LMFDB - Embedded newform 3150.2.m.a.1457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, 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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.a.2843.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.41421i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(3.41421 - 3.41421i) q^{17} -2.82843i q^{19} +(2.41421 + 2.41421i) q^{22} +(-0.828427 - 0.828427i) q^{23} +5.65685i q^{26} +(-0.707107 + 0.707107i) q^{28} +4.82843 q^{29} +10.2426 q^{31} +(-0.707107 + 0.707107i) q^{32} -4.82843i q^{34} +(2.24264 + 2.24264i) q^{37} +(-2.00000 - 2.00000i) q^{38} -8.82843i q^{41} +(8.07107 - 8.07107i) q^{43} +3.41421 q^{44} -1.17157 q^{46} +(0.757359 - 0.757359i) q^{47} +1.00000i q^{49} +(4.00000 + 4.00000i) q^{52} +(-5.41421 - 5.41421i) q^{53} +1.00000i q^{56} +(3.41421 - 3.41421i) q^{58} +2.82843 q^{59} +9.89949 q^{61} +(7.24264 - 7.24264i) q^{62} +1.00000i q^{64} +(-5.58579 - 5.58579i) q^{67} +(-3.41421 - 3.41421i) q^{68} +6.82843i q^{71} +(7.07107 - 7.07107i) q^{73} +3.17157 q^{74} -2.82843 q^{76} +(2.41421 - 2.41421i) q^{77} -5.65685i q^{79} +(-6.24264 - 6.24264i) q^{82} +(4.82843 + 4.82843i) q^{83} -11.4142i q^{86} +(2.41421 - 2.41421i) q^{88} -8.82843 q^{89} +5.65685 q^{91} +(-0.828427 + 0.828427i) q^{92} -1.07107i q^{94} +(7.41421 + 7.41421i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q - 16 q^{13} - 4 q^{14} - 4 q^{16} + 8 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{29} + 24 q^{31} - 8 q^{37} - 8 q^{38} + 4 q^{43} + 8 q^{44} - 16 q^{46} + 20 q^{47} + 16 q^{52} - 16 q^{53} + 8 q^{58} + 12 q^{62} - 28 q^{67} - 8 q^{68} + 24 q^{74} + 4 q^{77} - 8 q^{82} + 8 q^{83} + 4 q^{88} - 24 q^{89} + 8 q^{92} + 24 q^{97}+O(q^{100}) $ 4 * q - 16 * q^13 - 4 * q^14 - 4 * q^16 + 8 * q^17 + 4 * q^22 + 8 * q^23 + 8 * q^29 + 24 * q^31 - 8 * q^37 - 8 * q^38 + 4 * q^43 + 8 * q^44 - 16 * q^46 + 20 * q^47 + 16 * q^52 - 16 * q^53 + 8 * q^58 + 12 * q^62 - 28 * q^67 - 8 * q^68 + 24 * q^74 + 4 * q^77 - 8 * q^82 + 8 * q^83 + 4 * q^88 - 24 * q^89 + 8 * q^92 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			3.41421i			1.02942i	0.857363	+	0.514712i	$0.172101\pi$
$11$			3.41421i			1.02942i	−0.857363	+	0.514712i	$0.827899\pi$
$12$		0			0
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.116171	+	0.993229i	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.41421	−	3.41421i	0.828068	−	0.828068i	−0.159181	−	0.987249i	$-0.550885\pi$
$17$	3.41421	−	3.41421i	0.828068	−	0.828068i	0.987249	+	0.159181i	$0.0508853\pi$
$18$		0			0
$19$		−	2.82843i		−	0.648886i	−0.945905	−	0.324443i	$-0.894823\pi$
$19$		−	2.82843i		−	0.648886i	0.945905	−	0.324443i	$-0.105177\pi$
$20$		0			0
$21$		0			0
$22$	2.41421	+	2.41421i	0.514712	+	0.514712i
$23$	−0.828427	−	0.828427i	−0.172739	−	0.172739i	0.615443	−	0.788182i	$-0.288977\pi$
$23$	−0.828427	−	0.828427i	−0.172739	−	0.172739i	−0.788182	+	0.615443i	$0.788977\pi$
$24$		0			0
$25$		0			0
$26$			5.65685i			1.10940i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	4.82843			0.896616			0.448308	−	0.893879i	$-0.352027\pi$
$29$	4.82843			0.896616			0.448308	+	0.893879i	$0.352027\pi$
$30$		0			0
$31$	10.2426			1.83963			0.919816	−	0.392349i	$-0.128338\pi$
$31$	10.2426			1.83963			0.919816	+	0.392349i	$0.128338\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	4.82843i		−	0.828068i
$35$		0			0
$36$		0			0
$37$	2.24264	+	2.24264i	0.368688	+	0.368688i	0.866999	−	0.498311i	$-0.166046\pi$
$37$	2.24264	+	2.24264i	0.368688	+	0.368688i	−0.498311	+	0.866999i	$0.666046\pi$
$38$	−2.00000	−	2.00000i	−0.324443	−	0.324443i
$39$		0			0
$40$		0			0
$41$		−	8.82843i		−	1.37877i	−0.724396	−	0.689384i	$-0.757881\pi$
$41$		−	8.82843i		−	1.37877i	0.724396	−	0.689384i	$-0.242119\pi$
$42$		0			0
$43$	8.07107	−	8.07107i	1.23083	−	1.23083i	0.267180	−	0.963647i	$-0.413908\pi$
$43$	8.07107	−	8.07107i	1.23083	−	1.23083i	0.963647	−	0.267180i	$-0.0860917\pi$
$44$	3.41421			0.514712
$45$		0			0
$46$	−1.17157			−0.172739
$47$	0.757359	−	0.757359i	0.110472	−	0.110472i	−0.649710	−	0.760182i	$-0.725110\pi$
$47$	0.757359	−	0.757359i	0.110472	−	0.110472i	0.760182	+	0.649710i	$0.225110\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	−5.41421	−	5.41421i	−0.743699	−	0.743699i	0.229588	−	0.973288i	$-0.426262\pi$
$53$	−5.41421	−	5.41421i	−0.743699	−	0.743699i	−0.973288	+	0.229588i	$0.926262\pi$
$54$		0			0
$55$		0			0
$56$			1.00000i			0.133631i
$57$		0			0
$58$	3.41421	−	3.41421i	0.448308	−	0.448308i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	9.89949			1.26750			0.633750	−	0.773538i	$-0.281515\pi$
$61$	9.89949			1.26750			0.633750	+	0.773538i	$0.281515\pi$
$62$	7.24264	−	7.24264i	0.919816	−	0.919816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−5.58579	−	5.58579i	−0.682412	−	0.682412i	0.278131	−	0.960543i	$-0.410285\pi$
$67$	−5.58579	−	5.58579i	−0.682412	−	0.682412i	−0.960543	+	0.278131i	$0.910285\pi$
$68$	−3.41421	−	3.41421i	−0.414034	−	0.414034i
$69$		0			0
$70$		0			0
$71$			6.82843i			0.810385i	0.914231	+	0.405193i	$0.132796\pi$
$71$			6.82843i			0.810385i	−0.914231	+	0.405193i	$0.867204\pi$
$72$		0			0
$73$	7.07107	−	7.07107i	0.827606	−	0.827606i	−0.159579	−	0.987185i	$-0.551014\pi$
$73$	7.07107	−	7.07107i	0.827606	−	0.827606i	0.987185	+	0.159579i	$0.0510137\pi$
$74$	3.17157			0.368688
$75$		0			0
$76$	−2.82843			−0.324443
$77$	2.41421	−	2.41421i	0.275125	−	0.275125i
$78$		0			0
$79$		−	5.65685i		−	0.636446i	−0.948016	−	0.318223i	$-0.896914\pi$
$79$		−	5.65685i		−	0.636446i	0.948016	−	0.318223i	$-0.103086\pi$
$80$		0			0
$81$		0			0
$82$	−6.24264	−	6.24264i	−0.689384	−	0.689384i
$83$	4.82843	+	4.82843i	0.529989	+	0.529989i	0.920569	−	0.390580i	$-0.127726\pi$
$83$	4.82843	+	4.82843i	0.529989	+	0.529989i	−0.390580	+	0.920569i	$0.627726\pi$
$84$		0			0
$85$		0			0
$86$		−	11.4142i		−	1.23083i
$87$		0			0
$88$	2.41421	−	2.41421i	0.257356	−	0.257356i
$89$	−8.82843			−0.935811			−0.467906	−	0.883778i	$-0.654991\pi$
$89$	−8.82843			−0.935811			−0.467906	+	0.883778i	$0.654991\pi$
$90$		0			0
$91$	5.65685			0.592999
$92$	−0.828427	+	0.828427i	−0.0863695	+	0.0863695i
$93$		0			0
$94$		−	1.07107i		−	0.110472i
$95$		0			0
$96$		0			0
$97$	7.41421	+	7.41421i	0.752799	+	0.752799i	0.975001	−	0.222201i	$-0.0713243\pi$
$97$	7.41421	+	7.41421i	0.752799	+	0.752799i	−0.222201	+	0.975001i	$0.571324\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$			6.34315i			0.631167i	0.948898	+	0.315583i	$0.102200\pi$
$101$			6.34315i			0.631167i	−0.948898	+	0.315583i	$0.897800\pi$
$102$		0			0
$103$	4.58579	−	4.58579i	0.451851	−	0.451851i	−0.444118	−	0.895969i	$-0.646483\pi$
$103$	4.58579	−	4.58579i	0.451851	−	0.451851i	0.895969	+	0.444118i	$0.146483\pi$
$104$	5.65685			0.554700
$105$		0			0
$106$	−7.65685			−0.743699
$107$	−10.8284	+	10.8284i	−1.04682	+	1.04682i	−0.0479750	+	0.998849i	$0.515277\pi$
$107$	−10.8284	+	10.8284i	−1.04682	+	1.04682i	−0.998849	+	0.0479750i	$0.984723\pi$
$108$		0			0
$109$		−	13.3137i		−	1.27522i	−0.770358	−	0.637611i	$-0.779923\pi$
$109$		−	13.3137i		−	1.27522i	0.770358	−	0.637611i	$-0.220077\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	11.3137	+	11.3137i	1.06430	+	1.06430i	0.997785	+	0.0665190i	$0.0211893\pi$
$113$	11.3137	+	11.3137i	1.06430	+	1.06430i	0.0665190	+	0.997785i	$0.478811\pi$
$114$		0			0
$115$		0			0
$116$		−	4.82843i		−	0.448308i
$117$		0			0
$118$	2.00000	−	2.00000i	0.184115	−	0.184115i
$119$	−4.82843			−0.442621
$120$		0			0
$121$	−0.656854			−0.0597140
$122$	7.00000	−	7.00000i	0.633750	−	0.633750i
$123$		0			0
$124$		−	10.2426i		−	0.919816i
$125$		0			0
$126$		0			0
$127$	3.65685	+	3.65685i	0.324493	+	0.324493i	0.850488	−	0.525995i	$-0.176307\pi$
$127$	3.65685	+	3.65685i	0.324493	+	0.324493i	−0.525995	+	0.850488i	$0.676307\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	0.485281i		−	0.0423992i	−0.999775	−	0.0211996i	$-0.993251\pi$
$131$		−	0.485281i		−	0.0423992i	0.999775	−	0.0211996i	$-0.00674855\pi$
$132$		0			0
$133$	−2.00000	+	2.00000i	−0.173422	+	0.173422i
$134$	−7.89949			−0.682412
$135$		0			0
$136$	−4.82843			−0.414034
$137$	12.0000	−	12.0000i	1.02523	−	1.02523i	0.0255558	−	0.999673i	$-0.491864\pi$
$137$	12.0000	−	12.0000i	1.02523	−	1.02523i	0.999673	−	0.0255558i	$-0.00813555\pi$
$138$		0			0
$139$			6.34315i			0.538019i	0.963138	+	0.269009i	$0.0866962\pi$
$139$			6.34315i			0.538019i	−0.963138	+	0.269009i	$0.913304\pi$
$140$		0			0
$141$		0			0
$142$	4.82843	+	4.82843i	0.405193	+	0.405193i
$143$	−13.6569	−	13.6569i	−1.14204	−	1.14204i
$144$		0			0
$145$		0			0
$146$		−	10.0000i		−	0.827606i
$147$		0			0
$148$	2.24264	−	2.24264i	0.184344	−	0.184344i
$149$	−20.1421			−1.65011			−0.825054	−	0.565054i	$-0.808855\pi$
$149$	−20.1421			−1.65011			−0.825054	+	0.565054i	$0.808855\pi$
$150$		0			0
$151$	−13.1716			−1.07189			−0.535944	−	0.844254i	$-0.680044\pi$
$151$	−13.1716			−1.07189			−0.535944	+	0.844254i	$0.680044\pi$
$152$	−2.00000	+	2.00000i	−0.162221	+	0.162221i
$153$		0			0
$154$		−	3.41421i		−	0.275125i
$155$		0			0
$156$		0			0
$157$	−1.65685	−	1.65685i	−0.132231	−	0.132231i	0.637893	−	0.770125i	$-0.279806\pi$
$157$	−1.65685	−	1.65685i	−0.132231	−	0.132231i	−0.770125	+	0.637893i	$0.779806\pi$
$158$	−4.00000	−	4.00000i	−0.318223	−	0.318223i
$159$		0			0
$160$		0			0
$161$			1.17157i			0.0923329i
$162$		0			0
$163$	13.7279	−	13.7279i	1.07525	−	1.07525i	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	13.7279	−	13.7279i	1.07525	−	1.07525i	0.996928	−	0.0783260i	$-0.0249575\pi$
$164$	−8.82843			−0.689384
$165$		0			0
$166$	6.82843			0.529989
$167$	−10.4142	+	10.4142i	−0.805876	+	0.805876i	−0.984007	−	0.178131i	$-0.942995\pi$
$167$	−10.4142	+	10.4142i	−0.805876	+	0.805876i	0.178131	+	0.984007i	$0.442995\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$		0			0
$171$		0			0
$172$	−8.07107	−	8.07107i	−0.615413	−	0.615413i
$173$	5.48528	+	5.48528i	0.417038	+	0.417038i	0.884182	−	0.467143i	$-0.154717\pi$
$173$	5.48528	+	5.48528i	0.417038	+	0.417038i	−0.467143	+	0.884182i	$0.654717\pi$
$174$		0			0
$175$		0			0
$176$		−	3.41421i		−	0.257356i
$177$		0			0
$178$	−6.24264	+	6.24264i	−0.467906	+	0.467906i
$179$	−19.4142			−1.45109			−0.725543	−	0.688177i	$-0.758411\pi$
$179$	−19.4142			−1.45109			−0.725543	+	0.688177i	$0.758411\pi$
$180$		0			0
$181$	−4.92893			−0.366365			−0.183182	−	0.983079i	$-0.558640\pi$
$181$	−4.92893			−0.366365			−0.183182	+	0.983079i	$0.558640\pi$
$182$	4.00000	−	4.00000i	0.296500	−	0.296500i
$183$		0			0
$184$			1.17157i			0.0863695i
$185$		0			0
$186$		0			0
$187$	11.6569	+	11.6569i	0.852434	+	0.852434i
$188$	−0.757359	−	0.757359i	−0.0552361	−	0.0552361i
$189$		0			0
$190$		0			0
$191$		−	25.6569i		−	1.85646i	−0.372001	−	0.928232i	$-0.621328\pi$
$191$		−	25.6569i		−	1.85646i	0.372001	−	0.928232i	$-0.378672\pi$
$192$		0			0
$193$	3.48528	−	3.48528i	0.250876	−	0.250876i	−0.570454	−	0.821330i	$-0.693233\pi$
$193$	3.48528	−	3.48528i	0.250876	−	0.250876i	0.821330	+	0.570454i	$0.193233\pi$
$194$	10.4853			0.752799
$195$		0			0
$196$	1.00000			0.0714286
$197$	−1.75736	+	1.75736i	−0.125207	+	0.125207i	−0.766933	−	0.641727i	$-0.778218\pi$
$197$	−1.75736	+	1.75736i	−0.125207	+	0.125207i	0.641727	+	0.766933i	$0.278218\pi$
$198$		0			0
$199$			23.8995i			1.69419i	0.531441	+	0.847095i	$0.321651\pi$
$199$			23.8995i			1.69419i	−0.531441	+	0.847095i	$0.678349\pi$
$200$		0			0
$201$		0			0
$202$	4.48528	+	4.48528i	0.315583	+	0.315583i
$203$	−3.41421	−	3.41421i	−0.239631	−	0.239631i
$204$		0			0
$205$		0			0
$206$		−	6.48528i		−	0.451851i
$207$		0			0
$208$	4.00000	−	4.00000i	0.277350	−	0.277350i
$209$	9.65685			0.667979
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	−5.41421	+	5.41421i	−0.371850	+	0.371850i
$213$		0			0
$214$			15.3137i			1.04682i
$215$		0			0
$216$		0			0
$217$	−7.24264	−	7.24264i	−0.491662	−	0.491662i
$218$	−9.41421	−	9.41421i	−0.637611	−	0.637611i
$219$		0			0
$220$		0			0
$221$			27.3137i			1.83732i
$222$		0			0
$223$	15.3137	−	15.3137i	1.02548	−	1.02548i	0.0258150	−	0.999667i	$-0.491782\pi$
$223$	15.3137	−	15.3137i	1.02548	−	1.02548i	0.999667	−	0.0258150i	$-0.00821809\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	16.0000			1.06430
$227$	6.82843	−	6.82843i	0.453219	−	0.453219i	−0.443203	−	0.896421i	$-0.646158\pi$
$227$	6.82843	−	6.82843i	0.453219	−	0.453219i	0.896421	+	0.443203i	$0.146158\pi$
$228$		0			0
$229$			0.242641i			0.0160341i	0.999968	+	0.00801707i	$0.00255194\pi$
$229$			0.242641i			0.0160341i	−0.999968	+	0.00801707i	$0.997448\pi$
$230$		0			0
$231$		0			0
$232$	−3.41421	−	3.41421i	−0.224154	−	0.224154i
$233$	9.17157	+	9.17157i	0.600850	+	0.600850i	0.940538	−	0.339688i	$-0.110322\pi$
$233$	9.17157	+	9.17157i	0.600850	+	0.600850i	−0.339688	+	0.940538i	$0.610322\pi$
$234$		0			0
$235$		0			0
$236$		−	2.82843i		−	0.184115i
$237$		0			0
$238$	−3.41421	+	3.41421i	−0.221311	+	0.221311i
$239$	−2.34315			−0.151565			−0.0757827	−	0.997124i	$-0.524146\pi$
$239$	−2.34315			−0.151565			−0.0757827	+	0.997124i	$0.524146\pi$
$240$		0			0
$241$	24.1421			1.55513			0.777566	−	0.628802i	$-0.216454\pi$
$241$	24.1421			1.55513			0.777566	+	0.628802i	$0.216454\pi$
$242$	−0.464466	+	0.464466i	−0.0298570	+	0.0298570i
$243$		0			0
$244$		−	9.89949i		−	0.633750i
$245$		0			0
$246$		0			0
$247$	11.3137	+	11.3137i	0.719874	+	0.719874i
$248$	−7.24264	−	7.24264i	−0.459908	−	0.459908i
$249$		0			0
$250$		0			0
$251$			18.6274i			1.17575i	0.808951	+	0.587876i	$0.200036\pi$
$251$			18.6274i			1.17575i	−0.808951	+	0.587876i	$0.799964\pi$
$252$		0			0
$253$	2.82843	−	2.82843i	0.177822	−	0.177822i
$254$	5.17157			0.324493
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.4142	−	11.4142i	0.711999	−	0.711999i	−0.254954	−	0.966953i	$-0.582060\pi$
$257$	11.4142	−	11.4142i	0.711999	−	0.711999i	0.966953	+	0.254954i	$0.0820604\pi$
$258$		0			0
$259$		−	3.17157i		−	0.197072i
$260$		0			0
$261$		0			0
$262$	−0.343146	−	0.343146i	−0.0211996	−	0.0211996i
$263$	−3.65685	−	3.65685i	−0.225491	−	0.225491i	0.585315	−	0.810806i	$-0.300971\pi$
$263$	−3.65685	−	3.65685i	−0.225491	−	0.225491i	−0.810806	+	0.585315i	$0.800971\pi$
$264$		0			0
$265$		0			0
$266$			2.82843i			0.173422i
$267$		0			0
$268$	−5.58579	+	5.58579i	−0.341206	+	0.341206i
$269$	5.65685			0.344904			0.172452	−	0.985018i	$-0.444831\pi$
$269$	5.65685			0.344904			0.172452	+	0.985018i	$0.444831\pi$
$270$		0			0
$271$	23.8995			1.45179			0.725895	−	0.687805i	$-0.241426\pi$
$271$	23.8995			1.45179			0.725895	+	0.687805i	$0.241426\pi$
$272$	−3.41421	+	3.41421i	−0.207017	+	0.207017i
$273$		0			0
$274$		−	16.9706i		−	1.02523i
$275$		0			0
$276$		0			0
$277$	21.8995	+	21.8995i	1.31581	+	1.31581i	0.917057	+	0.398756i	$0.130558\pi$
$277$	21.8995	+	21.8995i	1.31581	+	1.31581i	0.398756	+	0.917057i	$0.369442\pi$
$278$	4.48528	+	4.48528i	0.269009	+	0.269009i
$279$		0			0
$280$		0			0
$281$		−	4.92893i		−	0.294035i	−0.989134	−	0.147018i	$-0.953033\pi$
$281$		−	4.92893i		−	0.294035i	0.989134	−	0.147018i	$-0.0469674\pi$
$282$		0			0
$283$	−1.31371	+	1.31371i	−0.0780919	+	0.0780919i	−0.745074	−	0.666982i	$-0.767586\pi$
$283$	−1.31371	+	1.31371i	−0.0780919	+	0.0780919i	0.666982	+	0.745074i	$0.267586\pi$
$284$	6.82843			0.405193
$285$		0			0
$286$	−19.3137			−1.14204
$287$	−6.24264	+	6.24264i	−0.368491	+	0.368491i
$288$		0			0
$289$		−	6.31371i		−	0.371395i
$290$		0			0
$291$		0			0
$292$	−7.07107	−	7.07107i	−0.413803	−	0.413803i
$293$	−2.65685	−	2.65685i	−0.155215	−	0.155215i	0.625227	−	0.780443i	$-0.285006\pi$
$293$	−2.65685	−	2.65685i	−0.155215	−	0.155215i	−0.780443	+	0.625227i	$0.785006\pi$
$294$		0			0
$295$		0			0
$296$		−	3.17157i		−	0.184344i
$297$		0			0
$298$	−14.2426	+	14.2426i	−0.825054	+	0.825054i
$299$	6.62742			0.383273
$300$		0			0
$301$	−11.4142			−0.657904
$302$	−9.31371	+	9.31371i	−0.535944	+	0.535944i
$303$		0			0
$304$			2.82843i			0.162221i
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	−2.41421	−	2.41421i	−0.137563	−	0.137563i
$309$		0			0
$310$		0			0
$311$			0.828427i			0.0469758i	0.999724	+	0.0234879i	$0.00747712\pi$
$311$			0.828427i			0.0469758i	−0.999724	+	0.0234879i	$0.992523\pi$
$312$		0			0
$313$	6.24264	−	6.24264i	0.352855	−	0.352855i	−0.508316	−	0.861171i	$-0.669732\pi$
$313$	6.24264	−	6.24264i	0.352855	−	0.352855i	0.861171	+	0.508316i	$0.169732\pi$
$314$	−2.34315			−0.132231
$315$		0			0
$316$	−5.65685			−0.318223
$317$	0.727922	−	0.727922i	0.0408842	−	0.0408842i	−0.686369	−	0.727253i	$-0.740797\pi$
$317$	0.727922	−	0.727922i	0.0408842	−	0.0408842i	0.727253	+	0.686369i	$0.240797\pi$
$318$		0			0
$319$			16.4853i			0.922999i
$320$		0			0
$321$		0			0
$322$	0.828427	+	0.828427i	0.0461664	+	0.0461664i
$323$	−9.65685	−	9.65685i	−0.537322	−	0.537322i
$324$		0			0
$325$		0			0
$326$		−	19.4142i		−	1.07525i
$327$		0			0
$328$	−6.24264	+	6.24264i	−0.344692	+	0.344692i
$329$	−1.07107			−0.0590499
$330$		0			0
$331$	−26.6274			−1.46358			−0.731788	−	0.681533i	$-0.761314\pi$
$331$	−26.6274			−1.46358			−0.731788	+	0.681533i	$0.761314\pi$
$332$	4.82843	−	4.82843i	0.264994	−	0.264994i
$333$		0			0
$334$			14.7279i			0.805876i
$335$		0			0
$336$		0			0
$337$	−15.8284	−	15.8284i	−0.862229	−	0.862229i	0.129367	−	0.991597i	$-0.458705\pi$
$337$	−15.8284	−	15.8284i	−0.862229	−	0.862229i	−0.991597	+	0.129367i	$0.958705\pi$
$338$	−13.4350	−	13.4350i	−0.730769	−	0.730769i
$339$		0			0
$340$		0			0
$341$			34.9706i			1.89376i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−11.4142			−0.615413
$345$		0			0
$346$	7.75736			0.417038
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	−0.441666	−	0.897180i	$-0.645612\pi$
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	0.897180	+	0.441666i	$0.145612\pi$
$348$		0			0
$349$		−	7.27208i		−	0.389265i	−0.980876	−	0.194633i	$-0.937649\pi$
$349$		−	7.27208i		−	0.389265i	0.980876	−	0.194633i	$-0.0623515\pi$
$350$		0			0
$351$		0			0
$352$	−2.41421	−	2.41421i	−0.128678	−	0.128678i
$353$	−18.3848	−	18.3848i	−0.978523	−	0.978523i	0.0212513	−	0.999774i	$-0.493235\pi$
$353$	−18.3848	−	18.3848i	−0.978523	−	0.978523i	−0.999774	+	0.0212513i	$0.993235\pi$
$354$		0			0
$355$		0			0
$356$			8.82843i			0.467906i
$357$		0			0
$358$	−13.7279	+	13.7279i	−0.725543	+	0.725543i
$359$	15.7990			0.833839			0.416919	−	0.908943i	$-0.363110\pi$
$359$	15.7990			0.833839			0.416919	+	0.908943i	$0.363110\pi$
$360$		0			0
$361$	11.0000			0.578947
$362$	−3.48528	+	3.48528i	−0.183182	+	0.183182i
$363$		0			0
$364$		−	5.65685i		−	0.296500i
$365$		0			0
$366$		0			0
$367$	1.75736	+	1.75736i	0.0917334	+	0.0917334i	0.751484	−	0.659751i	$-0.229338\pi$
$367$	1.75736	+	1.75736i	0.0917334	+	0.0917334i	−0.659751	+	0.751484i	$0.729338\pi$
$368$	0.828427	+	0.828427i	0.0431847	+	0.0431847i
$369$		0			0
$370$		0			0
$371$			7.65685i			0.397524i
$372$		0			0
$373$	−3.07107	+	3.07107i	−0.159014	+	0.159014i	−0.782130	−	0.623116i	$-0.785867\pi$
$373$	−3.07107	+	3.07107i	−0.159014	+	0.159014i	0.623116	+	0.782130i	$0.285867\pi$
$374$	16.4853			0.852434
$375$		0			0
$376$	−1.07107			−0.0552361
$377$	−19.3137	+	19.3137i	−0.994707	+	0.994707i
$378$		0			0
$379$			13.7990i			0.708806i	0.935093	+	0.354403i	$0.115316\pi$
$379$			13.7990i			0.708806i	−0.935093	+	0.354403i	$0.884684\pi$
$380$		0			0
$381$		0			0
$382$	−18.1421	−	18.1421i	−0.928232	−	0.928232i
$383$	1.58579	+	1.58579i	0.0810299	+	0.0810299i	0.746460	−	0.665430i	$-0.231752\pi$
$383$	1.58579	+	1.58579i	0.0810299	+	0.0810299i	−0.665430	+	0.746460i	$0.731752\pi$
$384$		0			0
$385$		0			0
$386$		−	4.92893i		−	0.250876i
$387$		0			0
$388$	7.41421	−	7.41421i	0.376400	−	0.376400i
$389$	−29.7990			−1.51087			−0.755434	−	0.655224i	$-0.772574\pi$
$389$	−29.7990			−1.51087			−0.755434	+	0.655224i	$0.772574\pi$
$390$		0			0
$391$	−5.65685			−0.286079
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$			2.48528i			0.125207i
$395$		0			0
$396$		0			0
$397$	15.0711	+	15.0711i	0.756395	+	0.756395i	0.975664	−	0.219269i	$-0.0703673\pi$
$397$	15.0711	+	15.0711i	0.756395	+	0.756395i	−0.219269	+	0.975664i	$0.570367\pi$
$398$	16.8995	+	16.8995i	0.847095	+	0.847095i
$399$		0			0
$400$		0			0
$401$		−	26.8701i		−	1.34183i	−0.741536	−	0.670913i	$-0.765902\pi$
$401$		−	26.8701i		−	1.34183i	0.741536	−	0.670913i	$-0.234098\pi$
$402$		0			0
$403$	−40.9706	+	40.9706i	−2.04089	+	2.04089i
$404$	6.34315			0.315583
$405$		0			0
$406$	−4.82843			−0.239631
$407$	−7.65685	+	7.65685i	−0.379536	+	0.379536i
$408$		0			0
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$		0			0
$411$		0			0
$412$	−4.58579	−	4.58579i	−0.225925	−	0.225925i
$413$	−2.00000	−	2.00000i	−0.0984136	−	0.0984136i
$414$		0			0
$415$		0			0
$416$		−	5.65685i		−	0.277350i
$417$		0			0
$418$	6.82843	−	6.82843i	0.333989	−	0.333989i
$419$	−26.6274			−1.30083			−0.650417	−	0.759577i	$-0.725406\pi$
$419$	−26.6274			−1.30083			−0.650417	+	0.759577i	$0.725406\pi$
$420$		0			0
$421$	4.62742			0.225527			0.112763	−	0.993622i	$-0.464030\pi$
$421$	4.62742			0.225527			0.112763	+	0.993622i	$0.464030\pi$
$422$	−2.82843	+	2.82843i	−0.137686	+	0.137686i
$423$		0			0
$424$			7.65685i			0.371850i
$425$		0			0
$426$		0			0
$427$	−7.00000	−	7.00000i	−0.338754	−	0.338754i
$428$	10.8284	+	10.8284i	0.523412	+	0.523412i
$429$		0			0
$430$		0			0
$431$		−	2.14214i		−	0.103183i	−0.998668	−	0.0515915i	$-0.983571\pi$
$431$		−	2.14214i		−	0.103183i	0.998668	−	0.0515915i	$-0.0164294\pi$
$432$		0			0
$433$	−9.75736	+	9.75736i	−0.468909	+	0.468909i	−0.901561	−	0.432652i	$-0.857578\pi$
$433$	−9.75736	+	9.75736i	−0.468909	+	0.468909i	0.432652	+	0.901561i	$0.357578\pi$
$434$	−10.2426			−0.491662
$435$		0			0
$436$	−13.3137			−0.637611
$437$	−2.34315	+	2.34315i	−0.112088	+	0.112088i
$438$		0			0
$439$		−	15.8995i		−	0.758841i	−0.925224	−	0.379421i	$-0.876123\pi$
$439$		−	15.8995i		−	0.758841i	0.925224	−	0.379421i	$-0.123877\pi$
$440$		0			0
$441$		0			0
$442$	19.3137	+	19.3137i	0.918659	+	0.918659i
$443$	−20.4853	−	20.4853i	−0.973285	−	0.973285i	0.0263672	−	0.999652i	$-0.491606\pi$
$443$	−20.4853	−	20.4853i	−0.973285	−	0.973285i	−0.999652	+	0.0263672i	$0.991606\pi$
$444$		0			0
$445$		0			0
$446$		−	21.6569i		−	1.02548i
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−8.72792			−0.411896			−0.205948	−	0.978563i	$-0.566028\pi$
$449$	−8.72792			−0.411896			−0.205948	+	0.978563i	$0.566028\pi$
$450$		0			0
$451$	30.1421			1.41934
$452$	11.3137	−	11.3137i	0.532152	−	0.532152i
$453$		0			0
$454$		−	9.65685i		−	0.453219i
$455$		0			0
$456$		0			0
$457$	−7.82843	−	7.82843i	−0.366198	−	0.366198i	0.499890	−	0.866089i	$-0.333374\pi$
$457$	−7.82843	−	7.82843i	−0.366198	−	0.366198i	−0.866089	+	0.499890i	$0.833374\pi$
$458$	0.171573	+	0.171573i	0.00801707	+	0.00801707i
$459$		0			0
$460$		0			0
$461$			17.3137i			0.806380i	0.915116	+	0.403190i	$0.132099\pi$
$461$			17.3137i			0.806380i	−0.915116	+	0.403190i	$0.867901\pi$
$462$		0			0
$463$	−19.7990	+	19.7990i	−0.920137	+	0.920137i	−0.997039	−	0.0769016i	$-0.975497\pi$
$463$	−19.7990	+	19.7990i	−0.920137	+	0.920137i	0.0769016	+	0.997039i	$0.475497\pi$
$464$	−4.82843			−0.224154
$465$		0			0
$466$	12.9706			0.600850
$467$	−14.0000	+	14.0000i	−0.647843	+	0.647843i	−0.952471	−	0.304629i	$-0.901468\pi$
$467$	−14.0000	+	14.0000i	−0.647843	+	0.647843i	0.304629	+	0.952471i	$0.401468\pi$
$468$		0			0
$469$			7.89949i			0.364765i
$470$		0			0
$471$		0			0
$472$	−2.00000	−	2.00000i	−0.0920575	−	0.0920575i
$473$	27.5563	+	27.5563i	1.26704	+	1.26704i
$474$		0			0
$475$		0			0
$476$			4.82843i			0.221311i
$477$		0			0
$478$	−1.65685	+	1.65685i	−0.0757827	+	0.0757827i
$479$	−24.8284			−1.13444			−0.567220	−	0.823566i	$-0.691981\pi$
$479$	−24.8284			−1.13444			−0.567220	+	0.823566i	$0.691981\pi$
$480$		0			0
$481$	−17.9411			−0.818045
$482$	17.0711	−	17.0711i	0.777566	−	0.777566i
$483$		0			0
$484$			0.656854i			0.0298570i
$485$		0			0
$486$		0			0
$487$	14.9706	+	14.9706i	0.678381	+	0.678381i	0.959634	−	0.281253i	$-0.0907499\pi$
$487$	14.9706	+	14.9706i	0.678381	+	0.678381i	−0.281253	+	0.959634i	$0.590750\pi$
$488$	−7.00000	−	7.00000i	−0.316875	−	0.316875i
$489$		0			0
$490$		0			0
$491$		−	1.27208i		−	0.0574081i	−0.999588	−	0.0287040i	$-0.990862\pi$
$491$		−	1.27208i		−	0.0574081i	0.999588	−	0.0287040i	$-0.00913803\pi$
$492$		0			0
$493$	16.4853	−	16.4853i	0.742460	−	0.742460i
$494$	16.0000			0.719874
$495$		0			0
$496$	−10.2426			−0.459908
$497$	4.82843	−	4.82843i	0.216585	−	0.216585i
$498$		0			0
$499$			27.4558i			1.22909i	0.788881	+	0.614546i	$0.210661\pi$
$499$			27.4558i			1.22909i	−0.788881	+	0.614546i	$0.789339\pi$
$500$		0			0
$501$		0			0
$502$	13.1716	+	13.1716i	0.587876	+	0.587876i
$503$	14.5563	+	14.5563i	0.649036	+	0.649036i	0.952760	−	0.303724i	$-0.0982302\pi$
$503$	14.5563	+	14.5563i	0.649036	+	0.649036i	−0.303724	+	0.952760i	$0.598230\pi$
$504$		0			0
$505$		0			0
$506$		−	4.00000i		−	0.177822i
$507$		0			0
$508$	3.65685	−	3.65685i	0.162247	−	0.162247i
$509$	29.6569			1.31452			0.657258	−	0.753665i	$-0.271716\pi$
$509$	29.6569			1.31452			0.657258	+	0.753665i	$0.271716\pi$
$510$		0			0
$511$	−10.0000			−0.442374
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	16.1421i		−	0.711999i
$515$		0			0
$516$		0			0
$517$	2.58579	+	2.58579i	0.113723	+	0.113723i
$518$	−2.24264	−	2.24264i	−0.0985360	−	0.0985360i
$519$		0			0
$520$		0			0
$521$		−	30.7696i		−	1.34804i	−0.738714	−	0.674019i	$-0.764566\pi$
$521$		−	30.7696i		−	1.34804i	0.738714	−	0.674019i	$-0.235434\pi$
$522$		0			0
$523$	2.68629	−	2.68629i	0.117463	−	0.117463i	−0.645932	−	0.763395i	$-0.723531\pi$
$523$	2.68629	−	2.68629i	0.117463	−	0.117463i	0.763395	+	0.645932i	$0.223531\pi$
$524$	−0.485281			−0.0211996
$525$		0			0
$526$	−5.17157			−0.225491
$527$	34.9706	−	34.9706i	1.52334	−	1.52334i
$528$		0			0
$529$		−	21.6274i		−	0.940322i
$530$		0			0
$531$		0			0
$532$	2.00000	+	2.00000i	0.0867110	+	0.0867110i
$533$	35.3137	+	35.3137i	1.52961	+	1.52961i
$534$		0			0
$535$		0			0
$536$			7.89949i			0.341206i
$537$		0			0
$538$	4.00000	−	4.00000i	0.172452	−	0.172452i
$539$	−3.41421			−0.147061
$540$		0			0
$541$	33.1127			1.42363			0.711813	−	0.702369i	$-0.247874\pi$
$541$	33.1127			1.42363			0.711813	+	0.702369i	$0.247874\pi$
$542$	16.8995	−	16.8995i	0.725895	−	0.725895i
$543$		0			0
$544$			4.82843i			0.207017i
$545$		0			0
$546$		0			0
$547$	−18.5563	−	18.5563i	−0.793412	−	0.793412i	0.188635	−	0.982047i	$-0.439594\pi$
$547$	−18.5563	−	18.5563i	−0.793412	−	0.793412i	−0.982047	+	0.188635i	$0.939594\pi$
$548$	−12.0000	−	12.0000i	−0.512615	−	0.512615i
$549$		0			0
$550$		0			0
$551$		−	13.6569i		−	0.581802i
$552$		0			0
$553$	−4.00000	+	4.00000i	−0.170097	+	0.170097i
$554$	30.9706			1.31581
$555$		0			0
$556$	6.34315			0.269009
$557$	−23.5563	+	23.5563i	−0.998115	+	0.998115i	−0.999998	−	0.00188368i	$-0.999400\pi$
$557$	−23.5563	+	23.5563i	−0.998115	+	0.998115i	0.00188368	+	0.999998i	$0.499400\pi$
$558$		0			0
$559$			64.5685i			2.73096i
$560$		0			0
$561$		0			0
$562$	−3.48528	−	3.48528i	−0.147018	−	0.147018i
$563$	29.3137	+	29.3137i	1.23543	+	1.23543i	0.961851	+	0.273575i	$0.0882061\pi$
$563$	29.3137	+	29.3137i	1.23543	+	1.23543i	0.273575	+	0.961851i	$0.411794\pi$
$564$		0			0
$565$		0			0
$566$			1.85786i			0.0780919i
$567$		0			0
$568$	4.82843	−	4.82843i	0.202596	−	0.202596i
$569$	33.8995			1.42114			0.710570	−	0.703626i	$-0.248437\pi$
$569$	33.8995			1.42114			0.710570	+	0.703626i	$0.248437\pi$
$570$		0			0
$571$	−44.9706			−1.88196			−0.940980	−	0.338463i	$-0.890093\pi$
$571$	−44.9706			−1.88196			−0.940980	+	0.338463i	$0.890093\pi$
$572$	−13.6569	+	13.6569i	−0.571022	+	0.571022i
$573$		0			0
$574$			8.82843i			0.368491i
$575$		0			0
$576$		0			0
$577$	−14.7279	−	14.7279i	−0.613131	−	0.613131i	0.330629	−	0.943761i	$-0.392739\pi$
$577$	−14.7279	−	14.7279i	−0.613131	−	0.613131i	−0.943761	+	0.330629i	$0.892739\pi$
$578$	−4.46447	−	4.46447i	−0.185697	−	0.185697i
$579$		0			0
$580$		0			0
$581$		−	6.82843i		−	0.283291i
$582$		0			0
$583$	18.4853	−	18.4853i	0.765582	−	0.765582i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	−3.75736			−0.155215
$587$	−21.7990	+	21.7990i	−0.899741	+	0.899741i	−0.995413	−	0.0956723i	$-0.969500\pi$
$587$	−21.7990	+	21.7990i	−0.899741	+	0.899741i	0.0956723	+	0.995413i	$0.469500\pi$
$588$		0			0
$589$		−	28.9706i		−	1.19371i
$590$		0			0
$591$		0			0
$592$	−2.24264	−	2.24264i	−0.0921720	−	0.0921720i
$593$	20.3848	+	20.3848i	0.837102	+	0.837102i	0.988477	−	0.151374i	$-0.0483698\pi$
$593$	20.3848	+	20.3848i	0.837102	+	0.837102i	−0.151374	+	0.988477i	$0.548370\pi$
$594$		0			0
$595$		0			0
$596$			20.1421i			0.825054i
$597$		0			0
$598$	4.68629	−	4.68629i	0.191637	−	0.191637i
$599$	−7.31371			−0.298830			−0.149415	−	0.988775i	$-0.547739\pi$
$599$	−7.31371			−0.298830			−0.149415	+	0.988775i	$0.547739\pi$
$600$		0			0
$601$	24.1421			0.984778			0.492389	−	0.870375i	$-0.336124\pi$
$601$	24.1421			0.984778			0.492389	+	0.870375i	$0.336124\pi$
$602$	−8.07107	+	8.07107i	−0.328952	+	0.328952i
$603$		0			0
$604$			13.1716i			0.535944i
$605$		0			0
$606$		0			0
$607$	−15.3137	−	15.3137i	−0.621564	−	0.621564i	0.324367	−	0.945931i	$-0.394849\pi$
$607$	−15.3137	−	15.3137i	−0.621564	−	0.621564i	−0.945931	+	0.324367i	$0.894849\pi$
$608$	2.00000	+	2.00000i	0.0811107	+	0.0811107i
$609$		0			0
$610$		0			0
$611$			6.05887i			0.245116i
$612$		0			0
$613$	−5.07107	+	5.07107i	−0.204818	+	0.204818i	−0.802061	−	0.597242i	$-0.796263\pi$
$613$	−5.07107	+	5.07107i	−0.204818	+	0.204818i	0.597242	+	0.802061i	$0.296263\pi$
$614$		0			0
$615$		0			0
$616$	−3.41421			−0.137563
$617$	−24.0416	+	24.0416i	−0.967880	+	0.967880i	−0.999500	−	0.0316203i	$-0.989933\pi$
$617$	−24.0416	+	24.0416i	−0.967880	+	0.967880i	0.0316203	+	0.999500i	$0.489933\pi$
$618$		0			0
$619$			46.1421i			1.85461i	0.374308	+	0.927305i	$0.377880\pi$
$619$			46.1421i			1.85461i	−0.374308	+	0.927305i	$0.622120\pi$
$620$		0			0
$621$		0			0
$622$	0.585786	+	0.585786i	0.0234879	+	0.0234879i
$623$	6.24264	+	6.24264i	0.250106	+	0.250106i
$624$		0			0
$625$		0			0
$626$		−	8.82843i		−	0.352855i
$627$		0			0
$628$	−1.65685	+	1.65685i	−0.0661157	+	0.0661157i
$629$	15.3137			0.610598
$630$		0			0
$631$	−39.7990			−1.58437			−0.792186	−	0.610279i	$-0.791057\pi$
$631$	−39.7990			−1.58437			−0.792186	+	0.610279i	$0.791057\pi$
$632$	−4.00000	+	4.00000i	−0.159111	+	0.159111i
$633$		0			0
$634$		−	1.02944i		−	0.0408842i
$635$		0			0
$636$		0			0
$637$	−4.00000	−	4.00000i	−0.158486	−	0.158486i
$638$	11.6569	+	11.6569i	0.461499	+	0.461499i
$639$		0			0
$640$		0			0
$641$			21.2132i			0.837871i	0.908016	+	0.418936i	$0.137597\pi$
$641$			21.2132i			0.837871i	−0.908016	+	0.418936i	$0.862403\pi$
$642$		0			0
$643$	−22.9706	+	22.9706i	−0.905871	+	0.905871i	−0.995936	−	0.0900653i	$-0.971292\pi$
$643$	−22.9706	+	22.9706i	−0.905871	+	0.905871i	0.0900653	+	0.995936i	$0.471292\pi$
$644$	1.17157			0.0461664
$645$		0			0
$646$	−13.6569			−0.537322
$647$	−24.7574	+	24.7574i	−0.973312	+	0.973312i	−0.999653	−	0.0263408i	$-0.991614\pi$
$647$	−24.7574	+	24.7574i	−0.973312	+	0.973312i	0.0263408	+	0.999653i	$0.491614\pi$
$648$		0			0
$649$			9.65685i			0.379065i
$650$		0			0
$651$		0			0
$652$	−13.7279	−	13.7279i	−0.537627	−	0.537627i
$653$	5.75736	+	5.75736i	0.225303	+	0.225303i	0.810727	−	0.585424i	$-0.199072\pi$
$653$	5.75736	+	5.75736i	0.225303	+	0.225303i	−0.585424	+	0.810727i	$0.699072\pi$
$654$		0			0
$655$		0			0
$656$			8.82843i			0.344692i
$657$		0			0
$658$	−0.757359	+	0.757359i	−0.0295249	+	0.0295249i
$659$	1.27208			0.0495531			0.0247766	−	0.999693i	$-0.492113\pi$
$659$	1.27208			0.0495531			0.0247766	+	0.999693i	$0.492113\pi$
$660$		0			0
$661$	−8.04163			−0.312783			−0.156392	−	0.987695i	$-0.549986\pi$
$661$	−8.04163			−0.312783			−0.156392	+	0.987695i	$0.549986\pi$
$662$	−18.8284	+	18.8284i	−0.731788	+	0.731788i
$663$		0			0
$664$		−	6.82843i		−	0.264994i
$665$		0			0
$666$		0			0
$667$	−4.00000	−	4.00000i	−0.154881	−	0.154881i
$668$	10.4142	+	10.4142i	0.402938	+	0.402938i
$669$		0			0
$670$		0			0
$671$			33.7990i			1.30480i
$672$		0			0
$673$	−14.6569	+	14.6569i	−0.564980	+	0.564980i	−0.930718	−	0.365738i	$-0.880817\pi$
$673$	−14.6569	+	14.6569i	−0.564980	+	0.564980i	0.365738	+	0.930718i	$0.380817\pi$
$674$	−22.3848			−0.862229
$675$		0			0
$676$	−19.0000			−0.730769
$677$	10.1716	−	10.1716i	0.390925	−	0.390925i	−0.484092	−	0.875017i	$-0.660850\pi$
$677$	10.1716	−	10.1716i	0.390925	−	0.390925i	0.875017	+	0.484092i	$0.160850\pi$
$678$		0			0
$679$		−	10.4853i		−	0.402388i
$680$		0			0
$681$		0			0
$682$	24.7279	+	24.7279i	0.946881	+	0.946881i
$683$	−12.3848	−	12.3848i	−0.473890	−	0.473890i	0.429281	−	0.903171i	$-0.358767\pi$
$683$	−12.3848	−	12.3848i	−0.473890	−	0.473890i	−0.903171	+	0.429281i	$0.858767\pi$
$684$		0			0
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	−8.07107	+	8.07107i	−0.307707	+	0.307707i
$689$	43.3137			1.65012
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	5.48528	−	5.48528i	0.208519	−	0.208519i
$693$		0			0
$694$		−	12.0000i		−	0.455514i
$695$		0			0
$696$		0			0
$697$	−30.1421	−	30.1421i	−1.14171	−	1.14171i
$698$	−5.14214	−	5.14214i	−0.194633	−	0.194633i
$699$		0			0
$700$		0			0
$701$			35.1716i			1.32841i	0.747550	+	0.664206i	$0.231230\pi$
$701$			35.1716i			1.32841i	−0.747550	+	0.664206i	$0.768770\pi$
$702$		0			0
$703$	6.34315	−	6.34315i	0.239236	−	0.239236i
$704$	−3.41421			−0.128678
$705$		0			0
$706$	−26.0000			−0.978523
$707$	4.48528	−	4.48528i	0.168686	−	0.168686i
$708$		0			0
$709$			35.1716i			1.32090i	0.750872	+	0.660448i	$0.229634\pi$
$709$			35.1716i			1.32090i	−0.750872	+	0.660448i	$0.770366\pi$
$710$		0			0
$711$		0			0
$712$	6.24264	+	6.24264i	0.233953	+	0.233953i
$713$	−8.48528	−	8.48528i	−0.317776	−	0.317776i
$714$		0			0
$715$		0			0
$716$			19.4142i			0.725543i
$717$		0			0
$718$	11.1716	−	11.1716i	0.416919	−	0.416919i
$719$	6.62742			0.247161			0.123580	−	0.992335i	$-0.460562\pi$
$719$	6.62742			0.247161			0.123580	+	0.992335i	$0.460562\pi$
$720$		0			0
$721$	−6.48528			−0.241524
$722$	7.77817	−	7.77817i	0.289474	−	0.289474i
$723$		0			0
$724$			4.92893i			0.183182i
$725$		0			0
$726$		0			0
$727$	−22.6274	−	22.6274i	−0.839204	−	0.839204i	0.149550	−	0.988754i	$-0.452218\pi$
$727$	−22.6274	−	22.6274i	−0.839204	−	0.839204i	−0.988754	+	0.149550i	$0.952218\pi$
$728$	−4.00000	−	4.00000i	−0.148250	−	0.148250i
$729$		0			0
$730$		0			0
$731$		−	55.1127i		−	2.03842i
$732$		0			0
$733$	31.5563	−	31.5563i	1.16556	−	1.16556i	0.182321	−	0.983239i	$-0.441639\pi$
$733$	31.5563	−	31.5563i	1.16556	−	1.16556i	0.983239	−	0.182321i	$-0.0583611\pi$
$734$	2.48528			0.0917334
$735$		0			0
$736$	1.17157			0.0431847
$737$	19.0711	−	19.0711i	0.702492	−	0.702492i
$738$		0			0
$739$		−	43.4558i		−	1.59855i	−0.600966	−	0.799275i	$-0.705217\pi$
$739$		−	43.4558i		−	1.59855i	0.600966	−	0.799275i	$-0.294783\pi$
$740$		0			0
$741$		0			0
$742$	5.41421	+	5.41421i	0.198762	+	0.198762i
$743$	31.1127	+	31.1127i	1.14141	+	1.14141i	0.988192	+	0.153222i	$0.0489651\pi$
$743$	31.1127	+	31.1127i	1.14141	+	1.14141i	0.153222	+	0.988192i	$0.451035\pi$
$744$		0			0
$745$		0			0
$746$			4.34315i			0.159014i
$747$		0			0
$748$	11.6569	−	11.6569i	0.426217	−	0.426217i
$749$	15.3137			0.559551
$750$		0			0
$751$	31.5147			1.14999			0.574994	−	0.818157i	$-0.305004\pi$
$751$	31.5147			1.14999			0.574994	+	0.818157i	$0.305004\pi$
$752$	−0.757359	+	0.757359i	−0.0276181	+	0.0276181i
$753$		0			0
$754$			27.3137i			0.994707i
$755$		0			0
$756$		0			0
$757$	−7.55635	−	7.55635i	−0.274640	−	0.274640i	0.556325	−	0.830965i	$-0.312211\pi$
$757$	−7.55635	−	7.55635i	−0.274640	−	0.274640i	−0.830965	+	0.556325i	$0.812211\pi$
$758$	9.75736	+	9.75736i	0.354403	+	0.354403i
$759$		0			0
$760$		0			0
$761$		−	14.9706i		−	0.542682i	−0.962483	−	0.271341i	$-0.912533\pi$
$761$		−	14.9706i		−	0.542682i	0.962483	−	0.271341i	$-0.0874672\pi$
$762$		0			0
$763$	−9.41421	+	9.41421i	−0.340817	+	0.340817i
$764$	−25.6569			−0.928232
$765$		0			0
$766$	2.24264			0.0810299
$767$	−11.3137	+	11.3137i	−0.408514	+	0.408514i
$768$		0			0
$769$		−	37.5980i		−	1.35582i	−0.735146	−	0.677909i	$-0.762886\pi$
$769$		−	37.5980i		−	1.35582i	0.735146	−	0.677909i	$-0.237114\pi$
$770$		0			0
$771$		0			0
$772$	−3.48528	−	3.48528i	−0.125438	−	0.125438i
$773$	−32.9411	−	32.9411i	−1.18481	−	1.18481i	−0.978483	−	0.206327i	$-0.933849\pi$
$773$	−32.9411	−	32.9411i	−1.18481	−	1.18481i	−0.206327	−	0.978483i	$-0.566151\pi$
$774$		0			0
$775$		0			0
$776$		−	10.4853i		−	0.376400i
$777$		0			0
$778$	−21.0711	+	21.0711i	−0.755434	+	0.755434i
$779$	−24.9706			−0.894663
$780$		0			0
$781$	−23.3137			−0.834230
$782$	−4.00000	+	4.00000i	−0.143040	+	0.143040i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	32.4853	+	32.4853i	1.15798	+	1.15798i	0.984910	+	0.173065i	$0.0553670\pi$
$787$	32.4853	+	32.4853i	1.15798	+	1.15798i	0.173065	+	0.984910i	$0.444633\pi$
$788$	1.75736	+	1.75736i	0.0626033	+	0.0626033i
$789$		0			0
$790$		0			0
$791$		−	16.0000i		−	0.568895i
$792$		0			0
$793$	−39.5980	+	39.5980i	−1.40617	+	1.40617i
$794$	21.3137			0.756395
$795$		0			0
$796$	23.8995			0.847095
$797$	25.8284	−	25.8284i	0.914890	−	0.914890i	−0.0817621	−	0.996652i	$-0.526055\pi$
$797$	25.8284	−	25.8284i	0.914890	−	0.914890i	0.996652	+	0.0817621i	$0.0260548\pi$
$798$		0			0
$799$		−	5.17157i		−	0.182957i
$800$		0			0
$801$		0			0
$802$	−19.0000	−	19.0000i	−0.670913	−	0.670913i
$803$	24.1421	+	24.1421i	0.851957	+	0.851957i
$804$		0			0
$805$		0			0
$806$			57.9411i			2.04089i
$807$		0			0
$808$	4.48528	−	4.48528i	0.157792	−	0.157792i
$809$	9.61522			0.338053			0.169027	−	0.985611i	$-0.445938\pi$
$809$	9.61522			0.338053			0.169027	+	0.985611i	$0.445938\pi$
$810$		0			0
$811$	−4.97056			−0.174540			−0.0872700	−	0.996185i	$-0.527814\pi$
$811$	−4.97056			−0.174540			−0.0872700	+	0.996185i	$0.527814\pi$
$812$	−3.41421	+	3.41421i	−0.119815	+	0.119815i
$813$		0			0
$814$			10.8284i			0.379536i
$815$		0			0
$816$		0			0
$817$	−22.8284	−	22.8284i	−0.798666	−	0.798666i
$818$	7.07107	+	7.07107i	0.247234	+	0.247234i
$819$		0			0
$820$		0			0
$821$			29.7990i			1.03999i	0.854169	+	0.519996i	$0.174067\pi$
$821$			29.7990i			1.03999i	−0.854169	+	0.519996i	$0.825933\pi$
$822$		0			0
$823$	−11.5147	+	11.5147i	−0.401378	+	0.401378i	−0.878718	−	0.477341i	$-0.841601\pi$
$823$	−11.5147	+	11.5147i	−0.401378	+	0.401378i	0.477341	+	0.878718i	$0.341601\pi$
$824$	−6.48528			−0.225925
$825$		0			0
$826$	−2.82843			−0.0984136
$827$	−5.75736	+	5.75736i	−0.200203	+	0.200203i	−0.800087	−	0.599884i	$-0.795213\pi$
$827$	−5.75736	+	5.75736i	−0.200203	+	0.200203i	0.599884	+	0.800087i	$0.295213\pi$
$828$		0			0
$829$			20.2426i			0.703056i	0.936177	+	0.351528i	$0.114338\pi$
$829$			20.2426i			0.703056i	−0.936177	+	0.351528i	$0.885662\pi$
$830$		0			0
$831$		0			0
$832$	−4.00000	−	4.00000i	−0.138675	−	0.138675i
$833$	3.41421	+	3.41421i	0.118295	+	0.118295i
$834$		0			0
$835$		0			0
$836$		−	9.65685i		−	0.333989i
$837$		0			0
$838$	−18.8284	+	18.8284i	−0.650417	+	0.650417i
$839$	13.5147			0.466580			0.233290	−	0.972407i	$-0.425051\pi$
$839$	13.5147			0.466580			0.233290	+	0.972407i	$0.425051\pi$
$840$		0			0
$841$	−5.68629			−0.196079
$842$	3.27208	−	3.27208i	0.112763	−	0.112763i
$843$		0			0
$844$			4.00000i			0.137686i
$845$		0			0
$846$		0			0
$847$	0.464466	+	0.464466i	0.0159592	+	0.0159592i
$848$	5.41421	+	5.41421i	0.185925	+	0.185925i
$849$		0			0
$850$		0			0
$851$		−	3.71573i		−	0.127374i
$852$		0			0
$853$	0.928932	−	0.928932i	0.0318060	−	0.0318060i	−0.691025	−	0.722831i	$-0.742841\pi$
$853$	0.928932	−	0.928932i	0.0318060	−	0.0318060i	0.722831	+	0.691025i	$0.242841\pi$
$854$	−9.89949			−0.338754
$855$		0			0
$856$	15.3137			0.523412
$857$	37.5563	−	37.5563i	1.28290	−	1.28290i	0.343891	−	0.939010i	$-0.388255\pi$
$857$	37.5563	−	37.5563i	1.28290	−	1.28290i	0.939010	−	0.343891i	$-0.111745\pi$
$858$		0			0
$859$		−	40.0000i		−	1.36478i	−0.730987	−	0.682391i	$-0.760940\pi$
$859$		−	40.0000i		−	1.36478i	0.730987	−	0.682391i	$-0.239060\pi$
$860$		0			0
$861$		0			0
$862$	−1.51472	−	1.51472i	−0.0515915	−	0.0515915i
$863$	−26.8284	−	26.8284i	−0.913250	−	0.913250i	0.0832762	−	0.996527i	$-0.473462\pi$
$863$	−26.8284	−	26.8284i	−0.913250	−	0.913250i	−0.996527	+	0.0832762i	$0.973462\pi$
$864$		0			0
$865$		0			0
$866$			13.7990i			0.468909i
$867$		0			0
$868$	−7.24264	+	7.24264i	−0.245831	+	0.245831i
$869$	19.3137			0.655173
$870$		0			0
$871$	44.6863			1.51414
$872$	−9.41421	+	9.41421i	−0.318805	+	0.318805i
$873$		0			0
$874$			3.31371i			0.112088i
$875$		0			0
$876$		0			0
$877$	−21.6985	−	21.6985i	−0.732706	−	0.732706i	0.238449	−	0.971155i	$-0.423361\pi$
$877$	−21.6985	−	21.6985i	−0.732706	−	0.732706i	−0.971155	+	0.238449i	$0.923361\pi$
$878$	−11.2426	−	11.2426i	−0.379421	−	0.379421i
$879$		0			0
$880$		0			0
$881$			36.6274i			1.23401i	0.786960	+	0.617005i	$0.211654\pi$
$881$			36.6274i			1.23401i	−0.786960	+	0.617005i	$0.788346\pi$
$882$		0			0
$883$	−0.615224	+	0.615224i	−0.0207039	+	0.0207039i	−0.717383	−	0.696679i	$-0.754660\pi$
$883$	−0.615224	+	0.615224i	−0.0207039	+	0.0207039i	0.696679	+	0.717383i	$0.254660\pi$
$884$	27.3137			0.918659
$885$		0			0
$886$	−28.9706			−0.973285
$887$	−14.2721	+	14.2721i	−0.479209	+	0.479209i	−0.904879	−	0.425669i	$-0.860039\pi$
$887$	−14.2721	+	14.2721i	−0.479209	+	0.479209i	0.425669	+	0.904879i	$0.360039\pi$
$888$		0			0
$889$		−	5.17157i		−	0.173449i
$890$		0			0
$891$		0			0
$892$	−15.3137	−	15.3137i	−0.512741	−	0.512741i
$893$	−2.14214	−	2.14214i	−0.0716838	−	0.0716838i
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−6.17157	+	6.17157i	−0.205948	+	0.205948i
$899$	49.4558			1.64944
$900$		0			0
$901$	−36.9706			−1.23167
$902$	21.3137	−	21.3137i	0.709669	−	0.709669i
$903$		0			0
$904$		−	16.0000i		−	0.532152i
$905$		0			0
$906$		0			0
$907$	−22.4142	−	22.4142i	−0.744252	−	0.744252i	0.229141	−	0.973393i	$-0.426408\pi$
$907$	−22.4142	−	22.4142i	−0.744252	−	0.744252i	−0.973393	+	0.229141i	$0.926408\pi$
$908$	−6.82843	−	6.82843i	−0.226609	−	0.226609i
$909$		0			0
$910$		0			0
$911$			4.00000i			0.132526i	0.997802	+	0.0662630i	$0.0211076\pi$
$911$			4.00000i			0.132526i	−0.997802	+	0.0662630i	$0.978892\pi$
$912$		0			0
$913$	−16.4853	+	16.4853i	−0.545583	+	0.545583i
$914$	−11.0711			−0.366198
$915$		0			0
$916$	0.242641			0.00801707
$917$	−0.343146	+	0.343146i	−0.0113317	+	0.0113317i
$918$		0			0
$919$		−	16.2010i		−	0.534422i	−0.963638	−	0.267211i	$-0.913898\pi$
$919$		−	16.2010i		−	0.534422i	0.963638	−	0.267211i	$-0.0861021\pi$
$920$		0			0
$921$		0			0
$922$	12.2426	+	12.2426i	0.403190	+	0.403190i
$923$	−27.3137	−	27.3137i	−0.899042	−	0.899042i
$924$		0			0
$925$		0			0
$926$			28.0000i			0.920137i
$927$		0			0
$928$	−3.41421	+	3.41421i	−0.112077	+	0.112077i
$929$	46.9706			1.54105			0.770527	−	0.637407i	$-0.219993\pi$
$929$	46.9706			1.54105			0.770527	+	0.637407i	$0.219993\pi$
$930$		0			0
$931$	2.82843			0.0926980
$932$	9.17157	−	9.17157i	0.300425	−	0.300425i
$933$		0			0
$934$			19.7990i			0.647843i
$935$		0			0
$936$		0			0
$937$	−13.2132	−	13.2132i	−0.431657	−	0.431657i	0.457535	−	0.889192i	$-0.348732\pi$
$937$	−13.2132	−	13.2132i	−0.431657	−	0.431657i	−0.889192	+	0.457535i	$0.848732\pi$
$938$	5.58579	+	5.58579i	0.182382	+	0.182382i
$939$		0			0
$940$		0			0
$941$		−	46.2843i		−	1.50882i	−0.656401	−	0.754412i	$-0.727922\pi$
$941$		−	46.2843i		−	1.50882i	0.656401	−	0.754412i	$-0.272078\pi$
$942$		0			0
$943$	−7.31371	+	7.31371i	−0.238167	+	0.238167i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	38.9706			1.26704
$947$	18.2426	−	18.2426i	0.592806	−	0.592806i	−0.345582	−	0.938388i	$-0.612319\pi$
$947$	18.2426	−	18.2426i	0.592806	−	0.592806i	0.938388	+	0.345582i	$0.112319\pi$
$948$		0			0
$949$			56.5685i			1.83629i
$950$		0			0
$951$		0			0
$952$	3.41421	+	3.41421i	0.110655	+	0.110655i
$953$	−36.2426	−	36.2426i	−1.17401	−	1.17401i	−0.981244	−	0.192770i	$-0.938253\pi$
$953$	−36.2426	−	36.2426i	−1.17401	−	1.17401i	−0.192770	−	0.981244i	$-0.561747\pi$
$954$		0			0
$955$		0			0
$956$			2.34315i			0.0757827i
$957$		0			0
$958$	−17.5563	+	17.5563i	−0.567220	+	0.567220i
$959$	−16.9706			−0.548008
$960$		0			0
$961$	73.9117			2.38425
$962$	−12.6863	+	12.6863i	−0.409022	+	0.409022i
$963$		0			0
$964$		−	24.1421i		−	0.777566i
$965$		0			0
$966$		0			0
$967$	36.2843	+	36.2843i	1.16682	+	1.16682i	0.982950	+	0.183874i	$0.0588637\pi$
$967$	36.2843	+	36.2843i	1.16682	+	1.16682i	0.183874	+	0.982950i	$0.441136\pi$
$968$	0.464466	+	0.464466i	0.0149285	+	0.0149285i
$969$		0			0
$970$		0			0
$971$		−	36.0000i		−	1.15529i	−0.816286	−	0.577647i	$-0.803971\pi$
$971$		−	36.0000i		−	1.15529i	0.816286	−	0.577647i	$-0.196029\pi$
$972$		0			0
$973$	4.48528	−	4.48528i	0.143792	−	0.143792i
$974$	21.1716			0.678381
$975$		0			0
$976$	−9.89949			−0.316875
$977$	−0.970563	+	0.970563i	−0.0310511	+	0.0310511i	−0.722462	−	0.691411i	$-0.756990\pi$
$977$	−0.970563	+	0.970563i	−0.0310511	+	0.0310511i	0.691411	+	0.722462i	$0.256990\pi$
$978$		0			0
$979$		−	30.1421i		−	0.963347i
$980$		0			0
$981$		0			0
$982$	−0.899495	−	0.899495i	−0.0287040	−	0.0287040i
$983$	9.44365	+	9.44365i	0.301206	+	0.301206i	0.841485	−	0.540280i	$-0.181682\pi$
$983$	9.44365	+	9.44365i	0.301206	+	0.301206i	−0.540280	+	0.841485i	$0.681682\pi$
$984$		0			0
$985$		0			0
$986$		−	23.3137i		−	0.742460i
$987$		0			0
$988$	11.3137	−	11.3137i	0.359937	−	0.359937i
$989$	−13.3726			−0.425223
$990$		0			0
$991$	−1.85786			−0.0590170			−0.0295085	−	0.999565i	$-0.509394\pi$
$991$	−1.85786			−0.0590170			−0.0295085	+	0.999565i	$0.509394\pi$
$992$	−7.24264	+	7.24264i	−0.229954	+	0.229954i
$993$		0			0
$994$		−	6.82843i		−	0.216585i
$995$		0			0
$996$		0			0
$997$	17.8995	+	17.8995i	0.566883	+	0.566883i	0.931254	−	0.364371i	$-0.118716\pi$
$997$	17.8995	+	17.8995i	0.566883	+	0.566883i	−0.364371	+	0.931254i	$0.618716\pi$
$998$	19.4142	+	19.4142i	0.614546	+	0.614546i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.a.1457.2		4
3.2	odd	2		3150.2.m.b.1457.1		4
5.2	odd	4		630.2.m.a.323.2	yes	4
5.3	odd	4		3150.2.m.b.2843.1		4
5.4	even	2		630.2.m.b.197.1	yes	4
15.2	even	4		630.2.m.b.323.1	yes	4
15.8	even	4	inner	3150.2.m.a.2843.2		4
15.14	odd	2		630.2.m.a.197.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.a.197.2	✓	4	15.14	odd	2
630.2.m.a.323.2	yes	4	5.2	odd	4
630.2.m.b.197.1	yes	4	5.4	even	2
630.2.m.b.323.1	yes	4	15.2	even	4
3150.2.m.a.1457.2		4	1.1	even	1	trivial
3150.2.m.a.2843.2		4	15.8	even	4	inner
3150.2.m.b.1457.1		4	3.2	odd	2
3150.2.m.b.2843.1		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.41421i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(3.41421 - 3.41421i) q^{17} -2.82843i q^{19} +(2.41421 + 2.41421i) q^{22} +(-0.828427 - 0.828427i) q^{23} +5.65685i q^{26} +(-0.707107 + 0.707107i) q^{28} +4.82843 q^{29} +10.2426 q^{31} +(-0.707107 + 0.707107i) q^{32} -4.82843i q^{34} +(2.24264 + 2.24264i) q^{37} +(-2.00000 - 2.00000i) q^{38} -8.82843i q^{41} +(8.07107 - 8.07107i) q^{43} +3.41421 q^{44} -1.17157 q^{46} +(0.757359 - 0.757359i) q^{47} +1.00000i q^{49} +(4.00000 + 4.00000i) q^{52} +(-5.41421 - 5.41421i) q^{53} +1.00000i q^{56} +(3.41421 - 3.41421i) q^{58} +2.82843 q^{59} +9.89949 q^{61} +(7.24264 - 7.24264i) q^{62} +1.00000i q^{64} +(-5.58579 - 5.58579i) q^{67} +(-3.41421 - 3.41421i) q^{68} +6.82843i q^{71} +(7.07107 - 7.07107i) q^{73} +3.17157 q^{74} -2.82843 q^{76} +(2.41421 - 2.41421i) q^{77} -5.65685i q^{79} +(-6.24264 - 6.24264i) q^{82} +(4.82843 + 4.82843i) q^{83} -11.4142i q^{86} +(2.41421 - 2.41421i) q^{88} -8.82843 q^{89} +5.65685 q^{91} +(-0.828427 + 0.828427i) q^{92} -1.07107i q^{94} +(7.41421 + 7.41421i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 16 q^{13} - 4 q^{14} - 4 q^{16} + 8 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{29} + 24 q^{31} - 8 q^{37} - 8 q^{38} + 4 q^{43} + 8 q^{44} - 16 q^{46} + 20 q^{47} + 16 q^{52} - 16 q^{53} + 8 q^{58} + 12 q^{62} - 28 q^{67} - 8 q^{68} + 24 q^{74} + 4 q^{77} - 8 q^{82} + 8 q^{83} + 4 q^{88} - 24 q^{89} + 8 q^{92} + 24 q^{97}+O(q^{100}) \) 4 * q - 16 * q^13 - 4 * q^14 - 4 * q^16 + 8 * q^17 + 4 * q^22 + 8 * q^23 + 8 * q^29 + 24 * q^31 - 8 * q^37 - 8 * q^38 + 4 * q^43 + 8 * q^44 - 16 * q^46 + 20 * q^47 + 16 * q^52 - 16 * q^53 + 8 * q^58 + 12 * q^62 - 28 * q^67 - 8 * q^68 + 24 * q^74 + 4 * q^77 - 8 * q^82 + 8 * q^83 + 4 * q^88 - 24 * q^89 + 8 * q^92 + 24 * q^97

Introduction

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