LMFDB - Embedded newform 51.5.f.a.38.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,5,Mod(38,51)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("51.38");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, 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:	$5.27186811728$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.12
Character	$\chi$	$=$	51.38
Dual form			51.5.f.a.47.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.828441 q^{2} +(-2.62611 - 8.60834i) q^{3} -15.3137 q^{4} +(20.1408 + 20.1408i) q^{5} +(-2.17558 - 7.13150i) q^{6} +(-53.5715 - 53.5715i) q^{7} -25.9415 q^{8} +(-67.2071 + 45.2130i) q^{9} +O(q^{10})$	\(q+0.828441 q^{2} +(-2.62611 - 8.60834i) q^{3} -15.3137 q^{4} +(20.1408 + 20.1408i) q^{5} +(-2.17558 - 7.13150i) q^{6} +(-53.5715 - 53.5715i) q^{7} -25.9415 q^{8} +(-67.2071 + 45.2130i) q^{9} +(16.6854 + 16.6854i) q^{10} +(-100.205 + 100.205i) q^{11} +(40.2155 + 131.825i) q^{12} -222.805 q^{13} +(-44.3808 - 44.3808i) q^{14} +(120.487 - 226.270i) q^{15} +223.528 q^{16} +(244.844 - 153.534i) q^{17} +(-55.6770 + 37.4563i) q^{18} -301.035i q^{19} +(-308.429 - 308.429i) q^{20} +(-320.477 + 601.847i) q^{21} +(-83.0135 + 83.0135i) q^{22} +(250.211 - 250.211i) q^{23} +(68.1254 + 223.313i) q^{24} +186.300i q^{25} -184.581 q^{26} +(565.702 + 459.807i) q^{27} +(820.378 + 820.378i) q^{28} +(-606.711 - 606.711i) q^{29} +(99.8159 - 187.452i) q^{30} +(377.336 - 377.336i) q^{31} +600.244 q^{32} +(1125.74 + 599.446i) q^{33} +(202.838 - 127.194i) q^{34} -2157.94i q^{35} +(1029.19 - 692.377i) q^{36} +(-993.473 + 993.473i) q^{37} -249.389i q^{38} +(585.112 + 1917.98i) q^{39} +(-522.482 - 522.482i) q^{40} +(-2098.29 + 2098.29i) q^{41} +(-265.496 + 498.594i) q^{42} -2576.64i q^{43} +(1534.50 - 1534.50i) q^{44} +(-2264.22 - 442.977i) q^{45} +(207.285 - 207.285i) q^{46} +1312.90i q^{47} +(-587.010 - 1924.20i) q^{48} +3338.82i q^{49} +154.338i q^{50} +(-1964.66 - 1704.50i) q^{51} +3411.97 q^{52} +484.122 q^{53} +(468.650 + 380.923i) q^{54} -4036.39 q^{55} +(1389.73 + 1389.73i) q^{56} +(-2591.41 + 790.551i) q^{57} +(-502.624 - 502.624i) q^{58} -1098.10 q^{59} +(-1845.09 + 3465.03i) q^{60} +(-544.654 - 544.654i) q^{61} +(312.600 - 312.600i) q^{62} +(6022.51 + 1178.26i) q^{63} -3079.18 q^{64} +(-4487.47 - 4487.47i) q^{65} +(932.611 + 496.605i) q^{66} -632.034 q^{67} +(-3749.46 + 2351.17i) q^{68} +(-2810.99 - 1496.82i) q^{69} -1787.73i q^{70} +(553.953 + 553.953i) q^{71} +(1743.45 - 1172.89i) q^{72} +(4527.21 - 4527.21i) q^{73} +(-823.033 + 823.033i) q^{74} +(1603.73 - 489.244i) q^{75} +4609.95i q^{76} +10736.2 q^{77} +(484.731 + 1588.94i) q^{78} +(-4286.76 - 4286.76i) q^{79} +(4502.02 + 4502.02i) q^{80} +(2472.58 - 6077.26i) q^{81} +(-1738.31 + 1738.31i) q^{82} -919.663 q^{83} +(4907.68 - 9216.50i) q^{84} +(8023.62 + 1839.05i) q^{85} -2134.59i q^{86} +(-3629.49 + 6816.07i) q^{87} +(2599.46 - 2599.46i) q^{88} +4806.29i q^{89} +(-1875.77 - 366.980i) q^{90} +(11936.0 + 11936.0i) q^{91} +(-3831.66 + 3831.66i) q^{92} +(-4239.16 - 2257.31i) q^{93} +1087.66i q^{94} +(6063.06 - 6063.06i) q^{95} +(-1576.31 - 5167.11i) q^{96} +(-5426.61 + 5426.61i) q^{97} +2766.01i q^{98} +(2203.91 - 11265.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7}+O(q^{10}) $ 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7	$ 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7} + 288 q^{10} - 234 q^{12} + 92 q^{13} + 960 q^{16} - 580 q^{18} - 1856 q^{21} + 120 q^{22} - 10 q^{24} + 378 q^{27} + 1648 q^{28} - 1248 q^{30} + 808 q^{31} + 2520 q^{33} - 5016 q^{34} - 5560 q^{37} + 152 q^{39} - 7020 q^{40} - 2696 q^{45} - 6620 q^{46} - 926 q^{48} + 11810 q^{51} + 5504 q^{52} + 6250 q^{54} + 9740 q^{55} + 16704 q^{57} + 4316 q^{58} + 9304 q^{61} + 27608 q^{63} - 6176 q^{64} + 23912 q^{67} - 3444 q^{69} - 54204 q^{72} + 14216 q^{73} - 5242 q^{75} - 25516 q^{78} + 4052 q^{79} + 6796 q^{81} + 14708 q^{82} - 59208 q^{84} - 32480 q^{85} - 28412 q^{88} - 21312 q^{90} - 38772 q^{91} - 56806 q^{96} - 92448 q^{97} - 18072 q^{99}+O(q^{100}) $ 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7 + 288 * q^10 - 234 * q^12 + 92 * q^13 + 960 * q^16 - 580 * q^18 - 1856 * q^21 + 120 * q^22 - 10 * q^24 + 378 * q^27 + 1648 * q^28 - 1248 * q^30 + 808 * q^31 + 2520 * q^33 - 5016 * q^34 - 5560 * q^37 + 152 * q^39 - 7020 * q^40 - 2696 * q^45 - 6620 * q^46 - 926 * q^48 + 11810 * q^51 + 5504 * q^52 + 6250 * q^54 + 9740 * q^55 + 16704 * q^57 + 4316 * q^58 + 9304 * q^61 + 27608 * q^63 - 6176 * q^64 + 23912 * q^67 - 3444 * q^69 - 54204 * q^72 + 14216 * q^73 - 5242 * q^75 - 25516 * q^78 + 4052 * q^79 + 6796 * q^81 + 14708 * q^82 - 59208 * q^84 - 32480 * q^85 - 28412 * q^88 - 21312 * q^90 - 38772 * q^91 - 56806 * q^96 - 92448 * q^97 - 18072 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.828441			0.207110			0.103555	−	0.994624i	$-0.466978\pi$
$2$	0.828441			0.207110			0.103555	+	0.994624i	$0.466978\pi$
$3$	−2.62611	−	8.60834i	−0.291790	−	0.956482i
$3$	−2.62611	−	8.60834i	−0.291790	−	0.956482i
$4$	−15.3137			−0.957105
$5$	20.1408	+	20.1408i	0.805630	+	0.805630i	0.983969	−	0.178339i	$-0.0570724\pi$
$5$	20.1408	+	20.1408i	0.805630	+	0.805630i	−0.178339	+	0.983969i	$0.557072\pi$
$6$	−2.17558	−	7.13150i	−0.0604328	−	0.198097i
$7$	−53.5715	−	53.5715i	−1.09330	−	1.09330i	−0.995174	−	0.0981222i	$-0.968716\pi$
$7$	−53.5715	−	53.5715i	−1.09330	−	1.09330i	−0.0981222	−	0.995174i	$-0.531284\pi$
$8$	−25.9415			−0.405336
$9$	−67.2071	+	45.2130i	−0.829717	+	0.558185i
$10$	16.6854	+	16.6854i	0.166854	+	0.166854i
$11$	−100.205	+	100.205i	−0.828137	+	0.828137i	−0.987259	−	0.159122i	$-0.949134\pi$
$11$	−100.205	+	100.205i	−0.828137	+	0.828137i	0.159122	+	0.987259i	$0.449134\pi$
$12$	40.2155	+	131.825i	0.279274	+	0.915454i
$13$	−222.805			−1.31837			−0.659187	−	0.751979i	$-0.729100\pi$
$13$	−222.805			−1.31837			−0.659187	+	0.751979i	$0.729100\pi$
$14$	−44.3808	−	44.3808i	−0.226433	−	0.226433i
$15$	120.487	−	226.270i	0.535496	−	1.00565i
$16$	223.528			0.873156
$17$	244.844	−	153.534i	0.847210	−	0.531259i
$17$	244.844	−	153.534i	0.847210	−	0.531259i
$18$	−55.6770	+	37.4563i	−0.171843	+	0.115606i
$19$		−	301.035i		−	0.833891i	−0.908931	−	0.416946i	$-0.863101\pi$
$19$		−	301.035i		−	0.833891i	0.908931	−	0.416946i	$-0.136899\pi$
$20$	−308.429	−	308.429i	−0.771073	−	0.771073i
$21$	−320.477	+	601.847i	−0.726705	+	1.36473i
$22$	−83.0135	+	83.0135i	−0.171515	+	0.171515i
$23$	250.211	−	250.211i	0.472989	−	0.472989i	−0.429891	−	0.902881i	$-0.641448\pi$
$23$	250.211	−	250.211i	0.472989	−	0.472989i	0.902881	+	0.429891i	$0.141448\pi$
$24$	68.1254	+	223.313i	0.118273	+	0.387697i
$25$			186.300i			0.298079i
$26$	−184.581			−0.273049
$27$	565.702	+	459.807i	0.775997	+	0.630736i
$28$	820.378	+	820.378i	1.04640	+	1.04640i
$29$	−606.711	−	606.711i	−0.721417	−	0.721417i	0.247477	−	0.968894i	$-0.420399\pi$
$29$	−606.711	−	606.711i	−0.721417	−	0.721417i	−0.968894	+	0.247477i	$0.920399\pi$
$30$	99.8159	−	187.452i	0.110907	−	0.208279i
$31$	377.336	−	377.336i	0.392649	−	0.392649i	−0.482982	−	0.875630i	$-0.660446\pi$
$31$	377.336	−	377.336i	0.392649	−	0.392649i	0.875630	+	0.482982i	$0.160446\pi$
$32$	600.244			0.586176
$33$	1125.74	+	599.446i	1.03374	+	0.550456i
$34$	202.838	−	127.194i	0.175466	−	0.110029i
$35$		−	2157.94i		−	1.76159i
$36$	1029.19	−	692.377i	0.794126	−	0.534242i
$37$	−993.473	+	993.473i	−0.725693	+	0.725693i	−0.969759	−	0.244066i	$-0.921519\pi$
$37$	−993.473	+	993.473i	−0.725693	+	0.725693i	0.244066	+	0.969759i	$0.421519\pi$
$38$		−	249.389i		−	0.172707i
$39$	585.112	+	1917.98i	0.384689	+	1.26100i
$40$	−522.482	−	522.482i	−0.326551	−	0.326551i
$41$	−2098.29	+	2098.29i	−1.24824	+	1.24824i	−0.291744	+	0.956497i	$0.594235\pi$
$41$	−2098.29	+	2098.29i	−1.24824	+	1.24824i	−0.956497	+	0.291744i	$0.905765\pi$
$42$	−265.496	+	498.594i	−0.150508	+	0.282650i
$43$		−	2576.64i		−	1.39353i	−0.717299	−	0.696766i	$-0.754622\pi$
$43$		−	2576.64i		−	1.39353i	0.717299	−	0.696766i	$-0.245378\pi$
$44$	1534.50	−	1534.50i	0.792614	−	0.792614i
$45$	−2264.22	−	442.977i	−1.11814	−	0.218754i
$46$	207.285	−	207.285i	0.0979609	−	0.0979609i
$47$			1312.90i			0.594341i	0.954824	+	0.297170i	$0.0960429\pi$
$47$			1312.90i			0.594341i	−0.954824	+	0.297170i	$0.903957\pi$
$48$	−587.010	−	1924.20i	−0.254779	−	0.835158i
$49$			3338.82i			1.39059i
$50$			154.338i			0.0617353i
$51$	−1964.66	−	1704.50i	−0.755347	−	0.655325i
$52$	3411.97			1.26182
$53$	484.122			0.172347			0.0861734	−	0.996280i	$-0.472536\pi$
$53$	484.122			0.172347			0.0861734	+	0.996280i	$0.472536\pi$
$54$	468.650	+	380.923i	0.160717	+	0.130632i
$55$	−4036.39			−1.33434
$56$	1389.73	+	1389.73i	0.443153	+	0.443153i
$57$	−2591.41	+	790.551i	−0.797602	+	0.243321i
$58$	−502.624	−	502.624i	−0.149413	−	0.149413i
$59$	−1098.10			−0.315456			−0.157728	−	0.987483i	$-0.550417\pi$
$59$	−1098.10			−0.315456			−0.157728	+	0.987483i	$0.550417\pi$
$60$	−1845.09	+	3465.03i	−0.512526	+	0.962509i
$61$	−544.654	−	544.654i	−0.146373	−	0.146373i	0.630123	−	0.776496i	$-0.283005\pi$
$61$	−544.654	−	544.654i	−0.146373	−	0.146373i	−0.776496	+	0.630123i	$0.783005\pi$
$62$	312.600	−	312.600i	0.0813216	−	0.0813216i
$63$	6022.51	+	1178.26i	1.51739	+	0.296865i
$64$	−3079.18			−0.751753
$65$	−4487.47	−	4487.47i	−1.06212	−	1.06212i
$66$	932.611	+	496.605i	0.214098	+	0.114005i
$67$	−632.034			−0.140796			−0.0703981	−	0.997519i	$-0.522427\pi$
$67$	−632.034			−0.140796			−0.0703981	+	0.997519i	$0.522427\pi$
$68$	−3749.46	+	2351.17i	−0.810869	+	0.508470i
$69$	−2810.99	−	1496.82i	−0.590419	−	0.314392i
$70$		−	1787.73i		−	0.364842i
$71$	553.953	+	553.953i	0.109890	+	0.109890i	0.759914	−	0.650024i	$-0.225241\pi$
$71$	553.953	+	553.953i	0.109890	+	0.109890i	−0.650024	+	0.759914i	$0.725241\pi$
$72$	1743.45	−	1172.89i	0.336314	−	0.226253i
$73$	4527.21	−	4527.21i	0.849543	−	0.849543i	−0.140533	−	0.990076i	$-0.544882\pi$
$73$	4527.21	−	4527.21i	0.849543	−	0.849543i	0.990076	+	0.140533i	$0.0448817\pi$
$74$	−823.033	+	823.033i	−0.150298	+	0.150298i
$75$	1603.73	−	489.244i	0.285108	−	0.0869767i
$76$			4609.95i			0.798122i
$77$	10736.2			1.81080
$78$	484.731	+	1588.94i	0.0796730	+	0.261166i
$79$	−4286.76	−	4286.76i	−0.686871	−	0.686871i	0.274668	−	0.961539i	$-0.411432\pi$
$79$	−4286.76	−	4286.76i	−0.686871	−	0.686871i	−0.961539	+	0.274668i	$0.911432\pi$
$80$	4502.02	+	4502.02i	0.703441	+	0.703441i
$81$	2472.58	−	6077.26i	0.376860	−	0.926270i
$82$	−1738.31	+	1738.31i	−0.258523	+	0.258523i
$83$	−919.663			−0.133497			−0.0667487	−	0.997770i	$-0.521263\pi$
$83$	−919.663			−0.133497			−0.0667487	+	0.997770i	$0.521263\pi$
$84$	4907.68	−	9216.50i	0.695534	−	1.30619i
$85$	8023.62	+	1839.05i	1.11054	+	0.254540i
$86$		−	2134.59i		−	0.288615i
$87$	−3629.49	+	6816.07i	−0.479520	+	0.900525i
$88$	2599.46	−	2599.46i	0.335674	−	0.335674i
$89$			4806.29i			0.606778i	0.952867	+	0.303389i	$0.0981181\pi$
$89$			4806.29i			0.606778i	−0.952867	+	0.303389i	$0.901882\pi$
$90$	−1875.77	−	366.980i	−0.231577	−	0.0453062i
$91$	11936.0	+	11936.0i	1.44137	+	1.44137i
$92$	−3831.66	+	3831.66i	−0.452700	+	0.452700i
$93$	−4239.16	−	2257.31i	−0.490133	−	0.260990i
$94$			1087.66i			0.123094i
$95$	6063.06	−	6063.06i	0.671808	−	0.671808i
$96$	−1576.31	−	5167.11i	−0.171041	−	0.560667i
$97$	−5426.61	+	5426.61i	−0.576747	+	0.576747i	−0.934005	−	0.357259i	$-0.883711\pi$
$97$	−5426.61	+	5426.61i	−0.576747	+	0.576747i	0.357259	+	0.934005i	$0.383711\pi$
$98$			2766.01i			0.288006i
$99$	2203.91	−	11265.0i	0.224866	−	1.14937i
$100$		−	2852.93i		−	0.285293i
$101$			20072.3i			1.96768i	0.179050	+	0.983840i	$0.442698\pi$
$101$			20072.3i			1.96768i	−0.179050	+	0.983840i	$0.557302\pi$
$102$	−1627.60	−	1412.08i	−0.156440	−	0.135724i
$103$	3120.21			0.294110			0.147055	−	0.989128i	$-0.453021\pi$
$103$	3120.21			0.294110			0.147055	+	0.989128i	$0.453021\pi$
$104$	5779.91			0.534385
$105$	−18576.3	+	5667.00i	−1.68492	+	0.514014i
$106$	401.066			0.0356948
$107$	−5137.86	−	5137.86i	−0.448760	−	0.448760i	0.446182	−	0.894942i	$-0.352783\pi$
$107$	−5137.86	−	5137.86i	−0.448760	−	0.448760i	−0.894942	+	0.446182i	$0.852783\pi$
$108$	−8662.98	−	7041.34i	−0.742711	−	0.603681i
$109$	−10289.9	−	10289.9i	−0.866080	−	0.866080i	0.125956	−	0.992036i	$-0.459800\pi$
$109$	−10289.9	−	10289.9i	−0.866080	−	0.866080i	−0.992036	+	0.125956i	$0.959800\pi$
$110$	−3343.91			−0.276356
$111$	11161.1	+	5943.18i	0.905862	+	0.482362i
$112$	−11974.7	−	11974.7i	−0.954619	−	0.954619i
$113$	6346.28	−	6346.28i	0.497007	−	0.497007i	−0.413498	−	0.910505i	$-0.635693\pi$
$113$	6346.28	−	6346.28i	0.497007	−	0.497007i	0.910505	+	0.413498i	$0.135693\pi$
$114$	−2146.83	+	654.925i	−0.165191	+	0.0503943i
$115$	10078.9			0.762109
$116$	9290.99	+	9290.99i	0.690472	+	0.690472i
$117$	14974.1	−	10073.7i	1.09388	−	0.735897i
$118$	−909.711			−0.0653340
$119$	−21341.7	−	4891.61i	−1.50707	−	0.345428i
$120$	−3125.60	+	5869.80i	−0.217056	+	0.407625i
$121$		−	5440.89i		−	0.371620i
$122$	−451.213	−	451.213i	−0.0303153	−	0.0303153i
$123$	23573.2	+	12552.5i	1.55814	+	0.829695i
$124$	−5778.40	+	5778.40i	−0.375806	+	0.375806i
$125$	8835.75	−	8835.75i	0.565488	−	0.565488i
$126$	4989.29	+	976.116i	0.314266	+	0.0614837i
$127$			7276.54i			0.451147i	0.974226	+	0.225573i	$0.0724255\pi$
$127$			7276.54i			0.451147i	−0.974226	+	0.225573i	$0.927574\pi$
$128$	−12154.8			−0.741872
$129$	−22180.6	+	6766.55i	−1.33289	+	0.406619i
$130$	−3717.60	−	3717.60i	−0.219976	−	0.219976i
$131$	−16251.7	−	16251.7i	−0.947013	−	0.947013i	0.0516521	−	0.998665i	$-0.483551\pi$
$131$	−16251.7	−	16251.7i	−0.947013	−	0.947013i	−0.998665	+	0.0516521i	$0.983551\pi$
$132$	−17239.3	−	9179.73i	−0.989398	−	0.526844i
$133$	−16126.9	+	16126.9i	−0.911690	+	0.911690i
$134$	−523.603			−0.0291603
$135$	2132.81	+	20654.5i	0.117027	+	1.13331i
$136$	−6351.62	+	3982.90i	−0.343405	+	0.215338i
$137$			18304.3i			0.975242i	0.873055	+	0.487621i	$0.162135\pi$
$137$			18304.3i			0.975242i	−0.873055	+	0.487621i	$0.837865\pi$
$138$	−2328.74	−	1240.03i	−0.122282	−	0.0651138i
$139$	−5646.17	+	5646.17i	−0.292230	+	0.292230i	−0.837961	−	0.545731i	$-0.816252\pi$
$139$	−5646.17	+	5646.17i	−0.292230	+	0.292230i	0.545731	+	0.837961i	$0.316252\pi$
$140$			33046.0i			1.68602i
$141$	11301.9	−	3447.82i	0.568476	−	0.173423i
$142$	458.917	+	458.917i	0.0227592	+	0.0227592i
$143$	22326.1	−	22326.1i	1.09179	−	1.09179i
$144$	−15022.7	+	10106.4i	−0.724472	+	0.487382i
$145$		−	24439.2i		−	1.16239i
$146$	3750.53	−	3750.53i	0.175949	−	0.175949i
$147$	28741.7	−	8768.12i	1.33008	−	0.405762i
$148$	15213.7	−	15213.7i	0.694564	−	0.694564i
$149$		−	26158.1i		−	1.17824i	−0.808046	−	0.589120i	$-0.799475\pi$
$149$		−	26158.1i		−	1.17824i	0.808046	−	0.589120i	$-0.200525\pi$
$150$	1328.60	−	405.310i	0.0590487	−	0.0180138i
$151$		−	1641.81i		−	0.0720062i	−0.999352	−	0.0360031i	$-0.988537\pi$
$151$		−	1641.81i		−	0.0720062i	0.999352	−	0.0360031i	$-0.0114626\pi$
$152$			7809.30i			0.338006i
$153$	−9513.50	+	21388.7i	−0.406404	+	0.913694i
$154$	8894.32			0.375035
$155$	15199.6			0.632659
$156$	−8960.22	−	29371.4i	−0.368188	−	1.20691i
$157$	15264.9			0.619293			0.309646	−	0.950852i	$-0.399789\pi$
$157$	15264.9			0.619293			0.309646	+	0.950852i	$0.399789\pi$
$158$	−3551.33	−	3551.33i	−0.142258	−	0.142258i
$159$	−1271.36	−	4167.49i	−0.0502891	−	0.164847i
$160$	12089.4	+	12089.4i	0.472241	+	0.472241i
$161$	−26808.4			−1.03423
$162$	2048.38	−	5034.65i	0.0780514	−	0.191840i
$163$	12059.2	+	12059.2i	0.453884	+	0.453884i	0.896641	−	0.442757i	$-0.146000\pi$
$163$	12059.2	+	12059.2i	0.453884	+	0.453884i	−0.442757	+	0.896641i	$0.646000\pi$
$164$	32132.6	−	32132.6i	1.19470	−	1.19470i
$165$	10600.0	+	34746.6i	0.389349	+	1.27628i
$166$	−761.886			−0.0276487
$167$	−13969.9	−	13969.9i	−0.500912	−	0.500912i	0.410809	−	0.911721i	$-0.365246\pi$
$167$	−13969.9	−	13969.9i	−0.500912	−	0.500912i	−0.911721	+	0.410809i	$0.865246\pi$
$168$	8313.66	−	15612.8i	0.294560	−	0.553176i
$169$	21081.2			0.738112
$170$	6647.09	+	1523.54i	0.230003	+	0.0527178i
$171$	13610.7	+	20231.7i	0.465465	+	0.691893i
$172$			39457.9i			1.33376i
$173$	−34341.1	−	34341.1i	−1.14742	−	1.14742i	−0.987059	−	0.160360i	$-0.948735\pi$
$173$	−34341.1	−	34341.1i	−1.14742	−	1.14742i	−0.160360	−	0.987059i	$-0.551265\pi$
$174$	−3006.81	+	5646.71i	−0.0993134	+	0.186508i
$175$	9980.36	−	9980.36i	0.325889	−	0.325889i
$176$	−22398.5	+	22398.5i	−0.723092	+	0.723092i
$177$	2883.74	+	9452.82i	0.0920469	+	0.301728i
$178$			3981.72i			0.125670i
$179$	28982.3			0.904538			0.452269	−	0.891881i	$-0.350615\pi$
$179$	28982.3			0.904538			0.452269	+	0.891881i	$0.350615\pi$
$180$	34673.6	+	6783.62i	1.07017	+	0.209371i
$181$	−21040.3	−	21040.3i	−0.642237	−	0.642237i	0.308868	−	0.951105i	$-0.400050\pi$
$181$	−21040.3	−	21040.3i	−0.642237	−	0.642237i	−0.951105	+	0.308868i	$0.900050\pi$
$182$	9888.29	+	9888.29i	0.298523	+	0.298523i
$183$	−3258.24	+	6118.89i	−0.0972929	+	0.182713i
$184$	−6490.86	+	6490.86i	−0.191720	+	0.191720i
$185$	−40018.6			−1.16928
$186$	−3511.89	−	1870.04i	−0.101511	−	0.0540538i
$187$	−9149.66	+	39919.2i	−0.261651	+	1.14156i
$188$		−	20105.3i		−	0.568847i
$189$	−5672.97	−	54938.1i	−0.158813	−	1.53798i
$190$	5022.89	−	5022.89i	0.139138	−	0.139138i
$191$		−	16312.3i		−	0.447145i	−0.974687	−	0.223572i	$-0.928228\pi$
$191$		−	16312.3i		−	0.447145i	0.974687	−	0.223572i	$-0.0717719\pi$
$192$	8086.28	+	26506.6i	0.219354	+	0.719039i
$193$	2588.64	+	2588.64i	0.0694955	+	0.0694955i	0.741000	−	0.671505i	$-0.234352\pi$
$193$	2588.64	+	2588.64i	0.0694955	+	0.0694955i	−0.671505	+	0.741000i	$0.734352\pi$
$194$	−4495.62	+	4495.62i	−0.119450	+	0.119450i
$195$	−26845.0	+	50414.2i	−0.705984	+	1.32582i
$196$		−	51129.6i		−	1.33095i
$197$	22623.4	−	22623.4i	0.582942	−	0.582942i	−0.352769	−	0.935711i	$-0.614760\pi$
$197$	22623.4	−	22623.4i	0.582942	−	0.582942i	0.935711	+	0.352769i	$0.114760\pi$
$198$	1825.81	−	9332.38i	0.0465719	−	0.238047i
$199$	45702.7	−	45702.7i	1.15408	−	1.15408i	0.168353	−	0.985727i	$-0.446155\pi$
$199$	45702.7	−	45702.7i	1.15408	−	1.15408i	0.985727	−	0.168353i	$-0.0538448\pi$
$200$		−	4832.90i		−	0.120822i
$201$	1659.79	+	5440.77i	0.0410830	+	0.134669i
$202$			16628.7i			0.407526i
$203$			65004.9i			1.57744i
$204$	30086.2	+	26102.2i	0.722947	+	0.627215i
$205$	−84522.3			−2.01124
$206$	2584.91			0.0609131
$207$	−5503.17	+	28128.8i	−0.128432	+	0.656462i
$208$	−49803.2			−1.15115
$209$	30165.0	+	30165.0i	0.690576	+	0.690576i
$210$	−15389.4	+	4694.77i	−0.348965	+	0.106457i
$211$	−7919.72	−	7919.72i	−0.177887	−	0.177887i	0.612547	−	0.790434i	$-0.290145\pi$
$211$	−7919.72	−	7919.72i	−0.177887	−	0.177887i	−0.790434	+	0.612547i	$0.790145\pi$
$212$	−7413.69			−0.164954
$213$	3313.87	−	6223.36i	0.0730427	−	0.137172i
$214$	−4256.41	−	4256.41i	−0.0929428	−	0.0929428i
$215$	51895.5	−	51895.5i	1.12267	−	1.12267i
$216$	−14675.2	−	11928.1i	−0.314540	−	0.255660i
$217$	−40428.9			−0.858563
$218$	−8524.57	−	8524.57i	−0.179374	−	0.179374i
$219$	−50860.8	−	27082.8i	−1.06046	−	0.564684i
$220$	61812.0			1.27711
$221$	−54552.5	+	34208.1i	−1.11694	+	0.700398i
$222$	9246.33	+	4923.57i	0.187613	+	0.0999020i
$223$		−	881.513i		−	0.0177263i	−0.999961	−	0.00886317i	$-0.997179\pi$
$223$		−	881.513i		−	0.0177263i	0.999961	−	0.00886317i	$-0.00282127\pi$
$224$	−32156.0	−	32156.0i	−0.640864	−	0.640864i
$225$	−8423.16	−	12520.7i	−0.166383	−	0.247321i
$226$	5257.52	−	5257.52i	0.102935	−	0.102935i
$227$	−23221.9	+	23221.9i	−0.450658	+	0.450658i	−0.895573	−	0.444915i	$-0.853234\pi$
$227$	−23221.9	+	23221.9i	−0.450658	+	0.450658i	0.444915	+	0.895573i	$0.353234\pi$
$228$	39684.0	−	12106.3i	0.763389	−	0.232884i
$229$		−	59725.7i		−	1.13891i	−0.822021	−	0.569456i	$-0.807154\pi$
$229$		−	59725.7i		−	1.13891i	0.822021	−	0.569456i	$-0.192846\pi$
$230$	8349.76			0.157840
$231$	−28194.5	−	92421.0i	−0.528373	−	1.73200i
$232$	15739.0	+	15739.0i	0.292416	+	0.292416i
$233$	57766.3	+	57766.3i	1.06405	+	1.06405i	0.997803	+	0.0662488i	$0.0211031\pi$
$233$	57766.3	+	57766.3i	1.06405	+	1.06405i	0.0662488	+	0.997803i	$0.478897\pi$
$234$	12405.1	−	8345.45i	0.226553	−	0.152412i
$235$	−26442.8	+	26442.8i	−0.478819	+	0.478819i
$236$	16816.0			0.301924
$237$	−25644.4	+	48159.4i	−0.456558	+	0.857402i
$238$	−17680.3	−	4052.41i	−0.312130	−	0.0715417i
$239$			28766.2i			0.503601i	0.967779	+	0.251800i	$0.0810226\pi$
$239$			28766.2i			0.503601i	−0.967779	+	0.251800i	$0.918977\pi$
$240$	26932.1	−	50577.7i	0.467571	−	0.878086i
$241$	−17055.2	+	17055.2i	−0.293645	+	0.293645i	−0.838519	−	0.544873i	$-0.816578\pi$
$241$	−17055.2	+	17055.2i	−0.293645	+	0.293645i	0.544873	+	0.838519i	$0.316578\pi$
$242$		−	4507.45i		−	0.0769663i
$243$	−58808.4	−	5325.20i	−0.995925	−	0.0901826i
$244$	8340.66	+	8340.66i	0.140094	+	0.140094i
$245$	−67246.3	+	67246.3i	−1.12030	+	1.12030i
$246$	19529.0	+	10399.0i	0.322707	+	0.171838i
$247$			67072.1i			1.09938i
$248$	−9788.66	+	9788.66i	−0.159155	+	0.159155i
$249$	2415.14	+	7916.78i	0.0389533	+	0.127688i
$250$	7319.90	−	7319.90i	0.117118	−	0.117118i
$251$		−	42828.8i		−	0.679811i	−0.940460	−	0.339906i	$-0.889605\pi$
$251$		−	42828.8i		−	0.679811i	0.940460	−	0.339906i	$-0.110395\pi$
$252$	−92226.9	−	18043.5i	−1.45230	−	0.284131i
$253$			50144.6i			0.783399i
$254$			6028.18i			0.0934370i
$255$	−5239.77	−	73899.6i	−0.0805809	−	1.13648i
$256$	39197.3			0.598104
$257$	65772.8			0.995818			0.497909	−	0.867229i	$-0.334101\pi$
$257$	65772.8			0.995818			0.497909	+	0.867229i	$0.334101\pi$
$258$	−18375.3	+	5605.68i	−0.276055	+	0.0842150i
$259$	106444.			1.58679
$260$	68719.7	+	68719.7i	1.01656	+	1.01656i
$261$	68206.5	+	13344.1i	1.00126	+	0.195888i
$262$	−13463.6	−	13463.6i	−0.196136	−	0.196136i
$263$	−89503.6			−1.29398			−0.646992	−	0.762497i	$-0.723973\pi$
$263$	−89503.6			−1.29398			−0.646992	+	0.762497i	$0.723973\pi$
$264$	−29203.5	−	15550.5i	−0.419012	−	0.223120i
$265$	9750.58	+	9750.58i	0.138848	+	0.138848i
$266$	−13360.2	+	13360.2i	−0.188820	+	0.188820i
$267$	41374.2	−	12621.9i	0.580372	−	0.177052i
$268$	9678.77			0.134757
$269$	−196.481	−	196.481i	−0.00271529	−	0.00271529i	0.705748	−	0.708463i	$-0.250611\pi$
$269$	−196.481	−	196.481i	−0.00271529	−	0.00271529i	−0.708463	+	0.705748i	$0.750611\pi$
$270$	1766.90	+	17111.0i	0.0242374	+	0.234719i
$271$	59286.3			0.807265			0.403632	−	0.914921i	$-0.367748\pi$
$271$	59286.3			0.807265			0.403632	+	0.914921i	$0.367748\pi$
$272$	54729.4	−	34319.1i	0.739746	−	0.463872i
$273$	71404.0	−	134095.i	0.958070	−	1.79923i
$274$			15164.0i			0.201982i
$275$	−18668.1	−	18668.1i	−0.246850	−	0.246850i
$276$	43046.6	+	22921.8i	0.565094	+	0.300906i
$277$	43418.0	−	43418.0i	0.565862	−	0.565862i	−0.365104	−	0.930967i	$-0.618967\pi$
$277$	43418.0	−	43418.0i	0.565862	−	0.565862i	0.930967	+	0.365104i	$0.118967\pi$
$278$	−4677.52	+	4677.52i	−0.0605238	+	0.0605238i
$279$	−8299.15	+	42420.1i	−0.106617	+	0.544958i
$280$			55980.3i			0.714034i
$281$	52233.9			0.661515			0.330758	−	0.943716i	$-0.392696\pi$
$281$	52233.9			0.661515			0.330758	+	0.943716i	$0.392696\pi$
$282$	9362.93	−	2856.32i	0.117737	−	0.0359176i
$283$	−91786.9	−	91786.9i	−1.14606	−	1.14606i	−0.987320	−	0.158741i	$-0.949257\pi$
$283$	−91786.9	−	91786.9i	−1.14606	−	1.14606i	−0.158741	−	0.987320i	$-0.550743\pi$
$284$	−8483.06	−	8483.06i	−0.105176	−	0.105176i
$285$	−68115.2	−	36270.6i	−0.838599	−	0.446545i
$286$	18495.8	−	18495.8i	0.226122	−	0.226122i
$287$	224817.			2.72939
$288$	−40340.6	+	27138.8i	−0.486360	+	0.327194i
$289$	36375.8	−	75183.5i	0.435529	−	0.900175i
$290$		−	20246.5i		−	0.240743i
$291$	60965.0	+	32463.2i	0.719937	+	0.383359i
$292$	−69328.3	+	69328.3i	−0.813102	+	0.813102i
$293$			40870.3i			0.476072i	0.971256	+	0.238036i	$0.0765037\pi$
$293$			40870.3i			0.476072i	−0.971256	+	0.238036i	$0.923496\pi$
$294$	23810.8	−	7263.86i	0.275473	−	0.0840375i
$295$	−22116.6	−	22116.6i	−0.254140	−	0.254140i
$296$	25772.2	−	25772.2i	0.294150	−	0.294150i
$297$	−102761.	+	10611.2i	−1.16497	+	0.120296i
$298$		−	21670.4i		−	0.244025i
$299$	−55748.4	+	55748.4i	−0.623577	+	0.623577i
$300$	−24559.0	+	7492.13i	−0.272878	+	0.0832459i
$301$	−138035.	+	138035.i	−1.52354	+	1.52354i
$302$		−	1360.14i		−	0.0149132i
$303$	172789.	−	52712.2i	1.88205	−	0.574150i
$304$		−	67289.7i		−	0.728117i
$305$		−	21939.5i		−	0.235845i
$306$	−7881.37	+	17719.2i	−0.0841703	+	0.189235i
$307$	−10850.8			−0.115129			−0.0575647	−	0.998342i	$-0.518334\pi$
$307$	−10850.8			−0.115129			−0.0575647	+	0.998342i	$0.518334\pi$
$308$	−164411.			−1.73312
$309$	−8194.02	−	26859.8i	−0.0858184	−	0.281311i
$310$	12592.0			0.131030
$311$	−69288.7	−	69288.7i	−0.716377	−	0.716377i	0.251485	−	0.967861i	$-0.419081\pi$
$311$	−69288.7	−	69288.7i	−0.716377	−	0.716377i	−0.967861	+	0.251485i	$0.919081\pi$
$312$	−15178.7	−	49755.4i	−0.155929	−	0.511130i
$313$	−1850.57	−	1850.57i	−0.0188894	−	0.0188894i	0.697599	−	0.716488i	$-0.254252\pi$
$313$	−1850.57	−	1850.57i	−0.0188894	−	0.0188894i	−0.716488	+	0.697599i	$0.754252\pi$
$314$	12646.1			0.128262
$315$	97566.9	+	145029.i	0.983290	+	1.46162i
$316$	65646.1	+	65646.1i	0.657408	+	0.657408i
$317$	−100049.	+	100049.i	−0.995618	+	0.995618i	−0.999990	−	0.00437273i	$-0.998608\pi$
$317$	−100049.	+	100049.i	−0.995618	+	0.995618i	0.00437273	+	0.999990i	$0.498608\pi$
$318$	−1053.25	−	3452.52i	−0.0104154	−	0.0341414i
$319$	121590.			1.19486
$320$	−62017.0	−	62017.0i	−0.605635	−	0.605635i
$321$	−30735.8	+	57721.0i	−0.298287	+	0.560175i
$322$	−22209.2			−0.214201
$323$	−46219.0	−	73706.4i	−0.443012	−	0.706481i
$324$	−37864.2	+	93065.3i	−0.360694	+	0.886538i
$325$		−	41508.6i		−	0.392980i
$326$	9990.37	+	9990.37i	0.0940040	+	0.0940040i
$327$	−61556.5	+	115601.i	−0.575676	+	1.08110i
$328$	54432.9	−	54432.9i	0.505957	−	0.505957i
$329$	70334.0	−	70334.0i	0.649791	−	0.649791i
$330$	8781.48	+	28785.5i	0.0806380	+	0.264330i
$331$			16831.8i			0.153630i	0.997045	+	0.0768148i	$0.0244750\pi$
$331$			16831.8i			0.153630i	−0.997045	+	0.0768148i	$0.975525\pi$
$332$	14083.4			0.127771
$333$	21850.5	−	111686.i	0.197049	−	1.00719i
$334$	−11573.3	−	11573.3i	−0.103744	−	0.103744i
$335$	−12729.6	−	12729.6i	−0.113430	−	0.113430i
$336$	−71635.6	+	134530.i	−0.634527	+	1.19162i
$337$	−106186.	+	106186.i	−0.934989	+	0.934989i	−0.998012	−	0.0630227i	$-0.979926\pi$
$337$	−106186.	+	106186.i	−0.934989	+	0.934989i	0.0630227	+	0.998012i	$0.479926\pi$
$338$	17464.5			0.152871
$339$	−71297.0	−	37964.9i	−0.620400	−	0.330357i
$340$	−122871.	−	28162.6i	−1.06290	−	0.243621i
$341$			75621.5i			0.650334i
$342$	11275.6	+	16760.7i	0.0964026	+	0.143298i
$343$	50240.3	−	50240.3i	0.427036	−	0.427036i
$344$			66842.0i			0.564849i
$345$	−26468.3	−	86762.5i	−0.222376	−	0.728943i
$346$	−28449.5	−	28449.5i	−0.237642	−	0.237642i
$347$	3855.76	−	3855.76i	0.0320222	−	0.0320222i	−0.690914	−	0.722937i	$-0.742792\pi$
$347$	3855.76	−	3855.76i	0.0320222	−	0.0320222i	0.722937	+	0.690914i	$0.242792\pi$
$348$	55580.8	−	104379.i	0.458951	−	0.861897i
$349$		−	120569.i		−	0.989884i	−0.868926	−	0.494942i	$-0.835189\pi$
$349$		−	120569.i		−	0.989884i	0.868926	−	0.494942i	$-0.164811\pi$
$350$	8268.13	−	8268.13i	0.0674950	−	0.0674950i
$351$	−126041.	−	102447.i	−1.02306	−	0.831547i
$352$	−60147.2	+	60147.2i	−0.485434	+	0.485434i
$353$		−	3717.14i		−	0.0298305i	−0.999889	−	0.0149152i	$-0.995252\pi$
$353$		−	3717.14i		−	0.0298305i	0.999889	−	0.0149152i	$-0.00474784\pi$
$354$	2389.01	+	7831.10i	0.0190638	+	0.0624908i
$355$			22314.1i			0.177061i
$356$		−	73602.0i		−	0.580750i
$357$	13937.1	+	196562.i	0.109354	+	1.54228i
$358$	24010.1			0.187339
$359$	12707.4			0.0985978			0.0492989	−	0.998784i	$-0.484301\pi$
$359$	12707.4			0.0985978			0.0492989	+	0.998784i	$0.484301\pi$
$360$	58737.4	+	11491.5i	0.453221	+	0.0886691i
$361$	39699.1			0.304626
$362$	−17430.7	−	17430.7i	−0.133014	−	0.133014i
$363$	−46837.0	+	14288.4i	−0.355448	+	0.108435i
$364$	−182785.	−	182785.i	−1.37955	−	1.37955i
$365$	182363.			1.36883
$366$	−2699.26	+	5069.14i	−0.0201504	+	0.0378418i
$367$	9098.48	+	9098.48i	0.0675518	+	0.0675518i	0.740076	−	0.672524i	$-0.234790\pi$
$367$	9098.48	+	9098.48i	0.0675518	+	0.0675518i	−0.672524	+	0.740076i	$0.734790\pi$
$368$	55929.2	−	55929.2i	0.412993	−	0.412993i
$369$	46150.0	−	235890.i	0.338937	−	1.73243i
$370$	−33153.0			−0.242170
$371$	−25935.2	−	25935.2i	−0.188426	−	0.188426i
$372$	64917.2	+	34567.7i	0.469109	+	0.249795i
$373$	150881.			1.08447			0.542234	−	0.840227i	$-0.317579\pi$
$373$	150881.			1.08447			0.542234	+	0.840227i	$0.317579\pi$
$374$	−7579.95	+	33070.7i	−0.0541905	+	0.236429i
$375$	−99264.9	−	52857.5i	−0.705884	−	0.375875i
$376$		−	34058.6i		−	0.240908i
$377$	135179.	+	135179.i	0.951098	+	0.951098i
$378$	−4699.72	−	45512.9i	−0.0328918	−	0.318531i
$379$	−173722.	+	173722.i	−1.20942	+	1.20942i	−0.238202	+	0.971216i	$0.576558\pi$
$379$	−173722.	+	173722.i	−1.20942	+	1.20942i	−0.971216	+	0.238202i	$0.923442\pi$
$380$	−92847.9	+	92847.9i	−0.642991	+	0.642991i
$381$	62639.0	−	19109.0i	0.431514	−	0.131640i
$382$		−	13513.8i		−	0.0926082i
$383$	−154602.			−1.05394			−0.526972	−	0.849883i	$-0.676673\pi$
$383$	−154602.			−1.05394			−0.526972	+	0.849883i	$0.676673\pi$
$384$	31920.0	+	104633.i	0.216471	+	0.709587i
$385$	216236.	+	216236.i	1.45883	+	1.45883i
$386$	2144.53	+	2144.53i	0.0143932	+	0.0143932i
$387$	116498.	+	173168.i	0.777848	+	1.15624i
$388$	83101.4	−	83101.4i	0.552007	−	0.552007i
$389$	−208476.			−1.37771			−0.688853	−	0.724901i	$-0.741885\pi$
$389$	−208476.			−1.37771			−0.688853	+	0.724901i	$0.741885\pi$
$390$	−22239.5	+	41765.2i	−0.146216	+	0.274590i
$391$	22846.8	−	99678.5i	0.149441	−	0.652001i
$392$		−	86614.0i		−	0.563659i
$393$	−97221.3	+	182579.i	−0.629472	+	1.18213i
$394$	18742.1	−	18742.1i	0.120733	−	0.120733i
$395$		−	172677.i		−	1.10673i
$396$	−33749.9	+	172509.i	−0.215220	+	1.10007i
$397$	62700.7	+	62700.7i	0.397824	+	0.397824i	0.877465	−	0.479641i	$-0.159233\pi$
$397$	62700.7	+	62700.7i	0.397824	+	0.397824i	−0.479641	+	0.877465i	$0.659233\pi$
$398$	37862.0	−	37862.0i	0.239022	−	0.239022i
$399$	181177.	+	96474.7i	1.13804	+	0.605993i
$400$			41643.2i			0.260270i
$401$	78840.5	−	78840.5i	0.490298	−	0.490298i	−0.418102	−	0.908400i	$-0.637304\pi$
$401$	78840.5	−	78840.5i	0.490298	−	0.490298i	0.908400	+	0.418102i	$0.137304\pi$
$402$	1375.04	+	4507.35i	0.00850870	+	0.0278913i
$403$	−84072.4	+	84072.4i	−0.517658	+	0.517658i
$404$		−	307381.i		−	1.88328i
$405$	172200.	−	72601.1i	1.04984	−	0.442622i
$406$			53852.7i			0.326705i
$407$		−	199101.i		−	1.20194i
$408$	50966.2	+	44217.3i	0.306170	+	0.265627i
$409$	276307.			1.65175			0.825875	−	0.563853i	$-0.190681\pi$
$409$	276307.			1.65175			0.825875	+	0.563853i	$0.190681\pi$
$410$	−70021.7			−0.416548
$411$	157570.	−	48069.2i	0.932802	−	0.284566i
$412$	−47781.9			−0.281494
$413$	58826.9	+	58826.9i	0.344886	+	0.344886i
$414$	−4559.05	+	23303.0i	−0.0265995	+	0.135960i
$415$	−18522.7	−	18522.7i	−0.107549	−	0.107549i
$416$	−133738.			−0.772799
$417$	63431.7	+	33776.7i	0.364783	+	0.194243i
$418$	24989.9	+	24989.9i	0.143025	+	0.143025i
$419$	16991.6	−	16991.6i	0.0967845	−	0.0967845i	−0.657057	−	0.753841i	$-0.728199\pi$
$419$	16991.6	−	16991.6i	0.0967845	−	0.0967845i	0.753841	+	0.657057i	$0.228199\pi$
$420$	284472.	−	86782.7i	1.61265	−	0.491965i
$421$	−49747.0			−0.280674			−0.140337	−	0.990104i	$-0.544819\pi$
$421$	−49747.0			−0.280674			−0.140337	+	0.990104i	$0.544819\pi$
$422$	−6561.02	−	6561.02i	−0.0368423	−	0.0368423i
$423$	−59360.0	−	88236.0i	−0.331752	−	0.493134i
$424$	−12558.9			−0.0698584
$425$	28603.3	+	45614.3i	0.158357	+	0.252536i
$426$	2745.35	−	5155.68i	0.0151279	−	0.0284097i
$427$			58355.9i			0.320058i
$428$	78679.6	+	78679.6i	0.429511	+	0.429511i
$429$	−250822.	−	133560.i	−1.36286	−	0.725707i
$430$	42992.3	−	42992.3i	0.232517	−	0.232517i
$431$	−41420.9	+	41420.9i	−0.222980	+	0.222980i	−0.809752	−	0.586772i	$-0.800398\pi$
$431$	−41420.9	+	41420.9i	−0.222980	+	0.222980i	0.586772	+	0.809752i	$0.300398\pi$
$432$	126450.	+	102780.i	0.677567	+	0.550731i
$433$		−	274926.i		−	1.46636i	−0.680035	−	0.733180i	$-0.738035\pi$
$433$		−	274926.i		−	1.46636i	0.680035	−	0.733180i	$-0.261965\pi$
$434$	−33492.9			−0.177817
$435$	−210381.	+	64180.2i	−1.11181	+	0.339174i
$436$	157576.	+	157576.i	0.828930	+	0.828930i
$437$	−75322.3	−	75322.3i	−0.394421	−	0.394421i
$438$	−42135.1	−	22436.5i	−0.219632	−	0.116952i
$439$	−164179.	+	164179.i	−0.851901	+	0.851901i	−0.990367	−	0.138466i	$-0.955783\pi$
$439$	−164179.	+	164179.i	−0.851901	+	0.851901i	0.138466	+	0.990367i	$0.455783\pi$
$440$	104710.			0.540858
$441$	−150958.	−	224392.i	−0.776209	−	1.15380i
$442$	−45193.5	+	28339.4i	−0.231330	+	0.145060i
$443$			119632.i			0.609592i	0.952418	+	0.304796i	$0.0985883\pi$
$443$			119632.i			0.609592i	−0.952418	+	0.304796i	$0.901412\pi$
$444$	−170918.	−	91012.0i	−0.867006	−	0.461671i
$445$	−96802.2	+	96802.2i	−0.488838	+	0.488838i
$446$		−	730.281i		−	0.00367130i
$447$	−225178.	+	68694.2i	−1.12697	+	0.343799i
$448$	164956.	+	164956.i	0.821889	+	0.821889i
$449$	123170.	−	123170.i	0.610959	−	0.610959i	−0.332237	−	0.943196i	$-0.607803\pi$
$449$	123170.	−	123170.i	0.610959	−	0.610959i	0.943196	+	0.332237i	$0.107803\pi$
$450$	−6978.09	−	10372.6i	−0.0344597	−	0.0512228i
$451$		−	420517.i		−	2.06743i
$452$	−97185.0	+	97185.0i	−0.475688	+	0.475688i
$453$	−14133.3	+	4311.59i	−0.0688726	+	0.0210107i
$454$	−19238.0	+	19238.0i	−0.0933358	+	0.0933358i
$455$			480801.i			2.32243i
$456$	67225.1	−	20508.1i	0.323297	−	0.0986270i
$457$		−	195720.i		−	0.937138i	−0.883427	−	0.468569i	$-0.844770\pi$
$457$		−	195720.i		−	0.937138i	0.883427	−	0.468569i	$-0.155230\pi$
$458$		−	49479.2i		−	0.235880i
$459$	209104.	+	25726.4i	0.992516	+	0.122111i
$460$	−154345.			−0.729418
$461$	−18750.9			−0.0882307			−0.0441153	−	0.999026i	$-0.514047\pi$
$461$	−18750.9			−0.0882307			−0.0441153	+	0.999026i	$0.514047\pi$
$462$	−23357.5	−	76565.3i	−0.109431	−	0.358714i
$463$	−214737.			−1.00172			−0.500859	−	0.865529i	$-0.666982\pi$
$463$	−214737.			−1.00172			−0.500859	+	0.865529i	$0.666982\pi$
$464$	−135617.	−	135617.i	−0.629909	−	0.629909i
$465$	−39916.0	−	130844.i	−0.184604	−	0.605128i
$466$	47856.0	+	47856.0i	0.220376	+	0.220376i
$467$	331873.			1.52173			0.760866	−	0.648909i	$-0.224775\pi$
$467$	331873.			1.52173			0.760866	+	0.648909i	$0.224775\pi$
$468$	−229309.	+	154265.i	−1.04696	+	0.704331i
$469$	33859.0	+	33859.0i	0.153932	+	0.153932i
$470$	−21906.3	+	21906.3i	−0.0991682	+	0.0991682i
$471$	−40087.5	−	131406.i	−0.180704	−	0.592343i
$472$	28486.4			0.127866
$473$	258191.	+	258191.i	1.15403	+	1.15403i
$474$	−21244.8	+	39897.2i	−0.0945577	+	0.177577i
$475$	56082.7			0.248566
$476$	326820.	+	74908.6i	1.44243	+	0.330611i
$477$	−32536.4	+	21888.6i	−0.142999	+	0.0962013i
$478$			23831.1i			0.104301i
$479$	−7175.67	−	7175.67i	−0.0312746	−	0.0312746i	0.691297	−	0.722571i	$-0.257040\pi$
$479$	−7175.67	−	7175.67i	−0.0312746	−	0.0312746i	−0.722571	+	0.691297i	$0.757040\pi$
$480$	72321.3	−	135817.i	0.313895	−	0.589485i
$481$	221351.	−	221351.i	0.956735	−	0.956735i
$482$	−14129.2	+	14129.2i	−0.0608170	+	0.0608170i
$483$	70401.9	+	230776.i	0.301780	+	0.989227i
$484$			83320.1i			0.355680i
$485$	−218592.			−0.929289
$486$	−48719.3	−	4411.61i	−0.206266	−	0.0186777i
$487$	200502.	+	200502.i	0.845397	+	0.845397i	0.989555	−	0.144157i	$-0.0460472\pi$
$487$	200502.	+	200502.i	0.845397	+	0.845397i	−0.144157	+	0.989555i	$0.546047\pi$
$488$	14129.2	+	14129.2i	0.0593303	+	0.0593303i
$489$	72141.1	−	135479.i	0.301693	−	0.566571i
$490$	−55709.6	+	55709.6i	−0.232026	+	0.232026i
$491$	−456883.			−1.89514			−0.947572	−	0.319541i	$-0.896471\pi$
$491$	−456883.			−1.89514			−0.947572	+	0.319541i	$0.896471\pi$
$492$	−360992.	−	192224.i	−1.49131	−	0.794106i
$493$	−241700.	−	55398.7i	−0.994450	−	0.227932i
$494$			55565.3i			0.227693i
$495$	271274.	−	182497.i	1.10713	−	0.744810i
$496$	84345.1	−	84345.1i	0.342844	−	0.342844i
$497$		−	59352.2i		−	0.240284i
$498$	2000.80	+	6558.58i	0.00806761	+	0.0264455i
$499$	−339228.	−	339228.i	−1.36236	−	1.36236i	−0.870903	−	0.491455i	$-0.836465\pi$
$499$	−339228.	−	339228.i	−1.36236	−	1.36236i	−0.491455	−	0.870903i	$-0.663535\pi$
$500$	−135308.	+	135308.i	−0.541232	+	0.541232i
$501$	−83571.3	+	156945.i	−0.332952	+	0.625275i
$502$		−	35481.1i		−	0.140796i
$503$	−152083.	+	152083.i	−0.601099	+	0.601099i	−0.940604	−	0.339505i	$-0.889740\pi$
$503$	−152083.	+	152083.i	−0.601099	+	0.601099i	0.339505	+	0.940604i	$0.389740\pi$
$504$	−156233.	−	30565.8i	−0.615052	−	0.120330i
$505$	−404271.	+	404271.i	−1.58522	+	1.58522i
$506$			41541.8i			0.162250i
$507$	−55361.7	−	181474.i	−0.215374	−	0.705991i
$508$		−	111431.i		−	0.431795i
$509$			458427.i			1.76943i	0.466129	+	0.884717i	$0.345648\pi$
$509$			458427.i			1.76943i	−0.466129	+	0.884717i	$0.654352\pi$
$510$	−4340.84	−	61221.4i	−0.0166891	−	0.235376i
$511$	−485059.			−1.85760
$512$	226950.			0.865745
$513$	138418.	−	170296.i	0.525965	−	0.647097i
$514$	54488.8			0.206244
$515$	62843.3	+	62843.3i	0.236944	+	0.236944i
$516$	339667.	−	103621.i	1.27571	−	0.389177i
$517$	−131558.	−	131558.i	−0.492195	−	0.492195i
$518$	88182.3			0.328641
$519$	−205436.	+	385803.i	−0.762680	+	1.43229i
$520$	116412.	+	116412.i	0.430517	+	0.430517i
$521$	−271673.	+	271673.i	−1.00085	+	1.00085i	−0.000853287		1.00000i	$0.500272\pi$
$521$	−271673.	+	271673.i	−1.00085	+	1.00085i	−1.00000		0.000853287i	$0.999728\pi$
$522$	56505.0	+	11054.8i	0.207370	+	0.0405703i
$523$	291238.			1.06474			0.532371	−	0.846511i	$-0.321301\pi$
$523$	291238.			1.06474			0.532371	+	0.846511i	$0.321301\pi$
$524$	248873.	+	248873.i	0.906391	+	0.906391i
$525$	−112124.	−	59704.8i	−0.406799	−	0.216616i
$526$	−74148.4			−0.267997
$527$	34454.5	−	150322.i	0.124058	−	0.541254i
$528$	251635.	+	133993.i	0.902617	+	0.480634i
$529$			154630.i			0.552562i
$530$	8077.78	+	8077.78i	0.0287568	+	0.0287568i
$531$	73800.1	−	49648.4i	0.261739	−	0.176082i
$532$	246962.	−	246962.i	0.872584	−	0.872584i
$533$	467511.	−	467511.i	1.64565	−	1.64565i
$534$	34276.0	−	10456.5i	0.120201	−	0.0366693i
$535$		−	206961.i		−	0.723070i
$536$	16395.9			0.0570698
$537$	−76110.9	−	249490.i	−0.263936	−	0.865175i
$538$	−162.773	−	162.773i	−0.000562364	−	0.000562364i
$539$	−334565.	−	334565.i	−1.15160	−	1.15160i
$540$	−32661.2	−	316297.i	−0.112007	−	1.08469i
$541$	138057.	−	138057.i	0.471697	−	0.471697i	−0.430766	−	0.902464i	$-0.641757\pi$
$541$	138057.	−	138057.i	0.471697	−	0.471697i	0.902464	+	0.430766i	$0.141757\pi$
$542$	49115.2			0.167193
$543$	−125868.	+	236377.i	−0.426890	+	0.801687i
$544$	146966.	−	92157.7i	0.496614	−	0.311411i
$545$		−	414492.i		−	1.39548i
$546$	59154.0	−	111089.i	0.198426	−	0.372638i
$547$	176637.	−	176637.i	0.590347	−	0.590347i	−0.347378	−	0.937725i	$-0.612928\pi$
$547$	176637.	−	176637.i	0.590347	−	0.590347i	0.937725	+	0.347378i	$0.112928\pi$
$548$		−	280307.i		−	0.933409i
$549$	61230.0	+	11979.2i	0.203151	+	0.0397449i
$550$	−15465.4	−	15465.4i	−0.0511252	−	0.0511252i
$551$	−182641.	+	182641.i	−0.601583	+	0.601583i
$552$	72921.3	+	38829.8i	0.239318	+	0.127435i
$553$			459297.i			1.50191i
$554$	35969.3	−	35969.3i	0.117196	−	0.117196i
$555$	105093.	+	344494.i	0.341185	+	1.11840i
$556$	86463.7	−	86463.7i	0.279695	−	0.279695i
$557$			400871.i			1.29210i	0.763297	+	0.646048i	$0.223579\pi$
$557$			400871.i			1.29210i	−0.763297	+	0.646048i	$0.776421\pi$
$558$	−6875.35	+	35142.5i	−0.0220814	+	0.112866i
$559$			574089.i			1.83720i
$560$		−	482360.i		−	1.53814i
$561$	367666.	−	26069.0i	1.16823	−	0.0828321i
$562$	43272.7			0.137007
$563$	277961.			0.876935			0.438467	−	0.898747i	$-0.355521\pi$
$563$	277961.			0.876935			0.438467	+	0.898747i	$0.355521\pi$
$564$	−173073.	+	52798.9i	−0.544092	+	0.165984i
$565$	255638.			0.800808
$566$	−76040.0	−	76040.0i	−0.237361	−	0.237361i
$567$	−458028.	+	193108.i	−1.42471	+	0.600669i
$568$	−14370.4	−	14370.4i	−0.0445422	−	0.0445422i
$569$	418515.			1.29267			0.646334	−	0.763055i	$-0.276301\pi$
$569$	418515.			1.29267			0.646334	+	0.763055i	$0.276301\pi$
$570$	−56429.4	−	30048.1i	−0.173682	−	0.0924840i
$571$	77013.7	+	77013.7i	0.236209	+	0.236209i	0.815278	−	0.579070i	$-0.196584\pi$
$571$	77013.7	+	77013.7i	0.236209	+	0.236209i	−0.579070	+	0.815278i	$0.696584\pi$
$572$	−341895.	+	341895.i	−1.04496	+	1.04496i
$573$	−140422.	+	42837.9i	−0.427686	+	0.130473i
$574$	186248.			0.565285
$575$	46614.3	+	46614.3i	0.140988	+	0.140988i
$576$	206943.	−	139219.i	0.623742	−	0.419617i
$577$	475977.			1.42967			0.714833	−	0.699295i	$-0.246503\pi$
$577$	475977.			1.42967			0.714833	+	0.699295i	$0.246503\pi$
$578$	30135.2	−	62285.1i	0.0902024	−	0.186435i
$579$	15485.8	−	29081.9i	0.0461931	−	0.0867493i
$580$			374255.i			1.11253i
$581$	49267.8	+	49267.8i	0.145952	+	0.145952i
$582$	50505.9	+	26893.8i	0.149106	+	0.0793975i
$583$	−48511.2	+	48511.2i	−0.142727	+	0.142727i
$584$	−117443.	+	117443.i	−0.344351	+	0.344351i
$585$	504481.	+	98697.7i	1.47412	+	0.288400i
$586$			33858.7i			0.0985994i
$587$	62715.1			0.182010			0.0910052	−	0.995850i	$-0.470992\pi$
$587$	62715.1			0.182010			0.0910052	+	0.995850i	$0.470992\pi$
$588$	−440141.	+	134272.i	−1.27303	+	0.388357i
$589$	−113591.	−	113591.i	−0.327426	−	0.327426i
$590$	−18322.3	−	18322.3i	−0.0526351	−	0.0526351i
$591$	−254162.	−	135338.i	−0.727671	−	0.387477i
$592$	−222069.	+	222069.i	−0.633643	+	0.633643i
$593$	−251754.			−0.715923			−0.357962	−	0.933736i	$-0.616528\pi$
$593$	−251754.			−0.715923			−0.357962	+	0.933736i	$0.616528\pi$
$594$	−85131.1	+	8790.73i	−0.241277	+	0.0249145i
$595$	−331317.	−	528358.i	−0.935857	−	1.49243i
$596$			400577.i			1.12770i
$597$	−513445.	−	273404.i	−1.44061	−	0.767107i
$598$	−46184.2	+	46184.2i	−0.129149	+	0.129149i
$599$		−	416021.i		−	1.15948i	−0.814803	−	0.579738i	$-0.803155\pi$
$599$		−	416021.i		−	1.15948i	0.814803	−	0.579738i	$-0.196845\pi$
$600$	−41603.2	+	12691.7i	−0.115565	+	0.0352548i
$601$	488387.	+	488387.i	1.35212	+	1.35212i	0.883286	+	0.468835i	$0.155326\pi$
$601$	488387.	+	488387.i	1.35212	+	1.35212i	0.468835	+	0.883286i	$0.344674\pi$
$602$	−114353.	+	114353.i	−0.315541	+	0.315541i
$603$	42477.2	−	28576.1i	0.116821	−	0.0785903i
$604$			25142.2i			0.0689175i
$605$	109584.	−	109584.i	0.299388	−	0.299388i
$606$	143146.	−	43668.9i	0.389792	−	0.118912i
$607$	263763.	−	263763.i	0.715874	−	0.715874i	−0.251884	−	0.967758i	$-0.581050\pi$
$607$	263763.	−	263763.i	0.715874	−	0.715874i	0.967758	+	0.251884i	$0.0810500\pi$
$608$		−	180694.i		−	0.488807i
$609$	559584.	−	170710.i	1.50880	−	0.460283i
$610$		−	18175.6i		−	0.0488459i
$611$		−	292521.i		−	0.783564i
$612$	145687.	−	327539.i	0.388971	−	0.874501i
$613$	−324402.			−0.863302			−0.431651	−	0.902041i	$-0.642069\pi$
$613$	−324402.			−0.863302			−0.431651	+	0.902041i	$0.642069\pi$
$614$	−8989.27			−0.0238445
$615$	221965.	+	727597.i	0.586860	+	1.92372i
$616$	−278514.			−0.733982
$617$	−248332.	−	248332.i	−0.652323	−	0.652323i	0.301229	−	0.953552i	$-0.402603\pi$
$617$	−248332.	−	248332.i	−0.652323	−	0.652323i	−0.953552	+	0.301229i	$0.902603\pi$
$618$	−6788.26	−	22251.8i	−0.0177739	−	0.0582623i
$619$	−372108.	−	372108.i	−0.971153	−	0.971153i	0.0284421	−	0.999595i	$-0.490945\pi$
$619$	−372108.	−	372108.i	−0.971153	−	0.971153i	−0.999595	+	0.0284421i	$0.990945\pi$
$620$	−232763.			−0.605522
$621$	256594.	−	26496.2i	0.665370	−	0.0687068i
$622$	−57401.5	−	57401.5i	−0.148369	−	0.148369i
$623$	257480.	−	257480.i	0.663388	−	0.663388i
$624$	130789.	+	428723.i	0.335894	+	1.10105i
$625$	472355.			1.20923
$626$	−1533.09	−	1533.09i	−0.00391218	−	0.00391218i
$627$	180454.	−	338888.i	0.459020	−	0.862027i
$628$	−233763.			−0.592728
$629$	−90713.9	+	395777.i	−0.229283	+	1.00034i
$630$	80828.4	+	120148.i	0.203649	+	0.302716i
$631$			420173.i			1.05528i	0.849467	+	0.527642i	$0.176924\pi$
$631$			420173.i			1.05528i	−0.849467	+	0.527642i	$0.823076\pi$
$632$	111205.	+	111205.i	0.278414	+	0.278414i
$633$	−47377.6	+	88973.7i	−0.118240	+	0.222052i
$634$	−82884.3	+	82884.3i	−0.206203	+	0.206203i
$635$	−146555.	+	146555.i	−0.363457	+	0.363457i
$636$	19469.2	+	63819.6i	0.0481320	+	0.157776i
$637$		−	743906.i		−	1.83333i
$638$	100730.			0.247468
$639$	−62275.4	−	12183.7i	−0.152516	−	0.0298385i
$640$	−244807.	−	244807.i	−0.597674	−	0.597674i
$641$	−116511.	−	116511.i	−0.283563	−	0.283563i	0.550965	−	0.834528i	$-0.314260\pi$
$641$	−116511.	−	116511.i	−0.283563	−	0.283563i	−0.834528	+	0.550965i	$0.814260\pi$
$642$	−25462.8	+	47818.4i	−0.0617784	+	0.116018i
$643$	−498081.	+	498081.i	−1.20470	+	1.20470i	−0.231975	+	0.972722i	$0.574519\pi$
$643$	−498081.	+	498081.i	−1.20470	+	1.20470i	−0.972722	+	0.231975i	$0.925481\pi$
$644$	410535.			0.989872
$645$	−583017.	−	310450.i	−1.40140	−	0.746230i
$646$	−38289.7	−	61061.4i	−0.0917522	−	0.146319i
$647$		−	711275.i		−	1.69914i	−0.527477	−	0.849569i	$-0.676862\pi$
$647$		−	711275.i		−	1.69914i	0.527477	−	0.849569i	$-0.323138\pi$
$648$	−64142.4	+	157653.i	−0.152755	+	0.375451i
$649$	110035.	−	110035.i	0.261240	−	0.261240i
$650$		−	34387.4i		−	0.0813902i
$651$	106171.	+	348026.i	0.250521	+	0.821201i
$652$	−184672.	−	184672.i	−0.434415	−	0.434415i
$653$	244805.	−	244805.i	0.574108	−	0.574108i	−0.359166	−	0.933274i	$-0.616939\pi$
$653$	244805.	−	244805.i	0.574108	−	0.574108i	0.933274	+	0.359166i	$0.116939\pi$
$654$	−50995.9	+	95768.9i	−0.119228	+	0.223908i
$655$		−	654642.i		−	1.52588i
$656$	−469027.	+	469027.i	−1.08991	+	1.08991i
$657$	−99571.9	+	508949.i	−0.230678	+	1.17908i
$658$	58267.5	−	58267.5i	0.134578	−	0.134578i
$659$			435078.i			1.00184i	0.865495	+	0.500918i	$0.167004\pi$
$659$			435078.i			1.00184i	−0.865495	+	0.500918i	$0.832996\pi$
$660$	−162325.	−	532099.i	−0.372648	−	1.22153i
$661$			300383.i			0.687499i	0.939061	+	0.343750i	$0.111697\pi$
$661$			300383.i			0.687499i	−0.939061	+	0.343750i	$0.888303\pi$
$662$			13944.2i			0.0318183i
$663$	437736.	+	379772.i	0.995831	+	0.863964i
$664$	23857.5			0.0541113
$665$	−649615.			−1.46897
$666$	18101.9	−	92525.4i	0.0408108	−	0.208599i
$667$	−303612.			−0.682445
$668$	213931.	+	213931.i	0.479426	+	0.479426i
$669$	−7588.36	+	2314.95i	−0.0169549	+	0.00517237i
$670$	−10545.8	−	10545.8i	−0.0234924	−	0.0234924i
$671$	109154.			0.242434
$672$	−192364.	+	361255.i	−0.425977	+	0.799973i
$673$	333744.	+	333744.i	0.736858	+	0.736858i	0.971969	−	0.235111i	$-0.0755453\pi$
$673$	333744.	+	333744.i	0.736858	+	0.736858i	−0.235111	+	0.971969i	$0.575545\pi$
$674$	−87968.6	+	87968.6i	−0.193646	+	0.193646i
$675$	−85661.8	+	105390.i	−0.188010	+	0.231309i
$676$	−322831.			−0.706451
$677$	−518731.	−	518731.i	−1.13179	−	1.13179i	−0.989880	−	0.141907i	$-0.954677\pi$
$677$	−518731.	−	518731.i	−1.13179	−	1.13179i	−0.141907	−	0.989880i	$-0.545323\pi$
$678$	−59065.4	−	31451.7i	−0.128491	−	0.0684202i
$679$	581423.			1.26111
$680$	−208145.	−	47707.7i	−0.450140	−	0.103174i
$681$	260886.	+	138919.i	0.562544	+	0.299548i
$682$			62647.9i			0.134691i
$683$	111373.	+	111373.i	0.238747	+	0.238747i	0.816331	−	0.577584i	$-0.196005\pi$
$683$	111373.	+	111373.i	0.238747	+	0.238747i	−0.577584	+	0.816331i	$0.696005\pi$
$684$	−208430.	−	309821.i	−0.445499	−	0.662215i
$685$	−368663.	+	368663.i	−0.785684	+	0.785684i
$686$	41621.1	−	41621.1i	0.0884435	−	0.0884435i
$687$	−514139.	+	156847.i	−1.08935	+	0.332324i
$688$		−	575951.i		−	1.21677i
$689$	−107865.			−0.227218
$690$	−21927.4	−	71877.6i	−0.0460563	−	0.150972i
$691$	−333135.	−	333135.i	−0.697693	−	0.697693i	0.266219	−	0.963912i	$-0.414225\pi$
$691$	−333135.	−	333135.i	−0.697693	−	0.697693i	−0.963912	+	0.266219i	$0.914225\pi$
$692$	525889.	+	525889.i	1.09820	+	1.09820i
$693$	−721550.	+	485416.i	−1.50245	+	1.01076i
$694$	3194.27	−	3194.27i	0.00663212	−	0.00663212i
$695$	−227436.			−0.470858
$696$	94154.4	−	176819.i	0.194367	−	0.365015i
$697$	−191595.	+	835912.i	−0.394383	+	1.72066i
$698$		−	99884.1i		−	0.205015i
$699$	345571.	−	648973.i	0.707267	−	1.32823i
$700$	−152836.	+	152836.i	−0.311910	+	0.311910i
$701$			721571.i			1.46839i	0.678936	+	0.734197i	$0.262441\pi$
$701$			721571.i			1.46839i	−0.678936	+	0.734197i	$0.737559\pi$
$702$	−104418.	−	84871.6i	−0.211885	−	0.172222i
$703$	299070.	+	299070.i	0.605148	+	0.605148i
$704$	308548.	−	308548.i	0.622554	−	0.622554i
$705$	297070.	+	158187.i	0.597696	+	0.318267i
$706$		−	3079.43i		−	0.00617819i
$707$	1.07530e6	−	1.07530e6i	2.15126	−	2.15126i
$708$	−44160.7	−	144758.i	−0.0880986	−	0.288785i
$709$	−28879.7	+	28879.7i	−0.0574514	+	0.0574514i	−0.735249	−	0.677797i	$-0.762935\pi$
$709$	−28879.7	+	28879.7i	−0.0574514	+	0.0574514i	0.677797	+	0.735249i	$0.262935\pi$
$710$			18485.9i			0.0366710i
$711$	481918.	+	94283.4i	0.953309	+	0.186507i
$712$		−	124682.i		−	0.245949i
$713$		−	188827.i		−	0.371437i
$714$	11546.0	+	162840.i	0.0226483	+	0.319422i
$715$	899329.			1.75916
$716$	−443826.			−0.865739
$717$	247629.	−	75543.2i	0.481685	−	0.146946i
$718$	10527.3			0.0204206
$719$	−366122.	−	366122.i	−0.708220	−	0.708220i	0.257941	−	0.966161i	$-0.416956\pi$
$719$	−366122.	−	366122.i	−0.708220	−	0.708220i	−0.966161	+	0.257941i	$0.916956\pi$
$720$	−506117.	−	99017.8i	−0.976306	−	0.191007i
$721$	−167154.	−	167154.i	−0.321549	−	0.321549i
$722$	32888.4			0.0630911
$723$	191606.	+	102028.i	0.366550	+	0.195184i
$724$	322205.	+	322205.i	0.614689	+	0.614689i
$725$	113030.	−	113030.i	0.215039	−	0.215039i
$726$	−38801.7	+	11837.1i	−0.0736169	+	0.0224580i
$727$	337029.			0.637673			0.318836	−	0.947810i	$-0.396708\pi$
$727$	337029.			0.637673			0.318836	+	0.947810i	$0.396708\pi$
$728$	−309639.	−	309639.i	−0.584242	−	0.584242i
$729$	108596.	+	520227.i	0.204343	+	0.978899i
$730$	151077.			0.283499
$731$	−395601.	−	630874.i	−0.740326	−	1.18061i
$732$	49895.7	−	93702.8i	0.0931196	−	0.174876i
$733$		−	482661.i		−	0.898326i	−0.893450	−	0.449163i	$-0.851722\pi$
$733$		−	482661.i		−	0.898326i	0.893450	−	0.449163i	$-0.148278\pi$
$734$	7537.55	+	7537.55i	0.0139907	+	0.0139907i
$735$	755475.	+	402283.i	1.39845	+	0.744658i
$736$	150188.	−	150188.i	0.277255	−	0.277255i
$737$	63332.7	−	63332.7i	0.116598	−	0.116598i
$738$	38232.5	−	195421.i	0.0701973	−	0.358805i
$739$			824830.i			1.51034i	0.655527	+	0.755172i	$0.272446\pi$
$739$			824830.i			1.51034i	−0.655527	+	0.755172i	$0.727554\pi$
$740$	612832.			1.11912
$741$	577380.	−	176139.i	1.05154	−	0.320789i
$742$	−21485.7	−	21485.7i	−0.0390250	−	0.0390250i
$743$	−261283.	−	261283.i	−0.473298	−	0.473298i	0.429682	−	0.902980i	$-0.358625\pi$
$743$	−261283.	−	261283.i	−0.473298	−	0.473298i	−0.902980	+	0.429682i	$0.858625\pi$
$744$	109970.	+	58558.0i	0.198669	+	0.105789i
$745$	526844.	−	526844.i	0.949225	−	0.949225i
$746$	124996.			0.224604
$747$	61807.9	−	41580.7i	0.110765	−	0.0745162i
$748$	140115.	−	611310.i	0.250427	−	1.09259i
$749$			550486.i			0.981257i
$750$	−82235.0	−	43789.3i	−0.146196	−	0.0778476i
$751$	395617.	−	395617.i	0.701447	−	0.701447i	−0.263274	−	0.964721i	$-0.584802\pi$
$751$	395617.	−	395617.i	0.701447	−	0.701447i	0.964721	+	0.263274i	$0.0848024\pi$
$752$			293470.i			0.518952i
$753$	−368685.	+	112473.i	−0.650228	+	0.198362i
$754$	111987.	+	111987.i	0.196982	+	0.196982i
$755$	33067.3	−	33067.3i	0.0580103	−	0.0580103i
$756$	86874.0	+	841304.i	0.152001	+	1.47201i
$757$		−	613709.i		−	1.07095i	−0.844550	−	0.535477i	$-0.820132\pi$
$757$		−	613709.i		−	1.07095i	0.844550	−	0.535477i	$-0.179868\pi$
$758$	−143918.	+	143918.i	−0.250483	+	0.250483i
$759$	431662.	−	131685.i	0.749307	−	0.228588i
$760$	−157285.	+	157285.i	−0.272308	+	0.272308i
$761$		−	116249.i		−	0.200734i	−0.994950	−	0.100367i	$-0.967998\pi$
$761$		−	116249.i		−	0.200734i	0.994950	−	0.100367i	$-0.0320017\pi$
$762$	51892.7	−	15830.7i	0.0893709	−	0.0272640i
$763$			1.10249e6i			1.89376i
$764$			249801.i			0.427964i
$765$	−622393.	+	239175.i	−1.06351	+	0.408688i
$766$	−128079.			−0.218282
$767$	244663.			0.415889
$768$	−102937.	−	337424.i	−0.174521	−	0.572076i
$769$	−864377.			−1.46167			−0.730837	−	0.682552i	$-0.760870\pi$
$769$	−864377.			−1.46167			−0.730837	+	0.682552i	$0.760870\pi$
$770$	179138.	+	179138.i	0.302139	+	0.302139i
$771$	−172727.	−	566194.i	−0.290570	−	0.952482i
$772$	−39641.6	−	39641.6i	−0.0665145	−	0.0665145i
$773$	−894829.			−1.49755			−0.748775	−	0.662824i	$-0.769358\pi$
$773$	−894829.			−1.49755			−0.748775	+	0.662824i	$0.769358\pi$
$774$	96511.3	+	143460.i	0.161100	+	0.239468i
$775$	70297.5	+	70297.5i	0.117041	+	0.117041i
$776$	140775.	−	140775.i	0.233776	−	0.233776i
$777$	−279533.	−	916304.i	−0.463011	−	1.51774i
$778$	−172710.			−0.285337
$779$	631659.	+	631659.i	1.04090	+	1.04090i
$780$	411097.	−	772028.i	0.675701	−	1.26895i
$781$	−111017.			−0.182007
$782$	18927.2	−	82577.7i	0.0309508	−	0.135036i
$783$	−64247.8	−	622188.i	−0.104794	−	1.01484i
$784$			746319.i			1.21421i
$785$	307447.	+	307447.i	0.498921	+	0.498921i
$786$	−80542.1	+	151256.i	−0.130370	+	0.244831i
$787$	326851.	−	326851.i	0.527716	−	0.527716i	−0.392175	−	0.919891i	$-0.628277\pi$
$787$	326851.	−	326851.i	0.527716	−	0.527716i	0.919891	+	0.392175i	$0.128277\pi$
$788$	−346448.	+	346448.i	−0.557937	+	0.557937i
$789$	235047.	+	770477.i	0.377572	+	1.23767i
$790$		−	143053.i		−	0.229215i
$791$	−679960.			−1.08675
$792$	−57172.7	+	292231.i	−0.0911462	+	0.465882i
$793$	121352.	+	121352.i	0.192974	+	0.192974i
$794$	51943.8	+	51943.8i	0.0823934	+	0.0823934i
$795$	58330.2	−	109542.i	0.0922910	−	0.173320i
$796$	−699877.	+	699877.i	−1.10458	+	1.10458i
$797$	1.03809e6			1.63426			0.817128	−	0.576456i	$-0.195565\pi$
$797$	1.03809e6			1.63426			0.817128	+	0.576456i	$0.195565\pi$
$798$	150094.	+	79923.5i	0.235699	+	0.125507i
$799$	201574.	+	321455.i	0.315749	+	0.503531i
$800$			111825.i			0.174727i
$801$	−217307.	−	323016.i	−0.338694	−	0.503454i
$802$	65314.7	−	65314.7i	0.101546	−	0.101546i
$803$			907294.i			1.40707i
$804$	−25417.6	−	83318.2i	−0.0393207	−	0.128893i
$805$	−539941.	−	539941.i	−0.833211	−	0.833211i
$806$	−69649.0	+	69649.0i	−0.107212	+	0.107212i
$807$	−1175.39	+	2207.36i	−0.00180483	+	0.00338942i
$808$		−	520706.i		−	0.797572i
$809$	41326.7	−	41326.7i	0.0631442	−	0.0631442i	−0.674829	−	0.737974i	$-0.735783\pi$
$809$	41326.7	−	41326.7i	0.0631442	−	0.0631442i	0.737974	+	0.674829i	$0.235783\pi$
$810$	142658.	−	60145.7i	0.217433	−	0.0916715i
$811$	−221582.	+	221582.i	−0.336893	+	0.336893i	−0.855197	−	0.518303i	$-0.826564\pi$
$811$	−221582.	+	221582.i	−0.336893	+	0.336893i	0.518303	+	0.855197i	$0.326564\pi$
$812$		−	995465.i		−	1.50978i
$813$	−155693.	−	510357.i	−0.235552	−	0.772134i
$814$		−	164943.i		−	0.248935i
$815$			485765.i			0.731325i
$816$	−439156.	−	381003.i	−0.659536	−	0.572201i
$817$	−775658.			−1.16205
$818$	228904.			0.342094
$819$	−1.34185e6	−	262522.i	−2.00049	−	0.391379i
$820$	1.29435e6			1.92497
$821$	526452.	+	526452.i	0.781039	+	0.781039i	0.980006	−	0.198967i	$-0.0637588\pi$
$821$	526452.	+	526452.i	0.781039	+	0.781039i	−0.198967	+	0.980006i	$0.563759\pi$
$822$	130537.	−	39822.5i	0.193193	−	0.0589366i
$823$	−240311.	−	240311.i	−0.354792	−	0.354792i	0.507097	−	0.861889i	$-0.330719\pi$
$823$	−240311.	−	240311.i	−0.354792	−	0.354792i	−0.861889	+	0.507097i	$0.830719\pi$
$824$	−80943.0			−0.119213
$825$	−111677.	+	209726.i	−0.164080	+	0.308137i
$826$	48734.6	+	48734.6i	0.0714295	+	0.0714295i
$827$	−234202.	+	234202.i	−0.342437	+	0.342437i	−0.857283	−	0.514846i	$-0.827849\pi$
$827$	−234202.	+	234202.i	−0.342437	+	0.342437i	0.514846	+	0.857283i	$0.327849\pi$
$828$	84273.8	−	430755.i	0.122923	−	0.628304i
$829$	−443593.			−0.645469			−0.322734	−	0.946490i	$-0.604602\pi$
$829$	−443593.			−0.645469			−0.322734	+	0.946490i	$0.604602\pi$
$830$	−15345.0	−	15345.0i	−0.0222746	−	0.0222746i
$831$	−487778.	−	259737.i	−0.706350	−	0.376124i
$832$	686058.			0.991092
$833$	512621.	+	817488.i	0.738765	+	1.17813i
$834$	52549.4	+	27982.0i	0.0755502	+	0.0402297i
$835$		−	562730.i		−	0.807100i
$836$	−461938.	−	461938.i	−0.660954	−	0.660954i
$837$	386961.	−	39958.0i	0.552352	−	0.0570365i
$838$	14076.5	−	14076.5i	0.0200450	−	0.0200450i
$839$	186640.	−	186640.i	0.265143	−	0.265143i	−0.561996	−	0.827140i	$-0.689967\pi$
$839$	186640.	−	186640.i	0.265143	−	0.265143i	0.827140	+	0.561996i	$0.189967\pi$
$840$	481898.	−	147011.i	0.682961	−	0.208348i
$841$			28916.5i			0.0408840i
$842$	−41212.4			−0.0581305
$843$	−137172.	−	449647.i	−0.193024	−	0.632728i
$844$	121280.	+	121280.i	0.170257	+	0.170257i
$845$	424592.	+	424592.i	0.594645	+	0.594645i
$846$	−49176.3	−	73098.3i	−0.0687092	−	0.102133i
$847$	−291477.	+	291477.i	−0.406291	+	0.406291i
$848$	108215.			0.150486
$849$	−549090.	+	1.03118e6i	−0.761777	+	1.43060i
$850$	23696.1	+	37788.7i	0.0327974	+	0.0523027i
$851$			497156.i			0.686489i
$852$	−50747.6	+	95302.6i	−0.0699095	+	0.131288i
$853$	−986343.	+	986343.i	−1.35560	+	1.35560i	−0.476327	+	0.879268i	$0.658032\pi$
$853$	−986343.	+	986343.i	−1.35560	+	1.35560i	−0.879268	+	0.476327i	$0.841968\pi$
$854$			48344.4i			0.0662873i
$855$	−133352.	+	681610.i	−0.182417	+	0.932403i
$856$	133284.	+	133284.i	0.181899	+	0.181899i
$857$	−602910.	+	602910.i	−0.820901	+	0.820901i	−0.986237	−	0.165336i	$-0.947129\pi$
$857$	−602910.	+	602910.i	−0.820901	+	0.820901i	0.165336	+	0.986237i	$0.447129\pi$
$858$	−207791.	−	110646.i	−0.282262	−	0.150301i
$859$		−	361011.i		−	0.489253i	−0.969617	−	0.244627i	$-0.921335\pi$
$859$		−	361011.i		−	0.489253i	0.969617	−	0.244627i	$-0.0786654\pi$
$860$	−794711.	+	794711.i	−1.07451	+	1.07451i
$861$	−590396.	−	1.93530e6i	−0.796411	−	2.61062i
$862$	−34314.8	+	34314.8i	−0.0461813	+	0.0461813i
$863$		−	530897.i		−	0.712834i	−0.934327	−	0.356417i	$-0.883998\pi$
$863$		−	530897.i		−	0.712834i	0.934327	−	0.356417i	$-0.116002\pi$
$864$	339559.	+	275996.i	0.454871	+	0.369722i
$865$		−	1.38331e6i		−	1.84879i
$866$		−	227760.i		−	0.303698i
$867$	−742732.	−	115695.i	−0.988084	−	0.153913i
$868$	619115.			0.821736
$869$	859106.			1.13765
$870$	−174288.	+	53169.5i	−0.230266	+	0.0702464i
$871$	140821.			0.185622
$872$	266936.	+	266936.i	0.351054	+	0.351054i
$873$	119353.	−	610059.i	0.156605	−	0.800467i
$874$	−62400.0	−	62400.0i	−0.0816887	−	0.0816887i
$875$	−946690.			−1.23649
$876$	778866.	+	414738.i	1.01497	+	0.540462i
$877$	−755819.	−	755819.i	−0.982694	−	0.982694i	0.0171584	−	0.999853i	$-0.494538\pi$
$877$	−755819.	−	755819.i	−0.982694	−	0.982694i	−0.999853	+	0.0171584i	$0.994538\pi$
$878$	−136013.	+	136013.i	−0.176437	+	0.176437i
$879$	351826.	−	107330.i	0.455355	−	0.138913i
$880$	−902246.			−1.16509
$881$	−428117.	−	428117.i	−0.551583	−	0.551583i	0.375315	−	0.926897i	$-0.377535\pi$
$881$	−428117.	−	428117.i	−0.551583	−	0.551583i	−0.926897	+	0.375315i	$0.877535\pi$
$882$	−125060.	−	185896.i	−0.160761	−	0.238964i
$883$	−187757.			−0.240810			−0.120405	−	0.992725i	$-0.538419\pi$
$883$	−187757.			−0.240810			−0.120405	+	0.992725i	$0.538419\pi$
$884$	835399.	−	523853.i	1.06903	−	0.670355i
$885$	−132306.	+	248468.i	−0.168925	+	0.317237i
$886$			99107.9i			0.126253i
$887$	−1.02112e6	−	1.02112e6i	−1.29787	−	1.29787i	−0.929798	−	0.368071i	$-0.880018\pi$
$887$	−1.02112e6	−	1.02112e6i	−1.29787	−	1.29787i	−0.368071	−	0.929798i	$-0.619982\pi$
$888$	−289537.	−	154175.i	−0.367179	−	0.195519i
$889$	389816.	−	389816.i	0.493237	−	0.493237i
$890$	−80194.9	+	80194.9i	−0.101243	+	0.101243i
$891$	361206.	+	856732.i	0.454987	+	1.07917i
$892$			13499.2i			0.0169660i
$893$	395228.			0.495615
$894$	−186546.	+	56909.0i	−0.233406	+	0.0712043i
$895$	583726.	+	583726.i	0.728723	+	0.728723i
$896$	651153.	+	651153.i	0.811086	+	0.811086i
$897$	626303.	+	333500.i	0.778394	+	0.414487i
$898$	102039.	−	102039.i	0.126536	−	0.126536i
$899$	−457868.			−0.566527
$900$	128990.	+	191737.i	0.159246	+	0.236713i
$901$	118534.	−	74329.1i	0.146014	−	0.0915607i
$902$		−	348373.i		−	0.428185i
$903$	1.55074e6	+	825754.i	1.90180	+	1.01269i
$904$	−164632.	+	164632.i	−0.201455	+	0.201455i
$905$		−	847536.i		−	1.03481i
$906$	−11708.6	+	3571.89i	−0.0142642	+	0.00435153i
$907$	915230.	+	915230.i	1.11254	+	1.11254i	0.992806	+	0.119733i	$0.0382040\pi$
$907$	915230.	+	915230.i	1.11254	+	1.11254i	0.119733	+	0.992806i	$0.461796\pi$
$908$	355613.	−	355613.i	0.431327	−	0.431327i
$909$	−907528.	−	1.34900e6i	−1.09833	−	1.63262i
$910$			398315.i			0.480999i
$911$	−27547.7	+	27547.7i	−0.0331931	+	0.0331931i	−0.723509	−	0.690315i	$-0.757472\pi$
$911$	−27547.7	+	27547.7i	−0.0331931	+	0.0331931i	0.690315	+	0.723509i	$0.257472\pi$
$912$	−579252.	+	176710.i	−0.696431	+	0.212458i
$913$	92154.4	−	92154.4i	0.110554	−	0.110554i
$914$		−	162143.i		−	0.194091i
$915$	−188863.	+	57615.6i	−0.225582	+	0.0688173i
$916$			914621.i			1.09006i
$917$			1.74126e6i			2.07073i
$918$	173231.	+	21312.8i	0.205560	+	0.0252904i
$919$	−518902.			−0.614405			−0.307202	−	0.951644i	$-0.599393\pi$
$919$	−518902.			−0.614405			−0.307202	+	0.951644i	$0.599393\pi$
$920$	−261462.			−0.308910
$921$	28495.5	+	93407.7i	0.0335937	+	0.110119i
$922$	−15534.0			−0.0182735
$923$	−123424.	−	123424.i	−0.144876	−	0.144876i
$924$	431762.	+	1.41531e6i	0.505709	+	1.65770i
$925$	−185084.	−	185084.i	−0.216314	−	0.216314i
$926$	−177897.			−0.207466
$927$	−209700.	+	141074.i	−0.244028	+	0.164167i
$928$	−364175.	−	364175.i	−0.422877	−	0.422877i
$929$	1.14055e6	−	1.14055e6i	1.32155	−	1.32155i	0.409020	−	0.912526i	$-0.365871\pi$
$929$	1.14055e6	−	1.14055e6i	1.32155	−	1.32155i	0.912526	−	0.409020i	$-0.134129\pi$
$930$	−33068.0	−	108396.i	−0.0382334	−	0.125328i
$931$	1.00510e6			1.15960
$932$	−884615.	−	884615.i	−1.01841	−	1.01841i
$933$	−414501.	+	778420.i	−0.476170	+	0.894234i
$934$	274937.			0.315166
$935$	−988284.	+	619722.i	−1.13047	+	0.708881i
$936$	−388451.	+	261327.i	−0.443388	+	0.298286i
$937$		−	508278.i		−	0.578925i	−0.957189	−	0.289463i	$-0.906523\pi$
$937$		−	508278.i		−	0.578925i	0.957189	−	0.289463i	$-0.0934766\pi$
$938$	28050.2	+	28050.2i	0.0318809	+	0.0318809i
$939$	−11070.5	+	20790.2i	−0.0125556	+	0.0235791i
$940$	404936.	−	404936.i	0.458280	−	0.458280i
$941$	78149.4	−	78149.4i	0.0882564	−	0.0882564i	−0.661600	−	0.749857i	$-0.730122\pi$
$941$	78149.4	−	78149.4i	0.0882564	−	0.0882564i	0.749857	+	0.661600i	$0.230122\pi$
$942$	−33210.1	−	108862.i	−0.0374256	−	0.122680i
$943$			1.05003e6i			1.18081i
$944$	−245456.			−0.275442
$945$	992236.	−	1.22075e6i	1.11110	−	1.36699i
$946$	213896.	+	213896.i	0.239012	+	0.239012i
$947$	482785.	+	482785.i	0.538336	+	0.538336i	0.923040	−	0.384704i	$-0.125696\pi$
$947$	482785.	+	482785.i	0.538336	+	0.538336i	−0.384704	+	0.923040i	$0.625696\pi$
$948$	392710.	−	737498.i	0.436974	−	0.820624i
$949$	−1.00869e6	+	1.00869e6i	−1.12002	+	1.12002i
$950$	46461.1			0.0514805
$951$	1.12399e6	+	598514.i	1.24280	+	0.661779i
$952$	553636.	+	126896.i	0.610872	+	0.140015i
$953$			33029.3i			0.0363675i	0.999835	+	0.0181837i	$0.00578838\pi$
$953$			33029.3i			0.0363675i	−0.999835	+	0.0181837i	$0.994212\pi$
$954$	−26954.5	+	18133.4i	−0.0296165	+	0.0199243i
$955$	328542.	−	328542.i	0.360233	−	0.360233i
$956$		−	440516.i		−	0.481999i
$957$	−319310.	−	1.04669e6i	−0.348650	−	1.14287i
$958$	−5944.61	−	5944.61i	−0.00647728	−	0.00647728i
$959$	980590.	−	980590.i	1.06623	−	1.06623i
$960$	−371000.	+	696727.i	−0.402561	+	0.755998i
$961$			638757.i			0.691654i
$962$	183376.	−	183376.i	0.198149	−	0.198149i
$963$	577598.	+	113003.i	0.622835	+	0.121853i
$964$	261178.	−	261178.i	0.281050	−	0.281050i
$965$			104274.i			0.111975i
$966$	58323.8	+	191184.i	0.0625017	+	0.204879i
$967$		−	1.05612e6i		−	1.12944i	−0.825284	−	0.564718i	$-0.808985\pi$
$967$		−	1.05612e6i		−	1.12944i	0.825284	−	0.564718i	$-0.191015\pi$
$968$			141145.i			0.150631i
$969$	−513114.	+	591430.i	−0.546470	+	0.629877i
$970$	−181090.			−0.192465
$971$	−21683.3			−0.0229979			−0.0114989	−	0.999934i	$-0.503660\pi$
$971$	−21683.3			−0.0229979			−0.0114989	+	0.999934i	$0.503660\pi$
$972$	900573.	+	81548.4i	0.953205	+	0.0863143i
$973$	604948.			0.638988
$974$	166104.	+	166104.i	0.175090	+	0.175090i
$975$	−357320.	+	109006.i	−0.375879	+	0.114668i
$976$	−121745.	−	121745.i	−0.127806	−	0.127806i
$977$	55537.0			0.0581826			0.0290913	−	0.999577i	$-0.490739\pi$
$977$	55537.0			0.0581826			0.0290913	+	0.999577i	$0.490739\pi$
$978$	59764.7	−	112236.i	0.0624837	−	0.117343i
$979$	−481612.	−	481612.i	−0.502495	−	0.502495i
$980$	1.02979e6	−	1.02979e6i	1.07225	−	1.07225i
$981$	1.15679e6	+	226317.i	1.20203	+	0.235168i
$982$	−378501.			−0.392504
$983$	676272.	+	676272.i	0.699865	+	0.699865i	0.964381	−	0.264516i	$-0.0852122\pi$
$983$	676272.	+	676272.i	0.699865	+	0.699865i	−0.264516	+	0.964381i	$0.585212\pi$
$984$	−611524.	−	325630.i	−0.631573	−	0.336306i
$985$	911304.			0.939271
$986$	−200234.	−	45894.6i	−0.205961	−	0.0472071i
$987$	−790164.	−	420754.i	−0.811116	−	0.431911i
$988$		−	1.02712e6i		−	1.05222i
$989$	−644704.	−	644704.i	−0.659125	−	0.659125i
$990$	224734.	−	151188.i	0.229297	−	0.154258i
$991$	697502.	−	697502.i	0.710229	−	0.710229i	−0.256354	−	0.966583i	$-0.582521\pi$
$991$	697502.	−	697502.i	0.710229	−	0.710229i	0.966583	+	0.256354i	$0.0825213\pi$
$992$	226493.	−	226493.i	0.230161	−	0.230161i
$993$	144894.	−	44202.3i	0.146944	−	0.0448277i
$994$		−	49169.8i		−	0.0497652i
$995$	1.84097e6			1.85952
$996$	−36984.7	−	121235.i	−0.0372824	−	0.122211i
$997$	−953020.	−	953020.i	−0.958764	−	0.958764i	0.0404192	−	0.999183i	$-0.487131\pi$
$997$	−953020.	−	953020.i	−0.958764	−	0.958764i	−0.999183	+	0.0404192i	$0.987131\pi$
$998$	−281031.	−	281031.i	−0.282158	−	0.282158i
$999$	−1.01882e6	+	105204.i	−1.02086	+	0.105415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.5.f.a.38.12	yes	44
3.2	odd	2	inner	51.5.f.a.38.11	✓	44
17.13	even	4	inner	51.5.f.a.47.11	yes	44
51.47	odd	4	inner	51.5.f.a.47.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.5.f.a.38.11	✓	44	3.2	odd	2	inner
51.5.f.a.38.12	yes	44	1.1	even	1	trivial
51.5.f.a.47.11	yes	44	17.13	even	4	inner
51.5.f.a.47.12	yes	44	51.47	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.828441 q^{2} +(-2.62611 - 8.60834i) q^{3} -15.3137 q^{4} +(20.1408 + 20.1408i) q^{5} +(-2.17558 - 7.13150i) q^{6} +(-53.5715 - 53.5715i) q^{7} -25.9415 q^{8} +(-67.2071 + 45.2130i) q^{9} +O(q^{10})\)	\(q+0.828441 q^{2} +(-2.62611 - 8.60834i) q^{3} -15.3137 q^{4} +(20.1408 + 20.1408i) q^{5} +(-2.17558 - 7.13150i) q^{6} +(-53.5715 - 53.5715i) q^{7} -25.9415 q^{8} +(-67.2071 + 45.2130i) q^{9} +(16.6854 + 16.6854i) q^{10} +(-100.205 + 100.205i) q^{11} +(40.2155 + 131.825i) q^{12} -222.805 q^{13} +(-44.3808 - 44.3808i) q^{14} +(120.487 - 226.270i) q^{15} +223.528 q^{16} +(244.844 - 153.534i) q^{17} +(-55.6770 + 37.4563i) q^{18} -301.035i q^{19} +(-308.429 - 308.429i) q^{20} +(-320.477 + 601.847i) q^{21} +(-83.0135 + 83.0135i) q^{22} +(250.211 - 250.211i) q^{23} +(68.1254 + 223.313i) q^{24} +186.300i q^{25} -184.581 q^{26} +(565.702 + 459.807i) q^{27} +(820.378 + 820.378i) q^{28} +(-606.711 - 606.711i) q^{29} +(99.8159 - 187.452i) q^{30} +(377.336 - 377.336i) q^{31} +600.244 q^{32} +(1125.74 + 599.446i) q^{33} +(202.838 - 127.194i) q^{34} -2157.94i q^{35} +(1029.19 - 692.377i) q^{36} +(-993.473 + 993.473i) q^{37} -249.389i q^{38} +(585.112 + 1917.98i) q^{39} +(-522.482 - 522.482i) q^{40} +(-2098.29 + 2098.29i) q^{41} +(-265.496 + 498.594i) q^{42} -2576.64i q^{43} +(1534.50 - 1534.50i) q^{44} +(-2264.22 - 442.977i) q^{45} +(207.285 - 207.285i) q^{46} +1312.90i q^{47} +(-587.010 - 1924.20i) q^{48} +3338.82i q^{49} +154.338i q^{50} +(-1964.66 - 1704.50i) q^{51} +3411.97 q^{52} +484.122 q^{53} +(468.650 + 380.923i) q^{54} -4036.39 q^{55} +(1389.73 + 1389.73i) q^{56} +(-2591.41 + 790.551i) q^{57} +(-502.624 - 502.624i) q^{58} -1098.10 q^{59} +(-1845.09 + 3465.03i) q^{60} +(-544.654 - 544.654i) q^{61} +(312.600 - 312.600i) q^{62} +(6022.51 + 1178.26i) q^{63} -3079.18 q^{64} +(-4487.47 - 4487.47i) q^{65} +(932.611 + 496.605i) q^{66} -632.034 q^{67} +(-3749.46 + 2351.17i) q^{68} +(-2810.99 - 1496.82i) q^{69} -1787.73i q^{70} +(553.953 + 553.953i) q^{71} +(1743.45 - 1172.89i) q^{72} +(4527.21 - 4527.21i) q^{73} +(-823.033 + 823.033i) q^{74} +(1603.73 - 489.244i) q^{75} +4609.95i q^{76} +10736.2 q^{77} +(484.731 + 1588.94i) q^{78} +(-4286.76 - 4286.76i) q^{79} +(4502.02 + 4502.02i) q^{80} +(2472.58 - 6077.26i) q^{81} +(-1738.31 + 1738.31i) q^{82} -919.663 q^{83} +(4907.68 - 9216.50i) q^{84} +(8023.62 + 1839.05i) q^{85} -2134.59i q^{86} +(-3629.49 + 6816.07i) q^{87} +(2599.46 - 2599.46i) q^{88} +4806.29i q^{89} +(-1875.77 - 366.980i) q^{90} +(11936.0 + 11936.0i) q^{91} +(-3831.66 + 3831.66i) q^{92} +(-4239.16 - 2257.31i) q^{93} +1087.66i q^{94} +(6063.06 - 6063.06i) q^{95} +(-1576.31 - 5167.11i) q^{96} +(-5426.61 + 5426.61i) q^{97} +2766.01i q^{98} +(2203.91 - 11265.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7}+O(q^{10}) \) 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7	\( 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7} + 288 q^{10} - 234 q^{12} + 92 q^{13} + 960 q^{16} - 580 q^{18} - 1856 q^{21} + 120 q^{22} - 10 q^{24} + 378 q^{27} + 1648 q^{28} - 1248 q^{30} + 808 q^{31} + 2520 q^{33} - 5016 q^{34} - 5560 q^{37} + 152 q^{39} - 7020 q^{40} - 2696 q^{45} - 6620 q^{46} - 926 q^{48} + 11810 q^{51} + 5504 q^{52} + 6250 q^{54} + 9740 q^{55} + 16704 q^{57} + 4316 q^{58} + 9304 q^{61} + 27608 q^{63} - 6176 q^{64} + 23912 q^{67} - 3444 q^{69} - 54204 q^{72} + 14216 q^{73} - 5242 q^{75} - 25516 q^{78} + 4052 q^{79} + 6796 q^{81} + 14708 q^{82} - 59208 q^{84} - 32480 q^{85} - 28412 q^{88} - 21312 q^{90} - 38772 q^{91} - 56806 q^{96} - 92448 q^{97} - 18072 q^{99}+O(q^{100}) \) 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7 + 288 * q^10 - 234 * q^12 + 92 * q^13 + 960 * q^16 - 580 * q^18 - 1856 * q^21 + 120 * q^22 - 10 * q^24 + 378 * q^27 + 1648 * q^28 - 1248 * q^30 + 808 * q^31 + 2520 * q^33 - 5016 * q^34 - 5560 * q^37 + 152 * q^39 - 7020 * q^40 - 2696 * q^45 - 6620 * q^46 - 926 * q^48 + 11810 * q^51 + 5504 * q^52 + 6250 * q^54 + 9740 * q^55 + 16704 * q^57 + 4316 * q^58 + 9304 * q^61 + 27608 * q^63 - 6176 * q^64 + 23912 * q^67 - 3444 * q^69 - 54204 * q^72 + 14216 * q^73 - 5242 * q^75 - 25516 * q^78 + 4052 * q^79 + 6796 * q^81 + 14708 * q^82 - 59208 * q^84 - 32480 * q^85 - 28412 * q^88 - 21312 * q^90 - 38772 * q^91 - 56806 * q^96 - 92448 * q^97 - 18072 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more