LMFDB - Embedded newform 1134.2.l.c.215.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(215,1134)]

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([5, 5]))

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

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

chi := DirichletCharacter("1134.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.215
Dual form			1134.2.l.c.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +(-1.50000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(3.00000 + 1.73205i) q^{13} +(-2.59808 + 0.500000i) q^{14} +1.00000 q^{16} +(-1.73205 - 3.00000i) q^{17} +(3.00000 + 1.73205i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.00000 - 1.73205i) q^{25} +(-1.73205 + 3.00000i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(2.59808 - 1.50000i) q^{29} -1.73205i q^{31} +1.00000i q^{32} +(3.00000 - 1.73205i) q^{34} +(-3.46410 + 3.00000i) q^{35} +(1.00000 - 1.73205i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(1.50000 - 0.866025i) q^{40} +(-3.46410 + 6.00000i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-2.59808 - 1.50000i) q^{44} +(-3.00000 - 5.19615i) q^{46} -6.92820 q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 + 1.00000i) q^{50} +(-3.00000 - 1.73205i) q^{52} +(-7.79423 + 4.50000i) q^{53} +5.19615i q^{55} +(2.59808 - 0.500000i) q^{56} +(1.50000 + 2.59808i) q^{58} +1.73205 q^{59} +1.73205 q^{62} -1.00000 q^{64} +6.00000i q^{65} +2.00000 q^{67} +(1.73205 + 3.00000i) q^{68} +(-3.00000 - 3.46410i) q^{70} -12.0000i q^{71} +(6.00000 - 3.46410i) q^{73} +(1.73205 + 1.00000i) q^{74} +(-3.00000 - 1.73205i) q^{76} +(-2.59808 + 7.50000i) q^{77} -1.00000 q^{79} +(0.866025 + 1.50000i) q^{80} +(-6.00000 - 3.46410i) q^{82} +(4.33013 + 7.50000i) q^{83} +(3.00000 - 5.19615i) q^{85} +(-6.92820 + 4.00000i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-3.00000 + 8.66025i) q^{91} +(5.19615 - 3.00000i) q^{92} -6.92820i q^{94} +6.00000i q^{95} +(-4.50000 + 2.59808i) q^{97} +(-2.59808 - 6.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^7	$ 4 q - 4 q^{4} + 2 q^{7} - 6 q^{10} + 12 q^{13} + 4 q^{16} + 12 q^{19} - 6 q^{22} + 4 q^{25} - 2 q^{28} + 12 q^{34} + 4 q^{37} + 6 q^{40} + 16 q^{43} - 12 q^{46} - 26 q^{49} - 12 q^{52} + 6 q^{58} - 4 q^{64} + 8 q^{67} - 12 q^{70} + 24 q^{73} - 12 q^{76} - 4 q^{79} - 24 q^{82} + 12 q^{85} + 6 q^{88} - 12 q^{91} - 18 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^7 - 6 * q^10 + 12 * q^13 + 4 * q^16 + 12 * q^19 - 6 * q^22 + 4 * q^25 - 2 * q^28 + 12 * q^34 + 4 * q^37 + 6 * q^40 + 16 * q^43 - 12 * q^46 - 26 * q^49 - 12 * q^52 + 6 * q^58 - 4 * q^64 + 8 * q^67 - 12 * q^70 + 24 * q^73 - 12 * q^76 - 4 * q^79 - 24 * q^82 + 12 * q^85 + 6 * q^88 - 12 * q^91 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.50000	+	0.866025i	−0.474342	+	0.273861i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$	−2.59808	+	0.500000i	−0.694365	+	0.133631i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	0.575863	−	0.817546i	$-0.304666\pi$
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	−0.995947	+	0.0899392i	$0.971333\pi$
$18$		0			0
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−0.866025	−	1.50000i	−0.193649	−	0.335410i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	−1.73205	+	3.00000i	−0.339683	+	0.588348i
$27$		0			0
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	2.59808	−	1.50000i	0.482451	−	0.278543i	−0.238987	−	0.971023i	$-0.576815\pi$
$29$	2.59808	−	1.50000i	0.482451	−	0.278543i	0.721437	+	0.692480i	$0.243482\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	3.00000	−	1.73205i	0.514496	−	0.297044i
$35$	−3.46410	+	3.00000i	−0.585540	+	0.507093i
$36$		0			0
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−1.73205	+	3.00000i	−0.280976	+	0.486664i
$39$		0			0
$40$	1.50000	−	0.866025i	0.237171	−	0.136931i
$41$	−3.46410	+	6.00000i	−0.541002	+	0.937043i	0.457845	+	0.889032i	$0.348621\pi$
$41$	−3.46410	+	6.00000i	−0.541002	+	0.937043i	−0.998847	+	0.0480106i	$0.984712\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−6.92820			−1.01058			−0.505291	−	0.862949i	$-0.668615\pi$
$47$	−6.92820			−1.01058			−0.505291	+	0.862949i	$0.668615\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	1.73205	+	1.00000i	0.244949	+	0.141421i
$51$		0			0
$52$	−3.00000	−	1.73205i	−0.416025	−	0.240192i
$53$	−7.79423	+	4.50000i	−1.07062	+	0.618123i	−0.928351	−	0.371706i	$-0.878773\pi$
$53$	−7.79423	+	4.50000i	−1.07062	+	0.618123i	−0.142269	+	0.989828i	$0.545440\pi$
$54$		0			0
$55$			5.19615i			0.700649i
$56$	2.59808	−	0.500000i	0.347183	−	0.0668153i
$57$		0			0
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	1.73205			0.225494			0.112747	−	0.993624i	$-0.464035\pi$
$59$	1.73205			0.225494			0.112747	+	0.993624i	$0.464035\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	1.73205			0.219971
$63$		0			0
$64$	−1.00000			−0.125000
$65$			6.00000i			0.744208i
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	1.73205	+	3.00000i	0.210042	+	0.363803i
$69$		0			0
$70$	−3.00000	−	3.46410i	−0.358569	−	0.414039i
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$		0			0
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$	1.73205	+	1.00000i	0.201347	+	0.116248i
$75$		0			0
$76$	−3.00000	−	1.73205i	−0.344124	−	0.198680i
$77$	−2.59808	+	7.50000i	−0.296078	+	0.854704i
$78$		0			0
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0.866025	+	1.50000i	0.0968246	+	0.167705i
$81$		0			0
$82$	−6.00000	−	3.46410i	−0.662589	−	0.382546i
$83$	4.33013	+	7.50000i	0.475293	+	0.823232i	0.999600	−	0.0282978i	$-0.00900866\pi$
$83$	4.33013	+	7.50000i	0.475293	+	0.823232i	−0.524306	+	0.851530i	$0.675675\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	−6.92820	+	4.00000i	−0.747087	+	0.431331i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$	−3.00000	+	8.66025i	−0.314485	+	0.907841i
$92$	5.19615	−	3.00000i	0.541736	−	0.312772i
$93$		0			0
$94$		−	6.92820i		−	0.714590i
$95$			6.00000i			0.615587i
$96$		0			0
$97$	−4.50000	+	2.59808i	−0.456906	+	0.263795i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−4.50000	+	2.59808i	−0.456906	+	0.263795i	0.253837	+	0.967247i	$0.418307\pi$
$98$	−2.59808	−	6.50000i	−0.262445	−	0.656599i
$99$		0			0
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	0.640464	+	0.767988i	$0.278742\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$		0			0
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$	2.59808	+	1.50000i	0.251166	+	0.145010i	0.620298	−	0.784366i	$-0.287012\pi$
$107$	2.59808	+	1.50000i	0.251166	+	0.145010i	−0.369132	+	0.929377i	$0.620345\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−5.19615			−0.495434
$111$		0			0
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−10.3923	−	6.00000i	−0.977626	−	0.564433i	−0.0760733	−	0.997102i	$-0.524238\pi$
$113$	−10.3923	−	6.00000i	−0.977626	−	0.564433i	−0.901553	+	0.432670i	$0.857572\pi$
$114$		0			0
$115$	−9.00000	−	5.19615i	−0.839254	−	0.484544i
$116$	−2.59808	+	1.50000i	−0.241225	+	0.139272i
$117$		0			0
$118$			1.73205i			0.159448i
$119$	6.92820	−	6.00000i	0.635107	−	0.550019i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$			1.73205i			0.155543i
$125$	12.1244			1.08444
$126$		0			0
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−6.00000			−0.526235
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		0			0
$133$	−3.00000	+	8.66025i	−0.260133	+	0.750939i
$134$			2.00000i			0.172774i
$135$		0			0
$136$	−3.00000	+	1.73205i	−0.257248	+	0.148522i
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$		0			0
$139$	15.0000	+	8.66025i	1.27228	+	0.734553i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	15.0000	+	8.66025i	1.27228	+	0.734553i	0.296866	+	0.954919i	$0.404058\pi$
$140$	3.46410	−	3.00000i	0.292770	−	0.253546i
$141$		0			0
$142$	12.0000			1.00702
$143$	5.19615	+	9.00000i	0.434524	+	0.752618i
$144$		0			0
$145$	4.50000	+	2.59808i	0.373705	+	0.215758i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	15.5885	−	9.00000i	1.27706	−	0.737309i	0.300750	−	0.953703i	$-0.402763\pi$
$149$	15.5885	−	9.00000i	1.27706	−	0.737309i	0.976306	+	0.216394i	$0.0694297\pi$
$150$		0			0
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	−0.972567	−	0.232623i	$-0.925269\pi$
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	0.687741	+	0.725956i	$0.258602\pi$
$152$	1.73205	−	3.00000i	0.140488	−	0.243332i
$153$		0			0
$154$	−7.50000	−	2.59808i	−0.604367	−	0.209359i
$155$	2.59808	−	1.50000i	0.208683	−	0.120483i
$156$		0			0
$157$		−	20.7846i		−	1.65879i	−0.558661	−	0.829396i	$-0.688685\pi$
$157$		−	20.7846i		−	1.65879i	0.558661	−	0.829396i	$-0.311315\pi$
$158$		−	1.00000i		−	0.0795557i
$159$		0			0
$160$	−1.50000	+	0.866025i	−0.118585	+	0.0684653i
$161$	−10.3923	−	12.0000i	−0.819028	−	0.945732i
$162$		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	$0.981949\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$		0			0
$166$	−7.50000	+	4.33013i	−0.582113	+	0.336083i
$167$	8.66025	−	15.0000i	0.670151	−	1.16073i	−0.307711	−	0.951480i	$-0.599563\pi$
$167$	8.66025	−	15.0000i	0.670151	−	1.16073i	0.977861	−	0.209255i	$-0.0671038\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	5.19615	+	3.00000i	0.398527	+	0.230089i
$171$		0			0
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$		0			0
$175$	5.00000	+	1.73205i	0.377964	+	0.130931i
$176$	2.59808	+	1.50000i	0.195837	+	0.113067i
$177$		0			0
$178$	−9.00000	−	5.19615i	−0.674579	−	0.389468i
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	−0.0585225	−	0.998286i	$-0.518639\pi$
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	0.835280	+	0.549825i	$0.185306\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$	−8.66025	−	3.00000i	−0.641941	−	0.222375i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	3.46410			0.254686
$186$		0			0
$187$		−	10.3923i		−	0.759961i
$188$	6.92820			0.505291
$189$		0			0
$190$	−6.00000			−0.435286
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$	−23.0000			−1.65558			−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−23.0000			−1.65558			−0.827788	+	0.561041i	$0.810401\pi$
$194$	−2.59808	−	4.50000i	−0.186531	−	0.323081i
$195$		0			0
$196$	6.50000	−	2.59808i	0.464286	−	0.185577i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$	9.00000	−	5.19615i	0.637993	−	0.368345i	−0.145848	−	0.989307i	$-0.546591\pi$
$199$	9.00000	−	5.19615i	0.637993	−	0.368345i	0.783841	+	0.620962i	$0.213258\pi$
$200$	−1.73205	−	1.00000i	−0.122474	−	0.0707107i
$201$		0			0
$202$		0			0
$203$	5.19615	+	6.00000i	0.364698	+	0.421117i
$204$		0			0
$205$	−12.0000			−0.838116
$206$	1.73205	+	3.00000i	0.120678	+	0.209020i
$207$		0			0
$208$	3.00000	+	1.73205i	0.208013	+	0.120096i
$209$	5.19615	+	9.00000i	0.359425	+	0.622543i
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	7.79423	−	4.50000i	0.535310	−	0.309061i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−6.92820	+	12.0000i	−0.472500	+	0.818393i
$216$		0			0
$217$	4.50000	−	0.866025i	0.305480	−	0.0587896i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$		0			0
$220$		−	5.19615i		−	0.350325i
$221$		−	12.0000i		−	0.807207i
$222$		0			0
$223$	22.5000	−	12.9904i	1.50671	−	0.869900i	0.506742	−	0.862098i	$-0.330850\pi$
$223$	22.5000	−	12.9904i	1.50671	−	0.869900i	0.999970	−	0.00780243i	$-0.00248362\pi$
$224$	−2.59808	+	0.500000i	−0.173591	+	0.0334077i
$225$		0			0
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	2.59808	−	4.50000i	0.172440	−	0.298675i	−0.766832	−	0.641848i	$-0.778168\pi$
$227$	2.59808	−	4.50000i	0.172440	−	0.298675i	0.939272	+	0.343172i	$0.111501\pi$
$228$		0			0
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	−0.0480291	−	0.998846i	$-0.515294\pi$
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	0.841011	+	0.541017i	$0.181961\pi$
$230$	5.19615	−	9.00000i	0.342624	−	0.593442i
$231$		0			0
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	15.5885	+	9.00000i	1.02123	+	0.589610i	0.914461	−	0.404674i	$-0.132615\pi$
$233$	15.5885	+	9.00000i	1.02123	+	0.589610i	0.106773	+	0.994283i	$0.465948\pi$
$234$		0			0
$235$	−6.00000	−	10.3923i	−0.391397	−	0.677919i
$236$	−1.73205			−0.112747
$237$		0			0
$238$	6.00000	+	6.92820i	0.388922	+	0.449089i
$239$	−5.19615	−	3.00000i	−0.336111	−	0.194054i	0.322440	−	0.946590i	$-0.395497\pi$
$239$	−5.19615	−	3.00000i	−0.336111	−	0.194054i	−0.658551	+	0.752536i	$0.728830\pi$
$240$		0			0
$241$	22.5000	+	12.9904i	1.44935	+	0.836784i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	22.5000	+	12.9904i	1.44935	+	0.836784i	0.450910	+	0.892570i	$0.351100\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$		0			0
$244$		0			0
$245$	−9.52628	−	7.50000i	−0.608612	−	0.479157i
$246$		0			0
$247$	6.00000	+	10.3923i	0.381771	+	0.661247i
$248$	−1.73205			−0.109985
$249$		0			0
$250$			12.1244i			0.766812i
$251$	19.0526			1.20259			0.601293	−	0.799028i	$-0.294652\pi$
$251$	19.0526			1.20259			0.601293	+	0.799028i	$0.294652\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$			11.0000i			0.690201i
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.19615	+	9.00000i	0.324127	+	0.561405i	0.981335	−	0.192304i	$-0.0615961\pi$
$257$	5.19615	+	9.00000i	0.324127	+	0.561405i	−0.657208	+	0.753709i	$0.728263\pi$
$258$		0			0
$259$	5.00000	+	1.73205i	0.310685	+	0.107624i
$260$		−	6.00000i		−	0.372104i
$261$		0			0
$262$	4.50000	−	2.59808i	0.278011	−	0.160510i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$	−13.5000	−	7.79423i	−0.829298	−	0.478796i
$266$	−8.66025	−	3.00000i	−0.530994	−	0.183942i
$267$		0			0
$268$	−2.00000			−0.122169
$269$	14.7224	+	25.5000i	0.897643	+	1.55476i	0.830500	+	0.557019i	$0.188055\pi$
$269$	14.7224	+	25.5000i	0.897643	+	1.55476i	0.0671428	+	0.997743i	$0.478612\pi$
$270$		0			0
$271$	4.50000	+	2.59808i	0.273356	+	0.157822i	0.630412	−	0.776261i	$-0.282886\pi$
$271$	4.50000	+	2.59808i	0.273356	+	0.157822i	−0.357056	+	0.934083i	$0.616219\pi$
$272$	−1.73205	−	3.00000i	−0.105021	−	0.181902i
$273$		0			0
$274$	9.00000	−	15.5885i	0.543710	−	0.941733i
$275$	5.19615	−	3.00000i	0.313340	−	0.180907i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−8.66025	+	15.0000i	−0.519408	+	0.899640i
$279$		0			0
$280$	3.00000	+	3.46410i	0.179284	+	0.207020i
$281$	25.9808	−	15.0000i	1.54988	−	0.894825i	0.551733	−	0.834021i	$-0.313967\pi$
$281$	25.9808	−	15.0000i	1.54988	−	0.894825i	0.998150	−	0.0608039i	$-0.0193664\pi$
$282$		0			0
$283$			27.7128i			1.64736i	0.567058	+	0.823678i	$0.308082\pi$
$283$			27.7128i			1.64736i	−0.567058	+	0.823678i	$0.691918\pi$
$284$			12.0000i			0.712069i
$285$		0			0
$286$	−9.00000	+	5.19615i	−0.532181	+	0.307255i
$287$	−17.3205	−	6.00000i	−1.02240	−	0.354169i
$288$		0			0
$289$	2.50000	−	4.33013i	0.147059	−	0.254713i
$290$	−2.59808	+	4.50000i	−0.152564	+	0.264249i
$291$		0			0
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	9.52628	−	16.5000i	0.556531	−	0.963940i	−0.441251	−	0.897384i	$-0.645465\pi$
$293$	9.52628	−	16.5000i	0.556531	−	0.963940i	0.997783	−	0.0665568i	$-0.0212014\pi$
$294$		0			0
$295$	1.50000	+	2.59808i	0.0873334	+	0.151266i
$296$	−1.73205	−	1.00000i	−0.100673	−	0.0581238i
$297$		0			0
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	−20.7846			−1.20201
$300$		0			0
$301$	−16.0000	+	13.8564i	−0.922225	+	0.798670i
$302$	−6.06218	−	3.50000i	−0.348839	−	0.201402i
$303$		0			0
$304$	3.00000	+	1.73205i	0.172062	+	0.0993399i
$305$		0			0
$306$		0			0
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$	2.59808	−	7.50000i	0.148039	−	0.427352i
$309$		0			0
$310$	1.50000	+	2.59808i	0.0851943	+	0.147561i
$311$	13.8564			0.785725			0.392862	−	0.919597i	$-0.371485\pi$
$311$	13.8564			0.785725			0.392862	+	0.919597i	$0.371485\pi$
$312$		0			0
$313$		−	1.73205i		−	0.0979013i	−0.998801	−	0.0489506i	$-0.984412\pi$
$313$		−	1.73205i		−	0.0979013i	0.998801	−	0.0489506i	$-0.0155877\pi$
$314$	20.7846			1.17294
$315$		0			0
$316$	1.00000			0.0562544
$317$		−	15.0000i		−	0.842484i	−0.906948	−	0.421242i	$-0.861594\pi$
$317$		−	15.0000i		−	0.842484i	0.906948	−	0.421242i	$-0.138406\pi$
$318$		0			0
$319$	9.00000			0.503903
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$		0			0
$322$	12.0000	−	10.3923i	0.668734	−	0.579141i
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$	6.00000	−	3.46410i	0.332820	−	0.192154i
$326$	−12.1244	−	7.00000i	−0.671506	−	0.387694i
$327$		0			0
$328$	6.00000	+	3.46410i	0.331295	+	0.191273i
$329$	−3.46410	−	18.0000i	−0.190982	−	0.992372i
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	−4.33013	−	7.50000i	−0.237647	−	0.411616i
$333$		0			0
$334$	15.0000	+	8.66025i	0.820763	+	0.473868i
$335$	1.73205	+	3.00000i	0.0946320	+	0.163908i
$336$		0			0
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$	0.866025	−	0.500000i	0.0471056	−	0.0271964i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	2.59808	−	4.50000i	0.140694	−	0.243689i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	6.92820	−	4.00000i	0.373544	−	0.215666i
$345$		0			0
$346$		0			0
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$		0			0
$349$	−9.00000	+	5.19615i	−0.481759	+	0.278144i	−0.721149	−	0.692780i	$-0.756386\pi$
$349$	−9.00000	+	5.19615i	−0.481759	+	0.278144i	0.239390	+	0.970923i	$0.423052\pi$
$350$	−1.73205	+	5.00000i	−0.0925820	+	0.267261i
$351$		0			0
$352$	−1.50000	+	2.59808i	−0.0799503	+	0.138478i
$353$	−17.3205	+	30.0000i	−0.921878	+	1.59674i	−0.125370	+	0.992110i	$0.540012\pi$
$353$	−17.3205	+	30.0000i	−0.921878	+	1.59674i	−0.796507	+	0.604629i	$0.793321\pi$
$354$		0			0
$355$	18.0000	−	10.3923i	0.955341	−	0.551566i
$356$	5.19615	−	9.00000i	0.275396	−	0.476999i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−5.19615	−	3.00000i	−0.274242	−	0.158334i	0.356572	−	0.934268i	$-0.383946\pi$
$359$	−5.19615	−	3.00000i	−0.274242	−	0.158334i	−0.630814	+	0.775934i	$0.717279\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$	6.92820			0.364138
$363$		0			0
$364$	3.00000	−	8.66025i	0.157243	−	0.453921i
$365$	10.3923	+	6.00000i	0.543958	+	0.314054i
$366$		0			0
$367$	19.5000	+	11.2583i	1.01789	+	0.587680i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	19.5000	+	11.2583i	1.01789	+	0.587680i	0.104399	+	0.994535i	$0.466708\pi$
$368$	−5.19615	+	3.00000i	−0.270868	+	0.156386i
$369$		0			0
$370$			3.46410i			0.180090i
$371$	−15.5885	−	18.0000i	−0.809312	−	0.934513i
$372$		0			0
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$	10.3923			0.537373
$375$		0			0
$376$			6.92820i			0.357295i
$377$	10.3923			0.535231
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		−	6.00000i		−	0.307794i
$381$		0			0
$382$		0			0
$383$	1.73205	+	3.00000i	0.0885037	+	0.153293i	0.906879	−	0.421392i	$-0.138458\pi$
$383$	1.73205	+	3.00000i	0.0885037	+	0.153293i	−0.818375	+	0.574684i	$0.805125\pi$
$384$		0			0
$385$	−13.5000	+	2.59808i	−0.688024	+	0.132410i
$386$		−	23.0000i		−	1.17067i
$387$		0			0
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$	15.5885	+	9.00000i	0.790366	+	0.456318i	0.840091	−	0.542445i	$-0.182501\pi$
$389$	15.5885	+	9.00000i	0.790366	+	0.456318i	−0.0497253	+	0.998763i	$0.515835\pi$
$390$		0			0
$391$	18.0000	+	10.3923i	0.910299	+	0.525561i
$392$	2.59808	+	6.50000i	0.131223	+	0.328300i
$393$		0			0
$394$	18.0000			0.906827
$395$	−0.866025	−	1.50000i	−0.0435745	−	0.0754732i
$396$		0			0
$397$	−24.0000	−	13.8564i	−1.20453	−	0.695433i	−0.242967	−	0.970034i	$-0.578121\pi$
$397$	−24.0000	−	13.8564i	−1.20453	−	0.695433i	−0.961558	+	0.274601i	$0.911454\pi$
$398$	5.19615	+	9.00000i	0.260460	+	0.451129i
$399$		0			0
$400$	1.00000	−	1.73205i	0.0500000	−	0.0866025i
$401$	−10.3923	+	6.00000i	−0.518967	+	0.299626i	−0.736512	−	0.676425i	$-0.763528\pi$
$401$	−10.3923	+	6.00000i	−0.518967	+	0.299626i	0.217545	+	0.976050i	$0.430195\pi$
$402$		0			0
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$		0			0
$405$		0			0
$406$	−6.00000	+	5.19615i	−0.297775	+	0.257881i
$407$	5.19615	−	3.00000i	0.257564	−	0.148704i
$408$		0			0
$409$			8.66025i			0.428222i	0.976809	+	0.214111i	$0.0686854\pi$
$409$			8.66025i			0.428222i	−0.976809	+	0.214111i	$0.931315\pi$
$410$		−	12.0000i		−	0.592638i
$411$		0			0
$412$	−3.00000	+	1.73205i	−0.147799	+	0.0853320i
$413$	0.866025	+	4.50000i	0.0426143	+	0.221431i
$414$		0			0
$415$	−7.50000	+	12.9904i	−0.368161	+	0.637673i
$416$	−1.73205	+	3.00000i	−0.0849208	+	0.147087i
$417$		0			0
$418$	−9.00000	+	5.19615i	−0.440204	+	0.254152i
$419$	−12.1244	+	21.0000i	−0.592314	+	1.02592i	0.401606	+	0.915812i	$0.368452\pi$
$419$	−12.1244	+	21.0000i	−0.592314	+	1.02592i	−0.993920	+	0.110105i	$0.964881\pi$
$420$		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	$-0.451342\pi$
$422$	−3.46410	−	2.00000i	−0.168630	−	0.0973585i
$423$		0			0
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−6.92820			−0.336067
$426$		0			0
$427$		0			0
$428$	−2.59808	−	1.50000i	−0.125583	−	0.0725052i
$429$		0			0
$430$	−12.0000	−	6.92820i	−0.578691	−	0.334108i
$431$	−20.7846	+	12.0000i	−1.00116	+	0.578020i	−0.908591	−	0.417687i	$-0.862841\pi$
$431$	−20.7846	+	12.0000i	−1.00116	+	0.578020i	−0.0925683	+	0.995706i	$0.529508\pi$
$432$		0			0
$433$		−	34.6410i		−	1.66474i	−0.554220	−	0.832370i	$-0.686983\pi$
$433$		−	34.6410i		−	1.66474i	0.554220	−	0.832370i	$-0.313017\pi$
$434$	0.866025	+	4.50000i	0.0415705	+	0.216007i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−20.7846			−0.994263
$438$		0			0
$439$		−	36.3731i		−	1.73599i	−0.496571	−	0.867996i	$-0.665408\pi$
$439$		−	36.3731i		−	1.73599i	0.496571	−	0.867996i	$-0.334592\pi$
$440$	5.19615			0.247717
$441$		0			0
$442$	12.0000			0.570782
$443$			9.00000i			0.427603i	0.976877	+	0.213801i	$0.0685846\pi$
$443$			9.00000i			0.427603i	−0.976877	+	0.213801i	$0.931415\pi$
$444$		0			0
$445$	−18.0000			−0.853282
$446$	12.9904	+	22.5000i	0.615112	+	1.06541i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$		−	30.0000i		−	1.41579i	−0.706319	−	0.707894i	$-0.749646\pi$
$449$		−	30.0000i		−	1.41579i	0.706319	−	0.707894i	$-0.250354\pi$
$450$		0			0
$451$	−18.0000	+	10.3923i	−0.847587	+	0.489355i
$452$	10.3923	+	6.00000i	0.488813	+	0.282216i
$453$		0			0
$454$	4.50000	+	2.59808i	0.211195	+	0.121934i
$455$	−15.5885	+	3.00000i	−0.730798	+	0.140642i
$456$		0			0
$457$	−5.00000			−0.233890			−0.116945	−	0.993138i	$-0.537310\pi$
$457$	−5.00000			−0.233890			−0.116945	+	0.993138i	$0.537310\pi$
$458$	6.92820	+	12.0000i	0.323734	+	0.560723i
$459$		0			0
$460$	9.00000	+	5.19615i	0.419627	+	0.242272i
$461$	6.92820	+	12.0000i	0.322679	+	0.558896i	0.981040	−	0.193806i	$-0.0620834\pi$
$461$	6.92820	+	12.0000i	0.322679	+	0.558896i	−0.658361	+	0.752702i	$0.728750\pi$
$462$		0			0
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	−0.815802	−	0.578331i	$-0.803704\pi$
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	0.908750	+	0.417340i	$0.137038\pi$
$464$	2.59808	−	1.50000i	0.120613	−	0.0696358i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	−15.5885	+	27.0000i	−0.721348	+	1.24941i	0.239112	+	0.970992i	$0.423144\pi$
$467$	−15.5885	+	27.0000i	−0.721348	+	1.24941i	−0.960460	+	0.278419i	$0.910190\pi$
$468$		0			0
$469$	1.00000	+	5.19615i	0.0461757	+	0.239936i
$470$	10.3923	−	6.00000i	0.479361	−	0.276759i
$471$		0			0
$472$		−	1.73205i		−	0.0797241i
$473$			24.0000i			1.10352i
$474$		0			0
$475$	6.00000	−	3.46410i	0.275299	−	0.158944i
$476$	−6.92820	+	6.00000i	−0.317554	+	0.275010i
$477$		0			0
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	−0.934248	−	0.356624i	$-0.883928\pi$
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	0.775969	+	0.630771i	$0.217261\pi$
$480$		0			0
$481$	6.00000	−	3.46410i	0.273576	−	0.157949i
$482$	−12.9904	+	22.5000i	−0.591696	+	1.02485i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−7.79423	−	4.50000i	−0.353918	−	0.204334i
$486$		0			0
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$		0			0
$489$		0			0
$490$	7.50000	−	9.52628i	0.338815	−	0.430353i
$491$	−28.5788	−	16.5000i	−1.28974	−	0.744635i	−0.311136	−	0.950365i	$-0.600710\pi$
$491$	−28.5788	−	16.5000i	−1.28974	−	0.744635i	−0.978609	+	0.205731i	$0.934043\pi$
$492$		0			0
$493$	−9.00000	−	5.19615i	−0.405340	−	0.234023i
$494$	−10.3923	+	6.00000i	−0.467572	+	0.269953i
$495$		0			0
$496$		−	1.73205i		−	0.0777714i
$497$	31.1769	−	6.00000i	1.39848	−	0.269137i
$498$		0			0
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$	−12.1244			−0.542218
$501$		0			0
$502$			19.0526i			0.850357i
$503$	38.1051			1.69902			0.849512	−	0.527570i	$-0.176897\pi$
$503$	38.1051			1.69902			0.849512	+	0.527570i	$0.176897\pi$
$504$		0			0
$505$		0			0
$506$		−	18.0000i		−	0.800198i
$507$		0			0
$508$	−11.0000			−0.488046
$509$	9.52628	+	16.5000i	0.422245	+	0.731350i	0.996159	−	0.0875661i	$-0.0279089\pi$
$509$	9.52628	+	16.5000i	0.422245	+	0.731350i	−0.573914	+	0.818916i	$0.694576\pi$
$510$		0			0
$511$	12.0000	+	13.8564i	0.530849	+	0.612971i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−9.00000	+	5.19615i	−0.396973	+	0.229192i
$515$	5.19615	+	3.00000i	0.228970	+	0.132196i
$516$		0			0
$517$	−18.0000	−	10.3923i	−0.791639	−	0.457053i
$518$	−1.73205	+	5.00000i	−0.0761019	+	0.219687i
$519$		0			0
$520$	6.00000			0.263117
$521$	−13.8564	−	24.0000i	−0.607060	−	1.05146i	−0.991722	−	0.128402i	$-0.959015\pi$
$521$	−13.8564	−	24.0000i	−0.607060	−	1.05146i	0.384662	−	0.923057i	$-0.374318\pi$
$522$		0			0
$523$	−33.0000	−	19.0526i	−1.44299	−	0.833110i	−0.444941	−	0.895560i	$-0.646775\pi$
$523$	−33.0000	−	19.0526i	−1.44299	−	0.833110i	−0.998048	+	0.0624496i	$0.980109\pi$
$524$	2.59808	+	4.50000i	0.113497	+	0.196583i
$525$		0			0
$526$		0			0
$527$	−5.19615	+	3.00000i	−0.226348	+	0.130682i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	7.79423	−	13.5000i	0.338560	−	0.586403i
$531$		0			0
$532$	3.00000	−	8.66025i	0.130066	−	0.375470i
$533$	−20.7846	+	12.0000i	−0.900281	+	0.519778i
$534$		0			0
$535$			5.19615i			0.224649i
$536$		−	2.00000i		−	0.0863868i
$537$		0			0
$538$	−25.5000	+	14.7224i	−1.09938	+	0.634729i
$539$	−20.7846	−	3.00000i	−0.895257	−	0.129219i
$540$		0			0
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$	−2.59808	+	4.50000i	−0.111597	+	0.193292i
$543$		0			0
$544$	3.00000	−	1.73205i	0.128624	−	0.0742611i
$545$	−1.73205	+	3.00000i	−0.0741929	+	0.128506i
$546$		0			0
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	0.843855	−	0.536571i	$-0.180281\pi$
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	−0.886612	+	0.462514i	$0.846947\pi$
$548$	15.5885	+	9.00000i	0.665906	+	0.384461i
$549$		0			0
$550$	3.00000	+	5.19615i	0.127920	+	0.221565i
$551$	10.3923			0.442727
$552$		0			0
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$	−6.92820	−	4.00000i	−0.294351	−	0.169944i
$555$		0			0
$556$	−15.0000	−	8.66025i	−0.636142	−	0.367277i
$557$	−2.59808	+	1.50000i	−0.110084	+	0.0635570i	−0.554031	−	0.832496i	$-0.686911\pi$
$557$	−2.59808	+	1.50000i	−0.110084	+	0.0635570i	0.443947	+	0.896053i	$0.353578\pi$
$558$		0			0
$559$			27.7128i			1.17213i
$560$	−3.46410	+	3.00000i	−0.146385	+	0.126773i
$561$		0			0
$562$	15.0000	+	25.9808i	0.632737	+	1.09593i
$563$	25.9808			1.09496			0.547479	−	0.836819i	$-0.315587\pi$
$563$	25.9808			1.09496			0.547479	+	0.836819i	$0.315587\pi$
$564$		0			0
$565$		−	20.7846i		−	0.874415i
$566$	−27.7128			−1.16486
$567$		0			0
$568$	−12.0000			−0.503509
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	−5.19615	−	9.00000i	−0.217262	−	0.376309i
$573$		0			0
$574$	6.00000	−	17.3205i	0.250435	−	0.722944i
$575$			12.0000i			0.500435i
$576$		0			0
$577$	−1.50000	+	0.866025i	−0.0624458	+	0.0360531i	−0.530898	−	0.847436i	$-0.678145\pi$
$577$	−1.50000	+	0.866025i	−0.0624458	+	0.0360531i	0.468452	+	0.883489i	$0.344812\pi$
$578$	4.33013	+	2.50000i	0.180110	+	0.103986i
$579$		0			0
$580$	−4.50000	−	2.59808i	−0.186852	−	0.107879i
$581$	−17.3205	+	15.0000i	−0.718576	+	0.622305i
$582$		0			0
$583$	−27.0000			−1.11823
$584$	−3.46410	−	6.00000i	−0.143346	−	0.248282i
$585$		0			0
$586$	16.5000	+	9.52628i	0.681609	+	0.393527i
$587$	7.79423	+	13.5000i	0.321702	+	0.557205i	0.980839	−	0.194818i	$-0.0624117\pi$
$587$	7.79423	+	13.5000i	0.321702	+	0.557205i	−0.659137	+	0.752023i	$0.729078\pi$
$588$		0			0
$589$	3.00000	−	5.19615i	0.123613	−	0.214104i
$590$	−2.59808	+	1.50000i	−0.106961	+	0.0617540i
$591$		0			0
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−19.0526	+	33.0000i	−0.782395	+	1.35515i	0.148148	+	0.988965i	$0.452669\pi$
$593$	−19.0526	+	33.0000i	−0.782395	+	1.35515i	−0.930543	+	0.366182i	$0.880665\pi$
$594$		0			0
$595$	15.0000	+	5.19615i	0.614940	+	0.213021i
$596$	−15.5885	+	9.00000i	−0.638528	+	0.368654i
$597$		0			0
$598$		−	20.7846i		−	0.849946i
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$		0			0
$601$	25.5000	−	14.7224i	1.04017	−	0.600541i	0.120286	−	0.992739i	$-0.461619\pi$
$601$	25.5000	−	14.7224i	1.04017	−	0.600541i	0.919881	+	0.392199i	$0.128285\pi$
$602$	−13.8564	−	16.0000i	−0.564745	−	0.652111i
$603$		0			0
$604$	3.50000	−	6.06218i	0.142413	−	0.246667i
$605$	1.73205	−	3.00000i	0.0704179	−	0.121967i
$606$		0			0
$607$	−19.5000	+	11.2583i	−0.791481	+	0.456962i	−0.840484	−	0.541837i	$-0.817729\pi$
$607$	−19.5000	+	11.2583i	−0.791481	+	0.456962i	0.0490029	+	0.998799i	$0.484396\pi$
$608$	−1.73205	+	3.00000i	−0.0702439	+	0.121666i
$609$		0			0
$610$		0			0
$611$	−20.7846	−	12.0000i	−0.840855	−	0.485468i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−24.2487			−0.978598
$615$		0			0
$616$	7.50000	+	2.59808i	0.302184	+	0.104679i
$617$	10.3923	+	6.00000i	0.418378	+	0.241551i	0.694383	−	0.719605i	$-0.255677\pi$
$617$	10.3923	+	6.00000i	0.418378	+	0.241551i	−0.276005	+	0.961156i	$0.589011\pi$
$618$		0			0
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	0.374550	−	0.927207i	$-0.377797\pi$
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	−0.615710	+	0.787973i	$0.711131\pi$
$620$	−2.59808	+	1.50000i	−0.104341	+	0.0602414i
$621$		0			0
$622$			13.8564i			0.555591i
$623$	−25.9808	−	9.00000i	−1.04090	−	0.360577i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	1.73205			0.0692267
$627$		0			0
$628$			20.7846i			0.829396i
$629$	−6.92820			−0.276246
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$			1.00000i			0.0397779i
$633$		0			0
$634$	15.0000			0.595726
$635$	9.52628	+	16.5000i	0.378039	+	0.654783i
$636$		0			0
$637$	−24.0000	−	3.46410i	−0.950915	−	0.137253i
$638$			9.00000i			0.356313i
$639$		0			0
$640$	1.50000	−	0.866025i	0.0592927	−	0.0342327i
$641$	−20.7846	−	12.0000i	−0.820943	−	0.473972i	0.0297987	−	0.999556i	$-0.490513\pi$
$641$	−20.7846	−	12.0000i	−0.820943	−	0.473972i	−0.850741	+	0.525584i	$0.823847\pi$
$642$		0			0
$643$	−15.0000	−	8.66025i	−0.591542	−	0.341527i	0.174165	−	0.984717i	$-0.444277\pi$
$643$	−15.0000	−	8.66025i	−0.591542	−	0.341527i	−0.765707	+	0.643189i	$0.777611\pi$
$644$	10.3923	+	12.0000i	0.409514	+	0.472866i
$645$		0			0
$646$	12.0000			0.472134
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$		0			0
$649$	4.50000	+	2.59808i	0.176640	+	0.101983i
$650$	3.46410	+	6.00000i	0.135873	+	0.235339i
$651$		0			0
$652$	7.00000	−	12.1244i	0.274141	−	0.474826i
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	−0.549973	−	0.835182i	$-0.685362\pi$
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	0.448303	+	0.893882i	$0.352029\pi$
$654$		0			0
$655$	4.50000	−	7.79423i	0.175830	−	0.304546i
$656$	−3.46410	+	6.00000i	−0.135250	+	0.234261i
$657$		0			0
$658$	18.0000	−	3.46410i	0.701713	−	0.135045i
$659$	10.3923	−	6.00000i	0.404827	−	0.233727i	−0.283738	−	0.958902i	$-0.591575\pi$
$659$	10.3923	−	6.00000i	0.404827	−	0.233727i	0.688565	+	0.725175i	$0.258241\pi$
$660$		0			0
$661$		−	6.92820i		−	0.269476i	−0.990881	−	0.134738i	$-0.956981\pi$
$661$		−	6.92820i		−	0.269476i	0.990881	−	0.134738i	$-0.0430193\pi$
$662$		−	8.00000i		−	0.310929i
$663$		0			0
$664$	7.50000	−	4.33013i	0.291056	−	0.168042i
$665$	−15.5885	+	3.00000i	−0.604494	+	0.116335i
$666$		0			0
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	−8.66025	+	15.0000i	−0.335075	+	0.580367i
$669$		0			0
$670$	−3.00000	+	1.73205i	−0.115900	+	0.0669150i
$671$		0			0
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$	−11.2583	−	6.50000i	−0.433655	−	0.250371i
$675$		0			0
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	5.19615			0.199704			0.0998522	−	0.995002i	$-0.468163\pi$
$677$	5.19615			0.199704			0.0998522	+	0.995002i	$0.468163\pi$
$678$		0			0
$679$	−9.00000	−	10.3923i	−0.345388	−	0.398820i
$680$	−5.19615	−	3.00000i	−0.199263	−	0.115045i
$681$		0			0
$682$	4.50000	+	2.59808i	0.172314	+	0.0994855i
$683$	−18.1865	+	10.5000i	−0.695888	+	0.401771i	−0.805814	−	0.592168i	$-0.798272\pi$
$683$	−18.1865	+	10.5000i	−0.695888	+	0.401771i	0.109926	+	0.993940i	$0.464939\pi$
$684$		0			0
$685$		−	31.1769i		−	1.19121i
$686$	15.5885	−	10.0000i	0.595170	−	0.381802i
$687$		0			0
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	−31.1769			−1.18775
$690$		0			0
$691$			6.92820i			0.263561i	0.991279	+	0.131781i	$0.0420694\pi$
$691$			6.92820i			0.263561i	−0.991279	+	0.131781i	$0.957931\pi$
$692$		0			0
$693$		0			0
$694$	12.0000			0.455514
$695$			30.0000i			1.13796i
$696$		0			0
$697$	24.0000			0.909065
$698$	−5.19615	−	9.00000i	−0.196677	−	0.340655i
$699$		0			0
$700$	−5.00000	−	1.73205i	−0.188982	−	0.0654654i
$701$		−	3.00000i		−	0.113308i	−0.998394	−	0.0566542i	$-0.981957\pi$
$701$		−	3.00000i		−	0.113308i	0.998394	−	0.0566542i	$-0.0180433\pi$
$702$		0			0
$703$	6.00000	−	3.46410i	0.226294	−	0.130651i
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	−30.0000	−	17.3205i	−1.12906	−	0.651866i
$707$		0			0
$708$		0			0
$709$	−38.0000			−1.42712			−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000			−1.42712			−0.713560	+	0.700594i	$0.752918\pi$
$710$	10.3923	+	18.0000i	0.390016	+	0.675528i
$711$		0			0
$712$	9.00000	+	5.19615i	0.337289	+	0.194734i
$713$	5.19615	+	9.00000i	0.194597	+	0.337053i
$714$		0			0
$715$	−9.00000	+	15.5885i	−0.336581	+	0.582975i
$716$	−10.3923	+	6.00000i	−0.388379	+	0.224231i
$717$		0			0
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$	22.5167	−	39.0000i	0.839730	−	1.45445i	−0.0503909	−	0.998730i	$-0.516047\pi$
$719$	22.5167	−	39.0000i	0.839730	−	1.45445i	0.890121	−	0.455725i	$-0.150620\pi$
$720$		0			0
$721$	6.00000	+	6.92820i	0.223452	+	0.258020i
$722$	6.06218	−	3.50000i	0.225611	−	0.130257i
$723$		0			0
$724$			6.92820i			0.257485i
$725$		−	6.00000i		−	0.222834i
$726$		0			0
$727$	−25.5000	+	14.7224i	−0.945743	+	0.546025i	−0.891756	−	0.452517i	$-0.850526\pi$
$727$	−25.5000	+	14.7224i	−0.945743	+	0.546025i	−0.0539868	+	0.998542i	$0.517193\pi$
$728$	8.66025	+	3.00000i	0.320970	+	0.111187i
$729$		0			0
$730$	−6.00000	+	10.3923i	−0.222070	+	0.384636i
$731$	13.8564	−	24.0000i	0.512498	−	0.887672i
$732$		0			0
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.938330	−	0.345740i	$-0.887628\pi$
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.169745	+	0.985488i	$0.554294\pi$
$734$	−11.2583	+	19.5000i	−0.415553	+	0.719758i
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	5.19615	+	3.00000i	0.191403	+	0.110506i
$738$		0			0
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	0.943215	−	0.332184i	$-0.107785\pi$
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	−0.759287	+	0.650756i	$0.774452\pi$
$740$	−3.46410			−0.127343
$741$		0			0
$742$	18.0000	−	15.5885i	0.660801	−	0.572270i
$743$	15.5885	+	9.00000i	0.571885	+	0.330178i	0.757902	−	0.652369i	$-0.226225\pi$
$743$	15.5885	+	9.00000i	0.571885	+	0.330178i	−0.186017	+	0.982547i	$0.559558\pi$
$744$		0			0
$745$	27.0000	+	15.5885i	0.989203	+	0.571117i
$746$	27.7128	−	16.0000i	1.01464	−	0.585802i
$747$		0			0
$748$			10.3923i			0.379980i
$749$	−2.59808	+	7.50000i	−0.0949316	+	0.274044i
$750$		0			0
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	0.948753	−	0.316017i	$-0.102346\pi$
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	−0.748056	+	0.663636i	$0.769012\pi$
$752$	−6.92820			−0.252646
$753$		0			0
$754$			10.3923i			0.378465i
$755$	−12.1244			−0.441250
$756$		0			0
$757$	4.00000			0.145382			0.0726912	−	0.997354i	$-0.476841\pi$
$757$	4.00000			0.145382			0.0726912	+	0.997354i	$0.476841\pi$
$758$			16.0000i			0.581146i
$759$		0			0
$760$	6.00000			0.217643
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	0.665276	−	0.746597i	$-0.268314\pi$
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	−0.979210	+	0.202848i	$0.934980\pi$
$762$		0			0
$763$	−4.00000	+	3.46410i	−0.144810	+	0.125409i
$764$		0			0
$765$		0			0
$766$	−3.00000	+	1.73205i	−0.108394	+	0.0625815i
$767$	5.19615	+	3.00000i	0.187622	+	0.108324i
$768$		0			0
$769$	16.5000	+	9.52628i	0.595005	+	0.343526i	0.767074	−	0.641558i	$-0.221712\pi$
$769$	16.5000	+	9.52628i	0.595005	+	0.343526i	−0.172069	+	0.985085i	$0.555045\pi$
$770$	−2.59808	−	13.5000i	−0.0936282	−	0.486506i
$771$		0			0
$772$	23.0000			0.827788
$773$	13.8564	+	24.0000i	0.498380	+	0.863220i	0.999998	−	0.00186926i	$-0.000595004\pi$
$773$	13.8564	+	24.0000i	0.498380	+	0.863220i	−0.501618	+	0.865089i	$0.667262\pi$
$774$		0			0
$775$	−3.00000	−	1.73205i	−0.107763	−	0.0622171i
$776$	2.59808	+	4.50000i	0.0932655	+	0.161541i
$777$		0			0
$778$	−9.00000	+	15.5885i	−0.322666	+	0.558873i
$779$	−20.7846	+	12.0000i	−0.744686	+	0.429945i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	−10.3923	+	18.0000i	−0.371628	+	0.643679i
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	31.1769	−	18.0000i	1.11275	−	0.642448i
$786$		0			0
$787$			41.5692i			1.48178i	0.671625	+	0.740891i	$0.265597\pi$
$787$			41.5692i			1.48178i	−0.671625	+	0.740891i	$0.734403\pi$
$788$			18.0000i			0.641223i
$789$		0			0
$790$	1.50000	−	0.866025i	0.0533676	−	0.0308118i
$791$	10.3923	−	30.0000i	0.369508	−	1.06668i
$792$		0			0
$793$		0			0
$794$	13.8564	−	24.0000i	0.491745	−	0.851728i
$795$		0			0
$796$	−9.00000	+	5.19615i	−0.318997	+	0.184173i
$797$	12.9904	−	22.5000i	0.460143	−	0.796991i	−0.538825	−	0.842418i	$-0.681132\pi$
$797$	12.9904	−	22.5000i	0.460143	−	0.796991i	0.998968	+	0.0454270i	$0.0144648\pi$
$798$		0			0
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$	1.73205	+	1.00000i	0.0612372	+	0.0353553i
$801$		0			0
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	20.7846			0.733473
$804$		0			0
$805$	9.00000	−	25.9808i	0.317208	−	0.915702i
$806$	5.19615	+	3.00000i	0.183027	+	0.105670i
$807$		0			0
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	−5.19615	−	6.00000i	−0.182349	−	0.210559i
$813$		0			0
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$	−24.2487			−0.849395
$816$		0			0
$817$			27.7128i			0.969549i
$818$	−8.66025			−0.302799
$819$		0			0
$820$	12.0000			0.419058
$821$			3.00000i			0.104701i	0.998629	+	0.0523504i	$0.0166713\pi$
$821$			3.00000i			0.104701i	−0.998629	+	0.0523504i	$0.983329\pi$
$822$		0			0
$823$	8.00000			0.278862			0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000			0.278862			0.139431	+	0.990232i	$0.455473\pi$
$824$	−1.73205	−	3.00000i	−0.0603388	−	0.104510i
$825$		0			0
$826$	−4.50000	+	0.866025i	−0.156575	+	0.0301329i
$827$		−	9.00000i		−	0.312961i	−0.987681	−	0.156480i	$-0.949985\pi$
$827$		−	9.00000i		−	0.312961i	0.987681	−	0.156480i	$-0.0500148\pi$
$828$		0			0
$829$	−15.0000	+	8.66025i	−0.520972	+	0.300783i	−0.737332	−	0.675530i	$-0.763915\pi$
$829$	−15.0000	+	8.66025i	−0.520972	+	0.300783i	0.216361	+	0.976314i	$0.430581\pi$
$830$	−12.9904	−	7.50000i	−0.450903	−	0.260329i
$831$		0			0
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$	19.0526	+	15.0000i	0.660132	+	0.519719i
$834$		0			0
$835$	30.0000			1.03819
$836$	−5.19615	−	9.00000i	−0.179713	−	0.311272i
$837$		0			0
$838$	−21.0000	−	12.1244i	−0.725433	−	0.418829i
$839$	−1.73205	−	3.00000i	−0.0597970	−	0.103572i	0.834577	−	0.550891i	$-0.185712\pi$
$839$	−1.73205	−	3.00000i	−0.0597970	−	0.103572i	−0.894374	+	0.447320i	$0.852379\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	27.7128	−	16.0000i	0.955047	−	0.551396i
$843$		0			0
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	0.866025	−	1.50000i	0.0297922	−	0.0516016i
$846$		0			0
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$	−7.79423	+	4.50000i	−0.267655	+	0.154531i
$849$		0			0
$850$		−	6.92820i		−	0.237635i
$851$			12.0000i			0.411355i
$852$		0			0
$853$	21.0000	−	12.1244i	0.719026	−	0.415130i	−0.0953679	−	0.995442i	$-0.530403\pi$
$853$	21.0000	−	12.1244i	0.719026	−	0.415130i	0.814394	+	0.580312i	$0.197069\pi$
$854$		0			0
$855$		0			0
$856$	1.50000	−	2.59808i	0.0512689	−	0.0888004i
$857$	−6.92820	+	12.0000i	−0.236663	+	0.409912i	−0.959755	−	0.280840i	$-0.909387\pi$
$857$	−6.92820	+	12.0000i	−0.236663	+	0.409912i	0.723092	+	0.690752i	$0.242720\pi$
$858$		0			0
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	−0.160437	−	0.987046i	$-0.551290\pi$
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	0.774589	+	0.632465i	$0.217957\pi$
$860$	6.92820	−	12.0000i	0.236250	−	0.409197i
$861$		0			0
$862$	−12.0000	−	20.7846i	−0.408722	−	0.707927i
$863$	46.7654	+	27.0000i	1.59191	+	0.919091i	0.992979	+	0.118291i	$0.0377417\pi$
$863$	46.7654	+	27.0000i	1.59191	+	0.919091i	0.598933	+	0.800799i	$0.295592\pi$
$864$		0			0
$865$		0			0
$866$	34.6410			1.17715
$867$		0			0
$868$	−4.50000	+	0.866025i	−0.152740	+	0.0293948i
$869$	−2.59808	−	1.50000i	−0.0881337	−	0.0508840i
$870$		0			0
$871$	6.00000	+	3.46410i	0.203302	+	0.117377i
$872$	1.73205	−	1.00000i	0.0586546	−	0.0338643i
$873$		0			0
$874$		−	20.7846i		−	0.703050i
$875$	6.06218	+	31.5000i	0.204939	+	1.06489i
$876$		0			0
$877$	−22.0000	−	38.1051i	−0.742887	−	1.28672i	−0.951175	−	0.308651i	$-0.900123\pi$
$877$	−22.0000	−	38.1051i	−0.742887	−	1.28672i	0.208288	−	0.978068i	$-0.433211\pi$
$878$	36.3731			1.22753
$879$		0			0
$880$			5.19615i			0.175162i
$881$	10.3923			0.350126			0.175063	−	0.984557i	$-0.443987\pi$
$881$	10.3923			0.350126			0.175063	+	0.984557i	$0.443987\pi$
$882$		0			0
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$			12.0000i			0.403604i
$885$		0			0
$886$	−9.00000			−0.302361
$887$	−12.1244	−	21.0000i	−0.407096	−	0.705111i	0.587467	−	0.809248i	$-0.300125\pi$
$887$	−12.1244	−	21.0000i	−0.407096	−	0.705111i	−0.994563	+	0.104137i	$0.966792\pi$
$888$		0			0
$889$	5.50000	+	28.5788i	0.184464	+	0.958503i
$890$		−	18.0000i		−	0.603361i
$891$		0			0
$892$	−22.5000	+	12.9904i	−0.753356	+	0.434950i
$893$	−20.7846	−	12.0000i	−0.695530	−	0.401565i
$894$		0			0
$895$	18.0000	+	10.3923i	0.601674	+	0.347376i
$896$	2.59808	−	0.500000i	0.0867956	−	0.0167038i
$897$		0			0
$898$	30.0000			1.00111
$899$	−2.59808	−	4.50000i	−0.0866507	−	0.150083i
$900$		0			0
$901$	27.0000	+	15.5885i	0.899500	+	0.519327i
$902$	−10.3923	−	18.0000i	−0.346026	−	0.599334i
$903$		0			0
$904$	−6.00000	+	10.3923i	−0.199557	+	0.345643i
$905$	10.3923	−	6.00000i	0.345452	−	0.199447i
$906$		0			0
$907$	13.0000	−	22.5167i	0.431658	−	0.747653i	−0.565358	−	0.824845i	$-0.691262\pi$
$907$	13.0000	−	22.5167i	0.431658	−	0.747653i	0.997016	+	0.0771920i	$0.0245954\pi$
$908$	−2.59808	+	4.50000i	−0.0862202	+	0.149338i
$909$		0			0
$910$	−3.00000	−	15.5885i	−0.0994490	−	0.516752i
$911$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$911$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$912$		0			0
$913$			25.9808i			0.859838i
$914$		−	5.00000i		−	0.165385i
$915$		0			0
$916$	−12.0000	+	6.92820i	−0.396491	+	0.228914i
$917$	10.3923	−	9.00000i	0.343184	−	0.297206i
$918$		0			0
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	−0.652616	−	0.757689i	$-0.726329\pi$
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	0.982486	+	0.186338i	$0.0596619\pi$
$920$	−5.19615	+	9.00000i	−0.171312	+	0.296721i
$921$		0			0
$922$	−12.0000	+	6.92820i	−0.395199	+	0.228168i
$923$	20.7846	−	36.0000i	0.684134	−	1.18495i
$924$		0			0
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$	3.46410	+	2.00000i	0.113837	+	0.0657241i
$927$		0			0
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	−48.4974			−1.59115			−0.795574	−	0.605856i	$-0.792831\pi$
$929$	−48.4974			−1.59115			−0.795574	+	0.605856i	$0.792831\pi$
$930$		0			0
$931$	−24.0000	−	3.46410i	−0.786568	−	0.113531i
$932$	−15.5885	−	9.00000i	−0.510617	−	0.294805i
$933$		0			0
$934$	−27.0000	−	15.5885i	−0.883467	−	0.510070i
$935$	15.5885	−	9.00000i	0.509797	−	0.294331i
$936$		0			0
$937$		−	22.5167i		−	0.735587i	−0.929907	−	0.367794i	$-0.880113\pi$
$937$		−	22.5167i		−	0.735587i	0.929907	−	0.367794i	$-0.119887\pi$
$938$	−5.19615	+	1.00000i	−0.169660	+	0.0326512i
$939$		0			0
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$	32.9090			1.07280			0.536401	−	0.843963i	$-0.319784\pi$
$941$	32.9090			1.07280			0.536401	+	0.843963i	$0.319784\pi$
$942$		0			0
$943$		−	41.5692i		−	1.35368i
$944$	1.73205			0.0563735
$945$		0			0
$946$	−24.0000			−0.780307
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$		0			0
$949$	24.0000			0.779073
$950$	3.46410	+	6.00000i	0.112390	+	0.194666i
$951$		0			0
$952$	−6.00000	−	6.92820i	−0.194461	−	0.224544i
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$		0			0
$955$		0			0
$956$	5.19615	+	3.00000i	0.168056	+	0.0970269i
$957$		0			0
$958$	−6.00000	−	3.46410i	−0.193851	−	0.111920i
$959$	15.5885	−	45.0000i	0.503378	−	1.45313i
$960$		0			0
$961$	28.0000			0.903226
$962$	3.46410	+	6.00000i	0.111687	+	0.193448i
$963$		0			0
$964$	−22.5000	−	12.9904i	−0.724676	−	0.418392i
$965$	−19.9186	−	34.5000i	−0.641202	−	1.11059i
$966$		0			0
$967$	3.50000	−	6.06218i	0.112552	−	0.194946i	−0.804246	−	0.594296i	$-0.797431\pi$
$967$	3.50000	−	6.06218i	0.112552	−	0.194946i	0.916799	+	0.399350i	$0.130764\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$		0			0
$970$	4.50000	−	7.79423i	0.144486	−	0.250258i
$971$	4.33013	−	7.50000i	0.138960	−	0.240686i	−0.788143	−	0.615492i	$-0.788957\pi$
$971$	4.33013	−	7.50000i	0.138960	−	0.240686i	0.927103	+	0.374806i	$0.122291\pi$
$972$		0			0
$973$	−15.0000	+	43.3013i	−0.480878	+	1.38817i
$974$	0.866025	−	0.500000i	0.0277492	−	0.0160210i
$975$		0			0
$976$		0			0
$977$		−	24.0000i		−	0.767828i	−0.923369	−	0.383914i	$-0.874576\pi$
$977$		−	24.0000i		−	0.767828i	0.923369	−	0.383914i	$-0.125424\pi$
$978$		0			0
$979$	−27.0000	+	15.5885i	−0.862924	+	0.498209i
$980$	9.52628	+	7.50000i	0.304306	+	0.239579i
$981$		0			0
$982$	16.5000	−	28.5788i	0.526536	−	0.911987i
$983$	6.92820	−	12.0000i	0.220975	−	0.382741i	−0.734129	−	0.679010i	$-0.762409\pi$
$983$	6.92820	−	12.0000i	0.220975	−	0.382741i	0.955104	+	0.296269i	$0.0957426\pi$
$984$		0			0
$985$	27.0000	−	15.5885i	0.860292	−	0.496690i
$986$	5.19615	−	9.00000i	0.165479	−	0.286618i
$987$		0			0
$988$	−6.00000	−	10.3923i	−0.190885	−	0.330623i
$989$	−41.5692	−	24.0000i	−1.32182	−	0.763156i
$990$		0			0
$991$	23.5000	+	40.7032i	0.746502	+	1.29298i	0.949490	+	0.313798i	$0.101602\pi$
$991$	23.5000	+	40.7032i	0.746502	+	1.29298i	−0.202988	+	0.979181i	$0.565065\pi$
$992$	1.73205			0.0549927
$993$		0			0
$994$	6.00000	+	31.1769i	0.190308	+	0.988872i
$995$	15.5885	+	9.00000i	0.494187	+	0.285319i
$996$		0			0
$997$	−15.0000	−	8.66025i	−0.475055	−	0.274273i	0.243299	−	0.969951i	$-0.421771\pi$
$997$	−15.0000	−	8.66025i	−0.475055	−	0.274273i	−0.718353	+	0.695678i	$0.755104\pi$
$998$	19.0526	−	11.0000i	0.603098	−	0.348199i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.l.c.215.2		4
3.2	odd	2	inner	1134.2.l.c.215.1		4
7.3	odd	6		1134.2.t.d.1025.1		4
9.2	odd	6		1134.2.t.d.593.1		4
9.4	even	3		42.2.f.a.5.1	✓	4
9.5	odd	6		42.2.f.a.5.2	yes	4
9.7	even	3		1134.2.t.d.593.2		4
21.17	even	6		1134.2.t.d.1025.2		4
36.23	even	6		336.2.bc.e.257.2		4
36.31	odd	6		336.2.bc.e.257.1		4
45.4	even	6		1050.2.s.b.551.2		4
45.13	odd	12		1050.2.u.a.299.1		4
45.14	odd	6		1050.2.s.b.551.1		4
45.22	odd	12		1050.2.u.d.299.2		4
45.23	even	12		1050.2.u.d.299.1		4
45.32	even	12		1050.2.u.a.299.2		4
63.4	even	3		294.2.f.a.227.2		4
63.5	even	6		294.2.d.a.293.1		4
63.13	odd	6		294.2.f.a.215.1		4
63.23	odd	6		294.2.d.a.293.2		4
63.31	odd	6		42.2.f.a.17.2	yes	4
63.32	odd	6		294.2.f.a.227.1		4
63.38	even	6	inner	1134.2.l.c.269.1		4
63.40	odd	6		294.2.d.a.293.4		4
63.41	even	6		294.2.f.a.215.2		4
63.52	odd	6	inner	1134.2.l.c.269.2		4
63.58	even	3		294.2.d.a.293.3		4
63.59	even	6		42.2.f.a.17.1	yes	4
252.23	even	6		2352.2.k.e.881.1		4
252.31	even	6		336.2.bc.e.17.2		4
252.59	odd	6		336.2.bc.e.17.1		4
252.103	even	6		2352.2.k.e.881.2		4
252.131	odd	6		2352.2.k.e.881.3		4
252.247	odd	6		2352.2.k.e.881.4		4
315.59	even	6		1050.2.s.b.101.2		4
315.94	odd	6		1050.2.s.b.101.1		4
315.122	odd	12		1050.2.u.a.899.1		4
315.157	even	12		1050.2.u.d.899.1		4
315.248	odd	12		1050.2.u.d.899.2		4
315.283	even	12		1050.2.u.a.899.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.f.a.5.1	✓	4	9.4	even	3
42.2.f.a.5.2	yes	4	9.5	odd	6
42.2.f.a.17.1	yes	4	63.59	even	6
42.2.f.a.17.2	yes	4	63.31	odd	6
294.2.d.a.293.1		4	63.5	even	6
294.2.d.a.293.2		4	63.23	odd	6
294.2.d.a.293.3		4	63.58	even	3
294.2.d.a.293.4		4	63.40	odd	6
294.2.f.a.215.1		4	63.13	odd	6
294.2.f.a.215.2		4	63.41	even	6
294.2.f.a.227.1		4	63.32	odd	6
294.2.f.a.227.2		4	63.4	even	3
336.2.bc.e.17.1		4	252.59	odd	6
336.2.bc.e.17.2		4	252.31	even	6
336.2.bc.e.257.1		4	36.31	odd	6
336.2.bc.e.257.2		4	36.23	even	6
1050.2.s.b.101.1		4	315.94	odd	6
1050.2.s.b.101.2		4	315.59	even	6
1050.2.s.b.551.1		4	45.14	odd	6
1050.2.s.b.551.2		4	45.4	even	6
1050.2.u.a.299.1		4	45.13	odd	12
1050.2.u.a.299.2		4	45.32	even	12
1050.2.u.a.899.1		4	315.122	odd	12
1050.2.u.a.899.2		4	315.283	even	12
1050.2.u.d.299.1		4	45.23	even	12
1050.2.u.d.299.2		4	45.22	odd	12
1050.2.u.d.899.1		4	315.157	even	12
1050.2.u.d.899.2		4	315.248	odd	12
1134.2.l.c.215.1		4	3.2	odd	2	inner
1134.2.l.c.215.2		4	1.1	even	1	trivial
1134.2.l.c.269.1		4	63.38	even	6	inner
1134.2.l.c.269.2		4	63.52	odd	6	inner
1134.2.t.d.593.1		4	9.2	odd	6
1134.2.t.d.593.2		4	9.7	even	3
1134.2.t.d.1025.1		4	7.3	odd	6
1134.2.t.d.1025.2		4	21.17	even	6
2352.2.k.e.881.1		4	252.23	even	6
2352.2.k.e.881.2		4	252.103	even	6
2352.2.k.e.881.3		4	252.131	odd	6
2352.2.k.e.881.4		4	252.247	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +(-1.50000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(3.00000 + 1.73205i) q^{13} +(-2.59808 + 0.500000i) q^{14} +1.00000 q^{16} +(-1.73205 - 3.00000i) q^{17} +(3.00000 + 1.73205i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.00000 - 1.73205i) q^{25} +(-1.73205 + 3.00000i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(2.59808 - 1.50000i) q^{29} -1.73205i q^{31} +1.00000i q^{32} +(3.00000 - 1.73205i) q^{34} +(-3.46410 + 3.00000i) q^{35} +(1.00000 - 1.73205i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(1.50000 - 0.866025i) q^{40} +(-3.46410 + 6.00000i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-2.59808 - 1.50000i) q^{44} +(-3.00000 - 5.19615i) q^{46} -6.92820 q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 + 1.00000i) q^{50} +(-3.00000 - 1.73205i) q^{52} +(-7.79423 + 4.50000i) q^{53} +5.19615i q^{55} +(2.59808 - 0.500000i) q^{56} +(1.50000 + 2.59808i) q^{58} +1.73205 q^{59} +1.73205 q^{62} -1.00000 q^{64} +6.00000i q^{65} +2.00000 q^{67} +(1.73205 + 3.00000i) q^{68} +(-3.00000 - 3.46410i) q^{70} -12.0000i q^{71} +(6.00000 - 3.46410i) q^{73} +(1.73205 + 1.00000i) q^{74} +(-3.00000 - 1.73205i) q^{76} +(-2.59808 + 7.50000i) q^{77} -1.00000 q^{79} +(0.866025 + 1.50000i) q^{80} +(-6.00000 - 3.46410i) q^{82} +(4.33013 + 7.50000i) q^{83} +(3.00000 - 5.19615i) q^{85} +(-6.92820 + 4.00000i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-3.00000 + 8.66025i) q^{91} +(5.19615 - 3.00000i) q^{92} -6.92820i q^{94} +6.00000i q^{95} +(-4.50000 + 2.59808i) q^{97} +(-2.59808 - 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^7	\( 4 q - 4 q^{4} + 2 q^{7} - 6 q^{10} + 12 q^{13} + 4 q^{16} + 12 q^{19} - 6 q^{22} + 4 q^{25} - 2 q^{28} + 12 q^{34} + 4 q^{37} + 6 q^{40} + 16 q^{43} - 12 q^{46} - 26 q^{49} - 12 q^{52} + 6 q^{58} - 4 q^{64} + 8 q^{67} - 12 q^{70} + 24 q^{73} - 12 q^{76} - 4 q^{79} - 24 q^{82} + 12 q^{85} + 6 q^{88} - 12 q^{91} - 18 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^7 - 6 * q^10 + 12 * q^13 + 4 * q^16 + 12 * q^19 - 6 * q^22 + 4 * q^25 - 2 * q^28 + 12 * q^34 + 4 * q^37 + 6 * q^40 + 16 * q^43 - 12 * q^46 - 26 * q^49 - 12 * q^52 + 6 * q^58 - 4 * q^64 + 8 * q^67 - 12 * q^70 + 24 * q^73 - 12 * q^76 - 4 * q^79 - 24 * q^82 + 12 * q^85 + 6 * q^88 - 12 * q^91 - 18 * q^97

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