LMFDB - Embedded newform 1860.2.s.a.433.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.13
Character	$\chi$	$=$	1860.433
Dual form			1860.2.s.a.1177.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.72803 - 1.41912i) q^{5} +(-0.575654 + 0.575654i) q^{7} -1.00000i q^{9} -5.07781i q^{11} +(0.293315 - 0.293315i) q^{13} +(2.22537 - 0.218435i) q^{15} +(-0.365849 - 0.365849i) q^{17} +0.439900i q^{19} -0.814097i q^{21} +(-4.26424 + 4.26424i) q^{23} +(0.972199 + 4.90457i) q^{25} +(0.707107 + 0.707107i) q^{27} -6.60907 q^{29} +(5.23909 + 1.88466i) q^{31} +(3.59055 + 3.59055i) q^{33} +(1.81167 - 0.177827i) q^{35} +(-0.849177 - 0.849177i) q^{37} +0.414810i q^{39} +10.3445 q^{41} +(6.93067 - 6.93067i) q^{43} +(-1.41912 + 1.72803i) q^{45} +(-3.89640 + 3.89640i) q^{47} +6.33725i q^{49} +0.517388 q^{51} +(-8.89919 + 8.89919i) q^{53} +(-7.20602 + 8.77462i) q^{55} +(-0.311057 - 0.311057i) q^{57} -8.14835i q^{59} +1.48893i q^{61} +(0.575654 + 0.575654i) q^{63} +(-0.923106 + 0.0906090i) q^{65} +(-6.46138 + 6.46138i) q^{67} -6.03054i q^{69} -11.3814 q^{71} +(-10.0788 + 10.0788i) q^{73} +(-4.15551 - 2.78061i) q^{75} +(2.92306 + 2.92306i) q^{77} -11.2244 q^{79} -1.00000 q^{81} +(-4.35534 + 4.35534i) q^{83} +(0.113016 + 1.15138i) q^{85} +(4.67332 - 4.67332i) q^{87} -4.17657 q^{89} +0.337695i q^{91} +(-5.03725 + 2.37194i) q^{93} +(0.624271 - 0.760163i) q^{95} +(-5.28842 + 5.28842i) q^{97} -5.07781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−1.72803	−	1.41912i	−0.772800	−	0.634650i
$5$	−1.72803	−	1.41912i	−0.772800	−	0.634650i
$6$		0			0
$7$	−0.575654	+	0.575654i	−0.217577	+	0.217577i	−0.807476	−	0.589900i	$-0.799167\pi$
$7$	−0.575654	+	0.575654i	−0.217577	+	0.217577i	0.589900	+	0.807476i	$0.299167\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	5.07781i		−	1.53102i	−0.643426	−	0.765508i	$-0.722488\pi$
$11$		−	5.07781i		−	1.53102i	0.643426	−	0.765508i	$-0.277512\pi$
$12$		0			0
$13$	0.293315	−	0.293315i	0.0813509	−	0.0813509i	−0.665260	−	0.746611i	$-0.731680\pi$
$13$	0.293315	−	0.293315i	0.0813509	−	0.0813509i	0.746611	+	0.665260i	$0.231680\pi$
$14$		0			0
$15$	2.22537	−	0.218435i	0.574589	−	0.0563997i
$16$		0			0
$17$	−0.365849	−	0.365849i	−0.0887314	−	0.0887314i	0.661348	−	0.750079i	$-0.269985\pi$
$17$	−0.365849	−	0.365849i	−0.0887314	−	0.0887314i	−0.750079	+	0.661348i	$0.769985\pi$
$18$		0			0
$19$			0.439900i			0.100920i	0.998726	+	0.0504600i	$0.0160688\pi$
$19$			0.439900i			0.100920i	−0.998726	+	0.0504600i	$0.983931\pi$
$20$		0			0
$21$		−	0.814097i		−	0.177651i
$22$		0			0
$23$	−4.26424	+	4.26424i	−0.889155	+	0.889155i	−0.994442	−	0.105287i	$-0.966424\pi$
$23$	−4.26424	+	4.26424i	−0.889155	+	0.889155i	0.105287	+	0.994442i	$0.466424\pi$
$24$		0			0
$25$	0.972199	+	4.90457i	0.194440	+	0.980914i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−6.60907			−1.22727			−0.613637	−	0.789589i	$-0.710294\pi$
$29$	−6.60907			−1.22727			−0.613637	+	0.789589i	$0.710294\pi$
$30$		0			0
$31$	5.23909	+	1.88466i	0.940968	+	0.338495i
$31$	5.23909	+	1.88466i	0.940968	+	0.338495i
$32$		0			0
$33$	3.59055	+	3.59055i	0.625035	+	0.625035i
$34$		0			0
$35$	1.81167	−	0.177827i	0.306228	−	0.0300583i
$36$		0			0
$37$	−0.849177	−	0.849177i	−0.139604	−	0.139604i	0.633851	−	0.773455i	$-0.281473\pi$
$37$	−0.849177	−	0.849177i	−0.139604	−	0.139604i	−0.773455	+	0.633851i	$0.781473\pi$
$38$		0			0
$39$			0.414810i			0.0664227i
$40$		0			0
$41$	10.3445			1.61554			0.807772	−	0.589495i	$-0.200673\pi$
$41$	10.3445			1.61554			0.807772	+	0.589495i	$0.200673\pi$
$42$		0			0
$43$	6.93067	−	6.93067i	1.05692	−	1.05692i	0.0586379	−	0.998279i	$-0.481324\pi$
$43$	6.93067	−	6.93067i	1.05692	−	1.05692i	0.998279	−	0.0586379i	$-0.0186757\pi$
$44$		0			0
$45$	−1.41912	+	1.72803i	−0.211550	+	0.257600i
$46$		0			0
$47$	−3.89640	+	3.89640i	−0.568348	+	0.568348i	−0.931666	−	0.363317i	$-0.881644\pi$
$47$	−3.89640	+	3.89640i	−0.568348	+	0.568348i	0.363317	+	0.931666i	$0.381644\pi$
$48$		0			0
$49$			6.33725i			0.905321i
$50$		0			0
$51$	0.517388			0.0724488
$52$		0			0
$53$	−8.89919	+	8.89919i	−1.22240	+	1.22240i	−0.255621	+	0.966777i	$0.582280\pi$
$53$	−8.89919	+	8.89919i	−1.22240	+	1.22240i	−0.966777	+	0.255621i	$0.917720\pi$
$54$		0			0
$55$	−7.20602	+	8.77462i	−0.971659	+	1.18317i
$56$		0			0
$57$	−0.311057	−	0.311057i	−0.0412005	−	0.0412005i
$58$		0			0
$59$		−	8.14835i		−	1.06082i	−0.847740	−	0.530412i	$-0.822037\pi$
$59$		−	8.14835i		−	1.06082i	0.847740	−	0.530412i	$-0.177963\pi$
$60$		0			0
$61$			1.48893i			0.190638i	0.995447	+	0.0953188i	$0.0303870\pi$
$61$			1.48893i			0.190638i	−0.995447	+	0.0953188i	$0.969613\pi$
$62$		0			0
$63$	0.575654	+	0.575654i	0.0725255	+	0.0725255i
$64$		0			0
$65$	−0.923106	+	0.0906090i	−0.114497	+	0.0112387i
$66$		0			0
$67$	−6.46138	+	6.46138i	−0.789383	+	0.789383i	−0.981393	−	0.192010i	$-0.938499\pi$
$67$	−6.46138	+	6.46138i	−0.789383	+	0.789383i	0.192010	+	0.981393i	$0.438499\pi$
$68$		0			0
$69$		−	6.03054i		−	0.725992i
$70$		0			0
$71$	−11.3814			−1.35072			−0.675361	−	0.737488i	$-0.736012\pi$
$71$	−11.3814			−1.35072			−0.675361	+	0.737488i	$0.736012\pi$
$72$		0			0
$73$	−10.0788	+	10.0788i	−1.17963	+	1.17963i	−0.199797	+	0.979837i	$0.564028\pi$
$73$	−10.0788	+	10.0788i	−1.17963	+	1.17963i	−0.979837	+	0.199797i	$0.935972\pi$
$74$		0			0
$75$	−4.15551	−	2.78061i	−0.479836	−	0.321077i
$76$		0			0
$77$	2.92306	+	2.92306i	0.333113	+	0.333113i
$78$		0			0
$79$	−11.2244			−1.26285			−0.631424	−	0.775438i	$-0.717529\pi$
$79$	−11.2244			−1.26285			−0.631424	+	0.775438i	$0.717529\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−4.35534	+	4.35534i	−0.478061	+	0.478061i	−0.904511	−	0.426450i	$-0.859764\pi$
$83$	−4.35534	+	4.35534i	−0.478061	+	0.478061i	0.426450	+	0.904511i	$0.359764\pi$
$84$		0			0
$85$	0.113016	+	1.15138i	0.0122583	+	0.124885i
$86$		0			0
$87$	4.67332	−	4.67332i	0.501032	−	0.501032i
$88$		0			0
$89$	−4.17657			−0.442716			−0.221358	−	0.975193i	$-0.571049\pi$
$89$	−4.17657			−0.442716			−0.221358	+	0.975193i	$0.571049\pi$
$90$		0			0
$91$			0.337695i			0.0354001i
$92$		0			0
$93$	−5.03725	+	2.37194i	−0.522339	+	0.245959i
$94$		0			0
$95$	0.624271	−	0.760163i	0.0640489	−	0.0779911i
$96$		0			0
$97$	−5.28842	+	5.28842i	−0.536958	+	0.536958i	−0.922634	−	0.385676i	$-0.873968\pi$
$97$	−5.28842	+	5.28842i	−0.536958	+	0.536958i	0.385676	+	0.922634i	$0.373968\pi$
$98$		0			0
$99$	−5.07781			−0.510339
$100$		0			0
$101$	7.71583			0.767754			0.383877	−	0.923384i	$-0.374589\pi$
$101$	7.71583			0.767754			0.383877	+	0.923384i	$0.374589\pi$
$102$		0			0
$103$	11.0295	+	11.0295i	1.08677	+	1.08677i	0.995859	+	0.0909079i	$0.0289769\pi$
$103$	11.0295	+	11.0295i	1.08677	+	1.08677i	0.0909079	+	0.995859i	$0.471023\pi$
$104$		0			0
$105$	−1.15530	+	1.40679i	−0.112746	+	0.137288i
$106$		0			0
$107$	11.7750	−	11.7750i	1.13833	−	1.13833i	0.149578	−	0.988750i	$-0.452209\pi$
$107$	11.7750	−	11.7750i	1.13833	−	1.13833i	0.988750	−	0.149578i	$-0.0477915\pi$
$108$		0			0
$109$			5.33906i			0.511389i	0.966758	+	0.255695i	$0.0823041\pi$
$109$			5.33906i			0.511389i	−0.966758	+	0.255695i	$0.917696\pi$
$110$		0			0
$111$	1.20092			0.113986
$112$		0			0
$113$	−5.34569	−	5.34569i	−0.502880	−	0.502880i	0.409452	−	0.912332i	$-0.365720\pi$
$113$	−5.34569	−	5.34569i	−0.502880	−	0.502880i	−0.912332	+	0.409452i	$0.865720\pi$
$114$		0			0
$115$	13.4202	−	1.31728i	1.25144	−	0.122837i
$116$		0			0
$117$	−0.293315	−	0.293315i	−0.0271170	−	0.0271170i
$118$		0			0
$119$	0.421204			0.0386117
$120$		0			0
$121$	−14.7841			−1.34401
$122$		0			0
$123$	−7.31469	+	7.31469i	−0.659543	+	0.659543i
$124$		0			0
$125$	5.28018	−	9.85493i	0.472274	−	0.881452i
$126$		0			0
$127$	1.85057	+	1.85057i	0.164212	+	0.164212i	0.784430	−	0.620218i	$-0.212956\pi$
$127$	1.85057	+	1.85057i	0.164212	+	0.164212i	−0.620218	+	0.784430i	$0.712956\pi$
$128$		0			0
$129$			9.80145i			0.862969i
$130$		0			0
$131$	−12.6937			−1.10906			−0.554528	−	0.832165i	$-0.687101\pi$
$131$	−12.6937			−1.10906			−0.554528	+	0.832165i	$0.687101\pi$
$132$		0			0
$133$	−0.253230	−	0.253230i	−0.0219579	−	0.0219579i
$134$		0			0
$135$	−0.218435	−	2.22537i	−0.0187999	−	0.191530i
$136$		0			0
$137$	8.40732	+	8.40732i	0.718286	+	0.718286i	0.968254	−	0.249968i	$-0.0804202\pi$
$137$	8.40732	+	8.40732i	0.718286	+	0.718286i	−0.249968	+	0.968254i	$0.580420\pi$
$138$		0			0
$139$	−20.3134			−1.72296			−0.861480	−	0.507791i	$-0.830462\pi$
$139$	−20.3134			−1.72296			−0.861480	+	0.507791i	$0.830462\pi$
$140$		0			0
$141$		−	5.51034i		−	0.464055i
$142$		0			0
$143$	−1.48940	−	1.48940i	−0.124550	−	0.124550i
$144$		0			0
$145$	11.4207	+	9.37906i	0.948437	+	0.778888i
$146$		0			0
$147$	−4.48111	−	4.48111i	−0.369596	−	0.369596i
$148$		0			0
$149$			18.9448i			1.55202i	0.630723	+	0.776008i	$0.282758\pi$
$149$			18.9448i			1.55202i	−0.630723	+	0.776008i	$0.717242\pi$
$150$		0			0
$151$		−	10.0823i		−	0.820483i	−0.911977	−	0.410241i	$-0.865444\pi$
$151$		−	10.0823i		−	0.820483i	0.911977	−	0.410241i	$-0.134556\pi$
$152$		0			0
$153$	−0.365849	+	0.365849i	−0.0295771	+	0.0295771i
$154$		0			0
$155$	−6.37877	−	10.6916i	−0.512355	−	0.858774i
$156$		0			0
$157$	−6.58857	+	6.58857i	−0.525825	+	0.525825i	−0.919325	−	0.393500i	$-0.871264\pi$
$157$	−6.58857	+	6.58857i	−0.525825	+	0.525825i	0.393500	+	0.919325i	$0.371264\pi$
$158$		0			0
$159$		−	12.5854i		−	0.998084i
$160$		0			0
$161$		−	4.90945i		−	0.386919i
$162$		0			0
$163$	16.2980	+	16.2980i	1.27656	+	1.27656i	0.942583	+	0.333973i	$0.108389\pi$
$163$	16.2980	+	16.2980i	1.27656	+	1.27656i	0.333973	+	0.942583i	$0.391611\pi$
$164$		0			0
$165$	−1.10917	−	11.3000i	−0.0863489	−	0.879705i
$166$		0			0
$167$	−13.5571	−	13.5571i	−1.04908	−	1.04908i	−0.998732	−	0.0503509i	$-0.983966\pi$
$167$	−13.5571	−	13.5571i	−1.04908	−	1.04908i	−0.0503509	−	0.998732i	$-0.516034\pi$
$168$		0			0
$169$			12.8279i			0.986764i
$170$		0			0
$171$	0.439900			0.0336400
$172$		0			0
$173$	8.44894	+	8.44894i	0.642361	+	0.642361i	0.951135	−	0.308774i	$-0.0999187\pi$
$173$	8.44894	+	8.44894i	0.642361	+	0.642361i	−0.308774	+	0.951135i	$0.599919\pi$
$174$		0			0
$175$	−3.38299	−	2.26368i	−0.255730	−	0.171118i
$176$		0			0
$177$	5.76175	+	5.76175i	0.433080	+	0.433080i
$178$		0			0
$179$	13.8628			1.03616			0.518079	−	0.855333i	$-0.326647\pi$
$179$	13.8628			1.03616			0.518079	+	0.855333i	$0.326647\pi$
$180$		0			0
$181$			2.66204i			0.197868i	0.995094	+	0.0989341i	$0.0315433\pi$
$181$			2.66204i			0.197868i	−0.995094	+	0.0989341i	$0.968457\pi$
$182$		0			0
$183$	−1.05283	−	1.05283i	−0.0778275	−	0.0778275i
$184$		0			0
$185$	0.262323	+	2.67249i	0.0192863	+	0.196485i
$186$		0			0
$187$	−1.85771	+	1.85771i	−0.135849	+	0.135849i
$188$		0			0
$189$	−0.814097			−0.0592169
$190$		0			0
$191$	23.8209			1.72362			0.861810	−	0.507232i	$-0.169331\pi$
$191$	23.8209			1.72362			0.861810	+	0.507232i	$0.169331\pi$
$192$		0			0
$193$	−13.3646	−	13.3646i	−0.962003	−	0.962003i	0.0373011	−	0.999304i	$-0.488124\pi$
$193$	−13.3646	−	13.3646i	−0.962003	−	0.962003i	−0.999304	+	0.0373011i	$0.988124\pi$
$194$		0			0
$195$	0.588665	−	0.716805i	0.0421551	−	0.0513315i
$196$		0			0
$197$	10.0820	+	10.0820i	0.718316	+	0.718316i	0.968260	−	0.249944i	$-0.0804122\pi$
$197$	10.0820	+	10.0820i	0.718316	+	0.718316i	−0.249944	+	0.968260i	$0.580412\pi$
$198$		0			0
$199$	8.47035			0.600448			0.300224	−	0.953869i	$-0.402939\pi$
$199$	8.47035			0.600448			0.300224	+	0.953869i	$0.402939\pi$
$200$		0			0
$201$		−	9.13777i		−	0.644528i
$202$		0			0
$203$	3.80454	−	3.80454i	0.267026	−	0.267026i
$204$		0			0
$205$	−17.8757	−	14.6801i	−1.24849	−	1.02530i
$206$		0			0
$207$	4.26424	+	4.26424i	0.296385	+	0.296385i
$208$		0			0
$209$	2.23373			0.154510
$210$		0			0
$211$	−21.0191			−1.44702			−0.723508	−	0.690316i	$-0.757471\pi$
$211$	−21.0191			−1.44702			−0.723508	+	0.690316i	$0.757471\pi$
$212$		0			0
$213$	8.04785	−	8.04785i	0.551430	−	0.551430i
$214$		0			0
$215$	−21.8119	+	2.14098i	−1.48756	+	0.146014i
$216$		0			0
$217$	−4.10081	+	1.93099i	−0.278381	+	0.131084i
$218$		0			0
$219$		−	14.2536i		−	0.963167i
$220$		0			0
$221$	−0.214618			−0.0144367
$222$		0			0
$223$	6.52316	−	6.52316i	0.436823	−	0.436823i	−0.454118	−	0.890941i	$-0.650046\pi$
$223$	6.52316	−	6.52316i	0.436823	−	0.436823i	0.890941	+	0.454118i	$0.150046\pi$
$224$		0			0
$225$	4.90457	−	0.972199i	0.326971	−	0.0648133i
$226$		0			0
$227$	−19.9575	+	19.9575i	−1.32463	+	1.32463i	−0.414641	+	0.909985i	$0.636093\pi$
$227$	−19.9575	+	19.9575i	−1.32463	+	1.32463i	−0.909985	+	0.414641i	$0.863907\pi$
$228$		0			0
$229$	5.62109			0.371452			0.185726	−	0.982602i	$-0.440536\pi$
$229$	5.62109			0.371452			0.185726	+	0.982602i	$0.440536\pi$
$230$		0			0
$231$	−4.13383			−0.271986
$232$		0			0
$233$	0.444489	+	0.444489i	0.0291195	+	0.0291195i	0.721517	−	0.692397i	$-0.243445\pi$
$233$	0.444489	+	0.444489i	0.0291195	+	0.0291195i	−0.692397	+	0.721517i	$0.743445\pi$
$234$		0			0
$235$	12.2626	−	1.20365i	0.799922	−	0.0785176i
$236$		0			0
$237$	7.93687	−	7.93687i	0.515555	−	0.515555i
$238$		0			0
$239$	−27.3608			−1.76983			−0.884913	−	0.465757i	$-0.845782\pi$
$239$	−27.3608			−1.76983			−0.884913	+	0.465757i	$0.845782\pi$
$240$		0			0
$241$			3.86122i			0.248723i	0.992237	+	0.124361i	$0.0396882\pi$
$241$			3.86122i			0.248723i	−0.992237	+	0.124361i	$0.960312\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	8.99331	−	10.9510i	0.574561	−	0.699632i
$246$		0			0
$247$	0.129029	+	0.129029i	0.00820994	+	0.00820994i
$248$		0			0
$249$		−	6.15938i		−	0.390335i
$250$		0			0
$251$		−	29.8469i		−	1.88392i	−0.335725	−	0.941960i	$-0.608981\pi$
$251$		−	29.8469i		−	1.88392i	0.335725	−	0.941960i	$-0.391019\pi$
$252$		0			0
$253$	21.6530	+	21.6530i	1.36131	+	1.36131i
$254$		0			0
$255$	−0.894064	−	0.734236i	−0.0559885	−	0.0459796i
$256$		0			0
$257$	11.2365	−	11.2365i	0.700917	−	0.700917i	−0.263691	−	0.964607i	$-0.584940\pi$
$257$	11.2365	−	11.2365i	0.700917	−	0.700917i	0.964607	+	0.263691i	$0.0849398\pi$
$258$		0			0
$259$	0.977664			0.0607491
$260$		0			0
$261$			6.60907i			0.409091i
$262$		0			0
$263$	−2.39013	+	2.39013i	−0.147382	+	0.147382i	−0.776947	−	0.629565i	$-0.783233\pi$
$263$	−2.39013	+	2.39013i	−0.147382	+	0.147382i	0.629565	+	0.776947i	$0.283233\pi$
$264$		0			0
$265$	28.0071	−	2.74908i	1.72046	−	0.168875i
$266$		0			0
$267$	2.95328	−	2.95328i	0.180738	−	0.180738i
$268$		0			0
$269$	−12.9537			−0.789801			−0.394901	−	0.918724i	$-0.629221\pi$
$269$	−12.9537			−0.789801			−0.394901	+	0.918724i	$0.629221\pi$
$270$		0			0
$271$		−	9.57319i		−	0.581530i	−0.956795	−	0.290765i	$-0.906090\pi$
$271$		−	9.57319i		−	0.581530i	0.956795	−	0.290765i	$-0.0939097\pi$
$272$		0			0
$273$	−0.238787	−	0.238787i	−0.0144520	−	0.0144520i
$274$		0			0
$275$	24.9045	−	4.93664i	1.50180	−	0.297691i
$276$		0			0
$277$	9.98683	+	9.98683i	0.600050	+	0.600050i	0.940326	−	0.340275i	$-0.110520\pi$
$277$	9.98683	+	9.98683i	0.600050	+	0.600050i	−0.340275	+	0.940326i	$0.610520\pi$
$278$		0			0
$279$	1.88466	−	5.23909i	0.112832	−	0.313656i
$280$		0			0
$281$	6.68935			0.399053			0.199527	−	0.979892i	$-0.436060\pi$
$281$	6.68935			0.399053			0.199527	+	0.979892i	$0.436060\pi$
$282$		0			0
$283$	−7.46041	−	7.46041i	−0.443475	−	0.443475i	0.449703	−	0.893178i	$-0.351530\pi$
$283$	−7.46041	−	7.46041i	−0.443475	−	0.443475i	−0.893178	+	0.449703i	$0.851530\pi$
$284$		0			0
$285$	0.0960897	+	0.978943i	0.00569186	+	0.0579876i
$286$		0			0
$287$	−5.95487	+	5.95487i	−0.351505	+	0.351505i
$288$		0			0
$289$		−	16.7323i		−	0.984253i
$290$		0			0
$291$		−	7.47896i		−	0.438424i
$292$		0			0
$293$	−5.50982	−	5.50982i	−0.321887	−	0.321887i	0.527604	−	0.849491i	$-0.323091\pi$
$293$	−5.50982	−	5.50982i	−0.321887	−	0.321887i	−0.849491	+	0.527604i	$0.823091\pi$
$294$		0			0
$295$	−11.5635	+	14.0806i	−0.673252	+	0.819806i
$296$		0			0
$297$	3.59055	−	3.59055i	0.208345	−	0.208345i
$298$		0			0
$299$			2.50153i			0.144667i
$300$		0			0
$301$			7.97933i			0.459921i
$302$		0			0
$303$	−5.45592	+	5.45592i	−0.313434	+	0.313434i
$304$		0			0
$305$	2.11297	−	2.57292i	0.120988	−	0.147325i
$306$		0			0
$307$	4.80394	−	4.80394i	0.274175	−	0.274175i	−0.556603	−	0.830778i	$-0.687896\pi$
$307$	4.80394	−	4.80394i	0.274175	−	0.274175i	0.830778	+	0.556603i	$0.187896\pi$
$308$		0			0
$309$	−15.5980			−0.887342
$310$		0			0
$311$	−23.7495			−1.34671			−0.673356	−	0.739318i	$-0.735148\pi$
$311$	−23.7495			−1.34671			−0.673356	+	0.739318i	$0.735148\pi$
$312$		0			0
$313$	−3.39387	+	3.39387i	−0.191833	+	0.191833i	−0.796488	−	0.604655i	$-0.793311\pi$
$313$	−3.39387	+	3.39387i	−0.191833	+	0.191833i	0.604655	+	0.796488i	$0.293311\pi$
$314$		0			0
$315$	−0.177827	−	1.81167i	−0.0100194	−	0.102076i
$316$		0			0
$317$	16.1463	−	16.1463i	0.906866	−	0.906866i	−0.0891519	−	0.996018i	$-0.528416\pi$
$317$	16.1463	−	16.1463i	0.906866	−	0.906866i	0.996018	+	0.0891519i	$0.0284156\pi$
$318$		0			0
$319$			33.5596i			1.87898i
$320$		0			0
$321$			16.6523i			0.929441i
$322$		0			0
$323$	0.160937	−	0.160937i	0.00895478	−	0.00895478i
$324$		0			0
$325$	1.72374	+	1.15342i	0.0956161	+	0.0639804i
$326$		0			0
$327$	−3.77528	−	3.77528i	−0.208774	−	0.208774i
$328$		0			0
$329$		−	4.48595i		−	0.247319i
$330$		0			0
$331$		−	27.2963i		−	1.50034i	−0.661245	−	0.750170i	$-0.729972\pi$
$331$		−	27.2963i		−	1.50034i	0.661245	−	0.750170i	$-0.270028\pi$
$332$		0			0
$333$	−0.849177	+	0.849177i	−0.0465346	+	0.0465346i
$334$		0			0
$335$	20.3349	−	1.99601i	1.11102	−	0.109054i
$336$		0			0
$337$	14.2054	+	14.2054i	0.773819	+	0.773819i	0.978772	−	0.204953i	$-0.0657041\pi$
$337$	14.2054	+	14.2054i	0.773819	+	0.773819i	−0.204953	+	0.978772i	$0.565704\pi$
$338$		0			0
$339$	7.55994			0.410600
$340$		0			0
$341$	9.56993	−	26.6031i	0.518241	−	1.44064i
$342$		0			0
$343$	−7.67763	−	7.67763i	−0.414553	−	0.414553i
$344$		0			0
$345$	−8.55806	+	10.4210i	−0.460750	+	0.561046i
$346$		0			0
$347$	12.1576	+	12.1576i	0.652652	+	0.652652i	0.953631	−	0.300979i	$-0.0973133\pi$
$347$	12.1576	+	12.1576i	0.652652	+	0.652652i	−0.300979	+	0.953631i	$0.597313\pi$
$348$		0			0
$349$			8.30114i			0.444350i	0.975007	+	0.222175i	$0.0713156\pi$
$349$			8.30114i			0.444350i	−0.975007	+	0.222175i	$0.928684\pi$
$350$		0			0
$351$	0.414810			0.0221409
$352$		0			0
$353$	6.60632	−	6.60632i	0.351619	−	0.351619i	−0.509093	−	0.860712i	$-0.670019\pi$
$353$	6.60632	−	6.60632i	0.351619	−	0.351619i	0.860712	+	0.509093i	$0.170019\pi$
$354$		0			0
$355$	19.6674	+	16.1515i	1.04384	+	0.857235i
$356$		0			0
$357$	−0.297836	+	0.297836i	−0.0157632	+	0.0157632i
$358$		0			0
$359$			10.2070i			0.538707i	0.963041	+	0.269353i	$0.0868099\pi$
$359$			10.2070i			0.538707i	−0.963041	+	0.269353i	$0.913190\pi$
$360$		0			0
$361$	18.8065			0.989815
$362$		0			0
$363$	10.4540	−	10.4540i	0.548690	−	0.548690i
$364$		0			0
$365$	31.7195	−	3.11348i	1.66028	−	0.162967i
$366$		0			0
$367$	4.28767	+	4.28767i	0.223815	+	0.223815i	0.810103	−	0.586288i	$-0.199411\pi$
$367$	4.28767	+	4.28767i	0.223815	+	0.223815i	−0.586288	+	0.810103i	$0.699411\pi$
$368$		0			0
$369$		−	10.3445i		−	0.538515i
$370$		0			0
$371$		−	10.2457i		−	0.531931i
$372$		0			0
$373$	2.94743	+	2.94743i	0.152612	+	0.152612i	0.779283	−	0.626672i	$-0.215583\pi$
$373$	2.94743	+	2.94743i	0.152612	+	0.152612i	−0.626672	+	0.779283i	$0.715583\pi$
$374$		0			0
$375$	3.23484	+	10.7021i	0.167046	+	0.552656i
$376$		0			0
$377$	−1.93854	+	1.93854i	−0.0998398	+	0.0998398i
$378$		0			0
$379$			4.60786i			0.236690i	0.992973	+	0.118345i	$0.0377588\pi$
$379$			4.60786i			0.236690i	−0.992973	+	0.118345i	$0.962241\pi$
$380$		0			0
$381$	−2.61711			−0.134078
$382$		0			0
$383$	−20.2250	+	20.2250i	−1.03345	+	1.03345i	−0.0340280	+	0.999421i	$0.510834\pi$
$383$	−20.2250	+	20.2250i	−1.03345	+	1.03345i	−0.999421	+	0.0340280i	$0.989166\pi$
$384$		0			0
$385$	−0.902973	−	9.19931i	−0.0460198	−	0.468840i
$386$		0			0
$387$	−6.93067	−	6.93067i	−0.352306	−	0.352306i
$388$		0			0
$389$	26.3586			1.33643			0.668217	−	0.743966i	$-0.267058\pi$
$389$	26.3586			1.33643			0.668217	+	0.743966i	$0.267058\pi$
$390$		0			0
$391$	3.12013			0.157792
$392$		0			0
$393$	8.97583	−	8.97583i	0.452771	−	0.452771i
$394$		0			0
$395$	19.3962	+	15.9288i	0.975929	+	0.801466i
$396$		0			0
$397$	2.18912	−	2.18912i	0.109869	−	0.109869i	−0.650035	−	0.759904i	$-0.725246\pi$
$397$	2.18912	−	2.18912i	0.109869	−	0.109869i	0.759904	+	0.650035i	$0.225246\pi$
$398$		0			0
$399$	0.358122			0.0179285
$400$		0			0
$401$			26.3320i			1.31496i	0.753473	+	0.657479i	$0.228377\pi$
$401$			26.3320i			1.31496i	−0.753473	+	0.657479i	$0.771623\pi$
$402$		0			0
$403$	2.08950	−	0.983904i	0.104085	−	0.0490118i
$404$		0			0
$405$	1.72803	+	1.41912i	0.0858667	+	0.0705166i
$406$		0			0
$407$	−4.31196	+	4.31196i	−0.213736	+	0.213736i
$408$		0			0
$409$	11.2663			0.557082			0.278541	−	0.960424i	$-0.410149\pi$
$409$	11.2663			0.557082			0.278541	+	0.960424i	$0.410149\pi$
$410$		0			0
$411$	−11.8897			−0.586478
$412$		0			0
$413$	4.69063	+	4.69063i	0.230811	+	0.230811i
$414$		0			0
$415$	13.7069	−	1.34543i	0.672847	−	0.0660444i
$416$		0			0
$417$	14.3637	−	14.3637i	0.703396	−	0.703396i
$418$		0			0
$419$		−	13.2921i		−	0.649361i	−0.945824	−	0.324680i	$-0.894743\pi$
$419$		−	13.2921i		−	0.649361i	0.945824	−	0.324680i	$-0.105257\pi$
$420$		0			0
$421$	−27.3668			−1.33377			−0.666887	−	0.745159i	$-0.732374\pi$
$421$	−27.3668			−1.33377			−0.666887	+	0.745159i	$0.732374\pi$
$422$		0			0
$423$	3.89640	+	3.89640i	0.189449	+	0.189449i
$424$		0			0
$425$	1.43865	−	2.15001i	0.0697850	−	0.104291i
$426$		0			0
$427$	−0.857106	−	0.857106i	−0.0414783	−	0.0414783i
$428$		0			0
$429$	2.10632			0.101694
$430$		0			0
$431$	5.25254			0.253006			0.126503	−	0.991966i	$-0.459625\pi$
$431$	5.25254			0.253006			0.126503	+	0.991966i	$0.459625\pi$
$432$		0			0
$433$	−16.1942	+	16.1942i	−0.778244	+	0.778244i	−0.979532	−	0.201288i	$-0.935487\pi$
$433$	−16.1942	+	16.1942i	−0.778244	+	0.778244i	0.201288	+	0.979532i	$0.435487\pi$
$434$		0			0
$435$	−14.7076	+	1.44365i	−0.705178	+	0.0692179i
$436$		0			0
$437$	−1.87584	−	1.87584i	−0.0897336	−	0.0897336i
$438$		0			0
$439$		−	18.2878i		−	0.872831i	−0.899745	−	0.436415i	$-0.856248\pi$
$439$		−	18.2878i		−	0.872831i	0.899745	−	0.436415i	$-0.143752\pi$
$440$		0			0
$441$	6.33725			0.301774
$442$		0			0
$443$	−11.5612	−	11.5612i	−0.549288	−	0.549288i	0.376947	−	0.926235i	$-0.376974\pi$
$443$	−11.5612	−	11.5612i	−0.549288	−	0.549288i	−0.926235	+	0.376947i	$0.876974\pi$
$444$		0			0
$445$	7.21726	+	5.92706i	0.342131	+	0.280970i
$446$		0			0
$447$	−13.3960	−	13.3960i	−0.633608	−	0.633608i
$448$		0			0
$449$	9.29786			0.438793			0.219397	−	0.975636i	$-0.429591\pi$
$449$	9.29786			0.438793			0.219397	+	0.975636i	$0.429591\pi$
$450$		0			0
$451$		−	52.5275i		−	2.47342i
$452$		0			0
$453$	7.12923	+	7.12923i	0.334961	+	0.334961i
$454$		0			0
$455$	0.479230	−	0.583549i	0.0224667	−	0.0273572i
$456$		0			0
$457$	−1.87262	−	1.87262i	−0.0875973	−	0.0875973i	0.661950	−	0.749548i	$-0.269729\pi$
$457$	−1.87262	−	1.87262i	−0.0875973	−	0.0875973i	−0.749548	+	0.661950i	$0.769729\pi$
$458$		0			0
$459$		−	0.517388i		−	0.0241496i
$460$		0			0
$461$		−	24.9462i		−	1.16186i	−0.813954	−	0.580930i	$-0.802689\pi$
$461$		−	24.9462i		−	1.16186i	0.813954	−	0.580930i	$-0.197311\pi$
$462$		0			0
$463$	−12.5924	+	12.5924i	−0.585219	+	0.585219i	−0.936333	−	0.351114i	$-0.885803\pi$
$463$	−12.5924	+	12.5924i	−0.585219	+	0.585219i	0.351114	+	0.936333i	$0.385803\pi$
$464$		0			0
$465$	12.0706	+	3.04967i	0.559761	+	0.141425i
$466$		0			0
$467$	−1.95220	+	1.95220i	−0.0903370	+	0.0903370i	−0.750831	−	0.660494i	$-0.770347\pi$
$467$	−1.95220	+	1.95220i	−0.0903370	+	0.0903370i	0.660494	+	0.750831i	$0.270347\pi$
$468$		0			0
$469$		−	7.43903i		−	0.343503i
$470$		0			0
$471$		−	9.31764i		−	0.429334i
$472$		0			0
$473$	−35.1926	−	35.1926i	−1.61816	−	1.61816i
$474$		0			0
$475$	−2.15752	+	0.427671i	−0.0989940	+	0.0196229i
$476$		0			0
$477$	8.89919	+	8.89919i	0.407466	+	0.407466i
$478$		0			0
$479$			12.3481i			0.564200i	0.959385	+	0.282100i	$0.0910310\pi$
$479$			12.3481i			0.564200i	−0.959385	+	0.282100i	$0.908969\pi$
$480$		0			0
$481$	−0.498152			−0.0227138
$482$		0			0
$483$	3.47150	+	3.47150i	0.157959	+	0.157959i
$484$		0			0
$485$	16.6435	−	1.63367i	0.755741	−	0.0741810i
$486$		0			0
$487$	5.83590	+	5.83590i	0.264450	+	0.264450i	0.826859	−	0.562409i	$-0.190125\pi$
$487$	5.83590	+	5.83590i	0.264450	+	0.264450i	−0.562409	+	0.826859i	$0.690125\pi$
$488$		0			0
$489$	−23.0488			−1.04230
$490$		0			0
$491$			2.22265i			0.100307i	0.998742	+	0.0501533i	$0.0159710\pi$
$491$			2.22265i			0.100307i	−0.998742	+	0.0501533i	$0.984029\pi$
$492$		0			0
$493$	2.41792	+	2.41792i	0.108898	+	0.108898i
$494$		0			0
$495$	8.77462	+	7.20602i	0.394390	+	0.323886i
$496$		0			0
$497$	6.55173	−	6.55173i	0.293885	−	0.293885i
$498$		0			0
$499$	11.3548			0.508312			0.254156	−	0.967163i	$-0.418202\pi$
$499$	11.3548			0.508312			0.254156	+	0.967163i	$0.418202\pi$
$500$		0			0
$501$	19.1727			0.856572
$502$		0			0
$503$	−19.0779	−	19.0779i	−0.850643	−	0.850643i	0.139569	−	0.990212i	$-0.455428\pi$
$503$	−19.0779	−	19.0779i	−0.850643	−	0.850643i	−0.990212	+	0.139569i	$0.955428\pi$
$504$		0			0
$505$	−13.3332	−	10.9497i	−0.593320	−	0.487255i
$506$		0			0
$507$	−9.07072	−	9.07072i	−0.402845	−	0.402845i
$508$		0			0
$509$	−6.25137			−0.277087			−0.138543	−	0.990356i	$-0.544242\pi$
$509$	−6.25137			−0.277087			−0.138543	+	0.990356i	$0.544242\pi$
$510$		0			0
$511$		−	11.6038i		−	0.513322i
$512$		0			0
$513$	−0.311057	+	0.311057i	−0.0137335	+	0.0137335i
$514$		0			0
$515$	−3.40716	−	34.7115i	−0.150137	−	1.52957i
$516$		0			0
$517$	19.7852	+	19.7852i	0.870151	+	0.870151i
$518$		0			0
$519$	−11.9486			−0.524486
$520$		0			0
$521$	7.50173			0.328657			0.164328	−	0.986406i	$-0.447454\pi$
$521$	7.50173			0.328657			0.164328	+	0.986406i	$0.447454\pi$
$522$		0			0
$523$	25.8067	−	25.8067i	1.12845	−	1.12845i	0.138016	−	0.990430i	$-0.455927\pi$
$523$	25.8067	−	25.8067i	1.12845	−	1.12845i	0.990430	−	0.138016i	$-0.0440726\pi$
$524$		0			0
$525$	3.99280	−	0.791465i	0.174260	−	0.0345424i
$526$		0			0
$527$	−1.22721	−	2.60621i	−0.0534583	−	0.113528i
$528$		0			0
$529$		−	13.3674i		−	0.581192i
$530$		0			0
$531$	−8.14835			−0.353608
$532$		0			0
$533$	3.03420	−	3.03420i	0.131426	−	0.131426i
$534$		0			0
$535$	−37.0576	+	3.63745i	−1.60214	+	0.157261i
$536$		0			0
$537$	−9.80251	+	9.80251i	−0.423010	+	0.423010i
$538$		0			0
$539$	32.1793			1.38606
$540$		0			0
$541$	−23.5126			−1.01089			−0.505443	−	0.862860i	$-0.668671\pi$
$541$	−23.5126			−1.01089			−0.505443	+	0.862860i	$0.668671\pi$
$542$		0			0
$543$	−1.88235	−	1.88235i	−0.0807793	−	0.0807793i
$544$		0			0
$545$	7.57676	−	9.22607i	0.324553	−	0.395201i
$546$		0			0
$547$	−6.68445	+	6.68445i	−0.285807	+	0.285807i	−0.835419	−	0.549613i	$-0.814775\pi$
$547$	−6.68445	+	6.68445i	−0.285807	+	0.285807i	0.549613	+	0.835419i	$0.314775\pi$
$548$		0			0
$549$	1.48893			0.0635459
$550$		0			0
$551$		−	2.90733i		−	0.123857i
$552$		0			0
$553$	6.46139	−	6.46139i	0.274766	−	0.274766i
$554$		0			0
$555$	−2.07523	−	1.70425i	−0.0880884	−	0.0723412i
$556$		0			0
$557$	25.6613	+	25.6613i	1.08730	+	1.08730i	0.995805	+	0.0914983i	$0.0291656\pi$
$557$	25.6613	+	25.6613i	1.08730	+	1.08730i	0.0914983	+	0.995805i	$0.470834\pi$
$558$		0			0
$559$		−	4.06574i		−	0.171962i
$560$		0			0
$561$		−	2.62720i		−	0.110920i
$562$		0			0
$563$	−23.8281	−	23.8281i	−1.00423	−	1.00423i	−0.999991	−	0.00424364i	$-0.998649\pi$
$563$	−23.8281	−	23.8281i	−1.00423	−	1.00423i	−0.00424364	−	0.999991i	$-0.501351\pi$
$564$		0			0
$565$	1.65136	+	16.8237i	0.0694731	+	0.707778i
$566$		0			0
$567$	0.575654	−	0.575654i	0.0241752	−	0.0241752i
$568$		0			0
$569$	−27.4294			−1.14990			−0.574951	−	0.818188i	$-0.694979\pi$
$569$	−27.4294			−1.14990			−0.574951	+	0.818188i	$0.694979\pi$
$570$		0			0
$571$		−	10.0366i		−	0.420019i	−0.977699	−	0.210010i	$-0.932650\pi$
$571$		−	10.0366i		−	0.420019i	0.977699	−	0.210010i	$-0.0673495\pi$
$572$		0			0
$573$	−16.8439	+	16.8439i	−0.703665	+	0.703665i
$574$		0			0
$575$	−25.0599	−	16.7686i	−1.04507	−	0.699297i
$576$		0			0
$577$	−4.32282	+	4.32282i	−0.179961	+	0.179961i	−0.791339	−	0.611378i	$-0.790616\pi$
$577$	−4.32282	+	4.32282i	−0.179961	+	0.179961i	0.611378	+	0.791339i	$0.290616\pi$
$578$		0			0
$579$	18.9004			0.785472
$580$		0			0
$581$		−	5.01434i		−	0.208030i
$582$		0			0
$583$	45.1884	+	45.1884i	1.87151	+	1.87151i
$584$		0			0
$585$	0.0906090	+	0.923106i	0.00374622	+	0.0381658i
$586$		0			0
$587$	−21.6379	−	21.6379i	−0.893090	−	0.893090i	0.101723	−	0.994813i	$-0.467565\pi$
$587$	−21.6379	−	21.6379i	−0.893090	−	0.893090i	−0.994813	+	0.101723i	$0.967565\pi$
$588$		0			0
$589$	−0.829062	+	2.30468i	−0.0341609	+	0.0949626i
$590$		0			0
$591$	−14.2582			−0.586503
$592$		0			0
$593$	−18.1551	−	18.1551i	−0.745541	−	0.745541i	0.228098	−	0.973638i	$-0.426749\pi$
$593$	−18.1551	−	18.1551i	−0.745541	−	0.745541i	−0.973638	+	0.228098i	$0.926749\pi$
$594$		0			0
$595$	−0.727855	−	0.597739i	−0.0298392	−	0.0245049i
$596$		0			0
$597$	−5.98945	+	5.98945i	−0.245132	+	0.245132i
$598$		0			0
$599$			5.05341i			0.206477i	0.994657	+	0.103238i	$0.0329204\pi$
$599$			5.05341i			0.206477i	−0.994657	+	0.103238i	$0.967080\pi$
$600$		0			0
$601$		−	6.47060i		−	0.263941i	−0.991254	−	0.131971i	$-0.957870\pi$
$601$		−	6.47060i		−	0.263941i	0.991254	−	0.131971i	$-0.0421305\pi$
$602$		0			0
$603$	6.46138	+	6.46138i	0.263128	+	0.263128i
$604$		0			0
$605$	25.5475	+	20.9804i	1.03865	+	0.852976i
$606$		0			0
$607$	25.7718	−	25.7718i	1.04605	−	1.04605i	0.0471585	−	0.998887i	$-0.484983\pi$
$607$	25.7718	−	25.7718i	1.04605	−	1.04605i	0.998887	−	0.0471585i	$-0.0150166\pi$
$608$		0			0
$609$			5.38043i			0.218026i
$610$		0			0
$611$			2.28574i			0.0924713i
$612$		0			0
$613$	−2.03353	+	2.03353i	−0.0821336	+	0.0821336i	−0.746980	−	0.664846i	$-0.768497\pi$
$613$	−2.03353	+	2.03353i	−0.0821336	+	0.0821336i	0.664846	+	0.746980i	$0.268497\pi$
$614$		0			0
$615$	23.0204	−	2.25961i	0.928274	−	0.0911162i
$616$		0			0
$617$	−26.2948	+	26.2948i	−1.05859	+	1.05859i	−0.0604158	+	0.998173i	$0.519243\pi$
$617$	−26.2948	+	26.2948i	−1.05859	+	1.05859i	−0.998173	+	0.0604158i	$0.980757\pi$
$618$		0			0
$619$	−8.62552			−0.346689			−0.173344	−	0.984861i	$-0.555457\pi$
$619$	−8.62552			−0.346689			−0.173344	+	0.984861i	$0.555457\pi$
$620$		0			0
$621$	−6.03054			−0.241997
$622$		0			0
$623$	2.40426	−	2.40426i	0.0963247	−	0.0963247i
$624$		0			0
$625$	−23.1097	+	9.53644i	−0.924386	+	0.381458i
$626$		0			0
$627$	−1.57949	+	1.57949i	−0.0630786	+	0.0630786i
$628$		0			0
$629$			0.621341i			0.0247745i
$630$		0			0
$631$			16.6281i			0.661954i	0.943639	+	0.330977i	$0.107378\pi$
$631$			16.6281i			0.661954i	−0.943639	+	0.330977i	$0.892622\pi$
$632$		0			0
$633$	14.8628	−	14.8628i	0.590742	−	0.590742i
$634$		0			0
$635$	−0.571668	−	5.82404i	−0.0226860	−	0.231120i
$636$		0			0
$637$	1.85881	+	1.85881i	0.0736486	+	0.0736486i
$638$		0			0
$639$			11.3814i			0.450240i
$640$		0			0
$641$		−	18.1311i		−	0.716137i	−0.933695	−	0.358068i	$-0.883435\pi$
$641$		−	18.1311i		−	0.716137i	0.933695	−	0.358068i	$-0.116565\pi$
$642$		0			0
$643$	−20.0275	+	20.0275i	−0.789807	+	0.789807i	−0.981462	−	0.191655i	$-0.938614\pi$
$643$	−20.0275	+	20.0275i	−0.789807	+	0.789807i	0.191655	+	0.981462i	$0.438614\pi$
$644$		0			0
$645$	13.9094	−	16.9372i	0.547683	−	0.666903i
$646$		0			0
$647$	7.68799	+	7.68799i	0.302246	+	0.302246i	0.841892	−	0.539646i	$-0.181442\pi$
$647$	7.68799	+	7.68799i	0.302246	+	0.302246i	−0.539646	+	0.841892i	$0.681442\pi$
$648$		0			0
$649$	−41.3758			−1.62414
$650$		0			0
$651$	1.53429	−	4.26513i	0.0601338	−	0.167164i
$652$		0			0
$653$	−1.59545	−	1.59545i	−0.0624348	−	0.0624348i	0.675200	−	0.737635i	$-0.264057\pi$
$653$	−1.59545	−	1.59545i	−0.0624348	−	0.0624348i	−0.737635	+	0.675200i	$0.764057\pi$
$654$		0			0
$655$	21.9352	+	18.0139i	0.857079	+	0.703862i
$656$		0			0
$657$	10.0788	+	10.0788i	0.393211	+	0.393211i
$658$		0			0
$659$			11.5424i			0.449629i	0.974402	+	0.224814i	$0.0721776\pi$
$659$			11.5424i			0.449629i	−0.974402	+	0.224814i	$0.927822\pi$
$660$		0			0
$661$	−5.01044			−0.194884			−0.0974418	−	0.995241i	$-0.531066\pi$
$661$	−5.01044			−0.194884			−0.0974418	+	0.995241i	$0.531066\pi$
$662$		0			0
$663$	0.151758	−	0.151758i	0.00589378	−	0.00589378i
$664$		0			0
$665$	0.0782264	+	0.796955i	0.00303349	+	0.0309046i
$666$		0			0
$667$	28.1826	−	28.1826i	1.09124	−	1.09124i
$668$		0			0
$669$			9.22514i			0.356664i
$670$		0			0
$671$	7.56048			0.291869
$672$		0			0
$673$	−19.2226	+	19.2226i	−0.740978	+	0.740978i	−0.972766	−	0.231788i	$-0.925542\pi$
$673$	−19.2226	+	19.2226i	−0.740978	+	0.740978i	0.231788	+	0.972766i	$0.425542\pi$
$674$		0			0
$675$	−2.78061	+	4.15551i	−0.107026	+	0.159945i
$676$		0			0
$677$	−18.0400	−	18.0400i	−0.693335	−	0.693335i	0.269629	−	0.962964i	$-0.413099\pi$
$677$	−18.0400	−	18.0400i	−0.693335	−	0.693335i	−0.962964	+	0.269629i	$0.913099\pi$
$678$		0			0
$679$		−	6.08860i		−	0.233659i
$680$		0			0
$681$		−	28.2242i		−	1.08155i
$682$		0			0
$683$	19.3030	+	19.3030i	0.738609	+	0.738609i	0.972309	−	0.233700i	$-0.0750834\pi$
$683$	19.3030	+	19.3030i	0.738609	+	0.738609i	−0.233700	+	0.972309i	$0.575083\pi$
$684$		0			0
$685$	−2.59714	−	26.4591i	−0.0992315	−	1.01095i
$686$		0			0
$687$	−3.97471	+	3.97471i	−0.151645	+	0.151645i
$688$		0			0
$689$			5.22053i			0.198886i
$690$		0			0
$691$	−28.2777			−1.07573			−0.537867	−	0.843030i	$-0.680770\pi$
$691$	−28.2777			−1.07573			−0.537867	+	0.843030i	$0.680770\pi$
$692$		0			0
$693$	2.92306	−	2.92306i	0.111038	−	0.111038i
$694$		0			0
$695$	35.1022	+	28.8272i	1.33150	+	1.09348i
$696$		0			0
$697$	−3.78453	−	3.78453i	−0.143349	−	0.143349i
$698$		0			0
$699$	−0.628603			−0.0237759
$700$		0			0
$701$	−40.7139			−1.53774			−0.768871	−	0.639403i	$-0.779181\pi$
$701$	−40.7139			−1.53774			−0.768871	+	0.639403i	$0.779181\pi$
$702$		0			0
$703$	0.373553	−	0.373553i	0.0140888	−	0.0140888i
$704$		0			0
$705$	−7.81983	+	9.52206i	−0.294512	+	0.358621i
$706$		0			0
$707$	−4.44165	+	4.44165i	−0.167045	+	0.167045i
$708$		0			0
$709$	33.8075			1.26967			0.634834	−	0.772649i	$-0.281069\pi$
$709$	33.8075			1.26967			0.634834	+	0.772649i	$0.281069\pi$
$710$		0			0
$711$			11.2244i			0.420949i
$712$		0			0
$713$	−30.3773	+	14.3041i	−1.13764	+	0.535692i
$714$		0			0
$715$	0.460095	+	4.68736i	0.0172066	+	0.175297i
$716$		0			0
$717$	19.3470	−	19.3470i	0.722528	−	0.722528i
$718$		0			0
$719$	−12.7320			−0.474822			−0.237411	−	0.971409i	$-0.576299\pi$
$719$	−12.7320			−0.474822			−0.237411	+	0.971409i	$0.576299\pi$
$720$		0			0
$721$	−12.6983			−0.472910
$722$		0			0
$723$	−2.73029	−	2.73029i	−0.101541	−	0.101541i
$724$		0			0
$725$	−6.42533	−	32.4147i	−0.238631	−	1.20385i
$726$		0			0
$727$	8.08237	−	8.08237i	0.299759	−	0.299759i	−0.541161	−	0.840919i	$-0.682015\pi$
$727$	8.08237	−	8.08237i	0.299759	−	0.299759i	0.840919	+	0.541161i	$0.182015\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−5.07115			−0.187563
$732$		0			0
$733$	5.30399	+	5.30399i	0.195907	+	0.195907i	0.798243	−	0.602336i	$-0.205763\pi$
$733$	5.30399	+	5.30399i	0.195907	+	0.195907i	−0.602336	+	0.798243i	$0.705763\pi$
$734$		0			0
$735$	1.38428	+	14.1027i	0.0510598	+	0.520187i
$736$		0			0
$737$	32.8096	+	32.8096i	1.20856	+	1.20856i
$738$		0			0
$739$	43.6596			1.60604			0.803021	−	0.595950i	$-0.203224\pi$
$739$	43.6596			1.60604			0.803021	+	0.595950i	$0.203224\pi$
$740$		0			0
$741$	−0.182475			−0.00670339
$742$		0			0
$743$	−7.66124	+	7.66124i	−0.281063	+	0.281063i	−0.833533	−	0.552470i	$-0.813686\pi$
$743$	−7.66124	+	7.66124i	−0.281063	+	0.281063i	0.552470	+	0.833533i	$0.313686\pi$
$744$		0			0
$745$	26.8849	−	32.7372i	0.984986	−	1.19940i
$746$		0			0
$747$	4.35534	+	4.35534i	0.159354	+	0.159354i
$748$		0			0
$749$			13.5566i			0.495347i
$750$		0			0
$751$	−21.3600			−0.779439			−0.389720	−	0.920934i	$-0.627428\pi$
$751$	−21.3600			−0.779439			−0.389720	+	0.920934i	$0.627428\pi$
$752$		0			0
$753$	21.1050	+	21.1050i	0.769107	+	0.769107i
$754$		0			0
$755$	−14.3079	+	17.4225i	−0.520719	+	0.634069i
$756$		0			0
$757$	−17.1881	−	17.1881i	−0.624713	−	0.624713i	0.322020	−	0.946733i	$-0.395638\pi$
$757$	−17.1881	−	17.1881i	−0.624713	−	0.624713i	−0.946733	+	0.322020i	$0.895638\pi$
$758$		0			0
$759$	−30.6219			−1.11151
$760$		0			0
$761$			24.6522i			0.893642i	0.894623	+	0.446821i	$0.147444\pi$
$761$			24.6522i			0.893642i	−0.894623	+	0.446821i	$0.852556\pi$
$762$		0			0
$763$	−3.07345	−	3.07345i	−0.111266	−	0.111266i
$764$		0			0
$765$	1.15138	−	0.113016i	0.0416283	−	0.00408609i
$766$		0			0
$767$	−2.39003	−	2.39003i	−0.0862990	−	0.0862990i
$768$		0			0
$769$		−	27.1546i		−	0.979220i	−0.871941	−	0.489610i	$-0.837139\pi$
$769$		−	27.1546i		−	0.979220i	0.871941	−	0.489610i	$-0.162861\pi$
$770$		0			0
$771$			15.8909i			0.572296i
$772$		0			0
$773$	−30.5805	+	30.5805i	−1.09990	+	1.09990i	−0.105482	+	0.994421i	$0.533639\pi$
$773$	−30.5805	+	30.5805i	−1.09990	+	1.09990i	−0.994421	+	0.105482i	$0.966361\pi$
$774$		0			0
$775$	−4.15000	+	27.5278i	−0.149072	+	0.988826i
$776$		0			0
$777$	−0.691313	+	0.691313i	−0.0248007	+	0.0248007i
$778$		0			0
$779$			4.55056i			0.163041i
$780$		0			0
$781$			57.7924i			2.06798i
$782$		0			0
$783$	−4.67332	−	4.67332i	−0.167011	−	0.167011i
$784$		0			0
$785$	20.7352	−	2.03530i	0.740072	−	0.0726430i
$786$		0			0
$787$	−14.7092	−	14.7092i	−0.524328	−	0.524328i	0.394548	−	0.918875i	$-0.370901\pi$
$787$	−14.7092	−	14.7092i	−0.524328	−	0.524328i	−0.918875	+	0.394548i	$0.870901\pi$
$788$		0			0
$789$		−	3.38016i		−	0.120337i
$790$		0			0
$791$	6.15453			0.218830
$792$		0			0
$793$	0.436724	+	0.436724i	0.0155085	+	0.0155085i
$794$		0			0
$795$	−17.8601	+	21.7479i	−0.633434	+	0.771319i
$796$		0			0
$797$	−21.5382	−	21.5382i	−0.762922	−	0.762922i	0.213927	−	0.976850i	$-0.431374\pi$
$797$	−21.5382	−	21.5382i	−0.762922	−	0.762922i	−0.976850	+	0.213927i	$0.931374\pi$
$798$		0			0
$799$	2.85099			0.100861
$800$		0			0
$801$			4.17657i			0.147572i
$802$		0			0
$803$	51.1782	+	51.1782i	1.80604	+	1.80604i
$804$		0			0
$805$	−6.96709	+	8.48369i	−0.245558	+	0.299011i
$806$		0			0
$807$	9.15965	−	9.15965i	0.322435	−	0.322435i
$808$		0			0
$809$	−56.4758			−1.98558			−0.992792	−	0.119851i	$-0.961758\pi$
$809$	−56.4758			−1.98558			−0.992792	+	0.119851i	$0.961758\pi$
$810$		0			0
$811$	32.6065			1.14497			0.572484	−	0.819916i	$-0.305980\pi$
$811$	32.6065			1.14497			0.572484	+	0.819916i	$0.305980\pi$
$812$		0			0
$813$	6.76926	+	6.76926i	0.237408	+	0.237408i
$814$		0			0
$815$	−5.03467	−	51.2922i	−0.176357	−	1.79669i
$816$		0			0
$817$	3.04881	+	3.04881i	0.106664	+	0.106664i
$818$		0			0
$819$	0.337695			0.0118000
$820$		0			0
$821$			28.7387i			1.00299i	0.865161	+	0.501494i	$0.167216\pi$
$821$			28.7387i			1.00299i	−0.865161	+	0.501494i	$0.832784\pi$
$822$		0			0
$823$	−10.5214	+	10.5214i	−0.366754	+	0.366754i	−0.866292	−	0.499538i	$-0.833503\pi$
$823$	−10.5214	+	10.5214i	−0.366754	+	0.366754i	0.499538	+	0.866292i	$0.333503\pi$
$824$		0			0
$825$	−14.1194	+	21.1009i	−0.491574	+	0.734637i
$826$		0			0
$827$	−4.30689	−	4.30689i	−0.149765	−	0.149765i	0.628248	−	0.778013i	$-0.283772\pi$
$827$	−4.30689	−	4.30689i	−0.149765	−	0.149765i	−0.778013	+	0.628248i	$0.783772\pi$
$828$		0			0
$829$	−43.3977			−1.50726			−0.753632	−	0.657297i	$-0.771700\pi$
$829$	−43.3977			−1.50726			−0.753632	+	0.657297i	$0.771700\pi$
$830$		0			0
$831$	−14.1235			−0.489939
$832$		0			0
$833$	2.31847	−	2.31847i	0.0803303	−	0.0803303i
$834$		0			0
$835$	4.18799	+	42.6664i	0.144931	+	1.47653i
$836$		0			0
$837$	2.37194	+	5.03725i	0.0819863	+	0.174113i
$838$		0			0
$839$			22.4676i			0.775668i	0.921729	+	0.387834i	$0.126777\pi$
$839$			22.4676i			0.775668i	−0.921729	+	0.387834i	$0.873223\pi$
$840$		0			0
$841$	14.6798			0.506200
$842$		0			0
$843$	−4.73009	+	4.73009i	−0.162913	+	0.162913i
$844$		0			0
$845$	18.2044	−	22.1671i	0.626249	−	0.762571i
$846$		0			0
$847$	8.51054	−	8.51054i	0.292426	−	0.292426i
$848$		0			0
$849$	10.5506			0.362096
$850$		0			0
$851$	7.24218			0.248259
$852$		0			0
$853$	−33.8441	−	33.8441i	−1.15880	−	1.15880i	−0.984734	−	0.174066i	$-0.944309\pi$
$853$	−33.8441	−	33.8441i	−1.15880	−	1.15880i	−0.174066	−	0.984734i	$-0.555691\pi$
$854$		0			0
$855$	−0.760163	−	0.624271i	−0.0259970	−	0.0213496i
$856$		0			0
$857$	16.4510	−	16.4510i	0.561955	−	0.561955i	−0.367908	−	0.929862i	$-0.619926\pi$
$857$	16.4510	−	16.4510i	0.561955	−	0.561955i	0.929862	+	0.367908i	$0.119926\pi$
$858$		0			0
$859$	−3.65653			−0.124759			−0.0623796	−	0.998052i	$-0.519869\pi$
$859$	−3.65653			−0.124759			−0.0623796	+	0.998052i	$0.519869\pi$
$860$		0			0
$861$		−	8.42145i		−	0.287002i
$862$		0			0
$863$	5.67721	−	5.67721i	0.193254	−	0.193254i	−0.603846	−	0.797101i	$-0.706366\pi$
$863$	5.67721	−	5.67721i	0.193254	−	0.193254i	0.797101	+	0.603846i	$0.206366\pi$
$864$		0			0
$865$	−2.61000	−	26.5901i	−0.0887425	−	0.904091i
$866$		0			0
$867$	11.8315	+	11.8315i	0.401820	+	0.401820i
$868$		0			0
$869$			56.9955i			1.93344i
$870$		0			0
$871$			3.79043i			0.128434i
$872$		0			0
$873$	5.28842	+	5.28842i	0.178986	+	0.178986i
$874$		0			0
$875$	2.63347	+	8.71258i	0.0890276	+	0.294539i
$876$		0			0
$877$	−1.31955	+	1.31955i	−0.0445579	+	0.0445579i	−0.729035	−	0.684477i	$-0.760031\pi$
$877$	−1.31955	+	1.31955i	−0.0445579	+	0.0445579i	0.684477	+	0.729035i	$0.260031\pi$
$878$		0			0
$879$	7.79206			0.262820
$880$		0			0
$881$		−	53.1298i		−	1.78999i	−0.446076	−	0.894995i	$-0.647179\pi$
$881$		−	53.1298i		−	1.78999i	0.446076	−	0.894995i	$-0.352821\pi$
$882$		0			0
$883$	7.16831	−	7.16831i	0.241233	−	0.241233i	−0.576127	−	0.817360i	$-0.695437\pi$
$883$	7.16831	−	7.16831i	0.241233	−	0.241233i	0.817360	+	0.576127i	$0.195437\pi$
$884$		0			0
$885$	−1.77989	−	18.1331i	−0.0598302	−	0.609538i
$886$		0			0
$887$	−17.5734	+	17.5734i	−0.590057	+	0.590057i	−0.937647	−	0.347590i	$-0.887000\pi$
$887$	−17.5734	+	17.5734i	−0.590057	+	0.590057i	0.347590	+	0.937647i	$0.387000\pi$
$888$		0			0
$889$	−2.13058			−0.0714573
$890$		0			0
$891$			5.07781i			0.170113i
$892$		0			0
$893$	−1.71403	−	1.71403i	−0.0573578	−	0.0573578i
$894$		0			0
$895$	−23.9555	−	19.6730i	−0.800743	−	0.657597i
$896$		0			0
$897$	−1.76885	−	1.76885i	−0.0590601	−	0.0590601i
$898$		0			0
$899$	−34.6255	−	12.4558i	−1.15483	−	0.415425i
$900$		0			0
$901$	6.51152			0.216930
$902$		0			0
$903$	−5.64224	−	5.64224i	−0.187762	−	0.187762i
$904$		0			0
$905$	3.77776	−	4.60010i	0.125577	−	0.152912i
$906$		0			0
$907$	33.1694	−	33.1694i	1.10137	−	1.10137i	0.107125	−	0.994246i	$-0.465836\pi$
$907$	33.1694	−	33.1694i	1.10137	−	1.10137i	0.994246	−	0.107125i	$-0.0341645\pi$
$908$		0			0
$909$		−	7.71583i		−	0.255918i
$910$		0			0
$911$		−	19.2876i		−	0.639027i	−0.947582	−	0.319514i	$-0.896480\pi$
$911$		−	19.2876i		−	0.639027i	0.947582	−	0.319514i	$-0.103520\pi$
$912$		0			0
$913$	22.1156	+	22.1156i	0.731919	+	0.731919i
$914$		0			0
$915$	0.325234	+	3.31342i	0.0107519	+	0.109538i
$916$		0			0
$917$	7.30720	−	7.30720i	0.241305	−	0.241305i
$918$		0			0
$919$			29.1593i			0.961876i	0.876754	+	0.480938i	$0.159704\pi$
$919$			29.1593i			0.961876i	−0.876754	+	0.480938i	$0.840296\pi$
$920$		0			0
$921$			6.79380i			0.223863i
$922$		0			0
$923$	−3.33833	+	3.33833i	−0.109882	+	0.109882i
$924$		0			0
$925$	3.33928	−	4.99042i	0.109795	−	0.164084i
$926$		0			0
$927$	11.0295	−	11.0295i	0.362256	−	0.362256i
$928$		0			0
$929$	15.0570			0.494004			0.247002	−	0.969015i	$-0.420555\pi$
$929$	15.0570			0.494004			0.247002	+	0.969015i	$0.420555\pi$
$930$		0			0
$931$	−2.78776			−0.0913651
$932$		0			0
$933$	16.7935	−	16.7935i	0.549793	−	0.549793i
$934$		0			0
$935$	5.84650	−	0.573872i	0.191201	−	0.0187676i
$936$		0			0
$937$	−19.4744	+	19.4744i	−0.636201	+	0.636201i	−0.949616	−	0.313415i	$-0.898527\pi$
$937$	−19.4744	+	19.4744i	−0.636201	+	0.636201i	0.313415	+	0.949616i	$0.398527\pi$
$938$		0			0
$939$		−	4.79965i		−	0.156631i
$940$		0			0
$941$			39.7367i			1.29538i	0.761904	+	0.647690i	$0.224265\pi$
$941$			39.7367i			1.29538i	−0.761904	+	0.647690i	$0.775735\pi$
$942$		0			0
$943$	−44.1115	+	44.1115i	−1.43647	+	1.43647i
$944$		0			0
$945$	1.40679	+	1.15530i	0.0457628	+	0.0375820i
$946$		0			0
$947$	23.3073	+	23.3073i	0.757384	+	0.757384i	0.975846	−	0.218461i	$-0.0701037\pi$
$947$	23.3073	+	23.3073i	0.757384	+	0.757384i	−0.218461	+	0.975846i	$0.570104\pi$
$948$		0			0
$949$			5.91252i			0.191929i
$950$		0			0
$951$			22.8343i			0.740453i
$952$		0			0
$953$	−0.489238	+	0.489238i	−0.0158480	+	0.0158480i	−0.714986	−	0.699138i	$-0.753567\pi$
$953$	−0.489238	+	0.489238i	−0.0158480	+	0.0158480i	0.699138	+	0.714986i	$0.253567\pi$
$954$		0			0
$955$	−41.1633	−	33.8047i	−1.33201	−	1.09389i
$956$		0			0
$957$	−23.7302	−	23.7302i	−0.767089	−	0.767089i
$958$		0			0
$959$	−9.67941			−0.312564
$960$		0			0
$961$	23.8961	+	19.7478i	0.770843	+	0.637025i
$962$		0			0
$963$	−11.7750	−	11.7750i	−0.379443	−	0.379443i
$964$		0			0
$965$	4.12850	+	42.0604i	0.132901	+	1.35397i
$966$		0			0
$967$	−41.4729	−	41.4729i	−1.33368	−	1.33368i	−0.902052	−	0.431627i	$-0.857940\pi$
$967$	−41.4729	−	41.4729i	−1.33368	−	1.33368i	−0.431627	−	0.902052i	$-0.642060\pi$
$968$		0			0
$969$			0.227599i			0.00731154i
$970$		0			0
$971$	−9.32210			−0.299161			−0.149580	−	0.988750i	$-0.547792\pi$
$971$	−9.32210			−0.299161			−0.149580	+	0.988750i	$0.547792\pi$
$972$		0			0
$973$	11.6935	−	11.6935i	0.374876	−	0.374876i
$974$		0			0
$975$	−2.03446	+	0.403278i	−0.0651550	+	0.0129152i
$976$		0			0
$977$	−41.0885	+	41.0885i	−1.31454	+	1.31454i	−0.396503	+	0.918034i	$0.629776\pi$
$977$	−41.0885	+	41.0885i	−1.31454	+	1.31454i	−0.918034	+	0.396503i	$0.870224\pi$
$978$		0			0
$979$			21.2078i			0.677806i
$980$		0			0
$981$	5.33906			0.170463
$982$		0			0
$983$	−14.4307	+	14.4307i	−0.460269	+	0.460269i	−0.898744	−	0.438474i	$-0.855519\pi$
$983$	−14.4307	+	14.4307i	−0.460269	+	0.460269i	0.438474	+	0.898744i	$0.355519\pi$
$984$		0			0
$985$	−3.11449	−	31.7298i	−0.0992358	−	1.01099i
$986$		0			0
$987$	3.17205	+	3.17205i	0.100967	+	0.100967i
$988$		0			0
$989$			59.1080i			1.87953i
$990$		0			0
$991$			46.5039i			1.47724i	0.674120	+	0.738622i	$0.264523\pi$
$991$			46.5039i			1.47724i	−0.674120	+	0.738622i	$0.735477\pi$
$992$		0			0
$993$	19.3014	+	19.3014i	0.612511	+	0.612511i
$994$		0			0
$995$	−14.6371	−	12.0204i	−0.464026	−	0.381074i
$996$		0			0
$997$	30.9891	−	30.9891i	0.981433	−	0.981433i	−0.0183976	−	0.999831i	$-0.505856\pi$
$997$	30.9891	−	30.9891i	0.981433	−	0.981433i	0.999831	+	0.0183976i	$0.00585648\pi$
$998$		0			0
$999$		−	1.20092i		−	0.0379954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.433.13	✓	64
5.2	odd	4	inner	1860.2.s.a.1177.20	yes	64
31.30	odd	2	inner	1860.2.s.a.433.20	yes	64
155.92	even	4	inner	1860.2.s.a.1177.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.13	✓	64	1.1	even	1	trivial
1860.2.s.a.433.20	yes	64	31.30	odd	2	inner
1860.2.s.a.1177.13	yes	64	155.92	even	4	inner
1860.2.s.a.1177.20	yes	64	5.2	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.72803 - 1.41912i) q^{5} +(-0.575654 + 0.575654i) q^{7} -1.00000i q^{9} -5.07781i q^{11} +(0.293315 - 0.293315i) q^{13} +(2.22537 - 0.218435i) q^{15} +(-0.365849 - 0.365849i) q^{17} +0.439900i q^{19} -0.814097i q^{21} +(-4.26424 + 4.26424i) q^{23} +(0.972199 + 4.90457i) q^{25} +(0.707107 + 0.707107i) q^{27} -6.60907 q^{29} +(5.23909 + 1.88466i) q^{31} +(3.59055 + 3.59055i) q^{33} +(1.81167 - 0.177827i) q^{35} +(-0.849177 - 0.849177i) q^{37} +0.414810i q^{39} +10.3445 q^{41} +(6.93067 - 6.93067i) q^{43} +(-1.41912 + 1.72803i) q^{45} +(-3.89640 + 3.89640i) q^{47} +6.33725i q^{49} +0.517388 q^{51} +(-8.89919 + 8.89919i) q^{53} +(-7.20602 + 8.77462i) q^{55} +(-0.311057 - 0.311057i) q^{57} -8.14835i q^{59} +1.48893i q^{61} +(0.575654 + 0.575654i) q^{63} +(-0.923106 + 0.0906090i) q^{65} +(-6.46138 + 6.46138i) q^{67} -6.03054i q^{69} -11.3814 q^{71} +(-10.0788 + 10.0788i) q^{73} +(-4.15551 - 2.78061i) q^{75} +(2.92306 + 2.92306i) q^{77} -11.2244 q^{79} -1.00000 q^{81} +(-4.35534 + 4.35534i) q^{83} +(0.113016 + 1.15138i) q^{85} +(4.67332 - 4.67332i) q^{87} -4.17657 q^{89} +0.337695i q^{91} +(-5.03725 + 2.37194i) q^{93} +(0.624271 - 0.760163i) q^{95} +(-5.28842 + 5.28842i) q^{97} -5.07781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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