LMFDB - Embedded newform 1344.2.u.a.1231.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 2]))

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.22
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-0.394206 + 0.394206i) q^{5} +(-0.0114637 + 2.64573i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.394206 + 0.394206i) q^{5} +(-0.0114637 + 2.64573i) q^{7} -1.00000i q^{9} +(-3.13004 + 3.13004i) q^{11} +(1.70772 + 1.70772i) q^{13} +0.557492i q^{15} -4.33838i q^{17} +(0.222492 - 0.222492i) q^{19} +(1.86271 + 1.87892i) q^{21} -0.538046 q^{23} +4.68920i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-5.16269 + 5.16269i) q^{29} -7.80935 q^{31} +4.42655i q^{33} +(-1.03844 - 1.04748i) q^{35} +(4.56570 + 4.56570i) q^{37} +2.41508 q^{39} -11.9367 q^{41} +(-4.29970 + 4.29970i) q^{43} +(0.394206 + 0.394206i) q^{45} +6.84515 q^{47} +(-6.99974 - 0.0606596i) q^{49} +(-3.06770 - 3.06770i) q^{51} +(9.04315 + 9.04315i) q^{53} -2.46776i q^{55} -0.314652i q^{57} +(-3.72516 - 3.72516i) q^{59} +(4.88759 + 4.88759i) q^{61} +(2.64573 + 0.0114637i) q^{63} -1.34639 q^{65} +(1.78508 + 1.78508i) q^{67} +(-0.380456 + 0.380456i) q^{69} +4.52303 q^{71} +14.2966 q^{73} +(3.31577 + 3.31577i) q^{75} +(-8.24535 - 8.31712i) q^{77} -0.0344876i q^{79} -1.00000 q^{81} +(0.301770 - 0.301770i) q^{83} +(1.71022 + 1.71022i) q^{85} +7.30114i q^{87} +4.54387 q^{89} +(-4.53774 + 4.49859i) q^{91} +(-5.52205 + 5.52205i) q^{93} +0.175416i q^{95} +0.0969036i q^{97} +(3.13004 + 3.13004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−0.394206	+	0.394206i	−0.176294	+	0.176294i	−0.789738	−	0.613444i	$-0.789784\pi$
$5$	−0.394206	+	0.394206i	−0.176294	+	0.176294i	0.613444	+	0.789738i	$0.289784\pi$
$6$		0			0
$7$	−0.0114637	+	2.64573i	−0.00433287	+	0.999991i
$7$	−0.0114637	+	2.64573i	−0.00433287	+	0.999991i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.13004	+	3.13004i	−0.943743	+	0.943743i	−0.998500	−	0.0547566i	$-0.982562\pi$
$11$	−3.13004	+	3.13004i	−0.943743	+	0.943743i	0.0547566	+	0.998500i	$0.482562\pi$
$12$		0			0
$13$	1.70772	+	1.70772i	0.473637	+	0.473637i	0.903089	−	0.429453i	$-0.141293\pi$
$13$	1.70772	+	1.70772i	0.473637	+	0.473637i	−0.429453	+	0.903089i	$0.641293\pi$
$14$		0			0
$15$			0.557492i			0.143944i
$16$		0			0
$17$		−	4.33838i		−	1.05221i	−0.850419	−	0.526106i	$-0.823652\pi$
$17$		−	4.33838i		−	1.05221i	0.850419	−	0.526106i	$-0.176348\pi$
$18$		0			0
$19$	0.222492	−	0.222492i	0.0510432	−	0.0510432i	−0.681124	−	0.732168i	$-0.738509\pi$
$19$	0.222492	−	0.222492i	0.0510432	−	0.0510432i	0.732168	+	0.681124i	$0.238509\pi$
$20$		0			0
$21$	1.86271	+	1.87892i	0.406476	+	0.410013i
$22$		0			0
$23$	−0.538046			−0.112190			−0.0560952	−	0.998425i	$-0.517865\pi$
$23$	−0.538046			−0.112190			−0.0560952	+	0.998425i	$0.517865\pi$
$24$		0			0
$25$			4.68920i			0.937841i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−5.16269	+	5.16269i	−0.958687	+	0.958687i	−0.999180	−	0.0404926i	$-0.987107\pi$
$29$	−5.16269	+	5.16269i	−0.958687	+	0.958687i	0.0404926	+	0.999180i	$0.487107\pi$
$30$		0			0
$31$	−7.80935			−1.40260			−0.701301	−	0.712866i	$-0.747397\pi$
$31$	−7.80935			−1.40260			−0.701301	+	0.712866i	$0.747397\pi$
$32$		0			0
$33$			4.42655i			0.770563i
$34$		0			0
$35$	−1.03844	−	1.04748i	−0.175529	−	0.177057i
$36$		0			0
$37$	4.56570	+	4.56570i	0.750597	+	0.750597i	0.974591	−	0.223994i	$-0.0719095\pi$
$37$	4.56570	+	4.56570i	0.750597	+	0.750597i	−0.223994	+	0.974591i	$0.571909\pi$
$38$		0			0
$39$	2.41508			0.386723
$40$		0			0
$41$	−11.9367			−1.86420			−0.932100	−	0.362201i	$-0.882025\pi$
$41$	−11.9367			−1.86420			−0.932100	+	0.362201i	$0.882025\pi$
$42$		0			0
$43$	−4.29970	+	4.29970i	−0.655698	+	0.655698i	−0.954359	−	0.298661i	$-0.903460\pi$
$43$	−4.29970	+	4.29970i	−0.655698	+	0.655698i	0.298661	+	0.954359i	$0.403460\pi$
$44$		0			0
$45$	0.394206	+	0.394206i	0.0587648	+	0.0587648i
$46$		0			0
$47$	6.84515			0.998468			0.499234	−	0.866467i	$-0.333615\pi$
$47$	6.84515			0.998468			0.499234	+	0.866467i	$0.333615\pi$
$48$		0			0
$49$	−6.99974	−	0.0606596i	−0.999962	−	0.00866566i
$50$		0			0
$51$	−3.06770	−	3.06770i	−0.429564	−	0.429564i
$52$		0			0
$53$	9.04315	+	9.04315i	1.24217	+	1.24217i	0.959098	+	0.283074i	$0.0913541\pi$
$53$	9.04315	+	9.04315i	1.24217	+	1.24217i	0.283074	+	0.959098i	$0.408646\pi$
$54$		0			0
$55$		−	2.46776i		−	0.332753i
$56$		0			0
$57$		−	0.314652i		−	0.0416766i
$58$		0			0
$59$	−3.72516	−	3.72516i	−0.484975	−	0.484975i	0.421742	−	0.906716i	$-0.361419\pi$
$59$	−3.72516	−	3.72516i	−0.484975	−	0.484975i	−0.906716	+	0.421742i	$0.861419\pi$
$60$		0			0
$61$	4.88759	+	4.88759i	0.625792	+	0.625792i	0.947006	−	0.321215i	$-0.104091\pi$
$61$	4.88759	+	4.88759i	0.625792	+	0.625792i	−0.321215	+	0.947006i	$0.604091\pi$
$62$		0			0
$63$	2.64573	+	0.0114637i	0.333330	+	0.00144429i
$64$		0			0
$65$	−1.34639			−0.166999
$66$		0			0
$67$	1.78508	+	1.78508i	0.218083	+	0.218083i	0.807690	−	0.589607i	$-0.200717\pi$
$67$	1.78508	+	1.78508i	0.218083	+	0.218083i	−0.589607	+	0.807690i	$0.700717\pi$
$68$		0			0
$69$	−0.380456	+	0.380456i	−0.0458015	+	0.0458015i
$70$		0			0
$71$	4.52303			0.536785			0.268393	−	0.963310i	$-0.413508\pi$
$71$	4.52303			0.536785			0.268393	+	0.963310i	$0.413508\pi$
$72$		0			0
$73$	14.2966			1.67329			0.836643	−	0.547749i	$-0.184515\pi$
$73$	14.2966			1.67329			0.836643	+	0.547749i	$0.184515\pi$
$74$		0			0
$75$	3.31577	+	3.31577i	0.382872	+	0.382872i
$76$		0			0
$77$	−8.24535	−	8.31712i	−0.939645	−	0.947823i
$78$		0			0
$79$		−	0.0344876i		−	0.00388016i	−0.999998	−	0.00194008i	$-0.999382\pi$
$79$		−	0.0344876i		−	0.00388016i	0.999998	−	0.00194008i	$-0.000617546\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	0.301770	−	0.301770i	0.0331236	−	0.0331236i	−0.690351	−	0.723475i	$-0.742544\pi$
$83$	0.301770	−	0.301770i	0.0331236	−	0.0331236i	0.723475	+	0.690351i	$0.242544\pi$
$84$		0			0
$85$	1.71022	+	1.71022i	0.185499	+	0.185499i
$86$		0			0
$87$			7.30114i			0.782765i
$88$		0			0
$89$	4.54387			0.481649			0.240824	−	0.970569i	$-0.422582\pi$
$89$	4.54387			0.481649			0.240824	+	0.970569i	$0.422582\pi$
$90$		0			0
$91$	−4.53774	+	4.49859i	−0.475684	+	0.471580i
$92$		0			0
$93$	−5.52205	+	5.52205i	−0.572610	+	0.572610i
$94$		0			0
$95$			0.175416i			0.0179973i
$96$		0			0
$97$			0.0969036i			0.00983907i	0.999988	+	0.00491954i	$0.00156594\pi$
$97$			0.0969036i			0.00983907i	−0.999988	+	0.00491954i	$0.998434\pi$
$98$		0			0
$99$	3.13004	+	3.13004i	0.314581	+	0.314581i
$100$		0			0
$101$	6.49968	−	6.49968i	0.646743	−	0.646743i	−0.305462	−	0.952204i	$-0.598811\pi$
$101$	6.49968	−	6.49968i	0.646743	−	0.646743i	0.952204	+	0.305462i	$0.0988108\pi$
$102$		0			0
$103$		−	6.04998i		−	0.596122i	−0.954547	−	0.298061i	$-0.903660\pi$
$103$		−	6.04998i		−	0.596122i	0.954547	−	0.298061i	$-0.0963399\pi$
$104$		0			0
$105$	−1.47497	−	0.00639091i	−0.143942	−	0.000623689i
$106$		0			0
$107$	−9.90493	+	9.90493i	−0.957546	+	0.957546i	−0.999135	−	0.0415886i	$-0.986758\pi$
$107$	−9.90493	+	9.90493i	−0.957546	+	0.957546i	0.0415886	+	0.999135i	$0.486758\pi$
$108$		0			0
$109$	−6.32076	+	6.32076i	−0.605419	+	0.605419i	−0.941746	−	0.336326i	$-0.890815\pi$
$109$	−6.32076	+	6.32076i	−0.605419	+	0.605419i	0.336326	+	0.941746i	$0.390815\pi$
$110$		0			0
$111$	6.45688			0.612860
$112$		0			0
$113$	−4.89913			−0.460871			−0.230435	−	0.973088i	$-0.574015\pi$
$113$	−4.89913			−0.460871			−0.230435	+	0.973088i	$0.574015\pi$
$114$		0			0
$115$	0.212101	−	0.212101i	0.0197785	−	0.0197785i
$116$		0			0
$117$	1.70772	−	1.70772i	0.157879	−	0.157879i
$118$		0			0
$119$	11.4782	+	0.0497339i	1.05220	+	0.00455910i
$120$		0			0
$121$		−	8.59432i		−	0.781302i
$122$		0			0
$123$	−8.44052	+	8.44052i	−0.761056	+	0.761056i
$124$		0			0
$125$	−3.81954	−	3.81954i	−0.341630	−	0.341630i
$126$		0			0
$127$			0.494752i			0.0439022i	0.999759	+	0.0219511i	$0.00698781\pi$
$127$			0.494752i			0.0439022i	−0.999759	+	0.0219511i	$0.993012\pi$
$128$		0			0
$129$			6.08069i			0.535375i
$130$		0			0
$131$	3.50569	−	3.50569i	0.306293	−	0.306293i	−0.537177	−	0.843470i	$-0.680509\pi$
$131$	3.50569	−	3.50569i	0.306293	−	0.306293i	0.843470	+	0.537177i	$0.180509\pi$
$132$		0			0
$133$	0.586103	+	0.591204i	0.0508216	+	0.0512639i
$134$		0			0
$135$	0.557492			0.0479812
$136$		0			0
$137$		−	15.8743i		−	1.35623i	−0.734956	−	0.678115i	$-0.762797\pi$
$137$		−	15.8743i		−	1.35623i	0.734956	−	0.678115i	$-0.237203\pi$
$138$		0			0
$139$	3.82317	+	3.82317i	0.324277	+	0.324277i	0.850405	−	0.526128i	$-0.176357\pi$
$139$	3.82317	+	3.82317i	0.324277	+	0.324277i	−0.526128	+	0.850405i	$0.676357\pi$
$140$		0			0
$141$	4.84025	−	4.84025i	0.407623	−	0.407623i
$142$		0			0
$143$	−10.6905			−0.893983
$144$		0			0
$145$		−	4.07033i		−	0.338022i
$146$		0			0
$147$	−4.99245	+	4.90667i	−0.411771	+	0.404695i
$148$		0			0
$149$	−2.93581	−	2.93581i	−0.240511	−	0.240511i	0.576550	−	0.817062i	$-0.304398\pi$
$149$	−2.93581	−	2.93581i	−0.240511	−	0.240511i	−0.817062	+	0.576550i	$0.804398\pi$
$150$		0			0
$151$	16.5324			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$151$	16.5324			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$152$		0			0
$153$	−4.33838			−0.350737
$154$		0			0
$155$	3.07850	−	3.07850i	0.247271	−	0.247271i
$156$		0			0
$157$	14.0002	+	14.0002i	1.11733	+	1.11733i	0.992131	+	0.125203i	$0.0399581\pi$
$157$	14.0002	+	14.0002i	1.11733	+	1.11733i	0.125203	+	0.992131i	$0.460042\pi$
$158$		0			0
$159$	12.7889			1.01423
$160$		0			0
$161$	0.00616800	−	1.42352i	0.000486106	−	0.112189i
$162$		0			0
$163$	5.09056	+	5.09056i	0.398724	+	0.398724i	0.877783	−	0.479059i	$-0.159022\pi$
$163$	5.09056	+	5.09056i	0.398724	+	0.398724i	−0.479059	+	0.877783i	$0.659022\pi$
$164$		0			0
$165$	−1.74497	−	1.74497i	−0.135846	−	0.135846i
$166$		0			0
$167$		−	16.6643i		−	1.28952i	−0.764385	−	0.644760i	$-0.776957\pi$
$167$		−	16.6643i		−	1.28952i	0.764385	−	0.644760i	$-0.223043\pi$
$168$		0			0
$169$		−	7.16737i		−	0.551337i
$170$		0			0
$171$	−0.222492	−	0.222492i	−0.0170144	−	0.0170144i
$172$		0			0
$173$	−11.9359	−	11.9359i	−0.907471	−	0.907471i	0.0885963	−	0.996068i	$-0.471762\pi$
$173$	−11.9359	−	11.9359i	−0.907471	−	0.907471i	−0.996068	+	0.0885963i	$0.971762\pi$
$174$		0			0
$175$	−12.4063	−	0.0537556i	−0.937832	−	0.00406354i
$176$		0			0
$177$	−5.26817			−0.395980
$178$		0			0
$179$	6.80074	+	6.80074i	0.508311	+	0.508311i	0.914008	−	0.405697i	$-0.132971\pi$
$179$	6.80074	+	6.80074i	0.508311	+	0.508311i	−0.405697	+	0.914008i	$0.632971\pi$
$180$		0			0
$181$	−13.9714	+	13.9714i	−1.03848	+	1.03848i	−0.0392553	+	0.999229i	$0.512499\pi$
$181$	−13.9714	+	13.9714i	−1.03848	+	1.03848i	−0.999229	+	0.0392553i	$0.987501\pi$
$182$		0			0
$183$	6.91209			0.510957
$184$		0			0
$185$	−3.59966			−0.264652
$186$		0			0
$187$	13.5793	+	13.5793i	0.993018	+	0.993018i
$188$		0			0
$189$	1.87892	−	1.86271i	0.136671	−	0.135492i
$190$		0			0
$191$		−	6.20721i		−	0.449138i	−0.974458	−	0.224569i	$-0.927903\pi$
$191$		−	6.20721i		−	0.449138i	0.974458	−	0.224569i	$-0.0720974\pi$
$192$		0			0
$193$	−6.29173			−0.452889			−0.226444	−	0.974024i	$-0.572710\pi$
$193$	−6.29173			−0.452889			−0.226444	+	0.974024i	$0.572710\pi$
$194$		0			0
$195$	−0.952041	+	0.952041i	−0.0681770	+	0.0681770i
$196$		0			0
$197$	−1.28099	−	1.28099i	−0.0912668	−	0.0912668i	0.659999	−	0.751266i	$-0.270557\pi$
$197$	−1.28099	−	1.28099i	−0.0912668	−	0.0912668i	−0.751266	+	0.659999i	$0.770557\pi$
$198$		0			0
$199$			12.7927i			0.906850i	0.891295	+	0.453425i	$0.149798\pi$
$199$			12.7927i			0.906850i	−0.891295	+	0.453425i	$0.850202\pi$
$200$		0			0
$201$	2.52449			0.178064
$202$		0			0
$203$	−13.5999	−	13.7182i	−0.954524	−	0.962832i
$204$		0			0
$205$	4.70552	−	4.70552i	0.328648	−	0.328648i
$206$		0			0
$207$			0.538046i			0.0373968i
$208$		0			0
$209$			1.39282i			0.0963434i
$210$		0			0
$211$	−16.8942	−	16.8942i	−1.16305	−	1.16305i	−0.983805	−	0.179241i	$-0.942636\pi$
$211$	−16.8942	−	16.8942i	−1.16305	−	1.16305i	−0.179241	−	0.983805i	$-0.557364\pi$
$212$		0			0
$213$	3.19827	−	3.19827i	0.219142	−	0.219142i
$214$		0			0
$215$		−	3.38994i		−	0.231192i
$216$		0			0
$217$	0.0895240	−	20.6614i	0.00607729	−	1.40259i
$218$		0			0
$219$	10.1092	−	10.1092i	0.683116	−	0.683116i
$220$		0			0
$221$	7.40874	−	7.40874i	0.498366	−	0.498366i
$222$		0			0
$223$	−19.1985			−1.28563			−0.642814	−	0.766022i	$-0.722233\pi$
$223$	−19.1985			−1.28563			−0.642814	+	0.766022i	$0.722233\pi$
$224$		0			0
$225$	4.68920			0.312614
$226$		0			0
$227$	−0.989181	+	0.989181i	−0.0656542	+	0.0656542i	−0.739172	−	0.673517i	$-0.764783\pi$
$227$	−0.989181	+	0.989181i	−0.0656542	+	0.0656542i	0.673517	+	0.739172i	$0.264783\pi$
$228$		0			0
$229$	−6.28226	+	6.28226i	−0.415144	+	0.415144i	−0.883526	−	0.468382i	$-0.844837\pi$
$229$	−6.28226	+	6.28226i	−0.415144	+	0.415144i	0.468382	+	0.883526i	$0.344837\pi$
$230$		0			0
$231$	−11.7114	−	0.0507446i	−0.770556	−	0.00333875i
$232$		0			0
$233$		−	9.79028i		−	0.641383i	−0.947184	−	0.320691i	$-0.896085\pi$
$233$		−	9.79028i		−	0.641383i	0.947184	−	0.320691i	$-0.103915\pi$
$234$		0			0
$235$	−2.69840	+	2.69840i	−0.176024	+	0.176024i
$236$		0			0
$237$	−0.0243864	−	0.0243864i	−0.00158407	−	0.00158407i
$238$		0			0
$239$			11.0560i			0.715156i	0.933883	+	0.357578i	$0.116397\pi$
$239$			11.0560i			0.715156i	−0.933883	+	0.357578i	$0.883603\pi$
$240$		0			0
$241$		−	25.3590i		−	1.63352i	−0.576978	−	0.816760i	$-0.695768\pi$
$241$		−	25.3590i		−	1.63352i	0.576978	−	0.816760i	$-0.304232\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	2.78325	−	2.73543i	0.177815	−	0.174760i
$246$		0			0
$247$	0.759910			0.0483519
$248$		0			0
$249$		−	0.426767i		−	0.0270453i
$250$		0			0
$251$	−16.6323	−	16.6323i	−1.04982	−	1.04982i	−0.998692	−	0.0511265i	$-0.983719\pi$
$251$	−16.6323	−	16.6323i	−1.04982	−	1.04982i	−0.0511265	−	0.998692i	$-0.516281\pi$
$252$		0			0
$253$	1.68411	−	1.68411i	0.105879	−	0.105879i
$254$		0			0
$255$	2.41861			0.151459
$256$		0			0
$257$			20.0104i			1.24822i	0.781338	+	0.624108i	$0.214538\pi$
$257$			20.0104i			1.24822i	−0.781338	+	0.624108i	$0.785462\pi$
$258$		0			0
$259$	−12.1319	+	12.0273i	−0.753842	+	0.747338i
$260$		0			0
$261$	5.16269	+	5.16269i	0.319562	+	0.319562i
$262$		0			0
$263$	−7.22258			−0.445363			−0.222682	−	0.974891i	$-0.571481\pi$
$263$	−7.22258			−0.445363			−0.222682	+	0.974891i	$0.571481\pi$
$264$		0			0
$265$	−7.12973			−0.437976
$266$		0			0
$267$	3.21300	−	3.21300i	0.196632	−	0.196632i
$268$		0			0
$269$	9.90386	+	9.90386i	0.603849	+	0.603849i	0.941332	−	0.337483i	$-0.109575\pi$
$269$	9.90386	+	9.90386i	0.603849	+	0.603849i	−0.337483	+	0.941332i	$0.609575\pi$
$270$		0			0
$271$	28.1109			1.70762			0.853808	−	0.520587i	$-0.174287\pi$
$271$	28.1109			1.70762			0.853808	+	0.520587i	$0.174287\pi$
$272$		0			0
$273$	−0.0276858	+	6.38965i	−0.00167562	+	0.386719i
$274$		0			0
$275$	−14.6774	−	14.6774i	−0.885081	−	0.885081i
$276$		0			0
$277$	10.1382	+	10.1382i	0.609145	+	0.609145i	0.942723	−	0.333577i	$-0.108256\pi$
$277$	10.1382	+	10.1382i	0.609145	+	0.609145i	−0.333577	+	0.942723i	$0.608256\pi$
$278$		0			0
$279$			7.80935i			0.467534i
$280$		0			0
$281$			12.2319i			0.729695i	0.931067	+	0.364847i	$0.118879\pi$
$281$			12.2319i			0.729695i	−0.931067	+	0.364847i	$0.881121\pi$
$282$		0			0
$283$	22.8215	+	22.8215i	1.35660	+	1.35660i	0.878075	+	0.478523i	$0.158828\pi$
$283$	22.8215	+	22.8215i	1.35660	+	1.35660i	0.478523	+	0.878075i	$0.341172\pi$
$284$		0			0
$285$	0.124038	+	0.124038i	0.00734736	+	0.00734736i
$286$		0			0
$287$	0.136839	−	31.5813i	0.00807733	−	1.86418i
$288$		0			0
$289$	−1.82154			−0.107149
$290$		0			0
$291$	0.0685212	+	0.0685212i	0.00401679	+	0.00401679i
$292$		0			0
$293$	−9.68214	+	9.68214i	−0.565637	+	0.565637i	−0.930903	−	0.365266i	$-0.880978\pi$
$293$	−9.68214	+	9.68214i	−0.565637	+	0.565637i	0.365266	+	0.930903i	$0.380978\pi$
$294$		0			0
$295$	2.93696			0.170997
$296$		0			0
$297$	4.42655			0.256854
$298$		0			0
$299$	−0.918833	−	0.918833i	−0.0531375	−	0.0531375i
$300$		0			0
$301$	−11.3265	−	11.4251i	−0.652851	−	0.658533i
$302$		0			0
$303$		−	9.19194i		−	0.528063i
$304$		0			0
$305$	−3.85344			−0.220647
$306$		0			0
$307$	22.2764	−	22.2764i	1.27138	−	1.27138i	0.326015	−	0.945365i	$-0.394294\pi$
$307$	22.2764	−	22.2764i	1.27138	−	1.27138i	0.945365	−	0.326015i	$-0.105706\pi$
$308$		0			0
$309$	−4.27798	−	4.27798i	−0.243366	−	0.243366i
$310$		0			0
$311$			1.16413i			0.0660120i	0.999455	+	0.0330060i	$0.0105080\pi$
$311$			1.16413i			0.0660120i	−0.999455	+	0.0330060i	$0.989492\pi$
$312$		0			0
$313$	26.2830			1.48561			0.742803	−	0.669511i	$-0.233496\pi$
$313$	26.2830			1.48561			0.742803	+	0.669511i	$0.233496\pi$
$314$		0			0
$315$	−1.04748	+	1.03844i	−0.0590189	+	0.0585096i
$316$		0			0
$317$	2.18295	−	2.18295i	0.122607	−	0.122607i	−0.643141	−	0.765748i	$-0.722369\pi$
$317$	2.18295	−	2.18295i	0.122607	−	0.122607i	0.765748	+	0.643141i	$0.222369\pi$
$318$		0			0
$319$		−	32.3189i		−	1.80951i
$320$		0			0
$321$			14.0077i			0.781833i
$322$		0			0
$323$	−0.965256	−	0.965256i	−0.0537083	−	0.0537083i
$324$		0			0
$325$	−8.00785	+	8.00785i	−0.444196	+	0.444196i
$326$		0			0
$327$			8.93891i			0.494323i
$328$		0			0
$329$	−0.0784707	+	18.1104i	−0.00432623	+	0.998458i
$330$		0			0
$331$	9.94175	−	9.94175i	0.546448	−	0.546448i	−0.378964	−	0.925412i	$-0.623719\pi$
$331$	9.94175	−	9.94175i	0.546448	−	0.546448i	0.925412	+	0.378964i	$0.123719\pi$
$332$		0			0
$333$	4.56570	−	4.56570i	0.250199	−	0.250199i
$334$		0			0
$335$	−1.40738			−0.0768935
$336$		0			0
$337$	29.4925			1.60656			0.803278	−	0.595604i	$-0.203087\pi$
$337$	29.4925			1.60656			0.803278	+	0.595604i	$0.203087\pi$
$338$		0			0
$339$	−3.46420	+	3.46420i	−0.188150	+	0.188150i
$340$		0			0
$341$	24.4436	−	24.4436i	1.32370	−	1.32370i
$342$		0			0
$343$	0.240732	−	18.5187i	0.0129983	−	0.999916i
$344$		0			0
$345$		−	0.299956i		−	0.0161491i
$346$		0			0
$347$	18.7346	−	18.7346i	1.00573	−	1.00573i	0.00574186	−	0.999984i	$-0.498172\pi$
$347$	18.7346	−	18.7346i	1.00573	−	1.00573i	0.999984	−	0.00574186i	$-0.00182770\pi$
$348$		0			0
$349$	−7.88445	−	7.88445i	−0.422045	−	0.422045i	0.463862	−	0.885907i	$-0.346463\pi$
$349$	−7.88445	−	7.88445i	−0.422045	−	0.422045i	−0.885907	+	0.463862i	$0.846463\pi$
$350$		0			0
$351$		−	2.41508i		−	0.128908i
$352$		0			0
$353$		−	23.6012i		−	1.25617i	−0.778147	−	0.628083i	$-0.783840\pi$
$353$		−	23.6012i		−	1.25617i	0.778147	−	0.628083i	$-0.216160\pi$
$354$		0			0
$355$	−1.78301	+	1.78301i	−0.0946323	+	0.0946323i
$356$		0			0
$357$	8.15146	−	8.08112i	0.431421	−	0.427698i
$358$		0			0
$359$	3.33994			0.176275			0.0881377	−	0.996108i	$-0.471908\pi$
$359$	3.33994			0.176275			0.0881377	+	0.996108i	$0.471908\pi$
$360$		0			0
$361$			18.9010i			0.994789i
$362$		0			0
$363$	−6.07710	−	6.07710i	−0.318965	−	0.318965i
$364$		0			0
$365$	−5.63579	+	5.63579i	−0.294991	+	0.294991i
$366$		0			0
$367$	−22.6750			−1.18363			−0.591813	−	0.806075i	$-0.701588\pi$
$367$	−22.6750			−1.18363			−0.591813	+	0.806075i	$0.701588\pi$
$368$		0			0
$369$			11.9367i			0.621400i
$370$		0			0
$371$	−24.0294	+	23.8220i	−1.24754	+	1.23678i
$372$		0			0
$373$	−22.4338	−	22.4338i	−1.16158	−	1.16158i	−0.984130	−	0.177447i	$-0.943216\pi$
$373$	−22.4338	−	22.4338i	−1.16158	−	1.16158i	−0.177447	−	0.984130i	$-0.556784\pi$
$374$		0			0
$375$	−5.40165			−0.278940
$376$		0			0
$377$	−17.6329			−0.908139
$378$		0			0
$379$	16.9076	−	16.9076i	0.868485	−	0.868485i	−0.123820	−	0.992305i	$-0.539514\pi$
$379$	16.9076	−	16.9076i	0.868485	−	0.868485i	0.992305	+	0.123820i	$0.0395144\pi$
$380$		0			0
$381$	0.349843	+	0.349843i	0.0179230	+	0.0179230i
$382$		0			0
$383$	25.9833			1.32768			0.663842	−	0.747873i	$-0.268925\pi$
$383$	25.9833			1.32768			0.663842	+	0.747873i	$0.268925\pi$
$384$		0			0
$385$	6.52903	+	0.0282897i	0.332750	+	0.00144178i
$386$		0			0
$387$	4.29970	+	4.29970i	0.218566	+	0.218566i
$388$		0			0
$389$	−1.49054	−	1.49054i	−0.0755733	−	0.0755733i	0.668310	−	0.743883i	$-0.267018\pi$
$389$	−1.49054	−	1.49054i	−0.0755733	−	0.0755733i	−0.743883	+	0.668310i	$0.767018\pi$
$390$		0			0
$391$			2.33425i			0.118048i
$392$		0			0
$393$		−	4.95779i		−	0.250087i
$394$		0			0
$395$	0.0135952	+	0.0135952i	0.000684050	+	0.000684050i
$396$		0			0
$397$	9.48340	+	9.48340i	0.475958	+	0.475958i	0.903836	−	0.427878i	$-0.140739\pi$
$397$	9.48340	+	9.48340i	0.475958	+	0.475958i	−0.427878	+	0.903836i	$0.640739\pi$
$398$		0			0
$399$	0.832482	+	0.00360707i	0.0416762	+	0.000180579i
$400$		0			0
$401$	28.6108			1.42875			0.714377	−	0.699761i	$-0.246710\pi$
$401$	28.6108			1.42875			0.714377	+	0.699761i	$0.246710\pi$
$402$		0			0
$403$	−13.3362	−	13.3362i	−0.664323	−	0.664323i
$404$		0			0
$405$	0.394206	−	0.394206i	0.0195883	−	0.0195883i
$406$		0			0
$407$	−28.5817			−1.41674
$408$		0			0
$409$	−31.8199			−1.57339			−0.786696	−	0.617341i	$-0.788210\pi$
$409$	−31.8199			−1.57339			−0.786696	+	0.617341i	$0.788210\pi$
$410$		0			0
$411$	−11.2248	−	11.2248i	−0.553678	−	0.553678i
$412$		0			0
$413$	9.89846	−	9.81305i	0.487071	−	0.482869i
$414$		0			0
$415$			0.237919i			0.0116790i
$416$		0			0
$417$	5.40678			0.264771
$418$		0			0
$419$	2.94563	−	2.94563i	0.143903	−	0.143903i	−0.631485	−	0.775388i	$-0.717554\pi$
$419$	2.94563	−	2.94563i	0.143903	−	0.143903i	0.775388	+	0.631485i	$0.217554\pi$
$420$		0			0
$421$	−1.19777	−	1.19777i	−0.0583755	−	0.0583755i	0.677316	−	0.735692i	$-0.263143\pi$
$421$	−1.19777	−	1.19777i	−0.0583755	−	0.0583755i	−0.735692	+	0.677316i	$0.763143\pi$
$422$		0			0
$423$		−	6.84515i		−	0.332823i
$424$		0			0
$425$	20.3435			0.986807
$426$		0			0
$427$	−12.9873	+	12.8752i	−0.628497	+	0.623074i
$428$		0			0
$429$	−7.55931	+	7.55931i	−0.364967	+	0.364967i
$430$		0			0
$431$			16.1774i			0.779238i	0.920976	+	0.389619i	$0.127393\pi$
$431$			16.1774i			0.779238i	−0.920976	+	0.389619i	$0.872607\pi$
$432$		0			0
$433$		−	19.4292i		−	0.933706i	−0.884335	−	0.466853i	$-0.845388\pi$
$433$		−	19.4292i		−	0.933706i	0.884335	−	0.466853i	$-0.154612\pi$
$434$		0			0
$435$	−2.87816	−	2.87816i	−0.137997	−	0.137997i
$436$		0			0
$437$	−0.119711	+	0.119711i	−0.00572656	+	0.00572656i
$438$		0			0
$439$			7.52105i			0.358960i	0.983762	+	0.179480i	$0.0574415\pi$
$439$			7.52105i			0.358960i	−0.983762	+	0.179480i	$0.942558\pi$
$440$		0			0
$441$	−0.0606596	+	6.99974i	−0.00288855	+	0.333321i
$442$		0			0
$443$	0.243233	−	0.243233i	0.0115564	−	0.0115564i	−0.701305	−	0.712861i	$-0.747399\pi$
$443$	0.243233	−	0.243233i	0.0115564	−	0.0115564i	0.712861	+	0.701305i	$0.247399\pi$
$444$		0			0
$445$	−1.79122	+	1.79122i	−0.0849120	+	0.0849120i
$446$		0			0
$447$	−4.15187			−0.196377
$448$		0			0
$449$	−22.2569			−1.05037			−0.525185	−	0.850988i	$-0.676004\pi$
$449$	−22.2569			−1.05037			−0.525185	+	0.850988i	$0.676004\pi$
$450$		0			0
$451$	37.3624	−	37.3624i	1.75933	−	1.75933i
$452$		0			0
$453$	11.6901	−	11.6901i	0.549251	−	0.549251i
$454$		0			0
$455$	0.0154346	−	3.56218i	0.000723585	−	0.166997i
$456$		0			0
$457$			20.7810i			0.972095i	0.873932	+	0.486047i	$0.161562\pi$
$457$			20.7810i			0.972095i	−0.873932	+	0.486047i	$0.838438\pi$
$458$		0			0
$459$	−3.06770	+	3.06770i	−0.143188	+	0.143188i
$460$		0			0
$461$	−15.0653	−	15.0653i	−0.701660	−	0.701660i	0.263106	−	0.964767i	$-0.415253\pi$
$461$	−15.0653	−	15.0653i	−0.701660	−	0.701660i	−0.964767	+	0.263106i	$0.915253\pi$
$462$		0			0
$463$			13.2284i			0.614777i	0.951584	+	0.307388i	$0.0994551\pi$
$463$			13.2284i			0.614777i	−0.951584	+	0.307388i	$0.900545\pi$
$464$		0			0
$465$		−	4.35365i		−	0.201896i
$466$		0			0
$467$	−2.60180	+	2.60180i	−0.120397	+	0.120397i	−0.764738	−	0.644341i	$-0.777132\pi$
$467$	−2.60180	+	2.60180i	−0.120397	+	0.120397i	0.644341	+	0.764738i	$0.277132\pi$
$468$		0			0
$469$	−4.74331	+	4.70238i	−0.219026	+	0.217136i
$470$		0			0
$471$	19.7992			0.912299
$472$		0			0
$473$		−	26.9165i		−	1.23762i
$474$		0			0
$475$	1.04331	+	1.04331i	0.0478704	+	0.0478704i
$476$		0			0
$477$	9.04315	−	9.04315i	0.414057	−	0.414057i
$478$		0			0
$479$	2.54238			0.116164			0.0580822	−	0.998312i	$-0.481501\pi$
$479$	2.54238			0.116164			0.0580822	+	0.998312i	$0.481501\pi$
$480$		0			0
$481$			15.5939i			0.711021i
$482$		0			0
$483$	−1.00222	−	1.01094i	−0.0456026	−	0.0459995i
$484$		0			0
$485$	−0.0382000	−	0.0382000i	−0.00173457	−	0.00173457i
$486$		0			0
$487$	−35.5909			−1.61278			−0.806388	−	0.591386i	$-0.798581\pi$
$487$	−35.5909			−1.61278			−0.806388	+	0.591386i	$0.798581\pi$
$488$		0			0
$489$	7.19914			0.325556
$490$		0			0
$491$	−3.87817	+	3.87817i	−0.175020	+	0.175020i	−0.789181	−	0.614161i	$-0.789494\pi$
$491$	−3.87817	+	3.87817i	−0.175020	+	0.175020i	0.614161	+	0.789181i	$0.289494\pi$
$492$		0			0
$493$	22.3977	+	22.3977i	1.00874	+	1.00874i
$494$		0			0
$495$	−2.46776			−0.110918
$496$		0			0
$497$	−0.0518507	+	11.9667i	−0.00232582	+	0.536780i
$498$		0			0
$499$	21.5149	+	21.5149i	0.963138	+	0.963138i	0.999344	−	0.0362059i	$-0.0115272\pi$
$499$	21.5149	+	21.5149i	0.963138	+	0.963138i	−0.0362059	+	0.999344i	$0.511527\pi$
$500$		0			0
$501$	−11.7834	−	11.7834i	−0.526444	−	0.526444i
$502$		0			0
$503$			23.0986i			1.02991i	0.857216	+	0.514957i	$0.172192\pi$
$503$			23.0986i			1.02991i	−0.857216	+	0.514957i	$0.827808\pi$
$504$		0			0
$505$			5.12443i			0.228034i
$506$		0			0
$507$	−5.06810	−	5.06810i	−0.225082	−	0.225082i
$508$		0			0
$509$	18.6469	+	18.6469i	0.826510	+	0.826510i	0.987032	−	0.160523i	$-0.0513180\pi$
$509$	18.6469	+	18.6469i	0.826510	+	0.826510i	−0.160523	+	0.987032i	$0.551318\pi$
$510$		0			0
$511$	−0.163891	+	37.8248i	−0.00725013	+	1.67327i
$512$		0			0
$513$	−0.314652			−0.0138922
$514$		0			0
$515$	2.38494	+	2.38494i	0.105093	+	0.105093i
$516$		0			0
$517$	−21.4256	+	21.4256i	−0.942297	+	0.942297i
$518$		0			0
$519$	−16.8799			−0.740947
$520$		0			0
$521$	−14.2643			−0.624932			−0.312466	−	0.949929i	$-0.601155\pi$
$521$	−14.2643			−0.624932			−0.312466	+	0.949929i	$0.601155\pi$
$522$		0			0
$523$	11.4011	+	11.4011i	0.498535	+	0.498535i	0.910982	−	0.412447i	$-0.135326\pi$
$523$	11.4011	+	11.4011i	0.498535	+	0.498535i	−0.412447	+	0.910982i	$0.635326\pi$
$524$		0			0
$525$	−8.81062	+	8.73460i	−0.384527	+	0.381209i
$526$		0			0
$527$			33.8799i			1.47583i
$528$		0			0
$529$	−22.7105			−0.987413
$530$		0			0
$531$	−3.72516	+	3.72516i	−0.161658	+	0.161658i
$532$		0			0
$533$	−20.3846	−	20.3846i	−0.882953	−	0.882953i
$534$		0			0
$535$		−	7.80917i		−	0.337620i
$536$		0			0
$537$	9.61770			0.415034
$538$		0			0
$539$	22.0993	−	21.7196i	0.951886	−	0.935530i
$540$		0			0
$541$	13.3232	−	13.3232i	0.572810	−	0.572810i	−0.360103	−	0.932913i	$-0.617258\pi$
$541$	13.3232	−	13.3232i	0.572810	−	0.572810i	0.932913	+	0.360103i	$0.117258\pi$
$542$		0			0
$543$			19.7585i			0.847919i
$544$		0			0
$545$		−	4.98337i		−	0.213464i
$546$		0			0
$547$	26.5641	+	26.5641i	1.13580	+	1.13580i	0.989195	+	0.146605i	$0.0468347\pi$
$547$	26.5641	+	26.5641i	1.13580	+	1.13580i	0.146605	+	0.989195i	$0.453165\pi$
$548$		0			0
$549$	4.88759	−	4.88759i	0.208597	−	0.208597i
$550$		0			0
$551$			2.29732i			0.0978690i
$552$		0			0
$553$	0.0912447		0.000395355i	0.00388012		1.68122e-5i
$554$		0			0
$555$	−2.54534	+	2.54534i	−0.108044	+	0.108044i
$556$		0			0
$557$	18.8028	−	18.8028i	0.796700	−	0.796700i	−0.185874	−	0.982574i	$-0.559512\pi$
$557$	18.8028	−	18.8028i	0.796700	−	0.796700i	0.982574	+	0.185874i	$0.0595116\pi$
$558$		0			0
$559$	−14.6854			−0.621125
$560$		0			0
$561$	19.2040			0.810795
$562$		0			0
$563$	23.9211	−	23.9211i	1.00815	−	1.00815i	0.00818785	−	0.999966i	$-0.497394\pi$
$563$	23.9211	−	23.9211i	1.00815	−	1.00815i	0.999966	−	0.00818785i	$-0.00260630\pi$
$564$		0			0
$565$	1.93127	−	1.93127i	0.0812489	−	0.0812489i
$566$		0			0
$567$	0.0114637	−	2.64573i	0.000481430	−	0.111110i
$568$		0			0
$569$			28.3011i			1.18644i	0.805039	+	0.593222i	$0.202145\pi$
$569$			28.3011i			1.18644i	−0.805039	+	0.593222i	$0.797855\pi$
$570$		0			0
$571$	14.6803	−	14.6803i	0.614350	−	0.614350i	−0.329727	−	0.944076i	$-0.606957\pi$
$571$	14.6803	−	14.6803i	0.614350	−	0.614350i	0.944076	+	0.329727i	$0.106957\pi$
$572$		0			0
$573$	−4.38916	−	4.38916i	−0.183360	−	0.183360i
$574$		0			0
$575$		−	2.52301i		−	0.105217i
$576$		0			0
$577$		−	30.7212i		−	1.27894i	−0.768816	−	0.639471i	$-0.779154\pi$
$577$		−	30.7212i		−	1.27894i	0.768816	−	0.639471i	$-0.220846\pi$
$578$		0			0
$579$	−4.44893	+	4.44893i	−0.184891	+	0.184891i
$580$		0			0
$581$	0.794941	+	0.801860i	0.0329797	+	0.0332668i
$582$		0			0
$583$	−56.6109			−2.34458
$584$		0			0
$585$			1.34639i			0.0556663i
$586$		0			0
$587$	13.0802	+	13.0802i	0.539876	+	0.539876i	0.923492	−	0.383617i	$-0.125322\pi$
$587$	13.0802	+	13.0802i	0.539876	+	0.539876i	−0.383617	+	0.923492i	$0.625322\pi$
$588$		0			0
$589$	−1.73752	+	1.73752i	−0.0715933	+	0.0715933i
$590$		0			0
$591$	−1.81160			−0.0745191
$592$		0			0
$593$			16.5125i			0.678085i	0.940771	+	0.339043i	$0.110103\pi$
$593$			16.5125i			0.678085i	−0.940771	+	0.339043i	$0.889897\pi$
$594$		0			0
$595$	−4.54437	+	4.50516i	−0.186301	+	0.184694i
$596$		0			0
$597$	9.04580	+	9.04580i	0.370220	+	0.370220i
$598$		0			0
$599$	28.8630			1.17931			0.589654	−	0.807656i	$-0.299264\pi$
$599$	28.8630			1.17931			0.589654	+	0.807656i	$0.299264\pi$
$600$		0			0
$601$	−21.5169			−0.877691			−0.438845	−	0.898563i	$-0.644612\pi$
$601$	−21.5169			−0.877691			−0.438845	+	0.898563i	$0.644612\pi$
$602$		0			0
$603$	1.78508	−	1.78508i	0.0726943	−	0.0726943i
$604$		0			0
$605$	3.38794	+	3.38794i	0.137739	+	0.137739i
$606$		0			0
$607$	−13.8828			−0.563486			−0.281743	−	0.959490i	$-0.590913\pi$
$607$	−13.8828			−0.563486			−0.281743	+	0.959490i	$0.590913\pi$
$608$		0			0
$609$	−19.3168	−	0.0836981i	−0.782758	−	0.00339162i
$610$		0			0
$611$	11.6896	+	11.6896i	0.472911	+	0.472911i
$612$		0			0
$613$	−16.3947	−	16.3947i	−0.662176	−	0.662176i	0.293717	−	0.955893i	$-0.405108\pi$
$613$	−16.3947	−	16.3947i	−0.662176	−	0.662176i	−0.955893	+	0.293717i	$0.905108\pi$
$614$		0			0
$615$		−	6.65461i		−	0.268340i
$616$		0			0
$617$			29.0118i			1.16797i	0.811764	+	0.583986i	$0.198508\pi$
$617$			29.0118i			1.16797i	−0.811764	+	0.583986i	$0.801492\pi$
$618$		0			0
$619$	2.96878	+	2.96878i	0.119325	+	0.119325i	0.764248	−	0.644923i	$-0.223110\pi$
$619$	2.96878	+	2.96878i	0.119325	+	0.119325i	−0.644923	+	0.764248i	$0.723110\pi$
$620$		0			0
$621$	0.380456	+	0.380456i	0.0152672	+	0.0152672i
$622$		0			0
$623$	−0.0520895	+	12.0218i	−0.00208692	+	0.481644i
$624$		0			0
$625$	−20.4346			−0.817386
$626$		0			0
$627$	0.984873	+	0.984873i	0.0393320	+	0.0393320i
$628$		0			0
$629$	19.8078	−	19.8078i	0.789787	−	0.789787i
$630$		0			0
$631$	33.1705			1.32050			0.660249	−	0.751047i	$-0.270451\pi$
$631$	33.1705			1.32050			0.660249	+	0.751047i	$0.270451\pi$
$632$		0			0
$633$	−23.8920			−0.949623
$634$		0			0
$635$	−0.195034	−	0.195034i	−0.00773971	−	0.00773971i
$636$		0			0
$637$	−11.8500	−	12.0572i	−0.469515	−	0.477723i
$638$		0			0
$639$		−	4.52303i		−	0.178928i
$640$		0			0
$641$	37.6332			1.48642			0.743211	−	0.669058i	$-0.233302\pi$
$641$	37.6332			1.48642			0.743211	+	0.669058i	$0.233302\pi$
$642$		0			0
$643$	−22.4745	+	22.4745i	−0.886308	+	0.886308i	−0.994166	−	0.107858i	$-0.965601\pi$
$643$	−22.4745	+	22.4745i	−0.886308	+	0.886308i	0.107858	+	0.994166i	$0.465601\pi$
$644$		0			0
$645$	−2.39705	−	2.39705i	−0.0943836	−	0.0943836i
$646$		0			0
$647$			48.2963i			1.89872i	0.314186	+	0.949361i	$0.398268\pi$
$647$			48.2963i			1.89872i	−0.314186	+	0.949361i	$0.601732\pi$
$648$		0			0
$649$	23.3198			0.915383
$650$		0			0
$651$	−14.5465	−	14.6731i	−0.570123	−	0.575085i
$652$		0			0
$653$	−20.7590	+	20.7590i	−0.812361	+	0.812361i	−0.984987	−	0.172626i	$-0.944775\pi$
$653$	−20.7590	+	20.7590i	−0.812361	+	0.812361i	0.172626	+	0.984987i	$0.444775\pi$
$654$		0			0
$655$			2.76393i			0.107996i
$656$		0			0
$657$		−	14.2966i		−	0.557762i
$658$		0			0
$659$	6.80846	+	6.80846i	0.265220	+	0.265220i	0.827171	−	0.561951i	$-0.189949\pi$
$659$	6.80846	+	6.80846i	0.265220	+	0.265220i	−0.561951	+	0.827171i	$0.689949\pi$
$660$		0			0
$661$	−6.37181	+	6.37181i	−0.247835	+	0.247835i	−0.820081	−	0.572247i	$-0.806072\pi$
$661$	−6.37181	+	6.37181i	−0.247835	+	0.247835i	0.572247	+	0.820081i	$0.306072\pi$
$662$		0			0
$663$		−	10.4775i		−	0.406914i
$664$		0			0
$665$	−0.464102	−	0.00201091i	−0.0179971	−	7.79798e-5i
$666$		0			0
$667$	2.77776	−	2.77776i	0.107555	−	0.107555i
$668$		0			0
$669$	−13.5754	+	13.5754i	−0.524855	+	0.524855i
$670$		0			0
$671$	−30.5967			−1.18117
$672$		0			0
$673$	9.86826			0.380393			0.190197	−	0.981746i	$-0.439087\pi$
$673$	9.86826			0.380393			0.190197	+	0.981746i	$0.439087\pi$
$674$		0			0
$675$	3.31577	−	3.31577i	0.127624	−	0.127624i
$676$		0			0
$677$	−2.58950	+	2.58950i	−0.0995228	+	0.0995228i	−0.755115	−	0.655592i	$-0.772419\pi$
$677$	−2.58950	+	2.58950i	−0.0995228	+	0.0995228i	0.655592	+	0.755115i	$0.272419\pi$
$678$		0			0
$679$	−0.256381	−	0.00111087i	−0.00983898	−	4.26314e-5i
$680$		0			0
$681$			1.39891i			0.0536065i
$682$		0			0
$683$	−21.3774	+	21.3774i	−0.817982	+	0.817982i	−0.985815	−	0.167833i	$-0.946323\pi$
$683$	−21.3774	+	21.3774i	−0.817982	+	0.817982i	0.167833	+	0.985815i	$0.446323\pi$
$684$		0			0
$685$	6.25773	+	6.25773i	0.239096	+	0.239096i
$686$		0			0
$687$			8.88446i			0.338963i
$688$		0			0
$689$			30.8864i			1.17668i
$690$		0			0
$691$	0.628457	−	0.628457i	0.0239076	−	0.0239076i	−0.695052	−	0.718960i	$-0.744619\pi$
$691$	0.628457	−	0.628457i	0.0239076	−	0.0239076i	0.718960	+	0.695052i	$0.244619\pi$
$692$		0			0
$693$	−8.31712	+	8.24535i	−0.315941	+	0.313215i
$694$		0			0
$695$	−3.01424			−0.114337
$696$		0			0
$697$			51.7860i			1.96153i
$698$		0			0
$699$	−6.92278	−	6.92278i	−0.261843	−	0.261843i
$700$		0			0
$701$	−27.5876	+	27.5876i	−1.04197	+	1.04197i	−0.0428904	+	0.999080i	$0.513657\pi$
$701$	−27.5876	+	27.5876i	−1.04197	+	1.04197i	−0.999080	+	0.0428904i	$0.986343\pi$
$702$		0			0
$703$	2.03167			0.0766258
$704$		0			0
$705$			3.81611i			0.143723i
$706$		0			0
$707$	17.1219	+	17.2709i	0.643934	+	0.649539i
$708$		0			0
$709$	−11.5424	−	11.5424i	−0.433484	−	0.433484i	0.456327	−	0.889812i	$-0.349165\pi$
$709$	−11.5424	−	11.5424i	−0.433484	−	0.433484i	−0.889812	+	0.456327i	$0.849165\pi$
$710$		0			0
$711$	−0.0344876			−0.00129339
$712$		0			0
$713$	4.20179			0.157358
$714$		0			0
$715$	4.21425	−	4.21425i	0.157604	−	0.157604i
$716$		0			0
$717$	7.81780	+	7.81780i	0.291961	+	0.291961i
$718$		0			0
$719$	40.8414			1.52313			0.761563	−	0.648091i	$-0.224432\pi$
$719$	40.8414			1.52313			0.761563	+	0.648091i	$0.224432\pi$
$720$		0			0
$721$	16.0066	+	0.0693551i	0.596117	+	0.00258292i
$722$		0			0
$723$	−17.9316	−	17.9316i	−0.666882	−	0.666882i
$724$		0			0
$725$	−24.2089	−	24.2089i	−0.899096	−	0.899096i
$726$		0			0
$727$		−	4.43184i		−	0.164368i	−0.996617	−	0.0821839i	$-0.973811\pi$
$727$		−	4.43184i		−	0.164368i	0.996617	−	0.0821839i	$-0.0261895\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	18.6537	+	18.6537i	0.689933	+	0.689933i
$732$		0			0
$733$	−26.1365	−	26.1365i	−0.965373	−	0.965373i	0.0340468	−	0.999420i	$-0.489160\pi$
$733$	−26.1365	−	26.1365i	−0.965373	−	0.965373i	−0.999420	+	0.0340468i	$0.989160\pi$
$734$		0			0
$735$	0.0338172	−	3.90230i	0.00124737	−	0.143938i
$736$		0			0
$737$	−11.1748			−0.411628
$738$		0			0
$739$	7.02298	+	7.02298i	0.258344	+	0.258344i	0.824380	−	0.566036i	$-0.191524\pi$
$739$	7.02298	+	7.02298i	0.258344	+	0.258344i	−0.566036	+	0.824380i	$0.691524\pi$
$740$		0			0
$741$	0.537337	−	0.537337i	0.0197396	−	0.0197396i
$742$		0			0
$743$	−46.4463			−1.70395			−0.851975	−	0.523582i	$-0.824595\pi$
$743$	−46.4463			−1.70395			−0.851975	+	0.523582i	$0.824595\pi$
$744$		0			0
$745$	2.31463			0.0848016
$746$		0			0
$747$	−0.301770	−	0.301770i	−0.0110412	−	0.0110412i
$748$		0			0
$749$	−26.0922	−	26.3193i	−0.953388	−	0.961686i
$750$		0			0
$751$			41.6120i			1.51844i	0.650833	+	0.759221i	$0.274420\pi$
$751$			41.6120i			1.51844i	−0.650833	+	0.759221i	$0.725580\pi$
$752$		0			0
$753$	−23.5216			−0.857173
$754$		0			0
$755$	−6.51716	+	6.51716i	−0.237184	+	0.237184i
$756$		0			0
$757$	6.26036	+	6.26036i	0.227537	+	0.227537i	0.811663	−	0.584126i	$-0.198563\pi$
$757$	6.26036	+	6.26036i	0.227537	+	0.227537i	−0.584126	+	0.811663i	$0.698563\pi$
$758$		0			0
$759$		−	2.38169i		−	0.0864497i
$760$		0			0
$761$	25.9132			0.939355			0.469677	−	0.882838i	$-0.344370\pi$
$761$	25.9132			0.939355			0.469677	+	0.882838i	$0.344370\pi$
$762$		0			0
$763$	−16.6505	−	16.7955i	−0.602790	−	0.608037i
$764$		0			0
$765$	1.71022	−	1.71022i	0.0618330	−	0.0618330i
$766$		0			0
$767$		−	12.7231i		−	0.459403i
$768$		0			0
$769$		−	32.6792i		−	1.17844i	−0.807972	−	0.589220i	$-0.799435\pi$
$769$		−	32.6792i		−	1.17844i	0.807972	−	0.589220i	$-0.200565\pi$
$770$		0			0
$771$	14.1495	+	14.1495i	0.509582	+	0.509582i
$772$		0			0
$773$	−35.9686	+	35.9686i	−1.29370	+	1.29370i	−0.361220	+	0.932480i	$0.617640\pi$
$773$	−35.9686	+	35.9686i	−1.29370	+	1.29370i	−0.932480	+	0.361220i	$0.882360\pi$
$774$		0			0
$775$		−	36.6196i		−	1.31542i
$776$		0			0
$777$	−0.0740197	+	17.0831i	−0.00265544	+	0.612854i
$778$		0			0
$779$	−2.65582	+	2.65582i	−0.0951548	+	0.0951548i
$780$		0			0
$781$	−14.1573	+	14.1573i	−0.506588	+	0.506588i
$782$		0			0
$783$	7.30114			0.260922
$784$		0			0
$785$	−11.0379			−0.393959
$786$		0			0
$787$	−1.99800	+	1.99800i	−0.0712211	+	0.0712211i	−0.741820	−	0.670599i	$-0.766037\pi$
$787$	−1.99800	+	1.99800i	−0.0712211	+	0.0712211i	0.670599	+	0.741820i	$0.266037\pi$
$788$		0			0
$789$	−5.10713	+	5.10713i	−0.181819	+	0.181819i
$790$		0			0
$791$	0.0561621	−	12.9617i	0.00199689	−	0.460867i
$792$		0			0
$793$			16.6933i			0.592796i
$794$		0			0
$795$	−5.04148	+	5.04148i	−0.178803	+	0.178803i
$796$		0			0
$797$	27.2412	+	27.2412i	0.964932	+	0.964932i	0.999406	−	0.0344735i	$-0.0109754\pi$
$797$	27.2412	+	27.2412i	0.964932	+	0.964932i	−0.0344735	+	0.999406i	$0.510975\pi$
$798$		0			0
$799$		−	29.6969i		−	1.05060i
$800$		0			0
$801$		−	4.54387i		−	0.160550i
$802$		0			0
$803$	−44.7488	+	44.7488i	−1.57915	+	1.57915i
$804$		0			0
$805$	0.558730	+	0.563593i	0.0196926	+	0.0198640i
$806$		0			0
$807$	14.0062			0.493041
$808$		0			0
$809$			22.6680i			0.796965i	0.917176	+	0.398482i	$0.130463\pi$
$809$			22.6680i			0.796965i	−0.917176	+	0.398482i	$0.869537\pi$
$810$		0			0
$811$	2.63633	+	2.63633i	0.0925741	+	0.0925741i	0.751877	−	0.659303i	$-0.229149\pi$
$811$	2.63633	+	2.63633i	0.0925741	+	0.0925741i	−0.659303	+	0.751877i	$0.729149\pi$
$812$		0			0
$813$	19.8774	−	19.8774i	0.697132	−	0.697132i
$814$		0			0
$815$	−4.01346			−0.140585
$816$		0			0
$817$			1.91330i			0.0669379i
$818$		0			0
$819$	4.49859	+	4.53774i	0.157193	+	0.158561i
$820$		0			0
$821$	24.2147	+	24.2147i	0.845098	+	0.845098i	0.989517	−	0.144419i	$-0.0461312\pi$
$821$	24.2147	+	24.2147i	0.845098	+	0.845098i	−0.144419	+	0.989517i	$0.546131\pi$
$822$		0			0
$823$	−22.0015			−0.766924			−0.383462	−	0.923557i	$-0.625268\pi$
$823$	−22.0015			−0.766924			−0.383462	+	0.923557i	$0.625268\pi$
$824$		0			0
$825$	−20.7570			−0.722665
$826$		0			0
$827$	−15.0680	+	15.0680i	−0.523966	+	0.523966i	−0.918767	−	0.394800i	$-0.870814\pi$
$827$	−15.0680	+	15.0680i	−0.523966	+	0.523966i	0.394800	+	0.918767i	$0.370814\pi$
$828$		0			0
$829$	−4.10935	−	4.10935i	−0.142724	−	0.142724i	0.632135	−	0.774858i	$-0.282179\pi$
$829$	−4.10935	−	4.10935i	−0.142724	−	0.142724i	−0.774858	+	0.632135i	$0.782179\pi$
$830$		0			0
$831$	14.3376			0.497365
$832$		0			0
$833$	−0.263164	+	30.3675i	−0.00911811	+	1.05217i
$834$		0			0
$835$	6.56916	+	6.56916i	0.227335	+	0.227335i
$836$		0			0
$837$	5.52205	+	5.52205i	0.190870	+	0.190870i
$838$		0			0
$839$		−	9.46675i		−	0.326829i	−0.986558	−	0.163414i	$-0.947749\pi$
$839$		−	9.46675i		−	0.326829i	0.986558	−	0.163414i	$-0.0522507\pi$
$840$		0			0
$841$		−	24.3067i		−	0.838162i
$842$		0			0
$843$	8.64927	+	8.64927i	0.297897	+	0.297897i
$844$		0			0
$845$	2.82542	+	2.82542i	0.0971975	+	0.0971975i
$846$		0			0
$847$	22.7382	+	0.0985227i	0.781295	+	0.00338528i
$848$		0			0
$849$	32.2745			1.10766
$850$		0			0
$851$	−2.45656	−	2.45656i	−0.0842097	−	0.0842097i
$852$		0			0
$853$	15.1346	−	15.1346i	0.518198	−	0.518198i	−0.398828	−	0.917026i	$-0.630583\pi$
$853$	15.1346	−	15.1346i	0.518198	−	0.518198i	0.917026	+	0.398828i	$0.130583\pi$
$854$		0			0
$855$	0.175416			0.00599909
$856$		0			0
$857$	34.9974			1.19549			0.597743	−	0.801687i	$-0.296064\pi$
$857$	34.9974			1.19549			0.597743	+	0.801687i	$0.296064\pi$
$858$		0			0
$859$	−24.0301	−	24.0301i	−0.819897	−	0.819897i	0.166196	−	0.986093i	$-0.446852\pi$
$859$	−24.0301	−	24.0301i	−0.819897	−	0.819897i	−0.986093	+	0.166196i	$0.946852\pi$
$860$		0			0
$861$	−22.2346	−	22.4281i	−0.757752	−	0.764347i
$862$		0			0
$863$		−	10.7529i		−	0.366032i	−0.983110	−	0.183016i	$-0.941414\pi$
$863$		−	10.7529i		−	0.366032i	0.983110	−	0.183016i	$-0.0585860\pi$
$864$		0			0
$865$	9.41043			0.319964
$866$		0			0
$867$	−1.28802	+	1.28802i	−0.0437436	+	0.0437436i
$868$		0			0
$869$	0.107948	+	0.107948i	0.00366187	+	0.00366187i
$870$		0			0
$871$			6.09686i			0.206584i
$872$		0			0
$873$	0.0969036			0.00327969
$874$		0			0
$875$	10.1493	−	10.0617i	0.343107	−	0.340147i
$876$		0			0
$877$	30.2332	−	30.2332i	1.02090	−	1.02090i	0.0211264	−	0.999777i	$-0.493275\pi$
$877$	30.2332	−	30.2332i	1.02090	−	1.02090i	0.999777	−	0.0211264i	$-0.00672524\pi$
$878$		0			0
$879$			13.6926i			0.461841i
$880$		0			0
$881$			20.9405i			0.705502i	0.935717	+	0.352751i	$0.114754\pi$
$881$			20.9405i			0.705502i	−0.935717	+	0.352751i	$0.885246\pi$
$882$		0			0
$883$	−35.8983	−	35.8983i	−1.20807	−	1.20807i	−0.971650	−	0.236422i	$-0.924025\pi$
$883$	−35.8983	−	35.8983i	−1.20807	−	1.20807i	−0.236422	−	0.971650i	$-0.575975\pi$
$884$		0			0
$885$	2.07675	−	2.07675i	0.0698091	−	0.0698091i
$886$		0			0
$887$		−	20.7226i		−	0.695796i	−0.937532	−	0.347898i	$-0.886896\pi$
$887$		−	20.7226i		−	0.695796i	0.937532	−	0.347898i	$-0.113104\pi$
$888$		0			0
$889$	−1.30898	−	0.00567169i	−0.0439018	−	0.000190222i
$890$		0			0
$891$	3.13004	−	3.13004i	0.104860	−	0.104860i
$892$		0			0
$893$	1.52299	−	1.52299i	0.0509650	−	0.0509650i
$894$		0			0
$895$	−5.36179			−0.179225
$896$		0			0
$897$	−1.29943			−0.0433866
$898$		0			0
$899$	40.3173	−	40.3173i	1.34466	−	1.34466i
$900$		0			0
$901$	39.2326	−	39.2326i	1.30703	−	1.30703i
$902$		0			0
$903$	−16.0879	−	0.0697072i	−0.535370	−	0.00231971i
$904$		0			0
$905$		−	11.0152i		−	0.366158i
$906$		0			0
$907$	1.14622	−	1.14622i	0.0380595	−	0.0380595i	−0.687821	−	0.725880i	$-0.741433\pi$
$907$	1.14622	−	1.14622i	0.0380595	−	0.0380595i	0.725880	+	0.687821i	$0.241433\pi$
$908$		0			0
$909$	−6.49968	−	6.49968i	−0.215581	−	0.215581i
$910$		0			0
$911$			42.5884i			1.41102i	0.708701	+	0.705508i	$0.249281\pi$
$911$			42.5884i			1.41102i	−0.708701	+	0.705508i	$0.750719\pi$
$912$		0			0
$913$			1.88911i			0.0625203i
$914$		0			0
$915$	−2.72479	+	2.72479i	−0.0900788	+	0.0900788i
$916$		0			0
$917$	9.23490	+	9.31528i	0.304963	+	0.307618i
$918$		0			0
$919$	20.0745			0.662196			0.331098	−	0.943596i	$-0.392581\pi$
$919$	20.0745			0.662196			0.331098	+	0.943596i	$0.392581\pi$
$920$		0			0
$921$		−	31.5035i		−	1.03808i
$922$		0			0
$923$	7.72408	+	7.72408i	0.254241	+	0.254241i
$924$		0			0
$925$	−21.4095	+	21.4095i	−0.703940	+	0.703940i
$926$		0			0
$927$	−6.04998			−0.198707
$928$		0			0
$929$			17.4771i			0.573405i	0.958020	+	0.286702i	$0.0925591\pi$
$929$			17.4771i			0.573405i	−0.958020	+	0.286702i	$0.907441\pi$
$930$		0			0
$931$	−1.57088	+	1.54389i	−0.0514836	+	0.0505990i
$932$		0			0
$933$	0.823167	+	0.823167i	0.0269493	+	0.0269493i
$934$		0			0
$935$	−10.7061			−0.350127
$936$		0			0
$937$	26.3097			0.859501			0.429750	−	0.902948i	$-0.358602\pi$
$937$	26.3097			0.859501			0.429750	+	0.902948i	$0.358602\pi$
$938$		0			0
$939$	18.5849	−	18.5849i	0.606496	−	0.606496i
$940$		0			0
$941$	32.4347	+	32.4347i	1.05734	+	1.05734i	0.998253	+	0.0590876i	$0.0188191\pi$
$941$	32.4347	+	32.4347i	1.05734	+	1.05734i	0.0590876	+	0.998253i	$0.481181\pi$
$942$		0			0
$943$	6.42250			0.209145
$944$		0			0
$945$	−0.00639091	+	1.47497i	−0.000207896	+	0.0479808i
$946$		0			0
$947$	−23.5630	−	23.5630i	−0.765696	−	0.765696i	0.211650	−	0.977346i	$-0.432116\pi$
$947$	−23.5630	−	23.5630i	−0.765696	−	0.765696i	−0.977346	+	0.211650i	$0.932116\pi$
$948$		0			0
$949$	24.4145	+	24.4145i	0.792530	+	0.792530i
$950$		0			0
$951$		−	3.08716i		−	0.100108i
$952$		0			0
$953$			13.2855i			0.430358i	0.976575	+	0.215179i	$0.0690335\pi$
$953$			13.2855i			0.430358i	−0.976575	+	0.215179i	$0.930966\pi$
$954$		0			0
$955$	2.44692	+	2.44692i	0.0791805	+	0.0791805i
$956$		0			0
$957$	−22.8529	−	22.8529i	−0.738729	−	0.738729i
$958$		0			0
$959$	41.9989	+	0.181978i	1.35622	+	0.00587636i
$960$		0			0
$961$	29.9860			0.967290
$962$		0			0
$963$	9.90493	+	9.90493i	0.319182	+	0.319182i
$964$		0			0
$965$	2.48024	−	2.48024i	0.0798417	−	0.0798417i
$966$		0			0
$967$	34.4697			1.10847			0.554236	−	0.832360i	$-0.313011\pi$
$967$	34.4697			1.10847			0.554236	+	0.832360i	$0.313011\pi$
$968$		0			0
$969$	−1.36508			−0.0438526
$970$		0			0
$971$	16.5015	+	16.5015i	0.529558	+	0.529558i	0.920440	−	0.390883i	$-0.127830\pi$
$971$	16.5015	+	16.5015i	0.529558	+	0.529558i	−0.390883	+	0.920440i	$0.627830\pi$
$972$		0			0
$973$	−10.1589	+	10.0712i	−0.325679	+	0.322869i
$974$		0			0
$975$			11.3248i			0.362684i
$976$		0			0
$977$	7.91766			0.253309			0.126654	−	0.991947i	$-0.459576\pi$
$977$	7.91766			0.253309			0.126654	+	0.991947i	$0.459576\pi$
$978$		0			0
$979$	−14.2225	+	14.2225i	−0.454553	+	0.454553i
$980$		0			0
$981$	6.32076	+	6.32076i	0.201806	+	0.201806i
$982$		0			0
$983$			14.3972i			0.459200i	0.973285	+	0.229600i	$0.0737417\pi$
$983$			14.3972i			0.459200i	−0.973285	+	0.229600i	$0.926258\pi$
$984$		0			0
$985$	1.00995			0.0321797
$986$		0			0
$987$	12.7505	+	12.8615i	0.405853	+	0.409385i
$988$		0			0
$989$	2.31344	−	2.31344i	0.0735630	−	0.0735630i
$990$		0			0
$991$			2.31554i			0.0735555i	0.999323	+	0.0367778i	$0.0117094\pi$
$991$			2.31554i			0.0735555i	−0.999323	+	0.0367778i	$0.988291\pi$
$992$		0			0
$993$		−	14.0598i		−	0.446173i
$994$		0			0
$995$	−5.04296	−	5.04296i	−0.159872	−	0.159872i
$996$		0			0
$997$	−19.6725	+	19.6725i	−0.623035	+	0.623035i	−0.946306	−	0.323271i	$-0.895217\pi$
$997$	−19.6725	+	19.6725i	−0.623035	+	0.623035i	0.323271	+	0.946306i	$0.395217\pi$
$998$		0			0
$999$		−	6.45688i		−	0.204287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.22		64
4.3	odd	2		336.2.u.a.139.25	✓	64
7.6	odd	2	inner	1344.2.u.a.1231.11		64
16.3	odd	4	inner	1344.2.u.a.559.11		64
16.13	even	4		336.2.u.a.307.26	yes	64
28.27	even	2		336.2.u.a.139.26	yes	64
112.13	odd	4		336.2.u.a.307.25	yes	64
112.83	even	4	inner	1344.2.u.a.559.22		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.25	✓	64	4.3	odd	2
336.2.u.a.139.26	yes	64	28.27	even	2
336.2.u.a.307.25	yes	64	112.13	odd	4
336.2.u.a.307.26	yes	64	16.13	even	4
1344.2.u.a.559.11		64	16.3	odd	4	inner
1344.2.u.a.559.22		64	112.83	even	4	inner
1344.2.u.a.1231.11		64	7.6	odd	2	inner
1344.2.u.a.1231.22		64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.394206 + 0.394206i) q^{5} +(-0.0114637 + 2.64573i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.394206 + 0.394206i) q^{5} +(-0.0114637 + 2.64573i) q^{7} -1.00000i q^{9} +(-3.13004 + 3.13004i) q^{11} +(1.70772 + 1.70772i) q^{13} +0.557492i q^{15} -4.33838i q^{17} +(0.222492 - 0.222492i) q^{19} +(1.86271 + 1.87892i) q^{21} -0.538046 q^{23} +4.68920i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-5.16269 + 5.16269i) q^{29} -7.80935 q^{31} +4.42655i q^{33} +(-1.03844 - 1.04748i) q^{35} +(4.56570 + 4.56570i) q^{37} +2.41508 q^{39} -11.9367 q^{41} +(-4.29970 + 4.29970i) q^{43} +(0.394206 + 0.394206i) q^{45} +6.84515 q^{47} +(-6.99974 - 0.0606596i) q^{49} +(-3.06770 - 3.06770i) q^{51} +(9.04315 + 9.04315i) q^{53} -2.46776i q^{55} -0.314652i q^{57} +(-3.72516 - 3.72516i) q^{59} +(4.88759 + 4.88759i) q^{61} +(2.64573 + 0.0114637i) q^{63} -1.34639 q^{65} +(1.78508 + 1.78508i) q^{67} +(-0.380456 + 0.380456i) q^{69} +4.52303 q^{71} +14.2966 q^{73} +(3.31577 + 3.31577i) q^{75} +(-8.24535 - 8.31712i) q^{77} -0.0344876i q^{79} -1.00000 q^{81} +(0.301770 - 0.301770i) q^{83} +(1.71022 + 1.71022i) q^{85} +7.30114i q^{87} +4.54387 q^{89} +(-4.53774 + 4.49859i) q^{91} +(-5.52205 + 5.52205i) q^{93} +0.175416i q^{95} +0.0969036i q^{97} +(3.13004 + 3.13004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

L-functions

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