LMFDB - Embedded newform 36.5.f.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23562 + 3.31693i) q^{2} +(3.18543 - 8.41742i) q^{3} +(-6.00404 - 14.8308i) q^{4} +(-23.3466 + 40.4374i) q^{5} +(20.7986 + 29.3840i) q^{6} +(-52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 - 53.6263i) q^{9} +O(q^{10})$	\(q+(-2.23562 + 3.31693i) q^{2} +(3.18543 - 8.41742i) q^{3} +(-6.00404 - 14.8308i) q^{4} +(-23.3466 + 40.4374i) q^{5} +(20.7986 + 29.3840i) q^{6} +(-52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 - 53.6263i) q^{9} +(-81.9341 - 167.841i) q^{10} +(-63.7631 + 36.8136i) q^{11} +(-143.962 + 3.29614i) q^{12} +(15.5924 - 27.0068i) q^{13} +(16.8104 - 241.609i) q^{14} +(266.010 + 325.329i) q^{15} +(-183.903 + 178.089i) q^{16} +53.8013 q^{17} +(313.590 - 81.4697i) q^{18} +54.9619i q^{19} +(739.891 + 103.459i) q^{20} +(87.7977 + 537.815i) q^{21} +(20.4416 - 293.799i) q^{22} +(243.863 + 140.795i) q^{23} +(310.911 - 484.882i) q^{24} +(-777.624 - 1346.88i) q^{25} +(54.7210 + 112.096i) q^{26} +(-644.770 + 340.165i) q^{27} +(763.818 + 595.904i) q^{28} +(223.597 + 387.282i) q^{29} +(-1673.79 + 155.026i) q^{30} +(240.584 + 138.901i) q^{31} +(-179.572 - 1008.13i) q^{32} +(106.763 + 653.989i) q^{33} +(-120.279 + 178.455i) q^{34} -2827.19i q^{35} +(-430.837 + 1222.29i) q^{36} +1016.51 q^{37} +(-182.305 - 122.874i) q^{38} +(-177.659 - 217.276i) q^{39} +(-1997.28 + 2222.87i) q^{40} +(-946.158 + 1638.79i) q^{41} +(-1980.18 - 911.129i) q^{42} +(666.266 - 384.669i) q^{43} +(928.811 + 724.625i) q^{44} +(3585.79 - 1202.81i) q^{45} +(-1012.19 + 494.115i) q^{46} +(-2374.81 + 1371.10i) q^{47} +(913.240 + 2115.28i) q^{48} +(632.546 - 1095.60i) q^{49} +(6205.98 + 431.792i) q^{50} +(171.381 - 452.869i) q^{51} +(-494.148 - 69.0969i) q^{52} -4647.69 q^{53} +(313.155 - 2899.14i) q^{54} -3437.89i q^{55} +(-3684.18 + 1201.32i) q^{56} +(462.637 + 175.078i) q^{57} +(-1784.46 - 124.157i) q^{58} +(262.792 + 151.723i) q^{59} +(3227.74 - 5898.42i) q^{60} +(-478.174 - 828.222i) q^{61} +(-998.577 + 487.469i) q^{62} +(4806.69 + 974.145i) q^{63} +(3745.36 + 1658.17i) q^{64} +(728.057 + 1261.03i) q^{65} +(-2407.91 - 1107.94i) q^{66} +(6010.96 + 3470.43i) q^{67} +(-323.026 - 797.915i) q^{68} +(1961.94 - 1604.21i) q^{69} +(9377.58 + 6320.51i) q^{70} +5971.60i q^{71} +(-3091.07 - 4161.63i) q^{72} -4339.17 q^{73} +(-2272.53 + 3371.70i) q^{74} +(-13814.4 + 2255.18i) q^{75} +(815.127 - 329.993i) q^{76} +(2229.00 - 3860.75i) q^{77} +(1117.87 - 103.537i) q^{78} +(-3294.15 + 1901.88i) q^{79} +(-2907.96 - 11594.3i) q^{80} +(809.440 + 6510.88i) q^{81} +(-3320.52 - 6802.05i) q^{82} +(2730.64 - 1576.53i) q^{83} +(7449.07 - 4531.17i) q^{84} +(-1256.08 + 2175.59i) q^{85} +(-213.596 + 3069.93i) q^{86} +(3972.17 - 648.452i) q^{87} +(-4479.99 + 1460.82i) q^{88} -7132.44 q^{89} +(-4026.82 + 14582.8i) q^{90} +1888.18i q^{91} +(623.925 - 4462.02i) q^{92} +(1935.55 - 1582.63i) q^{93} +(761.331 - 10942.3i) q^{94} +(-2222.52 - 1283.17i) q^{95} +(-9057.89 - 1699.80i) q^{96} +(980.405 + 1698.11i) q^{97} +(2219.91 + 4547.46i) q^{98} +(5844.98 + 1184.57i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.23562	+	3.31693i	−0.558904	+	0.829232i
$2$	−2.23562	+	3.31693i	−0.558904	+	0.829232i
$3$	3.18543	−	8.41742i	0.353937	−	0.935269i
$3$	3.18543	−	8.41742i	0.353937	−	0.935269i
$4$	−6.00404	−	14.8308i	−0.375253	−	0.926923i
$5$	−23.3466	+	40.4374i	−0.933862	+	1.61750i	−0.157212	+	0.987565i	$0.550251\pi$
$5$	−23.3466	+	40.4374i	−0.933862	+	1.61750i	−0.776650	+	0.629932i	$0.783083\pi$
$6$	20.7986	+	29.3840i	0.577739	+	0.816222i
$7$	−52.4363	+	30.2741i	−1.07013	+	0.617839i	−0.928217	−	0.372040i	$-0.878659\pi$
$7$	−52.4363	+	30.2741i	−1.07013	+	0.617839i	−0.141913	+	0.989879i	$0.545325\pi$
$8$	62.6153	+	13.2409i	0.978364	+	0.206889i
$9$	−60.7060	−	53.6263i	−0.749457	−	0.662053i
$10$	−81.9341	−	167.841i	−0.819341	−	1.67841i
$11$	−63.7631	+	36.8136i	−0.526968	+	0.304245i	−0.739781	−	0.672848i	$-0.765071\pi$
$11$	−63.7631	+	36.8136i	−0.526968	+	0.304245i	0.212813	+	0.977093i	$0.431737\pi$
$12$	−143.962	+	3.29614i	−0.999738	+	0.0228898i
$13$	15.5924	−	27.0068i	0.0922626	−	0.159803i	−0.816200	−	0.577769i	$-0.803923\pi$
$13$	15.5924	−	27.0068i	0.0922626	−	0.159803i	0.908463	+	0.417966i	$0.137257\pi$
$14$	16.8104	−	241.609i	0.0857671	−	1.23270i
$15$	266.010	+	325.329i	1.18227	+	1.44590i
$16$	−183.903	+	178.089i	−0.718371	+	0.695660i
$17$	53.8013			0.186164			0.0930819	−	0.995658i	$-0.470328\pi$
$17$	53.8013			0.186164			0.0930819	+	0.995658i	$0.470328\pi$
$18$	313.590	−	81.4697i	0.967870	−	0.251450i
$19$			54.9619i			0.152249i	0.997098	+	0.0761245i	$0.0242546\pi$
$19$			54.9619i			0.152249i	−0.997098	+	0.0761245i	$0.975745\pi$
$20$	739.891	+	103.459i	1.84973	+	0.258648i
$21$	87.7977	+	537.815i	0.199088	+	1.21954i
$22$	20.4416	−	293.799i	0.0422346	−	0.607023i
$23$	243.863	+	140.795i	0.460990	+	0.266152i	0.712460	−	0.701712i	$-0.247581\pi$
$23$	243.863	+	140.795i	0.460990	+	0.266152i	−0.251471	+	0.967865i	$0.580914\pi$
$24$	310.911	−	484.882i	0.539777	−	0.841808i
$25$	−777.624	−	1346.88i	−1.24420	−	2.15501i
$26$	54.7210	+	112.096i	0.0809483	+	0.165822i
$27$	−644.770	+	340.165i	−0.884459	+	0.466619i
$28$	763.818	+	595.904i	0.974258	+	0.760081i
$29$	223.597	+	387.282i	0.265871	+	0.460502i	0.967791	−	0.251753i	$-0.0810072\pi$
$29$	223.597	+	387.282i	0.265871	+	0.460502i	−0.701921	+	0.712255i	$0.747674\pi$
$30$	−1673.79	+	155.026i	−1.85976	+	0.172252i
$31$	240.584	+	138.901i	0.250347	+	0.144538i	0.619923	−	0.784663i	$-0.287164\pi$
$31$	240.584	+	138.901i	0.250347	+	0.144538i	−0.369576	+	0.929200i	$0.620497\pi$
$32$	−179.572	−	1008.13i	−0.175364	−	0.984504i
$33$	106.763	+	653.989i	0.0980375	+	0.600540i
$34$	−120.279	+	178.455i	−0.104048	+	0.154373i
$35$		−	2827.19i		−	2.30791i
$36$	−430.837	+	1222.29i	−0.332436	+	0.943126i
$37$	1016.51			0.742522			0.371261	−	0.928528i	$-0.378925\pi$
$37$	1016.51			0.742522			0.371261	+	0.928528i	$0.378925\pi$
$38$	−182.305	−	122.874i	−0.126250	−	0.0850926i
$39$	−177.659	−	217.276i	−0.116804	−	0.142851i
$40$	−1997.28	+	2222.87i	−1.24830	+	1.38930i
$41$	−946.158	+	1638.79i	−0.562854	+	0.974892i	0.434392	+	0.900724i	$0.356963\pi$
$41$	−946.158	+	1638.79i	−0.562854	+	0.974892i	−0.997246	+	0.0741680i	$0.976370\pi$
$42$	−1980.18	−	911.129i	−1.12255	−	0.516513i
$43$	666.266	−	384.669i	0.360339	−	0.208042i	−0.308891	−	0.951098i	$-0.599958\pi$
$43$	666.266	−	384.669i	0.360339	−	0.208042i	0.669229	+	0.743056i	$0.266624\pi$
$44$	928.811	+	724.625i	0.479758	+	0.374290i
$45$	3585.79	−	1202.81i	1.77076	−	0.593978i
$46$	−1012.19	+	494.115i	−0.478351	+	0.233514i
$47$	−2374.81	+	1371.10i	−1.07506	+	0.620687i	−0.929560	−	0.368671i	$-0.879813\pi$
$47$	−2374.81	+	1371.10i	−1.07506	+	0.620687i	−0.145502	+	0.989358i	$0.546480\pi$
$48$	913.240	+	2115.28i	0.396371	+	0.918090i
$49$	632.546	−	1095.60i	0.263451	−	0.456311i
$50$	6205.98	+	431.792i	2.48239	+	0.172717i
$51$	171.381	−	452.869i	0.0658903	−	0.174113i
$52$	−494.148	−	69.0969i	−0.182747	−	0.0255536i
$53$	−4647.69			−1.65457			−0.827286	−	0.561780i	$-0.810117\pi$
$53$	−4647.69			−1.65457			−0.827286	+	0.561780i	$0.810117\pi$
$54$	313.155	−	2899.14i	0.107392	−	0.994217i
$55$		−	3437.89i		−	1.13649i
$56$	−3684.18	+	1201.32i	−1.17480	+	0.383074i
$57$	462.637	+	175.078i	0.142394	+	0.0538866i
$58$	−1784.46	−	124.157i	−0.530459	−	0.0369076i
$59$	262.792	+	151.723i	0.0754934	+	0.0435861i	0.537272	−	0.843409i	$-0.319455\pi$
$59$	262.792	+	151.723i	0.0754934	+	0.0435861i	−0.461778	+	0.886995i	$0.652788\pi$
$60$	3227.74	−	5898.42i	0.896593	−	1.63845i
$61$	−478.174	−	828.222i	−0.128507	−	0.222580i	0.794591	−	0.607145i	$-0.207685\pi$
$61$	−478.174	−	828.222i	−0.128507	−	0.222580i	−0.923098	+	0.384564i	$0.874352\pi$
$62$	−998.577	+	487.469i	−0.259776	+	0.126813i
$63$	4806.69	+	974.145i	1.21106	+	0.245438i
$64$	3745.36	+	1658.17i	0.914394	+	0.404826i
$65$	728.057	+	1261.03i	0.172321	+	0.298469i
$66$	−2407.91	−	1107.94i	−0.552781	−	0.254349i
$67$	6010.96	+	3470.43i	1.33904	+	0.773096i	0.986665	−	0.162762i	$-0.0520403\pi$
$67$	6010.96	+	3470.43i	1.33904	+	0.773096i	0.352376	+	0.935858i	$0.385374\pi$
$68$	−323.026	−	797.915i	−0.0698585	−	0.172559i
$69$	1961.94	−	1604.21i	0.412086	−	0.336948i
$70$	9377.58	+	6320.51i	1.91379	+	1.28990i
$71$			5971.60i			1.18461i	0.805715	+	0.592303i	$0.201781\pi$
$71$			5971.60i			1.18461i	−0.805715	+	0.592303i	$0.798219\pi$
$72$	−3091.07	−	4161.63i	−0.596270	−	0.802784i
$73$	−4339.17			−0.814257			−0.407128	−	0.913371i	$-0.633470\pi$
$73$	−4339.17			−0.814257			−0.407128	+	0.913371i	$0.633470\pi$
$74$	−2272.53	+	3371.70i	−0.414999	+	0.615724i
$75$	−13814.4	+	2255.18i	−2.45589	+	0.400920i
$76$	815.127	−	329.993i	0.141123	−	0.0571318i
$77$	2229.00	−	3860.75i	0.375949	−	0.651163i
$78$	1117.87	−	103.537i	0.183739	−	0.0170179i
$79$	−3294.15	+	1901.88i	−0.527824	+	0.304740i	−0.740130	−	0.672464i	$-0.765236\pi$
$79$	−3294.15	+	1901.88i	−0.527824	+	0.304740i	0.212306	+	0.977203i	$0.431903\pi$
$80$	−2907.96	−	11594.3i	−0.454369	−	1.81161i
$81$	809.440	+	6510.88i	0.123371	+	0.992361i
$82$	−3320.52	−	6802.05i	−0.493831	−	1.01161i
$83$	2730.64	−	1576.53i	0.396376	−	0.228848i	−0.288543	−	0.957467i	$-0.593171\pi$
$83$	2730.64	−	1576.53i	0.396376	−	0.228848i	0.684919	+	0.728619i	$0.259837\pi$
$84$	7449.07	−	4531.17i	1.05571	−	0.642173i
$85$	−1256.08	+	2175.59i	−0.173851	+	0.301119i
$86$	−213.596	+	3069.93i	−0.0288799	+	0.415080i
$87$	3972.17	−	648.452i	0.524795	−	0.0856721i
$88$	−4479.99	+	1460.82i	−0.578512	+	0.188639i
$89$	−7132.44			−0.900447			−0.450224	−	0.892916i	$-0.648656\pi$
$89$	−7132.44			−0.900447			−0.450224	+	0.892916i	$0.648656\pi$
$90$	−4026.82	+	14582.8i	−0.497138	+	1.80035i
$91$			1888.18i			0.228014i
$92$	623.925	−	4462.02i	0.0737152	−	0.527176i
$93$	1935.55	−	1582.63i	0.223789	−	0.182985i
$94$	761.331	−	10942.3i	0.0861624	−	1.23838i
$95$	−2222.52	−	1283.17i	−0.246262	−	0.142180i
$96$	−9057.89	−	1699.80i	−0.982844	−	0.184440i
$97$	980.405	+	1698.11i	0.104199	+	0.180477i	0.913411	−	0.407040i	$-0.133439\pi$
$97$	980.405	+	1698.11i	0.104199	+	0.180477i	−0.809212	+	0.587517i	$0.800106\pi$
$98$	2219.91	+	4547.46i	0.231144	+	0.473496i
$99$	5844.98	+	1184.57i	0.596366	+	0.120862i
$100$	−15306.4	+	19619.5i	−1.53064	+	1.96195i
$101$	3849.96	+	6668.32i	0.377410	+	0.653693i	0.990685	−	0.136177i	$-0.0434815\pi$
$101$	3849.96	+	6668.32i	0.377410	+	0.653693i	−0.613275	+	0.789870i	$0.710148\pi$
$102$	1118.99	+	1580.90i	0.107554	+	0.151951i
$103$	−3195.22	−	1844.76i	−0.301180	−	0.173886i	0.341793	−	0.939775i	$-0.388966\pi$
$103$	−3195.22	−	1844.76i	−0.301180	−	0.173886i	−0.642973	+	0.765889i	$0.722299\pi$
$104$	1333.92	−	1484.58i	0.123328	−	0.137258i
$105$	−23797.6	−	9005.82i	−2.15852	−	0.816854i
$106$	10390.5	−	15416.1i	0.924747	−	1.37203i
$107$		−	13741.5i		−	1.20024i	−0.799911	−	0.600118i	$-0.795120\pi$
$107$		−	13741.5i		−	1.20024i	0.799911	−	0.600118i	$-0.204880\pi$
$108$	8916.14	+	7520.07i	0.764415	+	0.644725i
$109$	18709.9			1.57478			0.787388	−	0.616458i	$-0.211433\pi$
$109$	18709.9			1.57478			0.787388	+	0.616458i	$0.211433\pi$
$110$	11403.2	+	7685.80i	0.942416	+	0.635190i
$111$	3238.04	−	8556.42i	0.262806	−	0.694458i
$112$	4251.71	−	14905.8i	0.338944	−	1.18828i
$113$	5000.50	−	8661.12i	0.391613	−	0.678293i	−0.601050	−	0.799212i	$-0.705251\pi$
$113$	5000.50	−	8661.12i	0.391613	−	0.678293i	0.992662	+	0.120919i	$0.0385840\pi$
$114$	−1615.00	+	1143.13i	−0.124269	+	0.0879601i
$115$	−11386.7	+	6574.14i	−0.861002	+	0.497099i
$116$	4401.20	−	5641.38i	0.327081	−	0.419246i
$117$	−2394.83	+	803.313i	−0.174945	+	0.0586831i
$118$	−1090.76	+	532.469i	−0.0783366	+	0.0382411i
$119$	−2821.15	+	1628.79i	−0.199219	+	0.115019i
$120$	12348.7	+	23892.8i	0.857545	+	1.65922i
$121$	−4610.01	+	7984.77i	−0.314870	+	0.545371i
$122$	3816.17	+	265.516i	0.256394	+	0.0178390i
$123$	10780.5	+	13184.5i	0.712572	+	0.871471i
$124$	615.534	−	4402.00i	0.0400321	−	0.286291i
$125$	43436.1			2.77991
$126$	−13977.1	+	13765.6i	−0.880391	+	0.867072i
$127$		−	18883.8i		−	1.17080i	−0.810745	−	0.585400i	$-0.800937\pi$
$127$		−	18883.8i		−	1.17080i	0.810745	−	0.585400i	$-0.199063\pi$
$128$	−13873.2	+	8716.06i	−0.846753	+	0.531986i
$129$	−1115.57	−	6833.58i	−0.0670377	−	0.410647i
$130$	−5810.41	−	404.269i	−0.343811	−	0.0239212i
$131$	25700.9	+	14838.4i	1.49763	+	0.864660i	0.999996	−	0.00272458i	$-0.000867262\pi$
$131$	25700.9	+	14838.4i	1.49763	+	0.864660i	0.497639	+	0.867384i	$0.334201\pi$
$132$	9058.14	−	5509.95i	0.519866	−	0.316228i
$133$	−1663.92	−	2882.00i	−0.0940654	−	0.162926i
$134$	−24949.4	+	12179.4i	−1.38947	+	0.678290i
$135$	1297.77	−	34014.5i	0.0712080	−	1.86637i
$136$	3368.79	+	712.379i	0.182136	+	0.0385153i
$137$	−8332.79	−	14432.8i	−0.443965	−	0.768971i	0.554014	−	0.832507i	$-0.313095\pi$
$137$	−8332.79	−	14432.8i	−0.443965	−	0.768971i	−0.997980	+	0.0635366i	$0.979762\pi$
$138$	934.908	+	10094.0i	0.0490920	+	0.530036i
$139$	−3545.95	−	2047.25i	−0.183528	−	0.105960i	0.405421	−	0.914130i	$-0.367125\pi$
$139$	−3545.95	−	2047.25i	−0.183528	−	0.105960i	−0.588949	+	0.808170i	$0.700458\pi$
$140$	−41929.3	+	16974.5i	−2.13925	+	0.866048i
$141$	3976.30	+	24357.3i	0.200005	+	1.22516i
$142$	−19807.4	−	13350.2i	−0.982314	−	0.662081i
$143$			2296.05i			0.112282i
$144$	20714.3	−	949.039i	0.998952	−	0.0457677i
$145$	−20880.9			−0.993147
$146$	9700.73	−	14392.7i	0.455091	−	0.675208i
$147$	−7207.21	−	8814.38i	−0.333528	−	0.407903i
$148$	−6103.19	−	15075.7i	−0.278633	−	0.688261i
$149$	2934.59	−	5082.86i	0.132183	−	0.228947i	−0.792335	−	0.610086i	$-0.791135\pi$
$149$	2934.59	−	5082.86i	0.132183	−	0.228947i	0.924518	+	0.381139i	$0.124468\pi$
$150$	23403.3	−	50863.0i	1.04015	−	2.26058i
$151$	−28725.6	+	16584.7i	−1.25984	+	0.727369i	−0.973043	−	0.230622i	$-0.925924\pi$
$151$	−28725.6	+	16584.7i	−1.25984	+	0.727369i	−0.286797	+	0.957991i	$0.592591\pi$
$152$	−727.745	+	3441.46i	−0.0314987	+	0.148955i
$153$	−3266.07	−	2885.17i	−0.139522	−	0.123250i
$154$	7822.63	+	16024.6i	0.329846	+	0.675687i
$155$	−11233.6	+	6485.72i	−0.467579	+	0.269957i
$156$	−2155.70	+	3939.35i	−0.0885805	+	0.161873i
$157$	−11089.2	+	19207.1i	−0.449886	+	0.779226i	−0.998378	−	0.0569302i	$-0.981869\pi$
$157$	−11089.2	+	19207.1i	−0.449886	+	0.779226i	0.548492	+	0.836156i	$0.315202\pi$
$158$	1056.06	−	15178.3i	0.0423033	−	0.608009i
$159$	−14804.9	+	39121.6i	−0.585615	+	1.54747i
$160$	44958.6	+	16275.0i	1.75620	+	0.635741i
$161$	−17049.7			−0.657758
$162$	−23405.7	−	11871.0i	−0.891850	−	0.452331i
$163$		−	31303.8i		−	1.17821i	−0.808057	−	0.589104i	$-0.799481\pi$
$163$		−	31303.8i		−	1.17821i	0.808057	−	0.589104i	$-0.200519\pi$
$164$	29985.3	+	4192.86i	1.11486	+	0.155891i
$165$	−28938.2	−	10951.2i	−1.06293	−	0.402247i
$166$	−875.403	+	12581.8i	−0.0317682	+	0.456592i
$167$	−22551.7	−	13020.2i	−0.808622	−	0.466858i	0.0378548	−	0.999283i	$-0.487948\pi$
$167$	−22551.7	−	13020.2i	−0.808622	−	0.466858i	−0.846477	+	0.532425i	$0.821281\pi$
$168$	−1623.68	+	34838.0i	−0.0575284	+	1.23434i
$169$	13794.3	+	23892.4i	0.482975	+	0.836538i
$170$	−4408.17	−	9030.10i	−0.152532	−	0.312460i
$171$	2947.40	−	3336.52i	0.100797	−	0.114104i
$172$	−9705.23	−	7571.67i	−0.328057	−	0.255938i
$173$	−7830.38	−	13562.6i	−0.261632	−	0.453160i	0.705044	−	0.709164i	$-0.250927\pi$
$173$	−7830.38	−	13562.6i	−0.261632	−	0.453160i	−0.966676	+	0.256004i	$0.917594\pi$
$174$	−6729.38	+	14625.1i	−0.222268	+	0.483059i
$175$	81551.5	+	47083.8i	2.66290	+	1.53743i
$176$	5170.12	−	18125.6i	0.166907	−	0.585151i
$177$	2114.23	−	1728.73i	0.0674846	−	0.0551799i
$178$	15945.4	−	23657.8i	0.503264	−	0.746680i
$179$			36836.7i			1.14967i	0.818268	+	0.574837i	$0.194935\pi$
$179$			36836.7i			1.14967i	−0.818268	+	0.574837i	$0.805065\pi$
$180$	−39367.7	−	45958.2i	−1.21505	−	1.41846i
$181$	56961.0			1.73868			0.869342	−	0.494211i	$-0.164543\pi$
$181$	56961.0			1.73868			0.869342	+	0.494211i	$0.164543\pi$
$182$	−6262.97	−	4221.25i	−0.189076	−	0.127438i
$183$	−8494.68	+	1386.75i	−0.253656	+	0.0414090i
$184$	13405.3	+	12044.9i	0.395952	+	0.355768i
$185$	−23732.1	+	41105.2i	−0.693414	+	1.20103i
$186$	922.334	+	9958.25i	0.0266601	+	0.287844i
$187$	−3430.54	+	1980.62i	−0.0981024	+	0.0566394i
$188$	34592.9	+	26988.1i	0.978749	+	0.763584i
$189$	23511.2	−	37356.9i	0.658190	−	1.04580i
$190$	9224.88	−	4503.26i	0.255537	−	0.124744i
$191$	33837.1	−	19535.9i	0.927527	−	0.535508i	0.0414986	−	0.999139i	$-0.486787\pi$
$191$	33837.1	−	19535.9i	0.927527	−	0.535508i	0.886029	+	0.463630i	$0.153453\pi$
$192$	25888.1	−	26244.3i	0.702259	−	0.711921i
$193$	−2025.97	+	3509.08i	−0.0543898	+	0.0942059i	−0.891938	−	0.452157i	$-0.850655\pi$
$193$	−2025.97	+	3509.08i	−0.0543898	+	0.0942059i	0.837549	+	0.546363i	$0.183988\pi$
$194$	−7824.33	−	544.391i	−0.207895	−	0.0144646i
$195$	12933.8	−	2111.43i	0.340140	−	0.0555274i
$196$	−20046.5	−	2803.10i	−0.521826	−	0.0729670i
$197$	−44869.6			−1.15617			−0.578083	−	0.815978i	$-0.696199\pi$
$197$	−44869.6			−1.15617			−0.578083	+	0.815978i	$0.696199\pi$
$198$	−16996.3	+	16739.2i	−0.433534	+	0.426976i
$199$			56256.7i			1.42059i	0.703905	+	0.710294i	$0.251438\pi$
$199$			56256.7i			1.42059i	−0.703905	+	0.710294i	$0.748562\pi$
$200$	−30857.2	−	94632.0i	−0.771430	−	2.36580i
$201$	48359.6	−	39542.0i	1.19699	−	0.978737i
$202$	−30725.4	−	2137.77i	−0.752999	−	0.0523912i
$203$	−23449.3	−	13538.4i	−0.569032	−	0.328531i
$204$	−7745.36	+	177.337i	−0.186115	+	0.00426126i
$205$	−44179.1	−	76520.4i	−1.05126	−	1.82083i
$206$	13262.2	−	6474.13i	0.312523	−	0.152562i
$207$	−7253.68	−	21624.6i	−0.169285	−	0.504669i
$208$	1942.13	+	7743.46i	0.0448902	+	0.178982i
$209$	−2023.35	−	3504.54i	−0.0463210	−	0.0802303i
$210$	83074.0	−	58801.5i	1.88376	−	1.33337i
$211$	−63309.8	−	36552.0i	−1.42202	−	0.821005i	−0.425551	−	0.904935i	$-0.639920\pi$
$211$	−63309.8	−	36552.0i	−1.42202	−	0.821005i	−0.996472	+	0.0839298i	$0.973253\pi$
$212$	27905.0	+	68928.9i	0.620883	+	1.53366i
$213$	50265.5	+	19022.1i	1.10793	+	0.419276i
$214$	45579.6	+	30720.7i	0.995275	+	0.670817i
$215$			35922.8i			0.777129i
$216$	−44876.6	+	12762.2i	−0.961861	+	0.273538i
$217$	−16820.4			−0.357205
$218$	−41828.2	+	62059.5i	−0.880149	+	1.30586i
$219$	−13822.2	+	36524.7i	−0.288196	+	0.761549i
$220$	−50986.5	+	20641.2i	−1.05344	+	0.426472i
$221$	838.891	−	1453.00i	0.0171760	−	0.0297496i
$222$	21142.0	+	29869.2i	0.428984	+	0.606063i
$223$	65737.1	−	37953.3i	1.32191	−	0.763203i	0.337873	−	0.941192i	$-0.390292\pi$
$223$	65737.1	−	37953.3i	1.32191	−	0.763203i	0.984032	+	0.177989i	$0.0569591\pi$
$224$	39936.4	+	47426.3i	0.795927	+	0.945200i
$225$	−25022.0	+	123465.i	−0.494261	+	2.43881i
$226$	17549.1	+	35949.3i	0.343589	+	0.703839i
$227$	35712.5	−	20618.6i	0.693057	−	0.400136i	−0.111700	−	0.993742i	$-0.535629\pi$
$227$	35712.5	−	20618.6i	0.693057	−	0.400136i	0.804756	+	0.593606i	$0.202296\pi$
$228$	−181.162	−	7912.44i	−0.00348496	−	0.152209i
$229$	−13792.1	+	23888.7i	−0.263003	+	0.455534i	−0.967038	−	0.254630i	$-0.918046\pi$
$229$	−13792.1	+	23888.7i	−0.263003	+	0.455534i	0.704036	+	0.710165i	$0.251379\pi$
$230$	3650.43	−	52466.3i	0.0690063	−	0.991801i
$231$	−25397.2	−	31060.6i	−0.475950	−	0.582084i
$232$	8872.66	+	27210.4i	0.164846	+	0.505544i
$233$	49430.2			0.910502			0.455251	−	0.890363i	$-0.349550\pi$
$233$	49430.2			0.910502			0.455251	+	0.890363i	$0.349550\pi$
$234$	2689.38	−	9739.36i	0.0491157	−	0.177868i
$235$		−	128042.i		−	2.31855i
$236$	672.355	−	4808.36i	0.0120719	−	0.0863323i
$237$	5515.62	+	33786.6i	0.0981968	+	0.601517i
$238$	904.420	−	12998.9i	0.0159667	−	0.229484i
$239$	−97042.8	−	56027.7i	−1.69890	−	0.980859i	−0.946808	−	0.321800i	$-0.895712\pi$
$239$	−97042.8	−	56027.7i	−1.69890	−	0.980859i	−0.752091	−	0.659060i	$-0.770955\pi$
$240$	−106857.	−	12455.4i	−1.85516	−	0.216240i
$241$	−20548.3	−	35590.7i	−0.353787	−	0.612776i	0.633123	−	0.774051i	$-0.281773\pi$
$241$	−20548.3	−	35590.7i	−0.353787	−	0.612776i	−0.986910	+	0.161275i	$0.948439\pi$
$242$	−16178.7	−	33142.0i	−0.276257	−	0.565910i
$243$	57383.2	+	13926.6i	0.971790	+	0.235848i
$244$	−9412.18	+	12064.4i	−0.158092	+	0.202640i
$245$	29535.6	+	51157.1i	0.492054	+	0.852263i
$246$	−67833.0	+	6282.70i	−1.12091	+	0.103819i
$247$	1484.34	+	856.986i	0.0243299	+	0.0140469i
$248$	13225.0	+	11882.9i	0.215027	+	0.193205i
$249$	−4572.08	−	28006.9i	−0.0737421	−	0.451716i
$250$	−97106.5	+	144075.i	−1.55370	+	2.30519i
$251$		−	50848.1i		−	0.807099i	−0.914958	−	0.403550i	$-0.867776\pi$
$251$		−	50848.1i		−	0.807099i	0.914958	−	0.403550i	$-0.132224\pi$
$252$	−14412.3	−	77135.7i	−0.226950	−	1.21466i
$253$	−20732.7			−0.323902
$254$	62636.4	+	42217.0i	0.970865	+	0.654365i
$255$	14311.7	+	17503.1i	0.220095	+	0.269175i
$256$	2104.60	−	65502.2i	0.0321137	−	0.999484i
$257$	−6405.02	+	11093.8i	−0.0969738	+	0.167964i	−0.910431	−	0.413662i	$-0.864250\pi$
$257$	−6405.02	+	11093.8i	−0.0969738	+	0.167964i	0.813457	+	0.581625i	$0.197583\pi$
$258$	25160.5	+	11577.0i	0.377990	+	0.173923i
$259$	−53302.2	+	30774.1i	−0.794595	+	0.458760i
$260$	14330.8	−	18368.9i	0.211994	−	0.271730i
$261$	7194.80	−	35501.0i	0.105618	−	0.521147i
$262$	−106675.	+	52075.1i	−1.55404	+	0.758625i
$263$	−27445.5	+	15845.6i	−0.396789	+	0.229086i	−0.685097	−	0.728452i	$-0.740240\pi$
$263$	−27445.5	+	15845.6i	−0.396789	+	0.229086i	0.288309	+	0.957537i	$0.406907\pi$
$264$	−1974.41	+	42363.3i	−0.0283289	+	0.607830i
$265$	108508.	−	187941.i	1.54514	−	2.67627i
$266$	13279.3	+	923.929i	0.187677	+	0.0130580i
$267$	−22719.9	+	60036.8i	−0.318702	+	0.842161i
$268$	15379.1	−	109984.i	0.214121	−	1.53129i
$269$	−54892.9			−0.758598			−0.379299	−	0.925274i	$-0.623835\pi$
$269$	−54892.9			−0.758598			−0.379299	+	0.925274i	$0.623835\pi$
$270$	109923.	+	80348.0i	1.50785	+	1.10217i
$271$			106332.i			1.44785i	0.689877	+	0.723927i	$0.257665\pi$
$271$			106332.i			1.44785i	−0.689877	+	0.723927i	$0.742335\pi$
$272$	−9894.23	+	9581.43i	−0.133735	+	0.129507i
$273$	15893.6	+	6014.68i	0.213254	+	0.0807026i
$274$	66501.5	+	4626.96i	0.885789	+	0.0616303i
$275$	99167.4	+	57254.3i	1.31130	+	0.757082i
$276$	−35571.2	−	19465.3i	−0.466961	−	0.255531i
$277$	25166.6	+	43589.8i	0.327993	+	0.568100i	0.982113	−	0.188290i	$-0.0602945\pi$
$277$	25166.6	+	43589.8i	0.327993	+	0.568100i	−0.654121	+	0.756390i	$0.726961\pi$
$278$	14718.0	−	7184.78i	0.190440	−	0.0929660i
$279$	−7156.12	−	21333.7i	−0.0919326	−	0.274068i
$280$	37434.5	−	177025.i	0.477481	−	2.25797i
$281$	3048.20	+	5279.64i	0.0386039	+	0.0668640i	0.884682	−	0.466195i	$-0.154376\pi$
$281$	3048.20	+	5279.64i	0.0386039	+	0.0668640i	−0.846078	+	0.533059i	$0.821042\pi$
$282$	−89681.0	−	41264.5i	−1.12772	−	0.518894i
$283$	44494.8	+	25689.1i	0.555567	+	0.320757i	0.751364	−	0.659888i	$-0.229396\pi$
$283$	44494.8	+	25689.1i	0.555567	+	0.320757i	−0.195797	+	0.980644i	$0.562729\pi$
$284$	88563.4	−	35853.7i	1.09804	−	0.444527i
$285$	−17880.7	+	14620.4i	−0.220138	+	0.179999i
$286$	−7615.83	−	5133.08i	−0.0931076	−	0.0627547i
$287$		−	114576.i		−	1.39101i
$288$	−43161.3	+	70829.5i	−0.520366	+	0.853943i
$289$	−80626.4			−0.965343
$290$	46681.7	−	69260.5i	0.555074	−	0.823550i
$291$	17416.7	−	2843.26i	0.205675	−	0.0335761i
$292$	26052.6	+	64353.3i	0.305552	+	0.754753i
$293$	−45640.7	+	79051.9i	−0.531639	+	0.920825i	0.467679	+	0.883898i	$0.345090\pi$
$293$	−45640.7	+	79051.9i	−0.531639	+	0.920825i	−0.999318	+	0.0369270i	$0.988243\pi$
$294$	45349.2	−	4200.25i	0.524657	−	0.0485938i
$295$	−12270.6	+	7084.43i	−0.141001	+	0.0814068i
$296$	63649.3	+	13459.6i	0.726457	+	0.153620i
$297$	28589.8	−	45426.3i	0.324115	−	0.514985i
$298$	10298.9	+	21097.1i	0.115973	+	0.237570i
$299$	7604.82	−	4390.65i	0.0850642	−	0.0491118i
$300$	116388.	+	191337.i	1.29320	+	2.12597i
$301$	−23291.0	+	40341.3i	−0.257073	+	0.445263i
$302$	9209.03	−	132358.i	0.100972	−	1.45123i
$303$	68393.9	−	11165.2i	0.744958	−	0.121614i
$304$	−9788.11	−	10107.7i	−0.105914	−	0.109371i
$305$	44654.9			0.480031
$306$	16871.6	−	4383.18i	0.180182	−	0.0468109i
$307$			108180.i			1.14781i	0.818923	+	0.573904i	$0.194572\pi$
$307$			108180.i			1.14781i	−0.818923	+	0.573904i	$0.805428\pi$
$308$	−70640.8	−	9877.73i	−0.744654	−	0.104125i
$309$	−25706.3	+	21019.1i	−0.269229	+	0.220139i
$310$	3601.33	−	51760.6i	0.0374749	−	0.538612i
$311$	86673.2	+	50040.8i	0.896116	+	0.517373i	0.875938	−	0.482424i	$-0.160243\pi$
$311$	86673.2	+	50040.8i	0.896116	+	0.517373i	0.0201778	+	0.999796i	$0.493577\pi$
$312$	−8247.25	−	15957.2i	−0.0847227	−	0.163926i
$313$	75895.3	+	131455.i	0.774687	+	1.34180i	0.934970	+	0.354726i	$0.115426\pi$
$313$	75895.3	+	131455.i	0.774687	+	1.34180i	−0.160283	+	0.987071i	$0.551241\pi$
$314$	−38917.4	−	79722.0i	−0.394716	−	0.808572i
$315$	−151612.	+	171627.i	−1.52796	+	1.72968i
$316$	47984.5	+	37435.8i	0.480537	+	0.374898i
$317$	−56202.0	−	97344.7i	−0.559285	−	0.968710i	−0.997556	−	0.0698672i	$-0.977742\pi$
$317$	−56202.0	−	97344.7i	−0.559285	−	0.968710i	0.438271	−	0.898843i	$-0.355591\pi$
$318$	−96665.5	−	136568.i	−0.955910	−	1.35050i
$319$	−28514.5	−	16462.9i	−0.280211	−	0.161780i
$320$	−154493.	+	112740.i	−1.50872	+	1.10098i
$321$	−115668.	−	43772.7i	−1.12254	−	0.424808i
$322$	38116.7	−	56552.8i	0.367624	−	0.545434i
$323$			2957.02i			0.0283433i
$324$	91701.4	−	51096.2i	0.873546	−	0.486742i
$325$	−48500.0			−0.459172
$326$	103832.	+	69983.3i	0.977008	+	0.658505i
$327$	59599.2	−	157489.i	0.557372	−	1.47284i
$328$	−80943.1	+	90085.6i	−0.752371	+	0.837351i
$329$	83017.6	−	143791.i	0.766970	−	1.32843i
$330$	101019.	−	71503.2i	0.927629	−	0.656595i
$331$	99528.9	−	57463.0i	0.908433	−	0.524484i	0.0285065	−	0.999594i	$-0.490925\pi$
$331$	99528.9	−	57463.0i	0.908433	−	0.524484i	0.879927	+	0.475109i	$0.157592\pi$
$332$	−39776.0	−	31031.8i	−0.360865	−	0.281534i
$333$	−61708.5	−	54511.8i	−0.556488	−	0.491589i
$334$	93604.0	−	45694.1i	0.839076	−	0.409607i
$335$	−280670.	+	162045.i	−2.50096	+	1.44393i
$336$	−111925.	−	83270.0i	−0.991401	−	0.737581i
$337$	−61646.2	+	106774.i	−0.542808	+	0.940171i	0.455933	+	0.890014i	$0.349306\pi$
$337$	−61646.2	+	106774.i	−0.542808	+	0.940171i	−0.998741	+	0.0501573i	$0.984028\pi$
$338$	−110088.	−	7659.55i	−0.963621	−	0.0670456i
$339$	−56975.6	−	69680.8i	−0.495780	−	0.606336i
$340$	39807.2	+	5566.25i	0.344353	+	0.0481509i
$341$	−20453.8			−0.175900
$342$	4477.73	+	17235.5i	0.0382830	+	0.147357i
$343$		−	68777.2i		−	0.584597i
$344$	46811.9	−	15264.2i	0.395584	−	0.128990i
$345$	19065.6	+	116789.i	0.160181	+	0.981210i
$346$	62492.0	+	4347.99i	0.522002	+	0.0363192i
$347$	82843.4	+	47829.7i	0.688017	+	0.397227i	0.802869	−	0.596156i	$-0.203306\pi$
$347$	82843.4	+	47829.7i	0.688017	+	0.397227i	−0.114852	+	0.993383i	$0.536639\pi$
$348$	−33466.1	−	55017.0i	−0.276342	−	0.454295i
$349$	−21543.6	−	37314.5i	−0.176875	−	0.306357i	0.763934	−	0.645295i	$-0.223266\pi$
$349$	−21543.6	−	37314.5i	−0.176875	−	0.306357i	−0.940809	+	0.338938i	$0.889932\pi$
$350$	−338491.	+	165239.i	−2.76319	+	1.34889i
$351$	−866.734	+	22717.2i	−0.00703512	+	0.184391i
$352$	48563.1	+	57670.9i	0.391941	+	0.465448i
$353$	56436.9	+	97751.7i	0.452912	+	0.784467i	0.998565	−	0.0535440i	$-0.0170517\pi$
$353$	56436.9	+	97751.7i	0.452912	+	0.784467i	−0.545653	+	0.838011i	$0.683718\pi$
$354$	1007.48	+	10877.5i	0.00803949	+	0.0868007i
$355$	−241476.	−	139416.i	−1.91610	−	1.10626i
$356$	42823.5	+	105780.i	0.337895	+	0.834645i
$357$	4723.63	+	28935.2i	0.0370629	+	0.227033i
$358$	−122185.	−	82352.8i	−0.953348	−	0.642558i
$359$			223134.i			1.73132i	0.500632	+	0.865660i	$0.333101\pi$
$359$			223134.i			1.73132i	−0.500632	+	0.865660i	$0.666899\pi$
$360$	240451.	−	27835.0i	1.85533	−	0.214776i
$361$	127300.			0.976820
$362$	−127343.	+	188936.i	−0.971758	+	1.44177i
$363$	52526.3	+	64239.4i	0.398624	+	0.487515i
$364$	28003.2	−	11336.7i	0.211351	−	0.0855628i
$365$	101305.	−	175465.i	0.760404	−	1.31706i
$366$	14391.1	−	31276.5i	0.107432	−	0.233483i
$367$	92257.6	−	53265.0i	0.684968	−	0.395466i	−0.116756	−	0.993161i	$-0.537250\pi$
$367$	92257.6	−	53265.0i	0.684968	−	0.395466i	0.801724	+	0.597694i	$0.203916\pi$
$368$	−69921.2	+	17536.9i	−0.516313	+	0.129496i
$369$	145320.	−	48745.7i	1.06727	−	0.358000i
$370$	−83287.1	−	170613.i	−0.608379	−	1.24626i
$371$	243708.	−	140705.i	1.77061	−	1.02226i
$372$	−35092.8	−	19203.5i	−0.253590	−	0.138770i
$373$	−71440.5	+	123739.i	−0.513484	+	0.889380i	0.486394	+	0.873740i	$0.338312\pi$
$373$	−71440.5	+	123739.i	−0.513484	+	0.889380i	−0.999878	+	0.0156403i	$0.995021\pi$
$374$	1099.78	−	15806.8i	0.00786256	−	0.113006i
$375$	138363.	−	365620.i	0.983914	−	2.59997i
$376$	−166854.	+	54407.1i	−1.18022	+	0.384840i
$377$	13945.7			0.0981197
$378$	71348.1	+	161501.i	0.499343	+	1.13029i
$379$			95242.7i			0.663061i	0.943445	+	0.331530i	$0.107565\pi$
$379$			95242.7i			0.663061i	−0.943445	+	0.331530i	$0.892435\pi$
$380$	−5686.32	+	40665.8i	−0.0393789	+	0.281619i
$381$	−158953.	−	60153.2i	−1.09501	−	0.414390i
$382$	−10847.7	+	155910.i	−0.0743381	+	1.06843i
$383$	−46899.6	−	27077.5i	−0.319721	−	0.184591i	0.331547	−	0.943439i	$-0.392429\pi$
$383$	−46899.6	−	27077.5i	−0.319721	−	0.184591i	−0.651268	+	0.758848i	$0.725763\pi$
$384$	29174.6	+	144541.i	0.197853	+	0.980232i
$385$	104079.	+	180270.i	0.702169	+	1.21619i
$386$	−7110.07	−	14564.9i	−0.0477199	−	0.0977538i
$387$	−61074.8	−	12377.7i	−0.407793	−	0.0826451i
$388$	19297.9	−	24735.7i	0.128188	−	0.164309i
$389$	−6513.23	−	11281.2i	−0.0430425	−	0.0745518i	0.843702	−	0.536813i	$-0.180372\pi$
$389$	−6513.23	−	11281.2i	−0.0430425	−	0.0745518i	−0.886744	+	0.462261i	$0.847038\pi$
$390$	−21911.6	+	47620.9i	−0.144060	+	0.313089i
$391$	13120.2	+	7574.94i	0.0858196	+	0.0495480i
$392$	54113.9	−	60226.0i	0.352157	−	0.391933i
$393$	206770.	−	169069.i	1.33876	−	1.09466i
$394$	100311.	−	148829.i	0.646185	−	0.958730i
$395$		−	177609.i		−	1.13834i
$396$	−17525.5	−	93797.8i	−0.111758	−	0.598139i
$397$	54407.2			0.345204			0.172602	−	0.984992i	$-0.444783\pi$
$397$	54407.2			0.345204			0.172602	+	0.984992i	$0.444783\pi$
$398$	−186599.	−	125768.i	−1.17800	−	0.793972i
$399$	−29559.3	+	4825.53i	−0.185673	+	0.0303109i
$400$	382872.	+	109210.i	2.39295	+	0.682560i
$401$	−25211.2	+	43667.1i	−0.156785	+	0.271560i	−0.933708	−	0.358036i	$-0.883446\pi$
$401$	−25211.2	+	43667.1i	−0.156785	+	0.271560i	0.776922	+	0.629596i	$0.216780\pi$
$402$	23044.4	+	248806.i	0.142598	+	1.53960i
$403$	7502.54	−	4331.59i	0.0461953	−	0.0266709i
$404$	75781.0	−	97134.7i	0.464299	−	0.595130i
$405$	−282181.	−	119275.i	−1.72035	−	0.727175i
$406$	97329.6	−	47512.8i	0.590463	−	0.288243i
$407$	−64816.0	+	37421.6i	−0.391285	+	0.225909i
$408$	16727.4	−	26087.3i	0.100487	−	0.156714i
$409$	−20416.9	+	35363.2i	−0.122052	+	0.211400i	−0.920577	−	0.390562i	$-0.872281\pi$
$409$	−20416.9	+	35363.2i	−0.122052	+	0.211400i	0.798525	+	0.601962i	$0.205614\pi$
$410$	352580.	+	24531.4i	2.09744	+	0.145933i
$411$	−148031.	+	24165.8i	−0.876331	+	0.143060i
$412$	−8174.97	+	58463.5i	−0.0481606	+	0.344422i
$413$	−18373.2			−0.107717
$414$	87943.6	+	24284.3i	0.513102	+	0.141685i
$415$			147226.i			0.854850i
$416$	−30026.4	−	10869.5i	−0.173507	−	0.0628091i
$417$	−28528.0	+	23326.3i	−0.164059	+	0.134145i
$418$	16147.7	+	1123.51i	0.0924186	+	0.00643018i
$419$	−28866.9	−	16666.3i	−0.164427	−	0.0949318i	0.415529	−	0.909580i	$-0.363597\pi$
$419$	−28866.9	−	16666.3i	−0.164427	−	0.0949318i	−0.579955	+	0.814648i	$0.696930\pi$
$420$	9318.80	+	407008.i	0.0528276	+	2.30730i
$421$	−4180.31	−	7240.51i	−0.0235855	−	0.0408512i	0.853992	−	0.520287i	$-0.174175\pi$
$421$	−4180.31	−	7240.51i	−0.0235855	−	0.0408512i	−0.877577	+	0.479435i	$0.840842\pi$
$422$	262777.	−	128278.i	1.47558	−	0.720324i
$423$	217692.	+	44118.5i	1.21664	+	0.246570i
$424$	−291017.	−	61539.7i	−1.61877	−	0.342313i
$425$	−41837.2	−	72464.1i	−0.231625	−	0.401186i
$426$	−175469.	+	124201.i	−0.966901	+	0.684393i
$427$	50147.4	+	28952.6i	0.275038	+	0.158793i
$428$	−203797.	+	82504.6i	−1.11253	+	0.450392i
$429$	19326.8	+	7313.91i	0.105014	+	0.0397407i
$430$	−119153.	−	80309.6i	−0.644421	−	0.434341i
$431$		−	88445.3i		−	0.476124i	−0.971250	−	0.238062i	$-0.923488\pi$
$431$		−	88445.3i		−	0.476124i	0.971250	−	0.238062i	$-0.0765122\pi$
$432$	57995.5	−	177384.i	0.310761	−	0.950488i
$433$	119092.			0.635195			0.317598	−	0.948226i	$-0.397124\pi$
$433$	119092.			0.635195			0.317598	+	0.948226i	$0.397124\pi$
$434$	37604.0	−	55792.2i	0.199643	−	0.296206i
$435$	−66514.8	+	175763.i	−0.351512	+	0.928860i
$436$	−112335.	−	277482.i	−0.590939	−	1.45970i
$437$	−7738.34	+	13403.2i	−0.0405214	+	0.0701852i
$438$	−90248.7	−	127502.i	−0.470428	−	0.664614i
$439$	−103483.	+	59746.2i	−0.536960	+	0.310014i	−0.743846	−	0.668351i	$-0.767000\pi$
$439$	−103483.	+	59746.2i	−0.536960	+	0.310014i	0.206886	+	0.978365i	$0.433667\pi$
$440$	45520.7	−	215264.i	0.235128	−	1.11190i
$441$	−97152.5	+	32588.5i	−0.499547	+	0.167567i
$442$	2944.07	+	6030.90i	0.0150696	+	0.0308700i
$443$	176414.	−	101853.i	0.898930	−	0.518998i	0.0220772	−	0.999756i	$-0.492972\pi$
$443$	176414.	−	101853.i	0.898930	−	0.518998i	0.876853	+	0.480759i	$0.159639\pi$
$444$	−146340.	+	3350.57i	−0.742328	+	0.0169962i
$445$	166518.	−	288418.i	0.840894	−	1.45647i
$446$	−21074.4	+	302894.i	−0.105946	+	1.52272i
$447$	−33436.6	−	40892.8i	−0.167343	−	0.204659i
$448$	−246592.	+	26439.2i	−1.22864	+	0.131732i
$449$	77156.2			0.382717			0.191359	−	0.981520i	$-0.438711\pi$
$449$	77156.2			0.382717			0.191359	+	0.981520i	$0.438711\pi$
$450$	−353585.	−	359016.i	−1.74610	−	1.77292i
$451$		−	139326.i		−	0.684982i
$452$	−158474.	−	22159.5i	−0.775679	−	0.108463i
$453$	48097.2	+	294625.i	0.234382	+	1.43573i
$454$	−11448.9	+	164551.i	−0.0555461	+	0.798343i
$455$	−76353.2	−	44082.6i	−0.368812	−	0.212934i
$456$	26650.0	+	17088.3i	0.128164	+	0.0821804i
$457$	−140420.	−	243215.i	−0.672353	−	1.16455i	−0.977235	−	0.212159i	$-0.931951\pi$
$457$	−140420.	−	243215.i	−0.672353	−	1.16455i	0.304882	−	0.952390i	$-0.401383\pi$
$458$	−48403.1	−	99153.4i	−0.230750	−	0.472690i
$459$	−34689.5	+	18301.3i	−0.164654	+	0.0868675i
$460$	165866.	+	129403.i	0.783866	+	0.611544i
$461$	200811.	+	347814.i	0.944898	+	1.63661i	0.755956	+	0.654623i	$0.227173\pi$
$461$	200811.	+	347814.i	0.944898	+	1.63661i	0.188942	+	0.981988i	$0.439494\pi$
$462$	159804.	−	14801.1i	0.748694	−	0.0693441i
$463$	−51806.1	−	29910.3i	−0.241668	−	0.139527i	0.374275	−	0.927318i	$-0.377892\pi$
$463$	−51806.1	−	29910.3i	−0.241668	−	0.139527i	−0.615943	+	0.787791i	$0.711225\pi$
$464$	−110091.	−	31402.1i	−0.511347	−	0.145855i
$465$	18809.2	+	115218.i	0.0869888	+	0.532861i
$466$	−110507.	+	163957.i	−0.508883	+	0.755018i
$467$			208473.i			0.955909i	0.878385	+	0.477955i	$0.158622\pi$
$467$			208473.i			0.955909i	−0.878385	+	0.477955i	$0.841378\pi$
$468$	26292.4	+	30694.0i	0.120043	+	0.140140i
$469$	−420257.			−1.91060
$470$	424705.	+	286252.i	1.92261	+	1.29584i
$471$	126350.	+	154526.i	0.569554	+	0.696562i
$472$	14445.9	+	12979.8i	0.0648425	+	0.0582619i
$473$	−28322.1	+	49055.4i	−0.126591	+	0.219263i
$474$	−124399.	−	57238.9i	−0.553680	−	0.254762i
$475$	74027.3	−	42739.7i	0.328099	−	0.189428i
$476$	41094.5	+	32060.4i	0.181372	+	0.141500i
$477$	282143.	+	249239.i	1.24003	+	1.09541i
$478$	402790.	−	196628.i	1.76288	−	0.860575i
$479$	−138667.	+	80059.3i	−0.604368	+	0.348932i	−0.770758	−	0.637128i	$-0.780122\pi$
$479$	−138667.	+	80059.3i	−0.604368	+	0.348932i	0.166390	+	0.986060i	$0.446789\pi$
$480$	280206.	−	326593.i	1.21617	−	1.41750i
$481$	15849.9	−	27452.8i	0.0685070	−	0.118658i
$482$	163990.	+	11409.9i	0.705867	+	0.0491119i
$483$	−54310.8	+	143515.i	−0.232805	+	0.615181i
$484$	146099.	+	20429.1i	0.623672	+	0.0872083i
$485$	−91556.4			−0.389229
$486$	−174480.	+	159202.i	−0.738710	+	0.674023i
$487$			371960.i			1.56834i	0.620549	+	0.784168i	$0.286910\pi$
$487$			371960.i			1.56834i	−0.620549	+	0.784168i	$0.713090\pi$
$488$	−18974.6	−	58190.8i	−0.0796771	−	0.244351i
$489$	−263497.	−	99716.2i	−1.10194	−	0.417011i
$490$	−235715.	−	16400.2i	−0.981735	−	0.0683059i
$491$	−57863.4	−	33407.4i	−0.240016	−	0.138574i	0.375168	−	0.926957i	$-0.377585\pi$
$491$	−57863.4	−	33407.4i	−0.240016	−	0.138574i	−0.615184	+	0.788383i	$0.710918\pi$
$492$	130809.	−	239043.i	0.540392	−	0.987520i
$493$	12029.8	+	20836.3i	0.0494955	+	0.0857288i
$494$	−6160.99	+	3007.57i	−0.0252462	+	0.0123243i
$495$	−184361.	+	208700.i	−0.752418	+	0.851752i
$496$	−68980.8	+	17301.0i	−0.280391	+	0.0703246i
$497$	−180785.	−	313129.i	−0.731896	−	1.26768i
$498$	103118.	+	47447.3i	0.415792	+	0.191317i
$499$	−288151.	−	166364.i	−1.15723	−	0.668127i	−0.206591	−	0.978427i	$-0.566237\pi$
$499$	−288151.	−	166364.i	−1.15723	−	0.668127i	−0.950638	+	0.310301i	$0.899570\pi$
$500$	−260792.	−	644191.i	−1.04317	−	2.57676i
$501$	−181434.	+	148352.i	−0.722840	+	0.591041i
$502$	168659.	+	113677.i	0.669273	+	0.451091i
$503$			12673.0i			0.0500892i	0.999686	+	0.0250446i	$0.00797278\pi$
$503$			12673.0i			0.0500892i	−0.999686	+	0.0250446i	$0.992027\pi$
$504$	288074.	+	124641.i	1.13408	+	0.490683i
$505$	−359533.			−1.40980
$506$	46350.3	−	68768.8i	0.181030	−	0.268590i
$507$	245053.	−	40004.6i	0.953331	−	0.155630i
$508$	−280062.	+	113379.i	−1.08524	+	0.439346i
$509$	19452.7	−	33693.0i	0.0750834	−	0.130048i	−0.826039	−	0.563613i	$-0.809411\pi$
$509$	19452.7	−	33693.0i	0.0750834	−	0.130048i	0.901123	+	0.433564i	$0.142744\pi$
$510$	−90052.1	+	8340.63i	−0.346221	+	0.0320670i
$511$	227530.	−	131365.i	0.871360	−	0.503080i
$512$	212561.	+	153419.i	0.810856	+	0.585245i
$513$	−18696.1	−	35437.8i	−0.0710422	−	0.134658i
$514$	−22478.3	−	46046.5i	−0.0850817	−	0.174289i
$515$	149195.	−	86137.5i	0.562521	−	0.324772i
$516$	−94649.3	+	57573.9i	−0.355482	+	0.216235i
$517$	100950.	−	174851.i	0.377682	−	0.654164i
$518$	17087.9	−	245599.i	0.0636840	−	0.915306i
$519$	−139105.	+	22708.8i	−0.516428	+	0.0843062i
$520$	28890.3	+	88600.0i	0.106843	+	0.327663i
$521$	28001.3			0.103158			0.0515790	−	0.998669i	$-0.483575\pi$
$521$	28001.3			0.103158			0.0515790	+	0.998669i	$0.483575\pi$
$522$	101670.	+	103231.i	0.373122	+	0.378853i
$523$		−	306435.i		−	1.12030i	−0.828391	−	0.560151i	$-0.810743\pi$
$523$		−	306435.i		−	1.12030i	0.828391	−	0.560151i	$-0.189257\pi$
$524$	65755.8	−	470255.i	0.239481	−	1.71266i
$525$	656101.	−	536471.i	2.38041	−	1.94638i
$526$	8798.63	−	126459.i	0.0318012	−	0.457067i
$527$	12943.7	+	7473.06i	0.0466056	+	0.0269077i
$528$	−136102.	−	101257.i	−0.488199	−	0.363210i
$529$	−100274.	−	173680.i	−0.358326	−	0.620638i
$530$	380805.	+	780076.i	1.35566	+	2.77706i
$531$	−7816.72	−	23303.1i	−0.0277227	−	0.0826465i
$532$	−32752.0	+	41980.9i	−0.115722	+	0.148330i
$533$	29505.7	+	51105.4i	0.103861	+	0.179892i
$534$	−148345.	−	209580.i	−0.520223	−	0.734965i
$535$	555671.	+	320817.i	1.94138	+	1.12086i
$536$	330426.	+	296893.i	1.15013	+	1.03340i
$537$	310070.	+	117341.i	1.07526	+	0.406913i
$538$	122719.	−	182076.i	0.423983	−	0.629054i
$539$			93145.3i			0.320615i
$540$	−512253.	+	184978.i	−1.75670	+	0.634355i
$541$	387269.			1.32318			0.661590	−	0.749866i	$-0.269882\pi$
$541$	387269.			1.32318			0.661590	+	0.749866i	$0.269882\pi$
$542$	−352695.	−	237717.i	−1.20061	−	0.809211i
$543$	181446.	−	479465.i	0.615385	−	1.62614i
$544$	−9661.23	−	54238.9i	−0.0326464	−	0.183279i
$545$	−436812.	+	756581.i	−1.47062	+	2.54720i
$546$	−55482.3	+	39271.5i	−0.186110	+	0.131732i
$547$	−220183.	+	127123.i	−0.735883	+	0.424862i	−0.820570	−	0.571545i	$-0.806344\pi$
$547$	−220183.	+	127123.i	−0.735883	+	0.424862i	0.0846877	+	0.996408i	$0.473011\pi$
$548$	−164019.	+	210237.i	−0.546177	+	0.700080i
$549$	−15386.4	+	75920.7i	−0.0510497	+	0.251893i
$550$	−411609.	+	200933.i	−1.36069	+	0.664240i
$551$	−21285.8	+	12289.3i	−0.0701109	+	0.0404786i
$552$	144089.	−	74470.3i	0.472881	−	0.244402i
$553$	115156.	−	199455.i	0.376560	−	0.652221i
$554$	−200847.	−	13974.3i	−0.654404	−	0.0455312i
$555$	270403.	+	330701.i	0.877859	+	1.07362i
$556$	−9072.31	+	64880.9i	−0.0293473	+	0.209878i
$557$	−154243.			−0.497159			−0.248580	−	0.968611i	$-0.579964\pi$
$557$	−154243.			−0.497159			−0.248580	+	0.968611i	$0.579964\pi$
$558$	86760.8	+	23957.7i	0.278648	+	0.0769443i
$559$		−	23991.6i		−	0.0767779i
$560$	503491.	+	519928.i	1.60552	+	1.65793i
$561$	5743.98	+	35185.5i	0.0182510	+	0.111799i
$562$	−24326.8	−	1692.58i	−0.0770216	−	0.00535891i
$563$	−188653.	−	108919.i	−0.595177	−	0.343626i	0.171965	−	0.985103i	$-0.444988\pi$
$563$	−188653.	−	108919.i	−0.595177	−	0.343626i	−0.767142	+	0.641477i	$0.778322\pi$
$564$	337364.	−	205214.i	1.06057	−	0.645133i
$565$	233489.	+	404415.i	0.731425	+	1.26686i
$566$	−184682.	+	90155.2i	−0.576490	+	0.281422i
$567$	−239555.	−	316901.i	−0.745143	−	0.985730i
$568$	−79069.4	+	373914.i	−0.245082	+	1.15898i
$569$	−112165.	−	194275.i	−0.346443	−	0.600057i	0.639172	−	0.769064i	$-0.279277\pi$
$569$	−112165.	−	194275.i	−0.346443	−	0.600057i	−0.985615	+	0.169007i	$0.945944\pi$
$570$	−8520.54	−	91994.6i	−0.0262251	−	0.283147i
$571$	−227168.	−	131156.i	−0.696748	−	0.402268i	0.109387	−	0.993999i	$-0.465111\pi$
$571$	−227168.	−	131156.i	−0.696748	−	0.402268i	−0.806135	+	0.591732i	$0.798445\pi$
$572$	34052.2	−	13785.6i	0.104076	−	0.0421340i
$573$	−56655.8	−	347052.i	−0.172558	−	1.05702i
$574$	380042.	+	256149.i	1.15347	+	0.777443i
$575$		−	437941.i		−	1.32458i
$576$	−138444.	−	301510.i	−0.417282	−	0.908777i
$577$	450994.			1.35462			0.677312	−	0.735696i	$-0.263145\pi$
$577$	450994.			1.35462			0.677312	+	0.735696i	$0.263145\pi$
$578$	180250.	−	267432.i	0.539534	−	0.800494i
$579$	23083.8	+	28231.3i	0.0688573	+	0.0842121i
$580$	125370.	+	309680.i	0.372681	+	0.920570i
$581$	−95456.3	+	165335.i	−0.282782	+	0.489794i
$582$	−29506.2	+	64126.5i	−0.0871100	+	0.189318i
$583$	296351.	−	171099.i	0.871907	−	0.503396i
$584$	−271699.	−	57454.6i	−0.796640	−	0.168461i
$585$	23427.0	−	115595.i	0.0684550	−	0.337775i
$586$	−160175.	−	328117.i	−0.466443	−	0.955505i
$587$	−307738.	+	177673.i	−0.893111	+	0.515638i	−0.874959	−	0.484197i	$-0.839112\pi$
$587$	−307738.	+	177673.i	−0.893111	+	0.515638i	−0.0181523	+	0.999835i	$0.505778\pi$
$588$	−87451.6	+	159810.i	−0.252937	+	0.462222i
$589$	−7634.26	+	13222.9i	−0.0220058	+	0.0381151i
$590$	3933.78	−	56538.8i	0.0113007	−	0.162421i
$591$	−142929.	+	377686.i	−0.409210	+	1.08133i
$592$	−186940.	+	181030.i	−0.533406	+	0.516543i
$593$	89819.5			0.255424			0.127712	−	0.991811i	$-0.459237\pi$
$593$	89819.5			0.255424			0.127712	+	0.991811i	$0.459237\pi$
$594$	86760.0	+	196386.i	0.245893	+	0.556594i
$595$		−	152106.i		−	0.429649i
$596$	−93002.0	−	13004.5i	−0.261818	−	0.0366101i
$597$	473536.	+	179202.i	1.32863	+	0.502799i
$598$	−2438.00	+	35040.5i	−0.00681759	+	0.0979868i
$599$	−357687.	−	206511.i	−0.996896	−	0.575558i	−0.0895677	−	0.995981i	$-0.528549\pi$
$599$	−357687.	−	206511.i	−0.996896	−	0.575558i	−0.907328	+	0.420422i	$0.861882\pi$
$600$	−894851.	−	41706.0i	−2.48570	−	0.115850i
$601$	−129317.	−	223984.i	−0.358020	−	0.620110i	0.629610	−	0.776912i	$-0.283215\pi$
$601$	−129317.	−	223984.i	−0.358020	−	0.620110i	−0.987630	+	0.156802i	$0.949882\pi$
$602$	−81739.3	−	167442.i	−0.225548	−	0.462032i
$603$	−178795.	−	533021.i	−0.491723	−	1.46592i
$604$	418434.	+	326447.i	1.14697	+	0.894828i
$605$	−215256.	−	372834.i	−0.588090	−	1.01860i
$606$	−115868.	+	251819.i	−0.315514	+	0.685714i
$607$	267430.	+	154401.i	0.725825	+	0.419055i	0.816893	−	0.576789i	$-0.195695\pi$
$607$	267430.	+	154401.i	0.725825	+	0.419055i	−0.0910678	+	0.995845i	$0.529028\pi$
$608$	55408.8	−	9869.63i	0.149890	−	0.0266989i
$609$	−188655.	+	154256.i	−0.508667	+	0.415919i
$610$	−99831.1	+	148117.i	−0.268291	+	0.398057i
$611$			85514.7i			0.229065i
$612$	−23179.6	+	65760.9i	−0.0618876	+	0.175576i
$613$	−464349.			−1.23573			−0.617865	−	0.786284i	$-0.712002\pi$
$613$	−464349.			−1.23573			−0.617865	+	0.786284i	$0.712002\pi$
$614$	−358825.	−	241848.i	−0.951800	−	0.641515i
$615$	−784834.	+	128123.i	−2.07505	+	0.338749i
$616$	190689.	−	212228.i	0.502534	−	0.559295i
$617$	253688.	−	439401.i	0.666392	−	1.15423i	−0.312513	−	0.949913i	$-0.601171\pi$
$617$	253688.	−	439401.i	0.666392	−	1.15423i	0.978906	−	0.204312i	$-0.0654958\pi$
$618$	−12249.6	−	132257.i	−0.0320734	−	0.346290i
$619$	244884.	−	141384.i	0.639115	−	0.368993i	−0.145159	−	0.989408i	$-0.546369\pi$
$619$	244884.	−	141384.i	0.639115	−	0.368993i	0.784273	+	0.620415i	$0.213036\pi$
$620$	163635.	+	127662.i	0.425690	+	0.332108i
$621$	−205129.	−	7826.35i	−0.531918	−	0.0202944i
$622$	−359750.	+	175617.i	−0.929865	+	0.453927i
$623$	373999.	−	215929.i	0.963595	−	0.556332i
$624$	71366.5	+	8318.57i	0.183284	+	0.0213638i
$625$	−528069.	+	914643.i	−1.35186	+	2.34149i
$626$	−605698.	−	42142.5i	−1.54564	−	0.107540i
$627$	−35944.4	+	5867.89i	−0.0914317	+	0.0149261i
$628$	351437.	+	49141.5i	0.891103	+	0.124603i
$629$	54689.8			0.138231
$630$	−230330.	−	886578.i	−0.580323	−	2.23376i
$631$		−	403620.i		−	1.01371i	−0.862031	−	0.506855i	$-0.830808\pi$
$631$		−	403620.i		−	1.01371i	0.862031	−	0.506855i	$-0.169192\pi$
$632$	−231447.	+	75469.2i	−0.579452	+	0.188945i
$633$	−509343.	+	416472.i	−1.27117	+	1.03939i
$634$	448531.	+	31207.3i	1.11587	+	0.0776387i
$635$	763614.	+	440873.i	1.89377	+	1.09337i
$636$	669093.	−	15319.4i	1.65414	−	0.0378729i
$637$	−19725.8	−	34166.1i	−0.0486134	−	0.0842008i
$638$	118354.	−	57776.0i	0.290764	−	0.141940i
$639$	320235.	−	362512.i	0.784272	−	0.887811i
$640$	−28563.4	−	764487.i	−0.0697350	−	1.86642i
$641$	181028.	+	313549.i	0.440584	+	0.763114i	0.997733	−	0.0672990i	$-0.0214381\pi$
$641$	181028.	+	313549.i	0.440584	+	0.763114i	−0.557149	+	0.830413i	$0.688105\pi$
$642$	403780.	−	285804.i	0.979659	−	0.693423i
$643$	346651.	+	200139.i	0.838437	+	0.484072i	0.856733	−	0.515761i	$-0.172491\pi$
$643$	346651.	+	200139.i	0.838437	+	0.484072i	−0.0182957	+	0.999833i	$0.505824\pi$
$644$	102367.	+	252861.i	0.246825	+	0.609691i
$645$	302377.	+	114430.i	0.726825	+	0.275055i
$646$	−9808.24	−	6610.77i	−0.0235031	−	0.0158412i
$647$			98990.1i			0.236474i	0.992985	+	0.118237i	$0.0377242\pi$
$647$			98990.1i			0.236474i	−0.992985	+	0.118237i	$0.962276\pi$
$648$	−35526.6	+	418398.i	−0.0846064	+	0.996414i
$649$	−22341.9			−0.0530434
$650$	108427.	−	160871.i	0.256633	−	0.380760i
$651$	−53580.4	+	141585.i	−0.126428	+	0.334083i
$652$	−464259.	+	187949.i	−1.09211	+	0.442125i
$653$	269165.	−	466208.i	0.631237	−	1.09333i	−0.356062	−	0.934462i	$-0.615881\pi$
$653$	269165.	−	466208.i	0.631237	−	1.09333i	0.987299	−	0.158872i	$-0.0507859\pi$
$654$	389140.	+	549772.i	0.909809	+	1.28537i
$655$	−1.20006e6	+	692852.i	−2.79717	+	1.61495i
$656$	−117850.	−	469879.i	−0.273856	−	1.09189i
$657$	263414.	+	232694.i	0.610250	+	0.539081i
$658$	291348.	+	596824.i	0.672915	+	1.37846i
$659$	−126219.	+	72872.6i	−0.290639	+	0.167801i	−0.638230	−	0.769846i	$-0.720333\pi$
$659$	−126219.	+	72872.6i	−0.290639	+	0.167801i	0.347591	+	0.937646i	$0.387000\pi$
$660$	11331.7	+	494926.i	0.0260141	+	1.13619i
$661$	126176.	−	218543.i	0.288784	−	0.500189i	−0.684736	−	0.728792i	$-0.740082\pi$
$661$	126176.	−	218543.i	0.288784	−	0.500189i	0.973520	+	0.228603i	$0.0734157\pi$
$662$	−31907.6	+	458595.i	−0.0728077	+	1.04644i
$663$	−9558.30	−	11689.7i	−0.0217447	−	0.0265936i
$664$	191854.	−	62559.0i	0.435146	−	0.141891i
$665$	155388.			0.351377
$666$	318768.	−	82815.1i	0.718665	−	0.186707i
$667$			125925.i			0.283049i
$668$	−57698.5	+	412632.i	−0.129304	+	0.924720i
$669$	−110068.	−	674234.i	−0.245928	−	1.50646i
$670$	89979.0	−	1.29323e6i	0.200443	−	2.88090i
$671$	60979.7	+	35206.7i	0.135438	+	0.0781951i
$672$	526422.	−	185088.i	1.16572	−	0.409865i
$673$	−327332.	−	566956.i	−0.722701	−	1.25175i	−0.959913	−	0.280297i	$-0.909567\pi$
$673$	−327332.	−	566956.i	−0.722701	−	1.25175i	0.237213	−	0.971458i	$-0.423766\pi$
$674$	−216346.	−	443182.i	−0.476243	−	0.975580i
$675$	959551.	+	603910.i	2.10601	+	1.32545i
$676$	271520.	−	348030.i	0.594168	−	0.761594i
$677$	106756.	+	184907.i	0.232924	+	0.403437i	0.958667	−	0.284529i	$-0.0918372\pi$
$677$	106756.	+	184907.i	0.232924	+	0.403437i	−0.725743	+	0.687966i	$0.758504\pi$
$678$	358502.	−	33204.5i	0.779887	−	0.0722332i
$679$	−102818.	−	59361.8i	−0.223012	−	0.128756i
$680$	−107456.	+	119594.i	−0.232388	+	0.258637i
$681$	−59795.8	−	366287.i	−0.128937	−	0.789818i
$682$	45726.9	−	67843.8i	0.0983111	−	0.145862i
$683$			885039.i			1.89724i	0.316425	+	0.948618i	$0.397517\pi$
$683$			885039.i			1.89724i	−0.316425	+	0.948618i	$0.602483\pi$
$684$	−67179.4	−	23679.6i	−0.143590	−	0.0506131i
$685$	778168.			1.65841
$686$	228129.	+	153759.i	0.484767	+	0.326733i
$687$	157147.	+	192190.i	0.332961	+	0.407209i
$688$	−54023.0	+	189397.i	−0.114131	+	0.400124i
$689$	−72468.6	+	125519.i	−0.152655	+	0.264406i
$690$	−430003.	−	197855.i	−0.903177	−	0.415575i
$691$	−382656.	+	220927.i	−0.801406	+	0.462692i	−0.843963	−	0.536402i	$-0.819783\pi$
$691$	−382656.	+	220927.i	−0.801406	+	0.462692i	0.0425567	+	0.999094i	$0.486450\pi$
$692$	−154130.	+	197561.i	−0.321866	+	0.412562i
$693$	−342351.	+	114837.i	−0.712862	+	0.239120i
$694$	−343854.	+	167857.i	−0.713929	+	0.348514i
$695$	165571.	−	95592.6i	0.342780	−	0.197904i
$696$	257305.	+	11992.1i	0.531165	+	0.0247558i
$697$	−50904.6	+	88169.3i	−0.104783	+	0.181490i
$698$	171933.	+	11962.5i	0.352897	+	0.0245534i
$699$	157457.	−	416075.i	0.322260	−	0.851564i
$700$	208650.	−	1.49216e6i	0.425816	−	3.04523i
$701$	340679.			0.693281			0.346640	−	0.937998i	$-0.387322\pi$
$701$	340679.			0.693281			0.346640	+	0.937998i	$0.387322\pi$
$702$	−73413.5	−	53661.7i	−0.148971	−	0.108891i
$703$			55869.5i			0.113048i
$704$	−299859.	+	32150.4i	−0.605022	+	0.0648695i
$705$	−1.07778e6	−	407868.i	−2.16846	−	0.820619i
$706$	−450407.	−	31337.8i	−0.903640	−	0.0628723i
$707$	−403755.	−	233108.i	−0.807755	−	0.466357i
$708$	−38332.3	−	20976.2i	−0.0764713	−	0.0418467i
$709$	292720.	+	507006.i	0.582318	+	1.00860i	0.995204	+	0.0978214i	$0.0311874\pi$
$709$	292720.	+	507006.i	0.582318	+	1.00860i	−0.412886	+	0.910783i	$0.635479\pi$
$710$	1.00228e6	−	489278.i	1.98826	−	0.970597i
$711$	301966.	+	61197.7i	0.597335	+	0.121059i
$712$	−446600.	−	94440.0i	−0.880966	−	0.186293i
$713$	39113.0	+	67745.8i	0.0769383	+	0.133261i
$714$	−106536.	−	49020.0i	−0.208978	−	0.0961561i
$715$	−92846.3	−	53604.8i	−0.181615	−	0.104856i
$716$	546317.	−	221169.i	1.06566	−	0.431419i
$717$	−780732.	+	638378.i	−1.51867	+	1.24176i
$718$	−740121.	−	498843.i	−1.43567	−	0.967642i
$719$			306988.i			0.593832i	0.954904	+	0.296916i	$0.0959581\pi$
$719$			306988.i			0.593832i	−0.954904	+	0.296916i	$0.904042\pi$
$720$	−445230.	+	859789.i	−0.858855	+	1.65854i
$721$	223394.			0.429735
$722$	−284594.	+	422246.i	−0.545949	+	0.810011i
$723$	−365037.	+	59591.8i	−0.698329	+	0.114001i
$724$	−341996.	−	844775.i	−0.652446	−	1.61163i
$725$	347749.	−	602319.i	0.661592	−	1.14591i
$726$	−330506.	+	30611.5i	−0.627056	+	0.0580780i
$727$	488481.	−	282025.i	0.924227	−	0.533603i	0.0392459	−	0.999230i	$-0.487504\pi$
$727$	488481.	−	282025.i	0.924227	−	0.533603i	0.884981	+	0.465627i	$0.154171\pi$
$728$	−25001.2	+	118229.i	−0.0471736	+	0.223081i
$729$	300016.	−	438657.i	0.564534	−	0.825410i
$730$	355526.	+	728293.i	0.667154	+	1.36666i
$731$	35846.0	−	20695.7i	0.0670821	−	0.0387298i
$732$	71569.0	+	117657.i	0.133568	+	0.219581i
$733$	−290960.	+	503957.i	−0.541533	+	0.937963i	0.457283	+	0.889321i	$0.348823\pi$
$733$	−290960.	+	503957.i	−0.541533	+	0.937963i	−0.998816	+	0.0486418i	$0.984511\pi$
$734$	−29576.5	+	425092.i	−0.0548978	+	0.789025i
$735$	524694.	−	85655.7i	0.971252	−	0.158556i
$736$	98148.4	−	271129.i	0.181187	−	0.500519i
$737$	−511037.			−0.940843
$738$	−163194.	+	590993.i	−0.299633	+	1.08510i
$739$		−	193774.i		−	0.354818i	−0.984137	−	0.177409i	$-0.943228\pi$
$739$		−	193774.i		−	0.354818i	0.984137	−	0.177409i	$-0.0567715\pi$
$740$	752109.	+	105168.i	1.37346	+	0.192052i
$741$	11941.9	−	9764.48i	0.0217489	−	0.0177833i
$742$	−78129.4	+	1.12292e6i	−0.141908	+	2.03959i
$743$	−76480.8	−	44156.2i	−0.138540	−	0.0799861i	0.429128	−	0.903244i	$-0.358821\pi$
$743$	−76480.8	−	44156.2i	−0.138540	−	0.0799861i	−0.567668	+	0.823258i	$0.692154\pi$
$744$	142151.	−	73468.7i	0.256805	−	0.132726i
$745$	137025.	+	237334.i	0.246881	+	0.427610i
$746$	−250719.	−	513595.i	−0.450514	−	0.922875i
$747$	−250310.	−	50728.8i	−0.448576	−	0.0909104i
$748$	49971.3	+	38985.8i	0.0893135	+	0.0696792i
$749$	416012.	+	720554.i	0.741553	+	1.28441i
$750$	903410.	+	1.27633e6i	1.60606	+	2.26903i
$751$	−474180.	−	273768.i	−0.840743	−	0.485403i	0.0167738	−	0.999859i	$-0.494660\pi$
$751$	−474180.	−	273768.i	−0.840743	−	0.485403i	−0.857517	+	0.514456i	$0.827994\pi$
$752$	192557.	−	675077.i	0.340506	−	1.19376i
$753$	−428010.	−	161973.i	−0.754855	−	0.285662i
$754$	−31177.1	+	46256.8i	−0.0548395	+	0.0813640i
$755$		−	1.54879e6i		−	2.71705i
$756$	−695193.	−	124397.i	−1.21636	−	0.217653i
$757$	−45164.0			−0.0788135			−0.0394068	−	0.999223i	$-0.512547\pi$
$757$	−45164.0			−0.0788135			−0.0394068	+	0.999223i	$0.512547\pi$
$758$	−315913.	−	212926.i	−0.549831	−	0.370587i
$759$	−66042.5	+	174516.i	−0.114641	+	0.302936i
$760$	−122173.	−	109774.i	−0.211519	−	0.190052i
$761$	100185.	−	173525.i	0.172995	−	0.299636i	−0.766471	−	0.642279i	$-0.777989\pi$
$761$	100185.	−	173525.i	0.172995	−	0.299636i	0.939465	+	0.342644i	$0.111322\pi$
$762$	554882.	−	392757.i	0.955633	−	0.676416i
$763$	−981079.	+	566426.i	−1.68521	+	0.972959i
$764$	−492891.	−	384536.i	−0.844432	−	0.658795i
$765$	192920.	−	64712.5i	0.329651	−	0.110577i
$766$	194663.	−	95027.7i	0.331762	−	0.161954i
$767$	8195.11	−	4731.45i	0.0139304	−	0.00804273i
$768$	−544656.	−	226368.i	−0.923421	−	0.383790i
$769$	−212834.	+	368639.i	−0.359905	+	0.623374i	−0.987945	−	0.154807i	$-0.950524\pi$
$769$	−212834.	+	368639.i	−0.359905	+	0.623374i	0.628039	+	0.778181i	$0.283858\pi$
$770$	−830625.	−	57792.1i	−1.40095	−	0.0974736i
$771$	72978.6	+	89252.4i	0.122768	+	0.150145i
$772$	64206.2	+	8977.98i	0.107731	+	0.0150641i
$773$	199528.			0.333922			0.166961	−	0.985964i	$-0.446605\pi$
$773$	199528.			0.333922			0.166961	+	0.985964i	$0.446605\pi$
$774$	177596.	−	174909.i	0.296449	−	0.291965i
$775$		−	432051.i		−	0.719335i
$776$	38903.9	+	119309.i	0.0646055	+	0.198130i
$777$	89247.5	+	546696.i	0.147827	+	0.905532i
$778$	51980.2	+	3616.61i	0.0858774	+	0.00597506i
$779$	−90071.2	−	52002.6i	−0.148426	−	0.0856940i
$780$	−108969.	−	179141.i	−0.179108	−	0.294446i
$781$	−219836.	−	380768.i	−0.360411	−	0.624249i
$782$	−54457.2	+	26584.1i	−0.0890517	+	0.0434718i
$783$	−275909.	−	173648.i	−0.450031	−	0.283234i
$784$	78787.6	+	314134.i	0.128182	+	0.511073i
$785$	−517791.	−	896841.i	−0.840263	−	1.45538i
$786$	98530.5	+	1.06381e6i	0.159487	+	1.72195i
$787$	899924.	+	519571.i	1.45297	+	0.838872i	0.998649	−	0.0519669i	$-0.0165490\pi$
$787$	899924.	+	519571.i	1.45297	+	0.838872i	0.454320	+	0.890839i	$0.349882\pi$
$788$	269399.	+	665451.i	0.433854	+	1.07168i
$789$	45953.8	+	281495.i	0.0738188	+	0.452186i
$790$	589118.	+	397066.i	0.943948	+	0.636222i
$791$			605543.i			0.967815i
$792$	350301.	+	151565.i	0.558458	+	0.241629i
$793$	−29823.5			−0.0474255
$794$	−121634.	+	180465.i	−0.192936	+	0.286254i
$795$	−1.23633e6	−	1.51203e6i	−1.95615	−	2.39235i
$796$	834330.	−	337768.i	1.31677	−	0.533079i
$797$	−12577.0	+	21783.9i	−0.0197997	+	0.0342941i	−0.875755	−	0.482755i	$-0.839636\pi$
$797$	−12577.0	+	21783.9i	−0.0197997	+	0.0342941i	0.855956	+	0.517049i	$0.172970\pi$
$798$	50077.4	−	108834.i	0.0786386	−	0.170907i
$799$	−127768.	+	73766.9i	−0.200138	+	0.115549i
$800$	−1.21820e6	+	1.02581e6i	−1.90343	+	1.60283i
$801$	432982.	+	382487.i	0.674847	+	0.596144i
$802$	−88478.1	−	181247.i	−0.137558	−	0.281787i
$803$	276679.	−	159741.i	0.429087	−	0.247734i
$804$	−876790.	−	479798.i	−1.35639	−	0.742243i
$805$	398053.	−	689448.i	0.614255	−	1.06392i
$806$	−2405.21	+	34569.2i	−0.00370239	+	0.0532131i
$807$	−174858.	+	462057.i	−0.268496	+	0.709493i
$808$	152772.	+	468516.i	0.234002	+	0.717632i
$809$	975055.			1.48981			0.744907	−	0.667168i	$-0.232494\pi$
$809$	975055.			1.48981			0.744907	+	0.667168i	$0.232494\pi$
$810$	1.02647e6	−	669321.i	1.56451	−	1.02015i
$811$		−	240015.i		−	0.364919i	−0.983213	−	0.182460i	$-0.941594\pi$
$811$		−	240015.i		−	0.364919i	0.983213	−	0.182460i	$-0.0584059\pi$
$812$	−59995.0	+	429056.i	−0.0909919	+	0.650731i
$813$	895040.	+	338713.i	1.35413	+	0.512449i
$814$	20779.1	−	298650.i	0.0313601	−	0.450728i
$815$	1.26584e6	+	730836.i	1.90575	+	1.10028i
$816$	49133.5	+	113805.i	0.0737900	+	0.170915i
$817$	21142.1	+	36619.3i	0.0316741	+	0.0548612i
$818$	−71652.7	−	146780.i	−0.107084	−	0.219361i
$819$	101256.	−	114624.i	0.150957	−	0.170887i
$820$	−869603.	+	1.11464e6i	−1.29328	+	1.65770i
$821$	406806.	+	704608.i	0.603533	+	1.04535i	0.992282	+	0.124005i	$0.0395740\pi$
$821$	406806.	+	704608.i	0.603533	+	1.04535i	−0.388749	+	0.921344i	$0.627093\pi$
$822$	250783.	−	545033.i	0.371155	−	0.806638i
$823$	24117.0	+	13924.0i	0.0356061	+	0.0205572i	0.517697	−	0.855564i	$-0.326789\pi$
$823$	24117.0	+	13924.0i	0.0356061	+	0.0205572i	−0.482091	+	0.876121i	$0.660123\pi$
$824$	−175643.	−	157818.i	−0.258688	−	0.232435i
$825$	797825.	−	652354.i	1.17219	−	0.958463i
$826$	41075.3	−	60942.5i	0.0602034	−	0.0893223i
$827$		−	1.05969e6i		−	1.54941i	−0.632323	−	0.774705i	$-0.717898\pi$
$827$		−	1.05969e6i		−	1.54941i	0.632323	−	0.774705i	$-0.282102\pi$
$828$	−277158.	+	237413.i	−0.404265	+	0.346292i
$829$	−904280.			−1.31581			−0.657906	−	0.753100i	$-0.728558\pi$
$829$	−904280.			−1.31581			−0.657906	+	0.753100i	$0.728558\pi$
$830$	−488340.	−	329142.i	−0.708869	−	0.477779i
$831$	447080.	−	72985.3i	0.647416	−	0.105690i
$832$	103181.	−	75295.3i	0.149057	−	0.108773i
$833$	34031.8	−	58944.9i	0.0490451	−	0.0849486i
$834$	−13594.2	−	146774.i	−0.0195444	−	0.211017i
$835$	1.05301e6	−	607954.i	1.51028	−	0.871963i
$836$	−39826.7	+	51049.2i	−0.0569852	+	0.0730426i
$837$	−202370.	−	7721.09i	−0.288866	−	0.0110212i
$838$	119816.	−	58490.0i	0.170619	−	0.0832902i
$839$	−308829.	+	178303.i	−0.438727	+	0.253299i	−0.703058	−	0.711133i	$-0.748182\pi$
$839$	−308829.	+	178303.i	−0.438727	+	0.253299i	0.264330	+	0.964432i	$0.414849\pi$
$840$	−1.37085e6	−	879004.i	−1.94282	−	1.24575i
$841$	253649.	−	439333.i	0.358625	−	0.621157i
$842$	33361.8	+	2321.21i	0.0470571	+	0.00327408i
$843$	54150.9	−	8840.06i	0.0761992	−	0.0124394i
$844$	−161978.	+	1.15839e6i	−0.227390	+	1.62619i
$845$	−1.28819e6			−1.80413
$846$	−633014.	+	623438.i	−0.884449	+	0.871069i
$847$		−	558256.i		−	0.778156i
$848$	854725.	−	827703.i	1.18860	−	1.15102i
$849$	357971.	−	292701.i	0.496630	−	0.406077i
$850$	333890.	+	23231.0i	0.462132	+	0.0321536i
$851$	247890.	+	143120.i	0.342295	+	0.197624i
$852$	−19683.2	−	859685.i	−0.0271154	−	1.18430i
$853$	93966.4	+	162755.i	0.129144	+	0.223684i	0.923345	−	0.383971i	$-0.125444\pi$
$853$	93966.4	+	162755.i	0.129144	+	0.223684i	−0.794201	+	0.607655i	$0.792110\pi$
$854$	−208144.	+	101608.i	−0.285396	+	0.139320i
$855$	66108.5	+	197082.i	0.0904325	+	0.269596i
$856$	181950.	−	860429.i	0.248316	−	1.17427i
$857$	−424830.	−	735827.i	−0.578434	−	1.00188i	−0.995659	−	0.0930735i	$-0.970331\pi$
$857$	−424830.	−	735827.i	−0.578434	−	1.00188i	0.417226	−	0.908803i	$-0.363002\pi$
$858$	−67467.1	+	47754.6i	−0.0916468	+	0.0648695i
$859$	1.04585e6	+	603819.i	1.41736	+	0.818315i	0.996067	−	0.0886072i	$-0.0282416\pi$
$859$	1.04585e6	+	603819.i	1.41736	+	0.818315i	0.421297	+	0.906923i	$0.361575\pi$
$860$	532762.	−	215682.i	0.720339	−	0.291620i
$861$	−964438.	−	364976.i	−1.30097	−	0.492332i
$862$	293367.	+	197730.i	0.394818	+	0.266108i
$863$			77194.2i			0.103648i	0.998656	+	0.0518242i	$0.0165036\pi$
$863$			77194.2i			0.103648i	−0.998656	+	0.0518242i	$0.983496\pi$
$864$	458714.	+	588929.i	0.614490	+	0.788925i
$865$	731250.			0.977313
$866$	−266244.	+	395020.i	−0.355013	+	0.526725i
$867$	−256830.	+	678667.i	−0.341671	+	0.902856i
$868$	100991.	+	249460.i	0.134042	+	0.331101i
$869$	140030.	−	242539.i	0.185431	−	0.321176i
$870$	−434294.	−	613565.i	−0.573779	−	0.810628i
$871$	187450.	−	108224.i	0.247087	−	0.142656i
$872$	1.17153e6	+	247736.i	1.54070	+	0.325804i
$873$	31547.0	−	155661.i	0.0413932	−	0.204245i
$874$	−27157.5	−	55631.9i	−0.0355522	−	0.0728285i
$875$	−2.27763e6	+	1.31499e6i	−2.97487	+	1.71754i
$876$	624677.	−	14302.5i	0.814043	−	0.0186382i
$877$	−71455.2	+	123764.i	−0.0929040	+	0.160914i	−0.908732	−	0.417380i	$-0.862948\pi$
$877$	−71455.2	+	123764.i	−0.0929040	+	0.160914i	0.815828	+	0.578295i	$0.196282\pi$
$878$	33175.3	−	476817.i	0.0430354	−	0.618533i
$879$	520028.	+	635991.i	0.673053	+	0.823140i
$880$	612250.	+	632238.i	0.790612	+	0.816423i
$881$	−305226.			−0.393250			−0.196625	−	0.980479i	$-0.562998\pi$
$881$	−305226.			−0.393250			−0.196625	+	0.980479i	$0.562998\pi$
$882$	109102.	−	395103.i	0.140247	−	0.507895i
$883$			902045.i			1.15693i	0.815707	+	0.578465i	$0.196348\pi$
$883$			902045.i			1.15693i	−0.815707	+	0.578465i	$0.803652\pi$
$884$	−26585.9	−	3717.51i	−0.0340209	−	0.00475716i
$885$	20545.5	+	125854.i	0.0262319	+	0.160687i
$886$	−56555.9	+	812857.i	−0.0720461	+	1.03549i
$887$	−797270.	−	460304.i	−1.01335	−	0.585056i	−0.101177	−	0.994868i	$-0.532261\pi$
$887$	−797270.	−	460304.i	−1.01335	−	0.585056i	−0.912170	+	0.409813i	$0.865594\pi$
$888$	316045.	−	492888.i	0.400796	−	0.625061i
$889$	571692.	+	990199.i	0.723367	+	1.25291i
$890$	584391.	+	1.19712e6i	0.737774	+	1.51132i
$891$	−291302.	−	385355.i	−0.366934	−	0.485407i
$892$	−957564.	−	747057.i	−1.20348	−	0.938911i
$893$	−75358.1	−	130524.i	−0.0944990	−	0.163677i
$894$	210390.	−	19486.3i	0.263239	−	0.0243812i
$895$	−1.48958e6	−	860011.i	−1.85960	−	1.07364i
$896$	463589.	−	877037.i	0.577453	−	1.09245i
$897$	−12733.3	−	77999.1i	−0.0158254	−	0.0969404i
$898$	−172492.	+	255922.i	−0.213902	+	0.317362i
$899$			124232.i			0.153714i
$900$	1.98131e6	−	370194.i	2.44607	−	0.457030i
$901$	−250052.			−0.308022
$902$	462135.	+	311480.i	0.568010	+	0.382839i
$903$	265377.	+	324555.i	0.325453	+	0.398027i
$904$	427789.	−	476108.i	0.523471	−	0.582597i
$905$	−1.32984e6	+	2.30336e6i	−1.62369	+	2.81232i
$906$	−1.08478e6	−	499134.i	−1.32155	−	0.608080i
$907$	426945.	−	246497.i	0.518988	−	0.299638i	−0.217533	−	0.976053i	$-0.569801\pi$
$907$	426945.	−	246497.i	0.518988	−	0.299638i	0.736520	+	0.676415i	$0.236468\pi$
$908$	−520209.	−	405849.i	−0.630967	−	0.492258i
$909$	123882.	−	611266.i	0.149927	−	0.739780i
$910$	316915.	−	154707.i	0.382702	−	0.186821i
$911$	208640.	−	120458.i	0.251397	−	0.145144i	−0.369007	−	0.929427i	$-0.620302\pi$
$911$	208640.	−	120458.i	0.251397	−	0.145144i	0.620404	+	0.784283i	$0.286969\pi$
$912$	−116260.	+	50193.4i	−0.139778	+	0.0603471i
$913$	−116076.	+	201049.i	−0.139252	+	0.241191i
$914$	1.12065e6	+	77971.3i	1.34146	+	0.0933345i
$915$	142245.	−	375879.i	0.169901	−	0.448958i
$916$	437096.	+	61119.2i	0.520937	+	0.0728428i
$917$	−1.79688e6			−2.13688
$918$	16848.2	−	155977.i	0.0199925	−	0.185087i
$919$		−	155183.i		−	0.183744i	−0.995771	−	0.0918719i	$-0.970715\pi$
$919$		−	155183.i		−	0.183744i	0.995771	−	0.0918719i	$-0.0292850\pi$
$920$	−800032.	+	260871.i	−0.945218	+	0.308213i
$921$	910595.	+	344600.i	1.07351	+	0.406252i
$922$	−1.60261e6	−	111504.i	−1.88524	−	0.131169i
$923$	161274.	+	93111.4i	0.189304	+	0.109295i
$924$	−308167.	+	563149.i	−0.360946	+	0.659598i
$925$	−790464.	−	1.36912e6i	−0.923844	−	1.60015i
$926$	215029.	−	104969.i	0.250769	−	0.122417i
$927$	95041.2	+	283336.i	0.110599	+	0.329717i
$928$	350279.	−	294961.i	0.406742	−	0.342506i
$929$	352354.	+	610296.i	0.408271	+	0.707145i	0.994696	−	0.102858i	$-0.0327986\pi$
$929$	352354.	+	610296.i	0.408271	+	0.707145i	−0.586425	+	0.810003i	$0.699465\pi$
$930$	−424219.	−	195194.i	−0.490484	−	0.225684i
$931$	60216.4	+	34765.9i	0.0694729	+	0.0401102i
$932$	−296781.	−	733088.i	−0.341668	−	0.843965i
$933$	697306.	−	570163.i	0.801051	−	0.654992i
$934$	−691491.	−	466066.i	−0.792671	−	0.534262i
$935$		−	184963.i		−	0.211574i
$936$	−160589.	+	18590.0i	−0.183301	+	0.0212192i
$937$	−237273.			−0.270252			−0.135126	−	0.990828i	$-0.543144\pi$
$937$	−237273.			−0.270252			−0.135126	+	0.990828i	$0.543144\pi$
$938$	939533.	−	1.39396e6i	1.06784	−	1.58433i
$939$	1.34827e6	−	220103.i	1.52913	−	0.249629i
$940$	−1.89896e6	+	768768.i	−2.14911	+	0.870040i
$941$	−57476.2	+	99551.7i	−0.0649096	+	0.112427i	−0.896654	−	0.442732i	$-0.854009\pi$
$941$	−57476.2	+	99551.7i	−0.0649096	+	0.112427i	0.831744	+	0.555159i	$0.187343\pi$
$942$	−795023.	+	73635.1i	−0.895938	+	0.0829818i
$943$	−461467.	+	266428.i	−0.518940	+	0.299610i
$944$	−75348.5	+	18898.1i	−0.0845534	+	0.0212067i
$945$	961710.	+	1.82289e6i	1.07691	+	2.04125i
$946$	−99395.8	−	203612.i	−0.111067	−	0.227520i
$947$	890326.	−	514030.i	0.992772	−	0.573177i	0.0866700	−	0.996237i	$-0.472377\pi$
$947$	890326.	−	514030.i	0.992772	−	0.573177i	0.906102	+	0.423060i	$0.139044\pi$
$948$	467965.	−	284657.i	0.520711	−	0.316742i
$949$	−67658.0	+	117187.i	−0.0751254	+	0.130121i
$950$	−23732.1	+	341093.i	−0.0262960	+	0.377942i
$951$	−998419.	+	162991.i	−1.10396	+	0.180220i
$952$	−198214.	+	64632.6i	−0.218705	+	0.0713145i
$953$	837599.			0.922253			0.461127	−	0.887334i	$-0.347445\pi$
$953$	837599.			0.922253			0.461127	+	0.887334i	$0.347445\pi$
$954$	−1.45747e6	+	378646.i	−1.60141	+	0.416042i
$955$			1.82438e6i			2.00036i
$956$	−248284.	+	1.77561e6i	−0.271665	+	1.94282i
$957$	−229406.	+	187577.i	−0.250485	+	0.204813i
$958$	44454.6	−	638930.i	0.0484380	−	0.696181i
$959$	873882.	+	504536.i	0.950201	+	0.548599i
$960$	456853.	+	1.65956e6i	0.495717	+	1.80074i
$961$	−423174.	−	732958.i	−0.458218	−	0.793656i
$962$	55624.7	+	113947.i	0.0601059	+	0.123126i
$963$	−736906.	+	834192.i	−0.794620	+	0.899525i
$964$	−404464.	+	518435.i	−0.435237	+	0.557879i
$965$	−94598.6	−	163850.i	−0.101585	−	0.175951i
$966$	−354611.	−	500989.i	−0.380012	−	0.536876i
$967$	92494.4	+	53401.7i	0.0989151	+	0.0571087i	0.548642	−	0.836058i	$-0.315145\pi$
$967$	92494.4	+	53401.7i	0.0989151	+	0.0571087i	−0.449726	+	0.893166i	$0.648479\pi$
$968$	−394383.	+	438928.i	−0.420889	+	0.468428i
$969$	24890.5	+	9419.41i	0.0265086	+	0.0100317i
$970$	204685.	−	303686.i	0.217542	−	0.322761i
$971$			689120.i			0.730897i	0.930832	+	0.365448i	$0.119084\pi$
$971$			689120.i			0.730897i	−0.930832	+	0.365448i	$0.880916\pi$
$972$	−137990.	−	934653.i	−0.146054	−	0.989277i
$973$	247915.			0.261865
$974$	−1.23377e6	−	831561.i	−1.30051	−	0.876549i
$975$	−154494.	+	408245.i	−0.162518	+	0.429449i
$976$	235435.	+	67154.9i	0.247156	+	0.0704982i
$977$	293734.	−	508762.i	0.307726	−	0.532998i	−0.670138	−	0.742236i	$-0.733765\pi$
$977$	293734.	−	508762.i	0.307726	−	0.532998i	0.977865	+	0.209239i	$0.0670985\pi$
$978$	919830.	−	651075.i	0.961679	−	0.680696i
$979$	454787.	−	262571.i	0.474507	−	0.273957i
$980$	581366.	−	745184.i	0.605337	−	0.775910i
$981$	−1.13580e6	−	1.00334e6i	−1.18023	−	1.04259i
$982$	240170.	−	117243.i	0.249056	−	0.121580i
$983$	338570.	−	195474.i	0.350382	−	0.202293i	−0.314472	−	0.949267i	$-0.601827\pi$
$983$	338570.	−	195474.i	0.350382	−	0.202293i	0.664853	+	0.746974i	$0.268494\pi$
$984$	500450.	+	968294.i	0.516857	+	1.00004i
$985$	1.04755e6	−	1.81441e6i	1.07970	−	1.87009i
$986$	−96006.6	−	6679.82i	−0.0987523	−	0.00687086i
$987$	−945900.	−	1.15683e6i	−0.970981	−	1.18750i
$988$	3797.70	−	27159.3i	0.00389051	−	0.0278231i
$989$	216637.			0.221483
$990$	−280084.	−	1.07809e6i	−0.285771	−	1.09998i
$991$		−	462949.i		−	0.471396i	−0.971826	−	0.235698i	$-0.924262\pi$
$991$		−	462949.i		−	0.471396i	0.971826	−	0.235698i	$-0.0757376\pi$
$992$	96828.4	−	267483.i	0.0983964	−	0.271814i
$993$	−166648.	−	1.02082e6i	−0.169006	−	1.03526i
$994$	1.44279e6	+	100385.i	1.46026	+	0.101600i
$995$	−2.27488e6	−	1.31340e6i	−2.29780	−	1.32663i
$996$	−387912.	+	235962.i	−0.391034	+	0.237861i
$997$	−386642.	−	669683.i	−0.388972	−	0.673720i	0.603339	−	0.797485i	$-0.293836\pi$
$997$	−386642.	−	669683.i	−0.388972	−	0.673720i	−0.992312	+	0.123765i	$0.960503\pi$
$998$	1.19601e6	−	583851.i	1.20081	−	0.586193i
$999$	−655417.	+	345782.i	−0.656730	+	0.346475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.7	yes	44
3.2	odd	2		108.5.f.a.91.16		44
4.3	odd	2	inner	36.5.f.a.31.22	yes	44
9.2	odd	6		108.5.f.a.19.1		44
9.4	even	3		324.5.d.f.163.7		22
9.5	odd	6		324.5.d.e.163.16		22
9.7	even	3	inner	36.5.f.a.7.22	yes	44
12.11	even	2		108.5.f.a.91.1		44
36.7	odd	6	inner	36.5.f.a.7.7	✓	44
36.11	even	6		108.5.f.a.19.16		44
36.23	even	6		324.5.d.e.163.15		22
36.31	odd	6		324.5.d.f.163.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.7	✓	44	36.7	odd	6	inner
36.5.f.a.7.22	yes	44	9.7	even	3	inner
36.5.f.a.31.7	yes	44	1.1	even	1	trivial
36.5.f.a.31.22	yes	44	4.3	odd	2	inner
108.5.f.a.19.1		44	9.2	odd	6
108.5.f.a.19.16		44	36.11	even	6
108.5.f.a.91.1		44	12.11	even	2
108.5.f.a.91.16		44	3.2	odd	2
324.5.d.e.163.15		22	36.23	even	6
324.5.d.e.163.16		22	9.5	odd	6
324.5.d.f.163.7		22	9.4	even	3
324.5.d.f.163.8		22	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23562 + 3.31693i) q^{2} +(3.18543 - 8.41742i) q^{3} +(-6.00404 - 14.8308i) q^{4} +(-23.3466 + 40.4374i) q^{5} +(20.7986 + 29.3840i) q^{6} +(-52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 - 53.6263i) q^{9} +O(q^{10})\)	\(q+(-2.23562 + 3.31693i) q^{2} +(3.18543 - 8.41742i) q^{3} +(-6.00404 - 14.8308i) q^{4} +(-23.3466 + 40.4374i) q^{5} +(20.7986 + 29.3840i) q^{6} +(-52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 - 53.6263i) q^{9} +(-81.9341 - 167.841i) q^{10} +(-63.7631 + 36.8136i) q^{11} +(-143.962 + 3.29614i) q^{12} +(15.5924 - 27.0068i) q^{13} +(16.8104 - 241.609i) q^{14} +(266.010 + 325.329i) q^{15} +(-183.903 + 178.089i) q^{16} +53.8013 q^{17} +(313.590 - 81.4697i) q^{18} +54.9619i q^{19} +(739.891 + 103.459i) q^{20} +(87.7977 + 537.815i) q^{21} +(20.4416 - 293.799i) q^{22} +(243.863 + 140.795i) q^{23} +(310.911 - 484.882i) q^{24} +(-777.624 - 1346.88i) q^{25} +(54.7210 + 112.096i) q^{26} +(-644.770 + 340.165i) q^{27} +(763.818 + 595.904i) q^{28} +(223.597 + 387.282i) q^{29} +(-1673.79 + 155.026i) q^{30} +(240.584 + 138.901i) q^{31} +(-179.572 - 1008.13i) q^{32} +(106.763 + 653.989i) q^{33} +(-120.279 + 178.455i) q^{34} -2827.19i q^{35} +(-430.837 + 1222.29i) q^{36} +1016.51 q^{37} +(-182.305 - 122.874i) q^{38} +(-177.659 - 217.276i) q^{39} +(-1997.28 + 2222.87i) q^{40} +(-946.158 + 1638.79i) q^{41} +(-1980.18 - 911.129i) q^{42} +(666.266 - 384.669i) q^{43} +(928.811 + 724.625i) q^{44} +(3585.79 - 1202.81i) q^{45} +(-1012.19 + 494.115i) q^{46} +(-2374.81 + 1371.10i) q^{47} +(913.240 + 2115.28i) q^{48} +(632.546 - 1095.60i) q^{49} +(6205.98 + 431.792i) q^{50} +(171.381 - 452.869i) q^{51} +(-494.148 - 69.0969i) q^{52} -4647.69 q^{53} +(313.155 - 2899.14i) q^{54} -3437.89i q^{55} +(-3684.18 + 1201.32i) q^{56} +(462.637 + 175.078i) q^{57} +(-1784.46 - 124.157i) q^{58} +(262.792 + 151.723i) q^{59} +(3227.74 - 5898.42i) q^{60} +(-478.174 - 828.222i) q^{61} +(-998.577 + 487.469i) q^{62} +(4806.69 + 974.145i) q^{63} +(3745.36 + 1658.17i) q^{64} +(728.057 + 1261.03i) q^{65} +(-2407.91 - 1107.94i) q^{66} +(6010.96 + 3470.43i) q^{67} +(-323.026 - 797.915i) q^{68} +(1961.94 - 1604.21i) q^{69} +(9377.58 + 6320.51i) q^{70} +5971.60i q^{71} +(-3091.07 - 4161.63i) q^{72} -4339.17 q^{73} +(-2272.53 + 3371.70i) q^{74} +(-13814.4 + 2255.18i) q^{75} +(815.127 - 329.993i) q^{76} +(2229.00 - 3860.75i) q^{77} +(1117.87 - 103.537i) q^{78} +(-3294.15 + 1901.88i) q^{79} +(-2907.96 - 11594.3i) q^{80} +(809.440 + 6510.88i) q^{81} +(-3320.52 - 6802.05i) q^{82} +(2730.64 - 1576.53i) q^{83} +(7449.07 - 4531.17i) q^{84} +(-1256.08 + 2175.59i) q^{85} +(-213.596 + 3069.93i) q^{86} +(3972.17 - 648.452i) q^{87} +(-4479.99 + 1460.82i) q^{88} -7132.44 q^{89} +(-4026.82 + 14582.8i) q^{90} +1888.18i q^{91} +(623.925 - 4462.02i) q^{92} +(1935.55 - 1582.63i) q^{93} +(761.331 - 10942.3i) q^{94} +(-2222.52 - 1283.17i) q^{95} +(-9057.89 - 1699.80i) q^{96} +(980.405 + 1698.11i) q^{97} +(2219.91 + 4547.46i) q^{98} +(5844.98 + 1184.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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