LMFDB - Embedded newform 1368.2.e.f.379.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.9
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.f.379.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.847808 - 1.13191i) q^{2} +(-0.562443 + 1.91929i) q^{4} -2.55248i q^{5} +3.08957i q^{7} +(2.64930 - 0.990551i) q^{8} +O(q^{10})$	\(q+(-0.847808 - 1.13191i) q^{2} +(-0.562443 + 1.91929i) q^{4} -2.55248i q^{5} +3.08957i q^{7} +(2.64930 - 0.990551i) q^{8} +(-2.88918 + 2.16401i) q^{10} -5.76753 q^{11} +1.95212 q^{13} +(3.49711 - 2.61936i) q^{14} +(-3.36732 - 2.15898i) q^{16} -1.39823 q^{17} +(3.64002 + 2.39796i) q^{19} +(4.89893 + 1.43562i) q^{20} +(4.88976 + 6.52833i) q^{22} -1.59083i q^{23} -1.51514 q^{25} +(-1.65503 - 2.20963i) q^{26} +(-5.92976 - 1.73770i) q^{28} +7.86770 q^{29} -4.85075 q^{31} +(0.411070 + 5.64190i) q^{32} +(1.18543 + 1.58267i) q^{34} +7.88604 q^{35} +11.2538 q^{37} +(-0.371761 - 6.15319i) q^{38} +(-2.52836 - 6.76229i) q^{40} +6.86000i q^{41} -8.37466 q^{43} +(3.24391 - 11.0695i) q^{44} +(-1.80068 + 1.34872i) q^{46} +8.93785i q^{47} -2.54541 q^{49} +(1.28455 + 1.71500i) q^{50} +(-1.09796 + 3.74668i) q^{52} +10.5972 q^{53} +14.7215i q^{55} +(3.06037 + 8.18520i) q^{56} +(-6.67030 - 8.90553i) q^{58} +12.8365i q^{59} +6.56497i q^{61} +(4.11251 + 5.49062i) q^{62} +(6.03762 - 5.24854i) q^{64} -4.98275i q^{65} -16.2220i q^{67} +(0.786424 - 2.68360i) q^{68} +(-6.68585 - 8.92630i) q^{70} -4.47647 q^{71} +3.48486 q^{73} +(-9.54107 - 12.7383i) q^{74} +(-6.64968 + 5.63753i) q^{76} -17.8192i q^{77} +8.99879 q^{79} +(-5.51074 + 8.59500i) q^{80} +(7.76491 - 5.81597i) q^{82} +8.73861 q^{83} +3.56895i q^{85} +(7.10010 + 9.47936i) q^{86} +(-15.2799 + 5.71304i) q^{88} -9.05528i q^{89} +6.03121i q^{91} +(3.05325 + 0.894750i) q^{92} +(10.1168 - 7.57758i) q^{94} +(6.12075 - 9.29108i) q^{95} +14.6873i q^{97} +(2.15802 + 2.88118i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4}+O(q^{10}) $ 24 * q + 20 * q^4	$ 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) $ 24 * q + 20 * q^4 - 12 * q^16 + 24 * q^19 - 40 * q^25 - 40 * q^28 - 72 * q^49 - 104 * q^58 + 20 * q^64 + 80 * q^73 - 12 * q^76 + 56 * q^82

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−0.847808	−	1.13191i	−0.599491	−	0.800382i
$2$	−0.847808	−	1.13191i	−0.599491	−	0.800382i
$3$		0			0
$3$		0			0
$4$	−0.562443	+	1.91929i	−0.281221	+	0.959643i
$5$		−	2.55248i		−	1.14150i	−0.821123	−	0.570751i	$-0.806652\pi$
$5$		−	2.55248i		−	1.14150i	0.821123	−	0.570751i	$-0.193348\pi$
$6$		0			0
$7$			3.08957i			1.16775i	0.811845	+	0.583873i	$0.198463\pi$
$7$			3.08957i			1.16775i	−0.811845	+	0.583873i	$0.801537\pi$
$8$	2.64930	−	0.990551i	0.936670	−	0.350213i
$9$		0			0
$10$	−2.88918	+	2.16401i	−0.913637	+	0.684320i
$11$	−5.76753			−1.73898			−0.869488	−	0.493953i	$-0.835551\pi$
$11$	−5.76753			−1.73898			−0.869488	+	0.493953i	$0.835551\pi$
$12$		0			0
$13$	1.95212			0.541421			0.270711	−	0.962661i	$-0.412741\pi$
$13$	1.95212			0.541421			0.270711	+	0.962661i	$0.412741\pi$
$14$	3.49711	−	2.61936i	0.934642	−	0.700053i
$15$		0			0
$16$	−3.36732	−	2.15898i	−0.841829	−	0.539744i
$17$	−1.39823			−0.339120			−0.169560	−	0.985520i	$-0.554235\pi$
$17$	−1.39823			−0.339120			−0.169560	+	0.985520i	$0.554235\pi$
$18$		0			0
$19$	3.64002	+	2.39796i	0.835079	+	0.550131i
$19$	3.64002	+	2.39796i	0.835079	+	0.550131i
$20$	4.89893	+	1.43562i	1.09543	+	0.321015i
$21$		0			0
$22$	4.88976	+	6.52833i	1.04250	+	1.39185i
$23$		−	1.59083i		−	0.331711i	−0.986150	−	0.165855i	$-0.946962\pi$
$23$		−	1.59083i		−	0.331711i	0.986150	−	0.165855i	$-0.0530385\pi$
$24$		0			0
$25$	−1.51514			−0.303028
$26$	−1.65503	−	2.20963i	−0.324577	−	0.433344i
$27$		0			0
$28$	−5.92976	−	1.73770i	−1.12062	−	0.328395i
$29$	7.86770			1.46100			0.730498	−	0.682915i	$-0.239288\pi$
$29$	7.86770			1.46100			0.730498	+	0.682915i	$0.239288\pi$
$30$		0			0
$31$	−4.85075			−0.871221			−0.435611	−	0.900135i	$-0.643468\pi$
$31$	−4.85075			−0.871221			−0.435611	+	0.900135i	$0.643468\pi$
$32$	0.411070	+	5.64190i	0.0726676	+	0.997356i
$33$		0			0
$34$	1.18543	+	1.58267i	0.203300	+	0.271426i
$35$	7.88604			1.33298
$36$		0			0
$37$	11.2538			1.85011			0.925057	−	0.379828i	$-0.124017\pi$
$37$	11.2538			1.85011			0.925057	+	0.379828i	$0.124017\pi$
$38$	−0.371761	−	6.15319i	−0.0603077	−	0.998180i
$39$		0			0
$40$	−2.52836	−	6.76229i	−0.399769	−	1.06921i
$41$			6.86000i			1.07135i	0.844423	+	0.535676i	$0.179943\pi$
$41$			6.86000i			1.07135i	−0.844423	+	0.535676i	$0.820057\pi$
$42$		0			0
$43$	−8.37466			−1.27712			−0.638562	−	0.769571i	$-0.720470\pi$
$43$	−8.37466			−1.27712			−0.638562	+	0.769571i	$0.720470\pi$
$44$	3.24391	−	11.0695i	0.489037	−	1.66880i
$45$		0			0
$46$	−1.80068	+	1.34872i	−0.265495	+	0.198857i
$47$			8.93785i			1.30372i	0.758340	+	0.651859i	$0.226011\pi$
$47$			8.93785i			1.30372i	−0.758340	+	0.651859i	$0.773989\pi$
$48$		0			0
$49$	−2.54541			−0.363631
$50$	1.28455	+	1.71500i	0.181662	+	0.242538i
$51$		0			0
$52$	−1.09796	+	3.74668i	−0.152259	+	0.519571i
$53$	10.5972			1.45564			0.727820	−	0.685769i	$-0.240534\pi$
$53$	10.5972			1.45564			0.727820	+	0.685769i	$0.240534\pi$
$54$		0			0
$55$			14.7215i			1.98505i
$56$	3.06037	+	8.18520i	0.408960	+	1.09379i
$57$		0			0
$58$	−6.67030	−	8.90553i	−0.875853	−	1.16935i
$59$			12.8365i			1.67118i	0.549357	+	0.835588i	$0.314873\pi$
$59$			12.8365i			1.67118i	−0.549357	+	0.835588i	$0.685127\pi$
$60$		0			0
$61$			6.56497i			0.840559i	0.907395	+	0.420279i	$0.138068\pi$
$61$			6.56497i			0.840559i	−0.907395	+	0.420279i	$0.861932\pi$
$62$	4.11251	+	5.49062i	0.522289	+	0.697309i
$63$		0			0
$64$	6.03762	−	5.24854i	0.754702	−	0.656068i
$65$		−	4.98275i		−	0.618034i
$66$		0			0
$67$		−	16.2220i		−	1.98183i	−0.134477	−	0.990917i	$-0.542936\pi$
$67$		−	16.2220i		−	1.98183i	0.134477	−	0.990917i	$-0.457064\pi$
$68$	0.786424	−	2.68360i	0.0953679	−	0.325434i
$69$		0			0
$70$	−6.68585	−	8.92630i	−0.799112	−	1.06690i
$71$	−4.47647			−0.531259			−0.265629	−	0.964075i	$-0.585580\pi$
$71$	−4.47647			−0.531259			−0.265629	+	0.964075i	$0.585580\pi$
$72$		0			0
$73$	3.48486			0.407872			0.203936	−	0.978984i	$-0.434627\pi$
$73$	3.48486			0.407872			0.203936	+	0.978984i	$0.434627\pi$
$74$	−9.54107	−	12.7383i	−1.10913	−	1.48080i
$75$		0			0
$76$	−6.64968	+	5.63753i	−0.762771	+	0.646669i
$77$		−	17.8192i		−	2.03068i
$78$		0			0
$79$	8.99879			1.01244			0.506222	−	0.862403i	$-0.331042\pi$
$79$	8.99879			1.01244			0.506222	+	0.862403i	$0.331042\pi$
$80$	−5.51074	+	8.59500i	−0.616119	+	0.960950i
$81$		0			0
$82$	7.76491	−	5.81597i	0.857491	−	0.642266i
$83$	8.73861			0.959187			0.479594	−	0.877491i	$-0.340784\pi$
$83$	8.73861			0.959187			0.479594	+	0.877491i	$0.340784\pi$
$84$		0			0
$85$			3.56895i			0.387107i
$86$	7.10010	+	9.47936i	0.765624	+	1.02219i
$87$		0			0
$88$	−15.2799	+	5.71304i	−1.62885	+	0.609012i
$89$		−	9.05528i		−	0.959858i	−0.877307	−	0.479929i	$-0.840662\pi$
$89$		−	9.05528i		−	0.959858i	0.877307	−	0.479929i	$-0.159338\pi$
$90$		0			0
$91$			6.03121i			0.632243i
$92$	3.05325	+	0.894750i	0.318324	+	0.0932841i
$93$		0			0
$94$	10.1168	−	7.57758i	1.04347	−	0.781568i
$95$	6.12075	−	9.29108i	0.627975	−	0.953244i
$96$		0			0
$97$			14.6873i			1.49126i	0.666358	+	0.745632i	$0.267852\pi$
$97$			14.6873i			1.49126i	−0.666358	+	0.745632i	$0.732148\pi$
$98$	2.15802	+	2.88118i	0.217993	+	0.291043i
$99$		0			0
$100$	0.852178	−	2.90798i	0.0852178	−	0.290798i
$101$			9.05794i			0.901299i	0.892701	+	0.450649i	$0.148808\pi$
$101$			9.05794i			0.901299i	−0.892701	+	0.450649i	$0.851192\pi$
$102$		0			0
$103$	11.8596			1.16856			0.584280	−	0.811552i	$-0.301377\pi$
$103$	11.8596			1.16856			0.584280	+	0.811552i	$0.301377\pi$
$104$	5.17176	−	1.93368i	0.507133	−	0.189613i
$105$		0			0
$106$	−8.98440	−	11.9951i	−0.872642	−	1.16507i
$107$		−	0.428357i		−	0.0414108i	−0.999786	−	0.0207054i	$-0.993409\pi$
$107$		−	0.428357i		−	0.0414108i	0.999786	−	0.0207054i	$-0.00659121\pi$
$108$		0			0
$109$	3.65128			0.349729			0.174865	−	0.984592i	$-0.444051\pi$
$109$	3.65128			0.349729			0.174865	+	0.984592i	$0.444051\pi$
$110$	16.6634	−	12.4810i	1.58879	−	1.19002i
$111$		0			0
$112$	6.67030	−	10.4035i	0.630284	−	0.983043i
$113$		−	6.97033i		−	0.655714i	−0.944727	−	0.327857i	$-0.893674\pi$
$113$		−	6.97033i		−	0.655714i	0.944727	−	0.327857i	$-0.106326\pi$
$114$		0			0
$115$	−4.06055			−0.378648
$116$	−4.42513	+	15.1004i	−0.410863	+	1.40203i
$117$		0			0
$118$	14.5298	−	10.8829i	1.33758	−	1.00185i
$119$		−	4.31992i		−	0.396006i
$120$		0			0
$121$	22.2645			2.02404
$122$	7.43096	−	5.56584i	0.672768	−	0.503907i
$123$		0			0
$124$	2.72827	−	9.30998i	0.245006	−	0.836061i
$125$		−	8.89503i		−	0.795596i
$126$		0			0
$127$	−1.50237			−0.133313			−0.0666567	−	0.997776i	$-0.521233\pi$
$127$	−1.50237			−0.133313			−0.0666567	+	0.997776i	$0.521233\pi$
$128$	−11.0596	−	2.38428i	−0.977542	−	0.210743i
$129$		0			0
$130$	−5.64002	+	4.22441i	−0.494663	+	0.370506i
$131$	13.8282			1.20818			0.604088	−	0.796918i	$-0.293538\pi$
$131$	13.8282			1.20818			0.604088	+	0.796918i	$0.293538\pi$
$132$		0			0
$133$	−7.40867	+	11.2461i	−0.642413	+	0.975160i
$134$	−18.3619	+	13.7531i	−1.58622	+	1.18809i
$135$		0			0
$136$	−3.70433	+	1.38502i	−0.317644	+	0.118764i
$137$	−9.45889			−0.808128			−0.404064	−	0.914731i	$-0.632403\pi$
$137$	−9.45889			−0.808128			−0.404064	+	0.914731i	$0.632403\pi$
$138$		0			0
$139$	11.4049			0.967354			0.483677	−	0.875247i	$-0.339301\pi$
$139$	11.4049			0.967354			0.483677	+	0.875247i	$0.339301\pi$
$140$	−4.43545	+	15.1356i	−0.374864	+	1.27919i
$141$		0			0
$142$	3.79518	+	5.06696i	0.318485	+	0.425210i
$143$	−11.2589			−0.941519
$144$		0			0
$145$		−	20.0821i		−	1.66773i
$146$	−2.95449	−	3.94455i	−0.244516	−	0.326453i
$147$		0			0
$148$	−6.32962	+	21.5993i	−0.520292	+	1.77545i
$149$			12.2961i			1.00734i	0.863897	+	0.503669i	$0.168017\pi$
$149$			12.2961i			1.00734i	−0.863897	+	0.503669i	$0.831983\pi$
$150$		0			0
$151$	−3.39539			−0.276313			−0.138156	−	0.990410i	$-0.544118\pi$
$151$	−3.39539			−0.276313			−0.138156	+	0.990410i	$0.544118\pi$
$152$	12.0188	+	2.74730i	0.974856	+	0.222836i
$153$		0			0
$154$	−20.1697	+	15.1072i	−1.62532	+	1.21738i
$155$			12.3814i			0.994501i
$156$		0			0
$157$			3.95479i			0.315626i	0.987469	+	0.157813i	$0.0504444\pi$
$157$			3.95479i			0.315626i	−0.987469	+	0.157813i	$0.949556\pi$
$158$	−7.62925	−	10.1858i	−0.606950	−	0.810341i
$159$		0			0
$160$	14.4008	−	1.04925i	1.13848	−	0.0829502i
$161$	4.91497			0.387354
$162$		0			0
$163$	8.24977			0.646172			0.323086	−	0.946370i	$-0.395280\pi$
$163$	8.24977			0.646172			0.323086	+	0.946370i	$0.395280\pi$
$164$	−13.1663	−	3.85836i	−1.02812	−	0.301287i
$165$		0			0
$166$	−7.40867	−	9.89132i	−0.575024	−	0.767716i
$167$	−4.47647			−0.346399			−0.173200	−	0.984887i	$-0.555411\pi$
$167$	−4.47647			−0.346399			−0.173200	+	0.984887i	$0.555411\pi$
$168$		0			0
$169$	−9.18922			−0.706863
$170$	4.03973	−	3.02578i	0.309833	−	0.232067i
$171$		0			0
$172$	4.71026	−	16.0734i	0.359154	−	1.22558i
$173$	−1.64428			−0.125012			−0.0625061	−	0.998045i	$-0.519909\pi$
$173$	−1.64428			−0.125012			−0.0625061	+	0.998045i	$0.519909\pi$
$174$		0			0
$175$		−	4.68112i		−	0.353859i
$176$	19.4211	+	12.4520i	1.46392	+	0.938603i
$177$		0			0
$178$	−10.2498	+	7.67714i	−0.768253	+	0.575426i
$179$		−	10.3671i		−	0.774874i	−0.921896	−	0.387437i	$-0.873361\pi$
$179$		−	10.3671i		−	0.774874i	0.921896	−	0.387437i	$-0.126639\pi$
$180$		0			0
$181$	−14.7461			−1.09607			−0.548035	−	0.836455i	$-0.684624\pi$
$181$	−14.7461			−1.09607			−0.548035	+	0.836455i	$0.684624\pi$
$182$	6.82679	−	5.11331i	0.506035	−	0.379024i
$183$		0			0
$184$	−1.57580	−	4.21459i	−0.116169	−	0.310703i
$185$		−	28.7251i		−	2.11191i
$186$		0			0
$187$	8.06433			0.589722
$188$	−17.1543	−	5.02703i	−1.25110	−	0.366634i
$189$		0			0
$190$	−15.7059	+	0.948912i	−1.13942	+	0.0688413i
$191$		−	6.54828i		−	0.473817i	−0.971532	−	0.236909i	$-0.923866\pi$
$191$		−	6.54828i		−	0.473817i	0.971532	−	0.236909i	$-0.0761342\pi$
$192$		0			0
$193$			12.3619i			0.889828i	0.895573	+	0.444914i	$0.146766\pi$
$193$			12.3619i			0.889828i	−0.895573	+	0.444914i	$0.853234\pi$
$194$	16.6247	−	12.4520i	1.19358	−	0.893999i
$195$		0			0
$196$	1.43165	−	4.88538i	0.102261	−	0.348956i
$197$		−	8.35148i		−	0.595019i	−0.954719	−	0.297509i	$-0.903844\pi$
$197$		−	8.35148i		−	0.595019i	0.954719	−	0.297509i	$-0.0961559\pi$
$198$		0			0
$199$			4.04833i			0.286978i	0.989652	+	0.143489i	$0.0458322\pi$
$199$			4.04833i			0.286978i	−0.989652	+	0.143489i	$0.954168\pi$
$200$	−4.01406	+	1.50082i	−0.283837	+	0.106124i
$201$		0			0
$202$	10.2528	−	7.67940i	0.721383	−	0.540320i
$203$			24.3078i			1.70607i
$204$		0			0
$205$	17.5100			1.22295
$206$	−10.0547	−	13.4240i	−0.700541	−	0.935294i
$207$		0			0
$208$	−6.57341	−	4.21459i	−0.455784	−	0.292229i
$209$	−20.9940	−	13.8303i	−1.45218	−	0.956664i
$210$		0			0
$211$		−	18.5474i		−	1.27685i	−0.769683	−	0.638427i	$-0.779586\pi$
$211$		−	18.5474i		−	1.27685i	0.769683	−	0.638427i	$-0.220414\pi$
$212$	−5.96033	+	20.3391i	−0.409357	+	1.39689i
$213$		0			0
$214$	−0.484862	+	0.363165i	−0.0331445	+	0.0248254i
$215$			21.3761i			1.45784i
$216$		0			0
$217$		−	14.9867i		−	1.01737i
$218$	−3.09559	−	4.13292i	−0.209660	−	0.279917i
$219$		0			0
$220$	−28.2548	−	8.28000i	−1.90494	−	0.558237i
$221$	−2.72951			−0.183607
$222$		0			0
$223$	8.94886			0.599260			0.299630	−	0.954056i	$-0.403137\pi$
$223$	8.94886			0.599260			0.299630	+	0.954056i	$0.403137\pi$
$224$	−17.4310	+	1.27003i	−1.16466	+	0.0848573i
$225$		0			0
$226$	−7.88979	+	5.90951i	−0.524821	+	0.393094i
$227$			15.6679i			1.03991i	0.854193	+	0.519957i	$0.174052\pi$
$227$			15.6679i			1.03991i	−0.854193	+	0.519957i	$0.825948\pi$
$228$		0			0
$229$		−	3.56895i		−	0.235843i	−0.993023	−	0.117921i	$-0.962377\pi$
$229$		−	3.56895i		−	0.235843i	0.993023	−	0.117921i	$-0.0376231\pi$
$230$	3.44257	+	4.59618i	0.226996	+	0.303063i
$231$		0			0
$232$	20.8439	−	7.79336i	1.36847	−	0.511659i
$233$	−14.3739			−0.941663			−0.470831	−	0.882223i	$-0.656046\pi$
$233$	−14.3739			−0.941663			−0.470831	+	0.882223i	$0.656046\pi$
$234$		0			0
$235$	22.8136			1.48820
$236$	−24.6370	−	7.21982i	−1.60373	−	0.469970i
$237$		0			0
$238$	−4.88976	+	3.66246i	−0.316956	+	0.237402i
$239$			23.5188i			1.52131i	0.649158	+	0.760654i	$0.275122\pi$
$239$			23.5188i			1.52131i	−0.649158	+	0.760654i	$0.724878\pi$
$240$		0			0
$241$		−	17.4573i		−	1.12452i	−0.826960	−	0.562261i	$-0.809931\pi$
$241$		−	17.4573i		−	1.12452i	0.826960	−	0.562261i	$-0.190069\pi$
$242$	−18.8760	−	25.2014i	−1.21339	−	1.62001i
$243$		0			0
$244$	−12.6001	−	3.69242i	−0.806636	−	0.236383i
$245$			6.49711i			0.415085i
$246$		0			0
$247$	7.10577	+	4.68112i	0.452129	+	0.297852i
$248$	−12.8511	+	4.80492i	−0.816047	+	0.305113i
$249$		0			0
$250$	−10.0684	+	7.54128i	−0.636780	+	0.476952i
$251$	−2.97108			−0.187533			−0.0937663	−	0.995594i	$-0.529891\pi$
$251$	−2.97108			−0.187533			−0.0937663	+	0.995594i	$0.529891\pi$
$252$		0			0
$253$			9.17516i			0.576837i
$254$	1.27372	+	1.70054i	0.0799202	+	0.106702i
$255$		0			0
$256$	6.67764	+	14.5399i	0.417352	+	0.908745i
$257$			0.856714i			0.0534404i	0.999643	+	0.0267202i	$0.00850631\pi$
$257$			0.856714i			0.0534404i	−0.999643	+	0.0267202i	$0.991494\pi$
$258$		0			0
$259$			34.7694i			2.16046i
$260$	9.56332	+	2.80251i	0.593092	+	0.173804i
$261$		0			0
$262$	−11.7237	−	15.6523i	−0.724290	−	0.967001i
$263$			22.8813i			1.41092i	0.708749	+	0.705461i	$0.249260\pi$
$263$			22.8813i			1.41092i	−0.708749	+	0.705461i	$0.750740\pi$
$264$		0			0
$265$		−	27.0491i		−	1.66162i
$266$	19.0107	−	1.14858i	1.16562	−	0.0704240i
$267$		0			0
$268$	31.1347	+	9.12395i	1.90185	+	0.557334i
$269$	−8.42674			−0.513788			−0.256894	−	0.966440i	$-0.582699\pi$
$269$	−8.42674			−0.513788			−0.256894	+	0.966440i	$0.582699\pi$
$270$		0			0
$271$		−	3.72235i		−	0.226117i	−0.993588	−	0.113058i	$-0.963935\pi$
$271$		−	3.72235i		−	0.226117i	0.993588	−	0.113058i	$-0.0360647\pi$
$272$	4.70828	+	3.01874i	0.285481	+	0.183038i
$273$		0			0
$274$	8.01933	+	10.7066i	0.484465	+	0.646810i
$275$	8.73861			0.526958
$276$		0			0
$277$			18.9232i			1.13699i	0.822688	+	0.568493i	$0.192474\pi$
$277$			18.9232i			1.13699i	−0.822688	+	0.568493i	$0.807526\pi$
$278$	−9.66919	−	12.9094i	−0.579920	−	0.774252i
$279$		0			0
$280$	20.8925	−	7.81153i	1.24857	−	0.466828i
$281$			0.154199i			0.00919871i	0.999989	+	0.00459936i	$0.00146403\pi$
$281$			0.154199i			0.00919871i	−0.999989	+	0.00459936i	$0.998536\pi$
$282$		0			0
$283$	−30.6244			−1.82043			−0.910217	−	0.414132i	$-0.864085\pi$
$283$	−30.6244			−1.82043			−0.910217	+	0.414132i	$0.864085\pi$
$284$	2.51776	−	8.59162i	0.149401	−	0.509819i
$285$		0			0
$286$	9.54541	+	12.7441i	0.564432	+	0.753575i
$287$	−21.1944			−1.25107
$288$		0			0
$289$	−15.0450			−0.884997
$290$	−22.7312	+	17.0258i	−1.33482	+	0.999789i
$291$		0			0
$292$	−1.96004	+	6.68845i	−0.114702	+	0.391412i
$293$	17.3797			1.01533			0.507666	−	0.861554i	$-0.330508\pi$
$293$	17.3797			1.01533			0.507666	+	0.861554i	$0.330508\pi$
$294$		0			0
$295$	32.7650			1.90765
$296$	29.8147	−	11.1475i	1.73295	−	0.647934i
$297$		0			0
$298$	13.9181	−	10.4247i	0.806254	−	0.603889i
$299$		−	3.10549i		−	0.179595i
$300$		0			0
$301$		−	25.8740i		−	1.49136i
$302$	2.87864	+	3.84327i	0.165647	+	0.221155i
$303$		0			0
$304$	−7.07996	−	15.9334i	−0.406064	−	0.913845i
$305$	16.7569			0.959500
$306$		0			0
$307$			23.3433i			1.33227i	0.745830	+	0.666136i	$0.232053\pi$
$307$			23.3433i			1.33227i	−0.745830	+	0.666136i	$0.767947\pi$
$308$	34.2001	+	10.0223i	1.94873	+	0.571072i
$309$		0			0
$310$	14.0147	−	10.4971i	0.795980	−	0.596194i
$311$		−	20.4917i		−	1.16198i	−0.813911	−	0.580990i	$-0.802665\pi$
$311$		−	20.4917i		−	1.16198i	0.813911	−	0.580990i	$-0.197335\pi$
$312$		0			0
$313$	−10.6888			−0.604164			−0.302082	−	0.953282i	$-0.597682\pi$
$313$	−10.6888			−0.604164			−0.302082	+	0.953282i	$0.597682\pi$
$314$	4.47647	−	3.35290i	0.252622	−	0.189215i
$315$		0			0
$316$	−5.06130	+	17.2713i	−0.284721	+	0.971584i
$317$	−4.37379			−0.245657			−0.122828	−	0.992428i	$-0.539196\pi$
$317$	−4.37379			−0.245657			−0.122828	+	0.992428i	$0.539196\pi$
$318$		0			0
$319$	−45.3772			−2.54064
$320$	−13.3968	−	15.4109i	−0.748903	−	0.861494i
$321$		0			0
$322$	−4.16695	−	5.56330i	−0.232215	−	0.310031i
$323$	−5.08959	−	3.35290i	−0.283192	−	0.186560i
$324$		0			0
$325$	−2.95773			−0.164066
$326$	−6.99422	−	9.33800i	−0.387374	−	0.517184i
$327$		0			0
$328$	6.79518	+	18.1742i	0.375201	+	1.00350i
$329$	−27.6141			−1.52241
$330$		0			0
$331$		−	6.03121i		−	0.331505i	−0.986167	−	0.165753i	$-0.946995\pi$
$331$		−	6.03121i		−	0.331505i	0.986167	−	0.165753i	$-0.0530053\pi$
$332$	−4.91497	+	16.7719i	−0.269744	+	0.920477i
$333$		0			0
$334$	3.79518	+	5.06696i	0.207663	+	0.277252i
$335$	−41.4063			−2.26227
$336$		0			0
$337$			29.6740i			1.61644i	0.588878	+	0.808222i	$0.299570\pi$
$337$			29.6740i			1.61644i	−0.588878	+	0.808222i	$0.700430\pi$
$338$	7.79069	+	10.4014i	0.423758	+	0.565760i
$339$		0			0
$340$	−6.84983	−	2.00733i	−0.371484	−	0.108863i
$341$	27.9769			1.51503
$342$		0			0
$343$			13.7627i			0.743118i
$344$	−22.1870	+	8.29553i	−1.19624	+	0.447265i
$345$		0			0
$346$	1.39403	+	1.86118i	0.0749437	+	0.100058i
$347$	−2.97108			−0.159496			−0.0797479	−	0.996815i	$-0.525412\pi$
$347$	−2.97108			−0.159496			−0.0797479	+	0.996815i	$0.525412\pi$
$348$		0			0
$349$		−	20.6537i		−	1.10557i	−0.833325	−	0.552783i	$-0.813566\pi$
$349$		−	20.6537i		−	1.10557i	0.833325	−	0.552783i	$-0.186434\pi$
$350$	−5.29861	+	3.96869i	−0.283222	+	0.212135i
$351$		0			0
$352$	−2.37086	−	32.5398i	−0.126367	−	1.73438i
$353$	−23.8328			−1.26849			−0.634245	−	0.773132i	$-0.718689\pi$
$353$	−23.8328			−1.26849			−0.634245	+	0.773132i	$0.718689\pi$
$354$		0			0
$355$			11.4261i			0.606433i
$356$	17.3797	+	5.09308i	0.921121	+	0.269933i
$357$		0			0
$358$	−11.7346	+	8.78931i	−0.620195	+	0.464530i
$359$			8.30031i			0.438074i	0.975717	+	0.219037i	$0.0702915\pi$
$359$			8.30031i			0.438074i	−0.975717	+	0.219037i	$0.929709\pi$
$360$		0			0
$361$	7.49954	+	17.4573i	0.394713	+	0.918805i
$362$	12.5019	+	16.6913i	0.657084	+	0.877275i
$363$		0			0
$364$	−11.5756	−	3.39221i	−0.606727	−	0.177800i
$365$		−	8.89503i		−	0.465587i
$366$		0			0
$367$		−	5.63988i		−	0.294399i	−0.989107	−	0.147200i	$-0.952974\pi$
$367$		−	5.63988i		−	0.294399i	0.989107	−	0.147200i	$-0.0470260\pi$
$368$	−3.43456	+	5.35682i	−0.179039	+	0.279244i
$369$		0			0
$370$	−32.5142	+	24.3534i	−1.69033	+	1.26607i
$371$			32.7408i			1.69982i
$372$		0			0
$373$	6.45005			0.333971			0.166985	−	0.985959i	$-0.446597\pi$
$373$	6.45005			0.333971			0.166985	+	0.985959i	$0.446597\pi$
$374$	−6.83701	−	9.12810i	−0.353533	−	0.472003i
$375$		0			0
$376$	8.85340	+	23.6791i	0.456579	+	1.22115i
$377$	15.3587			0.791014
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	14.3897	+	16.9732i	0.738174	+	0.870705i
$381$		0			0
$382$	−7.41207	+	5.55169i	−0.379234	+	0.284049i
$383$	22.5179			1.15061			0.575305	−	0.817939i	$-0.304884\pi$
$383$	22.5179			1.15061			0.575305	+	0.817939i	$0.304884\pi$
$384$		0			0
$385$	−45.4830			−2.31803
$386$	13.9926	−	10.4805i	0.712202	−	0.533444i
$387$		0			0
$388$	−28.1890	−	8.26074i	−1.43108	−	0.419375i
$389$			3.25894i			0.165235i	0.996581	+	0.0826173i	$0.0263279\pi$
$389$			3.25894i			0.165235i	−0.996581	+	0.0826173i	$0.973672\pi$
$390$		0			0
$391$			2.22434i			0.112490i
$392$	−6.74357	+	2.52136i	−0.340602	+	0.127348i
$393$		0			0
$394$	−9.45313	+	7.08046i	−0.476242	+	0.356708i
$395$		−	22.9692i		−	1.15571i
$396$		0			0
$397$			36.0080i			1.80719i	0.428390	+	0.903594i	$0.359081\pi$
$397$			36.0080i			1.80719i	−0.428390	+	0.903594i	$0.640919\pi$
$398$	4.58235	−	3.43221i	0.229692	−	0.172041i
$399$		0			0
$400$	5.10195	+	3.27115i	0.255097	+	0.163557i
$401$			20.6903i			1.03323i	0.856219	+	0.516613i	$0.172807\pi$
$401$			20.6903i			1.03323i	−0.856219	+	0.516613i	$0.827193\pi$
$402$		0			0
$403$	−9.46927			−0.471698
$404$	−17.3848	−	5.09457i	−0.864925	−	0.253465i
$405$		0			0
$406$	27.5142	−	20.6083i	1.36551	−	1.02277i
$407$	−64.9067			−3.21731
$408$		0			0
$409$			22.8522i			1.12997i	0.825102	+	0.564983i	$0.191117\pi$
$409$			22.8522i			1.12997i	−0.825102	+	0.564983i	$0.808883\pi$
$410$	−14.8451	−	19.8198i	−0.733148	−	0.978828i
$411$		0			0
$412$	−6.67034	+	22.7620i	−0.328624	+	1.12140i
$413$	−39.6593			−1.95151
$414$		0			0
$415$		−	22.3051i		−	1.09491i
$416$	0.802459	+	11.0137i	0.0393438	+	0.539990i
$417$		0			0
$418$	2.14415	+	35.4888i	0.104874	+	1.73581i
$419$	21.7142			1.06081			0.530405	−	0.847744i	$-0.322040\pi$
$419$	21.7142			1.06081			0.530405	+	0.847744i	$0.322040\pi$
$420$		0			0
$421$	−34.3672			−1.67496			−0.837478	−	0.546472i	$-0.815971\pi$
$421$	−34.3672			−1.67496			−0.837478	+	0.546472i	$0.815971\pi$
$422$	−20.9940	+	15.7246i	−1.02197	+	0.765462i
$423$		0			0
$424$	28.0752	−	10.4971i	1.36345	−	0.509783i
$425$	2.11851			0.102763
$426$		0			0
$427$	−20.2829			−0.981559
$428$	0.822140	+	0.240926i	0.0397396	+	0.0116456i
$429$		0			0
$430$	24.1959	−	18.1228i	1.16683	−	0.873961i
$431$	9.93549			0.478576			0.239288	−	0.970949i	$-0.423086\pi$
$431$	9.93549			0.478576			0.239288	+	0.970949i	$0.423086\pi$
$432$		0			0
$433$			12.2167i			0.587097i	0.955944	+	0.293548i	$0.0948361\pi$
$433$			12.2167i			0.587097i	−0.955944	+	0.293548i	$0.905164\pi$
$434$	−16.9636	+	12.7059i	−0.814280	+	0.609901i
$435$		0			0
$436$	−2.05364	+	7.00785i	−0.0983514	+	0.335615i
$437$	3.81475	−	5.79065i	0.182484	−	0.277004i
$438$		0			0
$439$	−4.90069			−0.233897			−0.116949	−	0.993138i	$-0.537311\pi$
$439$	−4.90069			−0.233897			−0.116949	+	0.993138i	$0.537311\pi$
$440$	14.5824	+	39.0017i	0.695189	+	1.85933i
$441$		0			0
$442$	2.31410	+	3.08957i	0.110071	+	0.146956i
$443$	−2.97108			−0.141160			−0.0705800	−	0.997506i	$-0.522485\pi$
$443$	−2.97108			−0.141160			−0.0705800	+	0.997506i	$0.522485\pi$
$444$		0			0
$445$	−23.1134			−1.09568
$446$	−7.58691	−	10.1293i	−0.359251	−	0.479637i
$447$		0			0
$448$	16.2157	+	18.6536i	0.766120	+	0.881300i
$449$		−	24.5422i		−	1.15822i	−0.815250	−	0.579109i	$-0.803400\pi$
$449$		−	24.5422i		−	1.15822i	0.815250	−	0.579109i	$-0.196600\pi$
$450$		0			0
$451$		−	39.5653i		−	1.86306i
$452$	13.3781	+	3.92041i	0.629251	+	0.184401i
$453$		0			0
$454$	17.7346	−	13.2834i	0.832328	−	0.623419i
$455$	15.3945			0.721706
$456$		0			0
$457$	23.7640			1.11163			0.555816	−	0.831305i	$-0.312406\pi$
$457$	23.7640			1.11163			0.555816	+	0.831305i	$0.312406\pi$
$458$	−4.03973	+	3.02578i	−0.188764	+	0.141386i
$459$		0			0
$460$	2.28383	−	7.79336i	0.106484	−	0.363367i
$461$		−	24.1617i		−	1.12532i	−0.826687	−	0.562662i	$-0.809777\pi$
$461$		−	24.1617i		−	1.12532i	0.826687	−	0.562662i	$-0.190223\pi$
$462$		0			0
$463$		−	33.4913i		−	1.55647i	−0.627971	−	0.778237i	$-0.716114\pi$
$463$		−	33.4913i		−	1.55647i	0.627971	−	0.778237i	$-0.283886\pi$
$464$	−26.4930	−	16.9862i	−1.22991	−	0.788564i
$465$		0			0
$466$	12.1863	+	16.2699i	0.564518	+	0.753690i
$467$	−17.6518			−0.816830			−0.408415	−	0.912796i	$-0.633918\pi$
$467$	−17.6518			−0.816830			−0.408415	+	0.912796i	$0.633918\pi$
$468$		0			0
$469$	50.1189			2.31428
$470$	−19.3416	−	25.8230i	−0.892161	−	1.19113i
$471$		0			0
$472$	12.7153	+	34.0079i	0.585267	+	1.56534i
$473$	48.3011			2.22089
$474$		0			0
$475$	−5.51514	−	3.63325i	−0.253052	−	0.166705i
$476$	8.29116	+	2.42971i	0.380025	+	0.111365i
$477$		0			0
$478$	26.6212	−	19.9395i	1.21763	−	0.912010i
$479$			18.6470i			0.852004i	0.904722	+	0.426002i	$0.140078\pi$
$479$			18.6470i			0.852004i	−0.904722	+	0.426002i	$0.859922\pi$
$480$		0			0
$481$	21.9688			1.00169
$482$	−19.7601	+	14.8004i	−0.900047	+	0.674141i
$483$		0			0
$484$	−12.5225	+	42.7318i	−0.569204	+	1.94236i
$485$	37.4889			1.70228
$486$		0			0
$487$	13.8025			0.625453			0.312727	−	0.949843i	$-0.398758\pi$
$487$	13.8025			0.625453			0.312727	+	0.949843i	$0.398758\pi$
$488$	6.50294	+	17.3926i	0.294374	+	0.787326i
$489$		0			0
$490$	7.35415	−	5.50830i	0.332227	−	0.248840i
$491$	−3.47441			−0.156798			−0.0783989	−	0.996922i	$-0.524981\pi$
$491$	−3.47441			−0.156798			−0.0783989	+	0.996922i	$0.524981\pi$
$492$		0			0
$493$	−11.0008			−0.495453
$494$	−0.725724	−	12.0118i	−0.0326519	−	0.540436i
$495$		0			0
$496$	16.3340	+	10.4727i	0.733419	+	0.470237i
$497$		−	13.8303i		−	0.620375i
$498$		0			0
$499$	−17.7834			−0.796093			−0.398046	−	0.917365i	$-0.630312\pi$
$499$	−17.7834			−0.796093			−0.398046	+	0.917365i	$0.630312\pi$
$500$	17.0721	+	5.00294i	0.763488	+	0.223738i
$501$		0			0
$502$	2.51890	+	3.36299i	0.112424	+	0.150098i
$503$		−	23.2001i		−	1.03444i	−0.855852	−	0.517220i	$-0.826967\pi$
$503$		−	23.2001i		−	1.03444i	0.855852	−	0.517220i	$-0.173033\pi$
$504$		0			0
$505$	23.1202			1.02883
$506$	10.3855	−	7.77877i	0.461690	−	0.345809i
$507$		0			0
$508$	0.844995	−	2.88347i	0.0374906	−	0.127933i
$509$	22.2797			0.987529			0.493764	−	0.869596i	$-0.335621\pi$
$509$	22.2797			0.987529			0.493764	+	0.869596i	$0.335621\pi$
$510$		0			0
$511$			10.7667i			0.476291i
$512$	10.7965	−	19.8855i	0.477144	−	0.878825i
$513$		0			0
$514$	0.969724	−	0.726329i	0.0427727	−	0.0320370i
$515$		−	30.2713i		−	1.33391i
$516$		0			0
$517$		−	51.5493i		−	2.26714i
$518$	39.3558	−	29.4778i	1.72920	−	1.29518i
$519$		0			0
$520$	−4.93567	−	13.2008i	−0.216443	−	0.578894i
$521$			15.8179i			0.692996i	0.938051	+	0.346498i	$0.112629\pi$
$521$			15.8179i			0.692996i	−0.938051	+	0.346498i	$0.887371\pi$
$522$		0			0
$523$		−	22.2532i		−	0.973065i	−0.873662	−	0.486533i	$-0.838261\pi$
$523$		−	22.2532i		−	0.973065i	0.873662	−	0.486533i	$-0.161739\pi$
$524$	−7.77757	+	26.5403i	−0.339765	+	1.15942i
$525$		0			0
$526$	25.8996	−	19.3990i	1.12928	−	0.845835i
$527$	6.78247			0.295449
$528$		0			0
$529$	20.4693			0.889968
$530$	−30.6172	+	22.9325i	−1.32993	+	0.996123i
$531$		0			0
$532$	−17.4175	−	20.5446i	−0.755145	−	0.890723i
$533$			13.3916i			0.580053i
$534$		0			0
$535$	−1.09337			−0.0472706
$536$	−16.0687	−	42.9770i	−0.694063	−	1.85632i
$537$		0			0
$538$	7.14426	+	9.53832i	0.308011	+	0.411226i
$539$	14.6808			0.632345
$540$		0			0
$541$		−	33.3188i		−	1.43249i	−0.697851	−	0.716243i	$-0.745860\pi$
$541$		−	33.3188i		−	1.43249i	0.697851	−	0.716243i	$-0.254140\pi$
$542$	−4.21337	+	3.15584i	−0.180980	+	0.135555i
$543$		0			0
$544$	−0.574770	−	7.88867i	−0.0246431	−	0.338224i
$545$		−	9.31981i		−	0.399217i
$546$		0			0
$547$		−	5.88601i		−	0.251668i	−0.992051	−	0.125834i	$-0.959839\pi$
$547$		−	5.88601i		−	0.251668i	0.992051	−	0.125834i	$-0.0401606\pi$
$548$	5.32008	−	18.1543i	0.227263	−	0.775514i
$549$		0			0
$550$	−7.40867	−	9.89132i	−0.315907	−	0.421768i
$551$	28.6386	+	18.8665i	1.22005	+	0.803738i
$552$		0			0
$553$			27.8024i			1.18228i
$554$	21.4194	−	16.0433i	0.910023	−	0.681613i
$555$		0			0
$556$	−6.41462	+	21.8893i	−0.272041	+	0.928314i
$557$			17.6854i			0.749353i	0.927156	+	0.374677i	$0.122246\pi$
$557$			17.6854i			0.749353i	−0.927156	+	0.374677i	$0.877754\pi$
$558$		0			0
$559$	−16.3484			−0.691462
$560$	−26.5548	−	17.0258i	−1.12215	−	0.719471i
$561$		0			0
$562$	0.174539	−	0.130731i	0.00736248	−	0.00551454i
$563$		−	26.4633i		−	1.11530i	−0.830077	−	0.557648i	$-0.811704\pi$
$563$		−	26.4633i		−	1.11530i	0.830077	−	0.557648i	$-0.188296\pi$
$564$		0			0
$565$	−17.7916			−0.748499
$566$	25.9636	+	34.6641i	1.09133	+	1.45704i
$567$		0			0
$568$	−11.8595	+	4.43417i	−0.497614	+	0.186054i
$569$		−	24.0165i		−	1.00682i	−0.864047	−	0.503412i	$-0.832078\pi$
$569$		−	24.0165i		−	1.00682i	0.864047	−	0.503412i	$-0.167922\pi$
$570$		0			0
$571$	29.1807			1.22118			0.610588	−	0.791948i	$-0.290933\pi$
$571$	29.1807			1.22118			0.610588	+	0.791948i	$0.290933\pi$
$572$	6.33250	−	21.6091i	0.264775	−	0.903522i
$573$		0			0
$574$	17.9688	+	23.9902i	0.750004	+	1.00133i
$575$			2.41032i			0.100517i
$576$		0			0
$577$	−3.91629			−0.163037			−0.0815186	−	0.996672i	$-0.525977\pi$
$577$	−3.91629			−0.163037			−0.0815186	+	0.996672i	$0.525977\pi$
$578$	12.7552	+	17.0295i	0.530548	+	0.708336i
$579$		0			0
$580$	38.5433	+	11.2950i	1.60042	+	0.469001i
$581$			26.9985i			1.12009i
$582$		0			0
$583$	−61.1198			−2.53132
$584$	9.23246	−	3.45193i	0.382042	−	0.142842i
$585$		0			0
$586$	−14.7346	−	19.6722i	−0.608682	−	0.812653i
$587$	30.9562			1.27770			0.638849	−	0.769332i	$-0.279411\pi$
$587$	30.9562			1.27770			0.638849	+	0.769332i	$0.279411\pi$
$588$		0			0
$589$	−17.6569	−	11.6319i	−0.727538	−	0.479285i
$590$	−27.7784	−	37.0870i	−1.14362	−	1.52685i
$591$		0			0
$592$	−37.8951	−	24.2967i	−1.55748	−	0.998589i
$593$	−12.2130			−0.501528			−0.250764	−	0.968048i	$-0.580682\pi$
$593$	−12.2130			−0.501528			−0.250764	+	0.968048i	$0.580682\pi$
$594$		0			0
$595$	−11.0265			−0.452042
$596$	−23.5998	−	6.91586i	−0.966684	−	0.283285i
$597$		0			0
$598$	−3.51514	+	2.63286i	−0.143745	+	0.107666i
$599$	6.64694			0.271586			0.135793	−	0.990737i	$-0.456642\pi$
$599$	6.64694			0.271586			0.135793	+	0.990737i	$0.456642\pi$
$600$		0			0
$601$		−	26.6045i		−	1.08522i	−0.839985	−	0.542609i	$-0.817436\pi$
$601$		−	26.6045i		−	1.08522i	0.839985	−	0.542609i	$-0.182564\pi$
$602$	−29.2871	+	21.9362i	−1.19365	+	0.894054i
$603$		0			0
$604$	1.90971	−	6.51672i	0.0777050	−	0.265161i
$605$		−	56.8295i		−	2.31045i
$606$		0			0
$607$	−14.9143			−0.605351			−0.302676	−	0.953094i	$-0.597880\pi$
$607$	−14.9143			−0.605351			−0.302676	+	0.953094i	$0.597880\pi$
$608$	−12.0328	+	21.5224i	−0.487993	+	0.872848i
$609$		0			0
$610$	−14.2067	−	18.9674i	−0.575211	−	0.767966i
$611$			17.4478i			0.705861i
$612$		0			0
$613$		−	31.0944i		−	1.25589i	−0.778257	−	0.627946i	$-0.783896\pi$
$613$		−	31.0944i		−	1.25589i	0.778257	−	0.627946i	$-0.216104\pi$
$614$	26.4225	−	19.7906i	1.06633	−	0.798685i
$615$		0			0
$616$	−17.6508	−	47.2084i	−0.711171	−	1.90208i
$617$	−45.1554			−1.81789			−0.908944	−	0.416917i	$-0.863110\pi$
$617$	−45.1554			−1.81789			−0.908944	+	0.416917i	$0.863110\pi$
$618$		0			0
$619$	−4.22041			−0.169633			−0.0848163	−	0.996397i	$-0.527030\pi$
$619$	−4.22041			−0.169633			−0.0848163	+	0.996397i	$0.527030\pi$
$620$	−23.7635	−	6.96385i	−0.954366	−	0.279675i
$621$		0			0
$622$	−23.1948	+	17.3731i	−0.930028	+	0.696597i
$623$	27.9769			1.12087
$624$		0			0
$625$	−30.2800			−1.21120
$626$	9.06202	+	12.0987i	0.362191	+	0.483562i
$627$		0			0
$628$	−7.59037	−	2.22434i	−0.302889	−	0.0887609i
$629$	−15.7354			−0.627411
$630$		0			0
$631$		−	19.4026i		−	0.772406i	−0.922414	−	0.386203i	$-0.873786\pi$
$631$		−	19.4026i		−	0.772406i	0.922414	−	0.386203i	$-0.126214\pi$
$632$	23.8405	−	8.91376i	0.948325	−	0.354571i
$633$		0			0
$634$	3.70814	+	4.95074i	0.147269	+	0.196619i
$635$			3.83475i			0.152178i
$636$		0			0
$637$	−4.96896			−0.196877
$638$	38.4712	+	51.3630i	1.52309	+	2.03348i
$639$		0			0
$640$	−6.08583	+	28.2294i	−0.240564	+	1.11587i
$641$		−	15.0489i		−	0.594398i	−0.954816	−	0.297199i	$-0.903948\pi$
$641$		−	15.0489i		−	0.594398i	0.954816	−	0.297199i	$-0.0960524\pi$
$642$		0			0
$643$	5.99622			0.236468			0.118234	−	0.992986i	$-0.462277\pi$
$643$	5.99622			0.236468			0.118234	+	0.992986i	$0.462277\pi$
$644$	−2.76439	+	9.43323i	−0.108932	+	0.371721i
$645$		0			0
$646$	0.519808	+	8.60357i	0.0204516	+	0.338503i
$647$		−	0.565602i		−	0.0222361i	−0.999938	−	0.0111181i	$-0.996461\pi$
$647$		−	0.565602i		−	0.0222361i	0.999938	−	0.0111181i	$-0.00353906\pi$
$648$		0			0
$649$		−	74.0352i		−	2.90614i
$650$	2.50759	+	3.34789i	0.0983558	+	0.131315i
$651$		0			0
$652$	−4.64002	+	15.8337i	−0.181717	+	0.620094i
$653$			8.32237i			0.325679i	0.986653	+	0.162840i	$0.0520653\pi$
$653$			8.32237i			0.325679i	−0.986653	+	0.162840i	$0.947935\pi$
$654$		0			0
$655$		−	35.2962i		−	1.37913i
$656$	14.8106	−	23.0998i	0.578256	−	0.901896i
$657$		0			0
$658$	23.4114	+	31.2566i	0.912672	+	1.21851i
$659$			39.9756i			1.55723i	0.627502	+	0.778615i	$0.284077\pi$
$659$			39.9756i			1.55723i	−0.627502	+	0.778615i	$0.715923\pi$
$660$		0			0
$661$	35.1669			1.36783			0.683916	−	0.729561i	$-0.260275\pi$
$661$	35.1669			1.36783			0.683916	+	0.729561i	$0.260275\pi$
$662$	−6.82679	+	5.11331i	−0.265331	+	0.198734i
$663$		0			0
$664$	23.1512	−	8.65604i	0.898442	−	0.335920i
$665$	28.7054	+	18.9104i	1.11315	+	0.733316i
$666$		0			0
$667$		−	12.5162i		−	0.484628i
$668$	2.51776	−	8.59162i	0.0974149	−	0.332420i
$669$		0			0
$670$	35.1046	+	46.8682i	1.35621	+	1.81068i
$671$		−	37.8637i		−	1.46171i
$672$		0			0
$673$			27.3486i			1.05421i	0.849800	+	0.527106i	$0.176723\pi$
$673$			27.3486i			1.05421i	−0.849800	+	0.527106i	$0.823277\pi$
$674$	33.5883	−	25.1578i	1.29377	−	0.969044i
$675$		0			0
$676$	5.16841	−	17.6367i	0.198785	−	0.678336i
$677$	−7.86770			−0.302380			−0.151190	−	0.988505i	$-0.548311\pi$
$677$	−7.86770			−0.302380			−0.151190	+	0.988505i	$0.548311\pi$
$678$		0			0
$679$	−45.3772			−1.74142
$680$	3.53523	+	9.45522i	0.135570	+	0.362591i
$681$		0			0
$682$	−23.7190	−	31.6673i	−0.908249	−	1.21261i
$683$			17.3813i			0.665077i	0.943090	+	0.332539i	$0.107905\pi$
$683$			17.3813i			0.665077i	−0.943090	+	0.332539i	$0.892095\pi$
$684$		0			0
$685$			24.1436i			0.922480i
$686$	15.5782	−	11.6682i	0.594778	−	0.445492i
$687$		0			0
$688$	28.2001	+	18.0807i	1.07512	+	0.689320i
$689$	20.6871			0.788114
$690$		0			0
$691$	29.6547			1.12812			0.564059	−	0.825734i	$-0.309239\pi$
$691$	29.6547			1.12812			0.564059	+	0.825734i	$0.309239\pi$
$692$	0.924813	−	3.15584i	0.0351561	−	0.119967i
$693$		0			0
$694$	2.51890	+	3.36299i	0.0956162	+	0.127657i
$695$		−	29.1108i		−	1.10424i
$696$		0			0
$697$		−	9.59185i		−	0.363317i
$698$	−23.3781	+	17.5104i	−0.884875	+	0.662777i
$699$		0			0
$700$	8.98440	+	2.63286i	0.339579	+	0.0995128i
$701$		−	24.3454i		−	0.919513i	−0.888045	−	0.459757i	$-0.847937\pi$
$701$		−	24.3454i		−	0.919513i	0.888045	−	0.459757i	$-0.152063\pi$
$702$		0			0
$703$	40.9641	+	26.9862i	1.54499	+	1.01780i
$704$	−34.8222	+	30.2711i	−1.31241	+	1.14089i
$705$		0			0
$706$	20.2056	+	26.9765i	0.760448	+	1.01528i
$707$	−27.9851			−1.05249
$708$		0			0
$709$		−	45.9431i		−	1.72543i	−0.505690	−	0.862715i	$-0.668762\pi$
$709$		−	45.9431i		−	1.72543i	0.505690	−	0.862715i	$-0.331238\pi$
$710$	12.9333	−	9.68712i	0.485378	−	0.363551i
$711$		0			0
$712$	−8.96972	−	23.9902i	−0.336155	−	0.899071i
$713$			7.71672i			0.288993i
$714$		0			0
$715$			28.7382i			1.07475i
$716$	19.8974	+	5.83090i	0.743602	+	0.217911i
$717$		0			0
$718$	9.39521	−	7.03707i	0.350626	−	0.262621i
$719$		−	29.9952i		−	1.11863i	−0.828955	−	0.559316i	$-0.811064\pi$
$719$		−	29.9952i		−	1.11863i	0.828955	−	0.559316i	$-0.188936\pi$
$720$		0			0
$721$			36.6410i			1.36458i
$722$	13.4019	−	23.2892i	0.498768	−	0.866736i
$723$		0			0
$724$	8.29385	−	28.3020i	0.308238	−	1.05184i
$725$	−11.9207			−0.442722
$726$		0			0
$727$		−	17.4851i		−	0.648486i	−0.945974	−	0.324243i	$-0.894890\pi$
$727$		−	17.4851i		−	0.648486i	0.945974	−	0.324243i	$-0.105110\pi$
$728$	5.97422	+	15.9785i	0.221419	+	0.592203i
$729$		0			0
$730$	−10.0684	+	7.54128i	−0.372647	+	0.279115i
$731$	11.7097			0.433098
$732$		0			0
$733$		−	7.90958i		−	0.292147i	−0.989274	−	0.146073i	$-0.953336\pi$
$733$		−	7.90958i		−	0.292147i	0.989274	−	0.146073i	$-0.0466636\pi$
$734$	−6.38384	+	4.78154i	−0.235632	+	0.176490i
$735$		0			0
$736$	8.97529	−	0.653942i	0.330834	−	0.0241046i
$737$			93.5610i			3.44636i
$738$		0			0
$739$	8.55631			0.314749			0.157375	−	0.987539i	$-0.449697\pi$
$739$	8.55631			0.314749			0.157375	+	0.987539i	$0.449697\pi$
$740$	55.1316	+	16.1562i	2.02668	+	0.593914i
$741$		0			0
$742$	37.0596	−	27.7579i	1.36050	−	1.01902i
$743$	39.2358			1.43942			0.719711	−	0.694273i	$-0.244274\pi$
$743$	39.2358			1.43942			0.719711	+	0.694273i	$0.244274\pi$
$744$		0			0
$745$	31.3856			1.14988
$746$	−5.46841	−	7.30088i	−0.200213	−	0.267304i
$747$		0			0
$748$	−4.53573	+	15.4778i	−0.165843	+	0.565923i
$749$	1.32344			0.0483574
$750$		0			0
$751$	−11.0599			−0.403583			−0.201792	−	0.979428i	$-0.564676\pi$
$751$	−11.0599			−0.403583			−0.201792	+	0.979428i	$0.564676\pi$
$752$	19.2966	−	30.0966i	0.703675	−	1.09751i
$753$		0			0
$754$	−13.0212	−	17.3847i	−0.474206	−	0.633113i
$755$			8.66664i			0.315411i
$756$		0			0
$757$			17.6577i			0.641778i	0.947117	+	0.320889i	$0.103982\pi$
$757$			17.6577i			0.641778i	−0.947117	+	0.320889i	$0.896018\pi$
$758$		0			0
$759$		0			0
$760$	7.01243	−	30.6778i	0.254367	−	1.11280i
$761$	−0.635615			−0.0230410			−0.0115205	−	0.999934i	$-0.503667\pi$
$761$	−0.635615			−0.0230410			−0.0115205	+	0.999934i	$0.503667\pi$
$762$		0			0
$763$			11.2809i			0.408395i
$764$	12.5680	+	3.68303i	0.454695	+	0.133247i
$765$		0			0
$766$	−19.0908	−	25.4882i	−0.689780	−	0.920926i
$767$			25.0585i			0.904810i
$768$		0			0
$769$	−44.8236			−1.61638			−0.808191	−	0.588921i	$-0.799553\pi$
$769$	−44.8236			−1.61638			−0.808191	+	0.588921i	$0.799553\pi$
$770$	38.5609	+	51.4827i	1.38964	+	1.85531i
$771$		0			0
$772$	−23.7260	−	6.95285i	−0.853917	−	0.250239i
$773$	−31.2326			−1.12336			−0.561679	−	0.827355i	$-0.689844\pi$
$773$	−31.2326			−1.12336			−0.561679	+	0.827355i	$0.689844\pi$
$774$		0			0
$775$	7.34956			0.264004
$776$	14.5485	+	38.9110i	0.522260	+	1.39682i
$777$		0			0
$778$	3.68882	−	2.76295i	0.132251	−	0.0990566i
$779$	−16.4500	+	24.9706i	−0.589384	+	0.894664i
$780$		0			0
$781$	25.8182			0.923847
$782$	2.51776	−	1.88582i	0.0900348	−	0.0674366i
$783$		0			0
$784$	8.57121	+	5.49549i	0.306115	+	0.196267i
$785$	10.0945			0.360288
$786$		0			0
$787$			22.1080i			0.788066i	0.919096	+	0.394033i	$0.128920\pi$
$787$			22.1080i			0.788066i	−0.919096	+	0.394033i	$0.871080\pi$
$788$	16.0289	+	4.69723i	0.571005	+	0.167332i
$789$		0			0
$790$	−25.9991	+	19.4735i	−0.925006	+	0.692835i
$791$	21.5353			0.765707
$792$		0			0
$793$			12.8156i			0.455096i
$794$	40.7578	−	30.5278i	1.44644	−	1.08339i
$795$		0			0
$796$	−7.76990	−	2.27695i	−0.275397	−	0.0807045i
$797$	33.6741			1.19280			0.596399	−	0.802688i	$-0.296598\pi$
$797$	33.6741			1.19280			0.596399	+	0.802688i	$0.296598\pi$
$798$		0			0
$799$		−	12.4972i		−	0.442118i
$800$	−0.622828	−	8.54826i	−0.0220203	−	0.302226i
$801$		0			0
$802$	23.4196	−	17.5414i	0.826975	−	0.619410i
$803$	−20.0991			−0.709280
$804$		0			0
$805$		−	12.5453i		−	0.442165i
$806$	8.02812	+	10.7184i	0.282778	+	0.377538i
$807$		0			0
$808$	8.97236	+	23.9972i	0.315646	+	0.844220i
$809$	−3.10336			−0.109108			−0.0545542	−	0.998511i	$-0.517374\pi$
$809$	−3.10336			−0.109108			−0.0545542	+	0.998511i	$0.517374\pi$
$810$		0			0
$811$			23.4885i			0.824793i	0.911005	+	0.412396i	$0.135308\pi$
$811$			23.4885i			0.824793i	−0.911005	+	0.412396i	$0.864692\pi$
$812$	−46.6536	−	13.6717i	−1.63722	−	0.479784i
$813$		0			0
$814$	55.0284	+	73.4686i	1.92875	+	2.57507i
$815$		−	21.0573i		−	0.737607i
$816$		0			0
$817$	−30.4839	−	20.0821i	−1.06650	−	0.702584i
$818$	25.8666	−	19.3742i	0.904404	−	0.677405i
$819$		0			0
$820$	−9.84837	+	33.6067i	−0.343920	+	1.17360i
$821$			15.4088i			0.537773i	0.963172	+	0.268886i	$0.0866556\pi$
$821$			15.4088i			0.537773i	−0.963172	+	0.268886i	$0.913344\pi$
$822$		0			0
$823$		−	10.9991i		−	0.383406i	−0.981453	−	0.191703i	$-0.938599\pi$
$823$		−	10.9991i		−	0.383406i	0.981453	−	0.191703i	$-0.0614010\pi$
$824$	31.4197	−	11.7475i	1.09456	−	0.409245i
$825$		0			0
$826$	33.6235	+	44.8908i	1.16991	+	1.56195i
$827$		−	44.7336i		−	1.55554i	−0.628550	−	0.777770i	$-0.716351\pi$
$827$		−	44.7336i		−	1.55554i	0.628550	−	0.777770i	$-0.283649\pi$
$828$		0			0
$829$	−32.9618			−1.14481			−0.572405	−	0.819971i	$-0.693989\pi$
$829$	−32.9618			−1.14481			−0.572405	+	0.819971i	$0.693989\pi$
$830$	−25.2474	+	18.9104i	−0.876349	+	0.656391i
$831$		0			0
$832$	11.7862	−	10.2458i	0.408612	−	0.355209i
$833$	3.55907			0.123315
$834$		0			0
$835$			11.4261i			0.395416i
$836$	38.3523	−	32.5146i	1.32644	−	1.12454i
$837$		0			0
$838$	−18.4095	−	24.5786i	−0.635946	−	0.849053i
$839$	15.5301			0.536157			0.268078	−	0.963397i	$-0.413611\pi$
$839$	15.5301			0.536157			0.268078	+	0.963397i	$0.413611\pi$
$840$		0			0
$841$	32.9007			1.13451
$842$	29.1368	+	38.9006i	1.00412	+	1.34060i
$843$		0			0
$844$	35.5977	+	10.4318i	1.22532	+	0.359078i
$845$			23.4553i			0.806886i
$846$		0			0
$847$			68.7875i			2.36357i
$848$	−35.6842	−	22.8791i	−1.22540	−	0.785673i
$849$		0			0
$850$	−1.79609	−	2.39796i	−0.0616054	−	0.0822495i
$851$		−	17.9029i		−	0.613703i
$852$		0			0
$853$			36.1160i			1.23659i	0.785947	+	0.618295i	$0.212176\pi$
$853$			36.1160i			1.23659i	−0.785947	+	0.618295i	$0.787824\pi$
$854$	17.1960	+	22.9584i	0.588436	+	0.785622i
$855$		0			0
$856$	−0.424310	−	1.13485i	−0.0145026	−	0.0387883i
$857$		−	27.3297i		−	0.933564i	−0.884372	−	0.466782i	$-0.845413\pi$
$857$		−	27.3297i		−	0.933564i	0.884372	−	0.466782i	$-0.154587\pi$
$858$		0			0
$859$	2.97350			0.101455			0.0507273	−	0.998713i	$-0.483846\pi$
$859$	2.97350			0.101455			0.0507273	+	0.998713i	$0.483846\pi$
$860$	−41.0269	−	12.0228i	−1.39900	−	0.409975i
$861$		0			0
$862$	−8.42339	−	11.2461i	−0.286902	−	0.383043i
$863$	5.66437			0.192818			0.0964088	−	0.995342i	$-0.469264\pi$
$863$	5.66437			0.192818			0.0964088	+	0.995342i	$0.469264\pi$
$864$		0			0
$865$			4.19699i			0.142702i
$866$	13.8282	−	10.3574i	0.469901	−	0.351959i
$867$		0			0
$868$	28.7638	+	8.42917i	0.976307	+	0.286105i
$869$	−51.9008			−1.76062
$870$		0			0
$871$		−	31.6673i		−	1.07301i
$872$	9.67335	−	3.61678i	0.327581	−	0.122480i
$873$		0			0
$874$	−9.78867	+	0.591409i	−0.331107	+	0.0200047i
$875$	27.4818			0.929054
$876$		0			0
$877$	−15.7638			−0.532307			−0.266154	−	0.963931i	$-0.585753\pi$
$877$	−15.7638			−0.532307			−0.266154	+	0.963931i	$0.585753\pi$
$878$	4.15484	+	5.54714i	0.140219	+	0.187207i
$879$		0			0
$880$	31.7834	−	49.5719i	1.07142	−	1.67107i
$881$	20.3160			0.684464			0.342232	−	0.939616i	$-0.388817\pi$
$881$	20.3160			0.684464			0.342232	+	0.939616i	$0.388817\pi$
$882$		0			0
$883$	−47.2744			−1.59091			−0.795456	−	0.606012i	$-0.792768\pi$
$883$	−47.2744			−1.59091			−0.795456	+	0.606012i	$0.792768\pi$
$884$	1.53520	−	5.23872i	0.0516342	−	0.176197i
$885$		0			0
$886$	2.51890	+	3.36299i	0.0846242	+	0.112982i
$887$	7.97037			0.267619			0.133809	−	0.991007i	$-0.457279\pi$
$887$	7.97037			0.267619			0.133809	+	0.991007i	$0.457279\pi$
$888$		0			0
$889$		−	4.64166i		−	0.155676i
$890$	19.5957	+	26.1623i	0.656850	+	0.876962i
$891$		0			0
$892$	−5.03322	+	17.1754i	−0.168525	+	0.575076i
$893$	−21.4326	+	32.5340i	−0.717216	+	1.08871i
$894$		0			0
$895$	−26.4618			−0.884520
$896$	7.36640	−	34.1694i	0.246094	−	1.14152i
$897$		0			0
$898$	−27.7796	+	20.8071i	−0.927017	+	0.694342i
$899$	−38.1643			−1.27285
$900$		0			0
$901$	−14.8173			−0.493637
$902$	−44.7844	+	33.5438i	−1.49116	+	1.11689i
$903$		0			0
$904$	−6.90447	−	18.4665i	−0.229639	−	0.614188i
$905$			37.6391i			1.25117i
$906$		0			0
$907$		−	27.5029i		−	0.913218i	−0.889667	−	0.456609i	$-0.849064\pi$
$907$		−	27.5029i		−	0.913218i	0.889667	−	0.456609i	$-0.150936\pi$
$908$	−30.0711	−	8.81228i	−0.997946	−	0.292446i
$909$		0			0
$910$	−13.0516	−	17.4252i	−0.432656	−	0.577640i
$911$	32.3178			1.07074			0.535369	−	0.844618i	$-0.320173\pi$
$911$	32.3178			1.07074			0.535369	+	0.844618i	$0.320173\pi$
$912$		0			0
$913$	−50.4002			−1.66800
$914$	−20.1473	−	26.8987i	−0.666414	−	0.889730i
$915$		0			0
$916$	6.84983	+	2.00733i	0.226325	+	0.0663240i
$917$			42.7231i			1.41084i
$918$		0			0
$919$		−	20.9942i		−	0.692534i	−0.938136	−	0.346267i	$-0.887449\pi$
$919$		−	20.9942i		−	0.692534i	0.938136	−	0.346267i	$-0.112551\pi$
$920$	−10.7576	+	4.02219i	−0.354669	+	0.132608i
$921$		0			0
$922$	−27.3489	+	20.4845i	−0.900688	+	0.674621i
$923$	−8.73861			−0.287635
$924$		0			0
$925$	−17.0511			−0.560636
$926$	−37.9092	+	28.3942i	−1.24577	+	0.933092i
$927$		0			0
$928$	3.23417	+	44.3888i	0.106167	+	1.45713i
$929$	−54.6143			−1.79184			−0.895919	−	0.444218i	$-0.853482\pi$
$929$	−54.6143			−1.79184			−0.895919	+	0.444218i	$0.853482\pi$
$930$		0			0
$931$	−9.26537	−	6.10381i	−0.303660	−	0.200044i
$932$	8.08447	−	27.5875i	0.264816	−	0.903660i
$933$		0			0
$934$	14.9654	+	19.9803i	0.489682	+	0.653775i
$935$		−	20.5840i		−	0.673170i
$936$		0			0
$937$	15.8557			0.517984			0.258992	−	0.965879i	$-0.416610\pi$
$937$	15.8557			0.517984			0.258992	+	0.965879i	$0.416610\pi$
$938$	−42.4912	−	56.7302i	−1.38739	−	1.85231i
$939$		0			0
$940$	−12.8314	+	43.7859i	−0.418513	+	1.42814i
$941$	52.1390			1.69968			0.849842	−	0.527038i	$-0.176697\pi$
$941$	52.1390			1.69968			0.849842	+	0.527038i	$0.176697\pi$
$942$		0			0
$943$	10.9131			0.355379
$944$	27.7138	−	43.2247i	0.902007	−	1.40684i
$945$		0			0
$946$	−40.9501	−	54.6725i	−1.33140	−	1.77756i
$947$	−18.2398			−0.592715			−0.296357	−	0.955077i	$-0.595772\pi$
$947$	−18.2398			−0.592715			−0.296357	+	0.955077i	$0.595772\pi$
$948$		0			0
$949$	6.80288			0.220831
$950$	0.563270	+	9.32294i	0.0182749	+	0.302476i
$951$		0			0
$952$	−4.27910	−	11.4448i	−0.138687	−	0.370927i
$953$			45.0119i			1.45808i	0.684472	+	0.729039i	$0.260033\pi$
$953$			45.0119i			1.45808i	−0.684472	+	0.729039i	$0.739967\pi$
$954$		0			0
$955$	−16.7143			−0.540863
$956$	−45.1394	−	13.2280i	−1.45991	−	0.427824i
$957$		0			0
$958$	21.1068	−	15.8091i	0.681929	−	0.510769i
$959$		−	29.2239i		−	0.943688i
$960$		0			0
$961$	−7.47018			−0.240974
$962$	−18.6253	−	24.8667i	−0.600505	−	0.801735i
$963$		0			0
$964$	33.5055	+	9.81872i	1.07914	+	0.316240i
$965$	31.5534			1.01574
$966$		0			0
$967$			42.3405i			1.36158i	0.732479	+	0.680789i	$0.238363\pi$
$967$			42.3405i			1.36158i	−0.732479	+	0.680789i	$0.761637\pi$
$968$	58.9853	−	22.0541i	1.89586	−	0.708845i
$969$		0			0
$970$	−31.7834	−	42.4340i	−1.02050	−	1.36248i
$971$		−	26.2556i		−	0.842584i	−0.906925	−	0.421292i	$-0.861577\pi$
$971$		−	26.2556i		−	0.842584i	0.906925	−	0.421292i	$-0.138423\pi$
$972$		0			0
$973$			35.2363i			1.12962i
$974$	−11.7019	−	15.6232i	−0.374953	−	0.500601i
$975$		0			0
$976$	14.1736	−	22.1063i	0.453687	−	0.707607i
$977$		−	6.63934i		−	0.212411i	−0.994344	−	0.106206i	$-0.966130\pi$
$977$		−	6.63934i		−	0.212411i	0.994344	−	0.106206i	$-0.0338702\pi$
$978$		0			0
$979$			52.2267i			1.66917i
$980$	−12.4698	−	3.65425i	−0.398334	−	0.116731i
$981$		0			0
$982$	2.94563	+	3.93272i	0.0939988	+	0.125498i
$983$	−49.1713			−1.56832			−0.784161	−	0.620558i	$-0.786906\pi$
$983$	−49.1713			−1.56832			−0.784161	+	0.620558i	$0.786906\pi$
$984$		0			0
$985$	−21.3170			−0.679215
$986$	9.32661	+	12.4520i	0.297020	+	0.396552i
$987$		0			0
$988$	−12.9810	+	11.0051i	−0.412980	+	0.350120i
$989$			13.3226i			0.423635i
$990$		0			0
$991$	48.1910			1.53084			0.765419	−	0.643532i	$-0.222532\pi$
$991$	48.1910			1.53084			0.765419	+	0.643532i	$0.222532\pi$
$992$	−1.99400	−	27.3675i	−0.0633095	−	0.868918i
$993$		0			0
$994$	−15.6547	+	11.7255i	−0.496537	+	0.371909i
$995$	10.3333			0.327587
$996$		0			0
$997$			1.53168i			0.0485089i	0.999706	+	0.0242545i	$0.00772120\pi$
$997$			1.53168i			0.0485089i	−0.999706	+	0.0242545i	$0.992279\pi$
$998$	15.0769	+	20.1292i	0.477250	+	0.637178i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.f.379.9	✓	24
3.2	odd	2	inner	1368.2.e.f.379.16	yes	24
4.3	odd	2		5472.2.e.f.5167.21		24
8.3	odd	2	inner	1368.2.e.f.379.13	yes	24
8.5	even	2		5472.2.e.f.5167.14		24
12.11	even	2		5472.2.e.f.5167.8		24
19.18	odd	2	inner	1368.2.e.f.379.15	yes	24
24.5	odd	2		5472.2.e.f.5167.1		24
24.11	even	2	inner	1368.2.e.f.379.12	yes	24
57.56	even	2	inner	1368.2.e.f.379.10	yes	24
76.75	even	2		5472.2.e.f.5167.13		24
152.37	odd	2		5472.2.e.f.5167.22		24
152.75	even	2	inner	1368.2.e.f.379.11	yes	24
228.227	odd	2		5472.2.e.f.5167.2		24
456.227	odd	2	inner	1368.2.e.f.379.14	yes	24
456.341	even	2		5472.2.e.f.5167.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.e.f.379.9	✓	24	1.1	even	1	trivial
1368.2.e.f.379.10	yes	24	57.56	even	2	inner
1368.2.e.f.379.11	yes	24	152.75	even	2	inner
1368.2.e.f.379.12	yes	24	24.11	even	2	inner
1368.2.e.f.379.13	yes	24	8.3	odd	2	inner
1368.2.e.f.379.14	yes	24	456.227	odd	2	inner
1368.2.e.f.379.15	yes	24	19.18	odd	2	inner
1368.2.e.f.379.16	yes	24	3.2	odd	2	inner
5472.2.e.f.5167.1		24	24.5	odd	2
5472.2.e.f.5167.2		24	228.227	odd	2
5472.2.e.f.5167.7		24	456.341	even	2
5472.2.e.f.5167.8		24	12.11	even	2
5472.2.e.f.5167.13		24	76.75	even	2
5472.2.e.f.5167.14		24	8.5	even	2
5472.2.e.f.5167.21		24	4.3	odd	2
5472.2.e.f.5167.22		24	152.37	odd	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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.847808 - 1.13191i) q^{2} +(-0.562443 + 1.91929i) q^{4} -2.55248i q^{5} +3.08957i q^{7} +(2.64930 - 0.990551i) q^{8} +O(q^{10})\)	\(q+(-0.847808 - 1.13191i) q^{2} +(-0.562443 + 1.91929i) q^{4} -2.55248i q^{5} +3.08957i q^{7} +(2.64930 - 0.990551i) q^{8} +(-2.88918 + 2.16401i) q^{10} -5.76753 q^{11} +1.95212 q^{13} +(3.49711 - 2.61936i) q^{14} +(-3.36732 - 2.15898i) q^{16} -1.39823 q^{17} +(3.64002 + 2.39796i) q^{19} +(4.89893 + 1.43562i) q^{20} +(4.88976 + 6.52833i) q^{22} -1.59083i q^{23} -1.51514 q^{25} +(-1.65503 - 2.20963i) q^{26} +(-5.92976 - 1.73770i) q^{28} +7.86770 q^{29} -4.85075 q^{31} +(0.411070 + 5.64190i) q^{32} +(1.18543 + 1.58267i) q^{34} +7.88604 q^{35} +11.2538 q^{37} +(-0.371761 - 6.15319i) q^{38} +(-2.52836 - 6.76229i) q^{40} +6.86000i q^{41} -8.37466 q^{43} +(3.24391 - 11.0695i) q^{44} +(-1.80068 + 1.34872i) q^{46} +8.93785i q^{47} -2.54541 q^{49} +(1.28455 + 1.71500i) q^{50} +(-1.09796 + 3.74668i) q^{52} +10.5972 q^{53} +14.7215i q^{55} +(3.06037 + 8.18520i) q^{56} +(-6.67030 - 8.90553i) q^{58} +12.8365i q^{59} +6.56497i q^{61} +(4.11251 + 5.49062i) q^{62} +(6.03762 - 5.24854i) q^{64} -4.98275i q^{65} -16.2220i q^{67} +(0.786424 - 2.68360i) q^{68} +(-6.68585 - 8.92630i) q^{70} -4.47647 q^{71} +3.48486 q^{73} +(-9.54107 - 12.7383i) q^{74} +(-6.64968 + 5.63753i) q^{76} -17.8192i q^{77} +8.99879 q^{79} +(-5.51074 + 8.59500i) q^{80} +(7.76491 - 5.81597i) q^{82} +8.73861 q^{83} +3.56895i q^{85} +(7.10010 + 9.47936i) q^{86} +(-15.2799 + 5.71304i) q^{88} -9.05528i q^{89} +6.03121i q^{91} +(3.05325 + 0.894750i) q^{92} +(10.1168 - 7.57758i) q^{94} +(6.12075 - 9.29108i) q^{95} +14.6873i q^{97} +(2.15802 + 2.88118i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4}+O(q^{10}) \) 24 * q + 20 * q^4	\( 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) \) 24 * q + 20 * q^4 - 12 * q^16 + 24 * q^19 - 40 * q^25 - 40 * q^28 - 72 * q^49 - 104 * q^58 + 20 * q^64 + 80 * q^73 - 12 * q^76 + 56 * q^82

Introduction

L-functions

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