LMFDB - Embedded newform 120.4.b.b.11.13

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			11.13
Character	$\chi$	$=$	120.11
Dual form			120.4.b.b.11.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 - 3.42387i) q^{4} -5.00000 q^{5} +(-2.70986 + 14.4450i) q^{6} -11.8996i q^{7} +(-13.9338 + 17.8283i) q^{8} +(26.9313 - 1.92545i) q^{9} +O(q^{10})$	\(q+(0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 - 3.42387i) q^{4} -5.00000 q^{5} +(-2.70986 + 14.4450i) q^{6} -11.8996i q^{7} +(-13.9338 + 17.8283i) q^{8} +(26.9313 - 1.92545i) q^{9} +(-3.10183 + 13.7978i) q^{10} +19.5939i q^{11} +(38.1805 + 16.4392i) q^{12} +80.7203i q^{13} +(-32.8376 - 7.38212i) q^{14} +(25.9642 - 0.926975i) q^{15} +(40.5542 + 49.5111i) q^{16} +12.9580i q^{17} +(11.3938 - 75.5128i) q^{18} +81.9017 q^{19} +(36.1515 + 17.1193i) q^{20} +(2.20613 + 61.7928i) q^{21} +(54.0705 + 12.1554i) q^{22} -147.701 q^{23} +(69.0507 - 95.1630i) q^{24} +25.0000 q^{25} +(222.752 + 50.0762i) q^{26} +(-139.493 + 14.9915i) q^{27} +(-40.7427 + 86.0377i) q^{28} -217.553 q^{29} +(13.5493 - 72.2248i) q^{30} -139.101i q^{31} +(161.787 - 81.1966i) q^{32} +(-3.63262 - 101.748i) q^{33} +(35.7583 + 8.03870i) q^{34} +59.4981i q^{35} +(-201.313 - 78.2875i) q^{36} +272.588i q^{37} +(50.8090 - 226.012i) q^{38} +(-14.9651 - 419.168i) q^{39} +(69.6689 - 89.1417i) q^{40} +480.713i q^{41} +(171.889 + 32.2463i) q^{42} -24.1939 q^{43} +(67.0871 - 141.670i) q^{44} +(-134.656 + 9.62727i) q^{45} +(-91.6290 + 407.590i) q^{46} -370.290 q^{47} +(-219.771 - 249.585i) q^{48} +201.399 q^{49} +(15.5092 - 68.9889i) q^{50} +(-2.40235 - 67.2888i) q^{51} +(276.376 - 583.632i) q^{52} -271.318 q^{53} +(-45.1667 + 394.238i) q^{54} -97.9697i q^{55} +(212.150 + 165.807i) q^{56} +(-425.303 + 15.1842i) q^{57} +(-134.962 + 600.349i) q^{58} +323.342i q^{59} +(-190.903 - 82.1958i) q^{60} +79.6391i q^{61} +(-383.856 - 86.2932i) q^{62} +(-22.9122 - 320.472i) q^{63} +(-123.699 - 496.832i) q^{64} -403.602i q^{65} +(-283.033 - 53.0967i) q^{66} -563.244 q^{67} +(44.3665 - 93.6901i) q^{68} +(766.991 - 27.3831i) q^{69} +(164.188 + 36.9106i) q^{70} +537.552 q^{71} +(-340.927 + 506.968i) q^{72} +98.9937 q^{73} +(752.222 + 169.104i) q^{74} +(-129.821 + 4.63488i) q^{75} +(-592.173 - 280.421i) q^{76} +233.160 q^{77} +(-1166.00 - 218.741i) q^{78} +292.524i q^{79} +(-202.771 - 247.556i) q^{80} +(721.585 - 103.710i) q^{81} +(1326.56 + 298.218i) q^{82} -1235.15i q^{83} +(195.620 - 454.334i) q^{84} -64.7900i q^{85} +(-15.0091 + 66.7645i) q^{86} +(1129.72 - 40.3332i) q^{87} +(-349.327 - 273.018i) q^{88} -657.532i q^{89} +(-56.9692 + 377.564i) q^{90} +960.541 q^{91} +(1067.92 + 505.711i) q^{92} +(25.7885 + 722.327i) q^{93} +(-229.715 + 1021.83i) q^{94} -409.508 q^{95} +(-825.082 + 451.636i) q^{96} -574.564 q^{97} +(124.941 - 555.772i) q^{98} +(37.7272 + 527.689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 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 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * 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 $

$2$	0.620366	−	2.75956i	0.219333	−	0.975650i
$2$	0.620366	−	2.75956i	0.219333	−	0.975650i
$3$	−5.19284	+	0.185395i	−0.999363	+	0.0356793i
$3$	−5.19284	+	0.185395i	−0.999363	+	0.0356793i
$4$	−7.23029	−	3.42387i	−0.903786	−	0.427984i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−2.70986	+	14.4450i	−0.184382	+	0.982855i
$7$		−	11.8996i		−	0.642519i	−0.946991	−	0.321259i	$-0.895894\pi$
$7$		−	11.8996i		−	0.642519i	0.946991	−	0.321259i	$-0.104106\pi$
$8$	−13.9338	+	17.8283i	−0.615792	+	0.787909i
$9$	26.9313	−	1.92545i	0.997454	−	0.0713131i
$10$	−3.10183	+	13.7978i	−0.0980885	+	0.436324i
$11$			19.5939i			0.537072i	0.963270	+	0.268536i	$0.0865398\pi$
$11$			19.5939i			0.537072i	−0.963270	+	0.268536i	$0.913460\pi$
$12$	38.1805	+	16.4392i	0.918481	+	0.395465i
$13$			80.7203i			1.72214i	0.508488	+	0.861069i	$0.330205\pi$
$13$			80.7203i			1.72214i	−0.508488	+	0.861069i	$0.669795\pi$
$14$	−32.8376	−	7.38212i	−0.626874	−	0.140925i
$15$	25.9642	−	0.926975i	0.446929	−	0.0159563i
$16$	40.5542	+	49.5111i	0.633660	+	0.773612i
$17$			12.9580i			0.184869i	0.995719	+	0.0924345i	$0.0294649\pi$
$17$			12.9580i			0.184869i	−0.995719	+	0.0924345i	$0.970535\pi$
$18$	11.3938	−	75.5128i	0.149197	−	0.988807i
$19$	81.9017			0.988923			0.494462	−	0.869200i	$-0.335365\pi$
$19$	81.9017			0.988923			0.494462	+	0.869200i	$0.335365\pi$
$20$	36.1515	+	17.1193i	0.404186	+	0.191400i
$21$	2.20613	+	61.7928i	0.0229246	+	0.642110i
$22$	54.0705	+	12.1554i	0.523994	+	0.117797i
$23$	−147.701			−1.33904			−0.669519	−	0.742795i	$-0.733500\pi$
$23$	−147.701			−1.33904			−0.669519	+	0.742795i	$0.733500\pi$
$24$	69.0507	−	95.1630i	0.587288	−	0.809378i
$25$	25.0000			0.200000
$26$	222.752	+	50.0762i	1.68020	+	0.377721i
$27$	−139.493	+	14.9915i	−0.994274	+	0.106856i
$28$	−40.7427	+	86.0377i	−0.274988	+	0.580700i
$29$	−217.553			−1.39305			−0.696527	−	0.717531i	$-0.745272\pi$
$29$	−217.553			−1.39305			−0.696527	+	0.717531i	$0.745272\pi$
$30$	13.5493	−	72.2248i	0.0824583	−	0.439546i
$31$		−	139.101i		−	0.805909i	−0.915220	−	0.402955i	$-0.867983\pi$
$31$		−	139.101i		−	0.805909i	0.915220	−	0.402955i	$-0.132017\pi$
$32$	161.787	−	81.1966i	0.893757	−	0.448552i
$33$	−3.63262	−	101.748i	−0.0191624	−	0.536730i
$34$	35.7583	+	8.03870i	0.180368	+	0.0405478i
$35$			59.4981i			0.287343i
$36$	−201.313	−	78.2875i	−0.932006	−	0.362442i
$37$			272.588i			1.21117i	0.795781	+	0.605584i	$0.207060\pi$
$37$			272.588i			1.21117i	−0.795781	+	0.605584i	$0.792940\pi$
$38$	50.8090	−	226.012i	0.216903	−	0.964843i
$39$	−14.9651	−	419.168i	−0.0614447	−	1.72104i
$40$	69.6689	−	89.1417i	0.275391	−	0.352363i
$41$			480.713i			1.83109i	0.402212	+	0.915547i	$0.368242\pi$
$41$			480.713i			1.83109i	−0.402212	+	0.915547i	$0.631758\pi$
$42$	171.889	+	32.2463i	0.631503	+	0.118469i
$43$	−24.1939			−0.0858033			−0.0429016	−	0.999079i	$-0.513660\pi$
$43$	−24.1939			−0.0858033			−0.0429016	+	0.999079i	$0.513660\pi$
$44$	67.0871	−	141.670i	0.229858	−	0.485399i
$45$	−134.656	+	9.62727i	−0.446075	+	0.0318922i
$46$	−91.6290	+	407.590i	−0.293695	+	1.30643i
$47$	−370.290			−1.14920			−0.574599	−	0.818435i	$-0.694842\pi$
$47$	−370.290			−1.14920			−0.574599	+	0.818435i	$0.694842\pi$
$48$	−219.771	−	249.585i	−0.660858	−	0.750511i
$49$	201.399			0.587170
$50$	15.5092	−	68.9889i	0.0438665	−	0.195130i
$51$	−2.40235	−	67.2888i	−0.00659600	−	0.184751i
$52$	276.376	−	583.632i	0.737047	−	1.55645i
$53$	−271.318			−0.703178			−0.351589	−	0.936155i	$-0.614358\pi$
$53$	−271.318			−0.703178			−0.351589	+	0.936155i	$0.614358\pi$
$54$	−45.1667	+	394.238i	−0.113822	+	0.993501i
$55$		−	97.9697i		−	0.240186i
$56$	212.150	+	165.807i	0.506246	+	0.395658i
$57$	−425.303	+	15.1842i	−0.988293	+	0.0352841i
$58$	−134.962	+	600.349i	−0.305542	+	1.35913i
$59$			323.342i			0.713485i	0.934203	+	0.356742i	$0.116113\pi$
$59$			323.342i			0.713485i	−0.934203	+	0.356742i	$0.883887\pi$
$60$	−190.903	−	82.1958i	−0.410757	−	0.176857i
$61$			79.6391i			0.167160i	0.996501	+	0.0835799i	$0.0266354\pi$
$61$			79.6391i			0.167160i	−0.996501	+	0.0835799i	$0.973365\pi$
$62$	−383.856	−	86.2932i	−0.786286	−	0.176762i
$63$	−22.9122	−	320.472i	−0.0458200	−	0.640883i
$64$	−123.699	−	496.832i	−0.241600	−	0.970376i
$65$		−	403.602i		−	0.770164i
$66$	−283.033	−	53.0967i	−0.527864	−	0.0990266i
$67$	−563.244			−1.02703			−0.513517	−	0.858080i	$-0.671658\pi$
$67$	−563.244			−1.02703			−0.513517	+	0.858080i	$0.671658\pi$
$68$	44.3665	−	93.6901i	0.0791209	−	0.167082i
$69$	766.991	−	27.3831i	1.33819	−	0.0477759i
$70$	164.188	+	36.9106i	0.280346	+	0.0630237i
$71$	537.552			0.898531			0.449265	−	0.893398i	$-0.351686\pi$
$71$	537.552			0.898531			0.449265	+	0.893398i	$0.351686\pi$
$72$	−340.927	+	506.968i	−0.558036	+	0.829817i
$73$	98.9937			0.158717			0.0793585	−	0.996846i	$-0.474713\pi$
$73$	98.9937			0.158717			0.0793585	+	0.996846i	$0.474713\pi$
$74$	752.222	+	169.104i	1.18168	+	0.265649i
$75$	−129.821	+	4.63488i	−0.199873	+	0.00713586i
$76$	−592.173	−	280.421i	−0.893775	−	0.423243i
$77$	233.160			0.345079
$78$	−1166.00	−	218.741i	−1.69261	−	0.317532i
$79$			292.524i			0.416602i	0.978065	+	0.208301i	$0.0667933\pi$
$79$			292.524i			0.416602i	−0.978065	+	0.208301i	$0.933207\pi$
$80$	−202.771	−	247.556i	−0.283381	−	0.345970i
$81$	721.585	−	103.710i	0.989829	−	0.142263i
$82$	1326.56	+	298.218i	1.78651	+	0.401618i
$83$		−	1235.15i		−	1.63344i	−0.577033	−	0.816721i	$-0.695790\pi$
$83$		−	1235.15i		−	1.63344i	0.577033	−	0.816721i	$-0.304210\pi$
$84$	195.620	−	454.334i	0.254094	−	0.590141i
$85$		−	64.7900i		−	0.0826760i
$86$	−15.0091	+	66.7645i	−0.0188195	+	0.0837140i
$87$	1129.72	−	40.3332i	1.39217	−	0.0497032i
$88$	−349.327	−	273.018i	−0.423164	−	0.330725i
$89$		−	657.532i		−	0.783126i	−0.920151	−	0.391563i	$-0.871935\pi$
$89$		−	657.532i		−	0.783126i	0.920151	−	0.391563i	$-0.128065\pi$
$90$	−56.9692	+	377.564i	−0.0667231	+	0.442208i
$91$	960.541			1.10651
$92$	1067.92	+	505.711i	1.21021	+	0.573087i
$93$	25.7885	+	722.327i	0.0287543	+	0.805396i
$94$	−229.715	+	1021.83i	−0.252056	+	1.12122i
$95$	−409.508			−0.442260
$96$	−825.082	+	451.636i	−0.877184	+	0.480155i
$97$	−574.564			−0.601424			−0.300712	−	0.953715i	$-0.597224\pi$
$97$	−574.564			−0.601424			−0.300712	+	0.953715i	$0.597224\pi$
$98$	124.941	−	555.772i	0.128785	−	0.572872i
$99$	37.7272	+	527.689i	0.0383003	+	0.535705i
$100$	−180.757	−	85.5967i	−0.180757	−	0.0855967i
$101$	95.4087			0.0939953			0.0469976	−	0.998895i	$-0.485035\pi$
$101$	95.4087			0.0939953			0.0469976	+	0.998895i	$0.485035\pi$
$102$	−187.178	−	35.1143i	−0.181699	−	0.0340866i
$103$		−	190.207i		−	0.181957i	−0.995853	−	0.0909787i	$-0.971000\pi$
$103$		−	190.207i		−	0.181957i	0.995853	−	0.0909787i	$-0.0289995\pi$
$104$	−1439.11	−	1124.74i	−1.35689	−	1.06048i
$105$	−11.0306	−	308.964i	−0.0102522	−	0.287160i
$106$	−168.317	+	748.718i	−0.154230	+	0.686055i
$107$			1394.13i			1.25958i	0.776764	+	0.629792i	$0.216860\pi$
$107$			1394.13i			1.25958i	−0.776764	+	0.629792i	$0.783140\pi$
$108$	1059.90	+	369.212i	0.944345	+	0.328958i
$109$			1052.71i			0.925061i	0.886603	+	0.462531i	$0.153058\pi$
$109$			1052.71i			0.925061i	−0.886603	+	0.462531i	$0.846942\pi$
$110$	−270.353	−	60.7771i	−0.234337	−	0.0526806i
$111$	−50.5365	−	1415.51i	−0.0432136	−	1.21040i
$112$	589.164	−	482.580i	0.497060	−	0.407139i
$113$			1385.09i			1.15308i	0.817069	+	0.576540i	$0.195598\pi$
$113$			1385.09i			1.15308i	−0.817069	+	0.576540i	$0.804402\pi$
$114$	−221.942	+	1183.07i	−0.182340	+	0.971968i
$115$	738.507			0.598836
$116$	1572.97	+	744.873i	1.25902	+	0.596204i
$117$	155.423	+	2173.90i	0.122811	+	1.71775i
$118$	892.281	+	200.591i	0.696112	+	0.156490i
$119$	154.195			0.118782
$120$	−345.253	+	475.815i	−0.262643	+	0.361965i
$121$	947.078			0.711554
$122$	219.769	+	49.4054i	0.163089	+	0.0366636i
$123$	−89.1219	−	2496.27i	−0.0653321	−	1.82993i
$124$	−476.262	+	1005.74i	−0.344916	+	0.728370i
$125$	−125.000			−0.0894427
$126$	−898.573	−	135.582i	−0.635327	−	0.0958622i
$127$			345.019i			0.241067i	0.992709	+	0.120533i	$0.0384605\pi$
$127$			345.019i			0.241067i	−0.992709	+	0.120533i	$0.961540\pi$
$128$	−1447.78	+	33.1371i	−0.999738	+	0.0228823i
$129$	125.635	−	4.48544i	0.0857487	−	0.00306140i
$130$	−1113.76	−	250.381i	−0.751410	−	0.168922i
$131$			481.159i			0.320909i	0.987043	+	0.160454i	$0.0512960\pi$
$131$			481.159i			0.320909i	−0.987043	+	0.160454i	$0.948704\pi$
$132$	−322.108	+	748.107i	−0.212393	+	0.493291i
$133$		−	974.599i		−	0.635402i
$134$	−349.418	+	1554.30i	−0.225262	+	1.00203i
$135$	697.464	−	74.9575i	0.444653	−	0.0477875i
$136$	−231.019	−	180.554i	−0.145660	−	0.113841i
$137$		−	1207.42i		−	0.752967i	−0.926423	−	0.376483i	$-0.877133\pi$
$137$		−	1207.42i		−	0.752967i	0.926423	−	0.376483i	$-0.122867\pi$
$138$	400.250	−	2133.54i	0.246895	−	1.31608i
$139$	−2439.69			−1.48872			−0.744359	−	0.667779i	$-0.767245\pi$
$139$	−2439.69			−1.48872			−0.744359	+	0.667779i	$0.767245\pi$
$140$	203.714	−	430.188i	0.122978	−	0.259697i
$141$	1922.86	−	68.6499i	1.14847	−	0.0410026i
$142$	333.479	−	1483.40i	0.197077	−	0.876651i
$143$	−1581.63			−0.924912
$144$	1187.51	+	1255.31i	0.687215	+	0.726454i
$145$	1087.76			0.622993
$146$	61.4123	−	273.179i	0.0348118	−	0.154852i
$147$	−1045.83	+	37.3384i	−0.586796	+	0.0209498i
$148$	933.306	−	1970.89i	0.518360	−	1.09464i
$149$	−2052.93			−1.12874			−0.564372	−	0.825521i	$-0.690882\pi$
$149$	−2052.93			−1.12874			−0.564372	+	0.825521i	$0.690882\pi$
$150$	−67.7464	+	361.124i	−0.0368765	+	0.196571i
$151$			232.344i			0.125218i	0.998038	+	0.0626088i	$0.0199420\pi$
$151$			232.344i			0.125218i	−0.998038	+	0.0626088i	$0.980058\pi$
$152$	−1141.20	+	1460.17i	−0.608971	+	0.779181i
$153$	24.9500	+	348.975i	0.0131836	+	0.184398i
$154$	144.645	−	643.419i	0.0756870	−	0.336676i
$155$			695.503i			0.360414i
$156$	−1326.97	+	3081.95i	−0.681045	+	1.58175i
$157$		−	3057.94i		−	1.55446i	−0.629216	−	0.777231i	$-0.716624\pi$
$157$		−	3057.94i		−	1.55446i	0.629216	−	0.777231i	$-0.283376\pi$
$158$	807.236	+	181.472i	0.406457	+	0.0913743i
$159$	1408.91	−	50.3010i	0.702730	−	0.0250889i
$160$	−808.936	+	405.983i	−0.399700	+	0.200599i
$161$			1757.59i			0.860358i
$162$	161.454	−	2055.59i	0.0783026	−	0.996930i
$163$	621.974			0.298876			0.149438	−	0.988771i	$-0.452254\pi$
$163$	621.974			0.298876			0.149438	+	0.988771i	$0.452254\pi$
$164$	1645.90	−	3475.70i	0.783678	−	1.65492i
$165$	18.1631	+	508.741i	0.00856966	+	0.240033i
$166$	−3408.47	−	766.247i	−1.59367	−	0.358267i
$167$	1489.97			0.690402			0.345201	−	0.938529i	$-0.387811\pi$
$167$	1489.97			0.690402			0.345201	+	0.938529i	$0.387811\pi$
$168$	−1132.40	−	821.677i	−0.520041	−	0.377344i
$169$	−4318.77			−1.96576
$170$	−178.791	−	40.1935i	−0.0806628	−	0.0181335i
$171$	2205.72	−	157.698i	0.986405	−	0.0705232i
$172$	174.929	+	82.8369i	0.0775478	+	0.0367224i
$173$	2319.39			1.01930			0.509652	−	0.860381i	$-0.329774\pi$
$173$	2319.39			1.01930			0.509652	+	0.860381i	$0.329774\pi$
$174$	589.537	−	3142.54i	0.256855	−	1.36917i
$175$		−	297.490i		−	0.128504i
$176$	−970.118	+	794.617i	−0.415485	+	0.340321i
$177$	−59.9461	−	1679.07i	−0.0254566	−	0.713031i
$178$	−1814.49	−	407.910i	−0.764057	−	0.171765i
$179$		−	2525.19i		−	1.05442i	−0.849734	−	0.527212i	$-0.823237\pi$
$179$		−	2525.19i		−	1.05442i	0.849734	−	0.527212i	$-0.176763\pi$
$180$	1006.57	+	391.437i	0.416806	+	0.162089i
$181$		−	3943.26i		−	1.61934i	−0.586888	−	0.809668i	$-0.699647\pi$
$181$		−	3943.26i		−	1.61934i	0.586888	−	0.809668i	$-0.300353\pi$
$182$	595.887	−	2650.67i	0.242693	−	1.07956i
$183$	−14.7647	−	413.554i	−0.00596414	−	0.167053i
$184$	2058.04	−	2633.27i	0.824569	−	1.05504i
$185$		−	1362.94i		−	0.541651i
$186$	2009.30	+	376.942i	0.792092	+	0.148595i
$187$	−253.898			−0.0992880
$188$	2677.30	+	1267.82i	1.03863	+	0.491838i
$189$	178.393	+	1659.91i	0.0686571	+	0.638840i
$190$	−254.045	+	1130.06i	−0.0970020	+	0.431491i
$191$	−1918.68			−0.726862			−0.363431	−	0.931621i	$-0.618395\pi$
$191$	−1918.68			−0.726862			−0.363431	+	0.931621i	$0.618395\pi$
$192$	734.461	+	2557.04i	0.276069	+	0.961138i
$193$	−1417.65			−0.528731			−0.264365	−	0.964423i	$-0.585162\pi$
$193$	−1417.65			−0.528731			−0.264365	+	0.964423i	$0.585162\pi$
$194$	−356.440	+	1585.54i	−0.131912	+	0.586780i
$195$	74.8257	+	2095.84i	0.0274789	+	0.769673i
$196$	−1456.17	−	689.564i	−0.530676	−	0.251299i
$197$	−3744.03			−1.35407			−0.677033	−	0.735952i	$-0.736735\pi$
$197$	−3744.03			−1.35407			−0.677033	+	0.735952i	$0.736735\pi$
$198$	1479.59	+	223.250i	0.531061	+	0.0801298i
$199$			4872.55i			1.73571i	0.496820	+	0.867854i	$0.334501\pi$
$199$			4872.55i			1.73571i	−0.496820	+	0.867854i	$0.665499\pi$
$200$	−348.345	+	445.708i	−0.123158	+	0.157582i
$201$	2924.84	−	104.423i	1.02638	−	0.0366438i
$202$	59.1883	−	263.286i	0.0206162	−	0.0917065i
$203$			2588.80i			0.895063i
$204$	−213.018	+	494.743i	−0.0731092	+	0.169799i
$205$		−	2403.57i		−	0.818890i
$206$	−524.886	−	117.998i	−0.177527	−	0.0399092i
$207$	−3977.79	+	284.393i	−1.33563	+	0.0954911i
$208$	−3996.56	+	3273.55i	−1.33227	+	1.09125i
$209$			1604.78i			0.531123i
$210$	−859.447	−	161.231i	−0.282417	−	0.0529810i
$211$	2120.64			0.691900			0.345950	−	0.938253i	$-0.387557\pi$
$211$	2120.64			0.691900			0.345950	+	0.938253i	$0.387557\pi$
$212$	1961.71	+	928.958i	0.635523	+	0.300949i
$213$	−2791.42	+	99.6594i	−0.897958	+	0.0320589i
$214$	3847.18	+	864.870i	1.22891	+	0.276268i
$215$	120.970			0.0383724
$216$	1676.39	−	2695.81i	0.528073	−	0.849199i
$217$	−1655.24			−0.517812
$218$	2905.02	+	653.068i	0.902536	+	0.202896i
$219$	−514.059	+	18.3529i	−0.158616	+	0.00566291i
$220$	−335.435	+	708.349i	−0.102796	+	0.217077i
$221$	−1045.97			−0.318370
$222$	−3937.52	−	738.675i	−1.19040	−	0.223318i
$223$			5310.83i			1.59480i	0.603454	+	0.797398i	$0.293791\pi$
$223$			5310.83i			1.59480i	−0.603454	+	0.797398i	$0.706209\pi$
$224$	−966.209	−	1925.21i	−0.288203	−	0.574255i
$225$	673.281	−	48.1364i	0.199491	−	0.0142626i
$226$	3822.23	+	859.261i	1.12500	+	0.252908i
$227$			3911.60i			1.14371i	0.820355	+	0.571854i	$0.193776\pi$
$227$			3911.60i			1.14371i	−0.820355	+	0.571854i	$0.806224\pi$
$228$	3127.05	+	1346.39i	0.908307	+	0.391084i
$229$		−	5988.71i		−	1.72814i	−0.503368	−	0.864072i	$-0.667906\pi$
$229$		−	5988.71i		−	1.72814i	0.503368	−	0.864072i	$-0.332094\pi$
$230$	458.145	−	2037.95i	0.131344	−	0.584255i
$231$	−1210.76	+	43.2268i	−0.344859	+	0.0123122i
$232$	3031.34	−	3878.61i	0.857832	−	1.09760i
$233$			3640.14i			1.02349i	0.859137	+	0.511745i	$0.171001\pi$
$233$			3640.14i			1.02349i	−0.859137	+	0.511745i	$0.828999\pi$
$234$	6095.42	+	919.715i	1.70286	+	0.256939i
$235$	1851.45			0.513937
$236$	1107.08	−	2337.86i	0.305360	−	0.644838i
$237$	−54.2325	−	1519.03i	−0.0148640	−	0.416336i
$238$	95.6574	−	425.510i	0.0260527	−	0.115890i
$239$	−6300.66			−1.70525			−0.852627	−	0.522521i	$-0.824992\pi$
$239$	−6300.66			−1.70525			−0.852627	+	0.522521i	$0.824992\pi$
$240$	1098.85	+	1247.93i	0.295545	+	0.335639i
$241$	−186.979			−0.0499766			−0.0249883	−	0.999688i	$-0.507955\pi$
$241$	−186.979			−0.0499766			−0.0249883	+	0.999688i	$0.507955\pi$
$242$	587.535	−	2613.51i	0.156067	−	0.694227i
$243$	−3727.85	+	672.327i	−0.984123	+	0.177489i
$244$	272.674	−	575.814i	0.0715416	−	0.151077i
$245$	−1007.00			−0.262590
$246$	−6943.88	−	1302.66i	−1.79970	−	0.337621i
$247$			6611.13i			1.70306i
$248$	2479.93	+	1938.20i	0.634983	+	0.496273i
$249$	228.991	+	6413.96i	0.0582800	+	1.63240i
$250$	−77.5458	+	344.944i	−0.0196177	+	0.0872648i
$251$		−	5717.83i		−	1.43787i	−0.695075	−	0.718937i	$-0.744629\pi$
$251$		−	5717.83i		−	1.43787i	0.695075	−	0.718937i	$-0.255371\pi$
$252$	−931.591	+	2395.55i	−0.232876	+	0.598832i
$253$		−	2894.05i		−	0.719160i
$254$	952.098	+	214.038i	0.235197	+	0.0528738i
$255$	12.0117	+	336.444i	0.00294982	+	0.0826233i
$256$	−806.707	+	4015.77i	−0.196950	+	0.980414i
$257$		−	6608.04i		−	1.60388i	−0.597402	−	0.801942i	$-0.703800\pi$
$257$		−	6608.04i		−	1.60388i	0.597402	−	0.801942i	$-0.296200\pi$
$258$	65.5621	−	349.480i	0.0158206	−	0.0843321i
$259$	3243.69			0.778198
$260$	−1381.88	+	2918.16i	−0.329617	+	0.696063i
$261$	−5858.97	+	418.888i	−1.38951	+	0.0993431i
$262$	1327.79	+	298.495i	0.313095	+	0.0703858i
$263$	5341.51			1.25236			0.626182	−	0.779677i	$-0.284617\pi$
$263$	5341.51			1.25236			0.626182	+	0.779677i	$0.284617\pi$
$264$	1864.62	+	1352.97i	0.434694	+	0.315416i
$265$	1356.59			0.314471
$266$	−2689.46	−	604.608i	−0.619930	−	0.139364i
$267$	121.903	+	3414.46i	0.0279414	+	0.782627i
$268$	4072.42	+	1928.47i	0.928219	+	0.439553i
$269$	7051.54			1.59829			0.799144	−	0.601139i	$-0.205286\pi$
$269$	7051.54			1.59829			0.799144	+	0.601139i	$0.205286\pi$
$270$	225.834	−	1971.19i	0.0509030	−	0.444307i
$271$			4785.65i			1.07272i	0.843989	+	0.536361i	$0.180201\pi$
$271$			4785.65i			1.07272i	−0.843989	+	0.536361i	$0.819799\pi$
$272$	−641.565	+	525.502i	−0.143017	+	0.117144i
$273$	−4987.94	+	178.080i	−1.10580	+	0.0394794i
$274$	−3331.93	−	749.039i	−0.734632	−	0.165150i
$275$			489.848i			0.107414i
$276$	−5639.32	−	2428.09i	−1.22988	−	0.529543i
$277$			4080.47i			0.885097i	0.896745	+	0.442548i	$0.145926\pi$
$277$			4080.47i			0.885097i	−0.896745	+	0.442548i	$0.854074\pi$
$278$	−1513.50	+	6732.46i	−0.326524	+	1.45247i
$279$	−267.832	−	3746.15i	−0.0574719	−	0.803858i
$280$	−1060.75	−	829.033i	−0.226400	−	0.176944i
$281$		−	1042.56i		−	0.221331i	−0.993858	−	0.110665i	$-0.964702\pi$
$281$		−	1042.56i		−	0.221331i	0.993858	−	0.110665i	$-0.0352982\pi$
$282$	1003.43	−	5348.82i	0.211892	−	1.12949i
$283$	2816.83			0.591672			0.295836	−	0.955239i	$-0.404402\pi$
$283$	2816.83			0.591672			0.295836	+	0.955239i	$0.404402\pi$
$284$	−3886.66	−	1840.51i	−0.812080	−	0.384556i
$285$	2126.51	−	75.9208i	0.441978	−	0.0157795i
$286$	−981.189	+	4364.59i	−0.202863	+	0.902391i
$287$	5720.30			1.17651
$288$	4200.79	−	2498.24i	0.859493	−	0.511147i
$289$	4745.09			0.965823
$290$	674.812	−	3001.75i	0.136643	−	0.607823i
$291$	2983.62	−	106.521i	0.601041	−	0.0214584i
$292$	−715.754	−	338.942i	−0.143446	−	0.0679283i
$293$	4373.43			0.872009			0.436005	−	0.899944i	$-0.356393\pi$
$293$	4373.43			0.872009			0.436005	+	0.899944i	$0.356393\pi$
$294$	−545.763	+	2909.20i	−0.108264	+	0.577102i
$295$		−	1616.71i		−	0.319080i
$296$	−4859.79	−	3798.18i	−0.954290	−	0.745828i
$297$	−293.743	−	2733.21i	−0.0573895	−	0.533997i
$298$	−1273.57	+	5665.18i	−0.247570	+	1.10126i
$299$		−	11922.5i		−	2.30601i
$300$	954.514	+	410.979i	0.183696	+	0.0790929i
$301$			287.899i			0.0551302i
$302$	641.165	+	144.138i	0.122169	+	0.0274643i
$303$	−495.443	+	17.6883i	−0.0939354	+	0.00335369i
$304$	3321.46	+	4055.05i	0.626641	+	0.765042i
$305$		−	398.196i		−	0.0747561i
$306$	978.494	+	147.641i	0.182800	+	0.0275820i
$307$	−4848.29			−0.901324			−0.450662	−	0.892695i	$-0.648812\pi$
$307$	−4848.29			−0.901324			−0.450662	+	0.892695i	$0.648812\pi$
$308$	−1685.82	−	798.310i	−0.311878	−	0.147688i
$309$	35.2634	+	987.714i	0.00649211	+	0.181842i
$310$	1919.28	+	431.466i	0.351638	+	0.0790504i
$311$	4111.79			0.749705			0.374853	−	0.927084i	$-0.377693\pi$
$311$	4111.79			0.749705			0.374853	+	0.927084i	$0.377693\pi$
$312$	7681.59	+	5573.79i	1.39386	+	1.01139i
$313$	7169.64			1.29474			0.647368	−	0.762178i	$-0.275870\pi$
$313$	7169.64			1.29474			0.647368	+	0.762178i	$0.275870\pi$
$314$	−8438.57	−	1897.04i	−1.51661	−	0.340944i
$315$	114.561	+	1602.36i	0.0204913	+	0.286612i
$316$	1001.56	−	2115.03i	0.178299	−	0.376519i
$317$	4371.23			0.774489			0.387244	−	0.921977i	$-0.373427\pi$
$317$	4371.23			0.774489			0.387244	+	0.921977i	$0.373427\pi$
$318$	735.233	−	3919.18i	0.129654	−	0.691121i
$319$		−	4262.72i		−	0.748170i
$320$	618.497	+	2484.16i	0.108047	+	0.433965i
$321$	−258.465	−	7239.49i	−0.0449411	−	1.25878i
$322$	4850.17	+	1090.35i	0.839408	+	0.188704i
$323$			1061.28i			0.182821i
$324$	−5572.36	−	1720.76i	−0.955480	−	0.295055i
$325$			2018.01i			0.344428i
$326$	385.852	−	1716.37i	0.0655532	−	0.291598i
$327$	−195.168	−	5466.58i	−0.0330055	−	0.924472i
$328$	−8570.32	−	6698.16i	−1.44273	−	1.12757i
$329$			4406.31i			0.738381i
$330$	1415.17	+	265.484i	0.236068	+	0.0442861i
$331$	−5590.60			−0.928360			−0.464180	−	0.885741i	$-0.653651\pi$
$331$	−5590.60			−0.928360			−0.464180	+	0.885741i	$0.653651\pi$
$332$	−4229.00	+	8930.52i	−0.699086	+	1.47628i
$333$	524.856	+	7341.14i	0.0863722	+	1.20808i
$334$	924.325	−	4111.65i	0.151428	−	0.673590i
$335$	2816.22			0.459303
$336$	−2969.97	+	2615.19i	−0.482217	+	0.424614i
$337$	−7898.02			−1.27665			−0.638327	−	0.769765i	$-0.720373\pi$
$337$	−7898.02			−1.27665			−0.638327	+	0.769765i	$0.720373\pi$
$338$	−2679.22	+	11917.9i	−0.431155	+	1.91789i
$339$	−256.788	−	7192.54i	−0.0411411	−	1.15235i
$340$	−221.832	+	468.450i	−0.0353840	+	0.0747214i
$341$	2725.53			0.432831
$342$	933.175	−	6184.63i	0.147545	−	0.977854i
$343$		−	6478.14i		−	1.01979i
$344$	337.113	−	431.338i	0.0528370	−	0.0676052i
$345$	−3834.95	+	136.916i	−0.598455	+	0.0213661i
$346$	1438.87	−	6400.47i	0.223567	−	0.994484i
$347$			10863.8i			1.68069i	0.542048	+	0.840347i	$0.317649\pi$
$347$			10863.8i			1.68069i	−0.542048	+	0.840347i	$0.682351\pi$
$348$	−8306.29	−	3576.39i	−1.27949	−	0.550904i
$349$			4377.57i			0.671421i	0.941965	+	0.335711i	$0.108976\pi$
$349$			4377.57i			0.671421i	−0.941965	+	0.335711i	$0.891024\pi$
$350$	−820.941	−	184.553i	−0.125375	−	0.0281851i
$351$	−1210.12	−	11259.9i	−0.184021	−	1.71228i
$352$	1590.96	+	3170.05i	0.240905	+	0.480012i
$353$			1333.66i			0.201086i	0.994933	+	0.100543i	$0.0320580\pi$
$353$			1333.66i			0.201086i	−0.994933	+	0.100543i	$0.967942\pi$
$354$	−4670.67	−	876.212i	−0.701252	−	0.131554i
$355$	−2687.76			−0.401835
$356$	−2251.30	+	4754.15i	−0.335165	+	0.707779i
$357$	−800.711	+	28.5870i	−0.118706	+	0.00423805i
$358$	−6968.41	−	1566.54i	−1.02875	−	0.231269i
$359$	3527.91			0.518651			0.259326	−	0.965790i	$-0.416500\pi$
$359$	3527.91			0.518651			0.259326	+	0.965790i	$0.416500\pi$
$360$	1704.63	−	2534.84i	0.249561	−	0.371105i
$361$	−151.112			−0.0220312
$362$	−10881.6	−	2446.26i	−1.57991	−	0.355173i
$363$	−4918.03	+	175.584i	−0.711101	+	0.0253877i
$364$	−6944.99	−	3288.77i	−1.00005	−	0.473567i
$365$	−494.969			−0.0709804
$366$	−1150.38	−	215.811i	−0.164294	−	0.0308213i
$367$		−	4297.18i		−	0.611202i	−0.952160	−	0.305601i	$-0.901143\pi$
$367$		−	4297.18i		−	0.611202i	0.952160	−	0.305601i	$-0.0988574\pi$
$368$	−5989.92	−	7312.87i	−0.848495	−	1.03590i
$369$	925.592	+	12946.2i	0.130581	+	1.82643i
$370$	−3761.11	−	845.522i	−0.528462	−	0.118802i
$371$			3228.58i			0.451805i
$372$	2286.70	−	5310.93i	0.318709	−	0.740213i
$373$		−	1702.18i		−	0.236288i	−0.992996	−	0.118144i	$-0.962306\pi$
$373$		−	1702.18i		−	0.236288i	0.992996	−	0.118144i	$-0.0376944\pi$
$374$	−157.510	+	700.646i	−0.0217771	+	0.0968704i
$375$	649.105	−	23.1744i	0.0893858	−	0.00319125i
$376$	5159.54	−	6601.65i	0.707667	−	0.905463i
$377$		−	17560.9i		−	2.39903i
$378$	4691.29	+	537.467i	0.638343	+	0.0731331i
$379$	1377.13			0.186645			0.0933223	−	0.995636i	$-0.470251\pi$
$379$	1377.13			0.186645			0.0933223	+	0.995636i	$0.470251\pi$
$380$	2960.87	+	1402.10i	0.399708	+	0.189280i
$381$	−63.9648	−	1791.63i	−0.00860109	−	0.240913i
$382$	−1190.28	+	5294.70i	−0.159424	+	0.709163i
$383$	1957.46			0.261152			0.130576	−	0.991438i	$-0.458317\pi$
$383$	1957.46			0.261152			0.130576	+	0.991438i	$0.458317\pi$
$384$	7511.93	−	440.486i	0.998285	−	0.0585377i
$385$	−1165.80			−0.154324
$386$	−879.465	+	3912.10i	−0.115968	+	0.515856i
$387$	−651.573	+	46.5843i	−0.0855848	+	0.00611890i
$388$	4154.27	+	1967.23i	0.543559	+	0.257400i
$389$	−7121.90			−0.928264			−0.464132	−	0.885766i	$-0.653634\pi$
$389$	−7121.90			−0.928264			−0.464132	+	0.885766i	$0.653634\pi$
$390$	5830.01	+	1093.70i	0.756959	+	0.142005i
$391$		−	1913.91i		−	0.247547i
$392$	−2806.25	+	3590.61i	−0.361574	+	0.462636i
$393$	−89.2045	−	2498.58i	−0.0114498	−	0.320705i
$394$	−2322.67	+	10331.9i	−0.296991	+	1.32110i
$395$		−	1462.62i		−	0.186310i
$396$	1533.96	−	3944.52i	0.194658	−	0.500555i
$397$			3576.18i			0.452099i	0.974116	+	0.226050i	$0.0725811\pi$
$397$			3576.18i			0.452099i	−0.974116	+	0.226050i	$0.927419\pi$
$398$	13446.1	+	3022.76i	1.69344	+	0.380697i
$399$	180.686	+	5060.94i	0.0226707	+	0.634997i
$400$	1013.86	+	1237.78i	0.126732	+	0.154722i
$401$			4642.92i			0.578196i	0.957300	+	0.289098i	$0.0933553\pi$
$401$			4642.92i			0.578196i	−0.957300	+	0.289098i	$0.906645\pi$
$402$	1526.31	−	8136.03i	0.189367	−	1.00942i
$403$	11228.2			1.38789
$404$	−689.833	−	326.667i	−0.0849517	−	0.0402284i
$405$	−3607.93	+	518.549i	−0.442665	+	0.0636220i
$406$	7143.93	+	1606.00i	0.873269	+	0.196317i
$407$	−5341.07			−0.650485
$408$	1233.12	+	894.758i	0.149629	+	0.108571i
$409$	−2880.41			−0.348233			−0.174116	−	0.984725i	$-0.555707\pi$
$409$	−2880.41			−0.348233			−0.174116	+	0.984725i	$0.555707\pi$
$410$	−6632.78	−	1491.09i	−0.798950	−	0.179609i
$411$	223.849	+	6269.92i	0.0268653	+	0.752487i
$412$	−651.243	+	1375.25i	−0.0778748	+	0.164451i
$413$	3847.65			0.458427
$414$	−1682.89	+	11153.4i	−0.199781	+	1.32405i
$415$			6175.77i			0.730497i
$416$	6554.22	+	13059.5i	0.772469	+	1.53917i
$417$	12668.9	−	452.307i	1.48777	−	0.0531164i
$418$	4428.47	+	995.549i	0.518190	+	0.116493i
$419$		−	11503.6i		−	1.34126i	−0.741792	−	0.670630i	$-0.766024\pi$
$419$		−	11503.6i		−	1.34126i	0.741792	−	0.670630i	$-0.233976\pi$
$420$	−978.098	+	2271.67i	−0.113634	+	0.263919i
$421$			12380.8i			1.43327i	0.697450	+	0.716633i	$0.254318\pi$
$421$			12380.8i			1.43327i	−0.697450	+	0.716633i	$0.745682\pi$
$422$	1315.57	−	5852.03i	0.151756	−	0.675053i
$423$	−9972.37	+	712.976i	−1.14627	+	0.0819529i
$424$	3780.49	−	4837.15i	0.433011	−	0.554040i
$425$			323.950i			0.0369738i
$426$	−1456.69	+	7764.91i	−0.165673	+	0.883125i
$427$	947.675			0.107403
$428$	4773.31	−	10080.0i	0.539081	−	1.13840i
$429$	8213.15	−	293.226i	0.924323	−	0.0330002i
$430$	75.0455	−	333.823i	0.00841631	−	0.0374380i
$431$	1329.74			0.148611			0.0743053	−	0.997236i	$-0.476326\pi$
$431$	1329.74			0.148611			0.0743053	+	0.997236i	$0.476326\pi$
$432$	−6399.27	−	6298.48i	−0.712697	−	0.701472i
$433$	7568.50			0.839997			0.419999	−	0.907525i	$-0.362031\pi$
$433$	7568.50			0.839997			0.419999	+	0.907525i	$0.362031\pi$
$434$	−1026.86	+	4567.73i	−0.113573	+	0.505203i
$435$	−5648.59	+	201.666i	−0.622596	+	0.0222279i
$436$	3604.35	−	7611.43i	0.395911	−	0.836058i
$437$	−12097.0			−1.32421
$438$	−268.259	+	1429.96i	−0.0292646	+	0.155996i
$439$		−	6198.59i		−	0.673901i	−0.941522	−	0.336951i	$-0.890604\pi$
$439$		−	6198.59i		−	0.673901i	0.941522	−	0.336951i	$-0.109396\pi$
$440$	1746.64	+	1365.09i	0.189245	+	0.147905i
$441$	5423.93	−	387.785i	0.585675	−	0.0418729i
$442$	−648.887	+	2886.42i	−0.0698289	+	0.310618i
$443$		−	4385.56i		−	0.470349i	−0.971953	−	0.235174i	$-0.924434\pi$
$443$		−	4385.56i		−	0.470349i	0.971953	−	0.235174i	$-0.0755661\pi$
$444$	−4481.12	+	10407.6i	−0.478974	+	1.11244i
$445$			3287.66i			0.350225i
$446$	14655.5	+	3294.66i	1.55596	+	0.349791i
$447$	10660.6	−	380.604i	1.12803	−	0.0402728i
$448$	−5912.12	+	1471.97i	−0.623485	+	0.155233i
$449$			10366.2i			1.08955i	0.838581	+	0.544777i	$0.183386\pi$
$449$			10366.2i			1.08955i	−0.838581	+	0.544777i	$0.816614\pi$
$450$	284.846	−	1887.82i	0.0298395	−	0.197761i
$451$	−9419.07			−0.983429
$452$	4742.36	−	10014.6i	0.493499	−	1.04214i
$453$	−43.0754	−	1206.52i	−0.00446768	−	0.125138i
$454$	10794.3	+	2426.62i	1.11586	+	0.250852i
$455$	−4802.71			−0.494845
$456$	5655.37	−	7794.01i	0.580783	−	0.800413i
$457$	8503.91			0.870451			0.435226	−	0.900321i	$-0.356669\pi$
$457$	8503.91			0.870451			0.435226	+	0.900321i	$0.356669\pi$
$458$	−16526.2	−	3715.19i	−1.68606	−	0.379038i
$459$	−194.260	−	1807.55i	−0.0197544	−	0.183811i
$460$	−5339.62	−	2528.55i	−0.541220	−	0.256292i
$461$	14344.7			1.44924			0.724618	−	0.689151i	$-0.242016\pi$
$461$	14344.7			1.44924			0.724618	+	0.689151i	$0.242016\pi$
$462$	−631.831	+	3367.99i	−0.0636265	+	0.339162i
$463$		−	14521.6i		−	1.45762i	−0.684717	−	0.728809i	$-0.740074\pi$
$463$		−	14521.6i		−	1.45762i	0.684717	−	0.728809i	$-0.259926\pi$
$464$	−8822.69	−	10771.3i	−0.882723	−	1.07768i
$465$	−128.943	−	3611.64i	−0.0128593	−	0.360184i
$466$	10045.2	+	2258.22i	0.998569	+	0.224485i
$467$			15334.2i			1.51945i	0.650247	+	0.759723i	$0.274665\pi$
$467$			15334.2i			1.51945i	−0.650247	+	0.759723i	$0.725335\pi$
$468$	6319.39	−	16250.1i	0.624175	−	1.60504i
$469$			6702.39i			0.659888i
$470$	1148.58	−	5109.17i	0.112723	−	0.501423i
$471$	566.928	+	15879.4i	0.0554621	+	1.55347i
$472$	−5764.66	−	4505.38i	−0.562161	−	0.439358i
$473$		−	474.054i		−	0.0460825i
$474$	−4225.50	−	792.698i	−0.409459	−	0.0768140i
$475$	2047.54			0.197785
$476$	−1114.88	−	527.944i	−0.107353	−	0.0508367i
$477$	−7306.94	+	522.411i	−0.701387	+	0.0501458i
$478$	−3908.71	+	17387.0i	−0.374018	+	1.66373i
$479$	−2635.56			−0.251403			−0.125701	−	0.992068i	$-0.540118\pi$
$479$	−2635.56			−0.251403			−0.125701	+	0.992068i	$0.540118\pi$
$480$	4125.41	−	2258.18i	0.392288	−	0.214732i
$481$	−22003.4			−2.08580
$482$	−115.995	+	515.978i	−0.0109615	+	0.0487596i
$483$	−325.849	−	9126.90i	−0.0306969	−	0.859810i
$484$	−6847.65	−	3242.67i	−0.643092	−	0.304533i
$485$	2872.82			0.268965
$486$	−457.309	+	10704.3i	−0.0426830	+	0.999089i
$487$			627.098i			0.0583502i	0.999574	+	0.0291751i	$0.00928803\pi$
$487$			627.098i			0.0583502i	−0.999574	+	0.0291751i	$0.990712\pi$
$488$	−1419.83	−	1109.67i	−0.131707	−	0.102936i
$489$	−3229.82	+	115.311i	−0.298686	+	0.0106637i
$490$	−624.706	+	2778.86i	−0.0575946	+	0.256196i
$491$			106.671i			0.00980444i	0.999988	+	0.00490222i	$0.00156043\pi$
$491$			106.671i			0.00980444i	−0.999988	+	0.00490222i	$0.998440\pi$
$492$	−7902.52	+	18353.9i	−0.724133	+	1.68182i
$493$		−	2819.05i		−	0.257533i
$494$	18243.8	+	4101.32i	1.66159	+	0.373537i
$495$	−188.636	−	2638.45i	−0.0171284	−	0.239574i
$496$	6887.03	−	5641.12i	0.623461	−	0.510673i
$497$		−	6396.66i		−	0.577323i
$498$	17841.7	+	3347.09i	1.60544	+	0.301178i
$499$	3347.75			0.300332			0.150166	−	0.988661i	$-0.452019\pi$
$499$	3347.75			0.300332			0.150166	+	0.988661i	$0.452019\pi$
$500$	903.786	+	427.984i	0.0808371	+	0.0382800i
$501$	−7737.16	+	276.232i	−0.689962	+	0.0246330i
$502$	−15778.7	−	3547.15i	−1.40286	−	0.315373i
$503$	−574.905			−0.0509617			−0.0254809	−	0.999675i	$-0.508112\pi$
$503$	−574.905			−0.0509617			−0.0254809	+	0.999675i	$0.508112\pi$
$504$	6032.73	+	4056.90i	0.533173	+	0.358549i
$505$	−477.044			−0.0420360
$506$	−7986.30	−	1795.37i	−0.701649	−	0.157735i
$507$	22426.7	−	800.679i	1.96451	−	0.0701369i
$508$	1181.30	−	2494.59i	0.103173	−	0.217873i
$509$	846.131			0.0736819			0.0368410	−	0.999321i	$-0.488271\pi$
$509$	846.131			0.0736819			0.0368410	+	0.999321i	$0.488271\pi$
$510$	935.888	+	175.571i	0.0812585	+	0.0152440i
$511$		−	1177.99i		−	0.101979i
$512$	10581.3	+	4717.40i	0.913343	+	0.407191i
$513$	−11424.7	+	1227.83i	−0.983261	+	0.105673i
$514$	−18235.3	−	4099.40i	−1.56483	−	0.351784i
$515$			951.033i			0.0813739i
$516$	−923.738	−	397.728i	−0.0788087	−	0.0339322i
$517$		−	7255.43i		−	0.617202i
$518$	2012.28	−	8951.15i	0.170684	−	0.759249i
$519$	−12044.2	+	430.003i	−1.01866	+	0.0363680i
$520$	7195.55	+	5623.70i	0.606819	+	0.474261i
$521$			12770.5i			1.07387i	0.843624	+	0.536935i	$0.180418\pi$
$521$			12770.5i			1.07387i	−0.843624	+	0.536935i	$0.819582\pi$
$522$	−2478.76	+	16428.0i	−0.207840	+	1.37746i
$523$	−5813.64			−0.486067			−0.243033	−	0.970018i	$-0.578142\pi$
$523$	−5813.64			−0.486067			−0.243033	+	0.970018i	$0.578142\pi$
$524$	1647.43	−	3478.92i	0.137344	−	0.290033i
$525$	55.1532	+	1544.82i	0.00458492	+	0.128422i
$526$	3313.69	−	14740.2i	0.274684	−	1.22187i
$527$	1802.46			0.148988
$528$	4890.35	−	4306.18i	0.403078	−	0.354929i
$529$	9648.73			0.793025
$530$	841.583	−	3743.59i	0.0689736	−	0.306813i
$531$	622.581	+	8708.02i	0.0508808	+	0.711668i
$532$	−3336.90	+	7046.63i	−0.271942	+	0.574267i
$533$	−38803.4			−3.15340
$534$	9498.01	+	1781.82i	0.769699	+	0.144395i
$535$		−	6970.64i		−	0.563303i
$536$	7848.12	−	10041.7i	0.632439	−	0.809208i
$537$	468.158	+	13112.9i	0.0376211	+	1.05375i
$538$	4374.53	−	19459.1i	0.350557	−	1.55937i
$539$			3946.20i			0.315352i
$540$	−5299.51	−	1846.06i	−0.422324	−	0.147115i
$541$			4442.49i			0.353045i	0.984297	+	0.176523i	$0.0564849\pi$
$541$			4442.49i			0.353045i	−0.984297	+	0.176523i	$0.943515\pi$
$542$	13206.3	+	2968.85i	1.04660	+	0.235283i
$543$	731.060	+	20476.7i	0.0577768	+	1.61831i
$544$	1052.15	+	2096.44i	0.0829235	+	0.165228i
$545$		−	5263.57i		−	0.413700i
$546$	−2602.93	+	13875.0i	−0.204020	+	1.08753i
$547$	−2460.07			−0.192295			−0.0961473	−	0.995367i	$-0.530652\pi$
$547$	−2460.07			−0.192295			−0.0961473	+	0.995367i	$0.530652\pi$
$548$	−4134.03	+	8729.96i	−0.322257	+	0.680521i
$549$	153.342	+	2144.78i	0.0119207	+	0.166734i
$550$	1351.76	+	303.885i	0.104799	+	0.0235595i
$551$	−17818.0			−1.37762
$552$	−10198.9	+	14055.7i	−0.786401	+	1.08379i
$553$	3480.92			0.267674
$554$	11260.3	+	2531.39i	0.863545	+	0.194131i
$555$	252.682	+	7077.54i	0.0193257	+	0.541306i
$556$	17639.7	+	8353.18i	1.34548	+	0.637147i
$557$	20307.0			1.54477			0.772385	−	0.635155i	$-0.219064\pi$
$557$	20307.0			1.54477			0.772385	+	0.635155i	$0.219064\pi$
$558$	−10503.9	−	1584.89i	−0.796889	−	0.120240i
$559$		−	1952.94i		−	0.147765i
$560$	−2945.82	+	2412.90i	−0.222292	+	0.182078i
$561$	1318.45	−	47.0714i	0.0992248	−	0.00354253i
$562$	−2877.00	−	646.769i	−0.215941	−	0.0485450i
$563$		−	1927.79i		−	0.144310i	−0.997393	−	0.0721550i	$-0.977012\pi$
$563$		−	1927.79i		−	0.144310i	0.997393	−	0.0721550i	$-0.0229876\pi$
$564$	−14137.9	−	6087.25i	−1.05552	−	0.454467i
$565$		−	6925.44i		−	0.515673i
$566$	1747.47	−	7773.20i	0.129773	−	0.577265i
$567$	−1234.11	−	8586.59i	−0.0914068	−	0.635984i
$568$	−7490.13	+	9583.66i	−0.553308	+	0.707960i
$569$			5528.65i			0.407334i	0.979040	+	0.203667i	$0.0652861\pi$
$569$			5528.65i			0.407334i	−0.979040	+	0.203667i	$0.934714\pi$
$570$	1109.71	−	5915.33i	0.0815449	−	0.434677i
$571$	−22158.5			−1.62400			−0.812001	−	0.583656i	$-0.801621\pi$
$571$	−22158.5			−1.62400			−0.812001	+	0.583656i	$0.801621\pi$
$572$	11435.6	+	5415.29i	0.835923	+	0.395847i
$573$	9963.39	−	355.713i	0.726399	−	0.0259339i
$574$	3548.68	−	15785.5i	0.258047	−	1.14786i
$575$	−3692.54			−0.267808
$576$	−4288.01	−	13142.1i	−0.310186	−	0.950676i
$577$	16291.1			1.17541			0.587703	−	0.809077i	$-0.300032\pi$
$577$	16291.1			1.17541			0.587703	+	0.809077i	$0.300032\pi$
$578$	2943.69	−	13094.3i	0.211836	−	0.942306i
$579$	7361.66	−	262.826i	0.528394	−	0.0188647i
$580$	−7864.86	−	3724.36i	−0.563052	−	0.266631i
$581$	−14697.8			−1.04952
$582$	1556.99	−	8299.55i	0.110892	−	0.591112i
$583$		−	5316.19i		−	0.377657i
$584$	−1379.36	+	1764.89i	−0.0977367	+	0.125054i
$585$	−777.117	−	10869.5i	−0.0549228	−	0.768203i
$586$	2713.13	−	12068.7i	0.191260	−	0.850776i
$587$			14991.4i			1.05411i	0.849831	+	0.527055i	$0.176704\pi$
$587$			14991.4i			1.05411i	−0.849831	+	0.527055i	$0.823296\pi$
$588$	7689.53	+	3310.83i	0.539304	+	0.232205i
$589$		−	11392.6i		−	0.796982i
$590$	−4461.41	−	1002.95i	−0.311311	−	0.0699846i
$591$	19442.2	−	694.125i	1.35320	−	0.0483121i
$592$	−13496.2	+	11054.6i	−0.936974	+	0.767469i
$593$		−	11604.3i		−	0.803591i	−0.915729	−	0.401796i	$-0.868386\pi$
$593$		−	11604.3i		−	0.803591i	0.915729	−	0.401796i	$-0.131614\pi$
$594$	−7724.68	−	884.994i	−0.533582	−	0.0611309i
$595$	−770.976			−0.0531209
$596$	14843.3	+	7028.97i	1.02014	+	0.483084i
$597$	−903.346	−	25302.4i	−0.0619288	−	1.73460i
$598$	−32900.8	−	7396.32i	−2.24986	−	0.505783i
$599$	−2109.64			−0.143902			−0.0719511	−	0.997408i	$-0.522923\pi$
$599$	−2109.64			−0.143902			−0.0719511	+	0.997408i	$0.522923\pi$
$600$	1726.27	−	2379.08i	0.117458	−	0.161876i
$601$	−17029.9			−1.15585			−0.577923	−	0.816091i	$-0.696137\pi$
$601$	−17029.9			−1.15585			−0.577923	+	0.816091i	$0.696137\pi$
$602$	794.472	+	178.603i	0.0537878	+	0.0120919i
$603$	−15168.9	+	1084.50i	−1.02442	+	0.0732410i
$604$	795.514	−	1679.91i	0.0535911	−	0.113170i
$605$	−4735.39			−0.318216
$606$	−258.544	+	1378.17i	−0.0173311	+	0.0923837i
$607$		−	18341.5i		−	1.22646i	−0.789905	−	0.613229i	$-0.789870\pi$
$607$		−	18341.5i		−	1.22646i	0.789905	−	0.613229i	$-0.210130\pi$
$608$	13250.6	−	6650.14i	0.883856	−	0.443584i
$609$	−479.950	−	13443.2i	−0.0319352	−	0.894494i
$610$	−1098.84	−	247.027i	−0.0729358	−	0.0163964i
$611$		−	29889.9i		−	1.97908i
$612$	1014.45	−	2608.62i	0.0670043	−	0.172299i
$613$			9663.26i			0.636697i	0.947974	+	0.318349i	$0.103128\pi$
$613$			9663.26i			0.636697i	−0.947974	+	0.318349i	$0.896872\pi$
$614$	−3007.72	+	13379.1i	−0.197690	+	0.879377i
$615$	445.609	+	12481.3i	0.0292174	+	0.818368i
$616$	−3248.81	+	4156.86i	−0.212497	+	0.271891i
$617$			2815.64i			0.183717i	0.995772	+	0.0918586i	$0.0292808\pi$
$617$			2815.64i			0.183717i	−0.995772	+	0.0918586i	$0.970719\pi$
$618$	2747.53	+	515.433i	0.178838	+	0.0335498i
$619$	−14824.5			−0.962596			−0.481298	−	0.876557i	$-0.659834\pi$
$619$	−14824.5			−0.962596			−0.481298	+	0.876557i	$0.659834\pi$
$620$	2381.31	−	5028.69i	0.154251	−	0.325737i
$621$	20603.3	−	2214.27i	1.33137	−	0.143085i
$622$	2550.82	−	11346.7i	0.164435	−	0.731450i
$623$	−7824.37			−0.503173
$624$	20146.6	−	17740.0i	1.29248	−	1.13809i
$625$	625.000			0.0400000
$626$	4447.80	−	19785.0i	0.283978	−	1.26321i
$627$	−297.518	−	8333.35i	−0.0189501	−	0.530785i
$628$	−10470.0	+	22109.8i	−0.665284	+	1.40490i
$629$	−3532.20			−0.223908
$630$	4492.87	+	677.912i	0.284127	+	0.0428709i
$631$			2273.51i			0.143434i	0.997425	+	0.0717171i	$0.0228479\pi$
$631$			2273.51i			0.143434i	−0.997425	+	0.0717171i	$0.977152\pi$
$632$	−5215.22	−	4075.97i	−0.328244	−	0.256540i
$633$	−11012.2	+	393.156i	−0.691460	+	0.0246865i
$634$	2711.77	−	12062.7i	0.169871	−	0.755630i
$635$		−	1725.09i		−	0.107808i
$636$	−10359.1	−	4460.24i	−0.645856	−	0.278082i
$637$			16257.0i			1.01119i
$638$	−11763.2	−	2644.45i	−0.729953	−	0.164098i
$639$	14476.9	−	1035.03i	0.896243	−	0.0640770i
$640$	7238.88	−	165.686i	0.447096	−	0.0102333i
$641$			19455.2i			1.19880i	0.800448	+	0.599402i	$0.204595\pi$
$641$			19455.2i			1.19880i	−0.800448	+	0.599402i	$0.795405\pi$
$642$	−20138.1	−	3777.89i	−1.23799	−	0.232245i
$643$	15696.0			0.962657			0.481328	−	0.876540i	$-0.340154\pi$
$643$	15696.0			0.962657			0.481328	+	0.876540i	$0.340154\pi$
$644$	6017.76	−	12707.9i	0.368219	−	0.777580i
$645$	−628.177	+	22.4272i	−0.0383480	+	0.00136910i
$646$	2928.67	+	658.383i	0.178370	+	0.0400987i
$647$	10884.6			0.661389			0.330694	−	0.943738i	$-0.392717\pi$
$647$	10884.6			0.661389			0.330694	+	0.943738i	$0.392717\pi$
$648$	−8205.44	+	14309.7i	−0.497438	+	0.867499i
$649$	−6335.55			−0.383193
$650$	5568.81	+	1251.90i	0.336041	+	0.0755442i
$651$	8595.42	−	306.874i	0.517482	−	0.0184752i
$652$	−4497.06	−	2129.56i	−0.270120	−	0.127914i
$653$	27481.9			1.64694			0.823469	−	0.567361i	$-0.192036\pi$
$653$	27481.9			1.64694			0.823469	+	0.567361i	$0.192036\pi$
$654$	−15206.4	−	2852.70i	−0.909201	−	0.170565i
$655$		−	2405.80i		−	0.143515i
$656$	−23800.7	+	19495.0i	−1.41656	+	1.16029i
$657$	2666.03	−	190.608i	0.158313	−	0.0113186i
$658$	12159.4	+	2733.52i	0.720402	+	0.161951i
$659$			31077.7i			1.83705i	0.395367	+	0.918523i	$0.370617\pi$
$659$			31077.7i			1.83705i	−0.395367	+	0.918523i	$0.629383\pi$
$660$	1610.54	−	3740.54i	0.0949851	−	0.220606i
$661$			7446.83i			0.438197i	0.975703	+	0.219098i	$0.0703116\pi$
$661$			7446.83i			0.438197i	−0.975703	+	0.219098i	$0.929688\pi$
$662$	−3468.22	+	15427.6i	−0.203620	+	0.905755i
$663$	5431.58	−	193.918i	0.318167	−	0.0113592i
$664$	22020.7	+	17210.4i	1.28700	+	1.00586i
$665$			4872.99i			0.284160i
$666$	20583.9	+	3105.83i	1.19761	+	0.180703i
$667$	32132.9			1.86535
$668$	−10772.9	−	5101.45i	−0.623976	−	0.295481i
$669$	−984.602	−	27578.3i	−0.0569012	−	1.59378i
$670$	1747.09	−	7771.52i	0.100740	−	0.448119i
$671$	−1560.44			−0.0897768
$672$	5374.30	+	9818.16i	0.308509	+	0.563607i
$673$	11727.3			0.671700			0.335850	−	0.941915i	$-0.390976\pi$
$673$	11727.3			0.671700			0.335850	+	0.941915i	$0.390976\pi$
$674$	−4899.66	+	21795.0i	−0.280012	+	1.24557i
$675$	−3487.32	+	374.788i	−0.198855	+	0.0213712i
$676$	31226.0	+	14786.9i	1.77663	+	0.841313i
$677$	−16194.0			−0.919331			−0.459666	−	0.888092i	$-0.652031\pi$
$677$	−16194.0			−0.919331			−0.459666	+	0.888092i	$0.652031\pi$
$678$	−20007.5	−	3753.39i	−1.13331	−	0.212608i
$679$			6837.09i			0.386426i
$680$	1155.10	+	902.769i	0.0651411	+	0.0509112i
$681$	−725.190	−	20312.3i	−0.0408067	−	1.14298i
$682$	1690.82	−	7521.24i	0.0949340	−	0.422292i
$683$		−	22713.8i		−	1.27250i	−0.771481	−	0.636252i	$-0.780484\pi$
$683$		−	22713.8i		−	1.27250i	0.771481	−	0.636252i	$-0.219516\pi$
$684$	−16487.9	−	6411.88i	−0.921682	−	0.358427i
$685$			6037.08i			0.336737i
$686$	−17876.8	−	4018.82i	−0.994955	−	0.223672i
$687$	1110.28	+	31098.4i	0.0616590	+	1.72704i
$688$	−981.167	−	1197.87i	−0.0543701	−	0.0663784i
$689$		−	21900.9i		−	1.21097i
$690$	−2001.25	+	10667.7i	−0.110415	+	0.588569i
$691$	−10207.3			−0.561945			−0.280972	−	0.959716i	$-0.590657\pi$
$691$	−10207.3			−0.561945			−0.280972	+	0.959716i	$0.590657\pi$
$692$	−16769.8	−	7941.27i	−0.921233	−	0.436245i
$693$	6279.30	−	448.940i	0.344200	−	0.0246087i
$694$	29979.3	+	6739.55i	1.63977	+	0.368631i
$695$	12198.5			0.665775
$696$	−15022.2	+	20703.0i	−0.818124	+	1.12751i
$697$	−6229.08			−0.338513
$698$	12080.1	+	2715.70i	0.655072	+	0.147264i
$699$	−674.863	−	18902.7i	−0.0365174	−	1.02284i
$700$	−1018.57	+	2150.94i	−0.0549975	+	0.116140i
$701$	2137.78			0.115182			0.0575911	−	0.998340i	$-0.481658\pi$
$701$	2137.78			0.115182			0.0575911	+	0.998340i	$0.481658\pi$
$702$	−31823.1	−	3645.87i	−1.71095	−	0.196018i
$703$			22325.4i			1.19775i
$704$	9734.90	−	2423.76i	0.521162	−	0.129757i
$705$	−9614.28	+	343.249i	−0.513610	+	0.0183369i
$706$	3680.30	+	827.355i	0.196190	+	0.0441047i
$707$		−	1135.33i		−	0.0603937i
$708$	−5315.48	+	12345.4i	−0.282158	+	0.655322i
$709$			7932.80i			0.420201i	0.977680	+	0.210101i	$0.0673792\pi$
$709$			7932.80i			0.420201i	−0.977680	+	0.210101i	$0.932621\pi$
$710$	−1667.39	+	7417.02i	−0.0881355	+	0.392050i
$711$	563.242	+	7878.04i	0.0297092	+	0.415541i
$712$	11722.7	+	9161.90i	0.617032	+	0.482243i
$713$			20545.4i			1.07914i
$714$	−417.847	+	2227.34i	−0.0219013	+	0.116745i
$715$	7908.15			0.413633
$716$	−8645.93	+	18257.9i	−0.451276	+	0.952974i
$717$	32718.3	−	1168.11i	1.70417	−	0.0608422i
$718$	2188.59	−	9735.46i	0.113757	−	0.506022i
$719$	24949.4			1.29410			0.647048	−	0.762449i	$-0.276003\pi$
$719$	24949.4			1.29410			0.647048	+	0.762449i	$0.276003\pi$
$720$	−5937.54	−	6276.56i	−0.307332	−	0.324880i
$721$	−2263.39			−0.116911
$722$	−93.7447	+	417.002i	−0.00483216	+	0.0214947i
$723$	970.951	−	34.6649i	0.0499447	−	0.00178313i
$724$	−13501.2	+	28510.9i	−0.693050	+	1.46353i
$725$	−5438.82			−0.278611
$726$	−2566.44	+	13680.5i	−0.131198	+	0.699354i
$727$			13284.0i			0.677685i	0.940843	+	0.338843i	$0.110035\pi$
$727$			13284.0i			0.677685i	−0.940843	+	0.338843i	$0.889965\pi$
$728$	−13384.0	+	17124.9i	−0.681378	+	0.871826i
$729$	19233.5	−	4182.42i	0.977164	−	0.212489i
$730$	−307.062	+	1365.89i	−0.0155683	+	0.0692520i
$731$		−	313.505i		−	0.0158624i
$732$	−1309.20	+	3040.67i	−0.0661058	+	0.153533i
$733$		−	16860.0i		−	0.849575i	−0.905293	−	0.424788i	$-0.860349\pi$
$733$		−	16860.0i		−	0.849575i	0.905293	−	0.424788i	$-0.139651\pi$
$734$	−11858.3	−	2665.83i	−0.596319	−	0.134056i
$735$	5229.17	−	186.692i	0.262423	−	0.00936903i
$736$	−23896.2	+	11992.9i	−1.19677	+	0.600629i
$737$		−	11036.2i		−	0.551591i
$738$	36300.0	+	5477.17i	1.81060	+	0.273194i
$739$	21665.0			1.07843			0.539216	−	0.842168i	$-0.318721\pi$
$739$	21665.0			1.07843			0.539216	+	0.842168i	$0.318721\pi$
$740$	−4666.53	+	9854.46i	−0.231818	+	0.489537i
$741$	−1225.67	−	34330.6i	−0.0607640	−	1.70198i
$742$	8909.45	+	2002.90i	0.440804	+	0.0990955i
$743$	−23700.7			−1.17025			−0.585123	−	0.810944i	$-0.698954\pi$
$743$	−23700.7			−1.17025			−0.585123	+	0.810944i	$0.698954\pi$
$744$	−13237.2	−	9604.99i	−0.652285	−	0.473301i
$745$	10264.7			0.504790
$746$	−4697.25	−	1055.97i	−0.230534	−	0.0518256i
$747$	−2378.23	−	33264.2i	−0.116486	−	1.62928i
$748$	1835.76	+	869.314i	0.0897352	+	0.0424937i
$749$	16589.6			0.809307
$750$	338.732	−	1805.62i	0.0164917	−	0.0879092i
$751$			38822.5i			1.88636i	0.332286	+	0.943179i	$0.392180\pi$
$751$			38822.5i			1.88636i	−0.332286	+	0.943179i	$0.607820\pi$
$752$	−15016.8	−	18333.5i	−0.728201	−	0.889033i
$753$	1060.06	+	29691.8i	0.0513023	+	1.43696i
$754$	−48460.4	−	10894.2i	−2.34062	−	0.526186i
$755$		−	1161.72i		−	0.0559990i
$756$	4393.48	−	12612.4i	0.211362	−	0.606759i
$757$		−	21198.9i		−	1.01782i	−0.860821	−	0.508908i	$-0.830049\pi$
$757$		−	21198.9i		−	1.01782i	0.860821	−	0.508908i	$-0.169951\pi$
$758$	854.323	−	3800.26i	0.0409372	−	0.182100i
$759$	536.543	+	15028.4i	0.0256591	+	0.718702i
$760$	5706.00	−	7300.86i	0.272340	−	0.348460i
$761$			2028.32i			0.0966185i	0.998832	+	0.0483092i	$0.0153833\pi$
$761$			2028.32i			0.0966185i	−0.998832	+	0.0483092i	$0.984617\pi$
$762$	−4983.78	−	934.951i	−0.236933	−	0.0444484i
$763$	12526.9			0.594369
$764$	13872.6	+	6569.30i	0.656928	+	0.311085i
$765$	−124.750	−	1744.88i	−0.00589588	−	0.0824655i
$766$	1214.34	−	5401.71i	0.0572792	−	0.254793i
$767$	−26100.3			−1.22872
$768$	3444.60	−	21002.8i	0.161844	−	0.986816i
$769$	−257.053			−0.0120541			−0.00602703	−	0.999982i	$-0.501918\pi$
$769$	−257.053			−0.0120541			−0.00602703	+	0.999982i	$0.501918\pi$
$770$	−723.224	+	3217.09i	−0.0338483	+	0.150566i
$771$	1225.10	+	34314.5i	0.0572254	+	1.60286i
$772$	10250.1	+	4853.86i	0.477860	+	0.226288i
$773$	19191.4			0.892971			0.446486	−	0.894791i	$-0.352675\pi$
$773$	19191.4			0.892971			0.446486	+	0.894791i	$0.352675\pi$
$774$	−275.662	+	1826.95i	−0.0128016	+	0.0848429i
$775$		−	3477.51i		−	0.161182i
$776$	8005.85	−	10243.5i	0.370352	−	0.473867i
$777$	−16844.0	+	601.365i	−0.777703	+	0.0277656i
$778$	−4418.19	+	19653.3i	−0.203599	+	0.905661i
$779$			39371.2i			1.81081i
$780$	6634.87	−	15409.7i	0.304572	−	0.707381i
$781$			10532.8i			0.482576i
$782$	−5281.55	−	1187.33i	−0.241519	−	0.0542951i
$783$	30347.1	−	3261.45i	1.38508	−	0.148856i
$784$	8167.59	+	9971.50i	0.372066	+	0.454241i
$785$			15289.7i			0.695176i
$786$	−6950.32	−	1303.87i	−0.315407	−	0.0591699i
$787$	−41816.6			−1.89403			−0.947015	−	0.321191i	$-0.895917\pi$
$787$	−41816.6			−1.89403			−0.947015	+	0.321191i	$0.895917\pi$
$788$	27070.4	+	12819.1i	1.22379	+	0.579518i
$789$	−27737.6	+	990.289i	−1.25157	+	0.0446834i
$790$	−4036.18	−	907.360i	−0.181773	−	0.0408638i
$791$	16482.0			0.740876
$792$	−9933.51	−	6680.09i	−0.445671	−	0.299706i
$793$	−6428.50			−0.287872
$794$	9868.67	+	2218.54i	0.441090	+	0.0991600i
$795$	−7044.57	+	251.505i	−0.314270	+	0.0112201i
$796$	16683.0	−	35230.0i	0.742855	−	1.56871i
$797$	−25232.5			−1.12143			−0.560717	−	0.828008i	$-0.689474\pi$
$797$	−25232.5			−1.12143			−0.560717	+	0.828008i	$0.689474\pi$
$798$	14078.0	+	2641.02i	0.624507	+	0.117157i
$799$		−	4798.21i		−	0.212451i
$800$	4044.68	−	2029.92i	0.178751	−	0.0897105i
$801$	−1266.05	−	17708.2i	−0.0558472	−	0.781132i
$802$	12812.4	+	2880.31i	0.564117	+	0.126817i
$803$			1939.68i			0.0852425i
$804$	−21505.0	−	9259.26i	−0.943311	−	0.406155i
$805$		−	8787.96i		−	0.384764i
$806$	6965.62	−	30985.0i	0.304409	−	1.35409i
$807$	−36617.5	+	1307.32i	−1.59727	+	0.0570258i
$808$	−1329.40	+	1700.98i	−0.0578816	+	0.0740597i
$809$		−	35880.6i		−	1.55933i	−0.626199	−	0.779663i	$-0.715390\pi$
$809$		−	35880.6i		−	1.55933i	0.626199	−	0.779663i	$-0.284610\pi$
$810$	−807.270	+	10278.0i	−0.0350180	+	0.445840i
$811$	24028.6			1.04039			0.520196	−	0.854047i	$-0.325859\pi$
$811$	24028.6			1.04039			0.520196	+	0.854047i	$0.325859\pi$
$812$	8863.70	−	18717.8i	0.383073	−	0.808946i
$813$	−887.235	−	24851.1i	−0.0382739	−	1.07204i
$814$	−3313.42	+	14739.0i	−0.142672	+	0.634645i
$815$	−3109.87			−0.133661
$816$	3234.12	−	2847.79i	0.138746	−	0.122172i
$817$	−1981.52			−0.0848528
$818$	−1786.91	+	7948.66i	−0.0763788	+	0.339754i
$819$	25868.6	−	1849.48i	1.10369	−	0.0789084i
$820$	−8229.50	+	17378.5i	−0.350471	+	0.740102i
$821$	−9237.39			−0.392676			−0.196338	−	0.980536i	$-0.562905\pi$
$821$	−9237.39			−0.392676			−0.196338	+	0.980536i	$0.562905\pi$
$822$	17441.1	+	3271.92i	0.740057	+	0.138834i
$823$		−	2873.15i		−	0.121691i	−0.998147	−	0.0608454i	$-0.980620\pi$
$823$		−	2873.15i		−	0.121691i	0.998147	−	0.0608454i	$-0.0193797\pi$
$824$	3391.07	+	2650.30i	0.143366	+	0.112048i
$825$	−90.8154	−	2543.71i	−0.00383247	−	0.107346i
$826$	2386.95	−	10617.8i	0.100548	−	0.447265i
$827$		−	15113.0i		−	0.635465i	−0.948180	−	0.317733i	$-0.897079\pi$
$827$		−	15113.0i		−	0.635465i	0.948180	−	0.317733i	$-0.102921\pi$
$828$	29734.3	+	11563.2i	1.24799	+	0.485324i
$829$			10373.3i			0.434595i	0.976105	+	0.217298i	$0.0697242\pi$
$829$			10373.3i			0.434595i	−0.976105	+	0.217298i	$0.930276\pi$
$830$	17042.4	+	3831.24i	0.712710	+	0.160222i
$831$	−756.499	−	21189.3i	−0.0315796	−	0.884533i
$832$	40104.5	−	9985.05i	1.67112	−	0.416069i
$833$			2609.73i			0.108549i
$834$	6611.21	−	35241.2i	0.274493	−	1.46319i
$835$	−7449.83			−0.308757
$836$	5494.54	−	11603.0i	0.227312	−	0.480022i
$837$	2085.33	+	19403.5i	0.0861164	+	0.801295i
$838$	−31744.8	−	7136.45i	−1.30860	−	0.294182i
$839$	−14010.2			−0.576502			−0.288251	−	0.957555i	$-0.593074\pi$
$839$	−14010.2			−0.576502			−0.288251	+	0.957555i	$0.593074\pi$
$840$	5662.02	+	4108.38i	0.232569	+	0.168753i
$841$	22940.3			0.940599
$842$	34165.6	+	7680.65i	1.39837	+	0.314362i
$843$	193.285	+	5413.85i	0.00789692	+	0.221190i
$844$	−15332.9	−	7260.80i	−0.625330	−	0.296122i
$845$	21593.9			0.879114
$846$	−4219.02	+	27961.6i	−0.171457	+	1.13634i
$847$		−	11269.9i		−	0.457187i
$848$	−11003.1	−	13433.3i	−0.445576	−	0.543987i
$849$	−14627.4	+	522.227i	−0.591296	+	0.0211104i
$850$	893.957	+	200.967i	0.0360735	+	0.00810956i
$851$		−	40261.7i		−	1.62180i
$852$	20524.0	+	8836.90i	0.825283	+	0.355337i
$853$			11697.1i			0.469520i	0.972053	+	0.234760i	$0.0754304\pi$
$853$			11697.1i			0.469520i	−0.972053	+	0.234760i	$0.924570\pi$
$854$	587.905	−	2615.16i	0.0235570	−	0.104788i
$855$	−11028.6	+	788.490i	−0.441134	+	0.0315389i
$856$	−24855.0	−	19425.5i	−0.992437	−	0.775642i
$857$		−	4954.60i		−	0.197486i	−0.995113	−	0.0987432i	$-0.968518\pi$
$857$		−	4954.60i		−	0.197486i	0.995113	−	0.0987432i	$-0.0314822\pi$
$858$	4285.99	−	22846.6i	0.170538	−	0.909054i
$859$	−31596.1			−1.25500			−0.627499	−	0.778617i	$-0.715921\pi$
$859$	−31596.1			−1.25500			−0.627499	+	0.778617i	$0.715921\pi$
$860$	−874.646	−	414.184i	−0.0346805	−	0.0164228i
$861$	−29704.7	+	1060.52i	−1.17576	+	0.0419771i
$862$	824.924	−	3669.48i	0.0325952	−	0.144992i
$863$	6703.04			0.264396			0.132198	−	0.991223i	$-0.457796\pi$
$863$	6703.04			0.264396			0.132198	+	0.991223i	$0.457796\pi$
$864$	−21350.9	+	13751.8i	−0.840709	+	0.541488i
$865$	−11596.9			−0.455847
$866$	4695.24	−	20885.7i	0.184239	−	0.819544i
$867$	−24640.5	+	879.716i	−0.965208	+	0.0344599i
$868$	11967.9	+	5667.33i	0.467991	+	0.221615i
$869$	−5731.70			−0.223745
$870$	−2947.69	+	15712.7i	−0.114869	+	0.612311i
$871$		−	45465.3i		−	1.76869i
$872$	−18768.1	−	14668.3i	−0.728864	−	0.569645i
$873$	−15473.7	+	1106.30i	−0.599893	+	0.0428894i
$874$	−7504.57	+	33382.4i	−0.290442	+	1.29196i
$875$			1487.45i			0.0574686i
$876$	3779.63	+	1627.37i	0.145779	+	0.0627670i
$877$			2640.85i			0.101682i	0.998707	+	0.0508411i	$0.0161902\pi$
$877$			2640.85i			0.101682i	−0.998707	+	0.0508411i	$0.983810\pi$
$878$	−17105.4	−	3845.40i	−0.657492	−	0.147808i
$879$	−22710.6	+	810.813i	−0.871454	+	0.0311127i
$880$	4850.59	−	3973.09i	0.185811	−	0.152196i
$881$		−	948.785i		−	0.0362831i	−0.999835	−	0.0181415i	$-0.994225\pi$
$881$		−	948.785i		−	0.0362831i	0.999835	−	0.0181415i	$-0.00577495\pi$
$882$	2294.71	−	15208.2i	0.0876042	−	0.580598i
$883$	−7226.54			−0.275416			−0.137708	−	0.990473i	$-0.543974\pi$
$883$	−7226.54			−0.275416			−0.137708	+	0.990473i	$0.543974\pi$
$884$	7562.69	+	3581.28i	0.287739	+	0.136257i
$885$	299.730	+	8395.34i	0.0113846	+	0.318877i
$886$	−12102.2	−	2720.65i	−0.458896	−	0.103163i
$887$	48118.6			1.82149			0.910746	−	0.412966i	$-0.135507\pi$
$887$	48118.6			1.82149			0.910746	+	0.412966i	$0.135507\pi$
$888$	25940.3	+	18822.4i	0.980293	+	0.711304i
$889$	4105.59			0.154890
$890$	9072.47	+	2039.55i	0.341697	+	0.0768156i
$891$	2032.08	+	14138.7i	0.0764056	+	0.531609i
$892$	18183.6	−	38398.9i	0.682547	−	1.44136i
$893$	−30327.4			−1.13647
$894$	5563.15	−	29654.5i	0.208120	−	1.10939i
$895$			12626.0i			0.471553i
$896$	394.319	+	17228.0i	0.0147023	+	0.642351i
$897$	2210.37	+	61911.8i	0.0822768	+	2.30454i
$898$	28606.0	+	6430.82i	1.06302	+	0.238975i
$899$			30261.7i			1.12268i
$900$	−5032.83	−	1957.19i	−0.186401	−	0.0724884i
$901$		−	3515.74i		−	0.129996i
$902$	−5843.27	+	25992.4i	−0.215698	+	0.959483i
$903$	−53.3750	−	1495.01i	−0.00196701	−	0.0550951i
$904$	−24693.8	−	19299.5i	−0.908522	−	0.710058i
$905$			19716.3i			0.724189i
$906$	−3356.19	−	629.618i	−0.123071	−	0.0230879i
$907$	3998.99			0.146399			0.0731997	−	0.997317i	$-0.476679\pi$
$907$	3998.99			0.146399			0.0731997	+	0.997317i	$0.476679\pi$
$908$	13392.8	−	28282.0i	0.489488	−	1.03367i
$909$	2569.48	−	183.705i	0.0937560	−	0.00670310i
$910$	−2979.44	+	13253.3i	−0.108536	+	0.482795i
$911$	−44298.6			−1.61106			−0.805532	−	0.592552i	$-0.798120\pi$
$911$	−44298.6			−1.61106			−0.805532	+	0.592552i	$0.798120\pi$
$912$	−17999.6	−	20441.4i	−0.653538	−	0.742197i
$913$	24201.5			0.877276
$914$	5275.54	−	23467.0i	0.190918	−	0.849256i
$915$	73.8235	+	2067.77i	0.00266725	+	0.0747085i
$916$	−20504.6	+	43300.1i	−0.739618	+	1.56187i
$917$	5725.61			0.206190
$918$	−5108.54	−	585.270i	−0.183668	−	0.0210423i
$919$		−	2554.93i		−	0.0917078i	−0.998948	−	0.0458539i	$-0.985399\pi$
$919$		−	2554.93i		−	0.0917078i	0.998948	−	0.0458539i	$-0.0146009\pi$
$920$	−10290.2	+	13166.4i	−0.368759	+	0.471828i
$921$	25176.4	−	898.849i	0.900751	−	0.0321586i
$922$	8898.95	−	39584.9i	0.317865	−	1.41395i
$923$			43391.4i			1.54739i
$924$	8902.19	+	3832.96i	0.316949	+	0.136467i
$925$			6814.70i			0.242234i
$926$	−40073.2	−	9008.72i	−1.42213	−	0.319703i
$927$	−366.234	−	5122.51i	−0.0129760	−	0.181494i
$928$	−35197.3	+	17664.6i	−1.24505	+	0.624858i
$929$		−	11706.4i		−	0.413428i	−0.978401	−	0.206714i	$-0.933723\pi$
$929$		−	11706.4i		−	0.413428i	0.978401	−	0.206714i	$-0.0662770\pi$
$930$	−10046.5	−	1884.71i	−0.354234	−	0.0664539i
$931$	16494.9			0.580665
$932$	12463.4	−	26319.3i	0.438037	−	0.925017i
$933$	−21351.9	+	762.306i	−0.749228	+	0.0267490i
$934$	42315.5	+	9512.80i	1.48245	+	0.333264i
$935$	1269.49			0.0444030
$936$	−40922.7	−	27519.7i	−1.42906	−	0.961015i
$937$	−41893.6			−1.46062			−0.730311	−	0.683114i	$-0.760625\pi$
$937$	−41893.6			−1.46062			−0.730311	+	0.683114i	$0.760625\pi$
$938$	18495.6	+	4157.93i	0.643820	+	0.144735i
$939$	−37230.8	+	1329.22i	−1.29391	+	0.0461952i
$940$	−13386.5	−	6339.12i	−0.464489	−	0.219957i
$941$	3148.26			0.109065			0.0545326	−	0.998512i	$-0.482633\pi$
$941$	3148.26			0.109065			0.0545326	+	0.998512i	$0.482633\pi$
$942$	44171.9	+	8286.59i	1.52781	+	0.286615i
$943$		−	71002.1i		−	2.45190i
$944$	−16009.1	+	13112.9i	−0.551960	+	0.452107i
$945$	−891.966	−	8299.56i	−0.0307044	−	0.285698i
$946$	−1308.18	−	294.087i	−0.0449604	−	0.0101074i
$947$		−	24539.5i		−	0.842055i	−0.907048	−	0.421028i	$-0.861670\pi$
$947$		−	24539.5i		−	0.842055i	0.907048	−	0.421028i	$-0.138330\pi$
$948$	−4808.85	+	11168.7i	−0.164751	+	0.382641i
$949$			7990.81i			0.273333i
$950$	1270.23	−	5650.31i	0.0433806	−	0.192969i
$951$	−22699.1	+	810.405i	−0.773996	+	0.0276332i
$952$	−2148.52	+	2749.04i	−0.0731449	+	0.0935893i
$953$		−	34706.3i		−	1.17969i	−0.807515	−	0.589847i	$-0.799188\pi$
$953$		−	34706.3i		−	1.17969i	0.807515	−	0.589847i	$-0.200812\pi$
$954$	−3091.36	+	20488.0i	−0.104912	+	0.695307i
$955$	9593.39			0.325063
$956$	45555.6	+	21572.6i	1.54118	+	0.729820i
$957$	790.287	+	22135.6i	0.0266942	+	0.747694i
$958$	−1635.01	+	7272.99i	−0.0551408	+	0.245281i
$959$	−14367.8			−0.483795
$960$	−3672.31	−	12785.2i	−0.123462	−	0.429834i
$961$	10442.0			0.350510
$962$	−13650.2	+	60719.6i	−0.457483	+	2.03501i
$963$	2684.33	+	37545.6i	0.0898249	+	1.25638i
$964$	1351.91	+	640.190i	0.0451681	+	0.0213891i
$965$	7088.27			0.236455
$966$	−25388.3	−	4762.82i	−0.845606	−	0.158635i
$967$			8683.49i			0.288772i	0.989521	+	0.144386i	$0.0461207\pi$
$967$			8683.49i			0.288772i	−0.989521	+	0.144386i	$0.953879\pi$
$968$	−13196.4	+	16884.8i	−0.438169	+	0.560639i
$969$	−196.756	−	5511.07i	−0.00652293	−	0.182705i
$970$	1782.20	−	7927.71i	0.0589928	−	0.262416i
$971$		−	35296.8i		−	1.16656i	−0.812272	−	0.583279i	$-0.801769\pi$
$971$		−	35296.8i		−	1.16656i	0.812272	−	0.583279i	$-0.198231\pi$
$972$	29255.4	+	7902.56i	0.965399	+	0.260776i
$973$			29031.4i			0.956530i
$974$	1730.51	+	389.030i	0.0569293	+	0.0127981i
$975$	−374.129	−	10479.2i	−0.0122889	−	0.344208i
$976$	−3943.02	+	3229.70i	−0.129317	+	0.105922i
$977$			22443.3i			0.734927i	0.930038	+	0.367463i	$0.119774\pi$
$977$			22443.3i			0.734927i	−0.930038	+	0.367463i	$0.880226\pi$
$978$	−1685.46	+	8984.39i	−0.0551075	+	0.293752i
$979$	12883.6			0.420595
$980$	7280.87	+	3447.82i	0.237325	+	0.112384i
$981$	2026.95	+	28350.9i	0.0659690	+	0.922706i
$982$	294.364	+	66.1748i	0.00956570	+	0.00215043i
$983$	47336.6			1.53591			0.767957	−	0.640502i	$-0.221274\pi$
$983$	47336.6			1.53591			0.767957	+	0.640502i	$0.221274\pi$
$984$	45746.1	+	33193.6i	1.48205	+	1.07538i
$985$	18720.2			0.605557
$986$	−7779.32	−	1748.84i	−0.251262	−	0.0564853i
$987$	−816.907	−	22881.3i	−0.0263449	−	0.737911i
$988$	22635.7	−	47800.4i	0.728883	−	1.53920i
$989$	3573.48			0.114894
$990$	−7397.96	−	1116.25i	−0.237498	−	0.0358351i
$991$		−	34234.4i		−	1.09737i	−0.836030	−	0.548683i	$-0.815129\pi$
$991$		−	34234.4i		−	1.09737i	0.836030	−	0.548683i	$-0.184871\pi$
$992$	−11294.5	−	22504.7i	−0.361493	−	0.720287i
$993$	29031.1	−	1036.47i	0.927769	−	0.0331232i
$994$	−17651.9	−	3968.27i	−0.563265	−	0.126626i
$995$		−	24362.7i		−	0.776232i
$996$	20304.9	−	47158.8i	0.645969	−	1.50029i
$997$			50553.3i			1.60586i	0.596076	+	0.802928i	$0.296726\pi$
$997$			50553.3i			1.60586i	−0.596076	+	0.802928i	$0.703274\pi$
$998$	2076.83	−	9238.29i	0.0658726	−	0.293019i
$999$	−4086.51	−	38024.1i	−0.129421	−	1.20423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.b.11.13	yes	24
3.2	odd	2		120.4.b.a.11.12	yes	24
4.3	odd	2		480.4.b.a.431.23		24
8.3	odd	2		120.4.b.a.11.11	✓	24
8.5	even	2		480.4.b.b.431.23		24
12.11	even	2		480.4.b.b.431.24		24
24.5	odd	2		480.4.b.a.431.24		24
24.11	even	2	inner	120.4.b.b.11.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.11	✓	24	8.3	odd	2
120.4.b.a.11.12	yes	24	3.2	odd	2
120.4.b.b.11.13	yes	24	1.1	even	1	trivial
120.4.b.b.11.14	yes	24	24.11	even	2	inner
480.4.b.a.431.23		24	4.3	odd	2
480.4.b.a.431.24		24	24.5	odd	2
480.4.b.b.431.23		24	8.5	even	2
480.4.b.b.431.24		24	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 - 3.42387i) q^{4} -5.00000 q^{5} +(-2.70986 + 14.4450i) q^{6} -11.8996i q^{7} +(-13.9338 + 17.8283i) q^{8} +(26.9313 - 1.92545i) q^{9} +O(q^{10})\)	\(q+(0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 - 3.42387i) q^{4} -5.00000 q^{5} +(-2.70986 + 14.4450i) q^{6} -11.8996i q^{7} +(-13.9338 + 17.8283i) q^{8} +(26.9313 - 1.92545i) q^{9} +(-3.10183 + 13.7978i) q^{10} +19.5939i q^{11} +(38.1805 + 16.4392i) q^{12} +80.7203i q^{13} +(-32.8376 - 7.38212i) q^{14} +(25.9642 - 0.926975i) q^{15} +(40.5542 + 49.5111i) q^{16} +12.9580i q^{17} +(11.3938 - 75.5128i) q^{18} +81.9017 q^{19} +(36.1515 + 17.1193i) q^{20} +(2.20613 + 61.7928i) q^{21} +(54.0705 + 12.1554i) q^{22} -147.701 q^{23} +(69.0507 - 95.1630i) q^{24} +25.0000 q^{25} +(222.752 + 50.0762i) q^{26} +(-139.493 + 14.9915i) q^{27} +(-40.7427 + 86.0377i) q^{28} -217.553 q^{29} +(13.5493 - 72.2248i) q^{30} -139.101i q^{31} +(161.787 - 81.1966i) q^{32} +(-3.63262 - 101.748i) q^{33} +(35.7583 + 8.03870i) q^{34} +59.4981i q^{35} +(-201.313 - 78.2875i) q^{36} +272.588i q^{37} +(50.8090 - 226.012i) q^{38} +(-14.9651 - 419.168i) q^{39} +(69.6689 - 89.1417i) q^{40} +480.713i q^{41} +(171.889 + 32.2463i) q^{42} -24.1939 q^{43} +(67.0871 - 141.670i) q^{44} +(-134.656 + 9.62727i) q^{45} +(-91.6290 + 407.590i) q^{46} -370.290 q^{47} +(-219.771 - 249.585i) q^{48} +201.399 q^{49} +(15.5092 - 68.9889i) q^{50} +(-2.40235 - 67.2888i) q^{51} +(276.376 - 583.632i) q^{52} -271.318 q^{53} +(-45.1667 + 394.238i) q^{54} -97.9697i q^{55} +(212.150 + 165.807i) q^{56} +(-425.303 + 15.1842i) q^{57} +(-134.962 + 600.349i) q^{58} +323.342i q^{59} +(-190.903 - 82.1958i) q^{60} +79.6391i q^{61} +(-383.856 - 86.2932i) q^{62} +(-22.9122 - 320.472i) q^{63} +(-123.699 - 496.832i) q^{64} -403.602i q^{65} +(-283.033 - 53.0967i) q^{66} -563.244 q^{67} +(44.3665 - 93.6901i) q^{68} +(766.991 - 27.3831i) q^{69} +(164.188 + 36.9106i) q^{70} +537.552 q^{71} +(-340.927 + 506.968i) q^{72} +98.9937 q^{73} +(752.222 + 169.104i) q^{74} +(-129.821 + 4.63488i) q^{75} +(-592.173 - 280.421i) q^{76} +233.160 q^{77} +(-1166.00 - 218.741i) q^{78} +292.524i q^{79} +(-202.771 - 247.556i) q^{80} +(721.585 - 103.710i) q^{81} +(1326.56 + 298.218i) q^{82} -1235.15i q^{83} +(195.620 - 454.334i) q^{84} -64.7900i q^{85} +(-15.0091 + 66.7645i) q^{86} +(1129.72 - 40.3332i) q^{87} +(-349.327 - 273.018i) q^{88} -657.532i q^{89} +(-56.9692 + 377.564i) q^{90} +960.541 q^{91} +(1067.92 + 505.711i) q^{92} +(25.7885 + 722.327i) q^{93} +(-229.715 + 1021.83i) q^{94} -409.508 q^{95} +(-825.082 + 451.636i) q^{96} -574.564 q^{97} +(124.941 - 555.772i) q^{98} +(37.7272 + 527.689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

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