LMFDB - Embedded newform 45.5.i.a.11.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.11"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.817210 + 0.471817i) q^{2} +(-6.73136 + 5.97401i) q^{3} +(-7.55478 - 13.0853i) q^{4} +(9.68246 - 5.59017i) q^{5} +(-8.31957 + 1.70605i) q^{6} +(31.6912 - 54.8908i) q^{7} -29.3560i q^{8} +(9.62249 - 80.4264i) q^{9} +10.5501 q^{10} +(-1.86194 - 1.07499i) q^{11} +(129.025 + 42.9493i) q^{12} +(-49.0376 - 84.9356i) q^{13} +(51.7968 - 29.9049i) q^{14} +(-31.7804 + 95.4725i) q^{15} +(-107.026 + 185.374i) q^{16} -193.905i q^{17} +(45.8101 - 61.1852i) q^{18} -473.304 q^{19} +(-146.298 - 84.4650i) q^{20} +(114.593 + 558.814i) q^{21} +(-1.01440 - 1.75699i) q^{22} +(481.454 - 277.968i) q^{23} +(175.373 + 197.606i) q^{24} +(62.5000 - 108.253i) q^{25} -92.5470i q^{26} +(415.695 + 598.864i) q^{27} -957.681 q^{28} +(372.643 + 215.146i) q^{29} +(-71.0168 + 63.0266i) q^{30} +(556.847 + 964.488i) q^{31} +(-581.694 + 335.841i) q^{32} +(18.9554 - 3.88708i) q^{33} +(91.4876 - 158.461i) q^{34} -708.638i q^{35} +(-1125.10 + 481.691i) q^{36} -1638.40 q^{37} +(-386.789 - 223.313i) q^{38} +(837.495 + 278.781i) q^{39} +(-164.105 - 284.238i) q^{40} +(2103.45 - 1214.43i) q^{41} +(-170.011 + 510.735i) q^{42} +(766.741 - 1328.03i) q^{43} +32.4852i q^{44} +(-356.428 - 832.517i) q^{45} +524.599 q^{46} +(2182.02 + 1259.79i) q^{47} +(-386.997 - 1887.19i) q^{48} +(-808.170 - 1399.79i) q^{49} +(102.151 - 58.9771i) q^{50} +(1158.39 + 1305.25i) q^{51} +(-740.936 + 1283.34i) q^{52} -4493.75i q^{53} +(57.1565 + 685.530i) q^{54} -24.0375 q^{55} +(-1611.38 - 930.328i) q^{56} +(3185.98 - 2827.52i) q^{57} +(203.019 + 351.639i) q^{58} +(-4014.80 + 2317.95i) q^{59} +(1489.38 - 305.419i) q^{60} +(-26.4609 + 45.8316i) q^{61} +1050.92i q^{62} +(-4109.73 - 3077.00i) q^{63} +2791.00 q^{64} +(-949.609 - 548.257i) q^{65} +(17.3245 + 5.76690i) q^{66} +(1806.36 + 3128.71i) q^{67} +(-2537.30 + 1464.91i) q^{68} +(-1580.26 + 4747.31i) q^{69} +(334.347 - 579.106i) q^{70} +9591.70i q^{71} +(-2361.00 - 282.478i) q^{72} -302.318 q^{73} +(-1338.92 - 773.026i) q^{74} +(225.995 + 1102.07i) q^{75} +(3575.70 + 6193.30i) q^{76} +(-118.014 + 68.1355i) q^{77} +(552.876 + 622.967i) q^{78} +(5039.10 - 8727.97i) q^{79} +2393.17i q^{80} +(-6375.82 - 1547.81i) q^{81} +2291.95 q^{82} +(7732.71 + 4464.48i) q^{83} +(6446.50 - 5721.19i) q^{84} +(-1083.96 - 1877.48i) q^{85} +(1253.18 - 723.523i) q^{86} +(-3793.68 + 777.950i) q^{87} +(-31.5574 + 54.6590i) q^{88} +8738.71i q^{89} +(101.519 - 848.510i) q^{90} -6216.25 q^{91} +(-7274.55 - 4199.97i) q^{92} +(-9510.20 - 3165.71i) q^{93} +(1188.78 + 2059.02i) q^{94} +(-4582.74 + 2645.85i) q^{95} +(1909.28 - 5735.71i) q^{96} +(4805.23 - 8322.91i) q^{97} -1525.23i q^{98} +(-104.374 + 139.405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

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

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

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 $

$2$	0.817210	+	0.471817i	0.204303	+	0.117954i	0.598661	−	0.801003i	$-0.295700\pi$
$2$	0.817210	+	0.471817i	0.204303	+	0.117954i	−0.394358	+	0.918957i	$0.629033\pi$
$3$	−6.73136	+	5.97401i	−0.747929	+	0.663778i
$3$	−6.73136	+	5.97401i	−0.747929	+	0.663778i
$4$	−7.55478	−	13.0853i	−0.472174	−	0.817829i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$	−8.31957	+	1.70605i	−0.231099	+	0.0473903i
$7$	31.6912	−	54.8908i	0.646760	−	1.12022i	−0.337132	−	0.941457i	$-0.609457\pi$
$7$	31.6912	−	54.8908i	0.646760	−	1.12022i	0.983892	−	0.178764i	$-0.0572098\pi$
$8$		−	29.3560i		−	0.458688i
$9$	9.62249	−	80.4264i	0.118796	−	0.992919i
$10$	10.5501			0.105501
$11$	−1.86194	−	1.07499i	−0.0153879	−	0.00888421i	0.492286	−	0.870433i	$-0.336161\pi$
$11$	−1.86194	−	1.07499i	−0.0153879	−	0.00888421i	−0.507674	+	0.861549i	$0.669495\pi$
$12$	129.025	+	42.9493i	0.896010	+	0.298259i
$13$	−49.0376	−	84.9356i	−0.290163	−	0.502577i	0.683685	−	0.729777i	$-0.260376\pi$
$13$	−49.0376	−	84.9356i	−0.290163	−	0.502577i	−0.973848	+	0.227200i	$0.927043\pi$
$14$	51.7968	−	29.9049i	0.264269	−	0.152576i
$15$	−31.7804	+	95.4725i	−0.141246	+	0.424322i
$16$	−107.026	+	185.374i	−0.418070	+	0.724118i
$17$		−	193.905i		−	0.670952i	−0.942049	−	0.335476i	$-0.891103\pi$
$17$		−	193.905i		−	0.670952i	0.942049	−	0.335476i	$-0.108897\pi$
$18$	45.8101	−	61.1852i	0.141389	−	0.188843i
$19$	−473.304			−1.31109			−0.655545	−	0.755156i	$-0.727561\pi$
$19$	−473.304			−1.31109			−0.655545	+	0.755156i	$0.727561\pi$
$20$	−146.298	−	84.4650i	−0.365744	−	0.211162i
$21$	114.593	+	558.814i	0.259848	+	1.26715i
$22$	−1.01440	−	1.75699i	−0.00209586	−	0.00363013i
$23$	481.454	−	277.968i	0.910121	−	0.525458i	0.0296507	−	0.999560i	$-0.490561\pi$
$23$	481.454	−	277.968i	0.910121	−	0.525458i	0.880470	+	0.474102i	$0.157227\pi$
$24$	175.373	+	197.606i	0.304467	+	0.343066i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	92.5470i		−	0.136904i
$27$	415.695	+	598.864i	0.570227	+	0.821487i
$28$	−957.681			−1.22153
$29$	372.643	+	215.146i	0.443096	+	0.255821i	0.704910	−	0.709297i	$-0.250987\pi$
$29$	372.643	+	215.146i	0.443096	+	0.255821i	−0.261814	+	0.965118i	$0.584321\pi$
$30$	−71.0168	+	63.0266i	−0.0789076	+	0.0700296i
$31$	556.847	+	964.488i	0.579446	+	1.00363i	0.995543	+	0.0943090i	$0.0300642\pi$
$31$	556.847	+	964.488i	0.579446	+	1.00363i	−0.416097	+	0.909320i	$0.636602\pi$
$32$	−581.694	+	335.841i	−0.568060	+	0.327970i
$33$	18.9554	−	3.88708i	0.0174062	−	0.00356940i
$34$	91.4876	−	158.461i	0.0791415	−	0.137077i
$35$		−	708.638i		−	0.578480i
$36$	−1125.10	+	481.691i	−0.868130	+	0.371675i
$37$	−1638.40			−1.19679			−0.598395	−	0.801202i	$-0.704194\pi$
$37$	−1638.40			−1.19679			−0.598395	+	0.801202i	$0.704194\pi$
$38$	−386.789	−	223.313i	−0.267859	−	0.154649i
$39$	837.495	+	278.781i	0.550622	+	0.183288i
$40$	−164.105	−	284.238i	−0.102566	−	0.177649i
$41$	2103.45	−	1214.43i	1.25131	−	0.722445i	0.279941	−	0.960017i	$-0.409685\pi$
$41$	2103.45	−	1214.43i	1.25131	−	0.722445i	0.971370	+	0.237572i	$0.0763516\pi$
$42$	−170.011	+	510.735i	−0.0963782	+	0.289533i
$43$	766.741	−	1328.03i	0.414679	−	0.718245i	−0.580716	−	0.814106i	$-0.697227\pi$
$43$	766.741	−	1328.03i	0.414679	−	0.718245i	0.995395	+	0.0958614i	$0.0305606\pi$
$44$			32.4852i			0.0167796i
$45$	−356.428	−	832.517i	−0.176014	−	0.411119i
$46$	524.599			0.247920
$47$	2182.02	+	1259.79i	0.987784	+	0.570298i	0.904611	−	0.426237i	$-0.140161\pi$
$47$	2182.02	+	1259.79i	0.987784	+	0.570298i	0.0831731	+	0.996535i	$0.473495\pi$
$48$	−386.997	−	1887.19i	−0.167967	−	0.819094i
$49$	−808.170	−	1399.79i	−0.336597	−	0.583004i
$50$	102.151	−	58.9771i	0.0408605	−	0.0235908i
$51$	1158.39	+	1305.25i	0.445363	+	0.501824i
$52$	−740.936	+	1283.34i	−0.274015	+	0.474608i
$53$		−	4493.75i		−	1.59977i	−0.600154	−	0.799885i	$-0.704894\pi$
$53$		−	4493.75i		−	1.59977i	0.600154	−	0.799885i	$-0.295106\pi$
$54$	57.1565	+	685.530i	0.0196010	+	0.235093i
$55$	−24.0375			−0.00794628
$56$	−1611.38	−	930.328i	−0.513832	−	0.296661i
$57$	3185.98	−	2827.52i	0.980603	−	0.870274i
$58$	203.019	+	351.639i	0.0603504	+	0.104530i
$59$	−4014.80	+	2317.95i	−1.15335	+	0.665885i	−0.949701	−	0.313159i	$-0.898613\pi$
$59$	−4014.80	+	2317.95i	−1.15335	+	0.665885i	−0.203646	+	0.979045i	$0.565279\pi$
$60$	1489.38	−	305.419i	0.413716	−	0.0848385i
$61$	−26.4609	+	45.8316i	−0.00711123	+	0.0123170i	−0.869559	−	0.493829i	$-0.835597\pi$
$61$	−26.4609	+	45.8316i	−0.00711123	+	0.0123170i	0.862448	+	0.506146i	$0.168930\pi$
$62$			1050.92i			0.273392i
$63$	−4109.73	−	3077.00i	−1.03546	−	0.775258i
$64$	2791.00			0.681397
$65$	−949.609	−	548.257i	−0.224759	−	0.129765i
$66$	17.3245	+	5.76690i	0.00397716	+	0.00132390i
$67$	1806.36	+	3128.71i	0.402397	+	0.696972i	0.994015	−	0.109247i	$-0.0348439\pi$
$67$	1806.36	+	3128.71i	0.402397	+	0.696972i	−0.591618	+	0.806219i	$0.701511\pi$
$68$	−2537.30	+	1464.91i	−0.548724	+	0.316806i
$69$	−1580.26	+	4747.31i	−0.331918	+	0.997124i
$70$	334.347	−	579.106i	0.0682341	−	0.118185i
$71$			9591.70i			1.90274i	0.308053	+	0.951369i	$0.400323\pi$
$71$			9591.70i			1.90274i	−0.308053	+	0.951369i	$0.599677\pi$
$72$	−2361.00	−	282.478i	−0.455439	−	0.0544903i
$73$	−302.318			−0.0567307			−0.0283654	−	0.999598i	$-0.509030\pi$
$73$	−302.318			−0.0567307			−0.0283654	+	0.999598i	$0.509030\pi$
$74$	−1338.92	−	773.026i	−0.244507	−	0.141166i
$75$	225.995	+	1102.07i	0.0401769	+	0.195923i
$76$	3575.70	+	6193.30i	0.619062	+	1.07225i
$77$	−118.014	+	68.1355i	−0.0199046	+	0.0114919i
$78$	552.876	+	622.967i	0.0908738	+	0.102394i
$79$	5039.10	−	8727.97i	0.807418	−	1.39849i	−0.107228	−	0.994234i	$-0.534198\pi$
$79$	5039.10	−	8727.97i	0.807418	−	1.39849i	0.914646	−	0.404255i	$-0.132469\pi$
$80$			2393.17i			0.373933i
$81$	−6375.82	−	1547.81i	−0.971775	−	0.235910i
$82$	2291.95			0.340861
$83$	7732.71	+	4464.48i	1.12247	+	0.648060i	0.942031	−	0.335526i	$-0.108914\pi$
$83$	7732.71	+	4464.48i	1.12247	+	0.648060i	0.180441	+	0.983586i	$0.442247\pi$
$84$	6446.50	−	5721.19i	0.913620	−	0.810827i
$85$	−1083.96	−	1877.48i	−0.150029	−	0.259858i
$86$	1253.18	−	723.523i	0.169440	−	0.0978262i
$87$	−3793.68	+	777.950i	−0.501213	+	0.102781i
$88$	−31.5574	+	54.6590i	−0.00407508	+	0.00705824i
$89$			8738.71i			1.10323i	0.834098	+	0.551617i	$0.185989\pi$
$89$			8738.71i			1.10323i	−0.834098	+	0.551617i	$0.814011\pi$
$90$	101.519	−	848.510i	0.0125332	−	0.104754i
$91$	−6216.25			−0.750664
$92$	−7274.55	−	4199.97i	−0.859470	−	0.496215i
$93$	−9510.20	−	3165.71i	−1.09957	−	0.366020i
$94$	1188.78	+	2059.02i	0.134538	+	0.233027i
$95$	−4582.74	+	2645.85i	−0.507783	+	0.293169i
$96$	1909.28	−	5735.71i	0.207170	−	0.622365i
$97$	4805.23	−	8322.91i	0.510706	−	0.884569i	−0.489217	−	0.872162i	$-0.662717\pi$
$97$	4805.23	−	8322.91i	0.510706	−	0.884569i	0.999923	−	0.0124065i	$-0.00394922\pi$
$98$		−	1525.23i		−	0.158812i
$99$	−104.374	+	139.405i	−0.0106493	+	0.0142235i
$100$	−1888.69			−0.188869
$101$	−1468.67	−	847.935i	−0.143973	−	0.0831228i	0.426283	−	0.904590i	$-0.359823\pi$
$101$	−1468.67	−	847.935i	−0.143973	−	0.0831228i	−0.570256	+	0.821467i	$0.693156\pi$
$102$	330.812	+	1613.21i	0.0317966	+	0.155056i
$103$	9057.65	+	15688.3i	0.853771	+	1.47877i	0.877781	+	0.479062i	$0.159023\pi$
$103$	9057.65	+	15688.3i	0.853771	+	1.47877i	−0.0240103	+	0.999712i	$0.507643\pi$
$104$	−2493.37	+	1439.55i	−0.230526	+	0.133094i
$105$	4233.41	+	4770.10i	0.383982	+	0.432662i
$106$	2120.23	−	3672.34i	0.188699	−	0.326837i
$107$		−	14783.3i		−	1.29123i	−0.763661	−	0.645617i	$-0.776600\pi$
$107$		−	14783.3i		−	1.29123i	0.763661	−	0.645617i	$-0.223400\pi$
$108$	4695.81	−	9963.77i	0.402590	−	0.854233i
$109$	−11879.3			−0.999857			−0.499928	−	0.866067i	$-0.666640\pi$
$109$	−11879.3			−0.999857			−0.499928	+	0.866067i	$0.666640\pi$
$110$	−19.6437	−	11.3413i	−0.00162345	−	0.000937297i
$111$	11028.7	−	9787.84i	0.895113	−	0.794403i
$112$	6783.56	+	11749.5i	0.540781	+	0.936661i
$113$	12644.4	−	7300.26i	0.990244	−	0.571717i	0.0848964	−	0.996390i	$-0.472944\pi$
$113$	12644.4	−	7300.26i	0.990244	−	0.571717i	0.905347	+	0.424672i	$0.139611\pi$
$114$	3937.68	−	807.480i	0.302992	−	0.0621330i
$115$	3107.77	−	5382.82i	0.234992	−	0.407018i
$116$		−	6501.51i		−	0.483168i
$117$	−7302.93	+	3126.62i	−0.533489	+	0.228404i
$118$	−4374.58			−0.314176
$119$	−10643.6	−	6145.09i	−0.751614	−	0.433945i
$120$	2802.69	+	932.947i	0.194631	+	0.0647880i
$121$	−7318.19	−	12675.5i	−0.499842	−	0.865752i
$122$	−43.2482	+	24.9694i	−0.00290569	+	0.00167760i
$123$	−6904.10	+	20740.8i	−0.456349	+	1.37093i
$124$	8413.71	−	14573.0i	0.547198	−	0.947774i
$125$		−	1397.54i		−	0.0894427i
$126$	−1906.73	−	4453.59i	−0.120101	−	0.280524i
$127$	−10104.0			−0.626449			−0.313224	−	0.949679i	$-0.601409\pi$
$127$	−10104.0			−0.626449			−0.313224	+	0.949679i	$0.601409\pi$
$128$	11587.9	+	6690.30i	0.707272	+	0.408344i
$129$	2772.48	+	13520.0i	0.166605	+	0.812451i
$130$	−517.353	−	896.082i	−0.0306126	−	0.0530226i
$131$	18998.6	−	10968.8i	1.10708	−	0.639172i	0.169007	−	0.985615i	$-0.445944\pi$
$131$	18998.6	−	10968.8i	1.10708	−	0.639172i	0.938071	+	0.346443i	$0.112611\pi$
$132$	−194.067	−	218.670i	−0.0111379	−	0.0125499i
$133$	−14999.6	+	25980.0i	−0.847961	+	1.46871i
$134$			3409.08i			0.189857i
$135$	7372.71	+	3474.67i	0.404538	+	0.190654i
$136$	−5692.28			−0.307757
$137$	10545.6	+	6088.49i	0.561862	+	0.324391i	0.753892	−	0.656998i	$-0.228174\pi$
$137$	10545.6	+	6088.49i	0.561862	+	0.324391i	−0.192031	+	0.981389i	$0.561507\pi$
$138$	−3531.26	+	3133.96i	−0.185427	+	0.164564i
$139$	−13827.9	−	23950.7i	−0.715694	−	1.23962i	−0.962691	−	0.270602i	$-0.912777\pi$
$139$	−13827.9	−	23950.7i	−0.715694	−	1.23962i	0.246997	−	0.969016i	$-0.420556\pi$
$140$	−9272.71	+	5353.60i	−0.473097	+	0.273143i
$141$	−22213.9	+	4555.29i	−1.11734	+	0.229128i
$142$	−4525.52	+	7838.44i	−0.224436	+	0.388734i
$143$			210.860i			0.0103115i
$144$	13879.1	+	10391.5i	0.669325	+	0.501131i
$145$	4810.81			0.228814
$146$	−247.057	−	142.639i	−0.0115902	−	0.00669162i
$147$	13802.5	+	4594.49i	0.638736	+	0.212619i
$148$	12377.8	+	21438.9i	0.565092	+	0.978768i
$149$	−17886.6	+	10326.8i	−0.805667	+	0.465152i	−0.845449	−	0.534056i	$-0.820667\pi$
$149$	−17886.6	+	10326.8i	−0.805667	+	0.465152i	0.0397820	+	0.999208i	$0.487334\pi$
$150$	−335.288	+	1007.25i	−0.0149017	+	0.0447666i
$151$	−8454.63	+	14643.8i	−0.370801	+	0.642246i	−0.989689	−	0.143233i	$-0.954250\pi$
$151$	−8454.63	+	14643.8i	−0.370801	+	0.642246i	0.618888	+	0.785479i	$0.287583\pi$
$152$			13894.3i			0.601381i
$153$	−15595.1	−	1865.85i	−0.666200	−	0.0797065i
$154$	−128.590			−0.00542207
$155$	10783.3	+	6225.74i	0.448837	+	0.259136i
$156$	−2679.17	−	13065.0i	−0.110091	−	0.536858i
$157$	−13974.1	−	24203.9i	−0.566924	−	0.981942i	−0.996868	−	0.0790859i	$-0.974800\pi$
$157$	−13974.1	−	24203.9i	−0.566924	−	0.981942i	0.429943	−	0.902856i	$-0.358533\pi$
$158$	8236.00	−	4755.06i	0.329915	−	0.190477i
$159$	26845.7	+	30249.1i	1.06189	+	1.19651i
$160$	−3754.82	+	6503.54i	−0.146673	+	0.254044i
$161$		−	35236.5i		−	1.35938i
$162$	−4480.10	−	4273.10i	−0.170710	−	0.162822i
$163$	466.215			0.0175473			0.00877366	−	0.999962i	$-0.497207\pi$
$163$	466.215			0.0175473			0.00877366	+	0.999962i	$0.497207\pi$
$164$	−31782.3	−	18349.5i	−1.18167	−	0.682239i
$165$	161.805	−	143.600i	0.00594326	−	0.00527457i
$166$	4212.83	+	7296.84i	0.152883	+	0.264800i
$167$	28373.4	−	16381.4i	1.01737	−	0.587379i	0.104029	−	0.994574i	$-0.466827\pi$
$167$	28373.4	−	16381.4i	1.01737	−	0.587379i	0.913341	+	0.407195i	$0.133493\pi$
$168$	16404.5	−	3363.99i	0.581227	−	0.119189i
$169$	9471.13	−	16404.5i	0.331611	−	0.574367i
$170$		−	2045.72i		−	0.0707863i
$171$	−4554.36	+	38066.1i	−0.155753	+	1.30181i
$172$	−23170.2			−0.783202
$173$	8828.89	+	5097.36i	0.294995	+	0.170315i	0.640192	−	0.768215i	$-0.278855\pi$
$173$	8828.89	+	5097.36i	0.294995	+	0.170315i	−0.345198	+	0.938530i	$0.612188\pi$
$174$	−3467.28	−	1154.17i	−0.114523	−	0.0381217i
$175$	−3961.41	−	6861.36i	−0.129352	−	0.224044i
$176$	398.551	−	230.103i	0.0128664	−	0.00742844i
$177$	13177.7	−	39587.4i	0.420622	−	1.26360i
$178$	−4123.07	+	7141.37i	−0.130131	+	0.225393i
$179$			26275.1i			0.820046i	0.912075	+	0.410023i	$0.134479\pi$
$179$			26275.1i			0.820046i	−0.912075	+	0.410023i	$0.865521\pi$
$180$	−8200.96	+	10953.4i	−0.253116	+	0.338069i
$181$	33794.7			1.03155			0.515776	−	0.856723i	$-0.327504\pi$
$181$	33794.7			1.03155			0.515776	+	0.856723i	$0.327504\pi$
$182$	−5079.98	−	2932.93i	−0.153363	−	0.0885439i
$183$	−95.6805	−	466.587i	−0.00285707	−	0.0139325i
$184$	−8160.02	−	14133.6i	−0.241021	−	0.417461i
$185$	−15863.8	+	9158.96i	−0.463514	+	0.267610i
$186$	−6278.20	−	7074.12i	−0.181472	−	0.204478i
$187$	−208.446	+	361.039i	−0.00596088	+	0.0103245i
$188$		−	38069.7i		−	1.07712i
$189$	46046.1	−	3839.12i	1.28905	−	0.107475i
$190$	−4993.42			−0.138322
$191$	−4712.70	−	2720.88i	−0.129182	−	0.0745834i	0.434016	−	0.900905i	$-0.357096\pi$
$191$	−4712.70	−	2720.88i	−0.129182	−	0.0745834i	−0.563198	+	0.826322i	$0.690429\pi$
$192$	−18787.3	+	16673.5i	−0.509637	+	0.452297i
$193$	−11328.7	−	19621.9i	−0.304135	−	0.526777i	0.672934	−	0.739703i	$-0.265034\pi$
$193$	−11328.7	−	19621.9i	−0.304135	−	0.526777i	−0.977068	+	0.212926i	$0.931701\pi$
$194$	7853.77	−	4534.38i	0.208677	−	0.120480i
$195$	9667.45	−	1982.45i	0.254239	−	0.0521355i
$196$	−12211.1	+	21150.2i	−0.317865	+	0.550558i
$197$			13482.0i			0.347395i	0.984799	+	0.173697i	$0.0555714\pi$
$197$			13482.0i			0.347395i	−0.984799	+	0.173697i	$0.944429\pi$
$198$	−151.069	+	64.6776i	−0.00385341	+	0.00164977i
$199$	14137.4			0.356997			0.178498	−	0.983940i	$-0.442876\pi$
$199$	14137.4			0.356997			0.178498	+	0.983940i	$0.442876\pi$
$200$	−3177.88	−	1834.75i	−0.0794470	−	0.0458688i
$201$	−30850.2	−	10269.3i	−0.763599	−	0.254183i
$202$	−800.140	−	1385.88i	−0.0196094	−	0.0339644i
$203$	23619.1	−	13636.5i	0.573153	−	0.330910i
$204$	8328.09	−	25018.7i	0.200118	−	0.601179i
$205$	13577.7	−	23517.3i	0.323087	−	0.559603i
$206$			17094.2i			0.402823i
$207$	−17723.1	−	41396.3i	−0.413619	−	0.966098i
$208$	20993.1			0.485234
$209$	881.262	+	508.797i	0.0201749	+	0.0116480i
$210$	1208.97	+	5895.56i	0.0274143	+	0.133686i
$211$	18853.1	+	32654.5i	0.423464	+	0.733462i	0.996276	−	0.0862253i	$-0.0274805\pi$
$211$	18853.1	+	32654.5i	0.423464	+	0.733462i	−0.572811	+	0.819687i	$0.694147\pi$
$212$	−58801.9	+	33949.3i	−1.30834	+	0.755369i
$213$	−57300.9	−	64565.2i	−1.26300	−	1.42311i
$214$	6975.03	−	12081.1i	0.152307	−	0.263803i
$215$		−	17144.9i		−	0.370900i
$216$	17580.3	−	12203.2i	0.376806	−	0.261556i
$217$	70588.7			1.49905
$218$	−9707.89	−	5604.85i	−0.204273	−	0.117937i
$219$	2035.01	−	1806.05i	0.0424306	−	0.0376566i
$220$	181.598	+	314.537i	0.00375202	+	0.00649870i
$221$	−16469.4	+	9508.63i	−0.337205	+	0.194685i
$222$	13630.8	−	2795.20i	0.276577	−	0.0567162i
$223$	−14947.7	+	25890.2i	−0.300583	+	0.520626i	−0.976268	−	0.216565i	$-0.930515\pi$
$223$	−14947.7	+	25890.2i	−0.300583	+	0.520626i	0.675685	+	0.737191i	$0.263848\pi$
$224$			42572.9i			0.848471i
$225$	−8105.01	−	6068.32i	−0.160099	−	0.119868i
$226$	13777.5			0.269746
$227$	40759.1	+	23532.3i	0.790994	+	0.456681i	0.840312	−	0.542102i	$-0.182371\pi$
$227$	40759.1	+	23532.3i	0.790994	+	0.456681i	−0.0493182	+	0.998783i	$0.515705\pi$
$228$	−61068.2	−	20328.1i	−1.17475	−	0.391045i
$229$	−4858.77	−	8415.64i	−0.0926522	−	0.160478i	0.815974	−	0.578088i	$-0.196201\pi$
$229$	−4858.77	−	8415.64i	−0.0926522	−	0.160478i	−0.908626	+	0.417610i	$0.862868\pi$
$230$	5079.40	−	2932.60i	0.0960190	−	0.0554366i
$231$	387.354	−	1163.66i	0.00725913	−	0.0218074i
$232$	6315.82	−	10939.3i	0.117342	−	0.203242i
$233$			55316.3i			1.01892i	0.860493	+	0.509462i	$0.170155\pi$
$233$			55316.3i			1.01892i	−0.860493	+	0.509462i	$0.829845\pi$
$234$	−7443.22	−	890.532i	−0.135934	−	0.0162637i
$235$	28169.7			0.510090
$236$	60661.8	+	35023.1i	1.08916	+	0.628827i
$237$	18221.0	+	88854.7i	0.324395	+	1.58192i
$238$	−5798.71	−	10043.7i	−0.102371	−	0.177312i
$239$	−55750.4	+	32187.5i	−0.976006	+	0.563497i	−0.901062	−	0.433690i	$-0.857211\pi$
$239$	−55750.4	+	32187.5i	−0.976006	+	0.563497i	−0.0749442	+	0.997188i	$0.523878\pi$
$240$	−14296.8	−	16109.3i	−0.248209	−	0.279675i
$241$	−12059.0	+	20886.9i	−0.207624	+	0.359616i	−0.950966	−	0.309296i	$-0.899907\pi$
$241$	−12059.0	+	20886.9i	−0.207624	+	0.359616i	0.743341	+	0.668912i	$0.233240\pi$
$242$		−	13811.4i		−	0.235834i
$243$	52164.5	−	27670.3i	0.883411	−	0.468599i
$244$	799.625			0.0134309
$245$	−15650.1	−	9035.62i	−0.260727	−	0.150531i
$246$	−15428.0	+	13692.1i	−0.254940	+	0.226257i
$247$	23209.7	+	40200.3i	0.380430	+	0.658924i
$248$	28313.5	−	16346.8i	0.460352	−	0.265784i
$249$	−78722.5	+	16143.2i	−1.26970	+	0.260370i
$250$	659.384	−	1142.09i	0.0105501	−	0.0182734i
$251$			22668.3i			0.359808i	0.983684	+	0.179904i	$0.0575787\pi$
$251$			22668.3i			0.359808i	−0.983684	+	0.179904i	$0.942421\pi$
$252$	−9215.28	+	77022.9i	−0.145113	+	1.21288i
$253$	−1195.25			−0.0186731
$254$	−8257.09	−	4767.23i	−0.127985	−	0.0738922i
$255$	18512.6	+	6162.39i	0.284700	+	0.0947695i
$256$	−16014.8	−	27738.5i	−0.244367	−	0.423256i
$257$	−46787.4	+	27012.7i	−0.708374	+	0.408980i	−0.810459	−	0.585796i	$-0.800782\pi$
$257$	−46787.4	+	27012.7i	−0.708374	+	0.408980i	0.102084	+	0.994776i	$0.467449\pi$
$258$	−4113.27	+	12356.8i	−0.0617942	+	0.185638i
$259$	−51923.1	+	89933.4i	−0.774035	+	1.34067i
$260$			16567.8i			0.245086i
$261$	20889.2	−	27900.1i	0.306648	−	0.409567i
$262$	20701.1			0.301572
$263$	−91904.5	−	53061.1i	−1.32870	−	0.767123i	−0.343598	−	0.939117i	$-0.611646\pi$
$263$	−91904.5	−	53061.1i	−1.32870	−	0.767123i	−0.985098	+	0.171994i	$0.944979\pi$
$264$	−114.109	−	556.454i	−0.00163724	−	0.00798402i
$265$	−25120.8	−	43510.6i	−0.357719	−	0.619588i
$266$	−24515.6	+	14154.1i	−0.346481	+	0.200041i
$267$	−52205.1	−	58823.4i	−0.732303	−	0.825141i
$268$	27293.3	−	47273.4i	0.380002	−	0.658183i
$269$		−	7174.83i		−	0.0991533i	−0.998770	−	0.0495766i	$-0.984213\pi$
$269$		−	7174.83i		−	0.0991533i	0.998770	−	0.0495766i	$-0.0157872\pi$
$270$	4385.64	+	6318.10i	0.0601597	+	0.0866680i
$271$	50647.5			0.689636			0.344818	−	0.938670i	$-0.387941\pi$
$271$	50647.5			0.689636			0.344818	+	0.938670i	$0.387941\pi$
$272$	35945.0	+	20752.8i	0.485848	+	0.280504i
$273$	41843.8	−	37135.9i	0.561443	−	0.498275i
$274$	5745.30	+	9951.16i	0.0765265	+	0.132548i
$275$	−232.742	+	134.374i	−0.00307758	+	0.00177684i
$276$	74058.3	−	15186.7i	0.972200	−	0.199364i
$277$	−16570.9	+	28701.7i	−0.215967	+	0.374065i	−0.953571	−	0.301168i	$-0.902624\pi$
$277$	−16570.9	+	28701.7i	−0.215967	+	0.374065i	0.737605	+	0.675233i	$0.235957\pi$
$278$		−	26097.0i		−	0.337676i
$279$	82928.5	−	35504.4i	1.06536	−	0.456115i
$280$	−20802.8			−0.265342
$281$	−11828.7	−	6829.28i	−0.149804	−	0.0864893i	0.423224	−	0.906025i	$-0.360898\pi$
$281$	−11828.7	−	6829.28i	−0.149804	−	0.0864893i	−0.573028	+	0.819536i	$0.694232\pi$
$282$	−20302.7	−	6758.26i	−0.255303	−	0.0849840i
$283$	−7656.58	−	13261.6i	−0.0956009	−	0.165586i	0.814258	−	0.580503i	$-0.197144\pi$
$283$	−7656.58	−	13261.6i	−0.0956009	−	0.165586i	−0.909859	+	0.414917i	$0.863811\pi$
$284$	125510.	−	72463.2i	1.55611	−	0.898423i
$285$	15041.8	−	45187.5i	0.185187	−	0.556325i
$286$	−99.4870	+	172.317i	−0.00121628	+	0.00210666i
$287$		−	153947.i		−	1.86899i
$288$	21413.2	+	50015.2i	0.258164	+	0.602999i
$289$	45921.8			0.549824
$290$	3931.44	+	2269.82i	0.0467472	+	0.0269895i
$291$	17375.3	+	84731.0i	0.205186	+	1.00059i
$292$	2283.95	+	3955.91i	0.0267867	+	0.0463960i
$293$	4083.76	−	2357.76i	0.0475691	−	0.0274640i	−0.476027	−	0.879431i	$-0.657923\pi$
$293$	4083.76	−	2357.76i	0.0475691	−	0.0274640i	0.523596	+	0.851967i	$0.324590\pi$
$294$	9111.75	+	10266.9i	0.105416	+	0.118780i
$295$	−25915.4	+	44886.8i	−0.297793	+	0.515792i
$296$			48097.0i			0.548952i
$297$	−130.226	−	1561.92i	−0.00147633	−	0.0177070i
$298$	−19489.5			−0.219466
$299$	−47218.7	−	27261.7i	−0.528167	−	0.304937i
$300$	12713.5	−	11283.1i	0.141261	−	0.125367i
$301$	−48598.0	−	84174.2i	−0.536396	−	0.929064i
$302$	−13818.4	+	7978.07i	−0.151511	+	0.0874750i
$303$	14951.7	−	3066.07i	0.162857	−	0.0333961i
$304$	50655.7	−	87738.3i	0.548127	−	0.949384i
$305$			591.684i			0.00636048i
$306$	−11864.1	−	8882.81i	−0.126705	−	0.0948653i
$307$	−96040.5			−1.01901			−0.509504	−	0.860468i	$-0.670171\pi$
$307$	−96040.5			−1.01901			−0.509504	+	0.860468i	$0.670171\pi$
$308$	1783.14	+	1029.50i	0.0187968	+	0.0108524i
$309$	−154692.	−	51493.3i	−1.62014	−	0.539304i
$310$	5874.81	+	10175.5i	0.0611323	+	0.105884i
$311$	−14313.6	+	8263.98i	−0.147989	+	0.0854414i	−0.572166	−	0.820138i	$-0.693897\pi$
$311$	−14313.6	+	8263.98i	−0.147989	+	0.0854414i	0.424177	+	0.905579i	$0.360563\pi$
$312$	8183.91	−	24585.5i	0.0840720	−	0.252563i
$313$	18196.5	−	31517.3i	0.185737	−	0.321706i	−0.758087	−	0.652153i	$-0.773866\pi$
$313$	18196.5	−	31517.3i	0.185737	−	0.321706i	0.943825	+	0.330446i	$0.107199\pi$
$314$		−	26372.9i		−	0.267484i
$315$	−56993.2	−	6818.86i	−0.574383	−	0.0687212i
$316$	−152277.			−1.52497
$317$	115284.	+	66559.2i	1.14723	+	0.662353i	0.948210	−	0.317643i	$-0.102891\pi$
$317$	115284.	+	66559.2i	1.14723	+	0.662353i	0.199019	+	0.979996i	$0.436225\pi$
$318$	7666.57	+	37386.1i	0.0758136	+	0.369706i
$319$	−462.559	−	801.176i	−0.00454554	−	0.00787311i
$320$	27023.8	−	15602.2i	0.263904	−	0.152365i
$321$	88315.8	+	99512.1i	0.857094	+	0.965752i
$322$	16625.2	−	28795.7i	0.160345	−	0.277725i
$323$			91776.0i			0.879678i
$324$	27914.4	+	95122.5i	0.265913	+	0.906136i
$325$	−12259.4			−0.116065
$326$	380.995	+	219.968i	0.00358496	+	0.00206978i
$327$	79963.9	−	70967.0i	0.747822	−	0.663684i
$328$	−35650.8	−	61749.0i	−0.331377	−	0.573961i
$329$	138302.	−	79848.5i	1.27772	−	0.737692i
$330$	199.982	−	41.0092i	0.00183638	−	0.000376577i
$331$	−9077.72	+	15723.1i	−0.0828554	+	0.143510i	−0.904475	−	0.426526i	$-0.859737\pi$
$331$	−9077.72	+	15723.1i	−0.0828554	+	0.143510i	0.821620	+	0.570036i	$0.193071\pi$
$332$		−	134913.i		−	1.22399i
$333$	−15765.5	+	131771.i	−0.142174	+	1.18831i
$334$	30916.1			0.277135
$335$	34980.0	+	20195.7i	0.311695	+	0.179957i
$336$	−115854.	−	38564.9i	−1.02620	−	0.341597i
$337$	−35988.6	−	62334.2i	−0.316888	−	0.548866i	0.662949	−	0.748664i	$-0.269305\pi$
$337$	−35988.6	−	62334.2i	−0.316888	−	0.548866i	−0.979837	+	0.199799i	$0.935971\pi$
$338$	15479.8	−	8937.27i	0.135498	−	0.0782297i
$339$	−41502.4	+	124679.i	−0.361138	+	1.08491i
$340$	−16378.2	+	28367.9i	−0.141680	+	0.245397i
$341$		−	2394.42i		−	0.0205917i
$342$	−21682.1	+	28959.2i	−0.185374	+	0.247591i
$343$	49733.7			0.422729
$344$	−38985.8	−	22508.5i	−0.329450	−	0.190208i
$345$	11237.5	+	54799.5i	0.0944125	+	0.460404i
$346$	4810.04	+	8331.24i	0.0401788	+	0.0695917i
$347$	−103061.	+	59502.2i	−0.855923	+	0.494167i	−0.862645	−	0.505810i	$-0.831194\pi$
$347$	−103061.	+	59502.2i	−0.855923	+	0.494167i	0.00672178	+	0.999977i	$0.497860\pi$
$348$	38840.1	+	43764.1i	0.320717	+	0.361376i
$349$	−99984.5	+	173178.i	−0.820884	+	1.42181i	0.0841403	+	0.996454i	$0.473186\pi$
$349$	−99984.5	+	173178.i	−0.820884	+	1.42181i	−0.905025	+	0.425359i	$0.860148\pi$
$350$		−	7476.23i		−	0.0610304i
$351$	30480.2	−	64674.2i	0.247402	−	0.524948i
$352$	1444.10			0.0116550
$353$	−75467.4	−	43571.1i	−0.605634	−	0.349663i	0.165621	−	0.986189i	$-0.447037\pi$
$353$	−75467.4	−	43571.1i	−0.605634	−	0.349663i	−0.771255	+	0.636527i	$0.780371\pi$
$354$	29446.9	−	26133.8i	0.234981	−	0.208543i
$355$	53619.3	+	92871.3i	0.425465	+	0.736927i
$356$	114348.	−	66019.0i	0.902256	−	0.520918i
$357$	108357.	−	22220.2i	0.850198	−	0.174346i
$358$	−12397.0	+	21472.3i	−0.0967278	+	0.167538i
$359$			19954.8i			0.154831i	0.996999	+	0.0774156i	$0.0246668\pi$
$359$			19954.8i			0.154831i	−0.996999	+	0.0774156i	$0.975333\pi$
$360$	−24439.4	+	10463.3i	−0.188575	+	0.0807353i
$361$	93695.4			0.718958
$362$	27617.4	+	15944.9i	0.210749	+	0.121676i
$363$	124985.	+	41604.3i	0.948514	+	0.315737i
$364$	46962.4	+	81341.2i	0.354444	+	0.613914i
$365$	−2927.18	+	1690.01i	−0.0219717	+	0.0126854i
$366$	141.952	−	426.443i	0.00105969	−	0.00318346i
$367$	−71047.9	+	123059.i	−0.527496	+	0.913650i	0.471990	+	0.881604i	$0.343536\pi$
$367$	−71047.9	+	123059.i	−0.527496	+	0.913650i	−0.999486	+	0.0320462i	$0.989798\pi$
$368$			118999.i			0.878713i
$369$	−77431.8	−	180859.i	−0.568678	−	1.32827i
$370$	−17285.4			−0.126263
$371$	−246666.	−	142413.i	−1.79210	−	1.03467i
$372$	30423.3	+	148360.i	0.219847	+	1.07209i
$373$	12122.0	+	20996.0i	0.0871281	+	0.150910i	0.906296	−	0.422643i	$-0.138898\pi$
$373$	12122.0	+	20996.0i	0.0871281	+	0.150910i	−0.819168	+	0.573554i	$0.805564\pi$
$374$	−340.688	+	196.696i	−0.00243564	+	0.00140622i
$375$	8348.93	+	9407.37i	0.0593702	+	0.0668968i
$376$	36982.3	−	64055.3i	0.261588	−	0.453084i
$377$		−	42200.9i		−	0.296920i
$378$	39440.7	+	18587.9i	0.276033	+	0.130091i
$379$	−159354.			−1.10939			−0.554695	−	0.832054i	$-0.687165\pi$
$379$	−159354.			−1.10939			−0.554695	+	0.832054i	$0.687165\pi$
$380$	69243.2	+	39977.6i	0.479524	+	0.276853i
$381$	68013.6	−	60361.3i	0.468539	−	0.415823i
$382$	−2567.51	−	4447.06i	−0.0175948	−	0.0304751i
$383$	−27192.2	+	15699.4i	−0.185373	+	0.107025i	−0.589815	−	0.807539i	$-0.700799\pi$
$383$	−27192.2	+	15699.4i	−0.185373	+	0.107025i	0.404442	+	0.914564i	$0.367466\pi$
$384$	−117971.	+	24191.6i	−0.800039	+	0.164060i
$385$	−761.778	+	1319.44i	−0.00513934	+	0.00890159i
$386$		−	21380.3i		−	0.143496i
$387$	−99431.1	−	74445.3i	−0.663897	−	0.497067i
$388$	−145210.			−0.964567
$389$	157295.	+	90814.1i	1.03948	+	0.600142i	0.919685	−	0.392657i	$-0.128444\pi$
$389$	157295.	+	90814.1i	1.03948	+	0.600142i	0.119792	+	0.992799i	$0.461777\pi$
$390$	8835.69	+	2941.18i	0.0580913	+	0.0193372i
$391$	−53899.3	−	93356.3i	−0.352557	−	0.610647i
$392$	−41092.3	+	23724.6i	−0.267417	+	0.154393i
$393$	−62358.4	+	187333.i	−0.403748	+	1.21291i
$394$	−6361.05	+	11017.7i	−0.0409766	+	0.0709736i
$395$		−	112678.i		−	0.722177i
$396$	2612.67	+	312.589i	0.0166607	+	0.00199335i
$397$	−1823.10			−0.0115673			−0.00578363	−	0.999983i	$-0.501841\pi$
$397$	−1823.10			−0.0115673			−0.00578363	+	0.999983i	$0.501841\pi$
$398$	11553.3	+	6670.27i	0.0729354	+	0.0421092i
$399$	−54237.3	−	264489.i	−0.340684	−	1.66135i
$400$	13378.2	+	23171.8i	0.0836139	+	0.144824i
$401$	−90674.4	+	52350.9i	−0.563892	+	0.325563i	−0.754706	−	0.656063i	$-0.772221\pi$
$401$	−90674.4	+	52350.9i	−0.563892	+	0.325563i	0.190814	+	0.981626i	$0.438887\pi$
$402$	−20365.9	−	22947.8i	−0.126023	−	0.142000i
$403$	54612.9	−	94592.3i	0.336268	−	0.582432i
$404$			25623.9i			0.156994i
$405$	−70386.1	+	20655.3i	−0.429118	+	0.125928i
$406$	25735.7			0.156129
$407$	3050.61	+	1761.27i	0.0184161	+	0.0106325i
$408$	38316.8	−	34005.7i	0.230181	−	0.204283i
$409$	124392.	+	215453.i	0.743612	+	1.28797i	0.950841	+	0.309681i	$0.100222\pi$
$409$	124392.	+	215453.i	0.743612	+	1.28797i	−0.207229	+	0.978293i	$0.566444\pi$
$410$	22191.7	−	12812.4i	0.132015	−	0.0762189i
$411$	−107359.	+	22015.5i	−0.635557	+	0.130330i
$412$	136857.	−	237043.i	0.806256	−	1.39648i
$413$			293834.i			1.72267i
$414$	5047.95	−	42191.6i	0.0294520	−	0.246164i
$415$	99828.9			0.579642
$416$	57049.7	+	32937.7i	0.329660	+	0.190330i
$417$	236162.	+	78612.5i	1.35812	+	0.452085i
$418$	480.117	+	831.588i	0.00274786	+	0.00475944i
$419$	277596.	−	160270.i	1.58120	−	0.912904i	0.586510	−	0.809942i	$-0.300501\pi$
$419$	277596.	−	160270.i	1.58120	−	0.912904i	0.994685	−	0.102962i	$-0.0328321\pi$
$420$	30435.5	−	91432.3i	0.172537	−	0.518323i
$421$	165211.	−	286154.i	0.932127	−	1.61449i	0.152449	−	0.988311i	$-0.451284\pi$
$421$	165211.	−	286154.i	0.932127	−	1.61449i	0.779678	−	0.626180i	$-0.215383\pi$
$422$			35580.7i			0.199798i
$423$	122317.	−	163369.i	0.683604	−	0.913040i
$424$	−131919.			−0.733794
$425$	−20990.8	−	12119.1i	−0.116212	−	0.0670952i
$426$	−16363.9	−	79798.9i	−0.0901713	−	0.439721i
$427$	1677.16	+	2904.92i	0.00919852	+	0.0159323i
$428$	−193444.	+	111685.i	−1.05601	+	0.609687i
$429$	−1259.68	−	1419.37i	−0.00684454	−	0.00771226i
$430$	8089.23	−	14011.0i	0.0437492	−	0.0757758i
$431$		−	264920.i		−	1.42614i	−0.701095	−	0.713068i	$-0.747305\pi$
$431$		−	264920.i		−	1.42614i	0.701095	−	0.713068i	$-0.252695\pi$
$432$	−155504.	+	12965.3i	−0.833248	+	0.0694726i
$433$	183467.			0.978549			0.489274	−	0.872130i	$-0.337262\pi$
$433$	183467.			0.978549			0.489274	+	0.872130i	$0.337262\pi$
$434$	57685.8	+	33304.9i	0.306260	+	0.176819i
$435$	−32383.3	+	28739.8i	−0.171136	+	0.151882i
$436$	89745.5	+	155444.i	0.472106	+	0.817712i
$437$	−227874.	+	131563.i	−1.19325	+	0.688924i
$438$	2515.16	−	515.770i	0.0131104	−	0.00268849i
$439$	77277.4	−	133848.i	0.400981	−	0.694519i	−0.592864	−	0.805303i	$-0.702003\pi$
$439$	77277.4	−	133848.i	0.400981	−	0.694519i	0.993845	+	0.110784i	$0.0353360\pi$
$440$			705.645i			0.00364486i
$441$	−120357.	+	51528.7i	−0.618862	+	0.264955i
$442$	−17945.3			−0.0918558
$443$	−63499.5	−	36661.4i	−0.323566	−	0.186811i	0.329415	−	0.944185i	$-0.393148\pi$
$443$	−63499.5	−	36661.4i	−0.323566	−	0.186811i	−0.652981	+	0.757374i	$0.726482\pi$
$444$	−211396.	−	70368.4i	−1.07233	−	0.356953i
$445$	48850.9	+	84612.2i	0.246691	+	0.427281i
$446$	−24430.8	+	14105.2i	−0.122820	+	0.0709101i
$447$	58708.7	−	176368.i	0.293824	−	0.882685i
$448$	88450.4	−	153201.i	0.440701	−	0.763316i
$449$			196252.i			0.973468i	0.873550	+	0.486734i	$0.161812\pi$
$449$			196252.i			0.973468i	−0.873550	+	0.486734i	$0.838188\pi$
$450$	−3760.36	−	8783.17i	−0.0185697	−	0.0433737i
$451$	−5222.00			−0.0256734
$452$	−191052.	−	110304.i	−0.935134	−	0.539900i
$453$	−30571.3	−	149081.i	−0.148976	−	0.726484i
$454$	22205.9	+	38461.7i	0.107735	+	0.186602i
$455$	−60188.6	+	34749.9i	−0.290731	+	0.167854i
$456$	−83004.7	−	93527.6i	−0.399184	−	0.449790i
$457$	61210.4	−	106019.i	0.293084	−	0.507637i	−0.681453	−	0.731862i	$-0.738652\pi$
$457$	61210.4	−	106019.i	0.293084	−	0.507637i	0.974537	+	0.224225i	$0.0719850\pi$
$458$		−	9169.80i		−	0.0437148i
$459$	116123.	−	80605.4i	0.551178	−	0.382595i
$460$	−93914.1			−0.443828
$461$	177170.	+	102289.i	0.833658	+	0.481312i	0.855103	−	0.518458i	$-0.173494\pi$
$461$	177170.	+	102289.i	0.833658	+	0.481312i	−0.0214457	+	0.999770i	$0.506827\pi$
$462$	865.585	−	768.197i	0.00405533	−	0.00359906i
$463$	−14901.3	−	25809.8i	−0.0695123	−	0.120399i	0.829174	−	0.558990i	$-0.188811\pi$
$463$	−14901.3	−	25809.8i	−0.0695123	−	0.120399i	−0.898687	+	0.438591i	$0.855478\pi$
$464$	−79764.9	+	46052.3i	−0.370490	+	0.213902i
$465$	−109779.	+	22511.8i	−0.507707	+	0.104113i
$466$	−26099.2	+	45205.1i	−0.120186	+	0.208169i
$467$			83324.1i			0.382065i	0.981584	+	0.191032i	$0.0611836\pi$
$467$			83324.1i			0.382065i	−0.981584	+	0.191032i	$0.938816\pi$
$468$	96084.7	+	71939.7i	0.438695	+	0.328456i
$469$	228983.			1.04102
$470$	23020.6	+	13290.9i	0.104213	+	0.0601672i
$471$	238659.	+	79443.6i	1.07581	+	0.358111i
$472$	68045.6	+	117858.i	0.305433	+	0.529026i
$473$	−2855.25	+	1648.48i	−0.0127621	+	0.00736819i
$474$	−27032.8	+	81210.0i	−0.120319	+	0.361454i
$475$	−29581.5	+	51236.6i	−0.131109	+	0.227088i
$476$			185699.i			0.819589i
$477$	−361416.	−	43241.1i	−1.58844	−	0.190047i
$478$	−60746.5			−0.265867
$479$	−297654.	−	171850.i	−1.29730	−	0.748996i	−0.317362	−	0.948304i	$-0.602797\pi$
$479$	−297654.	−	171850.i	−1.29730	−	0.748996i	−0.979937	+	0.199309i	$0.936130\pi$
$480$	−13577.1	−	66209.0i	−0.0589285	−	0.287365i
$481$	80343.4	+	139159.i	0.347264	+	0.601479i
$482$	−19709.5	+	11379.3i	−0.0848364	+	0.0489803i
$483$	210503.	+	237190.i	0.902329	+	1.01672i
$484$	−110575.	+	191521.i	−0.472025	+	0.817571i
$485$		−	107448.i		−	0.456789i
$486$	55684.7	+	1999.61i	0.235756	+	0.00846591i
$487$	−250353.			−1.05559			−0.527795	−	0.849372i	$-0.676981\pi$
$487$	−250353.			−1.05559			−0.527795	+	0.849372i	$0.676981\pi$
$488$	1345.43	+	776.786i	0.00564966	+	0.00326183i
$489$	−3138.26	+	2785.17i	−0.0131241	+	0.0116475i
$490$	−8526.31	−	14768.0i	−0.0355115	−	0.0615077i
$491$	−306234.	+	176804.i	−1.27025	+	0.733380i	−0.975035	−	0.222050i	$-0.928725\pi$
$491$	−306234.	+	176804.i	−1.27025	+	0.733380i	−0.295216	+	0.955430i	$0.595392\pi$
$492$	323558.	−	66350.3i	1.33666	−	0.274102i
$493$	41717.8	−	72257.4i	0.171644	−	0.297296i
$494$			43802.8i			0.179493i
$495$	−231.301	+	1933.25i	−0.000943988	+	0.00789001i
$496$	−238388.			−0.968994
$497$	526497.	+	303973.i	2.13149	+	1.23062i
$498$	−71949.5	−	23950.2i	−0.290114	−	0.0965718i
$499$	25335.1	+	43881.8i	0.101747	+	0.176231i	0.912405	−	0.409290i	$-0.134223\pi$
$499$	25335.1	+	43881.8i	0.101747	+	0.176231i	−0.810657	+	0.585521i	$0.800890\pi$
$500$	−18287.2	+	10558.1i	−0.0731488	+	0.0422325i
$501$	−93129.2	+	279772.i	−0.371031	+	1.11463i
$502$	−10695.3	+	18524.7i	−0.0424408	+	0.0735097i
$503$		−	257570.i		−	1.01803i	−0.860758	−	0.509014i	$-0.830010\pi$
$503$		−	257570.i		−	1.01803i	0.860758	−	0.509014i	$-0.169990\pi$
$504$	−90328.4	+	120645.i	−0.355601	+	0.474951i
$505$	−18960.4			−0.0743473
$506$	−976.770	−	563.938i	−0.00381497	−	0.00220257i
$507$	34246.9	+	167005.i	0.133231	+	0.649702i
$508$	76333.4	+	132213.i	0.295793	+	0.512328i
$509$	437252.	−	252448.i	1.68771	−	0.974397i	0.731435	−	0.681911i	$-0.238851\pi$
$509$	437252.	−	252448.i	1.68771	−	0.974397i	0.956270	−	0.292486i	$-0.0944825\pi$
$510$	12221.2	+	13770.5i	0.0469864	+	0.0529432i
$511$	−9580.83	+	16594.5i	−0.0366912	+	0.0635510i
$512$		−	244314.i		−	0.931983i
$513$	−196750.	−	283445.i	−0.747619	−	1.07704i
$514$	−50980.2			−0.192964
$515$	175401.	+	101268.i	0.661328	+	0.381818i
$516$	155967.	−	138419.i	0.585780	−	0.519873i
$517$	−2708.52	−	4691.29i	−0.0101333	−	0.0175514i
$518$	−84864.1	+	48996.3i	−0.316275	+	0.182601i
$519$	−89882.2	+	18431.7i	−0.333687	+	0.0684273i
$520$	−16094.6	+	27876.7i	−0.0595216	+	0.103094i
$521$			434575.i			1.60099i	0.599337	+	0.800497i	$0.295431\pi$
$521$			434575.i			1.60099i	−0.599337	+	0.800497i	$0.704569\pi$
$522$	30234.6	−	12944.4i	0.110959	−	0.0475053i
$523$	−179044.			−0.654572			−0.327286	−	0.944925i	$-0.606134\pi$
$523$	−179044.			−0.654572			−0.327286	+	0.944925i	$0.606134\pi$
$524$	−287060.	−	165734.i	−1.04547	−	0.603600i
$525$	67655.4	+	22520.8i	0.245462	+	0.0817082i
$526$	−50070.2	−	86724.2i	−0.180971	−	0.313450i
$527$	187019.	−	107975.i	0.673387	−	0.388780i
$528$	−1308.15	+	3929.85i	−0.00469234	+	0.0140964i
$529$	14611.4	−	25307.6i	0.0522131	−	0.0904357i
$530$		−	47409.7i		−	0.168778i
$531$	147792.	+	345200.i	0.524156	+	1.22428i
$532$	453274.			1.60154
$533$	−206297.	−	119105.i	−0.726169	−	0.419254i
$534$	−14908.7	−	72702.4i	−0.0522826	−	0.254956i
$535$	−82641.4	−	143139.i	−0.288729	−	0.500093i
$536$	91846.3	−	53027.5i	0.319692	−	0.184574i
$537$	−156968.	−	176867.i	−0.544329	−	0.613337i
$538$	3385.20	−	5863.34i	0.0116955	−	0.0202573i
$539$			3475.10i			0.0119616i
$540$	−10232.2	−	122724.i	−0.0350899	−	0.420865i
$541$	125507.			0.428819			0.214409	−	0.976744i	$-0.431217\pi$
$541$	125507.			0.428819			0.214409	+	0.976744i	$0.431217\pi$
$542$	41389.7	+	23896.3i	0.140894	+	0.0813454i
$543$	−227484.	+	201890.i	−0.771528	+	0.684722i
$544$	65121.3	+	112793.i	0.220052	+	0.381141i
$545$	−115021.	+	66407.3i	−0.387243	+	0.223575i
$546$	51716.5	−	10605.2i	0.173478	−	0.0355742i
$547$	−274750.	+	475881.i	−0.918254	+	1.59046i	−0.116188	+	0.993227i	$0.537068\pi$
$547$	−274750.	+	475881.i	−0.918254	+	1.59046i	−0.802066	+	0.597235i	$0.796266\pi$
$548$		−	183989.i		−	0.612675i
$549$	3431.45	+	2569.17i	0.0113850	+	0.00852409i
$550$	−253.599			−0.000838344
$551$	−176373.	−	101829.i	−0.580938	−	0.335405i
$552$	139362.	+	46390.1i	0.457369	+	0.152247i
$553$	−319390.	−	553201.i	−1.04441	−	1.80897i
$554$	−27083.8	+	15636.9i	−0.0882451	+	0.0509483i
$555$	52069.2	−	156423.i	0.169042	−	0.507824i
$556$	−208934.	+	361884.i	−0.675864	+	1.17063i
$557$		−	51097.6i		−	0.164699i	−0.996604	−	0.0823494i	$-0.973758\pi$
$557$		−	51097.6i		−	0.164699i	0.996604	−	0.0823494i	$-0.0262423\pi$
$558$	84521.6	+	10112.5i	0.271456	+	0.0324779i
$559$	−150397.			−0.481298
$560$	131363.	+	75842.5i	0.418887	+	0.241845i
$561$	−753.724	−	3675.54i	−0.00239489	−	0.0116787i
$562$	−6444.34	−	11161.9i	−0.0204035	−	0.0353400i
$563$	184368.	−	106445.i	0.581660	−	0.335822i	−0.180133	−	0.983642i	$-0.557653\pi$
$563$	184368.	−	106445.i	0.581660	−	0.335822i	0.761793	+	0.647821i	$0.224319\pi$
$564$	227428.	+	256261.i	0.714968	+	0.805608i
$565$	81619.4	−	141369.i	0.255680	−	0.442850i
$566$		−	14450.0i		−	0.0451061i
$567$	−287018.	+	300922.i	−0.892777	+	0.936026i
$568$	281574.			0.872762
$569$	−6314.32	−	3645.57i	−0.0195030	−	0.0112601i	0.490217	−	0.871601i	$-0.336918\pi$
$569$	−6314.32	−	3645.57i	−0.0195030	−	0.0112601i	−0.509720	+	0.860340i	$0.670251\pi$
$570$	33612.5	−	29830.7i	0.103455	−	0.0918151i
$571$	−79579.8	−	137836.i	−0.244079	−	0.422757i	0.717793	−	0.696256i	$-0.245152\pi$
$571$	−79579.8	−	137836.i	−0.244079	−	0.422757i	−0.961872	+	0.273499i	$0.911819\pi$
$572$	2759.15	−	1593.00i	0.00843303	−	0.00486881i
$573$	47977.4	−	9838.47i	0.146126	−	0.0299653i
$574$	72634.8	−	125807.i	0.220456	−	0.381840i
$575$		−	69491.9i		−	0.210183i
$576$	26856.4	−	224470.i	0.0809474	−	0.676572i
$577$	−84239.2			−0.253024			−0.126512	−	0.991965i	$-0.540378\pi$
$577$	−84239.2			−0.253024			−0.126512	+	0.991965i	$0.540378\pi$
$578$	37527.8	+	21666.7i	0.112330	+	0.0648540i
$579$	193479.	+	64404.4i	0.577134	+	0.192114i
$580$	−36344.6	−	62950.6i	−0.108040	−	0.187130i
$581$	490118.	−	282970.i	1.45194	−	0.838278i
$582$	−25778.2	+	77441.0i	−0.0761038	+	0.228626i
$583$	−4830.74	+	8367.08i	−0.0142127	+	0.0246171i
$584$			8874.85i			0.0260217i
$585$	−53231.9	+	71098.0i	−0.155547	+	0.207752i
$586$	4449.72			0.0129580
$587$	−88195.6	−	50919.8i	−0.255959	−	0.147778i	0.366531	−	0.930406i	$-0.380546\pi$
$587$	−88195.6	−	50919.8i	−0.255959	−	0.147778i	−0.622490	+	0.782628i	$0.713879\pi$
$588$	−44154.3	−	215319.i	−0.127708	−	0.622770i
$589$	−263558.	−	456495.i	−0.759706	−	1.31585i
$590$	−42356.7	+	24454.7i	−0.121680	+	0.0702518i
$591$	−80541.8	−	90752.5i	−0.230593	−	0.259827i
$592$	175352.	−	303718.i	0.500341	−	0.866616i
$593$		−	382102.i		−	1.08660i	−0.839538	−	0.543300i	$-0.817174\pi$
$593$		−	382102.i		−	1.08660i	0.839538	−	0.543300i	$-0.182826\pi$
$594$	630.516	−	1337.86i	0.00178699	−	0.00379172i
$595$	−137408.			−0.388132
$596$	270259.	+	156034.i	0.760829	+	0.439265i
$597$	−95164.2	+	84457.1i	−0.267008	+	0.236967i
$598$	−25725.0	−	44557.1i	−0.0719372	−	0.124599i
$599$	149807.	−	86491.3i	0.417522	−	0.241057i	−0.276494	−	0.961016i	$-0.589173\pi$
$599$	149807.	−	86491.3i	0.417522	−	0.241057i	0.694017	+	0.719959i	$0.255839\pi$
$600$	32352.3	−	6634.31i	0.0898674	−	0.0184286i
$601$	103037.	−	178466.i	0.285263	−	0.494090i	−0.687410	−	0.726270i	$-0.741252\pi$
$601$	103037.	−	178466.i	0.285263	−	0.494090i	0.972673	+	0.232180i	$0.0745858\pi$
$602$		−	91717.3i		−	0.253080i
$603$	269012.	−	115173.i	0.739839	−	0.316750i
$604$	255491.			0.700329
$605$	−141716.	−	81819.8i	−0.387176	−	0.223536i
$606$	13665.3	+	4548.84i	0.0372112	+	0.0123867i
$607$	−34806.1	−	60285.9i	−0.0944665	−	0.163621i	0.814919	−	0.579574i	$-0.196781\pi$
$607$	−34806.1	−	60285.9i	−0.0944665	−	0.163621i	−0.909386	+	0.415954i	$0.863448\pi$
$608$	275318.	−	158955.i	0.744779	−	0.429998i
$609$	−77524.1	+	232893.i	−0.209027	+	0.627944i
$610$	−279.166	+	483.530i	−0.000750245	+	0.00129946i
$611$		−	247108.i		−	0.661917i
$612$	93402.3	+	218162.i	0.249376	+	0.582473i
$613$	−587239.			−1.56277			−0.781383	−	0.624052i	$-0.785485\pi$
$613$	−587239.			−1.56277			−0.781383	+	0.624052i	$0.785485\pi$
$614$	−78485.3	−	45313.5i	−0.208186	−	0.120196i
$615$	49096.0	+	239417.i	0.129806	+	0.633002i
$616$	2000.19	+	3464.43i	0.00527120	+	0.00912998i
$617$	−315735.	+	182290.i	−0.829378	+	0.478841i	−0.853640	−	0.520864i	$-0.825610\pi$
$617$	−315735.	+	182290.i	−0.829378	+	0.478841i	0.0242619	+	0.999706i	$0.492276\pi$
$618$	−102121.	−	115067.i	−0.267385	−	0.301283i
$619$	−269224.	+	466310.i	−0.702640	+	1.21701i	0.264897	+	0.964277i	$0.414662\pi$
$619$	−269224.	+	466310.i	−0.702640	+	1.21701i	−0.967537	+	0.252731i	$0.918671\pi$
$620$		−	188136.i		−	0.489429i
$621$	366603.	+	172776.i	0.950633	+	0.448022i
$622$	−15596.3			−0.0403127
$623$	479675.	+	276941.i	1.23587	+	0.713527i
$624$	−141312.	+	125413.i	−0.362920	+	0.322088i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	29740.7	−	17170.8i	0.0758932	−	0.0438170i
$627$	−8971.65	+	1839.77i	−0.0228211	+	0.00467981i
$628$	−211143.	+	365710.i	−0.535373	+	0.927294i
$629$			317695.i			0.802988i
$630$	−43358.2	−	32462.8i	−0.109242	−	0.0817908i
$631$	−239604.			−0.601778			−0.300889	−	0.953659i	$-0.597283\pi$
$631$	−239604.			−0.601778			−0.300889	+	0.953659i	$0.597283\pi$
$632$	−256218.	−	147928.i	−0.641470	−	0.370353i
$633$	−321985.	−	107181.i	−0.803578	−	0.267491i
$634$	62807.5	+	108786.i	0.156255	+	0.270641i
$635$	−97831.5	+	56483.0i	−0.242623	+	0.140078i
$636$	193004.	−	579808.i	0.477146	−	1.43341i
$637$	−79261.4	+	137285.i	−0.195336	+	0.338332i
$638$		−	872.972i		−	0.00214466i
$639$	771426.	+	92296.1i	1.88926	+	0.226038i
$640$	149600.			0.365234
$641$	−370466.	−	213889.i	−0.901639	−	0.520562i	−0.0239076	−	0.999714i	$-0.507611\pi$
$641$	−370466.	−	213889.i	−0.901639	−	0.520562i	−0.877732	+	0.479152i	$0.840944\pi$
$642$	25221.1	+	122991.i	0.0611920	+	0.298403i
$643$	377068.	+	653101.i	0.912007	+	1.57964i	0.811226	+	0.584733i	$0.198801\pi$
$643$	377068.	+	653101.i	0.912007	+	1.57964i	0.100781	+	0.994909i	$0.467866\pi$
$644$	−461079.	+	266204.i	−1.11174	+	0.641864i
$645$	102423.	+	115408.i	0.246196	+	0.277407i
$646$	−43301.4	+	75000.3i	−0.103762	+	0.179721i
$647$		−	101096.i		−	0.241506i	−0.992683	−	0.120753i	$-0.961469\pi$
$647$		−	101096.i		−	0.241506i	0.992683	−	0.120753i	$-0.0385309\pi$
$648$	−45437.4	+	187168.i	−0.108209	+	0.445741i
$649$	9967.07			0.0236635
$650$	−10018.5	−	5784.19i	−0.0237124	−	0.0136904i
$651$	−475158.	+	421697.i	−1.12118	+	0.995036i
$652$	−3522.15	−	6100.54i	−0.00828538	−	0.0143507i
$653$	−17824.9	+	10291.2i	−0.0418023	+	0.0241346i	−0.520756	−	0.853706i	$-0.674350\pi$
$653$	−17824.9	+	10291.2i	−0.0418023	+	0.0241346i	0.478953	+	0.877840i	$0.341016\pi$
$654$	98830.7	−	20266.7i	0.231066	−	0.0473835i
$655$	122635.	−	212410.i	0.285846	−	0.495100i
$656$			519901.i			1.20813i
$657$	−2909.05	+	24314.3i	−0.00673939	+	0.0563290i
$658$	150695.			0.348055
$659$	163706.	+	94515.6i	0.376958	+	0.217637i	0.676494	−	0.736448i	$-0.263498\pi$
$659$	163706.	+	94515.6i	0.376958	+	0.217637i	−0.299536	+	0.954085i	$0.596832\pi$
$660$	−3101.45	−	1032.39i	−0.00711994	−	0.00237005i
$661$	211019.	+	365495.i	0.482968	+	0.836525i	0.999809	−	0.0195568i	$-0.00622551\pi$
$661$	211019.	+	365495.i	0.482968	+	0.836525i	−0.516841	+	0.856081i	$0.672892\pi$
$662$	−14836.8	+	8566.04i	−0.0338551	+	0.0195463i
$663$	54057.1	−	162395.i	0.122978	−	0.369440i
$664$	131059.	−	227002.i	0.297257	−	0.514864i
$665$			335401.i			0.758439i
$666$	−75055.5	+	100246.i	−0.169213	+	0.226006i
$667$	239214.			0.537694
$668$	−428710.	−	247516.i	−0.960751	−	0.554690i
$669$	−54049.7	−	263574.i	−0.120765	−	0.588912i
$670$	19057.3	+	33008.3i	0.0424534	+	0.0735315i
$671$	98.5370	−	56.8904i	0.000218854	−	0.000126355i
$672$	−254331.	−	286574.i	−0.563197	−	0.634596i
$673$	−162001.	+	280593.i	−0.357673	+	0.619508i	−0.987572	−	0.157169i	$-0.949763\pi$
$673$	−162001.	+	280593.i	−0.357673	+	0.619508i	0.629899	+	0.776677i	$0.283096\pi$
$674$		−	67920.2i		−	0.149513i
$675$	90809.9	−	7571.34i	0.199308	−	0.0166175i
$676$	−286209.			−0.626311
$677$	575573.	+	332307.i	1.25581	+	0.725041i	0.972257	−	0.233916i	$-0.0751540\pi$
$677$	575573.	+	332307.i	1.25581	+	0.725041i	0.283551	+	0.958957i	$0.408487\pi$
$678$	−92741.6	+	82307.1i	−0.201751	+	0.179051i
$679$	−304568.	−	527526.i	−0.660608	−	1.14421i
$680$	−55115.2	+	31820.8i	−0.119194	+	0.0688166i
$681$	−414947.	+	85090.9i	−0.894743	+	0.183480i
$682$	1129.73	−	1956.74i	0.00242887	−	0.00420693i
$683$			502484.i			1.07716i	0.842574	+	0.538581i	$0.181039\pi$
$683$			502484.i			1.07716i	−0.842574	+	0.538581i	$0.818961\pi$
$684$	532512.	−	227986.i	1.13820	−	0.487300i
$685$	136143.			0.290144
$686$	40642.9	+	23465.2i	0.0863647	+	0.0498627i
$687$	82981.2	+	27622.4i	0.175819	+	0.0585259i
$688$	164122.	+	284268.i	0.346729	+	0.600553i
$689$	−381679.	+	220363.i	−0.804008	+	0.464194i
$690$	−16672.0	+	50084.8i	−0.0350178	+	0.105198i
$691$	88548.3	−	153370.i	0.185449	−	0.321207i	−0.758279	−	0.651930i	$-0.773959\pi$
$691$	88548.3	−	153370.i	0.185449	−	0.321207i	0.943728	+	0.330724i	$0.107293\pi$
$692$		−	154038.i		−	0.321673i
$693$	4344.31	+	10147.1i	0.00904594	+	0.0211288i
$694$	−112297.			−0.233156
$695$	−267777.	−	154601.i	−0.554374	−	0.320068i
$696$	22837.5	+	111367.i	0.0471444	+	0.229900i
$697$	−235484.	−	407870.i	−0.484726	−	0.839569i
$698$	−163417.	+	94348.7i	−0.335418	+	0.193653i
$699$	−330460.	−	372354.i	−0.676339	−	0.762082i
$700$	−59855.1	+	103672.i	−0.122153	+	0.211576i
$701$		−	434545.i		−	0.884298i	−0.896942	−	0.442149i	$-0.854216\pi$
$701$		−	434545.i		−	0.884298i	0.896942	−	0.442149i	$-0.145784\pi$
$702$	55423.1	−	38471.3i	0.112465	−	0.0780662i
$703$	775463.			1.56910
$704$	−5196.67	−	3000.30i	−0.0104853	−	0.00605368i
$705$	−189620.	+	168286.i	−0.381511	+	0.338587i
$706$	−41115.2	−	71213.6i	−0.0824884	−	0.142874i
$707$	−93087.8	+	53744.3i	−0.186232	+	0.107521i
$708$	−617565.	+	126641.i	−1.23202	+	0.252643i
$709$	359091.	−	621964.i	0.714352	−	1.23729i	−0.248857	−	0.968540i	$-0.580055\pi$
$709$	359091.	−	621964.i	0.714352	−	1.23729i	0.963209	−	0.268754i	$-0.0866118\pi$
$710$			101194.i			0.200742i
$711$	−653471.	−	489261.i	−1.29267	−	0.967836i
$712$	256534.			0.506040
$713$	536192.	+	309571.i	1.05473	+	0.608949i
$714$	99034.2	+	32966.0i	0.194262	+	0.0646651i
$715$	1178.74	+	2041.64i	0.00230572	+	0.00399362i
$716$	343817.	−	198503.i	0.670657	−	0.387204i
$717$	182988.	−	549720.i	0.355946	−	1.06931i
$718$	−9415.01	+	16307.3i	−0.0182630	+	0.0316324i
$719$			462730.i			0.895096i	0.894260	+	0.447548i	$0.147703\pi$
$719$			462730.i			0.895096i	−0.894260	+	0.447548i	$0.852297\pi$
$720$	192474.	+	23028.3i	0.371285	+	0.0444218i
$721$	1.14819e6			2.20874
$722$	76568.8	+	44207.0i	0.146885	+	0.0848041i
$723$	−43604.5	−	212638.i	−0.0834170	−	0.406784i
$724$	−255311.	−	442212.i	−0.487072	−	0.843633i
$725$	46580.4	−	26893.2i	0.0886191	−	0.0511643i
$726$	82509.2	+	92969.3i	0.156541	+	0.176387i
$727$	64484.9	−	111691.i	0.122008	−	0.211325i	−0.798551	−	0.601927i	$-0.794400\pi$
$727$	64484.9	−	111691.i	0.122008	−	0.211325i	0.920560	+	0.390602i	$0.127733\pi$
$728$			182484.i			0.344320i
$729$	−185836.	+	497890.i	−0.349683	+	0.936868i
$730$	−3189.50			−0.00598517
$731$	−257513.	−	148675.i	−0.481908	−	0.278230i
$732$	−5382.57	+	4776.96i	−0.0100454	+	0.00891517i
$733$	−1394.36	−	2415.10i	−0.00259517	−	0.00449497i	0.864725	−	0.502246i	$-0.167493\pi$
$733$	−1394.36	−	2415.10i	−0.00259517	−	0.00449497i	−0.867320	+	0.497751i	$0.834159\pi$
$734$	−116122.	+	67043.2i	−0.215538	+	0.124441i
$735$	159326.	−	32672.1i	0.294925	−	0.0604786i
$736$	−186706.	+	323384.i	−0.344669	+	0.596984i
$737$		−	7767.27i		−	0.0142999i
$738$	22054.3	−	184334.i	0.0404931	−	0.338448i
$739$	510348.			0.934496			0.467248	−	0.884126i	$-0.345245\pi$
$739$	510348.			0.934496			0.467248	+	0.884126i	$0.345245\pi$
$740$	239695.	+	138388.i	0.437719	+	0.252717i
$741$	−396390.	−	131948.i	−0.721915	−	0.240307i
$742$	−134385.	−	232762.i	−0.244087	−	0.422770i
$743$	841830.	−	486031.i	1.52492	−	0.880412i	0.525355	−	0.850883i	$-0.323933\pi$
$743$	841830.	−	486031.i	1.52492	−	0.880412i	0.999564	−	0.0295290i	$-0.00940074\pi$
$744$	−92932.5	+	279181.i	−0.167889	+	0.504360i
$745$	−115458.	+	199978.i	−0.208022	+	0.360305i
$746$			22877.5i			0.0411085i
$747$	433470.	−	578955.i	0.776816	−	1.03754i
$748$	6299.05			0.0112583
$749$	−811471.	−	468503.i	−1.44647	−	0.835119i
$750$	2384.28	+	11627.0i	0.00423872	+	0.0206701i
$751$	94820.1	+	164233.i	0.168120	+	0.291193i	0.937759	−	0.347287i	$-0.112897\pi$
$751$	94820.1	+	164233.i	0.168120	+	0.291193i	−0.769639	+	0.638480i	$0.779564\pi$
$752$	−467064.	+	269660.i	−0.825925	+	0.476848i
$753$	−135420.	−	152588.i	−0.238833	−	0.269111i
$754$	19911.1	−	34487.0i	0.0350229	−	0.0606615i
$755$			189051.i			0.331654i
$756$	−398104.	−	573521.i	−0.696551	−	1.00347i
$757$	−210860.			−0.367961			−0.183981	−	0.982930i	$-0.558898\pi$
$757$	−210860.			−0.367961			−0.183981	+	0.982930i	$0.558898\pi$
$758$	−130226.	−	75185.8i	−0.226651	−	0.130857i
$759$	8045.65	−	7140.42i	0.0139662	−	0.0123948i
$760$	77671.5	+	134531.i	0.134473	+	0.232914i
$761$	97647.9	−	56377.0i	0.168614	−	0.0973493i	−0.413318	−	0.910587i	$-0.635630\pi$
$761$	97647.9	−	56377.0i	0.168614	−	0.0973493i	0.581932	+	0.813237i	$0.302297\pi$
$762$	84060.9	−	17237.9i	0.144772	−	0.0296876i
$763$	−376470.	+	652065.i	−0.646668	+	1.12006i
$764$			82222.5i			0.140865i
$765$	−161429.	+	69113.2i	−0.275841	+	0.118097i
$766$	−29629.0			−0.0504962
$767$	393752.	+	227333.i	0.669318	+	0.386431i
$768$	273512.	+	91045.3i	0.463718	+	0.154360i
$769$	−219032.	−	379374.i	−0.370386	−	0.641528i	0.619239	−	0.785203i	$-0.287441\pi$
$769$	−219032.	−	379374.i	−0.370386	−	0.641528i	−0.989625	+	0.143675i	$0.954108\pi$
$770$	−1245.07	+	718.839i	−0.00209996	+	0.00121241i
$771$	153569.	−	461341.i	0.258342	−	0.776092i
$772$	−171172.	+	296478.i	−0.287209	+	0.497460i
$773$			348563.i			0.583340i	0.956519	+	0.291670i	$0.0942110\pi$
$773$			348563.i			0.583340i	−0.956519	+	0.291670i	$0.905789\pi$
$774$	−46131.6	−	107751.i	−0.0770046	−	0.179861i
$775$	139212.			0.231778
$776$	−244327.	−	141062.i	−0.405741	−	0.234254i
$777$	−187750.	−	915563.i	−0.310983	−	1.51651i
$778$	85695.2	+	148428.i	0.141579	+	0.245221i
$779$	−995573.	+	574794.i	−1.64058	+	0.947191i
$780$	−98976.3	−	111524.i	−0.162683	−	0.183307i
$781$	10311.0	−	17859.1i	0.0169043	−	0.0292792i
$782$		−	101722.i		−	0.166342i
$783$	26063.1	+	312598.i	0.0425110	+	0.509874i
$784$	345980.			0.562884
$785$	−270608.	−	156235.i	−0.439138	−	0.253536i
$786$	−139347.	+	123669.i	−0.225554	+	0.200177i
$787$	265282.	+	459482.i	0.428310	+	0.741855i	0.996723	−	0.0808885i	$-0.0257758\pi$
$787$	265282.	+	459482.i	0.428310	+	0.741855i	−0.568413	+	0.822743i	$0.692442\pi$
$788$	176416.	−	101854.i	0.284109	−	0.164031i
$789$	935630.	−	191865.i	1.50297	−	0.308206i
$790$	53163.2	−	92081.3i	0.0851837	−	0.147543i
$791$		−	925417.i		−	1.47906i
$792$	4092.37	+	3064.01i	0.00652416	+	0.00488471i
$793$	5190.31			0.00825367
$794$	−1489.86	−	860.171i	−0.00236322	−	0.00136441i
$795$	429030.	+	142813.i	0.678818	+	0.225962i
$796$	−106805.	−	184992.i	−0.168564	−	0.291962i
$797$	411680.	−	237683.i	0.648101	−	0.374181i	−0.139627	−	0.990204i	$-0.544590\pi$
$797$	411680.	−	237683.i	0.648101	−	0.374181i	0.787728	+	0.616023i	$0.211257\pi$
$798$	80466.9	−	241733.i	0.126360	−	0.379603i
$799$	244279.	−	423104.i	0.382642	−	0.662756i
$800$			83960.3i			0.131188i
$801$	702823.	+	84088.2i	1.09542	+	0.131060i
$802$	−98800.1			−0.153606
$803$	562.897	+	324.989i	0.000872967	+	0.000504008i
$804$	98690.3	+	481264.i	0.152673	+	0.744512i
$805$	−196978.	−	341176.i	−0.303967	−	0.526486i
$806$	89260.4	−	51534.5i	0.137401	−	0.0793283i
$807$	42862.5	+	48296.4i	0.0658158	+	0.0741596i
$808$	−24892.0	+	43114.2i	−0.0381274	+	0.0660386i
$809$		−	156996.i		−	0.239879i	−0.992781	−	0.119939i	$-0.961730\pi$
$809$		−	156996.i		−	0.239879i	0.992781	−	0.119939i	$-0.0382700\pi$
$810$	−67265.7	−	16329.6i	−0.102524	−	0.0248888i
$811$	93005.2			0.141405			0.0707026	−	0.997497i	$-0.477476\pi$
$811$	93005.2			0.141405			0.0707026	+	0.997497i	$0.477476\pi$
$812$	−356874.	−	206041.i	−0.541256	−	0.312494i
$813$	−340927.	+	302569.i	−0.515799	+	0.457765i
$814$	1661.99	+	2878.65i	0.00250830	+	0.00434451i
$815$	4514.10	−	2606.22i	0.00679605	−	0.00392370i
$816$	−365936.	+	75040.6i	−0.549573	+	0.112698i
$817$	−362901.	+	628564.i	−0.543682	+	0.941684i
$818$			234761.i			0.350848i
$819$	−59815.8	+	499950.i	−0.0891760	+	0.745348i
$820$	−410307.			−0.610213
$821$	593742.	+	342797.i	0.880869	+	0.508570i	0.870945	−	0.491381i	$-0.163508\pi$
$821$	593742.	+	342797.i	0.880869	+	0.508570i	0.00992415	+	0.999951i	$0.496841\pi$
$822$	−98122.0	−	32662.4i	−0.145219	−	0.0483397i
$823$	334766.	+	579831.i	0.494244	+	0.856055i	0.999978	−	0.00663403i	$-0.00211169\pi$
$823$	334766.	+	579831.i	0.494244	+	0.856055i	−0.505734	+	0.862689i	$0.668778\pi$
$824$	460546.	−	265897.i	0.678295	−	0.391614i
$825$	763.922	−	2294.92i	0.00112238	−	0.00337178i
$826$	−138636.	+	240124.i	−0.203196	+	0.351946i
$827$			101296.i			0.148109i	0.997254	+	0.0740547i	$0.0235939\pi$
$827$			101296.i			0.148109i	−0.997254	+	0.0740547i	$0.976406\pi$
$828$	−407788.	+	544652.i	−0.594803	+	0.794435i
$829$	−361713.			−0.526326			−0.263163	−	0.964751i	$-0.584766\pi$
$829$	−361713.			−0.526326			−0.263163	+	0.964751i	$0.584766\pi$
$830$	81581.2	+	47100.9i	0.118422	+	0.0683712i
$831$	−59919.1	−	292196.i	−0.0867687	−	0.423128i
$832$	−136864.	−	237056.i	−0.197716	−	0.342455i
$833$	−271427.	+	156708.i	−0.391167	+	0.225841i
$834$	155903.	+	175668.i	0.224142	+	0.252558i
$835$	183150.	−	317225.i	0.262684	−	0.454982i
$836$		−	15375.4i		−	0.0219995i
$837$	−346118.	+	734409.i	−0.494053	+	1.04830i
$838$	302473.			0.430723
$839$	441140.	+	254693.i	0.626690	+	0.361820i	0.779469	−	0.626441i	$-0.215489\pi$
$839$	441140.	+	254693.i	0.626690	+	0.361820i	−0.152779	+	0.988260i	$0.548822\pi$
$840$	140031.	−	124276.i	0.198457	−	0.176128i
$841$	−261065.	−	452178.i	−0.369111	−	0.639319i
$842$	270024.	−	155899.i	0.380872	−	0.219897i
$843$	120421.	−	24694.1i	0.169452	−	0.0347487i
$844$	284861.	−	493394.i	0.399898	−	0.692643i
$845$		−	211781.i		−	0.296602i
$846$	177039.	−	75796.1i	0.247359	−	0.105903i
$847$	−927690.			−1.29311
$848$	833025.	+	480947.i	1.15842	+	0.668815i
$849$	130764.	+	43528.1i	0.181415	+	0.0603885i
$850$	−11436.0	−	19807.6i	−0.0158283	−	0.0274154i
$851$	−788816.	+	455423.i	−1.08922	+	0.628863i
$852$	−411957.	+	1.23757e6i	−0.567509	+	1.70487i
$853$	−83946.1	+	145399.i	−0.115373	+	0.199831i	−0.917929	−	0.396746i	$-0.870140\pi$
$853$	−83946.1	+	145399.i	−0.115373	+	0.199831i	0.802556	+	0.596577i	$0.203473\pi$
$854$			3165.24i			0.00434002i
$855$	168699.	+	394033.i	0.230770	+	0.539015i
$856$	−433980.			−0.592273
$857$	−561598.	−	324239.i	−0.764652	−	0.441472i	0.0663117	−	0.997799i	$-0.478877\pi$
$857$	−561598.	−	324239.i	−0.764652	−	0.441472i	−0.830963	+	0.556327i	$0.812210\pi$
$858$	−359.737	−	1754.26i	−0.000488664	−	0.00238298i
$859$	485803.	+	841436.i	0.658376	+	1.14034i	0.981036	+	0.193826i	$0.0620896\pi$
$859$	485803.	+	841436.i	0.658376	+	1.14034i	−0.322660	+	0.946515i	$0.604577\pi$
$860$	−224345.	+	129526.i	−0.303333	+	0.175129i
$861$	919682.	+	1.03627e6i	1.24060	+	1.39788i
$862$	124994.	−	216496.i	0.168219	−	0.291363i
$863$		−	941752.i		−	1.26449i	−0.774769	−	0.632244i	$-0.782134\pi$
$863$		−	941752.i		−	1.26449i	0.774769	−	0.632244i	$-0.217866\pi$
$864$	−442931.	−	208748.i	−0.593346	−	0.279637i
$865$	113981.			0.152335
$866$	149931.	+	86562.8i	0.199920	+	0.115424i
$867$	−309117.	+	274337.i	−0.411229	+	0.364961i
$868$	−533282.	−	923672.i	−0.707811	−	1.22597i
$869$	−18765.0	+	10834.0i	−0.0248490	+	0.0143465i
$870$	−40023.9	+	8207.48i	−0.0528787	+	0.0108435i
$871$	177159.	−	306848.i	0.233521	−	0.404471i
$872$			348729.i			0.458622i
$873$	−623143.	−	466555.i	−0.817635	−	0.612173i
$874$	−248294.			−0.325046
$875$	−76712.3	−	44289.9i	−0.100196	−	0.0578480i
$876$	−39006.7	−	12984.4i	−0.0508313	−	0.0169205i
$877$	356636.	+	617711.i	0.463688	+	0.803131i	0.999141	−	0.0414340i	$-0.0131926\pi$
$877$	356636.	+	617711.i	0.463688	+	0.803131i	−0.535454	+	0.844565i	$0.679859\pi$
$878$	126304.	−	72921.6i	0.163843	−	0.0945947i
$879$	−13404.0	+	40267.3i	−0.0173483	+	0.0521165i
$880$	2572.63	−	4455.93i	0.00332210	−	0.00575404i
$881$			495061.i			0.637833i	0.947783	+	0.318916i	$0.103319\pi$
$881$			495061.i			0.637833i	−0.947783	+	0.318916i	$0.896681\pi$
$882$	−122669.	−	14676.5i	−0.157688	−	0.0188663i
$883$	−506755.			−0.649945			−0.324972	−	0.945724i	$-0.605355\pi$
$883$	−506755.			−0.649945			−0.324972	+	0.945724i	$0.605355\pi$
$884$	248846.	+	143671.i	0.318439	+	0.183851i
$885$	−93708.1	−	456968.i	−0.119644	−	0.583445i
$886$	−34594.9	−	59920.2i	−0.0440702	−	0.0763318i
$887$	−322197.	+	186020.i	−0.409519	+	0.236436i	−0.690583	−	0.723253i	$-0.742646\pi$
$887$	−322197.	+	186020.i	−0.409519	+	0.236436i	0.281064	+	0.959689i	$0.409313\pi$
$888$	−287332.	−	323758.i	−0.364383	−	0.410577i
$889$	−320208.	+	554617.i	−0.405162	+	0.701761i
$890$			92194.6i			0.116393i
$891$	10207.5	+	9735.85i	0.0128577	+	0.0122636i
$892$	451706.			0.567710
$893$	−1.03276e6	−	596262.i	−1.29507	−	0.747712i
$894$	131191.	−	116430.i	0.164145	−	0.145677i
$895$	146882.	+	254408.i	0.183368	+	0.317603i
$896$	734473.	−	424048.i	0.914870	−	0.528201i
$897$	480708.	−	98576.1i	0.597442	−	0.122514i
$898$	−92595.0	+	160379.i	−0.114825	+	0.198882i
$899$			479213.i			0.592938i
$900$	−18173.9	+	151901.i	−0.0224370	+	0.187532i
$901$	−871361.			−1.07337
$902$	−4267.47	−	2463.83i	−0.00524515	−	0.00302829i
$903$	829988.	+	276282.i	1.01788	+	0.338827i
$904$	−214306.	−	371190.i	−0.262240	−	0.454212i
$905$	327216.	−	188918.i	0.399518	−	0.230662i
$906$	45355.8	−	136255.i	0.0552556	−	0.165995i
$907$	538599.	−	932882.i	0.654714	−	1.13400i	−0.327252	−	0.944937i	$-0.606123\pi$
$907$	538599.	−	932882.i	0.654714	−	1.13400i	0.981966	−	0.189060i	$-0.0605441\pi$
$908$		−	711125.i		−	0.862531i
$909$	−82328.6	+	109960.i	−0.0996376	+	0.133079i
$910$	−65582.3			−0.0791961
$911$	781546.	+	451226.i	0.941711	+	0.543697i	0.890496	−	0.454991i	$-0.150357\pi$
$911$	781546.	+	451226.i	0.941711	+	0.543697i	0.0512146	+	0.998688i	$0.483691\pi$
$912$	183167.	+	893216.i	0.220220	+	1.07391i
$913$	−9598.55	−	16625.2i	−0.0115150	−	0.0199446i
$914$	100043.	−	57760.1i	0.119756	−	0.0691410i
$915$	−3534.72	−	3982.84i	−0.00422195	−	0.00475719i
$916$	−73413.9	+	127157.i	−0.0874958	+	0.151547i
$917$		−	1.39046e6i		−	1.65356i
$918$	132928.	−	11082.9i	0.157736	−	0.0131513i
$919$	−1.54236e6			−1.82623			−0.913114	−	0.407704i	$-0.866330\pi$
$919$	−1.54236e6			−1.82623			−0.913114	+	0.407704i	$0.866330\pi$
$920$	−158018.	−	91231.8i	−0.186694	−	0.107788i
$921$	646483.	−	573746.i	0.762146	−	0.676395i
$922$	96523.3	+	167183.i	0.113546	+	0.196667i
$923$	814677.	−	470354.i	0.956273	−	0.552105i
$924$	−18153.2	+	3722.58i	−0.0212623	+	0.00436014i
$925$	−102400.	+	177362.i	−0.119679	+	0.207290i
$926$		−	28122.7i		−	0.0327971i
$927$	1.34891e6	−	577514.i	1.56973	−	0.672052i
$928$	−289019.			−0.335607
$929$	213159.	+	123067.i	0.246985	+	0.142597i	0.618383	−	0.785877i	$-0.287788\pi$
$929$	213159.	+	123067.i	0.246985	+	0.142597i	−0.371398	+	0.928474i	$0.621121\pi$
$930$	−100334.	−	33398.7i	−0.116006	−	0.0386156i
$931$	382510.	+	662527.i	0.441310	+	0.764371i
$932$	723828.	−	417903.i	0.833305	−	0.481109i
$933$	46981.2	−	141138.i	0.0539710	−	0.162136i
$934$	−39313.7	+	68093.3i	−0.0450661	+	0.0780568i
$935$			4660.99i			0.00533157i
$936$	91785.2	+	214385.i	0.104766	+	0.244705i
$937$	1.11154e6			1.26603			0.633015	−	0.774139i	$-0.281817\pi$
$937$	1.11154e6			1.26603			0.633015	+	0.774139i	$0.281817\pi$
$938$	187127.	+	108038.i	0.212682	+	0.122792i
$939$	65797.1	+	320860.i	0.0746235	+	0.363902i
$940$	−212816.	−	368608.i	−0.240851	−	0.417166i
$941$	−1.41981e6	+	819726.i	−1.60343	+	0.925741i	−0.612636	+	0.790365i	$0.709891\pi$
$941$	−1.41981e6	+	819726.i	−1.60343	+	0.925741i	−0.990794	+	0.135376i	$0.956776\pi$
$942$	157552.	+	177525.i	0.177550	+	0.200059i
$943$	675144.	−	1.16938e6i	0.759230	−	1.31502i
$944$		−	992320.i		−	1.11355i
$945$	424378.	−	294577.i	0.475214	−	0.329865i
$946$	−3111.12			−0.00347643
$947$	−436626.	−	252086.i	−0.486866	−	0.281092i	0.236407	−	0.971654i	$-0.424030\pi$
$947$	−436626.	−	252086.i	−0.486866	−	0.281092i	−0.723273	+	0.690562i	$0.757363\pi$
$948$	1.02503e6	−	909704.i	1.14057	−	1.01224i
$949$	14824.9	+	25677.5i	0.0164612	+	0.0285116i
$950$	−48348.6	+	27914.1i	−0.0535718	+	0.0309297i
$951$	−1.17364e6	+	240673.i	−1.29770	+	0.266113i
$952$	−180395.	+	312454.i	−0.199045	+	0.344756i
$953$			185621.i			0.204381i	0.994765	+	0.102191i	$0.0325852\pi$
$953$			185621.i			0.204381i	−0.994765	+	0.102191i	$0.967415\pi$
$954$	−274951.	−	205859.i	−0.302106	−	0.226190i
$955$	−60840.6			−0.0667094
$956$	842365.	+	486339.i	0.921689	+	0.532137i
$957$	7899.88	+	2629.67i	0.00862575	+	0.00287130i
$958$	−162164.	−	280876.i	−0.176694	−	0.306043i
$959$	668405.	−	385904.i	0.726779	−	0.419606i
$960$	−88699.3	+	266464.i	−0.0962449	+	0.289132i
$961$	−158397.	+	274352.i	−0.171514	+	0.297071i
$962$			151629.i			0.163845i
$963$	−1.18897e6	−	142253.i	−1.28209	−	0.153394i
$964$	364413.			0.392139
$965$	−219380.	−	126659.i	−0.235582	−	0.136013i
$966$	60115.3	+	293153.i	0.0644215	+	0.314152i
$967$	31684.9	+	54879.9i	0.0338844	+	0.0586894i	0.882470	−	0.470368i	$-0.155879\pi$
$967$	31684.9	+	54879.9i	0.0338844	+	0.0586894i	−0.848586	+	0.529058i	$0.822546\pi$
$968$	−372101.	+	214833.i	−0.397110	+	0.229271i
$969$	−548270.	−	617777.i	−0.583912	−	0.657937i
$970$	50695.9	−	87807.8i	0.0538802	−	0.0933232i
$971$		−	602692.i		−	0.639230i	−0.947547	−	0.319615i	$-0.896446\pi$
$971$		−	602692.i		−	0.639230i	0.947547	−	0.319615i	$-0.103554\pi$
$972$	−756165.	−	473543.i	−0.800357	−	0.501218i
$973$	−1.75290e6			−1.85153
$974$	−204591.	−	118121.i	−0.215660	−	0.124511i
$975$	82522.4	−	73237.7i	0.0868086	−	0.0770416i
$976$	−5664.00	−	9810.33i	−0.00594598	−	0.0102987i
$977$	1.17363e6	−	677595.i	1.22954	−	0.709874i	0.262604	−	0.964904i	$-0.415419\pi$
$977$	1.17363e6	−	677595.i	1.22954	−	0.709874i	0.966933	+	0.255030i	$0.0820854\pi$
$978$	−3878.71	+	795.386i	−0.00405517	+	0.000831573i
$979$	9394.03	−	16270.9i	0.00980136	−	0.0169765i
$980$			273048.i			0.284307i
$981$	−114308.	+	955409.i	−0.118779	+	0.992777i
$982$	−333676.			−0.346021
$983$	−1.33442e6	−	770427.i	−1.38097	−	0.797305i	−0.388698	−	0.921365i	$-0.627075\pi$
$983$	−1.33442e6	−	770427.i	−1.38097	−	0.797305i	−0.992275	+	0.124060i	$0.960408\pi$
$984$	608868.	+	202677.i	0.628829	+	0.209322i
$985$	75366.9	+	130539.i	0.0776798	+	0.134545i
$986$	68184.5	−	39366.3i	0.0701345	−	0.0404922i
$987$	−453943.	+	1.36370e6i	−0.465980	+	1.39986i
$988$	350688.	−	607409.i	0.359258	−	0.622253i
$989$		−	852517.i		−	0.871586i
$990$	−1101.16	+	1470.74i	−0.00112352	+	0.00150060i
$991$	−1.26335e6			−1.28640			−0.643200	−	0.765698i	$-0.722394\pi$
$991$	−1.26335e6			−1.28640			−0.643200	+	0.765698i	$0.722394\pi$
$992$	−647829.	−	374024.i	−0.658320	−	0.380081i
$993$	−32824.3	−	160068.i	−0.0332887	−	0.162333i
$994$	286839.	+	496820.i	0.290312	+	0.502836i
$995$	136885.	−	79030.6i	0.138264	−	0.0798269i
$996$	805969.	+	908146.i	0.812456	+	0.915455i
$997$	191849.	−	332292.i	0.193005	−	0.334295i	−0.753240	−	0.657746i	$-0.771510\pi$
$997$	191849.	−	332292.i	0.193005	−	0.334295i	0.946245	+	0.323452i	$0.104843\pi$
$998$			47814.2i			0.0480060i
$999$	−681077.	−	981182.i	−0.682441	−	0.983147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.9	✓	32
3.2	odd	2		135.5.i.a.116.8		32
9.2	odd	6		405.5.c.b.161.17		32
9.4	even	3		135.5.i.a.71.8		32
9.5	odd	6	inner	45.5.i.a.41.9	yes	32
9.7	even	3		405.5.c.b.161.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.9	✓	32	1.1	even	1	trivial
45.5.i.a.41.9	yes	32	9.5	odd	6	inner
135.5.i.a.71.8		32	9.4	even	3
135.5.i.a.116.8		32	3.2	odd	2
405.5.c.b.161.16		32	9.7	even	3
405.5.c.b.161.17		32	9.2	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.817210 + 0.471817i) q^{2} +(-6.73136 + 5.97401i) q^{3} +(-7.55478 - 13.0853i) q^{4} +(9.68246 - 5.59017i) q^{5} +(-8.31957 + 1.70605i) q^{6} +(31.6912 - 54.8908i) q^{7} -29.3560i q^{8} +(9.62249 - 80.4264i) q^{9} +10.5501 q^{10} +(-1.86194 - 1.07499i) q^{11} +(129.025 + 42.9493i) q^{12} +(-49.0376 - 84.9356i) q^{13} +(51.7968 - 29.9049i) q^{14} +(-31.7804 + 95.4725i) q^{15} +(-107.026 + 185.374i) q^{16} -193.905i q^{17} +(45.8101 - 61.1852i) q^{18} -473.304 q^{19} +(-146.298 - 84.4650i) q^{20} +(114.593 + 558.814i) q^{21} +(-1.01440 - 1.75699i) q^{22} +(481.454 - 277.968i) q^{23} +(175.373 + 197.606i) q^{24} +(62.5000 - 108.253i) q^{25} -92.5470i q^{26} +(415.695 + 598.864i) q^{27} -957.681 q^{28} +(372.643 + 215.146i) q^{29} +(-71.0168 + 63.0266i) q^{30} +(556.847 + 964.488i) q^{31} +(-581.694 + 335.841i) q^{32} +(18.9554 - 3.88708i) q^{33} +(91.4876 - 158.461i) q^{34} -708.638i q^{35} +(-1125.10 + 481.691i) q^{36} -1638.40 q^{37} +(-386.789 - 223.313i) q^{38} +(837.495 + 278.781i) q^{39} +(-164.105 - 284.238i) q^{40} +(2103.45 - 1214.43i) q^{41} +(-170.011 + 510.735i) q^{42} +(766.741 - 1328.03i) q^{43} +32.4852i q^{44} +(-356.428 - 832.517i) q^{45} +524.599 q^{46} +(2182.02 + 1259.79i) q^{47} +(-386.997 - 1887.19i) q^{48} +(-808.170 - 1399.79i) q^{49} +(102.151 - 58.9771i) q^{50} +(1158.39 + 1305.25i) q^{51} +(-740.936 + 1283.34i) q^{52} -4493.75i q^{53} +(57.1565 + 685.530i) q^{54} -24.0375 q^{55} +(-1611.38 - 930.328i) q^{56} +(3185.98 - 2827.52i) q^{57} +(203.019 + 351.639i) q^{58} +(-4014.80 + 2317.95i) q^{59} +(1489.38 - 305.419i) q^{60} +(-26.4609 + 45.8316i) q^{61} +1050.92i q^{62} +(-4109.73 - 3077.00i) q^{63} +2791.00 q^{64} +(-949.609 - 548.257i) q^{65} +(17.3245 + 5.76690i) q^{66} +(1806.36 + 3128.71i) q^{67} +(-2537.30 + 1464.91i) q^{68} +(-1580.26 + 4747.31i) q^{69} +(334.347 - 579.106i) q^{70} +9591.70i q^{71} +(-2361.00 - 282.478i) q^{72} -302.318 q^{73} +(-1338.92 - 773.026i) q^{74} +(225.995 + 1102.07i) q^{75} +(3575.70 + 6193.30i) q^{76} +(-118.014 + 68.1355i) q^{77} +(552.876 + 622.967i) q^{78} +(5039.10 - 8727.97i) q^{79} +2393.17i q^{80} +(-6375.82 - 1547.81i) q^{81} +2291.95 q^{82} +(7732.71 + 4464.48i) q^{83} +(6446.50 - 5721.19i) q^{84} +(-1083.96 - 1877.48i) q^{85} +(1253.18 - 723.523i) q^{86} +(-3793.68 + 777.950i) q^{87} +(-31.5574 + 54.6590i) q^{88} +8738.71i q^{89} +(101.519 - 848.510i) q^{90} -6216.25 q^{91} +(-7274.55 - 4199.97i) q^{92} +(-9510.20 - 3165.71i) q^{93} +(1188.78 + 2059.02i) q^{94} +(-4582.74 + 2645.85i) q^{95} +(1909.28 - 5735.71i) q^{96} +(4805.23 - 8322.91i) q^{97} -1525.23i q^{98} +(-104.374 + 139.405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more