LMFDB - Embedded newform 45.5.h.a.14.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); 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([5, 3])) N = Newforms(chi, 5, names="a")

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

Newform invariants

comment:select newform

sage: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:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.11
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.316502 - 0.548197i) q^{2} +(-4.90909 + 7.54326i) q^{3} +(7.79965 - 13.5094i) q^{4} +(-24.0216 - 6.92551i) q^{5} +(5.68893 + 0.303692i) q^{6} +(73.2178 - 42.2723i) q^{7} -20.0025 q^{8} +(-32.8017 - 74.0611i) q^{9} +(3.80633 + 15.3605i) q^{10} +(148.474 - 85.7213i) q^{11} +(63.6157 + 125.154i) q^{12} +(-127.218 - 73.4493i) q^{13} +(-46.3471 - 26.7585i) q^{14} +(170.165 - 147.203i) q^{15} +(-118.464 - 205.185i) q^{16} -273.459 q^{17} +(-30.2183 + 41.4222i) q^{18} +229.656 q^{19} +(-280.920 + 270.501i) q^{20} +(-40.5615 + 759.820i) q^{21} +(-93.9843 - 54.2618i) q^{22} +(-194.631 + 337.110i) q^{23} +(98.1939 - 150.884i) q^{24} +(529.075 + 332.723i) q^{25} +92.9873i q^{26} +(719.689 + 116.141i) q^{27} -1318.84i q^{28} +(306.632 - 177.034i) q^{29} +(-134.554 - 46.6939i) q^{30} +(-310.913 + 538.517i) q^{31} +(-235.008 + 407.045i) q^{32} +(-82.2521 + 1540.79i) q^{33} +(86.5501 + 149.909i) q^{34} +(-2051.57 + 508.379i) q^{35} +(-1256.36 - 134.520i) q^{36} -730.131i q^{37} +(-72.6865 - 125.897i) q^{38} +(1178.57 - 599.069i) q^{39} +(480.491 + 138.527i) q^{40} +(-498.910 - 288.046i) q^{41} +(429.369 - 218.249i) q^{42} +(783.565 - 452.392i) q^{43} -2674.39i q^{44} +(275.038 + 2006.24i) q^{45} +246.404 q^{46} +(-396.417 - 686.614i) q^{47} +(2129.31 + 113.669i) q^{48} +(2373.40 - 4110.85i) q^{49} +(14.9450 - 395.345i) q^{50} +(1342.43 - 2062.77i) q^{51} +(-1984.51 + 1145.76i) q^{52} +3467.44 q^{53} +(-164.115 - 431.290i) q^{54} +(-4160.24 + 1030.91i) q^{55} +(-1464.54 + 845.551i) q^{56} +(-1127.40 + 1732.36i) q^{57} +(-194.099 - 112.063i) q^{58} +(2436.74 + 1406.85i) q^{59} +(-661.400 - 3446.96i) q^{60} +(2660.83 + 4608.69i) q^{61} +393.618 q^{62} +(-5532.41 - 4035.99i) q^{63} -3493.32 q^{64} +(2547.30 + 2645.42i) q^{65} +(870.688 - 442.572i) q^{66} +(-147.934 - 85.4097i) q^{67} +(-2132.88 + 3694.26i) q^{68} +(-1587.45 - 3123.05i) q^{69} +(928.016 + 963.760i) q^{70} +2798.11i q^{71} +(656.114 + 1481.40i) q^{72} +5866.22i q^{73} +(-400.255 + 231.088i) q^{74} +(-5107.10 + 2357.58i) q^{75} +(1791.24 - 3102.52i) q^{76} +(7247.28 - 12552.7i) q^{77} +(-701.428 - 456.483i) q^{78} +(1466.67 + 2540.34i) q^{79} +(1424.68 + 5749.29i) q^{80} +(-4409.10 + 4858.66i) q^{81} +364.668i q^{82} +(-3444.66 - 5966.32i) q^{83} +(9948.35 + 6474.30i) q^{84} +(6568.92 + 1893.84i) q^{85} +(-495.999 - 286.365i) q^{86} +(-169.869 + 3182.08i) q^{87} +(-2969.84 + 1714.64i) q^{88} -1031.26i q^{89} +(1012.76 - 785.751i) q^{90} -12419.5 q^{91} +(3036.10 + 5258.68i) q^{92} +(-2535.88 - 4988.93i) q^{93} +(-250.933 + 434.629i) q^{94} +(-5516.71 - 1590.48i) q^{95} +(-1916.77 - 3770.94i) q^{96} +(-12170.7 + 7026.75i) q^{97} -3004.74 q^{98} +(-11218.8 - 8184.32i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.316502	−	0.548197i	−0.0791254	−	0.137049i	0.823747	−	0.566957i	$-0.191879\pi$
$2$	−0.316502	−	0.548197i	−0.0791254	−	0.137049i	−0.902873	+	0.429908i	$0.858546\pi$
$3$	−4.90909	+	7.54326i	−0.545454	+	0.838140i
$3$	−4.90909	+	7.54326i	−0.545454	+	0.838140i
$4$	7.79965	−	13.5094i	0.487478	−	0.844337i
$5$	−24.0216	−	6.92551i	−0.960864	−	0.277020i
$5$	−24.0216	−	6.92551i	−0.960864	−	0.277020i
$6$	5.68893	+	0.303692i	0.158026	+	0.00843590i
$7$	73.2178	−	42.2723i	1.49424	−	0.862701i	0.494264	−	0.869312i	$-0.335438\pi$
$7$	73.2178	−	42.2723i	1.49424	−	0.862701i	0.999978	+	0.00661118i	$0.00210442\pi$
$8$	−20.0025			−0.312538
$9$	−32.8017	−	74.0611i	−0.404959	−	0.914335i
$10$	3.80633	+	15.3605i	0.0380633	+	0.153605i
$11$	148.474	−	85.7213i	1.22705	−	0.708440i	0.260642	−	0.965436i	$-0.416066\pi$
$11$	148.474	−	85.7213i	1.22705	−	0.708440i	0.966413	+	0.256995i	$0.0827325\pi$
$12$	63.6157	+	125.154i	0.441776	+	0.869123i
$13$	−127.218	−	73.4493i	−0.752769	−	0.434611i	0.0739247	−	0.997264i	$-0.476448\pi$
$13$	−127.218	−	73.4493i	−0.752769	−	0.434611i	−0.826693	+	0.562653i	$0.809781\pi$
$14$	−46.3471	−	26.7585i	−0.236465	−	0.136523i
$15$	170.165	−	147.203i	0.756289	−	0.654237i
$16$	−118.464	−	205.185i	−0.462749	−	0.801504i
$17$	−273.459			−0.946224			−0.473112	−	0.881002i	$-0.656869\pi$
$17$	−273.459			−0.946224			−0.473112	+	0.881002i	$0.656869\pi$
$18$	−30.2183	+	41.4222i	−0.0932663	+	0.127846i
$19$	229.656			0.636167			0.318083	−	0.948063i	$-0.396961\pi$
$19$	229.656			0.636167			0.318083	+	0.948063i	$0.396961\pi$
$20$	−280.920	+	270.501i	−0.702299	+	0.676252i
$21$	−40.5615	+	759.820i	−0.0919763	+	1.72295i
$22$	−93.9843	−	54.2618i	−0.194182	−	0.112111i
$23$	−194.631	+	337.110i	−0.367922	+	0.637259i	−0.989240	−	0.146299i	$-0.953264\pi$
$23$	−194.631	+	337.110i	−0.367922	+	0.637259i	0.621319	+	0.783558i	$0.286597\pi$
$24$	98.1939	−	150.884i	0.170475	−	0.261951i
$25$	529.075	+	332.723i	0.846520	+	0.532358i
$26$			92.9873i			0.137555i
$27$	719.689	+	116.141i	0.987228	+	0.159316i
$28$		−	1318.84i		−	1.68219i
$29$	306.632	−	177.034i	0.364604	−	0.210504i	−0.306494	−	0.951872i	$-0.599156\pi$
$29$	306.632	−	177.034i	0.364604	−	0.210504i	0.671098	+	0.741368i	$0.265823\pi$
$30$	−134.554	−	46.6939i	−0.149504	−	0.0518821i
$31$	−310.913	+	538.517i	−0.323531	+	0.560371i	−0.981214	−	0.192923i	$-0.938203\pi$
$31$	−310.913	+	538.517i	−0.323531	+	0.560371i	0.657683	+	0.753295i	$0.271537\pi$
$32$	−235.008	+	407.045i	−0.229500	+	0.397505i
$33$	−82.2521	+	1540.79i	−0.0755299	+	1.41487i
$34$	86.5501	+	149.909i	0.0748704	+	0.129679i
$35$	−2051.57	+	508.379i	−1.67475	+	0.415003i
$36$	−1256.36	−	134.520i	−0.969416	−	0.103797i
$37$		−	730.131i		−	0.533332i	−0.963789	−	0.266666i	$-0.914078\pi$
$37$		−	730.131i		−	0.533332i	0.963789	−	0.266666i	$-0.0859220\pi$
$38$	−72.6865	−	125.897i	−0.0503369	−	0.0871861i
$39$	1178.57	−	599.069i	0.774866	−	0.393865i
$40$	480.491	+	138.527i	0.300307	+	0.0865795i
$41$	−498.910	−	288.046i	−0.296794	−	0.171354i	0.344208	−	0.938893i	$-0.388148\pi$
$41$	−498.910	−	288.046i	−0.296794	−	0.171354i	−0.641002	+	0.767539i	$0.721481\pi$
$42$	429.369	−	218.249i	0.243406	−	0.123724i
$43$	783.565	−	452.392i	0.423778	−	0.244668i	−0.272914	−	0.962038i	$-0.587988\pi$
$43$	783.565	−	452.392i	0.423778	−	0.244668i	0.696692	+	0.717370i	$0.254654\pi$
$44$		−	2674.39i		−	1.38140i
$45$	275.038	+	2006.24i	0.135821	+	0.990733i
$46$	246.404			0.116448
$47$	−396.417	−	686.614i	−0.179455	−	0.310826i	0.762239	−	0.647296i	$-0.224100\pi$
$47$	−396.417	−	686.614i	−0.179455	−	0.310826i	−0.941694	+	0.336470i	$0.890767\pi$
$48$	2129.31	+	113.669i	0.924181	+	0.0493356i
$49$	2373.40	−	4110.85i	0.988506	−	1.71214i
$50$	14.9450	−	395.345i	0.00597798	−	0.158138i
$51$	1342.43	−	2062.77i	0.516122	−	0.793069i
$52$	−1984.51	+	1145.76i	−0.733917	+	0.423727i
$53$	3467.44			1.23440			0.617202	−	0.786805i	$-0.288266\pi$
$53$	3467.44			1.23440			0.617202	+	0.786805i	$0.288266\pi$
$54$	−164.115	−	431.290i	−0.0562807	−	0.147905i
$55$	−4160.24	+	1030.91i	−1.37529	+	0.340796i
$56$	−1464.54	+	845.551i	−0.467008	+	0.269627i
$57$	−1127.40	+	1732.36i	−0.347000	+	0.533197i
$58$	−194.099	−	112.063i	−0.0576989	−	0.0333125i
$59$	2436.74	+	1406.85i	0.700013	+	0.404152i	0.807352	−	0.590070i	$-0.200900\pi$
$59$	2436.74	+	1406.85i	0.700013	+	0.404152i	−0.107340	+	0.994222i	$0.534233\pi$
$60$	−661.400	−	3446.96i	−0.183722	−	0.957490i
$61$	2660.83	+	4608.69i	0.715084	+	1.23856i	0.962927	+	0.269762i	$0.0869450\pi$
$61$	2660.83	+	4608.69i	0.715084	+	1.23856i	−0.247843	+	0.968800i	$0.579722\pi$
$62$	393.618			0.102398
$63$	−5532.41	−	4035.99i	−1.39390	−	1.01688i
$64$	−3493.32			−0.852860
$65$	2547.30	+	2645.42i	0.602912	+	0.626135i
$66$	870.688	−	442.572i	0.199883	−	0.101601i
$67$	−147.934	−	85.4097i	−0.0329548	−	0.0190264i	0.483432	−	0.875382i	$-0.339390\pi$
$67$	−147.934	−	85.4097i	−0.0329548	−	0.0190264i	−0.516387	+	0.856355i	$0.672723\pi$
$68$	−2132.88	+	3694.26i	−0.461264	+	0.798932i
$69$	−1587.45	−	3123.05i	−0.333428	−	0.655966i
$70$	928.016	+	963.760i	0.189391	+	0.196686i
$71$			2798.11i			0.555071i	0.960715	+	0.277535i	$0.0895176\pi$
$71$			2798.11i			0.555071i	−0.960715	+	0.277535i	$0.910482\pi$
$72$	656.114	+	1481.40i	0.126565	+	0.285765i
$73$			5866.22i			1.10081i	0.834898	+	0.550405i	$0.185527\pi$
$73$			5866.22i			1.10081i	−0.834898	+	0.550405i	$0.814473\pi$
$74$	−400.255	+	231.088i	−0.0730927	+	0.0422001i
$75$	−5107.10	+	2357.58i	−0.907928	+	0.419126i
$76$	1791.24	−	3102.52i	0.310117	−	0.537139i
$77$	7247.28	−	12552.7i	1.22234	−	2.11716i
$78$	−701.428	−	456.483i	−0.115291	−	0.0750301i
$79$	1466.67	+	2540.34i	0.235005	+	0.407040i	0.959274	−	0.282477i	$-0.0911560\pi$
$79$	1466.67	+	2540.34i	0.235005	+	0.407040i	−0.724269	+	0.689517i	$0.757823\pi$
$80$	1424.68	+	5749.29i	0.222606	+	0.898327i
$81$	−4409.10	+	4858.66i	−0.672017	+	0.740536i
$82$			364.668i			0.0542338i
$83$	−3444.66	−	5966.32i	−0.500023	−	0.866065i	−1.00000		2.64929e-5i	$-0.999992\pi$
$83$	−3444.66	−	5966.32i	−0.500023	−	0.866065i	0.499977	−	0.866039i	$-0.333342\pi$
$84$	9948.35	+	6474.30i	1.40991	+	0.917559i
$85$	6568.92	+	1893.84i	0.909193	+	0.262123i
$86$	−495.999	−	286.365i	−0.0670632	−	0.0387189i
$87$	−169.869	+	3182.08i	−0.0224428	+	0.420410i
$88$	−2969.84	+	1714.64i	−0.383502	+	0.221415i
$89$		−	1031.26i		−	0.130193i	−0.997879	−	0.0650966i	$-0.979264\pi$
$89$		−	1031.26i		−	0.130193i	0.997879	−	0.0650966i	$-0.0207356\pi$
$90$	1012.76	−	785.751i	0.125032	−	0.0970063i
$91$	−12419.5			−1.49976
$92$	3036.10	+	5258.68i	0.358708	+	0.621300i
$93$	−2535.88	−	4988.93i	−0.293199	−	0.576821i
$94$	−250.933	+	434.629i	−0.0283990	+	0.0491884i
$95$	−5516.71	−	1590.48i	−0.611270	−	0.176231i
$96$	−1916.77	−	3770.94i	−0.207983	−	0.409174i
$97$	−12170.7	+	7026.75i	−1.29352	+	0.746811i	−0.979276	−	0.202532i	$-0.935083\pi$
$97$	−12170.7	+	7026.75i	−1.29352	+	0.746811i	−0.314240	+	0.949344i	$0.601750\pi$
$98$	−3004.74			−0.312864
$99$	−11218.8	−	8184.32i	−1.14466	−	0.835050i
$100$	8621.49	−	4552.35i	0.862149	−	0.455235i
$101$	11797.3	−	6811.17i	1.15648	−	0.667696i	0.206025	−	0.978547i	$-0.433947\pi$
$101$	11797.3	−	6811.17i	1.15648	−	0.667696i	0.950459	+	0.310851i	$0.100614\pi$
$102$	−1555.69	−	83.0474i	−0.149528	−	0.00798225i
$103$	14156.3	+	8173.15i	1.33437	+	0.770397i	0.985966	−	0.166948i	$-0.0533912\pi$
$103$	14156.3	+	8173.15i	1.33437	+	0.770397i	0.348402	+	0.937345i	$0.386724\pi$
$104$	2544.67	+	1469.17i	0.235269	+	0.135833i
$105$	6236.49	−	17971.2i	0.565668	−	1.63004i
$106$	−1097.45	−	1900.84i	−0.0976727	−	0.169174i
$107$	15293.8			1.33582			0.667909	−	0.744243i	$-0.267190\pi$
$107$	15293.8			1.33582			0.667909	+	0.744243i	$0.267190\pi$
$108$	7182.32	−	8816.70i	0.615768	−	0.755890i
$109$	−3110.73			−0.261824			−0.130912	−	0.991394i	$-0.541791\pi$
$109$	−3110.73			−0.261824			−0.130912	+	0.991394i	$0.541791\pi$
$110$	1881.86	+	1954.34i	0.155526	+	0.161516i
$111$	5507.57	+	3584.28i	0.447007	+	0.290908i
$112$	−17347.3	−	10015.5i	−1.38292	−	0.798427i
$113$	−4020.47	+	6963.67i	−0.314862	+	0.545357i	−0.979408	−	0.201890i	$-0.935292\pi$
$113$	−4020.47	+	6963.67i	−0.314862	+	0.545357i	0.664546	+	0.747247i	$0.268625\pi$
$114$	1306.50	+	69.7448i	0.100531	+	0.00536664i
$115$	7010.00	−	6750.01i	0.530057	−	0.510398i
$116$		−	5523.22i		−	0.410465i
$117$	−1266.78	+	11831.2i	−0.0925398	+	0.864282i
$118$		−	1781.09i		−	0.127915i
$119$	−20022.1	+	11559.7i	−1.41389	+	0.816308i
$120$	−3403.72	+	2944.43i	−0.236370	+	0.204474i
$121$	7375.77	−	12775.2i	0.503775	−	0.872564i
$122$	1684.31	−	2917.31i	0.113163	−	0.196003i
$123$	4622.00	−	2349.37i	0.305506	−	0.155289i
$124$	4850.02	+	8400.49i	0.315428	+	0.546338i
$125$	−10404.9	−	11656.7i	−0.665916	−	0.746026i
$126$	−461.503	+	4310.24i	−0.0290692	+	0.271494i
$127$		−	8105.72i		−	0.502555i	−0.967915	−	0.251278i	$-0.919149\pi$
$127$		−	8105.72i		−	0.502555i	0.967915	−	0.251278i	$-0.0808507\pi$
$128$	4865.76	+	8427.74i	0.296982	+	0.514389i
$129$	−434.083	+	8131.47i	−0.0260851	+	0.488641i
$130$	643.984	−	2233.70i	0.0381056	−	0.132172i
$131$	−5088.68	−	2937.95i	−0.296526	−	0.171199i	0.344355	−	0.938839i	$-0.388098\pi$
$131$	−5088.68	−	2937.95i	−0.296526	−	0.171199i	−0.640881	+	0.767640i	$0.721431\pi$
$132$	20173.6	+	13128.8i	1.15780	+	0.753489i
$133$	16814.9	−	9708.10i	0.950587	−	0.548821i
$134$			108.129i			0.00602190i
$135$	−16483.7	−	7774.10i	−0.904458	−	0.426563i
$136$	5469.85			0.295731
$137$	−17524.8	−	30353.8i	−0.933710	−	1.61723i	−0.776918	−	0.629601i	$-0.783218\pi$
$137$	−17524.8	−	30353.8i	−0.933710	−	1.61723i	−0.156792	−	0.987632i	$-0.550115\pi$
$138$	−1209.62	+	1858.69i	−0.0635170	+	0.0975996i
$139$	−5993.53	+	10381.1i	−0.310208	+	0.537296i	−0.978407	−	0.206686i	$-0.933732\pi$
$139$	−5993.53	+	10381.1i	−0.310208	+	0.537296i	0.668199	+	0.743982i	$0.267065\pi$
$140$	−9133.62	+	31680.6i	−0.466001	+	1.61636i
$141$	7125.36	+	380.374i	0.358401	+	0.0191325i
$142$	1533.92	−	885.606i	0.0760720	−	0.0439202i
$143$	−25184.7			−1.23158
$144$	−11310.4	+	15504.0i	−0.545449	+	0.747683i
$145$	−8591.84	+	2129.06i	−0.408649	+	0.101263i
$146$	3215.84	−	1856.67i	0.150865	−	0.0871021i
$147$	19358.0	+	38083.7i	0.895831	+	1.76240i
$148$	−9863.63	−	5694.77i	−0.450312	−	0.259988i
$149$	11303.5	+	6526.09i	0.509145	+	0.293955i	0.732482	−	0.680786i	$-0.238362\pi$
$149$	11303.5	+	6526.09i	0.509145	+	0.293955i	−0.223337	+	0.974741i	$0.571695\pi$
$150$	2908.82	+	2053.52i	0.129281	+	0.0912674i
$151$	14442.4	+	25014.9i	0.633409	+	1.09710i	0.986850	+	0.161639i	$0.0516781\pi$
$151$	14442.4	+	25014.9i	0.633409	+	1.09710i	−0.353441	+	0.935457i	$0.614989\pi$
$152$	−4593.69			−0.198826
$153$	8969.91	+	20252.7i	0.383182	+	0.865166i
$154$	−9175.10			−0.386874
$155$	11198.1	−	10782.8i	0.466103	−	0.448816i
$156$	1099.39	−	20594.3i	0.0451754	−	0.846249i
$157$	−18003.8	−	10394.5i	−0.730405	−	0.421700i	0.0881652	−	0.996106i	$-0.471900\pi$
$157$	−18003.8	−	10394.5i	−0.730405	−	0.421700i	−0.818570	+	0.574406i	$0.805233\pi$
$158$	928.404	−	1608.04i	0.0371897	−	0.0644145i
$159$	−17022.0	+	26155.8i	−0.673311	+	1.03460i
$160$	8464.25	−	8150.33i	0.330635	−	0.318372i
$161$			32910.0i			1.26963i
$162$	4058.99	+	879.282i	0.154663	+	0.0335041i
$163$		−	24195.2i		−	0.910654i	−0.890324	−	0.455327i	$-0.849522\pi$
$163$		−	24195.2i		−	0.910654i	0.890324	−	0.455327i	$-0.150478\pi$
$164$	−7782.66	+	4493.32i	−0.289361	+	0.167063i
$165$	12646.6	−	36442.6i	0.464520	−	1.33857i
$166$	−2180.48	+	3776.70i	−0.0791290	+	0.137055i
$167$	5184.25	−	8979.38i	0.185889	−	0.321969i	−0.757987	−	0.652270i	$-0.773817\pi$
$167$	5184.25	−	8979.38i	0.185889	−	0.321969i	0.943876	+	0.330301i	$0.107150\pi$
$168$	811.331	−	15198.3i	0.0287461	−	0.538488i
$169$	−3490.90	−	6046.42i	−0.122226	−	0.211702i
$170$	−1040.88	−	4200.46i	−0.0360165	−	0.145345i
$171$	−7533.10	−	17008.6i	−0.257621	−	0.581669i
$172$		−	14114.0i		−	0.477082i
$173$	19114.0	+	33106.4i	0.638644	+	1.10616i	0.985731	+	0.168331i	$0.0538376\pi$
$173$	19114.0	+	33106.4i	0.638644	+	1.10616i	−0.347087	+	0.937833i	$0.612829\pi$
$174$	1798.17	−	914.012i	0.0593926	−	0.0301893i
$175$	52802.7	+	1996.07i	1.72417	+	0.0651777i
$176$	−35177.5	−	20309.7i	−1.13564	−	0.655660i
$177$	−22574.5	+	11474.6i	−0.720561	+	0.366262i
$178$	−565.334	+	326.396i	−0.0178429	+	0.0103016i
$179$		−	29062.0i		−	0.907025i	−0.891250	−	0.453512i	$-0.850171\pi$
$179$		−	29062.0i		−	0.907025i	0.891250	−	0.453512i	$-0.149829\pi$
$180$	29248.2	+	11932.3i	0.902723	+	0.368282i
$181$	23849.6			0.727988			0.363994	−	0.931401i	$-0.381413\pi$
$181$	23849.6			0.727988			0.363994	+	0.931401i	$0.381413\pi$
$182$	3930.79	+	6808.33i	0.118669	+	0.205541i
$183$	−47826.8	−	2553.14i	−1.42813	−	0.0762382i
$184$	3893.09	−	6743.03i	0.114990	−	0.199168i
$185$	−5056.53	+	17538.9i	−0.147744	+	0.512459i
$186$	−1932.30	+	2969.16i	−0.0558534	+	0.0858238i
$187$	−40601.4	+	23441.2i	−1.16107	+	0.670343i
$188$	−12367.7			−0.349923
$189$	57603.6	−	21919.3i	1.61260	−	0.613626i
$190$	874.148	+	3527.63i	0.0242146	+	0.0977183i
$191$	−4976.77	+	2873.34i	−0.136421	+	0.0787626i	−0.566657	−	0.823954i	$-0.691764\pi$
$191$	−4976.77	+	2873.34i	−0.136421	+	0.0787626i	0.430236	+	0.902716i	$0.358430\pi$
$192$	17149.0	−	26351.0i	0.465196	−	0.714817i
$193$	−5427.21	−	3133.40i	−0.145701	−	0.0841204i	0.425377	−	0.905016i	$-0.360141\pi$
$193$	−5427.21	−	3133.40i	−0.145701	−	0.0841204i	−0.571078	+	0.820896i	$0.693475\pi$
$194$	7704.08	+	4447.95i	0.204700	+	0.118183i
$195$	−32460.0	+	6228.40i	−0.853650	+	0.163797i
$196$	−37023.4	−	64126.5i	−0.963750	−	1.66926i
$197$	55114.0			1.42013			0.710067	−	0.704134i	$-0.248665\pi$
$197$	55114.0			1.42013			0.710067	+	0.704134i	$0.248665\pi$
$198$	−935.852	+	8740.46i	−0.0238713	+	0.222948i
$199$	10375.3			0.261995			0.130998	−	0.991383i	$-0.458182\pi$
$199$	10375.3			0.261995			0.130998	+	0.991383i	$0.458182\pi$
$200$	−10582.8	−	6655.29i	−0.264570	−	0.166382i
$201$	1370.49	−	696.621i	0.0339222	−	0.0172427i
$202$	−7467.72	−	4311.49i	−0.183014	−	0.105663i
$203$	14967.3	−	25924.1i	0.363204	−	0.629088i
$204$	−17396.3	−	34224.4i	−0.418019	−	0.822385i
$205$	9989.76	+	10374.5i	0.237710	+	0.246866i
$206$		−	10347.3i		−	0.243832i
$207$	31351.0	+	3356.79i	0.731662	+	0.0783399i
$208$			34804.3i			0.804463i
$209$	34097.9	−	19686.4i	0.780611	−	0.450686i
$210$	−11825.6	+	2269.08i	−0.268154	+	0.0514532i
$211$	−25898.6	+	44857.7i	−0.581716	+	1.00756i	0.413560	+	0.910477i	$0.364285\pi$
$211$	−25898.6	+	44857.7i	−0.581716	+	1.00756i	−0.995276	+	0.0970851i	$0.969048\pi$
$212$	27044.8	−	46843.0i	0.601745	−	1.04225i
$213$	−21106.9	−	13736.2i	−0.465227	−	0.302766i
$214$	−4840.50	−	8384.00i	−0.105697	−	0.183073i
$215$	−21955.5	+	5440.59i	−0.474971	+	0.117698i
$216$	−14395.5	−	2323.11i	−0.308547	−	0.0497922i
$217$			52572.1i			1.11644i
$218$	984.552	+	1705.29i	0.0207169	+	0.0358828i
$219$	−44250.4	−	28797.8i	−0.922634	−	0.600442i
$220$	−18521.5	+	64243.0i	−0.382675	+	1.32733i
$221$	34788.9	+	20085.4i	0.712288	+	0.411240i
$222$	221.735	−	4153.66i	0.00449913	−	0.0842801i
$223$	22259.2	−	12851.4i	0.447611	−	0.258428i	−0.259210	−	0.965821i	$-0.583462\pi$
$223$	22259.2	−	12851.4i	0.447611	−	0.258428i	0.706821	+	0.707393i	$0.250129\pi$
$224$			39737.3i			0.791958i
$225$	7287.34	−	50097.8i	0.143947	−	0.989585i
$226$	5089.94			0.0996543
$227$	−17114.5	−	29643.2i	−0.332133	−	0.575272i	0.650797	−	0.759252i	$-0.274435\pi$
$227$	−17114.5	−	29643.2i	−0.332133	−	0.575272i	−0.982930	+	0.183980i	$0.941102\pi$
$228$	14609.7	+	28742.3i	0.281043	+	0.552907i
$229$	−2619.98	+	4537.93i	−0.0499605	+	0.0865341i	−0.889924	−	0.456109i	$-0.849243\pi$
$229$	−2619.98	+	4537.93i	−0.0499605	+	0.0865341i	0.839964	+	0.542643i	$0.182576\pi$
$230$	−5919.01	−	1706.47i	−0.111891	−	0.0322584i
$231$	59110.4	+	116290.i	1.10775	+	2.17931i
$232$	−6133.39	+	3541.12i	−0.113953	+	0.0657907i
$233$	44606.8			0.821654			0.410827	−	0.911713i	$-0.365240\pi$
$233$	44606.8			0.821654			0.410827	+	0.911713i	$0.365240\pi$
$234$	6886.74	−	3050.14i	0.125771	−	0.0557042i
$235$	4767.42	+	19239.0i	0.0863272	+	0.348374i
$236$	38011.5	−	21946.0i	0.682482	−	0.394031i
$237$	−26362.4	−	1407.31i	−0.469342	−	0.0250549i
$238$	12674.0	+	7317.35i	0.223749	+	0.129181i
$239$	−31245.6	−	18039.7i	−0.547008	−	0.315815i	0.200907	−	0.979610i	$-0.435611\pi$
$239$	−31245.6	−	18039.7i	−0.547008	−	0.315815i	−0.747914	+	0.663795i	$0.768945\pi$
$240$	−50362.3	−	17477.1i	−0.874346	−	0.303422i
$241$	−17018.3	−	29476.5i	−0.293009	−	0.507507i	0.681511	−	0.731808i	$-0.261323\pi$
$241$	−17018.3	−	29476.5i	−0.293009	−	0.507507i	−0.974520	+	0.224301i	$0.927990\pi$
$242$	−9337.78			−0.159446
$243$	−15005.5	−	57110.6i	−0.254119	−	0.967173i
$244$	83014.2			1.39435
$245$	−85482.7	+	82312.3i	−1.42412	+	1.37130i
$246$	−2750.79	−	1790.19i	−0.0454555	−	0.0295821i
$247$	−29216.4	−	16868.1i	−0.478886	−	0.276485i
$248$	6219.02	−	10771.7i	0.101116	−	0.175138i
$249$	61915.7	+	3305.25i	0.998624	+	0.0533096i
$250$	−3096.96	+	9393.31i	−0.0495514	+	0.150293i
$251$			60480.3i			0.959990i	0.877271	+	0.479995i	$0.159361\pi$
$251$			60480.3i			0.959990i	−0.877271	+	0.479995i	$0.840639\pi$
$252$	−97674.7	+	43260.1i	−1.53809	+	0.681219i
$253$			66735.9i			1.04260i
$254$	−4443.53	+	2565.47i	−0.0688748	+	0.0397649i
$255$	−46533.2	+	40254.1i	−0.715619	+	0.619055i
$256$	−24866.5	+	43070.0i	−0.379432	+	0.657196i
$257$	−7619.79	+	13197.9i	−0.115366	+	0.199819i	−0.917926	−	0.396752i	$-0.870137\pi$
$257$	−7619.79	+	13197.9i	−0.115366	+	0.199819i	0.802560	+	0.596571i	$0.203471\pi$
$258$	4595.03	−	2335.66i	0.0690318	−	0.0350889i
$259$	−30864.3	−	53458.6i	−0.460106	−	0.796926i
$260$	55606.1	−	13779.2i	0.822575	−	0.203834i
$261$	−23169.4	−	16902.5i	−0.340121	−	0.248125i
$262$			3719.46i			0.0541848i
$263$	−3230.92	−	5596.12i	−0.0467106	−	0.0809051i	0.841725	−	0.539907i	$-0.181541\pi$
$263$	−3230.92	−	5596.12i	−0.0467106	−	0.0809051i	−0.888435	+	0.459002i	$0.848207\pi$
$264$	1645.24	−	30819.6i	0.0236060	−	0.442200i
$265$	−83293.5	−	24013.8i	−1.18609	−	0.341955i
$266$	−10643.9	−	6145.26i	−0.150431	−	0.0868514i
$267$	7779.07	+	5062.55i	0.109120	+	0.0710145i
$268$	−2307.67	+	1332.33i	−0.0321295	+	0.0185500i
$269$		−	77325.2i		−	1.06860i	−0.845294	−	0.534301i	$-0.820575\pi$
$269$		−	77325.2i		−	1.06860i	0.845294	−	0.534301i	$-0.179425\pi$
$270$	955.393	+	11496.9i	0.0131055	+	0.157707i
$271$	−5856.99			−0.0797510			−0.0398755	−	0.999205i	$-0.512696\pi$
$271$	−5856.99			−0.0797510			−0.0398755	+	0.999205i	$0.512696\pi$
$272$	32394.9	+	56109.7i	0.437864	+	0.758403i
$273$	60968.4	−	93683.5i	0.818050	−	1.25701i
$274$	−11093.3	+	19214.1i	−0.147760	+	0.255928i
$275$	107075.	+	4047.69i	1.41587	+	0.0535232i
$276$	−54572.2	−	2913.23i	−0.716396	−	0.0382434i
$277$	45287.4	−	26146.7i	0.590225	−	0.340767i	−0.174961	−	0.984575i	$-0.555980\pi$
$277$	45287.4	−	26146.7i	0.590225	−	0.340767i	0.765187	+	0.643809i	$0.222647\pi$
$278$	7587.84			0.0981813
$279$	50081.6	+	5362.30i	0.643384	+	0.0688879i
$280$	41036.4	−	10168.8i	0.523423	−	0.129704i
$281$	9078.13	−	5241.26i	0.114970	−	0.0663779i	−0.441412	−	0.897304i	$-0.645522\pi$
$281$	9078.13	−	5241.26i	0.114970	−	0.0663779i	0.556382	+	0.830927i	$0.312189\pi$
$282$	−2046.67	−	4026.49i	−0.0257365	−	0.0506324i
$283$	−4813.64	−	2779.16i	−0.0601036	−	0.0347009i	0.469647	−	0.882854i	$-0.344381\pi$
$283$	−4813.64	−	2779.16i	−0.0601036	−	0.0347009i	−0.529751	+	0.848153i	$0.677715\pi$
$284$	37800.8	+	21824.3i	0.468667	+	0.270585i
$285$	39079.5	−	33806.2i	0.481126	−	0.416204i
$286$	7970.99	+	13806.2i	0.0974496	+	0.168788i
$287$	−48705.5			−0.591309
$288$	37854.8	+	4053.17i	0.456390	+	0.0488663i
$289$	−8741.28			−0.104660
$290$	3886.48	+	4036.17i	0.0462125	+	0.0479925i
$291$	6742.37	−	126302.i	0.0796208	−	1.49150i
$292$	79249.1	+	45754.5i	0.929455	+	0.536621i
$293$	−75376.9	+	130557.i	−0.878017	+	1.52077i	−0.0245037	+	0.999700i	$0.507801\pi$
$293$	−75376.9	+	130557.i	−0.878017	+	1.52077i	−0.853514	+	0.521071i	$0.825533\pi$
$294$	14750.5	−	22665.6i	0.170653	−	0.262224i
$295$	−48791.3	−	50670.6i	−0.560658	−	0.582253i
$296$			14604.4i			0.166687i
$297$	116811.	−	44448.8i	1.32425	−	0.503903i
$298$		−	8262.07i		−	0.0930371i
$299$	49521.0	−	28591.0i	0.553920	−	0.319806i
$300$	−7984.09	+	87382.1i	−0.0887121	+	0.970912i
$301$	38247.3	−	66246.3i	0.422151	−	0.731187i
$302$	9142.05	−	15834.5i	0.100237	−	0.173616i
$303$	−6535.51	+	122427.i	−0.0711860	+	1.33349i
$304$	−27205.9	−	47122.0i	−0.294385	−	0.509890i
$305$	−31999.9	−	129136.i	−0.343992	−	1.38818i
$306$	8263.46	−	11327.3i	0.0882509	−	0.120971i
$307$		−	140225.i		−	1.48781i	−0.668284	−	0.743906i	$-0.732971\pi$
$307$		−	140225.i		−	1.48781i	0.668284	−	0.743906i	$-0.267029\pi$
$308$	−113053.	−	195813.i	−1.19173	−	2.06414i
$309$	−131147.	+	66662.0i	−1.37354	+	0.698171i
$310$	−9455.32	−	2726.00i	−0.0983905	−	0.0283663i
$311$	−165187.	−	95370.9i	−1.70787	−	0.986041i	−0.937187	−	0.348827i	$-0.886580\pi$
$311$	−165187.	−	95370.9i	−1.70787	−	0.986041i	−0.770687	−	0.637214i	$-0.780087\pi$
$312$	−23574.3	+	11982.9i	−0.242175	+	0.123098i
$313$	−29158.8	+	16834.8i	−0.297633	+	0.171838i	−0.641379	−	0.767224i	$-0.721637\pi$
$313$	−29158.8	+	16834.8i	−0.297633	+	0.171838i	0.343746	+	0.939063i	$0.388304\pi$
$314$			13159.5i			0.133469i
$315$	104946.	+	135266.i	1.05766	+	1.36322i
$316$	45757.9			0.458239
$317$	39248.1	+	67979.6i	0.390571	+	0.676488i	0.992525	−	0.122042i	$-0.0389444\pi$
$317$	39248.1	+	67979.6i	0.390571	+	0.676488i	−0.601954	+	0.798531i	$0.705611\pi$
$318$	19726.0	+	1053.04i	0.195068	+	0.0104133i
$319$	30351.2	−	52569.8i	0.298259	−	0.516600i
$320$	83915.0	+	24193.0i	0.819483	+	0.236260i
$321$	−75078.5	+	115365.i	−0.728628	+	1.11960i
$322$	18041.1	−	10416.1i	0.174001	−	0.100460i
$323$	−62801.5			−0.601956
$324$	31248.1	+	97460.1i	0.297669	+	0.928404i
$325$	−42869.5	−	81188.6i	−0.405865	−	0.768649i
$326$	−13263.7	+	7657.81i	−0.124804	+	0.0720559i
$327$	15270.9	−	23465.1i	0.142813	−	0.219445i
$328$	9979.44	+	5761.63i	0.0927595	+	0.0535547i
$329$	−58049.6	−	33515.0i	−0.536300	−	0.309633i
$330$	−23980.4	+	4601.33i	−0.220205	+	0.0422528i
$331$	86246.3	+	149383.i	0.787199	+	1.36347i	0.927677	+	0.373384i	$0.121803\pi$
$331$	86246.3	+	149383.i	0.787199	+	1.36347i	−0.140478	+	0.990084i	$0.544864\pi$
$332$	−107469.			−0.975001
$333$	−54074.3	+	23949.5i	−0.487644	+	0.215977i
$334$	−6563.29			−0.0588340
$335$	2962.11	+	3076.20i	0.0263943	+	0.0274110i
$336$	160709.	−	81688.5i	1.42351	−	0.723573i
$337$	27972.6	+	16150.0i	0.246305	+	0.142204i	0.618071	−	0.786122i	$-0.287914\pi$
$337$	27972.6	+	16150.0i	0.246305	+	0.142204i	−0.371766	+	0.928326i	$0.621248\pi$
$338$	−2209.75	+	3827.40i	−0.0193424	+	0.0335020i
$339$	−32791.9	−	64512.8i	−0.285343	−	0.561366i
$340$	76819.9	−	73970.8i	0.664532	−	0.639886i
$341$			106607.i			0.916808i
$342$	−6939.81	+	9512.87i	−0.0593329	+	0.0813316i
$343$		−	198325.i		−	1.68574i
$344$	−15673.2	+	9048.94i	−0.132447	+	0.0764682i
$345$	16504.4	+	86014.7i	0.138663	+	0.722661i
$346$	12099.2	−	20956.4i	0.101066	−	0.175051i
$347$	−116127.	+	201138.i	−0.964440	+	1.67046i	−0.253329	+	0.967380i	$0.581526\pi$
$347$	−116127.	+	201138.i	−0.964440	+	1.67046i	−0.711111	+	0.703080i	$0.751808\pi$
$348$	41663.1	+	27114.0i	0.344027	+	0.223890i
$349$	82977.7	+	143722.i	0.681256	+	1.17997i	0.974598	+	0.223963i	$0.0718994\pi$
$349$	82977.7	+	143722.i	0.681256	+	1.17997i	−0.293342	+	0.956008i	$0.594767\pi$
$350$	−15617.9	−	29578.0i	−0.127493	−	0.241453i
$351$	−83026.9	−	67635.9i	−0.673914	−	0.548988i
$352$			80580.6i			0.650347i
$353$	64590.4	+	111874.i	0.518345	+	0.897800i	0.999773	+	0.0213140i	$0.00678497\pi$
$353$	64590.4	+	111874.i	0.518345	+	0.897800i	−0.481428	+	0.876486i	$0.659882\pi$
$354$	13435.2	+	8743.51i	0.107211	+	0.0697717i
$355$	19378.3	−	67215.1i	0.153766	−	0.533347i
$356$	−13931.7	−	8043.48i	−0.109927	−	0.0634664i
$357$	11091.9	−	207780.i	0.0870302	−	1.63030i
$358$	−15931.7	+	9198.16i	−0.124307	+	0.0717687i
$359$			205368.i			1.59347i	0.604331	+	0.796734i	$0.293441\pi$
$359$			205368.i			1.59347i	−0.604331	+	0.796734i	$0.706559\pi$
$360$	−5501.44	−	40129.6i	−0.0424493	−	0.309642i
$361$	−77579.1			−0.595292
$362$	−7548.44	−	13074.3i	−0.0576023	−	0.0997702i
$363$	60158.5	+	118352.i	0.456545	+	0.898179i
$364$	−96867.8	+	167780.i	−0.731100	+	1.26630i
$365$	40626.5	−	140916.i	0.304947	−	1.05773i
$366$	13737.6	+	27026.6i	0.102553	+	0.201757i
$367$	89820.1	−	51857.7i	0.666870	−	0.385018i	−0.128019	−	0.991772i	$-0.540862\pi$
$367$	89820.1	−	51857.7i	0.666870	−	0.385018i	0.794890	+	0.606754i	$0.207529\pi$
$368$	92226.6			0.681021
$369$	−4967.92	+	46398.3i	−0.0364856	+	0.340760i
$370$	11215.2	−	2779.12i	0.0819224	−	0.0203004i
$371$	253879.	−	146577.i	1.84450	−	1.06492i
$372$	−87176.3	−	4653.74i	−0.629960	−	0.0336292i
$373$	−156191.	−	90176.7i	−1.12263	−	0.648152i	−0.180560	−	0.983564i	$-0.557791\pi$
$373$	−156191.	−	90176.7i	−1.12263	−	0.648152i	−0.942071	+	0.335412i	$0.891124\pi$
$374$	25700.8	+	14838.4i	0.183740	+	0.106082i
$375$	139008.	−	21263.6i	0.988502	−	0.151208i
$376$	7929.31	+	13734.0i	0.0560867	+	0.0971450i
$377$	−52012.1			−0.365950
$378$	−30247.8	−	24640.6i	−0.211694	−	0.172452i
$379$	−145168.			−1.01063			−0.505317	−	0.862934i	$-0.668624\pi$
$379$	−145168.			−1.01063			−0.505317	+	0.862934i	$0.668624\pi$
$380$	−64514.9	+	62122.2i	−0.446779	+	0.430209i
$381$	61143.6	+	39791.7i	0.421212	+	0.274121i
$382$	3150.31	+	1818.83i	0.0215887	+	0.0124642i
$383$	56718.9	−	98240.0i	0.386661	−	0.669716i	−0.605337	−	0.795969i	$-0.706962\pi$
$383$	56718.9	−	98240.0i	0.386661	−	0.669716i	0.991998	+	0.126253i	$0.0402951\pi$
$384$	−87459.2	−	4668.84i	−0.593120	−	0.0316626i
$385$	−261025.	+	251344.i	−1.76100	+	1.69569i
$386$			3966.91i			0.0266242i
$387$	−59206.9	−	43192.5i	−0.395321	−	0.288394i
$388$			219225.i			1.45622i
$389$	−229341.	+	132410.i	−1.51559	+	0.875026i	−0.515757	+	0.856735i	$0.672489\pi$
$389$	−229341.	+	132410.i	−1.51559	+	0.875026i	−0.999833	+	0.0182911i	$0.994177\pi$
$390$	13688.0	+	15823.2i	0.0899937	+	0.104031i
$391$	53223.5	−	92185.7i	0.348137	−	0.602990i
$392$	−47473.9	+	82227.2i	−0.308946	+	0.535110i
$393$	47142.5	−	23962.6i	0.305230	−	0.155149i
$394$	−17443.7	−	30213.3i	−0.112369	−	0.194628i
$395$	−17638.5	−	71180.4i	−0.113049	−	0.456212i
$396$	−198068.	+	87724.3i	−1.26306	+	0.559409i
$397$			82700.5i			0.524719i	0.964970	+	0.262360i	$0.0845007\pi$
$397$			82700.5i			0.524719i	−0.964970	+	0.262360i	$0.915499\pi$
$398$	−3283.79	−	5687.70i	−0.0207305	−	0.0359063i
$399$	−9315.21	+	174497.i	−0.0585122	+	1.09608i
$400$	5593.76	−	147974.i	0.0349610	−	0.924837i
$401$	20868.1	+	12048.2i	0.129776	+	0.0749261i	0.563482	−	0.826128i	$-0.309461\pi$
$401$	20868.1	+	12048.2i	0.129776	+	0.0749261i	−0.433707	+	0.901054i	$0.642795\pi$
$402$	−815.647	−	530.816i	−0.00504720	−	0.00328467i
$403$	79107.4	−	45672.7i	0.487087	−	0.281220i
$404$		−	212499.i		−	1.30195i
$405$	139562.	−	86177.5i	0.850860	−	0.525392i
$406$	−18948.7			−0.114955
$407$	−62587.7	−	108405.i	−0.377834	−	0.654427i
$408$	−26852.0	+	41260.5i	−0.161308	+	0.247864i
$409$	83307.9	−	144294.i	0.498012	−	0.862582i	−0.501985	−	0.864876i	$-0.667397\pi$
$409$	83307.9	−	144294.i	0.498012	−	0.862582i	0.999997	+	0.00229409i	$0.000730232\pi$
$410$	2525.51	−	8759.91i	0.0150239	−	0.0521113i
$411$	314998.	+	16815.6i	1.86476	+	0.0995469i
$412$	220829.	−	127495.i	1.30095	−	0.751104i
$413$	237884.			1.39465
$414$	−8082.45	−	18248.9i	−0.0471566	−	0.106472i
$415$	41426.4	+	167177.i	0.240537	+	0.970687i
$416$	59794.3	−	34522.3i	0.345520	−	0.199486i
$417$	−48884.6	−	96172.5i	−0.281125	−	0.553068i
$418$	−21584.1	−	12461.6i	−0.123532	−	0.0713214i
$419$	93529.3	+	53999.2i	0.532745	+	0.307581i	0.742134	−	0.670252i	$-0.233814\pi$
$419$	93529.3	+	53999.2i	0.532745	+	0.307581i	−0.209388	+	0.977833i	$0.567147\pi$
$420$	−194137.	−	224420.i	−1.10055	−	1.27222i
$421$	−129425.	−	224171.i	−0.730222	−	1.26478i	−0.956788	−	0.290785i	$-0.906084\pi$
$421$	−129425.	−	224171.i	−0.730222	−	1.26478i	0.226567	−	0.973996i	$-0.427250\pi$
$422$	32787.8			0.184114
$423$	−37848.3	+	51881.2i	−0.211527	+	0.289954i
$424$	−69357.3			−0.385799
$425$	−144680.	−	90986.2i	−0.800997	−	0.503730i
$426$	−849.765	+	15918.3i	−0.00468252	+	0.0877155i
$427$	389640.	+	224959.i	2.13702	+	1.23381i
$428$	119286.	−	206610.i	0.651182	−	1.12788i
$429$	123634.	−	189975.i	0.671773	−	1.03224i
$430$	9931.47	+	10314.0i	0.0537127	+	0.0557815i
$431$		−	81054.9i		−	0.436340i	−0.975911	−	0.218170i	$-0.929991\pi$
$431$		−	81054.9i		−	0.436340i	0.975911	−	0.218170i	$-0.0700087\pi$
$432$	−61426.6	−	161428.i	−0.329146	−	0.864990i
$433$		−	173783.i		−	0.926897i	−0.886124	−	0.463448i	$-0.846612\pi$
$433$		−	173783.i		−	0.926897i	0.886124	−	0.463448i	$-0.153388\pi$
$434$	28819.8	−	16639.1i	0.153007	−	0.0883388i
$435$	26118.1	−	75262.3i	0.138026	−	0.397740i
$436$	−24262.6	+	42024.1i	−0.127634	+	0.221068i
$437$	−44698.1	+	77419.4i	−0.234060	+	0.405403i
$438$	−1781.53	+	33372.5i	−0.00928633	+	0.173956i
$439$	129440.	+	224196.i	0.671642	+	1.16332i	0.977438	+	0.211221i	$0.0677441\pi$
$439$	129440.	+	224196.i	0.671642	+	1.16332i	−0.305796	+	0.952097i	$0.598923\pi$
$440$	83215.0	−	20620.7i	0.429829	−	0.106512i
$441$	−382306.	−	40934.0i	−1.96578	−	0.210478i
$442$		−	25428.2i		−	0.130158i
$443$	96232.4	+	166679.i	0.490358	+	0.849326i	0.999938	−	0.0110976i	$-0.00353254\pi$
$443$	96232.4	+	166679.i	0.490358	+	0.849326i	−0.509580	+	0.860423i	$0.670199\pi$
$444$	91378.6	−	46447.8i	0.463531	−	0.235613i
$445$	−7142.00	+	24772.5i	−0.0360662	+	0.125098i
$446$	−14090.2	−	8134.96i	−0.0708347	−	0.0408964i
$447$	−104718.	+	53228.3i	−0.524091	+	0.266396i
$448$	−255773.	+	147671.i	−1.27438	+	0.735763i
$449$			56772.8i			0.281610i	0.990037	+	0.140805i	$0.0449690\pi$
$449$			56772.8i			0.281610i	−0.990037	+	0.140805i	$0.955031\pi$
$450$	−29769.9	+	11861.1i	−0.147012	+	0.0585734i
$451$	−98766.7			−0.485576
$452$	62716.6	+	108628.i	0.306977	+	0.531700i
$453$	−259593.	−	13857.9i	−1.26502	−	0.0675304i
$454$	−10833.5	+	18764.2i	−0.0525604	+	0.0910372i
$455$	298336.	+	86011.3i	1.44106	+	0.415463i
$456$	22550.8	−	34651.4i	0.108451	−	0.166645i
$457$	−271096.	+	156518.i	−1.29805	+	0.749429i	−0.980067	−	0.198667i	$-0.936339\pi$
$457$	−271096.	+	156518.i	−1.29805	+	0.749429i	−0.317983	+	0.948096i	$0.603005\pi$
$458$	3316.91			0.0158126
$459$	−196805.	−	31759.8i	−0.934139	−	0.150748i
$460$	−36513.0	−	147349.i	−0.172557	−	0.696354i
$461$	53494.0	−	30884.8i	0.251712	−	0.145326i	−0.368836	−	0.929494i	$-0.620244\pi$
$461$	53494.0	−	30884.8i	0.251712	−	0.145326i	0.620548	+	0.784169i	$0.286910\pi$
$462$	45041.4	−	69210.2i	0.211022	−	0.324255i
$463$	146977.	+	84857.4i	0.685628	+	0.395847i	0.801972	−	0.597362i	$-0.203784\pi$
$463$	146977.	+	84857.4i	0.685628	+	0.395847i	−0.116344	+	0.993209i	$0.537118\pi$
$464$	−72649.5	−	41944.2i	−0.337440	−	0.194821i
$465$	26365.0	+	137404.i	0.121933	+	0.635469i
$466$	−14118.1	−	24453.3i	−0.0650137	−	0.112607i
$467$	−76633.3			−0.351386			−0.175693	−	0.984445i	$-0.556217\pi$
$467$	−76633.3			−0.351386			−0.175693	+	0.984445i	$0.556217\pi$
$468$	149951.	+	109392.i	0.684635	+	0.499454i
$469$	−14441.9			−0.0656565
$470$	9037.84	−	8702.65i	0.0409137	−	0.0393963i
$471$	166790.	−	84779.7i	0.751846	−	0.382164i
$472$	−48740.9	−	28140.5i	−0.218781	−	0.126313i
$473$	77559.2	−	134336.i	0.346666	−	0.600443i
$474$	7572.27	+	14897.2i	0.0337031	+	0.0663054i
$475$	121505.	+	76412.0i	0.538527	+	0.338668i
$476$			360648.i			1.59173i
$477$	−113738.	−	256803.i	−0.499883	−	1.12866i
$478$			22838.3i			0.0999559i
$479$	−30431.7	+	17569.8i	−0.132634	+	0.0765763i	−0.564849	−	0.825194i	$-0.691066\pi$
$479$	−30431.7	+	17569.8i	−0.132634	+	0.0765763i	0.432215	+	0.901771i	$0.357732\pi$
$480$	19928.3	+	103859.i	0.0864944	+	0.450776i
$481$	−53627.6	+	92885.7i	−0.231792	+	0.401475i
$482$	−10772.6	+	18658.7i	−0.0463689	+	0.0803133i
$483$	−248249.	−	161558.i	−1.06412	−	0.692523i
$484$	−115057.	−	199285.i	−0.491159	−	0.850713i
$485$	341023.	−	84505.6i	1.44977	−	0.359254i
$486$	−26558.6	+	26301.5i	−0.112443	+	0.111355i
$487$			290883.i			1.22648i	0.789896	+	0.613240i	$0.210134\pi$
$487$			290883.i			1.22648i	−0.789896	+	0.613240i	$0.789866\pi$
$488$	−53223.1	−	92185.1i	−0.223491	−	0.387098i
$489$	182511.	+	118776.i	0.763256	+	0.496720i
$490$	72178.7	+	20809.4i	0.300619	+	0.0866695i
$491$	−384175.	−	221803.i	−1.59355	−	0.920037i	−0.992691	−	0.120682i	$-0.961492\pi$
$491$	−384175.	−	221803.i	−1.59355	−	0.920037i	−0.600860	−	0.799355i	$-0.705175\pi$
$492$	4311.47	−	80764.8i	0.0178113	−	0.333650i
$493$	−83851.2	+	48411.5i	−0.344997	+	0.199184i
$494$			21355.1i			0.0875080i
$495$	212813.	+	274296.i	0.868535	+	1.11946i
$496$	147327.			0.598853
$497$	118283.	+	204872.i	0.478860	+	0.829410i
$498$	−17784.5	−	34988.1i	−0.0717105	−	0.141079i
$499$	144661.	−	250561.i	0.580967	−	1.00626i	−0.414398	−	0.910096i	$-0.636008\pi$
$499$	144661.	−	250561.i	0.580967	−	1.00626i	0.995365	−	0.0961687i	$-0.0306588\pi$
$500$	−238629.	+	49646.6i	−0.954518	+	0.198586i
$501$	42283.9	+	83186.8i	0.168461	+	0.331420i
$502$	33155.1	−	19142.1i	0.131566	−	0.0759596i
$503$	−349897.			−1.38294			−0.691472	−	0.722403i	$-0.743037\pi$
$503$	−349897.			−1.38294			−0.691472	+	0.722403i	$0.743037\pi$
$504$	110662.	+	80729.8i	0.435649	+	0.317814i
$505$	−330561.	+	81913.0i	−1.29619	+	0.321196i
$506$	36584.4	−	21122.0i	0.142888	−	0.0824963i
$507$	62746.9	+	3349.62i	0.244105	+	0.0130311i
$508$	−109503.	−	63221.8i	−0.424326	−	0.244985i
$509$	406475.	+	234679.i	1.56891	+	0.905812i	0.996296	+	0.0859889i	$0.0274050\pi$
$509$	406475.	+	234679.i	1.56891	+	0.905812i	0.572617	+	0.819823i	$0.305928\pi$
$510$	36795.0	+	12768.9i	0.141465	+	0.0490921i
$511$	247979.	+	429512.i	0.949670	+	1.64488i
$512$	187185.			0.714056
$513$	165281.	+	26672.5i	0.628041	+	0.101351i
$514$	9646.70			0.0365134
$515$	−283454.	−	294372.i	−1.06873	−	1.10989i
$516$	106466.	+	69286.9i	0.399862	+	0.260226i
$517$	−117715.	−	67962.7i	−0.440403	−	0.254267i
$518$	−19537.2	+	33839.5i	−0.0728121	+	0.126114i
$519$	−343562.	−	18340.4i	−1.27547	−	0.0680886i
$520$	−50952.4	−	52914.9i	−0.188433	−	0.195691i
$521$			430054.i			1.58434i	0.610302	+	0.792169i	$0.291048\pi$
$521$			430054.i			1.58434i	−0.610302	+	0.792169i	$0.708952\pi$
$522$	−1932.75	+	18051.0i	−0.00709307	+	0.0662463i
$523$			21279.4i			0.0777959i	0.999243	+	0.0388980i	$0.0123847\pi$
$523$			21279.4i			0.0777959i	−0.999243	+	0.0388980i	$0.987615\pi$
$524$	−79379.9	+	45830.0i	−0.289100	+	0.166912i
$525$	−274270.	+	388506.i	−0.995084	+	1.40955i
$526$	−2045.18	+	3542.36i	−0.00739198	+	0.0128033i
$527$	85021.9	−	147262.i	0.306132	−	0.530237i
$528$	325891.	−	165651.i	1.16897	−	0.594190i
$529$	64158.3	+	111125.i	0.229267	+	0.397102i
$530$	13198.2	+	53261.6i	0.0469855	+	0.189611i
$531$	24264.0	−	226615.i	0.0860544	−	0.803711i
$532$		−	302879.i		−	1.07015i
$533$	42313.6	+	73289.2i	0.148945	+	0.257980i
$534$	313.186	−	5866.77i	0.00109830	−	0.0205739i
$535$	−367381.	−	105917.i	−1.28354	−	0.370049i
$536$	2959.04	+	1708.40i	0.0102996	+	0.00594649i
$537$	219222.	+	142668.i	0.760214	+	0.494741i
$538$	−42389.4	+	24473.5i	−0.146451	+	0.0845536i
$539$		−	813804.i		−	2.80119i
$540$	−233591.	+	162050.i	−0.801066	+	0.555728i
$541$	−127926.			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$541$	−127926.			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$542$	1853.75	+	3210.78i	0.00631033	+	0.0109298i
$543$	−117080.	+	179904.i	−0.397084	+	0.610156i
$544$	64264.9	−	111310.i	0.217158	−	0.376129i
$545$	74724.8	+	21543.4i	0.251577	+	0.0725306i
$546$	−70653.6	−	3771.71i	−0.237000	−	0.0126518i
$547$	437484.	−	252582.i	1.46214	−	0.844165i	0.463026	−	0.886345i	$-0.346764\pi$
$547$	437484.	−	252582.i	1.46214	−	0.844165i	0.999110	+	0.0421802i	$0.0134304\pi$
$548$	−546750.			−1.82065
$549$	254045.	−	348237.i	0.842881	−	1.15539i
$550$	−31670.5	−	59979.3i	−0.104696	−	0.198279i
$551$	70419.9	−	40657.0i	0.231949	−	0.133916i
$552$	31752.9	+	62468.8i	0.104209	+	0.205015i
$553$	214772.	+	123999.i	0.702308	+	0.405478i
$554$	−28667.1	−	16550.9i	−0.0934036	−	0.0539266i
$555$	−107478.	−	124243.i	−0.348925	−	0.403353i
$556$	93494.9	+	161938.i	0.302439	+	0.523840i
$557$	−277756.			−0.895268			−0.447634	−	0.894217i	$-0.647733\pi$
$557$	−277756.			−0.895268			−0.447634	+	0.894217i	$0.647733\pi$
$558$	−12911.3	−	29151.8i	−0.0414669	−	0.0936260i
$559$	−132911.			−0.425342
$560$	347348.	+	360727.i	1.10761	+	1.15028i
$561$	22492.5	−	421342.i	0.0714682	−	1.33878i
$562$	−5746.49	−	3317.74i	−0.0181941	−	0.0105043i
$563$	−80007.5	+	138577.i	−0.252414	+	0.437194i	−0.964190	−	0.265213i	$-0.914558\pi$
$563$	−80007.5	+	138577.i	−0.252414	+	0.437194i	0.711776	+	0.702407i	$0.247891\pi$
$564$	60714.0	−	93292.5i	0.190867	−	0.293284i
$565$	144805.	−	139435.i	0.453615	−	0.436791i
$566$			3518.43i			0.0109829i
$567$	−117438.	+	542123.i	−0.365294	+	1.68629i
$568$		−	55969.1i		−	0.173481i
$569$	152572.	−	88087.7i	0.471250	−	0.272076i	−0.245513	−	0.969393i	$-0.578956\pi$
$569$	152572.	−	88087.7i	0.471250	−	0.272076i	0.716763	+	0.697317i	$0.245623\pi$
$570$	−30901.1	−	10723.5i	−0.0951097	−	0.0330056i
$571$	227502.	−	394045.i	0.697770	−	1.20857i	−0.271467	−	0.962448i	$-0.587509\pi$
$571$	227502.	−	394045.i	0.697770	−	1.20857i	0.969238	−	0.246126i	$-0.0791577\pi$
$572$	−196432.	+	340230.i	−0.600371	+	1.03987i
$573$	2757.05	−	51646.5i	0.00839722	−	0.157301i
$574$	15415.4	+	26700.2i	0.0467876	+	0.0810384i
$575$	−215139.	+	113598.i	−0.650703	+	0.343586i
$576$	114587.	+	258719.i	0.345373	+	0.779800i
$577$		−	356530.i		−	1.07089i	−0.844571	−	0.535444i	$-0.820144\pi$
$577$		−	356530.i		−	1.07089i	0.844571	−	0.535444i	$-0.179856\pi$
$578$	2766.63	+	4791.94i	0.00828124	+	0.0143435i
$579$	50278.8	−	25556.7i	0.149978	−	0.0762339i
$580$	−38251.1	+	132677.i	−0.113707	+	0.394401i
$581$	−504421.	−	291228.i	−1.49431	−	0.862740i
$582$	−71372.1	+	36278.5i	−0.210709	+	0.107103i
$583$	514823.	−	297233.i	1.51468	−	0.874501i
$584$		−	117339.i		−	0.344046i
$585$	112367.	−	275430.i	0.328342	−	0.804823i
$586$	95427.6			0.277894
$587$	−253068.	−	438326.i	−0.734447	−	1.27210i	−0.954965	−	0.296717i	$-0.904108\pi$
$587$	−253068.	−	438326.i	−0.734447	−	1.27210i	0.220518	−	0.975383i	$-0.429225\pi$
$588$	665474.	+	35525.1i	1.92476	+	0.102750i
$589$	−71403.0	+	123674.i	−0.205819	+	0.356489i
$590$	−12334.9	+	42784.6i	−0.0354350	+	0.122909i
$591$	−270560.	+	415739.i	−0.774619	+	1.19027i
$592$	−149812.	+	86494.0i	−0.427467	+	0.246798i
$593$	412533.			1.17314			0.586570	−	0.809899i	$-0.300478\pi$
$593$	412533.			1.17314			0.586570	+	0.809899i	$0.300478\pi$
$594$	−61337.4	−	49967.1i	−0.173841	−	0.141616i
$595$	561019.	−	139021.i	1.58469	−	0.392686i
$596$	176327.	−	101802.i	0.496394	−	0.286593i
$597$	−50933.2	+	78263.5i	−0.142907	+	0.219589i
$598$	−31347.0	−	18098.2i	−0.0876583	−	0.0506095i
$599$	−43173.5	−	24926.2i	−0.120327	−	0.0694708i	0.438628	−	0.898668i	$-0.355464\pi$
$599$	−43173.5	−	24926.2i	−0.120327	−	0.0694708i	−0.558956	+	0.829198i	$0.688798\pi$
$600$	102154.	−	47157.4i	0.283762	−	0.130993i
$601$	−313761.	−	543450.i	−0.868660	−	1.50456i	−0.863367	−	0.504577i	$-0.831648\pi$
$601$	−313761.	−	543450.i	−0.868660	−	1.50456i	−0.00529310	−	0.999986i	$-0.501685\pi$
$602$	−48421.3			−0.133611
$603$	−1473.06	+	13757.7i	−0.00405122	+	0.0378366i
$604$	450581.			1.23509
$605$	−265653.	+	255800.i	−0.725778	+	0.698860i
$606$	69182.4	−	35165.5i	0.188387	−	0.0957572i
$607$	−281368.	−	162448.i	−0.763654	−	0.440896i	0.0669521	−	0.997756i	$-0.478673\pi$
$607$	−281368.	−	162448.i	−0.763654	−	0.440896i	−0.830606	+	0.556860i	$0.812006\pi$
$608$	−53970.9	+	93480.4i	−0.146000	+	0.252879i
$609$	122077.	+	240166.i	0.329153	+	0.647555i
$610$	−60663.8	+	58413.9i	−0.163031	+	0.156984i
$611$			116466.i			0.311973i
$612$	343563.	+	36785.8i	0.917285	+	0.0982148i
$613$			53253.9i			0.141720i	0.997486	+	0.0708599i	$0.0225743\pi$
$613$			53253.9i			0.141720i	−0.997486	+	0.0708599i	$0.977426\pi$
$614$	−76870.8	+	44381.4i	−0.203903	+	0.117724i
$615$	−127299.	+	24425.9i	−0.336568	+	0.0645803i
$616$	−144963.	+	251084.i	−0.382030	+	0.661695i
$617$	186658.	−	323301.i	0.490316	−	0.849252i	−0.509622	−	0.860398i	$-0.670215\pi$
$617$	186658.	−	323301.i	0.490316	−	0.849252i	0.999938	+	0.0111464i	$0.00354807\pi$
$618$	78052.1	+	50795.6i	0.204365	+	0.132999i
$619$	−251035.	−	434806.i	−0.655169	−	1.13479i	−0.981851	−	0.189652i	$-0.939264\pi$
$619$	−251035.	−	434806.i	−0.655169	−	1.13479i	0.326683	−	0.945134i	$-0.394069\pi$
$620$	−58327.7	−	235382.i	−0.151737	−	0.612336i
$621$	−179226.	+	220010.i	−0.464748	+	0.570504i
$622$			120740.i			0.312084i
$623$	−43593.8	−	75506.7i	−0.112318	−	0.194540i
$624$	−262538.	−	170857.i	−0.674253	−	0.438798i
$625$	169215.	+	352071.i	0.433191	+	0.901302i
$626$	18457.6	+	10656.5i	0.0471006	+	0.0271935i
$627$	−18889.7	+	353852.i	−0.0480496	+	0.900090i
$628$	−280846.	+	162147.i	−0.712113	+	0.411139i
$629$			199661.i			0.504651i
$630$	40936.7	−	100343.i	0.103141	−	0.252816i
$631$	−379130.			−0.952202			−0.476101	−	0.879391i	$-0.657950\pi$
$631$	−379130.			−0.952202			−0.476101	+	0.879391i	$0.657950\pi$
$632$	−29336.9	−	50813.0i	−0.0734481	−	0.127216i
$633$	−211235.	−	415570.i	−0.527179	−	1.03714i
$634$	24844.1	−	43031.3i	0.0618081	−	0.107055i
$635$	−56136.2	+	194712.i	−0.139218	+	0.482888i
$636$	220584.	+	433963.i	0.545330	+	1.07285i
$637$	−603879.	+	348649.i	−1.48823	+	0.859231i
$638$	−38424.8			−0.0943996
$639$	207231.	−	91782.7i	0.507520	−	0.224781i
$640$	−58517.0	−	236146.i	−0.142864	−	0.576528i
$641$	325664.	−	188022.i	0.792599	−	0.457607i	−0.0482776	−	0.998834i	$-0.515373\pi$
$641$	325664.	−	188022.i	0.792599	−	0.457607i	0.840877	+	0.541227i	$0.182040\pi$
$642$	87005.2	+	4644.60i	0.211094	+	0.0112688i
$643$	140867.	+	81329.8i	0.340713	+	0.196711i	0.660587	−	0.750749i	$-0.270307\pi$
$643$	140867.	+	81329.8i	0.340713	+	0.196711i	−0.319874	+	0.947460i	$0.603641\pi$
$644$	444594.	+	256686.i	1.07199	+	0.618915i
$645$	66741.9	−	192325.i	0.160428	−	0.462291i
$646$	19876.8	+	34427.6i	0.0476300	+	0.0824976i
$647$	344019.			0.821814			0.410907	−	0.911677i	$-0.365212\pi$
$647$	344019.			0.821814			0.410907	+	0.911677i	$0.365212\pi$
$648$	88192.9	−	97185.1i	0.210031	−	0.231446i
$649$	482389.			1.14527
$650$	−30939.0	+	49197.2i	−0.0732285	+	0.116443i
$651$	−396565.	−	258081.i	−0.935734	−	0.608967i
$652$	−326862.	−	188714.i	−0.768899	−	0.443924i
$653$	−263282.	+	456018.i	−0.617440	+	1.06944i	0.372511	+	0.928028i	$0.378497\pi$
$653$	−263282.	+	456018.i	−0.617440	+	1.06944i	−0.989951	+	0.141410i	$0.954836\pi$
$654$	−17696.7	−	944.706i	−0.0413750	−	0.00220872i
$655$	101891.	+	105816.i	0.237495	+	0.246643i
$656$			136492.i			0.317175i
$657$	434459.	−	192422.i	1.00651	−	0.445783i
$658$			42430.1i			0.0979992i
$659$	−417516.	+	241053.i	−0.961396	+	0.555062i	−0.896602	−	0.442837i	$-0.853972\pi$
$659$	−417516.	+	241053.i	−0.961396	+	0.555062i	−0.0647933	+	0.997899i	$0.520639\pi$
$660$	−393678.	−	455087.i	−0.903761	−	1.04474i
$661$	−185973.	+	322114.i	−0.425644	+	0.737237i	−0.996480	−	0.0838268i	$-0.973286\pi$
$661$	−185973.	+	322114.i	−0.425644	+	0.737237i	0.570836	+	0.821064i	$0.306619\pi$
$662$	54594.2	−	94559.9i	0.124575	−	0.215770i
$663$	−322291.	+	163821.i	−0.733197	+	0.372685i
$664$	68901.6	+	119341.i	0.156276	+	0.270679i
$665$	−471155.	+	116752.i	−1.06542	+	0.264011i
$666$	30243.6	+	22063.3i	0.0681845	+	0.0497419i
$667$			137825.i			0.309796i
$668$	−80870.7	−	140072.i	−0.181233	−	0.313905i
$669$	−12331.3	+	230996.i	−0.0275521	+	0.516121i
$670$	748.850	−	2597.44i	0.00166819	−	0.00578623i
$671$	790126.	+	456179.i	1.75489	+	1.01319i
$672$	−299749.	−	195074.i	−0.663772	−	0.431977i
$673$	243512.	−	140592.i	0.537638	−	0.310406i	−0.206483	−	0.978450i	$-0.566202\pi$
$673$	243512.	−	140592.i	0.537638	−	0.310406i	0.744121	+	0.668045i	$0.232868\pi$
$674$		−	20446.0i		−	0.0450078i
$675$	342126.	+	300905.i	0.750895	+	0.660422i
$676$	−108911.			−0.238330
$677$	134768.	+	233424.i	0.294041	+	0.509295i	0.974761	−	0.223249i	$-0.0716663\pi$
$677$	134768.	+	233424.i	0.294041	+	0.509295i	−0.680720	+	0.732544i	$0.738333\pi$
$678$	−24987.0	+	38394.8i	−0.0543569	+	0.0835243i
$679$	−594074.	+	1.02897e6i	−1.28855	+	2.23183i
$680$	−131395.	−	37881.5i	−0.284158	−	0.0819236i
$681$	307623.	+	16421.9i	0.663322	+	0.0354102i
$682$	58441.8	−	33741.4i	0.125648	−	0.0725428i
$683$	425001.			0.911063			0.455531	−	0.890220i	$-0.349449\pi$
$683$	425001.			0.911063			0.455531	+	0.890220i	$0.349449\pi$
$684$	−288531.	−	30893.4i	−0.616710	−	0.0660319i
$685$	210758.	+	850516.i	0.449162	+	1.81260i
$686$	−108721.	+	62770.3i	−0.231029	+	0.133385i
$687$	−21369.1	−	42040.3i	−0.0452766	−	0.0890743i
$688$	−185648.	−	107184.i	−0.392205	−	0.226440i
$689$	−441121.	−	254681.i	−0.929221	−	0.536486i
$690$	41929.3	−	36271.4i	0.0880683	−	0.0761845i
$691$	−204712.	−	354571.i	−0.428732	−	0.742586i	0.568028	−	0.823009i	$-0.307706\pi$
$691$	−204712.	−	354571.i	−0.428732	−	0.742586i	−0.996761	+	0.0804226i	$0.974373\pi$
$692$	596329.			1.24530
$693$	−1.16739e6	−	124994.i	−2.43079	−	0.260268i
$694$	147018.			0.305247
$695$	215868.	−	207862.i	0.446909	−	0.430334i
$696$	3397.80	−	63649.5i	0.00701423	−	0.131394i
$697$	136431.	+	78768.7i	0.280834	+	0.162139i
$698$	52525.1	−	90976.2i	0.107809	−	0.186731i
$699$	−218979.	+	336481.i	−0.448175	+	0.688662i
$700$	438809.	−	697764.i	0.895528	−	1.42401i
$701$		−	590764.i		−	1.20220i	−0.799172	−	0.601102i	$-0.794728\pi$
$701$		−	590764.i		−	1.20220i	0.799172	−	0.601102i	$-0.205272\pi$
$702$	−10799.6	+	66921.9i	−0.0219147	+	0.135798i
$703$		−	167679.i		−	0.339288i
$704$	−518665.	+	299451.i	−1.04651	+	0.604201i
$705$	−168528.	−	58483.9i	−0.339074	−	0.117668i
$706$	40885.9	−	70816.5i	0.0820285	−	0.142077i
$707$	575848.	−	997398.i	1.15204	−	1.99540i
$708$	−21057.8	+	394466.i	−0.0420094	+	0.786942i
$709$	−143727.	−	248942.i	−0.285920	−	0.495228i	0.686912	−	0.726741i	$-0.258966\pi$
$709$	−143727.	−	248942.i	−0.285920	−	0.495228i	−0.972832	+	0.231513i	$0.925632\pi$
$710$	−42980.4	+	10650.5i	−0.0852616	+	0.0211278i
$711$	140031.	−	191950.i	0.277004	−	0.379708i
$712$			20627.7i			0.0406904i
$713$	−121026.	−	209624.i	−0.238068	−	0.412346i
$714$	−117415.	+	59682.0i	−0.230317	+	0.117070i
$715$	604976.	+	174417.i	1.18339	+	0.341174i
$716$	−392610.	−	226673.i	−0.765835	−	0.442155i
$717$	289466.	−	147136.i	0.563065	−	0.286207i
$718$	112582.	−	64999.2i	0.218383	−	0.126084i
$719$			645625.i			1.24889i	0.781070	+	0.624443i	$0.214674\pi$
$719$			645625.i			1.24889i	−0.781070	+	0.624443i	$0.785326\pi$
$720$	379067.	−	294100.i	0.731226	−	0.567322i
$721$	1.38199e6			2.65849
$722$	24553.9	+	42528.6i	0.0471027	+	0.0815843i
$723$	305893.	+	16329.5i	0.585185	+	0.0312390i
$724$	186019.	−	322194.i	0.354878	−	0.614668i
$725$	221135.	+	8359.41i	0.420708	+	0.0159038i
$726$	45840.0	−	70437.3i	0.0869703	−	0.133638i
$727$	−462909.	+	267261.i	−0.875844	+	0.505669i	−0.869286	−	0.494310i	$-0.835421\pi$
$727$	−462909.	+	267261.i	−0.875844	+	0.505669i	−0.00655839	+	0.999978i	$0.502088\pi$
$728$	248420.			0.468732
$729$	504464.	+	167171.i	0.949237	+	0.314562i
$730$	−90108.0	+	22328.8i	−0.169090	+	0.0419005i
$731$	−214273.	+	123710.i	−0.400989	+	0.231511i
$732$	−407524.	+	626198.i	−0.760556	+	1.16866i
$733$	−163651.	−	94483.8i	−0.304586	−	0.175853i	0.339915	−	0.940456i	$-0.389602\pi$
$733$	−163651.	−	94483.8i	−0.304586	−	0.175853i	−0.644501	+	0.764603i	$0.722935\pi$
$734$	−56856.4	−	32826.1i	−0.105533	−	0.0609294i
$735$	−201261.	−	1.04890e6i	−0.372551	−	1.94159i
$736$	−91479.3	−	158447.i	−0.168876	−	0.292501i
$737$	−29285.7			−0.0539164
$738$	27007.7	−	11961.7i	0.0495879	−	0.0219625i
$739$	−683135.			−1.25089			−0.625443	−	0.780270i	$-0.715082\pi$
$739$	−683135.			−1.25089			−0.625443	+	0.780270i	$0.715082\pi$
$740$	197501.	+	205108.i	0.360666	+	0.374558i
$741$	270666.	−	137580.i	0.492944	−	0.250564i
$742$	−160706.	−	92783.6i	−0.291893	−	0.168525i
$743$	−150819.	+	261226.i	−0.273198	+	0.473193i	−0.969679	−	0.244382i	$-0.921415\pi$
$743$	−150819.	+	261226.i	−0.273198	+	0.473193i	0.696481	+	0.717576i	$0.254748\pi$
$744$	50723.7	+	99790.8i	0.0916359	+	0.180279i
$745$	−226332.	−	235050.i	−0.407787	−	0.423494i
$746$			114164.i			0.205141i
$747$	−328882.	+	450821.i	−0.589385	+	0.807909i
$748$			731334.i			1.30711i
$749$	1.11978e6	−	646504.i	1.99603	−	1.15241i
$750$	−55652.9	−	69473.8i	−0.0989386	−	0.123509i
$751$	−115004.	+	199192.i	−0.203907	+	0.353177i	−0.949784	−	0.312906i	$-0.898697\pi$
$751$	−115004.	+	199192.i	−0.203907	+	0.353177i	0.745877	+	0.666084i	$0.232031\pi$
$752$	−93922.0	+	162678.i	−0.166085	+	0.287669i
$753$	−456219.	−	296903.i	−0.804606	−	0.523631i
$754$	16461.9	+	28512.9i	0.0289559	+	0.0501532i
$755$	−173688.	−	700918.i	−0.304702	−	1.22963i
$756$	153171.	−	949154.i	0.267999	−	1.66071i
$757$			897739.i			1.56660i	0.621644	+	0.783300i	$0.286465\pi$
$757$			897739.i			1.56660i	−0.621644	+	0.783300i	$0.713535\pi$
$758$	45946.1	+	79580.9i	0.0799668	+	0.138507i
$759$	−503407.	−	327613.i	−0.873847	−	0.568692i
$760$	110348.	+	31813.6i	0.191045	+	0.0550790i
$761$	−343014.	−	198039.i	−0.592301	−	0.341965i	0.173706	−	0.984798i	$-0.444426\pi$
$761$	−343014.	−	198039.i	−0.592301	−	0.341965i	−0.766007	+	0.642833i	$0.777759\pi$
$762$	2461.64	−	46112.8i	0.00423951	−	0.0794167i
$763$	−227761.	+	131498.i	−0.391229	+	0.225876i
$764$			89644.1i			0.153580i
$765$	−75211.5	−	548623.i	−0.128517	−	0.937456i
$766$	−71806.5			−0.122379
$767$	−206665.	−	357954.i	−0.351298	−	0.608467i
$768$	−202817.	−	399009.i	−0.343860	−	0.676488i
$769$	−96241.3	+	166695.i	−0.162745	+	0.281883i	−0.935852	−	0.352392i	$-0.885368\pi$
$769$	−96241.3	+	166695.i	−0.162745	+	0.281883i	0.773107	+	0.634276i	$0.218702\pi$
$770$	220401.	+	63542.2i	0.371733	+	0.107172i
$771$	−62148.7	−	122268.i	−0.104550	−	0.205685i
$772$	−84660.7	+	48878.9i	−0.142052	+	0.0820138i
$773$	542226.			0.907447			0.453723	−	0.891143i	$-0.350095\pi$
$773$	542226.			0.907447			0.453723	+	0.891143i	$0.350095\pi$
$774$	−4938.93	+	46127.5i	−0.00824425	+	0.0769978i
$775$	−343673.	+	181468.i	−0.572193	+	0.302131i
$776$	243444.	−	140552.i	0.404273	−	0.233407i
$777$	554768.	+	29615.2i	0.918903	+	0.0490538i
$778$	145173.	+	83815.8i	0.239843	+	0.138474i
$779$	−114578.	−	66151.5i	−0.188810	−	0.109010i
$780$	−169035.	+	487095.i	−0.277836	+	0.800616i
$781$	239858.	+	415446.i	0.393234	+	0.681102i
$782$	−67381.2			−0.110186
$783$	241241.	−	91796.9i	0.393484	−	0.149729i
$784$	−1.12465e6			−1.82972
$785$	360492.	+	374377.i	0.585001	+	0.607533i
$786$	−28056.9	−	18259.2i	−0.0454145	−	0.0295554i
$787$	−852809.	−	492370.i	−1.37690	−	0.794954i	−0.385115	−	0.922869i	$-0.625838\pi$
$787$	−852809.	−	492370.i	−1.37690	−	0.794954i	−0.991785	+	0.127915i	$0.959172\pi$
$788$	429870.	−	744557.i	0.692285	−	1.19907i
$789$	58073.9	+	3100.17i	0.0932883	+	0.00498002i
$790$	−33438.3	+	32198.1i	−0.0535784	+	0.0515912i
$791$			679819.i			1.08653i
$792$	224404.	+	163707.i	0.357750	+	0.260985i
$793$		−	781744.i		−	1.24313i
$794$	45336.2	−	26174.8i	0.0719124	−	0.0415186i
$795$	590037.	−	510419.i	0.933567	−	0.807593i
$796$	80923.6	−	140164.i	0.127717	−	0.221213i
$797$	455717.	−	789324.i	0.717428	−	1.24262i	−0.244588	−	0.969627i	$-0.578653\pi$
$797$	455717.	−	789324.i	0.717428	−	1.24262i	0.962016	−	0.272994i	$-0.0880140\pi$
$798$	98607.2	−	50122.1i	0.154847	−	0.0787089i
$799$	108404.	+	187761.i	0.169805	+	0.294111i
$800$	−259770.	+	137165.i	−0.405891	+	0.214320i
$801$	−76376.3	+	33827.1i	−0.119040	+	0.0527229i
$802$		−	15253.1i		−	0.0237142i
$803$	502860.	+	870979.i	0.779859	+	1.35075i
$804$	1278.41	−	23947.9i	0.00197769	−	0.0370472i
$805$	227918.	−	790550.i	0.351712	−	1.21994i
$806$	−50075.2	−	28910.9i	−0.0770819	−	0.0445033i
$807$	583284.	+	379596.i	0.895639	+	0.582874i
$808$	−235975.	+	136240.i	−0.361446	+	0.208681i
$809$			485562.i			0.741904i	0.928652	+	0.370952i	$0.120969\pi$
$809$			485562.i			0.741904i	−0.928652	+	0.370952i	$0.879031\pi$
$810$	−91413.9	−	49232.3i	−0.139329	−	0.0750378i
$811$	157252.			0.239087			0.119543	−	0.992829i	$-0.461857\pi$
$811$	157252.			0.239087			0.119543	+	0.992829i	$0.461857\pi$
$812$	−233479.	−	404398.i	−0.354109	−	0.613334i
$813$	28752.5	−	44180.9i	0.0435005	−	0.0668425i
$814$	−39618.2	+	68620.8i	−0.0597924	+	0.103564i
$815$	−167564.	+	581207.i	−0.252270	+	0.875015i
$816$	−582280.	−	31083.9i	−0.874483	−	0.0466826i
$817$	179951.	−	103895.i	0.269593	−	0.155650i
$818$	−105468.			−0.157622
$819$	407380.	+	919802.i	0.607340	+	1.37128i
$820$	218070.	−	54037.9i	0.324316	−	0.0803657i
$821$	−492419.	+	284298.i	−0.730548	+	0.421782i	−0.818623	−	0.574332i	$-0.805262\pi$
$821$	−492419.	+	284298.i	−0.730548	+	0.421782i	0.0880747	+	0.996114i	$0.471929\pi$
$822$	−90479.1	−	178003.i	−0.133907	−	0.263441i
$823$	621801.	+	358997.i	0.918019	+	0.530018i	0.883002	−	0.469368i	$-0.155518\pi$
$823$	621801.	+	358997.i	0.918019	+	0.530018i	0.0350164	+	0.999387i	$0.488852\pi$
$824$	−283161.	−	163483.i	−0.417041	−	0.240779i
$825$	−556174.	+	787825.i	−0.817152	+	1.15750i
$826$	−75290.7	−	130407.i	−0.110352	−	0.191136i
$827$	39891.9			0.0583275			0.0291638	−	0.999575i	$-0.490716\pi$
$827$	39891.9			0.0583275			0.0291638	+	0.999575i	$0.490716\pi$
$828$	289875.	−	397351.i	0.422815	−	0.579580i
$829$	1.05219e6			1.53103			0.765515	−	0.643418i	$-0.222484\pi$
$829$	1.05219e6			1.53103			0.765515	+	0.643418i	$0.222484\pi$
$830$	78534.2	−	75621.5i	0.113999	−	0.109771i
$831$	−25088.5	+	469971.i	−0.0363306	+	0.680564i
$832$	444412.	+	256582.i	0.642007	+	0.370663i
$833$	−649028.	+	1.12415e6i	−0.935348	+	1.62007i
$834$	−37249.4	+	57237.1i	−0.0535534	+	0.0822897i
$835$	−186721.	+	179796.i	−0.267806	+	0.257873i
$836$		−	614189.i		−	0.878799i
$837$	−286304.	+	351455.i	−0.408674	+	0.501671i
$838$		−	68363.3i		−	0.0973498i
$839$	−849479.	+	490447.i	−1.20678	+	0.696736i	−0.962055	−	0.272856i	$-0.912032\pi$
$839$	−849479.	+	490447.i	−1.20678	+	0.696736i	−0.244727	+	0.969592i	$0.578698\pi$
$840$	−124745.	+	359468.i	−0.176793	+	0.509450i
$841$	−290958.	+	503955.i	−0.411376	+	0.712524i
$842$	−81926.5	+	141901.i	−0.115558	+	0.200153i
$843$	−5029.14	+	94208.6i	−0.00707683	+	0.132567i
$844$	404000.	+	699749.i	0.567148	+	0.982329i
$845$	41982.5	+	169421.i	0.0587970	+	0.237276i
$846$	40420.1	+	4327.84i	0.0564751	+	0.00604686i
$847$		−	1.24717e6i		−	1.73843i
$848$	−410766.	−	711467.i	−0.571219	−	0.989380i
$849$	44594.5	−	22667.4i	0.0618680	−	0.0314476i
$850$	−4086.83	+	108110.i	−0.00565651	+	0.149634i
$851$	246135.	+	142106.i	0.339870	+	0.196224i
$852$	−350194.	+	178004.i	−0.482425	+	0.245217i
$853$	608193.	−	351140.i	0.835879	−	0.482595i	−0.0199823	−	0.999800i	$-0.506361\pi$
$853$	608193.	−	351140.i	0.835879	−	0.482595i	0.855861	+	0.517205i	$0.173028\pi$
$854$		−	284799.i		−	0.390502i
$855$	63164.1	+	460744.i	0.0864049	+	0.630271i
$856$	−305913.			−0.417494
$857$	258863.	+	448364.i	0.352459	+	0.610476i	0.986680	−	0.162676i	$-0.0520124\pi$
$857$	258863.	+	448364.i	0.352459	+	0.610476i	−0.634221	+	0.773152i	$0.718679\pi$
$858$	−143274.	−	7648.39i	−0.194622	−	0.0103895i
$859$	324805.	−	562579.i	0.440186	−	0.762425i	−0.557517	−	0.830166i	$-0.688246\pi$
$859$	324805.	−	562579.i	0.440186	−	0.762425i	0.997703	+	0.0677408i	$0.0215791\pi$
$860$	−97746.5	+	339041.i	−0.132161	+	0.458411i
$861$	239100.	−	367399.i	0.322532	−	0.495600i
$862$	−44434.0	+	25654.0i	−0.0598000	+	0.0345255i
$863$	−1.39346e6			−1.87100			−0.935499	−	0.353329i	$-0.885050\pi$
$863$	−1.39346e6			−1.87100			−0.935499	+	0.353329i	$0.885050\pi$
$864$	−216407.	+	265652.i	−0.289897	+	0.355865i
$865$	−229870.	−	927642.i	−0.307220	−	1.23979i
$866$	−95267.2	+	55002.6i	−0.127030	+	0.0733410i
$867$	42911.7	−	65937.8i	0.0570871	−	0.0877195i
$868$	710217.	+	410044.i	0.942652	+	0.544240i
$869$	435522.	+	251449.i	0.576728	+	0.332974i
$870$	−49524.9	+	9502.79i	−0.0654313	+	0.0125549i
$871$	12546.6	+	21731.3i	0.0165382	+	0.0286450i
$872$	62222.3			0.0818301
$873$	919628.	+	670886.i	1.20666	+	0.880278i
$874$	56588.1			0.0740802
$875$	−1.25458e6	−	413634.i	−1.63864	−	0.540257i
$876$	−734179.	+	373184.i	−0.956740	+	0.486312i
$877$	−642695.	−	371060.i	−0.835614	−	0.482442i	0.0201572	−	0.999797i	$-0.493583\pi$
$877$	−642695.	−	371060.i	−0.835614	−	0.482442i	−0.855771	+	0.517355i	$0.826917\pi$
$878$	81935.6	−	141917.i	0.106288	−	0.184096i
$879$	−614791.	−	1.20950e6i	−0.795701	−	1.56541i
$880$	704364.	+	731493.i	0.909561	+	0.944594i
$881$		−	737962.i		−	0.950784i	−0.879774	−	0.475392i	$-0.842306\pi$
$881$		−	737962.i		−	0.950784i	0.879774	−	0.475392i	$-0.157694\pi$
$882$	98560.5	+	222535.i	0.126697	+	0.286062i
$883$		−	143168.i		−	0.183622i	−0.995776	−	0.0918109i	$-0.970734\pi$
$883$		−	143168.i		−	0.183622i	0.995776	−	0.0918109i	$-0.0292655\pi$
$884$	542682.	−	313318.i	0.694450	−	0.400941i
$885$	621742.	−	119299.i	0.793824	−	0.152318i
$886$	60915.4	−	105509.i	0.0775996	−	0.134406i
$887$	−504758.	+	874267.i	−0.641559	+	1.11121i	0.343526	+	0.939143i	$0.388379\pi$
$887$	−504758.	+	874267.i	−0.641559	+	1.11121i	−0.985085	+	0.172069i	$0.944955\pi$
$888$	−110165.	−	71694.4i	−0.139707	−	0.0909199i
$889$	−342648.	−	593483.i	−0.433555	−	0.750939i
$890$	15840.7	−	3925.32i	0.0199983	−	0.00495559i
$891$	−238145.	+	1.09934e6i	−0.299975	+	1.38476i
$892$		−	400945.i		−	0.503912i
$893$	−91039.6	−	157685.i	−0.114164	−	0.197737i
$894$	62323.0	+	40559.2i	0.0779782	+	0.0507475i
$895$	−201269.	+	698115.i	−0.251264	+	0.871528i
$896$	712521.	+	411374.i	0.887527	+	0.512414i
$897$	−27433.9	+	513906.i	−0.0340959	+	0.638702i
$898$	31122.7	−	17968.7i	0.0385944	−	0.0222825i
$899$			220169.i			0.272418i
$900$	−619952.	−	489193.i	−0.765373	−	0.603942i
$901$	−948202.			−1.16802
$902$	31259.8	+	54143.6i	0.0384214	+	0.0665478i
$903$	311954.	+	613719.i	0.382573	+	0.752651i
$904$	80419.4	−	139290.i	0.0984065	−	0.170445i
$905$	−572906.	−	165171.i	−0.699498	−	0.201667i
$906$	74564.7	+	146694.i	0.0908399	+	0.178713i
$907$	−415123.	+	239672.i	−0.504618	+	0.291341i	−0.730618	−	0.682786i	$-0.760768\pi$
$907$	−415123.	+	239672.i	−0.504618	+	0.291341i	0.226001	+	0.974127i	$0.427435\pi$
$908$	−533949.			−0.647631
$909$	−891414.	−	650303.i	−1.07883	−	0.787024i
$910$	−47272.8	−	190770.i	−0.0570858	−	0.230370i
$911$	755164.	−	435994.i	0.909923	−	0.525344i	0.0295167	−	0.999564i	$-0.490603\pi$
$911$	755164.	−	435994.i	0.909923	−	0.525344i	0.880406	+	0.474220i	$0.157270\pi$
$912$	489010.	+	26104.9i	0.587933	+	0.0313857i
$913$	−1.02288e6	−	590561.i	−1.22711	−	0.708473i
$914$	171605.	+	99076.1i	0.205417	+	0.118598i
$915$	1.13119e6	+	392555.i	1.35112	+	0.468877i
$916$	40869.8	+	70788.6i	0.0487093	+	0.0843670i
$917$	−496776.			−0.590775
$918$	44878.6	+	117940.i	0.0532542	+	0.139951i
$919$	411896.			0.487705			0.243852	−	0.969812i	$-0.421589\pi$
$919$	411896.			0.487705			0.243852	+	0.969812i	$0.421589\pi$
$920$	−140217.	+	135017.i	−0.165663	+	0.159519i
$921$	1.05775e6	+	688376.i	1.24700	+	0.811533i
$922$	−33861.9	−	19550.2i	−0.0398336	−	0.0229979i
$923$	205519.	−	355970.i	0.241240	−	0.417840i
$924$	2.03205e6	+	108477.i	2.38008	+	0.127056i
$925$	242932.	−	386294.i	0.283923	−	0.451476i
$926$		−	107430.i		−	0.125286i
$927$	140962.	−	1.31652e6i	0.164037	−	1.53204i
$928$			166417.i			0.193243i
$929$	756603.	−	436825.i	0.876671	−	0.506146i	0.00711192	−	0.999975i	$-0.497736\pi$
$929$	756603.	−	436825.i	0.876671	−	0.506146i	0.869559	+	0.493828i	$0.164403\pi$
$930$	66980.0	−	57941.8i	0.0774425	−	0.0669925i
$931$	545066.	−	944083.i	0.628854	−	1.08921i
$932$	347918.	−	602611.i	0.400539	−	0.693753i
$933$	1.53033e6	−	777867.i	1.75801	−	0.893597i
$934$	24254.6	+	42010.1i	0.0278035	+	0.0481571i
$935$	1.13765e6	−	281911.i	1.30133	−	0.322469i
$936$	25338.7	−	236652.i	0.0289222	−	0.270121i
$937$			271368.i			0.309086i	0.987986	+	0.154543i	$0.0493906\pi$
$937$			271368.i			0.309086i	−0.987986	+	0.154543i	$0.950609\pi$
$938$	4570.88	+	7916.99i	0.00519510	+	0.00899817i
$939$	16153.5	−	302596.i	0.0183204	−	0.343188i
$940$	297091.	+	85652.3i	0.336228	+	0.0969356i
$941$	554563.	+	320177.i	0.626284	+	0.361585i	0.779312	−	0.626636i	$-0.215569\pi$
$941$	554563.	+	320177.i	0.626284	+	0.361585i	−0.153027	+	0.988222i	$0.548902\pi$
$942$	−99265.4	−	64601.0i	−0.111865	−	0.0728010i
$943$	194207.	−	112125.i	0.218394	−	0.126090i
$944$		−	666644.i		−	0.748084i
$945$	−1.53553e6	+	127603.i	−1.71947	+	0.142889i
$946$	−98190.4			−0.109720
$947$	257159.	+	445412.i	0.286749	+	0.496663i	0.973032	−	0.230671i	$-0.0740922\pi$
$947$	257159.	+	445412.i	0.286749	+	0.496663i	−0.686283	+	0.727335i	$0.740759\pi$
$948$	−224630.	+	345164.i	−0.249949	+	0.384069i
$949$	430870.	−	746288.i	0.478425	−	0.828656i
$950$	3432.20	−	90793.3i	0.00380299	−	0.100602i
$951$	−705460.	−	37659.6i	−0.780031	−	0.0416404i
$952$	400491.	−	231223.i	0.441894	−	0.255128i
$953$	−926631.			−1.02028			−0.510142	−	0.860090i	$-0.670407\pi$
$953$	−926631.			−1.02028			−0.510142	+	0.860090i	$0.670407\pi$
$954$	−104780.	+	143629.i	−0.115128	+	0.157814i
$955$	139449.	−	34555.5i	0.152901	−	0.0378888i
$956$	−487410.	+	281406.i	−0.533309	+	0.307906i
$957$	247551.	+	487017.i	0.270297	+	0.531765i
$958$	19263.4	+	11121.7i	0.0209895	+	0.0121183i
$959$	−2.56626e6	−	1.48163e6i	−2.79038	−	1.61102i
$960$	−594441.	+	514228.i	−0.645009	+	0.557973i
$961$	268427.	+	464929.i	0.290656	+	0.503431i
$962$	67892.9			0.0733625
$963$	−501662.	−	1.13267e6i	−0.540951	−	1.22138i
$964$	−530946.			−0.571343
$965$	108670.	+	112856.i	0.116696	+	0.121190i
$966$	−9994.51	+	187222.i	−0.0107104	+	0.200634i
$967$	236777.	+	136703.i	0.253213	+	0.146193i	0.621235	−	0.783625i	$-0.286631\pi$
$967$	236777.	+	136703.i	0.253213	+	0.146193i	−0.368022	+	0.929817i	$0.619965\pi$
$968$	−147534.	+	255536.i	−0.157449	+	0.272710i
$969$	308298.	−	473728.i	0.328340	−	0.504524i
$970$	−154260.	−	160202.i	−0.163949	−	0.170264i
$971$		−	952676.i		−	1.01043i	−0.862993	−	0.505215i	$-0.831413\pi$
$971$		−	952676.i		−	1.01043i	0.862993	−	0.505215i	$-0.168587\pi$
$972$	−888567.	−	242728.i	−0.940498	−	0.256914i
$973$			1.01344e6i			1.07047i
$974$	159461.	−	92065.0i	0.168088	−	0.0970457i
$975$	822877.	+	75186.1i	0.865617	+	0.0790912i
$976$	630423.	−	1.09192e6i	0.661808	−	1.14629i
$977$	−551504.	+	955232.i	−0.577776	+	1.00074i	0.417958	+	0.908466i	$0.362746\pi$
$977$	−551504.	+	955232.i	−0.577776	+	1.00074i	−0.995734	+	0.0922705i	$0.970588\pi$
$978$	7347.89	−	137645.i	0.00768219	−	0.143907i
$979$	−88401.0	−	153115.i	−0.0922341	−	0.159754i
$980$	445254.	+	1.79683e6i	0.463613	+	1.87091i
$981$	102037.	+	230384.i	0.106028	+	0.239395i
$982$			280805.i			0.291193i
$983$	572312.	+	991274.i	0.592278	+	1.02586i	0.993925	+	0.110062i	$0.0351048\pi$
$983$	572312.	+	991274.i	0.592278	+	1.02586i	−0.401646	+	0.915795i	$0.631562\pi$
$984$	−92451.4	+	46993.2i	−0.0954824	+	0.0485338i
$985$	−1.32393e6	−	381692.i	−1.36456	−	0.393406i
$986$	53078.1	+	30644.6i	0.0545961	+	0.0315211i
$987$	537783.	−	273356.i	0.552043	−	0.280604i
$988$	−455755.	+	263130.i	−0.466893	+	0.269561i
$989$			352197.i			0.360075i
$990$	83012.8	−	203479.i	0.0846983	−	0.207610i
$991$	−320938.			−0.326794			−0.163397	−	0.986560i	$-0.552245\pi$
$991$	−320938.			−0.326794			−0.163397	+	0.986560i	$0.552245\pi$
$992$	−146134.	−	253111.i	−0.148500	−	0.257210i
$993$	−1.55023e6	−	82755.8i	−1.57216	−	0.0839267i
$994$	74873.3	−	129684.i	0.0757800	−	0.131255i
$995$	−249231.	−	71854.1i	−0.251742	−	0.0725780i
$996$	527573.	−	810664.i	0.531819	−	0.817188i
$997$	863459.	−	498518.i	0.868663	−	0.501523i	0.00175952	−	0.999998i	$-0.499440\pi$
$997$	863459.	−	498518.i	0.868663	−	0.501523i	0.866904	+	0.498475i	$0.166107\pi$
$998$	−183142.			−0.183877
$999$	84798.2	−	525467.i	0.0849680	−	0.526520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.11	✓	44
3.2	odd	2		135.5.h.a.44.12		44
5.4	even	2	inner	45.5.h.a.14.12	yes	44
9.2	odd	6	inner	45.5.h.a.29.12	yes	44
9.4	even	3		405.5.d.a.404.24		44
9.5	odd	6		405.5.d.a.404.22		44
9.7	even	3		135.5.h.a.89.11		44
15.14	odd	2		135.5.h.a.44.11		44
45.4	even	6		405.5.d.a.404.21		44
45.14	odd	6		405.5.d.a.404.23		44
45.29	odd	6	inner	45.5.h.a.29.11	yes	44
45.34	even	6		135.5.h.a.89.12		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.11	✓	44	1.1	even	1	trivial
45.5.h.a.14.12	yes	44	5.4	even	2	inner
45.5.h.a.29.11	yes	44	45.29	odd	6	inner
45.5.h.a.29.12	yes	44	9.2	odd	6	inner
135.5.h.a.44.11		44	15.14	odd	2
135.5.h.a.44.12		44	3.2	odd	2
135.5.h.a.89.11		44	9.7	even	3
135.5.h.a.89.12		44	45.34	even	6
405.5.d.a.404.21		44	45.4	even	6
405.5.d.a.404.22		44	9.5	odd	6
405.5.d.a.404.23		44	45.14	odd	6
405.5.d.a.404.24		44	9.4	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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.316502 - 0.548197i) q^{2} +(-4.90909 + 7.54326i) q^{3} +(7.79965 - 13.5094i) q^{4} +(-24.0216 - 6.92551i) q^{5} +(5.68893 + 0.303692i) q^{6} +(73.2178 - 42.2723i) q^{7} -20.0025 q^{8} +(-32.8017 - 74.0611i) q^{9} +(3.80633 + 15.3605i) q^{10} +(148.474 - 85.7213i) q^{11} +(63.6157 + 125.154i) q^{12} +(-127.218 - 73.4493i) q^{13} +(-46.3471 - 26.7585i) q^{14} +(170.165 - 147.203i) q^{15} +(-118.464 - 205.185i) q^{16} -273.459 q^{17} +(-30.2183 + 41.4222i) q^{18} +229.656 q^{19} +(-280.920 + 270.501i) q^{20} +(-40.5615 + 759.820i) q^{21} +(-93.9843 - 54.2618i) q^{22} +(-194.631 + 337.110i) q^{23} +(98.1939 - 150.884i) q^{24} +(529.075 + 332.723i) q^{25} +92.9873i q^{26} +(719.689 + 116.141i) q^{27} -1318.84i q^{28} +(306.632 - 177.034i) q^{29} +(-134.554 - 46.6939i) q^{30} +(-310.913 + 538.517i) q^{31} +(-235.008 + 407.045i) q^{32} +(-82.2521 + 1540.79i) q^{33} +(86.5501 + 149.909i) q^{34} +(-2051.57 + 508.379i) q^{35} +(-1256.36 - 134.520i) q^{36} -730.131i q^{37} +(-72.6865 - 125.897i) q^{38} +(1178.57 - 599.069i) q^{39} +(480.491 + 138.527i) q^{40} +(-498.910 - 288.046i) q^{41} +(429.369 - 218.249i) q^{42} +(783.565 - 452.392i) q^{43} -2674.39i q^{44} +(275.038 + 2006.24i) q^{45} +246.404 q^{46} +(-396.417 - 686.614i) q^{47} +(2129.31 + 113.669i) q^{48} +(2373.40 - 4110.85i) q^{49} +(14.9450 - 395.345i) q^{50} +(1342.43 - 2062.77i) q^{51} +(-1984.51 + 1145.76i) q^{52} +3467.44 q^{53} +(-164.115 - 431.290i) q^{54} +(-4160.24 + 1030.91i) q^{55} +(-1464.54 + 845.551i) q^{56} +(-1127.40 + 1732.36i) q^{57} +(-194.099 - 112.063i) q^{58} +(2436.74 + 1406.85i) q^{59} +(-661.400 - 3446.96i) q^{60} +(2660.83 + 4608.69i) q^{61} +393.618 q^{62} +(-5532.41 - 4035.99i) q^{63} -3493.32 q^{64} +(2547.30 + 2645.42i) q^{65} +(870.688 - 442.572i) q^{66} +(-147.934 - 85.4097i) q^{67} +(-2132.88 + 3694.26i) q^{68} +(-1587.45 - 3123.05i) q^{69} +(928.016 + 963.760i) q^{70} +2798.11i q^{71} +(656.114 + 1481.40i) q^{72} +5866.22i q^{73} +(-400.255 + 231.088i) q^{74} +(-5107.10 + 2357.58i) q^{75} +(1791.24 - 3102.52i) q^{76} +(7247.28 - 12552.7i) q^{77} +(-701.428 - 456.483i) q^{78} +(1466.67 + 2540.34i) q^{79} +(1424.68 + 5749.29i) q^{80} +(-4409.10 + 4858.66i) q^{81} +364.668i q^{82} +(-3444.66 - 5966.32i) q^{83} +(9948.35 + 6474.30i) q^{84} +(6568.92 + 1893.84i) q^{85} +(-495.999 - 286.365i) q^{86} +(-169.869 + 3182.08i) q^{87} +(-2969.84 + 1714.64i) q^{88} -1031.26i q^{89} +(1012.76 - 785.751i) q^{90} -12419.5 q^{91} +(3036.10 + 5258.68i) q^{92} +(-2535.88 - 4988.93i) q^{93} +(-250.933 + 434.629i) q^{94} +(-5516.71 - 1590.48i) q^{95} +(-1916.77 - 3770.94i) q^{96} +(-12170.7 + 7026.75i) q^{97} -3004.74 q^{98} +(-11218.8 - 8184.32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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