LMFDB - Embedded newform 504.2.j.a.323.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(323,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("504.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.j (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.8
Character	$\chi$	$=$	504.323
Dual form			504.2.j.a.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.619645 + 1.27124i) q^{2} +(-1.23208 - 1.57543i) q^{4} -0.753720 q^{5} +1.00000i q^{7} +(2.76619 - 0.590057i) q^{8} +O(q^{10})$	\(q+(-0.619645 + 1.27124i) q^{2} +(-1.23208 - 1.57543i) q^{4} -0.753720 q^{5} +1.00000i q^{7} +(2.76619 - 0.590057i) q^{8} +(0.467039 - 0.958156i) q^{10} +4.40413i q^{11} -4.28230i q^{13} +(-1.27124 - 0.619645i) q^{14} +(-0.963957 + 3.88211i) q^{16} +7.48403i q^{17} +0.157023 q^{19} +(0.928644 + 1.18743i) q^{20} +(-5.59869 - 2.72900i) q^{22} -2.84216 q^{23} -4.43191 q^{25} +(5.44381 + 2.65350i) q^{26} +(1.57543 - 1.23208i) q^{28} -5.03950 q^{29} +9.13728i q^{31} +(-4.33777 - 3.63095i) q^{32} +(-9.51396 - 4.63744i) q^{34} -0.753720i q^{35} +6.38541i q^{37} +(-0.0972987 + 0.199614i) q^{38} +(-2.08494 + 0.444738i) q^{40} +2.93539i q^{41} +1.50524 q^{43} +(6.93840 - 5.42624i) q^{44} +(1.76113 - 3.61306i) q^{46} +6.17443 q^{47} -1.00000 q^{49} +(2.74621 - 5.63400i) q^{50} +(-6.74646 + 5.27613i) q^{52} -10.5926 q^{53} -3.31948i q^{55} +(0.590057 + 2.76619i) q^{56} +(3.12270 - 6.40639i) q^{58} -6.17443i q^{59} -9.34822i q^{61} +(-11.6156 - 5.66187i) q^{62} +(7.30367 - 3.26443i) q^{64} +3.22765i q^{65} +11.5662 q^{67} +(11.7906 - 9.22092i) q^{68} +(0.958156 + 0.467039i) q^{70} +2.69634 q^{71} +1.74091 q^{73} +(-8.11736 - 3.95668i) q^{74} +(-0.193465 - 0.247379i) q^{76} -4.40413 q^{77} +12.2700i q^{79} +(0.726554 - 2.92603i) q^{80} +(-3.73157 - 1.81890i) q^{82} +8.29068i q^{83} -5.64087i q^{85} +(-0.932715 + 1.91352i) q^{86} +(2.59869 + 12.1827i) q^{88} -5.13323i q^{89} +4.28230 q^{91} +(3.50177 + 4.47762i) q^{92} +(-3.82596 + 7.84916i) q^{94} -0.118352 q^{95} +5.83722 q^{97} +(0.619645 - 1.27124i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.619645	+	1.27124i	−0.438155	+	0.898899i
$2$	−0.619645	+	1.27124i	−0.438155	+	0.898899i
$3$		0			0
$3$		0			0
$4$	−1.23208	−	1.57543i	−0.616040	−	0.787715i
$5$	−0.753720			−0.337074			−0.168537	−	0.985695i	$-0.553904\pi$
$5$	−0.753720			−0.337074			−0.168537	+	0.985695i	$0.553904\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.76619	−	0.590057i	0.977997	−	0.208617i
$9$		0			0
$10$	0.467039	−	0.958156i	0.147691	−	0.302996i
$11$			4.40413i			1.32790i	0.747779	+	0.663948i	$0.231120\pi$
$11$			4.40413i			1.32790i	−0.747779	+	0.663948i	$0.768880\pi$
$12$		0			0
$13$		−	4.28230i		−	1.18770i	−0.804578	−	0.593848i	$-0.797608\pi$
$13$		−	4.28230i		−	1.18770i	0.804578	−	0.593848i	$-0.202392\pi$
$14$	−1.27124	−	0.619645i	−0.339752	−	0.165607i
$15$		0			0
$16$	−0.963957	+	3.88211i	−0.240989	+	0.970528i
$17$			7.48403i			1.81514i	0.419897	+	0.907572i	$0.362066\pi$
$17$			7.48403i			1.81514i	−0.419897	+	0.907572i	$0.637934\pi$
$18$		0			0
$19$	0.157023			0.0360236			0.0180118	−	0.999838i	$-0.494266\pi$
$19$	0.157023			0.0360236			0.0180118	+	0.999838i	$0.494266\pi$
$20$	0.928644	+	1.18743i	0.207651	+	0.265518i
$21$		0			0
$22$	−5.59869	−	2.72900i	−1.19364	−	0.581824i
$23$	−2.84216			−0.592631			−0.296316	−	0.955090i	$-0.595758\pi$
$23$	−2.84216			−0.592631			−0.296316	+	0.955090i	$0.595758\pi$
$24$		0			0
$25$	−4.43191			−0.886381
$26$	5.44381	+	2.65350i	1.06762	+	0.520395i
$27$		0			0
$28$	1.57543	−	1.23208i	0.297728	−	0.232841i
$29$	−5.03950			−0.935812			−0.467906	−	0.883778i	$-0.654991\pi$
$29$	−5.03950			−0.935812			−0.467906	+	0.883778i	$0.654991\pi$
$30$		0			0
$31$			9.13728i			1.64110i	0.571572	+	0.820552i	$0.306334\pi$
$31$			9.13728i			1.64110i	−0.571572	+	0.820552i	$0.693666\pi$
$32$	−4.33777	−	3.63095i	−0.766816	−	0.641867i
$33$		0			0
$34$	−9.51396	−	4.63744i	−1.63163	−	0.795315i
$35$		−	0.753720i		−	0.127402i
$36$		0			0
$37$			6.38541i			1.04975i	0.851178	+	0.524877i	$0.175889\pi$
$37$			6.38541i			1.04975i	−0.851178	+	0.524877i	$0.824111\pi$
$38$	−0.0972987	+	0.199614i	−0.0157839	+	0.0323816i
$39$		0			0
$40$	−2.08494	+	0.444738i	−0.329658	+	0.0703193i
$41$			2.93539i			0.458431i	0.973376	+	0.229215i	$0.0736160\pi$
$41$			2.93539i			0.458431i	−0.973376	+	0.229215i	$0.926384\pi$
$42$		0			0
$43$	1.50524			0.229547			0.114774	−	0.993392i	$-0.463386\pi$
$43$	1.50524			0.229547			0.114774	+	0.993392i	$0.463386\pi$
$44$	6.93840	−	5.42624i	1.04600	−	0.818037i
$45$		0			0
$46$	1.76113	−	3.61306i	0.259665	−	0.532716i
$47$	6.17443			0.900634			0.450317	−	0.892869i	$-0.351311\pi$
$47$	6.17443			0.900634			0.450317	+	0.892869i	$0.351311\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	2.74621	−	5.63400i	0.388372	−	0.796767i
$51$		0			0
$52$	−6.74646	+	5.27613i	−0.935565	+	0.731668i
$53$	−10.5926			−1.45501			−0.727506	−	0.686102i	$-0.759320\pi$
$53$	−10.5926			−1.45501			−0.727506	+	0.686102i	$0.759320\pi$
$54$		0			0
$55$		−	3.31948i		−	0.447599i
$56$	0.590057	+	2.76619i	0.0788497	+	0.369648i
$57$		0			0
$58$	3.12270	−	6.40639i	0.410031	−	0.841201i
$59$		−	6.17443i		−	0.803843i	−0.915674	−	0.401921i	$-0.868343\pi$
$59$		−	6.17443i		−	0.803843i	0.915674	−	0.401921i	$-0.131657\pi$
$60$		0			0
$61$		−	9.34822i		−	1.19692i	−0.801154	−	0.598458i	$-0.795780\pi$
$61$		−	9.34822i		−	1.19692i	0.801154	−	0.598458i	$-0.204220\pi$
$62$	−11.6156	−	5.66187i	−1.47519	−	0.719058i
$63$		0			0
$64$	7.30367	−	3.26443i	0.912958	−	0.408053i
$65$			3.22765i			0.400341i
$66$		0			0
$67$	11.5662			1.41304			0.706521	−	0.707692i	$-0.250264\pi$
$67$	11.5662			1.41304			0.706521	+	0.707692i	$0.250264\pi$
$68$	11.7906	−	9.22092i	1.42982	−	1.11820i
$69$		0			0
$70$	0.958156	+	0.467039i	0.114522	+	0.0558219i
$71$	2.69634			0.319997			0.159998	−	0.987117i	$-0.448851\pi$
$71$	2.69634			0.319997			0.159998	+	0.987117i	$0.448851\pi$
$72$		0			0
$73$	1.74091			0.203758			0.101879	−	0.994797i	$-0.467515\pi$
$73$	1.74091			0.203758			0.101879	+	0.994797i	$0.467515\pi$
$74$	−8.11736	−	3.95668i	−0.943623	−	0.459955i
$75$		0			0
$76$	−0.193465	−	0.247379i	−0.0221920	−	0.0283763i
$77$	−4.40413			−0.501897
$78$		0			0
$79$			12.2700i			1.38048i	0.723581	+	0.690240i	$0.242495\pi$
$79$			12.2700i			1.38048i	−0.723581	+	0.690240i	$0.757505\pi$
$80$	0.726554	−	2.92603i	0.0812312	−	0.327140i
$81$		0			0
$82$	−3.73157	−	1.81890i	−0.412083	−	0.200864i
$83$			8.29068i			0.910021i	0.890486	+	0.455010i	$0.150364\pi$
$83$			8.29068i			0.910021i	−0.890486	+	0.455010i	$0.849636\pi$
$84$		0			0
$85$		−	5.64087i		−	0.611838i
$86$	−0.932715	+	1.91352i	−0.100577	+	0.206340i
$87$		0			0
$88$	2.59869	+	12.1827i	0.277021	+	1.29868i
$89$		−	5.13323i		−	0.544121i	−0.962280	−	0.272061i	$-0.912295\pi$
$89$		−	5.13323i		−	0.544121i	0.962280	−	0.272061i	$-0.0877052\pi$
$90$		0			0
$91$	4.28230			0.448907
$92$	3.50177	+	4.47762i	0.365085	+	0.466825i
$93$		0			0
$94$	−3.82596	+	7.84916i	−0.394617	+	0.809579i
$95$	−0.118352			−0.0121426
$96$		0			0
$97$	5.83722			0.592680			0.296340	−	0.955083i	$-0.404234\pi$
$97$	5.83722			0.592680			0.296340	+	0.955083i	$0.404234\pi$
$98$	0.619645	−	1.27124i	0.0625936	−	0.128414i
$99$		0			0
$100$	5.46046	+	6.98216i	0.546046	+	0.698216i
$101$	3.90513			0.388575			0.194287	−	0.980945i	$-0.437761\pi$
$101$	3.90513			0.388575			0.194287	+	0.980945i	$0.437761\pi$
$102$		0			0
$103$			15.9804i			1.57459i	0.616574	+	0.787297i	$0.288520\pi$
$103$			15.9804i			1.57459i	−0.616574	+	0.787297i	$0.711480\pi$
$104$	−2.52680	−	11.8457i	−0.247773	−	1.16156i
$105$		0			0
$106$	6.56368	−	13.4657i	0.637521	−	1.30791i
$107$		−	7.41901i		−	0.717223i	−0.933487	−	0.358612i	$-0.883250\pi$
$107$		−	7.41901i		−	0.717223i	0.933487	−	0.358612i	$-0.116750\pi$
$108$		0			0
$109$		−	10.9803i		−	1.05172i	−0.850572	−	0.525859i	$-0.823744\pi$
$109$		−	10.9803i		−	1.05172i	0.850572	−	0.525859i	$-0.176256\pi$
$110$	4.21985	+	2.05690i	0.402347	+	0.196118i
$111$		0			0
$112$	−3.88211	−	0.963957i	−0.366825	−	0.0910854i
$113$		−	10.0685i		−	0.947166i	−0.880749	−	0.473583i	$-0.842960\pi$
$113$		−	10.0685i		−	0.947166i	0.880749	−	0.473583i	$-0.157040\pi$
$114$		0			0
$115$	2.14219			0.199761
$116$	6.20907	+	7.93938i	0.576498	+	0.737153i
$117$		0			0
$118$	7.84916	+	3.82596i	0.722574	+	0.352208i
$119$	−7.48403			−0.686060
$120$		0			0
$121$	−8.39637			−0.763307
$122$	11.8838	+	5.79258i	1.07591	+	0.524435i
$123$		0			0
$124$	14.3951	−	11.2579i	1.29272	−	1.01099i
$125$	7.10902			0.635850
$126$		0			0
$127$		−	1.57353i		−	0.139628i	−0.997560	−	0.0698142i	$-0.977759\pi$
$127$		−	1.57353i		−	0.139628i	0.997560	−	0.0698142i	$-0.0222406\pi$
$128$	−0.375826	+	11.3075i	−0.0332186	+	0.999448i
$129$		0			0
$130$	−4.10311	−	2.00000i	−0.359867	−	0.175412i
$131$			2.80096i			0.244721i	0.992486	+	0.122361i	$0.0390464\pi$
$131$			2.80096i			0.244721i	−0.992486	+	0.122361i	$0.960954\pi$
$132$		0			0
$133$			0.157023i			0.0136157i
$134$	−7.16697	+	14.7034i	−0.619132	+	1.27018i
$135$		0			0
$136$	4.41600	+	20.7023i	0.378669	+	1.77521i
$137$			14.3363i			1.22483i	0.790536	+	0.612416i	$0.209802\pi$
$137$			14.3363i			1.22483i	−0.790536	+	0.612416i	$0.790198\pi$
$138$		0			0
$139$	14.7353			1.24983			0.624915	−	0.780693i	$-0.285134\pi$
$139$	14.7353			1.24983			0.624915	+	0.780693i	$0.285134\pi$
$140$	−1.18743	+	0.928644i	−0.100356	+	0.0784847i
$141$		0			0
$142$	−1.67077	+	3.42769i	−0.140208	+	0.287645i
$143$	18.8598			1.57714
$144$		0			0
$145$	3.79837			0.315438
$146$	−1.07874	+	2.21310i	−0.0892775	+	0.183158i
$147$		0			0
$148$	10.0598	−	7.86733i	0.826907	−	0.646691i
$149$	−9.30727			−0.762481			−0.381240	−	0.924476i	$-0.624503\pi$
$149$	−9.30727			−0.762481			−0.381240	+	0.924476i	$0.624503\pi$
$150$		0			0
$151$		−	10.7353i		−	0.873625i	−0.899553	−	0.436812i	$-0.856107\pi$
$151$		−	10.7353i		−	0.873625i	0.899553	−	0.436812i	$-0.143893\pi$
$152$	0.434357	−	0.0926527i	0.0352310	−	0.00751513i
$153$		0			0
$154$	2.72900	−	5.59869i	0.219909	−	0.451155i
$155$		−	6.88696i		−	0.553174i
$156$		0			0
$157$			13.8050i			1.10176i	0.834585	+	0.550879i	$0.185707\pi$
$157$			13.8050i			1.10176i	−0.834585	+	0.550879i	$0.814293\pi$
$158$	−15.5980	−	7.60302i	−1.24091	−	0.604864i
$159$		0			0
$160$	3.26946	+	2.73672i	0.258474	+	0.216357i
$161$		−	2.84216i		−	0.223994i
$162$		0			0
$163$	5.56294			0.435723			0.217861	−	0.975980i	$-0.430092\pi$
$163$	5.56294			0.435723			0.217861	+	0.975980i	$0.430092\pi$
$164$	4.62450	−	3.61663i	0.361113	−	0.282412i
$165$		0			0
$166$	−10.5394	−	5.13728i	−0.818017	−	0.398730i
$167$	25.5058			1.97370			0.986850	−	0.161638i	$-0.0516779\pi$
$167$	25.5058			1.97370			0.986850	+	0.161638i	$0.0516779\pi$
$168$		0			0
$169$	−5.33806			−0.410620
$170$	7.17087	+	3.49533i	0.549981	+	0.268080i
$171$		0			0
$172$	−1.85458	−	2.37140i	−0.141410	−	0.180818i
$173$	4.05978			0.308659			0.154330	−	0.988019i	$-0.450678\pi$
$173$	4.05978			0.308659			0.154330	+	0.988019i	$0.450678\pi$
$174$		0			0
$175$		−	4.43191i		−	0.335021i
$176$	−17.0973	−	4.24539i	−1.28876	−	0.320009i
$177$		0			0
$178$	6.52555	+	3.18078i	0.489110	+	0.238410i
$179$		−	24.3019i		−	1.81641i	−0.418528	−	0.908204i	$-0.637454\pi$
$179$		−	24.3019i		−	1.81641i	0.418528	−	0.908204i	$-0.362546\pi$
$180$		0			0
$181$		−	22.7424i		−	1.69043i	−0.534428	−	0.845214i	$-0.679473\pi$
$181$		−	22.7424i		−	1.69043i	0.534428	−	0.845214i	$-0.320527\pi$
$182$	−2.65350	+	5.44381i	−0.196691	+	0.403522i
$183$		0			0
$184$	−7.86197	+	1.67704i	−0.579592	+	0.123633i
$185$		−	4.81281i		−	0.353845i
$186$		0			0
$187$	−32.9606			−2.41032
$188$	−7.60740	−	9.72739i	−0.554826	−	0.709442i
$189$		0			0
$190$	0.0733361	−	0.150453i	0.00532036	−	0.0109150i
$191$	−9.59578			−0.694326			−0.347163	−	0.937805i	$-0.612855\pi$
$191$	−9.59578			−0.694326			−0.347163	+	0.937805i	$0.612855\pi$
$192$		0			0
$193$	7.47075			0.537756			0.268878	−	0.963174i	$-0.413347\pi$
$193$	7.47075			0.537756			0.268878	+	0.963174i	$0.413347\pi$
$194$	−3.61700	+	7.42048i	−0.259686	+	0.532759i
$195$		0			0
$196$	1.23208	+	1.57543i	0.0880057	+	0.112531i
$197$	−23.0306			−1.64086			−0.820431	−	0.571746i	$-0.806266\pi$
$197$	−23.0306			−1.64086			−0.820431	+	0.571746i	$0.806266\pi$
$198$		0			0
$199$			2.28608i			0.162056i	0.996712	+	0.0810279i	$0.0258203\pi$
$199$			2.28608i			0.162056i	−0.996712	+	0.0810279i	$0.974180\pi$
$200$	−12.2595	+	2.61508i	−0.866878	+	0.184914i
$201$		0			0
$202$	−2.41979	+	4.96434i	−0.170256	+	0.349290i
$203$		−	5.03950i		−	0.353704i
$204$		0			0
$205$		−	2.21246i		−	0.154525i
$206$	−20.3148	−	9.90217i	−1.41540	−	0.689917i
$207$		0			0
$208$	16.6244	+	4.12795i	1.15269	+	0.286222i
$209$			0.691552i			0.0478356i
$210$		0			0
$211$	−21.6480			−1.49031			−0.745154	−	0.666893i	$-0.767624\pi$
$211$	−21.6480			−1.49031			−0.745154	+	0.666893i	$0.767624\pi$
$212$	13.0510	+	16.6880i	0.896345	+	1.14613i
$213$		0			0
$214$	9.43131	+	4.59715i	0.644711	+	0.314255i
$215$	−1.13453			−0.0773744
$216$		0			0
$217$	−9.13728			−0.620279
$218$	13.9585	+	6.80386i	0.945389	+	0.460816i
$219$		0			0
$220$	−5.22961	+	4.08987i	−0.352580	+	0.275739i
$221$	32.0488			2.15584
$222$		0			0
$223$		−	5.85664i		−	0.392190i	−0.980585	−	0.196095i	$-0.937174\pi$
$223$		−	5.85664i		−	0.392190i	0.980585	−	0.196095i	$-0.0628260\pi$
$224$	3.63095	−	4.33777i	0.242603	−	0.289829i
$225$		0			0
$226$	12.7995	+	6.23891i	0.851407	+	0.415006i
$227$			18.5005i			1.22792i	0.789336	+	0.613961i	$0.210425\pi$
$227$			18.5005i			1.22792i	−0.789336	+	0.613961i	$0.789575\pi$
$228$		0			0
$229$			9.16399i			0.605573i	0.953058	+	0.302787i	$0.0979169\pi$
$229$			9.16399i			0.605573i	−0.953058	+	0.302787i	$0.902083\pi$
$230$	−1.32740	+	2.72323i	−0.0875262	+	0.179565i
$231$		0			0
$232$	−13.9402	+	2.97359i	−0.915221	+	0.195226i
$233$		−	5.29278i		−	0.346742i	−0.984857	−	0.173371i	$-0.944534\pi$
$233$		−	5.29278i		−	0.346742i	0.984857	−	0.173371i	$-0.0554659\pi$
$234$		0			0
$235$	−4.65380			−0.303580
$236$	−9.72739	+	7.60740i	−0.633199	+	0.495199i
$237$		0			0
$238$	4.63744	−	9.51396i	0.300601	−	0.616699i
$239$	−11.6411			−0.753002			−0.376501	−	0.926416i	$-0.622873\pi$
$239$	−11.6411			−0.753002			−0.376501	+	0.926416i	$0.622873\pi$
$240$		0			0
$241$	−29.2913			−1.88682			−0.943410	−	0.331628i	$-0.892402\pi$
$241$	−29.2913			−1.88682			−0.943410	+	0.331628i	$0.892402\pi$
$242$	5.20277	−	10.6738i	0.334447	−	0.686136i
$243$		0			0
$244$	−14.7275	+	11.5178i	−0.942829	+	0.737349i
$245$	0.753720			0.0481534
$246$		0			0
$247$		−	0.672421i		−	0.0427851i
$248$	5.39152	+	25.2755i	0.342362	+	1.60500i
$249$		0			0
$250$	−4.40507	+	9.03724i	−0.278601	+	0.571565i
$251$			4.92371i			0.310782i	0.987853	+	0.155391i	$0.0496637\pi$
$251$			4.92371i			0.310782i	−0.987853	+	0.155391i	$0.950336\pi$
$252$		0			0
$253$		−	12.5172i		−	0.786953i
$254$	2.00033	+	0.975031i	0.125512	+	0.0611789i
$255$		0			0
$256$	−14.1416	−	7.48438i	−0.883848	−	0.467774i
$257$		−	23.7193i		−	1.47957i	−0.672844	−	0.739784i	$-0.734928\pi$
$257$		−	23.7193i		−	1.47957i	0.672844	−	0.739784i	$-0.265072\pi$
$258$		0			0
$259$	−6.38541			−0.396770
$260$	5.08494	−	3.97673i	0.315355	−	0.246626i
$261$		0			0
$262$	−3.56068	−	1.73560i	−0.219980	−	0.107226i
$263$	−6.62803			−0.408702			−0.204351	−	0.978898i	$-0.565508\pi$
$263$	−6.62803			−0.408702			−0.204351	+	0.978898i	$0.565508\pi$
$264$		0			0
$265$	7.98389			0.490447
$266$	−0.199614	−	0.0972987i	−0.0122391	−	0.00596577i
$267$		0			0
$268$	−14.2505	−	18.2218i	−0.870491	−	1.11307i
$269$	21.7190			1.32423			0.662117	−	0.749401i	$-0.269658\pi$
$269$	21.7190			1.32423			0.662117	+	0.749401i	$0.269658\pi$
$270$		0			0
$271$		−	4.09127i		−	0.248527i	−0.992249	−	0.124263i	$-0.960343\pi$
$271$		−	4.09127i		−	0.248527i	0.992249	−	0.124263i	$-0.0396568\pi$
$272$	−29.0538	−	7.21428i	−1.76165	−	0.437430i
$273$		0			0
$274$	−18.2248	−	8.88340i	−1.10100	−	0.536666i
$275$		−	19.5187i		−	1.17702i
$276$		0			0
$277$			7.31594i			0.439572i	0.975548	+	0.219786i	$0.0705360\pi$
$277$			7.31594i			0.439572i	−0.975548	+	0.219786i	$0.929464\pi$
$278$	−9.13064	+	18.7320i	−0.547620	+	1.12347i
$279$		0			0
$280$	−0.444738	−	2.08494i	−0.0265782	−	0.124599i
$281$		−	1.40887i		−	0.0840459i	−0.999117	−	0.0420230i	$-0.986620\pi$
$281$		−	1.40887i		−	0.0840459i	0.999117	−	0.0420230i	$-0.0133803\pi$
$282$		0			0
$283$	18.0005			1.07002			0.535010	−	0.844846i	$-0.320308\pi$
$283$	18.0005			1.07002			0.535010	+	0.844846i	$0.320308\pi$
$284$	−3.32211	−	4.24790i	−0.197131	−	0.252066i
$285$		0			0
$286$	−11.6864	+	23.9752i	−0.691030	+	1.41769i
$287$	−2.93539			−0.173270
$288$		0			0
$289$	−39.0107			−2.29475
$290$	−2.35364	+	4.82863i	−0.138211	+	0.283547i
$291$		0			0
$292$	−2.14494	−	2.74268i	−0.125523	−	0.160503i
$293$	12.8759			0.752219			0.376110	−	0.926575i	$-0.377262\pi$
$293$	12.8759			0.752219			0.376110	+	0.926575i	$0.377262\pi$
$294$		0			0
$295$			4.65380i			0.270955i
$296$	3.76775	+	17.6633i	0.218996	+	1.02666i
$297$		0			0
$298$	5.76720	−	11.8317i	0.334085	−	0.685394i
$299$			12.1710i			0.703866i
$300$		0			0
$301$			1.50524i			0.0867607i
$302$	13.6471	+	6.65206i	0.785301	+	0.382783i
$303$		0			0
$304$	−0.151364	+	0.609582i	−0.00868131	+	0.0349619i
$305$			7.04594i			0.403450i
$306$		0			0
$307$	−18.0182			−1.02835			−0.514176	−	0.857685i	$-0.671902\pi$
$307$	−18.0182			−1.02835			−0.514176	+	0.857685i	$0.671902\pi$
$308$	5.42624	+	6.93840i	0.309189	+	0.395352i
$309$		0			0
$310$	8.75494	+	4.26747i	0.497247	+	0.242376i
$311$	−3.68495			−0.208954			−0.104477	−	0.994527i	$-0.533317\pi$
$311$	−3.68495			−0.208954			−0.104477	+	0.994527i	$0.533317\pi$
$312$		0			0
$313$	29.6789			1.67755			0.838777	−	0.544476i	$-0.183271\pi$
$313$	29.6789			1.67755			0.838777	+	0.544476i	$0.183271\pi$
$314$	−17.5494	−	8.55419i	−0.990369	−	0.482741i
$315$		0			0
$316$	19.3305	−	15.1176i	1.08742	−	0.850431i
$317$	12.2672			0.688995			0.344498	−	0.938787i	$-0.388049\pi$
$317$	12.2672			0.688995			0.344498	+	0.938787i	$0.388049\pi$
$318$		0			0
$319$		−	22.1946i		−	1.24266i
$320$	−5.50492	+	2.46046i	−0.307735	+	0.137544i
$321$		0			0
$322$	3.61306	+	1.76113i	0.201348	+	0.0981440i
$323$			1.17517i			0.0653881i
$324$		0			0
$325$			18.9787i			1.05275i
$326$	−3.44705	+	7.07180i	−0.190914	+	0.391671i
$327$		0			0
$328$	1.73205	+	8.11985i	0.0956363	+	0.448344i
$329$			6.17443i			0.340408i
$330$		0			0
$331$	0.587758			0.0323061			0.0161530	−	0.999870i	$-0.494858\pi$
$331$	0.587758			0.0323061			0.0161530	+	0.999870i	$0.494858\pi$
$332$	13.0614	−	10.2148i	0.716837	−	0.560609i
$333$		0			0
$334$	−15.8046	+	32.4239i	−0.864787	+	1.77416i
$335$	−8.71772			−0.476300
$336$		0			0
$337$	32.0318			1.74489			0.872443	−	0.488716i	$-0.162535\pi$
$337$	32.0318			1.74489			0.872443	+	0.488716i	$0.162535\pi$
$338$	3.30770	−	6.78594i	0.179915	−	0.369106i
$339$		0			0
$340$	−8.88679	+	6.95000i	−0.481954	+	0.376917i
$341$	−40.2418			−2.17921
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	4.16379	−	0.888178i	0.224497	−	0.0478874i
$345$		0			0
$346$	−2.51562	+	5.16093i	−0.135241	+	0.277454i
$347$			22.5357i			1.20978i	0.796309	+	0.604889i	$0.206783\pi$
$347$			22.5357i			1.20978i	−0.796309	+	0.604889i	$0.793217\pi$
$348$		0			0
$349$		−	9.66226i		−	0.517209i	−0.965983	−	0.258605i	$-0.916737\pi$
$349$		−	9.66226i		−	0.517209i	0.965983	−	0.258605i	$-0.0832627\pi$
$350$	5.63400	+	2.74621i	0.301150	+	0.146791i
$351$		0			0
$352$	15.9912	−	19.1041i	0.852332	−	1.01825i
$353$			8.41228i			0.447741i	0.974619	+	0.223870i	$0.0718692\pi$
$353$			8.41228i			0.447741i	−0.974619	+	0.223870i	$0.928131\pi$
$354$		0			0
$355$	−2.03229			−0.107863
$356$	−8.08704	+	6.32455i	−0.428613	+	0.335201i
$357$		0			0
$358$	30.8934	+	15.0585i	1.63277	+	0.795869i
$359$	20.2579			1.06917			0.534586	−	0.845114i	$-0.320467\pi$
$359$	20.2579			1.06917			0.534586	+	0.845114i	$0.320467\pi$
$360$		0			0
$361$	−18.9753			−0.998702
$362$	28.9109	+	14.0922i	1.51952	+	0.740670i
$363$		0			0
$364$	−5.27613	−	6.74646i	−0.276544	−	0.353610i
$365$	−1.31216			−0.0686814
$366$		0			0
$367$		−	37.5860i		−	1.96197i	−0.194082	−	0.980985i	$-0.562173\pi$
$367$		−	37.5860i		−	1.96197i	0.194082	−	0.980985i	$-0.437827\pi$
$368$	2.73972	−	11.0336i	0.142818	−	0.575165i
$369$		0			0
$370$	6.11822	+	2.98223i	0.318071	+	0.155039i
$371$		−	10.5926i		−	0.549943i
$372$		0			0
$373$			37.2643i			1.92947i	0.263215	+	0.964737i	$0.415217\pi$
$373$			37.2643i			1.92947i	−0.263215	+	0.964737i	$0.584783\pi$
$374$	20.4239	−	41.9007i	1.05609	−	2.16664i
$375$		0			0
$376$	17.0797	−	3.64327i	0.880817	−	0.187887i
$377$			21.5806i			1.11146i
$378$		0			0
$379$	−13.4549			−0.691131			−0.345565	−	0.938395i	$-0.612313\pi$
$379$	−13.4549			−0.691131			−0.345565	+	0.938395i	$0.612313\pi$
$380$	0.145819	+	0.186455i	0.00748035	+	0.00956493i
$381$		0			0
$382$	5.94598	−	12.1985i	0.304223	−	0.624129i
$383$	−17.8814			−0.913696			−0.456848	−	0.889545i	$-0.651022\pi$
$383$	−17.8814			−0.913696			−0.456848	+	0.889545i	$0.651022\pi$
$384$		0			0
$385$	3.31948			0.169177
$386$	−4.62921	+	9.49708i	−0.235621	+	0.483389i
$387$		0			0
$388$	−7.19192	−	9.19613i	−0.365114	−	0.466863i
$389$	7.56746			0.383685			0.191843	−	0.981426i	$-0.438554\pi$
$389$	7.56746			0.383685			0.191843	+	0.981426i	$0.438554\pi$
$390$		0			0
$391$		−	21.2708i		−	1.07571i
$392$	−2.76619	+	0.590057i	−0.139714	+	0.0298024i
$393$		0			0
$394$	14.2708	−	29.2773i	0.718952	−	1.47497i
$395$		−	9.24813i		−	0.465324i
$396$		0			0
$397$		−	0.422202i		−	0.0211897i	−0.999944	−	0.0105948i	$-0.996627\pi$
$397$		−	0.422202i		−	0.0211897i	0.999944	−	0.0105948i	$-0.00337251\pi$
$398$	−2.90614	−	1.41656i	−0.145672	−	0.0710056i
$399$		0			0
$400$	4.27217	−	17.2051i	0.213608	−	0.860257i
$401$		−	3.67413i		−	0.183477i	−0.995783	−	0.0917386i	$-0.970758\pi$
$401$		−	3.67413i		−	0.183477i	0.995783	−	0.0917386i	$-0.0292424\pi$
$402$		0			0
$403$	39.1285			1.94913
$404$	−4.81143	−	6.15226i	−0.239378	−	0.306086i
$405$		0			0
$406$	6.40639	+	3.12270i	0.317944	+	0.154977i
$407$	−28.1222			−1.39396
$408$		0			0
$409$	23.2115			1.14773			0.573867	−	0.818949i	$-0.305443\pi$
$409$	23.2115			1.14773			0.573867	+	0.818949i	$0.305443\pi$
$410$	2.81256	+	1.37094i	0.138902	+	0.0677060i
$411$		0			0
$412$	25.1760	−	19.6891i	1.24033	−	0.970013i
$413$	6.17443			0.303824
$414$		0			0
$415$		−	6.24886i		−	0.306744i
$416$	−15.5488	+	18.5756i	−0.762342	+	0.910744i
$417$		0			0
$418$	−0.879125	−	0.428516i	−0.0429994	−	0.0209594i
$419$			29.5694i			1.44456i	0.691601	+	0.722279i	$0.256906\pi$
$419$			29.5694i			1.44456i	−0.691601	+	0.722279i	$0.743094\pi$
$420$		0			0
$421$			35.9658i			1.75287i	0.481525	+	0.876433i	$0.340083\pi$
$421$			35.9658i			1.75287i	−0.481525	+	0.876433i	$0.659917\pi$
$422$	13.4141	−	27.5197i	0.652986	−	1.33964i
$423$		0			0
$424$	−29.3013	+	6.25026i	−1.42300	+	0.303540i
$425$		−	33.1685i		−	1.60891i
$426$		0			0
$427$	9.34822			0.452392
$428$	−11.6881	+	9.14082i	−0.564967	+	0.441838i
$429$		0			0
$430$	0.703007	−	1.44226i	0.0339020	−	0.0695518i
$431$	26.0881			1.25662			0.628309	−	0.777964i	$-0.283747\pi$
$431$	26.0881			1.25662			0.628309	+	0.777964i	$0.283747\pi$
$432$		0			0
$433$	37.4426			1.79938			0.899688	−	0.436533i	$-0.143794\pi$
$433$	37.4426			1.79938			0.899688	+	0.436533i	$0.143794\pi$
$434$	5.66187	−	11.6156i	0.271778	−	0.557568i
$435$		0			0
$436$	−17.2986	+	13.5286i	−0.828454	+	0.647900i
$437$	−0.446286			−0.0213487
$438$		0			0
$439$			32.9236i			1.57136i	0.618634	+	0.785679i	$0.287686\pi$
$439$			32.9236i			1.57136i	−0.618634	+	0.785679i	$0.712314\pi$
$440$	−1.95869	−	9.18234i	−0.0933766	−	0.437751i
$441$		0			0
$442$	−19.8589	+	40.7416i	−0.944591	+	1.93788i
$443$			3.82558i			0.181759i	0.995862	+	0.0908795i	$0.0289678\pi$
$443$			3.82558i			0.181759i	−0.995862	+	0.0908795i	$0.971032\pi$
$444$		0			0
$445$			3.86902i			0.183409i
$446$	7.44517	+	3.62904i	0.352539	+	0.171840i
$447$		0			0
$448$	3.26443	+	7.30367i	0.154230	+	0.345066i
$449$		−	20.9883i		−	0.990501i	−0.868750	−	0.495251i	$-0.835076\pi$
$449$		−	20.9883i		−	0.990501i	0.868750	−	0.495251i	$-0.164924\pi$
$450$		0			0
$451$	−12.9278			−0.608748
$452$	−15.8622	+	12.4052i	−0.746097	+	0.583492i
$453$		0			0
$454$	−23.5185	−	11.4638i	−1.10378	−	0.538021i
$455$	−3.22765			−0.151315
$456$		0			0
$457$	16.0953			0.752908			0.376454	−	0.926435i	$-0.377143\pi$
$457$	16.0953			0.752908			0.376454	+	0.926435i	$0.377143\pi$
$458$	−11.6496	−	5.67842i	−0.544349	−	0.265335i
$459$		0			0
$460$	−2.63936	−	3.37488i	−0.123061	−	0.157354i
$461$	28.0400			1.30595			0.652976	−	0.757378i	$-0.273520\pi$
$461$	28.0400			1.30595			0.652976	+	0.757378i	$0.273520\pi$
$462$		0			0
$463$			29.7148i			1.38097i	0.723349	+	0.690483i	$0.242602\pi$
$463$			29.7148i			1.38097i	−0.723349	+	0.690483i	$0.757398\pi$
$464$	4.85786	−	19.5639i	0.225521	−	0.908231i
$465$		0			0
$466$	6.72838	+	3.27965i	0.311686	+	0.151927i
$467$			34.8049i			1.61058i	0.592882	+	0.805289i	$0.297990\pi$
$467$			34.8049i			1.61058i	−0.592882	+	0.805289i	$0.702010\pi$
$468$		0			0
$469$			11.5662i			0.534080i
$470$	2.88370	−	5.91607i	0.133015	−	0.272888i
$471$		0			0
$472$	−3.64327	−	17.0797i	−0.167695	−	0.786156i
$473$			6.62928i			0.304815i
$474$		0			0
$475$	−0.695913			−0.0319307
$476$	9.22092	+	11.7906i	0.422640	+	0.540419i
$477$		0			0
$478$	7.21337	−	14.7986i	0.329932	−	0.676873i
$479$	−11.9604			−0.546483			−0.273241	−	0.961946i	$-0.588096\pi$
$479$	−11.9604			−0.546483			−0.273241	+	0.961946i	$0.588096\pi$
$480$		0			0
$481$	27.3442			1.24679
$482$	18.1502	−	37.2362i	0.826720	−	1.69606i
$483$		0			0
$484$	10.3450	+	13.2279i	0.470228	+	0.601268i
$485$	−4.39963			−0.199777
$486$		0			0
$487$		−	13.1035i		−	0.593775i	−0.954912	−	0.296888i	$-0.904051\pi$
$487$		−	13.1035i		−	0.593775i	0.954912	−	0.296888i	$-0.0959487\pi$
$488$	−5.51598	−	25.8590i	−0.249697	−	1.17058i
$489$		0			0
$490$	−0.467039	+	0.958156i	−0.0210987	+	0.0432851i
$491$			4.69315i			0.211799i	0.994377	+	0.105899i	$0.0337722\pi$
$491$			4.69315i			0.211799i	−0.994377	+	0.105899i	$0.966228\pi$
$492$		0			0
$493$		−	37.7158i		−	1.69863i
$494$	0.854805	+	0.416662i	0.0384595	+	0.0187465i
$495$		0			0
$496$	−35.4719	−	8.80795i	−1.59274	−	0.395488i
$497$			2.69634i			0.120947i
$498$		0			0
$499$	13.7443			0.615278			0.307639	−	0.951503i	$-0.400461\pi$
$499$	13.7443			0.615278			0.307639	+	0.951503i	$0.400461\pi$
$500$	−8.75888	−	11.1998i	−0.391709	−	0.500869i
$501$		0			0
$502$	−6.25919	−	3.05095i	−0.279361	−	0.136171i
$503$	−2.18114			−0.0972521			−0.0486261	−	0.998817i	$-0.515484\pi$
$503$	−2.18114			−0.0972521			−0.0486261	+	0.998817i	$0.515484\pi$
$504$		0			0
$505$	−2.94338			−0.130979
$506$	15.9124	+	7.75625i	0.707391	+	0.344807i
$507$		0			0
$508$	−2.47899	+	1.93872i	−0.109987	+	0.0860167i
$509$	−8.77140			−0.388786			−0.194393	−	0.980924i	$-0.562274\pi$
$509$	−8.77140			−0.388786			−0.194393	+	0.980924i	$0.562274\pi$
$510$		0			0
$511$			1.74091i			0.0770132i
$512$	18.2772	−	13.3396i	0.807744	−	0.589533i
$513$		0			0
$514$	30.1528	+	14.6975i	1.32998	+	0.648281i
$515$		−	12.0447i		−	0.530755i
$516$		0			0
$517$			27.1930i			1.19595i
$518$	3.95668	−	8.11736i	0.173847	−	0.356656i
$519$		0			0
$520$	1.90450	+	8.92832i	0.0835179	+	0.391533i
$521$			7.64302i			0.334847i	0.985885	+	0.167423i	$0.0535447\pi$
$521$			7.64302i			0.334847i	−0.985885	+	0.167423i	$0.946455\pi$
$522$		0			0
$523$	−29.0903			−1.27203			−0.636016	−	0.771676i	$-0.719419\pi$
$523$	−29.0903			−1.27203			−0.636016	+	0.771676i	$0.719419\pi$
$524$	4.41272	−	3.45101i	0.192770	−	0.150758i
$525$		0			0
$526$	4.10703	−	8.42579i	0.179075	−	0.367382i
$527$	−68.3837			−2.97884
$528$		0			0
$529$	−14.9221			−0.648788
$530$	−4.94718	+	10.1494i	−0.214892	+	0.440862i
$531$		0			0
$532$	0.247379	−	0.193465i	0.0107253	−	0.00838779i
$533$	12.5702			0.544476
$534$		0			0
$535$			5.59186i			0.241757i
$536$	31.9945	−	6.82475i	1.38195	−	0.294784i
$537$		0			0
$538$	−13.4581	+	27.6100i	−0.580220	+	1.19035i
$539$		−	4.40413i		−	0.189699i
$540$		0			0
$541$			16.6902i			0.717567i	0.933421	+	0.358784i	$0.116808\pi$
$541$			16.6902i			0.717567i	−0.933421	+	0.358784i	$0.883192\pi$
$542$	5.20096	+	2.53513i	0.223401	+	0.108893i
$543$		0			0
$544$	27.1741	−	32.4640i	1.16508	−	1.39188i
$545$			8.27605i			0.354507i
$546$		0			0
$547$	−6.06961			−0.259518			−0.129759	−	0.991546i	$-0.541420\pi$
$547$	−6.06961			−0.259518			−0.129759	+	0.991546i	$0.541420\pi$
$548$	22.5858	−	17.6634i	0.964818	−	0.754545i
$549$		0			0
$550$	24.8129	+	12.0947i	1.05802	+	0.515718i
$551$	−0.791319			−0.0337113
$552$		0			0
$553$	−12.2700			−0.521772
$554$	−9.30029	−	4.53329i	−0.395131	−	0.192601i
$555$		0			0
$556$	−18.1550	−	23.2144i	−0.769945	−	0.984510i
$557$	1.23215			0.0522079			0.0261039	−	0.999659i	$-0.491690\pi$
$557$	1.23215			0.0522079			0.0261039	+	0.999659i	$0.491690\pi$
$558$		0			0
$559$		−	6.44589i		−	0.272632i
$560$	2.92603	+	0.726554i	0.123647	+	0.0307025i
$561$		0			0
$562$	1.79100	+	0.872997i	0.0755488	+	0.0368252i
$563$		−	26.5142i		−	1.11744i	−0.829356	−	0.558720i	$-0.811293\pi$
$563$		−	26.5142i		−	1.11744i	0.829356	−	0.558720i	$-0.188707\pi$
$564$		0			0
$565$			7.58885i			0.319265i
$566$	−11.1539	+	22.8829i	−0.468835	+	0.961840i
$567$		0			0
$568$	7.45861	−	1.59100i	0.312956	−	0.0667567i
$569$		−	3.22646i		−	0.135260i	−0.997710	−	0.0676301i	$-0.978456\pi$
$569$		−	3.22646i		−	0.135260i	0.997710	−	0.0676301i	$-0.0215438\pi$
$570$		0			0
$571$	20.7231			0.867236			0.433618	−	0.901097i	$-0.357237\pi$
$571$	20.7231			0.867236			0.433618	+	0.901097i	$0.357237\pi$
$572$	−23.2368	−	29.7123i	−0.971579	−	1.24233i
$573$		0			0
$574$	1.81890	−	3.73157i	0.0759194	−	0.155753i
$575$	12.5962			0.525297
$576$		0			0
$577$	−6.99870			−0.291360			−0.145680	−	0.989332i	$-0.546537\pi$
$577$	−6.99870			−0.291360			−0.145680	+	0.989332i	$0.546537\pi$
$578$	24.1728	−	49.5918i	1.00545	−	2.06275i
$579$		0			0
$580$	−4.67990	−	5.98407i	−0.194322	−	0.248475i
$581$	−8.29068			−0.343956
$582$		0			0
$583$		−	46.6514i		−	1.93210i
$584$	4.81569	−	1.02723i	0.199275	−	0.0425073i
$585$		0			0
$586$	−7.97850	+	16.3683i	−0.329589	+	0.676169i
$587$			6.59578i			0.272237i	0.990693	+	0.136119i	$0.0434628\pi$
$587$			6.59578i			0.272237i	−0.990693	+	0.136119i	$0.956537\pi$
$588$		0			0
$589$			1.43477i			0.0591185i
$590$	−5.91607	−	2.88370i	−0.243561	−	0.118720i
$591$		0			0
$592$	−24.7889	−	6.15526i	−1.01882	−	0.252980i
$593$			17.4761i			0.717656i	0.933404	+	0.358828i	$0.116824\pi$
$593$			17.4761i			0.717656i	−0.933404	+	0.358828i	$0.883176\pi$
$594$		0			0
$595$	5.64087			0.231253
$596$	11.4673	+	14.6629i	0.469719	+	0.600617i
$597$		0			0
$598$	−15.4722	−	7.54168i	−0.632704	−	0.308402i
$599$	−17.4691			−0.713766			−0.356883	−	0.934149i	$-0.616161\pi$
$599$	−17.4691			−0.713766			−0.356883	+	0.934149i	$0.616161\pi$
$600$		0			0
$601$	−4.47159			−0.182400			−0.0912001	−	0.995833i	$-0.529070\pi$
$601$	−4.47159			−0.182400			−0.0912001	+	0.995833i	$0.529070\pi$
$602$	−1.91352	−	0.932715i	−0.0779891	−	0.0380146i
$603$		0			0
$604$	−16.9127	+	13.2267i	−0.688167	+	0.538188i
$605$	6.32852			0.257291
$606$		0			0
$607$			21.5209i			0.873507i	0.899581	+	0.436754i	$0.143872\pi$
$607$			21.5209i			0.873507i	−0.899581	+	0.436754i	$0.856128\pi$
$608$	−0.681131	−	0.570144i	−0.0276235	−	0.0231224i
$609$		0			0
$610$	−8.95705	−	4.36598i	−0.362661	−	0.176774i
$611$		−	26.4408i		−	1.06968i
$612$		0			0
$613$			26.0467i			1.05202i	0.850480	+	0.526008i	$0.176312\pi$
$613$			26.0467i			1.05202i	−0.850480	+	0.526008i	$0.823688\pi$
$614$	11.1649	−	22.9053i	0.450578	−	0.924385i
$615$		0			0
$616$	−12.1827	+	2.59869i	−0.490854	+	0.104704i
$617$		−	18.3524i		−	0.738838i	−0.929263	−	0.369419i	$-0.879557\pi$
$617$		−	18.3524i		−	0.738838i	0.929263	−	0.369419i	$-0.120443\pi$
$618$		0			0
$619$	25.2386			1.01443			0.507213	−	0.861821i	$-0.330676\pi$
$619$	25.2386			1.01443			0.507213	+	0.861821i	$0.330676\pi$
$620$	−10.8499	+	8.48528i	−0.435743	+	0.340777i
$621$		0			0
$622$	2.28336	−	4.68444i	0.0915545	−	0.187829i
$623$	5.13323			0.205659
$624$		0			0
$625$	16.8013			0.672053
$626$	−18.3904	+	37.7289i	−0.735029	+	1.50795i
$627$		0			0
$628$	21.7488	−	17.0088i	0.867871	−	0.678727i
$629$	−47.7886			−1.90545
$630$		0			0
$631$		−	10.3071i		−	0.410320i	−0.978728	−	0.205160i	$-0.934228\pi$
$631$		−	10.3071i		−	0.410320i	0.978728	−	0.205160i	$-0.0657715\pi$
$632$	7.23998	+	33.9411i	0.287991	+	1.35011i
$633$		0			0
$634$	−7.60132	+	15.5945i	−0.301887	+	0.619337i
$635$			1.18600i			0.0470651i
$636$		0			0
$637$			4.28230i			0.169671i
$638$	28.2146	+	13.7528i	1.11703	+	0.544478i
$639$		0			0
$640$	0.283268	−	8.52267i	0.0111971	−	0.336888i
$641$			9.80081i			0.387109i	0.981090	+	0.193554i	$0.0620016\pi$
$641$			9.80081i			0.387109i	−0.981090	+	0.193554i	$0.937998\pi$
$642$		0			0
$643$	6.91301			0.272622			0.136311	−	0.990666i	$-0.456475\pi$
$643$	6.91301			0.272622			0.136311	+	0.990666i	$0.456475\pi$
$644$	−4.47762	+	3.50177i	−0.176443	+	0.137989i
$645$		0			0
$646$	−1.49391	−	0.728187i	−0.0587773	−	0.0286501i
$647$	−34.5868			−1.35975			−0.679874	−	0.733329i	$-0.737966\pi$
$647$	−34.5868			−1.35975			−0.679874	+	0.733329i	$0.737966\pi$
$648$		0			0
$649$	27.1930			1.06742
$650$	−24.1264	−	11.7601i	−0.946317	−	0.461268i
$651$		0			0
$652$	−6.85398	−	8.76401i	−0.268423	−	0.343225i
$653$	8.32949			0.325958			0.162979	−	0.986630i	$-0.447890\pi$
$653$	8.32949			0.325958			0.162979	+	0.986630i	$0.447890\pi$
$654$		0			0
$655$		−	2.11114i		−	0.0824891i
$656$	−11.3955	−	2.82959i	−0.444920	−	0.110477i
$657$		0			0
$658$	−7.84916	−	3.82596i	−0.305992	−	0.149151i
$659$			43.5377i			1.69599i	0.530006	+	0.847994i	$0.322190\pi$
$659$			43.5377i			1.69599i	−0.530006	+	0.847994i	$0.677810\pi$
$660$		0			0
$661$		−	5.15619i		−	0.200552i	−0.994960	−	0.100276i	$-0.968027\pi$
$661$		−	5.15619i		−	0.200552i	0.994960	−	0.100276i	$-0.0319726\pi$
$662$	−0.364201	+	0.747178i	−0.0141551	+	0.0290399i
$663$		0			0
$664$	4.89198	+	22.9336i	0.189846	+	0.889998i
$665$		−	0.118352i		−	0.00458948i
$666$		0			0
$667$	14.3231			0.554591
$668$	−31.4252	−	40.1826i	−1.21588	−	1.55471i
$669$		0			0
$670$	5.40189	−	11.0823i	0.208693	−	0.428146i
$671$	41.1708			1.58938
$672$		0			0
$673$	−3.16066			−0.121834			−0.0609172	−	0.998143i	$-0.519403\pi$
$673$	−3.16066			−0.121834			−0.0609172	+	0.998143i	$0.519403\pi$
$674$	−19.8484	+	40.7200i	−0.764531	+	1.56848i
$675$		0			0
$676$	6.57692	+	8.40974i	0.252958	+	0.323452i
$677$	−2.51349			−0.0966012			−0.0483006	−	0.998833i	$-0.515381\pi$
$677$	−2.51349			−0.0966012			−0.0483006	+	0.998833i	$0.515381\pi$
$678$		0			0
$679$			5.83722i			0.224012i
$680$	−3.32843	−	15.6037i	−0.127640	−	0.598376i
$681$		0			0
$682$	24.9356	−	51.1568i	0.954834	−	1.95889i
$683$			1.45836i			0.0558026i	0.999611	+	0.0279013i	$0.00888241\pi$
$683$			1.45836i			0.0558026i	−0.999611	+	0.0279013i	$0.991118\pi$
$684$		0			0
$685$		−	10.8055i		−	0.412859i
$686$	1.27124	+	0.619645i	0.0485360	+	0.0236582i
$687$		0			0
$688$	−1.45099	+	5.84351i	−0.0553184	+	0.222782i
$689$			45.3608i			1.72811i
$690$		0			0
$691$	−47.4386			−1.80465			−0.902325	−	0.431055i	$-0.858141\pi$
$691$	−47.4386			−1.80465			−0.902325	+	0.431055i	$0.858141\pi$
$692$	−5.00197	−	6.39589i	−0.190146	−	0.243135i
$693$		0			0
$694$	−28.6482	−	13.9641i	−1.08747	−	0.530071i
$695$	−11.1063			−0.421285
$696$		0			0
$697$	−21.9685			−0.832117
$698$	12.2830	+	5.98717i	0.464919	+	0.226618i
$699$		0			0
$700$	−6.98216	+	5.46046i	−0.263901	+	0.206386i
$701$	17.9259			0.677051			0.338526	−	0.940957i	$-0.390072\pi$
$701$	17.9259			0.677051			0.338526	+	0.940957i	$0.390072\pi$
$702$		0			0
$703$			1.00266i			0.0378160i
$704$	14.3770	+	32.1663i	0.541852	+	1.21231i
$705$		0			0
$706$	−10.6940	−	5.21263i	−0.402474	−	0.196180i
$707$			3.90513i			0.146868i
$708$		0			0
$709$		−	27.5590i		−	1.03500i	−0.855683	−	0.517501i	$-0.826862\pi$
$709$		−	27.5590i		−	1.03500i	0.855683	−	0.517501i	$-0.173138\pi$
$710$	1.25930	−	2.58352i	0.0472606	−	0.0969577i
$711$		0			0
$712$	−3.02890	−	14.1995i	−0.113513	−	0.532149i
$713$		−	25.9696i		−	0.972570i
$714$		0			0
$715$	−14.2150			−0.531611
$716$	−38.2859	+	29.9419i	−1.43081	+	1.11898i
$717$		0			0
$718$	−12.5527	+	25.7526i	−0.468464	+	0.961079i
$719$	48.7684			1.81876			0.909378	−	0.415971i	$-0.136558\pi$
$719$	48.7684			1.81876			0.909378	+	0.415971i	$0.136558\pi$
$720$		0			0
$721$	−15.9804			−0.595141
$722$	11.7580	−	24.1221i	0.437587	−	0.897733i
$723$		0			0
$724$	−35.8290	+	28.0204i	−1.33157	+	1.04137i
$725$	22.3346			0.829486
$726$		0			0
$727$			26.4470i			0.980864i	0.871479	+	0.490432i	$0.163161\pi$
$727$			26.4470i			0.980864i	−0.871479	+	0.490432i	$0.836839\pi$
$728$	11.8457	−	2.52680i	0.439030	−	0.0936494i
$729$		0			0
$730$	0.813072	−	1.66806i	0.0300931	−	0.0617377i
$731$			11.2653i			0.416661i
$732$		0			0
$733$		−	35.5433i		−	1.31282i	−0.754403	−	0.656411i	$-0.772074\pi$
$733$		−	35.5433i		−	1.31282i	0.754403	−	0.656411i	$-0.227926\pi$
$734$	47.7806	+	23.2899i	1.76361	+	0.859648i
$735$		0			0
$736$	12.3286	+	10.3197i	0.454439	+	0.380391i
$737$			50.9393i			1.87637i
$738$		0			0
$739$	−27.3506			−1.00611			−0.503054	−	0.864255i	$-0.667790\pi$
$739$	−27.3506			−1.00611			−0.503054	+	0.864255i	$0.667790\pi$
$740$	−7.58225	+	5.92977i	−0.278729	+	0.217983i
$741$		0			0
$742$	13.4657	+	6.56368i	0.494343	+	0.240960i
$743$	29.2925			1.07464			0.537319	−	0.843379i	$-0.319437\pi$
$743$	29.2925			1.07464			0.537319	+	0.843379i	$0.319437\pi$
$744$		0			0
$745$	7.01508			0.257013
$746$	−47.3718	−	23.0907i	−1.73440	−	0.845409i
$747$		0			0
$748$	40.6102	+	51.9272i	1.48485	+	1.89865i
$749$	7.41901			0.271085
$750$		0			0
$751$		−	4.38966i		−	0.160181i	−0.996788	−	0.0800904i	$-0.974479\pi$
$751$		−	4.38966i		−	0.160181i	0.996788	−	0.0800904i	$-0.0255209\pi$
$752$	−5.95189	+	23.9698i	−0.217043	+	0.874090i
$753$		0			0
$754$	−27.4341	−	13.3723i	−0.999090	−	0.486992i
$755$			8.09140i			0.294476i
$756$		0			0
$757$		−	6.60965i		−	0.240232i	−0.992760	−	0.120116i	$-0.961673\pi$
$757$		−	6.60965i		−	0.240232i	0.992760	−	0.120116i	$-0.0383266\pi$
$758$	8.33725	−	17.1043i	0.302823	−	0.621257i
$759$		0			0
$760$	−0.327384	+	0.0698343i	−0.0118755	+	0.00253316i
$761$		−	9.83905i		−	0.356665i	−0.983970	−	0.178333i	$-0.942930\pi$
$761$		−	9.83905i		−	0.356665i	0.983970	−	0.178333i	$-0.0570703\pi$
$762$		0			0
$763$	10.9803			0.397512
$764$	11.8228	+	15.1175i	0.427733	+	0.546931i
$765$		0			0
$766$	11.0801	−	22.7315i	0.400341	−	0.821321i
$767$	−26.4408			−0.954720
$768$		0			0
$769$	−15.2643			−0.550446			−0.275223	−	0.961380i	$-0.588752\pi$
$769$	−15.2643			−0.550446			−0.275223	+	0.961380i	$0.588752\pi$
$770$	−2.05690	+	4.21985i	−0.0741256	+	0.152073i
$771$		0			0
$772$	−9.20456	−	11.7696i	−0.331279	−	0.423599i
$773$	−50.1053			−1.80216			−0.901082	−	0.433650i	$-0.857226\pi$
$773$	−50.1053			−1.80216			−0.901082	+	0.433650i	$0.857226\pi$
$774$		0			0
$775$		−	40.4956i		−	1.45464i
$776$	16.1469	−	3.44429i	0.579639	−	0.123643i
$777$		0			0
$778$	−4.68914	+	9.62003i	−0.168114	+	0.344895i
$779$			0.460925i			0.0165143i
$780$		0			0
$781$			11.8750i			0.424922i
$782$	27.0402	+	13.1804i	0.966956	+	0.471328i
$783$		0			0
$784$	0.963957	−	3.88211i	0.0344270	−	0.138647i
$785$		−	10.4051i		−	0.371374i
$786$		0			0
$787$	18.5548			0.661406			0.330703	−	0.943735i	$-0.392714\pi$
$787$	18.5548			0.661406			0.330703	+	0.943735i	$0.392714\pi$
$788$	28.3755	+	36.2831i	1.01084	+	1.29253i
$789$		0			0
$790$	11.7565	+	5.73056i	0.418279	+	0.203884i
$791$	10.0685			0.357995
$792$		0			0
$793$	−40.0318			−1.42157
$794$	0.536718	+	0.261615i	0.0190474	+	0.00928438i
$795$		0			0
$796$	3.60155	−	2.81663i	0.127654	−	0.0998328i
$797$	45.6932			1.61854			0.809268	−	0.587439i	$-0.199864\pi$
$797$	45.6932			1.61854			0.809268	+	0.587439i	$0.199864\pi$
$798$		0			0
$799$			46.2096i			1.63478i
$800$	19.2246	+	16.0920i	0.679691	+	0.568939i
$801$		0			0
$802$	4.67068	+	2.27665i	0.164927	+	0.0803915i
$803$			7.66718i			0.270569i
$804$		0			0
$805$			2.14219i			0.0755024i
$806$	−24.2458	+	49.7416i	−0.854022	+	1.75207i
$807$		0			0
$808$	10.8023	−	2.30425i	0.380025	−	0.0810632i
$809$			34.1703i			1.20136i	0.799489	+	0.600681i	$0.205104\pi$
$809$			34.1703i			1.20136i	−0.799489	+	0.600681i	$0.794896\pi$
$810$		0			0
$811$	−15.5443			−0.545834			−0.272917	−	0.962038i	$-0.587988\pi$
$811$	−15.5443			−0.545834			−0.272917	+	0.962038i	$0.587988\pi$
$812$	−7.93938	+	6.20907i	−0.278618	+	0.217896i
$813$		0			0
$814$	17.4258	−	35.7499i	0.610773	−	1.25303i
$815$	−4.19290			−0.146871
$816$		0			0
$817$	0.236358			0.00826912
$818$	−14.3829	+	29.5072i	−0.502885	+	1.03170i
$819$		0			0
$820$	−3.48558	+	2.72593i	−0.121722	+	0.0951936i
$821$	−21.3688			−0.745775			−0.372887	−	0.927877i	$-0.621632\pi$
$821$	−21.3688			−0.745775			−0.372887	+	0.927877i	$0.621632\pi$
$822$		0			0
$823$			34.9533i			1.21839i	0.793019	+	0.609197i	$0.208508\pi$
$823$			34.9533i			1.21839i	−0.793019	+	0.609197i	$0.791492\pi$
$824$	9.42934	+	44.2049i	0.328487	+	1.53995i
$825$		0			0
$826$	−3.82596	+	7.84916i	−0.133122	+	0.273107i
$827$			7.96828i			0.277084i	0.990357	+	0.138542i	$0.0442416\pi$
$827$			7.96828i			0.277084i	−0.990357	+	0.138542i	$0.955758\pi$
$828$		0			0
$829$		−	17.6279i		−	0.612241i	−0.951993	−	0.306120i	$-0.900969\pi$
$829$		−	17.6279i		−	0.612241i	0.951993	−	0.306120i	$-0.0990310\pi$
$830$	7.94377	+	3.87207i	0.275732	+	0.134402i
$831$		0			0
$832$	−13.9792	−	31.2765i	−0.484643	−	1.08432i
$833$		−	7.48403i		−	0.259306i
$834$		0			0
$835$	−19.2243			−0.665283
$836$	1.08949	−	0.852047i	0.0376808	−	0.0294687i
$837$		0			0
$838$	−37.5897	−	18.3225i	−1.29851	−	0.632941i
$839$	13.0585			0.450831			0.225415	−	0.974263i	$-0.427626\pi$
$839$	13.0585			0.450831			0.225415	+	0.974263i	$0.427626\pi$
$840$		0			0
$841$	−3.60344			−0.124256
$842$	−45.7210	−	22.2860i	−1.57565	−	0.768027i
$843$		0			0
$844$	26.6720	+	34.1048i	0.918089	+	1.17394i
$845$	4.02341			0.138409
$846$		0			0
$847$		−	8.39637i		−	0.288503i
$848$	10.2109	−	41.1218i	0.350642	−	1.41213i
$849$		0			0
$850$	42.1650	+	20.5527i	1.44625	+	0.704952i
$851$		−	18.1483i		−	0.622117i
$852$		0			0
$853$			35.6157i			1.21946i	0.792610	+	0.609729i	$0.208722\pi$
$853$			35.6157i			1.21946i	−0.792610	+	0.609729i	$0.791278\pi$
$854$	−5.79258	+	11.8838i	−0.198218	+	0.406655i
$855$		0			0
$856$	−4.37764	−	20.5224i	−0.149625	−	0.701442i
$857$		−	48.8491i		−	1.66865i	−0.551271	−	0.834327i	$-0.685857\pi$
$857$		−	48.8491i		−	1.66865i	0.551271	−	0.834327i	$-0.314143\pi$
$858$		0			0
$859$	−39.6213			−1.35186			−0.675930	−	0.736965i	$-0.736258\pi$
$859$	−39.6213			−1.35186			−0.675930	+	0.736965i	$0.736258\pi$
$860$	1.39783	+	1.78737i	0.0476657	+	0.0609490i
$861$		0			0
$862$	−16.1653	+	33.1641i	−0.550594	+	1.12957i
$863$	28.1238			0.957346			0.478673	−	0.877993i	$-0.341118\pi$
$863$	28.1238			0.957346			0.478673	+	0.877993i	$0.341118\pi$
$864$		0			0
$865$	−3.05994			−0.104041
$866$	−23.2011	+	47.5984i	−0.788406	+	1.61746i
$867$		0			0
$868$	11.2579	+	14.3951i	0.382117	+	0.488603i
$869$	−54.0386			−1.83313
$870$		0			0
$871$		−	49.5301i		−	1.67826i
$872$	−6.47898	−	30.3735i	−0.219406	−	1.02858i
$873$		0			0
$874$	0.276539	−	0.567334i	0.00935406	−	0.0191904i
$875$			7.10902i			0.240329i
$876$		0			0
$877$		−	18.6093i		−	0.628392i	−0.949358	−	0.314196i	$-0.898265\pi$
$877$		−	18.6093i		−	0.628392i	0.949358	−	0.314196i	$-0.101735\pi$
$878$	−41.8537	−	20.4010i	−1.41249	−	0.688499i
$879$		0			0
$880$	12.8866	+	3.19984i	0.434407	+	0.107867i
$881$		−	46.6579i		−	1.57195i	−0.618261	−	0.785973i	$-0.712162\pi$
$881$		−	46.6579i		−	1.57195i	0.618261	−	0.785973i	$-0.287838\pi$
$882$		0			0
$883$	18.2503			0.614173			0.307087	−	0.951682i	$-0.400646\pi$
$883$	18.2503			0.614173			0.307087	+	0.951682i	$0.400646\pi$
$884$	−39.4867	−	50.4907i	−1.32808	−	1.69819i
$885$		0			0
$886$	−4.86322	−	2.37050i	−0.163383	−	0.0796387i
$887$	−3.18771			−0.107033			−0.0535163	−	0.998567i	$-0.517043\pi$
$887$	−3.18771			−0.107033			−0.0535163	+	0.998567i	$0.517043\pi$
$888$		0			0
$889$	1.57353			0.0527746
$890$	−4.91844	−	2.39742i	−0.164866	−	0.0803617i
$891$		0			0
$892$	−9.22673	+	7.21585i	−0.308934	+	0.241605i
$893$	0.969530			0.0324441
$894$		0			0
$895$			18.3168i			0.612264i
$896$	−11.3075	−	0.375826i	−0.377756	−	0.0125555i
$897$		0			0
$898$	26.6811	+	13.0053i	0.890361	+	0.433993i
$899$		−	46.0473i		−	1.53576i
$900$		0			0
$901$		−	79.2756i		−	2.64105i
$902$	8.01067	−	16.4343i	0.266726	−	0.547203i
$903$		0			0
$904$	−5.94100	−	27.8515i	−0.197595	−	0.926326i
$905$			17.1414i			0.569799i
$906$		0			0
$907$	28.9992			0.962901			0.481451	−	0.876473i	$-0.340110\pi$
$907$	28.9992			0.962901			0.481451	+	0.876473i	$0.340110\pi$
$908$	29.1463	−	22.7941i	0.967253	−	0.756449i
$909$		0			0
$910$	2.00000	−	4.10311i	0.0662994	−	0.136017i
$911$	26.2517			0.869759			0.434880	−	0.900489i	$-0.356791\pi$
$911$	26.2517			0.869759			0.434880	+	0.900489i	$0.356791\pi$
$912$		0			0
$913$	−36.5133			−1.20841
$914$	−9.97340	+	20.4610i	−0.329891	+	0.676789i
$915$		0			0
$916$	14.4372	−	11.2908i	0.477019	−	0.373057i
$917$	−2.80096			−0.0924958
$918$		0			0
$919$			44.3857i			1.46415i	0.681224	+	0.732075i	$0.261448\pi$
$919$			44.3857i			1.46415i	−0.681224	+	0.732075i	$0.738552\pi$
$920$	5.92573	−	1.26402i	0.195365	−	0.0416734i
$921$		0			0
$922$	−17.3748	+	35.6454i	−0.572210	+	1.17392i
$923$		−	11.5465i		−	0.380059i
$924$		0			0
$925$		−	28.2995i		−	0.930482i
$926$	−37.7745	−	18.4126i	−1.24135	−	0.605077i
$927$		0			0
$928$	21.8602	+	18.2982i	0.717595	+	0.600667i
$929$		−	44.1182i		−	1.44747i	−0.690078	−	0.723735i	$-0.742424\pi$
$929$		−	44.1182i		−	1.44747i	0.690078	−	0.723735i	$-0.257576\pi$
$930$		0			0
$931$	−0.157023			−0.00514623
$932$	−8.33841	+	6.52113i	−0.273134	+	0.213607i
$933$		0			0
$934$	−44.2452	−	21.5667i	−1.44775	−	0.705683i
$935$	24.8431			0.812457
$936$		0			0
$937$	4.54976			0.148634			0.0743172	−	0.997235i	$-0.476322\pi$
$937$	4.54976			0.148634			0.0743172	+	0.997235i	$0.476322\pi$
$938$	−14.7034	−	7.16697i	−0.480084	−	0.234010i
$939$		0			0
$940$	5.73385	+	7.33173i	0.187018	+	0.239135i
$941$	33.4057			1.08899			0.544497	−	0.838763i	$-0.316721\pi$
$941$	33.4057			1.08899			0.544497	+	0.838763i	$0.316721\pi$
$942$		0			0
$943$		−	8.34284i		−	0.271680i
$944$	23.9698	+	5.95189i	0.780152	+	0.193717i
$945$		0			0
$946$	−8.42738	−	4.10780i	−0.273998	−	0.133556i
$947$		−	23.7401i		−	0.771451i	−0.922614	−	0.385725i	$-0.873951\pi$
$947$		−	23.7401i		−	0.771451i	0.922614	−	0.385725i	$-0.126049\pi$
$948$		0			0
$949$		−	7.45508i		−	0.242002i
$950$	0.431219	−	0.884669i	0.0139906	−	0.0287025i
$951$		0			0
$952$	−20.7023	+	4.41600i	−0.670965	+	0.143124i
$953$			14.0051i			0.453670i	0.973933	+	0.226835i	$0.0728378\pi$
$953$			14.0051i			0.453670i	−0.973933	+	0.226835i	$0.927162\pi$
$954$		0			0
$955$	7.23254			0.234039
$956$	14.3428	+	18.3398i	0.463880	+	0.593151i
$957$		0			0
$958$	7.41118	−	15.2044i	0.239444	−	0.491233i
$959$	−14.3363			−0.462943
$960$		0			0
$961$	−52.4899			−1.69322
$962$	−16.9437	+	34.7609i	−0.546287	+	1.12074i
$963$		0			0
$964$	36.0893	+	46.1464i	1.16236	+	1.48628i
$965$	−5.63086			−0.181264
$966$		0			0
$967$		−	18.5228i		−	0.595652i	−0.954620	−	0.297826i	$-0.903738\pi$
$967$		−	18.5228i		−	0.595652i	0.954620	−	0.297826i	$-0.0962616\pi$
$968$	−23.2260	+	4.95434i	−0.746512	+	0.159239i
$969$		0			0
$970$	2.72621	−	5.59297i	0.0875333	−	0.179579i
$971$		−	47.5729i		−	1.52669i	−0.645993	−	0.763343i	$-0.723557\pi$
$971$		−	47.5729i		−	1.52669i	0.645993	−	0.763343i	$-0.276443\pi$
$972$		0			0
$973$			14.7353i			0.472391i
$974$	16.6576	+	8.11951i	0.533744	+	0.260166i
$975$		0			0
$976$	36.2908	+	9.01128i	1.16164	+	0.288444i
$977$		−	7.09500i		−	0.226989i	−0.993539	−	0.113495i	$-0.963796\pi$
$977$		−	7.09500i		−	0.226989i	0.993539	−	0.113495i	$-0.0362045\pi$
$978$		0			0
$979$	22.6074			0.722536
$980$	−0.928644	−	1.18743i	−0.0296644	−	0.0379312i
$981$		0			0
$982$	−5.96610	−	2.90809i	−0.190386	−	0.0928008i
$983$	−9.29050			−0.296321			−0.148160	−	0.988963i	$-0.547335\pi$
$983$	−9.29050			−0.296321			−0.148160	+	0.988963i	$0.547335\pi$
$984$		0			0
$985$	17.3586			0.553092
$986$	47.9456	+	23.3704i	1.52690	+	0.744265i
$987$		0			0
$988$	−1.05935	+	0.828476i	−0.0337025	+	0.0263573i
$989$	−4.27814			−0.136037
$990$		0			0
$991$			35.4037i			1.12464i	0.826921	+	0.562319i	$0.190091\pi$
$991$			35.4037i			1.12464i	−0.826921	+	0.562319i	$0.809909\pi$
$992$	33.1770	−	39.6354i	1.05337	−	1.25843i
$993$		0			0
$994$	−3.42769	−	1.67077i	−0.108720	−	0.0529938i
$995$		−	1.72306i		−	0.0546248i
$996$		0			0
$997$			10.8948i			0.345041i	0.985006	+	0.172520i	$0.0551911\pi$
$997$			10.8948i			0.345041i	−0.985006	+	0.172520i	$0.944809\pi$
$998$	−8.51657	+	17.4722i	−0.269587	+	0.553073i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.j.a.323.8	yes	24
3.2	odd	2	inner	504.2.j.a.323.17	yes	24
4.3	odd	2		2016.2.j.a.1583.10		24
8.3	odd	2	inner	504.2.j.a.323.18	yes	24
8.5	even	2		2016.2.j.a.1583.16		24
12.11	even	2		2016.2.j.a.1583.15		24
24.5	odd	2		2016.2.j.a.1583.9		24
24.11	even	2	inner	504.2.j.a.323.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.j.a.323.7	✓	24	24.11	even	2	inner
504.2.j.a.323.8	yes	24	1.1	even	1	trivial
504.2.j.a.323.17	yes	24	3.2	odd	2	inner
504.2.j.a.323.18	yes	24	8.3	odd	2	inner
2016.2.j.a.1583.9		24	24.5	odd	2
2016.2.j.a.1583.10		24	4.3	odd	2
2016.2.j.a.1583.15		24	12.11	even	2
2016.2.j.a.1583.16		24	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.619645 + 1.27124i) q^{2} +(-1.23208 - 1.57543i) q^{4} -0.753720 q^{5} +1.00000i q^{7} +(2.76619 - 0.590057i) q^{8} +O(q^{10})\)	\(q+(-0.619645 + 1.27124i) q^{2} +(-1.23208 - 1.57543i) q^{4} -0.753720 q^{5} +1.00000i q^{7} +(2.76619 - 0.590057i) q^{8} +(0.467039 - 0.958156i) q^{10} +4.40413i q^{11} -4.28230i q^{13} +(-1.27124 - 0.619645i) q^{14} +(-0.963957 + 3.88211i) q^{16} +7.48403i q^{17} +0.157023 q^{19} +(0.928644 + 1.18743i) q^{20} +(-5.59869 - 2.72900i) q^{22} -2.84216 q^{23} -4.43191 q^{25} +(5.44381 + 2.65350i) q^{26} +(1.57543 - 1.23208i) q^{28} -5.03950 q^{29} +9.13728i q^{31} +(-4.33777 - 3.63095i) q^{32} +(-9.51396 - 4.63744i) q^{34} -0.753720i q^{35} +6.38541i q^{37} +(-0.0972987 + 0.199614i) q^{38} +(-2.08494 + 0.444738i) q^{40} +2.93539i q^{41} +1.50524 q^{43} +(6.93840 - 5.42624i) q^{44} +(1.76113 - 3.61306i) q^{46} +6.17443 q^{47} -1.00000 q^{49} +(2.74621 - 5.63400i) q^{50} +(-6.74646 + 5.27613i) q^{52} -10.5926 q^{53} -3.31948i q^{55} +(0.590057 + 2.76619i) q^{56} +(3.12270 - 6.40639i) q^{58} -6.17443i q^{59} -9.34822i q^{61} +(-11.6156 - 5.66187i) q^{62} +(7.30367 - 3.26443i) q^{64} +3.22765i q^{65} +11.5662 q^{67} +(11.7906 - 9.22092i) q^{68} +(0.958156 + 0.467039i) q^{70} +2.69634 q^{71} +1.74091 q^{73} +(-8.11736 - 3.95668i) q^{74} +(-0.193465 - 0.247379i) q^{76} -4.40413 q^{77} +12.2700i q^{79} +(0.726554 - 2.92603i) q^{80} +(-3.73157 - 1.81890i) q^{82} +8.29068i q^{83} -5.64087i q^{85} +(-0.932715 + 1.91352i) q^{86} +(2.59869 + 12.1827i) q^{88} -5.13323i q^{89} +4.28230 q^{91} +(3.50177 + 4.47762i) q^{92} +(-3.82596 + 7.84916i) q^{94} -0.118352 q^{95} +5.83722 q^{97} +(0.619645 - 1.27124i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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