LMFDB - Embedded newform 120.4.b.a.11.11

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			11.11
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 + 3.42387i) q^{4} +5.00000 q^{5} +(3.73307 + 14.2149i) q^{6} +11.8996i q^{7} +(13.9338 + 17.8283i) q^{8} +(26.9313 - 1.92545i) q^{9} +O(q^{10})$	\(q+(-0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 + 3.42387i) q^{4} +5.00000 q^{5} +(3.73307 + 14.2149i) 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} +(36.9110 - 19.1201i) 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} +(-22.0206 - 73.1238i) 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} +(-75.6613 - 89.9965i) 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} +(18.6654 + 71.0746i) 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} +(-188.128 + 106.131i) 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} +(-169.152 + 44.4221i) 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} +(-201.413 + 264.622i) 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} +(127.907 + 375.638i) 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} +(184.555 - 95.6004i) 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} +(-278.526 + 73.1456i) 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} +(409.582 + 453.311i) 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} +(1147.43 - 301.335i) 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} +(227.522 + 439.227i) 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} +(-110.103 - 365.619i) 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} +(855.189 + 391.647i) 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} + 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 $

$2$	−0.620366	−	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
$6$	3.73307	+	14.2149i	0.254003	+	0.967203i
$7$			11.8996i			0.642519i	0.946991	+	0.321259i	$0.104106\pi$
$7$			11.8996i			0.642519i	−0.946991	+	0.321259i	$0.895894\pi$
$8$	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	$0.913460\pi$
$12$	36.9110	−	19.1201i	0.887941	−	0.459958i
$13$		−	80.7203i		−	1.72214i	−0.508488	−	0.861069i	$-0.669795\pi$
$13$		−	80.7203i		−	1.72214i	0.508488	−	0.861069i	$-0.330205\pi$
$14$	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	$0.970535\pi$
$18$	−22.0206	−	73.1238i	−0.288351	−	0.957525i
$19$	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	$-0.266500\pi$
$23$	147.701			1.33904			0.669519	+	0.742795i	$0.266500\pi$
$24$	−75.6613	−	89.9965i	−0.643512	−	0.765436i
$25$	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	$-0.254728\pi$
$29$	217.553			1.39305			0.696527	+	0.717531i	$0.254728\pi$
$30$	18.6654	+	71.0746i	0.113594	+	0.432546i
$31$			139.101i			0.805909i	0.915220	+	0.402955i	$0.132017\pi$
$31$			139.101i			0.805909i	−0.915220	+	0.402955i	$0.867983\pi$
$32$	−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
$36$	−188.128	+	106.131i	−0.870965	+	0.491346i
$37$		−	272.588i		−	1.21117i	−0.795781	−	0.605584i	$-0.792940\pi$
$37$		−	272.588i		−	1.21117i	0.795781	−	0.605584i	$-0.207060\pi$
$38$	−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	$0.631758\pi$
$42$	−169.152	+	44.4221i	−0.621446	+	0.163202i
$43$	−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	$-0.305158\pi$
$47$	370.290			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$48$	−201.413	+	264.622i	−0.605655	+	0.795728i
$49$	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	$-0.385642\pi$
$53$	271.318			0.703178			0.351589	+	0.936155i	$0.385642\pi$
$54$	127.907	+	375.638i	0.322331	+	0.946627i
$55$			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	$0.883887\pi$
$60$	184.555	−	95.6004i	0.397099	−	0.205699i
$61$		−	79.6391i		−	0.167160i	−0.996501	−	0.0835799i	$-0.973365\pi$
$61$		−	79.6391i		−	0.167160i	0.996501	−	0.0835799i	$-0.0266354\pi$
$62$	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
$66$	−278.526	+	73.1456i	−0.519458	+	0.136418i
$67$	−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	$-0.648314\pi$
$71$	−537.552			−0.898531			−0.449265	+	0.893398i	$0.648314\pi$
$72$	409.582	+	453.311i	0.670413	+	0.741989i
$73$	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
$78$	1147.43	−	301.335i	1.66566	−	0.437429i
$79$		−	292.524i		−	0.416602i	−0.978065	−	0.208301i	$-0.933207\pi$
$79$		−	292.524i		−	0.416602i	0.978065	−	0.208301i	$-0.0667933\pi$
$80$	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	$-0.304210\pi$
$84$	227.522	+	439.227i	0.295531	+	0.570519i
$85$			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	$-0.128065\pi$
$90$	−110.103	−	365.619i	−0.128954	−	0.428218i
$91$	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
$96$	855.189	+	391.647i	0.909192	+	0.416378i
$97$	−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	$-0.514965\pi$
$101$	−95.4087			−0.0939953			−0.0469976	+	0.998895i	$0.514965\pi$
$102$	−184.197	+	48.3731i	−0.178806	+	0.0469574i
$103$			190.207i			0.181957i	0.995853	+	0.0909787i	$0.0289995\pi$
$103$			190.207i			0.181957i	−0.995853	+	0.0909787i	$0.971000\pi$
$104$	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	$0.783140\pi$
$108$	957.245	−	585.998i	0.852879	−	0.522108i
$109$		−	1052.71i		−	0.925061i	−0.886603	−	0.462531i	$-0.846942\pi$
$109$		−	1052.71i		−	0.925061i	0.886603	−	0.462531i	$-0.153058\pi$
$110$	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	$0.804402\pi$
$114$	305.745	+	1164.23i	0.251190	+	0.956490i
$115$	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
$120$	−378.306	−	449.983i	−0.287787	−	0.342313i
$121$	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
$126$	870.145	−	262.037i	0.615228	−	0.185271i
$127$		−	345.019i		−	0.241067i	−0.992709	−	0.120533i	$-0.961540\pi$
$127$		−	345.019i		−	0.241067i	0.992709	−	0.120533i	$-0.0384605\pi$
$128$	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	$0.948704\pi$
$132$	374.638	+	723.232i	0.247030	+	0.476888i
$133$			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	$-0.122867\pi$
$138$	551.380	+	2099.57i	0.340120	+	1.29512i
$139$	−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
$144$	996.845	−	1411.48i	0.576878	−	0.816830i
$145$	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	$-0.309118\pi$
$149$	2052.93			1.12874			0.564372	+	0.825521i	$0.309118\pi$
$150$	93.3268	+	355.373i	0.0508007	+	0.193441i
$151$		−	232.344i		−	0.125218i	−0.998038	−	0.0626088i	$-0.980058\pi$
$151$		−	232.344i		−	0.125218i	0.998038	−	0.0626088i	$-0.0199420\pi$
$152$	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
$156$	−1543.38	−	2979.47i	−0.792110	−	1.52916i
$157$			3057.94i			1.55446i	0.629216	+	0.777231i	$0.283376\pi$
$157$			3057.94i			1.55446i	−0.629216	+	0.777231i	$0.716624\pi$
$158$	−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
$162$	−733.840	−	1926.92i	−0.355901	−	0.934524i
$163$	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	$-0.612189\pi$
$167$	−1489.97			−0.690402			−0.345201	+	0.938529i	$0.612189\pi$
$168$	1070.92	−	900.340i	0.491807	−	0.413469i
$169$	−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	$-0.670226\pi$
$173$	−2319.39			−1.01930			−0.509652	+	0.860381i	$0.670226\pi$
$174$	812.141	+	3092.50i	0.353840	+	1.34737i
$175$			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	$-0.176763\pi$
$180$	−940.642	+	530.654i	−0.389507	+	0.219737i
$181$			3943.26i			1.61934i	0.586888	+	0.809668i	$0.300353\pi$
$181$			3943.26i			1.61934i	−0.586888	+	0.809668i	$0.699647\pi$
$182$	−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
$186$	−1977.30	+	519.272i	−0.779478	+	0.204704i
$187$	−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	$-0.381605\pi$
$191$	1918.68			0.726862			0.363431	+	0.931621i	$0.381605\pi$
$192$	550.241	−	2602.91i	0.206824	−	0.978378i
$193$	−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	$-0.263265\pi$
$197$	3744.03			1.35407			0.677033	+	0.735952i	$0.263265\pi$
$198$	1432.78	−	431.471i	0.514260	−	0.154865i
$199$		−	4872.55i		−	1.73571i	−0.496820	−	0.867854i	$-0.665499\pi$
$199$		−	4872.55i		−	1.73571i	0.496820	−	0.867854i	$-0.334501\pi$
$200$	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
$204$	247.758	+	478.293i	0.0850319	+	0.164153i
$205$			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
$210$	−845.761	+	222.111i	−0.277919	+	0.0729861i
$211$	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
$216$	−2210.94	−	2278.04i	−0.696459	−	0.717596i
$217$	−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
$222$	3874.82	−	1017.59i	1.17145	−	0.307641i
$223$		−	5310.83i		−	1.59480i	−0.603454	−	0.797398i	$-0.706209\pi$
$223$		−	5310.83i		−	1.59480i	0.603454	−	0.797398i	$-0.293791\pi$
$224$	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	$0.806224\pi$
$228$	3023.07	−	1565.97i	0.878105	−	0.454863i
$229$			5988.71i			1.72814i	0.503368	+	0.864072i	$0.332094\pi$
$229$			5988.71i			1.72814i	−0.503368	+	0.864072i	$0.667906\pi$
$230$	−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	$0.828999\pi$
$234$	−5902.58	+	1777.51i	−1.64899	+	0.496580i
$235$	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	$-0.175008\pi$
$239$	6300.66			1.70525			0.852627	+	0.522521i	$0.175008\pi$
$240$	−1007.06	+	1323.11i	−0.270857	+	0.355860i
$241$	−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
$246$	−6833.31	+	1794.54i	−1.77104	+	0.465104i
$247$		−	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	$-0.255371\pi$
$252$	−1262.91	−	2238.66i	−0.315699	−	0.559611i
$253$			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	$-0.296200\pi$
$258$	−90.3177	−	343.915i	−0.0217943	−	0.0829892i
$259$	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	$-0.715383\pi$
$263$	−5341.51			−1.25236			−0.626182	+	0.779677i	$0.715383\pi$
$264$	1763.39	−	1482.50i	0.411094	−	0.345612i
$265$	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	$-0.794714\pi$
$269$	−7051.54			−1.59829			−0.799144	+	0.601139i	$0.794714\pi$
$270$	639.533	+	1878.19i	0.144151	+	0.423344i
$271$		−	4785.65i		−	1.07272i	−0.843989	−	0.536361i	$-0.819799\pi$
$271$		−	4785.65i		−	1.07272i	0.843989	−	0.536361i	$-0.180201\pi$
$272$	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
$276$	5451.81	−	2824.06i	1.18899	−	0.615901i
$277$		−	4080.47i		−	0.885097i	−0.896745	−	0.442548i	$-0.854074\pi$
$277$		−	4080.47i		−	0.885097i	0.896745	−	0.442548i	$-0.145926\pi$
$278$	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	$-0.0352982\pi$
$282$	1382.32	+	5263.64i	0.291900	+	1.11151i
$283$	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
$288$	−4513.47	−	1875.21i	−0.923469	−	0.383674i
$289$	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	$-0.643607\pi$
$293$	−4373.43			−0.872009			−0.436005	+	0.899944i	$0.643607\pi$
$294$	751.838	+	2862.87i	0.149143	+	0.567912i
$295$			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
$300$	922.775	−	478.002i	0.177588	−	0.0919915i
$301$		−	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
$306$	947.538	−	285.343i	0.177017	−	0.0533071i
$307$	−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	$-0.622307\pi$
$311$	−4111.79			−0.749705			−0.374853	+	0.927084i	$0.622307\pi$
$312$	−7264.55	+	6107.40i	−1.31819	+	1.10822i
$313$	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	$-0.626573\pi$
$317$	−4371.23			−0.774489			−0.387244	+	0.921977i	$0.626573\pi$
$318$	1012.85	+	3856.77i	0.178610	+	0.680116i
$319$			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
$324$	−4862.18	+	3220.47i	−0.833708	+	0.552206i
$325$		−	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
$330$	−1392.63	+	365.728i	−0.232309	+	0.0610080i
$331$	−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
$336$	−3148.90	−	2396.73i	−0.511270	−	0.389145i
$337$	−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
$342$	−1803.53	−	5988.96i	−0.285157	−	0.946918i
$343$			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	$0.682351\pi$
$348$	8030.10	−	4159.63i	1.23695	−	0.640746i
$349$		−	4377.57i		−	0.671421i	−0.941965	−	0.335711i	$-0.891024\pi$
$349$		−	4377.57i		−	0.671421i	0.941965	−	0.335711i	$-0.108976\pi$
$350$	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	$0.967942\pi$
$354$	−4596.29	+	1207.06i	−0.690085	+	0.181228i
$355$	−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	$-0.583500\pi$
$359$	−3527.91			−0.518651			−0.259326	+	0.965790i	$0.583500\pi$
$360$	2047.91	+	2266.55i	0.299818	+	0.331827i
$361$	−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
$366$	1132.06	−	297.299i	0.161677	−	0.0424591i
$367$			4297.18i			0.611202i	0.952160	+	0.305601i	$0.0988574\pi$
$367$			4297.18i			0.611202i	−0.952160	+	0.305601i	$0.901143\pi$
$368$	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
$372$	2659.61	+	5134.34i	0.370684	+	0.715600i
$373$			1702.18i			0.236288i	0.992996	+	0.118144i	$0.0376944\pi$
$373$			1702.18i			0.236288i	−0.992996	+	0.118144i	$0.962306\pi$
$374$	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
$378$	−4469.95	+	1522.04i	−0.608226	+	0.207104i
$379$	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	$-0.541683\pi$
$383$	−1957.46			−0.261152			−0.130576	+	0.991438i	$0.541683\pi$
$384$	−7524.22	+	96.3346i	−0.999918	+	0.0128022i
$385$	−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	$-0.346366\pi$
$389$	7121.90			0.928264			0.464132	+	0.885766i	$0.346366\pi$
$390$	5737.17	−	1506.67i	0.744905	−	0.195624i
$391$			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
$396$	−2079.52	−	3686.17i	−0.263888	−	0.467771i
$397$		−	3576.18i		−	0.452099i	−0.974116	−	0.226050i	$-0.927419\pi$
$397$		−	3576.18i		−	0.452099i	0.974116	−	0.226050i	$-0.0725811\pi$
$398$	−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	$0.906645\pi$
$402$	−2102.63	−	8006.47i	−0.260870	−	0.993350i
$403$	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
$408$	1166.17	−	980.418i	0.141505	−	0.118965i
$409$	−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
$414$	−3252.48	−	10800.5i	−0.386113	−	1.28216i
$415$		−	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	$-0.233976\pi$
$420$	1137.61	+	2196.13i	0.132166	+	0.255144i
$421$		−	12380.8i		−	1.43327i	−0.697450	−	0.716633i	$-0.745682\pi$
$421$		−	12380.8i		−	1.43327i	0.697450	−	0.716633i	$-0.254318\pi$
$422$	−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
$426$	−2006.72	−	7641.26i	−0.228230	−	0.869062i
$427$	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	$-0.523674\pi$
$431$	−1329.74			−0.148611			−0.0743053	+	0.997236i	$0.523674\pi$
$432$	−4914.78	+	7514.42i	−0.547367	+	0.836893i
$433$	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
$438$	369.551	+	1407.19i	0.0403146	+	0.153512i
$439$			6198.59i			0.673901i	0.941522	+	0.336951i	$0.109396\pi$
$439$			6198.59i			0.673901i	−0.941522	+	0.336951i	$0.890604\pi$
$440$	−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	$-0.0755661\pi$
$444$	−5211.91	−	10061.5i	−0.557086	−	1.07545i
$445$		−	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	$0.816614\pi$
$450$	−550.516	−	1828.10i	−0.0576702	−	0.191505i
$451$	−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
$456$	−6196.79	−	7370.87i	−0.636384	−	0.756957i
$457$	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	$-0.757984\pi$
$461$	−14344.7			−1.44924			−0.724618	+	0.689151i	$0.757984\pi$
$462$	−870.404	−	3314.36i	−0.0876512	−	0.333762i
$463$			14521.6i			1.45762i	0.684717	+	0.728809i	$0.259926\pi$
$463$			14521.6i			1.45762i	−0.684717	+	0.728809i	$0.740074\pi$
$464$	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	$0.725335\pi$
$468$	8566.91	+	15185.8i	0.846165	+	1.49992i
$469$		−	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
$474$	4158.21	−	1092.01i	0.402938	−	0.105818i
$475$	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	$-0.459882\pi$
$479$	2635.56			0.251403			0.125701	+	0.992068i	$0.459882\pi$
$480$	4275.95	+	1958.23i	0.406603	+	0.186210i
$481$	−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
$486$	4167.96	+	9870.13i	0.389017	+	0.921230i
$487$		−	627.098i		−	0.0583502i	−0.999574	−	0.0291751i	$-0.990712\pi$
$487$		−	627.098i		−	0.0583502i	0.999574	−	0.0291751i	$-0.00928803\pi$
$488$	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	$0.998440\pi$
$492$	9191.28	+	17743.6i	0.842225	+	1.62590i
$493$			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
$498$	17557.6	−	4610.92i	1.57987	−	0.414900i
$499$	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	$-0.491888\pi$
$503$	574.905			0.0509617			0.0254809	+	0.999675i	$0.491888\pi$
$504$	−5394.22	+	4873.87i	−0.476742	+	0.430753i
$505$	−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	$-0.511729\pi$
$509$	−846.131			−0.0736819			−0.0368410	+	0.999321i	$0.511729\pi$
$510$	−920.985	+	241.866i	−0.0799645	+	0.0210000i
$511$			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
$516$	−893.023	+	462.590i	−0.0761882	+	0.0394659i
$517$			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	$0.819582\pi$
$522$	−4790.65	−	15908.3i	−0.401688	−	1.33388i
$523$	−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
$528$	−5184.99	−	3946.47i	−0.427363	−	0.325280i
$529$	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
$534$	9346.76	−	2454.61i	0.757442	−	0.198917i
$535$			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
$540$	4786.23	−	2929.99i	0.381419	−	0.233494i
$541$		−	4442.49i		−	0.353045i	−0.984297	−	0.176523i	$-0.943515\pi$
$541$		−	4442.49i		−	0.353045i	0.984297	−	0.176523i	$-0.0564849\pi$
$542$	−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
$546$	3585.77	+	13654.0i	0.281056	+	1.07022i
$547$	−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
$552$	−11175.3	−	13292.6i	−0.861688	−	1.02495i
$553$	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	$-0.780936\pi$
$557$	−20307.0			−1.54477			−0.772385	+	0.635155i	$0.780936\pi$
$558$	10171.6	−	3063.08i	0.771678	−	0.232385i
$559$			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	$-0.0229876\pi$
$564$	13667.8	−	7079.97i	1.02042	−	0.528582i
$565$			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	$0.934714\pi$
$570$	1528.72	+	5821.13i	0.112335	+	0.427755i
$571$	−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
$576$	−2374.75	+	13618.5i	−0.171785	+	0.985135i
$577$	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
$582$	−2144.89	−	8167.39i	−0.152764	−	0.581699i
$583$			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	$0.823296\pi$
$588$	7433.85	−	3850.77i	0.521372	−	0.270073i
$589$			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	$-0.131614\pi$
$594$	−7360.23	+	2506.19i	−0.508407	+	0.173115i
$595$	−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	$-0.477077\pi$
$599$	2109.64			0.143902			0.0719511	+	0.997408i	$0.477077\pi$
$600$	−1891.53	−	2249.91i	−0.128702	−	0.153087i
$601$	−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
$606$	−356.168	−	1356.23i	−0.0238751	−	0.0909126i
$607$			18341.5i			1.22646i	0.789905	+	0.613229i	$0.210130\pi$
$607$			18341.5i			1.22646i	−0.789905	+	0.613229i	$0.789870\pi$
$608$	−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
$612$	−1375.24	−	2437.77i	−0.0908347	−	0.161014i
$613$		−	9663.26i		−	0.636697i	−0.947974	−	0.318349i	$-0.896872\pi$
$613$		−	9663.26i		−	0.636697i	0.947974	−	0.318349i	$-0.103128\pi$
$614$	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	$0.970719\pi$
$618$	−2703.77	+	710.055i	−0.175990	+	0.0462178i
$619$	−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
$624$	21360.4	+	16258.1i	1.37035	+	1.04302i
$625$	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
$630$	4350.73	−	1310.19i	0.275138	−	0.0828556i
$631$		−	2273.51i		−	0.143434i	−0.997425	−	0.0717171i	$-0.977152\pi$
$631$		−	2273.51i		−	0.143434i	0.997425	−	0.0717171i	$-0.0228479\pi$
$632$	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
$636$	10014.6	−	5187.63i	0.624380	−	0.323432i
$637$		−	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	$0.795405\pi$
$642$	−19817.4	+	5204.38i	−1.21827	+	0.319939i
$643$	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	$-0.607283\pi$
$647$	−10884.6			−0.661389			−0.330694	+	0.943738i	$0.607283\pi$
$648$	11903.4	+	11419.6i	0.721619	+	0.692290i
$649$	−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	$-0.807964\pi$
$653$	−27481.9			−1.64694			−0.823469	+	0.567361i	$0.807964\pi$
$654$	14964.2	−	3929.86i	0.894722	−	0.234969i
$655$			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	$0.629383\pi$
$660$	1873.19	+	3616.16i	0.110475	+	0.213271i
$661$		−	7446.83i		−	0.438197i	−0.975703	−	0.219098i	$-0.929688\pi$
$661$		−	7446.83i		−	0.438197i	0.975703	−	0.219098i	$-0.0703116\pi$
$662$	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
$666$	−19932.7	+	6002.56i	−1.15972	+	0.349241i
$667$	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
$672$	−4660.45	+	10176.4i	−0.267531	+	0.584173i
$673$	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	$-0.347969\pi$
$677$	16194.0			0.919331			0.459666	+	0.888092i	$0.347969\pi$
$678$	−19688.9	+	5170.63i	−1.11526	+	0.292886i
$679$		−	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	$-0.219516\pi$
$684$	−15408.0	+	8692.28i	−0.861317	+	0.485903i
$685$		−	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
$690$	2756.90	+	10497.8i	0.152106	+	0.579196i
$691$	−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
$696$	−16460.3	−	19579.0i	−0.896447	−	1.06629i
$697$	−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	$-0.518342\pi$
$701$	−2137.78			−0.115182			−0.0575911	+	0.998340i	$0.518342\pi$
$702$	30321.6	−	10324.7i	1.63022	−	0.555098i
$703$		−	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
$708$	6182.33	+	11934.9i	0.328173	+	0.633532i
$709$		−	7932.80i		−	0.420201i	−0.977680	−	0.210101i	$-0.932621\pi$
$709$		−	7932.80i		−	0.420201i	0.977680	−	0.210101i	$-0.0673792\pi$
$710$	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
$714$	−575.622	−	2191.87i	−0.0301710	−	0.114886i
$715$	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	$-0.723997\pi$
$719$	−24949.4			−1.29410			−0.647048	+	0.762449i	$0.723997\pi$
$720$	4984.23	−	7057.41i	0.257988	−	0.365298i
$721$	−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
$726$	3535.51	+	13462.6i	0.180737	+	0.688217i
$727$		−	13284.0i		−	0.677685i	−0.940843	−	0.338843i	$-0.889965\pi$
$727$		−	13284.0i		−	0.677685i	0.940843	−	0.338843i	$-0.110035\pi$
$728$	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
$732$	−1522.71	−	2939.56i	−0.0768864	−	0.148428i
$733$			16860.0i			0.849575i	0.905293	+	0.424788i	$0.139651\pi$
$733$			16860.0i			0.849575i	−0.905293	+	0.424788i	$0.860349\pi$
$734$	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
$738$	35151.6	−	10585.6i	1.75332	−	0.527997i
$739$	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	$-0.301046\pi$
$743$	23700.7			1.17025			0.585123	+	0.810944i	$0.301046\pi$
$744$	12518.6	−	10524.5i	0.616872	−	0.518612i
$745$	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
$750$	466.634	+	1776.87i	0.0227188	+	0.0865093i
$751$		−	38822.5i		−	1.88636i	−0.332286	−	0.943179i	$-0.607820\pi$
$751$		−	38822.5i		−	1.88636i	0.332286	−	0.943179i	$-0.392180\pi$
$752$	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
$756$	6973.15	+	11390.8i	0.335464	+	0.547991i
$757$			21198.9i			1.01782i	0.860821	+	0.508908i	$0.169951\pi$
$757$			21198.9i			1.01782i	−0.860821	+	0.508908i	$0.830049\pi$
$758$	−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	$0.984617\pi$
$762$	4904.42	−	1287.98i	0.233160	−	0.0612317i
$763$	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
$768$	4933.61	+	20703.7i	0.231805	+	0.972762i
$769$	−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	$-0.647325\pi$
$773$	−19191.4			−0.892971			−0.446486	+	0.894791i	$0.647325\pi$
$774$	532.766	+	1769.15i	0.0247414	+	0.0821588i
$775$			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
$780$	−7716.90	−	14897.3i	−0.354243	−	0.683860i
$781$		−	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
$786$	−6839.64	+	1796.20i	−0.310384	+	0.0815119i
$787$	−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
$792$	−8882.14	+	8025.32i	−0.398501	+	0.360060i
$793$	−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	$-0.310526\pi$
$797$	25232.5			1.12143			0.560717	+	0.828008i	$0.310526\pi$
$798$	−13853.9	+	3638.25i	−0.614563	+	0.161394i
$799$			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
$804$	−20789.9	+	10769.3i	−0.911945	+	0.472392i
$805$			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	$-0.284610\pi$
$810$	−3669.20	−	9634.58i	−0.159164	−	0.417932i
$811$	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
$816$	−3428.97	−	2609.90i	−0.147105	−	0.111967i
$817$	−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	$-0.437095\pi$
$821$	9237.39			0.392676			0.196338	+	0.980536i	$0.437095\pi$
$822$	17163.3	−	4507.37i	0.728272	−	0.191256i
$823$			2873.15i			0.121691i	0.998147	+	0.0608454i	$0.0193797\pi$
$823$			2873.15i			0.121691i	−0.998147	+	0.0608454i	$0.980620\pi$
$824$	−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	$-0.102921\pi$
$828$	−27786.8	+	15675.7i	−1.16626	+	0.657931i
$829$		−	10373.3i		−	0.434595i	−0.976105	−	0.217298i	$-0.930276\pi$
$829$		−	10373.3i		−	0.434595i	0.976105	−	0.217298i	$-0.0697242\pi$
$830$	−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
$834$	−9107.54	−	34680.0i	−0.378140	−	1.43989i
$835$	−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	$-0.406926\pi$
$839$	14010.2			0.576502			0.288251	+	0.957555i	$0.406926\pi$
$840$	5354.62	−	4501.70i	0.219943	−	0.184909i
$841$	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
$846$	−8154.02	−	27077.0i	−0.331372	−	1.10039i
$847$			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
$852$	−19841.6	+	10278.0i	−0.797842	+	0.413286i
$853$		−	11697.1i		−	0.469520i	−0.972053	−	0.234760i	$-0.924570\pi$
$853$		−	11697.1i		−	0.469520i	0.972053	−	0.234760i	$-0.0754304\pi$
$854$	−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	$-0.0314822\pi$
$858$	5904.34	+	22482.7i	0.234931	+	0.894578i
$859$	−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	$-0.542204\pi$
$863$	−6703.04			−0.264396			−0.132198	+	0.991223i	$0.542204\pi$
$864$	23785.4	+	8900.92i	0.936570	+	0.350481i
$865$	−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
$870$	4060.70	+	15462.5i	0.158242	+	0.602561i
$871$			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
$876$	3653.96	−	1892.77i	0.140931	−	0.0730031i
$877$		−	2640.85i		−	0.101682i	−0.998707	−	0.0508411i	$-0.983810\pi$
$877$		−	2640.85i		−	0.101682i	0.998707	−	0.0508411i	$-0.0161902\pi$
$878$	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	$-0.00577495\pi$
$882$	−4434.94	−	14727.1i	−0.169311	−	0.562229i
$883$	−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	$-0.864493\pi$
$887$	−48118.6			−1.82149			−0.910746	+	0.412966i	$0.864493\pi$
$888$	−24532.0	+	20624.4i	−0.927072	+	0.779401i
$889$	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
$894$	7663.75	+	29182.3i	0.286705	+	1.09172i
$895$		−	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
$900$	−4703.21	+	2653.27i	−0.174193	+	0.0982692i
$901$			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
$906$	3302.75	−	867.356i	0.121111	−	0.0318057i
$907$	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	$-0.201880\pi$
$911$	44298.6			1.61106			0.805532	+	0.592552i	$0.201880\pi$
$912$	−16496.0	+	21673.0i	−0.598946	+	0.786913i
$913$	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
$918$	−4867.51	+	1657.41i	−0.175002	+	0.0595890i
$919$			2554.93i			0.0917078i	0.998948	+	0.0458539i	$0.0146009\pi$
$919$			2554.93i			0.0917078i	−0.998948	+	0.0458539i	$0.985399\pi$
$920$	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
$924$	−8606.18	+	4458.04i	−0.306410	+	0.158722i
$925$		−	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	$-0.0662770\pi$
$930$	−9886.52	+	2596.36i	−0.348593	+	0.0915463i
$931$	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
$936$	36591.4	−	33061.6i	1.27781	−	1.15454i
$937$	−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	$-0.517367\pi$
$941$	−3148.26			−0.109065			−0.0545326	+	0.998512i	$0.517367\pi$
$942$	−43468.5	+	11415.5i	−1.50348	+	0.394839i
$943$			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	$-0.138330\pi$
$948$	−5593.08	−	10797.4i	−0.191619	−	0.369918i
$949$		−	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	$-0.200812\pi$
$954$	−5974.60	−	19839.8i	−0.202762	−	0.673310i
$955$	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
$960$	2751.20	−	13014.5i	0.0924945	−	0.437544i
$961$	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
$966$	−24984.0	+	6561.21i	−0.832141	+	0.218534i
$967$		−	8683.49i		−	0.288772i	−0.989521	−	0.144386i	$-0.953879\pi$
$967$		−	8683.49i		−	0.288772i	0.989521	−	0.144386i	$-0.0461207\pi$
$968$	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	$-0.198231\pi$
$972$	24651.5	−	17624.8i	0.813475	−	0.581601i
$973$		−	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	$0.880226\pi$
$978$	2321.87	+	8841.32i	0.0759155	+	0.289074i
$979$	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	$-0.778726\pi$
$983$	−47336.6			−1.53591			−0.767957	+	0.640502i	$0.778726\pi$
$984$	43262.5	−	36371.4i	1.40158	−	1.17833i
$985$	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
$990$	7163.92	−	2157.35i	0.229984	−	0.0692578i
$991$			34234.4i			1.09737i	0.836030	+	0.548683i	$0.184871\pi$
$991$			34234.4i			1.09737i	−0.836030	+	0.548683i	$0.815129\pi$
$992$	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
$996$	−23616.2	−	45590.8i	−0.751314	−	1.45040i
$997$		−	50553.3i		−	1.60586i	−0.596076	−	0.802928i	$-0.703274\pi$
$997$		−	50553.3i		−	1.60586i	0.596076	−	0.802928i	$-0.296726\pi$
$998$	−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.a.11.11	✓	24
3.2	odd	2		120.4.b.b.11.14	yes	24
4.3	odd	2		480.4.b.b.431.23		24
8.3	odd	2		120.4.b.b.11.13	yes	24
8.5	even	2		480.4.b.a.431.23		24
12.11	even	2		480.4.b.a.431.24		24
24.5	odd	2		480.4.b.b.431.24		24
24.11	even	2	inner	120.4.b.a.11.12	yes	24

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

\(f(q)\)	\(=\)	\(q+(-0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 + 3.42387i) q^{4} +5.00000 q^{5} +(3.73307 + 14.2149i) q^{6} +11.8996i q^{7} +(13.9338 + 17.8283i) q^{8} +(26.9313 - 1.92545i) q^{9} +O(q^{10})\)	\(q+(-0.620366 - 2.75956i) q^{2} +(-5.19284 + 0.185395i) q^{3} +(-7.23029 + 3.42387i) q^{4} +5.00000 q^{5} +(3.73307 + 14.2149i) 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} +(36.9110 - 19.1201i) 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} +(-22.0206 - 73.1238i) 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} +(-75.6613 - 89.9965i) 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} +(18.6654 + 71.0746i) 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} +(-188.128 + 106.131i) 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} +(-169.152 + 44.4221i) 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} +(-201.413 + 264.622i) 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} +(127.907 + 375.638i) 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} +(184.555 - 95.6004i) 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} +(-278.526 + 73.1456i) 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} +(409.582 + 453.311i) 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} +(1147.43 - 301.335i) 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} +(227.522 + 439.227i) 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} +(-110.103 - 365.619i) 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} +(855.189 + 391.647i) q^{96} -574.564 q^{97} +(-124.941 - 555.772i) q^{98} +(37.7272 + 527.689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 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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