LMFDB - Embedded newform 120.4.b.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.638417 - 2.75544i) q^{2} +(-0.899959 - 5.11762i) q^{3} +(-7.18485 - 3.51823i) q^{4} +5.00000 q^{5} +(-14.6758 - 0.787399i) q^{6} -23.1184i q^{7} +(-14.2812 + 17.5513i) q^{8} +(-25.3801 + 9.21130i) q^{9} +O(q^{10})$	\(q+(0.638417 - 2.75544i) q^{2} +(-0.899959 - 5.11762i) q^{3} +(-7.18485 - 3.51823i) q^{4} +5.00000 q^{5} +(-14.6758 - 0.787399i) q^{6} -23.1184i q^{7} +(-14.2812 + 17.5513i) q^{8} +(-25.3801 + 9.21130i) q^{9} +(3.19208 - 13.7772i) q^{10} -5.98122i q^{11} +(-11.5389 + 39.9356i) q^{12} +3.38478i q^{13} +(-63.7014 - 14.7592i) q^{14} +(-4.49979 - 25.5881i) q^{15} +(39.2441 + 50.5559i) q^{16} +35.8894i q^{17} +(9.17803 + 75.8140i) q^{18} -51.7691 q^{19} +(-35.9242 - 17.5912i) q^{20} +(-118.311 + 20.8056i) q^{21} +(-16.4809 - 3.81851i) q^{22} +123.162 q^{23} +(102.673 + 57.2903i) q^{24} +25.0000 q^{25} +(9.32655 + 2.16090i) q^{26} +(69.9810 + 121.596i) q^{27} +(-81.3360 + 166.102i) q^{28} -130.020 q^{29} +(-73.3792 - 3.93700i) q^{30} -298.386i q^{31} +(164.358 - 75.8588i) q^{32} +(-30.6096 + 5.38285i) q^{33} +(98.8910 + 22.9124i) q^{34} -115.592i q^{35} +(214.760 + 23.1115i) q^{36} -343.478i q^{37} +(-33.0503 + 142.646i) q^{38} +(17.3220 - 3.04616i) q^{39} +(-71.4060 + 87.7564i) q^{40} -121.848i q^{41} +(-18.2034 + 339.282i) q^{42} -535.951 q^{43} +(-21.0433 + 42.9742i) q^{44} +(-126.901 + 46.0565i) q^{45} +(78.6290 - 339.366i) q^{46} +401.602 q^{47} +(223.408 - 246.335i) q^{48} -191.462 q^{49} +(15.9604 - 68.8859i) q^{50} +(183.669 - 32.2990i) q^{51} +(11.9085 - 24.3191i) q^{52} +67.6765 q^{53} +(379.728 - 115.199i) q^{54} -29.9061i q^{55} +(405.758 + 330.159i) q^{56} +(46.5900 + 264.935i) q^{57} +(-83.0072 + 358.263i) q^{58} -717.121i q^{59} +(-57.6946 + 199.678i) q^{60} -45.2695i q^{61} +(-822.184 - 190.495i) q^{62} +(212.951 + 586.749i) q^{63} +(-104.095 - 501.306i) q^{64} +16.9239i q^{65} +(-4.70961 + 87.7794i) q^{66} +722.381 q^{67} +(126.267 - 257.860i) q^{68} +(-110.841 - 630.299i) q^{69} +(-318.507 - 73.7960i) q^{70} +1033.71 q^{71} +(200.789 - 577.003i) q^{72} -331.455 q^{73} +(-946.432 - 219.282i) q^{74} +(-22.4990 - 127.941i) q^{75} +(371.953 + 182.136i) q^{76} -138.276 q^{77} +(2.66518 - 49.6745i) q^{78} +449.012i q^{79} +(196.220 + 252.780i) q^{80} +(559.304 - 467.568i) q^{81} +(-335.744 - 77.7897i) q^{82} +641.752i q^{83} +(923.249 + 266.762i) q^{84} +179.447i q^{85} +(-342.160 + 1476.78i) q^{86} +(117.013 + 665.395i) q^{87} +(104.978 + 85.4190i) q^{88} +855.504i q^{89} +(45.8901 + 379.070i) q^{90} +78.2509 q^{91} +(-884.903 - 433.314i) q^{92} +(-1527.03 + 268.535i) q^{93} +(256.389 - 1106.59i) q^{94} -258.845 q^{95} +(-536.132 - 772.851i) q^{96} +82.0025 q^{97} +(-122.233 + 527.561i) q^{98} +(55.0948 + 151.804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.638417	−	2.75544i	0.225714	−	0.974194i
$2$	0.638417	−	2.75544i	0.225714	−	0.974194i
$3$	−0.899959	−	5.11762i	−0.173197	−	0.984887i
$3$	−0.899959	−	5.11762i	−0.173197	−	0.984887i
$4$	−7.18485	−	3.51823i	−0.898106	−	0.439779i
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	−14.6758	−	0.787399i	−0.998564	−	0.0535757i
$7$		−	23.1184i		−	1.24828i	−0.781313	−	0.624139i	$-0.785450\pi$
$7$		−	23.1184i		−	1.24828i	0.781313	−	0.624139i	$-0.214550\pi$
$8$	−14.2812	+	17.5513i	−0.631145	+	0.775665i
$9$	−25.3801	+	9.21130i	−0.940006	+	0.341159i
$10$	3.19208	−	13.7772i	0.100943	−	0.435673i
$11$		−	5.98122i		−	0.163946i	−0.996635	−	0.0819730i	$-0.973878\pi$
$11$		−	5.98122i		−	0.163946i	0.996635	−	0.0819730i	$-0.0261221\pi$
$12$	−11.5389	+	39.9356i	−0.277583	+	0.960702i
$13$			3.38478i			0.0722131i	0.999348	+	0.0361065i	$0.0114956\pi$
$13$			3.38478i			0.0722131i	−0.999348	+	0.0361065i	$0.988504\pi$
$14$	−63.7014	−	14.7592i	−1.21606	−	0.281754i
$15$	−4.49979	−	25.5881i	−0.0774561	−	0.440455i
$16$	39.2441	+	50.5559i	0.613189	+	0.789936i
$17$			35.8894i			0.512028i	0.966673	+	0.256014i	$0.0824093\pi$
$17$			35.8894i			0.512028i	−0.966673	+	0.256014i	$0.917591\pi$
$18$	9.17803	+	75.8140i	0.120182	+	0.992752i
$19$	−51.7691			−0.625087			−0.312543	−	0.949904i	$-0.601181\pi$
$19$	−51.7691			−0.625087			−0.312543	+	0.949904i	$0.601181\pi$
$20$	−35.9242	−	17.5912i	−0.401645	−	0.196675i
$21$	−118.311	+	20.8056i	−1.22941	+	0.216198i
$22$	−16.4809	−	3.81851i	−0.159715	−	0.0370050i
$23$	123.162			1.11657			0.558286	−	0.829649i	$-0.311459\pi$
$23$	123.162			1.11657			0.558286	+	0.829649i	$0.311459\pi$
$24$	102.673	+	57.2903i	0.873255	+	0.487264i
$25$	25.0000			0.200000
$26$	9.32655	+	2.16090i	0.0703495	+	0.0162995i
$27$	69.9810	+	121.596i	0.498810	+	0.866712i
$28$	−81.3360	+	166.102i	−0.548967	+	1.12109i
$29$	−130.020			−0.832558			−0.416279	−	0.909237i	$-0.636666\pi$
$29$	−130.020			−0.832558			−0.416279	+	0.909237i	$0.636666\pi$
$30$	−73.3792	−	3.93700i	−0.446571	−	0.0239598i
$31$		−	298.386i		−	1.72877i	−0.502834	−	0.864383i	$-0.667709\pi$
$31$		−	298.386i		−	1.72877i	0.502834	−	0.864383i	$-0.332291\pi$
$32$	164.358	−	75.8588i	0.907956	−	0.419064i
$33$	−30.6096	+	5.38285i	−0.161468	+	0.0283950i
$34$	98.8910	+	22.9124i	0.498814	+	0.115572i
$35$		−	115.592i		−	0.558247i
$36$	214.760	+	23.1115i	0.994259	+	0.106998i
$37$		−	343.478i		−	1.52615i	−0.646312	−	0.763074i	$-0.723689\pi$
$37$		−	343.478i		−	1.52615i	0.646312	−	0.763074i	$-0.276311\pi$
$38$	−33.0503	+	142.646i	−0.141091	+	0.608955i
$39$	17.3220	−	3.04616i	0.0711217	−	0.0125071i
$40$	−71.4060	+	87.7564i	−0.282257	+	0.346888i
$41$		−	121.848i		−	0.464132i	−0.972700	−	0.232066i	$-0.925451\pi$
$41$		−	121.848i		−	0.464132i	0.972700	−	0.232066i	$-0.0745486\pi$
$42$	−18.2034	+	339.282i	−0.0668774	+	1.24649i
$43$	−535.951			−1.90074			−0.950370	−	0.311123i	$-0.899295\pi$
$43$	−535.951			−1.90074			−0.950370	+	0.311123i	$0.899295\pi$
$44$	−21.0433	+	42.9742i	−0.0721000	+	0.147241i
$45$	−126.901	+	46.0565i	−0.420383	+	0.152571i
$46$	78.6290	−	339.366i	0.252026	−	1.08776i
$47$	401.602			1.24638			0.623188	−	0.782072i	$-0.285837\pi$
$47$	401.602			1.24638			0.623188	+	0.782072i	$0.285837\pi$
$48$	223.408	−	246.335i	0.671796	−	0.740736i
$49$	−191.462			−0.558198
$50$	15.9604	−	68.8859i	0.0451429	−	0.194839i
$51$	183.669	−	32.2990i	0.504289	−	0.0886817i
$52$	11.9085	−	24.3191i	0.0317578	−	0.0648550i
$53$	67.6765			0.175398			0.0876989	−	0.996147i	$-0.472049\pi$
$53$	67.6765			0.175398			0.0876989	+	0.996147i	$0.472049\pi$
$54$	379.728	−	115.199i	0.956933	−	0.290308i
$55$		−	29.9061i		−	0.0733189i
$56$	405.758	+	330.159i	0.968245	+	0.787845i
$57$	46.5900	+	264.935i	0.108263	+	0.615640i
$58$	−83.0072	+	358.263i	−0.187920	+	0.811072i
$59$		−	717.121i		−	1.58239i	−0.611562	−	0.791197i	$-0.709458\pi$
$59$		−	717.121i		−	1.58239i	0.611562	−	0.791197i	$-0.290542\pi$
$60$	−57.6946	+	199.678i	−0.124139	+	0.429639i
$61$		−	45.2695i		−	0.0950192i	−0.998871	−	0.0475096i	$-0.984872\pi$
$61$		−	45.2695i		−	0.0950192i	0.998871	−	0.0475096i	$-0.0151285\pi$
$62$	−822.184	−	190.495i	−1.68415	−	0.390208i
$63$	212.951	+	586.749i	0.425862	+	1.17339i
$64$	−104.095	−	501.306i	−0.203311	−	0.979114i
$65$			16.9239i			0.0322947i
$66$	−4.70961	+	87.7794i	−0.00878353	+	0.163711i
$67$	722.381			1.31721			0.658604	−	0.752490i	$-0.271147\pi$
$67$	722.381			1.31721			0.658604	+	0.752490i	$0.271147\pi$
$68$	126.267	−	257.860i	0.225179	−	0.459855i
$69$	−110.841	−	630.299i	−0.193387	−	1.09970i
$70$	−318.507	−	73.7960i	−0.543841	−	0.126004i
$71$	1033.71			1.72787			0.863933	−	0.503607i	$-0.167994\pi$
$71$	1033.71			1.72787			0.863933	+	0.503607i	$0.167994\pi$
$72$	200.789	−	577.003i	0.328655	−	0.944450i
$73$	−331.455			−0.531423			−0.265711	−	0.964053i	$-0.585607\pi$
$73$	−331.455			−0.531423			−0.265711	+	0.964053i	$0.585607\pi$
$74$	−946.432	−	219.282i	−1.48676	−	0.344473i
$75$	−22.4990	−	127.941i	−0.0346394	−	0.196977i
$76$	371.953	+	182.136i	0.561394	+	0.274900i
$77$	−138.276			−0.204650
$78$	2.66518	−	49.6745i	0.00386887	−	0.0721093i
$79$			449.012i			0.639466i	0.947508	+	0.319733i	$0.103593\pi$
$79$			449.012i			0.639466i	−0.947508	+	0.319733i	$0.896407\pi$
$80$	196.220	+	252.780i	0.274226	+	0.353270i
$81$	559.304	−	467.568i	0.767221	−	0.641383i
$82$	−335.744	−	77.7897i	−0.452155	−	0.104761i
$83$			641.752i			0.848692i	0.905500	+	0.424346i	$0.139496\pi$
$83$			641.752i			0.848692i	−0.905500	+	0.424346i	$0.860504\pi$
$84$	923.249	+	266.762i	1.19922	+	0.346501i
$85$			179.447i			0.228986i
$86$	−342.160	+	1476.78i	−0.429024	+	1.85169i
$87$	117.013	+	665.395i	0.144197	+	0.819975i
$88$	104.978	+	85.4190i	0.127167	+	0.103474i
$89$			855.504i			1.01891i	0.860497	+	0.509456i	$0.170153\pi$
$89$			855.504i			1.01891i	−0.860497	+	0.509456i	$0.829847\pi$
$90$	45.8901	+	379.070i	0.0537472	+	0.443972i
$91$	78.2509			0.0901420
$92$	−884.903	−	433.314i	−1.00280	−	0.491045i
$93$	−1527.03	+	268.535i	−1.70264	+	0.299417i
$94$	256.389	−	1106.59i	0.281325	−	1.21421i
$95$	−258.845			−0.279547
$96$	−536.132	−	772.851i	−0.569987	−	0.821654i
$97$	82.0025			0.0858360			0.0429180	−	0.999079i	$-0.486335\pi$
$97$	82.0025			0.0858360			0.0429180	+	0.999079i	$0.486335\pi$
$98$	−122.233	+	527.561i	−0.125993	+	0.543793i
$99$	55.0948	+	151.804i	0.0559317	+	0.154110i
$100$	−179.621	−	87.9558i	−0.179621	−	0.0879558i
$101$	−967.336			−0.953006			−0.476503	−	0.879173i	$-0.658096\pi$
$101$	−967.336			−0.953006			−0.476503	+	0.879173i	$0.658096\pi$
$102$	28.2593	−	526.707i	0.0274323	−	0.511292i
$103$			249.178i			0.238371i	0.992872	+	0.119185i	$0.0380283\pi$
$103$			249.178i			0.238371i	−0.992872	+	0.119185i	$0.961972\pi$
$104$	−59.4073	−	48.3387i	−0.0560131	−	0.0455769i
$105$	−591.557	+	104.028i	−0.549810	+	0.0966868i
$106$	43.2058	−	186.478i	0.0395898	−	0.170871i
$107$			1073.12i			0.969557i	0.874637	+	0.484779i	$0.161100\pi$
$107$			1073.12i			0.969557i	−0.874637	+	0.484779i	$0.838900\pi$
$108$	−74.9992	−	1119.86i	−0.0668223	−	0.997765i
$109$			1529.06i			1.34364i	0.740712	+	0.671822i	$0.234488\pi$
$109$			1529.06i			1.34364i	−0.740712	+	0.671822i	$0.765512\pi$
$110$	−82.4043	−	19.0926i	−0.0714268	−	0.0165491i
$111$	−1757.79	+	309.116i	−1.50308	+	0.264324i
$112$	1168.77	−	907.262i	0.986060	−	0.765430i
$113$		−	1387.90i		−	1.15542i	−0.816242	−	0.577710i	$-0.803946\pi$
$113$		−	1387.90i		−	1.15542i	0.816242	−	0.577710i	$-0.196054\pi$
$114$	759.754	+	40.7630i	0.624189	+	0.0334895i
$115$	615.812			0.499346
$116$	934.176	+	457.442i	0.747725	+	0.366141i
$117$	−31.1782	−	85.9063i	−0.0246361	−	0.0678807i
$118$	−1975.98	−	457.822i	−1.54156	−	0.357169i
$119$	829.708			0.639153
$120$	513.367	+	286.452i	0.390531	+	0.217911i
$121$	1295.22			0.973122
$122$	−124.737	−	28.9008i	−0.0925671	−	0.0214472i
$123$	−623.571	+	109.658i	−0.457118	+	0.0803864i
$124$	−1049.79	+	2143.86i	−0.760275	+	1.55262i
$125$	125.000			0.0894427
$126$	1752.70	−	212.182i	1.23923	−	0.150021i
$127$		−	2100.84i		−	1.46787i	−0.679219	−	0.733936i	$-0.737681\pi$
$127$		−	2100.84i		−	1.46787i	0.679219	−	0.733936i	$-0.262319\pi$
$128$	−1447.77	−	33.2148i	−0.999737	−	0.0229360i
$129$	482.334	+	2742.80i	0.329203	+	1.87201i
$130$	46.6327	+	10.8045i	0.0314612	+	0.00728937i
$131$		−	1808.52i		−	1.20619i	−0.797670	−	0.603095i	$-0.793934\pi$
$131$		−	1808.52i		−	1.20619i	0.797670	−	0.603095i	$-0.206066\pi$
$132$	238.864	+	69.0169i	0.157503	+	0.0455087i
$133$			1196.82i			0.780282i
$134$	461.180	−	1990.47i	0.297313	−	1.28322i
$135$	349.905	+	607.981i	0.223074	+	0.387605i
$136$	−629.906	−	512.544i	−0.397162	−	0.323164i
$137$			1060.13i			0.661115i	0.943786	+	0.330558i	$0.107237\pi$
$137$			1060.13i			0.661115i	−0.943786	+	0.330558i	$0.892763\pi$
$138$	−1807.51	−	96.9780i	−1.11497	−	0.0598211i
$139$	−972.119			−0.593195			−0.296597	−	0.955003i	$-0.595852\pi$
$139$	−972.119			−0.593195			−0.296597	+	0.955003i	$0.595852\pi$
$140$	−406.680	+	830.512i	−0.245505	+	0.501365i
$141$	−361.425	−	2055.25i	−0.215869	−	1.22754i
$142$	659.936	−	2848.31i	0.390004	−	1.68328i
$143$	20.2451			0.0118390
$144$	−1461.71	−	921.628i	−0.845895	−	0.533350i
$145$	−650.102			−0.372331
$146$	−211.606	+	913.302i	−0.119950	+	0.517709i
$147$	172.308	+	979.831i	0.0966783	+	0.549762i
$148$	−1208.44	+	2467.84i	−0.671168	+	1.37064i
$149$	1341.22			0.737432			0.368716	−	0.929542i	$-0.379797\pi$
$149$	1341.22			0.737432			0.368716	+	0.929542i	$0.379797\pi$
$150$	−366.896	−	19.6850i	−0.199713	−	0.0107151i
$151$			211.509i			0.113989i	0.998374	+	0.0569946i	$0.0181518\pi$
$151$			211.509i			0.113989i	−0.998374	+	0.0569946i	$0.981848\pi$
$152$	739.324	−	908.614i	0.394521	−	0.484857i
$153$	−330.588	−	910.879i	−0.174683	−	0.481309i
$154$	−88.2780	+	381.012i	−0.0461925	+	0.199369i
$155$		−	1491.93i		−	0.773128i
$156$	−135.173	−	39.0567i	−0.0693752	−	0.0200451i
$157$			3123.57i			1.58782i	0.608036	+	0.793910i	$0.291958\pi$
$157$			3123.57i			1.58782i	−0.608036	+	0.793910i	$0.708042\pi$
$158$	1237.22	+	286.657i	0.622963	+	0.144337i
$159$	−60.9060	−	346.343i	−0.0303784	−	0.172747i
$160$	821.788	−	379.294i	0.406050	−	0.187411i
$161$		−	2847.32i		−	1.39379i
$162$	−931.285	−	1839.63i	−0.451658	−	0.892191i
$163$	−424.842			−0.204148			−0.102074	−	0.994777i	$-0.532548\pi$
$163$	−424.842			−0.204148			−0.102074	+	0.994777i	$0.532548\pi$
$164$	−428.689	+	875.458i	−0.204116	+	0.416840i
$165$	−153.048	+	26.9143i	−0.0722108	+	0.0126986i
$166$	1768.31	+	409.705i	0.826791	+	0.191562i
$167$	2358.82			1.09300			0.546500	−	0.837459i	$-0.315960\pi$
$167$	2358.82			1.09300			0.546500	+	0.837459i	$0.315960\pi$
$168$	1324.46	−	2373.65i	0.608241	−	1.09006i
$169$	2185.54			0.994785
$170$	494.455	+	114.562i	0.223076	+	0.0516854i
$171$	1313.91	−	476.861i	0.587585	−	0.213254i
$172$	3850.73	+	1885.60i	1.70707	+	0.835905i
$173$	3499.67			1.53800			0.769002	−	0.639246i	$-0.220753\pi$
$173$	3499.67			1.53800			0.769002	+	0.639246i	$0.220753\pi$
$174$	1908.16	+	102.378i	0.831362	+	0.0446049i
$175$		−	577.961i		−	0.249656i
$176$	302.386	−	234.728i	0.129507	−	0.100530i
$177$	−3669.96	+	645.379i	−1.55848	+	0.274066i
$178$	2357.29	+	546.168i	0.992618	+	0.229983i
$179$		−	593.563i		−	0.247849i	−0.992292	−	0.123925i	$-0.960452\pi$
$179$		−	593.563i		−	0.247849i	0.992292	−	0.123925i	$-0.0395481\pi$
$180$	1073.80	+	115.557i	0.444646	+	0.0478508i
$181$			356.562i			0.146426i	0.997316	+	0.0732128i	$0.0233252\pi$
$181$			356.562i			0.146426i	−0.997316	+	0.0732128i	$0.976675\pi$
$182$	49.9567	−	215.615i	0.0203463	−	0.0878157i
$183$	−231.672	+	40.7407i	−0.0935832	+	0.0164570i
$184$	−1758.91	+	2161.66i	−0.704719	+	0.866085i
$185$		−	1717.39i		−	0.682514i
$186$	−234.949	+	4379.07i	−0.0926200	+	1.72628i
$187$	214.663			0.0839449
$188$	−2885.45	−	1412.93i	−1.11938	−	0.548130i
$189$	2811.12	−	1617.85i	1.08190	−	0.622653i
$190$	−165.251	+	713.232i	−0.0630978	+	0.272333i
$191$	−3212.19			−1.21689			−0.608444	−	0.793597i	$-0.708206\pi$
$191$	−3212.19			−1.21689			−0.608444	+	0.793597i	$0.708206\pi$
$192$	−2471.82	+	983.875i	−0.929104	+	0.369818i
$193$	4916.33			1.83360			0.916800	−	0.399346i	$-0.130763\pi$
$193$	4916.33			1.83360			0.916800	+	0.399346i	$0.130763\pi$
$194$	52.3518	−	225.953i	0.0193744	−	0.0836209i
$195$	86.6102	−	15.2308i	0.0318066	−	0.00559334i
$196$	1375.63	+	673.608i	0.501321	+	0.245484i
$197$	2804.05			1.01411			0.507056	−	0.861913i	$-0.330734\pi$
$197$	2804.05			1.01411			0.507056	+	0.861913i	$0.330734\pi$
$198$	453.460	−	54.8958i	0.162758	−	0.0197034i
$199$		−	2328.27i		−	0.829382i	−0.909962	−	0.414691i	$-0.863890\pi$
$199$		−	2328.27i		−	0.829382i	0.909962	−	0.414691i	$-0.136110\pi$
$200$	−357.030	+	438.782i	−0.126229	+	0.155133i
$201$	−650.113	−	3696.88i	−0.228137	−	1.29730i
$202$	−617.564	+	2665.43i	−0.215107	+	0.928412i
$203$			3005.87i			1.03926i
$204$	−1433.27	−	414.126i	−0.491906	−	0.142130i
$205$		−	609.239i		−	0.207566i
$206$	686.593	+	159.079i	0.232219	+	0.0538037i
$207$	−3125.88	+	1134.49i	−1.04958	+	0.380929i
$208$	−171.121	+	132.833i	−0.0570437	+	0.0442802i
$209$			309.642i			0.102480i
$210$	−91.0172	+	1696.41i	−0.0299085	+	0.557445i
$211$	−2199.79			−0.717724			−0.358862	−	0.933391i	$-0.616835\pi$
$211$	−2199.79			−0.717724			−0.358862	+	0.933391i	$0.616835\pi$
$212$	−486.245	−	238.102i	−0.157526	−	0.0771363i
$213$	−930.293	−	5290.12i	−0.299261	−	1.70175i
$214$	2956.92	+	685.099i	0.944536	+	0.218843i
$215$	−2679.76			−0.850037
$216$	−3133.58	−	508.282i	−0.987099	−	0.160112i
$217$	−6898.22			−2.15798
$218$	4213.22	+	976.177i	1.30897	+	0.303280i
$219$	298.296	+	1696.26i	0.0920409	+	0.523391i
$220$	−105.217	+	214.871i	−0.0322441	+	0.0658481i
$221$	−121.478			−0.0369751
$222$	−270.454	+	5040.83i	−0.0817645	+	1.52396i
$223$		−	3517.53i		−	1.05628i	−0.849156	−	0.528142i	$-0.822889\pi$
$223$		−	3517.53i		−	1.05628i	0.849156	−	0.528142i	$-0.177111\pi$
$224$	−1753.74	−	3799.69i	−0.523109	−	1.13338i
$225$	−634.504	+	230.282i	−0.188001	+	0.0682318i
$226$	−3824.26	−	886.058i	−1.12560	−	0.260795i
$227$			4422.04i			1.29296i	0.762932	+	0.646479i	$0.223759\pi$
$227$			4422.04i			1.29296i	−0.762932	+	0.646479i	$0.776241\pi$
$228$	597.360	−	2067.43i	0.173514	−	0.600522i
$229$		−	2145.13i		−	0.619014i	−0.950897	−	0.309507i	$-0.899836\pi$
$229$		−	2145.13i		−	0.619014i	0.950897	−	0.309507i	$-0.100164\pi$
$230$	393.145	−	1696.83i	0.112710	−	0.486460i
$231$	124.443	+	707.647i	0.0354448	+	0.201557i
$232$	1856.85	−	2282.02i	0.525465	−	0.645785i
$233$			5668.46i			1.59379i	0.604118	+	0.796895i	$0.293526\pi$
$233$			5668.46i			1.59379i	−0.604118	+	0.796895i	$0.706474\pi$
$234$	−256.614	+	31.0656i	−0.0716896	+	0.00867873i
$235$	2008.01			0.557396
$236$	−2523.00	+	5152.41i	−0.695903	+	1.42116i
$237$	2297.87	−	404.092i	0.629802	−	0.110754i
$238$	529.699	−	2286.21i	0.144266	−	0.622659i
$239$	−5353.63			−1.44894			−0.724472	−	0.689304i	$-0.757916\pi$
$239$	−5353.63			−1.44894			−0.724472	+	0.689304i	$0.757916\pi$
$240$	1117.04	−	1231.67i	0.300436	−	0.331267i
$241$	−3097.05			−0.827795			−0.413897	−	0.910324i	$-0.635833\pi$
$241$	−3097.05			−0.827795			−0.413897	+	0.910324i	$0.635833\pi$
$242$	826.893	−	3568.91i	0.219648	−	0.948009i
$243$	−2896.19	−	2441.52i	−0.764570	−	0.644540i
$244$	−159.269	+	325.255i	−0.0417874	+	0.0853373i
$245$	−957.310			−0.249634
$246$	−95.9429	+	1788.22i	−0.0248662	+	0.463466i
$247$		−	175.227i		−	0.0451394i
$248$	5237.06	+	4261.31i	1.34094	+	1.09110i
$249$	3284.25	−	577.550i	0.835866	−	0.146991i
$250$	79.8021	−	344.429i	0.0201885	−	0.0871345i
$251$		−	2609.53i		−	0.656224i	−0.944639	−	0.328112i	$-0.893588\pi$
$251$		−	2609.53i		−	0.656224i	0.944639	−	0.328112i	$-0.106412\pi$
$252$	534.301	−	4964.92i	0.133563	−	1.24111i
$253$		−	736.662i		−	0.183057i
$254$	−5788.74	−	1341.21i	−1.42999	−	0.331320i
$255$	918.343	−	161.495i	0.225525	−	0.0396597i
$256$	−1015.80	+	3968.04i	−0.247999	+	0.968760i
$257$		−	895.782i		−	0.217422i	−0.994073	−	0.108711i	$-0.965328\pi$
$257$		−	895.782i		−	0.217422i	0.994073	−	0.108711i	$-0.0346723\pi$
$258$	7865.53	+	422.008i	1.89801	+	0.101834i
$259$	−7940.67			−1.90506
$260$	59.5423	−	121.596i	0.0142025	−	0.0290040i
$261$	3299.94	−	1197.66i	0.782609	−	0.284035i
$262$	−4983.25	−	1154.59i	−1.17506	−	0.272254i
$263$	−3402.86			−0.797829			−0.398915	−	0.916988i	$-0.630613\pi$
$263$	−3402.86			−0.797829			−0.398915	+	0.916988i	$0.630613\pi$
$264$	342.666	−	614.112i	0.0798850	−	0.143167i
$265$	338.382			0.0784403
$266$	3297.76	+	764.070i	0.760146	+	0.176121i
$267$	4378.15	−	769.918i	1.00351	−	0.176473i
$268$	−5190.20	−	2541.51i	−1.18299	−	0.579280i
$269$	−4014.61			−0.909944			−0.454972	−	0.890506i	$-0.650351\pi$
$269$	−4014.61			−0.909944			−0.454972	+	0.890506i	$0.650351\pi$
$270$	1898.64	−	575.996i	0.427954	−	0.129830i
$271$		−	2146.55i		−	0.481156i	−0.970630	−	0.240578i	$-0.922663\pi$
$271$		−	2146.55i		−	0.481156i	0.970630	−	0.240578i	$-0.0773370\pi$
$272$	−1814.42	+	1408.45i	−0.404469	+	0.313970i
$273$	−70.4225	−	400.458i	−0.0156123	−	0.0887797i
$274$	2921.11	+	676.803i	0.644054	+	0.149223i
$275$		−	149.531i		−	0.0327892i
$276$	−1421.16	+	4918.57i	−0.309942	+	1.07269i
$277$			117.069i			0.0253936i	0.999919	+	0.0126968i	$0.00404162\pi$
$277$			117.069i			0.0253936i	−0.999919	+	0.0126968i	$0.995958\pi$
$278$	−620.617	+	2678.61i	−0.133893	+	0.577887i
$279$	2748.53	+	7573.09i	0.589785	+	1.62505i
$280$	2028.79	+	1650.79i	0.433012	+	0.352335i
$281$			4176.32i			0.886614i	0.896370	+	0.443307i	$0.146195\pi$
$281$			4176.32i			0.886614i	−0.896370	+	0.443307i	$0.853805\pi$
$282$	−5893.84	−	316.221i	−1.24459	−	0.0667755i
$283$	3734.16			0.784357			0.392178	−	0.919889i	$-0.371722\pi$
$283$	3734.16			0.784357			0.392178	+	0.919889i	$0.371722\pi$
$284$	−7427.03	−	3636.82i	−1.55181	−	0.759879i
$285$	232.950	+	1324.67i	0.0484168	+	0.275322i
$286$	12.9248	−	55.7841i	0.00267224	−	0.0115335i
$287$	−2816.93			−0.579366
$288$	−3472.66	+	3439.25i	−0.710516	+	0.703681i
$289$	3624.95			0.737828
$290$	−415.036	+	1791.31i	−0.0840405	+	0.362723i
$291$	−73.7988	−	419.658i	−0.0148665	−	0.0845388i
$292$	2381.45	+	1166.14i	0.477274	+	0.233709i
$293$	2675.30			0.533423			0.266711	−	0.963776i	$-0.414063\pi$
$293$	2675.30			0.533423			0.266711	+	0.963776i	$0.414063\pi$
$294$	2809.86	+	150.757i	0.557397	+	0.0299059i
$295$		−	3585.61i		−	0.707668i
$296$	6028.48	+	4905.28i	1.18378	+	0.963221i
$297$	727.294	−	418.572i	0.142094	−	0.0817778i
$298$	856.260	−	3695.66i	0.166449	−	0.718401i
$299$			416.878i			0.0806310i
$300$	−288.473	+	998.390i	−0.0555167	+	0.192140i
$301$			12390.4i			2.37265i
$302$	582.799	+	135.031i	0.111047	+	0.0257290i
$303$	870.563	+	4950.46i	0.165058	+	0.938603i
$304$	−2031.63	−	2617.23i	−0.383296	−	0.493779i
$305$		−	226.348i		−	0.0424939i
$306$	−2720.92	+	329.394i	−0.508316	+	0.0615367i
$307$	9426.10			1.75236			0.876182	−	0.481980i	$-0.160082\pi$
$307$	9426.10			1.75236			0.876182	+	0.481980i	$0.160082\pi$
$308$	993.495	+	486.489i	0.183798	+	0.0900009i
$309$	1275.20	−	224.249i	0.234768	−	0.0412851i
$310$	−4110.92	−	952.474i	−0.753176	−	0.174506i
$311$	2253.75			0.410928			0.205464	−	0.978665i	$-0.434130\pi$
$311$	2253.75			0.410928			0.205464	+	0.978665i	$0.434130\pi$
$312$	−193.915	+	347.527i	−0.0351868	+	0.0630604i
$313$	6581.16			1.18846			0.594232	−	0.804294i	$-0.297456\pi$
$313$	6581.16			1.18846			0.594232	+	0.804294i	$0.297456\pi$
$314$	8606.78	+	1994.14i	1.54684	+	0.358394i
$315$	1064.75	+	2933.75i	0.190451	+	0.524755i
$316$	1579.73	−	3226.08i	0.281224	−	0.574308i
$317$	−4166.54			−0.738222			−0.369111	−	0.929385i	$-0.620338\pi$
$317$	−4166.54			−0.738222			−0.369111	+	0.929385i	$0.620338\pi$
$318$	−993.209	−	53.2884i	−0.175146	−	0.00939706i
$319$			777.680i			0.136494i
$320$	−520.476	−	2506.53i	−0.0909234	−	0.437873i
$321$	5491.84	−	965.765i	0.954905	−	0.167925i
$322$	−7845.61	−	1817.78i	−1.35782	−	0.314599i
$323$		−	1857.96i		−	0.320062i
$324$	−5663.53	+	1391.65i	−0.971112	+	0.238622i
$325$			84.6196i			0.0144426i
$326$	−271.226	+	1170.63i	−0.0460793	+	0.198880i
$327$	7825.15	−	1376.09i	1.32334	−	0.232715i
$328$	2138.59	+	1740.13i	0.360011	+	0.292935i
$329$		−	9284.41i		−	1.55582i
$330$	−23.5481	+	438.897i	−0.00392811	+	0.0732136i
$331$	−6581.83			−1.09296			−0.546480	−	0.837472i	$-0.684033\pi$
$331$	−6581.83			−1.09296			−0.546480	+	0.837472i	$0.684033\pi$
$332$	2257.83	−	4610.89i	0.373237	−	0.762216i
$333$	3163.88	+	8717.52i	0.520659	+	1.43459i
$334$	1505.91	−	6499.57i	0.246706	−	1.06479i
$335$	3611.91			0.589073
$336$	−5694.87	−	5164.85i	−0.924645	−	0.838588i
$337$	−7568.49			−1.22339			−0.611694	−	0.791094i	$-0.709512\pi$
$337$	−7568.49			−1.22339			−0.611694	+	0.791094i	$0.709512\pi$
$338$	1395.29	−	6022.12i	0.224537	−	0.969113i
$339$	−7102.74	+	1249.05i	−1.13796	+	0.200115i
$340$	631.337	−	1289.30i	0.100703	−	0.205653i
$341$	−1784.71			−0.283424
$342$	−475.138	−	3924.82i	−0.0751243	−	0.620556i
$343$		−	3503.32i		−	0.551491i
$344$	7654.02	−	9406.63i	1.19964	−	1.47434i
$345$	−554.205	−	3151.50i	−0.0864853	−	0.491799i
$346$	2234.25	−	9643.11i	0.347150	−	1.49831i
$347$			2676.22i			0.414025i	0.978338	+	0.207013i	$0.0663741\pi$
$347$			2676.22i			0.414025i	−0.978338	+	0.207013i	$0.933626\pi$
$348$	1500.29	−	5192.44i	0.231104	−	0.799839i
$349$			4165.96i			0.638964i	0.947592	+	0.319482i	$0.103509\pi$
$349$			4165.96i			0.638964i	−0.947592	+	0.319482i	$0.896491\pi$
$350$	−1592.53	−	368.980i	−0.243213	−	0.0563509i
$351$	−411.577	+	236.871i	−0.0625879	+	0.0360206i
$352$	−453.728	−	983.060i	−0.0687039	−	0.148856i
$353$			2421.76i			0.365149i	0.983192	+	0.182574i	$0.0584430\pi$
$353$			2421.76i			0.365149i	−0.983192	+	0.182574i	$0.941557\pi$
$354$	−564.661	+	10524.3i	−0.0847779	+	1.58012i
$355$	5168.53			0.772725
$356$	3009.86	−	6146.66i	0.448096	−	0.915091i
$357$	−746.703	−	4246.13i	−0.110699	−	0.629493i
$358$	−1635.53	−	378.941i	−0.241453	−	0.0559431i
$359$	503.494			0.0740206			0.0370103	−	0.999315i	$-0.488217\pi$
$359$	503.494			0.0740206			0.0370103	+	0.999315i	$0.488217\pi$
$360$	1003.94	−	2885.01i	0.146979	−	0.422371i
$361$	−4178.96			−0.609267
$362$	982.483	+	227.635i	0.142647	+	0.0330504i
$363$	−1165.65	−	6628.47i	−0.168542	−	0.958415i
$364$	−562.221	−	275.305i	−0.0809570	−	0.0396426i
$365$	−1657.27			−0.237659
$366$	−35.6452	+	664.368i	−0.00509072	+	0.0948827i
$367$			2029.60i			0.288676i	0.989528	+	0.144338i	$0.0461053\pi$
$367$			2029.60i			0.288676i	−0.989528	+	0.144338i	$0.953895\pi$
$368$	4833.40	+	6226.59i	0.684669	+	0.882020i
$369$	1122.38	+	3092.52i	0.158343	+	0.436287i
$370$	−4732.16	−	1096.41i	−0.664900	−	0.154053i
$371$		−	1564.57i		−	0.218945i
$372$	11916.2	+	3443.06i	1.66083	+	0.479877i
$373$		−	6340.20i		−	0.880116i	−0.897969	−	0.440058i	$-0.854958\pi$
$373$		−	6340.20i		−	0.880116i	0.897969	−	0.440058i	$-0.145042\pi$
$374$	137.044	−	591.489i	0.0189476	−	0.0817786i
$375$	−112.495	−	639.703i	−0.0154912	−	0.0880910i
$376$	−5735.35	+	7048.63i	−0.786644	+	0.966770i
$377$		−	440.090i		−	0.0601215i
$378$	−2663.22	−	8778.71i	−0.362385	−	1.19452i
$379$	−7822.99			−1.06026			−0.530132	−	0.847915i	$-0.677858\pi$
$379$	−7822.99			−1.06026			−0.530132	+	0.847915i	$0.677858\pi$
$380$	1859.77	+	910.679i	0.251063	+	0.122939i
$381$	−10751.3	+	1890.67i	−1.44569	+	0.254231i
$382$	−2050.71	+	8850.97i	−0.274669	+	1.18548i
$383$	13772.6			1.83746			0.918730	−	0.394886i	$-0.129216\pi$
$383$	13772.6			1.83746			0.918730	+	0.394886i	$0.129216\pi$
$384$	1132.96	+	7439.05i	0.150562	+	0.988601i
$385$	−691.382			−0.0915224
$386$	3138.67	−	13546.6i	0.413870	−	1.78628i
$387$	13602.5	−	4936.81i	1.78671	−	0.648455i
$388$	−589.175	−	288.504i	−0.0770898	−	0.0377489i
$389$	−5584.87			−0.727928			−0.363964	−	0.931413i	$-0.618577\pi$
$389$	−5584.87			−0.727928			−0.363964	+	0.931413i	$0.618577\pi$
$390$	13.3259	−	248.372i	0.00173021	−	0.0322483i
$391$			4420.23i			0.571715i
$392$	2734.31	−	3360.40i	0.352304	−	0.432975i
$393$	−9255.31	+	1627.59i	−1.18796	+	0.208909i
$394$	1790.15	−	7726.37i	0.228900	−	0.987941i
$395$			2245.06i			0.285978i
$396$	138.235	−	1284.53i	0.0175418	−	0.163005i
$397$			8932.39i			1.12923i	0.825355	+	0.564614i	$0.190975\pi$
$397$			8932.39i			1.12923i	−0.825355	+	0.564614i	$0.809025\pi$
$398$	−6415.41	−	1486.41i	−0.807978	−	0.187203i
$399$	6124.88	−	1077.09i	0.768490	−	0.135143i
$400$	981.102	+	1263.90i	0.122638	+	0.157987i
$401$			11678.7i			1.45438i	0.686437	+	0.727190i	$0.259174\pi$
$401$			11678.7i			1.45438i	−0.686437	+	0.727190i	$0.740826\pi$
$402$	−10601.5	−	568.803i	−1.31532	−	0.0705704i
$403$	1009.97			0.124840
$404$	6950.17	+	3403.31i	0.855900	+	0.419112i
$405$	2796.52	−	2337.84i	0.343112	−	0.286835i
$406$	8282.47	+	1919.00i	1.01244	+	0.234577i
$407$	−2054.42			−0.250206
$408$	−2056.12	+	3684.89i	−0.249493	+	0.447130i
$409$	14133.7			1.70873			0.854363	−	0.519677i	$-0.173948\pi$
$409$	14133.7			1.70873			0.854363	+	0.519677i	$0.173948\pi$
$410$	−1678.72	−	388.948i	−0.202210	−	0.0468507i
$411$	5425.33	−	954.071i	0.651124	−	0.114503i
$412$	876.664	−	1790.30i	0.104830	−	0.214082i
$413$	−16578.7			−1.97527
$414$	1130.39	+	9337.44i	0.134192	+	1.10848i
$415$			3208.76i			0.379547i
$416$	256.765	+	556.315i	0.0302619	+	0.0655663i
$417$	874.867	+	4974.94i	0.102740	+	0.584230i
$418$	853.200	+	197.681i	0.0998358	+	0.0231313i
$419$			1591.89i			0.185606i	0.995684	+	0.0928031i	$0.0295827\pi$
$419$			1591.89i			0.185606i	−0.995684	+	0.0928031i	$0.970417\pi$
$420$	4616.24	+	1333.81i	0.536309	+	0.154960i
$421$		−	16858.0i		−	1.95156i	−0.218755	−	0.975780i	$-0.570200\pi$
$421$		−	16858.0i		−	1.95156i	0.218755	−	0.975780i	$-0.429800\pi$
$422$	−1404.38	+	6061.38i	−0.162001	+	0.699202i
$423$	−10192.7	+	3699.28i	−1.17160	+	0.425213i
$424$	−966.501	+	1187.81i	−0.110701	+	0.136050i
$425$			897.236i			0.102406i
$426$	−15170.5	−	813.940i	−1.72538	−	0.0925717i
$427$	−1046.56			−0.118610
$428$	3775.49	−	7710.22i	0.426391	−	0.870765i
$429$	−18.2198	−	103.607i	−0.00205049	−	0.0116601i
$430$	−1710.80	+	7383.90i	−0.191866	+	0.828100i
$431$	−4285.05			−0.478895			−0.239447	−	0.970909i	$-0.576966\pi$
$431$	−4285.05			−0.478895			−0.239447	+	0.970909i	$0.576966\pi$
$432$	−3401.07	+	8309.89i	−0.378783	+	0.925486i
$433$	2085.76			0.231490			0.115745	−	0.993279i	$-0.463075\pi$
$433$	2085.76			0.231490			0.115745	+	0.993279i	$0.463075\pi$
$434$	−4403.94	+	19007.6i	−0.487088	+	2.10229i
$435$	585.065	+	3326.98i	0.0644867	+	0.366704i
$436$	5379.58	−	10986.1i	0.590907	−	1.20674i
$437$	−6376.01			−0.697954
$438$	4864.38	+	260.987i	0.530659	+	0.0284714i
$439$			8505.99i			0.924758i	0.886682	+	0.462379i	$0.153004\pi$
$439$			8505.99i			0.924758i	−0.886682	+	0.462379i	$0.846996\pi$
$440$	524.891	+	427.095i	0.0568709	+	0.0462749i
$441$	4859.33	−	1763.61i	0.524710	−	0.190435i
$442$	−77.5536	+	334.725i	−0.00834581	+	0.0360209i
$443$		−	6358.72i		−	0.681968i	−0.940069	−	0.340984i	$-0.889240\pi$
$443$		−	6358.72i		−	0.681968i	0.940069	−	0.340984i	$-0.110760\pi$
$444$	13717.0	+	3963.37i	1.46617	+	0.423633i
$445$			4277.52i			0.455672i
$446$	−9692.33	−	2245.65i	−1.02903	−	0.238419i
$447$	−1207.05	−	6863.88i	−0.127721	−	0.726287i
$448$	−11589.4	+	2406.52i	−1.22221	+	0.253789i
$449$		−	972.079i		−	0.102172i	−0.998694	−	0.0510860i	$-0.983732\pi$
$449$		−	972.079i		−	0.102172i	0.998694	−	0.0510860i	$-0.0162683\pi$
$450$	229.451	+	1895.35i	0.0240365	+	0.198550i
$451$	−728.799			−0.0760927
$452$	−4882.95	+	9971.84i	−0.508130	+	1.03769i
$453$	1082.42	−	190.349i	0.112266	−	0.0197426i
$454$	12184.7	+	2823.11i	1.25959	+	0.291839i
$455$	391.254			0.0403127
$456$	−5315.31	−	2965.87i	−0.545860	−	0.304582i
$457$	−11365.4			−1.16335			−0.581676	−	0.813421i	$-0.697603\pi$
$457$	−11365.4			−1.16335			−0.581676	+	0.813421i	$0.697603\pi$
$458$	−5910.77	−	1369.49i	−0.603039	−	0.139720i
$459$	−4364.02	+	2511.58i	−0.443780	+	0.255404i
$460$	−4424.52	−	2166.57i	−0.448466	−	0.219602i
$461$	14030.9			1.41754			0.708770	−	0.705440i	$-0.249250\pi$
$461$	14030.9			1.41754			0.708770	+	0.705440i	$0.249250\pi$
$462$	2029.32	+	108.879i	0.204356	+	0.0109643i
$463$			2762.89i			0.277327i	0.990340	+	0.138663i	$0.0442806\pi$
$463$			2762.89i			0.277327i	−0.990340	+	0.138663i	$0.955719\pi$
$464$	−5102.53	−	6573.30i	−0.510515	−	0.657668i
$465$	−7635.14	+	1342.68i	−0.761444	+	0.133904i
$466$	15619.1	+	3618.84i	1.55266	+	0.359741i
$467$		−	227.711i		−	0.0225636i	−0.999936	−	0.0112818i	$-0.996409\pi$
$467$		−	227.711i		−	0.0225636i	0.999936	−	0.0112818i	$-0.00359118\pi$
$468$	−78.2273	+	726.916i	−0.00772662	+	0.0717985i
$469$		−	16700.3i		−	1.64424i
$470$	1281.95	−	5532.94i	0.125812	−	0.543012i
$471$	15985.2	−	2811.08i	1.56382	−	0.275006i
$472$	12586.4	+	10241.3i	1.22741	+	0.998720i
$473$			3205.64i			0.311619i
$474$	353.552	−	6589.62i	0.0342599	−	0.638547i
$475$	−1294.23			−0.125017
$476$	−5961.32	−	2919.11i	−0.574027	−	0.281086i
$477$	−1717.64	+	623.388i	−0.164875	+	0.0598386i
$478$	−3417.85	+	14751.6i	−0.327048	+	1.41155i
$479$	10261.4			0.978819			0.489409	−	0.872054i	$-0.337212\pi$
$479$	10261.4			0.978819			0.489409	+	0.872054i	$0.337212\pi$
$480$	−2680.66	−	3864.26i	−0.254906	−	0.367455i
$481$	1162.60			0.110208
$482$	−1977.21	+	8533.72i	−0.186845	+	0.806432i
$483$	−14571.5	+	2562.47i	−1.37273	+	0.241401i
$484$	−9305.99	−	4556.90i	−0.873966	−	0.427959i
$485$	410.012			0.0383870
$486$	−8576.41	+	6421.56i	−0.800481	+	0.599358i
$487$		−	6652.96i		−	0.619044i	−0.950892	−	0.309522i	$-0.899831\pi$
$487$		−	6652.96i		−	0.619044i	0.950892	−	0.309522i	$-0.100169\pi$
$488$	794.538	+	646.503i	0.0737030	+	0.0599709i
$489$	382.340	+	2174.18i	0.0353579	+	0.201063i
$490$	−611.163	+	2637.81i	−0.0563460	+	0.243192i
$491$			4760.67i			0.437568i	0.975773	+	0.218784i	$0.0702090\pi$
$491$			4760.67i			0.437568i	−0.975773	+	0.218784i	$0.929791\pi$
$492$	4866.07	+	1405.99i	0.445893	+	0.128835i
$493$		−	4666.36i		−	0.426292i
$494$	−482.827	−	111.868i	−0.0439745	−	0.0101886i
$495$	275.474	+	759.021i	0.0250134	+	0.0689202i
$496$	15085.2	−	11709.9i	1.36562	−	1.06006i
$497$		−	23897.7i		−	2.15686i
$498$	505.315	−	9418.25i	0.0454693	−	0.847473i
$499$	−1378.04			−0.123626			−0.0618132	−	0.998088i	$-0.519688\pi$
$499$	−1378.04			−0.123626			−0.0618132	+	0.998088i	$0.519688\pi$
$500$	−898.106	−	439.779i	−0.0803290	−	0.0393350i
$501$	−2122.84	−	12071.5i	−0.189304	−	1.07648i
$502$	−7190.40	−	1665.97i	−0.639289	−	0.148119i
$503$	−10833.7			−0.960342			−0.480171	−	0.877175i	$-0.659425\pi$
$503$	−10833.7			−0.960342			−0.480171	+	0.877175i	$0.659425\pi$
$504$	−13339.4	−	4641.92i	−1.17894	−	0.410253i
$505$	−4836.68			−0.426197
$506$	−2029.82	−	470.297i	−0.178333	−	0.0413187i
$507$	−1966.90	−	11184.8i	−0.172294	−	0.979751i
$508$	−7391.26	+	15094.2i	−0.645539	+	1.31830i
$509$	−1103.26			−0.0960731			−0.0480366	−	0.998846i	$-0.515296\pi$
$509$	−1103.26			−0.0960731			−0.0480366	+	0.998846i	$0.515296\pi$
$510$	141.297	−	2633.54i	0.0122681	−	0.228657i
$511$			7662.72i			0.663363i
$512$	10285.2	+	5332.25i	0.887783	+	0.460262i
$513$	−3622.86	−	6294.93i	−0.311799	−	0.541770i
$514$	−2468.27	−	571.882i	−0.211811	−	0.0490752i
$515$			1245.89i			0.106603i
$516$	6184.30	−	21403.5i	0.527614	−	1.82604i
$517$		−	2402.07i		−	0.204338i
$518$	−5069.46	+	21880.0i	−0.429999	+	1.85589i
$519$	−3149.56	−	17910.0i	−0.266378	−	1.51476i
$520$	−297.036	−	241.694i	−0.0250498	−	0.0203826i
$521$			11844.2i			0.995973i	0.867185	+	0.497987i	$0.165927\pi$
$521$			11844.2i			0.995973i	−0.867185	+	0.497987i	$0.834073\pi$
$522$	−1193.33	−	9857.36i	−0.100059	−	0.826523i
$523$	−1501.84			−0.125566			−0.0627830	−	0.998027i	$-0.519998\pi$
$523$	−1501.84			−0.125566			−0.0627830	+	0.998027i	$0.519998\pi$
$524$	−6362.78	+	12993.9i	−0.530457	+	1.08329i
$525$	−2957.79	+	520.141i	−0.245883	+	0.0432396i
$526$	−2172.44	+	9376.35i	−0.180082	+	0.777240i
$527$	10708.9			0.885176
$528$	−1473.38	−	1336.25i	−0.121441	−	0.110138i
$529$	3001.99			0.246732
$530$	216.029	−	932.391i	0.0177051	−	0.0764160i
$531$	6605.62	+	18200.6i	0.539848	+	1.48746i
$532$	4210.69	−	8598.97i	0.343152	−	0.700776i
$533$	412.428			0.0335164
$534$	673.623	−	12555.2i	0.0545890	−	1.01745i
$535$			5365.61i			0.433599i
$536$	−10316.5	+	12678.7i	−0.831350	+	1.02171i
$537$	−3037.63	+	534.182i	−0.244104	+	0.0429268i
$538$	−2562.99	+	11062.0i	−0.205387	+	0.886461i
$539$			1145.18i			0.0915144i
$540$	−374.996	−	5599.30i	−0.0298838	−	0.446214i
$541$		−	2857.50i		−	0.227086i	−0.993533	−	0.113543i	$-0.963780\pi$
$541$		−	2857.50i		−	0.227086i	0.993533	−	0.113543i	$-0.0362200\pi$
$542$	−5914.67	−	1370.39i	−0.468739	−	0.108604i
$543$	1824.75	−	320.891i	0.144213	−	0.0253605i
$544$	2722.53	+	5898.71i	0.214573	+	0.464899i
$545$			7645.29i			0.600896i
$546$	−1148.40	−	61.6147i	−0.0900125	−	0.00482942i
$547$	15011.2			1.17337			0.586683	−	0.809817i	$-0.300434\pi$
$547$	15011.2			1.17337			0.586683	+	0.809817i	$0.300434\pi$
$548$	3729.77	−	7616.85i	0.290745	−	0.593752i
$549$	416.991	+	1148.95i	0.0324167	+	0.0893185i
$550$	−412.022	−	95.4628i	−0.0319430	−	0.00740100i
$551$	6731.03			0.520421
$552$	12645.5	+	7056.02i	0.975051	+	0.544065i
$553$	10380.5			0.798231
$554$	322.577	+	74.7391i	0.0247383	+	0.00573170i
$555$	−8788.96	+	1545.58i	−0.672199	+	0.118209i
$556$	6984.53	+	3420.14i	0.532752	+	0.260875i
$557$	−1755.01			−0.133505			−0.0667525	−	0.997770i	$-0.521264\pi$
$557$	−1755.01			−0.133505			−0.0667525	+	0.997770i	$0.521264\pi$
$558$	22621.9	−	2738.60i	1.71624	−	0.207767i
$559$		−	1814.08i		−	0.137258i
$560$	5843.87	−	4536.31i	0.440980	−	0.342311i
$561$	−193.188	−	1098.56i	−0.0145390	−	0.0826762i
$562$	11507.6	+	2666.23i	0.863733	+	0.200121i
$563$		−	4692.16i		−	0.351245i	−0.984458	−	0.175623i	$-0.943806\pi$
$563$		−	4692.16i		−	0.351245i	0.984458	−	0.175623i	$-0.0561938\pi$
$564$	−4634.06	+	16038.2i	−0.345973	+	1.19740i
$565$		−	6939.49i		−	0.516720i
$566$	2383.95	−	10289.2i	0.177041	−	0.764115i
$567$	−10809.4	−	12930.2i	−0.800625	−	0.957705i
$568$	−14762.6	+	18142.9i	−1.09053	+	1.34024i
$569$		−	1379.39i		−	0.101629i	−0.998708	−	0.0508146i	$-0.983818\pi$
$569$		−	1379.39i		−	0.101629i	0.998708	−	0.0508146i	$-0.0161817\pi$
$570$	3798.77	+	203.815i	0.279146	+	0.0149770i
$571$	885.908			0.0649283			0.0324642	−	0.999473i	$-0.489665\pi$
$571$	885.908			0.0649283			0.0324642	+	0.999473i	$0.489665\pi$
$572$	−145.458	−	71.2271i	−0.0106327	−	0.00520656i
$573$	2890.83	+	16438.8i	0.210761	+	1.19850i
$574$	−1798.38	+	7761.87i	−0.130771	+	0.564415i
$575$	3079.06			0.223314
$576$	7259.64	+	11764.4i	0.525147	+	0.851011i
$577$	−8524.86			−0.615069			−0.307534	−	0.951537i	$-0.599504\pi$
$577$	−8524.86			−0.615069			−0.307534	+	0.951537i	$0.599504\pi$
$578$	2314.23	−	9988.31i	0.166538	−	0.718787i
$579$	−4424.49	−	25159.9i	−0.317574	−	1.80589i
$580$	4670.88	+	2287.21i	0.334393	+	0.163743i
$581$	14836.3			1.05940
$582$	−1203.45	−	64.5687i	−0.0857127	−	0.00459873i
$583$		−	404.788i		−	0.0287558i
$584$	4733.57	−	5817.46i	0.335405	−	0.412206i
$585$	−155.891	−	429.531i	−0.0110176	−	0.0303572i
$586$	1707.96	−	7371.63i	0.120401	−	0.519657i
$587$		−	9805.07i		−	0.689435i	−0.938706	−	0.344718i	$-0.887975\pi$
$587$		−	9805.07i		−	0.689435i	0.938706	−	0.344718i	$-0.112025\pi$
$588$	2209.27	−	7646.15i	0.154947	−	0.536262i
$589$			15447.2i			1.08063i
$590$	−9879.90	−	2289.11i	−0.689405	−	0.159731i
$591$	−2523.53	−	14350.1i	−0.175641	−	0.998786i
$592$	17364.9	−	13479.5i	1.20556	−	0.935816i
$593$		−	6218.84i		−	0.430653i	−0.976542	−	0.215326i	$-0.930918\pi$
$593$		−	6218.84i		−	0.430653i	0.976542	−	0.215326i	$-0.0690815\pi$
$594$	−689.032	−	2271.24i	−0.0475948	−	0.156885i
$595$	4148.54			0.285838
$596$	−9636.49	−	4718.74i	−0.662292	−	0.324307i
$597$	−11915.2	+	2095.35i	−0.816847	+	0.143646i
$598$	1148.68	+	266.142i	0.0785502	+	0.0181996i
$599$	−16692.3			−1.13861			−0.569307	−	0.822125i	$-0.692788\pi$
$599$	−16692.3			−1.13861			−0.569307	+	0.822125i	$0.692788\pi$
$600$	2566.83	+	1432.26i	0.174651	+	0.0974528i
$601$	−13545.9			−0.919380			−0.459690	−	0.888080i	$-0.652039\pi$
$601$	−13545.9			−0.919380			−0.459690	+	0.888080i	$0.652039\pi$
$602$	34140.8	+	7910.21i	2.31142	+	0.535542i
$603$	−18334.1	+	6654.07i	−1.23818	+	0.449378i
$604$	744.138	−	1519.66i	0.0501300	−	0.102374i
$605$	6476.12			0.435193
$606$	14196.5	+	761.680i	0.951637	+	0.0510580i
$607$			7956.60i			0.532041i	0.963967	+	0.266020i	$0.0857088\pi$
$607$			7956.60i			0.532041i	−0.963967	+	0.266020i	$0.914291\pi$
$608$	−8508.65	+	3927.14i	−0.567551	+	0.261952i
$609$	15382.9	−	2705.16i	1.02356	−	0.179997i
$610$	−623.686	−	144.504i	−0.0413972	−	0.00959148i
$611$			1359.34i			0.0900046i
$612$	−829.458	+	7707.62i	−0.0547857	+	0.509088i
$613$		−	4425.02i		−	0.291558i	−0.989317	−	0.145779i	$-0.953431\pi$
$613$		−	4425.02i		−	0.291558i	0.989317	−	0.145779i	$-0.0465688\pi$
$614$	6017.78	−	25973.0i	0.395534	−	1.70714i
$615$	−3117.86	+	548.290i	−0.204429	+	0.0359499i
$616$	1974.75	−	2426.93i	0.129164	−	0.158740i
$617$		−	15603.2i		−	1.01809i	−0.860740	−	0.509044i	$-0.829999\pi$
$617$		−	15603.2i		−	1.01809i	0.860740	−	0.509044i	$-0.170001\pi$
$618$	196.202	−	3656.89i	0.0127709	−	0.238028i
$619$	21017.9			1.36475			0.682376	−	0.731002i	$-0.260947\pi$
$619$	21017.9			1.36475			0.682376	+	0.731002i	$0.260947\pi$
$620$	−5248.96	+	10719.3i	−0.340005	+	0.694351i
$621$	8619.04	+	14976.1i	0.556957	+	0.967745i
$622$	1438.83	−	6210.07i	0.0927524	−	0.400324i
$623$	19777.9			1.27189
$624$	833.789	+	756.188i	0.0534908	+	0.0485124i
$625$	625.000			0.0400000
$626$	4201.52	−	18134.0i	0.268253	−	1.15779i
$627$	1584.63	−	278.665i	0.100932	−	0.0177493i
$628$	10989.4	−	22442.3i	0.698290	−	1.42603i
$629$	12327.2			0.781429
$630$	8763.51	−	1060.91i	0.554201	−	0.0670914i
$631$			485.261i			0.0306148i	0.999883	+	0.0153074i	$0.00487268\pi$
$631$			485.261i			0.0306148i	−0.999883	+	0.0153074i	$0.995127\pi$
$632$	−7880.74	−	6412.43i	−0.496011	−	0.403596i
$633$	1979.72	+	11257.7i	0.124308	+	0.706877i
$634$	−2659.99	+	11480.6i	−0.166627	+	0.719171i
$635$		−	10504.2i		−	0.656452i
$636$	−780.914	+	2702.70i	−0.0486875	+	0.168505i
$637$		−	648.057i		−	0.0403092i
$638$	2142.85	+	496.484i	0.132972	+	0.0308088i
$639$	−26235.6	+	9521.78i	−1.62420	+	0.589477i
$640$	−7238.87	−	166.074i	−0.447096	−	0.0102573i
$641$			19080.5i			1.17572i	0.808963	+	0.587859i	$0.200029\pi$
$641$			19080.5i			1.17572i	−0.808963	+	0.587859i	$0.799971\pi$
$642$	844.976	−	15749.0i	0.0519448	−	0.968165i
$643$	5746.66			0.352451			0.176226	−	0.984350i	$-0.443611\pi$
$643$	5746.66			0.352451			0.176226	+	0.984350i	$0.443611\pi$
$644$	−10017.5	+	20457.6i	−0.612960	+	1.25177i
$645$	2411.67	+	13714.0i	0.147224	+	0.837190i
$646$	−5119.50	−	1186.16i	−0.311802	−	0.0722425i
$647$	−19272.4			−1.17106			−0.585529	−	0.810652i	$-0.699113\pi$
$647$	−19272.4			−1.17106			−0.585529	+	0.810652i	$0.699113\pi$
$648$	218.899	+	16493.9i	0.0132703	+	0.999912i
$649$	−4289.26			−0.259427
$650$	233.164	+	54.0225i	0.0140699	+	0.00325991i
$651$	6208.12	+	35302.5i	0.373756	+	2.12537i
$652$	3052.43	+	1494.69i	0.183347	+	0.0897802i
$653$	21075.3			1.26300			0.631501	−	0.775375i	$-0.282439\pi$
$653$	21075.3			1.26300			0.631501	+	0.775375i	$0.282439\pi$
$654$	1203.98	−	22440.2i	0.0719868	−	1.34171i
$655$		−	9042.58i		−	0.539424i
$656$	6160.13	−	4781.81i	0.366635	−	0.284601i
$657$	8412.37	−	3053.13i	0.499540	−	0.181300i
$658$	−25582.6	−	5927.32i	−1.51567	−	0.351172i
$659$		−	12251.3i		−	0.724194i	−0.932140	−	0.362097i	$-0.882061\pi$
$659$		−	12251.3i		−	0.724194i	0.932140	−	0.362097i	$-0.117939\pi$
$660$	1194.32	+	345.084i	0.0704376	+	0.0203521i
$661$			20389.7i			1.19980i	0.800074	+	0.599901i	$0.204793\pi$
$661$			20389.7i			1.19980i	−0.800074	+	0.599901i	$0.795207\pi$
$662$	−4201.95	+	18135.8i	−0.246697	+	1.06476i
$663$	109.325	+	621.678i	0.00640398	+	0.0364163i
$664$	−11263.6	−	9164.99i	−0.658301	−	0.535648i
$665$			5984.10i			0.348953i
$666$	26040.4	−	3152.45i	1.51509	−	0.183416i
$667$	−16013.6			−0.929610
$668$	−16947.8	−	8298.87i	−0.981629	−	0.480678i
$669$	−18001.4	+	3165.63i	−1.04032	+	0.182945i
$670$	2305.90	−	9952.37i	0.132962	−	0.573871i
$671$	−270.767			−0.0155780
$672$	−17867.1	+	12394.5i	−1.02565	+	0.711502i
$673$	7328.14			0.419731			0.209866	−	0.977730i	$-0.432697\pi$
$673$	7328.14			0.419731			0.209866	+	0.977730i	$0.432697\pi$
$674$	−4831.85	+	20854.5i	−0.276136	+	1.19182i
$675$	1749.53	+	3039.91i	0.0997619	+	0.173342i
$676$	−15702.8	−	7689.25i	−0.893423	−	0.437486i
$677$	22608.3			1.28347			0.641735	−	0.766926i	$-0.278215\pi$
$677$	22608.3			1.28347			0.641735	+	0.766926i	$0.278215\pi$
$678$	−1092.83	+	20368.6i	−0.0619025	+	1.15376i
$679$		−	1895.77i		−	0.107147i
$680$	−3149.53	−	2562.72i	−0.177616	−	0.144523i
$681$	22630.4	−	3979.66i	1.27342	−	0.223937i
$682$	−1139.39	+	4917.67i	−0.0639730	+	0.276110i
$683$			19092.3i			1.06961i	0.844975	+	0.534806i	$0.179615\pi$
$683$			19092.3i			1.06961i	−0.844975	+	0.534806i	$0.820385\pi$
$684$	−11117.9	−	1196.46i	−0.621498	−	0.0668828i
$685$			5300.64i			0.295660i
$686$	−9653.17	−	2236.58i	−0.537259	−	0.124480i
$687$	−10978.0	+	1930.53i	−0.609659	+	0.107211i
$688$	−21032.9	−	27095.5i	−1.16551	−	1.50146i
$689$			229.070i			0.0126660i
$690$	−9037.56	−	484.890i	−0.498629	−	0.0267528i
$691$	−20013.4			−1.10180			−0.550901	−	0.834571i	$-0.685716\pi$
$691$	−20013.4			−1.10180			−0.550901	+	0.834571i	$0.685716\pi$
$692$	−25144.6	−	12312.6i	−1.38129	−	0.676382i
$693$	3509.48	−	1273.71i	0.192372	−	0.0698183i
$694$	7374.14	+	1708.54i	0.403341	+	0.0934515i
$695$	−4860.60			−0.265285
$696$	−13349.6	−	7448.91i	−0.727035	−	0.405675i
$697$	4373.05			0.237649
$698$	11479.0	+	2659.62i	0.622475	+	0.144223i
$699$	29009.0	−	5101.38i	1.56970	−	0.276040i
$700$	−2033.40	+	4152.56i	−0.109793	+	0.224217i
$701$	−12648.4			−0.681490			−0.340745	−	0.940156i	$-0.610679\pi$
$701$	−12648.4			−0.681490			−0.340745	+	0.940156i	$0.610679\pi$
$702$	389.924	+	1285.30i	0.0209640	+	0.0691031i
$703$			17781.5i			0.953974i
$704$	−2998.42	+	622.617i	−0.160522	+	0.0333320i
$705$	−1807.13	−	10276.2i	−0.0965394	−	0.548972i
$706$	6673.01	+	1546.09i	0.355725	+	0.0824193i
$707$			22363.3i			1.18962i
$708$	28638.7	+	8274.81i	1.52021	+	0.439246i
$709$		−	28034.9i		−	1.48501i	−0.669840	−	0.742505i	$-0.733637\pi$
$709$		−	28034.9i		−	1.48501i	0.669840	−	0.742505i	$-0.266363\pi$
$710$	3299.68	−	14241.6i	0.174415	−	0.752783i
$711$	−4135.98	−	11396.0i	−0.218160	−	0.601101i
$712$	−15015.2	−	12217.6i	−0.790334	−	0.643082i
$713$		−	36750.0i		−	1.93029i
$714$	−12176.7	−	653.311i	−0.638235	−	0.0342431i
$715$	101.226			0.00529458
$716$	−2088.29	+	4264.66i	−0.108999	+	0.222595i
$717$	4818.05	+	27397.9i	0.250953	+	1.42705i
$718$	321.439	−	1387.34i	0.0167075	−	0.0721104i
$719$	10251.3			0.531721			0.265861	−	0.964011i	$-0.414344\pi$
$719$	10251.3			0.531721			0.265861	+	0.964011i	$0.414344\pi$
$720$	−7308.53	−	4608.14i	−0.378296	−	0.238521i
$721$	5760.59			0.297553
$722$	−2667.92	+	11514.9i	−0.137520	+	0.593544i
$723$	2787.22	+	15849.5i	0.143372	+	0.815284i
$724$	1254.47	−	2561.84i	0.0643949	−	0.131506i
$725$	−3250.51			−0.166512
$726$	−19008.5	−	1019.86i	−0.971724	−	0.0521357i
$727$			34232.2i			1.74636i	0.487399	+	0.873179i	$0.337946\pi$
$727$			34232.2i			1.74636i	−0.487399	+	0.873179i	$0.662054\pi$
$728$	−1117.52	+	1373.40i	−0.0568927	+	0.0699199i
$729$	−9888.31	+	17018.9i	−0.502378	+	0.864648i
$730$	−1058.03	+	4566.51i	−0.0536432	+	0.231526i
$731$		−	19235.0i		−	0.973231i
$732$	1807.87	+	522.362i	0.0912851	+	0.0263757i
$733$			4436.80i			0.223570i	0.993732	+	0.111785i	$0.0356568\pi$
$733$			4436.80i			0.223570i	−0.993732	+	0.111785i	$0.964343\pi$
$734$	5592.43	+	1295.73i	0.281226	+	0.0651584i
$735$	861.540	+	4899.15i	0.0432359	+	0.245861i
$736$	20242.7	−	9342.95i	1.01380	−	0.467915i
$737$		−	4320.72i		−	0.215951i
$738$	9237.77	−	1118.32i	0.460768	−	0.0557805i
$739$	−28539.2			−1.42061			−0.710306	−	0.703893i	$-0.751444\pi$
$739$	−28539.2			−1.42061			−0.710306	+	0.703893i	$0.751444\pi$
$740$	−6042.18	+	12339.2i	−0.300155	+	0.612970i
$741$	−896.746	+	157.697i	−0.0444572	+	0.00781802i
$742$	−4311.08	−	998.851i	−0.213295	−	0.0494191i
$743$	−22962.3			−1.13379			−0.566894	−	0.823791i	$-0.691855\pi$
$743$	−22962.3			−1.13379			−0.566894	+	0.823791i	$0.691855\pi$
$744$	17094.6	−	30636.3i	0.842366	−	1.50965i
$745$	6706.12			0.329790
$746$	−17470.0	−	4047.69i	−0.857403	−	0.198655i
$747$	−5911.37	−	16287.8i	−0.289539	−	0.797775i
$748$	−1542.32	−	755.233i	−0.0753914	−	0.0369172i
$749$	24808.9			1.21028
$750$	−1834.48	−	98.4249i	−0.0893143	−	0.00479196i
$751$			16176.5i			0.786003i	0.919538	+	0.393001i	$0.128563\pi$
$751$			16176.5i			0.786003i	−0.919538	+	0.393001i	$0.871437\pi$
$752$	15760.5	+	20303.4i	0.764264	+	0.984558i
$753$	−13354.6	+	2348.47i	−0.646307	+	0.113656i
$754$	−1212.64	−	280.961i	−0.0585700	−	0.0135703i
$755$			1057.54i			0.0509775i
$756$	−25889.4	+	1733.87i	−1.24549	+	0.0834128i
$757$		−	39134.4i		−	1.87895i	−0.342616	−	0.939475i	$-0.611313\pi$
$757$		−	39134.4i		−	1.87895i	0.342616	−	0.939475i	$-0.388687\pi$
$758$	−4994.33	+	21555.7i	−0.239317	+	1.03290i
$759$	−3769.96	+	662.965i	−0.180291	+	0.0317050i
$760$	3696.62	−	4543.07i	0.176435	−	0.216835i
$761$		−	22590.6i		−	1.07610i	−0.842914	−	0.538048i	$-0.819162\pi$
$761$		−	22590.6i		−	1.07610i	0.842914	−	0.538048i	$-0.180838\pi$
$762$	−1654.20	+	30831.6i	−0.0786423	+	1.46576i
$763$	35349.4			1.67724
$764$	23079.1	+	11301.2i	1.09289	+	0.535162i
$765$	−1652.94	−	4554.40i	−0.0781206	−	0.215248i
$766$	8792.66	−	37949.5i	0.414741	−	1.79004i
$767$	2427.30			0.114269
$768$	21221.1	+	1627.43i	0.997072	+	0.0764647i
$769$	−31121.3			−1.45938			−0.729689	−	0.683779i	$-0.760335\pi$
$769$	−31121.3			−1.45938			−0.729689	+	0.683779i	$0.760335\pi$
$770$	−441.390	+	1905.06i	−0.0206579	+	0.0891605i
$771$	−4584.28	+	806.167i	−0.214136	+	0.0376568i
$772$	−35323.1	−	17296.8i	−1.64677	−	0.806379i
$773$	−8798.80			−0.409406			−0.204703	−	0.978824i	$-0.565623\pi$
$773$	−8798.80			−0.409406			−0.204703	+	0.978824i	$0.565623\pi$
$774$	−4918.97	−	40632.6i	−0.228435	−	1.88696i
$775$		−	7459.66i		−	0.345753i
$776$	−1171.09	+	1439.25i	−0.0541750	+	0.0665799i
$777$	7146.28	+	40637.4i	0.329950	+	1.87627i
$778$	−3565.47	+	15388.7i	−0.164304	+	0.709143i
$779$			6307.95i			0.290123i
$780$	−675.867	−	195.284i	−0.0310255	−	0.00896446i
$781$		−	6182.83i		−	0.283277i
$782$	12179.7	+	2821.95i	0.556961	+	0.129044i
$783$	−9098.96	−	15810.0i	−0.415288	−	0.721587i
$784$	−7513.75	−	9679.54i	−0.342281	−	0.440941i
$785$			15617.8i			0.710094i
$786$	−1424.03	+	26541.5i	−0.0646225	+	1.20446i
$787$	1273.98			0.0577032			0.0288516	−	0.999584i	$-0.490815\pi$
$787$	1273.98			0.0577032			0.0288516	+	0.999584i	$0.490815\pi$
$788$	−20146.7	−	9865.29i	−0.910780	−	0.445985i
$789$	3062.43	+	17414.5i	0.138182	+	0.785772i
$790$	6186.12	+	1433.28i	0.278598	+	0.0645493i
$791$	−32086.0			−1.44229
$792$	−3451.18	−	1200.96i	−0.154839	−	0.0538817i
$793$	153.228			0.00686162
$794$	24612.6	+	5702.59i	1.10009	+	0.254883i
$795$	−304.530	−	1731.71i	−0.0135856	−	0.0772548i
$796$	−8191.41	+	16728.3i	−0.364745	+	0.744873i
$797$	−12686.8			−0.563853			−0.281927	−	0.959436i	$-0.590973\pi$
$797$	−12686.8			−0.563853			−0.281927	+	0.959436i	$0.590973\pi$
$798$	942.376	−	17564.3i	0.0418042	−	0.779161i
$799$			14413.3i			0.638179i
$800$	4108.94	−	1896.47i	0.181591	−	0.0838129i
$801$	−7880.30	−	21712.8i	−0.347611	−	0.957783i
$802$	32179.9	+	7455.87i	1.41685	+	0.328274i
$803$			1982.50i			0.0871246i
$804$	−8335.50	+	28848.7i	−0.365635	+	1.26544i
$805$		−	14236.6i		−	0.623323i
$806$	644.784	−	2782.91i	0.0281781	−	0.121618i
$807$	3612.98	+	20545.2i	0.157600	+	0.896192i
$808$	13814.7	−	16978.0i	0.601485	−	0.739213i
$809$			32453.4i			1.41038i	0.709017	+	0.705192i	$0.249139\pi$
$809$			32453.4i			1.41038i	−0.709017	+	0.705192i	$0.750861\pi$
$810$	−4656.43	−	9198.15i	−0.201988	−	0.399000i
$811$	−12428.5			−0.538131			−0.269065	−	0.963122i	$-0.586715\pi$
$811$	−12428.5			−0.538131			−0.269065	+	0.963122i	$0.586715\pi$
$812$	10575.3	−	21596.7i	0.457046	−	0.933369i
$813$	−10985.2	+	1931.80i	−0.473885	+	0.0833349i
$814$	−1311.58	+	5660.82i	−0.0564750	+	0.243749i
$815$	−2124.21			−0.0912980
$816$	8840.82	+	8018.00i	0.379277	+	0.343978i
$817$	27745.7			1.18813
$818$	9023.22	−	38944.6i	0.385684	−	1.66463i
$819$	−1986.02	+	720.792i	−0.0847340	+	0.0307528i
$820$	−2143.44	+	4377.29i	−0.0912833	+	0.186417i
$821$	4341.15			0.184540			0.0922699	−	0.995734i	$-0.470588\pi$
$821$	4341.15			0.184540			0.0922699	+	0.995734i	$0.470588\pi$
$822$	834.744	−	15558.3i	0.0354197	−	0.660166i
$823$		−	17283.8i		−	0.732048i	−0.930605	−	0.366024i	$-0.880719\pi$
$823$		−	17283.8i		−	0.732048i	0.930605	−	0.366024i	$-0.119281\pi$
$824$	−4373.39	−	3558.55i	−0.184896	−	0.150447i
$825$	−765.241	+	134.571i	−0.0322937	+	0.00567899i
$826$	−10584.1	+	45681.6i	−0.445846	+	1.92429i
$827$			22909.3i			0.963284i	0.876368	+	0.481642i	$0.159959\pi$
$827$			22909.3i			0.963284i	−0.876368	+	0.481642i	$0.840041\pi$
$828$	26450.4	+	2846.47i	1.11016	+	0.119470i
$829$			25856.8i			1.08329i	0.840609	+	0.541643i	$0.182197\pi$
$829$			25856.8i			1.08329i	−0.840609	+	0.541643i	$0.817803\pi$
$830$	8841.53	+	2048.53i	0.369752	+	0.0856692i
$831$	599.118	−	105.358i	0.0250098	−	0.00439810i
$832$	1696.81	−	352.340i	0.0707048	−	0.0146817i
$833$		−	6871.47i		−	0.285813i
$834$	14266.7	+	765.446i	0.592343	+	0.0317809i
$835$	11794.1			0.488804
$836$	1089.39	−	2224.73i	0.0450688	−	0.0920383i
$837$	36282.7	−	20881.4i	1.49834	−	0.862325i
$838$	4386.35	+	1016.29i	0.180816	+	0.0418940i
$839$	13028.4			0.536101			0.268051	−	0.963405i	$-0.413621\pi$
$839$	13028.4			0.536101			0.268051	+	0.963405i	$0.413621\pi$
$840$	6622.31	−	11868.2i	0.272014	−	0.487492i
$841$	−7483.71			−0.306848
$842$	−46451.0	−	10762.4i	−1.90120	−	0.440495i
$843$	21372.8	−	3758.52i	0.873214	−	0.153559i
$844$	15805.1	+	7739.37i	0.644592	+	0.315640i
$845$	10927.7			0.444881
$846$	3685.91	+	30447.1i	0.149792	+	1.23734i
$847$		−	29943.6i		−	1.21473i
$848$	2655.90	+	3421.45i	0.107552	+	0.138553i
$849$	−3360.59	−	19110.0i	−0.135848	−	0.772503i
$850$	2472.28	+	572.811i	0.0997628	+	0.0231144i
$851$		−	42303.6i		−	1.70405i
$852$	−11927.9	+	41281.7i	−0.479627	+	1.65996i
$853$		−	36530.1i		−	1.46632i	−0.680058	−	0.733158i	$-0.738045\pi$
$853$		−	36530.1i		−	1.46632i	0.680058	−	0.733158i	$-0.261955\pi$
$854$	−668.142	+	2883.73i	−0.0267721	+	0.115549i
$855$	6569.54	−	2384.30i	0.262776	−	0.0953701i
$856$	−18834.7	−	15325.5i	−0.752051	−	0.611932i
$857$		−	7069.49i		−	0.281784i	−0.990025	−	0.140892i	$-0.955003\pi$
$857$		−	7069.49i		−	0.281784i	0.990025	−	0.140892i	$-0.0449971\pi$
$858$	−297.114	−	15.9410i	−0.0118220	−	0.000634285i
$859$	23413.2			0.929974			0.464987	−	0.885317i	$-0.346059\pi$
$859$	23413.2			0.929974			0.464987	+	0.885317i	$0.346059\pi$
$860$	19253.6	+	9428.01i	0.763423	+	0.373828i
$861$	2535.12	+	14416.0i	0.100345	+	0.570611i
$862$	−2735.65	+	11807.2i	−0.108093	+	0.466536i
$863$	−31192.2			−1.23035			−0.615177	−	0.788389i	$-0.710915\pi$
$863$	−31192.2			−1.23035			−0.615177	+	0.788389i	$0.710915\pi$
$864$	20726.1	+	14676.6i	0.816105	+	0.577903i
$865$	17498.3			0.687817
$866$	1331.58	−	5747.16i	0.0522505	−	0.225516i
$867$	−3262.30	−	18551.1i	−0.127790	−	0.726677i
$868$	49562.7	+	24269.6i	1.93810	+	0.949035i
$869$	2685.64			0.104838
$870$	9540.78	+	511.890i	0.371796	+	0.0199479i
$871$			2445.10i			0.0951196i
$872$	−26836.9	−	21836.8i	−1.04222	−	0.848035i
$873$	−2081.24	+	755.349i	−0.0806863	+	0.0292837i
$874$	−4070.55	+	17568.7i	−0.157538	+	0.679942i
$875$		−	2889.80i		−	0.111649i
$876$	3824.63	−	13236.9i	0.147514	−	0.510539i
$877$			5427.10i			0.208962i	0.994527	+	0.104481i	$0.0333182\pi$
$877$			5427.10i			0.208962i	−0.994527	+	0.104481i	$0.966682\pi$
$878$	23437.7	+	5430.37i	0.900894	+	0.208731i
$879$	−2407.66	−	13691.2i	−0.0923873	−	0.525361i
$880$	1511.93	−	1173.64i	0.0579173	−	0.0449583i
$881$			30444.6i			1.16425i	0.813100	+	0.582124i	$0.197778\pi$
$881$			30444.6i			1.16425i	−0.813100	+	0.582124i	$0.802222\pi$
$882$	−1757.24	−	14515.5i	−0.0670856	−	0.554152i
$883$	−19742.5			−0.752423			−0.376211	−	0.926534i	$-0.622773\pi$
$883$	−19742.5			−0.752423			−0.376211	+	0.926534i	$0.622773\pi$
$884$	872.801	+	427.388i	0.0332075	+	0.0162609i
$885$	−18349.8	+	3226.90i	−0.696973	+	0.122566i
$886$	−17521.0	−	4059.51i	−0.664369	−	0.153930i
$887$	42628.0			1.61365			0.806825	−	0.590791i	$-0.201184\pi$
$887$	42628.0			1.61365			0.806825	+	0.590791i	$0.201184\pi$
$888$	19678.0	−	35266.0i	0.743637	−	1.33271i
$889$	−48568.2			−1.83231
$890$	11786.4	+	2730.84i	0.443912	+	0.102852i
$891$	−2796.63	−	3345.32i	−0.105152	−	0.125783i
$892$	−12375.5	+	25272.9i	−0.464532	+	0.948655i
$893$	−20790.6			−0.779093
$894$	−19683.6	−	1056.08i	−0.736373	−	0.0395085i
$895$		−	2967.82i		−	0.110842i
$896$	−767.875	+	33470.3i	−0.0286305	+	1.24795i
$897$	2133.42	−	375.173i	0.0794125	−	0.0139651i
$898$	−2678.50	−	620.592i	−0.0995353	−	0.0230617i
$899$			38796.3i			1.43930i
$900$	5369.00	+	577.787i	0.198852	+	0.0213995i
$901$			2428.87i			0.0898085i
$902$	−465.277	+	2008.16i	−0.0171752	+	0.0741290i
$903$	63409.2	−	11150.8i	2.33679	−	0.410936i
$904$	24359.4	+	19820.8i	0.896218	+	0.729238i
$905$			1782.81i			0.0654835i
$906$	166.542	−	3104.07i	0.00610705	−	0.113825i
$907$	−38664.1			−1.41546			−0.707729	−	0.706484i	$-0.750280\pi$
$907$	−38664.1			−1.41546			−0.707729	+	0.706484i	$0.750280\pi$
$908$	15557.8	−	31771.7i	0.568616	−	1.16121i
$909$	24551.1	−	8910.43i	0.895831	−	0.325127i
$910$	249.783	−	1078.08i	0.00909916	−	0.0392724i
$911$	42923.8			1.56107			0.780533	−	0.625115i	$-0.214948\pi$
$911$	42923.8			1.56107			0.780533	+	0.625115i	$0.214948\pi$
$912$	−11565.6	+	12752.5i	−0.419931	+	0.463024i
$913$	3838.46			0.139140
$914$	−7255.87	+	31316.7i	−0.262585	+	1.13333i
$915$	−1158.36	+	203.704i	−0.0418517	+	0.00735981i
$916$	−7547.07	+	15412.4i	−0.272229	+	0.555940i
$917$	−41810.1			−1.50566
$918$	4134.43	+	13628.2i	0.148646	+	0.489976i
$919$			8118.05i			0.291393i	0.989329	+	0.145696i	$0.0465422\pi$
$919$			8118.05i			0.291393i	−0.989329	+	0.145696i	$0.953458\pi$
$920$	−8794.53	+	10808.3i	−0.315160	+	0.387325i
$921$	−8483.10	−	48239.2i	−0.303505	−	1.72588i
$922$	8957.59	−	38661.3i	0.319959	−	1.38096i
$923$			3498.87i			0.124774i
$924$	1595.56	−	5522.16i	0.0568075	−	0.196608i
$925$		−	8586.95i		−	0.305229i
$926$	7612.96	+	1763.87i	0.270170	+	0.0625966i
$927$	−2295.25	−	6324.16i	−0.0813224	−	0.224070i
$928$	−21369.8	+	9863.18i	−0.755926	+	0.348895i
$929$		−	25104.2i		−	0.886588i	−0.896376	−	0.443294i	$-0.853810\pi$
$929$		−	25104.2i		−	0.886588i	0.896376	−	0.443294i	$-0.146190\pi$
$930$	−1174.75	+	21895.3i	−0.0414209	+	0.772018i
$931$	9911.82			0.348922
$932$	19943.0	−	40727.0i	0.700915	−	1.43139i
$933$	−2028.29	−	11533.9i	−0.0711716	−	0.404718i
$934$	−627.442	−	145.374i	−0.0219813	−	0.00509293i
$935$	1073.31			0.0375413
$936$	1953.03	+	679.626i	0.0682016	+	0.0237332i
$937$	35311.7			1.23115			0.615573	−	0.788080i	$-0.288925\pi$
$937$	35311.7			1.23115			0.615573	+	0.788080i	$0.288925\pi$
$938$	−46016.7	−	10661.8i	−1.60181	−	0.371129i
$939$	−5922.77	−	33679.9i	−0.205838	−	1.17050i
$940$	−14427.2	−	7064.65i	−0.500601	−	0.245131i
$941$	−27098.3			−0.938767			−0.469383	−	0.882994i	$-0.655524\pi$
$941$	−27098.3			−0.938767			−0.469383	+	0.882994i	$0.655524\pi$
$942$	2459.49	−	45840.9i	0.0850686	−	1.58554i
$943$		−	15007.1i		−	0.518237i
$944$	36254.7	−	28142.8i	1.24999	−	0.970306i
$945$	14055.6	−	8089.26i	0.483839	−	0.278459i
$946$	8832.94	+	2046.54i	0.303577	+	0.0703368i
$947$			10601.0i			0.363765i	0.983320	+	0.181883i	$0.0582191\pi$
$947$			10601.0i			0.363765i	−0.983320	+	0.181883i	$0.941781\pi$
$948$	−17931.6	−	5181.12i	−0.614336	−	0.177505i
$949$		−	1121.90i		−	0.0383757i
$950$	−826.257	+	3566.16i	−0.0282182	+	0.121791i
$951$	3749.71	+	21322.8i	0.127858	+	0.727065i
$952$	−11849.2	+	14562.4i	−0.403398	+	0.495768i
$953$		−	879.891i		−	0.0299081i	−0.999888	−	0.0149541i	$-0.995240\pi$
$953$		−	879.891i		−	0.0299081i	0.999888	−	0.0149541i	$-0.00476021\pi$
$954$	621.137	+	5130.83i	0.0210797	+	0.174126i
$955$	−16060.9			−0.544209
$956$	38465.0	+	18835.3i	1.30131	+	0.637215i
$957$	3979.88	−	699.880i	0.134432	−	0.0236405i
$958$	6551.03	−	28274.5i	0.220933	−	0.953559i
$959$	24508.5			0.825256
$960$	−12359.1	+	4919.38i	−0.415508	+	0.165388i
$961$	−59243.4			−1.98863
$962$	742.222	−	3203.46i	0.0248755	−	0.107364i
$963$	−9884.85	−	27236.0i	−0.330773	−	0.911389i
$964$	22251.8	+	10896.1i	0.743447	+	0.364047i
$965$	24581.6			0.820011
$966$	−2241.98	+	41786.8i	−0.0746734	+	1.39179i
$967$		−	41719.7i		−	1.38740i	−0.720264	−	0.693700i	$-0.755979\pi$
$967$		−	41719.7i		−	1.38740i	0.720264	−	0.693700i	$-0.244021\pi$
$968$	−18497.4	+	22732.9i	−0.614181	+	0.754816i
$969$	−9508.36	+	1672.09i	−0.315225	+	0.0554337i
$970$	261.759	−	1129.76i	0.00866450	−	0.0373964i
$971$		−	27246.3i		−	0.900491i	−0.892905	−	0.450245i	$-0.851336\pi$
$971$		−	27246.3i		−	0.900491i	0.892905	−	0.450245i	$-0.148664\pi$
$972$	12218.9	+	27731.4i	0.403210	+	0.915107i
$973$			22473.9i			0.740472i
$974$	−18331.8	−	4247.36i	−0.603069	−	0.139727i
$975$	433.051	−	76.1541i	0.0142243	−	0.00250142i
$976$	2288.64	−	1776.56i	0.0750591	−	0.0582647i
$977$			13023.4i			0.426466i	0.977001	+	0.213233i	$0.0683993\pi$
$977$			13023.4i			0.426466i	−0.977001	+	0.213233i	$0.931601\pi$
$978$	6234.91	+	334.520i	0.203855	+	0.0109374i
$979$	5116.96			0.167047
$980$	6878.13	+	3368.04i	0.224198	+	0.109784i
$981$	−14084.6	−	38807.7i	−0.458397	−	1.26303i
$982$	13117.7	+	3039.29i	0.426276	+	0.0987654i
$983$	15208.4			0.493460			0.246730	−	0.969084i	$-0.420644\pi$
$983$	15208.4			0.493460			0.246730	+	0.969084i	$0.420644\pi$
$984$	6980.70	−	12510.5i	0.226155	−	0.405306i
$985$	14020.2			0.453525
$986$	−12857.8	−	2979.08i	−0.415291	−	0.0962204i
$987$	−47514.1	+	8355.58i	−1.53231	+	0.269464i
$988$	−616.490	+	1258.98i	−0.0198514	+	0.0405400i
$989$	−66009.1			−2.12231
$990$	2267.30	−	274.479i	0.0727875	−	0.00881163i
$991$		−	7322.89i		−	0.234732i	−0.993089	−	0.117366i	$-0.962555\pi$
$991$		−	7322.89i		−	0.234732i	0.993089	−	0.117366i	$-0.0374451\pi$
$992$	−22635.2	−	49042.1i	−0.724465	−	1.56964i
$993$	5923.37	+	33683.3i	0.189298	+	1.07644i
$994$	−65848.5	−	15256.7i	−2.10120	−	0.486834i
$995$		−	11641.4i		−	0.370911i
$996$	−25628.8	−	7405.13i	−0.815340	−	0.235583i
$997$			33453.4i			1.06267i	0.847163	+	0.531333i	$0.178309\pi$
$997$			33453.4i			1.06267i	−0.847163	+	0.531333i	$0.821691\pi$
$998$	−879.765	+	3797.10i	−0.0279043	+	0.120436i
$999$	41765.6	−	24037.0i	1.32273	−	0.761257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.a.11.15	✓	24
3.2	odd	2		120.4.b.b.11.10	yes	24
4.3	odd	2		480.4.b.b.431.14		24
8.3	odd	2		120.4.b.b.11.9	yes	24
8.5	even	2		480.4.b.a.431.14		24
12.11	even	2		480.4.b.a.431.13		24
24.5	odd	2		480.4.b.b.431.13		24
24.11	even	2	inner	120.4.b.a.11.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.15	✓	24	1.1	even	1	trivial
120.4.b.a.11.16	yes	24	24.11	even	2	inner
120.4.b.b.11.9	yes	24	8.3	odd	2
120.4.b.b.11.10	yes	24	3.2	odd	2
480.4.b.a.431.13		24	12.11	even	2
480.4.b.a.431.14		24	8.5	even	2
480.4.b.b.431.13		24	24.5	odd	2
480.4.b.b.431.14		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.638417 - 2.75544i) q^{2} +(-0.899959 - 5.11762i) q^{3} +(-7.18485 - 3.51823i) q^{4} +5.00000 q^{5} +(-14.6758 - 0.787399i) q^{6} -23.1184i q^{7} +(-14.2812 + 17.5513i) q^{8} +(-25.3801 + 9.21130i) q^{9} +O(q^{10})\)	\(q+(0.638417 - 2.75544i) q^{2} +(-0.899959 - 5.11762i) q^{3} +(-7.18485 - 3.51823i) q^{4} +5.00000 q^{5} +(-14.6758 - 0.787399i) q^{6} -23.1184i q^{7} +(-14.2812 + 17.5513i) q^{8} +(-25.3801 + 9.21130i) q^{9} +(3.19208 - 13.7772i) q^{10} -5.98122i q^{11} +(-11.5389 + 39.9356i) q^{12} +3.38478i q^{13} +(-63.7014 - 14.7592i) q^{14} +(-4.49979 - 25.5881i) q^{15} +(39.2441 + 50.5559i) q^{16} +35.8894i q^{17} +(9.17803 + 75.8140i) q^{18} -51.7691 q^{19} +(-35.9242 - 17.5912i) q^{20} +(-118.311 + 20.8056i) q^{21} +(-16.4809 - 3.81851i) q^{22} +123.162 q^{23} +(102.673 + 57.2903i) q^{24} +25.0000 q^{25} +(9.32655 + 2.16090i) q^{26} +(69.9810 + 121.596i) q^{27} +(-81.3360 + 166.102i) q^{28} -130.020 q^{29} +(-73.3792 - 3.93700i) q^{30} -298.386i q^{31} +(164.358 - 75.8588i) q^{32} +(-30.6096 + 5.38285i) q^{33} +(98.8910 + 22.9124i) q^{34} -115.592i q^{35} +(214.760 + 23.1115i) q^{36} -343.478i q^{37} +(-33.0503 + 142.646i) q^{38} +(17.3220 - 3.04616i) q^{39} +(-71.4060 + 87.7564i) q^{40} -121.848i q^{41} +(-18.2034 + 339.282i) q^{42} -535.951 q^{43} +(-21.0433 + 42.9742i) q^{44} +(-126.901 + 46.0565i) q^{45} +(78.6290 - 339.366i) q^{46} +401.602 q^{47} +(223.408 - 246.335i) q^{48} -191.462 q^{49} +(15.9604 - 68.8859i) q^{50} +(183.669 - 32.2990i) q^{51} +(11.9085 - 24.3191i) q^{52} +67.6765 q^{53} +(379.728 - 115.199i) q^{54} -29.9061i q^{55} +(405.758 + 330.159i) q^{56} +(46.5900 + 264.935i) q^{57} +(-83.0072 + 358.263i) q^{58} -717.121i q^{59} +(-57.6946 + 199.678i) q^{60} -45.2695i q^{61} +(-822.184 - 190.495i) q^{62} +(212.951 + 586.749i) q^{63} +(-104.095 - 501.306i) q^{64} +16.9239i q^{65} +(-4.70961 + 87.7794i) q^{66} +722.381 q^{67} +(126.267 - 257.860i) q^{68} +(-110.841 - 630.299i) q^{69} +(-318.507 - 73.7960i) q^{70} +1033.71 q^{71} +(200.789 - 577.003i) q^{72} -331.455 q^{73} +(-946.432 - 219.282i) q^{74} +(-22.4990 - 127.941i) q^{75} +(371.953 + 182.136i) q^{76} -138.276 q^{77} +(2.66518 - 49.6745i) q^{78} +449.012i q^{79} +(196.220 + 252.780i) q^{80} +(559.304 - 467.568i) q^{81} +(-335.744 - 77.7897i) q^{82} +641.752i q^{83} +(923.249 + 266.762i) q^{84} +179.447i q^{85} +(-342.160 + 1476.78i) q^{86} +(117.013 + 665.395i) q^{87} +(104.978 + 85.4190i) q^{88} +855.504i q^{89} +(45.8901 + 379.070i) q^{90} +78.2509 q^{91} +(-884.903 - 433.314i) q^{92} +(-1527.03 + 268.535i) q^{93} +(256.389 - 1106.59i) q^{94} -258.845 q^{95} +(-536.132 - 772.851i) q^{96} +82.0025 q^{97} +(-122.233 + 527.561i) q^{98} +(55.0948 + 151.804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Introduction

L-functions

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