LMFDB - Embedded newform 675.2.k.a.424.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(199,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.k (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:	$5.38990213644$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.a.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.59808 + 1.50000i) q^{7} -3.00000i q^{8} +(-1.00000 + 1.73205i) q^{11} +(1.73205 - 1.00000i) q^{13} +(1.50000 + 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} -4.00000i q^{17} +8.00000 q^{19} +(-1.73205 + 1.00000i) q^{22} +(2.59808 - 1.50000i) q^{23} +2.00000 q^{26} -3.00000i q^{28} +(0.500000 - 0.866025i) q^{29} +(-4.33013 + 2.50000i) q^{32} +(2.00000 - 3.46410i) q^{34} -4.00000i q^{37} +(6.92820 + 4.00000i) q^{38} +(2.50000 + 4.33013i) q^{41} +(-6.92820 - 4.00000i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(6.06218 + 3.50000i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-1.73205 - 1.00000i) q^{52} -2.00000i q^{53} +(4.50000 - 7.79423i) q^{56} +(0.866025 - 0.500000i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} -7.00000 q^{64} +(-2.59808 + 1.50000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -2.00000 q^{71} -4.00000i q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.00000 - 6.92820i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(-3.00000 + 5.19615i) q^{79} +5.00000i q^{82} +(-7.79423 - 4.50000i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(5.19615 + 3.00000i) q^{88} -15.0000 q^{89} +6.00000 q^{91} +(-2.59808 - 1.50000i) q^{92} +(3.50000 + 6.06218i) q^{94} +(-1.73205 - 1.00000i) q^{97} +2.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} - 4 q^{11} + 6 q^{14} + 2 q^{16} + 32 q^{19} + 8 q^{26} + 2 q^{29} + 8 q^{34} + 10 q^{41} + 8 q^{44} + 12 q^{46} + 4 q^{49} + 18 q^{56} + 28 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{71} + 8 q^{74}+ \cdots + 14 q^{94}+O(q^{100}) $ 4 * q - 2 * q^4 - 4 * q^11 + 6 * q^14 + 2 * q^16 + 32 * q^19 + 8 * q^26 + 2 * q^29 + 8 * q^34 + 10 * q^41 + 8 * q^44 + 12 * q^46 + 4 * q^49 + 18 * q^56 + 28 * q^59 - 14 * q^61 - 28 * q^64 - 8 * q^71 + 8 * q^74 - 16 * q^76 - 12 * q^79 - 16 * q^86 - 60 * q^89 + 24 * q^91 + 14 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i	0.773893	−	0.633316i	$-0.218307\pi$
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i	−0.161521	+	0.986869i	$0.551640\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.59808	+	1.50000i	0.981981	+	0.566947i	0.902867	−	0.429919i	$-0.141458\pi$
$7$	2.59808	+	1.50000i	0.981981	+	0.566947i	0.0791130	+	0.996866i	$0.474791\pi$
$8$		−	3.00000i		−	1.06066i
$9$		0			0
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	1.73205	−	1.00000i	0.480384	−	0.277350i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$	1.73205	−	1.00000i	0.480384	−	0.277350i	0.720577	+	0.693375i	$0.243877\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		0			0
$19$	8.00000			1.83533			0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000			1.83533			0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$		0			0
$22$	−1.73205	+	1.00000i	−0.369274	+	0.213201i
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$		0			0
$25$		0			0
$26$	2.00000			0.392232
$27$		0			0
$28$		−	3.00000i		−	0.566947i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−4.33013	+	2.50000i	−0.765466	+	0.441942i
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$		0			0
$36$		0			0
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	6.92820	+	4.00000i	1.12390	+	0.648886i
$39$		0			0
$40$		0			0
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$		0			0
$43$	−6.92820	−	4.00000i	−1.05654	−	0.609994i	−0.132068	−	0.991241i	$-0.542162\pi$
$43$	−6.92820	−	4.00000i	−1.05654	−	0.609994i	−0.924473	+	0.381246i	$0.875495\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	3.00000			0.442326
$47$	6.06218	+	3.50000i	0.884260	+	0.510527i	0.872060	−	0.489398i	$-0.162783\pi$
$47$	6.06218	+	3.50000i	0.884260	+	0.510527i	0.0121990	+	0.999926i	$0.496117\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$		0			0
$51$		0			0
$52$	−1.73205	−	1.00000i	−0.240192	−	0.138675i
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$		0			0
$55$		0			0
$56$	4.50000	−	7.79423i	0.601338	−	1.04155i
$57$		0			0
$58$	0.866025	−	0.500000i	0.113715	−	0.0656532i
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.812198	+	0.583382i	$0.198271\pi$
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.0991242	+	0.995075i	$0.468396\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$		0			0
$64$	−7.00000			−0.875000
$65$		0			0
$66$		0			0
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	−0.650236	−	0.759733i	$-0.725330\pi$
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391996\pi$
$68$	−3.46410	+	2.00000i	−0.420084	+	0.242536i
$69$		0			0
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	−4.00000	−	6.92820i	−0.458831	−	0.794719i
$77$	−5.19615	+	3.00000i	−0.592157	+	0.341882i
$78$		0			0
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	−0.983967	−	0.178352i	$-0.942924\pi$
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	0.646440	+	0.762964i	$0.276257\pi$
$80$		0			0
$81$		0			0
$82$			5.00000i			0.552158i
$83$	−7.79423	−	4.50000i	−0.855528	−	0.493939i	0.00698436	−	0.999976i	$-0.497777\pi$
$83$	−7.79423	−	4.50000i	−0.855528	−	0.493939i	−0.862512	+	0.506036i	$0.831110\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	5.19615	+	3.00000i	0.553912	+	0.319801i
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	6.00000			0.628971
$92$	−2.59808	−	1.50000i	−0.270868	−	0.156386i
$93$		0			0
$94$	3.50000	+	6.06218i	0.360997	+	0.625266i
$95$		0			0
$96$		0			0
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$98$			2.00000i			0.202031i
$99$		0			0
$100$		0			0
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	−6.92820	+	4.00000i	−0.682656	+	0.394132i	−0.800855	−	0.598858i	$-0.795621\pi$
$103$	−6.92820	+	4.00000i	−0.682656	+	0.394132i	0.118199	+	0.992990i	$0.462288\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	1.00000	−	1.73205i	0.0971286	−	0.168232i
$107$		−	3.00000i		−	0.290021i	−0.989430	−	0.145010i	$-0.953678\pi$
$107$		−	3.00000i		−	0.290021i	0.989430	−	0.145010i	$-0.0463216\pi$
$108$		0			0
$109$	−5.00000			−0.478913			−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000			−0.478913			−0.239457	+	0.970907i	$0.576969\pi$
$110$		0			0
$111$		0			0
$112$	2.59808	−	1.50000i	0.245495	−	0.141737i
$113$	−6.92820	+	4.00000i	−0.651751	+	0.376288i	−0.789127	−	0.614231i	$-0.789466\pi$
$113$	−6.92820	+	4.00000i	−0.651751	+	0.376288i	0.137376	+	0.990519i	$0.456133\pi$
$114$		0			0
$115$		0			0
$116$	−1.00000			−0.0928477
$117$		0			0
$118$			14.0000i			1.28880i
$119$	6.00000	−	10.3923i	0.550019	−	0.952661i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−6.06218	+	3.50000i	−0.548844	+	0.316875i
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	5.00000i		−	0.443678i	−0.975083	−	0.221839i	$-0.928794\pi$
$127$		−	5.00000i		−	0.443678i	0.975083	−	0.221839i	$-0.0712060\pi$
$128$	2.59808	+	1.50000i	0.229640	+	0.132583i
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	20.7846	+	12.0000i	1.80225	+	1.04053i
$134$	−3.00000			−0.259161
$135$		0			0
$136$	−12.0000			−1.02899
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.873247	−	0.487278i	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$		0			0
$142$	−1.73205	−	1.00000i	−0.145350	−	0.0839181i
$143$			4.00000i			0.334497i
$144$		0			0
$145$		0			0
$146$	2.00000	−	3.46410i	0.165521	−	0.286691i
$147$		0			0
$148$	−3.46410	+	2.00000i	−0.284747	+	0.164399i
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	−0.969724	−	0.244202i	$-0.921474\pi$
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	0.273377	−	0.961907i	$-0.411859\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$		−	24.0000i		−	1.94666i
$153$		0			0
$154$	−6.00000			−0.483494
$155$		0			0
$156$		0			0
$157$	12.1244	−	7.00000i	0.967629	−	0.558661i	0.0691164	−	0.997609i	$-0.477982\pi$
$157$	12.1244	−	7.00000i	0.967629	−	0.558661i	0.898513	+	0.438948i	$0.144649\pi$
$158$	−5.19615	+	3.00000i	−0.413384	+	0.238667i
$159$		0			0
$160$		0			0
$161$	9.00000			0.709299
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	2.50000	−	4.33013i	0.195217	−	0.338126i
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	7.79423	−	4.50000i	0.603136	−	0.348220i	−0.167139	−	0.985933i	$-0.553453\pi$
$167$	7.79423	−	4.50000i	0.603136	−	0.348220i	0.770274	+	0.637713i	$0.220119\pi$
$168$		0			0
$169$	−4.50000	+	7.79423i	−0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$			8.00000i			0.609994i
$173$		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
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	−12.9904	−	7.50000i	−0.973670	−	0.562149i
$179$	−2.00000			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	5.19615	+	3.00000i	0.385164	+	0.222375i
$183$		0			0
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$		0			0
$186$		0			0
$187$	6.92820	+	4.00000i	0.506640	+	0.292509i
$188$		−	7.00000i		−	0.510527i
$189$		0			0
$190$		0			0
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$		0			0
$193$	8.66025	−	5.00000i	0.623379	−	0.359908i	−0.154805	−	0.987945i	$-0.549475\pi$
$193$	8.66025	−	5.00000i	0.623379	−	0.359908i	0.778183	+	0.628037i	$0.216141\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$	1.00000	−	1.73205i	0.0714286	−	0.123718i
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$		0			0
$202$	−15.5885	+	9.00000i	−1.09680	+	0.633238i
$203$	2.59808	−	1.50000i	0.182349	−	0.105279i
$204$		0			0
$205$		0			0
$206$	−8.00000			−0.557386
$207$		0			0
$208$		−	2.00000i		−	0.138675i
$209$	−8.00000	+	13.8564i	−0.553372	+	0.958468i
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	−1.73205	+	1.00000i	−0.118958	+	0.0686803i
$213$		0			0
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−4.33013	−	2.50000i	−0.293273	−	0.169321i
$219$		0			0
$220$		0			0
$221$	−4.00000	−	6.92820i	−0.269069	−	0.466041i
$222$		0			0
$223$	−16.4545	−	9.50000i	−1.10187	−	0.636167i	−0.165161	−	0.986267i	$-0.552814\pi$
$223$	−16.4545	−	9.50000i	−1.10187	−	0.636167i	−0.936713	+	0.350100i	$0.886148\pi$
$224$	−15.0000			−1.00223
$225$		0			0
$226$	−8.00000			−0.532152
$227$	−3.46410	−	2.00000i	−0.229920	−	0.132745i	0.380615	−	0.924734i	$-0.375712\pi$
$227$	−3.46410	−	2.00000i	−0.229920	−	0.132745i	−0.610535	+	0.791989i	$0.709046\pi$
$228$		0			0
$229$	7.50000	+	12.9904i	0.495614	+	0.858429i	0.999987	−	0.00505719i	$-0.00160976\pi$
$229$	7.50000	+	12.9904i	0.495614	+	0.858429i	−0.504373	+	0.863486i	$0.668276\pi$
$230$		0			0
$231$		0			0
$232$	−2.59808	−	1.50000i	−0.170572	−	0.0984798i
$233$			24.0000i			1.57229i	0.618041	+	0.786146i	$0.287927\pi$
$233$			24.0000i			1.57229i	−0.618041	+	0.786146i	$0.712073\pi$
$234$		0			0
$235$		0			0
$236$	7.00000	−	12.1244i	0.455661	−	0.789228i
$237$		0			0
$238$	10.3923	−	6.00000i	0.673633	−	0.388922i
$239$	4.00000	+	6.92820i	0.258738	+	0.448148i	0.965904	−	0.258900i	$-0.0833599\pi$
$239$	4.00000	+	6.92820i	0.258738	+	0.448148i	−0.707166	+	0.707048i	$0.750027\pi$
$240$		0			0
$241$	5.50000	−	9.52628i	0.354286	−	0.613642i	−0.632709	−	0.774389i	$-0.718057\pi$
$241$	5.50000	−	9.52628i	0.354286	−	0.613642i	0.986996	+	0.160748i	$0.0513906\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	7.00000			0.448129
$245$		0			0
$246$		0			0
$247$	13.8564	−	8.00000i	0.881662	−	0.509028i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$			6.00000i			0.377217i
$254$	2.50000	−	4.33013i	0.156864	−	0.271696i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	−0.329104	−	0.944294i	$-0.606747\pi$
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	0.653231	+	0.757159i	$0.273413\pi$
$258$		0			0
$259$	6.00000	−	10.3923i	0.372822	−	0.645746i
$260$		0			0
$261$		0			0
$262$		−	6.00000i		−	0.370681i
$263$	13.8564	+	8.00000i	0.854423	+	0.493301i	0.862141	−	0.506669i	$-0.169123\pi$
$263$	13.8564	+	8.00000i	0.854423	+	0.493301i	−0.00771799	+	0.999970i	$0.502457\pi$
$264$		0			0
$265$		0			0
$266$	12.0000	+	20.7846i	0.735767	+	1.27439i
$267$		0			0
$268$	2.59808	+	1.50000i	0.158703	+	0.0916271i
$269$	25.0000			1.52428			0.762138	−	0.647414i	$-0.224150\pi$
$269$	25.0000			1.52428			0.762138	+	0.647414i	$0.224150\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−3.46410	−	2.00000i	−0.210042	−	0.121268i
$273$		0			0
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	0.154172	−	0.988044i	$-0.450729\pi$
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	−0.778585	+	0.627539i	$0.784062\pi$
$278$		−	16.0000i		−	0.959616i
$279$		0			0
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$		0			0
$283$	−18.1865	+	10.5000i	−1.08108	+	0.624160i	−0.931187	−	0.364542i	$-0.881225\pi$
$283$	−18.1865	+	10.5000i	−1.08108	+	0.624160i	−0.149890	+	0.988703i	$0.547892\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$	−2.00000	+	3.46410i	−0.118262	+	0.204837i
$287$			15.0000i			0.885422i
$288$		0			0
$289$	1.00000			0.0588235
$290$		0			0
$291$		0			0
$292$	−3.46410	+	2.00000i	−0.202721	+	0.117041i
$293$	10.3923	−	6.00000i	0.607125	−	0.350524i	−0.164714	−	0.986341i	$-0.552670\pi$
$293$	10.3923	−	6.00000i	0.607125	−	0.350524i	0.771839	+	0.635818i	$0.219337\pi$
$294$		0			0
$295$		0			0
$296$	−12.0000			−0.697486
$297$		0			0
$298$		−	17.0000i		−	0.984784i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	−12.0000	−	20.7846i	−0.691669	−	1.19800i
$302$	1.73205	−	1.00000i	0.0996683	−	0.0575435i
$303$		0			0
$304$	4.00000	−	6.92820i	0.229416	−	0.397360i
$305$		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	$0.935985\pi$
$308$	5.19615	+	3.00000i	0.296078	+	0.170941i
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	12.1244	+	7.00000i	0.685309	+	0.395663i	0.801852	−	0.597522i	$-0.203848\pi$
$313$	12.1244	+	7.00000i	0.685309	+	0.395663i	−0.116543	+	0.993186i	$0.537181\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	6.00000			0.337526
$317$	−29.4449	−	17.0000i	−1.65379	−	0.954815i	−0.975494	−	0.220024i	$-0.929386\pi$
$317$	−29.4449	−	17.0000i	−1.65379	−	0.954815i	−0.678294	−	0.734791i	$-0.737280\pi$
$318$		0			0
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$		0			0
$321$		0			0
$322$	7.79423	+	4.50000i	0.434355	+	0.250775i
$323$		−	32.0000i		−	1.78053i
$324$		0			0
$325$		0			0
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	12.9904	−	7.50000i	0.717274	−	0.414118i
$329$	10.5000	+	18.1865i	0.578884	+	1.00266i
$330$		0			0
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	−0.771723	−	0.635959i	$-0.780605\pi$
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	0.936618	+	0.350352i	$0.113938\pi$
$332$			9.00000i			0.493939i
$333$		0			0
$334$	9.00000			0.492458
$335$		0			0
$336$		0			0
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	−0.676688	−	0.736270i	$-0.736585\pi$
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	0.299285	+	0.954164i	$0.403252\pi$
$338$	−7.79423	+	4.50000i	−0.423950	+	0.244768i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	−12.0000	+	20.7846i	−0.646997	+	1.12063i
$345$		0			0
$346$		0			0
$347$	−3.46410	+	2.00000i	−0.185963	+	0.107366i	−0.590091	−	0.807337i	$-0.700908\pi$
$347$	−3.46410	+	2.00000i	−0.185963	+	0.107366i	0.404128	+	0.914702i	$0.367575\pi$
$348$		0			0
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$		0			0
$351$		0			0
$352$		−	10.0000i		−	0.533002i
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.168397	−	0.985719i	$-0.553859\pi$
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.937856	+	0.347024i	$0.887192\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	+	12.9904i	0.397499	+	0.688489i
$357$		0			0
$358$	−1.73205	−	1.00000i	−0.0915417	−	0.0528516i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$	−6.06218	−	3.50000i	−0.318621	−	0.183956i
$363$		0			0
$364$	−3.00000	−	5.19615i	−0.157243	−	0.272352i
$365$		0			0
$366$		0			0
$367$	−20.7846	−	12.0000i	−1.08495	−	0.626395i	−0.152721	−	0.988269i	$-0.548804\pi$
$367$	−20.7846	−	12.0000i	−1.08495	−	0.626395i	−0.932227	+	0.361874i	$0.882137\pi$
$368$		−	3.00000i		−	0.156386i
$369$		0			0
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−8.66025	+	5.00000i	−0.448411	+	0.258890i	−0.707159	−	0.707055i	$-0.750023\pi$
$373$	−8.66025	+	5.00000i	−0.448411	+	0.258890i	0.258748	+	0.965945i	$0.416690\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$		0			0
$376$	10.5000	−	18.1865i	0.541496	−	0.937899i
$377$		−	2.00000i		−	0.103005i
$378$		0			0
$379$	26.0000			1.33553			0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000			1.33553			0.667765	+	0.744372i	$0.267251\pi$
$380$		0			0
$381$		0			0
$382$	6.92820	−	4.00000i	0.354478	−	0.204658i
$383$	31.1769	−	18.0000i	1.59307	−	0.919757i	0.600289	−	0.799783i	$-0.295052\pi$
$383$	31.1769	−	18.0000i	1.59307	−	0.919757i	0.992777	−	0.119974i	$-0.0382810\pi$
$384$		0			0
$385$		0			0
$386$	10.0000			0.508987
$387$		0			0
$388$			2.00000i			0.101535i
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$		0			0
$391$	−6.00000	−	10.3923i	−0.303433	−	0.525561i
$392$	5.19615	−	3.00000i	0.262445	−	0.151523i
$393$		0			0
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$		0			0
$396$		0			0
$397$			34.0000i			1.70641i	0.521575	+	0.853206i	$0.325345\pi$
$397$			34.0000i			1.70641i	−0.521575	+	0.853206i	$0.674655\pi$
$398$	−3.46410	−	2.00000i	−0.173640	−	0.100251i
$399$		0			0
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$		0			0
$404$	18.0000			0.895533
$405$		0			0
$406$	3.00000			0.148888
$407$	6.92820	+	4.00000i	0.343418	+	0.198273i
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$		0			0
$412$	6.92820	+	4.00000i	0.341328	+	0.197066i
$413$			42.0000i			2.06668i
$414$		0			0
$415$		0			0
$416$	−5.00000	+	8.66025i	−0.245145	+	0.424604i
$417$		0			0
$418$	−13.8564	+	8.00000i	−0.677739	+	0.391293i
$419$	−13.0000	−	22.5167i	−0.635092	−	1.10001i	−0.986496	−	0.163787i	$-0.947629\pi$
$419$	−13.0000	−	22.5167i	−0.635092	−	1.10001i	0.351404	−	0.936224i	$-0.385704\pi$
$420$		0			0
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	0.0706626	+	0.997500i	$0.477489\pi$
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	−0.899192	+	0.437555i	$0.855845\pi$
$422$			22.0000i			1.07094i
$423$		0			0
$424$	−6.00000			−0.291386
$425$		0			0
$426$		0			0
$427$	−18.1865	+	10.5000i	−0.880108	+	0.508131i
$428$	−2.59808	+	1.50000i	−0.125583	+	0.0725052i
$429$		0			0
$430$		0			0
$431$	30.0000			1.44505			0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000			1.44505			0.722525	+	0.691345i	$0.242982\pi$
$432$		0			0
$433$		−	28.0000i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$433$		−	28.0000i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$434$		0			0
$435$		0			0
$436$	2.50000	+	4.33013i	0.119728	+	0.207375i
$437$	20.7846	−	12.0000i	0.994263	−	0.574038i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$		0			0
$442$		−	8.00000i		−	0.380521i
$443$	−12.9904	−	7.50000i	−0.617192	−	0.356336i	0.158583	−	0.987346i	$-0.449307\pi$
$443$	−12.9904	−	7.50000i	−0.617192	−	0.356336i	−0.775775	+	0.631010i	$0.782641\pi$
$444$		0			0
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$		0			0
$448$	−18.1865	−	10.5000i	−0.859233	−	0.496078i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$		0			0
$451$	−10.0000			−0.470882
$452$	6.92820	+	4.00000i	0.325875	+	0.188144i
$453$		0			0
$454$	−2.00000	−	3.46410i	−0.0938647	−	0.162578i
$455$		0			0
$456$		0			0
$457$	17.3205	+	10.0000i	0.810219	+	0.467780i	0.847032	−	0.531542i	$-0.178387\pi$
$457$	17.3205	+	10.0000i	0.810219	+	0.467780i	−0.0368128	+	0.999322i	$0.511721\pi$
$458$			15.0000i			0.700904i
$459$		0			0
$460$		0			0
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	31.1769	−	18.0000i	1.44891	−	0.836531i	0.450497	−	0.892778i	$-0.351247\pi$
$463$	31.1769	−	18.0000i	1.44891	−	0.836531i	0.998417	+	0.0562469i	$0.0179134\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$		−	20.0000i		−	0.925490i	−0.886492	−	0.462745i	$-0.846865\pi$
$467$		−	20.0000i		−	0.925490i	0.886492	−	0.462745i	$-0.153135\pi$
$468$		0			0
$469$	−9.00000			−0.415581
$470$		0			0
$471$		0			0
$472$	36.3731	−	21.0000i	1.67421	−	0.966603i
$473$	13.8564	−	8.00000i	0.637118	−	0.367840i
$474$		0			0
$475$		0			0
$476$	−12.0000			−0.550019
$477$		0			0
$478$			8.00000i			0.365911i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$	9.52628	−	5.50000i	0.433910	−	0.250518i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$		0			0
$486$		0			0
$487$		−	16.0000i		−	0.725029i	−0.931978	−	0.362515i	$-0.881918\pi$
$487$		−	16.0000i		−	0.725029i	0.931978	−	0.362515i	$-0.118082\pi$
$488$	18.1865	+	10.5000i	0.823266	+	0.475313i
$489$		0			0
$490$		0			0
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	0.998467	−	0.0553560i	$-0.0176294\pi$
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	−0.547173	+	0.837020i	$0.684296\pi$
$492$		0			0
$493$	−3.46410	−	2.00000i	−0.156015	−	0.0900755i
$494$	16.0000			0.719874
$495$		0			0
$496$		0			0
$497$	−5.19615	−	3.00000i	−0.233079	−	0.134568i
$498$		0			0
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	0.246214	−	0.969216i	$-0.420813\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	7.00000i		−	0.312115i	−0.987748	−	0.156057i	$-0.950122\pi$
$503$		−	7.00000i		−	0.312115i	0.987748	−	0.156057i	$-0.0498784\pi$
$504$		0			0
$505$		0			0
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$		0			0
$508$	−4.33013	+	2.50000i	−0.192118	+	0.110920i
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.738945	−	0.673766i	$-0.764676\pi$
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.214026	−	0.976828i	$-0.568658\pi$
$510$		0			0
$511$	6.00000	−	10.3923i	0.265424	−	0.459728i
$512$			11.0000i			0.486136i
$513$		0			0
$514$	6.00000			0.264649
$515$		0			0
$516$		0			0
$517$	−12.1244	+	7.00000i	−0.533229	+	0.307860i
$518$	10.3923	−	6.00000i	0.456612	−	0.263625i
$519$		0			0
$520$		0			0
$521$	−11.0000			−0.481919			−0.240959	−	0.970535i	$-0.577462\pi$
$521$	−11.0000			−0.481919			−0.240959	+	0.970535i	$0.577462\pi$
$522$		0			0
$523$			29.0000i			1.26808i	0.773300	+	0.634041i	$0.218605\pi$
$523$			29.0000i			1.26808i	−0.773300	+	0.634041i	$0.781395\pi$
$524$	−3.00000	+	5.19615i	−0.131056	+	0.226995i
$525$		0			0
$526$	8.00000	+	13.8564i	0.348817	+	0.604168i
$527$		0			0
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		−	24.0000i		−	1.04053i
$533$	8.66025	+	5.00000i	0.375117	+	0.216574i
$534$		0			0
$535$		0			0
$536$	4.50000	+	7.79423i	0.194370	+	0.336659i
$537$		0			0
$538$	21.6506	+	12.5000i	0.933425	+	0.538913i
$539$	−4.00000			−0.172292
$540$		0			0
$541$	−39.0000			−1.67674			−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000			−1.67674			−0.838370	+	0.545101i	$0.816491\pi$
$542$	−6.92820	−	4.00000i	−0.297592	−	0.171815i
$543$		0			0
$544$	10.0000	+	17.3205i	0.428746	+	0.742611i
$545$		0			0
$546$		0			0
$547$	25.1147	+	14.5000i	1.07383	+	0.619975i	0.929225	−	0.369514i	$-0.120476\pi$
$547$	25.1147	+	14.5000i	1.07383	+	0.619975i	0.144604	+	0.989490i	$0.453809\pi$
$548$		−	12.0000i		−	0.512615i
$549$		0			0
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$	−15.5885	+	9.00000i	−0.662889	+	0.382719i
$554$	−6.00000	−	10.3923i	−0.254916	−	0.441527i
$555$		0			0
$556$	−8.00000	+	13.8564i	−0.339276	+	0.587643i
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	−12.9904	+	7.50000i	−0.547966	+	0.316368i
$563$	−18.1865	+	10.5000i	−0.766471	+	0.442522i	−0.831614	−	0.555354i	$-0.812583\pi$
$563$	−18.1865	+	10.5000i	−0.766471	+	0.442522i	0.0651433	+	0.997876i	$0.479250\pi$
$564$		0			0
$565$		0			0
$566$	−21.0000			−0.882696
$567$		0			0
$568$			6.00000i			0.251754i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	3.46410	−	2.00000i	0.144841	−	0.0836242i
$573$		0			0
$574$	−7.50000	+	12.9904i	−0.313044	+	0.542208i
$575$		0			0
$576$		0			0
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$		0			0
$580$		0			0
$581$	−13.5000	−	23.3827i	−0.560074	−	0.970077i
$582$		0			0
$583$	3.46410	+	2.00000i	0.143468	+	0.0828315i
$584$	−12.0000			−0.496564
$585$		0			0
$586$	12.0000			0.495715
$587$	−28.5788	−	16.5000i	−1.17957	−	0.681028i	−0.223659	−	0.974668i	$-0.571800\pi$
$587$	−28.5788	−	16.5000i	−1.17957	−	0.681028i	−0.955916	+	0.293640i	$0.905133\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−3.46410	−	2.00000i	−0.142374	−	0.0821995i
$593$			20.0000i			0.821302i	0.911793	+	0.410651i	$0.134698\pi$
$593$			20.0000i			0.821302i	−0.911793	+	0.410651i	$0.865302\pi$
$594$		0			0
$595$		0			0
$596$	−8.50000	+	14.7224i	−0.348174	+	0.603054i
$597$		0			0
$598$	5.19615	−	3.00000i	0.212486	−	0.122679i
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	0.949908	−	0.312531i	$-0.101177\pi$
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	−0.745613	+	0.666379i	$0.767843\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	−0.885700	−	0.464258i	$-0.846321\pi$
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	0.844909	+	0.534910i	$0.179654\pi$
$602$		−	24.0000i		−	0.978167i
$603$		0			0
$604$	−2.00000			−0.0813788
$605$		0			0
$606$		0			0
$607$	−35.5070	+	20.5000i	−1.44119	+	0.832069i	−0.997929	−	0.0643251i	$-0.979511\pi$
$607$	−35.5070	+	20.5000i	−1.44119	+	0.832069i	−0.443257	+	0.896394i	$0.646177\pi$
$608$	−34.6410	+	20.0000i	−1.40488	+	0.811107i
$609$		0			0
$610$		0			0
$611$	14.0000			0.566379
$612$		0			0
$613$			44.0000i			1.77714i	0.458738	+	0.888572i	$0.348302\pi$
$613$			44.0000i			1.77714i	−0.458738	+	0.888572i	$0.651698\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$		0			0
$616$	9.00000	+	15.5885i	0.362620	+	0.628077i
$617$	31.1769	−	18.0000i	1.25514	−	0.724653i	0.283011	−	0.959117i	$-0.408667\pi$
$617$	31.1769	−	18.0000i	1.25514	−	0.724653i	0.972125	+	0.234464i	$0.0753335\pi$
$618$		0			0
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−38.9711	−	22.5000i	−1.56135	−	0.901443i
$624$		0			0
$625$		0			0
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$		0			0
$628$	−12.1244	−	7.00000i	−0.483814	−	0.279330i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	15.5885	+	9.00000i	0.620076	+	0.358001i
$633$		0			0
$634$	−17.0000	−	29.4449i	−0.675156	−	1.16940i
$635$		0			0
$636$		0			0
$637$	3.46410	+	2.00000i	0.137253	+	0.0792429i
$638$			2.00000i			0.0791808i
$639$		0			0
$640$		0			0
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		0			0
$643$	7.79423	−	4.50000i	0.307374	−	0.177463i	−0.338377	−	0.941011i	$-0.609878\pi$
$643$	7.79423	−	4.50000i	0.307374	−	0.177463i	0.645751	+	0.763548i	$0.276544\pi$
$644$	−4.50000	−	7.79423i	−0.177325	−	0.307136i
$645$		0			0
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$			17.0000i			0.668339i	0.942513	+	0.334169i	$0.108456\pi$
$647$			17.0000i			0.668339i	−0.942513	+	0.334169i	$0.891544\pi$
$648$		0			0
$649$	−28.0000			−1.09910
$650$		0			0
$651$		0			0
$652$	3.46410	−	2.00000i	0.135665	−	0.0783260i
$653$	−3.46410	+	2.00000i	−0.135561	+	0.0782660i	−0.566247	−	0.824236i	$-0.691605\pi$
$653$	−3.46410	+	2.00000i	−0.135561	+	0.0782660i	0.430686	+	0.902502i	$0.358272\pi$
$654$		0			0
$655$		0			0
$656$	5.00000			0.195217
$657$		0			0
$658$			21.0000i			0.818665i
$659$	4.00000	−	6.92820i	0.155818	−	0.269884i	−0.777539	−	0.628835i	$-0.783532\pi$
$659$	4.00000	−	6.92820i	0.155818	−	0.269884i	0.933357	+	0.358951i	$0.116865\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	5.19615	−	3.00000i	0.201954	−	0.116598i
$663$		0			0
$664$	−13.5000	+	23.3827i	−0.523902	+	0.907424i
$665$		0			0
$666$		0			0
$667$		−	3.00000i		−	0.116160i
$668$	−7.79423	−	4.50000i	−0.301568	−	0.174110i
$669$		0			0
$670$		0			0
$671$	−7.00000	−	12.1244i	−0.270232	−	0.468056i
$672$		0			0
$673$	5.19615	+	3.00000i	0.200297	+	0.115642i	0.596794	−	0.802395i	$-0.296441\pi$
$673$	5.19615	+	3.00000i	0.200297	+	0.115642i	−0.396497	+	0.918036i	$0.629774\pi$
$674$	−8.00000			−0.308148
$675$		0			0
$676$	9.00000			0.346154
$677$	−36.3731	−	21.0000i	−1.39793	−	0.807096i	−0.403755	−	0.914867i	$-0.632295\pi$
$677$	−36.3731	−	21.0000i	−1.39793	−	0.807096i	−0.994176	+	0.107772i	$0.965628\pi$
$678$		0			0
$679$	−3.00000	−	5.19615i	−0.115129	−	0.199410i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$		0			0
$685$		0			0
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$		0			0
$688$	−6.92820	+	4.00000i	−0.264135	+	0.152499i
$689$	−2.00000	−	3.46410i	−0.0761939	−	0.131972i
$690$		0			0
$691$	7.00000	−	12.1244i	0.266293	−	0.461232i	−0.701609	−	0.712562i	$-0.747535\pi$
$691$	7.00000	−	12.1244i	0.266293	−	0.461232i	0.967901	+	0.251330i	$0.0808679\pi$
$692$		0			0
$693$		0			0
$694$	−4.00000			−0.151838
$695$		0			0
$696$		0			0
$697$	17.3205	−	10.0000i	0.656061	−	0.378777i
$698$	−4.33013	+	2.50000i	−0.163898	+	0.0946264i
$699$		0			0
$700$		0			0
$701$	−23.0000			−0.868698			−0.434349	−	0.900745i	$-0.643022\pi$
$701$	−23.0000			−0.868698			−0.434349	+	0.900745i	$0.643022\pi$
$702$		0			0
$703$		−	32.0000i		−	1.20690i
$704$	7.00000	−	12.1244i	0.263822	−	0.456954i
$705$		0			0
$706$	−12.0000	−	20.7846i	−0.451626	−	0.782239i
$707$	−46.7654	+	27.0000i	−1.75879	+	1.01544i
$708$		0			0
$709$	−20.5000	+	35.5070i	−0.769894	+	1.33349i	0.167727	+	0.985834i	$0.446357\pi$
$709$	−20.5000	+	35.5070i	−0.769894	+	1.33349i	−0.937620	+	0.347661i	$0.886976\pi$
$710$		0			0
$711$		0			0
$712$			45.0000i			1.68645i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.00000	+	1.73205i	0.0373718	+	0.0647298i
$717$		0			0
$718$	20.7846	+	12.0000i	0.775675	+	0.447836i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	38.9711	+	22.5000i	1.45036	+	0.837363i
$723$		0			0
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$		0			0
$726$		0			0
$727$	−19.9186	−	11.5000i	−0.738739	−	0.426511i	0.0828714	−	0.996560i	$-0.473591\pi$
$727$	−19.9186	−	11.5000i	−0.738739	−	0.426511i	−0.821611	+	0.570049i	$0.806924\pi$
$728$		−	18.0000i		−	0.667124i
$729$		0			0
$730$		0			0
$731$	−16.0000	+	27.7128i	−0.591781	+	1.02500i
$732$		0			0
$733$	29.4449	−	17.0000i	1.08757	−	0.627909i	0.154642	−	0.987971i	$-0.450578\pi$
$733$	29.4449	−	17.0000i	1.08757	−	0.627909i	0.932929	+	0.360061i	$0.117244\pi$
$734$	−12.0000	−	20.7846i	−0.442928	−	0.767174i
$735$		0			0
$736$	−7.50000	+	12.9904i	−0.276454	+	0.478832i
$737$		−	6.00000i		−	0.221013i
$738$		0			0
$739$	2.00000			0.0735712			0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000			0.0735712			0.0367856	+	0.999323i	$0.488288\pi$
$740$		0			0
$741$		0			0
$742$	5.19615	−	3.00000i	0.190757	−	0.110133i
$743$	−25.1147	+	14.5000i	−0.921370	+	0.531953i	−0.884072	−	0.467351i	$-0.845209\pi$
$743$	−25.1147	+	14.5000i	−0.921370	+	0.531953i	−0.0372984	+	0.999304i	$0.511875\pi$
$744$		0			0
$745$		0			0
$746$	−10.0000			−0.366126
$747$		0			0
$748$		−	8.00000i		−	0.292509i
$749$	4.50000	−	7.79423i	0.164426	−	0.284795i
$750$		0			0
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$	6.06218	−	3.50000i	0.221065	−	0.127632i
$753$		0			0
$754$	1.00000	−	1.73205i	0.0364179	−	0.0630776i
$755$		0			0
$756$		0			0
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$	22.5167	+	13.0000i	0.817842	+	0.472181i
$759$		0			0
$760$		0			0
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	0.969342	−	0.245716i	$-0.0790230\pi$
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	−0.697467	+	0.716617i	$0.745690\pi$
$762$		0			0
$763$	−12.9904	−	7.50000i	−0.470283	−	0.271518i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	36.0000			1.30073
$767$	24.2487	+	14.0000i	0.875570	+	0.505511i
$768$		0			0
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	0.907575	−	0.419890i	$-0.137931\pi$
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	−0.817423	+	0.576038i	$0.804598\pi$
$770$		0			0
$771$		0			0
$772$	−8.66025	−	5.00000i	−0.311689	−	0.179954i
$773$		−	24.0000i		−	0.863220i	−0.902060	−	0.431610i	$-0.857946\pi$
$773$		−	24.0000i		−	0.863220i	0.902060	−	0.431610i	$-0.142054\pi$
$774$		0			0
$775$		0			0
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$		0			0
$778$	−28.5788	+	16.5000i	−1.02460	+	0.591554i
$779$	20.0000	+	34.6410i	0.716574	+	1.24114i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		−	12.0000i		−	0.429119i
$783$		0			0
$784$	2.00000			0.0714286
$785$		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
$789$		0			0
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$			14.0000i			0.497155i
$794$	−17.0000	+	29.4449i	−0.603307	+	1.04496i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−22.5167	+	13.0000i	−0.797581	+	0.460484i	−0.842625	−	0.538501i	$-0.818991\pi$
$797$	−22.5167	+	13.0000i	−0.797581	+	0.460484i	0.0450436	+	0.998985i	$0.485657\pi$
$798$		0			0
$799$	14.0000	−	24.2487i	0.495284	−	0.857858i
$800$		0			0
$801$		0			0
$802$		−	18.0000i		−	0.635602i
$803$	6.92820	+	4.00000i	0.244491	+	0.141157i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	46.7654	+	27.0000i	1.64520	+	0.949857i
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$		0			0
$811$	−42.0000			−1.47482			−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000			−1.47482			−0.737410	+	0.675446i	$0.763951\pi$
$812$	−2.59808	−	1.50000i	−0.0911746	−	0.0526397i
$813$		0			0
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$		0			0
$816$		0			0
$817$	−55.4256	−	32.0000i	−1.93910	−	1.11954i
$818$			14.0000i			0.489499i
$819$		0			0
$820$		0			0
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		0			0
$823$	−45.8993	+	26.5000i	−1.59995	+	0.923732i	−0.608456	+	0.793588i	$0.708211\pi$
$823$	−45.8993	+	26.5000i	−1.59995	+	0.923732i	−0.991495	+	0.130144i	$0.958456\pi$
$824$	12.0000	+	20.7846i	0.418040	+	0.724066i
$825$		0			0
$826$	−21.0000	+	36.3731i	−0.730683	+	1.26558i
$827$		−	37.0000i		−	1.28662i	−0.765607	−	0.643308i	$-0.777561\pi$
$827$		−	37.0000i		−	1.28662i	0.765607	−	0.643308i	$-0.222439\pi$
$828$		0			0
$829$	3.00000			0.104194			0.0520972	−	0.998642i	$-0.483409\pi$
$829$	3.00000			0.104194			0.0520972	+	0.998642i	$0.483409\pi$
$830$		0			0
$831$		0			0
$832$	−12.1244	+	7.00000i	−0.420336	+	0.242681i
$833$	6.92820	−	4.00000i	0.240048	−	0.138592i
$834$		0			0
$835$		0			0
$836$	16.0000			0.553372
$837$		0			0
$838$		−	26.0000i		−	0.898155i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−29.4449	+	17.0000i	−1.01474	+	0.585859i
$843$		0			0
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$		0			0
$846$		0			0
$847$			21.0000i			0.721569i
$848$	−1.73205	−	1.00000i	−0.0594789	−	0.0343401i
$849$		0			0
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	−46.7654	−	27.0000i	−1.60122	−	0.924462i	−0.991245	−	0.132039i	$-0.957848\pi$
$853$	−46.7654	−	27.0000i	−1.60122	−	0.924462i	−0.609971	−	0.792424i	$-0.708819\pi$
$854$	−21.0000			−0.718605
$855$		0			0
$856$	−9.00000			−0.307614
$857$	8.66025	+	5.00000i	0.295829	+	0.170797i	0.640567	−	0.767902i	$-0.278699\pi$
$857$	8.66025	+	5.00000i	0.295829	+	0.170797i	−0.344739	+	0.938699i	$0.612033\pi$
$858$		0			0
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	0.990374	−	0.138416i	$-0.0442012\pi$
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	−0.615059	+	0.788481i	$0.710868\pi$
$860$		0			0
$861$		0			0
$862$	25.9808	+	15.0000i	0.884908	+	0.510902i
$863$			17.0000i			0.578687i	0.957225	+	0.289343i	$0.0934369\pi$
$863$			17.0000i			0.578687i	−0.957225	+	0.289343i	$0.906563\pi$
$864$		0			0
$865$		0			0
$866$	14.0000	−	24.2487i	0.475739	−	0.824005i
$867$		0			0
$868$		0			0
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−3.00000	+	5.19615i	−0.101651	+	0.176065i
$872$			15.0000i			0.507964i
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	−0.739543	−	0.673109i	$-0.764958\pi$
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	0.213158	+	0.977018i	$0.431625\pi$
$878$	24.2487	−	14.0000i	0.818354	−	0.472477i
$879$		0			0
$880$		0			0
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$		0			0
$883$		−	23.0000i		−	0.774012i	−0.922077	−	0.387006i	$-0.873509\pi$
$883$		−	23.0000i		−	0.774012i	0.922077	−	0.387006i	$-0.126491\pi$
$884$	−4.00000	+	6.92820i	−0.134535	+	0.233021i
$885$		0			0
$886$	−7.50000	−	12.9904i	−0.251967	−	0.436420i
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.921757	−	0.387768i	$-0.873246\pi$
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.125061	+	0.992149i	$0.539913\pi$
$888$		0			0
$889$	7.50000	−	12.9904i	0.251542	−	0.435683i
$890$		0			0
$891$		0			0
$892$			19.0000i			0.636167i
$893$	48.4974	+	28.0000i	1.62290	+	0.936984i
$894$		0			0
$895$		0			0
$896$	4.50000	+	7.79423i	0.150334	+	0.260387i
$897$		0			0
$898$	−22.5167	−	13.0000i	−0.751391	−	0.433816i
$899$		0			0
$900$		0			0
$901$	−8.00000			−0.266519
$902$	−8.66025	−	5.00000i	−0.288355	−	0.166482i
$903$		0			0
$904$	12.0000	+	20.7846i	0.399114	+	0.691286i
$905$		0			0
$906$		0			0
$907$	44.1673	+	25.5000i	1.46655	+	0.846714i	0.999300	−	0.0374111i	$-0.0119111\pi$
$907$	44.1673	+	25.5000i	1.46655	+	0.846714i	0.467251	+	0.884125i	$0.345244\pi$
$908$			4.00000i			0.132745i
$909$		0			0
$910$		0			0
$911$	−25.0000	+	43.3013i	−0.828287	+	1.43464i	0.0710941	+	0.997470i	$0.477351\pi$
$911$	−25.0000	+	43.3013i	−0.828287	+	1.43464i	−0.899381	+	0.437165i	$0.855982\pi$
$912$		0			0
$913$	15.5885	−	9.00000i	0.515903	−	0.297857i
$914$	10.0000	+	17.3205i	0.330771	+	0.572911i
$915$		0			0
$916$	7.50000	−	12.9904i	0.247807	−	0.429214i
$917$		−	18.0000i		−	0.594412i
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$		0			0
$921$		0			0
$922$	7.79423	−	4.50000i	0.256689	−	0.148200i
$923$	−3.46410	+	2.00000i	−0.114022	+	0.0658308i
$924$		0			0
$925$		0			0
$926$	36.0000			1.18303
$927$		0			0
$928$			5.00000i			0.164133i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$		0			0
$931$	8.00000	+	13.8564i	0.262189	+	0.454125i
$932$	20.7846	−	12.0000i	0.680823	−	0.393073i
$933$		0			0
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−7.79423	−	4.50000i	−0.254491	−	0.146930i
$939$		0			0
$940$		0			0
$941$	−3.50000	−	6.06218i	−0.114097	−	0.197621i	0.803322	−	0.595545i	$-0.203064\pi$
$941$	−3.50000	−	6.06218i	−0.114097	−	0.197621i	−0.917418	+	0.397924i	$0.869731\pi$
$942$		0			0
$943$	12.9904	+	7.50000i	0.423025	+	0.244234i
$944$	14.0000			0.455661
$945$		0			0
$946$	16.0000			0.520205
$947$	49.3634	+	28.5000i	1.60410	+	0.926126i	0.990656	+	0.136385i	$0.0435483\pi$
$947$	49.3634	+	28.5000i	1.60410	+	0.926126i	0.613441	+	0.789741i	$0.289785\pi$
$948$		0			0
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$		0			0
$952$	−31.1769	−	18.0000i	−1.01045	−	0.583383i
$953$		−	26.0000i		−	0.842223i	−0.907009	−	0.421111i	$-0.861640\pi$
$953$		−	26.0000i		−	0.842223i	0.907009	−	0.421111i	$-0.138360\pi$
$954$		0			0
$955$		0			0
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$		0			0
$958$	15.5885	−	9.00000i	0.503640	−	0.290777i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		−	8.00000i		−	0.257930i
$963$		0			0
$964$	−11.0000			−0.354286
$965$		0			0
$966$		0			0
$967$	35.5070	−	20.5000i	1.14183	−	0.659236i	0.194946	−	0.980814i	$-0.437547\pi$
$967$	35.5070	−	20.5000i	1.14183	−	0.659236i	0.946883	+	0.321578i	$0.104213\pi$
$968$	18.1865	−	10.5000i	0.584537	−	0.337483i
$969$		0			0
$970$		0			0
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$		0			0
$973$		−	48.0000i		−	1.53881i
$974$	8.00000	−	13.8564i	0.256337	−	0.443988i
$975$		0			0
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	32.9090	−	19.0000i	1.05285	−	0.607864i	0.129405	−	0.991592i	$-0.458693\pi$
$977$	32.9090	−	19.0000i	1.05285	−	0.607864i	0.923446	+	0.383728i	$0.125360\pi$
$978$		0			0
$979$	15.0000	−	25.9808i	0.479402	−	0.830349i
$980$		0			0
$981$		0			0
$982$			20.0000i			0.638226i
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	0.457995	−	0.888955i	$-0.348568\pi$
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	−0.540860	+	0.841112i	$0.681901\pi$
$984$		0			0
$985$		0			0
$986$	−2.00000	−	3.46410i	−0.0636930	−	0.110319i
$987$		0			0
$988$	−13.8564	−	8.00000i	−0.440831	−	0.254514i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	26.0000			0.825917			0.412959	−	0.910750i	$-0.364495\pi$
$991$	26.0000			0.825917			0.412959	+	0.910750i	$0.364495\pi$
$992$		0			0
$993$		0			0
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$		0			0
$997$	15.5885	+	9.00000i	0.493691	+	0.285033i	0.726105	−	0.687584i	$-0.241329\pi$
$997$	15.5885	+	9.00000i	0.493691	+	0.285033i	−0.232413	+	0.972617i	$0.574662\pi$
$998$		−	32.0000i		−	1.01294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.a.424.2		4
3.2	odd	2		225.2.k.a.124.1		4
5.2	odd	4		675.2.e.a.451.1		2
5.3	odd	4		135.2.e.a.46.1		2
5.4	even	2	inner	675.2.k.a.424.1		4
9.2	odd	6		2025.2.b.c.649.2		2
9.4	even	3	inner	675.2.k.a.199.1		4
9.5	odd	6		225.2.k.a.49.2		4
9.7	even	3		2025.2.b.d.649.1		2
15.2	even	4		225.2.e.a.151.1		2
15.8	even	4		45.2.e.a.16.1	✓	2
15.14	odd	2		225.2.k.a.124.2		4
20.3	even	4		2160.2.q.a.721.1		2
45.2	even	12		2025.2.a.b.1.1		1
45.4	even	6	inner	675.2.k.a.199.2		4
45.7	odd	12		2025.2.a.e.1.1		1
45.13	odd	12		135.2.e.a.91.1		2
45.14	odd	6		225.2.k.a.49.1		4
45.22	odd	12		675.2.e.a.226.1		2
45.23	even	12		45.2.e.a.31.1	yes	2
45.29	odd	6		2025.2.b.c.649.1		2
45.32	even	12		225.2.e.a.76.1		2
45.34	even	6		2025.2.b.d.649.2		2
45.38	even	12		405.2.a.e.1.1		1
45.43	odd	12		405.2.a.b.1.1		1
60.23	odd	4		720.2.q.d.241.1		2
180.23	odd	12		720.2.q.d.481.1		2
180.43	even	12		6480.2.a.x.1.1		1
180.83	odd	12		6480.2.a.k.1.1		1
180.103	even	12		2160.2.q.a.1441.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.a.16.1	✓	2	15.8	even	4
45.2.e.a.31.1	yes	2	45.23	even	12
135.2.e.a.46.1		2	5.3	odd	4
135.2.e.a.91.1		2	45.13	odd	12
225.2.e.a.76.1		2	45.32	even	12
225.2.e.a.151.1		2	15.2	even	4
225.2.k.a.49.1		4	45.14	odd	6
225.2.k.a.49.2		4	9.5	odd	6
225.2.k.a.124.1		4	3.2	odd	2
225.2.k.a.124.2		4	15.14	odd	2
405.2.a.b.1.1		1	45.43	odd	12
405.2.a.e.1.1		1	45.38	even	12
675.2.e.a.226.1		2	45.22	odd	12
675.2.e.a.451.1		2	5.2	odd	4
675.2.k.a.199.1		4	9.4	even	3	inner
675.2.k.a.199.2		4	45.4	even	6	inner
675.2.k.a.424.1		4	5.4	even	2	inner
675.2.k.a.424.2		4	1.1	even	1	trivial
720.2.q.d.241.1		2	60.23	odd	4
720.2.q.d.481.1		2	180.23	odd	12
2025.2.a.b.1.1		1	45.2	even	12
2025.2.a.e.1.1		1	45.7	odd	12
2025.2.b.c.649.1		2	45.29	odd	6
2025.2.b.c.649.2		2	9.2	odd	6
2025.2.b.d.649.1		2	9.7	even	3
2025.2.b.d.649.2		2	45.34	even	6
2160.2.q.a.721.1		2	20.3	even	4
2160.2.q.a.1441.1		2	180.103	even	12
6480.2.a.k.1.1		1	180.83	odd	12
6480.2.a.x.1.1		1	180.43	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.59808 + 1.50000i) q^{7} -3.00000i q^{8} +(-1.00000 + 1.73205i) q^{11} +(1.73205 - 1.00000i) q^{13} +(1.50000 + 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} -4.00000i q^{17} +8.00000 q^{19} +(-1.73205 + 1.00000i) q^{22} +(2.59808 - 1.50000i) q^{23} +2.00000 q^{26} -3.00000i q^{28} +(0.500000 - 0.866025i) q^{29} +(-4.33013 + 2.50000i) q^{32} +(2.00000 - 3.46410i) q^{34} -4.00000i q^{37} +(6.92820 + 4.00000i) q^{38} +(2.50000 + 4.33013i) q^{41} +(-6.92820 - 4.00000i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(6.06218 + 3.50000i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-1.73205 - 1.00000i) q^{52} -2.00000i q^{53} +(4.50000 - 7.79423i) q^{56} +(0.866025 - 0.500000i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} -7.00000 q^{64} +(-2.59808 + 1.50000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -2.00000 q^{71} -4.00000i q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.00000 - 6.92820i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(-3.00000 + 5.19615i) q^{79} +5.00000i q^{82} +(-7.79423 - 4.50000i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(5.19615 + 3.00000i) q^{88} -15.0000 q^{89} +6.00000 q^{91} +(-2.59808 - 1.50000i) q^{92} +(3.50000 + 6.06218i) q^{94} +(-1.73205 - 1.00000i) q^{97} +2.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} - 4 q^{11} + 6 q^{14} + 2 q^{16} + 32 q^{19} + 8 q^{26} + 2 q^{29} + 8 q^{34} + 10 q^{41} + 8 q^{44} + 12 q^{46} + 4 q^{49} + 18 q^{56} + 28 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{71} + 8 q^{74}+ \cdots + 14 q^{94}+O(q^{100}) \) 4 * q - 2 * q^4 - 4 * q^11 + 6 * q^14 + 2 * q^16 + 32 * q^19 + 8 * q^26 + 2 * q^29 + 8 * q^34 + 10 * q^41 + 8 * q^44 + 12 * q^46 + 4 * q^49 + 18 * q^56 + 28 * q^59 - 14 * q^61 - 28 * q^64 - 8 * q^71 + 8 * q^74 - 16 * q^76 - 12 * q^79 - 16 * q^86 - 60 * q^89 + 24 * q^91 + 14 * q^94

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