LMFDB - Embedded newform 36.5.f.a.7.2

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			7.2
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.93519 - 0.717143i) q^{2} +(2.22096 - 8.72166i) q^{3} +(14.9714 + 5.64418i) q^{4} +(-5.51579 - 9.55363i) q^{5} +(-14.9946 + 32.7286i) q^{6} +(-10.3188 - 5.95759i) q^{7} +(-54.8676 - 32.9476i) q^{8} +(-71.1347 - 38.7409i) q^{9} +O(q^{10})$	\(q+(-3.93519 - 0.717143i) q^{2} +(2.22096 - 8.72166i) q^{3} +(14.9714 + 5.64418i) q^{4} +(-5.51579 - 9.55363i) q^{5} +(-14.9946 + 32.7286i) 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} +(82.4775 - 118.040i) q^{12} +(18.5350 + 32.1036i) q^{13} +(36.3341 + 30.8443i) q^{14} +(-95.5738 + 26.8886i) q^{15} +(192.286 + 169.003i) q^{16} +284.021 q^{17} +(252.146 + 203.466i) q^{18} -45.4901i q^{19} +(-28.6568 - 174.163i) q^{20} +(-74.8777 + 76.7659i) q^{21} +(669.000 + 567.918i) q^{22} +(-174.319 + 100.643i) q^{23} +(-409.216 + 405.362i) 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} +(395.384 - 37.2718i) q^{30} +(1311.83 - 757.384i) q^{31} +(-635.484 - 802.954i) q^{32} +(-1378.68 + 1413.45i) q^{33} +(-1117.68 - 203.683i) q^{34} +131.443i q^{35} +(-846.326 - 981.503i) q^{36} -1521.29 q^{37} +(-32.6229 + 179.012i) q^{38} +(321.162 - 90.3555i) q^{39} +(-12.1303 + 705.917i) q^{40} +(1316.97 + 2281.07i) q^{41} +(349.710 - 248.390i) 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} +(1901.04 - 1301.71i) q^{48} +(-1129.51 - 1956.38i) q^{49} +(-1302.88 + 1534.78i) q^{50} +(630.798 - 2477.13i) q^{51} +(96.2969 + 585.252i) q^{52} +1415.13 q^{53} +(2334.57 - 1747.24i) q^{54} +2420.19i q^{55} +(369.883 + 666.859i) q^{56} +(-396.749 - 101.032i) q^{57} +(-3179.66 + 3745.60i) q^{58} +(-2453.33 + 1416.43i) q^{59} +(-1582.64 - 136.875i) 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} +(6439.01 - 4573.46i) q^{66} +(-805.917 + 465.296i) q^{67} +(4252.19 + 1603.07i) q^{68} +(490.620 + 1743.87i) q^{69} +(94.2635 - 517.254i) q^{70} -1162.75i q^{71} +(2626.58 + 4469.33i) q^{72} -2162.87 q^{73} +(5986.57 + 1090.98i) q^{74} +(-3242.64 - 3162.88i) q^{75} +(256.754 - 681.051i) q^{76} +(1307.02 + 2263.82i) q^{77} +(-1328.63 + 125.247i) 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} +(-1554.31 + 726.670i) q^{84} +(-1566.60 - 2713.43i) q^{85} +(-121.852 - 103.441i) q^{86} +(-7913.60 - 7718.96i) q^{87} +(6810.44 + 12278.5i) q^{88} -6739.71 q^{89} +(553.059 - 3531.18i) q^{90} -441.696i q^{91} +(-3177.85 + 522.881i) q^{92} +(-3692.13 - 13123.4i) q^{93} +(-8797.09 - 7467.91i) q^{94} +(-434.596 + 250.914i) q^{95} +(-8414.48 + 3759.15i) 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 $

$2$	−3.93519	−	0.717143i	−0.983797	−	0.179286i
$2$	−3.93519	−	0.717143i	−0.983797	−	0.179286i
$3$	2.22096	−	8.72166i	0.246773	−	0.969073i
$3$	2.22096	−	8.72166i	0.246773	−	0.969073i
$4$	14.9714	+	5.64418i	0.935713	+	0.352761i
$5$	−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	$0.904145\pi$
$6$	−14.9946	+	32.7286i	−0.416516	+	0.909129i
$7$	−10.3188	−	5.95759i	−0.210589	−	0.121583i	0.390996	−	0.920392i	$-0.372131\pi$
$7$	−10.3188	−	5.95759i	−0.210589	−	0.121583i	−0.601585	+	0.798809i	$0.705464\pi$
$8$	−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	$-0.972033\pi$
$11$	−189.995	−	109.694i	−1.57021	−	0.906559i	−0.574063	−	0.818811i	$-0.694633\pi$
$12$	82.4775	−	118.040i	0.572760	−	0.819723i
$13$	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	$0.798352\pi$
$14$	36.3341	+	30.8443i	0.185378	+	0.157369i
$15$	−95.5738	+	26.8886i	−0.424773	+	0.119505i
$16$	192.286	+	169.003i	0.751119	+	0.660167i
$17$	284.021			0.982771			0.491386	−	0.870942i	$-0.336491\pi$
$17$	284.021			0.982771			0.491386	+	0.870942i	$0.336491\pi$
$18$	252.146	+	203.466i	0.778227	+	0.627982i
$19$		−	45.4901i		−	0.126011i	−0.998013	−	0.0630057i	$-0.979931\pi$
$19$		−	45.4901i		−	0.126011i	0.998013	−	0.0630057i	$-0.0200686\pi$
$20$	−28.6568	−	174.163i	−0.0716419	−	0.435409i
$21$	−74.8777	+	76.7659i	−0.169791	+	0.174072i
$22$	669.000	+	567.918i	1.38223	+	1.17338i
$23$	−174.319	+	100.643i	−0.329525	+	0.190252i	−0.655630	−	0.755082i	$-0.727597\pi$
$23$	−174.319	+	100.643i	−0.329525	+	0.190252i	0.326105	+	0.945334i	$0.394264\pi$
$24$	−409.216	+	405.362i	−0.710445	+	0.703753i
$25$	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	$-0.0939366\pi$
$30$	395.384	−	37.2718i	0.439316	−	0.0414131i
$31$	1311.83	−	757.384i	1.36507	−	0.788121i	0.374773	−	0.927117i	$-0.377721\pi$
$31$	1311.83	−	757.384i	1.36507	−	0.788121i	0.990293	+	0.138996i	$0.0443875\pi$
$32$	−635.484	−	802.954i	−0.620590	−	0.784135i
$33$	−1378.68	+	1413.45i	−1.26601	+	1.29793i
$34$	−1117.68	−	203.683i	−0.966847	−	0.176197i
$35$			131.443i			0.107301i
$36$	−846.326	−	981.503i	−0.653030	−	0.757332i
$37$	−1521.29			−1.11124			−0.555622	−	0.831435i	$-0.687520\pi$
$37$	−1521.29			−1.11124			−0.555622	+	0.831435i	$0.687520\pi$
$38$	−32.6229	+	179.012i	−0.0225920	+	0.123970i
$39$	321.162	−	90.3555i	0.211152	−	0.0594053i
$40$	−12.1303	+	705.917i	−0.00758145	+	0.441198i
$41$	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	$0.546793\pi$
$42$	349.710	−	248.390i	0.198248	−	0.140811i
$43$	34.6057	+	19.9796i	0.0187159	+	0.0108056i	0.509329	−	0.860572i	$-0.329894\pi$
$43$	34.6057	+	19.9796i	0.0187159	+	0.0108056i	−0.490613	+	0.871378i	$0.663227\pi$
$44$	−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	$-0.106853\pi$
$47$	2498.36	+	1442.43i	1.13099	+	0.652978i	0.186807	+	0.982397i	$0.440186\pi$
$48$	1901.04	−	1301.71i	0.825106	−	0.564978i
$49$	−1129.51	−	1956.38i	−0.470435	−	0.814817i
$50$	−1302.88	+	1534.78i	−0.521153	+	0.613911i
$51$	630.798	−	2477.13i	0.242521	−	0.952377i
$52$	96.2969	+	585.252i	0.0356128	+	0.216439i
$53$	1415.13			0.503783			0.251892	−	0.967755i	$-0.418947\pi$
$53$	1415.13			0.503783			0.251892	+	0.967755i	$0.418947\pi$
$54$	2334.57	−	1747.24i	0.800607	−	0.599190i
$55$			2420.19i			0.800062i
$56$	369.883	+	666.859i	0.117947	+	0.212646i
$57$	−396.749	−	101.032i	−0.122114	−	0.0310962i
$58$	−3179.66	+	3745.60i	−0.945203	+	1.11344i
$59$	−2453.33	+	1416.43i	−0.704778	+	0.406904i	−0.809125	−	0.587637i	$-0.800058\pi$
$59$	−2453.33	+	1416.43i	−0.704778	+	0.406904i	0.104346	+	0.994541i	$0.466725\pi$
$60$	−1582.64	−	136.875i	−0.439622	−	0.0380209i
$61$	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
$66$	6439.01	−	4573.46i	1.47819	−	1.04992i
$67$	−805.917	+	465.296i	−0.179531	+	0.103653i	−0.587073	−	0.809534i	$-0.699720\pi$
$67$	−805.917	+	465.296i	−0.179531	+	0.103653i	0.407541	+	0.913187i	$0.366386\pi$
$68$	4252.19	+	1603.07i	0.919592	+	0.346684i
$69$	490.620	+	1743.87i	0.103050	+	0.366283i
$70$	94.2635	−	517.254i	0.0192375	−	0.105562i
$71$		−	1162.75i		−	0.230659i	−0.993327	−	0.115329i	$-0.963208\pi$
$71$		−	1162.75i		−	0.230659i	0.993327	−	0.115329i	$-0.0367923\pi$
$72$	2626.58	+	4469.33i	0.506670	+	0.862140i
$73$	−2162.87			−0.405867			−0.202934	−	0.979192i	$-0.565048\pi$
$73$	−2162.87			−0.405867			−0.202934	+	0.979192i	$0.565048\pi$
$74$	5986.57	+	1090.98i	1.09324	+	0.199230i
$75$	−3242.64	−	3162.88i	−0.576469	−	0.562290i
$76$	256.754	−	681.051i	0.0444519	−	0.117911i
$77$	1307.02	+	2263.82i	0.220445	+	0.381822i
$78$	−1328.63	+	125.247i	−0.218381	+	0.0205862i
$79$	−6482.54	−	3742.70i	−1.03870	−	0.599695i	−0.119237	−	0.992866i	$-0.538045\pi$
$79$	−6482.54	−	3742.70i	−1.03870	−	0.599695i	−0.919466	+	0.393171i	$0.871378\pi$
$80$	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	$-0.307515\pi$
$83$	966.756	+	558.157i	0.140333	+	0.0810215i	−0.428190	+	0.903689i	$0.640848\pi$
$84$	−1554.31	+	726.670i	−0.220282	+	0.102986i
$85$	−1566.60	−	2713.43i	−0.216830	−	0.375561i
$86$	−121.852	−	103.441i	−0.0164754	−	0.0139861i
$87$	−7913.60	−	7718.96i	−1.04553	−	1.01981i
$88$	6810.44	+	12278.5i	0.879447	+	1.58555i
$89$	−6739.71			−0.850866			−0.425433	−	0.904990i	$-0.639878\pi$
$89$	−6739.71			−0.850866			−0.425433	+	0.904990i	$0.639878\pi$
$90$	553.059	−	3531.18i	0.0682789	−	0.435949i
$91$		−	441.696i		−	0.0533385i
$92$	−3177.85	+	522.881i	−0.375455	+	0.0617771i
$93$	−3692.13	−	13123.4i	−0.426886	−	1.51734i
$94$	−8797.09	−	7467.91i	−0.995596	−	0.845168i
$95$	−434.596	+	250.914i	−0.0481546	+	0.0278021i
$96$	−8414.48	+	3759.15i	−0.913029	+	0.407894i
$97$	−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	$0.0115167\pi$
$102$	−4258.77	+	9295.61i	−0.409339	+	0.893465i
$103$	9962.26	−	5751.71i	0.939039	−	0.542154i	0.0493798	−	0.998780i	$-0.484276\pi$
$103$	9962.26	−	5751.71i	0.939039	−	0.542154i	0.889659	+	0.456626i	$0.150942\pi$
$104$	40.7622	−	2372.13i	0.00376870	−	0.219317i
$105$	1146.40	+	291.930i	0.103982	+	0.0264789i
$106$	−5568.79	−	1014.85i	−0.495620	−	0.0903211i
$107$		−	6602.72i		−	0.576707i	−0.957524	−	0.288353i	$-0.906892\pi$
$107$		−	6602.72i		−	0.576707i	0.957524	−	0.288353i	$-0.0931078\pi$
$108$	−10440.0	+	5201.50i	−0.895061	+	0.445944i
$109$	12045.3			1.01383			0.506913	−	0.861997i	$-0.330786\pi$
$109$	12045.3			1.01383			0.506913	+	0.861997i	$0.330786\pi$
$110$	1735.62	−	9523.89i	0.143440	−	0.787099i
$111$	−3378.73	+	13268.2i	−0.274225	+	1.07688i
$112$	−977.325	−	2889.48i	−0.0779117	−	0.230347i
$113$	−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	$0.880000\pi$
$114$	1488.83	+	682.104i	0.114561	+	0.0524857i
$115$	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
$120$	6129.83	+	1673.61i	0.425682	+	0.116223i
$121$	16744.9	+	29003.0i	1.14370	+	1.98094i
$122$	−13609.3	+	16031.5i	−0.914356	+	1.07710i
$123$	22819.6	−	6420.05i	1.50834	−	0.424354i
$124$	23914.7	−	3934.92i	1.55533	−	0.255913i
$125$	−12447.0			−0.796607
$126$	−1389.68	−	3601.72i	−0.0875336	−	0.226865i
$127$			26549.7i			1.64608i	0.567980	+	0.823042i	$0.307725\pi$
$127$			26549.7i			1.64608i	−0.567980	+	0.823042i	$0.692275\pi$
$128$	−4982.07	−	15608.2i	−0.304082	−	0.952646i
$129$	251.113	−	257.445i	0.0150900	−	0.0154706i
$130$	−1058.61	+	1247.03i	−0.0626396	+	0.0737886i
$131$	1142.84	−	659.821i	0.0665954	−	0.0384489i	−0.466333	−	0.884609i	$-0.654425\pi$
$131$	1142.84	−	659.821i	0.0665954	−	0.0384489i	0.532928	+	0.846161i	$0.321092\pi$
$132$	−28618.5	+	13379.8i	−1.64248	+	0.767892i
$133$	−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	$0.925310\pi$
$138$	−680.075	−	7214.32i	−0.0357107	−	0.378824i
$139$	11377.8	−	6569.00i	0.588885	−	0.339993i	−0.175772	−	0.984431i	$-0.556242\pi$
$139$	11377.8	−	6569.00i	0.588885	−	0.339993i	0.764656	+	0.644438i	$0.222909\pi$
$140$	−741.889	+	1967.89i	−0.0378515	+	0.100403i
$141$	18129.1	−	18586.3i	0.911881	−	0.934876i
$142$	−833.858	+	4575.64i	−0.0413538	+	0.226921i
$143$		−	8132.70i		−	0.397706i
$144$	−7130.92	−	19471.3i	−0.343891	−	0.939010i
$145$	−13550.2			−0.644478
$146$	8511.29	+	1551.08i	0.399291	+	0.0727662i
$147$	−19571.5	+	5506.21i	−0.905708	+	0.254811i
$148$	−22775.9	−	8586.46i	−1.03981	−	0.392004i
$149$	−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	$-0.365230\pi$
$150$	10492.2	+	14772.0i	0.466318	+	0.656532i
$151$	−24591.2	−	14197.8i	−1.07852	−	0.622681i	−0.148020	−	0.988984i	$-0.547290\pi$
$151$	−24591.2	−	14197.8i	−1.07852	−	0.622681i	−0.930496	+	0.366303i	$0.880623\pi$
$152$	−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
$156$	5318.24	+	459.950i	0.218534	+	0.0189000i
$157$	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	$0.797614\pi$
$158$	22826.0	+	19377.1i	0.914356	+	0.776203i
$159$	3142.94	−	12342.3i	0.124320	−	0.488203i
$160$	−4165.93	+	10500.1i	−0.162732	+	0.410161i
$161$	2398.36			0.0925257
$162$	−10053.8	−	24241.9i	−0.383091	−	0.923711i
$163$		−	407.281i		−	0.0153292i	−0.999971	−	0.00766459i	$-0.997560\pi$
$163$		−	407.281i		−	0.0153292i	0.999971	−	0.00766459i	$-0.00243974\pi$
$164$	6842.21	+	41584.0i	0.254395	+	1.54610i
$165$	21108.1	+	5375.13i	0.775319	+	0.197434i
$166$	−3404.09	−	2889.76i	−0.123534	−	0.104868i
$167$	20561.9	−	11871.4i	0.737277	−	0.425667i	−0.0838016	−	0.996482i	$-0.526706\pi$
$167$	20561.9	−	11871.4i	0.737277	−	0.425667i	0.821078	+	0.570816i	$0.193373\pi$
$168$	6637.61	−	1744.92i	0.235176	−	0.0618241i
$169$	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	$0.151630\pi$
$174$	25605.9	+	36050.7i	0.845750	+	1.19074i
$175$	−5193.52	+	2998.48i	−0.169584	+	0.0979095i
$176$	−17994.9	−	53202.2i	−0.580931	−	1.71753i
$177$	6904.89	+	24543.0i	0.220399	+	0.783395i
$178$	26522.0	+	4833.34i	0.837080	+	0.152548i
$179$			45743.4i			1.42765i	0.700323	+	0.713826i	$0.253039\pi$
$179$			45743.4i			1.42765i	−0.700323	+	0.713826i	$0.746961\pi$
$180$	−4708.75	+	13499.3i	−0.145332	+	0.416644i
$181$	−24226.2			−0.739483			−0.369742	−	0.929135i	$-0.620554\pi$
$181$	−24226.2			−0.739483			−0.369742	+	0.929135i	$0.620554\pi$
$182$	−316.759	+	1738.16i	−0.00956283	+	0.0524743i
$183$	−33871.0	−	33037.9i	−1.01141	−	0.986531i
$184$	12880.4	+	221.334i	0.380447	+	0.00653752i
$185$	8391.13	+	14533.9i	0.245176	+	0.424657i
$186$	5117.87	+	54291.0i	0.147932	+	1.56928i
$187$	−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	$-0.233446\pi$
$191$	19504.6	+	11261.0i	0.534651	+	0.308681i	−0.208257	+	0.978074i	$0.566779\pi$
$192$	35808.4	−	8758.58i	0.971365	−	0.237592i
$193$	−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	$0.912283\pi$
$194$	31184.4	−	36734.8i	0.828579	−	0.976055i
$195$	−2634.69	−	2569.88i	−0.0692883	−	0.0675841i
$196$	−5868.28	−	35664.9i	−0.152756	−	0.928387i
$197$	36300.2			0.935356			0.467678	−	0.883899i	$-0.345091\pi$
$197$	36300.2			0.935356			0.467678	+	0.883899i	$0.345091\pi$
$198$	−25587.4	−	66316.3i	−0.652674	−	1.69157i
$199$			47336.5i			1.19533i	0.801744	+	0.597667i	$0.203906\pi$
$199$			47336.5i			1.19533i	−0.801744	+	0.597667i	$0.796094\pi$
$200$	−28168.6	+	15624.1i	−0.704214	+	0.390602i
$201$	2268.25	+	8062.33i	0.0561434	+	0.199558i
$202$	−24735.1	+	29137.6i	−0.606194	+	0.714088i
$203$	−12674.7	+	7317.73i	−0.307571	+	0.177576i
$204$	23425.3	−	33525.8i	0.562892	−	0.805600i
$205$	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
$210$	−4301.96	−	1970.93i	−0.0975500	−	0.0446923i
$211$	40261.7	−	23245.1i	0.904330	−	0.522115i	0.0257275	−	0.999669i	$-0.491810\pi$
$211$	40261.7	−	23245.1i	0.904330	−	0.522115i	0.878602	+	0.477554i	$0.158476\pi$
$212$	21186.5	+	7987.24i	0.471397	+	0.177715i
$213$	−10141.1	−	2582.42i	−0.223525	−	0.0569203i
$214$	−4735.09	+	25982.9i	−0.103395	+	0.567363i
$215$		−	440.814i		−	0.00953626i
$216$	44813.5	−	12981.9i	0.960509	−	0.278247i
$217$	−18048.7			−0.383290
$218$	−47400.4	−	8638.18i	−0.997400	−	0.181765i
$219$	−4803.64	+	18863.8i	−0.100157	+	0.393315i
$220$	−13660.0	+	36233.6i	−0.282231	+	0.748629i
$221$	5264.34	+	9118.10i	0.107785	+	0.186689i
$222$	22811.1	−	49789.8i	0.462850	−	1.01026i
$223$	71531.9	+	41298.9i	1.43843	+	0.830480i	0.997741	−	0.0671780i	$-0.0213996\pi$
$223$	71531.9	+	41298.9i	1.43843	+	0.830480i	0.440693	+	0.897658i	$0.354733\pi$
$224$	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	$-0.426391\pi$
$227$	−25722.3	−	14850.8i	−0.499182	−	0.288203i	−0.728376	+	0.685178i	$0.759724\pi$
$228$	−5369.66	−	3751.91i	−0.103294	−	0.0721743i
$229$	−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	$0.975616\pi$
$230$	−6771.21	−	5748.13i	−0.128000	−	0.108660i
$231$	22647.1	−	6371.52i	0.424413	−	0.119404i
$232$	−68744.9	+	38130.3i	−1.27722	+	0.708425i
$233$	50931.3			0.938151			0.469075	−	0.883158i	$-0.344587\pi$
$233$	50931.3			0.938151			0.469075	+	0.883158i	$0.344587\pi$
$234$	−1858.48	+	11866.0i	−0.0339411	+	0.216708i
$235$		−	31824.5i		−	0.576270i
$236$	−44724.5	+	7358.94i	−0.803010	+	0.132127i
$237$	−47040.0	+	48226.2i	−0.837472	+	0.858590i
$238$	10319.7	+	8760.43i	0.182184	+	0.154658i
$239$	31946.2	−	18444.1i	0.559272	−	0.322896i	−0.193581	−	0.981084i	$-0.562010\pi$
$239$	31946.2	−	18444.1i	0.559272	−	0.322896i	0.752853	+	0.658188i	$0.228677\pi$
$240$	−22921.8	−	10981.9i	−0.397948	−	0.190658i
$241$	−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
$246$	−94403.6	+	8899.18i	−1.55998	+	0.147055i
$247$	1460.40	−	843.160i	0.0239374	−	0.0138203i
$248$	−96930.9	−	1665.64i	−1.57601	−	0.0270818i
$249$	7015.18	−	7192.08i	0.113146	−	0.115999i
$250$	48981.2	+	8926.26i	0.783699	+	0.142820i
$251$			1475.47i			0.0234198i	0.999931	+	0.0117099i	$0.00372746\pi$
$251$			1475.47i			0.0234198i	−0.999931	+	0.0117099i	$0.996273\pi$
$252$	2885.72	+	15170.0i	0.0454416	+	0.238883i
$253$	44159.6			0.689897
$254$	19039.9	−	104478.i	0.295119	−	1.61941i
$255$	−27145.0	+	7636.94i	−0.417454	+	0.117446i
$256$	8412.13	+	64993.9i	0.128359	+	0.991728i
$257$	−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	$0.917874\pi$
$258$	−1172.80	+	833.012i	−0.0176192	+	0.0125145i
$259$	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	$-0.289401\pi$
$263$	16482.5	+	9516.19i	0.238294	+	0.137579i	−0.376099	+	0.926580i	$0.622735\pi$
$264$	122215.	−	32128.3i	1.75354	−	0.460977i
$265$	−7805.54	−	13519.6i	−0.111151	−	0.192518i
$266$	1403.11	−	1652.84i	0.0198303	−	0.0233598i
$267$	−14968.6	+	58781.5i	−0.209971	+	0.824552i
$268$	−14691.9	+	2417.40i	−0.204555	+	0.0336573i
$269$	58724.1			0.811544			0.405772	−	0.913974i	$-0.367003\pi$
$269$	58724.1			0.811544			0.405772	+	0.913974i	$0.367003\pi$
$270$	−29569.5	−	12666.2i	−0.405617	−	0.173748i
$271$		−	31474.1i		−	0.428563i	−0.976772	−	0.214281i	$-0.931259\pi$
$271$		−	31474.1i		−	0.428563i	0.976772	−	0.214281i	$-0.0687409\pi$
$272$	54613.4	+	48000.3i	0.738178	+	0.648793i
$273$	−3852.32	−	980.988i	−0.0516889	−	0.0131625i
$274$	66820.8	−	78714.0i	0.890043	−	1.04846i
$275$	−95625.2	+	55209.2i	−1.26447	+	0.730040i
$276$	−2497.47	+	28877.4i	−0.0327856	+	0.379088i
$277$	−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	$-0.119862\pi$
$282$	−84670.5	+	60139.3i	−1.06472	+	0.756241i
$283$	47401.9	−	27367.5i	0.591865	−	0.341713i	−0.173970	−	0.984751i	$-0.555659\pi$
$283$	47401.9	−	27367.5i	0.591865	−	0.341713i	0.765835	+	0.643038i	$0.222326\pi$
$284$	6562.78	−	17408.0i	0.0813675	−	0.215830i
$285$	1223.17	+	4347.66i	0.0150590	+	0.0535262i
$286$	−5832.30	+	32003.7i	−0.0713030	+	0.391262i
$287$		−	31383.9i		−	0.381016i
$288$	14097.8	+	81737.1i	0.169968	+	0.985450i
$289$	−2853.15			−0.0341609
$290$	53322.4	+	9717.39i	0.634036	+	0.115546i
$291$	77612.4	+	75703.4i	0.916526	+	0.893983i
$292$	−32381.2	−	12207.6i	−0.379776	−	0.143174i
$293$	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	$0.660707\pi$
$294$	80966.1	−	7632.46i	0.936717	−	0.0883019i
$295$	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
$300$	−30695.0	−	65654.9i	−0.341055	−	0.729498i
$301$	−238.061	−	412.333i	−0.00262757	−	0.00455109i
$302$	86589.3	+	73506.3i	0.949403	+	0.805955i
$303$	−61561.3	−	60047.1i	−0.670536	−	0.654044i
$304$	7687.95	−	8747.13i	0.0831886	−	0.0946495i
$305$	−57996.0			−0.623446
$306$	71614.6	+	57788.7i	0.764820	+	0.617163i
$307$		−	123447.i		−	1.30980i	−0.755716	−	0.654900i	$-0.772711\pi$
$307$		−	123447.i		−	1.30980i	0.755716	−	0.654900i	$-0.227289\pi$
$308$	6790.48	+	41269.7i	0.0715813	+	0.435040i
$309$	−28038.7	−	99661.8i	−0.293658	−	1.04379i
$310$	50956.4	+	43257.2i	0.530243	+	0.450127i
$311$	52431.9	−	30271.6i	0.542094	−	0.312978i	−0.203833	−	0.979006i	$-0.565340\pi$
$311$	52431.9	−	30271.6i	0.542094	−	0.312978i	0.745927	+	0.666027i	$0.232007\pi$
$312$	−20598.4	−	5623.92i	−0.211604	−	0.0577737i
$313$	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	$0.125376\pi$
$318$	−21219.2	+	46315.2i	−0.209834	+	0.458004i
$319$	−233372.	+	134737.i	−2.29333	+	1.32406i
$320$	23923.8	−	38332.3i	0.233631	−	0.374339i
$321$	−57586.7	−	14664.4i	−0.558871	−	0.142316i
$322$	−9437.99	−	1719.97i	−0.0910265	−	0.0165885i
$323$		−	12920.1i		−	0.123840i
$324$	22178.9	+	102606.i	0.211276	+	0.977426i
$325$	18657.5			0.176639
$326$	−292.079	+	1602.73i	−0.00274830	+	0.0150808i
$327$	26752.0	−	105055.i	0.250185	−	0.982472i
$328$	2896.29	−	168548.i	0.0269212	−	1.56666i
$329$	−17186.8	−	29768.4i	−0.158783	−	0.275019i
$330$	−79209.4	−	36289.6i	−0.727359	−	0.333238i
$331$	−37439.2	−	21615.5i	−0.341720	−	0.197292i	0.319312	−	0.947650i	$-0.396548\pi$
$331$	−37439.2	−	21615.5i	−0.341720	−	0.197292i	−0.661032	+	0.750357i	$0.729881\pi$
$332$	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
$336$	−27371.6	+	2106.49i	−0.242450	+	0.0186587i
$337$	−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	$0.849951\pi$
$338$	−70377.3	+	82903.5i	−0.616027	+	0.725671i
$339$	−32321.5	+	9093.29i	−0.281249	+	0.0791264i
$340$	−8139.12	−	49466.1i	−0.0704076	−	0.427907i
$341$	−332321.			−2.85791
$342$	9255.70	−	11470.1i	0.0791329	−	0.0980655i
$343$			55525.0i			0.471955i
$344$	−1240.45	−	2236.41i	−0.0104825	−	0.0188988i
$345$	13954.2	−	14306.0i	0.117237	−	0.120194i
$346$	−7316.83	+	8619.12i	−0.0611182	+	0.0719964i
$347$	−25222.5	+	14562.2i	−0.209473	+	0.120940i	−0.601067	−	0.799199i	$-0.705257\pi$
$347$	−25222.5	+	14562.2i	−0.209473	+	0.120940i	0.391593	+	0.920138i	$0.371924\pi$
$348$	−74910.6	−	160230.i	−0.618564	−	1.32307i
$349$	−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	$0.953404\pi$
$354$	−9571.25	−	101533.i	−0.0763769	−	0.810216i
$355$	−11108.5	+	6413.49i	−0.0881451	+	0.0508906i
$356$	−100903.	−	38040.2i	−0.796167	−	0.300153i
$357$	−21266.8	+	21803.1i	−0.166866	+	0.171073i
$358$	32804.5	−	180009.i	0.255957	−	1.40452i
$359$		−	66839.6i		−	0.518615i	−0.965795	−	0.259307i	$-0.916506\pi$
$359$		−	66839.6i		−	0.518615i	0.965795	−	0.259307i	$-0.0834942\pi$
$360$	28210.7	−	49745.3i	0.217675	−	0.383837i
$361$	128252.			0.984121
$362$	95334.7	+	17373.6i	0.727501	+	0.132579i
$363$	290144.	−	81628.7i	2.20191	−	0.619483i
$364$	2493.01	−	6612.82i	0.0188158	−	0.0499096i
$365$	11929.9	+	20663.2i	0.0895472	+	0.155100i
$366$	109596.	+	154301.i	0.818149	+	1.15188i
$367$	81901.3	+	47285.7i	0.608077	+	0.351073i	0.772212	−	0.635364i	$-0.219150\pi$
$367$	81901.3	+	47285.7i	0.608077	+	0.351073i	−0.164136	+	0.986438i	$0.552483\pi$
$368$	−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
$372$	18794.6	−	217315.i	0.135815	−	1.57038i
$373$	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	$0.607811\pi$
$374$	190010.	+	161301.i	1.35842	+	1.15317i
$375$	−27644.2	+	108558.i	−0.196581	+	0.771970i
$376$	−89554.6	−	161457.i	−0.633450	−	1.14204i
$377$	45533.4			0.320366
$378$	−34499.4	+	4121.09i	−0.241450	+	0.0288422i
$379$			51191.3i			0.356384i	0.983996	+	0.178192i	$0.0570248\pi$
$379$			51191.3i			0.356384i	−0.983996	+	0.178192i	$0.942975\pi$
$380$	−7922.71	+	1303.60i	−0.0548664	+	0.00902769i
$381$	231557.	+	58965.7i	1.59518	+	0.406209i
$382$	−68678.6	−	58301.7i	−0.470646	−	0.399535i
$383$	132128.	−	76284.0i	0.900734	−	0.520039i	0.0232957	−	0.999729i	$-0.492584\pi$
$383$	132128.	−	76284.0i	0.900734	−	0.520039i	0.877438	+	0.479690i	$0.159251\pi$
$384$	−147194.	+	8786.92i	−0.998223	+	0.0595901i
$385$	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	$0.238692\pi$
$390$	8525.02	+	12002.4i	0.0560488	+	0.0789114i
$391$	−49510.2	+	28584.7i	−0.323848	+	0.186974i
$392$	−2484.03	+	144556.i	−0.0161653	+	0.940731i
$393$	−3216.53	−	11432.9i	−0.0208258	−	0.0740240i
$394$	−142848.	−	26032.5i	−0.920201	−	0.167696i
$395$			82575.7i			0.529247i
$396$	53133.1	+	279317.i	0.338825	+	1.78118i
$397$	−126087.			−0.799998			−0.399999	−	0.916516i	$-0.630990\pi$
$397$	−126087.			−0.799998			−0.399999	+	0.916516i	$0.630990\pi$
$398$	33947.0	−	186278.i	0.214306	−	1.17597i
$399$	3492.09	+	3406.20i	0.0219351	+	0.0213956i
$400$	122053.	−	41282.8i	0.762833	−	0.258017i
$401$	−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	$0.904079\pi$
$402$	−3144.14	−	33353.5i	−0.0194558	−	0.206390i
$403$	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
$408$	−116226.	+	115131.i	−0.698204	+	0.691628i
$409$	−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	$0.874880\pi$
$410$	−75217.6	+	88605.3i	−0.447458	+	0.527099i
$411$	166305.	+	162215.i	0.984513	+	0.960298i
$412$	181613.	−	29882.5i	1.06992	−	0.176044i
$413$	33754.1			0.197891
$414$	−64431.2	−	10091.3i	−0.375920	−	0.0588772i
$415$		−	12314.7i		−	0.0715036i
$416$	13999.0	−	35284.1i	0.0808930	−	0.203888i
$417$	−32022.9	−	113823.i	−0.184157	−	0.654573i
$418$	25834.7	−	30432.9i	0.147860	−	0.174177i
$419$	−182385.	+	105300.i	−1.03887	+	0.599792i	−0.919513	−	0.393060i	$-0.871417\pi$
$419$	−182385.	+	105300.i	−1.03887	+	0.599792i	−0.119357	+	0.992851i	$0.538083\pi$
$420$	15515.6	+	10841.1i	0.0879567	+	0.0614575i
$421$	−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
$426$	38055.2	+	17434.9i	0.209698	+	0.0960729i
$427$	−54249.0	+	31320.7i	−0.297533	+	0.171781i
$428$	37266.9	−	98852.0i	0.203440	−	0.539632i
$429$	−70930.6	−	18062.4i	−0.385407	−	0.0981432i
$430$	−316.126	+	1734.69i	−0.00170972	+	0.00938175i
$431$		−	150083.i		−	0.807933i	−0.914774	−	0.403967i	$-0.867631\pi$
$431$		−	150083.i		−	0.807933i	0.914774	−	0.403967i	$-0.132369\pi$
$432$	−185660.	+	18948.5i	−0.994832	+	0.101533i
$433$	71221.5			0.379871			0.189935	−	0.981797i	$-0.439172\pi$
$433$	71221.5			0.379871			0.189935	+	0.981797i	$0.439172\pi$
$434$	71025.1	+	12943.5i	0.377079	+	0.0687183i
$435$	−30094.3	+	118180.i	−0.159040	+	0.624546i
$436$	180335.	+	67985.7i	0.948651	+	0.357639i
$437$	4578.26	+	7929.78i	0.0239739	+	0.0415239i
$438$	32431.2	−	70787.7i	0.169050	−	0.368986i
$439$	94609.3	+	54622.7i	0.490913	+	0.283429i	0.724953	−	0.688798i	$-0.241861\pi$
$439$	94609.3	+	54622.7i	0.490913	+	0.283429i	−0.234040	+	0.972227i	$0.575195\pi$
$440$	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	$-0.533287\pi$
$443$	−199756.	−	115329.i	−1.01787	−	0.587666i	−0.913486	+	0.406871i	$0.866620\pi$
$444$	−125472.	+	179574.i	−0.636477	+	0.910912i
$445$	37174.8	+	64388.7i	0.187728	+	0.325154i
$446$	−251874.	−	213818.i	−1.26623	−	1.07491i
$447$	−224704.	+	63218.1i	−1.12460	+	0.316393i
$448$	1676.80	−	48775.7i	0.00835458	−	0.243023i
$449$	−9751.64			−0.0483710			−0.0241855	−	0.999707i	$-0.507699\pi$
$449$	−9751.64			−0.0483710			−0.0241855	+	0.999707i	$0.507699\pi$
$450$	152139.	−	58701.1i	0.751302	−	0.289882i
$451$		−	577854.i		−	2.84096i
$452$	−9691.23	−	58899.1i	−0.0474353	−	0.288292i
$453$	−178444.	+	182944.i	−0.869573	+	0.891500i
$454$	90572.1	+	76887.2i	0.439423	+	0.373029i
$455$	−4219.80	+	2436.30i	−0.0203831	+	0.0117682i
$456$	18440.0	+	18615.3i	0.0886809	+	0.0895241i
$457$	−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	$0.0324236\pi$
$462$	−93689.9	+	8831.90i	−0.438944	+	0.0413781i
$463$	150682.	−	86996.3i	0.702909	−	0.405825i	−0.105521	−	0.994417i	$-0.533651\pi$
$463$	150682.	−	86996.3i	0.702909	−	0.405825i	0.808430	+	0.588592i	$0.200318\pi$
$464$	297869.	−	100750.i	1.38353	−	0.467960i
$465$	−105011.	+	107659.i	−0.485658	+	0.497905i
$466$	−200424.	−	36525.0i	−0.922950	−	0.168197i
$467$		−	172090.i		−	0.789080i	−0.918879	−	0.394540i	$-0.870904\pi$
$467$		−	172090.i		−	0.789080i	0.918879	−	0.394540i	$-0.129096\pi$
$468$	15823.1	−	45362.3i	0.0722437	−	0.207111i
$469$	11088.2			0.0504097
$470$	−22822.7	+	125236.i	−0.103317	+	0.566933i
$471$	47826.6	−	13455.5i	0.215590	−	0.0606538i
$472$	181277.	+	3115.02i	0.813688	+	0.0139822i
$473$	−4383.27	−	7592.05i	−0.0195919	−	0.0339341i
$474$	219696.	−	156045.i	0.977836	−	0.694532i
$475$	−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	$-0.491223\pi$
$479$	−189138.	−	109199.i	−0.824343	−	0.475935i	−0.851912	+	0.523685i	$0.824557\pi$
$480$	82326.0	+	59654.1i	0.357318	+	0.258916i
$481$	−28197.2	−	48839.0i	−0.121875	−	0.211094i
$482$	21711.8	−	25576.2i	0.0934548	−	0.110088i
$483$	5326.65	−	20917.7i	0.0228328	−	0.0896642i
$484$	86996.3	+	528726.i	0.371373	+	2.25705i
$485$	132893.			0.564959
$486$	−233758.	+	33846.1i	−0.989680	+	0.143297i
$487$			392112.i			1.65330i	0.562716	+	0.826650i	$0.309757\pi$
$487$			392112.i			1.65330i	−0.562716	+	0.826650i	$0.690243\pi$
$488$	−294235.	+	163201.i	−1.23553	+	0.685306i
$489$	−3552.17	−	904.554i	−0.0148551	−	0.00378283i
$490$	64511.1	−	75993.1i	0.268684	−	0.316506i
$491$	−181620.	+	104859.i	−0.753358	+	0.434951i	−0.826906	−	0.562340i	$-0.809901\pi$
$491$	−181620.	+	104859.i	−0.753358	+	0.434951i	0.0735480	+	0.997292i	$0.476568\pi$
$492$	377878.	+	32680.9i	1.56107	+	0.135009i
$493$	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
$498$	−32763.8	+	23271.3i	−0.132110	+	0.0938344i
$499$	−117681.	+	67943.0i	−0.472611	+	0.272862i	−0.717332	−	0.696731i	$-0.754637\pi$
$499$	−117681.	+	67943.0i	−0.472611	+	0.272862i	0.244721	+	0.969594i	$0.421304\pi$
$500$	−186349.	−	70253.0i	−0.745395	−	0.281012i
$501$	−57871.4	−	205700.i	−0.230562	−	0.819518i
$502$	1058.12	−	5806.24i	0.00419883	−	0.0230403i
$503$			232332.i			0.918275i	0.888365	+	0.459137i	$0.151841\pi$
$503$			232332.i			0.918275i	−0.888365	+	0.459137i	$0.848159\pi$
$504$	−476.781	−	61766.4i	−0.00187697	−	0.243160i
$505$	−105409.			−0.413328
$506$	−173776.	−	31668.7i	−0.678718	−	0.123689i
$507$	−175156.	−	170848.i	−0.681413	−	0.664653i
$508$	−149851.	+	397486.i	−0.580675	+	1.54026i
$509$	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	$0.742849\pi$
$510$	112297.	−	10586.0i	0.431747	−	0.0406996i
$511$	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
$516$	5212.59	−	2436.99i	0.0195774	−	0.00915282i
$517$	−316450.	−	548108.i	−1.18393	−	2.05062i
$518$	−55274.9	−	46923.2i	−0.206001	−	0.174875i
$519$	−18210.3	−	17762.4i	−0.0676054	−	0.0659426i
$520$	−22887.3	+	12694.8i	−0.0846425	+	0.0469481i
$521$	443088.			1.63235			0.816177	−	0.577803i	$-0.196090\pi$
$521$	443088.			1.63235			0.816177	+	0.577803i	$0.196090\pi$
$522$	371292.	−	143259.i	1.36262	−	0.525752i
$523$		−	73202.4i		−	0.267622i	−0.991007	−	0.133811i	$-0.957278\pi$
$523$		−	73202.4i		−	0.267622i	0.991007	−	0.133811i	$-0.0427215\pi$
$524$	20834.1	−	3428.04i	0.0758775	−	0.0124848i
$525$	14617.1	+	51955.6i	0.0530327	+	0.188501i
$526$	−58037.4	−	49268.3i	−0.209767	−	0.178072i
$527$	372587.	−	215113.i	1.34155	−	0.774543i
$528$	−503978.	+	38785.6i	−1.80777	+	0.139124i
$529$	−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
$534$	101059.	−	220582.i	0.354399	−	0.773547i
$535$	−63079.9	+	36419.2i	−0.220386	+	0.127240i
$536$	59549.1	+	1023.28i	0.207274	+	0.00356176i
$537$	398958.	+	101594.i	1.38350	+	0.352306i
$538$	−231090.	−	42113.6i	−0.798394	−	0.145498i
$539$			495602.i			1.70591i
$540$	107278.	+	71049.4i	0.367894	+	0.243654i
$541$	438165.			1.49707			0.748536	−	0.663094i	$-0.230757\pi$
$541$	438165.			1.49707			0.748536	+	0.663094i	$0.230757\pi$
$542$	−22571.4	+	123856.i	−0.0768351	+	0.421619i
$543$	−53805.4	+	211293.i	−0.182485	+	0.716613i
$544$	−180491.	−	228056.i	−0.609898	−	0.770625i
$545$	−66439.2	−	115076.i	−0.223682	−	0.387429i
$546$	14456.1	+	6623.04i	0.0484916	+	0.0222163i
$547$	270221.	+	156012.i	0.903118	+	0.521416i	0.878211	−	0.478274i	$-0.158737\pi$
$547$	270221.	+	156012.i	0.903118	+	0.521416i	0.0249077	+	0.999690i	$0.492071\pi$
$548$	−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
$552$	30537.2	−	111847.i	0.100219	−	0.367068i
$553$	44594.9	+	77240.6i	0.145826	+	0.252578i
$554$	172227.	−	202881.i	0.561155	−	0.661032i
$555$	145396.	−	40905.5i	0.472026	−	0.132799i
$556$	207419.	−	34128.6i	0.670963	−	0.110400i
$557$	312549.			1.00741			0.503707	−	0.863874i	$-0.331969\pi$
$557$	312549.			1.00741			0.503707	+	0.863874i	$0.331969\pi$
$558$	484874.	+	75941.6i	1.55726	+	0.243900i
$559$			1481.29i			0.00474042i
$560$	−22214.3	+	25274.7i	−0.0708363	+	0.0805955i
$561$	−391574.	+	401448.i	−1.24419	+	1.27557i
$562$	−320268.	+	377272.i	−1.01401	+	1.19449i
$563$	74780.6	−	43174.6i	0.235924	−	0.136211i	−0.377378	−	0.926059i	$-0.623174\pi$
$563$	74780.6	−	43174.6i	0.235924	−	0.136211i	0.613302	+	0.789849i	$0.289841\pi$
$564$	376323.	−	175939.i	1.18305	−	0.553099i
$565$	−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	$0.838962\pi$
$570$	−1695.50	−	17986.1i	−0.00521852	−	0.0553588i
$571$	262848.	−	151755.i	0.806181	−	0.465449i	−0.0394467	−	0.999222i	$-0.512560\pi$
$571$	262848.	−	151755.i	0.806181	−	0.465449i	0.845628	+	0.533773i	$0.179226\pi$
$572$	45902.4	−	121758.i	0.140295	−	0.372139i
$573$	141533.	−	145102.i	0.431072	−	0.441942i
$574$	−22506.8	+	123502.i	−0.0683108	+	0.374843i
$575$			101308.i			0.306414i
$576$	3139.60	−	331761.i	0.00946301	−	0.999955i
$577$	−500884.			−1.50448			−0.752238	−	0.658892i	$-0.771026\pi$
$577$	−500884.			−1.50448			−0.752238	+	0.658892i	$0.771026\pi$
$578$	11227.7	+	2046.12i	0.0336074	+	0.00612456i
$579$	−158447.	+	44577.3i	−0.472636	+	0.132971i
$580$	−202865.	−	76479.5i	−0.603047	−	0.227347i
$581$	−6650.54	−	11519.1i	−0.0197017	−	0.0341244i
$582$	−251129.	−	353566.i	−0.741398	−	1.04382i
$583$	−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	$-0.0185658\pi$
$587$	498580.	+	287855.i	1.44697	+	0.835406i	0.448666	+	0.893699i	$0.351899\pi$
$588$	−324090.	−	28029.1i	−0.937371	−	0.0810688i
$589$	−34453.5	−	59675.2i	−0.0993122	−	0.172014i
$590$	−95296.8	−	80898.1i	−0.273763	−	0.232399i
$591$	80621.3	−	316598.i	0.230821	−	0.906429i
$592$	−292524.	−	257103.i	−0.834676	−	0.733607i
$593$	−138143.			−0.392843			−0.196421	−	0.980520i	$-0.562932\pi$
$593$	−138143.			−0.392843			−0.196421	+	0.980520i	$0.562932\pi$
$594$	−635217.	+	75879.2i	−1.80032	+	0.215055i
$595$			37332.6i			0.105452i
$596$	−67375.1	−	409477.i	−0.189674	−	1.15275i
$597$	412852.	+	105132.i	1.15837	+	0.294976i
$598$	22753.7	+	19315.8i	0.0636282	+	0.0540144i
$599$	165665.	−	95646.9i	0.461719	−	0.266574i	−0.251048	−	0.967975i	$-0.580775\pi$
$599$	165665.	−	95646.9i	0.461719	−	0.266574i	0.712767	+	0.701401i	$0.247442\pi$
$600$	73706.7	+	280377.i	0.204741	+	0.778825i
$601$	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
$606$	199193.	+	280445.i	0.542411	+	0.763664i
$607$	−59466.9	+	34333.2i	−0.161398	+	0.0931831i	−0.578523	−	0.815666i	$-0.696371\pi$
$607$	−59466.9	+	34333.2i	−0.161398	+	0.0931831i	0.417126	+	0.908849i	$0.363038\pi$
$608$	−36526.5	+	28908.2i	−0.0988100	+	0.0782014i
$609$	35672.9	+	126797.i	0.0961841	+	0.341880i
$610$	228225.	+	41591.4i	0.613344	+	0.111775i
$611$			106942.i			0.286461i
$612$	−240374.	−	278767.i	−0.641779	−	0.744284i
$613$	−572114.			−1.52252			−0.761258	−	0.648450i	$-0.775418\pi$
$613$	−572114.			−1.52252			−0.761258	+	0.648450i	$0.775418\pi$
$614$	−88529.3	+	485788.i	−0.234828	+	1.28858i
$615$	−187203.	−	182599.i	−0.494951	−	0.482778i
$616$	2874.39	−	167274.i	0.00757504	−	0.440825i
$617$	−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	$0.841855\pi$
$618$	38866.0	+	412296.i	0.101764	+	1.07952i
$619$	−388604.	−	224361.i	−1.01421	−	0.585552i	−0.101786	−	0.994806i	$-0.532456\pi$
$619$	−388604.	−	224361.i	−1.01421	−	0.585552i	−0.912420	+	0.409254i	$0.865789\pi$
$620$	−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
$624$	77025.5	+	36903.2i	0.197818	+	0.0947752i
$625$	−88627.6	−	153508.i	−0.226887	−	0.392979i
$626$	−135610.	+	159747.i	−0.346053	+	0.407646i
$627$	64297.8	+	62716.3i	0.163554	+	0.159531i
$628$	14340.3	+	87154.1i	0.0363612	+	0.220988i
$629$	−432079.			−1.09210
$630$	−26744.3	+	33142.8i	−0.0673829	+	0.0835042i
$631$			402529.i			1.01097i	0.862835	+	0.505486i	$0.168687\pi$
$631$			402529.i			1.01097i	−0.862835	+	0.505486i	$0.831313\pi$
$632$	232369.	+	418937.i	0.581760	+	1.04885i
$633$	−113316.	−	402775.i	−0.282804	−	1.00521i
$634$	−67298.3	+	79276.4i	−0.167427	+	0.197227i
$635$	253646.	−	146443.i	0.629043	−	0.363178i
$636$	116716.	−	167042.i	0.288547	−	0.412963i
$637$	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	$0.308348\pi$
$642$	216098.	+	99004.8i	0.524301	+	0.240207i
$643$	227886.	−	131570.i	0.551184	−	0.318226i	−0.198415	−	0.980118i	$-0.563580\pi$
$643$	227886.	−	131570.i	0.551184	−	0.318226i	0.749599	+	0.661892i	$0.230246\pi$
$644$	35906.8	+	13536.8i	0.0865775	+	0.0326395i
$645$	−3844.63	−	979.028i	−0.00924134	−	0.00235329i
$646$	−9265.58	+	50843.2i	−0.0222028	+	0.121834i
$647$		−	265174.i		−	0.633464i	−0.948515	−	0.316732i	$-0.897414\pi$
$647$		−	265174.i		−	0.633464i	0.948515	−	0.316732i	$-0.102586\pi$
$648$	−13694.8	−	419681.i	−0.0326142	−	0.999468i
$649$	621494.			1.47553
$650$	−73420.8	−	13380.1i	−0.173777	−	0.0316689i
$651$	−40085.5	+	157415.i	−0.0945856	+	0.371436i
$652$	2298.77	−	6097.57i	0.00540754	−	0.0143437i
$653$	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	$0.831139\pi$
$654$	−180614.	+	394225.i	−0.422274	+	0.921699i
$655$	−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	$-0.553809\pi$
$659$	−480334.	−	277321.i	−1.10604	−	0.638575i	−0.937802	+	0.347171i	$0.887142\pi$
$660$	285679.	+	199611.i	0.655829	+	0.458244i
$661$	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	$0.444355\pi$
$662$	131829.	+	111910.i	0.300812	+	0.255361i
$663$	91216.8	−	25662.8i	0.207514	−	0.0583818i
$664$	−34653.7	−	62477.0i	−0.0785984	−	0.141705i
$665$	5979.36			0.0135211
$666$	−383588.	−	309532.i	−0.864801	−	0.697842i
$667$			247241.i			0.555736i
$668$	374845.	−	61676.8i	0.840039	−	0.138219i
$669$	519065.	−	532153.i	1.15976	−	1.18901i
$670$	−31304.9	−	26574.9i	−0.0697368	−	0.0592001i
$671$	−998855.	+	576689.i	−2.21849	+	1.28085i
$672$	109223.	+	11339.9i	0.241867	+	0.0251114i
$673$	−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	$-0.104961\pi$
$678$	133712.	−	12604.7i	0.290879	−	0.0274204i
$679$	124307.	−	71768.4i	0.269621	−	0.155666i
$680$	−3445.26	+	200495.i	−0.00745083	+	0.433597i
$681$	−186652.	+	191358.i	−0.402474	+	0.412623i
$682$	1.30774e6	+	238321.i	2.81160	+	0.512382i
$683$		−	764551.i		−	1.63895i	−0.573117	−	0.819474i	$-0.694266\pi$
$683$		−	764551.i		−	1.63895i	0.573117	−	0.819474i	$-0.305734\pi$
$684$	−44648.7	+	38499.5i	−0.0954325	+	0.0822892i
$685$	284757.			0.606868
$686$	39819.4	−	218502.i	0.0846148	−	0.464308i
$687$	−392775.	+	110503.i	−0.832204	+	0.234131i
$688$	3277.60	+	9690.27i	0.00692435	+	0.0204719i
$689$	26229.4	+	45430.7i	0.0552523	+	0.0956998i
$690$	−65171.8	+	46289.8i	−0.136887	+	0.0972271i
$691$	−278107.	−	160565.i	−0.582445	−	0.336275i	0.179659	−	0.983729i	$-0.442500\pi$
$691$	−278107.	−	160565.i	−0.582445	−	0.336275i	−0.762105	+	0.647454i	$0.775834\pi$
$692$	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
$696$	179880.	+	684255.i	0.371334	+	1.41254i
$697$	374048.	+	647870.i	0.769949	+	1.33359i
$698$	310579.	−	365858.i	0.637472	−	0.750933i
$699$	113116.	−	444205.i	0.231510	−	0.909137i
$700$	−94678.2	+	15578.3i	−0.193221	+	0.0317925i
$701$	−621799.			−1.26536			−0.632680	−	0.774413i	$-0.718045\pi$
$701$	−621799.			−1.26536			−0.632680	+	0.774413i	$0.718045\pi$
$702$	99364.0	+	42563.0i	0.201630	+	0.0863690i
$703$			69203.8i			0.140029i
$704$	30873.9	−	898079.i	0.0622940	−	1.81205i
$705$	−277563.	−	70680.9i	−0.558448	−	0.142208i
$706$	400616.	−	471920.i	0.803745	−	0.946801i
$707$	−98598.6	+	56925.9i	−0.197257	+	0.113886i
$708$	−35149.0	+	406415.i	−0.0701207	+	0.810781i
$709$	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
$714$	99325.0	−	70548.0i	0.194833	−	0.138385i
$715$	−77696.8	+	44858.2i	−0.151982	+	0.0877466i
$716$	−258184.	+	684843.i	−0.503620	+	1.33587i
$717$	−89912.4	−	319588.i	−0.174897	−	0.621658i
$718$	−47933.5	+	263026.i	−0.0929801	+	0.510211i
$719$		−	348658.i		−	0.674438i	−0.941426	−	0.337219i	$-0.890514\pi$
$719$		−	348658.i		−	0.674438i	0.941426	−	0.337219i	$-0.109486\pi$
$720$	−146689.	+	175526.i	−0.282965	+	0.338591i
$721$	−137065.			−0.263668
$722$	−504694.	−	91974.7i	−0.968175	−	0.176439i
$723$	54036.7	+	52707.6i	0.103374	+	0.100832i
$724$	−362701.	−	136737.i	−0.691944	−	0.260861i
$725$	−309106.	−	535387.i	−0.588073	−	1.01857i
$726$	−1.20031e6	+	113150.i	−2.27730	+	0.214675i
$727$	−523789.	−	302410.i	−0.991032	−	0.572173i	−0.0854497	−	0.996342i	$-0.527233\pi$
$727$	−523789.	−	302410.i	−0.991032	−	0.572173i	−0.905583	+	0.424170i	$0.860566\pi$
$728$	−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
$732$	−320625.	−	685799.i	−0.598378	−	1.27990i
$733$	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	$0.687389\pi$
$734$	−288386.	−	244813.i	−0.535282	−	0.454404i
$735$	160556.	+	156607.i	0.297203	+	0.289893i
$736$	191589.	+	76013.1i	0.353683	+	0.140324i
$737$	204160.			0.375868
$738$	−132051.	+	843121.i	−0.242453	+	1.54802i
$739$			844449.i			1.54627i	0.634244	+	0.773133i	$0.281312\pi$
$739$			844449.i			1.54627i	−0.634244	+	0.773133i	$0.718688\pi$
$740$	43595.3	+	264954.i	0.0796116	+	0.483845i
$741$	−4110.28	−	14609.7i	−0.00748574	−	0.0266076i
$742$	51417.4	+	43648.6i	0.0933905	+	0.0792798i
$743$	537216.	−	310162.i	0.973131	−	0.561837i	0.0729415	−	0.997336i	$-0.476761\pi$
$743$	537216.	−	310162.i	0.973131	−	0.561837i	0.900189	+	0.435499i	$0.143428\pi$
$744$	−229806.	+	841699.i	−0.415161	+	1.52059i
$745$	−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
$750$	186637.	−	407373.i	0.331799	−	0.724218i
$751$	632847.	−	365374.i	1.12207	−	0.647825i	0.180139	−	0.983641i	$-0.442345\pi$
$751$	632847.	−	365374.i	1.12207	−	0.647825i	0.941928	+	0.335816i	$0.109012\pi$
$752$	236626.	+	699589.i	0.418434	+	1.23711i
$753$	12868.5	+	3276.95i	0.0226955	+	0.00577936i
$754$	−179182.	−	32653.9i	−0.315176	−	0.0574371i
$755$			313247.i			0.549533i
$756$	138717.	+	8523.71i	0.242709	+	0.0149137i
$757$	−769023.			−1.34198			−0.670992	−	0.741465i	$-0.734132\pi$
$757$	−769023.			−1.34198			−0.670992	+	0.741465i	$0.734132\pi$
$758$	36711.5	−	201447.i	0.0638945	−	0.350609i
$759$	98076.6	−	385145.i	0.170248	−	0.668560i
$760$	32112.2	+	551.810i	0.0555960	+	0.000955349i
$761$	−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	$0.909749\pi$
$762$	−868935.	−	398101.i	−1.49650	−	0.685620i
$763$	−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
$768$	585537.	+	70980.9i	0.992732	+	0.120342i
$769$	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	$0.819107\pi$
$770$	−74649.0	+	87935.4i	−0.125905	+	0.148314i
$771$	−300396.	+	84513.0i	−0.505341	+	0.142172i
$772$	−47508.6	−	288737.i	−0.0797145	−	0.484471i
$773$	−195309.			−0.326861			−0.163430	−	0.986555i	$-0.552256\pi$
$773$	−195309.			−0.326861			−0.163430	+	0.986555i	$0.552256\pi$
$774$	4660.50	+	12078.9i	0.00777949	+	0.0201625i
$775$		−	762389.i		−	1.26933i
$776$	674213.	−	373961.i	1.11963	−	0.621017i
$777$	113911.	−	116783.i	0.188679	−	0.193437i
$778$	175761.	−	207045.i	0.290379	−	0.342062i
$779$	103766.	−	59909.3i	0.170994	−	0.0987232i
$780$	−24940.1	−	53345.4i	−0.0409929	−	0.0876815i
$781$	−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
$786$	4458.60	+	47297.4i	0.00721695	+	0.0765583i
$787$	677438.	−	391119.i	1.09375	−	0.631480i	0.159181	−	0.987249i	$-0.449115\pi$
$787$	677438.	−	391119.i	1.09375	−	0.631480i	0.934574	+	0.355770i	$0.115781\pi$
$788$	543466.	+	204885.i	0.875225	+	0.329958i
$789$	119604.	−	122620.i	0.192128	−	0.196973i
$790$	59218.6	−	324951.i	0.0948864	−	0.520672i
$791$			44451.9i			0.0710456i
$792$	−8778.69	−	1.13727e6i	−0.0139952	−	1.81306i
$793$	194887.			0.309911
$794$	496176.	+	90422.3i	0.787036	+	0.143428i
$795$	−135249.	+	38050.9i	−0.213993	+	0.0602047i
$796$	−267176.	+	708694.i	−0.421668	+	1.11849i
$797$	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	$0.458520\pi$
$798$	−11299.3	−	15908.3i	−0.0177438	−	0.0249815i
$799$	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
$804$	−11546.4	+	133507.i	−0.0178622	+	0.206534i
$805$	−13228.8	−	22913.0i	−0.0204141	−	0.0353583i
$806$	−171232.	−	145360.i	−0.263581	−	0.223756i
$807$	130424.	−	512172.i	0.200267	−	0.786445i
$808$	−534778.	+	296622.i	−0.819126	+	0.454340i
$809$	−421614.			−0.644196			−0.322098	−	0.946706i	$-0.604388\pi$
$809$	−421614.			−0.644196			−0.322098	+	0.946706i	$0.604388\pi$
$810$	−176143.	+	229764.i	−0.268469	+	0.350196i
$811$			504037.i			0.766339i	0.923678	+	0.383169i	$0.125167\pi$
$811$			504037.i			0.766339i	−0.923678	+	0.383169i	$0.874833\pi$
$812$	−231061.	+	38018.6i	−0.350440	+	0.0576612i
$813$	−274506.	−	69902.6i	−0.415309	−	0.105758i
$814$	−1.01774e6	−	863970.i	−1.53600	−	1.30392i
$815$	−3891.01	+	2246.48i	−0.00585797	+	0.00338210i
$816$	539936.	−	369712.i	0.810890	−	0.555244i
$817$	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	$0.149763\pi$
$822$	−538110.	−	757609.i	−0.796394	−	1.12125i
$823$	−703826.	+	406354.i	−1.03912	+	0.599936i	−0.919584	−	0.392893i	$-0.871474\pi$
$823$	−703826.	+	406354.i	−1.03912	+	0.599936i	−0.119536	+	0.992830i	$0.538141\pi$
$824$	−736111.	−	12649.2i	−1.08415	−	0.0186298i
$825$	269137.	+	956628.i	0.395426	+	1.40551i
$826$	−132829.	−	24206.5i	−0.194685	−	0.0354790i
$827$			375951.i			0.549693i	0.961488	+	0.274847i	$0.0886271\pi$
$827$			375951.i			0.549693i	−0.961488	+	0.274847i	$0.911373\pi$
$828$	246312.	+	85917.6i	0.359273	+	0.125320i
$829$	423699.			0.616522			0.308261	−	0.951302i	$-0.400253\pi$
$829$	423699.			0.616522			0.308261	+	0.951302i	$0.400253\pi$
$830$	−8831.40	+	48460.7i	−0.0128196	+	0.0703450i
$831$	428643.	+	418100.i	0.620717	+	0.605449i
$832$	−80392.5	+	128810.i	−0.116137	+	0.186082i
$833$	−320806.	−	555652.i	−0.462330	−	0.800779i
$834$	44388.6	+	470880.i	0.0638175	+	0.676984i
$835$	−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	$-0.0448108\pi$
$839$	959899.	+	554198.i	1.36365	+	0.787302i	0.373539	+	0.927614i	$0.378144\pi$
$840$	−53282.0	−	53788.7i	−0.0755131	−	0.0762311i
$841$	−400727.	−	694079.i	−0.566573	−	0.981334i
$842$	217773.	−	256534.i	0.307171	−	0.361843i
$843$	−797090.	−	777485.i	−1.12164	−	1.09405i
$844$	733974.	−	120768.i	1.03038	−	0.169537i
$845$	−299914.			−0.420032
$846$	336465.	+	872034.i	0.470109	+	1.21841i
$847$		−	399036.i		−	0.556218i
$848$	272110.	+	239160.i	0.378401	+	0.332581i
$849$	−133412.	−	474205.i	−0.185089	−	0.657886i
$850$	−370046.	+	435909.i	−0.512174	+	0.603334i
$851$	265190.	−	153108.i	0.366183	−	0.211416i
$852$	−137251.	−	95900.8i	−0.189076	−	0.132112i
$853$	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	$0.0191129\pi$
$858$	266172.	+	121946.i	0.361566	+	0.165651i
$859$	−916830.	+	529332.i	−1.24252	+	0.717368i	−0.969606	−	0.244671i	$-0.921320\pi$
$859$	−916830.	+	529332.i	−1.24252	+	0.717368i	−0.272912	+	0.962039i	$0.587987\pi$
$860$	2488.03	−	6599.60i	0.00336403	−	0.00892321i
$861$	−273720.	−	69702.4i	−0.369233	−	0.0940246i
$862$	−107631.	+	590603.i	−0.144851	+	0.794842i
$863$			676878.i			0.908844i	0.890787	+	0.454422i	$0.150154\pi$
$863$			676878.i			0.908844i	−0.890787	+	0.454422i	$0.849846\pi$
$864$	744194.	+	58578.3i	0.996916	+	0.0784710i
$865$	−31180.7			−0.0416729
$866$	−280270.	−	51076.0i	−0.373716	−	0.0681053i
$867$	−6336.73	+	24884.2i	−0.00842999	+	0.0331044i
$868$	−270215.	−	101870.i	−0.358649	−	0.135210i
$869$	821100.	+	1.42219e6i	1.08732	+	1.88329i
$870$	203179.	−	443478.i	0.268435	−	0.585913i
$871$	−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
$876$	−178388.	+	255305.i	−0.232465	+	0.332699i
$877$	−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	$-0.575669\pi$
$878$	−333133.	−	282799.i	−0.432144	−	0.366850i
$879$	767755.	−	215999.i	0.993677	−	0.279560i
$880$	−409018.	+	465369.i	−0.528175	+	0.600942i
$881$	599513.			0.772408			0.386204	−	0.922413i	$-0.373786\pi$
$881$	599513.			0.772408			0.386204	+	0.922413i	$0.373786\pi$
$882$	113254.	−	723110.i	0.145586	−	0.929538i
$883$			729187.i			0.935229i	0.883933	+	0.467614i	$0.154886\pi$
$883$			729187.i			0.935229i	−0.883933	+	0.467614i	$0.845114\pi$
$884$	27350.3	+	166224.i	0.0349992	+	0.212710i
$885$	196388.	−	201341.i	0.250743	−	0.257066i
$886$	703369.	+	597094.i	0.896015	+	0.760634i
$887$	−1.26218e6	+	728722.i	−1.60426	+	0.926221i	−0.613641	+	0.789585i	$0.710296\pi$
$887$	−1.26218e6	+	728722.i	−1.60426	+	0.926221i	−0.990621	+	0.136636i	$0.956371\pi$
$888$	622538.	−	616674.i	0.789477	−	0.782041i
$889$	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
$894$	929590.	−	87630.0i	1.16310	−	0.109642i
$895$	437015.	−	252311.i	0.545570	−	0.314985i
$896$	−41577.7	+	190739.i	−0.0517898	+	0.237588i
$897$	−46891.0	+	48073.4i	−0.0582780	+	0.0597476i
$898$	38374.5	+	6993.32i	0.0475872	+	0.00867223i
$899$		−	1.86060e6i		−	2.30215i
$900$	−640792.	+	121895.i	−0.791101	+	0.150487i
$901$	401926.			0.495104
$902$	−414404.	+	2.27397e6i	−0.509344	+	2.79493i
$903$	−4124.95	+	1160.51i	−0.00505875	+	0.00142322i
$904$	−4102.27	+	238729.i	−0.00501981	+	0.292125i
$905$	133627.	+	231448.i	0.163153	+	0.282590i
$906$	833408.	−	591948.i	1.01532	−	0.721153i
$907$	−3010.76	−	1738.27i	−0.00365984	−	0.00211301i	0.498169	−	0.867080i	$-0.334006\pi$
$907$	−3010.76	−	1738.27i	−0.00365984	−	0.00211301i	−0.501829	+	0.864967i	$0.667339\pi$
$908$	−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	$-0.498455\pi$
$911$	−712683.	−	411468.i	−0.858736	−	0.495791i	−0.863589	+	0.504197i	$0.831789\pi$
$912$	−59214.9	−	86478.7i	−0.0711936	−	0.103973i
$913$	−122453.	−	212094.i	−0.146901	−	0.254441i
$914$	171211.	−	201685.i	0.204946	−	0.241424i
$915$	−128807.	+	505822.i	−0.153850	+	0.604164i
$916$	−117769.	−	715750.i	−0.140359	−	0.853042i
$917$	−15723.8			−0.0186990
$918$	663066.	−	496252.i	0.786813	−	0.588867i
$919$		−	873279.i		−	1.03400i	−0.855984	−	0.517002i	$-0.827048\pi$
$919$		−	873279.i		−	1.03400i	0.855984	−	0.517002i	$-0.172952\pi$
$920$	−68931.1	−	124276.i	−0.0814403	−	0.146828i
$921$	−1.07667e6	−	274171.i	−1.26929	−	0.323223i
$922$	−450398.	+	530563.i	−0.529828	+	0.624130i
$923$	37328.5	−	21551.6i	0.0438164	−	0.0252974i
$924$	375021.	+	32433.8i	0.439250	+	0.0379887i
$925$	−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	$0.230901\pi$
$930$	490447.	−	348352.i	0.567056	−	0.402765i
$931$	−88995.8	+	51381.7i	−0.102676	+	0.0592802i
$932$	762513.	+	287465.i	0.877840	+	0.330943i
$933$	−147569.	−	524525.i	−0.169525	−	0.602564i
$934$	−123413.	+	677205.i	−0.141471	+	0.776295i
$935$			687384.i			0.786278i
$936$	−94798.1	+	167162.i	−0.108205	+	0.190803i
$937$	−1.10958e6			−1.26380			−0.631901	−	0.775049i	$-0.717725\pi$
$937$	−1.10958e6			−1.26380			−0.631901	+	0.775049i	$0.717725\pi$
$938$	−43634.0	−	7951.80i	−0.0495929	−	0.00903774i
$939$	−337509.	−	329207.i	−0.382784	−	0.373369i
$940$	179623.	−	476458.i	0.203286	−	0.539224i
$941$	−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	$0.891632\pi$
$942$	−197856.	+	18651.4i	−0.222971	+	0.0210189i
$943$	−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	$-0.358101\pi$
$947$	−120742.	−	69710.2i	−0.134635	−	0.0777314i	−0.565805	+	0.824539i	$0.691434\pi$
$948$	−976452.	+	456511.i	−1.08651	+	0.507966i
$949$	−40088.8	−	69435.9i	−0.0445134	−	0.0770995i
$950$	69817.2	+	59268.3i	0.0773597	+	0.0656712i
$951$	−167493.	−	163374.i	−0.185198	−	0.180643i
$952$	105054.	+	189402.i	0.115915	+	0.208983i
$953$	1.68438e6			1.85462			0.927308	−	0.374300i	$-0.122117\pi$
$953$	1.68438e6			1.85462			0.927308	+	0.374300i	$0.122117\pi$
$954$	356818.	+	287931.i	0.392058	+	0.316367i
$955$		−	248453.i		−	0.272419i
$956$	582382.	−	95824.8i	0.637224	−	0.104848i
$957$	656824.	+	2.33463e6i	0.717175	+	2.54915i
$958$	665983.	+	565357.i	0.725658	+	0.616016i
$959$	266360.	−	153783.i	0.289622	−	0.167213i
$960$	−281188.	−	293790.i	−0.305108	−	0.318782i
$961$	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
$966$	−35962.3	+	78495.0i	−0.0385384	+	0.0841178i
$967$	−39280.8	+	22678.8i	−0.0420075	+	0.0242530i	−0.520857	−	0.853644i	$-0.674387\pi$
$967$	−39280.8	+	22678.8i	−0.0420075	+	0.0242530i	0.478849	+	0.877897i	$0.341054\pi$
$968$	36825.3	−	2.14303e6i	0.0393003	−	2.28706i
$969$	−112685.	−	28695.1i	−0.120010	−	0.0305605i
$970$	−522957.	−	95302.9i	−0.555805	−	0.101289i
$971$			1.18319e6i			1.25492i	0.778648	+	0.627461i	$0.215906\pi$
$971$			1.18319e6i			1.25492i	−0.778648	+	0.627461i	$0.784094\pi$
$972$	944156.	+	34447.3i	0.999335	+	0.0364605i
$973$	−156541.			−0.165350
$974$	281200.	−	1.54303e6i	0.296413	−	1.62651i
$975$	41437.6	−	162725.i	0.0435898	−	0.171176i
$976$	1.27491e6	−	431220.i	1.33838	−	0.452688i
$977$	−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	$-0.367453\pi$
$978$	13329.7	+	6107.00i	0.0139362	+	0.00638484i
$979$	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	$-0.580259\pi$
$983$	−1.17197e6	−	676638.i	−1.21286	−	0.700243i	−0.963381	+	0.268137i	$0.913592\pi$
$984$	−1.46358e6	−	399598.i	−1.51157	−	0.412699i
$985$	−200225.	−	346799.i	−0.206369	−	0.357442i
$986$	−903090.	+	1.06383e6i	−0.928918	+	1.09425i
$987$	−297801.	+	83783.0i	−0.305697	+	0.0860045i
$988$	26623.2	−	4380.56i	0.0272738	−	0.00448761i
$989$	−8043.24			−0.00822316
$990$	−492427.	+	610240.i	−0.502425	+	0.622630i
$991$		−	1.02847e6i		−	1.04724i	−0.851953	−	0.523619i	$-0.824582\pi$
$991$		−	1.02847e6i		−	1.04724i	0.851953	−	0.523619i	$-0.175418\pi$
$992$	−1.44179e6	−	572032.i	−1.46514	−	0.581296i
$993$	−271674.	+	278525.i	−0.275518	+	0.282466i
$994$	35864.2	−	42247.5i	0.0362985	−	0.0427591i
$995$	452235.	−	261098.i	0.456791	−	0.263729i
$996$	145621.	−	68080.6i	0.146793	−	0.0686285i
$997$	−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.7.2	✓	44
3.2	odd	2		108.5.f.a.19.21		44
4.3	odd	2	inner	36.5.f.a.7.16	yes	44
9.2	odd	6		324.5.d.e.163.9		22
9.4	even	3	inner	36.5.f.a.31.16	yes	44
9.5	odd	6		108.5.f.a.91.7		44
9.7	even	3		324.5.d.f.163.14		22
12.11	even	2		108.5.f.a.19.7		44
36.7	odd	6		324.5.d.f.163.13		22
36.11	even	6		324.5.d.e.163.10		22
36.23	even	6		108.5.f.a.91.21		44
36.31	odd	6	inner	36.5.f.a.31.2	yes	44

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

\(f(q)\)	\(=\)	\(q+(-3.93519 - 0.717143i) q^{2} +(2.22096 - 8.72166i) q^{3} +(14.9714 + 5.64418i) q^{4} +(-5.51579 - 9.55363i) q^{5} +(-14.9946 + 32.7286i) q^{6} +(-10.3188 - 5.95759i) q^{7} +(-54.8676 - 32.9476i) q^{8} +(-71.1347 - 38.7409i) q^{9} +O(q^{10})\)	\(q+(-3.93519 - 0.717143i) q^{2} +(2.22096 - 8.72166i) q^{3} +(14.9714 + 5.64418i) q^{4} +(-5.51579 - 9.55363i) q^{5} +(-14.9946 + 32.7286i) 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} +(82.4775 - 118.040i) q^{12} +(18.5350 + 32.1036i) q^{13} +(36.3341 + 30.8443i) q^{14} +(-95.5738 + 26.8886i) q^{15} +(192.286 + 169.003i) q^{16} +284.021 q^{17} +(252.146 + 203.466i) q^{18} -45.4901i q^{19} +(-28.6568 - 174.163i) q^{20} +(-74.8777 + 76.7659i) q^{21} +(669.000 + 567.918i) q^{22} +(-174.319 + 100.643i) q^{23} +(-409.216 + 405.362i) 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} +(395.384 - 37.2718i) q^{30} +(1311.83 - 757.384i) q^{31} +(-635.484 - 802.954i) q^{32} +(-1378.68 + 1413.45i) q^{33} +(-1117.68 - 203.683i) q^{34} +131.443i q^{35} +(-846.326 - 981.503i) q^{36} -1521.29 q^{37} +(-32.6229 + 179.012i) q^{38} +(321.162 - 90.3555i) q^{39} +(-12.1303 + 705.917i) q^{40} +(1316.97 + 2281.07i) q^{41} +(349.710 - 248.390i) 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} +(1901.04 - 1301.71i) q^{48} +(-1129.51 - 1956.38i) q^{49} +(-1302.88 + 1534.78i) q^{50} +(630.798 - 2477.13i) q^{51} +(96.2969 + 585.252i) q^{52} +1415.13 q^{53} +(2334.57 - 1747.24i) q^{54} +2420.19i q^{55} +(369.883 + 666.859i) q^{56} +(-396.749 - 101.032i) q^{57} +(-3179.66 + 3745.60i) q^{58} +(-2453.33 + 1416.43i) q^{59} +(-1582.64 - 136.875i) 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} +(6439.01 - 4573.46i) q^{66} +(-805.917 + 465.296i) q^{67} +(4252.19 + 1603.07i) q^{68} +(490.620 + 1743.87i) q^{69} +(94.2635 - 517.254i) q^{70} -1162.75i q^{71} +(2626.58 + 4469.33i) q^{72} -2162.87 q^{73} +(5986.57 + 1090.98i) q^{74} +(-3242.64 - 3162.88i) q^{75} +(256.754 - 681.051i) q^{76} +(1307.02 + 2263.82i) q^{77} +(-1328.63 + 125.247i) 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} +(-1554.31 + 726.670i) q^{84} +(-1566.60 - 2713.43i) q^{85} +(-121.852 - 103.441i) q^{86} +(-7913.60 - 7718.96i) q^{87} +(6810.44 + 12278.5i) q^{88} -6739.71 q^{89} +(553.059 - 3531.18i) q^{90} -441.696i q^{91} +(-3177.85 + 522.881i) q^{92} +(-3692.13 - 13123.4i) q^{93} +(-8797.09 - 7467.91i) q^{94} +(-434.596 + 250.914i) q^{95} +(-8414.48 + 3759.15i) 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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