LMFDB - Embedded newform 108.2.b.a.107.4

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:	$\Q(\sqrt{3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + x^{2} + 4 $ x^4 + x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.4
Root			$0.866025 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.2.b.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +2.23607i q^{5} -3.87298i q^{7} +(-2.59808 + 1.11803i) q^{8} +O(q^{10})$	\(q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +2.23607i q^{5} -3.87298i q^{7} +(-2.59808 + 1.11803i) q^{8} +(-2.50000 + 1.93649i) q^{10} +1.73205 q^{11} +2.00000 q^{13} +(4.33013 - 3.35410i) q^{14} +(-3.50000 - 1.93649i) q^{16} -4.47214i q^{17} +(-4.33013 - 1.11803i) q^{20} +(1.50000 + 1.93649i) q^{22} -6.92820 q^{23} +(1.73205 + 2.23607i) q^{26} +(7.50000 + 1.93649i) q^{28} -4.47214i q^{29} +3.87298i q^{31} +(-0.866025 - 5.59017i) q^{32} +(5.00000 - 3.87298i) q^{34} +8.66025 q^{35} -4.00000 q^{37} +(-2.50000 - 5.80948i) q^{40} +8.94427i q^{41} +7.74597i q^{43} +(-0.866025 + 3.35410i) q^{44} +(-6.00000 - 7.74597i) q^{46} -3.46410 q^{47} -8.00000 q^{49} +(-1.00000 + 3.87298i) q^{52} +2.23607i q^{53} +3.87298i q^{55} +(4.33013 + 10.0623i) q^{56} +(5.00000 - 3.87298i) q^{58} +3.46410 q^{59} -4.00000 q^{61} +(-4.33013 + 3.35410i) q^{62} +(5.50000 - 5.80948i) q^{64} +4.47214i q^{65} -7.74597i q^{67} +(8.66025 + 2.23607i) q^{68} +(7.50000 + 9.68246i) q^{70} -10.3923 q^{71} +5.00000 q^{73} +(-3.46410 - 4.47214i) q^{74} -6.70820i q^{77} +7.74597i q^{79} +(4.33013 - 7.82624i) q^{80} +(-10.0000 + 7.74597i) q^{82} +12.1244 q^{83} +10.0000 q^{85} +(-8.66025 + 6.70820i) q^{86} +(-4.50000 + 1.93649i) q^{88} -4.47214i q^{89} -7.74597i q^{91} +(3.46410 - 13.4164i) q^{92} +(-3.00000 - 3.87298i) q^{94} +11.0000 q^{97} +(-6.92820 - 8.94427i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4}+O(q^{10}) $ 4 * q - 2 * q^4	$ 4 q - 2 q^{4} - 10 q^{10} + 8 q^{13} - 14 q^{16} + 6 q^{22} + 30 q^{28} + 20 q^{34} - 16 q^{37} - 10 q^{40} - 24 q^{46} - 32 q^{49} - 4 q^{52} + 20 q^{58} - 16 q^{61} + 22 q^{64} + 30 q^{70} + 20 q^{73} - 40 q^{82} + 40 q^{85} - 18 q^{88} - 12 q^{94} + 44 q^{97}+O(q^{100}) $ 4 * q - 2 * q^4 - 10 * q^10 + 8 * q^13 - 14 * q^16 + 6 * q^22 + 30 * q^28 + 20 * q^34 - 16 * q^37 - 10 * q^40 - 24 * q^46 - 32 * q^49 - 4 * q^52 + 20 * q^58 - 16 * q^61 + 22 * q^64 + 30 * q^70 + 20 * q^73 - 40 * q^82 + 40 * q^85 - 18 * q^88 - 12 * q^94 + 44 * 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 $

$2$	0.866025	+	1.11803i	0.612372	+	0.790569i
$2$	0.866025	+	1.11803i	0.612372	+	0.790569i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	1.93649i	−0.250000	+	0.968246i
$5$			2.23607i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$5$			2.23607i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$		−	3.87298i		−	1.46385i	−0.681385	−	0.731925i	$-0.738622\pi$
$7$		−	3.87298i		−	1.46385i	0.681385	−	0.731925i	$-0.261378\pi$
$8$	−2.59808	+	1.11803i	−0.918559	+	0.395285i
$9$		0			0
$10$	−2.50000	+	1.93649i	−0.790569	+	0.612372i
$11$	1.73205			0.522233			0.261116	−	0.965307i	$-0.415909\pi$
$11$	1.73205			0.522233			0.261116	+	0.965307i	$0.415909\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	4.33013	−	3.35410i	1.15728	−	0.896421i
$15$		0			0
$16$	−3.50000	−	1.93649i	−0.875000	−	0.484123i
$17$		−	4.47214i		−	1.08465i	−0.840168	−	0.542326i	$-0.817544\pi$
$17$		−	4.47214i		−	1.08465i	0.840168	−	0.542326i	$-0.182456\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−4.33013	−	1.11803i	−0.968246	−	0.250000i
$21$		0			0
$22$	1.50000	+	1.93649i	0.319801	+	0.412861i
$23$	−6.92820			−1.44463			−0.722315	−	0.691564i	$-0.756922\pi$
$23$	−6.92820			−1.44463			−0.722315	+	0.691564i	$0.756922\pi$
$24$		0			0
$25$		0			0
$26$	1.73205	+	2.23607i	0.339683	+	0.438529i
$27$		0			0
$28$	7.50000	+	1.93649i	1.41737	+	0.365963i
$29$		−	4.47214i		−	0.830455i	−0.909718	−	0.415227i	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$		0			0
$31$			3.87298i			0.695608i	0.937567	+	0.347804i	$0.113073\pi$
$31$			3.87298i			0.695608i	−0.937567	+	0.347804i	$0.886927\pi$
$32$	−0.866025	−	5.59017i	−0.153093	−	0.988212i
$33$		0			0
$34$	5.00000	−	3.87298i	0.857493	−	0.664211i
$35$	8.66025			1.46385
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$		0			0
$40$	−2.50000	−	5.80948i	−0.395285	−	0.918559i
$41$			8.94427i			1.39686i	0.715678	+	0.698430i	$0.246118\pi$
$41$			8.94427i			1.39686i	−0.715678	+	0.698430i	$0.753882\pi$
$42$		0			0
$43$			7.74597i			1.18125i	0.806947	+	0.590624i	$0.201119\pi$
$43$			7.74597i			1.18125i	−0.806947	+	0.590624i	$0.798881\pi$
$44$	−0.866025	+	3.35410i	−0.130558	+	0.505650i
$45$		0			0
$46$	−6.00000	−	7.74597i	−0.884652	−	1.14208i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$		0			0
$49$	−8.00000			−1.14286
$50$		0			0
$51$		0			0
$52$	−1.00000	+	3.87298i	−0.138675	+	0.537086i
$53$			2.23607i			0.307148i	0.988137	+	0.153574i	$0.0490783\pi$
$53$			2.23607i			0.307148i	−0.988137	+	0.153574i	$0.950922\pi$
$54$		0			0
$55$			3.87298i			0.522233i
$56$	4.33013	+	10.0623i	0.578638	+	1.34463i
$57$		0			0
$58$	5.00000	−	3.87298i	0.656532	−	0.508548i
$59$	3.46410			0.450988			0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410			0.450988			0.225494	+	0.974245i	$0.427600\pi$
$60$		0			0
$61$	−4.00000			−0.512148			−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000			−0.512148			−0.256074	+	0.966657i	$0.582429\pi$
$62$	−4.33013	+	3.35410i	−0.549927	+	0.425971i
$63$		0			0
$64$	5.50000	−	5.80948i	0.687500	−	0.726184i
$65$			4.47214i			0.554700i
$66$		0			0
$67$		−	7.74597i		−	0.946320i	−0.880976	−	0.473160i	$-0.843113\pi$
$67$		−	7.74597i		−	0.946320i	0.880976	−	0.473160i	$-0.156887\pi$
$68$	8.66025	+	2.23607i	1.05021	+	0.271163i
$69$		0			0
$70$	7.50000	+	9.68246i	0.896421	+	1.15728i
$71$	−10.3923			−1.23334			−0.616670	−	0.787222i	$-0.711519\pi$
$71$	−10.3923			−1.23334			−0.616670	+	0.787222i	$0.711519\pi$
$72$		0			0
$73$	5.00000			0.585206			0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000			0.585206			0.292603	+	0.956234i	$0.405479\pi$
$74$	−3.46410	−	4.47214i	−0.402694	−	0.519875i
$75$		0			0
$76$		0			0
$77$		−	6.70820i		−	0.764471i
$78$		0			0
$79$			7.74597i			0.871489i	0.900070	+	0.435745i	$0.143515\pi$
$79$			7.74597i			0.871489i	−0.900070	+	0.435745i	$0.856485\pi$
$80$	4.33013	−	7.82624i	0.484123	−	0.875000i
$81$		0			0
$82$	−10.0000	+	7.74597i	−1.10432	+	0.855399i
$83$	12.1244			1.33082			0.665410	−	0.746478i	$-0.268257\pi$
$83$	12.1244			1.33082			0.665410	+	0.746478i	$0.268257\pi$
$84$		0			0
$85$	10.0000			1.08465
$86$	−8.66025	+	6.70820i	−0.933859	+	0.723364i
$87$		0			0
$88$	−4.50000	+	1.93649i	−0.479702	+	0.206431i
$89$		−	4.47214i		−	0.474045i	−0.971504	−	0.237023i	$-0.923828\pi$
$89$		−	4.47214i		−	0.474045i	0.971504	−	0.237023i	$-0.0761716\pi$
$90$		0			0
$91$		−	7.74597i		−	0.811998i
$92$	3.46410	−	13.4164i	0.361158	−	1.39876i
$93$		0			0
$94$	−3.00000	−	3.87298i	−0.309426	−	0.399468i
$95$		0			0
$96$		0			0
$97$	11.0000			1.11688			0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000			1.11688			0.558440	+	0.829545i	$0.311400\pi$
$98$	−6.92820	−	8.94427i	−0.699854	−	0.903508i
$99$		0			0
$100$		0			0
$101$			2.23607i			0.222497i	0.993793	+	0.111249i	$0.0354850\pi$
$101$			2.23607i			0.222497i	−0.993793	+	0.111249i	$0.964515\pi$
$102$		0			0
$103$		−	7.74597i		−	0.763233i	−0.924321	−	0.381616i	$-0.875368\pi$
$103$		−	7.74597i		−	0.763233i	0.924321	−	0.381616i	$-0.124632\pi$
$104$	−5.19615	+	2.23607i	−0.509525	+	0.219265i
$105$		0			0
$106$	−2.50000	+	1.93649i	−0.242821	+	0.188089i
$107$	−5.19615			−0.502331			−0.251166	−	0.967944i	$-0.580814\pi$
$107$	−5.19615			−0.502331			−0.251166	+	0.967944i	$0.580814\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	−4.33013	+	3.35410i	−0.412861	+	0.319801i
$111$		0			0
$112$	−7.50000	+	13.5554i	−0.708683	+	1.28087i
$113$		−	17.8885i		−	1.68281i	−0.540403	−	0.841406i	$-0.681728\pi$
$113$		−	17.8885i		−	1.68281i	0.540403	−	0.841406i	$-0.318272\pi$
$114$		0			0
$115$		−	15.4919i		−	1.44463i
$116$	8.66025	+	2.23607i	0.804084	+	0.207614i
$117$		0			0
$118$	3.00000	+	3.87298i	0.276172	+	0.356537i
$119$	−17.3205			−1.58777
$120$		0			0
$121$	−8.00000			−0.727273
$122$	−3.46410	−	4.47214i	−0.313625	−	0.404888i
$123$		0			0
$124$	−7.50000	−	1.93649i	−0.673520	−	0.173902i
$125$			11.1803i			1.00000i
$126$		0			0
$127$		−	11.6190i		−	1.03102i	−0.856885	−	0.515508i	$-0.827603\pi$
$127$		−	11.6190i		−	1.03102i	0.856885	−	0.515508i	$-0.172397\pi$
$128$	11.2583	+	1.11803i	0.995105	+	0.0988212i
$129$		0			0
$130$	−5.00000	+	3.87298i	−0.438529	+	0.339683i
$131$	19.0526			1.66463			0.832315	−	0.554303i	$-0.187015\pi$
$131$	19.0526			1.66463			0.832315	+	0.554303i	$0.187015\pi$
$132$		0			0
$133$		0			0
$134$	8.66025	−	6.70820i	0.748132	−	0.579501i
$135$		0			0
$136$	5.00000	+	11.6190i	0.428746	+	0.996317i
$137$		−	4.47214i		−	0.382080i	−0.981582	−	0.191040i	$-0.938814\pi$
$137$		−	4.47214i		−	0.382080i	0.981582	−	0.191040i	$-0.0611861\pi$
$138$		0			0
$139$			15.4919i			1.31401i	0.753887	+	0.657004i	$0.228177\pi$
$139$			15.4919i			1.31401i	−0.753887	+	0.657004i	$0.771823\pi$
$140$	−4.33013	+	16.7705i	−0.365963	+	1.41737i
$141$		0			0
$142$	−9.00000	−	11.6190i	−0.755263	−	0.975041i
$143$	3.46410			0.289683
$144$		0			0
$145$	10.0000			0.830455
$146$	4.33013	+	5.59017i	0.358364	+	0.462646i
$147$		0			0
$148$	2.00000	−	7.74597i	0.164399	−	0.636715i
$149$			2.23607i			0.183186i	0.995797	+	0.0915929i	$0.0291958\pi$
$149$			2.23607i			0.183186i	−0.995797	+	0.0915929i	$0.970804\pi$
$150$		0			0
$151$		−	3.87298i		−	0.315179i	−0.987505	−	0.157589i	$-0.949628\pi$
$151$		−	3.87298i		−	0.315179i	0.987505	−	0.157589i	$-0.0503723\pi$
$152$		0			0
$153$		0			0
$154$	7.50000	−	5.80948i	0.604367	−	0.468141i
$155$	−8.66025			−0.695608
$156$		0			0
$157$	20.0000			1.59617			0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000			1.59617			0.798087	+	0.602542i	$0.205846\pi$
$158$	−8.66025	+	6.70820i	−0.688973	+	0.533676i
$159$		0			0
$160$	12.5000	−	1.93649i	0.988212	−	0.153093i
$161$			26.8328i			2.11472i
$162$		0			0
$163$			23.2379i			1.82013i	0.414462	+	0.910066i	$0.363970\pi$
$163$			23.2379i			1.82013i	−0.414462	+	0.910066i	$0.636030\pi$
$164$	−17.3205	−	4.47214i	−1.35250	−	0.349215i
$165$		0			0
$166$	10.5000	+	13.5554i	0.814958	+	1.05211i
$167$	3.46410			0.268060			0.134030	−	0.990977i	$-0.457208\pi$
$167$	3.46410			0.268060			0.134030	+	0.990977i	$0.457208\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	8.66025	+	11.1803i	0.664211	+	0.857493i
$171$		0			0
$172$	−15.0000	−	3.87298i	−1.14374	−	0.295312i
$173$			15.6525i			1.19004i	0.803712	+	0.595018i	$0.202855\pi$
$173$			15.6525i			1.19004i	−0.803712	+	0.595018i	$0.797145\pi$
$174$		0			0
$175$		0			0
$176$	−6.06218	−	3.35410i	−0.456954	−	0.252825i
$177$		0			0
$178$	5.00000	−	3.87298i	0.374766	−	0.290292i
$179$	5.19615			0.388379			0.194189	−	0.980964i	$-0.437792\pi$
$179$	5.19615			0.388379			0.194189	+	0.980964i	$0.437792\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	8.66025	−	6.70820i	0.641941	−	0.497245i
$183$		0			0
$184$	18.0000	−	7.74597i	1.32698	−	0.571040i
$185$		−	8.94427i		−	0.657596i
$186$		0			0
$187$		−	7.74597i		−	0.566441i
$188$	1.73205	−	6.70820i	0.126323	−	0.489246i
$189$		0			0
$190$		0			0
$191$	17.3205			1.25327			0.626634	−	0.779314i	$-0.284432\pi$
$191$	17.3205			1.25327			0.626634	+	0.779314i	$0.284432\pi$
$192$		0			0
$193$	−25.0000			−1.79954			−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000			−1.79954			−0.899770	+	0.436365i	$0.856266\pi$
$194$	9.52628	+	12.2984i	0.683947	+	0.882972i
$195$		0			0
$196$	4.00000	−	15.4919i	0.285714	−	1.10657i
$197$		−	24.5967i		−	1.75245i	−0.481906	−	0.876223i	$-0.660055\pi$
$197$		−	24.5967i		−	1.75245i	0.481906	−	0.876223i	$-0.339945\pi$
$198$		0			0
$199$			11.6190i			0.823646i	0.911264	+	0.411823i	$0.135108\pi$
$199$			11.6190i			0.823646i	−0.911264	+	0.411823i	$0.864892\pi$
$200$		0			0
$201$		0			0
$202$	−2.50000	+	1.93649i	−0.175899	+	0.136251i
$203$	−17.3205			−1.21566
$204$		0			0
$205$	−20.0000			−1.39686
$206$	8.66025	−	6.70820i	0.603388	−	0.467383i
$207$		0			0
$208$	−7.00000	−	3.87298i	−0.485363	−	0.268543i
$209$		0			0
$210$		0			0
$211$			15.4919i			1.06651i	0.845955	+	0.533254i	$0.179031\pi$
$211$			15.4919i			1.06651i	−0.845955	+	0.533254i	$0.820969\pi$
$212$	−4.33013	−	1.11803i	−0.297394	−	0.0767869i
$213$		0			0
$214$	−4.50000	−	5.80948i	−0.307614	−	0.397128i
$215$	−17.3205			−1.18125
$216$		0			0
$217$	15.0000			1.01827
$218$	−3.46410	−	4.47214i	−0.234619	−	0.302891i
$219$		0			0
$220$	−7.50000	−	1.93649i	−0.505650	−	0.130558i
$221$		−	8.94427i		−	0.601657i
$222$		0			0
$223$			7.74597i			0.518708i	0.965782	+	0.259354i	$0.0835097\pi$
$223$			7.74597i			0.518708i	−0.965782	+	0.259354i	$0.916490\pi$
$224$	−21.6506	+	3.35410i	−1.44659	+	0.224105i
$225$		0			0
$226$	20.0000	−	15.4919i	1.33038	−	1.03051i
$227$	−3.46410			−0.229920			−0.114960	−	0.993370i	$-0.536674\pi$
$227$	−3.46410			−0.229920			−0.114960	+	0.993370i	$0.536674\pi$
$228$		0			0
$229$	2.00000			0.132164			0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000			0.132164			0.0660819	+	0.997814i	$0.478950\pi$
$230$	17.3205	−	13.4164i	1.14208	−	0.884652i
$231$		0			0
$232$	5.00000	+	11.6190i	0.328266	+	0.762821i
$233$		−	4.47214i		−	0.292979i	−0.989212	−	0.146490i	$-0.953202\pi$
$233$		−	4.47214i		−	0.292979i	0.989212	−	0.146490i	$-0.0467975\pi$
$234$		0			0
$235$		−	7.74597i		−	0.505291i
$236$	−1.73205	+	6.70820i	−0.112747	+	0.436667i
$237$		0			0
$238$	−15.0000	−	19.3649i	−0.972306	−	1.25524i
$239$	13.8564			0.896296			0.448148	−	0.893959i	$-0.352084\pi$
$239$	13.8564			0.896296			0.448148	+	0.893959i	$0.352084\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$	−6.92820	−	8.94427i	−0.445362	−	0.574960i
$243$		0			0
$244$	2.00000	−	7.74597i	0.128037	−	0.495885i
$245$		−	17.8885i		−	1.14286i
$246$		0			0
$247$		0			0
$248$	−4.33013	−	10.0623i	−0.274963	−	0.638957i
$249$		0			0
$250$	−12.5000	+	9.68246i	−0.790569	+	0.612372i
$251$	−10.3923			−0.655956			−0.327978	−	0.944685i	$-0.606367\pi$
$251$	−10.3923			−0.655956			−0.327978	+	0.944685i	$0.606367\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	12.9904	−	10.0623i	0.815089	−	0.631365i
$255$		0			0
$256$	8.50000	+	13.5554i	0.531250	+	0.847215i
$257$			22.3607i			1.39482i	0.716672	+	0.697410i	$0.245665\pi$
$257$			22.3607i			1.39482i	−0.716672	+	0.697410i	$0.754335\pi$
$258$		0			0
$259$			15.4919i			0.962622i
$260$	−8.66025	−	2.23607i	−0.537086	−	0.138675i
$261$		0			0
$262$	16.5000	+	21.3014i	1.01937	+	1.31601i
$263$	6.92820			0.427211			0.213606	−	0.976920i	$-0.431479\pi$
$263$	6.92820			0.427211			0.213606	+	0.976920i	$0.431479\pi$
$264$		0			0
$265$	−5.00000			−0.307148
$266$		0			0
$267$		0			0
$268$	15.0000	+	3.87298i	0.916271	+	0.236580i
$269$		−	4.47214i		−	0.272671i	−0.990663	−	0.136335i	$-0.956467\pi$
$269$		−	4.47214i		−	0.272671i	0.990663	−	0.136335i	$-0.0435325\pi$
$270$		0			0
$271$		−	11.6190i		−	0.705801i	−0.935661	−	0.352900i	$-0.885195\pi$
$271$		−	11.6190i		−	0.705801i	0.935661	−	0.352900i	$-0.114805\pi$
$272$	−8.66025	+	15.6525i	−0.525105	+	0.949071i
$273$		0			0
$274$	5.00000	−	3.87298i	0.302061	−	0.233975i
$275$		0			0
$276$		0			0
$277$	20.0000			1.20168			0.600842	−	0.799368i	$-0.294832\pi$
$277$	20.0000			1.20168			0.600842	+	0.799368i	$0.294832\pi$
$278$	−17.3205	+	13.4164i	−1.03882	+	0.804663i
$279$		0			0
$280$	−22.5000	+	9.68246i	−1.34463	+	0.578638i
$281$		−	4.47214i		−	0.266785i	−0.991063	−	0.133393i	$-0.957413\pi$
$281$		−	4.47214i		−	0.266785i	0.991063	−	0.133393i	$-0.0425871\pi$
$282$		0			0
$283$		−	30.9839i		−	1.84180i	−0.389799	−	0.920900i	$-0.627456\pi$
$283$		−	30.9839i		−	1.84180i	0.389799	−	0.920900i	$-0.372544\pi$
$284$	5.19615	−	20.1246i	0.308335	−	1.19418i
$285$		0			0
$286$	3.00000	+	3.87298i	0.177394	+	0.229014i
$287$	34.6410			2.04479
$288$		0			0
$289$	−3.00000			−0.176471
$290$	8.66025	+	11.1803i	0.508548	+	0.656532i
$291$		0			0
$292$	−2.50000	+	9.68246i	−0.146301	+	0.566623i
$293$			22.3607i			1.30632i	0.757218	+	0.653162i	$0.226558\pi$
$293$			22.3607i			1.30632i	−0.757218	+	0.653162i	$0.773442\pi$
$294$		0			0
$295$			7.74597i			0.450988i
$296$	10.3923	−	4.47214i	0.604040	−	0.259938i
$297$		0			0
$298$	−2.50000	+	1.93649i	−0.144821	+	0.112178i
$299$	−13.8564			−0.801337
$300$		0			0
$301$	30.0000			1.72917
$302$	4.33013	−	3.35410i	0.249171	−	0.193007i
$303$		0			0
$304$		0			0
$305$		−	8.94427i		−	0.512148i
$306$		0			0
$307$		−	23.2379i		−	1.32626i	−0.748506	−	0.663129i	$-0.769228\pi$
$307$		−	23.2379i		−	1.32626i	0.748506	−	0.663129i	$-0.230772\pi$
$308$	12.9904	+	3.35410i	0.740196	+	0.191118i
$309$		0			0
$310$	−7.50000	−	9.68246i	−0.425971	−	0.549927i
$311$	−27.7128			−1.57145			−0.785725	−	0.618576i	$-0.787710\pi$
$311$	−27.7128			−1.57145			−0.785725	+	0.618576i	$0.787710\pi$
$312$		0			0
$313$	5.00000			0.282617			0.141308	−	0.989966i	$-0.454869\pi$
$313$	5.00000			0.282617			0.141308	+	0.989966i	$0.454869\pi$
$314$	17.3205	+	22.3607i	0.977453	+	1.26189i
$315$		0			0
$316$	−15.0000	−	3.87298i	−0.843816	−	0.217872i
$317$			15.6525i			0.879131i	0.898211	+	0.439565i	$0.144867\pi$
$317$			15.6525i			0.879131i	−0.898211	+	0.439565i	$0.855133\pi$
$318$		0			0
$319$		−	7.74597i		−	0.433691i
$320$	12.9904	+	12.2984i	0.726184	+	0.687500i
$321$		0			0
$322$	−30.0000	+	23.2379i	−1.67183	+	1.29500i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	−25.9808	+	20.1246i	−1.43894	+	1.11460i
$327$		0			0
$328$	−10.0000	−	23.2379i	−0.552158	−	1.28310i
$329$			13.4164i			0.739671i
$330$		0			0
$331$			7.74597i			0.425757i	0.977079	+	0.212878i	$0.0682838\pi$
$331$			7.74597i			0.425757i	−0.977079	+	0.212878i	$0.931716\pi$
$332$	−6.06218	+	23.4787i	−0.332705	+	1.28856i
$333$		0			0
$334$	3.00000	+	3.87298i	0.164153	+	0.211920i
$335$	17.3205			0.946320
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	−7.79423	−	10.0623i	−0.423950	−	0.547317i
$339$		0			0
$340$	−5.00000	+	19.3649i	−0.271163	+	1.05021i
$341$			6.70820i			0.363270i
$342$		0			0
$343$			3.87298i			0.209121i
$344$	−8.66025	−	20.1246i	−0.466930	−	1.08505i
$345$		0			0
$346$	−17.5000	+	13.5554i	−0.940806	+	0.728745i
$347$	−32.9090			−1.76665			−0.883323	−	0.468765i	$-0.844699\pi$
$347$	−32.9090			−1.76665			−0.883323	+	0.468765i	$0.844699\pi$
$348$		0			0
$349$	−16.0000			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$350$		0			0
$351$		0			0
$352$	−1.50000	−	9.68246i	−0.0799503	−	0.516077i
$353$		−	17.8885i		−	0.952111i	−0.879415	−	0.476056i	$-0.842066\pi$
$353$		−	17.8885i		−	0.952111i	0.879415	−	0.476056i	$-0.157934\pi$
$354$		0			0
$355$		−	23.2379i		−	1.23334i
$356$	8.66025	+	2.23607i	0.458993	+	0.118511i
$357$		0			0
$358$	4.50000	+	5.80948i	0.237832	+	0.307040i
$359$	31.1769			1.64545			0.822727	−	0.568436i	$-0.192451\pi$
$359$	31.1769			1.64545			0.822727	+	0.568436i	$0.192451\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	−13.8564	−	17.8885i	−0.728277	−	0.940201i
$363$		0			0
$364$	15.0000	+	3.87298i	0.786214	+	0.202999i
$365$			11.1803i			0.585206i
$366$		0			0
$367$		−	27.1109i		−	1.41518i	−0.706625	−	0.707588i	$-0.749783\pi$
$367$		−	27.1109i		−	1.41518i	0.706625	−	0.707588i	$-0.250217\pi$
$368$	24.2487	+	13.4164i	1.26405	+	0.699379i
$369$		0			0
$370$	10.0000	−	7.74597i	0.519875	−	0.402694i
$371$	8.66025			0.449618
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	8.66025	−	6.70820i	0.447811	−	0.346873i
$375$		0			0
$376$	9.00000	−	3.87298i	0.464140	−	0.199734i
$377$		−	8.94427i		−	0.460653i
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	15.0000	+	19.3649i	0.767467	+	0.990795i
$383$	24.2487			1.23905			0.619526	−	0.784976i	$-0.287325\pi$
$383$	24.2487			1.23905			0.619526	+	0.784976i	$0.287325\pi$
$384$		0			0
$385$	15.0000			0.764471
$386$	−21.6506	−	27.9508i	−1.10199	−	1.42266i
$387$		0			0
$388$	−5.50000	+	21.3014i	−0.279220	+	1.08142i
$389$			2.23607i			0.113373i	0.998392	+	0.0566866i	$0.0180536\pi$
$389$			2.23607i			0.113373i	−0.998392	+	0.0566866i	$0.981946\pi$
$390$		0			0
$391$			30.9839i			1.56692i
$392$	20.7846	−	8.94427i	1.04978	−	0.451754i
$393$		0			0
$394$	27.5000	−	21.3014i	1.38543	−	1.07315i
$395$	−17.3205			−0.871489
$396$		0			0
$397$	14.0000			0.702640			0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000			0.702640			0.351320	+	0.936255i	$0.385733\pi$
$398$	−12.9904	+	10.0623i	−0.651149	+	0.504378i
$399$		0			0
$400$		0			0
$401$		−	17.8885i		−	0.893311i	−0.894706	−	0.446656i	$-0.852615\pi$
$401$		−	17.8885i		−	0.893311i	0.894706	−	0.446656i	$-0.147385\pi$
$402$		0			0
$403$			7.74597i			0.385854i
$404$	−4.33013	−	1.11803i	−0.215432	−	0.0556243i
$405$		0			0
$406$	−15.0000	−	19.3649i	−0.744438	−	0.961065i
$407$	−6.92820			−0.343418
$408$		0			0
$409$	−7.00000			−0.346128			−0.173064	−	0.984911i	$-0.555367\pi$
$409$	−7.00000			−0.346128			−0.173064	+	0.984911i	$0.555367\pi$
$410$	−17.3205	−	22.3607i	−0.855399	−	1.10432i
$411$		0			0
$412$	15.0000	+	3.87298i	0.738997	+	0.190808i
$413$		−	13.4164i		−	0.660178i
$414$		0			0
$415$			27.1109i			1.33082i
$416$	−1.73205	−	11.1803i	−0.0849208	−	0.548161i
$417$		0			0
$418$		0			0
$419$	−17.3205			−0.846162			−0.423081	−	0.906092i	$-0.639051\pi$
$419$	−17.3205			−0.846162			−0.423081	+	0.906092i	$0.639051\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−17.3205	+	13.4164i	−0.843149	+	0.653101i
$423$		0			0
$424$	−2.50000	−	5.80948i	−0.121411	−	0.282133i
$425$		0			0
$426$		0			0
$427$			15.4919i			0.749707i
$428$	2.59808	−	10.0623i	0.125583	−	0.486380i
$429$		0			0
$430$	−15.0000	−	19.3649i	−0.723364	−	0.933859i
$431$	−10.3923			−0.500580			−0.250290	−	0.968171i	$-0.580526\pi$
$431$	−10.3923			−0.500580			−0.250290	+	0.968171i	$0.580526\pi$
$432$		0			0
$433$	−13.0000			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$434$	12.9904	+	16.7705i	0.623558	+	0.805010i
$435$		0			0
$436$	2.00000	−	7.74597i	0.0957826	−	0.370965i
$437$		0			0
$438$		0			0
$439$		−	3.87298i		−	0.184847i	−0.995720	−	0.0924237i	$-0.970539\pi$
$439$		−	3.87298i		−	0.184847i	0.995720	−	0.0924237i	$-0.0294614\pi$
$440$	−4.33013	−	10.0623i	−0.206431	−	0.479702i
$441$		0			0
$442$	10.0000	−	7.74597i	0.475651	−	0.368438i
$443$	−24.2487			−1.15209			−0.576046	−	0.817418i	$-0.695405\pi$
$443$	−24.2487			−1.15209			−0.576046	+	0.817418i	$0.695405\pi$
$444$		0			0
$445$	10.0000			0.474045
$446$	−8.66025	+	6.70820i	−0.410075	+	0.317643i
$447$		0			0
$448$	−22.5000	−	21.3014i	−1.06303	−	1.00640i
$449$		−	17.8885i		−	0.844213i	−0.906546	−	0.422106i	$-0.861291\pi$
$449$		−	17.8885i		−	0.844213i	0.906546	−	0.422106i	$-0.138709\pi$
$450$		0			0
$451$			15.4919i			0.729487i
$452$	34.6410	+	8.94427i	1.62938	+	0.420703i
$453$		0			0
$454$	−3.00000	−	3.87298i	−0.140797	−	0.181768i
$455$	17.3205			0.811998
$456$		0			0
$457$	−31.0000			−1.45012			−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−31.0000			−1.45012			−0.725059	+	0.688686i	$0.758188\pi$
$458$	1.73205	+	2.23607i	0.0809334	+	0.104485i
$459$		0			0
$460$	30.0000	+	7.74597i	1.39876	+	0.361158i
$461$		−	38.0132i		−	1.77045i	−0.465164	−	0.885225i	$-0.654005\pi$
$461$		−	38.0132i		−	1.77045i	0.465164	−	0.885225i	$-0.345995\pi$
$462$		0			0
$463$			3.87298i			0.179993i	0.995942	+	0.0899964i	$0.0286856\pi$
$463$			3.87298i			0.179993i	−0.995942	+	0.0899964i	$0.971314\pi$
$464$	−8.66025	+	15.6525i	−0.402042	+	0.726648i
$465$		0			0
$466$	5.00000	−	3.87298i	0.231621	−	0.179412i
$467$	5.19615			0.240449			0.120225	−	0.992747i	$-0.461639\pi$
$467$	5.19615			0.240449			0.120225	+	0.992747i	$0.461639\pi$
$468$		0			0
$469$	−30.0000			−1.38527
$470$	8.66025	−	6.70820i	0.399468	−	0.309426i
$471$		0			0
$472$	−9.00000	+	3.87298i	−0.414259	+	0.178269i
$473$			13.4164i			0.616887i
$474$		0			0
$475$		0			0
$476$	8.66025	−	33.5410i	0.396942	−	1.53735i
$477$		0			0
$478$	12.0000	+	15.4919i	0.548867	+	0.708585i
$479$	17.3205			0.791394			0.395697	−	0.918381i	$-0.370503\pi$
$479$	17.3205			0.791394			0.395697	+	0.918381i	$0.370503\pi$
$480$		0			0
$481$	−8.00000			−0.364769
$482$	12.1244	+	15.6525i	0.552249	+	0.712951i
$483$		0			0
$484$	4.00000	−	15.4919i	0.181818	−	0.704179i
$485$			24.5967i			1.11688i
$486$		0			0
$487$		−	23.2379i		−	1.05301i	−0.850172	−	0.526505i	$-0.823502\pi$
$487$		−	23.2379i		−	1.05301i	0.850172	−	0.526505i	$-0.176498\pi$
$488$	10.3923	−	4.47214i	0.470438	−	0.202444i
$489$		0			0
$490$	20.0000	−	15.4919i	0.903508	−	0.699854i
$491$	8.66025			0.390832			0.195416	−	0.980720i	$-0.437394\pi$
$491$	8.66025			0.390832			0.195416	+	0.980720i	$0.437394\pi$
$492$		0			0
$493$	−20.0000			−0.900755
$494$		0			0
$495$		0			0
$496$	7.50000	−	13.5554i	0.336760	−	0.608657i
$497$			40.2492i			1.80542i
$498$		0			0
$499$			38.7298i			1.73379i	0.498495	+	0.866893i	$0.333886\pi$
$499$			38.7298i			1.73379i	−0.498495	+	0.866893i	$0.666114\pi$
$500$	−21.6506	−	5.59017i	−0.968246	−	0.250000i
$501$		0			0
$502$	−9.00000	−	11.6190i	−0.401690	−	0.518579i
$503$	−20.7846			−0.926740			−0.463370	−	0.886165i	$-0.653360\pi$
$503$	−20.7846			−0.926740			−0.463370	+	0.886165i	$0.653360\pi$
$504$		0			0
$505$	−5.00000			−0.222497
$506$	−10.3923	−	13.4164i	−0.461994	−	0.596432i
$507$		0			0
$508$	22.5000	+	5.80948i	0.998276	+	0.257754i
$509$		−	11.1803i		−	0.495560i	−0.968816	−	0.247780i	$-0.920299\pi$
$509$		−	11.1803i		−	0.495560i	0.968816	−	0.247780i	$-0.0797010\pi$
$510$		0			0
$511$		−	19.3649i		−	0.856653i
$512$	−7.79423	+	21.2426i	−0.344459	+	0.938801i
$513$		0			0
$514$	−25.0000	+	19.3649i	−1.10270	+	0.854150i
$515$	17.3205			0.763233
$516$		0			0
$517$	−6.00000			−0.263880
$518$	−17.3205	+	13.4164i	−0.761019	+	0.589483i
$519$		0			0
$520$	−5.00000	−	11.6190i	−0.219265	−	0.509525i
$521$			22.3607i			0.979639i	0.871824	+	0.489820i	$0.162937\pi$
$521$			22.3607i			0.979639i	−0.871824	+	0.489820i	$0.837063\pi$
$522$		0			0
$523$			23.2379i			1.01612i	0.861321	+	0.508061i	$0.169638\pi$
$523$			23.2379i			1.01612i	−0.861321	+	0.508061i	$0.830362\pi$
$524$	−9.52628	+	36.8951i	−0.416157	+	1.61177i
$525$		0			0
$526$	6.00000	+	7.74597i	0.261612	+	0.337740i
$527$	17.3205			0.754493
$528$		0			0
$529$	25.0000			1.08696
$530$	−4.33013	−	5.59017i	−0.188089	−	0.242821i
$531$		0			0
$532$		0			0
$533$			17.8885i			0.774839i
$534$		0			0
$535$		−	11.6190i		−	0.502331i
$536$	8.66025	+	20.1246i	0.374066	+	0.869251i
$537$		0			0
$538$	5.00000	−	3.87298i	0.215565	−	0.166976i
$539$	−13.8564			−0.596838
$540$		0			0
$541$	−4.00000			−0.171973			−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000			−0.171973			−0.0859867	+	0.996296i	$0.527404\pi$
$542$	12.9904	−	10.0623i	0.557985	−	0.432213i
$543$		0			0
$544$	−25.0000	+	3.87298i	−1.07187	+	0.166053i
$545$		−	8.94427i		−	0.383131i
$546$		0			0
$547$			7.74597i			0.331194i	0.986194	+	0.165597i	$0.0529550\pi$
$547$			7.74597i			0.331194i	−0.986194	+	0.165597i	$0.947045\pi$
$548$	8.66025	+	2.23607i	0.369948	+	0.0955201i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	30.0000			1.27573
$554$	17.3205	+	22.3607i	0.735878	+	0.950014i
$555$		0			0
$556$	−30.0000	−	7.74597i	−1.27228	−	0.328502i
$557$			15.6525i			0.663217i	0.943417	+	0.331608i	$0.107591\pi$
$557$			15.6525i			0.663217i	−0.943417	+	0.331608i	$0.892409\pi$
$558$		0			0
$559$			15.4919i			0.655239i
$560$	−30.3109	−	16.7705i	−1.28087	−	0.708683i
$561$		0			0
$562$	5.00000	−	3.87298i	0.210912	−	0.163372i
$563$	19.0526			0.802970			0.401485	−	0.915866i	$-0.368494\pi$
$563$	19.0526			0.802970			0.401485	+	0.915866i	$0.368494\pi$
$564$		0			0
$565$	40.0000			1.68281
$566$	34.6410	−	26.8328i	1.45607	−	1.12787i
$567$		0			0
$568$	27.0000	−	11.6190i	1.13289	−	0.487520i
$569$			35.7771i			1.49985i	0.661521	+	0.749927i	$0.269911\pi$
$569$			35.7771i			1.49985i	−0.661521	+	0.749927i	$0.730089\pi$
$570$		0			0
$571$		−	7.74597i		−	0.324159i	−0.986778	−	0.162079i	$-0.948180\pi$
$571$		−	7.74597i		−	0.324159i	0.986778	−	0.162079i	$-0.0518200\pi$
$572$	−1.73205	+	6.70820i	−0.0724207	+	0.280484i
$573$		0			0
$574$	30.0000	+	38.7298i	1.25218	+	1.61655i
$575$		0			0
$576$		0			0
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$	−2.59808	−	3.35410i	−0.108066	−	0.139512i
$579$		0			0
$580$	−5.00000	+	19.3649i	−0.207614	+	0.804084i
$581$		−	46.9574i		−	1.94812i
$582$		0			0
$583$			3.87298i			0.160403i
$584$	−12.9904	+	5.59017i	−0.537546	+	0.231323i
$585$		0			0
$586$	−25.0000	+	19.3649i	−1.03274	+	0.799957i
$587$	−19.0526			−0.786383			−0.393192	−	0.919457i	$-0.628629\pi$
$587$	−19.0526			−0.786383			−0.393192	+	0.919457i	$0.628629\pi$
$588$		0			0
$589$		0			0
$590$	−8.66025	+	6.70820i	−0.356537	+	0.276172i
$591$		0			0
$592$	14.0000	+	7.74597i	0.575396	+	0.318357i
$593$		−	4.47214i		−	0.183649i	−0.995775	−	0.0918243i	$-0.970730\pi$
$593$		−	4.47214i		−	0.183649i	0.995775	−	0.0918243i	$-0.0292698\pi$
$594$		0			0
$595$		−	38.7298i		−	1.58777i
$596$	−4.33013	−	1.11803i	−0.177369	−	0.0457965i
$597$		0			0
$598$	−12.0000	−	15.4919i	−0.490716	−	0.633512i
$599$	−17.3205			−0.707697			−0.353848	−	0.935303i	$-0.615127\pi$
$599$	−17.3205			−0.707697			−0.353848	+	0.935303i	$0.615127\pi$
$600$		0			0
$601$	−31.0000			−1.26452			−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000			−1.26452			−0.632258	+	0.774758i	$0.717872\pi$
$602$	25.9808	+	33.5410i	1.05890	+	1.36703i
$603$		0			0
$604$	7.50000	+	1.93649i	0.305171	+	0.0787947i
$605$		−	17.8885i		−	0.727273i
$606$		0			0
$607$		−	7.74597i		−	0.314399i	−0.987567	−	0.157200i	$-0.949753\pi$
$607$		−	7.74597i		−	0.314399i	0.987567	−	0.157200i	$-0.0502466\pi$
$608$		0			0
$609$		0			0
$610$	10.0000	−	7.74597i	0.404888	−	0.313625i
$611$	−6.92820			−0.280285
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$	25.9808	−	20.1246i	1.04850	−	0.812163i
$615$		0			0
$616$	7.50000	+	17.4284i	0.302184	+	0.702211i
$617$		−	17.8885i		−	0.720166i	−0.932920	−	0.360083i	$-0.882748\pi$
$617$		−	17.8885i		−	0.720166i	0.932920	−	0.360083i	$-0.117252\pi$
$618$		0			0
$619$		−	38.7298i		−	1.55668i	−0.627841	−	0.778342i	$-0.716061\pi$
$619$		−	38.7298i		−	1.55668i	0.627841	−	0.778342i	$-0.283939\pi$
$620$	4.33013	−	16.7705i	0.173902	−	0.673520i
$621$		0			0
$622$	−24.0000	−	30.9839i	−0.962312	−	1.24234i
$623$	−17.3205			−0.693932
$624$		0			0
$625$	−25.0000			−1.00000
$626$	4.33013	+	5.59017i	0.173067	+	0.223428i
$627$		0			0
$628$	−10.0000	+	38.7298i	−0.399043	+	1.54549i
$629$			17.8885i			0.713263i
$630$		0			0
$631$		−	34.8569i		−	1.38763i	−0.720154	−	0.693815i	$-0.755929\pi$
$631$		−	34.8569i		−	1.38763i	0.720154	−	0.693815i	$-0.244071\pi$
$632$	−8.66025	−	20.1246i	−0.344486	−	0.800514i
$633$		0			0
$634$	−17.5000	+	13.5554i	−0.695014	+	0.538355i
$635$	25.9808			1.03102
$636$		0			0
$637$	−16.0000			−0.633943
$638$	8.66025	−	6.70820i	0.342863	−	0.265580i
$639$		0			0
$640$	−2.50000	+	25.1744i	−0.0988212	+	0.995105i
$641$		−	44.7214i		−	1.76639i	−0.469008	−	0.883194i	$-0.655389\pi$
$641$		−	44.7214i		−	1.76639i	0.469008	−	0.883194i	$-0.344611\pi$
$642$		0			0
$643$		−	30.9839i		−	1.22188i	−0.791675	−	0.610942i	$-0.790791\pi$
$643$		−	30.9839i		−	1.22188i	0.791675	−	0.610942i	$-0.209209\pi$
$644$	−51.9615	−	13.4164i	−2.04757	−	0.528681i
$645$		0			0
$646$		0			0
$647$	20.7846			0.817127			0.408564	−	0.912730i	$-0.366030\pi$
$647$	20.7846			0.817127			0.408564	+	0.912730i	$0.366030\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$		0			0
$651$		0			0
$652$	−45.0000	−	11.6190i	−1.76234	−	0.455033i
$653$		−	11.1803i		−	0.437521i	−0.975779	−	0.218760i	$-0.929799\pi$
$653$		−	11.1803i		−	0.437521i	0.975779	−	0.218760i	$-0.0702013\pi$
$654$		0			0
$655$			42.6028i			1.66463i
$656$	17.3205	−	31.3050i	0.676252	−	1.22225i
$657$		0			0
$658$	−15.0000	+	11.6190i	−0.584761	+	0.452954i
$659$	−8.66025			−0.337356			−0.168678	−	0.985671i	$-0.553950\pi$
$659$	−8.66025			−0.337356			−0.168678	+	0.985671i	$0.553950\pi$
$660$		0			0
$661$	−16.0000			−0.622328			−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000			−0.622328			−0.311164	+	0.950356i	$0.600719\pi$
$662$	−8.66025	+	6.70820i	−0.336590	+	0.260722i
$663$		0			0
$664$	−31.5000	+	13.5554i	−1.22244	+	0.526053i
$665$		0			0
$666$		0			0
$667$			30.9839i			1.19970i
$668$	−1.73205	+	6.70820i	−0.0670151	+	0.259548i
$669$		0			0
$670$	15.0000	+	19.3649i	0.579501	+	0.748132i
$671$	−6.92820			−0.267460
$672$		0			0
$673$	23.0000			0.886585			0.443292	−	0.896377i	$-0.353810\pi$
$673$	23.0000			0.886585			0.443292	+	0.896377i	$0.353810\pi$
$674$	−8.66025	−	11.1803i	−0.333581	−	0.430651i
$675$		0			0
$676$	4.50000	−	17.4284i	0.173077	−	0.670324i
$677$			22.3607i			0.859391i	0.902974	+	0.429695i	$0.141379\pi$
$677$			22.3607i			0.859391i	−0.902974	+	0.429695i	$0.858621\pi$
$678$		0			0
$679$		−	42.6028i		−	1.63495i
$680$	−25.9808	+	11.1803i	−0.996317	+	0.428746i
$681$		0			0
$682$	−7.50000	+	5.80948i	−0.287190	+	0.222456i
$683$	10.3923			0.397650			0.198825	−	0.980035i	$-0.436287\pi$
$683$	10.3923			0.397650			0.198825	+	0.980035i	$0.436287\pi$
$684$		0			0
$685$	10.0000			0.382080
$686$	−4.33013	+	3.35410i	−0.165325	+	0.128060i
$687$		0			0
$688$	15.0000	−	27.1109i	0.571870	−	1.03359i
$689$			4.47214i			0.170375i
$690$		0			0
$691$		−	15.4919i		−	0.589341i	−0.955599	−	0.294670i	$-0.904790\pi$
$691$		−	15.4919i		−	0.589341i	0.955599	−	0.294670i	$-0.0952099\pi$
$692$	−30.3109	−	7.82624i	−1.15225	−	0.297509i
$693$		0			0
$694$	−28.5000	−	36.7933i	−1.08185	−	1.39666i
$695$	−34.6410			−1.31401
$696$		0			0
$697$	40.0000			1.51511
$698$	−13.8564	−	17.8885i	−0.524473	−	0.677091i
$699$		0			0
$700$		0			0
$701$			15.6525i			0.591186i	0.955314	+	0.295593i	$0.0955172\pi$
$701$			15.6525i			0.591186i	−0.955314	+	0.295593i	$0.904483\pi$
$702$		0			0
$703$		0			0
$704$	9.52628	−	10.0623i	0.359035	−	0.379237i
$705$		0			0
$706$	20.0000	−	15.4919i	0.752710	−	0.583047i
$707$	8.66025			0.325702
$708$		0			0
$709$	32.0000			1.20179			0.600893	−	0.799330i	$-0.294812\pi$
$709$	32.0000			1.20179			0.600893	+	0.799330i	$0.294812\pi$
$710$	25.9808	−	20.1246i	0.975041	−	0.755263i
$711$		0			0
$712$	5.00000	+	11.6190i	0.187383	+	0.435439i
$713$		−	26.8328i		−	1.00490i
$714$		0			0
$715$			7.74597i			0.289683i
$716$	−2.59808	+	10.0623i	−0.0970947	+	0.376046i
$717$		0			0
$718$	27.0000	+	34.8569i	1.00763	+	1.30085i
$719$	−20.7846			−0.775135			−0.387568	−	0.921841i	$-0.626685\pi$
$719$	−20.7846			−0.775135			−0.387568	+	0.921841i	$0.626685\pi$
$720$		0			0
$721$	−30.0000			−1.11726
$722$	16.4545	+	21.2426i	0.612372	+	0.790569i
$723$		0			0
$724$	8.00000	−	30.9839i	0.297318	−	1.15151i
$725$		0			0
$726$		0			0
$727$			42.6028i			1.58005i	0.613074	+	0.790026i	$0.289933\pi$
$727$			42.6028i			1.58005i	−0.613074	+	0.790026i	$0.710067\pi$
$728$	8.66025	+	20.1246i	0.320970	+	0.745868i
$729$		0			0
$730$	−12.5000	+	9.68246i	−0.462646	+	0.358364i
$731$	34.6410			1.28124
$732$		0			0
$733$	8.00000			0.295487			0.147743	−	0.989026i	$-0.452799\pi$
$733$	8.00000			0.295487			0.147743	+	0.989026i	$0.452799\pi$
$734$	30.3109	−	23.4787i	1.11880	−	0.866615i
$735$		0			0
$736$	6.00000	+	38.7298i	0.221163	+	1.42760i
$737$		−	13.4164i		−	0.494200i
$738$		0			0
$739$		−	23.2379i		−	0.854820i	−0.904058	−	0.427410i	$-0.859426\pi$
$739$		−	23.2379i		−	0.854820i	0.904058	−	0.427410i	$-0.140574\pi$
$740$	17.3205	+	4.47214i	0.636715	+	0.164399i
$741$		0			0
$742$	7.50000	+	9.68246i	0.275334	+	0.355454i
$743$	24.2487			0.889599			0.444799	−	0.895630i	$-0.353275\pi$
$743$	24.2487			0.889599			0.444799	+	0.895630i	$0.353275\pi$
$744$		0			0
$745$	−5.00000			−0.183186
$746$	−8.66025	−	11.1803i	−0.317074	−	0.409341i
$747$		0			0
$748$	15.0000	+	3.87298i	0.548454	+	0.141610i
$749$			20.1246i			0.735337i
$750$		0			0
$751$			3.87298i			0.141327i	0.997500	+	0.0706636i	$0.0225117\pi$
$751$			3.87298i			0.141327i	−0.997500	+	0.0706636i	$0.977488\pi$
$752$	12.1244	+	6.70820i	0.442130	+	0.244623i
$753$		0			0
$754$	10.0000	−	7.74597i	0.364179	−	0.282091i
$755$	8.66025			0.315179
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	17.8885i		−	0.648459i	−0.945978	−	0.324230i	$-0.894895\pi$
$761$		−	17.8885i		−	0.648459i	0.945978	−	0.324230i	$-0.105105\pi$
$762$		0			0
$763$			15.4919i			0.560846i
$764$	−8.66025	+	33.5410i	−0.313317	+	1.21347i
$765$		0			0
$766$	21.0000	+	27.1109i	0.758761	+	0.979556i
$767$	6.92820			0.250163
$768$		0			0
$769$	11.0000			0.396670			0.198335	−	0.980134i	$-0.436447\pi$
$769$	11.0000			0.396670			0.198335	+	0.980134i	$0.436447\pi$
$770$	12.9904	+	16.7705i	0.468141	+	0.604367i
$771$		0			0
$772$	12.5000	−	48.4123i	0.449885	−	1.74240i
$773$		−	4.47214i		−	0.160852i	−0.996761	−	0.0804258i	$-0.974372\pi$
$773$		−	4.47214i		−	0.160852i	0.996761	−	0.0804258i	$-0.0256280\pi$
$774$		0			0
$775$		0			0
$776$	−28.5788	+	12.2984i	−1.02592	+	0.441486i
$777$		0			0
$778$	−2.50000	+	1.93649i	−0.0896293	+	0.0694266i
$779$		0			0
$780$		0			0
$781$	−18.0000			−0.644091
$782$	−34.6410	+	26.8328i	−1.23876	+	0.959540i
$783$		0			0
$784$	28.0000	+	15.4919i	1.00000	+	0.553283i
$785$			44.7214i			1.59617i
$786$		0			0
$787$			15.4919i			0.552228i	0.961125	+	0.276114i	$0.0890467\pi$
$787$			15.4919i			0.552228i	−0.961125	+	0.276114i	$0.910953\pi$
$788$	47.6314	+	12.2984i	1.69680	+	0.438111i
$789$		0			0
$790$	−15.0000	−	19.3649i	−0.533676	−	0.688973i
$791$	−69.2820			−2.46339
$792$		0			0
$793$	−8.00000			−0.284088
$794$	12.1244	+	15.6525i	0.430277	+	0.555486i
$795$		0			0
$796$	−22.5000	−	5.80948i	−0.797491	−	0.205911i
$797$			42.4853i			1.50491i	0.658646	+	0.752453i	$0.271130\pi$
$797$			42.4853i			1.50491i	−0.658646	+	0.752453i	$0.728870\pi$
$798$		0			0
$799$			15.4919i			0.548065i
$800$		0			0
$801$		0			0
$802$	20.0000	−	15.4919i	0.706225	−	0.547039i
$803$	8.66025			0.305614
$804$		0			0
$805$	−60.0000			−2.11472
$806$	−8.66025	+	6.70820i	−0.305044	+	0.236286i
$807$		0			0
$808$	−2.50000	−	5.80948i	−0.0879497	−	0.204377i
$809$		−	4.47214i		−	0.157232i	−0.996905	−	0.0786160i	$-0.974950\pi$
$809$		−	4.47214i		−	0.157232i	0.996905	−	0.0786160i	$-0.0250501\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	8.66025	−	33.5410i	0.303915	−	1.17706i
$813$		0			0
$814$	−6.00000	−	7.74597i	−0.210300	−	0.271496i
$815$	−51.9615			−1.82013
$816$		0			0
$817$		0			0
$818$	−6.06218	−	7.82624i	−0.211959	−	0.273638i
$819$		0			0
$820$	10.0000	−	38.7298i	0.349215	−	1.35250i
$821$		−	4.47214i		−	0.156079i	−0.996950	−	0.0780393i	$-0.975134\pi$
$821$		−	4.47214i		−	0.156079i	0.996950	−	0.0780393i	$-0.0248660\pi$
$822$		0			0
$823$			27.1109i			0.945026i	0.881324	+	0.472513i	$0.156653\pi$
$823$			27.1109i			0.945026i	−0.881324	+	0.472513i	$0.843347\pi$
$824$	8.66025	+	20.1246i	0.301694	+	0.701074i
$825$		0			0
$826$	15.0000	−	11.6190i	0.521917	−	0.404275i
$827$	31.1769			1.08413			0.542064	−	0.840337i	$-0.317643\pi$
$827$	31.1769			1.08413			0.542064	+	0.840337i	$0.317643\pi$
$828$		0			0
$829$	38.0000			1.31979			0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000			1.31979			0.659897	+	0.751356i	$0.270600\pi$
$830$	−30.3109	+	23.4787i	−1.05211	+	0.814958i
$831$		0			0
$832$	11.0000	−	11.6190i	0.381356	−	0.402815i
$833$			35.7771i			1.23960i
$834$		0			0
$835$			7.74597i			0.268060i
$836$		0			0
$837$		0			0
$838$	−15.0000	−	19.3649i	−0.518166	−	0.668950i
$839$	38.1051			1.31553			0.657767	−	0.753221i	$-0.271501\pi$
$839$	38.1051			1.31553			0.657767	+	0.753221i	$0.271501\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	−3.46410	−	4.47214i	−0.119381	−	0.154120i
$843$		0			0
$844$	−30.0000	−	7.74597i	−1.03264	−	0.266627i
$845$		−	20.1246i		−	0.692308i
$846$		0			0
$847$			30.9839i			1.06462i
$848$	4.33013	−	7.82624i	0.148697	−	0.268754i
$849$		0			0
$850$		0			0
$851$	27.7128			0.949983
$852$		0			0
$853$	2.00000			0.0684787			0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000			0.0684787			0.0342393	+	0.999414i	$0.489099\pi$
$854$	−17.3205	+	13.4164i	−0.592696	+	0.459100i
$855$		0			0
$856$	13.5000	−	5.80948i	0.461421	−	0.198564i
$857$		−	4.47214i		−	0.152765i	−0.997079	−	0.0763826i	$-0.975663\pi$
$857$		−	4.47214i		−	0.152765i	0.997079	−	0.0763826i	$-0.0243370\pi$
$858$		0			0
$859$			15.4919i			0.528578i	0.964444	+	0.264289i	$0.0851373\pi$
$859$			15.4919i			0.528578i	−0.964444	+	0.264289i	$0.914863\pi$
$860$	8.66025	−	33.5410i	0.295312	−	1.14374i
$861$		0			0
$862$	−9.00000	−	11.6190i	−0.306541	−	0.395743i
$863$	20.7846			0.707516			0.353758	−	0.935337i	$-0.384904\pi$
$863$	20.7846			0.707516			0.353758	+	0.935337i	$0.384904\pi$
$864$		0			0
$865$	−35.0000			−1.19004
$866$	−11.2583	−	14.5344i	−0.382574	−	0.493900i
$867$		0			0
$868$	−7.50000	+	29.0474i	−0.254567	+	0.985932i
$869$			13.4164i			0.455120i
$870$		0			0
$871$		−	15.4919i		−	0.524924i
$872$	10.3923	−	4.47214i	0.351928	−	0.151446i
$873$		0			0
$874$		0			0
$875$	43.3013			1.46385
$876$		0			0
$877$	−34.0000			−1.14810			−0.574049	−	0.818821i	$-0.694628\pi$
$877$	−34.0000			−1.14810			−0.574049	+	0.818821i	$0.694628\pi$
$878$	4.33013	−	3.35410i	0.146135	−	0.113195i
$879$		0			0
$880$	7.50000	−	13.5554i	0.252825	−	0.456954i
$881$			22.3607i			0.753350i	0.926345	+	0.376675i	$0.122933\pi$
$881$			22.3607i			0.753350i	−0.926345	+	0.376675i	$0.877067\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	17.3205	+	4.47214i	0.582552	+	0.150414i
$885$		0			0
$886$	−21.0000	−	27.1109i	−0.705509	−	0.910808i
$887$	−38.1051			−1.27944			−0.639722	−	0.768606i	$-0.720951\pi$
$887$	−38.1051			−1.27944			−0.639722	+	0.768606i	$0.720951\pi$
$888$		0			0
$889$	−45.0000			−1.50925
$890$	8.66025	+	11.1803i	0.290292	+	0.374766i
$891$		0			0
$892$	−15.0000	−	3.87298i	−0.502237	−	0.129677i
$893$		0			0
$894$		0			0
$895$			11.6190i			0.388379i
$896$	4.33013	−	43.6033i	0.144659	−	1.45668i
$897$		0			0
$898$	20.0000	−	15.4919i	0.667409	−	0.516973i
$899$	17.3205			0.577671
$900$		0			0
$901$	10.0000			0.333148
$902$	−17.3205	+	13.4164i	−0.576710	+	0.446718i
$903$		0			0
$904$	20.0000	+	46.4758i	0.665190	+	1.54576i
$905$		−	35.7771i		−	1.18927i
$906$		0			0
$907$		−	15.4919i		−	0.514401i	−0.966358	−	0.257201i	$-0.917200\pi$
$907$		−	15.4919i		−	0.514401i	0.966358	−	0.257201i	$-0.0828001\pi$
$908$	1.73205	−	6.70820i	0.0574801	−	0.222620i
$909$		0			0
$910$	15.0000	+	19.3649i	0.497245	+	0.641941i
$911$	−45.0333			−1.49202			−0.746010	−	0.665934i	$-0.768033\pi$
$911$	−45.0333			−1.49202			−0.746010	+	0.665934i	$0.768033\pi$
$912$		0			0
$913$	21.0000			0.694999
$914$	−26.8468	−	34.6591i	−0.888013	−	1.14642i
$915$		0			0
$916$	−1.00000	+	3.87298i	−0.0330409	+	0.127967i
$917$		−	73.7902i		−	2.43677i
$918$		0			0
$919$			11.6190i			0.383274i	0.981466	+	0.191637i	$0.0613796\pi$
$919$			11.6190i			0.383274i	−0.981466	+	0.191637i	$0.938620\pi$
$920$	17.3205	+	40.2492i	0.571040	+	1.32698i
$921$		0			0
$922$	42.5000	−	32.9204i	1.39966	−	1.08417i
$923$	−20.7846			−0.684134
$924$		0			0
$925$		0			0
$926$	−4.33013	+	3.35410i	−0.142297	+	0.110223i
$927$		0			0
$928$	−25.0000	+	3.87298i	−0.820665	+	0.127137i
$929$		−	44.7214i		−	1.46726i	−0.679549	−	0.733630i	$-0.737825\pi$
$929$		−	44.7214i		−	1.46726i	0.679549	−	0.733630i	$-0.262175\pi$
$930$		0			0
$931$		0			0
$932$	8.66025	+	2.23607i	0.283676	+	0.0732448i
$933$		0			0
$934$	4.50000	+	5.80948i	0.147244	+	0.190092i
$935$	17.3205			0.566441
$936$		0			0
$937$	−31.0000			−1.01273			−0.506363	−	0.862320i	$-0.669010\pi$
$937$	−31.0000			−1.01273			−0.506363	+	0.862320i	$0.669010\pi$
$938$	−25.9808	−	33.5410i	−0.848302	−	1.09515i
$939$		0			0
$940$	15.0000	+	3.87298i	0.489246	+	0.126323i
$941$			42.4853i			1.38498i	0.721427	+	0.692490i	$0.243487\pi$
$941$			42.4853i			1.38498i	−0.721427	+	0.692490i	$0.756513\pi$
$942$		0			0
$943$		−	61.9677i		−	2.01795i
$944$	−12.1244	−	6.70820i	−0.394614	−	0.218333i
$945$		0			0
$946$	−15.0000	+	11.6190i	−0.487692	+	0.377765i
$947$	−50.2295			−1.63224			−0.816119	−	0.577883i	$-0.803879\pi$
$947$	−50.2295			−1.63224			−0.816119	+	0.577883i	$0.803879\pi$
$948$		0			0
$949$	10.0000			0.324614
$950$		0			0
$951$		0			0
$952$	45.0000	−	19.3649i	1.45846	−	0.627621i
$953$			35.7771i			1.15893i	0.814996	+	0.579467i	$0.196739\pi$
$953$			35.7771i			1.15893i	−0.814996	+	0.579467i	$0.803261\pi$
$954$		0			0
$955$			38.7298i			1.25327i
$956$	−6.92820	+	26.8328i	−0.224074	+	0.867835i
$957$		0			0
$958$	15.0000	+	19.3649i	0.484628	+	0.625652i
$959$	−17.3205			−0.559308
$960$		0			0
$961$	16.0000			0.516129
$962$	−6.92820	−	8.94427i	−0.223374	−	0.288375i
$963$		0			0
$964$	−7.00000	+	27.1109i	−0.225455	+	0.873183i
$965$		−	55.9017i		−	1.79954i
$966$		0			0
$967$			27.1109i			0.871827i	0.899989	+	0.435914i	$0.143575\pi$
$967$			27.1109i			0.871827i	−0.899989	+	0.435914i	$0.856425\pi$
$968$	20.7846	−	8.94427i	0.668043	−	0.287480i
$969$		0			0
$970$	−27.5000	+	21.3014i	−0.882972	+	0.683947i
$971$	36.3731			1.16727			0.583634	−	0.812017i	$-0.301630\pi$
$971$	36.3731			1.16727			0.583634	+	0.812017i	$0.301630\pi$
$972$		0			0
$973$	60.0000			1.92351
$974$	25.9808	−	20.1246i	0.832477	−	0.644834i
$975$		0			0
$976$	14.0000	+	7.74597i	0.448129	+	0.247942i
$977$			49.1935i			1.57384i	0.617055	+	0.786920i	$0.288325\pi$
$977$			49.1935i			1.57384i	−0.617055	+	0.786920i	$0.711675\pi$
$978$		0			0
$979$		−	7.74597i		−	0.247562i
$980$	34.6410	+	8.94427i	1.10657	+	0.285714i
$981$		0			0
$982$	7.50000	+	9.68246i	0.239335	+	0.308980i
$983$	−24.2487			−0.773414			−0.386707	−	0.922203i	$-0.626387\pi$
$983$	−24.2487			−0.773414			−0.386707	+	0.922203i	$0.626387\pi$
$984$		0			0
$985$	55.0000			1.75245
$986$	−17.3205	−	22.3607i	−0.551597	−	0.712109i
$987$		0			0
$988$		0			0
$989$		−	53.6656i		−	1.70647i
$990$		0			0
$991$		−	11.6190i		−	0.369088i	−0.982824	−	0.184544i	$-0.940919\pi$
$991$		−	11.6190i		−	0.369088i	0.982824	−	0.184544i	$-0.0590808\pi$
$992$	21.6506	−	3.35410i	0.687408	−	0.106493i
$993$		0			0
$994$	−45.0000	+	34.8569i	−1.42731	+	1.10559i
$995$	−25.9808			−0.823646
$996$		0			0
$997$	14.0000			0.443384			0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000			0.443384			0.221692	+	0.975117i	$0.428842\pi$
$998$	−43.3013	+	33.5410i	−1.37068	+	1.06172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.b.a.107.4	yes	4
3.2	odd	2	inner	108.2.b.a.107.1	✓	4
4.3	odd	2	inner	108.2.b.a.107.2	yes	4
8.3	odd	2		1728.2.c.c.1727.2		4
8.5	even	2		1728.2.c.c.1727.1		4
9.2	odd	6		324.2.h.d.215.2		8
9.4	even	3		324.2.h.d.107.1		8
9.5	odd	6		324.2.h.d.107.4		8
9.7	even	3		324.2.h.d.215.3		8
12.11	even	2	inner	108.2.b.a.107.3	yes	4
24.5	odd	2		1728.2.c.c.1727.3		4
24.11	even	2		1728.2.c.c.1727.4		4
36.7	odd	6		324.2.h.d.215.4		8
36.11	even	6		324.2.h.d.215.1		8
36.23	even	6		324.2.h.d.107.3		8
36.31	odd	6		324.2.h.d.107.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.b.a.107.1	✓	4	3.2	odd	2	inner
108.2.b.a.107.2	yes	4	4.3	odd	2	inner
108.2.b.a.107.3	yes	4	12.11	even	2	inner
108.2.b.a.107.4	yes	4	1.1	even	1	trivial
324.2.h.d.107.1		8	9.4	even	3
324.2.h.d.107.2		8	36.31	odd	6
324.2.h.d.107.3		8	36.23	even	6
324.2.h.d.107.4		8	9.5	odd	6
324.2.h.d.215.1		8	36.11	even	6
324.2.h.d.215.2		8	9.2	odd	6
324.2.h.d.215.3		8	9.7	even	3
324.2.h.d.215.4		8	36.7	odd	6
1728.2.c.c.1727.1		4	8.5	even	2
1728.2.c.c.1727.2		4	8.3	odd	2
1728.2.c.c.1727.3		4	24.5	odd	2
1728.2.c.c.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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +2.23607i q^{5} -3.87298i q^{7} +(-2.59808 + 1.11803i) q^{8} +O(q^{10})\)	\(q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +2.23607i q^{5} -3.87298i q^{7} +(-2.59808 + 1.11803i) q^{8} +(-2.50000 + 1.93649i) q^{10} +1.73205 q^{11} +2.00000 q^{13} +(4.33013 - 3.35410i) q^{14} +(-3.50000 - 1.93649i) q^{16} -4.47214i q^{17} +(-4.33013 - 1.11803i) q^{20} +(1.50000 + 1.93649i) q^{22} -6.92820 q^{23} +(1.73205 + 2.23607i) q^{26} +(7.50000 + 1.93649i) q^{28} -4.47214i q^{29} +3.87298i q^{31} +(-0.866025 - 5.59017i) q^{32} +(5.00000 - 3.87298i) q^{34} +8.66025 q^{35} -4.00000 q^{37} +(-2.50000 - 5.80948i) q^{40} +8.94427i q^{41} +7.74597i q^{43} +(-0.866025 + 3.35410i) q^{44} +(-6.00000 - 7.74597i) q^{46} -3.46410 q^{47} -8.00000 q^{49} +(-1.00000 + 3.87298i) q^{52} +2.23607i q^{53} +3.87298i q^{55} +(4.33013 + 10.0623i) q^{56} +(5.00000 - 3.87298i) q^{58} +3.46410 q^{59} -4.00000 q^{61} +(-4.33013 + 3.35410i) q^{62} +(5.50000 - 5.80948i) q^{64} +4.47214i q^{65} -7.74597i q^{67} +(8.66025 + 2.23607i) q^{68} +(7.50000 + 9.68246i) q^{70} -10.3923 q^{71} +5.00000 q^{73} +(-3.46410 - 4.47214i) q^{74} -6.70820i q^{77} +7.74597i q^{79} +(4.33013 - 7.82624i) q^{80} +(-10.0000 + 7.74597i) q^{82} +12.1244 q^{83} +10.0000 q^{85} +(-8.66025 + 6.70820i) q^{86} +(-4.50000 + 1.93649i) q^{88} -4.47214i q^{89} -7.74597i q^{91} +(3.46410 - 13.4164i) q^{92} +(-3.00000 - 3.87298i) q^{94} +11.0000 q^{97} +(-6.92820 - 8.94427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4}+O(q^{10}) \) 4 * q - 2 * q^4	\( 4 q - 2 q^{4} - 10 q^{10} + 8 q^{13} - 14 q^{16} + 6 q^{22} + 30 q^{28} + 20 q^{34} - 16 q^{37} - 10 q^{40} - 24 q^{46} - 32 q^{49} - 4 q^{52} + 20 q^{58} - 16 q^{61} + 22 q^{64} + 30 q^{70} + 20 q^{73} - 40 q^{82} + 40 q^{85} - 18 q^{88} - 12 q^{94} + 44 q^{97}+O(q^{100}) \) 4 * q - 2 * q^4 - 10 * q^10 + 8 * q^13 - 14 * q^16 + 6 * q^22 + 30 * q^28 + 20 * q^34 - 16 * q^37 - 10 * q^40 - 24 * q^46 - 32 * q^49 - 4 * q^52 + 20 * q^58 - 16 * q^61 + 22 * q^64 + 30 * q^70 + 20 * q^73 - 40 * q^82 + 40 * q^85 - 18 * q^88 - 12 * q^94 + 44 * q^97

Introduction

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