LMFDB - Embedded newform 675.2.e.a.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(226,675)]

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, 0]))

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

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

chi := DirichletCharacter("675.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	675.226
Dual form			675.2.e.a.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(-1.00000 - 1.73205i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} -8.00000 q^{19} +(-1.00000 + 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +2.00000 q^{26} -3.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(-2.50000 + 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{34} +4.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(2.50000 - 4.33013i) q^{41} +(-4.00000 - 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(-1.00000 + 1.73205i) q^{49} +(1.00000 + 1.73205i) q^{52} -2.00000 q^{53} +(4.50000 + 7.79423i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +7.00000 q^{64} +(-1.50000 + 2.59808i) q^{67} +(2.00000 - 3.46410i) q^{68} -2.00000 q^{71} -4.00000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(-3.00000 + 5.19615i) q^{77} +(3.00000 + 5.19615i) q^{79} -5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.00000 + 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{88} +15.0000 q^{89} +6.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(1.00000 + 1.73205i) q^{97} +2.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 2 * q - q^2 + q^4 - 3 * q^7 - 6 * q^8	$ 2 q - q^{2} + q^{4} - 3 q^{7} - 6 q^{8} - 2 q^{11} - 2 q^{13} - 3 q^{14} + q^{16} + 8 q^{17} - 16 q^{19} - 2 q^{22} - 3 q^{23} + 4 q^{26} - 6 q^{28} - q^{29} - 5 q^{32} - 4 q^{34} + 8 q^{37} + 8 q^{38} + 5 q^{41} - 8 q^{43} - 4 q^{44} + 6 q^{46} - 7 q^{47} - 2 q^{49} + 2 q^{52} - 4 q^{53} + 9 q^{56} - q^{58} - 14 q^{59} - 7 q^{61} + 14 q^{64} - 3 q^{67} + 4 q^{68} - 4 q^{71} - 8 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{77} + 6 q^{79} - 10 q^{82} - 9 q^{83} - 8 q^{86} + 6 q^{88} + 30 q^{89} + 12 q^{91} + 3 q^{92} - 7 q^{94} + 2 q^{97} + 4 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^4 - 3 * q^7 - 6 * q^8 - 2 * q^11 - 2 * q^13 - 3 * q^14 + q^16 + 8 * q^17 - 16 * q^19 - 2 * q^22 - 3 * q^23 + 4 * q^26 - 6 * q^28 - q^29 - 5 * q^32 - 4 * q^34 + 8 * q^37 + 8 * q^38 + 5 * q^41 - 8 * q^43 - 4 * q^44 + 6 * q^46 - 7 * q^47 - 2 * q^49 + 2 * q^52 - 4 * q^53 + 9 * q^56 - q^58 - 14 * q^59 - 7 * q^61 + 14 * q^64 - 3 * q^67 + 4 * q^68 - 4 * q^71 - 8 * q^73 - 4 * q^74 - 8 * q^76 - 6 * q^77 + 6 * q^79 - 10 * q^82 - 9 * q^83 - 8 * q^86 + 6 * q^88 + 30 * q^89 + 12 * q^91 + 3 * q^92 - 7 * q^94 + 2 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.50000	+	2.59808i	−0.400892	+	0.694365i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$		0			0
$26$	2.00000			0.392232
$27$		0			0
$28$	−3.00000			−0.566947
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$		0			0
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$		0			0
$36$		0			0
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	4.00000	+	6.92820i	0.648886	+	1.12390i
$39$		0			0
$40$		0			0
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	3.00000			0.442326
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$		0			0
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$		0			0
$56$	4.50000	+	7.79423i	0.601338	+	1.04155i
$57$		0			0
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.0991242	+	0.995075i	$0.531604\pi$
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.812198	+	0.583382i	$0.801729\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$		0			0
$64$	7.00000			0.875000
$65$		0			0
$66$		0			0
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		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
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$	−3.00000	+	5.19615i	−0.341882	+	0.592157i
$78$		0			0
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$		0			0
$81$		0			0
$82$	−5.00000			−0.552158
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$		0			0
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		0			0
$91$	6.00000			0.628971
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$		0			0
$96$		0			0
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	2.00000			0.202031
$99$		0			0
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	3.00000	−	5.19615i	0.294174	−	0.509525i
$105$		0			0
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$		0			0
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$		0			0
$112$	1.50000	−	2.59808i	0.141737	−	0.245495i
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$		0			0
$115$		0			0
$116$	−1.00000			−0.0928477
$117$		0			0
$118$	14.0000			1.28880
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−3.50000	+	6.06218i	−0.316875	+	0.548844i
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$		0			0
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	12.0000	+	20.7846i	1.04053	+	1.80225i
$134$	3.00000			0.259161
$135$		0			0
$136$	−12.0000			−1.02899
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$		0			0
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	4.00000			0.334497
$144$		0			0
$145$		0			0
$146$	2.00000	+	3.46410i	0.165521	+	0.286691i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	8.50000	−	14.7224i	0.696347	−	1.20611i	−0.273377	−	0.961907i	$-0.588141\pi$
$149$	8.50000	−	14.7224i	0.696347	−	1.20611i	0.969724	−	0.244202i	$-0.0785259\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	24.0000			1.94666
$153$		0			0
$154$	6.00000			0.483494
$155$		0			0
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$		0			0
$160$		0			0
$161$	9.00000			0.709299
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−2.50000	−	4.33013i	−0.195217	−	0.338126i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$	−8.00000			−0.609994
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	2.00000			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−3.00000	−	5.19615i	−0.222375	−	0.385164i
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	−7.00000			−0.510527
$189$		0			0
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	1.00000	+	1.73205i	0.0714286	+	0.123718i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$		0			0
$201$		0			0
$202$	−9.00000	+	15.5885i	−0.633238	+	1.09680i
$203$	−1.50000	+	2.59808i	−0.105279	+	0.182349i
$204$		0			0
$205$		0			0
$206$	−8.00000			−0.557386
$207$		0			0
$208$	−2.00000			−0.138675
$209$	8.00000	+	13.8564i	0.553372	+	0.958468i
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	−1.00000	+	1.73205i	−0.0686803	+	0.118958i
$213$		0			0
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−2.50000	−	4.33013i	−0.169321	−	0.293273i
$219$		0			0
$220$		0			0
$221$	−4.00000	+	6.92820i	−0.269069	+	0.466041i
$222$		0			0
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	−0.986267	−	0.165161i	$-0.947186\pi$
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	0.350100	−	0.936713i	$-0.386148\pi$
$224$	15.0000			1.00223
$225$		0			0
$226$	−8.00000			−0.532152
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	0.924734	−	0.380615i	$-0.124288\pi$
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	−0.791989	+	0.610535i	$0.790954\pi$
$228$		0			0
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	−0.999987	−	0.00505719i	$-0.998390\pi$
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	0.504373	+	0.863486i	$0.331724\pi$
$230$		0			0
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$		0			0
$235$		0			0
$236$	7.00000	+	12.1244i	0.455661	+	0.789228i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	−4.00000	+	6.92820i	−0.258738	+	0.448148i	−0.965904	−	0.258900i	$-0.916640\pi$
$239$	−4.00000	+	6.92820i	−0.258738	+	0.448148i	0.707166	+	0.707048i	$0.249973\pi$
$240$		0			0
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	−7.00000			−0.449977
$243$		0			0
$244$	−7.00000			−0.448129
$245$		0			0
$246$		0			0
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$		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
$253$	6.00000			0.377217
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$		0			0
$261$		0			0
$262$	6.00000			0.370681
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		0			0
$265$		0			0
$266$	12.0000	−	20.7846i	0.735767	−	1.27439i
$267$		0			0
$268$	1.50000	+	2.59808i	0.0916271	+	0.158703i
$269$	−25.0000			−1.52428			−0.762138	−	0.647414i	$-0.775850\pi$
$269$	−25.0000			−1.52428			−0.762138	+	0.647414i	$0.775850\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	6.00000	+	10.3923i	0.360505	+	0.624413i	0.988044	−	0.154172i	$-0.0492710\pi$
$277$	6.00000	+	10.3923i	0.360505	+	0.624413i	−0.627539	+	0.778585i	$0.715938\pi$
$278$	−16.0000			−0.959616
$279$		0			0
$280$		0			0
$281$	−7.50000	−	12.9904i	−0.447412	−	0.774941i	0.550804	−	0.834634i	$-0.314321\pi$
$281$	−7.50000	−	12.9904i	−0.447412	−	0.774941i	−0.998217	+	0.0596933i	$0.980988\pi$
$282$		0			0
$283$	10.5000	−	18.1865i	0.624160	−	1.08108i	−0.364542	−	0.931187i	$-0.618775\pi$
$283$	10.5000	−	18.1865i	0.624160	−	1.08108i	0.988703	−	0.149890i	$-0.0478921\pi$
$284$	−1.00000	+	1.73205i	−0.0593391	+	0.102778i
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	−15.0000			−0.885422
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$		0			0
$295$		0			0
$296$	−12.0000			−0.697486
$297$		0			0
$298$	−17.0000			−0.984784
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$	−12.0000	+	20.7846i	−0.691669	+	1.19800i
$302$	1.00000	−	1.73205i	0.0575435	−	0.0996683i
$303$		0			0
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$		0			0
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	6.00000			0.337526
$317$	17.0000	+	29.4449i	0.954815	+	1.65379i	0.734791	+	0.678294i	$0.237280\pi$
$317$	17.0000	+	29.4449i	0.954815	+	1.65379i	0.220024	+	0.975494i	$0.429386\pi$
$318$		0			0
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$		0			0
$321$		0			0
$322$	−4.50000	−	7.79423i	−0.250775	−	0.434355i
$323$	−32.0000			−1.78053
$324$		0			0
$325$		0			0
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$		0			0
$328$	−7.50000	+	12.9904i	−0.414118	+	0.717274i
$329$	−10.5000	+	18.1865i	−0.578884	+	1.00266i
$330$		0			0
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	0.936618	−	0.350352i	$-0.113938\pi$
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	−0.771723	+	0.635959i	$0.780605\pi$
$332$	−9.00000			−0.493939
$333$		0			0
$334$	−9.00000			−0.492458
$335$		0			0
$336$		0			0
$337$	−4.00000	+	6.92820i	−0.217894	+	0.377403i	−0.954164	−	0.299285i	$-0.903252\pi$
$337$	−4.00000	+	6.92820i	−0.217894	+	0.377403i	0.736270	+	0.676688i	$0.236585\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−15.0000			−0.809924
$344$	12.0000	+	20.7846i	0.646997	+	1.12063i
$345$		0			0
$346$		0			0
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$		0			0
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$		0			0
$352$	10.0000			0.533002
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	−	12.9904i	0.397499	−	0.688489i
$357$		0			0
$358$	−1.00000	−	1.73205i	−0.0528516	−	0.0915417i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$		0			0
$364$	3.00000	−	5.19615i	0.157243	−	0.272352i
$365$		0			0
$366$		0			0
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	0.988269	+	0.152721i	$0.0488036\pi$
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	−0.361874	+	0.932227i	$0.617863\pi$
$368$	−3.00000			−0.156386
$369$		0			0
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$		0			0
$376$	10.5000	+	18.1865i	0.541496	+	0.937899i
$377$	2.00000			0.103005
$378$		0			0
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$		0			0
$381$		0			0
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$		0			0
$385$		0			0
$386$	10.0000			0.508987
$387$		0			0
$388$	2.00000			0.101535
$389$	16.5000	+	28.5788i	0.836583	+	1.44900i	0.892735	+	0.450582i	$0.148784\pi$
$389$	16.5000	+	28.5788i	0.836583	+	1.44900i	−0.0561516	+	0.998422i	$0.517883\pi$
$390$		0			0
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$		0			0
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$		0			0
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	−2.00000	−	3.46410i	−0.100251	−	0.173640i
$399$		0			0
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$		0			0
$404$	−18.0000			−0.895533
$405$		0			0
$406$	3.00000			0.148888
$407$	−4.00000	−	6.92820i	−0.198273	−	0.343418i
$408$		0			0
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	42.0000			2.06668
$414$		0			0
$415$		0			0
$416$	−5.00000	−	8.66025i	−0.245145	−	0.424604i
$417$		0			0
$418$	8.00000	−	13.8564i	0.391293	−	0.677739i
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	−0.351404	−	0.936224i	$-0.614296\pi$
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	0.986496	−	0.163787i	$-0.0523710\pi$
$420$		0			0
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	−0.899192	−	0.437555i	$-0.855845\pi$
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	0.0706626	−	0.997500i	$-0.477489\pi$
$422$	−22.0000			−1.07094
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	−10.5000	+	18.1865i	−0.508131	+	0.880108i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$		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
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$		0			0
$435$		0			0
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		0			0
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$		0			0
$442$	8.00000			0.380521
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	0.631010	−	0.775775i	$-0.282641\pi$
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	−0.987346	+	0.158583i	$0.949307\pi$
$444$		0			0
$445$		0			0
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$		0			0
$448$	−10.5000	−	18.1865i	−0.496078	−	0.859233i
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$		0			0
$451$	−10.0000			−0.470882
$452$	−4.00000	−	6.92820i	−0.188144	−	0.325875i
$453$		0			0
$454$	2.00000	−	3.46410i	0.0938647	−	0.162578i
$455$		0			0
$456$		0			0
$457$	−10.0000	−	17.3205i	−0.467780	−	0.810219i	0.531542	−	0.847032i	$-0.321613\pi$
$457$	−10.0000	−	17.3205i	−0.467780	−	0.810219i	−0.999322	+	0.0368128i	$0.988279\pi$
$458$	15.0000			0.700904
$459$		0			0
$460$		0			0
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$		0			0
$463$	−18.0000	+	31.1769i	−0.836531	+	1.44891i	0.0562469	+	0.998417i	$0.482087\pi$
$463$	−18.0000	+	31.1769i	−0.836531	+	1.44891i	−0.892778	+	0.450497i	$0.851247\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$		0			0
$469$	9.00000			0.415581
$470$		0			0
$471$		0			0
$472$	21.0000	−	36.3731i	0.966603	−	1.67421i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$		0			0
$476$	−12.0000			−0.550019
$477$		0			0
$478$	8.00000			0.365911
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$	5.50000	−	9.52628i	0.250518	−	0.433910i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$		0			0
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	10.5000	+	18.1865i	0.475313	+	0.823266i
$489$		0			0
$490$		0			0
$491$	10.0000	−	17.3205i	0.451294	−	0.781664i	−0.547173	−	0.837020i	$-0.684296\pi$
$491$	10.0000	−	17.3205i	0.451294	−	0.781664i	0.998467	+	0.0553560i	$0.0176294\pi$
$492$		0			0
$493$	−2.00000	−	3.46410i	−0.0900755	−	0.156015i
$494$	−16.0000			−0.719874
$495$		0			0
$496$		0			0
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7.00000			−0.312115			−0.156057	−	0.987748i	$-0.549878\pi$
$503$	−7.00000			−0.312115			−0.156057	+	0.987748i	$0.549878\pi$
$504$		0			0
$505$		0			0
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$		0			0
$508$	2.50000	−	4.33013i	0.110920	−	0.192118i
$509$	21.5000	−	37.2391i	0.952971	−	1.65059i	0.214026	−	0.976828i	$-0.431342\pi$
$509$	21.5000	−	37.2391i	0.952971	−	1.65059i	0.738945	−	0.673766i	$-0.235324\pi$
$510$		0			0
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	−6.00000			−0.264649
$515$		0			0
$516$		0			0
$517$	−7.00000	+	12.1244i	−0.307860	+	0.533229i
$518$	−6.00000	+	10.3923i	−0.263625	+	0.456612i
$519$		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
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$	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
$532$	24.0000			1.04053
$533$	5.00000	+	8.66025i	0.216574	+	0.375117i
$534$		0			0
$535$		0			0
$536$	4.50000	−	7.79423i	0.194370	−	0.336659i
$537$		0			0
$538$	12.5000	+	21.6506i	0.538913	+	0.933425i
$539$	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	$0.816491\pi$
$542$	4.00000	+	6.92820i	0.171815	+	0.297592i
$543$		0			0
$544$	−10.0000	+	17.3205i	−0.428746	+	0.742611i
$545$		0			0
$546$		0			0
$547$	−14.5000	−	25.1147i	−0.619975	−	1.07383i	−0.989490	−	0.144604i	$-0.953809\pi$
$547$	−14.5000	−	25.1147i	−0.619975	−	1.07383i	0.369514	−	0.929225i	$-0.379524\pi$
$548$	−12.0000			−0.512615
$549$		0			0
$550$		0			0
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$		0			0
$553$	9.00000	−	15.5885i	0.382719	−	0.662889i
$554$	6.00000	−	10.3923i	0.254916	−	0.441527i
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	10.5000	−	18.1865i	0.442522	−	0.766471i	−0.555354	−	0.831614i	$-0.687417\pi$
$563$	10.5000	−	18.1865i	0.442522	−	0.766471i	0.997876	+	0.0651433i	$0.0207504\pi$
$564$		0			0
$565$		0			0
$566$	−21.0000			−0.882696
$567$		0			0
$568$	6.00000			0.251754
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$		0			0
$574$	7.50000	+	12.9904i	0.313044	+	0.542208i
$575$		0			0
$576$		0			0
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$		0			0
$580$		0			0
$581$	−13.5000	+	23.3827i	−0.560074	+	0.970077i
$582$		0			0
$583$	2.00000	+	3.46410i	0.0828315	+	0.143468i
$584$	12.0000			0.496564
$585$		0			0
$586$	12.0000			0.495715
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	20.0000			0.821302			0.410651	−	0.911793i	$-0.365302\pi$
$593$	20.0000			0.821302			0.410651	+	0.911793i	$0.365302\pi$
$594$		0			0
$595$		0			0
$596$	−8.50000	−	14.7224i	−0.348174	−	0.603054i
$597$		0			0
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	−0.949908	−	0.312531i	$-0.898823\pi$
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	0.745613	+	0.666379i	$0.232157\pi$
$600$		0			0
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$	24.0000			0.978167
$603$		0			0
$604$	2.00000			0.0813788
$605$		0			0
$606$		0			0
$607$	−20.5000	+	35.5070i	−0.832069	+	1.44119i	0.0643251	+	0.997929i	$0.479511\pi$
$607$	−20.5000	+	35.5070i	−0.832069	+	1.44119i	−0.896394	+	0.443257i	$0.853823\pi$
$608$	20.0000	−	34.6410i	0.811107	−	1.40488i
$609$		0			0
$610$		0			0
$611$	14.0000			0.566379
$612$		0			0
$613$	44.0000			1.77714			0.888572	−	0.458738i	$-0.151698\pi$
$613$	44.0000			1.77714			0.888572	+	0.458738i	$0.151698\pi$
$614$	3.50000	+	6.06218i	0.141249	+	0.244650i
$615$		0			0
$616$	9.00000	−	15.5885i	0.362620	−	0.628077i
$617$	18.0000	−	31.1769i	0.724653	−	1.25514i	−0.234464	−	0.972125i	$-0.575334\pi$
$617$	18.0000	−	31.1769i	0.724653	−	1.25514i	0.959117	−	0.283011i	$-0.0913331\pi$
$618$		0			0
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.5000	−	38.9711i	−0.901443	−	1.56135i
$624$		0			0
$625$		0			0
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	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	$0.396829\pi$
$632$	−9.00000	−	15.5885i	−0.358001	−	0.620076i
$633$		0			0
$634$	17.0000	−	29.4449i	0.675156	−	1.16940i
$635$		0			0
$636$		0			0
$637$	−2.00000	−	3.46410i	−0.0792429	−	0.137253i
$638$	2.00000			0.0791808
$639$		0			0
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	−4.50000	+	7.79423i	−0.177463	+	0.307374i	−0.941011	−	0.338377i	$-0.890122\pi$
$643$	−4.50000	+	7.79423i	−0.177463	+	0.307374i	0.763548	+	0.645751i	$0.223456\pi$
$644$	4.50000	−	7.79423i	0.177325	−	0.307136i
$645$		0			0
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	−17.0000			−0.668339			−0.334169	−	0.942513i	$-0.608456\pi$
$647$	−17.0000			−0.668339			−0.334169	+	0.942513i	$0.608456\pi$
$648$		0			0
$649$	28.0000			1.09910
$650$		0			0
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	2.00000	−	3.46410i	0.0782660	−	0.135561i	−0.824236	−	0.566247i	$-0.808395\pi$
$653$	2.00000	−	3.46410i	0.0782660	−	0.135561i	0.902502	+	0.430686i	$0.141728\pi$
$654$		0			0
$655$		0			0
$656$	5.00000			0.195217
$657$		0			0
$658$	21.0000			0.818665
$659$	−4.00000	−	6.92820i	−0.155818	−	0.269884i	0.777539	−	0.628835i	$-0.216468\pi$
$659$	−4.00000	−	6.92820i	−0.155818	−	0.269884i	−0.933357	+	0.358951i	$0.883135\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	3.00000	−	5.19615i	0.116598	−	0.201954i
$663$		0			0
$664$	13.5000	+	23.3827i	0.523902	+	0.907424i
$665$		0			0
$666$		0			0
$667$	3.00000			0.116160
$668$	−4.50000	−	7.79423i	−0.174110	−	0.301568i
$669$		0			0
$670$		0			0
$671$	−7.00000	+	12.1244i	−0.270232	+	0.468056i
$672$		0			0
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	0.918036	−	0.396497i	$-0.129774\pi$
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	−0.802395	+	0.596794i	$0.796441\pi$
$674$	8.00000			0.308148
$675$		0			0
$676$	9.00000			0.346154
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$		0			0
$679$	3.00000	−	5.19615i	0.115129	−	0.199410i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$		0			0
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$		0			0
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	0.967901	−	0.251330i	$-0.0808679\pi$
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	−0.701609	+	0.712562i	$0.747535\pi$
$692$		0			0
$693$		0			0
$694$	4.00000			0.151838
$695$		0			0
$696$		0			0
$697$	10.0000	−	17.3205i	0.378777	−	0.656061i
$698$	2.50000	−	4.33013i	0.0946264	−	0.163898i
$699$		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
$703$	−32.0000			−1.20690
$704$	−7.00000	−	12.1244i	−0.263822	−	0.456954i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−27.0000	+	46.7654i	−1.01544	+	1.75879i
$708$		0			0
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	0.937620	+	0.347661i	$0.113024\pi$
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	−0.167727	+	0.985834i	$0.553643\pi$
$710$		0			0
$711$		0			0
$712$	−45.0000			−1.68645
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.00000	−	1.73205i	0.0373718	−	0.0647298i
$717$		0			0
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	−22.5000	−	38.9711i	−0.837363	−	1.45036i
$723$		0			0
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$		0			0
$726$		0			0
$727$	11.5000	+	19.9186i	0.426511	+	0.738739i	0.996560	−	0.0828714i	$-0.0264091\pi$
$727$	11.5000	+	19.9186i	0.426511	+	0.738739i	−0.570049	+	0.821611i	$0.693076\pi$
$728$	−18.0000			−0.667124
$729$		0			0
$730$		0			0
$731$	−16.0000	−	27.7128i	−0.591781	−	1.02500i
$732$		0			0
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	0.360061	+	0.932929i	$0.382756\pi$
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	−0.987971	+	0.154642i	$0.950578\pi$
$734$	12.0000	−	20.7846i	0.442928	−	0.767174i
$735$		0			0
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	6.00000			0.221013
$738$		0			0
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$		0			0
$741$		0			0
$742$	3.00000	−	5.19615i	0.110133	−	0.190757i
$743$	14.5000	−	25.1147i	0.531953	−	0.921370i	−0.467351	−	0.884072i	$-0.654791\pi$
$743$	14.5000	−	25.1147i	0.531953	−	0.921370i	0.999304	−	0.0372984i	$-0.0118752\pi$
$744$		0			0
$745$		0			0
$746$	−10.0000			−0.366126
$747$		0			0
$748$	−8.00000			−0.292509
$749$	−4.50000	−	7.79423i	−0.164426	−	0.284795i
$750$		0			0
$751$	−5.00000	+	8.66025i	−0.182453	+	0.316017i	−0.942715	−	0.333599i	$-0.891737\pi$
$751$	−5.00000	+	8.66025i	−0.182453	+	0.316017i	0.760263	+	0.649616i	$0.225070\pi$
$752$	3.50000	−	6.06218i	0.127632	−	0.221065i
$753$		0			0
$754$	−1.00000	−	1.73205i	−0.0364179	−	0.0630776i
$755$		0			0
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	13.0000	+	22.5167i	0.472181	+	0.817842i
$759$		0			0
$760$		0			0
$761$	7.50000	−	12.9904i	0.271875	−	0.470901i	−0.697467	−	0.716617i	$-0.745690\pi$
$761$	7.50000	−	12.9904i	0.271875	−	0.470901i	0.969342	+	0.245716i	$0.0790230\pi$
$762$		0			0
$763$	−7.50000	−	12.9904i	−0.271518	−	0.470283i
$764$	8.00000			0.289430
$765$		0			0
$766$	36.0000			1.30073
$767$	−14.0000	−	24.2487i	−0.505511	−	0.875570i
$768$		0			0
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$		0			0
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$		0			0
$775$		0			0
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$		0			0
$778$	16.5000	−	28.5788i	0.591554	−	1.02460i
$779$	−20.0000	+	34.6410i	−0.716574	+	1.24114i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	12.0000			0.429119
$783$		0			0
$784$	−2.00000			−0.0714286
$785$		0			0
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$		0			0
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	14.0000			0.497155
$794$	17.0000	+	29.4449i	0.603307	+	1.04496i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−13.0000	+	22.5167i	−0.460484	+	0.797581i	−0.998985	−	0.0450436i	$-0.985657\pi$
$797$	−13.0000	+	22.5167i	−0.460484	+	0.797581i	0.538501	+	0.842625i	$0.318991\pi$
$798$		0			0
$799$	−14.0000	−	24.2487i	−0.495284	−	0.857858i
$800$		0			0
$801$		0			0
$802$	18.0000			0.635602
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	27.0000	+	46.7654i	0.949857	+	1.64520i
$809$	−26.0000			−0.914111			−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000			−0.914111			−0.457056	+	0.889438i	$0.651096\pi$
$810$		0			0
$811$	−42.0000			−1.47482			−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000			−1.47482			−0.737410	+	0.675446i	$0.763951\pi$
$812$	1.50000	+	2.59808i	0.0526397	+	0.0911746i
$813$		0			0
$814$	−4.00000	+	6.92820i	−0.140200	+	0.242833i
$815$		0			0
$816$		0			0
$817$	32.0000	+	55.4256i	1.11954	+	1.93910i
$818$	14.0000			0.489499
$819$		0			0
$820$		0			0
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	26.5000	−	45.8993i	0.923732	−	1.59995i	0.130144	−	0.991495i	$-0.458456\pi$
$823$	26.5000	−	45.8993i	0.923732	−	1.59995i	0.793588	−	0.608456i	$-0.208211\pi$
$824$	−12.0000	+	20.7846i	−0.418040	+	0.724066i
$825$		0			0
$826$	−21.0000	−	36.3731i	−0.730683	−	1.26558i
$827$	37.0000			1.28662			0.643308	−	0.765607i	$-0.277561\pi$
$827$	37.0000			1.28662			0.643308	+	0.765607i	$0.277561\pi$
$828$		0			0
$829$	−3.00000			−0.104194			−0.0520972	−	0.998642i	$-0.516591\pi$
$829$	−3.00000			−0.104194			−0.0520972	+	0.998642i	$0.516591\pi$
$830$		0			0
$831$		0			0
$832$	−7.00000	+	12.1244i	−0.242681	+	0.420336i
$833$	−4.00000	+	6.92820i	−0.138592	+	0.240048i
$834$		0			0
$835$		0			0
$836$	16.0000			0.553372
$837$		0			0
$838$	−26.0000			−0.898155
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	−0.971682	−	0.236293i	$-0.924067\pi$
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	0.281205	−	0.959648i	$-0.409266\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	−17.0000	+	29.4449i	−0.585859	+	1.01474i
$843$		0			0
$844$	−11.0000	−	19.0526i	−0.378636	−	0.655816i
$845$		0			0
$846$		0			0
$847$	−21.0000			−0.721569
$848$	−1.00000	−	1.73205i	−0.0343401	−	0.0594789i
$849$		0			0
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	−27.0000	−	46.7654i	−0.924462	−	1.60122i	−0.792424	−	0.609971i	$-0.791181\pi$
$853$	−27.0000	−	46.7654i	−0.924462	−	1.60122i	−0.132039	−	0.991245i	$-0.542152\pi$
$854$	21.0000			0.718605
$855$		0			0
$856$	−9.00000			−0.307614
$857$	−5.00000	−	8.66025i	−0.170797	−	0.295829i	0.767902	−	0.640567i	$-0.221301\pi$
$857$	−5.00000	−	8.66025i	−0.170797	−	0.295829i	−0.938699	+	0.344739i	$0.887967\pi$
$858$		0			0
$859$	−11.0000	+	19.0526i	−0.375315	+	0.650065i	−0.990374	−	0.138416i	$-0.955799\pi$
$859$	−11.0000	+	19.0526i	−0.375315	+	0.650065i	0.615059	+	0.788481i	$0.289132\pi$
$860$		0			0
$861$		0			0
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	17.0000			0.578687			0.289343	−	0.957225i	$-0.406563\pi$
$863$	17.0000			0.578687			0.289343	+	0.957225i	$0.406563\pi$
$864$		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
$872$	−15.0000			−0.507964
$873$		0			0
$874$	−24.0000			−0.811812
$875$		0			0
$876$		0			0
$877$	−9.00000	+	15.5885i	−0.303908	+	0.526385i	−0.977018	−	0.213158i	$-0.931625\pi$
$877$	−9.00000	+	15.5885i	−0.303908	+	0.526385i	0.673109	+	0.739543i	$0.264958\pi$
$878$	−14.0000	+	24.2487i	−0.472477	+	0.818354i
$879$		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
$883$	−23.0000			−0.774012			−0.387006	−	0.922077i	$-0.626491\pi$
$883$	−23.0000			−0.774012			−0.387006	+	0.922077i	$0.626491\pi$
$884$	4.00000	+	6.92820i	0.134535	+	0.233021i
$885$		0			0
$886$	−7.50000	+	12.9904i	−0.251967	+	0.436420i
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$		0			0
$889$	−7.50000	−	12.9904i	−0.251542	−	0.435683i
$890$		0			0
$891$		0			0
$892$	−19.0000			−0.636167
$893$	28.0000	+	48.4974i	0.936984	+	1.62290i
$894$		0			0
$895$		0			0
$896$	4.50000	−	7.79423i	0.150334	−	0.260387i
$897$		0			0
$898$	−13.0000	−	22.5167i	−0.433816	−	0.751391i
$899$		0			0
$900$		0			0
$901$	−8.00000			−0.266519
$902$	5.00000	+	8.66025i	0.166482	+	0.288355i
$903$		0			0
$904$	−12.0000	+	20.7846i	−0.399114	+	0.691286i
$905$		0			0
$906$		0			0
$907$	−25.5000	−	44.1673i	−0.846714	−	1.46655i	−0.884125	−	0.467251i	$-0.845244\pi$
$907$	−25.5000	−	44.1673i	−0.846714	−	1.46655i	0.0374111	−	0.999300i	$-0.488089\pi$
$908$	4.00000			0.132745
$909$		0			0
$910$		0			0
$911$	−25.0000	−	43.3013i	−0.828287	−	1.43464i	−0.899381	−	0.437165i	$-0.855982\pi$
$911$	−25.0000	−	43.3013i	−0.828287	−	1.43464i	0.0710941	−	0.997470i	$-0.477351\pi$
$912$		0			0
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$	−10.0000	+	17.3205i	−0.330771	+	0.572911i
$915$		0			0
$916$	7.50000	+	12.9904i	0.247807	+	0.429214i
$917$	18.0000			0.594412
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$		0			0
$922$	4.50000	−	7.79423i	0.148200	−	0.256689i
$923$	2.00000	−	3.46410i	0.0658308	−	0.114022i
$924$		0			0
$925$		0			0
$926$	36.0000			1.18303
$927$		0			0
$928$	5.00000			0.164133
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	8.00000	−	13.8564i	0.262189	−	0.454125i
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$		0			0
$934$	−10.0000	−	17.3205i	−0.327210	−	0.566744i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−4.50000	−	7.79423i	−0.146930	−	0.254491i
$939$		0			0
$940$		0			0
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	−0.917418	−	0.397924i	$-0.869731\pi$
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	0.803322	+	0.595545i	$0.203064\pi$
$942$		0			0
$943$	7.50000	+	12.9904i	0.244234	+	0.423025i
$944$	−14.0000			−0.455661
$945$		0			0
$946$	16.0000			0.520205
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.789741	−	0.613441i	$-0.789785\pi$
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.136385	−	0.990656i	$-0.543548\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$		0			0
$952$	18.0000	+	31.1769i	0.583383	+	1.01045i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$		0			0
$956$	4.00000	+	6.92820i	0.129369	+	0.224074i
$957$		0			0
$958$	−9.00000	+	15.5885i	−0.290777	+	0.503640i
$959$	−18.0000	+	31.1769i	−0.581250	+	1.00676i
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	8.00000			0.257930
$963$		0			0
$964$	11.0000			0.354286
$965$		0			0
$966$		0			0
$967$	20.5000	−	35.5070i	0.659236	−	1.14183i	−0.321578	−	0.946883i	$-0.604213\pi$
$967$	20.5000	−	35.5070i	0.659236	−	1.14183i	0.980814	−	0.194946i	$-0.0624533\pi$
$968$	−10.5000	+	18.1865i	−0.337483	+	0.584537i
$969$		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
$973$	−48.0000			−1.53881
$974$	−8.00000	−	13.8564i	−0.256337	−	0.443988i
$975$		0			0
$976$	3.50000	−	6.06218i	0.112032	−	0.194046i
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	−0.383728	−	0.923446i	$-0.625360\pi$
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	0.991592	−	0.129405i	$-0.0413067\pi$
$978$		0			0
$979$	−15.0000	−	25.9808i	−0.479402	−	0.830349i
$980$		0			0
$981$		0			0
$982$	−20.0000			−0.638226
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$		0			0
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$	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
$997$	−9.00000	−	15.5885i	−0.285033	−	0.493691i	0.687584	−	0.726105i	$-0.258671\pi$
$997$	−9.00000	−	15.5885i	−0.285033	−	0.493691i	−0.972617	+	0.232413i	$0.925338\pi$
$998$	−32.0000			−1.01294
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.a.16.1	✓	2	45.29	odd	6
45.2.e.a.31.1	yes	2	15.14	odd	2
135.2.e.a.46.1		2	45.34	even	6
135.2.e.a.91.1		2	5.4	even	2
225.2.e.a.76.1		2	3.2	odd	2
225.2.e.a.151.1		2	9.2	odd	6
225.2.k.a.49.1		4	15.2	even	4
225.2.k.a.49.2		4	15.8	even	4
225.2.k.a.124.1		4	45.38	even	12
225.2.k.a.124.2		4	45.2	even	12
405.2.a.b.1.1		1	45.4	even	6
405.2.a.e.1.1		1	45.14	odd	6
675.2.e.a.226.1		2	1.1	even	1	trivial
675.2.e.a.451.1		2	9.7	even	3	inner
675.2.k.a.199.1		4	5.3	odd	4
675.2.k.a.199.2		4	5.2	odd	4
675.2.k.a.424.1		4	45.7	odd	12
675.2.k.a.424.2		4	45.43	odd	12
720.2.q.d.241.1		2	180.119	even	6
720.2.q.d.481.1		2	60.59	even	2
2025.2.a.b.1.1		1	9.5	odd	6
2025.2.a.e.1.1		1	9.4	even	3
2025.2.b.c.649.1		2	45.32	even	12
2025.2.b.c.649.2		2	45.23	even	12
2025.2.b.d.649.1		2	45.13	odd	12
2025.2.b.d.649.2		2	45.22	odd	12
2160.2.q.a.721.1		2	180.79	odd	6
2160.2.q.a.1441.1		2	20.19	odd	2
6480.2.a.k.1.1		1	180.59	even	6
6480.2.a.x.1.1		1	180.139	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(-1.00000 - 1.73205i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} -8.00000 q^{19} +(-1.00000 + 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +2.00000 q^{26} -3.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(-2.50000 + 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{34} +4.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(2.50000 - 4.33013i) q^{41} +(-4.00000 - 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(-1.00000 + 1.73205i) q^{49} +(1.00000 + 1.73205i) q^{52} -2.00000 q^{53} +(4.50000 + 7.79423i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +7.00000 q^{64} +(-1.50000 + 2.59808i) q^{67} +(2.00000 - 3.46410i) q^{68} -2.00000 q^{71} -4.00000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(-3.00000 + 5.19615i) q^{77} +(3.00000 + 5.19615i) q^{79} -5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.00000 + 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{88} +15.0000 q^{89} +6.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(1.00000 + 1.73205i) q^{97} +2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 2 * q - q^2 + q^4 - 3 * q^7 - 6 * q^8	\( 2 q - q^{2} + q^{4} - 3 q^{7} - 6 q^{8} - 2 q^{11} - 2 q^{13} - 3 q^{14} + q^{16} + 8 q^{17} - 16 q^{19} - 2 q^{22} - 3 q^{23} + 4 q^{26} - 6 q^{28} - q^{29} - 5 q^{32} - 4 q^{34} + 8 q^{37} + 8 q^{38} + 5 q^{41} - 8 q^{43} - 4 q^{44} + 6 q^{46} - 7 q^{47} - 2 q^{49} + 2 q^{52} - 4 q^{53} + 9 q^{56} - q^{58} - 14 q^{59} - 7 q^{61} + 14 q^{64} - 3 q^{67} + 4 q^{68} - 4 q^{71} - 8 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{77} + 6 q^{79} - 10 q^{82} - 9 q^{83} - 8 q^{86} + 6 q^{88} + 30 q^{89} + 12 q^{91} + 3 q^{92} - 7 q^{94} + 2 q^{97} + 4 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^4 - 3 * q^7 - 6 * q^8 - 2 * q^11 - 2 * q^13 - 3 * q^14 + q^16 + 8 * q^17 - 16 * q^19 - 2 * q^22 - 3 * q^23 + 4 * q^26 - 6 * q^28 - q^29 - 5 * q^32 - 4 * q^34 + 8 * q^37 + 8 * q^38 + 5 * q^41 - 8 * q^43 - 4 * q^44 + 6 * q^46 - 7 * q^47 - 2 * q^49 + 2 * q^52 - 4 * q^53 + 9 * q^56 - q^58 - 14 * q^59 - 7 * q^61 + 14 * q^64 - 3 * q^67 + 4 * q^68 - 4 * q^71 - 8 * q^73 - 4 * q^74 - 8 * q^76 - 6 * q^77 + 6 * q^79 - 10 * q^82 - 9 * q^83 - 8 * q^86 + 6 * q^88 + 30 * q^89 + 12 * q^91 + 3 * q^92 - 7 * q^94 + 2 * q^97 + 4 * q^98

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