LMFDB - Embedded newform 525.2.r.b.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (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:	$4.19214610612$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.b.424.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.866025 - 2.50000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.866025 - 2.50000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.73205 - 1.00000i) q^{12} -1.00000i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-5.19615 + 3.00000i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-5.19615 - 3.00000i) q^{23} -1.00000i q^{27} +(-3.46410 + 4.00000i) q^{28} +6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} -2.00000 q^{36} +(-6.06218 - 3.50000i) q^{37} +(-0.500000 - 0.866025i) q^{39} +12.0000 q^{41} -1.00000i q^{43} +(5.19615 + 3.00000i) q^{47} +4.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(-1.73205 + 1.00000i) q^{52} -5.00000i q^{57} +(-3.00000 - 5.19615i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-2.59808 - 0.500000i) q^{63} +8.00000 q^{64} +(6.06218 - 3.50000i) q^{67} +(10.3923 + 6.00000i) q^{68} -6.00000 q^{69} +12.0000 q^{71} +(9.52628 - 5.50000i) q^{73} -10.0000 q^{76} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000i q^{83} +(-1.00000 + 5.19615i) q^{84} +(5.19615 - 3.00000i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-2.50000 + 0.866025i) q^{91} +12.0000i q^{92} +(-4.33013 - 2.50000i) q^{93} +10.0000i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^9	$ 4 q - 4 q^{4} + 2 q^{9} - 8 q^{16} + 10 q^{19} - 8 q^{21} + 24 q^{29} - 10 q^{31} - 8 q^{36} - 2 q^{39} + 48 q^{41} - 22 q^{49} - 12 q^{51} - 12 q^{59} - 4 q^{61} + 32 q^{64} - 24 q^{69} + 48 q^{71} - 40 q^{76} - 26 q^{79} - 2 q^{81} - 4 q^{84} + 12 q^{89} - 10 q^{91}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^9 - 8 * q^16 + 10 * q^19 - 8 * q^21 + 24 * q^29 - 10 * q^31 - 8 * q^36 - 2 * q^39 + 48 * q^41 - 22 * q^49 - 12 * q^51 - 12 * q^59 - 4 * q^61 + 32 * q^64 - 24 * q^69 + 48 * q^71 - 40 * q^76 - 26 * q^79 - 2 * q^81 - 4 * q^84 + 12 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.73205	−	1.00000i	−0.500000	−	0.288675i
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.973123	−	0.230285i	$-0.926034\pi$
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.287129	+	0.957892i	$0.592701\pi$
$18$		0			0
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		0			0
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.931831	+	0.362892i	$0.881789\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$	−3.46410	+	4.00000i	−0.654654	+	0.755929i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.0893706	−	0.995998i	$-0.528486\pi$
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.907245	+	0.420602i	$0.861819\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$		0			0
$43$		−	1.00000i		−	0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$		−	1.00000i		−	0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	0.828554	−	0.559908i	$-0.189164\pi$
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	−0.0706177	+	0.997503i	$0.522497\pi$
$48$			4.00000i			0.577350i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	5.00000i		−	0.662266i
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		0			0
$63$	−2.59808	−	0.500000i	−0.327327	−	0.0629941i
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$	10.3923	+	6.00000i	1.26025	+	0.727607i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	9.52628	−	5.50000i	1.11497	−	0.643726i	0.174855	−	0.984594i	$-0.444054\pi$
$73$	9.52628	−	5.50000i	1.11497	−	0.643726i	0.940111	+	0.340868i	$0.110721\pi$
$74$		0			0
$75$		0			0
$76$	−10.0000			−1.14708
$77$		0			0
$78$		0			0
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	0.225018	+	0.974355i	$0.427756\pi$
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	−1.00000	+	5.19615i	−0.109109	+	0.566947i
$85$		0			0
$86$		0			0
$87$	5.19615	−	3.00000i	0.557086	−	0.321634i
$88$		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
$91$	−2.50000	+	0.866025i	−0.262071	+	0.0907841i
$92$			12.0000i			1.25109i
$93$	−4.33013	−	2.50000i	−0.449013	−	0.259238i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	0.866025	+	0.500000i	0.0853320	+	0.0492665i	0.542059	−	0.840341i	$-0.317645\pi$
$103$	0.866025	+	0.500000i	0.0853320	+	0.0492665i	−0.456727	+	0.889607i	$0.650978\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.5885	+	9.00000i	1.50699	+	0.870063i	0.999967	+	0.00813215i	$0.00258857\pi$
$107$	15.5885	+	9.00000i	1.50699	+	0.870063i	0.507026	+	0.861931i	$0.330745\pi$
$108$	−1.73205	+	1.00000i	−0.166667	+	0.0962250i
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$		0			0
$111$	−7.00000			−0.664411
$112$	10.3923	+	2.00000i	0.981981	+	0.188982i
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000	−	10.3923i	−0.557086	−	0.964901i
$117$	−0.866025	−	0.500000i	−0.0800641	−	0.0462250i
$118$		0			0
$119$	12.0000	+	10.3923i	1.10004	+	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$	10.3923	−	6.00000i	0.937043	−	0.541002i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$		0			0
$126$		0			0
$127$		−	11.0000i		−	0.976092i	−0.872818	−	0.488046i	$-0.837710\pi$
$127$		−	11.0000i		−	0.976092i	0.872818	−	0.488046i	$-0.162290\pi$
$128$		0			0
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$	−12.9904	−	2.50000i	−1.12641	−	0.216777i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.19615	+	3.00000i	−0.443937	+	0.256307i	−0.705266	−	0.708942i	$-0.749173\pi$
$137$	−5.19615	+	3.00000i	−0.443937	+	0.256307i	0.261329	+	0.965250i	$0.415839\pi$
$138$		0			0
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$		0			0
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$		0			0
$146$		0			0
$147$	−2.59808	+	6.50000i	−0.214286	+	0.536111i
$148$			14.0000i			1.15079i
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.332896	+	0.942964i	$0.608026\pi$
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.650183	+	0.759778i	$0.725308\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$			6.00000i			0.485071i
$154$		0			0
$155$		0			0
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	8.66025	−	5.00000i	0.691164	−	0.399043i	−0.112884	−	0.993608i	$-0.536009\pi$
$157$	8.66025	−	5.00000i	0.691164	−	0.399043i	0.804048	+	0.594565i	$0.202676\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000	+	15.5885i	−0.236433	+	1.22854i
$162$		0			0
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	−12.0000	−	20.7846i	−0.937043	−	1.62301i
$165$		0			0
$166$		0			0
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	−1.73205	+	1.00000i	−0.132068	+	0.0762493i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.19615	−	3.00000i	−0.390567	−	0.225494i
$178$		0			0
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	0.977138	+	0.212607i	$0.0681952\pi$
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	−0.304446	+	0.952529i	$0.598471\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		−	12.0000i		−	0.875190i
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	6.92820	−	4.00000i	0.500000	−	0.288675i
$193$	4.33013	−	2.50000i	0.311689	−	0.179954i	−0.335993	−	0.941865i	$-0.609072\pi$
$193$	4.33013	−	2.50000i	0.311689	−	0.179954i	0.647682	+	0.761911i	$0.275738\pi$
$194$		0			0
$195$		0			0
$196$	13.0000	+	5.19615i	0.928571	+	0.371154i
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$		0			0
$203$	−5.19615	−	15.0000i	−0.364698	−	1.05279i
$204$	12.0000			0.840168
$205$		0			0
$206$		0			0
$207$	−5.19615	+	3.00000i	−0.361158	+	0.208514i
$208$	3.46410	+	2.00000i	0.240192	+	0.138675i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	10.3923	−	6.00000i	0.712069	−	0.411113i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.66025	+	10.0000i	−0.587896	+	0.678844i
$218$		0			0
$219$	5.50000	−	9.52628i	0.371656	−	0.643726i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	−0.803523	−	0.595274i	$-0.797043\pi$
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	0.113761	+	0.993508i	$0.463710\pi$
$228$	−8.66025	+	5.00000i	−0.573539	+	0.331133i
$229$	14.5000	−	25.1147i	0.958187	−	1.65963i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	14.5000	−	25.1147i	0.958187	−	1.65963i	0.726900	−	0.686743i	$-0.240960\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	0.320043	−	0.947403i	$-0.396303\pi$
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	−0.660454	+	0.750867i	$0.729636\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$			13.0000i			0.844441i
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	4.00000			0.256074
$245$		0			0
$246$		0			0
$247$	−4.33013	−	2.50000i	−0.275519	−	0.159071i
$248$		0			0
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	1.73205	+	5.00000i	0.109109	+	0.314970i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	−3.50000	+	18.1865i	−0.217479	+	1.13006i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	−10.3923	+	6.00000i	−0.640817	+	0.369976i	−0.784929	−	0.619586i	$-0.787301\pi$
$263$	−10.3923	+	6.00000i	−0.640817	+	0.369976i	0.144112	+	0.989561i	$0.453967\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	6.00000i		−	0.367194i
$268$	−12.1244	−	7.00000i	−0.740613	−	0.427593i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		−	24.0000i		−	1.45521i
$273$	−1.73205	+	2.00000i	−0.104828	+	0.121046i
$274$		0			0
$275$		0			0
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	−19.9186	+	11.5000i	−1.19679	+	0.690968i	−0.959839	−	0.280553i	$-0.909482\pi$
$277$	−19.9186	+	11.5000i	−1.19679	+	0.690968i	−0.236953	+	0.971521i	$0.576149\pi$
$278$		0			0
$279$	−5.00000			−0.299342
$280$		0			0
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		0			0
$283$	9.52628	−	5.50000i	0.566279	−	0.326941i	−0.189383	−	0.981903i	$-0.560649\pi$
$283$	9.52628	−	5.50000i	0.566279	−	0.326941i	0.755662	+	0.654962i	$0.227315\pi$
$284$	−12.0000	−	20.7846i	−0.712069	−	1.23334i
$285$		0			0
$286$		0			0
$287$	−10.3923	−	30.0000i	−0.613438	−	1.77084i
$288$		0			0
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−19.0526	−	11.0000i	−1.11497	−	0.643726i
$293$			12.0000i			0.701047i	0.936554	+	0.350524i	$0.113996\pi$
$293$			12.0000i			0.701047i	−0.936554	+	0.350524i	$0.886004\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$		0			0
$303$		0			0
$304$	10.0000	+	17.3205i	0.573539	+	0.993399i
$305$		0			0
$306$		0			0
$307$			7.00000i			0.399511i	0.979846	+	0.199756i	$0.0640148\pi$
$307$			7.00000i			0.399511i	−0.979846	+	0.199756i	$0.935985\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−14.7224	−	8.50000i	−0.832161	−	0.480448i	0.0224310	−	0.999748i	$-0.492859\pi$
$313$	−14.7224	−	8.50000i	−0.832161	−	0.480448i	−0.854592	+	0.519300i	$0.826193\pi$
$314$		0			0
$315$		0			0
$316$	26.0000			1.46261
$317$	5.19615	+	3.00000i	0.291845	+	0.168497i	0.638774	−	0.769395i	$-0.279442\pi$
$317$	5.19615	+	3.00000i	0.291845	+	0.168497i	−0.346929	+	0.937892i	$0.612775\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	18.0000			1.00466
$322$		0			0
$323$			30.0000i			1.66924i
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$		0			0
$326$		0			0
$327$	−6.06218	−	3.50000i	−0.335239	−	0.193550i
$328$		0			0
$329$	3.00000	−	15.5885i	0.165395	−	0.859419i
$330$		0			0
$331$	−11.5000	+	19.9186i	−0.632097	+	1.09482i	0.355025	+	0.934857i	$0.384472\pi$
$331$	−11.5000	+	19.9186i	−0.632097	+	1.09482i	−0.987122	+	0.159968i	$0.948861\pi$
$332$	−20.7846	+	12.0000i	−1.14070	+	0.658586i
$333$	−6.06218	+	3.50000i	−0.332205	+	0.191799i
$334$		0			0
$335$		0			0
$336$	10.0000	−	3.46410i	0.545545	−	0.188982i
$337$			13.0000i			0.708155i	0.935216	+	0.354078i	$0.115205\pi$
$337$			13.0000i			0.708155i	−0.935216	+	0.354078i	$0.884795\pi$
$338$		0			0
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	20.7846	−	12.0000i	1.11578	−	0.644194i	0.175457	−	0.984487i	$-0.443860\pi$
$347$	20.7846	−	12.0000i	1.11578	−	0.644194i	0.940319	+	0.340293i	$0.110526\pi$
$348$	−10.3923	−	6.00000i	−0.557086	−	0.321634i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$		0			0
$356$	−12.0000			−0.635999
$357$	15.5885	+	3.00000i	0.825029	+	0.158777i
$358$		0			0
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	−0.934268	−	0.356572i	$-0.883946\pi$
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	0.775934	+	0.630814i	$0.217279\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$		−	11.0000i		−	0.577350i
$364$	4.00000	+	3.46410i	0.209657	+	0.181568i
$365$		0			0
$366$		0			0
$367$	16.4545	−	9.50000i	0.858917	−	0.495896i	−0.00473247	−	0.999989i	$-0.501506\pi$
$367$	16.4545	−	9.50000i	0.858917	−	0.495896i	0.863649	+	0.504093i	$0.168173\pi$
$368$	20.7846	−	12.0000i	1.08347	−	0.625543i
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$		0			0
$371$		0			0
$372$			10.0000i			0.518476i
$373$	−14.7224	−	8.50000i	−0.762299	−	0.440113i	0.0678218	−	0.997697i	$-0.478395\pi$
$373$	−14.7224	−	8.50000i	−0.762299	−	0.440113i	−0.830120	+	0.557584i	$0.811728\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	6.00000i		−	0.309016i
$378$		0			0
$379$	25.0000			1.28416			0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000			1.28416			0.642082	+	0.766636i	$0.278071\pi$
$380$		0			0
$381$	−5.50000	−	9.52628i	−0.281774	−	0.488046i
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.866025	−	0.500000i	−0.0440225	−	0.0254164i
$388$	17.3205	−	10.0000i	0.879316	−	0.507673i
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$		0			0
$393$		−	6.00000i		−	0.302660i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	25.1147	+	14.5000i	1.26047	+	0.727734i	0.973166	−	0.230105i	$-0.0739068\pi$
$397$	25.1147	+	14.5000i	1.26047	+	0.727734i	0.287307	+	0.957839i	$0.407240\pi$
$398$		0			0
$399$	−12.5000	+	4.33013i	−0.625783	+	0.216777i
$400$		0			0
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$		0			0
$403$	−4.33013	+	2.50000i	−0.215699	+	0.124534i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$		0			0
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$		−	2.00000i		−	0.0985329i
$413$	−10.3923	+	12.0000i	−0.511372	+	0.590481i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−4.33013	+	2.50000i	−0.212047	+	0.122426i
$418$		0			0
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$		0			0
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.19615	+	1.00000i	0.251459	+	0.0483934i
$428$		−	36.0000i		−	1.74013i
$429$		0			0
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$	3.46410	+	2.00000i	0.166667	+	0.0962250i
$433$			29.0000i			1.39365i	0.717241	+	0.696826i	$0.245405\pi$
$433$			29.0000i			1.39365i	−0.717241	+	0.696826i	$0.754595\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	−25.9808	+	15.0000i	−1.24283	+	0.717547i
$438$		0			0
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$		0			0
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$	7.00000	+	12.1244i	0.332205	+	0.575396i
$445$		0			0
$446$		0			0
$447$			24.0000i			1.13516i
$448$	−6.92820	−	20.0000i	−0.327327	−	0.944911i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$		0			0
$452$	31.1769	−	18.0000i	1.46644	−	0.846649i
$453$	13.8564	+	8.00000i	0.651031	+	0.375873i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.52628	+	5.50000i	0.445621	+	0.257279i	0.705979	−	0.708233i	$-0.250507\pi$
$457$	9.52628	+	5.50000i	0.445621	+	0.257279i	−0.260358	+	0.965512i	$0.583841\pi$
$458$		0			0
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		0			0
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$		−	7.00000i		−	0.325318i	−0.986682	−	0.162659i	$-0.947993\pi$
$463$		−	7.00000i		−	0.325318i	0.986682	−	0.162659i	$-0.0520070\pi$
$464$	−12.0000	+	20.7846i	−0.557086	+	0.964901i
$465$		0			0
$466$		0			0
$467$	25.9808	+	15.0000i	1.20225	+	0.694117i	0.961054	−	0.276360i	$-0.0891283\pi$
$467$	25.9808	+	15.0000i	1.20225	+	0.694117i	0.241192	+	0.970477i	$0.422462\pi$
$468$			2.00000i			0.0924500i
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	6.00000	−	31.1769i	0.275010	−	1.42899i
$477$		0			0
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−3.50000	+	6.06218i	−0.159586	+	0.276412i
$482$		0			0
$483$	5.19615	+	15.0000i	0.236433	+	0.682524i
$484$	−22.0000			−1.00000
$485$		0			0
$486$		0			0
$487$	6.06218	−	3.50000i	0.274703	−	0.158600i	−0.356320	−	0.934364i	$-0.615969\pi$
$487$	6.06218	−	3.50000i	0.274703	−	0.158600i	0.631023	+	0.775764i	$0.282635\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−20.7846	−	12.0000i	−0.937043	−	0.541002i
$493$	−31.1769	+	18.0000i	−1.40414	+	0.810679i
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$	−10.3923	−	30.0000i	−0.466159	−	1.34568i
$498$		0			0
$499$	8.50000	−	14.7224i	0.380512	−	0.659067i	−0.610623	−	0.791921i	$-0.709081\pi$
$499$	8.50000	−	14.7224i	0.380512	−	0.659067i	0.991136	+	0.132855i	$0.0424144\pi$
$500$		0			0
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$		0			0
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	10.3923	−	6.00000i	0.461538	−	0.266469i
$508$	−19.0526	+	11.0000i	−0.845321	+	0.488046i
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$		0			0
$511$	−22.0000	−	19.0526i	−0.973223	−	0.842836i
$512$		0			0
$513$	−4.33013	−	2.50000i	−0.191180	−	0.110378i
$514$		0			0
$515$		0			0
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	0.999551	+	0.0299693i	$0.00954094\pi$
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	−0.473821	+	0.880621i	$0.657126\pi$
$522$		0			0
$523$	37.2391	+	21.5000i	1.62835	+	0.940129i	0.984585	+	0.174908i	$0.0559627\pi$
$523$	37.2391	+	21.5000i	1.62835	+	0.940129i	0.643767	+	0.765222i	$0.277371\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$		0			0
$527$	25.9808	+	15.0000i	1.13174	+	0.653410i
$528$		0			0
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	8.66025	+	25.0000i	0.375470	+	1.08389i
$533$		−	12.0000i		−	0.519778i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	15.5885	+	9.00000i	0.672692	+	0.388379i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	−0.586278	−	0.810110i	$-0.699407\pi$
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	0.994715	+	0.102677i	$0.0327407\pi$
$542$		0			0
$543$	−6.06218	+	3.50000i	−0.260153	+	0.150199i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	10.3923	+	6.00000i	0.443937	+	0.256307i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	15.0000	−	25.9808i	0.639021	−	1.10682i
$552$		0			0
$553$	33.7750	+	6.50000i	1.43626	+	0.276408i
$554$		0			0
$555$		0			0
$556$	5.00000	+	8.66025i	0.212047	+	0.367277i
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	−0.792469	−	0.609912i	$-0.791205\pi$
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	0.131965	+	0.991254i	$0.457871\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	−0.791123	−	0.611656i	$-0.790503\pi$
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	0.134148	+	0.990961i	$0.457170\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$		0			0
$566$		0			0
$567$	−1.73205	+	2.00000i	−0.0727393	+	0.0839921i
$568$		0			0
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	0.496928	+	0.867792i	$0.334461\pi$
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	−0.999994	+	0.00354413i	$0.998872\pi$
$570$		0			0
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	0.929921	−	0.367760i	$-0.119875\pi$
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	−0.783450	+	0.621455i	$0.786542\pi$
$572$		0			0
$573$		−	6.00000i		−	0.250654i
$574$		0			0
$575$		0			0
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	6.06218	−	3.50000i	0.252372	−	0.145707i	−0.368478	−	0.929636i	$-0.620121\pi$
$577$	6.06218	−	3.50000i	0.252372	−	0.145707i	0.620850	+	0.783930i	$0.286788\pi$
$578$		0			0
$579$	2.50000	−	4.33013i	0.103896	−	0.179954i
$580$		0			0
$581$	−30.0000	+	10.3923i	−1.24461	+	0.431145i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$			18.0000i			0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$			18.0000i			0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$	13.8564	−	2.00000i	0.571429	−	0.0824786i
$589$	−25.0000			−1.03011
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	24.2487	−	14.0000i	0.996616	−	0.575396i
$593$	−31.1769	−	18.0000i	−1.28028	−	0.739171i	−0.303383	−	0.952869i	$-0.598116\pi$
$593$	−31.1769	−	18.0000i	−1.28028	−	0.739171i	−0.976900	+	0.213697i	$0.931449\pi$
$594$		0			0
$595$		0			0
$596$	48.0000			1.96616
$597$	−13.8564	−	8.00000i	−0.567105	−	0.327418i
$598$		0			0
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	−1.00000			−0.0407909			−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000			−0.0407909			−0.0203954	+	0.999792i	$0.506493\pi$
$602$		0			0
$603$		−	7.00000i		−	0.285062i
$604$	16.0000	−	27.7128i	0.651031	−	1.12762i
$605$		0			0
$606$		0			0
$607$	−16.4545	−	9.50000i	−0.667867	−	0.385593i	0.127401	−	0.991851i	$-0.459336\pi$
$607$	−16.4545	−	9.50000i	−0.667867	−	0.385593i	−0.795268	+	0.606258i	$0.792670\pi$
$608$		0			0
$609$	−12.0000	−	10.3923i	−0.486265	−	0.421117i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	10.3923	−	6.00000i	0.420084	−	0.242536i
$613$	32.9090	−	19.0000i	1.32918	−	0.767403i	0.344008	−	0.938967i	$-0.388215\pi$
$613$	32.9090	−	19.0000i	1.32918	−	0.767403i	0.985173	+	0.171564i	$0.0548821\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			42.0000i			1.69086i	0.534089	+	0.845428i	$0.320655\pi$
$617$			42.0000i			1.69086i	−0.534089	+	0.845428i	$0.679345\pi$
$618$		0			0
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	0.967271	+	0.253744i	$0.0816620\pi$
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	−0.263887	+	0.964554i	$0.585005\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$		0			0
$623$	−15.5885	−	3.00000i	−0.624538	−	0.120192i
$624$	4.00000			0.160128
$625$		0			0
$626$		0			0
$627$		0			0
$628$	−17.3205	−	10.0000i	−0.691164	−	0.399043i
$629$	42.0000			1.67465
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$	−3.46410	+	2.00000i	−0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	4.33013	+	5.50000i	0.171566	+	0.217918i
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$		−	25.0000i		−	0.985904i	−0.870057	−	0.492952i	$-0.835918\pi$
$643$		−	25.0000i		−	0.985904i	0.870057	−	0.492952i	$-0.164082\pi$
$644$	30.0000	−	10.3923i	1.18217	−	0.409514i
$645$		0			0
$646$		0			0
$647$	20.7846	−	12.0000i	0.817127	−	0.471769i	−0.0322975	−	0.999478i	$-0.510282\pi$
$647$	20.7846	−	12.0000i	0.817127	−	0.471769i	0.849425	+	0.527710i	$0.176949\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−2.50000	+	12.9904i	−0.0979827	+	0.509133i
$652$		−	8.00000i		−	0.313304i
$653$	20.7846	+	12.0000i	0.813365	+	0.469596i	0.848123	−	0.529799i	$-0.177733\pi$
$653$	20.7846	+	12.0000i	0.813365	+	0.469596i	−0.0347583	+	0.999396i	$0.511066\pi$
$654$		0			0
$655$		0			0
$656$	−24.0000	+	41.5692i	−0.937043	+	1.62301i
$657$		−	11.0000i		−	0.429151i
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	0.964301	−	0.264807i	$-0.0853084\pi$
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	−0.711481	+	0.702706i	$0.751975\pi$
$662$		0			0
$663$	5.19615	+	3.00000i	0.201802	+	0.116510i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−31.1769	−	18.0000i	−1.20717	−	0.696963i
$668$	−20.7846	+	12.0000i	−0.804181	+	0.464294i
$669$	−2.00000	−	3.46410i	−0.0773245	−	0.133930i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	31.0000i		−	1.19496i	−0.801883	−	0.597481i	$-0.796168\pi$
$673$		−	31.0000i		−	1.19496i	0.801883	−	0.597481i	$-0.203832\pi$
$674$		0			0
$675$		0			0
$676$	−12.0000	−	20.7846i	−0.461538	−	0.799408i
$677$	−15.5885	−	9.00000i	−0.599113	−	0.345898i	0.169580	−	0.985517i	$-0.445759\pi$
$677$	−15.5885	−	9.00000i	−0.599113	−	0.345898i	−0.768693	+	0.639618i	$0.779092\pi$
$678$		0			0
$679$	25.0000	−	8.66025i	0.959412	−	0.332350i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	15.5885	−	9.00000i	0.596476	−	0.344375i	−0.171178	−	0.985240i	$-0.554757\pi$
$683$	15.5885	−	9.00000i	0.596476	−	0.344375i	0.767654	+	0.640865i	$0.221424\pi$
$684$	−5.00000	+	8.66025i	−0.191180	+	0.331133i
$685$		0			0
$686$		0			0
$687$		−	29.0000i		−	1.10642i
$688$	3.46410	+	2.00000i	0.132068	+	0.0762493i
$689$		0			0
$690$		0			0
$691$	−5.50000	+	9.52628i	−0.209230	+	0.362397i	−0.951472	−	0.307735i	$-0.900429\pi$
$691$	−5.50000	+	9.52628i	−0.209230	+	0.362397i	0.742242	+	0.670132i	$0.233762\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−62.3538	+	36.0000i	−2.36182	+	1.36360i
$698$		0			0
$699$	−6.00000			−0.226941
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	−30.3109	+	17.5000i	−1.14320	+	0.660025i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$			12.0000i			0.450988i
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$		0			0
$711$	6.50000	+	11.2583i	0.243769	+	0.422220i
$712$		0			0
$713$			30.0000i			1.12351i
$714$		0			0
$715$		0			0
$716$	18.0000	−	31.1769i	0.672692	−	1.16514i
$717$	5.19615	−	3.00000i	0.194054	−	0.112037i
$718$		0			0
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		0			0
$721$	0.500000	−	2.59808i	0.0186210	−	0.0967574i
$722$		0			0
$723$	−1.73205	−	1.00000i	−0.0644157	−	0.0371904i
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$		0			0
$726$		0			0
$727$			7.00000i			0.259616i	0.991539	+	0.129808i	$0.0414360\pi$
$727$			7.00000i			0.259616i	−0.991539	+	0.129808i	$0.958564\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$	3.46410	−	2.00000i	0.128037	−	0.0739221i
$733$	11.2583	+	6.50000i	0.415836	+	0.240083i	0.693294	−	0.720655i	$-0.256159\pi$
$733$	11.2583	+	6.50000i	0.415836	+	0.240083i	−0.277458	+	0.960738i	$0.589492\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	0.794443	−	0.607339i	$-0.207763\pi$
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	−0.923192	+	0.384338i	$0.874430\pi$
$740$		0			0
$741$	−5.00000			−0.183680
$742$		0			0
$743$		−	24.0000i		−	0.880475i	−0.897881	−	0.440237i	$-0.854894\pi$
$743$		−	24.0000i		−	0.880475i	0.897881	−	0.440237i	$-0.145106\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−10.3923	−	6.00000i	−0.380235	−	0.219529i
$748$		0			0
$749$	9.00000	−	46.7654i	0.328853	−	1.70877i
$750$		0			0
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	−0.638994	−	0.769212i	$-0.720649\pi$
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	0.985654	+	0.168779i	$0.0539825\pi$
$752$	−20.7846	+	12.0000i	−0.757937	+	0.437595i
$753$	−15.5885	+	9.00000i	−0.568075	+	0.327978i
$754$		0			0
$755$		0			0
$756$	4.00000	+	3.46410i	0.145479	+	0.125988i
$757$		−	50.0000i		−	1.81728i	−0.417579	−	0.908640i	$-0.637121\pi$
$757$		−	50.0000i		−	1.81728i	0.417579	−	0.908640i	$-0.362879\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$		0			0
$763$	−12.1244	+	14.0000i	−0.438931	+	0.506834i
$764$	−12.0000			−0.434145
$765$		0			0
$766$		0			0
$767$	−5.19615	+	3.00000i	−0.187622	+	0.108324i
$768$	−13.8564	−	8.00000i	−0.500000	−	0.288675i
$769$	13.0000			0.468792			0.234396	−	0.972141i	$-0.424689\pi$
$769$	13.0000			0.468792			0.234396	+	0.972141i	$0.424689\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	−8.66025	−	5.00000i	−0.311689	−	0.179954i
$773$	−20.7846	+	12.0000i	−0.747570	+	0.431610i	−0.824815	−	0.565402i	$-0.808721\pi$
$773$	−20.7846	+	12.0000i	−0.747570	+	0.431610i	0.0772449	+	0.997012i	$0.475388\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.06218	+	17.5000i	0.217479	+	0.627809i
$778$		0			0
$779$	30.0000	−	51.9615i	1.07486	−	1.86171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	6.00000i		−	0.214423i
$784$	−4.00000	−	27.7128i	−0.142857	−	0.989743i
$785$		0			0
$786$		0			0
$787$	24.2487	−	14.0000i	0.864373	−	0.499046i	−0.00110111	−	0.999999i	$-0.500350\pi$
$787$	24.2487	−	14.0000i	0.864373	−	0.499046i	0.865474	+	0.500953i	$0.167017\pi$
$788$	−10.3923	+	6.00000i	−0.370211	+	0.213741i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	45.0000	−	15.5885i	1.60002	−	0.554262i
$792$		0			0
$793$	1.73205	+	1.00000i	0.0615069	+	0.0355110i
$794$		0			0
$795$		0			0
$796$	−16.0000	+	27.7128i	−0.567105	+	0.982255i
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$		0			0
$804$	−14.0000			−0.493742
$805$		0			0
$806$		0			0
$807$	−15.5885	−	9.00000i	−0.548740	−	0.316815i
$808$		0			0
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−20.7846	+	24.0000i	−0.729397	+	0.842235i
$813$		−	16.0000i		−	0.561144i
$814$		0			0
$815$		0			0
$816$	−12.0000	−	20.7846i	−0.420084	−	0.727607i
$817$	−4.33013	−	2.50000i	−0.151492	−	0.0874639i
$818$		0			0
$819$	−0.500000	+	2.59808i	−0.0174714	+	0.0907841i
$820$		0			0
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$		0			0
$823$	−34.6410	+	20.0000i	−1.20751	+	0.697156i	−0.962215	−	0.272292i	$-0.912218\pi$
$823$	−34.6410	+	20.0000i	−1.20751	+	0.697156i	−0.245295	+	0.969448i	$0.578885\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			6.00000i			0.208640i	0.994544	+	0.104320i	$0.0332667\pi$
$827$			6.00000i			0.208640i	−0.994544	+	0.104320i	$0.966733\pi$
$828$	10.3923	+	6.00000i	0.361158	+	0.208514i
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	0.652553	−	0.757743i	$-0.273698\pi$
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	−0.982501	+	0.186256i	$0.940365\pi$
$830$		0			0
$831$	−11.5000	+	19.9186i	−0.398931	+	0.690968i
$832$		−	8.00000i		−	0.277350i
$833$	15.5885	−	39.0000i	0.540108	−	1.35127i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.33013	+	2.50000i	−0.149671	+	0.0864126i
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−20.7846	+	12.0000i	−0.715860	+	0.413302i
$844$	4.00000	+	6.92820i	0.137686	+	0.238479i
$845$		0			0
$846$		0			0
$847$	−28.5788	−	5.50000i	−0.981981	−	0.188982i
$848$		0			0
$849$	5.50000	−	9.52628i	0.188760	−	0.326941i
$850$		0			0
$851$	21.0000	+	36.3731i	0.719871	+	1.24685i
$852$	−20.7846	−	12.0000i	−0.712069	−	0.411113i
$853$			17.0000i			0.582069i	0.956713	+	0.291034i	$0.0939994\pi$
$853$			17.0000i			0.582069i	−0.956713	+	0.291034i	$0.906001\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−36.3731	+	21.0000i	−1.24248	+	0.717346i	−0.969599	−	0.244701i	$-0.921310\pi$
$857$	−36.3731	+	21.0000i	−1.24248	+	0.717346i	−0.272882	+	0.962048i	$0.587977\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$		0			0
$861$	−24.0000	−	20.7846i	−0.817918	−	0.708338i
$862$		0			0
$863$	5.19615	+	3.00000i	0.176879	+	0.102121i	0.585826	−	0.810437i	$-0.300770\pi$
$863$	5.19615	+	3.00000i	0.176879	+	0.102121i	−0.408946	+	0.912558i	$0.634104\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	19.0000i		−	0.645274i
$868$	25.9808	+	5.00000i	0.881845	+	0.169711i
$869$		0			0
$870$		0			0
$871$	−3.50000	−	6.06218i	−0.118593	−	0.205409i
$872$		0			0
$873$	8.66025	+	5.00000i	0.293105	+	0.169224i
$874$		0			0
$875$		0			0
$876$	−22.0000			−0.743311
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	0.528958	−	0.848648i	$-0.322583\pi$
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	−0.470471	+	0.882415i	$0.655916\pi$
$878$		0			0
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$		−	31.0000i		−	1.04323i	−0.853180	−	0.521617i	$-0.825329\pi$
$883$		−	31.0000i		−	1.04323i	0.853180	−	0.521617i	$-0.174671\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$		0			0
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	0.664218	−	0.747539i	$-0.268765\pi$
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	−0.315279	+	0.948999i	$0.602098\pi$
$888$		0			0
$889$	−27.5000	+	9.52628i	−0.922320	+	0.319501i
$890$		0			0
$891$		0			0
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$	25.9808	−	15.0000i	0.869413	−	0.501956i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			6.00000i			0.200334i
$898$		0			0
$899$	−15.0000	−	25.9808i	−0.500278	−	0.866507i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−1.73205	+	2.00000i	−0.0576390	+	0.0665558i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	26.8468	−	15.5000i	0.891433	−	0.514669i	0.0170220	−	0.999855i	$-0.494581\pi$
$907$	26.8468	−	15.5000i	0.891433	−	0.514669i	0.874411	+	0.485186i	$0.161248\pi$
$908$	20.7846	+	12.0000i	0.689761	+	0.398234i
$909$		0			0
$910$		0			0
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$	17.3205	+	10.0000i	0.573539	+	0.331133i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−58.0000			−1.91637
$917$	−15.5885	−	3.00000i	−0.514776	−	0.0990687i
$918$		0			0
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	−0.159492	−	0.987199i	$-0.550986\pi$
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	0.934686	−	0.355475i	$-0.115681\pi$
$920$		0			0
$921$	3.50000	+	6.06218i	0.115329	+	0.199756i
$922$		0			0
$923$		−	12.0000i		−	0.394985i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.866025	−	0.500000i	0.0284440	−	0.0164222i
$928$		0			0
$929$	−6.00000	+	10.3923i	−0.196854	+	0.340960i	−0.947507	−	0.319736i	$-0.896406\pi$
$929$	−6.00000	+	10.3923i	−0.196854	+	0.340960i	0.750653	+	0.660697i	$0.229739\pi$
$930$		0			0
$931$	5.00000	+	34.6410i	0.163868	+	1.13531i
$932$			12.0000i			0.393073i
$933$	−10.3923	−	6.00000i	−0.340229	−	0.196431i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	29.0000i		−	0.947389i	−0.880689	−	0.473694i	$-0.842920\pi$
$937$		−	29.0000i		−	0.947389i	0.880689	−	0.473694i	$-0.157080\pi$
$938$		0			0
$939$	−17.0000			−0.554774
$940$		0			0
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	0.999920	−	0.0126715i	$-0.00403357\pi$
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$942$		0			0
$943$	−62.3538	−	36.0000i	−2.03052	−	1.17232i
$944$	24.0000			0.781133
$945$		0			0
$946$		0			0
$947$	41.5692	+	24.0000i	1.35082	+	0.779895i	0.988364	−	0.152106i	$-0.0486057\pi$
$947$	41.5692	+	24.0000i	1.35082	+	0.779895i	0.362454	+	0.932002i	$0.381939\pi$
$948$	22.5167	−	13.0000i	0.731307	−	0.422220i
$949$	−5.50000	−	9.52628i	−0.178538	−	0.309236i
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$		0			0
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		0			0
$958$		0			0
$959$	12.0000	+	10.3923i	0.387500	+	0.335585i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	15.5885	−	9.00000i	0.502331	−	0.290021i
$964$	−2.00000	+	3.46410i	−0.0644157	+	0.111571i
$965$		0			0
$966$		0			0
$967$			55.0000i			1.76868i	0.466843	+	0.884340i	$0.345391\pi$
$967$			55.0000i			1.76868i	−0.466843	+	0.884340i	$0.654609\pi$
$968$		0			0
$969$	15.0000	+	25.9808i	0.481869	+	0.834622i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$			2.00000i			0.0641500i
$973$	4.33013	+	12.5000i	0.138817	+	0.400732i
$974$		0			0
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	−0.324462	−	0.945899i	$-0.605183\pi$
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	0.656941	+	0.753942i	$0.271850\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−7.00000			−0.223493
$982$		0			0
$983$	15.5885	−	9.00000i	0.497195	−	0.287055i	−0.230360	−	0.973106i	$-0.573990\pi$
$983$	15.5885	−	9.00000i	0.497195	−	0.287055i	0.727554	+	0.686050i	$0.240657\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.19615	−	15.0000i	−0.165395	−	0.477455i
$988$			10.0000i			0.318142i
$989$	−3.00000	+	5.19615i	−0.0953945	+	0.165228i
$990$		0			0
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	0.974070	+	0.226246i	$0.0726454\pi$
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	−0.291100	+	0.956693i	$0.594021\pi$
$992$		0			0
$993$			23.0000i			0.729883i
$994$		0			0
$995$		0			0
$996$	−12.0000	+	20.7846i	−0.380235	+	0.658586i
$997$	26.8468	−	15.5000i	0.850246	−	0.490890i	−0.0104877	−	0.999945i	$-0.503338\pi$
$997$	26.8468	−	15.5000i	0.850246	−	0.490890i	0.860734	+	0.509055i	$0.170005\pi$
$998$		0			0
$999$	−3.50000	+	6.06218i	−0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.b.499.2		4
5.2	odd	4		105.2.i.a.16.1	✓	2
5.3	odd	4		525.2.i.c.226.1		2
5.4	even	2	inner	525.2.r.b.499.1		4
7.4	even	3	inner	525.2.r.b.424.1		4
15.2	even	4		315.2.j.b.226.1		2
20.7	even	4		1680.2.bg.m.961.1		2
35.2	odd	12		735.2.a.e.1.1		1
35.4	even	6	inner	525.2.r.b.424.2		4
35.12	even	12		735.2.a.d.1.1		1
35.17	even	12		735.2.i.c.361.1		2
35.18	odd	12		525.2.i.c.151.1		2
35.23	odd	12		3675.2.a.h.1.1		1
35.27	even	4		735.2.i.c.226.1		2
35.32	odd	12		105.2.i.a.46.1	yes	2
35.33	even	12		3675.2.a.i.1.1		1
105.2	even	12		2205.2.a.f.1.1		1
105.32	even	12		315.2.j.b.46.1		2
105.47	odd	12		2205.2.a.d.1.1		1
140.67	even	12		1680.2.bg.m.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.a.16.1	✓	2	5.2	odd	4
105.2.i.a.46.1	yes	2	35.32	odd	12
315.2.j.b.46.1		2	105.32	even	12
315.2.j.b.226.1		2	15.2	even	4
525.2.i.c.151.1		2	35.18	odd	12
525.2.i.c.226.1		2	5.3	odd	4
525.2.r.b.424.1		4	7.4	even	3	inner
525.2.r.b.424.2		4	35.4	even	6	inner
525.2.r.b.499.1		4	5.4	even	2	inner
525.2.r.b.499.2		4	1.1	even	1	trivial
735.2.a.d.1.1		1	35.12	even	12
735.2.a.e.1.1		1	35.2	odd	12
735.2.i.c.226.1		2	35.27	even	4
735.2.i.c.361.1		2	35.17	even	12
1680.2.bg.m.961.1		2	20.7	even	4
1680.2.bg.m.1201.1		2	140.67	even	12
2205.2.a.d.1.1		1	105.47	odd	12
2205.2.a.f.1.1		1	105.2	even	12
3675.2.a.h.1.1		1	35.23	odd	12
3675.2.a.i.1.1		1	35.33	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.866025 - 2.50000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.866025 - 2.50000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.73205 - 1.00000i) q^{12} -1.00000i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-5.19615 + 3.00000i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-5.19615 - 3.00000i) q^{23} -1.00000i q^{27} +(-3.46410 + 4.00000i) q^{28} +6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} -2.00000 q^{36} +(-6.06218 - 3.50000i) q^{37} +(-0.500000 - 0.866025i) q^{39} +12.0000 q^{41} -1.00000i q^{43} +(5.19615 + 3.00000i) q^{47} +4.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(-1.73205 + 1.00000i) q^{52} -5.00000i q^{57} +(-3.00000 - 5.19615i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-2.59808 - 0.500000i) q^{63} +8.00000 q^{64} +(6.06218 - 3.50000i) q^{67} +(10.3923 + 6.00000i) q^{68} -6.00000 q^{69} +12.0000 q^{71} +(9.52628 - 5.50000i) q^{73} -10.0000 q^{76} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000i q^{83} +(-1.00000 + 5.19615i) q^{84} +(5.19615 - 3.00000i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-2.50000 + 0.866025i) q^{91} +12.0000i q^{92} +(-4.33013 - 2.50000i) q^{93} +10.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^9	\( 4 q - 4 q^{4} + 2 q^{9} - 8 q^{16} + 10 q^{19} - 8 q^{21} + 24 q^{29} - 10 q^{31} - 8 q^{36} - 2 q^{39} + 48 q^{41} - 22 q^{49} - 12 q^{51} - 12 q^{59} - 4 q^{61} + 32 q^{64} - 24 q^{69} + 48 q^{71} - 40 q^{76} - 26 q^{79} - 2 q^{81} - 4 q^{84} + 12 q^{89} - 10 q^{91}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^9 - 8 * q^16 + 10 * q^19 - 8 * q^21 + 24 * q^29 - 10 * q^31 - 8 * q^36 - 2 * q^39 + 48 * q^41 - 22 * q^49 - 12 * q^51 - 12 * q^59 - 4 * q^61 + 32 * q^64 - 24 * q^69 + 48 * q^71 - 40 * q^76 - 26 * q^79 - 2 * q^81 - 4 * q^84 + 12 * q^89 - 10 * q^91

Introduction

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