LMFDB - Embedded newform 82.5.h.b.13.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,5,Mod(7,82)] 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("82.7"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([39])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	82.h (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.47633697288$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	82.13
Dual form			82.5.h.b.19.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.52015 - 1.28408i) q^{2} +(1.08363 - 2.61611i) q^{3} +(4.70228 + 6.47214i) q^{4} +(16.3350 + 2.58721i) q^{5} +(-6.09020 + 5.20152i) q^{6} +(-18.3583 - 15.6794i) q^{7} +(-3.53971 - 22.3488i) q^{8} +(51.6059 + 51.6059i) q^{9} +(-37.8444 - 27.4956i) q^{10} +(61.9591 + 101.108i) q^{11} +(22.0274 - 5.28830i) q^{12} +(-22.1137 - 1.74039i) q^{13} +(26.1319 + 63.0880i) q^{14} +(24.4695 - 39.9306i) q^{15} +(-19.7771 + 60.8676i) q^{16} +(130.506 - 543.595i) q^{17} +(-63.7884 - 196.320i) q^{18} +(644.186 - 50.6985i) q^{19} +(60.0670 + 117.888i) q^{20} +(-60.9127 + 31.0366i) q^{21} +(-26.3153 - 334.367i) q^{22} +(576.632 - 187.359i) q^{23} +(-62.3028 - 14.9576i) q^{24} +(-334.272 - 108.612i) q^{25} +(53.4950 + 32.7818i) q^{26} +(402.833 - 166.859i) q^{27} +(15.1537 - 192.546i) q^{28} +(161.528 + 672.811i) q^{29} +(-112.941 + 69.2101i) q^{30} +(-134.005 + 184.442i) q^{31} +(128.000 - 128.000i) q^{32} +(331.650 - 52.5283i) q^{33} +(-1026.91 + 1202.36i) q^{34} +(-259.316 - 303.620i) q^{35} +(-91.3348 + 576.665i) q^{36} +(1228.24 - 892.371i) q^{37} +(-1688.54 - 699.418i) q^{38} +(-28.5161 + 55.9660i) q^{39} -374.226i q^{40} +(-1535.34 + 684.470i) q^{41} +193.362 q^{42} +(1632.77 + 831.936i) q^{43} +(-363.036 + 876.446i) q^{44} +(709.466 + 976.496i) q^{45} +(-1693.78 - 268.268i) q^{46} +(-2811.09 + 2400.90i) q^{47} +(137.805 + 117.697i) q^{48} +(-284.418 - 1795.75i) q^{49} +(702.949 + 702.949i) q^{50} +(-1280.68 - 930.472i) q^{51} +(-92.7209 - 151.307i) q^{52} +(-4113.67 + 987.605i) q^{53} +(-1229.46 - 96.7605i) q^{54} +(750.513 + 1811.90i) q^{55} +(-285.434 + 465.787i) q^{56} +(565.425 - 1740.20i) q^{57} +(456.869 - 1903.00i) q^{58} +(40.6297 + 125.045i) q^{59} +(373.498 - 29.3950i) q^{60} +(2585.55 + 5074.42i) q^{61} +(574.551 - 292.749i) q^{62} +(-138.243 - 1756.55i) q^{63} +(-486.941 + 158.217i) q^{64} +(-356.725 - 85.6420i) q^{65} +(-903.258 - 293.486i) q^{66} +(-1532.15 - 938.901i) q^{67} +(4131.89 - 1711.49i) q^{68} +(134.703 - 1711.56i) q^{69} +(263.642 + 1098.15i) q^{70} +(6751.25 - 4137.17i) q^{71} +(970.661 - 1336.00i) q^{72} +(1018.20 - 1018.20i) q^{73} +(-4241.23 + 671.744i) q^{74} +(-646.367 + 756.798i) q^{75} +(3357.27 + 3930.86i) q^{76} +(447.856 - 2827.65i) q^{77} +(143.730 - 104.426i) q^{78} +(4523.52 + 1873.70i) q^{79} +(-480.536 + 943.104i) q^{80} +4676.85i q^{81} +(4748.19 + 246.531i) q^{82} -6700.70 q^{83} +(-487.302 - 248.293i) q^{84} +(3538.20 - 8541.97i) q^{85} +(-3046.54 - 4193.20i) q^{86} +(1935.19 + 306.503i) q^{87} +(2040.33 - 1742.61i) q^{88} +(-9227.36 - 7880.91i) q^{89} +(-534.060 - 3371.92i) q^{90} +(378.681 + 378.681i) q^{91} +(3924.10 + 2851.02i) q^{92} +(337.310 + 550.439i) q^{93} +(10167.3 - 2440.96i) q^{94} +(10653.9 + 838.483i) q^{95} +(-196.158 - 473.567i) q^{96} +(1148.35 - 1873.94i) q^{97} +(-1589.10 + 4890.76i) q^{98} +(-2020.32 + 8415.22i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 56 q^{2} - 16 q^{3} + 16 q^{6} - 448 q^{8} - 24 q^{9} + 512 q^{11} - 576 q^{12} + 348 q^{13} - 192 q^{14} - 1036 q^{15} + 1792 q^{16} + 552 q^{17} + 416 q^{18} + 504 q^{19} + 876 q^{21} + 16 q^{22}+ \cdots + 36896 q^{99}+O(q^{100}) $ 112 * q + 56 * q^2 - 16 * q^3 + 16 * q^6 - 448 * q^8 - 24 * q^9 + 512 * q^11 - 576 * q^12 + 348 * q^13 - 192 * q^14 - 1036 * q^15 + 1792 * q^16 + 552 * q^17 + 416 * q^18 + 504 * q^19 + 876 * q^21 + 16 * q^22 + 800 * q^23 - 384 * q^24 - 3360 * q^25 + 1656 * q^26 - 964 * q^27 + 768 * q^28 + 4 * q^29 - 3544 * q^30 + 1380 * q^31 + 14336 * q^32 - 7392 * q^33 + 4224 * q^34 + 2264 * q^35 + 2048 * q^36 + 6212 * q^37 + 2624 * q^38 + 4928 * q^39 - 7460 * q^41 + 5056 * q^42 - 19816 * q^43 - 6560 * q^44 - 26000 * q^45 - 4400 * q^46 - 14660 * q^47 - 1536 * q^48 - 17808 * q^49 - 28720 * q^50 + 17948 * q^51 + 1152 * q^52 + 19032 * q^53 + 20152 * q^54 + 3160 * q^55 - 1536 * q^56 + 23432 * q^57 - 6752 * q^58 + 25136 * q^59 - 9536 * q^60 + 10080 * q^61 + 10496 * q^62 - 968 * q^63 - 57460 * q^65 - 2480 * q^66 + 280 * q^67 + 1568 * q^68 - 1876 * q^69 + 6792 * q^70 + 49672 * q^71 + 4480 * q^72 + 16196 * q^73 - 30984 * q^74 + 58748 * q^75 + 13312 * q^76 + 6444 * q^77 + 4928 * q^78 + 34556 * q^79 + 6888 * q^82 + 17304 * q^83 + 7008 * q^84 - 104144 * q^85 + 30800 * q^86 - 28492 * q^87 - 3648 * q^88 + 26732 * q^89 - 70336 * q^90 - 132748 * q^91 + 4160 * q^92 + 35360 * q^93 - 11160 * q^94 - 5644 * q^95 - 1024 * q^96 + 14036 * q^97 - 6528 * q^98 + 36896 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{31}{40}\right)$

Coefficient data

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

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

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

$2$	−2.52015	−	1.28408i	−0.630037	−	0.321020i
$2$	−2.52015	−	1.28408i	−0.630037	−	0.321020i
$3$	1.08363	−	2.61611i	0.120403	−	0.290679i	−0.852174	−	0.523258i	$-0.824716\pi$
$3$	1.08363	−	2.61611i	0.120403	−	0.290679i	0.972578	+	0.232579i	$0.0747164\pi$
$4$	4.70228	+	6.47214i	0.293893	+	0.404508i
$5$	16.3350	+	2.58721i	0.653399	+	0.103488i	0.474329	−	0.880348i	$-0.342691\pi$
$5$	16.3350	+	2.58721i	0.653399	+	0.103488i	0.179071	+	0.983836i	$0.442691\pi$
$6$	−6.09020	+	5.20152i	−0.169172	+	0.144487i
$7$	−18.3583	−	15.6794i	−0.374658	−	0.319989i	0.442103	−	0.896964i	$-0.354233\pi$
$7$	−18.3583	−	15.6794i	−0.374658	−	0.319989i	−0.816761	+	0.576976i	$0.804233\pi$
$8$	−3.53971	−	22.3488i	−0.0553079	−	0.349201i
$9$	51.6059	+	51.6059i	0.637109	+	0.637109i
$10$	−37.8444	−	27.4956i	−0.378444	−	0.274956i
$11$	61.9591	+	101.108i	0.512059	+	0.835604i	0.999290	−	0.0376692i	$-0.0119933\pi$
$11$	61.9591	+	101.108i	0.512059	+	0.835604i	−0.487232	+	0.873273i	$0.661993\pi$
$12$	22.0274	−	5.28830i	0.152968	−	0.0367243i
$13$	−22.1137	−	1.74039i	−0.130850	−	0.0102981i	0.0128648	−	0.999917i	$-0.495905\pi$
$13$	−22.1137	−	1.74039i	−0.130850	−	0.0102981i	−0.143715	+	0.989619i	$0.545905\pi$
$14$	26.1319	+	63.0880i	0.133326	+	0.321877i
$15$	24.4695	−	39.9306i	0.108753	−	0.177469i
$16$	−19.7771	+	60.8676i	−0.0772542	+	0.237764i
$17$	130.506	−	543.595i	0.451576	−	1.88095i	−0.0212138	−	0.999775i	$-0.506753\pi$
$17$	130.506	−	543.595i	0.451576	−	1.88095i	0.472790	−	0.881175i	$-0.343247\pi$
$18$	−63.7884	−	196.320i	−0.196878	−	0.605927i
$19$	644.186	−	50.6985i	1.78445	−	0.140439i	0.857224	−	0.514944i	$-0.172187\pi$
$19$	644.186	−	50.6985i	1.78445	−	0.140439i	0.927225	+	0.374505i	$0.122187\pi$
$20$	60.0670	+	117.888i	0.150167	+	0.294720i
$21$	−60.9127	+	31.0366i	−0.138124	+	0.0703777i
$22$	−26.3153	−	334.367i	−0.0543704	−	0.690842i
$23$	576.632	−	187.359i	1.09004	−	0.354176i	0.291779	−	0.956486i	$-0.405753\pi$
$23$	576.632	−	187.359i	1.09004	−	0.354176i	0.798262	+	0.602310i	$0.205753\pi$
$24$	−62.3028	−	14.9576i	−0.108165	−	0.0259680i
$25$	−334.272	−	108.612i	−0.534835	−	0.173779i
$26$	53.4950	+	32.7818i	0.0791346	+	0.0484938i
$27$	402.833	−	166.859i	0.552583	−	0.228888i
$28$	15.1537	−	192.546i	0.0193287	−	0.245595i
$29$	161.528	+	672.811i	0.192066	+	0.800013i	0.982316	+	0.187229i	$0.0599506\pi$
$29$	161.528	+	672.811i	0.192066	+	0.800013i	−0.790250	+	0.612784i	$0.790049\pi$
$30$	−112.941	+	69.2101i	−0.125490	+	0.0769002i
$31$	−134.005	+	184.442i	−0.139443	+	0.191927i	−0.873027	−	0.487672i	$-0.837846\pi$
$31$	−134.005	+	184.442i	−0.139443	+	0.191927i	0.733584	+	0.679599i	$0.237846\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	331.650	−	52.5283i	0.304546	−	0.0482353i
$34$	−1026.91	+	1202.36i	−0.888332	+	1.04010i
$35$	−259.316	−	303.620i	−0.211687	−	0.247853i
$36$	−91.3348	+	576.665i	−0.0704744	+	0.444958i
$37$	1228.24	−	892.371i	0.897182	−	0.651841i	−0.0405584	−	0.999177i	$-0.512914\pi$
$37$	1228.24	−	892.371i	0.897182	−	0.651841i	0.937741	+	0.347336i	$0.112914\pi$
$38$	−1688.54	−	699.418i	−1.16935	−	0.484362i
$39$	−28.5161	+	55.9660i	−0.0187483	+	0.0367955i
$40$		−	374.226i		−	0.233891i
$41$	−1535.34	+	684.470i	−0.913348	+	0.407180i
$41$	−1535.34	+	684.470i	−0.913348	+	0.407180i
$42$	193.362			0.109616
$43$	1632.77	+	831.936i	0.883053	+	0.449938i	0.835857	−	0.548948i	$-0.184971\pi$
$43$	1632.77	+	831.936i	0.883053	+	0.449938i	0.0471964	+	0.998886i	$0.484971\pi$
$44$	−363.036	+	876.446i	−0.187519	+	0.452710i
$45$	709.466	+	976.496i	0.350354	+	0.482220i
$46$	−1693.78	−	268.268i	−0.800463	−	0.126781i
$47$	−2811.09	+	2400.90i	−1.27256	+	1.08687i	−0.280670	+	0.959804i	$0.590557\pi$
$47$	−2811.09	+	2400.90i	−1.27256	+	1.08687i	−0.991894	+	0.127068i	$0.959443\pi$
$48$	137.805	+	117.697i	0.0598114	+	0.0510837i
$49$	−284.418	−	1795.75i	−0.118458	−	0.747915i
$50$	702.949	+	702.949i	0.281180	+	0.281180i
$51$	−1280.68	−	930.472i	−0.492381	−	0.357736i
$52$	−92.7209	−	151.307i	−0.0342903	−	0.0559566i
$53$	−4113.67	+	987.605i	−1.46446	+	0.351586i	−0.885832	−	0.464006i	$-0.846412\pi$
$53$	−4113.67	+	987.605i	−1.46446	+	0.351586i	−0.578628	+	0.815592i	$0.696412\pi$
$54$	−1229.46	−	96.7605i	−0.421625	−	0.0331826i
$55$	750.513	+	1811.90i	0.248104	+	0.598975i
$56$	−285.434	+	465.787i	−0.0910186	+	0.148529i
$57$	565.425	−	1740.20i	0.174031	−	0.535611i
$58$	456.869	−	1903.00i	0.135811	−	0.565695i
$59$	40.6297	+	125.045i	0.0116719	+	0.0359223i	0.956723	−	0.291001i	$-0.0939882\pi$
$59$	40.6297	+	125.045i	0.0116719	+	0.0359223i	−0.945051	+	0.326923i	$0.893988\pi$
$60$	373.498	−	29.3950i	0.103750	−	0.00816527i
$61$	2585.55	+	5074.42i	0.694852	+	1.36372i	0.920974	+	0.389625i	$0.127395\pi$
$61$	2585.55	+	5074.42i	0.694852	+	1.36372i	−0.226121	+	0.974099i	$0.572605\pi$
$62$	574.551	−	292.749i	0.149467	−	0.0761573i
$63$	−138.243	−	1756.55i	−0.0348307	−	0.442566i
$64$	−486.941	+	158.217i	−0.118882	+	0.0386271i
$65$	−356.725	−	85.6420i	−0.0844318	−	0.0202703i
$66$	−903.258	−	293.486i	−0.207360	−	0.0673752i
$67$	−1532.15	−	938.901i	−0.341311	−	0.209156i	0.341270	−	0.939965i	$-0.389143\pi$
$67$	−1532.15	−	938.901i	−0.341311	−	0.209156i	−0.682582	+	0.730809i	$0.739143\pi$
$68$	4131.89	−	1711.49i	0.893575	−	0.370131i
$69$	134.703	−	1711.56i	0.0282929	−	0.359496i
$70$	263.642	+	1098.15i	0.0538046	+	0.224112i
$71$	6751.25	−	4137.17i	1.33927	−	0.820705i	0.346191	−	0.938164i	$-0.387475\pi$
$71$	6751.25	−	4137.17i	1.33927	−	0.820705i	0.993078	+	0.117459i	$0.0374749\pi$
$72$	970.661	−	1336.00i	0.187242	−	0.257716i
$73$	1018.20	−	1018.20i	0.191069	−	0.191069i	−0.605089	−	0.796158i	$-0.706863\pi$
$73$	1018.20	−	1018.20i	0.191069	−	0.191069i	0.796158	+	0.605089i	$0.206863\pi$
$74$	−4241.23	+	671.744i	−0.774512	+	0.122671i
$75$	−646.367	+	756.798i	−0.114910	+	0.134542i
$76$	3357.27	+	3930.86i	0.581245	+	0.680551i
$77$	447.856	−	2827.65i	0.0755365	−	0.476919i
$78$	143.730	−	104.426i	0.0236242	−	0.0171640i
$79$	4523.52	+	1873.70i	0.724806	+	0.300225i	0.714416	−	0.699721i	$-0.246693\pi$
$79$	4523.52	+	1873.70i	0.724806	+	0.300225i	0.0103905	+	0.999946i	$0.496693\pi$
$80$	−480.536	+	943.104i	−0.0750837	+	0.147360i
$81$			4676.85i			0.712826i
$82$	4748.19	+	246.531i	0.706156	+	0.0366643i
$83$	−6700.70			−0.972666			−0.486333	−	0.873773i	$-0.661666\pi$
$83$	−6700.70			−0.972666			−0.486333	+	0.873773i	$0.661666\pi$
$84$	−487.302	−	248.293i	−0.0690620	−	0.0351889i
$85$	3538.20	−	8541.97i	0.489716	−	1.18228i
$86$	−3046.54	−	4193.20i	−0.411917	−	0.566955i
$87$	1935.19	+	306.503i	0.255672	+	0.0404945i
$88$	2040.33	−	1742.61i	0.263472	−	0.225027i
$89$	−9227.36	−	7880.91i	−1.16492	−	0.994938i	−0.999963	−	0.00863808i	$-0.997250\pi$
$89$	−9227.36	−	7880.91i	−1.16492	−	0.994938i	−0.164960	−	0.986300i	$-0.552750\pi$
$90$	−534.060	−	3371.92i	−0.0659334	−	0.416287i
$91$	378.681	+	378.681i	0.0457289	+	0.0457289i
$92$	3924.10	+	2851.02i	0.463622	+	0.336841i
$93$	337.310	+	550.439i	0.0389999	+	0.0636420i
$94$	10167.3	−	2440.96i	1.15067	−	0.276251i
$95$	10653.9	+	838.483i	1.18049	+	0.0929067i
$96$	−196.158	−	473.567i	−0.0212845	−	0.0513853i
$97$	1148.35	−	1873.94i	0.122048	−	0.199164i	−0.785781	−	0.618505i	$-0.787739\pi$
$97$	1148.35	−	1873.94i	0.122048	−	0.199164i	0.907829	+	0.419341i	$0.137739\pi$
$98$	−1589.10	+	4890.76i	−0.165463	+	0.509242i
$99$	−2020.32	+	8415.22i	−0.206134	+	0.858608i
$100$	−868.893	−	2674.18i	−0.0868893	−	0.267418i
$101$	−18371.9	+	1445.90i	−1.80099	+	0.141741i	−0.934158	−	0.356860i	$-0.883847\pi$
$101$	−18371.9	+	1445.90i	−1.80099	+	0.141741i	−0.866831	+	0.498601i	$0.833847\pi$
$102$	2032.71	+	3989.42i	0.195378	+	0.383451i
$103$	−11017.9	+	5613.91i	−1.03854	+	0.529164i	−0.888194	−	0.459468i	$-0.848040\pi$
$103$	−11017.9	+	5613.91i	−1.03854	+	0.529164i	−0.150350	+	0.988633i	$0.548040\pi$
$104$	39.3805	+	500.376i	0.00364095	+	0.0462626i
$105$	−1075.31	+	349.388i	−0.0975334	+	0.0316905i
$106$	11635.2	+	2793.37i	1.03553	+	0.248609i
$107$	7531.06	+	2446.99i	0.657792	+	0.213730i	0.618847	−	0.785512i	$-0.287600\pi$
$107$	7531.06	+	2446.99i	0.657792	+	0.213730i	0.0389455	+	0.999241i	$0.487600\pi$
$108$	2974.17	+	1822.57i	0.254987	+	0.156256i
$109$	6605.30	−	2736.01i	0.555955	−	0.230284i	−0.0869731	−	0.996211i	$-0.527719\pi$
$109$	6605.30	−	2736.01i	0.555955	−	0.230284i	0.642928	+	0.765927i	$0.277719\pi$
$110$	435.218	−	5529.97i	0.0359684	−	0.457022i
$111$	−1003.58	−	4180.22i	−0.0814529	−	0.339276i
$112$	1317.44	−	807.330i	0.105026	−	0.0643599i
$113$	−1996.66	+	2748.16i	−0.156368	+	0.215221i	−0.880012	−	0.474952i	$-0.842466\pi$
$113$	−1996.66	+	2748.16i	−0.156368	+	0.215221i	0.723644	+	0.690173i	$0.242466\pi$
$114$	−3659.51	+	3659.51i	−0.281587	+	0.281587i
$115$	9904.01	−	1568.64i	0.748885	−	0.118612i
$116$	−3594.98	+	4209.18i	−0.267165	+	0.312810i
$117$	−1051.38	−	1231.01i	−0.0768050	−	0.0899271i
$118$	58.1754	−	367.305i	0.00417806	−	0.0263793i
$119$	−10919.1	+	7933.20i	−0.771069	+	0.560215i
$120$	−979.017	−	405.522i	−0.0679873	−	0.0281612i
$121$	262.969	−	516.106i	0.0179611	−	0.0352507i
$122$		−	16108.3i		−	1.08226i
$123$	126.913	+	4758.33i	0.00838870	+	0.314517i
$124$	−1823.87			−0.118618
$125$	−14389.3	−	7331.73i	−0.920917	−	0.469231i
$126$	−1907.15	+	4604.27i	−0.120128	+	0.290014i
$127$	2718.44	+	3741.61i	0.168543	+	0.231980i	0.884931	−	0.465723i	$-0.154206\pi$
$127$	2718.44	+	3741.61i	0.168543	+	0.231980i	−0.716387	+	0.697703i	$0.754206\pi$
$128$	1430.33	+	226.541i	0.0873001	+	0.0138270i
$129$	3945.75	−	3369.99i	0.237110	−	0.202511i
$130$	789.027	+	673.893i	0.0466880	+	0.0398753i
$131$	1351.67	+	8534.13i	0.0787643	+	0.497298i	0.995260	+	0.0972529i	$0.0310056\pi$
$131$	1351.67	+	8534.13i	0.0787643	+	0.497298i	−0.916495	+	0.400045i	$0.868994\pi$
$132$	1899.48	+	1899.48i	0.109015	+	0.109015i
$133$	−12621.1	−	9169.74i	−0.713498	−	0.518387i
$134$	2655.61	+	4333.57i	0.147896	+	0.241344i
$135$	7011.97	−	1683.43i	0.384745	−	0.0923691i
$136$	−12610.7	−	992.480i	−0.681805	−	0.0536592i
$137$	−5953.26	−	14372.4i	−0.317186	−	0.765754i	−0.999401	−	0.0346028i	$-0.988983\pi$
$137$	−5953.26	−	14372.4i	−0.317186	−	0.765754i	0.682215	−	0.731151i	$-0.261017\pi$
$138$	−2537.25	+	4140.41i	−0.133231	+	0.217413i
$139$	−4415.81	+	13590.5i	−0.228550	+	0.703403i	0.769362	+	0.638813i	$0.220574\pi$
$139$	−4415.81	+	13590.5i	−0.228550	+	0.703403i	−0.997912	+	0.0645906i	$0.979426\pi$
$140$	745.693	−	3106.04i	0.0380456	−	0.158471i
$141$	3234.84	+	9955.82i	0.162710	+	0.500770i
$142$	−22326.6	+	1757.14i	−1.10725	+	0.0871425i
$143$	−1194.18	−	2343.71i	−0.0583979	−	0.114612i
$144$	−4161.74	+	2120.51i	−0.200701	+	0.102262i
$145$	897.850	+	11408.3i	0.0427039	+	0.542605i
$146$	−3873.48	+	1258.57i	−0.181717	+	0.0590434i
$147$	−5006.07	−	1201.85i	−0.231666	−	0.0556181i
$148$	11551.1	+	3753.18i	0.527351	+	0.171347i
$149$	−3103.41	−	1901.77i	−0.139787	−	0.0856615i	0.450847	−	0.892601i	$-0.351122\pi$
$149$	−3103.41	−	1901.77i	−0.139787	−	0.0856615i	−0.590634	+	0.806940i	$0.701122\pi$
$150$	2600.73	−	1077.26i	0.115588	−	0.0478781i
$151$	1096.50	−	13932.3i	0.0480899	−	0.611041i	−0.924903	−	0.380204i	$-0.875854\pi$
$151$	1096.50	−	13932.3i	0.0480899	−	0.611041i	0.972993	−	0.230837i	$-0.0741463\pi$
$152$	−3413.28	−	14217.4i	−0.147736	−	0.615363i
$153$	34787.5	−	21317.8i	1.48607	−	0.910668i
$154$	−4759.59	+	6551.02i	−0.200691	+	0.276228i
$155$	−2666.16	+	2666.16i	−0.110975	+	0.110975i
$156$	−496.310	+	78.6078i	−0.0203941	+	0.00323010i
$157$	−5504.91	+	6445.43i	−0.223332	+	0.261488i	−0.860748	−	0.509032i	$-0.830004\pi$
$157$	−5504.91	+	6445.43i	−0.223332	+	0.261488i	0.637415	+	0.770520i	$0.280004\pi$
$158$	−8993.95	−	10530.6i	−0.360277	−	0.421830i
$159$	−1874.01	+	11832.0i	−0.0741271	+	0.468020i
$160$	2422.04	−	1759.72i	0.0946110	−	0.0687389i
$161$	−13523.6	−	5601.68i	−0.521725	−	0.216106i
$162$	6005.44	−	11786.3i	0.228831	−	0.449106i
$163$			18760.8i			0.706116i	0.935601	+	0.353058i	$0.114858\pi$
$163$			18760.8i			0.706116i	−0.935601	+	0.353058i	$0.885142\pi$
$164$	−11649.6	−	6718.35i	−0.433134	−	0.249790i
$165$	5553.41			0.203982
$166$	16886.7	+	8604.23i	0.612815	+	0.312245i
$167$	−10334.8	+	24950.5i	−0.370570	+	0.894635i	0.623084	+	0.782155i	$0.285879\pi$
$167$	−10334.8	+	24950.5i	−0.370570	+	0.894635i	−0.993654	+	0.112480i	$0.964121\pi$
$168$	909.244	+	1251.47i	0.0322153	+	0.0443405i
$169$	−27723.4	−	4390.95i	−0.970673	−	0.153739i
$170$	−19885.3	+	16983.7i	−0.688074	+	0.587671i
$171$	35860.1	+	30627.4i	1.22636	+	1.04741i
$172$	2293.32	+	14479.5i	0.0775191	+	0.489436i
$173$	−6662.35	−	6662.35i	−0.222605	−	0.222605i	0.586989	−	0.809595i	$-0.300313\pi$
$173$	−6662.35	−	6662.35i	−0.222605	−	0.222605i	−0.809595	+	0.586989i	$0.800313\pi$
$174$	−4483.38	−	3257.36i	−0.148084	−	0.107589i
$175$	4433.69	+	7235.12i	0.144773	+	0.236249i
$176$	−7379.57	+	1771.68i	−0.238235	+	0.0571952i
$177$	371.160	+	29.2110i	0.0118472	+	0.000932394i
$178$	13134.6	+	31709.7i	0.414549	+	1.00081i
$179$	1090.18	−	1779.01i	0.0340245	−	0.0555229i	−0.835176	−	0.549983i	$-0.814634\pi$
$179$	1090.18	−	1779.01i	0.0340245	−	0.0555229i	0.869200	+	0.494460i	$0.164634\pi$
$180$	−2983.91	+	9183.52i	−0.0920959	+	0.283442i
$181$	8593.60	−	35794.9i	0.262312	−	1.09261i	−0.673241	−	0.739423i	$-0.735099\pi$
$181$	8593.60	−	35794.9i	0.262312	−	1.09261i	0.935553	−	0.353185i	$-0.114901\pi$
$182$	−468.076	−	1440.59i	−0.0141310	−	0.0434908i
$183$	16077.0	−	1265.29i	0.480068	−	0.0377822i
$184$	−6228.36	−	12223.8i	−0.183966	−	0.361054i
$185$	22372.1	−	11399.1i	0.653676	−	0.333065i
$186$	−143.262	−	1820.32i	−0.00414101	−	0.0526165i
$187$	63047.8	−	20485.5i	1.80296	−	0.585818i
$188$	−28757.5	−	6904.07i	−0.813646	−	0.195339i
$189$	−10011.6	−	3252.96i	−0.280271	−	0.0910657i
$190$	−25772.8	−	15793.6i	−0.713928	−	0.437496i
$191$	15801.7	−	6545.27i	0.433148	−	0.179416i	−0.155446	−	0.987844i	$-0.549681\pi$
$191$	15801.7	−	6545.27i	0.433148	−	0.179416i	0.588595	+	0.808428i	$0.299681\pi$
$192$	−113.751	+	1445.34i	−0.00308569	+	0.0392073i
$193$	−172.221	−	717.353i	−0.00462351	−	0.0192583i	0.970010	−	0.243063i	$-0.0781522\pi$
$193$	−172.221	−	717.353i	−0.00462351	−	0.0192583i	−0.974634	+	0.223805i	$0.928152\pi$
$194$	−5300.29	+	3248.02i	−0.140830	+	0.0863009i
$195$	−610.606	+	840.427i	−0.0160580	+	0.0221020i
$196$	10284.9	−	10284.9i	0.267724	−	0.267724i
$197$	5654.71	−	895.618i	0.145706	−	0.0230776i	−0.0831553	−	0.996537i	$-0.526500\pi$
$197$	5654.71	−	895.618i	0.145706	−	0.0230776i	0.228861	+	0.973459i	$0.426500\pi$
$198$	15897.3	−	18613.3i	0.405502	−	0.474782i
$199$	−38275.0	−	44814.2i	−0.966515	−	1.13164i	−0.991256	−	0.131950i	$-0.957876\pi$
$199$	−38275.0	−	44814.2i	−0.966515	−	1.13164i	0.0247412	−	0.999694i	$-0.492124\pi$
$200$	−1244.12	+	7855.05i	−0.0311029	+	0.196376i
$201$	−4116.55	+	2990.85i	−0.101892	+	0.0740290i
$202$	48156.5	+	19947.1i	1.18019	+	0.488851i
$203$	7583.94	−	14884.3i	0.184036	−	0.361191i
$204$		−	12664.1i		−	0.304308i
$205$	−26850.6	+	7208.57i	−0.638919	+	0.171530i
$206$	34975.5			0.824193
$207$	39426.4	+	20088.8i	0.920124	+	0.468827i
$208$	543.278	−	1311.59i	0.0125573	−	0.0303160i
$209$	45039.2	+	61991.2i	1.03109	+	1.41918i
$210$	3158.57	+	500.269i	0.0716229	+	0.0113440i
$211$	47135.3	−	40257.3i	1.05872	−	0.904232i	0.0631265	−	0.998006i	$-0.479893\pi$
$211$	47135.3	−	40257.3i	1.05872	−	0.904232i	0.995594	+	0.0937732i	$0.0298928\pi$
$212$	−25735.5	−	21980.2i	−0.572614	−	0.489058i
$213$	−3507.45	−	22145.2i	−0.0773095	−	0.488113i
$214$	−15837.3	−	15837.3i	−0.345822	−	0.345822i
$215$	24518.8	+	17814.0i	0.530423	+	0.385375i
$216$	−5155.02	−	8412.22i	−0.110490	−	0.180303i
$217$	5352.06	−	1284.91i	0.113658	−	0.0272869i
$218$	−20159.6	−	1586.59i	−0.424198	−	0.0333851i
$219$	−1560.38	−	3767.09i	−0.0325344	−	0.0785449i
$220$	−8197.73	+	13377.5i	−0.169375	+	0.276394i
$221$	−3832.03	+	11793.8i	−0.0784592	+	0.241473i
$222$	−2838.56	+	11823.4i	−0.0575959	+	0.239904i
$223$	968.916	+	2982.02i	0.0194839	+	0.0599653i	0.960326	−	0.278881i	$-0.0899634\pi$
$223$	968.916	+	2982.02i	0.0194839	+	0.0599653i	−0.940842	+	0.338846i	$0.889963\pi$
$224$	−4356.83	+	342.890i	−0.0868309	+	0.00683374i
$225$	−11645.4	−	22855.4i	−0.230033	−	0.451465i
$226$	8560.73	−	4361.91i	0.167608	−	0.0854004i
$227$	−5126.10	−	65133.3i	−0.0994800	−	1.26401i	−0.820721	−	0.571329i	$-0.806428\pi$
$227$	−5126.10	−	65133.3i	−0.0994800	−	1.26401i	0.721241	−	0.692684i	$-0.243572\pi$
$228$	13921.6	−	4523.40i	0.267806	−	0.0870153i
$229$	14446.5	+	3468.29i	0.275480	+	0.0661369i	0.368831	−	0.929496i	$-0.379758\pi$
$229$	14446.5	+	3468.29i	0.275480	+	0.0661369i	−0.0933513	+	0.995633i	$0.529758\pi$
$230$	−26973.8	−	8764.32i	−0.509902	−	0.165677i
$231$	−6912.14	−	4235.77i	−0.129535	−	0.0793794i
$232$	14464.8	−	5991.51i	0.268742	−	0.111317i
$233$	6150.11	−	78144.5i	0.113285	−	1.43942i	−0.633187	−	0.773999i	$-0.718253\pi$
$233$	6150.11	−	78144.5i	0.113285	−	1.43942i	0.746471	−	0.665418i	$-0.231747\pi$
$234$	1068.92	+	4452.39i	0.0195216	+	0.0813133i
$235$	−52130.8	+	31945.8i	−0.943971	+	0.578466i
$236$	−618.259	+	850.960i	−0.0111006	+	0.0152787i
$237$	9803.62	−	9803.62i	0.174538	−	0.174538i
$238$	37704.6	−	5971.83i	0.665642	−	0.105427i
$239$	−57397.9	+	67204.3i	−1.00485	+	1.17653i	−0.0205892	+	0.999788i	$0.506554\pi$
$239$	−57397.9	+	67204.3i	−1.00485	+	1.17653i	−0.984258	+	0.176737i	$0.943446\pi$
$240$	1946.54	+	2279.11i	0.0337942	+	0.0395679i
$241$	−11477.6	+	72466.9i	−0.197614	+	1.24769i	0.666927	+	0.745123i	$0.267609\pi$
$241$	−11477.6	+	72466.9i	−0.197614	+	1.24769i	−0.864541	+	0.502563i	$0.832391\pi$
$242$	−1325.44	+	962.989i	−0.0226323	+	0.0164434i
$243$	44864.6	+	18583.5i	0.759787	+	0.314714i
$244$	−20684.4	+	40595.3i	−0.347426	+	0.681862i
$245$		−	30069.3i		−	0.500947i
$246$	5790.23	−	12154.6i	0.0956809	−	0.200850i
$247$	−14333.6			−0.234942
$248$	4596.41	+	2341.99i	0.0747335	+	0.0380786i
$249$	−7261.07	+	17529.8i	−0.117112	+	0.282734i
$250$	26848.7	+	36954.1i	0.429579	+	0.591265i
$251$	−118490.	−	18767.0i	−1.88076	−	0.297883i	−0.892547	−	0.450955i	$-0.851084\pi$
$251$	−118490.	−	18767.0i	−1.88076	−	0.297883i	−0.988215	+	0.153071i	$0.951084\pi$
$252$	10718.5	−	9154.50i	0.168785	−	0.144156i
$253$	54671.1	+	46693.5i	0.854115	+	0.729483i
$254$	−2046.34	−	12920.1i	−0.0317183	−	0.200262i
$255$	−18512.6	−	18512.6i	−0.284700	−	0.284700i
$256$	−3313.73	−	2407.57i	−0.0505636	−	0.0367366i
$257$	12067.5	+	19692.4i	0.182705	+	0.298148i	0.930860	−	0.365377i	$-0.119060\pi$
$257$	12067.5	+	19692.4i	0.182705	+	0.298148i	−0.748154	+	0.663525i	$0.769060\pi$
$258$	−14271.2	+	3426.21i	−0.214398	+	0.0514724i
$259$	−36540.3	−	2875.78i	−0.544719	−	0.0428703i
$260$	−1123.13	−	2711.48i	−0.0166144	−	0.0401107i
$261$	−26385.2	+	43056.8i	−0.387329	+	0.632063i
$262$	7552.08	−	23242.9i	0.110018	−	0.338601i
$263$	−11140.8	+	46404.6i	−0.161066	+	0.670887i	0.832145	+	0.554558i	$0.187113\pi$
$263$	−11140.8	+	46404.6i	−0.161066	+	0.670887i	−0.993211	+	0.116329i	$0.962887\pi$
$264$	−2347.89	−	7226.07i	−0.0336876	−	0.103680i
$265$	−69751.9	+	5489.59i	−0.993263	+	0.0781715i
$266$	20032.3	+	39315.5i	0.283118	+	0.555650i
$267$	−30616.4	+	15599.8i	−0.429468	+	0.218825i
$268$	−1127.89	−	14331.2i	−0.0157036	−	0.199533i
$269$	−49507.7	+	16086.0i	−0.684176	+	0.222302i	−0.630423	−	0.776252i	$-0.717118\pi$
$269$	−49507.7	+	16086.0i	−0.684176	+	0.222302i	−0.0537532	+	0.998554i	$0.517118\pi$
$270$	−19832.9	−	4761.45i	−0.272056	−	0.0653148i
$271$	23661.3	+	7688.02i	0.322181	+	0.104683i	0.465642	−	0.884973i	$-0.345823\pi$
$271$	23661.3	+	7688.02i	0.322181	+	0.104683i	−0.143462	+	0.989656i	$0.545823\pi$
$272$	30506.3	+	18694.3i	0.412336	+	0.252680i
$273$	1401.02	−	580.322i	0.0187983	−	0.00778653i
$274$	−3452.26	+	43865.1i	−0.0459835	+	0.584276i
$275$	−9729.69	−	40527.1i	−0.128657	−	0.535895i
$276$	11710.9	−	7176.42i	0.153734	−	0.0942084i
$277$	41003.4	−	56436.3i	0.534392	−	0.735528i	−0.453399	−	0.891307i	$-0.649789\pi$
$277$	41003.4	−	56436.3i	0.534392	−	0.735528i	0.987792	+	0.155779i	$0.0497889\pi$
$278$	28579.7	−	28579.7i	0.369801	−	0.369801i
$279$	−16433.8	+	2602.85i	−0.211120	+	0.0334381i
$280$	−5867.65	+	6870.14i	−0.0748425	+	0.0876293i
$281$	18868.2	+	22091.8i	0.238955	+	0.279781i	0.866905	−	0.498473i	$-0.166106\pi$
$281$	18868.2	+	22091.8i	0.238955	+	0.279781i	−0.627950	+	0.778254i	$0.716106\pi$
$282$	4631.78	−	29243.9i	0.0582438	−	0.367737i
$283$	−51318.4	+	37285.0i	−0.640768	+	0.465545i	−0.860114	−	0.510102i	$-0.829608\pi$
$283$	−51318.4	+	37285.0i	−0.640768	+	0.465545i	0.219346	+	0.975647i	$0.429608\pi$
$284$	58522.6	+	24240.9i	0.725583	+	0.300546i
$285$	13738.5	−	26963.3i	0.169141	−	0.331958i
$286$			7439.91i			0.0909568i
$287$	38918.2	+	11507.6i	0.472487	+	0.139707i
$288$	13211.1			0.159277
$289$	−204046.	−	103966.i	−2.44305	−	1.24479i
$290$	12386.4	−	29903.4i	0.147282	−	0.355570i
$291$	−3658.04	−	5034.86i	−0.0431979	−	0.0594568i
$292$	11377.8	+	1802.07i	0.133443	+	0.0211352i
$293$	−125690.	+	107350.i	−1.46408	+	1.25045i	−0.556318	+	0.830970i	$0.687786\pi$
$293$	−125690.	+	107350.i	−1.46408	+	1.25045i	−0.907766	+	0.419477i	$0.862214\pi$
$294$	11072.8	+	9457.03i	0.128104	+	0.109411i
$295$	340.168	+	2147.73i	0.00390885	+	0.0246795i
$296$	−24291.1	−	24291.1i	−0.277245	−	0.277245i
$297$	41830.0	+	30391.2i	0.474214	+	0.344537i
$298$	5379.02	+	8777.77i	0.0605719	+	0.0988443i
$299$	−13077.5	+	3139.64i	−0.146280	+	0.0351186i
$300$	−7937.50	−	624.695i	−0.0881945	−	0.00694105i
$301$	−16930.5	−	40873.7i	−0.186868	−	0.451140i
$302$	−20653.6	+	33703.5i	−0.226455	+	0.369540i
$303$	−16125.7	+	49629.7i	−0.175644	+	0.540576i
$304$	−9654.23	+	40212.7i	−0.104465	+	0.435127i
$305$	29106.3	+	89579.9i	0.312887	+	0.962966i
$306$	−115043.	+	9054.11i	−1.22862	+	0.0966948i
$307$	−23142.0	−	45418.7i	−0.245541	−	0.481901i	0.735038	−	0.678026i	$-0.237164\pi$
$307$	−23142.0	−	45418.7i	−0.245541	−	0.481901i	−0.980579	+	0.196125i	$0.937164\pi$
$308$	20406.9	−	10397.8i	0.215117	−	0.109608i
$309$	2747.28	+	34907.5i	0.0287730	+	0.365596i
$310$	10142.7	−	3295.56i	0.105543	−	0.0342930i
$311$	154505.	+	37093.4i	1.59743	+	0.383509i	0.931858	−	0.362823i	$-0.118187\pi$
$311$	154505.	+	37093.4i	1.59743	+	0.383509i	0.665573	+	0.746332i	$0.268187\pi$
$312$	1351.71	+	439.198i	0.0138859	+	0.00451182i
$313$	53863.6	+	33007.7i	0.549803	+	0.336920i	0.769498	−	0.638649i	$-0.220506\pi$
$313$	53863.6	+	33007.7i	0.549803	+	0.336920i	−0.219695	+	0.975569i	$0.570506\pi$
$314$	22149.6	−	9174.68i	0.224650	−	0.0930532i
$315$	2286.35	−	29050.8i	0.0230421	−	0.292777i
$316$	9144.00	+	38087.5i	0.0915718	+	0.381424i
$317$	34205.7	−	20961.3i	0.340392	−	0.208593i	−0.341787	−	0.939777i	$-0.611032\pi$
$317$	34205.7	−	20961.3i	0.340392	−	0.208593i	0.682180	+	0.731185i	$0.261032\pi$
$318$	19916.0	−	27412.0i	0.196946	−	0.271073i
$319$	−58018.5	+	58018.5i	−0.570145	+	0.570145i
$320$	−8363.51	+	1324.65i	−0.0816749	+	0.0129360i
$321$	14562.5	−	17050.5i	0.141327	−	0.165473i
$322$	26888.6	+	31482.5i	0.259332	+	0.303639i
$323$	56510.4	−	356793.i	0.541656	−	3.41988i
$324$	−30269.2	+	21991.9i	−0.288344	+	0.209494i
$325$	7202.97	+	2983.57i	0.0681938	+	0.0282468i
$326$	24090.4	−	47280.0i	0.226677	−	0.444879i
$327$		−	20245.0i		−	0.189331i
$328$	20731.7	+	31890.2i	0.192703	+	0.296421i
$329$	89251.6			0.824564
$330$	−13995.4	−	7131.01i	−0.128516	−	0.0654822i
$331$	48271.8	−	116538.i	0.440593	−	1.06369i	−0.535148	−	0.844758i	$-0.679744\pi$
$331$	48271.8	−	116538.i	0.440593	−	1.06369i	0.975741	−	0.218928i	$-0.0702558\pi$
$332$	−31508.6	−	43367.8i	−0.285859	−	0.393452i
$333$	109436.	+	17333.0i	0.986897	+	0.156309i
$334$	58083.6	−	49608.1i	0.520668	−	0.444692i
$335$	−22598.5	−	19300.9i	−0.201368	−	0.171984i
$336$	−684.446	−	4321.42i	−0.00606263	−	0.0382779i
$337$	−90332.1	−	90332.1i	−0.795394	−	0.795394i	0.186971	−	0.982365i	$-0.440133\pi$
$337$	−90332.1	−	90332.1i	−0.795394	−	0.795394i	−0.982365	+	0.186971i	$0.940133\pi$
$338$	64228.7	+	46664.9i	0.562206	+	0.408467i
$339$	5025.86	+	8201.46i	0.0437332	+	0.0713661i
$340$	71922.4	−	17267.0i	0.622166	−	0.149369i
$341$	−26951.4	−	2121.12i	−0.231779	−	0.0182414i
$342$	−51044.7	−	123233.i	−0.436414	−	1.05360i
$343$	−53222.4	+	86851.0i	−0.452383	+	0.738221i
$344$	12813.3	−	39435.2i	0.108279	−	0.333248i
$345$	6628.53	−	27609.8i	0.0556902	−	0.231966i
$346$	8235.12	+	25345.1i	0.0687888	+	0.211710i
$347$	84906.5	−	6682.29i	0.705151	−	0.0554966i	0.279187	−	0.960237i	$-0.409935\pi$
$347$	84906.5	−	6682.29i	0.705151	−	0.0554966i	0.425964	+	0.904740i	$0.359935\pi$
$348$	7116.06	+	13966.0i	0.0587599	+	0.115323i
$349$	26947.8	−	13730.6i	0.221245	−	0.112730i	−0.339856	−	0.940478i	$-0.610378\pi$
$349$	26947.8	−	13730.6i	0.221245	−	0.112730i	0.561100	+	0.827748i	$0.310378\pi$
$350$	−1883.08	−	23926.8i	−0.0153721	−	0.195321i
$351$	−9198.54	+	2988.79i	−0.0746629	+	0.0242594i
$352$	20872.6	+	5011.07i	0.168458	+	0.0404431i
$353$	164402.	+	53417.4i	1.31934	+	0.428680i	0.882269	−	0.470746i	$-0.156015\pi$
$353$	164402.	+	53417.4i	1.31934	+	0.428680i	0.437073	+	0.899426i	$0.356015\pi$
$354$	−897.870	−	550.215i	−0.00716484	−	0.00439062i
$355$	120985.	−	50113.8i	0.960011	−	0.397649i
$356$	7616.67	−	96778.9i	0.0600987	−	0.763626i
$357$	8921.87	+	37162.3i	0.0700034	+	0.291585i
$358$	−5031.80	+	3083.49i	−0.0392606	+	0.0240590i
$359$	−141522.	+	194789.i	−1.09809	+	1.51138i	−0.260187	+	0.965558i	$0.583784\pi$
$359$	−141522.	+	194789.i	−1.09809	+	1.51138i	−0.837898	+	0.545826i	$0.816216\pi$
$360$	19312.3	−	19312.3i	0.149014	−	0.149014i
$361$	283689.	−	44931.9i	2.17685	−	0.344779i
$362$	−67620.7	+	79173.6i	−0.516015	+	0.604176i
$363$	−1065.23	−	1247.22i	−0.00808406	−	0.00946522i
$364$	−670.210	+	4231.54i	−0.00505834	+	0.0319371i
$365$	19266.7	−	13998.1i	0.144617	−	0.105071i
$366$	−42141.2	−	17455.4i	−0.314590	−	0.130307i
$367$	−55749.1	+	109414.i	−0.413910	+	0.812343i	0.586088	+	0.810247i	$0.300667\pi$
$367$	−55749.1	+	109414.i	−0.413910	+	0.812343i	−0.999998	+	0.00209613i	$0.999333\pi$
$368$			38803.6i			0.286534i
$369$	−114555.	−	43909.8i	−0.841321	−	0.322484i
$370$	−71018.3			−0.518761
$371$	91004.9	+	46369.3i	0.661176	+	0.336886i
$372$	−1976.39	+	4771.44i	−0.0142820	+	0.0344797i
$373$	3303.30	+	4546.61i	0.0237427	+	0.0326791i	0.820723	−	0.571326i	$-0.193571\pi$
$373$	3303.30	+	4546.61i	0.0237427	+	0.0326791i	−0.796981	+	0.604005i	$0.793571\pi$
$374$	−185195.	−	29331.9i	−1.32399	−	0.209700i
$375$	−34773.3	+	29699.2i	−0.247277	+	0.211194i
$376$	63607.8	+	54326.2i	0.449919	+	0.384267i
$377$	−2401.03	−	15159.5i	−0.0168933	−	0.106660i
$378$	21053.6	+	21053.6i	0.147347	+	0.147347i
$379$	−140887.	−	102360.i	−0.980828	−	0.712613i	−0.0229341	−	0.999737i	$-0.507301\pi$
$379$	−140887.	−	102360.i	−0.980828	−	0.712613i	−0.957893	+	0.287124i	$0.907301\pi$
$380$	44671.0	+	72896.5i	0.309356	+	0.504824i
$381$	12734.2	−	3057.22i	0.0877249	−	0.0210609i
$382$	−48227.2	−	3795.57i	−0.330496	−	0.0260106i
$383$	−29665.5	−	71618.8i	−0.202234	−	0.488236i	0.789927	−	0.613200i	$-0.210118\pi$
$383$	−29665.5	−	71618.8i	−0.202234	−	0.488236i	−0.992161	+	0.124965i	$0.960118\pi$
$384$	2142.60	−	3496.40i	0.0145304	−	0.0237115i
$385$	14631.4	−	45031.0i	0.0987111	−	0.303801i
$386$	−487.115	+	2028.98i	−0.00326932	+	0.0136177i
$387$	41327.5	+	127193.i	0.275942	+	0.849261i
$388$	17528.2	−	1379.50i	0.116433	−	0.00916344i
$389$	61336.2	+	120379.i	0.405338	+	0.795521i	0.999964	−	0.00848141i	$-0.00269975\pi$
$389$	61336.2	+	120379.i	0.405338	+	0.795521i	−0.594626	+	0.804003i	$0.702700\pi$
$390$	2617.99	−	1333.93i	0.0172123	−	0.00877011i
$391$	−26593.7	−	337905.i	−0.173950	−	2.21025i
$392$	−39126.1	+	12712.8i	−0.254621	+	0.0827313i
$393$	23790.9	+	5711.70i	0.154038	+	0.0369811i
$394$	−15400.7	−	5004.00i	−0.0992086	−	0.0322348i
$395$	69043.9	+	42310.2i	0.442518	+	0.271176i
$396$	−63964.5	+	26495.0i	−0.407895	+	0.168956i
$397$	−13003.0	+	165219.i	−0.0825018	+	1.04828i	0.806758	+	0.590882i	$0.201220\pi$
$397$	−13003.0	+	165219.i	−0.0825018	+	1.04828i	−0.889260	+	0.457403i	$0.848780\pi$
$398$	38913.5	+	162087.i	0.245660	+	1.02325i
$399$	−37665.6	+	23081.5i	−0.236592	+	0.144983i
$400$	13221.9	−	18198.3i	0.0826366	−	0.113740i
$401$	45999.5	−	45999.5i	0.286064	−	0.286064i	−0.549457	−	0.835522i	$-0.685166\pi$
$401$	45999.5	−	45999.5i	0.286064	−	0.286064i	0.835522	+	0.549457i	$0.185166\pi$
$402$	14214.8	−	2251.40i	0.0879606	−	0.0139316i
$403$	3284.35	−	3845.48i	0.0202227	−	0.0236778i
$404$	−95747.9	−	112106.i	−0.586633	−	0.686859i
$405$	−12100.0	+	76396.3i	−0.0737691	+	0.465760i
$406$	−38225.3	+	27772.3i	−0.231899	+	0.168484i
$407$	166327.	+	68894.7i	1.00409	+	0.415908i
$408$	−16261.7	+	31915.4i	−0.0976890	+	0.191726i
$409$			108216.i			0.646912i	0.946243	+	0.323456i	$0.104845\pi$
$409$			108216.i			0.646912i	−0.946243	+	0.323456i	$0.895155\pi$
$410$	76923.8	+	16311.6i	0.457607	+	0.0970353i
$411$	−44051.0			−0.260779
$412$	−88143.3	−	44911.2i	−0.519272	−	0.264582i
$413$	1214.75	−	2932.67i	0.00712176	−	0.0171935i
$414$	−73564.8	−	101253.i	−0.429209	−	0.590756i
$415$	−109456.	−	17336.1i	−0.635540	−	0.100660i
$416$	−3053.33	+	2607.79i	−0.0176436	+	0.0150690i
$417$	30769.1	+	26279.3i	0.176947	+	0.151127i
$418$	−33903.9	−	214061.i	−0.194043	−	1.22514i
$419$	−145997.	−	145997.i	−0.831604	−	0.831604i	0.156132	−	0.987736i	$-0.450097\pi$
$419$	−145997.	−	145997.i	−0.831604	−	0.831604i	−0.987736	+	0.156132i	$0.950097\pi$
$420$	−7317.68	−	5316.61i	−0.0414835	−	0.0301395i
$421$	35780.3	+	58388.1i	0.201873	+	0.329428i	0.937516	−	0.347943i	$-0.113120\pi$
$421$	35780.3	+	58388.1i	0.201873	+	0.329428i	−0.735642	+	0.677370i	$0.763120\pi$
$422$	−170481.	+	40929.0i	−0.957309	+	0.229830i
$423$	−268969.	−	21168.4i	−1.50322	−	0.118306i
$424$	36633.0	+	88439.9i	0.203770	+	0.491945i
$425$	−102665.	+	167534.i	−0.568388	+	0.927525i
$426$	−19596.9	+	60313.0i	−0.107986	+	0.332347i
$427$	32097.9	−	133697.i	0.176044	−	0.733276i
$428$	19575.9	+	60248.5i	0.106865	+	0.328896i
$429$	−7425.44	+	584.395i	−0.0403467	+	0.00317535i
$430$	−38916.5	−	76377.9i	−0.210473	−	0.413077i
$431$	−32617.8	+	16619.6i	−0.175590	+	0.0894677i	−0.539576	−	0.841937i	$-0.681416\pi$
$431$	−32617.8	+	16619.6i	−0.175590	+	0.0894677i	0.363986	+	0.931404i	$0.381416\pi$
$432$	2189.44	+	27819.5i	0.0117318	+	0.149067i
$433$	79453.9	−	25816.1i	0.423779	−	0.137694i	−0.0893607	−	0.995999i	$-0.528482\pi$
$433$	79453.9	−	25816.1i	0.423779	−	0.137694i	0.513139	+	0.858305i	$0.328482\pi$
$434$	−15137.9	−	3634.29i	−0.0803685	−	0.0192948i
$435$	30818.2	+	10013.5i	0.162866	+	0.0529182i
$436$	48767.8	+	29884.9i	0.256543	+	0.157210i
$437$	361959.	−	149928.i	1.89538	−	0.785093i
$438$	−904.855	+	11497.3i	−0.00471662	+	0.0599303i
$439$	37974.9	+	158177.i	0.197046	+	0.820755i	0.980052	+	0.198741i	$0.0636853\pi$
$439$	37974.9	+	158177.i	0.197046	+	0.820755i	−0.783006	+	0.622014i	$0.786315\pi$
$440$	37837.2	−	23186.7i	0.195440	−	0.119766i
$441$	77993.3	−	107349.i	0.401033	−	0.551975i
$442$	24801.4	−	24801.4i	0.126950	−	0.126950i
$443$	181727.	−	28782.7i	0.926003	−	0.146664i	0.324820	−	0.945776i	$-0.394696\pi$
$443$	181727.	−	28782.7i	0.926003	−	0.146664i	0.601183	+	0.799112i	$0.294696\pi$
$444$	22335.8	−	26151.9i	0.113302	−	0.132659i
$445$	−130339.	−	152608.i	−0.658196	−	0.770648i
$446$	1387.33	−	8759.28i	0.00697447	−	0.0440351i
$447$	−8338.19	+	6058.05i	−0.0417308	+	0.0303192i
$448$	11420.1	+	4730.38i	0.0569004	+	0.0235689i
$449$	−143700.	+	282026.i	−0.712792	+	1.39893i	0.195545	+	0.980695i	$0.437352\pi$
$449$	−143700.	+	282026.i	−0.712792	+	1.39893i	−0.908337	+	0.418238i	$0.862648\pi$
$450$			72552.6i			0.358284i
$451$	−164334.	−	112826.i	−0.807929	−	0.554697i
$452$	−27175.3			−0.133014
$453$	−35260.3	−	17966.0i	−0.171826	−	0.0875500i
$454$	−70717.8	+	170728.i	−0.343097	+	0.828310i
$455$	5206.03	+	7165.48i	0.0251468	+	0.0346117i
$456$	−40892.9	−	6476.80i	−0.196661	−	0.0311480i
$457$	−234648.	+	200408.i	−1.12353	+	0.959585i	−0.999466	−	0.0326888i	$-0.989593\pi$
$457$	−234648.	+	200408.i	−1.12353	+	0.959585i	−0.124064	+	0.992274i	$0.539593\pi$
$458$	−31953.6	−	27291.0i	−0.152331	−	0.130103i
$459$	−38131.7	−	240754.i	−0.180993	−	1.14274i
$460$	56723.9	+	56723.9i	0.268071	+	0.268071i
$461$	42322.8	+	30749.3i	0.199147	+	0.144688i	0.682890	−	0.730522i	$-0.260723\pi$
$461$	42322.8	+	30749.3i	0.199147	+	0.144688i	−0.483743	+	0.875210i	$0.660723\pi$
$462$	11980.6	+	19550.5i	0.0561297	+	0.0915954i
$463$	199625.	−	47925.8i	0.931223	−	0.223567i	0.260669	−	0.965428i	$-0.416057\pi$
$463$	199625.	−	47925.8i	0.931223	−	0.223567i	0.670553	+	0.741861i	$0.266057\pi$
$464$	−44147.0	−	3474.44i	−0.205052	−	0.0161380i
$465$	4085.85	+	9864.11i	0.0188963	+	0.0456197i
$466$	−115843.	+	189038.i	−0.533455	+	0.870519i
$467$	6633.35	−	20415.3i	0.0304158	−	0.0936101i	−0.934696	−	0.355448i	$-0.884328\pi$
$467$	6633.35	−	20415.3i	0.0304158	−	0.0936101i	0.965112	+	0.261837i	$0.0843284\pi$
$468$	3023.37	−	12593.3i	0.0138038	−	0.0574972i
$469$	13406.1	+	41259.8i	0.0609477	+	0.187578i
$470$	172398.	−	13568.0i	0.780436	−	0.0614216i
$471$	10896.7	+	21385.9i	0.0491193	+	0.0964020i
$472$	2650.80	−	1350.65i	0.0118985	−	0.00606261i
$473$	17049.3	+	216632.i	0.0762051	+	0.968277i
$474$	−37295.2	+	12117.9i	−0.165995	+	0.0539352i
$475$	−220840.	−	53019.0i	−0.978792	−	0.234987i
$476$	−102690.	−	33365.8i	−0.453223	−	0.147261i
$477$	−263256.	−	161323.i	−1.15702	−	0.709023i
$478$	230947.	−	95661.3i	1.01078	−	0.418678i
$479$	15793.9	−	200680.i	0.0688364	−	0.874649i	−0.861456	−	0.507832i	$-0.830447\pi$
$479$	15793.9	−	200680.i	0.0688364	−	0.874649i	0.930293	−	0.366818i	$-0.119553\pi$
$480$	−1979.02	−	8243.21i	−0.00858949	−	0.0357778i
$481$	−28714.1	+	17596.0i	−0.124109	+	0.0760543i
$482$	121978.	−	167889.i	0.525036	−	0.722650i
$483$	−29309.2	+	29309.2i	−0.125635	+	0.125635i
$484$	4576.86	−	724.903i	0.0195379	−	0.00309449i
$485$	23606.5	−	27639.7i	0.100357	−	0.117503i
$486$	−89202.8	−	104443.i	−0.377664	−	0.442188i
$487$	−22005.7	+	138938.i	−0.0927847	+	0.585820i	0.896864	+	0.442307i	$0.145840\pi$
$487$	−22005.7	+	138938.i	−0.0927847	+	0.585820i	−0.989648	+	0.143513i	$0.954160\pi$
$488$	104255.	−	75745.9i	0.437782	−	0.318068i
$489$	49080.4	+	20329.7i	0.205253	+	0.0850187i
$490$	−38611.4	+	75779.1i	−0.160814	+	0.315615i
$491$			256348.i			1.06333i	0.846956	+	0.531663i	$0.178433\pi$
$491$			256348.i			1.06333i	−0.846956	+	0.531663i	$0.821567\pi$
$492$	−30199.7	+	23196.4i	−0.124759	+	0.0958275i
$493$	386817.			1.59152
$494$	36122.7	+	18405.5i	0.148022	+	0.0754211i
$495$	−54773.7	+	132236.i	−0.223543	+	0.539682i
$496$	−8576.33	−	11804.3i	−0.0348609	−	0.0479819i
$497$	−188810.	−	29904.5i	−0.764385	−	0.121067i
$498$	40808.6	−	34853.8i	0.164548	−	0.140537i
$499$	115247.	+	98430.3i	0.462838	+	0.395301i	0.850060	−	0.526685i	$-0.176565\pi$
$499$	115247.	+	98430.3i	0.462838	+	0.395301i	−0.387222	+	0.921986i	$0.626565\pi$
$500$	−20210.7	−	127606.i	−0.0808430	−	0.510422i
$501$	54074.1	+	54074.1i	0.215434	+	0.215434i
$502$	274514.	+	199446.i	1.08932	+	0.791439i
$503$	8655.13	+	14123.9i	0.0342088	+	0.0558236i	0.869288	−	0.494307i	$-0.164578\pi$
$503$	8655.13	+	14123.9i	0.0342088	+	0.0558236i	−0.835079	+	0.550130i	$0.814578\pi$
$504$	−38767.4	+	9307.23i	−0.152618	+	0.0366403i
$505$	−303845.	−	23913.2i	−1.19143	−	0.0937679i
$506$	−77821.0	−	187876.i	−0.303945	−	0.733789i
$507$	−41529.1	+	67769.3i	−0.161561	+	0.263643i
$508$	−11433.3	+	35188.2i	−0.0443042	+	0.136354i
$509$	26783.7	−	111562.i	0.103380	−	0.430608i	−0.896544	−	0.442955i	$-0.853930\pi$
$509$	26783.7	−	111562.i	0.103380	−	0.430608i	0.999924	+	0.0123469i	$0.00393025\pi$
$510$	22882.9	+	70426.3i	0.0879772	+	0.270766i
$511$	−34657.3	+	2727.59i	−0.132725	+	0.0104457i
$512$	5259.59	+	10322.5i	0.0200637	+	0.0393773i
$513$	251040.	−	127911.i	0.953912	−	0.486042i
$514$	−5125.32	−	65123.3i	−0.0193997	−	0.246496i
$515$	−194502.	+	63197.5i	−0.733346	+	0.238279i
$516$	40365.0	+	9690.79i	0.151602	+	0.0363965i
$517$	−416923.	−	135467.i	−1.55982	−	0.506817i
$518$	88394.1	+	54168.0i	0.329431	+	0.201875i
$519$	−24649.0	+	10209.9i	−0.0915091	+	0.0379043i
$520$	−651.298	+	8275.53i	−0.00240865	+	0.0306048i
$521$	−10341.3	−	43074.7i	−0.0380979	−	0.158689i	0.950078	−	0.312011i	$-0.101003\pi$
$521$	−10341.3	−	43074.7i	−0.0380979	−	0.158689i	−0.988176	+	0.153322i	$0.951003\pi$
$522$	121783.	−	74628.7i	0.446936	−	0.273883i
$523$	190993.	−	262879.i	0.698254	−	0.961065i	−0.301716	−	0.953398i	$-0.597560\pi$
$523$	190993.	−	262879.i	0.698254	−	0.961065i	0.999971	−	0.00766681i	$-0.00244044\pi$
$524$	−48878.1	+	48878.1i	−0.178013	+	0.178013i
$525$	23732.4	−	3758.84i	0.0861038	−	0.0136375i
$526$	87663.5	−	102641.i	0.316845	−	0.370978i
$527$	82773.4	+	96915.2i	0.298037	+	0.348956i
$528$	−3361.81	+	21225.6i	−0.0120588	+	0.0761365i
$529$	71004.5	−	51587.8i	0.253732	−	0.184347i
$530$	182834.	+	75732.3i	0.650887	+	0.269606i
$531$	−4356.35	+	8549.81i	−0.0154502	+	0.0303227i
$532$		−	124804.i		−	0.440966i
$533$	35143.3	−	12464.1i	0.123705	−	0.0438739i
$534$	97189.1			0.340828
$535$	116689.	+	59456.0i	0.407683	+	0.207725i
$536$	−15560.0	+	37565.1i	−0.0541601	+	0.130754i
$537$	−3472.74	−	4779.82i	−0.0120427	−	0.0165753i
$538$	145422.	+	23032.6i	0.502419	+	0.0795754i
$539$	163942.	−	140020.i	0.564303	−	0.481961i
$540$	43867.6	+	37466.5i	0.150438	+	0.128486i
$541$	6098.65	+	38505.4i	0.0208372	+	0.131561i	0.995914	−	0.0903067i	$-0.0287847\pi$
$541$	6098.65	+	38505.4i	0.0208372	+	0.131561i	−0.975077	+	0.221868i	$0.928785\pi$
$542$	−49757.9	−	49757.9i	−0.169380	−	0.169380i
$543$	−84331.2	−	61270.2i	−0.286015	−	0.207802i
$544$	−52875.4	−	86284.8i	−0.178672	−	0.291566i
$545$	114976.	−	27603.3i	0.387092	−	0.0929327i
$546$	−4275.96	−	336.525i	−0.0143433	−	0.00112884i
$547$	−194351.	−	469205.i	−0.649549	−	1.56815i	−0.813426	−	0.581669i	$-0.802400\pi$
$547$	−194351.	−	469205.i	−0.649549	−	1.56815i	0.163877	−	0.986481i	$-0.447600\pi$
$548$	65026.5	−	106114.i	0.216535	−	0.353354i
$549$	−128440.	+	395299.i	−0.426145	+	1.31154i
$550$	−27519.7	+	114628.i	−0.0909743	+	0.378935i
$551$	138164.	+	425226.i	0.455086	+	1.40061i
$552$	−38728.2	+	3047.97i	−0.127101	+	0.0100031i
$553$	−53665.3	−	105324.i	−0.175486	−	0.344411i
$554$	−175803.	+	89576.3i	−0.572806	+	0.291859i
$555$	−5578.40	−	70880.3i	−0.0181102	−	0.230112i
$556$	−108724.	+	35326.5i	−0.351702	+	0.114275i
$557$	376868.	+	90478.0i	1.21473	+	0.291630i	0.789668	−	0.613535i	$-0.210253\pi$
$557$	376868.	+	90478.0i	1.21473	+	0.291630i	0.425060	+	0.905165i	$0.360253\pi$
$558$	44757.8	+	14542.7i	0.143747	+	0.0467064i
$559$	−34658.6	−	21238.8i	−0.110914	−	0.0679684i
$560$	23609.1	−	9779.23i	0.0752843	−	0.0311838i
$561$	14728.1	−	187139.i	0.0467974	−	0.594618i
$562$	−19182.9	−	79902.7i	−0.0607355	−	0.252982i
$563$	−100074.	+	61325.7i	−0.315723	+	0.193475i	−0.671327	−	0.741161i	$-0.734275\pi$
$563$	−100074.	+	61325.7i	−0.315723	+	0.193475i	0.355604	+	0.934637i	$0.384275\pi$
$564$	−49224.3	+	67751.4i	−0.154747	+	0.212990i
$565$	−39725.4	+	39725.4i	−0.124443	+	0.124443i
$566$	177207.	−	28066.8i	0.553156	−	0.0876114i
$567$	73330.4	−	85858.8i	0.228096	−	0.267066i
$568$	−116358.	−	136238.i	−0.360663	−	0.422282i
$569$	92195.5	−	582099.i	0.284764	−	1.79793i	−0.266753	−	0.963765i	$-0.585951\pi$
$569$	92195.5	−	582099.i	0.284764	−	1.79793i	0.551517	−	0.834164i	$-0.314049\pi$
$570$	−69246.0	+	50310.1i	−0.213130	+	0.154848i
$571$	596433.	+	247051.i	1.82932	+	0.757729i	0.968588	+	0.248671i	$0.0799940\pi$
$571$	596433.	+	247051.i	1.82932	+	0.757729i	0.860732	+	0.509058i	$0.170006\pi$
$572$	9553.43	−	18749.7i	0.0291989	−	0.0573062i
$573$		−	48431.6i		−	0.147509i
$574$	−83303.1	−	78974.8i	−0.252835	−	0.239698i
$575$	−213101.			−0.644541
$576$	−33293.9	−	16964.1i	−0.100351	−	0.0511312i
$577$	−165316.	+	399109.i	−0.496551	+	1.19878i	0.454778	+	0.890605i	$0.349718\pi$
$577$	−165316.	+	399109.i	−0.496551	+	1.19878i	−0.951329	+	0.308176i	$0.900282\pi$
$578$	380724.	+	524021.i	1.13961	+	1.56853i
$579$	−2063.30	−	326.794i	−0.00615467	−	0.000974804i
$580$	−69613.9	+	59455.9i	−0.206938	+	0.176742i
$581$	123013.	+	105063.i	0.364418	+	0.311242i
$582$	2753.64	+	17385.8i	0.00812945	+	0.0513273i
$583$	−354734.	−	354734.i	−1.04368	−	1.04368i
$584$	−26359.8	−	19151.5i	−0.0772889	−	0.0561537i
$585$	−13989.4	−	22828.7i	−0.0408779	−	0.0667067i
$586$	454603.	−	109141.i	1.32384	−	0.317827i
$587$	311754.	+	24535.6i	0.904765	+	0.0712066i	0.522299	−	0.852763i	$-0.325075\pi$
$587$	311754.	+	24535.6i	0.904765	+	0.0712066i	0.382467	+	0.923969i	$0.375075\pi$
$588$	−15761.4	−	38051.4i	−0.0455870	−	0.110057i
$589$	−76973.3	+	125609.i	−0.221876	+	0.362068i
$590$	1900.59	−	5849.41i	0.00545989	−	0.0168038i
$591$	3784.57	−	15763.9i	0.0108353	−	0.0451323i
$592$	30025.4	+	92408.7i	0.0856733	+	0.263675i
$593$	−141570.	+	11141.8i	−0.402588	+	0.0316844i	−0.278137	−	0.960541i	$-0.589717\pi$
$593$	−141570.	+	11141.8i	−0.402588	+	0.0316844i	−0.124451	+	0.992226i	$0.539717\pi$
$594$	−66392.9	−	130303.i	−0.188169	−	0.369303i
$595$	−198888.	+	101339.i	−0.561792	+	0.286247i
$596$	−2284.58	−	29028.4i	−0.00643153	−	0.0817203i
$597$	−158715.	+	51569.6i	−0.445317	+	0.144692i
$598$	36988.9	+	8880.24i	0.103435	+	0.0248326i
$599$	−174854.	−	56813.6i	−0.487330	−	0.158343i	0.0550379	−	0.998484i	$-0.482472\pi$
$599$	−174854.	−	56813.6i	−0.487330	−	0.158343i	−0.542368	+	0.840141i	$0.682472\pi$
$600$	19201.5	+	11766.7i	0.0533375	+	0.0326853i
$601$	320702.	−	132839.i	0.887877	−	0.367771i	0.108331	−	0.994115i	$-0.465450\pi$
$601$	320702.	−	132839.i	0.887877	−	0.367771i	0.779547	+	0.626344i	$0.215450\pi$
$602$	−9817.87	+	124748.i	−0.0270910	+	0.344223i
$603$	−30615.0	−	127521.i	−0.0841975	−	0.350708i
$604$	95328.0	−	58417.1i	0.261304	−	0.160128i
$605$	5630.87	−	7750.22i	0.0153838	−	0.0211740i
$606$	104368.	−	104368.i	0.284198	−	0.284198i
$607$	193677.	−	30675.4i	0.525654	−	0.0832554i	0.112033	−	0.993705i	$-0.464264\pi$
$607$	193677.	−	30675.4i	0.525654	−	0.0832554i	0.413621	+	0.910449i	$0.364264\pi$
$608$	75966.4	−	88945.2i	0.205501	−	0.240611i
$609$	−30720.8	−	35969.5i	−0.0828321	−	0.0969839i
$610$	41675.6	−	263129.i	0.112001	−	0.707147i
$611$	66342.2	−	48200.4i	0.177708	−	0.129113i
$612$	301553.	+	124907.i	0.805119	+	0.333491i
$613$	−239285.	+	469622.i	−0.636786	+	1.24976i	0.316757	+	0.948507i	$0.397406\pi$
$613$	−239285.	+	469622.i	−0.636786	+	1.24976i	−0.953543	+	0.301257i	$0.902594\pi$
$614$			144178.i			0.382439i
$615$	−10237.7	+	78055.5i	−0.0270676	+	0.206373i
$616$	−64780.0			−0.170718
$617$	−486411.	−	247839.i	−1.27771	−	0.651027i	−0.322394	−	0.946606i	$-0.604488\pi$
$617$	−486411.	−	247839.i	−1.27771	−	0.651027i	−0.955318	+	0.295579i	$0.904488\pi$
$618$	37900.4	−	91499.7i	0.0992355	−	0.239576i
$619$	−200020.	−	275305.i	−0.522027	−	0.718509i	0.463862	−	0.885907i	$-0.346463\pi$
$619$	−200020.	−	275305.i	−0.522027	−	0.718509i	−0.985889	+	0.167399i	$0.946463\pi$
$620$	−29792.8	−	4718.72i	−0.0775048	−	0.0122755i
$621$	201024.	−	171691.i	0.521272	−	0.445208i
$622$	−341745.	−	291878.i	−0.883326	−	0.754432i
$623$	45830.1	+	289360.i	0.118079	+	0.745524i
$624$	−2842.55	−	2842.55i	−0.00730027	−	0.00730027i
$625$	−38362.8	−	27872.2i	−0.0982088	−	0.0713529i
$626$	−93359.8	−	152349.i	−0.238238	−	0.388769i
$627$	210982.	−	50652.2i	0.536672	−	0.128844i
$628$	−67601.3	−	5320.34i	−0.171410	−	0.0134903i
$629$	−324795.	−	784125.i	−0.820934	−	1.98191i
$630$	−43065.5	+	70276.5i	−0.108505	+	0.177063i
$631$	−212771.	+	654842.i	−0.534384	+	1.64467i	0.210592	+	0.977574i	$0.432461\pi$
$631$	−212771.	+	654842.i	−0.534384	+	1.64467i	−0.744976	+	0.667091i	$0.767539\pi$
$632$	25863.1	−	107728.i	0.0647511	−	0.269708i
$633$	−54240.5	−	166935.i	−0.135368	−	0.416620i
$634$	−113119.	+	8902.68i	−0.281422	+	0.0221484i
$635$	34725.3	+	68152.2i	0.0861189	+	0.169018i
$636$	−85390.5	+	43508.6i	−0.211103	+	0.107563i
$637$	3164.25	+	40205.6i	0.00779815	+	0.0990849i
$638$	220716.	−	71714.8i	0.542240	−	0.176184i
$639$	561907.	+	134902.i	1.37614	+	0.330382i
$640$	22778.2	+	7401.10i	0.0556109	+	0.0180691i
$641$	−3717.13	−	2277.86i	−0.00904672	−	0.00554384i	0.517968	−	0.855400i	$-0.326689\pi$
$641$	−3717.13	−	2277.86i	−0.00904672	−	0.00554384i	−0.527015	+	0.849856i	$0.676689\pi$
$642$	−58593.7	+	24270.3i	−0.142161	+	0.0588851i
$643$	−23422.2	+	297608.i	−0.0566509	+	0.719818i	0.901357	+	0.433076i	$0.142572\pi$
$643$	−23422.2	+	297608.i	−0.0566509	+	0.719818i	−0.958008	+	0.286741i	$0.907428\pi$
$644$	−27337.2	−	113867.i	−0.0659146	−	0.274554i
$645$	73172.6	−	44840.2i	0.175885	−	0.107783i
$646$	−600564.	+	826606.i	−1.43911	+	1.98077i
$647$	−224694.	+	224694.i	−0.536764	+	0.536764i	−0.922577	−	0.385813i	$-0.873921\pi$
$647$	−224694.	+	224694.i	−0.536764	+	0.536764i	0.385813	+	0.922577i	$0.373921\pi$
$648$	104522.	−	16554.7i	0.248919	−	0.0394249i
$649$	−10125.7	+	11855.7i	−0.0240401	+	0.0281474i
$650$	−14321.4	−	16768.2i	−0.0338968	−	0.0396881i
$651$	2438.16	−	15393.9i	0.00575308	−	0.0363235i
$652$	−121423.	+	88218.6i	−0.285630	+	0.207522i
$653$	−32308.7	−	13382.7i	−0.0757693	−	0.0313847i	0.344477	−	0.938795i	$-0.388056\pi$
$653$	−32308.7	−	13382.7i	−0.0757693	−	0.0313847i	−0.420246	+	0.907410i	$0.638056\pi$
$654$	−25996.2	+	51020.4i	−0.0607791	+	0.119286i
$655$			142902.i			0.333085i
$656$	−11297.5	−	106989.i	−0.0262528	−	0.248618i
$657$	105091.			0.243463
$658$	−224927.	−	114606.i	−0.519505	−	0.264701i
$659$	47146.2	−	113821.i	0.108562	−	0.262091i	−0.860258	−	0.509860i	$-0.829697\pi$
$659$	47146.2	−	113821.i	0.108562	−	0.262091i	0.968819	+	0.247769i	$0.0796973\pi$
$660$	26113.7	+	35942.4i	0.0599488	+	0.0825124i
$661$	−567017.	−	89806.7i	−1.29776	−	0.205545i	−0.530940	−	0.847410i	$-0.678161\pi$
$661$	−567017.	−	89806.7i	−1.29776	−	0.205545i	−0.766818	+	0.641865i	$0.778161\pi$
$662$	−271297.	+	231709.i	−0.619054	+	0.528722i
$663$	26701.3	+	22805.1i	0.0607443	+	0.0518805i
$664$	23718.5	+	149753.i	0.0537962	+	0.339656i
$665$	−182441.	−	182441.i	−0.412552	−	0.412552i
$666$	−253538.	−	184206.i	−0.571603	−	0.415294i
$667$	219199.	+	357701.i	0.492705	+	0.804022i
$668$	−210080.	+	50435.8i	−0.470795	+	0.113028i
$669$	8851.23	+	696.607i	0.0197766	+	0.00155645i
$670$	32167.6	+	77659.4i	0.0716587	+	0.172999i
$671$	−352866.	+	575826.i	−0.783728	+	1.27893i
$672$	−3824.14	+	11769.5i	−0.00846829	+	0.0260627i
$673$	1966.72	−	8191.97i	0.00434222	−	0.0180867i	−0.970157	−	0.242479i	$-0.922040\pi$
$673$	1966.72	−	8191.97i	0.00434222	−	0.0180867i	0.974499	+	0.224392i	$0.0720396\pi$
$674$	111657.	+	343644.i	0.245790	+	0.756465i
$675$	−152779.	+	12023.9i	−0.335317	+	0.0263900i
$676$	−101944.	−	200077.i	−0.223085	−	0.437828i
$677$	85449.5	−	43538.7i	0.186437	−	0.0949944i	−0.358281	−	0.933614i	$-0.616637\pi$
$677$	85449.5	−	43538.7i	0.186437	−	0.0949944i	0.544718	+	0.838620i	$0.316637\pi$
$678$	−2134.59	−	27122.5i	−0.00464360	−	0.0590025i
$679$	−50464.0	+	16396.7i	−0.109457	+	0.0355646i
$680$	−203427.	−	48838.5i	−0.439938	−	0.105620i
$681$	−175951.	−	57169.9i	−0.379400	−	0.123274i
$682$	65197.9	+	39953.3i	0.140173	+	0.0858982i
$683$	409624.	−	169672.i	0.878099	−	0.363721i	0.102340	−	0.994749i	$-0.467367\pi$
$683$	409624.	−	169672.i	0.878099	−	0.363721i	0.775759	+	0.631029i	$0.217367\pi$
$684$	−29600.5	+	376110.i	−0.0632685	+	0.803902i
$685$	−60061.9	−	250176.i	−0.128002	−	0.533168i
$686$	245652.	−	150536.i	0.522001	−	0.319883i
$687$	24728.0	−	34035.2i	0.0523933	−	0.0721132i
$688$	−82929.3	+	82929.3i	−0.175199	+	0.175199i
$689$	92687.3	−	14680.2i	0.195246	−	0.0309239i
$690$	−52158.0	+	61069.2i	−0.109553	+	0.128270i
$691$	−113800.	−	133243.i	−0.238334	−	0.279054i	0.628328	−	0.777948i	$-0.283739\pi$
$691$	−113800.	−	133243.i	−0.238334	−	0.279054i	−0.866663	+	0.498895i	$0.833739\pi$
$692$	11791.4	−	74447.9i	0.0246237	−	0.155468i
$693$	169035.	−	122811.i	0.351975	−	0.255724i
$694$	−222558.	−	92186.3i	−0.462087	−	0.191403i
$695$	−107293.	+	210575.i	−0.222128	+	0.435951i
$696$		−	44334.1i		−	0.0915206i
$697$	171704.	+	923928.i	0.353439	+	1.90183i
$698$	−85543.7			−0.175581
$699$	−197770.	−	100769.i	−0.404768	−	0.206240i
$700$	−25978.2	+	62717.0i	−0.0530168	+	0.127994i
$701$	205416.	+	282731.i	0.418021	+	0.575357i	0.965152	−	0.261690i	$-0.0842799\pi$
$701$	205416.	+	282731.i	0.418021	+	0.575357i	−0.547130	+	0.837047i	$0.684280\pi$
$702$	27019.5	+	4279.47i	0.0548281	+	0.00868392i
$703$	745975.	−	637123.i	1.50943	−	1.28918i
$704$	−46167.4	−	39430.7i	−0.0931515	−	0.0795589i
$705$	27083.3	+	170997.i	0.0544909	+	0.344042i
$706$	−345725.	−	345725.i	−0.693619	−	0.693619i
$707$	359947.	+	261517.i	0.720111	+	0.523192i
$708$	1556.24	+	2539.56i	0.00310464	+	0.00506631i
$709$	−490445.	+	117746.i	−0.975659	+	0.234235i	−0.689771	−	0.724028i	$-0.742289\pi$
$709$	−490445.	+	117746.i	−0.975659	+	0.234235i	−0.285889	+	0.958263i	$0.592289\pi$
$710$	−369251.	−	29060.7i	−0.732495	−	0.0576486i
$711$	136746.	+	330134.i	0.270505	+	0.653057i
$712$	−143467.	+	234117.i	−0.283004	+	0.461820i
$713$	−42714.7	+	131462.i	−0.0840230	+	0.258596i
$714$	25234.9	−	105111.i	0.0494999	−	0.206182i
$715$	−13443.2	−	41374.0i	−0.0262961	−	0.0809311i
$716$	16640.3	−	1309.62i	0.0324590	−	0.00255458i
$717$	113616.	+	222984.i	0.221004	+	0.433745i
$718$	606781.	−	309170.i	1.17702	−	0.599721i
$719$	46755.6	+	594087.i	0.0904432	+	1.14919i	0.859890	+	0.510479i	$0.170532\pi$
$719$	46755.6	+	594087.i	0.0904432	+	1.14919i	−0.769447	+	0.638711i	$0.779468\pi$
$720$	−73468.2	+	23871.3i	−0.141721	+	0.0460479i
$721$	290293.	+	69693.1i	0.558426	+	0.134066i
$722$	−772634.	−	251044.i	−1.48217	−	0.481588i
$723$	177144.	+	108554.i	0.338883	+	0.207668i
$724$	272079.	−	112699.i	0.519061	−	0.215002i
$725$	19080.9	−	242446.i	0.0363014	−	0.461253i
$726$	1083.00	+	4511.02i	0.00205473	+	0.00855858i
$727$	249612.	−	152963.i	0.472278	−	0.289412i	−0.265922	−	0.963995i	$-0.585676\pi$
$727$	249612.	−	152963.i	0.472278	−	0.289412i	0.738200	+	0.674582i	$0.235676\pi$
$728$	7122.66	−	9803.50i	0.0134394	−	0.0184977i
$729$	−170636.	+	170636.i	−0.321082	+	0.321082i
$730$	−66529.4	+	10537.2i	−0.124844	+	0.0197734i
$731$	665321.	−	778990.i	1.24508	−	1.45780i
$732$	83787.8	+	98102.9i	0.156372	+	0.183088i
$733$	105237.	−	664441.i	0.195867	−	1.23666i	−0.672261	−	0.740314i	$-0.734677\pi$
$733$	105237.	−	664441.i	0.195867	−	1.23666i	0.868128	−	0.496341i	$-0.165323\pi$
$734$	280992.	−	204152.i	0.521557	−	0.378933i
$735$	−78664.7	−	32584.0i	−0.145615	−	0.0603156i
$736$	49826.9	−	97790.8i	0.0919831	−	0.180527i
$737$		−	213086.i		−	0.392301i
$738$	232312.	+	257757.i	0.426539	+	0.473258i
$739$	390883.			0.715744			0.357872	−	0.933771i	$-0.383502\pi$
$739$	390883.			0.715744			0.357872	+	0.933771i	$0.383502\pi$
$740$	178977.	+	91193.1i	0.326838	+	0.166532i
$741$	−15532.3	+	37498.2i	−0.0282878	+	0.0682927i
$742$	−169804.	−	233715.i	−0.308418	−	0.424501i
$743$	−853400.	−	135165.i	−1.54588	−	0.244843i	−0.675549	−	0.737315i	$-0.736093\pi$
$743$	−853400.	−	135165.i	−1.54588	−	0.244843i	−0.870328	+	0.492472i	$0.836093\pi$
$744$	11107.7	−	9486.87i	0.0200668	−	0.0171387i
$745$	−45773.9	−	39094.6i	−0.0824717	−	0.0704375i
$746$	−2486.61	−	15699.8i	−0.00446817	−	0.0282109i
$747$	−345795.	−	345795.i	−0.619695	−	0.619695i
$748$	429053.	+	311725.i	0.766846	+	0.557146i
$749$	−99889.8	−	163005.i	−0.178056	−	0.290562i
$750$	125770.	−	30194.7i	0.223591	−	0.0536795i
$751$	−41697.6	−	3281.67i	−0.0739317	−	0.00581855i	0.0414393	−	0.999141i	$-0.486806\pi$
$751$	−41697.6	−	3281.67i	−0.0739317	−	0.00581855i	−0.115371	+	0.993322i	$0.536806\pi$
$752$	−90541.9	−	218587.i	−0.160108	−	0.386536i
$753$	−177495.	+	289646.i	−0.313038	+	0.510832i
$754$	−13415.0	+	41287.2i	−0.0235966	+	0.0726228i
$755$	53957.1	−	224748.i	0.0946575	−	0.394277i
$756$	−26023.7	−	80092.6i	−0.0455329	−	0.140136i
$757$	927648.	−	73007.5i	1.61879	−	0.127402i	0.763593	−	0.645698i	$-0.223434\pi$
$757$	927648.	−	73007.5i	1.61879	−	0.127402i	0.855201	+	0.518297i	$0.173434\pi$
$758$	223617.	+	438873.i	0.389195	+	0.763837i
$759$	181398.	−	92427.1i	0.314884	−	0.160441i
$760$	−18972.7	−	241071.i	−0.0328475	−	0.417367i
$761$	480514.	−	156129.i	0.829730	−	0.269596i	0.136799	−	0.990599i	$-0.456319\pi$
$761$	480514.	−	156129.i	0.829730	−	0.269596i	0.692932	+	0.721003i	$0.256319\pi$
$762$	−36017.8	−	8647.12i	−0.0620308	−	0.0148923i
$763$	−164161.	−	53339.1i	−0.281982	−	0.0916214i
$764$	116666.	+	71493.0i	0.199874	+	0.122483i
$765$	623407.	−	258224.i	1.06524	−	0.441238i
$766$	−17202.8	+	218583.i	−0.0293185	+	0.372527i
$767$	−680.847	−	2835.93i	−0.00115733	−	0.00482064i
$768$	−9889.32	+	6060.18i	−0.0167666	+	0.0102746i
$769$	319654.	−	439966.i	0.540540	−	0.743989i	−0.448151	−	0.893958i	$-0.647917\pi$
$769$	319654.	−	439966.i	0.540540	−	0.743989i	0.988691	+	0.149969i	$0.0479173\pi$
$770$	−94696.7	+	94696.7i	−0.159718	+	0.159718i
$771$	64594.1	−	10230.7i	0.108664	−	0.0172106i
$772$	3832.97	−	4487.83i	0.00643134	−	0.00753013i
$773$	−763637.	−	894104.i	−1.27799	−	1.49634i	−0.774871	−	0.632119i	$-0.782185\pi$
$773$	−763637.	−	894104.i	−1.27799	−	1.49634i	−0.503120	−	0.864216i	$-0.667815\pi$
$774$	59174.5	−	373613.i	0.0987762	−	0.623649i
$775$	64826.8	−	47099.4i	0.107932	−	0.0784173i
$776$	−45945.1	−	19031.1i	−0.0762985	−	0.0316039i
$777$	−47119.5	+	92477.1i	−0.0780474	+	0.153177i
$778$		−	382133.i		−	0.631329i
$779$	−954342.	+	518765.i	−1.57264	+	0.854862i
$780$	−8310.60			−0.0136598
$781$	836603.	+	426270.i	1.37157	+	0.698849i
$782$	−366877.	+	885719.i	−0.599939	+	1.44838i
$783$	177333.	+	244078.i	0.289246	+	0.398113i
$784$	114928.	+	18202.8i	0.186979	+	0.0296145i
$785$	−106598.	+	91043.6i	−0.172986	+	0.147744i
$786$	−52622.4	−	44943.8i	−0.0851776	−	0.0727486i
$787$	−115994.	−	732355.i	−0.187277	−	1.18242i	−0.884839	−	0.465897i	$-0.845732\pi$
$787$	−115994.	−	732355.i	−0.187277	−	1.18242i	0.697562	−	0.716525i	$-0.254268\pi$
$788$	32386.6	+	32386.6i	0.0521570	+	0.0521570i
$789$	109327.	+	79430.8i	0.175620	+	0.127595i
$790$	−119671.	−	195286.i	−0.191750	−	0.312908i
$791$	79744.8	−	19145.0i	0.127453	−	0.0305987i
$792$	195222.	+	15364.3i	0.311227	+	0.0244941i
$793$	−48344.6	−	116714.i	−0.0768778	−	0.185600i
$794$	244924.	−	399680.i	0.388499	−	0.633973i
$795$	−61223.7	+	188427.i	−0.0968692	+	0.298133i
$796$	110064.	−	458450.i	0.173708	−	0.723545i
$797$	−341196.	−	1.05009e6i	−0.537139	−	1.65314i	−0.738981	−	0.673726i	$-0.764693\pi$
$797$	−341196.	−	1.05009e6i	−0.537139	−	1.65314i	0.201842	−	0.979418i	$-0.435307\pi$
$798$	124561.	−	9803.19i	0.195604	−	0.0153944i
$799$	938253.	+	1.84143e6i	1.46969	+	2.88443i
$800$	−56689.1	+	28884.6i	−0.0885768	+	0.0451321i
$801$	−69484.7	−	882887.i	−0.108299	−	1.37607i
$802$	−174992.	+	56858.5i	−0.272063	+	0.0883988i
$803$	166036.	+	39861.6i	0.257496	+	0.0618193i
$804$	−38714.3	−	12579.1i	−0.0598907	−	0.0194597i
$805$	−206416.	−	126492.i	−0.318531	−	0.195196i
$806$	−13215.0	+	5473.82i	−0.0203421	+	0.00842597i
$807$	−11565.1	+	146949.i	−0.0177584	+	0.225641i
$808$	97345.3	+	405472.i	0.149105	+	0.621067i
$809$	16893.6	−	10352.4i	0.0258122	−	0.0158177i	−0.509533	−	0.860451i	$-0.670182\pi$
$809$	16893.6	−	10352.4i	0.0258122	−	0.0158177i	0.535345	+	0.844634i	$0.320182\pi$
$810$	128593.	−	176992.i	0.195995	−	0.269765i
$811$	684089.	−	684089.i	1.04009	−	1.04009i	0.0409276	−	0.999162i	$-0.486969\pi$
$811$	684089.	−	684089.i	1.04009	−	1.04009i	0.999162	−	0.0409276i	$-0.0130313\pi$
$812$	131995.	−	20906.0i	0.200192	−	0.0317072i
$813$	45752.7	−	53569.6i	0.0692207	−	0.0810470i
$814$	−330701.	−	387201.i	−0.499099	−	0.584370i
$815$	−48538.1	+	306458.i	−0.0730748	+	0.461376i
$816$	81963.8	−	59550.2i	0.123095	−	0.0894340i
$817$	1.09398e6	+	453142.i	1.63895	+	0.678876i
$818$	138958.	−	272721.i	0.207672	−	0.407578i
$819$			39084.3i			0.0582687i
$820$	−172914.	−	139884.i	−0.257159	−	0.208037i
$821$	−424019.			−0.629070			−0.314535	−	0.949246i	$-0.601849\pi$
$821$	−424019.			−0.629070			−0.314535	+	0.949246i	$0.601849\pi$
$822$	111015.	+	56565.0i	0.164300	+	0.0837151i
$823$	−88513.3	+	213690.i	−0.130680	+	0.315489i	−0.975653	−	0.219319i	$-0.929616\pi$
$823$	−88513.3	+	213690.i	−0.130680	+	0.315489i	0.844973	+	0.534809i	$0.179616\pi$
$824$	164464.	+	226366.i	0.242224	+	0.333393i
$825$	−116567.	−	18462.4i	−0.171264	−	0.0271256i
$826$	−6827.13	+	5830.92i	−0.0100064	+	0.00854628i
$827$	−625711.	−	534407.i	−0.914877	−	0.781378i	0.0613533	−	0.998116i	$-0.480458\pi$
$827$	−625711.	−	534407.i	−0.914877	−	0.781378i	−0.976230	+	0.216738i	$0.930458\pi$
$828$	55376.9	+	349636.i	0.0807733	+	0.509983i
$829$	103290.	+	103290.i	0.150296	+	0.150296i	0.778250	−	0.627954i	$-0.216108\pi$
$829$	103290.	+	103290.i	0.150296	+	0.150296i	−0.627954	+	0.778250i	$0.716108\pi$
$830$	253584.	+	184239.i	0.368100	+	0.267440i
$831$	−103211.	−	168425.i	−0.149460	−	0.243897i
$832$	11043.4	−	2651.29i	0.0159536	−	0.00383011i
$833$	−1.01328e6	−	79746.5i	−1.46028	−	0.114927i
$834$	−43797.9	−	105737.i	−0.0629682	−	0.152019i
$835$	−233371.	+	380827.i	−0.334714	+	0.546204i
$836$	−189428.	+	583000.i	−0.271039	+	0.834172i
$837$	−23205.9	+	96659.5i	−0.0331243	+	0.137973i
$838$	180462.	+	555406.i	0.256980	+	0.790902i
$839$	40521.7	−	3189.13i	0.0575657	−	0.00453052i	−0.0496436	−	0.998767i	$-0.515809\pi$
$839$	40521.7	−	3189.13i	0.0575657	−	0.00453052i	0.107209	+	0.994236i	$0.465809\pi$
$840$	11614.7	+	22795.1i	0.0164607	+	0.0323060i
$841$	203608.	−	103744.i	0.287874	−	0.146679i
$842$	−15196.6	−	193091.i	−0.0214349	−	0.272357i
$843$	78240.6	−	25421.9i	0.110097	−	0.0357728i
$844$	482194.	+	115765.i	0.676920	+	0.162514i
$845$	−441501.	−	143452.i	−0.618327	−	0.200907i
$846$	650661.	+	398725.i	0.909105	+	0.557100i
$847$	−12919.9	+	5351.60i	−0.0180091	+	0.00745962i
$848$	21243.3	−	269921.i	0.0295413	−	0.375358i
$849$	41931.6	+	174658.i	0.0581737	+	0.242311i
$850$	473858.	−	290381.i	0.655859	−	0.401911i
$851$	541050.	−	744691.i	0.747099	−	1.02829i
$852$	126834.	−	126834.i	0.174725	−	0.174725i
$853$	−552633.	+	87528.4i	−0.759519	+	0.120296i	−0.524168	−	0.851615i	$-0.675624\pi$
$853$	−552633.	+	87528.4i	−0.759519	+	0.120296i	−0.235350	+	0.971911i	$0.575624\pi$
$854$	−252570.	+	295721.i	−0.346310	+	0.405477i
$855$	506535.	+	593076.i	0.692911	+	0.811294i
$856$	28029.6	−	176972.i	0.0382534	−	0.241522i
$857$	−1.08467e6	+	788057.i	−1.47685	+	1.07299i	−0.498289	+	0.867011i	$0.666038\pi$
$857$	−1.08467e6	+	788057.i	−1.47685	+	1.07299i	−0.978556	+	0.205980i	$0.933962\pi$
$858$	19463.6	+	8062.09i	0.0264392	+	0.0109515i
$859$	−229307.	+	450040.i	−0.310764	+	0.609908i	−0.992577	−	0.121618i	$-0.961192\pi$
$859$	−229307.	+	450040.i	−0.310764	+	0.609908i	0.681813	+	0.731526i	$0.261192\pi$
$860$			242455.i			0.327820i
$861$	72278.0	−	89344.5i	0.0974989	−	0.120521i
$862$	103543.			0.139349
$863$	−570255.	−	290559.i	−0.765680	−	0.390134i	0.0271065	−	0.999633i	$-0.491371\pi$
$863$	−570255.	−	290559.i	−0.765680	−	0.390134i	−0.792787	+	0.609499i	$0.791371\pi$
$864$	30204.7	−	72920.6i	0.0404620	−	0.0976839i
$865$	−91592.6	−	126066.i	−0.122413	−	0.168487i
$866$	−233385.	−	36964.6i	−0.311199	−	0.0492890i
$867$	−493097.	+	421145.i	−0.655986	+	0.560265i
$868$	33483.0	+	28597.2i	0.0444411	+	0.0379563i
$869$	90826.6	+	573457.i	0.120275	+	0.759383i
$870$	−64808.4	−	64808.4i	−0.0856235	−	0.0856235i
$871$	32247.4	+	23429.1i	0.0425068	+	0.0308830i
$872$	−84527.4	−	137936.i	−0.111164	−	0.181403i
$873$	155968.	−	37444.5i	0.204647	−	0.0491315i
$874$	−1.10471e6	−	86942.6i	−1.44619	−	0.113818i
$875$	149206.	+	360215.i	0.194881	+	0.470484i
$876$	17043.8	−	27812.9i	0.0222105	−	0.0362442i
$877$	17802.5	−	54790.3i	0.0231462	−	0.0712368i	−0.938816	−	0.344419i	$-0.888076\pi$
$877$	17802.5	−	54790.3i	0.0231462	−	0.0712368i	0.961962	+	0.273182i	$0.0880761\pi$
$878$	107409.	−	447391.i	0.139332	−	0.580361i
$879$	144637.	+	445146.i	0.187198	+	0.576136i
$880$	−125129.	+	9847.86i	−0.161582	+	0.0127168i
$881$	−113841.	−	223425.i	−0.146671	−	0.287859i	0.805969	−	0.591958i	$-0.201645\pi$
$881$	−113841.	−	223425.i	−0.146671	−	0.287859i	−0.952641	+	0.304099i	$0.901645\pi$
$882$	−334399.	+	170385.i	−0.429860	+	0.219025i
$883$	−15924.2	−	202336.i	−0.0204237	−	0.259508i	−0.998649	−	0.0519625i	$-0.983452\pi$
$883$	−15924.2	−	202336.i	−0.0204237	−	0.259508i	0.978225	−	0.207546i	$-0.0665476\pi$
$884$	−94350.1	+	30656.2i	−0.120736	+	0.0392296i
$885$	5987.33	+	1437.43i	0.00764445	+	0.00183527i
$886$	−494938.	−	160815.i	−0.630498	−	0.204861i
$887$	−185071.	−	113412.i	−0.235229	−	0.144148i	0.399889	−	0.916563i	$-0.369049\pi$
$887$	−185071.	−	113412.i	−0.235229	−	0.144148i	−0.635118	+	0.772415i	$0.719049\pi$
$888$	−89870.6	+	37225.6i	−0.113970	+	0.0472080i
$889$	8760.52	−	111313.i	0.0110848	−	0.140845i
$890$	132514.	+	551959.i	0.167294	+	0.696830i
$891$	−472867.	+	289773.i	−0.595640	+	0.365008i
$892$	−14743.9	+	20293.2i	−0.0185303	+	0.0255048i
$893$	−1.68915e6	+	1.68915e6i	−2.11819	+	2.11819i
$894$	28792.5	−	4560.28i	0.0360250	−	0.00570580i
$895$	22410.7	−	26239.6i	0.0279776	−	0.0327575i
$896$	−22706.3	−	26585.6i	−0.0282833	−	0.0331154i
$897$	−5957.55	+	37614.5i	−0.00740428	+	0.0467488i
$898$	724288.	−	526226.i	0.898170	−	0.652559i
$899$	−145740.	−	60367.7i	−0.180327	−	0.0746939i
$900$	93163.3	−	182843.i	0.115016	−	0.225732i
$901$			2.36506e6i			2.91334i
$902$	269267.	+	495355.i	0.330956	+	0.608840i
$903$	−125277.			−0.153636
$904$	68485.8	+	34895.3i	0.0838038	+	0.0427002i
$905$	232985.	−	562476.i	0.284467	−	0.686763i
$906$	65791.4	+	90554.1i	0.0801517	+	0.110319i
$907$	525627.	+	83251.2i	0.638945	+	0.101199i	0.467498	−	0.883994i	$-0.345156\pi$
$907$	525627.	+	83251.2i	0.638945	+	0.101199i	0.171447	+	0.985193i	$0.445156\pi$
$908$	397447.	−	339452.i	0.482067	−	0.411725i
$909$	−1.02271e6	−	873480.i	−1.23773	−	1.05712i
$910$	−3918.91	−	24743.0i	−0.00473241	−	0.0298793i
$911$	−919683.	−	919683.i	−1.10816	−	1.10816i	−0.993393	−	0.114764i	$-0.963389\pi$
$911$	−919683.	−	919683.i	−1.10816	−	1.10816i	−0.114764	−	0.993393i	$-0.536611\pi$
$912$	94739.4	+	68832.2i	0.113905	+	0.0827565i
$913$	−415169.	−	677494.i	−0.498062	−	0.812763i
$914$	848688.	−	203752.i	1.01591	−	0.243899i
$915$	265891.	+	20926.1i	0.317586	+	0.0249946i
$916$	45484.1	+	109808.i	0.0542086	+	0.130871i
$917$	108996.	−	177865.i	0.129620	−	0.211521i
$918$	−213050.	+	655700.i	−0.252811	+	0.778072i
$919$	312652.	−	1.30229e6i	0.370195	−	1.54197i	−0.407425	−	0.913239i	$-0.633573\pi$
$919$	312652.	−	1.30229e6i	0.370195	−	1.54197i	0.777620	−	0.628734i	$-0.216427\pi$
$920$	−70114.6	−	215790.i	−0.0828386	−	0.254951i
$921$	−143898.	+	11325.0i	−0.169642	+	0.0133511i
$922$	−67175.2	−	131839.i	−0.0790218	−	0.155089i
$923$	−156496.	+	79738.5i	−0.183696	+	0.0935976i
$924$	−5088.39	−	64654.1i	−0.00595986	−	0.0757272i
$925$	−507489.	+	164893.i	−0.593121	+	0.192717i
$926$	−564626.	−	135555.i	−0.658474	−	0.158086i
$927$	−858299.	−	278878.i	−0.998802	−	0.324530i
$928$	106795.	+	65444.3i	0.124010	+	0.0759934i
$929$	627837.	−	260059.i	0.727471	−	0.301328i	0.0119587	−	0.999928i	$-0.496193\pi$
$929$	627837.	−	260059.i	0.727471	−	0.301328i	0.715512	+	0.698600i	$0.246193\pi$
$930$	2369.36	−	30105.6i	0.00273946	−	0.0348081i
$931$	−274260.	−	1.14237e6i	−0.316419	−	1.31798i
$932$	534681.	−	327653.i	0.615550	−	0.377209i
$933$	264467.	−	364007.i	0.303814	−	0.418164i
$934$	−42931.9	+	42931.9i	−0.0492138	+	0.0492138i
$935$	1.08288e6	−	171512.i	1.23868	−	0.196188i
$936$	−23790.1	+	27854.6i	−0.0271547	+	0.0317940i
$937$	−37472.8	−	43875.1i	−0.0426813	−	0.0499734i	0.738655	−	0.674084i	$-0.235461\pi$
$937$	−37472.8	−	43875.1i	−0.0426813	−	0.0499734i	−0.781336	+	0.624111i	$0.785461\pi$
$938$	19195.4	−	121195.i	0.0218169	−	0.137746i
$939$	144720.	−	105145.i	0.164133	−	0.119250i
$940$	−451891.	−	187180.i	−0.511421	−	0.211837i
$941$	−459018.	+	900873.i	−0.518382	+	1.01738i	0.472332	+	0.881421i	$0.343412\pi$
$941$	−459018.	+	900873.i	−0.518382	+	1.01738i	−0.990714	+	0.135962i	$0.956588\pi$
$942$		−	67887.8i		−	0.0765051i
$943$	−757083.	+	682346.i	−0.851373	+	0.767329i
$944$	−8414.76			−0.00944273
$945$	−155123.	−	79039.1i	−0.173705	−	0.0885071i
$946$	235205.	−	567836.i	0.262824	−	0.634513i
$947$	656639.	+	903786.i	0.732195	+	1.00778i	0.999030	+	0.0440376i	$0.0140221\pi$
$947$	656639.	+	903786.i	0.732195	+	1.00778i	−0.266835	+	0.963742i	$0.585978\pi$
$948$	109550.	+	17351.0i	0.121898	+	0.0193067i
$949$	−24288.4	+	20744.2i	−0.0269691	+	0.0230337i
$950$	488469.	+	417192.i	0.541239	+	0.462262i
$951$	−17770.7	−	112200.i	−0.0196492	−	0.124060i
$952$	215948.	+	215948.i	0.238274	+	0.238274i
$953$	−70442.6	−	51179.6i	−0.0775621	−	0.0563522i	0.548328	−	0.836263i	$-0.315264\pi$
$953$	−70442.6	−	51179.6i	−0.0775621	−	0.0563522i	−0.625891	+	0.779911i	$0.715264\pi$
$954$	456291.	+	744599.i	0.501355	+	0.818137i
$955$	275054.	−	66034.7i	0.301586	−	0.0724045i
$956$	−704856.	−	55473.4i	−0.771232	−	0.0606972i
$957$	88912.4	+	214653.i	0.0970819	+	0.234376i
$958$	−297492.	+	485464.i	−0.324149	+	0.528963i
$959$	−116060.	+	357197.i	−0.126196	+	0.388392i
$960$	−5597.51	+	23315.3i	−0.00607369	+	0.0252987i
$961$	269322.	+	828888.i	0.291625	+	0.897530i
$962$	94958.4	−	7473.39i	0.102608	−	0.00807546i
$963$	262368.	+	514926.i	0.282917	+	0.555255i
$964$	−522986.	+	266475.i	−0.562777	+	0.286749i
$965$	−957.290	−	12163.5i	−0.00102799	−	0.0130619i
$966$	111499.	−	36228.2i	0.119486	−	0.0388233i
$967$	−299851.	−	71987.8i	−0.320666	−	0.0769850i	0.0699172	−	0.997553i	$-0.477726\pi$
$967$	−299851.	−	71987.8i	−0.320666	−	0.0769850i	−0.390583	+	0.920568i	$0.627726\pi$
$968$	−12465.2	−	4050.19i	−0.0133030	−	0.00432239i
$969$	−872173.	−	534468.i	−0.928870	−	0.569212i
$970$	−94983.5	+	39343.5i	−0.100950	+	0.0418147i
$971$	−99939.8	+	1.26986e6i	−0.105999	+	1.34684i	0.682086	+	0.731272i	$0.261073\pi$
$971$	−99939.8	+	1.26986e6i	−0.105999	+	1.34684i	−0.788084	+	0.615567i	$0.788927\pi$
$972$	90691.0	+	377755.i	0.0959912	+	0.399832i
$973$	294157.	−	180260.i	0.310709	−	0.190403i
$974$	233865.	−	321888.i	0.246517	−	0.339302i
$975$	15610.7	−	15610.7i	0.0164215	−	0.0164215i
$976$	−360002.	+	57018.8i	−0.377925	+	0.0598574i
$977$	1.09995e6	−	1.28788e6i	1.15235	−	1.34923i	0.225304	−	0.974289i	$-0.427663\pi$
$977$	1.09995e6	−	1.28788e6i	1.15235	−	1.34923i	0.927048	−	0.374942i	$-0.122337\pi$
$978$	−97584.7	−	114257.i	−0.102024	−	0.119455i
$979$	225104.	−	1.42125e6i	0.234865	−	1.48288i
$980$	194613.	−	141394.i	0.202637	−	0.147225i
$981$	482066.	+	199678.i	0.500920	+	0.207488i
$982$	329171.	−	646034.i	0.341349	−	0.669935i
$983$			637414.i			0.659652i	0.944042	+	0.329826i	$0.106990\pi$
$983$			637414.i			0.659652i	−0.944042	+	0.329826i	$0.893010\pi$
$984$	105894.	−	19679.4i	0.109365	−	0.0203246i
$985$	94686.7			0.0975925
$986$	−974835.	−	496703.i	−1.00271	−	0.510909i
$987$	96715.6	−	233492.i	0.0992801	−	0.239683i
$988$	−67400.5	−	92768.9i	−0.0690478	−	0.0950361i
$989$	1.09737e6	+	173807.i	1.12192	+	0.177695i
$990$	307839.	−	262919.i	0.314089	−	0.268257i
$991$	680071.	+	580836.i	0.692480	+	0.591434i	0.924456	−	0.381288i	$-0.124519\pi$
$991$	680071.	+	580836.i	0.692480	+	0.591434i	−0.231976	+	0.972721i	$0.574519\pi$
$992$	6455.95	+	40761.3i	0.00656050	+	0.0414214i
$993$	−252569.	−	252569.i	−0.256142	−	0.256142i
$994$	437429.	+	317811.i	0.442726	+	0.321659i
$995$	−509277.	−	831065.i	−0.514409	−	0.839439i
$996$	−147599.	+	35435.3i	−0.148787	+	0.0357205i
$997$	243636.	+	19174.6i	0.245105	+	0.0192902i	0.200416	−	0.979711i	$-0.435770\pi$
$997$	243636.	+	19174.6i	0.245105	+	0.0192902i	0.0446884	+	0.999001i	$0.485770\pi$
$998$	−164047.	−	396045.i	−0.164706	−	0.397634i
$999$	345877.	−	564420.i	0.346570	−	0.565550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.h.b.13.5	✓	112
41.19	odd	40	inner	82.5.h.b.19.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.h.b.13.5	✓	112	1.1	even	1	trivial
82.5.h.b.19.5	yes	112	41.19	odd	40	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	82.h (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52015 - 1.28408i) q^{2} +(1.08363 - 2.61611i) q^{3} +(4.70228 + 6.47214i) q^{4} +(16.3350 + 2.58721i) q^{5} +(-6.09020 + 5.20152i) q^{6} +(-18.3583 - 15.6794i) q^{7} +(-3.53971 - 22.3488i) q^{8} +(51.6059 + 51.6059i) q^{9} +(-37.8444 - 27.4956i) q^{10} +(61.9591 + 101.108i) q^{11} +(22.0274 - 5.28830i) q^{12} +(-22.1137 - 1.74039i) q^{13} +(26.1319 + 63.0880i) q^{14} +(24.4695 - 39.9306i) q^{15} +(-19.7771 + 60.8676i) q^{16} +(130.506 - 543.595i) q^{17} +(-63.7884 - 196.320i) q^{18} +(644.186 - 50.6985i) q^{19} +(60.0670 + 117.888i) q^{20} +(-60.9127 + 31.0366i) q^{21} +(-26.3153 - 334.367i) q^{22} +(576.632 - 187.359i) q^{23} +(-62.3028 - 14.9576i) q^{24} +(-334.272 - 108.612i) q^{25} +(53.4950 + 32.7818i) q^{26} +(402.833 - 166.859i) q^{27} +(15.1537 - 192.546i) q^{28} +(161.528 + 672.811i) q^{29} +(-112.941 + 69.2101i) q^{30} +(-134.005 + 184.442i) q^{31} +(128.000 - 128.000i) q^{32} +(331.650 - 52.5283i) q^{33} +(-1026.91 + 1202.36i) q^{34} +(-259.316 - 303.620i) q^{35} +(-91.3348 + 576.665i) q^{36} +(1228.24 - 892.371i) q^{37} +(-1688.54 - 699.418i) q^{38} +(-28.5161 + 55.9660i) q^{39} -374.226i q^{40} +(-1535.34 + 684.470i) q^{41} +193.362 q^{42} +(1632.77 + 831.936i) q^{43} +(-363.036 + 876.446i) q^{44} +(709.466 + 976.496i) q^{45} +(-1693.78 - 268.268i) q^{46} +(-2811.09 + 2400.90i) q^{47} +(137.805 + 117.697i) q^{48} +(-284.418 - 1795.75i) q^{49} +(702.949 + 702.949i) q^{50} +(-1280.68 - 930.472i) q^{51} +(-92.7209 - 151.307i) q^{52} +(-4113.67 + 987.605i) q^{53} +(-1229.46 - 96.7605i) q^{54} +(750.513 + 1811.90i) q^{55} +(-285.434 + 465.787i) q^{56} +(565.425 - 1740.20i) q^{57} +(456.869 - 1903.00i) q^{58} +(40.6297 + 125.045i) q^{59} +(373.498 - 29.3950i) q^{60} +(2585.55 + 5074.42i) q^{61} +(574.551 - 292.749i) q^{62} +(-138.243 - 1756.55i) q^{63} +(-486.941 + 158.217i) q^{64} +(-356.725 - 85.6420i) q^{65} +(-903.258 - 293.486i) q^{66} +(-1532.15 - 938.901i) q^{67} +(4131.89 - 1711.49i) q^{68} +(134.703 - 1711.56i) q^{69} +(263.642 + 1098.15i) q^{70} +(6751.25 - 4137.17i) q^{71} +(970.661 - 1336.00i) q^{72} +(1018.20 - 1018.20i) q^{73} +(-4241.23 + 671.744i) q^{74} +(-646.367 + 756.798i) q^{75} +(3357.27 + 3930.86i) q^{76} +(447.856 - 2827.65i) q^{77} +(143.730 - 104.426i) q^{78} +(4523.52 + 1873.70i) q^{79} +(-480.536 + 943.104i) q^{80} +4676.85i q^{81} +(4748.19 + 246.531i) q^{82} -6700.70 q^{83} +(-487.302 - 248.293i) q^{84} +(3538.20 - 8541.97i) q^{85} +(-3046.54 - 4193.20i) q^{86} +(1935.19 + 306.503i) q^{87} +(2040.33 - 1742.61i) q^{88} +(-9227.36 - 7880.91i) q^{89} +(-534.060 - 3371.92i) q^{90} +(378.681 + 378.681i) q^{91} +(3924.10 + 2851.02i) q^{92} +(337.310 + 550.439i) q^{93} +(10167.3 - 2440.96i) q^{94} +(10653.9 + 838.483i) q^{95} +(-196.158 - 473.567i) q^{96} +(1148.35 - 1873.94i) q^{97} +(-1589.10 + 4890.76i) q^{98} +(-2020.32 + 8415.22i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 56 q^{2} - 16 q^{3} + 16 q^{6} - 448 q^{8} - 24 q^{9} + 512 q^{11} - 576 q^{12} + 348 q^{13} - 192 q^{14} - 1036 q^{15} + 1792 q^{16} + 552 q^{17} + 416 q^{18} + 504 q^{19} + 876 q^{21} + 16 q^{22}+ \cdots + 36896 q^{99}+O(q^{100}) \) 112 * q + 56 * q^2 - 16 * q^3 + 16 * q^6 - 448 * q^8 - 24 * q^9 + 512 * q^11 - 576 * q^12 + 348 * q^13 - 192 * q^14 - 1036 * q^15 + 1792 * q^16 + 552 * q^17 + 416 * q^18 + 504 * q^19 + 876 * q^21 + 16 * q^22 + 800 * q^23 - 384 * q^24 - 3360 * q^25 + 1656 * q^26 - 964 * q^27 + 768 * q^28 + 4 * q^29 - 3544 * q^30 + 1380 * q^31 + 14336 * q^32 - 7392 * q^33 + 4224 * q^34 + 2264 * q^35 + 2048 * q^36 + 6212 * q^37 + 2624 * q^38 + 4928 * q^39 - 7460 * q^41 + 5056 * q^42 - 19816 * q^43 - 6560 * q^44 - 26000 * q^45 - 4400 * q^46 - 14660 * q^47 - 1536 * q^48 - 17808 * q^49 - 28720 * q^50 + 17948 * q^51 + 1152 * q^52 + 19032 * q^53 + 20152 * q^54 + 3160 * q^55 - 1536 * q^56 + 23432 * q^57 - 6752 * q^58 + 25136 * q^59 - 9536 * q^60 + 10080 * q^61 + 10496 * q^62 - 968 * q^63 - 57460 * q^65 - 2480 * q^66 + 280 * q^67 + 1568 * q^68 - 1876 * q^69 + 6792 * q^70 + 49672 * q^71 + 4480 * q^72 + 16196 * q^73 - 30984 * q^74 + 58748 * q^75 + 13312 * q^76 + 6444 * q^77 + 4928 * q^78 + 34556 * q^79 + 6888 * q^82 + 17304 * q^83 + 7008 * q^84 - 104144 * q^85 + 30800 * q^86 - 28492 * q^87 - 3648 * q^88 + 26732 * q^89 - 70336 * q^90 - 132748 * q^91 + 4160 * q^92 + 35360 * q^93 - 11160 * q^94 - 5644 * q^95 - 1024 * q^96 + 14036 * q^97 - 6528 * q^98 + 36896 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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