LMFDB - Embedded newform 36.5.f.a.31.16

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			31.16
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.58866 - 3.04940i) q^{2} +(-2.22096 - 8.72166i) q^{3} +(-2.59770 - 15.7877i) q^{4} +(-5.51579 + 9.55363i) q^{5} +(-32.3451 - 15.8048i) q^{6} +(10.3188 - 5.95759i) q^{7} +(-54.8676 - 32.9476i) q^{8} +(-71.1347 + 38.7409i) q^{9} +O(q^{10})$	\(q+(2.58866 - 3.04940i) q^{2} +(-2.22096 - 8.72166i) q^{3} +(-2.59770 - 15.7877i) q^{4} +(-5.51579 + 9.55363i) q^{5} +(-32.3451 - 15.8048i) q^{6} +(10.3188 - 5.95759i) q^{7} +(-54.8676 - 32.9476i) q^{8} +(-71.1347 + 38.7409i) q^{9} +(14.8544 + 41.5509i) q^{10} +(189.995 - 109.694i) q^{11} +(-131.926 + 57.7201i) q^{12} +(18.5350 - 32.1036i) q^{13} +(8.54488 - 46.8884i) q^{14} +(95.5738 + 26.8886i) q^{15} +(-242.504 + 82.0235i) q^{16} +284.021 q^{17} +(-66.0069 + 317.205i) q^{18} -45.4901i q^{19} +(165.158 + 62.2643i) q^{20} +(-74.8777 - 76.7659i) q^{21} +(157.332 - 863.330i) q^{22} +(174.319 + 100.643i) q^{23} +(-165.499 + 551.712i) q^{24} +(251.652 + 435.874i) q^{25} +(-49.9160 - 139.626i) q^{26} +(495.872 + 534.371i) q^{27} +(-120.862 - 147.435i) q^{28} +(614.153 + 1063.74i) q^{29} +(329.402 - 221.838i) q^{30} +(-1311.83 - 757.384i) q^{31} +(-377.637 + 951.823i) q^{32} +(-1378.68 - 1413.45i) q^{33} +(735.233 - 866.094i) q^{34} +131.443i q^{35} +(796.416 + 1022.42i) q^{36} -1521.29 q^{37} +(-138.718 - 117.758i) q^{38} +(-321.162 - 90.3555i) q^{39} +(617.407 - 342.453i) q^{40} +(1316.97 - 2281.07i) q^{41} +(-427.923 + 29.6117i) q^{42} +(-34.6057 + 19.9796i) q^{43} +(-2225.36 - 2714.63i) q^{44} +(22.2482 - 893.281i) q^{45} +(758.153 - 271.038i) q^{46} +(-2498.36 + 1442.43i) q^{47} +(1253.97 + 1932.87i) q^{48} +(-1129.51 + 1956.38i) q^{49} +(1980.60 + 360.941i) q^{50} +(-630.798 - 2477.13i) q^{51} +(-554.991 - 209.230i) q^{52} +1415.13 q^{53} +(2913.15 - 128.809i) q^{54} +2420.19i q^{55} +(-762.458 - 13.1019i) q^{56} +(-396.749 + 101.032i) q^{57} +(4833.61 + 880.870i) q^{58} +(2453.33 + 1416.43i) q^{59} +(176.238 - 1578.74i) q^{60} +(2628.64 + 4552.93i) q^{61} +(-5705.44 + 2039.68i) q^{62} +(-503.226 + 823.552i) q^{63} +(1924.92 + 3615.51i) q^{64} +(204.471 + 354.154i) q^{65} +(-7879.10 + 545.223i) q^{66} +(805.917 + 465.296i) q^{67} +(-737.801 - 4484.04i) q^{68} +(490.620 - 1743.87i) q^{69} +(400.823 + 340.261i) q^{70} -1162.75i q^{71} +(5179.41 + 218.094i) q^{72} -2162.87 q^{73} +(-3938.11 + 4639.03i) q^{74} +(3242.64 - 3162.88i) q^{75} +(-718.185 + 118.170i) q^{76} +(1307.02 - 2263.82i) q^{77} +(-1106.91 + 745.454i) q^{78} +(6482.54 - 3742.70i) q^{79} +(553.978 - 2769.22i) q^{80} +(3559.29 - 5511.64i) q^{81} +(-3546.69 - 9920.88i) q^{82} +(-966.756 + 558.157i) q^{83} +(-1017.45 + 1381.56i) q^{84} +(-1566.60 + 2713.43i) q^{85} +(-28.6565 + 157.247i) q^{86} +(7913.60 - 7718.96i) q^{87} +(-14038.7 - 241.238i) q^{88} -6739.71 q^{89} +(-2666.38 - 2380.24i) q^{90} -441.696i q^{91} +(1136.10 - 3013.54i) q^{92} +(-3692.13 + 13123.4i) q^{93} +(-2068.85 + 11352.5i) q^{94} +(434.596 + 250.914i) q^{95} +(9140.19 + 1179.66i) q^{96} +(-6023.28 - 10432.6i) q^{97} +(3041.85 + 8508.73i) q^{98} +(-9265.60 + 15163.6i) 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 $

$2$	2.58866	−	3.04940i	0.647164	−	0.762350i
$2$	2.58866	−	3.04940i	0.647164	−	0.762350i
$3$	−2.22096	−	8.72166i	−0.246773	−	0.969073i
$3$	−2.22096	−	8.72166i	−0.246773	−	0.969073i
$4$	−2.59770	−	15.7877i	−0.162356	−	0.986732i
$5$	−5.51579	+	9.55363i	−0.220632	+	0.382145i	−0.955000	−	0.296606i	$-0.904145\pi$
$5$	−5.51579	+	9.55363i	−0.220632	+	0.382145i	0.734368	+	0.678751i	$0.237479\pi$
$6$	−32.3451	−	15.8048i	−0.898476	−	0.439022i
$7$	10.3188	−	5.95759i	0.210589	−	0.121583i	−0.390996	−	0.920392i	$-0.627869\pi$
$7$	10.3188	−	5.95759i	0.210589	−	0.121583i	0.601585	+	0.798809i	$0.294536\pi$
$8$	−54.8676	−	32.9476i	−0.857307	−	0.514806i
$9$	−71.1347	+	38.7409i	−0.878206	+	0.478282i
$10$	14.8544	+	41.5509i	0.148544	+	0.415509i
$11$	189.995	−	109.694i	1.57021	−	0.906559i	0.574063	−	0.818811i	$-0.305367\pi$
$11$	189.995	−	109.694i	1.57021	−	0.906559i	0.996143	−	0.0877473i	$-0.0279668\pi$
$12$	−131.926	+	57.7201i	−0.916151	+	0.400834i
$13$	18.5350	−	32.1036i	0.109675	−	0.189962i	−0.805964	−	0.591965i	$-0.798352\pi$
$13$	18.5350	−	32.1036i	0.109675	−	0.189962i	0.915639	+	0.402003i	$0.131686\pi$
$14$	8.54488	−	46.8884i	0.0435963	−	0.239227i
$15$	95.5738	+	26.8886i	0.424773	+	0.119505i
$16$	−242.504	+	82.0235i	−0.947281	+	0.320404i
$17$	284.021			0.982771			0.491386	−	0.870942i	$-0.336491\pi$
$17$	284.021			0.982771			0.491386	+	0.870942i	$0.336491\pi$
$18$	−66.0069	+	317.205i	−0.203725	+	0.979028i
$19$		−	45.4901i		−	0.126011i	−0.998013	−	0.0630057i	$-0.979931\pi$
$19$		−	45.4901i		−	0.126011i	0.998013	−	0.0630057i	$-0.0200686\pi$
$20$	165.158	+	62.2643i	0.412896	+	0.155661i
$21$	−74.8777	−	76.7659i	−0.169791	−	0.174072i
$22$	157.332	−	863.330i	0.325066	−	1.78374i
$23$	174.319	+	100.643i	0.329525	+	0.190252i	0.655630	−	0.755082i	$-0.272403\pi$
$23$	174.319	+	100.643i	0.329525	+	0.190252i	−0.326105	+	0.945334i	$0.605736\pi$
$24$	−165.499	+	551.712i	−0.287324	+	0.957833i
$25$	251.652	+	435.874i	0.402643	+	0.697399i
$26$	−49.9160	−	139.626i	−0.0738402	−	0.206547i
$27$	495.872	+	534.371i	0.680208	+	0.733019i
$28$	−120.862	−	147.435i	−0.154161	−	0.188055i
$29$	614.153	+	1063.74i	0.730265	+	1.26486i	0.956770	+	0.290846i	$0.0939366\pi$
$29$	614.153	+	1063.74i	0.730265	+	1.26486i	−0.226505	+	0.974010i	$0.572730\pi$
$30$	329.402	−	221.838i	0.366003	−	0.246486i
$31$	−1311.83	−	757.384i	−1.36507	−	0.788121i	−0.374773	−	0.927117i	$-0.622279\pi$
$31$	−1311.83	−	757.384i	−1.36507	−	0.788121i	−0.990293	+	0.138996i	$0.955613\pi$
$32$	−377.637	+	951.823i	−0.368786	+	0.929514i
$33$	−1378.68	−	1413.45i	−1.26601	−	1.29793i
$34$	735.233	−	866.094i	0.636015	−	0.749216i
$35$			131.443i			0.107301i
$36$	796.416	+	1022.42i	0.614519	+	0.788902i
$37$	−1521.29			−1.11124			−0.555622	−	0.831435i	$-0.687520\pi$
$37$	−1521.29			−1.11124			−0.555622	+	0.831435i	$0.687520\pi$
$38$	−138.718	−	117.758i	−0.0960648	−	0.0815501i
$39$	−321.162	−	90.3555i	−0.211152	−	0.0594053i
$40$	617.407	−	342.453i	0.385879	−	0.214033i
$41$	1316.97	−	2281.07i	0.783447	−	1.35697i	−0.146476	−	0.989214i	$-0.546793\pi$
$41$	1316.97	−	2281.07i	0.783447	−	1.35697i	0.929923	−	0.367755i	$-0.119874\pi$
$42$	−427.923	+	29.6117i	−0.242587	+	0.0167867i
$43$	−34.6057	+	19.9796i	−0.0187159	+	0.0108056i	−0.509329	−	0.860572i	$-0.670106\pi$
$43$	−34.6057	+	19.9796i	−0.0187159	+	0.0108056i	0.490613	+	0.871378i	$0.336773\pi$
$44$	−2225.36	−	2714.63i	−1.14946	−	1.40219i
$45$	22.2482	−	893.281i	0.0109868	−	0.441126i
$46$	758.153	−	271.038i	0.358295	−	0.128090i
$47$	−2498.36	+	1442.43i	−1.13099	+	0.652978i	−0.944184	−	0.329419i	$-0.893147\pi$
$47$	−2498.36	+	1442.43i	−1.13099	+	0.652978i	−0.186807	+	0.982397i	$0.559814\pi$
$48$	1253.97	+	1932.87i	0.544259	+	0.838917i
$49$	−1129.51	+	1956.38i	−0.470435	+	0.814817i
$50$	1980.60	+	360.941i	0.792239	+	0.144376i
$51$	−630.798	−	2477.13i	−0.242521	−	0.952377i
$52$	−554.991	−	209.230i	−0.205248	−	0.0773780i
$53$	1415.13			0.503783			0.251892	−	0.967755i	$-0.418947\pi$
$53$	1415.13			0.503783			0.251892	+	0.967755i	$0.418947\pi$
$54$	2913.15	−	128.809i	0.999024	−	0.0441732i
$55$			2420.19i			0.800062i
$56$	−762.458	−	13.1019i	−0.243131	−	0.00417791i
$57$	−396.749	+	101.032i	−0.122114	+	0.0310962i
$58$	4833.61	+	880.870i	1.43686	+	0.261852i
$59$	2453.33	+	1416.43i	0.704778	+	0.406904i	0.809125	−	0.587637i	$-0.199942\pi$
$59$	2453.33	+	1416.43i	0.704778	+	0.406904i	−0.104346	+	0.994541i	$0.533275\pi$
$60$	176.238	−	1578.74i	0.0489550	−	0.438539i
$61$	2628.64	+	4552.93i	0.706433	+	1.22358i	0.966172	+	0.257899i	$0.0830300\pi$
$61$	2628.64	+	4552.93i	0.706433	+	1.22358i	−0.259739	+	0.965679i	$0.583637\pi$
$62$	−5705.44	+	2039.68i	−1.48425	+	0.530614i
$63$	−503.226	+	823.552i	−0.126789	+	0.207496i
$64$	1924.92	+	3615.51i	0.469950	+	0.882693i
$65$	204.471	+	354.154i	0.0483954	+	0.0838233i
$66$	−7879.10	+	545.223i	−1.80879	+	0.125166i
$67$	805.917	+	465.296i	0.179531	+	0.103653i	0.587073	−	0.809534i	$-0.300280\pi$
$67$	805.917	+	465.296i	0.179531	+	0.103653i	−0.407541	+	0.913187i	$0.633614\pi$
$68$	−737.801	−	4484.04i	−0.159559	−	0.969732i
$69$	490.620	−	1743.87i	0.103050	−	0.366283i
$70$	400.823	+	340.261i	0.0818006	+	0.0694411i
$71$		−	1162.75i		−	0.230659i	−0.993327	−	0.115329i	$-0.963208\pi$
$71$		−	1162.75i		−	0.230659i	0.993327	−	0.115329i	$-0.0367923\pi$
$72$	5179.41	+	218.094i	0.999115	+	0.0420707i
$73$	−2162.87			−0.405867			−0.202934	−	0.979192i	$-0.565048\pi$
$73$	−2162.87			−0.405867			−0.202934	+	0.979192i	$0.565048\pi$
$74$	−3938.11	+	4639.03i	−0.719158	+	0.847157i
$75$	3242.64	−	3162.88i	0.576469	−	0.562290i
$76$	−718.185	+	118.170i	−0.124339	+	0.0204587i
$77$	1307.02	−	2263.82i	0.220445	−	0.381822i
$78$	−1106.91	+	745.454i	−0.181938	+	0.122527i
$79$	6482.54	−	3742.70i	1.03870	−	0.599695i	0.119237	−	0.992866i	$-0.461955\pi$
$79$	6482.54	−	3742.70i	1.03870	−	0.599695i	0.919466	+	0.393171i	$0.128622\pi$
$80$	553.978	−	2769.22i	0.0865591	−	0.432690i
$81$	3559.29	−	5511.64i	0.542492	−	0.840061i
$82$	−3546.69	−	9920.88i	−0.527467	−	1.47544i
$83$	−966.756	+	558.157i	−0.140333	+	0.0810215i	−0.568523	−	0.822667i	$-0.692485\pi$
$83$	−966.756	+	558.157i	−0.140333	+	0.0810215i	0.428190	+	0.903689i	$0.359152\pi$
$84$	−1017.45	+	1381.56i	−0.144196	+	0.195800i
$85$	−1566.60	+	2713.43i	−0.216830	+	0.375561i
$86$	−28.6565	+	157.247i	−0.00387459	+	0.0212611i
$87$	7913.60	−	7718.96i	1.04553	−	1.01981i
$88$	−14038.7	−	241.238i	−1.81285	−	0.0311516i
$89$	−6739.71			−0.850866			−0.425433	−	0.904990i	$-0.639878\pi$
$89$	−6739.71			−0.850866			−0.425433	+	0.904990i	$0.639878\pi$
$90$	−2666.38	−	2380.24i	−0.329183	−	0.293857i
$91$		−	441.696i		−	0.0533385i
$92$	1136.10	−	3013.54i	0.134227	−	0.356042i
$93$	−3692.13	+	13123.4i	−0.426886	+	1.51734i
$94$	−2068.85	+	11352.5i	−0.234139	+	1.28480i
$95$	434.596	+	250.914i	0.0481546	+	0.0278021i
$96$	9140.19	+	1179.66i	0.991774	+	0.128002i
$97$	−6023.28	−	10432.6i	−0.640161	−	1.10879i	−0.985396	−	0.170276i	$-0.945534\pi$
$97$	−6023.28	−	10432.6i	−0.640161	−	1.10879i	0.345235	−	0.938516i	$-0.387799\pi$
$98$	3041.85	+	8508.73i	0.316727	+	0.885957i
$99$	−9265.60	+	15163.6i	−0.945373	+	1.54715i
$100$	6227.74	−	5105.28i	0.622774	−	0.510528i
$101$	4777.60	+	8275.04i	0.468346	+	0.811199i	0.999346	−	0.0361728i	$-0.0115167\pi$
$101$	4777.60	+	8275.04i	0.468346	+	0.811199i	−0.530999	+	0.847372i	$0.678183\pi$
$102$	−9186.70	−	4488.89i	−0.882996	−	0.431458i
$103$	−9962.26	−	5751.71i	−0.939039	−	0.542154i	−0.0493798	−	0.998780i	$-0.515724\pi$
$103$	−9962.26	−	5751.71i	−0.939039	−	0.542154i	−0.889659	+	0.456626i	$0.849058\pi$
$104$	−2074.71	+	1150.77i	−0.191819	+	0.106395i
$105$	1146.40	−	291.930i	0.103982	−	0.0264789i
$106$	3663.28	−	4315.29i	0.326031	−	0.384059i
$107$		−	6602.72i		−	0.576707i	−0.957524	−	0.288353i	$-0.906892\pi$
$107$		−	6602.72i		−	0.576707i	0.957524	−	0.288353i	$-0.0931078\pi$
$108$	7148.37	−	9216.82i	0.612857	−	0.790194i
$109$	12045.3			1.01383			0.506913	−	0.861997i	$-0.330786\pi$
$109$	12045.3			1.01383			0.506913	+	0.861997i	$0.330786\pi$
$110$	7380.12	+	6265.04i	0.609928	+	0.517772i
$111$	3378.73	+	13268.2i	0.274225	+	1.07688i
$112$	−2013.70	+	2291.13i	−0.160531	+	0.182647i
$113$	−1865.35	+	3230.88i	−0.146084	+	0.253025i	−0.929777	−	0.368124i	$-0.880000\pi$
$113$	−1865.35	+	3230.88i	−0.146084	+	0.253025i	0.783693	+	0.621149i	$0.213334\pi$
$114$	−718.962	+	1471.38i	−0.0553218	+	0.113218i
$115$	−1923.01	+	1110.25i	−0.145407	+	0.0839510i
$116$	15198.7	−	12459.4i	1.12951	−	0.925933i
$117$	−74.7620	+	3001.74i	−0.00546146	+	0.219281i
$118$	10670.1	−	3814.54i	0.766311	−	0.273954i
$119$	2930.77	−	1692.08i	0.206960	−	0.119489i
$120$	−4358.00	−	4624.24i	−0.302639	−	0.321128i
$121$	16744.9	−	29003.0i	1.14370	−	1.98094i
$122$	20688.4	+	3770.21i	1.38997	+	0.253307i
$123$	−22819.6	−	6420.05i	−1.50834	−	0.424354i
$124$	−8549.63	+	22678.2i	−0.556037	+	1.47491i
$125$	−12447.0			−0.796607
$126$	1208.66	+	3666.43i	0.0761314	+	0.230942i
$127$			26549.7i			1.64608i	0.567980	+	0.823042i	$0.307725\pi$
$127$			26549.7i			1.64608i	−0.567980	+	0.823042i	$0.692275\pi$
$128$	16008.1	+	3489.47i	0.977056	+	0.212981i
$129$	251.113	+	257.445i	0.0150900	+	0.0154706i
$130$	1609.26	+	293.269i	0.0952226	+	0.0173532i
$131$	−1142.84	−	659.821i	−0.0665954	−	0.0384489i	0.466333	−	0.884609i	$-0.345575\pi$
$131$	−1142.84	−	659.821i	−0.0665954	−	0.0384489i	−0.532928	+	0.846161i	$0.678908\pi$
$132$	−18733.7	+	25437.9i	−1.07517	+	1.45994i
$133$	−271.011	−	469.405i	−0.0153209	−	0.0265366i
$134$	3505.12	−	1253.07i	0.195206	−	0.0697856i
$135$	−7840.31	+	1789.90i	−0.430195	+	0.0982111i
$136$	−15583.6	−	9357.79i	−0.842537	−	0.505936i
$137$	−12906.5	−	22354.7i	−0.687648	−	1.19104i	−0.972597	−	0.232499i	$-0.925310\pi$
$137$	−12906.5	−	22354.7i	−0.687648	−	1.19104i	0.284949	−	0.958543i	$-0.408023\pi$
$138$	−4047.73	−	6010.39i	−0.212546	−	0.315605i
$139$	−11377.8	−	6569.00i	−0.588885	−	0.339993i	0.175772	−	0.984431i	$-0.443758\pi$
$139$	−11377.8	−	6569.00i	−0.588885	−	0.339993i	−0.764656	+	0.644438i	$0.777091\pi$
$140$	2075.19	−	341.450i	0.105877	−	0.0174209i
$141$	18129.1	+	18586.3i	0.911881	+	0.934876i
$142$	−3545.69	−	3009.96i	−0.175843	−	0.149274i
$143$		−	8132.70i		−	0.397706i
$144$	14072.8	−	15229.5i	0.678664	−	0.734449i
$145$	−13550.2			−0.644478
$146$	−5598.92	+	6595.45i	−0.262663	+	0.309413i
$147$	19571.5	+	5506.21i	0.905708	+	0.254811i
$148$	3951.86	+	24017.7i	0.180417	+	1.09650i
$149$	−12968.2	+	22461.6i	−0.584128	+	1.01174i	0.410856	+	0.911700i	$0.365230\pi$
$149$	−12968.2	+	22461.6i	−0.584128	+	1.01174i	−0.994984	+	0.100038i	$0.968103\pi$
$150$	−1250.82	−	18075.7i	−0.0555919	−	0.803366i
$151$	24591.2	−	14197.8i	1.07852	−	0.622681i	0.148020	−	0.988984i	$-0.452710\pi$
$151$	24591.2	−	14197.8i	1.07852	−	0.622681i	0.930496	+	0.366303i	$0.119377\pi$
$152$	−1498.79	+	2495.93i	−0.0648714	+	0.108030i
$153$	−20203.7	+	11003.2i	−0.863076	+	0.470042i
$154$	−3519.88	−	9845.88i	−0.148418	−	0.415158i
$155$	14471.5	−	8355.15i	0.602353	−	0.347769i
$156$	−592.223	+	5305.14i	−0.0243353	+	0.217995i
$157$	2760.19	−	4780.78i	0.111980	−	0.193954i	−0.804589	−	0.593832i	$-0.797614\pi$
$157$	2760.19	−	4780.78i	0.111980	−	0.193954i	0.916568	+	0.399878i	$0.130948\pi$
$158$	5368.10	−	29456.4i	0.215033	−	1.17996i
$159$	−3142.94	−	12342.3i	−0.124320	−	0.488203i
$160$	−7010.39	−	8857.86i	−0.273844	−	0.346010i
$161$	2398.36			0.0925257
$162$	−7593.42	−	25121.5i	−0.289339	−	0.957227i
$163$		−	407.281i		−	0.0153292i	−0.999971	−	0.00766459i	$-0.997560\pi$
$163$		−	407.281i		−	0.0153292i	0.999971	−	0.00766459i	$-0.00243974\pi$
$164$	−39433.9	−	14866.5i	−1.46616	−	0.552739i
$165$	21108.1	−	5375.13i	0.775319	−	0.197434i
$166$	−800.556	+	4392.91i	−0.0290520	+	0.159417i
$167$	−20561.9	−	11871.4i	−0.737277	−	0.425667i	0.0838016	−	0.996482i	$-0.473294\pi$
$167$	−20561.9	−	11871.4i	−0.737277	−	0.425667i	−0.821078	+	0.570816i	$0.806627\pi$
$168$	1579.12	+	6679.00i	0.0559494	+	0.236643i
$169$	13593.4	+	23544.5i	0.475943	+	0.824357i
$170$	4218.95	+	11801.3i	0.145984	+	0.408351i
$171$	1762.33	+	3235.92i	0.0602690	+	0.110664i
$172$	405.328	+	494.444i	0.0137009	+	0.0167132i
$173$	1413.25	+	2447.82i	0.0472200	+	0.0817874i	0.888669	−	0.458549i	$-0.151630\pi$
$173$	1413.25	+	2447.82i	0.0472200	+	0.0817874i	−0.841449	+	0.540336i	$0.818297\pi$
$174$	−3052.60	−	44113.5i	−0.100826	−	1.45705i
$175$	5193.52	+	2998.48i	0.169584	+	0.0979095i
$176$	−37077.0	+	42185.2i	−1.19696	+	1.36187i
$177$	6904.89	−	24543.0i	0.220399	−	0.783395i
$178$	−17446.8	+	20552.1i	−0.550650	+	0.648658i
$179$			45743.4i			1.42765i	0.700323	+	0.713826i	$0.253039\pi$
$179$			45743.4i			1.42765i	−0.700323	+	0.713826i	$0.746961\pi$
$180$	−14160.7	+	1969.23i	−0.437057	+	0.0607787i
$181$	−24226.2			−0.739483			−0.369742	−	0.929135i	$-0.620554\pi$
$181$	−24226.2			−0.739483			−0.369742	+	0.929135i	$0.620554\pi$
$182$	−1346.91	−	1143.40i	−0.0406626	−	0.0345188i
$183$	33871.0	−	33037.9i	1.01141	−	0.986531i
$184$	−6248.52	−	11265.4i	−0.184562	−	0.332745i
$185$	8391.13	−	14533.9i	0.245176	−	0.424657i
$186$	30461.0	+	45230.9i	0.880476	+	1.30740i
$187$	53962.5	−	31155.3i	1.54315	−	0.890940i
$188$	29262.6	+	35696.4i	0.827938	+	1.00997i
$189$	8300.38	+	2559.89i	0.232367	+	0.0716634i
$190$	1890.16	−	675.726i	0.0523589	−	0.0187182i
$191$	−19504.6	+	11261.0i	−0.534651	+	0.308681i	−0.742908	−	0.669393i	$-0.766554\pi$
$191$	−19504.6	+	11261.0i	−0.534651	+	0.308681i	0.208257	+	0.978074i	$0.433221\pi$
$192$	27258.1	−	24818.4i	0.739423	−	0.673241i
$193$	−9144.35	+	15838.5i	−0.245493	+	0.425205i	−0.962270	−	0.272097i	$-0.912283\pi$
$193$	−9144.35	+	15838.5i	−0.245493	+	0.425205i	0.716777	+	0.697302i	$0.245616\pi$
$194$	−47405.5	−	8639.10i	−1.25958	−	0.229544i
$195$	2634.69	−	2569.88i	0.0692883	−	0.0675841i
$196$	33820.9	+	12750.4i	0.880385	+	0.331903i
$197$	36300.2			0.935356			0.467678	−	0.883899i	$-0.345091\pi$
$197$	36300.2			0.935356			0.467678	+	0.883899i	$0.345091\pi$
$198$	22254.4	+	67507.9i	0.567656	+	1.72196i
$199$			47336.5i			1.19533i	0.801744	+	0.597667i	$0.203906\pi$
$199$			47336.5i			1.19533i	−0.801744	+	0.597667i	$0.796094\pi$
$200$	553.433	−	32206.7i	0.0138358	−	0.805168i
$201$	2268.25	−	8062.33i	0.0561434	−	0.199558i
$202$	37601.5	+	6852.44i	0.921515	+	0.167935i
$203$	12674.7	+	7317.73i	0.307571	+	0.177576i
$204$	−37469.6	+	16393.7i	−0.900366	+	0.393928i
$205$	14528.3	+	25163.8i	0.345706	+	0.598781i
$206$	−43328.2	+	15489.7i	−1.02102	+	0.365014i
$207$	−16299.1	−	405.949i	−0.380385	−	0.00947394i
$208$	−1861.57	+	9305.56i	−0.0430280	+	0.215088i
$209$	−4989.97	−	8642.89i	−0.114237	−	0.197864i
$210$	2077.43	−	4251.55i	0.0471073	−	0.0964070i
$211$	−40261.7	−	23245.1i	−0.904330	−	0.522115i	−0.0257275	−	0.999669i	$-0.508190\pi$
$211$	−40261.7	−	23245.1i	−0.904330	−	0.522115i	−0.878602	+	0.477554i	$0.841524\pi$
$212$	−3676.08	−	22341.6i	−0.0817924	−	0.497099i
$213$	−10141.1	+	2582.42i	−0.223525	+	0.0569203i
$214$	−20134.3	−	17092.2i	−0.439653	−	0.373224i
$215$		−	440.814i		−	0.00953626i
$216$	−9601.10	−	45657.4i	−0.205785	−	0.978597i
$217$	−18048.7			−0.383290
$218$	31181.1	−	36730.9i	0.656113	−	0.772891i
$219$	4803.64	+	18863.8i	0.100157	+	0.393315i
$220$	38209.2	−	6286.92i	0.789447	−	0.129895i
$221$	5264.34	−	9118.10i	0.107785	−	0.186689i
$222$	49206.4	+	24043.7i	0.998426	+	0.487861i
$223$	−71531.9	+	41298.9i	−1.43843	+	0.830480i	−0.997741	−	0.0671780i	$-0.978600\pi$
$223$	−71531.9	+	41298.9i	−1.43843	+	0.830480i	−0.440693	+	0.897658i	$0.645267\pi$
$224$	1773.79	+	12071.5i	0.0353514	+	0.240583i
$225$	−34787.3	−	21256.6i	−0.687157	−	0.419883i
$226$	5023.49	+	14051.8i	0.0983533	+	0.275116i
$227$	25722.3	−	14850.8i	0.499182	−	0.288203i	−0.229194	−	0.973381i	$-0.573609\pi$
$227$	25722.3	−	14850.8i	0.499182	−	0.288203i	0.728376	+	0.685178i	$0.240276\pi$
$228$	2625.69	+	6001.31i	0.0505096	+	0.115445i
$229$	−22667.9	+	39262.0i	−0.432256	+	0.748690i	−0.997067	−	0.0765307i	$-0.975616\pi$
$229$	−22667.9	+	39262.0i	−0.432256	+	0.748690i	0.564811	+	0.825220i	$0.308949\pi$
$230$	−1592.42	+	8738.10i	−0.0301024	+	0.165182i
$231$	−22647.1	−	6371.52i	−0.424413	−	0.119404i
$232$	1350.64	−	78599.9i	0.0250937	−	1.46031i
$233$	50931.3			0.938151			0.469075	−	0.883158i	$-0.344587\pi$
$233$	50931.3			0.938151			0.469075	+	0.883158i	$0.344587\pi$
$234$	8959.99	+	7998.47i	0.163635	+	0.146075i
$235$		−	31824.5i		−	0.576270i
$236$	15989.2	−	42412.0i	0.287080	−	0.761491i
$237$	−47040.0	−	48226.2i	−0.837472	−	0.858590i
$238$	2426.92	−	13317.3i	0.0428452	−	0.235105i
$239$	−31946.2	−	18444.1i	−0.559272	−	0.322896i	0.193581	−	0.981084i	$-0.437990\pi$
$239$	−31946.2	−	18444.1i	−0.559272	−	0.322896i	−0.752853	+	0.658188i	$0.771323\pi$
$240$	−25382.5	+	1318.70i	−0.440669	+	0.0228941i
$241$	−4193.64	−	7263.59i	−0.0722033	−	0.125060i	0.827663	−	0.561225i	$-0.189670\pi$
$241$	−4193.64	−	7263.59i	−0.0722033	−	0.125060i	−0.899867	+	0.436165i	$0.856336\pi$
$242$	−45094.9	−	126141.i	−0.770011	−	2.15389i
$243$	−55975.7	−	18801.8i	−0.947953	−	0.318410i
$244$	65052.0	−	53327.3i	1.09265	−	0.895715i
$245$	−12460.3	−	21581.9i	−0.207586	−	0.359549i
$246$	−78649.5	+	52966.9i	−1.29965	+	0.875254i
$247$	−1460.40	−	843.160i	−0.0239374	−	0.0138203i
$248$	47023.0	+	84777.4i	0.764551	+	1.37840i
$249$	7015.18	+	7192.08i	0.113146	+	0.115999i
$250$	−32221.0	+	37955.8i	−0.515536	+	0.607293i
$251$			1475.47i			0.0234198i	0.999931	+	0.0117099i	$0.00372746\pi$
$251$			1475.47i			0.0234198i	−0.999931	+	0.0117099i	$0.996273\pi$
$252$	14309.2	+	5805.44i	0.225328	+	0.0914185i
$253$	44159.6			0.689897
$254$	80960.7	+	68728.1i	1.25489	+	1.06529i
$255$	27145.0	+	7636.94i	0.417454	+	0.117446i
$256$	52080.3	−	39782.1i	0.794682	−	0.607026i
$257$	−17336.5	+	30027.8i	−0.262480	+	0.454629i	−0.966900	−	0.255154i	$-0.917874\pi$
$257$	−17336.5	+	30027.8i	−0.262480	+	0.454629i	0.704420	+	0.709783i	$0.251207\pi$
$258$	1435.10	−	99.3072i	0.0215597	−	0.00149191i
$259$	−15698.0	+	9063.23i	−0.234015	+	0.135109i
$260$	5060.12	−	4148.11i	0.0748539	−	0.0613626i
$261$	−84897.9	−	51876.3i	−1.24628	−	0.761531i
$262$	−4970.49	+	1776.94i	−0.0724097	+	0.0258863i
$263$	−16482.5	+	9516.19i	−0.238294	+	0.137579i	−0.614392	−	0.789001i	$-0.710599\pi$
$263$	−16482.5	+	9516.19i	−0.238294	+	0.137579i	0.376099	+	0.926580i	$0.377265\pi$
$264$	29075.4	+	122977.i	0.417174	+	1.76447i
$265$	−7805.54	+	13519.6i	−0.111151	+	0.192518i
$266$	−2132.96	−	388.707i	−0.0301453	−	0.00549363i
$267$	14968.6	+	58781.5i	0.209971	+	0.824552i
$268$	5252.43	−	13932.3i	0.0731292	−	0.193978i
$269$	58724.1			0.811544			0.405772	−	0.913974i	$-0.367003\pi$
$269$	58724.1			0.811544			0.405772	+	0.913974i	$0.367003\pi$
$270$	−14837.8	+	28541.7i	−0.203536	+	0.391518i
$271$		−	31474.1i		−	0.428563i	−0.976772	−	0.214281i	$-0.931259\pi$
$271$		−	31474.1i		−	0.428563i	0.976772	−	0.214281i	$-0.0687409\pi$
$272$	−68876.2	+	23296.4i	−0.930960	+	0.314884i
$273$	−3852.32	+	980.988i	−0.0516889	+	0.0131625i
$274$	−101579.	−	18511.6i	−1.35301	−	0.246571i
$275$	95625.2	+	55209.2i	1.26447	+	0.730040i
$276$	−28806.3	−	3215.70i	−0.378154	−	0.0422141i
$277$	−33265.8	−	57618.0i	−0.433549	−	0.750929i	0.563627	−	0.826029i	$-0.309405\pi$
$277$	−33265.8	−	57618.0i	−0.433549	−	0.750929i	−0.997176	+	0.0751008i	$0.976072\pi$
$278$	−49484.8	+	17690.7i	−0.640299	+	0.228905i
$279$	122658.	+	3054.95i	1.57575	+	0.0392460i
$280$	4330.73	−	7211.98i	0.0552389	−	0.0919895i
$281$	61859.9	+	107145.i	0.783424	+	1.35693i	0.929936	+	0.367721i	$0.119862\pi$
$281$	61859.9	+	107145.i	0.783424	+	1.35693i	−0.146512	+	0.989209i	$0.546805\pi$
$282$	103607.	−	7169.48i	1.30284	−	0.0901549i
$283$	−47401.9	−	27367.5i	−0.591865	−	0.341713i	0.173970	−	0.984751i	$-0.444341\pi$
$283$	−47401.9	−	27367.5i	−0.591865	−	0.341713i	−0.765835	+	0.643038i	$0.777674\pi$
$284$	−18357.2	+	3020.48i	−0.227598	+	0.0374489i
$285$	1223.17	−	4347.66i	0.0150590	−	0.0535262i
$286$	−24799.9	−	21052.8i	−0.303192	−	0.257381i
$287$		−	31383.9i		−	0.381016i
$288$	−10011.3	−	82337.6i	−0.120700	−	0.992689i
$289$	−2853.15			−0.0341609
$290$	−35076.7	+	41319.9i	−0.417083	+	0.491318i
$291$	−77612.4	+	75703.4i	−0.916526	+	0.893983i
$292$	5618.48	+	34146.7i	0.0658951	+	0.400482i
$293$	44309.0	−	76745.4i	0.516127	−	0.893958i	−0.483698	−	0.875235i	$-0.660707\pi$
$293$	44309.0	−	76745.4i	0.516127	−	0.893958i	0.999825	−	0.0187226i	$-0.00595995\pi$
$294$	67454.4	−	45427.5i	0.780398	−	0.525562i
$295$	−27064.1	+	15625.5i	−0.310993	+	0.179552i
$296$	83469.8	+	50122.9i	0.952677	+	0.572075i
$297$	152830.	+	47133.8i	1.73259	+	0.534342i
$298$	34924.2	+	97690.7i	0.393273	+	1.10007i
$299$	6462.01	−	3730.84i	0.0722812	−	0.0417316i
$300$	−58358.1	−	42977.6i	−0.648423	−	0.477529i
$301$	−238.061	+	412.333i	−0.00262757	+	0.00455109i
$302$	20363.6	−	111742.i	0.223276	−	1.22518i
$303$	61561.3	−	60047.1i	0.670536	−	0.654044i
$304$	3731.26	+	11031.5i	0.0403746	+	0.119368i
$305$	−57996.0			−0.623446
$306$	−18747.3	+	90092.9i	−0.200215	+	0.962161i
$307$		−	123447.i		−	1.30980i	−0.755716	−	0.654900i	$-0.772711\pi$
$307$		−	123447.i		−	1.30980i	0.755716	−	0.654900i	$-0.227289\pi$
$308$	−39135.8	−	14754.1i	−0.412547	−	0.155529i
$309$	−28038.7	+	99661.8i	−0.293658	+	1.04379i
$310$	11983.7	−	65758.1i	0.124700	−	0.684268i
$311$	−52431.9	−	30271.6i	−0.542094	−	0.312978i	0.203833	−	0.979006i	$-0.434660\pi$
$311$	−52431.9	−	30271.6i	−0.542094	−	0.312978i	−0.745927	+	0.666027i	$0.767993\pi$
$312$	14644.4	+	15539.1i	0.150440	+	0.159631i
$313$	26193.1	+	45367.8i	0.267361	+	0.463083i	0.968180	−	0.250257i	$-0.0805150\pi$
$313$	26193.1	+	45367.8i	0.267361	+	0.463083i	−0.700818	+	0.713340i	$0.747182\pi$
$314$	−7433.35	−	20792.7i	−0.0753920	−	0.210888i
$315$	−5092.22	−	9350.17i	−0.0513200	−	0.0942320i
$316$	−75928.4	−	92622.1i	−0.760378	−	0.927557i
$317$	12998.7	+	22514.4i	0.129354	+	0.224048i	0.923427	−	0.383775i	$-0.125376\pi$
$317$	12998.7	+	22514.4i	0.129354	+	0.224048i	−0.794072	+	0.607823i	$0.792043\pi$
$318$	−45772.5	−	22365.8i	−0.452637	−	0.221172i
$319$	233372.	+	134737.i	2.29333	+	1.32406i
$320$	−45158.7	−	1552.45i	−0.441003	−	0.0151607i
$321$	−57586.7	+	14664.4i	−0.558871	+	0.142316i
$322$	6208.53	−	7313.56i	0.0598794	−	0.0705370i
$323$		−	12920.1i		−	0.123840i
$324$	−96262.2	−	41875.5i	−0.916992	−	0.398905i
$325$	18657.5			0.176639
$326$	−1241.96	−	1054.31i	−0.0116862	−	0.00992050i
$327$	−26752.0	−	105055.i	−0.250185	−	0.982472i
$328$	−147415.	+	81765.6i	−1.37023	+	0.760017i
$329$	−17186.8	+	29768.4i	−0.158783	+	0.275019i
$330$	38250.6	−	78281.3i	0.351245	−	0.718837i
$331$	37439.2	−	21615.5i	0.341720	−	0.197292i	−0.319312	−	0.947650i	$-0.603452\pi$
$331$	37439.2	−	21615.5i	0.341720	−	0.197292i	0.661032	+	0.750357i	$0.270119\pi$
$332$	11323.4	+	13812.9i	0.102731	+	0.125317i
$333$	108217.	−	58936.2i	0.975901	−	0.531488i
$334$	−89428.5	+	31970.5i	−0.801647	+	0.286587i
$335$	−8890.54	+	5132.95i	−0.0792206	+	0.0457381i
$336$	24454.8	+	12474.3i	0.216613	+	0.110494i
$337$	−5926.38	+	10264.8i	−0.0521831	+	0.0903837i	−0.890937	−	0.454127i	$-0.849951\pi$
$337$	−5926.38	+	10264.8i	−0.0521831	+	0.0903837i	0.838754	+	0.544511i	$0.183285\pi$
$338$	106985.	+	19496.8i	0.936462	+	0.170659i
$339$	32321.5	+	9093.29i	0.281249	+	0.0791264i
$340$	46908.4	+	17684.3i	0.405782	+	0.152979i
$341$	−332321.			−2.85791
$342$	14429.7	+	3002.66i	0.123369	+	0.0256717i
$343$			55525.0i			0.471955i
$344$	2557.01	+	43.9392i	0.0216081	+	0.000371309i
$345$	13954.2	+	14306.0i	0.117237	+	0.120194i
$346$	11122.8	+	2027.00i	0.0929098	+	0.0169317i
$347$	25222.5	+	14562.2i	0.209473	+	0.120940i	0.601067	−	0.799199i	$-0.294743\pi$
$347$	25222.5	+	14562.2i	0.209473	+	0.120940i	−0.391593	+	0.920138i	$0.628076\pi$
$348$	−142422.	−	104886.i	−1.17603	−	0.866083i
$349$	−59988.4	−	103903.i	−0.492512	−	0.853055i	0.507451	−	0.861681i	$-0.330588\pi$
$349$	−59988.4	−	103903.i	−0.492512	−	0.853055i	−0.999963	+	0.00862528i	$0.997254\pi$
$350$	22587.8	−	8075.08i	0.184390	−	0.0659191i
$351$	26346.2	−	6014.70i	0.213848	−	0.0488202i
$352$	32659.8	+	222266.i	0.263589	+	1.79385i
$353$	−77379.0	−	134024.i	−0.620975	−	1.07556i	−0.989305	−	0.145865i	$-0.953404\pi$
$353$	−77379.0	−	134024.i	−0.620975	−	1.07556i	0.368330	−	0.929695i	$-0.379930\pi$
$354$	−56967.0	−	84589.1i	−0.454587	−	0.675007i
$355$	11108.5	+	6413.49i	0.0881451	+	0.0508906i
$356$	17507.8	+	106405.i	0.138144	+	0.839577i
$357$	−21266.8	−	21803.1i	−0.166866	−	0.171073i
$358$	139490.	+	118414.i	1.08837	+	0.923925i
$359$		−	66839.6i		−	0.518615i	−0.965795	−	0.259307i	$-0.916506\pi$
$359$		−	66839.6i		−	0.518615i	0.965795	−	0.259307i	$-0.0834942\pi$
$360$	−30652.1	+	48279.2i	−0.236513	+	0.372525i
$361$	128252.			0.984121
$362$	−62713.4	+	73875.4i	−0.478567	+	0.563745i
$363$	−290144.	−	81628.7i	−2.20191	−	0.619483i
$364$	−6973.37	+	1147.39i	−0.0526308	+	0.00865984i
$365$	11929.9	−	20663.2i	0.0895472	−	0.155100i
$366$	−13065.4	−	188810.i	−0.0975352	−	1.40949i
$367$	−81901.3	+	47285.7i	−0.608077	+	0.351073i	−0.772212	−	0.635364i	$-0.780850\pi$
$367$	−81901.3	+	47285.7i	−0.608077	+	0.351073i	0.164136	+	0.986438i	$0.447517\pi$
$368$	−50528.1	−	10108.1i	−0.373110	−	0.0746403i
$369$	−5312.08	+	213284.i	−0.0390132	+	1.56641i
$370$	−22597.8	−	63211.2i	−0.165068	−	0.461732i
$371$	14602.5	−	8430.74i	0.106091	−	0.0612517i
$372$	216780.	+	24199.6i	1.56651	+	0.174873i
$373$	90530.4	−	156803.i	0.650694	−	1.12704i	−0.332260	−	0.943188i	$-0.607811\pi$
$373$	90530.4	−	156803.i	0.650694	−	1.12704i	0.982955	−	0.183848i	$-0.0588554\pi$
$374$	44685.5	−	245204.i	0.319465	−	1.75301i
$375$	27644.2	+	108558.i	0.196581	+	0.771970i
$376$	184604.	+	3172.19i	1.30576	+	0.0224379i
$377$	45533.4			0.320366
$378$	29293.0	−	18684.5i	0.205012	−	0.130767i
$379$			51191.3i			0.356384i	0.983996	+	0.178192i	$0.0570248\pi$
$379$			51191.3i			0.356384i	−0.983996	+	0.178192i	$0.942975\pi$
$380$	2832.41	−	7513.07i	0.0196150	−	0.0520296i
$381$	231557.	−	58965.7i	1.59518	−	0.406209i
$382$	−16151.5	+	88628.2i	−0.110684	+	0.607359i
$383$	−132128.	−	76284.0i	−0.900734	−	0.520039i	−0.0232957	−	0.999729i	$-0.507416\pi$
$383$	−132128.	−	76284.0i	−0.900734	−	0.520039i	−0.877438	+	0.479690i	$0.840749\pi$
$384$	−5119.29	−	147367.i	−0.0347174	−	0.999397i
$385$	14418.5	+	24973.5i	0.0972742	+	0.168484i
$386$	24626.3	+	68885.2i	0.165282	+	0.462329i
$387$	1687.64	−	2761.90i	0.0112683	−	0.0184411i
$388$	−149061.	+	122195.i	−0.990147	+	0.811687i
$389$	−33948.4	−	58800.3i	−0.224347	−	0.388580i	0.731776	−	0.681545i	$-0.238692\pi$
$389$	−33948.4	−	58800.3i	−0.224347	−	0.388580i	−0.956123	+	0.292965i	$0.905358\pi$
$390$	−1016.31	−	14686.8i	−0.00668183	−	0.0965600i
$391$	49510.2	+	28584.7i	0.323848	+	0.186974i
$392$	126432.	−	70127.0i	0.822780	−	0.456366i
$393$	−3216.53	+	11432.9i	−0.0208258	+	0.0740240i
$394$	93968.9	−	110694.i	0.605329	−	0.713069i
$395$			82575.7i			0.529247i
$396$	263468.	+	106892.i	1.68011	+	0.681641i
$397$	−126087.			−0.799998			−0.399999	−	0.916516i	$-0.630990\pi$
$397$	−126087.			−0.799998			−0.399999	+	0.916516i	$0.630990\pi$
$398$	144348.	+	122538.i	0.911264	+	0.773578i
$399$	−3492.09	+	3406.20i	−0.0219351	+	0.0213956i
$400$	−96778.6	−	85059.8i	−0.604866	−	0.531624i
$401$	−35445.4	+	61393.2i	−0.220430	+	0.381796i	−0.954939	−	0.296803i	$-0.904079\pi$
$401$	−35445.4	+	61393.2i	−0.220430	+	0.381796i	0.734509	+	0.678599i	$0.237413\pi$
$402$	−18713.6	−	27787.4i	−0.115799	−	0.171948i
$403$	−48629.5	+	28076.3i	−0.299426	+	0.172874i
$404$	118233.	−	96923.5i	0.724398	−	0.593836i
$405$	33023.9	+	64405.2i	0.201334	+	0.392655i
$406$	55125.1	−	19707.1i	0.334424	−	0.119556i
$407$	−289038.	+	166876.i	−1.74488	+	1.00741i
$408$	−47005.1	+	156698.i	−0.282374	+	0.941331i
$409$	−21772.1	+	37710.4i	−0.130153	+	0.225432i	−0.923735	−	0.383031i	$-0.874880\pi$
$409$	−21772.1	+	37710.4i	−0.130153	+	0.225432i	0.793582	+	0.608463i	$0.208214\pi$
$410$	114343.	+	20837.7i	0.680209	+	0.123960i
$411$	−166305.	+	162215.i	−0.984513	+	0.960298i
$412$	−64927.4	+	172223.i	−0.382502	+	1.01460i
$413$	33754.1			0.197891
$414$	−43430.8	+	48651.7i	−0.253394	+	0.283856i
$415$		−	12314.7i		−	0.0715036i
$416$	23557.4	+	29765.6i	0.136126	+	0.172000i
$417$	−32022.9	+	113823.i	−0.184157	+	0.654573i
$418$	−39273.0	−	7157.04i	−0.224771	−	0.0409620i
$419$	182385.	+	105300.i	1.03887	+	0.599792i	0.919513	−	0.393060i	$-0.128583\pi$
$419$	182385.	+	105300.i	1.03887	+	0.599792i	0.119357	+	0.992851i	$0.461917\pi$
$420$	−7586.91	−	17340.7i	−0.0430097	−	0.0983035i
$421$	−42063.0	−	72855.3i	−0.237321	−	0.411052i	0.722624	−	0.691242i	$-0.242936\pi$
$421$	−42063.0	−	72855.3i	−0.237321	−	0.411052i	−0.959945	+	0.280190i	$0.909603\pi$
$422$	−175107.	+	62600.4i	−0.983285	+	0.351522i
$423$	121839.	−	199395.i	0.680935	−	1.11438i
$424$	−77644.7	−	46625.0i	−0.431897	−	0.259350i
$425$	71474.4	+	123797.i	0.395706	+	0.685383i
$426$	−18377.0	+	37609.3i	−0.101264	+	0.207241i
$427$	54249.0	+	31320.7i	0.297533	+	0.171781i
$428$	−104242.	+	17151.9i	−0.569055	+	0.0936320i
$429$	−70930.6	+	18062.4i	−0.385407	+	0.0981432i
$430$	−1344.22	−	1141.12i	−0.00726997	−	0.00617153i
$431$		−	150083.i		−	0.807933i	−0.914774	−	0.403967i	$-0.867631\pi$
$431$		−	150083.i		−	0.807933i	0.914774	−	0.403967i	$-0.132369\pi$
$432$	−164082.	−	88913.9i	−0.879211	−	0.476433i
$433$	71221.5			0.379871			0.189935	−	0.981797i	$-0.439172\pi$
$433$	71221.5			0.379871			0.189935	+	0.981797i	$0.439172\pi$
$434$	−46722.0	+	55037.8i	−0.248051	+	0.292201i
$435$	30094.3	+	118180.i	0.159040	+	0.624546i
$436$	−31290.0	−	190167.i	−0.164601	−	1.00038i
$437$	4578.26	−	7929.78i	0.0239739	−	0.0415239i
$438$	69958.3	+	34183.7i	0.364662	+	0.178185i
$439$	−94609.3	+	54622.7i	−0.490913	+	0.283429i	−0.724953	−	0.688798i	$-0.758139\pi$
$439$	−94609.3	+	54622.7i	−0.490913	+	0.283429i	0.234040	+	0.972227i	$0.424805\pi$
$440$	79739.3	−	132790.i	0.411876	−	0.685899i
$441$	4555.95	−	182925.i	0.0234262	−	0.940578i
$442$	−14177.2	−	39656.7i	−0.0725680	−	0.202989i
$443$	199756.	−	115329.i	1.01787	−	0.587666i	0.104382	−	0.994537i	$-0.466713\pi$
$443$	199756.	−	115329.i	1.01787	−	0.587666i	0.913486	+	0.406871i	$0.133380\pi$
$444$	200698.	−	87809.2i	1.01807	−	0.445424i
$445$	37174.8	−	64388.7i	0.187728	−	0.325154i
$446$	−59234.5	+	325038.i	−0.297786	+	1.63405i
$447$	224704.	+	63218.1i	1.12460	+	0.316393i
$448$	41402.6	+	25840.0i	0.206287	+	0.128747i
$449$	−9751.64			−0.0483710			−0.0241855	−	0.999707i	$-0.507699\pi$
$449$	−9751.64			−0.0483710			−0.0241855	+	0.999707i	$0.507699\pi$
$450$	−154872.	+	51054.6i	−0.764802	+	0.252122i
$451$		−	577854.i		−	2.84096i
$452$	55853.8	+	21056.7i	0.273386	+	0.103066i
$453$	−178444.	−	182944.i	−0.869573	−	0.891500i
$454$	21300.3	−	116881.i	0.103341	−	0.567066i
$455$	4219.80	+	2436.30i	0.0203831	+	0.0117682i
$456$	25097.4	+	7528.55i	0.120698	+	0.0362061i
$457$	−33069.5	−	57278.1i	−0.158342	−	0.274256i	0.775929	−	0.630820i	$-0.217281\pi$
$457$	−33069.5	−	57278.1i	−0.158342	−	0.274256i	−0.934271	+	0.356564i	$0.883948\pi$
$458$	61046.1	+	170760.i	0.291023	+	0.814056i
$459$	140838.	+	151772.i	0.668489	+	0.720390i
$460$	22523.8	+	27475.9i	0.106445	+	0.129848i
$461$	86994.6	+	150679.i	0.409346	+	0.709008i	0.994817	−	0.101686i	$-0.0324236\pi$
$461$	86994.6	+	150679.i	0.409346	+	0.709008i	−0.585471	+	0.810694i	$0.699090\pi$
$462$	−78054.9	+	52566.5i	−0.365693	+	0.246278i
$463$	−150682.	−	86996.3i	−0.702909	−	0.405825i	0.105521	−	0.994417i	$-0.466349\pi$
$463$	−150682.	−	86996.3i	−0.702909	−	0.405825i	−0.808430	+	0.588592i	$0.799682\pi$
$464$	−236186.	−	207587.i	−1.09703	−	0.964194i
$465$	−105011.	−	107659.i	−0.485658	−	0.497905i
$466$	131844.	−	155310.i	0.607138	−	0.715200i
$467$		−	172090.i		−	0.789080i	−0.918879	−	0.394540i	$-0.870904\pi$
$467$		−	172090.i		−	0.789080i	0.918879	−	0.394540i	$-0.129096\pi$
$468$	47584.9	−	6617.31i	0.217259	−	0.0302127i
$469$	11088.2			0.0504097
$470$	−97045.8	−	82382.8i	−0.439320	−	0.372942i
$471$	−47826.6	−	13455.5i	−0.215590	−	0.0606538i
$472$	−87940.6	−	158548.i	−0.394735	−	0.711665i
$473$	−4383.27	+	7592.05i	−0.0195919	+	0.0339341i
$474$	−268831.	+	18602.8i	−1.19653	+	0.0827983i
$475$	19828.0	−	11447.7i	0.0878802	−	0.0507376i
$476$	−34327.3	−	41874.6i	−0.151505	−	0.184815i
$477$	−100665.	+	54823.3i	−0.442426	+	0.240951i
$478$	−138941.	+	49671.2i	−0.608101	+	0.217395i
$479$	189138.	−	109199.i	0.824343	−	0.475935i	−0.0275690	−	0.999620i	$-0.508777\pi$
$479$	189138.	−	109199.i	0.824343	−	0.475935i	0.851912	+	0.523685i	$0.175443\pi$
$480$	−61685.4	+	80815.2i	−0.267732	+	0.350760i
$481$	−28197.2	+	48839.0i	−0.121875	+	0.211094i
$482$	−33005.5	−	6014.87i	−0.142067	−	0.0258900i
$483$	−5326.65	−	20917.7i	−0.0228328	−	0.0896642i
$484$	−501389.	−	189022.i	−2.14034	−	0.806904i
$485$	132893.			0.564959
$486$	−202236.	+	122021.i	−0.856222	+	0.516609i
$487$			392112.i			1.65330i	0.562716	+	0.826650i	$0.309757\pi$
$487$			392112.i			1.65330i	−0.562716	+	0.826650i	$0.690243\pi$
$488$	5780.89	−	336416.i	0.0242748	−	1.41266i
$489$	−3552.17	+	904.554i	−0.0148551	+	0.00378283i
$490$	−98067.5	−	17871.7i	−0.408444	−	0.0744343i
$491$	181620.	+	104859.i	0.753358	+	0.434951i	0.826906	−	0.562340i	$-0.190099\pi$
$491$	181620.	+	104859.i	0.753358	+	0.434951i	−0.0735480	+	0.997292i	$0.523432\pi$
$492$	−42079.3	+	376947.i	−0.173836	+	1.55722i
$493$	174432.	+	302125.i	0.717683	+	1.24306i
$494$	−6351.60	+	2270.68i	−0.0260273	+	0.00930470i
$495$	−93760.2	−	172159.i	−0.382655	−	0.702619i
$496$	380247.	+	76067.9i	1.54562	+	0.309199i
$497$	−6927.19	−	11998.2i	−0.0280443	−	0.0485741i
$498$	40091.4	−	2774.28i	0.161656	−	0.0111864i
$499$	117681.	+	67943.0i	0.472611	+	0.272862i	0.717332	−	0.696731i	$-0.245363\pi$
$499$	117681.	+	67943.0i	0.472611	+	0.272862i	−0.244721	+	0.969594i	$0.578696\pi$
$500$	32333.5	+	196509.i	0.129334	+	0.786037i
$501$	−57871.4	+	205700.i	−0.230562	+	0.819518i
$502$	4499.29	+	3819.48i	0.0178541	+	0.0151564i
$503$			232332.i			0.918275i	0.888365	+	0.459137i	$0.151841\pi$
$503$			232332.i			0.918275i	−0.888365	+	0.459137i	$0.848159\pi$
$504$	54744.8	−	28606.3i	0.215517	−	0.112616i
$505$	−105409.			−0.413328
$506$	114314.	−	134660.i	0.446477	−	0.525943i
$507$	175156.	−	170848.i	0.681413	−	0.664653i
$508$	419159.	−	68968.2i	1.62424	−	0.267252i
$509$	72659.4	−	125850.i	0.280451	−	0.485755i	−0.691045	−	0.722812i	$-0.742849\pi$
$509$	72659.4	−	125850.i	0.280451	−	0.485755i	0.971496	+	0.237057i	$0.0761827\pi$
$510$	93557.1	−	63006.5i	0.359697	−	0.242239i
$511$	−22318.3	+	12885.5i	−0.0854711	+	0.0493467i
$512$	13506.6	−	261796.i	0.0515234	−	0.998672i
$513$	24308.6	−	22557.3i	0.0923687	−	0.0857140i
$514$	46688.3	+	130598.i	0.176719	+	0.494321i
$515$	109899.	−	63450.5i	0.414363	−	0.239233i
$516$	3412.16	−	4633.27i	0.0128153	−	0.0174016i
$517$	−316450.	+	548108.i	−1.18393	+	2.05062i
$518$	−12999.3	+	71331.1i	−0.0484461	+	0.265839i
$519$	18210.3	−	17762.4i	0.0676054	−	0.0659426i
$520$	449.672	−	26168.4i	0.00166299	−	0.0967766i
$521$	443088.			1.63235			0.816177	−	0.577803i	$-0.196090\pi$
$521$	443088.			1.63235			0.816177	+	0.577803i	$0.196090\pi$
$522$	−377963.	+	124598.i	−1.38710	+	0.457267i
$523$		−	73202.4i		−	0.267622i	−0.991007	−	0.133811i	$-0.957278\pi$
$523$		−	73202.4i		−	0.267622i	0.991007	−	0.133811i	$-0.0427215\pi$
$524$	−7448.30	+	19756.9i	−0.0271266	+	0.0719543i
$525$	14617.1	−	51955.6i	0.0530327	−	0.188501i
$526$	−13648.9	+	74896.0i	−0.0493318	+	0.270699i
$527$	−372587.	−	215113.i	−1.34155	−	0.774543i
$528$	450271.	+	229682.i	1.61513	+	0.823870i
$529$	−119662.	−	207261.i	−0.427609	−	0.740640i
$530$	21020.8	+	58799.9i	0.0748338	+	0.209327i
$531$	−229391.	−	5713.25i	−0.813555	−	0.0202626i
$532$	−6706.83	+	5498.02i	−0.0236970	+	0.0194260i
$533$	−48820.3	−	84559.2i	−0.171849	−	0.297651i
$534$	217997.	+	106520.i	0.764483	+	0.373549i
$535$	63079.9	+	36419.2i	0.220386	+	0.127240i
$536$	−28888.4	−	52082.7i	−0.100553	−	0.181286i
$537$	398958.	−	101594.i	1.38350	−	0.352306i
$538$	152017.	−	179073.i	0.525202	−	0.618681i
$539$			495602.i			1.70591i
$540$	48625.2	+	119131.i	0.166753	+	0.408542i
$541$	438165.			1.49707			0.748536	−	0.663094i	$-0.230757\pi$
$541$	438165.			1.49707			0.748536	+	0.663094i	$0.230757\pi$
$542$	−95977.1	−	81475.6i	−0.326715	−	0.277351i
$543$	53805.4	+	211293.i	0.182485	+	0.716613i
$544$	−107257.	+	270337.i	−0.362432	+	0.913500i
$545$	−66439.2	+	115076.i	−0.223682	+	0.387429i
$546$	−6980.92	+	14286.7i	−0.0234168	+	0.0479234i
$547$	−270221.	+	156012.i	−0.903118	+	0.521416i	−0.878211	−	0.478274i	$-0.841263\pi$
$547$	−270221.	+	156012.i	−0.903118	+	0.521416i	−0.0249077	+	0.999690i	$0.507929\pi$
$548$	−319402.	+	261834.i	−1.06359	+	0.871898i
$549$	−363372.	−	222036.i	−1.20561	−	0.736679i
$550$	415896.	−	148682.i	1.37486	−	0.491510i
$551$	48389.8	−	27937.9i	0.159386	−	0.0920217i
$552$	−84375.5	+	79517.5i	−0.276910	+	0.260967i
$553$	44594.9	−	77240.6i	0.145826	−	0.252578i
$554$	−261814.	−	47712.6i	−0.853048	−	0.155458i
$555$	−145396.	−	40905.5i	−0.472026	−	0.132799i
$556$	−74153.2	+	196694.i	−0.239873	+	0.636271i
$557$	312549.			1.00741			0.503707	−	0.863874i	$-0.331969\pi$
$557$	312549.			1.00741			0.503707	+	0.863874i	$0.331969\pi$
$558$	326836.	−	366126.i	1.04969	−	1.17588i
$559$			1481.29i			0.00474042i
$560$	−10781.4	−	31875.5i	−0.0343796	−	0.101644i
$561$	−391574.	−	401448.i	−1.24419	−	1.27557i
$562$	486861.	+	88724.8i	1.54146	+	0.280913i
$563$	−74780.6	−	43174.6i	−0.235924	−	0.136211i	0.377378	−	0.926059i	$-0.376826\pi$
$563$	−74780.6	−	43174.6i	−0.235924	−	0.136211i	−0.613302	+	0.789849i	$0.710159\pi$
$564$	246341.	−	334499.i	0.774422	−	1.05157i
$565$	−20577.7	−	35641.7i	−0.0644615	−	0.111651i
$566$	−206162.	+	73702.3i	−0.643539	+	0.230064i
$567$	3891.69	−	78078.5i	0.0121052	−	0.242865i
$568$	−38309.8	+	63797.4i	−0.118744	+	0.197745i
$569$	−277479.	−	480608.i	−0.857049	−	1.48445i	−0.874731	−	0.484609i	$-0.838962\pi$
$569$	−277479.	−	480608.i	−0.857049	−	1.48445i	0.0176822	−	0.999844i	$-0.494371\pi$
$570$	−10091.4	−	14984.5i	−0.0310601	−	0.0461205i
$571$	−262848.	−	151755.i	−0.806181	−	0.465449i	0.0394467	−	0.999222i	$-0.487440\pi$
$571$	−262848.	−	151755.i	−0.806181	−	0.465449i	−0.845628	+	0.533773i	$0.820774\pi$
$572$	−128397.	+	21126.3i	−0.392430	+	0.0645701i
$573$	141533.	+	145102.i	0.431072	+	0.441942i
$574$	−95702.2	−	81242.3i	−0.290468	−	0.246580i
$575$			101308.i			0.306414i
$576$	−276996.	−	182615.i	−0.834890	−	0.550417i
$577$	−500884.			−1.50448			−0.752238	−	0.658892i	$-0.771026\pi$
$577$	−500884.			−1.50448			−0.752238	+	0.658892i	$0.771026\pi$
$578$	−7385.83	+	8700.40i	−0.0221077	+	0.0260426i
$579$	158447.	+	44577.3i	0.472636	+	0.132971i
$580$	35199.2	+	213926.i	0.104635	+	0.635927i
$581$	−6650.54	+	11519.1i	−0.0197017	+	0.0341244i
$582$	29938.2	+	432641.i	0.0883853	+	1.27727i
$583$	268867.	−	155230.i	0.791043	−	0.456709i
$584$	118671.	+	71261.2i	0.347953	+	0.208943i
$585$	−28265.2	−	17271.2i	−0.0825924	−	0.0504675i
$586$	−119327.	−	333783.i	−0.347490	−	0.972007i
$587$	−498580.	+	287855.i	−1.44697	+	0.835406i	−0.998300	−	0.0582932i	$-0.981434\pi$
$587$	−498580.	+	287855.i	−1.44697	+	0.835406i	−0.448666	+	0.893699i	$0.648101\pi$
$588$	36089.7	−	323292.i	0.104383	−	0.935062i
$589$	−34453.5	+	59675.2i	−0.0993122	+	0.172014i
$590$	−22411.4	+	122978.i	−0.0643821	+	0.353285i
$591$	−80621.3	−	316598.i	−0.230821	−	0.906429i
$592$	368919.	−	124782.i	1.05266	−	0.356048i
$593$	−138143.			−0.392843			−0.196421	−	0.980520i	$-0.562932\pi$
$593$	−138143.			−0.392843			−0.196421	+	0.980520i	$0.562932\pi$
$594$	539355.	−	344027.i	1.52863	−	0.975035i
$595$			37332.6i			0.105452i
$596$	388305.	+	146390.i	1.09315	+	0.412115i
$597$	412852.	−	105132.i	1.15837	−	0.294976i
$598$	5351.10	−	29363.2i	0.0149637	−	0.0821108i
$599$	−165665.	−	95646.9i	−0.461719	−	0.266574i	0.251048	−	0.967975i	$-0.419225\pi$
$599$	−165665.	−	95646.9i	−0.461719	−	0.266574i	−0.712767	+	0.701401i	$0.752558\pi$
$600$	−282125.	+	66702.9i	−0.783681	+	0.185286i
$601$	203120.	+	351814.i	0.562346	+	0.974012i	0.997291	+	0.0735551i	$0.0234345\pi$
$601$	203120.	+	351814.i	0.562346	+	0.974012i	−0.434945	+	0.900457i	$0.643232\pi$
$602$	641.112	+	1793.33i	0.00176905	+	0.00494843i
$603$	−75354.6	−	1876.80i	−0.207241	−	0.00516158i
$604$	−288031.	−	351358.i	−0.789524	−	0.963110i
$605$	184722.	+	319948.i	0.504671	+	0.874117i
$606$	−23746.7	−	343167.i	−0.0646633	−	0.934458i
$607$	59466.9	+	34333.2i	0.161398	+	0.0931831i	0.578523	−	0.815666i	$-0.303629\pi$
$607$	59466.9	+	34333.2i	0.161398	+	0.0931831i	−0.417126	+	0.908849i	$0.636962\pi$
$608$	43298.5	+	17178.7i	0.117129	+	0.0464712i
$609$	35672.9	−	126797.i	0.0961841	−	0.341880i
$610$	−150132.	+	176853.i	−0.403472	+	0.475284i
$611$			106942.i			0.286461i
$612$	226199.	+	290388.i	0.603931	+	0.775310i
$613$	−572114.			−1.52252			−0.761258	−	0.648450i	$-0.775418\pi$
$613$	−572114.			−1.52252			−0.761258	+	0.648450i	$0.775418\pi$
$614$	−376440.	−	319563.i	−0.998526	−	0.847655i
$615$	187203.	−	182599.i	0.494951	−	0.482778i
$616$	−146300.	+	81147.5i	−0.385553	+	0.213852i
$617$	−10190.4	+	17650.3i	−0.0267684	+	0.0463642i	−0.879099	−	0.476639i	$-0.841855\pi$
$617$	−10190.4	+	17650.3i	−0.0267684	+	0.0463642i	0.852331	+	0.523003i	$0.175188\pi$
$618$	231326.	+	343492.i	0.605686	+	0.899371i
$619$	388604.	−	224361.i	1.01421	−	0.585552i	0.101786	−	0.994806i	$-0.467544\pi$
$619$	388604.	−	224361.i	1.01421	−	0.585552i	0.912420	+	0.409254i	$0.134211\pi$
$620$	−169501.	−	206768.i	−0.440951	−	0.537899i
$621$	32659.1	+	143057.i	0.0846878	+	0.370959i
$622$	−228038.	+	81523.2i	−0.589423	+	0.210717i
$623$	−69546.0	+	40152.4i	−0.179183	+	0.103451i
$624$	85294.4	−	4431.31i	0.219054	−	0.0113806i
$625$	−88627.6	+	153508.i	−0.226887	+	0.392979i
$626$	206150.	+	37568.4i	0.526058	+	0.0958680i
$627$	−64297.8	+	62716.3i	−0.163554	+	0.159531i
$628$	−82647.8	−	31158.0i	−0.209562	−	0.0790042i
$629$	−432079.			−1.09210
$630$	−41694.5	−	8676.16i	−0.105050	−	0.0218598i
$631$			402529.i			1.01097i	0.862835	+	0.505486i	$0.168687\pi$
$631$			402529.i			1.01097i	−0.862835	+	0.505486i	$0.831313\pi$
$632$	−478995.	−	8230.94i	−1.19921	−	0.0206070i
$633$	−113316.	+	402775.i	−0.282804	+	1.00521i
$634$	102304.	+	18643.8i	0.254517	+	0.0463827i
$635$	−253646.	−	146443.i	−0.629043	−	0.363178i
$636$	−186692.	+	81681.3i	−0.461541	+	0.201933i
$637$	41871.2	+	72523.0i	0.103190	+	0.178730i
$638$	1.01499e6	−	362856.i	2.49356	−	0.891441i
$639$	45046.0	+	82711.9i	0.110320	+	0.202566i
$640$	−121634.	+	133688.i	−0.296959	+	0.326387i
$641$	−176906.	−	306411.i	−0.430554	−	0.745741i	0.566367	−	0.824153i	$-0.308348\pi$
$641$	−176906.	−	306411.i	−0.430554	−	0.745741i	−0.996921	+	0.0784117i	$0.975015\pi$
$642$	−104355.	+	213566.i	−0.253187	+	0.518157i
$643$	−227886.	−	131570.i	−0.551184	−	0.318226i	0.198415	−	0.980118i	$-0.436420\pi$
$643$	−227886.	−	131570.i	−0.551184	−	0.318226i	−0.749599	+	0.661892i	$0.769754\pi$
$644$	−6230.22	−	37864.6i	−0.0150221	−	0.0912981i
$645$	−3844.63	+	979.028i	−0.00924134	+	0.00235329i
$646$	−39398.7	−	33445.8i	−0.0944097	−	0.0801451i
$647$		−	265174.i		−	0.633464i	−0.948515	−	0.316732i	$-0.897414\pi$
$647$		−	265174.i		−	0.633464i	0.948515	−	0.316732i	$-0.102586\pi$
$648$	−376885.	+	185141.i	−0.897550	+	0.440912i
$649$	621494.			1.47553
$650$	48297.9	−	56894.3i	0.114315	−	0.134661i
$651$	40085.5	+	157415.i	0.0945856	+	0.371436i
$652$	−6430.04	+	1057.99i	−0.0151258	+	0.00248879i
$653$	2938.96	−	5090.43i	0.00689235	−	0.0119379i	−0.862559	−	0.505957i	$-0.831139\pi$
$653$	2938.96	−	5090.43i	0.00689235	−	0.0119379i	0.869451	+	0.494019i	$0.164473\pi$
$654$	−389606.	−	190373.i	−0.910899	−	0.445092i
$655$	12607.4	−	7278.87i	0.0293861	−	0.0169661i
$656$	−132270.	+	661190.i	−0.307365	+	1.53645i
$657$	153855.	−	83791.4i	0.356435	−	0.194119i
$658$	46285.0	+	129470.i	0.106903	+	0.299031i
$659$	480334.	−	277321.i	1.10604	−	0.638575i	0.168242	−	0.985746i	$-0.446191\pi$
$659$	480334.	−	277321.i	1.10604	−	0.638575i	0.937802	+	0.347171i	$0.112858\pi$
$660$	−139693.	−	319285.i	−0.320692	−	0.732977i
$661$	410614.	−	711204.i	0.939789	−	1.62776i	0.173926	−	0.984759i	$-0.444355\pi$
$661$	410614.	−	711204.i	0.939789	−	1.62776i	0.765863	−	0.643004i	$-0.222312\pi$
$662$	31002.8	−	170122.i	0.0707433	−	0.388191i
$663$	−91216.8	−	25662.8i	−0.207514	−	0.0583818i
$664$	71433.6	+	1227.50i	0.162019	+	0.00278410i
$665$	5979.36			0.0135211
$666$	100416.	−	482562.i	0.226388	−	1.08794i
$667$			247241.i			0.555736i
$668$	−134009.	+	355464.i	−0.300318	+	0.796604i
$669$	519065.	+	532153.i	1.15976	+	1.18901i
$670$	−7362.12	+	40398.3i	−0.0164004	+	0.0899939i
$671$	998855.	+	576689.i	2.21849	+	1.28085i
$672$	101344.	−	42280.7i	0.224419	−	0.0936276i
$673$	−258432.	−	447618.i	−0.570580	−	0.988274i	−0.996506	−	0.0835158i	$-0.973385\pi$
$673$	−258432.	−	447618.i	−0.570580	−	0.988274i	0.425926	−	0.904758i	$-0.359948\pi$
$674$	15960.1	+	44643.9i	0.0351330	+	0.0982749i
$675$	−108131.	+	350613.i	−0.237325	+	0.769522i
$676$	336402.	−	275770.i	0.736148	−	0.603468i
$677$	345343.	+	598152.i	0.753483	+	1.30507i	0.946125	+	0.323801i	$0.104961\pi$
$677$	345343.	+	598152.i	0.753483	+	1.30507i	−0.192642	+	0.981269i	$0.561706\pi$
$678$	111398.	−	75021.7i	0.242337	−	0.163203i
$679$	−124307.	−	71768.4i	−0.269621	−	0.155666i
$680$	175357.	−	97263.9i	0.379231	−	0.210346i
$681$	−186652.	−	191358.i	−0.402474	−	0.412623i
$682$	−860265.	+	1.01338e6i	−1.84954	+	2.17873i
$683$		−	764551.i		−	1.63895i	−0.573117	−	0.819474i	$-0.694266\pi$
$683$		−	764551.i		−	1.63895i	0.573117	−	0.819474i	$-0.305734\pi$
$684$	46509.9	−	36229.1i	0.0994106	−	0.0774364i
$685$	284757.			0.606868
$686$	169318.	+	143735.i	0.359795	+	0.305433i
$687$	392775.	+	110503.i	0.832204	+	0.234131i
$688$	6753.22	−	7683.62i	0.0142671	−	0.0162326i
$689$	26229.4	−	45430.7i	0.0552523	−	0.0956998i
$690$	79747.4	−	5518.42i	0.167501	−	0.0115909i
$691$	278107.	−	160565.i	0.582445	−	0.336275i	−0.179659	−	0.983729i	$-0.557500\pi$
$691$	278107.	−	160565.i	0.582445	−	0.336275i	0.762105	+	0.647454i	$0.224166\pi$
$692$	34974.2	−	28670.6i	0.0730358	−	0.0598722i
$693$	−5271.92	+	211671.i	−0.0109775	+	0.440753i
$694$	109698.	−	39216.9i	0.227762	−	0.0814244i
$695$	125516.	−	72466.4i	0.259853	−	0.150026i
$696$	−688522.	+	162787.i	−1.42134	+	0.336048i
$697$	374048.	−	647870.i	0.769949	−	1.33359i
$698$	−472131.	−	86040.5i	−0.969063	−	0.176601i
$699$	−113116.	−	444205.i	−0.231510	−	0.909137i
$700$	33847.9	−	89782.9i	0.0690774	−	0.183230i
$701$	−621799.			−1.26536			−0.632680	−	0.774413i	$-0.718045\pi$
$701$	−621799.			−1.26536			−0.632680	+	0.774413i	$0.718045\pi$
$702$	49860.2	−	95910.2i	0.101176	−	0.194621i
$703$			69203.8i			0.140029i
$704$	762323.	+	475777.i	1.53813	+	0.959972i
$705$	−277563.	+	70680.9i	−0.558448	+	0.142208i
$706$	−609002.	−	110984.i	−1.22183	−	0.222664i
$707$	98598.6	+	56925.9i	0.197257	+	0.113886i
$708$	−405414.	−	45257.2i	−0.808784	−	0.0902861i
$709$	262435.	+	454550.i	0.522070	+	0.904252i	0.999670	+	0.0256748i	$0.00817343\pi$
$709$	262435.	+	454550.i	0.522070	+	0.904252i	−0.477600	+	0.878577i	$0.658493\pi$
$710$	48313.4	−	17271.9i	0.0958409	−	0.0342629i
$711$	−316138.	+	517375.i	−0.625371	+	1.02345i
$712$	369792.	+	222057.i	0.729454	+	0.438031i
$713$	−152451.	−	264053.i	−0.299882	−	0.519412i
$714$	−121539.	+	8410.35i	−0.238407	+	0.0164975i
$715$	77696.8	+	44858.2i	0.151982	+	0.0877466i
$716$	722183.	−	118828.i	1.40871	−	0.231788i
$717$	−89912.4	+	319588.i	−0.174897	+	0.621658i
$718$	−203821.	−	173025.i	−0.395366	−	0.335629i
$719$		−	348658.i		−	0.674438i	−0.941426	−	0.337219i	$-0.890514\pi$
$719$		−	348658.i		−	0.674438i	0.941426	−	0.337219i	$-0.109486\pi$
$720$	67874.8	+	218449.i	0.130931	+	0.421391i
$721$	−137065.			−0.263668
$722$	332000.	−	391091.i	0.636888	−	0.750245i
$723$	−54036.7	+	52707.6i	−0.103374	+	0.100832i
$724$	62932.5	+	382476.i	0.120060	+	0.729672i
$725$	−309106.	+	535387.i	−0.588073	+	1.01857i
$726$	−1.00000e6	+	673456.i	−1.89726	+	1.27772i
$727$	523789.	−	302410.i	0.991032	−	0.572173i	0.0854497	−	0.996342i	$-0.472767\pi$
$727$	523789.	−	302410.i	0.991032	−	0.572173i	0.905583	+	0.424170i	$0.139434\pi$
$728$	−14552.8	+	24234.8i	−0.0274590	+	0.0457275i
$729$	−39663.4	+	529959.i	−0.0746336	+	0.997211i
$730$	−32128.0	−	89869.2i	−0.0602890	−	0.168642i
$731$	−9828.75	+	5674.63i	−0.0183935	+	0.0106195i
$732$	−609580.	−	448923.i	−1.13765	−	0.837819i
$733$	237805.	−	411891.i	0.442602	−	0.766609i	−0.555280	−	0.831664i	$-0.687389\pi$
$733$	237805.	−	411891.i	0.442602	−	0.766609i	0.997882	+	0.0650546i	$0.0207222\pi$
$734$	−67821.2	+	372156.i	−0.125885	+	0.690770i
$735$	−160556.	+	156607.i	−0.297203	+	0.289893i
$736$	−161624.	+	127914.i	−0.298366	+	0.236136i
$737$	204160.			0.375868
$738$	636636.	+	568317.i	1.16890	+	1.04347i
$739$			844449.i			1.54627i	0.634244	+	0.773133i	$0.281312\pi$
$739$			844449.i			1.54627i	−0.634244	+	0.773133i	$0.718688\pi$
$740$	−251254.	−	94722.2i	−0.458828	−	0.172977i
$741$	−4110.28	+	14609.7i	−0.00748574	+	0.0266076i
$742$	12092.1	−	66353.1i	0.0219631	−	0.120518i
$743$	−537216.	−	310162.i	−0.973131	−	0.561837i	−0.0729415	−	0.997336i	$-0.523239\pi$
$743$	−537216.	−	310162.i	−0.973131	−	0.561837i	−0.900189	+	0.435499i	$0.856572\pi$
$744$	634964.	−	598405.i	1.14710	−	1.08106i
$745$	−143060.	−	247787.i	−0.257754	−	0.446443i
$746$	−243804.	−	681974.i	−0.438090	−	1.22543i
$747$	47146.4	−	77157.3i	0.0844905	−	0.138273i
$748$	−632049.	−	771013.i	−1.12966	−	1.37803i
$749$	−39336.3	−	68132.4i	−0.0701180	−	0.121448i
$750$	402599.	+	196722.i	0.715732	+	0.349728i
$751$	−632847.	−	365374.i	−1.12207	−	0.647825i	−0.180139	−	0.983641i	$-0.557655\pi$
$751$	−632847.	−	365374.i	−1.12207	−	0.647825i	−0.941928	+	0.335816i	$0.890988\pi$
$752$	487549.	−	554719.i	0.862149	−	0.980928i
$753$	12868.5	−	3276.95i	0.0226955	−	0.00577936i
$754$	117870.	−	138849.i	0.207330	−	0.244231i
$755$			313247.i			0.549533i
$756$	18852.9	−	137694.i	0.0329864	−	0.240919i
$757$	−769023.			−1.34198			−0.670992	−	0.741465i	$-0.734132\pi$
$757$	−769023.			−1.34198			−0.670992	+	0.741465i	$0.734132\pi$
$758$	156103.	+	132517.i	0.271689	+	0.230639i
$759$	−98076.6	−	385145.i	−0.170248	−	0.668560i
$760$	−15578.2	−	28085.9i	−0.0269706	−	0.0486252i
$761$	−137697.	+	238498.i	−0.237769	+	0.411828i	−0.960074	−	0.279747i	$-0.909749\pi$
$761$	−137697.	+	238498.i	−0.237769	+	0.411828i	0.722305	+	0.691575i	$0.243083\pi$
$762$	419613.	−	858754.i	0.722668	−	1.47897i
$763$	124293.	−	71760.8i	0.213500	−	0.123264i
$764$	228452.	+	278680.i	0.391389	+	0.477441i
$765$	6318.96	−	253710.i	0.0107975	−	0.433526i
$766$	−574654.	+	205437.i	−0.979375	+	0.350124i
$767$	90945.2	−	52507.2i	0.154593	−	0.0892541i
$768$	−462634.	−	365872.i	−0.784359	−	0.620307i
$769$	26421.1	−	45762.6i	0.0446784	−	0.0773853i	−0.842821	−	0.538193i	$-0.819107\pi$
$769$	26421.1	−	45762.6i	0.0446784	−	0.0773853i	0.887500	+	0.460808i	$0.152440\pi$
$770$	113479.	+	20680.2i	0.191396	+	0.0348798i
$771$	300396.	+	84513.0i	0.505341	+	0.142172i
$772$	273808.	+	103225.i	0.459421	+	0.173201i
$773$	−195309.			−0.326861			−0.163430	−	0.986555i	$-0.552256\pi$
$773$	−195309.			−0.326861			−0.163430	+	0.986555i	$0.552256\pi$
$774$	−4053.42	−	12295.9i	−0.00676612	−	0.0205248i
$775$		−	762389.i		−	1.26933i
$776$	−13246.4	+	770866.i	−0.0219975	+	1.28013i
$777$	113911.	+	116783.i	0.188679	+	0.193437i
$778$	−267187.	−	48691.7i	−0.441423	−	0.0804443i
$779$	−103766.	−	59909.3i	−0.170994	−	0.0987232i
$780$	−47416.7	−	34919.9i	−0.0779368	−	0.0573963i
$781$	−127546.	−	220917.i	−0.209106	−	0.362182i
$782$	215331.	−	76980.4i	0.352122	−	0.125883i
$783$	−263893.	+	855666.i	−0.430431	+	1.39566i
$784$	113443.	−	567076.i	0.184563	−	0.922590i
$785$	30449.2	+	52739.6i	0.0494125	+	0.0855849i
$786$	26537.1	+	39404.4i	0.0429545	+	0.0637823i
$787$	−677438.	−	391119.i	−1.09375	−	0.631480i	−0.159181	−	0.987249i	$-0.550885\pi$
$787$	−677438.	−	391119.i	−1.09375	−	0.631480i	−0.934574	+	0.355770i	$0.884219\pi$
$788$	−94297.2	−	573098.i	−0.151861	−	0.922946i
$789$	119604.	+	122620.i	0.192128	+	0.196973i
$790$	251807.	+	213760.i	0.403472	+	0.342510i
$791$			44451.9i			0.0710456i
$792$	1.00798e6	−	526711.i	1.60695	−	0.839696i
$793$	194887.			0.309911
$794$	−326396.	+	384490.i	−0.517730	+	0.609879i
$795$	135249.	+	38050.9i	0.213993	+	0.0602047i
$796$	747335.	−	122966.i	1.17948	−	0.194070i
$797$	586714.	−	1.01622e6i	0.923655	−	1.59982i	0.129944	−	0.991521i	$-0.458520\pi$
$797$	586714.	−	1.01622e6i	0.923655	−	1.59982i	0.793711	−	0.608296i	$-0.208146\pi$
$798$	1347.04	+	19466.3i	0.00211531	+	0.0305687i
$799$	−709586.	+	409680.i	−1.11151	+	0.641728i
$800$	−509908.	+	74926.0i	−0.796731	+	0.117072i
$801$	479427.	−	261102.i	0.747236	−	0.406954i
$802$	95456.6	+	267013.i	0.148408	+	0.415130i
$803$	−410934.	+	237253.i	−0.637295	+	0.367943i
$804$	−133178.	−	14866.9i	−0.206025	−	0.0229990i
$805$	−13228.8	+	22913.0i	−0.0204141	+	0.0353583i
$806$	−40269.4	+	220971.i	−0.0619876	+	0.340146i
$807$	−130424.	−	512172.i	−0.200267	−	0.786445i
$808$	10506.9	−	611442.i	0.0160935	−	0.936554i
$809$	−421614.			−0.644196			−0.322098	−	0.946706i	$-0.604388\pi$
$809$	−421614.			−0.644196			−0.322098	+	0.946706i	$0.604388\pi$
$810$	281885.	+	66020.0i	0.429637	+	0.100625i
$811$			504037.i			0.766339i	0.923678	+	0.383169i	$0.125167\pi$
$811$			504037.i			0.766339i	−0.923678	+	0.383169i	$0.874833\pi$
$812$	82605.3	−	219114.i	0.125284	−	0.332321i
$813$	−274506.	+	69902.6i	−0.415309	+	0.105758i
$814$	−239348.	+	1.31338e6i	−0.361228	+	1.98217i
$815$	3891.01	+	2246.48i	0.00585797	+	0.00338210i
$816$	356154.	+	548974.i	0.534882	+	0.824464i
$817$	908.875	+	1574.22i	0.00136163	+	0.00235842i
$818$	58633.6	+	164011.i	0.0876275	+	0.245113i
$819$	17111.7	+	31419.9i	0.0255109	+	0.0468422i
$820$	359538.	−	294737.i	0.534709	−	0.438335i
$821$	35777.1	+	61967.7i	0.0530785	+	0.0919346i	0.891344	−	0.453328i	$-0.149763\pi$
$821$	35777.1	+	61967.7i	0.0530785	+	0.0919346i	−0.838265	+	0.545262i	$0.816430\pi$
$822$	64150.6	+	927049.i	0.0949417	+	1.37201i
$823$	703826.	+	406354.i	1.03912	+	0.599936i	0.919584	−	0.392893i	$-0.128526\pi$
$823$	703826.	+	406354.i	1.03912	+	0.599936i	0.119536	+	0.992830i	$0.461859\pi$
$824$	357101.	+	643815.i	0.525940	+	0.948215i
$825$	269137.	−	956628.i	0.395426	−	1.40551i
$826$	87377.7	−	102930.i	0.128068	−	0.150862i
$827$			375951.i			0.549693i	0.961488	+	0.274847i	$0.0886271\pi$
$827$			375951.i			0.549693i	−0.961488	+	0.274847i	$0.911373\pi$
$828$	35931.2	+	258380.i	0.0524097	+	0.376876i
$829$	423699.			0.616522			0.308261	−	0.951302i	$-0.400253\pi$
$829$	423699.			0.616522			0.308261	+	0.951302i	$0.400253\pi$
$830$	−37552.5	−	31878.6i	−0.0545108	−	0.0462746i
$831$	−428643.	+	418100.i	−0.620717	+	0.605449i
$832$	151749.	+	5216.79i	0.219220	+	0.00753628i
$833$	−320806.	+	555652.i	−0.462330	+	0.800779i
$834$	264196.	+	392300.i	0.379834	+	0.564009i
$835$	226830.	−	130961.i	0.325333	−	0.187831i
$836$	−123489.	+	101232.i	−0.176691	+	0.144845i
$837$	−245774.	−	1.07657e6i	−0.350821	−	1.53671i
$838$	793234.	−	283579.i	1.12957	−	0.403819i
$839$	−959899.	+	554198.i	−1.36365	+	0.787302i	−0.990107	−	0.140313i	$-0.955189\pi$
$839$	−959899.	+	554198.i	−1.36365	+	0.787302i	−0.373539	+	0.927614i	$0.621856\pi$
$840$	−72518.8	−	21753.7i	−0.102776	−	0.0308300i
$841$	−400727.	+	694079.i	−0.566573	+	0.981334i
$842$	−331052.	−	60330.3i	−0.466951	−	0.0850965i
$843$	797090.	−	777485.i	1.12164	−	1.09405i
$844$	−262399.	+	696024.i	−0.368364	+	0.977100i
$845$	−299914.			−0.420032
$846$	−292637.	−	887702.i	−0.408872	−	1.24030i
$847$		−	399036.i		−	0.556218i
$848$	−343174.	+	116074.i	−0.477224	+	0.161414i
$849$	−133412.	+	474205.i	−0.185089	+	0.657886i
$850$	562531.	+	102515.i	0.778589	+	0.141889i
$851$	−265190.	−	153108.i	−0.366183	−	0.211416i
$852$	67114.1	+	153397.i	0.0924559	+	0.211318i
$853$	254659.	+	441083.i	0.349995	+	0.606209i	0.986248	−	0.165272i	$-0.0528501\pi$
$853$	254659.	+	441083.i	0.349995	+	0.606209i	−0.636253	+	0.771480i	$0.719517\pi$
$854$	235941.	−	84348.4i	0.323510	−	0.115654i
$855$	−40635.4	−	1012.07i	−0.0555869	−	0.00138446i
$856$	−217543.	+	362276.i	−0.296892	+	0.494415i
$857$	328394.	+	568795.i	0.447130	+	0.774452i	0.998198	−	0.0600088i	$-0.0191129\pi$
$857$	328394.	+	568795.i	0.447130	+	0.774452i	−0.551068	+	0.834460i	$0.685780\pi$
$858$	−128536.	+	263053.i	−0.174602	+	0.357330i
$859$	916830.	+	529332.i	1.24252	+	0.717368i	0.969606	−	0.244671i	$-0.0786799\pi$
$859$	916830.	+	529332.i	1.24252	+	0.717368i	0.272912	+	0.962039i	$0.412013\pi$
$860$	−6959.44	+	1145.10i	−0.00940974	+	0.00154827i
$861$	−273720.	+	69702.4i	−0.369233	+	0.0940246i
$862$	−457662.	−	388512.i	−0.615928	−	0.522866i
$863$			676878.i			0.908844i	0.890787	+	0.454422i	$0.150154\pi$
$863$			676878.i			0.908844i	−0.890787	+	0.454422i	$0.849846\pi$
$864$	−695886.	+	270184.i	−0.932203	+	0.361936i
$865$	−31180.7			−0.0416729
$866$	184368.	−	217183.i	0.245839	−	0.289594i
$867$	6336.73	+	24884.2i	0.00842999	+	0.0331044i
$868$	46885.2	+	284948.i	0.0622295	+	0.378204i
$869$	821100.	−	1.42219e6i	1.08732	−	1.88329i
$870$	438282.	+	214157.i	0.579048	+	0.282940i
$871$	29875.4	−	17248.6i	0.0393801	−	0.0227361i
$872$	−660896.	−	396862.i	−0.869161	−	0.521924i
$873$	832633.	+	508775.i	1.09251	+	0.667570i
$874$	−12329.5	−	34488.5i	−0.0161408	−	0.0451493i
$875$	−128438.	+	74154.0i	−0.167756	+	0.0968541i
$876$	285338.	−	124841.i	0.371836	−	0.162685i
$877$	−737914.	+	1.27810e6i	−0.959415	+	1.66176i	−0.235490	+	0.971877i	$0.575669\pi$
$877$	−737914.	+	1.27810e6i	−0.959415	+	1.66176i	−0.723925	+	0.689879i	$0.757664\pi$
$878$	−78344.6	+	429901.i	−0.101629	+	0.557673i
$879$	−767755.	−	215999.i	−0.993677	−	0.279560i
$880$	−198512.	−	586905.i	−0.256343	−	0.757883i
$881$	599513.			0.772408			0.386204	−	0.922413i	$-0.373786\pi$
$881$	599513.			0.772408			0.386204	+	0.922413i	$0.373786\pi$
$882$	−546017.	−	487422.i	−0.701890	−	0.626568i
$883$			729187.i			0.935229i	0.883933	+	0.467614i	$0.154886\pi$
$883$			729187.i			0.935229i	−0.883933	+	0.467614i	$0.845114\pi$
$884$	−157629.	−	59425.7i	−0.201712	−	0.0760449i
$885$	196388.	+	201341.i	0.250743	+	0.257066i
$886$	165415.	−	907682.i	0.210720	−	1.15629i
$887$	1.26218e6	+	728722.i	1.60426	+	0.926221i	0.990621	+	0.136636i	$0.0436290\pi$
$887$	1.26218e6	+	728722.i	1.60426	+	0.926221i	0.613641	+	0.789585i	$0.289704\pi$
$888$	251772.	−	839316.i	0.319287	−	1.06439i
$889$	158172.	+	273962.i	0.200137	+	0.346647i
$890$	−100114.	−	280041.i	−0.126391	−	0.353543i
$891$	71655.4	−	1.43761e6i	0.0902596	−	1.81087i
$892$	837834.	+	1.02204e6i	1.05300	+	1.28452i
$893$	65616.2	+	113651.i	0.0822826	+	0.142518i
$894$	774460.	−	521564.i	0.969000	−	0.652578i
$895$	−437015.	−	252311.i	−0.545570	−	0.314985i
$896$	185974.	−	59362.3i	0.231652	−	0.0739426i
$897$	−46891.0	−	48073.4i	−0.0582780	−	0.0597476i
$898$	−25243.7	+	29736.7i	−0.0313040	+	0.0368757i
$899$		−	1.86060e6i		−	2.30215i
$900$	−245225.	+	604431.i	−0.302747	+	0.746211i
$901$	401926.			0.495104
$902$	−1.76211e6	−	1.49587e6i	−2.16581	−	1.83857i
$903$	4124.95	+	1160.51i	0.00505875	+	0.00142322i
$904$	208797.	−	115812.i	0.255498	−	0.141715i
$905$	133627.	−	231448.i	0.163153	−	0.282590i
$906$	−1.01980e6	+	70568.9i	−1.24239	+	0.0859719i
$907$	3010.76	−	1738.27i	0.00365984	−	0.00211301i	−0.498169	−	0.867080i	$-0.665994\pi$
$907$	3010.76	−	1738.27i	0.00365984	−	0.00211301i	0.501829	+	0.864967i	$0.332661\pi$
$908$	−301279.	−	367519.i	−0.365424	−	0.445767i
$909$	−660435.	−	403554.i	−0.799287	−	0.488399i
$910$	18352.9	−	6561.11i	0.0221627	−	0.00792309i
$911$	712683.	−	411468.i	0.858736	−	0.495791i	−0.00485282	−	0.999988i	$-0.501545\pi$
$911$	712683.	−	411468.i	0.858736	−	0.495791i	0.863589	+	0.504197i	$0.168211\pi$
$912$	87926.3	−	57043.3i	0.105713	−	0.0685828i
$913$	−122453.	+	212094.i	−0.146901	+	0.254441i
$914$	−260270.	−	47431.1i	−0.311552	−	0.0567768i
$915$	128807.	+	505822.i	0.153850	+	0.604164i
$916$	678742.	+	255884.i	0.808936	+	0.304967i
$917$	−15723.8			−0.0186990
$918$	827396.	−	36584.4i	0.981812	−	0.0434121i
$919$		−	873279.i		−	1.03400i	−0.855984	−	0.517002i	$-0.827048\pi$
$919$		−	873279.i		−	1.03400i	0.855984	−	0.517002i	$-0.172952\pi$
$920$	142091.	+	2441.67i	0.167877	+	0.00288477i
$921$	−1.07667e6	+	274171.i	−1.26929	+	0.323223i
$922$	684680.	+	124775.i	0.805427	+	0.146780i
$923$	−37328.5	−	21551.6i	−0.0438164	−	0.0252974i
$924$	−41761.2	+	374097.i	−0.0489136	+	0.438168i
$925$	−382837.	−	663092.i	−0.447435	−	0.774980i
$926$	−655351.	+	234286.i	−0.764279	+	0.273228i
$927$	931489.	+	23199.8i	1.08397	+	0.0269976i
$928$	−1.24442e6	+	182856.i	−1.44501	+	0.212330i
$929$	−172980.	−	299611.i	−0.200431	−	0.347157i	0.748236	−	0.663433i	$-0.230901\pi$
$929$	−172980.	−	299611.i	−0.200431	−	0.347157i	−0.948667	+	0.316275i	$0.897568\pi$
$930$	−600135.	+	41528.6i	−0.693878	+	0.0480155i
$931$	88995.8	+	51381.7i	0.102676	+	0.0592802i
$932$	−132304.	−	804088.i	−0.152315	−	0.925704i
$933$	−147569.	+	524525.i	−0.169525	+	0.602564i
$934$	−524771.	−	445481.i	−0.601556	−	0.510665i
$935$			687384.i			0.786278i
$936$	103002.	−	162235.i	0.117569	−	0.185180i
$937$	−1.10958e6			−1.26380			−0.631901	−	0.775049i	$-0.717725\pi$
$937$	−1.10958e6			−1.26380			−0.631901	+	0.775049i	$0.717725\pi$
$938$	28703.5	−	33812.3i	0.0326234	−	0.0384299i
$939$	337509.	−	329207.i	0.382784	−	0.373369i
$940$	−502437.	+	82670.6i	−0.568624	+	0.0935611i
$941$	−161271.	+	279330.i	−0.182129	+	0.315456i	−0.942605	−	0.333909i	$-0.891632\pi$
$941$	−161271.	+	279330.i	−0.182129	+	0.315456i	0.760477	+	0.649365i	$0.224965\pi$
$942$	−164838.	+	111011.i	−0.185761	+	0.125102i
$943$	459147.	−	265089.i	0.516331	−	0.298104i
$944$	−711124.	−	142259.i	−0.797997	−	0.159638i
$945$	−70239.4	+	65179.0i	−0.0786533	+	0.0729867i
$946$	11804.4	+	33019.6i	0.0131905	+	0.0368969i
$947$	120742.	−	69710.2i	0.134635	−	0.0777314i	−0.431170	−	0.902271i	$-0.641899\pi$
$947$	120742.	−	69710.2i	0.134635	−	0.0777314i	0.565805	+	0.824539i	$0.308566\pi$
$948$	−639185.	+	867931.i	−0.711230	+	0.965758i
$949$	−40088.8	+	69435.9i	−0.0445134	+	0.0770995i
$950$	16419.2	−	90097.6i	0.0181931	−	0.0998311i
$951$	167493.	−	163374.i	0.185198	−	0.180643i
$952$	−216554.	−	3721.22i	−0.238942	−	0.00410593i
$953$	1.68438e6			1.85462			0.927308	−	0.374300i	$-0.122117\pi$
$953$	1.68438e6			1.85462			0.927308	+	0.374300i	$0.122117\pi$
$954$	−93408.2	+	448886.i	−0.102633	+	0.493218i
$955$		−	248453.i		−	0.272419i
$956$	−208204.	+	552270.i	−0.227811	+	0.604276i
$957$	656824.	−	2.33463e6i	0.717175	−	2.54915i
$958$	156622.	−	859436.i	0.170656	−	0.936446i
$959$	−266360.	−	153783.i	−0.289622	−	0.167213i
$960$	86755.5	+	397307.i	0.0941358	+	0.431105i
$961$	685501.	+	1.18732e6i	0.742269	+	1.28565i
$962$	75936.8	+	212412.i	0.0820545	+	0.229525i
$963$	255795.	+	469682.i	0.275829	+	0.506468i
$964$	−103782.	+	85076.6i	−0.111678	+	0.0915495i
$965$	−100877.	−	174723.i	−0.108327	−	0.187628i
$966$	−77575.3	−	37905.6i	−0.0831321	−	0.0406208i
$967$	39280.8	+	22678.8i	0.0420075	+	0.0242530i	0.520857	−	0.853644i	$-0.325613\pi$
$967$	39280.8	+	22678.8i	0.0420075	+	0.0242530i	−0.478849	+	0.877897i	$0.658946\pi$
$968$	−1.87433e6	+	1.03962e6i	−2.00030	+	1.10949i
$969$	−112685.	+	28695.1i	−0.120010	+	0.0305605i
$970$	344013.	−	405243.i	0.365622	−	0.430697i
$971$			1.18319e6i			1.25492i	0.778648	+	0.627461i	$0.215906\pi$
$971$			1.18319e6i			1.25492i	−0.778648	+	0.627461i	$0.784094\pi$
$972$	−151429.	+	932570.i	−0.160279	+	0.987072i
$973$	−156541.			−0.165350
$974$	1.19571e6	+	1.01504e6i	1.26039	+	1.06996i
$975$	−41437.6	−	162725.i	−0.0435898	−	0.171176i
$976$	−1.01090e6	−	888494.i	−1.06123	−	0.932727i
$977$	−562965.	+	975083.i	−0.589783	+	1.02153i	0.404478	+	0.914548i	$0.367453\pi$
$977$	−562965.	+	975083.i	−0.589783	+	1.02153i	−0.994261	+	0.106986i	$0.965880\pi$
$978$	−6436.99	+	13173.6i	−0.00672985	+	0.0137729i
$979$	−1.28051e6	+	739303.i	−1.33604	+	0.771360i
$980$	−308361.	+	252784.i	−0.321076	+	0.263206i
$981$	−856837.	+	466644.i	−0.890349	+	0.484895i
$982$	789909.	−	282390.i	0.819132	−	0.292838i
$983$	1.17197e6	−	676638.i	1.21286	−	0.700243i	0.249476	−	0.968381i	$-0.419741\pi$
$983$	1.17197e6	−	676638.i	1.21286	−	0.700243i	0.963381	+	0.268137i	$0.0864081\pi$
$984$	1.04053e6	+	1.10410e6i	1.07465	+	1.14030i
$985$	−200225.	+	346799.i	−0.206369	+	0.357442i
$986$	1.37285e6	+	250185.i	1.41211	+	0.257341i
$987$	297801.	+	83783.0i	0.305697	+	0.0860045i
$988$	−9517.90	+	25246.6i	−0.00975051	+	0.0258636i
$989$	−8043.24			−0.00822316
$990$	−767696.	−	159749.i	−0.783283	−	0.162993i
$991$		−	1.02847e6i		−	1.04724i	−0.851953	−	0.523619i	$-0.824582\pi$
$991$		−	1.02847e6i		−	1.04724i	0.851953	−	0.523619i	$-0.175418\pi$
$992$	1.21629e6	−	962611.i	1.23599	−	0.978200i
$993$	−271674.	−	278525.i	−0.275518	−	0.282466i
$994$	−54519.6	−	9935.56i	−0.0551797	−	0.0100559i
$995$	−452235.	−	261098.i	−0.456791	−	0.263729i
$996$	95323.1	−	129437.i	0.0960903	−	0.130478i
$997$	−564030.	−	976929.i	−0.567430	−	0.982817i	−0.996819	−	0.0796977i	$-0.974605\pi$
$997$	−564030.	−	976929.i	−0.567430	−	0.982817i	0.429389	−	0.903119i	$-0.358729\pi$
$998$	511821.	−	182975.i	0.513874	−	0.183709i
$999$	−754366.	−	812935.i	−0.755877	−	0.814563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.16	yes	44
3.2	odd	2		108.5.f.a.91.7		44
4.3	odd	2	inner	36.5.f.a.31.2	yes	44
9.2	odd	6		108.5.f.a.19.21		44
9.4	even	3		324.5.d.f.163.14		22
9.5	odd	6		324.5.d.e.163.9		22
9.7	even	3	inner	36.5.f.a.7.2	✓	44
12.11	even	2		108.5.f.a.91.21		44
36.7	odd	6	inner	36.5.f.a.7.16	yes	44
36.11	even	6		108.5.f.a.19.7		44
36.23	even	6		324.5.d.e.163.10		22
36.31	odd	6		324.5.d.f.163.13		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.2	✓	44	9.7	even	3	inner
36.5.f.a.7.16	yes	44	36.7	odd	6	inner
36.5.f.a.31.2	yes	44	4.3	odd	2	inner
36.5.f.a.31.16	yes	44	1.1	even	1	trivial
108.5.f.a.19.7		44	36.11	even	6
108.5.f.a.19.21		44	9.2	odd	6
108.5.f.a.91.7		44	3.2	odd	2
108.5.f.a.91.21		44	12.11	even	2
324.5.d.e.163.9		22	9.5	odd	6
324.5.d.e.163.10		22	36.23	even	6
324.5.d.f.163.13		22	36.31	odd	6
324.5.d.f.163.14		22	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.58866 - 3.04940i) q^{2} +(-2.22096 - 8.72166i) q^{3} +(-2.59770 - 15.7877i) q^{4} +(-5.51579 + 9.55363i) q^{5} +(-32.3451 - 15.8048i) q^{6} +(10.3188 - 5.95759i) q^{7} +(-54.8676 - 32.9476i) q^{8} +(-71.1347 + 38.7409i) q^{9} +O(q^{10})\)	\(q+(2.58866 - 3.04940i) q^{2} +(-2.22096 - 8.72166i) q^{3} +(-2.59770 - 15.7877i) q^{4} +(-5.51579 + 9.55363i) q^{5} +(-32.3451 - 15.8048i) q^{6} +(10.3188 - 5.95759i) q^{7} +(-54.8676 - 32.9476i) q^{8} +(-71.1347 + 38.7409i) q^{9} +(14.8544 + 41.5509i) q^{10} +(189.995 - 109.694i) q^{11} +(-131.926 + 57.7201i) q^{12} +(18.5350 - 32.1036i) q^{13} +(8.54488 - 46.8884i) q^{14} +(95.5738 + 26.8886i) q^{15} +(-242.504 + 82.0235i) q^{16} +284.021 q^{17} +(-66.0069 + 317.205i) q^{18} -45.4901i q^{19} +(165.158 + 62.2643i) q^{20} +(-74.8777 - 76.7659i) q^{21} +(157.332 - 863.330i) q^{22} +(174.319 + 100.643i) q^{23} +(-165.499 + 551.712i) q^{24} +(251.652 + 435.874i) q^{25} +(-49.9160 - 139.626i) q^{26} +(495.872 + 534.371i) q^{27} +(-120.862 - 147.435i) q^{28} +(614.153 + 1063.74i) q^{29} +(329.402 - 221.838i) q^{30} +(-1311.83 - 757.384i) q^{31} +(-377.637 + 951.823i) q^{32} +(-1378.68 - 1413.45i) q^{33} +(735.233 - 866.094i) q^{34} +131.443i q^{35} +(796.416 + 1022.42i) q^{36} -1521.29 q^{37} +(-138.718 - 117.758i) q^{38} +(-321.162 - 90.3555i) q^{39} +(617.407 - 342.453i) q^{40} +(1316.97 - 2281.07i) q^{41} +(-427.923 + 29.6117i) q^{42} +(-34.6057 + 19.9796i) q^{43} +(-2225.36 - 2714.63i) q^{44} +(22.2482 - 893.281i) q^{45} +(758.153 - 271.038i) q^{46} +(-2498.36 + 1442.43i) q^{47} +(1253.97 + 1932.87i) q^{48} +(-1129.51 + 1956.38i) q^{49} +(1980.60 + 360.941i) q^{50} +(-630.798 - 2477.13i) q^{51} +(-554.991 - 209.230i) q^{52} +1415.13 q^{53} +(2913.15 - 128.809i) q^{54} +2420.19i q^{55} +(-762.458 - 13.1019i) q^{56} +(-396.749 + 101.032i) q^{57} +(4833.61 + 880.870i) q^{58} +(2453.33 + 1416.43i) q^{59} +(176.238 - 1578.74i) q^{60} +(2628.64 + 4552.93i) q^{61} +(-5705.44 + 2039.68i) q^{62} +(-503.226 + 823.552i) q^{63} +(1924.92 + 3615.51i) q^{64} +(204.471 + 354.154i) q^{65} +(-7879.10 + 545.223i) q^{66} +(805.917 + 465.296i) q^{67} +(-737.801 - 4484.04i) q^{68} +(490.620 - 1743.87i) q^{69} +(400.823 + 340.261i) q^{70} -1162.75i q^{71} +(5179.41 + 218.094i) q^{72} -2162.87 q^{73} +(-3938.11 + 4639.03i) q^{74} +(3242.64 - 3162.88i) q^{75} +(-718.185 + 118.170i) q^{76} +(1307.02 - 2263.82i) q^{77} +(-1106.91 + 745.454i) q^{78} +(6482.54 - 3742.70i) q^{79} +(553.978 - 2769.22i) q^{80} +(3559.29 - 5511.64i) q^{81} +(-3546.69 - 9920.88i) q^{82} +(-966.756 + 558.157i) q^{83} +(-1017.45 + 1381.56i) q^{84} +(-1566.60 + 2713.43i) q^{85} +(-28.6565 + 157.247i) q^{86} +(7913.60 - 7718.96i) q^{87} +(-14038.7 - 241.238i) q^{88} -6739.71 q^{89} +(-2666.38 - 2380.24i) q^{90} -441.696i q^{91} +(1136.10 - 3013.54i) q^{92} +(-3692.13 + 13123.4i) q^{93} +(-2068.85 + 11352.5i) q^{94} +(434.596 + 250.914i) q^{95} +(9140.19 + 1179.66i) q^{96} +(-6023.28 - 10432.6i) q^{97} +(3041.85 + 8508.73i) q^{98} +(-9265.60 + 15163.6i) 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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