LMFDB - Embedded newform 16.5.f.a.11.3

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			11.3
Root			$2.79265 - 0.448449i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.5.f.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.34420 - 3.24110i) q^{2} +(-4.63552 - 4.63552i) q^{3} +(-5.00945 + 15.1956i) q^{4} +(-29.2002 - 29.2002i) q^{5} +(-4.15759 + 25.8908i) q^{6} +59.6196 q^{7} +(60.9935 - 19.3854i) q^{8} -38.0239i q^{9} +(-26.1896 + 163.092i) q^{10} +(-18.0837 + 18.0837i) q^{11} +(93.6607 - 47.2180i) q^{12} +(50.7721 - 50.7721i) q^{13} +(-139.760 - 193.233i) q^{14} +270.716i q^{15} +(-205.811 - 152.243i) q^{16} -223.769 q^{17} +(-123.239 + 89.1358i) q^{18} +(14.7360 + 14.7360i) q^{19} +(589.990 - 297.436i) q^{20} +(-276.368 - 276.368i) q^{21} +(101.003 + 16.2192i) q^{22} +739.082 q^{23} +(-372.598 - 192.875i) q^{24} +1080.30i q^{25} +(-283.577 - 45.5374i) q^{26} +(-551.738 + 551.738i) q^{27} +(-298.661 + 905.954i) q^{28} +(938.904 - 938.904i) q^{29} +(877.416 - 634.612i) q^{30} -938.741i q^{31} +(-10.9723 + 1023.94i) q^{32} +167.655 q^{33} +(524.560 + 725.259i) q^{34} +(-1740.90 - 1740.90i) q^{35} +(577.796 + 190.479i) q^{36} +(263.837 + 263.837i) q^{37} +(13.2167 - 82.3049i) q^{38} -470.710 q^{39} +(-2347.08 - 1214.96i) q^{40} +248.841i q^{41} +(-247.874 + 1543.60i) q^{42} +(1035.00 - 1035.00i) q^{43} +(-184.203 - 365.381i) q^{44} +(-1110.31 + 1110.31i) q^{45} +(-1732.56 - 2395.44i) q^{46} +2018.46i q^{47} +(248.315 + 1659.76i) q^{48} +1153.50 q^{49} +(3501.35 - 2532.44i) q^{50} +(1037.29 + 1037.29i) q^{51} +(517.171 + 1025.85i) q^{52} +(833.240 + 833.240i) q^{53} +(3081.62 + 494.853i) q^{54} +1056.09 q^{55} +(3636.41 - 1155.75i) q^{56} -136.618i q^{57} +(-5244.06 - 842.101i) q^{58} +(-2223.17 + 2223.17i) q^{59} +(-4113.68 - 1356.14i) q^{60} +(-341.374 + 341.374i) q^{61} +(-3042.55 + 2200.60i) q^{62} -2266.97i q^{63} +(3344.42 - 2364.76i) q^{64} -2965.11 q^{65} +(-393.016 - 543.385i) q^{66} +(4845.43 + 4845.43i) q^{67} +(1120.96 - 3400.30i) q^{68} +(-3426.03 - 3426.03i) q^{69} +(-1561.41 + 9723.46i) q^{70} -4180.93 q^{71} +(-737.108 - 2319.21i) q^{72} -9071.36i q^{73} +(236.635 - 1473.61i) q^{74} +(5007.74 - 5007.74i) q^{75} +(-297.741 + 150.103i) q^{76} +(-1078.14 + 1078.14i) q^{77} +(1103.44 + 1525.62i) q^{78} +735.536i q^{79} +(1564.19 + 10455.2i) q^{80} +2035.24 q^{81} +(806.518 - 583.333i) q^{82} +(1441.90 + 1441.90i) q^{83} +(5584.02 - 2815.12i) q^{84} +(6534.10 + 6534.10i) q^{85} +(-5780.81 - 928.294i) q^{86} -8704.61 q^{87} +(-752.429 + 1453.55i) q^{88} -5071.77i q^{89} +(6201.39 + 995.831i) q^{90} +(3027.01 - 3027.01i) q^{91} +(-3702.39 + 11230.8i) q^{92} +(-4351.55 + 4351.55i) q^{93} +(6542.05 - 4731.69i) q^{94} -860.586i q^{95} +(4797.36 - 4695.64i) q^{96} -2523.85 q^{97} +(-2704.03 - 3738.60i) q^{98} +(687.613 + 687.613i) 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 $

$2$	−2.34420	−	3.24110i	−0.586050	−	0.810275i
$2$	−2.34420	−	3.24110i	−0.586050	−	0.810275i
$3$	−4.63552	−	4.63552i	−0.515058	−	0.515058i	0.401014	−	0.916072i	$-0.368658\pi$
$3$	−4.63552	−	4.63552i	−0.515058	−	0.515058i	−0.916072	+	0.401014i	$0.868658\pi$
$4$	−5.00945	+	15.1956i	−0.313090	+	0.949723i
$5$	−29.2002	−	29.2002i	−1.16801	−	1.16801i	−0.982676	−	0.185330i	$-0.940665\pi$
$5$	−29.2002	−	29.2002i	−1.16801	−	1.16801i	−0.185330	−	0.982676i	$-0.559335\pi$
$6$	−4.15759	+	25.8908i	−0.115489	+	0.719188i
$7$	59.6196			1.21673			0.608363	−	0.793659i	$-0.291826\pi$
$7$	59.6196			1.21673			0.608363	+	0.793659i	$0.291826\pi$
$8$	60.9935	−	19.3854i	0.953024	−	0.302896i
$9$		−	38.0239i		−	0.469431i
$10$	−26.1896	+	163.092i	−0.261896	+	1.63092i
$11$	−18.0837	+	18.0837i	−0.149452	+	0.149452i	−0.777873	−	0.628421i	$-0.783701\pi$
$11$	−18.0837	+	18.0837i	−0.149452	+	0.149452i	0.628421	+	0.777873i	$0.283701\pi$
$12$	93.6607	−	47.2180i	0.650422	−	0.327903i
$13$	50.7721	−	50.7721i	0.300427	−	0.300427i	−0.540754	−	0.841181i	$-0.681861\pi$
$13$	50.7721	−	50.7721i	0.300427	−	0.300427i	0.841181	+	0.540754i	$0.181861\pi$
$14$	−139.760	−	193.233i	−0.713063	−	0.985883i
$15$			270.716i			1.20318i
$16$	−205.811	−	152.243i	−0.803949	−	0.594699i
$17$	−223.769			−0.774289			−0.387144	−	0.922019i	$-0.626538\pi$
$17$	−223.769			−0.774289			−0.387144	+	0.922019i	$0.626538\pi$
$18$	−123.239	+	89.1358i	−0.380368	+	0.275110i
$19$	14.7360	+	14.7360i	0.0408199	+	0.0408199i	0.727222	−	0.686402i	$-0.240811\pi$
$19$	14.7360	+	14.7360i	0.0408199	+	0.0408199i	−0.686402	+	0.727222i	$0.740811\pi$
$20$	589.990	−	297.436i	1.47497	−	0.743591i
$21$	−276.368	−	276.368i	−0.626684	−	0.626684i
$22$	101.003	+	16.2192i	0.208684	+	0.0335108i
$23$	739.082			1.39713			0.698565	−	0.715547i	$-0.253822\pi$
$23$	739.082			1.39713			0.698565	+	0.715547i	$0.253822\pi$
$24$	−372.598	−	192.875i	−0.646871	−	0.334853i
$25$			1080.30i			1.72848i
$26$	−283.577	−	45.5374i	−0.419493	−	0.0673631i
$27$	−551.738	+	551.738i	−0.756842	+	0.756842i
$28$	−298.661	+	905.954i	−0.380946	+	1.15555i
$29$	938.904	−	938.904i	1.11641	−	1.11641i	0.124150	−	0.992263i	$-0.460380\pi$
$29$	938.904	−	938.904i	1.11641	−	1.11641i	0.992263	−	0.124150i	$-0.0396204\pi$
$30$	877.416	−	634.612i	0.974907	−	0.705124i
$31$		−	938.741i		−	0.976838i	−0.872609	−	0.488419i	$-0.837574\pi$
$31$		−	938.741i		−	0.976838i	0.872609	−	0.488419i	$-0.162426\pi$
$32$	−10.9723	+	1023.94i	−0.0107151	+	0.999943i
$33$	167.655			0.153953
$34$	524.560	+	725.259i	0.453772	+	0.627387i
$35$	−1740.90	−	1740.90i	−1.42114	−	1.42114i
$36$	577.796	+	190.479i	0.445830	+	0.146975i
$37$	263.837	+	263.837i	0.192722	+	0.192722i	0.796871	−	0.604149i	$-0.206487\pi$
$37$	263.837	+	263.837i	0.192722	+	0.192722i	−0.604149	+	0.796871i	$0.706487\pi$
$38$	13.2167	−	82.3049i	0.00915283	−	0.0569979i
$39$	−470.710			−0.309474
$40$	−2347.08	−	1214.96i	−1.46692	−	0.759353i
$41$			248.841i			0.148031i	0.997257	+	0.0740157i	$0.0235815\pi$
$41$			248.841i			0.148031i	−0.997257	+	0.0740157i	$0.976418\pi$
$42$	−247.874	+	1543.60i	−0.140518	+	0.875055i
$43$	1035.00	−	1035.00i	0.559765	−	0.559765i	−0.369476	−	0.929240i	$-0.620463\pi$
$43$	1035.00	−	1035.00i	0.559765	−	0.559765i	0.929240	+	0.369476i	$0.120463\pi$
$44$	−184.203	−	365.381i	−0.0951461	−	0.188730i
$45$	−1110.31	+	1110.31i	−0.548299	+	0.548299i
$46$	−1732.56	−	2395.44i	−0.818788	−	1.13206i
$47$			2018.46i			0.913746i	0.889532	+	0.456873i	$0.151031\pi$
$47$			2018.46i			0.913746i	−0.889532	+	0.456873i	$0.848969\pi$
$48$	248.315	+	1659.76i	0.107776	+	0.720384i
$49$	1153.50			0.480424
$50$	3501.35	−	2532.44i	1.40054	−	1.01297i
$51$	1037.29	+	1037.29i	0.398803	+	0.398803i
$52$	517.171	+	1025.85i	0.191261	+	0.379383i
$53$	833.240	+	833.240i	0.296632	+	0.296632i	0.839693	−	0.543061i	$-0.182735\pi$
$53$	833.240	+	833.240i	0.296632	+	0.296632i	−0.543061	+	0.839693i	$0.682735\pi$
$54$	3081.62	+	494.853i	1.05680	+	0.169703i
$55$	1056.09			0.349122
$56$	3636.41	−	1155.75i	1.15957	−	0.368542i
$57$		−	136.618i		−	0.0420492i
$58$	−5244.06	−	842.101i	−1.55888	−	0.250327i
$59$	−2223.17	+	2223.17i	−0.638660	+	0.638660i	−0.950225	−	0.311565i	$-0.899147\pi$
$59$	−2223.17	+	2223.17i	−0.638660	+	0.638660i	0.311565	+	0.950225i	$0.399147\pi$
$60$	−4113.68	−	1356.14i	−1.14269	−	0.376704i
$61$	−341.374	+	341.374i	−0.0917425	+	0.0917425i	−0.751489	−	0.659746i	$-0.770664\pi$
$61$	−341.374	+	341.374i	−0.0917425	+	0.0917425i	0.659746	+	0.751489i	$0.270664\pi$
$62$	−3042.55	+	2200.60i	−0.791507	+	0.572476i
$63$		−	2266.97i		−	0.571170i
$64$	3344.42	−	2364.76i	0.816508	−	0.577334i
$65$	−2965.11			−0.701800
$66$	−393.016	−	543.385i	−0.0902240	−	0.124744i
$67$	4845.43	+	4845.43i	1.07940	+	1.07940i	0.996563	+	0.0828379i	$0.0263984\pi$
$67$	4845.43	+	4845.43i	1.07940	+	1.07940i	0.0828379	+	0.996563i	$0.473602\pi$
$68$	1120.96	−	3400.30i	0.242422	−	0.735360i
$69$	−3426.03	−	3426.03i	−0.719602	−	0.719602i
$70$	−1561.41	+	9723.46i	−0.318656	+	1.98438i
$71$	−4180.93			−0.829386			−0.414693	−	0.909961i	$-0.636111\pi$
$71$	−4180.93			−0.829386			−0.414693	+	0.909961i	$0.636111\pi$
$72$	−737.108	−	2319.21i	−0.142189	−	0.447379i
$73$		−	9071.36i		−	1.70226i	−0.524953	−	0.851131i	$-0.675917\pi$
$73$		−	9071.36i		−	1.70226i	0.524953	−	0.851131i	$-0.324083\pi$
$74$	236.635	−	1473.61i	0.0432131	−	0.269103i
$75$	5007.74	−	5007.74i	0.890265	−	0.890265i
$76$	−297.741	+	150.103i	−0.0515479	+	0.0259873i
$77$	−1078.14	+	1078.14i	−0.181842	+	0.181842i
$78$	1103.44	+	1525.62i	0.181367	+	0.250759i
$79$			735.536i			0.117855i	0.998262	+	0.0589277i	$0.0187682\pi$
$79$			735.536i			0.117855i	−0.998262	+	0.0589277i	$0.981232\pi$
$80$	1564.19	+	10455.2i	0.244405	+	1.63363i
$81$	2035.24			0.310203
$82$	806.518	−	583.333i	0.119946	−	0.0867539i
$83$	1441.90	+	1441.90i	0.209305	+	0.209305i	0.803972	−	0.594667i	$-0.202716\pi$
$83$	1441.90	+	1441.90i	0.209305	+	0.209305i	−0.594667	+	0.803972i	$0.702716\pi$
$84$	5584.02	−	2815.12i	0.791385	−	0.398968i
$85$	6534.10	+	6534.10i	0.904374	+	0.904374i
$86$	−5780.81	−	928.294i	−0.781613	−	0.125513i
$87$	−8704.61			−1.15003
$88$	−752.429	+	1453.55i	−0.0971628	+	0.187700i
$89$		−	5071.77i		−	0.640294i	−0.947368	−	0.320147i	$-0.896268\pi$
$89$		−	5071.77i		−	0.640294i	0.947368	−	0.320147i	$-0.103732\pi$
$90$	6201.39	+	995.831i	0.765603	+	0.122942i
$91$	3027.01	−	3027.01i	0.365537	−	0.365537i
$92$	−3702.39	+	11230.8i	−0.437428	+	1.32689i
$93$	−4351.55	+	4351.55i	−0.503128	+	0.503128i
$94$	6542.05	−	4731.69i	0.740385	−	0.535501i
$95$		−	860.586i		−	0.0953558i
$96$	4797.36	−	4695.64i	0.520547	−	0.509509i
$97$	−2523.85			−0.268238			−0.134119	−	0.990965i	$-0.542820\pi$
$97$	−2523.85			−0.268238			−0.134119	+	0.990965i	$0.542820\pi$
$98$	−2704.03	−	3738.60i	−0.281552	−	0.389275i
$99$	687.613	+	687.613i	0.0701575	+	0.0701575i
$100$	−16415.7	−	5411.70i	−1.64157	−	0.541170i
$101$	425.990	+	425.990i	0.0417596	+	0.0417596i	0.727678	−	0.685919i	$-0.240599\pi$
$101$	425.990	+	425.990i	0.0417596	+	0.0417596i	−0.685919	+	0.727678i	$0.740599\pi$
$102$	930.341	−	5793.56i	0.0894215	−	0.556859i
$103$	13178.6			1.24221			0.621103	−	0.783729i	$-0.286685\pi$
$103$	13178.6			1.24221			0.621103	+	0.783729i	$0.286685\pi$
$104$	2112.53	−	4081.00i	0.195316	−	0.377312i
$105$			16140.0i			1.46394i
$106$	747.332	−	4653.90i	0.0665123	−	0.414195i
$107$	−10821.5	+	10821.5i	−0.945190	+	0.945190i	−0.998574	−	0.0533845i	$-0.982999\pi$
$107$	−10821.5	+	10821.5i	−0.945190	+	0.945190i	0.0533845	+	0.998574i	$0.482999\pi$
$108$	−5620.07	−	11147.9i	−0.481830	−	0.955750i
$109$	−1428.57	+	1428.57i	−0.120240	+	0.120240i	−0.764666	−	0.644426i	$-0.777096\pi$
$109$	−1428.57	+	1428.57i	−0.120240	+	0.120240i	0.644426	+	0.764666i	$0.277096\pi$
$110$	−2475.69	−	3422.90i	−0.204603	−	0.282885i
$111$		−	2446.04i		−	0.198526i
$112$	−12270.4	−	9076.66i	−0.978186	−	0.723586i
$113$	20121.5			1.57581			0.787904	−	0.615798i	$-0.211166\pi$
$113$	20121.5			1.57581			0.787904	+	0.615798i	$0.211166\pi$
$114$	−442.792	+	320.260i	−0.0340714	+	0.0246429i
$115$	−21581.3	−	21581.3i	−1.63186	−	1.63186i
$116$	9563.79	+	18970.6i	0.710745	+	1.40982i
$117$	−1930.56	−	1930.56i	−0.141030	−	0.141030i
$118$	12417.1	+	1993.96i	0.891776	+	0.143203i
$119$	−13341.0			−0.942098
$120$	5247.92	+	16511.9i	0.364439	+	1.14666i
$121$			13987.0i			0.955328i
$122$	1906.68	+	306.178i	0.128102	+	0.0205709i
$123$	1153.51	−	1153.51i	0.0762447	−	0.0762447i
$124$	14264.7	+	4702.57i	0.927725	+	0.305839i
$125$	13294.8	−	13294.8i	0.850865	−	0.850865i
$126$	−7347.48	+	5314.24i	−0.462804	+	0.334734i
$127$			2630.54i			0.163094i	0.996669	+	0.0815470i	$0.0259861\pi$
$127$			2630.54i			0.163094i	−0.996669	+	0.0815470i	$0.974014\pi$
$128$	−15504.4	−	5296.11i	−0.946314	−	0.323249i
$129$	−9595.57			−0.576622
$130$	6950.80	+	9610.20i	0.411290	+	0.568651i
$131$	12437.0	+	12437.0i	0.724722	+	0.724722i	0.969563	−	0.244841i	$-0.0787357\pi$
$131$	12437.0	+	12437.0i	0.724722	+	0.724722i	−0.244841	+	0.969563i	$0.578736\pi$
$132$	−839.857	+	2547.61i	−0.0482011	+	0.146213i
$133$	878.554	+	878.554i	0.0496667	+	0.0496667i
$134$	4345.86	−	27063.2i	0.242028	−	1.50719i
$135$	32221.6			1.76799
$136$	−13648.5	+	4337.85i	−0.737915	+	0.234529i
$137$		−	15392.0i		−	0.820078i	−0.912068	−	0.410039i	$-0.865515\pi$
$137$		−	15392.0i		−	0.820078i	0.912068	−	0.410039i	$-0.134485\pi$
$138$	−3072.80	+	19135.4i	−0.161353	+	1.00480i
$139$	12151.3	−	12151.3i	0.628915	−	0.628915i	−0.318880	−	0.947795i	$-0.603307\pi$
$139$	12151.3	−	12151.3i	0.628915	−	0.628915i	0.947795	+	0.318880i	$0.103307\pi$
$140$	35175.0	−	17733.0i	1.79464	−	0.904747i
$141$	9356.63	−	9356.63i	0.470632	−	0.470632i
$142$	9800.95	+	13550.8i	0.486062	+	0.672030i
$143$			1836.29i			0.0897987i
$144$	−5788.87	+	7825.74i	−0.279170	+	0.377399i
$145$	−54832.3			−2.60796
$146$	−29401.2	+	21265.1i	−1.37930	+	0.997611i
$147$	−5347.06	−	5347.06i	−0.247446	−	0.247446i
$148$	−5330.83	+	2687.48i	−0.243373	+	0.122693i
$149$	−20803.7	−	20803.7i	−0.937062	−	0.937062i	0.0610710	−	0.998133i	$-0.480548\pi$
$149$	−20803.7	−	20803.7i	−0.937062	−	0.937062i	−0.998133	+	0.0610710i	$0.980548\pi$
$150$	−27969.7	−	4491.44i	−1.24310	−	0.199619i
$151$	−7756.67			−0.340190			−0.170095	−	0.985428i	$-0.554407\pi$
$151$	−7756.67			−0.340190			−0.170095	+	0.985428i	$0.554407\pi$
$152$	1184.46	+	613.137i	0.0512665	+	0.0265381i
$153$			8508.60i			0.363475i
$154$	6021.75	+	966.985i	0.253911	+	0.0407735i
$155$	−27411.4	+	27411.4i	−1.14095	+	1.14095i
$156$	2358.00	−	7152.71i	0.0968934	−	0.293915i
$157$	7040.20	−	7040.20i	0.285618	−	0.285618i	−0.549727	−	0.835345i	$-0.685268\pi$
$157$	7040.20	−	7040.20i	0.285618	−	0.285618i	0.835345	+	0.549727i	$0.185268\pi$
$158$	2383.95	−	1724.24i	0.0954953	−	0.0690692i
$159$		−	7725.00i		−	0.305565i
$160$	30219.6	−	29578.8i	1.18045	−	1.15542i
$161$	44063.8			1.69993
$162$	−4771.01	−	6596.41i	−0.181794	−	0.251349i
$163$	7273.43	+	7273.43i	0.273756	+	0.273756i	0.830610	−	0.556854i	$-0.187992\pi$
$163$	7273.43	+	7273.43i	0.273756	+	0.273756i	−0.556854	+	0.830610i	$0.687992\pi$
$164$	−3781.28	−	1246.56i	−0.140589	−	0.0463472i
$165$	−4895.54	−	4895.54i	−0.179818	−	0.179818i
$166$	1293.24	−	8053.46i	0.0469313	−	0.292258i
$167$	30069.6			1.07819			0.539095	−	0.842245i	$-0.318766\pi$
$167$	30069.6			1.07819			0.539095	+	0.842245i	$0.318766\pi$
$168$	−22214.1	−	11499.2i	−0.787065	−	0.407425i
$169$			23405.4i			0.819488i
$170$	5860.43	−	36494.9i	0.202783	−	1.26280i
$171$	560.320	−	560.320i	0.0191621	−	0.0191621i
$172$	10542.7	+	20912.3i	0.356365	+	0.706878i
$173$	−8329.72	+	8329.72i	−0.278316	+	0.278316i	−0.832436	−	0.554121i	$-0.813055\pi$
$173$	−8329.72	+	8329.72i	−0.278316	+	0.278316i	0.554121	+	0.832436i	$0.313055\pi$
$174$	20405.3	+	28212.5i	0.673978	+	0.931844i
$175$			64406.9i			2.10308i
$176$	6474.93	−	968.707i	0.209031	−	0.0312728i
$177$	20611.1			0.657893
$178$	−16438.1	+	11889.2i	−0.518814	+	0.375244i
$179$	−7537.56	−	7537.56i	−0.235247	−	0.235247i	0.579632	−	0.814879i	$-0.303197\pi$
$179$	−7537.56	−	7537.56i	−0.235247	−	0.235247i	−0.814879	+	0.579632i	$0.803197\pi$
$180$	−11309.7	−	22433.7i	−0.349065	−	0.692399i
$181$	3802.64	+	3802.64i	0.116072	+	0.116072i	0.762757	−	0.646685i	$-0.223845\pi$
$181$	3802.64	+	3802.64i	0.116072	+	0.116072i	−0.646685	+	0.762757i	$0.723845\pi$
$182$	−16906.8	−	2714.92i	−0.510409	−	0.0819624i
$183$	3164.89			0.0945054
$184$	45079.2	−	14327.4i	1.33150	−	0.423185i
$185$		−	15408.2i		−	0.450202i
$186$	24304.7	+	3902.90i	0.702530	+	0.112814i
$187$	4046.58	−	4046.58i	0.115719	−	0.115719i
$188$	−30671.7	−	10111.4i	−0.867806	−	0.286085i
$189$	−32894.4	+	32894.4i	−0.920869	+	0.920869i
$190$	−2789.25	+	2017.39i	−0.0772644	+	0.0558833i
$191$		−	52248.1i		−	1.43220i	−0.697997	−	0.716100i	$-0.745925\pi$
$191$		−	52248.1i		−	1.43220i	0.697997	−	0.716100i	$-0.254075\pi$
$192$	−26465.0	−	4541.21i	−0.717909	−	0.123188i
$193$	−24380.0			−0.654514			−0.327257	−	0.944935i	$-0.606124\pi$
$193$	−24380.0			−0.654514			−0.327257	+	0.944935i	$0.606124\pi$
$194$	5916.41	+	8180.04i	0.157201	+	0.217346i
$195$	13744.8	+	13744.8i	0.361468	+	0.361468i
$196$	−5778.38	+	17528.0i	−0.150416	+	0.456269i
$197$	31537.9	+	31537.9i	0.812644	+	0.812644i	0.985030	−	0.172386i	$-0.0551476\pi$
$197$	31537.9	+	31537.9i	0.812644	+	0.812644i	−0.172386	+	0.985030i	$0.555148\pi$
$198$	616.720	−	3840.53i	0.0157310	−	0.0979626i
$199$	−71129.4			−1.79615			−0.898076	−	0.439841i	$-0.855035\pi$
$199$	−71129.4			−1.79615			−0.898076	+	0.439841i	$0.855035\pi$
$200$	20942.0	+	65891.2i	0.523549	+	1.64728i
$201$		−	44922.2i		−	1.11191i
$202$	382.069	−	2379.28i	0.00936353	−	0.0583099i
$203$	55977.1	−	55977.1i	1.35837	−	1.35837i
$204$	−20958.4	+	10565.9i	−0.503614	+	0.253891i
$205$	7266.19	−	7266.19i	0.172902	−	0.172902i
$206$	−30893.2	−	42713.0i	−0.727995	−	1.00653i
$207$		−	28102.8i		−	0.655857i
$208$	−18179.1	+	2719.76i	−0.420191	+	0.0628643i
$209$	−532.962			−0.0122012
$210$	52311.2	−	37835.3i	1.18620	−	0.857943i
$211$	−13393.4	−	13393.4i	−0.300833	−	0.300833i	0.540507	−	0.841340i	$-0.318233\pi$
$211$	−13393.4	−	13393.4i	−0.300833	−	0.300833i	−0.841340	+	0.540507i	$0.818233\pi$
$212$	−16835.6	+	8487.49i	−0.374591	+	0.188846i
$213$	19380.8	+	19380.8i	0.427181	+	0.427181i
$214$	60441.2	+	9705.77i	1.31979	+	0.211935i
$215$	−60444.6			−1.30762
$216$	−22956.8	+	44348.0i	−0.492044	+	0.950532i
$217$		−	55967.4i		−	1.18854i
$218$	7978.99	+	1281.28i	0.167894	+	0.0269607i
$219$	−42050.4	+	42050.4i	−0.876763	+	0.876763i
$220$	−5290.44	+	16047.9i	−0.109307	+	0.331569i
$221$	−11361.2	+	11361.2i	−0.232617	+	0.232617i
$222$	−7927.86	+	5734.01i	−0.160861	+	0.116346i
$223$		−	54266.9i		−	1.09125i	−0.838029	−	0.545626i	$-0.816292\pi$
$223$		−	54266.9i		−	1.09125i	0.838029	−	0.545626i	$-0.183708\pi$
$224$	−654.161	+	61047.0i	−0.0130373	+	1.21666i
$225$	41077.2			0.811401
$226$	−47168.8	−	65215.7i	−0.923502	−	1.27684i
$227$	14529.0	+	14529.0i	0.281957	+	0.281957i	0.833889	−	0.551932i	$-0.186109\pi$
$227$	14529.0	+	14529.0i	0.281957	+	0.281957i	−0.551932	+	0.833889i	$0.686109\pi$
$228$	2075.99	+	684.380i	0.0399351	+	0.0131652i
$229$	21618.1	+	21618.1i	0.412237	+	0.412237i	0.882517	−	0.470280i	$-0.155847\pi$
$229$	21618.1	+	21618.1i	0.412237	+	0.412237i	−0.470280	+	0.882517i	$0.655847\pi$
$230$	−19356.2	+	120538.i	−0.365902	+	2.27860i
$231$	9995.50			0.187318
$232$	39066.0	−	75468.0i	0.725811	−	1.40213i
$233$			92103.6i			1.69654i	0.529562	+	0.848271i	$0.322356\pi$
$233$			92103.6i			1.69654i	−0.529562	+	0.848271i	$0.677644\pi$
$234$	−1731.51	+	10782.7i	−0.0316223	+	0.196923i
$235$	58939.5	−	58939.5i	1.06726	−	1.06726i
$236$	−22645.5	−	44919.3i	−0.406592	−	0.806508i
$237$	3409.59	−	3409.59i	0.0607024	−	0.0607024i
$238$	31274.1	+	43239.6i	0.552116	+	0.763358i
$239$			70411.0i			1.23266i	0.787487	+	0.616332i	$0.211382\pi$
$239$			70411.0i			1.23266i	−0.787487	+	0.616332i	$0.788618\pi$
$240$	41214.5	−	55716.2i	0.715530	−	0.967296i
$241$	22402.6			0.385714			0.192857	−	0.981227i	$-0.438225\pi$
$241$	22402.6			0.385714			0.192857	+	0.981227i	$0.438225\pi$
$242$	45333.1	−	32788.2i	0.774078	−	0.559870i
$243$	35256.4	+	35256.4i	0.597070	+	0.597070i
$244$	−3477.28	−	6897.47i	−0.0584063	−	0.115854i
$245$	−33682.3	−	33682.3i	−0.561138	−	0.561138i
$246$	−6442.68	−	1034.58i	−0.106462	−	0.0170959i
$247$	1496.35			0.0245268
$248$	−18197.8	−	57257.1i	−0.295880	−	0.930949i
$249$		−	13367.9i		−	0.215608i
$250$	−74255.3	−	11924.1i	−1.18808	−	0.190785i
$251$	−72407.6	+	72407.6i	−1.14931	+	1.14931i	−0.162621	+	0.986689i	$0.551995\pi$
$251$	−72407.6	+	72407.6i	−1.14931	+	1.14931i	−0.986689	+	0.162621i	$0.948005\pi$
$252$	34447.9	+	11356.3i	0.542453	+	0.178828i
$253$	−13365.3	+	13365.3i	−0.208804	+	0.208804i
$254$	8525.85	−	6166.52i	0.132151	−	0.0955813i
$255$		−	60577.9i		−	0.931609i
$256$	19180.2	+	62666.5i	0.292667	+	0.956214i
$257$	−56466.3			−0.854916			−0.427458	−	0.904035i	$-0.640591\pi$
$257$	−56466.3			−0.854916			−0.427458	+	0.904035i	$0.640591\pi$
$258$	22493.9	+	31100.2i	0.337929	+	0.467222i
$259$	15729.9	+	15729.9i	0.234490	+	0.234490i
$260$	14853.5	−	45056.5i	0.219727	−	0.666516i
$261$	−35700.8	−	35700.8i	−0.524080	−	0.524080i
$262$	11154.7	−	69464.1i	0.162501	−	1.01195i
$263$	76515.5			1.10621			0.553105	−	0.833111i	$-0.313443\pi$
$263$	76515.5			1.10621			0.553105	+	0.833111i	$0.313443\pi$
$264$	10225.8	−	3250.04i	0.146721	−	0.0466317i
$265$		−	48661.5i		−	0.692937i
$266$	787.974	−	4906.99i	0.0111365	−	0.0693508i
$267$	−23510.3	+	23510.3i	−0.329788	+	0.329788i
$268$	−97902.0	+	49356.2i	−1.36308	+	0.687182i
$269$	1928.97	−	1928.97i	0.0266576	−	0.0266576i	−0.693652	−	0.720310i	$-0.744000\pi$
$269$	1928.97	−	1928.97i	0.0266576	−	0.0266576i	0.720310	+	0.693652i	$0.244000\pi$
$270$	−75534.0	−	104434.i	−1.03613	−	1.43256i
$271$			128685.i			1.75222i	0.482109	+	0.876111i	$0.339871\pi$
$271$			128685.i			1.75222i	−0.482109	+	0.876111i	$0.660129\pi$
$272$	46054.2	+	34067.3i	0.622488	+	0.460468i
$273$	−28063.5			−0.376545
$274$	−49887.1	+	36082.0i	−0.664488	+	0.480607i
$275$	−19535.8	−	19535.8i	−0.258324	−	0.258324i
$276$	69222.9	−	34897.9i	0.908724	−	0.458122i
$277$	56674.5	+	56674.5i	0.738632	+	0.738632i	0.972313	−	0.233681i	$-0.0750772\pi$
$277$	56674.5	+	56674.5i	0.738632	+	0.738632i	−0.233681	+	0.972313i	$0.575077\pi$
$278$	−67868.5	−	10898.5i	−0.878170	−	0.141018i
$279$	−35694.6			−0.458558
$280$	−139932.	−	72435.7i	−1.78484	−	0.923925i
$281$		−	10599.7i		−	0.134240i	−0.997745	−	0.0671200i	$-0.978619\pi$
$281$		−	10599.7i		−	0.134240i	0.997745	−	0.0671200i	$-0.0213810\pi$
$282$	−52259.6	−	8391.95i	−0.657155	−	0.105527i
$283$	63293.6	−	63293.6i	0.790291	−	0.790291i	−0.191251	−	0.981541i	$-0.561254\pi$
$283$	63293.6	−	63293.6i	0.790291	−	0.790291i	0.981541	+	0.191251i	$0.0612543\pi$
$284$	20944.2	−	63531.7i	0.259673	−	0.787687i
$285$	−3989.26	+	3989.26i	−0.0491137	+	0.0491137i
$286$	5951.61	−	4304.64i	0.0727617	−	0.0526266i
$287$			14835.8i			0.180114i
$288$	38934.3	+	417.208i	0.469405	+	0.00503000i
$289$	−33448.2			−0.400477
$290$	128538.	+	177717.i	1.52839	+	2.11316i
$291$	11699.3	+	11699.3i	0.138158	+	0.138158i
$292$	137844.	+	45442.5i	1.61668	+	0.532962i
$293$	−89072.9	−	89072.9i	−1.03755	−	1.03755i	−0.999267	−	0.0382867i	$-0.987810\pi$
$293$	−89072.9	−	89072.9i	−1.03755	−	1.03755i	−0.0382867	−	0.999267i	$-0.512190\pi$
$294$	−4795.77	+	29864.9i	−0.0554835	+	0.345515i
$295$	129834.			1.49192
$296$	21206.9	+	10977.8i	0.242044	+	0.125294i
$297$		−	19954.9i		−	0.226223i
$298$	−18658.8	+	116195.i	−0.210113	+	1.30844i
$299$	37524.7	−	37524.7i	0.419735	−	0.419735i
$300$	51009.5	+	101182.i	0.566772	+	1.12424i
$301$	61706.6	−	61706.6i	0.681080	−	0.681080i
$302$	18183.2	+	25140.1i	0.199368	+	0.275647i
$303$		−	3949.36i		−	0.0430172i
$304$	−789.377	−	5276.27i	−0.00854157	−	0.0570927i
$305$	19936.3			0.214312
$306$	27577.2	−	19945.9i	0.294515	−	0.213015i
$307$	−124227.	−	124227.i	−1.31807	−	1.31807i	−0.915302	−	0.402769i	$-0.868048\pi$
$307$	−124227.	−	124227.i	−1.31807	−	1.31807i	−0.402769	−	0.915302i	$-0.631952\pi$
$308$	−10982.1	−	21783.9i	−0.115767	−	0.229633i
$309$	−61089.5	−	61089.5i	−0.639808	−	0.639808i
$310$	153101.	+	24585.2i	1.59314	+	0.255830i
$311$	15733.9			0.162673			0.0813364	−	0.996687i	$-0.474081\pi$
$311$	15733.9			0.162673			0.0813364	+	0.996687i	$0.474081\pi$
$312$	−28710.3	+	9124.88i	−0.294936	+	0.0937385i
$313$			104554.i			1.06721i	0.845733	+	0.533606i	$0.179163\pi$
$313$			104554.i			1.06721i	−0.845733	+	0.533606i	$0.820837\pi$
$314$	−39321.6	−	6314.34i	−0.398816	−	0.0640426i
$315$	−66196.0	+	66196.0i	−0.667130	+	0.667130i
$316$	−11176.9	−	3684.63i	−0.111930	−	0.0368994i
$317$	45847.9	−	45847.9i	0.456248	−	0.456248i	−0.441174	−	0.897422i	$-0.645438\pi$
$317$	45847.9	−	45847.9i	0.456248	−	0.456248i	0.897422	+	0.441174i	$0.145438\pi$
$318$	−25037.5	+	18108.9i	−0.247592	+	0.179077i
$319$			33957.7i			0.333700i
$320$	−166709.	−	28606.1i	−1.62802	−	0.279356i
$321$	100326.			0.973654
$322$	−103294.	−	142815.i	−0.996241	−	1.37741i
$323$	−3297.46	−	3297.46i	−0.0316064	−	0.0316064i
$324$	−10195.4	+	30926.6i	−0.0971215	+	0.294607i
$325$	54849.0	+	54849.0i	0.519281	+	0.519281i
$326$	6523.53	−	40624.3i	0.0613829	−	0.382253i
$327$	13244.3			0.123861
$328$	4823.87	+	15177.7i	0.0448382	+	0.141077i
$329$			120340.i			1.11178i
$330$	−4390.80	+	27343.1i	−0.0403196	+	0.251084i
$331$	−137545.	+	137545.i	−1.25542	+	1.25542i	−0.302159	+	0.953258i	$0.597707\pi$
$331$	−137545.	+	137545.i	−1.25542	+	1.25542i	−0.953258	+	0.302159i	$0.902293\pi$
$332$	−29133.7	+	14687.4i	−0.264313	+	0.133250i
$333$	10032.1	−	10032.1i	0.0904700	−	0.0904700i
$334$	−70489.2	−	97458.6i	−0.631873	−	0.873630i
$335$		−	282975.i		−	2.52149i
$336$	14804.5	+	98954.5i	0.131134	+	0.876510i
$337$	−40849.6			−0.359690			−0.179845	−	0.983695i	$-0.557560\pi$
$337$	−40849.6			−0.359690			−0.179845	+	0.983695i	$0.557560\pi$
$338$	75859.2	−	54866.9i	0.664010	−	0.480261i
$339$	−93273.5	−	93273.5i	−0.811632	−	0.811632i
$340$	−132022.	+	66557.2i	−1.14206	+	0.575754i
$341$	16975.9	+	16975.9i	0.145990	+	0.145990i
$342$	−3129.56	−	502.551i	−0.0267566	−	0.00429663i
$343$	−74375.6			−0.632182
$344$	43064.6	−	83192.5i	0.363918	−	0.703019i
$345$			200081.i			1.68100i
$346$	46524.0	+	7470.91i	0.388619	+	0.0624053i
$347$	21361.1	−	21361.1i	0.177404	−	0.177404i	−0.612819	−	0.790223i	$-0.709965\pi$
$347$	21361.1	−	21361.1i	0.177404	−	0.177404i	0.790223	+	0.612819i	$0.209965\pi$
$348$	43605.3	−	132272.i	0.360065	−	1.09221i
$349$	139275.	−	139275.i	1.14347	−	1.14347i	0.155654	−	0.987812i	$-0.450252\pi$
$349$	139275.	−	139275.i	1.14347	−	1.14347i	0.987812	−	0.155654i	$-0.0497484\pi$
$350$	208749.	−	150983.i	1.70408	−	1.23251i
$351$			56025.8i			0.454751i
$352$	−18318.2	−	18715.1i	−0.147842	−	0.151045i
$353$	−100461.			−0.806209			−0.403105	−	0.915154i	$-0.632069\pi$
$353$	−100461.			−0.806209			−0.403105	+	0.915154i	$0.632069\pi$
$354$	−48316.6	−	66802.7i	−0.385558	−	0.533074i
$355$	122084.	+	122084.i	0.968728	+	0.968728i
$356$	77068.4	+	25406.7i	0.608102	+	0.200470i
$357$	61842.6	+	61842.6i	0.485234	+	0.485234i
$358$	−6760.42	+	42099.5i	−0.0527482	+	0.328482i
$359$	96352.7			0.747609			0.373805	−	0.927507i	$-0.378053\pi$
$359$	96352.7			0.747609			0.373805	+	0.927507i	$0.378053\pi$
$360$	−46197.7	+	89245.1i	−0.356464	+	0.688619i
$361$		−	129887.i		−	0.996667i
$362$	3410.58	−	21238.9i	0.0260262	−	0.162074i
$363$	64836.8	−	64836.8i	0.492049	−	0.492049i
$364$	30833.5	+	61160.9i	0.232713	+	0.461605i
$365$	−264885.	+	264885.i	−1.98825	+	1.98825i
$366$	−7419.14	−	10257.7i	−0.0553849	−	0.0765753i
$367$			190661.i			1.41557i	0.706429	+	0.707784i	$0.250305\pi$
$367$			190661.i			1.41557i	−0.706429	+	0.707784i	$0.749695\pi$
$368$	−152111.	−	112520.i	−1.12322	−	0.830871i
$369$	9461.91			0.0694906
$370$	−49939.4	+	36119.8i	−0.364787	+	0.263841i
$371$	49677.5	+	49677.5i	0.360920	+	0.360920i
$372$	−44325.4	−	87923.2i	−0.320308	−	0.635356i
$373$	51771.9	+	51771.9i	0.372114	+	0.372114i	0.868247	−	0.496133i	$-0.165247\pi$
$373$	51771.9	+	51771.9i	0.372114	+	0.372114i	−0.496133	+	0.868247i	$0.665247\pi$
$374$	−22601.3	−	3629.37i	−0.161581	−	0.0259471i
$375$	−123256.			−0.876489
$376$	39128.7	+	123113.i	0.276770	+	0.870821i
$377$		−	95340.2i		−	0.670801i
$378$	183725.	+	29502.9i	1.28583	+	0.206482i
$379$	121232.	−	121232.i	0.843990	−	0.843990i	−0.145385	−	0.989375i	$-0.546442\pi$
$379$	121232.	−	121232.i	0.843990	−	0.843990i	0.989375	+	0.145385i	$0.0464420\pi$
$380$	13077.1	+	4311.06i	0.0905616	+	0.0298550i
$381$	12193.9	−	12193.9i	0.0840028	−	0.0840028i
$382$	−169341.	+	122480.i	−1.16048	+	0.839341i
$383$		−	8262.20i		−	0.0563246i	−0.999603	−	0.0281623i	$-0.991034\pi$
$383$		−	8262.20i		−	0.0563246i	0.999603	−	0.0281623i	$-0.00896552\pi$
$384$	47320.8	+	96421.2i	0.320914	+	0.653898i
$385$	62963.9			0.424786
$386$	57151.6	+	79018.0i	0.383578	+	0.530336i
$387$	−39355.0	−	39355.0i	−0.262771	−	0.262771i
$388$	12643.1	−	38351.3i	0.0839826	−	0.254752i
$389$	43964.9	+	43964.9i	0.290541	+	0.290541i	0.837294	−	0.546753i	$-0.184136\pi$
$389$	43964.9	+	43964.9i	0.290541	+	0.290541i	−0.546753	+	0.837294i	$0.684136\pi$
$390$	12327.7	−	76768.9i	0.0810499	−	0.504726i
$391$	−165384.			−1.08178
$392$	70355.8	−	22360.9i	0.457855	−	0.145518i
$393$		−	115303.i		−	0.746547i
$394$	28286.3	−	176149.i	0.182215	−	1.13471i
$395$	21477.8	−	21477.8i	0.137656	−	0.137656i
$396$	−13893.2	+	7004.12i	−0.0885958	+	0.0446645i
$397$	72864.3	−	72864.3i	0.462311	−	0.462311i	−0.437101	−	0.899412i	$-0.643995\pi$
$397$	72864.3	−	72864.3i	0.462311	−	0.462311i	0.899412	+	0.437101i	$0.143995\pi$
$398$	166742.	+	230537.i	1.05263	+	1.45538i
$399$		−	8145.10i		−	0.0511624i
$400$	164468.	−	222337.i	1.02792	−	1.38961i
$401$	237249.			1.47542			0.737711	−	0.675116i	$-0.235907\pi$
$401$	237249.			1.47542			0.737711	+	0.675116i	$0.235907\pi$
$402$	−145597.	+	105307.i	−0.900950	+	0.651633i
$403$	−47661.9	−	47661.9i	−0.293468	−	0.293468i
$404$	−8607.13	+	4339.18i	−0.0527346	+	0.0265855i
$405$	−59429.3	−	59429.3i	−0.362319	−	0.362319i
$406$	−312649.	−	50205.8i	−1.89673	−	0.304580i
$407$	−9542.29			−0.0576055
$408$	83376.0	+	43159.6i	0.500865	+	0.259273i
$409$		−	150042.i		−	0.896945i	−0.893797	−	0.448473i	$-0.851968\pi$
$409$		−	150042.i		−	0.896945i	0.893797	−	0.448473i	$-0.148032\pi$
$410$	−40583.9	−	6517.04i	−0.241427	−	0.0387688i
$411$	−71350.1	+	71350.1i	−0.422387	+	0.422387i
$412$	−66017.3	+	200256.i	−0.388923	+	1.17975i
$413$	−132545.	+	132545.i	−0.777074	+	0.777074i
$414$	−91084.0	+	65878.6i	−0.531424	+	0.384365i
$415$		−	84207.5i		−	0.488939i
$416$	51430.6	+	52544.7i	0.297190	+	0.303629i
$417$	−112655.			−0.647855
$418$	1249.37	+	1727.38i	0.00715053	+	0.00988635i
$419$	71760.1	+	71760.1i	0.408747	+	0.408747i	0.881302	−	0.472554i	$-0.156668\pi$
$419$	71760.1	+	71760.1i	0.408747	+	0.408747i	−0.472554	+	0.881302i	$0.656668\pi$
$420$	−245256.	−	80852.3i	−1.39034	−	0.458346i
$421$	−209821.	−	209821.i	−1.18382	−	1.18382i	−0.978747	−	0.205070i	$-0.934258\pi$
$421$	−209821.	−	209821.i	−1.18382	−	1.18382i	−0.205070	−	0.978747i	$-0.565742\pi$
$422$	−12012.5	+	74806.1i	−0.0674542	+	0.420061i
$423$	76750.0			0.428941
$424$	66974.9	+	34669.6i	0.372546	+	0.192849i
$425$		−	241738.i		−	1.33834i
$426$	17382.6	−	108248.i	0.0957846	−	0.596484i
$427$	−20352.6	+	20352.6i	−0.111626	+	0.111626i
$428$	−110229.	−	218648.i	−0.601739	−	1.19360i
$429$	8512.18	−	8512.18i	0.0462515	−	0.0462515i
$430$	141694.	+	195907.i	0.766329	+	1.05953i
$431$		−	123853.i		−	0.666731i	−0.942798	−	0.333366i	$-0.891816\pi$
$431$		−	123853.i		−	0.666731i	0.942798	−	0.333366i	$-0.108184\pi$
$432$	197552.	−	29555.5i	1.05855	−	0.158369i
$433$	−265114.			−1.41402			−0.707012	−	0.707202i	$-0.749957\pi$
$433$	−265114.			−1.41402			−0.707012	+	0.707202i	$0.749957\pi$
$434$	−181396.	+	131199.i	−0.963047	+	0.696547i
$435$	254176.	+	254176.i	1.34325	+	1.34325i
$436$	−14551.6	−	28864.3i	−0.0765486	−	0.151841i
$437$	10891.1	+	10891.1i	0.0570307	+	0.0570307i
$438$	234864.	+	37715.0i	1.22425	+	0.196592i
$439$	186089.			0.965590			0.482795	−	0.875734i	$-0.339622\pi$
$439$	186089.			0.965590			0.482795	+	0.875734i	$0.339622\pi$
$440$	64414.8	−	20472.7i	0.332721	−	0.105748i
$441$		−	43860.5i		−	0.225526i
$442$	63456.0	+	10189.9i	0.324809	+	0.0521585i
$443$	25618.8	−	25618.8i	0.130542	−	0.130542i	−0.638817	−	0.769359i	$-0.720576\pi$
$443$	25618.8	−	25618.8i	0.130542	−	0.130542i	0.769359	+	0.638817i	$0.220576\pi$
$444$	37169.0	+	12253.3i	0.188545	+	0.0621567i
$445$	−148096.	+	148096.i	−0.747867	+	0.747867i
$446$	−175884.	+	127212.i	−0.884214	+	0.639529i
$447$			192872.i			0.965282i
$448$	199393.	−	140986.i	0.993467	−	0.702458i
$449$	−2307.59			−0.0114463			−0.00572316	−	0.999984i	$-0.501822\pi$
$449$	−2307.59			−0.0114463			−0.00572316	+	0.999984i	$0.501822\pi$
$450$	−96293.2	−	133135.i	−0.475522	−	0.657458i
$451$	−4499.96	−	4499.96i	−0.0221236	−	0.0221236i
$452$	−100798.	+	305758.i	−0.493370	+	1.49658i
$453$	35956.2	+	35956.2i	0.175217	+	0.175217i
$454$	13031.0	−	81148.6i	0.0632217	−	0.393704i
$455$	−176778.			−0.853899
$456$	−2648.39	−	8332.80i	−0.0127365	−	0.0400739i
$457$			262378.i			1.25631i	0.778090	+	0.628153i	$0.216189\pi$
$457$			262378.i			1.25631i	−0.778090	+	0.628153i	$0.783811\pi$
$458$	19389.3	−	120744.i	0.0924338	−	0.575617i
$459$	123462.	−	123462.i	0.586014	−	0.586014i
$460$	436051.	−	219830.i	2.06073	−	1.03889i
$461$	136771.	−	136771.i	0.643564	−	0.643564i	−0.307866	−	0.951430i	$-0.599615\pi$
$461$	136771.	−	136771.i	0.643564	−	0.643564i	0.951430	+	0.307866i	$0.0996148\pi$
$462$	−23431.5	−	32396.4i	−0.109778	−	0.151779i
$463$			22250.8i			0.103797i	0.998652	+	0.0518983i	$0.0165272\pi$
$463$			22250.8i			0.103797i	−0.998652	+	0.0518983i	$0.983473\pi$
$464$	−336178.	+	50295.2i	−1.56147	+	0.233610i
$465$	254132.			1.17531
$466$	298517.	−	215909.i	1.37467	−	0.994259i
$467$	175541.	+	175541.i	0.804906	+	0.804906i	0.983858	−	0.178952i	$-0.0572708\pi$
$467$	175541.	+	175541.i	0.804906	+	0.804906i	−0.178952	+	0.983858i	$0.557271\pi$
$468$	39006.9	−	19664.9i	0.178094	−	0.0897842i
$469$	288883.	+	288883.i	1.31334	+	1.31334i
$470$	−329195.	−	52862.7i	−1.49024	−	0.239306i
$471$	−65269.9			−0.294219
$472$	−92502.2	+	178696.i	−0.415210	+	0.802105i
$473$			37433.4i			0.167316i
$474$	−19043.6	−	3058.06i	−0.0847602	−	0.0136110i
$475$	−15919.3	+	15919.3i	−0.0705563	+	0.0705563i
$476$	66831.3	−	202725.i	0.294962	−	0.894732i
$477$	31683.1	−	31683.1i	0.139249	−	0.139249i
$478$	228209.	−	165057.i	0.998796	−	0.722403i
$479$			117920.i			0.513945i	0.966419	+	0.256973i	$0.0827250\pi$
$479$			117920.i			0.513945i	−0.966419	+	0.256973i	$0.917275\pi$
$480$	−277197.	−	2970.36i	−1.20311	−	0.0128922i
$481$	26791.1			0.115798
$482$	−52516.3	−	72609.2i	−0.226048	−	0.312534i
$483$	−204258.	−	204258.i	−0.875559	−	0.875559i
$484$	−212540.	−	70066.9i	−0.907297	−	0.299104i
$485$	73696.7	+	73696.7i	0.313303	+	0.313303i
$486$	31621.4	−	196917.i	0.133878	−	0.833703i
$487$	−449942.			−1.89714			−0.948568	−	0.316574i	$-0.897467\pi$
$487$	−449942.			−1.89714			−0.948568	+	0.316574i	$0.897467\pi$
$488$	−14203.9	+	27439.2i	−0.0596443	+	0.115221i
$489$		−	67432.3i		−	0.282001i
$490$	−30209.6	+	188126.i	−0.125821	+	0.783531i
$491$	−122509.	+	122509.i	−0.508166	+	0.508166i	−0.913963	−	0.405797i	$-0.866994\pi$
$491$	−122509.	+	122509.i	−0.508166	+	0.508166i	0.405797	+	0.913963i	$0.366994\pi$
$492$	11749.8	+	23306.6i	0.0485399	+	0.0962829i
$493$	−210098.	+	210098.i	−0.864426	+	0.864426i
$494$	−3507.75	−	4849.83i	−0.0143739	−	0.0198734i
$495$		−	40156.8i		−	0.163889i
$496$	−142917.	+	193203.i	−0.580924	+	0.785327i
$497$	−249266.			−1.00914
$498$	−43326.8	+	31337.1i	−0.174702	+	0.126357i
$499$	−44886.9	−	44886.9i	−0.180268	−	0.180268i	0.611205	−	0.791473i	$-0.290685\pi$
$499$	−44886.9	−	44886.9i	−0.180268	−	0.180268i	−0.791473	+	0.611205i	$0.790685\pi$
$500$	135422.	+	268621.i	0.541689	+	1.07448i
$501$	−139388.	−	139388.i	−0.555330	−	0.555330i
$502$	404418.	+	64942.3i	1.60481	+	0.257704i
$503$	235778.			0.931896			0.465948	−	0.884812i	$-0.345713\pi$
$503$	235778.			0.931896			0.465948	+	0.884812i	$0.345713\pi$
$504$	−43946.1	−	138271.i	−0.173005	−	0.544338i
$505$		−	24877.9i		−	0.0975509i
$506$	74649.4	+	11987.3i	0.291558	+	0.0468190i
$507$	108496.	−	108496.i	0.422083	−	0.422083i
$508$	−39972.6	−	13177.6i	−0.154894	−	0.0510632i
$509$	227812.	−	227812.i	0.879308	−	0.879308i	−0.114155	−	0.993463i	$-0.536416\pi$
$509$	227812.	−	227812.i	0.879308	−	0.879308i	0.993463	+	0.114155i	$0.0364161\pi$
$510$	−196339.	+	142007.i	−0.754859	+	0.545970i
$511$		−	540831.i		−	2.07119i
$512$	158146.	−	209068.i	0.603279	−	0.797530i
$513$	−16260.8			−0.0617884
$514$	132368.	+	183013.i	0.501024	+	0.692717i
$515$	−384816.	−	384816.i	−1.45090	−	1.45090i
$516$	48068.5	−	145810.i	0.180535	−	0.547631i
$517$	−36501.3	−	36501.3i	−0.136561	−	0.136561i
$518$	14108.1	−	87856.0i	0.0525785	−	0.327425i
$519$	77225.1			0.286697
$520$	−180852.	+	57479.6i	−0.668832	+	0.212573i
$521$			539683.i			1.98822i	0.108395	+	0.994108i	$0.465429\pi$
$521$			539683.i			1.98822i	−0.108395	+	0.994108i	$0.534571\pi$
$522$	−32020.0	+	199400.i	−0.117512	+	0.731785i
$523$	−175071.	+	175071.i	−0.640044	+	0.640044i	−0.950566	−	0.310522i	$-0.899496\pi$
$523$	−175071.	+	175071.i	−0.640044	+	0.640044i	0.310522	+	0.950566i	$0.399496\pi$
$524$	−251289.	+	126684.i	−0.915189	+	0.461382i
$525$	298560.	−	298560.i	1.08321	−	1.08321i
$526$	−179368.	−	247994.i	−0.648295	−	0.896334i
$527$			210062.i			0.756354i
$528$	−34505.1	−	25524.2i	−0.123770	−	0.0915555i
$529$	266401.			0.951972
$530$	−157717.	+	114072.i	−0.561469	+	0.406096i
$531$	84533.9	+	84533.9i	0.299807	+	0.299807i
$532$	−17751.2	+	8949.06i	−0.0627198	+	0.0316194i
$533$	12634.2	+	12634.2i	0.0444726	+	0.0444726i
$534$	131312.	+	21086.3i	0.460491	+	0.0739466i
$535$	631977.			2.20797
$536$	389470.	+	201609.i	1.35564	+	0.701748i
$537$			69880.9i			0.242332i
$538$	−10773.9	−	1730.09i	−0.0372227	−	0.00597729i
$539$	−20859.5	+	20859.5i	−0.0718003	+	0.0718003i
$540$	−161413.	+	489626.i	−0.553541	+	1.67910i
$541$	−142203.	+	142203.i	−0.485863	+	0.485863i	−0.906998	−	0.421135i	$-0.861632\pi$
$541$	−142203.	+	142203.i	−0.485863	+	0.485863i	0.421135	+	0.906998i	$0.361632\pi$
$542$	417081.	−	301663.i	1.41978	−	1.02689i
$543$		−	35254.4i		−	0.119568i
$544$	2455.25	−	229127.i	0.00829657	−	0.774244i
$545$	83428.9			0.280882
$546$	65786.6	+	90956.7i	0.220674	+	0.305105i
$547$	−265412.	−	265412.i	−0.887045	−	0.887045i	0.107193	−	0.994238i	$-0.465814\pi$
$547$	−265412.	−	265412.i	−0.887045	−	0.887045i	−0.994238	+	0.107193i	$0.965814\pi$
$548$	233891.	+	77105.6i	0.778847	+	0.256758i
$549$	12980.4	+	12980.4i	0.0430668	+	0.0430668i
$550$	−17521.6	+	109113.i	−0.0579227	+	0.360705i
$551$	27671.3			0.0911438
$552$	−275380.	−	142551.i	−0.903763	−	0.467833i
$553$			43852.4i			0.143398i
$554$	50831.3	−	316544.i	0.165620	−	1.03137i
$555$	−71424.8	+	71424.8i	−0.231880	+	0.231880i
$556$	123774.	+	245517.i	0.400388	+	0.794203i
$557$	168105.	−	168105.i	0.541837	−	0.541837i	−0.382230	−	0.924067i	$-0.624844\pi$
$557$	168105.	−	168105.i	0.541837	−	0.541837i	0.924067	+	0.382230i	$0.124844\pi$
$558$	83675.4	+	115690.i	0.268738	+	0.371558i
$559$		−	105099.i		−	0.336336i
$560$	93256.6	+	623336.i	0.297374	+	1.98768i
$561$	−37516.0			−0.119204
$562$	−34354.8	+	24847.9i	−0.108771	+	0.0786714i
$563$	−181113.	−	181113.i	−0.571389	−	0.571389i	0.361127	−	0.932517i	$-0.382392\pi$
$563$	−181113.	−	181113.i	−0.571389	−	0.571389i	−0.932517	+	0.361127i	$0.882392\pi$
$564$	95307.8	+	189051.i	0.299620	+	0.594320i
$565$	−587551.	−	587551.i	−1.84055	−	1.84055i
$566$	−353514.	−	56767.9i	−1.10350	−	0.177203i
$567$	121340.			0.377432
$568$	−255010.	+	81048.9i	−0.790424	+	0.251218i
$569$		−	124083.i		−	0.383254i	−0.981468	−	0.191627i	$-0.938624\pi$
$569$		−	124083.i		−	0.383254i	0.981468	−	0.191627i	$-0.0613765\pi$
$570$	22281.2	+	3577.96i	0.0685787	+	0.0110125i
$571$	−92801.0	+	92801.0i	−0.284630	+	0.284630i	−0.834952	−	0.550322i	$-0.814505\pi$
$571$	−92801.0	+	92801.0i	−0.284630	+	0.284630i	0.550322	+	0.834952i	$0.314505\pi$
$572$	−27903.5	−	9198.82i	−0.0852840	−	0.0281151i
$573$	−242197.	+	242197.i	−0.737666	+	0.737666i
$574$	48084.3	−	34778.1i	0.145942	−	0.105556i
$575$			798429.i			2.41491i
$576$	−89917.6	−	127168.i	−0.271019	−	0.383294i
$577$	182478.			0.548098			0.274049	−	0.961716i	$-0.411637\pi$
$577$	182478.			0.548098			0.274049	+	0.961716i	$0.411637\pi$
$578$	78409.4	+	108409.i	0.234700	+	0.324496i
$579$	113014.	+	113014.i	0.337112	+	0.337112i
$580$	274679.	−	833208.i	0.816526	−	2.47684i
$581$	85965.6	+	85965.6i	0.254667	+	0.254667i
$582$	10493.1	−	65344.3i	0.0309784	−	0.192913i
$583$	−30136.1			−0.0886646
$584$	−175851.	−	553294.i	−0.515609	−	1.62230i
$585$			112745.i			0.329447i
$586$	−79889.4	+	497499.i	−0.232645	+	1.44876i
$587$	197015.	−	197015.i	0.571772	−	0.571772i	−0.360851	−	0.932623i	$-0.617514\pi$
$587$	197015.	−	197015.i	0.571772	−	0.571772i	0.932623	+	0.360851i	$0.117514\pi$
$588$	108037.	−	54465.8i	0.312478	−	0.157532i
$589$	13833.3	−	13833.3i	0.0398744	−	0.0398744i
$590$	−304357.	−	420805.i	−0.874338	−	1.20886i
$591$		−	292389.i		−	0.837116i
$592$	−14133.2	−	94467.8i	−0.0403272	−	0.269551i
$593$	−478257.			−1.36004			−0.680020	−	0.733194i	$-0.738029\pi$
$593$	−478257.			−1.36004			−0.680020	+	0.733194i	$0.738029\pi$
$594$	−64675.8	+	46778.3i	−0.183303	+	0.132578i
$595$	389561.	+	389561.i	1.10038	+	1.10038i
$596$	420340.	−	211909.i	1.18334	−	0.596565i
$597$	329722.	+	329722.i	0.925121	+	0.925121i
$598$	−209587.	−	33655.9i	−0.586087	−	0.0941150i
$599$	−141800.			−0.395206			−0.197603	−	0.980282i	$-0.563316\pi$
$599$	−141800.			−0.395206			−0.197603	+	0.980282i	$0.563316\pi$
$600$	208363.	−	402516.i	0.578786	−	1.11810i
$601$			50813.1i			0.140678i	0.997523	+	0.0703391i	$0.0224081\pi$
$601$			50813.1i			0.140678i	−0.997523	+	0.0703391i	$0.977592\pi$
$602$	−344650.	−	55344.5i	−0.951010	−	0.152715i
$603$	184242.	−	184242.i	0.506705	−	0.506705i
$604$	38856.6	−	117867.i	0.106510	−	0.323086i
$605$	408421.	−	408421.i	1.11583	−	1.11583i
$606$	−12800.3	+	9258.10i	−0.0348557	+	0.0252102i
$607$			448023.i			1.21597i	0.793948	+	0.607985i	$0.208022\pi$
$607$			448023.i			1.21597i	−0.793948	+	0.607985i	$0.791978\pi$
$608$	−15250.5	+	14927.1i	−0.0412550	+	0.0403802i
$609$	−518965.			−1.39928
$610$	−46734.8	−	64615.7i	−0.125597	−	0.173651i
$611$	102482.	+	102482.i	0.274514	+	0.274514i
$612$	−129293.	−	42623.4i	−0.345201	−	0.113801i
$613$	8742.04	+	8742.04i	0.0232644	+	0.0232644i	0.718643	−	0.695379i	$-0.244763\pi$
$613$	8742.04	+	8742.04i	0.0232644	+	0.0232644i	−0.695379	+	0.718643i	$0.744763\pi$
$614$	−111419.	+	693844.i	−0.295544	+	1.84045i
$615$	−67365.1			−0.178109
$616$	−44859.5	+	86659.9i	−0.118221	+	0.228379i
$617$		−	488336.i		−	1.28277i	−0.767220	−	0.641384i	$-0.778361\pi$
$617$		−	488336.i		−	1.28277i	0.767220	−	0.641384i	$-0.221639\pi$
$618$	−54791.1	+	341203.i	−0.143461	+	0.893380i
$619$	−416206.	+	416206.i	−1.08624	+	1.08624i	−0.0903309	+	0.995912i	$0.528792\pi$
$619$	−416206.	+	416206.i	−1.08624	+	1.08624i	−0.995912	+	0.0903309i	$0.971208\pi$
$620$	−279216.	−	553847.i	−0.726368	−	1.44081i
$621$	−407779.	+	407779.i	−1.05741	+	1.05741i
$622$	−36883.4	−	50995.1i	−0.0953344	−	0.131810i
$623$		−	302377.i		−	0.779062i
$624$	96877.2	+	71662.2i	0.248801	+	0.184044i
$625$	−101233.			−0.259155
$626$	338869.	−	245095.i	0.864734	−	0.625439i
$627$	2470.56	+	2470.56i	0.00628434	+	0.00628434i
$628$	71712.3	+	142247.i	0.181834	+	0.360682i
$629$	−59038.6	−	59038.6i	−0.149223	−	0.149223i
$630$	369724.	+	59371.1i	0.931530	+	0.149587i
$631$	77166.0			0.193806			0.0969030	−	0.995294i	$-0.469106\pi$
$631$	77166.0			0.193806			0.0969030	+	0.995294i	$0.469106\pi$
$632$	14258.6	+	44862.9i	0.0356980	+	0.112319i
$633$			124171.i			0.309893i
$634$	−256074.	−	41120.9i	−0.637070	−	0.102302i
$635$	76812.3	−	76812.3i	0.190495	−	0.190495i
$636$	117386.	+	38698.0i	0.290203	+	0.0956696i
$637$	58565.5	−	58565.5i	0.144332	−	0.144332i
$638$	110060.	−	79603.6i	0.270389	−	0.195565i
$639$			158976.i			0.389340i
$640$	298084.	+	607378.i	0.727744	+	1.48286i
$641$	692532.			1.68548			0.842740	−	0.538321i	$-0.180941\pi$
$641$	692532.			1.68548			0.842740	+	0.538321i	$0.180941\pi$
$642$	−235185.	−	325167.i	−0.570610	−	0.788927i
$643$	515879.	+	515879.i	1.24774	+	1.24774i	0.956714	+	0.291031i	$0.0939984\pi$
$643$	515879.	+	515879.i	1.24774	+	1.24774i	0.291031	+	0.956714i	$0.406002\pi$
$644$	−220735.	+	669574.i	−0.532230	+	1.61446i
$645$	280192.	+	280192.i	0.673498	+	0.673498i
$646$	−2957.49	+	18417.3i	−0.00708693	+	0.0441328i
$647$	−187947.			−0.448980			−0.224490	−	0.974476i	$-0.572072\pi$
$647$	−187947.			−0.448980			−0.224490	+	0.974476i	$0.572072\pi$
$648$	124136.	−	39453.8i	0.295630	−	0.0939592i
$649$		−	80406.4i		−	0.190898i
$650$	49194.0	−	306348.i	0.116435	−	0.725084i
$651$	−259438.	+	259438.i	−0.612169	+	0.612169i
$652$	−146960.	+	74088.1i	−0.345703	+	0.174282i
$653$	363478.	−	363478.i	0.852415	−	0.852415i	−0.138015	−	0.990430i	$-0.544072\pi$
$653$	363478.	−	363478.i	0.852415	−	0.852415i	0.990430	+	0.138015i	$0.0440722\pi$
$654$	−31047.3	−	42926.2i	−0.0725887	−	0.100361i
$655$		−	726322.i		−	1.69296i
$656$	37884.2	−	51214.2i	0.0880341	−	0.119010i
$657$	−344929.			−0.799096
$658$	390034.	−	282101.i	0.900847	−	0.651558i
$659$	−59401.3	−	59401.3i	−0.136781	−	0.136781i	0.635401	−	0.772182i	$-0.280835\pi$
$659$	−59401.3	−	59401.3i	−0.136781	−	0.136781i	−0.772182	+	0.635401i	$0.780835\pi$
$660$	98914.5	−	49866.6i	0.227076	−	0.114478i
$661$	−352242.	−	352242.i	−0.806191	−	0.806191i	0.177864	−	0.984055i	$-0.443081\pi$
$661$	−352242.	−	352242.i	−0.806191	−	0.806191i	−0.984055	+	0.177864i	$0.943081\pi$
$662$	768228.	+	123364.i	1.75297	+	0.281495i
$663$	105331.			0.239622
$664$	115898.	+	59994.9i	0.262870	+	0.136075i
$665$		−	51307.8i		−	0.116022i
$666$	−56032.4	−	8997.80i	−0.126325	−	0.0202856i
$667$	693927.	−	693927.i	1.55977	−	1.55977i
$668$	−150632.	+	456925.i	−0.337571	+	1.02398i
$669$	−251555.	+	251555.i	−0.562058	+	0.562058i
$670$	−917149.	+	663349.i	−2.04310	+	1.47772i
$671$		−	12346.6i		−	0.0274222i
$672$	286017.	−	279952.i	0.633363	−	0.619933i
$673$	678354.			1.49771			0.748853	−	0.662736i	$-0.230605\pi$
$673$	678354.			1.49771			0.748853	+	0.662736i	$0.230605\pi$
$674$	95759.7	+	132398.i	0.210796	+	0.291448i
$675$	−596041.	−	596041.i	−1.30818	−	1.30818i
$676$	−355658.	−	117248.i	−0.778287	−	0.256574i
$677$	−348304.	−	348304.i	−0.759943	−	0.759943i	0.216369	−	0.976312i	$-0.430579\pi$
$677$	−348304.	−	348304.i	−0.759943	−	0.759943i	−0.976312	+	0.216369i	$0.930579\pi$
$678$	−83656.9	+	520961.i	−0.181988	+	1.13330i
$679$	−150471.			−0.326372
$680$	525204.	+	271872.i	1.13582	+	0.587958i
$681$		−	134699.i		−	0.290448i
$682$	15225.7	−	94815.5i	0.0327346	−	0.203850i
$683$	−218970.	+	218970.i	−0.469401	+	0.469401i	−0.901721	−	0.432319i	$-0.857695\pi$
$683$	−218970.	+	218970.i	−0.469401	+	0.469401i	0.432319	+	0.901721i	$0.357695\pi$
$684$	5707.49	+	11321.3i	0.0121993	+	0.0241982i
$685$	−449450.	+	449450.i	−0.957856	+	0.957856i
$686$	174351.	+	241059.i	0.370491	+	0.512241i
$687$		−	200422.i		−	0.424652i
$688$	−370587.	+	55443.1i	−0.782913	+	0.117131i
$689$	84610.7			0.178233
$690$	648482.	−	469030.i	1.36207	−	0.985150i
$691$	166441.	+	166441.i	0.348581	+	0.348581i	0.859581	−	0.511000i	$-0.170725\pi$
$691$	166441.	+	166441.i	0.348581	+	0.348581i	−0.511000	+	0.859581i	$0.670725\pi$
$692$	−84847.5	−	168302.i	−0.177185	−	0.351461i
$693$	40995.2	+	40995.2i	0.0853625	+	0.0853625i
$694$	−119308.	−	19158.7i	−0.247714	−	0.0397784i
$695$	−709638.			−1.46915
$696$	−530925.	+	168742.i	−1.09601	+	0.348341i
$697$		−	55683.0i		−	0.114619i
$698$	−777894.	−	124916.i	−1.59665	−	0.256393i
$699$	426948.	−	426948.i	0.873817	−	0.873817i
$700$	−978700.	−	322643.i	−1.99735	−	0.658455i
$701$	−606601.	+	606601.i	−1.23443	+	1.23443i	−0.272188	+	0.962244i	$0.587747\pi$
$701$	−606601.	+	606601.i	−1.23443	+	1.23443i	−0.962244	+	0.272188i	$0.912253\pi$
$702$	181585.	−	131336.i	0.368473	−	0.266507i
$703$			7775.80i			0.0157338i
$704$	−17715.8	+	103243.i	−0.0357450	+	0.208313i
$705$	−546430.			−1.09940
$706$	235501.	+	325604.i	0.472479	+	0.653251i
$707$	25397.3	+	25397.3i	0.0508100	+	0.0508100i
$708$	−103250.	+	313198.i	−0.205980	+	0.624816i
$709$	590171.	+	590171.i	1.17405	+	1.17405i	0.981236	+	0.192811i	$0.0617603\pi$
$709$	590171.	+	590171.i	1.17405	+	1.17405i	0.192811	+	0.981236i	$0.438240\pi$
$710$	109497.	−	681875.i	0.217213	−	1.35266i
$711$	27968.0			0.0553251
$712$	−98318.0	−	309345.i	−0.193942	−	0.610215i
$713$		−	693806.i		−	1.36477i
$714$	55466.6	−	345410.i	0.108802	−	0.677545i
$715$	53620.1	−	53620.1i	0.104885	−	0.104885i
$716$	152296.	−	76778.5i	0.297073	−	0.149766i
$717$	326391.	−	326391.i	0.634893	−	0.634893i
$718$	−225870.	−	312289.i	−0.438137	−	0.605769i
$719$			319294.i			0.617637i	0.951121	+	0.308819i	$0.0999336\pi$
$719$			319294.i			0.617637i	−0.951121	+	0.308819i	$0.900066\pi$
$720$	397549.	−	59476.8i	0.766877	−	0.114732i
$721$	785701.			1.51143
$722$	−420976.	+	304480.i	−0.807575	+	0.584097i
$723$	−103848.	−	103848.i	−0.198665	−	0.198665i
$724$	−76832.4	+	38734.2i	−0.146578	+	0.0738954i
$725$	1.01430e6	+	1.01430e6i	1.92969	+	1.92969i
$726$	−362133.	−	58152.0i	−0.687060	−	0.110330i
$727$	−295780.			−0.559628			−0.279814	−	0.960054i	$-0.590273\pi$
$727$	−295780.			−0.559628			−0.279814	+	0.960054i	$0.590273\pi$
$728$	125948.	−	243308.i	0.237646	−	0.459085i
$729$		−	491717.i		−	0.925253i
$730$	1.47946e6	+	237575.i	2.77625	+	0.445815i
$731$	−231602.	+	231602.i	−0.433419	+	0.433419i
$732$	−15854.4	+	48092.3i	−0.0295887	+	0.0897539i
$733$	353645.	−	353645.i	0.658203	−	0.658203i	−0.296752	−	0.954955i	$-0.595903\pi$
$733$	353645.	−	353645.i	0.658203	−	0.658203i	0.954955	+	0.296752i	$0.0959033\pi$
$734$	617953.	−	446949.i	1.14700	−	0.829594i
$735$			312270.i			0.578036i
$736$	−8109.39	+	756776.i	−0.0149704	+	1.39705i
$737$	−175247.			−0.322637
$738$	−22180.6	−	30667.0i	−0.0407250	−	0.0563065i
$739$	−23782.9	−	23782.9i	−0.0435488	−	0.0435488i	0.684997	−	0.728546i	$-0.259803\pi$
$739$	−23782.9	−	23782.9i	−0.0435488	−	0.0435488i	−0.728546	+	0.684997i	$0.759803\pi$
$740$	234136.	+	77186.4i	0.427567	+	0.140954i
$741$	−6936.38	−	6936.38i	−0.0126327	−	0.0126327i
$742$	44555.6	−	277463.i	0.0809273	−	0.503962i
$743$	−912931.			−1.65371			−0.826857	−	0.562412i	$-0.809873\pi$
$743$	−912931.			−1.65371			−0.826857	+	0.562412i	$0.809873\pi$
$744$	−181060.	+	349773.i	−0.327097	+	0.631888i
$745$			1.21494e6i			2.18899i
$746$	46434.1	−	289161.i	0.0834372	−	0.519592i
$747$	54826.8	−	54826.8i	0.0982543	−	0.0982543i
$748$	41218.9	+	81761.2i	0.0736705	+	0.146132i
$749$	−645172.	+	645172.i	−1.15004	+	1.15004i
$750$	288937.	+	399486.i	0.513667	+	0.710197i
$751$		−	799005.i		−	1.41667i	−0.705875	−	0.708336i	$-0.749446\pi$
$751$		−	799005.i		−	1.41667i	0.705875	−	0.708336i	$-0.250554\pi$
$752$	307297.	−	415422.i	0.543404	−	0.734605i
$753$	671294.			1.18392
$754$	−309007.	+	223497.i	−0.543533	+	0.393123i
$755$	226496.	+	226496.i	0.397344	+	0.397344i
$756$	−335066.	−	664632.i	−0.586256	−	1.16289i
$757$	−24122.0	−	24122.0i	−0.0420940	−	0.0420940i	0.685746	−	0.727841i	$-0.259476\pi$
$757$	−24122.0	−	24122.0i	−0.0420940	−	0.0420940i	−0.727841	+	0.685746i	$0.759476\pi$
$758$	−677115.	−	108732.i	−1.17848	−	0.189243i
$759$	123910.			0.215092
$760$	−16682.8	−	52490.2i	−0.0288829	−	0.0908763i
$761$			97444.6i			0.168263i	0.996455	+	0.0841315i	$0.0268116\pi$
$761$			97444.6i			0.168263i	−0.996455	+	0.0841315i	$0.973188\pi$
$762$	−68106.8	−	10936.7i	−0.117295	−	0.0188355i
$763$	−85170.8	+	85170.8i	−0.146299	+	0.146299i
$764$	793940.	+	261734.i	1.36019	+	0.448408i
$765$	248452.	−	248452.i	0.424542	−	0.424542i
$766$	−26778.6	+	19368.3i	−0.0456384	+	0.0330090i
$767$			225750.i			0.383741i
$768$	201581.	−	379402.i	0.341765	−	0.643246i
$769$	−747937.			−1.26477			−0.632386	−	0.774653i	$-0.717924\pi$
$769$	−747937.			−1.26477			−0.632386	+	0.774653i	$0.717924\pi$
$770$	−147600.	−	204072.i	−0.248946	−	0.344193i
$771$	261751.	+	261751.i	0.440331	+	0.440331i
$772$	122130.	−	370468.i	0.204922	−	0.621607i
$773$	−328529.	−	328529.i	−0.549813	−	0.549813i	0.376574	−	0.926387i	$-0.377102\pi$
$773$	−328529.	−	328529.i	−0.549813	−	0.549813i	−0.926387	+	0.376574i	$0.877102\pi$
$774$	−35297.4	+	219809.i	−0.0589198	+	0.366914i
$775$	1.01412e6			1.68844
$776$	−153938.	+	48925.7i	−0.255637	+	0.0812481i
$777$		−	145832.i		−	0.241552i
$778$	39432.1	−	245557.i	0.0651464	−	0.405689i
$779$	−3666.92	+	3666.92i	−0.00604263	+	0.00604263i
$780$	−277714.	+	140006.i	−0.456466	+	0.230122i
$781$	75606.7	−	75606.7i	0.123953	−	0.123953i
$782$	387693.	+	536026.i	0.633978	+	0.876541i
$783$			1.03606e6i			1.68990i
$784$	−237402.	−	175612.i	−0.386236	−	0.285707i
$785$	−411150.			−0.667207
$786$	−373710.	+	270295.i	−0.604909	+	0.437514i
$787$	−76254.3	−	76254.3i	−0.123116	−	0.123116i	0.642864	−	0.765980i	$-0.277746\pi$
$787$	−76254.3	−	76254.3i	−0.123116	−	0.123116i	−0.765980	+	0.642864i	$0.777746\pi$
$788$	−637224.	+	321249.i	−1.02622	+	0.517356i
$789$	−354689.	−	354689.i	−0.569762	−	0.569762i
$790$	−119960.	−	19263.4i	−0.192212	−	0.0308659i
$791$	1.19964e6			1.91733
$792$	55269.6	+	28610.3i	0.0881122	+	0.0456113i
$793$			34664.5i			0.0551238i
$794$	−406969.	−	65351.9i	−0.645536	−	0.103661i
$795$	−225571.	+	225571.i	−0.356902	+	0.356902i
$796$	356319.	−	1.08085e6i	0.562358	−	1.70585i
$797$	10472.2	−	10472.2i	0.0164862	−	0.0164862i	−0.698816	−	0.715302i	$-0.746289\pi$
$797$	10472.2	−	10472.2i	0.0164862	−	0.0164862i	0.715302	+	0.698816i	$0.246289\pi$
$798$	−26399.1	+	19093.8i	−0.0414556	+	0.0299837i
$799$		−	451671.i		−	0.707503i
$800$	−1.10616e6	−	11853.3i	−1.72838	−	0.0185208i
$801$	−192849.			−0.300574
$802$	−556160.	−	768949.i	−0.864671	−	1.19550i
$803$	164044.	+	164044.i	0.254407	+	0.254407i
$804$	682618.	+	225035.i	1.05600	+	0.348128i
$805$	−1.28667e6	−	1.28667e6i	−1.98552	−	1.98552i
$806$	−42747.9	+	266206.i	−0.0658028	+	0.409777i
$807$	−17883.5			−0.0274604
$808$	34240.6	+	17724.6i	0.0524467	+	0.0271491i
$809$			569939.i			0.870826i	0.900231	+	0.435413i	$0.143398\pi$
$809$			569939.i			0.870826i	−0.900231	+	0.435413i	$0.856602\pi$
$810$	−53302.1	+	331931.i	−0.0812408	+	0.505914i
$811$	−207525.	+	207525.i	−0.315521	+	0.315521i	−0.847044	−	0.531523i	$-0.821620\pi$
$811$	−207525.	+	207525.i	−0.315521	+	0.315521i	0.531523	+	0.847044i	$0.321620\pi$
$812$	570189.	+	1.13102e6i	0.864783	+	1.71537i
$813$	596522.	−	596522.i	0.902496	−	0.902496i
$814$	22369.0	+	30927.5i	0.0337597	+	0.0466763i
$815$		−	424771.i		−	0.639498i
$816$	−55565.4	−	371405.i	−0.0834496	−	0.557785i
$817$	30503.6			0.0456991
$818$	−486301.	+	351728.i	−0.726772	+	0.525655i
$819$	−115099.	−	115099.i	−0.171595	−	0.171595i
$820$	74014.3	+	146814.i	0.110075	+	0.218343i
$821$	−597985.	−	597985.i	−0.887163	−	0.887163i	0.107086	−	0.994250i	$-0.465848\pi$
$821$	−597985.	−	597985.i	−0.887163	−	0.887163i	−0.994250	+	0.107086i	$0.965848\pi$
$822$	398511.	+	63993.8i	0.589790	+	0.0947096i
$823$	−17487.0			−0.0258176			−0.0129088	−	0.999917i	$-0.504109\pi$
$823$	−17487.0			−0.0258176			−0.0129088	+	0.999917i	$0.504109\pi$
$824$	803807.	−	255471.i	1.18385	−	0.376260i
$825$			181117.i			0.266104i
$826$	740302.	+	118879.i	1.08505	+	0.174239i
$827$	108277.	−	108277.i	0.158316	−	0.158316i	−0.623504	−	0.781820i	$-0.714291\pi$
$827$	108277.	−	108277.i	0.158316	−	0.158316i	0.781820	+	0.623504i	$0.214291\pi$
$828$	427038.	+	140780.i	0.622882	+	0.205343i
$829$	368289.	−	368289.i	0.535895	−	0.535895i	−0.386426	−	0.922321i	$-0.626290\pi$
$829$	368289.	−	368289.i	0.535895	−	0.535895i	0.922321	+	0.386426i	$0.126290\pi$
$830$	−272925.	+	197399.i	−0.396175	+	0.286543i
$831$		−	525431.i		−	0.760876i
$832$	49739.1	−	289867.i	0.0718541	−	0.418747i
$833$	−258117.			−0.371987
$834$	264086.	+	365126.i	0.379676	+	0.524941i
$835$	−878038.	−	878038.i	−1.25933	−	1.25933i
$836$	2669.85	−	8098.66i	0.00382009	−	0.0115878i
$837$	517939.	+	517939.i	0.739311	+	0.739311i
$838$	64361.5	−	400802.i	0.0916512	−	0.570744i
$839$	−105615.			−0.150038			−0.0750188	−	0.997182i	$-0.523902\pi$
$839$	−105615.			−0.150038			−0.0750188	+	0.997182i	$0.523902\pi$
$840$	312879.	+	984433.i	0.443422	+	1.39517i
$841$		−	1.05580e6i		−	1.49276i
$842$	−188188.	+	1.17191e6i	−0.265441	+	1.65299i
$843$	−49135.2	+	49135.2i	−0.0691414	+	0.0691414i
$844$	270614.	−	136427.i	0.379896	−	0.191520i
$845$	683441.	−	683441.i	0.957167	−	0.957167i
$846$	−179917.	−	248754.i	−0.251381	−	0.347560i
$847$			833897.i			1.16237i
$848$	−44635.0	−	298345.i	−0.0620703	−	0.414884i
$849$	−586797.			−0.814090
$850$	−783496.	+	566682.i	−1.08442	+	0.784334i
$851$	194997.	+	194997.i	0.269258	+	0.269258i
$852$	−391589.	+	197415.i	−0.539451	+	0.271958i
$853$	1.00366e6	+	1.00366e6i	1.37939	+	1.37939i	0.845647	+	0.533742i	$0.179215\pi$
$853$	1.00366e6	+	1.00366e6i	1.37939	+	1.37939i	0.533742	+	0.845647i	$0.320785\pi$
$854$	113675.	+	18254.2i	0.155866	+	0.0250292i
$855$	−32722.9			−0.0447630
$856$	−450262.	+	869818.i	−0.614494	+	1.18708i
$857$			677179.i			0.922024i	0.887394	+	0.461012i	$0.152513\pi$
$857$			677179.i			0.922024i	−0.887394	+	0.461012i	$0.847487\pi$
$858$	−47543.0	−	7634.56i	−0.0645821	−	0.0103707i
$859$	−750520.	+	750520.i	−1.01713	+	1.01713i	−0.0172783	+	0.999851i	$0.505500\pi$
$859$	−750520.	+	750520.i	−1.01713	+	1.01713i	−0.999851	+	0.0172783i	$0.994500\pi$
$860$	302794.	−	918490.i	0.409402	−	1.24187i
$861$	68771.6	−	68771.6i	0.0927690	−	0.0927690i
$862$	−401419.	+	290335.i	−0.540236	+	0.390738i
$863$		−	61525.8i		−	0.0826106i	−0.999147	−	0.0413053i	$-0.986848\pi$
$863$		−	61525.8i		−	0.0826106i	0.999147	−	0.0413053i	$-0.0131516\pi$
$864$	−558893.	−	571001.i	−0.748689	−	0.764908i
$865$	486458.			0.650149
$866$	621480.	+	859260.i	0.828688	+	1.14575i
$867$	155050.	+	155050.i	0.206269	+	0.206269i
$868$	850456.	+	280366.i	1.12879	+	0.372122i
$869$	−13301.2	−	13301.2i	−0.0176137	−	0.0176137i
$870$	227970.	−	1.41965e6i	0.301189	−	1.87561i
$871$	492025.			0.648562
$872$	−59440.2	+	114827.i	−0.0781712	+	0.151012i
$873$			95966.7i			0.125919i
$874$	9768.21	−	60830.1i	0.0127877	−	0.0796334i
$875$	792629.	−	792629.i	1.03527	−	1.03527i
$876$	−428331.	−	849630.i	−0.558176	−	1.10719i
$877$	−818941.	+	818941.i	−1.06476	+	1.06476i	−0.0670114	+	0.997752i	$0.521346\pi$
$877$	−818941.	+	818941.i	−1.06476	+	1.06476i	−0.997752	+	0.0670114i	$0.978654\pi$
$878$	−436231.	−	603134.i	−0.565884	−	0.782393i
$879$			825798.i			1.06880i
$880$	−217355.	−	160783.i	−0.280676	−	0.207622i
$881$	349159.			0.449853			0.224927	−	0.974376i	$-0.427786\pi$
$881$	349159.			0.449853			0.224927	+	0.974376i	$0.427786\pi$
$882$	−142156.	+	102818.i	−0.182738	+	0.132170i
$883$	353886.	+	353886.i	0.453881	+	0.453881i	0.896640	−	0.442760i	$-0.146001\pi$
$883$	353886.	+	353886.i	0.453881	+	0.453881i	−0.442760	+	0.896640i	$0.646001\pi$
$884$	−115727.	−	229554.i	−0.148092	−	0.293752i
$885$	−601848.	−	601848.i	−0.768423	−	0.768423i
$886$	−143089.	−	22977.4i	−0.182279	−	0.0292708i
$887$	1.16958e6			1.48656			0.743282	−	0.668978i	$-0.233268\pi$
$887$	1.16958e6			1.48656			0.743282	+	0.668978i	$0.233268\pi$
$888$	−47417.4	−	149193.i	−0.0601328	−	0.189200i
$889$			156832.i			0.198441i
$890$	827163.	+	132827.i	1.04427	+	0.167690i
$891$	−36804.6	+	36804.6i	−0.0463604	+	0.0463604i
$892$	824617.	+	271847.i	1.03639	+	0.341661i
$893$	−29744.1	+	29744.1i	−0.0372990	+	0.0372990i
$894$	625117.	−	452131.i	0.782144	−	0.565704i
$895$			440196.i			0.549540i
$896$	−924367.	−	315752.i	−1.15141	−	0.393306i
$897$	−347893.			−0.432375
$898$	5409.45	+	7479.13i	0.00670812	+	0.00927466i
$899$	−881387.	−	881387.i	−1.09055	−	1.09055i
$900$	−205774.	+	624192.i	−0.254042	+	0.770607i
$901$	−186454.	−	186454.i	−0.229679	−	0.229679i
$902$	−4036.01	+	25133.6i	−0.00496066	+	0.0308917i
$903$	−572084.			−0.701591
$904$	1.22728e6	−	390062.i	1.50178	−	0.477306i
$905$		−	222075.i		−	0.271146i
$906$	32249.0	−	200826.i	0.0392880	−	0.244660i
$907$	110870.	−	110870.i	0.134772	−	0.134772i	−0.636503	−	0.771274i	$-0.719620\pi$
$907$	110870.	−	110870.i	0.134772	−	0.134772i	0.771274	+	0.636503i	$0.219620\pi$
$908$	−293558.	+	147994.i	−0.356059	+	0.179503i
$909$	16197.8	−	16197.8i	0.0196033	−	0.0196033i
$910$	414404.	+	572957.i	0.500428	+	0.691893i
$911$		−	162563.i		−	0.195877i	−0.995192	−	0.0979387i	$-0.968775\pi$
$911$		−	162563.i		−	0.195877i	0.995192	−	0.0979387i	$-0.0312249\pi$
$912$	−20799.1	+	28117.4i	−0.0250066	+	0.0338054i
$913$	−52149.8			−0.0625621
$914$	850394.	−	615068.i	1.01795	−	0.736259i
$915$	−92415.3	−	92415.3i	−0.110383	−	0.110383i
$916$	−436795.	+	220205.i	−0.520579	+	0.262444i
$917$	741487.	+	741487.i	0.881789	+	0.881789i
$918$	−689572.	−	110733.i	−0.818266	−	0.131399i
$919$	−615695.			−0.729012			−0.364506	−	0.931201i	$-0.618762\pi$
$919$	−615695.			−0.729012			−0.364506	+	0.931201i	$0.618762\pi$
$920$	−1.73468e6	−	897958.i	−2.04948	−	1.06091i
$921$			1.15171e6i			1.35776i
$922$	−763906.	−	122670.i	−0.898624	−	0.144303i
$923$	−212275.	+	212275.i	−0.249170	+	0.249170i
$924$	−50071.9	+	151887.i	−0.0586476	+	0.177901i
$925$	−285023.	+	285023.i	−0.333116	+	0.333116i
$926$	72117.0	−	52160.3i	0.0841038	−	0.0608301i
$927$		−	501101.i		−	0.583131i
$928$	951080.	+	971684.i	1.10439	+	1.12831i
$929$	228015.			0.264199			0.132099	−	0.991236i	$-0.457828\pi$
$929$	228015.			0.264199			0.132099	+	0.991236i	$0.457828\pi$
$930$	−595736.	−	823667.i	−0.688792	−	0.952326i
$931$	16997.9	+	16997.9i	0.0196108	+	0.0196108i
$932$	−1.39957e6	−	461388.i	−1.61125	−	0.531171i
$933$	−72934.7	−	72934.7i	−0.0837859	−	0.0837859i
$934$	157443.	−	980449.i	0.180480	−	1.12391i
$935$	−236321.			−0.270321
$936$	−155176.	−	80326.9i	−0.177122	−	0.0916873i
$937$			431768.i			0.491781i	0.969298	+	0.245890i	$0.0790803\pi$
$937$			431768.i			0.491781i	−0.969298	+	0.245890i	$0.920920\pi$
$938$	259098.	−	1.61350e6i	0.294482	−	1.83384i
$939$	484660.	−	484660.i	0.549675	−	0.549675i
$940$	600365.	+	1.19087e6i	0.679453	+	1.34775i
$941$	−532946.	+	532946.i	−0.601871	+	0.601871i	−0.940809	−	0.338938i	$-0.889932\pi$
$941$	−532946.	+	532946.i	−0.601871	+	0.601871i	0.338938	+	0.940809i	$0.389932\pi$
$942$	153006.	+	211546.i	0.172427	+	0.238399i
$943$			183914.i			0.206819i
$944$	796016.	−	119091.i	0.893260	−	0.133640i
$945$	1.92104e6			2.15116
$946$	121325.	−	87751.4i	0.135572	−	0.0980555i
$947$	−1.02432e6	−	1.02432e6i	−1.14218	−	1.14218i	−0.988051	−	0.154128i	$-0.950743\pi$
$947$	−1.02432e6	−	1.02432e6i	−1.14218	−	1.14218i	−0.154128	−	0.988051i	$-0.549257\pi$
$948$	34730.5	+	68890.8i	0.0386451	+	0.0766558i
$949$	−460572.	−	460572.i	−0.511405	−	0.511405i
$950$	88913.8	+	14278.0i	0.0985195	+	0.0158205i
$951$	−425057.			−0.469988
$952$	−813717.	+	258621.i	−0.897841	+	0.285358i
$953$			264733.i			0.291490i	0.989322	+	0.145745i	$0.0465578\pi$
$953$			264733.i			0.291490i	−0.989322	+	0.145745i	$0.953442\pi$
$954$	−176960.	−	28416.5i	−0.194436	−	0.0312230i
$955$	−1.52565e6	+	1.52565e6i	−1.67282	+	1.67282i
$956$	−1.06994e6	−	352720.i	−1.17069	−	0.385935i
$957$	157411.	−	157411.i	0.171875	−	0.171875i
$958$	382191.	−	276428.i	0.416437	−	0.301198i
$959$		−	917667.i		−	0.997810i
$960$	640178.	+	905386.i	0.694638	+	0.982407i
$961$	42286.5			0.0457883
$962$	−62803.8	−	86832.7i	−0.0678634	−	0.0938281i
$963$	411475.	+	411475.i	0.443702	+	0.443702i
$964$	−112225.	+	340421.i	−0.120763	+	0.366321i
$965$	711899.	+	711899.i	0.764476	+	0.764476i
$966$	−183199.	+	1.14084e6i	−0.196322	+	1.22257i
$967$	61058.3			0.0652967			0.0326484	−	0.999467i	$-0.489606\pi$
$967$	61058.3			0.0652967			0.0326484	+	0.999467i	$0.489606\pi$
$968$	271142.	+	853114.i	0.289365	+	0.910450i
$969$			30570.9i			0.0325582i
$970$	66098.5	−	411618.i	0.0702503	−	0.437473i
$971$	404297.	−	404297.i	0.428807	−	0.428807i	−0.459415	−	0.888222i	$-0.651941\pi$
$971$	404297.	−	404297.i	0.428807	−	0.428807i	0.888222	+	0.459415i	$0.151941\pi$
$972$	−712355.	+	359126.i	−0.753988	+	0.380114i
$973$	724454.	−	724454.i	0.765218	−	0.765218i
$974$	1.05475e6	+	1.45831e6i	1.11182	+	1.53720i
$975$		−	508507.i		−	0.534919i
$976$	122230.	−	18286.7i	0.128315	−	0.0191971i
$977$	−1.83431e6			−1.92169			−0.960845	−	0.277086i	$-0.910631\pi$
$977$	−1.83431e6			−1.92169			−0.960845	+	0.277086i	$0.910631\pi$
$978$	−218555.	+	158075.i	−0.228498	+	0.165267i
$979$	91716.3	+	91716.3i	0.0956932	+	0.0956932i
$980$	680551.	−	343092.i	0.708612	−	0.357239i
$981$	54319.9	+	54319.9i	0.0564444	+	0.0564444i
$982$	684251.	+	109878.i	0.709565	+	0.113943i
$983$	586823.			0.607296			0.303648	−	0.952784i	$-0.401795\pi$
$983$	586823.			0.607296			0.303648	+	0.952784i	$0.401795\pi$
$984$	47995.3	−	92717.5i	0.0495688	−	0.0957572i
$985$		−	1.84182e6i		−	1.89835i
$986$	1.17346e6	+	188437.i	1.20702	+	0.193826i
$987$	557839.	−	557839.i	0.572630	−	0.572630i
$988$	−7495.91	+	22738.0i	−0.00767910	+	0.0232937i
$989$	764953.	−	764953.i	0.782064	−	0.782064i
$990$	−130152.	+	94135.7i	−0.132795	+	0.0960470i
$991$		−	1.20757e6i		−	1.22961i	−0.788680	−	0.614804i	$-0.789235\pi$
$991$		−	1.20757e6i		−	1.22961i	0.788680	−	0.614804i	$-0.210765\pi$
$992$	961216.	+	10300.1i	0.976782	+	0.0104669i
$993$	1.27518e6			1.29322
$994$	584329.	+	807894.i	0.591404	+	0.817677i
$995$	2.07699e6	+	2.07699e6i	2.09792	+	2.09792i
$996$	203133.	+	66965.9i	0.204768	+	0.0675049i
$997$	833662.	+	833662.i	0.838686	+	0.838686i	0.988686	−	0.150000i	$-0.0479272\pi$
$997$	833662.	+	833662.i	0.838686	+	0.838686i	−0.150000	+	0.988686i	$0.547927\pi$
$998$	−40259.0	+	250707.i	−0.0404206	+	0.251713i
$999$	−291138.			−0.291721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.5.f.a.11.3	yes	14
3.2	odd	2		144.5.m.a.91.5		14
4.3	odd	2		64.5.f.a.15.5		14
8.3	odd	2		128.5.f.a.31.3		14
8.5	even	2		128.5.f.b.31.5		14
12.11	even	2		576.5.m.a.271.7		14
16.3	odd	4	inner	16.5.f.a.3.3	✓	14
16.5	even	4		128.5.f.a.95.3		14
16.11	odd	4		128.5.f.b.95.5		14
16.13	even	4		64.5.f.a.47.5		14
48.29	odd	4		576.5.m.a.559.7		14
48.35	even	4		144.5.m.a.19.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.3	✓	14	16.3	odd	4	inner
16.5.f.a.11.3	yes	14	1.1	even	1	trivial
64.5.f.a.15.5		14	4.3	odd	2
64.5.f.a.47.5		14	16.13	even	4
128.5.f.a.31.3		14	8.3	odd	2
128.5.f.a.95.3		14	16.5	even	4
128.5.f.b.31.5		14	8.5	even	2
128.5.f.b.95.5		14	16.11	odd	4
144.5.m.a.19.5		14	48.35	even	4
144.5.m.a.91.5		14	3.2	odd	2
576.5.m.a.271.7		14	12.11	even	2
576.5.m.a.559.7		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+(-2.34420 - 3.24110i) q^{2} +(-4.63552 - 4.63552i) q^{3} +(-5.00945 + 15.1956i) q^{4} +(-29.2002 - 29.2002i) q^{5} +(-4.15759 + 25.8908i) q^{6} +59.6196 q^{7} +(60.9935 - 19.3854i) q^{8} -38.0239i q^{9} +(-26.1896 + 163.092i) q^{10} +(-18.0837 + 18.0837i) q^{11} +(93.6607 - 47.2180i) q^{12} +(50.7721 - 50.7721i) q^{13} +(-139.760 - 193.233i) q^{14} +270.716i q^{15} +(-205.811 - 152.243i) q^{16} -223.769 q^{17} +(-123.239 + 89.1358i) q^{18} +(14.7360 + 14.7360i) q^{19} +(589.990 - 297.436i) q^{20} +(-276.368 - 276.368i) q^{21} +(101.003 + 16.2192i) q^{22} +739.082 q^{23} +(-372.598 - 192.875i) q^{24} +1080.30i q^{25} +(-283.577 - 45.5374i) q^{26} +(-551.738 + 551.738i) q^{27} +(-298.661 + 905.954i) q^{28} +(938.904 - 938.904i) q^{29} +(877.416 - 634.612i) q^{30} -938.741i q^{31} +(-10.9723 + 1023.94i) q^{32} +167.655 q^{33} +(524.560 + 725.259i) q^{34} +(-1740.90 - 1740.90i) q^{35} +(577.796 + 190.479i) q^{36} +(263.837 + 263.837i) q^{37} +(13.2167 - 82.3049i) q^{38} -470.710 q^{39} +(-2347.08 - 1214.96i) q^{40} +248.841i q^{41} +(-247.874 + 1543.60i) q^{42} +(1035.00 - 1035.00i) q^{43} +(-184.203 - 365.381i) q^{44} +(-1110.31 + 1110.31i) q^{45} +(-1732.56 - 2395.44i) q^{46} +2018.46i q^{47} +(248.315 + 1659.76i) q^{48} +1153.50 q^{49} +(3501.35 - 2532.44i) q^{50} +(1037.29 + 1037.29i) q^{51} +(517.171 + 1025.85i) q^{52} +(833.240 + 833.240i) q^{53} +(3081.62 + 494.853i) q^{54} +1056.09 q^{55} +(3636.41 - 1155.75i) q^{56} -136.618i q^{57} +(-5244.06 - 842.101i) q^{58} +(-2223.17 + 2223.17i) q^{59} +(-4113.68 - 1356.14i) q^{60} +(-341.374 + 341.374i) q^{61} +(-3042.55 + 2200.60i) q^{62} -2266.97i q^{63} +(3344.42 - 2364.76i) q^{64} -2965.11 q^{65} +(-393.016 - 543.385i) q^{66} +(4845.43 + 4845.43i) q^{67} +(1120.96 - 3400.30i) q^{68} +(-3426.03 - 3426.03i) q^{69} +(-1561.41 + 9723.46i) q^{70} -4180.93 q^{71} +(-737.108 - 2319.21i) q^{72} -9071.36i q^{73} +(236.635 - 1473.61i) q^{74} +(5007.74 - 5007.74i) q^{75} +(-297.741 + 150.103i) q^{76} +(-1078.14 + 1078.14i) q^{77} +(1103.44 + 1525.62i) q^{78} +735.536i q^{79} +(1564.19 + 10455.2i) q^{80} +2035.24 q^{81} +(806.518 - 583.333i) q^{82} +(1441.90 + 1441.90i) q^{83} +(5584.02 - 2815.12i) q^{84} +(6534.10 + 6534.10i) q^{85} +(-5780.81 - 928.294i) q^{86} -8704.61 q^{87} +(-752.429 + 1453.55i) q^{88} -5071.77i q^{89} +(6201.39 + 995.831i) q^{90} +(3027.01 - 3027.01i) q^{91} +(-3702.39 + 11230.8i) q^{92} +(-4351.55 + 4351.55i) q^{93} +(6542.05 - 4731.69i) q^{94} -860.586i q^{95} +(4797.36 - 4695.64i) q^{96} -2523.85 q^{97} +(-2704.03 - 3738.60i) q^{98} +(687.613 + 687.613i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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