LMFDB - Embedded newform 1148.2.i.a.821.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			821.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1148.821
Dual form			1148.2.i.a.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -4.00000 q^{13} -3.00000 q^{15} +(3.50000 - 6.06218i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{27} +6.00000 q^{29} +(5.00000 + 8.66025i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(1.50000 - 7.79423i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} -1.00000 q^{41} -4.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(5.50000 - 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{53} -9.00000 q^{55} -7.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.00000 - 5.19615i) q^{63} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +6.00000 q^{69} -9.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(-6.00000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(-3.00000 - 5.19615i) q^{87} +(6.00000 - 10.3923i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(5.00000 - 8.66025i) q^{93} +(-10.5000 - 18.1865i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 3 q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 + 3 * q^5 + 5 * q^7 + 2 * q^9	$ 2 q - q^{3} + 3 q^{5} + 5 q^{7} + 2 q^{9} - 3 q^{11} - 8 q^{13} - 6 q^{15} + 7 q^{19} - 4 q^{21} - 6 q^{23} - 4 q^{25} - 10 q^{27} + 12 q^{29} + 10 q^{31} - 3 q^{33} + 3 q^{35} - 2 q^{37} + 4 q^{39} - 2 q^{41} - 8 q^{43} - 6 q^{45} - 12 q^{47} + 11 q^{49} + 6 q^{53} - 18 q^{55} - 14 q^{57} - 6 q^{59} + 13 q^{61} + 2 q^{63} - 12 q^{65} + 4 q^{67} + 12 q^{69} - 18 q^{71} - 14 q^{73} - 4 q^{75} - 12 q^{77} + q^{79} - q^{81} + 24 q^{83} - 6 q^{87} + 12 q^{89} - 20 q^{91} + 10 q^{93} - 21 q^{95} + 4 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q - q^3 + 3 * q^5 + 5 * q^7 + 2 * q^9 - 3 * q^11 - 8 * q^13 - 6 * q^15 + 7 * q^19 - 4 * q^21 - 6 * q^23 - 4 * q^25 - 10 * q^27 + 12 * q^29 + 10 * q^31 - 3 * q^33 + 3 * q^35 - 2 * q^37 + 4 * q^39 - 2 * q^41 - 8 * q^43 - 6 * q^45 - 12 * q^47 + 11 * q^49 + 6 * q^53 - 18 * q^55 - 14 * q^57 - 6 * q^59 + 13 * q^61 + 2 * q^63 - 12 * q^65 + 4 * q^67 + 12 * q^69 - 18 * q^71 - 14 * q^73 - 4 * q^75 - 12 * q^77 + q^79 - q^81 + 24 * q^83 - 6 * q^87 + 12 * q^89 - 20 * q^91 + 10 * q^93 - 21 * q^95 + 4 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.830014	+	0.557743i	$0.188333\pi$
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.0680129	+	0.997684i	$0.478334\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$	1.50000	−	7.79423i	0.253546	−	1.31747i
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$		0			0
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$	−7.00000			−0.927173
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$	1.00000	−	5.19615i	0.125988	−	0.654654i
$64$		0			0
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$		0			0
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$		0			0
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$		0			0
$77$	−6.00000	−	5.19615i	−0.683763	−	0.592157i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$		0			0
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	−10.5000	−	18.1865i	−1.07728	−	1.86590i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$		0			0
$105$	−7.50000	+	2.59808i	−0.731925	+	0.253546i
$106$		0			0
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$		0			0
$109$	−4.00000	−	6.92820i	−0.383131	−	0.663602i	0.608377	−	0.793648i	$-0.291821\pi$
$109$	−4.00000	−	6.92820i	−0.383131	−	0.663602i	−0.991508	+	0.130046i	$0.958487\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	−3.00000			−0.282216			−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000			−0.282216			−0.141108	+	0.989994i	$0.545067\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$		0			0
$117$	−4.00000	+	6.92820i	−0.369800	+	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	14.0000			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$		0			0
$133$	3.50000	−	18.1865i	0.303488	−	1.57697i
$134$		0			0
$135$	−7.50000	+	12.9904i	−0.645497	+	1.11803i
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$		0			0
$143$	6.00000	+	10.3923i	0.501745	+	0.869048i
$144$		0			0
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$		0			0
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$		0			0
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	0.935857	−	0.352381i	$-0.114628\pi$
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	−0.773099	+	0.634285i	$0.781294\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	30.0000			2.40966
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$	−3.00000	+	15.5885i	−0.236433	+	1.22854i
$162$		0			0
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$		0			0
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$		0			0
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−7.00000	−	12.1244i	−0.535303	−	0.927173i
$172$		0			0
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127601\pi$
$174$		0			0
$175$	−8.00000	−	6.92820i	−0.604743	−	0.523723i
$176$		0			0
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$		0			0
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$		0			0
$183$	−13.0000			−0.960988
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−12.5000	+	4.33013i	−0.909241	+	0.314970i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$		0			0
$195$	12.0000			0.859338
$196$		0			0
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$		0			0
$203$	15.0000	−	5.19615i	1.05279	−	0.364698i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$		0			0
$209$	−21.0000			−1.45260
$210$		0			0
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$		0			0
$213$	4.50000	+	7.79423i	0.308335	+	0.534052i
$214$		0			0
$215$	−6.00000	+	10.3923i	−0.409197	+	0.708749i
$216$		0			0
$217$	20.0000	+	17.3205i	1.35769	+	1.17579i
$218$		0			0
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	−8.00000			−0.533333
$226$		0			0
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$		0			0
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$		0			0
$231$	−1.50000	+	7.79423i	−0.0986928	+	0.512823i
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	18.0000	+	31.1769i	1.17419	+	2.03376i
$236$		0			0
$237$	−1.00000			−0.0649570
$238$		0			0
$239$	−27.0000			−1.74648			−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000			−1.74648			−0.873242	+	0.487286i	$0.837987\pi$
$240$		0			0
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$		0			0
$245$	−3.00000	−	20.7846i	−0.191663	−	1.32788i
$246$		0			0
$247$	−14.0000	+	24.2487i	−0.890799	+	1.54291i
$248$		0			0
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−1.00000	+	5.19615i	−0.0621370	+	0.322873i
$260$		0			0
$261$	6.00000	−	10.3923i	0.371391	−	0.643268i
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	18.0000			1.10573
$266$		0			0
$267$	−12.0000			−0.734388
$268$		0			0
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$		0			0
$273$	8.00000	+	6.92820i	0.484182	+	0.419314i
$274$		0			0
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	0.992522	−	0.122068i	$-0.0389525\pi$
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	−0.601975	+	0.798515i	$0.705619\pi$
$278$		0			0
$279$	20.0000			1.19737
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	−0.936039	−	0.351895i	$-0.885537\pi$
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	0.163270	−	0.986581i	$-0.447796\pi$
$284$		0			0
$285$	−10.5000	+	18.1865i	−0.621966	+	1.07728i
$286$		0			0
$287$	−2.50000	+	0.866025i	−0.147570	+	0.0511199i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−1.00000	−	1.73205i	−0.0586210	−	0.101535i
$292$		0			0
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	−18.0000			−1.04800
$296$		0			0
$297$	7.50000	+	12.9904i	0.435194	+	0.753778i
$298$		0			0
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$	−10.0000	+	3.46410i	−0.576390	+	0.199667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−19.5000	−	33.7750i	−1.11657	−	1.93395i
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−10.0000	+	17.3205i	−0.565233	+	0.979013i	0.431795	+	0.901972i	$0.357881\pi$
$313$	−10.0000	+	17.3205i	−0.565233	+	0.979013i	−0.997028	+	0.0770410i	$0.975453\pi$
$314$		0			0
$315$	−12.0000	−	10.3923i	−0.676123	−	0.585540i
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$		0			0
$324$		0			0
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$		0			0
$327$	−4.00000	+	6.92820i	−0.221201	+	0.383131i
$328$		0			0
$329$	−6.00000	+	31.1769i	−0.330791	+	1.71884i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$		0			0
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$		0			0
$335$	12.0000			0.655630
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$		0			0
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$		0			0
$341$	15.0000	−	25.9808i	0.812296	−	1.40694i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	9.00000	−	15.5885i	0.484544	−	0.839254i
$346$		0			0
$347$	7.50000	+	12.9904i	0.402621	+	0.697360i	0.994041	−	0.109003i	$-0.0347659\pi$
$347$	7.50000	+	12.9904i	0.402621	+	0.697360i	−0.591420	+	0.806363i	$0.701433\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$		0			0
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		0			0
$355$	−13.5000	+	23.3827i	−0.716506	+	1.24102i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.204595	+	0.978847i	$0.565588\pi$
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.745409	+	0.666608i	$0.767746\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	−2.00000			−0.104973
$364$		0			0
$365$	−42.0000			−2.19838
$366$		0			0
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$		0			0
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$		0			0
$371$	12.0000	+	10.3923i	0.623009	+	0.539542i
$372$		0			0
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$		0			0
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	−7.00000	−	12.1244i	−0.358621	−	0.621150i
$382$		0			0
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	−0.282079	−	0.959391i	$-0.591024\pi$
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	0.971897	−	0.235408i	$-0.0756427\pi$
$384$		0			0
$385$	−22.5000	+	7.79423i	−1.14671	+	0.397231i
$386$		0			0
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$		0			0
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	18.0000			0.907980
$394$		0			0
$395$	−1.50000	−	2.59808i	−0.0754732	−	0.130723i
$396$		0			0
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$		0			0
$399$	−17.5000	+	6.06218i	−0.876096	+	0.303488i
$400$		0			0
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$		0			0
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$		0			0
$405$	−3.00000			−0.149071
$406$		0			0
$407$	6.00000			0.297409
$408$		0			0
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	0.939490	+	0.342578i	$0.111300\pi$
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	−0.173064	+	0.984911i	$0.555367\pi$
$410$		0			0
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$		0			0
$413$	−12.0000	−	10.3923i	−0.590481	−	0.511372i
$414$		0			0
$415$	18.0000	−	31.1769i	0.883585	−	1.53041i
$416$		0			0
$417$	−7.00000	−	12.1244i	−0.342791	−	0.593732i
$418$		0			0
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$	12.0000	+	20.7846i	0.583460	+	1.01058i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.50000	−	33.7750i	0.314557	−	1.63449i
$428$		0			0
$429$	6.00000	−	10.3923i	0.289683	−	0.501745i
$430$		0			0
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$		0			0
$433$	23.0000			1.10531			0.552655	−	0.833410i	$-0.313615\pi$
$433$	23.0000			1.10531			0.552655	+	0.833410i	$0.313615\pi$
$434$		0			0
$435$	−18.0000			−0.863034
$436$		0			0
$437$	21.0000	+	36.3731i	1.00457	+	1.73996i
$438$		0			0
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	−0.853847	−	0.520524i	$-0.825737\pi$
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	0.877711	+	0.479191i	$0.159070\pi$
$440$		0			0
$441$	−2.00000	−	13.8564i	−0.0952381	−	0.659829i
$442$		0			0
$443$	−9.00000	+	15.5885i	−0.427603	+	0.740630i	−0.996660	−	0.0816684i	$-0.973975\pi$
$443$	−9.00000	+	15.5885i	−0.427603	+	0.740630i	0.569057	+	0.822298i	$0.307309\pi$
$444$		0			0
$445$	−18.0000	−	31.1769i	−0.853282	−	1.47793i
$446$		0			0
$447$	18.0000			0.851371
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	1.50000	+	2.59808i	0.0706322	+	0.122339i
$452$		0			0
$453$	2.00000	−	3.46410i	0.0939682	−	0.162758i
$454$		0			0
$455$	−6.00000	+	31.1769i	−0.281284	+	1.46160i
$456$		0			0
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	−0.615986	−	0.787757i	$-0.711242\pi$
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	0.990211	+	0.139581i	$0.0445757\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	27.0000			1.25752			0.628758	−	0.777601i	$-0.283564\pi$
$461$	27.0000			1.25752			0.628758	+	0.777601i	$0.283564\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$		0			0
$465$	−15.0000	−	25.9808i	−0.695608	−	1.20483i
$466$		0			0
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	0.276360	+	0.961054i	$0.410872\pi$
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	−0.970477	+	0.241192i	$0.922462\pi$
$468$		0			0
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$		0			0
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$		0			0
$475$	−28.0000			−1.28473
$476$		0			0
$477$	12.0000			0.549442
$478$		0			0
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	0.519973	−	0.854183i	$-0.325942\pi$
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	−0.999730	+	0.0232187i	$0.992609\pi$
$480$		0			0
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$		0			0
$483$	15.0000	−	5.19615i	0.682524	−	0.236433i
$484$		0			0
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$		0			0
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	0.761052	−	0.648691i	$-0.224683\pi$
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	−0.942309	+	0.334744i	$0.891350\pi$
$488$		0			0
$489$	14.0000			0.633102
$490$		0			0
$491$	−42.0000			−1.89543			−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000			−1.89543			−0.947717	+	0.319113i	$0.896615\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−9.00000	+	15.5885i	−0.404520	+	0.700649i
$496$		0			0
$497$	−22.5000	+	7.79423i	−1.00926	+	0.349619i
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$		0			0
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$		0			0
$503$	9.00000			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$		0			0
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	−28.0000	−	24.2487i	−1.23865	−	1.07270i
$512$		0			0
$513$	−17.5000	+	30.3109i	−0.772644	+	1.33826i
$514$		0			0
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$		0			0
$517$	36.0000			1.58328
$518$		0			0
$519$	−21.0000			−0.921798
$520$		0			0
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$		0			0
$523$	−19.0000	+	32.9090i	−0.830812	+	1.43901i	0.0665832	+	0.997781i	$0.478790\pi$
$523$	−19.0000	+	32.9090i	−0.830812	+	1.43901i	−0.897395	+	0.441228i	$0.854543\pi$
$524$		0			0
$525$	−2.00000	+	10.3923i	−0.0872872	+	0.453557i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	4.00000			0.173259
$534$		0			0
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	−1.50000	+	2.59808i	−0.0647298	+	0.112115i
$538$		0			0
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		0			0
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	−0.976352	−	0.216186i	$-0.930638\pi$
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	0.675399	+	0.737453i	$0.263972\pi$
$542$		0			0
$543$	2.00000	+	3.46410i	0.0858282	+	0.148659i
$544$		0			0
$545$	−24.0000			−1.02805
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$		0			0
$549$	−13.0000	−	22.5167i	−0.554826	−	0.960988i
$550$		0			0
$551$	21.0000	−	36.3731i	0.894630	−	1.54954i
$552$		0			0
$553$	0.500000	−	2.59808i	0.0212622	−	0.110481i
$554$		0			0
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$		0			0
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.50000	+	12.9904i	0.316087	+	0.547479i	0.979668	−	0.200625i	$-0.0642974\pi$
$563$	7.50000	+	12.9904i	0.316087	+	0.547479i	−0.663581	+	0.748105i	$0.730964\pi$
$564$		0			0
$565$	−4.50000	+	7.79423i	−0.189316	+	0.327906i
$566$		0			0
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	24.0000			1.00087
$576$		0			0
$577$	−10.0000	−	17.3205i	−0.416305	−	0.721062i	0.579259	−	0.815144i	$-0.303342\pi$
$577$	−10.0000	−	17.3205i	−0.416305	−	0.721062i	−0.995565	+	0.0940813i	$0.970009\pi$
$578$		0			0
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$		0			0
$581$	30.0000	−	10.3923i	1.24461	−	0.431145i
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$		0			0
$585$	12.0000	+	20.7846i	0.496139	+	0.859338i
$586$		0			0
$587$	−33.0000			−1.36206			−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000			−1.36206			−0.681028	+	0.732257i	$0.738467\pi$
$588$		0			0
$589$	70.0000			2.88430
$590$		0			0
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$		0			0
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$		0			0
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	−0.428497	−	0.903543i	$-0.640957\pi$
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	0.996740	−	0.0806818i	$-0.0257098\pi$
$608$		0			0
$609$	−12.0000	−	10.3923i	−0.486265	−	0.421117i
$610$		0			0
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$		0			0
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	0.928010	−	0.372554i	$-0.121518\pi$
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	−0.786647	+	0.617403i	$0.788185\pi$
$614$		0			0
$615$	3.00000			0.120972
$616$		0			0
$617$	−27.0000			−1.08698			−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000			−1.08698			−0.543490	+	0.839416i	$0.682897\pi$
$618$		0			0
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$		0			0
$621$	15.0000	−	25.9808i	0.601929	−	1.04257i
$622$		0			0
$623$	6.00000	−	31.1769i	0.240385	−	1.24908i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	10.5000	+	18.1865i	0.419330	+	0.726300i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$		0			0
$633$	−11.5000	−	19.9186i	−0.457084	−	0.791693i
$634$		0			0
$635$	21.0000	−	36.3731i	0.833360	−	1.44342i
$636$		0			0
$637$	−22.0000	+	17.3205i	−0.871672	+	0.686264i
$638$		0			0
$639$	−9.00000	+	15.5885i	−0.356034	+	0.616670i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$		0			0
$643$	5.00000			0.197181			0.0985904	−	0.995128i	$-0.468567\pi$
$643$	5.00000			0.197181			0.0985904	+	0.995128i	$0.468567\pi$
$644$		0			0
$645$	12.0000			0.472500
$646$		0			0
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$		0			0
$649$	−9.00000	+	15.5885i	−0.353281	+	0.611900i
$650$		0			0
$651$	5.00000	−	25.9808i	0.195965	−	1.01827i
$652$		0			0
$653$	−18.0000	+	31.1769i	−0.704394	+	1.22005i	0.262515	+	0.964928i	$0.415448\pi$
$653$	−18.0000	+	31.1769i	−0.704394	+	1.22005i	−0.966910	+	0.255119i	$0.917885\pi$
$654$		0			0
$655$	27.0000	+	46.7654i	1.05498	+	1.82727i
$656$		0			0
$657$	−28.0000			−1.09238
$658$		0			0
$659$	−48.0000			−1.86981			−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000			−1.86981			−0.934907	+	0.354892i	$0.884518\pi$
$660$		0			0
$661$	15.5000	+	26.8468i	0.602880	+	1.04422i	0.992383	+	0.123194i	$0.0393136\pi$
$661$	15.5000	+	26.8468i	0.602880	+	1.04422i	−0.389503	+	0.921025i	$0.627353\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−42.0000	−	36.3731i	−1.62869	−	1.41049i
$666$		0			0
$667$	−18.0000	+	31.1769i	−0.696963	+	1.20717i
$668$		0			0
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$		0			0
$671$	−39.0000			−1.50558
$672$		0			0
$673$	−22.0000			−0.848038			−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000			−0.848038			−0.424019	+	0.905653i	$0.639381\pi$
$674$		0			0
$675$	10.0000	+	17.3205i	0.384900	+	0.666667i
$676$		0			0
$677$	7.50000	−	12.9904i	0.288248	−	0.499261i	−0.685143	−	0.728408i	$-0.740260\pi$
$677$	7.50000	−	12.9904i	0.288248	−	0.499261i	0.973392	+	0.229147i	$0.0735938\pi$
$678$		0			0
$679$	5.00000	−	1.73205i	0.191882	−	0.0664700i
$680$		0			0
$681$	−10.5000	+	18.1865i	−0.402361	+	0.696909i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$	36.0000			1.37549
$686$		0			0
$687$	−4.00000			−0.152610
$688$		0			0
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$		0			0
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	−0.856358	−	0.516382i	$-0.827278\pi$
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	0.875379	+	0.483437i	$0.160612\pi$
$692$		0			0
$693$	−15.0000	+	5.19615i	−0.569803	+	0.197386i
$694$		0			0
$695$	21.0000	−	36.3731i	0.796575	−	1.37971i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	6.00000			0.226941
$700$		0			0
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	7.00000	+	12.1244i	0.264010	+	0.457279i
$704$		0			0
$705$	18.0000	−	31.1769i	0.677919	−	1.17419i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$		0			0
$713$	−60.0000			−2.24702
$714$		0			0
$715$	36.0000			1.34632
$716$		0			0
$717$	13.5000	+	23.3827i	0.504167	+	0.873242i
$718$		0			0
$719$	−1.50000	+	2.59808i	−0.0559406	+	0.0968919i	−0.892640	−	0.450771i	$-0.851149\pi$
$719$	−1.50000	+	2.59808i	−0.0559406	+	0.0968919i	0.836699	+	0.547663i	$0.184482\pi$
$720$		0			0
$721$	2.00000	−	10.3923i	0.0744839	−	0.387030i
$722$		0			0
$723$	11.0000	−	19.0526i	0.409094	−	0.708572i
$724$		0			0
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	−40.0000			−1.48352			−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000			−1.48352			−0.741759	+	0.670667i	$0.766008\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$	−16.5000	+	12.9904i	−0.608612	+	0.479157i
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$	28.0000			1.02861
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	27.0000	+	46.7654i	0.989203	+	1.71335i
$746$		0			0
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$		0			0
$749$	−3.00000	+	15.5885i	−0.109618	+	0.569590i
$750$		0			0
$751$	21.5000	−	37.2391i	0.784546	−	1.35887i	−0.144724	−	0.989472i	$-0.546229\pi$
$751$	21.5000	−	37.2391i	0.784546	−	1.35887i	0.929270	−	0.369402i	$-0.120437\pi$
$752$		0			0
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$		0			0
$755$	12.0000			0.436725
$756$		0			0
$757$	−40.0000			−1.45382			−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000			−1.45382			−0.726912	+	0.686730i	$0.759045\pi$
$758$		0			0
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$	−16.0000	−	13.8564i	−0.579239	−	0.501636i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$		0			0
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	−18.0000	−	31.1769i	−0.647415	−	1.12136i	−0.983738	−	0.179609i	$-0.942517\pi$
$773$	−18.0000	−	31.1769i	−0.647415	−	1.12136i	0.336323	−	0.941747i	$-0.390817\pi$
$774$		0			0
$775$	20.0000	−	34.6410i	0.718421	−	1.24434i
$776$		0			0
$777$	5.00000	−	1.73205i	0.179374	−	0.0621370i
$778$		0			0
$779$	−3.50000	+	6.06218i	−0.125401	+	0.217200i
$780$		0			0
$781$	13.5000	+	23.3827i	0.483068	+	0.836698i
$782$		0			0
$783$	−30.0000			−1.07211
$784$		0			0
$785$	−42.0000			−1.49904
$786$		0			0
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$		0			0
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	−7.50000	+	2.59808i	−0.266669	+	0.0923770i
$792$		0			0
$793$	−26.0000	+	45.0333i	−0.923287	+	1.59918i
$794$		0			0
$795$	−9.00000	−	15.5885i	−0.319197	−	0.552866i
$796$		0			0
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−12.0000	−	20.7846i	−0.423999	−	0.734388i
$802$		0			0
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$		0			0
$805$	36.0000	+	31.1769i	1.26883	+	1.09884i
$806$		0			0
$807$	7.50000	−	12.9904i	0.264013	−	0.457283i
$808$		0			0
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$		0			0
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$		0			0
$813$	8.00000			0.280572
$814$		0			0
$815$	21.0000	+	36.3731i	0.735598	+	1.27409i
$816$		0			0
$817$	−14.0000	+	24.2487i	−0.489798	+	0.848355i
$818$		0			0
$819$	−4.00000	+	20.7846i	−0.139771	+	0.726273i
$820$		0			0
$821$	4.50000	−	7.79423i	0.157051	−	0.272020i	−0.776753	−	0.629805i	$-0.783135\pi$
$821$	4.50000	−	7.79423i	0.157051	−	0.272020i	0.933804	+	0.357785i	$0.116468\pi$
$822$		0			0
$823$	−2.50000	−	4.33013i	−0.0871445	−	0.150939i	0.819159	−	0.573567i	$-0.194441\pi$
$823$	−2.50000	−	4.33013i	−0.0871445	−	0.150939i	−0.906303	+	0.422628i	$0.861108\pi$
$824$		0			0
$825$	12.0000			0.417786
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$		0			0
$831$	6.50000	−	11.2583i	0.225483	−	0.390547i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	18.0000	−	31.1769i	0.622916	−	1.07892i
$836$		0			0
$837$	−25.0000	−	43.3013i	−0.864126	−	1.49671i
$838$		0			0
$839$	−3.00000			−0.103572			−0.0517858	−	0.998658i	$-0.516491\pi$
$839$	−3.00000			−0.103572			−0.0517858	+	0.998658i	$0.516491\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$		0			0
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	1.00000	−	5.19615i	0.0343604	−	0.178542i
$848$		0			0
$849$	−13.0000	+	22.5167i	−0.446159	+	0.772770i
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$		0			0
$855$	−42.0000			−1.43637
$856$		0			0
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	0.890507	−	0.454969i	$-0.150350\pi$
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	−0.839268	+	0.543718i	$0.817016\pi$
$858$		0			0
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	−0.926161	−	0.377128i	$-0.876912\pi$
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	0.789683	+	0.613515i	$0.210245\pi$
$860$		0			0
$861$	2.00000	+	1.73205i	0.0681598	+	0.0590281i
$862$		0			0
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$		0			0
$865$	−31.5000	−	54.5596i	−1.07103	−	1.85508i
$866$		0			0
$867$	−17.0000			−0.577350
$868$		0			0
$869$	−3.00000			−0.101768
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$		0			0
$873$	2.00000	−	3.46410i	0.0676897	−	0.117242i
$874$		0			0
$875$	7.50000	−	2.59808i	0.253546	−	0.0878310i
$876$		0			0
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$		0			0
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	45.0000			1.51609			0.758044	−	0.652203i	$-0.226155\pi$
$881$	45.0000			1.51609			0.758044	+	0.652203i	$0.226155\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$		0			0
$885$	9.00000	+	15.5885i	0.302532	+	0.524000i
$886$		0			0
$887$	−1.50000	+	2.59808i	−0.0503651	+	0.0872349i	−0.890109	−	0.455748i	$-0.849372\pi$
$887$	−1.50000	+	2.59808i	−0.0503651	+	0.0872349i	0.839744	+	0.542983i	$0.182705\pi$
$888$		0			0
$889$	35.0000	−	12.1244i	1.17386	−	0.406638i
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$	42.0000	+	72.7461i	1.40548	+	2.43436i
$894$		0			0
$895$	−9.00000			−0.300837
$896$		0			0
$897$	−24.0000			−0.801337
$898$		0			0
$899$	30.0000	+	51.9615i	1.00056	+	1.73301i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	8.00000	+	6.92820i	0.266223	+	0.230556i
$904$		0			0
$905$	−6.00000	+	10.3923i	−0.199447	+	0.345452i
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$		0			0
$915$	−19.5000	+	33.7750i	−0.644650	+	1.11657i
$916$		0			0
$917$	−9.00000	+	46.7654i	−0.297206	+	1.54433i
$918$		0			0
$919$	−29.5000	+	51.0955i	−0.973115	+	1.68548i	−0.287096	+	0.957902i	$0.592690\pi$
$919$	−29.5000	+	51.0955i	−0.973115	+	1.68548i	−0.686020	+	0.727583i	$0.740644\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$		0			0
$923$	36.0000			1.18495
$924$		0			0
$925$	8.00000			0.263038
$926$		0			0
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		0			0
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$	−7.00000	−	48.4974i	−0.229416	−	1.58944i
$932$		0			0
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	20.0000			0.652675
$940$		0			0
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	0.955387	+	0.295355i	$0.0954381\pi$
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	−0.221908	+	0.975068i	$0.571229\pi$
$942$		0			0
$943$	3.00000	−	5.19615i	0.0976934	−	0.169210i
$944$		0			0
$945$	−7.50000	+	38.9711i	−0.243975	+	1.26773i
$946$		0			0
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721926\pi$
$948$		0			0
$949$	28.0000	+	48.4974i	0.908918	+	1.57429i
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−9.00000	+	15.5885i	−0.290929	+	0.503903i
$958$		0			0
$959$	24.0000	+	20.7846i	0.775000	+	0.671170i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$		0			0
$965$	−42.0000			−1.35203
$966$		0			0
$967$	23.0000			0.739630			0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000			0.739630			0.369815	+	0.929105i	$0.379421\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	35.0000	−	12.1244i	1.12205	−	0.388689i
$974$		0			0
$975$	8.00000	−	13.8564i	0.256205	−	0.443760i
$976$		0			0
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$	−16.0000			−0.510841
$982$		0			0
$983$	−6.00000	−	10.3923i	−0.191370	−	0.331463i	0.754334	−	0.656490i	$-0.227960\pi$
$983$	−6.00000	−	10.3923i	−0.191370	−	0.331463i	−0.945705	+	0.325027i	$0.894626\pi$
$984$		0			0
$985$	4.50000	−	7.79423i	0.143382	−	0.248345i
$986$		0			0
$987$	30.0000	−	10.3923i	0.954911	−	0.330791i
$988$		0			0
$989$	12.0000	−	20.7846i	0.381578	−	0.660912i
$990$		0			0
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	0.974070	+	0.226246i	$0.0726454\pi$
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	−0.291100	+	0.956693i	$0.594021\pi$
$992$		0			0
$993$	−28.0000			−0.888553
$994$		0			0
$995$	48.0000			1.52170
$996$		0			0
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$		0			0
$999$	5.00000	−	8.66025i	0.158193	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.a.821.1	yes	2
7.2	even	3		8036.2.a.d.1.1		1
7.4	even	3	inner	1148.2.i.a.165.1	✓	2
7.5	odd	6		8036.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.a.165.1	✓	2	7.4	even	3	inner
1148.2.i.a.821.1	yes	2	1.1	even	1	trivial
8036.2.a.c.1.1		1	7.5	odd	6
8036.2.a.d.1.1		1	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -4.00000 q^{13} -3.00000 q^{15} +(3.50000 - 6.06218i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{27} +6.00000 q^{29} +(5.00000 + 8.66025i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(1.50000 - 7.79423i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} -1.00000 q^{41} -4.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(5.50000 - 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{53} -9.00000 q^{55} -7.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.00000 - 5.19615i) q^{63} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +6.00000 q^{69} -9.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(-6.00000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(-3.00000 - 5.19615i) q^{87} +(6.00000 - 10.3923i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(5.00000 - 8.66025i) q^{93} +(-10.5000 - 18.1865i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 3 q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 + 3 * q^5 + 5 * q^7 + 2 * q^9	\( 2 q - q^{3} + 3 q^{5} + 5 q^{7} + 2 q^{9} - 3 q^{11} - 8 q^{13} - 6 q^{15} + 7 q^{19} - 4 q^{21} - 6 q^{23} - 4 q^{25} - 10 q^{27} + 12 q^{29} + 10 q^{31} - 3 q^{33} + 3 q^{35} - 2 q^{37} + 4 q^{39} - 2 q^{41} - 8 q^{43} - 6 q^{45} - 12 q^{47} + 11 q^{49} + 6 q^{53} - 18 q^{55} - 14 q^{57} - 6 q^{59} + 13 q^{61} + 2 q^{63} - 12 q^{65} + 4 q^{67} + 12 q^{69} - 18 q^{71} - 14 q^{73} - 4 q^{75} - 12 q^{77} + q^{79} - q^{81} + 24 q^{83} - 6 q^{87} + 12 q^{89} - 20 q^{91} + 10 q^{93} - 21 q^{95} + 4 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q - q^3 + 3 * q^5 + 5 * q^7 + 2 * q^9 - 3 * q^11 - 8 * q^13 - 6 * q^15 + 7 * q^19 - 4 * q^21 - 6 * q^23 - 4 * q^25 - 10 * q^27 + 12 * q^29 + 10 * q^31 - 3 * q^33 + 3 * q^35 - 2 * q^37 + 4 * q^39 - 2 * q^41 - 8 * q^43 - 6 * q^45 - 12 * q^47 + 11 * q^49 + 6 * q^53 - 18 * q^55 - 14 * q^57 - 6 * q^59 + 13 * q^61 + 2 * q^63 - 12 * q^65 + 4 * q^67 + 12 * q^69 - 18 * q^71 - 14 * q^73 - 4 * q^75 - 12 * q^77 + q^79 - q^81 + 24 * q^83 - 6 * q^87 + 12 * q^89 - 20 * q^91 + 10 * q^93 - 21 * q^95 + 4 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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