LMFDB - Embedded newform 56.5.k.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,5,Mod(11,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("56.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	56.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.78871793270$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	56.11
Dual form			56.5.k.a.51.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27052 - 3.79286i) q^{2} +(4.42688 - 7.66758i) q^{3} +(-12.7715 - 9.63782i) q^{4} +(-19.7872 + 11.4241i) q^{5} +(-23.4576 - 26.5324i) q^{6} +(-24.1747 - 42.6214i) q^{7} +(-52.7814 + 36.1956i) q^{8} +(1.30543 + 2.26108i) q^{9} +(18.1900 + 89.5645i) q^{10} +(78.0757 - 135.231i) q^{11} +(-130.437 + 55.2614i) q^{12} +56.7703i q^{13} +(-192.371 + 37.5395i) q^{14} +202.293i q^{15} +(70.2247 + 246.180i) q^{16} +(92.7903 - 160.717i) q^{17} +(10.2345 - 2.07857i) q^{18} +(-254.563 - 440.916i) q^{19} +(362.816 + 44.8015i) q^{20} +(-433.822 - 3.31882i) q^{21} +(-413.715 - 467.944i) q^{22} +(103.705 - 59.8743i) q^{23} +(43.8754 + 564.940i) q^{24} +(-51.4787 + 89.1637i) q^{25} +(215.322 + 72.1279i) q^{26} +740.271 q^{27} +(-102.030 + 777.333i) q^{28} -981.672i q^{29} +(767.269 + 257.018i) q^{30} +(434.293 + 250.739i) q^{31} +(1022.95 + 46.4249i) q^{32} +(-691.264 - 1197.30i) q^{33} +(-491.686 - 556.136i) q^{34} +(965.261 + 567.183i) q^{35} +(5.11947 - 41.4590i) q^{36} +(1544.20 - 891.543i) q^{37} +(-1995.76 + 405.327i) q^{38} +(435.291 + 251.315i) q^{39} +(630.892 - 1319.19i) q^{40} -235.209 q^{41} +(-563.768 + 1641.21i) q^{42} +3200.11 q^{43} +(-2300.48 + 974.630i) q^{44} +(-51.6617 - 29.8269i) q^{45} +(-95.3347 - 469.411i) q^{46} +(-2725.37 + 1573.49i) q^{47} +(2198.48 + 551.355i) q^{48} +(-1232.17 + 2060.72i) q^{49} +(272.780 + 308.536i) q^{50} +(-821.543 - 1422.95i) q^{51} +(547.142 - 725.044i) q^{52} +(-1747.11 - 1008.69i) q^{53} +(940.531 - 2807.74i) q^{54} +3567.79i q^{55} +(2818.68 + 1374.60i) q^{56} -4507.68 q^{57} +(-3723.34 - 1247.24i) q^{58} +(-1840.92 + 3188.58i) q^{59} +(1949.66 - 2583.59i) q^{60} +(2038.00 - 1176.64i) q^{61} +(1502.80 - 1328.64i) q^{62} +(64.8120 - 110.300i) q^{63} +(1475.76 - 3820.91i) q^{64} +(-648.551 - 1123.32i) q^{65} +(-5419.47 + 1100.66i) q^{66} +(-541.370 + 937.680i) q^{67} +(-2734.04 + 1158.31i) q^{68} -1060.23i q^{69} +(3377.63 - 2940.48i) q^{70} +2275.41i q^{71} +(-150.744 - 72.0920i) q^{72} +(-4272.40 + 7400.01i) q^{73} +(-1419.56 - 6989.65i) q^{74} +(455.780 + 789.434i) q^{75} +(-998.309 + 8084.61i) q^{76} +(-7651.20 - 58.5332i) q^{77} +(1506.25 - 1331.69i) q^{78} +(10768.3 - 6217.08i) q^{79} +(-4201.94 - 4068.95i) q^{80} +(3171.35 - 5492.94i) q^{81} +(-298.838 + 892.114i) q^{82} -155.884 q^{83} +(5508.59 + 4223.48i) q^{84} +4240.19i q^{85} +(4065.81 - 12137.6i) q^{86} +(-7527.06 - 4345.75i) q^{87} +(773.819 + 9963.69i) q^{88} +(4388.50 + 7601.10i) q^{89} +(-178.766 + 158.050i) q^{90} +(2419.63 - 1372.40i) q^{91} +(-1901.54 - 234.807i) q^{92} +(3845.13 - 2219.99i) q^{93} +(2505.39 + 12336.1i) q^{94} +(10074.2 + 5816.32i) q^{95} +(4884.43 - 7638.02i) q^{96} +10581.9 q^{97} +(6250.50 + 7291.64i) q^{98} +407.691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 28 q^{6} - 4 q^{8} - 704 q^{9} + 66 q^{10} + 94 q^{11} + 46 q^{12} + 6 q^{14} + 120 q^{16} - 2 q^{17} - 730 q^{18} - 2 q^{19} - 1872 q^{20} + 2160 q^{22} + 550 q^{24}+ \cdots + 640 q^{99}+O(q^{100}) $ 60 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 28 * q^6 - 4 * q^8 - 704 * q^9 + 66 * q^10 + 94 * q^11 + 46 * q^12 + 6 * q^14 + 120 * q^16 - 2 * q^17 - 730 * q^18 - 2 * q^19 - 1872 * q^20 + 2160 * q^22 + 550 * q^24 + 2748 * q^25 + 438 * q^26 + 316 * q^27 - 2038 * q^28 + 168 * q^30 - 2764 * q^32 + 322 * q^33 + 1212 * q^34 - 3846 * q^35 + 7600 * q^36 - 2384 * q^38 + 4886 * q^40 - 8 * q^41 + 7054 * q^42 - 5576 * q^43 + 1018 * q^44 + 2970 * q^46 - 7352 * q^48 + 1500 * q^49 - 10216 * q^50 + 7202 * q^51 - 8888 * q^52 - 15700 * q^54 + 9576 * q^56 + 7804 * q^57 - 4638 * q^58 - 6530 * q^59 + 5950 * q^60 + 20448 * q^62 - 24616 * q^64 + 1248 * q^65 + 20560 * q^66 - 8002 * q^67 - 18320 * q^68 - 19122 * q^70 - 6404 * q^72 + 3678 * q^73 - 3876 * q^74 + 1572 * q^75 + 25012 * q^76 + 29140 * q^78 + 21732 * q^80 - 12898 * q^81 + 31314 * q^82 + 10552 * q^83 - 24068 * q^84 + 5452 * q^86 - 8922 * q^88 - 6818 * q^89 - 51340 * q^90 + 18240 * q^91 + 16188 * q^92 - 26760 * q^94 + 40208 * q^96 - 6984 * q^97 - 3142 * q^98 + 640 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.27052	−	3.79286i	0.317631	−	0.948215i
$2$	1.27052	−	3.79286i	0.317631	−	0.948215i
$3$	4.42688	−	7.66758i	0.491876	−	0.851954i	−0.508080	−	0.861310i	$-0.669645\pi$
$3$	4.42688	−	7.66758i	0.491876	−	0.851954i	0.999956	+	0.00935579i	$0.00297808\pi$
$4$	−12.7715	−	9.63782i	−0.798221	−	0.602364i
$5$	−19.7872	+	11.4241i	−0.791487	+	0.456965i	−0.840486	−	0.541834i	$-0.817730\pi$
$5$	−19.7872	+	11.4241i	−0.791487	+	0.456965i	0.0489990	+	0.998799i	$0.484397\pi$
$6$	−23.4576	−	26.5324i	−0.651600	−	0.737010i
$7$	−24.1747	−	42.6214i	−0.493360	−	0.869825i
$7$	−24.1747	−	42.6214i	−0.493360	−	0.869825i
$8$	−52.7814	+	36.1956i	−0.824710	+	0.565556i
$9$	1.30543	+	2.26108i	0.0161165	+	0.0279145i
$10$	18.1900	+	89.5645i	0.181900	+	0.895645i
$11$	78.0757	−	135.231i	0.645254	−	1.11761i	−0.338989	−	0.940790i	$-0.610085\pi$
$11$	78.0757	−	135.231i	0.645254	−	1.11761i	0.984243	−	0.176822i	$-0.0565817\pi$
$12$	−130.437	+	55.2614i	−0.905812	+	0.383760i
$13$			56.7703i			0.335919i	0.985794	+	0.167959i	$0.0537177\pi$
$13$			56.7703i			0.335919i	−0.985794	+	0.167959i	$0.946282\pi$
$14$	−192.371	+	37.5395i	−0.981487	+	0.191528i
$15$			202.293i			0.899080i
$16$	70.2247	+	246.180i	0.274315	+	0.961640i
$17$	92.7903	−	160.717i	0.321074	−	0.556116i	−0.659636	−	0.751585i	$-0.729290\pi$
$17$	92.7903	−	160.717i	0.321074	−	0.556116i	0.980710	+	0.195469i	$0.0626230\pi$
$18$	10.2345	−	2.07857i	0.0315881	−	0.00641535i
$19$	−254.563	−	440.916i	−0.705160	−	1.22137i	−0.966634	−	0.256163i	$-0.917542\pi$
$19$	−254.563	−	440.916i	−0.705160	−	1.22137i	0.261473	−	0.965211i	$-0.415792\pi$
$20$	362.816	+	44.8015i	0.907041	+	0.112004i
$21$	−433.822	−	3.31882i	−0.983723	−	0.00752568i
$22$	−413.715	−	467.944i	−0.854784	−	0.966827i
$23$	103.705	−	59.8743i	0.196040	−	0.113184i	−0.398767	−	0.917052i	$-0.630562\pi$
$23$	103.705	−	59.8743i	0.196040	−	0.113184i	0.594807	+	0.803868i	$0.297228\pi$
$24$	43.8754	+	564.940i	0.0761726	+	0.980798i
$25$	−51.4787	+	89.1637i	−0.0823659	+	0.142662i
$26$	215.322	+	72.1279i	0.318523	+	0.106698i
$27$	740.271			1.01546
$28$	−102.030	+	777.333i	−0.130141	+	0.991496i
$29$		−	981.672i		−	1.16727i	−0.812017	−	0.583634i	$-0.801630\pi$
$29$		−	981.672i		−	1.16727i	0.812017	−	0.583634i	$-0.198370\pi$
$30$	767.269	+	257.018i	0.852521	+	0.285575i
$31$	434.293	+	250.739i	0.451918	+	0.260915i	0.708640	−	0.705570i	$-0.249309\pi$
$31$	434.293	+	250.739i	0.451918	+	0.260915i	−0.256722	+	0.966485i	$0.582642\pi$
$32$	1022.95	+	46.4249i	0.998972	+	0.0453368i
$33$	−691.264	−	1197.30i	−0.634769	−	1.09945i
$34$	−491.686	−	556.136i	−0.425334	−	0.481086i
$35$	965.261	+	567.183i	0.787968	+	0.463007i
$36$	5.11947	−	41.4590i	0.00395021	−	0.0319900i
$37$	1544.20	−	891.543i	1.12797	−	0.651237i	0.184550	−	0.982823i	$-0.440917\pi$
$37$	1544.20	−	891.543i	1.12797	−	0.651237i	0.943425	+	0.331587i	$0.107584\pi$
$38$	−1995.76	+	405.327i	−1.38210	+	0.280698i
$39$	435.291	+	251.315i	0.286187	+	0.165230i
$40$	630.892	−	1319.19i	0.394308	−	0.824494i
$41$	−235.209			−0.139922			−0.0699610	−	0.997550i	$-0.522287\pi$
$41$	−235.209			−0.139922			−0.0699610	+	0.997550i	$0.522287\pi$
$42$	−563.768	+	1641.21i	−0.319596	+	0.930390i
$43$	3200.11			1.73072			0.865362	−	0.501148i	$-0.167089\pi$
$43$	3200.11			1.73072			0.865362	+	0.501148i	$0.167089\pi$
$44$	−2300.48	+	974.630i	−1.18826	+	0.503424i
$45$	−51.6617	−	29.8269i	−0.0255119	−	0.0147293i
$46$	−95.3347	−	469.411i	−0.0450542	−	0.221839i
$47$	−2725.37	+	1573.49i	−1.23376	+	0.712309i	−0.967811	−	0.251679i	$-0.919017\pi$
$47$	−2725.37	+	1573.49i	−1.23376	+	0.712309i	−0.265945	+	0.963988i	$0.585684\pi$
$48$	2198.48	+	551.355i	0.954202	+	0.239304i
$49$	−1232.17	+	2060.72i	−0.513191	+	0.858274i
$50$	272.780	+	308.536i	0.109112	+	0.123414i
$51$	−821.543	−	1422.95i	−0.315857	−	0.547080i
$52$	547.142	−	725.044i	0.202345	−	0.268138i
$53$	−1747.11	−	1008.69i	−0.621969	−	0.359094i	0.155666	−	0.987810i	$-0.450248\pi$
$53$	−1747.11	−	1008.69i	−0.621969	−	0.359094i	−0.777635	+	0.628716i	$0.783581\pi$
$54$	940.531	−	2807.74i	0.322541	−	0.962875i
$55$			3567.79i			1.17943i
$56$	2818.68	+	1374.60i	0.898814	+	0.438331i
$57$	−4507.68			−1.38741
$58$	−3723.34	−	1247.24i	−1.10682	−	0.370760i
$59$	−1840.92	+	3188.58i	−0.528849	+	0.915994i	0.470585	+	0.882355i	$0.344043\pi$
$59$	−1840.92	+	3188.58i	−0.528849	+	0.915994i	−0.999434	+	0.0336392i	$0.989290\pi$
$60$	1949.66	−	2583.59i	0.541574	−	0.717665i
$61$	2038.00	−	1176.64i	0.547702	−	0.316216i	−0.200493	−	0.979695i	$-0.564254\pi$
$61$	2038.00	−	1176.64i	0.547702	−	0.316216i	0.748195	+	0.663479i	$0.230921\pi$
$62$	1502.80	−	1328.64i	0.390947	−	0.345641i
$63$	64.8120	−	110.300i	0.0163295	−	0.0277904i
$64$	1475.76	−	3820.91i	0.360293	−	0.932839i
$65$	−648.551	−	1123.32i	−0.153503	−	0.265875i
$66$	−5419.47	+	1100.66i	−1.24414	+	0.252678i
$67$	−541.370	+	937.680i	−0.120599	+	0.208884i	−0.920004	−	0.391909i	$-0.871815\pi$
$67$	−541.370	+	937.680i	−0.120599	+	0.208884i	0.799405	+	0.600793i	$0.205148\pi$
$68$	−2734.04	+	1158.31i	−0.591272	+	0.250500i
$69$		−	1060.23i		−	0.222690i
$70$	3377.63	−	2940.48i	0.689312	−	0.600097i
$71$			2275.41i			0.451381i	0.974199	+	0.225691i	$0.0724639\pi$
$71$			2275.41i			0.451381i	−0.974199	+	0.225691i	$0.927536\pi$
$72$	−150.744	−	72.0920i	−0.0290786	−	0.0139066i
$73$	−4272.40	+	7400.01i	−0.801726	+	1.38863i	0.116754	+	0.993161i	$0.462751\pi$
$73$	−4272.40	+	7400.01i	−0.801726	+	1.38863i	−0.918479	+	0.395469i	$0.870582\pi$
$74$	−1419.56	−	6989.65i	−0.259233	−	1.27641i
$75$	455.780	+	789.434i	0.0810276	+	0.140344i
$76$	−998.309	+	8084.61i	−0.172837	+	1.39969i
$77$	−7651.20	−	58.5332i	−1.29047	−	0.00987235i
$78$	1506.25	−	1331.69i	0.247576	−	0.218885i
$79$	10768.3	−	6217.08i	1.72541	−	0.996167i	0.818970	−	0.573836i	$-0.194545\pi$
$79$	10768.3	−	6217.08i	1.72541	−	0.996167i	0.906442	−	0.422331i	$-0.138788\pi$
$80$	−4201.94	−	4068.95i	−0.656553	−	0.635773i
$81$	3171.35	−	5492.94i	0.483364	−	0.837211i
$82$	−298.838	+	892.114i	−0.0444435	+	0.132676i
$83$	−155.884			−0.0226279			−0.0113140	−	0.999936i	$-0.503601\pi$
$83$	−155.884			−0.0226279			−0.0113140	+	0.999936i	$0.503601\pi$
$84$	5508.59	+	4223.48i	0.780695	+	0.598566i
$85$			4240.19i			0.586878i
$86$	4065.81	−	12137.6i	0.549731	−	1.64110i
$87$	−7527.06	−	4345.75i	−0.994458	−	0.574151i
$88$	773.819	+	9963.69i	0.0999250	+	1.28663i
$89$	4388.50	+	7601.10i	0.554033	+	0.959614i	0.997978	+	0.0635595i	$0.0202453\pi$
$89$	4388.50	+	7601.10i	0.554033	+	0.959614i	−0.443945	+	0.896054i	$0.646421\pi$
$90$	−178.766	+	158.050i	−0.0220699	+	0.0195123i
$91$	2419.63	−	1372.40i	0.292191	−	0.165729i
$92$	−1901.54	−	234.807i	−0.224662	−	0.0277418i
$93$	3845.13	−	2219.99i	0.444575	−	0.256676i
$94$	2505.39	+	12336.1i	0.283543	+	1.39612i
$95$	10074.2	+	5816.32i	1.11625	+	0.644467i
$96$	4884.43	−	7638.02i	0.529995	−	0.828778i
$97$	10581.9			1.12466			0.562328	−	0.826914i	$-0.309906\pi$
$97$	10581.9			1.12466			0.562328	+	0.826914i	$0.309906\pi$
$98$	6250.50	+	7291.64i	0.650823	+	0.759230i
$99$	407.691			0.0415968
$100$	1516.81	−	642.615i	0.151681	−	0.0642615i
$101$	4694.78	+	2710.53i	0.460228	+	0.265713i	0.712140	−	0.702037i	$-0.247726\pi$
$101$	4694.78	+	2710.53i	0.460228	+	0.265713i	−0.251912	+	0.967750i	$0.581059\pi$
$102$	−6440.85	+	1308.10i	−0.619075	+	0.125731i
$103$	−10557.4	+	6095.33i	−0.995138	+	0.574543i	−0.906806	−	0.421548i	$-0.861487\pi$
$103$	−10557.4	+	6095.33i	−0.995138	+	0.574543i	−0.0883319	+	0.996091i	$0.528154\pi$
$104$	−2054.83	−	2996.42i	−0.189981	−	0.277036i
$105$	8622.02	−	4890.36i	0.782042	−	0.443570i
$106$	−6045.58	+	5344.97i	−0.538055	+	0.475701i
$107$	−4568.28	−	7912.50i	−0.399012	−	0.691108i	0.594593	−	0.804027i	$-0.297313\pi$
$107$	−4568.28	−	7912.50i	−0.399012	−	0.691108i	−0.993604	+	0.112919i	$0.963980\pi$
$108$	−9454.40	−	7134.60i	−0.810563	−	0.611677i
$109$	7296.36	+	4212.56i	0.614120	+	0.354563i	0.774576	−	0.632480i	$-0.217963\pi$
$109$	7296.36	+	4212.56i	0.614120	+	0.354563i	−0.160456	+	0.987043i	$0.551296\pi$
$110$	13532.1	+	4532.95i	1.11836	+	0.374624i
$111$		−	15787.0i		−	1.28131i
$112$	8794.88	−	8944.39i	0.701122	−	0.713041i
$113$	−13900.8			−1.08863			−0.544317	−	0.838879i	$-0.683211\pi$
$113$	−13900.8			−1.08863			−0.544317	+	0.838879i	$0.683211\pi$
$114$	−5727.11	+	17097.0i	−0.440682	+	1.31556i
$115$	−1368.02	+	2369.49i	−0.103442	+	0.179167i
$116$	−9461.19	+	12537.5i	−0.703120	+	0.931738i
$117$	−128.362	+	74.1098i	−0.00937702	+	0.00541382i
$118$	9754.88	+	11033.5i	0.700580	+	0.792411i
$119$	−9093.18	−	69.5646i	−0.642128	−	0.00491241i
$120$	−7322.11	−	10677.3i	−0.508480	−	0.741480i
$121$	−4871.13	−	8437.05i	−0.332705	−	0.576262i
$122$	−1873.50	−	9224.79i	−0.125874	−	0.619779i
$123$	−1041.24	+	1803.48i	−0.0688243	+	0.119207i
$124$	−3130.02	−	7387.97i	−0.203565	−	0.480487i
$125$		−	16632.6i		−	1.06448i
$126$	−336.008	−	385.961i	−0.0211645	−	0.0243110i
$127$		−	20643.9i		−	1.27992i	−0.768408	−	0.639961i	$-0.778951\pi$
$127$		−	20643.9i		−	1.27992i	0.768408	−	0.639961i	$-0.221049\pi$
$128$	−12617.2	−	10451.9i	−0.770091	−	0.637933i
$129$	14166.5	−	24537.1i	0.851301	−	1.47450i
$130$	−5084.60	+	1032.65i	−0.300864	+	0.0611038i
$131$	−9837.91	−	17039.8i	−0.573271	−	0.992935i	−0.996227	−	0.0867849i	$-0.972341\pi$
$131$	−9837.91	−	17039.8i	−0.573271	−	0.992935i	0.422956	−	0.906150i	$-0.360993\pi$
$132$	−2710.90	+	21953.7i	−0.155584	+	1.25997i
$133$	−12638.5	+	21508.8i	−0.714483	+	1.21594i
$134$	2868.67	+	3244.68i	0.159761	+	0.180702i
$135$	−14647.9	+	8456.95i	−0.803724	+	0.464030i
$136$	919.657	+	11841.5i	0.0497220	+	0.640219i
$137$	8083.84	−	14001.6i	0.430702	−	0.745997i	−0.566232	−	0.824246i	$-0.691599\pi$
$137$	8083.84	−	14001.6i	0.430702	−	0.745997i	0.996934	+	0.0782485i	$0.0249328\pi$
$138$	−4021.29	−	1347.04i	−0.211158	−	0.0707331i
$139$	−10532.5			−0.545133			−0.272567	−	0.962137i	$-0.587873\pi$
$139$	−10532.5			−0.545133			−0.272567	+	0.962137i	$0.587873\pi$
$140$	−6861.46	−	16546.8i	−0.350074	−	0.844225i
$141$			27862.6i			1.40147i
$142$	8630.32	+	2890.96i	0.428006	+	0.143373i
$143$	7677.10	+	4432.38i	0.375427	+	0.216753i
$144$	−464.958	+	480.155i	−0.0224227	+	0.0231556i
$145$	11214.7	+	19424.5i	0.533401	+	0.923877i
$146$	22639.0	+	25606.5i	1.06207	+	1.20128i
$147$	10346.0	+	18570.3i	0.478784	+	0.859380i
$148$	−28314.3	−	3496.33i	−1.29266	−	0.159620i
$149$	−4054.85	+	2341.07i	−0.182643	+	0.105449i	−0.588534	−	0.808473i	$-0.700295\pi$
$149$	−4054.85	+	2341.07i	−0.182643	+	0.105449i	0.405891	+	0.913921i	$0.366961\pi$
$150$	3573.29	−	725.715i	0.158813	−	0.0322540i
$151$	22733.0	+	13124.9i	0.997019	+	0.575629i	0.907365	−	0.420344i	$-0.138091\pi$
$151$	22733.0	+	13124.9i	0.997019	+	0.575629i	0.0896539	+	0.995973i	$0.471424\pi$
$152$	29395.4	+	14058.1i	1.27231	+	0.608471i
$153$	484.526			0.0206983
$154$	−9943.03	+	28945.5i	−0.419254	+	1.22051i
$155$	−11457.9			−0.476916
$156$	−3137.20	−	7404.94i	−0.128912	−	0.304279i
$157$	−22152.8	−	12789.9i	−0.898732	−	0.518883i	−0.0219433	−	0.999759i	$-0.506985\pi$
$157$	−22152.8	−	12789.9i	−0.898732	−	0.518883i	−0.876789	+	0.480876i	$0.840319\pi$
$158$	−9899.13	−	48741.6i	−0.396536	−	1.95247i
$159$	−15468.5	+	8930.75i	−0.611863	+	0.353259i
$160$	−20771.6	+	10767.7i	−0.811390	+	0.420612i
$161$	−5058.97	−	2972.63i	−0.195169	−	0.114680i
$162$	−16804.7	−	19007.4i	−0.640324	−	0.724257i
$163$	2613.72	+	4527.09i	0.0983748	+	0.170390i	0.911012	−	0.412380i	$-0.135302\pi$
$163$	2613.72	+	4527.09i	0.0983748	+	0.170390i	−0.812637	+	0.582770i	$0.801969\pi$
$164$	3003.98	+	2266.90i	0.111689	+	0.0842840i
$165$	27356.3	+	15794.2i	1.00482	+	0.580135i
$166$	−198.054	+	591.245i	−0.00718733	+	0.0214561i
$167$		−	39756.1i		−	1.42551i	−0.701412	−	0.712756i	$-0.747447\pi$
$167$		−	39756.1i		−	1.42551i	0.701412	−	0.712756i	$-0.252553\pi$
$168$	23017.9	−	15527.3i	0.815542	−	0.550144i
$169$	25338.1			0.887159
$170$	16082.4	+	5387.26i	0.556486	+	0.186410i
$171$	664.630	−	1151.17i	0.0227294	−	0.0393685i
$172$	−40870.3	−	30842.1i	−1.38150	−	1.04253i
$173$	20341.2	−	11744.0i	0.679647	−	0.392394i	−0.120075	−	0.992765i	$-0.538314\pi$
$173$	20341.2	−	11744.0i	0.679647	−	0.392394i	0.799722	+	0.600371i	$0.204980\pi$
$174$	−26046.1	+	23027.7i	−0.860289	+	0.760592i
$175$	5044.76	+	38.5934i	0.164727	+	0.00126019i
$176$	38774.0	+	9724.10i	1.25174	+	0.313924i
$177$	16299.1	+	28230.9i	0.520256	+	0.901111i
$178$	34405.6	−	6987.57i	1.08590	−	0.220540i
$179$	−8118.38	+	14061.4i	−0.253375	+	0.438858i	−0.964453	−	0.264255i	$-0.914874\pi$
$179$	−8118.38	+	14061.4i	−0.253375	+	0.438858i	0.711078	+	0.703113i	$0.248207\pi$
$180$	372.333	+	878.842i	0.0114918	+	0.0271247i
$181$		−	21278.0i		−	0.649491i	−0.945802	−	0.324745i	$-0.894721\pi$
$181$		−	21278.0i		−	0.649491i	0.945802	−	0.324745i	$-0.105279\pi$
$182$	−2131.13	−	10921.0i	−0.0643379	−	0.329700i
$183$		−	20835.4i		−	0.622156i
$184$	−3306.53	+	6913.93i	−0.0976646	+	0.204216i
$185$	−20370.2	+	35282.2i	−0.595185	+	1.03089i
$186$	−3534.77	−	17404.6i	−0.102173	−	0.503081i
$187$	−14489.3	−	25096.3i	−0.414348	−	0.717672i
$188$	49972.1	+	6170.69i	1.41388	+	0.174590i
$189$	−17895.8	−	31551.4i	−0.500988	−	0.883273i
$190$	34859.9	−	30820.1i	0.965648	−	0.853742i
$191$	17556.3	−	10136.2i	0.481246	−	0.277848i	−0.239690	−	0.970850i	$-0.577046\pi$
$191$	17556.3	−	10136.2i	0.481246	−	0.277848i	0.720936	+	0.693002i	$0.243712\pi$
$192$	−22764.1	−	28230.2i	−0.617516	−	0.765794i
$193$	−24834.4	+	43014.4i	−0.666712	+	1.15478i	0.312106	+	0.950047i	$0.398966\pi$
$193$	−24834.4	+	43014.4i	−0.666712	+	1.15478i	−0.978818	+	0.204732i	$0.934368\pi$
$194$	13444.5	−	40135.6i	0.357225	−	1.06642i
$195$	−11484.2			−0.302018
$196$	35597.6	−	14443.1i	0.926634	−	0.375965i
$197$			43766.4i			1.12774i	0.825864	+	0.563869i	$0.190688\pi$
$197$			43766.4i			1.12774i	−0.825864	+	0.563869i	$0.809312\pi$
$198$	517.980	−	1546.31i	0.0132124	−	0.0394427i
$199$	47355.1	+	27340.5i	1.19581	+	0.690399i	0.959618	−	0.281308i	$-0.0907683\pi$
$199$	47355.1	+	27340.5i	1.19581	+	0.690399i	0.236189	+	0.971707i	$0.424102\pi$
$200$	−510.212	−	6569.49i	−0.0127553	−	0.164237i
$201$	4793.16	+	8302.00i	0.118640	+	0.205490i
$202$	16245.5	−	14362.9i	0.398135	−	0.351996i
$203$	−41840.3	+	23731.6i	−1.01532	+	0.575884i
$204$	−3221.81	+	26091.2i	−0.0774176	+	0.626952i
$205$	4654.12	−	2687.06i	0.110746	−	0.0639395i
$206$	9705.28	+	47787.0i	0.228704	+	1.12610i
$207$	270.761	+	156.324i	0.00631896	+	0.00364825i
$208$	−13975.7	+	3986.67i	−0.323033	+	0.0921476i
$209$	−79500.7			−1.82003
$210$	−7593.99	−	38915.4i	−0.172199	−	0.882436i
$211$	69955.1			1.57128			0.785642	−	0.618682i	$-0.212333\pi$
$211$	69955.1			1.57128			0.785642	+	0.618682i	$0.212333\pi$
$212$	12591.7	+	29720.9i	0.280164	+	0.661288i
$213$	17446.9	+	10073.0i	0.384556	+	0.222024i
$214$	−35815.1	+	7273.84i	−0.782057	+	0.158831i
$215$	−63321.1	+	36558.4i	−1.36984	+	0.790880i
$216$	−39072.6	+	26794.5i	−0.837461	+	0.574300i
$217$	187.979	−	24571.7i	0.00399199	−	0.521815i
$218$	25247.8	−	22321.9i	0.531265	−	0.469698i
$219$	37826.8	+	65517.9i	0.788699	+	1.36607i
$220$	34385.7	−	45566.1i	0.710448	−	0.941449i
$221$	9123.97	+	5267.73i	0.186810	+	0.107855i
$222$	−59877.9	−	20057.8i	−1.21496	−	0.406983i
$223$		−	13285.7i		−	0.267162i	−0.991038	−	0.133581i	$-0.957352\pi$
$223$		−	13285.7i		−	0.267162i	0.991038	−	0.133581i	$-0.0426476\pi$
$224$	−22750.7	−	44721.8i	−0.453418	−	0.891298i
$225$	−268.808			−0.00530979
$226$	−17661.3	+	52723.7i	−0.345784	+	1.03226i
$227$	5519.94	−	9560.82i	0.107123	−	0.185542i	−0.807481	−	0.589894i	$-0.799169\pi$
$227$	5519.94	−	9560.82i	0.107123	−	0.185542i	0.914604	+	0.404352i	$0.132503\pi$
$228$	57570.0	+	43444.2i	1.10746	+	0.835723i
$229$	−53523.0	+	30901.5i	−1.02063	+	0.589262i	−0.914287	−	0.405067i	$-0.867248\pi$
$229$	−53523.0	+	30901.5i	−1.02063	+	0.589262i	−0.106345	+	0.994329i	$0.533915\pi$
$230$	7249.02	+	8199.20i	0.137032	+	0.154994i
$231$	−34319.7	+	58407.1i	−0.643162	+	1.09456i
$232$	35532.2	+	51814.1i	0.660155	+	0.962657i
$233$	−42214.0	−	73116.8i	−0.777579	−	1.34681i	−0.933334	−	0.359011i	$-0.883114\pi$
$233$	−42214.0	−	73116.8i	−0.777579	−	1.34681i	0.155755	−	0.987796i	$-0.450219\pi$
$234$	118.001	+	581.017i	0.00215504	+	0.0106110i
$235$	35951.5	−	62269.8i	0.651001	−	1.12757i
$236$	54242.4	−	22980.5i	0.973901	−	0.412606i
$237$		−	110089.i		−	1.95996i
$238$	−11816.9	+	34400.8i	−0.208618	+	0.607315i
$239$			64606.7i			1.13105i	0.824731	+	0.565525i	$0.191326\pi$
$239$			64606.7i			1.13105i	−0.824731	+	0.565525i	$0.808674\pi$
$240$	−49800.5	+	14206.0i	−0.864591	+	0.246631i
$241$	30086.4	−	52111.1i	0.518007	−	0.897214i	−0.481774	−	0.876295i	$-0.660007\pi$
$241$	30086.4	−	52111.1i	0.518007	−	0.897214i	0.999781	−	0.0209189i	$-0.00665918\pi$
$242$	−38189.4	+	7756.05i	−0.652097	+	0.132437i
$243$	1902.57	+	3295.35i	0.0322202	+	0.0558071i
$244$	−37368.6	−	4614.38i	−0.627665	−	0.0775057i
$245$	839.310	−	54852.2i	0.0139827	−	0.913823i
$246$	5517.44	+	6240.65i	0.0911732	+	0.103124i
$247$	25030.9	−	14451.6i	0.410282	−	0.236877i
$248$	−31998.3	+	2485.11i	−0.520264	+	0.0404057i
$249$	−690.079	+	1195.25i	−0.0111301	+	0.0192780i
$250$	−63084.9	−	21132.0i	−1.00936	−	0.338113i
$251$	67264.1			1.06767			0.533834	−	0.845590i	$-0.320751\pi$
$251$	67264.1			1.06767			0.533834	+	0.845590i	$0.320751\pi$
$252$	−1890.80	+	784.058i	−0.0297745	+	0.0123466i
$253$		−	18698.9i		−	0.292129i
$254$	−78299.2	−	26228.5i	−1.21364	−	0.406542i
$255$	32512.0	+	18770.8i	0.499993	+	0.288671i
$256$	−55673.0	+	34575.8i	−0.849502	+	0.527585i
$257$	3699.03	+	6406.91i	0.0560044	+	0.0970024i	0.892668	−	0.450714i	$-0.148831\pi$
$257$	3699.03	+	6406.91i	0.0560044	+	0.0970024i	−0.836664	+	0.547716i	$0.815497\pi$
$258$	−75066.8	−	84906.4i	−1.12774	−	1.27556i
$259$	−75329.3	−	44263.2i	−1.12296	−	0.659846i
$260$	−2543.39	+	20597.2i	−0.0376242	+	0.304692i
$261$	2219.64	−	1281.51i	0.0325837	−	0.0188122i
$262$	−77128.7	+	15664.4i	−1.12360	+	0.228198i
$263$	−29807.8	−	17209.6i	−0.430942	−	0.248804i	0.268806	−	0.963194i	$-0.413371\pi$
$263$	−29807.8	−	17209.6i	−0.430942	−	0.248804i	−0.699748	+	0.714390i	$0.746704\pi$
$264$	79823.0	+	38174.7i	1.14530	+	0.547732i
$265$	46093.8			0.656374
$266$	65522.4	+	75263.5i	0.926033	+	1.06370i
$267$	77709.4			1.09006
$268$	15951.3	−	6758.00i	0.222089	−	0.0940911i
$269$	−35810.6	−	20675.3i	−0.494888	−	0.285724i	0.231712	−	0.972784i	$-0.425567\pi$
$269$	−35810.6	−	20675.3i	−0.494888	−	0.285724i	−0.726600	+	0.687061i	$0.758901\pi$
$270$	13465.6	+	66302.0i	0.184713	+	0.909493i
$271$	−43880.2	+	25334.2i	−0.597489	+	0.344960i	−0.768053	−	0.640386i	$-0.778774\pi$
$271$	−43880.2	+	25334.2i	−0.597489	+	0.344960i	0.170564	+	0.985347i	$0.445441\pi$
$272$	46081.6	+	11556.8i	0.622858	+	0.156206i
$273$	188.410	−	24628.2i	0.00252802	−	0.330451i
$274$	−42835.5	−	48450.2i	−0.570561	−	0.645349i
$275$	8038.47	+	13923.0i	0.106294	+	0.184106i
$276$	−10218.3	+	13540.7i	−0.134140	+	0.177756i
$277$	39389.9	+	22741.8i	0.513364	+	0.296391i	0.734215	−	0.678917i	$-0.237550\pi$
$277$	39389.9	+	22741.8i	0.513364	+	0.296391i	−0.220851	+	0.975307i	$0.570884\pi$
$278$	−13381.8	+	39948.4i	−0.173151	+	0.516903i
$279$			1309.30i			0.0168201i
$280$	−71477.4	+	5001.43i	−0.911701	+	0.0637937i
$281$	−151297.			−1.91610			−0.958050	−	0.286600i	$-0.907475\pi$
$281$	−151297.			−1.91610			−0.958050	+	0.286600i	$0.907475\pi$
$282$	105679.	+	35400.1i	1.32889	+	0.445150i
$283$	−129.566	+	224.415i	−0.00161778	+	0.00280207i	−0.866833	−	0.498598i	$-0.833848\pi$
$283$	−129.566	+	224.415i	−0.00161778	+	0.00280207i	0.865215	+	0.501400i	$0.167182\pi$
$284$	21930.0	−	29060.5i	0.271896	−	0.360302i
$285$	89194.2	−	51496.3i	1.09811	−	0.633996i
$286$	26565.3	−	23486.7i	0.324775	−	0.287138i
$287$	5686.10	+	10024.9i	0.0690320	+	0.121708i
$288$	1230.42	+	2373.57i	0.0148343	+	0.0286165i
$289$	24540.4	+	42505.3i	0.293823	+	0.508917i
$290$	87923.0	−	17856.7i	1.04546	−	0.212327i
$291$	46844.8	−	81137.6i	0.553191	−	0.958156i
$292$	125885.	−	53332.9i	1.47642	−	0.625503i
$293$			159992.i			1.86364i	0.362922	+	0.931820i	$0.381779\pi$
$293$			159992.i			1.86364i	−0.362922	+	0.931820i	$0.618221\pi$
$294$	83579.5	−	15647.0i	0.966953	−	0.181024i
$295$		−	84123.8i		−	0.966663i
$296$	−49235.1	+	102950.i	−0.561941	+	1.17501i
$297$	57797.2	−	100108.i	0.655230	−	1.13489i
$298$	3727.56	+	18353.9i	0.0419752	+	0.206678i
$299$	3399.08	+	5887.38i	0.0380206	+	0.0658536i
$300$	1787.41	−	14475.0i	0.0198602	−	0.160834i
$301$	−77361.5	−	136393.i	−0.853870	−	1.50543i
$302$	78663.8	−	69547.6i	0.862504	−	0.762550i
$303$	41566.5	−	23998.4i	0.452750	−	0.261395i
$304$	90668.0	−	93631.4i	0.981085	−	1.01315i
$305$	−26884.1	+	46564.7i	−0.288999	+	0.500561i
$306$	615.602	−	1837.74i	0.00657441	−	0.0196264i
$307$	−5421.20			−0.0575200			−0.0287600	−	0.999586i	$-0.509156\pi$
$307$	−5421.20			−0.0575200			−0.0287600	+	0.999586i	$0.509156\pi$
$308$	97153.4	+	74488.4i	1.02413	+	0.785213i
$309$			107933.i			1.13042i
$310$	−14557.5	+	43458.3i	−0.151483	+	0.452219i
$311$	102588.	+	59229.5i	1.06066	+	0.612374i	0.925616	−	0.378465i	$-0.123548\pi$
$311$	102588.	+	59229.5i	1.06066	+	0.612374i	0.135048	+	0.990839i	$0.456881\pi$
$312$	−32071.8	+	2490.82i	−0.329468	+	0.0255878i
$313$	52842.7	+	91526.2i	0.539382	+	0.934236i	0.998937	+	0.0460875i	$0.0146753\pi$
$313$	52842.7	+	91526.2i	0.539382	+	0.934236i	−0.459556	+	0.888149i	$0.651991\pi$
$314$	−76656.1	+	67772.7i	−0.777477	+	0.687377i
$315$	−22.3611	+	2922.95i	−0.000225358	+	0.0294578i
$316$	−197447.	−	24381.3i	−1.97732	−	0.244164i
$317$	−17243.5	+	9955.53i	−0.171596	+	0.0990708i	−0.583338	−	0.812229i	$-0.698254\pi$
$317$	−17243.5	+	9955.53i	−0.171596	+	0.0990708i	0.411742	+	0.911300i	$0.364920\pi$
$318$	14220.0	+	70016.6i	0.140619	+	0.692383i
$319$	−132753.	−	76644.8i	−1.30455	−	0.753184i
$320$	14449.4	+	92464.2i	0.141108	+	0.902971i
$321$	−80893.0			−0.785057
$322$	−17702.3	+	15411.2i	−0.170733	+	0.148636i
$323$	−94483.8			−0.905634
$324$	−93443.1	+	39588.4i	−0.890137	+	0.377119i
$325$	−5061.85	−	2922.46i	−0.0479228	−	0.0276682i
$326$	20491.4	−	4161.69i	0.192813	−	0.0391593i
$327$	64600.3	−	37297.0i	0.604142	−	0.348801i
$328$	12414.7	−	8513.52i	0.115395	−	0.0791337i
$329$	132949.	+	78120.4i	1.22827	+	0.721726i
$330$	94661.9	−	83691.7i	0.869255	−	0.768519i
$331$	−37744.9	−	65376.1i	−0.344510	−	0.596709i	0.640754	−	0.767746i	$-0.278622\pi$
$331$	−37744.9	−	65376.1i	−0.344510	−	0.596709i	−0.985265	+	0.171037i	$0.945288\pi$
$332$	1990.88	+	1502.38i	0.0180621	+	0.0136303i
$333$	4031.70	+	2327.70i	0.0363579	+	0.0209913i
$334$	−150789.	−	50511.0i	−1.35169	−	0.452786i
$335$		−	24738.7i		−	0.220439i
$336$	−29648.0	−	107031.i	−0.262613	−	0.948051i
$337$	89399.3			0.787180			0.393590	−	0.919286i	$-0.371233\pi$
$337$	89399.3			0.787180			0.393590	+	0.919286i	$0.371233\pi$
$338$	32192.7	−	96104.0i	0.281789	−	0.841217i
$339$	−61537.1	+	106585.i	−0.535473	+	0.927467i
$340$	40866.2	−	54153.8i	0.353514	−	0.468458i
$341$	67815.5	−	39153.3i	0.583204	−	0.336713i
$342$	−3521.81	−	3983.44i	−0.0301102	−	0.0340570i
$343$	117618.	+	2699.83i	0.999737	+	0.0229481i
$344$	−168906.	+	115830.i	−1.42734	+	0.978821i
$345$	12112.2	+	20978.9i	0.101761	+	0.176256i
$346$	−18699.3	−	92072.1i	−0.156197	−	0.769087i
$347$	−38274.9	+	66294.1i	−0.317874	+	0.550574i	−0.980044	−	0.198779i	$-0.936302\pi$
$347$	−38274.9	+	66294.1i	−0.317874	+	0.550574i	0.662170	+	0.749354i	$0.269636\pi$
$348$	54248.6	+	128046.i	0.447950	+	1.05733i
$349$			176503.i			1.44911i	0.689216	+	0.724556i	$0.257955\pi$
$349$			176503.i			1.44911i	−0.689216	+	0.724556i	$0.742045\pi$
$350$	6555.87	−	19085.0i	0.0535173	−	0.155796i
$351$			42025.4i			0.341112i
$352$	86145.4	−	134710.i	0.695259	−	1.08721i
$353$	57092.3	−	98886.8i	0.458172	−	0.793577i	−0.540693	−	0.841220i	$-0.681838\pi$
$353$	57092.3	−	98886.8i	0.458172	−	0.793577i	0.998864	+	0.0476435i	$0.0151711\pi$
$354$	127784.	−	25952.2i	1.01970	−	0.207094i
$355$	−25994.6	−	45024.0i	−0.206266	−	0.357262i
$356$	17210.2	−	139373.i	0.135796	−	1.09971i
$357$	−40787.8	+	69414.8i	−0.320033	+	0.544647i
$358$	43018.5	+	48657.2i	0.335652	+	0.379648i
$359$	57826.8	−	33386.3i	0.448684	−	0.259048i	−0.258590	−	0.965987i	$-0.583258\pi$
$359$	57826.8	−	33386.3i	0.448684	−	0.259048i	0.707274	+	0.706939i	$0.249925\pi$
$360$	3806.38	−	295.618i	0.0293702	−	0.00228101i
$361$	−64444.0	+	111620.i	−0.494502	+	0.856503i
$362$	−80704.3	−	27034.1i	−0.615856	−	0.206298i
$363$	−86255.7			−0.654598
$364$	−44129.4	−	5792.28i	−0.333062	−	0.0437166i
$365$		−	195234.i		−	1.46544i
$366$	−79025.6	−	26471.8i	−0.589937	−	0.197616i
$367$	−95866.5	−	55348.5i	−0.711762	−	0.410936i	0.0999512	−	0.994992i	$-0.468131\pi$
$367$	−95866.5	−	55348.5i	−0.711762	−	0.410936i	−0.811713	+	0.584056i	$0.801465\pi$
$368$	22022.5	+	21325.5i	0.162619	+	0.157472i
$369$	−307.050	−	531.826i	−0.00225505	−	0.00390586i
$370$	107940.	+	122088.i	0.788456	+	0.891805i
$371$	−756.216	+	98849.2i	−0.00549412	+	0.718167i
$372$	−70504.1	−	8706.03i	−0.509482	−	0.0629121i
$373$	−173952.	+	100431.i	−1.25029	+	0.721857i	−0.971168	−	0.238397i	$-0.923378\pi$
$373$	−173952.	+	100431.i	−1.25029	+	0.721857i	−0.279126	+	0.960255i	$0.590045\pi$
$374$	−113596.	+	23070.6i	−0.812116	+	0.164936i
$375$	−127532.	−	73630.3i	−0.906891	−	0.523594i
$376$	86895.3	−	181697.i	0.614640	−	1.28521i
$377$	55729.8			0.392107
$378$	−142407.	+	27789.4i	−0.996662	+	0.194489i
$379$	−24930.1			−0.173559			−0.0867793	−	0.996228i	$-0.527657\pi$
$379$	−24930.1			−0.173559			−0.0867793	+	0.996228i	$0.527657\pi$
$380$	−72605.9	−	171376.i	−0.502811	−	1.18682i
$381$	−158288.	−	91387.9i	−1.09043	−	0.629562i
$382$	−16139.3	−	79466.9i	−0.110601	−	0.544577i
$383$	−199763.	+	115333.i	−1.36182	+	0.786244i	−0.989865	−	0.142009i	$-0.954644\pi$
$383$	−199763.	+	115333.i	−1.36182	+	0.786244i	−0.371950	+	0.928253i	$0.621311\pi$
$384$	−135996.	+	50473.9i	−0.922279	+	0.342298i
$385$	152064.	−	86250.0i	1.02590	−	0.581886i
$386$	131595.	+	148844.i	0.883210	+	0.998979i
$387$	4177.53	+	7235.69i	0.0278931	+	0.0483123i
$388$	−135147.	−	101986.i	−0.897725	−	0.677453i
$389$	230118.	+	132859.i	1.52073	+	0.877992i	0.999701	+	0.0244507i	$0.00778367\pi$
$389$	230118.	+	132859.i	1.52073	+	0.877992i	0.521025	+	0.853541i	$0.325550\pi$
$390$	−14591.0	+	43558.0i	−0.0959301	+	0.286378i
$391$		−	22223.0i		−	0.145361i
$392$	−9553.01	−	153367.i	−0.0621681	−	0.998066i
$393$	−174205.			−1.12791
$394$	166000.	+	55606.2i	1.06934	+	0.358204i
$395$	−142049.	+	246037.i	−0.910427	+	1.57691i
$396$	−5206.84	−	3929.25i	−0.0332035	−	0.0250564i
$397$	91360.2	−	52746.8i	0.579663	−	0.334669i	−0.181336	−	0.983421i	$-0.558042\pi$
$397$	91360.2	−	52746.8i	0.579663	−	0.334669i	0.761000	+	0.648752i	$0.224709\pi$
$398$	163864.	−	144875.i	1.03447	−	0.914589i
$399$	108972.	+	192124.i	0.684491	+	1.20680i
$400$	−25565.4	−	6411.52i	−0.159784	−	0.0400720i
$401$	−79917.5	−	138421.i	−0.496996	−	0.860823i	0.502998	−	0.864288i	$-0.332230\pi$
$401$	−79917.5	−	138421.i	−0.496996	−	0.860823i	−0.999994	+	0.00346478i	$0.998897\pi$
$402$	37578.1	−	7631.90i	0.232532	−	0.0472260i
$403$	−14234.5	+	24655.0i	−0.0876463	+	0.151808i
$404$	−33836.0	−	79865.2i	−0.207308	−	0.489322i
$405$			144920.i			0.883522i
$406$	36851.5	+	188846.i	0.223565	+	1.14566i
$407$		−	278431.i		−	1.68085i
$408$	94866.9	+	45369.4i	0.569894	+	0.272548i
$409$	−48043.3	+	83213.4i	−0.287201	+	0.497447i	−0.973141	−	0.230212i	$-0.926058\pi$
$409$	−48043.3	+	83213.4i	−0.287201	+	0.497447i	0.685940	+	0.727658i	$0.259391\pi$
$410$	−4278.46	−	21066.4i	−0.0254519	−	0.125321i
$411$	−71572.4	−	123967.i	−0.423703	−	0.733876i
$412$	193580.	+	23903.8i	1.14042	+	0.140823i
$413$	180405.	+	1380.14i	1.05767	+	0.00809137i
$414$	936.922	−	828.345i	0.00546642	−	0.00483293i
$415$	3084.50	−	1780.84i	0.0179097	−	0.0103402i
$416$	−2635.55	+	58073.0i	−0.0152295	+	0.335573i
$417$	−46626.2	+	80759.0i	−0.268138	+	0.464428i
$418$	−101007.	+	301535.i	−0.578097	+	1.72578i
$419$	160888.			0.916423			0.458212	−	0.888843i	$-0.348490\pi$
$419$	160888.			0.916423			0.458212	+	0.888843i	$0.348490\pi$
$420$	−157249.	−	20640.0i	−0.891434	−	0.117007i
$421$			287246.i			1.62065i	0.585980	+	0.810326i	$0.300710\pi$
$421$			287246.i			1.62065i	−0.585980	+	0.810326i	$0.699290\pi$
$422$	88879.6	−	265330.i	0.499088	−	1.48991i
$423$	−7115.57	−	4108.18i	−0.0397676	−	0.0229598i
$424$	128725.	−	9997.32i	0.716032	−	0.0556099i
$425$	9553.44	+	16547.0i	0.0528910	+	0.0916099i
$426$	60372.1	−	53375.7i	0.332673	−	0.294120i
$427$	−99418.0	−	58417.6i	−0.545267	−	0.320397i
$428$	−17915.2	+	145083.i	−0.0977992	+	0.792008i
$429$	67971.3	−	39243.2i	0.369327	−	0.213231i
$430$	58210.1	+	286616.i	0.314819	+	1.55011i
$431$	−19194.7	−	11082.1i	−0.103330	−	0.0596576i	0.447444	−	0.894312i	$-0.352334\pi$
$431$	−19194.7	−	11082.1i	−0.103330	−	0.0596576i	−0.550774	+	0.834654i	$0.685668\pi$
$432$	51985.3	+	182240.i	0.278556	+	0.976508i
$433$	151870.			0.810022			0.405011	−	0.914312i	$-0.367268\pi$
$433$	151870.			0.810022			0.405011	+	0.914312i	$0.367268\pi$
$434$	−92958.3	−	31931.9i	−0.493525	−	0.169530i
$435$	198585.			1.04947
$436$	−52585.9	−	124122.i	−0.276628	−	0.652944i
$437$	−52799.1	−	30483.5i	−0.276480	−	0.159626i
$438$	296560.	−	60229.6i	1.54584	−	0.313951i
$439$	245952.	−	142001.i	1.27621	−	0.736820i	0.300060	−	0.953920i	$-0.402993\pi$
$439$	245952.	−	142001.i	1.27621	−	0.736820i	0.976149	+	0.217100i	$0.0696598\pi$
$440$	−129138.	−	188313.i	−0.667036	−	0.972691i
$441$	−6267.96	−	95.9079i	−0.0322292	−	0.000493148i
$442$	31572.0	−	27913.2i	0.161606	−	0.142878i
$443$	−31778.5	−	55041.9i	−0.161929	−	0.280470i	0.773631	−	0.633636i	$-0.218438\pi$
$443$	−31778.5	−	55041.9i	−0.161929	−	0.280470i	−0.935561	+	0.353166i	$0.885105\pi$
$444$	−152153.	+	201625.i	−0.771815	+	1.02277i
$445$	−173672.	−	100269.i	−0.877020	−	0.506348i
$446$	−50390.7	−	16879.8i	−0.253327	−	0.0848588i
$447$			41454.5i			0.207471i
$448$	−198529.	+	29470.1i	−0.989161	+	0.146834i
$449$	61415.1			0.304637			0.152318	−	0.988331i	$-0.451326\pi$
$449$	61415.1			0.304637			0.152318	+	0.988331i	$0.451326\pi$
$450$	−341.527	+	1019.55i	−0.00168655	+	0.00503482i
$451$	−18364.1	+	31807.6i	−0.0902852	+	0.156379i
$452$	177534.	+	133973.i	0.868972	+	0.655754i
$453$	201273.	−	116205.i	0.980819	−	0.566276i
$454$	−29249.6	−	33083.6i	−0.141909	−	0.160510i
$455$	−32199.1	+	54798.1i	−0.155533	+	0.264693i
$456$	237922.	−	163158.i	1.14421	−	0.784655i
$457$	31000.6	+	53694.7i	0.148436	+	0.257098i	0.930649	−	0.365912i	$-0.119243\pi$
$457$	31000.6	+	53694.7i	0.148436	+	0.257098i	−0.782214	+	0.623010i	$0.785910\pi$
$458$	49202.9	+	242266.i	0.234563	+	1.15495i
$459$	68689.9	−	118974.i	0.326038	−	0.564714i
$460$	40308.5	−	17077.2i	0.190494	−	0.0807052i
$461$		−	310281.i		−	1.46000i	−0.683447	−	0.730000i	$-0.739520\pi$
$461$		−	310281.i		−	1.46000i	0.683447	−	0.730000i	$-0.260480\pi$
$462$	177926.	+	204377.i	0.833594	+	0.957522i
$463$		−	154072.i		−	0.718724i	−0.933198	−	0.359362i	$-0.882994\pi$
$463$		−	154072.i		−	0.718724i	0.933198	−	0.359362i	$-0.117006\pi$
$464$	241668.	−	68937.6i	1.12249	−	0.320199i
$465$	−50722.8	+	87854.5i	−0.234584	+	0.406311i
$466$	−330955.	+	67215.1i	−1.52404	+	0.309525i
$467$	−82179.2	−	142339.i	−0.376815	−	0.652663i	0.613782	−	0.789476i	$-0.289647\pi$
$467$	−82179.2	−	142339.i	−0.376815	−	0.652663i	−0.990597	+	0.136813i	$0.956314\pi$
$468$	2353.64	+	290.633i	0.0107460	+	0.00132695i
$469$	53052.7	+	405.864i	0.241191	+	0.00184516i
$470$	−190503.	−	215474.i	−0.862397	−	0.975438i
$471$	−196136.	+	113239.i	−0.884129	+	0.510452i
$472$	−18245.7	−	234931.i	−0.0818984	−	1.05452i
$473$	249851.	−	432754.i	1.11676	−	1.93428i
$474$	−417552.	−	139871.i	−1.85846	−	0.622544i
$475$	52418.2			0.232325
$476$	115464.	+	88526.9i	0.509602	+	0.390716i
$477$		−	5267.14i		−	0.0231493i
$478$	245044.	+	82084.3i	1.07248	+	0.359256i
$479$	−155445.	−	89746.1i	−0.677493	−	0.391151i	0.121417	−	0.992602i	$-0.461256\pi$
$479$	−155445.	−	89746.1i	−0.677493	−	0.391151i	−0.798910	+	0.601451i	$0.794590\pi$
$480$	−9391.43	+	206935.i	−0.0407614	+	0.898156i
$481$	50613.1	+	87664.5i	0.218763	+	0.378908i
$482$	−159425.	−	180322.i	−0.686217	−	0.776164i
$483$	−45188.3	+	25630.6i	−0.193701	+	0.109866i
$484$	−19102.9	+	154701.i	−0.0815472	+	0.660394i
$485$	−209386.	+	120889.i	−0.890151	+	0.513929i
$486$	14916.1	−	3029.37i	0.0631512	−	0.0128257i
$487$	169310.	+	97751.1i	0.713878	+	0.412158i	0.812495	−	0.582968i	$-0.198109\pi$
$487$	169310.	+	97751.1i	0.713878	+	0.412158i	−0.0986171	+	0.995125i	$0.531442\pi$
$488$	−64979.4	+	135871.i	−0.272858	+	0.570542i
$489$	46282.5			0.193553
$490$	−206980.	−	72874.4i	−0.862059	−	0.303517i
$491$	280280.			1.16260			0.581299	−	0.813690i	$-0.302545\pi$
$491$	280280.			1.16260			0.581299	+	0.813690i	$0.302545\pi$
$492$	30679.9	−	12998.0i	0.126743	−	0.0536964i
$493$	−157772.	−	91089.6i	−0.649136	−	0.374779i
$494$	−23010.5	−	113300.i	−0.0942916	−	0.464275i
$495$	−8067.04	+	4657.51i	−0.0329233	+	0.0190083i
$496$	−31228.9	+	124522.i	−0.126938	+	0.506156i
$497$	96981.4	−	55007.3i	0.392623	−	0.222694i
$498$	3656.66	+	4135.97i	0.0147444	+	0.0166770i
$499$	66200.3	+	114662.i	0.265864	+	0.460489i	0.967789	−	0.251761i	$-0.0810096\pi$
$499$	66200.3	+	114662.i	0.265864	+	0.460489i	−0.701926	+	0.712250i	$0.747676\pi$
$500$	−160302.	+	212423.i	−0.641207	+	0.849694i
$501$	−304833.	−	175996.i	−1.21447	−	0.701175i
$502$	85460.6	−	255123.i	0.339124	−	1.01238i
$503$			503435.i			1.98979i	0.100918	+	0.994895i	$0.467822\pi$
$503$			503435.i			1.98979i	−0.100918	+	0.994895i	$0.532178\pi$
$504$	571.512	+	8167.71i	0.00224991	+	0.0321543i
$505$	−123862.			−0.485686
$506$	−70922.3	−	23757.4i	−0.277001	−	0.0927893i
$507$	112169.	−	194282.i	0.436372	−	0.755818i
$508$	−198962.	+	263654.i	−0.770979	+	1.02166i
$509$	122732.	−	70859.5i	0.473722	−	0.273503i	−0.244075	−	0.969756i	$-0.578484\pi$
$509$	122732.	−	70859.5i	0.473722	−	0.273503i	0.717796	+	0.696253i	$0.245151\pi$
$510$	112502.	−	99464.7i	0.432535	−	0.382410i
$511$	418683.	+	3203.01i	1.60340	+	0.0122664i
$512$	60407.3	+	255089.i	0.230435	+	0.973088i
$513$	−188445.	−	326397.i	−0.716063	−	1.24026i
$514$	29000.2	−	5889.78i	0.109768	−	0.0222932i
$515$	139268.	−	241219.i	0.525092	−	0.909487i
$516$	−417412.	+	176842.i	−1.56771	+	0.664182i
$517$			491405.i			1.83848i
$518$	−263591.	+	229476.i	−0.982362	+	0.855219i
$519$		−	207957.i		−	0.772037i
$520$	74890.8	+	35815.9i	0.276963	+	0.132455i
$521$	−96305.6	+	166806.i	−0.354794	+	0.614521i	−0.987083	−	0.160212i	$-0.948782\pi$
$521$	−96305.6	+	166806.i	−0.354794	+	0.614521i	0.632289	+	0.774733i	$0.282116\pi$
$522$	−2040.48	−	10047.0i	−0.00748844	−	0.0368717i
$523$	−219141.	−	379563.i	−0.801161	−	1.38765i	−0.918853	−	0.394601i	$-0.870883\pi$
$523$	−219141.	−	379563.i	−0.801161	−	1.38765i	0.117692	−	0.993050i	$-0.462451\pi$
$524$	−38580.9	+	312440.i	−0.140511	+	1.13790i
$525$	22628.5	−	38510.3i	0.0820988	−	0.139720i
$526$	−103145.	+	91191.7i	−0.372800	+	0.329597i
$527$	80596.4	−	46532.4i	0.290198	−	0.167546i
$528$	246208.	−	254255.i	0.883151	−	0.912016i
$529$	−132751.	+	229931.i	−0.474379	+	0.821648i
$530$	58563.3	−	174827.i	0.208484	−	0.622383i
$531$	−9612.82			−0.0340927
$532$	368711.	−	152893.i	1.30276	−	0.540213i
$533$		−	13352.9i		−	0.0470024i
$534$	98731.6	−	294741.i	0.346237	−	1.03361i
$535$	180787.	+	104377.i	0.631625	+	0.364669i
$536$	−5365.59	−	69087.3i	−0.0186762	−	0.240474i
$537$	71878.2	+	124497.i	0.249258	+	0.431727i
$538$	−123917.	+	109556.i	−0.428119	+	0.378506i
$539$	182470.	+	327520.i	0.628079	+	1.12735i
$540$	268582.	+	33165.3i	0.921065	+	0.113735i
$541$	5879.67	−	3394.63i	0.0200890	−	0.0115984i	−0.489922	−	0.871766i	$-0.662975\pi$
$541$	5879.67	−	3394.63i	0.0200890	−	0.0115984i	0.510011	+	0.860168i	$0.329641\pi$
$542$	40338.4	+	198619.i	0.137316	+	0.676117i
$543$	−163151.	−	94195.0i	−0.553336	−	0.319469i
$544$	102381.	−	160098.i	0.345956	−	0.540988i
$545$	−192499.			−0.648091
$546$	−93171.8	−	32005.3i	−0.312535	−	0.107358i
$547$	−380486.			−1.27164			−0.635820	−	0.771837i	$-0.719338\pi$
$547$	−380486.			−1.27164			−0.635820	+	0.771837i	$0.719338\pi$
$548$	−238188.	+	100912.i	−0.793157	+	0.336032i
$549$	5320.95	+	3072.05i	0.0176540	+	0.0101926i
$550$	63021.2	−	12799.2i	0.208334	−	0.0423115i
$551$	−432835.	+	249897.i	−1.42567	+	0.823111i
$552$	38375.5	+	55960.2i	0.125943	+	0.183654i
$553$	−525301.	−	308664.i	−1.71774	−	1.00934i
$554$	136302.	−	120506.i	0.444102	−	0.392636i
$555$	180353.	+	312380.i	0.585514	+	1.01414i
$556$	134517.	+	101511.i	0.435137	+	0.328369i
$557$	−219883.	−	126950.i	−0.708731	−	0.409186i	0.101860	−	0.994799i	$-0.467521\pi$
$557$	−219883.	−	126950.i	−0.708731	−	0.409186i	−0.810591	+	0.585612i	$0.800854\pi$
$558$	4965.97	+	1663.49i	0.0159491	+	0.00534259i
$559$			181671.i			0.581382i
$560$	−71843.9	+	277458.i	−0.229094	+	0.884751i
$561$	−256570.			−0.815231
$562$	−192227.	+	573849.i	−0.608612	+	1.81687i
$563$	118636.	−	205484.i	0.374284	−	0.648278i	−0.615936	−	0.787796i	$-0.711222\pi$
$563$	118636.	−	205484.i	0.374284	−	0.648278i	0.990220	+	0.139518i	$0.0445553\pi$
$564$	268535.	−	355849.i	0.844195	−	1.11868i
$565$	275057.	−	158804.i	0.861640	−	0.497468i
$566$	686.557	+	776.550i	0.00214311	+	0.00242402i
$567$	−310783.	−	2377.55i	−0.966700	−	0.00739545i
$568$	−82359.9	−	120100.i	−0.255281	−	0.372259i
$569$	154203.	+	267087.i	0.476286	+	0.824952i	0.999631	−	0.0271692i	$-0.00864928\pi$
$569$	154203.	+	267087.i	0.476286	+	0.824952i	−0.523345	+	0.852121i	$0.675316\pi$
$570$	−81994.9	−	403728.i	−0.252370	−	1.24262i
$571$	−120713.	+	209082.i	−0.370240	+	0.641274i	−0.989602	−	0.143831i	$-0.954058\pi$
$571$	−120713.	+	209082.i	−0.370240	+	0.641274i	0.619363	+	0.785105i	$0.287391\pi$
$572$	−55330.0	−	130599.i	−0.169110	−	0.399160i
$573$		−	179486.i		−	0.546666i
$574$	45247.5	−	8829.64i	0.137332	−	0.0267990i
$575$			12329.0i			0.0372900i
$576$	10565.9	−	1651.14i	0.0318464	−	0.00497666i
$577$	−55637.9	+	96367.7i	−0.167116	+	0.289454i	−0.937405	−	0.348242i	$-0.886779\pi$
$577$	−55637.9	+	96367.7i	−0.167116	+	0.289454i	0.770288	+	0.637696i	$0.220112\pi$
$578$	192396.	−	39074.5i	0.575890	−	0.116960i
$579$	219878.	+	380839.i	0.655879	+	1.13602i
$580$	43980.4	−	356167.i	0.130738	−	1.05876i
$581$	3768.44	+	6643.99i	0.0111637	+	0.0196823i
$582$	−248226.	−	280763.i	−0.732826	−	0.828884i
$583$	−272814.	+	157509.i	−0.802656	+	0.463413i
$584$	−42344.3	−	545225.i	−0.124156	−	1.59864i
$585$	1693.28	−	2932.85i	0.00494786	−	0.00856994i
$586$	606825.	+	203273.i	1.76713	+	0.591949i
$587$	269391.			0.781821			0.390911	−	0.920429i	$-0.372160\pi$
$587$	269391.			0.781821			0.390911	+	0.920429i	$0.372160\pi$
$588$	46842.7	−	336885.i	0.135484	−	0.974377i
$589$		−	255316.i		−	0.735948i
$590$	−319070.	−	106881.i	−0.916604	−	0.307042i
$591$	335582.	+	193749.i	0.960781	+	0.554707i
$592$	327921.	+	317542.i	0.935675	+	0.906061i
$593$	−42445.8	−	73518.4i	−0.120705	−	0.209067i	0.799341	−	0.600878i	$-0.205182\pi$
$593$	−42445.8	−	73518.4i	−0.120705	−	0.209067i	−0.920046	+	0.391810i	$0.871849\pi$
$594$	−306261.	−	346405.i	−0.867999	−	0.981775i
$595$	180723.	−	102505.i	0.510481	−	0.289542i
$596$	74349.5	+	9180.87i	0.209308	+	0.0258459i
$597$	419271.	−	242066.i	1.17638	−	0.679181i
$598$	26648.6	−	5412.18i	0.0745199	−	0.0151346i
$599$	−112218.	−	64789.3i	−0.312759	−	0.180572i	0.335401	−	0.942075i	$-0.391128\pi$
$599$	−112218.	−	64789.3i	−0.312759	−	0.180572i	−0.648161	+	0.761504i	$0.724461\pi$
$600$	−52630.8	−	25170.3i	−0.146197	−	0.0699174i
$601$	−184056.			−0.509567			−0.254783	−	0.966998i	$-0.582004\pi$
$601$	−184056.			−0.509567			−0.254783	+	0.966998i	$0.582004\pi$
$602$	−615609.	+	120131.i	−1.69868	+	0.331482i
$603$	−2826.89			−0.00777454
$604$	−163840.	−	386722.i	−0.449104	−	1.06005i
$605$	192772.	+	111297.i	0.526663	+	0.304069i
$606$	−38211.5	−	188146.i	−0.104052	−	0.512331i
$607$	151789.	−	87635.2i	0.411966	−	0.237849i	−0.279668	−	0.960097i	$-0.590224\pi$
$607$	151789.	−	87635.2i	0.411966	−	0.237849i	0.691634	+	0.722248i	$0.256891\pi$
$608$	−239935.	−	462852.i	−0.649062	−	1.25209i
$609$	−3258.00	+	425871.i	−0.00878448	+	1.14827i
$610$	142456.	+	161129.i	0.382844	+	0.433027i
$611$	−89327.5	−	154720.i	−0.239278	−	0.414441i
$612$	−6188.15	−	4669.78i	−0.0165218	−	0.0124679i
$613$	63503.2	+	36663.6i	0.168995	+	0.0975695i	0.582112	−	0.813109i	$-0.302226\pi$
$613$	63503.2	+	36663.6i	0.168995	+	0.0975695i	−0.413117	+	0.910678i	$0.635560\pi$
$614$	−6887.76	+	20561.8i	−0.0182701	+	0.0545413i
$615$		−	47581.1i		−	0.125801i
$616$	405960.	−	273850.i	1.06985	−	0.721691i
$617$	77651.3			0.203976			0.101988	−	0.994786i	$-0.467480\pi$
$617$	77651.3			0.203976			0.101988	+	0.994786i	$0.467480\pi$
$618$	409375.	+	137132.i	1.07188	+	0.359055i
$619$	2997.08	−	5191.09i	0.00782199	−	0.0135481i	−0.862088	−	0.506759i	$-0.830843\pi$
$619$	2997.08	−	5191.09i	0.00782199	−	0.0135481i	0.869910	+	0.493211i	$0.164177\pi$
$620$	146335.	+	110429.i	0.380685	+	0.287277i
$621$	76770.0	−	44323.2i	0.199071	−	0.114934i
$622$	354990.	−	313851.i	0.917561	−	0.811227i
$623$	217879.	−	370798.i	0.561358	−	0.955347i
$624$	−31300.6	+	124808.i	−0.0803865	+	0.320534i
$625$	157838.	+	273384.i	0.404066	+	0.699863i
$626$	414284.	−	84138.7i	1.05718	−	0.214707i
$627$	−351940.	+	609578.i	−0.895228	+	1.55058i
$628$	159659.	+	376853.i	0.404831	+	0.955547i
$629$		−	330906.i		−	0.836379i
$630$	11057.9	+	3798.49i	0.0278607	+	0.00957039i
$631$			112623.i			0.282857i	0.989948	+	0.141429i	$0.0451696\pi$
$631$			112623.i			0.282857i	−0.989948	+	0.141429i	$0.954830\pi$
$632$	−343335.	+	717911.i	−0.859576	+	1.79737i
$633$	309683.	−	536387.i	0.772876	−	1.33866i
$634$	15851.7	+	78050.8i	0.0394363	+	0.194177i
$635$	235838.	+	408483.i	0.584879	+	1.01304i
$636$	283630.	+	35023.3i	0.701193	+	0.0865851i
$637$	−116987.	−	69950.7i	−0.288310	−	0.172391i
$638$	−459368.	+	406133.i	−1.12855	+	0.997762i
$639$	−5144.89	+	2970.40i	−0.0126001	+	0.00727467i
$640$	369062.	+	62673.3i	0.901030	+	0.153011i
$641$	−126822.	+	219663.i	−0.308659	+	0.534614i	−0.978069	−	0.208279i	$-0.933214\pi$
$641$	−126822.	+	219663.i	−0.308659	+	0.534614i	0.669410	+	0.742893i	$0.266547\pi$
$642$	−102776.	+	306816.i	−0.249358	+	0.744402i
$643$	−215232.			−0.520576			−0.260288	−	0.965531i	$-0.583818\pi$
$643$	−215232.			−0.520576			−0.260288	+	0.965531i	$0.583818\pi$
$644$	35961.2	+	86722.5i	0.0867086	+	0.209103i
$645$			647359.i			1.55606i
$646$	−120044.	+	358364.i	−0.287657	+	0.858735i
$647$	196020.	+	113172.i	0.468266	+	0.270354i	0.715514	−	0.698599i	$-0.246193\pi$
$647$	196020.	+	113172.i	0.468266	+	0.270354i	−0.247248	+	0.968952i	$0.579526\pi$
$648$	31431.7	+	404714.i	0.0748545	+	0.963826i
$649$	287463.	+	497901.i	0.682484	+	1.18210i
$650$	−17515.7	+	15485.8i	−0.0414572	+	0.0366528i
$651$	−187574.	−	110218.i	−0.442599	−	0.260069i
$652$	10250.1	−	83008.5i	0.0241120	−	0.195266i
$653$	68023.7	−	39273.5i	0.159527	−	0.0921029i	−0.418111	−	0.908396i	$-0.637308\pi$
$653$	68023.7	−	39273.5i	0.159527	−	0.0921029i	0.577638	+	0.816293i	$0.303974\pi$
$654$	−59386.1	−	292406.i	−0.138845	−	0.683646i
$655$	389329.	+	224779.i	0.907473	+	0.523930i
$656$	−16517.5	−	57903.7i	−0.0383827	−	0.134555i
$657$	−22309.3			−0.0516839
$658$	465214.	−	405004.i	1.07449	−	0.935421i
$659$	417721.			0.961868			0.480934	−	0.876757i	$-0.340298\pi$
$659$	417721.			0.961868			0.480934	+	0.876757i	$0.340298\pi$
$660$	−197161.	−	465371.i	−0.452619	−	1.06835i
$661$	−65859.8	−	38024.2i	−0.150736	−	0.0870276i	0.422735	−	0.906253i	$-0.361070\pi$
$661$	−65859.8	−	38024.2i	−0.150736	−	0.0870276i	−0.573471	+	0.819226i	$0.694404\pi$
$662$	−295918.	+	60099.2i	−0.675236	+	0.137136i
$663$	80781.5	−	46639.2i	0.183774	−	0.106102i
$664$	8227.77	−	5642.31i	0.0186615	−	0.0127974i
$665$	4360.48	−	569982.i	0.00986032	−	1.28890i
$666$	13951.0	−	12334.3i	0.0314526	−	0.0278077i
$667$	−58776.9	−	101805.i	−0.132116	−	0.228832i
$668$	−383162.	+	507747.i	−0.858677	+	1.13787i
$669$	−101869.	−	58814.2i	−0.227609	−	0.131410i
$670$	−93830.5	−	31431.1i	−0.209023	−	0.0700181i
$671$		−	367468.i		−	0.816158i
$672$	−443623.	−	23535.1i	−0.982370	−	0.0521168i
$673$	101557.			0.224223			0.112112	−	0.993696i	$-0.464239\pi$
$673$	101557.			0.224223			0.112112	+	0.993696i	$0.464239\pi$
$674$	113584.	−	339079.i	0.250033	−	0.746416i
$675$	−38108.2	+	66005.3i	−0.0836393	+	0.144868i
$676$	−323607.	−	244205.i	−0.708149	−	0.534392i
$677$	−674994.	+	389708.i	−1.47273	+	0.850280i	−0.999529	−	0.0306750i	$-0.990234\pi$
$677$	−674994.	+	389708.i	−1.47273	+	0.850280i	−0.473199	+	0.880955i	$0.656901\pi$
$678$	326079.	+	368821.i	0.709355	+	0.802335i
$679$	−255814.	−	451015.i	−0.554861	−	0.978255i
$680$	−153476.	−	223803.i	−0.331912	−	0.484004i
$681$	−48872.3	−	84649.2i	−0.105382	−	0.182528i
$682$	−62341.8	−	306960.i	−0.134033	−	0.659953i
$683$	3932.13	−	6810.65i	0.00842920	−	0.0145998i	−0.861780	−	0.507282i	$-0.830650\pi$
$683$	3932.13	−	6810.65i	0.00842920	−	0.0145998i	0.870209	+	0.492682i	$0.163984\pi$
$684$	−19583.2	+	8296.67i	−0.0418572	+	0.0177334i
$685$			369403.i			0.787263i
$686$	159676.	−	442678.i	0.339307	−	0.940676i
$687$			547189.i			1.15938i
$688$	224726.	+	787802.i	0.474763	+	1.66433i
$689$	57263.9	−	99184.0i	0.120626	−	0.208931i
$690$	94958.6	−	19285.6i	0.199451	−	0.0405074i
$691$	−326474.	−	565469.i	−0.683742	−	1.18428i	−0.973830	−	0.227276i	$-0.927018\pi$
$691$	−326474.	−	565469.i	−0.683742	−	1.18428i	0.290088	−	0.957000i	$-0.406315\pi$
$692$	−372974.	−	46055.8i	−0.778873	−	0.0961773i
$693$	−9855.78	−	17376.4i	−0.0205222	−	0.0361820i
$694$	202815.	+	229399.i	0.421096	+	0.476292i
$695$	208409.	−	120325.i	0.431466	−	0.249107i
$696$	554586.	−	43071.3i	1.14485	−	0.0889139i
$697$	−21825.1	+	37802.2i	−0.0449253	+	0.0778129i
$698$	669452.	+	224251.i	1.37407	+	0.460282i
$699$	−747505.			−1.52989
$700$	−64057.5	−	49113.4i	−0.130729	−	0.100232i
$701$			107649.i			0.219065i	0.993983	+	0.109532i	$0.0349353\pi$
$701$			107649.i			0.219065i	−0.993983	+	0.109532i	$0.965065\pi$
$702$	159396.	+	53394.2i	0.323448	+	0.108348i
$703$	−786191.	−	453907.i	−1.59081	−	0.918452i
$704$	−401485.	−	497889.i	−0.810072	−	1.00459i
$705$	−318306.	−	551322.i	−0.640423	−	1.10924i
$706$	−302526.	−	342181.i	−0.606952	−	0.686509i
$707$	2032.08	−	265625.i	0.00406539	−	0.531410i
$708$	63919.6	−	517640.i	0.127517	−	1.03267i
$709$	−368435.	+	212716.i	−0.732941	+	0.423164i	−0.819497	−	0.573083i	$-0.805747\pi$
$709$	−368435.	+	212716.i	−0.732941	+	0.423164i	0.0865562	+	0.996247i	$0.472414\pi$
$710$	−203796.	+	41389.9i	−0.404278	+	0.0821065i
$711$	28114.6	+	16232.0i	0.0556151	+	0.0321094i
$712$	−506757.	−	242353.i	−0.999632	−	0.478066i
$713$	60051.4			0.118126
$714$	211459.	+	242895.i	0.414790	+	0.476456i
$715$	−202544.			−0.396194
$716$	239206.	−	101343.i	0.466601	−	0.197682i
$717$	495377.	+	286006.i	0.963602	+	0.556336i
$718$	−53159.3	−	261747.i	−0.103117	−	0.507730i
$719$	42026.4	−	24264.0i	0.0812952	−	0.0469358i	−0.458801	−	0.888539i	$-0.651721\pi$
$719$	42026.4	−	24264.0i	0.0812952	−	0.0469358i	0.540097	+	0.841603i	$0.318388\pi$
$720$	3714.85	−	14812.6i	0.00716600	−	0.0285738i
$721$	515014.	+	302620.i	0.990714	+	0.582139i
$722$	341482.	+	386243.i	0.655079	+	0.740946i
$723$	−266378.	−	461379.i	−0.509590	−	0.882636i
$724$	−205073.	+	271752.i	−0.391230	+	0.518437i
$725$	87529.5	+	50535.2i	0.166525	+	0.0961431i
$726$	−109590.	+	327156.i	−0.207920	+	0.620699i
$727$		−	43615.9i		−	0.0825232i	−0.999148	−	0.0412616i	$-0.986862\pi$
$727$		−	43615.9i		−	0.0825232i	0.999148	−	0.0412616i	$-0.0131377\pi$
$728$	−78036.7	+	160017.i	−0.147243	+	0.301928i
$729$	547449.			1.03012
$730$	−740493.	−	248049.i	−1.38955	−	0.465469i
$731$	296939.	−	514313.i	0.555690	−	0.962483i
$732$	−200808.	+	266100.i	−0.374764	+	0.496618i
$733$	−383469.	+	221396.i	−0.713711	+	0.412061i	−0.812434	−	0.583054i	$-0.801858\pi$
$733$	−383469.	+	221396.i	−0.713711	+	0.412061i	0.0987225	+	0.995115i	$0.468524\pi$
$734$	−331730.	+	293286.i	−0.615733	+	0.544377i
$735$	−416869.	−	249260.i	−0.771657	−	0.461400i
$736$	108865.	−	56433.7i	0.200970	−	0.104180i
$737$	84535.7	+	146420.i	0.155634	+	0.269566i
$738$	−2407.25	+	488.899i	−0.00441987	+	0.000897649i
$739$	−32621.6	+	56502.2i	−0.0597332	+	0.103461i	−0.894346	−	0.447377i	$-0.852358\pi$
$739$	−32621.6	+	56502.2i	−0.0597332	+	0.103461i	0.834612	+	0.550838i	$0.185692\pi$
$740$	600203.	−	254284.i	1.09606	−	0.464361i
$741$		−	255902.i		−	0.466055i
$742$	373960.	+	128458.i	0.679231	+	0.233321i
$743$		−	83279.8i		−	0.150856i	−0.997151	−	0.0754279i	$-0.975968\pi$
$743$		−	83279.8i		−	0.150856i	0.997151	−	0.0754279i	$-0.0240323\pi$
$744$	−122598.	+	256351.i	−0.221481	+	0.463115i
$745$	53489.3	−	92646.2i	0.0963728	−	0.166923i
$746$	159912.	+	787376.i	0.287344	+	1.41483i
$747$	−203.496	−	352.466i	−0.000364682	−	0.000631648i
$748$	−56822.2	+	460164.i	−0.101558	+	0.822449i
$749$	−226805.	+	385989.i	−0.404287	+	0.688036i
$750$	−441301.	+	390160.i	−0.784535	+	0.693618i
$751$	599685.	−	346228.i	1.06327	−	0.613879i	0.136935	−	0.990580i	$-0.456275\pi$
$751$	599685.	−	346228.i	1.06327	−	0.613879i	0.926335	+	0.376701i	$0.122942\pi$
$752$	−578749.	−	560432.i	−1.02342	−	0.991031i
$753$	297770.	−	515753.i	0.525160	−	0.909603i
$754$	70806.0	−	211375.i	0.124545	−	0.371802i
$755$	−599763.			−1.05217
$756$	−75530.0	+	575437.i	−0.132153	+	1.00682i
$757$		−	802762.i		−	1.40086i	−0.713720	−	0.700431i	$-0.752991\pi$
$757$		−	802762.i		−	1.40086i	0.713720	−	0.700431i	$-0.247009\pi$
$758$	−31674.3	+	94556.5i	−0.0551275	+	0.164571i
$759$	−143375.	−	82777.9i	−0.248881	−	0.143691i
$760$	−742253.	+	57646.3i	−1.28506	+	0.0998032i
$761$	123294.	+	213551.i	0.212898	+	0.368750i	0.952620	−	0.304162i	$-0.0983764\pi$
$761$	123294.	+	213551.i	0.212898	+	0.368750i	−0.739722	+	0.672912i	$0.765043\pi$
$762$	−547730.	+	484255.i	−0.943315	+	0.833997i
$763$	3158.14	−	412819.i	0.00542479	−	0.709104i
$764$	−321912.	−	39750.5i	−0.551506	−	0.0681014i
$765$	−9587.40	+	5535.29i	−0.0163824	+	0.00945840i
$766$	183639.	+	904208.i	0.312974	+	1.54103i
$767$	−181016.	−	104510.i	−0.307700	−	0.177650i
$768$	18655.0	+	579940.i	0.0316281	+	0.983243i
$769$	683555.			1.15590			0.577951	−	0.816072i	$-0.303853\pi$
$769$	683555.			1.15590			0.577951	+	0.816072i	$0.303853\pi$
$770$	−133933.	−	686340.i	−0.225895	−	1.15760i
$771$	65500.7			0.110189
$772$	731738.	−	310011.i	1.22778	−	0.520166i
$773$	885806.	+	511420.i	1.48245	+	0.855892i	0.999802	−	0.0199237i	$-0.00634232\pi$
$773$	885806.	+	511420.i	1.48245	+	0.855892i	0.482646	+	0.875815i	$0.339676\pi$
$774$	32751.6	−	6651.66i	0.0546702	−	0.0111032i
$775$	−44713.7	+	25815.5i	−0.0744453	+	0.0429810i
$776$	−558528.	+	383018.i	−0.927516	+	0.636056i
$777$	−672865.	+	381646.i	−1.11452	+	0.632147i
$778$	796284.	−	704004.i	1.31555	−	1.16310i
$779$	59875.5	+	103707.i	0.0986675	+	0.170897i
$780$	146671.	+	110683.i	0.241077	+	0.181925i
$781$	307707.	+	177655.i	0.504469	+	0.291256i
$782$	−84288.7	−	28234.8i	−0.137834	−	0.0461713i
$783$		−	726703.i		−	1.18531i
$784$	−593836.	−	158623.i	−0.966127	−	0.258068i
$785$	584456.			0.948446
$786$	−221332.	+	660735.i	−0.358260	+	1.06950i
$787$	122136.	−	211546.i	0.197195	−	0.341551i	−0.750423	−	0.660958i	$-0.770150\pi$
$787$	122136.	−	211546.i	0.197195	−	0.341551i	0.947618	+	0.319407i	$0.103484\pi$
$788$	421813.	−	558964.i	0.679309	−	0.900185i
$789$	−263911.	+	152369.i	−0.423940	+	0.244762i
$790$	752705.	+	851368.i	1.20607	+	1.36415i
$791$	336047.	+	592471.i	0.537089	+	0.946922i
$792$	−21518.5	+	14756.6i	−0.0343053	+	0.0235253i
$793$	66798.1	+	115698.i	0.106223	+	0.183983i
$794$	−83986.0	−	413532.i	−0.133219	−	0.655946i
$795$	204052.	−	353428.i	0.322854	−	0.559200i
$796$	−341295.	−	805581.i	−0.538647	−	1.27140i
$797$		−	374969.i		−	0.590308i	−0.955450	−	0.295154i	$-0.904629\pi$
$797$		−	374969.i		−	0.590308i	0.955450	−	0.295154i	$-0.0953710\pi$
$798$	867149.	−	169216.i	1.36172	−	0.265727i
$799$			584018.i			0.914814i
$800$	−56799.4	+	88819.8i	−0.0887490	+	0.138781i
$801$	−11457.8	+	19845.5i	−0.0178581	+	0.0309312i
$802$	−626549.	+	127249.i	−0.974106	+	0.197835i
$803$	667141.	+	1.15552e6i	1.03463	+	1.79204i
$804$	18797.1	−	152225.i	0.0290790	−	0.235491i
$805$	134062.	+	1025.60i	0.206878	+	0.00158266i
$806$	75427.4	+	85314.3i	0.116107	+	0.131326i
$807$	−317059.	+	183054.i	−0.486847	+	0.281081i
$808$	−345907.	+	26864.5i	−0.529830	+	0.0411487i
$809$	387718.	−	671547.i	0.592405	−	1.02608i	−0.401503	−	0.915858i	$-0.631512\pi$
$809$	387718.	−	671547.i	0.592405	−	1.02608i	0.993908	−	0.110217i	$-0.0351547\pi$
$810$	549660.	+	184124.i	0.837768	+	0.280634i
$811$	710759.			1.08064			0.540319	−	0.841460i	$-0.318303\pi$
$811$	710759.			1.08064			0.540319	+	0.841460i	$0.318303\pi$
$812$	763086.	+	100160.i	1.15734	+	0.151909i
$813$			448606.i			0.678710i
$814$	−1.05605e6	−	353753.i	−1.59381	−	0.533890i
$815$	−103436.	−	59718.9i	−0.155725	−	0.0899076i
$816$	292610.	−	302174.i	0.439449	−	0.453813i
$817$	−814629.	−	1.41098e6i	−1.22044	−	2.11386i
$818$	254576.	+	287946.i	0.380462	+	0.430332i
$819$	6261.77	+	3679.39i	0.00933533	+	0.00548540i
$820$	−85337.7	−	10537.7i	−0.126915	−	0.0156718i
$821$	119625.	−	69065.3i	0.177474	−	0.102465i	−0.408631	−	0.912699i	$-0.633994\pi$
$821$	119625.	−	69065.3i	0.177474	−	0.102465i	0.586105	+	0.810235i	$0.300661\pi$
$822$	−561124.	+	113961.i	−0.830453	+	0.168660i
$823$	46567.3	+	26885.6i	0.0687514	+	0.0396936i	0.533982	−	0.845496i	$-0.320695\pi$
$823$	46567.3	+	26885.6i	0.0687514	+	0.0396936i	−0.465230	+	0.885190i	$0.654028\pi$
$824$	336612.	−	703852.i	0.495764	−	1.03664i
$825$	142341.			0.209133
$826$	234444.	−	682498.i	0.343620	−	1.00033i
$827$	−621540.			−0.908779			−0.454390	−	0.890803i	$-0.650143\pi$
$827$	−621540.			−0.908779			−0.454390	+	0.890803i	$0.650143\pi$
$828$	−1951.41	−	4606.04i	−0.00284635	−	0.00671842i
$829$	−77797.1	−	44916.2i	−0.113202	−	0.0653573i	0.442330	−	0.896852i	$-0.354152\pi$
$829$	−77797.1	−	44916.2i	−0.113202	−	0.0653573i	−0.555532	+	0.831495i	$0.687485\pi$
$830$	−2835.53	−	13961.7i	−0.00411603	−	0.0202666i
$831$	348749.	−	201350.i	0.505023	−	0.291575i
$832$	216914.	+	83779.3i	0.313358	+	0.121029i
$833$	216860.	+	389246.i	0.312528	+	0.560963i
$834$	247068.	+	279453.i	0.355209	+	0.401769i
$835$	454179.	+	786661.i	0.651409	+	1.12827i
$836$	1.01535e6	+	766214.i	1.45279	+	1.09632i
$837$	321495.	+	185615.i	0.458905	+	0.264949i
$838$	204412.	−	610226.i	0.291084	−	0.868966i
$839$		−	652138.i		−	0.926436i	−0.886244	−	0.463218i	$-0.846695\pi$
$839$		−	652138.i		−	0.926436i	0.886244	−	0.463218i	$-0.153305\pi$
$840$	−278073.	+	570199.i	−0.394094	+	0.808106i
$841$	−256400.			−0.362514
$842$	1.08948e6	+	364952.i	1.53673	+	0.514769i
$843$	−669775.	+	1.16008e6i	−0.942483	+	1.63243i
$844$	−893435.	−	674215.i	−1.25423	−	0.946485i
$845$	−501370.	+	289466.i	−0.702174	+	0.405400i
$846$	−24622.2	+	21768.8i	−0.0344022	+	0.0304154i
$847$	−241841.	+	411577.i	−0.337103	+	0.573700i
$848$	125630.	−	500939.i	0.174704	−	0.696615i
$849$	1147.15	+	1986.92i	0.00159149	+	0.00275654i
$850$	74898.5	−	15211.4i	0.103666	−	0.0210539i
$851$	106761.	−	184915.i	0.147419	−	0.255337i
$852$	−125742.	−	296798.i	−0.173222	−	0.408867i
$853$		−	782387.i		−	1.07528i	−0.843173	−	0.537642i	$-0.819315\pi$
$853$		−	782387.i		−	1.07528i	0.843173	−	0.537642i	$-0.180685\pi$
$854$	−347882.	+	302857.i	−0.476998	+	0.415262i
$855$			30371.3i			0.0415461i
$856$	527518.	+	252281.i	0.719929	+	0.344301i
$857$	−630022.	+	1.09123e6i	−0.857815	+	1.48578i	0.0161931	+	0.999869i	$0.494845\pi$
$857$	−630022.	+	1.09123e6i	−0.857815	+	1.48578i	−0.874008	+	0.485911i	$0.838488\pi$
$858$	−62485.0	−	307665.i	−0.0848791	−	0.417930i
$859$	261915.	+	453650.i	0.354956	+	0.614802i	0.987110	−	0.160041i	$-0.0511626\pi$
$859$	261915.	+	453650.i	0.354956	+	0.614802i	−0.632155	+	0.774842i	$0.717829\pi$
$860$	1.16105e6	+	143370.i	1.56984	+	0.193848i
$861$	102039.	+	780.617i	0.137644	+	0.00105301i
$862$	−66419.9	+	58722.7i	−0.0893890	+	0.0790299i
$863$	−223973.	+	129311.i	−0.300728	+	0.173625i	−0.642770	−	0.766059i	$-0.722215\pi$
$863$	−223973.	+	129311.i	−0.300728	+	0.173625i	0.342042	+	0.939685i	$0.388881\pi$
$864$	757258.	+	34367.0i	1.01442	+	0.0460377i
$865$	−268329.	+	464760.i	−0.358621	+	0.621150i
$866$	192955.	−	576022.i	0.257288	−	0.768075i
$867$	434550.			0.578099
$868$	−239219.	+	312007.i	−0.317509	+	0.414119i
$869$		−	1.94161e6i		−	2.57112i
$870$	252307.	−	753206.i	0.333343	−	0.995120i
$871$	−53232.4	−	30733.7i	−0.0701681	−	0.0405116i
$872$	−537589.	+	41751.2i	−0.706996	+	0.0549081i
$873$	13814.0	+	23926.5i	0.0181255	+	0.0313943i
$874$	−182702.	+	161529.i	−0.239178	+	0.211460i
$875$	−708903.	+	402086.i	−0.925914	+	0.525174i
$876$	148344.	−	1.20133e6i	0.193313	−	1.56551i
$877$	−93683.6	+	54088.3i	−0.121805	+	0.0703241i	−0.559665	−	0.828719i	$-0.689070\pi$
$877$	−93683.6	+	54088.3i	−0.121805	+	0.0703241i	0.437860	+	0.899043i	$0.355737\pi$
$878$	−226100.	−	1.11328e6i	−0.293300	−	1.44416i
$879$	1.22675e6	+	708264.i	1.58773	+	0.916679i
$880$	−878317.	+	250547.i	−1.13419	+	0.323536i
$881$	−969918.			−1.24964			−0.624818	−	0.780771i	$-0.714827\pi$
$881$	−969918.			−1.24964			−0.624818	+	0.780771i	$0.714827\pi$
$882$	−8327.35	+	23651.6i	−0.0107046	+	0.0304035i
$883$	−1.26147e6			−1.61791			−0.808956	−	0.587869i	$-0.799967\pi$
$883$	−1.26147e6			−1.61791			−0.808956	+	0.587869i	$0.799967\pi$
$884$	−65757.8	−	155212.i	−0.0841478	−	0.198619i
$885$	−645027.	−	372406.i	−0.823552	−	0.475478i
$886$	−249142.	+	50599.2i	−0.317379	+	0.0644579i
$887$	751111.	−	433654.i	0.954678	−	0.551184i	0.0601472	−	0.998190i	$-0.480843\pi$
$887$	751111.	−	433654.i	0.954678	−	0.551184i	0.894531	+	0.447006i	$0.147510\pi$
$888$	571420.	+	833262.i	0.724652	+	1.05671i
$889$	−879871.	+	499058.i	−1.11331	+	0.631462i
$890$	−600962.	+	531318.i	−0.758694	+	0.670771i
$891$	−495211.	−	857731.i	−0.623785	−	1.08043i
$892$	−128045.	+	169679.i	−0.160929	+	0.213254i
$893$	1.38755e6	+	801104.i	1.73999	+	1.00458i
$894$	157231.	+	52668.9i	0.196727	+	0.0658991i
$895$		−	370981.i		−	0.463133i
$896$	−140459.	+	790433.i	−0.174958	+	0.984576i
$897$	60189.3			0.0748057
$898$	78029.3	−	232939.i	0.0967620	−	0.288861i
$899$	246144.	−	426334.i	0.304558	−	0.527510i
$900$	3433.09	+	2590.72i	0.00423839	+	0.00319843i
$901$	−324230.	+	187194.i	−0.399396	+	0.230591i
$902$	97309.6	+	110065.i	0.119603	+	0.135280i
$903$	−1.38828e6	−	10620.6i	−1.70255	−	0.0130249i
$904$	733703.	−	503147.i	0.897808	−	0.615684i
$905$	243082.	+	421031.i	0.296794	+	0.514063i
$906$	−185027.	−	911040.i	−0.225413	−	1.10989i
$907$	273897.	−	474404.i	0.332946	−	0.576679i	−0.650142	−	0.759812i	$-0.725291\pi$
$907$	273897.	−	474404.i	0.332946	−	0.576679i	0.983088	+	0.183134i	$0.0586241\pi$
$908$	−162644.	+	68906.2i	−0.197272	+	0.0835770i
$909$			14153.7i			0.0171294i
$910$	166932.	+	191749.i	0.201584	+	0.231553i
$911$			1.09543e6i			1.31992i	0.751302	+	0.659959i	$0.229426\pi$
$911$			1.09543e6i			1.31992i	−0.751302	+	0.659959i	$0.770574\pi$
$912$	−316550.	−	1.10970e6i	−0.380586	−	1.33418i
$913$	−12170.7	+	21080.3i	−0.0146008	+	0.0252893i
$914$	243043.	−	49360.7i	0.290932	−	0.0590866i
$915$	238026.	+	412273.i	0.284303	+	0.492428i
$916$	981395.	+	121185.i	1.16964	+	0.144430i
$917$	−488431.	+	831236.i	−0.580851	+	0.988521i
$918$	−363981.	−	411691.i	−0.431910	−	0.488524i
$919$	−529967.	+	305976.i	−0.627506	+	0.362291i	−0.779785	−	0.626047i	$-0.784672\pi$
$919$	−529967.	+	305976.i	−0.627506	+	0.362291i	0.152280	+	0.988337i	$0.451339\pi$
$920$	−13558.7	−	174581.i	−0.0160192	−	0.206263i
$921$	−23999.0	+	41567.5i	−0.0282927	+	0.0490044i
$922$	−1.17685e6	−	394219.i	−1.38439	−	0.463741i
$923$	−129176.			−0.151627
$924$	1.00123e6	−	415181.i	1.17271	−	0.486288i
$925$			183582.i			0.214559i
$926$	−584374.	−	195752.i	−0.681505	−	0.228289i
$927$	−27564.0	−	15914.1i	−0.0320762	−	0.0185192i
$928$	45574.0	−	1.00420e6i	0.0529202	−	1.16607i
$929$	−226502.	−	392313.i	−0.262446	−	0.454570i	0.704445	−	0.709758i	$-0.251196\pi$
$929$	−226502.	−	392313.i	−0.262446	−	0.454570i	−0.966891	+	0.255188i	$0.917863\pi$
$930$	268775.	+	304006.i	0.310759	+	0.351492i
$931$	1.22227e6	+	18702.3i	1.41016	+	0.0215772i
$932$	−165549.	+	1.34067e6i	−0.190587	+	1.54344i
$933$	908294.	−	524404.i	1.04343	−	0.602424i
$934$	−644281.	+	130850.i	−0.738552	+	0.149996i
$935$	573406.	+	331056.i	0.655902	+	0.378685i
$936$	4092.68	−	8557.76i	0.00467150	−	0.00976806i
$937$	505558.			0.575827			0.287913	−	0.957656i	$-0.407038\pi$
$937$	505558.			0.575827			0.287913	+	0.957656i	$0.407038\pi$
$938$	68944.1	−	200706.i	0.0783594	−	0.228115i
$939$	935713.			1.06124
$940$	−1.05930e6	+	448788.i	−1.19885	+	0.507908i
$941$	−370039.	−	213642.i	−0.417896	−	0.241272i	0.276281	−	0.961077i	$-0.410898\pi$
$941$	−370039.	−	213642.i	−0.417896	−	0.241272i	−0.694177	+	0.719805i	$0.744231\pi$
$942$	180305.	+	887789.i	0.203192	+	1.00048i
$943$	−24392.4	+	14083.0i	−0.0274304	+	0.0158369i
$944$	−914241.	−	229282.i	−1.02593	−	0.257292i
$945$	714554.	+	419869.i	0.800150	+	0.470165i
$946$	−1.32393e6	−	1.49747e6i	−1.47939	−	1.67331i
$947$	−345861.	−	599049.i	−0.385658	−	0.667979i	0.606202	−	0.795310i	$-0.292692\pi$
$947$	−345861.	−	599049.i	−0.385658	−	0.667979i	−0.991860	+	0.127331i	$0.959359\pi$
$948$	−1.06102e6	+	1.40601e6i	−1.18061	+	1.56448i
$949$	−420100.	−	242545.i	−0.466467	−	0.269315i
$950$	66598.6	−	198815.i	0.0737934	−	0.220294i
$951$			176288.i			0.194922i
$952$	482469.	−	325461.i	0.532348	−	0.359108i
$953$	−242314.			−0.266804			−0.133402	−	0.991062i	$-0.542590\pi$
$953$	−242314.			−0.266804			−0.133402	+	0.991062i	$0.542590\pi$
$954$	−19977.5	−	6692.02i	−0.0219505	−	0.00735293i
$955$	−231593.	+	401132.i	−0.253933	+	0.439825i
$956$	622668.	−	825127.i	0.681304	−	0.902828i
$957$	−1.17536e6	+	678595.i	−1.28336	+	0.740946i
$958$	−537890.	+	475555.i	−0.586088	+	0.518167i
$959$	−792193.	−	6060.44i	−0.861378	−	0.00658972i
$960$	772943.	+	298536.i	0.838697	+	0.323932i
$961$	−336020.	−	582004.i	−0.363847	−	0.630201i
$962$	396804.	−	80588.6i	0.428772	−	0.0870811i
$963$	11927.2	−	20658.5i	0.0128613	−	0.0222765i
$964$	−886487.	+	375572.i	−0.953934	+	0.404147i
$965$		−	1.13484e6i		−	1.21866i
$966$	39800.4	+	203957.i	0.0426514	+	0.218567i
$967$			1.24936e6i			1.33609i	0.744123	+	0.668043i	$0.232868\pi$
$967$			1.24936e6i			1.33609i	−0.744123	+	0.668043i	$0.767132\pi$
$968$	562489.	+	269006.i	0.600293	+	0.287086i
$969$	−418269.	+	724463.i	−0.445459	+	0.771558i
$970$	192485.	+	947762.i	0.204576	+	1.00729i
$971$	−363188.	−	629061.i	−0.385206	−	0.667197i	0.606591	−	0.795014i	$-0.292536\pi$
$971$	−363188.	−	629061.i	−0.385206	−	0.667197i	−0.991798	+	0.127817i	$0.959203\pi$
$972$	7461.24	−	60423.4i	0.00789730	−	0.0639547i
$973$	254620.	+	448911.i	0.268947	+	0.474171i
$974$	585868.	−	517973.i	0.617564	−	0.545996i
$975$	−44816.4	+	25874.8i	−0.0471441	+	0.0272187i
$976$	432783.	+	419085.i	0.454329	+	0.439949i
$977$	−794738.	+	1.37653e6i	−0.832597	+	1.44210i	0.0633759	+	0.997990i	$0.479813\pi$
$977$	−794738.	+	1.37653e6i	−0.832597	+	1.44210i	−0.895972	+	0.444110i	$0.853520\pi$
$978$	58803.0	−	175543.i	0.0614783	−	0.183529i
$979$	1.37054e6			1.42997
$980$	−539376.	+	692459.i	−0.561615	+	0.721011i
$981$			21996.9i			0.0228572i
$982$	356102.	−	1.06306e6i	0.369277	−	1.10239i
$983$	174387.	+	100683.i	0.180471	+	0.104195i	0.587514	−	0.809214i	$-0.300107\pi$
$983$	174387.	+	100683.i	0.180471	+	0.104195i	−0.407043	+	0.913409i	$0.633440\pi$
$984$	−10319.9	−	132879.i	−0.0106582	−	0.137235i
$985$	−499993.	−	866013.i	−0.515337	−	0.892590i
$986$	−545943.	+	482675.i	−0.561556	+	0.496479i
$987$	1.18754e6	−	673569.i	1.21903	−	0.691430i
$988$	−458965.	−	56674.2i	−0.470182	−	0.0580593i
$989$	331868.	−	191604.i	0.339292	−	0.195890i
$990$	7415.91	+	36514.6i	0.00756648	+	0.0372560i
$991$	−1.07286e6	−	619416.i	−1.09244	−	0.630718i	−0.158212	−	0.987405i	$-0.550573\pi$
$991$	−1.07286e6	−	619416.i	−1.09244	−	0.630718i	−0.934224	+	0.356687i	$0.883906\pi$
$992$	432619.	+	276655.i	0.439625	+	0.281135i
$993$	−668369.			−0.677825
$994$	−85418.0	−	437725.i	−0.0864523	−	0.443025i
$995$	−1.24937e6			−1.26195
$996$	20333.0	−	8614.36i	0.0204967	−	0.00868369i
$997$	−324948.	−	187609.i	−0.326906	−	0.188739i	0.327560	−	0.944830i	$-0.393774\pi$
$997$	−324948.	−	187609.i	−0.326906	−	0.188739i	−0.654467	+	0.756091i	$0.727107\pi$
$998$	519007.	−	105407.i	0.521089	−	0.105830i
$999$	1.14312e6	−	659983.i	1.14541	−	0.661305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.5.k.a.11.19	yes	60
4.3	odd	2		224.5.o.a.207.8		60
7.2	even	3	inner	56.5.k.a.51.2	yes	60
8.3	odd	2	inner	56.5.k.a.11.2	✓	60
8.5	even	2		224.5.o.a.207.7		60
28.23	odd	6		224.5.o.a.79.7		60
56.37	even	6		224.5.o.a.79.8		60
56.51	odd	6	inner	56.5.k.a.51.19	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.5.k.a.11.2	✓	60	8.3	odd	2	inner
56.5.k.a.11.19	yes	60	1.1	even	1	trivial
56.5.k.a.51.2	yes	60	7.2	even	3	inner
56.5.k.a.51.19	yes	60	56.51	odd	6	inner
224.5.o.a.79.7		60	28.23	odd	6
224.5.o.a.79.8		60	56.37	even	6
224.5.o.a.207.7		60	8.5	even	2
224.5.o.a.207.8		60	4.3	odd	2

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	56.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27052 - 3.79286i) q^{2} +(4.42688 - 7.66758i) q^{3} +(-12.7715 - 9.63782i) q^{4} +(-19.7872 + 11.4241i) q^{5} +(-23.4576 - 26.5324i) q^{6} +(-24.1747 - 42.6214i) q^{7} +(-52.7814 + 36.1956i) q^{8} +(1.30543 + 2.26108i) q^{9} +(18.1900 + 89.5645i) q^{10} +(78.0757 - 135.231i) q^{11} +(-130.437 + 55.2614i) q^{12} +56.7703i q^{13} +(-192.371 + 37.5395i) q^{14} +202.293i q^{15} +(70.2247 + 246.180i) q^{16} +(92.7903 - 160.717i) q^{17} +(10.2345 - 2.07857i) q^{18} +(-254.563 - 440.916i) q^{19} +(362.816 + 44.8015i) q^{20} +(-433.822 - 3.31882i) q^{21} +(-413.715 - 467.944i) q^{22} +(103.705 - 59.8743i) q^{23} +(43.8754 + 564.940i) q^{24} +(-51.4787 + 89.1637i) q^{25} +(215.322 + 72.1279i) q^{26} +740.271 q^{27} +(-102.030 + 777.333i) q^{28} -981.672i q^{29} +(767.269 + 257.018i) q^{30} +(434.293 + 250.739i) q^{31} +(1022.95 + 46.4249i) q^{32} +(-691.264 - 1197.30i) q^{33} +(-491.686 - 556.136i) q^{34} +(965.261 + 567.183i) q^{35} +(5.11947 - 41.4590i) q^{36} +(1544.20 - 891.543i) q^{37} +(-1995.76 + 405.327i) q^{38} +(435.291 + 251.315i) q^{39} +(630.892 - 1319.19i) q^{40} -235.209 q^{41} +(-563.768 + 1641.21i) q^{42} +3200.11 q^{43} +(-2300.48 + 974.630i) q^{44} +(-51.6617 - 29.8269i) q^{45} +(-95.3347 - 469.411i) q^{46} +(-2725.37 + 1573.49i) q^{47} +(2198.48 + 551.355i) q^{48} +(-1232.17 + 2060.72i) q^{49} +(272.780 + 308.536i) q^{50} +(-821.543 - 1422.95i) q^{51} +(547.142 - 725.044i) q^{52} +(-1747.11 - 1008.69i) q^{53} +(940.531 - 2807.74i) q^{54} +3567.79i q^{55} +(2818.68 + 1374.60i) q^{56} -4507.68 q^{57} +(-3723.34 - 1247.24i) q^{58} +(-1840.92 + 3188.58i) q^{59} +(1949.66 - 2583.59i) q^{60} +(2038.00 - 1176.64i) q^{61} +(1502.80 - 1328.64i) q^{62} +(64.8120 - 110.300i) q^{63} +(1475.76 - 3820.91i) q^{64} +(-648.551 - 1123.32i) q^{65} +(-5419.47 + 1100.66i) q^{66} +(-541.370 + 937.680i) q^{67} +(-2734.04 + 1158.31i) q^{68} -1060.23i q^{69} +(3377.63 - 2940.48i) q^{70} +2275.41i q^{71} +(-150.744 - 72.0920i) q^{72} +(-4272.40 + 7400.01i) q^{73} +(-1419.56 - 6989.65i) q^{74} +(455.780 + 789.434i) q^{75} +(-998.309 + 8084.61i) q^{76} +(-7651.20 - 58.5332i) q^{77} +(1506.25 - 1331.69i) q^{78} +(10768.3 - 6217.08i) q^{79} +(-4201.94 - 4068.95i) q^{80} +(3171.35 - 5492.94i) q^{81} +(-298.838 + 892.114i) q^{82} -155.884 q^{83} +(5508.59 + 4223.48i) q^{84} +4240.19i q^{85} +(4065.81 - 12137.6i) q^{86} +(-7527.06 - 4345.75i) q^{87} +(773.819 + 9963.69i) q^{88} +(4388.50 + 7601.10i) q^{89} +(-178.766 + 158.050i) q^{90} +(2419.63 - 1372.40i) q^{91} +(-1901.54 - 234.807i) q^{92} +(3845.13 - 2219.99i) q^{93} +(2505.39 + 12336.1i) q^{94} +(10074.2 + 5816.32i) q^{95} +(4884.43 - 7638.02i) q^{96} +10581.9 q^{97} +(6250.50 + 7291.64i) q^{98} +407.691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 28 q^{6} - 4 q^{8} - 704 q^{9} + 66 q^{10} + 94 q^{11} + 46 q^{12} + 6 q^{14} + 120 q^{16} - 2 q^{17} - 730 q^{18} - 2 q^{19} - 1872 q^{20} + 2160 q^{22} + 550 q^{24}+ \cdots + 640 q^{99}+O(q^{100}) \) 60 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 28 * q^6 - 4 * q^8 - 704 * q^9 + 66 * q^10 + 94 * q^11 + 46 * q^12 + 6 * q^14 + 120 * q^16 - 2 * q^17 - 730 * q^18 - 2 * q^19 - 1872 * q^20 + 2160 * q^22 + 550 * q^24 + 2748 * q^25 + 438 * q^26 + 316 * q^27 - 2038 * q^28 + 168 * q^30 - 2764 * q^32 + 322 * q^33 + 1212 * q^34 - 3846 * q^35 + 7600 * q^36 - 2384 * q^38 + 4886 * q^40 - 8 * q^41 + 7054 * q^42 - 5576 * q^43 + 1018 * q^44 + 2970 * q^46 - 7352 * q^48 + 1500 * q^49 - 10216 * q^50 + 7202 * q^51 - 8888 * q^52 - 15700 * q^54 + 9576 * q^56 + 7804 * q^57 - 4638 * q^58 - 6530 * q^59 + 5950 * q^60 + 20448 * q^62 - 24616 * q^64 + 1248 * q^65 + 20560 * q^66 - 8002 * q^67 - 18320 * q^68 - 19122 * q^70 - 6404 * q^72 + 3678 * q^73 - 3876 * q^74 + 1572 * q^75 + 25012 * q^76 + 29140 * q^78 + 21732 * q^80 - 12898 * q^81 + 31314 * q^82 + 10552 * q^83 - 24068 * q^84 + 5452 * q^86 - 8922 * q^88 - 6818 * q^89 - 51340 * q^90 + 18240 * q^91 + 16188 * q^92 - 26760 * q^94 + 40208 * q^96 - 6984 * q^97 - 3142 * q^98 + 640 * q^99

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