LMFDB - Embedded newform 82.5.h.a.11.1

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)

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")

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);

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			11.1
Character	$\chi$	$=$	82.11
Dual form			82.5.h.a.15.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.79360 + 0.442463i) q^{2} +(-12.8086 - 5.30550i) q^{3} +(7.60845 - 2.47214i) q^{4} +(10.8792 - 21.3516i) q^{5} +(38.1297 + 9.15413i) q^{6} +(64.4592 - 15.4753i) q^{7} +(-20.1612 + 10.2726i) q^{8} +(78.6367 + 78.6367i) q^{9} +(-20.9448 + 64.4615i) q^{10} +(-102.282 - 87.3569i) q^{11} +(-110.570 - 8.70202i) q^{12} +(-34.8488 - 56.8681i) q^{13} +(-173.226 + 71.7527i) q^{14} +(-252.628 + 215.765i) q^{15} +(51.7771 - 37.6183i) q^{16} +(-27.3153 - 347.074i) q^{17} +(-254.474 - 184.886i) q^{18} +(-80.2239 + 130.914i) q^{19} +(29.9896 - 189.347i) q^{20} +(-907.738 - 143.772i) q^{21} +(324.387 + 198.785i) q^{22} +(-485.403 + 668.101i) q^{23} +(312.738 - 24.6130i) q^{24} +(29.8326 + 41.0610i) q^{25} +(122.516 + 143.448i) q^{26} +(-160.274 - 386.936i) q^{27} +(452.178 - 277.095i) q^{28} +(52.7712 - 670.521i) q^{29} +(610.275 - 714.540i) q^{30} +(-1079.98 - 350.908i) q^{31} +(-128.000 + 128.000i) q^{32} +(846.616 + 1661.58i) q^{33} +(229.876 + 957.502i) q^{34} +(370.841 - 1544.66i) q^{35} +(792.704 + 403.903i) q^{36} +(34.2228 + 105.327i) q^{37} +(166.189 - 401.217i) q^{38} +(144.651 + 913.292i) q^{39} +542.230i q^{40} +(-1435.45 + 874.781i) q^{41} +2599.47 q^{42} +(-168.806 + 26.7363i) q^{43} +(-994.165 - 411.796i) q^{44} +(2534.52 - 823.515i) q^{45} +(1060.42 - 2081.18i) q^{46} +(-1555.37 - 373.411i) q^{47} +(-862.777 + 207.134i) q^{48} +(1776.20 - 905.021i) q^{49} +(-101.508 - 101.508i) q^{50} +(-1491.53 + 4590.46i) q^{51} +(-405.731 - 346.527i) q^{52} +(5083.84 + 400.107i) q^{53} +(618.948 + 1010.03i) q^{54} +(-2977.95 + 1233.51i) q^{55} +(-1140.60 + 974.166i) q^{56} +(1722.12 - 1251.19i) q^{57} +(149.259 + 1896.52i) q^{58} +(-4513.27 - 3279.08i) q^{59} +(-1388.71 + 2266.17i) q^{60} +(719.158 - 4540.58i) q^{61} +(3172.31 + 502.444i) q^{62} +(6285.79 + 3851.94i) q^{63} +(300.946 - 414.217i) q^{64} +(-1593.35 + 125.399i) q^{65} +(-3100.30 - 4267.20i) q^{66} +(1824.97 + 2136.76i) q^{67} +(-1065.84 - 2573.17i) q^{68} +(9761.96 - 5982.13i) q^{69} +(-352.526 + 4479.26i) q^{70} +(3093.15 - 3621.62i) q^{71} +(-2393.21 - 777.602i) q^{72} +(-2960.76 + 2960.76i) q^{73} +(-142.208 - 279.099i) q^{74} +(-164.265 - 684.212i) q^{75} +(-286.744 + 1194.37i) q^{76} +(-7944.88 - 4048.12i) q^{77} +(-808.197 - 2487.37i) q^{78} +(-3698.55 + 8929.09i) q^{79} +(-239.917 - 1514.78i) q^{80} -3201.48i q^{81} +(3623.02 - 3078.93i) q^{82} -10252.3 q^{83} +(-7261.90 + 1150.17i) q^{84} +(-7707.75 - 3192.65i) q^{85} +(459.748 - 149.381i) q^{86} +(-4233.38 + 8308.47i) q^{87} +(2959.51 + 710.515i) q^{88} +(-8918.74 + 2141.20i) q^{89} +(-6716.07 + 3422.01i) q^{90} +(-3126.38 - 3126.38i) q^{91} +(-2041.53 + 6283.19i) q^{92} +(11971.3 + 10224.5i) q^{93} +(4510.30 + 354.969i) q^{94} +(1922.44 + 3137.14i) q^{95} +(2318.61 - 960.399i) q^{96} +(-1230.93 + 1051.31i) q^{97} +(-4561.57 + 3314.17i) q^{98} +(-1173.64 - 14912.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 56 q^{2} - 16 q^{6} + 448 q^{8} - 24 q^{9} - 512 q^{11} + 576 q^{12} + 60 q^{13} - 192 q^{14} + 340 q^{15} + 1792 q^{16} + 1416 q^{17} - 416 q^{18} - 600 q^{19} - 1300 q^{21} + 2608 q^{22} - 800 q^{23}+ \cdots + 106864 q^{99}+O(q^{100}) $ 112 * q - 56 * q^2 - 16 * q^6 + 448 * q^8 - 24 * q^9 - 512 * q^11 + 576 * q^12 + 60 * q^13 - 192 * q^14 + 340 * q^15 + 1792 * q^16 + 1416 * q^17 - 416 * q^18 - 600 * q^19 - 1300 * q^21 + 2608 * q^22 - 800 * q^23 - 128 * q^24 + 3360 * q^25 - 1848 * q^26 - 2148 * q^27 - 768 * q^28 + 2564 * q^29 - 6952 * q^30 - 8220 * q^31 - 14336 * q^32 + 16000 * q^33 + 3840 * q^34 + 12184 * q^35 + 2048 * q^36 + 3908 * q^37 + 1984 * q^38 + 4928 * q^39 + 2396 * q^41 - 16320 * q^42 + 9608 * q^43 - 1312 * q^44 - 26000 * q^45 - 5072 * q^46 - 16900 * q^47 - 2560 * q^48 - 2832 * q^49 + 27952 * q^50 - 16452 * q^51 + 2688 * q^52 + 22296 * q^53 + 29576 * q^54 - 35048 * q^55 - 1536 * q^56 - 1912 * q^57 + 1696 * q^58 - 25136 * q^59 + 1472 * q^60 + 2880 * q^61 - 2816 * q^62 + 28536 * q^63 - 1844 * q^65 + 2480 * q^66 - 45464 * q^67 + 5152 * q^68 - 19924 * q^69 - 16392 * q^70 + 9512 * q^71 - 4480 * q^72 + 25412 * q^73 + 26376 * q^74 + 21900 * q^75 - 15104 * q^76 + 45036 * q^77 - 4928 * q^78 + 21116 * q^79 - 29544 * q^82 - 14952 * q^83 - 10400 * q^84 + 44656 * q^85 - 30800 * q^86 + 22580 * q^87 + 3648 * q^88 - 40436 * q^89 + 40640 * q^90 - 5068 * q^91 - 6848 * q^92 - 4704 * q^93 + 13848 * q^94 + 52372 * q^95 + 1024 * q^96 + 36404 * q^97 - 10368 * q^98 + 106864 * q^99

Character values

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

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{40}\right)$

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 $

$2$	−2.79360	+	0.442463i	−0.698401	+	0.110616i
$2$	−2.79360	+	0.442463i	−0.698401	+	0.110616i
$3$	−12.8086	−	5.30550i	−1.42318	−	0.589500i	−0.467522	−	0.883981i	$-0.654853\pi$
$3$	−12.8086	−	5.30550i	−1.42318	−	0.589500i	−0.955657	+	0.294481i	$0.904853\pi$
$4$	7.60845	−	2.47214i	0.475528	−	0.154508i
$5$	10.8792	−	21.3516i	0.435167	−	0.854063i	−0.564425	−	0.825484i	$-0.690902\pi$
$5$	10.8792	−	21.3516i	0.435167	−	0.854063i	0.999592	−	0.0285783i	$-0.00909799\pi$
$6$	38.1297	+	9.15413i	1.05916	+	0.254281i
$7$	64.4592	−	15.4753i	1.31549	−	0.315822i	0.485815	−	0.874062i	$-0.338523\pi$
$7$	64.4592	−	15.4753i	1.31549	−	0.315822i	0.829680	+	0.558239i	$0.188523\pi$
$8$	−20.1612	+	10.2726i	−0.315018	+	0.160510i
$9$	78.6367	+	78.6367i	0.970823	+	0.970823i
$10$	−20.9448	+	64.4615i	−0.209448	+	0.644615i
$11$	−102.282	−	87.3569i	−0.845304	−	0.721958i	0.117234	−	0.993104i	$-0.462597\pi$
$11$	−102.282	−	87.3569i	−0.845304	−	0.721958i	−0.962538	+	0.271146i	$0.912597\pi$
$12$	−110.570	−	8.70202i	−0.767845	−	0.0604307i
$13$	−34.8488	−	56.8681i	−0.206206	−	0.336498i	0.732772	−	0.680474i	$-0.238226\pi$
$13$	−34.8488	−	56.8681i	−0.206206	−	0.336498i	−0.938978	+	0.343976i	$0.888226\pi$
$14$	−173.226	+	71.7527i	−0.883808	+	0.366085i
$15$	−252.628	+	215.765i	−1.12279	+	0.958954i
$16$	51.7771	−	37.6183i	0.202254	−	0.146946i
$17$	−27.3153	−	347.074i	−0.0945167	−	1.20095i	−0.843044	−	0.537845i	$-0.819239\pi$
$17$	−27.3153	−	347.074i	−0.0945167	−	1.20095i	0.748527	−	0.663104i	$-0.230761\pi$
$18$	−254.474	−	184.886i	−0.785413	−	0.570636i
$19$	−80.2239	+	130.914i	−0.222227	+	0.362641i	−0.944251	−	0.329227i	$-0.893212\pi$
$19$	−80.2239	+	130.914i	−0.222227	+	0.362641i	0.722024	+	0.691868i	$0.243212\pi$
$20$	29.9896	−	189.347i	0.0749741	−	0.473368i
$21$	−907.738	−	143.772i	−2.05836	−	0.326013i
$22$	324.387	+	198.785i	0.670222	+	0.410712i
$23$	−485.403	+	668.101i	−0.917587	+	1.26295i	0.0469217	+	0.998899i	$0.485059\pi$
$23$	−485.403	+	668.101i	−0.917587	+	1.26295i	−0.964509	+	0.264051i	$0.914941\pi$
$24$	312.738	−	24.6130i	0.542948	−	0.0427310i
$25$	29.8326	+	41.0610i	0.0477321	+	0.0656976i
$26$	122.516	+	143.448i	0.181237	+	0.212201i
$27$	−160.274	−	386.936i	−0.219855	−	0.530777i
$28$	452.178	−	277.095i	0.576758	−	0.353438i
$29$	52.7712	−	670.521i	0.0627481	−	0.797290i	−0.882369	−	0.470558i	$-0.844053\pi$
$29$	52.7712	−	670.521i	0.0627481	−	0.797290i	0.945117	−	0.326732i	$-0.105947\pi$
$30$	610.275	−	714.540i	0.678083	−	0.793933i
$31$	−1079.98	−	350.908i	−1.12381	−	0.365148i	−0.312590	−	0.949888i	$-0.601197\pi$
$31$	−1079.98	−	350.908i	−1.12381	−	0.365148i	−0.811221	+	0.584740i	$0.801197\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	846.616	+	1661.58i	0.777426	+	1.52578i
$34$	229.876	+	957.502i	0.198855	+	0.828289i
$35$	370.841	−	1544.66i	0.302727	−	1.26095i
$36$	792.704	+	403.903i	0.611654	+	0.311653i
$37$	34.2228	+	105.327i	0.0249984	+	0.0769371i	0.962777	−	0.270296i	$-0.0871214\pi$
$37$	34.2228	+	105.327i	0.0249984	+	0.0769371i	−0.937779	+	0.347233i	$0.887121\pi$
$38$	166.189	−	401.217i	0.115090	−	0.277851i
$39$	144.651	+	913.292i	0.0951028	+	0.600455i
$40$			542.230i			0.338894i
$41$	−1435.45	+	874.781i	−0.853927	+	0.520393i
$41$	−1435.45	+	874.781i	−0.853927	+	0.520393i
$42$	2599.47			1.47363
$43$	−168.806	+	26.7363i	−0.0912959	+	0.0144599i	−0.201915	−	0.979403i	$-0.564717\pi$
$43$	−168.806	+	26.7363i	−0.0912959	+	0.0144599i	0.110619	+	0.993863i	$0.464717\pi$
$44$	−994.165	−	411.796i	−0.513515	−	0.212705i
$45$	2534.52	−	823.515i	1.25161	−	0.406674i
$46$	1060.42	−	2081.18i	0.501141	−	0.983545i
$47$	−1555.37	−	373.411i	−0.704105	−	0.169041i	−0.134445	−	0.990921i	$-0.542925\pi$
$47$	−1555.37	−	373.411i	−0.704105	−	0.169041i	−0.569660	+	0.821880i	$0.692925\pi$
$48$	−862.777	+	207.134i	−0.374469	+	0.0899021i
$49$	1776.20	−	905.021i	0.739776	−	0.376935i
$50$	−101.508	−	101.508i	−0.0406034	−	0.0406034i
$51$	−1491.53	+	4590.46i	−0.573445	+	1.76488i
$52$	−405.731	−	346.527i	−0.150049	−	0.128154i
$53$	5083.84	+	400.107i	1.80984	+	0.142438i	0.937840	−	0.347067i	$-0.112822\pi$
$53$	5083.84	+	400.107i	1.80984	+	0.142438i	0.872001	+	0.489505i	$0.162822\pi$
$54$	618.948	+	1010.03i	0.212259	+	0.346376i
$55$	−2977.95	+	1233.51i	−0.984446	+	0.407771i
$56$	−1140.60	+	974.166i	−0.363712	+	0.310640i
$57$	1722.12	−	1251.19i	0.530046	−	0.385101i
$58$	149.259	+	1896.52i	0.0443696	+	0.563770i
$59$	−4513.27	−	3279.08i	−1.29654	−	0.941993i	−0.296627	−	0.954993i	$-0.595862\pi$
$59$	−4513.27	−	3279.08i	−1.29654	−	0.941993i	−0.999915	+	0.0129998i	$0.995862\pi$
$60$	−1388.71	+	2266.17i	−0.385752	+	0.629490i
$61$	719.158	−	4540.58i	0.193270	−	1.22026i	−0.680070	−	0.733147i	$-0.738051\pi$
$61$	719.158	−	4540.58i	0.193270	−	1.22026i	0.873340	−	0.487111i	$-0.161949\pi$
$62$	3172.31	+	502.444i	0.825262	+	0.130709i
$63$	6285.79	+	3851.94i	1.58372	+	0.970505i
$64$	300.946	−	414.217i	0.0734732	−	0.101127i
$65$	−1593.35	+	125.399i	−0.377124	+	0.0296803i
$66$	−3100.30	−	4267.20i	−0.711731	−	0.979613i
$67$	1824.97	+	2136.76i	0.406543	+	0.476000i	0.925472	−	0.378817i	$-0.123669\pi$
$67$	1824.97	+	2136.76i	0.406543	+	0.476000i	−0.518929	+	0.854817i	$0.673669\pi$
$68$	−1065.84	−	2573.17i	−0.230502	−	0.556481i
$69$	9761.96	−	5982.13i	2.05040	−	1.25649i
$70$	−352.526	+	4479.26i	−0.0719440	+	0.914136i
$71$	3093.15	−	3621.62i	0.613599	−	0.718432i	−0.363410	−	0.931629i	$-0.618388\pi$
$71$	3093.15	−	3621.62i	0.613599	−	0.718432i	0.977009	+	0.213197i	$0.0683877\pi$
$72$	−2393.21	−	777.602i	−0.461654	−	0.150000i
$73$	−2960.76	+	2960.76i	−0.555593	+	0.555593i	−0.928050	−	0.372457i	$-0.878516\pi$
$73$	−2960.76	+	2960.76i	−0.555593	+	0.555593i	0.372457	+	0.928050i	$0.378516\pi$
$74$	−142.208	−	279.099i	−0.0259694	−	0.0509677i
$75$	−164.265	−	684.212i	−0.0292026	−	0.121638i
$76$	−286.744	+	1194.37i	−0.0496440	+	0.206782i
$77$	−7944.88	−	4048.12i	−1.34000	−	0.682766i
$78$	−808.197	−	2487.37i	−0.132840	−	0.408839i
$79$	−3698.55	+	8929.09i	−0.592621	+	1.43071i	0.288341	+	0.957528i	$0.406896\pi$
$79$	−3698.55	+	8929.09i	−0.592621	+	1.43071i	−0.880962	+	0.473186i	$0.843104\pi$
$80$	−239.917	−	1514.78i	−0.0374871	−	0.236684i
$81$		−	3201.48i		−	0.487956i
$82$	3623.02	−	3078.93i	0.538820	−	0.457901i
$83$	−10252.3			−1.48821			−0.744106	−	0.668062i	$-0.767124\pi$
$83$	−10252.3			−1.48821			−0.744106	+	0.668062i	$0.767124\pi$
$84$	−7261.90	+	1150.17i	−1.02918	+	0.163006i
$85$	−7707.75	−	3192.65i	−1.06682	−	0.441890i
$86$	459.748	−	149.381i	0.0621617	−	0.0201976i
$87$	−4233.38	+	8308.47i	−0.559305	+	1.09770i
$88$	2959.51	+	710.515i	0.382168	+	0.0917504i
$89$	−8918.74	+	2141.20i	−1.12596	+	0.270320i	−0.753319	−	0.657655i	$-0.771548\pi$
$89$	−8918.74	+	2141.20i	−1.12596	+	0.270320i	−0.372643	+	0.927975i	$0.621548\pi$
$90$	−6716.07	+	3422.01i	−0.829144	+	0.422470i
$91$	−3126.38	−	3126.38i	−0.377536	−	0.377536i
$92$	−2041.53	+	6283.19i	−0.241202	+	0.742343i
$93$	11971.3	+	10224.5i	1.38413	+	1.18216i
$94$	4510.30	+	354.969i	0.510446	+	0.0401730i
$95$	1922.44	+	3137.14i	0.213013	+	0.347605i
$96$	2318.61	−	960.399i	0.251585	−	0.104210i
$97$	−1230.93	+	1051.31i	−0.130824	+	0.111735i	−0.712453	−	0.701720i	$-0.752416\pi$
$97$	−1230.93	+	1051.31i	−0.130824	+	0.111735i	0.581628	+	0.813455i	$0.302416\pi$
$98$	−4561.57	+	3314.17i	−0.474966	+	0.345083i
$99$	−1173.64	−	14912.6i	−0.119747	−	1.52153i
$100$	328.488	+	238.661i	0.0328488	+	0.0238661i
$101$	10217.3	−	16673.2i	1.00160	−	1.63447i	0.257645	−	0.966240i	$-0.417054\pi$
$101$	10217.3	−	16673.2i	1.00160	−	1.63447i	0.743958	−	0.668227i	$-0.232946\pi$
$102$	2135.64	−	13483.9i	0.205271	−	1.29603i
$103$	19105.6	+	3026.03i	1.80089	+	0.285232i	0.964727	−	0.263253i	$-0.0847955\pi$
$103$	19105.6	+	3026.03i	1.80089	+	0.285232i	0.836160	+	0.548486i	$0.184795\pi$
$104$	1286.78	+	788.539i	0.118970	+	0.0729048i
$105$	−12945.2	+	17817.5i	−1.17417	+	1.61610i
$106$	−14379.3	+	1131.67i	−1.27975	+	0.100719i
$107$	−7875.67	−	10839.9i	−0.687891	−	0.946801i	0.312104	−	0.950048i	$-0.398966\pi$
$107$	−7875.67	−	10839.9i	−0.687891	−	0.946801i	−0.999995	+	0.00324709i	$0.998966\pi$
$108$	−2176.00	−	2547.77i	−0.186557	−	0.218430i
$109$	4405.27	+	10635.3i	0.370783	+	0.895149i	0.993618	+	0.112796i	$0.0359806\pi$
$109$	4405.27	+	10635.3i	0.370783	+	0.895149i	−0.622835	+	0.782353i	$0.714019\pi$
$110$	7773.43	−	4763.56i	0.642432	−	0.393683i
$111$	120.466	−	1530.66i	0.00977726	−	0.124232i
$112$	2755.36	−	3226.11i	0.219655	−	0.257184i
$113$	12352.1	+	4013.44i	0.967351	+	0.314311i	0.749746	−	0.661726i	$-0.230176\pi$
$113$	12352.1	+	4013.44i	0.967351	+	0.314311i	0.217605	+	0.976037i	$0.430176\pi$
$114$	−4257.31	+	4257.31i	−0.327587	+	0.327587i
$115$	8984.21	+	17632.5i	0.679335	+	1.33327i
$116$	−1256.11	−	5232.09i	−0.0933497	−	0.388829i
$117$	1731.52	−	7212.32i	0.126490	−	0.526869i
$118$	14059.2	+	7163.50i	1.00971	+	0.514471i
$119$	−7131.80	−	21949.4i	−0.503623	−	1.54999i
$120$	2876.81	−	6945.22i	0.199778	−	0.482307i
$121$	539.982	+	3409.31i	0.0368815	+	0.232860i
$122$			13002.8i			0.873609i
$123$	23027.3	−	3588.94i	1.52206	−	0.237222i
$124$	−9084.49			−0.590823
$125$	15994.0	−	2533.20i	1.02362	−	0.162125i
$126$	−19264.3	−	7979.55i	−1.21343	−	0.502617i
$127$	4164.50	−	1353.13i	0.258199	−	0.0838940i	−0.177057	−	0.984201i	$-0.556658\pi$
$127$	4164.50	−	1353.13i	0.258199	−	0.0838940i	0.435256	+	0.900307i	$0.356658\pi$
$128$	−657.448	+	1290.32i	−0.0401275	+	0.0787546i
$129$	2304.02	+	553.147i	0.138455	+	0.0332400i
$130$	4395.70	−	1055.32i	0.260101	−	0.0624447i
$131$	−2269.31	+	1156.27i	−0.132237	+	0.0673780i	−0.518857	−	0.854861i	$-0.673642\pi$
$131$	−2269.31	+	1156.27i	−0.132237	+	0.0673780i	0.386620	+	0.922239i	$0.373642\pi$
$132$	10549.1	+	10549.1i	0.605434	+	0.605434i
$133$	−3145.25	+	9680.08i	−0.177808	+	0.547237i
$134$	−6043.68	−	5161.79i	−0.336583	−	0.287469i
$135$	−10005.3	−	787.438i	−0.548990	−	0.0432065i
$136$	4116.07	+	6716.82i	0.222539	+	0.363150i
$137$	298.922	−	123.818i	0.0159264	−	0.00659693i	−0.374706	−	0.927144i	$-0.622256\pi$
$137$	298.922	−	123.818i	0.0159264	−	0.00659693i	0.390632	+	0.920547i	$0.372256\pi$
$138$	−24624.2	+	21031.0i	−1.29301	+	1.10434i
$139$	15159.1	−	11013.8i	0.784593	−	0.570040i	−0.121761	−	0.992559i	$-0.538854\pi$
$139$	15159.1	−	11013.8i	0.784593	−	0.570040i	0.906354	+	0.422519i	$0.138854\pi$
$140$	−997.094	−	12669.3i	−0.0508721	−	0.646392i
$141$	17941.0	+	13034.9i	0.902418	+	0.655645i
$142$	−7038.61	+	11486.0i	−0.349068	+	0.569627i
$143$	−1403.42	+	8860.86i	−0.0686304	+	0.433315i
$144$	7029.75	+	1113.40i	0.339012	+	0.0536942i
$145$	−13742.6	−	8421.46i	−0.653630	−	0.400545i
$146$	6961.15	−	9581.21i	0.326569	−	0.449484i
$147$	−27552.3	+	2168.41i	−1.27504	+	0.100348i
$148$	520.765	+	716.771i	0.0237749	+	0.0327233i
$149$	−15390.8	−	18020.3i	−0.693246	−	0.811687i	0.296423	−	0.955057i	$-0.404206\pi$
$149$	−15390.8	−	18020.3i	−0.693246	−	0.811687i	−0.989669	+	0.143369i	$0.954206\pi$
$150$	761.629	+	1838.74i	0.0338502	+	0.0817216i
$151$	5435.91	−	3331.13i	0.238407	−	0.146096i	−0.398164	−	0.917314i	$-0.630352\pi$
$151$	5435.91	−	3331.13i	0.238407	−	0.146096i	0.636570	+	0.771219i	$0.280352\pi$
$152$	272.582	−	3463.48i	0.0117980	−	0.149908i
$153$	25144.8	−	29440.8i	1.07415	−	1.25767i
$154$	23986.0	+	7793.53i	1.01139	+	0.328619i
$155$	−19241.7	+	19241.7i	−0.800905	+	0.800905i
$156$	3358.36	+	6591.14i	0.137999	+	0.270839i
$157$	−900.874	−	3752.41i	−0.0365481	−	0.152234i	0.951112	−	0.308846i	$-0.0999428\pi$
$157$	−900.874	−	3752.41i	−0.0365481	−	0.152234i	−0.987660	+	0.156612i	$0.949943\pi$
$158$	6381.49	−	26580.8i	0.255628	−	1.06477i
$159$	−62994.2	−	32097.2i	−2.49176	−	1.26962i
$160$	1340.47	+	4125.53i	0.0523620	+	0.161154i
$161$	−20949.7	+	50577.0i	−0.808213	+	1.95120i
$162$	1416.54	+	8943.66i	0.0539757	+	0.340789i
$163$		−	3720.33i		−	0.140025i	−0.997546	−	0.0700127i	$-0.977696\pi$
$163$		−	3720.33i		−	0.140025i	0.997546	−	0.0700127i	$-0.0223040\pi$
$164$	−8758.99	+	10204.4i	−0.325661	+	0.379401i
$165$	44687.8			1.64142
$166$	28640.8	−	4536.26i	1.03937	−	0.164620i
$167$	42028.8	+	17408.9i	1.50700	+	0.624220i	0.974937	−	0.222483i	$-0.0714162\pi$
$167$	42028.8	+	17408.9i	1.50700	+	0.624220i	0.532065	+	0.846703i	$0.321416\pi$
$168$	19778.0	−	6426.26i	0.700750	−	0.227688i
$169$	10946.9	−	21484.5i	0.383281	−	0.752231i
$170$	22945.0	+	5508.61i	0.793946	+	0.190609i
$171$	−16603.2	+	3986.06i	−0.567804	+	0.136318i
$172$	−1218.26	+	620.733i	−0.0411796	+	0.0209821i
$173$	−1338.37	−	1338.37i	−0.0447182	−	0.0447182i	0.684394	−	0.729112i	$-0.260067\pi$
$173$	−1338.37	−	1338.37i	−0.0447182	−	0.0447182i	−0.729112	+	0.684394i	$0.760067\pi$
$174$	8150.19	−	25083.7i	0.269196	−	0.828501i
$175$	2558.42	+	2185.09i	0.0835402	+	0.0713500i
$176$	−8582.07	−	675.424i	−0.277055	−	0.0218047i
$177$	40411.5	+	65945.6i	1.28991	+	2.10494i
$178$	23968.0	−	9927.89i	0.756471	−	0.313341i
$179$	−30938.4	+	26423.9i	−0.965588	+	0.824690i	−0.984545	−	0.175130i	$-0.943965\pi$
$179$	−30938.4	+	26423.9i	−0.965588	+	0.824690i	0.0189570	+	0.999820i	$0.493965\pi$
$180$	17247.9	−	12531.3i	0.532343	−	0.386770i
$181$	−3635.63	−	46195.1i	−0.110974	−	1.41006i	−0.760309	−	0.649561i	$-0.774953\pi$
$181$	−3635.63	−	46195.1i	−0.110974	−	1.41006i	0.649335	−	0.760503i	$-0.275047\pi$
$182$	10117.2	+	7350.56i	0.305433	+	0.221910i
$183$	−33301.5	+	54343.1i	−0.994401	+	1.62272i
$184$	2923.15	−	18456.1i	0.0863408	−	0.545134i
$185$	2621.21	+	415.159i	0.0765876	+	0.0121303i
$186$	−37967.2	−	23266.3i	−1.09744	−	0.672515i
$187$	−27525.5	+	37885.6i	−0.787139	+	1.08340i
$188$	−12757.1	+	1004.00i	−0.360940	+	0.0284066i
$189$	−16319.1	−	22461.3i	−0.456849	−	0.628799i
$190$	−6758.61	−	7913.31i	−0.187219	−	0.219205i
$191$	−11944.8	−	28837.4i	−0.327427	−	0.790478i	−0.998782	−	0.0493421i	$-0.984288\pi$
$191$	−11944.8	−	28837.4i	−0.327427	−	0.790478i	0.671355	−	0.741136i	$-0.265712\pi$
$192$	−6052.33	+	3708.87i	−0.164180	+	0.100610i
$193$	705.244	−	8960.98i	0.0189332	−	0.240570i	−0.980168	−	0.198171i	$-0.936500\pi$
$193$	705.244	−	8960.98i	0.0189332	−	0.240570i	0.999101	−	0.0423989i	$-0.0135000\pi$
$194$	2973.56	−	3481.59i	0.0790083	−	0.0925069i
$195$	21073.9	+	6847.33i	0.554212	+	0.180074i
$196$	11276.8	−	11276.8i	0.293545	−	0.293545i
$197$	−22874.0	−	44892.7i	−0.589399	−	1.15676i	−0.972467	−	0.233040i	$-0.925133\pi$
$197$	−22874.0	−	44892.7i	−0.589399	−	1.15676i	0.383069	−	0.923720i	$-0.374867\pi$
$198$	9876.96	+	41140.5i	0.251938	+	1.04940i
$199$	11095.7	−	46216.8i	0.280187	−	1.16706i	−0.637721	−	0.770267i	$-0.720123\pi$
$199$	11095.7	−	46216.8i	0.280187	−	1.16706i	0.917908	−	0.396794i	$-0.129877\pi$
$200$	−1023.26	−	521.379i	−0.0255816	−	0.0130345i
$201$	−12038.7	−	37051.4i	−0.297981	−	0.917091i
$202$	−21165.9	+	51099.1i	−0.518722	+	1.25231i
$203$	−6974.93	−	44037.9i	−0.169257	−	1.06865i
$204$			38613.6i			0.927854i
$205$	3061.42	+	40166.0i	0.0728477	+	0.955765i
$206$	−54712.4			−1.28929
$207$	−90707.7	+	14366.7i	−2.11692	+	0.335287i
$208$	−3943.65	−	1633.51i	−0.0911531	−	0.0377569i
$209$	19641.7	−	6381.96i	0.449661	−	0.146104i
$210$	28280.1	−	55502.9i	0.641273	−	1.25857i
$211$	−10619.6	−	2549.55i	−0.238531	−	0.0572662i	0.112417	−	0.993661i	$-0.464141\pi$
$211$	−10619.6	−	2549.55i	−0.238531	−	0.0572662i	−0.350948	+	0.936395i	$0.614141\pi$
$212$	39669.3	−	9523.76i	0.882638	−	0.211903i
$213$	−58833.5	+	29977.2i	−1.29678	+	0.660741i
$214$	26797.8	+	26797.8i	0.585155	+	0.585155i
$215$	−1265.61	+	3895.14i	−0.0273793	+	0.0842649i
$216$	7206.17	+	6154.65i	0.154453	+	0.131916i
$217$	−75045.3	−	5906.19i	−1.59369	−	0.125426i
$218$	−17012.3	−	27761.5i	−0.357973	−	0.584158i
$219$	53631.5	−	22214.9i	1.11823	−	0.463187i
$220$	−19608.2	+	16747.0i	−0.405128	+	0.346012i
$221$	−18785.5	+	13648.5i	−0.384627	+	0.279448i
$222$	340.728	+	4329.36i	0.00691357	+	0.0878452i
$223$	−7435.04	−	5401.88i	−0.149511	−	0.108626i	0.510515	−	0.859869i	$-0.329455\pi$
$223$	−7435.04	−	5401.88i	−0.149511	−	0.108626i	−0.660026	+	0.751243i	$0.729455\pi$
$224$	−6269.95	+	10231.6i	−0.124959	+	0.203915i
$225$	−882.968	+	5574.84i	−0.0174413	+	0.110120i
$226$	−36282.7	−	5746.61i	−0.710367	−	0.112511i
$227$	5511.47	+	3377.43i	0.106959	+	0.0655443i	0.574949	−	0.818189i	$-0.305022\pi$
$227$	5511.47	+	3377.43i	0.106959	+	0.0655443i	−0.467990	+	0.883734i	$0.655022\pi$
$228$	10009.5	−	13777.0i	0.192551	−	0.265023i
$229$	−52634.2	+	4142.40i	−1.00368	+	0.0789916i	−0.569635	−	0.821898i	$-0.692915\pi$
$229$	−52634.2	+	4142.40i	−1.00368	+	0.0789916i	−0.434049	+	0.900889i	$0.642915\pi$
$230$	−32900.1	−	45283.1i	−0.621929	−	0.856012i
$231$	80285.7	+	94002.4i	1.50458	+	1.76163i
$232$	5824.09	+	14060.6i	0.108206	+	0.261233i
$233$	−1078.31	+	660.786i	−0.0198623	+	0.0121716i	−0.532394	−	0.846497i	$-0.678708\pi$
$233$	−1078.31	+	660.786i	−0.0198623	+	0.0121716i	0.512532	+	0.858668i	$0.328708\pi$
$234$	−1646.01	+	20914.5i	−0.0300607	+	0.381958i
$235$	−24894.0	+	29147.1i	−0.450774	+	0.527789i
$236$	−42445.3	−	13791.3i	−0.762089	−	0.247618i
$237$	94746.6	−	94746.6i	1.68681	−	1.68681i
$238$	29635.3	+	58162.5i	0.523184	+	1.02681i
$239$	−7431.50	−	30954.4i	−0.130101	−	0.541910i	−0.998906	−	0.0467559i	$-0.985112\pi$
$239$	−7431.50	−	30954.4i	−0.130101	−	0.541910i	0.868805	−	0.495154i	$-0.164888\pi$
$240$	−4963.65	+	20675.1i	−0.0861745	+	0.358942i
$241$	−75349.3	−	38392.4i	−1.29731	−	0.661014i	−0.337413	−	0.941357i	$-0.609552\pi$
$241$	−75349.3	−	38392.4i	−1.29731	−	0.661014i	−0.959900	+	0.280343i	$0.909552\pi$
$242$	−3016.99	−	9285.34i	−0.0515161	−	0.158550i
$243$	−29967.7	+	72348.4i	−0.507505	+	1.22523i
$244$	−5753.26	−	36324.7i	−0.0966350	−	0.610129i
$245$		−	47770.6i		−	0.795845i
$246$	−62741.2	+	20214.8i	−1.03677	+	0.334041i
$247$	10240.5			0.167853
$248$	25378.5	−	4019.55i	0.412631	−	0.0653544i
$249$	131318.	+	54393.6i	2.11799	+	0.877301i
$250$	−43560.1	+	14153.5i	−0.696962	+	0.226457i
$251$	36566.5	−	71765.8i	0.580412	−	1.13912i	−0.394990	−	0.918685i	$-0.629252\pi$
$251$	36566.5	−	71765.8i	0.580412	−	1.13912i	0.975401	−	0.220436i	$-0.0707481\pi$
$252$	57347.6	+	13767.9i	0.903055	+	0.216804i
$253$	108011.	−	25931.2i	1.68744	−	0.405118i
$254$	−11035.2	+	5622.74i	−0.171047	+	0.0871526i
$255$	81787.0	+	81787.0i	1.25778	+	1.25778i
$256$	1265.73	−	3895.53i	0.0193136	−	0.0594410i
$257$	83107.0	+	70980.1i	1.25826	+	1.07466i	0.993906	+	0.110233i	$0.0351597\pi$
$257$	83107.0	+	70980.1i	1.25826	+	1.07466i	0.264357	+	0.964425i	$0.414840\pi$
$258$	−6681.28	−	525.828i	−0.100374	−	0.00789958i
$259$	3835.94	+	6259.68i	0.0571837	+	0.0933153i
$260$	−11812.9	+	4893.07i	−0.174747	+	0.0723827i
$261$	56877.3	−	48577.8i	0.834945	−	0.713111i
$262$	5827.96	−	4234.26i	0.0849012	−	0.0616843i
$263$	−7360.42	−	93523.0i	−0.106412	−	1.35209i	−0.785876	−	0.618384i	$-0.787787\pi$
$263$	−7360.42	−	93523.0i	−0.106412	−	1.35209i	0.679464	−	0.733709i	$-0.262213\pi$
$264$	−34137.6	−	24802.4i	−0.489807	−	0.355865i
$265$	63850.9	−	104195.i	0.909233	−	1.48373i
$266$	4503.50	−	28434.0i	0.0636483	−	0.401859i
$267$	125597.	+	19892.6i	1.76180	+	0.279042i
$268$	19167.6	+	11745.9i	0.266869	+	0.163537i
$269$	−27349.4	+	37643.2i	−0.377958	+	0.520214i	−0.955042	−	0.296470i	$-0.904190\pi$
$269$	−27349.4	+	37643.2i	−0.377958	+	0.520214i	0.577084	+	0.816685i	$0.304190\pi$
$270$	28299.4	−	2227.21i	0.388195	−	0.0305516i
$271$	62424.6	+	85920.1i	0.849997	+	1.16992i	0.983863	+	0.178921i	$0.0572607\pi$
$271$	62424.6	+	85920.1i	0.849997	+	1.16992i	−0.133866	+	0.990999i	$0.542739\pi$
$272$	−14470.6	−	16942.9i	−0.195591	−	0.229008i
$273$	23457.6	+	56631.6i	0.314744	+	0.759860i
$274$	−780.286	+	478.160i	−0.0103933	+	0.00636901i
$275$	535.634	−	6805.88i	0.00708277	−	0.0899951i
$276$	59484.7	−	69647.7i	0.780885	−	0.914299i
$277$	22856.8	+	7426.63i	0.297890	+	0.0967903i	0.454149	−	0.890926i	$-0.349943\pi$
$277$	22856.8	+	7426.63i	0.297890	+	0.0967903i	−0.156259	+	0.987716i	$0.549943\pi$
$278$	−37475.4	+	37475.4i	−0.484905	+	0.484905i
$279$	−57332.1	−	112520.i	−0.736528	−	1.44552i
$280$	8391.18	+	34951.8i	0.107030	+	0.445813i
$281$	−35751.2	+	148915.i	−0.452771	+	1.88593i	0.0109396	+	0.999940i	$0.496518\pi$
$281$	−35751.2	+	148915.i	−0.452771	+	1.88593i	−0.463711	+	0.885987i	$0.653482\pi$
$282$	−55887.5	−	28476.1i	−0.702775	−	0.358082i
$283$	−25795.5	−	79390.3i	−0.322085	−	0.991277i	−0.972739	−	0.231902i	$-0.925505\pi$
$283$	−25795.5	−	79390.3i	−0.322085	−	0.991277i	0.650654	−	0.759374i	$-0.274495\pi$
$284$	14581.0	−	35201.6i	0.180780	−	0.436441i
$285$	−7979.71	−	50381.9i	−0.0982420	−	0.620276i
$286$		−	25374.7i		−	0.310219i
$287$	−78990.6	+	78601.7i	−0.958985	+	0.954263i
$288$	−20131.0			−0.242706
$289$	−37221.7	+	5895.33i	−0.445656	+	0.0705850i
$290$	42117.5	+	17445.6i	0.500803	+	0.207439i
$291$	21344.2	−	6935.16i	0.252054	−	0.0818974i
$292$	−15207.4	+	29846.2i	−0.178356	+	0.350044i
$293$	147325.	+	35369.6i	1.71609	+	0.411997i	0.967870	−	0.251451i	$-0.0809077\pi$
$293$	147325.	+	35369.6i	1.71609	+	0.411997i	0.748222	+	0.663448i	$0.230908\pi$
$294$	76010.8	−	18248.6i	0.879388	−	0.211122i
$295$	−119114.	+	60691.6i	−1.36873	+	0.697405i
$296$	−1771.96	−	1771.96i	−0.0202241	−	0.0202241i
$297$	−17408.4	+	53577.6i	−0.197354	+	0.607394i
$298$	50969.0	+	43531.7i	0.573950	+	0.490199i
$299$	54909.4	+	4321.46i	0.614192	+	0.0483379i
$300$	−2941.27	−	4799.71i	−0.0326807	−	0.0533301i
$301$	−10467.4	+	4335.72i	−0.115533	+	0.0478552i
$302$	−13711.9	+	11711.0i	−0.150343	+	0.128405i
$303$	−219330.	+	159352.i	−2.38898	+	1.73569i
$304$	770.978	+	9796.21i	0.00834248	+	0.106001i
$305$	−89124.7	−	64752.9i	−0.958073	−	0.696081i
$306$	−57218.1	+	93371.5i	−0.611070	+	0.997175i
$307$	18911.4	−	119402.i	0.200653	−	1.26687i	−0.657490	−	0.753463i	$-0.728382\pi$
$307$	18911.4	−	119402.i	0.200653	−	1.26687i	0.858143	−	0.513411i	$-0.171618\pi$
$308$	−70455.8	−	11159.1i	−0.742703	−	0.117633i
$309$	−228662.	−	140124.i	−2.39484	−	1.46756i
$310$	45240.1	−	62267.6i	0.470760	−	0.647946i
$311$	56900.8	−	4478.19i	0.588298	−	0.0463001i	0.219183	−	0.975684i	$-0.429661\pi$
$311$	56900.8	−	4478.19i	0.588298	−	0.0463001i	0.369115	+	0.929384i	$0.379661\pi$
$312$	−12298.3	−	16927.1i	−0.126338	−	0.173890i
$313$	10529.8	+	12328.9i	0.107481	+	0.125844i	0.811539	−	0.584299i	$-0.198630\pi$
$313$	10529.8	+	12328.9i	0.107481	+	0.125844i	−0.704057	+	0.710143i	$0.748630\pi$
$314$	4176.99	+	10084.2i	0.0423647	+	0.102277i
$315$	150629.	−	92305.6i	1.51805	−	0.930265i
$316$	−6066.31	+	77079.8i	−0.0607506	+	0.771910i
$317$	−950.299	+	1112.66i	−0.00945674	+	0.0110724i	−0.765114	−	0.643895i	$-0.777318\pi$
$317$	−950.299	+	1112.66i	−0.00945674	+	0.0110724i	0.755657	+	0.654967i	$0.227318\pi$
$318$	190183.	+	61794.1i	1.88069	+	0.611073i
$319$	−63972.2	+	63972.2i	−0.628652	+	0.628652i
$320$	−5570.13	−	10932.0i	−0.0543958	−	0.106758i
$321$	43365.1	+	180629.i	0.420853	+	1.75298i
$322$	36146.7	−	150562.i	0.348623	−	1.45212i
$323$	47628.1	+	24267.7i	0.456518	+	0.232608i
$324$	−7914.49	−	24358.3i	−0.0753933	−	0.232037i
$325$	1295.43	−	3127.45i	0.0122644	−	0.0296090i
$326$	1646.11	+	10393.1i	0.0154890	+	0.0977939i
$327$		−	159595.i		−	1.49253i
$328$	19954.1	−	32382.5i	0.185474	−	0.300997i
$329$	−106036.			−0.979633
$330$	−124840.	+	19772.7i	−1.14637	+	0.181568i
$331$	132077.	+	54708.0i	1.20551	+	0.499338i	0.892775	−	0.450503i	$-0.148755\pi$
$331$	132077.	+	54708.0i	1.20551	+	0.499338i	0.312734	+	0.949841i	$0.398755\pi$
$332$	−78004.1	+	25345.1i	−0.707687	+	0.229941i
$333$	−5591.39	+	10973.7i	−0.0504233	+	0.0989613i
$334$	−125115.	−	30037.3i	−1.12154	−	0.269258i
$335$	65477.4	−	15719.7i	0.583448	−	0.140073i
$336$	−52408.5	+	26703.5i	−0.464219	+	0.236531i
$337$	−87000.4	−	87000.4i	−0.766058	−	0.766058i	0.211352	−	0.977410i	$-0.432213\pi$
$337$	−87000.4	−	87000.4i	−0.766058	−	0.766058i	−0.977410	+	0.211352i	$0.932213\pi$
$338$	−21075.2	+	64862.7i	−0.184475	+	0.567756i
$339$	−136920.	−	116941.i	−1.19143	−	1.01758i
$340$	−66536.7	−	5236.55i	−0.575577	−	0.0452989i
$341$	79808.4	+	130235.i	0.686341	+	1.12001i
$342$	44619.0	−	18481.8i	0.381476	−	0.158013i
$343$	−20542.3	+	17544.8i	−0.174607	+	0.149128i
$344$	3128.68	−	2273.12i	0.0264389	−	0.0192090i
$345$	−21526.0	−	273514.i	−0.180853	−	2.29795i
$346$	4331.06	+	3146.70i	0.0361778	+	0.0262847i
$347$	−10005.7	+	16327.7i	−0.0830972	+	0.135602i	−0.891489	−	0.453043i	$-0.850338\pi$
$347$	−10005.7	+	16327.7i	−0.0830972	+	0.135602i	0.808392	+	0.588645i	$0.200338\pi$
$348$	−11669.8	+	73680.1i	−0.0963617	+	0.608404i
$349$	41030.8	+	6498.65i	0.336868	+	0.0533546i	0.322577	−	0.946543i	$-0.395451\pi$
$349$	41030.8	+	6498.65i	0.336868	+	0.0533546i	0.0142909	+	0.999898i	$0.495451\pi$
$350$	−8114.03	−	4972.28i	−0.0662370	−	0.0405901i
$351$	−16419.0	+	22598.8i	−0.133270	+	0.183430i
$352$	24273.8	−	1910.39i	0.195908	−	0.0154183i
$353$	−53196.4	−	73218.5i	−0.426906	−	0.587586i	0.540333	−	0.841451i	$-0.318298\pi$
$353$	−53196.4	−	73218.5i	−0.426906	−	0.587586i	−0.967240	+	0.253865i	$0.918298\pi$
$354$	−142072.	−	166345.i	−1.13371	−	1.32741i
$355$	−43676.3	−	105444.i	−0.346568	−	0.836690i
$356$	−62564.5	+	38339.6i	−0.493660	+	0.302515i
$357$	−25104.2	+	318980.i	−0.196975	+	2.50280i
$358$	74738.1	−	87507.0i	0.583144	−	0.682774i
$359$	88929.1	+	28894.8i	0.690009	+	0.224198i	0.632972	−	0.774174i	$-0.281835\pi$
$359$	88929.1	+	28894.8i	0.690009	+	0.224198i	0.0570371	+	0.998372i	$0.481835\pi$
$360$	−42639.2	+	42639.2i	−0.329006	+	0.329006i
$361$	48462.0	+	95112.1i	0.371867	+	0.729829i
$362$	30596.2	+	127442.i	0.233480	+	0.972515i
$363$	11171.7	−	46533.4i	0.0847823	−	0.353144i
$364$	−31515.7	−	16058.1i	−0.237862	−	0.121197i
$365$	31006.2	+	95427.3i	0.232736	+	0.716287i
$366$	68986.4	−	166548.i	0.514993	−	1.24330i
$367$	−34234.4	−	216148.i	−0.254174	−	1.60479i	−0.703012	−	0.711178i	$-0.748162\pi$
$367$	−34234.4	−	216148.i	−0.254174	−	1.60479i	0.448838	−	0.893613i	$-0.351838\pi$
$368$			52852.3i			0.390273i
$369$	−181669.	−	44089.3i	−1.33422	−	0.323803i
$370$	−7506.31			−0.0548306
$371$	333893.	−	52883.4i	2.42582	−	0.384212i
$372$	116360.	+	48197.8i	0.840847	+	0.348290i
$373$	−129004.	+	41915.8i	−0.927223	+	0.301273i	−0.733426	−	0.679769i	$-0.762080\pi$
$373$	−129004.	+	41915.8i	−0.927223	+	0.301273i	−0.193796	+	0.981042i	$0.562080\pi$
$374$	60132.3	−	118016.i	0.429897	−	0.843721i
$375$	−218301.	−	52409.5i	−1.55236	−	0.372690i
$376$	35194.0	−	8449.32i	0.248939	−	0.0597649i
$377$	−39970.3	+	20365.9i	−0.281225	+	0.143292i
$378$	55527.5	+	55527.5i	0.388619	+	0.388619i
$379$	12344.2	−	37991.6i	0.0859380	−	0.264490i	−0.898848	−	0.438260i	$-0.855595\pi$
$379$	12344.2	−	37991.6i	0.0859380	−	0.264490i	0.984786	+	0.173770i	$0.0555949\pi$
$380$	22382.2	+	19116.2i	0.155002	+	0.132384i
$381$	−60520.5	−	4763.06i	−0.416920	−	0.0328123i
$382$	46128.7	+	75275.2i	0.316114	+	0.515852i
$383$	131395.	−	54425.5i	0.895736	−	0.371026i	0.113157	−	0.993577i	$-0.463904\pi$
$383$	131395.	−	54425.5i	0.895736	−	0.371026i	0.782579	+	0.622551i	$0.213904\pi$
$384$	15266.8	−	13039.1i	0.103534	−	0.0884268i
$385$	−172867.	+	125596.i	−1.16625	+	0.847330i
$386$	1994.73	+	25345.5i	0.0133878	+	0.170108i
$387$	−15376.8	−	11171.9i	−0.102670	−	0.0745942i
$388$	−6766.47	+	11041.9i	−0.0449468	+	0.0733465i
$389$	−16125.7	+	101813.i	−0.106566	+	0.672831i	0.875347	+	0.483496i	$0.160633\pi$
$389$	−16125.7	+	101813.i	−0.106566	+	0.672831i	−0.981913	+	0.189335i	$0.939367\pi$
$390$	−61901.9	−	9804.29i	−0.406981	−	0.0644595i
$391$	245139.	+	150222.i	1.60347	+	0.982605i
$392$	−26513.4	+	36492.6i	−0.172541	+	0.237483i
$393$	35201.4	−	2770.41i	0.227916	−	0.0179374i
$394$	83764.2	+	115292.i	0.539593	+	0.742686i
$395$	150413.	+	176111.i	0.964030	+	1.12873i
$396$	−45795.5	−	110560.i	−0.292033	−	0.705031i
$397$	−14381.5	+	8813.01i	−0.0912481	+	0.0559169i	−0.567374	−	0.823460i	$-0.692041\pi$
$397$	−14381.5	+	8813.01i	−0.0912481	+	0.0559169i	0.476126	+	0.879377i	$0.342041\pi$
$398$	−10547.7	+	134021.i	−0.0665871	+	0.846070i
$399$	91644.0	−	107301.i	0.575649	−	0.673999i
$400$	3089.29	+	1003.77i	0.0193081	+	0.00627357i
$401$	−102145.	+	102145.i	−0.635225	+	0.635225i	−0.949374	−	0.314149i	$-0.898281\pi$
$401$	−102145.	+	102145.i	−0.635225	+	0.635225i	0.314149	+	0.949374i	$0.398281\pi$
$402$	50025.3	+	98180.2i	0.309555	+	0.607536i
$403$	17680.7	+	73645.3i	0.108865	+	0.453456i
$404$	36519.8	−	152116.i	0.223751	−	0.931991i
$405$	−68356.6	−	34829.4i	−0.416745	−	0.212342i
$406$	38970.4	+	119938.i	0.236419	+	0.727623i
$407$	5700.66	−	13762.6i	0.0344141	−	0.0830830i
$408$	−17085.1	−	107871.i	−0.102635	−	0.648014i
$409$		−	66156.2i		−	0.395479i	−0.980255	−	0.197740i	$-0.936640\pi$
$409$		−	66156.2i		−	0.395479i	0.980255	−	0.197740i	$-0.0633601\pi$
$410$	−26324.4	−	110853.i	−0.156600	−	0.659449i
$411$	−4485.70			−0.0265550
$412$	152845.	−	24208.2i	0.900443	−	0.142616i
$413$	−341666.	−	141523.i	−2.00310	−	0.829710i
$414$	247045.	−	80269.7i	1.44137	−	0.468329i
$415$	−111536.	+	218903.i	−0.647620	+	1.27103i
$416$	11739.8	+	2818.47i	0.0678380	+	0.0162865i
$417$	−252601.	+	60644.1i	−1.45266	+	0.348752i
$418$	−52047.2	+	26519.4i	−0.297883	+	0.151779i
$419$	6558.31	+	6558.31i	0.0373563	+	0.0373563i	0.725538	−	0.688182i	$-0.241591\pi$
$419$	6558.31	+	6558.31i	0.0373563	+	0.0373563i	−0.688182	+	0.725538i	$0.741591\pi$
$420$	−54445.5	+	167566.i	−0.308648	+	0.949921i
$421$	−79177.5	−	67624.0i	−0.446722	−	0.381537i	0.397437	−	0.917629i	$-0.369900\pi$
$421$	−79177.5	−	67624.0i	−0.446722	−	0.381537i	−0.844159	+	0.536093i	$0.819900\pi$
$422$	30795.1	+	2423.63i	0.172925	+	0.0136095i
$423$	−92945.2	−	151673.i	−0.519453	−	0.847670i
$424$	−106606.	+	44157.8i	−0.592996	+	0.245627i
$425$	13436.3	−	11475.7i	0.0743880	−	0.0635334i
$426$	151094.	−	109776.i	0.832582	−	0.604907i
$427$	−23910.5	−	303812.i	−0.131139	−	1.66628i
$428$	−86719.4	−	63005.3i	−0.473401	−	0.343946i
$429$	64987.2	−	106050.i	0.353113	−	0.576228i
$430$	1812.15	−	11441.5i	0.00980072	−	0.0618793i
$431$	70477.1	+	11162.5i	0.379397	+	0.0600905i	0.343220	−	0.939255i	$-0.388482\pi$
$431$	70477.1	+	11162.5i	0.379397	+	0.0600905i	0.0361762	+	0.999345i	$0.488482\pi$
$432$	−22854.4	−	14005.2i	−0.122462	−	0.0750450i
$433$	63682.7	−	87651.7i	0.339661	−	0.467503i	−0.604681	−	0.796468i	$-0.706700\pi$
$433$	63682.7	−	87651.7i	0.339661	−	0.467503i	0.944342	+	0.328964i	$0.106700\pi$
$434$	212260.	−	16705.2i	1.12691	−	0.0886897i
$435$	131343.	+	180779.i	0.694112	+	0.955363i
$436$	59809.1	+	70027.5i	0.314626	+	0.368379i
$437$	−48522.4	−	117144.i	−0.254085	−	0.613417i
$438$	−139996.	+	85789.6i	−0.729738	+	0.447184i
$439$	19772.5	−	251234.i	0.102597	−	1.30361i	−0.703017	−	0.711173i	$-0.748164\pi$
$439$	19772.5	−	251234.i	0.102597	−	1.30361i	0.805614	−	0.592441i	$-0.201836\pi$
$440$	47367.6	−	55460.3i	0.244667	−	0.286469i
$441$	210843.	+	68506.9i	1.08413	+	0.352255i
$442$	46440.4	−	46440.4i	0.237712	−	0.237712i
$443$	8399.67	+	16485.3i	0.0428011	+	0.0840018i	0.911417	−	0.411485i	$-0.134990\pi$
$443$	8399.67	+	16485.3i	0.0428011	+	0.0840018i	−0.868616	+	0.495487i	$0.834990\pi$
$444$	−2867.44	−	11943.8i	−0.0145455	−	0.0605864i
$445$	−51310.5	+	213724.i	−0.259111	+	1.07928i
$446$	23160.7	+	11801.0i	0.116435	+	0.0593264i
$447$	101528.	+	312471.i	0.508124	+	1.56385i
$448$	12988.6	−	31357.3i	0.0647153	−	0.156237i
$449$	−25053.1	−	158179.i	−0.124271	−	0.784614i	−0.968570	−	0.248742i	$-0.919983\pi$
$449$	−25053.1	−	158179.i	−0.124271	−	0.784614i	0.844299	−	0.535872i	$-0.180017\pi$
$450$		−	15964.6i		−	0.0788374i
$451$	223239.	+	35922.5i	1.09753	+	0.176609i
$452$	103902.			0.508566
$453$	−87299.8	+	13826.9i	−0.425419	+	0.0673797i
$454$	−16891.3	−	6996.59i	−0.0819503	−	0.0339449i
$455$	−100766.	+	32740.7i	−0.486731	+	0.158149i
$456$	−21866.9	+	42916.2i	−0.105162	+	0.206392i
$457$	192830.	+	46294.4i	0.923299	+	0.221664i	0.667107	−	0.744962i	$-0.267532\pi$
$457$	192830.	+	46294.4i	0.923299	+	0.221664i	0.256192	+	0.966626i	$0.417532\pi$
$458$	145206.	−	34860.9i	0.692236	−	0.166191i
$459$	−129918.	+	66196.4i	−0.616656	+	0.314202i
$460$	111946.	+	111946.i	0.529045	+	0.529045i
$461$	−8479.33	+	26096.7i	−0.0398988	+	0.122796i	−0.969022	−	0.246974i	$-0.920564\pi$
$461$	−8479.33	+	26096.7i	−0.0398988	+	0.122796i	0.929123	+	0.369770i	$0.120564\pi$
$462$	−265879.	−	227082.i	−1.24566	−	1.06390i
$463$	60200.6	+	4737.89i	0.280827	+	0.0221016i	0.218090	−	0.975929i	$-0.430017\pi$
$463$	60200.6	+	4737.89i	0.280827	+	0.0221016i	0.0627366	+	0.998030i	$0.480017\pi$
$464$	−22491.5	−	36702.8i	−0.104468	−	0.170476i
$465$	348547.	−	144373.i	1.61197	−	0.667698i
$466$	2719.98	−	2323.09i	0.0125255	−	0.0106978i
$467$	−248377.	+	180456.i	−1.13888	+	0.827444i	−0.986963	−	0.160950i	$-0.948544\pi$
$467$	−248377.	+	180456.i	−1.13888	+	0.827444i	−0.151916	+	0.988393i	$0.548544\pi$
$468$	−4655.61	−	59155.1i	−0.0212562	−	0.270085i
$469$	150703.	+	109492.i	0.685136	+	0.497781i
$470$	56647.5	−	92440.3i	0.256439	−	0.418471i
$471$	−8369.48	+	52842.8i	−0.0377274	+	0.238201i
$472$	124678.	+	19747.0i	0.559634	+	0.0886373i
$473$	19601.4	+	12011.8i	0.0876122	+	0.0536889i
$474$	−222763.	+	306606.i	−0.991484	+	1.36466i
$475$	−7768.73	+	611.412i	−0.0344321	+	0.00270986i
$476$	−108524.	−	149370.i	−0.478974	−	0.659251i
$477$	368314.	+	431240.i	1.61875	+	1.89532i
$478$	34456.9	+	83186.3i	0.150807	+	0.364079i
$479$	145816.	−	89355.9i	0.635525	−	0.389450i	−0.167095	−	0.985941i	$-0.553439\pi$
$479$	145816.	−	89355.9i	0.635525	−	0.389450i	0.802620	+	0.596491i	$0.203439\pi$
$480$	4718.50	−	59954.2i	0.0204796	−	0.260218i
$481$	4797.12	−	5616.70i	0.0207343	−	0.0242768i
$482$	227483.	+	73913.8i	0.979164	+	0.318150i
$483$	536673.	−	536673.i	2.30046	−	2.30046i
$484$	12536.7	+	24604.7i	0.0535171	+	0.105033i
$485$	9055.68	+	37719.6i	0.0384980	+	0.160356i
$486$	51706.3	−	215372.i	0.218913	−	0.911837i
$487$	−236162.	−	120331.i	−0.995755	−	0.507363i	−0.121376	−	0.992607i	$-0.538731\pi$
$487$	−236162.	−	120331.i	−0.995755	−	0.507363i	−0.874379	+	0.485244i	$0.838731\pi$
$488$	32144.7	+	98931.1i	0.134980	+	0.415426i
$489$	−19738.2	+	47652.3i	−0.0825450	+	0.199281i
$490$	21136.7	+	133452.i	0.0880331	+	0.555819i
$491$			392112.i			1.62647i	0.581934	+	0.813236i	$0.302296\pi$
$491$			392112.i			1.62647i	−0.581934	+	0.813236i	$0.697704\pi$
$492$	166330.	−	84232.9i	0.687131	−	0.347978i
$493$	−234162.			−0.963436
$494$	−28608.0	+	4531.05i	−0.117228	+	0.0185672i
$495$	−331175.	−	137177.i	−1.35160	−	0.559850i
$496$	−69118.9	+	22458.1i	−0.280953	+	0.0912871i
$497$	143337.	−	281314.i	0.580289	−	1.13888i
$498$	−390917.	−	93850.8i	−1.57625	−	0.378425i
$499$	−176636.	+	42406.6i	−0.709379	+	0.170307i	−0.572050	−	0.820219i	$-0.693852\pi$
$499$	−176636.	+	42406.6i	−0.709379	+	0.170307i	−0.137329	+	0.990525i	$0.543852\pi$
$500$	115427.	−	58813.1i	0.461709	−	0.235253i
$501$	−445968.	−	445968.i	−1.77676	−	1.77676i
$502$	−70398.6	+	216665.i	−0.279355	+	0.859767i
$503$	325691.	+	278167.i	1.28727	+	1.09943i	0.989460	+	0.144808i	$0.0462566\pi$
$503$	325691.	+	278167.i	1.28727	+	1.09943i	0.297811	+	0.954625i	$0.403743\pi$
$504$	−166298.	−	13088.0i	−0.654677	−	0.0515242i
$505$	−244843.	−	399547.i	−0.960073	−	1.56670i
$506$	−290267.	+	120232.i	−1.13370	+	0.469592i
$507$	−254200.	+	217108.i	−0.988918	+	0.844616i
$508$	28340.3	−	20590.4i	0.109819	−	0.0797880i
$509$	7592.12	+	96467.1i	0.0293041	+	0.372343i	0.994032	+	0.109093i	$0.0347946\pi$
$509$	7592.12	+	96467.1i	0.0293041	+	0.372343i	−0.964728	+	0.263250i	$0.915205\pi$
$510$	−264668.	−	192293.i	−1.01756	−	0.739303i
$511$	−145030.	+	236667.i	−0.555411	+	0.906349i
$512$	−1812.33	+	11442.6i	−0.00691349	+	0.0436501i
$513$	63513.0	+	10059.5i	0.241339	+	0.0382244i
$514$	−263574.	−	161518.i	−0.997646	−	0.611358i
$515$	272464.	−	375014.i	1.02729	−	1.41395i
$516$	18897.5	−	1487.27i	0.0709749	−	0.00558585i
$517$	126466.	+	174065.i	0.473143	+	0.651225i
$518$	−13485.8	−	15789.8i	−0.0502593	−	0.0588461i
$519$	10042.0	+	24243.4i	0.0372806	+	0.0900034i
$520$	30835.6	−	18896.1i	0.114037	−	0.0698820i
$521$	−28873.8	+	366876.i	−0.106372	+	1.35159i	0.679718	+	0.733474i	$0.262102\pi$
$521$	−28873.8	+	366876.i	−0.106372	+	1.35159i	−0.786090	+	0.618112i	$0.787898\pi$
$522$	−137399.	+	160873.i	−0.504245	+	0.590396i
$523$	−165751.	−	53855.6i	−0.605971	−	0.196892i	−0.0100691	−	0.999949i	$-0.503205\pi$
$523$	−165751.	−	53855.6i	−0.605971	−	0.196892i	−0.595901	+	0.803058i	$0.703205\pi$
$524$	−14407.5	+	14407.5i	−0.0524718	+	0.0524718i
$525$	−21176.8	−	41561.7i	−0.0768318	−	0.150791i
$526$	61942.6	+	258009.i	0.223881	+	0.932533i
$527$	−92290.9	+	384419.i	−0.332306	+	1.38415i
$528$	106341.	+	54183.4i	0.381446	+	0.194356i
$529$	−124266.	−	382452.i	−0.444060	−	1.36668i
$530$	−132272.	+	319332.i	−0.470885	+	1.13682i
$531$	−97052.3	−	612764.i	−0.344205	−	2.17322i
$532$			81425.9i			0.287700i
$533$	99770.9	+	51146.3i	0.351196	+	0.180036i
$534$	−359670.			−1.26131
$535$	−317130.	+	50228.5i	−1.10797	+	0.175486i
$536$	−58743.7	−	24332.5i	−0.204471	−	0.0846947i
$537$	536470.	−	174310.i	1.86036	−	0.604468i
$538$	59747.6	−	117261.i	0.206422	−	0.405126i
$539$	−260733.	−	62596.5i	−0.897467	−	0.215463i
$540$	−78071.9	+	18743.4i	−0.267736	+	0.0642778i
$541$	116224.	−	59219.1i	0.397101	−	0.202333i	−0.244025	−	0.969769i	$-0.578468\pi$
$541$	116224.	−	59219.1i	0.397101	−	0.202333i	0.641126	+	0.767436i	$0.278468\pi$
$542$	−212406.	−	212406.i	−0.723051	−	0.723051i
$543$	−198521.	+	610984.i	−0.673297	+	2.07219i
$544$	47921.9	+	40929.1i	0.161933	+	0.138304i
$545$	275005.	+	21643.4i	0.925866	+	0.0728672i
$546$	−90588.6	−	147827.i	−0.303870	−	0.495871i
$547$	492682.	−	204076.i	1.64661	−	0.682050i	0.649674	−	0.760213i	$-0.274905\pi$
$547$	492682.	−	204076.i	1.64661	−	0.682050i	0.996941	+	0.0781628i	$0.0249054\pi$
$548$	1968.24	−	1681.04i	0.00655417	−	0.00559779i
$549$	413609.	−	300504.i	1.37229	−	0.997025i
$550$	1515.00	+	19249.9i	0.00500827	+	0.0636361i
$551$	83546.8	+	60700.3i	0.275186	+	0.199935i
$552$	−135360.	+	220888.i	−0.444235	+	0.724926i
$553$	−100225.	+	632798.i	−0.327739	+	2.06926i
$554$	−67138.9	−	10633.8i	−0.218753	−	0.0346471i
$555$	−31371.4	−	19224.4i	−0.101847	−	0.0624120i
$556$	88110.0	−	121273.i	0.285020	−	0.392297i
$557$	290157.	−	22835.9i	0.935240	−	0.0736050i	0.398328	−	0.917243i	$-0.369591\pi$
$557$	290157.	−	22835.9i	0.935240	−	0.0736050i	0.536912	+	0.843638i	$0.319591\pi$
$558$	209949.	+	288970.i	0.674289	+	0.928079i
$559$	7403.14	+	8667.96i	0.0236915	+	0.0277392i
$560$	−38906.5	−	93928.6i	−0.124064	−	0.299517i
$561$	553565.	−	339225.i	1.75891	−	1.07786i
$562$	33985.5	−	431827.i	0.107602	−	1.36722i
$563$	53226.8	−	62320.6i	0.167924	−	0.196614i	−0.670062	−	0.742305i	$-0.733733\pi$
$563$	53226.8	−	62320.6i	0.167924	−	0.196614i	0.837987	+	0.545691i	$0.183733\pi$
$564$	168727.	+	54822.8i	0.530428	+	0.172347i
$565$	220074.	−	220074.i	0.689400	−	0.689400i
$566$	107190.	+	210372.i	0.334596	+	0.656681i
$567$	−49543.8	−	206365.i	−0.154107	−	0.641903i
$568$	−25158.1	+	104791.i	−0.0779795	+	0.324808i
$569$	−121342.	−	61826.8i	−0.374789	−	0.190964i	0.256442	−	0.966560i	$-0.417450\pi$
$569$	−121342.	−	61826.8i	−0.374789	−	0.190964i	−0.631231	+	0.775595i	$0.717450\pi$
$570$	44584.3	+	137216.i	0.137225	+	0.422334i
$571$	−42546.2	+	102716.i	−0.130493	+	0.315039i	−0.975599	−	0.219561i	$-0.929538\pi$
$571$	−42546.2	+	102716.i	−0.130493	+	0.315039i	0.845105	+	0.534600i	$0.179538\pi$
$572$	11227.4	+	70886.9i	0.0343152	+	0.216658i
$573$			432741.i			1.31801i
$574$	185890.	−	254533.i	0.564199	−	0.772538i
$575$	−41913.7			−0.126771
$576$	56238.0	−	8907.23i	0.169506	−	0.0268471i
$577$	−129299.	−	53557.4i	−0.388368	−	0.160867i	0.179951	−	0.983676i	$-0.442406\pi$
$577$	−129299.	−	53557.4i	−0.388368	−	0.160867i	−0.568319	+	0.822808i	$0.692406\pi$
$578$	101374.	−	32938.4i	0.303439	−	0.0985933i
$579$	−56575.7	+	111036.i	−0.168761	+	0.331213i
$580$	−125379.	−	30100.8i	−0.372707	−	0.0894791i
$581$	−660855.	+	158657.i	−1.95774	+	0.470011i
$582$	−56558.8	+	28818.1i	−0.166976	+	0.0850785i
$583$	−485033.	−	485033.i	−1.42703	−	1.42703i
$584$	29277.6	−	90107.1i	0.0858439	−	0.264200i
$585$	−135157.	−	115435.i	−0.394935	−	0.337307i
$586$	−427217.	−	33622.7i	−1.24409	−	0.0979123i
$587$	−97333.9	−	158835.i	−0.282480	−	0.460966i	0.679657	−	0.733530i	$-0.262128\pi$
$587$	−97333.9	−	158835.i	−0.282480	−	0.460966i	−0.962138	+	0.272564i	$0.912128\pi$
$588$	−204270.	+	84611.3i	−0.590812	+	0.244722i
$589$	132579.	−	113233.i	0.382159	−	0.326395i
$590$	305904.	−	222252.i	0.878781	−	0.638472i
$591$	54805.6	+	696371.i	0.156910	+	1.99373i
$592$	5734.17	+	4166.12i	0.0163616	+	0.0118874i
$593$	131244.	−	214171.i	0.373225	−	0.609047i	−0.609793	−	0.792561i	$-0.708747\pi$
$593$	131244.	−	214171.i	0.373225	−	0.609047i	0.983017	+	0.183514i	$0.0587472\pi$
$594$	24926.1	−	157377.i	0.0706450	−	0.446035i
$595$	−546243.	−	86516.4i	−1.54295	−	0.244379i
$596$	−161648.	−	99058.3i	−0.455071	−	0.278868i
$597$	−387323.	+	533105.i	−1.08674	+	1.49577i
$598$	−155307.	+	12222.9i	−0.434299	+	0.0341801i
$599$	290057.	+	399230.i	0.808407	+	1.11268i	0.991567	+	0.129594i	$0.0413674\pi$
$599$	290057.	+	399230.i	0.808407	+	1.11268i	−0.183160	+	0.983083i	$0.558633\pi$
$600$	10340.4	+	12107.1i	0.0287234	+	0.0336308i
$601$	−260629.	−	629214.i	−0.721562	−	1.74201i	−0.668852	−	0.743396i	$-0.733214\pi$
$601$	−260629.	−	629214.i	−0.721562	−	1.74201i	−0.0527102	−	0.998610i	$-0.516786\pi$
$602$	27323.3	−	16743.7i	0.0753945	−	0.0462018i
$603$	−24518.5	+	311538.i	−0.0674311	+	0.856793i
$604$	33123.8	−	38783.0i	0.0907960	−	0.106308i
$605$	78668.7	+	25561.0i	0.214927	+	0.0698340i
$606$	542213.	−	542213.i	1.47647	−	1.47647i
$607$	−240767.	−	472532.i	−0.653461	−	1.28249i	−0.945356	−	0.326039i	$-0.894286\pi$
$607$	−240767.	−	472532.i	−0.653461	−	1.28249i	0.291895	−	0.956450i	$-0.405714\pi$
$608$	−6488.27	−	27025.6i	−0.0175518	−	0.0731085i
$609$	−144304.	+	601071.i	−0.389085	+	1.62066i
$610$	277630.	+	141460.i	0.746117	+	0.380166i
$611$	32967.6	+	101464.i	0.0883089	+	0.271787i
$612$	118531.	−	286160.i	0.316468	−	0.764022i
$613$	42084.9	+	265714.i	0.111997	+	0.707120i	0.978237	+	0.207492i	$0.0665299\pi$
$613$	42084.9	+	265714.i	0.111997	+	0.707120i	−0.866240	+	0.499628i	$0.833470\pi$
$614$			341928.i			0.906982i
$615$	173888.	−	530714.i	0.459748	−	1.40317i
$616$	201763.			0.531717
$617$	36246.0	−	5740.80i	0.0952116	−	0.0150800i	−0.108647	−	0.994080i	$-0.534652\pi$
$617$	36246.0	−	5740.80i	0.0952116	−	0.0150800i	0.203858	+	0.979000i	$0.434652\pi$
$618$	700790.	+	290277.i	1.83490	+	0.760038i
$619$	244117.	−	79318.3i	0.637113	−	0.207010i	0.0273895	−	0.999625i	$-0.491281\pi$
$619$	244117.	−	79318.3i	0.637113	−	0.207010i	0.609723	+	0.792614i	$0.291281\pi$
$620$	−98831.7	+	193968.i	−0.257106	+	0.504600i
$621$	336310.	+	80740.9i	0.872081	+	0.209368i
$622$	−156977.	+	37686.8i	−0.405747	+	0.0974112i
$623$	−541760.	+	276040.i	−1.39582	+	0.711208i
$624$	41846.1	+	41846.1i	0.107470	+	0.107470i
$625$	110111.	−	338888.i	0.281885	−	0.867553i
$626$	−34871.3	−	29782.9i	−0.0889855	−	0.0760008i
$627$	−285442.	−	22464.8i	−0.726077	−	0.0571435i
$628$	−16130.7	−	26323.0i	−0.0409011	−	0.0667445i
$629$	35621.4	−	14754.9i	0.0900347	−	0.0372936i
$630$	−379956.	+	324513.i	−0.957309	+	0.817619i
$631$	293114.	−	212960.i	0.736171	−	0.534859i	−0.155339	−	0.987861i	$-0.549647\pi$
$631$	293114.	−	212960.i	0.736171	−	0.534859i	0.891509	+	0.453002i	$0.149647\pi$
$632$	−17158.1	−	218015.i	−0.0429572	−	0.545823i
$633$	122496.	+	88998.7i	0.305714	+	0.222114i
$634$	2162.45	−	3528.80i	0.00537981	−	0.00877906i
$635$	16414.9	−	103639.i	0.0407090	−	0.257026i
$636$	−558637.	−	88479.4i	−1.38107	−	0.218740i
$637$	−113365.	−	69470.4i	−0.279384	−	0.171207i
$638$	150408.	−	207018.i	0.369512	−	0.508590i
$639$	528027.	−	41556.6i	1.29317	−	0.101774i
$640$	20397.8	+	28075.1i	0.0497992	+	0.0685428i
$641$	−360702.	−	422328.i	−0.877875	−	1.02786i	−0.999378	−	0.0352687i	$-0.988771\pi$
$641$	−360702.	−	422328.i	−0.877875	−	1.02786i	0.121503	−	0.992591i	$-0.461229\pi$
$642$	−201067.	−	485418.i	−0.487832	−	1.17773i
$643$	180410.	−	110556.i	0.436354	−	0.267398i	−0.286926	−	0.957953i	$-0.592633\pi$
$643$	180410.	−	110556.i	0.436354	−	0.267398i	0.723280	+	0.690554i	$0.242633\pi$
$644$	−34361.4	+	436603.i	−0.0828513	+	1.05273i
$645$	36876.4	−	43176.7i	0.0886399	−	0.103784i
$646$	−143792.	−	46720.7i	−0.344563	−	0.111955i
$647$	15190.2	−	15190.2i	0.0362873	−	0.0362873i	−0.688730	−	0.725018i	$-0.741832\pi$
$647$	15190.2	−	15190.2i	0.0362873	−	0.0362873i	0.725018	+	0.688730i	$0.241832\pi$
$648$	32887.6	+	64545.6i	0.0783217	+	0.153715i
$649$	175175.	+	729655.i	0.415893	+	1.73232i
$650$	−2235.14	+	9310.04i	−0.00529028	+	0.0220356i
$651$	929891.	+	473803.i	2.19417	+	1.11798i
$652$	−9197.17	−	28306.0i	−0.0216351	−	0.0665860i
$653$	195987.	−	473155.i	0.459622	−	1.10963i	−0.508928	−	0.860809i	$-0.669958\pi$
$653$	195987.	−	473155.i	0.459622	−	1.10963i	0.968550	−	0.248818i	$-0.0800420\pi$
$654$	70615.0	+	445846.i	0.165098	+	1.04239i
$655$			61032.7i			0.142259i
$656$	−41415.8	+	99292.8i	−0.0962405	+	0.230733i
$657$	−465648.			−1.07877
$658$	296224.	−	46917.3i	0.684177	−	0.108363i
$659$	−526036.	−	217891.i	−1.21128	−	0.501729i	−0.316653	−	0.948541i	$-0.602559\pi$
$659$	−526036.	−	217891.i	−1.21128	−	0.501729i	−0.894628	+	0.446812i	$0.852559\pi$
$660$	340005.	−	110474.i	0.780544	−	0.253614i
$661$	−317663.	+	623450.i	−0.727050	+	1.42692i	0.170208	+	0.985408i	$0.445556\pi$
$661$	−317663.	+	623450.i	−0.727050	+	1.42692i	−0.897257	+	0.441508i	$0.854444\pi$
$662$	−393177.	−	94393.3i	−0.897164	−	0.215390i
$663$	313029.	−	75151.6i	0.712127	−	0.170967i
$664$	206698.	−	105318.i	0.468814	−	0.238873i
$665$	172467.	+	172467.i	0.389999	+	0.389999i
$666$	10764.7	−	33130.2i	0.0242690	−	0.0746923i
$667$	422360.	+	360730.i	0.949361	+	0.810831i
$668$	362811.	+	28553.8i	0.813069	+	0.0639899i
$669$	66573.0	+	108637.i	0.148746	+	0.242732i
$670$	−175963.	+	72886.1i	−0.391986	+	0.162366i
$671$	−470208.	+	401596.i	−1.04435	+	0.891957i
$672$	134593.	−	97787.7i	0.298047	−	0.216544i
$673$	18925.6	+	240472.i	0.0417849	+	0.530927i	0.981816	+	0.189837i	$0.0607961\pi$
$673$	18925.6	+	240472.i	0.0417849	+	0.530927i	−0.940031	+	0.341090i	$0.889204\pi$
$674$	281539.	+	204550.i	0.619754	+	0.450277i
$675$	11106.6	−	18124.3i	0.0243766	−	0.0397791i
$676$	30176.3	−	190526.i	0.0660348	−	0.416927i
$677$	−391765.	−	62049.5i	−0.854768	−	0.135382i	−0.286353	−	0.958124i	$-0.592443\pi$
$677$	−391765.	−	62049.5i	−0.854768	−	0.135382i	−0.568415	+	0.822742i	$0.692443\pi$
$678$	434242.	+	266104.i	0.944654	+	0.578885i
$679$	−63075.3	+	86815.7i	−0.136811	+	0.188304i
$680$	188194.	−	14811.2i	0.406994	−	0.0320312i
$681$	−52675.4	−	72501.4i	−0.113583	−	0.156334i
$682$	−280578.	−	328514.i	−0.603232	−	0.706294i
$683$	73191.6	+	176700.i	0.156899	+	0.378787i	0.982708	−	0.185162i	$-0.0592811\pi$
$683$	73191.6	+	176700.i	0.156899	+	0.378787i	−0.825809	+	0.563950i	$0.809281\pi$
$684$	−116470.	+	71373.0i	−0.248945	+	0.152553i
$685$	608.325	−	7729.50i	0.00129645	−	0.0164729i
$686$	49624.1	−	58102.4i	0.105450	−	0.123466i
$687$	696148.	+	226192.i	1.47499	+	0.479252i
$688$	−7734.52	+	7734.52i	−0.0163402	+	0.0163402i
$689$	−154413.	−	303052.i	−0.325270	−	0.638379i
$690$	181155.	+	754565.i	0.380498	+	1.58489i
$691$	118392.	−	493140.i	0.247952	−	1.03280i	−0.699939	−	0.714202i	$-0.746790\pi$
$691$	118392.	−	493140.i	0.247952	−	1.03280i	0.947892	−	0.318593i	$-0.103210\pi$
$692$	−13491.6	−	6874.30i	−0.0281741	−	0.0143554i
$693$	−306429.	−	943090.i	−0.638062	−	1.96375i
$694$	20727.4	−	50040.4i	0.0430354	−	0.103897i
$695$	−70242.2	−	443492.i	−0.145421	−	0.918155i
$696$		−	210997.i		−	0.435569i
$697$	342824.	+	474313.i	0.705676	+	0.976337i
$698$	−117499.			−0.241171
$699$	17317.4	−	2742.81i	0.0354428	−	0.00561359i
$700$	24867.4	+	10300.4i	0.0507499	+	0.0210213i
$701$	56973.7	−	18511.9i	0.115941	−	0.0376716i	−0.250472	−	0.968124i	$-0.580586\pi$
$701$	56973.7	−	18511.9i	0.115941	−	0.0376716i	0.366413	+	0.930452i	$0.380586\pi$
$702$	35869.0	−	70396.8i	0.0727855	−	0.142850i
$703$	−16534.2	−	3969.51i	−0.0334559	−	0.00803205i
$704$	−66966.0	+	16077.1i	−0.135117	+	0.0324387i
$705$	473498.	−	241259.i	0.952665	−	0.485407i
$706$	181006.	+	181006.i	0.363148	+	0.363148i
$707$	400580.	−	1.23286e6i	0.801402	−	2.46646i
$708$	470496.	+	401841.i	0.938619	+	0.801656i
$709$	254087.	+	19997.1i	0.505464	+	0.0397809i	0.328628	−	0.944459i	$-0.393414\pi$
$709$	254087.	+	19997.1i	0.505464	+	0.0397809i	0.176836	+	0.984240i	$0.443414\pi$
$710$	168669.	+	275243.i	0.334595	+	0.546009i
$711$	−992995.	+	411312.i	−1.96430	+	0.813640i
$712$	157817.	−	134788.i	0.311310	−	0.265884i
$713$	758669.	−	551205.i	1.49236	−	1.08426i
$714$	−71005.5	−	902211.i	−0.139282	−	1.76975i
$715$	173925.	+	126364.i	0.340213	+	0.247179i
$716$	−170070.	+	277529.i	−0.331743	+	0.541355i
$717$	−69041.6	+	435911.i	−0.134299	+	0.847930i
$718$	−261218.	−	41372.8i	−0.506703	−	0.0802539i
$719$	−590867.	−	362084.i	−1.14296	−	0.700408i	−0.183716	−	0.982979i	$-0.558813\pi$
$719$	−590867.	−	362084.i	−1.14296	−	0.700408i	−0.959246	+	0.282571i	$0.908813\pi$
$720$	100251.	−	137983.i	0.193385	−	0.266172i
$721$	1.27836e6	−	100609.i	2.45914	−	0.193539i
$722$	−177467.	−	244263.i	−0.340443	−	0.468579i
$723$	761429.	+	891519.i	1.45664	+	1.70551i
$724$	−141862.	−	342485.i	−0.270638	−	0.653379i
$725$	29106.6	−	17836.5i	0.0553752	−	0.0339340i
$726$	−10619.9	+	134939.i	−0.0201488	+	0.256014i
$727$	−183654.	+	215032.i	−0.347482	+	0.406849i	−0.906432	−	0.422352i	$-0.861205\pi$
$727$	−183654.	+	215032.i	−0.347482	+	0.406849i	0.558950	+	0.829202i	$0.311205\pi$
$728$	95147.6	+	30915.3i	0.179529	+	0.0583326i
$729$	584322.	−	584322.i	1.09951	−	1.09951i
$730$	−128842.	−	252867.i	−0.241776	−	0.474511i
$731$	13890.5	+	57858.0i	0.0259945	+	0.108275i
$732$	−119029.	+	495793.i	−0.222143	+	0.925290i
$733$	167397.	+	85292.8i	0.311558	+	0.158747i	0.602777	−	0.797910i	$-0.294061\pi$
$733$	167397.	+	85292.8i	0.311558	+	0.158747i	−0.291219	+	0.956656i	$0.594061\pi$
$734$	191275.	+	588684.i	0.355031	+	1.09267i
$735$	−253447.	+	611875.i	−0.469151	+	1.13263i
$736$	−23385.2	−	147649.i	−0.0431704	−	0.272567i
$737$		−	377976.i		−	0.695872i
$738$	527019.	+	42786.1i	0.967640	+	0.0785580i
$739$	−969519.			−1.77528			−0.887642	−	0.460535i	$-0.847658\pi$
$739$	−969519.			−1.77528			−0.887642	+	0.460535i	$0.847658\pi$
$740$	20969.7	−	3321.27i	0.0382938	−	0.00606514i
$741$	−131167.	−	54331.1i	−0.238884	−	0.0989491i
$742$	−909365.	+	295470.i	−1.65170	+	0.536669i
$743$	−289628.	+	568426.i	−0.524641	+	1.02967i	0.464893	+	0.885367i	$0.346093\pi$
$743$	−289628.	+	568426.i	−0.524641	+	1.02967i	−0.989534	+	0.144299i	$0.953907\pi$
$744$	−346389.	−	83160.6i	−0.625775	−	0.150235i
$745$	−552200.	+	132571.i	−0.994910	+	0.238857i
$746$	341839.	−	174176.i	0.614248	−	0.312975i
$747$	−806206.	−	806206.i	−1.44479	−	1.44479i
$748$	−115768.	+	356297.i	−0.206912	+	0.636809i
$749$	−675411.	−	576855.i	−1.20394	−	1.02826i
$750$	633036.	+	49821.1i	1.12540	+	0.0885708i
$751$	84503.1	+	137897.i	0.149828	+	0.244497i	0.918745	−	0.394852i	$-0.129204\pi$
$751$	84503.1	+	137897.i	0.149828	+	0.244497i	−0.768917	+	0.639349i	$0.779204\pi$
$752$	−94579.5	+	39176.1i	−0.167248	+	0.0692764i
$753$	−849120.	+	725217.i	−1.49754	+	1.27902i
$754$	102650.	−	74579.6i	0.180558	−	0.131183i
$755$	−11986.7	−	152305.i	−0.0210283	−	0.267190i
$756$	−179691.	−	130553.i	−0.314400	−	0.228425i
$757$	165135.	−	269475.i	0.288168	−	0.470248i	−0.675496	−	0.737363i	$-0.736071\pi$
$757$	165135.	−	269475.i	0.288168	−	0.470248i	0.963665	+	0.267116i	$0.0860705\pi$
$758$	−17675.0	+	111595.i	−0.0307624	+	0.194226i
$759$	−1.52105e6	−	240911.i	−2.64034	−	0.418189i
$760$	−70985.3	−	43499.9i	−0.122897	−	0.0753114i
$761$	−563750.	+	775936.i	−0.973458	+	1.33985i	−0.0331781	+	0.999449i	$0.510563\pi$
$761$	−563750.	+	775936.i	−0.973458	+	1.33985i	−0.940280	+	0.340401i	$0.889437\pi$
$762$	171178.	−	13472.0i	0.294807	−	0.0232018i
$763$	448544.	+	617368.i	0.770471	+	1.06046i
$764$	−162172.	−	189879.i	−0.277836	−	0.325304i
$765$	−355052.	−	857171.i	−0.606693	−	1.46469i
$766$	−342984.	+	210181.i	−0.584542	+	0.358208i
$767$	−29193.1	+	370933.i	−0.0496237	+	0.630528i
$768$	−36880.0	+	43181.0i	−0.0625272	+	0.0732099i
$769$	687015.	+	223225.i	1.16175	+	0.377476i	0.825558	−	0.564317i	$-0.190860\pi$
$769$	687015.	+	223225.i	1.16175	+	0.377476i	0.336193	+	0.941793i	$0.390860\pi$
$770$	427352.	−	427352.i	0.720782	−	0.720782i
$771$	−687901.	−	1.35008e6i	−1.15722	−	2.27118i
$772$	−16786.9	−	69922.6i	−0.0281668	−	0.117323i
$773$	−197743.	+	823657.i	−0.330934	+	1.37844i	0.520449	+	0.853893i	$0.325765\pi$
$773$	−197743.	+	823657.i	−0.330934	+	1.37844i	−0.851382	+	0.524545i	$0.824235\pi$
$774$	47899.9	+	24406.2i	0.0799563	+	0.0407398i
$775$	−17810.0	−	54813.7i	−0.0296525	−	0.0912611i
$776$	14017.2	−	33840.5i	0.0232776	−	0.0561971i
$777$	−15922.3	−	100529.i	−0.0263733	−	0.166514i
$778$		−	291561.i		−	0.481694i
$779$	636.903	−	258098.i	0.00104954	−	0.425315i
$780$	177267.			0.291366
$781$	−632746.	+	100217.i	−1.03736	+	0.164301i
$782$	−751290.	−	311195.i	−1.22855	−	0.508884i
$783$	−267907.	+	87048.2i	−0.436979	+	0.141983i
$784$	57921.3	−	113677.i	0.0942337	−	0.184944i
$785$	−89920.7	−	21588.0i	−0.145922	−	0.0350327i
$786$	−97113.0	+	23314.8i	−0.157193	+	0.0377386i
$787$	−56.0736	+	28.5709i	−9.05334e−5	+	4.61291e-5i	−0.454036	−	0.890983i	$-0.650016\pi$
$787$	−56.0736	+	28.5709i	−9.05334e−5	+	4.61291e-5i	0.453945	+	0.891030i	$0.350016\pi$
$788$	−285016.	−	285016.i	−0.459005	−	0.459005i
$789$	−401910.	+	1.23695e6i	−0.645616	+	1.98700i
$790$	−498117.	−	425432.i	−0.798136	−	0.681672i
$791$	858316.	+	67551.0i	1.37181	+	0.107964i
$792$	176853.	+	288598.i	0.281944	+	0.460091i
$793$	−283276.	+	117337.i	−0.450468	+	0.186590i
$794$	36276.9	−	30983.4i	0.0575425	−	0.0491459i
$795$	−1.37065e6	+	995835.i	−2.16866	+	1.57563i
$796$	−29833.3	−	379068.i	−0.0470842	−	0.598262i
$797$	−362849.	−	263625.i	−0.571228	−	0.415021i	0.264323	−	0.964434i	$-0.414851\pi$
$797$	−362849.	−	263625.i	−0.571228	−	0.415021i	−0.835551	+	0.549413i	$0.814851\pi$
$798$	−208540.	+	340306.i	−0.327479	+	0.534398i
$799$	−87115.8	+	550028.i	−0.136459	+	0.861571i
$800$	−9074.38	−	1437.24i	−0.0141787	−	0.00224569i
$801$	−869717.	−	532963.i	−1.35554	−	0.830677i
$802$	240157.	−	330548.i	0.373376	−	0.513908i
$803$	561474.	−	44189.0i	0.870760	−	0.0685303i
$804$	−183192.	−	252142.i	−0.283397	−	0.390062i
$805$	851984.	+	997545.i	1.31474	+	1.53936i
$806$	−81978.2	−	197913.i	−0.126191	−	0.304652i
$807$	550024.	−	337055.i	0.844568	−	0.517552i
$808$	−34716.1	+	441110.i	−0.0531751	+	0.675654i
$809$	307986.	−	360606.i	0.470581	−	0.550980i	−0.473457	−	0.880817i	$-0.656994\pi$
$809$	307986.	−	360606.i	0.470581	−	0.550980i	0.944038	+	0.329837i	$0.106994\pi$
$810$	206372.	+	67054.3i	0.314544	+	0.102201i
$811$	−527207.	+	527207.i	−0.801566	+	0.801566i	−0.983340	−	0.181774i	$-0.941816\pi$
$811$	−527207.	+	527207.i	−0.801566	+	0.801566i	0.181774	+	0.983340i	$0.441816\pi$
$812$	−161936.	−	317818.i	−0.245602	−	0.482021i
$813$	−343724.	−	1.43171e6i	−0.520030	−	2.16608i
$814$	−9835.94	+	40969.7i	−0.0148446	+	0.0618320i
$815$	−79435.0	−	40474.1i	−0.119590	−	0.0609344i
$816$	95458.0	+	293790.i	0.143361	+	0.441221i
$817$	10042.2	−	24243.9i	0.0150447	−	0.0363211i
$818$	29271.7	+	184814.i	0.0437463	+	0.276203i
$819$		−	491696.i		−	0.733042i
$820$	122589.	+	298033.i	0.182315	+	0.443238i
$821$	−18407.3			−0.0273089			−0.0136545	−	0.999907i	$-0.504346\pi$
$821$	−18407.3			−0.0273089			−0.0136545	+	0.999907i	$0.504346\pi$
$822$	12531.3	−	1984.76i	0.0185460	−	0.00293741i
$823$	408002.	+	169000.i	0.602369	+	0.249509i	0.662962	−	0.748653i	$-0.269299\pi$
$823$	408002.	+	169000.i	0.602369	+	0.249509i	−0.0605931	+	0.998163i	$0.519299\pi$
$824$	−416277.	+	135257.i	−0.613095	+	0.199207i
$825$	−42969.4	+	84332.1i	−0.0631322	+	0.123904i
$826$	1.01710e6	+	244184.i	1.49074	+	0.357896i
$827$	995435.	−	238983.i	1.45546	−	0.349426i	0.572903	−	0.819623i	$-0.305817\pi$
$827$	995435.	−	238983.i	1.45546	−	0.349426i	0.882562	+	0.470197i	$0.155817\pi$
$828$	−654629.	+	333550.i	−0.954849	+	0.486520i
$829$	925988.	+	925988.i	1.34740	+	1.34740i	0.888476	+	0.458923i	$0.151765\pi$
$829$	925988.	+	925988.i	1.34740	+	1.34740i	0.458923	+	0.888476i	$0.348235\pi$
$830$	214732.	−	660878.i	0.311703	−	0.959323i
$831$	−253362.	−	216392.i	−0.366893	−	0.313356i
$832$	−34043.3	−	2679.27i	−0.0491797	−	0.00387052i
$833$	−362627.	−	591753.i	−0.522601	−	0.852807i
$834$	678834.	−	281182.i	0.975959	−	0.404256i
$835$	828945.	−	707986.i	1.18892	−	1.01543i
$836$	133666.	−	97113.7i	0.191252	−	0.138953i
$837$	37314.5	+	474126.i	0.0532632	+	0.676773i
$838$	−21223.1	−	15419.5i	−0.0302219	−	0.0219575i
$839$	291256.	−	475286.i	0.413762	−	0.675198i	−0.576077	−	0.817396i	$-0.695417\pi$
$839$	291256.	−	475286.i	0.413762	−	0.675198i	0.989838	+	0.142198i	$0.0454170\pi$
$840$	77957.3	−	492203.i	0.110484	−	0.697567i
$841$	251759.	+	39874.7i	0.355954	+	0.0563775i
$842$	251112.	+	153881.i	0.354195	+	0.217051i
$843$	1.24799e6	−	1.71771e6i	1.75613	−	2.41710i
$844$	−87101.8	+	6855.06i	−0.122276	+	0.00962335i
$845$	−339634.	−	467466.i	−0.475661	−	0.654692i
$846$	326762.	+	382589.i	0.456552	+	0.534554i
$847$	87566.9	+	211405.i	0.122060	+	0.294679i
$848$	278278.	−	170529.i	0.386979	−	0.237141i
$849$	−90801.2	+	1.15374e6i	−0.125973	+	1.60063i
$850$	−32458.2	+	38003.7i	−0.0449249	+	0.0526003i
$851$	−86980.8	−	28261.8i	−0.120106	−	0.0390248i
$852$	−373524.	+	373524.i	−0.514564	+	0.514564i
$853$	263552.	+	517251.i	0.362217	+	0.710891i	0.998147	−	0.0608563i	$-0.0193831\pi$
$853$	263552.	+	517251.i	0.362217	+	0.710891i	−0.635930	+	0.771747i	$0.719383\pi$
$854$	201222.	+	838150.i	0.275905	+	1.14923i
$855$	−95519.7	+	397868.i	−0.130666	+	0.544261i
$856$	270137.	+	137642.i	0.368669	+	0.187846i
$857$	146637.	+	451301.i	0.199655	+	0.614475i	0.999891	+	0.0147895i	$0.00470782\pi$
$857$	146637.	+	451301.i	0.199655	+	0.614475i	−0.800235	+	0.599686i	$0.795292\pi$
$858$	−134626.	+	325015.i	−0.182874	+	0.441498i
$859$	99073.0	+	625522.i	0.134267	+	0.847728i	0.959248	+	0.282567i	$0.0911859\pi$
$859$	99073.0	+	625522.i	0.134267	+	0.847728i	−0.824981	+	0.565161i	$0.808814\pi$
$860$			32764.8i			0.0443007i
$861$	1.42878e6	−	587695.i	1.92735	−	0.792767i
$862$	−201824.			−0.271618
$863$	−946054.	+	149840.i	−1.27027	+	0.201190i	−0.754934	−	0.655801i	$-0.772331\pi$
$863$	−946054.	+	149840.i	−1.27027	+	0.201190i	−0.515331	+	0.856991i	$0.672331\pi$
$864$	70043.0	+	29012.7i	0.0938290	+	0.0388652i
$865$	−43136.7	+	14016.0i	−0.0576520	+	0.0187323i
$866$	−139122.	+	273042.i	−0.185506	+	0.364077i
$867$	508036.	+	121969.i	0.675859	+	0.162259i
$868$	−585579.	+	140585.i	−0.777224	+	0.186595i
$869$	1.15831e6	−	590189.i	1.53386	−	0.781541i
$870$	−446909.	−	446909.i	−0.590447	−	0.590447i
$871$	57915.7	−	178246.i	0.0763414	−	0.234955i
$872$	−198068.	−	169166.i	−0.260484	−	0.222474i
$873$	−179468.	−	14124.4i	−0.235482	−	0.0185328i
$874$	187384.	+	305783.i	0.245307	+	0.400305i
$875$	991760.	−	410801.i	1.29536	−	0.536556i
$876$	353134.	−	301605.i	0.460184	−	0.393034i
$877$	293087.	−	212940.i	0.381063	−	0.276859i	−0.380720	−	0.924690i	$-0.624324\pi$
$877$	293087.	−	212940.i	0.381063	−	0.276859i	0.761784	+	0.647832i	$0.224324\pi$
$878$	55925.2	+	710597.i	0.0725468	+	0.921794i
$879$	−1.69937e6	−	1.23467e6i	−2.19944	−	1.59798i
$880$	−107787.	+	175893.i	−0.139188	+	0.227134i
$881$	−82423.0	+	520398.i	−0.106193	+	0.670477i	0.875958	+	0.482387i	$0.160230\pi$
$881$	−82423.0	+	520398.i	−0.106193	+	0.670477i	−0.982152	+	0.188091i	$0.939770\pi$
$882$	−619322.	−	98091.0i	−0.796122	−	0.126093i
$883$	351678.	+	215508.i	0.451049	+	0.276403i	0.729414	−	0.684072i	$-0.239793\pi$
$883$	351678.	+	215508.i	0.451049	+	0.276403i	−0.278366	+	0.960475i	$0.589793\pi$
$884$	−109188.	+	150284.i	−0.139724	+	0.192313i
$885$	1.84769e6	−	145416.i	2.35907	−	0.185663i
$886$	−30759.5	−	42336.8i	−0.0391843	−	0.0539325i
$887$	100095.	+	117196.i	0.127223	+	0.148959i	0.820361	−	0.571846i	$-0.193772\pi$
$887$	100095.	+	117196.i	0.127223	+	0.148959i	−0.693138	+	0.720805i	$0.743772\pi$
$888$	13295.2	+	32097.4i	0.0168604	+	0.0407047i
$889$	247500.	−	151668.i	0.313164	−	0.191907i
$890$	48776.4	−	619762.i	0.0615785	−	0.782429i
$891$	−279671.	+	327453.i	−0.352284	+	0.412471i
$892$	−69923.3	−	22719.5i	−0.0878805	−	0.0285541i
$893$	173662.	−	173662.i	0.217772	−	0.217772i
$894$	−421885.	−	827997.i	−0.527861	−	1.03599i
$895$	227608.	+	948054.i	0.284145	+	1.18355i
$896$	−22410.6	+	93347.0i	−0.0279150	+	0.116274i
$897$	−680385.	−	346674.i	−0.845610	−	0.430860i
$898$	139977.	+	430804.i	0.173581	+	0.534229i
$899$	−292283.	+	705634.i	−0.361646	+	0.873092i
$900$	7063.74	+	44598.7i	0.00872067	+	0.0550601i
$901$		−	1.77540e6i		−	2.18699i
$902$	−639535.	−	1578.17i	−0.786052	−	0.00193972i
$903$	157076.			0.192634
$904$	−290262.	+	45972.9i	−0.355183	+	0.0562555i
$905$	−1.02589e6	−	424938.i	−1.25258	−	0.518834i
$906$	237763.	−	77253.9i	0.289660	−	0.0941161i
$907$	−522523.	+	1.02551e6i	−0.635172	+	1.24659i	0.319119	+	0.947715i	$0.396613\pi$
$907$	−522523.	+	1.02551e6i	−0.635172	+	1.24659i	−0.954291	+	0.298880i	$0.903387\pi$
$908$	50283.3	+	12071.9i	0.0609890	+	0.0146422i
$909$	2.11458e6	−	507666.i	2.55916	−	0.614399i
$910$	267012.	−	136050.i	0.322440	−	0.164291i
$911$	−232483.	−	232483.i	−0.280126	−	0.280126i	0.553033	−	0.833159i	$-0.313470\pi$
$911$	−232483.	−	232483.i	−0.280126	−	0.280126i	−0.833159	+	0.553033i	$0.813470\pi$
$912$	42098.6	−	129566.i	0.0506149	−	0.155777i
$913$	1.04862e6	+	895609.i	1.25799	+	1.07443i
$914$	−559175.	−	44008.0i	−0.669353	−	0.0526792i
$915$	798018.	+	1.30225e6i	0.953170	+	1.55543i
$916$	−390224.	+	161636.i	−0.465075	+	0.192640i
$917$	−128385.	+	109651.i	−0.152677	+	0.130399i
$918$	333649.	−	242410.i	0.395917	−	0.287651i
$919$	−95114.5	−	1.20854e6i	−0.112620	−	1.43097i	−0.750517	−	0.660851i	$-0.770195\pi$
$919$	−95114.5	−	1.20854e6i	−0.112620	−	1.43097i	0.637897	−	0.770122i	$-0.279805\pi$
$920$	−362264.	−	263201.i	−0.428006	−	0.310965i
$921$	−875714.	+	1.42904e6i	−1.03239	+	1.68470i
$922$	12141.1	−	76655.6i	0.0142822	−	0.0901742i
$923$	−313747.	−	49692.7i	−0.368278	−	0.0583296i
$924$	843236.	+	516736.i	0.987655	+	0.605236i
$925$	−3303.88	+	4547.39i	−0.00386136	+	0.00531471i
$926$	−170273.	+	13400.8i	−0.198575	+	0.0156282i
$927$	1.26444e6	+	1.74036e6i	1.47143	+	2.02525i
$928$	79072.0	+	92581.4i	0.0918178	+	0.107505i
$929$	499528.	+	1.20597e6i	0.578799	+	1.39735i	0.893891	+	0.448284i	$0.147965\pi$
$929$	499528.	+	1.20597e6i	0.578799	+	1.39735i	−0.315092	+	0.949061i	$0.602035\pi$
$930$	−909823.	+	557541.i	−1.05194	+	0.644630i
$931$	−24014.5	+	305133.i	−0.0277060	+	0.352039i
$932$	−6570.68	+	7693.28i	−0.00756447	+	0.00885686i
$933$	−752580.	−	244528.i	−0.864548	−	0.280909i
$934$	614021.	−	614021.i	0.703866	−	0.703866i
$935$	509462.	+	999876.i	0.582758	+	1.14373i
$936$	39179.9	+	163196.i	0.0447210	+	0.186276i
$937$	257944.	−	1.07441e6i	0.293796	−	1.22375i	−0.608822	−	0.793307i	$-0.708358\pi$
$937$	257944.	−	1.07441e6i	0.293796	−	1.22375i	0.902618	−	0.430442i	$-0.141642\pi$
$938$	−469452.	−	239198.i	−0.533562	−	0.271864i
$939$	−69461.9	−	213782.i	−0.0787799	−	0.242460i
$940$	−117349.	+	283306.i	−0.132808	+	0.320627i
$941$	−204163.	−	1.28903e6i	−0.230567	−	1.45574i	−0.782914	−	0.622130i	$-0.786267\pi$
$941$	−204163.	−	1.28903e6i	−0.230567	−	1.45574i	0.552346	−	0.833615i	$-0.313733\pi$
$942$		−	151325.i		−	0.170533i
$943$	112332.	−	1.38365e6i	0.126322	−	1.55597i
$944$	−357037.			−0.400654
$945$	−657123.	+	104078.i	−0.735840	+	0.116546i
$946$	−60073.3	−	24883.2i	−0.0671273	−	0.0278051i
$947$	−404933.	+	131571.i	−0.451527	+	0.146710i	−0.525948	−	0.850517i	$-0.676289\pi$
$947$	−404933.	+	131571.i	−0.451527	+	0.146710i	0.0744208	+	0.997227i	$0.476289\pi$
$948$	486648.	−	955101.i	0.541500	−	1.06275i
$949$	271551.	+	65193.7i	0.301522	+	0.0723891i
$950$	21432.2	−	5145.42i	0.0237476	−	0.00570130i
$951$	18075.2	−	9209.78i	0.0199858	−	0.0101833i
$952$	369264.	+	369264.i	0.407439	+	0.407439i
$953$	−89890.5	+	276654.i	−0.0989755	+	0.304615i	−0.988269	−	0.152721i	$-0.951196\pi$
$953$	−89890.5	+	276654.i	−0.0989755	+	0.304615i	0.889294	+	0.457336i	$0.151196\pi$
$954$	−1.21973e6	−	1.04175e6i	−1.34019	−	1.14463i
$955$	−745674.	−	58685.8i	−0.817603	−	0.0643467i
$956$	−133066.	−	217144.i	−0.145596	−	0.237592i
$957$	1.15880e6	−	479991.i	1.26527	−	0.524094i
$958$	−367814.	+	314143.i	−0.400772	+	0.342292i
$959$	17352.2	−	12607.1i	0.0188676	−	0.0137081i
$960$	13345.9	+	169576.i	0.0144813	+	0.184002i
$961$	296083.	+	215117.i	0.320602	+	0.232931i
$962$	−10916.1	+	17813.4i	−0.0117955	+	0.0192485i
$963$	233099.	−	1.47173e6i	0.251356	−	1.58700i
$964$	−668202.	−	105833.i	−0.719041	−	0.113885i
$965$	−183658.	−	112546.i	−0.197222	−	0.120858i
$966$	−1.26179e6	+	1.73671e6i	−1.35218	+	1.86111i
$967$	−977871.	+	76960.1i	−1.04575	+	0.0823024i	−0.589677	−	0.807639i	$-0.700745\pi$
$967$	−977871.	+	76960.1i	−1.04575	+	0.0823024i	−0.456074	+	0.889942i	$0.650745\pi$
$968$	−45909.2	−	63188.7i	−0.0489947	−	0.0674355i
$969$	−481297.	−	563527.i	−0.512585	−	0.600160i
$970$	−41987.6	−	101367.i	−0.0446249	−	0.107734i
$971$	−324740.	+	199001.i	−0.344427	+	0.211065i	−0.683944	−	0.729535i	$-0.739737\pi$
$971$	−324740.	+	199001.i	−0.344427	+	0.211065i	0.339516	+	0.940600i	$0.389737\pi$
$972$	−49152.6	+	624543.i	−0.0520252	+	0.661043i
$973$	806705.	−	944530.i	0.852097	−	0.997677i
$974$	712986.	+	231663.i	0.751559	+	0.244196i
$975$	−33185.4	+	33185.4i	−0.0349090	+	0.0349090i
$976$	−133573.	−	262152.i	−0.140223	−	0.275203i
$977$	98065.9	+	408474.i	0.102737	+	0.427932i	0.999905	−	0.0137573i	$-0.00437924\pi$
$977$	98065.9	+	408474.i	0.102737	+	0.427932i	−0.897168	+	0.441690i	$0.854379\pi$
$978$	34056.4	−	141855.i	0.0356059	−	0.148309i
$979$	1.09927e6	+	560108.i	1.14694	+	0.584395i
$980$	−118095.	−	363460.i	−0.122965	−	0.378447i
$981$	−489906.	+	1.18274e6i	−0.509067	+	1.22900i
$982$	−173495.	−	1.09540e6i	−0.179914	−	1.13593i
$983$		−	1.41750e6i		−	1.46695i	−0.679714	−	0.733477i	$-0.737896\pi$
$983$		−	1.41750e6i		−	1.46695i	0.679714	−	0.733477i	$-0.262104\pi$
$984$	−427390.	+	308908.i	−0.441401	+	0.319036i
$985$	−1.20738e6			−1.24443
$986$	654156.	−	103608.i	0.672865	−	0.106571i
$987$	1.35818e6	+	562577.i	1.39419	+	0.577494i
$988$	77914.5	−	25315.9i	0.0798186	−	0.0259346i
$989$	64076.6	−	125757.i	0.0655099	−	0.128570i
$990$	985868.	+	236686.i	1.00588	+	0.241492i
$991$	993258.	−	238460.i	1.01138	−	0.242811i	0.306298	−	0.951936i	$-0.400910\pi$
$991$	993258.	−	238460.i	1.01138	−	0.242811i	0.705083	+	0.709125i	$0.250910\pi$
$992$	183154.	−	93321.6i	0.186120	−	0.0948329i
$993$	−1.40147e6	−	1.40147e6i	−1.42130	−	1.42130i
$994$	−275955.	+	849301.i	−0.279296	+	0.859586i
$995$	−866089.	−	739710.i	−0.874816	−	0.747163i
$996$	1.13359e6	+	89215.7i	1.14272	+	0.0899337i
$997$	16098.3	+	26270.0i	0.0161953	+	0.0264283i	0.860635	−	0.509222i	$-0.170067\pi$
$997$	16098.3	+	26270.0i	0.0161953	+	0.0264283i	−0.844440	+	0.535650i	$0.820067\pi$
$998$	474688.	−	196622.i	0.476593	−	0.197411i
$999$	35269.8	−	30123.2i	0.0353404	−	0.0301836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.h.a.11.1	✓	112
41.15	odd	40	inner	82.5.h.a.15.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.h.a.11.1	✓	112	1.1	even	1	trivial
82.5.h.a.15.1	yes	112	41.15	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+(-2.79360 + 0.442463i) q^{2} +(-12.8086 - 5.30550i) q^{3} +(7.60845 - 2.47214i) q^{4} +(10.8792 - 21.3516i) q^{5} +(38.1297 + 9.15413i) q^{6} +(64.4592 - 15.4753i) q^{7} +(-20.1612 + 10.2726i) q^{8} +(78.6367 + 78.6367i) q^{9} +(-20.9448 + 64.4615i) q^{10} +(-102.282 - 87.3569i) q^{11} +(-110.570 - 8.70202i) q^{12} +(-34.8488 - 56.8681i) q^{13} +(-173.226 + 71.7527i) q^{14} +(-252.628 + 215.765i) q^{15} +(51.7771 - 37.6183i) q^{16} +(-27.3153 - 347.074i) q^{17} +(-254.474 - 184.886i) q^{18} +(-80.2239 + 130.914i) q^{19} +(29.9896 - 189.347i) q^{20} +(-907.738 - 143.772i) q^{21} +(324.387 + 198.785i) q^{22} +(-485.403 + 668.101i) q^{23} +(312.738 - 24.6130i) q^{24} +(29.8326 + 41.0610i) q^{25} +(122.516 + 143.448i) q^{26} +(-160.274 - 386.936i) q^{27} +(452.178 - 277.095i) q^{28} +(52.7712 - 670.521i) q^{29} +(610.275 - 714.540i) q^{30} +(-1079.98 - 350.908i) q^{31} +(-128.000 + 128.000i) q^{32} +(846.616 + 1661.58i) q^{33} +(229.876 + 957.502i) q^{34} +(370.841 - 1544.66i) q^{35} +(792.704 + 403.903i) q^{36} +(34.2228 + 105.327i) q^{37} +(166.189 - 401.217i) q^{38} +(144.651 + 913.292i) q^{39} +542.230i q^{40} +(-1435.45 + 874.781i) q^{41} +2599.47 q^{42} +(-168.806 + 26.7363i) q^{43} +(-994.165 - 411.796i) q^{44} +(2534.52 - 823.515i) q^{45} +(1060.42 - 2081.18i) q^{46} +(-1555.37 - 373.411i) q^{47} +(-862.777 + 207.134i) q^{48} +(1776.20 - 905.021i) q^{49} +(-101.508 - 101.508i) q^{50} +(-1491.53 + 4590.46i) q^{51} +(-405.731 - 346.527i) q^{52} +(5083.84 + 400.107i) q^{53} +(618.948 + 1010.03i) q^{54} +(-2977.95 + 1233.51i) q^{55} +(-1140.60 + 974.166i) q^{56} +(1722.12 - 1251.19i) q^{57} +(149.259 + 1896.52i) q^{58} +(-4513.27 - 3279.08i) q^{59} +(-1388.71 + 2266.17i) q^{60} +(719.158 - 4540.58i) q^{61} +(3172.31 + 502.444i) q^{62} +(6285.79 + 3851.94i) q^{63} +(300.946 - 414.217i) q^{64} +(-1593.35 + 125.399i) q^{65} +(-3100.30 - 4267.20i) q^{66} +(1824.97 + 2136.76i) q^{67} +(-1065.84 - 2573.17i) q^{68} +(9761.96 - 5982.13i) q^{69} +(-352.526 + 4479.26i) q^{70} +(3093.15 - 3621.62i) q^{71} +(-2393.21 - 777.602i) q^{72} +(-2960.76 + 2960.76i) q^{73} +(-142.208 - 279.099i) q^{74} +(-164.265 - 684.212i) q^{75} +(-286.744 + 1194.37i) q^{76} +(-7944.88 - 4048.12i) q^{77} +(-808.197 - 2487.37i) q^{78} +(-3698.55 + 8929.09i) q^{79} +(-239.917 - 1514.78i) q^{80} -3201.48i q^{81} +(3623.02 - 3078.93i) q^{82} -10252.3 q^{83} +(-7261.90 + 1150.17i) q^{84} +(-7707.75 - 3192.65i) q^{85} +(459.748 - 149.381i) q^{86} +(-4233.38 + 8308.47i) q^{87} +(2959.51 + 710.515i) q^{88} +(-8918.74 + 2141.20i) q^{89} +(-6716.07 + 3422.01i) q^{90} +(-3126.38 - 3126.38i) q^{91} +(-2041.53 + 6283.19i) q^{92} +(11971.3 + 10224.5i) q^{93} +(4510.30 + 354.969i) q^{94} +(1922.44 + 3137.14i) q^{95} +(2318.61 - 960.399i) q^{96} +(-1230.93 + 1051.31i) q^{97} +(-4561.57 + 3314.17i) q^{98} +(-1173.64 - 14912.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 56 q^{2} - 16 q^{6} + 448 q^{8} - 24 q^{9} - 512 q^{11} + 576 q^{12} + 60 q^{13} - 192 q^{14} + 340 q^{15} + 1792 q^{16} + 1416 q^{17} - 416 q^{18} - 600 q^{19} - 1300 q^{21} + 2608 q^{22} - 800 q^{23}+ \cdots + 106864 q^{99}+O(q^{100}) \) 112 * q - 56 * q^2 - 16 * q^6 + 448 * q^8 - 24 * q^9 - 512 * q^11 + 576 * q^12 + 60 * q^13 - 192 * q^14 + 340 * q^15 + 1792 * q^16 + 1416 * q^17 - 416 * q^18 - 600 * q^19 - 1300 * q^21 + 2608 * q^22 - 800 * q^23 - 128 * q^24 + 3360 * q^25 - 1848 * q^26 - 2148 * q^27 - 768 * q^28 + 2564 * q^29 - 6952 * q^30 - 8220 * q^31 - 14336 * q^32 + 16000 * q^33 + 3840 * q^34 + 12184 * q^35 + 2048 * q^36 + 3908 * q^37 + 1984 * q^38 + 4928 * q^39 + 2396 * q^41 - 16320 * q^42 + 9608 * q^43 - 1312 * q^44 - 26000 * q^45 - 5072 * q^46 - 16900 * q^47 - 2560 * q^48 - 2832 * q^49 + 27952 * q^50 - 16452 * q^51 + 2688 * q^52 + 22296 * q^53 + 29576 * q^54 - 35048 * q^55 - 1536 * q^56 - 1912 * q^57 + 1696 * q^58 - 25136 * q^59 + 1472 * q^60 + 2880 * q^61 - 2816 * q^62 + 28536 * q^63 - 1844 * q^65 + 2480 * q^66 - 45464 * q^67 + 5152 * q^68 - 19924 * q^69 - 16392 * q^70 + 9512 * q^71 - 4480 * q^72 + 25412 * q^73 + 26376 * q^74 + 21900 * q^75 - 15104 * q^76 + 45036 * q^77 - 4928 * q^78 + 21116 * q^79 - 29544 * q^82 - 14952 * q^83 - 10400 * q^84 + 44656 * q^85 - 30800 * q^86 + 22580 * q^87 + 3648 * q^88 - 40436 * q^89 + 40640 * q^90 - 5068 * q^91 - 6848 * q^92 - 4704 * q^93 + 13848 * q^94 + 52372 * q^95 + 1024 * q^96 + 36404 * q^97 - 10368 * q^98 + 106864 * q^99

Introduction

L-functions

Modular forms

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Database

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