LMFDB - Embedded newform 36.5.f.a.7.16

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			7.16
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.16

$q$-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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	0.734368	−	0.678751i	$-0.237479\pi$
$5$	−5.51579	−	9.55363i	−0.220632	−	0.382145i	−0.955000	+	0.296606i	$0.904145\pi$
$6$	−32.3451	+	15.8048i	−0.898476	+	0.439022i
$7$	10.3188	+	5.95759i	0.210589	+	0.121583i	0.601585	−	0.798809i	$-0.294536\pi$
$7$	10.3188	+	5.95759i	0.210589	+	0.121583i	−0.390996	+	0.920392i	$0.627869\pi$
$8$	−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	0.996143	+	0.0877473i	$0.0279668\pi$
$11$	189.995	+	109.694i	1.57021	+	0.906559i	0.574063	+	0.818811i	$0.305367\pi$
$12$	−131.926	−	57.7201i	−0.916151	−	0.400834i
$13$	18.5350	+	32.1036i	0.109675	+	0.189962i	0.915639	−	0.402003i	$-0.131686\pi$
$13$	18.5350	+	32.1036i	0.109675	+	0.189962i	−0.805964	+	0.591965i	$0.798352\pi$
$14$	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	$0.0200686\pi$
$19$			45.4901i			0.126011i	−0.998013	+	0.0630057i	$0.979931\pi$
$20$	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	−0.326105	−	0.945334i	$-0.605736\pi$
$23$	174.319	−	100.643i	0.329525	−	0.190252i	0.655630	+	0.755082i	$0.272403\pi$
$24$	−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	−0.226505	−	0.974010i	$-0.572730\pi$
$29$	614.153	−	1063.74i	0.730265	−	1.26486i	0.956770	−	0.290846i	$-0.0939366\pi$
$30$	329.402	+	221.838i	0.366003	+	0.246486i
$31$	−1311.83	+	757.384i	−1.36507	+	0.788121i	−0.990293	−	0.138996i	$-0.955613\pi$
$31$	−1311.83	+	757.384i	−1.36507	+	0.788121i	−0.374773	+	0.927117i	$0.622279\pi$
$32$	−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	0.929923	+	0.367755i	$0.119874\pi$
$41$	1316.97	+	2281.07i	0.783447	+	1.35697i	−0.146476	+	0.989214i	$0.546793\pi$
$42$	−427.923	−	29.6117i	−0.242587	−	0.0167867i
$43$	−34.6057	−	19.9796i	−0.0187159	−	0.0108056i	0.490613	−	0.871378i	$-0.336773\pi$
$43$	−34.6057	−	19.9796i	−0.0187159	−	0.0108056i	−0.509329	+	0.860572i	$0.670106\pi$
$44$	−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	−0.186807	−	0.982397i	$-0.559814\pi$
$47$	−2498.36	−	1442.43i	−1.13099	−	0.652978i	−0.944184	+	0.329419i	$0.893147\pi$
$48$	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	−0.104346	−	0.994541i	$-0.533275\pi$
$59$	2453.33	−	1416.43i	0.704778	−	0.406904i	0.809125	+	0.587637i	$0.199942\pi$
$60$	176.238	+	1578.74i	0.0489550	+	0.438539i
$61$	2628.64	−	4552.93i	0.706433	−	1.22358i	−0.259739	−	0.965679i	$-0.583637\pi$
$61$	2628.64	−	4552.93i	0.706433	−	1.22358i	0.966172	−	0.257899i	$-0.0830300\pi$
$62$	−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	−0.407541	−	0.913187i	$-0.633614\pi$
$67$	805.917	−	465.296i	0.179531	−	0.103653i	0.587073	+	0.809534i	$0.300280\pi$
$68$	−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	$0.0367923\pi$
$71$			1162.75i			0.230659i	−0.993327	+	0.115329i	$0.963208\pi$
$72$	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	0.919466	−	0.393171i	$-0.128622\pi$
$79$	6482.54	+	3742.70i	1.03870	+	0.599695i	0.119237	+	0.992866i	$0.461955\pi$
$80$	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	0.428190	−	0.903689i	$-0.359152\pi$
$83$	−966.756	−	558.157i	−0.140333	−	0.0810215i	−0.568523	+	0.822667i	$0.692485\pi$
$84$	−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	0.345235	+	0.938516i	$0.387799\pi$
$97$	−6023.28	+	10432.6i	−0.640161	+	1.10879i	−0.985396	+	0.170276i	$0.945534\pi$
$98$	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	−0.530999	−	0.847372i	$-0.678183\pi$
$101$	4777.60	−	8275.04i	0.468346	−	0.811199i	0.999346	+	0.0361728i	$0.0115167\pi$
$102$	−9186.70	+	4488.89i	−0.882996	+	0.431458i
$103$	−9962.26	+	5751.71i	−0.939039	+	0.542154i	−0.889659	−	0.456626i	$-0.849058\pi$
$103$	−9962.26	+	5751.71i	−0.939039	+	0.542154i	−0.0493798	+	0.998780i	$0.515724\pi$
$104$	−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	$0.0931078\pi$
$107$			6602.72i			0.576707i	−0.957524	+	0.288353i	$0.906892\pi$
$108$	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	0.783693	−	0.621149i	$-0.213334\pi$
$113$	−1865.35	−	3230.88i	−0.146084	−	0.253025i	−0.929777	+	0.368124i	$0.880000\pi$
$114$	−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	$-0.692275\pi$
$127$		−	26549.7i		−	1.64608i	0.567980	−	0.823042i	$-0.307725\pi$
$128$	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	−0.532928	−	0.846161i	$-0.678908\pi$
$131$	−1142.84	+	659.821i	−0.0665954	+	0.0384489i	0.466333	+	0.884609i	$0.345575\pi$
$132$	−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	0.284949	+	0.958543i	$0.408023\pi$
$137$	−12906.5	+	22354.7i	−0.687648	+	1.19104i	−0.972597	+	0.232499i	$0.925310\pi$
$138$	−4047.73	+	6010.39i	−0.212546	+	0.315605i
$139$	−11377.8	+	6569.00i	−0.588885	+	0.339993i	−0.764656	−	0.644438i	$-0.777091\pi$
$139$	−11377.8	+	6569.00i	−0.588885	+	0.339993i	0.175772	+	0.984431i	$0.443758\pi$
$140$	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	−0.994984	−	0.100038i	$-0.968103\pi$
$149$	−12968.2	−	22461.6i	−0.584128	−	1.01174i	0.410856	−	0.911700i	$-0.365230\pi$
$150$	−1250.82	+	18075.7i	−0.0555919	+	0.803366i
$151$	24591.2	+	14197.8i	1.07852	+	0.622681i	0.930496	−	0.366303i	$-0.119377\pi$
$151$	24591.2	+	14197.8i	1.07852	+	0.622681i	0.148020	+	0.988984i	$0.452710\pi$
$152$	−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	0.916568	−	0.399878i	$-0.130948\pi$
$157$	2760.19	+	4780.78i	0.111980	+	0.193954i	−0.804589	+	0.593832i	$0.797614\pi$
$158$	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	$0.00243974\pi$
$163$			407.281i			0.0153292i	−0.999971	+	0.00766459i	$0.997560\pi$
$164$	−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	−0.821078	−	0.570816i	$-0.806627\pi$
$167$	−20561.9	+	11871.4i	−0.737277	+	0.425667i	0.0838016	+	0.996482i	$0.473294\pi$
$168$	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	−0.841449	−	0.540336i	$-0.818297\pi$
$173$	1413.25	−	2447.82i	0.0472200	−	0.0817874i	0.888669	+	0.458549i	$0.151630\pi$
$174$	−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	$-0.746961\pi$
$179$		−	45743.4i		−	1.42765i	0.700323	−	0.713826i	$-0.253039\pi$
$180$	−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	0.208257	−	0.978074i	$-0.433221\pi$
$191$	−19504.6	−	11261.0i	−0.534651	−	0.308681i	−0.742908	+	0.669393i	$0.766554\pi$
$192$	27258.1	+	24818.4i	0.739423	+	0.673241i
$193$	−9144.35	−	15838.5i	−0.245493	−	0.425205i	0.716777	−	0.697302i	$-0.245616\pi$
$193$	−9144.35	−	15838.5i	−0.245493	−	0.425205i	−0.962270	+	0.272097i	$0.912283\pi$
$194$	−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	$-0.796094\pi$
$199$		−	47336.5i		−	1.19533i	0.801744	−	0.597667i	$-0.203906\pi$
$200$	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	−0.878602	−	0.477554i	$-0.841524\pi$
$211$	−40261.7	+	23245.1i	−0.904330	+	0.522115i	−0.0257275	+	0.999669i	$0.508190\pi$
$212$	−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	−0.440693	−	0.897658i	$-0.645267\pi$
$223$	−71531.9	−	41298.9i	−1.43843	−	0.830480i	−0.997741	+	0.0671780i	$0.978600\pi$
$224$	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	0.728376	−	0.685178i	$-0.240276\pi$
$227$	25722.3	+	14850.8i	0.499182	+	0.288203i	−0.229194	+	0.973381i	$0.573609\pi$
$228$	2625.69	−	6001.31i	0.0505096	−	0.115445i
$229$	−22667.9	−	39262.0i	−0.432256	−	0.748690i	0.564811	−	0.825220i	$-0.308949\pi$
$229$	−22667.9	−	39262.0i	−0.432256	−	0.748690i	−0.997067	+	0.0765307i	$0.975616\pi$
$230$	−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	−0.752853	−	0.658188i	$-0.771323\pi$
$239$	−31946.2	+	18444.1i	−0.559272	+	0.322896i	0.193581	+	0.981084i	$0.437990\pi$
$240$	−25382.5	−	1318.70i	−0.440669	−	0.0228941i
$241$	−4193.64	+	7263.59i	−0.0722033	+	0.125060i	−0.899867	−	0.436165i	$-0.856336\pi$
$241$	−4193.64	+	7263.59i	−0.0722033	+	0.125060i	0.827663	+	0.561225i	$0.189670\pi$
$242$	−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	$-0.996273\pi$
$251$		−	1475.47i		−	0.0234198i	0.999931	−	0.0117099i	$-0.00372746\pi$
$252$	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	0.704420	−	0.709783i	$-0.251207\pi$
$257$	−17336.5	−	30027.8i	−0.262480	−	0.454629i	−0.966900	+	0.255154i	$0.917874\pi$
$258$	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	0.376099	−	0.926580i	$-0.377265\pi$
$263$	−16482.5	−	9516.19i	−0.238294	−	0.137579i	−0.614392	+	0.789001i	$0.710599\pi$
$264$	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	$0.0687409\pi$
$271$			31474.1i			0.428563i	−0.976772	+	0.214281i	$0.931259\pi$
$272$	−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	−0.997176	−	0.0751008i	$-0.976072\pi$
$277$	−33265.8	+	57618.0i	−0.433549	+	0.750929i	0.563627	+	0.826029i	$0.309405\pi$
$278$	−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	−0.146512	−	0.989209i	$-0.546805\pi$
$281$	61859.9	−	107145.i	0.783424	−	1.35693i	0.929936	−	0.367721i	$-0.119862\pi$
$282$	103607.	+	7169.48i	1.30284	+	0.0901549i
$283$	−47401.9	+	27367.5i	−0.591865	+	0.341713i	−0.765835	−	0.643038i	$-0.777674\pi$
$283$	−47401.9	+	27367.5i	−0.591865	+	0.341713i	0.173970	+	0.984751i	$0.444341\pi$
$284$	−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	0.999825	+	0.0187226i	$0.00595995\pi$
$293$	44309.0	+	76745.4i	0.516127	+	0.893958i	−0.483698	+	0.875235i	$0.660707\pi$
$294$	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	$0.227289\pi$
$307$			123447.i			1.30980i	−0.755716	+	0.654900i	$0.772711\pi$
$308$	−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	−0.745927	−	0.666027i	$-0.767993\pi$
$311$	−52431.9	+	30271.6i	−0.542094	+	0.312978i	0.203833	+	0.979006i	$0.434660\pi$
$312$	14644.4	−	15539.1i	0.150440	−	0.159631i
$313$	26193.1	−	45367.8i	0.267361	−	0.463083i	−0.700818	−	0.713340i	$-0.747182\pi$
$313$	26193.1	−	45367.8i	0.267361	−	0.463083i	0.968180	+	0.250257i	$0.0805150\pi$
$314$	−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	−0.794072	−	0.607823i	$-0.792043\pi$
$317$	12998.7	−	22514.4i	0.129354	−	0.224048i	0.923427	+	0.383775i	$0.125376\pi$
$318$	−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	0.661032	−	0.750357i	$-0.270119\pi$
$331$	37439.2	+	21615.5i	0.341720	+	0.197292i	−0.319312	+	0.947650i	$0.603452\pi$
$332$	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	0.838754	−	0.544511i	$-0.183285\pi$
$337$	−5926.38	−	10264.8i	−0.0521831	−	0.0903837i	−0.890937	+	0.454127i	$0.849951\pi$
$338$	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	−0.391593	−	0.920138i	$-0.628076\pi$
$347$	25222.5	−	14562.2i	0.209473	−	0.120940i	0.601067	+	0.799199i	$0.294743\pi$
$348$	−142422.	+	104886.i	−1.17603	+	0.866083i
$349$	−59988.4	+	103903.i	−0.492512	+	0.853055i	−0.999963	−	0.00862528i	$-0.997254\pi$
$349$	−59988.4	+	103903.i	−0.492512	+	0.853055i	0.507451	+	0.861681i	$0.330588\pi$
$350$	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	0.368330	+	0.929695i	$0.379930\pi$
$353$	−77379.0	+	134024.i	−0.620975	+	1.07556i	−0.989305	+	0.145865i	$0.953404\pi$
$354$	−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	$0.0834942\pi$
$359$			66839.6i			0.518615i	−0.965795	+	0.259307i	$0.916506\pi$
$360$	−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	0.164136	−	0.986438i	$-0.447517\pi$
$367$	−81901.3	−	47285.7i	−0.608077	−	0.351073i	−0.772212	+	0.635364i	$0.780850\pi$
$368$	−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	0.982955	+	0.183848i	$0.0588554\pi$
$373$	90530.4	+	156803.i	0.650694	+	1.12704i	−0.332260	+	0.943188i	$0.607811\pi$
$374$	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	$-0.942975\pi$
$379$		−	51191.3i		−	0.356384i	0.983996	−	0.178192i	$-0.0570248\pi$
$380$	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	−0.877438	−	0.479690i	$-0.840749\pi$
$383$	−132128.	+	76284.0i	−0.900734	+	0.520039i	−0.0232957	+	0.999729i	$0.507416\pi$
$384$	−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	−0.956123	−	0.292965i	$-0.905358\pi$
$389$	−33948.4	+	58800.3i	−0.224347	+	0.388580i	0.731776	+	0.681545i	$0.238692\pi$
$390$	−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	0.734509	−	0.678599i	$-0.237413\pi$
$401$	−35445.4	−	61393.2i	−0.220430	−	0.381796i	−0.954939	+	0.296803i	$0.904079\pi$
$402$	−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	0.793582	−	0.608463i	$-0.208214\pi$
$409$	−21772.1	−	37710.4i	−0.130153	−	0.225432i	−0.923735	+	0.383031i	$0.874880\pi$
$410$	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	0.119357	−	0.992851i	$-0.461917\pi$
$419$	182385.	−	105300.i	1.03887	−	0.599792i	0.919513	+	0.393060i	$0.128583\pi$
$420$	−7586.91	+	17340.7i	−0.0430097	+	0.0983035i
$421$	−42063.0	+	72855.3i	−0.237321	+	0.411052i	−0.959945	−	0.280190i	$-0.909603\pi$
$421$	−42063.0	+	72855.3i	−0.237321	+	0.411052i	0.722624	+	0.691242i	$0.242936\pi$
$422$	−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	$0.132369\pi$
$431$			150083.i			0.807933i	−0.914774	+	0.403967i	$0.867631\pi$
$432$	−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	0.234040	−	0.972227i	$-0.424805\pi$
$439$	−94609.3	−	54622.7i	−0.490913	−	0.283429i	−0.724953	+	0.688798i	$0.758139\pi$
$440$	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	0.913486	−	0.406871i	$-0.133380\pi$
$443$	199756.	+	115329.i	1.01787	+	0.587666i	0.104382	+	0.994537i	$0.466713\pi$
$444$	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	−0.934271	−	0.356564i	$-0.883948\pi$
$457$	−33069.5	+	57278.1i	−0.158342	+	0.274256i	0.775929	+	0.630820i	$0.217281\pi$
$458$	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	−0.585471	−	0.810694i	$-0.699090\pi$
$461$	86994.6	−	150679.i	0.409346	−	0.709008i	0.994817	+	0.101686i	$0.0324236\pi$
$462$	−78054.9	−	52566.5i	−0.365693	−	0.246278i
$463$	−150682.	+	86996.3i	−0.702909	+	0.405825i	−0.808430	−	0.588592i	$-0.799682\pi$
$463$	−150682.	+	86996.3i	−0.702909	+	0.405825i	0.105521	+	0.994417i	$0.466349\pi$
$464$	−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	$0.129096\pi$
$467$			172090.i			0.789080i	−0.918879	+	0.394540i	$0.870904\pi$
$468$	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	0.851912	−	0.523685i	$-0.175443\pi$
$479$	189138.	+	109199.i	0.824343	+	0.475935i	−0.0275690	+	0.999620i	$0.508777\pi$
$480$	−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	$-0.690243\pi$
$487$		−	392112.i		−	1.65330i	0.562716	−	0.826650i	$-0.309757\pi$
$488$	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	−0.0735480	−	0.997292i	$-0.523432\pi$
$491$	181620.	−	104859.i	0.753358	−	0.434951i	0.826906	+	0.562340i	$0.190099\pi$
$492$	−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	−0.244721	−	0.969594i	$-0.578696\pi$
$499$	117681.	−	67943.0i	0.472611	−	0.272862i	0.717332	+	0.696731i	$0.245363\pi$
$500$	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	$-0.848159\pi$
$503$		−	232332.i		−	0.918275i	0.888365	−	0.459137i	$-0.151841\pi$
$504$	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	0.971496	−	0.237057i	$-0.0761827\pi$
$509$	72659.4	+	125850.i	0.280451	+	0.485755i	−0.691045	+	0.722812i	$0.742849\pi$
$510$	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	$0.0427215\pi$
$523$			73202.4i			0.267622i	−0.991007	+	0.133811i	$0.957278\pi$
$524$	−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	−0.0249077	−	0.999690i	$-0.507929\pi$
$547$	−270221.	−	156012.i	−0.903118	−	0.521416i	−0.878211	+	0.478274i	$0.841263\pi$
$548$	−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	−0.613302	−	0.789849i	$-0.710159\pi$
$563$	−74780.6	+	43174.6i	−0.235924	+	0.136211i	0.377378	+	0.926059i	$0.376826\pi$
$564$	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	0.0176822	+	0.999844i	$0.494371\pi$
$569$	−277479.	+	480608.i	−0.857049	+	1.48445i	−0.874731	+	0.484609i	$0.838962\pi$
$570$	−10091.4	+	14984.5i	−0.0310601	+	0.0461205i
$571$	−262848.	+	151755.i	−0.806181	+	0.465449i	−0.845628	−	0.533773i	$-0.820774\pi$
$571$	−262848.	+	151755.i	−0.806181	+	0.465449i	0.0394467	+	0.999222i	$0.487440\pi$
$572$	−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	−0.448666	−	0.893699i	$-0.648101\pi$
$587$	−498580.	−	287855.i	−1.44697	−	0.835406i	−0.998300	+	0.0582932i	$0.981434\pi$
$588$	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	−0.712767	−	0.701401i	$-0.752558\pi$
$599$	−165665.	+	95646.9i	−0.461719	+	0.266574i	0.251048	+	0.967975i	$0.419225\pi$
$600$	−282125.	−	66702.9i	−0.783681	−	0.185286i
$601$	203120.	−	351814.i	0.562346	−	0.974012i	−0.434945	−	0.900457i	$-0.643232\pi$
$601$	203120.	−	351814.i	0.562346	−	0.974012i	0.997291	−	0.0735551i	$-0.0234345\pi$
$602$	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	−0.417126	−	0.908849i	$-0.636962\pi$
$607$	59466.9	−	34333.2i	0.161398	−	0.0931831i	0.578523	+	0.815666i	$0.303629\pi$
$608$	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	0.852331	−	0.523003i	$-0.175188\pi$
$617$	−10190.4	−	17650.3i	−0.0267684	−	0.0463642i	−0.879099	+	0.476639i	$0.841855\pi$
$618$	231326.	−	343492.i	0.605686	−	0.899371i
$619$	388604.	+	224361.i	1.01421	+	0.585552i	0.912420	−	0.409254i	$-0.134211\pi$
$619$	388604.	+	224361.i	1.01421	+	0.585552i	0.101786	+	0.994806i	$0.467544\pi$
$620$	−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	$-0.831313\pi$
$631$		−	402529.i		−	1.01097i	0.862835	−	0.505486i	$-0.168687\pi$
$632$	−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	−0.996921	−	0.0784117i	$-0.975015\pi$
$641$	−176906.	+	306411.i	−0.430554	+	0.745741i	0.566367	+	0.824153i	$0.308348\pi$
$642$	−104355.	−	213566.i	−0.253187	−	0.518157i
$643$	−227886.	+	131570.i	−0.551184	+	0.318226i	−0.749599	−	0.661892i	$-0.769754\pi$
$643$	−227886.	+	131570.i	−0.551184	+	0.318226i	0.198415	+	0.980118i	$0.436420\pi$
$644$	−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	$0.102586\pi$
$647$			265174.i			0.633464i	−0.948515	+	0.316732i	$0.897414\pi$
$648$	−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	0.869451	−	0.494019i	$-0.164473\pi$
$653$	2938.96	+	5090.43i	0.00689235	+	0.0119379i	−0.862559	+	0.505957i	$0.831139\pi$
$654$	−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	0.937802	−	0.347171i	$-0.112858\pi$
$659$	480334.	+	277321.i	1.10604	+	0.638575i	0.168242	+	0.985746i	$0.446191\pi$
$660$	−139693.	+	319285.i	−0.320692	+	0.732977i
$661$	410614.	+	711204.i	0.939789	+	1.62776i	0.765863	+	0.643004i	$0.222312\pi$
$661$	410614.	+	711204.i	0.939789	+	1.62776i	0.173926	+	0.984759i	$0.444355\pi$
$662$	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	0.425926	+	0.904758i	$0.359948\pi$
$673$	−258432.	+	447618.i	−0.570580	+	0.988274i	−0.996506	+	0.0835158i	$0.973385\pi$
$674$	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	−0.192642	−	0.981269i	$-0.561706\pi$
$677$	345343.	−	598152.i	0.753483	−	1.30507i	0.946125	−	0.323801i	$-0.104961\pi$
$678$	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	$0.305734\pi$
$683$			764551.i			1.63895i	−0.573117	+	0.819474i	$0.694266\pi$
$684$	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	0.762105	−	0.647454i	$-0.224166\pi$
$691$	278107.	+	160565.i	0.582445	+	0.336275i	−0.179659	+	0.983729i	$0.557500\pi$
$692$	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	−0.477600	−	0.878577i	$-0.658493\pi$
$709$	262435.	−	454550.i	0.522070	−	0.904252i	0.999670	−	0.0256748i	$-0.00817343\pi$
$710$	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	$0.109486\pi$
$719$			348658.i			0.674438i	−0.941426	+	0.337219i	$0.890514\pi$
$720$	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	0.905583	−	0.424170i	$-0.139434\pi$
$727$	523789.	+	302410.i	0.991032	+	0.572173i	0.0854497	+	0.996342i	$0.472767\pi$
$728$	−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	0.997882	−	0.0650546i	$-0.0207222\pi$
$733$	237805.	+	411891.i	0.442602	+	0.766609i	−0.555280	+	0.831664i	$0.687389\pi$
$734$	−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	$-0.718688\pi$
$739$		−	844449.i		−	1.54627i	0.634244	−	0.773133i	$-0.281312\pi$
$740$	−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	−0.900189	−	0.435499i	$-0.856572\pi$
$743$	−537216.	+	310162.i	−0.973131	+	0.561837i	−0.0729415	+	0.997336i	$0.523239\pi$
$744$	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	−0.941928	−	0.335816i	$-0.890988\pi$
$751$	−632847.	+	365374.i	−1.12207	+	0.647825i	−0.180139	+	0.983641i	$0.557655\pi$
$752$	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	0.722305	−	0.691575i	$-0.243083\pi$
$761$	−137697.	−	238498.i	−0.237769	−	0.411828i	−0.960074	+	0.279747i	$0.909749\pi$
$762$	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	0.887500	−	0.460808i	$-0.152440\pi$
$769$	26421.1	+	45762.6i	0.0446784	+	0.0773853i	−0.842821	+	0.538193i	$0.819107\pi$
$770$	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	−0.934574	−	0.355770i	$-0.884219\pi$
$787$	−677438.	+	391119.i	−1.09375	+	0.631480i	−0.159181	+	0.987249i	$0.550885\pi$
$788$	−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	0.793711	+	0.608296i	$0.208146\pi$
$797$	586714.	+	1.01622e6i	0.923655	+	1.59982i	0.129944	+	0.991521i	$0.458520\pi$
$798$	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	$-0.874833\pi$
$811$		−	504037.i		−	0.766339i	0.923678	−	0.383169i	$-0.125167\pi$
$812$	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	−0.838265	−	0.545262i	$-0.816430\pi$
$821$	35777.1	−	61967.7i	0.0530785	−	0.0919346i	0.891344	+	0.453328i	$0.149763\pi$
$822$	64150.6	−	927049.i	0.0949417	−	1.37201i
$823$	703826.	−	406354.i	1.03912	−	0.599936i	0.119536	−	0.992830i	$-0.461859\pi$
$823$	703826.	−	406354.i	1.03912	−	0.599936i	0.919584	+	0.392893i	$0.128526\pi$
$824$	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	$-0.911373\pi$
$827$		−	375951.i		−	0.549693i	0.961488	−	0.274847i	$-0.0886271\pi$
$828$	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	−0.373539	−	0.927614i	$-0.621856\pi$
$839$	−959899.	−	554198.i	−1.36365	−	0.787302i	−0.990107	+	0.140313i	$0.955189\pi$
$840$	−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	−0.636253	−	0.771480i	$-0.719517\pi$
$853$	254659.	−	441083.i	0.349995	−	0.606209i	0.986248	+	0.165272i	$0.0528501\pi$
$854$	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	−0.551068	−	0.834460i	$-0.685780\pi$
$857$	328394.	−	568795.i	0.447130	−	0.774452i	0.998198	+	0.0600088i	$0.0191129\pi$
$858$	−128536.	−	263053.i	−0.174602	−	0.357330i
$859$	916830.	−	529332.i	1.24252	−	0.717368i	0.272912	−	0.962039i	$-0.412013\pi$
$859$	916830.	−	529332.i	1.24252	−	0.717368i	0.969606	+	0.244671i	$0.0786799\pi$
$860$	−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	$-0.849846\pi$
$863$		−	676878.i		−	0.908844i	0.890787	−	0.454422i	$-0.150154\pi$
$864$	−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	−0.723925	−	0.689879i	$-0.757664\pi$
$877$	−737914.	−	1.27810e6i	−0.959415	−	1.66176i	−0.235490	−	0.971877i	$-0.575669\pi$
$878$	−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	$-0.845114\pi$
$883$		−	729187.i		−	0.935229i	0.883933	−	0.467614i	$-0.154886\pi$
$884$	−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	0.613641	−	0.789585i	$-0.289704\pi$
$887$	1.26218e6	−	728722.i	1.60426	−	0.926221i	0.990621	−	0.136636i	$-0.0436290\pi$
$888$	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	0.501829	−	0.864967i	$-0.332661\pi$
$907$	3010.76	+	1738.27i	0.00365984	+	0.00211301i	−0.498169	+	0.867080i	$0.665994\pi$
$908$	−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	0.863589	−	0.504197i	$-0.168211\pi$
$911$	712683.	+	411468.i	0.858736	+	0.495791i	−0.00485282	+	0.999988i	$0.501545\pi$
$912$	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	$0.172952\pi$
$919$			873279.i			1.03400i	−0.855984	+	0.517002i	$0.827048\pi$
$920$	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	−0.948667	−	0.316275i	$-0.897568\pi$
$929$	−172980.	+	299611.i	−0.200431	+	0.347157i	0.748236	+	0.663433i	$0.230901\pi$
$930$	−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	0.760477	−	0.649365i	$-0.224965\pi$
$941$	−161271.	−	279330.i	−0.182129	−	0.315456i	−0.942605	+	0.333909i	$0.891632\pi$
$942$	−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	0.565805	−	0.824539i	$-0.308566\pi$
$947$	120742.	+	69710.2i	0.134635	+	0.0777314i	−0.431170	+	0.902271i	$0.641899\pi$
$948$	−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	−0.478849	−	0.877897i	$-0.658946\pi$
$967$	39280.8	−	22678.8i	0.0420075	−	0.0242530i	0.520857	+	0.853644i	$0.325613\pi$
$968$	−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	$-0.784094\pi$
$971$		−	1.18319e6i		−	1.25492i	0.778648	−	0.627461i	$-0.215906\pi$
$972$	−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	−0.994261	−	0.106986i	$-0.965880\pi$
$977$	−562965.	−	975083.i	−0.589783	−	1.02153i	0.404478	−	0.914548i	$-0.367453\pi$
$978$	−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	0.963381	−	0.268137i	$-0.0864081\pi$
$983$	1.17197e6	+	676638.i	1.21286	+	0.700243i	0.249476	+	0.968381i	$0.419741\pi$
$984$	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	$0.175418\pi$
$991$			1.02847e6i			1.04724i	−0.851953	+	0.523619i	$0.824582\pi$
$992$	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	0.429389	+	0.903119i	$0.358729\pi$
$997$	−564030.	+	976929.i	−0.567430	+	0.982817i	−0.996819	+	0.0796977i	$0.974605\pi$
$998$	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.7.16	yes	44
3.2	odd	2		108.5.f.a.19.7		44
4.3	odd	2	inner	36.5.f.a.7.2	✓	44
9.2	odd	6		324.5.d.e.163.10		22
9.4	even	3	inner	36.5.f.a.31.2	yes	44
9.5	odd	6		108.5.f.a.91.21		44
9.7	even	3		324.5.d.f.163.13		22
12.11	even	2		108.5.f.a.19.21		44
36.7	odd	6		324.5.d.f.163.14		22
36.11	even	6		324.5.d.e.163.9		22
36.23	even	6		108.5.f.a.91.7		44
36.31	odd	6	inner	36.5.f.a.31.16	yes	44

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

\(f(q)\)	\(=\)	\(q+(2.58866 + 3.04940i) q^{2} +(-2.22096 + 8.72166i) q^{3} +(-2.59770 + 15.7877i) q^{4} +(-5.51579 - 9.55363i) q^{5} +(-32.3451 + 15.8048i) q^{6} +(10.3188 + 5.95759i) q^{7} +(-54.8676 + 32.9476i) q^{8} +(-71.1347 - 38.7409i) q^{9} +O(q^{10})\)	\(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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