LMFDB - Embedded newform 24.4.f.b.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,4,Mod(11,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("24.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	24.f (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:	$1.41604584014$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 10x^{6} + 120x^{4} - 640x^{2} + 4096 $ x^8 - 10x^6 + 120x^4 - 640*x^2 + 4096
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.7
Root			$2.58576 - 1.14624i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.4.f.b.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.58576 - 1.14624i) q^{2} +(1.37228 + 5.01167i) q^{3} +(5.37228 - 5.92778i) q^{4} -12.2683 q^{5} +(9.29295 + 11.3860i) q^{6} -14.0624i q^{7} +(7.09677 - 21.4857i) q^{8} +(-23.2337 + 13.7548i) q^{9} +O(q^{10})$	\(q+(2.58576 - 1.14624i) q^{2} +(1.37228 + 5.01167i) q^{3} +(5.37228 - 5.92778i) q^{4} -12.2683 q^{5} +(9.29295 + 11.3860i) q^{6} -14.0624i q^{7} +(7.09677 - 21.4857i) q^{8} +(-23.2337 + 13.7548i) q^{9} +(-31.7228 + 14.0624i) q^{10} +0.853445i q^{11} +(37.0804 + 18.7895i) q^{12} +75.5470i q^{13} +(-16.1188 - 36.3619i) q^{14} +(-16.8355 - 61.4846i) q^{15} +(-6.27719 - 63.6914i) q^{16} -49.2633i q^{17} +(-44.3104 + 62.1980i) q^{18} +86.1902 q^{19} +(-65.9087 + 72.7237i) q^{20} +(70.4759 - 19.2975i) q^{21} +(0.978251 + 2.20680i) q^{22} +131.817 q^{23} +(117.418 + 6.08225i) q^{24} +25.5109 q^{25} +(86.5947 + 195.346i) q^{26} +(-100.818 - 97.5641i) q^{27} +(-83.3586 - 75.5470i) q^{28} -128.684 q^{29} +(-114.009 - 139.687i) q^{30} +137.032i q^{31} +(-89.2367 - 157.495i) q^{32} +(-4.27719 + 1.17117i) q^{33} +(-56.4674 - 127.383i) q^{34} +172.521i q^{35} +(-43.2822 + 211.619i) q^{36} -188.046i q^{37} +(222.867 - 98.7944i) q^{38} +(-378.617 + 103.672i) q^{39} +(-87.0652 + 263.593i) q^{40} +133.935i q^{41} +(160.114 - 130.681i) q^{42} -243.038 q^{43} +(5.05904 + 4.58495i) q^{44} +(285.038 - 168.748i) q^{45} +(340.848 - 151.094i) q^{46} +36.5380 q^{47} +(310.586 - 118.862i) q^{48} +145.250 q^{49} +(65.9649 - 29.2415i) q^{50} +(246.891 - 67.6031i) q^{51} +(447.826 + 405.860i) q^{52} -245.099 q^{53} +(-372.522 - 136.716i) q^{54} -10.4703i q^{55} +(-302.140 - 99.7974i) q^{56} +(118.277 + 431.957i) q^{57} +(-332.745 + 147.502i) q^{58} -146.936i q^{59} +(-454.913 - 230.515i) q^{60} -191.332i q^{61} +(157.071 + 354.330i) q^{62} +(193.426 + 326.721i) q^{63} +(-411.272 - 304.958i) q^{64} -926.832i q^{65} +(-9.71733 + 7.93102i) q^{66} -135.299 q^{67} +(-292.022 - 264.656i) q^{68} +(180.891 + 660.625i) q^{69} +(197.750 + 446.098i) q^{70} +622.549 q^{71} +(130.648 + 596.807i) q^{72} -716.195 q^{73} +(-215.545 - 486.241i) q^{74} +(35.0081 + 127.852i) q^{75} +(463.038 - 510.917i) q^{76} +12.0015 q^{77} +(-860.178 + 702.054i) q^{78} -959.221i q^{79} +(77.0103 + 781.385i) q^{80} +(350.609 - 639.152i) q^{81} +(153.522 + 346.324i) q^{82} -73.7766i q^{83} +(264.225 - 521.438i) q^{84} +604.376i q^{85} +(-628.437 + 278.579i) q^{86} +(-176.590 - 644.920i) q^{87} +(18.3369 + 6.05671i) q^{88} +1608.62i q^{89} +(543.612 - 763.063i) q^{90} +1062.37 q^{91} +(708.160 - 781.385i) q^{92} +(-686.757 + 188.046i) q^{93} +(94.4785 - 41.8812i) q^{94} -1057.41 q^{95} +(666.857 - 663.353i) q^{96} +33.0106 q^{97} +(375.581 - 166.491i) q^{98} +(-11.7390 - 19.8287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9	$ 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9} - 24 q^{10} + 36 q^{12} - 280 q^{16} + 264 q^{18} + 184 q^{19} - 176 q^{22} + 264 q^{24} + 296 q^{25} - 324 q^{27} + 528 q^{28} - 624 q^{30} - 264 q^{33} - 176 q^{34} - 516 q^{36} - 1248 q^{40} + 1320 q^{42} - 152 q^{43} + 1440 q^{46} + 1080 q^{48} - 952 q^{49} + 1056 q^{51} + 2112 q^{52} - 1584 q^{54} + 1176 q^{57} - 2616 q^{58} - 2640 q^{60} - 1360 q^{64} + 792 q^{66} - 1496 q^{67} + 3696 q^{70} + 2640 q^{72} + 1072 q^{73} - 708 q^{75} + 1912 q^{76} - 3696 q^{78} - 504 q^{81} - 2816 q^{82} - 4224 q^{84} - 1232 q^{88} + 4104 q^{90} + 3168 q^{91} + 4800 q^{94} + 4752 q^{96} - 3872 q^{97} + 2112 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9 - 24 * q^10 + 36 * q^12 - 280 * q^16 + 264 * q^18 + 184 * q^19 - 176 * q^22 + 264 * q^24 + 296 * q^25 - 324 * q^27 + 528 * q^28 - 624 * q^30 - 264 * q^33 - 176 * q^34 - 516 * q^36 - 1248 * q^40 + 1320 * q^42 - 152 * q^43 + 1440 * q^46 + 1080 * q^48 - 952 * q^49 + 1056 * q^51 + 2112 * q^52 - 1584 * q^54 + 1176 * q^57 - 2616 * q^58 - 2640 * q^60 - 1360 * q^64 + 792 * q^66 - 1496 * q^67 + 3696 * q^70 + 2640 * q^72 + 1072 * q^73 - 708 * q^75 + 1912 * q^76 - 3696 * q^78 - 504 * q^81 - 2816 * q^82 - 4224 * q^84 - 1232 * q^88 + 4104 * q^90 + 3168 * q^91 + 4800 * q^94 + 4752 * q^96 - 3872 * q^97 + 2112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	2.58576	−	1.14624i	0.914203	−	0.405256i
$2$	2.58576	−	1.14624i	0.914203	−	0.405256i
$3$	1.37228	+	5.01167i	0.264096	+	0.964496i
$3$	1.37228	+	5.01167i	0.264096	+	0.964496i
$4$	5.37228	−	5.92778i	0.671535	−	0.740973i
$5$	−12.2683			−1.09731			−0.548654	−	0.836049i	$-0.684860\pi$
$5$	−12.2683			−1.09731			−0.548654	+	0.836049i	$0.684860\pi$
$6$	9.29295	+	11.3860i	0.632305	+	0.774719i
$7$		−	14.0624i		−	0.759296i	−0.925131	−	0.379648i	$-0.876045\pi$
$7$		−	14.0624i		−	0.759296i	0.925131	−	0.379648i	$-0.123955\pi$
$8$	7.09677	−	21.4857i	0.313636	−	0.949543i
$9$	−23.2337	+	13.7548i	−0.860507	+	0.509439i
$10$	−31.7228	+	14.0624i	−1.00316	+	0.444691i
$11$			0.853445i			0.0233930i	0.999932	+	0.0116965i	$0.00372320\pi$
$11$			0.853445i			0.0233930i	−0.999932	+	0.0116965i	$0.996277\pi$
$12$	37.0804	+	18.7895i	0.892015	+	0.452006i
$13$			75.5470i			1.61177i	0.592075	+	0.805883i	$0.298309\pi$
$13$			75.5470i			1.61177i	−0.592075	+	0.805883i	$0.701691\pi$
$14$	−16.1188	−	36.3619i	−0.307709	−	0.694151i
$15$	−16.8355	−	61.4846i	−0.289795	−	1.05835i
$16$	−6.27719	−	63.6914i	−0.0980810	−	0.995178i
$17$		−	49.2633i		−	0.702829i	−0.936220	−	0.351415i	$-0.885701\pi$
$17$		−	49.2633i		−	0.702829i	0.936220	−	0.351415i	$-0.114299\pi$
$18$	−44.3104	+	62.1980i	−0.580225	+	0.814456i
$19$	86.1902			1.04070			0.520352	−	0.853952i	$-0.325801\pi$
$19$	86.1902			1.04070			0.520352	+	0.853952i	$0.325801\pi$
$20$	−65.9087	+	72.7237i	−0.736882	+	0.813076i
$21$	70.4759	−	19.2975i	0.732339	−	0.200527i
$22$	0.978251	+	2.20680i	0.00948017	+	0.0213860i
$23$	131.817			1.19504			0.597518	−	0.801856i	$-0.296154\pi$
$23$	131.817			1.19504			0.597518	+	0.801856i	$0.296154\pi$
$24$	117.418	+	6.08225i	0.998661	+	0.0517306i
$25$	25.5109			0.204087
$26$	86.5947	+	195.346i	0.653178	+	1.47348i
$27$	−100.818	−	97.5641i	−0.718608	−	0.695415i
$28$	−83.3586	−	75.5470i	−0.562618	−	0.509894i
$29$	−128.684			−0.823998			−0.411999	−	0.911184i	$-0.635169\pi$
$29$	−128.684			−0.823998			−0.411999	+	0.911184i	$0.635169\pi$
$30$	−114.009	−	139.687i	−0.693834	−	0.850107i
$31$			137.032i			0.793923i	0.917835	+	0.396961i	$0.129935\pi$
$31$			137.032i			0.793923i	−0.917835	+	0.396961i	$0.870065\pi$
$32$	−89.2367	−	157.495i	−0.492968	−	0.870047i
$33$	−4.27719	+	1.17117i	−0.0225625	+	0.00617800i
$34$	−56.4674	−	127.383i	−0.284826	−	0.642529i
$35$			172.521i			0.833183i
$36$	−43.2822	+	211.619i	−0.200381	+	0.979718i
$37$		−	188.046i		−	0.835529i	−0.908555	−	0.417764i	$-0.862814\pi$
$37$		−	188.046i		−	0.835529i	0.908555	−	0.417764i	$-0.137186\pi$
$38$	222.867	−	98.7944i	0.951415	−	0.421752i
$39$	−378.617	+	103.672i	−1.55454	+	0.425661i
$40$	−87.0652	+	263.593i	−0.344156	+	1.04194i
$41$			133.935i			0.510175i	0.966918	+	0.255087i	$0.0821042\pi$
$41$			133.935i			0.510175i	−0.966918	+	0.255087i	$0.917896\pi$
$42$	160.114	−	130.681i	0.588242	−	0.480107i
$43$	−243.038			−0.861929			−0.430964	−	0.902369i	$-0.641827\pi$
$43$	−243.038			−0.861929			−0.430964	+	0.902369i	$0.641827\pi$
$44$	5.05904	+	4.58495i	0.0173336	+	0.0157092i
$45$	285.038	−	168.748i	0.944242	−	0.559012i
$46$	340.848	−	151.094i	1.09251	−	0.484295i
$47$	36.5380			0.113396			0.0566981	−	0.998391i	$-0.481943\pi$
$47$	36.5380			0.113396			0.0566981	+	0.998391i	$0.481943\pi$
$48$	310.586	−	118.862i	0.933943	−	0.357421i
$49$	145.250			0.423469
$50$	65.9649	−	29.2415i	0.186577	−	0.0827075i
$51$	246.891	−	67.6031i	0.677876	−	0.185614i
$52$	447.826	+	405.860i	1.19427	+	1.08236i
$53$	−245.099			−0.635225			−0.317613	−	0.948221i	$-0.602881\pi$
$53$	−245.099			−0.635225			−0.317613	+	0.948221i	$0.602881\pi$
$54$	−372.522	−	136.716i	−0.938775	−	0.344531i
$55$		−	10.4703i		−	0.0256694i
$56$	−302.140	−	99.7974i	−0.720985	−	0.238143i
$57$	118.277	+	431.957i	0.274846	+	1.00376i
$58$	−332.745	+	147.502i	−0.753302	+	0.333930i
$59$		−	146.936i		−	0.324229i	−0.986772	−	0.162114i	$-0.948169\pi$
$59$		−	146.936i		−	0.324229i	0.986772	−	0.162114i	$-0.0518313\pi$
$60$	−454.913	−	230.515i	−0.978816	−	0.495990i
$61$		−	191.332i		−	0.401599i	−0.979632	−	0.200800i	$-0.935646\pi$
$61$		−	191.332i		−	0.401599i	0.979632	−	0.200800i	$-0.0643540\pi$
$62$	157.071	+	354.330i	0.321742	+	0.725807i
$63$	193.426	+	326.721i	0.386815	+	0.653380i
$64$	−411.272	−	304.958i	−0.803265	−	0.595622i
$65$		−	926.832i		−	1.76861i
$66$	−9.71733	+	7.93102i	−0.0181230	+	0.0147915i
$67$	−135.299			−0.246707			−0.123354	−	0.992363i	$-0.539365\pi$
$67$	−135.299			−0.246707			−0.123354	+	0.992363i	$0.539365\pi$
$68$	−292.022	−	264.656i	−0.520777	−	0.471975i
$69$	180.891	+	660.625i	0.315604	+	1.15261i
$70$	197.750	+	446.098i	0.337652	+	0.761698i
$71$	622.549			1.04061			0.520303	−	0.853982i	$-0.325819\pi$
$71$	622.549			1.04061			0.520303	+	0.853982i	$0.325819\pi$
$72$	130.648	+	596.807i	0.213848	+	0.976867i
$73$	−716.195			−1.14828			−0.574139	−	0.818758i	$-0.694663\pi$
$73$	−716.195			−1.14828			−0.574139	+	0.818758i	$0.694663\pi$
$74$	−215.545	−	486.241i	−0.338603	−	0.763843i
$75$	35.0081	+	127.852i	0.0538985	+	0.196841i
$76$	463.038	−	510.917i	0.698870	−	0.771134i
$77$	12.0015			0.0177622
$78$	−860.178	+	702.054i	−1.24867	+	1.01913i
$79$		−	959.221i		−	1.36609i	−0.730378	−	0.683043i	$-0.760656\pi$
$79$		−	959.221i		−	1.36609i	0.730378	−	0.683043i	$-0.239344\pi$
$80$	77.0103	+	781.385i	0.107625	+	1.09202i
$81$	350.609	−	639.152i	0.480944	−	0.876751i
$82$	153.522	+	346.324i	0.206751	+	0.466403i
$83$		−	73.7766i		−	0.0975667i	−0.998809	−	0.0487833i	$-0.984466\pi$
$83$		−	73.7766i		−	0.0975667i	0.998809	−	0.0487833i	$-0.0155344\pi$
$84$	264.225	−	521.438i	0.343206	−	0.677304i
$85$			604.376i			0.771221i
$86$	−628.437	+	278.579i	−0.787978	+	0.349302i
$87$	−176.590	−	644.920i	−0.217614	−	0.794743i
$88$	18.3369	+	6.05671i	0.0222127	+	0.00733690i
$89$			1608.62i			1.91588i	0.286970	+	0.957940i	$0.407352\pi$
$89$			1608.62i			1.91588i	−0.286970	+	0.957940i	$0.592648\pi$
$90$	543.612	−	763.063i	0.636686	−	0.893710i
$91$	1062.37			1.22381
$92$	708.160	−	781.385i	0.802509	−	0.885489i
$93$	−686.757	+	188.046i	−0.765736	+	0.209672i
$94$	94.4785	−	41.8812i	0.103667	−	0.0459545i
$95$	−1057.41			−1.14197
$96$	666.857	−	663.353i	0.708967	−	0.705242i
$97$	33.0106			0.0345538			0.0172769	−	0.999851i	$-0.494500\pi$
$97$	33.0106			0.0345538			0.0172769	+	0.999851i	$0.494500\pi$
$98$	375.581	−	166.491i	0.387137	−	0.171613i
$99$	−11.7390	−	19.8287i	−0.0119173	−	0.0201299i
$100$	137.052	−	151.223i	0.137052	−	0.151223i
$101$	287.905			0.283639			0.141820	−	0.989893i	$-0.454705\pi$
$101$	287.905			0.283639			0.141820	+	0.989893i	$0.454705\pi$
$102$	560.912	−	457.801i	0.544495	−	0.444402i
$103$			330.007i			0.315695i	0.987464	+	0.157847i	$0.0504554\pi$
$103$			330.007i			0.315695i	−0.987464	+	0.157847i	$0.949545\pi$
$104$	1623.18	+	536.140i	1.53044	+	0.505508i
$105$	−864.619	+	236.748i	−0.803602	+	0.220040i
$106$	−633.766	+	280.941i	−0.580725	+	0.257429i
$107$			879.693i			0.794796i	0.917646	+	0.397398i	$0.130087\pi$
$107$			879.693i			0.794796i	−0.917646	+	0.397398i	$0.869913\pi$
$108$	−1119.96	+	73.4848i	−0.997854	+	0.0654730i
$109$			419.616i			0.368733i	0.982858	+	0.184367i	$0.0590234\pi$
$109$			419.616i			0.368733i	−0.982858	+	0.184367i	$0.940977\pi$
$110$	−12.0015	−	27.0737i	−0.0104027	−	0.0234670i
$111$	942.424	−	258.052i	0.805864	−	0.220659i
$112$	−895.652	+	88.2721i	−0.755635	+	0.0744726i
$113$		−	874.828i		−	0.728291i	−0.931342	−	0.364145i	$-0.881361\pi$
$113$		−	874.828i		−	0.728291i	0.931342	−	0.364145i	$-0.118639\pi$
$114$	800.961	+	981.362i	0.658043	+	0.806254i
$115$	−1617.17			−1.31132
$116$	−691.325	+	762.808i	−0.553344	+	0.610560i
$117$	−1039.14	−	1755.24i	−0.821096	−	1.38694i
$118$	−168.424	−	379.942i	−0.131396	−	0.296411i
$119$	−692.758			−0.533656
$120$	−1440.52	−	74.6188i	−1.09584	−	0.0567644i
$121$	1330.27			0.999453
$122$	−219.312	−	494.738i	−0.162751	−	0.367144i
$123$	−671.239	+	183.797i	−0.492062	+	0.134735i
$124$	812.293	+	736.172i	0.588275	+	0.533147i
$125$	1220.56			0.873362
$126$	874.651	+	623.109i	0.618414	+	0.440563i
$127$			2139.85i			1.49512i	0.664192	+	0.747562i	$0.268776\pi$
$127$			2139.85i			1.49512i	−0.664192	+	0.747562i	$0.731224\pi$
$128$	−1413.00	−	317.134i	−0.975727	−	0.218992i
$129$	−333.516	−	1218.03i	−0.227632	−	0.831327i
$130$	−1062.37	−	2396.56i	−0.716738	−	1.61687i
$131$		−	1844.04i		−	1.22988i	−0.788573	−	0.614941i	$-0.789180\pi$
$131$		−	1844.04i		−	1.22988i	0.788573	−	0.614941i	$-0.210820\pi$
$132$	−16.0358	+	31.6461i	−0.0105738	+	0.0208669i
$133$		−	1212.04i		−	0.790203i
$134$	−349.850	+	155.085i	−0.225541	+	0.0999797i
$135$	1236.86	+	1196.94i	0.788535	+	0.763086i
$136$	−1058.46	−	349.610i	−0.667367	−	0.220433i
$137$			1322.68i			0.824849i	0.910992	+	0.412425i	$0.135318\pi$
$137$			1322.68i			0.824849i	−0.910992	+	0.412425i	$0.864682\pi$
$138$	1224.97	+	1500.87i	0.755627	+	0.925818i
$139$	1768.23			1.07899			0.539495	−	0.841989i	$-0.318615\pi$
$139$	1768.23			1.07899			0.539495	+	0.841989i	$0.318615\pi$
$140$	1022.67	+	926.832i	0.617366	+	0.559511i
$141$	50.1405	+	183.117i	0.0299474	+	0.109370i
$142$	1609.76	−	713.589i	0.951325	−	0.421711i
$143$	−64.4752			−0.0377041
$144$	1021.91	+	1393.44i	0.591382	+	0.806392i
$145$	1578.73			0.904181
$146$	−1851.91	+	820.930i	−1.04976	+	0.465347i
$147$	199.324	+	727.945i	0.111836	+	0.408434i
$148$	−1114.70	−	1010.24i	−0.619104	−	0.561087i
$149$	2268.03			1.24701			0.623505	−	0.781820i	$-0.285708\pi$
$149$	2268.03			1.24701			0.623505	+	0.781820i	$0.285708\pi$
$150$	237.071	+	290.467i	0.129045	+	0.158110i
$151$			14.6741i			0.00790833i	0.999992	+	0.00395417i	$0.00125865\pi$
$151$			14.6741i			0.00790833i	−0.999992	+	0.00395417i	$0.998741\pi$
$152$	611.672	−	1851.86i	0.326402	−	0.988194i
$153$	677.609	+	1144.57i	0.358048	+	0.604789i
$154$	31.0329	−	13.7565i	0.0162383	−	0.00719826i
$155$		−	1681.14i		−	0.871178i
$156$	−1419.49	+	2801.31i	−0.728527	+	1.43772i
$157$		−	367.876i		−	0.187005i	−0.995619	−	0.0935023i	$-0.970194\pi$
$157$		−	367.876i		−	0.187005i	0.995619	−	0.0935023i	$-0.0298062\pi$
$158$	−1099.49	−	2480.31i	−0.553615	−	1.24888i
$159$	−336.345	−	1228.36i	−0.167760	−	0.612672i
$160$	1094.78	+	1932.20i	0.540938	+	0.954711i
$161$		−	1853.66i		−	0.907386i
$162$	173.969	−	2054.57i	0.0843724	−	0.996434i
$163$	−872.288			−0.419159			−0.209579	−	0.977792i	$-0.567209\pi$
$163$	−872.288			−0.419159			−0.209579	+	0.977792i	$0.567209\pi$
$164$	793.939	+	719.538i	0.378026	+	0.342600i
$165$	52.4738	−	14.3682i	0.0247580	−	0.00677918i
$166$	−84.5655	−	190.768i	−0.0395395	−	0.0891958i
$167$	−2964.46			−1.37363			−0.686816	−	0.726831i	$-0.740992\pi$
$167$	−2964.46			−1.37363			−0.686816	+	0.726831i	$0.740992\pi$
$168$	85.5308	−	1651.18i	0.0392788	−	0.758280i
$169$	−3510.35			−1.59779
$170$	692.758	+	1562.77i	0.312542	+	0.705053i
$171$	−2002.52	+	1185.53i	−0.895533	+	0.530175i
$172$	−1305.67	+	1440.68i	−0.578816	+	0.638666i
$173$	−1962.66			−0.862533			−0.431267	−	0.902225i	$-0.641933\pi$
$173$	−1962.66			−0.862533			−0.431267	+	0.902225i	$0.641933\pi$
$174$	−1195.85	−	1465.19i	−0.521018	−	0.638367i
$175$		−	358.743i		−	0.154963i
$176$	54.3571	−	5.35724i	0.0232802	−	0.00229441i
$177$	736.397	−	201.638i	0.312717	−	0.0856273i
$178$	1843.86	+	4159.50i	0.776422	+	1.75150i
$179$			2427.54i			1.01365i	0.862050	+	0.506823i	$0.169180\pi$
$179$			2427.54i			1.01365i	−0.862050	+	0.506823i	$0.830820\pi$
$180$	530.998	−	2596.20i	0.219879	−	1.07505i
$181$			1808.20i			0.742554i	0.928522	+	0.371277i	$0.121080\pi$
$181$			1808.20i			0.742554i	−0.928522	+	0.371277i	$0.878920\pi$
$182$	2747.03	−	1217.73i	1.11881	−	0.495956i
$183$	958.894	−	262.561i	0.387341	−	0.106061i
$184$	935.478	−	2832.19i	0.374806	−	1.13474i
$185$			2307.00i			0.916833i
$186$	−1560.24	+	1273.43i	−0.615067	+	0.502001i
$187$	42.0435			0.0164413
$188$	196.293	−	216.589i	0.0761495	−	0.0840235i
$189$	−1371.98	+	1417.74i	−0.528026	+	0.545636i
$190$	−2734.20	+	1212.04i	−1.04400	+	0.462792i
$191$	3182.95			1.20581			0.602907	−	0.797812i	$-0.294009\pi$
$191$	3182.95			1.20581			0.602907	+	0.797812i	$0.294009\pi$
$192$	963.971	−	2479.65i	0.362336	−	0.932047i
$193$	−858.152			−0.320058			−0.160029	−	0.987112i	$-0.551159\pi$
$193$	−858.152			−0.320058			−0.160029	+	0.987112i	$0.551159\pi$
$194$	85.3575	−	37.8380i	0.0315892	−	0.0140032i
$195$	4644.98	−	1271.87i	1.70581	−	0.467081i
$196$	780.323	−	861.010i	0.284374	−	0.313779i
$197$	−3610.74			−1.30586			−0.652931	−	0.757418i	$-0.726461\pi$
$197$	−3610.74			−1.30586			−0.652931	+	0.757418i	$0.726461\pi$
$198$	−53.0826	−	37.8165i	−0.0190526	−	0.0135732i
$199$		−	3781.55i		−	1.34707i	−0.739155	−	0.673536i	$-0.764775\pi$
$199$		−	3781.55i		−	1.34707i	0.739155	−	0.673536i	$-0.235225\pi$
$200$	181.045	−	548.119i	0.0640090	−	0.193789i
$201$	−185.668	−	678.074i	−0.0651544	−	0.237948i
$202$	744.451	−	330.007i	0.259304	−	0.114947i
$203$			1809.60i			0.625659i
$204$	925.633	−	1826.70i	0.317683	−	0.626934i
$205$		−	1643.16i		−	0.559819i
$206$	378.266	+	853.318i	0.127937	+	0.288609i
$207$	−3062.60	+	1813.13i	−1.02834	+	0.608797i
$208$	4811.69	−	474.223i	1.60400	−	0.158084i
$209$			73.5586i			0.0243452i
$210$	−1964.33	+	1603.23i	−0.645483	+	0.526826i
$211$	−446.299			−0.145614			−0.0728069	−	0.997346i	$-0.523196\pi$
$211$	−446.299			−0.145614			−0.0728069	+	0.997346i	$0.523196\pi$
$212$	−1316.74	+	1452.89i	−0.426576	+	0.470684i
$213$	854.312	+	3120.01i	0.274819	+	1.00366i
$214$	1008.34	+	2274.67i	0.322096	+	0.726605i
$215$	2981.66			0.945802
$216$	−2811.72	+	1473.75i	−0.885708	+	0.464242i
$217$	1926.99			0.602823
$218$	480.980	+	1085.03i	0.149431	+	0.337097i
$219$	−982.821	−	3589.33i	−0.303255	−	1.10751i
$220$	−62.0657	−	56.2495i	−0.0190203	−	0.0172379i
$221$	3721.69			1.13280
$222$	2141.09	−	1747.50i	0.647300	−	0.528309i
$223$		−	4865.50i		−	1.46107i	−0.682877	−	0.730534i	$-0.739271\pi$
$223$		−	4865.50i		−	1.46107i	0.682877	−	0.730534i	$-0.260729\pi$
$224$	−2214.76	+	1254.88i	−0.660624	+	0.374309i
$225$	−592.712	+	350.898i	−0.175618	+	0.103970i
$226$	−1002.76	−	2262.09i	−0.295144	−	0.665806i
$227$			1373.72i			0.401661i	0.979626	+	0.200831i	$0.0643641\pi$
$227$			1373.72i			0.401661i	−0.979626	+	0.200831i	$0.935636\pi$
$228$	3195.96	+	1619.47i	0.928324	+	0.470404i
$229$			2419.15i			0.698086i	0.937107	+	0.349043i	$0.113493\pi$
$229$			2419.15i			0.698086i	−0.937107	+	0.349043i	$0.886507\pi$
$230$	−4181.62	+	1853.66i	−1.19882	+	0.531422i
$231$	16.4694	+	60.1474i	0.00469093	+	0.0171316i
$232$	−913.238	+	2764.86i	−0.258435	+	0.782422i
$233$		−	5250.61i		−	1.47630i	−0.674634	−	0.738152i	$-0.735699\pi$
$233$		−	5250.61i		−	1.47630i	0.674634	−	0.738152i	$-0.264301\pi$
$234$	−4698.87	−	3347.51i	−1.31271	−	0.935187i
$235$	−448.259			−0.124431
$236$	−871.007	−	789.383i	−0.240244	−	0.217731i
$237$	4807.30	−	1316.32i	1.31759	−	0.360777i
$238$	−1791.30	+	794.065i	−0.487870	+	0.216267i
$239$	467.796			0.126608			0.0633038	−	0.997994i	$-0.479836\pi$
$239$	467.796			0.126608			0.0633038	+	0.997994i	$0.479836\pi$
$240$	−3810.36	+	1458.23i	−1.02482	+	0.392201i
$241$	−2777.11			−0.742279			−0.371140	−	0.928577i	$-0.621033\pi$
$241$	−2777.11			−0.742279			−0.371140	+	0.928577i	$0.621033\pi$
$242$	3439.76	−	1524.81i	0.913703	−	0.405034i
$243$	3684.35	+	880.039i	0.972639	+	0.232323i
$244$	−1134.17	−	1027.89i	−0.297574	−	0.269688i
$245$	−1781.97			−0.464676
$246$	−1524.99	+	1244.65i	−0.395242	+	0.322586i
$247$			6511.41i			1.67737i
$248$	2944.22	+	972.482i	0.753864	+	0.249003i
$249$	369.744	−	101.242i	0.0941027	−	0.0257669i
$250$	3156.07	−	1399.05i	0.798431	−	0.353935i
$251$		−	4896.97i		−	1.23145i	−0.787961	−	0.615725i	$-0.788863\pi$
$251$		−	4896.97i		−	1.23145i	0.787961	−	0.615725i	$-0.211137\pi$
$252$	2975.87	+	608.650i	0.743896	+	0.152148i
$253$			112.499i			0.0279555i
$254$	2452.77	+	5533.13i	0.605908	+	1.36685i
$255$	−3028.93	+	829.374i	−0.743840	+	0.203676i
$256$	−4017.19	+	799.606i	−0.980760	+	0.195216i
$257$			4089.12i			0.992500i	0.868180	+	0.496250i	$0.165290\pi$
$257$			4089.12i			0.992500i	−0.868180	+	0.496250i	$0.834710\pi$
$258$	−2258.54	−	2767.23i	−0.545002	−	0.667753i
$259$	−2644.37			−0.634414
$260$	−5494.06	−	4979.20i	−1.31049	−	1.18768i
$261$	2989.79	−	1770.02i	0.709056	−	0.419777i
$262$	−2113.71	−	4768.24i	−0.498417	−	1.12436i
$263$	1391.98			0.326362			0.163181	−	0.986596i	$-0.447824\pi$
$263$	1391.98			0.326362			0.163181	+	0.986596i	$0.447824\pi$
$264$	−5.19087	+	100.210i	−0.00121014	+	0.0233617i
$265$	3006.94			0.697038
$266$	−1389.28	−	3134.04i	−0.320235	−	0.722406i
$267$	−8061.87	+	2207.48i	−1.84786	+	0.505975i
$268$	−726.864	+	802.023i	−0.165673	+	0.182803i
$269$	−8301.36			−1.88157			−0.940786	−	0.339001i	$-0.889911\pi$
$269$	−8301.36			−1.88157			−0.940786	+	0.339001i	$0.889911\pi$
$270$	4570.21	+	1677.27i	1.03013	+	0.378057i
$271$			5322.68i			1.19310i	0.802576	+	0.596549i	$0.203462\pi$
$271$			5322.68i			1.19310i	−0.802576	+	0.596549i	$0.796538\pi$
$272$	−3137.65	+	309.235i	−0.699440	+	0.0689342i
$273$	1457.87	+	5324.25i	0.323202	+	1.18036i
$274$	1516.11	+	3420.14i	0.334275	+	0.754080i
$275$			21.7721i			0.00477422i
$276$	4887.84	+	2476.79i	1.06599	+	0.540163i
$277$		−	8320.83i		−	1.80487i	−0.430821	−	0.902437i	$-0.641776\pi$
$277$		−	8320.83i		−	1.80487i	0.430821	−	0.902437i	$-0.358224\pi$
$278$	4572.22	−	2026.81i	0.986416	−	0.437267i
$279$	−1884.85	−	3183.75i	−0.404455	−	0.683176i
$280$	3706.74	+	1224.34i	0.791143	+	0.261316i
$281$		−	5048.08i		−	1.07168i	−0.844318	−	0.535842i	$-0.819994\pi$
$281$		−	5048.08i		−	1.07168i	0.844318	−	0.535842i	$-0.180006\pi$
$282$	339.546	+	416.022i	0.0717010	+	0.0878502i
$283$	6998.62			1.47005			0.735026	−	0.678038i	$-0.237170\pi$
$283$	6998.62			1.47005			0.735026	+	0.678038i	$0.237170\pi$
$284$	3344.51	−	3690.33i	0.698803	−	0.771060i
$285$	−1451.06	−	5299.37i	−0.301590	−	1.10143i
$286$	−166.717	+	73.9039i	−0.0344692	+	0.0152798i
$287$	1883.45			0.387374
$288$	4239.62	+	2431.76i	0.867438	+	0.497545i
$289$	2486.13			0.506031
$290$	4082.21	−	1809.60i	0.826605	−	0.366425i
$291$	45.2999	+	165.438i	0.00912552	+	0.0333271i
$292$	−3847.60	+	4245.45i	−0.771109	+	0.850843i
$293$	3412.85			0.680480			0.340240	−	0.940339i	$-0.389492\pi$
$293$	3412.85			0.680480			0.340240	+	0.940339i	$0.389492\pi$
$294$	1349.80	+	1653.82i	0.267762	+	0.328070i
$295$			1802.66i			0.355779i
$296$	−4040.30	−	1334.52i	−0.793371	−	0.262052i
$297$	83.2656	−	86.0426i	0.0162679	−	0.0168104i
$298$	5864.58	−	2599.70i	1.14002	−	0.505358i
$299$			9958.41i			1.92612i
$300$	945.953	+	479.337i	0.182049	+	0.0922485i
$301$			3417.69i			0.654459i
$302$	16.8200	+	37.9436i	0.00320490	+	0.00722982i
$303$	395.086	+	1442.88i	0.0749079	+	0.273569i
$304$	−541.032	−	5489.58i	−0.102073	−	1.03569i
$305$			2347.32i			0.440679i
$306$	3064.08	+	2182.87i	0.572424	+	0.407799i
$307$	−5000.60			−0.929640			−0.464820	−	0.885405i	$-0.653881\pi$
$307$	−5000.60			−0.929640			−0.464820	+	0.885405i	$0.653881\pi$
$308$	64.4752	−	71.1420i	0.0119280	−	0.0131613i
$309$	−1653.89	+	452.862i	−0.304486	+	0.0833736i
$310$	−1926.99	−	4347.03i	−0.353050	−	0.796434i
$311$	−6995.65			−1.27552			−0.637761	−	0.770235i	$-0.720139\pi$
$311$	−6995.65			−1.27552			−0.637761	+	0.770235i	$0.720139\pi$
$312$	−459.495	+	8870.58i	−0.0833776	+	1.60961i
$313$	430.510			0.0777440			0.0388720	−	0.999244i	$-0.487624\pi$
$313$	430.510			0.0777440			0.0388720	+	0.999244i	$0.487624\pi$
$314$	−421.673	−	951.239i	−0.0757847	−	0.170960i
$315$	−2373.00	−	4008.30i	−0.424456	−	0.716960i
$316$	−5686.05	−	5153.21i	−1.01223	−	0.917375i
$317$	1426.59			0.252761			0.126381	−	0.991982i	$-0.459664\pi$
$317$	1426.59			0.252761			0.126381	+	0.991982i	$0.459664\pi$
$318$	−2277.69	−	2790.70i	−0.401656	−	0.492121i
$319$		−	109.824i		−	0.0192758i
$320$	5045.60	+	3741.32i	0.881430	+	0.653581i
$321$	−4408.73	+	1207.19i	−0.766578	+	0.209902i
$322$	−2124.74	−	4793.13i	−0.367724	−	0.829536i
$323$		−	4246.01i		−	0.731437i
$324$	−1905.18	−	5512.03i	−0.326677	−	0.945136i
$325$			1927.27i			0.328941i
$326$	−2255.53	+	999.849i	−0.383196	+	0.169867i
$327$	−2102.98	+	575.831i	−0.355642	+	0.0973809i
$328$	2877.69	+	950.508i	0.484433	+	0.160009i
$329$		−	513.811i		−	0.0861013i
$330$	119.215	−	97.3001i	0.0198866	−	0.0162309i
$331$	5851.84			0.971741			0.485871	−	0.874031i	$-0.338503\pi$
$331$	5851.84			0.971741			0.485871	+	0.874031i	$0.338503\pi$
$332$	−437.332	−	396.349i	−0.0722943	−	0.0655195i
$333$	2586.54	+	4369.00i	0.425651	+	0.718978i
$334$	−7665.37	+	3397.97i	−1.25578	+	0.556673i
$335$	1659.89			0.270714
$336$	−1671.48	−	4367.58i	−0.271389	−	0.709140i
$337$	−1089.58			−0.176121			−0.0880607	−	0.996115i	$-0.528067\pi$
$337$	−1089.58			−0.176121			−0.0880607	+	0.996115i	$0.528067\pi$
$338$	−9076.90	+	4023.69i	−1.46071	+	0.647514i
$339$	4384.35	−	1200.51i	0.702434	−	0.192338i
$340$	3582.61	+	3246.88i	0.571454	+	0.517902i
$341$	−116.949			−0.0185723
$342$	−3819.12	+	5360.86i	−0.603843	+	0.847608i
$343$		−	6865.95i		−	1.08083i
$344$	−1724.79	+	5221.84i	−0.270332	+	0.818439i
$345$	−2219.22	−	8104.74i	−0.346315	−	1.26477i
$346$	−5074.96	+	2249.67i	−0.788530	+	0.349547i
$347$		−	9333.60i		−	1.44396i	−0.691914	−	0.721980i	$-0.743232\pi$
$347$		−	9333.60i		−	1.44396i	0.691914	−	0.721980i	$-0.256768\pi$
$348$	−4771.64	−	2417.90i	−0.735019	−	0.372452i
$349$			9558.32i			1.46603i	0.680212	+	0.733016i	$0.261888\pi$
$349$			9558.32i			1.46603i	−0.680212	+	0.733016i	$0.738112\pi$
$350$	−411.205	−	927.623i	−0.0627995	−	0.141667i
$351$	7370.67	−	7616.49i	1.12085	−	1.15823i
$352$	134.414	−	76.1587i	0.0203531	−	0.0115320i
$353$			7314.79i			1.10291i	0.834205	+	0.551454i	$0.185927\pi$
$353$			7314.79i			1.10291i	−0.834205	+	0.551454i	$0.814073\pi$
$354$	1673.02	−	1365.47i	0.251186	−	0.205011i
$355$	−7637.61			−1.14187
$356$	9535.54	+	8641.95i	1.41961	+	1.28658i
$357$	−950.659	−	3471.87i	−0.140936	−	0.514709i
$358$	2782.53	+	6277.02i	0.410786	+	0.926678i
$359$	11172.2			1.64247			0.821235	−	0.570590i	$-0.193286\pi$
$359$	11172.2			1.64247			0.821235	+	0.570590i	$0.193286\pi$
$360$	−1602.83	−	7321.80i	−0.234657	−	1.07192i
$361$	569.749			0.0830659
$362$	2072.62	+	4675.56i	0.300925	+	0.678846i
$363$	1825.51	+	6666.88i	0.263951	+	0.963969i
$364$	5707.35	−	6297.49i	0.821830	−	0.906809i
$365$	8786.49			1.26002
$366$	2178.51	−	1778.04i	0.311127	−	0.253933i
$367$		−	804.841i		−	0.114475i	−0.998361	−	0.0572375i	$-0.981771\pi$
$367$		−	804.841i		−	0.114475i	0.998361	−	0.0572375i	$-0.0182292\pi$
$368$	−827.442	−	8395.64i	−0.117210	−	1.18927i
$369$	−1842.26	−	3111.81i	−0.259903	−	0.439009i
$370$	2644.37	+	5965.35i	0.371552	+	0.838172i
$371$			3446.67i			0.482324i
$372$	−2574.76	+	5081.18i	−0.358858	+	0.708191i
$373$			2302.52i			0.319625i	0.987147	+	0.159812i	$0.0510889\pi$
$373$			2302.52i			0.319625i	−0.987147	+	0.159812i	$0.948911\pi$
$374$	108.714	−	48.1918i	0.0150307	−	0.00666294i
$375$	1674.95	+	6117.05i	0.230651	+	0.842355i
$376$	259.302	−	785.046i	0.0355651	−	0.107675i
$377$		−	9721.66i		−	1.32809i
$378$	−1922.55	+	5238.54i	−0.261601	+	0.712808i
$379$	12398.1			1.68034			0.840168	−	0.542327i	$-0.182457\pi$
$379$	12398.1			1.68034			0.840168	+	0.542327i	$0.182457\pi$
$380$	−5680.68	+	6268.07i	−0.766876	+	0.846172i
$381$	−10724.2	+	2936.47i	−1.44204	+	0.394856i
$382$	8230.35	−	3648.42i	1.10236	−	0.488663i
$383$	−13466.2			−1.79658			−0.898289	−	0.439405i	$-0.855189\pi$
$383$	−13466.2			−1.79658			−0.898289	+	0.439405i	$0.855189\pi$
$384$	−349.668	−	7516.70i	−0.0464686	−	0.998920i
$385$	−147.237			−0.0194907
$386$	−2218.97	+	983.645i	−0.292598	+	0.129705i
$387$	5646.67	−	3342.95i	0.741696	−	0.439100i
$388$	177.342	−	195.680i	0.0232041	−	0.0256035i
$389$	−3152.95			−0.410953			−0.205477	−	0.978662i	$-0.565874\pi$
$389$	−3152.95			−0.410953			−0.205477	+	0.978662i	$0.565874\pi$
$390$	10552.9	−	8613.00i	1.37017	−	1.11830i
$391$		−	6493.75i		−	0.839906i
$392$	1030.81	−	3120.80i	0.132815	−	0.402102i
$393$	9241.72	−	2530.54i	1.18622	−	0.324806i
$394$	−9336.50	+	4138.77i	−1.19382	+	0.529208i
$395$			11768.0i			1.49902i
$396$	−180.605	−	36.9390i	−0.0229186	−	0.00468751i
$397$		−	8857.87i		−	1.11981i	−0.828557	−	0.559904i	$-0.810838\pi$
$397$		−	8857.87i		−	1.11981i	0.828557	−	0.559904i	$-0.189162\pi$
$398$	−4334.56	−	9778.18i	−0.545909	−	1.23150i
$399$	6074.34	−	1663.26i	0.762148	−	0.208689i
$400$	−160.137	−	1624.82i	−0.0200171	−	0.203103i
$401$			10688.2i			1.33103i	0.746382	+	0.665517i	$0.231789\pi$
$401$			10688.2i			1.33103i	−0.746382	+	0.665517i	$0.768211\pi$
$402$	−1257.33	−	1540.51i	−0.155994	−	0.191129i
$403$	−10352.3			−1.27962
$404$	1546.70	−	1706.64i	0.190474	−	0.210169i
$405$	−4301.37	+	7841.29i	−0.527745	+	0.962067i
$406$	2074.23	+	4679.18i	0.253552	+	0.571979i
$407$	160.487			0.0195456
$408$	299.631	−	5784.40i	0.0363578	−	0.701888i
$409$	−6348.22			−0.767479			−0.383740	−	0.923441i	$-0.625364\pi$
$409$	−6348.22			−0.767479			−0.383740	+	0.923441i	$0.625364\pi$
$410$	−1883.45	−	4248.80i	−0.226870	−	0.511789i
$411$	−6628.85	+	1815.09i	−0.795564	+	0.217839i
$412$	1956.21	+	1772.89i	0.233921	+	0.212000i
$413$	−2066.27			−0.246186
$414$	−5840.88	+	8198.78i	−0.693390	+	0.973304i
$415$			905.113i			0.107061i
$416$	11898.3	−	6741.57i	1.40231	−	0.794549i
$417$	2426.51	+	8861.81i	0.284957	+	1.04068i
$418$	84.3156	+	190.205i	0.00986605	+	0.0222565i
$419$		−	9356.80i		−	1.09095i	−0.838126	−	0.545477i	$-0.816349\pi$
$419$		−	9356.80i		−	1.09095i	0.838126	−	0.545477i	$-0.183651\pi$
$420$	−3241.59	+	6397.15i	−0.376603	+	0.743212i
$421$			2066.06i			0.239177i	0.992824	+	0.119588i	$0.0381575\pi$
$421$			2066.06i			0.239177i	−0.992824	+	0.119588i	$0.961842\pi$
$422$	−1154.02	+	511.565i	−0.133121	+	0.0590109i
$423$	−848.913	+	502.575i	−0.0975782	+	0.0577684i
$424$	−1739.41	+	5266.12i	−0.199229	+	0.603174i
$425$		−	1256.75i		−	0.143438i
$426$	5785.31	+	7088.34i	0.657980	+	0.806177i
$427$	−2690.58			−0.304933
$428$	5214.63	+	4725.96i	0.588922	+	0.533733i
$429$	−88.4781	−	323.129i	−0.00995749	−	0.0363655i
$430$	7709.85	−	3417.69i	0.864655	−	0.383292i
$431$	−11533.3			−1.28895			−0.644475	−	0.764625i	$-0.722924\pi$
$431$	−11533.3			−1.28895			−0.644475	+	0.764625i	$0.722924\pi$
$432$	−5581.14	+	7033.66i	−0.621581	+	0.783350i
$433$	−15962.0			−1.77156			−0.885781	−	0.464104i	$-0.846376\pi$
$433$	−15962.0			−1.77156			−0.885781	+	0.464104i	$0.846376\pi$
$434$	4982.72	−	2208.79i	0.551102	−	0.244297i
$435$	2166.46	+	7912.06i	0.238790	+	0.872079i
$436$	2487.39	+	2254.30i	0.273221	+	0.247617i
$437$	11361.4			1.24368
$438$	−6655.57	−	8154.60i	−0.726062	−	0.889594i
$439$			3062.84i			0.332988i	0.986043	+	0.166494i	$0.0532446\pi$
$439$			3062.84i			0.332988i	−0.986043	+	0.166494i	$0.946755\pi$
$440$	−224.962	−	74.3054i	−0.0243742	−	0.00805085i
$441$	−3374.69	+	1997.89i	−0.364398	+	0.215732i
$442$	9623.39	−	4265.94i	1.03561	−	0.459073i
$443$		−	16006.6i		−	1.71670i	−0.513064	−	0.858350i	$-0.671490\pi$
$443$		−	16006.6i		−	1.71670i	0.513064	−	0.858350i	$-0.328510\pi$
$444$	3533.29	−	6972.81i	0.377664	−	0.745304i
$445$		−	19735.0i		−	2.10231i
$446$	−5577.02	−	12581.0i	−0.592106	−	1.33571i
$447$	3112.38	+	11366.6i	0.329330	+	1.20274i
$448$	−4288.44	+	5783.45i	−0.452254	+	0.609916i
$449$		−	276.966i		−	0.0291110i	−0.999894	−	0.0145555i	$-0.995367\pi$
$449$		−	276.966i		−	0.0291110i	0.999894	−	0.0145555i	$-0.00463332\pi$
$450$	−1130.40	+	1586.73i	−0.118416	+	0.166220i
$451$	−114.306			−0.0119345
$452$	−5185.79	−	4699.82i	−0.539644	−	0.489073i
$453$	−73.5416	+	20.1369i	−0.00762756	+	0.00208856i
$454$	1574.61	+	3552.11i	0.162776	+	0.367200i
$455$	−13033.5			−1.34290
$456$	10120.3	+	524.230i	1.03931	+	0.0538362i
$457$	15283.1			1.56436			0.782180	−	0.623053i	$-0.214108\pi$
$457$	15283.1			1.56436			0.782180	+	0.623053i	$0.214108\pi$
$458$	2772.92	+	6255.33i	0.282904	+	0.638193i
$459$	−4806.32	+	4966.62i	−0.488758	+	0.505059i
$460$	−8687.91	+	9586.25i	−0.880600	+	0.971655i
$461$	923.721			0.0933231			0.0466616	−	0.998911i	$-0.485142\pi$
$461$	923.721			0.0933231			0.0466616	+	0.998911i	$0.485142\pi$
$462$	111.529	+	136.649i	0.0112312	+	0.0137608i
$463$		−	4589.60i		−	0.460684i	−0.973110	−	0.230342i	$-0.926015\pi$
$463$		−	4589.60i		−	0.460684i	0.973110	−	0.230342i	$-0.0739846\pi$
$464$	807.771	+	8196.04i	0.0808186	+	0.820025i
$465$	8425.34	−	2307.00i	0.840249	−	0.230074i
$466$	−6018.45	−	13576.8i	−0.598281	−	1.34964i
$467$			7091.05i			0.702644i	0.936255	+	0.351322i	$0.114268\pi$
$467$			7091.05i			0.702644i	−0.936255	+	0.351322i	$0.885732\pi$
$468$	−15987.2	−	3269.84i	−1.57908	−	0.322967i
$469$			1902.62i			0.187324i
$470$	−1159.09	+	513.811i	−0.113755	+	0.0504263i
$471$	1843.67	−	504.830i	0.180365	−	0.0493871i
$472$	−3157.03	−	1042.77i	−0.307869	−	0.101690i
$473$		−	207.420i		−	0.0201631i
$474$	10921.7	−	8913.99i	1.05833	−	0.863783i
$475$	2198.79			0.212394
$476$	−3721.69	+	4106.52i	−0.358369	+	0.395424i
$477$	5694.55	−	3371.30i	0.546616	−	0.323608i
$478$	1209.61	−	536.205i	0.115745	−	0.0513085i
$479$	8879.04			0.846960			0.423480	−	0.905906i	$-0.360808\pi$
$479$	8879.04			0.846960			0.423480	+	0.905906i	$0.360808\pi$
$480$	−8181.20	+	8138.21i	−0.777956	+	0.773868i
$481$	14206.3			1.34668
$482$	−7180.93	+	3183.22i	−0.678594	+	0.300813i
$483$	9289.95	−	2543.75i	0.875171	−	0.239637i
$484$	7146.59	−	7885.56i	0.671168	−	0.740567i
$485$	−404.984			−0.0379162
$486$	10535.6	−	1947.57i	0.983340	−	0.181777i
$487$			19238.1i			1.79006i	0.446003	+	0.895031i	$0.352847\pi$
$487$			19238.1i			1.79006i	−0.446003	+	0.895031i	$0.647153\pi$
$488$	−4110.91	−	1357.84i	−0.381336	−	0.125956i
$489$	−1197.02	−	4371.62i	−0.110698	−	0.404277i
$490$	−4607.73	+	2042.56i	−0.424809	+	0.188313i
$491$			5230.16i			0.480720i	0.970684	+	0.240360i	$0.0772656\pi$
$491$			5230.16i			0.480720i	−0.970684	+	0.240360i	$0.922734\pi$
$492$	−2516.58	+	4966.37i	−0.230602	+	0.455084i
$493$			6339.37i			0.579130i
$494$	7463.62	+	16836.9i	0.679765	+	1.53346i
$495$	144.018	+	243.264i	0.0130770	+	0.0220887i
$496$	8727.74	−	860.173i	0.790095	−	0.0778688i
$497$		−	8754.51i		−	0.790128i
$498$	840.021	−	685.602i	0.0755868	−	0.0616919i
$499$	−5766.04			−0.517281			−0.258641	−	0.965974i	$-0.583275\pi$
$499$	−5766.04			−0.517281			−0.258641	+	0.965974i	$0.583275\pi$
$500$	6557.20	−	7235.22i	0.586494	−	0.647138i
$501$	−4068.07	−	14856.9i	−0.362770	−	1.32486i
$502$	−5613.08	−	12662.4i	−0.499052	−	1.12579i
$503$	17836.2			1.58106			0.790532	−	0.612421i	$-0.209804\pi$
$503$	17836.2			1.58106			0.790532	+	0.612421i	$0.209804\pi$
$504$	8392.52	−	1837.23i	0.741731	−	0.162374i
$505$	−3532.10			−0.311240
$506$	128.950	+	290.895i	0.0113291	+	0.0255570i
$507$	−4817.18	−	17592.7i	−0.421970	−	1.54106i
$508$	12684.6	+	11495.9i	1.10785	+	1.00403i
$509$	7614.87			0.663110			0.331555	−	0.943436i	$-0.392427\pi$
$509$	7614.87			0.663110			0.331555	+	0.943436i	$0.392427\pi$
$510$	−6881.43	+	5616.43i	−0.597480	+	0.487647i
$511$			10071.4i			0.871884i
$512$	−9470.95	+	6672.24i	−0.817502	+	0.575926i
$513$	−8689.51	−	8409.07i	−0.747859	−	0.723722i
$514$	4687.11	+	10573.5i	0.402217	+	0.907347i
$515$		−	4048.62i		−	0.346414i
$516$	−9011.94	−	4566.57i	−0.768853	−	0.389597i
$517$			31.1832i			0.00265268i
$518$	−6837.70	+	3031.08i	−0.579983	+	0.257100i
$519$	−2693.32	−	9836.20i	−0.227791	−	0.831910i
$520$	−19913.6	−	6577.52i	−1.67937	−	0.554698i
$521$			15729.5i			1.32269i	0.750082	+	0.661345i	$0.230014\pi$
$521$			15729.5i			1.32269i	−0.750082	+	0.661345i	$0.769986\pi$
$522$	5702.02	−	8003.86i	0.478104	−	0.671110i
$523$	−8194.99			−0.685166			−0.342583	−	0.939488i	$-0.611302\pi$
$523$	−8194.99			−0.685166			−0.342583	+	0.939488i	$0.611302\pi$
$524$	−10931.1	−	9906.70i	−0.911309	−	0.825909i
$525$	1797.90	−	492.297i	0.149461	−	0.0409249i
$526$	3599.33	−	1595.54i	0.298362	−	0.132260i
$527$	6750.62			0.557992
$528$	101.442	+	265.068i	0.00836117	+	0.0218478i
$529$	5208.82			0.428111
$530$	7775.23	−	3446.67i	0.637235	−	0.282479i
$531$	2021.09	+	3413.87i	0.165175	+	0.279001i
$532$	−7184.70	−	6511.41i	−0.585519	−	0.530649i
$533$	−10118.4			−0.822283
$534$	−18315.7	+	14948.8i	−1.48427	+	1.21142i
$535$		−	10792.3i		−	0.872137i
$536$	−960.186	+	2906.99i	−0.0773763	+	0.234259i
$537$	−12166.0	+	3331.26i	−0.977658	+	0.267699i
$538$	−21465.3	+	9515.33i	−1.72014	+	0.762518i
$539$			123.963i			0.00990623i
$540$	13740.0	−	901.533i	1.09495	−	0.0718441i
$541$			9756.26i			0.775331i	0.921800	+	0.387666i	$0.126719\pi$
$541$			9756.26i			0.775331i	−0.921800	+	0.387666i	$0.873281\pi$
$542$	6101.05	+	13763.2i	0.483510	+	1.09073i
$543$	−9062.09	+	2481.36i	−0.716191	+	0.196105i
$544$	−7758.74	+	4396.09i	−0.611495	+	0.346472i
$545$		−	5147.97i		−	0.404614i
$546$	9872.54	+	12096.1i	0.773820	+	0.948108i
$547$	19760.8			1.54463			0.772313	−	0.635242i	$-0.219100\pi$
$547$	19760.8			1.54463			0.772313	+	0.635242i	$0.219100\pi$
$548$	7840.57	+	7105.82i	0.611191	+	0.553915i
$549$	2631.74	+	4445.35i	0.204590	+	0.345579i
$550$	24.9560	+	56.2975i	0.00193478	+	0.00436460i
$551$	−11091.3			−0.857539
$552$	15477.7	+	801.746i	1.19344	+	0.0618199i
$553$	−13488.9			−1.03726
$554$	−9537.64	−	21515.6i	−0.731436	−	1.65002i
$555$	−11561.9	+	3165.85i	−0.884282	+	0.242132i
$556$	9499.45	−	10481.7i	0.724580	−	0.799502i
$557$	−13411.5			−1.02022			−0.510111	−	0.860109i	$-0.670396\pi$
$557$	−13411.5			−1.02022			−0.510111	+	0.860109i	$0.670396\pi$
$558$	−8523.09	−	6071.92i	−0.646615	−	0.460654i
$559$		−	18360.8i		−	1.38923i
$560$	10988.1	−	1082.95i	0.829165	−	0.0817194i
$561$	57.6955	+	210.708i	0.00434208	+	0.0158576i
$562$	−5786.29	−	13053.1i	−0.434306	−	0.979736i
$563$			15737.1i			1.17804i	0.808117	+	0.589021i	$0.200487\pi$
$563$			15737.1i			1.17804i	−0.808117	+	0.589021i	$0.799513\pi$
$564$	1354.84	+	686.532i	0.101151	+	0.0512557i
$565$			10732.6i			0.799160i
$566$	18096.7	−	8022.08i	1.34393	−	0.595748i
$567$	−8987.98	−	4930.38i	−0.665714	−	0.365179i
$568$	4418.09	−	13375.9i	0.326371	−	0.988100i
$569$		−	61.6242i		−	0.00454028i	−0.999997	−	0.00227014i	$-0.999277\pi$
$569$		−	61.6242i		−	0.00454028i	0.999997	−	0.00227014i	$-0.000722609\pi$
$570$	−9826.42	−	12039.6i	−0.722076	−	0.884710i
$571$	7189.49			0.526919			0.263460	−	0.964670i	$-0.415136\pi$
$571$	7189.49			0.526919			0.263460	+	0.964670i	$0.415136\pi$
$572$	−346.379	+	382.195i	−0.0253196	+	0.0279377i
$573$	4367.91	+	15951.9i	0.318450	+	1.16300i
$574$	4870.13	−	2158.88i	0.354138	−	0.156986i
$575$	3362.78			0.243891
$576$	13750.0	+	1428.33i	0.994648	+	0.103323i
$577$	6614.86			0.477262			0.238631	−	0.971110i	$-0.423301\pi$
$577$	6614.86			0.477262			0.238631	+	0.971110i	$0.423301\pi$
$578$	6428.53	−	2849.70i	0.462615	−	0.205072i
$579$	−1177.63	−	4300.77i	−0.0845258	−	0.308694i
$580$	8481.37	−	9358.35i	0.607189	−	0.669973i
$581$	−1037.47			−0.0740820
$582$	306.766	+	375.859i	0.0218486	+	0.0267695i
$583$		−	209.179i		−	0.0148598i
$584$	−5082.68	+	15388.0i	−0.360141	+	1.09034i
$585$	12748.4	+	21533.7i	0.900996	+	1.52190i
$586$	8824.80	−	3911.93i	0.622097	−	0.275769i
$587$			11536.9i			0.811208i	0.914049	+	0.405604i	$0.132939\pi$
$587$			11536.9i			0.811208i	−0.914049	+	0.405604i	$0.867061\pi$
$588$	5385.92	+	2729.18i	0.377741	+	0.191410i
$589$			11810.8i			0.826239i
$590$	2066.27	+	4661.23i	0.144182	+	0.325254i
$591$	−4954.95	−	18095.9i	−0.344872	−	1.25950i
$592$	−11976.9	+	1180.40i	−0.831500	+	0.0819495i
$593$		−	10962.6i		−	0.759154i	−0.925160	−	0.379577i	$-0.876070\pi$
$593$		−	10962.6i		−	0.759154i	0.925160	−	0.379577i	$-0.123930\pi$
$594$	116.679	−	317.927i	0.00805962	−	0.0219608i
$595$	8498.95			0.585585
$596$	12184.5	−	13444.4i	0.837411	−	0.924000i
$597$	18951.9	−	5189.35i	1.29925	−	0.355756i
$598$	11414.7	+	25750.0i	0.780571	+	1.76086i
$599$	−3971.66			−0.270914			−0.135457	−	0.990783i	$-0.543250\pi$
$599$	−3971.66			−0.270914			−0.135457	+	0.990783i	$0.543250\pi$
$600$	2995.44	+	155.163i	0.203814	+	0.0105575i
$601$	261.374			0.0177399			0.00886996	−	0.999961i	$-0.497177\pi$
$601$	261.374			0.0177399			0.00886996	+	0.999961i	$0.497177\pi$
$602$	3917.48	+	8837.31i	0.265224	+	0.598309i
$603$	3143.49	−	1861.02i	0.212293	−	0.125682i
$604$	86.9846	+	78.8332i	0.00585986	+	0.00531072i
$605$	−16320.2			−1.09671
$606$	2675.48	+	3278.08i	0.179347	+	0.219741i
$607$			3406.07i			0.227757i	0.993495	+	0.113878i	$0.0363274\pi$
$607$			3406.07i			0.227757i	−0.993495	+	0.113878i	$0.963673\pi$
$608$	−7691.33	−	13574.6i	−0.513034	−	0.905462i
$609$	−9069.10	+	2483.27i	−0.603446	+	0.165234i
$610$	2690.58	+	6069.59i	0.178588	+	0.402870i
$611$			2760.34i			0.182768i
$612$	10425.0	+	2132.22i	0.688575	+	0.140833i
$613$		−	16854.4i		−	1.11051i	−0.831680	−	0.555255i	$-0.812621\pi$
$613$		−	16854.4i		−	1.11051i	0.831680	−	0.555255i	$-0.187379\pi$
$614$	−12930.3	+	5731.88i	−0.849880	+	0.376742i
$615$	8234.96	−	2254.87i	0.539944	−	0.147846i
$616$	85.1716	−	257.860i	0.00557088	−	0.0168660i
$617$			1136.77i			0.0741726i	0.999312	+	0.0370863i	$0.0118076\pi$
$617$			1136.77i			0.0741726i	−0.999312	+	0.0370863i	$0.988192\pi$
$618$	−3757.46	+	3066.74i	−0.244575	+	0.199615i
$619$	6524.80			0.423673			0.211837	−	0.977305i	$-0.432056\pi$
$619$	6524.80			0.423673			0.211837	+	0.977305i	$0.432056\pi$
$620$	−9965.45	−	9031.57i	−0.645519	−	0.585027i
$621$	−13289.6	−	12860.6i	−0.858762	−	0.831046i
$622$	−18089.1	+	8018.68i	−1.16609	+	0.516913i
$623$	22621.0			1.45472
$624$	8979.65	+	23463.9i	0.576079	+	1.50530i
$625$	−18163.1			−1.16244
$626$	1113.19	−	493.466i	0.0710738	−	0.0315062i
$627$	−368.652	+	100.943i	−0.0234809	+	0.00642947i
$628$	−2180.69	−	1976.33i	−0.138565	−	0.125580i
$629$	−9263.75			−0.587234
$630$	−10730.5	−	7644.47i	−0.678591	−	0.483434i
$631$		−	5941.20i		−	0.374826i	−0.982281	−	0.187413i	$-0.939990\pi$
$631$		−	5941.20i		−	0.374826i	0.982281	−	0.187413i	$-0.0600103\pi$
$632$	−20609.6	−	6807.37i	−1.29716	−	0.428454i
$633$	−612.448	−	2236.71i	−0.0384560	−	0.140444i
$634$	3688.82	−	1635.21i	0.231075	−	0.102433i
$635$		−	26252.3i		−	1.64061i
$636$	−9088.36	−	4605.29i	−0.566630	−	0.287125i
$637$			10973.2i			0.682533i
$638$	−125.885	−	283.979i	−0.00781164	−	0.0176220i
$639$	−14464.1	+	8563.06i	−0.895448	+	0.530124i
$640$	17335.1	+	3890.69i	1.07067	+	0.240301i
$641$		−	19637.2i		−	1.21002i	−0.796219	−	0.605009i	$-0.793170\pi$
$641$		−	19637.2i		−	1.21002i	0.796219	−	0.605009i	$-0.206830\pi$
$642$	−10016.2	+	8174.94i	−0.615744	+	0.502553i
$643$	−19004.4			−1.16557			−0.582785	−	0.812627i	$-0.698037\pi$
$643$	−19004.4			−1.16557			−0.582785	+	0.812627i	$0.698037\pi$
$644$	−10988.1	−	9958.41i	−0.672349	−	0.609342i
$645$	4091.68	+	14943.1i	0.249782	+	0.912223i
$646$	−4866.93	−	10979.2i	−0.296419	−	0.668683i
$647$	22086.6			1.34206			0.671030	−	0.741430i	$-0.265852\pi$
$647$	22086.6			1.34206			0.671030	+	0.741430i	$0.265852\pi$
$648$	−11244.4	−	12069.0i	−0.681672	−	0.731658i
$649$	125.402			0.00758469
$650$	2209.11	+	4983.45i	0.133305	+	0.300719i
$651$	2644.37	+	9657.43i	0.159203	+	0.581420i
$652$	−4686.18	+	5170.73i	−0.281480	+	0.310585i
$653$	4365.25			0.261601			0.130800	−	0.991409i	$-0.458245\pi$
$653$	4365.25			0.261601			0.130800	+	0.991409i	$0.458245\pi$
$654$	−4777.75	+	3899.47i	−0.285665	+	0.233152i
$655$			22623.2i			1.34956i
$656$	8530.52	−	840.736i	0.507715	−	0.0500385i
$657$	16639.9	−	9851.15i	0.988101	−	0.584977i
$658$	−588.949	−	1328.59i	−0.0348931	−	0.0787141i
$659$		−	10561.6i		−	0.624313i	−0.950031	−	0.312157i	$-0.898949\pi$
$659$		−	10561.6i		−	0.624313i	0.950031	−	0.312157i	$-0.101051\pi$
$660$	196.732	−	388.243i	0.0116027	−	0.0228975i
$661$		−	6097.14i		−	0.358777i	−0.983778	−	0.179388i	$-0.942588\pi$
$661$		−	6097.14i		−	0.358777i	0.983778	−	0.179388i	$-0.0574118\pi$
$662$	15131.4	−	6707.60i	0.888369	−	0.393804i
$663$	5107.21	+	18651.9i	0.299167	+	1.09258i
$664$	−1585.14	−	523.576i	−0.0926438	−	0.0306004i
$665$			14869.6i			0.867097i
$666$	11696.1	+	8332.38i	0.680501	+	0.484795i
$667$	−16962.7			−0.984707
$668$	−15925.9	+	17572.7i	−0.922442	+	1.01782i
$669$	24384.3	−	6676.84i	1.40919	−	0.385862i
$670$	4292.06	−	1902.62i	0.247488	−	0.109709i
$671$	163.291			0.00939463
$672$	−9328.31	−	9377.59i	−0.535487	−	0.538316i
$673$	18846.7			1.07948			0.539739	−	0.841832i	$-0.318523\pi$
$673$	18846.7			1.07948			0.539739	+	0.841832i	$0.318523\pi$
$674$	−2817.38	+	1248.91i	−0.161011	+	0.0713743i
$675$	−2571.95	−	2488.94i	−0.146659	−	0.141925i
$676$	−18858.6	+	20808.6i	−1.07297	+	1.18392i
$677$	6123.61			0.347636			0.173818	−	0.984778i	$-0.444390\pi$
$677$	6123.61			0.347636			0.173818	+	0.984778i	$0.444390\pi$
$678$	9960.79	−	8129.73i	0.564221	−	0.460502i
$679$		−	464.208i		−	0.0262366i
$680$	12985.4	+	4289.12i	0.732308	+	0.241883i
$681$	−6884.64	+	1885.13i	−0.387401	+	0.106077i
$682$	−302.402	+	134.051i	−0.0169788	+	0.00752652i
$683$			17482.3i			0.979417i	0.871886	+	0.489709i	$0.162897\pi$
$683$			17482.3i			0.979417i	−0.871886	+	0.489709i	$0.837103\pi$
$684$	−3730.50	+	18239.5i	−0.208537	+	1.01960i
$685$		−	16227.0i		−	0.905115i
$686$	−7870.00	−	17753.7i	−0.438015	−	0.988103i
$687$	−12124.0	+	3319.75i	−0.673302	+	0.184361i
$688$	1525.59	+	15479.4i	0.0845389	+	0.857773i
$689$		−	18516.5i		−	1.02383i
$690$	−15028.3	−	18413.1i	−0.829157	−	1.01591i
$691$	−2578.54			−0.141957			−0.0709786	−	0.997478i	$-0.522612\pi$
$691$	−2578.54			−0.141957			−0.0709786	+	0.997478i	$0.522612\pi$
$692$	−10544.0	+	11634.2i	−0.579221	+	0.639113i
$693$	−278.838	+	165.078i	−0.0152845	+	0.00904878i
$694$	−10698.5	−	24134.4i	−0.585173	−	1.32007i
$695$	−21693.2			−1.18399
$696$	−15109.8	−	782.686i	−0.822895	−	0.0426259i
$697$	6598.09			0.358566
$698$	10956.1	+	24715.5i	0.594118	+	1.34025i
$699$	26314.3	−	7205.32i	1.42389	−	0.389886i
$700$	−2126.55	−	1927.27i	−0.114823	−	0.104063i
$701$	14569.0			0.784969			0.392484	−	0.919759i	$-0.371616\pi$
$701$	14569.0			0.784969			0.392484	+	0.919759i	$0.371616\pi$
$702$	10328.5	−	28142.9i	0.555303	−	1.51309i
$703$		−	16207.7i		−	0.869538i
$704$	260.265	−	350.998i	0.0139334	−	0.0187908i
$705$	−615.138	−	2246.53i	−0.0328616	−	0.120013i
$706$	8384.48	+	18914.3i	0.446960	+	1.00828i
$707$		−	4048.62i		−	0.215366i
$708$	2760.86	−	5448.45i	0.146553	−	0.289217i
$709$		−	16092.3i		−	0.852409i	−0.904627	−	0.426205i	$-0.859850\pi$
$709$		−	16092.3i		−	0.852409i	0.904627	−	0.426205i	$-0.140150\pi$
$710$	−19749.0	+	8754.51i	−1.04390	+	0.462748i
$711$	13193.9	+	22286.2i	0.695937	+	1.17553i
$712$	34562.3	+	11416.0i	1.81921	+	0.600889i
$713$			18063.1i			0.948766i
$714$	−6437.76	−	7887.75i	−0.337433	−	0.413433i
$715$	791.000			0.0413731
$716$	14389.9	+	13041.4i	0.751084	+	0.680699i
$717$	641.948	+	2344.44i	0.0334365	+	0.122113i
$718$	28888.6	−	12806.0i	1.50155	−	0.665621i
$719$	−18037.4			−0.935582			−0.467791	−	0.883839i	$-0.654950\pi$
$719$	−18037.4			−0.935582			−0.467791	+	0.883839i	$0.654950\pi$
$720$	−12537.1	−	17095.2i	−0.648929	−	0.884861i
$721$	4640.68			0.239706
$722$	1473.23	−	653.067i	0.0759391	−	0.0336629i
$723$	−3810.97	−	13918.0i	−0.196033	−	0.715925i
$724$	10718.6	+	9714.15i	0.550212	+	0.498651i
$725$	−3282.83			−0.168167
$726$	12362.1	+	15146.5i	0.631959	+	0.774296i
$727$		−	5954.34i		−	0.303761i	−0.988399	−	0.151881i	$-0.951467\pi$
$727$		−	5954.34i		−	0.303761i	0.988399	−	0.151881i	$-0.0485329\pi$
$728$	7539.39	−	22825.8i	0.383830	−	1.16206i
$729$	645.501	+	19672.4i	0.0327949	+	0.999462i
$730$	22719.7	−	10071.4i	1.15191	−	0.510629i
$731$			11972.8i			0.605789i
$732$	3595.04	−	7094.67i	0.181525	−	0.358233i
$733$		−	26466.1i		−	1.33363i	−0.745225	−	0.666813i	$-0.767658\pi$
$733$		−	26466.1i		−	1.33363i	0.745225	−	0.666813i	$-0.232342\pi$
$734$	−922.539	−	2081.12i	−0.0463917	−	0.104654i
$735$	−2445.36	−	8930.63i	−0.122719	−	0.448179i
$736$	−11763.0	−	20760.6i	−0.589114	−	1.03974i
$737$		−	115.470i		−	0.00577124i
$738$	−8330.50	−	5934.72i	−0.415515	−	0.296016i
$739$	−17526.6			−0.872433			−0.436216	−	0.899842i	$-0.643682\pi$
$739$	−17526.6			−0.872433			−0.436216	+	0.899842i	$0.643682\pi$
$740$	13675.4	+	12393.9i	0.679348	+	0.615686i
$741$	−32633.0	+	8935.48i	−1.61782	+	0.442987i
$742$	3950.70	+	8912.25i	0.195465	+	0.440942i
$743$	−9846.17			−0.486165			−0.243083	−	0.970006i	$-0.578159\pi$
$743$	−9846.17			−0.486165			−0.243083	+	0.970006i	$0.578159\pi$
$744$	−833.460	+	16090.0i	−0.0410701	+	0.792860i
$745$	−27824.9			−1.36835
$746$	2639.24	+	5953.76i	0.129530	+	0.292202i
$747$	1014.79	+	1714.10i	0.0497042	+	0.0839568i
$748$	225.870	−	249.225i	0.0110409	−	0.0121826i
$749$	12370.6			0.603486
$750$	11342.6	+	13897.3i	0.552232	+	0.676611i
$751$			14295.5i			0.694609i	0.937752	+	0.347305i	$0.112903\pi$
$751$			14295.5i			0.694609i	−0.937752	+	0.347305i	$0.887097\pi$
$752$	−229.356	−	2327.16i	−0.0111220	−	0.112849i
$753$	24542.0	−	6720.01i	1.18773	−	0.325220i
$754$	−11143.3	−	25137.8i	−0.538217	−	1.21415i
$755$		−	180.026i		−	0.00867788i
$756$	1033.37	+	15749.3i	0.0497134	+	0.757667i
$757$			15060.1i			0.723078i	0.932357	+	0.361539i	$0.117749\pi$
$757$			15060.1i			0.723078i	−0.932357	+	0.361539i	$0.882251\pi$
$758$	32058.4	−	14211.1i	1.53617	−	0.680966i
$759$	−563.808	+	154.380i	−0.0269630	+	0.00738293i
$760$	−7504.17	+	22719.1i	−0.358164	+	1.08435i
$761$			34534.2i			1.64503i	0.568746	+	0.822513i	$0.307429\pi$
$761$			34534.2i			1.64503i	−0.568746	+	0.822513i	$0.692571\pi$
$762$	−24364.3	+	19885.5i	−1.15830	+	0.945375i
$763$	5900.80			0.279978
$764$	17099.7	−	18867.9i	0.809746	−	0.893475i
$765$	−8313.10	−	14041.9i	−0.392890	−	0.663641i
$766$	−34820.3	+	15435.4i	−1.64244	+	0.728074i
$767$	11100.6			0.522581
$768$	−9520.08	−	19035.6i	−0.447300	−	0.894384i
$769$	−1513.63			−0.0709789			−0.0354894	−	0.999370i	$-0.511299\pi$
$769$	−1513.63			−0.0709789			−0.0354894	+	0.999370i	$0.511299\pi$
$770$	−380.720	+	168.769i	−0.0178184	+	0.00789871i
$771$	−20493.3	+	5611.43i	−0.957263	+	0.262115i
$772$	−4610.23	+	5086.94i	−0.214930	+	0.237154i
$773$	5140.81			0.239201			0.119600	−	0.992822i	$-0.461839\pi$
$773$	5140.81			0.239201			0.119600	+	0.992822i	$0.461839\pi$
$774$	10769.1	−	15116.5i	0.500113	−	0.702003i
$775$			3495.80i			0.162029i
$776$	234.269	−	709.257i	0.0108373	−	0.0328104i
$777$	−3628.82	−	13252.7i	−0.167546	−	0.611890i
$778$	−8152.76	+	3614.03i	−0.375695	+	0.166541i
$779$			11543.9i			0.530941i
$780$	17414.7	−	34367.3i	0.799420	−	1.57762i
$781$			531.311i			0.0243429i
$782$	−7443.38	−	16791.3i	−0.340377	−	0.767845i
$783$	12973.6	+	12554.9i	0.592132	+	0.573021i
$784$	−911.761	−	9251.17i	−0.0415343	−	0.421427i
$785$			4513.21i			0.205202i
$786$	20996.2	−	17136.6i	0.952813	−	0.777660i
$787$	12562.3			0.568994			0.284497	−	0.958677i	$-0.408173\pi$
$787$	12562.3			0.568994			0.284497	+	0.958677i	$0.408173\pi$
$788$	−19397.9	+	21403.7i	−0.876932	+	0.967608i
$789$	1910.19	+	6976.16i	0.0861909	+	0.314775i
$790$	13488.9	+	30429.2i	0.607486	+	1.37041i
$791$	−12302.1			−0.552989
$792$	−509.342	+	111.501i	−0.0228519	+	0.00500256i
$793$	14454.6			0.647284
$794$	−10153.2	−	22904.3i	−0.453809	−	1.02373i
$795$	4126.37	+	15069.8i	0.184085	+	0.672291i
$796$	−22416.2	−	20315.6i	−0.998143	−	0.904606i
$797$	−35384.0			−1.57260			−0.786302	−	0.617842i	$-0.788007\pi$
$797$	−35384.0			−1.57260			−0.786302	+	0.617842i	$0.788007\pi$
$798$	13800.3	−	11263.4i	0.612186	−	0.499649i
$799$		−	1799.98i		−	0.0796981i
$800$	−2276.51	−	4017.85i	−0.100608	−	0.177565i
$801$	−22126.3	−	37374.1i	−0.976023	−	1.64863i
$802$	12251.3	+	27637.2i	0.539410	+	1.21684i
$803$		−	611.233i		−	0.0268617i
$804$	−5016.93	−	2542.20i	−0.220067	−	0.111513i
$805$			22741.3i			0.995683i
$806$	−26768.6	+	11866.2i	−1.16983	+	0.518573i
$807$	−11391.8	−	41603.7i	−0.496915	−	1.81477i
$808$	2043.19	−	6185.83i	0.0889595	−	0.269328i
$809$		−	18988.2i		−	0.825203i	−0.910912	−	0.412601i	$-0.864620\pi$
$809$		−	18988.2i		−	0.825203i	0.910912	−	0.412601i	$-0.135380\pi$
$810$	−2134.31	+	25206.1i	−0.0925826	+	1.09340i
$811$	−2403.78			−0.104079			−0.0520396	−	0.998645i	$-0.516572\pi$
$811$	−2403.78			−0.104079			−0.0520396	+	0.998645i	$0.516572\pi$
$812$	10726.9	+	9721.66i	0.463596	+	0.420152i
$813$	−26675.5	+	7304.21i	−1.15074	+	0.315092i
$814$	414.980	−	183.956i	0.0178686	−	0.00792095i
$815$	10701.5			0.459947
$816$	−5855.52	−	15300.5i	−0.251206	−	0.656403i
$817$	−20947.5			−0.897013
$818$	−16414.9	+	7276.56i	−0.701632	+	0.311026i
$819$	−24682.8	+	14612.7i	−1.05310	+	0.623455i
$820$	−9740.27	−	8827.50i	−0.414811	−	0.375938i
$821$	25305.3			1.07572			0.537858	−	0.843036i	$-0.319234\pi$
$821$	25305.3			1.07572			0.537858	+	0.843036i	$0.319234\pi$
$822$	−15060.1	+	12291.6i	−0.639027	+	0.521556i
$823$			5546.84i			0.234934i	0.993077	+	0.117467i	$0.0374774\pi$
$823$			5546.84i			0.234934i	−0.993077	+	0.117467i	$0.962523\pi$
$824$	7090.43	+	2341.98i	0.299766	+	0.0990132i
$825$	−109.115	+	29.8775i	−0.00460471	+	0.00126085i
$826$	−5342.88	+	2368.44i	−0.225064	+	0.0997682i
$827$		−	25938.6i		−	1.09066i	−0.838222	−	0.545329i	$-0.816405\pi$
$827$		−	25938.6i		−	1.09066i	0.838222	−	0.545329i	$-0.183595\pi$
$828$	−5705.35	+	27895.1i	−0.239462	+	1.17080i
$829$			22109.0i			0.926268i	0.886288	+	0.463134i	$0.153275\pi$
$829$			22109.0i			0.926268i	−0.886288	+	0.463134i	$0.846725\pi$
$830$	1037.47	+	2340.40i	0.0433870	+	0.0978753i
$831$	41701.3	−	11418.5i	1.74080	−	0.476660i
$832$	23038.7	−	31070.3i	0.960003	−	1.29468i
$833$		−	7155.48i		−	0.297626i
$834$	16432.1	+	20133.1i	0.682251	+	0.835915i
$835$	36368.8			1.50730
$836$	436.039	+	395.178i	0.0180392	+	0.0163487i
$837$	13369.4	−	13815.2i	0.552106	−	0.570519i
$838$	−10725.1	−	24194.4i	−0.442116	−	0.997353i
$839$	−4634.41			−0.190700			−0.0953502	−	0.995444i	$-0.530397\pi$
$839$	−4634.41			−0.190700			−0.0953502	+	0.995444i	$0.530397\pi$
$840$	−1049.32	+	20257.1i	−0.0431010	+	0.832067i
$841$	−7829.53			−0.321027
$842$	2368.19	+	5342.32i	0.0969279	+	0.218656i
$843$	25299.3	−	6927.38i	1.03363	−	0.283027i
$844$	−2397.65	+	2645.57i	−0.0977848	+	0.107896i
$845$	43065.9			1.75327
$846$	−1619.01	+	2272.59i	−0.0657953	+	0.0923562i
$847$		−	18706.8i		−	0.758881i
$848$	1538.53	+	15610.7i	0.0623035	+	0.632162i
$849$	9604.08	+	35074.8i	0.388235	+	1.41786i
$850$	−1440.53	−	3249.65i	−0.0581292	−	0.131132i
$851$		−	24787.7i		−	0.998487i
$852$	23084.3	+	11697.4i	0.928235	+	0.470359i
$853$			3798.64i			0.152477i	0.997090	+	0.0762385i	$0.0242910\pi$
$853$			3798.64i			0.152477i	−0.997090	+	0.0762385i	$0.975709\pi$
$854$	−6957.19	+	3084.04i	−0.278771	+	0.123576i
$855$	24567.4	−	14544.5i	0.982677	−	0.581766i
$856$	18900.8	+	6242.98i	0.754693	+	0.249277i
$857$		−	7495.91i		−	0.298781i	−0.988778	−	0.149391i	$-0.952269\pi$
$857$		−	7495.91i		−	0.298781i	0.988778	−	0.149391i	$-0.0477312\pi$
$858$	−599.165	−	734.115i	−0.0238405	−	0.0292101i
$859$	4024.01			0.159834			0.0799170	−	0.996802i	$-0.474534\pi$
$859$	4024.01			0.159834			0.0799170	+	0.996802i	$0.474534\pi$
$860$	16018.3	−	17674.6i	0.635139	−	0.700814i
$861$	2584.62	+	9439.21i	0.102304	+	0.373621i
$862$	−29822.2	+	13219.8i	−1.17836	+	0.522355i
$863$	−33138.4			−1.30712			−0.653559	−	0.756875i	$-0.726725\pi$
$863$	−33138.4			−1.30712			−0.653559	+	0.756875i	$0.726725\pi$
$864$	−6369.23	+	24584.7i	−0.250794	+	0.968041i
$865$	24078.5			0.946465
$866$	−41273.9	+	18296.3i	−1.61957	+	0.717936i
$867$	3411.67	+	12459.7i	0.133641	+	0.488065i
$868$	10352.3	−	11422.8i	0.404817	−	0.446675i
$869$	818.643			0.0319569
$870$	14671.0	+	17975.4i	0.571718	+	0.700486i
$871$		−	10221.4i		−	0.397635i
$872$	9015.75	+	2977.92i	0.350128	+	0.115648i
$873$	−766.959	+	454.056i	−0.0297338	+	0.0176031i
$874$	29377.7	−	13022.8i	1.13698	−	0.504008i
$875$		−	17164.0i		−	0.663141i
$876$	−26556.8	−	13457.0i	−1.02428	−	0.519028i
$877$			30457.0i			1.17270i	0.810057	+	0.586351i	$0.199436\pi$
$877$			30457.0i			1.17270i	−0.810057	+	0.586351i	$0.800564\pi$
$878$	3510.74	+	7919.77i	0.134945	+	0.304418i
$879$	4683.39	+	17104.1i	0.179712	+	0.656321i
$880$	−666.869	+	65.7241i	−0.0255456	+	0.00251768i
$881$			3443.70i			0.131693i	0.997830	+	0.0658463i	$0.0209747\pi$
$881$			3443.70i			0.131693i	−0.997830	+	0.0658463i	$0.979025\pi$
$882$	−6436.08	+	9034.25i	−0.245707	+	0.344897i
$883$	26019.5			0.991649			0.495824	−	0.868423i	$-0.334866\pi$
$883$	26019.5			0.991649			0.495824	+	0.868423i	$0.334866\pi$
$884$	19994.0	−	22061.4i	0.760713	−	0.839371i
$885$	−9034.32	+	2473.75i	−0.343147	+	0.0939597i
$886$	−18347.4	−	41389.3i	−0.695703	−	1.56941i
$887$	26980.3			1.02132			0.510659	−	0.859783i	$-0.329401\pi$
$887$	26980.3			1.02132			0.510659	+	0.859783i	$0.329401\pi$
$888$	1143.74	−	22080.0i	0.0432224	−	0.834410i
$889$	30091.3			1.13524
$890$	−22621.0	−	51029.9i	−0.851974	−	1.92194i
$891$	545.481	+	299.225i	0.0205099	+	0.0112508i
$892$	−28841.6	−	26138.8i	−1.08261	−	0.981158i
$893$	3149.22			0.118012
$894$	21076.7	+	25823.8i	0.788491	+	0.966083i
$895$		−	29781.7i		−	1.11228i
$896$	−4459.65	+	19870.2i	−0.166280	+	0.740866i
$897$	−49908.2	+	13665.7i	−1.85773	+	0.508680i
$898$	−317.469	−	716.167i	−0.0117974	−	0.0266134i
$899$		−	17633.7i		−	0.654191i
$900$	−1104.17	+	5398.59i	−0.0408951	+	0.199948i
$901$			12074.4i			0.446455i
$902$	−295.569	+	131.022i	−0.0109106	+	0.00483654i
$903$	−17128.3	+	4690.03i	−0.631224	+	0.172840i
$904$	−18796.3	−	6208.45i	−0.691544	−	0.228418i
$905$		−	22183.5i		−	0.814811i
$906$	−167.079	+	136.365i	−0.00612674	+	0.00500048i
$907$	−45386.2			−1.66155			−0.830775	−	0.556609i	$-0.812102\pi$
$907$	−45386.2			−1.66155			−0.830775	+	0.556609i	$0.812102\pi$
$908$	8143.12	+	7380.02i	0.297620	+	0.269730i
$909$	−6689.08	+	3960.08i	−0.244074	+	0.144497i
$910$	−33701.3	+	14939.4i	−1.22768	+	0.544217i
$911$	−36921.1			−1.34276			−0.671378	−	0.741115i	$-0.734297\pi$
$911$	−36921.1			−1.34276			−0.671378	+	0.741115i	$0.734297\pi$
$912$	26769.5	−	10244.7i	0.971959	−	0.371970i
$913$	62.9643			0.00228238
$914$	39518.3	−	17518.0i	1.43014	−	0.633966i
$915$	−11764.0	+	3221.18i	−0.425033	+	0.116381i
$916$	14340.2	+	12996.3i	0.517263	+	0.468789i
$917$	−25931.6			−0.933845
$918$	−6735.07	+	18351.7i	−0.242146	+	0.659798i
$919$			47257.0i			1.69626i	0.529786	+	0.848131i	$0.322272\pi$
$919$			47257.0i			1.69626i	−0.529786	+	0.848131i	$0.677728\pi$
$920$	−11476.7	+	34746.1i	−0.411278	+	1.24516i
$921$	−6862.23	−	25061.4i	−0.245514	−	0.896634i
$922$	2388.52	−	1058.80i	0.0853163	−	0.0378198i
$923$			47031.7i			1.67721i
$924$	445.019	+	225.502i	0.0158442	+	0.00802864i
$925$		−	4797.22i		−	0.170521i
$926$	−5260.77	−	11867.6i	−0.186695	−	0.421159i
$927$	−4539.19	−	7667.28i	−0.160827	−	0.271657i
$928$	11483.3	+	20267.1i	0.406205	+	0.716917i
$929$			31093.6i			1.09811i	0.835785	+	0.549057i	$0.185013\pi$
$929$			31093.6i			1.09811i	−0.835785	+	0.549057i	$0.814987\pi$
$930$	19141.5	−	15622.8i	0.674919	−	0.550851i
$931$	12519.1			0.440706
$932$	−31124.5	−	28207.8i	−1.09390	−	0.991391i
$933$	−9600.01	−	35059.9i	−0.336860	−	1.23024i
$934$	8128.03	+	18335.7i	0.284751	+	0.642359i
$935$	−515.802			−0.0180412
$936$	−45087.0	+	9870.09i	−1.57448	+	0.344673i
$937$	−32860.5			−1.14569			−0.572843	−	0.819665i	$-0.694159\pi$
$937$	−32860.5			−1.14569			−0.572843	+	0.819665i	$0.694159\pi$
$938$	2180.86	+	4919.72i	0.0759142	+	0.171252i
$939$	590.781	+	2157.57i	0.0205318	+	0.0749838i
$940$	−2408.17	+	2657.18i	−0.0835595	+	0.0921997i
$941$	8534.60			0.295664			0.147832	−	0.989012i	$-0.452770\pi$
$941$	8534.60			0.295664			0.147832	+	0.989012i	$0.452770\pi$
$942$	4188.64	−	3418.66i	0.144876	−	0.118244i
$943$			17655.0i			0.609677i
$944$	−9358.58	+	922.347i	−0.322665	+	0.0318007i
$945$	16831.9	−	17393.2i	0.579408	−	0.598732i
$946$	−237.752	−	536.337i	−0.00817123	−	0.0184332i
$947$			51719.4i			1.77471i	0.461084	+	0.887357i	$0.347461\pi$
$947$			51719.4i			1.77471i	−0.461084	+	0.887357i	$0.652539\pi$
$948$	18023.3	−	35568.3i	0.617479	−	1.21857i
$949$		−	54106.4i		−	1.85076i
$950$	5685.53	−	2520.33i	0.194172	−	0.0860740i
$951$	1957.68	+	7149.60i	0.0667531	+	0.243787i
$952$	−4916.35	+	14884.4i	−0.167374	+	0.506729i
$953$			1815.12i			0.0616973i	0.999524	+	0.0308486i	$0.00982098\pi$
$953$			1815.12i			0.0616973i	−0.999524	+	0.0308486i	$0.990179\pi$
$954$	10860.4	−	15244.7i	0.368574	−	0.517363i
$955$	−39049.4			−1.32315
$956$	2513.13	−	2772.99i	0.0850214	−	0.0938127i
$957$	550.404	−	150.710i	0.0185915	−	0.00509066i
$958$	22959.0	−	10177.5i	0.774293	−	0.343235i
$959$	18600.0			0.626305
$960$	−11826.3	+	30421.0i	−0.397595	+	1.02274i
$961$	11013.3			0.369687
$962$	36734.0	−	16283.8i	1.23114	−	0.545749i
$963$	−12100.0	−	20438.5i	−0.404900	−	0.683927i
$964$	−14919.4	+	16462.1i	−0.498466	+	0.550008i
$965$	10528.1			0.351202
$966$	21105.8	−	17226.0i	0.702970	−	0.573745i
$967$		−	7342.85i		−	0.244188i	−0.992519	−	0.122094i	$-0.961039\pi$
$967$		−	7342.85i		−	0.244188i	0.992519	−	0.122094i	$-0.0389610\pi$
$968$	9440.64	−	28581.8i	0.313464	−	0.949024i
$969$	21279.6	−	5826.72i	0.705469	−	0.193169i
$970$	−1047.19	+	464.208i	−0.0346631	+	0.0153658i
$971$		−	56846.0i		−	1.87876i	−0.342881	−	0.939379i	$-0.611403\pi$
$971$		−	56846.0i		−	1.87876i	0.342881	−	0.939379i	$-0.388597\pi$
$972$	25010.0	−	17112.2i	0.825306	−	0.564686i
$973$		−	24865.5i		−	0.819273i
$974$	22051.4	+	49745.0i	0.725434	+	1.63648i
$975$	−9658.84	+	2644.76i	−0.317262	+	0.0868718i
$976$	−12186.2	+	1201.03i	−0.399663	+	0.0393893i
$977$			29034.3i			0.950758i	0.879781	+	0.475379i	$0.157689\pi$
$977$			29034.3i			0.950758i	−0.879781	+	0.475379i	$0.842311\pi$
$978$	−8106.13	−	9931.88i	−0.265036	−	0.324731i
$979$	−1372.87			−0.0448182
$980$	−9573.23	+	10563.1i	−0.312047	+	0.344313i
$981$	−5771.75	−	9749.23i	−0.187847	−	0.317298i
$982$	5995.00	+	13523.9i	0.194815	+	0.439476i
$983$	8726.42			0.283143			0.141571	−	0.989928i	$-0.454784\pi$
$983$	8726.42			0.283143			0.141571	+	0.989928i	$0.454784\pi$
$984$	−814.627	+	15726.4i	−0.0263916	+	0.509492i
$985$	44297.6			1.43293
$986$	7266.43	+	16392.1i	0.234696	+	0.529442i
$987$	2575.05	−	705.093i	0.0830444	−	0.0227390i
$988$	38598.2	+	34981.1i	1.24289	+	1.12641i
$989$	−32036.6			−1.03004
$990$	651.232	+	463.943i	0.0209066	+	0.0148940i
$991$			42872.7i			1.37426i	0.726532	+	0.687132i	$0.241131\pi$
$991$			42872.7i			1.37426i	−0.726532	+	0.687132i	$0.758869\pi$
$992$	21581.8	−	12228.3i	0.690750	−	0.391378i
$993$	8030.38	+	29327.5i	0.256633	+	0.937241i
$994$	−10034.7	−	22637.0i	−0.320204	−	0.722337i
$995$			46393.2i			1.47815i
$996$	1386.23	−	2735.66i	0.0441007	−	0.0870310i
$997$			5601.07i			0.177921i	0.996035	+	0.0889607i	$0.0283545\pi$
$997$			5601.07i			0.177921i	−0.996035	+	0.0889607i	$0.971645\pi$
$998$	−14909.6	+	6609.24i	−0.472900	+	0.209631i
$999$	−18346.5	+	18958.4i	−0.581039	+	0.600417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.4.f.b.11.7	yes	8
3.2	odd	2	inner	24.4.f.b.11.2	yes	8
4.3	odd	2		96.4.f.b.47.1		8
8.3	odd	2	inner	24.4.f.b.11.1	✓	8
8.5	even	2		96.4.f.b.47.2		8
12.11	even	2		96.4.f.b.47.4		8
16.3	odd	4		768.4.c.v.767.14		16
16.5	even	4		768.4.c.v.767.13		16
16.11	odd	4		768.4.c.v.767.3		16
16.13	even	4		768.4.c.v.767.4		16
24.5	odd	2		96.4.f.b.47.3		8
24.11	even	2	inner	24.4.f.b.11.8	yes	8
48.5	odd	4		768.4.c.v.767.2		16
48.11	even	4		768.4.c.v.767.16		16
48.29	odd	4		768.4.c.v.767.15		16
48.35	even	4		768.4.c.v.767.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.f.b.11.1	✓	8	8.3	odd	2	inner
24.4.f.b.11.2	yes	8	3.2	odd	2	inner
24.4.f.b.11.7	yes	8	1.1	even	1	trivial
24.4.f.b.11.8	yes	8	24.11	even	2	inner
96.4.f.b.47.1		8	4.3	odd	2
96.4.f.b.47.2		8	8.5	even	2
96.4.f.b.47.3		8	24.5	odd	2
96.4.f.b.47.4		8	12.11	even	2
768.4.c.v.767.1		16	48.35	even	4
768.4.c.v.767.2		16	48.5	odd	4
768.4.c.v.767.3		16	16.11	odd	4
768.4.c.v.767.4		16	16.13	even	4
768.4.c.v.767.13		16	16.5	even	4
768.4.c.v.767.14		16	16.3	odd	4
768.4.c.v.767.15		16	48.29	odd	4
768.4.c.v.767.16		16	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58576 - 1.14624i) q^{2} +(1.37228 + 5.01167i) q^{3} +(5.37228 - 5.92778i) q^{4} -12.2683 q^{5} +(9.29295 + 11.3860i) q^{6} -14.0624i q^{7} +(7.09677 - 21.4857i) q^{8} +(-23.2337 + 13.7548i) q^{9} +O(q^{10})\)	\(q+(2.58576 - 1.14624i) q^{2} +(1.37228 + 5.01167i) q^{3} +(5.37228 - 5.92778i) q^{4} -12.2683 q^{5} +(9.29295 + 11.3860i) q^{6} -14.0624i q^{7} +(7.09677 - 21.4857i) q^{8} +(-23.2337 + 13.7548i) q^{9} +(-31.7228 + 14.0624i) q^{10} +0.853445i q^{11} +(37.0804 + 18.7895i) q^{12} +75.5470i q^{13} +(-16.1188 - 36.3619i) q^{14} +(-16.8355 - 61.4846i) q^{15} +(-6.27719 - 63.6914i) q^{16} -49.2633i q^{17} +(-44.3104 + 62.1980i) q^{18} +86.1902 q^{19} +(-65.9087 + 72.7237i) q^{20} +(70.4759 - 19.2975i) q^{21} +(0.978251 + 2.20680i) q^{22} +131.817 q^{23} +(117.418 + 6.08225i) q^{24} +25.5109 q^{25} +(86.5947 + 195.346i) q^{26} +(-100.818 - 97.5641i) q^{27} +(-83.3586 - 75.5470i) q^{28} -128.684 q^{29} +(-114.009 - 139.687i) q^{30} +137.032i q^{31} +(-89.2367 - 157.495i) q^{32} +(-4.27719 + 1.17117i) q^{33} +(-56.4674 - 127.383i) q^{34} +172.521i q^{35} +(-43.2822 + 211.619i) q^{36} -188.046i q^{37} +(222.867 - 98.7944i) q^{38} +(-378.617 + 103.672i) q^{39} +(-87.0652 + 263.593i) q^{40} +133.935i q^{41} +(160.114 - 130.681i) q^{42} -243.038 q^{43} +(5.05904 + 4.58495i) q^{44} +(285.038 - 168.748i) q^{45} +(340.848 - 151.094i) q^{46} +36.5380 q^{47} +(310.586 - 118.862i) q^{48} +145.250 q^{49} +(65.9649 - 29.2415i) q^{50} +(246.891 - 67.6031i) q^{51} +(447.826 + 405.860i) q^{52} -245.099 q^{53} +(-372.522 - 136.716i) q^{54} -10.4703i q^{55} +(-302.140 - 99.7974i) q^{56} +(118.277 + 431.957i) q^{57} +(-332.745 + 147.502i) q^{58} -146.936i q^{59} +(-454.913 - 230.515i) q^{60} -191.332i q^{61} +(157.071 + 354.330i) q^{62} +(193.426 + 326.721i) q^{63} +(-411.272 - 304.958i) q^{64} -926.832i q^{65} +(-9.71733 + 7.93102i) q^{66} -135.299 q^{67} +(-292.022 - 264.656i) q^{68} +(180.891 + 660.625i) q^{69} +(197.750 + 446.098i) q^{70} +622.549 q^{71} +(130.648 + 596.807i) q^{72} -716.195 q^{73} +(-215.545 - 486.241i) q^{74} +(35.0081 + 127.852i) q^{75} +(463.038 - 510.917i) q^{76} +12.0015 q^{77} +(-860.178 + 702.054i) q^{78} -959.221i q^{79} +(77.0103 + 781.385i) q^{80} +(350.609 - 639.152i) q^{81} +(153.522 + 346.324i) q^{82} -73.7766i q^{83} +(264.225 - 521.438i) q^{84} +604.376i q^{85} +(-628.437 + 278.579i) q^{86} +(-176.590 - 644.920i) q^{87} +(18.3369 + 6.05671i) q^{88} +1608.62i q^{89} +(543.612 - 763.063i) q^{90} +1062.37 q^{91} +(708.160 - 781.385i) q^{92} +(-686.757 + 188.046i) q^{93} +(94.4785 - 41.8812i) q^{94} -1057.41 q^{95} +(666.857 - 663.353i) q^{96} +33.0106 q^{97} +(375.581 - 166.491i) q^{98} +(-11.7390 - 19.8287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9	\( 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9} - 24 q^{10} + 36 q^{12} - 280 q^{16} + 264 q^{18} + 184 q^{19} - 176 q^{22} + 264 q^{24} + 296 q^{25} - 324 q^{27} + 528 q^{28} - 624 q^{30} - 264 q^{33} - 176 q^{34} - 516 q^{36} - 1248 q^{40} + 1320 q^{42} - 152 q^{43} + 1440 q^{46} + 1080 q^{48} - 952 q^{49} + 1056 q^{51} + 2112 q^{52} - 1584 q^{54} + 1176 q^{57} - 2616 q^{58} - 2640 q^{60} - 1360 q^{64} + 792 q^{66} - 1496 q^{67} + 3696 q^{70} + 2640 q^{72} + 1072 q^{73} - 708 q^{75} + 1912 q^{76} - 3696 q^{78} - 504 q^{81} - 2816 q^{82} - 4224 q^{84} - 1232 q^{88} + 4104 q^{90} + 3168 q^{91} + 4800 q^{94} + 4752 q^{96} - 3872 q^{97} + 2112 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9 - 24 * q^10 + 36 * q^12 - 280 * q^16 + 264 * q^18 + 184 * q^19 - 176 * q^22 + 264 * q^24 + 296 * q^25 - 324 * q^27 + 528 * q^28 - 624 * q^30 - 264 * q^33 - 176 * q^34 - 516 * q^36 - 1248 * q^40 + 1320 * q^42 - 152 * q^43 + 1440 * q^46 + 1080 * q^48 - 952 * q^49 + 1056 * q^51 + 2112 * q^52 - 1584 * q^54 + 1176 * q^57 - 2616 * q^58 - 2640 * q^60 - 1360 * q^64 + 792 * q^66 - 1496 * q^67 + 3696 * q^70 + 2640 * q^72 + 1072 * q^73 - 708 * q^75 + 1912 * q^76 - 3696 * q^78 - 504 * q^81 - 2816 * q^82 - 4224 * q^84 - 1232 * q^88 + 4104 * q^90 + 3168 * q^91 + 4800 * q^94 + 4752 * q^96 - 3872 * q^97 + 2112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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