LMFDB - Embedded newform 143.4.b.a.12.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.b (of order $2$, degree $1$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.2
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.22956i q^{2} +1.03843 q^{3} -19.3483 q^{4} -12.1782i q^{5} -5.43054i q^{6} +36.1879i q^{7} +59.3469i q^{8} -25.9217 q^{9} +O(q^{10})$	\(q-5.22956i q^{2} +1.03843 q^{3} -19.3483 q^{4} -12.1782i q^{5} -5.43054i q^{6} +36.1879i q^{7} +59.3469i q^{8} -25.9217 q^{9} -63.6866 q^{10} +11.0000i q^{11} -20.0919 q^{12} +(-39.4437 - 25.3218i) q^{13} +189.247 q^{14} -12.6462i q^{15} +155.571 q^{16} -65.0001 q^{17} +135.559i q^{18} -38.0407i q^{19} +235.628i q^{20} +37.5786i q^{21} +57.5252 q^{22} +81.9036 q^{23} +61.6276i q^{24} -23.3081 q^{25} +(-132.422 + 206.273i) q^{26} -54.9555 q^{27} -700.175i q^{28} -187.949 q^{29} -66.1341 q^{30} -45.8009i q^{31} -338.796i q^{32} +11.4227i q^{33} +339.922i q^{34} +440.702 q^{35} +501.541 q^{36} -266.793i q^{37} -198.936 q^{38} +(-40.9595 - 26.2950i) q^{39} +722.737 q^{40} +290.682i q^{41} +196.520 q^{42} -227.140 q^{43} -212.832i q^{44} +315.679i q^{45} -428.320i q^{46} -101.910i q^{47} +161.550 q^{48} -966.562 q^{49} +121.891i q^{50} -67.4981 q^{51} +(763.170 + 489.936i) q^{52} -219.078 q^{53} +287.393i q^{54} +133.960 q^{55} -2147.64 q^{56} -39.5026i q^{57} +982.890i q^{58} +66.6592i q^{59} +244.683i q^{60} -258.906 q^{61} -239.519 q^{62} -938.050i q^{63} -527.184 q^{64} +(-308.374 + 480.352i) q^{65} +59.7359 q^{66} -786.161i q^{67} +1257.64 q^{68} +85.0513 q^{69} -2304.68i q^{70} +1147.95i q^{71} -1538.37i q^{72} +175.023i q^{73} -1395.21 q^{74} -24.2039 q^{75} +736.023i q^{76} -398.067 q^{77} +(-137.511 + 214.200i) q^{78} -318.790 q^{79} -1894.58i q^{80} +642.817 q^{81} +1520.14 q^{82} +742.741i q^{83} -727.083i q^{84} +791.583i q^{85} +1187.85i q^{86} -195.172 q^{87} -652.815 q^{88} -1281.00i q^{89} +1650.86 q^{90} +(916.344 - 1427.38i) q^{91} -1584.70 q^{92} -47.5610i q^{93} -532.945 q^{94} -463.266 q^{95} -351.816i q^{96} +517.050i q^{97} +5054.70i q^{98} -285.138i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) $ 36 * q - 152 * q^4 + 360 * q^9	$ 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) $ 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	5.22956i		−	1.84893i	−0.381267	−	0.924465i	$-0.624512\pi$
$2$		−	5.22956i		−	1.84893i	0.381267	−	0.924465i	$-0.375488\pi$
$3$	1.03843			0.199846			0.0999230	−	0.994995i	$-0.468140\pi$
$3$	1.03843			0.199846			0.0999230	+	0.994995i	$0.468140\pi$
$4$	−19.3483			−2.41854
$5$		−	12.1782i		−	1.08925i	−0.838680	−	0.544625i	$-0.816672\pi$
$5$		−	12.1782i		−	1.08925i	0.838680	−	0.544625i	$-0.183328\pi$
$6$		−	5.43054i		−	0.369501i
$7$			36.1879i			1.95396i	0.213328	+	0.976981i	$0.431570\pi$
$7$			36.1879i			1.95396i	−0.213328	+	0.976981i	$0.568430\pi$
$8$			59.3469i			2.62279i
$9$	−25.9217			−0.960062
$10$	−63.6866			−2.01395
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	−20.0919			−0.483336
$13$	−39.4437	−	25.3218i	−0.841516	−	0.540232i
$13$	−39.4437	−	25.3218i	−0.841516	−	0.540232i
$14$	189.247			3.61274
$15$		−	12.6462i		−	0.217682i
$16$	155.571			2.43080
$17$	−65.0001			−0.927344			−0.463672	−	0.886007i	$-0.653468\pi$
$17$	−65.0001			−0.927344			−0.463672	+	0.886007i	$0.653468\pi$
$18$			135.559i			1.77509i
$19$		−	38.0407i		−	0.459322i	−0.973271	−	0.229661i	$-0.926238\pi$
$19$		−	38.0407i		−	0.459322i	0.973271	−	0.229661i	$-0.0737618\pi$
$20$			235.628i			2.63440i
$21$			37.5786i			0.390491i
$22$	57.5252			0.557473
$23$	81.9036			0.742526			0.371263	−	0.928528i	$-0.378925\pi$
$23$	81.9036			0.742526			0.371263	+	0.928528i	$0.378925\pi$
$24$			61.6276i			0.524153i
$25$	−23.3081			−0.186465
$26$	−132.422	+	206.273i	−0.998851	+	1.55590i
$27$	−54.9555			−0.391711
$28$		−	700.175i		−	4.72574i
$29$	−187.949			−1.20349			−0.601745	−	0.798688i	$-0.705528\pi$
$29$	−187.949			−1.20349			−0.601745	+	0.798688i	$0.705528\pi$
$30$	−66.1341			−0.402479
$31$		−	45.8009i		−	0.265357i	−0.991159	−	0.132679i	$-0.957642\pi$
$31$		−	45.8009i		−	0.265357i	0.991159	−	0.132679i	$-0.0423579\pi$
$32$		−	338.796i		−	1.87160i
$33$			11.4227i			0.0602559i
$34$			339.922i			1.71459i
$35$	440.702			2.12835
$36$	501.541			2.32195
$37$		−	266.793i		−	1.18542i	−0.805416	−	0.592710i	$-0.798058\pi$
$37$		−	266.793i		−	1.18542i	0.805416	−	0.592710i	$-0.201942\pi$
$38$	−198.936			−0.849255
$39$	−40.9595	−	26.2950i	−0.168174	−	0.107963i
$40$	722.737			2.85687
$41$			290.682i			1.10724i	0.832769	+	0.553621i	$0.186754\pi$
$41$			290.682i			1.10724i	−0.832769	+	0.553621i	$0.813246\pi$
$42$	196.520			0.721991
$43$	−227.140			−0.805548			−0.402774	−	0.915299i	$-0.631954\pi$
$43$	−227.140			−0.805548			−0.402774	+	0.915299i	$0.631954\pi$
$44$		−	212.832i		−	0.729218i
$45$			315.679i			1.04575i
$46$		−	428.320i		−	1.37288i
$47$		−	101.910i		−	0.316279i	−0.987417	−	0.158139i	$-0.949450\pi$
$47$		−	101.910i		−	0.316279i	0.987417	−	0.158139i	$-0.0505495\pi$
$48$	161.550			0.485787
$49$	−966.562			−2.81796
$50$			121.891i			0.344761i
$51$	−67.4981			−0.185326
$52$	763.170	+	489.936i	2.03524	+	1.30657i
$53$	−219.078			−0.567786			−0.283893	−	0.958856i	$-0.591626\pi$
$53$	−219.078			−0.567786			−0.283893	+	0.958856i	$0.591626\pi$
$54$			287.393i			0.724245i
$55$	133.960			0.328421
$56$	−2147.64			−5.12482
$57$		−	39.5026i		−	0.0917938i
$58$			982.890i			2.22517i
$59$			66.6592i			0.147090i	0.997292	+	0.0735448i	$0.0234312\pi$
$59$			66.6592i			0.147090i	−0.997292	+	0.0735448i	$0.976569\pi$
$60$			244.683i			0.526474i
$61$	−258.906			−0.543435			−0.271718	−	0.962377i	$-0.587592\pi$
$61$	−258.906			−0.543435			−0.271718	+	0.962377i	$0.587592\pi$
$62$	−239.519			−0.490627
$63$		−	938.050i		−	1.87592i
$64$	−527.184			−1.02966
$65$	−308.374	+	480.352i	−0.588448	+	0.916621i
$66$	59.7359			0.111409
$67$		−	786.161i		−	1.43351i	−0.697327	−	0.716753i	$-0.745627\pi$
$67$		−	786.161i		−	1.43351i	0.697327	−	0.716753i	$-0.254373\pi$
$68$	1257.64			2.24282
$69$	85.0513			0.148391
$70$		−	2304.68i		−	3.93517i
$71$			1147.95i			1.91883i	0.282006	+	0.959413i	$0.409000\pi$
$71$			1147.95i			1.91883i	−0.282006	+	0.959413i	$0.591000\pi$
$72$		−	1538.37i		−	2.51804i
$73$			175.023i			0.280616i	0.990108	+	0.140308i	$0.0448092\pi$
$73$			175.023i			0.280616i	−0.990108	+	0.140308i	$0.955191\pi$
$74$	−1395.21			−2.19176
$75$	−24.2039			−0.0372643
$76$			736.023i			1.11089i
$77$	−398.067			−0.589141
$78$	−137.511	+	214.200i	−0.199616	+	0.310941i
$79$	−318.790			−0.454009			−0.227004	−	0.973894i	$-0.572893\pi$
$79$	−318.790			−0.454009			−0.227004	+	0.973894i	$0.572893\pi$
$80$		−	1894.58i		−	2.64775i
$81$	642.817			0.881780
$82$	1520.14			2.04721
$83$			742.741i			0.982246i	0.871090	+	0.491123i	$0.163413\pi$
$83$			742.741i			0.982246i	−0.871090	+	0.491123i	$0.836587\pi$
$84$		−	727.083i		−	0.944420i
$85$			791.583i			1.01011i
$86$			1187.85i			1.48940i
$87$	−195.172			−0.240513
$88$	−652.815			−0.790800
$89$		−	1281.00i		−	1.52568i	−0.646585	−	0.762842i	$-0.723803\pi$
$89$		−	1281.00i		−	1.52568i	0.646585	−	0.762842i	$-0.276197\pi$
$90$	1650.86			1.93351
$91$	916.344	−	1427.38i	1.05559	−	1.64429i
$92$	−1584.70			−1.79583
$93$		−	47.5610i		−	0.0530306i
$94$	−532.945			−0.584777
$95$	−463.266			−0.500317
$96$		−	351.816i		−	0.374032i
$97$			517.050i			0.541222i	0.962689	+	0.270611i	$0.0872257\pi$
$97$			517.050i			0.541222i	−0.962689	+	0.270611i	$0.912774\pi$
$98$			5054.70i			5.21022i
$99$		−	285.138i		−	0.289469i
$100$	450.974			0.450974
$101$	1185.67			1.16811			0.584054	−	0.811715i	$-0.301466\pi$
$101$	1185.67			1.16811			0.584054	+	0.811715i	$0.301466\pi$
$102$			352.986i			0.342655i
$103$	−363.361			−0.347602			−0.173801	−	0.984781i	$-0.555605\pi$
$103$	−363.361			−0.347602			−0.173801	+	0.984781i	$0.555605\pi$
$104$	1502.77	−	2340.86i	1.41691	−	2.20712i
$105$	457.639			0.425343
$106$			1145.68i			1.04980i
$107$	837.900			0.757036			0.378518	−	0.925594i	$-0.376434\pi$
$107$	837.900			0.757036			0.378518	+	0.925594i	$0.376434\pi$
$108$	1063.30			0.947369
$109$		−	1990.28i		−	1.74894i	−0.485082	−	0.874469i	$-0.661210\pi$
$109$		−	1990.28i		−	1.74894i	0.485082	−	0.874469i	$-0.338790\pi$
$110$		−	700.552i		−	0.607228i
$111$		−	277.046i		−	0.236902i
$112$			5629.80i			4.74970i
$113$	636.309			0.529725			0.264863	−	0.964286i	$-0.414673\pi$
$113$	636.309			0.529725			0.264863	+	0.964286i	$0.414673\pi$
$114$	−206.581			−0.169720
$115$		−	997.438i		−	0.808796i
$116$	3636.50			2.91069
$117$	1022.45	+	656.384i	0.807907	+	0.518656i
$118$	348.599			0.271958
$119$		−	2352.22i		−	1.81199i
$120$	750.512			0.570934
$121$	−121.000			−0.0909091
$122$			1353.97i			1.00477i
$123$			301.853i			0.221278i
$124$			886.171i			0.641778i
$125$		−	1238.42i		−	0.886143i
$126$	−4905.59			−3.46845
$127$	−2121.68			−1.48243			−0.741215	−	0.671268i	$-0.765750\pi$
$127$	−2121.68			−1.48243			−0.741215	+	0.671268i	$0.765750\pi$
$128$			46.5733i			0.0321605i
$129$	−235.870			−0.160986
$130$	2512.03	+	1612.66i	1.69477	+	1.08800i
$131$	−1305.18			−0.870489			−0.435244	−	0.900312i	$-0.643338\pi$
$131$	−1305.18			−0.870489			−0.435244	+	0.900312i	$0.643338\pi$
$132$		−	221.011i		−	0.145731i
$133$	1376.61			0.897498
$134$	−4111.28			−2.65045
$135$			669.258i			0.426671i
$136$		−	3857.55i		−	2.43222i
$137$		−	2234.06i		−	1.39320i	−0.717460	−	0.696600i	$-0.754695\pi$
$137$		−	2234.06i		−	1.39320i	0.717460	−	0.696600i	$-0.245305\pi$
$138$		−	444.781i		−	0.274364i
$139$	2671.68			1.63028			0.815141	−	0.579263i	$-0.196659\pi$
$139$	2671.68			1.63028			0.815141	+	0.579263i	$0.196659\pi$
$140$	−8526.86			−5.14751
$141$		−	105.826i		−	0.0632071i
$142$	6003.28			3.54777
$143$	278.540	−	433.881i	0.162886	−	0.253727i
$144$	−4032.67			−2.33372
$145$			2288.87i			1.31090i
$146$	915.297			0.518839
$147$	−1003.71			−0.563159
$148$			5162.01i			2.86699i
$149$		−	1787.03i		−	0.982546i	−0.871006	−	0.491273i	$-0.836532\pi$
$149$		−	1787.03i		−	0.982546i	0.871006	−	0.491273i	$-0.163468\pi$
$150$			126.576i			0.0688991i
$151$			1740.94i			0.938251i	0.883131	+	0.469126i	$0.155431\pi$
$151$			1740.94i			0.938251i	−0.883131	+	0.469126i	$0.844569\pi$
$152$	2257.59			1.20470
$153$	1684.91			0.890307
$154$			2081.71i			1.08928i
$155$	−557.772			−0.289041
$156$	792.499	+	508.764i	0.406735	+	0.261114i
$157$	−2673.97			−1.35927			−0.679637	−	0.733549i	$-0.737863\pi$
$157$	−2673.97			−1.35927			−0.679637	+	0.733549i	$0.737863\pi$
$158$			1667.13i			0.839430i
$159$	−227.497			−0.113470
$160$	−4125.92			−2.03864
$161$			2963.92i			1.45087i
$162$		−	3361.65i		−	1.63035i
$163$			741.519i			0.356321i	0.984001	+	0.178160i	$0.0570146\pi$
$163$			741.519i			0.356321i	−0.984001	+	0.178160i	$0.942985\pi$
$164$		−	5624.22i		−	2.67791i
$165$	139.108			0.0656337
$166$	3884.21			1.81610
$167$			2644.12i			1.22520i	0.790393	+	0.612600i	$0.209876\pi$
$167$			2644.12i			1.22520i	−0.790393	+	0.612600i	$0.790124\pi$
$168$	−2230.17			−1.02418
$169$	914.608	+	1997.57i	0.416299	+	0.909228i
$170$	4139.64			1.86762
$171$			986.077i			0.440978i
$172$	4394.79			1.94825
$173$	1886.55			0.829086			0.414543	−	0.910030i	$-0.363941\pi$
$173$	1886.55			0.829086			0.414543	+	0.910030i	$0.363941\pi$
$174$			1020.66i			0.444691i
$175$		−	843.472i		−	0.364346i
$176$			1711.29i			0.732915i
$177$			69.2209i			0.0293953i
$178$	−6699.08			−2.82088
$179$	−908.468			−0.379341			−0.189671	−	0.981848i	$-0.560742\pi$
$179$	−908.468			−0.379341			−0.189671	+	0.981848i	$0.560742\pi$
$180$		−	6107.86i		−	2.52918i
$181$	1546.76			0.635192			0.317596	−	0.948226i	$-0.397124\pi$
$181$	1546.76			0.635192			0.317596	+	0.948226i	$0.397124\pi$
$182$	−7464.59	−	4792.08i	−3.04018	−	1.95172i
$183$	−268.856			−0.108603
$184$			4860.72i			1.94749i
$185$	−3249.06			−1.29122
$186$	−248.723			−0.0980500
$187$		−	715.001i		−	0.279605i
$188$			1971.79i			0.764934i
$189$		−	1988.72i		−	0.765387i
$190$			2422.68i			0.925051i
$191$	982.973			0.372384			0.186192	−	0.982513i	$-0.440385\pi$
$191$	982.973			0.372384			0.186192	+	0.982513i	$0.440385\pi$
$192$	−547.444			−0.205773
$193$			1514.27i			0.564764i	0.959302	+	0.282382i	$0.0911245\pi$
$193$			1514.27i			0.564764i	−0.959302	+	0.282382i	$0.908875\pi$
$194$	2703.95			1.00068
$195$	−320.225	+	498.813i	−0.117599	+	0.183183i
$196$	18701.4			6.81537
$197$		−	1075.66i		−	0.389022i	−0.980900	−	0.194511i	$-0.937688\pi$
$197$		−	1075.66i		−	0.389022i	0.980900	−	0.194511i	$-0.0623120\pi$
$198$	−1491.15			−0.535209
$199$	−4118.70			−1.46717			−0.733585	−	0.679597i	$-0.762154\pi$
$199$	−4118.70			−1.46717			−0.733585	+	0.679597i	$0.762154\pi$
$200$		−	1383.27i		−	0.489058i
$201$		−	816.374i		−	0.286481i
$202$		−	6200.55i		−	2.15975i
$203$		−	6801.46i		−	2.35157i
$204$	1305.98			0.448219
$205$	3539.98			1.20606
$206$			1900.22i			0.642692i
$207$	−2123.08			−0.712870
$208$	−6136.31	−	3939.36i	−2.04556	−	1.31320i
$209$	418.447			0.138491
$210$		−	2393.25i		−	0.786429i
$211$	−2303.92			−0.751698			−0.375849	−	0.926681i	$-0.622649\pi$
$211$	−2303.92			−0.751698			−0.375849	+	0.926681i	$0.622649\pi$
$212$	4238.79			1.37321
$213$			1192.07i			0.383470i
$214$		−	4381.85i		−	1.39971i
$215$			2766.16i			0.877444i
$216$		−	3261.43i		−	1.02737i
$217$	1657.44			0.518498
$218$	−10408.3			−3.23366
$219$			181.750i			0.0560800i
$220$	−2591.90			−0.794300
$221$	2563.84	+	1645.92i	0.780375	+	0.500981i
$222$	−1448.83			−0.438014
$223$			832.363i			0.249951i	0.992160	+	0.124976i	$0.0398853\pi$
$223$			832.363i			0.249951i	−0.992160	+	0.124976i	$0.960115\pi$
$224$	12260.3			3.65704
$225$	604.186			0.179018
$226$		−	3327.62i		−	0.979425i
$227$		−	1695.88i		−	0.495858i	−0.968778	−	0.247929i	$-0.920250\pi$
$227$		−	1695.88i		−	0.495858i	0.968778	−	0.247929i	$-0.0797500\pi$
$228$			764.309i			0.222007i
$229$		−	786.997i		−	0.227101i	−0.993532	−	0.113551i	$-0.963778\pi$
$229$		−	786.997i		−	0.227101i	0.993532	−	0.113551i	$-0.0362225\pi$
$230$	−5216.16			−1.49541
$231$	−413.364			−0.117738
$232$		−	11154.2i		−	3.15650i
$233$	−1243.87			−0.349735			−0.174868	−	0.984592i	$-0.555950\pi$
$233$	−1243.87			−0.349735			−0.174868	+	0.984592i	$0.555950\pi$
$234$	3432.60	−	5346.95i	0.958959	−	1.49376i
$235$	−1241.08			−0.344507
$236$		−	1289.74i		−	0.355742i
$237$	−331.041			−0.0907318
$238$	−12301.1			−3.35025
$239$			3136.83i			0.848974i	0.905434	+	0.424487i	$0.139546\pi$
$239$			3136.83i			0.848974i	−0.905434	+	0.424487i	$0.860454\pi$
$240$		−	1967.39i		−	0.529143i
$241$		−	1916.63i		−	0.512285i	−0.966639	−	0.256143i	$-0.917548\pi$
$241$		−	1916.63i		−	0.512285i	0.966639	−	0.256143i	$-0.0824517\pi$
$242$			632.777i			0.168085i
$243$	2151.32			0.567931
$244$	5009.41			1.31432
$245$			11771.0i			3.06947i
$246$	1578.56			0.409128
$247$	−963.260	+	1500.46i	−0.248141	+	0.386527i
$248$	2718.14			0.695976
$249$			771.285i			0.196298i
$250$	−6476.41			−1.63842
$251$	−103.535			−0.0260360			−0.0130180	−	0.999915i	$-0.504144\pi$
$251$	−103.535			−0.0260360			−0.0130180	+	0.999915i	$0.504144\pi$
$252$			18149.7i			4.53700i
$253$			900.940i			0.223880i
$254$			11095.5i			2.74091i
$255$			822.004i			0.201866i
$256$	−3973.91			−0.970194
$257$	−7415.84			−1.79995			−0.899976	−	0.435940i	$-0.856416\pi$
$257$	−7415.84			−1.79995			−0.899976	+	0.435940i	$0.856416\pi$
$258$			1233.49i			0.297651i
$259$	9654.68			2.31626
$260$	5966.53	−	9294.02i	1.42319	−	2.21689i
$261$	4871.94			1.15542
$262$			6825.52i			1.60947i
$263$	5900.70			1.38347			0.691735	−	0.722152i	$-0.256847\pi$
$263$	5900.70			1.38347			0.691735	+	0.722152i	$0.256847\pi$
$264$	−677.903			−0.158038
$265$			2667.97i			0.618461i
$266$		−	7199.07i		−	1.65941i
$267$		−	1330.23i		−	0.304902i
$268$			15210.9i			3.46699i
$269$	1618.54			0.366854			0.183427	−	0.983033i	$-0.441281\pi$
$269$	1618.54			0.366854			0.183427	+	0.983033i	$0.441281\pi$
$270$	3499.93			0.788884
$271$		−	1537.62i		−	0.344662i	−0.985039	−	0.172331i	$-0.944870\pi$
$271$		−	1537.62i		−	0.344662i	0.985039	−	0.172331i	$-0.0551299\pi$
$272$	−10112.2			−2.25419
$273$	951.559	−	1482.24i	0.210956	−	0.328605i
$274$	−11683.1			−2.57593
$275$		−	256.390i		−	0.0562214i
$276$	−1645.60			−0.358889
$277$	−843.367			−0.182935			−0.0914675	−	0.995808i	$-0.529156\pi$
$277$	−843.367			−0.182935			−0.0914675	+	0.995808i	$0.529156\pi$
$278$		−	13971.7i		−	3.01428i
$279$			1187.24i			0.254760i
$280$			26154.3i			5.58221i
$281$			6797.17i			1.44301i	0.692410	+	0.721504i	$0.256549\pi$
$281$			6797.17i			1.44301i	−0.692410	+	0.721504i	$0.743451\pi$
$282$	−553.426			−0.116865
$283$	−1323.77			−0.278057			−0.139029	−	0.990288i	$-0.544398\pi$
$283$	−1323.77			−0.278057			−0.139029	+	0.990288i	$0.544398\pi$
$284$		−	22210.9i		−	4.64076i
$285$	−481.070			−0.0999863
$286$	−2269.01	−	1456.64i	−0.469123	−	0.301165i
$287$	−10519.2			−2.16351
$288$			8782.16i			1.79685i
$289$	−687.985			−0.140033
$290$	11969.8			2.42376
$291$			536.921i			0.108161i
$292$		−	3386.41i		−	0.678681i
$293$			1511.28i			0.301331i	0.988585	+	0.150666i	$0.0481417\pi$
$293$			1511.28i			0.301331i	−0.988585	+	0.150666i	$0.951858\pi$
$294$			5248.95i			1.04124i
$295$	811.788			0.160217
$296$	15833.3			3.10910
$297$		−	604.510i		−	0.118105i
$298$	−9345.39			−1.81666
$299$	−3230.58	−	2073.95i	−0.624847	−	0.401136i
$300$	468.305			0.0901254
$301$		−	8219.73i		−	1.57401i
$302$	9104.37			1.73476
$303$	1231.24			0.233442
$304$		−	5918.04i		−	1.11652i
$305$			3153.01i			0.591937i
$306$		−	8811.35i		−	1.64612i
$307$			1011.24i			0.187996i	0.995572	+	0.0939980i	$0.0299647\pi$
$307$			1011.24i			0.187996i	−0.995572	+	0.0939980i	$0.970035\pi$
$308$	7701.93			1.42486
$309$	−377.325			−0.0694669
$310$			2916.90i			0.534416i
$311$	−1025.89			−0.187051			−0.0935255	−	0.995617i	$-0.529814\pi$
$311$	−1025.89			−0.187051			−0.0935255	+	0.995617i	$0.529814\pi$
$312$	1560.52	−	2430.82i	0.283164	−	0.441083i
$313$	−8341.83			−1.50642			−0.753208	−	0.657783i	$-0.771494\pi$
$313$	−8341.83			−1.50642			−0.753208	+	0.657783i	$0.771494\pi$
$314$			13983.7i			2.51320i
$315$	−11423.7			−2.04335
$316$	6168.06			1.09804
$317$			7325.39i			1.29790i	0.760830	+	0.648951i	$0.224792\pi$
$317$			7325.39i			1.29790i	−0.760830	+	0.648951i	$0.775208\pi$
$318$			1189.71i			0.209798i
$319$		−	2067.44i		−	0.362866i
$320$			6420.14i			1.12155i
$321$	870.101			0.151291
$322$	15500.0			2.68255
$323$			2472.65i			0.425950i
$324$	−12437.4			−2.13262
$325$	919.359	+	590.205i	0.156913	+	0.100734i
$326$	3877.82			0.658812
$327$		−	2066.77i		−	0.349518i
$328$	−17251.1			−2.90406
$329$	3687.91			0.617997
$330$		−	727.475i		−	0.121352i
$331$		−	6571.14i		−	1.09119i	−0.838051	−	0.545593i	$-0.816305\pi$
$331$		−	6571.14i		−	1.09119i	0.838051	−	0.545593i	$-0.183695\pi$
$332$		−	14370.8i		−	2.37560i
$333$			6915.72i			1.13808i
$334$	13827.6			2.26531
$335$	−9574.02			−1.56145
$336$			5846.16i			0.949208i
$337$	−1379.12			−0.222924			−0.111462	−	0.993769i	$-0.535553\pi$
$337$	−1379.12			−0.222924			−0.111462	+	0.993769i	$0.535553\pi$
$338$	10446.4	−	4783.00i	1.68110	−	0.769707i
$339$	660.763			0.105863
$340$		−	15315.8i		−	2.44299i
$341$	503.810			0.0800083
$342$	5156.75			0.815337
$343$		−	22565.4i		−	3.55223i
$344$		−	13480.1i		−	2.11278i
$345$		−	1035.77i		−	0.161635i
$346$		−	9865.85i		−	1.53292i
$347$	7654.45			1.18419			0.592093	−	0.805870i	$-0.298302\pi$
$347$	7654.45			1.18419			0.592093	+	0.805870i	$0.298302\pi$
$348$	3776.25			0.581690
$349$			7741.39i			1.18736i	0.804703	+	0.593678i	$0.202325\pi$
$349$			7741.39i			1.18736i	−0.804703	+	0.593678i	$0.797675\pi$
$350$	−4410.99			−0.673650
$351$	2167.65	+	1391.57i	0.329631	+	0.211615i
$352$	3726.76			0.564309
$353$			11416.1i			1.72129i	0.509202	+	0.860647i	$0.329941\pi$
$353$			11416.1i			1.72129i	−0.509202	+	0.860647i	$0.670059\pi$
$354$	361.995			0.0543498
$355$	13979.9			2.09008
$356$			24785.2i			3.68993i
$357$		−	2442.61i		−	0.362120i
$358$			4750.89i			0.701376i
$359$			2574.25i			0.378450i	0.981934	+	0.189225i	$0.0605976\pi$
$359$			2574.25i			0.378450i	−0.981934	+	0.189225i	$0.939402\pi$
$360$	−18734.5			−2.74277
$361$	5411.91			0.789023
$362$		−	8088.88i		−	1.17443i
$363$	−125.650			−0.0181678
$364$	−17729.7	+	27617.5i	−2.55299	+	3.97678i
$365$	2131.47			0.305661
$366$			1406.00i			0.200800i
$367$	9928.39			1.41215			0.706073	−	0.708139i	$-0.250465\pi$
$367$	9928.39			1.41215			0.706073	+	0.708139i	$0.250465\pi$
$368$	12741.9			1.80493
$369$		−	7534.97i		−	1.06302i
$370$			16991.2i			2.38737i
$371$		−	7927.96i		−	1.10943i
$372$			920.227i			0.128257i
$373$	−6517.28			−0.904697			−0.452348	−	0.891841i	$-0.649414\pi$
$373$	−6517.28			−0.904697			−0.452348	+	0.891841i	$0.649414\pi$
$374$	−3739.14			−0.516969
$375$		−	1286.02i		−	0.177092i
$376$	6048.04			0.829531
$377$	7413.39	+	4759.21i	1.01276	+	0.650164i
$378$	−10400.1			−1.41515
$379$			43.3123i			0.00587019i	0.999996	+	0.00293509i	$0.000934271\pi$
$379$			43.3123i			0.00587019i	−0.999996	+	0.00293509i	$0.999066\pi$
$380$	8963.43			1.21004
$381$	−2203.22			−0.296258
$382$		−	5140.52i		−	0.688512i
$383$			1478.09i			0.197198i	0.995127	+	0.0985989i	$0.0314361\pi$
$383$			1478.09i			0.197198i	−0.995127	+	0.0985989i	$0.968564\pi$
$384$			48.3632i			0.00642714i
$385$			4847.73i			0.641722i
$386$	7918.96			1.04421
$387$	5887.86			0.773376
$388$		−	10004.1i		−	1.30897i
$389$	7207.75			0.939453			0.469727	−	0.882812i	$-0.344353\pi$
$389$	7207.75			0.939453			0.469727	+	0.882812i	$0.344353\pi$
$390$	2608.57	+	1674.64i	0.338693	+	0.217432i
$391$	−5323.75			−0.688577
$392$		−	57362.4i		−	7.39091i
$393$	−1355.34			−0.173964
$394$	−5625.22			−0.719275
$395$			3882.28i			0.494529i
$396$			5516.95i			0.700094i
$397$			8844.17i			1.11808i	0.829142	+	0.559038i	$0.188829\pi$
$397$			8844.17i			1.11808i	−0.829142	+	0.559038i	$0.811171\pi$
$398$			21539.0i			2.71270i
$399$	1429.51			0.179361
$400$	−3626.08			−0.453260
$401$		−	9013.84i		−	1.12252i	−0.827640	−	0.561259i	$-0.810317\pi$
$401$		−	9013.84i		−	1.12252i	0.827640	−	0.561259i	$-0.189683\pi$
$402$	−4269.28			−0.529682
$403$	−1159.76	+	1806.56i	−0.143355	+	0.223303i
$404$	−22940.8			−2.82512
$405$		−	7828.35i		−	0.960478i
$406$	−35568.7			−4.34789
$407$	2934.73			0.357418
$408$		−	4005.80i		−	0.486070i
$409$		−	5390.45i		−	0.651689i	−0.945423	−	0.325845i	$-0.894351\pi$
$409$		−	5390.45i		−	0.651689i	0.945423	−	0.325845i	$-0.105649\pi$
$410$		−	18512.6i		−	2.22993i
$411$		−	2319.91i		−	0.278426i
$412$	7030.43			0.840690
$413$	−2412.25			−0.287407
$414$			11102.8i			1.31805i
$415$	9045.23			1.06991
$416$	−8578.94	+	13363.4i	−1.01110	+	1.57498i
$417$	2774.36			0.325805
$418$		−	2188.30i		−	0.256060i
$419$	−4206.31			−0.490434			−0.245217	−	0.969468i	$-0.578859\pi$
$419$	−4206.31			−0.490434			−0.245217	+	0.969468i	$0.578859\pi$
$420$	−8854.55			−1.02871
$421$		−	7744.99i		−	0.896598i	−0.893884	−	0.448299i	$-0.852030\pi$
$421$		−	7744.99i		−	0.896598i	0.893884	−	0.448299i	$-0.147970\pi$
$422$			12048.5i			1.38984i
$423$			2641.68i			0.303647i
$424$		−	13001.6i		−	1.48918i
$425$	1515.03			0.172917
$426$	6233.99			0.709009
$427$		−	9369.27i		−	1.06185i
$428$	−16212.0			−1.83092
$429$	289.245	−	450.555i	0.0325521	−	0.0507063i
$430$	14465.8			1.62233
$431$		−	8379.07i		−	0.936440i	−0.883612	−	0.468220i	$-0.844896\pi$
$431$		−	8379.07i		−	0.936440i	0.883612	−	0.468220i	$-0.155104\pi$
$432$	−8549.50			−0.952172
$433$	1111.22			0.123329			0.0616647	−	0.998097i	$-0.480359\pi$
$433$	1111.22			0.123329			0.0616647	+	0.998097i	$0.480359\pi$
$434$		−	8667.67i		−	0.958667i
$435$			2376.84i			0.261978i
$436$			38508.6i			4.22988i
$437$		−	3115.67i		−	0.341059i
$438$	950.472			0.103688
$439$	−450.553			−0.0489834			−0.0244917	−	0.999700i	$-0.507797\pi$
$439$	−450.553			−0.0489834			−0.0244917	+	0.999700i	$0.507797\pi$
$440$			7950.11i			0.861378i
$441$	25054.9			2.70542
$442$	8607.46	−	13407.8i	0.926278	−	1.44286i
$443$	−17620.9			−1.88983			−0.944915	−	0.327316i	$-0.893856\pi$
$443$	−17620.9			−1.88983			−0.944915	+	0.327316i	$0.893856\pi$
$444$			5360.39i			0.572956i
$445$	−15600.3			−1.66185
$446$	4352.90			0.462143
$447$		−	1855.71i		−	0.196358i
$448$		−	19077.7i		−	2.01191i
$449$			21.8810i			0.00229984i	0.999999	+	0.00114992i	$0.000366031\pi$
$449$			21.8810i			0.00229984i	−0.999999	+	0.00114992i	$0.999634\pi$
$450$		−	3159.63i		−	0.330992i
$451$	−3197.50			−0.333846
$452$	−12311.5			−1.28116
$453$			1807.85i			0.187506i
$454$	−8868.73			−0.916807
$455$	−17382.9	−	11159.4i	−1.79104	−	1.14980i
$456$	2344.35			0.240755
$457$		−	1231.96i		−	0.126102i	−0.998010	−	0.0630509i	$-0.979917\pi$
$457$		−	1231.96i		−	0.126102i	0.998010	−	0.0630509i	$-0.0200830\pi$
$458$	−4115.65			−0.419895
$459$	3572.11			0.363250
$460$			19298.8i			1.95611i
$461$		−	16.5907i		−	0.00167615i	−1.00000		0.000838076i	$-0.999733\pi$
$461$		−	16.5907i		−	0.00167615i	1.00000		0.000838076i	$-0.000266768\pi$
$462$			2161.72i			0.217689i
$463$		−	13452.2i		−	1.35027i	−0.737694	−	0.675135i	$-0.764085\pi$
$463$		−	13452.2i		−	1.35027i	0.737694	−	0.675135i	$-0.235915\pi$
$464$	−29239.5			−2.92545
$465$	−579.207			−0.0577636
$466$			6504.87i			0.646636i
$467$	−5005.39			−0.495978			−0.247989	−	0.968763i	$-0.579770\pi$
$467$	−5005.39			−0.495978			−0.247989	+	0.968763i	$0.579770\pi$
$468$	−19782.6	−	12699.9i	−1.95396	−	1.25439i
$469$	28449.5			2.80102
$470$			6490.30i			0.636969i
$471$	−2776.73			−0.271645
$472$	−3956.01			−0.385784
$473$		−	2498.54i		−	0.242882i
$474$			1731.20i			0.167757i
$475$			886.657i			0.0856476i
$476$			45511.5i			4.38238i
$477$	5678.86			0.545110
$478$	16404.3			1.56969
$479$			8324.26i			0.794040i	0.917810	+	0.397020i	$0.129956\pi$
$479$			8324.26i			0.794040i	−0.917810	+	0.397020i	$0.870044\pi$
$480$	−4284.48			−0.407414
$481$	−6755.70	+	10523.3i	−0.640402	+	0.997550i
$482$	−10023.1			−0.947180
$483$			3077.82i			0.289950i
$484$	2341.15			0.219867
$485$	6296.73			0.589526
$486$		−	11250.5i		−	1.05006i
$487$			14551.6i			1.35399i	0.735986	+	0.676997i	$0.236719\pi$
$487$			14551.6i			1.35399i	−0.735986	+	0.676997i	$0.763281\pi$
$488$		−	15365.3i		−	1.42531i
$489$			770.016i			0.0712093i
$490$	61557.0			5.67523
$491$	−10777.1			−0.990554			−0.495277	−	0.868735i	$-0.664933\pi$
$491$	−10777.1			−0.990554			−0.495277	+	0.868735i	$0.664933\pi$
$492$		−	5840.36i		−	0.535170i
$493$	12216.7			1.11605
$494$	7846.77	+	5037.43i	0.714662	+	0.458795i
$495$	−3472.47			−0.315305
$496$		−	7125.31i		−	0.645032i
$497$	−41541.9			−3.74931
$498$	4033.48			0.362941
$499$		−	12570.8i		−	1.12775i	−0.825861	−	0.563873i	$-0.809311\pi$
$499$		−	12570.8i		−	1.12775i	0.825861	−	0.563873i	$-0.190689\pi$
$500$			23961.4i			2.14317i
$501$			2745.74i			0.244851i
$502$			541.441i			0.0481388i
$503$	20941.6			1.85634			0.928169	−	0.372158i	$-0.121382\pi$
$503$	20941.6			1.85634			0.928169	+	0.372158i	$0.121382\pi$
$504$	55670.3			4.92014
$505$		−	14439.3i		−	1.27236i
$506$	4711.52			0.413938
$507$	949.757	+	2074.34i	0.0831957	+	0.181706i
$508$	41051.0			3.58532
$509$			13815.8i			1.20309i	0.798839	+	0.601545i	$0.205448\pi$
$509$			13815.8i			1.20309i	−0.798839	+	0.601545i	$0.794552\pi$
$510$	4298.72			0.373237
$511$	−6333.73			−0.548312
$512$			21154.4i			1.82598i
$513$			2090.54i			0.179921i
$514$			38781.6i			3.32798i
$515$			4425.07i			0.378625i
$516$	4563.68			0.389351
$517$	1121.01			0.0953616
$518$		−	50489.8i		−	4.28261i
$519$	1959.05			0.165690
$520$	−28507.4	−	18301.0i	−2.40410	−	1.54337i
$521$	1106.23			0.0930230			0.0465115	−	0.998918i	$-0.485190\pi$
$521$	1106.23			0.0930230			0.0465115	+	0.998918i	$0.485190\pi$
$522$		−	25478.1i		−	2.13630i
$523$	−3729.93			−0.311852			−0.155926	−	0.987769i	$-0.549836\pi$
$523$	−3729.93			−0.311852			−0.155926	+	0.987769i	$0.549836\pi$
$524$	25253.0			2.10531
$525$		−	875.887i		−	0.0728131i
$526$		−	30858.1i		−	2.55794i
$527$			2977.06i			0.246078i
$528$			1777.05i			0.146470i
$529$	−5458.79			−0.448656
$530$	13952.3			1.14349
$531$		−	1727.92i		−	0.141215i
$532$	−26635.1			−2.17064
$533$	7360.61	−	11465.6i	0.598168	−	0.931762i
$534$	−6956.53			−0.563742
$535$		−	10204.1i		−	0.824602i
$536$	46656.2			3.75978
$537$	−943.381			−0.0758099
$538$		−	8464.23i		−	0.678288i
$539$		−	10632.2i		−	0.849648i
$540$		−	12949.0i		−	1.03192i
$541$			1670.73i			0.132773i	0.997794	+	0.0663865i	$0.0211470\pi$
$541$			1670.73i			0.132773i	−0.997794	+	0.0663865i	$0.978853\pi$
$542$	−8041.06			−0.637257
$543$	1606.20			0.126941
$544$			22021.8i			1.73562i
$545$	−24238.0			−1.90503
$546$	−7751.46	−	4976.24i	−0.607567	−	0.390043i
$547$	−10877.0			−0.850214			−0.425107	−	0.905143i	$-0.639764\pi$
$547$	−10877.0			−0.850214			−0.425107	+	0.905143i	$0.639764\pi$
$548$			43225.3i			3.36951i
$549$	6711.28			0.521731
$550$	−1340.81			−0.103949
$551$			7149.69i			0.552790i
$552$			5047.52i			0.389197i
$553$		−	11536.3i		−	0.887115i
$554$			4410.44i			0.338234i
$555$	−3373.92			−0.258045
$556$	−51692.6			−3.94291
$557$			740.936i			0.0563635i	0.999603	+	0.0281817i	$0.00897171\pi$
$557$			740.936i			0.0563635i	−0.999603	+	0.0281817i	$0.991028\pi$
$558$	6208.72			0.471033
$559$	8959.25	+	5751.61i	0.677882	+	0.435183i
$560$	68560.7			5.17361
$561$		−	742.479i		−	0.0558779i
$562$	35546.2			2.66802
$563$	−17939.1			−1.34289			−0.671443	−	0.741056i	$-0.734325\pi$
$563$	−17939.1			−1.34289			−0.671443	+	0.741056i	$0.734325\pi$
$564$			2047.57i			0.152869i
$565$		−	7749.09i		−	0.577003i
$566$			6922.76i			0.514108i
$567$			23262.2i			1.72296i
$568$	−68127.2			−5.03267
$569$	12054.7			0.888154			0.444077	−	0.895989i	$-0.353532\pi$
$569$	12054.7			0.888154			0.444077	+	0.895989i	$0.353532\pi$
$570$			2515.78i			0.184868i
$571$	3582.24			0.262543			0.131272	−	0.991346i	$-0.458094\pi$
$571$	3582.24			0.262543			0.131272	+	0.991346i	$0.458094\pi$
$572$	−5389.29	+	8394.87i	−0.393947	+	0.613649i
$573$	1020.75			0.0744195
$574$			55010.7i			4.00018i
$575$	−1909.02			−0.138455
$576$	13665.5			0.988533
$577$			8815.90i			0.636067i	0.948079	+	0.318034i	$0.103022\pi$
$577$			8815.90i			0.636067i	−0.948079	+	0.318034i	$0.896978\pi$
$578$			3597.86i			0.258912i
$579$			1572.46i			0.112866i
$580$		−	44285.9i		−	3.17047i
$581$	−26878.2			−1.91927
$582$	2807.86			0.199982
$583$		−	2409.86i		−	0.171194i
$584$	−10387.1			−0.735995
$585$	7993.57	−	12451.5i	0.564946	−	0.880013i
$586$	7903.34			0.557140
$587$			11576.7i			0.814005i	0.913427	+	0.407002i	$0.133426\pi$
$587$			11576.7i			0.814005i	−0.913427	+	0.407002i	$0.866574\pi$
$588$	19420.1			1.36202
$589$	−1742.30			−0.121885
$590$		−	4245.30i		−	0.296231i
$591$		−	1116.99i		−	0.0777446i
$592$		−	41505.4i		−	2.88152i
$593$		−	21222.8i		−	1.46967i	−0.678246	−	0.734835i	$-0.737259\pi$
$593$		−	21222.8i		−	1.46967i	0.678246	−	0.734835i	$-0.262741\pi$
$594$	−3161.32			−0.218368
$595$	−28645.7			−1.97371
$596$			34576.1i			2.37633i
$597$	−4276.98			−0.293208
$598$	−10845.9	+	16894.5i	−0.741673	+	1.15530i
$599$	−1105.67			−0.0754197			−0.0377099	−	0.999289i	$-0.512006\pi$
$599$	−1105.67			−0.0754197			−0.0377099	+	0.999289i	$0.512006\pi$
$600$		−	1436.42i		−	0.0977363i
$601$	−12552.4			−0.851953			−0.425976	−	0.904734i	$-0.640069\pi$
$601$	−12552.4			−0.851953			−0.425976	+	0.904734i	$0.640069\pi$
$602$	−42985.6			−2.91024
$603$			20378.6i			1.37625i
$604$		−	33684.3i		−	2.26920i
$605$			1473.56i			0.0990227i
$606$		−	6438.84i		−	0.431617i
$607$	−7119.14			−0.476041			−0.238021	−	0.971260i	$-0.576499\pi$
$607$	−7119.14			−0.476041			−0.238021	+	0.971260i	$0.576499\pi$
$608$	−12888.0			−0.859668
$609$		−	7062.85i		−	0.469952i
$610$	16488.9			1.09445
$611$	−2580.55	+	4019.71i	−0.170864	+	0.266154i
$612$	−32600.2			−2.15325
$613$			19933.5i			1.31339i	0.754157	+	0.656694i	$0.228046\pi$
$613$			19933.5i			1.31339i	−0.754157	+	0.656694i	$0.771954\pi$
$614$	5288.37			0.347591
$615$	3676.02			0.241027
$616$		−	23624.0i		−	1.54519i
$617$			8240.78i			0.537701i	0.963182	+	0.268850i	$0.0866437\pi$
$617$			8240.78i			0.537701i	−0.963182	+	0.268850i	$0.913356\pi$
$618$			1973.25i			0.128439i
$619$		−	30187.8i		−	1.96018i	−0.198562	−	0.980088i	$-0.563627\pi$
$619$		−	30187.8i		−	1.96018i	0.198562	−	0.980088i	$-0.436373\pi$
$620$	10792.0			0.699057
$621$	−4501.05			−0.290855
$622$			5364.95i			0.345844i
$623$	46356.7			2.98113
$624$	−6372.13	−	4090.75i	−0.408797	−	0.262437i
$625$	−17995.2			−1.15170
$626$			43624.1i			2.78526i
$627$	434.528			0.0276769
$628$	51736.9			3.28746
$629$			17341.6i			1.09929i
$630$			59741.2i			3.77801i
$631$		−	6770.50i		−	0.427146i	−0.976927	−	0.213573i	$-0.931490\pi$
$631$		−	6770.50i		−	0.427146i	0.976927	−	0.213573i	$-0.0685102\pi$
$632$		−	18919.2i		−	1.19077i
$633$	−2392.46			−0.150224
$634$	38308.6			2.39973
$635$			25838.2i			1.61474i
$636$	4401.69			0.274432
$637$	38124.8	+	24475.1i	2.37136	+	1.52235i
$638$	−10811.8			−0.670914
$639$		−	29756.8i		−	1.84219i
$640$	567.179			0.0350308
$641$	28823.4			1.77606			0.888030	−	0.459785i	$-0.152074\pi$
$641$	28823.4			1.77606			0.888030	+	0.459785i	$0.152074\pi$
$642$		−	4550.25i		−	0.279726i
$643$			2166.36i			0.132866i	0.997791	+	0.0664332i	$0.0211619\pi$
$643$			2166.36i			0.132866i	−0.997791	+	0.0664332i	$0.978838\pi$
$644$		−	57346.9i		−	3.50898i
$645$			2872.46i			0.175354i
$646$	12930.9			0.787551
$647$	14042.1			0.853248			0.426624	−	0.904429i	$-0.359703\pi$
$647$	14042.1			0.853248			0.426624	+	0.904429i	$0.359703\pi$
$648$			38149.2i			2.31272i
$649$	−733.251			−0.0443492
$650$	3086.52	−	4807.85i	0.186251	−	0.290122i
$651$	1721.13			0.103620
$652$		−	14347.2i		−	0.861777i
$653$	−17080.2			−1.02358			−0.511792	−	0.859110i	$-0.671018\pi$
$653$	−17080.2			−1.02358			−0.511792	+	0.859110i	$0.671018\pi$
$654$	−10808.3			−0.646235
$655$			15894.7i			0.948180i
$656$			45221.9i			2.69149i
$657$		−	4536.90i		−	0.269408i
$658$		−	19286.1i		−	1.14263i
$659$	−11060.3			−0.653789			−0.326895	−	0.945061i	$-0.606002\pi$
$659$	−11060.3			−0.653789			−0.326895	+	0.945061i	$0.606002\pi$
$660$	−2691.51			−0.158738
$661$			21419.7i			1.26041i	0.776431	+	0.630203i	$0.217028\pi$
$661$			21419.7i			1.26041i	−0.776431	+	0.630203i	$0.782972\pi$
$662$	−34364.2			−2.01753
$663$	2662.37	+	1709.18i	0.155955	+	0.100119i
$664$	−44079.3			−2.57622
$665$		−	16764.6i		−	0.977600i
$666$	36166.2			2.10422
$667$	−15393.7			−0.893622
$668$		−	51159.4i		−	2.96320i
$669$			864.352i			0.0499518i
$670$			50067.9i			2.88700i
$671$		−	2847.97i		−	0.163852i
$672$	12731.5			0.730844
$673$	−4828.11			−0.276538			−0.138269	−	0.990395i	$-0.544154\pi$
$673$	−4828.11			−0.276538			−0.138269	+	0.990395i	$0.544154\pi$
$674$			7212.18i			0.412170i
$675$	1280.91			0.0730404
$676$	−17696.1	−	38649.7i	−1.00684	−	2.19901i
$677$	−4401.28			−0.249860			−0.124930	−	0.992166i	$-0.539871\pi$
$677$	−4401.28			−0.249860			−0.124930	+	0.992166i	$0.539871\pi$
$678$		−	3455.50i		−	0.195734i
$679$	−18710.9			−1.05753
$680$	−46978.0			−2.64930
$681$		−	1761.06i		−	0.0990953i
$682$		−	2634.71i		−	0.147930i
$683$			6626.66i			0.371248i	0.982621	+	0.185624i	$0.0594306\pi$
$683$			6626.66i			0.371248i	−0.982621	+	0.185624i	$0.940569\pi$
$684$		−	19079.0i		−	1.06652i
$685$	−27206.8			−1.51754
$686$	−118007.			−6.56783
$687$		−	817.242i		−	0.0453853i
$688$	−35336.6			−1.95813
$689$	8641.24	+	5547.46i	0.477801	+	0.306736i
$690$	−5416.62			−0.298851
$691$		−	14053.1i		−	0.773668i	−0.922149	−	0.386834i	$-0.873569\pi$
$691$		−	14053.1i		−	0.773668i	0.922149	−	0.386834i	$-0.126431\pi$
$692$	−36501.7			−2.00518
$693$	10318.5			0.565612
$694$		−	40029.4i		−	2.18948i
$695$		−	32536.2i		−	1.77578i
$696$		−	11582.8i		−	0.630813i
$697$		−	18894.4i		−	1.02679i
$698$	40484.1			2.19534
$699$	−1291.67			−0.0698932
$700$			16319.8i			0.881185i
$701$	6447.55			0.347390			0.173695	−	0.984799i	$-0.444429\pi$
$701$	6447.55			0.347390			0.173695	+	0.984799i	$0.444429\pi$
$702$	7277.32	−	11335.8i	0.391261	−	0.609464i
$703$	−10149.0			−0.544490
$704$		−	5799.02i		−	0.310453i
$705$	−1288.77			−0.0688483
$706$	59701.2			3.18255
$707$			42907.0i			2.28244i
$708$		−	1339.31i		−	0.0710937i
$709$		−	24784.5i		−	1.31283i	−0.754398	−	0.656417i	$-0.772071\pi$
$709$		−	24784.5i		−	1.31283i	0.754398	−	0.656417i	$-0.227929\pi$
$710$		−	73109.0i		−	3.86441i
$711$	8263.57			0.435876
$712$	76023.4			4.00154
$713$		−	3751.26i		−	0.197035i
$714$	−12773.8			−0.669534
$715$	−5283.88	−	3392.11i	−0.276372	−	0.177424i
$716$	17577.3			0.917453
$717$			3257.38i			0.169664i
$718$	13462.2			0.699728
$719$	7207.86			0.373864			0.186932	−	0.982373i	$-0.440146\pi$
$719$	7207.86			0.373864			0.186932	+	0.982373i	$0.440146\pi$
$720$			49110.6i			2.54201i
$721$		−	13149.3i		−	0.679201i
$722$		−	28301.9i		−	1.45885i
$723$		−	1990.28i		−	0.102378i
$724$	−29927.2			−1.53624
$725$	4380.74			0.224409
$726$			657.095i			0.0335910i
$727$	−3645.68			−0.185985			−0.0929924	−	0.995667i	$-0.529643\pi$
$727$	−3645.68			−0.185985			−0.0929924	+	0.995667i	$0.529643\pi$
$728$	84710.7	+	54382.1i	4.31262	+	2.76859i
$729$	−15122.1			−0.768281
$730$		−	11146.6i		−	0.565145i
$731$	14764.2			0.747020
$732$	5201.92			0.262662
$733$			24419.8i			1.23051i	0.788326	+	0.615257i	$0.210948\pi$
$733$			24419.8i			1.23051i	−0.788326	+	0.615257i	$0.789052\pi$
$734$		−	51921.1i		−	2.61096i
$735$			12223.3i			0.613421i
$736$		−	27748.6i		−	1.38971i
$737$	8647.78			0.432218
$738$	−39404.6			−1.96545
$739$			15262.7i			0.759742i	0.925040	+	0.379871i	$0.124032\pi$
$739$			15262.7i			0.759742i	−0.925040	+	0.379871i	$0.875968\pi$
$740$	62863.9			3.12287
$741$	−1000.28	+	1558.13i	−0.0495899	+	0.0772459i
$742$	−41459.8			−2.05126
$743$		−	25663.7i		−	1.26717i	−0.773672	−	0.633586i	$-0.781582\pi$
$743$		−	25663.7i		−	1.26717i	0.773672	−	0.633586i	$-0.218418\pi$
$744$	2822.60			0.139088
$745$	−21762.8			−1.07024
$746$			34082.5i			1.67272i
$747$		−	19253.1i		−	0.943016i
$748$			13834.1i			0.676236i
$749$			30321.8i			1.47922i
$750$	−6725.30			−0.327431
$751$	14278.3			0.693773			0.346886	−	0.937907i	$-0.387239\pi$
$751$	14278.3			0.693773			0.346886	+	0.937907i	$0.387239\pi$
$752$		−	15854.3i		−	0.768812i
$753$	−107.514			−0.00520320
$754$	24888.6	−	38768.8i	1.20211	−	1.87252i
$755$	21201.5			1.02199
$756$			38478.5i			1.85112i
$757$	−1131.95			−0.0543478			−0.0271739	−	0.999631i	$-0.508651\pi$
$757$	−1131.95			−0.0543478			−0.0271739	+	0.999631i	$0.508651\pi$
$758$	226.504			0.0108536
$759$			935.564i			0.0447415i
$760$		−	27493.4i		−	1.31222i
$761$		−	6084.34i		−	0.289825i	−0.989444	−	0.144913i	$-0.953710\pi$
$761$		−	6084.34i		−	0.289825i	0.989444	−	0.144913i	$-0.0462901\pi$
$762$			11521.9i			0.547760i
$763$	72024.0			3.41736
$764$	−19018.9			−0.900627
$765$		−	20519.2i		−	0.969767i
$766$	7729.76			0.364605
$767$	1687.93	−	2629.28i	0.0794625	−	0.123778i
$768$	−4126.63			−0.193889
$769$		−	31295.1i		−	1.46753i	−0.679403	−	0.733765i	$-0.737761\pi$
$769$		−	31295.1i		−	1.46753i	0.679403	−	0.733765i	$-0.262239\pi$
$770$	25351.5			1.18650
$771$	−7700.84			−0.359713
$772$		−	29298.6i		−	1.36591i
$773$		−	18477.7i		−	0.859762i	−0.902886	−	0.429881i	$-0.858556\pi$
$773$		−	18477.7i		−	0.859762i	0.902886	−	0.429881i	$-0.141444\pi$
$774$		−	30790.9i		−	1.42992i
$775$			1067.53i			0.0494799i
$776$	−30685.3			−1.41951
$777$	10025.7			0.462896
$778$		−	37693.4i		−	1.73698i
$779$	11057.7			0.508581
$780$	6195.82	−	9651.19i	0.284418	−	0.443036i
$781$	−12627.5			−0.578548
$782$			27840.9i			1.27313i
$783$	10328.8			0.471420
$784$	−150369.			−6.84992
$785$			32564.1i			1.48059i
$786$			7087.82i			0.321647i
$787$			22265.7i			1.00849i	0.863559	+	0.504247i	$0.168230\pi$
$787$			22265.7i			1.00849i	−0.863559	+	0.504247i	$0.831770\pi$
$788$			20812.2i			0.940867i
$789$	6127.46			0.276481
$790$	20302.7			0.914349
$791$			23026.7i			1.03506i
$792$	16922.1			0.759216
$793$	10212.2	+	6555.98i	0.457310	+	0.293581i
$794$	46251.2			2.06724
$795$			2770.50i			0.123597i
$796$	79690.0			3.54841
$797$	−33315.8			−1.48069			−0.740344	−	0.672229i	$-0.765337\pi$
$797$	−33315.8			−1.48069			−0.740344	+	0.672229i	$0.765337\pi$
$798$		−	7475.74i		−	0.331627i
$799$			6624.16i			0.293299i
$800$			7896.71i			0.348988i
$801$			33205.7i			1.46475i
$802$	−47138.5			−2.07546
$803$	−1925.26			−0.0846088
$804$			15795.5i			0.692865i
$805$	36095.1			1.58036
$806$	9447.50	+	6065.05i	0.412871	+	0.265053i
$807$	1680.74			0.0733144
$808$			70366.0i			3.06370i
$809$	7766.42			0.337519			0.168759	−	0.985657i	$-0.446024\pi$
$809$	7766.42			0.337519			0.168759	+	0.985657i	$0.446024\pi$
$810$	−40938.8			−1.77586
$811$		−	11454.6i		−	0.495964i	−0.968765	−	0.247982i	$-0.920233\pi$
$811$		−	11454.6i		−	0.495964i	0.968765	−	0.247982i	$-0.0797673\pi$
$812$			131597.i			5.68738i
$813$		−	1596.71i		−	0.0688794i
$814$		−	15347.3i		−	0.660840i
$815$	9030.36			0.388122
$816$	−10500.8			−0.450491
$817$			8640.57i			0.370006i
$818$	−28189.7			−1.20493
$819$	−23753.1	+	37000.1i	−1.01343	+	1.57862i
$820$	−68492.7			−2.91692
$821$			15606.4i			0.663419i	0.943382	+	0.331710i	$0.107625\pi$
$821$			15606.4i			0.663419i	−0.943382	+	0.331710i	$0.892375\pi$
$822$	−12132.1			−0.514789
$823$	−20464.2			−0.866752			−0.433376	−	0.901213i	$-0.642678\pi$
$823$	−20464.2			−0.866752			−0.433376	+	0.901213i	$0.642678\pi$
$824$		−	21564.3i		−	0.911685i
$825$		−	266.243i		−	0.0112356i
$826$			12615.0i			0.531396i
$827$		−	12021.3i		−	0.505469i	−0.967536	−	0.252734i	$-0.918670\pi$
$827$		−	12021.3i		−	0.505469i	0.967536	−	0.252734i	$-0.0813299\pi$
$828$	41078.0			1.72411
$829$	−13196.8			−0.552886			−0.276443	−	0.961030i	$-0.589156\pi$
$829$	−13196.8			−0.552886			−0.276443	+	0.961030i	$0.589156\pi$
$830$		−	47302.6i		−	1.97819i
$831$	−875.778			−0.0365589
$832$	20794.1	+	13349.3i	0.866472	+	0.556253i
$833$	62826.6			2.61322
$834$		−	14508.7i		−	0.602391i
$835$	32200.6			1.33455
$836$	−8096.26			−0.334946
$837$			2517.01i			0.103943i
$838$			21997.2i			0.906777i
$839$		−	3180.02i		−	0.130854i	−0.997857	−	0.0654270i	$-0.979159\pi$
$839$		−	3180.02i		−	0.130854i	0.997857	−	0.0654270i	$-0.0208409\pi$
$840$			27159.4i			1.11558i
$841$	10935.7			0.448388
$842$	−40502.9			−1.65775
$843$			7058.39i			0.288379i
$844$	44577.0			1.81801
$845$	24326.8	−	11138.3i	0.990376	−	0.453453i
$846$	13814.8			0.561422
$847$		−	4378.73i		−	0.177633i
$848$	−34082.3			−1.38018
$849$	−1374.65			−0.0555686
$850$		−	7922.96i		−	0.319712i
$851$		−	21851.3i		−	0.880205i
$852$		−	23064.5i		−	0.927438i
$853$			26200.4i			1.05168i	0.850583	+	0.525840i	$0.176249\pi$
$853$			26200.4i			1.05168i	−0.850583	+	0.525840i	$0.823751\pi$
$854$	−48997.2			−1.96329
$855$	12008.6			0.480335
$856$			49726.7i			1.98554i
$857$	−14528.8			−0.579106			−0.289553	−	0.957162i	$-0.593507\pi$
$857$	−14528.8			−0.579106			−0.289553	+	0.957162i	$0.593507\pi$
$858$	−2356.21	−	1512.62i	−0.0937523	−	0.0601866i
$859$	−34941.5			−1.38788			−0.693939	−	0.720033i	$-0.744126\pi$
$859$	−34941.5			−1.38788			−0.693939	+	0.720033i	$0.744126\pi$
$860$		−	53520.5i		−	2.12213i
$861$	−10923.4			−0.432369
$862$	−43818.9			−1.73141
$863$		−	8791.23i		−	0.346764i	−0.984855	−	0.173382i	$-0.944531\pi$
$863$		−	8791.23i		−	0.346764i	0.984855	−	0.173382i	$-0.0554695\pi$
$864$			18618.7i			0.733126i
$865$		−	22974.8i		−	0.903082i
$866$		−	5811.17i		−	0.228027i
$867$	−714.424			−0.0279851
$868$	−32068.6			−1.25401
$869$		−	3506.69i		−	0.136889i
$870$	12429.8			0.484380
$871$	−19907.1	+	31009.1i	−0.774426	+	1.20632i
$872$	118117.			4.58709
$873$		−	13402.8i		−	0.519606i
$874$	−16293.6			−0.630594
$875$	44815.9			1.73149
$876$		−	3516.56i		−	0.135632i
$877$		−	28581.8i		−	1.10050i	−0.834999	−	0.550251i	$-0.814532\pi$
$877$		−	28581.8i		−	1.10050i	0.834999	−	0.550251i	$-0.185468\pi$
$878$			2356.20i			0.0905669i
$879$			1569.36i			0.0602198i
$880$	20840.4			0.798328
$881$	−20330.7			−0.777480			−0.388740	−	0.921348i	$-0.627090\pi$
$881$	−20330.7			−0.777480			−0.388740	+	0.921348i	$0.627090\pi$
$882$		−	131026.i		−	5.00213i
$883$	−4523.51			−0.172399			−0.0861995	−	0.996278i	$-0.527472\pi$
$883$	−4523.51			−0.172399			−0.0861995	+	0.996278i	$0.527472\pi$
$884$	−49606.1	−	31845.9i	−1.88737	−	1.21164i
$885$	842.985			0.0320188
$886$			92149.7i			3.49416i
$887$	−36611.9			−1.38592			−0.692959	−	0.720977i	$-0.743693\pi$
$887$	−36611.9			−1.38592			−0.692959	+	0.720977i	$0.743693\pi$
$888$	16441.8			0.621342
$889$		−	76779.0i		−	2.89661i
$890$			81582.6i			3.07265i
$891$			7070.99i			0.265867i
$892$		−	16104.8i		−	0.604518i
$893$	−3876.72			−0.145274
$894$	−9704.54			−0.363052
$895$			11063.5i			0.413197i
$896$	−1685.39			−0.0628403
$897$	−3354.73	−	2153.65i	−0.124873	−	0.0801655i
$898$	114.428			0.00425224
$899$			8608.22i			0.319355i
$900$	−11690.0			−0.432963
$901$	14240.1			0.526533
$902$			16721.6i			0.617258i
$903$		−	8535.61i		−	0.314560i
$904$			37763.0i			1.38936i
$905$		−	18836.7i		−	0.691883i
$906$	9454.26			0.346685
$907$	−24453.1			−0.895205			−0.447603	−	0.894233i	$-0.647722\pi$
$907$	−24453.1			−0.895205			−0.447603	+	0.894233i	$0.647722\pi$
$908$			32812.5i			1.19925i
$909$	−30734.6			−1.12146
$910$	−58358.8	+	90905.1i	−2.12591	+	3.31151i
$911$	−6317.71			−0.229764			−0.114882	−	0.993379i	$-0.536649\pi$
$911$	−6317.71			−0.229764			−0.114882	+	0.993379i	$0.536649\pi$
$912$		−	6145.47i		−	0.223133i
$913$	−8170.15			−0.296158
$914$	−6442.59			−0.233153
$915$			3274.18i			0.118296i
$916$			15227.1i			0.549255i
$917$		−	47231.6i		−	1.70090i
$918$		−	18680.6i		−	0.671625i
$919$	23233.9			0.833969			0.416984	−	0.908914i	$-0.363087\pi$
$919$	23233.9			0.833969			0.416984	+	0.908914i	$0.363087\pi$
$920$	59194.8			2.12130
$921$			1050.11i			0.0375703i
$922$	−86.7621			−0.00309909
$923$	29068.2	−	45279.4i	1.03661	−	1.61472i
$924$	7997.91			0.284753
$925$			6218.46i			0.221040i
$926$	−70348.9			−2.49655
$927$	9418.92			0.333719
$928$			63676.3i			2.25245i
$929$		−	223.698i		−	0.00790020i	−0.999992	−	0.00395010i	$-0.998743\pi$
$929$		−	223.698i		−	0.00790020i	0.999992	−	0.00395010i	$-0.00125736\pi$
$930$			3029.00i			0.106801i
$931$			36768.6i			1.29435i
$932$	24066.7			0.845850
$933$	−1065.31			−0.0373814
$934$			26176.0i			0.917029i
$935$	−8707.42			−0.304559
$936$	−38954.3	+	60678.9i	−1.36032	+	2.11897i
$937$	33965.3			1.18420			0.592101	−	0.805864i	$-0.298299\pi$
$937$	33965.3			1.18420			0.592101	+	0.805864i	$0.298299\pi$
$938$		−	148779.i		−	5.17888i
$939$	−8662.41			−0.301051
$940$	24012.8			0.833204
$941$		−	7921.13i		−	0.274412i	−0.990543	−	0.137206i	$-0.956188\pi$
$941$		−	7921.13i		−	0.274412i	0.990543	−	0.137206i	$-0.0438122\pi$
$942$			14521.1i			0.502253i
$943$			23807.9i			0.822156i
$944$			10370.3i			0.357546i
$945$	−24219.0			−0.833698
$946$	−13066.3			−0.449072
$947$		−	9441.25i		−	0.323970i	−0.986793	−	0.161985i	$-0.948210\pi$
$947$		−	9441.25i		−	0.323970i	0.986793	−	0.161985i	$-0.0517896\pi$
$948$	6405.10			0.219439
$949$	4431.92	−	6903.57i	0.151598	−	0.236143i
$950$	4636.83			0.158356
$951$			7606.91i			0.259381i
$952$	139597.			4.75247
$953$	−48172.4			−1.63741			−0.818707	−	0.574211i	$-0.805309\pi$
$953$	−48172.4			−1.63741			−0.818707	+	0.574211i	$0.805309\pi$
$954$		−	29698.0i		−	1.00787i
$955$		−	11970.8i		−	0.405620i
$956$		−	60692.5i		−	2.05328i
$957$		−	2146.89i		−	0.0725173i
$958$	43532.3			1.46812
$959$	80845.8			2.72226
$960$			6666.87i			0.224138i
$961$	27693.3			0.929585
$962$	55032.3	+	35329.4i	1.84440	+	1.18406i
$963$	−21719.8			−0.726801
$964$			37083.5i			1.23898i
$965$	18441.0			0.615169
$966$	16095.7			0.536097
$967$			17859.9i			0.593936i	0.954887	+	0.296968i	$0.0959754\pi$
$967$			17859.9i			0.593936i	−0.954887	+	0.296968i	$0.904025\pi$
$968$		−	7180.97i		−	0.238435i
$969$			2567.67i			0.0851244i
$970$		−	32929.2i		−	1.08999i
$971$	−7255.22			−0.239785			−0.119892	−	0.992787i	$-0.538255\pi$
$971$	−7255.22			−0.239785			−0.119892	+	0.992787i	$0.538255\pi$
$972$	−41624.4			−1.37356
$973$			96682.5i			3.18551i
$974$	76098.4			2.50344
$975$	954.691	+	612.887i	0.0313585	+	0.0201314i
$976$	−40278.4			−1.32098
$977$		−	14646.9i		−	0.479628i	−0.970819	−	0.239814i	$-0.922914\pi$
$977$		−	14646.9i		−	0.479628i	0.970819	−	0.239814i	$-0.0770864\pi$
$978$	4026.85			0.131661
$979$	14091.0			0.460011
$980$		−	227749.i		−	7.42364i
$981$			51591.3i			1.67909i
$982$			56359.3i			1.83146i
$983$			22170.7i			0.719366i	0.933075	+	0.359683i	$0.117115\pi$
$983$			22170.7i			0.719366i	−0.933075	+	0.359683i	$0.882885\pi$
$984$	−17914.0			−0.580365
$985$	−13099.5			−0.423742
$986$		−	63888.0i		−	2.06350i
$987$	3829.63			0.123504
$988$	18637.5	−	29031.5i	0.600139	−	0.934832i
$989$	−18603.6			−0.598140
$990$			18159.5i			0.582976i
$991$	41873.8			1.34225			0.671123	−	0.741346i	$-0.265812\pi$
$991$	41873.8			1.34225			0.671123	+	0.741346i	$0.265812\pi$
$992$	−15517.2			−0.496643
$993$		−	6823.67i		−	0.218069i
$994$			217246.i			6.93221i
$995$			50158.3i			1.59812i
$996$		−	14923.1i		−	0.474755i
$997$	36262.5			1.15190			0.575950	−	0.817485i	$-0.304632\pi$
$997$	36262.5			1.15190			0.575950	+	0.817485i	$0.304632\pi$
$998$	−65739.7			−2.08512
$999$			14661.7i			0.464342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.2	✓	36
13.5	odd	4		1859.4.a.j.1.1		18
13.8	odd	4		1859.4.a.k.1.18		18
13.12	even	2	inner	143.4.b.a.12.35	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.2	✓	36	1.1	even	1	trivial
143.4.b.a.12.35	yes	36	13.12	even	2	inner
1859.4.a.j.1.1		18	13.5	odd	4
1859.4.a.k.1.18		18	13.8	odd	4

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.22956i q^{2} +1.03843 q^{3} -19.3483 q^{4} -12.1782i q^{5} -5.43054i q^{6} +36.1879i q^{7} +59.3469i q^{8} -25.9217 q^{9} +O(q^{10})\)	\(q-5.22956i q^{2} +1.03843 q^{3} -19.3483 q^{4} -12.1782i q^{5} -5.43054i q^{6} +36.1879i q^{7} +59.3469i q^{8} -25.9217 q^{9} -63.6866 q^{10} +11.0000i q^{11} -20.0919 q^{12} +(-39.4437 - 25.3218i) q^{13} +189.247 q^{14} -12.6462i q^{15} +155.571 q^{16} -65.0001 q^{17} +135.559i q^{18} -38.0407i q^{19} +235.628i q^{20} +37.5786i q^{21} +57.5252 q^{22} +81.9036 q^{23} +61.6276i q^{24} -23.3081 q^{25} +(-132.422 + 206.273i) q^{26} -54.9555 q^{27} -700.175i q^{28} -187.949 q^{29} -66.1341 q^{30} -45.8009i q^{31} -338.796i q^{32} +11.4227i q^{33} +339.922i q^{34} +440.702 q^{35} +501.541 q^{36} -266.793i q^{37} -198.936 q^{38} +(-40.9595 - 26.2950i) q^{39} +722.737 q^{40} +290.682i q^{41} +196.520 q^{42} -227.140 q^{43} -212.832i q^{44} +315.679i q^{45} -428.320i q^{46} -101.910i q^{47} +161.550 q^{48} -966.562 q^{49} +121.891i q^{50} -67.4981 q^{51} +(763.170 + 489.936i) q^{52} -219.078 q^{53} +287.393i q^{54} +133.960 q^{55} -2147.64 q^{56} -39.5026i q^{57} +982.890i q^{58} +66.6592i q^{59} +244.683i q^{60} -258.906 q^{61} -239.519 q^{62} -938.050i q^{63} -527.184 q^{64} +(-308.374 + 480.352i) q^{65} +59.7359 q^{66} -786.161i q^{67} +1257.64 q^{68} +85.0513 q^{69} -2304.68i q^{70} +1147.95i q^{71} -1538.37i q^{72} +175.023i q^{73} -1395.21 q^{74} -24.2039 q^{75} +736.023i q^{76} -398.067 q^{77} +(-137.511 + 214.200i) q^{78} -318.790 q^{79} -1894.58i q^{80} +642.817 q^{81} +1520.14 q^{82} +742.741i q^{83} -727.083i q^{84} +791.583i q^{85} +1187.85i q^{86} -195.172 q^{87} -652.815 q^{88} -1281.00i q^{89} +1650.86 q^{90} +(916.344 - 1427.38i) q^{91} -1584.70 q^{92} -47.5610i q^{93} -532.945 q^{94} -463.266 q^{95} -351.816i q^{96} +517.050i q^{97} +5054.70i q^{98} -285.138i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 36 * q - 152 * q^4 + 360 * q^9	\( 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) \) 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Introduction

L-functions

Modular forms

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