LMFDB - Embedded newform 1134.2.e.f.919.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(865,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.e (of order $3$, degree $2$, not 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:	$9.05503558921$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.f.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(2.00000 - 3.46410i) q^{13} +(0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +8.00000 q^{31} -1.00000 q^{32} +(-3.00000 - 5.19615i) q^{34} +(-7.50000 + 2.59808i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 2.59808i) q^{56} +(1.50000 + 2.59808i) q^{58} +3.00000 q^{59} -10.0000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} -10.0000 q^{67} +(3.00000 + 5.19615i) q^{68} +(7.50000 - 2.59808i) q^{70} -6.00000 q^{71} +(3.50000 + 6.06218i) q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +17.0000 q^{79} +(1.50000 + 2.59808i) q^{80} +(3.00000 - 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(-9.00000 + 15.5885i) q^{85} +(4.00000 + 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{89} +(8.00000 + 6.92820i) q^{91} +(3.00000 + 5.19615i) q^{92} +6.00000 q^{94} +12.0000 q^{95} +(5.00000 + 8.66025i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} - 2 q^{8} - 3 q^{10} + 4 q^{13} + q^{14} + 2 q^{16} + 6 q^{17} + 4 q^{19} + 3 q^{20} + 6 q^{23} - 4 q^{25} - 4 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} - 2 q^{32} - 6 q^{34} - 15 q^{35} - 8 q^{37} - 4 q^{38} - 3 q^{40} - 6 q^{41} - 8 q^{43} - 6 q^{46} - 12 q^{47} - 13 q^{49} + 4 q^{50} + 4 q^{52} + 9 q^{53} + q^{56} + 3 q^{58} + 6 q^{59} - 20 q^{61} - 16 q^{62} + 2 q^{64} + 24 q^{65} - 20 q^{67} + 6 q^{68} + 15 q^{70} - 12 q^{71} + 7 q^{73} + 8 q^{74} + 4 q^{76} + 34 q^{79} + 3 q^{80} + 6 q^{82} - 12 q^{83} - 18 q^{85} + 8 q^{86} + 6 q^{89} + 16 q^{91} + 6 q^{92} + 12 q^{94} + 24 q^{95} + 10 q^{97} + 13 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 - 2 * q^8 - 3 * q^10 + 4 * q^13 + q^14 + 2 * q^16 + 6 * q^17 + 4 * q^19 + 3 * q^20 + 6 * q^23 - 4 * q^25 - 4 * q^26 - q^28 - 3 * q^29 + 16 * q^31 - 2 * q^32 - 6 * q^34 - 15 * q^35 - 8 * q^37 - 4 * q^38 - 3 * q^40 - 6 * q^41 - 8 * q^43 - 6 * q^46 - 12 * q^47 - 13 * q^49 + 4 * q^50 + 4 * q^52 + 9 * q^53 + q^56 + 3 * q^58 + 6 * q^59 - 20 * q^61 - 16 * q^62 + 2 * q^64 + 24 * q^65 - 20 * q^67 + 6 * q^68 + 15 * q^70 - 12 * q^71 + 7 * q^73 + 8 * q^74 + 4 * q^76 + 34 * q^79 + 3 * q^80 + 6 * q^82 - 12 * q^83 - 18 * q^85 + 8 * q^86 + 6 * q^89 + 16 * q^91 + 6 * q^92 + 12 * q^94 + 24 * q^95 + 10 * q^97 + 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$		0			0
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	−7.50000	+	2.59808i	−1.26773	+	0.439155i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$		0			0
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		0			0
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	3.00000			0.390567			0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000			0.390567			0.195283	+	0.980747i	$0.437437\pi$
$60$		0			0
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	12.0000			1.48842
$66$		0			0
$67$	−10.0000			−1.22169			−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000			−1.22169			−0.610847	+	0.791748i	$0.709171\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$	7.50000	−	2.59808i	0.896421	−	0.310530i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$		0			0
$78$		0			0
$79$	17.0000			1.91265			0.956325	−	0.292306i	$-0.0944227\pi$
$79$	17.0000			1.91265			0.956325	+	0.292306i	$0.0944227\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$		0			0
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	8.00000	+	6.92820i	0.838628	+	0.726273i
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$		0			0
$94$	6.00000			0.618853
$95$	12.0000			1.23117
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	6.50000	+	2.59808i	0.656599	+	0.262445i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$		0			0
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	−9.00000	+	15.5885i	−0.839254	+	1.45363i
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	−15.0000	+	5.19615i	−1.37505	+	0.476331i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	10.0000			0.905357
$123$		0			0
$124$	8.00000			0.718421
$125$	3.00000			0.268328
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−12.0000			−1.05247
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$	8.00000	+	6.92820i	0.693688	+	0.600751i
$134$	10.0000			0.863868
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$	−7.50000	+	2.59808i	−0.633866	+	0.219578i
$141$		0			0
$142$	6.00000			0.503509
$143$		0			0
$144$		0			0
$145$	4.50000	−	7.79423i	0.373705	−	0.647275i
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$		0			0
$154$		0			0
$155$	12.0000	+	20.7846i	0.963863	+	1.66946i
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−17.0000			−1.35245
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$	−15.0000	+	5.19615i	−1.18217	+	0.409514i
$162$		0			0
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	9.00000	−	15.5885i	0.690268	−	1.19558i
$171$		0			0
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	9.00000			0.684257			0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000			0.684257			0.342129	+	0.939653i	$0.388852\pi$
$174$		0			0
$175$	−8.00000	−	6.92820i	−0.604743	−	0.523723i
$176$		0			0
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−8.00000	−	6.92820i	−0.592999	−	0.513553i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	−24.0000			−1.76452
$186$		0			0
$187$		0			0
$188$	−6.00000			−0.437595
$189$		0			0
$190$	−12.0000			−0.870572
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$		0			0
$193$	26.0000			1.87152			0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000			1.87152			0.935760	+	0.352636i	$0.114715\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$		0			0
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$		0			0
$202$	7.50000	−	12.9904i	0.527698	−	0.914000i
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		0			0
$205$	−18.0000			−1.25717
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$		0			0
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$	12.0000	−	20.7846i	0.818393	−	1.41750i
$216$		0			0
$217$	−4.00000	+	20.7846i	−0.271538	+	1.41095i
$218$	−2.00000	−	3.46410i	−0.135457	−	0.234619i
$219$		0			0
$220$		0			0
$221$	24.0000			1.61441
$222$		0			0
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	0.500000	−	2.59808i	0.0334077	−	0.173591i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$	9.00000	−	15.5885i	0.593442	−	1.02787i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$	−9.00000	−	15.5885i	−0.587095	−	1.01688i
$236$	3.00000			0.195283
$237$		0			0
$238$	15.0000	−	5.19615i	0.972306	−	0.336817i
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$		0			0
$244$	−10.0000			−0.640184
$245$	−3.00000	−	20.7846i	−0.191663	−	1.32788i
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	−8.00000			−0.508001
$249$		0			0
$250$	−3.00000			−0.189737
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$		0			0
$254$	−5.00000			−0.313728
$255$		0			0
$256$	1.00000			0.0625000
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$	12.0000			0.744208
$261$		0			0
$262$	6.00000	+	10.3923i	0.370681	+	0.642039i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	−13.5000	+	23.3827i	−0.829298	+	1.43639i
$266$	−8.00000	−	6.92820i	−0.490511	−	0.424795i
$267$		0			0
$268$	−10.0000			−0.610847
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	12.5000	−	21.6506i	0.759321	−	1.31518i	−0.183876	−	0.982949i	$-0.558865\pi$
$271$	12.5000	−	21.6506i	0.759321	−	1.31518i	0.943197	−	0.332233i	$-0.107802\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	14.0000	−	24.2487i	0.841178	−	1.45696i	−0.0477206	−	0.998861i	$-0.515196\pi$
$277$	14.0000	−	24.2487i	0.841178	−	1.45696i	0.888899	−	0.458103i	$-0.151471\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$		0			0
$280$	7.50000	−	2.59808i	0.448211	−	0.155265i
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$		0			0
$287$	−12.0000	−	10.3923i	−0.708338	−	0.613438i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$		0			0
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	−0.906509	−	0.422186i	$-0.861263\pi$
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	0.818878	+	0.573967i	$0.194596\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$	10.5000	+	18.1865i	0.608249	+	1.05352i
$299$	24.0000			1.38796
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$	4.00000	−	6.92820i	0.230174	−	0.398673i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−15.0000	−	25.9808i	−0.858898	−	1.48765i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$		0			0
$310$	−12.0000	−	20.7846i	−0.681554	−	1.18049i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	5.00000			0.282617			0.141308	−	0.989966i	$-0.454869\pi$
$313$	5.00000			0.282617			0.141308	+	0.989966i	$0.454869\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	17.0000			0.956325
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$		0			0
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$	15.0000	−	5.19615i	0.835917	−	0.289570i
$323$	24.0000			1.33540
$324$		0			0
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$	1.00000	−	1.73205i	0.0553849	−	0.0959294i
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	3.00000	−	15.5885i	0.165395	−	0.859419i
$330$		0			0
$331$	2.00000			0.109930			0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000			0.109930			0.0549650	+	0.998488i	$0.482495\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$		0			0
$334$	−3.00000	+	5.19615i	−0.164153	+	0.284321i
$335$	−15.0000	−	25.9808i	−0.819538	−	1.41948i
$336$		0			0
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$		0			0
$340$	−9.00000	+	15.5885i	−0.488094	+	0.845403i
$341$		0			0
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	−9.00000			−0.483843
$347$	−33.0000			−1.77153			−0.885766	−	0.464131i	$-0.846367\pi$
$347$	−33.0000			−1.77153			−0.885766	+	0.464131i	$0.846367\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	8.00000	+	6.92820i	0.427618	+	0.370328i
$351$		0			0
$352$		0			0
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	−0.920677	+	0.390324i	$0.872363\pi$
$354$		0			0
$355$	−9.00000	−	15.5885i	−0.477670	−	0.827349i
$356$	3.00000	−	5.19615i	0.159000	−	0.275396i
$357$		0			0
$358$	7.50000	+	12.9904i	0.396387	+	0.686563i
$359$	18.0000	−	31.1769i	0.950004	−	1.64545i	0.204595	−	0.978847i	$-0.434412\pi$
$359$	18.0000	−	31.1769i	0.950004	−	1.64545i	0.745409	−	0.666608i	$-0.232254\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	10.0000			0.525588
$363$		0			0
$364$	8.00000	+	6.92820i	0.419314	+	0.363137i
$365$	−10.5000	+	18.1865i	−0.549595	+	0.951927i
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	24.0000			1.24770
$371$	−22.5000	+	7.79423i	−1.16814	+	0.404656i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$		0			0
$376$	6.00000			0.309426
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$	12.0000			0.615587
$381$		0			0
$382$	−18.0000			−0.920960
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$		0			0
$386$	−26.0000			−1.32337
$387$		0			0
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	−0.957263	−	0.289220i	$-0.906604\pi$
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	0.729103	+	0.684403i	$0.239937\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$		0			0
$394$	−15.0000			−0.755689
$395$	25.5000	+	44.1673i	1.28304	+	2.22230i
$396$		0			0
$397$	−16.0000	+	27.7128i	−0.803017	+	1.39087i	0.114605	+	0.993411i	$0.463440\pi$
$397$	−16.0000	+	27.7128i	−0.803017	+	1.39087i	−0.917622	+	0.397455i	$0.869893\pi$
$398$	5.50000	+	9.52628i	0.275690	+	0.477509i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	16.0000	−	27.7128i	0.797017	−	1.38047i
$404$	−7.50000	+	12.9904i	−0.373139	+	0.646296i
$405$		0			0
$406$	−7.50000	+	2.59808i	−0.372219	+	0.128940i
$407$		0			0
$408$		0			0
$409$	−25.0000			−1.23617			−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000			−1.23617			−0.618085	+	0.786111i	$0.712091\pi$
$410$	18.0000			0.888957
$411$		0			0
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	−1.50000	+	7.79423i	−0.0738102	+	0.383529i
$414$		0			0
$415$	18.0000	−	31.1769i	0.883585	−	1.53041i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$		0			0
$418$		0			0
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	−0.932061	−	0.362301i	$-0.881991\pi$
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	0.152269	−	0.988339i	$-0.451342\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$		0			0
$424$	−4.50000	−	7.79423i	−0.218539	−	0.378521i
$425$	−24.0000			−1.16417
$426$		0			0
$427$	5.00000	−	25.9808i	0.241967	−	1.25730i
$428$	−1.50000	+	2.59808i	−0.0725052	+	0.125583i
$429$		0			0
$430$	−12.0000	+	20.7846i	−0.578691	+	1.00232i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	4.00000	−	20.7846i	0.192006	−	0.997693i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	24.0000			1.14808
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	39.0000			1.85295			0.926473	−	0.376361i	$-0.122825\pi$
$443$	39.0000			1.85295			0.926473	+	0.376361i	$0.122825\pi$
$444$		0			0
$445$	18.0000			0.853282
$446$	−0.500000	−	0.866025i	−0.0236757	−	0.0410075i
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$		0			0
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$	−6.00000	+	31.1769i	−0.281284	+	1.46160i
$456$		0			0
$457$	−1.00000			−0.0467780			−0.0233890	−	0.999726i	$-0.507446\pi$
$457$	−1.00000			−0.0467780			−0.0233890	+	0.999726i	$0.507446\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$		0			0
$460$	−9.00000	+	15.5885i	−0.419627	+	0.726816i
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	−0.938386	−	0.345589i	$-0.887679\pi$
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	0.169904	−	0.985461i	$-0.445654\pi$
$462$		0			0
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	−0.556299	−	0.830982i	$-0.687779\pi$
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	0.997801	+	0.0662777i	$0.0211123\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	−16.5000	+	28.5788i	−0.763529	+	1.32247i	0.177492	+	0.984122i	$0.443202\pi$
$467$	−16.5000	+	28.5788i	−0.763529	+	1.32247i	−0.941021	+	0.338349i	$0.890132\pi$
$468$		0			0
$469$	5.00000	−	25.9808i	0.230879	−	1.19968i
$470$	9.00000	+	15.5885i	0.415139	+	0.719042i
$471$		0			0
$472$	−3.00000			−0.138086
$473$		0			0
$474$		0			0
$475$	8.00000	+	13.8564i	0.367065	+	0.635776i
$476$	−15.0000	+	5.19615i	−0.687524	+	0.238165i
$477$		0			0
$478$		0			0
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	−0.500000	+	0.866025i	−0.0227744	+	0.0394464i
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−15.0000	+	25.9808i	−0.681115	+	1.17973i
$486$		0			0
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	0.974879	−	0.222737i	$-0.0714992\pi$
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	−0.680335	+	0.732901i	$0.738166\pi$
$488$	10.0000			0.452679
$489$		0			0
$490$	3.00000	+	20.7846i	0.135526	+	0.938953i
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	−0.382118	−	0.924113i	$-0.624805\pi$
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	0.991365	−	0.131132i	$-0.0418613\pi$
$492$		0			0
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	8.00000	+	13.8564i	0.359937	+	0.623429i
$495$		0			0
$496$	8.00000			0.359211
$497$	3.00000	−	15.5885i	0.134568	−	0.699238i
$498$		0			0
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	0.842774	−	0.538267i	$-0.180921\pi$
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	−0.887540	+	0.460730i	$0.847588\pi$
$500$	3.00000			0.134164
$501$		0			0
$502$	9.00000			0.401690
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	−45.0000			−2.00247
$506$		0			0
$507$		0			0
$508$	5.00000			0.221839
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−17.5000	+	6.06218i	−0.774154	+	0.268175i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		0			0
$515$	12.0000	−	20.7846i	0.528783	−	0.915879i
$516$		0			0
$517$		0			0
$518$	16.0000	+	13.8564i	0.703000	+	0.608816i
$519$		0			0
$520$	−12.0000			−0.526235
$521$	−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
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	9.00000	−	15.5885i	0.392419	−	0.679689i
$527$	24.0000	+	41.5692i	1.04546	+	1.81078i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	13.5000	−	23.3827i	0.586403	−	1.01568i
$531$		0			0
$532$	8.00000	+	6.92820i	0.346844	+	0.300376i
$533$	12.0000	+	20.7846i	0.519778	+	0.900281i
$534$		0			0
$535$	−9.00000			−0.389104
$536$	10.0000			0.431934
$537$		0			0
$538$	−10.5000	−	18.1865i	−0.452687	−	0.784077i
$539$		0			0
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−12.5000	+	21.6506i	−0.536921	+	0.929974i
$543$		0			0
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$	−6.00000	+	10.3923i	−0.257012	+	0.445157i
$546$		0			0
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	0.993028	+	0.117875i	$0.0376081\pi$
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	−0.394432	+	0.918925i	$0.629059\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$		0			0
$550$		0			0
$551$	−12.0000			−0.511217
$552$		0			0
$553$	−8.50000	+	44.1673i	−0.361457	+	1.87818i
$554$	−14.0000	+	24.2487i	−0.594803	+	1.03023i
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	−3.00000	−	5.19615i	−0.127114	−	0.220168i	0.795443	−	0.606028i	$-0.207238\pi$
$557$	−3.00000	−	5.19615i	−0.127114	−	0.220168i	−0.922557	+	0.385860i	$0.873905\pi$
$558$		0			0
$559$	−32.0000			−1.35346
$560$	−7.50000	+	2.59808i	−0.316933	+	0.109789i
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−15.0000			−0.632175			−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000			−0.632175			−0.316087	+	0.948730i	$0.602369\pi$
$564$		0			0
$565$	−18.0000			−0.757266
$566$	4.00000			0.168133
$567$		0			0
$568$	6.00000			0.251754
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$		0			0
$574$	12.0000	+	10.3923i	0.500870	+	0.433766i
$575$	−24.0000			−1.00087
$576$		0			0
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	0.520952	−	0.853586i	$-0.325577\pi$
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	−0.999703	+	0.0243645i	$0.992244\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$		0			0
$580$	4.50000	−	7.79423i	0.186852	−	0.323638i
$581$	30.0000	−	10.3923i	1.24461	−	0.431145i
$582$		0			0
$583$		0			0
$584$	−3.50000	−	6.06218i	−0.144831	−	0.250855i
$585$		0			0
$586$	1.50000	−	2.59808i	0.0619644	−	0.107326i
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	0.668708	−	0.743525i	$-0.266848\pi$
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	−0.978266	+	0.207355i	$0.933514\pi$
$588$		0			0
$589$	16.0000	−	27.7128i	0.659269	−	1.14189i
$590$	−4.50000	−	7.79423i	−0.185262	−	0.320883i
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	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
$595$	−36.0000	−	31.1769i	−1.47586	−	1.27813i
$596$	−10.5000	−	18.1865i	−0.430097	−	0.744949i
$597$		0			0
$598$	−24.0000			−0.981433
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	0.999934	+	0.0114528i	$0.00364562\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$	−20.0000	+	6.92820i	−0.815139	+	0.282372i
$603$		0			0
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−16.5000	+	28.5788i	−0.670820	+	1.16190i
$606$		0			0
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	0.732551	−	0.680712i	$-0.238329\pi$
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	−0.955789	+	0.294052i	$0.904996\pi$
$608$	−2.00000	+	3.46410i	−0.0811107	+	0.140488i
$609$		0			0
$610$	15.0000	+	25.9808i	0.607332	+	1.05193i
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−8.00000			−0.322854
$615$		0			0
$616$		0			0
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	−0.988343	−	0.152242i	$-0.951351\pi$
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	0.626017	+	0.779809i	$0.284684\pi$
$618$		0			0
$619$	8.00000	−	13.8564i	0.321547	−	0.556936i	−0.659260	−	0.751915i	$-0.729130\pi$
$619$	8.00000	−	13.8564i	0.321547	−	0.556936i	0.980807	+	0.194979i	$0.0624638\pi$
$620$	12.0000	+	20.7846i	0.481932	+	0.834730i
$621$		0			0
$622$	12.0000			0.481156
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−5.00000			−0.199840
$627$		0			0
$628$	14.0000			0.558661
$629$	−48.0000			−1.91389
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−17.0000			−0.676224
$633$		0			0
$634$	−18.0000			−0.714871
$635$	7.50000	+	12.9904i	0.297628	+	0.515508i
$636$		0			0
$637$	−22.0000	+	17.3205i	−0.871672	+	0.686264i
$638$		0			0
$639$		0			0
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	−0.525584	−	0.850741i	$-0.676153\pi$
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	0.999556	+	0.0297987i	$0.00948663\pi$
$642$		0			0
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$	−15.0000	+	5.19615i	−0.591083	+	0.204757i
$645$		0			0
$646$	−24.0000			−0.944267
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$		0			0
$649$		0			0
$650$	−8.00000	−	13.8564i	−0.313786	−	0.543493i
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$		0			0
$655$	18.0000	−	31.1769i	0.703318	−	1.21818i
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$	−3.00000	+	15.5885i	−0.116952	+	0.607701i
$659$	10.5000	+	18.1865i	0.409022	+	0.708447i	0.994780	−	0.102039i	$-0.0325366\pi$
$659$	10.5000	+	18.1865i	0.409022	+	0.708447i	−0.585758	+	0.810486i	$0.699203\pi$
$660$		0			0
$661$	32.0000			1.24466			0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000			1.24466			0.622328	+	0.782757i	$0.286187\pi$
$662$	−2.00000			−0.0777322
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	−6.00000	+	31.1769i	−0.232670	+	1.20899i
$666$		0			0
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$		0			0
$670$	15.0000	+	25.9808i	0.579501	+	1.00372i
$671$		0			0
$672$		0			0
$673$	21.5000	+	37.2391i	0.828764	+	1.43546i	0.899008	+	0.437932i	$0.144289\pi$
$673$	21.5000	+	37.2391i	0.828764	+	1.43546i	−0.0702442	+	0.997530i	$0.522378\pi$
$674$	−3.50000	+	6.06218i	−0.134815	+	0.233506i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	21.0000			0.807096			0.403548	−	0.914959i	$-0.367777\pi$
$677$	21.0000			0.807096			0.403548	+	0.914959i	$0.367777\pi$
$678$		0			0
$679$	−25.0000	+	8.66025i	−0.959412	+	0.332350i
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$		0			0
$682$		0			0
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$		0			0
$685$	36.0000			1.37549
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$		0			0
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	36.0000			1.37149
$690$		0			0
$691$	8.00000			0.304334			0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000			0.304334			0.152167	+	0.988355i	$0.451375\pi$
$692$	9.00000			0.342129
$693$		0			0
$694$	33.0000			1.25266
$695$	−6.00000			−0.227593
$696$		0			0
$697$	−36.0000			−1.36360
$698$	−5.00000	−	8.66025i	−0.189253	−	0.327795i
$699$		0			0
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$		0			0
$705$		0			0
$706$	15.0000	−	25.9808i	0.564532	−	0.977799i
$707$	−30.0000	−	25.9808i	−1.12827	−	0.977107i
$708$		0			0
$709$	8.00000			0.300446			0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000			0.300446			0.150223	+	0.988652i	$0.452001\pi$
$710$	9.00000	+	15.5885i	0.337764	+	0.585024i
$711$		0			0
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	24.0000	+	41.5692i	0.898807	+	1.55678i
$714$		0			0
$715$		0			0
$716$	−7.50000	−	12.9904i	−0.280288	−	0.485473i
$717$		0			0
$718$	−18.0000	+	31.1769i	−0.671754	+	1.16351i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$		0			0
$721$	20.0000	−	6.92820i	0.744839	−	0.258020i
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	−10.0000			−0.371647
$725$	12.0000			0.445669
$726$		0			0
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	0.570049	−	0.821611i	$-0.306924\pi$
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	−0.996560	+	0.0828714i	$0.973591\pi$
$728$	−8.00000	−	6.92820i	−0.296500	−	0.256776i
$729$		0			0
$730$	10.5000	−	18.1865i	0.388622	−	0.673114i
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$		0			0
$733$	−22.0000	−	38.1051i	−0.812589	−	1.40744i	−0.911047	−	0.412303i	$-0.864724\pi$
$733$	−22.0000	−	38.1051i	−0.812589	−	1.40744i	0.0984580	−	0.995141i	$-0.468609\pi$
$734$	−9.50000	+	16.4545i	−0.350651	+	0.607346i
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$		0			0
$738$		0			0
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	0.708072	−	0.706140i	$-0.249565\pi$
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	−0.965571	+	0.260138i	$0.916232\pi$
$740$	−24.0000			−0.882258
$741$		0			0
$742$	22.5000	−	7.79423i	0.826001	−	0.286135i
$743$	12.0000	−	20.7846i	0.440237	−	0.762513i	−0.557470	−	0.830197i	$-0.688228\pi$
$743$	12.0000	−	20.7846i	0.440237	−	0.762513i	0.997707	+	0.0676840i	$0.0215610\pi$
$744$		0			0
$745$	31.5000	−	54.5596i	1.15407	−	1.99891i
$746$	−5.00000	−	8.66025i	−0.183063	−	0.317074i
$747$		0			0
$748$		0			0
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	0.929270	+	0.369402i	$0.120437\pi$
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	−0.144724	+	0.989472i	$0.546229\pi$
$752$	−6.00000			−0.218797
$753$		0			0
$754$	12.0000			0.437014
$755$	−24.0000			−0.873449
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	10.0000			0.363216
$759$		0			0
$760$	−12.0000			−0.435286
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$		0			0
$763$	−10.0000	+	3.46410i	−0.362024	+	0.125409i
$764$	18.0000			0.651217
$765$		0			0
$766$	−3.00000	−	5.19615i	−0.108394	−	0.187745i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$		0			0
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	−0.999364	−	0.0356685i	$-0.988644\pi$
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	0.530572	+	0.847640i	$0.321977\pi$
$770$		0			0
$771$		0			0
$772$	26.0000			0.935760
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$	−16.0000	+	27.7128i	−0.574737	+	0.995474i
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$		0			0
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$		0			0
$782$	18.0000	−	31.1769i	0.643679	−	1.11488i
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$	21.0000	+	36.3731i	0.749522	+	1.29821i
$786$		0			0
$787$	−22.0000			−0.784215			−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000			−0.784215			−0.392108	+	0.919919i	$0.628254\pi$
$788$	15.0000			0.534353
$789$		0			0
$790$	−25.5000	−	44.1673i	−0.907249	−	1.57140i
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		0			0
$793$	−20.0000	+	34.6410i	−0.710221	+	1.23014i
$794$	16.0000	−	27.7128i	0.567819	−	0.983491i
$795$		0			0
$796$	−5.50000	−	9.52628i	−0.194942	−	0.337650i
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	−0.661441	−	0.749997i	$-0.730055\pi$
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	0.980237	+	0.197826i	$0.0633881\pi$
$798$		0			0
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$		0			0
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$		0			0
$804$		0			0
$805$	−36.0000	−	31.1769i	−1.26883	−	1.09884i
$806$	−16.0000	+	27.7128i	−0.563576	+	0.976142i
$807$		0			0
$808$	7.50000	−	12.9904i	0.263849	−	0.457000i
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	0.996125	−	0.0879478i	$-0.0280309\pi$
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	−0.574228	+	0.818696i	$0.694698\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	7.50000	−	2.59808i	0.263198	−	0.0911746i
$813$		0			0
$814$		0			0
$815$	−6.00000			−0.210171
$816$		0			0
$817$	−32.0000			−1.11954
$818$	25.0000			0.874105
$819$		0			0
$820$	−18.0000			−0.628587
$821$	−21.0000			−0.732905			−0.366453	−	0.930437i	$-0.619428\pi$
$821$	−21.0000			−0.732905			−0.366453	+	0.930437i	$0.619428\pi$
$822$		0			0
$823$	23.0000			0.801730			0.400865	−	0.916137i	$-0.368710\pi$
$823$	23.0000			0.801730			0.400865	+	0.916137i	$0.368710\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	1.50000	−	7.79423i	0.0521917	−	0.271196i
$827$	−21.0000			−0.730242			−0.365121	−	0.930960i	$-0.618972\pi$
$827$	−21.0000			−0.730242			−0.365121	+	0.930960i	$0.618972\pi$
$828$		0			0
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	−0.997848	−	0.0655624i	$-0.979116\pi$
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	0.442145	−	0.896943i	$-0.354217\pi$
$830$	−18.0000	+	31.1769i	−0.624789	+	1.08217i
$831$		0			0
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	−6.00000	−	41.5692i	−0.207888	−	1.44029i
$834$		0			0
$835$	18.0000			0.622916
$836$		0			0
$837$		0			0
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	16.0000	+	27.7128i	0.551396	+	0.955047i
$843$		0			0
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	−27.5000	+	9.52628i	−0.944911	+	0.327327i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$		0			0
$850$	24.0000			0.823193
$851$	−48.0000			−1.64542
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$	−5.00000	+	25.9808i	−0.171096	+	0.889043i
$855$		0			0
$856$	1.50000	−	2.59808i	0.0512689	−	0.0888004i
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$	12.0000	−	20.7846i	0.409197	−	0.708749i
$861$		0			0
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	21.0000	−	36.3731i	0.714848	−	1.23815i	−0.248170	−	0.968717i	$-0.579829\pi$
$863$	21.0000	−	36.3731i	0.714848	−	1.23815i	0.963018	−	0.269437i	$-0.0868376\pi$
$864$		0			0
$865$	13.5000	+	23.3827i	0.459014	+	0.795035i
$866$	7.00000			0.237870
$867$		0			0
$868$	−4.00000	+	20.7846i	−0.135769	+	0.705476i
$869$		0			0
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−2.00000	−	3.46410i	−0.0677285	−	0.117309i
$873$		0			0
$874$	−24.0000			−0.811812
$875$	−1.50000	+	7.79423i	−0.0507093	+	0.263493i
$876$		0			0
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	−8.00000			−0.269987
$879$		0			0
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$	24.0000			0.807207
$885$		0			0
$886$	−39.0000			−1.31023
$887$	−21.0000	−	36.3731i	−0.705111	−	1.22129i	−0.966651	−	0.256096i	$-0.917564\pi$
$887$	−21.0000	−	36.3731i	−0.705111	−	1.22129i	0.261540	−	0.965193i	$-0.415770\pi$
$888$		0			0
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$	−18.0000			−0.603361
$891$		0			0
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$	22.5000	−	38.9711i	0.752092	−	1.30266i
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	6.00000			0.200223
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$		0			0
$901$	−27.0000	+	46.7654i	−0.899500	+	1.55798i
$902$		0			0
$903$		0			0
$904$	3.00000	−	5.19615i	0.0997785	−	0.172821i
$905$	−15.0000	−	25.9808i	−0.498617	−	0.863630i
$906$		0			0
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$		0			0
$910$	6.00000	−	31.1769i	0.198898	−	1.03350i
$911$	−27.0000	−	46.7654i	−0.894550	−	1.54941i	−0.834361	−	0.551219i	$-0.814163\pi$
$911$	−27.0000	−	46.7654i	−0.894550	−	1.54941i	−0.0601892	−	0.998187i	$-0.519170\pi$
$912$		0			0
$913$		0			0
$914$	1.00000			0.0330771
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	30.0000	−	10.3923i	0.990687	−	0.343184i
$918$		0			0
$919$	18.5000	−	32.0429i	0.610259	−	1.05700i	−0.380938	−	0.924601i	$-0.624399\pi$
$919$	18.5000	−	32.0429i	0.610259	−	1.05700i	0.991197	−	0.132398i	$-0.0422678\pi$
$920$	9.00000	−	15.5885i	0.296721	−	0.513936i
$921$		0			0
$922$	16.5000	+	28.5788i	0.543399	+	0.941194i
$923$	−12.0000	+	20.7846i	−0.394985	+	0.684134i
$924$		0			0
$925$	−16.0000	−	27.7128i	−0.526077	−	0.911192i
$926$	−9.50000	+	16.4545i	−0.312189	+	0.540728i
$927$		0			0
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$	−22.0000	+	17.3205i	−0.721021	+	0.567657i
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$		0			0
$934$	16.5000	−	28.5788i	0.539896	−	0.935128i
$935$		0			0
$936$		0			0
$937$	−1.00000			−0.0326686			−0.0163343	−	0.999867i	$-0.505200\pi$
$937$	−1.00000			−0.0326686			−0.0163343	+	0.999867i	$0.505200\pi$
$938$	−5.00000	+	25.9808i	−0.163256	+	0.848302i
$939$		0			0
$940$	−9.00000	−	15.5885i	−0.293548	−	0.508439i
$941$	−18.0000			−0.586783			−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000			−0.586783			−0.293392	+	0.955992i	$0.594784\pi$
$942$		0			0
$943$	−36.0000			−1.17232
$944$	3.00000			0.0976417
$945$		0			0
$946$		0			0
$947$	−45.0000			−1.46230			−0.731152	−	0.682215i	$-0.761017\pi$
$947$	−45.0000			−1.46230			−0.731152	+	0.682215i	$0.761017\pi$
$948$		0			0
$949$	28.0000			0.908918
$950$	−8.00000	−	13.8564i	−0.259554	−	0.449561i
$951$		0			0
$952$	15.0000	−	5.19615i	0.486153	−	0.168408i
$953$	48.0000			1.55487			0.777436	−	0.628962i	$-0.216520\pi$
$953$	48.0000			1.55487			0.777436	+	0.628962i	$0.216520\pi$
$954$		0			0
$955$	27.0000	+	46.7654i	0.873699	+	1.51329i
$956$		0			0
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	24.0000	+	20.7846i	0.775000	+	0.671170i
$960$		0			0
$961$	33.0000			1.06452
$962$	−16.0000	−	27.7128i	−0.515861	−	0.893497i
$963$		0			0
$964$	0.500000	−	0.866025i	0.0161039	−	0.0278928i
$965$	39.0000	+	67.5500i	1.25545	+	2.17451i
$966$		0			0
$967$	18.5000	−	32.0429i	0.594920	−	1.03043i	−0.398638	−	0.917108i	$-0.630517\pi$
$967$	18.5000	−	32.0429i	0.594920	−	1.03043i	0.993558	−	0.113323i	$-0.0361496\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$		0			0
$970$	15.0000	−	25.9808i	0.481621	−	0.834192i
$971$	−1.50000	+	2.59808i	−0.0481373	+	0.0833762i	−0.889090	−	0.457732i	$-0.848662\pi$
$971$	−1.50000	+	2.59808i	−0.0481373	+	0.0833762i	0.840953	+	0.541108i	$0.181995\pi$
$972$		0			0
$973$	−4.00000	−	3.46410i	−0.128234	−	0.111054i
$974$	−6.50000	−	11.2583i	−0.208273	−	0.360740i
$975$		0			0
$976$	−10.0000			−0.320092
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$		0			0
$980$	−3.00000	−	20.7846i	−0.0958315	−	0.663940i
$981$		0			0
$982$	−13.5000	+	23.3827i	−0.430802	+	0.746171i
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	22.5000	+	38.9711i	0.716910	+	1.24172i
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$		0			0
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	0.623516	−	0.781810i	$-0.285704\pi$
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	−0.988826	+	0.149076i	$0.952370\pi$
$992$	−8.00000			−0.254000
$993$		0			0
$994$	−3.00000	+	15.5885i	−0.0951542	+	0.494436i
$995$	16.5000	−	28.5788i	0.523085	−	0.906010i
$996$		0			0
$997$	−16.0000	+	27.7128i	−0.506725	+	0.877674i	0.493245	+	0.869891i	$0.335811\pi$
$997$	−16.0000	+	27.7128i	−0.506725	+	0.877674i	−0.999970	+	0.00778294i	$0.997523\pi$
$998$	1.00000	+	1.73205i	0.0316544	+	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.e.f.919.1		2
3.2	odd	2		1134.2.e.j.919.1		2
7.4	even	3		1134.2.h.k.109.1		2
9.2	odd	6		1134.2.h.g.541.1		2
9.4	even	3		378.2.g.f.163.1	yes	2
9.5	odd	6		378.2.g.a.163.1	yes	2
9.7	even	3		1134.2.h.k.541.1		2
21.11	odd	6		1134.2.h.g.109.1		2
63.4	even	3		378.2.g.f.109.1	yes	2
63.5	even	6		2646.2.a.r.1.1		1
63.11	odd	6		1134.2.e.j.865.1		2
63.23	odd	6		2646.2.a.bc.1.1		1
63.25	even	3	inner	1134.2.e.f.865.1		2
63.32	odd	6		378.2.g.a.109.1	✓	2
63.40	odd	6		2646.2.a.m.1.1		1
63.58	even	3		2646.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.a.109.1	✓	2	63.32	odd	6
378.2.g.a.163.1	yes	2	9.5	odd	6
378.2.g.f.109.1	yes	2	63.4	even	3
378.2.g.f.163.1	yes	2	9.4	even	3
1134.2.e.f.865.1		2	63.25	even	3	inner
1134.2.e.f.919.1		2	1.1	even	1	trivial
1134.2.e.j.865.1		2	63.11	odd	6
1134.2.e.j.919.1		2	3.2	odd	2
1134.2.h.g.109.1		2	21.11	odd	6
1134.2.h.g.541.1		2	9.2	odd	6
1134.2.h.k.109.1		2	7.4	even	3
1134.2.h.k.541.1		2	9.7	even	3
2646.2.a.b.1.1		1	63.58	even	3
2646.2.a.m.1.1		1	63.40	odd	6
2646.2.a.r.1.1		1	63.5	even	6
2646.2.a.bc.1.1		1	63.23	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(2.00000 - 3.46410i) q^{13} +(0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +8.00000 q^{31} -1.00000 q^{32} +(-3.00000 - 5.19615i) q^{34} +(-7.50000 + 2.59808i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 2.59808i) q^{56} +(1.50000 + 2.59808i) q^{58} +3.00000 q^{59} -10.0000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} -10.0000 q^{67} +(3.00000 + 5.19615i) q^{68} +(7.50000 - 2.59808i) q^{70} -6.00000 q^{71} +(3.50000 + 6.06218i) q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +17.0000 q^{79} +(1.50000 + 2.59808i) q^{80} +(3.00000 - 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(-9.00000 + 15.5885i) q^{85} +(4.00000 + 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{89} +(8.00000 + 6.92820i) q^{91} +(3.00000 + 5.19615i) q^{92} +6.00000 q^{94} +12.0000 q^{95} +(5.00000 + 8.66025i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} - 2 q^{8} - 3 q^{10} + 4 q^{13} + q^{14} + 2 q^{16} + 6 q^{17} + 4 q^{19} + 3 q^{20} + 6 q^{23} - 4 q^{25} - 4 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} - 2 q^{32} - 6 q^{34} - 15 q^{35} - 8 q^{37} - 4 q^{38} - 3 q^{40} - 6 q^{41} - 8 q^{43} - 6 q^{46} - 12 q^{47} - 13 q^{49} + 4 q^{50} + 4 q^{52} + 9 q^{53} + q^{56} + 3 q^{58} + 6 q^{59} - 20 q^{61} - 16 q^{62} + 2 q^{64} + 24 q^{65} - 20 q^{67} + 6 q^{68} + 15 q^{70} - 12 q^{71} + 7 q^{73} + 8 q^{74} + 4 q^{76} + 34 q^{79} + 3 q^{80} + 6 q^{82} - 12 q^{83} - 18 q^{85} + 8 q^{86} + 6 q^{89} + 16 q^{91} + 6 q^{92} + 12 q^{94} + 24 q^{95} + 10 q^{97} + 13 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 - 2 * q^8 - 3 * q^10 + 4 * q^13 + q^14 + 2 * q^16 + 6 * q^17 + 4 * q^19 + 3 * q^20 + 6 * q^23 - 4 * q^25 - 4 * q^26 - q^28 - 3 * q^29 + 16 * q^31 - 2 * q^32 - 6 * q^34 - 15 * q^35 - 8 * q^37 - 4 * q^38 - 3 * q^40 - 6 * q^41 - 8 * q^43 - 6 * q^46 - 12 * q^47 - 13 * q^49 + 4 * q^50 + 4 * q^52 + 9 * q^53 + q^56 + 3 * q^58 + 6 * q^59 - 20 * q^61 - 16 * q^62 + 2 * q^64 + 24 * q^65 - 20 * q^67 + 6 * q^68 + 15 * q^70 - 12 * q^71 + 7 * q^73 + 8 * q^74 + 4 * q^76 + 34 * q^79 + 3 * q^80 + 6 * q^82 - 12 * q^83 - 18 * q^85 + 8 * q^86 + 6 * q^89 + 16 * q^91 + 6 * q^92 + 12 * q^94 + 24 * q^95 + 10 * q^97 + 13 * q^98

Introduction

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