LMFDB - Embedded newform 1350.2.j.e.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(199,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, 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("1350.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (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:	$10.7798042729$
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 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1350.199
Dual form			1350.2.j.e.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(3.00000 + 5.19615i) q^{11} +(1.73205 + 1.00000i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.00000 q^{19} +(-5.19615 - 3.00000i) q^{22} +(-7.79423 - 4.50000i) q^{23} -2.00000 q^{26} +1.00000i q^{28} +(-1.50000 - 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} +8.00000i q^{37} +(-3.46410 + 2.00000i) q^{38} +(-1.50000 + 2.59808i) q^{41} +(-6.92820 + 4.00000i) q^{43} +6.00000 q^{44} +9.00000 q^{46} +(2.59808 - 1.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(1.73205 - 1.00000i) q^{52} +6.00000i q^{53} +(-0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000i q^{62} -1.00000 q^{64} +(11.2583 + 6.50000i) q^{67} +6.00000 q^{71} +4.00000i q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-5.19615 - 3.00000i) q^{77} +(-5.00000 - 8.66025i) q^{79} -3.00000i q^{82} +(-7.79423 + 4.50000i) q^{83} +(4.00000 - 6.92820i) q^{86} +(-5.19615 + 3.00000i) q^{88} +9.00000 q^{89} -2.00000 q^{91} +(-7.79423 + 4.50000i) q^{92} +(-1.50000 + 2.59808i) q^{94} +(1.73205 - 1.00000i) q^{97} -6.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 12 q^{11} + 2 q^{14} - 2 q^{16} + 16 q^{19} - 8 q^{26} - 6 q^{29} + 8 q^{31} - 6 q^{41} + 24 q^{44} + 36 q^{46} - 12 q^{49} - 2 q^{56} - 12 q^{59} + 26 q^{61} - 4 q^{64} + 24 q^{71} - 16 q^{74}+ \cdots - 6 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 + 12 * q^11 + 2 * q^14 - 2 * q^16 + 16 * q^19 - 8 * q^26 - 6 * q^29 + 8 * q^31 - 6 * q^41 + 24 * q^44 + 36 * q^46 - 12 * q^49 - 2 * q^56 - 12 * q^59 + 26 * q^61 - 4 * q^64 + 24 * q^71 - 16 * q^74 + 8 * q^76 - 20 * q^79 + 16 * q^86 + 36 * q^89 - 8 * q^91 - 6 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$		0			0
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	0.720577	−	0.693375i	$-0.243877\pi$
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	−0.240192	+	0.970725i	$0.577210\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$	−5.19615	−	3.00000i	−1.10782	−	0.639602i
$23$	−7.79423	−	4.50000i	−1.62521	−	0.938315i	−0.985496	−	0.169701i	$-0.945720\pi$
$23$	−7.79423	−	4.50000i	−1.62521	−	0.938315i	−0.639713	−	0.768613i	$-0.720947\pi$
$24$		0			0
$25$		0			0
$26$	−2.00000			−0.392232
$27$		0			0
$28$			1.00000i			0.188982i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	−3.46410	+	2.00000i	−0.561951	+	0.324443i
$39$		0			0
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−6.92820	+	4.00000i	−1.05654	+	0.609994i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$	−6.92820	+	4.00000i	−1.05654	+	0.609994i	−0.132068	+	0.991241i	$0.542162\pi$
$44$	6.00000			0.904534
$45$		0			0
$46$	9.00000			1.32698
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	−0.298401	−	0.954441i	$-0.596453\pi$
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	0.677369	+	0.735643i	$0.263120\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$	1.73205	−	1.00000i	0.240192	−	0.138675i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	2.59808	+	1.50000i	0.341144	+	0.196960i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$			4.00000i			0.508001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	11.2583	+	6.50000i	1.37542	+	0.794101i	0.991605	−	0.129307i	$-0.0412752\pi$
$67$	11.2583	+	6.50000i	1.37542	+	0.794101i	0.383819	+	0.923408i	$0.374609\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−5.19615	−	3.00000i	−0.592157	−	0.341882i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$		0			0
$82$		−	3.00000i		−	0.331295i
$83$	−7.79423	+	4.50000i	−0.855528	+	0.493939i	−0.862512	−	0.506036i	$-0.831110\pi$
$83$	−7.79423	+	4.50000i	−0.855528	+	0.493939i	0.00698436	+	0.999976i	$0.497777\pi$
$84$		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
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$	−7.79423	+	4.50000i	−0.812605	+	0.469157i
$93$		0			0
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$		0			0
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	−0.409484	−	0.912317i	$-0.634291\pi$
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$98$		−	6.00000i		−	0.606092i
$99$		0			0
$100$		0			0
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	0.800855	−	0.598858i	$-0.204379\pi$
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	−0.118199	+	0.992990i	$0.537712\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$			3.00000i			0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$			3.00000i			0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$		0			0
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$		0			0
$111$		0			0
$112$	0.866025	+	0.500000i	0.0818317	+	0.0472456i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000			−0.278543
$117$		0			0
$118$		−	6.00000i		−	0.552345i
$119$		0			0
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−11.2583	−	6.50000i	−1.01928	−	0.588482i
$123$		0			0
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		0			0
$126$		0			0
$127$		−	7.00000i		−	0.621150i	−0.950549	−	0.310575i	$-0.899478\pi$
$127$		−	7.00000i		−	0.621150i	0.950549	−	0.310575i	$-0.100522\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$		0			0
$133$	−3.46410	+	2.00000i	−0.300376	+	0.173422i
$134$	−13.0000			−1.12303
$135$		0			0
$136$		0			0
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		0			0
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$			12.0000i			1.00349i
$144$		0			0
$145$		0			0
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$		0			0
$148$	6.92820	+	4.00000i	0.569495	+	0.328798i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$			4.00000i			0.324443i
$153$		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	$-0.522018\pi$
$157$	−12.1244	−	7.00000i	−0.967629	−	0.558661i	−0.898513	+	0.438948i	$0.855351\pi$
$158$	8.66025	+	5.00000i	0.688973	+	0.397779i
$159$		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	$0.949930\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$		0			0
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$			8.00000i			0.609994i
$173$	20.7846	−	12.0000i	1.58022	−	0.912343i	0.585399	−	0.810745i	$-0.300938\pi$
$173$	20.7846	−	12.0000i	1.58022	−	0.912343i	0.994826	−	0.101598i	$-0.0323955\pi$
$174$		0			0
$175$		0			0
$176$	3.00000	−	5.19615i	0.226134	−	0.391675i
$177$		0			0
$178$	−7.79423	+	4.50000i	−0.584202	+	0.337289i
$179$	−18.0000			−1.34538			−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	1.73205	−	1.00000i	0.128388	−	0.0741249i
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		−	3.00000i		−	0.218797i
$189$		0			0
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	1.73205	+	1.00000i	0.124676	+	0.0719816i	0.561041	−	0.827788i	$-0.310401\pi$
$193$	1.73205	+	1.00000i	0.124676	+	0.0719816i	−0.436365	+	0.899770i	$0.643734\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$			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
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$		0			0
$202$	−5.19615	−	3.00000i	−0.365600	−	0.211079i
$203$	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
$209$	12.0000	+	20.7846i	0.830057	+	1.43770i
$210$		0			0
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$		0			0
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$		0			0
$217$			4.00000i			0.271538i
$218$	−6.06218	+	3.50000i	−0.410582	+	0.237050i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.866025	−	0.500000i	0.0579934	−	0.0334825i	−0.470723	−	0.882281i	$-0.656007\pi$
$223$	0.866025	−	0.500000i	0.0579934	−	0.0334825i	0.528716	+	0.848799i	$0.322674\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$		0			0
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$		0			0
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$		0			0
$231$		0			0
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$		−	12.0000i		−	0.786146i	−0.919507	−	0.393073i	$-0.871412\pi$
$233$		−	12.0000i		−	0.786146i	0.919507	−	0.393073i	$-0.128588\pi$
$234$		0			0
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−14.5000	−	25.1147i	−0.934027	−	1.61778i	−0.776360	−	0.630290i	$-0.782936\pi$
$241$	−14.5000	−	25.1147i	−0.934027	−	1.61778i	−0.157667	−	0.987492i	$-0.550397\pi$
$242$		−	25.0000i		−	1.60706i
$243$		0			0
$244$	13.0000			0.832240
$245$		0			0
$246$		0			0
$247$	6.92820	+	4.00000i	0.440831	+	0.254514i
$248$	3.46410	+	2.00000i	0.219971	+	0.127000i
$249$		0			0
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	54.0000i		−	3.39495i
$254$	3.50000	+	6.06218i	0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.899961	−	0.435970i	$-0.143595\pi$
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.0724199	+	0.997374i	$0.476928\pi$
$258$		0			0
$259$	−4.00000	−	6.92820i	−0.248548	−	0.430498i
$260$		0			0
$261$		0			0
$262$		−	18.0000i		−	1.11204i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$		0			0
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$		0			0
$268$	11.2583	−	6.50000i	0.687712	−	0.397051i
$269$	21.0000			1.28039			0.640196	−	0.768211i	$-0.278853\pi$
$269$	21.0000			1.28039			0.640196	+	0.768211i	$0.278853\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$		0			0
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	6.92820	−	4.00000i	0.416275	−	0.240337i	−0.277207	−	0.960810i	$-0.589409\pi$
$277$	6.92820	−	4.00000i	0.416275	−	0.240337i	0.693482	+	0.720473i	$0.256075\pi$
$278$		−	16.0000i		−	0.959616i
$279$		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
$283$	−11.2583	−	6.50000i	−0.669238	−	0.386385i	0.126550	−	0.991960i	$-0.459610\pi$
$283$	−11.2583	−	6.50000i	−0.669238	−	0.386385i	−0.795788	+	0.605575i	$0.792943\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$		−	3.00000i		−	0.177084i
$288$		0			0
$289$	17.0000			1.00000
$290$		0			0
$291$		0			0
$292$	3.46410	+	2.00000i	0.202721	+	0.117041i
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$		0			0
$295$		0			0
$296$	−8.00000			−0.464991
$297$		0			0
$298$			3.00000i			0.173785i
$299$	−9.00000	−	15.5885i	−0.520483	−	0.901504i
$300$		0			0
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$	12.1244	+	7.00000i	0.697678	+	0.402805i
$303$		0			0
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$		−	7.00000i		−	0.399511i	−0.979846	−	0.199756i	$-0.935985\pi$
$307$		−	7.00000i		−	0.399511i	0.979846	−	0.199756i	$-0.0640148\pi$
$308$	−5.19615	+	3.00000i	−0.296078	+	0.170941i
$309$		0			0
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−1.73205	+	1.00000i	−0.0979013	+	0.0565233i	−0.548151	−	0.836379i	$-0.684668\pi$
$313$	−1.73205	+	1.00000i	−0.0979013	+	0.0565233i	0.450250	+	0.892903i	$0.351335\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−10.0000			−0.562544
$317$	5.19615	−	3.00000i	0.291845	−	0.168497i	−0.346929	−	0.937892i	$-0.612775\pi$
$317$	5.19615	−	3.00000i	0.291845	−	0.168497i	0.638774	+	0.769395i	$0.279442\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$		0			0
$322$	−7.79423	+	4.50000i	−0.434355	+	0.250775i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$		0			0
$328$	−2.59808	−	1.50000i	−0.143455	−	0.0828236i
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		0			0
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$			9.00000i			0.493939i
$333$		0			0
$334$	3.00000			0.164153
$335$		0			0
$336$		0			0
$337$	−6.92820	−	4.00000i	−0.377403	−	0.217894i	0.299285	−	0.954164i	$-0.403252\pi$
$337$	−6.92820	−	4.00000i	−0.377403	−	0.217894i	−0.676688	+	0.736270i	$0.736585\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$		0			0
$340$		0			0
$341$	24.0000			1.29967
$342$		0			0
$343$		−	13.0000i		−	0.701934i
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	−12.0000	+	20.7846i	−0.645124	+	1.11739i
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$		0			0
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	0.990282	+	0.139072i	$0.0444119\pi$
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$			6.00000i			0.319801i
$353$	20.7846	−	12.0000i	1.10625	−	0.638696i	0.168397	−	0.985719i	$-0.446141\pi$
$353$	20.7846	−	12.0000i	1.10625	−	0.638696i	0.937856	+	0.347024i	$0.112808\pi$
$354$		0			0
$355$		0			0
$356$	4.50000	−	7.79423i	0.238500	−	0.413093i
$357$		0			0
$358$	15.5885	−	9.00000i	0.823876	−	0.475665i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−4.33013	+	2.50000i	−0.227586	+	0.131397i
$363$		0			0
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$		0			0
$366$		0			0
$367$	6.92820	−	4.00000i	0.361649	−	0.208798i	−0.308155	−	0.951336i	$-0.599711\pi$
$367$	6.92820	−	4.00000i	0.361649	−	0.208798i	0.669804	+	0.742538i	$0.266378\pi$
$368$			9.00000i			0.469157i
$369$		0			0
$370$		0			0
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.952703	−	0.303902i	$-0.0982894\pi$
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.213165	+	0.977016i	$0.431623\pi$
$374$		0			0
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$		−	6.00000i		−	0.309016i
$378$		0			0
$379$	22.0000			1.13006			0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000			1.13006			0.565032	+	0.825069i	$0.308864\pi$
$380$		0			0
$381$		0			0
$382$	10.3923	+	6.00000i	0.531717	+	0.306987i
$383$	10.3923	+	6.00000i	0.531022	+	0.306586i	0.741433	−	0.671027i	$-0.234147\pi$
$383$	10.3923	+	6.00000i	0.531022	+	0.306586i	−0.210411	+	0.977613i	$0.567480\pi$
$384$		0			0
$385$		0			0
$386$	−2.00000			−0.101797
$387$		0			0
$388$		−	2.00000i		−	0.101535i
$389$	−10.5000	−	18.1865i	−0.532371	−	0.922094i	−0.999286	−	0.0377914i	$-0.987968\pi$
$389$	−10.5000	−	18.1865i	−0.532371	−	0.922094i	0.466915	−	0.884302i	$-0.345366\pi$
$390$		0			0
$391$		0			0
$392$	−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
$397$			2.00000i			0.100377i	0.998740	+	0.0501886i	$0.0159822\pi$
$397$			2.00000i			0.100377i	−0.998740	+	0.0501886i	$0.984018\pi$
$398$	6.92820	−	4.00000i	0.347279	−	0.200502i
$399$		0			0
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$	6.92820	−	4.00000i	0.345118	−	0.199254i
$404$	6.00000			0.298511
$405$		0			0
$406$	−3.00000			−0.148888
$407$	−41.5692	+	24.0000i	−2.06051	+	1.18964i
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$		0			0
$411$		0			0
$412$	6.92820	−	4.00000i	0.341328	−	0.197066i
$413$		−	6.00000i		−	0.295241i
$414$		0			0
$415$		0			0
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	−20.7846	−	12.0000i	−1.01661	−	0.586939i
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	−0.222885	−	0.974845i	$-0.571547\pi$
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	0.955683	−	0.294398i	$-0.0951193\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$		−	2.00000i		−	0.0973585i
$423$		0			0
$424$	−6.00000			−0.291386
$425$		0			0
$426$		0			0
$427$	−11.2583	−	6.50000i	−0.544829	−	0.314557i
$428$	2.59808	+	1.50000i	0.125583	+	0.0725052i
$429$		0			0
$430$		0			0
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$		0			0
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$	−2.00000	−	3.46410i	−0.0960031	−	0.166282i
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−31.1769	−	18.0000i	−1.49139	−	0.861057i
$438$		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
$442$		0			0
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$		0			0
$445$		0			0
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$		0			0
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$		0			0
$453$		0			0
$454$	−6.00000	+	10.3923i	−0.281594	+	0.487735i
$455$		0			0
$456$		0			0
$457$	6.92820	−	4.00000i	0.324088	−	0.187112i	−0.329125	−	0.944286i	$-0.606754\pi$
$457$	6.92820	−	4.00000i	0.324088	−	0.187112i	0.653213	+	0.757174i	$0.273421\pi$
$458$		−	13.0000i		−	0.607450i
$459$		0			0
$460$		0			0
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	−0.987801	−	0.155719i	$-0.950230\pi$
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	0.359044	−	0.933321i	$-0.383103\pi$
$462$		0			0
$463$	−3.46410	−	2.00000i	−0.160990	−	0.0929479i	0.417340	−	0.908750i	$-0.362962\pi$
$463$	−3.46410	−	2.00000i	−0.160990	−	0.0929479i	−0.578331	+	0.815802i	$0.696296\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		0			0
$469$	−13.0000			−0.600284
$470$		0			0
$471$		0			0
$472$	−5.19615	−	3.00000i	−0.239172	−	0.138086i
$473$	−41.5692	−	24.0000i	−1.91135	−	1.10352i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	0.973321	+	0.229447i	$0.0736918\pi$
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	−0.287954	+	0.957644i	$0.592975\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	25.1147	+	14.5000i	1.14394	+	0.660457i
$483$		0			0
$484$	12.5000	+	21.6506i	0.568182	+	0.984120i
$485$		0			0
$486$		0			0
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$	−11.2583	+	6.50000i	−0.509641	+	0.294241i
$489$		0			0
$490$		0			0
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−5.19615	+	3.00000i	−0.233079	+	0.134568i
$498$		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
$502$	10.3923	−	6.00000i	0.463831	−	0.267793i
$503$			27.0000i			1.20387i	0.798545	+	0.601935i	$0.205603\pi$
$503$			27.0000i			1.20387i	−0.798545	+	0.601935i	$0.794397\pi$
$504$		0			0
$505$		0			0
$506$	27.0000	+	46.7654i	1.20030	+	2.07897i
$507$		0			0
$508$	−6.06218	−	3.50000i	−0.268966	−	0.155287i
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−18.0000			−0.793946
$515$		0			0
$516$		0			0
$517$	15.5885	+	9.00000i	0.685580	+	0.395820i
$518$	6.92820	+	4.00000i	0.304408	+	0.175750i
$519$		0			0
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$			19.0000i			0.830812i	0.909636	+	0.415406i	$0.136360\pi$
$523$			19.0000i			0.830812i	−0.909636	+	0.415406i	$0.863640\pi$
$524$	9.00000	+	15.5885i	0.393167	+	0.680985i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	29.0000	+	50.2295i	1.26087	+	2.18389i
$530$		0			0
$531$		0			0
$532$			4.00000i			0.173422i
$533$	−5.19615	+	3.00000i	−0.225070	+	0.129944i
$534$		0			0
$535$		0			0
$536$	−6.50000	+	11.2583i	−0.280757	+	0.486286i
$537$		0			0
$538$	−18.1865	+	10.5000i	−0.784077	+	0.452687i
$539$	−36.0000			−1.55063
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	3.46410	−	2.00000i	0.148796	−	0.0859074i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−37.2391	+	21.5000i	−1.59223	+	0.919274i	−0.599305	+	0.800521i	$0.704556\pi$
$547$	−37.2391	+	21.5000i	−1.59223	+	0.919274i	−0.992924	+	0.118753i	$0.962110\pi$
$548$		−	12.0000i		−	0.512615i
$549$		0			0
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$	8.66025	+	5.00000i	0.368271	+	0.212622i
$554$	−4.00000	+	6.92820i	−0.169944	+	0.294351i
$555$		0			0
$556$	8.00000	+	13.8564i	0.339276	+	0.587643i
$557$			6.00000i			0.254228i	0.991888	+	0.127114i	$0.0405714\pi$
$557$			6.00000i			0.254228i	−0.991888	+	0.127114i	$0.959429\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	12.9904	+	7.50000i	0.547966	+	0.316368i
$563$	2.59808	+	1.50000i	0.109496	+	0.0632175i	0.553748	−	0.832684i	$-0.313197\pi$
$563$	2.59808	+	1.50000i	0.109496	+	0.0632175i	−0.444252	+	0.895902i	$0.646530\pi$
$564$		0			0
$565$		0			0
$566$	13.0000			0.546431
$567$		0			0
$568$			6.00000i			0.251754i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	−0.0554391	−	0.998462i	$-0.517656\pi$
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	0.892413	−	0.451219i	$-0.149011\pi$
$572$	10.3923	+	6.00000i	0.434524	+	0.250873i
$573$		0			0
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$		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	$-0.0667451\pi$
$578$	−14.7224	+	8.50000i	−0.612372	+	0.353553i
$579$		0			0
$580$		0			0
$581$	4.50000	−	7.79423i	0.186691	−	0.323359i
$582$		0			0
$583$	−31.1769	+	18.0000i	−1.29122	+	0.745484i
$584$	−4.00000			−0.165521
$585$		0			0
$586$		0			0
$587$	12.9904	−	7.50000i	0.536170	−	0.309558i	−0.207355	−	0.978266i	$-0.566486\pi$
$587$	12.9904	−	7.50000i	0.536170	−	0.309558i	0.743525	+	0.668708i	$0.233152\pi$
$588$		0			0
$589$	8.00000	−	13.8564i	0.329634	−	0.570943i
$590$		0			0
$591$		0			0
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$			24.0000i			0.985562i	0.870153	+	0.492781i	$0.164020\pi$
$593$			24.0000i			0.985562i	−0.870153	+	0.492781i	$0.835980\pi$
$594$		0			0
$595$		0			0
$596$	−1.50000	−	2.59808i	−0.0614424	−	0.106421i
$597$		0			0
$598$	15.5885	+	9.00000i	0.637459	+	0.368037i
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$			8.00000i			0.326056i
$603$		0			0
$604$	−14.0000			−0.569652
$605$		0			0
$606$		0			0
$607$	−25.1147	−	14.5000i	−1.01938	−	0.588537i	−0.105453	−	0.994424i	$-0.533629\pi$
$607$	−25.1147	−	14.5000i	−1.01938	−	0.588537i	−0.913923	+	0.405887i	$0.866962\pi$
$608$	3.46410	+	2.00000i	0.140488	+	0.0811107i
$609$		0			0
$610$		0			0
$611$	6.00000			0.242734
$612$		0			0
$613$			40.0000i			1.61558i	0.589467	+	0.807792i	$0.299338\pi$
$613$			40.0000i			1.61558i	−0.589467	+	0.807792i	$0.700662\pi$
$614$	3.50000	+	6.06218i	0.141249	+	0.244650i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	10.3923	+	6.00000i	0.418378	+	0.241551i	0.694383	−	0.719605i	$-0.255677\pi$
$617$	10.3923	+	6.00000i	0.418378	+	0.241551i	−0.276005	+	0.961156i	$0.589011\pi$
$618$		0			0
$619$	−20.0000	−	34.6410i	−0.803868	−	1.39234i	−0.917053	−	0.398766i	$-0.869439\pi$
$619$	−20.0000	−	34.6410i	−0.803868	−	1.39234i	0.113185	−	0.993574i	$-0.463895\pi$
$620$		0			0
$621$		0			0
$622$			12.0000i			0.481156i
$623$	−7.79423	+	4.50000i	−0.312269	+	0.180289i
$624$		0			0
$625$		0			0
$626$	1.00000	−	1.73205i	0.0399680	−	0.0692267i
$627$		0			0
$628$	−12.1244	+	7.00000i	−0.483814	+	0.279330i
$629$		0			0
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	8.66025	−	5.00000i	0.344486	−	0.198889i
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$		0			0
$636$		0			0
$637$	−10.3923	+	6.00000i	−0.411758	+	0.237729i
$638$			18.0000i			0.712627i
$639$		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
$643$	−26.8468	−	15.5000i	−1.05873	−	0.611260i	−0.133652	−	0.991028i	$-0.542670\pi$
$643$	−26.8468	−	15.5000i	−1.05873	−	0.611260i	−0.925082	+	0.379768i	$0.876004\pi$
$644$	4.50000	−	7.79423i	0.177325	−	0.307136i
$645$		0			0
$646$		0			0
$647$			3.00000i			0.117942i	0.998260	+	0.0589711i	$0.0187820\pi$
$647$			3.00000i			0.117942i	−0.998260	+	0.0589711i	$0.981218\pi$
$648$		0			0
$649$	−36.0000			−1.41312
$650$		0			0
$651$		0			0
$652$	3.46410	+	2.00000i	0.135665	+	0.0783260i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$		0			0
$656$	3.00000			0.117130
$657$		0			0
$658$		−	3.00000i		−	0.116952i
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.0602929	−	0.998181i	$-0.480797\pi$
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.834303	−	0.551306i	$-0.185870\pi$
$662$	−8.66025	−	5.00000i	−0.336590	−	0.194331i
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$		0			0
$666$		0			0
$667$			27.0000i			1.04544i
$668$	−2.59808	+	1.50000i	−0.100523	+	0.0580367i
$669$		0			0
$670$		0			0
$671$	−39.0000	+	67.5500i	−1.50558	+	2.60774i
$672$		0			0
$673$	39.8372	−	23.0000i	1.53561	−	0.886585i	0.536522	−	0.843886i	$-0.319738\pi$
$673$	39.8372	−	23.0000i	1.53561	−	0.886585i	0.999088	−	0.0426985i	$-0.0135955\pi$
$674$	8.00000			0.308148
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	−0.768693	−	0.639618i	$-0.779092\pi$
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	0.169580	+	0.985517i	$0.445759\pi$
$678$		0			0
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$		0			0
$681$		0			0
$682$	−20.7846	+	12.0000i	−0.795884	+	0.459504i
$683$			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
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$		0			0
$688$	6.92820	+	4.00000i	0.264135	+	0.152499i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	0.945319	−	0.326146i	$-0.105750\pi$
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	−0.755110	+	0.655598i	$0.772417\pi$
$692$		−	24.0000i		−	0.912343i
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−19.9186	−	11.5000i	−0.753930	−	0.435281i
$699$		0			0
$700$		0			0
$701$	45.0000			1.69963			0.849813	−	0.527084i	$-0.176715\pi$
$701$	45.0000			1.69963			0.849813	+	0.527084i	$0.176715\pi$
$702$		0			0
$703$			32.0000i			1.20690i
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−5.19615	−	3.00000i	−0.195421	−	0.112827i
$708$		0			0
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$		0			0
$711$		0			0
$712$			9.00000i			0.337289i
$713$	−31.1769	+	18.0000i	−1.16758	+	0.674105i
$714$		0			0
$715$		0			0
$716$	−9.00000	+	15.5885i	−0.336346	+	0.582568i
$717$		0			0
$718$	10.3923	−	6.00000i	0.387837	−	0.223918i
$719$	−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
$721$	−8.00000			−0.297936
$722$	2.59808	−	1.50000i	0.0966904	−	0.0558242i
$723$		0			0
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$		0			0
$726$		0			0
$727$	45.8993	−	26.5000i	1.70231	−	0.982831i	0.758901	−	0.651206i	$-0.225737\pi$
$727$	45.8993	−	26.5000i	1.70231	−	0.982831i	0.943411	−	0.331625i	$-0.107597\pi$
$728$		−	2.00000i		−	0.0741249i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	12.1244	+	7.00000i	0.447823	+	0.258551i	0.706910	−	0.707303i	$-0.250088\pi$
$733$	12.1244	+	7.00000i	0.447823	+	0.258551i	−0.259087	+	0.965854i	$0.583422\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	−4.50000	−	7.79423i	−0.165872	−	0.287299i
$737$			78.0000i			2.87317i
$738$		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
$742$	5.19615	+	3.00000i	0.190757	+	0.110133i
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	0.718986	−	0.695024i	$-0.244606\pi$
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	−0.242415	+	0.970173i	$0.577940\pi$
$744$		0			0
$745$		0			0
$746$	−26.0000			−0.951928
$747$		0			0
$748$		0			0
$749$	−1.50000	−	2.59808i	−0.0548088	−	0.0949316i
$750$		0			0
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	−0.883694	−	0.468065i	$-0.844951\pi$
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	0.847203	+	0.531269i	$0.178285\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$		0			0
$754$	3.00000	+	5.19615i	0.109254	+	0.189233i
$755$		0			0
$756$		0			0
$757$		−	46.0000i		−	1.67190i	−0.548807	−	0.835949i	$-0.684918\pi$
$757$		−	46.0000i		−	1.67190i	0.548807	−	0.835949i	$-0.315082\pi$
$758$	−19.0526	+	11.0000i	−0.692020	+	0.399538i
$759$		0			0
$760$		0			0
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	0.394973	+	0.918693i	$0.370754\pi$
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	−0.993098	+	0.117289i	$0.962579\pi$
$762$		0			0
$763$	−6.06218	+	3.50000i	−0.219466	+	0.126709i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−12.0000			−0.433578
$767$	−10.3923	+	6.00000i	−0.375244	+	0.216647i
$768$		0			0
$769$	14.5000	−	25.1147i	0.522883	−	0.905661i	−0.476762	−	0.879032i	$-0.658190\pi$
$769$	14.5000	−	25.1147i	0.522883	−	0.905661i	0.999645	−	0.0266282i	$-0.00847701\pi$
$770$		0			0
$771$		0			0
$772$	1.73205	−	1.00000i	0.0623379	−	0.0359908i
$773$		−	48.0000i		−	1.72644i	−0.504828	−	0.863220i	$-0.668444\pi$
$773$		−	48.0000i		−	1.72644i	0.504828	−	0.863220i	$-0.331556\pi$
$774$		0			0
$775$		0			0
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$	18.1865	+	10.5000i	0.652019	+	0.376443i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$		0			0
$784$	6.00000			0.214286
$785$		0			0
$786$		0			0
$787$	−17.3205	−	10.0000i	−0.617409	−	0.356462i	0.158450	−	0.987367i	$-0.449350\pi$
$787$	−17.3205	−	10.0000i	−0.617409	−	0.356462i	−0.775860	+	0.630905i	$0.782684\pi$
$788$	10.3923	+	6.00000i	0.370211	+	0.213741i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$			26.0000i			0.923287i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.310031	−	0.950726i	$-0.600340\pi$
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.978369	+	0.206868i	$0.933673\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$			6.00000i			0.211867i
$803$	−20.7846	+	12.0000i	−0.733473	+	0.423471i
$804$		0			0
$805$		0			0
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$		0			0
$808$	−5.19615	+	3.00000i	−0.182800	+	0.105540i
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	2.59808	−	1.50000i	0.0911746	−	0.0526397i
$813$		0			0
$814$	24.0000	−	41.5692i	0.841200	−	1.45700i
$815$		0			0
$816$		0			0
$817$	−27.7128	+	16.0000i	−0.969549	+	0.559769i
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$		0			0
$821$	13.5000	+	23.3827i	0.471153	+	0.816061i	0.999456	−	0.0329950i	$-0.0105045\pi$
$821$	13.5000	+	23.3827i	0.471153	+	0.816061i	−0.528302	+	0.849056i	$0.677171\pi$
$822$		0			0
$823$	−21.6506	−	12.5000i	−0.754694	−	0.435723i	0.0726937	−	0.997354i	$-0.476840\pi$
$823$	−21.6506	−	12.5000i	−0.754694	−	0.435723i	−0.827387	+	0.561632i	$0.810174\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$		−	3.00000i		−	0.104320i	−0.998639	−	0.0521601i	$-0.983389\pi$
$827$		−	3.00000i		−	0.104320i	0.998639	−	0.0521601i	$-0.0166106\pi$
$828$		0			0
$829$	7.00000			0.243120			0.121560	−	0.992584i	$-0.461210\pi$
$829$	7.00000			0.243120			0.121560	+	0.992584i	$0.461210\pi$
$830$		0			0
$831$		0			0
$832$	−1.73205	−	1.00000i	−0.0600481	−	0.0346688i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	24.0000			0.830057
$837$		0			0
$838$			30.0000i			1.03633i
$839$	−18.0000	−	31.1769i	−0.621429	−	1.07635i	−0.989220	−	0.146438i	$-0.953219\pi$
$839$	−18.0000	−	31.1769i	−0.621429	−	1.07635i	0.367791	−	0.929909i	$-0.380114\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−19.0526	−	11.0000i	−0.656595	−	0.379085i
$843$		0			0
$844$	1.00000	+	1.73205i	0.0344214	+	0.0596196i
$845$		0			0
$846$		0			0
$847$		−	25.0000i		−	0.859010i
$848$	5.19615	−	3.00000i	0.178437	−	0.103020i
$849$		0			0
$850$		0			0
$851$	36.0000	−	62.3538i	1.23406	−	2.13746i
$852$		0			0
$853$	8.66025	−	5.00000i	0.296521	−	0.171197i	−0.344358	−	0.938839i	$-0.611903\pi$
$853$	8.66025	−	5.00000i	0.296521	−	0.171197i	0.640879	+	0.767642i	$0.278570\pi$
$854$	13.0000			0.444851
$855$		0			0
$856$	−3.00000			−0.102538
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.272882	−	0.962048i	$-0.412023\pi$
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.969599	+	0.244701i	$0.0786899\pi$
$858$		0			0
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	0.415442	+	0.909620i	$0.363627\pi$
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	−0.995475	+	0.0950262i	$0.969707\pi$
$860$		0			0
$861$		0			0
$862$	5.19615	−	3.00000i	0.176982	−	0.102180i
$863$			3.00000i			0.102121i	0.998696	+	0.0510606i	$0.0162602\pi$
$863$			3.00000i			0.102121i	−0.998696	+	0.0510606i	$0.983740\pi$
$864$		0			0
$865$		0			0
$866$	−8.00000	−	13.8564i	−0.271851	−	0.470860i
$867$		0			0
$868$	3.46410	+	2.00000i	0.117579	+	0.0678844i
$869$	30.0000	−	51.9615i	1.01768	−	1.76267i
$870$		0			0
$871$	13.0000	+	22.5167i	0.440488	+	0.762948i
$872$			7.00000i			0.237050i
$873$		0			0
$874$	36.0000			1.21772
$875$		0			0
$876$		0			0
$877$	19.0526	+	11.0000i	0.643359	+	0.371444i	0.785907	−	0.618344i	$-0.212196\pi$
$877$	19.0526	+	11.0000i	0.643359	+	0.371444i	−0.142548	+	0.989788i	$0.545530\pi$
$878$	24.2487	+	14.0000i	0.818354	+	0.472477i
$879$		0			0
$880$		0			0
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$		0			0
$883$			31.0000i			1.04323i	0.853180	+	0.521617i	$0.174671\pi$
$883$			31.0000i			1.04323i	−0.853180	+	0.521617i	$0.825329\pi$
$884$		0			0
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	31.1769	+	18.0000i	1.04682	+	0.604381i	0.921757	−	0.387768i	$-0.126754\pi$
$887$	31.1769	+	18.0000i	1.04682	+	0.604381i	0.125061	+	0.992149i	$0.460087\pi$
$888$		0			0
$889$	3.50000	+	6.06218i	0.117386	+	0.203319i
$890$		0			0
$891$		0			0
$892$		−	1.00000i		−	0.0334825i
$893$	10.3923	−	6.00000i	0.347765	−	0.200782i
$894$		0			0
$895$		0			0
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−5.19615	+	3.00000i	−0.173398	+	0.100111i
$899$	−12.0000			−0.400222
$900$		0			0
$901$		0			0
$902$	15.5885	−	9.00000i	0.519039	−	0.299667i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−32.0429	+	18.5000i	−1.06397	+	0.614282i	−0.926527	−	0.376228i	$-0.877221\pi$
$907$	−32.0429	+	18.5000i	−1.06397	+	0.614282i	−0.137441	+	0.990510i	$0.543888\pi$
$908$		−	12.0000i		−	0.398234i
$909$		0			0
$910$		0			0
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	0.503022	−	0.864274i	$-0.332222\pi$
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	−0.999994	+	0.00349271i	$0.998888\pi$
$912$		0			0
$913$	−46.7654	−	27.0000i	−1.54771	−	0.893570i
$914$	−4.00000	+	6.92820i	−0.132308	+	0.229165i
$915$		0			0
$916$	6.50000	+	11.2583i	0.214766	+	0.371986i
$917$		−	18.0000i		−	0.594412i
$918$		0			0
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$		0			0
$921$		0			0
$922$	23.3827	+	13.5000i	0.770068	+	0.444599i
$923$	10.3923	+	6.00000i	0.342067	+	0.197492i
$924$		0			0
$925$		0			0
$926$	4.00000			0.131448
$927$		0			0
$928$		−	3.00000i		−	0.0984798i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$	−12.0000	+	20.7846i	−0.393284	+	0.681188i
$932$	−10.3923	−	6.00000i	−0.340411	−	0.196537i
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$		0			0
$936$		0			0
$937$			56.0000i			1.82944i	0.404088	+	0.914720i	$0.367589\pi$
$937$			56.0000i			1.82944i	−0.404088	+	0.914720i	$0.632411\pi$
$938$	11.2583	−	6.50000i	0.367598	−	0.212233i
$939$		0			0
$940$		0			0
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$		0			0
$943$	23.3827	−	13.5000i	0.761445	−	0.439620i
$944$	6.00000			0.195283
$945$		0			0
$946$	48.0000			1.56061
$947$	−33.7750	+	19.5000i	−1.09754	+	0.633665i	−0.935574	−	0.353131i	$-0.885117\pi$
$947$	−33.7750	+	19.5000i	−1.09754	+	0.633665i	−0.161966	+	0.986796i	$0.551783\pi$
$948$		0			0
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−25.9808	−	15.0000i	−0.839400	−	0.484628i
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		−	16.0000i		−	0.515861i
$963$		0			0
$964$	−29.0000			−0.934027
$965$		0			0
$966$		0			0
$967$	32.0429	+	18.5000i	1.03043	+	0.594920i	0.917108	−	0.398638i	$-0.130517\pi$
$967$	32.0429	+	18.5000i	1.03043	+	0.594920i	0.113323	+	0.993558i	$0.463850\pi$
$968$	−21.6506	−	12.5000i	−0.695878	−	0.401765i
$969$		0			0
$970$		0			0
$971$	24.0000			0.770197			0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000			0.770197			0.385098	+	0.922876i	$0.374168\pi$
$972$		0			0
$973$		−	16.0000i		−	0.512936i
$974$	−4.00000	−	6.92820i	−0.128168	−	0.221994i
$975$		0			0
$976$	6.50000	−	11.2583i	0.208060	−	0.360370i
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.211495	−	0.977379i	$-0.567833\pi$
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.952183	+	0.305530i	$0.901167\pi$
$978$		0			0
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$		0			0
$981$		0			0
$982$			12.0000i			0.382935i
$983$	7.79423	−	4.50000i	0.248597	−	0.143528i	−0.370525	−	0.928823i	$-0.620822\pi$
$983$	7.79423	−	4.50000i	0.248597	−	0.143528i	0.619122	+	0.785295i	$0.287489\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	6.92820	−	4.00000i	0.220416	−	0.127257i
$989$	72.0000			2.28947
$990$		0			0
$991$	−10.0000			−0.317660			−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000			−0.317660			−0.158830	+	0.987306i	$0.550772\pi$
$992$	3.46410	−	2.00000i	0.109985	−	0.0635001i
$993$		0			0
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$		0			0
$997$	−8.66025	+	5.00000i	−0.274273	+	0.158352i	−0.630828	−	0.775923i	$-0.717285\pi$
$997$	−8.66025	+	5.00000i	−0.274273	+	0.158352i	0.356555	+	0.934274i	$0.383951\pi$
$998$			32.0000i			1.01294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.j.e.199.1		4
3.2	odd	2		450.2.j.c.49.2		4
5.2	odd	4		1350.2.e.b.901.1		2
5.3	odd	4		270.2.e.b.91.1		2
5.4	even	2	inner	1350.2.j.e.199.2		4
9.2	odd	6		450.2.j.c.349.1		4
9.4	even	3		4050.2.c.a.649.1		2
9.5	odd	6		4050.2.c.t.649.2		2
9.7	even	3	inner	1350.2.j.e.1099.2		4
15.2	even	4		450.2.e.e.301.1		2
15.8	even	4		90.2.e.a.31.1	✓	2
15.14	odd	2		450.2.j.c.49.1		4
20.3	even	4		2160.2.q.b.1441.1		2
45.2	even	12		450.2.e.e.151.1		2
45.4	even	6		4050.2.c.a.649.2		2
45.7	odd	12		1350.2.e.b.451.1		2
45.13	odd	12		810.2.a.b.1.1		1
45.14	odd	6		4050.2.c.t.649.1		2
45.22	odd	12		4050.2.a.ba.1.1		1
45.23	even	12		810.2.a.g.1.1		1
45.29	odd	6		450.2.j.c.349.2		4
45.32	even	12		4050.2.a.n.1.1		1
45.34	even	6	inner	1350.2.j.e.1099.1		4
45.38	even	12		90.2.e.a.61.1	yes	2
45.43	odd	12		270.2.e.b.181.1		2
60.23	odd	4		720.2.q.b.481.1		2
180.23	odd	12		6480.2.a.g.1.1		1
180.43	even	12		2160.2.q.b.721.1		2
180.83	odd	12		720.2.q.b.241.1		2
180.103	even	12		6480.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.a.31.1	✓	2	15.8	even	4
90.2.e.a.61.1	yes	2	45.38	even	12
270.2.e.b.91.1		2	5.3	odd	4
270.2.e.b.181.1		2	45.43	odd	12
450.2.e.e.151.1		2	45.2	even	12
450.2.e.e.301.1		2	15.2	even	4
450.2.j.c.49.1		4	15.14	odd	2
450.2.j.c.49.2		4	3.2	odd	2
450.2.j.c.349.1		4	9.2	odd	6
450.2.j.c.349.2		4	45.29	odd	6
720.2.q.b.241.1		2	180.83	odd	12
720.2.q.b.481.1		2	60.23	odd	4
810.2.a.b.1.1		1	45.13	odd	12
810.2.a.g.1.1		1	45.23	even	12
1350.2.e.b.451.1		2	45.7	odd	12
1350.2.e.b.901.1		2	5.2	odd	4
1350.2.j.e.199.1		4	1.1	even	1	trivial
1350.2.j.e.199.2		4	5.4	even	2	inner
1350.2.j.e.1099.1		4	45.34	even	6	inner
1350.2.j.e.1099.2		4	9.7	even	3	inner
2160.2.q.b.721.1		2	180.43	even	12
2160.2.q.b.1441.1		2	20.3	even	4
4050.2.a.n.1.1		1	45.32	even	12
4050.2.a.ba.1.1		1	45.22	odd	12
4050.2.c.a.649.1		2	9.4	even	3
4050.2.c.a.649.2		2	45.4	even	6
4050.2.c.t.649.1		2	45.14	odd	6
4050.2.c.t.649.2		2	9.5	odd	6
6480.2.a.g.1.1		1	180.23	odd	12
6480.2.a.v.1.1		1	180.103	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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(3.00000 + 5.19615i) q^{11} +(1.73205 + 1.00000i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.00000 q^{19} +(-5.19615 - 3.00000i) q^{22} +(-7.79423 - 4.50000i) q^{23} -2.00000 q^{26} +1.00000i q^{28} +(-1.50000 - 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} +8.00000i q^{37} +(-3.46410 + 2.00000i) q^{38} +(-1.50000 + 2.59808i) q^{41} +(-6.92820 + 4.00000i) q^{43} +6.00000 q^{44} +9.00000 q^{46} +(2.59808 - 1.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(1.73205 - 1.00000i) q^{52} +6.00000i q^{53} +(-0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000i q^{62} -1.00000 q^{64} +(11.2583 + 6.50000i) q^{67} +6.00000 q^{71} +4.00000i q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-5.19615 - 3.00000i) q^{77} +(-5.00000 - 8.66025i) q^{79} -3.00000i q^{82} +(-7.79423 + 4.50000i) q^{83} +(4.00000 - 6.92820i) q^{86} +(-5.19615 + 3.00000i) q^{88} +9.00000 q^{89} -2.00000 q^{91} +(-7.79423 + 4.50000i) q^{92} +(-1.50000 + 2.59808i) q^{94} +(1.73205 - 1.00000i) q^{97} -6.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 12 q^{11} + 2 q^{14} - 2 q^{16} + 16 q^{19} - 8 q^{26} - 6 q^{29} + 8 q^{31} - 6 q^{41} + 24 q^{44} + 36 q^{46} - 12 q^{49} - 2 q^{56} - 12 q^{59} + 26 q^{61} - 4 q^{64} + 24 q^{71} - 16 q^{74}+ \cdots - 6 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 + 12 * q^11 + 2 * q^14 - 2 * q^16 + 16 * q^19 - 8 * q^26 - 6 * q^29 + 8 * q^31 - 6 * q^41 + 24 * q^44 + 36 * q^46 - 12 * q^49 - 2 * q^56 - 12 * q^59 + 26 * q^61 - 4 * q^64 + 24 * q^71 - 16 * q^74 + 8 * q^76 - 20 * q^79 + 16 * q^86 + 36 * q^89 - 8 * q^91 - 6 * q^94

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