LMFDB - Embedded newform 108.2.b.b.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.b (of order $2$, degree $1$, 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.3
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.2.b.b.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.82843i q^{5} -1.73205i q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.82843i q^{5} -1.73205i q^{7} -2.82843i q^{8} +(2.00000 + 3.46410i) q^{10} -4.89898 q^{11} -1.00000 q^{13} +(-1.22474 - 2.12132i) q^{14} +(-2.00000 - 3.46410i) q^{16} +2.82843i q^{17} +5.19615i q^{19} +(4.89898 + 2.82843i) q^{20} +(-6.00000 + 3.46410i) q^{22} +4.89898 q^{23} -3.00000 q^{25} +(-1.22474 + 0.707107i) q^{26} +(-3.00000 - 1.73205i) q^{28} -5.65685i q^{29} -3.46410i q^{31} +(-4.89898 - 2.82843i) q^{32} +(2.00000 + 3.46410i) q^{34} +4.89898 q^{35} -1.00000 q^{37} +(3.67423 + 6.36396i) q^{38} +8.00000 q^{40} -5.65685i q^{41} +3.46410i q^{43} +(-4.89898 + 8.48528i) q^{44} +(6.00000 - 3.46410i) q^{46} -4.89898 q^{47} +4.00000 q^{49} +(-3.67423 + 2.12132i) q^{50} +(-1.00000 + 1.73205i) q^{52} -5.65685i q^{53} -13.8564i q^{55} -4.89898 q^{56} +(-4.00000 - 6.92820i) q^{58} +4.89898 q^{59} +11.0000 q^{61} +(-2.44949 - 4.24264i) q^{62} -8.00000 q^{64} -2.82843i q^{65} +12.1244i q^{67} +(4.89898 + 2.82843i) q^{68} +(6.00000 - 3.46410i) q^{70} -1.00000 q^{73} +(-1.22474 + 0.707107i) q^{74} +(9.00000 + 5.19615i) q^{76} +8.48528i q^{77} -1.73205i q^{79} +(9.79796 - 5.65685i) q^{80} +(-4.00000 - 6.92820i) q^{82} +9.79796 q^{83} -8.00000 q^{85} +(2.44949 + 4.24264i) q^{86} +13.8564i q^{88} +2.82843i q^{89} +1.73205i q^{91} +(4.89898 - 8.48528i) q^{92} +(-6.00000 + 3.46410i) q^{94} -14.6969 q^{95} -13.0000 q^{97} +(4.89898 - 2.82843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4}+O(q^{10}) $ 4 * q + 4 * q^4	$ 4 q + 4 q^{4} + 8 q^{10} - 4 q^{13} - 8 q^{16} - 24 q^{22} - 12 q^{25} - 12 q^{28} + 8 q^{34} - 4 q^{37} + 32 q^{40} + 24 q^{46} + 16 q^{49} - 4 q^{52} - 16 q^{58} + 44 q^{61} - 32 q^{64} + 24 q^{70} - 4 q^{73} + 36 q^{76} - 16 q^{82} - 32 q^{85} - 24 q^{94} - 52 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 + 8 * q^10 - 4 * q^13 - 8 * q^16 - 24 * q^22 - 12 * q^25 - 12 * q^28 + 8 * q^34 - 4 * q^37 + 32 * q^40 + 24 * q^46 + 16 * q^49 - 4 * q^52 - 16 * q^58 + 44 * q^61 - 32 * q^64 + 24 * q^70 - 4 * q^73 + 36 * q^76 - 16 * q^82 - 32 * q^85 - 24 * q^94 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$			2.82843i			1.26491i	0.774597	+	0.632456i	$0.217953\pi$
$5$			2.82843i			1.26491i	−0.774597	+	0.632456i	$0.782047\pi$
$6$		0			0
$7$		−	1.73205i		−	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$		−	1.73205i		−	0.654654i	0.944911	−	0.327327i	$-0.106148\pi$
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	−4.89898			−1.47710			−0.738549	−	0.674200i	$-0.764489\pi$
$11$	−4.89898			−1.47710			−0.738549	+	0.674200i	$0.764489\pi$
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.22474	−	2.12132i	−0.327327	−	0.566947i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$		0			0
$19$			5.19615i			1.19208i	0.802955	+	0.596040i	$0.203260\pi$
$19$			5.19615i			1.19208i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	4.89898	+	2.82843i	1.09545	+	0.632456i
$21$		0			0
$22$	−6.00000	+	3.46410i	−1.27920	+	0.738549i
$23$	4.89898			1.02151			0.510754	−	0.859727i	$-0.329366\pi$
$23$	4.89898			1.02151			0.510754	+	0.859727i	$0.329366\pi$
$24$		0			0
$25$	−3.00000			−0.600000
$26$	−1.22474	+	0.707107i	−0.240192	+	0.138675i
$27$		0			0
$28$	−3.00000	−	1.73205i	−0.566947	−	0.327327i
$29$		−	5.65685i		−	1.05045i	−0.850963	−	0.525226i	$-0.823981\pi$
$29$		−	5.65685i		−	1.05045i	0.850963	−	0.525226i	$-0.176019\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$		0			0
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	4.89898			0.828079
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	3.67423	+	6.36396i	0.596040	+	1.03237i
$39$		0			0
$40$	8.00000			1.26491
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	−4.89898	+	8.48528i	−0.738549	+	1.27920i
$45$		0			0
$46$	6.00000	−	3.46410i	0.884652	−	0.510754i
$47$	−4.89898			−0.714590			−0.357295	−	0.933992i	$-0.616301\pi$
$47$	−4.89898			−0.714590			−0.357295	+	0.933992i	$0.616301\pi$
$48$		0			0
$49$	4.00000			0.571429
$50$	−3.67423	+	2.12132i	−0.519615	+	0.300000i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$		0			0
$55$		−	13.8564i		−	1.86840i
$56$	−4.89898			−0.654654
$57$		0			0
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	4.89898			0.637793			0.318896	−	0.947790i	$-0.396688\pi$
$59$	4.89898			0.637793			0.318896	+	0.947790i	$0.396688\pi$
$60$		0			0
$61$	11.0000			1.40841			0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000			1.40841			0.704203	+	0.709999i	$0.251305\pi$
$62$	−2.44949	−	4.24264i	−0.311086	−	0.538816i
$63$		0			0
$64$	−8.00000			−1.00000
$65$		−	2.82843i		−	0.350823i
$66$		0			0
$67$			12.1244i			1.48123i	0.671932	+	0.740613i	$0.265465\pi$
$67$			12.1244i			1.48123i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	4.89898	+	2.82843i	0.594089	+	0.342997i
$69$		0			0
$70$	6.00000	−	3.46410i	0.717137	−	0.414039i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−1.22474	+	0.707107i	−0.142374	+	0.0821995i
$75$		0			0
$76$	9.00000	+	5.19615i	1.03237	+	0.596040i
$77$			8.48528i			0.966988i
$78$		0			0
$79$		−	1.73205i		−	0.194871i	−0.995242	−	0.0974355i	$-0.968936\pi$
$79$		−	1.73205i		−	0.194871i	0.995242	−	0.0974355i	$-0.0310640\pi$
$80$	9.79796	−	5.65685i	1.09545	−	0.632456i
$81$		0			0
$82$	−4.00000	−	6.92820i	−0.441726	−	0.765092i
$83$	9.79796			1.07547			0.537733	−	0.843115i	$-0.319281\pi$
$83$	9.79796			1.07547			0.537733	+	0.843115i	$0.319281\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	2.44949	+	4.24264i	0.264135	+	0.457496i
$87$		0			0
$88$			13.8564i			1.47710i
$89$			2.82843i			0.299813i	0.988700	+	0.149906i	$0.0478972\pi$
$89$			2.82843i			0.299813i	−0.988700	+	0.149906i	$0.952103\pi$
$90$		0			0
$91$			1.73205i			0.181568i
$92$	4.89898	−	8.48528i	0.510754	−	0.884652i
$93$		0			0
$94$	−6.00000	+	3.46410i	−0.618853	+	0.357295i
$95$	−14.6969			−1.50787
$96$		0			0
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	4.89898	−	2.82843i	0.494872	−	0.285714i
$99$		0			0
$100$	−3.00000	+	5.19615i	−0.300000	+	0.519615i
$101$			11.3137i			1.12576i	0.826540	+	0.562878i	$0.190306\pi$
$101$			11.3137i			1.12576i	−0.826540	+	0.562878i	$0.809694\pi$
$102$		0			0
$103$		−	8.66025i		−	0.853320i	−0.904412	−	0.426660i	$-0.859690\pi$
$103$		−	8.66025i		−	0.853320i	0.904412	−	0.426660i	$-0.140310\pi$
$104$			2.82843i			0.277350i
$105$		0			0
$106$	−4.00000	−	6.92820i	−0.388514	−	0.672927i
$107$	−14.6969			−1.42081			−0.710403	−	0.703795i	$-0.751487\pi$
$107$	−14.6969			−1.42081			−0.710403	+	0.703795i	$0.751487\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−9.79796	−	16.9706i	−0.934199	−	1.61808i
$111$		0			0
$112$	−6.00000	+	3.46410i	−0.566947	+	0.327327i
$113$			2.82843i			0.266076i	0.991111	+	0.133038i	$0.0424732\pi$
$113$			2.82843i			0.266076i	−0.991111	+	0.133038i	$0.957527\pi$
$114$		0			0
$115$			13.8564i			1.29212i
$116$	−9.79796	−	5.65685i	−0.909718	−	0.525226i
$117$		0			0
$118$	6.00000	−	3.46410i	0.552345	−	0.318896i
$119$	4.89898			0.449089
$120$		0			0
$121$	13.0000			1.18182
$122$	13.4722	−	7.77817i	1.21972	−	0.704203i
$123$		0			0
$124$	−6.00000	−	3.46410i	−0.538816	−	0.311086i
$125$			5.65685i			0.505964i
$126$		0			0
$127$			10.3923i			0.922168i	0.887357	+	0.461084i	$0.152539\pi$
$127$			10.3923i			0.922168i	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$		0			0
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−9.79796			−0.856052			−0.428026	−	0.903767i	$-0.640791\pi$
$131$	−9.79796			−0.856052			−0.428026	+	0.903767i	$0.640791\pi$
$132$		0			0
$133$	9.00000			0.780399
$134$	8.57321	+	14.8492i	0.740613	+	1.28278i
$135$		0			0
$136$	8.00000			0.685994
$137$			19.7990i			1.69154i	0.533546	+	0.845771i	$0.320859\pi$
$137$			19.7990i			1.69154i	−0.533546	+	0.845771i	$0.679141\pi$
$138$		0			0
$139$		−	8.66025i		−	0.734553i	−0.930112	−	0.367277i	$-0.880290\pi$
$139$		−	8.66025i		−	0.734553i	0.930112	−	0.367277i	$-0.119710\pi$
$140$	4.89898	−	8.48528i	0.414039	−	0.717137i
$141$		0			0
$142$		0			0
$143$	4.89898			0.409673
$144$		0			0
$145$	16.0000			1.32873
$146$	−1.22474	+	0.707107i	−0.101361	+	0.0585206i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$		−	22.6274i		−	1.85371i	−0.375419	−	0.926855i	$-0.622501\pi$
$149$		−	22.6274i		−	1.85371i	0.375419	−	0.926855i	$-0.377499\pi$
$150$		0			0
$151$		−	22.5167i		−	1.83238i	−0.400744	−	0.916190i	$-0.631248\pi$
$151$		−	22.5167i		−	1.83238i	0.400744	−	0.916190i	$-0.368752\pi$
$152$	14.6969			1.19208
$153$		0			0
$154$	6.00000	+	10.3923i	0.483494	+	0.837436i
$155$	9.79796			0.786991
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−1.22474	−	2.12132i	−0.0974355	−	0.168763i
$159$		0			0
$160$	8.00000	−	13.8564i	0.632456	−	1.09545i
$161$		−	8.48528i		−	0.668734i
$162$		0			0
$163$			5.19615i			0.406994i	0.979076	+	0.203497i	$0.0652307\pi$
$163$			5.19615i			0.406994i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	−9.79796	−	5.65685i	−0.765092	−	0.441726i
$165$		0			0
$166$	12.0000	−	6.92820i	0.931381	−	0.537733i
$167$	4.89898			0.379094			0.189547	−	0.981872i	$-0.439298\pi$
$167$	4.89898			0.379094			0.189547	+	0.981872i	$0.439298\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−9.79796	+	5.65685i	−0.751469	+	0.433861i
$171$		0			0
$172$	6.00000	+	3.46410i	0.457496	+	0.264135i
$173$		−	5.65685i		−	0.430083i	−0.976605	−	0.215041i	$-0.931011\pi$
$173$		−	5.65685i		−	0.430083i	0.976605	−	0.215041i	$-0.0689886\pi$
$174$		0			0
$175$			5.19615i			0.392792i
$176$	9.79796	+	16.9706i	0.738549	+	1.27920i
$177$		0			0
$178$	2.00000	+	3.46410i	0.149906	+	0.259645i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	1.22474	+	2.12132i	0.0907841	+	0.157243i
$183$		0			0
$184$		−	13.8564i		−	1.02151i
$185$		−	2.82843i		−	0.207950i
$186$		0			0
$187$		−	13.8564i		−	1.01328i
$188$	−4.89898	+	8.48528i	−0.357295	+	0.618853i
$189$		0			0
$190$	−18.0000	+	10.3923i	−1.30586	+	0.753937i
$191$	24.4949			1.77239			0.886194	−	0.463314i	$-0.153340\pi$
$191$	24.4949			1.77239			0.886194	+	0.463314i	$0.153340\pi$
$192$		0			0
$193$	−1.00000			−0.0719816			−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000			−0.0719816			−0.0359908	+	0.999352i	$0.511459\pi$
$194$	−15.9217	+	9.19239i	−1.14311	+	0.659975i
$195$		0			0
$196$	4.00000	−	6.92820i	0.285714	−	0.494872i
$197$			2.82843i			0.201517i	0.994911	+	0.100759i	$0.0321270\pi$
$197$			2.82843i			0.201517i	−0.994911	+	0.100759i	$0.967873\pi$
$198$		0			0
$199$			5.19615i			0.368345i	0.982894	+	0.184173i	$0.0589606\pi$
$199$			5.19615i			0.368345i	−0.982894	+	0.184173i	$0.941039\pi$
$200$			8.48528i			0.600000i
$201$		0			0
$202$	8.00000	+	13.8564i	0.562878	+	0.974933i
$203$	−9.79796			−0.687682
$204$		0			0
$205$	16.0000			1.11749
$206$	−6.12372	−	10.6066i	−0.426660	−	0.738997i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$		−	25.4558i		−	1.76082i
$210$		0			0
$211$			12.1244i			0.834675i	0.908752	+	0.417338i	$0.137037\pi$
$211$			12.1244i			0.834675i	−0.908752	+	0.417338i	$0.862963\pi$
$212$	−9.79796	−	5.65685i	−0.672927	−	0.388514i
$213$		0			0
$214$	−18.0000	+	10.3923i	−1.23045	+	0.710403i
$215$	−9.79796			−0.668215
$216$		0			0
$217$	−6.00000			−0.407307
$218$	−12.2474	+	7.07107i	−0.829502	+	0.478913i
$219$		0			0
$220$	−24.0000	−	13.8564i	−1.61808	−	0.934199i
$221$		−	2.82843i		−	0.190261i
$222$		0			0
$223$			24.2487i			1.62381i	0.583787	+	0.811907i	$0.301570\pi$
$223$			24.2487i			1.62381i	−0.583787	+	0.811907i	$0.698430\pi$
$224$	−4.89898	+	8.48528i	−0.327327	+	0.566947i
$225$		0			0
$226$	2.00000	+	3.46410i	0.133038	+	0.230429i
$227$	−19.5959			−1.30063			−0.650313	−	0.759666i	$-0.725362\pi$
$227$	−19.5959			−1.30063			−0.650313	+	0.759666i	$0.725362\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	9.79796	+	16.9706i	0.646058	+	1.11901i
$231$		0			0
$232$	−16.0000			−1.05045
$233$		−	22.6274i		−	1.48237i	−0.671300	−	0.741186i	$-0.734264\pi$
$233$		−	22.6274i		−	1.48237i	0.671300	−	0.741186i	$-0.265736\pi$
$234$		0			0
$235$		−	13.8564i		−	0.903892i
$236$	4.89898	−	8.48528i	0.318896	−	0.552345i
$237$		0			0
$238$	6.00000	−	3.46410i	0.388922	−	0.224544i
$239$	19.5959			1.26755			0.633777	−	0.773516i	$-0.281504\pi$
$239$	19.5959			1.26755			0.633777	+	0.773516i	$0.281504\pi$
$240$		0			0
$241$	−25.0000			−1.61039			−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000			−1.61039			−0.805196	+	0.593009i	$0.797940\pi$
$242$	15.9217	−	9.19239i	1.02348	−	0.590909i
$243$		0			0
$244$	11.0000	−	19.0526i	0.704203	−	1.21972i
$245$			11.3137i			0.722806i
$246$		0			0
$247$		−	5.19615i		−	0.330623i
$248$	−9.79796			−0.622171
$249$		0			0
$250$	4.00000	+	6.92820i	0.252982	+	0.438178i
$251$	29.3939			1.85533			0.927663	−	0.373420i	$-0.121815\pi$
$251$	29.3939			1.85533			0.927663	+	0.373420i	$0.121815\pi$
$252$		0			0
$253$	−24.0000			−1.50887
$254$	7.34847	+	12.7279i	0.461084	+	0.798621i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$			28.2843i			1.76432i	0.470946	+	0.882162i	$0.343913\pi$
$257$			28.2843i			1.76432i	−0.470946	+	0.882162i	$0.656087\pi$
$258$		0			0
$259$			1.73205i			0.107624i
$260$	−4.89898	−	2.82843i	−0.303822	−	0.175412i
$261$		0			0
$262$	−12.0000	+	6.92820i	−0.741362	+	0.428026i
$263$	−19.5959			−1.20834			−0.604168	−	0.796857i	$-0.706494\pi$
$263$	−19.5959			−1.20834			−0.604168	+	0.796857i	$0.706494\pi$
$264$		0			0
$265$	16.0000			0.982872
$266$	11.0227	−	6.36396i	0.675845	−	0.390199i
$267$		0			0
$268$	21.0000	+	12.1244i	1.28278	+	0.740613i
$269$			2.82843i			0.172452i	0.996276	+	0.0862261i	$0.0274808\pi$
$269$			2.82843i			0.172452i	−0.996276	+	0.0862261i	$0.972519\pi$
$270$		0			0
$271$			5.19615i			0.315644i	0.987468	+	0.157822i	$0.0504472\pi$
$271$			5.19615i			0.315644i	−0.987468	+	0.157822i	$0.949553\pi$
$272$	9.79796	−	5.65685i	0.594089	−	0.342997i
$273$		0			0
$274$	14.0000	+	24.2487i	0.845771	+	1.46492i
$275$	14.6969			0.886259
$276$		0			0
$277$	14.0000			0.841178			0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000			0.841178			0.420589	+	0.907251i	$0.361823\pi$
$278$	−6.12372	−	10.6066i	−0.367277	−	0.636142i
$279$		0			0
$280$		−	13.8564i		−	0.828079i
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$		0			0
$283$		−	24.2487i		−	1.44144i	−0.693228	−	0.720718i	$-0.743812\pi$
$283$		−	24.2487i		−	1.44144i	0.693228	−	0.720718i	$-0.256188\pi$
$284$		0			0
$285$		0			0
$286$	6.00000	−	3.46410i	0.354787	−	0.204837i
$287$	−9.79796			−0.578355
$288$		0			0
$289$	9.00000			0.529412
$290$	19.5959	−	11.3137i	1.15071	−	0.664364i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$			2.82843i			0.165238i	0.996581	+	0.0826192i	$0.0263285\pi$
$293$			2.82843i			0.165238i	−0.996581	+	0.0826192i	$0.973671\pi$
$294$		0			0
$295$			13.8564i			0.806751i
$296$			2.82843i			0.164399i
$297$		0			0
$298$	−16.0000	−	27.7128i	−0.926855	−	1.60536i
$299$	−4.89898			−0.283315
$300$		0			0
$301$	6.00000			0.345834
$302$	−15.9217	−	27.5772i	−0.916190	−	1.58689i
$303$		0			0
$304$	18.0000	−	10.3923i	1.03237	−	0.596040i
$305$			31.1127i			1.78151i
$306$		0			0
$307$		−	10.3923i		−	0.593120i	−0.955014	−	0.296560i	$-0.904160\pi$
$307$		−	10.3923i		−	0.593120i	0.955014	−	0.296560i	$-0.0958395\pi$
$308$	14.6969	+	8.48528i	0.837436	+	0.483494i
$309$		0			0
$310$	12.0000	−	6.92820i	0.681554	−	0.393496i
$311$	−24.4949			−1.38898			−0.694489	−	0.719503i	$-0.744370\pi$
$311$	−24.4949			−1.38898			−0.694489	+	0.719503i	$0.744370\pi$
$312$		0			0
$313$	11.0000			0.621757			0.310878	−	0.950450i	$-0.399377\pi$
$313$	11.0000			0.621757			0.310878	+	0.950450i	$0.399377\pi$
$314$	−12.2474	+	7.07107i	−0.691164	+	0.399043i
$315$		0			0
$316$	−3.00000	−	1.73205i	−0.168763	−	0.0974355i
$317$		−	5.65685i		−	0.317721i	−0.987301	−	0.158860i	$-0.949218\pi$
$317$		−	5.65685i		−	0.317721i	0.987301	−	0.158860i	$-0.0507819\pi$
$318$		0			0
$319$			27.7128i			1.55162i
$320$		−	22.6274i		−	1.26491i
$321$		0			0
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$	−14.6969			−0.817760
$324$		0			0
$325$	3.00000			0.166410
$326$	3.67423	+	6.36396i	0.203497	+	0.352467i
$327$		0			0
$328$	−16.0000			−0.883452
$329$			8.48528i			0.467809i
$330$		0			0
$331$		−	22.5167i		−	1.23763i	−0.785538	−	0.618814i	$-0.787614\pi$
$331$		−	22.5167i		−	1.23763i	0.785538	−	0.618814i	$-0.212386\pi$
$332$	9.79796	−	16.9706i	0.537733	−	0.931381i
$333$		0			0
$334$	6.00000	−	3.46410i	0.328305	−	0.189547i
$335$	−34.2929			−1.87362
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	−14.6969	+	8.48528i	−0.799408	+	0.461538i
$339$		0			0
$340$	−8.00000	+	13.8564i	−0.433861	+	0.751469i
$341$			16.9706i			0.919007i
$342$		0			0
$343$		−	19.0526i		−	1.02874i
$344$	9.79796			0.528271
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	19.5959			1.05196			0.525982	−	0.850496i	$-0.323698\pi$
$347$	19.5959			1.05196			0.525982	+	0.850496i	$0.323698\pi$
$348$		0			0
$349$	23.0000			1.23116			0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000			1.23116			0.615581	+	0.788074i	$0.288921\pi$
$350$	3.67423	+	6.36396i	0.196396	+	0.340168i
$351$		0			0
$352$	24.0000	+	13.8564i	1.27920	+	0.738549i
$353$			11.3137i			0.602168i	0.953598	+	0.301084i	$0.0973484\pi$
$353$			11.3137i			0.602168i	−0.953598	+	0.301084i	$0.902652\pi$
$354$		0			0
$355$		0			0
$356$	4.89898	+	2.82843i	0.259645	+	0.149906i
$357$		0			0
$358$		0			0
$359$	14.6969			0.775675			0.387837	−	0.921728i	$-0.373222\pi$
$359$	14.6969			0.775675			0.387837	+	0.921728i	$0.373222\pi$
$360$		0			0
$361$	−8.00000			−0.421053
$362$	13.4722	−	7.77817i	0.708083	−	0.408812i
$363$		0			0
$364$	3.00000	+	1.73205i	0.157243	+	0.0907841i
$365$		−	2.82843i		−	0.148047i
$366$		0			0
$367$			19.0526i			0.994535i	0.867597	+	0.497268i	$0.165663\pi$
$367$			19.0526i			0.994535i	−0.867597	+	0.497268i	$0.834337\pi$
$368$	−9.79796	−	16.9706i	−0.510754	−	0.884652i
$369$		0			0
$370$	−2.00000	−	3.46410i	−0.103975	−	0.180090i
$371$	−9.79796			−0.508685
$372$		0			0
$373$	−25.0000			−1.29445			−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−25.0000			−1.29445			−0.647225	+	0.762299i	$0.724071\pi$
$374$	−9.79796	−	16.9706i	−0.506640	−	0.877527i
$375$		0			0
$376$			13.8564i			0.714590i
$377$			5.65685i			0.291343i
$378$		0			0
$379$		−	15.5885i		−	0.800725i	−0.916357	−	0.400363i	$-0.868884\pi$
$379$		−	15.5885i		−	0.800725i	0.916357	−	0.400363i	$-0.131116\pi$
$380$	−14.6969	+	25.4558i	−0.753937	+	1.30586i
$381$		0			0
$382$	30.0000	−	17.3205i	1.53493	−	0.886194i
$383$	19.5959			1.00130			0.500652	−	0.865648i	$-0.333094\pi$
$383$	19.5959			1.00130			0.500652	+	0.865648i	$0.333094\pi$
$384$		0			0
$385$	−24.0000			−1.22315
$386$	−1.22474	+	0.707107i	−0.0623379	+	0.0359908i
$387$		0			0
$388$	−13.0000	+	22.5167i	−0.659975	+	1.14311i
$389$		−	14.1421i		−	0.717035i	−0.933523	−	0.358517i	$-0.883282\pi$
$389$		−	14.1421i		−	0.717035i	0.933523	−	0.358517i	$-0.116718\pi$
$390$		0			0
$391$			13.8564i			0.700749i
$392$		−	11.3137i		−	0.571429i
$393$		0			0
$394$	2.00000	+	3.46410i	0.100759	+	0.174519i
$395$	4.89898			0.246494
$396$		0			0
$397$	−10.0000			−0.501886			−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000			−0.501886			−0.250943	+	0.968002i	$0.580741\pi$
$398$	3.67423	+	6.36396i	0.184173	+	0.318997i
$399$		0			0
$400$	6.00000	+	10.3923i	0.300000	+	0.519615i
$401$		−	22.6274i		−	1.12996i	−0.825105	−	0.564980i	$-0.808884\pi$
$401$		−	22.6274i		−	1.12996i	0.825105	−	0.564980i	$-0.191116\pi$
$402$		0			0
$403$			3.46410i			0.172559i
$404$	19.5959	+	11.3137i	0.974933	+	0.562878i
$405$		0			0
$406$	−12.0000	+	6.92820i	−0.595550	+	0.343841i
$407$	4.89898			0.242833
$408$		0			0
$409$	−1.00000			−0.0494468			−0.0247234	−	0.999694i	$-0.507871\pi$
$409$	−1.00000			−0.0494468			−0.0247234	+	0.999694i	$0.507871\pi$
$410$	19.5959	−	11.3137i	0.967773	−	0.558744i
$411$		0			0
$412$	−15.0000	−	8.66025i	−0.738997	−	0.426660i
$413$		−	8.48528i		−	0.417533i
$414$		0			0
$415$			27.7128i			1.36037i
$416$	4.89898	+	2.82843i	0.240192	+	0.138675i
$417$		0			0
$418$	−18.0000	−	31.1769i	−0.880409	−	1.52491i
$419$	4.89898			0.239331			0.119665	−	0.992814i	$-0.461818\pi$
$419$	4.89898			0.239331			0.119665	+	0.992814i	$0.461818\pi$
$420$		0			0
$421$	−25.0000			−1.21843			−0.609213	−	0.793007i	$-0.708514\pi$
$421$	−25.0000			−1.21843			−0.609213	+	0.793007i	$0.708514\pi$
$422$	8.57321	+	14.8492i	0.417338	+	0.722850i
$423$		0			0
$424$	−16.0000			−0.777029
$425$		−	8.48528i		−	0.411597i
$426$		0			0
$427$		−	19.0526i		−	0.922018i
$428$	−14.6969	+	25.4558i	−0.710403	+	1.23045i
$429$		0			0
$430$	−12.0000	+	6.92820i	−0.578691	+	0.334108i
$431$	14.6969			0.707927			0.353963	−	0.935259i	$-0.384834\pi$
$431$	14.6969			0.707927			0.353963	+	0.935259i	$0.384834\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	−7.34847	+	4.24264i	−0.352738	+	0.203653i
$435$		0			0
$436$	−10.0000	+	17.3205i	−0.478913	+	0.829502i
$437$			25.4558i			1.21772i
$438$		0			0
$439$		−	17.3205i		−	0.826663i	−0.910581	−	0.413331i	$-0.864365\pi$
$439$		−	17.3205i		−	0.826663i	0.910581	−	0.413331i	$-0.135635\pi$
$440$	−39.1918			−1.86840
$441$		0			0
$442$	−2.00000	−	3.46410i	−0.0951303	−	0.164771i
$443$	9.79796			0.465515			0.232758	−	0.972535i	$-0.425225\pi$
$443$	9.79796			0.465515			0.232758	+	0.972535i	$0.425225\pi$
$444$		0			0
$445$	−8.00000			−0.379236
$446$	17.1464	+	29.6985i	0.811907	+	1.40626i
$447$		0			0
$448$			13.8564i			0.654654i
$449$		−	31.1127i		−	1.46830i	−0.678988	−	0.734150i	$-0.737581\pi$
$449$		−	31.1127i		−	1.46830i	0.678988	−	0.734150i	$-0.262419\pi$
$450$		0			0
$451$			27.7128i			1.30495i
$452$	4.89898	+	2.82843i	0.230429	+	0.133038i
$453$		0			0
$454$	−24.0000	+	13.8564i	−1.12638	+	0.650313i
$455$	−4.89898			−0.229668
$456$		0			0
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$	−12.2474	+	7.07107i	−0.572286	+	0.330409i
$459$		0			0
$460$	24.0000	+	13.8564i	1.11901	+	0.646058i
$461$		−	14.1421i		−	0.658665i	−0.944214	−	0.329332i	$-0.893176\pi$
$461$		−	14.1421i		−	0.658665i	0.944214	−	0.329332i	$-0.106824\pi$
$462$		0			0
$463$			12.1244i			0.563467i	0.959493	+	0.281733i	$0.0909093\pi$
$463$			12.1244i			0.563467i	−0.959493	+	0.281733i	$0.909091\pi$
$464$	−19.5959	+	11.3137i	−0.909718	+	0.525226i
$465$		0			0
$466$	−16.0000	−	27.7128i	−0.741186	−	1.28377i
$467$	−14.6969			−0.680093			−0.340047	−	0.940409i	$-0.610443\pi$
$467$	−14.6969			−0.680093			−0.340047	+	0.940409i	$0.610443\pi$
$468$		0			0
$469$	21.0000			0.969690
$470$	−9.79796	−	16.9706i	−0.451946	−	0.782794i
$471$		0			0
$472$		−	13.8564i		−	0.637793i
$473$		−	16.9706i		−	0.780307i
$474$		0			0
$475$		−	15.5885i		−	0.715247i
$476$	4.89898	−	8.48528i	0.224544	−	0.388922i
$477$		0			0
$478$	24.0000	−	13.8564i	1.09773	−	0.633777i
$479$	9.79796			0.447680			0.223840	−	0.974626i	$-0.428141\pi$
$479$	9.79796			0.447680			0.223840	+	0.974626i	$0.428141\pi$
$480$		0			0
$481$	1.00000			0.0455961
$482$	−30.6186	+	17.6777i	−1.39464	+	0.805196i
$483$		0			0
$484$	13.0000	−	22.5167i	0.590909	−	1.02348i
$485$		−	36.7696i		−	1.66962i
$486$		0			0
$487$			25.9808i			1.17730i	0.808388	+	0.588650i	$0.200341\pi$
$487$			25.9808i			1.17730i	−0.808388	+	0.588650i	$0.799659\pi$
$488$		−	31.1127i		−	1.40841i
$489$		0			0
$490$	8.00000	+	13.8564i	0.361403	+	0.625969i
$491$	−24.4949			−1.10544			−0.552720	−	0.833367i	$-0.686410\pi$
$491$	−24.4949			−1.10544			−0.552720	+	0.833367i	$0.686410\pi$
$492$		0			0
$493$	16.0000			0.720604
$494$	−3.67423	−	6.36396i	−0.165312	−	0.286328i
$495$		0			0
$496$	−12.0000	+	6.92820i	−0.538816	+	0.311086i
$497$		0			0
$498$		0			0
$499$		−	24.2487i		−	1.08552i	−0.839887	−	0.542761i	$-0.817379\pi$
$499$		−	24.2487i		−	1.08552i	0.839887	−	0.542761i	$-0.182621\pi$
$500$	9.79796	+	5.65685i	0.438178	+	0.252982i
$501$		0			0
$502$	36.0000	−	20.7846i	1.60676	−	0.927663i
$503$	14.6969			0.655304			0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969			0.655304			0.327652	+	0.944798i	$0.393743\pi$
$504$		0			0
$505$	−32.0000			−1.42398
$506$	−29.3939	+	16.9706i	−1.30672	+	0.754434i
$507$		0			0
$508$	18.0000	+	10.3923i	0.798621	+	0.461084i
$509$			19.7990i			0.877575i	0.898591	+	0.438787i	$0.144592\pi$
$509$			19.7990i			0.877575i	−0.898591	+	0.438787i	$0.855408\pi$
$510$		0			0
$511$			1.73205i			0.0766214i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	20.0000	+	34.6410i	0.882162	+	1.52795i
$515$	24.4949			1.07937
$516$		0			0
$517$	24.0000			1.05552
$518$	1.22474	+	2.12132i	0.0538122	+	0.0932055i
$519$		0			0
$520$	−8.00000			−0.350823
$521$			19.7990i			0.867409i	0.901055	+	0.433705i	$0.142794\pi$
$521$			19.7990i			0.867409i	−0.901055	+	0.433705i	$0.857206\pi$
$522$		0			0
$523$		−	15.5885i		−	0.681636i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$		−	15.5885i		−	0.681636i	0.940129	−	0.340818i	$-0.110704\pi$
$524$	−9.79796	+	16.9706i	−0.428026	+	0.741362i
$525$		0			0
$526$	−24.0000	+	13.8564i	−1.04645	+	0.604168i
$527$	9.79796			0.426806
$528$		0			0
$529$	1.00000			0.0434783
$530$	19.5959	−	11.3137i	0.851192	−	0.491436i
$531$		0			0
$532$	9.00000	−	15.5885i	0.390199	−	0.675845i
$533$			5.65685i			0.245026i
$534$		0			0
$535$		−	41.5692i		−	1.79719i
$536$	34.2929			1.48123
$537$		0			0
$538$	2.00000	+	3.46410i	0.0862261	+	0.149348i
$539$	−19.5959			−0.844056
$540$		0			0
$541$	−1.00000			−0.0429934			−0.0214967	−	0.999769i	$-0.506843\pi$
$541$	−1.00000			−0.0429934			−0.0214967	+	0.999769i	$0.506843\pi$
$542$	3.67423	+	6.36396i	0.157822	+	0.273356i
$543$		0			0
$544$	8.00000	−	13.8564i	0.342997	−	0.594089i
$545$		−	28.2843i		−	1.21157i
$546$		0			0
$547$		−	22.5167i		−	0.962743i	−0.876517	−	0.481371i	$-0.840139\pi$
$547$		−	22.5167i		−	0.962743i	0.876517	−	0.481371i	$-0.159861\pi$
$548$	34.2929	+	19.7990i	1.46492	+	0.845771i
$549$		0			0
$550$	18.0000	−	10.3923i	0.767523	−	0.443129i
$551$	29.3939			1.25222
$552$		0			0
$553$	−3.00000			−0.127573
$554$	17.1464	−	9.89949i	0.728482	−	0.420589i
$555$		0			0
$556$	−15.0000	−	8.66025i	−0.636142	−	0.367277i
$557$			2.82843i			0.119844i	0.998203	+	0.0599222i	$0.0190852\pi$
$557$			2.82843i			0.119844i	−0.998203	+	0.0599222i	$0.980915\pi$
$558$		0			0
$559$		−	3.46410i		−	0.146516i
$560$	−9.79796	−	16.9706i	−0.414039	−	0.717137i
$561$		0			0
$562$	−4.00000	−	6.92820i	−0.168730	−	0.292249i
$563$	−9.79796			−0.412935			−0.206467	−	0.978453i	$-0.566197\pi$
$563$	−9.79796			−0.412935			−0.206467	+	0.978453i	$0.566197\pi$
$564$		0			0
$565$	−8.00000			−0.336563
$566$	−17.1464	−	29.6985i	−0.720718	−	1.24832i
$567$		0			0
$568$		0			0
$569$			19.7990i			0.830017i	0.909818	+	0.415008i	$0.136221\pi$
$569$			19.7990i			0.830017i	−0.909818	+	0.415008i	$0.863779\pi$
$570$		0			0
$571$			32.9090i			1.37720i	0.725143	+	0.688599i	$0.241774\pi$
$571$			32.9090i			1.37720i	−0.725143	+	0.688599i	$0.758226\pi$
$572$	4.89898	−	8.48528i	0.204837	−	0.354787i
$573$		0			0
$574$	−12.0000	+	6.92820i	−0.500870	+	0.289178i
$575$	−14.6969			−0.612905
$576$		0			0
$577$	35.0000			1.45707			0.728535	−	0.685009i	$-0.240202\pi$
$577$	35.0000			1.45707			0.728535	+	0.685009i	$0.240202\pi$
$578$	11.0227	−	6.36396i	0.458484	−	0.264706i
$579$		0			0
$580$	16.0000	−	27.7128i	0.664364	−	1.15071i
$581$		−	16.9706i		−	0.704058i
$582$		0			0
$583$			27.7128i			1.14775i
$584$			2.82843i			0.117041i
$585$		0			0
$586$	2.00000	+	3.46410i	0.0826192	+	0.143101i
$587$	−4.89898			−0.202203			−0.101101	−	0.994876i	$-0.532237\pi$
$587$	−4.89898			−0.202203			−0.101101	+	0.994876i	$0.532237\pi$
$588$		0			0
$589$	18.0000			0.741677
$590$	9.79796	+	16.9706i	0.403376	+	0.698667i
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$			28.2843i			1.16150i	0.814083	+	0.580748i	$0.197240\pi$
$593$			28.2843i			1.16150i	−0.814083	+	0.580748i	$0.802760\pi$
$594$		0			0
$595$			13.8564i			0.568057i
$596$	−39.1918	−	22.6274i	−1.60536	−	0.926855i
$597$		0			0
$598$	−6.00000	+	3.46410i	−0.245358	+	0.141658i
$599$	−9.79796			−0.400334			−0.200167	−	0.979762i	$-0.564148\pi$
$599$	−9.79796			−0.400334			−0.200167	+	0.979762i	$0.564148\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	7.34847	−	4.24264i	0.299501	−	0.172917i
$603$		0			0
$604$	−39.0000	−	22.5167i	−1.58689	−	0.916190i
$605$			36.7696i			1.49489i
$606$		0			0
$607$			12.1244i			0.492112i	0.969256	+	0.246056i	$0.0791348\pi$
$607$			12.1244i			0.492112i	−0.969256	+	0.246056i	$0.920865\pi$
$608$	14.6969	−	25.4558i	0.596040	−	1.03237i
$609$		0			0
$610$	22.0000	+	38.1051i	0.890754	+	1.54283i
$611$	4.89898			0.198191
$612$		0			0
$613$	11.0000			0.444286			0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000			0.444286			0.222143	+	0.975014i	$0.428695\pi$
$614$	−7.34847	−	12.7279i	−0.296560	−	0.513657i
$615$		0			0
$616$	24.0000			0.966988
$617$			2.82843i			0.113868i	0.998378	+	0.0569341i	$0.0181325\pi$
$617$			2.82843i			0.113868i	−0.998378	+	0.0569341i	$0.981868\pi$
$618$		0			0
$619$			19.0526i			0.765787i	0.923792	+	0.382893i	$0.125072\pi$
$619$			19.0526i			0.765787i	−0.923792	+	0.382893i	$0.874928\pi$
$620$	9.79796	−	16.9706i	0.393496	−	0.681554i
$621$		0			0
$622$	−30.0000	+	17.3205i	−1.20289	+	0.694489i
$623$	4.89898			0.196273
$624$		0			0
$625$	−31.0000			−1.24000
$626$	13.4722	−	7.77817i	0.538457	−	0.310878i
$627$		0			0
$628$	−10.0000	+	17.3205i	−0.399043	+	0.691164i
$629$		−	2.82843i		−	0.112777i
$630$		0			0
$631$		−	36.3731i		−	1.44799i	−0.689806	−	0.723994i	$-0.742304\pi$
$631$		−	36.3731i		−	1.44799i	0.689806	−	0.723994i	$-0.257696\pi$
$632$	−4.89898			−0.194871
$633$		0			0
$634$	−4.00000	−	6.92820i	−0.158860	−	0.275154i
$635$	−29.3939			−1.16646
$636$		0			0
$637$	−4.00000			−0.158486
$638$	19.5959	+	33.9411i	0.775810	+	1.34374i
$639$		0			0
$640$	−16.0000	−	27.7128i	−0.632456	−	1.09545i
$641$			45.2548i			1.78746i	0.448607	+	0.893729i	$0.351920\pi$
$641$			45.2548i			1.78746i	−0.448607	+	0.893729i	$0.648080\pi$
$642$		0			0
$643$			17.3205i			0.683054i	0.939872	+	0.341527i	$0.110944\pi$
$643$			17.3205i			0.683054i	−0.939872	+	0.341527i	$0.889056\pi$
$644$	−14.6969	−	8.48528i	−0.579141	−	0.334367i
$645$		0			0
$646$	−18.0000	+	10.3923i	−0.708201	+	0.408880i
$647$	−29.3939			−1.15559			−0.577796	−	0.816181i	$-0.696087\pi$
$647$	−29.3939			−1.15559			−0.577796	+	0.816181i	$0.696087\pi$
$648$		0			0
$649$	−24.0000			−0.942082
$650$	3.67423	−	2.12132i	0.144115	−	0.0832050i
$651$		0			0
$652$	9.00000	+	5.19615i	0.352467	+	0.203497i
$653$		−	5.65685i		−	0.221370i	−0.993856	−	0.110685i	$-0.964696\pi$
$653$		−	5.65685i		−	0.221370i	0.993856	−	0.110685i	$-0.0353044\pi$
$654$		0			0
$655$		−	27.7128i		−	1.08283i
$656$	−19.5959	+	11.3137i	−0.765092	+	0.441726i
$657$		0			0
$658$	6.00000	+	10.3923i	0.233904	+	0.405134i
$659$	9.79796			0.381674			0.190837	−	0.981622i	$-0.438880\pi$
$659$	9.79796			0.381674			0.190837	+	0.981622i	$0.438880\pi$
$660$		0			0
$661$	−37.0000			−1.43913			−0.719567	−	0.694423i	$-0.755660\pi$
$661$	−37.0000			−1.43913			−0.719567	+	0.694423i	$0.755660\pi$
$662$	−15.9217	−	27.5772i	−0.618814	−	1.07182i
$663$		0			0
$664$		−	27.7128i		−	1.07547i
$665$			25.4558i			0.987135i
$666$		0			0
$667$		−	27.7128i		−	1.07304i
$668$	4.89898	−	8.48528i	0.189547	−	0.328305i
$669$		0			0
$670$	−42.0000	+	24.2487i	−1.62260	+	0.936809i
$671$	−53.8888			−2.08035
$672$		0			0
$673$	11.0000			0.424019			0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000			0.424019			0.212009	+	0.977268i	$0.431999\pi$
$674$	13.4722	−	7.77817i	0.518930	−	0.299604i
$675$		0			0
$676$	−12.0000	+	20.7846i	−0.461538	+	0.799408i
$677$		−	14.1421i		−	0.543526i	−0.962364	−	0.271763i	$-0.912393\pi$
$677$		−	14.1421i		−	0.543526i	0.962364	−	0.271763i	$-0.0876068\pi$
$678$		0			0
$679$			22.5167i			0.864110i
$680$			22.6274i			0.867722i
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	−56.0000			−2.13965
$686$	−13.4722	−	23.3345i	−0.514371	−	0.890916i
$687$		0			0
$688$	12.0000	−	6.92820i	0.457496	−	0.264135i
$689$			5.65685i			0.215509i
$690$		0			0
$691$			45.0333i			1.71315i	0.516024	+	0.856574i	$0.327412\pi$
$691$			45.0333i			1.71315i	−0.516024	+	0.856574i	$0.672588\pi$
$692$	−9.79796	−	5.65685i	−0.372463	−	0.215041i
$693$		0			0
$694$	24.0000	−	13.8564i	0.911028	−	0.525982i
$695$	24.4949			0.929144
$696$		0			0
$697$	16.0000			0.606043
$698$	28.1691	−	16.2635i	1.06622	−	0.615581i
$699$		0			0
$700$	9.00000	+	5.19615i	0.340168	+	0.196396i
$701$			2.82843i			0.106828i	0.998572	+	0.0534141i	$0.0170103\pi$
$701$			2.82843i			0.106828i	−0.998572	+	0.0534141i	$0.982990\pi$
$702$		0			0
$703$		−	5.19615i		−	0.195977i
$704$	39.1918			1.47710
$705$		0			0
$706$	8.00000	+	13.8564i	0.301084	+	0.521493i
$707$	19.5959			0.736980
$708$		0			0
$709$	−25.0000			−0.938895			−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000			−0.938895			−0.469447	+	0.882960i	$0.655547\pi$
$710$		0			0
$711$		0			0
$712$	8.00000			0.299813
$713$		−	16.9706i		−	0.635553i
$714$		0			0
$715$			13.8564i			0.518200i
$716$		0			0
$717$		0			0
$718$	18.0000	−	10.3923i	0.671754	−	0.387837i
$719$	−29.3939			−1.09621			−0.548103	−	0.836411i	$-0.684650\pi$
$719$	−29.3939			−1.09621			−0.548103	+	0.836411i	$0.684650\pi$
$720$		0			0
$721$	−15.0000			−0.558629
$722$	−9.79796	+	5.65685i	−0.364642	+	0.210526i
$723$		0			0
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$			16.9706i			0.630271i
$726$		0			0
$727$		−	17.3205i		−	0.642382i	−0.947014	−	0.321191i	$-0.895917\pi$
$727$		−	17.3205i		−	0.642382i	0.947014	−	0.321191i	$-0.104083\pi$
$728$	4.89898			0.181568
$729$		0			0
$730$	−2.00000	−	3.46410i	−0.0740233	−	0.128212i
$731$	−9.79796			−0.362391
$732$		0			0
$733$	38.0000			1.40356			0.701781	−	0.712393i	$-0.252388\pi$
$733$	38.0000			1.40356			0.701781	+	0.712393i	$0.252388\pi$
$734$	13.4722	+	23.3345i	0.497268	+	0.861293i
$735$		0			0
$736$	−24.0000	−	13.8564i	−0.884652	−	0.510754i
$737$		−	59.3970i		−	2.18792i
$738$		0			0
$739$		−	10.3923i		−	0.382287i	−0.981562	−	0.191144i	$-0.938780\pi$
$739$		−	10.3923i		−	0.382287i	0.981562	−	0.191144i	$-0.0612196\pi$
$740$	−4.89898	−	2.82843i	−0.180090	−	0.103975i
$741$		0			0
$742$	−12.0000	+	6.92820i	−0.440534	+	0.254342i
$743$	34.2929			1.25808			0.629041	−	0.777372i	$-0.283448\pi$
$743$	34.2929			1.25808			0.629041	+	0.777372i	$0.283448\pi$
$744$		0			0
$745$	64.0000			2.34478
$746$	−30.6186	+	17.6777i	−1.12103	+	0.647225i
$747$		0			0
$748$	−24.0000	−	13.8564i	−0.877527	−	0.506640i
$749$			25.4558i			0.930136i
$750$		0			0
$751$		−	29.4449i		−	1.07446i	−0.843436	−	0.537229i	$-0.819471\pi$
$751$		−	29.4449i		−	1.07446i	0.843436	−	0.537229i	$-0.180529\pi$
$752$	9.79796	+	16.9706i	0.357295	+	0.618853i
$753$		0			0
$754$	4.00000	+	6.92820i	0.145671	+	0.252310i
$755$	63.6867			2.31780
$756$		0			0
$757$	47.0000			1.70824			0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000			1.70824			0.854122	+	0.520073i	$0.174095\pi$
$758$	−11.0227	−	19.0919i	−0.400363	−	0.693448i
$759$		0			0
$760$			41.5692i			1.50787i
$761$			2.82843i			0.102530i	0.998685	+	0.0512652i	$0.0163254\pi$
$761$			2.82843i			0.102530i	−0.998685	+	0.0512652i	$0.983675\pi$
$762$		0			0
$763$			17.3205i			0.627044i
$764$	24.4949	−	42.4264i	0.886194	−	1.53493i
$765$		0			0
$766$	24.0000	−	13.8564i	0.867155	−	0.500652i
$767$	−4.89898			−0.176892
$768$		0			0
$769$	−1.00000			−0.0360609			−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000			−0.0360609			−0.0180305	+	0.999837i	$0.505740\pi$
$770$	−29.3939	+	16.9706i	−1.05928	+	0.611577i
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$			28.2843i			1.01731i	0.860969	+	0.508657i	$0.169858\pi$
$773$			28.2843i			1.01731i	−0.860969	+	0.508657i	$0.830142\pi$
$774$		0			0
$775$			10.3923i			0.373303i
$776$			36.7696i			1.31995i
$777$		0			0
$778$	−10.0000	−	17.3205i	−0.358517	−	0.620970i
$779$	29.3939			1.05314
$780$		0			0
$781$		0			0
$782$	9.79796	+	16.9706i	0.350374	+	0.606866i
$783$		0			0
$784$	−8.00000	−	13.8564i	−0.285714	−	0.494872i
$785$		−	28.2843i		−	1.00951i
$786$		0			0
$787$		−	8.66025i		−	0.308705i	−0.988016	−	0.154352i	$-0.950671\pi$
$787$		−	8.66025i		−	0.308705i	0.988016	−	0.154352i	$-0.0493291\pi$
$788$	4.89898	+	2.82843i	0.174519	+	0.100759i
$789$		0			0
$790$	6.00000	−	3.46410i	0.213470	−	0.123247i
$791$	4.89898			0.174188
$792$		0			0
$793$	−11.0000			−0.390621
$794$	−12.2474	+	7.07107i	−0.434646	+	0.250943i
$795$		0			0
$796$	9.00000	+	5.19615i	0.318997	+	0.184173i
$797$		−	22.6274i		−	0.801504i	−0.916187	−	0.400752i	$-0.868749\pi$
$797$		−	22.6274i		−	0.801504i	0.916187	−	0.400752i	$-0.131251\pi$
$798$		0			0
$799$		−	13.8564i		−	0.490204i
$800$	14.6969	+	8.48528i	0.519615	+	0.300000i
$801$		0			0
$802$	−16.0000	−	27.7128i	−0.564980	−	0.978573i
$803$	4.89898			0.172881
$804$		0			0
$805$	24.0000			0.845889
$806$	2.44949	+	4.24264i	0.0862796	+	0.149441i
$807$		0			0
$808$	32.0000			1.12576
$809$		−	22.6274i		−	0.795538i	−0.917486	−	0.397769i	$-0.869785\pi$
$809$		−	22.6274i		−	0.795538i	0.917486	−	0.397769i	$-0.130215\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−9.79796	+	16.9706i	−0.343841	+	0.595550i
$813$		0			0
$814$	6.00000	−	3.46410i	0.210300	−	0.121417i
$815$	−14.6969			−0.514811
$816$		0			0
$817$	−18.0000			−0.629740
$818$	−1.22474	+	0.707107i	−0.0428222	+	0.0247234i
$819$		0			0
$820$	16.0000	−	27.7128i	0.558744	−	0.967773i
$821$		−	31.1127i		−	1.08584i	−0.839784	−	0.542920i	$-0.817319\pi$
$821$		−	31.1127i		−	1.08584i	0.839784	−	0.542920i	$-0.182681\pi$
$822$		0			0
$823$		−	50.2295i		−	1.75089i	−0.483318	−	0.875445i	$-0.660569\pi$
$823$		−	50.2295i		−	1.75089i	0.483318	−	0.875445i	$-0.339431\pi$
$824$	−24.4949			−0.853320
$825$		0			0
$826$	−6.00000	−	10.3923i	−0.208767	−	0.361595i
$827$	−14.6969			−0.511063			−0.255531	−	0.966801i	$-0.582250\pi$
$827$	−14.6969			−0.511063			−0.255531	+	0.966801i	$0.582250\pi$
$828$		0			0
$829$	11.0000			0.382046			0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000			0.382046			0.191023	+	0.981586i	$0.438820\pi$
$830$	19.5959	+	33.9411i	0.680184	+	1.17811i
$831$		0			0
$832$	8.00000			0.277350
$833$			11.3137i			0.391997i
$834$		0			0
$835$			13.8564i			0.479521i
$836$	−44.0908	−	25.4558i	−1.52491	−	0.880409i
$837$		0			0
$838$	6.00000	−	3.46410i	0.207267	−	0.119665i
$839$	−48.9898			−1.69132			−0.845658	−	0.533726i	$-0.820792\pi$
$839$	−48.9898			−1.69132			−0.845658	+	0.533726i	$0.820792\pi$
$840$		0			0
$841$	−3.00000			−0.103448
$842$	−30.6186	+	17.6777i	−1.05519	+	0.609213i
$843$		0			0
$844$	21.0000	+	12.1244i	0.722850	+	0.417338i
$845$		−	33.9411i		−	1.16761i
$846$		0			0
$847$		−	22.5167i		−	0.773682i
$848$	−19.5959	+	11.3137i	−0.672927	+	0.388514i
$849$		0			0
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	−4.89898			−0.167935
$852$		0			0
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	−13.4722	−	23.3345i	−0.461009	−	0.798491i
$855$		0			0
$856$			41.5692i			1.42081i
$857$		−	56.5685i		−	1.93234i	−0.257897	−	0.966172i	$-0.583030\pi$
$857$		−	56.5685i		−	1.93234i	0.257897	−	0.966172i	$-0.416970\pi$
$858$		0			0
$859$			12.1244i			0.413678i	0.978375	+	0.206839i	$0.0663176\pi$
$859$			12.1244i			0.413678i	−0.978375	+	0.206839i	$0.933682\pi$
$860$	−9.79796	+	16.9706i	−0.334108	+	0.578691i
$861$		0			0
$862$	18.0000	−	10.3923i	0.613082	−	0.353963i
$863$	14.6969			0.500290			0.250145	−	0.968208i	$-0.419522\pi$
$863$	14.6969			0.500290			0.250145	+	0.968208i	$0.419522\pi$
$864$		0			0
$865$	16.0000			0.544016
$866$	31.8434	−	18.3848i	1.08208	−	0.624740i
$867$		0			0
$868$	−6.00000	+	10.3923i	−0.203653	+	0.352738i
$869$			8.48528i			0.287843i
$870$		0			0
$871$		−	12.1244i		−	0.410818i
$872$			28.2843i			0.957826i
$873$		0			0
$874$	18.0000	+	31.1769i	0.608859	+	1.05457i
$875$	9.79796			0.331231
$876$		0			0
$877$	−1.00000			−0.0337676			−0.0168838	−	0.999857i	$-0.505375\pi$
$877$	−1.00000			−0.0337676			−0.0168838	+	0.999857i	$0.505375\pi$
$878$	−12.2474	−	21.2132i	−0.413331	−	0.715911i
$879$		0			0
$880$	−48.0000	+	27.7128i	−1.61808	+	0.934199i
$881$			19.7990i			0.667045i	0.942742	+	0.333522i	$0.108237\pi$
$881$			19.7990i			0.667045i	−0.942742	+	0.333522i	$0.891763\pi$
$882$		0			0
$883$			5.19615i			0.174864i	0.996170	+	0.0874322i	$0.0278661\pi$
$883$			5.19615i			0.174864i	−0.996170	+	0.0874322i	$0.972134\pi$
$884$	−4.89898	−	2.82843i	−0.164771	−	0.0951303i
$885$		0			0
$886$	12.0000	−	6.92820i	0.403148	−	0.232758i
$887$	48.9898			1.64492			0.822458	−	0.568826i	$-0.192602\pi$
$887$	48.9898			1.64492			0.822458	+	0.568826i	$0.192602\pi$
$888$		0			0
$889$	18.0000			0.603701
$890$	−9.79796	+	5.65685i	−0.328428	+	0.189618i
$891$		0			0
$892$	42.0000	+	24.2487i	1.40626	+	0.811907i
$893$		−	25.4558i		−	0.851847i
$894$		0			0
$895$		0			0
$896$	9.79796	+	16.9706i	0.327327	+	0.566947i
$897$		0			0
$898$	−22.0000	−	38.1051i	−0.734150	−	1.27158i
$899$	−19.5959			−0.653560
$900$		0			0
$901$	16.0000			0.533037
$902$	19.5959	+	33.9411i	0.652473	+	1.13012i
$903$		0			0
$904$	8.00000			0.266076
$905$			31.1127i			1.03422i
$906$		0			0
$907$		−	1.73205i		−	0.0575118i	−0.999586	−	0.0287559i	$-0.990845\pi$
$907$		−	1.73205i		−	0.0575118i	0.999586	−	0.0287559i	$-0.00915455\pi$
$908$	−19.5959	+	33.9411i	−0.650313	+	1.12638i
$909$		0			0
$910$	−6.00000	+	3.46410i	−0.198898	+	0.114834i
$911$	9.79796			0.324621			0.162310	−	0.986740i	$-0.448105\pi$
$911$	9.79796			0.324621			0.162310	+	0.986740i	$0.448105\pi$
$912$		0			0
$913$	−48.0000			−1.58857
$914$	2.44949	−	1.41421i	0.0810219	−	0.0467780i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$			16.9706i			0.560417i
$918$		0			0
$919$			10.3923i			0.342811i	0.985201	+	0.171405i	$0.0548307\pi$
$919$			10.3923i			0.342811i	−0.985201	+	0.171405i	$0.945169\pi$
$920$	39.1918			1.29212
$921$		0			0
$922$	−10.0000	−	17.3205i	−0.329332	−	0.570421i
$923$		0			0
$924$		0			0
$925$	3.00000			0.0986394
$926$	8.57321	+	14.8492i	0.281733	+	0.487976i
$927$		0			0
$928$	−16.0000	+	27.7128i	−0.525226	+	0.909718i
$929$			45.2548i			1.48476i	0.669977	+	0.742381i	$0.266304\pi$
$929$			45.2548i			1.48476i	−0.669977	+	0.742381i	$0.733696\pi$
$930$		0			0
$931$			20.7846i			0.681188i
$932$	−39.1918	−	22.6274i	−1.28377	−	0.741186i
$933$		0			0
$934$	−18.0000	+	10.3923i	−0.588978	+	0.340047i
$935$	39.1918			1.28171
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	25.7196	−	14.8492i	0.839776	−	0.484845i
$939$		0			0
$940$	−24.0000	−	13.8564i	−0.782794	−	0.451946i
$941$		−	48.0833i		−	1.56747i	−0.621096	−	0.783735i	$-0.713312\pi$
$941$		−	48.0833i		−	1.56747i	0.621096	−	0.783735i	$-0.286688\pi$
$942$		0			0
$943$		−	27.7128i		−	0.902453i
$944$	−9.79796	−	16.9706i	−0.318896	−	0.552345i
$945$		0			0
$946$	−12.0000	−	20.7846i	−0.390154	−	0.675766i
$947$	−34.2929			−1.11437			−0.557184	−	0.830389i	$-0.688118\pi$
$947$	−34.2929			−1.11437			−0.557184	+	0.830389i	$0.688118\pi$
$948$		0			0
$949$	1.00000			0.0324614
$950$	−11.0227	−	19.0919i	−0.357624	−	0.619422i
$951$		0			0
$952$		−	13.8564i		−	0.449089i
$953$			2.82843i			0.0916217i	0.998950	+	0.0458109i	$0.0145872\pi$
$953$			2.82843i			0.0916217i	−0.998950	+	0.0458109i	$0.985413\pi$
$954$		0			0
$955$			69.2820i			2.24191i
$956$	19.5959	−	33.9411i	0.633777	−	1.09773i
$957$		0			0
$958$	12.0000	−	6.92820i	0.387702	−	0.223840i
$959$	34.2929			1.10737
$960$		0			0
$961$	19.0000			0.612903
$962$	1.22474	−	0.707107i	0.0394874	−	0.0227980i
$963$		0			0
$964$	−25.0000	+	43.3013i	−0.805196	+	1.39464i
$965$		−	2.82843i		−	0.0910503i
$966$		0			0
$967$			53.6936i			1.72667i	0.504632	+	0.863334i	$0.331628\pi$
$967$			53.6936i			1.72667i	−0.504632	+	0.863334i	$0.668372\pi$
$968$		−	36.7696i		−	1.18182i
$969$		0			0
$970$	−26.0000	−	45.0333i	−0.834810	−	1.44593i
$971$	14.6969			0.471647			0.235824	−	0.971796i	$-0.424221\pi$
$971$	14.6969			0.471647			0.235824	+	0.971796i	$0.424221\pi$
$972$		0			0
$973$	−15.0000			−0.480878
$974$	18.3712	+	31.8198i	0.588650	+	1.01957i
$975$		0			0
$976$	−22.0000	−	38.1051i	−0.704203	−	1.21972i
$977$		−	5.65685i		−	0.180979i	−0.995897	−	0.0904894i	$-0.971157\pi$
$977$		−	5.65685i		−	0.180979i	0.995897	−	0.0904894i	$-0.0288431\pi$
$978$		0			0
$979$		−	13.8564i		−	0.442853i
$980$	19.5959	+	11.3137i	0.625969	+	0.361403i
$981$		0			0
$982$	−30.0000	+	17.3205i	−0.957338	+	0.552720i
$983$	−34.2929			−1.09377			−0.546886	−	0.837207i	$-0.684187\pi$
$983$	−34.2929			−1.09377			−0.546886	+	0.837207i	$0.684187\pi$
$984$		0			0
$985$	−8.00000			−0.254901
$986$	19.5959	−	11.3137i	0.624061	−	0.360302i
$987$		0			0
$988$	−9.00000	−	5.19615i	−0.286328	−	0.165312i
$989$			16.9706i			0.539633i
$990$		0			0
$991$		−	36.3731i		−	1.15543i	−0.816239	−	0.577714i	$-0.803945\pi$
$991$		−	36.3731i		−	1.15543i	0.816239	−	0.577714i	$-0.196055\pi$
$992$	−9.79796	+	16.9706i	−0.311086	+	0.538816i
$993$		0			0
$994$		0			0
$995$	−14.6969			−0.465924
$996$		0			0
$997$	−34.0000			−1.07679			−0.538395	−	0.842692i	$-0.680969\pi$
$997$	−34.0000			−1.07679			−0.538395	+	0.842692i	$0.680969\pi$
$998$	−17.1464	−	29.6985i	−0.542761	−	0.940089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.b.b.107.3	yes	4
3.2	odd	2	inner	108.2.b.b.107.2	yes	4
4.3	odd	2	inner	108.2.b.b.107.1	✓	4
8.3	odd	2		1728.2.c.d.1727.2		4
8.5	even	2		1728.2.c.d.1727.1		4
9.2	odd	6		324.2.h.b.215.2		4
9.4	even	3		324.2.h.a.107.2		4
9.5	odd	6		324.2.h.a.107.1		4
9.7	even	3		324.2.h.b.215.1		4
12.11	even	2	inner	108.2.b.b.107.4	yes	4
24.5	odd	2		1728.2.c.d.1727.3		4
24.11	even	2		1728.2.c.d.1727.4		4
36.7	odd	6		324.2.h.a.215.2		4
36.11	even	6		324.2.h.a.215.1		4
36.23	even	6		324.2.h.b.107.1		4
36.31	odd	6		324.2.h.b.107.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.b.b.107.1	✓	4	4.3	odd	2	inner
108.2.b.b.107.2	yes	4	3.2	odd	2	inner
108.2.b.b.107.3	yes	4	1.1	even	1	trivial
108.2.b.b.107.4	yes	4	12.11	even	2	inner
324.2.h.a.107.1		4	9.5	odd	6
324.2.h.a.107.2		4	9.4	even	3
324.2.h.a.215.1		4	36.11	even	6
324.2.h.a.215.2		4	36.7	odd	6
324.2.h.b.107.1		4	36.23	even	6
324.2.h.b.107.2		4	36.31	odd	6
324.2.h.b.215.1		4	9.7	even	3
324.2.h.b.215.2		4	9.2	odd	6
1728.2.c.d.1727.1		4	8.5	even	2
1728.2.c.d.1727.2		4	8.3	odd	2
1728.2.c.d.1727.3		4	24.5	odd	2
1728.2.c.d.1727.4		4	24.11	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.82843i q^{5} -1.73205i q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.82843i q^{5} -1.73205i q^{7} -2.82843i q^{8} +(2.00000 + 3.46410i) q^{10} -4.89898 q^{11} -1.00000 q^{13} +(-1.22474 - 2.12132i) q^{14} +(-2.00000 - 3.46410i) q^{16} +2.82843i q^{17} +5.19615i q^{19} +(4.89898 + 2.82843i) q^{20} +(-6.00000 + 3.46410i) q^{22} +4.89898 q^{23} -3.00000 q^{25} +(-1.22474 + 0.707107i) q^{26} +(-3.00000 - 1.73205i) q^{28} -5.65685i q^{29} -3.46410i q^{31} +(-4.89898 - 2.82843i) q^{32} +(2.00000 + 3.46410i) q^{34} +4.89898 q^{35} -1.00000 q^{37} +(3.67423 + 6.36396i) q^{38} +8.00000 q^{40} -5.65685i q^{41} +3.46410i q^{43} +(-4.89898 + 8.48528i) q^{44} +(6.00000 - 3.46410i) q^{46} -4.89898 q^{47} +4.00000 q^{49} +(-3.67423 + 2.12132i) q^{50} +(-1.00000 + 1.73205i) q^{52} -5.65685i q^{53} -13.8564i q^{55} -4.89898 q^{56} +(-4.00000 - 6.92820i) q^{58} +4.89898 q^{59} +11.0000 q^{61} +(-2.44949 - 4.24264i) q^{62} -8.00000 q^{64} -2.82843i q^{65} +12.1244i q^{67} +(4.89898 + 2.82843i) q^{68} +(6.00000 - 3.46410i) q^{70} -1.00000 q^{73} +(-1.22474 + 0.707107i) q^{74} +(9.00000 + 5.19615i) q^{76} +8.48528i q^{77} -1.73205i q^{79} +(9.79796 - 5.65685i) q^{80} +(-4.00000 - 6.92820i) q^{82} +9.79796 q^{83} -8.00000 q^{85} +(2.44949 + 4.24264i) q^{86} +13.8564i q^{88} +2.82843i q^{89} +1.73205i q^{91} +(4.89898 - 8.48528i) q^{92} +(-6.00000 + 3.46410i) q^{94} -14.6969 q^{95} -13.0000 q^{97} +(4.89898 - 2.82843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4}+O(q^{10}) \) 4 * q + 4 * q^4	\( 4 q + 4 q^{4} + 8 q^{10} - 4 q^{13} - 8 q^{16} - 24 q^{22} - 12 q^{25} - 12 q^{28} + 8 q^{34} - 4 q^{37} + 32 q^{40} + 24 q^{46} + 16 q^{49} - 4 q^{52} - 16 q^{58} + 44 q^{61} - 32 q^{64} + 24 q^{70} - 4 q^{73} + 36 q^{76} - 16 q^{82} - 32 q^{85} - 24 q^{94} - 52 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 + 8 * q^10 - 4 * q^13 - 8 * q^16 - 24 * q^22 - 12 * q^25 - 12 * q^28 + 8 * q^34 - 4 * q^37 + 32 * q^40 + 24 * q^46 + 16 * q^49 - 4 * q^52 - 16 * q^58 + 44 * q^61 - 32 * q^64 + 24 * q^70 - 4 * q^73 + 36 * q^76 - 16 * q^82 - 32 * q^85 - 24 * q^94 - 52 * q^97

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