LMFDB - Embedded newform 184.2.h.a.91.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,2,Mod(91,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	184.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.46924739719$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	184.91
Dual form			184.2.h.a.91.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} -2.00000 q^{3} +2.00000i q^{4} +3.74166 q^{5} +(-2.00000 - 2.00000i) q^{6} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(3.74166 + 3.74166i) q^{10} +3.74166i q^{11} -4.00000i q^{12} +4.00000i q^{13} -7.48331 q^{15} -4.00000 q^{16} -7.48331i q^{17} +(1.00000 + 1.00000i) q^{18} -3.74166i q^{19} +7.48331i q^{20} +(-3.74166 + 3.74166i) q^{22} +(3.74166 - 3.00000i) q^{23} +(4.00000 - 4.00000i) q^{24} +9.00000 q^{25} +(-4.00000 + 4.00000i) q^{26} +4.00000 q^{27} +(-7.48331 - 7.48331i) q^{30} -2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} -7.48331i q^{33} +(7.48331 - 7.48331i) q^{34} +2.00000i q^{36} -3.74166 q^{37} +(3.74166 - 3.74166i) q^{38} -8.00000i q^{39} +(-7.48331 + 7.48331i) q^{40} -4.00000 q^{41} -3.74166i q^{43} -7.48331 q^{44} +3.74166 q^{45} +(6.74166 + 0.741657i) q^{46} -4.00000i q^{47} +8.00000 q^{48} -7.00000 q^{49} +(9.00000 + 9.00000i) q^{50} +14.9666i q^{51} -8.00000 q^{52} -3.74166 q^{53} +(4.00000 + 4.00000i) q^{54} +14.0000i q^{55} +7.48331i q^{57} -2.00000 q^{59} -14.9666i q^{60} +11.2250 q^{61} +(2.00000 - 2.00000i) q^{62} -8.00000i q^{64} +14.9666i q^{65} +(7.48331 - 7.48331i) q^{66} -11.2250i q^{67} +14.9666 q^{68} +(-7.48331 + 6.00000i) q^{69} +12.0000i q^{71} +(-2.00000 + 2.00000i) q^{72} +8.00000 q^{73} +(-3.74166 - 3.74166i) q^{74} -18.0000 q^{75} +7.48331 q^{76} +(8.00000 - 8.00000i) q^{78} -7.48331 q^{79} -14.9666 q^{80} -11.0000 q^{81} +(-4.00000 - 4.00000i) q^{82} +11.2250i q^{83} -28.0000i q^{85} +(3.74166 - 3.74166i) q^{86} +(-7.48331 - 7.48331i) q^{88} +7.48331i q^{89} +(3.74166 + 3.74166i) q^{90} +(6.00000 + 7.48331i) q^{92} +4.00000i q^{93} +(4.00000 - 4.00000i) q^{94} -14.0000i q^{95} +(8.00000 + 8.00000i) q^{96} -7.48331i q^{97} +(-7.00000 - 7.00000i) q^{98} +3.74166i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} + 4 q^{9} - 16 q^{16} + 4 q^{18} + 16 q^{24} + 36 q^{25} - 16 q^{26} + 16 q^{27} - 16 q^{32} - 16 q^{41} + 12 q^{46} + 32 q^{48} - 28 q^{49} + 36 q^{50} - 32 q^{52}+ \cdots - 28 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 + 4 * q^9 - 16 * q^16 + 4 * q^18 + 16 * q^24 + 36 * q^25 - 16 * q^26 + 16 * q^27 - 16 * q^32 - 16 * q^41 + 12 * q^46 + 32 * q^48 - 28 * q^49 + 36 * q^50 - 32 * q^52 + 16 * q^54 - 8 * q^59 + 8 * q^62 - 8 * q^72 + 32 * q^73 - 72 * q^75 + 32 * q^78 - 44 * q^81 - 16 * q^82 + 24 * q^92 + 16 * q^94 + 32 * q^96 - 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	−2.00000			−1.15470			−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$			2.00000i			1.00000i
$5$	3.74166			1.67332			0.836660	−	0.547723i	$-0.184505\pi$
$5$	3.74166			1.67332			0.836660	+	0.547723i	$0.184505\pi$
$6$	−2.00000	−	2.00000i	−0.816497	−	0.816497i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	1.00000			0.333333
$10$	3.74166	+	3.74166i	1.18322	+	1.18322i
$11$			3.74166i			1.12815i	0.825723	+	0.564076i	$0.190768\pi$
$11$			3.74166i			1.12815i	−0.825723	+	0.564076i	$0.809232\pi$
$12$		−	4.00000i		−	1.15470i
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	−7.48331			−1.93218
$16$	−4.00000			−1.00000
$17$		−	7.48331i		−	1.81497i	−0.420084	−	0.907485i	$-0.637999\pi$
$17$		−	7.48331i		−	1.81497i	0.420084	−	0.907485i	$-0.362001\pi$
$18$	1.00000	+	1.00000i	0.235702	+	0.235702i
$19$		−	3.74166i		−	0.858395i	−0.903211	−	0.429198i	$-0.858796\pi$
$19$		−	3.74166i		−	0.858395i	0.903211	−	0.429198i	$-0.141204\pi$
$20$			7.48331i			1.67332i
$21$		0			0
$22$	−3.74166	+	3.74166i	−0.797724	+	0.797724i
$23$	3.74166	−	3.00000i	0.780189	−	0.625543i
$23$	3.74166	−	3.00000i	0.780189	−	0.625543i
$24$	4.00000	−	4.00000i	0.816497	−	0.816497i
$25$	9.00000			1.80000
$26$	−4.00000	+	4.00000i	−0.784465	+	0.784465i
$27$	4.00000			0.769800
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−7.48331	−	7.48331i	−1.36626	−	1.36626i
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		−	7.48331i		−	1.30268i
$34$	7.48331	−	7.48331i	1.28338	−	1.28338i
$35$		0			0
$36$			2.00000i			0.333333i
$37$	−3.74166			−0.615125			−0.307562	−	0.951528i	$-0.599513\pi$
$37$	−3.74166			−0.615125			−0.307562	+	0.951528i	$0.599513\pi$
$38$	3.74166	−	3.74166i	0.606977	−	0.606977i
$39$		−	8.00000i		−	1.28103i
$40$	−7.48331	+	7.48331i	−1.18322	+	1.18322i
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$		−	3.74166i		−	0.570597i	−0.958439	−	0.285299i	$-0.907907\pi$
$43$		−	3.74166i		−	0.570597i	0.958439	−	0.285299i	$-0.0920928\pi$
$44$	−7.48331			−1.12815
$45$	3.74166			0.557773
$46$	6.74166	+	0.741657i	0.994003	+	0.109351i
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$	8.00000			1.15470
$49$	−7.00000			−1.00000
$50$	9.00000	+	9.00000i	1.27279	+	1.27279i
$51$			14.9666i			2.09575i
$52$	−8.00000			−1.10940
$53$	−3.74166			−0.513956			−0.256978	−	0.966417i	$-0.582727\pi$
$53$	−3.74166			−0.513956			−0.256978	+	0.966417i	$0.582727\pi$
$54$	4.00000	+	4.00000i	0.544331	+	0.544331i
$55$			14.0000i			1.88776i
$56$		0			0
$57$			7.48331i			0.991189i
$58$		0			0
$59$	−2.00000			−0.260378			−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000			−0.260378			−0.130189	+	0.991489i	$0.541558\pi$
$60$		−	14.9666i		−	1.93218i
$61$	11.2250			1.43721			0.718605	−	0.695418i	$-0.244781\pi$
$61$	11.2250			1.43721			0.718605	+	0.695418i	$0.244781\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$			14.9666i			1.85638i
$66$	7.48331	−	7.48331i	0.921132	−	0.921132i
$67$		−	11.2250i		−	1.37135i	−0.727908	−	0.685674i	$-0.759507\pi$
$67$		−	11.2250i		−	1.37135i	0.727908	−	0.685674i	$-0.240493\pi$
$68$	14.9666			1.81497
$69$	−7.48331	+	6.00000i	−0.900885	+	0.722315i
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	−2.00000	+	2.00000i	−0.235702	+	0.235702i
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$	−3.74166	−	3.74166i	−0.434959	−	0.434959i
$75$	−18.0000			−2.07846
$76$	7.48331			0.858395
$77$		0			0
$78$	8.00000	−	8.00000i	0.905822	−	0.905822i
$79$	−7.48331			−0.841939			−0.420969	−	0.907075i	$-0.638310\pi$
$79$	−7.48331			−0.841939			−0.420969	+	0.907075i	$0.638310\pi$
$80$	−14.9666			−1.67332
$81$	−11.0000			−1.22222
$82$	−4.00000	−	4.00000i	−0.441726	−	0.441726i
$83$			11.2250i			1.23210i	0.787707	+	0.616050i	$0.211268\pi$
$83$			11.2250i			1.23210i	−0.787707	+	0.616050i	$0.788732\pi$
$84$		0			0
$85$		−	28.0000i		−	3.03703i
$86$	3.74166	−	3.74166i	0.403473	−	0.403473i
$87$		0			0
$88$	−7.48331	−	7.48331i	−0.797724	−	0.797724i
$89$			7.48331i			0.793230i	0.917985	+	0.396615i	$0.129815\pi$
$89$			7.48331i			0.793230i	−0.917985	+	0.396615i	$0.870185\pi$
$90$	3.74166	+	3.74166i	0.394405	+	0.394405i
$91$		0			0
$92$	6.00000	+	7.48331i	0.625543	+	0.780189i
$93$			4.00000i			0.414781i
$94$	4.00000	−	4.00000i	0.412568	−	0.412568i
$95$		−	14.0000i		−	1.43637i
$96$	8.00000	+	8.00000i	0.816497	+	0.816497i
$97$		−	7.48331i		−	0.759815i	−0.925024	−	0.379908i	$-0.875956\pi$
$97$		−	7.48331i		−	0.759815i	0.925024	−	0.379908i	$-0.124044\pi$
$98$	−7.00000	−	7.00000i	−0.707107	−	0.707107i
$99$			3.74166i			0.376051i
$100$			18.0000i			1.80000i
$101$			16.0000i			1.59206i	0.605257	+	0.796030i	$0.293070\pi$
$101$			16.0000i			1.59206i	−0.605257	+	0.796030i	$0.706930\pi$
$102$	−14.9666	+	14.9666i	−1.48192	+	1.48192i
$103$	7.48331			0.737353			0.368676	−	0.929558i	$-0.379811\pi$
$103$	7.48331			0.737353			0.368676	+	0.929558i	$0.379811\pi$
$104$	−8.00000	−	8.00000i	−0.784465	−	0.784465i
$105$		0			0
$106$	−3.74166	−	3.74166i	−0.363422	−	0.363422i
$107$			3.74166i			0.361720i	0.983509	+	0.180860i	$0.0578880\pi$
$107$			3.74166i			0.361720i	−0.983509	+	0.180860i	$0.942112\pi$
$108$			8.00000i			0.769800i
$109$	−3.74166			−0.358386			−0.179193	−	0.983814i	$-0.557349\pi$
$109$	−3.74166			−0.358386			−0.179193	+	0.983814i	$0.557349\pi$
$110$	−14.0000	+	14.0000i	−1.33485	+	1.33485i
$111$	7.48331			0.710285
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	−7.48331	+	7.48331i	−0.700877	+	0.700877i
$115$	14.0000	−	11.2250i	1.30551	−	1.04673i
$116$		0			0
$117$			4.00000i			0.369800i
$118$	−2.00000	−	2.00000i	−0.184115	−	0.184115i
$119$		0			0
$120$	14.9666	−	14.9666i	1.36626	−	1.36626i
$121$	−3.00000			−0.272727
$122$	11.2250	+	11.2250i	1.01626	+	1.01626i
$123$	8.00000			0.721336
$124$	4.00000			0.359211
$125$	14.9666			1.33866
$126$		0			0
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$			7.48331i			0.658869i
$130$	−14.9666	+	14.9666i	−1.31266	+	1.31266i
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$	14.9666			1.30268
$133$		0			0
$134$	11.2250	−	11.2250i	0.969690	−	0.969690i
$135$	14.9666			1.28812
$136$	14.9666	+	14.9666i	1.28338	+	1.28338i
$137$		−	14.9666i		−	1.27869i	−0.768922	−	0.639343i	$-0.779207\pi$
$137$		−	14.9666i		−	1.27869i	0.768922	−	0.639343i	$-0.220793\pi$
$138$	−13.4833	−	1.48331i	−1.14778	−	0.126268i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$			8.00000i			0.673722i
$142$	−12.0000	+	12.0000i	−1.00702	+	1.00702i
$143$	−14.9666			−1.25157
$144$	−4.00000			−0.333333
$145$		0			0
$146$	8.00000	+	8.00000i	0.662085	+	0.662085i
$147$	14.0000			1.15470
$148$		−	7.48331i		−	0.615125i
$149$	−11.2250			−0.919586			−0.459793	−	0.888026i	$-0.652076\pi$
$149$	−11.2250			−0.919586			−0.459793	+	0.888026i	$0.652076\pi$
$150$	−18.0000	−	18.0000i	−1.46969	−	1.46969i
$151$		−	6.00000i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$151$		−	6.00000i		−	0.488273i	0.969741	−	0.244137i	$-0.0785045\pi$
$152$	7.48331	+	7.48331i	0.606977	+	0.606977i
$153$		−	7.48331i		−	0.604990i
$154$		0			0
$155$		−	7.48331i		−	0.601074i
$156$	16.0000			1.28103
$157$	−11.2250			−0.895850			−0.447925	−	0.894071i	$-0.647837\pi$
$157$	−11.2250			−0.895850			−0.447925	+	0.894071i	$0.647837\pi$
$158$	−7.48331	−	7.48331i	−0.595341	−	0.595341i
$159$	7.48331			0.593465
$160$	−14.9666	−	14.9666i	−1.18322	−	1.18322i
$161$		0			0
$162$	−11.0000	−	11.0000i	−0.864242	−	0.864242i
$163$	−6.00000			−0.469956			−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000			−0.469956			−0.234978	+	0.972001i	$0.575502\pi$
$164$		−	8.00000i		−	0.624695i
$165$		−	28.0000i		−	2.17980i
$166$	−11.2250	+	11.2250i	−0.871227	+	0.871227i
$167$			20.0000i			1.54765i	0.633402	+	0.773823i	$0.281658\pi$
$167$			20.0000i			1.54765i	−0.633402	+	0.773823i	$0.718342\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	28.0000	−	28.0000i	2.14750	−	2.14750i
$171$		−	3.74166i		−	0.286132i
$172$	7.48331			0.570597
$173$			12.0000i			0.912343i	0.889892	+	0.456172i	$0.150780\pi$
$173$			12.0000i			0.912343i	−0.889892	+	0.456172i	$0.849220\pi$
$174$		0			0
$175$		0			0
$176$		−	14.9666i		−	1.12815i
$177$	4.00000			0.300658
$178$	−7.48331	+	7.48331i	−0.560898	+	0.560898i
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$			7.48331i			0.557773i
$181$	−26.1916			−1.94681			−0.973403	−	0.229099i	$-0.926422\pi$
$181$	−26.1916			−1.94681			−0.973403	+	0.229099i	$0.926422\pi$
$182$		0			0
$183$	−22.4499			−1.65955
$184$	−1.48331	+	13.4833i	−0.109351	+	0.994003i
$185$	−14.0000			−1.02930
$186$	−4.00000	+	4.00000i	−0.293294	+	0.293294i
$187$	28.0000			2.04756
$188$	8.00000			0.583460
$189$		0			0
$190$	14.0000	−	14.0000i	1.01567	−	1.01567i
$191$	7.48331			0.541474			0.270737	−	0.962653i	$-0.412733\pi$
$191$	7.48331			0.541474			0.270737	+	0.962653i	$0.412733\pi$
$192$			16.0000i			1.15470i
$193$	10.0000			0.719816			0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000			0.719816			0.359908	+	0.932988i	$0.382808\pi$
$194$	7.48331	−	7.48331i	0.537271	−	0.537271i
$195$		−	29.9333i		−	2.14357i
$196$		−	14.0000i		−	1.00000i
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	−3.74166	+	3.74166i	−0.265908	+	0.265908i
$199$	14.9666			1.06096			0.530478	−	0.847699i	$-0.322012\pi$
$199$	14.9666			1.06096			0.530478	+	0.847699i	$0.322012\pi$
$200$	−18.0000	+	18.0000i	−1.27279	+	1.27279i
$201$			22.4499i			1.58350i
$202$	−16.0000	+	16.0000i	−1.12576	+	1.12576i
$203$		0			0
$204$	−29.9333			−2.09575
$205$	−14.9666			−1.04531
$206$	7.48331	+	7.48331i	0.521387	+	0.521387i
$207$	3.74166	−	3.00000i	0.260063	−	0.208514i
$208$		−	16.0000i		−	1.10940i
$209$	14.0000			0.968400
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$		−	7.48331i		−	0.513956i
$213$		−	24.0000i		−	1.64445i
$214$	−3.74166	+	3.74166i	−0.255774	+	0.255774i
$215$		−	14.0000i		−	0.954792i
$216$	−8.00000	+	8.00000i	−0.544331	+	0.544331i
$217$		0			0
$218$	−3.74166	−	3.74166i	−0.253417	−	0.253417i
$219$	−16.0000			−1.08118
$220$	−28.0000			−1.88776
$221$	29.9333			2.01353
$222$	7.48331	+	7.48331i	0.502247	+	0.502247i
$223$		−	10.0000i		−	0.669650i	−0.942280	−	0.334825i	$-0.891323\pi$
$223$		−	10.0000i		−	0.669650i	0.942280	−	0.334825i	$-0.108677\pi$
$224$		0			0
$225$	9.00000			0.600000
$226$		0			0
$227$		−	18.7083i		−	1.24171i	−0.783924	−	0.620856i	$-0.786785\pi$
$227$		−	18.7083i		−	1.24171i	0.783924	−	0.620856i	$-0.213215\pi$
$228$	−14.9666			−0.991189
$229$	11.2250			0.741767			0.370884	−	0.928679i	$-0.379055\pi$
$229$	11.2250			0.741767			0.370884	+	0.928679i	$0.379055\pi$
$230$	25.2250	+	2.77503i	1.66329	+	0.182980i
$231$		0			0
$232$		0			0
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$	−4.00000	+	4.00000i	−0.261488	+	0.261488i
$235$		−	14.9666i		−	0.976315i
$236$		−	4.00000i		−	0.260378i
$237$	14.9666			0.972187
$238$		0			0
$239$			18.0000i			1.16432i	0.813073	+	0.582162i	$0.197793\pi$
$239$			18.0000i			1.16432i	−0.813073	+	0.582162i	$0.802207\pi$
$240$	29.9333			1.93218
$241$			22.4499i			1.44613i	0.690781	+	0.723064i	$0.257267\pi$
$241$			22.4499i			1.44613i	−0.690781	+	0.723064i	$0.742733\pi$
$242$	−3.00000	−	3.00000i	−0.192847	−	0.192847i
$243$	10.0000			0.641500
$244$			22.4499i			1.43721i
$245$	−26.1916			−1.67332
$246$	8.00000	+	8.00000i	0.510061	+	0.510061i
$247$	14.9666			0.952304
$248$	4.00000	+	4.00000i	0.254000	+	0.254000i
$249$		−	22.4499i		−	1.42271i
$250$	14.9666	+	14.9666i	0.946573	+	0.946573i
$251$			18.7083i			1.18086i	0.807090	+	0.590428i	$0.201041\pi$
$251$			18.7083i			1.18086i	−0.807090	+	0.590428i	$0.798959\pi$
$252$		0			0
$253$	11.2250	+	14.0000i	0.705708	+	0.880172i
$254$	−4.00000	+	4.00000i	−0.250982	+	0.250982i
$255$			56.0000i			3.50686i
$256$	16.0000			1.00000
$257$	12.0000			0.748539			0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000			0.748539			0.374270	+	0.927320i	$0.377893\pi$
$258$	−7.48331	+	7.48331i	−0.465891	+	0.465891i
$259$		0			0
$260$	−29.9333			−1.85638
$261$		0			0
$262$	−18.0000	−	18.0000i	−1.11204	−	1.11204i
$263$	−7.48331			−0.461441			−0.230720	−	0.973020i	$-0.574108\pi$
$263$	−7.48331			−0.461441			−0.230720	+	0.973020i	$0.574108\pi$
$264$	14.9666	+	14.9666i	0.921132	+	0.921132i
$265$	−14.0000			−0.860013
$266$		0			0
$267$		−	14.9666i		−	0.915943i
$268$	22.4499			1.37135
$269$		−	16.0000i		−	0.975537i	−0.872973	−	0.487769i	$-0.837811\pi$
$269$		−	16.0000i		−	0.975537i	0.872973	−	0.487769i	$-0.162189\pi$
$270$	14.9666	+	14.9666i	0.910840	+	0.910840i
$271$		−	4.00000i		−	0.242983i	−0.992592	−	0.121491i	$-0.961232\pi$
$271$		−	4.00000i		−	0.242983i	0.992592	−	0.121491i	$-0.0387677\pi$
$272$			29.9333i			1.81497i
$273$		0			0
$274$	14.9666	−	14.9666i	0.904167	−	0.904167i
$275$			33.6749i			2.03067i
$276$	−12.0000	−	14.9666i	−0.722315	−	0.900885i
$277$			8.00000i			0.480673i	0.970690	+	0.240337i	$0.0772579\pi$
$277$			8.00000i			0.480673i	−0.970690	+	0.240337i	$0.922742\pi$
$278$	10.0000	+	10.0000i	0.599760	+	0.599760i
$279$		−	2.00000i		−	0.119737i
$280$		0			0
$281$		−	7.48331i		−	0.446417i	−0.974771	−	0.223209i	$-0.928347\pi$
$281$		−	7.48331i		−	0.446417i	0.974771	−	0.223209i	$-0.0716531\pi$
$282$	−8.00000	+	8.00000i	−0.476393	+	0.476393i
$283$			3.74166i			0.222418i	0.993797	+	0.111209i	$0.0354724\pi$
$283$			3.74166i			0.222418i	−0.993797	+	0.111209i	$0.964528\pi$
$284$	−24.0000			−1.42414
$285$			28.0000i			1.65858i
$286$	−14.9666	−	14.9666i	−0.884995	−	0.884995i
$287$		0			0
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	−39.0000			−2.29412
$290$		0			0
$291$			14.9666i			0.877359i
$292$			16.0000i			0.936329i
$293$	3.74166			0.218590			0.109295	−	0.994009i	$-0.465141\pi$
$293$	3.74166			0.218590			0.109295	+	0.994009i	$0.465141\pi$
$294$	14.0000	+	14.0000i	0.816497	+	0.816497i
$295$	−7.48331			−0.435695
$296$	7.48331	−	7.48331i	0.434959	−	0.434959i
$297$			14.9666i			0.868452i
$298$	−11.2250	−	11.2250i	−0.650245	−	0.650245i
$299$	12.0000	+	14.9666i	0.693978	+	0.865543i
$300$		−	36.0000i		−	2.07846i
$301$		0			0
$302$	6.00000	−	6.00000i	0.345261	−	0.345261i
$303$		−	32.0000i		−	1.83835i
$304$			14.9666i			0.858395i
$305$	42.0000			2.40491
$306$	7.48331	−	7.48331i	0.427793	−	0.427793i
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$		0			0
$309$	−14.9666			−0.851422
$310$	7.48331	−	7.48331i	0.425024	−	0.425024i
$311$		−	22.0000i		−	1.24751i	−0.781622	−	0.623753i	$-0.785607\pi$
$311$		−	22.0000i		−	1.24751i	0.781622	−	0.623753i	$-0.214393\pi$
$312$	16.0000	+	16.0000i	0.905822	+	0.905822i
$313$		−	29.9333i		−	1.69193i	−0.533240	−	0.845964i	$-0.679026\pi$
$313$		−	29.9333i		−	1.69193i	0.533240	−	0.845964i	$-0.320974\pi$
$314$	−11.2250	−	11.2250i	−0.633462	−	0.633462i
$315$		0			0
$316$		−	14.9666i		−	0.841939i
$317$			12.0000i			0.673987i	0.941507	+	0.336994i	$0.109410\pi$
$317$			12.0000i			0.673987i	−0.941507	+	0.336994i	$0.890590\pi$
$318$	7.48331	+	7.48331i	0.419643	+	0.419643i
$319$		0			0
$320$		−	29.9333i		−	1.67332i
$321$		−	7.48331i		−	0.417678i
$322$		0			0
$323$	−28.0000			−1.55796
$324$		−	22.0000i		−	1.22222i
$325$			36.0000i			1.99692i
$326$	−6.00000	−	6.00000i	−0.332309	−	0.332309i
$327$	7.48331			0.413828
$328$	8.00000	−	8.00000i	0.441726	−	0.441726i
$329$		0			0
$330$	28.0000	−	28.0000i	1.54135	−	1.54135i
$331$	−26.0000			−1.42909			−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000			−1.42909			−0.714545	+	0.699590i	$0.753366\pi$
$332$	−22.4499			−1.23210
$333$	−3.74166			−0.205042
$334$	−20.0000	+	20.0000i	−1.09435	+	1.09435i
$335$		−	42.0000i		−	2.29471i
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−3.00000	−	3.00000i	−0.163178	−	0.163178i
$339$		0			0
$340$	56.0000			3.03703
$341$	7.48331			0.405244
$342$	3.74166	−	3.74166i	0.202326	−	0.202326i
$343$		0			0
$344$	7.48331	+	7.48331i	0.403473	+	0.403473i
$345$	−28.0000	+	22.4499i	−1.50747	+	1.20866i
$346$	−12.0000	+	12.0000i	−0.645124	+	0.645124i
$347$	−22.0000			−1.18102			−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000			−1.18102			−0.590511	+	0.807030i	$0.701074\pi$
$348$		0			0
$349$		−	20.0000i		−	1.07058i	−0.844670	−	0.535288i	$-0.820203\pi$
$349$		−	20.0000i		−	1.07058i	0.844670	−	0.535288i	$-0.179797\pi$
$350$		0			0
$351$			16.0000i			0.854017i
$352$	14.9666	−	14.9666i	0.797724	−	0.797724i
$353$	−2.00000			−0.106449			−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000			−0.106449			−0.0532246	+	0.998583i	$0.516950\pi$
$354$	4.00000	+	4.00000i	0.212598	+	0.212598i
$355$			44.8999i			2.38304i
$356$	−14.9666			−0.793230
$357$		0			0
$358$	6.00000	+	6.00000i	0.317110	+	0.317110i
$359$	−29.9333			−1.57982			−0.789908	−	0.613225i	$-0.789872\pi$
$359$	−29.9333			−1.57982			−0.789908	+	0.613225i	$0.789872\pi$
$360$	−7.48331	+	7.48331i	−0.394405	+	0.394405i
$361$	5.00000			0.263158
$362$	−26.1916	−	26.1916i	−1.37660	−	1.37660i
$363$	6.00000			0.314918
$364$		0			0
$365$	29.9333			1.56678
$366$	−22.4499	−	22.4499i	−1.17348	−	1.17348i
$367$	22.4499			1.17188			0.585939	−	0.810355i	$-0.300726\pi$
$367$	22.4499			1.17188			0.585939	+	0.810355i	$0.300726\pi$
$368$	−14.9666	+	12.0000i	−0.780189	+	0.625543i
$369$	−4.00000			−0.208232
$370$	−14.0000	−	14.0000i	−0.727825	−	0.727825i
$371$		0			0
$372$	−8.00000			−0.414781
$373$	26.1916			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$373$	26.1916			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$374$	28.0000	+	28.0000i	1.44785	+	1.44785i
$375$	−29.9333			−1.54575
$376$	8.00000	+	8.00000i	0.412568	+	0.412568i
$377$		0			0
$378$		0			0
$379$			18.7083i			0.960980i	0.877000	+	0.480490i	$0.159541\pi$
$379$			18.7083i			0.960980i	−0.877000	+	0.480490i	$0.840459\pi$
$380$	28.0000			1.43637
$381$		−	8.00000i		−	0.409852i
$382$	7.48331	+	7.48331i	0.382880	+	0.382880i
$383$	−14.9666			−0.764759			−0.382380	−	0.924005i	$-0.624895\pi$
$383$	−14.9666			−0.764759			−0.382380	+	0.924005i	$0.624895\pi$
$384$	−16.0000	+	16.0000i	−0.816497	+	0.816497i
$385$		0			0
$386$	10.0000	+	10.0000i	0.508987	+	0.508987i
$387$		−	3.74166i		−	0.190199i
$388$	14.9666			0.759815
$389$	26.1916			1.32797			0.663983	−	0.747747i	$-0.268865\pi$
$389$	26.1916			1.32797			0.663983	+	0.747747i	$0.268865\pi$
$390$	29.9333	−	29.9333i	1.51573	−	1.51573i
$391$	−22.4499	−	28.0000i	−1.13534	−	1.41602i
$392$	14.0000	−	14.0000i	0.707107	−	0.707107i
$393$	36.0000			1.81596
$394$	12.0000	−	12.0000i	0.604551	−	0.604551i
$395$	−28.0000			−1.40883
$396$	−7.48331			−0.376051
$397$		−	12.0000i		−	0.602263i	−0.953583	−	0.301131i	$-0.902636\pi$
$397$		−	12.0000i		−	0.602263i	0.953583	−	0.301131i	$-0.0973643\pi$
$398$	14.9666	+	14.9666i	0.750209	+	0.750209i
$399$		0			0
$400$	−36.0000			−1.80000
$401$			7.48331i			0.373699i	0.982389	+	0.186849i	$0.0598277\pi$
$401$			7.48331i			0.373699i	−0.982389	+	0.186849i	$0.940172\pi$
$402$	−22.4499	+	22.4499i	−1.11970	+	1.11970i
$403$	8.00000			0.398508
$404$	−32.0000			−1.59206
$405$	−41.1582			−2.04517
$406$		0			0
$407$		−	14.0000i		−	0.693954i
$408$	−29.9333	−	29.9333i	−1.48192	−	1.48192i
$409$	30.0000			1.48340			0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000			1.48340			0.741702	+	0.670729i	$0.234019\pi$
$410$	−14.9666	−	14.9666i	−0.739149	−	0.739149i
$411$			29.9333i			1.47650i
$412$			14.9666i			0.737353i
$413$		0			0
$414$	6.74166	+	0.741657i	0.331334	+	0.0364505i
$415$			42.0000i			2.06170i
$416$	16.0000	−	16.0000i	0.784465	−	0.784465i
$417$	−20.0000			−0.979404
$418$	14.0000	+	14.0000i	0.684762	+	0.684762i
$419$		−	3.74166i		−	0.182792i	−0.995815	−	0.0913960i	$-0.970867\pi$
$419$		−	3.74166i		−	0.182792i	0.995815	−	0.0913960i	$-0.0291329\pi$
$420$		0			0
$421$	−11.2250			−0.547072			−0.273536	−	0.961862i	$-0.588193\pi$
$421$	−11.2250			−0.547072			−0.273536	+	0.961862i	$0.588193\pi$
$422$	−10.0000	−	10.0000i	−0.486792	−	0.486792i
$423$		−	4.00000i		−	0.194487i
$424$	7.48331	−	7.48331i	0.363422	−	0.363422i
$425$		−	67.3498i		−	3.26695i
$426$	24.0000	−	24.0000i	1.16280	−	1.16280i
$427$		0			0
$428$	−7.48331			−0.361720
$429$	29.9333			1.44519
$430$	14.0000	−	14.0000i	0.675140	−	0.675140i
$431$	−37.4166			−1.80229			−0.901146	−	0.433515i	$-0.857273\pi$
$431$	−37.4166			−1.80229			−0.901146	+	0.433515i	$0.857273\pi$
$432$	−16.0000			−0.769800
$433$		−	7.48331i		−	0.359625i	−0.983701	−	0.179813i	$-0.942451\pi$
$433$		−	7.48331i		−	0.359625i	0.983701	−	0.179813i	$-0.0575491\pi$
$434$		0			0
$435$		0			0
$436$		−	7.48331i		−	0.358386i
$437$	−11.2250	−	14.0000i	−0.536963	−	0.669711i
$438$	−16.0000	−	16.0000i	−0.764510	−	0.764510i
$439$			4.00000i			0.190910i	0.995434	+	0.0954548i	$0.0304305\pi$
$439$			4.00000i			0.190910i	−0.995434	+	0.0954548i	$0.969569\pi$
$440$	−28.0000	−	28.0000i	−1.33485	−	1.33485i
$441$	−7.00000			−0.333333
$442$	29.9333	+	29.9333i	1.42378	+	1.42378i
$443$	−6.00000			−0.285069			−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000			−0.285069			−0.142534	+	0.989790i	$0.545525\pi$
$444$			14.9666i			0.710285i
$445$			28.0000i			1.32733i
$446$	10.0000	−	10.0000i	0.473514	−	0.473514i
$447$	22.4499			1.06185
$448$		0			0
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$	9.00000	+	9.00000i	0.424264	+	0.424264i
$451$		−	14.9666i		−	0.704751i
$452$		0			0
$453$			12.0000i			0.563809i
$454$	18.7083	−	18.7083i	0.878023	−	0.878023i
$455$		0			0
$456$	−14.9666	−	14.9666i	−0.700877	−	0.700877i
$457$			14.9666i			0.700109i	0.936729	+	0.350055i	$0.113837\pi$
$457$			14.9666i			0.700109i	−0.936729	+	0.350055i	$0.886163\pi$
$458$	11.2250	+	11.2250i	0.524509	+	0.524509i
$459$		−	29.9333i		−	1.39716i
$460$	22.4499	+	28.0000i	1.04673	+	1.30551i
$461$			24.0000i			1.11779i	0.829238	+	0.558896i	$0.188775\pi$
$461$			24.0000i			1.11779i	−0.829238	+	0.558896i	$0.811225\pi$
$462$		0			0
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$		0			0
$465$			14.9666i			0.694061i
$466$	−14.0000	−	14.0000i	−0.648537	−	0.648537i
$467$		−	33.6749i		−	1.55829i	−0.626844	−	0.779145i	$-0.715654\pi$
$467$		−	33.6749i		−	1.55829i	0.626844	−	0.779145i	$-0.284346\pi$
$468$	−8.00000			−0.369800
$469$		0			0
$470$	14.9666	−	14.9666i	0.690359	−	0.690359i
$471$	22.4499			1.03444
$472$	4.00000	−	4.00000i	0.184115	−	0.184115i
$473$	14.0000			0.643721
$474$	14.9666	+	14.9666i	0.687440	+	0.687440i
$475$		−	33.6749i		−	1.54511i
$476$		0			0
$477$	−3.74166			−0.171319
$478$	−18.0000	+	18.0000i	−0.823301	+	0.823301i
$479$	29.9333			1.36769			0.683843	−	0.729629i	$-0.260307\pi$
$479$	29.9333			1.36769			0.683843	+	0.729629i	$0.260307\pi$
$480$	29.9333	+	29.9333i	1.36626	+	1.36626i
$481$		−	14.9666i		−	0.682420i
$482$	−22.4499	+	22.4499i	−1.02257	+	1.02257i
$483$		0			0
$484$		−	6.00000i		−	0.272727i
$485$		−	28.0000i		−	1.27141i
$486$	10.0000	+	10.0000i	0.453609	+	0.453609i
$487$			28.0000i			1.26880i	0.773004	+	0.634401i	$0.218753\pi$
$487$			28.0000i			1.26880i	−0.773004	+	0.634401i	$0.781247\pi$
$488$	−22.4499	+	22.4499i	−1.01626	+	1.01626i
$489$	12.0000			0.542659
$490$	−26.1916	−	26.1916i	−1.18322	−	1.18322i
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$			16.0000i			0.721336i
$493$		0			0
$494$	14.9666	+	14.9666i	0.673380	+	0.673380i
$495$			14.0000i			0.629253i
$496$			8.00000i			0.359211i
$497$		0			0
$498$	22.4499	−	22.4499i	1.00601	−	1.00601i
$499$	2.00000			0.0895323			0.0447661	−	0.998997i	$-0.485746\pi$
$499$	2.00000			0.0895323			0.0447661	+	0.998997i	$0.485746\pi$
$500$			29.9333i			1.33866i
$501$		−	40.0000i		−	1.78707i
$502$	−18.7083	+	18.7083i	−0.834992	+	0.834992i
$503$	−29.9333			−1.33466			−0.667329	−	0.744763i	$-0.732563\pi$
$503$	−29.9333			−1.33466			−0.667329	+	0.744763i	$0.732563\pi$
$504$		0			0
$505$			59.8665i			2.66403i
$506$	−2.77503	+	25.2250i	−0.123365	+	1.12139i
$507$	6.00000			0.266469
$508$	−8.00000			−0.354943
$509$			44.0000i			1.95027i	0.221621	+	0.975133i	$0.428865\pi$
$509$			44.0000i			1.95027i	−0.221621	+	0.975133i	$0.571135\pi$
$510$	−56.0000	+	56.0000i	−2.47972	+	2.47972i
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		−	14.9666i		−	0.660793i
$514$	12.0000	+	12.0000i	0.529297	+	0.529297i
$515$	28.0000			1.23383
$516$	−14.9666			−0.658869
$517$	14.9666			0.658232
$518$		0			0
$519$		−	24.0000i		−	1.05348i
$520$	−29.9333	−	29.9333i	−1.31266	−	1.31266i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$			33.6749i			1.47250i	0.676709	+	0.736251i	$0.263406\pi$
$523$			33.6749i			1.47250i	−0.676709	+	0.736251i	$0.736594\pi$
$524$		−	36.0000i		−	1.57267i
$525$		0			0
$526$	−7.48331	−	7.48331i	−0.326288	−	0.326288i
$527$	−14.9666			−0.651957
$528$			29.9333i			1.30268i
$529$	5.00000	−	22.4499i	0.217391	−	0.976085i
$530$	−14.0000	−	14.0000i	−0.608121	−	0.608121i
$531$	−2.00000			−0.0867926
$532$		0			0
$533$		−	16.0000i		−	0.693037i
$534$	14.9666	−	14.9666i	0.647669	−	0.647669i
$535$			14.0000i			0.605273i
$536$	22.4499	+	22.4499i	0.969690	+	0.969690i
$537$	−12.0000			−0.517838
$538$	16.0000	−	16.0000i	0.689809	−	0.689809i
$539$		−	26.1916i		−	1.12815i
$540$			29.9333i			1.28812i
$541$		−	16.0000i		−	0.687894i	−0.938989	−	0.343947i	$-0.888236\pi$
$541$		−	16.0000i		−	0.687894i	0.938989	−	0.343947i	$-0.111764\pi$
$542$	4.00000	−	4.00000i	0.171815	−	0.171815i
$543$	52.3832			2.24798
$544$	−29.9333	+	29.9333i	−1.28338	+	1.28338i
$545$	−14.0000			−0.599694
$546$		0			0
$547$	−18.0000			−0.769624			−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000			−0.769624			−0.384812	+	0.922995i	$0.625734\pi$
$548$	29.9333			1.27869
$549$	11.2250			0.479070
$550$	−33.6749	+	33.6749i	−1.43590	+	1.43590i
$551$		0			0
$552$	2.96663	−	26.9666i	0.126268	−	1.14778i
$553$		0			0
$554$	−8.00000	+	8.00000i	−0.339887	+	0.339887i
$555$	28.0000			1.18853
$556$			20.0000i			0.848189i
$557$	−33.6749			−1.42685			−0.713426	−	0.700731i	$-0.752858\pi$
$557$	−33.6749			−1.42685			−0.713426	+	0.700731i	$0.752858\pi$
$558$	2.00000	−	2.00000i	0.0846668	−	0.0846668i
$559$	14.9666			0.633021
$560$		0			0
$561$	−56.0000			−2.36432
$562$	7.48331	−	7.48331i	0.315665	−	0.315665i
$563$			18.7083i			0.788460i	0.919012	+	0.394230i	$0.128989\pi$
$563$			18.7083i			0.788460i	−0.919012	+	0.394230i	$0.871011\pi$
$564$	−16.0000			−0.673722
$565$		0			0
$566$	−3.74166	+	3.74166i	−0.157274	+	0.157274i
$567$		0			0
$568$	−24.0000	−	24.0000i	−1.00702	−	1.00702i
$569$		−	14.9666i		−	0.627434i	−0.949517	−	0.313717i	$-0.898426\pi$
$569$		−	14.9666i		−	0.627434i	0.949517	−	0.313717i	$-0.101574\pi$
$570$	−28.0000	+	28.0000i	−1.17279	+	1.17279i
$571$			11.2250i			0.469750i	0.972026	+	0.234875i	$0.0754682\pi$
$571$			11.2250i			0.469750i	−0.972026	+	0.234875i	$0.924532\pi$
$572$		−	29.9333i		−	1.25157i
$573$	−14.9666			−0.625240
$574$		0			0
$575$	33.6749	−	27.0000i	1.40434	−	1.12598i
$576$		−	8.00000i		−	0.333333i
$577$	−20.0000			−0.832611			−0.416305	−	0.909225i	$-0.636675\pi$
$577$	−20.0000			−0.832611			−0.416305	+	0.909225i	$0.636675\pi$
$578$	−39.0000	−	39.0000i	−1.62219	−	1.62219i
$579$	−20.0000			−0.831172
$580$		0			0
$581$		0			0
$582$	−14.9666	+	14.9666i	−0.620387	+	0.620387i
$583$		−	14.0000i		−	0.579821i
$584$	−16.0000	+	16.0000i	−0.662085	+	0.662085i
$585$			14.9666i			0.618794i
$586$	3.74166	+	3.74166i	0.154566	+	0.154566i
$587$	46.0000			1.89862			0.949312	−	0.314337i	$-0.101782\pi$
$587$	46.0000			1.89862			0.949312	+	0.314337i	$0.101782\pi$
$588$			28.0000i			1.15470i
$589$	−7.48331			−0.308345
$590$	−7.48331	−	7.48331i	−0.308083	−	0.308083i
$591$			24.0000i			0.987228i
$592$	14.9666			0.615125
$593$	−12.0000			−0.492781			−0.246390	−	0.969171i	$-0.579245\pi$
$593$	−12.0000			−0.492781			−0.246390	+	0.969171i	$0.579245\pi$
$594$	−14.9666	+	14.9666i	−0.614088	+	0.614088i
$595$		0			0
$596$		−	22.4499i		−	0.919586i
$597$	−29.9333			−1.22509
$598$	−2.96663	+	26.9666i	−0.121315	+	1.10275i
$599$			22.0000i			0.898896i	0.893307	+	0.449448i	$0.148379\pi$
$599$			22.0000i			0.898896i	−0.893307	+	0.449448i	$0.851621\pi$
$600$	36.0000	−	36.0000i	1.46969	−	1.46969i
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$		−	11.2250i		−	0.457116i
$604$	12.0000			0.488273
$605$	−11.2250			−0.456360
$606$	32.0000	−	32.0000i	1.29991	−	1.29991i
$607$		−	38.0000i		−	1.54237i	−0.636610	−	0.771186i	$-0.719664\pi$
$607$		−	38.0000i		−	1.54237i	0.636610	−	0.771186i	$-0.280336\pi$
$608$	−14.9666	+	14.9666i	−0.606977	+	0.606977i
$609$		0			0
$610$	42.0000	+	42.0000i	1.70053	+	1.70053i
$611$	16.0000			0.647291
$612$	14.9666			0.604990
$613$	−11.2250			−0.453372			−0.226686	−	0.973968i	$-0.572789\pi$
$613$	−11.2250			−0.453372			−0.226686	+	0.973968i	$0.572789\pi$
$614$	6.00000	+	6.00000i	0.242140	+	0.242140i
$615$	29.9333			1.20703
$616$		0			0
$617$			22.4499i			0.903801i	0.892068	+	0.451900i	$0.149254\pi$
$617$			22.4499i			0.903801i	−0.892068	+	0.451900i	$0.850746\pi$
$618$	−14.9666	−	14.9666i	−0.602046	−	0.602046i
$619$		−	18.7083i		−	0.751950i	−0.926630	−	0.375975i	$-0.877308\pi$
$619$		−	18.7083i		−	0.751950i	0.926630	−	0.375975i	$-0.122692\pi$
$620$	14.9666			0.601074
$621$	14.9666	−	12.0000i	0.600590	−	0.481543i
$622$	22.0000	−	22.0000i	0.882120	−	0.882120i
$623$		0			0
$624$			32.0000i			1.28103i
$625$	11.0000			0.440000
$626$	29.9333	−	29.9333i	1.19637	−	1.19637i
$627$	−28.0000			−1.11821
$628$		−	22.4499i		−	0.895850i
$629$			28.0000i			1.11643i
$630$		0			0
$631$	22.4499			0.893718			0.446859	−	0.894604i	$-0.352543\pi$
$631$	22.4499			0.893718			0.446859	+	0.894604i	$0.352543\pi$
$632$	14.9666	−	14.9666i	0.595341	−	0.595341i
$633$	20.0000			0.794929
$634$	−12.0000	+	12.0000i	−0.476581	+	0.476581i
$635$			14.9666i			0.593933i
$636$			14.9666i			0.593465i
$637$		−	28.0000i		−	1.10940i
$638$		0			0
$639$			12.0000i			0.474713i
$640$	29.9333	−	29.9333i	1.18322	−	1.18322i
$641$		−	22.4499i		−	0.886719i	−0.896344	−	0.443360i	$-0.853786\pi$
$641$		−	22.4499i		−	0.886719i	0.896344	−	0.443360i	$-0.146214\pi$
$642$	7.48331	−	7.48331i	0.295343	−	0.295343i
$643$		−	33.6749i		−	1.32801i	−0.747729	−	0.664005i	$-0.768856\pi$
$643$		−	33.6749i		−	1.32801i	0.747729	−	0.664005i	$-0.231144\pi$
$644$		0			0
$645$			28.0000i			1.10250i
$646$	−28.0000	−	28.0000i	−1.10165	−	1.10165i
$647$			30.0000i			1.17942i	0.807614	+	0.589711i	$0.200758\pi$
$647$			30.0000i			1.17942i	−0.807614	+	0.589711i	$0.799242\pi$
$648$	22.0000	−	22.0000i	0.864242	−	0.864242i
$649$		−	7.48331i		−	0.293746i
$650$	−36.0000	+	36.0000i	−1.41204	+	1.41204i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$			16.0000i			0.626128i	0.949732	+	0.313064i	$0.101356\pi$
$653$			16.0000i			0.626128i	−0.949732	+	0.313064i	$0.898644\pi$
$654$	7.48331	+	7.48331i	0.292621	+	0.292621i
$655$	−67.3498			−2.63158
$656$	16.0000			0.624695
$657$	8.00000			0.312110
$658$		0			0
$659$			3.74166i			0.145754i	0.997341	+	0.0728771i	$0.0232181\pi$
$659$			3.74166i			0.145754i	−0.997341	+	0.0728771i	$0.976782\pi$
$660$	56.0000			2.17980
$661$	18.7083			0.727668			0.363834	−	0.931464i	$-0.381468\pi$
$661$	18.7083			0.727668			0.363834	+	0.931464i	$0.381468\pi$
$662$	−26.0000	−	26.0000i	−1.01052	−	1.01052i
$663$	−59.8665			−2.32502
$664$	−22.4499	−	22.4499i	−0.871227	−	0.871227i
$665$		0			0
$666$	−3.74166	−	3.74166i	−0.144986	−	0.144986i
$667$		0			0
$668$	−40.0000			−1.54765
$669$			20.0000i			0.773245i
$670$	42.0000	−	42.0000i	1.62260	−	1.62260i
$671$			42.0000i			1.62139i
$672$		0			0
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$		0			0
$675$	36.0000			1.38564
$676$		−	6.00000i		−	0.230769i
$677$	−26.1916			−1.00663			−0.503313	−	0.864104i	$-0.667886\pi$
$677$	−26.1916			−1.00663			−0.503313	+	0.864104i	$0.667886\pi$
$678$		0			0
$679$		0			0
$680$	56.0000	+	56.0000i	2.14750	+	2.14750i
$681$			37.4166i			1.43381i
$682$	7.48331	+	7.48331i	0.286551	+	0.286551i
$683$	−14.0000			−0.535695			−0.267848	−	0.963461i	$-0.586312\pi$
$683$	−14.0000			−0.535695			−0.267848	+	0.963461i	$0.586312\pi$
$684$	7.48331			0.286132
$685$		−	56.0000i		−	2.13965i
$686$		0			0
$687$	−22.4499			−0.856519
$688$			14.9666i			0.570597i
$689$		−	14.9666i		−	0.570183i
$690$	−50.4499	−	5.55006i	−1.92060	−	0.211287i
$691$	−2.00000			−0.0760836			−0.0380418	−	0.999276i	$-0.512112\pi$
$691$	−2.00000			−0.0760836			−0.0380418	+	0.999276i	$0.512112\pi$
$692$	−24.0000			−0.912343
$693$		0			0
$694$	−22.0000	−	22.0000i	−0.835109	−	0.835109i
$695$	37.4166			1.41929
$696$		0			0
$697$			29.9333i			1.13380i
$698$	20.0000	−	20.0000i	0.757011	−	0.757011i
$699$	28.0000			1.05906
$700$		0			0
$701$	26.1916			0.989243			0.494622	−	0.869108i	$-0.335307\pi$
$701$	26.1916			0.989243			0.494622	+	0.869108i	$0.335307\pi$
$702$	−16.0000	+	16.0000i	−0.603881	+	0.603881i
$703$			14.0000i			0.528020i
$704$	29.9333			1.12815
$705$			29.9333i			1.12735i
$706$	−2.00000	−	2.00000i	−0.0752710	−	0.0752710i
$707$		0			0
$708$			8.00000i			0.300658i
$709$	18.7083			0.702604			0.351302	−	0.936262i	$-0.385739\pi$
$709$	18.7083			0.702604			0.351302	+	0.936262i	$0.385739\pi$
$710$	−44.8999	+	44.8999i	−1.68506	+	1.68506i
$711$	−7.48331			−0.280646
$712$	−14.9666	−	14.9666i	−0.560898	−	0.560898i
$713$	−6.00000	−	7.48331i	−0.224702	−	0.280252i
$714$		0			0
$715$	−56.0000			−2.09428
$716$			12.0000i			0.448461i
$717$		−	36.0000i		−	1.34444i
$718$	−29.9333	−	29.9333i	−1.11710	−	1.11710i
$719$		−	30.0000i		−	1.11881i	−0.828894	−	0.559406i	$-0.811029\pi$
$719$		−	30.0000i		−	1.11881i	0.828894	−	0.559406i	$-0.188971\pi$
$720$	−14.9666			−0.557773
$721$		0			0
$722$	5.00000	+	5.00000i	0.186081	+	0.186081i
$723$		−	44.8999i		−	1.66984i
$724$		−	52.3832i		−	1.94681i
$725$		0			0
$726$	6.00000	+	6.00000i	0.222681	+	0.222681i
$727$	14.9666			0.555082			0.277541	−	0.960714i	$-0.410481\pi$
$727$	14.9666			0.555082			0.277541	+	0.960714i	$0.410481\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	29.9333	+	29.9333i	1.10788	+	1.10788i
$731$	−28.0000			−1.03562
$732$		−	44.8999i		−	1.65955i
$733$	11.2250			0.414604			0.207302	−	0.978277i	$-0.433532\pi$
$733$	11.2250			0.414604			0.207302	+	0.978277i	$0.433532\pi$
$734$	22.4499	+	22.4499i	0.828643	+	0.828643i
$735$	52.3832			1.93218
$736$	−26.9666	−	2.96663i	−0.994003	−	0.109351i
$737$	42.0000			1.54709
$738$	−4.00000	−	4.00000i	−0.147242	−	0.147242i
$739$	14.0000			0.514998			0.257499	−	0.966279i	$-0.417102\pi$
$739$	14.0000			0.514998			0.257499	+	0.966279i	$0.417102\pi$
$740$		−	28.0000i		−	1.02930i
$741$	−29.9333			−1.09963
$742$		0			0
$743$	37.4166			1.37268			0.686340	−	0.727280i	$-0.259216\pi$
$743$	37.4166			1.37268			0.686340	+	0.727280i	$0.259216\pi$
$744$	−8.00000	−	8.00000i	−0.293294	−	0.293294i
$745$	−42.0000			−1.53876
$746$	26.1916	+	26.1916i	0.958943	+	0.958943i
$747$			11.2250i			0.410700i
$748$			56.0000i			2.04756i
$749$		0			0
$750$	−29.9333	−	29.9333i	−1.09301	−	1.09301i
$751$	−14.9666			−0.546140			−0.273070	−	0.961994i	$-0.588039\pi$
$751$	−14.9666			−0.546140			−0.273070	+	0.961994i	$0.588039\pi$
$752$			16.0000i			0.583460i
$753$		−	37.4166i		−	1.36354i
$754$		0			0
$755$		−	22.4499i		−	0.817037i
$756$		0			0
$757$	3.74166			0.135993			0.0679964	−	0.997686i	$-0.478339\pi$
$757$	3.74166			0.135993			0.0679964	+	0.997686i	$0.478339\pi$
$758$	−18.7083	+	18.7083i	−0.679516	+	0.679516i
$759$	−22.4499	−	28.0000i	−0.814881	−	1.01634i
$760$	28.0000	+	28.0000i	1.01567	+	1.01567i
$761$	18.0000			0.652499			0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000			0.652499			0.326250	+	0.945284i	$0.394215\pi$
$762$	8.00000	−	8.00000i	0.289809	−	0.289809i
$763$		0			0
$764$			14.9666i			0.541474i
$765$		−	28.0000i		−	1.01234i
$766$	−14.9666	−	14.9666i	−0.540766	−	0.540766i
$767$		−	8.00000i		−	0.288863i
$768$	−32.0000			−1.15470
$769$		−	7.48331i		−	0.269855i	−0.990855	−	0.134928i	$-0.956920\pi$
$769$		−	7.48331i		−	0.269855i	0.990855	−	0.134928i	$-0.0430802\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$			20.0000i			0.719816i
$773$	26.1916			0.942046			0.471023	−	0.882121i	$-0.343885\pi$
$773$	26.1916			0.942046			0.471023	+	0.882121i	$0.343885\pi$
$774$	3.74166	−	3.74166i	0.134491	−	0.134491i
$775$		−	18.0000i		−	0.646579i
$776$	14.9666	+	14.9666i	0.537271	+	0.537271i
$777$		0			0
$778$	26.1916	+	26.1916i	0.939014	+	0.939014i
$779$			14.9666i			0.536235i
$780$	59.8665			2.14357
$781$	−44.8999			−1.60664
$782$	5.55006	−	50.4499i	0.198470	−	1.80409i
$783$		0			0
$784$	28.0000			1.00000
$785$	−42.0000			−1.49904
$786$	36.0000	+	36.0000i	1.28408	+	1.28408i
$787$			3.74166i			0.133376i	0.997774	+	0.0666878i	$0.0212432\pi$
$787$			3.74166i			0.133376i	−0.997774	+	0.0666878i	$0.978757\pi$
$788$	24.0000			0.854965
$789$	14.9666			0.532826
$790$	−28.0000	−	28.0000i	−0.996195	−	0.996195i
$791$		0			0
$792$	−7.48331	−	7.48331i	−0.265908	−	0.265908i
$793$			44.8999i			1.59444i
$794$	12.0000	−	12.0000i	0.425864	−	0.425864i
$795$	28.0000			0.993058
$796$			29.9333i			1.06096i
$797$	−11.2250			−0.397609			−0.198804	−	0.980039i	$-0.563706\pi$
$797$	−11.2250			−0.397609			−0.198804	+	0.980039i	$0.563706\pi$
$798$		0			0
$799$	−29.9333			−1.05896
$800$	−36.0000	−	36.0000i	−1.27279	−	1.27279i
$801$			7.48331i			0.264410i
$802$	−7.48331	+	7.48331i	−0.264245	+	0.264245i
$803$			29.9333i			1.05632i
$804$	−44.8999			−1.58350
$805$		0			0
$806$	8.00000	+	8.00000i	0.281788	+	0.281788i
$807$			32.0000i			1.12645i
$808$	−32.0000	−	32.0000i	−1.12576	−	1.12576i
$809$	14.0000			0.492214			0.246107	−	0.969243i	$-0.420849\pi$
$809$	14.0000			0.492214			0.246107	+	0.969243i	$0.420849\pi$
$810$	−41.1582	−	41.1582i	−1.44615	−	1.44615i
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$		0			0
$813$			8.00000i			0.280572i
$814$	14.0000	−	14.0000i	0.490700	−	0.490700i
$815$	−22.4499			−0.786387
$816$		−	59.8665i		−	2.09575i
$817$	−14.0000			−0.489798
$818$	30.0000	+	30.0000i	1.04893	+	1.04893i
$819$		0			0
$820$		−	29.9333i		−	1.04531i
$821$			44.0000i			1.53561i	0.640683	+	0.767805i	$0.278651\pi$
$821$			44.0000i			1.53561i	−0.640683	+	0.767805i	$0.721349\pi$
$822$	−29.9333	+	29.9333i	−1.04404	+	1.04404i
$823$			18.0000i			0.627441i	0.949515	+	0.313720i	$0.101575\pi$
$823$			18.0000i			0.627441i	−0.949515	+	0.313720i	$0.898425\pi$
$824$	−14.9666	+	14.9666i	−0.521387	+	0.521387i
$825$		−	67.3498i		−	2.34482i
$826$		0			0
$827$		−	18.7083i		−	0.650551i	−0.945619	−	0.325275i	$-0.894543\pi$
$827$		−	18.7083i		−	0.650551i	0.945619	−	0.325275i	$-0.105457\pi$
$828$	6.00000	+	7.48331i	0.208514	+	0.260063i
$829$		−	8.00000i		−	0.277851i	−0.990303	−	0.138926i	$-0.955635\pi$
$829$		−	8.00000i		−	0.277851i	0.990303	−	0.138926i	$-0.0443649\pi$
$830$	−42.0000	+	42.0000i	−1.45784	+	1.45784i
$831$		−	16.0000i		−	0.555034i
$832$	32.0000			1.10940
$833$			52.3832i			1.81497i
$834$	−20.0000	−	20.0000i	−0.692543	−	0.692543i
$835$			74.8331i			2.58971i
$836$			28.0000i			0.968400i
$837$		−	8.00000i		−	0.276520i
$838$	3.74166	−	3.74166i	0.129253	−	0.129253i
$839$	−7.48331			−0.258353			−0.129176	−	0.991622i	$-0.541233\pi$
$839$	−7.48331			−0.258353			−0.129176	+	0.991622i	$0.541233\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−11.2250	−	11.2250i	−0.386838	−	0.386838i
$843$			14.9666i			0.515478i
$844$		−	20.0000i		−	0.688428i
$845$	−11.2250			−0.386151
$846$	4.00000	−	4.00000i	0.137523	−	0.137523i
$847$		0			0
$848$	14.9666			0.513956
$849$		−	7.48331i		−	0.256827i
$850$	67.3498	−	67.3498i	2.31008	−	2.31008i
$851$	−14.0000	+	11.2250i	−0.479914	+	0.384787i
$852$	48.0000			1.64445
$853$		−	20.0000i		−	0.684787i	−0.939557	−	0.342393i	$-0.888762\pi$
$853$		−	20.0000i		−	0.684787i	0.939557	−	0.342393i	$-0.111238\pi$
$854$		0			0
$855$		−	14.0000i		−	0.478790i
$856$	−7.48331	−	7.48331i	−0.255774	−	0.255774i
$857$	−30.0000			−1.02478			−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000			−1.02478			−0.512390	+	0.858753i	$0.671240\pi$
$858$	29.9333	+	29.9333i	1.02190	+	1.02190i
$859$	−18.0000			−0.614152			−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000			−0.614152			−0.307076	+	0.951685i	$0.599351\pi$
$860$	28.0000			0.954792
$861$		0			0
$862$	−37.4166	−	37.4166i	−1.27441	−	1.27441i
$863$			42.0000i			1.42970i	0.699280	+	0.714848i	$0.253504\pi$
$863$			42.0000i			1.42970i	−0.699280	+	0.714848i	$0.746496\pi$
$864$	−16.0000	−	16.0000i	−0.544331	−	0.544331i
$865$			44.8999i			1.52664i
$866$	7.48331	−	7.48331i	0.254293	−	0.254293i
$867$	78.0000			2.64902
$868$		0			0
$869$		−	28.0000i		−	0.949835i
$870$		0			0
$871$	44.8999			1.52137
$872$	7.48331	−	7.48331i	0.253417	−	0.253417i
$873$		−	7.48331i		−	0.253272i
$874$	2.77503	−	25.2250i	0.0938667	−	0.853247i
$875$		0			0
$876$		−	32.0000i		−	1.08118i
$877$			20.0000i			0.675352i	0.941262	+	0.337676i	$0.109641\pi$
$877$			20.0000i			0.675352i	−0.941262	+	0.337676i	$0.890359\pi$
$878$	−4.00000	+	4.00000i	−0.134993	+	0.134993i
$879$	−7.48331			−0.252406
$880$		−	56.0000i		−	1.88776i
$881$			29.9333i			1.00848i	0.863564	+	0.504239i	$0.168227\pi$
$881$			29.9333i			1.00848i	−0.863564	+	0.504239i	$0.831773\pi$
$882$	−7.00000	−	7.00000i	−0.235702	−	0.235702i
$883$	10.0000			0.336527			0.168263	−	0.985742i	$-0.446184\pi$
$883$	10.0000			0.336527			0.168263	+	0.985742i	$0.446184\pi$
$884$			59.8665i			2.01353i
$885$	14.9666			0.503098
$886$	−6.00000	−	6.00000i	−0.201574	−	0.201574i
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$	−14.9666	+	14.9666i	−0.502247	+	0.502247i
$889$		0			0
$890$	−28.0000	+	28.0000i	−0.938562	+	0.938562i
$891$		−	41.1582i		−	1.37885i
$892$	20.0000			0.669650
$893$	−14.9666			−0.500839
$894$	22.4499	+	22.4499i	0.750838	+	0.750838i
$895$	22.4499			0.750419
$896$		0			0
$897$	−24.0000	−	29.9333i	−0.801337	−	0.999442i
$898$	24.0000	+	24.0000i	0.800890	+	0.800890i
$899$		0			0
$900$			18.0000i			0.600000i
$901$			28.0000i			0.932815i
$902$	14.9666	−	14.9666i	0.498334	−	0.498334i
$903$		0			0
$904$		0			0
$905$	−98.0000			−3.25763
$906$	−12.0000	+	12.0000i	−0.398673	+	0.398673i
$907$		−	33.6749i		−	1.11816i	−0.829115	−	0.559079i	$-0.811155\pi$
$907$		−	33.6749i		−	1.11816i	0.829115	−	0.559079i	$-0.188845\pi$
$908$	37.4166			1.24171
$909$			16.0000i			0.530687i
$910$		0			0
$911$	−22.4499			−0.743800			−0.371900	−	0.928273i	$-0.621294\pi$
$911$	−22.4499			−0.743800			−0.371900	+	0.928273i	$0.621294\pi$
$912$		−	29.9333i		−	0.991189i
$913$	−42.0000			−1.39000
$914$	−14.9666	+	14.9666i	−0.495052	+	0.495052i
$915$	−84.0000			−2.77695
$916$			22.4499i			0.741767i
$917$		0			0
$918$	29.9333	−	29.9333i	0.987945	−	0.987945i
$919$	−44.8999			−1.48111			−0.740555	−	0.671995i	$-0.765437\pi$
$919$	−44.8999			−1.48111			−0.740555	+	0.671995i	$0.765437\pi$
$920$	−5.55006	+	50.4499i	−0.182980	+	1.66329i
$921$	−12.0000			−0.395413
$922$	−24.0000	+	24.0000i	−0.790398	+	0.790398i
$923$	−48.0000			−1.57994
$924$		0			0
$925$	−33.6749			−1.10722
$926$	4.00000	−	4.00000i	0.131448	−	0.131448i
$927$	7.48331			0.245784
$928$		0			0
$929$	32.0000			1.04989			0.524943	−	0.851137i	$-0.324087\pi$
$929$	32.0000			1.04989			0.524943	+	0.851137i	$0.324087\pi$
$930$	−14.9666	+	14.9666i	−0.490775	+	0.490775i
$931$			26.1916i			0.858395i
$932$		−	28.0000i		−	0.917170i
$933$			44.0000i			1.44050i
$934$	33.6749	−	33.6749i	1.10188	−	1.10188i
$935$	104.766			3.42623
$936$	−8.00000	−	8.00000i	−0.261488	−	0.261488i
$937$			22.4499i			0.733408i	0.930338	+	0.366704i	$0.119514\pi$
$937$			22.4499i			0.733408i	−0.930338	+	0.366704i	$0.880486\pi$
$938$		0			0
$939$			59.8665i			1.95367i
$940$	29.9333			0.976315
$941$	18.7083			0.609873			0.304936	−	0.952373i	$-0.401365\pi$
$941$	18.7083			0.609873			0.304936	+	0.952373i	$0.401365\pi$
$942$	22.4499	+	22.4499i	0.731459	+	0.731459i
$943$	−14.9666	+	12.0000i	−0.487381	+	0.390774i
$944$	8.00000			0.260378
$945$		0			0
$946$	14.0000	+	14.0000i	0.455179	+	0.455179i
$947$	26.0000			0.844886			0.422443	−	0.906389i	$-0.361173\pi$
$947$	26.0000			0.844886			0.422443	+	0.906389i	$0.361173\pi$
$948$			29.9333i			0.972187i
$949$			32.0000i			1.03876i
$950$	33.6749	−	33.6749i	1.09256	−	1.09256i
$951$		−	24.0000i		−	0.778253i
$952$		0			0
$953$			29.9333i			0.969633i	0.874616	+	0.484817i	$0.161114\pi$
$953$			29.9333i			0.969633i	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−3.74166	−	3.74166i	−0.121141	−	0.121141i
$955$	28.0000			0.906059
$956$	−36.0000			−1.16432
$957$		0			0
$958$	29.9333	+	29.9333i	0.967100	+	0.967100i
$959$		0			0
$960$			59.8665i			1.93218i
$961$	27.0000			0.870968
$962$	14.9666	−	14.9666i	0.482544	−	0.482544i
$963$			3.74166i			0.120573i
$964$	−44.8999			−1.44613
$965$	37.4166			1.20448
$966$		0			0
$967$			54.0000i			1.73652i	0.496107	+	0.868261i	$0.334762\pi$
$967$			54.0000i			1.73652i	−0.496107	+	0.868261i	$0.665238\pi$
$968$	6.00000	−	6.00000i	0.192847	−	0.192847i
$969$	56.0000			1.79898
$970$	28.0000	−	28.0000i	0.899026	−	0.899026i
$971$		−	3.74166i		−	0.120075i	−0.998196	−	0.0600377i	$-0.980878\pi$
$971$		−	3.74166i		−	0.120075i	0.998196	−	0.0600377i	$-0.0191221\pi$
$972$			20.0000i			0.641500i
$973$		0			0
$974$	−28.0000	+	28.0000i	−0.897178	+	0.897178i
$975$		−	72.0000i		−	2.30585i
$976$	−44.8999			−1.43721
$977$			22.4499i			0.718237i	0.933292	+	0.359119i	$0.116923\pi$
$977$			22.4499i			0.718237i	−0.933292	+	0.359119i	$0.883077\pi$
$978$	12.0000	+	12.0000i	0.383718	+	0.383718i
$979$	−28.0000			−0.894884
$980$		−	52.3832i		−	1.67332i
$981$	−3.74166			−0.119462
$982$	26.0000	+	26.0000i	0.829693	+	0.829693i
$983$	59.8665			1.90945			0.954723	−	0.297497i	$-0.0961519\pi$
$983$	59.8665			1.90945			0.954723	+	0.297497i	$0.0961519\pi$
$984$	−16.0000	+	16.0000i	−0.510061	+	0.510061i
$985$		−	44.8999i		−	1.43063i
$986$		0			0
$987$		0			0
$988$			29.9333i			0.952304i
$989$	−11.2250	−	14.0000i	−0.356933	−	0.445174i
$990$	−14.0000	+	14.0000i	−0.444949	+	0.444949i
$991$		−	10.0000i		−	0.317660i	−0.987306	−	0.158830i	$-0.949228\pi$
$991$		−	10.0000i		−	0.317660i	0.987306	−	0.158830i	$-0.0507723\pi$
$992$	−8.00000	+	8.00000i	−0.254000	+	0.254000i
$993$	52.0000			1.65017
$994$		0			0
$995$	56.0000			1.77532
$996$	44.8999			1.42271
$997$			8.00000i			0.253363i	0.991943	+	0.126681i	$0.0404325\pi$
$997$			8.00000i			0.253363i	−0.991943	+	0.126681i	$0.959567\pi$
$998$	2.00000	+	2.00000i	0.0633089	+	0.0633089i
$999$	−14.9666			−0.473523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.2.h.a.91.4	yes	4
4.3	odd	2		736.2.h.a.367.3		4
8.3	odd	2	inner	184.2.h.a.91.1	✓	4
8.5	even	2		736.2.h.a.367.1		4
23.22	odd	2	inner	184.2.h.a.91.3	yes	4
92.91	even	2		736.2.h.a.367.2		4
184.45	odd	2		736.2.h.a.367.4		4
184.91	even	2	inner	184.2.h.a.91.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.h.a.91.1	✓	4	8.3	odd	2	inner
184.2.h.a.91.2	yes	4	184.91	even	2	inner
184.2.h.a.91.3	yes	4	23.22	odd	2	inner
184.2.h.a.91.4	yes	4	1.1	even	1	trivial
736.2.h.a.367.1		4	8.5	even	2
736.2.h.a.367.2		4	92.91	even	2
736.2.h.a.367.3		4	4.3	odd	2
736.2.h.a.367.4		4	184.45	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -2.00000 q^{3} +2.00000i q^{4} +3.74166 q^{5} +(-2.00000 - 2.00000i) q^{6} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(3.74166 + 3.74166i) q^{10} +3.74166i q^{11} -4.00000i q^{12} +4.00000i q^{13} -7.48331 q^{15} -4.00000 q^{16} -7.48331i q^{17} +(1.00000 + 1.00000i) q^{18} -3.74166i q^{19} +7.48331i q^{20} +(-3.74166 + 3.74166i) q^{22} +(3.74166 - 3.00000i) q^{23} +(4.00000 - 4.00000i) q^{24} +9.00000 q^{25} +(-4.00000 + 4.00000i) q^{26} +4.00000 q^{27} +(-7.48331 - 7.48331i) q^{30} -2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} -7.48331i q^{33} +(7.48331 - 7.48331i) q^{34} +2.00000i q^{36} -3.74166 q^{37} +(3.74166 - 3.74166i) q^{38} -8.00000i q^{39} +(-7.48331 + 7.48331i) q^{40} -4.00000 q^{41} -3.74166i q^{43} -7.48331 q^{44} +3.74166 q^{45} +(6.74166 + 0.741657i) q^{46} -4.00000i q^{47} +8.00000 q^{48} -7.00000 q^{49} +(9.00000 + 9.00000i) q^{50} +14.9666i q^{51} -8.00000 q^{52} -3.74166 q^{53} +(4.00000 + 4.00000i) q^{54} +14.0000i q^{55} +7.48331i q^{57} -2.00000 q^{59} -14.9666i q^{60} +11.2250 q^{61} +(2.00000 - 2.00000i) q^{62} -8.00000i q^{64} +14.9666i q^{65} +(7.48331 - 7.48331i) q^{66} -11.2250i q^{67} +14.9666 q^{68} +(-7.48331 + 6.00000i) q^{69} +12.0000i q^{71} +(-2.00000 + 2.00000i) q^{72} +8.00000 q^{73} +(-3.74166 - 3.74166i) q^{74} -18.0000 q^{75} +7.48331 q^{76} +(8.00000 - 8.00000i) q^{78} -7.48331 q^{79} -14.9666 q^{80} -11.0000 q^{81} +(-4.00000 - 4.00000i) q^{82} +11.2250i q^{83} -28.0000i q^{85} +(3.74166 - 3.74166i) q^{86} +(-7.48331 - 7.48331i) q^{88} +7.48331i q^{89} +(3.74166 + 3.74166i) q^{90} +(6.00000 + 7.48331i) q^{92} +4.00000i q^{93} +(4.00000 - 4.00000i) q^{94} -14.0000i q^{95} +(8.00000 + 8.00000i) q^{96} -7.48331i q^{97} +(-7.00000 - 7.00000i) q^{98} +3.74166i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} + 4 q^{9} - 16 q^{16} + 4 q^{18} + 16 q^{24} + 36 q^{25} - 16 q^{26} + 16 q^{27} - 16 q^{32} - 16 q^{41} + 12 q^{46} + 32 q^{48} - 28 q^{49} + 36 q^{50} - 32 q^{52}+ \cdots - 28 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 + 4 * q^9 - 16 * q^16 + 4 * q^18 + 16 * q^24 + 36 * q^25 - 16 * q^26 + 16 * q^27 - 16 * q^32 - 16 * q^41 + 12 * q^46 + 32 * q^48 - 28 * q^49 + 36 * q^50 - 32 * q^52 + 16 * q^54 - 8 * q^59 + 8 * q^62 - 8 * q^72 + 32 * q^73 - 72 * q^75 + 32 * q^78 - 44 * q^81 - 16 * q^82 + 24 * q^92 + 16 * q^94 + 32 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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