LMFDB - Embedded newform 429.2.f.a.131.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.48
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70555 q^{2} +(-1.68970 + 0.380676i) q^{3} +5.32000 q^{4} -2.40031i q^{5} +(-4.57157 + 1.02994i) q^{6} +4.64879i q^{7} +8.98243 q^{8} +(2.71017 - 1.28646i) q^{9} +O(q^{10})$	\(q+2.70555 q^{2} +(-1.68970 + 0.380676i) q^{3} +5.32000 q^{4} -2.40031i q^{5} +(-4.57157 + 1.02994i) q^{6} +4.64879i q^{7} +8.98243 q^{8} +(2.71017 - 1.28646i) q^{9} -6.49415i q^{10} +(0.588530 - 3.26399i) q^{11} +(-8.98921 + 2.02520i) q^{12} +1.00000i q^{13} +12.5775i q^{14} +(0.913739 + 4.05580i) q^{15} +13.6624 q^{16} -2.96873 q^{17} +(7.33251 - 3.48057i) q^{18} -0.907622i q^{19} -12.7696i q^{20} +(-1.76968 - 7.85505i) q^{21} +(1.59230 - 8.83089i) q^{22} -0.745744i q^{23} +(-15.1776 + 3.41940i) q^{24} -0.761477 q^{25} +2.70555i q^{26} +(-4.08965 + 3.20542i) q^{27} +24.7316i q^{28} -4.15417 q^{29} +(2.47217 + 10.9732i) q^{30} -2.63982 q^{31} +18.9995 q^{32} +(0.248083 + 5.73920i) q^{33} -8.03206 q^{34} +11.1585 q^{35} +(14.4181 - 6.84395i) q^{36} -9.06415 q^{37} -2.45562i q^{38} +(-0.380676 - 1.68970i) q^{39} -21.5606i q^{40} -4.58710 q^{41} +(-4.78796 - 21.2522i) q^{42} +6.71382i q^{43} +(3.13098 - 17.3644i) q^{44} +(-3.08789 - 6.50525i) q^{45} -2.01765i q^{46} +6.35638i q^{47} +(-23.0854 + 5.20095i) q^{48} -14.6112 q^{49} -2.06021 q^{50} +(5.01627 - 1.13013i) q^{51} +5.32000i q^{52} -6.81627i q^{53} +(-11.0648 + 8.67243i) q^{54} +(-7.83458 - 1.41265i) q^{55} +41.7574i q^{56} +(0.345510 + 1.53361i) q^{57} -11.2393 q^{58} -5.61923i q^{59} +(4.86109 + 21.5769i) q^{60} -5.76709i q^{61} -7.14217 q^{62} +(5.98046 + 12.5990i) q^{63} +24.0793 q^{64} +2.40031 q^{65} +(0.671201 + 15.5277i) q^{66} +8.08809 q^{67} -15.7937 q^{68} +(0.283887 + 1.26008i) q^{69} +30.1899 q^{70} +0.0134651i q^{71} +(24.3439 - 11.5555i) q^{72} -4.80852i q^{73} -24.5235 q^{74} +(1.28667 - 0.289876i) q^{75} -4.82855i q^{76} +(15.1736 + 2.73595i) q^{77} +(-1.02994 - 4.57157i) q^{78} +8.17275i q^{79} -32.7940i q^{80} +(5.69006 - 6.97303i) q^{81} -12.4106 q^{82} +1.87173 q^{83} +(-9.41470 - 41.7889i) q^{84} +7.12587i q^{85} +18.1646i q^{86} +(7.01931 - 1.58139i) q^{87} +(5.28643 - 29.3186i) q^{88} +6.88831i q^{89} +(-8.35444 - 17.6003i) q^{90} -4.64879 q^{91} -3.96736i q^{92} +(4.46051 - 1.00492i) q^{93} +17.1975i q^{94} -2.17857 q^{95} +(-32.1035 + 7.23265i) q^{96} +13.4578 q^{97} -39.5314 q^{98} +(-2.60396 - 9.60309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	2.70555			1.91311			0.956556	−	0.291547i	$-0.0941700\pi$
$2$	2.70555			1.91311			0.956556	+	0.291547i	$0.0941700\pi$
$3$	−1.68970	+	0.380676i	−0.975549	+	0.219783i
$3$	−1.68970	+	0.380676i	−0.975549	+	0.219783i
$4$	5.32000			2.66000
$5$		−	2.40031i		−	1.07345i	−0.843757	−	0.536725i	$-0.819661\pi$
$5$		−	2.40031i		−	1.07345i	0.843757	−	0.536725i	$-0.180339\pi$
$6$	−4.57157	+	1.02994i	−1.86633	+	0.420470i
$7$			4.64879i			1.75708i	0.477673	+	0.878538i	$0.341481\pi$
$7$			4.64879i			1.75708i	−0.477673	+	0.878538i	$0.658519\pi$
$8$	8.98243			3.17577
$9$	2.71017	−	1.28646i	0.903391	−	0.428819i
$10$		−	6.49415i		−	2.05363i
$11$	0.588530	−	3.26399i	0.177448	−	0.984130i
$11$	0.588530	−	3.26399i	0.177448	−	0.984130i
$12$	−8.98921	+	2.02520i	−2.59496	+	0.584624i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$			12.5775i			3.36148i
$15$	0.913739	+	4.05580i	0.235926	+	1.04720i
$16$	13.6624			3.41561
$17$	−2.96873			−0.720024			−0.360012	−	0.932948i	$-0.617227\pi$
$17$	−2.96873			−0.720024			−0.360012	+	0.932948i	$0.617227\pi$
$18$	7.33251	−	3.48057i	1.72829	−	0.820378i
$19$		−	0.907622i		−	0.208223i	−0.994566	−	0.104111i	$-0.966800\pi$
$19$		−	0.907622i		−	0.208223i	0.994566	−	0.104111i	$-0.0331999\pi$
$20$		−	12.7696i		−	2.85538i
$21$	−1.76968	−	7.85505i	−0.386176	−	1.71411i
$22$	1.59230	−	8.83089i	0.339479	−	1.88275i
$23$		−	0.745744i		−	0.155498i	−0.996973	−	0.0777492i	$-0.975227\pi$
$23$		−	0.745744i		−	0.155498i	0.996973	−	0.0777492i	$-0.0247734\pi$
$24$	−15.1776	+	3.41940i	−3.09812	+	0.697981i
$25$	−0.761477			−0.152295
$26$			2.70555i			0.530602i
$27$	−4.08965	+	3.20542i	−0.787054	+	0.616884i
$28$			24.7316i			4.67382i
$29$	−4.15417			−0.771411			−0.385705	−	0.922622i	$-0.626042\pi$
$29$	−4.15417			−0.771411			−0.385705	+	0.922622i	$0.626042\pi$
$30$	2.47217	+	10.9732i	0.451354	+	2.00342i
$31$	−2.63982			−0.474126			−0.237063	−	0.971494i	$-0.576185\pi$
$31$	−2.63982			−0.474126			−0.237063	+	0.971494i	$0.576185\pi$
$32$	18.9995			3.35867
$33$	0.248083	+	5.73920i	0.0431857	+	0.999067i
$34$	−8.03206			−1.37749
$35$	11.1585			1.88613
$36$	14.4181	−	6.84395i	2.40302	−	1.14066i
$37$	−9.06415			−1.49014			−0.745069	−	0.666988i	$-0.767583\pi$
$37$	−9.06415			−1.49014			−0.745069	+	0.666988i	$0.767583\pi$
$38$		−	2.45562i		−	0.398354i
$39$	−0.380676	−	1.68970i	−0.0609569	−	0.270569i
$40$		−	21.5606i		−	3.40903i
$41$	−4.58710			−0.716385			−0.358192	−	0.933648i	$-0.616607\pi$
$41$	−4.58710			−0.716385			−0.358192	+	0.933648i	$0.616607\pi$
$42$	−4.78796	−	21.2522i	−0.738798	−	3.27929i
$43$			6.71382i			1.02385i	0.859031	+	0.511924i	$0.171067\pi$
$43$			6.71382i			1.02385i	−0.859031	+	0.511924i	$0.828933\pi$
$44$	3.13098	−	17.3644i	0.472013	−	2.61779i
$45$	−3.08789	−	6.50525i	−0.460315	−	0.969745i
$46$		−	2.01765i		−	0.297486i
$47$			6.35638i			0.927173i	0.886052	+	0.463587i	$0.153438\pi$
$47$			6.35638i			0.927173i	−0.886052	+	0.463587i	$0.846562\pi$
$48$	−23.0854	+	5.20095i	−3.33209	+	0.750693i
$49$	−14.6112			−2.08732
$50$	−2.06021			−0.291358
$51$	5.01627	−	1.13013i	0.702418	−	0.158249i
$52$			5.32000i			0.737752i
$53$		−	6.81627i		−	0.936287i	−0.883652	−	0.468143i	$-0.844923\pi$
$53$		−	6.81627i		−	0.936287i	0.883652	−	0.468143i	$-0.155077\pi$
$54$	−11.0648	+	8.67243i	−1.50572	+	1.18017i
$55$	−7.83458	−	1.41265i	−1.05641	−	0.190482i
$56$			41.7574i			5.58007i
$57$	0.345510	+	1.53361i	0.0457639	+	0.203132i
$58$	−11.2393			−1.47580
$59$		−	5.61923i		−	0.731561i	−0.930701	−	0.365781i	$-0.880802\pi$
$59$		−	5.61923i		−	0.731561i	0.930701	−	0.365781i	$-0.119198\pi$
$60$	4.86109	+	21.5769i	0.627565	+	2.78556i
$61$		−	5.76709i		−	0.738400i	−0.929350	−	0.369200i	$-0.879632\pi$
$61$		−	5.76709i		−	0.738400i	0.929350	−	0.369200i	$-0.120368\pi$
$62$	−7.14217			−0.907056
$63$	5.98046	+	12.5990i	0.753467	+	1.58733i
$64$	24.0793			3.00991
$65$	2.40031			0.297722
$66$	0.671201	+	15.5277i	0.0826192	+	1.91133i
$67$	8.08809			0.988117			0.494059	−	0.869429i	$-0.335513\pi$
$67$	8.08809			0.988117			0.494059	+	0.869429i	$0.335513\pi$
$68$	−15.7937			−1.91526
$69$	0.283887	+	1.26008i	0.0341760	+	0.151696i
$70$	30.1899			3.60839
$71$			0.0134651i			0.00159802i	1.00000		0.000799009i	$0.000254333\pi$
$71$			0.0134651i			0.00159802i	−1.00000		0.000799009i	$0.999746\pi$
$72$	24.3439	−	11.5555i	2.86896	−	1.36183i
$73$		−	4.80852i		−	0.562795i	−0.959591	−	0.281398i	$-0.909202\pi$
$73$		−	4.80852i		−	0.562795i	0.959591	−	0.281398i	$-0.0907980\pi$
$74$	−24.5235			−2.85080
$75$	1.28667	−	0.289876i	0.148572	−	0.0334720i
$76$		−	4.82855i		−	0.553873i
$77$	15.1736	+	2.73595i	1.72919	+	0.311790i
$78$	−1.02994	−	4.57157i	−0.116617	−	0.517628i
$79$			8.17275i			0.919506i	0.888047	+	0.459753i	$0.152062\pi$
$79$			8.17275i			0.919506i	−0.888047	+	0.459753i	$0.847938\pi$
$80$		−	32.7940i		−	3.66648i
$81$	5.69006	−	6.97303i	0.632229	−	0.774781i
$82$	−12.4106			−1.37052
$83$	1.87173			0.205449			0.102724	−	0.994710i	$-0.467244\pi$
$83$	1.87173			0.205449			0.102724	+	0.994710i	$0.467244\pi$
$84$	−9.41470	−	41.7889i	−1.02723	−	4.55954i
$85$			7.12587i			0.772910i
$86$			18.1646i			1.95874i
$87$	7.01931	−	1.58139i	0.752549	−	0.169543i
$88$	5.28643	−	29.3186i	0.563536	−	3.12537i
$89$			6.88831i			0.730159i	0.930976	+	0.365080i	$0.118958\pi$
$89$			6.88831i			0.730159i	−0.930976	+	0.365080i	$0.881042\pi$
$90$	−8.35444	−	17.6003i	−0.880635	−	1.85523i
$91$	−4.64879			−0.487325
$92$		−	3.96736i		−	0.413626i
$93$	4.46051	−	1.00492i	0.462533	−	0.104205i
$94$			17.1975i			1.77379i
$95$	−2.17857			−0.223517
$96$	−32.1035	+	7.23265i	−3.27655	+	0.738179i
$97$	13.4578			1.36643			0.683217	−	0.730215i	$-0.260580\pi$
$97$	13.4578			1.36643			0.683217	+	0.730215i	$0.260580\pi$
$98$	−39.5314			−3.99327
$99$	−2.60396	−	9.60309i	−0.261708	−	0.965147i
$100$	−4.05106			−0.405106
$101$	−5.10627			−0.508093			−0.254046	−	0.967192i	$-0.581762\pi$
$101$	−5.10627			−0.508093			−0.254046	+	0.967192i	$0.581762\pi$
$102$	13.5718	−	3.05761i	1.34381	−	0.302749i
$103$	−3.16632			−0.311987			−0.155993	−	0.987758i	$-0.549858\pi$
$103$	−3.16632			−0.311987			−0.155993	+	0.987758i	$0.549858\pi$
$104$			8.98243i			0.880800i
$105$	−18.8545	+	4.24778i	−1.84002	+	0.414541i
$106$		−	18.4418i		−	1.79122i
$107$	12.6023			1.21831			0.609156	−	0.793050i	$-0.291508\pi$
$107$	12.6023			1.21831			0.609156	+	0.793050i	$0.291508\pi$
$108$	−21.7570	+	17.0528i	−2.09357	+	1.64091i
$109$		−	14.0453i		−	1.34529i	−0.739963	−	0.672647i	$-0.765157\pi$
$109$		−	14.0453i		−	1.34529i	0.739963	−	0.672647i	$-0.234843\pi$
$110$	−21.1969	−	3.82200i	−2.02104	−	0.364414i
$111$	15.3157	−	3.45050i	1.45370	−	0.327507i
$112$			63.5137i			6.00148i
$113$			2.86467i			0.269486i	0.990881	+	0.134743i	$0.0430208\pi$
$113$			2.86467i			0.269486i	−0.990881	+	0.134743i	$0.956979\pi$
$114$	0.934794	+	4.14926i	0.0875515	+	0.388614i
$115$	−1.79002			−0.166920
$116$	−22.1002			−2.05195
$117$	1.28646	+	2.71017i	0.118933	+	0.250555i
$118$		−	15.2031i		−	1.39956i
$119$		−	13.8010i		−	1.26514i
$120$	8.20760	+	36.4310i	0.749248	+	3.32568i
$121$	−10.3073	−	3.84191i	−0.937024	−	0.349265i
$122$		−	15.6031i		−	1.41264i
$123$	7.75082	−	1.74620i	0.698868	−	0.157449i
$124$	−14.0439			−1.26118
$125$		−	10.1738i		−	0.909969i
$126$	16.1804	+	34.0872i	1.44147	+	3.03673i
$127$		−	10.8973i		−	0.966976i	−0.875351	−	0.483488i	$-0.839370\pi$
$127$		−	10.8973i		−	0.966976i	0.875351	−	0.483488i	$-0.160630\pi$
$128$	27.1487			2.39963
$129$	−2.55579	−	11.3443i	−0.225025	−	0.998814i
$130$	6.49415			0.569575
$131$	21.5642			1.88407			0.942036	−	0.335512i	$-0.108909\pi$
$131$	21.5642			1.88407			0.942036	+	0.335512i	$0.108909\pi$
$132$	1.31980	+	30.5326i	0.114874	+	2.65752i
$133$	4.21934			0.365863
$134$	21.8827			1.89038
$135$	7.69400	+	9.81643i	0.662194	+	0.844864i
$136$	−26.6665			−2.28663
$137$			21.2168i			1.81267i	0.422555	+	0.906337i	$0.361133\pi$
$137$			21.2168i			1.81267i	−0.422555	+	0.906337i	$0.638867\pi$
$138$	0.768070	+	3.40922i	0.0653825	+	0.290212i
$139$			15.4534i			1.31074i	0.755309	+	0.655369i	$0.227487\pi$
$139$			15.4534i			1.31074i	−0.755309	+	0.655369i	$0.772513\pi$
$140$	59.3633			5.01712
$141$	−2.41972	−	10.7404i	−0.203777	−	0.904503i
$142$			0.0364306i			0.00305719i
$143$	3.26399	+	0.588530i	0.272949	+	0.0492154i
$144$	37.0275	−	17.5761i	3.08563	−	1.46468i
$145$			9.97129i			0.828071i
$146$		−	13.0097i		−	1.07669i
$147$	24.6886	−	5.56213i	2.03628	−	0.458757i
$148$	−48.2213			−3.96377
$149$	12.6919			1.03976			0.519880	−	0.854239i	$-0.325977\pi$
$149$	12.6919			1.03976			0.519880	+	0.854239i	$0.325977\pi$
$150$	3.48114	−	0.784274i	0.284234	−	0.0640357i
$151$		−	4.45438i		−	0.362492i	−0.983438	−	0.181246i	$-0.941987\pi$
$151$		−	4.45438i		−	0.362492i	0.983438	−	0.181246i	$-0.0580131\pi$
$152$		−	8.15266i		−	0.661268i
$153$	−8.04578	+	3.81914i	−0.650463	+	0.308760i
$154$	41.0529	+	7.40225i	3.30814	+	0.596490i
$155$			6.33638i			0.508950i
$156$	−2.02520	−	8.98921i	−0.162145	−	0.719713i
$157$	13.7663			1.09867			0.549335	−	0.835602i	$-0.314881\pi$
$157$	13.7663			1.09867			0.549335	+	0.835602i	$0.314881\pi$
$158$			22.1118i			1.75912i
$159$	2.59479	+	11.5175i	0.205780	+	0.913393i
$160$		−	45.6047i		−	3.60536i
$161$	3.46681			0.273223
$162$	15.3948	−	18.8659i	1.20953	−	1.48224i
$163$	−9.13240			−0.715305			−0.357653	−	0.933855i	$-0.616423\pi$
$163$	−9.13240			−0.715305			−0.357653	+	0.933855i	$0.616423\pi$
$164$	−24.4034			−1.90558
$165$	13.7759	−	0.595476i	1.07245	−	0.0463577i
$166$	5.06405			0.393046
$167$	−5.90115			−0.456644			−0.228322	−	0.973586i	$-0.573324\pi$
$167$	−5.90115			−0.456644			−0.228322	+	0.973586i	$0.573324\pi$
$168$	−15.8960	−	70.5575i	−1.22641	−	5.44363i
$169$	−1.00000			−0.0769231
$170$			19.2794i			1.47866i
$171$	−1.16762	−	2.45981i	−0.0892898	−	0.188107i
$172$			35.7175i			2.72344i
$173$	−13.0937			−0.995497			−0.497748	−	0.867322i	$-0.665840\pi$
$173$	−13.0937			−0.995497			−0.497748	+	0.867322i	$0.665840\pi$
$174$	18.9911	−	4.27854i	1.43971	−	0.324355i
$175$		−	3.53994i		−	0.267595i
$176$	8.04075	−	44.5940i	0.606094	−	3.36140i
$177$	2.13910	+	9.49481i	0.160785	+	0.713674i
$178$			18.6367i			1.39688i
$179$			22.5404i			1.68475i	0.538893	+	0.842374i	$0.318843\pi$
$179$			22.5404i			1.68475i	−0.538893	+	0.842374i	$0.681157\pi$
$180$	−16.4276	−	34.6079i	−1.22444	−	2.57952i
$181$	2.44801			0.181959			0.0909796	−	0.995853i	$-0.471000\pi$
$181$	2.44801			0.181959			0.0909796	+	0.995853i	$0.471000\pi$
$182$	−12.5775			−0.932308
$183$	2.19539	+	9.74465i	0.162288	+	0.720345i
$184$		−	6.69860i		−	0.493827i
$185$			21.7568i			1.59959i
$186$	12.0681	−	2.71885i	0.884878	−	0.199356i
$187$	−1.74719	+	9.68992i	−0.127767	+	0.708597i
$188$			33.8160i			2.46628i
$189$	−14.9013	−	19.0119i	−1.08391	−	1.38291i
$190$	−5.89424			−0.427613
$191$		−	19.6329i		−	1.42059i	−0.703907	−	0.710293i	$-0.748563\pi$
$191$		−	19.6329i		−	1.42059i	0.703907	−	0.710293i	$-0.251437\pi$
$192$	−40.6867	+	9.16639i	−2.93631	+	0.661528i
$193$			15.8242i			1.13905i	0.821974	+	0.569526i	$0.192873\pi$
$193$			15.8242i			1.13905i	−0.821974	+	0.569526i	$0.807127\pi$
$194$	36.4108			2.61414
$195$	−4.05580	+	0.913739i	−0.290442	+	0.0654342i
$196$	−77.7317			−5.55226
$197$	5.90304			0.420574			0.210287	−	0.977640i	$-0.432560\pi$
$197$	5.90304			0.420574			0.210287	+	0.977640i	$0.432560\pi$
$198$	−7.04515	−	25.9816i	−0.500677	−	1.84644i
$199$	9.39740			0.666164			0.333082	−	0.942898i	$-0.391911\pi$
$199$	9.39740			0.666164			0.333082	+	0.942898i	$0.391911\pi$
$200$	−6.83992			−0.483655
$201$	−13.6664	+	3.07894i	−0.963957	+	0.217172i
$202$	−13.8153			−0.972039
$203$		−	19.3119i		−	1.35543i
$204$	26.6866	−	6.01227i	1.86843	−	0.420943i
$205$			11.0104i			0.769003i
$206$	−8.56663			−0.596865
$207$	−0.959367	−	2.02110i	−0.0666806	−	0.140476i
$208$			13.6624i			0.947319i
$209$	−2.96247	−	0.534163i	−0.204918	−	0.0369488i
$210$	−51.0119	+	11.4926i	−3.52016	+	0.793063i
$211$		−	0.229443i		−	0.0157955i	−0.999969	−	0.00789775i	$-0.997486\pi$
$211$		−	0.229443i		−	0.0157955i	0.999969	−	0.00789775i	$-0.00251396\pi$
$212$		−	36.2626i		−	2.49052i
$213$	−0.00512585	−	0.0227521i	−0.000351218	−	0.00155895i
$214$	34.0962			2.33077
$215$	16.1152			1.09905
$216$	−36.7351	+	28.7925i	−2.49950	+	1.95908i
$217$		−	12.2720i		−	0.833075i
$218$		−	38.0002i		−	2.57370i
$219$	1.83049	+	8.12496i	0.123693	+	0.549034i
$220$	−41.6800	−	7.51532i	−2.81006	−	0.506683i
$221$		−	2.96873i		−	0.199699i
$222$	41.4374	−	9.33551i	2.78110	−	0.626558i
$223$	5.90391			0.395355			0.197678	−	0.980267i	$-0.436660\pi$
$223$	5.90391			0.395355			0.197678	+	0.980267i	$0.436660\pi$
$224$			88.3246i			5.90144i
$225$	−2.06373	+	0.979607i	−0.137582	+	0.0653071i
$226$			7.75052i			0.515557i
$227$	−2.05068			−0.136108			−0.0680541	−	0.997682i	$-0.521679\pi$
$227$	−2.05068			−0.136108			−0.0680541	+	0.997682i	$0.521679\pi$
$228$	1.83811	+	8.15881i	0.121732	+	0.540330i
$229$	14.9772			0.989722			0.494861	−	0.868972i	$-0.335219\pi$
$229$	14.9772			0.989722			0.494861	+	0.868972i	$0.335219\pi$
$230$	−4.84298			−0.319337
$231$	−26.6803	+	1.15328i	−1.75544	+	0.0758806i
$232$	−37.3146			−2.44982
$233$	−10.9417			−0.716814			−0.358407	−	0.933565i	$-0.616680\pi$
$233$	−10.9417			−0.716814			−0.358407	+	0.933565i	$0.616680\pi$
$234$	3.48057	+	7.33251i	0.227532	+	0.479341i
$235$	15.2573			0.995274
$236$		−	29.8943i		−	1.94595i
$237$	−3.11117	−	13.8095i	−0.202092	−	0.897023i
$238$		−	37.3393i		−	2.42035i
$239$	−21.9971			−1.42287			−0.711436	−	0.702751i	$-0.751955\pi$
$239$	−21.9971			−1.42287			−0.711436	+	0.702751i	$0.751955\pi$
$240$	12.4839	+	55.4120i	0.805832	+	3.57683i
$241$			3.54849i			0.228578i	0.993448	+	0.114289i	$0.0364590\pi$
$241$			3.54849i			0.228578i	−0.993448	+	0.114289i	$0.963541\pi$
$242$	−27.8868	−	10.3945i	−1.79263	−	0.668183i
$243$	−6.96003	+	13.9484i	−0.446486	+	0.894790i
$244$		−	30.6809i		−	1.96414i
$245$			35.0714i			2.24063i
$246$	20.9702	−	4.72443i	1.33701	−	0.301218i
$247$	0.907622			0.0577506
$248$	−23.7120			−1.50571
$249$	−3.16265	+	0.712521i	−0.200425	+	0.0451542i
$250$		−	27.5256i		−	1.74087i
$251$		−	15.5158i		−	0.979346i	−0.871906	−	0.489673i	$-0.837116\pi$
$251$		−	15.5158i		−	0.979346i	0.871906	−	0.489673i	$-0.162884\pi$
$252$	31.8160	+	67.0268i	2.00422	+	4.22229i
$253$	−2.43410	−	0.438893i	−0.153031	−	0.0275930i
$254$		−	29.4831i		−	1.84993i
$255$	−2.71265	−	12.0406i	−0.169873	−	0.754011i
$256$	25.2935			1.58085
$257$			7.59761i			0.473926i	0.971519	+	0.236963i	$0.0761520\pi$
$257$			7.59761i			0.473926i	−0.971519	+	0.236963i	$0.923848\pi$
$258$	−6.91482	−	30.6927i	−0.430498	−	1.91084i
$259$		−	42.1373i		−	2.61828i
$260$	12.7696			0.791940
$261$	−11.2585	+	5.34416i	−0.696885	+	0.330795i
$262$	58.3430			3.60444
$263$	6.37999			0.393407			0.196703	−	0.980463i	$-0.436976\pi$
$263$	6.37999			0.393407			0.196703	+	0.980463i	$0.436976\pi$
$264$	2.22839	+	51.5520i	0.137148	+	3.17281i
$265$	−16.3611			−1.00506
$266$	11.4156			0.699938
$267$	−2.62221	−	11.6392i	−0.160477	−	0.712306i
$268$	43.0286			2.62839
$269$		−	27.4691i		−	1.67482i	−0.546576	−	0.837409i	$-0.684069\pi$
$269$		−	27.4691i		−	1.67482i	0.546576	−	0.837409i	$-0.315931\pi$
$270$	20.8165	+	26.5588i	1.26685	+	1.61632i
$271$			10.7347i			0.652088i	0.945355	+	0.326044i	$0.105716\pi$
$271$			10.7347i			0.652088i	−0.945355	+	0.326044i	$0.894284\pi$
$272$	−40.5601			−2.45932
$273$	7.85505	−	1.76968i	0.475409	−	0.107106i
$274$			57.4031i			3.46785i
$275$	−0.448152	+	2.48545i	−0.0270246	+	0.149878i
$276$	1.51028	+	6.70365i	0.0909081	+	0.403512i
$277$			12.1941i			0.732671i	0.930483	+	0.366336i	$0.119388\pi$
$277$			12.1941i			0.732671i	−0.930483	+	0.366336i	$0.880612\pi$
$278$			41.8099i			2.50759i
$279$	−7.15437	+	3.39601i	−0.428321	+	0.203314i
$280$	100.231			5.98993
$281$	29.1873			1.74117			0.870583	−	0.492022i	$-0.163742\pi$
$281$	29.1873			1.74117			0.870583	+	0.492022i	$0.163742\pi$
$282$	−6.54668	−	29.0586i	−0.389849	−	1.73042i
$283$		−	11.3887i		−	0.676989i	−0.940968	−	0.338494i	$-0.890082\pi$
$283$		−	11.3887i		−	0.676989i	0.940968	−	0.338494i	$-0.109918\pi$
$284$			0.0716346i			0.00425073i
$285$	3.68113	−	0.829330i	0.218052	−	0.0491253i
$286$	8.83089	+	1.59230i	0.522181	+	0.0941545i
$287$		−	21.3244i		−	1.25874i
$288$	51.4919	−	24.4420i	3.03419	−	1.44026i
$289$	−8.18662			−0.481566
$290$			26.9778i			1.58419i
$291$	−22.7397	+	5.12307i	−1.33302	+	0.300320i
$292$		−	25.5814i		−	1.49704i
$293$	−16.9662			−0.991178			−0.495589	−	0.868557i	$-0.665048\pi$
$293$	−16.9662			−0.991178			−0.495589	+	0.868557i	$0.665048\pi$
$294$	66.7961	−	15.0486i	3.89563	−	0.877654i
$295$	−13.4879			−0.785294
$296$	−81.4181			−4.73233
$297$	8.05558	+	15.2351i	0.467432	+	0.884029i
$298$	34.3385			1.98918
$299$	0.745744			0.0431275
$300$	6.84508	−	1.54214i	0.395201	−	0.0890355i
$301$	−31.2111			−1.79898
$302$		−	12.0516i		−	0.693489i
$303$	8.62806	−	1.94383i	0.495669	−	0.111670i
$304$		−	12.4003i		−	0.711207i
$305$	−13.8428			−0.792636
$306$	−21.7683	+	10.3329i	−1.24441	+	0.590692i
$307$		−	27.4337i		−	1.56572i	−0.622196	−	0.782862i	$-0.713759\pi$
$307$		−	27.4337i		−	1.56572i	0.622196	−	0.782862i	$-0.286241\pi$
$308$	80.7235	+	14.5553i	4.59965	+	0.829363i
$309$	5.35013	−	1.20534i	0.304358	−	0.0685694i
$310$			17.1434i			0.973680i
$311$			4.04707i			0.229488i	0.993395	+	0.114744i	$0.0366048\pi$
$311$			4.04707i			0.229488i	−0.993395	+	0.114744i	$0.963395\pi$
$312$	−3.41940	−	15.1776i	−0.193585	−	0.859263i
$313$	24.0372			1.35866			0.679332	−	0.733831i	$-0.262270\pi$
$313$	24.0372			1.35866			0.679332	+	0.733831i	$0.262270\pi$
$314$	37.2454			2.10188
$315$	30.2415	−	14.3549i	1.70392	−	0.808809i
$316$			43.4790i			2.44589i
$317$		−	4.26641i		−	0.239625i	−0.992797	−	0.119813i	$-0.961771\pi$
$317$		−	4.26641i		−	0.239625i	0.992797	−	0.119813i	$-0.0382294\pi$
$318$	7.02033	+	31.1610i	0.393681	+	1.74742i
$319$	−2.44486	+	13.5592i	−0.136886	+	0.759168i
$320$		−	57.7976i		−	3.23099i
$321$	−21.2941	+	4.79740i	−1.18852	+	0.267765i
$322$	9.37962			0.522706
$323$			2.69449i			0.149925i
$324$	30.2711	−	37.0966i	1.68173	−	2.06092i
$325$		−	0.761477i		−	0.0422391i
$326$	−24.7082			−1.36846
$327$	5.34670	+	23.7323i	0.295673	+	1.31240i
$328$	−41.2033			−2.27507
$329$	−29.5495			−1.62911
$330$	37.2713	−	1.61109i	2.05172	−	0.0886875i
$331$	−10.1438			−0.557556			−0.278778	−	0.960356i	$-0.589929\pi$
$331$	−10.1438			−0.557556			−0.278778	+	0.960356i	$0.589929\pi$
$332$	9.95758			0.546493
$333$	−24.5654	+	11.6606i	−1.34618	+	0.638999i
$334$	−15.9658			−0.873612
$335$		−	19.4139i		−	1.06069i
$336$	−24.1781	−	107.319i	−1.31902	−	5.85473i
$337$		−	10.7437i		−	0.585245i	−0.956228	−	0.292622i	$-0.905472\pi$
$337$		−	10.7437i		−	0.585245i	0.956228	−	0.292622i	$-0.0945279\pi$
$338$	−2.70555			−0.147163
$339$	−1.09051	−	4.84044i	−0.0592285	−	0.262896i
$340$			37.9097i			2.05594i
$341$	−1.55361	+	8.61635i	−0.0841329	+	0.466601i
$342$	−3.15904	−	6.65515i	−0.170822	−	0.359869i
$343$		−	35.3829i		−	1.91050i
$344$			60.3064i			3.25151i
$345$	3.02459	−	0.681416i	0.162838	−	0.0366862i
$346$	−35.4257			−1.90450
$347$	−15.0847			−0.809788			−0.404894	−	0.914364i	$-0.632692\pi$
$347$	−15.0847			−0.809788			−0.404894	+	0.914364i	$0.632692\pi$
$348$	37.3427	−	8.41302i	2.00178	−	0.450985i
$349$			20.5817i			1.10171i	0.834600	+	0.550856i	$0.185699\pi$
$349$			20.5817i			1.10171i	−0.834600	+	0.550856i	$0.814301\pi$
$350$		−	9.57749i		−	0.511939i
$351$	−3.20542	−	4.08965i	−0.171093	−	0.218290i
$352$	11.1818	−	62.0142i	0.595991	−	3.30537i
$353$		−	19.7474i		−	1.05105i	−0.850779	−	0.525524i	$-0.823869\pi$
$353$		−	19.7474i		−	1.05105i	0.850779	−	0.525524i	$-0.176131\pi$
$354$	5.78745	+	25.6887i	0.307600	+	1.36534i
$355$	0.0323205			0.00171539
$356$			36.6458i			1.94223i
$357$	5.25371	+	23.3196i	0.278056	+	1.23420i
$358$			60.9842i			3.22311i
$359$	−15.2603			−0.805408			−0.402704	−	0.915330i	$-0.631930\pi$
$359$	−15.2603			−0.805408			−0.402704	+	0.915330i	$0.631930\pi$
$360$	−27.7368	−	58.4329i	−1.46186	−	3.07969i
$361$	18.1762			0.956643
$362$	6.62322			0.348109
$363$	18.8787	+	2.56795i	0.990875	+	0.134783i
$364$	−24.7316			−1.29629
$365$	−11.5419			−0.604133
$366$	5.93974	+	26.3646i	0.310475	+	1.37810i
$367$	15.8794			0.828898			0.414449	−	0.910073i	$-0.363974\pi$
$367$	15.8794			0.828898			0.414449	+	0.910073i	$0.363974\pi$
$368$		−	10.1887i		−	0.531121i
$369$	−12.4318	+	5.90110i	−0.647175	+	0.307199i
$370$			58.8640i			3.06019i
$371$	31.6874			1.64513
$372$	23.7299	−	5.34616i	1.23034	−	0.277185i
$373$			19.6181i			1.01579i	0.861420	+	0.507894i	$0.169576\pi$
$373$			19.6181i			1.01579i	−0.861420	+	0.507894i	$0.830424\pi$
$374$	−4.72711	+	26.2166i	−0.244433	+	1.35563i
$375$	3.87290	+	17.1906i	0.199996	+	0.887719i
$376$			57.0958i			2.94449i
$377$		−	4.15417i		−	0.213951i
$378$	−40.3163	−	51.4377i	−2.07364	−	2.64567i
$379$	−12.0138			−0.617106			−0.308553	−	0.951207i	$-0.599845\pi$
$379$	−12.0138			−0.617106			−0.308553	+	0.951207i	$0.599845\pi$
$380$	−11.5900			−0.594555
$381$	4.14833	+	18.4131i	0.212525	+	0.943333i
$382$		−	53.1177i		−	2.71774i
$383$		−	20.5930i		−	1.05225i	−0.850407	−	0.526125i	$-0.823644\pi$
$383$		−	20.5930i		−	1.05225i	0.850407	−	0.526125i	$-0.176356\pi$
$384$	−45.8731	+	10.3348i	−2.34095	+	0.527398i
$385$	6.56712	−	36.4213i	0.334691	−	1.85620i
$386$			42.8132i			2.17913i
$387$	8.63703	+	18.1956i	0.439045	+	0.924935i
$388$	71.5957			3.63472
$389$		−	9.37067i		−	0.475112i	−0.971374	−	0.237556i	$-0.923654\pi$
$389$		−	9.37067i		−	0.475112i	0.971374	−	0.237556i	$-0.0763463\pi$
$390$	−10.9732	+	2.47217i	−0.555648	+	0.125183i
$391$			2.21392i			0.111963i
$392$	−131.244			−6.62883
$393$	−36.4370	+	8.20896i	−1.83800	+	0.414087i
$394$	15.9710			0.804606
$395$	19.6171			0.987044
$396$	−13.8531	−	51.0885i	−0.696144	−	2.56729i
$397$	8.54019			0.428620			0.214310	−	0.976766i	$-0.431250\pi$
$397$	8.54019			0.428620			0.214310	+	0.976766i	$0.431250\pi$
$398$	25.4251			1.27445
$399$	−7.12942	+	1.60620i	−0.356918	+	0.0804106i
$400$	−10.4036			−0.520181
$401$		−	0.437486i		−	0.0218470i	−0.999940	−	0.0109235i	$-0.996523\pi$
$401$		−	0.437486i		−	0.0218470i	0.999940	−	0.0109235i	$-0.00347713\pi$
$402$	−36.9752	+	8.33023i	−1.84416	+	0.415474i
$403$		−	2.63982i		−	0.131499i
$404$	−27.1654			−1.35153
$405$	−16.7374	−	13.6579i	−0.831689	−	0.678667i
$406$		−	52.2492i		−	2.59308i
$407$	−5.33452	+	29.5853i	−0.264423	+	1.46649i
$408$	45.0583	−	10.1513i	2.23072	−	0.502563i
$409$		−	14.4152i		−	0.712783i	−0.934337	−	0.356392i	$-0.884007\pi$
$409$		−	14.4152i		−	0.712783i	0.934337	−	0.356392i	$-0.115993\pi$
$410$			29.7893i			1.47119i
$411$	−8.07673	−	35.8500i	−0.398395	−	1.76835i
$412$	−16.8448			−0.829885
$413$	26.1226			1.28541
$414$	−2.59562	−	5.46818i	−0.127568	−	0.268746i
$415$		−	4.49272i		−	0.220539i
$416$			18.9995i			0.931527i
$417$	−5.88272	−	26.1116i	−0.288078	−	1.27869i
$418$	−8.01511	−	1.44520i	−0.392032	−	0.0706873i
$419$			40.5181i			1.97944i	0.143017	+	0.989720i	$0.454320\pi$
$419$			40.5181i			1.97944i	−0.143017	+	0.989720i	$0.545680\pi$
$420$	−100.306	+	22.5982i	−4.89444	+	1.10268i
$421$	−14.5428			−0.708771			−0.354386	−	0.935099i	$-0.615310\pi$
$421$	−14.5428			−0.708771			−0.354386	+	0.935099i	$0.615310\pi$
$422$		−	0.620769i		−	0.0302186i
$423$	8.17720	+	17.2269i	0.397589	+	0.837600i
$424$		−	61.2267i		−	2.97343i
$425$	2.26062			0.109656
$426$	−0.0138683	−	0.0615568i	−0.000671919	−	0.00298244i
$427$	26.8100			1.29742
$428$	67.0444			3.24071
$429$	−5.73920	+	0.248083i	−0.277091	+	0.0119776i
$430$	43.6006			2.10261
$431$	−18.9139			−0.911049			−0.455524	−	0.890223i	$-0.650548\pi$
$431$	−18.9139			−0.911049			−0.455524	+	0.890223i	$0.650548\pi$
$432$	−55.8746	+	43.7938i	−2.68827	+	2.10703i
$433$	−29.8901			−1.43643			−0.718213	−	0.695824i	$-0.755040\pi$
$433$	−29.8901			−1.43643			−0.718213	+	0.695824i	$0.755040\pi$
$434$		−	33.2024i		−	1.59377i
$435$	−3.79583	−	16.8485i	−0.181996	−	0.807824i
$436$		−	74.7210i		−	3.57849i
$437$	−0.676854			−0.0323783
$438$	4.95248	+	21.9825i	0.236639	+	1.05036i
$439$			28.1904i			1.34545i	0.739891	+	0.672727i	$0.234877\pi$
$439$			28.1904i			1.34545i	−0.739891	+	0.672727i	$0.765123\pi$
$440$	−70.3736	−	12.6891i	−3.35493	−	0.604927i
$441$	−39.5989	+	18.7967i	−1.88566	+	0.895080i
$442$		−	8.03206i		−	0.382046i
$443$			18.4814i			0.878079i	0.898468	+	0.439039i	$0.144681\pi$
$443$			18.4814i			0.878079i	−0.898468	+	0.439039i	$0.855319\pi$
$444$	81.4795	−	18.3567i	3.86685	−	0.871170i
$445$	16.5341			0.783790
$446$	15.9733			0.756359
$447$	−21.4455	+	4.83150i	−1.01434	+	0.228522i
$448$			111.939i			5.28864i
$449$		−	27.7393i		−	1.30910i	−0.756019	−	0.654550i	$-0.772858\pi$
$449$		−	27.7393i		−	1.30910i	0.756019	−	0.654550i	$-0.227142\pi$
$450$	−5.58354	+	2.65037i	−0.263210	+	0.124940i
$451$	−2.69965	+	14.9722i	−0.127121	+	0.705016i
$452$			15.2401i			0.716832i
$453$	1.69568	+	7.52657i	0.0796698	+	0.353629i
$454$	−5.54821			−0.260390
$455$			11.1585i			0.523119i
$456$	3.10352	+	13.7755i	0.145336	+	0.645099i
$457$		−	9.88017i		−	0.462175i	−0.972933	−	0.231088i	$-0.925772\pi$
$457$		−	9.88017i		−	0.462175i	0.972933	−	0.231088i	$-0.0742284\pi$
$458$	40.5216			1.89345
$459$	12.1411	−	9.51604i	0.566698	−	0.444171i
$460$	−9.52289			−0.444007
$461$	−0.122017			−0.00568292			−0.00284146	−	0.999996i	$-0.500904\pi$
$461$	−0.122017			−0.00568292			−0.00284146	+	0.999996i	$0.500904\pi$
$462$	−72.1850	+	3.12027i	−3.35835	+	0.145168i
$463$	−32.4447			−1.50784			−0.753918	−	0.656969i	$-0.771838\pi$
$463$	−32.4447			−1.50784			−0.753918	+	0.656969i	$0.771838\pi$
$464$	−56.7561			−2.63483
$465$	−2.41211	−	10.7066i	−0.111859	−	0.496506i
$466$	−29.6033			−1.37135
$467$			2.06150i			0.0953948i	0.998862	+	0.0476974i	$0.0151883\pi$
$467$			2.06150i			0.0953948i	−0.998862	+	0.0476974i	$0.984812\pi$
$468$	6.84395	+	14.4181i	0.316362	+	0.666478i
$469$			37.5998i			1.73620i
$470$	41.2793			1.90407
$471$	−23.2609	+	5.24050i	−1.07181	+	0.241469i
$472$		−	50.4743i		−	2.32327i
$473$	21.9138	+	3.95128i	1.00760	+	0.181680i
$474$	−8.41742	−	37.3623i	−0.386625	−	1.71611i
$475$			0.691134i			0.0317114i
$476$		−	73.4214i		−	3.36526i
$477$	−8.76883	−	18.4733i	−0.401497	−	0.845833i
$478$	−59.5142			−2.72212
$479$	−19.1463			−0.874815			−0.437408	−	0.899263i	$-0.644103\pi$
$479$	−19.1463			−0.874815			−0.437408	+	0.899263i	$0.644103\pi$
$480$	17.3606	+	77.0582i	0.792399	+	3.51721i
$481$		−	9.06415i		−	0.413290i
$482$			9.60062i			0.437296i
$483$	−5.85786	+	1.31973i	−0.266542	+	0.0600498i
$484$	−54.8347	−	20.4390i	−2.49249	−	0.929045i
$485$		−	32.3029i		−	1.46680i
$486$	−18.8307	+	37.7381i	−0.854179	+	1.71184i
$487$	7.65812			0.347022			0.173511	−	0.984832i	$-0.444489\pi$
$487$	7.65812			0.347022			0.173511	+	0.984832i	$0.444489\pi$
$488$		−	51.8025i		−	2.34499i
$489$	15.4310	−	3.47649i	0.697815	−	0.157212i
$490$			94.8874i			4.28658i
$491$	15.4009			0.695031			0.347516	−	0.937674i	$-0.387025\pi$
$491$	15.4009			0.695031			0.347516	+	0.937674i	$0.387025\pi$
$492$	41.2344	−	9.28978i	1.85899	−	0.418815i
$493$	12.3326			0.555434
$494$	2.45562			0.110483
$495$	−23.0504	+	6.25031i	−1.03604	+	0.280931i
$496$	−36.0663			−1.61943
$497$	−0.0625966			−0.00280784
$498$	−8.55672	+	1.92776i	−0.383436	+	0.0863850i
$499$	−14.3159			−0.640868			−0.320434	−	0.947271i	$-0.603829\pi$
$499$	−14.3159			−0.640868			−0.320434	+	0.947271i	$0.603829\pi$
$500$		−	54.1244i		−	2.42052i
$501$	9.97116	−	2.24642i	0.445479	−	0.100363i
$502$		−	41.9787i		−	1.87360i
$503$	−12.7139			−0.566885			−0.283442	−	0.958989i	$-0.591476\pi$
$503$	−12.7139			−0.566885			−0.283442	+	0.958989i	$0.591476\pi$
$504$	53.7191	+	113.170i	2.39284	+	5.04098i
$505$			12.2566i			0.545412i
$506$	−6.58559	−	1.18745i	−0.292765	−	0.0527885i
$507$	1.68970	−	0.380676i	0.0750422	−	0.0169064i
$508$		−	57.9735i		−	2.57216i
$509$		−	10.7626i		−	0.477045i	−0.971137	−	0.238523i	$-0.923337\pi$
$509$		−	10.7626i		−	0.477045i	0.971137	−	0.238523i	$-0.0766631\pi$
$510$	−7.33921	−	32.5764i	−0.324986	−	1.44251i
$511$	22.3538			0.988874
$512$	14.1356			0.624712
$513$	2.90931	+	3.71186i	0.128449	+	0.163883i
$514$			20.5557i			0.906674i
$515$			7.60014i			0.334902i
$516$	−13.5968	−	60.3519i	−0.598566	−	2.65685i
$517$	20.7472	+	3.74092i	0.912459	+	0.164526i
$518$		−	114.005i		−	5.00907i
$519$	22.1244	−	4.98446i	0.971155	−	0.218794i
$520$	21.5606			0.945495
$521$		−	13.0706i		−	0.572632i	−0.958135	−	0.286316i	$-0.907569\pi$
$521$		−	13.0706i		−	0.572632i	0.958135	−	0.286316i	$-0.0924307\pi$
$522$	−30.4605	+	14.4589i	−1.33322	+	0.632849i
$523$			4.52508i			0.197868i	0.995094	+	0.0989339i	$0.0315432\pi$
$523$			4.52508i			0.197868i	−0.995094	+	0.0989339i	$0.968457\pi$
$524$	114.722			5.01163
$525$	1.34757	+	5.98144i	0.0588128	+	0.261052i
$526$	17.2614			0.752632
$527$	7.83693			0.341382
$528$	3.38942	+	78.4114i	0.147505	+	3.41242i
$529$	22.4439			0.975820
$530$	−44.2659			−1.92279
$531$	−7.22889	−	15.2291i	−0.313707	−	0.660885i
$532$	22.4469			0.973197
$533$		−	4.58710i		−	0.198689i
$534$	−7.09453	−	31.4904i	−0.307010	−	1.36272i
$535$		−	30.2495i		−	1.30780i
$536$	72.6507			3.13803
$537$	−8.58058	−	38.0865i	−0.370279	−	1.64355i
$538$		−	74.3189i		−	3.20412i
$539$	−8.59913	+	47.6908i	−0.370391	+	2.05419i
$540$	40.9321	+	52.2234i	1.76144	+	2.24734i
$541$			8.78739i			0.377799i	0.981996	+	0.188900i	$0.0604921\pi$
$541$			8.78739i			0.377799i	−0.981996	+	0.188900i	$0.939508\pi$
$542$			29.0434i			1.24752i
$543$	−4.13640	+	0.931899i	−0.177510	+	0.0399916i
$544$	−56.4045			−2.41832
$545$	−33.7130			−1.44411
$546$	21.2522	−	4.78796i	0.909512	−	0.204906i
$547$			43.5328i			1.86133i	0.365875	+	0.930664i	$0.380770\pi$
$547$			43.5328i			1.86133i	−0.365875	+	0.930664i	$0.619230\pi$
$548$			112.873i			4.82172i
$549$	−7.41910	−	15.6298i	−0.316640	−	0.667064i
$550$	−1.21250	+	6.72452i	−0.0517011	+	0.286734i
$551$			3.77042i			0.160625i
$552$	2.55000	+	11.3186i	0.108535	+	0.481753i
$553$	−37.9933			−1.61564
$554$			32.9917i			1.40168i
$555$	−8.28227	−	36.7624i	−0.351563	−	1.56048i
$556$			82.2119i			3.48656i
$557$	15.9263			0.674817			0.337409	−	0.941358i	$-0.390450\pi$
$557$	15.9263			0.674817			0.337409	+	0.941358i	$0.390450\pi$
$558$	−19.3565	+	9.18808i	−0.819426	+	0.388963i
$559$	−6.71382			−0.283964
$560$	152.452			6.44229
$561$	−0.736493	−	17.0382i	−0.0310947	−	0.719352i
$562$	78.9676			3.33105
$563$	25.5134			1.07526			0.537630	−	0.843181i	$-0.319320\pi$
$563$	25.5134			1.07526			0.537630	+	0.843181i	$0.319320\pi$
$564$	−12.8729	−	57.1388i	−0.542048	−	2.40598i
$565$	6.87610			0.289280
$566$		−	30.8127i		−	1.29516i
$567$	32.4161	+	26.4519i	1.36135	+	1.11087i
$568$			0.120950i			0.00507494i
$569$	39.9270			1.67383			0.836913	−	0.547336i	$-0.184358\pi$
$569$	39.9270			1.67383			0.836913	+	0.547336i	$0.184358\pi$
$570$	9.95950	−	2.24379i	0.417157	−	0.0939822i
$571$			24.5956i			1.02929i	0.857402	+	0.514647i	$0.172077\pi$
$571$			24.5956i			1.02929i	−0.857402	+	0.514647i	$0.827923\pi$
$572$	17.3644	+	3.13098i	0.726044	+	0.130913i
$573$	7.47376	+	33.1737i	0.312221	+	1.38585i
$574$		−	57.6943i		−	2.40812i
$575$			0.567867i			0.0236817i
$576$	65.2589	−	30.9769i	2.71912	−	1.29070i
$577$	38.2383			1.59188			0.795941	−	0.605374i	$-0.206976\pi$
$577$	38.2383			1.59188			0.795941	+	0.605374i	$0.206976\pi$
$578$	−22.1493			−0.921290
$579$	−6.02389	−	26.7382i	−0.250344	−	1.11120i
$580$			53.0473i			2.20267i
$581$			8.70125i			0.360989i
$582$	−61.5234	+	13.8607i	−2.55023	+	0.574545i
$583$	−22.2482	−	4.01158i	−0.921428	−	0.166143i
$584$		−	43.1923i		−	1.78731i
$585$	6.50525	−	3.08789i	0.268959	−	0.127669i
$586$	−45.9030			−1.89624
$587$			7.39147i			0.305079i	0.988297	+	0.152539i	$0.0487451\pi$
$587$			7.39147i			0.305079i	−0.988297	+	0.152539i	$0.951255\pi$
$588$	131.343	−	29.5906i	5.41650	−	1.22029i
$589$			2.39596i			0.0987238i
$590$	−36.4921			−1.50236
$591$	−9.97437	+	2.24715i	−0.410291	+	0.0924352i
$592$	−123.838			−5.08972
$593$	10.0660			0.413362			0.206681	−	0.978408i	$-0.433734\pi$
$593$	10.0660			0.413362			0.206681	+	0.978408i	$0.433734\pi$
$594$	21.7948	+	41.2193i	0.894250	+	1.69125i
$595$	−33.1267			−1.35806
$596$	67.5209			2.76576
$597$	−15.8788	+	3.57736i	−0.649875	+	0.146412i
$598$	2.01765			0.0825078
$599$		−	4.65033i		−	0.190008i	−0.995477	−	0.0950038i	$-0.969714\pi$
$599$		−	4.65033i		−	0.190008i	0.995477	−	0.0950038i	$-0.0302863\pi$
$600$	11.5574	−	2.60379i	0.471829	−	0.106299i
$601$			8.64295i			0.352553i	0.984341	+	0.176277i	$0.0564053\pi$
$601$			8.64295i			0.352553i	−0.984341	+	0.176277i	$0.943595\pi$
$602$	−84.4432			−3.44165
$603$	21.9201	−	10.4050i	0.892656	−	0.423723i
$604$		−	23.6973i		−	0.964230i
$605$	−9.22177	+	24.7406i	−0.374918	+	1.00585i
$606$	23.3436	−	5.25914i	0.948271	−	0.213638i
$607$			32.9707i			1.33824i	0.743155	+	0.669120i	$0.233329\pi$
$607$			32.9707i			1.33824i	−0.743155	+	0.669120i	$0.766671\pi$
$608$		−	17.2444i		−	0.699352i
$609$	7.35156	+	32.6313i	0.297900	+	1.32229i
$610$	−37.4524			−1.51640
$611$	−6.35638			−0.257152
$612$	−42.8036	+	20.3179i	−1.73023	+	0.821301i
$613$			23.5803i			0.952398i	0.879338	+	0.476199i	$0.157986\pi$
$613$			23.5803i			0.952398i	−0.879338	+	0.476199i	$0.842014\pi$
$614$		−	74.2232i		−	2.99541i
$615$	−4.19141	−	18.6044i	−0.169014	−	0.750200i
$616$	136.296	+	24.5755i	5.49151	+	0.990175i
$617$		−	12.0090i		−	0.483465i	−0.970343	−	0.241732i	$-0.922284\pi$
$617$		−	12.0090i		−	0.483465i	0.970343	−	0.241732i	$-0.0777156\pi$
$618$	14.4750	−	3.26111i	0.582271	−	0.131181i
$619$	33.8834			1.36189			0.680944	−	0.732336i	$-0.261570\pi$
$619$	33.8834			1.36189			0.680944	+	0.732336i	$0.261570\pi$
$620$			33.7096i			1.35381i
$621$	2.39042	+	3.04984i	0.0959245	+	0.122386i
$622$			10.9496i			0.439037i
$623$	−32.0223			−1.28295
$624$	−5.20095	−	23.0854i	−0.208205	−	0.924155i
$625$	−28.2275			−1.12910
$626$	65.0339			2.59928
$627$	5.20903	−	0.225166i	0.208029	−	0.00899225i
$628$	73.2368			2.92247
$629$	26.9091			1.07293
$630$	81.8199	−	38.8380i	3.25978	−	1.54734i
$631$	26.8591			1.06924			0.534621	−	0.845092i	$-0.320454\pi$
$631$	26.8591			1.06924			0.534621	+	0.845092i	$0.320454\pi$
$632$			73.4112i			2.92014i
$633$	0.0873433	+	0.387689i	0.00347159	+	0.0154093i
$634$		−	11.5430i		−	0.458430i
$635$	−26.1568			−1.03800
$636$	13.8043	+	61.2729i	0.547376	+	2.42963i
$637$		−	14.6112i		−	0.578917i
$638$	−6.61468	+	36.6850i	−0.261878	+	1.45237i
$639$	0.0173223	+	0.0364929i	0.000685260	+	0.00144364i
$640$		−	65.1651i		−	2.57588i
$641$			20.2051i			0.798053i	0.916939	+	0.399027i	$0.130652\pi$
$641$			20.2051i			0.798053i	−0.916939	+	0.399027i	$0.869348\pi$
$642$	−57.6124	+	12.9796i	−2.27378	+	0.512264i
$643$	−25.2247			−0.994765			−0.497382	−	0.867531i	$-0.665705\pi$
$643$	−25.2247			−0.994765			−0.497382	+	0.867531i	$0.665705\pi$
$644$	18.4434			0.726772
$645$	−27.2299	+	6.13468i	−1.07218	+	0.241553i
$646$			7.29008i			0.286824i
$647$			27.8084i			1.09326i	0.837374	+	0.546631i	$0.184090\pi$
$647$			27.8084i			1.09326i	−0.837374	+	0.546631i	$0.815910\pi$
$648$	51.1106	−	62.6348i	2.00781	−	2.46053i
$649$	−18.3411	−	3.30708i	−0.719951	−	0.129814i
$650$		−	2.06021i		−	0.0808083i
$651$	4.67164	+	20.7359i	0.183096	+	0.812705i
$652$	−48.5844			−1.90271
$653$		−	34.9648i		−	1.36828i	−0.729351	−	0.684140i	$-0.760178\pi$
$653$		−	34.9648i		−	1.36828i	0.729351	−	0.684140i	$-0.239822\pi$
$654$	14.4658	+	64.2090i	0.565656	+	2.51077i
$655$		−	51.7607i		−	2.02246i
$656$	−62.6709			−2.44689
$657$	−6.18595	−	13.0319i	−0.241337	−	0.508424i
$658$	−79.9475			−3.11668
$659$	−50.7710			−1.97776			−0.988879	−	0.148720i	$-0.952485\pi$
$659$	−50.7710			−1.97776			−0.988879	+	0.148720i	$0.952485\pi$
$660$	73.2876	−	3.16793i	2.85272	−	0.123312i
$661$	−17.8821			−0.695532			−0.347766	−	0.937581i	$-0.613060\pi$
$661$	−17.8821			−0.695532			−0.347766	+	0.937581i	$0.613060\pi$
$662$	−27.4447			−1.06667
$663$	1.13013	+	5.01627i	0.0438904	+	0.194816i
$664$	16.8126			0.652457
$665$		−	10.1277i		−	0.392736i
$666$	−66.4629	+	31.5484i	−2.57539	+	1.22248i
$667$			3.09795i			0.119953i
$668$	−31.3941			−1.21467
$669$	−9.97584	+	2.24748i	−0.385688	+	0.0868925i
$670$		−	52.5253i		−	2.02923i
$671$	−18.8237	−	3.39410i	−0.726682	−	0.131028i
$672$	−33.6230	−	149.242i	−1.29704	−	5.75714i
$673$		−	34.4034i		−	1.32615i	−0.748552	−	0.663077i	$-0.769250\pi$
$673$		−	34.4034i		−	1.32615i	0.748552	−	0.663077i	$-0.230750\pi$
$674$		−	29.0675i		−	1.11964i
$675$	3.11418	−	2.44085i	0.119865	−	0.0939485i
$676$	−5.32000			−0.204615
$677$	−32.3052			−1.24159			−0.620795	−	0.783973i	$-0.713190\pi$
$677$	−32.3052			−1.24159			−0.620795	+	0.783973i	$0.713190\pi$
$678$	−2.95043	−	13.0960i	−0.113311	−	0.502951i
$679$			62.5625i			2.40093i
$680$			64.0077i			2.45458i
$681$	3.46503	−	0.780643i	0.132780	−	0.0299143i
$682$	−4.20338	+	23.3120i	−0.160956	+	0.892661i
$683$		−	27.4993i		−	1.05223i	−0.850413	−	0.526116i	$-0.823648\pi$
$683$		−	27.4993i		−	1.05223i	0.850413	−	0.526116i	$-0.176352\pi$
$684$	−6.21172	−	13.0862i	−0.237511	−	0.500364i
$685$	50.9269			1.94582
$686$		−	95.7301i		−	3.65499i
$687$	−25.3070	+	5.70146i	−0.965522	+	0.217524i
$688$			91.7270i			3.49706i
$689$	6.81627			0.259679
$690$	8.18318	−	1.84360i	0.311528	−	0.0701848i
$691$	35.6772			1.35722			0.678612	−	0.734497i	$-0.262582\pi$
$691$	35.6772			1.35722			0.678612	+	0.734497i	$0.262582\pi$
$692$	−69.6586			−2.64802
$693$	44.6427	−	12.1053i	1.69584	−	0.459841i
$694$	−40.8124			−1.54922
$695$	37.0928			1.40701
$696$	63.0505	−	14.2048i	2.38992	−	0.538430i
$697$	13.6179			0.515814
$698$			55.6848i			2.10770i
$699$	18.4882	−	4.16524i	0.699287	−	0.157544i
$700$		−	18.8325i		−	0.711802i
$701$	33.0189			1.24711			0.623554	−	0.781780i	$-0.285688\pi$
$701$	33.0189			1.24711			0.623554	+	0.781780i	$0.285688\pi$
$702$	−8.67243	−	11.0648i	−0.327320	−	0.417613i
$703$			8.22683i			0.310281i
$704$	14.1714	−	78.5945i	0.534104	−	2.96214i
$705$	−25.7802	+	5.80807i	−0.970939	+	0.218745i
$706$		−	53.4276i		−	2.01077i
$707$		−	23.7379i		−	0.892757i
$708$	11.3800	+	50.5124i	0.427688	+	1.89837i
$709$	27.3389			1.02673			0.513367	−	0.858169i	$-0.328398\pi$
$709$	27.3389			1.02673			0.513367	+	0.858169i	$0.328398\pi$
$710$	0.0874447			0.00328174
$711$	10.5139	+	22.1495i	0.394301	+	0.830673i
$712$			61.8738i			2.31882i
$713$			1.96863i			0.0737258i
$714$	14.2142	+	63.0922i	0.531952	+	2.36117i
$715$	1.41265	−	7.83458i	0.0528302	−	0.292997i
$716$			119.915i			4.48143i
$717$	37.1685	−	8.37375i	1.38808	−	0.312724i
$718$	−41.2875			−1.54084
$719$			27.5207i			1.02635i	0.858285	+	0.513174i	$0.171530\pi$
$719$			27.5207i			1.02635i	−0.858285	+	0.513174i	$0.828470\pi$
$720$	−42.1881	−	88.8774i	−1.57226	−	3.31227i
$721$		−	14.7195i		−	0.548184i
$722$	49.1767			1.83017
$723$	−1.35082	−	5.99588i	−0.0502377	−	0.222989i
$724$	13.0234			0.484012
$725$	3.16331			0.117482
$726$	51.0773	+	6.94773i	1.89566	+	0.257854i
$727$	23.5273			0.872580			0.436290	−	0.899806i	$-0.356292\pi$
$727$	23.5273			0.872580			0.436290	+	0.899806i	$0.356292\pi$
$728$	−41.7574			−1.54763
$729$	6.45055	−	26.2181i	0.238909	−	0.971042i
$730$	−31.2273			−1.15577
$731$		−	19.9315i		−	0.737195i
$732$	11.6795	+	51.8416i	0.431686	+	1.91612i
$733$		−	40.4706i		−	1.49482i	−0.664365	−	0.747408i	$-0.731298\pi$
$733$		−	40.4706i		−	1.49482i	0.664365	−	0.747408i	$-0.268702\pi$
$734$	42.9625			1.58578
$735$	−13.3508	−	59.2601i	−0.492453	−	2.18584i
$736$		−	14.1688i		−	0.522268i
$737$	4.76008	−	26.3994i	0.175340	−	0.972436i
$738$	−33.6349	+	15.9657i	−1.23812	+	0.587706i
$739$		−	21.7703i		−	0.800832i	−0.916333	−	0.400416i	$-0.868866\pi$
$739$		−	21.7703i		−	0.800832i	0.916333	−	0.400416i	$-0.131134\pi$
$740$			115.746i			4.25491i
$741$	−1.53361	+	0.345510i	−0.0563386	+	0.0126926i
$742$	85.7318			3.14731
$743$	−19.9234			−0.730918			−0.365459	−	0.930827i	$-0.619088\pi$
$743$	−19.9234			−0.730918			−0.365459	+	0.930827i	$0.619088\pi$
$744$	40.0662	−	9.02659i	1.46890	−	0.330931i
$745$		−	30.4644i		−	1.11613i
$746$			53.0778i			1.94332i
$747$	5.07270	−	2.40789i	0.185600	−	0.0881002i
$748$	−9.29505	+	51.5504i	−0.339861	+	1.88487i
$749$			58.5855i			2.14067i
$750$	10.4783	+	46.5100i	0.382615	+	1.69831i
$751$	16.4501			0.600272			0.300136	−	0.953896i	$-0.402968\pi$
$751$	16.4501			0.600272			0.300136	+	0.953896i	$0.402968\pi$
$752$			86.8436i			3.16686i
$753$	5.90647	+	26.2170i	0.215244	+	0.955399i
$754$		−	11.2393i		−	0.409312i
$755$	−10.6919			−0.389118
$756$	−79.2750	−	101.144i	−2.88321	−	3.67855i
$757$	−35.7661			−1.29994			−0.649970	−	0.759960i	$-0.725219\pi$
$757$	−35.7661			−1.29994			−0.649970	+	0.759960i	$0.725219\pi$
$758$	−32.5039			−1.18059
$759$	4.27998	−	0.185007i	0.155353	−	0.00671531i
$760$	−19.5689			−0.709838
$761$	−35.0961			−1.27223			−0.636117	−	0.771593i	$-0.719460\pi$
$761$	−35.0961			−1.27223			−0.636117	+	0.771593i	$0.719460\pi$
$762$	11.2235	+	49.8176i	0.406585	+	1.80470i
$763$	65.2935			2.36378
$764$		−	104.447i		−	3.77876i
$765$	9.16712	+	19.3123i	0.331438	+	0.698239i
$766$		−	55.7153i		−	2.01307i
$767$	5.61923			0.202899
$768$	−42.7385	+	9.62864i	−1.54219	+	0.347444i
$769$		−	39.6385i		−	1.42940i	−0.699431	−	0.714700i	$-0.746563\pi$
$769$		−	39.6385i		−	1.42940i	0.699431	−	0.714700i	$-0.253437\pi$
$770$	17.7677	−	98.5396i	0.640303	−	3.55112i
$771$	−2.89223	−	12.8377i	−0.104161	−	0.462338i
$772$			84.1848i			3.02988i
$773$		−	8.43042i		−	0.303221i	−0.988440	−	0.151611i	$-0.951554\pi$
$773$		−	8.43042i		−	0.303221i	0.988440	−	0.151611i	$-0.0484459\pi$
$774$	23.3679	+	49.2291i	0.839943	+	1.76950i
$775$	2.01016			0.0722072
$776$	120.884			4.33948
$777$	16.0406	+	71.1994i	0.575455	+	2.55426i
$778$		−	25.3528i		−	0.908943i
$779$			4.16335i			0.149168i
$780$	−21.5769	+	4.86109i	−0.772576	+	0.174055i
$781$	0.0439501	+	0.00792464i	0.00157266	+	0.000283566i
$782$			5.98986i			0.214197i
$783$	16.9891	−	13.3159i	0.607142	−	0.475871i
$784$	−199.624			−7.12945
$785$		−	33.0434i		−	1.17937i
$786$	−98.5821	+	22.2098i	−3.51631	+	0.792196i
$787$		−	18.8892i		−	0.673328i	−0.941625	−	0.336664i	$-0.890701\pi$
$787$		−	18.8892i		−	0.673328i	0.941625	−	0.336664i	$-0.109299\pi$
$788$	31.4042			1.11873
$789$	−10.7803	+	2.42871i	−0.383788	+	0.0864643i
$790$	53.0751			1.88833
$791$	−13.3173			−0.473507
$792$	−23.3899	−	86.2591i	−0.831124	−	3.06509i
$793$	5.76709			0.204795
$794$	23.1059			0.819998
$795$	27.6454	−	6.22829i	0.980482	−	0.220895i
$796$	49.9942			1.77200
$797$		−	7.57802i		−	0.268427i	−0.990952	−	0.134214i	$-0.957149\pi$
$797$		−	7.57802i		−	0.268427i	0.990952	−	0.134214i	$-0.0428508\pi$
$798$	−19.2890	+	4.34566i	−0.682824	+	0.153835i
$799$		−	18.8704i		−	0.667587i
$800$	−14.4677			−0.511510
$801$	8.86151	+	18.6685i	0.313106	+	0.659619i
$802$		−	1.18364i		−	0.0417958i
$803$	−15.6950	−	2.82996i	−0.553864	−	0.0998671i
$804$	−72.7055	+	16.3800i	−2.56413	+	0.577677i
$805$		−	8.32140i		−	0.293291i
$806$		−	7.14217i		−	0.251572i
$807$	10.4568	+	46.4145i	0.368097	+	1.63387i
$808$	−45.8667			−1.61359
$809$	−22.3252			−0.784914			−0.392457	−	0.919770i	$-0.628375\pi$
$809$	−22.3252			−0.784914			−0.392457	+	0.919770i	$0.628375\pi$
$810$	−45.2839	−	36.9521i	−1.59112	−	1.29837i
$811$			42.1574i			1.48035i	0.672416	+	0.740174i	$0.265257\pi$
$811$			42.1574i			1.48035i	−0.672416	+	0.740174i	$0.734743\pi$
$812$		−	102.739i		−	3.60544i
$813$	−4.08645	−	18.1385i	−0.143318	−	0.636144i
$814$	−14.4328	+	80.0445i	−0.505870	+	2.80556i
$815$			21.9206i			0.767844i
$816$	68.5344	−	15.4402i	2.39918	−	0.540517i
$817$	6.09361			0.213189
$818$		−	39.0009i		−	1.36364i
$819$	−12.5990	+	5.98046i	−0.440245	+	0.208974i
$820$			58.5756i			2.04555i
$821$	20.9868			0.732443			0.366221	−	0.930528i	$-0.380651\pi$
$821$	20.9868			0.732443			0.366221	+	0.930528i	$0.380651\pi$
$822$	−21.8520	−	96.9941i	−0.762176	−	3.38306i
$823$	−8.85694			−0.308733			−0.154367	−	0.988014i	$-0.549334\pi$
$823$	−8.85694			−0.308733			−0.154367	+	0.988014i	$0.549334\pi$
$824$	−28.4412			−0.990797
$825$	−0.188910	−	4.37027i	−0.00657699	−	0.152153i
$826$	70.6760			2.45913
$827$	11.5953			0.403209			0.201605	−	0.979467i	$-0.435384\pi$
$827$	11.5953			0.403209			0.201605	+	0.979467i	$0.435384\pi$
$828$	−5.10384	−	10.7522i	−0.177371	−	0.373666i
$829$	−10.6080			−0.368430			−0.184215	−	0.982886i	$-0.558974\pi$
$829$	−10.6080			−0.368430			−0.184215	+	0.982886i	$0.558974\pi$
$830$		−	12.1553i		−	0.421916i
$831$	−4.64199	−	20.6043i	−0.161029	−	0.714757i
$832$			24.0793i			0.834798i
$833$	43.3768			1.50292
$834$	−15.9160	−	70.6461i	−0.551126	−	2.44627i
$835$			14.1646i			0.490185i
$836$	−15.7604	−	2.84175i	−0.545083	−	0.0982839i
$837$	10.7960	−	8.46174i	0.373163	−	0.292480i
$838$			109.624i			3.78689i
$839$		−	14.1872i		−	0.489795i	−0.969549	−	0.244897i	$-0.921246\pi$
$839$		−	14.1872i		−	0.489795i	0.969549	−	0.244897i	$-0.0787543\pi$
$840$	−169.360	+	38.1554i	−5.84346	+	1.31649i
$841$	−11.7428			−0.404926
$842$	−39.3462			−1.35596
$843$	−49.3177	+	11.1109i	−1.69859	+	0.382679i
$844$		−	1.22064i		−	0.0420160i
$845$			2.40031i			0.0825731i
$846$	22.1238	+	46.6082i	0.760633	+	1.60242i
$847$	17.8602	−	47.9163i	0.613685	−	1.64642i
$848$		−	93.1268i		−	3.19799i
$849$	4.33541	+	19.2435i	0.148791	+	0.660436i
$850$	6.11623			0.209785
$851$			6.75954i			0.231714i
$852$	−0.0272696	−	0.121041i	−0.000934240	−	0.00414680i
$853$			4.40579i			0.150851i	0.997151	+	0.0754256i	$0.0240315\pi$
$853$			4.40579i			0.150851i	−0.997151	+	0.0754256i	$0.975968\pi$
$854$	72.5357			2.48212
$855$	−5.90431	+	2.80264i	−0.201923	+	0.0958482i
$856$	113.200			3.86908
$857$	−4.94679			−0.168979			−0.0844895	−	0.996424i	$-0.526926\pi$
$857$	−4.94679			−0.168979			−0.0844895	+	0.996424i	$0.526926\pi$
$858$	−15.5277	+	0.671201i	−0.530107	+	0.0229144i
$859$	−27.1208			−0.925351			−0.462676	−	0.886528i	$-0.653111\pi$
$859$	−27.1208			−0.925351			−0.462676	+	0.886528i	$0.653111\pi$
$860$	85.7331			2.92347
$861$	8.11770	+	36.0319i	0.276650	+	1.22796i
$862$	−51.1724			−1.74294
$863$		−	17.0607i		−	0.580752i	−0.956913	−	0.290376i	$-0.906220\pi$
$863$		−	17.0607i		−	0.580752i	0.956913	−	0.290376i	$-0.0937805\pi$
$864$	−77.7014	+	60.9014i	−2.64346	+	2.07191i
$865$			31.4289i			1.06862i
$866$	−80.8691			−2.74804
$867$	13.8329	−	3.11645i	0.469791	−	0.105840i
$868$		−	65.2869i		−	2.21598i
$869$	26.6758	+	4.80991i	0.904913	+	0.163165i
$870$	−10.2698	−	45.5845i	−0.348179	−	1.54546i
$871$			8.08809i			0.274054i
$872$		−	126.161i		−	4.27235i
$873$	36.4730	−	17.3129i	1.23442	−	0.585953i
$874$	−1.83126			−0.0619434
$875$	47.2956			1.59888
$876$	9.73821	+	43.2248i	0.329023	+	1.46043i
$877$		−	48.8134i		−	1.64831i	−0.566363	−	0.824156i	$-0.691650\pi$
$877$		−	48.8134i		−	1.64831i	0.566363	−	0.824156i	$-0.308350\pi$
$878$			76.2705i			2.57401i
$879$	28.6678	−	6.45863i	0.966942	−	0.217844i
$880$	−107.039	−	19.3003i	−3.60830	−	0.650612i
$881$			23.2768i			0.784215i	0.919919	+	0.392107i	$0.128254\pi$
$881$			23.2768i			0.784215i	−0.919919	+	0.392107i	$0.871746\pi$
$882$	−107.137	+	50.8553i	−3.60748	+	1.71239i
$883$	6.19019			0.208317			0.104158	−	0.994561i	$-0.466785\pi$
$883$	6.19019			0.208317			0.104158	+	0.994561i	$0.466785\pi$
$884$		−	15.7937i		−	0.531199i
$885$	22.7905	−	5.13451i	0.766093	−	0.172595i
$886$			50.0024i			1.67986i
$887$	−0.793840			−0.0266545			−0.0133273	−	0.999911i	$-0.504242\pi$
$887$	−0.793840			−0.0266545			−0.0133273	+	0.999911i	$0.504242\pi$
$888$	137.572	−	30.9939i	4.61662	−	1.04009i
$889$	50.6591			1.69905
$890$	44.7337			1.49948
$891$	−19.4111	−	22.6761i	−0.650298	−	0.759680i
$892$	31.4088			1.05165
$893$	5.76919			0.193059
$894$	−58.0218	+	13.0719i	−1.94054	+	0.437188i
$895$	54.1039			1.80849
$896$			126.208i			4.21632i
$897$	−1.26008	+	0.283887i	−0.0420730	+	0.00947871i
$898$		−	75.0501i		−	2.50445i
$899$	10.9663			0.365746
$900$	−10.9791	+	5.21151i	−0.365969	+	0.173717i
$901$			20.2357i			0.674149i
$902$	−7.30403	+	40.5082i	−0.243197	+	1.34877i
$903$	52.7374	−	11.8813i	1.75499	−	0.395385i
$904$			25.7317i			0.855825i
$905$		−	5.87598i		−	0.195324i
$906$	4.58774	+	20.3635i	0.152417	+	0.676532i
$907$	10.9991			0.365219			0.182609	−	0.983186i	$-0.441546\pi$
$907$	10.9991			0.365219			0.182609	+	0.983186i	$0.441546\pi$
$908$	−10.9096			−0.362048
$909$	−13.8389	+	6.56899i	−0.459006	+	0.217880i
$910$			30.1899i			1.00079i
$911$			7.69798i			0.255046i	0.991836	+	0.127523i	$0.0407026\pi$
$911$			7.69798i			0.255046i	−0.991836	+	0.127523i	$0.959297\pi$
$912$	4.72050	+	20.9528i	0.156311	+	0.693817i
$913$	1.10157	−	6.10929i	0.0364565	−	0.202188i
$914$		−	26.7313i		−	0.884193i
$915$	23.3902	−	5.26961i	0.773255	−	0.174208i
$916$	79.6788			2.63266
$917$			100.247i			3.31046i
$918$	32.8483	−	25.7461i	1.08416	−	0.849749i
$919$		−	26.3226i		−	0.868301i	−0.900840	−	0.434151i	$-0.857049\pi$
$919$		−	26.3226i		−	0.868301i	0.900840	−	0.434151i	$-0.142951\pi$
$920$	−16.0787			−0.530099
$921$	10.4433	+	46.3547i	0.344120	+	1.52744i
$922$	−0.330124			−0.0108721
$923$	−0.0134651			−0.000443211
$924$	−141.939	+	6.13548i	−4.66946	+	0.201842i
$925$	6.90214			0.226941
$926$	−87.7809			−2.88466
$927$	−8.58126	+	4.07333i	−0.281846	+	0.133786i
$928$	−78.9272			−2.59091
$929$		−	47.6720i		−	1.56407i	−0.623236	−	0.782034i	$-0.714182\pi$
$929$		−	47.6720i		−	1.56407i	0.623236	−	0.782034i	$-0.285818\pi$
$930$	−6.52608	−	28.9672i	−0.213999	−	0.949872i
$931$			13.2615i			0.434627i
$932$	−58.2099			−1.90673
$933$	−1.54062	−	6.83834i	−0.0504377	−	0.223877i
$934$			5.57749i			0.182501i
$935$	23.2588	+	4.19379i	0.760644	+	0.137152i
$936$	11.5555	+	24.3439i	0.377703	+	0.795707i
$937$			36.0674i			1.17827i	0.808034	+	0.589135i	$0.200531\pi$
$937$			36.0674i			1.17827i	−0.808034	+	0.589135i	$0.799469\pi$
$938$			101.728i			3.32154i
$939$	−40.6157	+	9.15038i	−1.32544	+	0.298611i
$940$	81.1687			2.64743
$941$	−5.65441			−0.184329			−0.0921643	−	0.995744i	$-0.529378\pi$
$941$	−5.65441			−0.184329			−0.0921643	+	0.995744i	$0.529378\pi$
$942$	−62.9336	+	14.1784i	−2.05049	+	0.461958i
$943$			3.42080i			0.111397i
$944$		−	76.7723i		−	2.49872i
$945$	−45.6345	+	35.7677i	−1.48449	+	1.16352i
$946$	59.2890	+	10.6904i	1.92765	+	0.347575i
$947$		−	10.0116i		−	0.325333i	−0.986681	−	0.162666i	$-0.947991\pi$
$947$		−	10.0116i		−	0.325333i	0.986681	−	0.162666i	$-0.0520094\pi$
$948$	−16.5514	−	73.4665i	−0.537565	−	2.38608i
$949$	4.80852			0.156091
$950$			1.86990i			0.0606675i
$951$	1.62412	+	7.20895i	0.0526657	+	0.233766i
$952$		−	123.967i		−	4.01778i
$953$	−10.1129			−0.327588			−0.163794	−	0.986495i	$-0.552373\pi$
$953$	−10.1129			−0.327588			−0.163794	+	0.986495i	$0.552373\pi$
$954$	−23.7245	−	49.9804i	−0.768110	−	1.61817i
$955$	−47.1250			−1.52493
$956$	−117.025			−3.78484
$957$	−1.03058	−	23.8416i	−0.0333139	−	0.770691i
$958$	−51.8012			−1.67362
$959$	−98.6324			−3.18501
$960$	22.0022	+	97.6607i	0.710117	+	3.15198i
$961$	−24.0313			−0.775205
$962$		−	24.5235i		−	0.790670i
$963$	34.1545	−	16.2123i	1.10061	−	0.522435i
$964$			18.8780i			0.608019i
$965$	37.9830			1.22271
$966$	−15.8487	+	3.57059i	−0.509925	+	0.114882i
$967$			24.8226i			0.798243i	0.916898	+	0.399121i	$0.130685\pi$
$967$			24.8226i			0.798243i	−0.916898	+	0.399121i	$0.869315\pi$
$968$	−92.5843	−	34.5097i	−2.97577	−	1.10918i
$969$	−1.02573	−	4.55288i	−0.0329511	−	0.146260i
$970$		−	87.3972i		−	2.80615i
$971$			39.0524i			1.25325i	0.779320	+	0.626626i	$0.215565\pi$
$971$			39.0524i			1.25325i	−0.779320	+	0.626626i	$0.784435\pi$
$972$	−37.0274	+	74.2055i	−1.18765	+	2.38014i
$973$	−71.8394			−2.30306
$974$	20.7194			0.663893
$975$	0.289876	+	1.28667i	0.00928346	+	0.0412063i
$976$		−	78.7924i		−	2.52208i
$977$			4.91859i			0.157360i	0.996900	+	0.0786799i	$0.0250705\pi$
$977$			4.91859i			0.157360i	−0.996900	+	0.0786799i	$0.974930\pi$
$978$	41.7494	−	9.40581i	1.33500	−	0.300765i
$979$	22.4834	+	4.05398i	0.718572	+	0.129566i
$980$			186.580i			5.96008i
$981$	−18.0686	−	38.0651i	−0.576887	−	1.21533i
$982$	41.6678			1.32967
$983$		−	37.1938i		−	1.18630i	−0.805093	−	0.593148i	$-0.797885\pi$
$983$		−	37.1938i		−	1.18630i	0.805093	−	0.593148i	$-0.202115\pi$
$984$	69.6212	−	15.6851i	2.21944	−	0.500023i
$985$		−	14.1691i		−	0.451466i
$986$	33.3666			1.06261
$987$	49.9297	−	11.2488i	1.58928	−	0.358052i
$988$	4.82855			0.153617
$989$	5.00679			0.159207
$990$	−62.3640	+	16.9105i	−1.98206	+	0.537452i
$991$	−15.4387			−0.490425			−0.245213	−	0.969469i	$-0.578858\pi$
$991$	−15.4387			−0.490425			−0.245213	+	0.969469i	$0.578858\pi$
$992$	−50.1553			−1.59243
$993$	17.1400	−	3.86151i	0.543923	−	0.122541i
$994$	−0.169358			−0.00537171
$995$		−	22.5567i		−	0.715094i
$996$	−16.8253	+	3.79061i	−0.533131	+	0.120110i
$997$			29.8330i			0.944821i	0.881379	+	0.472411i	$0.156616\pi$
$997$			29.8330i			0.944821i	−0.881379	+	0.472411i	$0.843384\pi$
$998$	−38.7324			−1.22605
$999$	37.0692	−	29.0544i	1.17282	−	0.919241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.48	yes	48
3.2	odd	2	inner	429.2.f.a.131.1	✓	48
11.10	odd	2	inner	429.2.f.a.131.2	yes	48
33.32	even	2	inner	429.2.f.a.131.47	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.1	✓	48	3.2	odd	2	inner
429.2.f.a.131.2	yes	48	11.10	odd	2	inner
429.2.f.a.131.47	yes	48	33.32	even	2	inner
429.2.f.a.131.48	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.70555 q^{2} +(-1.68970 + 0.380676i) q^{3} +5.32000 q^{4} -2.40031i q^{5} +(-4.57157 + 1.02994i) q^{6} +4.64879i q^{7} +8.98243 q^{8} +(2.71017 - 1.28646i) q^{9} +O(q^{10})\)	\(q+2.70555 q^{2} +(-1.68970 + 0.380676i) q^{3} +5.32000 q^{4} -2.40031i q^{5} +(-4.57157 + 1.02994i) q^{6} +4.64879i q^{7} +8.98243 q^{8} +(2.71017 - 1.28646i) q^{9} -6.49415i q^{10} +(0.588530 - 3.26399i) q^{11} +(-8.98921 + 2.02520i) q^{12} +1.00000i q^{13} +12.5775i q^{14} +(0.913739 + 4.05580i) q^{15} +13.6624 q^{16} -2.96873 q^{17} +(7.33251 - 3.48057i) q^{18} -0.907622i q^{19} -12.7696i q^{20} +(-1.76968 - 7.85505i) q^{21} +(1.59230 - 8.83089i) q^{22} -0.745744i q^{23} +(-15.1776 + 3.41940i) q^{24} -0.761477 q^{25} +2.70555i q^{26} +(-4.08965 + 3.20542i) q^{27} +24.7316i q^{28} -4.15417 q^{29} +(2.47217 + 10.9732i) q^{30} -2.63982 q^{31} +18.9995 q^{32} +(0.248083 + 5.73920i) q^{33} -8.03206 q^{34} +11.1585 q^{35} +(14.4181 - 6.84395i) q^{36} -9.06415 q^{37} -2.45562i q^{38} +(-0.380676 - 1.68970i) q^{39} -21.5606i q^{40} -4.58710 q^{41} +(-4.78796 - 21.2522i) q^{42} +6.71382i q^{43} +(3.13098 - 17.3644i) q^{44} +(-3.08789 - 6.50525i) q^{45} -2.01765i q^{46} +6.35638i q^{47} +(-23.0854 + 5.20095i) q^{48} -14.6112 q^{49} -2.06021 q^{50} +(5.01627 - 1.13013i) q^{51} +5.32000i q^{52} -6.81627i q^{53} +(-11.0648 + 8.67243i) q^{54} +(-7.83458 - 1.41265i) q^{55} +41.7574i q^{56} +(0.345510 + 1.53361i) q^{57} -11.2393 q^{58} -5.61923i q^{59} +(4.86109 + 21.5769i) q^{60} -5.76709i q^{61} -7.14217 q^{62} +(5.98046 + 12.5990i) q^{63} +24.0793 q^{64} +2.40031 q^{65} +(0.671201 + 15.5277i) q^{66} +8.08809 q^{67} -15.7937 q^{68} +(0.283887 + 1.26008i) q^{69} +30.1899 q^{70} +0.0134651i q^{71} +(24.3439 - 11.5555i) q^{72} -4.80852i q^{73} -24.5235 q^{74} +(1.28667 - 0.289876i) q^{75} -4.82855i q^{76} +(15.1736 + 2.73595i) q^{77} +(-1.02994 - 4.57157i) q^{78} +8.17275i q^{79} -32.7940i q^{80} +(5.69006 - 6.97303i) q^{81} -12.4106 q^{82} +1.87173 q^{83} +(-9.41470 - 41.7889i) q^{84} +7.12587i q^{85} +18.1646i q^{86} +(7.01931 - 1.58139i) q^{87} +(5.28643 - 29.3186i) q^{88} +6.88831i q^{89} +(-8.35444 - 17.6003i) q^{90} -4.64879 q^{91} -3.96736i q^{92} +(4.46051 - 1.00492i) q^{93} +17.1975i q^{94} -2.17857 q^{95} +(-32.1035 + 7.23265i) q^{96} +13.4578 q^{97} -39.5314 q^{98} +(-2.60396 - 9.60309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

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