LMFDB - Embedded newform 684.2.c.b.647.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(647,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, 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("684.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.c (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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			647.28
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28221 + 0.596605i) q^{2} +(1.28813 + 1.52995i) q^{4} +0.875520i q^{5} +1.57625i q^{7} +(0.738874 + 2.73021i) q^{8} +O(q^{10})$	\(q+(1.28221 + 0.596605i) q^{2} +(1.28813 + 1.52995i) q^{4} +0.875520i q^{5} +1.57625i q^{7} +(0.738874 + 2.73021i) q^{8} +(-0.522340 + 1.12260i) q^{10} -1.17159 q^{11} +1.22802 q^{13} +(-0.940399 + 2.02108i) q^{14} +(-0.681467 + 3.94152i) q^{16} +1.69830i q^{17} +1.00000i q^{19} +(-1.33950 + 1.12778i) q^{20} +(-1.50222 - 0.698976i) q^{22} -2.82059 q^{23} +4.23346 q^{25} +(1.57458 + 0.732645i) q^{26} +(-2.41158 + 2.03041i) q^{28} -3.36748i q^{29} +0.711161i q^{31} +(-3.22532 + 4.64729i) q^{32} +(-1.01321 + 2.17757i) q^{34} -1.38004 q^{35} +4.09715 q^{37} +(-0.596605 + 1.28221i) q^{38} +(-2.39036 + 0.646899i) q^{40} -2.74242i q^{41} -0.560484i q^{43} +(-1.50915 - 1.79247i) q^{44} +(-3.61659 - 1.68278i) q^{46} -5.51577 q^{47} +4.51543 q^{49} +(5.42819 + 2.52571i) q^{50} +(1.58185 + 1.87881i) q^{52} -2.34318i q^{53} -1.02575i q^{55} +(-4.30350 + 1.16465i) q^{56} +(2.00906 - 4.31782i) q^{58} +5.11852 q^{59} +12.9257 q^{61} +(-0.424282 + 0.911858i) q^{62} +(-6.90813 + 4.03457i) q^{64} +1.07516i q^{65} -10.0216i q^{67} +(-2.59830 + 2.18762i) q^{68} +(-1.76950 - 0.823338i) q^{70} -5.22020 q^{71} +4.48272 q^{73} +(5.25340 + 2.44438i) q^{74} +(-1.52995 + 1.28813i) q^{76} -1.84672i q^{77} -6.92030i q^{79} +(-3.45088 - 0.596638i) q^{80} +(1.63614 - 3.51636i) q^{82} -12.4321 q^{83} -1.48689 q^{85} +(0.334387 - 0.718658i) q^{86} +(-0.865657 - 3.19869i) q^{88} +6.17734i q^{89} +1.93567i q^{91} +(-3.63328 - 4.31535i) q^{92} +(-7.07237 - 3.29073i) q^{94} -0.875520 q^{95} +7.36164 q^{97} +(5.78974 + 2.69393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.28221	+	0.596605i	0.906659	+	0.421863i
$2$	1.28221	+	0.596605i	0.906659	+	0.421863i
$3$		0			0
$3$		0			0
$4$	1.28813	+	1.52995i	0.644063	+	0.764973i
$5$			0.875520i			0.391545i	0.980649	+	0.195772i	$0.0627213\pi$
$5$			0.875520i			0.391545i	−0.980649	+	0.195772i	$0.937279\pi$
$6$		0			0
$7$			1.57625i			0.595767i	0.954602	+	0.297883i	$0.0962806\pi$
$7$			1.57625i			0.595767i	−0.954602	+	0.297883i	$0.903719\pi$
$8$	0.738874	+	2.73021i	0.261231	+	0.965276i
$9$		0			0
$10$	−0.522340	+	1.12260i	−0.165178	+	0.354998i
$11$	−1.17159			−0.353247			−0.176624	−	0.984278i	$-0.556518\pi$
$11$	−1.17159			−0.353247			−0.176624	+	0.984278i	$0.556518\pi$
$12$		0			0
$13$	1.22802			0.340592			0.170296	−	0.985393i	$-0.445528\pi$
$13$	1.22802			0.340592			0.170296	+	0.985393i	$0.445528\pi$
$14$	−0.940399	+	2.02108i	−0.251332	+	0.540157i
$15$		0			0
$16$	−0.681467	+	3.94152i	−0.170367	+	0.985381i
$17$			1.69830i			0.411897i	0.978563	+	0.205949i	$0.0660280\pi$
$17$			1.69830i			0.411897i	−0.978563	+	0.205949i	$0.933972\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.33950	+	1.12778i	−0.299521	+	0.252179i
$21$		0			0
$22$	−1.50222	−	0.698976i	−0.320275	−	0.149022i
$23$	−2.82059			−0.588134			−0.294067	−	0.955785i	$-0.595009\pi$
$23$	−2.82059			−0.588134			−0.294067	+	0.955785i	$0.595009\pi$
$24$		0			0
$25$	4.23346			0.846693
$26$	1.57458	+	0.732645i	0.308801	+	0.143683i
$27$		0			0
$28$	−2.41158	+	2.03041i	−0.455745	+	0.383711i
$29$		−	3.36748i		−	0.625326i	−0.949864	−	0.312663i	$-0.898779\pi$
$29$		−	3.36748i		−	0.625326i	0.949864	−	0.312663i	$-0.101221\pi$
$30$		0			0
$31$			0.711161i			0.127728i	0.997959	+	0.0638642i	$0.0203424\pi$
$31$			0.711161i			0.127728i	−0.997959	+	0.0638642i	$0.979658\pi$
$32$	−3.22532	+	4.64729i	−0.570161	+	0.821533i
$33$		0			0
$34$	−1.01321	+	2.17757i	−0.173764	+	0.373450i
$35$	−1.38004			−0.233269
$36$		0			0
$37$	4.09715			0.673567			0.336783	−	0.941582i	$-0.390661\pi$
$37$	4.09715			0.673567			0.336783	+	0.941582i	$0.390661\pi$
$38$	−0.596605	+	1.28221i	−0.0967821	+	0.208002i
$39$		0			0
$40$	−2.39036	+	0.646899i	−0.377949	+	0.102284i
$41$		−	2.74242i		−	0.428294i	−0.976801	−	0.214147i	$-0.931303\pi$
$41$		−	2.74242i		−	0.428294i	0.976801	−	0.214147i	$-0.0686972\pi$
$42$		0			0
$43$		−	0.560484i		−	0.0854730i	−0.999086	−	0.0427365i	$-0.986392\pi$
$43$		−	0.560484i		−	0.0854730i	0.999086	−	0.0427365i	$-0.0136076\pi$
$44$	−1.50915	−	1.79247i	−0.227513	−	0.270225i
$45$		0			0
$46$	−3.61659	−	1.68278i	−0.533237	−	0.248112i
$47$	−5.51577			−0.804557			−0.402279	−	0.915517i	$-0.631782\pi$
$47$	−5.51577			−0.804557			−0.402279	+	0.915517i	$0.631782\pi$
$48$		0			0
$49$	4.51543			0.645062
$50$	5.42819	+	2.52571i	0.767662	+	0.357189i
$51$		0			0
$52$	1.58185	+	1.87881i	0.219363	+	0.260544i
$53$		−	2.34318i		−	0.321860i	−0.986966	−	0.160930i	$-0.948551\pi$
$53$		−	2.34318i		−	0.321860i	0.986966	−	0.160930i	$-0.0514494\pi$
$54$		0			0
$55$		−	1.02575i		−	0.138312i
$56$	−4.30350	+	1.16465i	−0.575079	+	0.155633i
$57$		0			0
$58$	2.00906	−	4.31782i	0.263802	−	0.566957i
$59$	5.11852			0.666375			0.333187	−	0.942861i	$-0.391876\pi$
$59$	5.11852			0.666375			0.333187	+	0.942861i	$0.391876\pi$
$60$		0			0
$61$	12.9257			1.65497			0.827486	−	0.561486i	$-0.189770\pi$
$61$	12.9257			1.65497			0.827486	+	0.561486i	$0.189770\pi$
$62$	−0.424282	+	0.911858i	−0.0538839	+	0.115806i
$63$		0			0
$64$	−6.90813	+	4.03457i	−0.863516	+	0.504321i
$65$			1.07516i			0.133357i
$66$		0			0
$67$		−	10.0216i		−	1.22434i	−0.790728	−	0.612168i	$-0.790298\pi$
$67$		−	10.0216i		−	1.22434i	0.790728	−	0.612168i	$-0.209702\pi$
$68$	−2.59830	+	2.18762i	−0.315090	+	0.265288i
$69$		0			0
$70$	−1.76950	−	0.823338i	−0.211496	−	0.0984077i
$71$	−5.22020			−0.619523			−0.309762	−	0.950814i	$-0.600249\pi$
$71$	−5.22020			−0.619523			−0.309762	+	0.950814i	$0.600249\pi$
$72$		0			0
$73$	4.48272			0.524662			0.262331	−	0.964978i	$-0.415509\pi$
$73$	4.48272			0.524662			0.262331	+	0.964978i	$0.415509\pi$
$74$	5.25340	+	2.44438i	0.610696	+	0.284153i
$75$		0			0
$76$	−1.52995	+	1.28813i	−0.175497	+	0.147758i
$77$		−	1.84672i		−	0.210453i
$78$		0			0
$79$		−	6.92030i		−	0.778595i	−0.921112	−	0.389297i	$-0.872718\pi$
$79$		−	6.92030i		−	0.778595i	0.921112	−	0.389297i	$-0.127282\pi$
$80$	−3.45088	−	0.596638i	−0.385820	−	0.0667062i
$81$		0			0
$82$	1.63614	−	3.51636i	0.180682	−	0.388317i
$83$	−12.4321			−1.36460			−0.682301	−	0.731071i	$-0.739021\pi$
$83$	−12.4321			−1.36460			−0.682301	+	0.731071i	$0.739021\pi$
$84$		0			0
$85$	−1.48689			−0.161276
$86$	0.334387	−	0.718658i	0.0360579	−	0.0774949i
$87$		0			0
$88$	−0.865657	−	3.19869i	−0.0922793	−	0.340981i
$89$			6.17734i			0.654797i	0.944886	+	0.327398i	$0.106172\pi$
$89$			6.17734i			0.654797i	−0.944886	+	0.327398i	$0.893828\pi$
$90$		0			0
$91$			1.93567i			0.202914i
$92$	−3.63328	−	4.31535i	−0.378795	−	0.449907i
$93$		0			0
$94$	−7.07237	−	3.29073i	−0.729459	−	0.339413i
$95$	−0.875520			−0.0898265
$96$		0			0
$97$	7.36164			0.747461			0.373731	−	0.927537i	$-0.378078\pi$
$97$	7.36164			0.747461			0.373731	+	0.927537i	$0.378078\pi$
$98$	5.78974	+	2.69393i	0.584852	+	0.272128i
$99$		0			0
$100$	5.45323	+	6.47697i	0.545323	+	0.647697i
$101$		−	13.7324i		−	1.36643i	−0.730218	−	0.683215i	$-0.760581\pi$
$101$		−	13.7324i		−	1.36643i	0.730218	−	0.683215i	$-0.239419\pi$
$102$		0			0
$103$		−	13.7131i		−	1.35119i	−0.737274	−	0.675594i	$-0.763887\pi$
$103$		−	13.7131i		−	1.35119i	0.737274	−	0.675594i	$-0.236113\pi$
$104$	0.907354	+	3.35277i	0.0889734	+	0.328766i
$105$		0			0
$106$	1.39795	−	3.00445i	0.135781	−	0.291818i
$107$	10.7901			1.04312			0.521561	−	0.853214i	$-0.325350\pi$
$107$	10.7901			1.04312			0.521561	+	0.853214i	$0.325350\pi$
$108$		0			0
$109$	−11.0027			−1.05387			−0.526936	−	0.849905i	$-0.676659\pi$
$109$	−11.0027			−1.05387			−0.526936	+	0.849905i	$0.676659\pi$
$110$	0.611967	−	1.31523i	0.0583488	−	0.125402i
$111$		0			0
$112$	−6.21283	−	1.07416i	−0.587057	−	0.101499i
$113$		−	9.23206i		−	0.868479i	−0.900797	−	0.434240i	$-0.857017\pi$
$113$		−	9.23206i		−	0.868479i	0.900797	−	0.434240i	$-0.142983\pi$
$114$		0			0
$115$		−	2.46949i		−	0.230281i
$116$	5.15206	−	4.33774i	0.478357	−	0.402749i
$117$		0			0
$118$	6.56302	+	3.05374i	0.604175	+	0.281119i
$119$	−2.67694			−0.245395
$120$		0			0
$121$	−9.62738			−0.875216
$122$	16.5735	+	7.71156i	1.50050	+	0.698172i
$123$		0			0
$124$	−1.08804	+	0.916065i	−0.0977087	+	0.0822650i
$125$			8.08408i			0.723062i
$126$		0			0
$127$			5.26930i			0.467575i	0.972288	+	0.233787i	$0.0751119\pi$
$127$			5.26930i			0.467575i	−0.972288	+	0.233787i	$0.924888\pi$
$128$	−11.2647	+	1.05174i	−0.995670	+	0.0929615i
$129$		0			0
$130$	−0.641445	+	1.37858i	−0.0562585	+	0.120909i
$131$	19.7081			1.72190			0.860951	−	0.508687i	$-0.169869\pi$
$131$	19.7081			1.72190			0.860951	+	0.508687i	$0.169869\pi$
$132$		0			0
$133$	−1.57625			−0.136678
$134$	5.97895	−	12.8498i	0.516503	−	1.11006i
$135$		0			0
$136$	−4.63671	+	1.25483i	−0.397595	+	0.107600i
$137$		−	7.58624i		−	0.648136i	−0.946034	−	0.324068i	$-0.894949\pi$
$137$		−	7.58624i		−	0.648136i	0.946034	−	0.324068i	$-0.105051\pi$
$138$		0			0
$139$			3.08331i			0.261523i	0.991414	+	0.130761i	$0.0417422\pi$
$139$			3.08331i			0.261523i	−0.991414	+	0.130761i	$0.958258\pi$
$140$	−1.77766	−	2.11138i	−0.150240	−	0.178445i
$141$		0			0
$142$	−6.69339	−	3.11440i	−0.561697	−	0.261354i
$143$	−1.43874			−0.120313
$144$		0			0
$145$	2.94830			0.244843
$146$	5.74778	+	2.67441i	0.475690	+	0.221336i
$147$		0			0
$148$	5.27764	+	6.26841i	0.433819	+	0.515260i
$149$		−	12.7351i		−	1.04330i	−0.853160	−	0.521649i	$-0.825317\pi$
$149$		−	12.7351i		−	1.04330i	0.853160	−	0.521649i	$-0.174683\pi$
$150$		0			0
$151$			8.49238i			0.691100i	0.938400	+	0.345550i	$0.112308\pi$
$151$			8.49238i			0.691100i	−0.938400	+	0.345550i	$0.887692\pi$
$152$	−2.73021	+	0.738874i	−0.221450	+	0.0599306i
$153$		0			0
$154$	1.10176	−	2.36788i	0.0887824	−	0.190809i
$155$	−0.622636			−0.0500113
$156$		0			0
$157$	−7.11561			−0.567887			−0.283944	−	0.958841i	$-0.591643\pi$
$157$	−7.11561			−0.567887			−0.283944	+	0.958841i	$0.591643\pi$
$158$	4.12869	−	8.87328i	0.328461	−	0.705920i
$159$		0			0
$160$	−4.06880	−	2.82383i	−0.321667	−	0.223243i
$161$		−	4.44596i		−	0.350391i
$162$		0			0
$163$		−	2.51124i		−	0.196695i	−0.995152	−	0.0983476i	$-0.968644\pi$
$163$		−	2.51124i		−	0.196695i	0.995152	−	0.0983476i	$-0.0313557\pi$
$164$	4.19575	−	3.53258i	0.327633	−	0.275848i
$165$		0			0
$166$	−15.9406	−	7.41706i	−1.23723	−	0.575676i
$167$	−0.610148			−0.0472146			−0.0236073	−	0.999721i	$-0.507515\pi$
$167$	−0.610148			−0.0472146			−0.0236073	+	0.999721i	$0.507515\pi$
$168$		0			0
$169$	−11.4920			−0.883997
$170$	−1.90651	−	0.887087i	−0.146222	−	0.0680365i
$171$		0			0
$172$	0.857510	−	0.721974i	0.0653845	−	0.0550500i
$173$		−	5.17208i		−	0.393226i	−0.980481	−	0.196613i	$-0.937006\pi$
$173$		−	5.17208i		−	0.393226i	0.980481	−	0.196613i	$-0.0629943\pi$
$174$		0			0
$175$			6.67300i			0.504431i
$176$	0.798399	−	4.61785i	0.0601816	−	0.348083i
$177$		0			0
$178$	−3.68543	+	7.92065i	−0.276235	+	0.593678i
$179$	19.0678			1.42519			0.712597	−	0.701574i	$-0.247519\pi$
$179$	19.0678			1.42519			0.712597	+	0.701574i	$0.247519\pi$
$180$		0			0
$181$	1.43223			0.106456			0.0532282	−	0.998582i	$-0.483049\pi$
$181$	1.43223			0.106456			0.0532282	+	0.998582i	$0.483049\pi$
$182$	−1.15483	+	2.48194i	−0.0856018	+	0.183973i
$183$		0			0
$184$	−2.08406	−	7.70082i	−0.153639	−	0.567712i
$185$			3.58714i			0.263731i
$186$		0			0
$187$		−	1.98970i		−	0.145502i
$188$	−7.10500	−	8.43882i	−0.518185	−	0.615464i
$189$		0			0
$190$	−1.12260	−	0.522340i	−0.0814420	−	0.0378945i
$191$	−6.19439			−0.448210			−0.224105	−	0.974565i	$-0.571946\pi$
$191$	−6.19439			−0.448210			−0.224105	+	0.974565i	$0.571946\pi$
$192$		0			0
$193$	−17.0662			−1.22845			−0.614227	−	0.789129i	$-0.710532\pi$
$193$	−17.0662			−1.22845			−0.614227	+	0.789129i	$0.710532\pi$
$194$	9.43917	+	4.39199i	0.677693	+	0.315327i
$195$		0			0
$196$	5.81645	+	6.90837i	0.415460	+	0.493455i
$197$			15.6500i			1.11501i	0.830172	+	0.557507i	$0.188242\pi$
$197$			15.6500i			1.11501i	−0.830172	+	0.557507i	$0.811758\pi$
$198$		0			0
$199$			22.2997i			1.58078i	0.612602	+	0.790392i	$0.290123\pi$
$199$			22.2997i			1.58078i	−0.612602	+	0.790392i	$0.709877\pi$
$200$	3.12800	+	11.5583i	0.221183	+	0.817292i
$201$		0			0
$202$	8.19284	−	17.6079i	0.576446	−	1.23889i
$203$	5.30800			0.372548
$204$		0			0
$205$	2.40104			0.167696
$206$	8.18128	−	17.5830i	0.570017	−	1.22507i
$207$		0			0
$208$	−0.836857	+	4.84028i	−0.0580256	+	0.335613i
$209$		−	1.17159i		−	0.0810405i
$210$		0			0
$211$		−	5.82733i		−	0.401170i	−0.979676	−	0.200585i	$-0.935716\pi$
$211$		−	5.82733i		−	0.401170i	0.979676	−	0.200585i	$-0.0642843\pi$
$212$	3.58493	−	3.01831i	0.246214	−	0.207298i
$213$		0			0
$214$	13.8352	+	6.43745i	0.945756	+	0.440055i
$215$	0.490715			0.0334665
$216$		0			0
$217$	−1.12097			−0.0760963
$218$	−14.1078	−	6.56429i	−0.955503	−	0.444590i
$219$		0			0
$220$	1.56934	−	1.32129i	0.105805	−	0.0890816i
$221$			2.08555i			0.140289i
$222$		0			0
$223$			8.67750i			0.581089i	0.956862	+	0.290544i	$0.0938364\pi$
$223$			8.67750i			0.581089i	−0.956862	+	0.290544i	$0.906164\pi$
$224$	−7.32530	−	5.08390i	−0.489442	−	0.339683i
$225$		0			0
$226$	5.50789	−	11.8374i	0.366380	−	0.787415i
$227$	9.67095			0.641883			0.320942	−	0.947099i	$-0.396001\pi$
$227$	9.67095			0.641883			0.320942	+	0.947099i	$0.396001\pi$
$228$		0			0
$229$	−18.5767			−1.22759			−0.613793	−	0.789467i	$-0.710357\pi$
$229$	−18.5767			−1.22759			−0.613793	+	0.789467i	$0.710357\pi$
$230$	1.47331	−	3.16640i	0.0971470	−	0.208786i
$231$		0			0
$232$	9.19394	−	2.48815i	0.603612	−	0.163355i
$233$			12.6346i			0.827720i	0.910341	+	0.413860i	$0.135820\pi$
$233$			12.6346i			0.827720i	−0.910341	+	0.413860i	$0.864180\pi$
$234$		0			0
$235$		−	4.82916i		−	0.315020i
$236$	6.59330	+	7.83106i	0.429187	+	0.509759i
$237$		0			0
$238$	−3.43240	−	1.59707i	−0.222489	−	0.103523i
$239$	9.59098			0.620389			0.310194	−	0.950673i	$-0.399606\pi$
$239$	9.59098			0.620389			0.310194	+	0.950673i	$0.399606\pi$
$240$		0			0
$241$	10.0365			0.646506			0.323253	−	0.946313i	$-0.395224\pi$
$241$	10.0365			0.646506			0.323253	+	0.946313i	$0.395224\pi$
$242$	−12.3443	−	5.74374i	−0.793523	−	0.369222i
$243$		0			0
$244$	16.6500	+	19.7757i	1.06591	+	1.26601i
$245$			3.95335i			0.252571i
$246$		0			0
$247$			1.22802i			0.0781372i
$248$	−1.94162	+	0.525459i	−0.123293	+	0.0333666i
$249$		0			0
$250$	−4.82300	+	10.3655i	−0.305034	+	0.655571i
$251$	9.94743			0.627876			0.313938	−	0.949443i	$-0.398352\pi$
$251$	9.94743			0.627876			0.313938	+	0.949443i	$0.398352\pi$
$252$		0			0
$253$	3.30458			0.207757
$254$	−3.14369	+	6.75635i	−0.197253	+	0.423931i
$255$		0			0
$256$	−15.0712	−	5.37203i	−0.941950	−	0.335752i
$257$			16.8455i			1.05079i	0.850858	+	0.525396i	$0.176083\pi$
$257$			16.8455i			1.05079i	−0.850858	+	0.525396i	$0.823917\pi$
$258$		0			0
$259$			6.45813i			0.401289i
$260$	−1.64493	+	1.38494i	−0.102015	+	0.0858903i
$261$		0			0
$262$	25.2699	+	11.7579i	1.56118	+	0.726408i
$263$	−26.5036			−1.63428			−0.817139	−	0.576440i	$-0.804441\pi$
$263$	−26.5036			−1.63428			−0.817139	+	0.576440i	$0.804441\pi$
$264$		0			0
$265$	2.05150			0.126023
$266$	−2.02108	−	0.940399i	−0.123921	−	0.0576595i
$267$		0			0
$268$	15.3325	−	12.9091i	0.936584	−	0.788549i
$269$			19.0041i			1.15870i	0.815080	+	0.579349i	$0.196693\pi$
$269$			19.0041i			1.15870i	−0.815080	+	0.579349i	$0.803307\pi$
$270$		0			0
$271$		−	6.80319i		−	0.413265i	−0.978419	−	0.206632i	$-0.933750\pi$
$271$		−	6.80319i		−	0.413265i	0.978419	−	0.206632i	$-0.0662504\pi$
$272$	−6.69387	−	1.15733i	−0.405876	−	0.0701736i
$273$		0			0
$274$	4.52599	−	9.72715i	0.273425	−	0.587639i
$275$	−4.95988			−0.299092
$276$		0			0
$277$	−12.8041			−0.769325			−0.384662	−	0.923057i	$-0.625682\pi$
$277$	−12.8041			−0.769325			−0.384662	+	0.923057i	$0.625682\pi$
$278$	−1.83952	+	3.95345i	−0.110327	+	0.237112i
$279$		0			0
$280$	−1.01968	−	3.76780i	−0.0609372	−	0.225169i
$281$		−	17.6648i		−	1.05379i	−0.849929	−	0.526897i	$-0.823355\pi$
$281$		−	17.6648i		−	1.05379i	0.849929	−	0.526897i	$-0.176645\pi$
$282$		0			0
$283$			1.21184i			0.0720364i	0.999351	+	0.0360182i	$0.0114674\pi$
$283$			1.21184i			0.0720364i	−0.999351	+	0.0360182i	$0.988533\pi$
$284$	−6.72427	−	7.98662i	−0.399012	−	0.473919i
$285$		0			0
$286$	−1.84476	−	0.858358i	−0.109083	−	0.0507558i
$287$	4.32274			0.255163
$288$		0			0
$289$	14.1158			0.830341
$290$	3.78034	+	1.75897i	0.221989	+	0.103290i
$291$		0			0
$292$	5.77430	+	6.85831i	0.337915	+	0.401352i
$293$			28.0167i			1.63675i	0.574684	+	0.818375i	$0.305125\pi$
$293$			28.0167i			1.63675i	−0.574684	+	0.818375i	$0.694875\pi$
$294$		0			0
$295$			4.48137i			0.260915i
$296$	3.02728	+	11.1861i	0.175957	+	0.650178i
$297$		0			0
$298$	7.59780	−	16.3290i	0.440129	−	0.945915i
$299$	−3.46375			−0.200314
$300$		0			0
$301$	0.883463			0.0509220
$302$	−5.06659	+	10.8890i	−0.291550	+	0.626592i
$303$		0			0
$304$	−3.94152	−	0.681467i	−0.226062	−	0.0390848i
$305$			11.3167i			0.647995i
$306$		0			0
$307$		−	16.2810i		−	0.929204i	−0.885520	−	0.464602i	$-0.846197\pi$
$307$		−	16.2810i		−	0.929204i	0.885520	−	0.464602i	$-0.153803\pi$
$308$	2.82538	−	2.37880i	0.160991	−	0.135545i
$309$		0			0
$310$	−0.798350	−	0.371468i	−0.0453432	−	0.0210979i
$311$	−27.6225			−1.56633			−0.783163	−	0.621816i	$-0.786395\pi$
$311$	−27.6225			−1.56633			−0.783163	+	0.621816i	$0.786395\pi$
$312$		0			0
$313$	−9.21609			−0.520924			−0.260462	−	0.965484i	$-0.583875\pi$
$313$	−9.21609			−0.520924			−0.260462	+	0.965484i	$0.583875\pi$
$314$	−9.12370	−	4.24521i	−0.514880	−	0.239571i
$315$		0			0
$316$	10.5877	−	8.91422i	0.595604	−	0.501464i
$317$			14.5060i			0.814740i	0.913263	+	0.407370i	$0.133554\pi$
$317$			14.5060i			0.814740i	−0.913263	+	0.407370i	$0.866446\pi$
$318$		0			0
$319$			3.94531i			0.220895i
$320$	−3.53235	−	6.04821i	−0.197464	−	0.338105i
$321$		0			0
$322$	2.65248	−	5.70066i	0.147817	−	0.317685i
$323$	−1.69830			−0.0944957
$324$		0			0
$325$	5.19879			0.288377
$326$	1.49822	−	3.21993i	0.0829785	−	0.178335i
$327$		0			0
$328$	7.48739	−	2.02630i	0.413422	−	0.111884i
$329$		−	8.69423i		−	0.479328i
$330$		0			0
$331$		−	36.1018i		−	1.98433i	−0.124918	−	0.992167i	$-0.539867\pi$
$331$		−	36.1018i		−	1.98433i	0.124918	−	0.992167i	$-0.460133\pi$
$332$	−16.0141	−	19.0205i	−0.878889	−	1.04388i
$333$		0			0
$334$	−0.782337	−	0.364017i	−0.0428076	−	0.0199181i
$335$	8.77413			0.479382
$336$		0			0
$337$	−33.7434			−1.83812			−0.919060	−	0.394117i	$-0.871051\pi$
$337$	−33.7434			−1.83812			−0.919060	+	0.394117i	$0.871051\pi$
$338$	−14.7351	−	6.85616i	−0.801484	−	0.372926i
$339$		0			0
$340$	−1.91530	−	2.27486i	−0.103872	−	0.123372i
$341$		−	0.833189i		−	0.0451197i
$342$		0			0
$343$			18.1512i			0.980073i
$344$	1.53024	−	0.414127i	0.0825051	−	0.0223282i
$345$		0			0
$346$	3.08569	−	6.63170i	0.165888	−	0.356522i
$347$	0.637441			0.0342196			0.0171098	−	0.999854i	$-0.494554\pi$
$347$	0.637441			0.0342196			0.0171098	+	0.999854i	$0.494554\pi$
$348$		0			0
$349$	−11.9214			−0.638139			−0.319069	−	0.947731i	$-0.603370\pi$
$349$	−11.9214			−0.638139			−0.319069	+	0.947731i	$0.603370\pi$
$350$	−3.98114	+	8.55619i	−0.212801	+	0.457347i
$351$		0			0
$352$	3.77874	−	5.44472i	0.201408	−	0.290204i
$353$			20.2177i			1.07608i	0.842919	+	0.538041i	$0.180835\pi$
$353$			20.2177i			1.07608i	−0.842919	+	0.538041i	$0.819165\pi$
$354$		0			0
$355$		−	4.57039i		−	0.242571i
$356$	−9.45099	+	7.95719i	−0.500902	+	0.421730i
$357$		0			0
$358$	24.4489	+	11.3759i	1.29217	+	0.601237i
$359$	−9.41793			−0.497060			−0.248530	−	0.968624i	$-0.579947\pi$
$359$	−9.41793			−0.497060			−0.248530	+	0.968624i	$0.579947\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	1.83641	+	0.854473i	0.0965198	+	0.0449101i
$363$		0			0
$364$	−2.96147	+	2.49339i	−0.155223	+	0.130689i
$365$			3.92471i			0.205429i
$366$		0			0
$367$			27.8731i			1.45497i	0.686126	+	0.727483i	$0.259310\pi$
$367$			27.8731i			1.45497i	−0.686126	+	0.727483i	$0.740690\pi$
$368$	1.92214	−	11.1174i	0.100199	−	0.579536i
$369$		0			0
$370$	−2.14010	+	4.59946i	−0.111259	+	0.239115i
$371$	3.69344			0.191754
$372$		0			0
$373$	24.9736			1.29308			0.646542	−	0.762879i	$-0.276215\pi$
$373$	24.9736			1.29308			0.646542	+	0.762879i	$0.276215\pi$
$374$	1.18707	−	2.55122i	0.0613818	−	0.131920i
$375$		0			0
$376$	−4.07546	−	15.0592i	−0.210176	−	0.776620i
$377$		−	4.13535i		−	0.212981i
$378$		0			0
$379$			35.6475i			1.83109i	0.402214	+	0.915546i	$0.368241\pi$
$379$			35.6475i			1.83109i	−0.402214	+	0.915546i	$0.631759\pi$
$380$	−1.12778	−	1.33950i	−0.0578539	−	0.0687148i
$381$		0			0
$382$	−7.94250	−	3.69560i	−0.406374	−	0.189083i
$383$	−33.6422			−1.71904			−0.859519	−	0.511104i	$-0.829237\pi$
$383$	−33.6422			−1.71904			−0.859519	+	0.511104i	$0.829237\pi$
$384$		0			0
$385$	1.61684			0.0824017
$386$	−21.8825	−	10.1818i	−1.11379	−	0.518240i
$387$		0			0
$388$	9.48272	+	11.2629i	0.481412	+	0.571788i
$389$		−	23.9119i		−	1.21238i	−0.795318	−	0.606192i	$-0.792696\pi$
$389$		−	23.9119i		−	1.21238i	0.795318	−	0.606192i	$-0.207304\pi$
$390$		0			0
$391$		−	4.79020i		−	0.242251i
$392$	3.33634	+	12.3281i	0.168510	+	0.622663i
$393$		0			0
$394$	−9.33685	+	20.0666i	−0.470384	+	1.01094i
$395$	6.05886			0.304855
$396$		0			0
$397$	10.0545			0.504622			0.252311	−	0.967646i	$-0.418809\pi$
$397$	10.0545			0.504622			0.252311	+	0.967646i	$0.418809\pi$
$398$	−13.3041	+	28.5929i	−0.666875	+	1.43323i
$399$		0			0
$400$	−2.88497	+	16.6863i	−0.144248	+	0.834315i
$401$		−	23.9729i		−	1.19715i	−0.801066	−	0.598576i	$-0.795734\pi$
$401$		−	23.9729i		−	1.19715i	0.801066	−	0.598576i	$-0.204266\pi$
$402$		0			0
$403$			0.873322i			0.0435033i
$404$	21.0099	−	17.6891i	1.04528	−	0.880066i
$405$		0			0
$406$	6.80596	+	3.16678i	0.337774	+	0.157164i
$407$	−4.80017			−0.237936
$408$		0			0
$409$	−19.1002			−0.944442			−0.472221	−	0.881480i	$-0.656548\pi$
$409$	−19.1002			−0.944442			−0.472221	+	0.881480i	$0.656548\pi$
$410$	3.07864	+	1.43247i	0.152043	+	0.0707449i
$411$		0			0
$412$	20.9802	−	17.6641i	1.03362	−	0.870250i
$413$			8.06807i			0.397004i
$414$		0			0
$415$		−	10.8846i		−	0.534302i
$416$	−3.96076	+	5.70698i	−0.194192	+	0.279808i
$417$		0			0
$418$	0.698976	−	1.50222i	0.0341880	−	0.0734761i
$419$	−6.79093			−0.331759			−0.165879	−	0.986146i	$-0.553046\pi$
$419$	−6.79093			−0.331759			−0.165879	+	0.986146i	$0.553046\pi$
$420$		0			0
$421$	−14.8350			−0.723014			−0.361507	−	0.932369i	$-0.617738\pi$
$421$	−14.8350			−0.723014			−0.361507	+	0.932369i	$0.617738\pi$
$422$	3.47661	−	7.47186i	0.169239	−	0.363725i
$423$		0			0
$424$	6.39738	−	1.73131i	0.310684	−	0.0840800i
$425$			7.18967i			0.348750i
$426$		0			0
$427$			20.3742i			0.985977i
$428$	13.8990	+	16.5083i	0.671836	+	0.797960i
$429$		0			0
$430$	0.629200	+	0.292763i	0.0303427	+	0.0141183i
$431$	29.7003			1.43061			0.715306	−	0.698812i	$-0.246287\pi$
$431$	29.7003			1.43061			0.715306	+	0.698812i	$0.246287\pi$
$432$		0			0
$433$	17.0227			0.818060			0.409030	−	0.912521i	$-0.365867\pi$
$433$	17.0227			0.818060			0.409030	+	0.912521i	$0.365867\pi$
$434$	−1.43732	−	0.668775i	−0.0689934	−	0.0321022i
$435$		0			0
$436$	−14.1729	−	16.8336i	−0.678759	−	0.806183i
$437$		−	2.82059i		−	0.134927i
$438$		0			0
$439$			38.3145i			1.82865i	0.404982	+	0.914324i	$0.367278\pi$
$439$			38.3145i			1.82865i	−0.404982	+	0.914324i	$0.632722\pi$
$440$	2.80052	−	0.757900i	0.133509	−	0.0361315i
$441$		0			0
$442$	−1.24425	+	2.67411i	−0.0591828	+	0.127194i
$443$	0.275281			0.0130790			0.00653950	−	0.999979i	$-0.497918\pi$
$443$	0.275281			0.0130790			0.00653950	+	0.999979i	$0.497918\pi$
$444$		0			0
$445$	−5.40838			−0.256382
$446$	−5.17704	+	11.1264i	−0.245140	+	0.526849i
$447$		0			0
$448$	−6.35949	−	10.8889i	−0.300458	−	0.514454i
$449$			30.9508i			1.46066i	0.683094	+	0.730330i	$0.260634\pi$
$449$			30.9508i			1.46066i	−0.683094	+	0.730330i	$0.739366\pi$
$450$		0			0
$451$			3.21299i			0.151294i
$452$	14.1246	−	11.8921i	0.664363	−	0.559355i
$453$		0			0
$454$	12.4002	+	5.76973i	0.581969	+	0.270787i
$455$	−1.69472			−0.0794497
$456$		0			0
$457$	−1.95918			−0.0916467			−0.0458233	−	0.998950i	$-0.514591\pi$
$457$	−1.95918			−0.0916467			−0.0458233	+	0.998950i	$0.514591\pi$
$458$	−23.8193	−	11.0830i	−1.11300	−	0.517874i
$459$		0			0
$460$	3.77818	−	3.18101i	0.176159	−	0.148315i
$461$		−	4.32505i		−	0.201438i	−0.994915	−	0.100719i	$-0.967886\pi$
$461$		−	4.32505i		−	0.201438i	0.994915	−	0.100719i	$-0.0321143\pi$
$462$		0			0
$463$		−	25.1142i		−	1.16716i	−0.812057	−	0.583578i	$-0.801652\pi$
$463$		−	25.1142i		−	1.16716i	0.812057	−	0.583578i	$-0.198348\pi$
$464$	13.2730	+	2.29483i	0.616184	+	0.106535i
$465$		0			0
$466$	−7.53786	+	16.2002i	−0.349185	+	0.750460i
$467$	40.6445			1.88080			0.940401	−	0.340068i	$-0.110450\pi$
$467$	40.6445			1.88080			0.940401	+	0.340068i	$0.110450\pi$
$468$		0			0
$469$	15.7966			0.729419
$470$	2.88110	−	6.19200i	0.132895	−	0.285616i
$471$		0			0
$472$	3.78194	+	13.9747i	0.174078	+	0.643236i
$473$			0.656657i			0.0301931i
$474$		0			0
$475$			4.23346i			0.194245i
$476$	−3.44823	−	4.09557i	−0.158049	−	0.187720i
$477$		0			0
$478$	12.2976	+	5.72202i	0.562481	+	0.261719i
$479$	21.8446			0.998104			0.499052	−	0.866572i	$-0.333682\pi$
$479$	21.8446			0.998104			0.499052	+	0.866572i	$0.333682\pi$
$480$		0			0
$481$	5.03139			0.229412
$482$	12.8689	+	5.98781i	0.586161	+	0.272737i
$483$		0			0
$484$	−12.4013	−	14.7294i	−0.563694	−	0.669517i
$485$			6.44527i			0.292664i
$486$		0			0
$487$			3.68887i			0.167159i	0.996501	+	0.0835794i	$0.0266352\pi$
$487$			3.68887i			0.167159i	−0.996501	+	0.0835794i	$0.973365\pi$
$488$	9.55050	+	35.2900i	0.432331	+	1.59750i
$489$		0			0
$490$	−2.35859	+	5.06903i	−0.106550	+	0.228995i
$491$	−23.2115			−1.04752			−0.523759	−	0.851866i	$-0.675471\pi$
$491$	−23.2115			−1.04752			−0.523759	+	0.851866i	$0.675471\pi$
$492$		0			0
$493$	5.71898			0.257570
$494$	−0.732645	+	1.57458i	−0.0329632	+	0.0708439i
$495$		0			0
$496$	−2.80306	−	0.484633i	−0.125861	−	0.0217607i
$497$		−	8.22834i		−	0.369091i
$498$		0			0
$499$		−	36.5684i		−	1.63703i	−0.574488	−	0.818513i	$-0.694799\pi$
$499$		−	36.5684i		−	1.63703i	0.574488	−	0.818513i	$-0.305201\pi$
$500$	−12.3682	+	10.4133i	−0.553123	+	0.465698i
$501$		0			0
$502$	12.7547	+	5.93468i	0.569270	+	0.264878i
$503$	−16.7949			−0.748848			−0.374424	−	0.927258i	$-0.622160\pi$
$503$	−16.7949			−0.748848			−0.374424	+	0.927258i	$0.622160\pi$
$504$		0			0
$505$	12.0230			0.535018
$506$	4.23716	+	1.97153i	0.188365	+	0.0876450i
$507$		0			0
$508$	−8.06174	+	6.78752i	−0.357682	+	0.301147i
$509$		−	0.402260i		−	0.0178299i	−0.999960	−	0.00891493i	$-0.997162\pi$
$509$		−	0.402260i		−	0.0178299i	0.999960	−	0.00891493i	$-0.00283775\pi$
$510$		0			0
$511$			7.06588i			0.312576i
$512$	−16.1195	−	15.8796i	−0.712387	−	0.701787i
$513$		0			0
$514$	−10.0501	+	21.5994i	−0.443291	+	0.952710i
$515$	12.0061			0.529050
$516$		0			0
$517$	6.46221			0.284208
$518$	−3.85295	+	8.28068i	−0.169289	+	0.363832i
$519$		0			0
$520$	−2.93541	+	0.794407i	−0.128726	+	0.0348371i
$521$			20.9261i			0.916789i	0.888749	+	0.458394i	$0.151575\pi$
$521$			20.9261i			0.916789i	−0.888749	+	0.458394i	$0.848425\pi$
$522$		0			0
$523$		−	13.2699i		−	0.580252i	−0.956989	−	0.290126i	$-0.906303\pi$
$523$		−	13.2699i		−	0.580252i	0.956989	−	0.290126i	$-0.0936971\pi$
$524$	25.3865	+	30.1523i	1.10901	+	1.31721i
$525$		0			0
$526$	−33.9831	−	15.8121i	−1.48173	−	0.689442i
$527$	−1.20776			−0.0526109
$528$		0			0
$529$	−15.0443			−0.654098
$530$	2.63045	+	1.22393i	0.114260	+	0.0531643i
$531$		0			0
$532$	−2.03041	−	2.41158i	−0.0880293	−	0.104555i
$533$		−	3.36776i		−	0.145874i
$534$		0			0
$535$			9.44698i			0.408428i
$536$	27.3612	−	7.40472i	1.18182	−	0.319835i
$537$		0			0
$538$	−11.3379	+	24.3672i	−0.488812	+	1.05054i
$539$	−5.29023			−0.227866
$540$		0			0
$541$	−12.0161			−0.516611			−0.258305	−	0.966063i	$-0.583164\pi$
$541$	−12.0161			−0.516611			−0.258305	+	0.966063i	$0.583164\pi$
$542$	4.05882	−	8.72312i	0.174341	−	0.374690i
$543$		0			0
$544$	−7.89248	−	5.47754i	−0.338387	−	0.234848i
$545$		−	9.63312i		−	0.412638i
$546$		0			0
$547$		−	12.3917i		−	0.529832i	−0.964272	−	0.264916i	$-0.914656\pi$
$547$		−	12.3917i		−	0.529832i	0.964272	−	0.264916i	$-0.0853442\pi$
$548$	11.6065	−	9.77202i	0.495806	−	0.417440i
$549$		0			0
$550$	−6.35961	−	2.95909i	−0.271175	−	0.126176i
$551$	3.36748			0.143460
$552$		0			0
$553$	10.9081			0.463861
$554$	−16.4176	−	7.63900i	−0.697515	−	0.324550i
$555$		0			0
$556$	−4.71730	+	3.97169i	−0.200058	+	0.168437i
$557$		−	11.9614i		−	0.506820i	−0.967359	−	0.253410i	$-0.918448\pi$
$557$		−	11.9614i		−	0.506820i	0.967359	−	0.253410i	$-0.0815521\pi$
$558$		0			0
$559$		−	0.688287i		−	0.0291115i
$560$	0.940451	−	5.43946i	0.0397413	−	0.229859i
$561$		0			0
$562$	10.5389	−	22.6500i	0.444557	−	0.955433i
$563$	31.1491			1.31278			0.656389	−	0.754423i	$-0.272083\pi$
$563$	31.1491			1.31278			0.656389	+	0.754423i	$0.272083\pi$
$564$		0			0
$565$	8.08286			0.340048
$566$	−0.722989	+	1.55383i	−0.0303895	+	0.0653125i
$567$		0			0
$568$	−3.85707	−	14.2523i	−0.161839	−	0.598011i
$569$		−	19.6945i		−	0.825637i	−0.910813	−	0.412819i	$-0.864544\pi$
$569$		−	19.6945i		−	0.825637i	0.910813	−	0.412819i	$-0.135456\pi$
$570$		0			0
$571$		−	18.8382i		−	0.788354i	−0.919034	−	0.394177i	$-0.871030\pi$
$571$		−	18.8382i		−	0.788354i	0.919034	−	0.394177i	$-0.128970\pi$
$572$	−1.85328	−	2.20119i	−0.0774893	−	0.0920364i
$573$		0			0
$574$	5.54266	+	2.57897i	0.231346	+	0.107644i
$575$	−11.9409			−0.497969
$576$		0			0
$577$	−26.8024			−1.11580			−0.557900	−	0.829908i	$-0.688393\pi$
$577$	−26.8024			−1.11580			−0.557900	+	0.829908i	$0.688393\pi$
$578$	18.0994	+	8.42155i	0.752836	+	0.350290i
$579$		0			0
$580$	3.79778	+	4.51074i	0.157694	+	0.187298i
$581$		−	19.5961i		−	0.812984i
$582$		0			0
$583$			2.74524i			0.113696i
$584$	3.31216	+	12.2388i	0.137058	+	0.506444i
$585$		0			0
$586$	−16.7149	+	35.9232i	−0.690485	+	1.48398i
$587$	−11.0171			−0.454724			−0.227362	−	0.973810i	$-0.573010\pi$
$587$	−11.0171			−0.454724			−0.227362	+	0.973810i	$0.573010\pi$
$588$		0			0
$589$	−0.711161			−0.0293029
$590$	−2.67361	+	5.74606i	−0.110071	+	0.236561i
$591$		0			0
$592$	−2.79207	+	16.1490i	−0.114753	+	0.663720i
$593$			6.15338i			0.252689i	0.991986	+	0.126344i	$0.0403245\pi$
$593$			6.15338i			0.252689i	−0.991986	+	0.126344i	$0.959676\pi$
$594$		0			0
$595$		−	2.34371i		−	0.0960829i
$596$	19.4840	−	16.4044i	0.798094	−	0.671949i
$597$		0			0
$598$	−4.44126	−	2.06649i	−0.181617	−	0.0845051i
$599$	6.41240			0.262004			0.131002	−	0.991382i	$-0.458181\pi$
$599$	6.41240			0.262004			0.131002	+	0.991382i	$0.458181\pi$
$600$		0			0
$601$	32.4377			1.32316			0.661582	−	0.749873i	$-0.269886\pi$
$601$	32.4377			1.32316			0.661582	+	0.749873i	$0.269886\pi$
$602$	1.13279	+	0.527078i	0.0461689	+	0.0214821i
$603$		0			0
$604$	−12.9929	+	10.9392i	−0.528673	+	0.445112i
$605$		−	8.42896i		−	0.342686i
$606$		0			0
$607$			23.8190i			0.966783i	0.875404	+	0.483391i	$0.160595\pi$
$607$			23.8190i			0.966783i	−0.875404	+	0.483391i	$0.839405\pi$
$608$	−4.64729	−	3.22532i	−0.188473	−	0.130804i
$609$		0			0
$610$	−6.75163	+	14.5104i	−0.273365	+	0.587511i
$611$	−6.77349			−0.274026
$612$		0			0
$613$	1.36726			0.0552231			0.0276115	−	0.999619i	$-0.491210\pi$
$613$	1.36726			0.0552231			0.0276115	+	0.999619i	$0.491210\pi$
$614$	9.71331	−	20.8756i	0.391997	−	0.842472i
$615$		0			0
$616$	5.04193	−	1.36449i	0.203145	−	0.0549769i
$617$		−	15.2765i		−	0.615009i	−0.951547	−	0.307504i	$-0.900506\pi$
$617$		−	15.2765i		−	0.615009i	0.951547	−	0.307504i	$-0.0994939\pi$
$618$		0			0
$619$		−	3.16259i		−	0.127115i	−0.997978	−	0.0635576i	$-0.979755\pi$
$619$		−	3.16259i		−	0.127115i	0.997978	−	0.0635576i	$-0.0202447\pi$
$620$	−0.802033	−	0.952599i	−0.0322104	−	0.0382573i
$621$		0			0
$622$	−35.4178	−	16.4797i	−1.42012	−	0.660776i
$623$	−9.73703			−0.390106
$624$		0			0
$625$	14.0895			0.563582
$626$	−11.8170	−	5.49836i	−0.472301	−	0.219759i
$627$		0			0
$628$	−9.16579	−	10.8865i	−0.365755	−	0.434418i
$629$			6.95817i			0.277440i
$630$		0			0
$631$		−	36.6985i		−	1.46094i	−0.682943	−	0.730472i	$-0.739300\pi$
$631$		−	36.6985i		−	1.46094i	0.682943	−	0.730472i	$-0.260700\pi$
$632$	18.8939	−	5.11323i	0.751559	−	0.203393i
$633$		0			0
$634$	−8.65437	+	18.5998i	−0.343709	+	0.738692i
$635$	−4.61338			−0.183076
$636$		0			0
$637$	5.54506			0.219703
$638$	−2.35379	+	5.05871i	−0.0931874	+	0.200276i
$639$		0			0
$640$	−0.920819	−	9.86249i	−0.0363986	−	0.389849i
$641$		−	45.6693i		−	1.80383i	−0.431916	−	0.901914i	$-0.642162\pi$
$641$		−	45.6693i		−	1.80383i	0.431916	−	0.901914i	$-0.357838\pi$
$642$		0			0
$643$		−	33.7577i		−	1.33127i	−0.746276	−	0.665636i	$-0.768160\pi$
$643$		−	33.7577i		−	1.33127i	0.746276	−	0.665636i	$-0.231840\pi$
$644$	6.80208	−	5.72695i	0.268039	−	0.225674i
$645$		0			0
$646$	−2.17757	−	1.01321i	−0.0856754	−	0.0398643i
$647$	−32.2578			−1.26819			−0.634093	−	0.773257i	$-0.718626\pi$
$647$	−32.2578			−1.26819			−0.634093	+	0.773257i	$0.718626\pi$
$648$		0			0
$649$	−5.99680			−0.235395
$650$	6.66594	+	3.10162i	0.261460	+	0.121656i
$651$		0			0
$652$	3.84205	−	3.23479i	0.150466	−	0.126684i
$653$		−	15.3265i		−	0.599774i	−0.953975	−	0.299887i	$-0.903051\pi$
$653$		−	15.3265i		−	0.599774i	0.953975	−	0.299887i	$-0.0969489\pi$
$654$		0			0
$655$			17.2548i			0.674202i
$656$	10.8093	+	1.86887i	0.422033	+	0.0729671i
$657$		0			0
$658$	5.18702	−	11.1478i	0.202211	−	0.434588i
$659$	47.6605			1.85659			0.928295	−	0.371845i	$-0.121275\pi$
$659$	47.6605			1.85659			0.928295	+	0.371845i	$0.121275\pi$
$660$		0			0
$661$	−8.07105			−0.313927			−0.156964	−	0.987604i	$-0.550171\pi$
$661$	−8.07105			−0.313927			−0.156964	+	0.987604i	$0.550171\pi$
$662$	21.5385	−	46.2901i	0.837118	−	1.79912i
$663$		0			0
$664$	−9.18577	−	33.9423i	−0.356477	−	1.31722i
$665$		−	1.38004i		−	0.0535156i
$666$		0			0
$667$			9.49830i			0.367776i
$668$	−0.785946	−	0.933493i	−0.0304092	−	0.0361179i
$669$		0			0
$670$	11.2503	+	5.23469i	0.434636	+	0.202234i
$671$	−15.1437			−0.584614
$672$		0			0
$673$	−2.05598			−0.0792521			−0.0396260	−	0.999215i	$-0.512617\pi$
$673$	−2.05598			−0.0792521			−0.0396260	+	0.999215i	$0.512617\pi$
$674$	−43.2661	−	20.1315i	−1.66655	−	0.775436i
$675$		0			0
$676$	−14.8031	−	17.5821i	−0.569349	−	0.676234i
$677$		−	28.5633i		−	1.09778i	−0.835895	−	0.548889i	$-0.815051\pi$
$677$		−	28.5633i		−	1.09778i	0.835895	−	0.548889i	$-0.184949\pi$
$678$		0			0
$679$			11.6038i			0.445313i
$680$	−1.09863	−	4.05953i	−0.0421304	−	0.155676i
$681$		0			0
$682$	0.497084	−	1.06832i	0.0190343	−	0.0409082i
$683$	25.0112			0.957029			0.478514	−	0.878080i	$-0.341175\pi$
$683$	25.0112			0.957029			0.478514	+	0.878080i	$0.341175\pi$
$684$		0			0
$685$	6.64190			0.253774
$686$	−10.8291	+	23.2737i	−0.413457	+	0.888593i
$687$		0			0
$688$	2.20916	+	0.381951i	0.0842235	+	0.0145618i
$689$		−	2.87748i		−	0.109623i
$690$		0			0
$691$		−	37.8565i		−	1.44013i	−0.693908	−	0.720064i	$-0.744112\pi$
$691$		−	37.8565i		−	1.44013i	0.693908	−	0.720064i	$-0.255888\pi$
$692$	7.91300	−	6.66229i	0.300807	−	0.253262i
$693$		0			0
$694$	0.817333	+	0.380300i	0.0310255	+	0.0144360i
$695$	−2.69950			−0.102398
$696$		0			0
$697$	4.65744			0.176413
$698$	−15.2858	−	7.11238i	−0.578575	−	0.269207i
$699$		0			0
$700$	−10.2093	+	8.59566i	−0.385876	+	0.324885i
$701$		−	29.3202i		−	1.10741i	−0.832713	−	0.553704i	$-0.813214\pi$
$701$		−	29.3202i		−	1.10741i	0.832713	−	0.553704i	$-0.186786\pi$
$702$		0			0
$703$			4.09715i			0.154527i
$704$	8.09349	−	4.72686i	0.305035	−	0.178150i
$705$		0			0
$706$	−12.0620	+	25.9234i	−0.453959	+	0.975639i
$707$	21.6458			0.814073
$708$		0			0
$709$	15.5881			0.585424			0.292712	−	0.956201i	$-0.405442\pi$
$709$	15.5881			0.585424			0.292712	+	0.956201i	$0.405442\pi$
$710$	2.72672	−	5.86020i	0.102332	−	0.219929i
$711$		0			0
$712$	−16.8655	+	4.56428i	−0.632060	+	0.171053i
$713$		−	2.00590i		−	0.0751214i
$714$		0			0
$715$		−	1.25964i		−	0.0471080i
$716$	24.5617	+	29.1727i	0.917914	+	1.09023i
$717$		0			0
$718$	−12.0758	−	5.61879i	−0.450664	−	0.209691i
$719$	−16.0671			−0.599203			−0.299601	−	0.954064i	$-0.596854\pi$
$719$	−16.0671			−0.599203			−0.299601	+	0.954064i	$0.596854\pi$
$720$		0			0
$721$	21.6152			0.804993
$722$	−1.28221	−	0.596605i	−0.0477189	−	0.0222033i
$723$		0			0
$724$	1.84489	+	2.19123i	0.0685646	+	0.0814363i
$725$		−	14.2561i		−	0.529459i
$726$		0			0
$727$		−	45.2899i		−	1.67971i	−0.542810	−	0.839856i	$-0.682640\pi$
$727$		−	45.2899i		−	1.67971i	0.542810	−	0.839856i	$-0.317360\pi$
$728$	−5.28480	+	1.43022i	−0.195868	+	0.0530074i
$729$		0			0
$730$	−2.34150	+	5.03230i	−0.0866628	+	0.186254i
$731$	0.951867			0.0352061
$732$		0			0
$733$	26.9615			0.995847			0.497923	−	0.867221i	$-0.334096\pi$
$733$	26.9615			0.995847			0.497923	+	0.867221i	$0.334096\pi$
$734$	−16.6293	+	35.7392i	−0.613797	+	1.31916i
$735$		0			0
$736$	9.09730	−	13.1081i	0.335331	−	0.483172i
$737$			11.7412i			0.432494i
$738$		0			0
$739$		−	6.52370i		−	0.239978i	−0.992775	−	0.119989i	$-0.961714\pi$
$739$		−	6.52370i		−	0.239978i	0.992775	−	0.119989i	$-0.0382860\pi$
$740$	−5.48812	+	4.62068i	−0.201747	+	0.169860i
$741$		0			0
$742$	4.73576	+	2.20352i	0.173855	+	0.0808938i
$743$	−38.5862			−1.41559			−0.707795	−	0.706418i	$-0.750310\pi$
$743$	−38.5862			−1.41559			−0.707795	+	0.706418i	$0.750310\pi$
$744$		0			0
$745$	11.1498			0.408497
$746$	32.0214	+	14.8994i	1.17239	+	0.545505i
$747$		0			0
$748$	3.04414	−	2.56299i	0.111305	−	0.0937121i
$749$			17.0080i			0.621457i
$750$		0			0
$751$		−	12.7257i		−	0.464369i	−0.972672	−	0.232184i	$-0.925413\pi$
$751$		−	12.7257i		−	0.464369i	0.972672	−	0.232184i	$-0.0745872\pi$
$752$	3.75881	−	21.7405i	0.137070	−	0.792795i
$753$		0			0
$754$	2.46717	−	5.30238i	0.0898489	−	0.193101i
$755$	−7.43525			−0.270596
$756$		0			0
$757$	−50.9986			−1.85358			−0.926788	−	0.375584i	$-0.877442\pi$
$757$	−50.9986			−1.85358			−0.926788	+	0.375584i	$0.877442\pi$
$758$	−21.2675	+	45.7076i	−0.772470	+	1.66018i
$759$		0			0
$760$	−0.646899	−	2.39036i	−0.0234655	−	0.0867074i
$761$		−	41.1183i		−	1.49054i	−0.666764	−	0.745269i	$-0.732321\pi$
$761$		−	41.1183i		−	1.49054i	0.666764	−	0.745269i	$-0.267679\pi$
$762$		0			0
$763$		−	17.3431i		−	0.627862i
$764$	−7.97915	−	9.47707i	−0.288675	−	0.342868i
$765$		0			0
$766$	−43.1364	−	20.0711i	−1.55858	−	0.725199i
$767$	6.28566			0.226962
$768$		0			0
$769$	23.4244			0.844705			0.422352	−	0.906432i	$-0.361204\pi$
$769$	23.4244			0.844705			0.422352	+	0.906432i	$0.361204\pi$
$770$	2.07313	+	0.964614i	0.0747103	+	0.0347623i
$771$		0			0
$772$	−21.9834	−	26.1104i	−0.791201	−	0.939734i
$773$			24.8030i			0.892101i	0.895008	+	0.446050i	$0.147170\pi$
$773$			24.8030i			0.892101i	−0.895008	+	0.446050i	$0.852830\pi$
$774$		0			0
$775$			3.01068i			0.108147i
$776$	5.43933	+	20.0989i	0.195260	+	0.721507i
$777$		0			0
$778$	14.2660	−	30.6601i	0.511460	−	1.09922i
$779$	2.74242			0.0982574
$780$		0			0
$781$	6.11593			0.218845
$782$	2.85786	−	6.14204i	0.102197	−	0.219639i
$783$		0			0
$784$	−3.07712	+	17.7977i	−0.109897	+	0.635632i
$785$		−	6.22986i		−	0.222353i
$786$		0			0
$787$		−	25.1092i		−	0.895046i	−0.894272	−	0.447523i	$-0.852306\pi$
$787$		−	25.1092i		−	0.895046i	0.894272	−	0.447523i	$-0.147694\pi$
$788$	−23.9436	+	20.1591i	−0.852956	+	0.718139i
$789$		0			0
$790$	7.76874	+	3.61475i	0.276399	+	0.128607i
$791$	14.5520			0.517411
$792$		0			0
$793$	15.8731			0.563671
$794$	12.8920	+	5.99857i	0.457520	+	0.212881i
$795$		0			0
$796$	−34.1173	+	28.7248i	−1.20926	+	1.01812i
$797$		−	21.6563i		−	0.767105i	−0.923519	−	0.383553i	$-0.874700\pi$
$797$		−	21.6563i		−	0.767105i	0.923519	−	0.383553i	$-0.125300\pi$
$798$		0			0
$799$		−	9.36740i		−	0.331395i
$800$	−13.6543	+	19.6742i	−0.482751	+	0.695586i
$801$		0			0
$802$	14.3024	−	30.7383i	0.505034	−	1.08541i
$803$	−5.25190			−0.185336
$804$		0			0
$805$	3.89253			0.137194
$806$	−0.521028	+	1.11978i	−0.0183524	+	0.0394427i
$807$		0			0
$808$	37.4925	−	10.1465i	1.31898	−	0.356954i
$809$			7.65555i			0.269155i	0.990903	+	0.134577i	$0.0429677\pi$
$809$			7.65555i			0.269155i	−0.990903	+	0.134577i	$0.957032\pi$
$810$		0			0
$811$			8.69259i			0.305238i	0.988285	+	0.152619i	$0.0487707\pi$
$811$			8.69259i			0.305238i	−0.988285	+	0.152619i	$0.951229\pi$
$812$	6.83736	+	8.12094i	0.239944	+	0.284989i
$813$		0			0
$814$	−6.15483	−	2.86381i	−0.215727	−	0.100376i
$815$	2.19864			0.0770149
$816$		0			0
$817$	0.560484			0.0196089
$818$	−24.4904	−	11.3952i	−0.856287	−	0.398425i
$819$		0			0
$820$	3.09285	+	3.67347i	0.108007	+	0.128283i
$821$		−	5.50155i		−	0.192005i	−0.995381	−	0.0960027i	$-0.969394\pi$
$821$		−	5.50155i		−	0.192005i	0.995381	−	0.0960027i	$-0.0306058\pi$
$822$		0			0
$823$			41.2351i			1.43736i	0.695339	+	0.718682i	$0.255254\pi$
$823$			41.2351i			1.43736i	−0.695339	+	0.718682i	$0.744746\pi$
$824$	37.4396	−	10.1322i	1.30427	−	0.352973i
$825$		0			0
$826$	−4.81345	+	10.3450i	−0.167481	+	0.359947i
$827$	−17.4625			−0.607231			−0.303616	−	0.952795i	$-0.598194\pi$
$827$	−17.4625			−0.607231			−0.303616	+	0.952795i	$0.598194\pi$
$828$		0			0
$829$	2.15205			0.0747438			0.0373719	−	0.999301i	$-0.488101\pi$
$829$	2.15205			0.0747438			0.0373719	+	0.999301i	$0.488101\pi$
$830$	6.49379	−	13.9563i	0.225403	−	0.484430i
$831$		0			0
$832$	−8.48334	+	4.95454i	−0.294107	+	0.171768i
$833$			7.66854i			0.265699i
$834$		0			0
$835$		−	0.534197i		−	0.0184866i
$836$	1.79247	−	1.50915i	0.0619938	−	0.0521952i
$837$		0			0
$838$	−8.70740	−	4.05150i	−0.300792	−	0.139957i
$839$	−46.5057			−1.60556			−0.802778	−	0.596278i	$-0.796646\pi$
$839$	−46.5057			−1.60556			−0.802778	+	0.596278i	$0.796646\pi$
$840$		0			0
$841$	17.6601			0.608968
$842$	−19.0216	−	8.85064i	−0.655528	−	0.305013i
$843$		0			0
$844$	8.91550	−	7.50633i	0.306884	−	0.258379i
$845$		−	10.0614i		−	0.346124i
$846$		0			0
$847$		−	15.1752i		−	0.521425i
$848$	9.23569	+	1.59680i	0.317155	+	0.0548343i
$849$		0			0
$850$	−4.28939	+	9.21867i	−0.147125	+	0.316198i
$851$	−11.5564			−0.396148
$852$		0			0
$853$	14.5849			0.499378			0.249689	−	0.968326i	$-0.419672\pi$
$853$	14.5849			0.499378			0.249689	+	0.968326i	$0.419672\pi$
$854$	−12.1554	+	26.1240i	−0.415948	+	0.893945i
$855$		0			0
$856$	7.97255	+	29.4594i	0.272496	+	1.00690i
$857$			23.3828i			0.798743i	0.916789	+	0.399371i	$0.130772\pi$
$857$			23.3828i			0.798743i	−0.916789	+	0.399371i	$0.869228\pi$
$858$		0			0
$859$			8.89552i			0.303511i	0.988418	+	0.151756i	$0.0484927\pi$
$859$			8.89552i			0.303511i	−0.988418	+	0.151756i	$0.951507\pi$
$860$	0.632102	+	0.750767i	0.0215545	+	0.0256010i
$861$		0			0
$862$	38.0820	+	17.7193i	1.29708	+	0.603523i
$863$	−11.5412			−0.392868			−0.196434	−	0.980517i	$-0.562936\pi$
$863$	−11.5412			−0.392868			−0.196434	+	0.980517i	$0.562936\pi$
$864$		0			0
$865$	4.52826			0.153966
$866$	21.8267	+	10.1558i	0.741702	+	0.345110i
$867$		0			0
$868$	−1.44395	−	1.71502i	−0.0490108	−	0.0582116i
$869$			8.10775i			0.275037i
$870$		0			0
$871$		−	12.3068i		−	0.417000i
$872$	−8.12964	−	30.0398i	−0.275304	−	1.01728i
$873$		0			0
$874$	1.68278	−	3.61659i	0.0569209	−	0.122333i
$875$	−12.7425			−0.430777
$876$		0			0
$877$	−8.70329			−0.293889			−0.146945	−	0.989145i	$-0.546944\pi$
$877$	−8.70329			−0.293889			−0.146945	+	0.989145i	$0.546944\pi$
$878$	−22.8586	+	49.1272i	−0.771440	+	1.65796i
$879$		0			0
$880$	4.04302	+	0.699015i	0.136290	+	0.0235638i
$881$		−	7.29206i		−	0.245676i	−0.992427	−	0.122838i	$-0.960800\pi$
$881$		−	7.29206i		−	0.245676i	0.992427	−	0.122838i	$-0.0391995\pi$
$882$		0			0
$883$			56.2222i			1.89203i	0.324127	+	0.946014i	$0.394930\pi$
$883$			56.2222i			1.89203i	−0.324127	+	0.946014i	$0.605070\pi$
$884$	−3.19077	+	2.68644i	−0.107317	+	0.0903549i
$885$		0			0
$886$	0.352968	+	0.164234i	0.0118582	+	0.00551755i
$887$	41.3843			1.38955			0.694775	−	0.719227i	$-0.255504\pi$
$887$	41.3843			1.38955			0.694775	+	0.719227i	$0.255504\pi$
$888$		0			0
$889$	−8.30573			−0.278565
$890$	−6.93469	−	3.22667i	−0.232451	−	0.108158i
$891$		0			0
$892$	−13.2761	+	11.1777i	−0.444517	+	0.374257i
$893$		−	5.51577i		−	0.184578i
$894$		0			0
$895$			16.6942i			0.558027i
$896$	−1.65780	−	17.7560i	−0.0553833	−	0.593187i
$897$		0			0
$898$	−18.4654	+	39.6855i	−0.616199	+	1.32432i
$899$	2.39482			0.0798718
$900$		0			0
$901$	3.97941			0.132573
$902$	−1.91689	+	4.11973i	−0.0638253	+	0.137172i
$903$		0			0
$904$	25.2055	−	6.82133i	0.838322	−	0.226874i
$905$			1.25394i			0.0416825i
$906$		0			0
$907$			26.3682i			0.875542i	0.899086	+	0.437771i	$0.144232\pi$
$907$			26.3682i			0.875542i	−0.899086	+	0.437771i	$0.855768\pi$
$908$	12.4574	+	14.7960i	0.413413	+	0.491023i
$909$		0			0
$910$	−2.17299	−	1.01108i	−0.0720338	−	0.0335169i
$911$	26.4879			0.877583			0.438792	−	0.898589i	$-0.355407\pi$
$911$	26.4879			0.877583			0.438792	+	0.898589i	$0.355407\pi$
$912$		0			0
$913$	14.5653			0.482042
$914$	−2.51208	−	1.16886i	−0.0830923	−	0.0386624i
$915$		0			0
$916$	−23.9292	−	28.4214i	−0.790642	−	0.939070i
$917$			31.0649i			1.02585i
$918$		0			0
$919$		−	43.7471i		−	1.44308i	−0.692371	−	0.721541i	$-0.743434\pi$
$919$		−	43.7471i		−	1.44308i	0.692371	−	0.721541i	$-0.256566\pi$
$920$	6.74222	−	1.82464i	0.222285	−	0.0601566i
$921$		0			0
$922$	2.58035	−	5.54563i	0.0849793	−	0.182636i
$923$	−6.41052			−0.211005
$924$		0			0
$925$	17.3451			0.570304
$926$	14.9832	−	32.2017i	0.492380	−	1.05821i
$927$		0			0
$928$	15.6497	+	10.8612i	0.513726	+	0.356536i
$929$			14.5115i			0.476108i	0.971252	+	0.238054i	$0.0765095\pi$
$929$			14.5115i			0.476108i	−0.971252	+	0.238054i	$0.923490\pi$
$930$		0			0
$931$			4.51543i			0.147987i
$932$	−19.3302	+	16.2749i	−0.633183	+	0.533103i
$933$		0			0
$934$	52.1148	+	24.2487i	1.70525	+	0.793441i
$935$	1.74203			0.0569704
$936$		0			0
$937$	−35.4067			−1.15669			−0.578343	−	0.815794i	$-0.696301\pi$
$937$	−35.4067			−1.15669			−0.578343	+	0.815794i	$0.696301\pi$
$938$	20.2545	+	9.42432i	0.661334	+	0.307715i
$939$		0			0
$940$	7.38836	−	6.22057i	0.240982	−	0.202893i
$941$			7.00918i			0.228493i	0.993452	+	0.114246i	$0.0364453\pi$
$941$			7.00918i			0.228493i	−0.993452	+	0.114246i	$0.963555\pi$
$942$		0			0
$943$			7.73525i			0.251894i
$944$	−3.48810	+	20.1748i	−0.113528	+	0.656633i
$945$		0			0
$946$	−0.391765	+	0.841972i	−0.0127374	+	0.0273749i
$947$	−30.0496			−0.976482			−0.488241	−	0.872709i	$-0.662361\pi$
$947$	−30.0496			−0.976482			−0.488241	+	0.872709i	$0.662361\pi$
$948$		0			0
$949$	5.50488			0.178696
$950$	−2.52571	+	5.42819i	−0.0819447	+	0.176114i
$951$		0			0
$952$	−1.97792	−	7.30861i	−0.0641048	−	0.236874i
$953$			39.6998i			1.28600i	0.765865	+	0.643002i	$0.222311\pi$
$953$			39.6998i			1.28600i	−0.765865	+	0.643002i	$0.777689\pi$
$954$		0			0
$955$		−	5.42331i		−	0.175494i
$956$	12.3544	+	14.6737i	0.399569	+	0.474581i
$957$		0			0
$958$	28.0093	+	13.0326i	0.904940	+	0.421064i
$959$	11.9578			0.386138
$960$		0			0
$961$	30.4942			0.983685
$962$	6.45130	+	3.00175i	0.207998	+	0.0967804i
$963$		0			0
$964$	12.9282	+	15.3553i	0.416390	+	0.494559i
$965$		−	14.9418i		−	0.480995i
$966$		0			0
$967$			55.5448i			1.78620i	0.449857	+	0.893101i	$0.351475\pi$
$967$			55.5448i			1.78620i	−0.449857	+	0.893101i	$0.648525\pi$
$968$	−7.11342	−	26.2848i	−0.228634	−	0.844825i
$969$		0			0
$970$	−3.84528	+	8.26418i	−0.123464	+	0.265347i
$971$	12.8080			0.411027			0.205514	−	0.978654i	$-0.434114\pi$
$971$	12.8080			0.411027			0.205514	+	0.978654i	$0.434114\pi$
$972$		0			0
$973$	−4.86007			−0.155807
$974$	−2.20080	+	4.72991i	−0.0705182	+	0.151556i
$975$		0			0
$976$	−8.80847	+	50.9471i	−0.281952	+	1.63078i
$977$			24.6068i			0.787242i	0.919273	+	0.393621i	$0.128778\pi$
$977$			24.6068i			0.787242i	−0.919273	+	0.393621i	$0.871222\pi$
$978$		0			0
$979$		−	7.23730i		−	0.231305i
$980$	−6.04842	+	5.09242i	−0.193210	+	0.162671i
$981$		0			0
$982$	−29.7620	−	13.8481i	−0.949743	−	0.441910i
$983$	−18.0995			−0.577284			−0.288642	−	0.957437i	$-0.593204\pi$
$983$	−18.0995			−0.577284			−0.288642	+	0.957437i	$0.593204\pi$
$984$		0			0
$985$	−13.7019			−0.436578
$986$	7.33293	+	3.41197i	0.233528	+	0.108659i
$987$		0			0
$988$	−1.87881	+	1.58185i	−0.0597729	+	0.0503253i
$989$			1.58090i			0.0502696i
$990$		0			0
$991$		−	45.3924i		−	1.44194i	−0.692967	−	0.720969i	$-0.743697\pi$
$991$		−	45.3924i		−	1.44194i	0.692967	−	0.720969i	$-0.256303\pi$
$992$	−3.30497	−	2.29372i	−0.104933	−	0.0728257i
$993$		0			0
$994$	4.90907	−	10.5505i	0.155706	−	0.334640i
$995$	−19.5238			−0.618947
$996$		0			0
$997$	−13.5460			−0.429005			−0.214503	−	0.976723i	$-0.568813\pi$
$997$	−13.5460			−0.429005			−0.214503	+	0.976723i	$0.568813\pi$
$998$	21.8169	−	46.8883i	0.690601	−	1.48422i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.28	yes	32
3.2	odd	2	inner	684.2.c.b.647.5	✓	32
4.3	odd	2	inner	684.2.c.b.647.6	yes	32
12.11	even	2	inner	684.2.c.b.647.27	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.5	✓	32	3.2	odd	2	inner
684.2.c.b.647.6	yes	32	4.3	odd	2	inner
684.2.c.b.647.27	yes	32	12.11	even	2	inner
684.2.c.b.647.28	yes	32	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28221 + 0.596605i) q^{2} +(1.28813 + 1.52995i) q^{4} +0.875520i q^{5} +1.57625i q^{7} +(0.738874 + 2.73021i) q^{8} +O(q^{10})\)	\(q+(1.28221 + 0.596605i) q^{2} +(1.28813 + 1.52995i) q^{4} +0.875520i q^{5} +1.57625i q^{7} +(0.738874 + 2.73021i) q^{8} +(-0.522340 + 1.12260i) q^{10} -1.17159 q^{11} +1.22802 q^{13} +(-0.940399 + 2.02108i) q^{14} +(-0.681467 + 3.94152i) q^{16} +1.69830i q^{17} +1.00000i q^{19} +(-1.33950 + 1.12778i) q^{20} +(-1.50222 - 0.698976i) q^{22} -2.82059 q^{23} +4.23346 q^{25} +(1.57458 + 0.732645i) q^{26} +(-2.41158 + 2.03041i) q^{28} -3.36748i q^{29} +0.711161i q^{31} +(-3.22532 + 4.64729i) q^{32} +(-1.01321 + 2.17757i) q^{34} -1.38004 q^{35} +4.09715 q^{37} +(-0.596605 + 1.28221i) q^{38} +(-2.39036 + 0.646899i) q^{40} -2.74242i q^{41} -0.560484i q^{43} +(-1.50915 - 1.79247i) q^{44} +(-3.61659 - 1.68278i) q^{46} -5.51577 q^{47} +4.51543 q^{49} +(5.42819 + 2.52571i) q^{50} +(1.58185 + 1.87881i) q^{52} -2.34318i q^{53} -1.02575i q^{55} +(-4.30350 + 1.16465i) q^{56} +(2.00906 - 4.31782i) q^{58} +5.11852 q^{59} +12.9257 q^{61} +(-0.424282 + 0.911858i) q^{62} +(-6.90813 + 4.03457i) q^{64} +1.07516i q^{65} -10.0216i q^{67} +(-2.59830 + 2.18762i) q^{68} +(-1.76950 - 0.823338i) q^{70} -5.22020 q^{71} +4.48272 q^{73} +(5.25340 + 2.44438i) q^{74} +(-1.52995 + 1.28813i) q^{76} -1.84672i q^{77} -6.92030i q^{79} +(-3.45088 - 0.596638i) q^{80} +(1.63614 - 3.51636i) q^{82} -12.4321 q^{83} -1.48689 q^{85} +(0.334387 - 0.718658i) q^{86} +(-0.865657 - 3.19869i) q^{88} +6.17734i q^{89} +1.93567i q^{91} +(-3.63328 - 4.31535i) q^{92} +(-7.07237 - 3.29073i) q^{94} -0.875520 q^{95} +7.36164 q^{97} +(5.78974 + 2.69393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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