LMFDB - Embedded newform 16.5.f.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,5,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, 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("16.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	16.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:	$1.65391940934$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.7
Root			$-2.40693 - 1.48549i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.5.f.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.89242 + 0.921438i) q^{2} +(-0.0461995 - 0.0461995i) q^{3} +(14.3019 + 7.17325i) q^{4} +(-8.04297 - 8.04297i) q^{5} +(-0.137258 - 0.222398i) q^{6} -49.8797 q^{7} +(49.0594 + 41.0996i) q^{8} -80.9957i q^{9} +(-23.8955 - 38.7177i) q^{10} +(-84.2573 + 84.2573i) q^{11} +(-0.329340 - 0.992142i) q^{12} +(19.4838 - 19.4838i) q^{13} +(-194.153 - 45.9610i) q^{14} +0.743162i q^{15} +(153.089 + 205.182i) q^{16} +437.855 q^{17} +(74.6325 - 315.270i) q^{18} +(349.021 + 349.021i) q^{19} +(-57.3356 - 172.724i) q^{20} +(2.30442 + 2.30442i) q^{21} +(-405.603 + 250.327i) q^{22} -404.840 q^{23} +(-0.367736 - 4.16530i) q^{24} -495.621i q^{25} +(93.7922 - 57.8860i) q^{26} +(-7.48412 + 7.48412i) q^{27} +(-713.374 - 357.799i) q^{28} +(-1031.65 + 1031.65i) q^{29} +(-0.684778 + 2.89270i) q^{30} -1506.15i q^{31} +(406.824 + 939.718i) q^{32} +7.78529 q^{33} +(1704.32 + 403.456i) q^{34} +(401.181 + 401.181i) q^{35} +(581.003 - 1158.39i) q^{36} +(-434.262 - 434.262i) q^{37} +(1036.94 + 1680.14i) q^{38} -1.80028 q^{39} +(-64.0199 - 725.146i) q^{40} +696.847i q^{41} +(6.84639 + 11.0931i) q^{42} +(917.612 - 917.612i) q^{43} +(-1809.44 + 600.641i) q^{44} +(-651.446 + 651.446i) q^{45} +(-1575.81 - 373.035i) q^{46} +111.917i q^{47} +(2.40668 - 16.5520i) q^{48} +86.9810 q^{49} +(456.684 - 1929.17i) q^{50} +(-20.2287 - 20.2287i) q^{51} +(418.417 - 138.893i) q^{52} +(1041.19 + 1041.19i) q^{53} +(-36.0275 + 22.2352i) q^{54} +1355.36 q^{55} +(-2447.06 - 2050.04i) q^{56} -32.2492i q^{57} +(-4966.23 + 3065.02i) q^{58} +(-1711.60 + 1711.60i) q^{59} +(-5.33089 + 10.6286i) q^{60} +(3711.24 - 3711.24i) q^{61} +(1387.83 - 5862.58i) q^{62} +4040.04i q^{63} +(717.641 + 4032.64i) q^{64} -313.415 q^{65} +(30.3036 + 7.17366i) q^{66} +(-1854.18 - 1854.18i) q^{67} +(6262.16 + 3140.84i) q^{68} +(18.7034 + 18.7034i) q^{69} +(1191.90 + 1931.23i) q^{70} -1161.89 q^{71} +(3328.89 - 3973.60i) q^{72} -905.295i q^{73} +(-1290.19 - 2090.48i) q^{74} +(-22.8975 + 22.8975i) q^{75} +(2488.05 + 7495.28i) q^{76} +(4202.72 - 4202.72i) q^{77} +(-7.00746 - 1.65885i) q^{78} +5869.63i q^{79} +(418.984 - 2881.56i) q^{80} -6559.96 q^{81} +(-642.101 + 2712.42i) q^{82} +(-7560.06 - 7560.06i) q^{83} +(16.4274 + 49.4877i) q^{84} +(-3521.65 - 3521.65i) q^{85} +(4417.25 - 2726.21i) q^{86} +95.3236 q^{87} +(-7596.55 + 670.665i) q^{88} +6439.80i q^{89} +(-3135.97 + 1935.44i) q^{90} +(-971.844 + 971.844i) q^{91} +(-5789.98 - 2904.02i) q^{92} +(-69.5835 + 69.5835i) q^{93} +(-103.125 + 435.628i) q^{94} -5614.33i q^{95} +(24.6194 - 62.2096i) q^{96} -413.032 q^{97} +(338.567 + 80.1476i) q^{98} +(6824.48 + 6824.48i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20}+ \cdots + 49214 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	3.89242	+	0.921438i	0.973106	+	0.230359i
$2$	3.89242	+	0.921438i	0.973106	+	0.230359i
$3$	−0.0461995	−	0.0461995i	−0.00513328	−	0.00513328i	0.704535	−	0.709669i	$-0.251155\pi$
$3$	−0.0461995	−	0.0461995i	−0.00513328	−	0.00513328i	−0.709669	+	0.704535i	$0.751155\pi$
$4$	14.3019	+	7.17325i	0.893869	+	0.448328i
$5$	−8.04297	−	8.04297i	−0.321719	−	0.321719i	0.527707	−	0.849426i	$-0.323052\pi$
$5$	−8.04297	−	8.04297i	−0.321719	−	0.321719i	−0.849426	+	0.527707i	$0.823052\pi$
$6$	−0.137258	−	0.222398i	−0.00381272	−	0.00617772i
$7$	−49.8797			−1.01795			−0.508976	−	0.860781i	$-0.669976\pi$
$7$	−49.8797			−1.01795			−0.508976	+	0.860781i	$0.669976\pi$
$8$	49.0594	+	41.0996i	0.766552	+	0.642182i
$9$		−	80.9957i		−	0.999947i
$10$	−23.8955	−	38.7177i	−0.238955	−	0.387177i
$11$	−84.2573	+	84.2573i	−0.696341	+	0.696341i	−0.963619	−	0.267278i	$-0.913876\pi$
$11$	−84.2573	+	84.2573i	−0.696341	+	0.696341i	0.267278	+	0.963619i	$0.413876\pi$
$12$	−0.329340	−	0.992142i	−0.00228709	−	0.00688987i
$13$	19.4838	−	19.4838i	0.115289	−	0.115289i	−0.647109	−	0.762398i	$-0.724022\pi$
$13$	19.4838	−	19.4838i	0.115289	−	0.115289i	0.762398	+	0.647109i	$0.224022\pi$
$14$	−194.153	−	45.9610i	−0.990575	−	0.234495i
$15$			0.743162i			0.00330294i
$16$	153.089	+	205.182i	0.598004	+	0.801493i
$17$	437.855			1.51507			0.757535	−	0.652795i	$-0.226404\pi$
$17$	437.855			1.51507			0.757535	+	0.652795i	$0.226404\pi$
$18$	74.6325	−	315.270i	0.230347	−	0.973054i
$19$	349.021	+	349.021i	0.966817	+	0.966817i	0.999467	−	0.0326494i	$-0.0103945\pi$
$19$	349.021	+	349.021i	0.966817	+	0.966817i	−0.0326494	+	0.999467i	$0.510394\pi$
$20$	−57.3356	−	172.724i	−0.143339	−	0.431810i
$21$	2.30442	+	2.30442i	0.00522543	+	0.00522543i
$22$	−405.603	+	250.327i	−0.838022	+	0.517205i
$23$	−404.840			−0.765293			−0.382647	−	0.923895i	$-0.624987\pi$
$23$	−404.840			−0.765293			−0.382647	+	0.923895i	$0.624987\pi$
$24$	−0.367736	−	4.16530i	−0.000638430	−	0.00723143i
$25$		−	495.621i		−	0.792994i
$26$	93.7922	−	57.8860i	0.138746	−	0.0856302i
$27$	−7.48412	+	7.48412i	−0.0102663	+	0.0102663i
$28$	−713.374	−	357.799i	−0.909916	−	0.456377i
$29$	−1031.65	+	1031.65i	−1.22670	+	1.22670i	−0.261490	+	0.965206i	$0.584214\pi$
$29$	−1031.65	+	1031.65i	−1.22670	+	1.22670i	−0.965206	+	0.261490i	$0.915786\pi$
$30$	−0.684778	+	2.89270i	−0.000760864	+	0.00321411i
$31$		−	1506.15i		−	1.56728i	−0.621217	−	0.783638i	$-0.713362\pi$
$31$		−	1506.15i		−	1.56728i	0.621217	−	0.783638i	$-0.286638\pi$
$32$	406.824	+	939.718i	0.397290	+	0.917693i
$33$	7.78529			0.00714903
$34$	1704.32	+	403.456i	1.47432	+	0.349011i
$35$	401.181	+	401.181i	0.327494	+	0.327494i
$36$	581.003	−	1158.39i	0.448304	−	0.893822i
$37$	−434.262	−	434.262i	−0.317211	−	0.317211i	0.530484	−	0.847695i	$-0.322010\pi$
$37$	−434.262	−	434.262i	−0.317211	−	0.317211i	−0.847695	+	0.530484i	$0.822010\pi$
$38$	1036.94	+	1680.14i	0.718100	+	1.16353i
$39$	−1.80028			−0.00118362
$40$	−64.0199	−	725.146i	−0.0400124	−	0.453216i
$41$			696.847i			0.414543i	0.978283	+	0.207272i	$0.0664584\pi$
$41$			696.847i			0.414543i	−0.978283	+	0.207272i	$0.933542\pi$
$42$	6.84639	+	11.0931i	0.00388117	+	0.00628863i
$43$	917.612	−	917.612i	0.496275	−	0.496275i	−0.414002	−	0.910276i	$-0.635869\pi$
$43$	917.612	−	917.612i	0.496275	−	0.496275i	0.910276	+	0.414002i	$0.135869\pi$
$44$	−1809.44	+	600.641i	−0.934627	+	0.310249i
$45$	−651.446	+	651.446i	−0.321702	+	0.321702i
$46$	−1575.81	−	373.035i	−0.744711	−	0.176292i
$47$			111.917i			0.0506641i	0.999679	+	0.0253321i	$0.00806431\pi$
$47$			111.917i			0.0506641i	−0.999679	+	0.0253321i	$0.991936\pi$
$48$	2.40668	−	16.5520i	0.00104457	−	0.00718401i
$49$	86.9810			0.0362270
$50$	456.684	−	1929.17i	0.182674	−	0.771667i
$51$	−20.2287	−	20.2287i	−0.00777728	−	0.00777728i
$52$	418.417	−	138.893i	0.154740	−	0.0513658i
$53$	1041.19	+	1041.19i	0.370663	+	0.370663i	0.867719	−	0.497056i	$-0.165586\pi$
$53$	1041.19	+	1041.19i	0.370663	+	0.370663i	−0.497056	+	0.867719i	$0.665586\pi$
$54$	−36.0275	+	22.2352i	−0.0123551	+	0.00762525i
$55$	1355.36			0.448052
$56$	−2447.06	−	2050.04i	−0.780314	−	0.653710i
$57$		−	32.2492i		−	0.00992589i
$58$	−4966.23	+	3065.02i	−1.47629	+	0.911124i
$59$	−1711.60	+	1711.60i	−0.491697	+	0.491697i	−0.908841	−	0.417144i	$-0.863031\pi$
$59$	−1711.60	+	1711.60i	−0.491697	+	0.491697i	0.417144	+	0.908841i	$0.363031\pi$
$60$	−5.33089	+	10.6286i	−0.00148080	+	0.00295240i
$61$	3711.24	−	3711.24i	0.997376	−	0.997376i	−0.00262076	−	0.999997i	$-0.500834\pi$
$61$	3711.24	−	3711.24i	0.997376	−	0.997376i	0.999997	+	0.00262076i	$0.000834216\pi$
$62$	1387.83	−	5862.58i	0.361037	−	1.52513i
$63$			4040.04i			1.01790i
$64$	717.641	+	4032.64i	0.175205	+	0.984532i
$65$	−313.415			−0.0741810
$66$	30.3036	+	7.17366i	0.00695676	+	0.00164685i
$67$	−1854.18	−	1854.18i	−0.413049	−	0.413049i	0.469750	−	0.882799i	$-0.344344\pi$
$67$	−1854.18	−	1854.18i	−0.413049	−	0.413049i	−0.882799	+	0.469750i	$0.844344\pi$
$68$	6262.16	+	3140.84i	1.35427	+	0.679248i
$69$	18.7034	+	18.7034i	0.00392846	+	0.00392846i
$70$	1191.90	+	1931.23i	0.243245	+	0.394128i
$71$	−1161.89			−0.230489			−0.115244	−	0.993337i	$-0.536765\pi$
$71$	−1161.89			−0.230489			−0.115244	+	0.993337i	$0.536765\pi$
$72$	3328.89	−	3973.60i	0.642148	−	0.766512i
$73$		−	905.295i		−	0.169881i	−0.996386	−	0.0849404i	$-0.972930\pi$
$73$		−	905.295i		−	0.169881i	0.996386	−	0.0849404i	$-0.0270700\pi$
$74$	−1290.19	−	2090.48i	−0.235608	−	0.381753i
$75$	−22.8975	+	22.8975i	−0.00407066	+	0.00407066i
$76$	2488.05	+	7495.28i	0.430757	+	1.29766i
$77$	4202.72	−	4202.72i	0.708842	−	0.708842i
$78$	−7.00746	−	1.65885i	−0.00115178	−	0.000272657i
$79$			5869.63i			0.940495i	0.882535	+	0.470247i	$0.155835\pi$
$79$			5869.63i			0.940495i	−0.882535	+	0.470247i	$0.844165\pi$
$80$	418.984	−	2881.56i	0.0654663	−	0.450244i
$81$	−6559.96			−0.999842
$82$	−642.101	+	2712.42i	−0.0954939	+	0.403394i
$83$	−7560.06	−	7560.06i	−1.09741	−	1.09741i	−0.994713	−	0.102698i	$-0.967252\pi$
$83$	−7560.06	−	7560.06i	−1.09741	−	1.09741i	−0.102698	−	0.994713i	$-0.532748\pi$
$84$	16.4274	+	49.4877i	0.00232815	+	0.00701356i
$85$	−3521.65	−	3521.65i	−0.487426	−	0.487426i
$86$	4417.25	−	2726.21i	0.597249	−	0.368606i
$87$	95.3236			0.0125939
$88$	−7596.55	+	670.665i	−0.980959	+	0.0866045i
$89$			6439.80i			0.813004i	0.913650	+	0.406502i	$0.133252\pi$
$89$			6439.80i			0.813004i	−0.913650	+	0.406502i	$0.866748\pi$
$90$	−3135.97	+	1935.44i	−0.387157	+	0.238943i
$91$	−971.844	+	971.844i	−0.117358	+	0.117358i
$92$	−5789.98	−	2904.02i	−0.684072	−	0.343102i
$93$	−69.5835	+	69.5835i	−0.00804527	+	0.00804527i
$94$	−103.125	+	435.628i	−0.0116710	+	0.0493015i
$95$		−	5614.33i		−	0.622087i
$96$	24.6194	−	62.2096i	0.00267138	−	0.00675017i
$97$	−413.032			−0.0438976			−0.0219488	−	0.999759i	$-0.506987\pi$
$97$	−413.032			−0.0438976			−0.0219488	+	0.999759i	$0.506987\pi$
$98$	338.567	+	80.1476i	0.0352527	+	0.00834523i
$99$	6824.48	+	6824.48i	0.696304	+	0.696304i
$100$	3555.22	−	7088.33i	0.355522	−	0.708833i
$101$	8460.63	+	8460.63i	0.829392	+	0.829392i	0.987433	−	0.158041i	$-0.0505177\pi$
$101$	8460.63	+	8460.63i	0.829392	+	0.829392i	−0.158041	+	0.987433i	$0.550518\pi$
$102$	−60.0991	−	97.3781i	−0.00577654	−	0.00935968i
$103$	17007.9			1.60316			0.801578	−	0.597891i	$-0.203994\pi$
$103$	17007.9			1.60316			0.801578	+	0.597891i	$0.203994\pi$
$104$	1756.64	−	155.086i	0.162411	−	0.0143385i
$105$		−	37.0687i		−	0.00336224i
$106$	3093.37	+	5012.15i	0.275309	+	0.446080i
$107$	9368.65	−	9368.65i	0.818294	−	0.818294i	−0.167567	−	0.985861i	$-0.553591\pi$
$107$	9368.65	−	9368.65i	0.818294	−	0.818294i	0.985861	+	0.167567i	$0.0535909\pi$
$108$	−160.723	+	53.3518i	−0.0137794	+	0.00457405i
$109$	−8308.73	+	8308.73i	−0.699329	+	0.699329i	−0.964266	−	0.264937i	$-0.914649\pi$
$109$	−8308.73	+	8308.73i	−0.699329	+	0.699329i	0.264937	+	0.964266i	$0.414649\pi$
$110$	5275.62	+	1248.88i	0.436002	+	0.103213i
$111$			40.1254i			0.00325667i
$112$	−7636.03	−	10234.4i	−0.608740	−	0.815882i
$113$	5814.63			0.455371			0.227685	−	0.973735i	$-0.426884\pi$
$113$	5814.63			0.455371			0.227685	+	0.973735i	$0.426884\pi$
$114$	29.7156	−	125.528i	0.00228652	−	0.00965894i
$115$	3256.12	+	3256.12i	0.246209	+	0.246209i
$116$	−22154.9	+	7354.29i	−1.64647	+	0.546544i
$117$	−1578.10	−	1578.10i	−0.115283	−	0.115283i
$118$	−8239.39	+	5085.13i	−0.591740	+	0.365206i
$119$	−21840.1			−1.54227
$120$	−30.5437	+	36.4591i	−0.00212109	+	0.00253188i
$121$			442.428i			0.0302185i
$122$	17865.4	−	11026.0i	1.20031	−	0.740797i
$123$	32.1940	−	32.1940i	0.00212797	−	0.00212797i
$124$	10804.0	−	21540.9i	0.702654	−	1.40094i
$125$	−9013.12	+	9013.12i	−0.576840	+	0.576840i
$126$	−3722.64	+	15725.5i	−0.234483	+	0.990523i
$127$		−	20367.1i		−	1.26276i	−0.775472	−	0.631382i	$-0.782488\pi$
$127$		−	20367.1i		−	1.26276i	0.775472	−	0.631382i	$-0.217512\pi$
$128$	−922.465	+	16358.0i	−0.0563028	+	0.998414i
$129$	−84.7864			−0.00509503
$130$	−1219.94	−	288.792i	−0.0721860	−	0.0170883i
$131$	4414.52	+	4414.52i	0.257242	+	0.257242i	0.823931	−	0.566690i	$-0.191776\pi$
$131$	4414.52	+	4414.52i	0.257242	+	0.257242i	−0.566690	+	0.823931i	$0.691776\pi$
$132$	111.344	+	55.8458i	0.00639029	+	0.00320511i
$133$	−17409.1	−	17409.1i	−0.984174	−	0.984174i
$134$	−5508.74	−	8925.76i	−0.306791	−	0.497091i
$135$	120.389			0.00660571
$136$	21480.9	+	17995.7i	1.16138	+	0.972950i
$137$		−	11018.7i		−	0.587067i	−0.955949	−	0.293533i	$-0.905169\pi$
$137$		−	11018.7i		−	0.587067i	0.955949	−	0.293533i	$-0.0948312\pi$
$138$	55.5676	+	90.0356i	0.00291785	+	0.00472777i
$139$	−14957.2	+	14957.2i	−0.774140	+	0.774140i	−0.978827	−	0.204688i	$-0.934382\pi$
$139$	−14957.2	+	14957.2i	−0.774140	+	0.774140i	0.204688	+	0.978827i	$0.434382\pi$
$140$	2859.88	+	8615.41i	0.145912	+	0.439562i
$141$	5.17051	−	5.17051i	0.000260073	−	0.000260073i
$142$	−4522.59	−	1070.61i	−0.224290	−	0.0530953i
$143$			3283.30i			0.160560i
$144$	16618.9	−	12399.6i	0.801451	−	0.597972i
$145$	16595.1			0.789302
$146$	834.173	−	3523.79i	0.0391336	−	0.165312i
$147$	−4.01848	−	4.01848i	−0.000185963	−	0.000185963i
$148$	−3095.71	−	9325.85i	−0.141331	−	0.425760i
$149$	15393.9	+	15393.9i	0.693388	+	0.693388i	0.962976	−	0.269588i	$-0.0868876\pi$
$149$	15393.9	+	15393.9i	0.693388	+	0.693388i	−0.269588	+	0.962976i	$0.586888\pi$
$150$	−110.225	+	68.0280i	−0.00489890	+	0.00302347i
$151$	−16971.9			−0.744347			−0.372174	−	0.928163i	$-0.621387\pi$
$151$	−16971.9			−0.744347			−0.372174	+	0.928163i	$0.621387\pi$
$152$	2778.11	+	31467.4i	0.120244	+	1.36199i
$153$		−	35464.4i		−	1.51499i
$154$	20231.3	−	12486.2i	0.853066	−	0.526490i
$155$	−12113.9	+	12113.9i	−0.504222	+	0.504222i
$156$	−25.7475	−	12.9139i	−0.00105800	−	0.000530649i
$157$	1167.73	−	1167.73i	0.0473744	−	0.0473744i	−0.683023	−	0.730397i	$-0.739335\pi$
$157$	1167.73	−	1167.73i	0.0473744	−	0.0473744i	0.730397	+	0.683023i	$0.239335\pi$
$158$	−5408.50	+	22847.1i	−0.216652	+	0.915201i
$159$		−	96.2051i		−	0.00380543i
$160$	4286.05	−	10830.2i	0.167424	−	0.423055i
$161$	20193.3			0.779032
$162$	−25534.1	−	6044.60i	−0.972952	−	0.230323i
$163$	28076.2	+	28076.2i	1.05673	+	1.05673i	0.998291	+	0.0584383i	$0.0186121\pi$
$163$	28076.2	+	28076.2i	1.05673	+	1.05673i	0.0584383	+	0.998291i	$0.481388\pi$
$164$	−4998.66	+	9966.24i	−0.185851	+	0.370547i
$165$	−62.6168	−	62.6168i	−0.00229998	−	0.00229998i
$166$	−22460.8	−	36393.1i	−0.815098	−	1.32070i
$167$	−2929.82			−0.105053			−0.0525264	−	0.998620i	$-0.516727\pi$
$167$	−2929.82			−0.105053			−0.0525264	+	0.998620i	$0.516727\pi$
$168$	18.3425	+	207.764i	0.000649891	+	0.00736125i
$169$			27801.8i			0.973417i
$170$	−10462.8	−	16952.8i	−0.362034	−	0.586600i
$171$	28269.2	−	28269.2i	0.966767	−	0.966767i
$172$	19705.9	−	6541.34i	0.666098	−	0.221111i
$173$	8560.97	−	8560.97i	0.286043	−	0.286043i	−0.549470	−	0.835513i	$-0.685171\pi$
$173$	8560.97	−	8560.97i	0.286043	−	0.286043i	0.835513	+	0.549470i	$0.185171\pi$
$174$	371.040	+	87.8347i	0.0122552	+	0.00290113i
$175$			24721.4i			0.807230i
$176$	−30187.0	−	4389.23i	−0.974527	−	0.141698i
$177$	158.150			0.00504804
$178$	−5933.88	+	25066.4i	−0.187283	+	0.791139i
$179$	−24420.1	−	24420.1i	−0.762153	−	0.762153i	0.214558	−	0.976711i	$-0.431169\pi$
$179$	−24420.1	−	24420.1i	−0.762153	−	0.762153i	−0.976711	+	0.214558i	$0.931169\pi$
$180$	−13989.9	+	4643.94i	−0.431787	+	0.143331i
$181$	−10946.5	−	10946.5i	−0.334133	−	0.334133i	0.520021	−	0.854154i	$-0.325924\pi$
$181$	−10946.5	−	10946.5i	−0.334133	−	0.334133i	−0.854154	+	0.520021i	$0.825924\pi$
$182$	−4678.32	+	2887.33i	−0.141237	+	0.0871674i
$183$	−342.915			−0.0102396
$184$	−19861.2	−	16638.8i	−0.586637	−	0.491457i
$185$			6985.52i			0.204106i
$186$	−334.965	+	206.732i	−0.00968220	+	0.00597559i
$187$	−36892.5	+	36892.5i	−1.05501	+	1.05501i
$188$	−802.809	+	1600.63i	−0.0227141	+	0.0452871i
$189$	373.306	−	373.306i	0.0104506	−	0.0104506i
$190$	5173.26	−	21853.3i	0.143303	−	0.605356i
$191$		−	22384.9i		−	0.613604i	−0.951773	−	0.306802i	$-0.900741\pi$
$191$		−	22384.9i		−	0.613604i	0.951773	−	0.306802i	$-0.0992590\pi$
$192$	153.151	−	219.461i	0.00415450	−	0.00595326i
$193$	−30429.5			−0.816920			−0.408460	−	0.912776i	$-0.633934\pi$
$193$	−30429.5			−0.816920			−0.408460	+	0.912776i	$0.633934\pi$
$194$	−1607.70	−	380.584i	−0.0427170	−	0.0101122i
$195$	14.4796	+	14.4796i	0.000380792	+	0.000380792i
$196$	1243.99	+	623.937i	0.0323822	+	0.0162416i
$197$	19093.9	+	19093.9i	0.491997	+	0.491997i	0.908935	−	0.416938i	$-0.136897\pi$
$197$	19093.9	+	19093.9i	0.491997	+	0.491997i	−0.416938	+	0.908935i	$0.636897\pi$
$198$	20275.4	+	32852.1i	0.517177	+	0.837978i
$199$	67963.8			1.71621			0.858107	−	0.513470i	$-0.171640\pi$
$199$	67963.8			1.71621			0.858107	+	0.513470i	$0.171640\pi$
$200$	20369.9	−	24314.9i	0.509246	−	0.607872i
$201$			171.324i			0.00424060i
$202$	25136.4	+	40728.3i	0.616028	+	0.998144i
$203$	51458.4	−	51458.4i	1.24872	−	1.24872i
$204$	−144.203	−	434.414i	−0.00346510	−	0.0104386i
$205$	5604.72	−	5604.72i	0.133366	−	0.133366i
$206$	66201.8	+	15671.7i	1.56004	+	0.369302i
$207$			32790.3i			0.765253i
$208$	6980.48	+	1014.97i	0.161346	+	0.0234600i
$209$	−58815.1			−1.34647
$210$	34.1565	−	144.287i	0.000774523	−	0.00327181i
$211$	−55219.8	−	55219.8i	−1.24031	−	1.24031i	−0.959872	−	0.280438i	$-0.909520\pi$
$211$	−55219.8	−	55219.8i	−1.24031	−	1.24031i	−0.280438	−	0.959872i	$-0.590480\pi$
$212$	7422.30	+	22359.8i	0.165146	+	0.497503i
$213$	53.6790	+	53.6790i	0.00118316	+	0.00118316i
$214$	45099.4	−	27834.1i	0.984788	−	0.607785i
$215$	−14760.6			−0.319322
$216$	−674.761	+	59.5716i	−0.0144625	+	0.00127683i
$217$			75126.4i			1.59541i
$218$	−39997.1	+	24685.1i	−0.841618	+	0.519424i
$219$	−41.8242	+	41.8242i	−0.000872046	+	0.000872046i
$220$	19384.2	+	9722.31i	0.400500	+	0.200874i
$221$	8531.07	−	8531.07i	0.174670	−	0.174670i
$222$	−36.9731	+	156.185i	−0.000750204	+	0.00316908i
$223$		−	40417.5i		−	0.812754i	−0.913705	−	0.406377i	$-0.866792\pi$
$223$		−	40417.5i		−	0.812754i	0.913705	−	0.406377i	$-0.133208\pi$
$224$	−20292.3	−	46872.8i	−0.404422	−	0.934168i
$225$	−40143.2			−0.792952
$226$	22633.0	+	5357.82i	0.443124	+	0.104899i
$227$	−1672.85	−	1672.85i	−0.0324643	−	0.0324643i	0.690688	−	0.723153i	$-0.257308\pi$
$227$	−1672.85	−	1672.85i	−0.0324643	−	0.0324643i	−0.723153	+	0.690688i	$0.757308\pi$
$228$	231.332	−	461.225i	0.00445005	−	0.00887244i
$229$	−26519.0	−	26519.0i	−0.505691	−	0.505691i	0.407510	−	0.913201i	$-0.366397\pi$
$229$	−26519.0	−	26519.0i	−0.505691	−	0.505691i	−0.913201	+	0.407510i	$0.866397\pi$
$230$	9673.87	+	15674.5i	0.182871	+	0.296304i
$231$	−388.328			−0.00727737
$232$	−93012.7	+	8211.67i	−1.72809	+	0.152565i
$233$		−	24163.3i		−	0.445087i	−0.974923	−	0.222543i	$-0.928564\pi$
$233$		−	24163.3i		−	0.445087i	0.974923	−	0.222543i	$-0.0714359\pi$
$234$	−4688.52	−	7596.76i	−0.0856257	−	0.138738i
$235$	900.145	−	900.145i	0.0162996	−	0.0162996i
$236$	−36756.8	+	12201.4i	−0.659954	+	0.219071i
$237$	271.174	−	271.174i	0.00482782	−	0.00482782i
$238$	−85010.8	−	20124.3i	−1.50079	−	0.355276i
$239$			76356.4i			1.33675i	0.743825	+	0.668374i	$0.233010\pi$
$239$			76356.4i			1.33675i	−0.743825	+	0.668374i	$0.766990\pi$
$240$	−152.484	+	113.770i	−0.00264729	+	0.00197517i
$241$	40548.1			0.698130			0.349065	−	0.937099i	$-0.386499\pi$
$241$	40548.1			0.698130			0.349065	+	0.937099i	$0.386499\pi$
$242$	−407.670	+	1722.12i	−0.00696111	+	0.0294058i
$243$	909.281	+	909.281i	0.0153988	+	0.0153988i
$244$	79699.4	−	26456.1i	1.33867	−	0.444372i
$245$	−699.586	−	699.586i	−0.0116549	−	0.0116549i
$246$	154.977	−	95.6479i	0.00256093	−	0.00158054i
$247$	13600.5			0.222926
$248$	61902.3	−	73890.9i	1.00648	−	1.20140i
$249$			698.542i			0.0112666i
$250$	−43387.9	+	26777.8i	−0.694206	+	0.428446i
$251$	−10536.0	+	10536.0i	−0.167235	+	0.167235i	−0.785763	−	0.618528i	$-0.787729\pi$
$251$	−10536.0	+	10536.0i	−0.167235	+	0.167235i	0.618528	+	0.785763i	$0.287729\pi$
$252$	−28980.2	+	57780.3i	−0.456353	+	0.909868i
$253$	34110.7	−	34110.7i	0.532905	−	0.532905i
$254$	18767.0	−	79277.4i	0.290889	−	1.22880i
$255$			325.397i			0.00500419i
$256$	−18663.5	+	62822.3i	−0.284783	+	0.958592i
$257$	37983.9			0.575086			0.287543	−	0.957768i	$-0.407162\pi$
$257$	37983.9			0.575086			0.287543	+	0.957768i	$0.407162\pi$
$258$	−330.025	−	78.1254i	−0.00495800	−	0.00117369i
$259$	21660.9	+	21660.9i	0.322906	+	0.322906i
$260$	−4482.43	−	2248.20i	−0.0663081	−	0.0332574i
$261$	83559.4	+	83559.4i	1.22663	+	1.22663i
$262$	13115.5	+	21250.9i	0.191065	+	0.309581i
$263$	37545.0			0.542801			0.271400	−	0.962467i	$-0.412513\pi$
$263$	37545.0			0.542801			0.271400	+	0.962467i	$0.412513\pi$
$264$	381.941	+	319.972i	0.00548010	+	0.00459097i
$265$		−	16748.6i		−	0.238498i
$266$	−51722.0	−	83804.8i	−0.730992	−	1.18442i
$267$	297.516	−	297.516i	0.00417338	−	0.00417338i
$268$	−13217.8	−	39818.8i	−0.184031	−	0.554394i
$269$	4676.63	−	4676.63i	0.0646291	−	0.0646291i	−0.674053	−	0.738683i	$-0.735448\pi$
$269$	4676.63	−	4676.63i	0.0646291	−	0.0646291i	0.738683	+	0.674053i	$0.235448\pi$
$270$	468.605	+	110.931i	0.00642806	+	0.00152169i
$271$			2746.12i			0.0373922i	0.999825	+	0.0186961i	$0.00595149\pi$
$271$			2746.12i			0.0373922i	−0.999825	+	0.0186961i	$0.994049\pi$
$272$	67030.8	+	89840.1i	0.906018	+	1.21432i
$273$	89.7975			0.00120487
$274$	10153.0	−	42889.3i	0.135236	−	0.571278i
$275$	41759.7	+	41759.7i	0.552194	+	0.552194i
$276$	133.330	+	401.659i	0.00175029	+	0.00527277i
$277$	−33056.5	−	33056.5i	−0.430822	−	0.430822i	0.458086	−	0.888908i	$-0.348535\pi$
$277$	−33056.5	−	33056.5i	−0.430822	−	0.430822i	−0.888908	+	0.458086i	$0.848535\pi$
$278$	−72001.7	+	44437.5i	−0.931650	+	0.574989i
$279$	−121992.			−1.56719
$280$	3193.29	+	36170.0i	0.0407307	+	0.461352i
$281$		−	80033.0i		−	1.01358i	−0.862071	−	0.506788i	$-0.830833\pi$
$281$		−	80033.0i		−	1.01358i	0.862071	−	0.506788i	$-0.169167\pi$
$282$	24.8901	−	15.3615i	0.000312989	−	0.000193168i
$283$	−72284.3	+	72284.3i	−0.902549	+	0.902549i	−0.995656	−	0.0931068i	$-0.970320\pi$
$283$	−72284.3	+	72284.3i	−0.902549	+	0.902549i	0.0931068	+	0.995656i	$0.470320\pi$
$284$	−16617.3	−	8334.56i	−0.206027	−	0.103335i
$285$	−259.379	+	259.379i	−0.00319334	+	0.00319334i
$286$	−3025.35	+	12780.0i	−0.0369866	+	0.156242i
$287$		−	34758.5i		−	0.421985i
$288$	76113.1	−	32951.0i	0.917645	−	0.397269i
$289$	108196.			1.29544
$290$	64595.1	+	15291.3i	0.768075	+	0.181823i
$291$	19.0819	+	19.0819i	0.000225339	+	0.000225339i
$292$	6493.91	−	12947.4i	0.0761623	−	0.151851i
$293$	−84911.3	−	84911.3i	−0.989077	−	0.989077i	0.0108641	−	0.999941i	$-0.496542\pi$
$293$	−84911.3	−	84911.3i	−0.989077	−	0.989077i	−0.999941	+	0.0108641i	$0.996542\pi$
$294$	−11.9388	−	19.3444i	−0.000138124	−	0.000223800i
$295$	27532.6			0.316376
$296$	−3456.61	−	39152.7i	−0.0394518	−	0.446867i
$297$		−	1261.18i		−	0.0142977i
$298$	45735.0	+	74104.1i	0.515011	+	0.834468i
$299$	−7887.81	+	7887.81i	−0.0882296	+	0.0882296i
$300$	−491.727	+	163.228i	−0.00546363	+	0.00181365i
$301$	−45770.2	+	45770.2i	−0.505184	+	0.505184i
$302$	−66061.7	−	15638.5i	−0.724329	−	0.171467i
$303$		−	781.754i		−	0.00851500i
$304$	−18181.6	+	125044.i	−0.196737	+	1.35306i
$305$	−59698.7			−0.641749
$306$	32678.2	−	138042.i	0.348992	−	1.47425i
$307$	−55472.5	−	55472.5i	−0.588574	−	0.588574i	0.348671	−	0.937245i	$-0.386633\pi$
$307$	−55472.5	−	55472.5i	−0.588574	−	0.588574i	−0.937245	+	0.348671i	$0.886633\pi$
$308$	90254.1	−	29959.8i	0.951406	−	0.315818i
$309$	−785.756	−	785.756i	−0.00822944	−	0.00822944i
$310$	−58314.8	+	35990.3i	−0.606814	+	0.374509i
$311$	−127048.			−1.31355			−0.656777	−	0.754084i	$-0.728081\pi$
$311$	−127048.			−1.31355			−0.656777	+	0.754084i	$0.728081\pi$
$312$	−88.3207	−	73.9909i	−0.000907305	−	0.000760097i
$313$		−	25469.3i		−	0.259974i	−0.991516	−	0.129987i	$-0.958507\pi$
$313$		−	25469.3i		−	0.259974i	0.991516	−	0.129987i	$-0.0414935\pi$
$314$	5621.29	−	3469.31i	0.0570134	−	0.0351871i
$315$	32493.9	−	32493.9i	0.327477	−	0.327477i
$316$	−42104.3	+	83946.9i	−0.421650	+	0.840679i
$317$	−94218.4	+	94218.4i	−0.937599	+	0.937599i	−0.998164	−	0.0605656i	$-0.980710\pi$
$317$	−94218.4	+	94218.4i	−0.937599	+	0.937599i	0.0605656	+	0.998164i	$0.480710\pi$
$318$	88.6470	−	374.471i	0.000876617	−	0.00370309i
$319$		−	173848.i		−	1.70840i
$320$	26662.4	−	38206.4i	0.260375	−	0.373109i
$321$	−865.654			−0.00840107
$322$	78600.8	+	18606.9i	0.758080	+	0.179457i
$323$	152821.	+	152821.i	1.46480	+	1.46480i
$324$	−93820.0	−	47056.2i	−0.893728	−	0.448257i
$325$	−9656.57	−	9656.57i	−0.0914232	−	0.0914232i
$326$	83414.1	+	135155.i	0.784882	+	1.27174i
$327$	767.719			0.00717971
$328$	−28640.2	+	34186.9i	−0.266212	+	0.317769i
$329$		−	5582.38i		−	0.0515737i
$330$	−186.034	−	301.429i	−0.00170830	−	0.00276794i
$331$	65141.3	−	65141.3i	0.594567	−	0.594567i	−0.344295	−	0.938862i	$-0.611882\pi$
$331$	65141.3	−	65141.3i	0.594567	−	0.594567i	0.938862	+	0.344295i	$0.111882\pi$
$332$	−53893.1	−	162354.i	−0.488942	−	1.47294i
$333$	−35173.4	+	35173.4i	−0.317195	+	0.317195i
$334$	−11404.1	−	2699.64i	−0.102227	−	0.0241999i
$335$			29826.2i			0.265771i
$336$	−120.045	+	825.606i	−0.00106332	+	0.00731298i
$337$	135004.			1.18874			0.594369	−	0.804193i	$-0.297402\pi$
$337$	135004.			1.18874			0.594369	+	0.804193i	$0.297402\pi$
$338$	−25617.6	+	108216.i	−0.224236	+	0.947238i
$339$	−268.633	−	268.633i	−0.00233754	−	0.00233754i
$340$	−25104.7	−	75628.1i	−0.217168	−	0.654222i
$341$	126904.	+	126904.i	1.09136	+	1.09136i
$342$	136084.	−	83987.4i	1.16347	−	0.718062i
$343$	115422.			0.981075
$344$	82730.9	−	7303.94i	0.699119	−	0.0617221i
$345$		−	300.862i		−	0.00252772i
$346$	41211.3	−	25434.5i	0.344242	−	0.212457i
$347$	10849.2	−	10849.2i	0.0901025	−	0.0901025i	−0.660619	−	0.750721i	$-0.729706\pi$
$347$	10849.2	−	10849.2i	0.0901025	−	0.0901025i	0.750721	+	0.660619i	$0.229706\pi$
$348$	1363.31	+	683.780i	0.0112573	+	0.00564622i
$349$	−6073.15	+	6073.15i	−0.0498612	+	0.0498612i	−0.731598	−	0.681737i	$-0.761225\pi$
$349$	−6073.15	+	6073.15i	−0.0498612	+	0.0498612i	0.681737	+	0.731598i	$0.261225\pi$
$350$	−22779.3	+	96226.2i	−0.185953	+	0.785520i
$351$			291.638i			0.00236717i
$352$	−113456.	−	44900.1i	−0.915676	−	0.362378i
$353$	−143445.			−1.15116			−0.575579	−	0.817746i	$-0.695223\pi$
$353$	−143445.			−1.15116			−0.575579	+	0.817746i	$0.695223\pi$
$354$	615.586	+	145.725i	0.00491227	+	0.00116286i
$355$	9345.08	+	9345.08i	0.0741526	+	0.0741526i
$356$	−46194.3	+	92101.5i	−0.364492	+	0.726719i
$357$	1009.00	+	1009.00i	0.00791690	+	0.00791690i
$358$	−72551.9	−	117555.i	−0.566086	−	0.917225i
$359$	124076.			0.962718			0.481359	−	0.876523i	$-0.340143\pi$
$359$	124076.			0.962718			0.481359	+	0.876523i	$0.340143\pi$
$360$	−58733.7	+	5185.34i	−0.453192	+	0.0400103i
$361$			113310.i			0.869472i
$362$	−32522.0	−	52695.0i	−0.248176	−	0.402117i
$363$	20.4400	−	20.4400i	0.000155120	−	0.000155120i
$364$	−20870.5	+	6927.94i	−0.157518	+	0.0522879i
$365$	−7281.26	+	7281.26i	−0.0546538	+	0.0546538i
$366$	−1334.77	−	315.974i	−0.00996423	−	0.00235879i
$367$		−	126240.i		−	0.937268i	−0.883392	−	0.468634i	$-0.844746\pi$
$367$		−	126240.i		−	0.937268i	0.883392	−	0.468634i	$-0.155254\pi$
$368$	−61976.6	−	83066.0i	−0.457648	−	0.613377i
$369$	56441.7			0.414521
$370$	−6436.72	+	27190.6i	−0.0470177	+	0.198616i
$371$	−51934.3	−	51934.3i	−0.377317	−	0.377317i
$372$	−1494.32	+	496.037i	−0.0107983	+	0.00358450i
$373$	−95513.7	−	95513.7i	−0.686512	−	0.686512i	0.274948	−	0.961459i	$-0.411339\pi$
$373$	−95513.7	−	95513.7i	−0.686512	−	0.686512i	−0.961459	+	0.274948i	$0.911339\pi$
$374$	−177595.	+	109607.i	−1.26966	+	0.783601i
$375$	832.804			0.00592216
$376$	−4599.75	+	5490.58i	−0.0325356	+	0.0388367i
$377$			40200.9i			0.282848i
$378$	1797.04	−	1109.09i	0.0125769	−	0.00776214i
$379$	−31220.0	+	31220.0i	−0.217347	+	0.217347i	−0.807380	−	0.590032i	$-0.799115\pi$
$379$	−31220.0	+	31220.0i	−0.217347	+	0.217347i	0.590032	+	0.807380i	$0.299115\pi$
$380$	40273.0	−	80295.6i	0.278899	−	0.556064i
$381$	−940.951	+	940.951i	−0.00648212	+	0.00648212i
$382$	20626.3	−	87131.5i	0.141350	−	0.597102i
$383$			253102.i			1.72543i	0.505689	+	0.862716i	$0.331238\pi$
$383$			253102.i			1.72543i	−0.505689	+	0.862716i	$0.668762\pi$
$384$	798.350	−	713.115i	0.00541415	−	0.00483612i
$385$	−67604.7			−0.456095
$386$	−118444.	−	28038.9i	−0.794950	−	0.188185i
$387$	−74322.6	−	74322.6i	−0.496248	−	0.496248i
$388$	−5907.15	−	2962.78i	−0.0392387	−	0.0196805i
$389$	−43279.4	−	43279.4i	−0.286011	−	0.286011i	0.549490	−	0.835500i	$-0.314822\pi$
$389$	−43279.4	−	43279.4i	−0.286011	−	0.286011i	−0.835500	+	0.549490i	$0.814822\pi$
$390$	43.0187	+	69.7028i	0.000282832	+	0.000458270i
$391$	−177261.			−1.15947
$392$	4267.23	+	3574.89i	0.0277699	+	0.0232643i
$393$		−	407.898i		−	0.00264099i
$394$	56727.7	+	91915.4i	0.365429	+	0.592101i
$395$	47209.2	−	47209.2i	0.302575	−	0.302575i
$396$	48649.4	+	146557.i	0.310232	+	0.934578i
$397$	198533.	−	198533.i	1.25965	−	1.25965i	0.308395	−	0.951258i	$-0.400208\pi$
$397$	198533.	−	198533.i	1.25965	−	1.25965i	0.951258	−	0.308395i	$-0.0997920\pi$
$398$	264544.	+	62624.4i	1.67006	+	0.395346i
$399$			1608.58i			0.0101041i
$400$	101693.	−	75874.2i	0.635579	−	0.474214i
$401$	−89330.8			−0.555536			−0.277768	−	0.960648i	$-0.589595\pi$
$401$	−89330.8			−0.555536			−0.277768	+	0.960648i	$0.589595\pi$
$402$	−157.865	+	666.867i	−0.000976861	+	0.00412655i
$403$	−29345.5	−	29345.5i	−0.180689	−	0.180689i
$404$	60312.9	+	181693.i	0.369528	+	1.11321i
$405$	52761.6	+	52761.6i	0.321668	+	0.321668i
$406$	247714.	−	152882.i	1.50279	−	0.927481i
$407$	73179.5			0.441775
$408$	−161.015	−	1823.80i	−0.000967266	−	0.0109561i
$409$			26716.3i			0.159709i	0.996807	+	0.0798545i	$0.0254456\pi$
$409$			26716.3i			0.159709i	−0.996807	+	0.0798545i	$0.974554\pi$
$410$	26980.3	−	16651.5i	0.160502	−	0.0990573i
$411$	−509.057	+	509.057i	−0.00301358	+	0.00301358i
$412$	243245.	+	122002.i	1.43301	+	0.718739i
$413$	85373.9	−	85373.9i	0.500524	−	0.500524i
$414$	−30214.2	+	127634.i	−0.176283	+	0.744672i
$415$			121611.i			0.706115i
$416$	26235.7	+	10382.8i	0.151603	+	0.0599966i
$417$	1382.03			0.00794775
$418$	−228933.	−	54194.5i	−1.31026	−	0.310172i
$419$	−119011.	−	119011.i	−0.677889	−	0.677889i	0.281633	−	0.959522i	$-0.409124\pi$
$419$	−119011.	−	119011.i	−0.677889	−	0.677889i	−0.959522	+	0.281633i	$0.909124\pi$
$420$	265.903	−	530.153i	0.00150739	−	0.00300540i
$421$	126967.	+	126967.i	0.716355	+	0.716355i	0.967857	−	0.251502i	$-0.0809245\pi$
$421$	126967.	+	126967.i	0.716355	+	0.716355i	−0.251502	+	0.967857i	$0.580925\pi$
$422$	−164057.	−	265821.i	−0.921236	−	1.49267i
$423$	9064.80			0.0506614
$424$	8287.61	+	93872.8i	0.0460996	+	0.522166i
$425$		−	217010.i		−	1.20144i
$426$	159.479	+	258.403i	0.000878791	+	0.00142390i
$427$	−185115.	+	185115.i	−1.01528	+	1.01528i
$428$	201193.	−	66785.9i	1.09831	−	0.364584i
$429$	151.687	−	151.687i	0.000824201	−	0.000824201i
$430$	−57454.7	−	13601.0i	−0.310734	−	0.0735587i
$431$			82986.1i			0.446736i	0.974734	+	0.223368i	$0.0717051\pi$
$431$			82986.1i			0.446736i	−0.974734	+	0.223368i	$0.928295\pi$
$432$	−2681.35	−	389.872i	−0.0143676	−	0.00208908i
$433$	−153228.			−0.817265			−0.408633	−	0.912699i	$-0.633994\pi$
$433$	−153228.			−0.817265			−0.408633	+	0.912699i	$0.633994\pi$
$434$	−69224.3	+	292424.i	−0.367518	+	1.55251i
$435$	−766.685	−	766.685i	−0.00405171	−	0.00405171i
$436$	−178431.	+	59230.1i	−0.938638	+	0.311580i
$437$	−141298.	−	141298.i	−0.739899	−	0.739899i
$438$	−201.336	+	124.259i	−0.00104948	+	0.000647709i
$439$	48984.2			0.254172			0.127086	−	0.991892i	$-0.459438\pi$
$439$	48984.2			0.254172			0.127086	+	0.991892i	$0.459438\pi$
$440$	66492.9	+	55704.7i	0.343455	+	0.287731i
$441$		−	7045.09i		−	0.0362251i
$442$	41067.4	−	25345.7i	0.210210	−	0.129736i
$443$	5464.01	−	5464.01i	0.0278422	−	0.0278422i	−0.693049	−	0.720891i	$-0.743733\pi$
$443$	5464.01	−	5464.01i	0.0278422	−	0.0278422i	0.720891	+	0.693049i	$0.243733\pi$
$444$	−287.830	+	573.870i	−0.00146006	+	0.00291104i
$445$	51795.1	−	51795.1i	0.261559	−	0.261559i
$446$	37242.2	−	157322.i	0.187226	−	0.790896i
$447$		−	1422.38i		−	0.00711870i
$448$	−35795.7	−	201147.i	−0.178351	−	1.00221i
$449$	140068.			0.694776			0.347388	−	0.937721i	$-0.387069\pi$
$449$	140068.			0.694776			0.347388	+	0.937721i	$0.387069\pi$
$450$	−156254.	−	36989.5i	−0.771626	−	0.182664i
$451$	−58714.4	−	58714.4i	−0.288664	−	0.288664i
$452$	83160.3	+	41709.8i	0.407042	+	0.204155i
$453$	784.092	+	784.092i	0.00382094	+	0.00382094i
$454$	−4970.02	−	8052.88i	−0.0241127	−	0.0390696i
$455$	15633.0			0.0755127
$456$	1325.43	−	1582.13i	0.00637422	−	0.00760871i
$457$			219788.i			1.05238i	0.850368	+	0.526188i	$0.176379\pi$
$457$			219788.i			1.05238i	−0.850368	+	0.526188i	$0.823621\pi$
$458$	−78787.4	−	127659.i	−0.375600	−	0.608582i
$459$	−3276.96	+	3276.96i	−0.0155541	+	0.0155541i
$460$	23211.7	+	69925.6i	0.109696	+	0.330461i
$461$	124163.	−	124163.i	0.584239	−	0.584239i	−0.351826	−	0.936065i	$-0.614439\pi$
$461$	124163.	−	124163.i	0.584239	−	0.584239i	0.936065	+	0.351826i	$0.114439\pi$
$462$	−1511.54	−	357.820i	−0.00708165	−	0.00167641i
$463$			236566.i			1.10354i	0.833995	+	0.551772i	$0.186048\pi$
$463$			236566.i			1.10354i	−0.833995	+	0.551772i	$0.813952\pi$
$464$	−369611.	−	53742.1i	−1.71676	−	0.249619i
$465$	1119.32			0.00517663
$466$	22265.0	−	94053.8i	0.102530	−	0.433116i
$467$	73415.5	+	73415.5i	0.336631	+	0.336631i	0.855098	−	0.518467i	$-0.173497\pi$
$467$	73415.5	+	73415.5i	0.336631	+	0.336631i	−0.518467	+	0.855098i	$0.673497\pi$
$468$	−11249.8	−	33890.0i	−0.0513631	−	0.154732i
$469$	92485.8	+	92485.8i	0.420465	+	0.420465i
$470$	4333.17	−	2674.32i	0.0196160	−	0.0121065i
$471$	−107.897			−0.000486372
$472$	−154316.	+	13623.9i	−0.692670	+	0.0611528i
$473$			154631.i			0.691153i
$474$	1305.39	−	805.654i	0.00581012	−	0.00358585i
$475$	172982.	−	172982.i	0.766681	−	0.766681i
$476$	−312355.	−	156664.i	−1.37859	−	0.691442i
$477$	84332.1	−	84332.1i	0.370643	−	0.370643i
$478$	−70357.7	+	297211.i	−0.307933	+	1.30080i
$479$		−	212004.i		−	0.924003i	−0.886879	−	0.462002i	$-0.847131\pi$
$479$		−	212004.i		−	0.924003i	0.886879	−	0.462002i	$-0.152869\pi$
$480$	−698.363	+	302.337i	−0.00303109	+	0.00131223i
$481$	−16922.1			−0.0731417
$482$	157830.	+	37362.5i	0.679354	+	0.160821i
$483$	−932.920	−	932.920i	−0.00399899	−	0.00399899i
$484$	−3173.65	+	6327.57i	−0.0135478	+	0.0270113i
$485$	3322.01	+	3322.01i	0.0141227	+	0.0141227i
$486$	2701.46	+	4377.15i	0.0114374	+	0.0185319i
$487$	26716.3			0.112647			0.0563234	−	0.998413i	$-0.482062\pi$
$487$	26716.3			0.112647			0.0563234	+	0.998413i	$0.482062\pi$
$488$	334601.	−	29540.4i	1.40504	−	0.124044i
$489$		−	2594.22i		−	0.0108490i
$490$	−2078.46	−	3367.71i	−0.00865664	−	0.0140263i
$491$	99544.8	−	99544.8i	0.412910	−	0.412910i	−0.469841	−	0.882751i	$-0.655689\pi$
$491$	99544.8	−	99544.8i	0.412910	−	0.412910i	0.882751	+	0.469841i	$0.155689\pi$
$492$	691.371	−	229.500i	0.00285615	−	0.000948096i
$493$	−451714.	+	451714.i	−1.85853	+	1.85853i
$494$	52938.9	+	12532.0i	0.216931	+	0.0513531i
$495$		−	109778.i		−	0.448028i
$496$	309036.	−	230575.i	1.25616	−	0.937238i
$497$	57954.9			0.234627
$498$	−643.663	+	2719.02i	−0.00259537	+	0.0109636i
$499$	189887.	+	189887.i	0.762597	+	0.762597i	0.976791	−	0.214194i	$-0.0687125\pi$
$499$	189887.	+	189887.i	0.762597	+	0.762597i	−0.214194	+	0.976791i	$0.568713\pi$
$500$	−193558.	+	64251.5i	−0.774233	+	0.257006i
$501$	135.356	+	135.356i	0.000539265	+	0.000539265i
$502$	−50718.8	+	31302.3i	−0.201262	+	0.124213i
$503$	188872.			0.746502			0.373251	−	0.927730i	$-0.378243\pi$
$503$	188872.			0.746502			0.373251	+	0.927730i	$0.378243\pi$
$504$	−166044.	+	198202.i	−0.653676	+	0.780273i
$505$		−	136097.i		−	0.533662i
$506$	164204.	−	101342.i	0.641332	−	0.395813i
$507$	1284.43	−	1284.43i	0.00499682	−	0.00499682i
$508$	146098.	−	291289.i	0.566132	−	1.12875i
$509$	−14343.5	+	14343.5i	−0.0553629	+	0.0553629i	−0.734246	−	0.678883i	$-0.762464\pi$
$509$	−14343.5	+	14343.5i	−0.0553629	+	0.0553629i	0.678883	+	0.734246i	$0.262464\pi$
$510$	−299.833	+	1266.58i	−0.00115276	+	0.00486961i
$511$			45155.8i			0.172931i
$512$	−130533.	+	227334.i	−0.497944	+	0.867209i
$513$	−5224.23			−0.0198513
$514$	147849.	+	34999.8i	0.559620	+	0.132477i
$515$	−136794.	−	136794.i	−0.515765	−	0.515765i
$516$	−1212.61	−	608.194i	−0.00455429	−	0.00228425i
$517$	−9429.82	−	9429.82i	−0.0352795	−	0.0352795i
$518$	64354.1	+	104272.i	0.239837	+	0.388606i
$519$	−791.025			−0.00293667
$520$	−15375.9	−	12881.2i	−0.0568636	−	0.0476377i
$521$		−	65377.4i		−	0.240853i	−0.992722	−	0.120427i	$-0.961574\pi$
$521$		−	65377.4i		−	0.240853i	0.992722	−	0.120427i	$-0.0384262\pi$
$522$	248254.	+	402243.i	0.911076	+	1.47621i
$523$	−143634.	+	143634.i	−0.525113	+	0.525113i	−0.919111	−	0.393998i	$-0.871092\pi$
$523$	−143634.	+	143634.i	−0.525113	+	0.525113i	0.393998	+	0.919111i	$0.371092\pi$
$524$	31469.6	+	94802.6i	0.114612	+	0.345269i
$525$	1142.12	−	1142.12i	0.00414374	−	0.00414374i
$526$	146141.	+	34595.4i	0.528203	+	0.125039i
$527$		−	659477.i		−	2.37453i
$528$	1191.84	+	1597.40i	0.00427515	+	0.00572989i
$529$	−115946.			−0.414327
$530$	15432.7	−	65192.4i	0.0549404	−	0.232084i
$531$	138632.	+	138632.i	0.491671	+	0.491671i
$532$	−124103.	−	373862.i	−0.438490	−	1.32096i
$533$	13577.2	+	13577.2i	0.0477921	+	0.0477921i
$534$	1432.20	−	883.915i	0.00502251	−	0.00309976i
$535$	−150704.			−0.526521
$536$	−14758.8	−	167171.i	−0.0513713	−	0.581877i
$537$			2256.40i			0.00782469i
$538$	22512.6	−	13894.2i	0.0777789	−	0.0480030i
$539$	−7328.78	+	7328.78i	−0.0252263	+	0.0252263i
$540$	1721.79	+	863.581i	0.00590464	+	0.00296153i
$541$	−275122.	+	275122.i	−0.940007	+	0.940007i	−0.998300	−	0.0582928i	$-0.981434\pi$
$541$	−275122.	+	275122.i	−0.940007	+	0.940007i	0.0582928	+	0.998300i	$0.481434\pi$
$542$	−2530.38	+	10689.0i	−0.00861363	+	0.0363865i
$543$			1011.45i			0.00343039i
$544$	178130.	+	411460.i	0.601921	+	1.39037i
$545$	133654.			0.449975
$546$	349.530	+	82.7427i	0.00117246	+	0.000277552i
$547$	−1032.53	−	1032.53i	−0.00345087	−	0.00345087i	0.705379	−	0.708830i	$-0.250777\pi$
$547$	−1032.53	−	1032.53i	−0.00345087	−	0.00345087i	−0.708830	+	0.705379i	$0.750777\pi$
$548$	79039.6	−	157588.i	0.263199	−	0.524761i
$549$	−300594.	−	300594.i	−0.997323	−	0.997323i
$550$	124067.	+	201025.i	0.410140	+	0.664547i
$551$	−720136.			−2.37198
$552$	148.874	+	1686.28i	0.000488586	+	0.00553416i
$553$		−	292775.i		−	0.957379i
$554$	−98210.4	−	159129.i	−0.319991	−	0.518479i
$555$	322.727	−	322.727i	0.00104773	−	0.00104773i
$556$	−321207.	+	106624.i	−1.03905	+	0.344911i
$557$	−223266.	+	223266.i	−0.719635	+	0.719635i	−0.968530	−	0.248895i	$-0.919933\pi$
$557$	−223266.	+	223266.i	−0.719635	+	0.719635i	0.248895	+	0.968530i	$0.419933\pi$
$558$	−474844.	−	112408.i	−1.52505	−	0.361018i
$559$		−	35757.1i		−	0.114430i
$560$	−20898.8	+	143731.i	−0.0666416	+	0.458327i
$561$	3408.83			0.0108313
$562$	73745.4	−	311522.i	0.233487	−	0.986317i
$563$	191551.	+	191551.i	0.604322	+	0.604322i	0.941457	−	0.337134i	$-0.109458\pi$
$563$	191551.	+	191551.i	0.604322	+	0.604322i	−0.337134	+	0.941457i	$0.609458\pi$
$564$	111.038	−	36.8588i	0.000349069	−	0.000115873i
$565$	−46766.9	−	46766.9i	−0.146501	−	0.146501i
$566$	−347966.	+	214755.i	−1.08619	+	0.670365i
$567$	327209.			1.01779
$568$	−57001.8	−	47753.4i	−0.176682	−	0.148016i
$569$			119746.i			0.369858i	0.982752	+	0.184929i	$0.0592055\pi$
$569$			119746.i			0.369858i	−0.982752	+	0.184929i	$0.940795\pi$
$570$	−1248.62	+	770.612i	−0.00384308	+	0.00237184i
$571$	375516.	−	375516.i	1.15175	−	1.15175i	0.165544	−	0.986202i	$-0.447062\pi$
$571$	375516.	−	375516.i	1.15175	−	1.15175i	0.986202	−	0.165544i	$-0.0529379\pi$
$572$	−23551.9	+	46957.4i	−0.0719837	+	0.143520i
$573$	−1034.17	+	1034.17i	−0.00314980	+	0.00314980i
$574$	32027.8	−	135295.i	0.0972083	−	0.410636i
$575$			200647.i			0.606873i
$576$	326627.	−	58125.9i	0.984480	−	0.175196i
$577$	185281.			0.556518			0.278259	−	0.960506i	$-0.410243\pi$
$577$	185281.			0.556518			0.278259	+	0.960506i	$0.410243\pi$
$578$	421145.	+	99696.0i	1.26060	+	0.298416i
$579$	1405.83	+	1405.83i	0.00419348	+	0.00419348i
$580$	237341.	+	119041.i	0.705533	+	0.353866i
$581$	377093.	+	377093.i	1.11711	+	1.11711i
$582$	56.6920	+	91.8576i	0.000167369	+	0.000271187i
$583$	−175456.			−0.516216
$584$	37207.3	−	44413.2i	0.109094	−	0.130223i
$585$			25385.3i			0.0741771i
$586$	−252270.	−	408751.i	−0.734633	−	1.19032i
$587$	−483071.	+	483071.i	−1.40196	+	1.40196i	−0.608081	+	0.793875i	$0.708060\pi$
$587$	−483071.	+	483071.i	−1.40196	+	1.40196i	−0.793875	+	0.608081i	$0.791940\pi$
$588$	−28.6464	−	86.2975i	−8.28543e−5	−	0.000249599i
$589$	525679.	−	525679.i	1.51527	−	1.51527i
$590$	107169.	+	25369.6i	0.307868	+	0.0728803i
$591$		−	1764.26i		−	0.00505112i
$592$	22622.1	−	155584.i	0.0645491	−	0.443936i
$593$	636299.			1.80947			0.904736	−	0.425973i	$-0.140068\pi$
$593$	636299.			1.80947			0.904736	+	0.425973i	$0.140068\pi$
$594$	1162.10	−	4909.06i	0.00329360	−	0.0139131i
$595$	175659.	+	175659.i	0.496177	+	0.496177i
$596$	109738.	+	330586.i	0.308933	+	0.930663i
$597$	−3139.90	−	3139.90i	−0.00880981	−	0.00880981i
$598$	−37970.8	+	23434.6i	−0.106181	+	0.0655322i
$599$	410280.			1.14347			0.571737	−	0.820437i	$-0.306270\pi$
$599$	410280.			1.14347			0.571737	+	0.820437i	$0.306270\pi$
$600$	−2064.41	+	182.258i	−0.00573448	+	0.000506271i
$601$		−	531872.i		−	1.47251i	−0.676704	−	0.736255i	$-0.736592\pi$
$601$		−	531872.i		−	1.47251i	0.676704	−	0.736255i	$-0.263408\pi$
$602$	−220331.	+	135982.i	−0.607971	+	0.375223i
$603$	−150181.	+	150181.i	−0.413028	+	0.413028i
$604$	−242730.	−	121743.i	−0.665349	−	0.333712i
$605$	3558.44	−	3558.44i	0.00972184	−	0.00972184i
$606$	720.337	−	3042.92i	0.00196151	−	0.00828599i
$607$			505448.i			1.37182i	0.727684	+	0.685912i	$0.240597\pi$
$607$			505448.i			1.37182i	−0.727684	+	0.685912i	$0.759403\pi$
$608$	−185991.	+	469972.i	−0.503135	+	1.27135i
$609$	−4754.71			−0.0128200
$610$	−232373.	−	55008.6i	−0.624489	−	0.147833i
$611$	2180.57	+	2180.57i	0.00584099	+	0.00584099i
$612$	254395.	−	507208.i	0.679212	−	1.35420i
$613$	−31334.4	−	31334.4i	−0.0833873	−	0.0833873i	0.664183	−	0.747570i	$-0.268780\pi$
$613$	−31334.4	−	31334.4i	−0.0833873	−	0.0833873i	−0.747570	+	0.664183i	$0.768780\pi$
$614$	−164808.	−	267037.i	−0.437161	−	0.708329i
$615$	−517.871			−0.00136921
$616$	378913.	−	33452.6i	0.998570	−	0.0881592i
$617$			481833.i			1.26569i	0.774280	+	0.632844i	$0.218112\pi$
$617$			481833.i			1.26569i	−0.774280	+	0.632844i	$0.781888\pi$
$618$	−2334.47	−	3782.52i	−0.00611239	−	0.00990385i
$619$	55035.5	−	55035.5i	0.143635	−	0.143635i	−0.631632	−	0.775268i	$-0.717615\pi$
$619$	55035.5	−	55035.5i	0.143635	−	0.143635i	0.775268	+	0.631632i	$0.217615\pi$
$620$	−260149.	+	86356.1i	−0.676766	+	0.224652i
$621$	3029.87	−	3029.87i	0.00785672	−	0.00785672i
$622$	−494526.	−	117067.i	−1.27823	−	0.302590i
$623$		−	321215.i		−	0.827599i
$624$	−275.603	−	369.386i	−0.000707808	−	0.000948661i
$625$	−164779.			−0.421834
$626$	23468.4	−	99137.5i	0.0598873	−	0.252982i
$627$	2717.23	+	2717.23i	0.00691180	+	0.00691180i
$628$	25077.2	−	8324.36i	0.0635858	−	0.0211072i
$629$	−190144.	−	190144.i	−0.480597	−	0.480597i
$630$	156421.	−	96538.9i	0.394107	−	0.243232i
$631$	−188802.			−0.474184			−0.237092	−	0.971487i	$-0.576194\pi$
$631$	−188802.			−0.474184			−0.237092	+	0.971487i	$0.576194\pi$
$632$	−241240.	+	287960.i	−0.603969	+	0.720939i
$633$			5102.26i			0.0127337i
$634$	−453554.	+	279921.i	−1.12837	+	0.696398i
$635$	−163812.	+	163812.i	−0.406255	+	0.406255i
$636$	690.103	−	1375.92i	0.00170608	−	0.00340156i
$637$	1694.72	−	1694.72i	0.00417656	−	0.00417656i
$638$	160190.	−	676691.i	0.393545	−	1.66245i
$639$			94108.5i			0.230477i
$640$	138986.	−	124148.i	0.339322	−	0.303095i
$641$	−442081.			−1.07593			−0.537967	−	0.842966i	$-0.680807\pi$
$641$	−442081.			−1.07593			−0.537967	+	0.842966i	$0.680807\pi$
$642$	−3369.49	−	797.646i	−0.00817512	−	0.00193526i
$643$	−246339.	−	246339.i	−0.595814	−	0.595814i	0.343382	−	0.939196i	$-0.388427\pi$
$643$	−246339.	−	246339.i	−0.595814	−	0.595814i	−0.939196	+	0.343382i	$0.888427\pi$
$644$	288802.	+	144851.i	0.696353	+	0.349262i
$645$	681.935	+	681.935i	0.00163917	+	0.00163917i
$646$	454028.	+	735657.i	1.08797	+	1.76283i
$647$	−54549.4			−0.130311			−0.0651555	−	0.997875i	$-0.520754\pi$
$647$	−54549.4			−0.130311			−0.0651555	+	0.997875i	$0.520754\pi$
$648$	−321828.	−	269612.i	−0.766431	−	0.642080i
$649$		−	288429.i		−	0.684778i
$650$	−28689.5	−	46485.4i	−0.0679042	−	0.110025i
$651$	3470.80	−	3470.80i	0.00818970	−	0.00818970i
$652$	200146.	+	602942.i	0.470816	+	1.41834i
$653$	231745.	−	231745.i	0.543481	−	0.543481i	−0.381066	−	0.924548i	$-0.624443\pi$
$653$	231745.	−	231745.i	0.543481	−	0.543481i	0.924548	+	0.381066i	$0.124443\pi$
$654$	2988.29	+	707.405i	0.00698661	+	0.00165391i
$655$		−	71011.8i		−	0.165519i
$656$	−142981.	+	106680.i	−0.332254	+	0.247899i
$657$	−73325.0			−0.169872
$658$	5143.82	−	21729.0i	0.0118805	−	0.0501866i
$659$	−479757.	−	479757.i	−1.10472	−	1.10472i	−0.993833	−	0.110883i	$-0.964632\pi$
$659$	−479757.	−	479757.i	−1.10472	−	1.10472i	−0.110883	−	0.993833i	$-0.535368\pi$
$660$	−446.374	−	1344.71i	−0.00102473	−	0.00308702i
$661$	515798.	+	515798.i	1.18053	+	1.18053i	0.979607	+	0.200922i	$0.0643937\pi$
$661$	515798.	+	515798.i	1.18053	+	1.18053i	0.200922	+	0.979607i	$0.435606\pi$
$662$	313581.	−	193534.i	0.715541	−	0.441612i
$663$	−788.263			−0.00179326
$664$	−60176.1	−	681608.i	−0.136486	−	1.54596i
$665$			280041.i			0.633254i
$666$	−169320.	+	104500.i	−0.381733	+	0.235595i
$667$	417654.	−	417654.i	0.938782	−	0.938782i
$668$	−41902.0	−	21016.3i	−0.0939034	−	0.0470981i
$669$	−1867.27	+	1867.27i	−0.00417210	+	0.00417210i
$670$	−27483.0	+	116096.i	−0.0612230	+	0.258624i
$671$			625397.i			1.38903i
$672$	−1228.01	+	3102.99i	−0.00271934	+	0.00687136i
$673$	−505551.			−1.11618			−0.558090	−	0.829780i	$-0.688466\pi$
$673$	−505551.			−1.11618			−0.558090	+	0.829780i	$0.688466\pi$
$674$	525492.	+	124398.i	1.15677	+	0.273837i
$675$	3709.29	+	3709.29i	0.00814111	+	0.00814111i
$676$	−199429.	+	397618.i	−0.436410	+	0.870107i
$677$	−460825.	−	460825.i	−1.00545	−	1.00545i	−0.999985	−	0.00546007i	$-0.998262\pi$
$677$	−460825.	−	460825.i	−1.00545	−	1.00545i	−0.00546007	−	0.999985i	$-0.501738\pi$
$678$	−798.104	−	1293.16i	−0.00173620	−	0.00281315i
$679$	20601.9			0.0446857
$680$	−28031.4	−	317509.i	−0.0606216	−	0.686654i
$681$			154.570i			0.000333297i
$682$	377031.	+	610900.i	0.810603	+	1.31341i
$683$	120242.	−	120242.i	0.257761	−	0.257761i	−0.566382	−	0.824143i	$-0.691657\pi$
$683$	120242.	−	120242.i	0.257761	−	0.257761i	0.824143	+	0.566382i	$0.191657\pi$
$684$	607086.	−	201522.i	1.29759	−	0.430734i
$685$	−88622.7	+	88622.7i	−0.188870	+	0.188870i
$686$	449273.	+	106355.i	0.954690	+	0.226000i
$687$			2450.33i			0.00519171i
$688$	328754.	+	47801.4i	0.694535	+	0.100987i
$689$	40572.7			0.0854664
$690$	277.225	−	1171.08i	0.000582284	−	0.00245974i
$691$	166965.	+	166965.i	0.349678	+	0.349678i	0.859990	−	0.510311i	$-0.170470\pi$
$691$	166965.	+	166965.i	0.349678	+	0.349678i	−0.510311	+	0.859990i	$0.670470\pi$
$692$	183848.	−	61028.2i	0.383926	−	0.127444i
$693$	−340403.	−	340403.i	−0.708805	−	0.708805i
$694$	52226.3	−	32232.7i	0.108435	−	0.0669233i
$695$	240600.			0.498111
$696$	4676.51	+	3917.76i	0.00965392	+	0.00808760i
$697$			305118.i			0.628062i
$698$	−29235.3	+	18043.2i	−0.0600062	+	0.0370342i
$699$	−1116.33	+	1116.33i	−0.00228475	+	0.00228475i
$700$	−177333.	+	353564.i	−0.361904	+	0.721558i
$701$	39689.8	−	39689.8i	0.0807687	−	0.0807687i	−0.665568	−	0.746337i	$-0.731811\pi$
$701$	39689.8	−	39689.8i	0.0807687	−	0.0807687i	0.746337	+	0.665568i	$0.231811\pi$
$702$	−268.726	+	1135.18i	−0.000545300	+	0.00230351i
$703$		−	303133.i		−	0.613371i
$704$	−400246.	−	279313.i	−0.807573	−	0.563567i
$705$	−83.1725			−0.000167341
$706$	−558347.	−	132175.i	−1.12020	−	0.265180i
$707$	−422013.	−	422013.i	−0.844281	−	0.844281i
$708$	2261.85	+	1134.45i	0.00451228	+	0.00226318i
$709$	250742.	+	250742.i	0.498809	+	0.498809i	0.911067	−	0.412258i	$-0.135260\pi$
$709$	250742.	+	250742.i	0.498809	+	0.498809i	−0.412258	+	0.911067i	$0.635260\pi$
$710$	27764.1	+	44985.9i	0.0550766	+	0.0892401i
$711$	475415.			0.940445
$712$	−264674.	+	315933.i	−0.522096	+	0.623210i
$713$			609751.i			1.19943i
$714$	2997.73	+	4857.19i	0.00588024	+	0.00952771i
$715$	26407.5	−	26407.5i	0.0516553	−	0.0516553i
$716$	−174083.	−	524426.i	−0.339570	−	1.02296i
$717$	3527.63	−	3527.63i	0.00686190	−	0.00686190i
$718$	482957.	+	114328.i	0.936826	+	0.221771i
$719$		−	133454.i		−	0.258152i	−0.991635	−	0.129076i	$-0.958799\pi$
$719$		−	133454.i		−	0.258152i	0.991635	−	0.129076i	$-0.0412011\pi$
$720$	−233394.	−	33935.9i	−0.450221	−	0.0654628i
$721$	−848347.			−1.63194
$722$	−104409.	+	441052.i	−0.200291	+	0.846088i
$723$	−1873.30	−	1873.30i	−0.00358370	−	0.00358370i
$724$	−78034.0	−	235078.i	−0.148870	−	0.448472i
$725$	511309.	+	511309.i	0.972763	+	0.972763i
$726$	98.3952	−	60.7269i	0.000186681	−	0.000115215i
$727$	583370.			1.10376			0.551881	−	0.833923i	$-0.313910\pi$
$727$	583370.			1.10376			0.551881	+	0.833923i	$0.313910\pi$
$728$	−87620.5	+	7735.62i	−0.165327	+	0.0145959i
$729$			531273.i			0.999684i
$730$	−35051.0	+	21632.5i	−0.0657740	+	0.0405939i
$731$	401781.	−	401781.i	0.751891	−	0.751891i
$732$	−4904.33	−	2459.81i	−0.00915288	−	0.00459071i
$733$	534516.	−	534516.i	0.994838	−	0.994838i	−0.00514857	−	0.999987i	$-0.501639\pi$
$733$	534516.	−	534516.i	0.994838	−	0.994838i	0.999987	+	0.00514857i	$0.00163885\pi$
$734$	116322.	−	491378.i	0.215909	−	0.912061i
$735$			64.6410i			0.000119656i
$736$	−164699.	−	380435.i	−0.304043	−	0.702304i
$737$	312456.			0.575247
$738$	219695.	+	52007.5i	0.403373	+	0.0954889i
$739$	−91929.4	−	91929.4i	−0.168332	−	0.168332i	0.617914	−	0.786246i	$-0.287978\pi$
$739$	−91929.4	−	91929.4i	−0.168332	−	0.168332i	−0.786246	+	0.617914i	$0.787978\pi$
$740$	−50108.9	+	99906.2i	−0.0915063	+	0.182444i
$741$	−628.336	−	628.336i	−0.00114434	−	0.00114434i
$742$	−154296.	−	250005.i	−0.280251	−	0.454088i
$743$	83329.2			0.150945			0.0754727	−	0.997148i	$-0.475953\pi$
$743$	83329.2			0.150945			0.0754727	+	0.997148i	$0.475953\pi$
$744$	−6273.58	+	553.866i	−0.0113336	+	0.00100060i
$745$		−	247625.i		−	0.446151i
$746$	−283770.	−	459789.i	−0.509904	−	0.826193i
$747$	−612333.	+	612333.i	−1.09735	+	1.09735i
$748$	−792272.	+	262994.i	−1.41602	+	0.470048i
$749$	−467305.	+	467305.i	−0.832985	+	0.832985i
$750$	3241.62	+	767.377i	0.00576289	+	0.00136422i
$751$			318689.i			0.565051i	0.959260	+	0.282525i	$0.0911722\pi$
$751$			318689.i			0.565051i	−0.959260	+	0.282525i	$0.908828\pi$
$752$	−22963.4	+	17133.3i	−0.0406069	+	0.0302973i
$753$	973.515			0.00171693
$754$	−37042.7	+	156479.i	−0.0651567	+	0.275241i
$755$	136504.	+	136504.i	0.239470	+	0.239470i
$756$	8016.80	−	2661.17i	0.0140268	−	0.00465617i
$757$	−428881.	−	428881.i	−0.748419	−	0.748419i	0.225763	−	0.974182i	$-0.427512\pi$
$757$	−428881.	−	428881.i	−0.748419	−	0.748419i	−0.974182	+	0.225763i	$0.927512\pi$
$758$	−150288.	+	92754.0i	−0.261570	+	0.161434i
$759$	−3151.80			−0.00547110
$760$	230747.	−	275435.i	0.399493	−	0.476862i
$761$		−	718933.i		−	1.24142i	−0.784040	−	0.620711i	$-0.786844\pi$
$761$		−	718933.i		−	1.24142i	0.784040	−	0.620711i	$-0.213156\pi$
$762$	−4529.61	+	2795.55i	−0.00780100	+	0.00481457i
$763$	414437.	−	414437.i	0.711884	−	0.711884i
$764$	160572.	−	320147.i	0.275096	−	0.548482i
$765$	−285239.	+	285239.i	−0.487401	+	0.487401i
$766$	−233218.	+	985179.i	−0.397469	+	1.67903i
$767$			66696.8i			0.113374i
$768$	3764.60	−	2040.11i	0.00638259	−	0.00345885i
$769$	421326.			0.712468			0.356234	−	0.934397i	$-0.384061\pi$
$769$	421326.			0.712468			0.356234	+	0.934397i	$0.384061\pi$
$770$	−263146.	−	62293.6i	−0.443829	−	0.105066i
$771$	−1754.84	−	1754.84i	−0.00295208	−	0.00295208i
$772$	−435199.	−	218278.i	−0.730220	−	0.366248i
$773$	455325.	+	455325.i	0.762013	+	0.762013i	0.976686	−	0.214673i	$-0.0688685\pi$
$773$	455325.	+	455325.i	0.762013	+	0.762013i	−0.214673	+	0.976686i	$0.568868\pi$
$774$	−220811.	−	357779.i	−0.368587	−	0.597218i
$775$	−746482.			−1.24284
$776$	−20263.1	−	16975.5i	−0.0336498	−	0.0281902i
$777$		−	2001.44i		−	0.00331513i
$778$	−128582.	−	208341.i	−0.212433	−	0.344204i
$779$	−243214.	+	243214.i	−0.400788	+	0.400788i
$780$	103.220	+	310.952i	0.000169658	+	0.000511098i
$781$	97898.1	−	97898.1i	0.160499	−	0.160499i
$782$	−689976.	−	163335.i	−1.12829	−	0.267095i
$783$		−	15442.0i		−	0.0251872i
$784$	13315.8	+	17847.0i	0.0216639	+	0.0290357i
$785$	−18784.0			−0.0304825
$786$	375.852	−	1587.71i	0.000608376	−	0.00256996i
$787$	541211.	+	541211.i	0.873811	+	0.873811i	0.992885	−	0.119074i	$-0.0379927\pi$
$787$	541211.	+	541211.i	0.873811	+	0.873811i	−0.119074	+	0.992885i	$0.537993\pi$
$788$	136114.	+	410045.i	0.219205	+	0.660357i
$789$	−1734.56	−	1734.56i	−0.00278635	−	0.00278635i
$790$	227259.	−	140258.i	0.364138	−	0.224736i
$791$	−290032.			−0.463546
$792$	54321.0	+	615288.i	0.0865999	+	0.980908i
$793$		−	144618.i		−	0.229972i
$794$	955709.	−	589838.i	1.51595	−	0.935603i
$795$	−773.775	+	773.775i	−0.00122428	+	0.00122428i
$796$	972012.	+	487521.i	1.53407	+	0.769427i
$797$	481291.	−	481291.i	0.757690	−	0.757690i	−0.218212	−	0.975901i	$-0.570022\pi$
$797$	481291.	−	481291.i	0.757690	−	0.757690i	0.975901	+	0.218212i	$0.0700224\pi$
$798$	−1482.21	+	6261.27i	−0.00232757	+	0.00983234i
$799$			49003.4i			0.0767597i
$800$	465744.	−	201631.i	0.727725	−	0.315048i
$801$	521597.			0.812961
$802$	−347713.	−	82312.7i	−0.540595	−	0.127973i
$803$	76277.7	+	76277.7i	0.118295	+	0.118295i
$804$	−1228.95	+	2450.26i	−0.00190118	+	0.00379054i
$805$	−162414.	−	162414.i	−0.250629	−	0.250629i
$806$	−87185.2	−	141265.i	−0.134206	−	0.217453i
$807$	−432.116			−0.000663518
$808$	67344.3	+	762802.i	0.103152	+	1.16839i
$809$			34438.5i			0.0526195i	0.999654	+	0.0263097i	$0.00837562\pi$
$809$			34438.5i			0.0526195i	−0.999654	+	0.0263097i	$0.991624\pi$
$810$	156754.	+	253987.i	0.238918	+	0.387116i
$811$	227480.	−	227480.i	0.345862	−	0.345862i	−0.512704	−	0.858566i	$-0.671356\pi$
$811$	227480.	−	227480.i	0.345862	−	0.345862i	0.858566	+	0.512704i	$0.171356\pi$
$812$	1.10508e6	−	366830.i	1.67603	−	0.556355i
$813$	126.869	−	126.869i	0.000191944	−	0.000191944i
$814$	284846.	+	67430.4i	0.429893	+	0.101767i
$815$		−	451633.i		−	0.679939i
$816$	1053.78	−	7247.36i	0.00158259	−	0.0108843i
$817$	640532.			0.959614
$818$	−24617.4	+	103991.i	−0.0367905	+	0.155414i
$819$	78715.2	+	78715.2i	0.117352	+	0.117352i
$820$	120362.	−	39954.1i	0.179004	−	0.0594202i
$821$	−807677.	−	807677.i	−1.19826	−	1.19826i	−0.974687	−	0.223573i	$-0.928228\pi$
$821$	−807677.	−	807677.i	−1.19826	−	1.19826i	−0.223573	−	0.974687i	$-0.571772\pi$
$822$	−2450.53	+	1512.40i	−0.00362674	+	0.00223832i
$823$	−703593.			−1.03878			−0.519388	−	0.854539i	$-0.673840\pi$
$823$	−703593.			−1.03878			−0.519388	+	0.854539i	$0.673840\pi$
$824$	834395.	+	699017.i	1.22890	+	1.02952i
$825$		−	3858.56i		−	0.00566914i
$826$	410978.	−	253645.i	0.602363	−	0.371762i
$827$	−775918.	+	775918.i	−1.13450	+	1.13450i	−0.145081	+	0.989420i	$0.546344\pi$
$827$	−775918.	+	775918.i	−1.13450	+	1.13450i	−0.989420	+	0.145081i	$0.953656\pi$
$828$	−235213.	+	468964.i	−0.343084	+	0.684036i
$829$	−804056.	+	804056.i	−1.16998	+	1.16998i	−0.187763	+	0.982214i	$0.560124\pi$
$829$	−804056.	+	804056.i	−1.16998	+	1.16998i	−0.982214	+	0.187763i	$0.939876\pi$
$830$	−112057.	+	473360.i	−0.162660	+	0.687125i
$831$			3054.39i			0.00442305i
$832$	92553.5	+	64588.7i	0.133704	+	0.0933061i
$833$	38085.1			0.0548864
$834$	5379.43	+	1273.45i	0.00773400	+	0.00183084i
$835$	23564.4	+	23564.4i	0.0337974	+	0.0337974i
$836$	−841168.	−	421896.i	−1.20357	−	0.603660i
$837$	11272.2	+	11272.2i	0.0160901	+	0.0160901i
$838$	−353580.	−	572902.i	−0.503500	−	0.815816i
$839$	−248652.			−0.353239			−0.176619	−	0.984279i	$-0.556516\pi$
$839$	−248652.			−0.353239			−0.176619	+	0.984279i	$0.556516\pi$
$840$	1523.51	−	1818.57i	0.00215917	−	0.00257733i
$841$		−	1.42133e6i		−	2.00957i
$842$	377218.	+	611203.i	0.532070	+	0.862108i
$843$	−3697.49	+	3697.49i	−0.00520297	+	0.00520297i
$844$	−393643.	−	1.18585e6i	−0.552609	−	1.66474i
$845$	223609.	−	223609.i	0.313166	−	0.313166i
$846$	35284.0	+	8352.65i	0.0492989	+	0.0116703i
$847$		−	22068.2i		−	0.0307610i
$848$	−54239.1	+	373029.i	−0.0754259	+	0.518742i
$849$	6679.00			0.00926608
$850$	199961.	−	844696.i	0.276763	−	1.16913i
$851$	175807.	+	175807.i	0.242760	+	0.242760i
$852$	382.659	+	1152.76i	0.000527148	+	0.00158804i
$853$	779867.	+	779867.i	1.07182	+	1.07182i	0.997213	+	0.0746081i	$0.0237706\pi$
$853$	779867.	+	779867.i	1.07182	+	1.07182i	0.0746081	+	0.997213i	$0.476229\pi$
$854$	−891119.	+	549974.i	−1.22186	+	0.754096i
$855$	−454737.			−0.622054
$856$	844668.	−	74571.9i	1.15276	−	0.101772i
$857$		−	481792.i		−	0.655992i	−0.944679	−	0.327996i	$-0.893627\pi$
$857$		−	481792.i		−	0.655992i	0.944679	−	0.327996i	$-0.106373\pi$
$858$	730.199	−	450.659i	0.000991897	−	0.000612172i
$859$	−947889.	+	947889.i	−1.28461	+	1.28461i	−0.346594	+	0.938015i	$0.612662\pi$
$859$	−947889.	+	947889.i	−1.28461	+	1.28461i	−0.938015	+	0.346594i	$0.887338\pi$
$860$	−211105.	−	105882.i	−0.285432	−	0.143161i
$861$	−1605.83	+	1605.83i	−0.00216617	+	0.00216617i
$862$	−76466.5	+	323017.i	−0.102910	+	0.434721i
$863$		−	1.00011e6i		−	1.34284i	−0.741077	−	0.671421i	$-0.765684\pi$
$863$		−	1.00011e6i		−	1.34284i	0.741077	−	0.671421i	$-0.234316\pi$
$864$	−10077.7	−	3988.24i	−0.0135000	−	0.00534262i
$865$	−137711.			−0.184051
$866$	−596429.	−	141190.i	−0.795285	−	0.188265i
$867$	−4998.61	−	4998.61i	−0.00664984	−	0.00664984i
$868$	−538900.	+	1.07445e6i	−0.715268	+	1.42609i
$869$	−494559.	−	494559.i	−0.654905	−	0.654905i
$870$	−2277.81	−	3690.71i	−0.00300939	−	0.00487609i
$871$	−72252.8			−0.0952398
$872$	−749107.	+	66135.3i	−0.985169	+	0.0869761i
$873$			33453.9i			0.0438953i
$874$	−419793.	−	680187.i	−0.549557	−	0.890442i
$875$	449571.	−	449571.i	0.587195	−	0.587195i
$876$	−898.181	+	298.150i	−0.00117046	+	0.000388532i
$877$	−747906.	+	747906.i	−0.972406	+	0.972406i	−0.999629	−	0.0272234i	$-0.991333\pi$
$877$	−747906.	+	747906.i	−0.972406	+	0.972406i	0.0272234	+	0.999629i	$0.491333\pi$
$878$	190667.	+	45135.9i	0.247336	+	0.0585508i
$879$			7845.72i			0.0101544i
$880$	207490.	+	278095.i	0.267937	+	0.359110i
$881$	−53961.8			−0.0695240			−0.0347620	−	0.999396i	$-0.511067\pi$
$881$	−53961.8			−0.0695240			−0.0347620	+	0.999396i	$0.511067\pi$
$882$	6491.61	−	27422.5i	0.00834479	−	0.0352508i
$883$	−629494.	−	629494.i	−0.807366	−	0.807366i	0.176869	−	0.984234i	$-0.443403\pi$
$883$	−629494.	−	629494.i	−0.807366	−	0.807366i	−0.984234	+	0.176869i	$0.943403\pi$
$884$	183206.	−	60815.1i	0.234442	−	0.0778228i
$885$	−1271.99	−	1271.99i	−0.00162405	−	0.00162405i
$886$	26303.0	−	16233.5i	0.0335072	−	0.0206797i
$887$	880807.			1.11952			0.559762	−	0.828653i	$-0.310893\pi$
$887$	880807.			1.11952			0.559762	+	0.828653i	$0.310893\pi$
$888$	−1649.14	+	1968.53i	−0.00209137	+	0.00249641i
$889$			1.01590e6i			1.28543i
$890$	249335.	−	153883.i	0.314777	−	0.194272i
$891$	552724.	−	552724.i	0.696231	−	0.696231i
$892$	289925.	−	578047.i	0.364381	−	0.726496i
$893$	−39061.4	+	39061.4i	−0.0489829	+	0.0489829i
$894$	1310.64	−	5536.51i	0.00163986	−	0.00692725i
$895$			392821.i			0.490398i
$896$	46012.3	−	815932.i	0.0573136	−	1.01634i
$897$	728.826			0.000905814
$898$	545202.	+	129063.i	0.676090	+	0.160048i
$899$	1.55383e6	+	1.55383e6i	1.92257	+	1.92257i
$900$	−574124.	−	287957.i	−0.708796	−	0.355503i
$901$	455891.	+	455891.i	0.561580	+	0.561580i
$902$	−174440.	−	282643.i	−0.214404	−	0.347396i
$903$	4229.12			0.00518650
$904$	285262.	+	238979.i	0.349065	+	0.292431i
$905$			176085.i			0.214994i
$906$	2329.52	+	3774.51i	0.00283799	+	0.00459837i
$907$	662568.	−	662568.i	0.805408	−	0.805408i	−0.178527	−	0.983935i	$-0.557133\pi$
$907$	662568.	−	662568.i	0.805408	−	0.805408i	0.983935	+	0.178527i	$0.0571333\pi$
$908$	−11925.2	−	35924.8i	−0.0144642	−	0.0435735i
$909$	685275.	−	685275.i	0.829348	−	0.829348i
$910$	60850.3	+	14404.9i	0.0734819	+	0.0173951i
$911$			817906.i			0.985522i	0.870165	+	0.492761i	$0.164012\pi$
$911$			817906.i			0.985522i	−0.870165	+	0.492761i	$0.835988\pi$
$912$	6616.97	−	4937.00i	0.00795553	−	0.00593572i
$913$	1.27398e6			1.52834
$914$	−202521.	+	855506.i	−0.242425	+	1.02407i
$915$	2758.05	+	2758.05i	0.00329428	+	0.00329428i
$916$	−189045.	−	569499.i	−0.225306	−	0.678737i
$917$	−220195.	−	220195.i	−0.261860	−	0.261860i
$918$	−15774.8	+	9735.81i	−0.0187189	+	0.0115528i
$919$	−33891.9			−0.0401296			−0.0200648	−	0.999799i	$-0.506387\pi$
$919$	−33891.9			−0.0401296			−0.0200648	+	0.999799i	$0.506387\pi$
$920$	25917.8	+	293568.i	0.0306212	+	0.346843i
$921$			5125.61i			0.00604263i
$922$	597704.	−	368887.i	0.703111	−	0.433941i
$923$	−22638.1	+	22638.1i	−0.0265728	+	0.0265728i
$924$	−5553.82	−	2785.57i	−0.00650501	−	0.00326265i
$925$	−215230.	+	215230.i	−0.251547	+	0.251547i
$926$	−217980.	+	920813.i	−0.254212	+	1.07386i
$927$		−	1.37757e6i		−	1.60307i
$928$	−1.38916e6	−	549760.i	−1.61308	−	0.638377i
$929$	−207783.			−0.240757			−0.120378	−	0.992728i	$-0.538411\pi$
$929$	−207783.			−0.240757			−0.120378	+	0.992728i	$0.538411\pi$
$930$	4356.85	+	1031.38i	0.00503741	+	0.00119248i
$931$	30358.2	+	30358.2i	0.0350249	+	0.0350249i
$932$	173329.	−	345581.i	0.199545	−	0.397849i
$933$	5869.57	+	5869.57i	0.00674284	+	0.00674284i
$934$	218116.	+	353412.i	0.250032	+	0.405124i
$935$	593450.			0.678830
$936$	−12561.3	−	142280.i	−0.0143378	−	0.162402i
$937$			1.12361e6i			1.27979i	0.768464	+	0.639893i	$0.221022\pi$
$937$			1.12361e6i			1.27979i	−0.768464	+	0.639893i	$0.778978\pi$
$938$	274774.	+	445214.i	0.312299	+	0.506015i
$939$	−1176.67	+	1176.67i	−0.00133452	+	0.00133452i
$940$	19330.8	−	6416.83i	0.0218773	−	0.00726214i
$941$	−856765.	+	856765.i	−0.967570	+	0.967570i	−0.999490	−	0.0319200i	$-0.989838\pi$
$941$	−856765.	+	856765.i	−0.967570	+	0.967570i	0.0319200	+	0.999490i	$0.489838\pi$
$942$	−419.982	−	99.4206i	−0.000473291	−	0.000112040i
$943$		−	282112.i		−	0.317247i
$944$	−613216.	−	89162.7i	−0.688129	−	0.100055i
$945$	−6004.97			−0.00672430
$946$	−142483.	+	601889.i	−0.159214	+	0.672565i
$947$	−246666.	−	246666.i	−0.275048	−	0.275048i	0.556080	−	0.831129i	$-0.312305\pi$
$947$	−246666.	−	246666.i	−0.275048	−	0.275048i	−0.831129	+	0.556080i	$0.812305\pi$
$948$	5823.50	−	1933.11i	0.00647989	−	0.00215099i
$949$	−17638.6	−	17638.6i	−0.0195853	−	0.0195853i
$950$	832713.	−	513928.i	0.922673	−	0.569449i
$951$	8705.68			0.00962591
$952$	−1.07146e6	−	897619.i	−1.18223	−	0.990417i
$953$		−	219446.i		−	0.241625i	−0.992675	−	0.120812i	$-0.961450\pi$
$953$		−	219446.i		−	0.241625i	0.992675	−	0.120812i	$-0.0385500\pi$
$954$	405963.	−	250549.i	0.446056	−	0.275294i
$955$	−180041.	+	180041.i	−0.197408	+	0.197408i
$956$	−547724.	+	1.09204e6i	−0.599302	+	1.19488i
$957$	−8031.71	+	8031.71i	−0.00876968	+	0.00876968i
$958$	195349.	−	825210.i	0.212853	−	0.899153i
$959$			549607.i			0.597606i
$960$	−2996.91	+	533.324i	−0.00325185	+	0.000578694i
$961$	−1.34498e6			−1.45636
$962$	−65868.1	−	15592.7i	−0.0711746	−	0.0168489i
$963$	−758821.	−	758821.i	−0.818251	−	0.818251i
$964$	579915.	+	290861.i	0.624037	+	0.312991i
$965$	244743.	+	244743.i	0.262819	+	0.262819i
$966$	−2771.69	−	4490.95i	−0.00297023	−	0.00481264i
$967$	650799.			0.695975			0.347988	−	0.937499i	$-0.386865\pi$
$967$	650799.			0.695975			0.347988	+	0.937499i	$0.386865\pi$
$968$	−18183.6	+	21705.3i	−0.0194057	+	0.0231640i
$969$		−	14120.5i		−	0.0150384i
$970$	9869.63	+	15991.7i	0.0104896	+	0.0169961i
$971$	790825.	−	790825.i	0.838768	−	0.838768i	−0.149929	−	0.988697i	$-0.547904\pi$
$971$	790825.	−	790825.i	0.838768	−	0.838768i	0.988697	+	0.149929i	$0.0479044\pi$
$972$	6481.95	+	19527.0i	0.00686078	+	0.0206682i
$973$	746058.	−	746058.i	0.788037	−	0.788037i
$974$	103991.	+	24617.4i	0.109617	+	0.0259492i
$975$			892.258i			0.000938602i
$976$	1.32963e6	+	193330.i	1.39582	+	0.202955i
$977$	−1.40812e6			−1.47520			−0.737600	−	0.675237i	$-0.764041\pi$
$977$	−1.40812e6			−1.47520			−0.737600	+	0.675237i	$0.764041\pi$
$978$	2390.41	−	10097.8i	0.00249916	−	0.0105572i
$979$	−542600.	−	542600.i	−0.566128	−	0.566128i
$980$	−4987.11	−	15023.7i	−0.00519274	−	0.0156432i
$981$	672972.	+	672972.i	0.699292	+	0.699292i
$982$	479195.	−	295746.i	0.496923	−	0.306688i
$983$	−208227.			−0.215491			−0.107746	−	0.994179i	$-0.534363\pi$
$983$	−208227.			−0.215491			−0.107746	+	0.994179i	$0.534363\pi$
$984$	2902.58	−	256.256i	0.00299774	−	0.000264657i
$985$		−	307144.i		−	0.316569i
$986$	−2.17449e6	+	1.34204e6i	−2.23668	+	1.38042i
$987$	−257.903	+	257.903i	−0.000264742	+	0.000264742i
$988$	194513.	+	97559.7i	0.199267	+	0.0999440i
$989$	−371486.	+	371486.i	−0.379796	+	0.379796i
$990$	101154.	−	427303.i	0.103208	−	0.435979i
$991$			170063.i			0.173166i	0.996245	+	0.0865831i	$0.0275948\pi$
$991$			170063.i			0.173166i	−0.996245	+	0.0865831i	$0.972405\pi$
$992$	1.41536e6	−	612740.i	1.43828	−	0.622663i
$993$	−6019.00			−0.00610416
$994$	225585.	+	53401.8i	0.228317	+	0.0540485i
$995$	−546631.	−	546631.i	−0.552138	−	0.552138i
$996$	−5010.82	+	9990.49i	−0.00505115	+	0.0100709i
$997$	−917799.	−	917799.i	−0.923331	−	0.923331i	0.0739326	−	0.997263i	$-0.476445\pi$
$997$	−917799.	−	917799.i	−0.923331	−	0.923331i	−0.997263	+	0.0739326i	$0.976445\pi$
$998$	564153.	+	914091.i	0.566416	+	0.917759i
$999$	6500.15			0.00651317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.5.f.a.11.7	yes	14
3.2	odd	2		144.5.m.a.91.1		14
4.3	odd	2		64.5.f.a.15.4		14
8.3	odd	2		128.5.f.a.31.4		14
8.5	even	2		128.5.f.b.31.4		14
12.11	even	2		576.5.m.a.271.5		14
16.3	odd	4	inner	16.5.f.a.3.7	✓	14
16.5	even	4		128.5.f.a.95.4		14
16.11	odd	4		128.5.f.b.95.4		14
16.13	even	4		64.5.f.a.47.4		14
48.29	odd	4		576.5.m.a.559.5		14
48.35	even	4		144.5.m.a.19.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.7	✓	14	16.3	odd	4	inner
16.5.f.a.11.7	yes	14	1.1	even	1	trivial
64.5.f.a.15.4		14	4.3	odd	2
64.5.f.a.47.4		14	16.13	even	4
128.5.f.a.31.4		14	8.3	odd	2
128.5.f.a.95.4		14	16.5	even	4
128.5.f.b.31.4		14	8.5	even	2
128.5.f.b.95.4		14	16.11	odd	4
144.5.m.a.19.1		14	48.35	even	4
144.5.m.a.91.1		14	3.2	odd	2
576.5.m.a.271.5		14	12.11	even	2
576.5.m.a.559.5		14	48.29	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.89242 + 0.921438i) q^{2} +(-0.0461995 - 0.0461995i) q^{3} +(14.3019 + 7.17325i) q^{4} +(-8.04297 - 8.04297i) q^{5} +(-0.137258 - 0.222398i) q^{6} -49.8797 q^{7} +(49.0594 + 41.0996i) q^{8} -80.9957i q^{9} +(-23.8955 - 38.7177i) q^{10} +(-84.2573 + 84.2573i) q^{11} +(-0.329340 - 0.992142i) q^{12} +(19.4838 - 19.4838i) q^{13} +(-194.153 - 45.9610i) q^{14} +0.743162i q^{15} +(153.089 + 205.182i) q^{16} +437.855 q^{17} +(74.6325 - 315.270i) q^{18} +(349.021 + 349.021i) q^{19} +(-57.3356 - 172.724i) q^{20} +(2.30442 + 2.30442i) q^{21} +(-405.603 + 250.327i) q^{22} -404.840 q^{23} +(-0.367736 - 4.16530i) q^{24} -495.621i q^{25} +(93.7922 - 57.8860i) q^{26} +(-7.48412 + 7.48412i) q^{27} +(-713.374 - 357.799i) q^{28} +(-1031.65 + 1031.65i) q^{29} +(-0.684778 + 2.89270i) q^{30} -1506.15i q^{31} +(406.824 + 939.718i) q^{32} +7.78529 q^{33} +(1704.32 + 403.456i) q^{34} +(401.181 + 401.181i) q^{35} +(581.003 - 1158.39i) q^{36} +(-434.262 - 434.262i) q^{37} +(1036.94 + 1680.14i) q^{38} -1.80028 q^{39} +(-64.0199 - 725.146i) q^{40} +696.847i q^{41} +(6.84639 + 11.0931i) q^{42} +(917.612 - 917.612i) q^{43} +(-1809.44 + 600.641i) q^{44} +(-651.446 + 651.446i) q^{45} +(-1575.81 - 373.035i) q^{46} +111.917i q^{47} +(2.40668 - 16.5520i) q^{48} +86.9810 q^{49} +(456.684 - 1929.17i) q^{50} +(-20.2287 - 20.2287i) q^{51} +(418.417 - 138.893i) q^{52} +(1041.19 + 1041.19i) q^{53} +(-36.0275 + 22.2352i) q^{54} +1355.36 q^{55} +(-2447.06 - 2050.04i) q^{56} -32.2492i q^{57} +(-4966.23 + 3065.02i) q^{58} +(-1711.60 + 1711.60i) q^{59} +(-5.33089 + 10.6286i) q^{60} +(3711.24 - 3711.24i) q^{61} +(1387.83 - 5862.58i) q^{62} +4040.04i q^{63} +(717.641 + 4032.64i) q^{64} -313.415 q^{65} +(30.3036 + 7.17366i) q^{66} +(-1854.18 - 1854.18i) q^{67} +(6262.16 + 3140.84i) q^{68} +(18.7034 + 18.7034i) q^{69} +(1191.90 + 1931.23i) q^{70} -1161.89 q^{71} +(3328.89 - 3973.60i) q^{72} -905.295i q^{73} +(-1290.19 - 2090.48i) q^{74} +(-22.8975 + 22.8975i) q^{75} +(2488.05 + 7495.28i) q^{76} +(4202.72 - 4202.72i) q^{77} +(-7.00746 - 1.65885i) q^{78} +5869.63i q^{79} +(418.984 - 2881.56i) q^{80} -6559.96 q^{81} +(-642.101 + 2712.42i) q^{82} +(-7560.06 - 7560.06i) q^{83} +(16.4274 + 49.4877i) q^{84} +(-3521.65 - 3521.65i) q^{85} +(4417.25 - 2726.21i) q^{86} +95.3236 q^{87} +(-7596.55 + 670.665i) q^{88} +6439.80i q^{89} +(-3135.97 + 1935.44i) q^{90} +(-971.844 + 971.844i) q^{91} +(-5789.98 - 2904.02i) q^{92} +(-69.5835 + 69.5835i) q^{93} +(-103.125 + 435.628i) q^{94} -5614.33i q^{95} +(24.6194 - 62.2096i) q^{96} -413.032 q^{97} +(338.567 + 80.1476i) q^{98} +(6824.48 + 6824.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20}+ \cdots + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

Introduction

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