LMFDB - Embedded newform 45.5.i.a.11.8

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			11.8
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06605 - 0.615486i) q^{2} +(1.63702 - 8.84987i) q^{3} +(-7.24235 - 12.5441i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-7.19213 + 8.42687i) q^{6} +(-21.1314 + 36.6007i) q^{7} +37.5258i q^{8} +(-75.6403 - 28.9748i) q^{9} +13.7627 q^{10} +(23.9316 + 13.8169i) q^{11} +(-122.870 + 43.5589i) q^{12} +(-118.307 - 204.914i) q^{13} +(45.0545 - 26.0122i) q^{14} +(33.6219 + 94.8397i) q^{15} +(-92.7810 + 160.701i) q^{16} -304.483i q^{17} +(62.8030 + 77.4443i) q^{18} -315.542 q^{19} +(140.248 + 80.9720i) q^{20} +(289.319 + 246.927i) q^{21} +(-17.0082 - 29.4591i) q^{22} +(728.193 - 420.423i) q^{23} +(332.099 + 61.4306i) q^{24} +(62.5000 - 108.253i) q^{25} +291.266i q^{26} +(-380.248 + 621.974i) q^{27} +612.165 q^{28} +(672.277 + 388.139i) q^{29} +(22.5298 - 121.798i) q^{30} +(-833.118 - 1443.00i) q^{31} +(717.792 - 414.418i) q^{32} +(161.454 - 189.173i) q^{33} +(-187.405 + 324.595i) q^{34} -472.513i q^{35} +(184.350 + 1158.69i) q^{36} -209.474 q^{37} +(336.385 + 194.212i) q^{38} +(-2007.13 + 711.554i) q^{39} +(-209.776 - 363.342i) q^{40} +(-1821.60 + 1051.70i) q^{41} +(-156.450 - 441.309i) q^{42} +(805.510 - 1395.19i) q^{43} -400.267i q^{44} +(894.359 - 142.295i) q^{45} -1035.06 q^{46} +(-320.976 - 185.316i) q^{47} +(1270.30 + 1084.17i) q^{48} +(307.425 + 532.476i) q^{49} +(-133.257 + 76.9358i) q^{50} +(-2694.63 - 498.445i) q^{51} +(-1713.64 + 2968.12i) q^{52} -2527.06i q^{53} +(788.182 - 429.020i) q^{54} -308.955 q^{55} +(-1373.47 - 792.975i) q^{56} +(-516.550 + 2792.51i) q^{57} +(-477.789 - 827.554i) q^{58} +(1192.13 - 688.279i) q^{59} +(946.179 - 1108.62i) q^{60} +(-400.200 + 693.167i) q^{61} +2051.09i q^{62} +(2658.89 - 2156.21i) q^{63} +1948.72 q^{64} +(2291.01 + 1322.71i) q^{65} +(-288.552 + 102.295i) q^{66} +(-1192.70 - 2065.81i) q^{67} +(-3819.47 + 2205.17i) q^{68} +(-2528.62 - 7132.66i) q^{69} +(-290.825 + 503.724i) q^{70} +1978.96i q^{71} +(1087.31 - 2838.47i) q^{72} +10301.8 q^{73} +(223.311 + 128.929i) q^{74} +(-855.712 - 730.330i) q^{75} +(2285.27 + 3958.20i) q^{76} +(-1011.42 + 583.942i) q^{77} +(2577.66 + 476.808i) q^{78} +(-2915.77 + 5050.26i) q^{79} -2074.65i q^{80} +(4881.92 + 4383.33i) q^{81} +2589.23 q^{82} +(-147.535 - 85.1792i) q^{83} +(1002.13 - 5417.58i) q^{84} +(1702.11 + 2948.14i) q^{85} +(-1717.43 + 991.561i) q^{86} +(4535.51 - 5314.17i) q^{87} +(-518.491 + 898.052i) q^{88} +11188.1i q^{89} +(-1041.01 - 398.772i) q^{90} +9999.99 q^{91} +(-10547.7 - 6089.70i) q^{92} +(-14134.2 + 5010.76i) q^{93} +(228.119 + 395.113i) q^{94} +(3055.23 - 1763.94i) q^{95} +(-2492.50 - 7030.78i) q^{96} +(516.445 - 894.509i) q^{97} -756.864i q^{98} +(-1409.85 - 1738.53i) 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 $

$2$	−1.06605	−	0.615486i	−0.266513	−	0.153872i	0.360789	−	0.932648i	$-0.382508\pi$
$2$	−1.06605	−	0.615486i	−0.266513	−	0.153872i	−0.627302	+	0.778776i	$0.715841\pi$
$3$	1.63702	−	8.84987i	0.181891	−	0.983319i
$3$	1.63702	−	8.84987i	0.181891	−	0.983319i
$4$	−7.24235	−	12.5441i	−0.452647	−	0.784008i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$	−7.19213	+	8.42687i	−0.199781	+	0.234080i
$7$	−21.1314	+	36.6007i	−0.431254	+	0.746953i	−0.996982	−	0.0776387i	$-0.975262\pi$
$7$	−21.1314	+	36.6007i	−0.431254	+	0.746953i	0.565728	+	0.824592i	$0.308595\pi$
$8$			37.5258i			0.586341i
$9$	−75.6403	−	28.9748i	−0.933831	−	0.357714i
$10$	13.7627			0.137627
$11$	23.9316	+	13.8169i	0.197782	+	0.114189i	0.595620	−	0.803266i	$-0.296906\pi$
$11$	23.9316	+	13.8169i	0.197782	+	0.114189i	−0.397839	+	0.917455i	$0.630240\pi$
$12$	−122.870	+	43.5589i	−0.853262	+	0.302492i
$13$	−118.307	−	204.914i	−0.700042	−	1.21251i	−0.968451	−	0.249203i	$-0.919831\pi$
$13$	−118.307	−	204.914i	−0.700042	−	1.21251i	0.268409	−	0.963305i	$-0.413502\pi$
$14$	45.0545	−	26.0122i	0.229870	−	0.132715i
$15$	33.6219	+	94.8397i	0.149431	+	0.421510i
$16$	−92.7810	+	160.701i	−0.362426	+	0.627740i
$17$		−	304.483i		−	1.05357i	−0.849997	−	0.526787i	$-0.823397\pi$
$17$		−	304.483i		−	1.05357i	0.849997	−	0.526787i	$-0.176603\pi$
$18$	62.8030	+	77.4443i	0.193836	+	0.239026i
$19$	−315.542			−0.874079			−0.437039	−	0.899442i	$-0.643973\pi$
$19$	−315.542			−0.874079			−0.437039	+	0.899442i	$0.643973\pi$
$20$	140.248	+	80.9720i	0.350619	+	0.202430i
$21$	289.319	+	246.927i	0.656052	+	0.559924i
$22$	−17.0082	−	29.4591i	−0.0351410	−	0.0608659i
$23$	728.193	−	420.423i	1.37655	−	0.794750i	0.384805	−	0.922998i	$-0.374269\pi$
$23$	728.193	−	420.423i	1.37655	−	0.794750i	0.991742	+	0.128248i	$0.0409354\pi$
$24$	332.099	+	61.4306i	0.576560	+	0.106650i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$			291.266i			0.430866i
$27$	−380.248	+	621.974i	−0.521603	+	0.853188i
$28$	612.165			0.780823
$29$	672.277	+	388.139i	0.799378	+	0.461521i	0.843254	−	0.537516i	$-0.180637\pi$
$29$	672.277	+	388.139i	0.799378	+	0.461521i	−0.0438757	+	0.999037i	$0.513971\pi$
$30$	22.5298	−	121.798i	0.0250331	−	0.135331i
$31$	−833.118	−	1443.00i	−0.866928	−	1.50156i	−0.865120	−	0.501565i	$-0.832758\pi$
$31$	−833.118	−	1443.00i	−0.866928	−	1.50156i	−0.00180801	−	0.999998i	$-0.500576\pi$
$32$	717.792	−	414.418i	0.700969	−	0.404705i
$33$	161.454	−	189.173i	0.148259	−	0.173712i
$34$	−187.405	+	324.595i	−0.162115	+	0.280792i
$35$		−	472.513i		−	0.385725i
$36$	184.350	+	1158.69i	0.142245	+	0.894049i
$37$	−209.474			−0.153013			−0.0765063	−	0.997069i	$-0.524377\pi$
$37$	−209.474			−0.153013			−0.0765063	+	0.997069i	$0.524377\pi$
$38$	336.385	+	194.212i	0.232954	+	0.134496i
$39$	−2007.13	+	711.554i	−1.31961	+	0.467820i
$40$	−209.776	−	363.342i	−0.131110	−	0.227089i
$41$	−1821.60	+	1051.70i	−1.08364	+	0.625641i	−0.931877	−	0.362775i	$-0.881829\pi$
$41$	−1821.60	+	1051.70i	−1.08364	+	0.625641i	−0.151766	+	0.988417i	$0.548496\pi$
$42$	−156.450	−	441.309i	−0.0886902	−	0.250175i
$43$	805.510	−	1395.19i	0.435647	−	0.754562i	−0.561702	−	0.827340i	$-0.689853\pi$
$43$	805.510	−	1395.19i	0.435647	−	0.754562i	0.997348	+	0.0727779i	$0.0231864\pi$
$44$		−	400.267i		−	0.206750i
$45$	894.359	−	142.295i	0.441659	−	0.0702689i
$46$	−1035.06			−0.489158
$47$	−320.976	−	185.316i	−0.145304	−	0.0838912i	0.425586	−	0.904918i	$-0.360068\pi$
$47$	−320.976	−	185.316i	−0.145304	−	0.0838912i	−0.570889	+	0.821027i	$0.693401\pi$
$48$	1270.30	+	1084.17i	0.551346	+	0.470560i
$49$	307.425	+	532.476i	0.128040	+	0.221773i
$50$	−133.257	+	76.9358i	−0.0533027	+	0.0307743i
$51$	−2694.63	−	498.445i	−1.03600	−	0.191636i
$52$	−1713.64	+	2968.12i	−0.633744	+	1.09768i
$53$		−	2527.06i		−	0.899631i	−0.893121	−	0.449816i	$-0.851490\pi$
$53$		−	2527.06i		−	0.899631i	0.893121	−	0.449816i	$-0.148510\pi$
$54$	788.182	−	429.020i	0.270296	−	0.147126i
$55$	−308.955			−0.102134
$56$	−1373.47	−	792.975i	−0.437970	−	0.252862i
$57$	−516.550	+	2792.51i	−0.158987	+	0.859498i
$58$	−477.789	−	827.554i	−0.142030	−	0.246003i
$59$	1192.13	−	688.279i	0.342469	−	0.197724i	−0.318894	−	0.947790i	$-0.603312\pi$
$59$	1192.13	−	688.279i	0.342469	−	0.197724i	0.661363	+	0.750066i	$0.269978\pi$
$60$	946.179	−	1108.62i	0.262828	−	0.307950i
$61$	−400.200	+	693.167i	−0.107552	+	0.186285i	−0.914778	−	0.403957i	$-0.867634\pi$
$61$	−400.200	+	693.167i	−0.107552	+	0.186285i	0.807226	+	0.590242i	$0.200968\pi$
$62$			2051.09i			0.533582i
$63$	2658.89	−	2156.21i	0.669914	−	0.543263i
$64$	1948.72			0.475761
$65$	2291.01	+	1322.71i	0.542250	+	0.313068i
$66$	−288.552	+	102.295i	−0.0662424	+	0.0234838i
$67$	−1192.70	−	2065.81i	−0.265693	−	0.460194i	0.702052	−	0.712126i	$-0.252268\pi$
$67$	−1192.70	−	2065.81i	−0.265693	−	0.460194i	−0.967745	+	0.251932i	$0.918934\pi$
$68$	−3819.47	+	2205.17i	−0.826010	+	0.476897i
$69$	−2528.62	−	7132.66i	−0.531110	−	1.49814i
$70$	−290.825	+	503.724i	−0.0593521	+	0.102801i
$71$			1978.96i			0.392573i	0.980547	+	0.196287i	$0.0628883\pi$
$71$			1978.96i			0.392573i	−0.980547	+	0.196287i	$0.937112\pi$
$72$	1087.31	−	2838.47i	0.209743	−	0.547544i
$73$	10301.8			1.93315			0.966577	−	0.256376i	$-0.0825285\pi$
$73$	10301.8			1.93315			0.966577	+	0.256376i	$0.0825285\pi$
$74$	223.311	+	128.929i	0.0407799	+	0.0235443i
$75$	−855.712	−	730.330i	−0.152127	−	0.129836i
$76$	2285.27	+	3958.20i	0.395649	+	0.685284i
$77$	−1011.42	+	583.942i	−0.170588	+	0.0984891i
$78$	2577.66	+	476.808i	0.423679	+	0.0783708i
$79$	−2915.77	+	5050.26i	−0.467196	+	0.809207i	−0.999298	−	0.0374731i	$-0.988069\pi$
$79$	−2915.77	+	5050.26i	−0.467196	+	0.809207i	0.532101	+	0.846681i	$0.321402\pi$
$80$		−	2074.65i		−	0.324164i
$81$	4881.92	+	4383.33i	0.744081	+	0.668089i
$82$	2589.23			0.385074
$83$	−147.535	−	85.1792i	−0.0214160	−	0.0123645i	0.489254	−	0.872141i	$-0.337269\pi$
$83$	−147.535	−	85.1792i	−0.0214160	−	0.0123645i	−0.510670	+	0.859777i	$0.670603\pi$
$84$	1002.13	−	5417.58i	0.142025	−	0.767798i
$85$	1702.11	+	2948.14i	0.235586	+	0.408048i
$86$	−1717.43	+	991.561i	−0.232211	+	0.134067i
$87$	4535.51	−	5314.17i	0.599222	−	0.702097i
$88$	−518.491	+	898.052i	−0.0669539	+	0.115968i
$89$			11188.1i			1.41246i	0.707982	+	0.706230i	$0.249606\pi$
$89$			11188.1i			1.41246i	−0.707982	+	0.706230i	$0.750394\pi$
$90$	−1041.01	−	398.772i	−0.128520	−	0.0492311i
$91$	9999.99			1.20758
$92$	−10547.7	−	6089.70i	−1.24618	−	0.719482i
$93$	−14134.2	+	5010.76i	−1.63420	+	0.579345i
$94$	228.119	+	395.113i	0.0258169	+	0.0447163i
$95$	3055.23	−	1763.94i	0.338529	−	0.195450i
$96$	−2492.50	−	7030.78i	−0.270454	−	0.762888i
$97$	516.445	−	894.509i	0.0548884	−	0.0950695i	−0.837276	−	0.546781i	$-0.815853\pi$
$97$	516.445	−	894.509i	0.0548884	−	0.0950695i	0.892164	+	0.451711i	$0.149186\pi$
$98$		−	756.864i		−	0.0788072i
$99$	−1409.85	−	1738.53i	−0.143847	−	0.177383i
$100$	−1810.59			−0.181059
$101$	−3794.12	−	2190.54i	−0.371936	−	0.214737i	0.302368	−	0.953191i	$-0.402223\pi$
$101$	−3794.12	−	2190.54i	−0.371936	−	0.214737i	−0.674304	+	0.738454i	$0.735556\pi$
$102$	2565.84	+	2189.88i	0.246620	+	0.210484i
$103$	−5855.56	−	10142.1i	−0.551942	−	0.955992i	−0.998134	−	0.0610549i	$-0.980554\pi$
$103$	−5855.56	−	10142.1i	−0.551942	−	0.955992i	0.446192	−	0.894937i	$-0.352780\pi$
$104$	7689.57	−	4439.57i	0.710944	−	0.410464i
$105$	−4181.68	−	773.514i	−0.379291	−	0.0701600i
$106$	−1555.37	+	2693.99i	−0.138428	+	0.239764i
$107$		−	1773.37i		−	0.154893i	−0.996997	−	0.0774464i	$-0.975323\pi$
$107$		−	1773.37i		−	0.154893i	0.996997	−	0.0774464i	$-0.0246767\pi$
$108$	10556.0	+	265.324i	0.905008	+	0.0227473i
$109$	−7552.17			−0.635651			−0.317826	−	0.948149i	$-0.602953\pi$
$109$	−7552.17			−0.635651			−0.317826	+	0.948149i	$0.602953\pi$
$110$	329.363	+	190.158i	0.0272201	+	0.0157155i
$111$	−342.914	+	1853.82i	−0.0278317	+	0.150460i
$112$	−3921.19	−	6791.70i	−0.312595	−	0.541430i
$113$	−21753.9	+	12559.6i	−1.70365	+	0.983603i	−0.761651	+	0.647988i	$0.775611\pi$
$113$	−21753.9	+	12559.6i	−1.70365	+	0.983603i	−0.941999	+	0.335615i	$0.891056\pi$
$114$	2269.42	−	2659.03i	0.174625	−	0.204604i
$115$	−4700.47	+	8141.45i	−0.355423	+	0.615610i
$116$		−	11244.2i		−	0.835625i
$117$	3011.44	+	18927.7i	0.219990	+	1.38269i
$118$	−1694.50			−0.121697
$119$	11144.3	+	6434.16i	0.786971	+	0.454358i
$120$	−3558.94	+	1261.69i	−0.247149	+	0.0876173i
$121$	−6938.69	−	12018.2i	−0.473922	−	0.820856i
$122$	853.270	−	492.635i	0.0573280	−	0.0330983i
$123$	6325.43	+	17842.6i	0.418099	+	1.17936i
$124$	−12067.5	+	20901.5i	−0.784825	+	1.35936i
$125$			1397.54i			0.0894427i
$126$	−4161.64	+	662.126i	−0.262134	+	0.0417061i
$127$	11630.0			0.721063			0.360531	−	0.932747i	$-0.382595\pi$
$127$	11630.0			0.721063			0.360531	+	0.932747i	$0.382595\pi$
$128$	−13562.1	−	7830.09i	−0.827766	−	0.477911i
$129$	−11028.6	−	9412.61i	−0.662735	−	0.565628i
$130$	−1628.22	−	2820.17i	−0.0963446	−	0.166874i
$131$	22854.3	−	13194.9i	1.33176	−	0.768891i	0.346190	−	0.938165i	$-0.387475\pi$
$131$	22854.3	−	13194.9i	1.33176	−	0.768891i	0.985569	+	0.169273i	$0.0541420\pi$
$132$	−3542.31	−	655.246i	−0.203301	−	0.0376060i
$133$	6667.86	−	11549.1i	0.376950	−	0.652896i
$134$			2936.36i			0.163531i
$135$	204.797	−	8147.89i	0.0112371	−	0.447072i
$136$	11426.0			0.617754
$137$	28449.8	+	16425.5i	1.51579	+	0.875141i	0.999828	+	0.0185276i	$0.00589784\pi$
$137$	28449.8	+	16425.5i	1.51579	+	0.875141i	0.515960	+	0.856613i	$0.327435\pi$
$138$	−1694.41	+	9160.12i	−0.0889735	+	0.480998i
$139$	−5839.17	−	10113.7i	−0.302219	−	0.523459i	0.674419	−	0.738349i	$-0.264394\pi$
$139$	−5839.17	−	10113.7i	−0.302219	−	0.523459i	−0.976638	+	0.214890i	$0.931061\pi$
$140$	−5927.26	+	3422.11i	−0.302411	+	0.174597i
$141$	−2165.46	+	2537.23i	−0.108921	+	0.127621i
$142$	1218.02	−	2109.68i	0.0604059	−	0.104626i
$143$		−	6538.55i		−	0.319749i
$144$	11674.3	−	9467.19i	0.562996	−	0.456558i
$145$	−8679.06			−0.412797
$146$	−10982.2	−	6340.60i	−0.515212	−	0.297458i
$147$	5215.60	−	1849.00i	0.241363	−	0.0855661i
$148$	1517.09	+	2627.67i	0.0692607	+	0.119963i
$149$	33279.3	−	19213.8i	1.49900	−	0.865447i	0.498999	−	0.866602i	$-0.333701\pi$
$149$	33279.3	−	19213.8i	1.49900	−	0.865447i	0.999999	+	0.00115510i	$0.000367679\pi$
$150$	462.728	+	1305.25i	0.0205657	+	0.0580111i
$151$	20864.3	−	36138.0i	0.915060	−	1.58493i	0.108248	−	0.994124i	$-0.465476\pi$
$151$	20864.3	−	36138.0i	0.915060	−	1.58493i	0.806813	−	0.590807i	$-0.201191\pi$
$152$		−	11841.0i		−	0.512508i
$153$	−8822.35	+	23031.2i	−0.376878	+	0.983860i
$154$	1437.63			0.0606187
$155$	16133.3	+	9314.54i	0.671520	+	0.387702i
$156$	23462.2	+	20024.4i	0.964094	+	0.822830i
$157$	−424.982	−	736.090i	−0.0172413	−	0.0298629i	0.857276	−	0.514857i	$-0.172155\pi$
$157$	−424.982	−	736.090i	−0.0172413	−	0.0298629i	−0.874517	+	0.484994i	$0.838822\pi$
$158$	6216.74	−	3589.23i	0.249028	−	0.143776i
$159$	−22364.2	−	4136.86i	−0.884624	−	0.163635i
$160$	−4633.33	+	8025.16i	−0.180989	+	0.313483i
$161$			35536.5i			1.37095i
$162$	−2506.50	−	7677.62i	−0.0955077	−	0.292548i
$163$	−13884.8			−0.522594			−0.261297	−	0.965259i	$-0.584150\pi$
$163$	−13884.8			−0.522594			−0.261297	+	0.965259i	$0.584150\pi$
$164$	26385.4	+	15233.6i	0.981015	+	0.566389i
$165$	−505.766	+	2734.21i	−0.0185773	+	0.100430i
$166$	104.853	+	181.611i	0.00380510	+	0.00659062i
$167$	−3956.62	+	2284.36i	−0.141870	+	0.0819088i	−0.569255	−	0.822161i	$-0.692768\pi$
$167$	−3956.62	+	2284.36i	−0.141870	+	0.0819088i	0.427385	+	0.904070i	$0.359435\pi$
$168$	−9266.13	+	10856.9i	−0.328307	+	0.384670i
$169$	−13712.6	+	23751.0i	−0.480118	+	0.831588i
$170$		−	4190.50i		−	0.145000i
$171$	23867.7	+	9142.79i	0.816242	+	0.312670i
$172$	−23335.2			−0.788777
$173$	−24613.7	−	14210.8i	−0.822405	−	0.474815i	0.0288404	−	0.999584i	$-0.490819\pi$
$173$	−24613.7	−	14210.8i	−0.822405	−	0.474815i	−0.851245	+	0.524769i	$0.824152\pi$
$174$	−8105.90	+	2873.64i	−0.267733	+	0.0949149i
$175$	2641.43	+	4575.09i	0.0862507	+	0.149391i
$176$	−4440.79	+	2563.89i	−0.143362	+	0.0827703i
$177$	−4139.63	−	11677.0i	−0.132134	−	0.372720i
$178$	6886.12	−	11927.1i	0.217337	−	0.376440i
$179$		−	28162.8i		−	0.878963i	−0.898252	−	0.439481i	$-0.855162\pi$
$179$		−	28162.8i		−	0.878963i	0.898252	−	0.439481i	$-0.144838\pi$
$180$	−8262.22	−	10188.4i	−0.255007	−	0.314457i
$181$	−44153.7			−1.34775			−0.673876	−	0.738844i	$-0.735372\pi$
$181$	−44153.7			−1.34775			−0.673876	+	0.738844i	$0.735372\pi$
$182$	−10660.5	−	6154.86i	−0.321837	−	0.185813i
$183$	5479.30	+	4676.45i	0.163615	+	0.139641i
$184$	15776.7	+	27326.1i	0.465995	+	0.807126i
$185$	2028.23	−	1171.00i	0.0592615	−	0.0342147i
$186$	18151.9	+	3357.68i	0.524681	+	0.0970540i
$187$	4207.01	−	7286.75i	0.120307	−	0.208378i
$188$			5368.49i			0.151892i
$189$	−14729.5	−	27060.6i	−0.412349	−	0.757554i
$190$	−4342.71			−0.120297
$191$	−25628.1	−	14796.4i	−0.702504	−	0.405591i	0.105775	−	0.994390i	$-0.466268\pi$
$191$	−25628.1	−	14796.4i	−0.702504	−	0.405591i	−0.808279	+	0.588799i	$0.799601\pi$
$192$	3190.09	−	17245.9i	0.0865368	−	0.467825i
$193$	3379.59	+	5853.63i	0.0907298	+	0.157149i	0.907818	−	0.419363i	$-0.137747\pi$
$193$	3379.59	+	5853.63i	0.0907298	+	0.157149i	−0.817089	+	0.576512i	$0.804413\pi$
$194$	−1101.12	+	635.730i	−0.0292570	+	0.0168915i
$195$	15456.3	−	18109.8i	0.406477	−	0.476260i
$196$	4452.96	−	7712.76i	0.115914	−	0.200769i
$197$		−	21665.5i		−	0.558259i	−0.960253	−	0.279130i	$-0.909954\pi$
$197$		−	21665.5i		−	0.558259i	0.960253	−	0.279130i	$-0.0900459\pi$
$198$	432.934	+	2721.11i	0.0110431	+	0.0694089i
$199$	−55987.8			−1.41380			−0.706899	−	0.707314i	$-0.749907\pi$
$199$	−55987.8			−1.41380			−0.706899	+	0.707314i	$0.749907\pi$
$200$	4062.29	+	2345.37i	0.101557	+	0.0586341i
$201$	−20234.6	+	7173.44i	−0.500845	+	0.177556i
$202$	2696.49	+	4670.46i	0.0660839	+	0.114461i
$203$	−28412.3	+	16403.9i	−0.689469	+	0.398065i
$204$	13262.9	+	37411.7i	0.318698	+	0.898975i
$205$	11758.4	−	20366.1i	0.279795	−	0.484619i
$206$			14416.1i			0.339713i
$207$	−67262.5	+	10701.6i	−1.56976	+	0.249752i
$208$	43906.6			1.01485
$209$	−7551.43	−	4359.82i	−0.172877	−	0.0998104i
$210$	3981.81	+	3398.37i	0.0902904	+	0.0770606i
$211$	22165.0	+	38391.0i	0.497856	+	0.862311i	0.999997	−	0.00247445i	$-0.000787644\pi$
$211$	22165.0	+	38391.0i	0.497856	+	0.862311i	−0.502141	+	0.864786i	$0.667454\pi$
$212$	−31699.8	+	18301.9i	−0.705318	+	0.407216i
$213$	17513.6	+	3239.60i	0.386025	+	0.0714057i
$214$	−1091.48	+	1890.50i	−0.0238336	+	0.0412810i
$215$			18011.8i			0.389654i
$216$	−23340.1	−	14269.1i	−0.500260	−	0.305837i
$217$	70419.9			1.49546
$218$	8051.02	+	4648.26i	0.169410	+	0.0978086i
$219$	16864.2	−	91169.4i	0.351624	−	1.90091i
$220$	2237.56	+	3875.57i	0.0462306	+	0.0800738i
$221$	−62392.8	+	36022.5i	−1.27747	+	0.737546i
$222$	1506.56	−	1765.21i	0.0305690	−	0.0358171i
$223$	32214.1	−	55796.5i	0.647794	−	1.12201i	−0.335855	−	0.941914i	$-0.609025\pi$
$223$	32214.1	−	55796.5i	0.647794	−	1.12201i	0.983649	−	0.180098i	$-0.0576415\pi$
$224$			35028.9i			0.698122i
$225$	−7864.14	+	6377.38i	−0.155341	+	0.125973i
$226$	30921.1			0.605394
$227$	13673.6	+	7894.48i	0.265358	+	0.153205i	0.626776	−	0.779199i	$-0.284374\pi$
$227$	13673.6	+	7894.48i	0.265358	+	0.153205i	−0.361418	+	0.932404i	$0.617707\pi$
$228$	38770.6	−	13744.7i	0.745818	−	0.264402i
$229$	18299.9	+	31696.4i	0.348962	+	0.604420i	0.986065	−	0.166359i	$-0.0532009\pi$
$229$	18299.9	+	31696.4i	0.348962	+	0.604420i	−0.637103	+	0.770778i	$0.719868\pi$
$230$	10021.9	−	5786.15i	0.189450	−	0.109379i
$231$	3512.10	+	9906.83i	0.0658177	+	0.185657i
$232$	−14565.2	+	25227.8i	−0.270609	+	0.468708i
$233$		−	5152.64i		−	0.0949114i	−0.998873	−	0.0474557i	$-0.984889\pi$
$233$		−	5152.64i		−	0.0949114i	0.998873	−	0.0474557i	$-0.0151113\pi$
$234$	8439.38	−	22031.4i	0.154127	−	0.402356i
$235$	4143.78			0.0750346
$236$	−17267.7	−	9969.51i	−0.310035	−	0.178999i
$237$	39921.0	+	34071.6i	0.710730	+	0.606590i
$238$	−7920.28	−	13718.3i	−0.139825	−	0.242185i
$239$	22898.9	−	13220.7i	0.400885	−	0.231451i	−0.285981	−	0.958235i	$-0.592319\pi$
$239$	22898.9	−	13220.7i	0.400885	−	0.231451i	0.686866	+	0.726784i	$0.258986\pi$
$240$	−18360.3	−	3396.24i	−0.318756	−	0.0589625i
$241$	−6406.70	+	11096.7i	−0.110306	+	0.191056i	−0.915894	−	0.401421i	$-0.868517\pi$
$241$	−6406.70	+	11096.7i	−0.110306	+	0.191056i	0.805587	+	0.592477i	$0.201850\pi$
$242$			17082.7i			0.291692i
$243$	46783.7	−	36028.7i	0.792286	−	0.610149i
$244$	11593.6			0.194732
$245$	−5953.26	−	3437.12i	−0.0991797	−	0.0572615i
$246$	4238.63	−	22914.4i	0.0700415	−	0.378650i
$247$	37330.9	+	64659.0i	0.611892	+	1.05983i
$248$	54149.9	−	31263.4i	0.880429	−	0.508316i
$249$	−995.342	+	1166.22i	−0.0160536	+	0.0188097i
$250$	860.168	−	1489.86i	0.0137627	−	0.0238377i
$251$		−	73021.8i		−	1.15906i	−0.814952	−	0.579529i	$-0.803236\pi$
$251$		−	73021.8i		−	1.15906i	0.814952	−	0.579529i	$-0.196764\pi$
$252$	−46304.4	−	17737.4i	−0.729157	−	0.279311i
$253$	23235.7			0.363007
$254$	−12398.2	−	7158.12i	−0.192173	−	0.110951i
$255$	28877.1	−	10237.3i	0.444092	−	0.157436i
$256$	−5951.12	−	10307.6i	−0.0908069	−	0.157282i
$257$	−79049.4	+	45639.2i	−1.19683	+	0.690990i	−0.959847	−	0.280524i	$-0.909492\pi$
$257$	−79049.4	+	45639.2i	−1.19683	+	0.690990i	−0.236983	+	0.971514i	$0.576159\pi$
$258$	5963.71	+	16822.3i	0.0895936	+	0.252723i
$259$	4426.49	−	7666.91i	0.0659872	−	0.114293i
$260$		−	38318.2i		−	0.566838i
$261$	−39605.0	−	48838.1i	−0.581391	−	0.716931i
$262$	−32485.2			−0.473242
$263$	−37880.4	−	21870.3i	−0.547651	−	0.316186i	0.200523	−	0.979689i	$-0.435736\pi$
$263$	−37880.4	−	21870.3i	−0.547651	−	0.316186i	−0.748174	+	0.663503i	$0.769069\pi$
$264$	7098.86	+	6058.71i	0.101855	+	0.0869305i
$265$	14126.7	+	24468.2i	0.201164	+	0.348426i
$266$	−14216.6	+	8207.96i	−0.200924	+	0.116004i
$267$	99013.2	+	18315.2i	1.38890	+	0.256914i
$268$	−17275.9	+	29922.7i	−0.240531	+	0.416611i
$269$			102008.i			1.40970i	0.709355	+	0.704852i	$0.248986\pi$
$269$			102008.i			1.40970i	−0.709355	+	0.704852i	$0.751014\pi$
$270$	−5233.24	+	8560.04i	−0.0717866	+	0.117422i
$271$	−112531.			−1.53227			−0.766135	−	0.642680i	$-0.777822\pi$
$271$	−112531.			−1.53227			−0.766135	+	0.642680i	$0.777822\pi$
$272$	48930.8	+	28250.2i	0.661371	+	0.381842i
$273$	16370.2	−	88498.6i	0.219649	−	1.18744i
$274$	−20219.4	−	35021.0i	−0.269319	−	0.466473i
$275$	2991.45	−	1727.11i	0.0395563	−	0.0228378i
$276$	−71159.8	+	83376.5i	−0.934150	+	1.09452i
$277$	25079.3	−	43438.6i	0.326855	−	0.566130i	−0.655031	−	0.755602i	$-0.727344\pi$
$277$	25079.3	−	43438.6i	0.326855	−	0.566130i	0.981886	+	0.189472i	$0.0606777\pi$
$278$			14375.7i			0.186012i
$279$	21206.5	+	133289.i	0.272434	+	1.71232i
$280$	17731.5			0.226167
$281$	104136.	+	60123.2i	1.31883	+	0.761429i	0.983541	−	0.180685i	$-0.0578315\pi$
$281$	104136.	+	60123.2i	1.31883	+	0.761429i	0.335292	+	0.942114i	$0.391165\pi$
$282$	3870.13	−	1372.01i	0.0486662	−	0.0172528i
$283$	34116.3	+	59091.2i	0.425980	+	0.737819i	0.996511	−	0.0834569i	$-0.0265961\pi$
$283$	34116.3	+	59091.2i	0.425980	+	0.737819i	−0.570531	+	0.821276i	$0.693263\pi$
$284$	24824.4	−	14332.3i	0.307781	−	0.177697i
$285$	−10609.1	−	29925.9i	−0.130614	−	0.368433i
$286$	−4024.39	+	6970.44i	−0.0492003	+	0.0852174i
$287$		−	88895.9i		−	1.07924i
$288$	−66301.7	+	10548.8i	−0.799355	+	0.127179i
$289$	−9188.85			−0.110018
$290$	9252.34	+	5341.84i	0.110016	+	0.0635177i
$291$	−7070.86	−	6034.80i	−0.0834999	−	0.0712651i
$292$	−74609.1	−	129227.i	−0.875037	−	1.51561i
$293$	98072.6	−	56622.2i	1.14238	−	0.659556i	0.195365	−	0.980731i	$-0.437411\pi$
$293$	98072.6	−	56622.2i	1.14238	−	0.659556i	0.947020	+	0.321175i	$0.104078\pi$
$294$	−6698.15	−	1239.00i	−0.0774926	−	0.0143343i
$295$	−7695.19	+	13328.5i	−0.0884250	+	0.153157i
$296$		−	7860.70i		−	0.0897176i
$297$	−17693.7	+	9630.97i	−0.200588	+	0.109184i
$298$	−47303.3			−0.532671
$299$	−172301.	−	99478.0i	−1.92728	−	1.11272i
$300$	−2963.97	+	16023.5i	−0.0329330	+	0.178039i
$301$	34043.2	+	58964.5i	0.375748	+	0.650815i
$302$	−44484.9	+	25683.4i	−0.487752	+	0.281604i
$303$	−25597.0	+	29991.5i	−0.278807	+	0.326673i
$304$	29276.3	−	50708.1i	0.316789	−	0.548694i
$305$		−	8948.75i		−	0.0961972i
$306$	23580.5	−	19122.4i	0.251831	−	0.204221i
$307$	−149777.			−1.58916			−0.794579	−	0.607161i	$-0.792308\pi$
$307$	−149777.			−1.58916			−0.794579	+	0.607161i	$0.792308\pi$
$308$	14650.1	+	8458.22i	0.154432	+	0.0891616i
$309$	−99342.1	+	35218.0i	−1.04044	+	0.368849i
$310$	−11465.9	−	19859.6i	−0.119313	−	0.206656i
$311$	33215.4	−	19176.9i	0.343414	−	0.198270i	−0.318367	−	0.947968i	$-0.603134\pi$
$311$	33215.4	−	19176.9i	0.343414	−	0.198270i	0.661781	+	0.749697i	$0.269801\pi$
$312$	−26701.7	−	75319.3i	−0.274302	−	0.773744i
$313$	−11580.1	+	20057.3i	−0.118202	+	0.204731i	−0.919055	−	0.394129i	$-0.871046\pi$
$313$	−11580.1	+	20057.3i	−0.118202	+	0.204731i	0.800853	+	0.598860i	$0.204380\pi$
$314$			1046.28i			0.0106118i
$315$	−13691.0	+	35741.0i	−0.137979	+	0.360202i
$316$	84468.2			0.845900
$317$	64166.9	+	37046.7i	0.638546	+	0.368665i	0.784054	−	0.620692i	$-0.213148\pi$
$317$	64166.9	+	37046.7i	0.638546	+	0.368665i	−0.145508	+	0.989357i	$0.546482\pi$
$318$	21295.2	+	18175.0i	0.210585	+	0.179730i
$319$	10725.8	+	18577.6i	0.105401	+	0.182561i
$320$	−18868.4	+	10893.7i	−0.184262	+	0.106383i
$321$	−15694.1	−	2903.04i	−0.152309	−	0.0281736i
$322$	21872.2	−	37883.8i	0.210951	−	0.365378i
$323$			96077.3i			0.920907i
$324$	19628.5	−	92985.0i	0.186981	−	0.885774i
$325$	−29576.8			−0.280017
$326$	14801.9	+	8545.90i	0.139278	+	0.0804123i
$327$	−12363.1	+	66835.7i	−0.115619	+	0.625048i
$328$	−39466.0	−	68357.2i	−0.366839	−	0.635384i
$329$	13565.4	−	7831.97i	0.125326	−	0.0723568i
$330$	2222.04	−	2603.53i	0.0204045	−	0.0239075i
$331$	−9919.31	+	17180.8i	−0.0905369	+	0.156814i	−0.907737	−	0.419539i	$-0.862192\pi$
$331$	−9919.31	+	17180.8i	−0.0905369	+	0.156814i	0.817200	+	0.576354i	$0.195525\pi$
$332$			2467.59i			0.0223871i
$333$	15844.7	+	6069.48i	0.142888	+	0.0547348i
$334$	5623.96			0.0504138
$335$	23096.5	+	13334.8i	0.205805	+	0.118822i
$336$	−66524.7	+	23583.9i	−0.589257	+	0.208899i
$337$	22224.6	+	38494.1i	0.195692	+	0.338949i	0.947127	−	0.320858i	$-0.103971\pi$
$337$	22224.6	+	38494.1i	0.195692	+	0.338949i	−0.751435	+	0.659807i	$0.770638\pi$
$338$	29236.8	−	16879.9i	0.255916	−	0.147753i
$339$	75539.4	+	213080.i	0.657316	+	1.85414i
$340$	24654.6	−	42703.0i	0.213275	−	0.369403i
$341$		−	46044.4i		−	0.395975i
$342$	−19817.0	−	24437.0i	−0.169428	−	0.208927i
$343$	−127458.			−1.08338
$344$	52355.5	+	30227.5i	0.442431	+	0.255438i
$345$	64356.0	+	54926.2i	0.540693	+	0.461468i
$346$	17493.0	+	30298.8i	0.146121	+	0.253089i
$347$	107096.	−	61832.1i	0.889438	−	0.513518i	0.0156796	−	0.999877i	$-0.495009\pi$
$347$	107096.	−	61832.1i	0.889438	−	0.513518i	0.873759	+	0.486360i	$0.161675\pi$
$348$	−99509.4	−	18406.9i	−0.821685	−	0.151993i
$349$	93775.0	−	162423.i	0.769903	−	1.33351i	−0.167712	−	0.985836i	$-0.553638\pi$
$349$	93775.0	−	162423.i	0.769903	−	1.33351i	0.937615	−	0.347675i	$-0.113029\pi$
$350$		−	6503.05i		−	0.0530862i
$351$	172437.	+	4334.19i	1.39964	+	0.0351799i
$352$	22903.9			0.184852
$353$	−31677.2	−	18288.8i	−0.254212	−	0.146770i	0.367479	−	0.930032i	$-0.380221\pi$
$353$	−31677.2	−	18288.8i	−0.254212	−	0.146770i	−0.621692	+	0.783262i	$0.713554\pi$
$354$	−2773.94	+	14996.1i	−0.0221356	+	0.119667i
$355$	−11062.7	−	19161.2i	−0.0877821	−	0.152043i
$356$	140345.	−	81028.1i	1.10738	−	0.639346i
$357$	75184.9	−	88092.7i	0.589922	−	0.691199i
$358$	−17333.8	+	30023.1i	−0.135247	+	0.234255i
$359$		−	31290.3i		−	0.242785i	−0.992605	−	0.121392i	$-0.961264\pi$
$359$		−	31290.3i		−	0.242785i	0.992605	−	0.121392i	$-0.0387359\pi$
$360$	5339.72	+	33561.6i	0.0412016	+	0.258963i
$361$	−30754.0			−0.235986
$362$	47070.2	+	27176.0i	0.359194	+	0.207381i
$363$	−117718.	+	41732.5i	−0.893366	+	0.316709i
$364$	−72423.5	−	125441.i	−0.546609	−	0.946754i
$365$	−99746.6	+	57588.7i	−0.748707	+	0.432266i
$366$	−2962.94	−	8357.78i	−0.0221187	−	0.0623920i
$367$	−68681.5	+	118960.i	−0.509927	+	0.883219i	0.490007	+	0.871718i	$0.336994\pi$
$367$	−68681.5	+	118960.i	−0.509927	+	0.883219i	−0.999934	+	0.0115003i	$0.996339\pi$
$368$			156029.i			1.15215i
$369$	168260.	−	26770.5i	1.23574	−	0.196609i
$370$	−2882.93			−0.0210587
$371$	92492.4	+	53400.5i	0.671983	+	0.387969i
$372$	165221.	+	141012.i	1.19393	+	1.01899i
$373$	18921.5	+	32773.0i	0.136000	+	0.235558i	0.925979	−	0.377575i	$-0.123242\pi$
$373$	18921.5	+	32773.0i	0.136000	+	0.235558i	−0.789979	+	0.613133i	$0.789909\pi$
$374$	−8969.80	+	5178.71i	−0.0641268	+	0.0370236i
$375$	12368.1	+	2287.81i	0.0879507	+	0.0162688i
$376$	6954.13	−	12044.9i	0.0491889	−	0.0851976i
$377$		−	183679.i		−	1.29234i
$378$	−952.961	+	37913.8i	−0.00666947	+	0.265347i
$379$	257039.			1.78945			0.894727	−	0.446613i	$-0.147370\pi$
$379$	257039.			1.78945			0.894727	+	0.446613i	$0.147370\pi$
$380$	−44254.1	−	25550.1i	−0.306469	−	0.176940i
$381$	19038.6	−	102924.i	0.131155	−	0.709035i
$382$	18213.9	+	31547.4i	0.124818	+	0.216191i
$383$	76927.3	−	44414.0i	0.524425	−	0.302777i	−0.214318	−	0.976764i	$-0.568753\pi$
$383$	76927.3	−	44414.0i	0.524425	−	0.302777i	0.738743	+	0.673987i	$0.235420\pi$
$384$	−91496.8	+	107205.i	−0.620502	+	0.727030i
$385$	6528.67	−	11308.0i	0.0440457	−	0.0762893i
$386$		−	8320.37i		−	0.0558429i
$387$	−101354.	+	82192.7i	−0.676738	+	0.548797i
$388$	−14961.1			−0.0993803
$389$	−216424.	−	124953.i	−1.43023	−	0.825746i	−0.433096	−	0.901348i	$-0.642579\pi$
$389$	−216424.	−	124953.i	−1.43023	−	0.825746i	−0.997138	+	0.0756023i	$0.975912\pi$
$390$	−27623.5	+	9792.90i	−0.181614	+	0.0643846i
$391$	−128011.	−	221722.i	−0.837328	−	1.45029i
$392$	−19981.6	+	11536.4i	−0.130034	+	0.0750754i
$393$	−79360.5	−	223858.i	−0.513830	−	1.44940i
$394$	−13334.8	+	23096.6i	−0.0859002	+	0.148784i
$395$		−	65198.6i		−	0.417873i
$396$	−11597.7	+	30276.4i	−0.0739573	+	0.193069i
$397$	253790.			1.61025			0.805124	−	0.593107i	$-0.202099\pi$
$397$	253790.			1.61025			0.805124	+	0.593107i	$0.202099\pi$
$398$	59686.0	+	34459.7i	0.376796	+	0.217543i
$399$	−91292.4	−	77915.8i	−0.573441	−	0.489418i
$400$	11597.6	+	20087.7i	0.0724852	+	0.125548i
$401$	−79498.2	+	45898.3i	−0.494388	+	0.285435i	−0.726393	−	0.687279i	$-0.758805\pi$
$401$	−79498.2	+	45898.3i	−0.494388	+	0.285435i	0.232005	+	0.972715i	$0.425472\pi$
$402$	25986.4	+	4806.88i	0.160803	+	0.0297448i
$403$	−197128.	+	341435.i	−1.21377	+	2.10232i
$404$			63458.5i			0.388801i
$405$	−71772.5	−	15150.7i	−0.437571	−	0.0923682i
$406$	40385.4			0.245004
$407$	−5013.05	−	2894.28i	−0.0302631	−	0.0174724i
$408$	18704.6	−	101118.i	0.112364	−	0.607449i
$409$	−6862.22	−	11885.7i	−0.0410221	−	0.0710524i	0.844785	−	0.535105i	$-0.179728\pi$
$409$	−6862.22	−	11885.7i	−0.0410221	−	0.0710524i	−0.885807	+	0.464053i	$0.846395\pi$
$410$	−25070.2	+	14474.3i	−0.149138	+	0.0861051i
$411$	191937.	−	224888.i	1.13625	−	1.33132i
$412$	−84816.0	+	146906.i	−0.499670	+	0.865454i
$413$			58177.3i			0.341078i
$414$	78292.1	+	29990.6i	0.456791	+	0.174979i
$415$	1904.66			0.0110592
$416$	−169840.	−	98057.1i	−0.981416	−	0.566621i
$417$	−99064.1	+	35119.5i	−0.569697	+	0.201965i
$418$	5366.82	+	9295.60i	0.0307160	+	0.0532016i
$419$	−91362.5	+	52748.2i	−0.520403	+	0.300455i	−0.737100	−	0.675784i	$-0.763805\pi$
$419$	−91362.5	+	52748.2i	−0.520403	+	0.300455i	0.216696	+	0.976239i	$0.430472\pi$
$420$	20582.1	+	58057.6i	0.116679	+	0.329125i
$421$	1303.65	−	2257.99i	0.00735523	−	0.0127396i	−0.862324	−	0.506356i	$-0.830992\pi$
$421$	1303.65	−	2257.99i	0.00735523	−	0.0127396i	0.869680	+	0.493617i	$0.164325\pi$
$422$		−	54569.1i		−	0.306423i
$423$	18909.2	+	23317.6i	0.105680	+	0.130317i
$424$	94830.2			0.527491
$425$	−32961.2	−	19030.2i	−0.182484	−	0.105357i
$426$	−16676.5	−	14232.9i	−0.0918935	−	0.0784288i
$427$	−16913.6	−	29295.2i	−0.0927642	−	0.160672i
$428$	−22245.3	+	12843.4i	−0.121437	+	0.0701118i
$429$	−57865.3	−	10703.7i	−0.314415	−	0.0581596i
$430$	11086.0	−	19201.5i	0.0599567	−	0.103848i
$431$			298817.i			1.60861i	0.594218	+	0.804304i	$0.297461\pi$
$431$			298817.i			1.60861i	−0.594218	+	0.804304i	$0.702539\pi$
$432$	−64672.3	−	118814.i	−0.346538	−	0.636648i
$433$	29.3738			0.000156669			7.83347e−5	−	1.00000i	$-0.499975\pi$
$433$	29.3738			0.000156669			7.83347e−5		1.00000i	$0.499975\pi$
$434$	−75071.4	−	43342.5i	−0.398561	−	0.230109i
$435$	−14207.8	+	76808.5i	−0.0750842	+	0.405911i
$436$	54695.5	+	94735.4i	0.287726	+	0.498355i
$437$	−229776.	+	132661.i	−1.20321	+	0.694674i
$438$	−74091.7	+	86811.8i	−0.386208	+	0.452512i
$439$	11935.9	−	20673.5i	0.0619334	−	0.107272i	−0.833396	−	0.552676i	$-0.813607\pi$
$439$	11935.9	−	20673.5i	0.0619334	−	0.107272i	0.895330	+	0.445404i	$0.146940\pi$
$440$		−	11593.8i		−	0.0598854i
$441$	−7825.33	−	49184.3i	−0.0402370	−	0.252900i
$442$	88685.4			0.453950
$443$	−6015.60	−	3473.11i	−0.0306529	−	0.0176975i	0.484595	−	0.874739i	$-0.338967\pi$
$443$	−6015.60	−	3473.11i	−0.0306529	−	0.0176975i	−0.515248	+	0.857041i	$0.672300\pi$
$444$	25738.0	−	9124.46i	0.130560	−	0.0462851i
$445$	−62543.4	−	108328.i	−0.315836	−	0.547043i
$446$	−68684.0	+	39654.7i	−0.345291	+	0.199354i
$447$	−115561.	−	325971.i	−0.578356	−	1.63141i
$448$	−41179.2	+	71324.5i	−0.205174	+	0.355372i
$449$			218791.i			1.08527i	0.839969	+	0.542635i	$0.182573\pi$
$449$			218791.i			1.08527i	−0.839969	+	0.542635i	$0.817427\pi$
$450$	12308.8	−	1958.36i	0.0607841	−	0.00967089i
$451$	−58125.1			−0.285766
$452$	315099.	+	181922.i	1.54230	+	0.890450i
$453$	−285661.	−	243805.i	−1.39205	−	1.18808i
$454$	−9717.88	−	16831.9i	−0.0471476	−	0.0816621i
$455$	−96824.5	+	55901.7i	−0.467695	+	0.270024i
$456$	−104791.	−	19384.0i	−0.503959	−	0.0932208i
$457$	66614.5	−	115380.i	0.318960	−	0.552455i	−0.661311	−	0.750112i	$-0.730000\pi$
$457$	66614.5	−	115380.i	0.318960	−	0.552455i	0.980271	+	0.197657i	$0.0633331\pi$
$458$		−	45053.4i		−	0.214781i
$459$	189381.	+	115779.i	0.898897	+	0.549547i
$460$	136170.			0.643524
$461$	113670.	+	65627.6i	0.534866	+	0.308805i	0.742996	−	0.669296i	$-0.233404\pi$
$461$	113670.	+	65627.6i	0.534866	+	0.308805i	−0.208130	+	0.978101i	$0.566738\pi$
$462$	2353.44	−	12722.9i	0.0110260	−	0.0596075i
$463$	104000.	+	180134.i	0.485147	+	0.840299i	0.999854	−	0.0170669i	$-0.00543281\pi$
$463$	104000.	+	180134.i	0.485147	+	0.840299i	−0.514708	+	0.857366i	$0.672099\pi$
$464$	−124749.	+	72023.9i	−0.579430	+	0.334534i
$465$	108843.	−	127529.i	0.503378	−	0.589798i
$466$	−3171.38	+	5493.00i	−0.0146042	+	0.0252952i
$467$		−	389941.i		−	1.78799i	−0.448076	−	0.893995i	$-0.647891\pi$
$467$		−	389941.i		−	1.78799i	0.448076	−	0.893995i	$-0.352109\pi$
$468$	215621.	−	174857.i	0.984464	−	0.798346i
$469$	100814.			0.458325
$470$	−4417.50	−	2550.44i	−0.0199977	−	0.0115457i
$471$	−7210.01	+	2556.04i	−0.0325008	+	0.0115219i
$472$	25828.2	+	44735.8i	0.115934	+	0.200804i
$473$	38554.3	−	22259.3i	0.172326	−	0.0994923i
$474$	−21587.3	−	60893.0i	−0.0960820	−	0.271026i
$475$	−19721.4	+	34158.5i	−0.0874079	+	0.151395i
$476$		−	186394.i		−	0.822655i
$477$	−73221.3	+	191148.i	−0.321811	+	0.840104i
$478$	−32548.6			−0.142455
$479$	−133392.	−	77014.0i	−0.581379	−	0.335659i	0.180302	−	0.983611i	$-0.442292\pi$
$479$	−133392.	−	77014.0i	−0.581379	−	0.335659i	−0.761681	+	0.647952i	$0.775626\pi$
$480$	63436.8	+	54141.7i	0.275333	+	0.234990i
$481$	24782.3	+	42924.2i	0.107115	+	0.185529i
$482$	13659.8	−	7886.47i	0.0587962	−	0.0339460i
$483$	314494.	+	58174.1i	1.34809	+	0.249365i
$484$	−100505.	+	174079.i	−0.429038	+	0.743116i
$485$			11548.1i			0.0490937i
$486$	−72049.1	+	9613.79i	−0.305040	+	0.0407026i
$487$	−209417.			−0.882987			−0.441493	−	0.897265i	$-0.645551\pi$
$487$	−209417.			−0.882987			−0.441493	+	0.897265i	$0.645551\pi$
$488$	−26011.7	−	15017.8i	−0.109227	−	0.0630620i
$489$	−22729.7	+	122879.i	−0.0950552	+	0.513876i
$490$	4231.00	+	7328.31i	0.0176218	+	0.0305219i
$491$	247730.	−	143027.i	1.02758	−	0.593273i	0.111289	−	0.993788i	$-0.464502\pi$
$491$	247730.	−	143027.i	1.02758	−	0.593273i	0.916290	+	0.400515i	$0.131169\pi$
$492$	178009.	−	208569.i	0.735379	−	0.861629i
$493$	118182.	−	204697.i	0.486247	−	0.842204i
$494$		−	91906.7i		−	0.376611i
$495$	23369.5	+	8951.93i	0.0953759	+	0.0365348i
$496$	309190.			1.25679
$497$	−72431.4	−	41818.3i	−0.293234	−	0.169299i
$498$	1778.88	−	630.636i	0.00717279	−	0.00254285i
$499$	−14256.2	−	24692.5i	−0.0572537	−	0.0991664i	0.835978	−	0.548763i	$-0.184901\pi$
$499$	−14256.2	−	24692.5i	−0.0572537	−	0.0991664i	−0.893232	+	0.449597i	$0.851568\pi$
$500$	17530.9	−	10121.5i	0.0701238	−	0.0404860i
$501$	13739.2	+	38755.1i	0.0547375	+	0.154402i
$502$	−44943.9	+	77845.2i	−0.178346	+	0.308905i
$503$		−	48257.4i		−	0.190734i	−0.995442	−	0.0953670i	$-0.969598\pi$
$503$		−	48257.4i		−	0.190734i	0.995442	−	0.0953670i	$-0.0304025\pi$
$504$	80913.6	+	99777.0i	0.318537	+	0.392798i
$505$	48981.9			0.192067
$506$	−24770.6	−	14301.3i	−0.0967464	−	0.0558565i
$507$	187745.	+	160236.i	0.730387	+	0.623367i
$508$	−84228.7	−	145888.i	−0.326387	−	0.565319i
$509$	352744.	−	203657.i	1.36152	−	0.786075i	0.371695	−	0.928355i	$-0.378777\pi$
$509$	352744.	−	203657.i	1.36152	−	0.786075i	0.989826	+	0.142280i	$0.0454433\pi$
$510$	−37085.4	−	6859.95i	−0.142581	−	0.0263743i
$511$	−217691.	+	377052.i	−0.833680	+	1.44398i
$512$			265214.i			1.01171i
$513$	119984.	−	196259.i	0.455922	−	0.745754i
$514$	112361.			0.425295
$515$	113392.	+	65467.1i	0.427533	+	0.246836i
$516$	−38200.2	+	206513.i	−0.143472	+	0.775619i
$517$	−5120.98	−	8869.79i	−0.0191589	−	0.0331843i
$518$	−9437.75	+	5448.89i	−0.0351730	+	0.0203071i
$519$	−166057.	+	194565.i	−0.616483	+	0.722321i
$520$	−49635.9	+	85972.0i	−0.183565	+	0.317944i
$521$			294195.i			1.08382i	0.840435	+	0.541912i	$0.182300\pi$
$521$			294195.i			1.08382i	−0.840435	+	0.541912i	$0.817700\pi$
$522$	12161.8	+	76440.3i	0.0446332	+	0.280531i
$523$	236625.			0.865083			0.432541	−	0.901614i	$-0.357617\pi$
$523$	236625.			0.865083			0.432541	+	0.901614i	$0.357617\pi$
$524$	−331038.	−	191125.i	−1.20563	−	0.696073i
$525$	44813.0	−	15886.8i	0.162587	−	0.0576391i
$526$	26921.7	+	46629.8i	0.0973041	+	0.168536i
$527$	−439370.	+	253670.i	−1.58201	+	0.913373i
$528$	15420.4	+	43497.6i	0.0553132	+	0.156026i
$529$	213590.	−	369948.i	0.763254	−	1.32199i
$530$		−	34779.2i		−	0.123814i
$531$	−110116.	+	17519.7i	−0.390537	+	0.0621353i
$532$	−193164.			−0.682501
$533$	431017.	+	248848.i	1.51719	+	0.875950i
$534$	−94280.6	−	80466.2i	−0.330628	−	0.282183i
$535$	9913.43	+	17170.6i	0.0346351	+	0.0599897i
$536$	77521.4	−	44757.0i	0.269831	−	0.155787i
$537$	−249237.	−	46103.2i	−0.864301	−	0.159876i
$538$	62784.2	−	108745.i	0.216913	−	0.375705i
$539$			16990.7i			0.0584834i
$540$	−103691.	+	56440.9i	−0.355595	+	0.193556i
$541$	−230383.			−0.787147			−0.393573	−	0.919293i	$-0.628761\pi$
$541$	−230383.			−0.787147			−0.393573	+	0.919293i	$0.628761\pi$
$542$	119964.	+	69261.5i	0.408370	+	0.235773i
$543$	−72280.6	+	390754.i	−0.245144	+	1.32527i
$544$	−126183.	−	218556.i	−0.426386	−	0.738523i
$545$	73123.6	−	42217.9i	0.246187	−	0.142136i
$546$	−71921.2	+	84268.6i	−0.241252	+	0.282671i
$547$	124150.	−	215034.i	0.414928	−	0.718676i	−0.580493	−	0.814265i	$-0.697140\pi$
$547$	124150.	−	215034.i	0.414928	−	0.718676i	0.995421	+	0.0955893i	$0.0304735\pi$
$548$		−	475837.i		−	1.58452i
$549$	50355.7	−	40835.6i	0.167072	−	0.135486i
$550$	−4252.06			−0.0140564
$551$	−212132.	−	122474.i	−0.698719	−	0.403406i
$552$	267659.	−	94888.5i	0.878423	−	0.311412i
$553$	−123229.	−	213439.i	−0.402960	−	0.697947i
$554$	−53471.7	+	30871.9i	−0.174223	+	0.100587i
$555$	−7042.92	−	19866.5i	−0.0228648	−	0.0644963i
$556$	−84578.7	+	146495.i	−0.273597	+	0.473884i
$557$			93331.8i			0.300829i	0.988623	+	0.150414i	$0.0480608\pi$
$557$			93331.8i			0.300829i	−0.988623	+	0.150414i	$0.951939\pi$
$558$	59430.0	−	155145.i	0.190870	−	0.498276i
$559$	−381190.			−1.21988
$560$	75933.5	+	43840.2i	0.242135	+	0.139797i
$561$	−57599.9	−	49160.1i	−0.183019	−	0.156202i
$562$	−74010.0	−	128189.i	−0.234325	−	0.405862i
$563$	293214.	−	169287.i	0.925056	−	0.534081i	0.0398114	−	0.999207i	$-0.487324\pi$
$563$	293214.	−	169287.i	0.925056	−	0.534081i	0.885245	+	0.465126i	$0.153991\pi$
$564$	47510.4	+	8788.33i	0.149359	+	0.0276279i
$565$	140421.	−	243216.i	0.439881	−	0.761895i
$566$		−	83992.5i		−	0.262185i
$567$	−263595.	+	86055.5i	−0.819919	+	0.267678i
$568$	−74262.2			−0.230182
$569$	32183.5	+	18581.1i	0.0994050	+	0.0573915i	0.548878	−	0.835902i	$-0.315055\pi$
$569$	32183.5	+	18581.1i	0.0994050	+	0.0573915i	−0.449473	+	0.893294i	$0.648388\pi$
$570$	−7109.11	+	38432.4i	−0.0218809	+	0.118290i
$571$	−148933.	−	257960.i	−0.456793	−	0.791189i	0.541996	−	0.840381i	$-0.317669\pi$
$571$	−148933.	−	257960.i	−0.456793	−	0.791189i	−0.998789	+	0.0491922i	$0.984335\pi$
$572$	−82020.4	+	47354.5i	−0.250686	+	0.144733i
$573$	−172900.	+	202583.i	−0.526605	+	0.617012i
$574$	−54714.2	+	94767.8i	−0.166064	+	0.287632i
$575$		−	105106.i		−	0.317900i
$576$	−147402.	−	56463.8i	−0.444281	−	0.170187i
$577$	−54793.5			−0.164580			−0.0822900	−	0.996608i	$-0.526223\pi$
$577$	−54793.5			−0.164580			−0.0822900	+	0.996608i	$0.526223\pi$
$578$	9795.81	+	5655.61i	0.0293214	+	0.0169287i
$579$	57336.3	−	20326.4i	0.171030	−	0.0606323i
$580$	62856.8	+	108871.i	0.186851	+	0.323636i
$581$	6235.24	−	3599.92i	0.0184714	−	0.0106645i
$582$	3823.57	+	10785.4i	0.0112882	+	0.0318414i
$583$	34916.2	−	60476.6i	0.102728	−	0.177931i
$584$			386583.i			1.13349i
$585$	−134967.	−	166432.i	−0.394381	−	0.486324i
$586$	−139401.			−0.405948
$587$	323152.	+	186572.i	0.937843	+	0.541464i	0.889284	−	0.457356i	$-0.151204\pi$
$587$	323152.	+	186572.i	0.937843	+	0.541464i	0.0485596	+	0.998820i	$0.484537\pi$
$588$	−60967.3	−	52034.1i	−0.176337	−	0.150499i
$589$	262884.	+	455328.i	0.757763	+	1.31248i
$590$	16407.0	−	9472.57i	0.0471329	−	0.0272122i
$591$	−191737.	−	35466.8i	−0.548947	−	0.101542i
$592$	19435.2	−	33662.8i	0.0554557	−	0.0960521i
$593$			150209.i			0.427155i	0.976926	+	0.213578i	$0.0685117\pi$
$593$			150209.i			0.427155i	−0.976926	+	0.213578i	$0.931488\pi$
$594$	24790.2	+	623.098i	0.0702597	+	0.00176597i
$595$	−143872.			−0.406390
$596$	−482040.	−	278306.i	−1.35703	−	0.783484i
$597$	−91653.3	+	495485.i	−0.257158	+	1.39021i
$598$	122455.	+	212098.i	0.342431	+	0.593108i
$599$	421258.	−	243214.i	1.17407	−	0.677851i	0.219436	−	0.975627i	$-0.429578\pi$
$599$	421258.	−	243214.i	1.17407	−	0.677851i	0.954636	+	0.297776i	$0.0962449\pi$
$600$	27406.2	−	32111.3i	0.0761284	−	0.0891981i
$601$	126705.	−	219460.i	0.350789	−	0.607585i	−0.635599	−	0.772020i	$-0.719247\pi$
$601$	126705.	−	219460.i	0.350789	−	0.607585i	0.986388	+	0.164435i	$0.0525801\pi$
$602$		−	83812.4i		−	0.231268i
$603$	30359.4	+	190817.i	0.0834947	+	0.524786i
$604$	−604426.			−1.65680
$605$	134367.	+	77576.9i	0.367098	+	0.211944i
$606$	45747.1	−	16217.9i	0.124571	−	0.0441622i
$607$	−26509.2	−	45915.3i	−0.0719482	−	0.124618i	0.827807	−	0.561013i	$-0.189588\pi$
$607$	−26509.2	−	45915.3i	−0.0719482	−	0.124618i	−0.899755	+	0.436395i	$0.856255\pi$
$608$	−226494.	+	130766.i	−0.612702	+	0.353744i
$609$	98660.5	+	278299.i	0.266017	+	0.750373i
$610$	−5507.83	+	9539.84i	−0.0148020	+	0.0256379i
$611$			87696.7i			0.234910i
$612$	352801.	−	56131.4i	0.941947	−	0.149866i
$613$	22974.2			0.0611391			0.0305695	−	0.999533i	$-0.490268\pi$
$613$	22974.2			0.0611391			0.0305695	+	0.999533i	$0.490268\pi$
$614$	159670.	+	92185.4i	0.423532	+	0.244526i
$615$	−160989.	−	137400.i	−0.425643	−	0.363276i
$616$	−21912.9	−	37954.3i	−0.0577482	−	0.100023i
$617$	147334.	−	85063.2i	0.387019	−	0.223445i	−0.293849	−	0.955852i	$-0.594936\pi$
$617$	147334.	−	85063.2i	0.387019	−	0.223445i	0.680868	+	0.732407i	$0.261603\pi$
$618$	127580.	+	23599.4i	0.334046	+	0.0617908i
$619$	−119354.	+	206727.i	−0.311498	+	0.539530i	−0.978687	−	0.205359i	$-0.934164\pi$
$619$	−119354.	+	206727.i	−0.311498	+	0.539530i	0.667189	+	0.744888i	$0.267497\pi$
$620$		−	269837.i		−	0.701969i
$621$	−15402.2	+	612783.i	−0.0399393	+	1.58900i
$622$	−47212.5			−0.122033
$623$	−409492.	−	236420.i	−1.05504	−	0.609129i
$624$	71876.1	−	388568.i	0.184593	−	0.997924i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	24690.0	−	14254.8i	0.0630047	−	0.0363758i
$627$	−50945.7	+	59692.0i	−0.129590	+	0.151838i
$628$	−6155.74	+	10662.1i	−0.0156085	+	0.0270347i
$629$			63781.3i			0.161210i
$630$	36593.5	−	29675.3i	0.0921982	−	0.0747676i
$631$	−196615.			−0.493809			−0.246904	−	0.969040i	$-0.579413\pi$
$631$	−196615.			−0.493809			−0.246904	+	0.969040i	$0.579413\pi$
$632$	−189515.	−	109417.i	−0.474472	−	0.273936i
$633$	376039.	−	133311.i	0.938482	−	0.332704i
$634$	−45603.5	−	78987.6i	−0.113454	−	0.196508i
$635$	−112607.	+	65013.8i	−0.279266	+	0.161235i
$636$	110076.	+	310500.i	0.272131	+	0.767621i
$637$	72741.2	−	125991.i	0.179267	−	0.310500i
$638$		−	26406.2i		−	0.0648732i
$639$	57340.1	−	149689.i	0.140429	−	0.366597i
$640$	175086.			0.427456
$641$	508194.	+	293406.i	1.23684	+	0.714090i	0.968447	−	0.249219i	$-0.0801738\pi$
$641$	508194.	+	293406.i	1.23684	+	0.714090i	0.268394	+	0.963309i	$0.413507\pi$
$642$	14943.9	+	12754.3i	0.0362573	+	0.0309447i
$643$	−171870.	−	297688.i	−0.415699	−	0.720012i	0.579802	−	0.814757i	$-0.303130\pi$
$643$	−171870.	−	297688.i	−0.415699	−	0.720012i	−0.995502	+	0.0947452i	$0.969796\pi$
$644$	445775.	−	257368.i	1.07484	−	0.620559i
$645$	159402.	+	29485.6i	0.383154	+	0.0708747i
$646$	59134.2	−	102424.i	0.141701	−	0.245434i
$647$		−	497153.i		−	1.18763i	−0.804601	−	0.593816i	$-0.797621\pi$
$647$		−	497153.i		−	1.18763i	0.804601	−	0.593816i	$-0.202379\pi$
$648$	−164488.	+	183198.i	−0.391728	+	0.436285i
$649$	38039.5			0.0903120
$650$	31530.4	+	18204.1i	0.0746282	+	0.0430866i
$651$	115279.	−	623207.i	0.272012	−	1.47052i
$652$	100559.	+	174173.i	0.236550	+	0.409717i
$653$	−64622.8	+	37310.0i	−0.151551	+	0.0874981i	−0.573858	−	0.818955i	$-0.694554\pi$
$653$	−64622.8	+	37310.0i	−0.151551	+	0.0874981i	0.422307	+	0.906453i	$0.361221\pi$
$654$	54316.2	−	63641.2i	0.126991	−	0.148793i
$655$	−147524.	+	255519.i	−0.343859	+	0.595581i
$656$		−	390312.i		−	0.906994i
$657$	−779230.	−	298492.i	−1.80524	−	0.691517i
$658$	−19281.9			−0.0445346
$659$	551847.	+	318609.i	1.27071	+	0.733647i	0.975122	−	0.221667i	$-0.0711497\pi$
$659$	551847.	+	318609.i	1.27071	+	0.733647i	0.295592	+	0.955314i	$0.404483\pi$
$660$	37961.2	−	13457.7i	0.0871470	−	0.0308947i
$661$	205877.	+	356590.i	0.471201	+	0.816143i	0.999457	−	0.0329413i	$-0.0104874\pi$
$661$	205877.	+	356590.i	0.471201	+	0.816143i	−0.528257	+	0.849085i	$0.677154\pi$
$662$	21149.0	−	12210.4i	0.0482586	−	0.0278621i
$663$	216656.	+	611138.i	0.492883	+	1.39031i
$664$	3196.42	−	5536.36i	0.00724983	−	0.0125571i
$665$			149098.i			0.337154i
$666$	−13155.6	−	16222.6i	−0.0296594	−	0.0365739i
$667$	652730.			1.46717
$668$	57310.5	+	33088.2i	0.128434	+	0.0741516i
$669$	−441057.	−	376431.i	−0.985467	−	0.841072i
$670$	−16414.7	−	28431.2i	−0.0365666	−	0.0633352i
$671$	−19154.8	+	11059.1i	−0.0425435	+	0.0245625i
$672$	310002.	+	57343.1i	0.686476	+	0.126982i
$673$	223336.	−	386830.i	0.493094	−	0.854063i	−0.506875	−	0.862020i	$-0.669199\pi$
$673$	223336.	−	386830.i	0.493094	−	0.854063i	0.999968	+	0.00795662i	$0.00253270\pi$
$674$		−	54715.7i		−	0.120446i
$675$	43565.2	+	80036.5i	0.0956163	+	0.175663i
$676$	397247.			0.869296
$677$	−258957.	−	149509.i	−0.565002	−	0.326204i	0.190148	−	0.981755i	$-0.439103\pi$
$677$	−258957.	−	149509.i	−0.565002	−	0.326204i	−0.755151	+	0.655551i	$0.772436\pi$
$678$	50618.5	−	273648.i	0.110116	−	0.595295i
$679$	21826.5	+	37804.5i	0.0473417	+	0.0819982i
$680$	−110632.	+	63873.2i	−0.239255	+	0.138134i
$681$	92249.1	−	108086.i	0.198915	−	0.233065i
$682$	−28339.7	+	49085.8i	−0.0609294	+	0.105533i
$683$			540348.i			1.15833i	0.815210	+	0.579165i	$0.196621\pi$
$683$			540348.i			1.15833i	−0.815210	+	0.579165i	$0.803379\pi$
$684$	−58170.2	−	365615.i	−0.124334	−	0.781469i
$685$	−367286.			−0.782749
$686$	135878.	+	78448.9i	0.288735	+	0.166701i
$687$	310466.	−	110064.i	0.657810	−	0.233202i
$688$	149472.	+	258893.i	0.315779	+	0.546945i
$689$	−517831.	+	298970.i	−1.09081	+	0.629780i
$690$	−34800.6	−	98164.5i	−0.0730951	−	0.206185i
$691$	184050.	−	318784.i	0.385460	−	0.667637i	−0.606373	−	0.795181i	$-0.707376\pi$
$691$	184050.	−	318784.i	0.385460	−	0.667637i	0.991833	+	0.127544i	$0.0407093\pi$
$692$			411677.i			0.859695i
$693$	93423.5	−	14863.9i	0.194531	−	0.0309504i
$694$	−152227.			−0.316063
$695$	113075.	+	65283.9i	0.234098	+	0.135156i
$696$	199419.	+	170199.i	0.411668	+	0.351349i
$697$	320225.	+	554647.i	0.659159	+	1.14170i
$698$	−199938.	+	115434.i	−0.410379	+	0.236932i
$699$	−45600.2	−	8434.99i	−0.0933281	−	0.0172636i
$700$	38260.3	−	66268.8i	0.0780823	−	0.135242i
$701$			578017.i			1.17626i	0.808765	+	0.588132i	$0.200136\pi$
$701$			578017.i			1.17626i	−0.808765	+	0.588132i	$0.799864\pi$
$702$	−181160.	−	110753.i	−0.367610	−	0.224741i
$703$	66098.0			0.133745
$704$	46635.9	+	26925.3i	0.0940968	+	0.0543268i
$705$	6783.46	−	36671.9i	0.0136481	−	0.0737829i
$706$	22513.0	+	38993.7i	0.0451674	+	0.0782322i
$707$	160350.	−	92578.3i	0.320797	−	0.185212i
$708$	−116496.	+	136497.i	−0.232405	+	0.272305i
$709$	−280670.	+	486135.i	−0.558346	+	0.967084i	0.439288	+	0.898346i	$0.355231\pi$
$709$	−280670.	+	486135.i	−0.558346	+	0.967084i	−0.997635	+	0.0687381i	$0.978103\pi$
$710$			27235.9i			0.0540287i
$711$	366880.	−	297520.i	0.725747	−	0.588540i
$712$	−419843.			−0.828184
$713$	−1.21334e6	−	700523.i	−2.38673	−	1.37798i
$714$	−134371.	+	47636.2i	−0.263578	+	0.0934417i
$715$	36551.6	+	63309.2i	0.0714981	+	0.123838i
$716$	−353278.	+	203965.i	−0.689114	+	0.397860i
$717$	−79515.4	−	224295.i	−0.154672	−	0.436296i
$718$	−19258.8	+	33357.2i	−0.0373577	+	0.0647054i
$719$		−	578659.i		−	1.11935i	−0.828713	−	0.559674i	$-0.810926\pi$
$719$		−	578659.i		−	1.11935i	0.828713	−	0.559674i	$-0.189074\pi$
$720$	−60112.6	+	156927.i	−0.115958	+	0.302714i
$721$	494945.			0.952109
$722$	32785.4	+	18928.7i	0.0628936	+	0.0363116i
$723$	87716.7	+	74864.0i	0.167805	+	0.143218i
$724$	319777.	+	553870.i	0.610056	+	1.05665i
$725$	84034.6	−	48517.4i	0.159876	−	0.0923042i
$726$	151179.	+	27964.7i	0.286826	+	0.0530563i
$727$	178554.	−	309265.i	0.337833	−	0.585144i	−0.646192	−	0.763175i	$-0.723639\pi$
$727$	178554.	−	309265.i	0.337833	−	0.585144i	0.984025	+	0.178031i	$0.0569728\pi$
$728$			375258.i			0.708056i
$729$	−242263.	−	473010.i	−0.455861	−	0.890051i
$730$	141780.			0.266054
$731$	−424810.	−	245264.i	−0.794987	−	0.458986i
$732$	18978.9	−	102602.i	0.0354200	−	0.191484i
$733$	80064.6	+	138676.i	0.149016	+	0.258103i	0.930864	−	0.365366i	$-0.119056\pi$
$733$	80064.6	+	138676.i	0.149016	+	0.258103i	−0.781848	+	0.623469i	$0.785723\pi$
$734$	146436.	−	84545.0i	0.271805	−	0.156926i
$735$	−40163.7	+	47059.0i	−0.0743462	+	0.0871099i
$736$	348461.	−	603552.i	0.643278	−	1.11419i
$737$		−	65917.5i		−	0.121357i
$738$	−195851.	−	75022.7i	−0.359594	−	0.137746i
$739$	251930.			0.461307			0.230654	−	0.973036i	$-0.425914\pi$
$739$	251930.			0.461307			0.230654	+	0.973036i	$0.425914\pi$
$740$	−29378.3	−	16961.5i	−0.0536491	−	0.0309743i
$741$	633335.	−	224525.i	1.15345	−	0.408911i
$742$	−65734.5	−	113856.i	−0.119395	−	0.206798i
$743$	−457432.	+	264099.i	−0.828608	+	0.478397i	−0.853376	−	0.521296i	$-0.825449\pi$
$743$	−457432.	+	264099.i	−0.828608	+	0.478397i	0.0247676	+	0.999693i	$0.492115\pi$
$744$	−188033.	−	530398.i	−0.339694	−	0.958200i
$745$	−214817.	+	372074.i	−0.387040	+	0.670373i
$746$		−	46583.6i		−	0.0837058i
$747$	8691.52	+	10717.8i	0.0155759	+	0.0192072i
$748$	−121875.			−0.217826
$749$	64906.5	+	37473.8i	0.115698	+	0.0667981i
$750$	−11776.9	−	10051.3i	−0.0209367	−	0.0178690i
$751$	−480235.	−	831791.i	−0.851479	−	1.47480i	−0.879873	−	0.475208i	$-0.842373\pi$
$751$	−480235.	−	831791.i	−0.851479	−	1.47480i	0.0283945	−	0.999597i	$-0.490961\pi$
$752$	59561.0	−	34387.6i	0.105324	−	0.0608087i
$753$	−646234.	−	119538.i	−1.13972	−	0.210823i
$754$	−113052.	+	195811.i	−0.198854	+	0.344425i
$755$			466540.i			0.818455i
$756$	−232775.	+	380751.i	−0.407279	+	0.666189i
$757$	−487728.			−0.851111			−0.425555	−	0.904932i	$-0.639921\pi$
$757$	−487728.			−0.851111			−0.425555	+	0.904932i	$0.639921\pi$
$758$	−274017.	−	158204.i	−0.476914	−	0.275346i
$759$	38037.4	−	205633.i	0.0660279	−	0.356952i
$760$	66193.2	+	114650.i	0.114600	+	0.198494i
$761$	−726268.	+	419311.i	−1.25409	+	0.724047i	−0.971919	−	0.235317i	$-0.924387\pi$
$761$	−726268.	+	419311.i	−1.25409	+	0.724047i	−0.282168	+	0.959365i	$0.591054\pi$
$762$	−83644.6	+	98004.7i	−0.144055	+	0.168786i
$763$	159588.	−	276415.i	0.274127	−	0.474802i
$764$			428642.i			0.734358i
$765$	−43326.2	−	272317.i	−0.0740335	−	0.465320i
$766$	−109345.			−0.186355
$767$	−282076.	−	162857.i	−0.479485	−	0.276831i
$768$	−100963.	+	35792.8i	−0.171175	+	0.0606839i
$769$	112322.	+	194548.i	0.189939	+	0.328984i	0.945230	−	0.326406i	$-0.105838\pi$
$769$	112322.	+	194548.i	0.189939	+	0.328984i	−0.755291	+	0.655390i	$0.772504\pi$
$770$	−13919.8	+	8036.61i	−0.0234775	+	0.0135547i
$771$	274495.	+	774289.i	0.461771	+	1.30255i
$772$	48952.4	−	84788.1i	0.0821371	−	0.142266i
$773$		−	734461.i		−	1.22916i	−0.788853	−	0.614582i	$-0.789325\pi$
$773$		−	734461.i		−	1.22916i	0.788853	−	0.614582i	$-0.210675\pi$
$774$	158638.	−	25239.6i	0.264804	−	0.0421309i
$775$	−208279.			−0.346771
$776$	33567.2	+	19380.0i	0.0557432	+	0.0321833i
$777$	−60604.8	−	51724.7i	−0.100384	−	0.0856754i
$778$	153813.	+	266412.i	0.254118	+	0.440145i
$779$	574793.	−	331857.i	0.947188	−	0.546860i
$780$	−339111.	−	62727.8i	−0.557382	−	0.103103i
$781$	−27343.1	+	47359.7i	−0.0448277	+	0.0776438i
$782$			315157.i			0.515364i
$783$	−497045.	+	270550.i	−0.810722	+	0.441289i
$784$	−114093.			−0.185621
$785$	8229.74	+	4751.44i	0.0133551	+	0.00771056i
$786$	−53179.0	+	287490.i	−0.0860786	+	0.465348i
$787$	142394.	+	246634.i	0.229902	+	0.398202i	0.957779	−	0.287506i	$-0.0928260\pi$
$787$	142394.	+	246634.i	0.229902	+	0.398202i	−0.727877	+	0.685708i	$0.759493\pi$
$788$	−271774.	+	156909.i	−0.437679	+	0.252694i
$789$	−255560.	+	299435.i	−0.410525	+	0.481004i
$790$	−40128.9	+	69505.2i	−0.0642988	+	0.111369i
$791$		−	1.06161e6i		−	1.69673i
$792$	65239.7	−	52905.8i	0.104007	−	0.0843437i
$793$	189386.			0.301163
$794$	−270553.	−	156204.i	−0.429153	−	0.247771i
$795$	239666.	−	84964.7i	0.379203	−	0.134432i
$796$	405484.	+	702318.i	0.639952	+	1.10843i
$797$	−64271.3	+	37107.0i	−0.101181	+	0.0584170i	−0.549737	−	0.835338i	$-0.685272\pi$
$797$	−64271.3	+	37107.0i	−0.101181	+	0.0584170i	0.448555	+	0.893755i	$0.351939\pi$
$798$	49366.5	+	139252.i	0.0775222	+	0.218673i
$799$	−56425.5	+	97731.8i	−0.0883856	+	0.153088i
$800$		−	103604.i		−	0.161882i
$801$	324173.	−	846271.i	0.505257	−	1.31900i
$802$	112999.			0.175682
$803$	246538.	+	142339.i	0.382342	+	0.220745i
$804$	236531.	+	201873.i	0.365911	+	0.312296i
$805$	−198655.	−	344081.i	−0.306555	−	0.530969i
$806$	420297.	−	242659.i	0.646973	−	0.373530i
$807$	902753.	+	166989.i	1.38619	+	0.256413i
$808$	82201.7	−	142377.i	0.125909	−	0.218081i
$809$			1.01875e6i			1.55657i	0.627911	+	0.778285i	$0.283910\pi$
$809$			1.01875e6i			1.55657i	−0.627911	+	0.778285i	$0.716090\pi$
$810$	67188.3	+	60326.5i	0.102406	+	0.0919471i
$811$	63192.0			0.0960772			0.0480386	−	0.998845i	$-0.484703\pi$
$811$	63192.0			0.0960772			0.0480386	+	0.998845i	$0.484703\pi$
$812$	411544.	+	237605.i	0.624173	+	0.360366i
$813$	−184216.	+	995888.i	−0.278706	+	1.50671i
$814$	3562.78	+	6170.92i	0.00537701	+	0.00931325i
$815$	134439.	−	77618.3i	0.202400	−	0.116855i
$816$	330112.	−	386785.i	0.495770	−	0.580884i
$817$	−254173.	+	440240.i	−0.380789	+	0.659547i
$818$			16894.4i			0.0252486i
$819$	−756403.	−	289748.i	−1.12768	−	0.431970i
$820$	−340634.			−0.506594
$821$	308222.	+	177952.i	0.457275	+	0.264008i	0.710898	−	0.703295i	$-0.248289\pi$
$821$	308222.	+	177952.i	0.457275	+	0.264008i	−0.253623	+	0.967303i	$0.581622\pi$
$822$	−343030.	+	121609.i	−0.507679	+	0.179978i
$823$	−48452.4	−	83922.0i	−0.0715345	−	0.123901i	0.828039	−	0.560670i	$-0.189456\pi$
$823$	−48452.4	−	83922.0i	−0.0715345	−	0.123901i	−0.899574	+	0.436768i	$0.856123\pi$
$824$	380592.	−	219735.i	0.560538	−	0.323627i
$825$	−10387.7	−	29301.2i	−0.0152619	−	0.0430505i
$826$	35807.3	−	62020.1i	0.0524821	−	0.0909017i
$827$		−	1.06487e6i		−	1.55699i	−0.627650	−	0.778496i	$-0.715983\pi$
$827$		−	1.06487e6i		−	1.55699i	0.627650	−	0.778496i	$-0.284017\pi$
$828$	621381.	+	766244.i	0.906353	+	1.11765i
$829$	−733212.			−1.06689			−0.533446	−	0.845834i	$-0.679103\pi$
$829$	−733212.			−1.06689			−0.533446	+	0.845834i	$0.679103\pi$
$830$	−2030.47	−	1172.29i	−0.00294742	−	0.00170169i
$831$	−343370.	−	293058.i	−0.497234	−	0.424377i
$832$	−230547.	−	399320.i	−0.333053	−	0.576865i
$833$	162130.	−	93605.7i	0.233654	−	0.134900i
$834$	127223.	+	23533.4i	0.182909	+	0.0338339i
$835$	25539.9	−	44236.4i	0.0366307	−	0.0634463i
$836$			126301.i			0.180716i
$837$	1.21430e6	+	30521.4i	1.73331	+	0.0435665i
$838$	129863.			0.184926
$839$	435879.	+	251655.i	0.619216	+	0.357505i	0.776564	−	0.630039i	$-0.216961\pi$
$839$	435879.	+	251655.i	0.619216	+	0.357505i	−0.157347	+	0.987543i	$0.550294\pi$
$840$	29026.8	−	156921.i	0.0411377	−	0.222394i
$841$	−52336.4	−	90649.4i	−0.0739967	−	0.128166i
$842$	−2779.52	+	1604.76i	−0.00392054	+	0.00226352i
$843$	702556.	−	823170.i	0.988611	−	1.15834i
$844$	321054.	−	556082.i	0.450706	−	0.780645i
$845$		−	306624.i		−	0.429430i
$846$	−5806.62	−	36496.2i	−0.00811303	−	0.0509925i
$847$	586498.			0.817522
$848$	406103.	+	234464.i	0.564735	+	0.326050i
$849$	578798.	−	205191.i	0.802993	−	0.284671i
$850$	23425.6	+	40574.4i	0.0324230	+	0.0561583i
$851$	−152538.	+	88067.7i	−0.210629	+	0.121607i
$852$	−86201.4	−	243155.i	−0.118750	−	0.334968i
$853$	247436.	−	428571.i	0.340067	−	0.589013i	−0.644378	−	0.764707i	$-0.722884\pi$
$853$	247436.	−	428571.i	0.340067	−	0.589013i	0.984445	+	0.175694i	$0.0562169\pi$
$854$			41640.4i			0.0570951i
$855$	−282208.	+	44900.0i	−0.386044	+	0.0614205i
$856$	66547.1			0.0908200
$857$	318771.	+	184043.i	0.434028	+	0.250586i	0.701061	−	0.713101i	$-0.252710\pi$
$857$	318771.	+	184043.i	0.434028	+	0.250586i	−0.267033	+	0.963687i	$0.586043\pi$
$858$	55099.5	+	47026.1i	0.0748468	+	0.0638799i
$859$	253556.	+	439172.i	0.343627	+	0.595180i	0.985103	−	0.171963i	$-0.0550109\pi$
$859$	253556.	+	439172.i	0.343627	+	0.595180i	−0.641476	+	0.767143i	$0.721678\pi$
$860$	225942.	−	130448.i	0.305492	−	0.176376i
$861$	−786717.	−	145525.i	−1.06124	−	0.196304i
$862$	183918.	−	318554.i	0.247519	−	0.428715i
$863$			968158.i			1.29994i	0.759958	+	0.649972i	$0.225219\pi$
$863$			968158.i			1.29994i	−0.759958	+	0.649972i	$0.774781\pi$
$864$	−15182.2	+	604030.i	−0.0203380	+	0.809154i
$865$	317762.			0.424688
$866$	−31.3140	−	18.0792i	−4.17545e−5	−	2.41070e-5i
$867$	−15042.3	+	81320.1i	−0.0200114	+	0.108183i
$868$	−510006.	−	883356.i	−0.676917	−	1.17246i
$869$	−139558.	+	80573.8i	−0.184806	+	0.106698i
$870$	62420.9	−	73137.3i	0.0824691	−	0.0966274i
$871$	−282209.	+	488801.i	−0.371993	+	0.644311i
$872$		−	283402.i		−	0.372708i
$873$	−64982.4	+	52697.1i	−0.0852642	+	0.0691445i
$874$	326605.			0.427562
$875$	−51151.1	−	29532.1i	−0.0668095	−	0.0385725i
$876$	−1.26578e6	+	448734.i	−1.64949	+	0.584764i
$877$	−104983.	−	181836.i	−0.136496	−	0.236418i	0.789672	−	0.613529i	$-0.210251\pi$
$877$	−104983.	−	181836.i	−0.136496	−	0.236418i	−0.926168	+	0.377111i	$0.876917\pi$
$878$	−25448.6	+	14692.7i	−0.0330122	+	0.0190596i
$879$	−340552.	−	960621.i	−0.440764	−	1.24330i
$880$	28665.2	−	49649.5i	0.0370160	−	0.0641136i
$881$		−	253953.i		−	0.327192i	−0.986527	−	0.163596i	$-0.947691\pi$
$881$		−	253953.i		−	0.327192i	0.986527	−	0.163596i	$-0.0523093\pi$
$882$	−21930.0	+	57249.4i	−0.0281904	+	0.0735926i
$883$	−396178.			−0.508123			−0.254062	−	0.967188i	$-0.581767\pi$
$883$	−396178.			−0.508123			−0.254062	+	0.967188i	$0.581767\pi$
$884$	903741.	+	521775.i	1.15648	+	0.667696i
$885$	105358.	+	89920.4i	0.134518	+	0.114808i
$886$	4275.30	+	7405.05i	0.00544628	+	0.00943323i
$887$	−124411.	+	71828.5i	−0.158128	+	0.0912955i	−0.576976	−	0.816761i	$-0.695767\pi$
$887$	−124411.	+	71828.5i	−0.158128	+	0.0912955i	0.418848	+	0.908056i	$0.362434\pi$
$888$	−69566.1	−	12868.1i	−0.0882210	−	0.0163188i
$889$	−245759.	+	425667.i	−0.310961	+	0.538600i
$890$			153978.i			0.194393i
$891$	56267.9	+	172353.i	0.0708769	+	0.217102i
$892$	−933225.			−1.17289
$893$	101282.	+	58475.0i	0.127007	+	0.0733275i
$894$	−77436.5	+	418628.i	−0.0968882	+	0.523785i
$895$	157435.	+	272686.i	0.196542	+	0.340421i
$896$	573174.	−	330922.i	0.713954	−	0.412202i
$897$	−1.16243e6	+	1.36199e6i	−1.44471	+	1.69274i
$898$	134663.	−	233243.i	0.166992	−	0.289239i
$899$		−	1.29346e6i		−	1.60042i
$900$	136953.	+	52461.5i	0.169078	+	0.0647673i
$901$	−769448.			−0.947828
$902$	61964.4	+	35775.2i	0.0761605	+	0.0439713i
$903$	577558.	−	204751.i	0.708304	−	0.251103i
$904$	−471310.	−	816334.i	−0.576727	−	0.998920i
$905$	427516.	−	246827.i	0.521982	−	0.301367i
$906$	154472.	+	435730.i	0.188188	+	0.530837i
$907$	−79023.9	+	136873.i	−0.0960603	+	0.166381i	−0.910051	−	0.414497i	$-0.863958\pi$
$907$	−79023.9	+	136873.i	−0.0960603	+	0.166381i	0.813990	+	0.580878i	$0.197291\pi$
$908$		−	228698.i		−	0.277390i
$909$	223518.	+	275627.i	0.270511	+	0.333575i
$910$	137627.			0.166196
$911$	423337.	+	244414.i	0.510093	+	0.294503i	0.732872	−	0.680366i	$-0.238179\pi$
$911$	423337.	+	244414.i	0.510093	+	0.294503i	−0.222779	+	0.974869i	$0.571513\pi$
$912$	−400834.	−	342102.i	−0.481920	−	0.411307i
$913$	−2353.82	−	4076.94i	−0.00282379	−	0.00489095i
$914$	−142029.	+	82000.6i	−0.170014	+	0.0981578i
$915$	−79195.2	−	14649.3i	−0.0945925	−	0.0174974i
$916$	265069.	−	459113.i	0.315913	−	0.547178i
$917$			1.11531e6i			1.32635i
$918$	−130629.	−	239988.i	−0.155008	−	0.284776i
$919$	193983.			0.229685			0.114843	−	0.993384i	$-0.463364\pi$
$919$	193983.			0.229685			0.114843	+	0.993384i	$0.463364\pi$
$920$	−305515.	−	176389.i	−0.360958	−	0.208399i
$921$	−245187.	+	1.32550e6i	−0.289054	+	1.56265i
$922$	−80785.8	−	139925.i	−0.0950327	−	0.164601i
$923$	405517.	−	234125.i	0.475999	−	0.274818i
$924$	98836.7	−	115805.i	0.115764	−	0.135639i
$925$	−13092.1	+	22676.3i	−0.0153013	+	0.0265026i
$926$		−	256043.i		−	0.298601i
$927$	149050.	+	936817.i	0.173449	+	1.09017i
$928$	643407.			0.747119
$929$	−293388.	−	169388.i	−0.339947	−	0.196269i	0.320301	−	0.947316i	$-0.396216\pi$
$929$	−293388.	−	169388.i	−0.339947	−	0.196269i	−0.660249	+	0.751047i	$0.729549\pi$
$930$	−194525.	+	68961.5i	−0.224910	+	0.0797335i
$931$	−97005.7	−	168019.i	−0.111917	−	0.193847i
$932$	−64635.4	+	37317.3i	−0.0744113	+	0.0429614i
$933$	−115339.	−	325345.i	−0.132499	−	0.373749i
$934$	−240003.	+	415698.i	−0.275121	+	0.476523i
$935$			94071.6i			0.107606i
$936$	−710277.	+	113007.i	−0.810730	+	0.128989i
$937$	576017.			0.656079			0.328039	−	0.944664i	$-0.393612\pi$
$937$	576017.			0.656079			0.328039	+	0.944664i	$0.393612\pi$
$938$	−107473.	−	62049.4i	−0.122150	−	0.0705232i
$939$	158548.	+	135317.i	0.179816	+	0.153469i
$940$	−30010.8	−	51980.1i	−0.0339642	−	0.0588277i
$941$	−38906.8	+	22462.8i	−0.0439386	+	0.0253679i	−0.521808	−	0.853063i	$-0.674742\pi$
$941$	−38906.8	+	22462.8i	−0.0439386	+	0.0253679i	0.477870	+	0.878431i	$0.341409\pi$
$942$	9259.46	+	1712.79i	0.0104348	+	0.00193020i
$943$	−884319.	+	1.53169e6i	−0.994456	+	1.72245i
$944$			255437.i			0.286642i
$945$	293891.	+	179672.i	0.329096	+	0.201195i
$946$	−54801.2			−0.0612362
$947$	−624982.	−	360833.i	−0.696895	−	0.402353i	0.109295	−	0.994009i	$-0.465141\pi$
$947$	−624982.	−	360833.i	−0.696895	−	0.402353i	−0.806190	+	0.591657i	$0.798474\pi$
$948$	138276.	−	747532.i	0.153862	−	0.831789i
$949$	−1.21877e6	−	2.11098e6i	−1.35329	−	2.34397i
$950$	42048.1	−	24276.5i	0.0465907	−	0.0268992i
$951$	432901.	−	507222.i	0.478661	−	0.560837i
$952$	−241447.	+	418199.i	−0.266409	+	0.461433i
$953$		−	1.51930e6i		−	1.67286i	−0.548077	−	0.836428i	$-0.684640\pi$
$953$		−	1.51930e6i		−	1.67286i	0.548077	−	0.836428i	$-0.315360\pi$
$954$	195707.	−	158707.i	0.215035	−	0.174381i
$955$	330857.			0.362772
$956$	−331684.	−	191498.i	−0.362918	−	0.209531i
$957$	181967.	−	64509.7i	0.198687	−	0.0704370i
$958$	94802.1	+	164202.i	0.103297	+	0.178915i
$959$	−1.20237e6	+	694189.i	−1.30738	+	0.754815i
$960$	65519.6	+	184816.i	0.0710933	+	0.200538i
$961$	−926410.	+	1.60459e6i	−1.00313	+	1.73747i
$962$		−	61012.6i		−	0.0659280i
$963$	−51383.1	+	134138.i	−0.0554073	+	0.144644i
$964$	185598.			0.199719
$965$	−65445.5	−	37785.0i	−0.0702790	−	0.0405756i
$966$	−299462.	−	255583.i	−0.320913	−	0.273891i
$967$	−798261.	−	1.38263e6i	−0.853673	−	1.47861i	−0.877870	−	0.478898i	$-0.841036\pi$
$967$	−798261.	−	1.38263e6i	−0.853673	−	1.47861i	0.0241969	−	0.999707i	$-0.492297\pi$
$968$	450991.	−	260380.i	0.481302	−	0.277880i
$969$	850271.	+	157281.i	0.905545	+	0.167505i
$970$	7107.68	−	12310.9i	0.00755413	−	0.0130841i
$971$			1.11408e6i			1.18162i	0.806809	+	0.590812i	$0.201193\pi$
$971$			1.11408e6i			1.18162i	−0.806809	+	0.590812i	$0.798807\pi$
$972$	−790773.	−	325928.i	−0.836988	−	0.344976i
$973$	493560.			0.521332
$974$	223250.	+	128893.i	0.235328	+	0.135867i
$975$	−48417.8	+	261751.i	−0.0509326	+	0.275346i
$976$	−74261.9	−	128625.i	−0.0779591	−	0.135029i
$977$	104336.	−	60238.7i	0.109307	−	0.0631083i	−0.444350	−	0.895853i	$-0.646565\pi$
$977$	104336.	−	60238.7i	0.109307	−	0.0631083i	0.553657	+	0.832745i	$0.313232\pi$
$978$	99861.1	−	117005.i	0.104404	−	0.122329i
$979$	−154585.	+	267749.i	−0.161288	+	0.279359i
$980$			99571.3i			0.103677i
$981$	571249.	+	218823.i	0.593591	+	0.227381i
$982$	−352124.			−0.365152
$983$	−56127.0	−	32404.9i	−0.0580851	−	0.0335354i	0.470676	−	0.882306i	$-0.344010\pi$
$983$	−56127.0	−	32404.9i	−0.0580851	−	0.0335354i	−0.528761	+	0.848771i	$0.677343\pi$
$984$	−669559.	+	237367.i	−0.691510	+	0.245149i
$985$	121114.	+	209775.i	0.124831	+	0.216213i
$986$	−251976.	+	145479.i	−0.259182	+	0.149639i
$987$	−47105.1	−	132873.i	−0.0483541	−	0.136396i
$988$	540727.	−	936567.i	0.553942	−	0.959456i
$989$		−	1.35462e6i		−	1.38492i
$990$	−19403.3	−	23926.8i	−0.0197973	−	0.0244126i
$991$	551476.			0.561539			0.280769	−	0.959775i	$-0.409410\pi$
$991$	551476.			0.561539			0.280769	+	0.959775i	$0.409410\pi$
$992$	−1.19601e6	−	690517.i	−1.21538	−	0.701700i
$993$	135809.	+	115910.i	0.137731	+	0.117550i
$994$	51477.2	+	89161.1i	0.0521005	+	0.0902408i
$995$	542100.	−	312981.i	0.547562	−	0.316135i
$996$	21837.9	+	4039.50i	0.0220136	+	0.00407201i
$997$	−345429.	+	598300.i	−0.347511	+	0.601906i	−0.985807	−	0.167885i	$-0.946306\pi$
$997$	−345429.	+	598300.i	−0.347511	+	0.601906i	0.638296	+	0.769791i	$0.279640\pi$
$998$			35098.1i			0.0352389i
$999$	79652.2	−	130288.i	0.0798118	−	0.130549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.8	✓	32
3.2	odd	2		135.5.i.a.116.9		32
9.2	odd	6		405.5.c.b.161.14		32
9.4	even	3		135.5.i.a.71.9		32
9.5	odd	6	inner	45.5.i.a.41.8	yes	32
9.7	even	3		405.5.c.b.161.19		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.8	✓	32	1.1	even	1	trivial
45.5.i.a.41.8	yes	32	9.5	odd	6	inner
135.5.i.a.71.9		32	9.4	even	3
135.5.i.a.116.9		32	3.2	odd	2
405.5.c.b.161.14		32	9.2	odd	6
405.5.c.b.161.19		32	9.7	even	3

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+(-1.06605 - 0.615486i) q^{2} +(1.63702 - 8.84987i) q^{3} +(-7.24235 - 12.5441i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-7.19213 + 8.42687i) q^{6} +(-21.1314 + 36.6007i) q^{7} +37.5258i q^{8} +(-75.6403 - 28.9748i) q^{9} +13.7627 q^{10} +(23.9316 + 13.8169i) q^{11} +(-122.870 + 43.5589i) q^{12} +(-118.307 - 204.914i) q^{13} +(45.0545 - 26.0122i) q^{14} +(33.6219 + 94.8397i) q^{15} +(-92.7810 + 160.701i) q^{16} -304.483i q^{17} +(62.8030 + 77.4443i) q^{18} -315.542 q^{19} +(140.248 + 80.9720i) q^{20} +(289.319 + 246.927i) q^{21} +(-17.0082 - 29.4591i) q^{22} +(728.193 - 420.423i) q^{23} +(332.099 + 61.4306i) q^{24} +(62.5000 - 108.253i) q^{25} +291.266i q^{26} +(-380.248 + 621.974i) q^{27} +612.165 q^{28} +(672.277 + 388.139i) q^{29} +(22.5298 - 121.798i) q^{30} +(-833.118 - 1443.00i) q^{31} +(717.792 - 414.418i) q^{32} +(161.454 - 189.173i) q^{33} +(-187.405 + 324.595i) q^{34} -472.513i q^{35} +(184.350 + 1158.69i) q^{36} -209.474 q^{37} +(336.385 + 194.212i) q^{38} +(-2007.13 + 711.554i) q^{39} +(-209.776 - 363.342i) q^{40} +(-1821.60 + 1051.70i) q^{41} +(-156.450 - 441.309i) q^{42} +(805.510 - 1395.19i) q^{43} -400.267i q^{44} +(894.359 - 142.295i) q^{45} -1035.06 q^{46} +(-320.976 - 185.316i) q^{47} +(1270.30 + 1084.17i) q^{48} +(307.425 + 532.476i) q^{49} +(-133.257 + 76.9358i) q^{50} +(-2694.63 - 498.445i) q^{51} +(-1713.64 + 2968.12i) q^{52} -2527.06i q^{53} +(788.182 - 429.020i) q^{54} -308.955 q^{55} +(-1373.47 - 792.975i) q^{56} +(-516.550 + 2792.51i) q^{57} +(-477.789 - 827.554i) q^{58} +(1192.13 - 688.279i) q^{59} +(946.179 - 1108.62i) q^{60} +(-400.200 + 693.167i) q^{61} +2051.09i q^{62} +(2658.89 - 2156.21i) q^{63} +1948.72 q^{64} +(2291.01 + 1322.71i) q^{65} +(-288.552 + 102.295i) q^{66} +(-1192.70 - 2065.81i) q^{67} +(-3819.47 + 2205.17i) q^{68} +(-2528.62 - 7132.66i) q^{69} +(-290.825 + 503.724i) q^{70} +1978.96i q^{71} +(1087.31 - 2838.47i) q^{72} +10301.8 q^{73} +(223.311 + 128.929i) q^{74} +(-855.712 - 730.330i) q^{75} +(2285.27 + 3958.20i) q^{76} +(-1011.42 + 583.942i) q^{77} +(2577.66 + 476.808i) q^{78} +(-2915.77 + 5050.26i) q^{79} -2074.65i q^{80} +(4881.92 + 4383.33i) q^{81} +2589.23 q^{82} +(-147.535 - 85.1792i) q^{83} +(1002.13 - 5417.58i) q^{84} +(1702.11 + 2948.14i) q^{85} +(-1717.43 + 991.561i) q^{86} +(4535.51 - 5314.17i) q^{87} +(-518.491 + 898.052i) q^{88} +11188.1i q^{89} +(-1041.01 - 398.772i) q^{90} +9999.99 q^{91} +(-10547.7 - 6089.70i) q^{92} +(-14134.2 + 5010.76i) q^{93} +(228.119 + 395.113i) q^{94} +(3055.23 - 1763.94i) q^{95} +(-2492.50 - 7030.78i) q^{96} +(516.445 - 894.509i) q^{97} -756.864i q^{98} +(-1409.85 - 1738.53i) 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

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