LMFDB - Embedded newform 1350.2.f.f.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(107,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1350.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1350.107
Dual form			1350.2.f.f.593.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.44949 - 1.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.44949 - 1.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.09638i q^{11} +(-4.22474 + 4.22474i) q^{13} -2.04989 q^{14} -1.00000 q^{16} +(-4.17121 + 4.17121i) q^{17} -4.44949i q^{19} +(-0.775255 - 0.775255i) q^{22} +(-4.48905 - 4.48905i) q^{23} +5.97469i q^{26} +(-1.44949 + 1.44949i) q^{28} -3.14626 q^{29} -1.44949 q^{31} +(-0.707107 + 0.707107i) q^{32} +5.89898i q^{34} +(-3.14626 - 3.14626i) q^{38} +4.87832i q^{41} +(7.22474 - 7.22474i) q^{43} -1.09638 q^{44} -6.34847 q^{46} +(-7.31747 + 7.31747i) q^{47} -2.79796i q^{49} +(4.22474 + 4.22474i) q^{52} +(5.65685 + 5.65685i) q^{53} +2.04989i q^{56} +(-2.22474 + 2.22474i) q^{58} +2.82843 q^{59} -8.44949 q^{61} +(-1.02494 + 1.02494i) q^{62} +1.00000i q^{64} +(-2.00000 - 2.00000i) q^{67} +(4.17121 + 4.17121i) q^{68} +13.9993i q^{71} +(4.44949 - 4.44949i) q^{73} -4.44949 q^{76} +(-1.58919 + 1.58919i) q^{77} -5.44949i q^{79} +(3.44949 + 3.44949i) q^{82} +(-10.2173 - 10.2173i) q^{83} -10.2173i q^{86} +(-0.775255 + 0.775255i) q^{88} -17.4634 q^{89} +12.2474 q^{91} +(-4.48905 + 4.48905i) q^{92} +10.3485i q^{94} +(-8.44949 - 8.44949i) q^{97} +(-1.97846 - 1.97846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 q^{7} - 24 q^{13} - 8 q^{16} - 16 q^{22} + 8 q^{28} + 8 q^{31} + 48 q^{43} + 8 q^{46} + 24 q^{52} - 8 q^{58} - 48 q^{61} - 16 q^{67} + 16 q^{73} - 16 q^{76} + 8 q^{82} - 16 q^{88} - 48 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 - 24 * q^13 - 8 * q^16 - 16 * q^22 + 8 * q^28 + 8 * q^31 + 48 * q^43 + 8 * q^46 + 24 * q^52 - 8 * q^58 - 48 * q^61 - 16 * q^67 + 16 * q^73 - 16 * q^76 + 8 * q^82 - 16 * q^88 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.44949	−	1.44949i	−0.547856	−	0.547856i	0.377964	−	0.925820i	$-0.376624\pi$
$7$	−1.44949	−	1.44949i	−0.547856	−	0.547856i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	1.09638i		−	0.330570i	−0.986246	−	0.165285i	$-0.947146\pi$
$11$		−	1.09638i		−	0.330570i	0.986246	−	0.165285i	$-0.0528544\pi$
$12$		0			0
$13$	−4.22474	+	4.22474i	−1.17173	+	1.17173i	−0.189937	+	0.981796i	$0.560828\pi$
$13$	−4.22474	+	4.22474i	−1.17173	+	1.17173i	−0.981796	+	0.189937i	$0.939172\pi$
$14$	−2.04989			−0.547856
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.17121	+	4.17121i	−1.01167	+	1.01167i	−0.0117355	+	0.999931i	$0.503736\pi$
$17$	−4.17121	+	4.17121i	−1.01167	+	1.01167i	−0.999931	+	0.0117355i	$0.996264\pi$
$18$		0			0
$19$		−	4.44949i		−	1.02078i	−0.859942	−	0.510391i	$-0.829501\pi$
$19$		−	4.44949i		−	1.02078i	0.859942	−	0.510391i	$-0.170499\pi$
$20$		0			0
$21$		0			0
$22$	−0.775255	−	0.775255i	−0.165285	−	0.165285i
$23$	−4.48905	−	4.48905i	−0.936031	−	0.936031i	0.0620428	−	0.998073i	$-0.480238\pi$
$23$	−4.48905	−	4.48905i	−0.936031	−	0.936031i	−0.998073	+	0.0620428i	$0.980238\pi$
$24$		0			0
$25$		0			0
$26$			5.97469i			1.17173i
$27$		0			0
$28$	−1.44949	+	1.44949i	−0.273928	+	0.273928i
$29$	−3.14626			−0.584247			−0.292123	−	0.956381i	$-0.594362\pi$
$29$	−3.14626			−0.584247			−0.292123	+	0.956381i	$0.594362\pi$
$30$		0			0
$31$	−1.44949			−0.260336			−0.130168	−	0.991492i	$-0.541552\pi$
$31$	−1.44949			−0.260336			−0.130168	+	0.991492i	$0.541552\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			5.89898i			1.01167i
$35$		0			0
$36$		0			0
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	−3.14626	−	3.14626i	−0.510391	−	0.510391i
$39$		0			0
$40$		0			0
$41$			4.87832i			0.761865i	0.924603	+	0.380932i	$0.124397\pi$
$41$			4.87832i			0.761865i	−0.924603	+	0.380932i	$0.875603\pi$
$42$		0			0
$43$	7.22474	−	7.22474i	1.10176	−	1.10176i	0.107565	−	0.994198i	$-0.465695\pi$
$43$	7.22474	−	7.22474i	1.10176	−	1.10176i	0.994198	−	0.107565i	$-0.0343054\pi$
$44$	−1.09638			−0.165285
$45$		0			0
$46$	−6.34847			−0.936031
$47$	−7.31747	+	7.31747i	−1.06736	+	1.06736i	−0.0698023	+	0.997561i	$0.522237\pi$
$47$	−7.31747	+	7.31747i	−1.06736	+	1.06736i	−0.997561	+	0.0698023i	$0.977763\pi$
$48$		0			0
$49$		−	2.79796i		−	0.399708i
$50$		0			0
$51$		0			0
$52$	4.22474	+	4.22474i	0.585867	+	0.585867i
$53$	5.65685	+	5.65685i	0.777029	+	0.777029i	0.979324	−	0.202296i	$-0.0648402\pi$
$53$	5.65685	+	5.65685i	0.777029	+	0.777029i	−0.202296	+	0.979324i	$0.564840\pi$
$54$		0			0
$55$		0			0
$56$			2.04989i			0.273928i
$57$		0			0
$58$	−2.22474	+	2.22474i	−0.292123	+	0.292123i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	−8.44949			−1.08185			−0.540923	−	0.841072i	$-0.681925\pi$
$61$	−8.44949			−1.08185			−0.540923	+	0.841072i	$0.681925\pi$
$62$	−1.02494	+	1.02494i	−0.130168	+	0.130168i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−2.00000	−	2.00000i	−0.244339	−	0.244339i	0.574304	−	0.818642i	$-0.305273\pi$
$67$	−2.00000	−	2.00000i	−0.244339	−	0.244339i	−0.818642	+	0.574304i	$0.805273\pi$
$68$	4.17121	+	4.17121i	0.505833	+	0.505833i
$69$		0			0
$70$		0			0
$71$			13.9993i			1.66141i	0.556714	+	0.830704i	$0.312062\pi$
$71$			13.9993i			1.66141i	−0.556714	+	0.830704i	$0.687938\pi$
$72$		0			0
$73$	4.44949	−	4.44949i	0.520773	−	0.520773i	−0.397032	−	0.917805i	$-0.629960\pi$
$73$	4.44949	−	4.44949i	0.520773	−	0.520773i	0.917805	+	0.397032i	$0.129960\pi$
$74$		0			0
$75$		0			0
$76$	−4.44949			−0.510391
$77$	−1.58919	+	1.58919i	−0.181105	+	0.181105i
$78$		0			0
$79$		−	5.44949i		−	0.613115i	−0.951852	−	0.306558i	$-0.900823\pi$
$79$		−	5.44949i		−	0.613115i	0.951852	−	0.306558i	$-0.0991773\pi$
$80$		0			0
$81$		0			0
$82$	3.44949	+	3.44949i	0.380932	+	0.380932i
$83$	−10.2173	−	10.2173i	−1.12150	−	1.12150i	−0.991516	−	0.129981i	$-0.958508\pi$
$83$	−10.2173	−	10.2173i	−1.12150	−	1.12150i	−0.129981	−	0.991516i	$-0.541492\pi$
$84$		0			0
$85$		0			0
$86$		−	10.2173i		−	1.10176i
$87$		0			0
$88$	−0.775255	+	0.775255i	−0.0826425	+	0.0826425i
$89$	−17.4634			−1.85111			−0.925557	−	0.378609i	$-0.876403\pi$
$89$	−17.4634			−1.85111			−0.925557	+	0.378609i	$0.876403\pi$
$90$		0			0
$91$	12.2474			1.28388
$92$	−4.48905	+	4.48905i	−0.468015	+	0.468015i
$93$		0			0
$94$			10.3485i			1.06736i
$95$		0			0
$96$		0			0
$97$	−8.44949	−	8.44949i	−0.857916	−	0.857916i	0.133177	−	0.991092i	$-0.457482\pi$
$97$	−8.44949	−	8.44949i	−0.857916	−	0.857916i	−0.991092	+	0.133177i	$0.957482\pi$
$98$	−1.97846	−	1.97846i	−0.199854	−	0.199854i
$99$		0			0
$100$		0			0
$101$		−	8.16744i		−	0.812691i	−0.913719	−	0.406346i	$-0.866803\pi$
$101$		−	8.16744i		−	0.812691i	0.913719	−	0.406346i	$-0.133197\pi$
$102$		0			0
$103$	−1.55051	+	1.55051i	−0.152776	+	0.152776i	−0.779357	−	0.626580i	$-0.784454\pi$
$103$	−1.55051	+	1.55051i	−0.152776	+	0.152776i	0.626580	+	0.779357i	$0.284454\pi$
$104$	5.97469			0.585867
$105$		0			0
$106$	8.00000			0.777029
$107$	−3.60697	+	3.60697i	−0.348699	+	0.348699i	−0.859625	−	0.510926i	$-0.829303\pi$
$107$	−3.60697	+	3.60697i	−0.348699	+	0.348699i	0.510926	+	0.859625i	$0.329303\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$		0			0
$112$	1.44949	+	1.44949i	0.136964	+	0.136964i
$113$	−5.72829	−	5.72829i	−0.538872	−	0.538872i	0.384326	−	0.923198i	$-0.374434\pi$
$113$	−5.72829	−	5.72829i	−0.538872	−	0.538872i	−0.923198	+	0.384326i	$0.874434\pi$
$114$		0			0
$115$		0			0
$116$			3.14626i			0.292123i
$117$		0			0
$118$	2.00000	−	2.00000i	0.184115	−	0.184115i
$119$	12.0922			1.10849
$120$		0			0
$121$	9.79796			0.890724
$122$	−5.97469	+	5.97469i	−0.540923	+	0.540923i
$123$		0			0
$124$			1.44949i			0.130168i
$125$		0			0
$126$		0			0
$127$	4.55051	+	4.55051i	0.403792	+	0.403792i	0.879567	−	0.475775i	$-0.157832\pi$
$127$	4.55051	+	4.55051i	0.403792	+	0.403792i	−0.475775	+	0.879567i	$0.657832\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$			9.29593i			0.812189i	0.913831	+	0.406095i	$0.133110\pi$
$131$			9.29593i			0.812189i	−0.913831	+	0.406095i	$0.866890\pi$
$132$		0			0
$133$	−6.44949	+	6.44949i	−0.559242	+	0.559242i
$134$	−2.82843			−0.244339
$135$		0			0
$136$	5.89898			0.505833
$137$	15.4135	−	15.4135i	1.31686	−	1.31686i	0.400617	−	0.916245i	$-0.368796\pi$
$137$	15.4135	−	15.4135i	1.31686	−	1.31686i	0.916245	−	0.400617i	$-0.131204\pi$
$138$		0			0
$139$			8.24745i			0.699539i	0.936836	+	0.349770i	$0.113740\pi$
$139$			8.24745i			0.699539i	−0.936836	+	0.349770i	$0.886260\pi$
$140$		0			0
$141$		0			0
$142$	9.89898	+	9.89898i	0.830704	+	0.830704i
$143$	4.63191	+	4.63191i	0.387340	+	0.387340i
$144$		0			0
$145$		0			0
$146$		−	6.29253i		−	0.520773i
$147$		0			0
$148$		0			0
$149$	4.41761			0.361905			0.180952	−	0.983492i	$-0.442082\pi$
$149$	4.41761			0.361905			0.180952	+	0.983492i	$0.442082\pi$
$150$		0			0
$151$	24.1464			1.96501			0.982504	−	0.186240i	$-0.0596303\pi$
$151$	24.1464			1.96501			0.982504	+	0.186240i	$0.0596303\pi$
$152$	−3.14626	+	3.14626i	−0.255196	+	0.255196i
$153$		0			0
$154$			2.24745i			0.181105i
$155$		0			0
$156$		0			0
$157$	−8.02270	−	8.02270i	−0.640281	−	0.640281i	0.310343	−	0.950625i	$-0.399556\pi$
$157$	−8.02270	−	8.02270i	−0.640281	−	0.640281i	−0.950625	+	0.310343i	$0.899556\pi$
$158$	−3.85337	−	3.85337i	−0.306558	−	0.306558i
$159$		0			0
$160$		0			0
$161$			13.0137i			1.02562i
$162$		0			0
$163$	4.12372	−	4.12372i	0.322995	−	0.322995i	−0.526920	−	0.849915i	$-0.676653\pi$
$163$	4.12372	−	4.12372i	0.322995	−	0.322995i	0.849915	+	0.526920i	$0.176653\pi$
$164$	4.87832			0.380932
$165$		0			0
$166$	−14.4495			−1.12150
$167$	5.51399	−	5.51399i	0.426685	−	0.426685i	−0.460812	−	0.887498i	$-0.652442\pi$
$167$	5.51399	−	5.51399i	0.426685	−	0.426685i	0.887498	+	0.460812i	$0.152442\pi$
$168$		0			0
$169$		−	22.6969i		−	1.74592i
$170$		0			0
$171$		0			0
$172$	−7.22474	−	7.22474i	−0.550882	−	0.550882i
$173$	5.33902	+	5.33902i	0.405918	+	0.405918i	0.880312	−	0.474394i	$-0.157333\pi$
$173$	5.33902	+	5.33902i	0.405918	+	0.405918i	−0.474394	+	0.880312i	$0.657333\pi$
$174$		0			0
$175$		0			0
$176$			1.09638i			0.0826425i
$177$		0			0
$178$	−12.3485	+	12.3485i	−0.925557	+	0.925557i
$179$	−7.84961			−0.586707			−0.293354	−	0.956004i	$-0.594771\pi$
$179$	−7.84961			−0.586707			−0.293354	+	0.956004i	$0.594771\pi$
$180$		0			0
$181$	−4.24745			−0.315710			−0.157855	−	0.987462i	$-0.550458\pi$
$181$	−4.24745			−0.315710			−0.157855	+	0.987462i	$0.550458\pi$
$182$	8.66025	−	8.66025i	0.641941	−	0.641941i
$183$		0			0
$184$			6.34847i			0.468015i
$185$		0			0
$186$		0			0
$187$	4.57321	+	4.57321i	0.334427	+	0.334427i
$188$	7.31747	+	7.31747i	0.533682	+	0.533682i
$189$		0			0
$190$		0			0
$191$		−	16.0492i		−	1.16128i	−0.814162	−	0.580638i	$-0.802803\pi$
$191$		−	16.0492i		−	1.16128i	0.814162	−	0.580638i	$-0.197197\pi$
$192$		0			0
$193$	6.79796	−	6.79796i	0.489328	−	0.489328i	−0.418766	−	0.908094i	$-0.637537\pi$
$193$	6.79796	−	6.79796i	0.489328	−	0.489328i	0.908094	+	0.418766i	$0.137537\pi$
$194$	−11.9494			−0.857916
$195$		0			0
$196$	−2.79796			−0.199854
$197$	−6.75323	+	6.75323i	−0.481148	+	0.481148i	−0.905498	−	0.424350i	$-0.860503\pi$
$197$	−6.75323	+	6.75323i	−0.481148	+	0.481148i	0.424350	+	0.905498i	$0.360503\pi$
$198$		0			0
$199$			12.5505i			0.889682i	0.895610	+	0.444841i	$0.146740\pi$
$199$			12.5505i			0.889682i	−0.895610	+	0.444841i	$0.853260\pi$
$200$		0			0
$201$		0			0
$202$	−5.77526	−	5.77526i	−0.406346	−	0.406346i
$203$	4.56048	+	4.56048i	0.320083	+	0.320083i
$204$		0			0
$205$		0			0
$206$			2.19275i			0.152776i
$207$		0			0
$208$	4.22474	−	4.22474i	0.292933	−	0.292933i
$209$	−4.87832			−0.337440
$210$		0			0
$211$	8.24745			0.567778			0.283889	−	0.958857i	$-0.408375\pi$
$211$	8.24745			0.567778			0.283889	+	0.958857i	$0.408375\pi$
$212$	5.65685	−	5.65685i	0.388514	−	0.388514i
$213$		0			0
$214$			5.10102i			0.348699i
$215$		0			0
$216$		0			0
$217$	2.10102	+	2.10102i	0.142627	+	0.142627i
$218$	−2.82843	−	2.82843i	−0.191565	−	0.191565i
$219$		0			0
$220$		0			0
$221$		−	35.2446i		−	2.37081i
$222$		0			0
$223$	12.7980	−	12.7980i	0.857015	−	0.857015i	−0.133971	−	0.990985i	$-0.542773\pi$
$223$	12.7980	−	12.7980i	0.857015	−	0.857015i	0.990985	+	0.133971i	$0.0427728\pi$
$224$	2.04989			0.136964
$225$		0			0
$226$	−8.10102			−0.538872
$227$	5.33902	−	5.33902i	0.354363	−	0.354363i	−0.507367	−	0.861730i	$-0.669381\pi$
$227$	5.33902	−	5.33902i	0.354363	−	0.354363i	0.861730	+	0.507367i	$0.169381\pi$
$228$		0			0
$229$			4.65153i			0.307382i	0.988119	+	0.153691i	$0.0491160\pi$
$229$			4.65153i			0.307382i	−0.988119	+	0.153691i	$0.950884\pi$
$230$		0			0
$231$		0			0
$232$	2.22474	+	2.22474i	0.146062	+	0.146062i
$233$	3.46410	+	3.46410i	0.226941	+	0.226941i	0.811413	−	0.584473i	$-0.198699\pi$
$233$	3.46410	+	3.46410i	0.226941	+	0.226941i	−0.584473	+	0.811413i	$0.698699\pi$
$234$		0			0
$235$		0			0
$236$		−	2.82843i		−	0.184115i
$237$		0			0
$238$	8.55051	−	8.55051i	0.554247	−	0.554247i
$239$	−6.14966			−0.397789			−0.198894	−	0.980021i	$-0.563735\pi$
$239$	−6.14966			−0.397789			−0.198894	+	0.980021i	$0.563735\pi$
$240$		0			0
$241$	−19.6969			−1.26879			−0.634396	−	0.773008i	$-0.718751\pi$
$241$	−19.6969			−1.26879			−0.634396	+	0.773008i	$0.718751\pi$
$242$	6.92820	−	6.92820i	0.445362	−	0.445362i
$243$		0			0
$244$			8.44949i			0.540923i
$245$		0			0
$246$		0			0
$247$	18.7980	+	18.7980i	1.19609	+	1.19609i
$248$	1.02494	+	1.02494i	0.0650840	+	0.0650840i
$249$		0			0
$250$		0			0
$251$		−	1.73205i		−	0.109326i	−0.998505	−	0.0546630i	$-0.982592\pi$
$251$		−	1.73205i		−	0.109326i	0.998505	−	0.0546630i	$-0.0174085\pi$
$252$		0			0
$253$	−4.92168	+	4.92168i	−0.309424	+	0.309424i
$254$	6.43539			0.403792
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.61413	−	2.61413i	0.163065	−	0.163065i	−0.620858	−	0.783923i	$-0.713216\pi$
$257$	2.61413	−	2.61413i	0.163065	−	0.163065i	0.783923	+	0.620858i	$0.213216\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	6.57321	+	6.57321i	0.406095	+	0.406095i
$263$	−0.921404	−	0.921404i	−0.0568162	−	0.0568162i	0.678128	−	0.734944i	$-0.262792\pi$
$263$	−0.921404	−	0.921404i	−0.0568162	−	0.0568162i	−0.734944	+	0.678128i	$0.762792\pi$
$264$		0			0
$265$		0			0
$266$			9.12096i			0.559242i
$267$		0			0
$268$	−2.00000	+	2.00000i	−0.122169	+	0.122169i
$269$	24.5665			1.49785			0.748924	−	0.662655i	$-0.230571\pi$
$269$	24.5665			1.49785			0.748924	+	0.662655i	$0.230571\pi$
$270$		0			0
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	4.17121	−	4.17121i	0.252917	−	0.252917i
$273$		0			0
$274$		−	21.7980i		−	1.31686i
$275$		0			0
$276$		0			0
$277$	−9.55051	−	9.55051i	−0.573835	−	0.573835i	0.359363	−	0.933198i	$-0.382994\pi$
$277$	−9.55051	−	9.55051i	−0.573835	−	0.573835i	−0.933198	+	0.359363i	$0.882994\pi$
$278$	5.83183	+	5.83183i	0.349770	+	0.349770i
$279$		0			0
$280$		0			0
$281$			8.83523i			0.527065i	0.964650	+	0.263533i	$0.0848877\pi$
$281$			8.83523i			0.527065i	−0.964650	+	0.263533i	$0.915112\pi$
$282$		0			0
$283$	−0.898979	+	0.898979i	−0.0534388	+	0.0534388i	−0.733321	−	0.679882i	$-0.762031\pi$
$283$	−0.898979	+	0.898979i	−0.0534388	+	0.0534388i	0.679882	+	0.733321i	$0.262031\pi$
$284$	13.9993			0.830704
$285$		0			0
$286$	6.55051			0.387340
$287$	7.07107	−	7.07107i	0.417392	−	0.417392i
$288$		0			0
$289$		−	17.7980i		−	1.04694i
$290$		0			0
$291$		0			0
$292$	−4.44949	−	4.44949i	−0.260387	−	0.260387i
$293$	4.24264	+	4.24264i	0.247858	+	0.247858i	0.820091	−	0.572233i	$-0.193923\pi$
$293$	4.24264	+	4.24264i	0.247858	+	0.247858i	−0.572233	+	0.820091i	$0.693923\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$	3.12372	−	3.12372i	0.180952	−	0.180952i
$299$	37.9301			2.19356
$300$		0			0
$301$	−20.9444			−1.20721
$302$	17.0741	−	17.0741i	0.982504	−	0.982504i
$303$		0			0
$304$			4.44949i			0.255196i
$305$		0			0
$306$		0			0
$307$	−21.6742	−	21.6742i	−1.23701	−	1.23701i	−0.961216	−	0.275798i	$-0.911058\pi$
$307$	−21.6742	−	21.6742i	−1.23701	−	1.23701i	−0.275798	−	0.961216i	$-0.588942\pi$
$308$	1.58919	+	1.58919i	0.0905523	+	0.0905523i
$309$		0			0
$310$		0			0
$311$		−	32.2412i		−	1.82823i	−0.405455	−	0.914115i	$-0.632887\pi$
$311$		−	32.2412i		−	1.82823i	0.405455	−	0.914115i	$-0.367113\pi$
$312$		0			0
$313$	−3.24745	+	3.24745i	−0.183557	+	0.183557i	−0.792904	−	0.609347i	$-0.791432\pi$
$313$	−3.24745	+	3.24745i	−0.183557	+	0.183557i	0.609347	+	0.792904i	$0.291432\pi$
$314$	−11.3458			−0.640281
$315$		0			0
$316$	−5.44949			−0.306558
$317$	−1.55708	+	1.55708i	−0.0874542	+	0.0874542i	−0.749481	−	0.662026i	$-0.769697\pi$
$317$	−1.55708	+	1.55708i	−0.0874542	+	0.0874542i	0.662026	+	0.749481i	$0.269697\pi$
$318$		0			0
$319$			3.44949i			0.193134i
$320$		0			0
$321$		0			0
$322$	9.20204	+	9.20204i	0.512810	+	0.512810i
$323$	18.5597	+	18.5597i	1.03269	+	1.03269i
$324$		0			0
$325$		0			0
$326$		−	5.83183i		−	0.322995i
$327$		0			0
$328$	3.44949	−	3.44949i	0.190466	−	0.190466i
$329$	21.2132			1.16952
$330$		0			0
$331$	−21.1010			−1.15982			−0.579908	−	0.814682i	$-0.696912\pi$
$331$	−21.1010			−1.15982			−0.579908	+	0.814682i	$0.696912\pi$
$332$	−10.2173	+	10.2173i	−0.560749	+	0.560749i
$333$		0			0
$334$		−	7.79796i		−	0.426685i
$335$		0			0
$336$		0			0
$337$	7.10102	+	7.10102i	0.386817	+	0.386817i	0.873551	−	0.486733i	$-0.161812\pi$
$337$	7.10102	+	7.10102i	0.386817	+	0.386817i	−0.486733	+	0.873551i	$0.661812\pi$
$338$	−16.0492	−	16.0492i	−0.872959	−	0.872959i
$339$		0			0
$340$		0			0
$341$			1.58919i			0.0860593i
$342$		0			0
$343$	−14.2020	+	14.2020i	−0.766838	+	0.766838i
$344$	−10.2173			−0.550882
$345$		0			0
$346$	7.55051			0.405918
$347$	10.0745	−	10.0745i	0.540826	−	0.540826i	−0.382945	−	0.923771i	$-0.625090\pi$
$347$	10.0745	−	10.0745i	0.540826	−	0.540826i	0.923771	+	0.382945i	$0.125090\pi$
$348$		0			0
$349$			20.0454i			1.07301i	0.843898	+	0.536503i	$0.180255\pi$
$349$			20.0454i			1.07301i	−0.843898	+	0.536503i	$0.819745\pi$
$350$		0			0
$351$		0			0
$352$	0.775255	+	0.775255i	0.0413212	+	0.0413212i
$353$	1.34278	+	1.34278i	0.0714690	+	0.0714690i	0.741938	−	0.670469i	$-0.233907\pi$
$353$	1.34278	+	1.34278i	0.0714690	+	0.0714690i	−0.670469	+	0.741938i	$0.733907\pi$
$354$		0			0
$355$		0			0
$356$			17.4634i			0.925557i
$357$		0			0
$358$	−5.55051	+	5.55051i	−0.293354	+	0.293354i
$359$	−24.0416			−1.26887			−0.634434	−	0.772977i	$-0.718767\pi$
$359$	−24.0416			−1.26887			−0.634434	+	0.772977i	$0.718767\pi$
$360$		0			0
$361$	−0.797959			−0.0419978
$362$	−3.00340	+	3.00340i	−0.157855	+	0.157855i
$363$		0			0
$364$		−	12.2474i		−	0.641941i
$365$		0			0
$366$		0			0
$367$	−20.2474	−	20.2474i	−1.05691	−	1.05691i	−0.998280	−	0.0586283i	$-0.981327\pi$
$367$	−20.2474	−	20.2474i	−1.05691	−	1.05691i	−0.0586283	−	0.998280i	$-0.518673\pi$
$368$	4.48905	+	4.48905i	0.234008	+	0.234008i
$369$		0			0
$370$		0			0
$371$		−	16.3991i		−	0.851399i
$372$		0			0
$373$	−19.3712	+	19.3712i	−1.00300	+	1.00300i	−0.00300584	+	0.999995i	$0.500957\pi$
$373$	−19.3712	+	19.3712i	−1.00300	+	1.00300i	−0.999995	+	0.00300584i	$0.999043\pi$
$374$	6.46750			0.334427
$375$		0			0
$376$	10.3485			0.533682
$377$	13.2922	−	13.2922i	0.684581	−	0.684581i
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$		0			0
$381$		0			0
$382$	−11.3485	−	11.3485i	−0.580638	−	0.580638i
$383$	14.2457	+	14.2457i	0.727920	+	0.727920i	0.970205	−	0.242285i	$-0.0778969\pi$
$383$	14.2457	+	14.2457i	0.727920	+	0.727920i	−0.242285	+	0.970205i	$0.577897\pi$
$384$		0			0
$385$		0			0
$386$		−	9.61377i		−	0.489328i
$387$		0			0
$388$	−8.44949	+	8.44949i	−0.428958	+	0.428958i
$389$	−9.43879			−0.478566			−0.239283	−	0.970950i	$-0.576912\pi$
$389$	−9.43879			−0.478566			−0.239283	+	0.970950i	$0.576912\pi$
$390$		0			0
$391$	37.4495			1.89390
$392$	−1.97846	+	1.97846i	−0.0999271	+	0.0999271i
$393$		0			0
$394$			9.55051i			0.481148i
$395$		0			0
$396$		0			0
$397$	19.5732	+	19.5732i	0.982351	+	0.982351i	0.999847	−	0.0174955i	$-0.00556927\pi$
$397$	19.5732	+	19.5732i	0.982351	+	0.982351i	−0.0174955	+	0.999847i	$0.505569\pi$
$398$	8.87455	+	8.87455i	0.444841	+	0.444841i
$399$		0			0
$400$		0			0
$401$			10.0424i			0.501492i	0.968053	+	0.250746i	$0.0806758\pi$
$401$			10.0424i			0.501492i	−0.968053	+	0.250746i	$0.919324\pi$
$402$		0			0
$403$	6.12372	−	6.12372i	0.305044	−	0.305044i
$404$	−8.16744			−0.406346
$405$		0			0
$406$	6.44949			0.320083
$407$		0			0
$408$		0			0
$409$		−	30.7980i		−	1.52286i	−0.648247	−	0.761431i	$-0.724497\pi$
$409$		−	30.7980i		−	1.52286i	0.648247	−	0.761431i	$-0.275503\pi$
$410$		0			0
$411$		0			0
$412$	1.55051	+	1.55051i	0.0763882	+	0.0763882i
$413$	−4.09978	−	4.09978i	−0.201737	−	0.201737i
$414$		0			0
$415$		0			0
$416$		−	5.97469i		−	0.292933i
$417$		0			0
$418$	−3.44949	+	3.44949i	−0.168720	+	0.168720i
$419$	−34.1161			−1.66668			−0.833340	−	0.552760i	$-0.813574\pi$
$419$	−34.1161			−1.66668			−0.833340	+	0.552760i	$0.813574\pi$
$420$		0			0
$421$	−13.5505			−0.660411			−0.330206	−	0.943909i	$-0.607118\pi$
$421$	−13.5505			−0.660411			−0.330206	+	0.943909i	$0.607118\pi$
$422$	5.83183	−	5.83183i	0.283889	−	0.283889i
$423$		0			0
$424$		−	8.00000i		−	0.388514i
$425$		0			0
$426$		0			0
$427$	12.2474	+	12.2474i	0.592696	+	0.592696i
$428$	3.60697	+	3.60697i	0.174349	+	0.174349i
$429$		0			0
$430$		0			0
$431$			22.6274i			1.08992i	0.838461	+	0.544962i	$0.183456\pi$
$431$			22.6274i			1.08992i	−0.838461	+	0.544962i	$0.816544\pi$
$432$		0			0
$433$	−14.2474	+	14.2474i	−0.684689	+	0.684689i	−0.961053	−	0.276364i	$-0.910870\pi$
$433$	−14.2474	+	14.2474i	−0.684689	+	0.684689i	0.276364	+	0.961053i	$0.410870\pi$
$434$	2.97129			0.142627
$435$		0			0
$436$	−4.00000			−0.191565
$437$	−19.9740	+	19.9740i	−0.955484	+	0.955484i
$438$		0			0
$439$			3.59592i			0.171624i	0.996311	+	0.0858119i	$0.0273484\pi$
$439$			3.59592i			0.171624i	−0.996311	+	0.0858119i	$0.972652\pi$
$440$		0			0
$441$		0			0
$442$	−24.9217	−	24.9217i	−1.18540	−	1.18540i
$443$	−4.41761	−	4.41761i	−0.209887	−	0.209887i	0.594332	−	0.804220i	$-0.297416\pi$
$443$	−4.41761	−	4.41761i	−0.209887	−	0.209887i	−0.804220	+	0.594332i	$0.797416\pi$
$444$		0			0
$445$		0			0
$446$		−	18.0990i		−	0.857015i
$447$		0			0
$448$	1.44949	−	1.44949i	0.0684820	−	0.0684820i
$449$	15.5563			0.734150			0.367075	−	0.930191i	$-0.380359\pi$
$449$	15.5563			0.734150			0.367075	+	0.930191i	$0.380359\pi$
$450$		0			0
$451$	5.34847			0.251850
$452$	−5.72829	+	5.72829i	−0.269436	+	0.269436i
$453$		0			0
$454$		−	7.55051i		−	0.354363i
$455$		0			0
$456$		0			0
$457$	−14.6969	−	14.6969i	−0.687494	−	0.687494i	0.274184	−	0.961677i	$-0.411592\pi$
$457$	−14.6969	−	14.6969i	−0.687494	−	0.687494i	−0.961677	+	0.274184i	$0.911592\pi$
$458$	3.28913	+	3.28913i	0.153691	+	0.153691i
$459$		0			0
$460$		0			0
$461$		−	2.82843i		−	0.131733i	−0.997828	−	0.0658665i	$-0.979019\pi$
$461$		−	2.82843i		−	0.131733i	0.997828	−	0.0658665i	$-0.0209811\pi$
$462$		0			0
$463$	11.3485	−	11.3485i	0.527408	−	0.527408i	−0.392391	−	0.919799i	$-0.628352\pi$
$463$	11.3485	−	11.3485i	0.527408	−	0.527408i	0.919799	+	0.392391i	$0.128352\pi$
$464$	3.14626			0.146062
$465$		0			0
$466$	4.89898			0.226941
$467$	6.61037	−	6.61037i	0.305891	−	0.305891i	−0.537422	−	0.843313i	$-0.680602\pi$
$467$	6.61037	−	6.61037i	0.305891	−	0.305891i	0.843313	+	0.537422i	$0.180602\pi$
$468$		0			0
$469$			5.79796i			0.267725i
$470$		0			0
$471$		0			0
$472$	−2.00000	−	2.00000i	−0.0920575	−	0.0920575i
$473$	−7.92104	−	7.92104i	−0.364210	−	0.364210i
$474$		0			0
$475$		0			0
$476$		−	12.0922i		−	0.554247i
$477$		0			0
$478$	−4.34847	+	4.34847i	−0.198894	+	0.198894i
$479$	−18.3848			−0.840022			−0.420011	−	0.907519i	$-0.637974\pi$
$479$	−18.3848			−0.840022			−0.420011	+	0.907519i	$0.637974\pi$
$480$		0			0
$481$		0			0
$482$	−13.9278	+	13.9278i	−0.634396	+	0.634396i
$483$		0			0
$484$		−	9.79796i		−	0.445362i
$485$		0			0
$486$		0			0
$487$	14.6969	+	14.6969i	0.665982	+	0.665982i	0.956783	−	0.290802i	$-0.0939219\pi$
$487$	14.6969	+	14.6969i	0.665982	+	0.665982i	−0.290802	+	0.956783i	$0.593922\pi$
$488$	5.97469	+	5.97469i	0.270462	+	0.270462i
$489$		0			0
$490$		0			0
$491$			25.1701i			1.13591i	0.823059	+	0.567956i	$0.192266\pi$
$491$			25.1701i			1.13591i	−0.823059	+	0.567956i	$0.807734\pi$
$492$		0			0
$493$	13.1237	−	13.1237i	0.591063	−	0.591063i
$494$	26.5843			1.19609
$495$		0			0
$496$	1.44949			0.0650840
$497$	20.2918	−	20.2918i	0.910212	−	0.910212i
$498$		0			0
$499$			5.79796i			0.259552i	0.991543	+	0.129776i	$0.0414259\pi$
$499$			5.79796i			0.259552i	−0.991543	+	0.129776i	$0.958574\pi$
$500$		0			0
$501$		0			0
$502$	−1.22474	−	1.22474i	−0.0546630	−	0.0546630i
$503$	−26.1951	−	26.1951i	−1.16798	−	1.16798i	−0.982682	−	0.185297i	$-0.940675\pi$
$503$	−26.1951	−	26.1951i	−1.16798	−	1.16798i	−0.185297	−	0.982682i	$-0.559325\pi$
$504$		0			0
$505$		0			0
$506$			6.96031i			0.309424i
$507$		0			0
$508$	4.55051	−	4.55051i	0.201896	−	0.201896i
$509$	18.8455			0.835311			0.417656	−	0.908605i	$-0.362852\pi$
$509$	18.8455			0.835311			0.417656	+	0.908605i	$0.362852\pi$
$510$		0			0
$511$	−12.8990			−0.570617
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	3.69694i		−	0.163065i
$515$		0			0
$516$		0			0
$517$	8.02270	+	8.02270i	0.352838	+	0.352838i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			4.59259i			0.201205i	0.994927	+	0.100602i	$0.0320770\pi$
$521$			4.59259i			0.201205i	−0.994927	+	0.100602i	$0.967923\pi$
$522$		0			0
$523$	−4.77526	+	4.77526i	−0.208807	+	0.208807i	−0.803760	−	0.594953i	$-0.797171\pi$
$523$	−4.77526	+	4.77526i	−0.208807	+	0.208807i	0.594953	+	0.803760i	$0.297171\pi$
$524$	9.29593			0.406095
$525$		0			0
$526$	−1.30306			−0.0568162
$527$	6.04612	−	6.04612i	0.263373	−	0.263373i
$528$		0			0
$529$			17.3031i			0.752307i
$530$		0			0
$531$		0			0
$532$	6.44949	+	6.44949i	0.279621	+	0.279621i
$533$	−20.6096	−	20.6096i	−0.892702	−	0.892702i
$534$		0			0
$535$		0			0
$536$			2.82843i			0.122169i
$537$		0			0
$538$	17.3712	−	17.3712i	0.748924	−	0.748924i
$539$	−3.06762			−0.132132
$540$		0			0
$541$	−9.59592			−0.412561			−0.206280	−	0.978493i	$-0.566136\pi$
$541$	−9.59592			−0.412561			−0.206280	+	0.978493i	$0.566136\pi$
$542$	−4.24264	+	4.24264i	−0.182237	+	0.182237i
$543$		0			0
$544$		−	5.89898i		−	0.252917i
$545$		0			0
$546$		0			0
$547$	13.4722	+	13.4722i	0.576029	+	0.576029i	0.933807	−	0.357777i	$-0.116465\pi$
$547$	13.4722	+	13.4722i	0.576029	+	0.576029i	−0.357777	+	0.933807i	$0.616465\pi$
$548$	−15.4135	−	15.4135i	−0.658431	−	0.658431i
$549$		0			0
$550$		0			0
$551$			13.9993i			0.596389i
$552$		0			0
$553$	−7.89898	+	7.89898i	−0.335899	+	0.335899i
$554$	−13.5065			−0.573835
$555$		0			0
$556$	8.24745			0.349770
$557$	−12.1244	+	12.1244i	−0.513725	+	0.513725i	−0.915666	−	0.401940i	$-0.868336\pi$
$557$	−12.1244	+	12.1244i	−0.513725	+	0.513725i	0.401940	+	0.915666i	$0.368336\pi$
$558$		0			0
$559$			61.0454i			2.58195i
$560$		0			0
$561$		0			0
$562$	6.24745	+	6.24745i	0.263533	+	0.263533i
$563$	13.6814	+	13.6814i	0.576604	+	0.576604i	0.933966	−	0.357362i	$-0.116324\pi$
$563$	13.6814	+	13.6814i	0.576604	+	0.576604i	−0.357362	+	0.933966i	$0.616324\pi$
$564$		0			0
$565$		0			0
$566$			1.27135i			0.0534388i
$567$		0			0
$568$	9.89898	−	9.89898i	0.415352	−	0.415352i
$569$	−22.0560			−0.924634			−0.462317	−	0.886715i	$-0.652982\pi$
$569$	−22.0560			−0.924634			−0.462317	+	0.886715i	$0.652982\pi$
$570$		0			0
$571$	−1.55051			−0.0648868			−0.0324434	−	0.999474i	$-0.510329\pi$
$571$	−1.55051			−0.0648868			−0.0324434	+	0.999474i	$0.510329\pi$
$572$	4.63191	−	4.63191i	0.193670	−	0.193670i
$573$		0			0
$574$		−	10.0000i		−	0.417392i
$575$		0			0
$576$		0			0
$577$	−4.00000	−	4.00000i	−0.166522	−	0.166522i	0.618927	−	0.785449i	$-0.287568\pi$
$577$	−4.00000	−	4.00000i	−0.166522	−	0.166522i	−0.785449	+	0.618927i	$0.787568\pi$
$578$	−12.5851	−	12.5851i	−0.523469	−	0.523469i
$579$		0			0
$580$		0			0
$581$			29.6198i			1.22884i
$582$		0			0
$583$	6.20204	−	6.20204i	0.256862	−	0.256862i
$584$	−6.29253			−0.260387
$585$		0			0
$586$	6.00000			0.247858
$587$	−24.0737	+	24.0737i	−0.993630	+	0.993630i	−0.999980	−	0.00635031i	$-0.997979\pi$
$587$	−24.0737	+	24.0737i	−0.993630	+	0.993630i	0.00635031	+	0.999980i	$0.497979\pi$
$588$		0			0
$589$			6.44949i			0.265747i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−23.9702	−	23.9702i	−0.984338	−	0.984338i	0.0155412	−	0.999879i	$-0.495053\pi$
$593$	−23.9702	−	23.9702i	−0.984338	−	0.984338i	−0.999879	+	0.0155412i	$0.995053\pi$
$594$		0			0
$595$		0			0
$596$		−	4.41761i		−	0.180952i
$597$		0			0
$598$	26.8207	−	26.8207i	1.09678	−	1.09678i
$599$	18.5919			0.759643			0.379821	−	0.925060i	$-0.375985\pi$
$599$	18.5919			0.759643			0.379821	+	0.925060i	$0.375985\pi$
$600$		0			0
$601$	−18.3939			−0.750302			−0.375151	−	0.926964i	$-0.622409\pi$
$601$	−18.3939			−0.750302			−0.375151	+	0.926964i	$0.622409\pi$
$602$	−14.8099	+	14.8099i	−0.603607	+	0.603607i
$603$		0			0
$604$		−	24.1464i		−	0.982504i
$605$		0			0
$606$		0			0
$607$	16.6515	+	16.6515i	0.675865	+	0.675865i	0.959062	−	0.283197i	$-0.0913950\pi$
$607$	16.6515	+	16.6515i	0.675865	+	0.675865i	−0.283197	+	0.959062i	$0.591395\pi$
$608$	3.14626	+	3.14626i	0.127598	+	0.127598i
$609$		0			0
$610$		0			0
$611$		−	61.8289i		−	2.50133i
$612$		0			0
$613$	10.4722	−	10.4722i	0.422968	−	0.422968i	−0.463256	−	0.886224i	$-0.653319\pi$
$613$	10.4722	−	10.4722i	0.422968	−	0.422968i	0.886224	+	0.463256i	$0.153319\pi$
$614$	−30.6520			−1.23701
$615$		0			0
$616$	2.24745			0.0905523
$617$	3.67840	−	3.67840i	0.148087	−	0.148087i	−0.629176	−	0.777263i	$-0.716608\pi$
$617$	3.67840	−	3.67840i	0.148087	−	0.148087i	0.777263	+	0.629176i	$0.216608\pi$
$618$		0			0
$619$			8.69694i			0.349559i	0.984608	+	0.174780i	$0.0559213\pi$
$619$			8.69694i			0.349559i	−0.984608	+	0.174780i	$0.944079\pi$
$620$		0			0
$621$		0			0
$622$	−22.7980	−	22.7980i	−0.914115	−	0.914115i
$623$	25.3130	+	25.3130i	1.01414	+	1.01414i
$624$		0			0
$625$		0			0
$626$			4.59259i			0.183557i
$627$		0			0
$628$	−8.02270	+	8.02270i	−0.320141	+	0.320141i
$629$		0			0
$630$		0			0
$631$	4.49490			0.178939			0.0894695	−	0.995990i	$-0.471483\pi$
$631$	4.49490			0.178939			0.0894695	+	0.995990i	$0.471483\pi$
$632$	−3.85337	+	3.85337i	−0.153279	+	0.153279i
$633$		0			0
$634$			2.20204i			0.0874542i
$635$		0			0
$636$		0			0
$637$	11.8207	+	11.8207i	0.468352	+	0.468352i
$638$	2.43916	+	2.43916i	0.0965672	+	0.0965672i
$639$		0			0
$640$		0			0
$641$			27.8557i			1.10023i	0.835088	+	0.550117i	$0.185417\pi$
$641$			27.8557i			1.10023i	−0.835088	+	0.550117i	$0.814583\pi$
$642$		0			0
$643$	32.8207	−	32.8207i	1.29432	−	1.29432i	0.362233	−	0.932088i	$-0.382014\pi$
$643$	32.8207	−	32.8207i	1.29432	−	1.29432i	0.932088	−	0.362233i	$-0.117986\pi$
$644$	13.0137			0.512810
$645$		0			0
$646$	26.2474			1.03269
$647$	−6.00680	+	6.00680i	−0.236152	+	0.236152i	−0.815254	−	0.579103i	$-0.803403\pi$
$647$	−6.00680	+	6.00680i	−0.236152	+	0.236152i	0.579103	+	0.815254i	$0.303403\pi$
$648$		0			0
$649$		−	3.10102i		−	0.121726i
$650$		0			0
$651$		0			0
$652$	−4.12372	−	4.12372i	−0.161498	−	0.161498i
$653$	−10.5673	−	10.5673i	−0.413530	−	0.413530i	0.469437	−	0.882966i	$-0.344457\pi$
$653$	−10.5673	−	10.5673i	−0.413530	−	0.413530i	−0.882966	+	0.469437i	$0.844457\pi$
$654$		0			0
$655$		0			0
$656$		−	4.87832i		−	0.190466i
$657$		0			0
$658$	15.0000	−	15.0000i	0.584761	−	0.584761i
$659$	−32.0983			−1.25037			−0.625186	−	0.780475i	$-0.714977\pi$
$659$	−32.0983			−1.25037			−0.625186	+	0.780475i	$0.714977\pi$
$660$		0			0
$661$	−20.0454			−0.779676			−0.389838	−	0.920883i	$-0.627469\pi$
$661$	−20.0454			−0.779676			−0.389838	+	0.920883i	$0.627469\pi$
$662$	−14.9207	+	14.9207i	−0.579908	+	0.579908i
$663$		0			0
$664$			14.4495i			0.560749i
$665$		0			0
$666$		0			0
$667$	14.1237	+	14.1237i	0.546873	+	0.546873i
$668$	−5.51399	−	5.51399i	−0.213343	−	0.213343i
$669$		0			0
$670$		0			0
$671$			9.26382i			0.357626i
$672$		0			0
$673$	−34.7980	+	34.7980i	−1.34136	+	1.34136i	−0.446658	+	0.894705i	$0.647386\pi$
$673$	−34.7980	+	34.7980i	−1.34136	+	1.34136i	−0.894705	+	0.446658i	$0.852614\pi$
$674$	10.0424			0.386817
$675$		0			0
$676$	−22.6969			−0.872959
$677$	−33.6554	+	33.6554i	−1.29348	+	1.29348i	−0.360863	+	0.932619i	$0.617518\pi$
$677$	−33.6554	+	33.6554i	−1.29348	+	1.29348i	−0.932619	+	0.360863i	$0.882482\pi$
$678$		0			0
$679$			24.4949i			0.940028i
$680$		0			0
$681$		0			0
$682$	1.12372	+	1.12372i	0.0430296	+	0.0430296i
$683$	6.92820	+	6.92820i	0.265100	+	0.265100i	0.827122	−	0.562022i	$-0.189976\pi$
$683$	6.92820	+	6.92820i	0.265100	+	0.265100i	−0.562022	+	0.827122i	$0.689976\pi$
$684$		0			0
$685$		0			0
$686$			20.0847i			0.766838i
$687$		0			0
$688$	−7.22474	+	7.22474i	−0.275441	+	0.275441i
$689$	−47.7975			−1.82094
$690$		0			0
$691$	22.8990			0.871118			0.435559	−	0.900160i	$-0.356551\pi$
$691$	22.8990			0.871118			0.435559	+	0.900160i	$0.356551\pi$
$692$	5.33902	−	5.33902i	0.202959	−	0.202959i
$693$		0			0
$694$		−	14.2474i		−	0.540826i
$695$		0			0
$696$		0			0
$697$	−20.3485	−	20.3485i	−0.770753	−	0.770753i
$698$	14.1742	+	14.1742i	0.536503	+	0.536503i
$699$		0			0
$700$		0			0
$701$		−	13.8243i		−	0.522137i	−0.965320	−	0.261068i	$-0.915925\pi$
$701$		−	13.8243i		−	0.522137i	0.965320	−	0.261068i	$-0.0840748\pi$
$702$		0			0
$703$		0			0
$704$	1.09638			0.0413212
$705$		0			0
$706$	1.89898			0.0714690
$707$	−11.8386	+	11.8386i	−0.445237	+	0.445237i
$708$		0			0
$709$		−	8.00000i		−	0.300446i	−0.988652	−	0.150223i	$-0.952001\pi$
$709$		−	8.00000i		−	0.300446i	0.988652	−	0.150223i	$-0.0479992\pi$
$710$		0			0
$711$		0			0
$712$	12.3485	+	12.3485i	0.462778	+	0.462778i
$713$	6.50683	+	6.50683i	0.243683	+	0.243683i
$714$		0			0
$715$		0			0
$716$			7.84961i			0.293354i
$717$		0			0
$718$	−17.0000	+	17.0000i	−0.634434	+	0.634434i
$719$	29.7627			1.10996			0.554981	−	0.831863i	$-0.312726\pi$
$719$	29.7627			1.10996			0.554981	+	0.831863i	$0.312726\pi$
$720$		0			0
$721$	4.49490			0.167399
$722$	−0.564242	+	0.564242i	−0.0209989	+	0.0209989i
$723$		0			0
$724$			4.24745i			0.157855i
$725$		0			0
$726$		0			0
$727$	24.4949	+	24.4949i	0.908465	+	0.908465i	0.996148	−	0.0876830i	$-0.0279462\pi$
$727$	24.4949	+	24.4949i	0.908465	+	0.908465i	−0.0876830	+	0.996148i	$0.527946\pi$
$728$	−8.66025	−	8.66025i	−0.320970	−	0.320970i
$729$		0			0
$730$		0			0
$731$			60.2718i			2.22923i
$732$		0			0
$733$	−23.5959	+	23.5959i	−0.871535	+	0.871535i	−0.992640	−	0.121105i	$-0.961356\pi$
$733$	−23.5959	+	23.5959i	−0.871535	+	0.871535i	0.121105	+	0.992640i	$0.461356\pi$
$734$	−28.6342			−1.05691
$735$		0			0
$736$	6.34847			0.234008
$737$	−2.19275	+	2.19275i	−0.0807711	+	0.0807711i
$738$		0			0
$739$			9.84337i			0.362094i	0.983474	+	0.181047i	$0.0579486\pi$
$739$			9.84337i			0.362094i	−0.983474	+	0.181047i	$0.942051\pi$
$740$		0			0
$741$		0			0
$742$	−11.5959	−	11.5959i	−0.425700	−	0.425700i
$743$	−19.7597	−	19.7597i	−0.724912	−	0.724912i	0.244690	−	0.969601i	$-0.421314\pi$
$743$	−19.7597	−	19.7597i	−0.724912	−	0.724912i	−0.969601	+	0.244690i	$0.921314\pi$
$744$		0			0
$745$		0			0
$746$			27.3950i			1.00300i
$747$		0			0
$748$	4.57321	−	4.57321i	0.167213	−	0.167213i
$749$	10.4565			0.382073
$750$		0			0
$751$	25.0454			0.913920			0.456960	−	0.889487i	$-0.348938\pi$
$751$	25.0454			0.913920			0.456960	+	0.889487i	$0.348938\pi$
$752$	7.31747	−	7.31747i	0.266841	−	0.266841i
$753$		0			0
$754$		−	18.7980i		−	0.684581i
$755$		0			0
$756$		0			0
$757$	−2.02270	−	2.02270i	−0.0735164	−	0.0735164i	0.669393	−	0.742909i	$-0.266554\pi$
$757$	−2.02270	−	2.02270i	−0.0735164	−	0.0735164i	−0.742909	+	0.669393i	$0.766554\pi$
$758$	2.82843	+	2.82843i	0.102733	+	0.102733i
$759$		0			0
$760$		0			0
$761$			4.52837i			0.164153i	0.996626	+	0.0820766i	$0.0261552\pi$
$761$			4.52837i			0.164153i	−0.996626	+	0.0820766i	$0.973845\pi$
$762$		0			0
$763$	−5.79796	+	5.79796i	−0.209900	+	0.209900i
$764$	−16.0492			−0.580638
$765$		0			0
$766$	20.1464			0.727920
$767$	−11.9494	+	11.9494i	−0.431467	+	0.431467i
$768$		0			0
$769$			31.6969i			1.14302i	0.820595	+	0.571510i	$0.193642\pi$
$769$			31.6969i			1.14302i	−0.820595	+	0.571510i	$0.806358\pi$
$770$		0			0
$771$		0			0
$772$	−6.79796	−	6.79796i	−0.244664	−	0.244664i
$773$	1.12848	+	1.12848i	0.0405888	+	0.0405888i	0.727110	−	0.686521i	$-0.240863\pi$
$773$	1.12848	+	1.12848i	0.0405888	+	0.0405888i	−0.686521	+	0.727110i	$0.740863\pi$
$774$		0			0
$775$		0			0
$776$			11.9494i			0.428958i
$777$		0			0
$778$	−6.67423	+	6.67423i	−0.239283	+	0.239283i
$779$	21.7060			0.777699
$780$		0			0
$781$	15.3485			0.549211
$782$	26.4808	−	26.4808i	0.946951	−	0.946951i
$783$		0			0
$784$			2.79796i			0.0999271i
$785$		0			0
$786$		0			0
$787$	−12.5732	−	12.5732i	−0.448187	−	0.448187i	0.446565	−	0.894751i	$-0.352647\pi$
$787$	−12.5732	−	12.5732i	−0.448187	−	0.448187i	−0.894751	+	0.446565i	$0.852647\pi$
$788$	6.75323	+	6.75323i	0.240574	+	0.240574i
$789$		0			0
$790$		0			0
$791$			16.6062i			0.590448i
$792$		0			0
$793$	35.6969	−	35.6969i	1.26764	−	1.26764i
$794$	27.6807			0.982351
$795$		0			0
$796$	12.5505			0.444841
$797$	−18.7026	+	18.7026i	−0.662481	+	0.662481i	−0.955964	−	0.293484i	$-0.905185\pi$
$797$	−18.7026	+	18.7026i	−0.662481	+	0.662481i	0.293484	+	0.955964i	$0.405185\pi$
$798$		0			0
$799$		−	61.0454i		−	2.15963i
$800$		0			0
$801$		0			0
$802$	7.10102	+	7.10102i	0.250746	+	0.250746i
$803$	−4.87832	−	4.87832i	−0.172152	−	0.172152i
$804$		0			0
$805$		0			0
$806$		−	8.66025i		−	0.305044i
$807$		0			0
$808$	−5.77526	+	5.77526i	−0.203173	+	0.203173i
$809$	15.6992			0.551955			0.275977	−	0.961164i	$-0.410998\pi$
$809$	15.6992			0.551955			0.275977	+	0.961164i	$0.410998\pi$
$810$		0			0
$811$	30.8990			1.08501			0.542505	−	0.840053i	$-0.317476\pi$
$811$	30.8990			1.08501			0.542505	+	0.840053i	$0.317476\pi$
$812$	4.56048	−	4.56048i	0.160041	−	0.160041i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−32.1464	−	32.1464i	−1.12466	−	1.12466i
$818$	−21.7774	−	21.7774i	−0.761431	−	0.761431i
$819$		0			0
$820$		0			0
$821$		−	5.08540i		−	0.177482i	−0.996055	−	0.0887408i	$-0.971716\pi$
$821$		−	5.08540i		−	0.177482i	0.996055	−	0.0887408i	$-0.0282843\pi$
$822$		0			0
$823$	4.00000	−	4.00000i	0.139431	−	0.139431i	−0.633946	−	0.773377i	$-0.718566\pi$
$823$	4.00000	−	4.00000i	0.139431	−	0.139431i	0.773377	+	0.633946i	$0.218566\pi$
$824$	2.19275			0.0763882
$825$		0			0
$826$	−5.79796			−0.201737
$827$	−17.7491	+	17.7491i	−0.617197	+	0.617197i	−0.944811	−	0.327615i	$-0.893755\pi$
$827$	−17.7491	+	17.7491i	−0.617197	+	0.617197i	0.327615	+	0.944811i	$0.393755\pi$
$828$		0			0
$829$		−	25.7980i		−	0.896000i	−0.894034	−	0.448000i	$-0.852136\pi$
$829$		−	25.7980i		−	0.896000i	0.894034	−	0.448000i	$-0.147864\pi$
$830$		0			0
$831$		0			0
$832$	−4.22474	−	4.22474i	−0.146467	−	0.146467i
$833$	11.6709	+	11.6709i	0.404372	+	0.404372i
$834$		0			0
$835$		0			0
$836$			4.87832i			0.168720i
$837$		0			0
$838$	−24.1237	+	24.1237i	−0.833340	+	0.833340i
$839$	−8.54950			−0.295161			−0.147581	−	0.989050i	$-0.547149\pi$
$839$	−8.54950			−0.295161			−0.147581	+	0.989050i	$0.547149\pi$
$840$		0			0
$841$	−19.1010			−0.658656
$842$	−9.58166	+	9.58166i	−0.330206	+	0.330206i
$843$		0			0
$844$		−	8.24745i		−	0.283889i
$845$		0			0
$846$		0			0
$847$	−14.2020	−	14.2020i	−0.487988	−	0.487988i
$848$	−5.65685	−	5.65685i	−0.194257	−	0.194257i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−16.4268	+	16.4268i	−0.562442	+	0.562442i	−0.930001	−	0.367558i	$-0.880194\pi$
$853$	−16.4268	+	16.4268i	−0.562442	+	0.562442i	0.367558	+	0.930001i	$0.380194\pi$
$854$	17.3205			0.592696
$855$		0			0
$856$	5.10102			0.174349
$857$	−24.2487	+	24.2487i	−0.828320	+	0.828320i	−0.987284	−	0.158964i	$-0.949185\pi$
$857$	−24.2487	+	24.2487i	−0.828320	+	0.828320i	0.158964	+	0.987284i	$0.449185\pi$
$858$		0			0
$859$		−	2.89898i		−	0.0989119i	−0.998776	−	0.0494560i	$-0.984251\pi$
$859$		−	2.89898i		−	0.0989119i	0.998776	−	0.0494560i	$-0.0157487\pi$
$860$		0			0
$861$		0			0
$862$	16.0000	+	16.0000i	0.544962	+	0.544962i
$863$	−7.95315	−	7.95315i	−0.270728	−	0.270728i	0.558665	−	0.829393i	$-0.311314\pi$
$863$	−7.95315	−	7.95315i	−0.270728	−	0.270728i	−0.829393	+	0.558665i	$0.811314\pi$
$864$		0			0
$865$		0			0
$866$			20.1489i			0.684689i
$867$		0			0
$868$	2.10102	−	2.10102i	0.0713133	−	0.0713133i
$869$	−5.97469			−0.202678
$870$		0			0
$871$	16.8990			0.572600
$872$	−2.82843	+	2.82843i	−0.0957826	+	0.0957826i
$873$		0			0
$874$			28.2474i			0.955484i
$875$		0			0
$876$		0			0
$877$	24.9217	+	24.9217i	0.841545	+	0.841545i	0.989060	−	0.147514i	$-0.0471273\pi$
$877$	24.9217	+	24.9217i	0.841545	+	0.841545i	−0.147514	+	0.989060i	$0.547127\pi$
$878$	2.54270	+	2.54270i	0.0858119	+	0.0858119i
$879$		0			0
$880$		0			0
$881$		−	40.2337i		−	1.35551i	−0.735290	−	0.677753i	$-0.762954\pi$
$881$		−	40.2337i		−	1.35551i	0.735290	−	0.677753i	$-0.237046\pi$
$882$		0			0
$883$	−33.1464	+	33.1464i	−1.11547	+	1.11547i	−0.123068	+	0.992398i	$0.539273\pi$
$883$	−33.1464	+	33.1464i	−1.11547	+	1.11547i	−0.992398	+	0.123068i	$0.960727\pi$
$884$	−35.2446			−1.18540
$885$		0			0
$886$	−6.24745			−0.209887
$887$	−10.4316	+	10.4316i	−0.350260	+	0.350260i	−0.860206	−	0.509946i	$-0.829665\pi$
$887$	−10.4316	+	10.4316i	−0.350260	+	0.350260i	0.509946	+	0.860206i	$0.329665\pi$
$888$		0			0
$889$		−	13.1918i		−	0.442440i
$890$		0			0
$891$		0			0
$892$	−12.7980	−	12.7980i	−0.428507	−	0.428507i
$893$	32.5590	+	32.5590i	1.08955	+	1.08955i
$894$		0			0
$895$		0			0
$896$		−	2.04989i		−	0.0684820i
$897$		0			0
$898$	11.0000	−	11.0000i	0.367075	−	0.367075i
$899$	4.56048			0.152100
$900$		0			0
$901$	−47.1918			−1.57219
$902$	3.78194	−	3.78194i	0.125925	−	0.125925i
$903$		0			0
$904$			8.10102i			0.269436i
$905$		0			0
$906$		0			0
$907$	1.62883	+	1.62883i	0.0540843	+	0.0540843i	0.733632	−	0.679547i	$-0.237824\pi$
$907$	1.62883	+	1.62883i	0.0540843	+	0.0540843i	−0.679547	+	0.733632i	$0.737824\pi$
$908$	−5.33902	−	5.33902i	−0.177182	−	0.177182i
$909$		0			0
$910$		0			0
$911$		−	43.4120i		−	1.43830i	−0.694852	−	0.719152i	$-0.744530\pi$
$911$		−	43.4120i		−	1.43830i	0.694852	−	0.719152i	$-0.255470\pi$
$912$		0			0
$913$	−11.2020	+	11.2020i	−0.370733	+	0.370733i
$914$	−20.7846			−0.687494
$915$		0			0
$916$	4.65153			0.153691
$917$	13.4744	−	13.4744i	0.444962	−	0.444962i
$918$		0			0
$919$		−	5.65153i		−	0.186427i	−0.995646	−	0.0932134i	$-0.970286\pi$
$919$		−	5.65153i		−	0.186427i	0.995646	−	0.0932134i	$-0.0297139\pi$
$920$		0			0
$921$		0			0
$922$	−2.00000	−	2.00000i	−0.0658665	−	0.0658665i
$923$	−59.1433	−	59.1433i	−1.94673	−	1.94673i
$924$		0			0
$925$		0			0
$926$		−	16.0492i		−	0.527408i
$927$		0			0
$928$	2.22474	−	2.22474i	0.0730308	−	0.0730308i
$929$	39.8051			1.30596			0.652981	−	0.757374i	$-0.273518\pi$
$929$	39.8051			1.30596			0.652981	+	0.757374i	$0.273518\pi$
$930$		0			0
$931$	−12.4495			−0.408016
$932$	3.46410	−	3.46410i	0.113470	−	0.113470i
$933$		0			0
$934$		−	9.34847i		−	0.305891i
$935$		0			0
$936$		0			0
$937$	−19.4949	−	19.4949i	−0.636871	−	0.636871i	0.312912	−	0.949782i	$-0.398696\pi$
$937$	−19.4949	−	19.4949i	−0.636871	−	0.636871i	−0.949782	+	0.312912i	$0.898696\pi$
$938$	4.09978	+	4.09978i	0.133862	+	0.133862i
$939$		0			0
$940$		0			0
$941$			33.3376i			1.08677i	0.839483	+	0.543387i	$0.182858\pi$
$941$			33.3376i			1.08677i	−0.839483	+	0.543387i	$0.817142\pi$
$942$		0			0
$943$	21.8990	−	21.8990i	0.713129	−	0.713129i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	−11.2020			−0.364210
$947$	33.4804	−	33.4804i	1.08797	−	1.08797i	0.0922298	−	0.995738i	$-0.470601\pi$
$947$	33.4804	−	33.4804i	1.08797	−	1.08797i	0.995738	−	0.0922298i	$-0.0293995\pi$
$948$		0			0
$949$			37.5959i			1.22042i
$950$		0			0
$951$		0			0
$952$	−8.55051	−	8.55051i	−0.277124	−	0.277124i
$953$	−3.67840	−	3.67840i	−0.119155	−	0.119155i	0.645015	−	0.764170i	$-0.276851\pi$
$953$	−3.67840	−	3.67840i	−0.119155	−	0.119155i	−0.764170	+	0.645015i	$0.776851\pi$
$954$		0			0
$955$		0			0
$956$			6.14966i			0.198894i
$957$		0			0
$958$	−13.0000	+	13.0000i	−0.420011	+	0.420011i
$959$	−44.6834			−1.44290
$960$		0			0
$961$	−28.8990			−0.932225
$962$		0			0
$963$		0			0
$964$			19.6969i			0.634396i
$965$		0			0
$966$		0			0
$967$	−11.3485	−	11.3485i	−0.364942	−	0.364942i	0.500687	−	0.865629i	$-0.333081\pi$
$967$	−11.3485	−	11.3485i	−0.364942	−	0.364942i	−0.865629	+	0.500687i	$0.833081\pi$
$968$	−6.92820	−	6.92820i	−0.222681	−	0.222681i
$969$		0			0
$970$		0			0
$971$		−	37.8659i		−	1.21518i	−0.794253	−	0.607588i	$-0.792137\pi$
$971$		−	37.8659i		−	1.21518i	0.794253	−	0.607588i	$-0.207863\pi$
$972$		0			0
$973$	11.9546	−	11.9546i	0.383247	−	0.383247i
$974$	20.7846			0.665982
$975$		0			0
$976$	8.44949			0.270462
$977$	14.0707	−	14.0707i	0.450162	−	0.450162i	−0.445246	−	0.895408i	$-0.646884\pi$
$977$	14.0707	−	14.0707i	0.450162	−	0.450162i	0.895408	+	0.445246i	$0.146884\pi$
$978$		0			0
$979$			19.1464i			0.611922i
$980$		0			0
$981$		0			0
$982$	17.7980	+	17.7980i	0.567956	+	0.567956i
$983$	12.1958	+	12.1958i	0.388985	+	0.388985i	0.874325	−	0.485340i	$-0.161304\pi$
$983$	12.1958	+	12.1958i	0.388985	+	0.388985i	−0.485340	+	0.874325i	$0.661304\pi$
$984$		0			0
$985$		0			0
$986$		−	18.5597i		−	0.591063i
$987$		0			0
$988$	18.7980	−	18.7980i	0.598043	−	0.598043i
$989$	−64.8644			−2.06257
$990$		0			0
$991$	−41.7423			−1.32599			−0.662995	−	0.748624i	$-0.730715\pi$
$991$	−41.7423			−1.32599			−0.662995	+	0.748624i	$0.730715\pi$
$992$	1.02494	−	1.02494i	0.0325420	−	0.0325420i
$993$		0			0
$994$		−	28.6969i		−	0.910212i
$995$		0			0
$996$		0			0
$997$	14.9217	+	14.9217i	0.472574	+	0.472574i	0.902747	−	0.430172i	$-0.141547\pi$
$997$	14.9217	+	14.9217i	0.472574	+	0.472574i	−0.430172	+	0.902747i	$0.641547\pi$
$998$	4.09978	+	4.09978i	0.129776	+	0.129776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.f.f.107.3		8
3.2	odd	2	inner	1350.2.f.f.107.1		8
5.2	odd	4		270.2.f.a.53.3	yes	8
5.3	odd	4	inner	1350.2.f.f.593.1		8
5.4	even	2		270.2.f.a.107.1	yes	8
15.2	even	4		270.2.f.a.53.2	✓	8
15.8	even	4	inner	1350.2.f.f.593.3		8
15.14	odd	2		270.2.f.a.107.4	yes	8
20.7	even	4		2160.2.w.f.593.3		8
20.19	odd	2		2160.2.w.f.1457.1		8
45.2	even	12		810.2.m.a.53.1		8
45.4	even	6		810.2.m.a.107.1		8
45.7	odd	12		810.2.m.h.53.2		8
45.14	odd	6		810.2.m.h.107.2		8
45.22	odd	12		810.2.m.a.593.1		8
45.29	odd	6		810.2.m.a.377.1		8
45.32	even	12		810.2.m.h.593.2		8
45.34	even	6		810.2.m.h.377.2		8
60.47	odd	4		2160.2.w.f.593.2		8
60.59	even	2		2160.2.w.f.1457.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.f.a.53.2	✓	8	15.2	even	4
270.2.f.a.53.3	yes	8	5.2	odd	4
270.2.f.a.107.1	yes	8	5.4	even	2
270.2.f.a.107.4	yes	8	15.14	odd	2
810.2.m.a.53.1		8	45.2	even	12
810.2.m.a.107.1		8	45.4	even	6
810.2.m.a.377.1		8	45.29	odd	6
810.2.m.a.593.1		8	45.22	odd	12
810.2.m.h.53.2		8	45.7	odd	12
810.2.m.h.107.2		8	45.14	odd	6
810.2.m.h.377.2		8	45.34	even	6
810.2.m.h.593.2		8	45.32	even	12
1350.2.f.f.107.1		8	3.2	odd	2	inner
1350.2.f.f.107.3		8	1.1	even	1	trivial
1350.2.f.f.593.1		8	5.3	odd	4	inner
1350.2.f.f.593.3		8	15.8	even	4	inner
2160.2.w.f.593.2		8	60.47	odd	4
2160.2.w.f.593.3		8	20.7	even	4
2160.2.w.f.1457.1		8	20.19	odd	2
2160.2.w.f.1457.4		8	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.44949 - 1.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.44949 - 1.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.09638i q^{11} +(-4.22474 + 4.22474i) q^{13} -2.04989 q^{14} -1.00000 q^{16} +(-4.17121 + 4.17121i) q^{17} -4.44949i q^{19} +(-0.775255 - 0.775255i) q^{22} +(-4.48905 - 4.48905i) q^{23} +5.97469i q^{26} +(-1.44949 + 1.44949i) q^{28} -3.14626 q^{29} -1.44949 q^{31} +(-0.707107 + 0.707107i) q^{32} +5.89898i q^{34} +(-3.14626 - 3.14626i) q^{38} +4.87832i q^{41} +(7.22474 - 7.22474i) q^{43} -1.09638 q^{44} -6.34847 q^{46} +(-7.31747 + 7.31747i) q^{47} -2.79796i q^{49} +(4.22474 + 4.22474i) q^{52} +(5.65685 + 5.65685i) q^{53} +2.04989i q^{56} +(-2.22474 + 2.22474i) q^{58} +2.82843 q^{59} -8.44949 q^{61} +(-1.02494 + 1.02494i) q^{62} +1.00000i q^{64} +(-2.00000 - 2.00000i) q^{67} +(4.17121 + 4.17121i) q^{68} +13.9993i q^{71} +(4.44949 - 4.44949i) q^{73} -4.44949 q^{76} +(-1.58919 + 1.58919i) q^{77} -5.44949i q^{79} +(3.44949 + 3.44949i) q^{82} +(-10.2173 - 10.2173i) q^{83} -10.2173i q^{86} +(-0.775255 + 0.775255i) q^{88} -17.4634 q^{89} +12.2474 q^{91} +(-4.48905 + 4.48905i) q^{92} +10.3485i q^{94} +(-8.44949 - 8.44949i) q^{97} +(-1.97846 - 1.97846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} - 24 q^{13} - 8 q^{16} - 16 q^{22} + 8 q^{28} + 8 q^{31} + 48 q^{43} + 8 q^{46} + 24 q^{52} - 8 q^{58} - 48 q^{61} - 16 q^{67} + 16 q^{73} - 16 q^{76} + 8 q^{82} - 16 q^{88} - 48 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 - 24 * q^13 - 8 * q^16 - 16 * q^22 + 8 * q^28 + 8 * q^31 + 48 * q^43 + 8 * q^46 + 24 * q^52 - 8 * q^58 - 48 * q^61 - 16 * q^67 + 16 * q^73 - 16 * q^76 + 8 * q^82 - 16 * q^88 - 48 * q^97

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