LMFDB - Embedded newform 60.4.e.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("60.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.e (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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	60.11
Dual form			60.4.e.a.11.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.235442 - 2.81861i) q^{2} +(5.18580 + 0.327893i) q^{3} +(-7.88913 - 1.32724i) q^{4} -5.00000i q^{5} +(2.14516 - 14.5395i) q^{6} -26.3120i q^{7} +(-5.59840 + 21.9239i) q^{8} +(26.7850 + 3.40077i) q^{9} +O(q^{10})$	\(q+(0.235442 - 2.81861i) q^{2} +(5.18580 + 0.327893i) q^{3} +(-7.88913 - 1.32724i) q^{4} -5.00000i q^{5} +(2.14516 - 14.5395i) q^{6} -26.3120i q^{7} +(-5.59840 + 21.9239i) q^{8} +(26.7850 + 3.40077i) q^{9} +(-14.0931 - 1.17721i) q^{10} +41.8165 q^{11} +(-40.4763 - 9.46957i) q^{12} -62.0996 q^{13} +(-74.1633 - 6.19495i) q^{14} +(1.63946 - 25.9290i) q^{15} +(60.4769 + 20.9415i) q^{16} +57.4334i q^{17} +(15.8917 - 74.6957i) q^{18} +72.8787i q^{19} +(-6.63619 + 39.4457i) q^{20} +(8.62751 - 136.449i) q^{21} +(9.84535 - 117.864i) q^{22} +144.939 q^{23} +(-36.2208 + 111.857i) q^{24} -25.0000 q^{25} +(-14.6208 + 175.035i) q^{26} +(137.786 + 26.4183i) q^{27} +(-34.9223 + 207.579i) q^{28} +100.810i q^{29} +(-72.6977 - 10.7258i) q^{30} +130.044i q^{31} +(73.2648 - 165.530i) q^{32} +(216.852 + 13.7113i) q^{33} +(161.882 + 13.5222i) q^{34} -131.560 q^{35} +(-206.797 - 62.3792i) q^{36} +10.8369 q^{37} +(205.417 + 17.1587i) q^{38} +(-322.036 - 20.3620i) q^{39} +(109.620 + 27.9920i) q^{40} +17.9491i q^{41} +(-382.565 - 56.4433i) q^{42} -366.646i q^{43} +(-329.896 - 55.5004i) q^{44} +(17.0038 - 133.925i) q^{45} +(34.1247 - 408.526i) q^{46} -257.954 q^{47} +(306.754 + 128.428i) q^{48} -349.322 q^{49} +(-5.88605 + 70.4653i) q^{50} +(-18.8320 + 297.838i) q^{51} +(489.912 + 82.4209i) q^{52} -147.704i q^{53} +(106.904 - 382.146i) q^{54} -209.083i q^{55} +(576.862 + 147.305i) q^{56} +(-23.8964 + 377.934i) q^{57} +(284.143 + 23.7348i) q^{58} -442.815 q^{59} +(-47.3479 + 202.381i) q^{60} -279.593 q^{61} +(366.544 + 30.6178i) q^{62} +(89.4811 - 704.766i) q^{63} +(-449.316 - 245.478i) q^{64} +310.498i q^{65} +(89.7029 - 607.993i) q^{66} +735.331i q^{67} +(76.2278 - 453.100i) q^{68} +(751.623 + 47.5244i) q^{69} +(-30.9747 + 370.817i) q^{70} +299.317 q^{71} +(-224.511 + 568.193i) q^{72} -740.346 q^{73} +(2.55145 - 30.5449i) q^{74} +(-129.645 - 8.19732i) q^{75} +(96.7274 - 574.950i) q^{76} -1100.28i q^{77} +(-133.213 + 902.899i) q^{78} -209.278i q^{79} +(104.708 - 302.384i) q^{80} +(705.870 + 182.179i) q^{81} +(50.5915 + 4.22596i) q^{82} -89.4750 q^{83} +(-249.164 + 1065.01i) q^{84} +287.167 q^{85} +(-1033.43 - 86.3238i) q^{86} +(-33.0547 + 522.778i) q^{87} +(-234.105 + 916.781i) q^{88} -353.462i q^{89} +(-373.479 - 79.4587i) q^{90} +1633.96i q^{91} +(-1143.44 - 192.368i) q^{92} +(-42.6405 + 674.383i) q^{93} +(-60.7331 + 727.071i) q^{94} +364.393 q^{95} +(434.212 - 834.383i) q^{96} +902.465 q^{97} +(-82.2450 + 984.602i) q^{98} +(1120.05 + 142.208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.235442	−	2.81861i	0.0832413	−	0.996529i
$2$	0.235442	−	2.81861i	0.0832413	−	0.996529i
$3$	5.18580	+	0.327893i	0.998007	+	0.0631030i
$3$	5.18580	+	0.327893i	0.998007	+	0.0631030i
$4$	−7.88913	−	1.32724i	−0.986142	−	0.165905i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$	2.14516	−	14.5395i	0.145959	−	0.989291i
$7$		−	26.3120i		−	1.42072i	−0.703841	−	0.710358i	$-0.748533\pi$
$7$		−	26.3120i		−	1.42072i	0.703841	−	0.710358i	$-0.251467\pi$
$8$	−5.59840	+	21.9239i	−0.247417	+	0.968909i
$9$	26.7850	+	3.40077i	0.992036	+	0.125954i
$10$	−14.0931	−	1.17721i	−0.445662	−	0.0372266i
$11$	41.8165			1.14620			0.573098	−	0.819487i	$-0.305742\pi$
$11$	41.8165			1.14620			0.573098	+	0.819487i	$0.305742\pi$
$12$	−40.4763	−	9.46957i	−0.973707	−	0.227803i
$13$	−62.0996			−1.32487			−0.662436	−	0.749119i	$-0.730477\pi$
$13$	−62.0996			−1.32487			−0.662436	+	0.749119i	$0.730477\pi$
$14$	−74.1633	−	6.19495i	−1.41578	−	0.118262i
$15$	1.63946	−	25.9290i	0.0282205	−	0.446322i
$16$	60.4769	+	20.9415i	0.944951	+	0.327211i
$17$			57.4334i			0.819391i	0.912222	+	0.409696i	$0.134365\pi$
$17$			57.4334i			0.819391i	−0.912222	+	0.409696i	$0.865635\pi$
$18$	15.8917	−	74.6957i	0.208096	−	0.978108i
$19$			72.8787i			0.879975i	0.898004	+	0.439987i	$0.145017\pi$
$19$			72.8787i			0.879975i	−0.898004	+	0.439987i	$0.854983\pi$
$20$	−6.63619	+	39.4457i	−0.0741949	+	0.441016i
$21$	8.62751	−	136.449i	0.0896513	−	1.41788i
$22$	9.84535	−	117.864i	0.0954108	−	1.14222i
$23$	144.939			1.31399			0.656996	−	0.753894i	$-0.271827\pi$
$23$	144.939			1.31399			0.656996	+	0.753894i	$0.271827\pi$
$24$	−36.2208	+	111.857i	−0.308065	+	0.951365i
$25$	−25.0000			−0.200000
$26$	−14.6208	+	175.035i	−0.110284	+	1.32027i
$27$	137.786	+	26.4183i	0.982111	+	0.188304i
$28$	−34.9223	+	207.579i	−0.235703	+	1.40103i
$29$			100.810i			0.645513i	0.946482	+	0.322757i	$0.104610\pi$
$29$			100.810i			0.645513i	−0.946482	+	0.322757i	$0.895390\pi$
$30$	−72.6977	−	10.7258i	−0.442424	−	0.0652750i
$31$			130.044i			0.753440i	0.926327	+	0.376720i	$0.122948\pi$
$31$			130.044i			0.753440i	−0.926327	+	0.376720i	$0.877052\pi$
$32$	73.2648	−	165.530i	0.404734	−	0.914434i
$33$	216.852	+	13.7113i	1.14391	+	0.0723283i
$34$	161.882	+	13.5222i	0.816547	+	0.0682071i
$35$	−131.560			−0.635363
$36$	−206.797	−	62.3792i	−0.957392	−	0.288792i
$37$	10.8369			0.0481505			0.0240752	−	0.999710i	$-0.492336\pi$
$37$	10.8369			0.0481505			0.0240752	+	0.999710i	$0.492336\pi$
$38$	205.417	+	17.1587i	0.876921	+	0.0732502i
$39$	−322.036	−	20.3620i	−1.32223	−	0.0836033i
$40$	109.620	+	27.9920i	0.433309	+	0.110648i
$41$			17.9491i			0.0683701i	0.999416	+	0.0341851i	$0.0108836\pi$
$41$			17.9491i			0.0683701i	−0.999416	+	0.0341851i	$0.989116\pi$
$42$	−382.565	−	56.4433i	−1.40550	−	0.207367i
$43$		−	366.646i		−	1.30030i	−0.759805	−	0.650151i	$-0.774706\pi$
$43$		−	366.646i		−	1.30030i	0.759805	−	0.650151i	$-0.225294\pi$
$44$	−329.896	−	55.5004i	−1.13031	−	0.190159i
$45$	17.0038	−	133.925i	0.0563285	−	0.443652i
$46$	34.1247	−	408.526i	0.109378	−	1.30943i
$47$	−257.954			−0.800562			−0.400281	−	0.916392i	$-0.631088\pi$
$47$	−257.954			−0.800562			−0.400281	+	0.916392i	$0.631088\pi$
$48$	306.754	+	128.428i	0.922420	+	0.386188i
$49$	−349.322			−1.01843
$50$	−5.88605	+	70.4653i	−0.0166483	+	0.199306i
$51$	−18.8320	+	297.838i	−0.0517060	+	0.817758i
$52$	489.912	+	82.4209i	1.30651	+	0.219802i
$53$		−	147.704i		−	0.382806i	−0.981512	−	0.191403i	$-0.938696\pi$
$53$		−	147.704i		−	0.382806i	0.981512	−	0.191403i	$-0.0613038\pi$
$54$	106.904	−	382.146i	0.269402	−	0.963028i
$55$		−	209.083i		−	0.512594i
$56$	576.862	+	147.305i	1.37654	+	0.351509i
$57$	−23.8964	+	377.934i	−0.0555290	+	0.878221i
$58$	284.143	+	23.7348i	0.643273	+	0.0537333i
$59$	−442.815			−0.977112			−0.488556	−	0.872533i	$-0.662476\pi$
$59$	−442.815			−0.977112			−0.488556	+	0.872533i	$0.662476\pi$
$60$	−47.3479	+	202.381i	−0.101876	+	0.435455i
$61$	−279.593			−0.586856			−0.293428	−	0.955981i	$-0.594796\pi$
$61$	−279.593			−0.586856			−0.293428	+	0.955981i	$0.594796\pi$
$62$	366.544	+	30.6178i	0.750825	+	0.0627173i
$63$	89.4811	−	704.766i	0.178945	−	1.40940i
$64$	−449.316	−	245.478i	−0.877570	−	0.479448i
$65$			310.498i			0.592500i
$66$	89.7029	−	607.993i	0.167298	−	1.13392i
$67$			735.331i			1.34082i	0.741991	+	0.670410i	$0.233882\pi$
$67$			735.331i			1.34082i	−0.741991	+	0.670410i	$0.766118\pi$
$68$	76.2278	−	453.100i	0.135941	−	0.808036i
$69$	751.623	+	47.5244i	1.31137	+	0.0829168i
$70$	−30.9747	+	370.817i	−0.0528884	+	0.633158i
$71$	299.317			0.500315			0.250157	−	0.968205i	$-0.419518\pi$
$71$	299.317			0.500315			0.250157	+	0.968205i	$0.419518\pi$
$72$	−224.511	+	568.193i	−0.367485	+	0.930030i
$73$	−740.346			−1.18700			−0.593500	−	0.804834i	$-0.702254\pi$
$73$	−740.346			−1.18700			−0.593500	+	0.804834i	$0.702254\pi$
$74$	2.55145	−	30.5449i	0.00400811	−	0.0479834i
$75$	−129.645	−	8.19732i	−0.199601	−	0.0126206i
$76$	96.7274	−	574.950i	0.145992	−	0.867780i
$77$		−	1100.28i		−	1.62842i
$78$	−133.213	+	902.899i	−0.193377	+	1.31068i
$79$		−	209.278i		−	0.298046i	−0.988834	−	0.149023i	$-0.952387\pi$
$79$		−	209.278i		−	0.298046i	0.988834	−	0.149023i	$-0.0476128\pi$
$80$	104.708	−	302.384i	0.146333	−	0.422595i
$81$	705.870	+	182.179i	0.968271	+	0.249903i
$82$	50.5915	+	4.22596i	0.0681329	+	0.00569122i
$83$	−89.4750			−0.118327			−0.0591636	−	0.998248i	$-0.518843\pi$
$83$	−89.4750			−0.118327			−0.0591636	+	0.998248i	$0.518843\pi$
$84$	−249.164	+	1065.01i	−0.323643	+	1.38336i
$85$	287.167			0.366443
$86$	−1033.43	−	86.3238i	−1.29579	−	0.108239i
$87$	−33.0547	+	522.778i	−0.0407338	+	0.644227i
$88$	−234.105	+	916.781i	−0.283588	+	1.11056i
$89$		−	353.462i		−	0.420976i	−0.977596	−	0.210488i	$-0.932495\pi$
$89$		−	353.462i		−	0.420976i	0.977596	−	0.210488i	$-0.0675053\pi$
$90$	−373.479	−	79.4587i	−0.437423	−	0.0930632i
$91$			1633.96i			1.88226i
$92$	−1143.44	−	192.368i	−1.29578	−	0.217998i
$93$	−42.6405	+	674.383i	−0.0475443	+	0.751938i
$94$	−60.7331	+	727.071i	−0.0666398	+	0.797784i
$95$	364.393			0.393537
$96$	434.212	−	834.383i	0.461631	−	0.887072i
$97$	902.465			0.944654			0.472327	−	0.881424i	$-0.343414\pi$
$97$	902.465			0.944654			0.472327	+	0.881424i	$0.343414\pi$
$98$	−82.2450	+	984.602i	−0.0847755	+	1.01490i
$99$	1120.05	+	142.208i	1.13707	+	0.144368i
$100$	197.228	+	33.1809i	0.197228	+	0.0331809i
$101$			1092.24i			1.07606i	0.842925	+	0.538031i	$0.180831\pi$
$101$			1092.24i			1.07606i	−0.842925	+	0.538031i	$0.819169\pi$
$102$	835.056	+	123.204i	0.810616	+	0.119598i
$103$		−	1871.41i		−	1.79025i	−0.445813	−	0.895126i	$-0.647085\pi$
$103$		−	1871.41i		−	1.79025i	0.445813	−	0.895126i	$-0.352915\pi$
$104$	347.658	−	1361.47i	0.327795	−	1.28368i
$105$	−682.244	−	43.1376i	−0.634097	−	0.0400933i
$106$	−416.321	−	34.7758i	−0.381478	−	0.0318653i
$107$	1142.20			1.03197			0.515985	−	0.856598i	$-0.327426\pi$
$107$	1142.20			1.03197			0.515985	+	0.856598i	$0.327426\pi$
$108$	−1051.95	−	391.293i	−0.937260	−	0.348631i
$109$	−1091.23			−0.958906			−0.479453	−	0.877568i	$-0.659165\pi$
$109$	−1091.23			−0.958906			−0.479453	+	0.877568i	$0.659165\pi$
$110$	−589.322	−	49.2268i	−0.510815	−	0.0426690i
$111$	56.1977	+	3.55332i	0.0480545	+	0.00303844i
$112$	551.013	−	1591.27i	0.464874	−	1.34251i
$113$		−	1143.42i		−	0.951893i	−0.879474	−	0.475947i	$-0.842106\pi$
$113$		−	1143.42i		−	0.951893i	0.879474	−	0.475947i	$-0.157894\pi$
$114$	1059.62	+	156.336i	0.870551	+	0.128441i
$115$		−	724.694i		−	0.587635i
$116$	133.798	−	795.301i	0.107094	−	0.636567i
$117$	−1663.34	−	211.186i	−1.31432	−	0.166873i
$118$	−104.257	+	1248.12i	−0.0813360	+	0.973720i
$119$	1511.19			1.16412
$120$	559.286	+	181.104i	0.425464	+	0.137771i
$121$	417.620			0.313764
$122$	−65.8279	+	788.064i	−0.0488506	+	0.584819i
$123$	−5.88537	+	93.0803i	−0.00431436	+	0.0682339i
$124$	172.600	−	1025.94i	0.124999	−	0.742998i
$125$			125.000i			0.0894427i
$126$	−1965.39	−	418.144i	−1.38961	−	0.295645i
$127$		−	1454.56i		−	1.01631i	−0.861266	−	0.508155i	$-0.830328\pi$
$127$		−	1454.56i		−	1.01631i	0.861266	−	0.508155i	$-0.169672\pi$
$128$	−797.694	+	1208.65i	−0.550835	+	0.834614i
$129$	120.220	−	1901.35i	0.0820529	−	1.29771i
$130$	875.173	+	73.1042i	0.590444	+	0.0493205i
$131$	−748.305			−0.499082			−0.249541	−	0.968364i	$-0.580280\pi$
$131$	−748.305			−0.499082			−0.249541	+	0.968364i	$0.580280\pi$
$132$	−1692.58	−	395.984i	−1.11606	−	0.261106i
$133$	1917.59			1.25019
$134$	2072.61	+	173.128i	1.33617	+	0.111612i
$135$	132.091	−	688.932i	0.0842120	−	0.439213i
$136$	−1259.17	−	321.535i	−0.793916	−	0.202731i
$137$			1259.05i			0.785165i	0.919717	+	0.392582i	$0.128418\pi$
$137$			1259.05i			0.785165i	−0.919717	+	0.392582i	$0.871582\pi$
$138$	310.916	−	2107.34i	0.191789	−	1.29992i
$139$			2071.90i			1.26429i	0.774849	+	0.632146i	$0.217826\pi$
$139$			2071.90i			1.26429i	−0.774849	+	0.632146i	$0.782174\pi$
$140$	1037.89	+	174.611i	0.626558	+	0.105410i
$141$	−1337.70	−	84.5812i	−0.798967	−	0.0505179i
$142$	70.4717	−	843.657i	0.0416468	−	0.498578i
$143$	−2596.79			−1.51856
$144$	1548.65	+	766.586i	0.896212	+	0.443626i
$145$	504.048			0.288682
$146$	−174.308	+	2086.75i	−0.0988073	+	1.18288i
$147$	−1811.51	−	114.540i	−1.01640	−	0.0642660i
$148$	−85.4934	−	14.3831i	−0.0474832	−	0.00798839i
$149$			3570.32i			1.96303i	0.191382	+	0.981516i	$0.438703\pi$
$149$			3570.32i			1.96303i	−0.191382	+	0.981516i	$0.561297\pi$
$150$	−53.6289	+	363.489i	−0.0291919	+	0.197858i
$151$		−	208.116i		−	0.112161i	−0.998426	−	0.0560803i	$-0.982140\pi$
$151$		−	208.116i		−	0.112161i	0.998426	−	0.0560803i	$-0.0178603\pi$
$152$	−1597.79	−	408.004i	−0.852616	−	0.217720i
$153$	−195.318	+	1538.35i	−0.103206	+	0.812866i
$154$	−3101.25	−	259.051i	−1.62277	−	0.135551i
$155$	650.221			0.336948
$156$	2513.56	+	588.057i	1.29004	+	0.301809i
$157$	2057.73			1.04602			0.523010	−	0.852327i	$-0.324809\pi$
$157$	2057.73			1.04602			0.523010	+	0.852327i	$0.324809\pi$
$158$	−589.873	−	49.2728i	−0.297011	−	0.0248097i
$159$	48.4311	−	765.964i	0.0241562	−	0.382043i
$160$	−827.651	−	366.324i	−0.408947	−	0.181003i
$161$		−	3813.63i		−	1.86681i
$162$	679.683	−	1946.68i	0.329635	−	0.944108i
$163$			1088.30i			0.522957i	0.965209	+	0.261478i	$0.0842100\pi$
$163$			1088.30i			0.522957i	−0.965209	+	0.261478i	$0.915790\pi$
$164$	23.8227	−	141.603i	0.0113429	−	0.0674226i
$165$	68.5566	−	1084.26i	0.0323462	−	0.511573i
$166$	−21.0662	+	252.195i	−0.00984971	+	0.117917i
$167$	−1395.62			−0.646686			−0.323343	−	0.946282i	$-0.604807\pi$
$167$	−1395.62			−0.646686			−0.323343	+	0.946282i	$0.604807\pi$
$168$	2943.19	+	953.043i	1.35162	+	0.437672i
$169$	1659.36			0.755283
$170$	67.6111	−	809.412i	0.0305032	−	0.365171i
$171$	−247.844	+	1952.05i	−0.110837	+	0.872967i
$172$	−486.626	+	2892.52i	−0.215726	+	1.28228i
$173$			158.379i			0.0696030i	0.999394	+	0.0348015i	$0.0110799\pi$
$173$			158.379i			0.0696030i	−0.999394	+	0.0348015i	$0.988920\pi$
$174$	1465.73	+	216.252i	0.638600	+	0.0942187i
$175$			657.800i			0.284143i
$176$	2528.93	+	875.701i	1.08310	+	0.375048i
$177$	−2296.35	−	145.196i	−0.975164	−	0.0616586i
$178$	−996.272	−	83.2197i	−0.419515	−	0.0350426i
$179$	−403.729			−0.168582			−0.0842909	−	0.996441i	$-0.526862\pi$
$179$	−403.729			−0.168582			−0.0842909	+	0.996441i	$0.526862\pi$
$180$	−311.896	+	1033.98i	−0.129152	+	0.428159i
$181$	218.428			0.0896996			0.0448498	−	0.998994i	$-0.485719\pi$
$181$	218.428			0.0896996			0.0448498	+	0.998994i	$0.485719\pi$
$182$	4605.51	+	384.704i	1.87573	+	0.156682i
$183$	−1449.91	−	91.6765i	−0.585686	−	0.0370323i
$184$	−811.425	+	3177.63i	−0.325104	+	1.27314i
$185$		−	54.1843i		−	0.0215336i
$186$	1890.78	+	278.965i	0.745371	+	0.109972i
$187$			2401.66i			0.939182i
$188$	2035.03	+	342.366i	0.789468	+	0.132817i
$189$	695.118	−	3625.44i	0.267526	−	1.39530i
$190$	85.7935	−	1027.08i	0.0327585	−	0.392171i
$191$	−1680.33			−0.636566			−0.318283	−	0.947996i	$-0.603106\pi$
$191$	−1680.33			−0.636566			−0.318283	+	0.947996i	$0.603106\pi$
$192$	−2249.57	−	1420.32i	−0.845566	−	0.533870i
$193$	−4835.77			−1.80356			−0.901779	−	0.432198i	$-0.857738\pi$
$193$	−4835.77			−1.80356			−0.901779	+	0.432198i	$0.857738\pi$
$194$	212.478	−	2543.70i	0.0786342	−	0.941375i
$195$	−101.810	+	1610.18i	−0.0373885	+	0.591319i
$196$	2755.85	+	463.633i	1.00432	+	0.168963i
$197$			3000.08i			1.08501i	0.840053	+	0.542504i	$0.182524\pi$
$197$			3000.08i			1.08501i	−0.840053	+	0.542504i	$0.817476\pi$
$198$	664.537	−	3123.51i	0.238518	−	1.12110i
$199$		−	3482.66i		−	1.24060i	−0.784365	−	0.620300i	$-0.787011\pi$
$199$		−	3482.66i		−	1.24060i	0.784365	−	0.620300i	$-0.212989\pi$
$200$	139.960	−	548.098i	0.0494833	−	0.193782i
$201$	−241.110	+	3813.28i	−0.0846098	+	1.33815i
$202$	3078.61	+	257.160i	1.07233	+	0.0895727i
$203$	2652.50			0.917090
$204$	543.870	−	2324.69i	0.186659	−	0.797847i
$205$	89.7454			0.0305761
$206$	−5274.79	−	440.609i	−1.78404	−	0.149023i
$207$	3882.18	+	492.903i	1.30353	+	0.165503i
$208$	−3755.59	−	1300.46i	−1.25194	−	0.433513i
$209$			3047.53i			1.00862i
$210$	−282.217	+	1912.82i	−0.0927372	+	0.628559i
$211$		−	4616.43i		−	1.50620i	−0.657906	−	0.753100i	$-0.728558\pi$
$211$		−	4616.43i		−	1.50620i	0.657906	−	0.753100i	$-0.271442\pi$
$212$	−196.039	+	1165.26i	−0.0635094	+	0.377501i
$213$	1552.20	+	98.1437i	0.499318	+	0.0315713i
$214$	268.922	−	3219.42i	0.0859025	−	1.02839i
$215$	−1833.23			−0.581513
$216$	−1350.58	+	2872.92i	−0.425440	+	0.904987i
$217$	3421.72			1.07042
$218$	−256.921	+	3075.75i	−0.0798205	+	0.955578i
$219$	−3839.28	−	242.754i	−1.18463	−	0.0749032i
$220$	−277.502	+	1649.48i	−0.0850418	+	0.505491i
$221$		−	3566.59i		−	1.08559i
$222$	23.2467	−	157.563i	0.00702801	−	0.0476348i
$223$			3869.17i			1.16188i	0.813947	+	0.580940i	$0.197315\pi$
$223$			3869.17i			1.16188i	−0.813947	+	0.580940i	$0.802685\pi$
$224$	−4355.43	−	1927.74i	−1.29915	−	0.575012i
$225$	−669.624	−	85.0192i	−0.198407	−	0.0251909i
$226$	−3222.86	−	269.209i	−0.948589	−	0.0792368i
$227$	−345.177			−0.100926			−0.0504630	−	0.998726i	$-0.516070\pi$
$227$	−345.177			−0.100926			−0.0504630	+	0.998726i	$0.516070\pi$
$228$	690.130	−	2949.86i	0.200460	−	0.856838i
$229$	−3839.52			−1.10796			−0.553979	−	0.832530i	$-0.686891\pi$
$229$	−3839.52			−1.10796			−0.553979	+	0.832530i	$0.686891\pi$
$230$	−2042.63	−	170.623i	−0.585596	−	0.0489155i
$231$	360.772	−	5705.81i	0.102758	−	1.62517i
$232$	−2210.14	−	564.373i	−0.625444	−	0.159711i
$233$		−	4045.88i		−	1.13757i	−0.822486	−	0.568786i	$-0.807413\pi$
$233$		−	4045.88i		−	1.13757i	0.822486	−	0.568786i	$-0.192587\pi$
$234$	−986.871	+	4638.57i	−0.275700	+	1.29587i
$235$			1289.77i			0.358022i
$236$	3493.43	+	587.721i	0.963571	+	0.162107i
$237$	68.6207	−	1085.27i	0.0188076	−	0.297452i
$238$	355.797	−	4259.45i	0.0969029	−	1.16008i
$239$	2154.87			0.583208			0.291604	−	0.956539i	$-0.405811\pi$
$239$	2154.87			0.583208			0.291604	+	0.956539i	$0.405811\pi$
$240$	642.142	−	1533.77i	0.172709	−	0.412519i
$241$	2662.28			0.711587			0.355793	−	0.934565i	$-0.384211\pi$
$241$	2662.28			0.711587			0.355793	+	0.934565i	$0.384211\pi$
$242$	98.3252	−	1177.11i	0.0261181	−	0.312675i
$243$	3600.76	+	1176.19i	0.950572	+	0.310505i
$244$	2205.75	+	371.086i	0.578723	+	0.0973622i
$245$			1746.61i			0.455456i
$246$	260.971	+	38.5036i	0.0676379	+	0.00997926i
$247$		−	4525.74i		−	1.16585i
$248$	−2851.08	−	728.039i	−0.730015	−	0.186413i
$249$	−463.999	−	29.3382i	−0.118091	−	0.00746680i
$250$	352.326	+	29.4302i	0.0891323	+	0.00744532i
$251$	5028.01			1.26440			0.632202	−	0.774804i	$-0.282151\pi$
$251$	5028.01			1.26440			0.632202	+	0.774804i	$0.282151\pi$
$252$	−1641.32	+	5441.23i	−0.410292	+	1.36018i
$253$	6060.83			1.50609
$254$	−4099.84	−	342.464i	−1.01278	−	0.0845989i
$255$	1489.19	+	94.1600i	0.365713	+	0.0231236i
$256$	3218.91	+	2532.95i	0.785866	+	0.618397i
$257$		−	6527.24i		−	1.58427i	−0.610344	−	0.792136i	$-0.708969\pi$
$257$		−	6527.24i		−	1.58427i	0.610344	−	0.792136i	$-0.291031\pi$
$258$	−5330.86	−	786.512i	−1.28638	−	0.189791i
$259$		−	285.139i		−	0.0684081i
$260$	412.105	−	2449.56i	0.0982986	−	0.584289i
$261$	−342.830	+	2700.18i	−0.0813052	+	0.640372i
$262$	−176.182	+	2109.18i	−0.0415442	+	0.497350i
$263$	5689.37			1.33392			0.666962	−	0.745092i	$-0.267594\pi$
$263$	5689.37			1.33392			0.666962	+	0.745092i	$0.267594\pi$
$264$	−1514.63	+	4677.48i	−0.353102	+	1.09045i
$265$	−738.521			−0.171196
$266$	451.480	−	5404.93i	0.104068	−	1.24585i
$267$	115.898	−	1832.98i	0.0265649	−	0.420137i
$268$	975.959	−	5801.13i	0.222448	−	1.32224i
$269$			1257.39i			0.284998i	0.989795	+	0.142499i	$0.0455138\pi$
$269$			1257.39i			0.284998i	−0.989795	+	0.142499i	$0.954486\pi$
$270$	−1910.73	−	534.518i	−0.430679	−	0.120480i
$271$			1301.08i			0.291642i	0.989311	+	0.145821i	$0.0465824\pi$
$271$			1301.08i			0.291642i	−0.989311	+	0.145821i	$0.953418\pi$
$272$	−1202.74	+	3473.39i	−0.268114	+	0.774285i
$273$	−535.765	+	8473.41i	−0.118776	+	1.87851i
$274$	3548.76	+	296.432i	0.782440	+	0.0653581i
$275$	−1045.41			−0.229239
$276$	−5866.58	−	1372.51i	−1.27944	−	0.299331i
$277$	−8335.26			−1.80800			−0.904002	−	0.427528i	$-0.859385\pi$
$277$	−8335.26			−1.80800			−0.904002	+	0.427528i	$0.859385\pi$
$278$	5839.89	+	487.813i	1.25990	+	0.105241i
$279$	−442.250	+	3483.23i	−0.0948990	+	0.747439i
$280$	736.526	−	2884.31i	0.157199	−	0.615609i
$281$			2714.03i			0.576177i	0.957604	+	0.288088i	$0.0930197\pi$
$281$			2714.03i			0.576177i	−0.957604	+	0.288088i	$0.906980\pi$
$282$	−553.351	+	3750.53i	−0.116850	+	0.791989i
$283$			6298.67i			1.32303i	0.749933	+	0.661514i	$0.230086\pi$
$283$			6298.67i			1.32303i	−0.749933	+	0.661514i	$0.769914\pi$
$284$	−2361.35	−	397.264i	−0.493381	−	0.0830046i
$285$	1889.67	+	119.482i	0.392752	+	0.0248333i
$286$	−611.392	+	7319.33i	−0.126407	+	1.51329i
$287$	472.276			0.0971345
$288$	2525.33	−	4184.57i	0.516688	−	0.856174i
$289$	1614.40			0.328598
$290$	118.674	−	1420.72i	0.0240303	−	0.287680i
$291$	4680.00	+	295.911i	0.942771	+	0.0596104i
$292$	5840.69	+	982.616i	1.17055	+	0.196929i
$293$		−	8362.65i		−	1.66741i	−0.552210	−	0.833705i	$-0.686215\pi$
$293$		−	8362.65i		−	1.66741i	0.552210	−	0.833705i	$-0.313785\pi$
$294$	−749.350	+	5078.98i	−0.148650	+	1.00752i
$295$			2214.07i			0.436978i
$296$	−60.6690	+	237.586i	−0.0119132	+	0.0466534i
$297$	5761.74	+	1104.72i	1.12569	+	0.215833i
$298$	10063.3	+	840.602i	1.95622	+	0.163405i
$299$	−9000.64			−1.74087
$300$	1011.91	+	236.739i	0.194741	+	0.0455605i
$301$	−9647.19			−1.84736
$302$	−586.599	−	48.9993i	−0.111771	−	0.00933639i
$303$	−358.138	+	5664.15i	−0.0679026	+	1.07392i
$304$	−1526.19	+	4407.48i	−0.287938	+	0.831533i
$305$			1397.96i			0.262450i
$306$	4290.03	+	912.717i	0.801453	+	0.170512i
$307$		−	3054.26i		−	0.567805i	−0.958853	−	0.283902i	$-0.908371\pi$
$307$		−	3054.26i		−	0.567805i	0.958853	−	0.283902i	$-0.0916292\pi$
$308$	−1460.33	+	8680.23i	−0.270162	+	1.60585i
$309$	613.623	−	9704.78i	0.112970	−	1.78668i
$310$	153.089	−	1832.72i	0.0280480	−	0.335779i
$311$	−3174.41			−0.578792			−0.289396	−	0.957210i	$-0.593454\pi$
$311$	−3174.41			−0.578792			−0.289396	+	0.957210i	$0.593454\pi$
$312$	2249.30	−	6946.29i	0.408146	−	1.26044i
$313$	−1929.89			−0.348510			−0.174255	−	0.984701i	$-0.555752\pi$
$313$	−1929.89			−0.348510			−0.174255	+	0.984701i	$0.555752\pi$
$314$	484.477	−	5799.95i	0.0870720	−	1.04239i
$315$	−3523.83	−	447.405i	−0.630303	−	0.0800268i
$316$	−277.761	+	1651.02i	−0.0494472	+	0.293915i
$317$			2361.25i			0.418362i	0.977877	+	0.209181i	$0.0670798\pi$
$317$			2361.25i			0.418362i	−0.977877	+	0.209181i	$0.932920\pi$
$318$	−2147.55	−	316.848i	−0.378707	−	0.0558741i
$319$			4215.51i			0.739884i
$320$	−1227.39	+	2246.58i	−0.214416	+	0.392461i
$321$	5923.23	+	374.520i	1.02991	+	0.0651204i
$322$	−10749.1	−	897.888i	−1.86033	−	0.155396i
$323$	−4185.67			−0.721043
$324$	−5326.90	−	2374.09i	−0.913392	−	0.407080i
$325$	1552.49			0.264974
$326$	3067.48	+	256.230i	0.521142	+	0.0435316i
$327$	−5658.89	−	357.806i	−0.956995	−	0.0605098i
$328$	−393.514	−	100.486i	−0.0662445	−	0.0169159i
$329$			6787.28i			1.13737i
$330$	−3039.96	−	448.514i	−0.507105	−	0.0748179i
$331$		−	9926.27i		−	1.64833i	−0.566350	−	0.824165i	$-0.691645\pi$
$331$		−	9926.27i		−	1.64833i	0.566350	−	0.824165i	$-0.308355\pi$
$332$	705.881	+	118.755i	0.116687	+	0.0196310i
$333$	290.265	+	36.8536i	0.0477670	+	0.00606477i
$334$	−328.588	+	3933.72i	−0.0538310	+	0.644442i
$335$	3676.66			0.599633
$336$	3379.21	−	8071.32i	0.548663	−	1.31050i
$337$	−7538.30			−1.21851			−0.609254	−	0.792975i	$-0.708531\pi$
$337$	−7538.30			−1.21851			−0.609254	+	0.792975i	$0.708531\pi$
$338$	390.682	−	4677.08i	0.0628707	−	0.752662i
$339$	374.919	−	5929.54i	0.0600673	−	0.949996i
$340$	−2265.50	−	381.139i	−0.361365	−	0.0607946i
$341$			5437.99i			0.863589i
$342$	5443.73	+	1158.17i	0.860711	+	0.183119i
$343$			166.342i			0.0261855i
$344$	8038.31	+	2052.63i	1.25987	+	0.321716i
$345$	237.622	−	3758.12i	0.0370815	−	0.586464i
$346$	446.408	+	37.2890i	0.0693614	+	0.00579384i
$347$	1157.23			0.179030			0.0895148	−	0.995985i	$-0.471468\pi$
$347$	1157.23			0.179030			0.0895148	+	0.995985i	$0.471468\pi$
$348$	954.624	−	4080.40i	0.147050	−	0.628541i
$349$	7043.61			1.08033			0.540166	−	0.841558i	$-0.318361\pi$
$349$	7043.61			1.08033			0.540166	+	0.841558i	$0.318361\pi$
$350$	1854.08	+	154.874i	0.283157	+	0.0236524i
$351$	−8556.47	−	1640.56i	−1.30117	−	0.249478i
$352$	3063.68	−	6921.90i	0.463905	−	1.04812i
$353$			421.398i			0.0635376i	0.999495	+	0.0317688i	$0.0101140\pi$
$353$			421.398i			0.0635376i	−0.999495	+	0.0317688i	$0.989886\pi$
$354$	−949.907	+	6438.33i	−0.142619	+	0.966647i
$355$		−	1496.58i		−	0.223748i
$356$	−469.128	+	2788.51i	−0.0698420	+	0.415142i
$357$	7836.72	+	495.508i	1.16180	+	0.0734595i
$358$	−95.0547	+	1137.96i	−0.0140330	+	0.167997i
$359$	4581.36			0.673523			0.336762	−	0.941590i	$-0.390668\pi$
$359$	4581.36			0.673523			0.336762	+	0.941590i	$0.390668\pi$
$360$	2840.96	+	1122.56i	0.415922	+	0.164344i
$361$	1547.70			0.225645
$362$	51.4271	−	615.664i	0.00746671	−	0.0893883i
$363$	2165.69	+	136.935i	0.313139	+	0.0197994i
$364$	2168.66	−	12890.6i	0.312277	−	1.85618i
$365$			3701.73i			0.530842i
$366$	−599.770	+	4065.15i	−0.0856571	+	0.580571i
$367$			3683.56i			0.523925i	0.965078	+	0.261963i	$0.0843697\pi$
$367$			3683.56i			0.523925i	−0.965078	+	0.261963i	$0.915630\pi$
$368$	8765.45	+	3035.24i	1.24166	+	0.429953i
$369$	−61.0407	+	480.766i	−0.00861152	+	0.0678256i
$370$	−152.724	−	12.7572i	−0.0214588	−	0.00179248i
$371$	−3886.39			−0.543859
$372$	1231.46	−	5263.70i	0.171635	−	0.733630i
$373$	−4542.08			−0.630510			−0.315255	−	0.949007i	$-0.602090\pi$
$373$	−4542.08			−0.630510			−0.315255	+	0.949007i	$0.602090\pi$
$374$	6769.36	+	565.452i	0.935923	+	0.0781787i
$375$	−40.9866	+	648.225i	−0.00564410	+	0.0892645i
$376$	1444.13	−	5655.36i	0.198072	−	0.775672i
$377$		−	6260.24i		−	0.855222i
$378$	−10055.0	−	2812.85i	−1.36819	−	0.382744i
$379$			63.4024i			0.00859304i	0.999991	+	0.00429652i	$0.00136763\pi$
$379$			63.4024i			0.00859304i	−0.999991	+	0.00429652i	$0.998632\pi$
$380$	−2874.75	−	483.637i	−0.388083	−	0.0652896i
$381$	476.940	−	7543.05i	0.0641322	−	1.01428i
$382$	−395.619	+	4736.18i	−0.0529885	+	0.634357i
$383$	−12158.8			−1.62216			−0.811078	−	0.584938i	$-0.801119\pi$
$383$	−12158.8			−1.62216			−0.811078	+	0.584938i	$0.801119\pi$
$384$	−4532.98	+	6006.26i	−0.602403	+	0.798192i
$385$	−5501.38			−0.728250
$386$	−1138.54	+	13630.2i	−0.150130	+	1.79730i
$387$	1246.88	−	9820.60i	0.163779	−	1.28995i
$388$	−7119.66	−	1197.79i	−0.931562	−	0.156722i
$389$			4854.49i			0.632731i	0.948637	+	0.316365i	$0.102463\pi$
$389$			4854.49i			0.632731i	−0.948637	+	0.316365i	$0.897537\pi$
$390$	4514.50	+	666.066i	0.586155	+	0.0864809i
$391$			8324.33i			1.07667i
$392$	1955.64	−	7658.50i	0.251977	−	0.986767i
$393$	−3880.56	−	245.364i	−0.498087	−	0.0314936i
$394$	8456.05	+	706.344i	1.08124	+	0.0903175i
$395$	−1046.39			−0.133290
$396$	−8647.51	−	2608.48i	−1.09736	−	0.331013i
$397$	1031.79			0.130438			0.0652191	−	0.997871i	$-0.479225\pi$
$397$	1031.79			0.130438			0.0652191	+	0.997871i	$0.479225\pi$
$398$	−9816.27	−	819.965i	−1.23629	−	0.103269i
$399$	9944.21	+	628.762i	1.24770	+	0.0788909i
$400$	−1511.92	−	523.538i	−0.188990	−	0.0654422i
$401$		−	10339.2i		−	1.28757i	−0.765207	−	0.643784i	$-0.777364\pi$
$401$		−	10339.2i		−	1.28757i	0.765207	−	0.643784i	$-0.222636\pi$
$402$	10691.4	+	1577.40i	1.32646	+	0.195705i
$403$		−	8075.69i		−	0.998210i
$404$	1449.67	−	8616.85i	0.178524	−	1.06115i
$405$	910.895	−	3529.35i	0.111760	−	0.433024i
$406$	624.510	−	7476.38i	0.0763397	−	0.913907i
$407$	453.159			0.0551899
$408$	−6424.35	−	2080.29i	−0.779540	−	0.252425i
$409$	−9261.32			−1.11966			−0.559832	−	0.828606i	$-0.689134\pi$
$409$	−9261.32			−1.11966			−0.559832	+	0.828606i	$0.689134\pi$
$410$	21.1298	−	252.957i	0.00254519	−	0.0304699i
$411$	−412.832	+	6529.16i	−0.0495462	+	0.783600i
$412$	−2483.81	+	14763.8i	−0.297011	+	1.76544i
$413$			11651.3i			1.38820i
$414$	2303.33	−	10826.3i	0.273436	−	1.28523i
$415$			447.375i			0.0529175i
$416$	−4549.71	+	10279.4i	−0.536221	+	1.21151i
$417$	−679.362	+	10744.5i	−0.0797806	+	1.26177i
$418$	8589.81	+	717.517i	1.00512	+	0.0839591i
$419$	3057.12			0.356444			0.178222	−	0.983990i	$-0.442966\pi$
$419$	3057.12			0.356444			0.178222	+	0.983990i	$0.442966\pi$
$420$	5325.06	+	1245.82i	0.618658	+	0.144737i
$421$	9355.98			1.08309			0.541547	−	0.840670i	$-0.317839\pi$
$421$	9355.98			1.08309			0.541547	+	0.840670i	$0.317839\pi$
$422$	−13011.9	−	1086.90i	−1.50097	−	0.125378i
$423$	−6909.29	−	877.241i	−0.794187	−	0.100834i
$424$	3238.25	+	826.907i	0.370905	+	0.0947126i
$425$		−	1435.84i		−	0.163878i
$426$	642.081	−	4351.93i	0.0730256	−	0.494957i
$427$			7356.65i			0.833755i
$428$	−9010.98	−	1515.97i	−1.01767	−	0.171209i
$429$	−13466.4	−	851.467i	−1.51553	−	0.0958257i
$430$	−431.619	+	5167.16i	−0.0484058	+	0.579494i
$431$	4915.07			0.549306			0.274653	−	0.961543i	$-0.411437\pi$
$431$	4915.07			0.549306			0.274653	+	0.961543i	$0.411437\pi$
$432$	7779.65	+	4483.15i	0.866432	+	0.499296i
$433$	13859.1			1.53816			0.769082	−	0.639150i	$-0.220714\pi$
$433$	13859.1			1.53816			0.769082	+	0.639150i	$0.220714\pi$
$434$	805.617	−	9644.51i	0.0891034	−	1.06671i
$435$	2613.89	+	165.274i	0.288107	+	0.0182167i
$436$	8608.85	+	1448.32i	0.945617	+	0.159087i
$437$			10563.0i			1.15628i
$438$	−1588.16	+	10764.3i	−0.173254	+	1.17429i
$439$		−	7001.72i		−	0.761216i	−0.924736	−	0.380608i	$-0.875715\pi$
$439$		−	7001.72i		−	0.761216i	0.924736	−	0.380608i	$-0.124285\pi$
$440$	4583.91	+	1170.53i	0.496657	+	0.126824i
$441$	−9356.58	−	1187.96i	−1.01032	−	0.128276i
$442$	−10052.8	−	839.725i	−1.08182	−	0.0903657i
$443$	12384.9			1.32828			0.664138	−	0.747610i	$-0.268799\pi$
$443$	12384.9			1.32828			0.664138	+	0.747610i	$0.268799\pi$
$444$	−438.635	−	102.620i	−0.0468845	−	0.0109688i
$445$	−1767.31			−0.188266
$446$	10905.7	+	910.965i	1.15785	+	0.0967163i
$447$	−1170.68	+	18514.9i	−0.123873	+	1.95912i
$448$	−6459.01	+	11822.4i	−0.681160	+	1.24678i
$449$		−	10889.4i		−	1.14455i	−0.820061	−	0.572277i	$-0.806060\pi$
$449$		−	10889.4i		−	1.14455i	0.820061	−	0.572277i	$-0.193940\pi$
$450$	−397.294	+	1867.39i	−0.0416191	+	0.195622i
$451$			750.568i			0.0783655i
$452$	−1517.59	+	9020.59i	−0.157924	+	0.938701i
$453$	68.2398	−	1079.25i	0.00707767	−	0.111937i
$454$	−81.2691	+	972.919i	−0.00840120	+	0.100576i
$455$	8169.82			0.841774
$456$	−8152.01	−	2639.73i	−0.837178	−	0.271089i
$457$	5583.72			0.571543			0.285772	−	0.958298i	$-0.407750\pi$
$457$	5583.72			0.571543			0.285772	+	0.958298i	$0.407750\pi$
$458$	−903.983	+	10822.1i	−0.0922279	+	1.10411i
$459$	−1517.29	+	7913.54i	−0.154294	+	0.804733i
$460$	−961.841	+	5717.21i	−0.0974915	+	0.579492i
$461$			3455.46i			0.349103i	0.984648	+	0.174552i	$0.0558476\pi$
$461$			3455.46i			0.349103i	−0.984648	+	0.174552i	$0.944152\pi$
$462$	−15997.5	−	2360.26i	−1.61098	−	0.237683i
$463$		−	1399.18i		−	0.140444i	−0.997531	−	0.0702220i	$-0.977629\pi$
$463$		−	1399.18i		−	0.140444i	0.997531	−	0.0702220i	$-0.0223708\pi$
$464$	−2111.11	+	6096.65i	−0.211219	+	0.609978i
$465$	3371.91	+	213.203i	0.336277	+	0.0212624i
$466$	−11403.8	−	952.569i	−1.13362	−	0.0946929i
$467$	3413.27			0.338217			0.169109	−	0.985597i	$-0.445911\pi$
$467$	3413.27			0.338217			0.169109	+	0.985597i	$0.445911\pi$
$468$	12842.0	+	3873.72i	1.26842	+	0.382613i
$469$	19348.0			1.90492
$470$	3635.36	+	303.666i	0.356780	+	0.0298022i
$471$	10671.0	+	674.716i	1.04393	+	0.0660069i
$472$	2479.05	−	9708.23i	0.241754	−	0.946732i
$473$		−	15331.9i		−	1.49040i
$474$	−3042.80	−	448.933i	−0.294854	−	0.0435025i
$475$		−	1821.97i		−	0.175995i
$476$	−11922.0	−	2005.71i	−1.14799	−	0.193133i
$477$	502.308	−	3956.25i	0.0482161	−	0.379758i
$478$	507.346	−	6073.73i	0.0485470	−	0.581184i
$479$	18073.4			1.72399			0.861996	−	0.506914i	$-0.169214\pi$
$479$	18073.4			1.72399			0.861996	+	0.506914i	$0.169214\pi$
$480$	−4171.92	−	2171.06i	−0.396711	−	0.206448i
$481$	−672.964			−0.0637932
$482$	626.812	−	7503.93i	0.0592334	−	0.709117i
$483$	1250.46	−	19776.7i	0.117801	−	1.86309i
$484$	−3294.66	−	554.281i	−0.309416	−	0.0520549i
$485$		−	4512.32i		−	0.422462i
$486$	4163.00	−	9872.22i	0.388554	−	0.921426i
$487$			5637.63i			0.524570i	0.964991	+	0.262285i	$0.0844760\pi$
$487$			5637.63i			0.524570i	−0.964991	+	0.262285i	$0.915524\pi$
$488$	1565.27	−	6129.77i	0.145198	−	0.568610i
$489$	−356.844	+	5643.68i	−0.0330001	+	0.521914i
$490$	4923.01	+	411.225i	0.453876	+	0.0379128i
$491$	153.464			0.0141054			0.00705269	−	0.999975i	$-0.497755\pi$
$491$	153.464			0.0141054			0.00705269	+	0.999975i	$0.497755\pi$
$492$	169.970	−	726.512i	0.0155749	−	0.0665725i
$493$	−5789.84			−0.528928
$494$	−12756.3	−	1065.55i	−1.16181	−	0.0970471i
$495$	711.041	−	5600.27i	0.0645635	−	0.508512i
$496$	−2723.32	+	7864.67i	−0.246534	+	0.711964i
$497$		−	7875.62i		−	0.710805i
$498$	−191.938	+	1300.93i	−0.0172710	+	0.117060i
$499$		−	12507.6i		−	1.12208i	−0.827790	−	0.561038i	$-0.810402\pi$
$499$		−	12507.6i		−	1.12208i	0.827790	−	0.561038i	$-0.189598\pi$
$500$	165.905	−	986.142i	0.0148390	−	0.0882032i
$501$	−7237.42	−	457.615i	−0.645398	−	0.0408078i
$502$	1183.80	−	14172.0i	0.105251	−	1.26001i
$503$	−18132.9			−1.60737			−0.803683	−	0.595058i	$-0.797129\pi$
$503$	−18132.9			−1.60737			−0.803683	+	0.595058i	$0.797129\pi$
$504$	14950.3	+	5907.34i	1.32131	+	0.522091i
$505$	5461.21			0.481229
$506$	1426.97	−	17083.1i	0.125369	−	1.50087i
$507$	8605.09	+	544.091i	0.753778	+	0.0476606i
$508$	−1930.55	+	11475.2i	−0.168611	+	1.00223i
$509$			10913.0i			0.950312i	0.879902	+	0.475156i	$0.157608\pi$
$509$			10913.0i			0.950312i	−0.879902	+	0.475156i	$0.842392\pi$
$510$	616.018	−	4175.28i	0.0534858	−	0.362518i
$511$			19480.0i			1.68639i
$512$	7897.28	−	8476.48i	0.681667	−	0.731662i
$513$	−1925.33	+	10041.7i	−0.165703	+	0.864233i
$514$	−18397.7	−	1536.79i	−1.57877	−	0.131877i
$515$	−9357.07			−0.800625
$516$	−3471.98	+	14840.5i	−0.296212	+	1.26611i
$517$	−10786.7			−0.917601
$518$	−803.697	−	67.1338i	−0.0681707	−	0.00569438i
$519$	−51.9312	+	821.320i	−0.00439215	+	0.0694642i
$520$	−6807.33	−	1738.29i	−0.574079	−	0.146594i
$521$			4652.88i			0.391260i	0.980678	+	0.195630i	$0.0626751\pi$
$521$			4652.88i			0.391260i	−0.980678	+	0.195630i	$0.937325\pi$
$522$	7530.05	+	1602.04i	0.631382	+	0.134328i
$523$		−	18369.3i		−	1.53582i	−0.640556	−	0.767911i	$-0.721296\pi$
$523$		−	18369.3i		−	1.53582i	0.640556	−	0.767911i	$-0.278704\pi$
$524$	5903.48	+	993.179i	0.492166	+	0.0828001i
$525$	−215.688	+	3411.22i	−0.0179303	+	0.283577i
$526$	1339.52	−	16036.1i	0.111037	−	1.32929i
$527$	−7468.88			−0.617362
$528$	12827.4	+	5370.43i	1.05727	+	0.442647i
$529$	8840.26			0.726577
$530$	−173.879	+	2081.60i	−0.0142506	+	0.170602i
$531$	−11860.8	−	1505.91i	−0.969330	−	0.123072i
$532$	−15128.1	−	2545.09i	−1.23287	−	0.207413i
$533$		−	1114.63i		−	0.0905816i
$534$	−5139.17	−	758.231i	−0.416468	−	0.0614454i
$535$		−	5711.01i		−	0.461511i
$536$	−16121.3	−	4116.68i	−1.29913	−	0.331741i
$537$	−2093.66	−	132.380i	−0.168246	−	0.0106380i
$538$	3544.10	+	296.042i	0.284009	+	0.0237236i
$539$	−14607.4			−1.16732
$540$	−1956.46	+	5259.76i	−0.155913	+	0.419155i
$541$	4665.50			0.370768			0.185384	−	0.982666i	$-0.440647\pi$
$541$	4665.50			0.370768			0.185384	+	0.982666i	$0.440647\pi$
$542$	3667.24	+	306.329i	0.290630	+	0.0242766i
$543$	1132.72	+	71.6209i	0.0895208	+	0.00566031i
$544$	9506.97	+	4207.85i	0.749279	+	0.331636i
$545$			5456.14i			0.428836i
$546$	23757.1	+	3505.11i	1.86211	+	0.274734i
$547$		−	10501.6i		−	0.820873i	−0.911889	−	0.410437i	$-0.865376\pi$
$547$		−	10501.6i		−	0.820873i	0.911889	−	0.410437i	$-0.134624\pi$
$548$	1671.05	−	9932.78i	0.130263	−	0.774284i
$549$	−7488.89	−	950.831i	−0.582182	−	0.0739171i
$550$	−246.134	+	2946.61i	−0.0190822	+	0.228444i
$551$	−7346.87			−0.568035
$552$	−5249.81	+	16212.5i	−0.404795	+	1.25009i
$553$	−5506.52			−0.423438
$554$	−1962.47	+	23493.9i	−0.150501	+	1.80173i
$555$	17.7666	−	280.989i	0.00135883	−	0.0214906i
$556$	2749.91	−	16345.5i	0.209752	−	1.24677i
$557$		−	11169.6i		−	0.849680i	−0.905268	−	0.424840i	$-0.860330\pi$
$557$		−	11169.6i		−	0.849680i	0.905268	−	0.424840i	$-0.139670\pi$
$558$	9713.75	+	2066.63i	0.736946	+	0.156787i
$559$			22768.6i			1.72273i
$560$	−7956.34	−	2755.07i	−0.600387	−	0.207898i
$561$	−787.488	+	12454.5i	−0.0592652	+	0.937311i
$562$	7649.81	+	638.997i	0.574177	+	0.0479617i
$563$	22377.8			1.67515			0.837576	−	0.546321i	$-0.183972\pi$
$563$	22377.8			1.67515			0.837576	+	0.546321i	$0.183972\pi$
$564$	10441.0	+	2442.71i	0.779513	+	0.182370i
$565$	−5717.10			−0.425699
$566$	17753.5	+	1482.97i	1.31844	+	0.110131i
$567$	4793.50	−	18572.8i	0.355040	−	1.37564i
$568$	−1675.69	+	6562.19i	−0.123786	+	0.484760i
$569$		−	21371.4i		−	1.57458i	−0.616585	−	0.787288i	$-0.711484\pi$
$569$		−	21371.4i		−	1.57458i	0.616585	−	0.787288i	$-0.288516\pi$
$570$	781.681	−	5298.11i	0.0574403	−	0.389322i
$571$			10994.1i			0.805757i	0.915254	+	0.402878i	$0.131990\pi$
$571$			10994.1i			0.805757i	−0.915254	+	0.402878i	$0.868010\pi$
$572$	20486.4	+	3446.55i	1.49752	+	0.251936i
$573$	−8713.83	−	550.966i	−0.635297	−	0.0401692i
$574$	111.194	−	1331.16i	0.00808560	−	0.0967974i
$575$	−3623.47			−0.262799
$576$	−11200.1	−	8103.13i	−0.810192	−	0.586164i
$577$	2014.98			0.145381			0.0726906	−	0.997355i	$-0.476841\pi$
$577$	2014.98			0.145381			0.0726906	+	0.997355i	$0.476841\pi$
$578$	380.098	−	4550.37i	0.0273529	−	0.327458i
$579$	−25077.3	−	1585.61i	−1.79996	−	0.113810i
$580$	−3976.50	−	668.992i	−0.284682	−	0.0478937i
$581$			2354.27i			0.168109i
$582$	1935.93	−	13121.4i	0.137881	−	0.934537i
$583$		−	6176.47i		−	0.438771i
$584$	4144.75	−	16231.3i	0.293683	−	1.15009i
$585$	−1055.93	+	8316.68i	−0.0746280	+	0.587782i
$586$	−23571.1	−	1968.92i	−1.66162	−	0.138797i
$587$	−17180.7			−1.20804			−0.604022	−	0.796968i	$-0.706436\pi$
$587$	−17180.7			−1.20804			−0.604022	+	0.796968i	$0.706436\pi$
$588$	14139.2	+	3307.93i	0.991654	+	0.232001i
$589$	−9477.45			−0.663008
$590$	6240.61	+	521.286i	0.435461	+	0.0363746i
$591$	−983.703	+	15557.8i	−0.0684672	+	1.08285i
$592$	655.379	+	226.940i	0.0454999	+	0.0157554i
$593$			6700.22i			0.463988i	0.972717	+	0.231994i	$0.0745250\pi$
$593$			6700.22i			0.463988i	−0.972717	+	0.231994i	$0.925475\pi$
$594$	4470.33	−	15980.0i	0.308788	−	1.10382i
$595$		−	7555.94i		−	0.520611i
$596$	4738.66	−	28166.7i	0.325676	−	1.93583i
$597$	1141.94	−	18060.4i	0.0782856	−	1.23813i
$598$	−2119.13	+	25369.3i	−0.144912	+	1.73483i
$599$	−1618.60			−0.110407			−0.0552037	−	0.998475i	$-0.517581\pi$
$599$	−1618.60			−0.110407			−0.0552037	+	0.998475i	$0.517581\pi$
$600$	905.521	−	2796.43i	0.0616129	−	0.190273i
$601$	6101.93			0.414148			0.207074	−	0.978325i	$-0.433606\pi$
$601$	6101.93			0.414148			0.207074	+	0.978325i	$0.433606\pi$
$602$	−2271.35	+	27191.7i	−0.153776	+	1.84095i
$603$	−2500.69	+	19695.8i	−0.168882	+	1.33014i
$604$	−276.220	+	1641.86i	−0.0186080	+	0.110606i
$605$		−	2088.10i		−	0.140320i
$606$	15880.7	+	2343.03i	1.06454	+	0.157061i
$607$			3490.58i			0.233407i	0.993167	+	0.116704i	$0.0372328\pi$
$607$			3490.58i			0.233407i	−0.993167	+	0.116704i	$0.962767\pi$
$608$	12063.6	+	5339.44i	0.804679	+	0.356156i
$609$	13755.3	+	869.737i	0.915262	+	0.0578711i
$610$	3940.32	+	329.139i	0.261539	+	0.0218467i
$611$	16018.8			1.06064
$612$	3582.65	−	11877.0i	0.236634	−	0.784478i
$613$	14259.5			0.939535			0.469767	−	0.882790i	$-0.344338\pi$
$613$	14259.5			0.939535			0.469767	+	0.882790i	$0.344338\pi$
$614$	−8608.78	−	719.102i	−0.565834	−	0.0472648i
$615$	465.401	+	29.4269i	0.0305151	+	0.00192944i
$616$	24122.4	+	6159.79i	1.57779	+	0.402897i
$617$			24504.0i			1.59886i	0.600763	+	0.799428i	$0.294864\pi$
$617$			24504.0i			1.59886i	−0.600763	+	0.799428i	$0.705136\pi$
$618$	−27209.5	−	4014.48i	−1.77108	−	0.261304i
$619$			20921.7i			1.35850i	0.733906	+	0.679251i	$0.237695\pi$
$619$			20921.7i			1.35850i	−0.733906	+	0.679251i	$0.762305\pi$
$620$	−5129.68	−	862.998i	−0.332279	−	0.0559013i
$621$	19970.6	+	3829.04i	1.29049	+	0.247430i
$622$	−747.389	+	8947.42i	−0.0481793	+	0.576783i
$623$	−9300.29			−0.598087
$624$	−19049.3	−	7975.35i	−1.22209	−	0.511650i
$625$	625.000			0.0400000
$626$	−454.376	+	5439.60i	−0.0290104	+	0.347301i
$627$	−999.263	+	15803.9i	−0.0636471	+	1.00661i
$628$	−16233.7	−	2731.10i	−1.03152	−	0.173540i
$629$			622.398i			0.0394541i
$630$	−2090.72	+	9826.97i	−0.132216	+	0.621454i
$631$		−	21088.4i		−	1.33045i	−0.746642	−	0.665226i	$-0.768335\pi$
$631$		−	21088.4i		−	1.33045i	0.746642	−	0.665226i	$-0.231665\pi$
$632$	4588.19	+	1171.62i	0.288779	+	0.0737414i
$633$	1513.69	−	23939.9i	0.0950457	−	1.50320i
$634$	6655.43	+	555.936i	0.416910	+	0.0348250i
$635$	−7272.80			−0.454508
$636$	−1398.70	+	5978.51i	−0.0872043	+	0.372741i
$637$	21692.7			1.34929
$638$	11881.9	+	992.507i	0.737316	+	0.0615889i
$639$	8017.19	+	1017.91i	0.496330	+	0.0630168i
$640$	6043.25	+	3988.47i	0.373251	+	0.246341i
$641$		−	1545.86i		−	0.0952537i	−0.998865	−	0.0476269i	$-0.984834\pi$
$641$		−	1545.86i		−	0.0952537i	0.998865	−	0.0476269i	$-0.0151658\pi$
$642$	2450.20	−	16607.1i	0.150626	−	1.02092i
$643$		−	3919.16i		−	0.240368i	−0.992752	−	0.120184i	$-0.961652\pi$
$643$		−	3919.16i		−	0.240368i	0.992752	−	0.120184i	$-0.0383484\pi$
$644$	−5061.60	+	30086.3i	−0.309712	+	1.84094i
$645$	−9506.76	−	601.102i	−0.580354	−	0.0366952i
$646$	−985.482	+	11797.8i	−0.0600206	+	0.718541i
$647$	10568.6			0.642187			0.321094	−	0.947047i	$-0.395950\pi$
$647$	10568.6			0.642187			0.321094	+	0.947047i	$0.395950\pi$
$648$	−7945.82	+	14455.5i	−0.481699	+	0.876337i
$649$	−18517.0			−1.11996
$650$	365.521	−	4375.86i	0.0220568	−	0.264055i
$651$	17744.4	+	1121.96i	1.06829	+	0.0675469i
$652$	1444.43	−	8585.71i	0.0867610	−	0.515709i
$653$			17960.1i			1.07631i	0.842845	+	0.538156i	$0.180879\pi$
$653$			17960.1i			1.07631i	−0.842845	+	0.538156i	$0.819121\pi$
$654$	−2340.85	+	15866.0i	−0.139961	+	0.948637i
$655$			3741.53i			0.223196i
$656$	−375.881	+	1085.50i	−0.0223715	+	0.0646064i
$657$	−19830.2	−	2517.75i	−1.17755	−	0.149508i
$658$	19130.7	+	1598.01i	1.13342	+	0.0946762i
$659$	−30263.9			−1.78894			−0.894472	−	0.447124i	$-0.852448\pi$
$659$	−30263.9			−1.78894			−0.894472	+	0.447124i	$0.852448\pi$
$660$	−1979.92	+	8462.88i	−0.116770	+	0.499117i
$661$	732.138			0.0430815			0.0215408	−	0.999768i	$-0.493143\pi$
$661$	732.138			0.0430815			0.0215408	+	0.999768i	$0.493143\pi$
$662$	−27978.3	−	2337.06i	−1.64261	−	0.137209i
$663$	1169.46	−	18495.6i	0.0685038	−	1.08342i
$664$	500.917	−	1961.64i	0.0292761	−	0.114648i
$665$		−	9587.93i		−	0.559103i
$666$	172.217	−	809.467i	0.0100199	−	0.0470964i
$667$			14611.2i			0.848199i
$668$	11010.3	+	1852.32i	0.637724	+	0.107288i
$669$	−1268.67	+	20064.7i	−0.0733180	+	1.15956i
$670$	865.638	−	10363.1i	0.0499142	−	0.597552i
$671$	−11691.6			−0.672652
$672$	−21954.3	−	11425.0i	−1.26028	−	0.655847i
$673$	1970.80			0.112881			0.0564404	−	0.998406i	$-0.482025\pi$
$673$	1970.80			0.112881			0.0564404	+	0.998406i	$0.482025\pi$
$674$	−1774.83	+	21247.5i	−0.101430	+	1.21428i
$675$	−3444.66	−	660.457i	−0.196422	−	0.0376608i
$676$	−13090.9	−	2202.36i	−0.744816	−	0.125305i
$677$		−	12741.7i		−	0.723341i	−0.932306	−	0.361671i	$-0.882207\pi$
$677$		−	12741.7i		−	0.723341i	0.932306	−	0.361671i	$-0.117793\pi$
$678$	−16624.8	−	2452.81i	−0.941699	−	0.138938i
$679$		−	23745.7i		−	1.34208i
$680$	−1607.68	+	6295.83i	−0.0906641	+	0.355050i
$681$	−1790.02	−	113.181i	−0.100725	−	0.00636873i
$682$	15327.6	+	1280.33i	0.860592	+	0.0718862i
$683$	31694.1			1.77561			0.887805	−	0.460220i	$-0.152230\pi$
$683$	31694.1			1.77561			0.887805	+	0.460220i	$0.152230\pi$
$684$	4546.11	−	15071.1i	0.254130	−	0.842481i
$685$	6295.23			0.351136
$686$	468.853	+	39.1638i	0.0260946	+	0.00217971i
$687$	−19911.0	−	1258.95i	−1.10575	−	0.0699155i
$688$	7678.12	−	22173.6i	0.425473	−	1.22872i
$689$			9172.37i			0.507169i
$690$	−10536.7	−	1554.58i	−0.581342	−	0.0857709i
$691$			7103.88i			0.391092i	0.980695	+	0.195546i	$0.0626479\pi$
$691$			7103.88i			0.391092i	−0.980695	+	0.195546i	$0.937352\pi$
$692$	210.206	−	1249.47i	0.0115475	−	0.0686384i
$693$	3741.79	−	29470.9i	0.205106	−	1.61545i
$694$	272.460	−	3261.78i	0.0149026	−	0.178408i
$695$	10359.5			0.565409
$696$	−11276.3	−	3651.41i	−0.614119	−	0.198860i
$697$	−1030.88			−0.0560219
$698$	1658.36	−	19853.2i	0.0899282	−	1.07658i
$699$	1326.61	−	20981.1i	0.0717841	−	1.13530i
$700$	873.057	−	5189.47i	0.0471407	−	0.280205i
$701$		−	6869.08i		−	0.370102i	−0.982729	−	0.185051i	$-0.940755\pi$
$701$		−	6869.08i		−	0.370102i	0.982729	−	0.185051i	$-0.0592451\pi$
$702$	−6638.67	+	23731.1i	−0.356923	+	1.27589i
$703$			789.776i			0.0423712i
$704$	−18788.8	−	10265.0i	−1.00587	−	0.549542i
$705$	−422.906	+	6688.48i	−0.0225923	+	0.357309i
$706$	1187.76	+	99.2147i	0.0633170	+	0.00528895i
$707$	28739.1			1.52878
$708$	17923.5	+	4193.27i	0.951421	+	0.222589i
$709$	−4579.11			−0.242556			−0.121278	−	0.992619i	$-0.538699\pi$
$709$	−4579.11			−0.242556			−0.121278	+	0.992619i	$0.538699\pi$
$710$	−4218.29	−	352.358i	−0.222971	−	0.0186250i
$711$	711.706	−	5605.50i	0.0375401	−	0.295672i
$712$	7749.27	+	1978.82i	0.407888	+	0.104157i
$713$			18848.5i			0.990014i
$714$	3241.73	−	21972.0i	0.169914	−	1.15165i
$715$			12983.9i			0.679121i
$716$	3185.07	+	535.845i	0.166245	+	0.0279685i
$717$	11174.7	+	706.565i	0.582046	+	0.0368022i
$718$	1078.64	−	12913.1i	0.0560649	−	0.671186i
$719$	13012.9			0.674967			0.337483	−	0.941332i	$-0.390424\pi$
$719$	13012.9			0.674967			0.337483	+	0.941332i	$0.390424\pi$
$720$	3832.93	−	7743.27i	0.198396	−	0.400798i
$721$	−49240.7			−2.54344
$722$	364.392	−	4362.35i	0.0187829	−	0.224861i
$723$	13806.0	+	872.941i	0.710169	+	0.0449032i
$724$	−1723.21	−	289.906i	−0.0884565	−	0.0148816i
$725$		−	2520.24i		−	0.129103i
$726$	895.860	−	6072.00i	0.0457968	−	0.310404i
$727$		−	8777.55i		−	0.447787i	−0.974614	−	0.223894i	$-0.928123\pi$
$727$		−	8777.55i		−	0.447787i	0.974614	−	0.223894i	$-0.0718768\pi$
$728$	−35822.9	−	9147.59i	−1.82374	−	0.465703i
$729$	18287.1	+	7280.16i	0.929083	+	0.369870i
$730$	10433.7	+	871.542i	0.529000	+	0.0441880i
$731$	21057.7			1.06546
$732$	11316.9	+	2647.63i	0.571426	+	0.133687i
$733$	−36538.2			−1.84116			−0.920580	−	0.390554i	$-0.872283\pi$
$733$	−36538.2			−1.84116			−0.920580	+	0.390554i	$0.872283\pi$
$734$	10382.5	+	867.265i	0.522107	+	0.0436122i
$735$	−572.700	+	9057.56i	−0.0287406	+	0.454549i
$736$	10618.9	−	23991.8i	0.531818	−	1.20156i
$737$			30749.0i			1.53684i
$738$	1340.72	+	285.242i	0.0668734	+	0.0142275i
$739$		−	11350.7i		−	0.565008i	−0.959266	−	0.282504i	$-0.908835\pi$
$739$		−	11350.7i		−	0.565008i	0.959266	−	0.282504i	$-0.0911651\pi$
$740$	−71.9154	+	427.467i	−0.00357252	+	0.0212351i
$741$	1483.96	−	23469.5i	0.0735688	−	1.16353i
$742$	−915.020	+	10954.2i	−0.0452715	+	0.541971i
$743$	−9663.11			−0.477127			−0.238563	−	0.971127i	$-0.576676\pi$
$743$	−9663.11			−0.477127			−0.238563	+	0.971127i	$0.576676\pi$
$744$	−14546.4	−	4710.31i	−0.716796	−	0.232108i
$745$	17851.6			0.877894
$746$	−1069.40	+	12802.4i	−0.0524844	+	0.628322i
$747$	−2396.59	−	304.284i	−0.117385	−	0.0149038i
$748$	3187.58	−	18947.1i	0.155815	−	0.926167i
$749$		−	30053.6i		−	1.46614i
$750$	1817.44	+	268.144i	0.0884848	+	0.0130550i
$751$		−	15714.3i		−	0.763548i	−0.924256	−	0.381774i	$-0.875313\pi$
$751$		−	15714.3i		−	0.763548i	0.924256	−	0.381774i	$-0.124687\pi$
$752$	−15600.2	−	5401.94i	−0.756492	−	0.261953i
$753$	26074.2	+	1648.65i	1.26188	+	0.0797876i
$754$	−17645.2	−	1473.92i	−0.852253	−	0.0711897i
$755$	−1040.58			−0.0501598
$756$	−10295.7	+	27679.0i	−0.495305	+	1.33158i
$757$	−21007.8			−1.00864			−0.504321	−	0.863516i	$-0.668257\pi$
$757$	−21007.8			−1.00864			−0.504321	+	0.863516i	$0.668257\pi$
$758$	178.707	+	14.9276i	0.00856322	+	0.000715296i
$759$	31430.3	+	1987.30i	1.50309	+	0.0950389i
$760$	−2040.02	+	7988.93i	−0.0973675	+	0.381301i
$761$		−	13202.6i		−	0.628901i	−0.949274	−	0.314451i	$-0.898180\pi$
$761$		−	13202.6i		−	0.628901i	0.949274	−	0.314451i	$-0.101820\pi$
$762$	−21148.6	−	3120.26i	−1.00543	−	0.148340i
$763$			28712.4i			1.36233i
$764$	13256.3	+	2230.19i	0.627744	+	0.105609i
$765$	7691.76	+	976.589i	0.363525	+	0.0461551i
$766$	−2862.69	+	34270.9i	−0.135030	+	1.61653i
$767$	27498.6			1.29455
$768$	15862.1	+	14190.8i	0.745277	+	0.666755i
$769$	−5051.50			−0.236881			−0.118441	−	0.992961i	$-0.537790\pi$
$769$	−5051.50			−0.236881			−0.118441	+	0.992961i	$0.537790\pi$
$770$	−1295.26	+	15506.3i	−0.0606205	+	0.725723i
$771$	2140.23	−	33848.9i	0.0999723	−	1.58112i
$772$	38150.1	+	6418.22i	1.77856	+	0.299219i
$773$			21369.0i			0.994296i	0.867666	+	0.497148i	$0.165619\pi$
$773$			21369.0i			0.994296i	−0.867666	+	0.497148i	$0.834381\pi$
$774$	−27386.9	−	5826.64i	−1.27184	−	0.270587i
$775$		−	3251.10i		−	0.150688i
$776$	−5052.36	+	19785.6i	−0.233723	+	0.915284i
$777$	93.4951	−	1478.68i	0.00431676	−	0.0682718i
$778$	13682.9	+	1142.95i	0.630535	+	0.0526693i
$779$	−1308.11			−0.0601640
$780$	2940.28	−	12567.8i	0.134973	−	0.576922i
$781$	12516.4			0.573458
$782$	23463.0	+	1959.90i	1.07294	+	0.0896237i
$783$	−2663.22	+	13890.2i	−0.121553	+	0.633965i
$784$	−21125.9	−	7315.33i	−0.962368	−	0.333242i
$785$		−	10288.7i		−	0.467794i
$786$	−1605.23	+	10880.0i	−0.0728457	+	0.493737i
$787$		−	14306.2i		−	0.647981i	−0.946060	−	0.323991i	$-0.894975\pi$
$787$		−	14306.2i		−	0.647981i	0.946060	−	0.323991i	$-0.105025\pi$
$788$	3981.82	−	23668.0i	0.180008	−	1.06997i
$789$	29503.9	+	1865.50i	1.33126	+	0.0841745i
$790$	−246.364	+	2949.36i	−0.0110952	+	0.132827i
$791$	−30085.7			−1.35237
$792$	−9388.27	+	23759.8i	−0.421209	+	1.06600i
$793$	17362.6			0.777508
$794$	242.926	−	2908.21i	0.0108578	−	0.129985i
$795$	−3829.82	−	242.156i	−0.170855	−	0.0108030i
$796$	−4622.32	+	27475.2i	−0.205821	+	1.22341i
$797$			12905.8i			0.573587i	0.957992	+	0.286793i	$0.0925893\pi$
$797$			12905.8i			0.573587i	−0.957992	+	0.286793i	$0.907411\pi$
$798$	4113.52	−	27880.8i	0.182477	−	1.23680i
$799$		−	14815.2i		−	0.655974i
$800$	−1831.62	+	4138.26i	−0.0809469	+	0.182887i
$801$	1202.04	−	9467.47i	0.0530238	−	0.417624i
$802$	−29142.2	−	2434.28i	−1.28310	−	0.107179i
$803$	−30958.7			−1.36053
$804$	6963.27	−	29763.4i	0.305442	−	1.30557i
$805$	−19068.2			−0.834862
$806$	−22762.2	−	1901.36i	−0.994746	−	0.0830923i
$807$	−412.289	+	6520.57i	−0.0179842	+	0.284430i
$808$	−23946.2	−	6114.81i	−1.04261	−	0.266235i
$809$		−	7580.76i		−	0.329450i	−0.986340	−	0.164725i	$-0.947326\pi$
$809$		−	7580.76i		−	0.329450i	0.986340	−	0.164725i	$-0.0526737\pi$
$810$	−9733.39	−	3398.41i	−0.422218	−	0.147417i
$811$			14898.1i			0.645058i	0.946560	+	0.322529i	$0.104533\pi$
$811$			14898.1i			0.645058i	−0.946560	+	0.322529i	$0.895467\pi$
$812$	−20926.0	−	3520.50i	−0.904381	−	0.152150i
$813$	−426.615	+	6747.14i	−0.0184035	+	0.291061i
$814$	106.693	−	1277.28i	0.00459407	−	0.0549983i
$815$	5441.48			0.233873
$816$	−7376.08	+	17617.9i	−0.316439	+	0.755823i
$817$	26720.7			1.14423
$818$	−2180.50	+	26104.0i	−0.0932022	+	1.11578i
$819$	−5556.74	+	43765.7i	−0.237079	+	1.86727i
$820$	−708.014	−	119.113i	−0.0301523	−	0.00507271i
$821$			23658.4i			1.00570i	0.864372	+	0.502852i	$0.167716\pi$
$821$			23658.4i			1.00570i	−0.864372	+	0.502852i	$0.832284\pi$
$822$	18306.0	+	2700.85i	0.776756	+	0.114602i
$823$			27699.9i			1.17322i	0.809870	+	0.586609i	$0.199538\pi$
$823$			27699.9i			1.17322i	−0.809870	+	0.586609i	$0.800462\pi$
$824$	41028.7	+	10476.9i	1.73459	+	0.442938i
$825$	−5421.30	−	342.783i	−0.228782	−	0.0144657i
$826$	32840.6	+	2743.22i	1.38338	+	0.115555i
$827$	−34271.4			−1.44103			−0.720516	−	0.693438i	$-0.756095\pi$
$827$	−34271.4			−1.44103			−0.720516	+	0.693438i	$0.756095\pi$
$828$	−29972.9	−	9041.16i	−1.25801	−	0.379471i
$829$	−18183.3			−0.761799			−0.380899	−	0.924617i	$-0.624386\pi$
$829$	−18183.3			−0.761799			−0.380899	+	0.924617i	$0.624386\pi$
$830$	1260.98	+	105.331i	0.0527339	+	0.00440492i
$831$	−43225.0	−	2733.07i	−1.80440	−	0.114090i
$832$	27902.3	+	15244.1i	1.16267	+	0.635207i
$833$		−	20062.7i		−	0.834493i
$834$	30124.5	+	4444.56i	1.25075	+	0.184535i
$835$			6978.12i			0.289207i
$836$	4044.80	−	24042.4i	0.167335	−	0.994645i
$837$	−3435.55	+	17918.3i	−0.141876	+	0.739961i
$838$	719.773	−	8616.83i	0.0296708	−	0.355207i
$839$	25752.3			1.05967			0.529837	−	0.848099i	$-0.322253\pi$
$839$	25752.3			1.05967			0.529837	+	0.848099i	$0.322253\pi$
$840$	4765.22	−	14715.9i	0.195733	−	0.604462i
$841$	14226.4			0.583313
$842$	2202.79	−	26370.9i	0.0901581	−	1.07934i
$843$	−889.912	+	14074.4i	−0.0363585	+	0.575029i
$844$	−6127.10	+	36419.6i	−0.249886	+	1.48533i
$845$		−	8296.79i		−	0.337773i
$846$	−4099.34	+	19268.0i	−0.166594	+	0.783037i
$847$		−	10988.4i		−	0.445769i
$848$	3093.15	−	8932.69i	0.125258	−	0.361733i
$849$	−2065.29	+	32663.6i	−0.0834870	+	1.32039i
$850$	−4047.06	−	338.056i	−0.163309	−	0.0136414i
$851$	1570.68			0.0632694
$852$	−12115.2	−	2834.40i	−0.487160	−	0.113973i
$853$	−32006.5			−1.28474			−0.642369	−	0.766395i	$-0.722049\pi$
$853$	−32006.5			−1.28474			−0.642369	+	0.766395i	$0.722049\pi$
$854$	20735.5	+	1732.06i	0.830861	+	0.0694028i
$855$	9760.27	+	1239.22i	0.390403	+	0.0495677i
$856$	−6394.50	+	25041.5i	−0.255327	+	0.999885i
$857$		−	46463.2i		−	1.85199i	−0.377539	−	0.925994i	$-0.623230\pi$
$857$		−	46463.2i		−	1.85199i	0.377539	−	0.925994i	$-0.376770\pi$
$858$	−5570.51	+	37756.1i	−0.221648	+	1.50230i
$859$			33474.7i			1.32962i	0.747013	+	0.664809i	$0.231487\pi$
$859$			33474.7i			1.32962i	−0.747013	+	0.664809i	$0.768513\pi$
$860$	14462.6	+	2433.13i	0.573454	+	0.0964757i
$861$	2449.13	+	154.856i	0.0969409	+	0.00612947i
$862$	1157.21	−	13853.7i	0.0457249	−	0.547399i
$863$	−183.100			−0.00722223			−0.00361112	−	0.999993i	$-0.501149\pi$
$863$	−183.100			−0.00722223			−0.00361112	+	0.999993i	$0.501149\pi$
$864$	14467.9	−	20872.3i	0.569686	−	0.821863i
$865$	791.894			0.0311274
$866$	3263.01	−	39063.4i	0.128039	−	1.53283i
$867$	8371.96	+	529.351i	0.327943	+	0.0207355i
$868$	−26994.4	−	4541.44i	−1.05559	−	0.177588i
$869$		−	8751.27i		−	0.341618i
$870$	1081.26	−	7328.63i	0.0421359	−	0.285591i
$871$		−	45663.7i		−	1.77641i
$872$	6109.13	−	23924.0i	0.237249	−	0.929093i
$873$	24172.5	+	3069.07i	0.937130	+	0.118983i
$874$	29772.8	+	2486.96i	1.15227	+	0.0962502i
$875$	3289.00			0.127073
$876$	29966.4	+	7010.76i	1.15579	+	0.270402i
$877$	19800.4			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$877$	19800.4			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$878$	−19735.1	−	1648.50i	−0.758574	−	0.0633646i
$879$	2742.05	−	43367.0i	0.105219	−	1.66409i
$880$	4378.50	−	12644.7i	0.167727	−	0.484377i
$881$			16266.4i			0.622053i	0.950401	+	0.311026i	$0.100673\pi$
$881$			16266.4i			0.622053i	−0.950401	+	0.311026i	$0.899327\pi$
$882$	−5551.34	+	26092.9i	−0.211931	+	0.996136i
$883$			45218.6i			1.72336i	0.507453	+	0.861679i	$0.330587\pi$
$883$			45218.6i			1.72336i	−0.507453	+	0.861679i	$0.669413\pi$
$884$	−4733.71	+	28137.3i	−0.180104	+	1.07054i
$885$	−725.979	+	11481.7i	−0.0275746	+	0.436107i
$886$	2915.93	−	34908.3i	0.110567	−	1.32367i
$887$	−48410.6			−1.83255			−0.916273	−	0.400553i	$-0.868818\pi$
$887$	−48410.6			−1.83255			−0.916273	+	0.400553i	$0.868818\pi$
$888$	−392.520	+	1212.18i	−0.0148335	+	0.0458087i
$889$	−38272.4			−1.44389
$890$	−416.099	+	4981.36i	−0.0156715	+	0.187613i
$891$	29517.0	+	7618.09i	1.10983	+	0.286437i
$892$	5135.31	−	30524.4i	0.192761	−	1.14578i
$893$		−	18799.3i		−	0.704475i
$894$	51910.8	+	7658.88i	1.94201	+	0.286523i
$895$			2018.65i			0.0753920i
$896$	31802.0	+	20988.9i	1.18575	+	0.782579i
$897$	−46675.5	−	2951.24i	−1.73740	−	0.109854i
$898$	−30693.1	−	2563.83i	−1.14058	−	0.0952741i
$899$	−13109.7			−0.486355
$900$	5169.92	+	1559.48i	0.191478	+	0.0577585i
$901$	8483.16			0.313668
$902$	2115.56	+	176.715i	0.0780936	+	0.00652325i
$903$	−50028.4	−	3163.24i	−1.84368	−	0.116574i
$904$	25068.2	+	6401.32i	0.922298	+	0.235514i
$905$		−	1092.14i		−	0.0401149i
$906$	−3025.91	−	446.442i	−0.110959	−	0.0163709i
$907$		−	23267.3i		−	0.851795i	−0.904771	−	0.425898i	$-0.859958\pi$
$907$		−	23267.3i		−	0.851795i	0.904771	−	0.425898i	$-0.140042\pi$
$908$	2723.15	+	458.132i	0.0995273	+	0.0167441i
$909$	−3714.46	+	29255.7i	−0.135535	+	1.06749i
$910$	1923.52	−	23027.6i	0.0700703	−	0.838853i
$911$	3858.37			0.140322			0.0701610	−	0.997536i	$-0.477649\pi$
$911$	3858.37			0.140322			0.0701610	+	0.997536i	$0.477649\pi$
$912$	−9359.69	+	22355.8i	−0.339836	+	0.811706i
$913$	−3741.53			−0.135626
$914$	1314.64	−	15738.3i	0.0475760	−	0.569560i
$915$	−458.382	+	7249.56i	−0.0165614	+	0.261927i
$916$	30290.5	+	5095.95i	1.09260	+	0.183816i
$917$			19689.4i			0.709053i
$918$	21948.0	+	6139.84i	0.789096	+	0.220746i
$919$		−	3155.27i		−	0.113257i	−0.998395	−	0.0566284i	$-0.981965\pi$
$919$		−	3155.27i		−	0.113257i	0.998395	−	0.0566284i	$-0.0180350\pi$
$920$	15888.1	+	4057.13i	0.569365	+	0.145391i
$921$	1001.47	−	15838.8i	0.0358302	−	0.566673i
$922$	9739.59	+	813.559i	0.347892	+	0.0290598i
$923$	−18587.4			−0.662852
$924$	−10419.1	+	44535.1i	−0.370958	+	1.58560i
$925$	−270.921			−0.00963010
$926$	−3943.75	−	329.426i	−0.139957	−	0.0116907i
$927$	6364.25	−	50125.8i	0.225490	−	1.77599i
$928$	16687.0	+	7385.79i	0.590279	+	0.261261i
$929$		−	47364.8i		−	1.67275i	−0.548155	−	0.836377i	$-0.684670\pi$
$929$		−	47364.8i		−	1.67275i	0.548155	−	0.836377i	$-0.315330\pi$
$930$	1394.82	−	9453.92i	0.0491808	−	0.333340i
$931$		−	25458.1i		−	0.896194i
$932$	−5369.84	+	31918.5i	−0.188729	+	1.12181i
$933$	−16461.8	−	1040.87i	−0.577638	−	0.0365235i
$934$	803.627	−	9620.69i	0.0281536	−	0.337043i
$935$	12008.3			0.420015
$936$	13942.0	−	35284.5i	0.486870	−	1.23217i
$937$	12573.9			0.438389			0.219194	−	0.975681i	$-0.429657\pi$
$937$	12573.9			0.438389			0.219194	+	0.975681i	$0.429657\pi$
$938$	4555.34	−	54534.6i	0.158568	−	1.89831i
$939$	−10008.0	−	632.796i	−0.347816	−	0.0219920i
$940$	1711.83	−	10175.2i	0.0593976	−	0.353061i
$941$			9368.78i			0.324563i	0.986745	+	0.162281i	$0.0518852\pi$
$941$			9368.78i			0.324563i	−0.986745	+	0.162281i	$0.948115\pi$
$942$	4414.16	−	29918.5i	0.152676	−	1.03482i
$943$			2601.52i			0.0898379i
$944$	−26780.1	−	9273.21i	−0.923323	−	0.319722i
$945$	−18127.2	−	3475.59i	−0.623997	−	0.119641i
$946$	−43214.5	−	3609.76i	−1.48523	−	0.124063i
$947$	6725.68			0.230787			0.115393	−	0.993320i	$-0.463187\pi$
$947$	6725.68			0.230787			0.115393	+	0.993320i	$0.463187\pi$
$948$	−1981.77	+	8470.78i	−0.0678955	+	0.290209i
$949$	45975.2			1.57262
$950$	−5135.42	−	428.967i	−0.175384	−	0.0146500i
$951$	−774.235	+	12244.9i	−0.0263999	+	0.417528i
$952$	−8460.24	+	33131.2i	−0.288023	+	1.12793i
$953$			53834.3i			1.82987i	0.403602	+	0.914935i	$0.367758\pi$
$953$			53834.3i			1.82987i	−0.403602	+	0.914935i	$0.632242\pi$
$954$	−11032.9	−	2347.28i	−0.374426	−	0.0796603i
$955$			8401.63i			0.284681i
$956$	−17000.0	−	2860.02i	−0.575126	−	0.0967570i
$957$	−1382.23	+	21860.8i	−0.0466889	+	0.738410i
$958$	4255.22	−	50941.8i	0.143507	−	1.71801i
$959$	33128.0			1.11550
$960$	−7101.62	+	11247.9i	−0.238754	+	0.378149i
$961$	12879.5			0.432329
$962$	−158.444	+	1896.82i	−0.00531022	+	0.0635718i
$963$	30593.8	+	3884.36i	1.02375	+	0.129981i
$964$	−21003.1	−	3533.48i	−0.701725	−	0.118056i
$965$			24178.9i			0.806575i
$966$	−55448.5	−	8180.83i	−1.84682	−	0.272478i
$967$		−	5199.14i		−	0.172899i	−0.996256	−	0.0864494i	$-0.972448\pi$
$967$		−	5199.14i		−	0.172899i	0.996256	−	0.0864494i	$-0.0275521\pi$
$968$	−2338.00	+	9155.86i	−0.0776304	+	0.304009i
$969$	−21706.0	−	1372.45i	−0.719606	−	0.0455000i
$970$	−12718.5	−	1062.39i	−0.420996	−	0.0351663i
$971$	−31817.8			−1.05158			−0.525788	−	0.850616i	$-0.676230\pi$
$971$	−31817.8			−1.05158			−0.525788	+	0.850616i	$0.676230\pi$
$972$	−26845.8	−	14058.2i	−0.885884	−	0.463907i
$973$	54516.0			1.79620
$974$	15890.3	+	1327.33i	0.522749	+	0.0436658i
$975$	8050.89	+	509.050i	0.264446	+	0.0167207i
$976$	−16908.9	−	5855.10i	−0.554550	−	0.192026i
$977$		−	49441.8i		−	1.61902i	−0.587107	−	0.809510i	$-0.699733\pi$
$977$		−	49441.8i		−	1.61902i	0.587107	−	0.809510i	$-0.300267\pi$
$978$	15823.3	+	2334.56i	0.517356	+	0.0763304i
$979$		−	14780.5i		−	0.482521i
$980$	2318.17	−	13779.2i	0.0755624	−	0.449144i
$981$	−29228.5	−	3711.02i	−0.951269	−	0.120778i
$982$	36.1319	−	432.556i	0.00117415	−	0.0140564i
$983$	−6929.51			−0.224839			−0.112420	−	0.993661i	$-0.535860\pi$
$983$	−6929.51			−0.224839			−0.112420	+	0.993661i	$0.535860\pi$
$984$	−2007.74	−	650.131i	−0.0650450	−	0.0210624i
$985$	15000.4			0.485230
$986$	−1363.17	+	16319.3i	−0.0440286	+	0.527092i
$987$	−2225.50	+	35197.5i	−0.0717715	+	1.13510i
$988$	−6006.73	+	35704.1i	−0.193421	+	1.14970i
$989$		−	53141.2i		−	1.70859i
$990$	−15617.6	−	3322.69i	−0.501373	−	0.106669i
$991$		−	18340.4i		−	0.587893i	−0.955822	−	0.293947i	$-0.905031\pi$
$991$		−	18340.4i		−	0.587893i	0.955822	−	0.293947i	$-0.0949688\pi$
$992$	21526.3	+	9527.66i	0.688971	+	0.304943i
$993$	3254.75	−	51475.6i	0.104015	−	1.64505i
$994$	−22198.3	−	1854.25i	−0.708338	−	0.0591683i
$995$	−17413.3			−0.554813
$996$	3621.61	+	847.290i	0.115216	+	0.0269552i
$997$	−11489.5			−0.364970			−0.182485	−	0.983209i	$-0.558414\pi$
$997$	−11489.5			−0.364970			−0.182485	+	0.983209i	$0.558414\pi$
$998$	−35254.0	−	2944.80i	−1.11818	−	0.0934030i
$999$	1493.17	+	286.291i	0.0472891	+	0.00906692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.e.a.11.13	yes	24
3.2	odd	2	inner	60.4.e.a.11.12	yes	24
4.3	odd	2	inner	60.4.e.a.11.11	✓	24
8.3	odd	2		960.4.h.d.191.24		24
8.5	even	2		960.4.h.d.191.1		24
12.11	even	2	inner	60.4.e.a.11.14	yes	24
24.5	odd	2		960.4.h.d.191.23		24
24.11	even	2		960.4.h.d.191.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.e.a.11.11	✓	24	4.3	odd	2	inner
60.4.e.a.11.12	yes	24	3.2	odd	2	inner
60.4.e.a.11.13	yes	24	1.1	even	1	trivial
60.4.e.a.11.14	yes	24	12.11	even	2	inner
960.4.h.d.191.1		24	8.5	even	2
960.4.h.d.191.2		24	24.11	even	2
960.4.h.d.191.23		24	24.5	odd	2
960.4.h.d.191.24		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.235442 - 2.81861i) q^{2} +(5.18580 + 0.327893i) q^{3} +(-7.88913 - 1.32724i) q^{4} -5.00000i q^{5} +(2.14516 - 14.5395i) q^{6} -26.3120i q^{7} +(-5.59840 + 21.9239i) q^{8} +(26.7850 + 3.40077i) q^{9} +O(q^{10})\)	\(q+(0.235442 - 2.81861i) q^{2} +(5.18580 + 0.327893i) q^{3} +(-7.88913 - 1.32724i) q^{4} -5.00000i q^{5} +(2.14516 - 14.5395i) q^{6} -26.3120i q^{7} +(-5.59840 + 21.9239i) q^{8} +(26.7850 + 3.40077i) q^{9} +(-14.0931 - 1.17721i) q^{10} +41.8165 q^{11} +(-40.4763 - 9.46957i) q^{12} -62.0996 q^{13} +(-74.1633 - 6.19495i) q^{14} +(1.63946 - 25.9290i) q^{15} +(60.4769 + 20.9415i) q^{16} +57.4334i q^{17} +(15.8917 - 74.6957i) q^{18} +72.8787i q^{19} +(-6.63619 + 39.4457i) q^{20} +(8.62751 - 136.449i) q^{21} +(9.84535 - 117.864i) q^{22} +144.939 q^{23} +(-36.2208 + 111.857i) q^{24} -25.0000 q^{25} +(-14.6208 + 175.035i) q^{26} +(137.786 + 26.4183i) q^{27} +(-34.9223 + 207.579i) q^{28} +100.810i q^{29} +(-72.6977 - 10.7258i) q^{30} +130.044i q^{31} +(73.2648 - 165.530i) q^{32} +(216.852 + 13.7113i) q^{33} +(161.882 + 13.5222i) q^{34} -131.560 q^{35} +(-206.797 - 62.3792i) q^{36} +10.8369 q^{37} +(205.417 + 17.1587i) q^{38} +(-322.036 - 20.3620i) q^{39} +(109.620 + 27.9920i) q^{40} +17.9491i q^{41} +(-382.565 - 56.4433i) q^{42} -366.646i q^{43} +(-329.896 - 55.5004i) q^{44} +(17.0038 - 133.925i) q^{45} +(34.1247 - 408.526i) q^{46} -257.954 q^{47} +(306.754 + 128.428i) q^{48} -349.322 q^{49} +(-5.88605 + 70.4653i) q^{50} +(-18.8320 + 297.838i) q^{51} +(489.912 + 82.4209i) q^{52} -147.704i q^{53} +(106.904 - 382.146i) q^{54} -209.083i q^{55} +(576.862 + 147.305i) q^{56} +(-23.8964 + 377.934i) q^{57} +(284.143 + 23.7348i) q^{58} -442.815 q^{59} +(-47.3479 + 202.381i) q^{60} -279.593 q^{61} +(366.544 + 30.6178i) q^{62} +(89.4811 - 704.766i) q^{63} +(-449.316 - 245.478i) q^{64} +310.498i q^{65} +(89.7029 - 607.993i) q^{66} +735.331i q^{67} +(76.2278 - 453.100i) q^{68} +(751.623 + 47.5244i) q^{69} +(-30.9747 + 370.817i) q^{70} +299.317 q^{71} +(-224.511 + 568.193i) q^{72} -740.346 q^{73} +(2.55145 - 30.5449i) q^{74} +(-129.645 - 8.19732i) q^{75} +(96.7274 - 574.950i) q^{76} -1100.28i q^{77} +(-133.213 + 902.899i) q^{78} -209.278i q^{79} +(104.708 - 302.384i) q^{80} +(705.870 + 182.179i) q^{81} +(50.5915 + 4.22596i) q^{82} -89.4750 q^{83} +(-249.164 + 1065.01i) q^{84} +287.167 q^{85} +(-1033.43 - 86.3238i) q^{86} +(-33.0547 + 522.778i) q^{87} +(-234.105 + 916.781i) q^{88} -353.462i q^{89} +(-373.479 - 79.4587i) q^{90} +1633.96i q^{91} +(-1143.44 - 192.368i) q^{92} +(-42.6405 + 674.383i) q^{93} +(-60.7331 + 727.071i) q^{94} +364.393 q^{95} +(434.212 - 834.383i) q^{96} +902.465 q^{97} +(-82.2450 + 984.602i) q^{98} +(1120.05 + 142.208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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