LMFDB - Embedded newform 230.5.f.a.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	230.47
Dual form			230.5.f.a.93.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +(-2.34537 + 2.34537i) q^{3} +8.00000i q^{4} +(-23.4912 - 8.55343i) q^{5} +9.38149 q^{6} +(-59.8209 - 59.8209i) q^{7} +(16.0000 - 16.0000i) q^{8} +69.9985i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +(-2.34537 + 2.34537i) q^{3} +8.00000i q^{4} +(-23.4912 - 8.55343i) q^{5} +9.38149 q^{6} +(-59.8209 - 59.8209i) q^{7} +(16.0000 - 16.0000i) q^{8} +69.9985i q^{9} +(29.8756 + 64.0894i) q^{10} -73.2042 q^{11} +(-18.7630 - 18.7630i) q^{12} +(-43.3186 + 43.3186i) q^{13} +239.284i q^{14} +(75.1567 - 35.0347i) q^{15} -64.0000 q^{16} +(-284.950 - 284.950i) q^{17} +(139.997 - 139.997i) q^{18} -280.309i q^{19} +(68.4275 - 187.930i) q^{20} +280.604 q^{21} +(146.408 + 146.408i) q^{22} +(77.9968 - 77.9968i) q^{23} +75.0519i q^{24} +(478.678 + 401.862i) q^{25} +173.274 q^{26} +(-354.147 - 354.147i) q^{27} +(478.567 - 478.567i) q^{28} +1451.92i q^{29} +(-220.383 - 80.2439i) q^{30} -425.672 q^{31} +(128.000 + 128.000i) q^{32} +(171.691 - 171.691i) q^{33} +1139.80i q^{34} +(893.593 + 1916.94i) q^{35} -559.988 q^{36} +(-131.607 - 131.607i) q^{37} +(-560.617 + 560.617i) q^{38} -203.196i q^{39} +(-512.715 + 239.005i) q^{40} +2387.94 q^{41} +(-561.209 - 561.209i) q^{42} +(842.868 - 842.868i) q^{43} -585.634i q^{44} +(598.727 - 1644.35i) q^{45} -311.987 q^{46} +(1590.91 + 1590.91i) q^{47} +(150.104 - 150.104i) q^{48} +4756.08i q^{49} +(-153.632 - 1761.08i) q^{50} +1336.63 q^{51} +(-346.549 - 346.549i) q^{52} +(498.490 - 498.490i) q^{53} +1416.59i q^{54} +(1719.66 + 626.147i) q^{55} -1914.27 q^{56} +(657.428 + 657.428i) q^{57} +(2903.85 - 2903.85i) q^{58} -5054.42i q^{59} +(280.278 + 601.253i) q^{60} +2107.22 q^{61} +(851.343 + 851.343i) q^{62} +(4187.37 - 4187.37i) q^{63} -512.000i q^{64} +(1388.13 - 647.086i) q^{65} -686.764 q^{66} +(3227.11 + 3227.11i) q^{67} +(2279.60 - 2279.60i) q^{68} +365.863i q^{69} +(2046.70 - 5621.07i) q^{70} -1162.18 q^{71} +(1119.98 + 1119.98i) q^{72} +(-1372.64 + 1372.64i) q^{73} +526.427i q^{74} +(-2065.19 + 180.162i) q^{75} +2242.47 q^{76} +(4379.14 + 4379.14i) q^{77} +(-406.393 + 406.393i) q^{78} +103.775i q^{79} +(1503.44 + 547.420i) q^{80} -4008.66 q^{81} +(-4775.87 - 4775.87i) q^{82} +(-1873.09 + 1873.09i) q^{83} +2244.83i q^{84} +(4256.53 + 9131.13i) q^{85} -3371.47 q^{86} +(-3405.30 - 3405.30i) q^{87} +(-1171.27 + 1171.27i) q^{88} +7525.52i q^{89} +(-4486.16 + 2091.25i) q^{90} +5182.72 q^{91} +(623.974 + 623.974i) q^{92} +(998.358 - 998.358i) q^{93} -6363.64i q^{94} +(-2397.60 + 6584.80i) q^{95} -600.415 q^{96} +(-11007.7 - 11007.7i) q^{97} +(9512.15 - 9512.15i) q^{98} -5124.18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−2.34537	+	2.34537i	−0.260597	+	0.260597i	−0.825296	−	0.564700i	$-0.808992\pi$
$3$	−2.34537	+	2.34537i	−0.260597	+	0.260597i	0.564700	+	0.825296i	$0.308992\pi$
$4$			8.00000i			0.500000i
$5$	−23.4912	−	8.55343i	−0.939650	−	0.342137i
$5$	−23.4912	−	8.55343i	−0.939650	−	0.342137i
$6$	9.38149			0.260597
$7$	−59.8209	−	59.8209i	−1.22083	−	1.22083i	−0.967336	−	0.253499i	$-0.918419\pi$
$7$	−59.8209	−	59.8209i	−1.22083	−	1.22083i	−0.253499	−	0.967336i	$-0.581581\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$			69.9985i			0.864179i
$10$	29.8756	+	64.0894i	0.298756	+	0.640894i
$11$	−73.2042			−0.604994			−0.302497	−	0.953150i	$-0.597820\pi$
$11$	−73.2042			−0.604994			−0.302497	+	0.953150i	$0.597820\pi$
$12$	−18.7630	−	18.7630i	−0.130298	−	0.130298i
$13$	−43.3186	+	43.3186i	−0.256323	+	0.256323i	−0.823557	−	0.567234i	$-0.808014\pi$
$13$	−43.3186	+	43.3186i	−0.256323	+	0.256323i	0.567234	+	0.823557i	$0.308014\pi$
$14$			239.284i			1.22083i
$15$	75.1567	−	35.0347i	0.334030	−	0.155710i
$16$	−64.0000			−0.250000
$17$	−284.950	−	284.950i	−0.985986	−	0.985986i	0.0139172	−	0.999903i	$-0.495570\pi$
$17$	−284.950	−	284.950i	−0.985986	−	0.985986i	−0.999903	+	0.0139172i	$0.995570\pi$
$18$	139.997	−	139.997i	0.432089	−	0.432089i
$19$		−	280.309i		−	0.776478i	−0.921559	−	0.388239i	$-0.873083\pi$
$19$		−	280.309i		−	0.776478i	0.921559	−	0.388239i	$-0.126917\pi$
$20$	68.4275	−	187.930i	0.171069	−	0.469825i
$21$	280.604			0.636291
$22$	146.408	+	146.408i	0.302497	+	0.302497i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$			75.0519i			0.130298i
$25$	478.678	+	401.862i	0.765884	+	0.642979i
$26$	173.274			0.256323
$27$	−354.147	−	354.147i	−0.485799	−	0.485799i
$28$	478.567	−	478.567i	0.610417	−	0.610417i
$29$			1451.92i			1.72643i	0.504840	+	0.863213i	$0.331551\pi$
$29$			1451.92i			1.72643i	−0.504840	+	0.863213i	$0.668449\pi$
$30$	−220.383	−	80.2439i	−0.244870	−	0.0891599i
$31$	−425.672			−0.442947			−0.221473	−	0.975166i	$-0.571087\pi$
$31$	−425.672			−0.442947			−0.221473	+	0.975166i	$0.571087\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	171.691	−	171.691i	0.157659	−	0.157659i
$34$			1139.80i			0.985986i
$35$	893.593	+	1916.94i	0.729464	+	1.56485i
$36$	−559.988			−0.432089
$37$	−131.607	−	131.607i	−0.0961335	−	0.0961335i	0.657404	−	0.753538i	$-0.271654\pi$
$37$	−131.607	−	131.607i	−0.0961335	−	0.0961335i	−0.753538	+	0.657404i	$0.771654\pi$
$38$	−560.617	+	560.617i	−0.388239	+	0.388239i
$39$		−	203.196i		−	0.133594i
$40$	−512.715	+	239.005i	−0.320447	+	0.149378i
$41$	2387.94			1.42055			0.710273	−	0.703927i	$-0.248572\pi$
$41$	2387.94			1.42055			0.710273	+	0.703927i	$0.248572\pi$
$42$	−561.209	−	561.209i	−0.318146	−	0.318146i
$43$	842.868	−	842.868i	0.455851	−	0.455851i	−0.441440	−	0.897291i	$-0.645532\pi$
$43$	842.868	−	842.868i	0.455851	−	0.455851i	0.897291	+	0.441440i	$0.145532\pi$
$44$		−	585.634i		−	0.302497i
$45$	598.727	−	1644.35i	0.295668	−	0.812025i
$46$	−311.987			−0.147442
$47$	1590.91	+	1590.91i	0.720194	+	0.720194i	0.968645	−	0.248450i	$-0.0799213\pi$
$47$	1590.91	+	1590.91i	0.720194	+	0.720194i	−0.248450	+	0.968645i	$0.579921\pi$
$48$	150.104	−	150.104i	0.0651492	−	0.0651492i
$49$			4756.08i			1.98087i
$50$	−153.632	−	1761.08i	−0.0614528	−	0.704431i
$51$	1336.63			0.513890
$52$	−346.549	−	346.549i	−0.128162	−	0.128162i
$53$	498.490	−	498.490i	0.177462	−	0.177462i	−0.612787	−	0.790248i	$-0.709952\pi$
$53$	498.490	−	498.490i	0.177462	−	0.177462i	0.790248	+	0.612787i	$0.209952\pi$
$54$			1416.59i			0.485799i
$55$	1719.66	+	626.147i	0.568482	+	0.206991i
$56$	−1914.27			−0.610417
$57$	657.428	+	657.428i	0.202348	+	0.202348i
$58$	2903.85	−	2903.85i	0.863213	−	0.863213i
$59$		−	5054.42i		−	1.45200i	−0.687694	−	0.726001i	$-0.741377\pi$
$59$		−	5054.42i		−	1.45200i	0.687694	−	0.726001i	$-0.258623\pi$
$60$	280.278	+	601.253i	0.0778550	+	0.167015i
$61$	2107.22			0.566305			0.283152	−	0.959075i	$-0.408620\pi$
$61$	2107.22			0.566305			0.283152	+	0.959075i	$0.408620\pi$
$62$	851.343	+	851.343i	0.221473	+	0.221473i
$63$	4187.37	−	4187.37i	1.05502	−	1.05502i
$64$		−	512.000i		−	0.125000i
$65$	1388.13	−	647.086i	0.328552	−	0.153156i
$66$	−686.764			−0.157659
$67$	3227.11	+	3227.11i	0.718893	+	0.718893i	0.968378	−	0.249486i	$-0.0802616\pi$
$67$	3227.11	+	3227.11i	0.718893	+	0.718893i	−0.249486	+	0.968378i	$0.580262\pi$
$68$	2279.60	−	2279.60i	0.492993	−	0.492993i
$69$			365.863i			0.0768458i
$70$	2046.70	−	5621.07i	0.417693	−	1.14716i
$71$	−1162.18			−0.230546			−0.115273	−	0.993334i	$-0.536774\pi$
$71$	−1162.18			−0.230546			−0.115273	+	0.993334i	$0.536774\pi$
$72$	1119.98	+	1119.98i	0.216045	+	0.216045i
$73$	−1372.64	+	1372.64i	−0.257579	+	0.257579i	−0.824069	−	0.566490i	$-0.808301\pi$
$73$	−1372.64	+	1372.64i	−0.257579	+	0.257579i	0.566490	+	0.824069i	$0.308301\pi$
$74$			526.427i			0.0961335i
$75$	−2065.19	+	180.162i	−0.367145	+	0.0320288i
$76$	2242.47			0.388239
$77$	4379.14	+	4379.14i	0.738597	+	0.738597i
$78$	−406.393	+	406.393i	−0.0667970	+	0.0667970i
$79$			103.775i			0.0166280i	0.999965	+	0.00831401i	$0.00264646\pi$
$79$			103.775i			0.0166280i	−0.999965	+	0.00831401i	$0.997354\pi$
$80$	1503.44	+	547.420i	0.234912	+	0.0855343i
$81$	−4008.66			−0.610983
$82$	−4775.87	−	4775.87i	−0.710273	−	0.710273i
$83$	−1873.09	+	1873.09i	−0.271896	+	0.271896i	−0.829863	−	0.557967i	$-0.811582\pi$
$83$	−1873.09	+	1873.09i	−0.271896	+	0.271896i	0.557967	+	0.829863i	$0.311582\pi$
$84$			2244.83i			0.318146i
$85$	4256.53	+	9131.13i	0.589139	+	1.26382i
$86$	−3371.47			−0.455851
$87$	−3405.30	−	3405.30i	−0.449901	−	0.449901i
$88$	−1171.27	+	1171.27i	−0.151248	+	0.151248i
$89$			7525.52i			0.950071i	0.879967	+	0.475036i	$0.157565\pi$
$89$			7525.52i			0.950071i	−0.879967	+	0.475036i	$0.842435\pi$
$90$	−4486.16	+	2091.25i	−0.553847	+	0.258179i
$91$	5182.72			0.625856
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	998.358	−	998.358i	0.115430	−	0.115430i
$94$		−	6363.64i		−	0.720194i
$95$	−2397.60	+	6584.80i	−0.265662	+	0.729618i
$96$	−600.415			−0.0651492
$97$	−11007.7	−	11007.7i	−1.16991	−	1.16991i	−0.982230	−	0.187683i	$-0.939902\pi$
$97$	−11007.7	−	11007.7i	−1.16991	−	1.16991i	−0.187683	−	0.982230i	$-0.560098\pi$
$98$	9512.15	−	9512.15i	0.990436	−	0.990436i
$99$		−	5124.18i		−	0.522823i
$100$	−3214.89	+	3829.42i	−0.321489	+	0.382942i
$101$	5671.64			0.555988			0.277994	−	0.960583i	$-0.410330\pi$
$101$	5671.64			0.555988			0.277994	+	0.960583i	$0.410330\pi$
$102$	−2673.25	−	2673.25i	−0.256945	−	0.256945i
$103$	−3304.74	+	3304.74i	−0.311504	+	0.311504i	−0.845492	−	0.533988i	$-0.820693\pi$
$103$	−3304.74	+	3304.74i	−0.311504	+	0.311504i	0.533988	+	0.845492i	$0.320693\pi$
$104$			1386.20i			0.128162i
$105$	−6591.75	−	2400.13i	−0.597891	−	0.217699i
$106$	−1993.96			−0.177462
$107$	11124.0	+	11124.0i	0.971617	+	0.971617i	0.999608	−	0.0279915i	$-0.00891113\pi$
$107$	11124.0	+	11124.0i	0.971617	+	0.971617i	−0.0279915	+	0.999608i	$0.508911\pi$
$108$	2833.18	−	2833.18i	0.242900	−	0.242900i
$109$		−	17224.7i		−	1.44977i	−0.688869	−	0.724886i	$-0.741892\pi$
$109$		−	17224.7i		−	1.44977i	0.688869	−	0.724886i	$-0.258108\pi$
$110$	−2187.02	−	4691.61i	−0.180746	−	0.387737i
$111$	617.334			0.0501042
$112$	3828.54	+	3828.54i	0.305209	+	0.305209i
$113$	5675.71	−	5675.71i	0.444492	−	0.444492i	−0.449027	−	0.893518i	$-0.648229\pi$
$113$	5675.71	−	5675.71i	0.444492	−	0.444492i	0.893518	+	0.449027i	$0.148229\pi$
$114$		−	2629.71i		−	0.202348i
$115$	−2499.38	+	1165.10i	−0.188989	+	0.0880984i
$116$	−11615.4			−0.863213
$117$	−3032.24	−	3032.24i	−0.221509	−	0.221509i
$118$	−10108.8	+	10108.8i	−0.726001	+	0.726001i
$119$			34091.9i			2.40745i
$120$	641.951	−	1763.06i	0.0445799	−	0.122435i
$121$	−9282.14			−0.633983
$122$	−4214.44	−	4214.44i	−0.283152	−	0.283152i
$123$	−5600.60	+	5600.60i	−0.370190	+	0.370190i
$124$		−	3405.37i		−	0.221473i
$125$	−7807.44	−	13534.6i	−0.499676	−	0.866212i
$126$	−16749.5			−1.05502
$127$	671.931	+	671.931i	0.0416598	+	0.0416598i	0.727630	−	0.685970i	$-0.240622\pi$
$127$	671.931	+	671.931i	0.0416598	+	0.0416598i	−0.685970	+	0.727630i	$0.740622\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$			3953.68i			0.237587i
$130$	−4070.43	−	1482.09i	−0.240854	−	0.0876977i
$131$	−26734.4			−1.55786			−0.778929	−	0.627112i	$-0.784237\pi$
$131$	−26734.4			−1.55786			−0.778929	+	0.627112i	$0.784237\pi$
$132$	1373.53	+	1373.53i	0.0788297	+	0.0788297i
$133$	−16768.3	+	16768.3i	−0.947952	+	0.947952i
$134$		−	12908.4i		−	0.718893i
$135$	5290.19	+	11348.5i	0.290271	+	0.622691i
$136$	−9118.40			−0.492993
$137$	12027.9	+	12027.9i	0.640837	+	0.640837i	0.950761	−	0.309924i	$-0.100304\pi$
$137$	12027.9	+	12027.9i	0.640837	+	0.640837i	−0.309924	+	0.950761i	$0.600304\pi$
$138$	731.726	−	731.726i	0.0384229	−	0.0384229i
$139$			11511.6i			0.595808i	0.954596	+	0.297904i	$0.0962875\pi$
$139$			11511.6i			0.595808i	−0.954596	+	0.297904i	$0.903712\pi$
$140$	−15335.5	+	7148.75i	−0.782425	+	0.364732i
$141$	−7462.54			−0.375361
$142$	2324.37	+	2324.37i	0.115273	+	0.115273i
$143$	3171.11	−	3171.11i	0.155074	−	0.155074i
$144$		−	4479.90i		−	0.216045i
$145$	12418.9	−	34107.5i	0.590675	−	1.62224i
$146$	5490.56			0.257579
$147$	−11154.8	−	11154.8i	−0.516209	−	0.516209i
$148$	1052.85	−	1052.85i	0.0480668	−	0.0480668i
$149$			43238.2i			1.94758i	0.227447	+	0.973790i	$0.426962\pi$
$149$			43238.2i			1.94758i	−0.227447	+	0.973790i	$0.573038\pi$
$150$	4490.71	+	3770.06i	0.199587	+	0.167558i
$151$	3447.40			0.151195			0.0755975	−	0.997138i	$-0.475914\pi$
$151$	3447.40			0.151195			0.0755975	+	0.997138i	$0.475914\pi$
$152$	−4484.94	−	4484.94i	−0.194120	−	0.194120i
$153$	19946.1	−	19946.1i	0.852068	−	0.852068i
$154$		−	17516.6i		−	0.738597i
$155$	9999.56	+	3640.95i	0.416215	+	0.151549i
$156$	1625.57			0.0667970
$157$	−34241.1	−	34241.1i	−1.38915	−	1.38915i	−0.827119	−	0.562027i	$-0.810022\pi$
$157$	−34241.1	−	34241.1i	−1.38915	−	1.38915i	−0.562027	−	0.827119i	$-0.689978\pi$
$158$	207.551	−	207.551i	0.00831401	−	0.00831401i
$159$			2338.29i			0.0924919i
$160$	−1912.04	−	4101.72i	−0.0746891	−	0.160223i
$161$	−9331.67			−0.360004
$162$	8017.32	+	8017.32i	0.305492	+	0.305492i
$163$	22799.9	−	22799.9i	0.858140	−	0.858140i	−0.132979	−	0.991119i	$-0.542454\pi$
$163$	22799.9	−	22799.9i	0.858140	−	0.858140i	0.991119	+	0.132979i	$0.0424543\pi$
$164$			19103.5i			0.710273i
$165$	−5501.79	+	2564.69i	−0.202086	+	0.0942035i
$166$	7492.37			0.271896
$167$	−17821.9	−	17821.9i	−0.639031	−	0.639031i	0.311286	−	0.950316i	$-0.399240\pi$
$167$	−17821.9	−	17821.9i	−0.639031	−	0.639031i	−0.950316	+	0.311286i	$0.899240\pi$
$168$	4489.67	−	4489.67i	0.159073	−	0.159073i
$169$			24808.0i			0.868597i
$170$	9749.20	−	26775.3i	0.337343	−	0.926482i
$171$	19621.2			0.671016
$172$	6742.94	+	6742.94i	0.227925	+	0.227925i
$173$	7632.13	−	7632.13i	0.255008	−	0.255008i	−0.568012	−	0.823020i	$-0.692287\pi$
$173$	7632.13	−	7632.13i	0.255008	−	0.255008i	0.823020	+	0.568012i	$0.192287\pi$
$174$			13621.2i			0.449901i
$175$	−4595.20	−	52674.6i	−0.150047	−	1.71999i
$176$	4685.07			0.151248
$177$	11854.5	+	11854.5i	0.378387	+	0.378387i
$178$	15051.0	−	15051.0i	0.475036	−	0.475036i
$179$			16221.9i			0.506285i	0.967429	+	0.253143i	$0.0814642\pi$
$179$			16221.9i			0.506285i	−0.967429	+	0.253143i	$0.918536\pi$
$180$	13154.8	+	4789.82i	0.406013	+	0.147834i
$181$	−56673.3			−1.72990			−0.864951	−	0.501856i	$-0.832651\pi$
$181$	−56673.3			−1.72990			−0.864951	+	0.501856i	$0.832651\pi$
$182$	−10365.4	−	10365.4i	−0.312928	−	0.312928i
$183$	−4942.21	+	4942.21i	−0.147577	+	0.147577i
$184$		−	2495.90i		−	0.0737210i
$185$	1965.92	+	4217.30i	0.0574410	+	0.123223i
$186$	−3993.43			−0.115430
$187$	20859.5	+	20859.5i	0.596515	+	0.596515i
$188$	−12727.3	+	12727.3i	−0.360097	+	0.360097i
$189$			42370.8i			1.18616i
$190$	17964.8	−	8374.40i	0.497640	−	0.231978i
$191$	−13043.9			−0.357554			−0.178777	−	0.983890i	$-0.557214\pi$
$191$	−13043.9			−0.357554			−0.178777	+	0.983890i	$0.557214\pi$
$192$	1200.83	+	1200.83i	0.0325746	+	0.0325746i
$193$	14226.9	−	14226.9i	0.381941	−	0.381941i	−0.489860	−	0.871801i	$-0.662952\pi$
$193$	14226.9	−	14226.9i	0.381941	−	0.381941i	0.871801	+	0.489860i	$0.162952\pi$
$194$			44030.8i			1.16991i
$195$	−1738.03	+	4773.34i	−0.0457075	+	0.125532i
$196$	−38048.6			−0.990436
$197$	7405.12	+	7405.12i	0.190809	+	0.190809i	0.796046	−	0.605236i	$-0.206921\pi$
$197$	7405.12	+	7405.12i	0.190809	+	0.190809i	−0.605236	+	0.796046i	$0.706921\pi$
$198$	−10248.4	+	10248.4i	−0.261411	+	0.261411i
$199$		−	15947.4i		−	0.402702i	−0.979519	−	0.201351i	$-0.935467\pi$
$199$		−	15947.4i		−	0.402702i	0.979519	−	0.201351i	$-0.0645332\pi$
$200$	14088.6	−	1229.06i	0.352216	−	0.0307264i
$201$	−15137.5			−0.374682
$202$	−11343.3	−	11343.3i	−0.277994	−	0.277994i
$203$	86855.4	−	86855.4i	2.10768	−	2.10768i
$204$			10693.0i			0.256945i
$205$	−56095.6	−	20425.1i	−1.33482	−	0.486022i
$206$	13219.0			0.311504
$207$	5459.66	+	5459.66i	0.127416	+	0.127416i
$208$	2772.39	−	2772.39i	0.0640808	−	0.0640808i
$209$			20519.8i			0.469765i
$210$	8383.23	+	17983.8i	0.190096	+	0.407795i
$211$	36053.4			0.809807			0.404903	−	0.914359i	$-0.367305\pi$
$211$	36053.4			0.809807			0.404903	+	0.914359i	$0.367305\pi$
$212$	3987.92	+	3987.92i	0.0887308	+	0.0887308i
$213$	2725.75	−	2725.75i	0.0600797	−	0.0600797i
$214$		−	44496.2i		−	0.971617i
$215$	−27009.4	+	12590.6i	−0.584304	+	0.272377i
$216$	−11332.7			−0.242900
$217$	25464.1	+	25464.1i	0.540764	+	0.540764i
$218$	−34449.5	+	34449.5i	−0.724886	+	0.724886i
$219$		−	6438.70i		−	0.134249i
$220$	−5009.18	+	13757.3i	−0.103495	+	0.284241i
$221$	24687.3			0.505462
$222$	−1234.67	−	1234.67i	−0.0250521	−	0.0250521i
$223$	17609.1	−	17609.1i	0.354101	−	0.354101i	−0.507532	−	0.861633i	$-0.669442\pi$
$223$	17609.1	−	17609.1i	0.354101	−	0.354101i	0.861633	+	0.507532i	$0.169442\pi$
$224$		−	15314.1i		−	0.305209i
$225$	−28129.7	+	33506.7i	−0.555648	+	0.661861i
$226$	−22702.9			−0.444492
$227$	48395.2	+	48395.2i	0.939184	+	0.939184i	0.998254	−	0.0590696i	$-0.0188134\pi$
$227$	48395.2	+	48395.2i	0.939184	+	0.939184i	−0.0590696	+	0.998254i	$0.518813\pi$
$228$	−5259.42	+	5259.42i	−0.101174	+	0.101174i
$229$		−	34895.4i		−	0.665422i	−0.943029	−	0.332711i	$-0.892037\pi$
$229$		−	34895.4i		−	0.665422i	0.943029	−	0.332711i	$-0.107963\pi$
$230$	7328.97	+	2668.56i	0.138544	+	0.0504454i
$231$	−20541.4			−0.384952
$232$	23230.8	+	23230.8i	0.431606	+	0.431606i
$233$	−38201.2	+	38201.2i	−0.703663	+	0.703663i	−0.965195	−	0.261532i	$-0.915772\pi$
$233$	−38201.2	+	38201.2i	−0.703663	+	0.703663i	0.261532	+	0.965195i	$0.415772\pi$
$234$			12128.9i			0.221509i
$235$	−23764.7	−	50980.2i	−0.430325	−	0.923136i
$236$	40435.4			0.726001
$237$	−243.392	−	243.392i	−0.00433321	−	0.00433321i
$238$	68183.8	−	68183.8i	1.20373	−	1.20373i
$239$		−	7017.53i		−	0.122854i	−0.998112	−	0.0614268i	$-0.980435\pi$
$239$		−	7017.53i		−	0.122854i	0.998112	−	0.0614268i	$-0.0195651\pi$
$240$	−4810.03	+	2242.22i	−0.0835074	+	0.0389275i
$241$	62945.8			1.08376			0.541879	−	0.840456i	$-0.317713\pi$
$241$	62945.8			1.08376			0.541879	+	0.840456i	$0.317713\pi$
$242$	18564.3	+	18564.3i	0.316991	+	0.316991i
$243$	38087.7	−	38087.7i	0.645019	−	0.645019i
$244$			16857.8i			0.283152i
$245$	40680.8	−	111726.i	0.677730	−	1.86133i
$246$	22402.4			0.370190
$247$	12142.6	+	12142.6i	0.199029	+	0.199029i
$248$	−6810.75	+	6810.75i	−0.110737	+	0.110737i
$249$		−	8786.19i		−	0.141710i
$250$	−11454.3	+	42684.0i	−0.183268	+	0.682944i
$251$	100166.			1.58990			0.794952	−	0.606672i	$-0.207496\pi$
$251$	100166.			1.58990			0.794952	+	0.606672i	$0.207496\pi$
$252$	33499.0	+	33499.0i	0.527509	+	0.527509i
$253$	−5709.70	+	5709.70i	−0.0892015	+	0.0892015i
$254$		−	2687.73i		−	0.0416598i
$255$	−31399.0	−	11432.7i	−0.482876	−	0.175821i
$256$	4096.00			0.0625000
$257$	65834.1	+	65834.1i	0.996747	+	0.996747i	0.999995	−	0.00324791i	$-0.00103385\pi$
$257$	65834.1	+	65834.1i	0.996747	+	0.996747i	−0.00324791	+	0.999995i	$0.501034\pi$
$258$	7907.35	−	7907.35i	0.118793	−	0.118793i
$259$			15745.7i			0.234726i
$260$	5176.68	+	11105.0i	0.0765782	+	0.164276i
$261$	−101632.			−1.49194
$262$	53468.8	+	53468.8i	0.778929	+	0.778929i
$263$	3333.79	−	3333.79i	0.0481977	−	0.0481977i	−0.682597	−	0.730795i	$-0.739150\pi$
$263$	3333.79	−	3333.79i	0.0481977	−	0.0481977i	0.730795	+	0.682597i	$0.239150\pi$
$264$		−	5494.12i		−	0.0788297i
$265$	−15973.9	+	7446.35i	−0.227468	+	0.106036i
$266$	67073.3			0.947952
$267$	−17650.1	−	17650.1i	−0.247586	−	0.247586i
$268$	−25816.9	+	25816.9i	−0.359446	+	0.359446i
$269$			81887.8i			1.13166i	0.824523	+	0.565828i	$0.191443\pi$
$269$			81887.8i			1.13166i	−0.824523	+	0.565828i	$0.808557\pi$
$270$	12116.7	−	33277.5i	0.166210	−	0.456481i
$271$	−11234.4			−0.152972			−0.0764862	−	0.997071i	$-0.524370\pi$
$271$	−11234.4			−0.152972			−0.0764862	+	0.997071i	$0.524370\pi$
$272$	18236.8	+	18236.8i	0.246496	+	0.246496i
$273$	−12155.4	+	12155.4i	−0.163096	+	0.163096i
$274$		−	48111.5i		−	0.640837i
$275$	−35041.2	−	29418.0i	−0.463355	−	0.388998i
$276$	−2926.90			−0.0384229
$277$	35187.8	+	35187.8i	0.458599	+	0.458599i	0.898195	−	0.439596i	$-0.144879\pi$
$277$	35187.8	+	35187.8i	0.458599	+	0.458599i	−0.439596	+	0.898195i	$0.644879\pi$
$278$	23023.2	−	23023.2i	0.297904	−	0.297904i
$279$		−	29796.4i		−	0.382785i
$280$	44968.6	+	16373.6i	0.573578	+	0.208846i
$281$	38051.9			0.481907			0.240954	−	0.970537i	$-0.422540\pi$
$281$	38051.9			0.481907			0.240954	+	0.970537i	$0.422540\pi$
$282$	14925.1	+	14925.1i	0.187680	+	0.187680i
$283$	81314.3	−	81314.3i	1.01530	−	1.01530i	0.0154182	−	0.999881i	$-0.495092\pi$
$283$	81314.3	−	81314.3i	1.01530	−	1.01530i	0.999881	−	0.0154182i	$-0.00490796\pi$
$284$		−	9297.47i		−	0.115273i
$285$	−9820.54	−	21067.1i	−0.120905	−	0.259367i
$286$	−12684.4			−0.155074
$287$	−142848.	−	142848.i	−1.73425	−	1.73425i
$288$	−8959.80	+	8959.80i	−0.108022	+	0.108022i
$289$			78871.9i			0.944337i
$290$	−93052.9	+	43377.1i	−1.10646	+	0.515781i
$291$	51634.3			0.609751
$292$	−10981.1	−	10981.1i	−0.128790	−	0.128790i
$293$	−104242.	+	104242.i	−1.21424	+	1.21424i	−0.244627	+	0.969617i	$0.578666\pi$
$293$	−104242.	+	104242.i	−1.21424	+	1.21424i	−0.969617	+	0.244627i	$0.921334\pi$
$294$			44619.1i			0.516209i
$295$	−43232.6	+	118735.i	−0.496784	+	1.36437i
$296$	−4211.42			−0.0480668
$297$	25925.1	+	25925.1i	0.293905	+	0.293905i
$298$	86476.5	−	86476.5i	0.973790	−	0.973790i
$299$			6757.43i			0.0755856i
$300$	−1441.30	−	16521.5i	−0.0160144	−	0.183573i
$301$	−100842.			−1.11304
$302$	−6894.79	−	6894.79i	−0.0755975	−	0.0755975i
$303$	−13302.1	+	13302.1i	−0.144889	+	0.144889i
$304$			17939.8i			0.194120i
$305$	−49501.2	−	18024.0i	−0.532128	−	0.193754i
$306$	−79784.2			−0.852068
$307$	−6464.11	−	6464.11i	−0.0685855	−	0.0685855i	0.671982	−	0.740567i	$-0.265443\pi$
$307$	−6464.11	−	6464.11i	−0.0685855	−	0.0685855i	−0.740567	+	0.671982i	$0.765443\pi$
$308$	−35033.1	+	35033.1i	−0.369299	+	0.369299i
$309$		−	15501.7i		−	0.162354i
$310$	−12717.2	−	27281.0i	−0.132333	−	0.283882i
$311$	121044.			1.25147			0.625736	−	0.780035i	$-0.284799\pi$
$311$	121044.			1.25147			0.625736	+	0.780035i	$0.284799\pi$
$312$	−3251.14	−	3251.14i	−0.0333985	−	0.0333985i
$313$	−81792.6	+	81792.6i	−0.834882	+	0.834882i	−0.988180	−	0.153298i	$-0.951011\pi$
$313$	−81792.6	+	81792.6i	−0.834882	+	0.834882i	0.153298	+	0.988180i	$0.451011\pi$
$314$			136964.i			1.38915i
$315$	−134183.	+	62550.2i	−1.35231	+	0.630387i
$316$	−830.204			−0.00831401
$317$	7026.34	+	7026.34i	0.0699215	+	0.0699215i	0.741203	−	0.671281i	$-0.234256\pi$
$317$	7026.34	+	7026.34i	0.0699215	+	0.0699215i	−0.671281	+	0.741203i	$0.734256\pi$
$318$	4676.58	−	4676.58i	0.0462459	−	0.0462459i
$319$		−	106287.i		−	1.04448i
$320$	−4379.36	+	12027.5i	−0.0427672	+	0.117456i
$321$	−52180.0			−0.506400
$322$	18663.3	+	18663.3i	0.180002	+	0.180002i
$323$	−79874.0	+	79874.0i	−0.765597	+	0.765597i
$324$		−	32069.3i		−	0.305492i
$325$	−38143.7	+	3327.56i	−0.361124	+	0.0315035i
$326$	−91199.7			−0.858140
$327$	40398.4	+	40398.4i	0.377806	+	0.377806i
$328$	38207.0	−	38207.0i	0.355136	−	0.355136i
$329$		−	190339.i		−	1.75848i
$330$	16133.0	+	5874.19i	0.148145	+	0.0539412i
$331$	193823.			1.76909			0.884544	−	0.466457i	$-0.154470\pi$
$331$	193823.			1.76909			0.884544	+	0.466457i	$0.154470\pi$
$332$	−14984.7	−	14984.7i	−0.135948	−	0.135948i
$333$	9212.28	−	9212.28i	0.0830766	−	0.0830766i
$334$			71287.7i			0.639031i
$335$	−48206.0	−	103412.i	−0.429548	−	0.921468i
$336$	−17958.7			−0.159073
$337$	57627.0	+	57627.0i	0.507418	+	0.507418i	0.913733	−	0.406315i	$-0.133186\pi$
$337$	57627.0	+	57627.0i	0.507418	+	0.507418i	−0.406315	+	0.913733i	$0.633186\pi$
$338$	49616.0	−	49616.0i	0.434298	−	0.434298i
$339$			26623.3i			0.231666i
$340$	−73049.0	+	34052.2i	−0.631912	+	0.294570i
$341$	31161.0			0.267980
$342$	−39242.4	−	39242.4i	−0.335508	−	0.335508i
$343$	140883.	−	140883.i	1.19748	−	1.19748i
$344$		−	26971.8i		−	0.227925i
$345$	3129.38	−	8594.58i	0.0262918	−	0.0722082i
$346$	−30528.5			−0.255008
$347$	−109603.	−	109603.i	−0.910255	−	0.910255i	0.0860366	−	0.996292i	$-0.472580\pi$
$347$	−109603.	−	109603.i	−0.910255	−	0.910255i	−0.996292	+	0.0860366i	$0.972580\pi$
$348$	27242.4	−	27242.4i	0.224950	−	0.224950i
$349$		−	184332.i		−	1.51339i	−0.653770	−	0.756693i	$-0.726814\pi$
$349$		−	184332.i		−	1.51339i	0.653770	−	0.756693i	$-0.273186\pi$
$350$	−96158.9	+	114540.i	−0.784970	+	0.935018i
$351$	30682.4			0.249043
$352$	−9370.14	−	9370.14i	−0.0756242	−	0.0756242i
$353$	76882.3	−	76882.3i	0.616989	−	0.616989i	−0.327769	−	0.944758i	$-0.606297\pi$
$353$	76882.3	−	76882.3i	0.616989	−	0.616989i	0.944758	+	0.327769i	$0.106297\pi$
$354$		−	47418.0i		−	0.378387i
$355$	27301.2	+	9940.66i	0.216633	+	0.0788785i
$356$	−60204.1			−0.475036
$357$	−79958.2	−	79958.2i	−0.627374	−	0.627374i
$358$	32443.8	−	32443.8i	0.253143	−	0.253143i
$359$			224307.i			1.74042i	0.492680	+	0.870211i	$0.336017\pi$
$359$			224307.i			1.74042i	−0.492680	+	0.870211i	$0.663983\pi$
$360$	−16730.0	−	35889.3i	−0.129089	−	0.276923i
$361$	51748.0			0.397081
$362$	113347.	+	113347.i	0.864951	+	0.864951i
$363$	21770.1	−	21770.1i	0.165214	−	0.165214i
$364$			41461.7i			0.312928i
$365$	43985.8	−	20504.2i	0.330162	−	0.153907i
$366$	19768.8			0.147577
$367$	15570.7	+	15570.7i	0.115605	+	0.115605i	0.762543	−	0.646938i	$-0.223951\pi$
$367$	15570.7	+	15570.7i	0.115605	+	0.115605i	−0.646938	+	0.762543i	$0.723951\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$			167152.i			1.22760i
$370$	4502.76	−	12366.4i	0.0328909	−	0.0903319i
$371$	−59640.2			−0.433303
$372$	7986.87	+	7986.87i	0.0577152	+	0.0577152i
$373$	−81252.5	+	81252.5i	−0.584008	+	0.584008i	−0.936002	−	0.351994i	$-0.885504\pi$
$373$	−81252.5	+	81252.5i	−0.584008	+	0.584008i	0.351994	+	0.936002i	$0.385504\pi$
$374$		−	83438.2i		−	0.596515i
$375$	50054.9	+	13432.2i	0.355946	+	0.0955182i
$376$	50909.1			0.360097
$377$	−62895.3	−	62895.3i	−0.442523	−	0.442523i
$378$	84741.7	−	84741.7i	0.593080	−	0.593080i
$379$		−	123157.i		−	0.857398i	−0.903447	−	0.428699i	$-0.858972\pi$
$379$		−	123157.i		−	0.857398i	0.903447	−	0.428699i	$-0.141028\pi$
$380$	−52678.4	−	19180.8i	−0.364809	−	0.132831i
$381$	−3151.86			−0.0217128
$382$	26087.9	+	26087.9i	0.178777	+	0.178777i
$383$	85486.9	−	85486.9i	0.582776	−	0.582776i	−0.352889	−	0.935665i	$-0.614801\pi$
$383$	85486.9	−	85486.9i	0.582776	−	0.582776i	0.935665	+	0.352889i	$0.114801\pi$
$384$		−	4803.32i		−	0.0325746i
$385$	−65414.8	−	140328.i	−0.441321	−	0.946724i
$386$	−56907.7			−0.381941
$387$	58999.5	+	58999.5i	0.393936	+	0.393936i
$388$	88061.6	−	88061.6i	0.584956	−	0.584956i
$389$			15954.2i			0.105433i	0.998610	+	0.0527164i	$0.0167879\pi$
$389$			15954.2i			0.105433i	−0.998610	+	0.0527164i	$0.983212\pi$
$390$	13022.7	−	6070.62i	0.0856195	−	0.0399121i
$391$	−44450.4			−0.290751
$392$	76097.2	+	76097.2i	0.495218	+	0.495218i
$393$	62702.1	−	62702.1i	0.405973	−	0.405973i
$394$		−	29620.5i		−	0.190809i
$395$	887.637	−	2437.82i	0.00568907	−	0.0156245i
$396$	40993.5			0.261411
$397$	−45383.6	−	45383.6i	−0.287951	−	0.287951i	0.548319	−	0.836269i	$-0.315268\pi$
$397$	−45383.6	−	45383.6i	−0.287951	−	0.287951i	−0.836269	+	0.548319i	$0.815268\pi$
$398$	−31894.8	+	31894.8i	−0.201351	+	0.201351i
$399$		−	78655.8i		−	0.494066i
$400$	−30635.4	−	25719.1i	−0.191471	−	0.160745i
$401$	163737.			1.01826			0.509130	−	0.860690i	$-0.329967\pi$
$401$	163737.			1.01826			0.509130	+	0.860690i	$0.329967\pi$
$402$	30275.1	+	30275.1i	0.187341	+	0.187341i
$403$	18439.5	−	18439.5i	0.113537	−	0.113537i
$404$			45373.1i			0.277994i
$405$	94168.5	+	34287.8i	0.574110	+	0.209040i
$406$	−347421.			−2.10768
$407$	9634.18	+	9634.18i	0.0581602	+	0.0581602i
$408$	21386.0	−	21386.0i	0.128472	−	0.128472i
$409$			102150.i			0.610652i	0.952248	+	0.305326i	$0.0987654\pi$
$409$			102150.i			0.610652i	−0.952248	+	0.305326i	$0.901235\pi$
$410$	71341.1	+	153041.i	0.424397	+	0.910418i
$411$	−56419.7			−0.334000
$412$	−26437.9	−	26437.9i	−0.155752	−	0.155752i
$413$	−302360.	+	302360.i	−1.77265	+	1.77265i
$414$		−	21838.6i		−	0.127416i
$415$	60022.6	−	27979.9i	0.348513	−	0.162461i
$416$	−11089.6			−0.0640808
$417$	−26999.0	−	26999.0i	−0.155266	−	0.155266i
$418$	41039.6	−	41039.6i	0.234882	−	0.234882i
$419$			40931.4i			0.233146i	0.993182	+	0.116573i	$0.0371910\pi$
$419$			40931.4i			0.233146i	−0.993182	+	0.116573i	$0.962809\pi$
$420$	19201.0	−	52734.0i	0.108849	−	0.298945i
$421$	−349093.			−1.96960			−0.984798	−	0.173701i	$-0.944427\pi$
$421$	−349093.			−1.96960			−0.984798	+	0.173701i	$0.944427\pi$
$422$	−72106.8	−	72106.8i	−0.404903	−	0.404903i
$423$	−111361.	+	111361.i	−0.622376	+	0.622376i
$424$		−	15951.7i		−	0.0887308i
$425$	−21888.7	−	250910.i	−0.121183	−	1.38912i
$426$	−10903.0			−0.0600797
$427$	−126056.	−	126056.i	−0.691364	−	0.691364i
$428$	−88992.3	+	88992.3i	−0.485808	+	0.485808i
$429$			14874.8i			0.0808235i
$430$	79200.1	+	28837.7i	0.428340	+	0.155964i
$431$	−302745.			−1.62976			−0.814879	−	0.579632i	$-0.803196\pi$
$431$	−302745.			−1.62976			−0.814879	+	0.579632i	$0.803196\pi$
$432$	22665.4	+	22665.4i	0.121450	+	0.121450i
$433$	−156144.	+	156144.i	−0.832816	+	0.832816i	−0.987901	−	0.155085i	$-0.950435\pi$
$433$	−156144.	+	156144.i	−0.832816	+	0.832816i	0.155085	+	0.987901i	$0.450435\pi$
$434$		−	101856.i		−	0.540764i
$435$	50867.8	+	109122.i	0.268822	+	0.576677i
$436$	137798.			0.724886
$437$	−21863.2	−	21863.2i	−0.114485	−	0.114485i
$438$	−12877.4	+	12877.4i	−0.0671244	+	0.0671244i
$439$			62981.5i			0.326802i	0.986560	+	0.163401i	$0.0522464\pi$
$439$			62981.5i			0.326802i	−0.986560	+	0.163401i	$0.947754\pi$
$440$	37532.9	−	17496.2i	0.193868	−	0.0903729i
$441$	−332918.			−1.71183
$442$	−49374.5	−	49374.5i	−0.252731	−	0.252731i
$443$	−62961.6	+	62961.6i	−0.320825	+	0.320825i	−0.849084	−	0.528259i	$-0.822845\pi$
$443$	−62961.6	+	62961.6i	−0.320825	+	0.320825i	0.528259	+	0.849084i	$0.322845\pi$
$444$			4938.67i			0.0250521i
$445$	64369.0	−	176784.i	0.325055	−	0.892735i
$446$	−70436.4			−0.354101
$447$	−101410.	−	101410.i	−0.507533	−	0.507533i
$448$	−30628.3	+	30628.3i	−0.152604	+	0.152604i
$449$			205207.i			1.01789i	0.860800	+	0.508944i	$0.169964\pi$
$449$			205207.i			1.01789i	−0.860800	+	0.508944i	$0.830036\pi$
$450$	123273.	−	10754.0i	0.608755	−	0.0531062i
$451$	−174807.			−0.859421
$452$	45405.7	+	45405.7i	0.222246	+	0.222246i
$453$	−8085.43	+	8085.43i	−0.0394009	+	0.0394009i
$454$		−	193581.i		−	0.939184i
$455$	−121748.	−	44330.0i	−0.588086	−	0.214129i
$456$	21037.7			0.101174
$457$	206501.	+	206501.i	0.988756	+	0.988756i	0.999937	−	0.0111813i	$-0.00355920\pi$
$457$	206501.	+	206501.i	0.988756	+	0.988756i	−0.0111813	+	0.999937i	$0.503559\pi$
$458$	−69790.7	+	69790.7i	−0.332711	+	0.332711i
$459$			201829.i			0.957982i
$460$	−9320.81	−	19995.1i	−0.0440492	−	0.0944946i
$461$	400955.			1.88666			0.943329	−	0.331858i	$-0.107676\pi$
$461$	400955.			1.88666			0.943329	+	0.331858i	$0.107676\pi$
$462$	41082.9	+	41082.9i	0.192476	+	0.192476i
$463$	191583.	−	191583.i	0.893708	−	0.893708i	−0.101162	−	0.994870i	$-0.532256\pi$
$463$	191583.	−	191583.i	0.893708	−	0.893708i	0.994870	+	0.101162i	$0.0322560\pi$
$464$		−	92923.1i		−	0.431606i
$465$	−31992.1	+	14913.3i	−0.147957	+	0.0689712i
$466$	152805.			0.703663
$467$	234264.	+	234264.i	1.07417	+	1.07417i	0.997020	+	0.0771452i	$0.0245805\pi$
$467$	234264.	+	234264.i	1.07417	+	1.07417i	0.0771452	+	0.997020i	$0.475419\pi$
$468$	24257.9	−	24257.9i	0.110754	−	0.110754i
$469$		−	386097.i		−	1.75530i
$470$	−54430.9	+	149490.i	−0.246405	+	0.676730i
$471$	160616.			0.724014
$472$	−80870.7	−	80870.7i	−0.363001	−	0.363001i
$473$	−61701.5	+	61701.5i	−0.275787	+	0.275787i
$474$			973.568i			0.00433321i
$475$	112645.	−	134178.i	0.499259	−	0.594693i
$476$	−272735.			−1.20373
$477$	34893.5	+	34893.5i	0.153359	+	0.153359i
$478$	−14035.1	+	14035.1i	−0.0614268	+	0.0614268i
$479$			448733.i			1.95577i	0.209152	+	0.977883i	$0.432930\pi$
$479$			448733.i			1.95577i	−0.209152	+	0.977883i	$0.567070\pi$
$480$	14104.5	+	5135.61i	0.0612174	+	0.0222900i
$481$	11402.1			0.0492825
$482$	−125892.	−	125892.i	−0.541879	−	0.541879i
$483$	21886.2	−	21886.2i	0.0938160	−	0.0938160i
$484$		−	74257.1i		−	0.316991i
$485$	164431.	+	352738.i	0.699037	+	1.49958i
$486$	−152351.			−0.645019
$487$	264836.	+	264836.i	1.11665	+	1.11665i	0.992229	+	0.124424i	$0.0397083\pi$
$487$	264836.	+	264836.i	1.11665	+	1.11665i	0.124424	+	0.992229i	$0.460292\pi$
$488$	33715.5	−	33715.5i	0.141576	−	0.141576i
$489$			106949.i			0.447257i
$490$	−304814.	+	142091.i	−1.26953	+	0.591798i
$491$	380949.			1.58017			0.790085	−	0.612997i	$-0.210036\pi$
$491$	380949.			1.58017			0.790085	+	0.612997i	$0.210036\pi$
$492$	−44804.8	−	44804.8i	−0.185095	−	0.185095i
$493$	413726.	−	413726.i	1.70223	−	1.70223i
$494$		−	48570.3i		−	0.199029i
$495$	−43829.4	+	120373.i	−0.178877	+	0.491270i
$496$	27243.0			0.110737
$497$	69522.9	+	69522.9i	0.281459	+	0.281459i
$498$	−17572.4	+	17572.4i	−0.0708552	+	0.0708552i
$499$		−	135067.i		−	0.542437i	−0.962518	−	0.271219i	$-0.912573\pi$
$499$		−	135067.i		−	0.542437i	0.962518	−	0.271219i	$-0.0874266\pi$
$500$	108277.	−	62459.5i	0.433106	−	0.249838i
$501$	83598.1			0.333059
$502$	−200331.	−	200331.i	−0.794952	−	0.794952i
$503$	−146031.	+	146031.i	−0.577176	+	0.577176i	−0.934124	−	0.356948i	$-0.883817\pi$
$503$	−146031.	+	146031.i	−0.577176	+	0.577176i	0.356948	+	0.934124i	$0.383817\pi$
$504$		−	133996.i		−	0.527509i
$505$	−133234.	−	48512.0i	−0.522434	−	0.190224i
$506$	22838.8			0.0892015
$507$	−58184.0	−	58184.0i	−0.226354	−	0.226354i
$508$	−5375.45	+	5375.45i	−0.0208299	+	0.0208299i
$509$		−	53167.2i		−	0.205215i	−0.994722	−	0.102607i	$-0.967281\pi$
$509$		−	53167.2i		−	0.205215i	0.994722	−	0.102607i	$-0.0327185\pi$
$510$	39932.6	+	85663.6i	0.153528	+	0.329349i
$511$	164225.			0.628923
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−99270.6	+	99270.6i	−0.377212	+	0.377212i
$514$		−	263337.i		−	0.996747i
$515$	105899.	−	49365.6i	0.399281	−	0.186127i
$516$	−31629.4			−0.118793
$517$	−116461.	−	116461.i	−0.435713	−	0.435713i
$518$	31491.3	−	31491.3i	0.117363	−	0.117363i
$519$			35800.3i			0.132908i
$520$	11856.7	−	32563.5i	0.0438489	−	0.120427i
$521$	142704.			0.525728			0.262864	−	0.964833i	$-0.415333\pi$
$521$	142704.			0.525728			0.262864	+	0.964833i	$0.415333\pi$
$522$	203265.	+	203265.i	0.745970	+	0.745970i
$523$	−273664.	+	273664.i	−1.00049	+	1.00049i	−0.000494852		1.00000i	$0.500158\pi$
$523$	−273664.	+	273664.i	−1.00049	+	1.00049i	−1.00000		0.000494852i	$0.999842\pi$
$524$		−	213875.i		−	0.778929i
$525$	134319.	+	112764.i	0.487325	+	0.409122i
$526$	−13335.2			−0.0481977
$527$	121295.	+	121295.i	0.436739	+	0.436739i
$528$	−10988.2	+	10988.2i	−0.0394149	+	0.0394149i
$529$		−	12167.0i		−	0.0434783i
$530$	46840.6	+	17055.2i	0.166752	+	0.0607163i
$531$	353802.			1.25479
$532$	−134147.	−	134147.i	−0.473976	−	0.473976i
$533$	−103442.	+	103442.i	−0.364119	+	0.364119i
$534$			70600.5i			0.247586i
$535$	−166169.	−	356466.i	−0.580553	−	1.24541i
$536$	103268.			0.359446
$537$	−38046.3	−	38046.3i	−0.131936	−	0.131936i
$538$	163776.	−	163776.i	0.565828	−	0.565828i
$539$		−	348165.i		−	1.19842i
$540$	−90788.3	+	42321.5i	−0.311345	+	0.145136i
$541$	−124212.			−0.424395			−0.212198	−	0.977227i	$-0.568062\pi$
$541$	−124212.			−0.424395			−0.212198	+	0.977227i	$0.568062\pi$
$542$	22468.9	+	22468.9i	0.0764862	+	0.0764862i
$543$	132920.	−	132920.i	0.450807	−	0.450807i
$544$		−	72947.2i		−	0.246496i
$545$	−147331.	+	404631.i	−0.496021	+	1.36228i
$546$	48621.6			0.163096
$547$	−68566.6	−	68566.6i	−0.229159	−	0.229159i	0.583182	−	0.812341i	$-0.301807\pi$
$547$	−68566.6	−	68566.6i	−0.229159	−	0.229159i	−0.812341	+	0.583182i	$0.801807\pi$
$548$	−96223.0	+	96223.0i	−0.320419	+	0.320419i
$549$			147502.i			0.489388i
$550$	11246.5	+	128918.i	0.0371785	+	0.426177i
$551$	406987.			1.34053
$552$	5853.81	+	5853.81i	0.0192115	+	0.0192115i
$553$	6207.94	−	6207.94i	0.0203001	−	0.0203001i
$554$		−	140751.i		−	0.458599i
$555$	−14501.9	−	5280.32i	−0.0470804	−	0.0171425i
$556$	−92092.8			−0.297904
$557$	60764.0	+	60764.0i	0.195855	+	0.195855i	0.798221	−	0.602365i	$-0.205775\pi$
$557$	60764.0	+	60764.0i	0.195855	+	0.195855i	−0.602365	+	0.798221i	$0.705775\pi$
$558$	−59592.7	+	59592.7i	−0.191392	+	0.191392i
$559$			73023.7i			0.233690i
$560$	−57190.0	−	122684.i	−0.182366	−	0.391212i
$561$	−97846.7			−0.310900
$562$	−76103.7	−	76103.7i	−0.240954	−	0.240954i
$563$	−20873.0	+	20873.0i	−0.0658520	+	0.0658520i	−0.739266	−	0.673414i	$-0.764827\pi$
$563$	−20873.0	+	20873.0i	−0.0658520	+	0.0658520i	0.673414	+	0.739266i	$0.264827\pi$
$564$		−	59700.4i		−	0.187680i
$565$	−181876.	+	84782.8i	−0.569744	+	0.265589i
$566$	−325257.			−1.01530
$567$	239802.	+	239802.i	0.745909	+	0.745909i
$568$	−18594.9	+	18594.9i	−0.0576366	+	0.0576366i
$569$			362289.i			1.11900i	0.828830	+	0.559501i	$0.189007\pi$
$569$			362289.i			1.11900i	−0.828830	+	0.559501i	$0.810993\pi$
$570$	−22493.1	+	61775.2i	−0.0692307	+	0.190136i
$571$	43128.5			0.132279			0.0661397	−	0.997810i	$-0.478932\pi$
$571$	43128.5			0.132279			0.0661397	+	0.997810i	$0.478932\pi$
$572$	25368.8	+	25368.8i	0.0775369	+	0.0775369i
$573$	30592.9	−	30592.9i	0.0931775	−	0.0931775i
$574$			571394.i			1.73425i
$575$	68679.2	−	5991.40i	0.207725	−	0.0181214i
$576$	35839.2			0.108022
$577$	−217134.	−	217134.i	−0.652193	−	0.652193i	0.301328	−	0.953521i	$-0.402570\pi$
$577$	−217134.	−	217134.i	−0.652193	−	0.652193i	−0.953521	+	0.301328i	$0.902570\pi$
$578$	157744.	−	157744.i	0.472168	−	0.472168i
$579$			66734.8i			0.199065i
$580$	272860.	+	99351.5i	0.811118	+	0.295337i
$581$	224100.			0.663880
$582$	−103269.	−	103269.i	−0.304875	−	0.304875i
$583$	−36491.6	+	36491.6i	−0.107363	+	0.107363i
$584$			43924.5i			0.128790i
$585$	45295.0	+	97167.1i	0.132354	+	0.283927i
$586$	416967.			1.21424
$587$	−116674.	−	116674.i	−0.338609	−	0.338609i	0.517235	−	0.855844i	$-0.326961\pi$
$587$	−116674.	−	116674.i	−0.338609	−	0.338609i	−0.855844	+	0.517235i	$0.826961\pi$
$588$	89238.1	−	89238.1i	0.258105	−	0.258105i
$589$			119319.i			0.343938i
$590$	323935.	−	151004.i	0.930579	−	0.433795i
$591$	−34735.5			−0.0994486
$592$	8422.84	+	8422.84i	0.0240334	+	0.0240334i
$593$	−49304.6	+	49304.6i	−0.140210	+	0.140210i	−0.773728	−	0.633518i	$-0.781610\pi$
$593$	−49304.6	+	49304.6i	−0.140210	+	0.140210i	0.633518	+	0.773728i	$0.281610\pi$
$594$		−	103700.i		−	0.293905i
$595$	291603.	−	800862.i	0.823679	−	2.26216i
$596$	−345906.			−0.973790
$597$	37402.6	+	37402.6i	0.104943	+	0.104943i
$598$	13514.9	−	13514.9i	0.0377928	−	0.0377928i
$599$		−	604183.i		−	1.68389i	−0.539560	−	0.841947i	$-0.681409\pi$
$599$		−	604183.i		−	1.68389i	0.539560	−	0.841947i	$-0.318591\pi$
$600$	−30160.5	+	35925.7i	−0.0837791	+	0.0997935i
$601$	364311.			1.00861			0.504305	−	0.863526i	$-0.331749\pi$
$601$	364311.			1.00861			0.504305	+	0.863526i	$0.331749\pi$
$602$	201684.	+	201684.i	0.556518	+	0.556518i
$603$	−225893.	+	225893.i	−0.621252	+	0.621252i
$604$			27579.2i			0.0755975i
$605$	218049.	+	79394.2i	0.595722	+	0.216909i
$606$	53208.4			0.144889
$607$	262536.	+	262536.i	0.712545	+	0.712545i	0.967067	−	0.254522i	$-0.0819182\pi$
$607$	262536.	+	262536.i	0.712545	+	0.712545i	−0.254522	+	0.967067i	$0.581918\pi$
$608$	35879.5	−	35879.5i	0.0970598	−	0.0970598i
$609$			407416.i			1.09851i
$610$	62954.5	+	135050.i	0.169187	+	0.362941i
$611$	−137832.			−0.369205
$612$	159568.	+	159568.i	0.426034	+	0.426034i
$613$	−245240.	+	245240.i	−0.652636	+	0.652636i	−0.953627	−	0.300991i	$-0.902683\pi$
$613$	−245240.	+	245240.i	−0.652636	+	0.652636i	0.300991	+	0.953627i	$0.402683\pi$
$614$			25856.5i			0.0685855i
$615$	179469.	−	83660.7i	0.474504	−	0.221193i
$616$	140133.			0.369299
$617$	−109830.	−	109830.i	−0.288504	−	0.288504i	0.547984	−	0.836489i	$-0.315395\pi$
$617$	−109830.	−	109830.i	−0.288504	−	0.288504i	−0.836489	+	0.547984i	$0.815395\pi$
$618$	−31003.4	+	31003.4i	−0.0811769	+	0.0811769i
$619$		−	575966.i		−	1.50320i	−0.659621	−	0.751598i	$-0.729283\pi$
$619$		−	575966.i		−	1.50320i	0.659621	−	0.751598i	$-0.270717\pi$
$620$	−29127.6	+	79996.5i	−0.0757743	+	0.208107i
$621$	−55244.7			−0.143254
$622$	−242087.	−	242087.i	−0.625736	−	0.625736i
$623$	450183.	−	450183.i	1.15988	−	1.15988i
$624$			13004.6i			0.0333985i
$625$	67639.5	+	384724.i	0.173157	+	0.984894i
$626$	327170.			0.834882
$627$	−48126.5	−	48126.5i	−0.122419	−	0.122419i
$628$	273928.	−	273928.i	0.694573	−	0.694573i
$629$			75002.7i			0.189573i
$630$	393466.	+	143266.i	0.991348	+	0.360961i
$631$	500379.			1.25672			0.628362	−	0.777921i	$-0.283726\pi$
$631$	500379.			1.25672			0.628362	+	0.777921i	$0.283726\pi$
$632$	1660.41	+	1660.41i	0.00415701	+	0.00415701i
$633$	−84558.6	+	84558.6i	−0.211033	+	0.211033i
$634$		−	28105.4i		−	0.0699215i
$635$	−10037.2	−	21531.8i	−0.0248923	−	0.0533990i
$636$	−18706.3			−0.0462459
$637$	−206027.	−	206027.i	−0.507744	−	0.507744i
$638$	−212574.	+	212574.i	−0.522238	+	0.522238i
$639$		−	81351.1i		−	0.199233i
$640$	32813.8	−	15296.3i	0.0801117	−	0.0373445i
$641$	−155077.			−0.377425			−0.188712	−	0.982032i	$-0.560431\pi$
$641$	−155077.			−0.377425			−0.188712	+	0.982032i	$0.560431\pi$
$642$	104360.	+	104360.i	0.253200	+	0.253200i
$643$	−406795.	+	406795.i	−0.983907	+	0.983907i	−0.999873	−	0.0159656i	$-0.994918\pi$
$643$	−406795.	+	406795.i	−0.983907	+	0.983907i	0.0159656	+	0.999873i	$0.494918\pi$
$644$		−	74653.4i		−	0.180002i
$645$	33817.5	−	92876.8i	0.0812872	−	0.223248i
$646$	319496.			0.765597
$647$	−533161.	−	533161.i	−1.27365	−	1.27365i	−0.944159	−	0.329489i	$-0.893124\pi$
$647$	−533161.	−	533161.i	−1.27365	−	1.27365i	−0.329489	−	0.944159i	$-0.606876\pi$
$648$	−64138.6	+	64138.6i	−0.152746	+	0.152746i
$649$			370005.i			0.878452i
$650$	82942.6	+	69632.4i	0.196314	+	0.164810i
$651$	−119445.			−0.281843
$652$	182399.	+	182399.i	0.429070	+	0.429070i
$653$	26192.1	−	26192.1i	0.0614248	−	0.0614248i	−0.675727	−	0.737152i	$-0.736170\pi$
$653$	26192.1	−	26192.1i	0.0614248	−	0.0614248i	0.737152	+	0.675727i	$0.236170\pi$
$654$		−	161594.i		−	0.377806i
$655$	628025.	+	228671.i	1.46384	+	0.533001i
$656$	−152828.			−0.355136
$657$	−96082.7	−	96082.7i	−0.222595	−	0.222595i
$658$	−380678.	+	380678.i	−0.879238	+	0.879238i
$659$		−	407184.i		−	0.937604i	−0.883303	−	0.468802i	$-0.844686\pi$
$659$		−	407184.i		−	0.937604i	0.883303	−	0.468802i	$-0.155314\pi$
$660$	−20517.5	−	44014.3i	−0.0471018	−	0.101043i
$661$	340027.			0.778235			0.389118	−	0.921188i	$-0.372780\pi$
$661$	340027.			0.778235			0.389118	+	0.921188i	$0.372780\pi$
$662$	−387646.	−	387646.i	−0.884544	−	0.884544i
$663$	−57900.8	+	57900.8i	−0.131722	+	0.131722i
$664$			59938.9i			0.135948i
$665$	537335.	−	250482.i	1.21507	−	0.566413i
$666$	−36849.1			−0.0830766
$667$	113245.	+	113245.i	0.254548	+	0.254548i
$668$	142575.	−	142575.i	0.319515	−	0.319515i
$669$			82599.7i			0.184555i
$670$	−110411.	+	303235.i	−0.245960	+	0.675508i
$671$	−154257.			−0.342611
$672$	35917.4	+	35917.4i	0.0795364	+	0.0795364i
$673$	−73653.5	+	73653.5i	−0.162616	+	0.162616i	−0.783725	−	0.621109i	$-0.786683\pi$
$673$	−73653.5	+	73653.5i	−0.162616	+	0.162616i	0.621109	+	0.783725i	$0.286683\pi$
$674$		−	230508.i		−	0.507418i
$675$	−27204.2	−	311841.i	−0.0597074	−	0.684424i
$676$	−198464.			−0.434298
$677$	−485682.	−	485682.i	−1.05968	−	1.05968i	−0.998102	−	0.0615768i	$-0.980387\pi$
$677$	−485682.	−	485682.i	−1.05968	−	1.05968i	−0.0615768	−	0.998102i	$-0.519613\pi$
$678$	53246.6	−	53246.6i	0.115833	−	0.115833i
$679$			1.31698e6i			2.85654i
$680$	214203.	+	77993.6i	0.463241	+	0.168671i
$681$	−227010.			−0.489497
$682$	−62321.9	−	62321.9i	−0.133990	−	0.133990i
$683$	150888.	−	150888.i	0.323455	−	0.323455i	−0.526636	−	0.850091i	$-0.676547\pi$
$683$	150888.	−	150888.i	0.323455	−	0.323455i	0.850091	+	0.526636i	$0.176547\pi$
$684$			156969.i			0.335508i
$685$	−179670.	−	385430.i	−0.382909	−	0.821417i
$686$	−563531.			−1.19748
$687$	81842.6	+	81842.6i	0.173407	+	0.173407i
$688$	−53943.6	+	53943.6i	−0.113963	+	0.113963i
$689$			43187.8i			0.0909751i
$690$	−23447.9	+	10930.4i	−0.0492500	+	0.0229582i
$691$	665264.			1.39328			0.696639	−	0.717422i	$-0.254678\pi$
$691$	665264.			1.39328			0.696639	+	0.717422i	$0.254678\pi$
$692$	61057.0	+	61057.0i	0.127504	+	0.127504i
$693$	−306533.	+	306533.i	−0.638280	+	0.638280i
$694$			438412.i			0.910255i
$695$	98463.7	−	270422.i	0.203848	−	0.559851i
$696$	−108970.			−0.224950
$697$	−680442.	−	680442.i	−1.40064	−	1.40064i
$698$	−368664.	+	368664.i	−0.756693	+	0.756693i
$699$		−	179192.i		−	0.366745i
$700$	421397.	−	36761.6i	0.859994	−	0.0750237i
$701$	−798934.			−1.62583			−0.812914	−	0.582383i	$-0.802120\pi$
$701$	−798934.			−1.62583			−0.812914	+	0.582383i	$0.802120\pi$
$702$	−61364.7	−	61364.7i	−0.124522	−	0.124522i
$703$	−36890.5	+	36890.5i	−0.0746456	+	0.0746456i
$704$			37480.6i			0.0756242i
$705$	175304.	+	63830.4i	0.352708	+	0.128425i
$706$	−307529.			−0.616989
$707$	−339282.	−	339282.i	−0.678770	−	0.678770i
$708$	−94835.9	+	94835.9i	−0.189194	+	0.189194i
$709$		−	482660.i		−	0.960172i	−0.877221	−	0.480086i	$-0.840605\pi$
$709$		−	482660.i		−	0.960172i	0.877221	−	0.480086i	$-0.159395\pi$
$710$	−34721.0	−	74483.7i	−0.0688772	−	0.147756i
$711$	−7264.13			−0.0143696
$712$	120408.	+	120408.i	0.237518	+	0.237518i
$713$	−33201.0	+	33201.0i	−0.0653089	+	0.0653089i
$714$			319833.i			0.627374i
$715$	−101617.	+	47369.4i	−0.198772	+	0.0926586i
$716$	−129775.			−0.253143
$717$	16458.7	+	16458.7i	0.0320153	+	0.0320153i
$718$	448614.	−	448614.i	0.870211	−	0.870211i
$719$			113475.i			0.219505i	0.993959	+	0.109752i	$0.0350058\pi$
$719$			113475.i			0.219505i	−0.993959	+	0.109752i	$0.964994\pi$
$720$	−38318.5	+	105238.i	−0.0739169	+	0.203006i
$721$	395385.			0.760589
$722$	−103496.	−	103496.i	−0.198541	−	0.198541i
$723$	−147631.	+	147631.i	−0.282424	+	0.282424i
$724$		−	453387.i		−	0.864951i
$725$	−583472.	+	695003.i	−1.11005	+	1.32224i
$726$	−87080.3			−0.165214
$727$	9797.75	+	9797.75i	0.0185378	+	0.0185378i	0.716315	−	0.697777i	$-0.245827\pi$
$727$	9797.75	+	9797.75i	0.0185378	+	0.0185378i	−0.697777	+	0.716315i	$0.745827\pi$
$728$	82923.4	−	82923.4i	0.156464	−	0.156464i
$729$		−	146042.i		−	0.274803i
$730$	−128980.	−	46963.1i	−0.242034	−	0.0881275i
$731$	−480350.			−0.898925
$732$	−39537.7	−	39537.7i	−0.0737886	−	0.0737886i
$733$	−63790.7	+	63790.7i	−0.118727	+	0.118727i	−0.763974	−	0.645247i	$-0.776754\pi$
$733$	−63790.7	+	63790.7i	−0.118727	+	0.118727i	0.645247	+	0.763974i	$0.276754\pi$
$734$		−	62282.9i		−	0.115605i
$735$	166628.	+	357451.i	0.308442	+	0.661670i
$736$	19967.2			0.0368605
$737$	−236238.	−	236238.i	−0.434926	−	0.434926i
$738$	334304.	−	334304.i	0.613802	−	0.613802i
$739$			429550.i			0.786547i	0.919421	+	0.393274i	$0.128658\pi$
$739$			429550.i			0.786547i	−0.919421	+	0.393274i	$0.871342\pi$
$740$	−33738.4	+	15727.3i	−0.0616114	+	0.0287205i
$741$	−56957.7			−0.103733
$742$	119280.	+	119280.i	0.216651	+	0.216651i
$743$	361809.	−	361809.i	0.655394	−	0.655394i	−0.298893	−	0.954287i	$-0.596617\pi$
$743$	361809.	−	361809.i	0.655394	−	0.655394i	0.954287	+	0.298893i	$0.0966173\pi$
$744$		−	31947.5i		−	0.0577152i
$745$	369835.	−	1.01572e6i	0.666340	−	1.83004i
$746$	325010.			0.584008
$747$	−131114.	−	131114.i	−0.234967	−	0.234967i
$748$	−166876.	+	166876.i	−0.298258	+	0.298258i
$749$		−	1.33090e6i		−	2.37237i
$750$	−73245.4	−	126974.i	−0.130214	−	0.225732i
$751$	−282515.			−0.500912			−0.250456	−	0.968128i	$-0.580581\pi$
$751$	−282515.			−0.500912			−0.250456	+	0.968128i	$0.580581\pi$
$752$	−101818.	−	101818.i	−0.180049	−	0.180049i
$753$	−234925.	+	234925.i	−0.414324	+	0.414324i
$754$			251581.i			0.442523i
$755$	−80983.7	−	29487.1i	−0.142070	−	0.0517294i
$756$	−338967.			−0.593080
$757$	−130770.	−	130770.i	−0.228201	−	0.228201i	0.583740	−	0.811941i	$-0.301589\pi$
$757$	−130770.	−	130770.i	−0.228201	−	0.228201i	−0.811941	+	0.583740i	$0.801589\pi$
$758$	−246315.	+	246315.i	−0.428699	+	0.428699i
$759$		−	26782.7i		−	0.0464912i
$760$	66995.2	+	143718.i	0.115989	+	0.248820i
$761$	805976.			1.39172			0.695862	−	0.718176i	$-0.255023\pi$
$761$	805976.			1.39172			0.695862	+	0.718176i	$0.255023\pi$
$762$	6303.71	+	6303.71i	0.0108564	+	0.0108564i
$763$	−1.03040e6	+	1.03040e6i	−1.76993	+	1.76993i
$764$		−	104352.i		−	0.178777i
$765$	−639165.	+	297951.i	−1.09217	+	0.509121i
$766$	−341948.			−0.582776
$767$	218950.	+	218950.i	0.372182	+	0.372182i
$768$	−9606.64	+	9606.64i	−0.0162873	+	0.0162873i
$769$			788267.i			1.33297i	0.745518	+	0.666485i	$0.232202\pi$
$769$			788267.i			1.33297i	−0.745518	+	0.666485i	$0.767798\pi$
$770$	−149827.	+	411486.i	−0.252702	+	0.694023i
$771$	−308811.			−0.519498
$772$	113815.	+	113815.i	0.190970	+	0.190970i
$773$	−594992.	+	594992.i	−0.995755	+	0.995755i	−0.999991	−	0.00423640i	$-0.998652\pi$
$773$	−594992.	+	594992.i	−0.995755	+	0.995755i	0.00423640	+	0.999991i	$0.498652\pi$
$774$		−	235998.i		−	0.393936i
$775$	−203760.	−	171061.i	−0.339246	−	0.284805i
$776$	−352247.			−0.584956
$777$	−36929.4	−	36929.4i	−0.0611689	−	0.0611689i
$778$	31908.4	−	31908.4i	0.0527164	−	0.0527164i
$779$		−	669359.i		−	1.10302i
$780$	−38186.7	−	13904.2i	−0.0627658	−	0.0228537i
$781$	85076.8			0.139479
$782$	88900.7	+	88900.7i	0.145376	+	0.145376i
$783$	514195.	−	514195.i	0.838696	−	0.838696i
$784$		−	304389.i		−	0.495218i
$785$	511487.	+	1.09724e6i	0.830032	+	1.78059i
$786$	−250808.			−0.405973
$787$	−437528.	−	437528.i	−0.706409	−	0.706409i	0.259369	−	0.965778i	$-0.416485\pi$
$787$	−437528.	−	437528.i	−0.706409	−	0.706409i	−0.965778	+	0.259369i	$0.916485\pi$
$788$	−59241.0	+	59241.0i	−0.0954047	+	0.0954047i
$789$			15637.9i			0.0251203i
$790$	−6650.91	+	3100.36i	−0.0106568	+	0.00496773i
$791$	−679052.			−1.08530
$792$	−81987.0	−	81987.0i	−0.130706	−	0.130706i
$793$	−91281.8	+	91281.8i	−0.145157	+	0.145157i
$794$			181534.i			0.287951i
$795$	20000.4	−	54929.3i	0.0316449	−	0.0869100i
$796$	127579.			0.201351
$797$	−421744.	−	421744.i	−0.663946	−	0.663946i	0.292362	−	0.956308i	$-0.405559\pi$
$797$	−421744.	−	421744.i	−0.663946	−	0.663946i	−0.956308	+	0.292362i	$0.905559\pi$
$798$	−157312.	+	157312.i	−0.247033	+	0.247033i
$799$		−	906659.i		−	1.42020i
$800$	9832.44	+	112709.i	0.0153632	+	0.176108i
$801$	−526775.			−0.821031
$802$	−327474.	−	327474.i	−0.509130	−	0.509130i
$803$	100483.	−	100483.i	0.155834	−	0.155834i
$804$		−	121100.i		−	0.187341i
$805$	219213.	+	79817.8i	0.338278	+	0.123171i
$806$	−73758.0			−0.113537
$807$	−192057.	−	192057.i	−0.294906	−	0.294906i
$808$	90746.2	−	90746.2i	0.138997	−	0.138997i
$809$		−	155479.i		−	0.237561i	−0.992921	−	0.118780i	$-0.962102\pi$
$809$		−	155479.i		−	0.237561i	0.992921	−	0.118780i	$-0.0378984\pi$
$810$	−119761.	−	256913.i	−0.182535	−	0.391575i
$811$	375643.			0.571128			0.285564	−	0.958360i	$-0.407819\pi$
$811$	375643.			0.571128			0.285564	+	0.958360i	$0.407819\pi$
$812$	694843.	+	694843.i	1.05384	+	1.05384i
$813$	26348.9	−	26348.9i	0.0398641	−	0.0398641i
$814$		−	38536.7i		−	0.0581602i
$815$	−730616.	+	340581.i	−1.09995	+	0.512749i
$816$	−85544.1			−0.128472
$817$	−236263.	−	236263.i	−0.353958	−	0.353958i
$818$	204301.	−	204301.i	0.305326	−	0.305326i
$819$			362782.i			0.540852i
$820$	163400.	−	448765.i	0.243011	−	0.667408i
$821$	1.30690e6			1.93891			0.969453	−	0.245277i	$-0.0788790\pi$
$821$	1.30690e6			1.93891			0.969453	+	0.245277i	$0.0788790\pi$
$822$	112839.	+	112839.i	0.167000	+	0.167000i
$823$	−843105.	+	843105.i	−1.24475	+	1.24475i	−0.286742	+	0.958008i	$0.592572\pi$
$823$	−843105.	+	843105.i	−1.24475	+	1.24475i	−0.958008	+	0.286742i	$0.907428\pi$
$824$			105752.i			0.155752i
$825$	151181.	−	13188.6i	0.222120	−	0.0193772i
$826$	1.20944e6			1.77265
$827$	−500614.	−	500614.i	−0.731967	−	0.731967i	0.239042	−	0.971009i	$-0.423167\pi$
$827$	−500614.	−	500614.i	−0.731967	−	0.731967i	−0.971009	+	0.239042i	$0.923167\pi$
$828$	−43677.2	+	43677.2i	−0.0637081	+	0.0637081i
$829$		−	707262.i		−	1.02913i	−0.857451	−	0.514566i	$-0.827953\pi$
$829$		−	707262.i		−	1.02913i	0.857451	−	0.514566i	$-0.172047\pi$
$830$	−176005.	−	64085.4i	−0.255487	−	0.0930258i
$831$	−165057.			−0.239019
$832$	22179.1	+	22179.1i	0.0320404	+	0.0320404i
$833$	1.35524e6	−	1.35524e6i	1.95311	−	1.95311i
$834$			107996.i			0.155266i
$835$	266221.	+	571098.i	0.381829	+	0.819101i
$836$	−164158.			−0.234882
$837$	150751.	+	150751.i	0.215183	+	0.215183i
$838$	81862.8	−	81862.8i	0.116573	−	0.116573i
$839$			1.22810e6i			1.74465i	0.488926	+	0.872325i	$0.337389\pi$
$839$			1.22810e6i			1.74465i	−0.488926	+	0.872325i	$0.662611\pi$
$840$	−143870.	+	67065.9i	−0.203897	+	0.0950480i
$841$	−1.40080e6			−1.98054
$842$	698187.	+	698187.i	0.984798	+	0.984798i
$843$	−89245.8	+	89245.8i	−0.125583	+	0.125583i
$844$			288427.i			0.404903i
$845$	212194.	−	582771.i	0.297179	−	0.816177i
$846$	445445.			0.622376
$847$	555266.	+	555266.i	0.773988	+	0.773988i
$848$	−31903.4	+	31903.4i	−0.0443654	+	0.0443654i
$849$			381424.i			0.529168i
$850$	−458042.	+	545597.i	−0.633968	+	0.755151i
$851$	−20529.8			−0.0283482
$852$	21806.0	+	21806.0i	0.0300398	+	0.0300398i
$853$	−387702.	+	387702.i	−0.532844	+	0.532844i	−0.921418	−	0.388573i	$-0.872968\pi$
$853$	−387702.	+	387702.i	−0.532844	+	0.532844i	0.388573	+	0.921418i	$0.372968\pi$
$854$			504223.i			0.691364i
$855$	−460926.	−	167828.i	−0.630520	−	0.229580i
$856$	355969.			0.485808
$857$	−758556.	−	758556.i	−1.03282	−	1.03282i	−0.999443	−	0.0333802i	$-0.989373\pi$
$857$	−758556.	−	758556.i	−1.03282	−	1.03282i	−0.0333802	−	0.999443i	$-0.510627\pi$
$858$	29749.7	−	29749.7i	0.0404118	−	0.0404118i
$859$		−	519654.i		−	0.704251i	−0.935953	−	0.352126i	$-0.885459\pi$
$859$		−	519654.i		−	0.704251i	0.935953	−	0.352126i	$-0.114541\pi$
$860$	−100725.	−	216076.i	−0.136188	−	0.292152i
$861$	670065.			0.903880
$862$	605491.	+	605491.i	0.814879	+	0.814879i
$863$	−941955.	+	941955.i	−1.26476	+	1.26476i	−0.316003	+	0.948758i	$0.602341\pi$
$863$	−941955.	+	941955.i	−1.26476	+	1.26476i	−0.948758	+	0.316003i	$0.897659\pi$
$864$		−	90661.8i		−	0.121450i
$865$	−244569.	+	114007.i	−0.326866	+	0.152370i
$866$	624575.			0.832816
$867$	−184984.	−	184984.i	−0.246091	−	0.246091i
$868$	−203712.	+	203712.i	−0.270382	+	0.270382i
$869$		−	7596.81i		−	0.0100598i
$870$	116508.	−	319979.i	0.153928	−	0.422749i
$871$	−279588.			−0.368538
$872$	−275596.	−	275596.i	−0.362443	−	0.362443i
$873$	770522.	−	770522.i	1.01101	−	1.01101i
$874$			87452.7i			0.114485i
$875$	−342602.	+	1.27670e6i	−0.447480	+	1.66752i
$876$	51509.6			0.0671244
$877$	−694115.	−	694115.i	−0.902469	−	0.902469i	0.0931799	−	0.995649i	$-0.470297\pi$
$877$	−694115.	−	694115.i	−0.902469	−	0.902469i	−0.995649	+	0.0931799i	$0.970297\pi$
$878$	125963.	−	125963.i	0.163401	−	0.163401i
$879$		−	488971.i		−	0.632856i
$880$	−110058.	−	40073.4i	−0.142121	−	0.0517477i
$881$	688672.			0.887279			0.443640	−	0.896205i	$-0.353687\pi$
$881$	688672.			0.887279			0.443640	+	0.896205i	$0.353687\pi$
$882$	665836.	+	665836.i	0.855914	+	0.855914i
$883$	−281308.	+	281308.i	−0.360795	+	0.360795i	−0.864105	−	0.503311i	$-0.832115\pi$
$883$	−281308.	+	281308.i	−0.360795	+	0.360795i	0.503311	+	0.864105i	$0.332115\pi$
$884$			197498.i			0.252731i
$885$	−177080.	−	379873.i	−0.226091	−	0.485012i
$886$	251846.			0.320825
$887$	733241.	+	733241.i	0.931965	+	0.931965i	0.997829	−	0.0658635i	$-0.0209802\pi$
$887$	733241.	+	733241.i	0.931965	+	0.931965i	−0.0658635	+	0.997829i	$0.520980\pi$
$888$	9877.34	−	9877.34i	0.0125260	−	0.0125260i
$889$		−	80391.1i		−	0.101719i
$890$	−482305.	+	224830.i	−0.608895	+	0.283840i
$891$	293451.			0.369641
$892$	140873.	+	140873.i	0.177051	+	0.177051i
$893$	445946.	−	445946.i	0.559215	−	0.559215i
$894$			405639.i			0.507533i
$895$	138753.	−	381072.i	0.173219	−	0.475731i
$896$	122513.			0.152604
$897$	−15848.7	−	15848.7i	−0.0196974	−	0.0196974i
$898$	410415.	−	410415.i	0.508944	−	0.508944i
$899$		−	618043.i		−	0.764714i
$900$	−268054.	−	225038.i	−0.330930	−	0.277824i
$901$	−284089.			−0.349949
$902$	349614.	+	349614.i	0.429710	+	0.429710i
$903$	236512.	−	236512.i	0.290054	−	0.290054i
$904$		−	181623.i		−	0.222246i
$905$	1.33133e6	+	484752.i	1.62550	+	0.591864i
$906$	32341.7			0.0394009
$907$	309922.	+	309922.i	0.376736	+	0.376736i	0.869923	−	0.493187i	$-0.164168\pi$
$907$	309922.	+	309922.i	0.376736	+	0.376736i	−0.493187	+	0.869923i	$0.664168\pi$
$908$	−387162.	+	387162.i	−0.469592	+	0.469592i
$909$			397006.i			0.480473i
$910$	154837.	+	332157.i	0.186979	+	0.401107i
$911$	−1.24901e6			−1.50497			−0.752486	−	0.658609i	$-0.771145\pi$
$911$	−1.24901e6			−1.50497			−0.752486	+	0.658609i	$0.771145\pi$
$912$	−42075.4	−	42075.4i	−0.0505870	−	0.0505870i
$913$	137118.	−	137118.i	0.164495	−	0.164495i
$914$		−	826003.i		−	0.988756i
$915$	158372.	−	73825.9i	0.189163	−	0.0881792i
$916$	279163.			0.332711
$917$	1.59928e6	+	1.59928e6i	1.90189	+	1.90189i
$918$	403657.	−	403657.i	0.478991	−	0.478991i
$919$		−	862437.i		−	1.02117i	−0.859828	−	0.510583i	$-0.829430\pi$
$919$		−	862437.i		−	1.02117i	0.859828	−	0.510583i	$-0.170570\pi$
$920$	−21348.5	+	58631.7i	−0.0252227	+	0.0692719i
$921$	30321.5			0.0357463
$922$	−801909.	−	801909.i	−0.943329	−	0.943329i
$923$	50344.2	−	50344.2i	0.0590944	−	0.0590944i
$924$		−	164331.i		−	0.192476i
$925$	−10109.5	−	115885.i	−0.0118153	−	0.135439i
$926$	−766333.			−0.893708
$927$	−231327.	−	231327.i	−0.269195	−	0.269195i
$928$	−185846.	+	185846.i	−0.215803	+	0.215803i
$929$		−	1.04494e6i		−	1.21077i	−0.795935	−	0.605383i	$-0.793020\pi$
$929$		−	1.04494e6i		−	1.21077i	0.795935	−	0.605383i	$-0.206980\pi$
$930$	93810.7	+	34157.6i	0.108464	+	0.0394931i
$931$	1.33317e6			1.53811
$932$	−305609.	−	305609.i	−0.351832	−	0.351832i
$933$	−283892.	+	283892.i	−0.326130	+	0.326130i
$934$		−	937054.i		−	1.07417i
$935$	−311596.	−	668437.i	−0.356425	−	0.764606i
$936$	−97031.6			−0.110754
$937$	1.20971e6	+	1.20971e6i	1.37785	+	1.37785i	0.848249	+	0.529598i	$0.177657\pi$
$937$	1.20971e6	+	1.20971e6i	1.37785	+	1.37785i	0.529598	+	0.848249i	$0.322343\pi$
$938$	−772194.	+	772194.i	−0.877649	+	0.877649i
$939$		−	383668.i		−	0.435135i
$940$	407841.	−	190118.i	0.461568	−	0.215163i
$941$	1.11630e6			1.26067			0.630334	−	0.776324i	$-0.282918\pi$
$941$	1.11630e6			1.26067			0.630334	+	0.776324i	$0.282918\pi$
$942$	−321232.	−	321232.i	−0.362007	−	0.362007i
$943$	186251.	−	186251.i	0.209448	−	0.209448i
$944$			323483.i			0.363001i
$945$	362416.	−	995344.i	0.405830	−	1.11458i
$946$	246806.			0.275787
$947$	807531.	+	807531.i	0.900450	+	0.900450i	0.995475	−	0.0950253i	$-0.0302932\pi$
$947$	807531.	+	807531.i	0.900450	+	0.900450i	−0.0950253	+	0.995475i	$0.530293\pi$
$948$	1947.14	−	1947.14i	0.00216660	−	0.00216660i
$949$		−	118922.i		−	0.132047i
$950$	−493646.	+	43064.4i	−0.546976	+	0.0477168i
$951$	−32958.8			−0.0364426
$952$	545471.	+	545471.i	0.601863	+	0.601863i
$953$	1.06225e6	−	1.06225e6i	1.16961	−	1.16961i	0.187312	−	0.982300i	$-0.440022\pi$
$953$	1.06225e6	−	1.06225e6i	1.16961	−	1.16961i	0.982300	−	0.187312i	$-0.0599776\pi$
$954$		−	139574.i		−	0.153359i
$955$	306418.	+	111570.i	0.335976	+	0.122333i
$956$	56140.2			0.0614268
$957$	249282.	+	249282.i	0.272187	+	0.272187i
$958$	897466.	−	897466.i	0.977883	−	0.977883i
$959$		−	1.43904e6i		−	1.56471i
$960$	−17937.8	−	38480.2i	−0.0194637	−	0.0417537i
$961$	−742325.			−0.803798
$962$	−22804.1	−	22804.1i	−0.0246413	−	0.0246413i
$963$	−778666.	+	778666.i	−0.839650	+	0.839650i
$964$			503566.i			0.541879i
$965$	−455897.	+	212519.i	−0.489567	+	0.228215i
$966$	−87545.0			−0.0938160
$967$	719392.	+	719392.i	0.769330	+	0.769330i	0.977988	−	0.208659i	$-0.0669098\pi$
$967$	719392.	+	719392.i	0.769330	+	0.769330i	−0.208659	+	0.977988i	$0.566910\pi$
$968$	−148514.	+	148514.i	−0.158496	+	0.158496i
$969$		−	374668.i		−	0.399024i
$970$	376615.	−	1.03434e6i	0.400271	−	1.09931i
$971$	−188478.			−0.199904			−0.0999520	−	0.994992i	$-0.531869\pi$
$971$	−188478.			−0.199904			−0.0999520	+	0.994992i	$0.531869\pi$
$972$	304702.	+	304702.i	0.322510	+	0.322510i
$973$	688634.	−	688634.i	0.727383	−	0.727383i
$974$		−	1.05934e6i		−	1.11665i
$975$	81656.9	−	97265.6i	0.0858981	−	0.102318i
$976$	−134862.			−0.141576
$977$	−706505.	−	706505.i	−0.740161	−	0.740161i	0.232448	−	0.972609i	$-0.425326\pi$
$977$	−706505.	−	706505.i	−0.740161	−	0.740161i	−0.972609	+	0.232448i	$0.925326\pi$
$978$	213897.	−	213897.i	0.223628	−	0.223628i
$979$		−	550900.i		−	0.574787i
$980$	893809.	+	325446.i	0.930664	+	0.338865i
$981$	1.20571e6			1.25286
$982$	−761898.	−	761898.i	−0.790085	−	0.790085i
$983$	−642922.	+	642922.i	−0.665351	+	0.665351i	−0.956636	−	0.291285i	$-0.905917\pi$
$983$	−642922.	+	642922.i	−0.665351	+	0.665351i	0.291285	+	0.956636i	$0.405917\pi$
$984$			179219.i			0.185095i
$985$	−110616.	−	237295.i	−0.114011	−	0.244577i
$986$	−1.65490e6			−1.70223
$987$	446416.	+	446416.i	0.458253	+	0.458253i
$988$	−97140.7	+	97140.7i	−0.0995147	+	0.0995147i
$989$		−	131482.i		−	0.134423i
$990$	328406.	−	153088.i	0.335074	−	0.156197i
$991$	914743.			0.931434			0.465717	−	0.884934i	$-0.345796\pi$
$991$	914743.			0.931434			0.465717	+	0.884934i	$0.345796\pi$
$992$	−54486.0	−	54486.0i	−0.0553683	−	0.0553683i
$993$	−454587.	+	454587.i	−0.461019	+	0.461019i
$994$		−	278092.i		−	0.281459i
$995$	−136405.	+	374624.i	−0.137779	+	0.378399i
$996$	70289.5			0.0708552
$997$	854230.	+	854230.i	0.859378	+	0.859378i	0.991265	−	0.131887i	$-0.0421035\pi$
$997$	854230.	+	854230.i	0.859378	+	0.859378i	−0.131887	+	0.991265i	$0.542103\pi$
$998$	−270135.	+	270135.i	−0.271219	+	0.271219i
$999$			93216.5i			0.0934032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.a.47.8	✓	44
5.3	odd	4	inner	230.5.f.a.93.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.a.47.8	✓	44	1.1	even	1	trivial
230.5.f.a.93.8	yes	44	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-2.34537 + 2.34537i) q^{3} +8.00000i q^{4} +(-23.4912 - 8.55343i) q^{5} +9.38149 q^{6} +(-59.8209 - 59.8209i) q^{7} +(16.0000 - 16.0000i) q^{8} +69.9985i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-2.34537 + 2.34537i) q^{3} +8.00000i q^{4} +(-23.4912 - 8.55343i) q^{5} +9.38149 q^{6} +(-59.8209 - 59.8209i) q^{7} +(16.0000 - 16.0000i) q^{8} +69.9985i q^{9} +(29.8756 + 64.0894i) q^{10} -73.2042 q^{11} +(-18.7630 - 18.7630i) q^{12} +(-43.3186 + 43.3186i) q^{13} +239.284i q^{14} +(75.1567 - 35.0347i) q^{15} -64.0000 q^{16} +(-284.950 - 284.950i) q^{17} +(139.997 - 139.997i) q^{18} -280.309i q^{19} +(68.4275 - 187.930i) q^{20} +280.604 q^{21} +(146.408 + 146.408i) q^{22} +(77.9968 - 77.9968i) q^{23} +75.0519i q^{24} +(478.678 + 401.862i) q^{25} +173.274 q^{26} +(-354.147 - 354.147i) q^{27} +(478.567 - 478.567i) q^{28} +1451.92i q^{29} +(-220.383 - 80.2439i) q^{30} -425.672 q^{31} +(128.000 + 128.000i) q^{32} +(171.691 - 171.691i) q^{33} +1139.80i q^{34} +(893.593 + 1916.94i) q^{35} -559.988 q^{36} +(-131.607 - 131.607i) q^{37} +(-560.617 + 560.617i) q^{38} -203.196i q^{39} +(-512.715 + 239.005i) q^{40} +2387.94 q^{41} +(-561.209 - 561.209i) q^{42} +(842.868 - 842.868i) q^{43} -585.634i q^{44} +(598.727 - 1644.35i) q^{45} -311.987 q^{46} +(1590.91 + 1590.91i) q^{47} +(150.104 - 150.104i) q^{48} +4756.08i q^{49} +(-153.632 - 1761.08i) q^{50} +1336.63 q^{51} +(-346.549 - 346.549i) q^{52} +(498.490 - 498.490i) q^{53} +1416.59i q^{54} +(1719.66 + 626.147i) q^{55} -1914.27 q^{56} +(657.428 + 657.428i) q^{57} +(2903.85 - 2903.85i) q^{58} -5054.42i q^{59} +(280.278 + 601.253i) q^{60} +2107.22 q^{61} +(851.343 + 851.343i) q^{62} +(4187.37 - 4187.37i) q^{63} -512.000i q^{64} +(1388.13 - 647.086i) q^{65} -686.764 q^{66} +(3227.11 + 3227.11i) q^{67} +(2279.60 - 2279.60i) q^{68} +365.863i q^{69} +(2046.70 - 5621.07i) q^{70} -1162.18 q^{71} +(1119.98 + 1119.98i) q^{72} +(-1372.64 + 1372.64i) q^{73} +526.427i q^{74} +(-2065.19 + 180.162i) q^{75} +2242.47 q^{76} +(4379.14 + 4379.14i) q^{77} +(-406.393 + 406.393i) q^{78} +103.775i q^{79} +(1503.44 + 547.420i) q^{80} -4008.66 q^{81} +(-4775.87 - 4775.87i) q^{82} +(-1873.09 + 1873.09i) q^{83} +2244.83i q^{84} +(4256.53 + 9131.13i) q^{85} -3371.47 q^{86} +(-3405.30 - 3405.30i) q^{87} +(-1171.27 + 1171.27i) q^{88} +7525.52i q^{89} +(-4486.16 + 2091.25i) q^{90} +5182.72 q^{91} +(623.974 + 623.974i) q^{92} +(998.358 - 998.358i) q^{93} -6363.64i q^{94} +(-2397.60 + 6584.80i) q^{95} -600.415 q^{96} +(-11007.7 - 11007.7i) q^{97} +(9512.15 - 9512.15i) q^{98} -5124.18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more