.5	+	74917.9i	−0.407812	+	0.962448i
$280$			111170.i			1.41799i
$281$		−	56013.8i		−	0.709386i	−0.934983	−	0.354693i	$-0.884585\pi$
$281$		−	56013.8i		−	0.709386i	0.934983	−	0.354693i	$-0.115415\pi$
$282$	−4798.43	+	23623.5i	−0.0603394	+	0.297061i
$283$	−108561.			−1.35551			−0.677753	−	0.735290i	$-0.737046\pi$
$283$	−108561.			−1.35551			−0.677753	+	0.735290i	$0.737046\pi$
$284$			86822.0i			1.07645i
$285$	12338.1	−	60742.7i	0.151900	−	0.747832i
$286$	−3427.77			−0.0419063
$287$	−208060.			−2.52596
$288$	−66304.4	−	28094.8i	−0.799388	−	0.338720i
$289$	−24206.2			−0.289821
$290$	−40392.5	−	6201.85i	−0.480292	−	0.0737437i
$291$	99001.9	+	20109.4i	1.16912	+	0.237472i
$292$		−	54497.2i		−	0.639158i
$293$	−69709.4			−0.812000			−0.406000	−	0.913873i	$-0.633077\pi$
$293$	−69709.4			−0.812000			−0.406000	+	0.913873i	$0.633077\pi$
$294$	−8196.32	+	40351.9i	−0.0948253	+	0.466842i
$295$	171331.			1.96875
$296$		−	12925.4i		−	0.147523i
$297$	75405.1	−	109940.i	0.854846	−	1.24636i
$298$			6673.79i			0.0751519i
$299$			1979.80i			0.0221452i
$300$	−16414.2	+	80810.0i	−0.182380	+	0.897889i
$301$			107973.i			1.19174i
$302$	25935.4			0.284367
$303$	−8378.27	+	41247.7i	−0.0912576	+	0.449277i
$304$		−	32893.5i		−	0.355929i
$305$	210655.			2.26450
$306$	−24740.2	−	10483.0i	−0.264217	−	0.111955i
$307$			6168.44i			0.0654484i	0.999464	+	0.0327242i	$0.0104183\pi$
$307$			6168.44i			0.0654484i	−0.999464	+	0.0327242i	$0.989582\pi$
$308$	−196316.			−2.06945
$309$	−9528.40	+	46910.0i	−0.0997937	+	0.491302i
$310$	−48811.5			−0.507924
$311$	26520.8			0.274199			0.137099	−	0.990557i	$-0.456222\pi$
$311$	26520.8			0.274199			0.137099	+	0.990557i	$0.456222\pi$
$312$	−1012.26	+	4983.54i	−0.0103988	+	0.0511952i
$313$	−66317.5			−0.676923			−0.338462	−	0.940980i	$-0.609907\pi$
$313$	−66317.5			−0.676923			−0.338462	+	0.940980i	$0.609907\pi$
$314$			37722.9i			0.382600i
$315$	−85564.3	+	201934.i	−0.862326	+	2.03511i
$316$		−	159500.i		−	1.59730i
$317$	122227.			1.21633			0.608163	−	0.793812i	$-0.291907\pi$
$317$	122227.			1.21633			0.608163	+	0.793812i	$0.291907\pi$
$318$	34879.1	+	7084.68i	0.344914	+	0.0700593i
$319$	23340.3	−	152015.i	0.229363	−	1.49384i
$320$			54062.1i			0.527951i
$321$	73309.1	+	14890.6i	0.711456	+	0.144512i
$322$		−	14871.6i		−	0.143432i
$323$		−	47015.5i		−	0.450647i
$324$	−64552.1	−	66675.6i	−0.614922	−	0.635151i
$325$	8914.01			0.0843930
$326$			56822.0i			0.534665i
$327$	35223.8	−	173413.i	0.329413	−	1.62176i
$328$	112560.			1.04626
$329$	149244.			1.37881
$330$	78375.0	+	15919.6i	0.719697	+	0.146185i
$331$		−	94844.4i		−	0.865677i	−0.901472	−	0.432838i	$-0.857512\pi$
$331$		−	94844.4i		−	0.865677i	0.901472	−	0.432838i	$-0.142488\pi$
$332$			3756.08i			0.0340768i
$333$	9948.31	−	23478.3i	0.0897141	−	0.211728i
$334$			47291.7i			0.423928i
$335$		−	4792.19i		−	0.0427016i
$336$	−23167.5	+	114058.i	−0.205211	+	1.01029i
$337$			91228.7i			0.803289i	0.915796	+	0.401644i	$0.131561\pi$
$337$			91228.7i			0.803289i	−0.915796	+	0.401644i	$0.868439\pi$
$338$	−38643.7			−0.338255
$339$	−26746.9	+	131679.i	−0.232741	+	1.14583i
$340$			122899.i			1.06314i
$341$		−	183699.i		−	1.57979i
$342$	−8309.31	+	19610.2i	−0.0710416	+	0.167660i
$343$	72705.0			0.617983
$344$		−	58413.4i		−	0.493623i
$345$	9194.80	−	45267.6i	0.0772510	−	0.380320i
$346$		−	40517.4i		−	0.338446i
$347$		−	195509.i		−	1.62370i	−0.583864	−	0.811852i	$-0.698460\pi$
$347$		−	195509.i		−	1.62370i	0.583864	−	0.811852i	$-0.301540\pi$
$348$	−100470.	−	36987.2i	−0.829618	−	0.305417i
$349$	−159382.			−1.30854			−0.654271	−	0.756260i	$-0.727024\pi$
$349$	−159382.			−1.30854			−0.654271	+	0.756260i	$0.727024\pi$
$350$	−66959.0			−0.546604
$351$	−5674.40	+	8273.21i	−0.0460581	+	0.0671522i
$352$	162579.			1.31213
$353$			136025.i			1.09162i	0.837910	+	0.545808i	$0.183777\pi$
$353$			136025.i			1.09162i	−0.837910	+	0.545808i	$0.816223\pi$
$354$	−57692.8	−	11718.6i	−0.460378	−	0.0935125i
$355$	−218979.			−1.73759
$356$	15471.7			0.122078
$357$	−33113.9	+	163025.i	−0.259821	+	1.27914i
$358$			61273.6i			0.478087i
$359$	−114459.			−0.888095			−0.444047	−	0.896003i	$-0.646458\pi$
$359$	−114459.			−0.888095			−0.444047	+	0.896003i	$0.646458\pi$
$360$	46290.2	−	109246.i	0.357177	−	0.842948i
$361$	93054.4			0.714040
$362$	22143.9			0.168981
$363$	−33682.9	+	165827.i	−0.255621	+	1.25847i
$364$	14773.2			0.111500
$365$	137451.			1.03172
$366$	−70934.8	−	14408.3i	−0.529538	−	0.107560i
$367$			149962.i			1.11339i	0.830716	+	0.556696i	$0.187931\pi$
$367$			149962.i			1.11339i	−0.830716	+	0.556696i	$0.812069\pi$
$368$		−	24513.5i		−	0.181013i
$369$	204460.	+	86634.4i	1.50160	+	0.636265i
$370$	15296.9			0.111738
$371$		−	220353.i		−	1.60092i
$372$	−125319.	−	25455.0i	−0.905591	−	0.183945i
$373$	172008.			1.23632			0.618161	−	0.786051i	$-0.287878\pi$
$373$	172008.			1.23632			0.618161	+	0.786051i	$0.287878\pi$
$374$	60663.1			0.433692
$375$	−7157.03	−	1453.74i	−0.0508945	−	0.0103377i
$376$	−80740.9			−0.571108
$377$	−1756.41	+	11439.4i	−0.0123578	+	0.0804863i
$378$	42624.2	−	62145.6i	0.298313	−	0.434937i
$379$			13988.3i			0.0973838i	0.998814	+	0.0486919i	$0.0155052\pi$
$379$			13988.3i			0.0973838i	−0.998814	+	0.0486919i	$0.984495\pi$
$380$	97415.4			0.674622
$381$	−26033.9	−	5288.03i	−0.179345	−	0.0364287i
$382$	−14233.5			−0.0975408
$383$			186557.i			1.27179i	0.771777	+	0.635893i	$0.219368\pi$
$383$			186557.i			1.27179i	−0.771777	+	0.635893i	$0.780632\pi$
$384$	29180.8	−	143662.i	0.197895	−	0.974272i
$385$		−	495143.i		−	3.34048i
$386$		−	72548.4i		−	0.486915i
$387$	44959.0	−	106105.i	0.300189	−	0.708455i
$388$			158773.i			1.05466i
$389$	10807.0			0.0714178			0.0357089	−	0.999362i	$-0.488631\pi$
$389$	10807.0			0.0714178			0.0357089	+	0.999362i	$0.488631\pi$
$390$	−5897.89	−	1197.98i	−0.0387764	−	0.00787630i
$391$		−	35037.7i		−	0.229183i
$392$	−137916.			−0.897514
$393$	43643.2	−	214863.i	0.282574	−	1.39116i
$394$			33257.5i			0.214238i
$395$	402286.			2.57834
$396$	192919.	+	81744.3i	1.23022	+	0.521276i
$397$	−147468.			−0.935658			−0.467829	−	0.883819i	$-0.654964\pi$
$397$	−147468.			−0.935658			−0.467829	+	0.883819i	$0.654964\pi$
$398$	77217.2			0.487470
$399$	129221.	+	26247.5i	0.811685	+	0.164870i
$400$	−110371.			−0.689819
$401$			209902.i			1.30535i	0.757638	+	0.652675i	$0.226353\pi$
$401$			209902.i			1.30535i	−0.757638	+	0.652675i	$0.773647\pi$
$402$	−327.774	+	1613.69i	−0.00202826	+	0.00998546i
$403$			13823.8i			0.0851169i
$404$	−66150.6			−0.405295
$405$	168167.	−	162811.i	1.02525	−	0.992599i
$406$	13193.5	−	85929.2i	0.0800403	−	0.521301i
$407$			57568.8i			0.347535i
$408$	17914.6	−	88196.5i	0.107618	−	0.529824i
$409$		−	267299.i		−	1.59791i	−0.601394	−	0.798953i	$-0.705388\pi$
$409$		−	267299.i		−	1.59791i	0.601394	−	0.798953i	$-0.294612\pi$
$410$			133212.i			0.792458i
$411$	34803.6	−	171344.i	0.206035	−	1.01435i
$412$	−75231.4			−0.443205
$413$			364481.i			2.13685i
$414$	−6192.40	+	14614.2i	−0.0361292	+	0.0852659i
$415$	−9473.45			−0.0550062
$416$	−12234.4			−0.0706962
$417$	−14497.6	+	71374.1i	−0.0833726	+	0.410458i
$418$		−	48084.3i		−	0.275201i
$419$		−	28344.6i		−	0.161451i	−0.996736	−	0.0807257i	$-0.974276\pi$
$419$		−	28344.6i		−	0.161451i	0.996736	−	0.0807257i	$-0.0257238\pi$
$420$	−337786.	−	68611.4i	−1.91489	−	0.388954i
$421$			194730.i			1.09867i	0.835601	+	0.549337i	$0.185120\pi$
$421$			194730.i			1.09867i	−0.835601	+	0.549337i	$0.814880\pi$
$422$		−	52966.1i		−	0.297422i
$423$	−146661.	−	62143.9i	−0.819662	−	0.347310i
$424$			119211.i			0.663106i
$425$	−157756.			−0.873390
$426$	73737.8	+	14977.7i	0.406322	+	0.0825326i
$427$			448138.i			2.45786i
$428$			117569.i			0.641807i
$429$	4508.54	−	22196.3i	0.0244975	−	0.120605i
$430$	69130.6			0.373881
$431$			139802.i			0.752593i	0.926499	+	0.376296i	$0.122803\pi$
$431$			139802.i			0.752593i	−0.926499	+	0.376296i	$0.877197\pi$
$432$	70259.1	−	102437.i	0.376474	−	0.548895i
$433$			76893.1i			0.410121i	0.978749	+	0.205060i	$0.0657391\pi$
$433$			76893.1i			0.410121i	−0.978749	+	0.205060i	$0.934261\pi$
$434$		−	103839.i		−	0.551293i
$435$	93287.9	−	253402.i	0.493000	−	1.33916i
$436$	278109.			1.46299
$437$	−27772.4			−0.145429
$438$	−46284.4	−	9401.32i	−0.241260	−	0.0490050i
$439$	171807.			0.891478			0.445739	−	0.895163i	$-0.352941\pi$
$439$	171807.			0.891478			0.445739	+	0.895163i	$0.352941\pi$
$440$			267872.i			1.38363i
$441$	−250516.	−	106150.i	−1.28812	−	0.545809i
$442$	−4565.03			−0.0233668
$443$	−212396.			−1.08228			−0.541140	−	0.840933i	$-0.682007\pi$
$443$	−212396.			−1.08228			−0.541140	+	0.840933i	$0.682007\pi$
$444$	39273.4	+	7977.25i	0.199220	+	0.0404657i
$445$			39022.3i			0.197057i
$446$	−3737.82			−0.0187909
$447$	−43215.7	−	8778.02i	−0.216285	−	0.0439321i
$448$	−115009.			−0.573029
$449$	375838.			1.86427			0.932134	−	0.362114i	$-0.117945\pi$
$449$	375838.			1.86427			0.932134	+	0.362114i	$0.117945\pi$
$450$	65800.1	+	27881.1i	0.324939	+	0.137684i
$451$	−501335.			−2.46476
$452$	−211180.			−1.03365
$453$	−34112.7	+	167943.i	−0.166234	+	0.818399i
$454$		−	6742.65i		−	0.0327129i
$455$			37260.6i			0.179981i
$456$	−69908.4	−	14199.9i	−0.336202	−	0.0682896i
$457$	286801.			1.37325			0.686624	−	0.727013i	$-0.259092\pi$
$457$	286801.			1.37325			0.686624	+	0.727013i	$0.259092\pi$
$458$			75990.2i			0.362265i
$459$	100423.	−	146416.i	0.476659	−	0.694964i
$460$	72597.5			0.343088
$461$	−68070.5			−0.320300			−0.160150	−	0.987093i	$-0.551198\pi$
$461$	−68070.5			−0.320300			−0.160150	+	0.987093i	$0.551198\pi$
$462$	−33866.6	+	166731.i	−0.158667	+	0.781147i
$463$	64690.2			0.301770			0.150885	−	0.988551i	$-0.451788\pi$
$463$	64690.2			0.301770			0.150885	+	0.988551i	$0.451788\pi$
$464$	21747.4	−	141640.i	0.101012	−	0.657887i
$465$	64201.7	−	316076.i	0.296921	−	1.46179i
$466$			139906.i			0.644265i
$467$	−224909.			−1.03127			−0.515636	−	0.856807i	$-0.672444\pi$
$467$	−224909.			−1.03127			−0.515636	+	0.856807i	$0.672444\pi$
$468$	−14517.6	−	6151.44i	−0.0662830	−	0.0280857i
$469$	10194.7			0.0463476
$470$		−	95554.7i		−	0.432570i
$471$	−244272.	−	49616.8i	−1.10111	−	0.223659i
$472$		−	197184.i		−	0.885089i
$473$			260169.i			1.16287i
$474$	−135463.	−	27515.4i	−0.602927	−	0.122467i
$475$			125044.i			0.554213i
$476$	−261450.			−1.15392
$477$	−91752.8	+	216539.i	−0.403258	+	0.951699i
$478$		−	49703.8i		−	0.217537i
$479$	96339.8			0.419889			0.209945	−	0.977713i	$-0.432672\pi$
$479$	96339.8			0.419889			0.209945	+	0.977713i	$0.432672\pi$
$480$	279736.	+	56820.2i	1.21413	+	0.246616i
$481$		−	4332.18i		−	0.0187248i
$482$	38718.3			0.166657
$483$	96300.2	+	19560.6i	0.412794	+	0.0838470i
$484$	−265943.			−1.13527
$485$	−400452.			−1.70242
$486$	−67763.3	+	43321.7i	−0.286895	+	0.183414i
$487$	−221881.			−0.935539			−0.467769	−	0.883851i	$-0.654942\pi$
$487$	−221881.			−0.935539			−0.467769	+	0.883851i	$0.654942\pi$
$488$		−	242442.i		−	1.01805i
$489$	−367948.	−	74737.9i	−1.53875	−	0.312552i
$490$		−	163219.i		−	0.679797i
$491$	89492.1			0.371212			0.185606	−	0.982624i	$-0.440575\pi$
$491$	89492.1			0.371212			0.185606	+	0.982624i	$0.440575\pi$
$492$	−69469.5	+	342011.i	−0.286988	+	1.41289i
$493$	31084.1	−	202450.i	0.127892	−	0.832960i
$494$			3618.45i			0.0148275i
$495$	−206173.	+	486573.i	−0.841436	+	1.98581i
$496$		−	171162.i		−	0.695737i
$497$		−	465847.i		−	1.88595i
$498$	3190.03	+	647.962i	0.0128628	+	0.00261271i
$499$	332788.			1.33649			0.668246	−	0.743940i	$-0.267045\pi$
$499$	332788.			1.33649			0.668246	+	0.743940i	$0.267045\pi$
$500$		−	11478.0i		−	0.0459121i
$501$	−306235.	−	62202.7i	−1.22005	−	0.247818i
$502$	−136603.			−0.542065
$503$	−266566.			−1.05358			−0.526792	−	0.849994i	$-0.676605\pi$
$503$	−266566.			−1.05358			−0.526792	+	0.849994i	$0.676605\pi$
$504$	232405.	+	98475.5i	0.914922	+	0.387674i
$505$		−	166843.i		−	0.654221i
$506$		−	35834.1i		−	0.139957i
$507$	50827.9	−	250235.i	0.197736	−	0.973490i
$508$		−	41751.6i		−	0.161788i
$509$			235686.i			0.909702i	0.890568	+	0.454851i	$0.150307\pi$
$509$			235686.i			0.909702i	−0.890568	+	0.454851i	$0.849693\pi$
$510$	104378.	+	21201.4i	0.401300	+	0.0815125i
$511$			292407.i			1.11981i
$512$	263421.			1.00487
$513$	−116055.	−	79599.7i	−0.440992	−	0.302466i
$514$		−	81617.6i		−	0.308928i
$515$		−	189746.i		−	0.715416i
$516$	177487.	+	36051.3i	0.666602	+	0.135401i
$517$	359614.			1.34541
$518$			32541.8i			0.121278i
$519$	262368.	+	53292.4i	0.974038	+	0.197847i
$520$		−	20157.9i		−	0.0745485i
$521$			349903.i			1.28906i	0.764580	+	0.644529i	$0.222947\pi$
$521$			349903.i			1.28906i	−0.764580	+	0.644529i	$0.777053\pi$
$522$	−48745.3	+	78948.4i	−0.178892	+	0.289736i
$523$	195801.			0.715833			0.357917	−	0.933754i	$-0.383487\pi$
$523$	195801.			0.715833			0.357917	+	0.933754i	$0.383487\pi$
$524$	344585.			1.25497
$525$	88071.0	−	433589.i	0.319532	−	1.57311i
$526$	32720.2			0.118262
$527$		−	244647.i		−	0.880883i
$528$	−55823.6	+	274830.i	−0.200240	+	0.985815i
$529$	259144.			0.926040
$530$	−141082.			−0.502251
$531$	151766.	−	358173.i	0.538253	−	1.27029i
$532$			207237.i			0.732224i
$533$	37726.6			0.132798
$534$	2669.03	−	13140.1i	0.00935991	−	0.0460805i
$535$	−296528.			−1.03600
$536$	−5515.31			−0.0191973
$537$	−396773.	−	80593.0i	−1.37592	−	0.279479i
$538$	1488.69			0.00514327
$539$	614265.			2.11436
$540$	303371.	+	208075.i	1.04037	+	0.713563i
$541$		−	82978.2i		−	0.283511i	−0.989902	−	0.141755i	$-0.954725\pi$
$541$		−	82978.2i		−	0.283511i	0.989902	−	0.141755i	$-0.0452746\pi$
$542$			70306.4i			0.239330i
$543$	−29125.8	+	143392.i	−0.0987822	+	0.486322i
$544$	216519.			0.731641
$545$			701438.i			2.36154i
$546$	2548.54	−	12546.9i	0.00854881	−	0.0420873i
$547$	−391364.			−1.30800			−0.653998	−	0.756496i	$-0.726910\pi$
$547$	−391364.			−1.30800			−0.653998	+	0.756496i	$0.726910\pi$
$548$	274792.			0.915045
$549$	186601.	−	440383.i	0.619111	−	1.46112i
$550$	−161342.			−0.533362
$551$	−160471.	−	24638.6i	−0.528558	−	0.0811545i
$552$	−52098.3	−	10582.3i	−0.170980	−	0.0347296i
$553$			855805.i			2.79849i
$554$	114071.			0.371670
$555$	−20119.9	+	99054.0i	−0.0653192	+	0.321578i
$556$	−114465.			−0.370275
$557$		−	675.650i		−	0.00217777i	−0.999999	−	0.00108888i	$-0.999653\pi$
$557$		−	675.650i		−	0.00217777i	0.999999	−	0.00108888i	$-0.000346602\pi$
$558$	−43237.7	+	102042.i	−0.138866	+	0.327726i
$559$		−	19578.3i		−	0.0626542i
$560$		−	461352.i		−	1.47115i
$561$	−79790.1	+	392821.i	−0.253526	+	1.24815i
$562$		−	76293.8i		−	0.241555i
$563$	−525405.			−1.65759			−0.828795	−	0.559552i	$-0.810973\pi$
$563$	−525405.			−1.65759			−0.828795	+	0.559552i	$0.810973\pi$
$564$	49831.3	−	245328.i	0.156655	−	0.771240i
$565$		−	532630.i		−	1.66851i
$566$	−147866.			−0.461568
$567$	346356.	+	357750.i	1.07735	+	1.11279i
$568$			252022.i			0.781165i
$569$	316924.			0.978882			0.489441	−	0.872036i	$-0.337201\pi$
$569$	316924.			0.978882			0.489441	+	0.872036i	$0.337201\pi$
$570$	16805.2	−	82734.7i	0.0517241	−	0.254647i
$571$	143325.			0.439592			0.219796	−	0.975546i	$-0.429461\pi$
$571$	143325.			0.439592			0.219796	+	0.975546i	$0.429461\pi$
$572$	35597.1			0.108798
$573$	18721.3	−	92168.5i	0.0570201	−	0.280720i
$574$	−283389.			−0.860121
$575$			93187.6i			0.281853i
$576$	113019.	+	47888.8i	0.340648	+	0.144341i
$577$		−	94297.7i		−	0.283237i	−0.989921	−	0.141618i	$-0.954769\pi$
$577$		−	94297.7i		−	0.283237i	0.989921	−	0.141618i	$-0.0452305\pi$
$578$	−32970.1			−0.0986880
$579$	469783.	+	95422.8i	1.40133	+	0.284639i
$580$	419473.	+	64405.7i	1.24695	+	0.191456i
$581$		−	20153.4i		−	0.0597029i
$582$	134846.	+	27390.0i	0.398099	+	0.0808623i
$583$		−	530954.i		−	1.56214i
$584$		−	158192.i		−	0.463829i
$585$	15515.0	−	36615.7i	0.0453355	−	0.106993i
$586$	−94947.9			−0.276497
$587$		−	447749.i		−	1.29945i	−0.760170	−	0.649724i	$-0.774885\pi$
$587$		−	447749.i		−	1.29945i	0.760170	−	0.649724i	$-0.225115\pi$
$588$	85118.1	−	419051.i	0.246188	−	1.21203i
$589$	−193918.			−0.558968
$590$	233361.			0.670386
$591$	−215357.	−	43743.5i	−0.616572	−	0.125239i
$592$			53640.0i			0.153054i
$593$			31495.2i			0.0895644i	0.998997	+	0.0447822i	$0.0142594\pi$
$593$			31495.2i			0.0895644i	−0.998997	+	0.0447822i	$0.985741\pi$
$594$	102706.	−	149744.i	0.291087	−	0.424401i
$595$		−	659421.i		−	1.86264i
$596$		−	69306.8i		−	0.195112i
$597$	−101564.	+	500015.i	−0.284963	+	1.40293i
$598$			2696.60i			0.00754073i
$599$	112532.			0.313632			0.156816	−	0.987628i	$-0.449877\pi$
$599$	112532.			0.313632			0.156816	+	0.987628i	$0.449877\pi$
$600$	−47646.3	+	234571.i	−0.132351	+	0.651586i
$601$			201583.i			0.558092i	0.960278	+	0.279046i	$0.0900182\pi$
$601$			201583.i			0.558092i	−0.960278	+	0.279046i	$0.909982\pi$
$602$			147065.i			0.405805i
$603$	−10018.2	−	4244.97i	−0.0275522	−	0.0116745i
$604$	−269337.			−0.738281
$605$		−	670753.i		−	1.83253i
$606$	−11411.6	+	56181.5i	−0.0310744	+	0.152985i
$607$		−	221596.i		−	0.601429i	−0.953714	−	0.300714i	$-0.902775\pi$
$607$		−	221596.i		−	0.601429i	0.953714	−	0.300714i	$-0.0972251\pi$
$608$		−	171622.i		−	0.464266i
$609$	539076.	+	198456.i	1.45350	+	0.535094i
$610$	286924.			0.771093
$611$	−27061.7			−0.0724891
$612$	256925.	+	108865.i	0.685969	+	0.290661i
$613$	−213080.			−0.567049			−0.283525	−	0.958965i	$-0.591504\pi$
$613$	−213080.			−0.567049			−0.283525	+	0.958965i	$0.591504\pi$
$614$			8401.75i			0.0222860i
$615$	−862607.	−	175214.i	−2.28067	−	0.463252i
$616$	−569857.			−1.50177
$617$	224424.			0.589522			0.294761	−	0.955571i	$-0.404760\pi$
$617$	224424.			0.589522			0.294761	+	0.955571i	$0.404760\pi$
$618$	−12978.2	+	63893.9i	−0.0339811	+	0.167295i
$619$			124945.i			0.326091i	0.986619	+	0.163045i	$0.0521317\pi$
$619$			124945.i			0.326091i	−0.986619	+	0.163045i	$0.947868\pi$
$620$	506904.			1.31869
$621$	−86488.7	−	59320.6i	−0.224273	−	0.153823i
$622$	36122.7			0.0933683
$623$	−83014.2			−0.213883
$624$	4200.85	−	20681.5i	0.0107887	−	0.0531145i
$625$	−375892.			−0.962282
$626$	−90328.0			−0.230501
$627$	311367.	+	63245.1i	0.792022	+	0.160876i
$628$		−	391749.i		−	0.993318i
$629$			76669.0i			0.193784i
$630$	−116543.	+	275045.i	−0.293633	+	0.692983i
$631$	541414.			1.35979			0.679893	−	0.733312i	$-0.262026\pi$
$631$	541414.			1.35979			0.679893	+	0.733312i	$0.262026\pi$
$632$		−	462989.i		−	1.15914i
$633$	342979.	+	69666.2i	0.855973	+	0.173866i
$634$	166480.			0.414175
$635$	105304.			0.261156
$636$	−362217.	−	73573.8i	−0.895477	−	0.181890i
$637$	−46224.8			−0.113919
$638$	31790.7	−	207052.i	0.0781013	−	0.508672i
$639$	−193974.	+	457784.i	−0.475053	+	1.12114i
$640$			581099.i			1.41870i
$641$	−350348.			−0.852674			−0.426337	−	0.904564i	$-0.640196\pi$
$641$	−350348.			−0.852674			−0.426337	+	0.904564i	$0.640196\pi$
$642$	99850.9	+	20281.8i	0.242260	+	0.0492081i
$643$	−20695.6			−0.0500560			−0.0250280	−	0.999687i	$-0.507967\pi$
$643$	−20695.6			−0.0500560			−0.0250280	+	0.999687i	$0.507967\pi$
$644$			154440.i			0.372383i
$645$	−90927.3	+	447651.i	−0.218562	+	1.07602i
$646$		−	64037.6i		−	0.153451i
$647$		−	102590.i		−	0.245073i	−0.992464	−	0.122537i	$-0.960897\pi$
$647$		−	102590.i		−	0.245073i	0.992464	−	0.122537i	$-0.0391029\pi$
$648$	−187378.	−	193542.i	−0.446241	−	0.460921i
$649$			878240.i			2.08509i
$650$	12141.3			0.0287369
$651$	672405.	+	136580.i	1.58661	+	0.322273i
$652$		−	590092.i		−	1.38811i
$653$	−125065.			−0.293298			−0.146649	−	0.989189i	$-0.546849\pi$
$653$	−125065.			−0.293298			−0.146649	+	0.989189i	$0.546849\pi$
$654$	47976.7	−	236198.i	0.112170	−	0.552230i
$655$			869099.i			2.02575i
$656$	−467122.			−1.08548
$657$	121755.	−	287346.i	0.282070	−	0.665694i
$658$	203278.			0.469504
$659$	−68769.7			−0.158353			−0.0791765	−	0.996861i	$-0.525229\pi$
$659$	−68769.7			−0.158353			−0.0791765	+	0.996861i	$0.525229\pi$
$660$	−813918.	−	165324.i	−1.86850	−	0.379531i
$661$	394976.			0.903998			0.451999	−	0.892018i	$-0.350711\pi$
$661$	394976.			0.903998			0.451999	+	0.892018i	$0.350711\pi$
$662$		−	129183.i		−	0.294774i
$663$	6004.38	−	29560.6i	0.0136597	−	0.0672491i
$664$			10902.9i			0.0247291i
$665$	−522686.			−1.18195
$666$	13550.1	−	31978.7i	0.0305488	−	0.0720961i
$667$	−119589.	−	18361.6i	−0.268806	−	0.0412723i
$668$		−	491120.i		−	1.10061i
$669$	4916.34	−	24204.0i	0.0109847	−	0.0540798i
$670$		−	6527.21i		−	0.0145405i
$671$			1.07982e6i			2.39831i
$672$	−120877.	+	595097.i	−0.267673	+	1.31780i
$673$	474542.			1.04772			0.523860	−	0.851805i	$-0.324492\pi$
$673$	474542.			1.04772			0.523860	+	0.851805i	$0.324492\pi$
$674$			124258.i			0.273530i
$675$	−267089.	+	389413.i	−0.586204	+	0.854679i
$676$	401311.			0.878189
$677$	−472531.			−1.03099			−0.515493	−	0.856894i	$-0.672391\pi$
$677$	−472531.			−1.03099			−0.515493	+	0.856894i	$0.672391\pi$
$678$	−36430.7	+	179354.i	−0.0792515	+	0.390169i
$679$		−	851903.i		−	1.84778i
$680$			356746.i			0.771509i
$681$	43661.6	+	8868.59i	0.0941469	+	0.0191232i
$682$		−	250208.i		−	0.537938i
$683$			230478.i			0.494069i	0.969007	+	0.247035i	$0.0794561\pi$
$683$			230478.i			0.494069i	−0.969007	+	0.247035i	$0.920544\pi$
$684$	86291.5	−	203650.i	0.184440	−	0.435284i
$685$			693070.i			1.47705i
$686$	99028.1			0.210431
$687$	−492070.	−	99949.8i	−1.04259	−	0.211772i
$688$			242413.i			0.512129i
$689$			39955.5i			0.0841663i
$690$	12523.8	−	61656.9i	0.0263050	−	0.129504i
$691$	−185295.			−0.388067			−0.194034	−	0.980995i	$-0.562157\pi$
$691$	−185295.			−0.388067			−0.194034	+	0.980995i	$0.562157\pi$
$692$			420770.i			0.878683i
$693$	−1.03511e6	−	438602.i	−2.15537	−	0.913281i
$694$		−	266293.i		−	0.552893i
$695$		−	288701.i		−	0.597693i
$696$	−291639.	−	107365.i	−0.602043	−	0.221637i
$697$	−667668.			−1.37434
$698$	−217086.			−0.445576
$699$	−905953.	−	184018.i	−1.85418	−	0.376622i
$700$	695364.			1.41911
$701$		−	536002.i		−	1.09076i	−0.838188	−	0.545381i	$-0.816385\pi$
$701$		−	536002.i		−	1.09076i	0.838188	−	0.545381i	$-0.183615\pi$
$702$	−7728.84	+	11268.6i	−0.0156834	+	0.0228662i
$703$	60771.2			0.122967
$704$	−277122.			−0.559147
$705$	618758.	+	125683.i	1.24492	+	0.252870i
$706$			185274.i			0.371710i
$707$	354933.			0.710081
$708$	599135.	+	121697.i	1.19525	+	0.242780i
$709$	−236313.			−0.470106			−0.235053	−	0.971983i	$-0.575526\pi$
$709$	−236313.			−0.470106			−0.235053	+	0.971983i	$0.575526\pi$
$710$	−298262.			−0.591672
$711$	356349.	−	840993.i	0.704915	−	1.66362i
$712$	44910.6			0.0885908
$713$	−144514.			−0.284271
$714$	−45102.9	+	222049.i	−0.0884724	+	0.435565i
$715$			89781.8i			0.175621i
$716$		−	636321.i		−	1.24122i
$717$	321854.	+	65375.3i	0.626067	+	0.127167i
$718$	−155899.			−0.302408
$719$		−	711787.i		−	1.37687i	−0.725299	−	0.688434i	$-0.758299\pi$
$719$		−	711787.i		−	1.37687i	0.725299	−	0.688434i	$-0.241701\pi$
$720$	−192103.	+	453367.i	−0.370568	+	0.874551i
$721$	403657.			0.776501
$722$	126745.			0.243140
$723$	−50926.1	+	250718.i	−0.0974236	+	0.479633i
$724$	−229963.			−0.438713
$725$	−82672.5	+	538444.i	−0.157284	+	1.02439i
$726$	−45877.9	+	225865.i	−0.0870424	+	0.428525i
$727$			61413.5i			0.116197i	0.998311	+	0.0580985i	$0.0185038\pi$
$727$			61413.5i			0.116197i	−0.998311	+	0.0580985i	$0.981496\pi$
$728$	42883.0			0.0809138
$729$	−191398.	−	495778.i	−0.360150	−	0.932895i
$730$	187215.			0.351314
$731$			346487.i			0.648414i
$732$	736652.	+	149629.i	1.37480	+	0.279251i
$733$			347280.i			0.646355i	0.946338	+	0.323178i	$0.104751\pi$
$733$			347280.i			0.646355i	−0.946338	+	0.323178i	$0.895249\pi$
$734$			204256.i			0.379125i
$735$	1.05692e6	+	214682.i	1.95644	+	0.397394i
$736$		−	127899.i		−	0.236109i
$737$	24564.7			0.0452249
$738$	278485.	+	118001.i	0.511315	+	0.216657i
$739$		−	68601.3i		−	0.125616i	−0.998026	−	0.0628078i	$-0.979994\pi$
$739$		−	68601.3i		−	0.125616i	0.998026	−	0.0628078i	$-0.0200055\pi$
$740$	−158857.			−0.290096
$741$	−23431.0	−	4759.33i	−0.0426732	−	0.00866782i
$742$		−	300132.i		−	0.545136i
$743$	−358973.			−0.650255			−0.325127	−	0.945670i	$-0.605407\pi$
$743$	−358973.			−0.650255			−0.325127	+	0.945670i	$0.605407\pi$
$744$	−363770.	−	73889.4i	−0.657176	−	0.133486i
$745$	174803.			0.314947
$746$	234285.			0.420984
$747$	−8391.67	+	19804.6i	−0.0150386	+	0.0354915i
$748$	−629982.			−1.12596
$749$		−	630819.i		−	1.12445i
$750$	−9748.26	−	1980.08i	−0.0173302	−	0.00352014i
$751$		−	689652.i		−	1.22278i	−0.791328	−	0.611392i	$-0.790610\pi$
$751$		−	689652.i		−	1.22278i	0.791328	−	0.611392i	$-0.209390\pi$
$752$	335072.			0.592519
$753$	179673.	−	884562.i	0.316879	−	1.56005i
$754$	−2392.32	+	15581.1i	−0.00420800	+	0.0274067i
$755$		−	679312.i		−	1.19172i
$756$	−442649.	+	645377.i	−0.774490	+	1.12920i
$757$		−	163123.i		−	0.284657i	−0.989819	−	0.142329i	$-0.954541\pi$
$757$		−	163123.i		−	0.284657i	0.989819	−	0.142329i	$-0.0454590\pi$
$758$			19052.8i			0.0331605i
$759$	232042.	+	47132.5i	0.402794	+	0.0818158i
$760$	282772.			0.489564
$761$			393303.i			0.679139i	0.940581	+	0.339569i	$0.110281\pi$
$761$			393303.i			0.679139i	−0.940581	+	0.339569i	$0.889719\pi$
$762$	−35459.6	−	7202.58i	−0.0610694	−	0.0124045i
$763$	−1.49221e6			−2.56318
$764$	147814.			0.253238
$765$	−274577.	+	648009.i	−0.469182	+	1.10728i
$766$			254101.i			0.433060i
$767$		−	66089.5i		−	0.112342i
$768$	−3691.25	+	18172.7i	−0.00625823	+	0.0308103i
$769$			486149.i			0.822085i	0.911616	+	0.411042i	$0.134835\pi$
$769$			486149.i			0.822085i	−0.911616	+	0.411042i	$0.865165\pi$
$770$		−	674411.i		−	1.13748i
$771$	528510.	+	107351.i	0.889087	+	0.180592i
$772$			753410.i			1.26414i
$773$	−420711.			−0.704085			−0.352042	−	0.935984i	$-0.614513\pi$
$773$	−420711.			−0.704085			−0.352042	+	0.935984i	$0.614513\pi$
$774$	61236.6	−	144520.i	0.102218	−	0.241238i
$775$			650672.i			1.08332i
$776$			460879.i			0.765355i
$777$	−210723.	−	42802.2i	−0.349035	−	0.0708964i
$778$	14719.7			0.0243187
$779$			529223.i			0.872095i
$780$	61249.1	+	12441.0i	0.100672	+	0.0204487i
$781$		−	1.12249e6i		−	1.84026i
$782$		−	47723.2i		−	0.0780397i
$783$	−447111.	−	419488.i	−0.729276	−	0.684220i
$784$	572345.			0.931163
$785$	988055.			1.60340
$786$	59444.4	−	292655.i	0.0962201	−	0.473708i
$787$	−387504.			−0.625643			−0.312822	−	0.949812i	$-0.601274\pi$
$787$	−387504.			−0.625643			−0.312822	+	0.949812i	$0.601274\pi$
$788$		−	345377.i		−	0.556212i
$789$	−43036.7	+	211877.i	−0.0691330	+	0.340354i
$790$	547935.			0.877960
$791$	1.13309e6			1.81097
$792$	559995.	+	237283.i	0.892758	+	0.378283i
$793$		−	81258.8i		−	0.129218i
$794$	−200859.			−0.318604
$795$	185565.	−	913571.i	0.293605	−	1.44547i
$796$	−801894.			−1.26558
$797$	−649072.			−1.02182			−0.510912	−	0.859633i	$-0.670692\pi$
$797$	−649072.			−1.02182			−0.510912	+	0.859633i	$0.670692\pi$
$798$	176006.	+	35750.5i	0.276389	+	0.0561405i
$799$	478926.			0.750197
$800$	−575862.			−0.899785
$801$	81577.5	+	34566.3i	0.127147	+	0.0538751i
$802$			285897.i			0.444489i
$803$			704573.i			1.09269i
$804$	3403.91	−	16758.1i	0.00526582	−	0.0259246i
$805$	−389524.			−0.601095
$806$			18828.7i			0.0289834i
$807$	−1958.07	+	9639.92i	−0.00300664	+	0.0148022i
$808$	−192018.			−0.294117
$809$	−285520.			−0.436254			−0.218127	−	0.975920i	$-0.569995\pi$
$809$	−285520.			−0.436254			−0.218127	+	0.975920i	$0.569995\pi$
$810$	229052.	−	221757.i	0.349112	−	0.337993i
$811$	−206731.			−0.314314			−0.157157	−	0.987574i	$-0.550233\pi$
$811$	−206731.			−0.314314			−0.157157	+	0.987574i	$0.550233\pi$
$812$	−137014.	+	892368.i	−0.207803	+	1.35342i
$813$	−455265.	−	92473.9i	−0.688784	−	0.139906i
$814$			78411.7i			0.118340i
$815$	1.48831e6			2.24067
$816$	−74344.8	+	366012.i	−0.111653	+	0.549687i
$817$	274641.			0.411454
$818$		−	364076.i		−	0.544108i
$819$	77894.5	+	33005.8i	0.116129	+	0.0492065i
$820$		−	1.38340e6i		−	2.05740i
$821$			542980.i			0.805559i	0.915297	+	0.402780i	$0.131956\pi$
$821$			542980.i			0.805559i	−0.915297	+	0.402780i	$0.868044\pi$
$822$	47404.4	−	233380.i	0.0701576	−	0.345398i
$823$		−	336410.i		−	0.496672i	−0.968674	−	0.248336i	$-0.920116\pi$
$823$		−	336410.i		−	0.496672i	0.968674	−	0.248336i	$-0.0798837\pi$
$824$	−218378.			−0.321628
$825$	212213.	−	1.04476e6i	0.311791	−	1.53500i
$826$			496442.i			0.727626i
$827$	795389.			1.16297			0.581485	−	0.813557i	$-0.302472\pi$
$827$	795389.			1.16297			0.581485	+	0.813557i	$0.302472\pi$
$828$	64307.6	−	151768.i	0.0937997	−	0.221370i
$829$		−	408766.i		−	0.594793i	−0.954754	−	0.297397i	$-0.903882\pi$
$829$		−	408766.i		−	0.594793i	0.954754	−	0.297397i	$-0.0961184\pi$
$830$	−12903.3			−0.0187304
$831$	−150038.	+	738663.i	−0.217270	+	1.06966i
$832$	20854.1			0.0301262
$833$	818066.			1.17896
$834$	−19746.5	+	97215.3i	−0.0283895	+	0.139766i
$835$	1.23869e6			1.77660
$836$			499351.i			0.714486i
$837$	−603898.	−	414199.i	−0.862010	−	0.591233i
$838$		−	38606.8i		−	0.0549764i
$839$	325659.			0.462635			0.231318	−	0.972878i	$-0.425696\pi$
$839$	325659.			0.462635			0.231318	+	0.972878i	$0.425696\pi$
$840$	−980508.	−	199162.i	−1.38961	−	0.282259i
$841$	−674702.	−	212189.i	−0.953937	−	0.300006i
$842$			265233.i			0.374113i
$843$	494036.	+	100349.i	0.695190	+	0.141208i
$844$			550049.i			0.772176i
$845$			1.01217e6i			1.41756i
$846$	−199760.	−	84643.3i	−0.279106	−	0.118264i
$847$	1.42693e6			1.98900
$848$		−	494719.i		−	0.687967i
$849$	194488.	−	957497.i	0.269822	−	1.32838i
$850$	−214872.			−0.297401
$851$	45288.9			0.0625363
$852$	−765761.	−	155542.i	−1.05491	−	0.214274i
$853$		−	660217.i		−	0.907378i	−0.891160	−	0.453689i	$-0.850108\pi$
$853$		−	660217.i		−	0.907378i	0.891160	−	0.453689i	$-0.149892\pi$
$854$			610388.i			0.836932i
$855$	513640.	+	217642.i	0.702630	+	0.297721i
$856$			341272.i			0.465751i
$857$			158040.i			0.215182i	0.994195	+	0.107591i	$0.0343137\pi$
$857$			158040.i			0.215182i	−0.994195	+	0.107591i	$0.965686\pi$
$858$	6140.87	−	30232.6i	0.00834171	−	0.0410677i
$859$			322395.i			0.436919i	0.975846	+	0.218460i	$0.0701032\pi$
$859$			322395.i			0.436919i	−0.975846	+	0.218460i	$0.929897\pi$
$860$	−717916.			−0.970681
$861$	372741.	−	1.83507e6i	0.502807	−	2.47541i
$862$			190418.i			0.256268i
$863$		−	682045.i		−	0.915781i	−0.889009	−	0.457891i	$-0.848605\pi$
$863$		−	682045.i		−	0.915781i	0.889009	−	0.457891i	$-0.151395\pi$
$864$	366578.	−	534466.i	0.491064	−	0.715966i
$865$	−1.06125e6			−1.41836
$866$			104733.i			0.139652i
$867$	43365.5	−	213496.i	0.0576907	−	0.284021i
$868$			1.07836e6i			1.43128i
$869$			2.06212e6i			2.73070i
$870$	127063.	−	345147.i	0.167873	−	0.456001i
$871$	−1848.55			−0.00243666
$872$	807281.			1.06168
$873$	−354725.	+	837160.i	−0.465439	+	1.09845i
$874$	−37827.5			−0.0495204
$875$			61585.7i			0.0804385i
$876$	480659.	+	97632.0i	0.626367	+	0.127228i
$877$	−142648.			−0.185466			−0.0927332	−	0.995691i	$-0.529560\pi$
$877$	−142648.			−0.185466			−0.0927332	+	0.995691i	$0.529560\pi$
$878$	234010.			0.303560
$879$	124885.	−	614830.i	0.161634	−	0.795751i
$880$		−	1.11166e6i		−	1.43551i
$881$	651206.			0.839009			0.419505	−	0.907753i	$-0.362204\pi$
$881$	651206.			0.839009			0.419505	+	0.907753i	$0.362204\pi$
$882$	−341216.	−	144581.i	−0.438624	−	0.185855i
$883$	204565.			0.262367			0.131183	−	0.991358i	$-0.458122\pi$
$883$	204565.			0.262367			0.131183	+	0.991358i	$0.458122\pi$
$884$	47407.5			0.0606656
$885$	−306940.	+	1.51112e6i	−0.391892	+	1.92935i
$886$	−289295.			−0.368531
$887$	387335.			0.492311			0.246156	−	0.969230i	$-0.420833\pi$
$887$	387335.			0.492311			0.246156	+	0.969230i	$0.420833\pi$
$888$	114001.	+	23155.9i	0.144571	+	0.0293654i
$889$			224020.i			0.283454i
$890$			53150.4i			0.0671007i
$891$	834569.	+	862023.i	1.05125	+	1.08583i
$892$	38816.9			0.0487856
$893$		−	379618.i		−	0.476040i
$894$	−58862.1	−	11956.1i	−0.0736480	−	0.0149595i
$895$	1.60491e6			2.00357
$896$	−1.23620e6			−1.53983
$897$	−17461.7	−	3546.83i	−0.0217020	−	0.00440814i
$898$	511912.			0.634808
$899$	−835014.	−	128208.i	−1.03318	−	0.158633i
$900$	−683329.	−	289543.i	−0.843616	−	0.357460i
$901$		−	707115.i		−	0.871044i
$902$	−682845.			−0.839285
$903$	−952312.	−	193435.i	−1.16789	−	0.237224i
$904$	−613001.			−0.750109
$905$		−	580004.i		−	0.708164i
$906$	−46463.3	+	228747.i	−0.0566049	+	0.278676i
$907$			470466.i			0.571892i	0.958246	+	0.285946i	$0.0923077\pi$
$907$			470466.i			0.571892i	−0.958246	+	0.285946i	$0.907692\pi$
$908$			70021.9i			0.0849302i
$909$	−348790.	−	147791.i	−0.422121	−	0.178863i
$910$			50750.9i			0.0612859i
$911$	1.62568e6			1.95883			0.979417	−	0.201848i	$-0.0646948\pi$
$911$	1.62568e6			1.95883			0.979417	+	0.201848i	$0.0646948\pi$
$912$	290117.	+	58928.9i	0.348806	+	0.0708499i
$913$		−	48560.9i		−	0.0582566i
$914$	390639.			0.467609
$915$	−377390.	+	1.85796e6i	−0.450763	+	2.21919i
$916$		−	789152.i		−	0.940524i
$917$	−1.84888e6			−2.19872
$918$	136782.	−	199426.i	0.162309	−	0.236644i
$919$	729069.			0.863253			0.431626	−	0.902053i	$-0.357940\pi$
$919$	729069.			0.863253			0.431626	+	0.902053i	$0.357940\pi$
$920$	210732.			0.248975
$921$	−54405.0	−	11050.8i	−0.0641386	−	0.0130279i
$922$	−92715.6			−0.109066
$923$			84469.7i			0.0991511i
$924$	351702.	−	1.73149e6i	0.411937	−	2.02804i
$925$		−	203912.i		−	0.238319i
$926$	88111.5			0.102757
$927$	−396671.	−	168079.i	−0.461605	−	0.195593i
$928$	113467.	−	739010.i	0.131757	−	0.858133i
$929$			583266.i			0.675827i	0.941177	+	0.337914i	$0.109721\pi$
$929$			583266.i			0.675827i	−0.941177	+	0.337914i	$0.890279\pi$
$930$	87446.1	−	430512.i	0.101105	−	0.497760i
$931$		−	648435.i		−	0.748113i
$932$		−	1.45291e6i		−	1.67266i
$933$	−47512.1	+	233910.i	−0.0545809	+	0.268711i
$934$	−306338.			−0.351162
$935$		−	1.58892e6i		−	1.81752i
$936$	−42140.9	−	17856.1i	−0.0481007	−	0.0203814i
$937$	−1.13702e6			−1.29506			−0.647529	−	0.762041i	$-0.724198\pi$
$937$	−1.13702e6			−1.29506			−0.647529	+	0.762041i	$0.724198\pi$
$938$	13885.7			0.0157820
$939$	118808.	−	584913.i	0.134746	−	0.663377i
$940$			992327.i			1.12305i
$941$		−	581978.i		−	0.657245i	−0.944461	−	0.328623i	$-0.893416\pi$
$941$		−	581978.i		−	0.657245i	0.944461	−	0.328623i	$-0.106584\pi$
$942$	−332712.	−	67580.7i	−0.374944	−	0.0761589i
$943$			394396.i			0.443516i
$944$			818305.i			0.918271i
$945$	−1.62775e6	−	1.11643e6i	−1.82273	−	1.25017i
$946$			354363.i			0.395974i
$947$	−400856.			−0.446981			−0.223490	−	0.974706i	$-0.571745\pi$
$947$	−400856.			−0.446981			−0.223490	+	0.974706i	$0.571745\pi$
$948$	1.40678e6	+	285746.i	1.56534	+	0.317953i
$949$		−	53020.7i		−	0.0588726i
$950$			170317.i			0.188717i
$951$	−218971.	+	1.07803e6i	−0.242117	+	1.19199i
$952$	−758924.			−0.837384
$953$			305454.i			0.336326i	0.985759	+	0.168163i	$0.0537834\pi$
$953$			305454.i			0.336326i	−0.985759	+	0.168163i	$0.946217\pi$
$954$	−124972.	+	294938.i	−0.137315	+	0.324066i
$955$			372812.i			0.408774i
$956$			516170.i			0.564777i
$957$	1.29894e6	+	478194.i	1.41829	+	0.522131i
$958$	131220.			0.142978
$959$	−1.47440e6			−1.60317
$960$	−476822.	−	96852.6i	−0.517385	−	0.105092i
$961$	−85534.7			−0.0926180
$962$		−	5900.66i		−	0.00637603i
$963$	−262667.	+	619902.i	−0.283239	+	0.668452i
$964$	−402087.			−0.432679
$965$	−1.90022e6			−2.04056
$966$	131166.	+	26642.6i	0.140562	+	0.0285510i
$967$			125843.i			0.134578i	0.997734	+	0.0672891i	$0.0214350\pi$
$967$			125843.i			0.134578i	−0.997734	+	0.0672891i	$0.978565\pi$
$968$	−771967.			−0.823849
$969$	414672.	+	84228.6i	0.441628	+	0.0897040i
$970$	−545437.			−0.579697
$971$	−873471.			−0.926424			−0.463212	−	0.886247i	$-0.653303\pi$
$971$	−873471.			−0.926424			−0.463212	+	0.886247i	$0.653303\pi$
$972$	703717.	−	449893.i	0.744844	−	0.476186i
$973$	614168.			0.648727
$974$	−302213.			−0.318563
$975$	−15969.5	+	78620.6i	−0.0167989	+	0.0827041i
$976$			1.00613e6i			1.05622i
$977$			557751.i			0.584321i	0.956369	+	0.292160i	$0.0943741\pi$
$977$			557751.i			0.584321i	−0.956369	+	0.292160i	$0.905626\pi$
$978$	−501164.	−	101797.i	−0.523965	−	0.106428i
$979$	−200028.			−0.208702
$980$			1.69502e6i			1.76491i
$981$	1.46638e6	+	621341.i	1.52373	+	0.645642i
$982$	121893.			0.126403
$983$	794671.			0.822395			0.411197	−	0.911546i	$-0.365111\pi$
$983$	794671.			0.822395			0.411197	+	0.911546i	$0.365111\pi$
$984$	−201653.	+	992771.i	−0.208264	+	1.02532i
$985$	871097.			0.897830
$986$	42338.2	−	275748.i	0.0435490	−	0.283634i
$987$	−267372.	+	1.31632e6i	−0.274461	+	1.35122i
$988$		−	37577.3i		−	0.0384956i
$989$	204672.			0.209251
$990$	−280818.	+	662739.i	−0.286520	+	0.676195i
$991$	276418.			0.281462			0.140731	−	0.990048i	$-0.455055\pi$
$991$	276418.			0.281462			0.140731	+	0.990048i	$0.455055\pi$
$992$		−	893041.i		−	0.907503i
$993$	836518.	+	169914.i	0.848353	+	0.172318i
$994$		−	634508.i		−	0.642191i
$995$		−	2.02251e6i		−	2.04289i
$996$	−33128.2	−	6729.03i	−0.0333948	−	0.00678319i
$997$			1.39752e6i			1.40595i	0.711217	+	0.702973i	$0.248144\pi$
$997$			1.39752e6i			1.40595i	−0.711217	+	0.702973i	$0.751856\pi$
$998$	453275.			0.455094
$999$	189253.	+	129804.i	0.189633	+	0.130064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.5.d.c.86.20	yes	32
3.2	odd	2	inner	87.5.d.c.86.14	yes	32
29.28	even	2	inner	87.5.d.c.86.13	✓	32
87.86	odd	2	inner	87.5.d.c.86.19	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.5.d.c.86.13	✓	32	29.28	even	2	inner
87.5.d.c.86.14	yes	32	3.2	odd	2	inner
87.5.d.c.86.19	yes	32	87.86	odd	2	inner
87.5.d.c.86.20	yes	32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	87.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.36205 q^{2} +(-1.79151 + 8.81989i) q^{3} -14.1448 q^{4} -35.6756i q^{5} +(-2.44013 + 12.0132i) q^{6} +75.8945 q^{7} -41.0588 q^{8} +(-74.5810 - 31.6018i) q^{9} -48.5920i q^{10} +182.873 q^{11} +(25.3405 - 124.756i) q^{12} -13.7616 q^{13} +103.372 q^{14} +(314.655 + 63.9130i) q^{15} +170.393 q^{16} +243.546 q^{17} +(-101.583 - 43.0433i) q^{18} -193.045i q^{19} +504.624i q^{20} +(-135.965 + 669.381i) q^{21} +249.083 q^{22} -143.864i q^{23} +(73.5571 - 362.135i) q^{24} -647.746 q^{25} -18.7440 q^{26} +(412.336 - 601.182i) q^{27} -1073.51 q^{28} +(127.631 - 831.259i) q^{29} +(428.576 + 87.0528i) q^{30} -1004.52i q^{31} +889.025 q^{32} +(-327.618 + 1612.92i) q^{33} +331.723 q^{34} -2707.58i q^{35} +(1054.93 + 447.001i) q^{36} +314.802i q^{37} -262.938i q^{38} +(24.6539 - 121.376i) q^{39} +1464.80i q^{40} -2741.44 q^{41} +(-185.192 + 911.733i) q^{42} +1422.67i q^{43} -2586.70 q^{44} +(-1127.41 + 2660.72i) q^{45} -195.951i q^{46} +1966.47 q^{47} +(-305.259 + 1502.85i) q^{48} +3358.98 q^{49} -882.264 q^{50} +(-436.315 + 2148.05i) q^{51} +194.655 q^{52} -2903.41i q^{53} +(561.624 - 818.842i) q^{54} -6524.09i q^{55} -3116.14 q^{56} +(1702.64 + 345.842i) q^{57} +(173.840 - 1132.22i) q^{58} +4802.46i q^{59} +(-4450.73 - 904.037i) q^{60} +5904.75i q^{61} -1368.21i q^{62} +(-5660.29 - 2398.40i) q^{63} -1515.38 q^{64} +490.952i q^{65} +(-446.233 + 2196.88i) q^{66} +134.327 q^{67} -3444.92 q^{68} +(1268.87 + 257.734i) q^{69} -3687.87i q^{70} -6138.08i q^{71} +(3062.21 + 1297.53i) q^{72} +3852.80i q^{73} +428.777i q^{74} +(1160.44 - 5713.05i) q^{75} +2730.59i q^{76} +13879.0 q^{77} +(33.5800 - 165.320i) q^{78} +11276.2i q^{79} -6078.85i q^{80} +(4563.66 + 4713.78i) q^{81} -3733.99 q^{82} -265.544i q^{83} +(1923.20 - 9468.27i) q^{84} -8688.65i q^{85} +1937.76i q^{86} +(7102.96 + 2614.90i) q^{87} -7508.55 q^{88} -1093.81 q^{89} +(-1535.59 + 3624.04i) q^{90} -1044.43 q^{91} +2034.94i q^{92} +(8859.74 + 1799.60i) q^{93} +2678.43 q^{94} -6887.01 q^{95} +(-1592.69 + 7841.11i) q^{96} -11224.8i q^{97} +4575.10 q^{98} +(-13638.8 - 5779.10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 188 q^{4} - 36 q^{6} - 84 q^{7} - 452 q^{9} - 224 q^{13} - 52 q^{16} - 4216 q^{22} - 832 q^{24} - 7684 q^{25} - 396 q^{28} + 3384 q^{30} - 3308 q^{33} + 9124 q^{34} - 3680 q^{36} + 19764 q^{42} + 44 q^{45}+ \cdots + 13884 q^{96}+O(q^{100}) \) 32 * q + 188 * q^4 - 36 * q^6 - 84 * q^7 - 452 * q^9 - 224 * q^13 - 52 * q^16 - 4216 * q^22 - 832 * q^24 - 7684 * q^25 - 396 * q^28 + 3384 * q^30 - 3308 * q^33 + 9124 * q^34 - 3680 * q^36 + 19764 * q^42 + 44 * q^45 + 4796 * q^49 - 7052 * q^51 + 34048 * q^52 + 3008 * q^54 + 7976 * q^57 + 5936 * q^58 - 22848 * q^63 - 14668 * q^64 - 1872 * q^67 + 15192 * q^78 - 41088 * q^81 - 27028 * q^82 - 35572 * q^87 - 60032 * q^88 - 34272 * q^91 + 38000 * q^93 + 59636 * q^94 + 13884 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more