LMFDB - Embedded newform 45.5.h.a.14.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(14,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("45.14");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.9
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02189 - 1.76997i) q^{2} +(8.99991 + 0.0407214i) q^{3} +(5.91148 - 10.2390i) q^{4} +(15.4498 + 19.6546i) q^{5} +(-9.12485 - 15.9711i) q^{6} +(-2.09732 + 1.21089i) q^{7} -56.8640 q^{8} +(80.9967 + 0.732978i) q^{9} +(19.0000 - 47.4305i) q^{10} +(117.697 - 67.9523i) q^{11} +(53.6197 - 91.9092i) q^{12} +(-136.503 - 78.8098i) q^{13} +(4.28647 + 2.47479i) q^{14} +(138.247 + 177.519i) q^{15} +(-36.4748 - 63.1763i) q^{16} +258.165 q^{17} +(-81.4724 - 144.110i) q^{18} -363.338 q^{19} +(292.574 - 42.0027i) q^{20} +(-18.9250 + 10.8125i) q^{21} +(-240.547 - 138.880i) q^{22} +(-392.923 + 680.562i) q^{23} +(-511.771 - 2.31559i) q^{24} +(-147.606 + 607.320i) q^{25} +322.140i q^{26} +(728.933 + 9.89504i) q^{27} +28.6326i q^{28} +(-629.935 + 363.693i) q^{29} +(172.929 - 426.096i) q^{30} +(-463.170 + 802.234i) q^{31} +(-529.459 + 917.050i) q^{32} +(1062.03 - 606.772i) q^{33} +(-263.817 - 456.944i) q^{34} +(-56.2028 - 22.5140i) q^{35} +(486.315 - 824.991i) q^{36} -1997.88i q^{37} +(371.292 + 643.096i) q^{38} +(-1225.30 - 714.839i) q^{39} +(-878.539 - 1117.64i) q^{40} +(1250.71 + 722.098i) q^{41} +(38.4770 + 22.4474i) q^{42} +(542.092 - 312.977i) q^{43} -1606.79i q^{44} +(1236.98 + 1603.28i) q^{45} +1606.10 q^{46} +(188.637 + 326.730i) q^{47} +(-325.698 - 570.066i) q^{48} +(-1197.57 + 2074.25i) q^{49} +(1225.77 - 359.356i) q^{50} +(2323.46 + 10.5129i) q^{51} +(-1613.86 + 931.765i) q^{52} -694.739 q^{53} +(-727.376 - 1300.30i) q^{54} +(3153.97 + 1263.43i) q^{55} +(119.262 - 68.8560i) q^{56} +(-3270.01 - 14.7956i) q^{57} +(1287.45 + 743.309i) q^{58} +(-2222.20 - 1282.99i) q^{59} +(2634.85 - 366.106i) q^{60} +(-2577.00 - 4463.50i) q^{61} +1893.24 q^{62} +(-170.764 + 96.5407i) q^{63} +997.001 q^{64} +(-559.965 - 3900.50i) q^{65} +(-2159.24 - 1259.70i) q^{66} +(5671.56 + 3274.48i) q^{67} +(1526.14 - 2643.35i) q^{68} +(-3563.98 + 6109.00i) q^{69} +(17.5841 + 122.484i) q^{70} +3331.47i q^{71} +(-4605.80 - 41.6801i) q^{72} +1735.66i q^{73} +(-3536.18 + 2041.61i) q^{74} +(-1353.17 + 5459.81i) q^{75} +(-2147.86 + 3720.21i) q^{76} +(-164.565 + 285.036i) q^{77} +(-13.1180 + 2899.23i) q^{78} +(-3695.54 - 6400.86i) q^{79} +(678.175 - 1692.96i) q^{80} +(6559.93 + 118.738i) q^{81} -2951.62i q^{82} +(-5465.06 - 9465.75i) q^{83} +(-1.16596 + 257.691i) q^{84} +(3988.60 + 5074.13i) q^{85} +(-1107.92 - 639.657i) q^{86} +(-5684.17 + 3247.55i) q^{87} +(-6692.72 + 3864.04i) q^{88} -2325.29i q^{89} +(1573.70 - 3827.79i) q^{90} +381.719 q^{91} +(4645.51 + 8046.26i) q^{92} +(-4201.15 + 7201.17i) q^{93} +(385.534 - 667.764i) q^{94} +(-5613.50 - 7141.26i) q^{95} +(-4802.42 + 8231.80i) q^{96} +(14265.5 - 8236.22i) q^{97} +4895.13 q^{98} +(9582.86 - 5417.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.02189	−	1.76997i	−0.255473	−	0.442492i	0.709551	−	0.704654i	$-0.248898\pi$
$2$	−1.02189	−	1.76997i	−0.255473	−	0.442492i	−0.965024	+	0.262162i	$0.915564\pi$
$3$	8.99991	+	0.0407214i	0.999990	+	0.00452460i
$3$	8.99991	+	0.0407214i	0.999990	+	0.00452460i
$4$	5.91148	−	10.2390i	0.369467	−	0.639936i
$5$	15.4498	+	19.6546i	0.617993	+	0.786184i
$5$	15.4498	+	19.6546i	0.617993	+	0.786184i
$6$	−9.12485	−	15.9711i	−0.253468	−	0.443643i
$7$	−2.09732	+	1.21089i	−0.0428025	+	0.0247120i	−0.521249	−	0.853405i	$-0.674534\pi$
$7$	−2.09732	+	1.21089i	−0.0428025	+	0.0247120i	0.478446	+	0.878117i	$0.341200\pi$
$8$	−56.8640			−0.888501
$9$	80.9967	+	0.732978i	0.999959	+	0.00904912i
$10$	19.0000	−	47.4305i	0.190000	−	0.474305i
$11$	117.697	−	67.9523i	0.972701	−	0.561589i	0.0726425	−	0.997358i	$-0.476857\pi$
$11$	117.697	−	67.9523i	0.972701	−	0.561589i	0.900059	+	0.435769i	$0.143523\pi$
$12$	53.6197	−	91.9092i	0.372359	−	0.638258i
$13$	−136.503	−	78.8098i	−0.807707	−	0.466330i	0.0384518	−	0.999260i	$-0.487757\pi$
$13$	−136.503	−	78.8098i	−0.807707	−	0.466330i	−0.846159	+	0.532930i	$0.821091\pi$
$14$	4.28647	+	2.47479i	0.0218697	+	0.0126265i
$15$	138.247	+	177.519i	0.614429	+	0.788972i
$16$	−36.4748	−	63.1763i	−0.142480	−	0.246782i
$17$	258.165			0.893305			0.446652	−	0.894708i	$-0.352616\pi$
$17$	258.165			0.893305			0.446652	+	0.894708i	$0.352616\pi$
$18$	−81.4724	−	144.110i	−0.251458	−	0.444785i
$19$	−363.338			−1.00648			−0.503238	−	0.864148i	$-0.667858\pi$
$19$	−363.338			−1.00648			−0.503238	+	0.864148i	$0.667858\pi$
$20$	292.574	−	42.0027i	0.731436	−	0.105007i
$21$	−18.9250	+	10.8125i	−0.0429138	+	0.0245181i
$22$	−240.547	−	138.880i	−0.496997	−	0.286941i
$23$	−392.923	+	680.562i	−0.742765	+	1.28651i	0.208467	+	0.978029i	$0.433153\pi$
$23$	−392.923	+	680.562i	−0.742765	+	1.28651i	−0.951232	+	0.308477i	$0.900181\pi$
$24$	−511.771	−	2.31559i	−0.888491	−	0.00402011i
$25$	−147.606	+	607.320i	−0.236170	+	0.971712i
$26$			322.140i			0.476538i
$27$	728.933	+	9.89504i	0.999908	+	0.0135734i
$28$			28.6326i			0.0365211i
$29$	−629.935	+	363.693i	−0.749031	+	0.432453i	−0.825344	−	0.564631i	$-0.809019\pi$
$29$	−629.935	+	363.693i	−0.749031	+	0.432453i	0.0763129	+	0.997084i	$0.475685\pi$
$30$	172.929	−	426.096i	0.192144	−	0.473440i
$31$	−463.170	+	802.234i	−0.481967	+	0.834790i	−0.999786	−	0.0206996i	$-0.993411\pi$
$31$	−463.170	+	802.234i	−0.481967	+	0.834790i	0.517819	+	0.855490i	$0.326744\pi$
$32$	−529.459	+	917.050i	−0.517050	+	0.895556i
$33$	1062.03	−	606.772i	0.975232	−	0.557182i
$34$	−263.817	−	456.944i	−0.228215	−	0.395280i
$35$	−56.2028	−	22.5140i	−0.0458798	−	0.0183788i
$36$	486.315	−	824.991i	0.375243	−	0.636567i
$37$		−	1997.88i		−	1.45937i	−0.683783	−	0.729685i	$-0.739667\pi$
$37$		−	1997.88i		−	1.45937i	0.683783	−	0.729685i	$-0.260333\pi$
$38$	371.292	+	643.096i	0.257127	+	0.445357i
$39$	−1225.30	−	714.839i	−0.805589	−	0.469980i
$40$	−878.539	−	1117.64i	−0.549087	−	0.698525i
$41$	1250.71	+	722.098i	0.744027	+	0.429564i	0.823532	−	0.567270i	$-0.192000\pi$
$41$	1250.71	+	722.098i	0.744027	+	0.429564i	−0.0795044	+	0.996835i	$0.525334\pi$
$42$	38.4770	+	22.4474i	0.0218124	+	0.0127253i
$43$	542.092	−	312.977i	0.293181	−	0.169268i	−0.346194	−	0.938163i	$-0.612526\pi$
$43$	542.092	−	312.977i	0.293181	−	0.169268i	0.639376	+	0.768895i	$0.279193\pi$
$44$		−	1606.79i		−	0.829956i
$45$	1236.98	+	1603.28i	0.610853	+	0.791744i
$46$	1606.10			0.759025
$47$	188.637	+	326.730i	0.0853950	+	0.147908i	0.905559	−	0.424219i	$-0.139451\pi$
$47$	188.637	+	326.730i	0.0853950	+	0.147908i	−0.820164	+	0.572128i	$0.806118\pi$
$48$	−325.698	−	570.066i	−0.141362	−	0.247425i
$49$	−1197.57	+	2074.25i	−0.498779	+	0.863910i
$50$	1225.77	−	359.356i	0.490309	−	0.143742i
$51$	2323.46	+	10.5129i	0.893296	+	0.00404185i
$52$	−1613.86	+	931.765i	−0.596843	+	0.344588i
$53$	−694.739			−0.247326			−0.123663	−	0.992324i	$-0.539464\pi$
$53$	−694.739			−0.247326			−0.123663	+	0.992324i	$0.539464\pi$
$54$	−727.376	−	1300.30i	−0.249443	−	0.445918i
$55$	3153.97	+	1263.43i	1.04263	+	0.417664i
$56$	119.262	−	68.8560i	0.0380300	−	0.0219566i
$57$	−3270.01	−	14.7956i	−1.00647	−	0.00455391i
$58$	1287.45	+	743.309i	0.382714	+	0.220960i
$59$	−2222.20	−	1282.99i	−0.638381	−	0.368569i	0.145610	−	0.989342i	$-0.453486\pi$
$59$	−2222.20	−	1282.99i	−0.638381	−	0.368569i	−0.783991	+	0.620773i	$0.786819\pi$
$60$	2634.85	−	366.106i	0.731903	−	0.101696i
$61$	−2577.00	−	4463.50i	−0.692556	−	1.19954i	−0.970998	−	0.239089i	$-0.923151\pi$
$61$	−2577.00	−	4463.50i	−0.692556	−	1.19954i	0.278441	−	0.960453i	$-0.410182\pi$
$62$	1893.24			0.492517
$63$	−170.764	+	96.5407i	−0.0430243	+	0.0243237i
$64$	997.001			0.243408
$65$	−559.965	−	3900.50i	−0.132536	−	0.923195i
$66$	−2159.24	−	1259.70i	−0.495694	−	0.289187i
$67$	5671.56	+	3274.48i	1.26344	+	0.729445i	0.973738	−	0.227673i	$-0.0731117\pi$
$67$	5671.56	+	3274.48i	1.26344	+	0.729445i	0.289698	+	0.957118i	$0.406445\pi$
$68$	1526.14	−	2643.35i	0.330047	−	0.571658i
$69$	−3563.98	+	6109.00i	−0.748578	+	1.28313i
$70$	17.5841	+	122.484i	0.00358858	+	0.0249967i
$71$			3331.47i			0.660875i	0.943828	+	0.330438i	$0.107196\pi$
$71$			3331.47i			0.660875i	−0.943828	+	0.330438i	$0.892804\pi$
$72$	−4605.80	−	41.6801i	−0.888464	−	0.00804014i
$73$			1735.66i			0.325701i	0.986651	+	0.162850i	$0.0520688\pi$
$73$			1735.66i			0.325701i	−0.986651	+	0.162850i	$0.947931\pi$
$74$	−3536.18	+	2041.61i	−0.645759	+	0.372829i
$75$	−1353.17	+	5459.81i	−0.240564	+	0.970633i
$76$	−2147.86	+	3720.21i	−0.371860	+	0.644081i
$77$	−164.565	+	285.036i	−0.0277560	+	0.0480748i
$78$	−13.1180	+	2899.23i	−0.00215615	+	0.476533i
$79$	−3695.54	−	6400.86i	−0.592139	−	1.02561i	−0.993944	−	0.109889i	$-0.964950\pi$
$79$	−3695.54	−	6400.86i	−0.592139	−	1.02561i	0.401805	−	0.915725i	$-0.368383\pi$
$80$	678.175	−	1692.96i	0.105965	−	0.264525i
$81$	6559.93	+	118.738i	0.999836	+	0.0180975i
$82$		−	2951.62i		−	0.438968i
$83$	−5465.06	−	9465.75i	−0.793302	−	1.37404i	−0.923912	−	0.382605i	$-0.875027\pi$
$83$	−5465.06	−	9465.75i	−0.793302	−	1.37404i	0.130610	−	0.991434i	$-0.458306\pi$
$84$	−1.16596	+	257.691i	−0.000165244	+	0.0365208i
$85$	3988.60	+	5074.13i	0.552056	+	0.702302i
$86$	−1107.92	−	639.657i	−0.149800	−	0.0864868i
$87$	−5684.17	+	3247.55i	−0.750980	+	0.429060i
$88$	−6692.72	+	3864.04i	−0.864245	+	0.498972i
$89$		−	2325.29i		−	0.293560i	−0.989169	−	0.146780i	$-0.953109\pi$
$89$		−	2325.29i		−	0.293560i	0.989169	−	0.146780i	$-0.0468909\pi$
$90$	1573.70	−	3827.79i	0.194284	−	0.472566i
$91$	381.719			0.0460958
$92$	4645.51	+	8046.26i	0.548855	+	0.950645i
$93$	−4201.15	+	7201.17i	−0.485739	+	0.832601i
$94$	385.534	−	667.764i	0.0436321	−	0.0755731i
$95$	−5613.50	−	7141.26i	−0.621995	−	0.791275i
$96$	−4802.42	+	8231.80i	−0.521096	+	0.893208i
$97$	14265.5	−	8236.22i	1.51616	−	0.875355i	0.516340	−	0.856384i	$-0.327294\pi$
$97$	14265.5	−	8236.22i	1.51616	−	0.875355i	0.999820	−	0.0189715i	$-0.00603918\pi$
$98$	4895.13			0.509697
$99$	9582.86	−	5417.64i	0.977743	−	0.552764i
$100$	5345.77	+	5101.50i	0.534577	+	0.510150i
$101$	2850.51	−	1645.74i	0.279434	−	0.161332i	−0.353733	−	0.935346i	$-0.615088\pi$
$101$	2850.51	−	1645.74i	0.279434	−	0.161332i	0.633167	+	0.774015i	$0.281755\pi$
$102$	−2355.72	−	4123.19i	−0.226424	−	0.396308i
$103$	−1997.64	−	1153.34i	−0.188297	−	0.108713i	0.402888	−	0.915249i	$-0.368006\pi$
$103$	−1997.64	−	1153.34i	−0.188297	−	0.108713i	−0.591185	+	0.806536i	$0.701340\pi$
$104$	7762.08	+	4481.44i	0.717648	+	0.414334i
$105$	−504.903	−	204.912i	−0.0457962	−	0.0185862i
$106$	709.948	+	1229.67i	0.0631851	+	0.109440i
$107$	−3623.64			−0.316503			−0.158251	−	0.987399i	$-0.550586\pi$
$107$	−3623.64			−0.316503			−0.158251	+	0.987399i	$0.550586\pi$
$108$	4410.39	−	7405.04i	0.378120	−	0.634863i
$109$	17380.4			1.46288			0.731438	−	0.681908i	$-0.238850\pi$
$109$	17380.4			1.46288			0.731438	+	0.681908i	$0.238850\pi$
$110$	−986.777	−	6873.51i	−0.0815518	−	0.568059i
$111$	81.3564	−	17980.7i	0.00660307	−	1.45936i
$112$	152.999	+	88.3340i	0.0121970	+	0.00704193i
$113$	5120.93	−	8869.71i	0.401044	−	0.694628i	−0.592808	−	0.805343i	$-0.701981\pi$
$113$	5120.93	−	8869.71i	0.401044	−	0.694628i	0.993852	+	0.110715i	$0.0353142\pi$
$114$	3315.40	+	5802.92i	0.255109	+	0.446516i
$115$	−19446.8	+	2791.82i	−1.47045	+	0.211102i
$116$			8599.86i			0.639109i
$117$	−10998.5	−	6483.38i	−0.803454	−	0.473620i
$118$			5244.30i			0.376638i
$119$	−541.455	+	312.609i	−0.0382357	+	0.0220754i
$120$	−7861.26	−	10094.4i	−0.545921	−	0.701002i
$121$	1914.53	−	3316.06i	0.130765	−	0.226492i
$122$	−5266.83	+	9122.41i	−0.353858	+	0.612901i
$123$	11226.9	+	6549.75i	0.742076	+	0.432926i
$124$	5476.04	+	9484.78i	0.356142	+	0.616856i
$125$	−14217.1	+	6481.84i	−0.909895	+	0.414838i
$126$	345.376	+	203.592i	0.0217546	+	0.0128239i
$127$		−	27661.2i		−	1.71500i	−0.514484	−	0.857500i	$-0.672017\pi$
$127$		−	27661.2i		−	1.71500i	0.514484	−	0.857500i	$-0.327983\pi$
$128$	7452.52	+	12908.1i	0.454866	+	0.787850i
$129$	4891.52	−	2794.69i	0.293944	−	0.167940i
$130$	−6331.53	+	4977.00i	−0.374647	+	0.294497i
$131$	−11192.2	−	6461.79i	−0.652185	−	0.376539i	0.137108	−	0.990556i	$-0.456219\pi$
$131$	−11192.2	−	6461.79i	−0.652185	−	0.376539i	−0.789293	+	0.614017i	$0.789553\pi$
$132$	65.4310	−	14461.0i	0.00375522	−	0.829947i
$133$	762.036	−	439.962i	0.0430797	−	0.0248721i
$134$		−	13384.6i		−	0.745413i
$135$	11067.4	+	14479.8i	0.607265	+	0.794500i
$136$	−14680.3			−0.793702
$137$	17968.9	+	31123.0i	0.957369	+	1.65821i	0.728850	+	0.684673i	$0.240055\pi$
$137$	17968.9	+	31123.0i	0.957369	+	1.65821i	0.228519	+	0.973539i	$0.426612\pi$
$138$	14454.7	+	65.4025i	0.759017	+	0.00343429i
$139$	−9010.90	+	15607.3i	−0.466379	+	0.807792i	−0.999263	−	0.0383967i	$-0.987775\pi$
$139$	−9010.90	+	15607.3i	−0.466379	+	0.807792i	0.532884	+	0.846188i	$0.321108\pi$
$140$	−562.762	+	442.368i	−0.0287123	+	0.0225698i
$141$	1684.41	+	2948.22i	0.0847249	+	0.148293i
$142$	5896.59	−	3404.40i	0.292432	−	0.168836i
$143$	−21421.2			−1.04754
$144$	−2908.03	−	5143.81i	−0.140241	−	0.248062i
$145$	−16880.6	−	6762.12i	−0.802883	−	0.321623i
$146$	3072.06	−	1773.65i	0.144120	−	0.0832077i
$147$	−10862.5	+	18619.3i	−0.502682	+	0.861644i
$148$	−20456.2	−	11810.4i	−0.933904	−	0.539190i
$149$	30500.0	+	17609.2i	1.37381	+	0.793172i	0.991406	−	0.130822i	$-0.0417617\pi$
$149$	30500.0	+	17609.2i	1.37381	+	0.793172i	0.382408	+	0.923994i	$0.375095\pi$
$150$	11046.5	−	3184.26i	0.490955	−	0.141523i
$151$	−5908.59	−	10234.0i	−0.259137	−	0.448839i	0.706874	−	0.707340i	$-0.250105\pi$
$151$	−5908.59	−	10234.0i	−0.259137	−	0.448839i	−0.966011	+	0.258501i	$0.916771\pi$
$152$	20660.9			0.894255
$153$	20910.5	+	189.229i	0.893268	+	0.00808362i
$154$	672.671			0.0283636
$155$	−22923.5	+	3290.95i	−0.954151	+	0.136980i
$156$	−14562.6	+	8320.08i	−0.598396	+	0.341884i
$157$	−4657.79	−	2689.18i	−0.188965	−	0.109099i	0.402533	−	0.915405i	$-0.368130\pi$
$157$	−4657.79	−	2689.18i	−0.188965	−	0.109099i	−0.591498	+	0.806307i	$0.701463\pi$
$158$	−7552.87	+	13082.0i	−0.302550	+	0.524033i
$159$	−6252.59	−	28.2908i	−0.247324	−	0.00111905i
$160$	−26204.3	+	3761.95i	−1.02360	+	0.146951i
$161$		−	1903.14i		−	0.0734209i
$162$	−6493.36	−	11732.2i	−0.247423	−	0.447043i
$163$			12593.5i			0.473991i	0.971511	+	0.236995i	$0.0761626\pi$
$163$			12593.5i			0.473991i	−0.971511	+	0.236995i	$0.923837\pi$
$164$	14787.1	−	8537.33i	0.549788	−	0.317420i
$165$	28334.0	+	11499.2i	1.04073	+	0.422377i
$166$	−11169.4	+	19345.9i	−0.405334	+	0.702059i
$167$	−17707.1	+	30669.5i	−0.634912	+	1.09970i	0.351622	+	0.936142i	$0.385630\pi$
$167$	−17707.1	+	30669.5i	−0.634912	+	1.09970i	−0.986534	+	0.163558i	$0.947703\pi$
$168$	1076.15	−	614.841i	0.0381290	−	0.0217843i
$169$	−1858.54	−	3219.09i	−0.0650727	−	0.112709i
$170$	4905.13	−	12244.9i	0.169728	−	0.423699i
$171$	−29429.2	−	266.319i	−1.00644	−	0.00910772i
$172$		−	7400.63i		−	0.250156i
$173$	−10598.2	−	18356.6i	−0.354112	−	0.613340i	0.632854	−	0.774271i	$-0.281883\pi$
$173$	−10598.2	−	18356.6i	−0.354112	−	0.613340i	−0.986966	+	0.160932i	$0.948550\pi$
$174$	11556.7	+	6742.14i	0.381710	+	0.222689i
$175$	−425.819	−	1452.48i	−0.0139043	−	0.0474279i
$176$	−8585.95	−	4957.10i	−0.277181	−	0.160030i
$177$	−19947.4	−	11637.3i	−0.636707	−	0.371454i
$178$	−4115.68	+	2376.19i	−0.129898	+	0.0749965i
$179$			16660.9i			0.519986i	0.965611	+	0.259993i	$0.0837202\pi$
$179$			16660.9i			0.519986i	−0.965611	+	0.259993i	$0.916280\pi$
$180$	23728.3	−	3187.63i	0.732356	−	0.0983835i
$181$	45130.9			1.37758			0.688791	−	0.724960i	$-0.258142\pi$
$181$	45130.9			1.37758			0.688791	+	0.724960i	$0.258142\pi$
$182$	−390.076	−	675.631i	−0.0117762	−	0.0203970i
$183$	−23011.0	−	40276.0i	−0.687122	−	1.20266i
$184$	22343.2	−	38699.5i	0.659947	−	1.14306i
$185$	39267.5	−	30866.8i	1.14733	−	0.901880i
$186$	17038.9	+	77.0953i	0.492512	+	0.00222844i
$187$	30385.2	−	17542.9i	0.868919	−	0.501670i
$188$	4460.51			0.126203
$189$	−1540.79	+	861.904i	−0.0431340	+	0.0241288i
$190$	−6903.40	+	17233.3i	−0.191230	+	0.477377i
$191$	30912.8	−	17847.5i	0.847367	−	0.489228i	−0.0123943	−	0.999923i	$-0.503945\pi$
$191$	30912.8	−	17847.5i	0.847367	−	0.489228i	0.859762	+	0.510695i	$0.170612\pi$
$192$	8972.92	+	40.5993i	0.243406	+	0.00110133i
$193$	21060.2	+	12159.1i	0.565390	+	0.326428i	0.755306	−	0.655372i	$-0.227488\pi$
$193$	21060.2	+	12159.1i	0.565390	+	0.326428i	−0.189916	+	0.981800i	$0.560822\pi$
$194$	−29155.7	−	16833.0i	−0.774675	−	0.447259i
$195$	−4880.80	−	35126.9i	−0.128358	−	0.923785i
$196$	14158.8	+	24523.7i	0.368565	+	0.638373i
$197$	13918.9			0.358652			0.179326	−	0.983790i	$-0.442608\pi$
$197$	13918.9			0.358652			0.179326	+	0.983790i	$0.442608\pi$
$198$	−19381.7	−	11425.1i	−0.494380	−	0.291427i
$199$	−41162.0			−1.03942			−0.519709	−	0.854343i	$-0.673960\pi$
$199$	−41162.0			−1.03942			−0.519709	+	0.854343i	$0.673960\pi$
$200$	8393.49	−	34534.7i	0.209837	−	0.863366i
$201$	50910.2	+	29701.0i	1.26012	+	0.735154i
$202$	−5825.82	−	3363.54i	−0.142776	−	0.0824316i
$203$	880.784	−	1525.56i	0.0213736	−	0.0370201i
$204$	13842.7	−	23727.7i	0.332630	−	0.570159i
$205$	5130.70	+	35738.5i	0.122087	+	0.850410i
$206$			4714.34i			0.111093i
$207$	−32324.3	+	54835.3i	−0.754376	+	1.27973i
$208$			11498.3i			0.265771i
$209$	−42763.7	+	24689.6i	−0.979001	+	0.565226i
$210$	153.267	+	1103.06i	0.00347545	+	0.0250127i
$211$	24325.2	−	42132.5i	0.546377	−	0.946352i	−0.452142	−	0.891946i	$-0.649340\pi$
$211$	24325.2	−	42132.5i	0.546377	−	0.946352i	0.998519	−	0.0544061i	$-0.0173266\pi$
$212$	−4106.94	+	7113.42i	−0.0913790	+	0.158273i
$213$	−135.662	+	29982.9i	−0.00299020	+	0.660869i
$214$	3702.96	+	6413.72i	0.0808577	+	0.140050i
$215$	14526.7	+	5819.16i	0.314260	+	0.125888i
$216$	−41450.1	−	562.672i	−0.888419	−	0.0120600i
$217$		−	2243.39i		−	0.0476415i
$218$	−17760.9	−	30762.8i	−0.373725	−	0.647310i
$219$	−70.6786	+	15620.8i	−0.00147367	+	0.325698i
$220$	31580.9	−	24824.7i	0.652498	−	0.512907i
$221$	−35240.2	−	20345.9i	−0.721529	−	0.416575i
$222$	−31908.4	+	18230.3i	−0.647439	+	0.369903i
$223$	24767.9	−	14299.7i	0.498057	−	0.287553i	−0.229854	−	0.973225i	$-0.573825\pi$
$223$	24767.9	−	14299.7i	0.498057	−	0.287553i	0.727911	+	0.685672i	$0.240491\pi$
$224$		−	2564.46i		−	0.0511094i
$225$	−12400.8	+	49082.7i	−0.244954	+	0.969535i
$226$	−20932.1			−0.409823
$227$	4539.31	+	7862.32i	0.0880923	+	0.152580i	0.906705	−	0.421766i	$-0.138590\pi$
$227$	4539.31	+	7862.32i	0.0880923	+	0.152580i	−0.818612	+	0.574346i	$0.805256\pi$
$228$	−19482.1	+	33394.1i	−0.374771	+	0.642392i
$229$	−11598.2	+	20088.6i	−0.221166	+	0.383071i	−0.955162	−	0.296082i	$-0.904320\pi$
$229$	−11598.2	+	20088.6i	−0.221166	+	0.383071i	0.733996	+	0.679154i	$0.237653\pi$
$230$	24813.9	+	31567.2i	0.469072	+	0.596733i
$231$	−1492.68	+	2558.59i	−0.0279732	+	0.0479487i
$232$	35820.6	−	20681.1i	0.665514	−	0.384235i
$233$	18159.1			0.334490			0.167245	−	0.985915i	$-0.446513\pi$
$233$	18159.1			0.334490			0.167245	+	0.985915i	$0.446513\pi$
$234$	−236.122	+	26092.3i	−0.00431225	+	0.476519i
$235$	−3507.33	+	8755.51i	−0.0635097	+	0.158542i
$236$	−26273.0	+	15168.7i	−0.471722	+	0.272349i
$237$	−32998.8	−	57757.6i	−0.587492	−	1.02828i
$238$	1106.62	+	638.905i	0.0195363	+	0.0112793i
$239$	−28454.7	−	16428.3i	−0.498147	−	0.287605i	0.229801	−	0.973238i	$-0.426193\pi$
$239$	−28454.7	−	16428.3i	−0.498147	−	0.287605i	−0.727948	+	0.685632i	$0.759526\pi$
$240$	6172.45	−	15208.9i	0.107161	−	0.264043i
$241$	17841.6	+	30902.5i	0.307185	+	0.532060i	0.977745	−	0.209795i	$-0.0672797\pi$
$241$	17841.6	+	30902.5i	0.307185	+	0.532060i	−0.670561	+	0.741855i	$0.733946\pi$
$242$	−7825.76			−0.133627
$243$	59033.9	+	1335.76i	0.999744	+	0.0226212i
$244$	−60935.6			−1.02351
$245$	−59270.7	+	8509.04i	−0.987434	+	0.141758i
$246$	120.194	−	26564.3i	0.00198616	−	0.438963i
$247$	49596.5	+	28634.6i	0.812938	+	0.469350i
$248$	26337.7	−	45618.2i	0.428228	−	0.741712i
$249$	−48799.5	−	85413.5i	−0.787077	−	1.37761i
$250$	26001.0	+	18540.1i	0.416016	+	0.296641i
$251$		−	7904.26i		−	0.125462i	−0.998030	−	0.0627312i	$-0.980019\pi$
$251$		−	7904.26i		−	0.125462i	0.998030	−	0.0627312i	$-0.0199811\pi$
$252$	−20.9871	+	2319.14i	−0.000330484	+	0.0365197i
$253$			106800.i			1.66852i
$254$	−48959.5	+	28266.8i	−0.758873	+	0.438136i
$255$	35690.4	+	45829.1i	0.548873	+	0.704793i
$256$	23207.3	−	40196.3i	0.354116	−	0.613346i
$257$	37848.7	−	65555.8i	0.573039	−	0.992533i	−0.423213	−	0.906030i	$-0.639098\pi$
$257$	37848.7	−	65555.8i	0.573039	−	0.992533i	0.996252	−	0.0865023i	$-0.0275690\pi$
$258$	−9945.11	−	5801.97i	−0.149407	−	0.0871637i
$259$	2419.21	+	4190.19i	0.0360640	+	0.0624646i
$260$	−43247.4	−	17324.2i	−0.639754	−	0.256276i
$261$	−51289.2	+	28996.2i	−0.752913	+	0.425657i
$262$			26413.0i			0.384782i
$263$	9619.50	+	16661.5i	0.139072	+	0.240881i	0.927146	−	0.374701i	$-0.122255\pi$
$263$	9619.50	+	16661.5i	0.139072	+	0.240881i	−0.788073	+	0.615581i	$0.788921\pi$
$264$	−60391.2	+	34503.5i	−0.866494	+	0.495057i
$265$	−10733.6	−	13654.8i	−0.152846	−	0.194444i
$266$	−1557.44	−	899.186i	−0.0220114	−	0.0127083i
$267$	94.6891	−	20927.4i	0.00132824	−	0.293557i
$268$	67054.7	−	38714.0i	0.933597	−	0.539012i
$269$		−	44799.5i		−	0.619111i	−0.950881	−	0.309556i	$-0.899820\pi$
$269$		−	44799.5i		−	0.619111i	0.950881	−	0.309556i	$-0.100180\pi$
$270$	14319.0	−	34385.6i	0.196420	−	0.471682i
$271$	−18271.5			−0.248792			−0.124396	−	0.992233i	$-0.539699\pi$
$271$	−18271.5			−0.248792			−0.124396	+	0.992233i	$0.539699\pi$
$272$	−9416.53	−	16309.9i	−0.127278	−	0.220452i
$273$	3435.44	+	15.5442i	0.0460953	+	0.000208565i
$274$	36724.4	−	63608.6i	0.489163	−	0.847256i
$275$	23896.0	+	81509.8i	0.315980	+	1.07782i
$276$	41481.5	+	72604.8i	0.544548	+	0.953118i
$277$	−100122.	+	57805.4i	−1.30488	+	0.753371i	−0.981236	−	0.192809i	$-0.938240\pi$
$277$	−100122.	+	57805.4i	−1.30488	+	0.753371i	−0.323641	+	0.946180i	$0.604907\pi$
$278$	36832.6			0.476588
$279$	−38103.2	+	64638.8i	−0.489501	+	0.830395i
$280$	3195.92	+	1280.24i	0.0407642	+	0.0163295i
$281$	104701.	−	60449.1i	1.32598	−	0.765557i	0.341308	−	0.939952i	$-0.389130\pi$
$281$	104701.	−	60449.1i	1.32598	−	0.765557i	0.984676	+	0.174395i	$0.0557968\pi$
$282$	3496.96	−	5994.11i	0.0439736	−	0.0753749i
$283$	−123681.	−	71407.4i	−1.54430	−	0.891600i	−0.998560	−	0.0536438i	$-0.982916\pi$
$283$	−123681.	−	71407.4i	−1.54430	−	0.891600i	−0.545737	−	0.837957i	$-0.683750\pi$
$284$	34110.9	+	19693.9i	0.422918	+	0.244172i
$285$	−50230.2	−	64499.3i	−0.618408	−	0.794082i
$286$	21890.1	+	37914.8i	0.267619	+	0.463529i
$287$	−3497.52			−0.0424616
$288$	−43556.6	+	73889.9i	−0.525133	+	0.890841i
$289$	−16871.8			−0.202006
$290$	5281.41	+	36788.3i	0.0627992	+	0.437435i
$291$	128724.	−	73544.3i	1.52010	−	0.868486i
$292$	17771.4	+	10260.3i	0.208428	+	0.120336i
$293$	−24499.4	+	42434.3i	−0.285378	+	0.494290i	−0.972701	−	0.232063i	$-0.925453\pi$
$293$	−24499.4	+	42434.3i	−0.285378	+	0.494290i	0.687323	+	0.726352i	$0.258786\pi$
$294$	44055.7	+	199.337i	0.509692	+	0.00230618i
$295$	−9115.99	−	63498.5i	−0.104751	−	0.729658i
$296$			113607.i			1.29665i
$297$	86465.5	−	48368.0i	0.980234	−	0.548335i
$298$		−	71978.7i		−	0.810535i
$299$	107270.	−	61932.3i	1.19987	−	0.692747i
$300$	47903.7	+	46130.7i	0.532263	+	0.512563i
$301$	−757.961	+	1312.83i	−0.00836592	+	0.0144902i
$302$	−12075.9	+	20916.0i	−0.132405	+	0.229332i
$303$	25721.3	−	14695.5i	0.280161	−	0.160066i
$304$	13252.7	+	22954.3i	0.143403	+	0.248381i
$305$	47914.1	−	119610.i	0.515066	−	1.28579i
$306$	−21033.3	−	37204.3i	−0.224629	−	0.397329i
$307$		−	116431.i		−	1.23536i	−0.786430	−	0.617680i	$-0.788073\pi$
$307$		−	116431.i		−	1.23536i	0.786430	−	0.617680i	$-0.211927\pi$
$308$	1945.65	+	3369.96i	0.0205099	+	0.0355242i
$309$	−17931.6	−	10461.3i	−0.187803	−	0.109564i
$310$	29250.1	+	37210.8i	0.304372	+	0.387209i
$311$	−33284.3	−	19216.7i	−0.344127	−	0.198682i	0.317968	−	0.948101i	$-0.396999\pi$
$311$	−33284.3	−	19216.7i	−0.344127	−	0.198682i	−0.662096	+	0.749419i	$0.730333\pi$
$312$	69675.6	+	40648.6i	0.715766	+	0.417577i
$313$	−67083.4	+	38730.6i	−0.684741	+	0.395335i	−0.801639	−	0.597809i	$-0.796038\pi$
$313$	−67083.4	+	38730.6i	−0.684741	+	0.395335i	0.116898	+	0.993144i	$0.462705\pi$
$314$			10992.2i			0.111487i
$315$	−4535.73	−	1864.75i	−0.0457116	−	0.0187932i
$316$	−87384.4			−0.875104
$317$	2741.17	+	4747.85i	0.0272783	+	0.0472475i	0.879342	−	0.476190i	$-0.157983\pi$
$317$	2741.17	+	4747.85i	0.0272783	+	0.0472475i	−0.852064	+	0.523438i	$0.824649\pi$
$318$	6339.39	+	11095.8i	0.0626893	+	0.109725i
$319$	−49427.6	+	85611.0i	−0.485722	+	0.841295i
$320$	15403.5	+	19595.7i	0.150425	+	0.191364i
$321$	−32612.4	−	147.560i	−0.316499	−	0.00143205i
$322$	−3368.50	+	1944.80i	−0.0324881	+	0.0187570i
$323$	−93801.2			−0.899090
$324$	39994.6	−	66465.0i	0.380988	−	0.633145i
$325$	68011.4	−	71267.9i	0.643895	−	0.674725i
$326$	22290.0	−	12869.1i	0.209737	−	0.121092i
$327$	156422.	+	707.756i	1.46286	+	0.00661893i
$328$	−71120.4	−	41061.4i	−0.661069	−	0.381668i
$329$	−791.267	−	456.838i	−0.00731023	−	0.00422056i
$330$	−8601.01	−	61901.1i	−0.0789808	−	0.568422i
$331$	−33569.2	−	58143.6i	−0.306397	−	0.530696i	0.671174	−	0.741300i	$-0.265790\pi$
$331$	−33569.2	−	58143.6i	−0.306397	−	0.530696i	−0.977571	+	0.210604i	$0.932457\pi$
$332$	−129226.			−1.17240
$333$	1464.40	−	161821.i	0.0132060	−	1.45931i
$334$	72378.7			0.648811
$335$	23266.1	+	162062.i	0.207316	+	1.44408i
$336$	1373.38	+	801.228i	0.0121650	+	0.00709705i
$337$	−80579.2	−	46522.4i	−0.709517	−	0.409640i	0.101365	−	0.994849i	$-0.467679\pi$
$337$	−80579.2	−	46522.4i	−0.709517	−	0.409640i	−0.810882	+	0.585209i	$0.801012\pi$
$338$	−3798.45	+	6579.11i	−0.0332486	+	0.0575882i
$339$	46449.1	−	79618.0i	0.404182	−	0.692806i
$340$	75532.5	−	10843.6i	0.653395	−	0.0938030i
$341$			125894.i			1.08267i
$342$	29602.0	+	52360.8i	0.253087	+	0.447666i
$343$		−	11615.2i		−	0.0987273i
$344$	−30825.5	+	17797.1i	−0.260492	+	0.150395i
$345$	−175133.	+	24334.2i	−1.47139	+	0.204446i
$346$	−21660.4	+	37517.0i	−0.180932	+	0.313383i
$347$	−25688.7	+	44494.1i	−0.213345	+	0.369525i	−0.952759	−	0.303726i	$-0.901769\pi$
$347$	−25688.7	+	44494.1i	−0.213345	+	0.369525i	0.739414	+	0.673251i	$0.235103\pi$
$348$	−350.198	+	77397.9i	−0.00289172	+	0.639103i
$349$	−5628.71	−	9749.21i	−0.0462123	−	0.0800421i	0.841994	−	0.539487i	$-0.181382\pi$
$349$	−5628.71	−	9749.21i	−0.0462123	−	0.0800421i	−0.888206	+	0.459445i	$0.848048\pi$
$350$	−2135.70	+	2237.96i	−0.0174343	+	0.0182691i
$351$	−98721.3	−	58797.7i	−0.801303	−	0.477250i
$352$			143912.i			1.16148i
$353$	78993.2	+	136820.i	0.633929	+	1.09800i	0.986741	+	0.162302i	$0.0518920\pi$
$353$	78993.2	+	136820.i	0.633929	+	1.09800i	−0.352812	+	0.935694i	$0.614775\pi$
$354$	−213.556	+	47198.2i	−0.00170414	+	0.376634i
$355$	−65478.8	+	51470.6i	−0.519570	+	0.408416i
$356$	−23808.6	−	13745.9i	−0.187860	−	0.108461i
$357$	−4885.78	+	2791.41i	−0.0383352	+	0.0219021i
$358$	29489.2	−	17025.6i	0.230089	−	0.132842i
$359$			101263.i			0.785710i	0.919600	+	0.392855i	$0.128513\pi$
$359$			101263.i			0.785710i	−0.919600	+	0.392855i	$0.871487\pi$
$360$	−70339.5	−	91169.1i	−0.542743	−	0.703465i
$361$	1693.47			0.0129946
$362$	−46118.9	−	79880.2i	−0.351934	−	0.609568i
$363$	17365.6	−	29766.3i	0.131788	−	0.225898i
$364$	2256.53	−	3908.42i	0.0170309	−	0.0294984i
$365$	−34113.7	+	26815.6i	−0.256061	+	0.201281i
$366$	−47772.4	+	81886.4i	−0.356628	+	0.611293i
$367$	−170900.	+	98669.4i	−1.26885	+	0.732572i	−0.974771	−	0.223208i	$-0.928347\pi$
$367$	−170900.	+	98669.4i	−1.26885	+	0.732572i	−0.294082	+	0.955780i	$0.595014\pi$
$368$	57327.2			0.423316
$369$	100774.	+	59404.3i	0.740110	+	0.436280i
$370$	−94760.3	−	37959.6i	−0.692187	−	0.277280i
$371$	1457.09	−	841.252i	0.0105862	−	0.00611193i
$372$	48897.6	+	85585.1i	0.353347	+	0.618461i
$373$	207774.	+	119959.i	1.49339	+	0.862212i	0.999971	−	0.00757777i	$-0.00241210\pi$
$373$	207774.	+	119959.i	1.49339	+	0.862212i	0.493423	+	0.869789i	$0.335745\pi$
$374$	−62100.7	−	35853.9i	−0.443970	−	0.256326i
$375$	−128217.	+	57757.0i	−0.911763	+	0.410716i
$376$	−10726.7	−	18579.2i	−0.0758735	−	0.131417i
$377$	114650.			0.806663
$378$	3100.06	+	1846.37i	0.0216963	+	0.0129222i
$379$	201753.			1.40456			0.702282	−	0.711898i	$-0.252164\pi$
$379$	201753.			1.40456			0.702282	+	0.711898i	$0.252164\pi$
$380$	−106303.	+	15261.2i	−0.736173	+	0.105687i
$381$	1126.41	−	248949.i	0.00775970	−	1.71498i
$382$	−63179.0	−	36476.4i	−0.432958	−	0.249969i
$383$	−30536.6	+	52891.0i	−0.208173	+	0.360565i	−0.951139	−	0.308763i	$-0.900085\pi$
$383$	−30536.6	+	52891.0i	−0.208173	+	0.360565i	0.742966	+	0.669329i	$0.233418\pi$
$384$	66546.3	+	116476.i	0.451296	+	0.789900i
$385$	−8144.76	+	1169.28i	−0.0549487	+	0.00788856i
$386$		−	49701.1i		−	0.333574i
$387$	44137.1	−	24952.8i	0.294701	−	0.166608i
$388$		−	194753.i		−	1.29366i
$389$	49647.1	−	28663.8i	0.328091	−	0.189424i	−0.326902	−	0.945058i	$-0.606005\pi$
$389$	49647.1	−	28663.8i	0.328091	−	0.189424i	0.654993	+	0.755635i	$0.272671\pi$
$390$	−57185.8	+	44534.7i	−0.375975	+	0.292799i
$391$	−101439.	+	175697.i	−0.663516	+	1.14924i
$392$	68098.5	−	117950.i	0.443165	−	0.767584i
$393$	−100465.	−	58611.3i	−0.650475	−	0.379486i
$394$	−14223.6	−	24636.0i	−0.0916258	−	0.158701i
$395$	68710.9	−	171526.i	0.440384	−	1.09935i
$396$	1177.75	−	130145.i	0.00751037	−	0.829922i
$397$			258112.i			1.63767i	0.574029	+	0.818835i	$0.305380\pi$
$397$			258112.i			1.63767i	−0.574029	+	0.818835i	$0.694620\pi$
$398$	42063.1	+	72855.4i	0.265543	+	0.459934i
$399$	6876.17	−	3928.59i	0.0431918	−	0.0246769i
$400$	43752.1	−	12826.7i	0.273451	−	0.0801667i
$401$	−159961.	−	92353.5i	−0.994776	−	0.574334i	−0.0880773	−	0.996114i	$-0.528072\pi$
$401$	−159961.	−	92353.5i	−0.994776	−	0.574334i	−0.906698	+	0.421780i	$0.861406\pi$
$402$	545.042	−	120460.i	0.00337270	−	0.745405i
$403$	126448.	−	73004.6i	0.778576	−	0.449511i
$404$		−	38915.1i		−	0.238427i
$405$	99015.9	+	130767.i	0.603663	+	0.797239i
$406$	−3600.26			−0.0218415
$407$	−135760.	−	235144.i	−0.819566	−	1.41953i
$408$	−132121.	−	597.803i	−0.793694	−	0.00359119i
$409$	25843.5	−	44762.2i	0.154491	−	0.267587i	−0.778382	−	0.627790i	$-0.783959\pi$
$409$	25843.5	−	44762.2i	0.154491	−	0.267587i	0.932874	+	0.360204i	$0.117293\pi$
$410$	58012.9	−	45602.0i	0.345109	−	0.271279i
$411$	160451.	+	280836.i	0.949857	+	1.66253i
$412$	−23618.0	+	13635.9i	−0.139139	+	0.0803320i
$413$	6214.23			0.0364324
$414$	130088.	+	1177.23i	0.758994	+	0.00686850i
$415$	101611.	−	253658.i	0.589993	−	1.47283i
$416$	144545.	−	83453.1i	0.835250	−	0.482232i
$417$	−81732.9	+	140098.i	−0.470029	+	0.805673i
$418$	87399.7	+	50460.2i	0.500216	+	0.288800i
$419$	293177.	+	169266.i	1.66994	+	0.964142i	0.967665	+	0.252239i	$0.0811668\pi$
$419$	293177.	+	169266.i	1.66994	+	0.964142i	0.702278	+	0.711903i	$0.252167\pi$
$420$	−5082.82	+	3958.36i	−0.0288142	+	0.0224397i
$421$	−112147.	−	194245.i	−0.632740	−	1.09594i	−0.986989	−	0.160787i	$-0.948597\pi$
$421$	−112147.	−	194245.i	−0.632740	−	1.09594i	0.354249	−	0.935151i	$-0.384736\pi$
$422$	−99430.9			−0.558337
$423$	15039.5	+	26602.3i	0.0840530	+	0.148675i
$424$	39505.7			0.219749
$425$	−38106.8	+	156789.i	−0.210972	+	0.868035i
$426$	53207.4	−	30399.2i	0.293193	−	0.167511i
$427$	10809.6	+	6240.93i	0.0592862	+	0.0342289i
$428$	−21421.1	+	37102.4i	−0.116937	+	0.202541i
$429$	−192789.	−	872.303i	−1.04753	−	0.00473972i
$430$	−4544.93	−	31658.3i	−0.0245805	−	0.171218i
$431$			334739.i			1.80199i	0.433833	+	0.900993i	$0.357161\pi$
$431$			334739.i			1.80199i	−0.433833	+	0.900993i	$0.642839\pi$
$432$	−25962.6	−	46412.2i	−0.139117	−	0.248694i
$433$			79690.3i			0.425040i	0.977157	+	0.212520i	$0.0681671\pi$
$433$			79690.3i			0.425040i	−0.977157	+	0.212520i	$0.931833\pi$
$434$	−3970.72	+	2292.50i	−0.0210809	+	0.0121711i
$435$	−151649.	−	61545.9i	−0.801420	−	0.325252i
$436$	102744.	−	177958.i	0.540485	−	0.936147i
$437$	142764.	−	247274.i	0.747575	−	1.29484i
$438$	27720.5	−	15837.6i	0.144495	−	0.0825547i
$439$	25448.4	+	44077.8i	0.132048	+	0.228713i	0.924466	−	0.381265i	$-0.124511\pi$
$439$	25448.4	+	44077.8i	0.132048	+	0.228713i	−0.792418	+	0.609978i	$0.791178\pi$
$440$	−179347.	−	71843.9i	−0.926381	−	0.371095i
$441$	−98519.4	+	167129.i	−0.506576	+	0.859361i
$442$			83165.3i			0.425694i
$443$	−145297.	−	251662.i	−0.740372	−	1.28236i	−0.952326	−	0.305082i	$-0.901316\pi$
$443$	−145297.	−	251662.i	−0.740372	−	1.28236i	0.211955	−	0.977280i	$-0.432017\pi$
$444$	−183623.	−	107126.i	−0.931455	−	0.543410i
$445$	45702.6	−	35925.3i	0.230792	−	0.181418i
$446$	−50620.1	−	29225.6i	−0.254480	−	0.146924i
$447$	273780.	+	159723.i	1.37021	+	0.799379i
$448$	−2091.03	+	1207.26i	−0.0104185	+	0.00601511i
$449$		−	361637.i		−	1.79382i	−0.442210	−	0.896912i	$-0.645805\pi$
$449$		−	361637.i		−	1.79382i	0.442210	−	0.896912i	$-0.354195\pi$
$450$	99547.0	−	28208.2i	0.491590	−	0.139300i
$451$	196273.			0.964955
$452$	−60544.5	−	104866.i	−0.296345	−	0.513285i
$453$	−52760.0	−	92345.4i	−0.257104	−	0.450007i
$454$	9277.36	−	16068.9i	0.0450104	−	0.0779602i
$455$	5897.50	+	7502.54i	0.0284869	+	0.0362398i
$456$	185946.	+	841.340i	0.894246	+	0.00404615i
$457$	−63960.2	+	36927.5i	−0.306251	+	0.176814i	−0.645248	−	0.763973i	$-0.723246\pi$
$457$	−63960.2	+	36927.5i	−0.306251	+	0.176814i	0.338997	+	0.940788i	$0.389912\pi$
$458$	47408.3			0.226008
$459$	188185.	+	2554.55i	0.893223	+	0.0121252i
$460$	−86373.7	+	215619.i	−0.408193	+	1.01899i
$461$	5305.41	−	3063.08i	0.0249642	−	0.0144131i	−0.487466	−	0.873142i	$-0.662079\pi$
$461$	5305.41	−	3063.08i	0.0249642	−	0.0144131i	0.512430	+	0.858729i	$0.328745\pi$
$462$	6053.98	+	27.3921i	0.0283633	+	0.000128334i
$463$	207709.	+	119921.i	0.968933	+	0.559414i	0.898911	−	0.438132i	$-0.144360\pi$
$463$	207709.	+	119921.i	0.968933	+	0.559414i	0.0700222	+	0.997545i	$0.477693\pi$
$464$	45953.6	+	26531.3i	0.213444	+	0.123232i
$465$	−206443.	+	28684.7i	−0.954761	+	0.132662i
$466$	−18556.6	−	32141.0i	−0.0854530	−	0.148009i
$467$	−55135.6			−0.252812			−0.126406	−	0.991979i	$-0.540344\pi$
$467$	−55135.6			−0.252812			−0.126406	+	0.991979i	$0.540344\pi$
$468$	−131401.	+	74286.9i	−0.599937	+	0.339173i
$469$	−15860.1			−0.0721042
$470$	19081.1	−	2739.32i	0.0863787	−	0.0124007i
$471$	−41810.2	−	24392.0i	−0.188469	−	0.109953i
$472$	126364.	+	72956.0i	0.567202	+	0.327474i
$473$	42535.0	−	73672.8i	0.190118	−	0.329295i
$474$	−68507.9	+	117429.i	−0.304918	+	0.522659i
$475$	53631.0	−	220662.i	0.237700	−	0.978005i
$476$			7391.93i			0.0326245i
$477$	−56271.6	−	509.229i	−0.247316	−	0.00223808i
$478$			67151.7i			0.293901i
$479$	−315795.	+	182324.i	−1.37637	+	0.794645i	−0.991720	−	0.128419i	$-0.959010\pi$
$479$	−315795.	+	182324.i	−1.37637	+	0.794645i	−0.384646	+	0.923064i	$0.625676\pi$
$480$	−235989.	+	32790.1i	−1.02426	+	0.142318i
$481$	−157452.	+	272715.i	−0.680548	+	1.17874i
$482$	36464.3	−	63158.0i	0.156955	−	0.271853i
$483$	77.4987	−	17128.1i	0.000332200	−	0.0734201i
$484$	−22635.4	−	39205.7i	−0.0966268	−	0.167363i
$485$	382280.	+	153136.i	1.62517	+	0.651017i
$486$	−57961.9	−	105853.i	−0.245398	−	0.448157i
$487$		−	119653.i		−	0.504505i	−0.967661	−	0.252253i	$-0.918829\pi$
$487$		−	119653.i		−	0.504505i	0.967661	−	0.252253i	$-0.0811714\pi$
$488$	146539.	+	253813.i	0.615337	+	1.06579i
$489$	−512.824	+	113340.i	−0.00214462	+	0.473986i
$490$	75628.9	+	96211.8i	0.314989	+	0.400716i
$491$	−91852.2	−	53030.9i	−0.381001	−	0.219971i	0.297253	−	0.954799i	$-0.403930\pi$
$491$	−91852.2	−	53030.9i	−0.381001	−	0.219971i	−0.678254	+	0.734828i	$0.737263\pi$
$492$	133430.	−	76233.1i	0.551218	−	0.314929i
$493$	−162627.	+	93892.9i	−0.669113	+	0.386312i
$494$		−	117046.i		−	0.479624i
$495$	254535.	+	104646.i	1.03881	+	0.427082i
$496$	67576.2			0.274682
$497$	−4034.04	−	6987.17i	−0.0163316	−	0.0282871i
$498$	−101311.	+	173657.i	−0.408506	+	0.700218i
$499$	−95907.1	+	166116.i	−0.385167	+	0.667129i	−0.991792	−	0.127859i	$-0.959190\pi$
$499$	−95907.1	+	166116.i	−0.385167	+	0.667129i	0.606625	+	0.794988i	$0.292523\pi$
$500$	−17676.8	+	183886.i	−0.0707071	+	0.735544i
$501$	−160611.	+	275302.i	−0.639881	+	1.09682i
$502$	−13990.3	+	8077.29i	−0.0555161	+	0.0320522i
$503$	−155699.			−0.615391			−0.307696	−	0.951485i	$-0.599558\pi$
$503$	−155699.			−0.615391			−0.307696	+	0.951485i	$0.599558\pi$
$504$	9710.31	−	5489.69i	0.0382272	−	0.0216116i
$505$	76386.3	+	30599.2i	0.299525	+	0.119985i
$506$	189032.	−	109138.i	0.738304	−	0.426260i
$507$	−16595.6	−	29047.2i	−0.0645621	−	0.113002i
$508$	−283223.	−	163519.i	−1.09749	−	0.633637i
$509$	−253416.	−	146310.i	−0.978132	−	0.564725i	−0.0764267	−	0.997075i	$-0.524351\pi$
$509$	−253416.	−	146310.i	−0.978132	−	0.564725i	−0.901706	+	0.432350i	$0.857684\pi$
$510$	44644.3	−	110003.i	0.171643	−	0.422927i
$511$	−2101.69	−	3640.24i	−0.00804873	−	0.0139408i
$512$	143619.			0.547864
$513$	−264849.	−	3595.24i	−1.00638	−	0.0136613i
$514$	−154709.			−0.585583
$515$	−8194.78	−	57081.7i	−0.0308975	−	0.215220i
$516$	301.364	−	66605.0i	0.00113186	−	0.250154i
$517$	44404.1	+	25636.7i	0.166128	+	0.0959138i
$518$	4944.33	−	8563.83i	0.0184267	−	0.0319160i
$519$	−94635.5	−	165640.i	−0.351333	−	0.614936i
$520$	31841.9	+	221798.i	0.117758	+	0.820259i
$521$		−	28599.3i		−	0.105361i	−0.998611	−	0.0526805i	$-0.983224\pi$
$521$		−	28599.3i		−	0.105361i	0.998611	−	0.0526805i	$-0.0167765\pi$
$522$	103734.	+	61149.2i	0.380699	+	0.224414i
$523$		−	255598.i		−	0.934444i	−0.884140	−	0.467222i	$-0.845255\pi$
$523$		−	255598.i		−	0.934444i	0.884140	−	0.467222i	$-0.154745\pi$
$524$	−132324.	+	76397.5i	−0.481923	+	0.278238i
$525$	−3773.18	−	13089.5i	−0.0136896	−	0.0474903i
$526$	19660.2	−	34052.4i	0.0710584	−	0.123077i
$527$	−119574.	+	207109.i	−0.430543	+	0.745722i
$528$	−77070.9	−	44963.1i	−0.276454	−	0.161283i
$529$	−168856.	−	292467.i	−0.603400	−	1.04512i
$530$	−13200.0	+	32951.8i	−0.0469919	+	0.117308i
$531$	−179051.	−	105547.i	−0.635020	−	0.374331i
$532$		−	10403.3i		−	0.0367577i
$533$	−113817.	−	197136.i	−0.400638	−	0.693925i
$534$	−37137.5	+	21217.9i	−0.130236	+	0.0744080i
$535$	−55984.5	−	71221.1i	−0.195596	−	0.248829i
$536$	−322508.	−	186200.i	−1.12256	−	0.648112i
$537$	−678.454	+	149946.i	−0.00235273	+	0.519981i
$538$	−79293.6	+	45780.2i	−0.273952	+	0.158166i
$539$			325510.i			1.12043i
$540$	213683.	−	27722.1i	0.732794	−	0.0950689i
$541$	222986.			0.761874			0.380937	−	0.924601i	$-0.375601\pi$
$541$	222986.			0.761874			0.380937	+	0.924601i	$0.375601\pi$
$542$	18671.5	+	32339.9i	0.0635595	+	0.110088i
$543$	406174.	+	1837.80i	1.37757	+	0.00623301i
$544$	−136688.	+	236750.i	−0.461883	+	0.800005i
$545$	268524.	+	341605.i	0.904046	+	1.15009i
$546$	−3483.13	−	6096.50i	−0.0116838	−	0.0204501i
$547$	92696.0	−	53518.0i	0.309803	−	0.178865i	−0.337035	−	0.941492i	$-0.609424\pi$
$547$	92696.0	−	53518.0i	0.309803	−	0.178865i	0.646838	+	0.762627i	$0.276091\pi$
$548$	424890.			1.41487
$549$	−205457.	−	363417.i	−0.681673	−	1.20576i
$550$	119851.	−	125589.i	0.396200	−	0.415171i
$551$	228879.	−	132143.i	0.753882	−	0.435254i
$552$	202662.	−	347382.i	0.665112	−	1.14006i
$553$	15501.5	+	8949.77i	0.0506900	+	0.0292659i
$554$	204627.	+	118142.i	0.666721	+	0.384931i
$555$	354661.	−	276200.i	1.15140	−	0.896679i
$556$	106536.	+	184525.i	0.344624	+	0.596906i
$557$	−165757.			−0.534272			−0.267136	−	0.963659i	$-0.586077\pi$
$557$	−165757.			−0.534272			−0.267136	+	0.963659i	$0.586077\pi$
$558$	153346.	+	1387.70i	0.492497	+	0.00445684i
$559$	−98662.6			−0.315740
$560$	627.637	+	4371.88i	0.00200139	+	0.0139409i
$561$	274179.	−	156647.i	0.871180	−	0.497734i
$562$	−213986.	−	123545.i	−0.677505	−	0.391158i
$563$	−198623.	+	344026.i	−0.626634	+	1.08536i	0.361589	+	0.932338i	$0.382234\pi$
$563$	−198623.	+	344026.i	−0.626634	+	1.08536i	−0.988223	+	0.153024i	$0.951099\pi$
$564$	40144.1	+	181.638i	0.126201	+	0.000571017i
$565$	253448.	−	36385.6i	0.793947	−	0.113981i
$566$			291882.i			0.911118i
$567$	−13902.0	+	7694.31i	−0.0432427	+	0.0239334i
$568$		−	189441.i		−	0.587188i
$569$	−39485.1	+	22796.7i	−0.121957	+	0.0704122i	−0.559738	−	0.828670i	$-0.689098\pi$
$569$	−39485.1	+	22796.7i	−0.121957	+	0.0704122i	0.437780	+	0.899082i	$0.355765\pi$
$570$	−62831.8	+	154817.i	−0.193388	+	0.476507i
$571$	137353.	−	237902.i	0.421275	−	0.729669i	−0.574790	−	0.818301i	$-0.694916\pi$
$571$	137353.	−	237902.i	0.421275	−	0.729669i	0.996064	+	0.0886320i	$0.0282495\pi$
$572$	−126631.	+	219331.i	−0.387033	+	0.670361i
$573$	278939.	−	159367.i	0.849572	−	0.485389i
$574$	3574.08	+	6190.49i	0.0108478	+	0.0187889i
$575$	−355321.	−	339085.i	−1.07469	−	1.02559i
$576$	80753.8	+	730.780i	0.243398	+	0.00220263i
$577$		−	85338.7i		−	0.256327i	−0.991753	−	0.128164i	$-0.959092\pi$
$577$		−	85338.7i		−	0.256327i	0.991753	−	0.128164i	$-0.0409082\pi$
$578$	17241.1	+	29862.5i	0.0516071	+	0.0893861i
$579$	189045.	+	110288.i	0.563907	+	0.328983i
$580$	−169027.	+	132866.i	−0.502457	+	0.394965i
$581$	22924.0	+	13235.2i	0.0679106	+	0.0392082i
$582$	−261713.	−	152683.i	−0.772643	−	0.450759i
$583$	−81768.6	+	47209.1i	−0.240574	+	0.138896i
$584$		−	98696.7i		−	0.289385i
$585$	−42496.3	−	316338.i	−0.124177	−	0.924356i
$586$	100143.			0.291625
$587$	183601.	+	318006.i	0.532843	+	0.922910i	0.999264	+	0.0383480i	$0.0122095\pi$
$587$	183601.	+	318006.i	0.532843	+	0.922910i	−0.466422	+	0.884562i	$0.654457\pi$
$588$	126429.	+	221288.i	0.365673	+	0.640034i
$589$	168287.	−	291482.i	0.485088	−	0.840197i
$590$	−103075.	+	81023.5i	−0.296106	+	0.232759i
$591$	125269.	+	566.799i	0.358648	+	0.00162276i
$592$	−126218.	+	72872.3i	−0.360147	+	0.207931i
$593$	−203932.			−0.579930			−0.289965	−	0.957037i	$-0.593644\pi$
$593$	−203932.			−0.579930			−0.289965	+	0.957037i	$0.593644\pi$
$594$	−173968.	−	103614.i	−0.493056	−	0.293661i
$595$	−14509.6	−	5812.33i	−0.0409847	−	0.0164178i
$596$	360601.	−	208193.i	1.01516	−	0.586102i
$597$	−370454.	−	1676.18i	−1.03941	−	0.00470296i
$598$	−219236.	−	126576.i	−0.613070	−	0.353956i
$599$	150018.	+	86613.1i	0.418110	+	0.241396i	0.694268	−	0.719716i	$-0.255728\pi$
$599$	150018.	+	86613.1i	0.418110	+	0.241396i	−0.276158	+	0.961112i	$0.589061\pi$
$600$	76947.0	−	310467.i	0.213742	−	0.862408i
$601$	194986.	+	337727.i	0.539828	+	0.935010i	0.998913	+	0.0466173i	$0.0148441\pi$
$601$	194986.	+	337727.i	0.539828	+	0.935010i	−0.459085	+	0.888393i	$0.651823\pi$
$602$	3098.21			0.00854906
$603$	456978.	+	269379.i	1.25678	+	0.740848i
$604$	−139714.			−0.382971
$605$	94755.0	−	13603.3i	0.258876	−	0.0371648i
$606$	−52294.9	−	30508.8i	−0.142401	−	0.0830767i
$607$	−162922.	−	94063.2i	−0.442184	−	0.255295i	0.262340	−	0.964976i	$-0.415506\pi$
$607$	−162922.	−	94063.2i	−0.442184	−	0.255295i	−0.704524	+	0.709681i	$0.748839\pi$
$608$	192373.	−	333199.i	0.520398	−	0.901356i
$609$	7989.10	−	13694.1i	0.0215409	−	0.0369230i
$610$	−260669.	+	37422.2i	−0.700535	+	0.100570i
$611$		−	59465.9i		−	0.159289i
$612$	125550.	−	212984.i	0.335207	−	0.568648i
$613$			105068.i			0.279608i	0.990179	+	0.139804i	$0.0446472\pi$
$613$			105068.i			0.279608i	−0.990179	+	0.139804i	$0.955353\pi$
$614$	−206080.	+	118980.i	−0.546636	+	0.315601i
$615$	44720.5	+	321852.i	0.118238	+	0.850954i
$616$	9357.85	−	16208.3i	0.0246612	−	0.0427145i
$617$	−40749.7	+	70580.5i	−0.107042	+	0.185402i	−0.914571	−	0.404426i	$-0.867471\pi$
$617$	−40749.7	+	70580.5i	−0.107042	+	0.185402i	0.807529	+	0.589828i	$0.200805\pi$
$618$	−191.975	+	42428.6i	−0.000502652	+	0.111092i
$619$	−61533.5	−	106579.i	−0.160594	−	0.278158i	0.774488	−	0.632589i	$-0.218008\pi$
$619$	−61533.5	−	106579.i	−0.160594	−	0.278158i	−0.935082	+	0.354431i	$0.884674\pi$
$620$	−101816.	+	254167.i	−0.264869	+	0.661205i
$621$	−293148.	+	492196.i	−0.760159	+	1.27631i
$622$			78549.5i			0.203031i
$623$	2815.67	+	4876.88i	0.00725446	+	0.0125651i
$624$	−468.227	+	103484.i	−0.00120251	+	0.265768i
$625$	−347050.	−	179289.i	−0.888447	−	0.458979i
$626$	137104.	+	79156.9i	0.349865	+	0.201995i
$627$	−385875.	+	220463.i	−0.981548	+	0.560791i
$628$	−55068.9	+	31794.0i	−0.139633	+	0.0806170i
$629$		−	515782.i		−	1.30366i
$630$	1334.47	+	9933.67i	0.00336224	+	0.0250281i
$631$	−760006.			−1.90879			−0.954396	−	0.298545i	$-0.903499\pi$
$631$	−760006.			−1.90879			−0.954396	+	0.298545i	$0.903499\pi$
$632$	210143.	+	363979.i	0.526116	+	0.911259i
$633$	220641.	−	378198.i	0.550653	−	0.943870i
$634$	5602.36	−	9703.57i	0.0139377	−	0.0241409i
$635$	543670.	−	427361.i	1.34831	−	1.05986i
$636$	−37251.7	+	63852.9i	−0.0920942	+	0.157858i
$637$	326942.	−	188760.i	0.805734	−	0.465191i
$638$	202038.			0.496355
$639$	−2441.90	+	269838.i	−0.00598034	+	0.660848i
$640$	−138564.	+	345905.i	−0.338292	+	0.844494i
$641$	−209786.	+	121120.i	−0.510577	+	0.294782i	−0.733071	−	0.680152i	$-0.761914\pi$
$641$	−209786.	+	121120.i	−0.510577	+	0.294782i	0.222494	+	0.974934i	$0.428580\pi$
$642$	33065.1	+	57873.6i	0.0802232	+	0.140414i
$643$	335283.	+	193576.i	0.810941	+	0.468197i	0.847283	−	0.531142i	$-0.178237\pi$
$643$	335283.	+	193576.i	0.810941	+	0.468197i	−0.0363415	+	0.999339i	$0.511570\pi$
$644$	−19486.2	−	11250.4i	−0.0469847	−	0.0271266i
$645$	130502.	+	52963.5i	0.313687	+	0.127308i
$646$	95854.5	+	166025.i	0.229693	+	0.397840i
$647$	174684.			0.417297			0.208649	−	0.977991i	$-0.433093\pi$
$647$	174684.			0.417297			0.208649	+	0.977991i	$0.433093\pi$
$648$	−373024.	−	6751.90i	−0.888355	−	0.0160796i
$649$	−348729.			−0.827939
$650$	−195642.	−	47549.9i	−0.463058	−	0.112544i
$651$	91.3540	−	20190.3i	0.000215559	−	0.0476410i
$652$	128944.	+	74446.0i	0.303324	+	0.175124i
$653$	149972.	−	259759.i	0.351709	−	0.609178i	−0.634840	−	0.772644i	$-0.718934\pi$
$653$	149972.	−	259759.i	0.351709	−	0.609178i	0.986549	+	0.163466i	$0.0522673\pi$
$654$	−158594.	−	277585.i	−0.370792	−	0.648995i
$655$	−45912.8	−	319811.i	−0.107017	−	0.745436i
$656$		−	105354.i		−	0.244817i
$657$	−1272.20	+	140583.i	−0.00294731	+	0.325688i
$658$			1867.35i			0.00431295i
$659$	206766.	−	119376.i	0.476111	−	0.274883i	−0.242683	−	0.970106i	$-0.578028\pi$
$659$	206766.	−	119376.i	0.476111	−	0.274883i	0.718794	+	0.695223i	$0.244694\pi$
$660$	285236.	−	222134.i	0.654812	−	0.509949i
$661$	174605.	−	302425.i	0.399627	−	0.692174i	−0.594053	−	0.804426i	$-0.702473\pi$
$661$	174605.	−	302425.i	0.399627	−	0.692174i	0.993680	+	0.112252i	$0.0358063\pi$
$662$	−68608.1	+	118833.i	−0.156552	+	0.271157i
$663$	−316330.	−	184547.i	−0.719637	−	0.419835i
$664$	310765.	+	538261.i	0.704849	+	1.22083i
$665$	20420.6	+	8180.19i	0.0461769	+	0.0184978i
$666$	−287915.	+	162772.i	−0.649106	+	0.366970i
$667$		−	571613.i		−	1.28484i
$668$	209350.	+	362605.i	0.469159	+	0.812607i
$669$	223491.	−	127688.i	0.499353	−	0.285297i
$670$	263070.	−	206790.i	0.586032	−	0.460660i
$671$	−606610.	−	350226.i	−1.34730	−	0.777864i
$672$	104.429	−	23079.9i	0.000231250	−	0.0511088i
$673$	−154058.	+	88945.3i	−0.340137	+	0.196378i	−0.660332	−	0.750973i	$-0.729585\pi$
$673$	−154058.	+	88945.3i	−0.340137	+	0.196378i	0.320196	+	0.947351i	$0.396251\pi$
$674$			190163.i			0.418607i
$675$	−113605.	+	441235.i	−0.249338	+	0.968417i
$676$	−43946.9			−0.0961690
$677$	−23441.0	−	40601.0i	−0.0511444	−	0.0885848i	0.839320	−	0.543638i	$-0.182954\pi$
$677$	−23441.0	−	40601.0i	−0.0511444	−	0.0885848i	−0.890464	+	0.455053i	$0.849620\pi$
$678$	−188387.	−	852.385i	−0.409819	−	0.00185429i
$679$	−19946.3	+	34548.0i	−0.0432636	+	0.0749347i
$680$	−226808.	−	288536.i	−0.490502	−	0.623996i
$681$	40533.2	+	70945.0i	0.0874011	+	0.152977i
$682$	222828.	−	128650.i	0.479072	−	0.276592i
$683$	−880813.			−1.88817			−0.944087	−	0.329696i	$-0.893054\pi$
$683$	−880813.			−1.88817			−0.944087	+	0.329696i	$0.893054\pi$
$684$	−176697.	+	299750.i	−0.377673	+	0.640689i
$685$	−334094.	+	834015.i	−0.712013	+	1.77743i
$686$	−20558.5	+	11869.4i	−0.0436860	+	0.0252221i
$687$	−105201.	+	180324.i	−0.222897	+	0.382067i
$688$	−39545.5	−	22831.6i	−0.0835449	−	0.0482346i
$689$	94833.7	+	54752.2i	0.199767	+	0.115336i
$690$	222037.	+	285112.i	0.466367	+	0.598849i
$691$	43555.7	+	75440.8i	0.0912198	+	0.157997i	0.908025	−	0.418917i	$-0.137590\pi$
$691$	43555.7	+	75440.8i	0.0912198	+	0.157997i	−0.816805	+	0.576914i	$0.804257\pi$
$692$	−250605.			−0.523331
$693$	−13538.2	+	22966.3i	−0.0281899	+	0.0478217i
$694$	105004.			0.218016
$695$	−445973.	+	64024.9i	−0.923292	+	0.132550i
$696$	323225.	−	184669.i	0.667246	−	0.381220i
$697$	322890.	+	186420.i	0.664643	+	0.383732i
$698$	−11503.9	+	19925.3i	−0.0236120	+	0.0408971i
$699$	163430.	+	739.465i	0.334486	+	0.00151343i
$700$	−17389.1	−	4226.35i	−0.0354880	−	0.00862520i
$701$			595389.i			1.21162i	0.795611	+	0.605808i	$0.207150\pi$
$701$			595389.i			1.21162i	−0.795611	+	0.605808i	$0.792850\pi$
$702$	−3187.59	+	234818.i	−0.00646826	+	0.476494i
$703$			725905.i			1.46882i
$704$	117344.	−	67748.5i	0.236764	−	0.136696i
$705$	−31922.1	+	78655.9i	−0.0642264	+	0.158253i
$706$	161445.	−	279631.i	0.323903	−	0.561016i
$707$	−3985.62	+	6903.30i	−0.00797365	+	0.0138108i
$708$	−237073.	+	135447.i	−0.472949	+	0.270212i
$709$	323680.	+	560629.i	0.643906	+	1.11528i	0.984553	+	0.175087i	$0.0560207\pi$
$709$	323680.	+	560629.i	0.643906	+	1.11528i	−0.340647	+	0.940191i	$0.610646\pi$
$710$	158013.	+	63297.8i	0.313456	+	0.125566i
$711$	−294635.	−	521157.i	−0.582834	−	1.03093i
$712$			132225.i			0.260828i
$713$	−363980.	−	630432.i	−0.715976	−	1.24011i
$714$	9933.42	+	5795.15i	0.0194851	+	0.0113676i
$715$	−330954.	−	421025.i	−0.647374	−	0.823562i
$716$	170590.	+	98490.4i	0.332758	+	0.192118i
$717$	−255420.	−	149012.i	−0.496841	−	0.289856i
$718$	179232.	−	103480.i	0.347670	−	0.200727i
$719$			234792.i			0.454178i	0.973874	+	0.227089i	$0.0729209\pi$
$719$			234792.i			0.454178i	−0.973874	+	0.227089i	$0.927079\pi$
$720$	56170.8	−	136627.i	0.108354	−	0.263555i
$721$	5586.26			0.0107461
$722$	−1730.54	−	2997.39i	−0.00331977	−	0.00575001i
$723$	159314.	+	278847.i	0.304774	+	0.533444i
$724$	266791.	−	462095.i	0.508971	−	0.881564i
$725$	−127896.	−	436255.i	−0.243321	−	0.829974i
$726$	−70431.1	−	318.676i	−0.133626	−	0.000604611i
$727$	772639.	−	446083.i	1.46187	−	0.844009i	0.462769	−	0.886479i	$-0.346856\pi$
$727$	772639.	−	446083.i	1.46187	−	0.844009i	0.999098	+	0.0424699i	$0.0135227\pi$
$728$	−21706.1			−0.0409562
$729$	531245.	+	14425.6i	0.999632	+	0.0271444i
$730$	82323.2	+	32977.5i	0.154482	+	0.0618830i
$731$	139949.	−	80799.8i	0.261900	−	0.151208i
$732$	−548415.	−	2481.38i	−1.02350	−	0.00463097i
$733$	354772.	+	204828.i	0.660300	+	0.381224i	0.792391	−	0.610013i	$-0.208836\pi$
$733$	354772.	+	204828.i	0.660300	+	0.381224i	−0.132092	+	0.991238i	$0.542169\pi$
$734$	349283.	+	201659.i	0.648314	+	0.374304i
$735$	−533777.	+	74167.0i	−0.988065	+	0.137289i
$736$	−416073.	−	720659.i	−0.768093	−	1.33038i
$737$	890033.			1.63859
$738$	2163.47	−	239071.i	0.00397227	−	0.438950i
$739$	635453.			1.16357			0.581787	−	0.813341i	$-0.302354\pi$
$739$	635453.			1.16357			0.581787	+	0.813341i	$0.302354\pi$
$740$	−83916.2	−	584528.i	−0.153244	−	1.06744i
$741$	445198.	+	259728.i	0.810806	+	0.473024i
$742$	−2977.98	−	1719.34i	−0.00540896	−	0.00312286i
$743$	22811.7	−	39511.0i	0.0413219	−	0.0715716i	−0.844625	−	0.535359i	$-0.820176\pi$
$743$	22811.7	−	39511.0i	0.0413219	−	0.0715716i	0.885947	+	0.463787i	$0.153510\pi$
$744$	238895.	−	409487.i	0.431579	−	0.739767i
$745$	125118.	+	871525.i	0.225428	+	1.57024i
$746$		−	490338.i		−	0.881086i
$747$	−435713.	−	770700.i	−0.780835	−	1.38116i
$748$		−	414818.i		−	0.741404i
$749$	7599.93	−	4387.82i	0.0135471	−	0.00782142i
$750$	233251.	+	167918.i	0.414669	+	0.298521i
$751$	−134221.	+	232478.i	−0.237981	+	0.412195i	−0.960135	−	0.279538i	$-0.909819\pi$
$751$	−134221.	+	232478.i	−0.237981	+	0.412195i	0.722154	+	0.691732i	$0.243152\pi$
$752$	13761.0	−	23834.8i	0.0243341	−	0.0421479i
$753$	321.873	−	71137.6i	0.000567668	−	0.125461i
$754$	−117160.	−	202927.i	−0.206080	−	0.356942i
$755$	109858.	−	274244.i	0.192725	−	0.481108i
$756$	−283.320	+	20871.2i	−0.000495718	+	0.0365178i
$757$		−	453292.i		−	0.791018i	−0.918462	−	0.395509i	$-0.870568\pi$
$757$		−	453292.i		−	0.791018i	0.918462	−	0.395509i	$-0.129432\pi$
$758$	−206170.	−	357096.i	−0.358828	−	0.621508i
$759$	−4349.05	+	961190.i	−0.00754937	+	1.66850i
$760$	319207.	+	406081.i	0.552643	+	0.703049i
$761$	20609.8	+	11899.1i	0.0355881	+	0.0205468i	0.517689	−	0.855569i	$-0.326793\pi$
$761$	20609.8	+	11899.1i	0.0355881	+	0.0205468i	−0.482100	+	0.876116i	$0.660126\pi$
$762$	−441782.	+	252404.i	−0.760848	+	0.434697i
$763$	−36452.3	+	21045.8i	−0.0626147	+	0.0361506i
$764$		−	422021.i		−	0.723015i
$765$	319344.	+	413911.i	0.545678	+	0.707269i
$766$	124820.			0.212730
$767$	202224.	+	350263.i	0.343750	+	0.595392i
$768$	210501.	−	360818.i	0.356887	−	0.611738i
$769$	424556.	−	735352.i	0.717930	−	1.24349i	−0.243888	−	0.969803i	$-0.578423\pi$
$769$	424556.	−	735352.i	0.717930	−	1.24349i	0.961818	−	0.273688i	$-0.0882437\pi$
$770$	10392.6	+	13221.1i	0.0175285	+	0.0222990i
$771$	343304.	−	588455.i	0.577524	−	0.989930i
$772$	248994.	−	143757.i	0.417786	−	0.241209i
$773$	367992.			0.615857			0.307928	−	0.951410i	$-0.400364\pi$
$773$	367992.			0.615857			0.307928	+	0.951410i	$0.400364\pi$
$774$	−89268.8	−	52622.1i	−0.149011	−	0.0878388i
$775$	−418846.	−	399707.i	−0.697350	−	0.665485i
$776$	−811197.	+	468345.i	−1.34711	+	0.777754i
$777$	21602.0	+	37809.8i	0.0357810	+	0.0626272i
$778$	−101468.	−	58582.5i	−0.167637	−	0.0967851i
$779$	−454430.	−	262366.i	−0.748846	−	0.432346i
$780$	−388517.	−	157678.i	−0.638588	−	0.259168i
$781$	226381.	+	392104.i	0.371140	+	0.642834i
$782$	414638.			0.678040
$783$	−462779.	+	258875.i	−0.754832	+	0.422246i
$784$	174724.			0.284264
$785$	−19107.3	−	133094.i	−0.0310071	−	0.215983i
$786$	−1075.57	+	237714.i	−0.00174099	+	0.384778i
$787$	−9633.41	−	5561.85i	−0.0155536	−	0.00897987i	0.492203	−	0.870480i	$-0.336192\pi$
$787$	−9633.41	−	5561.85i	−0.0155536	−	0.00897987i	−0.507757	+	0.861501i	$0.669525\pi$
$788$	82281.5	−	142516.i	0.132510	−	0.229515i
$789$	85896.2	+	150343.i	0.137981	+	0.241507i
$790$	−373811.	+	53665.2i	−0.598960	+	0.0859881i
$791$			24803.5i			0.0396424i
$792$	−544920.	+	308069.i	−0.868725	+	0.491131i
$793$			812372.i			1.29184i
$794$	456849.	−	263762.i	0.724655	−	0.418380i
$795$	−96045.3	−	123329.i	−0.151964	−	0.195133i
$796$	−243328.	+	421457.i	−0.384031	+	0.665162i
$797$	131296.	−	227411.i	0.206697	−	0.358009i	−0.743975	−	0.668207i	$-0.767062\pi$
$797$	131296.	−	227411.i	0.206697	−	0.358009i	0.950672	+	0.310198i	$0.100395\pi$
$798$	−13980.2	−	8156.01i	−0.0219536	−	0.0128077i
$799$	48699.6	+	84350.2i	0.0762837	+	0.132127i
$800$	−478791.	−	456913.i	−0.748111	−	0.713927i
$801$	1704.39	−	188341.i	0.00265646	−	0.293548i
$802$			377501.i			0.586906i
$803$	117942.	+	204282.i	0.182910	+	0.316810i
$804$	605062.	−	345692.i	0.936026	−	0.534783i
$805$	37405.5	−	29403.2i	0.0577223	−	0.0453736i
$806$	−258431.	−	149205.i	−0.397810	−	0.229675i
$807$	1824.30	−	403191.i	0.00280123	−	0.619105i
$808$	−162092.	+	93583.6i	−0.248278	+	0.143343i
$809$			1.09146e6i			1.66767i	0.552012	+	0.833836i	$0.313860\pi$
$809$			1.09146e6i			1.66767i	−0.552012	+	0.833836i	$0.686140\pi$
$810$	130270.	−	308885.i	0.198552	−	0.470789i
$811$	−380079.			−0.577873			−0.288936	−	0.957348i	$-0.593302\pi$
$811$	−380079.			−0.577873			−0.288936	+	0.957348i	$0.593302\pi$
$812$	−10413.5	−	18036.7i	−0.0157937	−	0.0273555i
$813$	−164442.	−	744.042i	−0.248789	−	0.00112568i
$814$	−277464.	+	480583.i	−0.418754	+	0.725303i
$815$	−247519.	+	194567.i	−0.372644	+	0.292923i
$816$	−84083.8	−	147171.i	−0.126279	−	0.221026i
$817$	−196963.	+	113716.i	−0.295080	+	0.170365i
$818$	−105637.			−0.157873
$819$	30918.0	+	279.792i	0.0460939	+	0.000417126i
$820$	396256.	+	158734.i	0.589316	+	0.236071i
$821$	468285.	−	270364.i	0.694743	−	0.401110i	−0.110644	−	0.993860i	$-0.535291\pi$
$821$	468285.	−	270364.i	0.694743	−	0.401110i	0.805386	+	0.592750i	$0.201958\pi$
$822$	333107.	−	570976.i	0.492992	−	0.845034i
$823$	41821.1	+	24145.4i	0.0617441	+	0.0356480i	0.530554	−	0.847651i	$-0.321984\pi$
$823$	41821.1	+	24145.4i	0.0617441	+	0.0356480i	−0.468810	+	0.883299i	$0.655317\pi$
$824$	113594.	+	65583.5i	0.167302	+	0.0965917i
$825$	211742.	+	734554.i	0.311100	+	1.07923i
$826$	−6350.27	−	10999.0i	−0.00930748	−	0.0161210i
$827$	−433990.			−0.634554			−0.317277	−	0.948333i	$-0.602768\pi$
$827$	−433990.			−0.634554			−0.317277	+	0.948333i	$0.602768\pi$
$828$	370373.	+	655125.i	0.540230	+	0.955573i
$829$	−126257.			−0.183716			−0.0918578	−	0.995772i	$-0.529281\pi$
$829$	−126257.			−0.183716			−0.0918578	+	0.995772i	$0.529281\pi$
$830$	−552801.	+	79361.5i	−0.802441	+	0.115200i
$831$	−903442.	+	516166.i	−1.30827	+	0.747459i
$832$	−136093.	−	78573.4i	−0.196603	−	0.113509i
$833$	−309170.	+	535498.i	−0.445561	+	0.771735i
$834$	331490.	+	1499.88i	0.476583	+	0.00215637i
$835$	−876368.	+	125813.i	−1.25694	+	0.180449i
$836$			583809.i			0.835331i
$837$	−345558.	+	580191.i	−0.493253	+	0.828172i
$838$		−	691884.i		−	0.985247i
$839$	130170.	−	75153.9i	0.184922	−	0.106765i	−0.404681	−	0.914458i	$-0.632618\pi$
$839$	130170.	−	75153.9i	0.184922	−	0.106765i	0.589603	+	0.807693i	$0.299284\pi$
$840$	28710.8	+	11652.2i	0.0406899	+	0.0165138i
$841$	−89095.3	+	154318.i	−0.125969	+	0.218184i
$842$	−229205.	+	396994.i	−0.323295	+	0.559964i
$843$	944761.	−	539773.i	1.32943	−	0.759550i
$844$	−287596.	−	498131.i	−0.403737	−	0.699292i
$845$	34555.7	−	86263.2i	0.0483957	−	0.120813i
$846$	31716.4	−	53804.1i	0.0443142	−	0.0751752i
$847$			9273.13i			0.0129259i
$848$	25340.5	+	43891.1i	0.0352390	+	0.0610358i
$849$	−1.11021e6	−	647696.i	−1.54025	−	0.898579i
$850$	316452.	−	92773.2i	0.437996	−	0.128406i
$851$	1.35968e6	+	785011.i	1.87749	+	1.08397i
$852$	306193.	+	178633.i	0.421809	+	0.246083i
$853$	247353.	−	142809.i	0.339953	−	0.196272i	−0.320298	−	0.947317i	$-0.603783\pi$
$853$	247353.	−	142809.i	0.339953	−	0.196272i	0.660251	+	0.751045i	$0.270450\pi$
$854$		−	25510.2i		−	0.0349782i
$855$	−449441.	−	582533.i	−0.614809	−	0.796872i
$856$	206055.			0.281213
$857$	604631.	+	1.04725e6i	0.823244	+	1.42590i	0.903254	+	0.429106i	$0.141171\pi$
$857$	604631.	+	1.04725e6i	0.823244	+	1.42590i	−0.0800099	+	0.996794i	$0.525495\pi$
$858$	195465.	+	342121.i	0.265519	+	0.464735i
$859$	−322885.	+	559253.i	−0.437584	+	0.757918i	−0.997503	−	0.0706299i	$-0.977499\pi$
$859$	−322885.	+	559253.i	−0.437584	+	0.757918i	0.559919	+	0.828548i	$0.310832\pi$
$860$	145456.	−	114338.i	0.196669	−	0.154595i
$861$	−31477.4	−	142.424i	−0.0424612	−	0.000192122i
$862$	592477.	−	342067.i	0.797364	−	0.460358i
$863$	753393.			1.01158			0.505790	−	0.862657i	$-0.331201\pi$
$863$	753393.			1.01158			0.505790	+	0.862657i	$0.331201\pi$
$864$	−395014.	+	663229.i	−0.529158	+	0.888456i
$865$	197052.	−	491910.i	0.263359	−	0.657437i
$866$	141049.	−	81434.8i	0.188077	−	0.108586i
$867$	−151844.	−	687.043i	−0.202004	−	0.000913998i
$868$	−22970.0	−	13261.7i	−0.0304875	−	0.0176020i
$869$	−869906.	−	502241.i	−1.15195	−	0.665077i
$870$	46034.1	+	331306.i	0.0608193	+	0.437715i
$871$	−516122.	−	893949.i	−0.680324	−	1.17836i
$872$	−988321.			−1.29977
$873$	1.16150e6	−	656650.i	1.52402	−	0.861600i
$874$	−583556.			−0.763940
$875$	21969.1	−	30809.8i	0.0286943	−	0.0402414i
$876$	159523.	+	93065.6i	0.207881	+	0.121278i
$877$	−765073.	−	441715.i	−0.994726	−	0.574306i	−0.0880427	−	0.996117i	$-0.528061\pi$
$877$	−765073.	−	441715.i	−0.994726	−	0.574306i	−0.906684	+	0.421811i	$0.861395\pi$
$878$	52010.9	−	90085.5i	0.0674691	−	0.116860i
$879$	−222221.	+	380907.i	−0.287612	+	0.492993i
$880$	−35221.5	−	245340.i	−0.0454824	−	0.316813i
$881$		−	404743.i		−	0.521468i	−0.965411	−	0.260734i	$-0.916035\pi$
$881$		−	404743.i		−	0.521468i	0.965411	−	0.260734i	$-0.0839646\pi$
$882$	396489.	+	3588.03i	0.509676	+	0.00461231i
$883$			27686.5i			0.0355096i	0.999842	+	0.0177548i	$0.00565183\pi$
$883$			27686.5i			0.0355096i	−0.999842	+	0.0177548i	$0.994348\pi$
$884$	−416643.	+	240549.i	−0.533163	+	0.307822i
$885$	−79457.4	−	571852.i	−0.101449	−	0.730125i
$886$	−296956.	+	514342.i	−0.378289	+	0.655216i
$887$	−636301.	+	1.10210e6i	−0.808752	+	1.40080i	0.104978	+	0.994475i	$0.466523\pi$
$887$	−636301.	+	1.10210e6i	−0.808752	+	1.40080i	−0.913729	+	0.406324i	$0.866810\pi$
$888$	−4626.26	+	1.02246e6i	−0.00586683	+	1.29664i
$889$	33494.7	+	58014.5i	0.0423811	+	0.0734062i
$890$	−110290.	−	44180.4i	−0.139237	−	0.0557763i
$891$	780151.	−	431787.i	0.982705	−	0.543894i
$892$		−	338131.i		−	0.424967i
$893$	−68539.1	−	118713.i	−0.0859480	−	0.148866i
$894$	2931.08	−	647802.i	0.00366735	−	0.810526i
$895$	−327463.	+	257407.i	−0.408804	+	0.321347i
$896$	−31260.6	−	18048.3i	−0.0389387	−	0.0224813i
$897$	967941.	−	553017.i	1.20300	−	0.687311i
$898$	−640085.	+	369553.i	−0.793752	+	0.458273i
$899$		−	673807.i		−	0.833712i
$900$	429250.	+	417123.i	0.529938	+	0.514966i
$901$	−179357.			−0.220938
$902$	−200569.	−	347396.i	−0.246520	−	0.426985i
$903$	−6875.04	+	11784.5i	−0.00843140	+	0.0144522i
$904$	−291197.	+	504367.i	−0.356328	+	0.617177i
$905$	697265.	+	887030.i	0.851335	+	1.08303i
$906$	−109533.	+	187750.i	−0.133441	+	0.228731i
$907$	−479947.	+	277097.i	−0.583416	+	0.336836i	−0.762490	−	0.647000i	$-0.776023\pi$
$907$	−479947.	+	277097.i	−0.583416	+	0.336836i	0.179074	+	0.983836i	$0.442690\pi$
$908$	107336.			0.130189
$909$	232088.	−	131210.i	0.280883	−	0.158796i
$910$	7252.65	−	18105.1i	0.00875818	−	0.0218635i
$911$	−771670.	+	445524.i	−0.929811	+	0.536827i	−0.886752	−	0.462246i	$-0.847044\pi$
$911$	−771670.	+	445524.i	−0.929811	+	0.536827i	−0.0430595	+	0.999073i	$0.513711\pi$
$912$	118338.	+	207127.i	0.142277	+	0.249027i
$913$	−1.28644e6	−	742726.i	−1.54329	−	0.891019i
$914$	130721.	+	75471.6i	0.156478	+	0.0903424i
$915$	436093.	−	1.07453e6i	0.520879	−	1.28344i
$916$	137125.	+	237507.i	0.163427	+	0.283065i
$917$	31298.1			0.0372202
$918$	−187783.	−	335692.i	−0.222829	−	0.398341i
$919$	242131.			0.286695			0.143347	−	0.989672i	$-0.454213\pi$
$919$	242131.			0.286695			0.143347	+	0.989672i	$0.454213\pi$
$920$	1.10582e6	−	158754.i	1.30650	−	0.187564i
$921$	4741.26	−	1.04787e6i	0.00558951	−	1.23535i
$922$	−10843.1	−	6260.27i	−0.0127553	−	0.00736430i
$923$	262553.	−	454754.i	0.308186	−	0.533794i
$924$	17373.4	+	30408.6i	0.0203489	+	0.0356166i
$925$	1.21335e6	+	294899.i	1.41809	+	0.344660i
$926$		−	490184.i		−	0.571660i
$927$	−160957.	−	94880.8i	−0.187305	−	0.110413i
$928$		−	770242.i		−	0.894399i
$929$	953051.	−	550244.i	1.10429	−	0.637565i	0.166949	−	0.985966i	$-0.446609\pi$
$929$	953051.	−	550244.i	1.10429	−	0.637565i	0.937346	+	0.348401i	$0.113275\pi$
$930$	261733.	+	336085.i	0.302617	+	0.388582i
$931$	435122.	−	753653.i	0.502009	−	0.869505i
$932$	107347.	−	185931.i	0.123583	−	0.214052i
$933$	−298773.	−	174304.i	−0.343225	−	0.200237i
$934$	56342.5	+	97588.1i	0.0645866	+	0.111867i
$935$	814245.	+	326174.i	0.931391	+	0.373101i
$936$	625418.	+	368671.i	0.713870	+	0.420812i
$937$		−	580897.i		−	0.661637i	−0.943694	−	0.330819i	$-0.892675\pi$
$937$		−	580897.i		−	0.661637i	0.943694	−	0.330819i	$-0.107325\pi$
$938$	16207.3	+	28071.9i	0.0184207	+	0.0319055i
$939$	−605321.	+	345840.i	−0.686523	+	0.392233i
$940$	68914.0	+	87669.4i	0.0779923	+	0.0992185i
$941$	721653.	+	416647.i	0.814985	+	0.470532i	0.848684	−	0.528900i	$-0.177396\pi$
$941$	721653.	+	416647.i	0.814985	+	0.470532i	−0.0336993	+	0.999432i	$0.510729\pi$
$942$	−447.617	+	98928.6i	−0.000504435	+	0.111486i
$943$	−982865.	+	567457.i	−1.10528	+	0.638131i
$944$			187188.i			0.210055i
$945$	−40745.3	−	16967.3i	−0.0456261	−	0.0189998i
$946$	−173865.			−0.194280
$947$	78904.6	+	136667.i	0.0879837	+	0.152392i	0.906659	−	0.421865i	$-0.138624\pi$
$947$	78904.6	+	136667.i	0.0879837	+	0.152392i	−0.818675	+	0.574257i	$0.805291\pi$
$948$	−786451.	−	3558.42i	−0.875095	−	0.00395950i
$949$	136787.	−	236922.i	0.151884	−	0.263071i
$950$	−445370.	+	130568.i	−0.493485	+	0.144673i
$951$	24477.0	+	42841.8i	0.0270643	+	0.0473704i
$952$	30789.3	−	17776.2i	0.0339724	−	0.0196140i
$953$	−904204.			−0.995590			−0.497795	−	0.867295i	$-0.665857\pi$
$953$	−904204.			−0.995590			−0.497795	+	0.867295i	$0.665857\pi$
$954$	56602.1	+	100119.i	0.0621922	+	0.110007i
$955$	828383.	+	331838.i	0.908290	+	0.363847i
$956$	−336418.	+	194231.i	−0.368098	+	0.212522i
$957$	−448330.	+	768479.i	−0.489524	+	0.839089i
$958$	645415.	+	372631.i	0.703247	+	0.406020i
$959$	−75373.0	−	43516.6i	−0.0819556	−	0.0473171i
$960$	137832.	+	176986.i	0.149557	+	0.192042i
$961$	32708.0	+	56651.8i	0.0354166	+	0.0613433i
$962$	643596.			0.695446
$963$	−293503.	−	2656.05i	−0.316490	−	0.00286407i
$964$	421881.			0.453979
$965$	86393.8	+	601786.i	0.0927743	+	0.646230i
$966$	−30395.4	+	17365.9i	−0.0325727	+	0.0186098i
$967$	605117.	+	349365.i	0.647122	+	0.373616i	0.787353	−	0.616503i	$-0.211451\pi$
$967$	605117.	+	349365.i	0.647122	+	0.373616i	−0.140230	+	0.990119i	$0.544784\pi$
$968$	−108868.	+	188565.i	−0.116185	+	0.201238i
$969$	−844202.	−	3819.72i	−0.899081	−	0.00406803i
$970$	−119603.	−	833110.i	−0.127116	−	0.885439i
$971$		−	1.63052e6i		−	1.72937i	−0.502311	−	0.864687i	$-0.667517\pi$
$971$		−	1.63052e6i		−	1.72937i	0.502311	−	0.864687i	$-0.332483\pi$
$972$	362654.	−	596551.i	0.383849	−	0.631415i
$973$		−	43644.8i		−	0.0461006i
$974$	−211782.	+	122272.i	−0.223239	+	0.128887i
$975$	614998.	−	638635.i	0.646941	−	0.671805i
$976$	−187992.	+	325611.i	−0.197351	+	0.341821i
$977$	260634.	−	451431.i	0.273050	−	0.472936i	−0.696592	−	0.717468i	$-0.745301\pi$
$977$	260634.	−	451431.i	0.273050	−	0.472936i	0.969641	+	0.244532i	$0.0786344\pi$
$978$	201132.	−	114913.i	0.210283	−	0.120141i
$979$	−158009.	−	273679.i	−0.164860	−	0.285546i
$980$	−263254.	+	657173.i	−0.274108	+	0.684270i
$981$	1.40776e6	+	12739.5i	1.46282	+	0.0132377i
$982$			216767.i			0.224786i
$983$	275182.	+	476630.i	0.284783	+	0.493258i	0.972556	−	0.232667i	$-0.0747452\pi$
$983$	275182.	+	476630.i	0.284783	+	0.493258i	−0.687774	+	0.725925i	$0.741412\pi$
$984$	−638405.	−	372445.i	−0.659335	−	0.384655i
$985$	215045.	+	273571.i	0.221644	+	0.281967i
$986$	332374.	+	191896.i	0.341880	+	0.197385i
$987$	−7102.72	−	4143.72i	−0.00729106	−	0.00425360i
$988$	586378.	−	338545.i	0.600708	−	0.346819i
$989$			491903.i			0.502906i
$990$	−74887.6	−	557455.i	−0.0764081	−	0.568773i
$991$	1.51931e6			1.54703			0.773516	−	0.633777i	$-0.218496\pi$
$991$	1.51931e6			1.54703			0.773516	+	0.633777i	$0.218496\pi$
$992$	−490459.	−	849499.i	−0.498401	−	0.863256i
$993$	−299752.	−	524654.i	−0.303993	−	0.532077i
$994$	−8244.70	+	14280.2i	−0.00834454	+	0.0144532i
$995$	−635946.	−	809023.i	−0.642353	−	0.817174i
$996$	−1.16302e6	−	5262.28i	−1.17238	−	0.00530463i
$997$	−1.62802e6	+	939936.i	−1.63783	+	0.945601i	−0.656250	+	0.754544i	$0.727858\pi$
$997$	−1.62802e6	+	939936.i	−1.63783	+	0.945601i	−0.981579	+	0.191057i	$0.938808\pi$
$998$	392026.			0.393599
$999$	19769.1	−	1.45632e6i	0.0198087	−	1.45924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.9	✓	44
3.2	odd	2		135.5.h.a.44.14		44
5.4	even	2	inner	45.5.h.a.14.14	yes	44
9.2	odd	6	inner	45.5.h.a.29.14	yes	44
9.4	even	3		405.5.d.a.404.27		44
9.5	odd	6		405.5.d.a.404.17		44
9.7	even	3		135.5.h.a.89.9		44
15.14	odd	2		135.5.h.a.44.9		44
45.4	even	6		405.5.d.a.404.18		44
45.14	odd	6		405.5.d.a.404.28		44
45.29	odd	6	inner	45.5.h.a.29.9	yes	44
45.34	even	6		135.5.h.a.89.14		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.9	✓	44	1.1	even	1	trivial
45.5.h.a.14.14	yes	44	5.4	even	2	inner
45.5.h.a.29.9	yes	44	45.29	odd	6	inner
45.5.h.a.29.14	yes	44	9.2	odd	6	inner
135.5.h.a.44.9		44	15.14	odd	2
135.5.h.a.44.14		44	3.2	odd	2
135.5.h.a.89.9		44	9.7	even	3
135.5.h.a.89.14		44	45.34	even	6
405.5.d.a.404.17		44	9.5	odd	6
405.5.d.a.404.18		44	45.4	even	6
405.5.d.a.404.27		44	9.4	even	3
405.5.d.a.404.28		44	45.14	odd	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02189 - 1.76997i) q^{2} +(8.99991 + 0.0407214i) q^{3} +(5.91148 - 10.2390i) q^{4} +(15.4498 + 19.6546i) q^{5} +(-9.12485 - 15.9711i) q^{6} +(-2.09732 + 1.21089i) q^{7} -56.8640 q^{8} +(80.9967 + 0.732978i) q^{9} +(19.0000 - 47.4305i) q^{10} +(117.697 - 67.9523i) q^{11} +(53.6197 - 91.9092i) q^{12} +(-136.503 - 78.8098i) q^{13} +(4.28647 + 2.47479i) q^{14} +(138.247 + 177.519i) q^{15} +(-36.4748 - 63.1763i) q^{16} +258.165 q^{17} +(-81.4724 - 144.110i) q^{18} -363.338 q^{19} +(292.574 - 42.0027i) q^{20} +(-18.9250 + 10.8125i) q^{21} +(-240.547 - 138.880i) q^{22} +(-392.923 + 680.562i) q^{23} +(-511.771 - 2.31559i) q^{24} +(-147.606 + 607.320i) q^{25} +322.140i q^{26} +(728.933 + 9.89504i) q^{27} +28.6326i q^{28} +(-629.935 + 363.693i) q^{29} +(172.929 - 426.096i) q^{30} +(-463.170 + 802.234i) q^{31} +(-529.459 + 917.050i) q^{32} +(1062.03 - 606.772i) q^{33} +(-263.817 - 456.944i) q^{34} +(-56.2028 - 22.5140i) q^{35} +(486.315 - 824.991i) q^{36} -1997.88i q^{37} +(371.292 + 643.096i) q^{38} +(-1225.30 - 714.839i) q^{39} +(-878.539 - 1117.64i) q^{40} +(1250.71 + 722.098i) q^{41} +(38.4770 + 22.4474i) q^{42} +(542.092 - 312.977i) q^{43} -1606.79i q^{44} +(1236.98 + 1603.28i) q^{45} +1606.10 q^{46} +(188.637 + 326.730i) q^{47} +(-325.698 - 570.066i) q^{48} +(-1197.57 + 2074.25i) q^{49} +(1225.77 - 359.356i) q^{50} +(2323.46 + 10.5129i) q^{51} +(-1613.86 + 931.765i) q^{52} -694.739 q^{53} +(-727.376 - 1300.30i) q^{54} +(3153.97 + 1263.43i) q^{55} +(119.262 - 68.8560i) q^{56} +(-3270.01 - 14.7956i) q^{57} +(1287.45 + 743.309i) q^{58} +(-2222.20 - 1282.99i) q^{59} +(2634.85 - 366.106i) q^{60} +(-2577.00 - 4463.50i) q^{61} +1893.24 q^{62} +(-170.764 + 96.5407i) q^{63} +997.001 q^{64} +(-559.965 - 3900.50i) q^{65} +(-2159.24 - 1259.70i) q^{66} +(5671.56 + 3274.48i) q^{67} +(1526.14 - 2643.35i) q^{68} +(-3563.98 + 6109.00i) q^{69} +(17.5841 + 122.484i) q^{70} +3331.47i q^{71} +(-4605.80 - 41.6801i) q^{72} +1735.66i q^{73} +(-3536.18 + 2041.61i) q^{74} +(-1353.17 + 5459.81i) q^{75} +(-2147.86 + 3720.21i) q^{76} +(-164.565 + 285.036i) q^{77} +(-13.1180 + 2899.23i) q^{78} +(-3695.54 - 6400.86i) q^{79} +(678.175 - 1692.96i) q^{80} +(6559.93 + 118.738i) q^{81} -2951.62i q^{82} +(-5465.06 - 9465.75i) q^{83} +(-1.16596 + 257.691i) q^{84} +(3988.60 + 5074.13i) q^{85} +(-1107.92 - 639.657i) q^{86} +(-5684.17 + 3247.55i) q^{87} +(-6692.72 + 3864.04i) q^{88} -2325.29i q^{89} +(1573.70 - 3827.79i) q^{90} +381.719 q^{91} +(4645.51 + 8046.26i) q^{92} +(-4201.15 + 7201.17i) q^{93} +(385.534 - 667.764i) q^{94} +(-5613.50 - 7141.26i) q^{95} +(-4802.42 + 8231.80i) q^{96} +(14265.5 - 8236.22i) q^{97} +4895.13 q^{98} +(9582.86 - 5417.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more