LMFDB - Embedded newform 1156.2.h.e.757.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1156,2,Mod(733,1156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1156, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("1156.733");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1156 = 2^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1156.h (of order $8$, degree $4$, 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:	$9.23070647366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	16.0.229607785695641627262976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 799x^{8} + 6561 $ x^16 + 799*x^8 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			757.4
Root			$2.12749 - 0.881234i$ of defining polynomial
Character	$\chi$	$=$	1156.757
Dual form			1156.2.h.e.733.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00872 + 1.24625i) q^{3} +(0.541196 - 1.30656i) q^{5} +(-1.24625 - 3.00872i) q^{7} +(5.37794 + 5.37794i) q^{9} +O(q^{10})$	\(q+(3.00872 + 1.24625i) q^{3} +(0.541196 - 1.30656i) q^{5} +(-1.24625 - 3.00872i) q^{7} +(5.37794 + 5.37794i) q^{9} +(-0.395595 + 0.163861i) q^{11} -2.60555i q^{13} +(3.25662 - 3.25662i) q^{15} +(0.428189 - 0.428189i) q^{19} -10.6056i q^{21} +(5.62185 - 2.32865i) q^{23} +(2.12132 + 2.12132i) q^{25} +(5.73968 + 13.8568i) q^{27} +(-0.868918 + 2.09775i) q^{29} +(5.62185 + 2.32865i) q^{31} -1.39445 q^{33} -4.60555 q^{35} +(-3.91969 - 1.62359i) q^{37} +(3.24718 - 7.83938i) q^{39} +(-0.541196 - 1.30656i) q^{41} +(2.40024 + 2.40024i) q^{43} +(9.93713 - 4.11609i) q^{45} +4.00000i q^{47} +(-2.54951 + 2.54951i) q^{49} +(-3.68481 + 3.68481i) q^{53} +0.605551i q^{55} +(1.82194 - 0.754670i) q^{57} +(-6.08504 - 6.08504i) q^{59} +(-3.36142 - 8.11520i) q^{61} +(9.47844 - 22.8830i) q^{63} +(-3.40432 - 1.41011i) q^{65} -9.21110 q^{67} +19.8167 q^{69} +(-3.79991 - 1.57398i) q^{71} +(3.78837 - 9.14594i) q^{73} +(3.73876 + 9.02616i) q^{75} +(0.986024 + 0.986024i) q^{77} +(-0.395595 + 0.163861i) q^{79} +26.0278i q^{81} +(-12.5983 + 12.5983i) q^{83} +(-5.22866 + 5.22866i) q^{87} +7.81665i q^{89} +(-7.83938 + 3.24718i) q^{91} +(14.0125 + 14.0125i) q^{93} +(-0.327722 - 0.791191i) q^{95} +(-4.11609 + 9.93713i) q^{97} +(-3.00872 - 1.24625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 80 q^{33} - 16 q^{35} - 32 q^{67} + 144 q^{69}+O(q^{100}) $ 16 * q - 80 * q^33 - 16 * q^35 - 32 * q^67 + 144 * q^69

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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
$3$	3.00872	+	1.24625i	1.73709	+	0.719525i	0.998995	+	0.0448236i	$0.0142726\pi$
$3$	3.00872	+	1.24625i	1.73709	+	0.719525i	0.738091	+	0.674701i	$0.235727\pi$
$4$		0			0
$5$	0.541196	−	1.30656i	0.242030	−	0.584313i	−0.755454	−	0.655202i	$-0.772584\pi$
$5$	0.541196	−	1.30656i	0.242030	−	0.584313i	0.997484	+	0.0708890i	$0.0225836\pi$
$6$		0			0
$7$	−1.24625	−	3.00872i	−0.471039	−	1.13719i	−0.963705	−	0.266971i	$-0.913977\pi$
$7$	−1.24625	−	3.00872i	−0.471039	−	1.13719i	0.492665	−	0.870219i	$-0.336023\pi$
$8$		0			0
$9$	5.37794	+	5.37794i	1.79265	+	1.79265i
$10$		0			0
$11$	−0.395595	+	0.163861i	−0.119277	+	0.0494059i	−0.441524	−	0.897250i	$-0.645562\pi$
$11$	−0.395595	+	0.163861i	−0.119277	+	0.0494059i	0.322247	+	0.946656i	$0.395562\pi$
$12$		0			0
$13$		−	2.60555i		−	0.722650i	−0.932440	−	0.361325i	$-0.882325\pi$
$13$		−	2.60555i		−	0.722650i	0.932440	−	0.361325i	$-0.117675\pi$
$14$		0			0
$15$	3.25662	−	3.25662i	0.840855	−	0.840855i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$	0.428189	−	0.428189i	0.0982334	−	0.0982334i	−0.656282	−	0.754516i	$-0.727872\pi$
$19$	0.428189	−	0.428189i	0.0982334	−	0.0982334i	0.754516	+	0.656282i	$0.227872\pi$
$20$		0			0
$21$		−	10.6056i		−	2.31432i
$22$		0			0
$23$	5.62185	−	2.32865i	1.17224	−	0.485556i	0.290305	−	0.956934i	$-0.406243\pi$
$23$	5.62185	−	2.32865i	1.17224	−	0.485556i	0.881931	+	0.471378i	$0.156243\pi$
$24$		0			0
$25$	2.12132	+	2.12132i	0.424264	+	0.424264i
$26$		0			0
$27$	5.73968	+	13.8568i	1.10460	+	2.66675i
$28$		0			0
$29$	−0.868918	+	2.09775i	−0.161354	+	0.389543i	−0.983792	−	0.179311i	$-0.942613\pi$
$29$	−0.868918	+	2.09775i	−0.161354	+	0.389543i	0.822438	+	0.568854i	$0.192613\pi$
$30$		0			0
$31$	5.62185	+	2.32865i	1.00971	+	0.418237i	0.825350	−	0.564621i	$-0.190978\pi$
$31$	5.62185	+	2.32865i	1.00971	+	0.418237i	0.184363	+	0.982858i	$0.440978\pi$
$32$		0			0
$33$	−1.39445			−0.242742
$34$		0			0
$35$	−4.60555			−0.778480
$36$		0			0
$37$	−3.91969	−	1.62359i	−0.644393	−	0.266916i	0.0364615	−	0.999335i	$-0.488391\pi$
$37$	−3.91969	−	1.62359i	−0.644393	−	0.266916i	−0.680854	+	0.732419i	$0.738391\pi$
$38$		0			0
$39$	3.24718	−	7.83938i	0.519964	−	1.25531i
$40$		0			0
$41$	−0.541196	−	1.30656i	−0.0845206	−	0.204051i	0.875969	−	0.482368i	$-0.160223\pi$
$41$	−0.541196	−	1.30656i	−0.0845206	−	0.204051i	−0.960489	+	0.278317i	$0.910223\pi$
$42$		0			0
$43$	2.40024	+	2.40024i	0.366033	+	0.366033i	0.866028	−	0.499995i	$-0.166665\pi$
$43$	2.40024	+	2.40024i	0.366033	+	0.366033i	−0.499995	+	0.866028i	$0.666665\pi$
$44$		0			0
$45$	9.93713	−	4.11609i	1.48134	−	0.613591i
$46$		0			0
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$		0			0
$49$	−2.54951	+	2.54951i	−0.364216	+	0.364216i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.68481	+	3.68481i	−0.506147	+	0.506147i	−0.913341	−	0.407194i	$-0.866507\pi$
$53$	−3.68481	+	3.68481i	−0.506147	+	0.506147i	0.407194	+	0.913341i	$0.366507\pi$
$54$		0			0
$55$			0.605551i			0.0816525i
$56$		0			0
$57$	1.82194	−	0.754670i	0.241321	−	0.0999585i
$58$		0			0
$59$	−6.08504	−	6.08504i	−0.792205	−	0.792205i	0.189647	−	0.981852i	$-0.439266\pi$
$59$	−6.08504	−	6.08504i	−0.792205	−	0.792205i	−0.981852	+	0.189647i	$0.939266\pi$
$60$		0			0
$61$	−3.36142	−	8.11520i	−0.430386	−	1.03904i	−0.979163	−	0.203076i	$-0.934906\pi$
$61$	−3.36142	−	8.11520i	−0.430386	−	1.03904i	0.548777	−	0.835969i	$-0.315094\pi$
$62$		0			0
$63$	9.47844	−	22.8830i	1.19417	−	2.88299i
$64$		0			0
$65$	−3.40432	−	1.41011i	−0.422254	−	0.174903i
$66$		0			0
$67$	−9.21110			−1.12532			−0.562658	−	0.826690i	$-0.690221\pi$
$67$	−9.21110			−1.12532			−0.562658	+	0.826690i	$0.690221\pi$
$68$		0			0
$69$	19.8167			2.38564
$70$		0			0
$71$	−3.79991	−	1.57398i	−0.450967	−	0.186796i	0.145628	−	0.989339i	$-0.453480\pi$
$71$	−3.79991	−	1.57398i	−0.450967	−	0.186796i	−0.596594	+	0.802543i	$0.703480\pi$
$72$		0			0
$73$	3.78837	−	9.14594i	0.443395	−	1.07045i	−0.531354	−	0.847150i	$-0.678317\pi$
$73$	3.78837	−	9.14594i	0.443395	−	1.07045i	0.974749	−	0.223301i	$-0.0716834\pi$
$74$		0			0
$75$	3.73876	+	9.02616i	0.431715	+	1.04225i
$76$		0			0
$77$	0.986024	+	0.986024i	0.112368	+	0.112368i
$78$		0			0
$79$	−0.395595	+	0.163861i	−0.0445080	+	0.0184358i	−0.404826	−	0.914394i	$-0.632668\pi$
$79$	−0.395595	+	0.163861i	−0.0445080	+	0.0184358i	0.360318	+	0.932829i	$0.382668\pi$
$80$		0			0
$81$			26.0278i			2.89197i
$82$		0			0
$83$	−12.5983	+	12.5983i	−1.38284	+	1.38284i	−0.543305	+	0.839535i	$0.682827\pi$
$83$	−12.5983	+	12.5983i	−1.38284	+	1.38284i	−0.839535	+	0.543305i	$0.817173\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.22866	+	5.22866i	−0.560572	+	0.560572i
$88$		0			0
$89$			7.81665i			0.828564i	0.910149	+	0.414282i	$0.135967\pi$
$89$			7.81665i			0.828564i	−0.910149	+	0.414282i	$0.864033\pi$
$90$		0			0
$91$	−7.83938	+	3.24718i	−0.821790	+	0.340397i
$92$		0			0
$93$	14.0125	+	14.0125i	1.45303	+	1.45303i
$94$		0			0
$95$	−0.327722	−	0.791191i	−0.0336236	−	0.0811745i
$96$		0			0
$97$	−4.11609	+	9.93713i	−0.417926	+	1.00896i	0.565021	+	0.825076i	$0.308868\pi$
$97$	−4.11609	+	9.93713i	−0.417926	+	1.00896i	−0.982947	+	0.183887i	$0.941132\pi$
$98$		0			0
$99$	−3.00872	−	1.24625i	−0.302388	−	0.125253i
$100$		0			0
$101$	−10.6056			−1.05529			−0.527646	−	0.849464i	$-0.676925\pi$
$101$	−10.6056			−1.05529			−0.527646	+	0.849464i	$0.676925\pi$
$102$		0			0
$103$	−13.2111			−1.30173			−0.650864	−	0.759194i	$-0.725593\pi$
$103$	−13.2111			−1.30173			−0.650864	+	0.759194i	$0.725593\pi$
$104$		0			0
$105$	−13.8568	−	5.73968i	−1.35229	−	0.560136i
$106$		0			0
$107$	−3.08332	+	7.44378i	−0.298075	+	0.719618i	0.701898	+	0.712278i	$0.252336\pi$
$107$	−3.08332	+	7.44378i	−0.298075	+	0.719618i	−0.999973	+	0.00733983i	$0.997664\pi$
$108$		0			0
$109$	3.36142	+	8.11520i	0.321966	+	0.777295i	0.999140	+	0.0414716i	$0.0132046\pi$
$109$	3.36142	+	8.11520i	0.321966	+	0.777295i	−0.677174	+	0.735823i	$0.736795\pi$
$110$		0			0
$111$	−9.76985	−	9.76985i	−0.927313	−	0.927313i
$112$		0			0
$113$	12.5503	−	5.19849i	1.18063	−	0.489033i	0.295936	−	0.955208i	$-0.404368\pi$
$113$	12.5503	−	5.19849i	1.18063	−	0.489033i	0.884692	+	0.466175i	$0.154368\pi$
$114$		0			0
$115$		−	8.60555i		−	0.802472i
$116$		0			0
$117$	14.0125	−	14.0125i	1.29546	−	1.29546i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.64853	+	7.64853i	−0.695321	+	0.695321i
$122$		0			0
$123$		−	4.60555i		−	0.415269i
$124$		0			0
$125$	10.4525	−	4.32957i	0.934900	−	0.387248i
$126$		0			0
$127$	−0.428189	−	0.428189i	−0.0379957	−	0.0379957i	0.687854	−	0.725849i	$-0.258553\pi$
$127$	−0.428189	−	0.428189i	−0.0379957	−	0.0379957i	−0.725849	+	0.687854i	$0.758553\pi$
$128$		0			0
$129$	4.23034	+	10.2130i	0.372461	+	0.899200i
$130$		0			0
$131$	−3.41104	+	8.23497i	−0.298024	+	0.719493i	0.701950	+	0.712226i	$0.252313\pi$
$131$	−3.41104	+	8.23497i	−0.298024	+	0.719493i	−0.999974	+	0.00726659i	$0.997687\pi$
$132$		0			0
$133$	−1.82194	−	0.754670i	−0.157982	−	0.0654382i
$134$		0			0
$135$	21.2111			1.82556
$136$		0			0
$137$	−2.60555			−0.222607			−0.111304	−	0.993786i	$-0.535503\pi$
$137$	−2.60555			−0.222607			−0.111304	+	0.993786i	$0.535503\pi$
$138$		0			0
$139$	−0.395595	−	0.163861i	−0.0335540	−	0.0138985i	0.365843	−	0.930676i	$-0.380781\pi$
$139$	−0.395595	−	0.163861i	−0.0335540	−	0.0138985i	−0.399397	+	0.916778i	$0.630781\pi$
$140$		0			0
$141$	−4.98501	+	12.0349i	−0.419814	+	1.01352i
$142$		0			0
$143$	0.426948	+	1.03074i	0.0357032	+	0.0861952i
$144$		0			0
$145$	2.27059	+	2.27059i	0.188562	+	0.188562i
$146$		0			0
$147$	−10.8481	+	4.49343i	−0.894736	+	0.370612i
$148$		0			0
$149$		−	8.42221i		−	0.689974i	−0.938607	−	0.344987i	$-0.887883\pi$
$149$		−	8.42221i		−	0.689974i	0.938607	−	0.344987i	$-0.112117\pi$
$150$		0			0
$151$	−3.25662	+	3.25662i	−0.265020	+	0.265020i	−0.827090	−	0.562070i	$-0.810005\pi$
$151$	−3.25662	+	3.25662i	−0.265020	+	0.265020i	0.562070	+	0.827090i	$0.310005\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.08504	−	6.08504i	0.488762	−	0.488762i
$156$		0			0
$157$		−	8.42221i		−	0.672165i	−0.941833	−	0.336083i	$-0.890898\pi$
$157$		−	8.42221i		−	0.672165i	0.941833	−	0.336083i	$-0.109102\pi$
$158$		0			0
$159$	−15.6788	+	6.49435i	−1.24341	+	0.515036i
$160$		0			0
$161$	−14.0125	−	14.0125i	−1.10434	−	1.10434i
$162$		0			0
$163$	−2.32865	−	5.62185i	−0.182394	−	0.440337i	0.806065	−	0.591827i	$-0.201593\pi$
$163$	−2.32865	−	5.62185i	−0.182394	−	0.440337i	−0.988459	+	0.151490i	$0.951593\pi$
$164$		0			0
$165$	−0.754670	+	1.82194i	−0.0587510	+	0.141837i
$166$		0			0
$167$	19.4787	+	8.06833i	1.50730	+	0.624346i	0.975000	−	0.222207i	$-0.0713260\pi$
$167$	19.4787	+	8.06833i	1.50730	+	0.624346i	0.532305	+	0.846553i	$0.321326\pi$
$168$		0			0
$169$	6.21110			0.477777
$170$		0			0
$171$	4.60555			0.352195
$172$		0			0
$173$	19.3589	+	8.01872i	1.47183	+	0.609652i	0.967275	−	0.253729i	$-0.0816570\pi$
$173$	19.3589	+	8.01872i	1.47183	+	0.609652i	0.504554	+	0.863380i	$0.331657\pi$
$174$		0			0
$175$	3.73876	−	9.02616i	0.282624	−	0.682314i
$176$		0			0
$177$	−10.7247	−	25.8917i	−0.806117	−	1.94614i
$178$		0			0
$179$	10.6262	+	10.6262i	0.794242	+	0.794242i	0.982181	−	0.187939i	$-0.0601808\pi$
$179$	10.6262	+	10.6262i	0.794242	+	0.794242i	−0.187939	+	0.982181i	$0.560181\pi$
$180$		0			0
$181$	−16.9853	+	7.03555i	−1.26251	+	0.522948i	−0.910679	−	0.413116i	$-0.864441\pi$
$181$	−16.9853	+	7.03555i	−1.26251	+	0.522948i	−0.351830	+	0.936064i	$0.614441\pi$
$182$		0			0
$183$		−	28.6056i		−	2.11458i
$184$		0			0
$185$	−4.24264	+	4.24264i	−0.311925	+	0.311925i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	34.5382	−	34.5382i	2.51229	−	2.51229i
$190$		0			0
$191$			6.78890i			0.491227i	0.969368	+	0.245614i	$0.0789895\pi$
$191$			6.78890i			0.491227i	−0.969368	+	0.245614i	$0.921011\pi$
$192$		0			0
$193$	10.7283	−	4.44382i	0.772242	−	0.319873i	0.0384615	−	0.999260i	$-0.487754\pi$
$193$	10.7283	−	4.44382i	0.772242	−	0.319873i	0.733780	+	0.679387i	$0.237754\pi$
$194$		0			0
$195$	−8.48528	−	8.48528i	−0.607644	−	0.607644i
$196$		0			0
$197$	−9.52806	−	23.0028i	−0.678846	−	1.63888i	−0.766122	−	0.642695i	$-0.777816\pi$
$197$	−9.52806	−	23.0028i	−0.678846	−	1.63888i	0.0872765	−	0.996184i	$-0.472184\pi$
$198$		0			0
$199$	−5.47660	+	13.2217i	−0.388226	+	0.937259i	0.602090	+	0.798428i	$0.294335\pi$
$199$	−5.47660	+	13.2217i	−0.388226	+	0.937259i	−0.990316	+	0.138832i	$0.955665\pi$
$200$		0			0
$201$	−27.7136	−	11.4794i	−1.95477	−	0.809692i
$202$		0			0
$203$	7.39445			0.518989
$204$		0			0
$205$	−2.00000			−0.139686
$206$		0			0
$207$	42.7572	+	17.7106i	2.97183	+	1.23097i
$208$		0			0
$209$	−0.0992262	+	0.239553i	−0.00686362	+	0.0165702i
$210$		0			0
$211$	−8.39605	−	20.2699i	−0.578008	−	1.39543i	−0.894598	−	0.446872i	$-0.852538\pi$
$211$	−8.39605	−	20.2699i	−0.578008	−	1.39543i	0.316590	−	0.948563i	$-0.397462\pi$
$212$		0			0
$213$	−9.47131	−	9.47131i	−0.648963	−	0.648963i
$214$		0			0
$215$	4.43506	−	1.83706i	0.302469	−	0.125287i
$216$		0			0
$217$		−	19.8167i		−	1.34524i
$218$		0			0
$219$	22.7963	−	22.7963i	1.54043	−	1.54043i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−12.5983	+	12.5983i	−0.843643	+	0.843643i	−0.989331	−	0.145688i	$-0.953461\pi$
$223$	−12.5983	+	12.5983i	−0.843643	+	0.843643i	0.145688	+	0.989331i	$0.453461\pi$
$224$		0			0
$225$			22.8167i			1.52111i
$226$		0			0
$227$	0.395595	−	0.163861i	0.0262566	−	0.0108758i	−0.369516	−	0.929224i	$-0.620477\pi$
$227$	0.395595	−	0.163861i	0.0262566	−	0.0108758i	0.395773	+	0.918348i	$0.370477\pi$
$228$		0			0
$229$	3.25662	+	3.25662i	0.215203	+	0.215203i	0.806474	−	0.591270i	$-0.201373\pi$
$229$	3.25662	+	3.25662i	0.215203	+	0.215203i	−0.591270	+	0.806474i	$0.701373\pi$
$230$		0			0
$231$	1.73784	+	4.19551i	0.114341	+	0.276044i
$232$		0			0
$233$	3.03370	−	7.32401i	0.198744	−	0.479812i	−0.792815	−	0.609462i	$-0.791386\pi$
$233$	3.03370	−	7.32401i	0.198744	−	0.479812i	0.991560	+	0.129650i	$0.0413855\pi$
$234$		0			0
$235$	5.22625	+	2.16478i	0.340923	+	0.141215i
$236$		0			0
$237$	−1.39445			−0.0905792
$238$		0			0
$239$	−14.7889			−0.956614			−0.478307	−	0.878193i	$-0.658749\pi$
$239$	−14.7889			−0.956614			−0.478307	+	0.878193i	$0.658749\pi$
$240$		0			0
$241$	−11.7591	−	4.87076i	−0.757468	−	0.313754i	−0.0296835	−	0.999559i	$-0.509450\pi$
$241$	−11.7591	−	4.87076i	−0.757468	−	0.313754i	−0.727785	+	0.685806i	$0.759450\pi$
$242$		0			0
$243$	−15.2181	+	36.7398i	−0.976243	+	2.35686i
$244$		0			0
$245$	1.95131	+	4.71088i	0.124665	+	0.300967i
$246$		0			0
$247$	−1.11567	−	1.11567i	−0.0709883	−	0.0709883i
$248$		0			0
$249$	−53.6053	+	22.2041i	−3.39710	+	1.40713i
$250$		0			0
$251$			12.0000i			0.757433i	0.925513	+	0.378717i	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$		0			0
$253$	−1.84240	+	1.84240i	−0.115831	+	0.115831i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.7139	−	13.7139i	0.855452	−	0.855452i	−0.135346	−	0.990798i	$-0.543215\pi$
$257$	13.7139	−	13.7139i	0.855452	−	0.855452i	0.990798	+	0.135346i	$0.0432146\pi$
$258$		0			0
$259$			13.8167i			0.858525i
$260$		0			0
$261$	−15.9546	+	6.60860i	−0.987563	+	0.409062i
$262$		0			0
$263$	16.2831	+	16.2831i	1.00406	+	1.00406i	0.999992	+	0.00406616i	$0.00129430\pi$
$263$	16.2831	+	16.2831i	1.00406	+	1.00406i	0.00406616	+	0.999992i	$0.498706\pi$
$264$		0			0
$265$	2.82023	+	6.80863i	0.173245	+	0.418251i
$266$		0			0
$267$	−9.74153	+	23.5181i	−0.596172	+	1.43929i
$268$		0			0
$269$	22.7632	+	9.42883i	1.38790	+	0.574886i	0.946581	−	0.322466i	$-0.104512\pi$
$269$	22.7632	+	9.42883i	1.38790	+	0.574886i	0.441316	+	0.897352i	$0.354512\pi$
$270$		0			0
$271$	−1.21110			−0.0735692			−0.0367846	−	0.999323i	$-0.511712\pi$
$271$	−1.21110			−0.0735692			−0.0367846	+	0.999323i	$0.511712\pi$
$272$		0			0
$273$	−27.6333			−1.67244
$274$		0			0
$275$	−1.18679	−	0.491583i	−0.0715659	−	0.0296436i
$276$		0			0
$277$	−1.95131	+	4.71088i	−0.117243	+	0.283049i	−0.971597	−	0.236642i	$-0.923953\pi$
$277$	−1.95131	+	4.71088i	−0.117243	+	0.283049i	0.854354	+	0.519691i	$0.173953\pi$
$278$		0			0
$279$	17.7106	+	42.7572i	1.06031	+	2.55981i
$280$		0			0
$281$	−13.0265	−	13.0265i	−0.777094	−	0.777094i	0.202242	−	0.979336i	$-0.435177\pi$
$281$	−13.0265	−	13.0265i	−0.777094	−	0.777094i	−0.979336	+	0.202242i	$0.935177\pi$
$282$		0			0
$283$	2.76917	−	1.14703i	0.164610	−	0.0681837i	−0.298857	−	0.954298i	$-0.596605\pi$
$283$	2.76917	−	1.14703i	0.164610	−	0.0681837i	0.463467	+	0.886114i	$0.346605\pi$
$284$		0			0
$285$		−	2.78890i		−	0.165200i
$286$		0			0
$287$	−3.25662	+	3.25662i	−0.192232	+	0.192232i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	−24.7684	+	24.7684i	−1.45195	+	1.45195i
$292$		0			0
$293$		−	21.6333i		−	1.26383i	−0.775037	−	0.631916i	$-0.782269\pi$
$293$		−	21.6333i		−	1.26383i	0.775037	−	0.631916i	$-0.217731\pi$
$294$		0			0
$295$	−11.2437	+	4.65729i	−0.654633	+	0.271158i
$296$		0			0
$297$	−4.54118	−	4.54118i	−0.263506	−	0.263506i
$298$		0			0
$299$	−6.06740	−	14.6480i	−0.350887	−	0.847116i
$300$		0			0
$301$	4.23034	−	10.2130i	0.243833	−	0.588665i
$302$		0			0
$303$	−31.9091	−	13.2172i	−1.83313	−	0.759308i
$304$		0			0
$305$	−12.4222			−0.711293
$306$		0			0
$307$	21.2111			1.21058			0.605291	−	0.796004i	$-0.293057\pi$
$307$	21.2111			1.21058			0.605291	+	0.796004i	$0.293057\pi$
$308$		0			0
$309$	−39.7485	−	16.4644i	−2.26121	−	0.936626i
$310$		0			0
$311$	−10.2331	+	24.7049i	−0.580267	+	1.40089i	0.312305	+	0.949982i	$0.398899\pi$
$311$	−10.2331	+	24.7049i	−0.580267	+	1.40089i	−0.892572	+	0.450906i	$0.851101\pi$
$312$		0			0
$313$	−3.36142	−	8.11520i	−0.189999	−	0.458698i	0.799960	−	0.600053i	$-0.204854\pi$
$313$	−3.36142	−	8.11520i	−0.189999	−	0.458698i	−0.989959	+	0.141355i	$0.954854\pi$
$314$		0			0
$315$	−24.7684	−	24.7684i	−1.39554	−	1.39554i
$316$		0			0
$317$	25.6159	−	10.6104i	1.43873	−	0.595942i	0.479241	−	0.877683i	$-0.340912\pi$
$317$	25.6159	−	10.6104i	1.43873	−	0.595942i	0.959490	+	0.281741i	$0.0909119\pi$
$318$		0			0
$319$		−	0.972244i		−	0.0544352i
$320$		0			0
$321$	−18.5537	+	18.5537i	−1.03557	+	1.03557i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	5.52721	−	5.52721i	0.306594	−	0.306594i
$326$		0			0
$327$			28.6056i			1.58189i
$328$		0			0
$329$	12.0349	−	4.98501i	0.663505	−	0.274833i
$330$		0			0
$331$	−2.40024	−	2.40024i	−0.131929	−	0.131929i	0.638059	−	0.769988i	$-0.279738\pi$
$331$	−2.40024	−	2.40024i	−0.131929	−	0.131929i	−0.769988	+	0.638059i	$0.779738\pi$
$332$		0			0
$333$	−12.3483	−	29.8114i	−0.676682	−	1.63365i
$334$		0			0
$335$	−4.98501	+	12.0349i	−0.272360	+	0.657536i
$336$		0			0
$337$	−21.1808	−	8.77339i	−1.15379	−	0.477917i	−0.277989	−	0.960584i	$-0.589668\pi$
$337$	−21.1808	−	8.77339i	−1.15379	−	0.477917i	−0.875804	+	0.482667i	$0.839668\pi$
$338$		0			0
$339$	44.2389			2.40273
$340$		0			0
$341$	−2.60555			−0.141099
$342$		0			0
$343$	−10.2130	−	4.23034i	−0.551447	−	0.228417i
$344$		0			0
$345$	10.7247	−	25.8917i	0.577398	−	1.39396i
$346$		0			0
$347$	2.98409	+	7.20423i	0.160194	+	0.386743i	0.983513	−	0.180836i	$-0.0578802\pi$
$347$	2.98409	+	7.20423i	0.160194	+	0.386743i	−0.823319	+	0.567579i	$0.807880\pi$
$348$		0			0
$349$	−16.7113	−	16.7113i	−0.894534	−	0.894534i	0.100412	−	0.994946i	$-0.467984\pi$
$349$	−16.7113	−	16.7113i	−0.894534	−	0.894534i	−0.994946	+	0.100412i	$0.967984\pi$
$350$		0			0
$351$	36.1047	−	14.9550i	1.92712	−	0.798241i
$352$		0			0
$353$			31.2111i			1.66120i	0.556870	+	0.830600i	$0.312002\pi$
$353$			31.2111i			1.66120i	−0.556870	+	0.830600i	$0.687998\pi$
$354$		0			0
$355$	−4.11300	+	4.11300i	−0.218295	+	0.218295i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.7419	−	11.7419i	0.619714	−	0.619714i	−0.325744	−	0.945458i	$-0.605615\pi$
$359$	11.7419	−	11.7419i	0.619714	−	0.619714i	0.945458	+	0.325744i	$0.105615\pi$
$360$		0			0
$361$			18.6333i			0.980700i
$362$		0			0
$363$	−32.5443	+	13.4803i	−1.70813	+	0.707532i
$364$		0			0
$365$	−9.89949	−	9.89949i	−0.518163	−	0.518163i
$366$		0			0
$367$	−3.73876	−	9.02616i	−0.195162	−	0.471162i	0.795758	−	0.605614i	$-0.207073\pi$
$367$	−3.73876	−	9.02616i	−0.195162	−	0.471162i	−0.990920	+	0.134452i	$0.957073\pi$
$368$		0			0
$369$	4.11609	−	9.93713i	0.214275	−	0.517306i
$370$		0			0
$371$	15.6788	+	6.49435i	0.814000	+	0.337170i
$372$		0			0
$373$	−21.0278			−1.08878			−0.544388	−	0.838834i	$-0.683238\pi$
$373$	−21.0278			−1.08878			−0.544388	+	0.838834i	$0.683238\pi$
$374$		0			0
$375$	36.8444			1.90264
$376$		0			0
$377$	5.46581	+	2.26401i	0.281503	+	0.116602i
$378$		0			0
$379$	11.2163	−	27.0785i	0.576142	−	1.39093i	−0.320109	−	0.947381i	$-0.603720\pi$
$379$	11.2163	−	27.0785i	0.576142	−	1.39093i	0.896251	−	0.443548i	$-0.146280\pi$
$380$		0			0
$381$	−0.754670	−	1.82194i	−0.0386629	−	0.0933406i
$382$		0			0
$383$	13.7139	+	13.7139i	0.700750	+	0.700750i	0.964571	−	0.263822i	$-0.0849830\pi$
$383$	13.7139	+	13.7139i	0.700750	+	0.700750i	−0.263822	+	0.964571i	$0.584983\pi$
$384$		0			0
$385$	1.82194	−	0.754670i	0.0928544	−	0.0384616i
$386$		0			0
$387$			25.8167i			1.31233i
$388$		0			0
$389$	−7.20071	+	7.20071i	−0.365091	+	0.365091i	−0.865683	−	0.500592i	$-0.833116\pi$
$389$	−7.20071	+	7.20071i	−0.365091	+	0.365091i	0.500592	+	0.865683i	$0.333116\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−20.5257	+	20.5257i	−1.03539	+	1.03539i
$394$		0			0
$395$			0.605551i			0.0304686i
$396$		0			0
$397$	11.7591	−	4.87076i	0.590171	−	0.244457i	−0.0675534	−	0.997716i	$-0.521519\pi$
$397$	11.7591	−	4.87076i	0.590171	−	0.244457i	0.657724	+	0.753259i	$0.271519\pi$
$398$		0			0
$399$	−4.54118	−	4.54118i	−0.227344	−	0.227344i
$400$		0			0
$401$	−3.78837	−	9.14594i	−0.189182	−	0.456726i	0.800620	−	0.599172i	$-0.204503\pi$
$401$	−3.78837	−	9.14594i	−0.189182	−	0.456726i	−0.989803	+	0.142445i	$0.954503\pi$
$402$		0			0
$403$	6.06740	−	14.6480i	0.302239	−	0.729669i
$404$		0			0
$405$	34.0069	+	14.0861i	1.68982	+	0.699945i
$406$		0			0
$407$	1.81665			0.0900482
$408$		0			0
$409$	23.2111			1.14772			0.573858	−	0.818955i	$-0.305446\pi$
$409$	23.2111			1.14772			0.573858	+	0.818955i	$0.305446\pi$
$410$		0			0
$411$	−7.83938	−	3.24718i	−0.386688	−	0.160171i
$412$		0			0
$413$	−10.7247	+	25.8917i	−0.527728	+	1.27405i
$414$		0			0
$415$	9.64230	+	23.2786i	0.473322	+	1.14270i
$416$		0			0
$417$	−0.986024	−	0.986024i	−0.0482858	−	0.0482858i
$418$		0			0
$419$	3.00872	−	1.24625i	0.146986	−	0.0608835i	−0.307978	−	0.951394i	$-0.599652\pi$
$419$	3.00872	−	1.24625i	0.146986	−	0.0608835i	0.454964	+	0.890510i	$0.349652\pi$
$420$		0			0
$421$		−	18.6056i		−	0.906779i	−0.891312	−	0.453390i	$-0.850215\pi$
$421$		−	18.6056i		−	0.906779i	0.891312	−	0.453390i	$-0.149785\pi$
$422$		0			0
$423$	−21.5117	+	21.5117i	−1.04594	+	1.04594i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−20.2272	+	20.2272i	−0.978862	+	0.978862i
$428$		0			0
$429$			3.63331i			0.175418i
$430$		0			0
$431$	2.45708	−	1.01776i	0.118354	−	0.0490237i	−0.322721	−	0.946494i	$-0.604597\pi$
$431$	2.45708	−	1.01776i	0.118354	−	0.0490237i	0.441074	+	0.897471i	$0.354597\pi$
$432$		0			0
$433$	−10.6262	−	10.6262i	−0.510664	−	0.510664i	0.404066	−	0.914730i	$-0.367597\pi$
$433$	−10.6262	−	10.6262i	−0.510664	−	0.510664i	−0.914730	+	0.404066i	$0.867597\pi$
$434$		0			0
$435$	4.00185	+	9.66131i	0.191874	+	0.463224i
$436$		0			0
$437$	1.41011	−	3.40432i	0.0674549	−	0.162851i
$438$		0			0
$439$	−34.3662	−	14.2350i	−1.64021	−	0.679398i	−0.643891	−	0.765117i	$-0.722681\pi$
$439$	−34.3662	−	14.2350i	−1.64021	−	0.679398i	−0.996319	+	0.0857193i	$0.972681\pi$
$440$		0			0
$441$	−27.4222			−1.30582
$442$		0			0
$443$	−17.2111			−0.817724			−0.408862	−	0.912596i	$-0.634074\pi$
$443$	−17.2111			−0.817724			−0.408862	+	0.912596i	$0.634074\pi$
$444$		0			0
$445$	10.2130	+	4.23034i	0.484140	+	0.200537i
$446$		0			0
$447$	10.4962	−	25.3401i	0.496453	−	1.19854i
$448$		0			0
$449$	9.10111	+	21.9720i	0.429508	+	1.03692i	0.979444	+	0.201717i	$0.0646521\pi$
$449$	9.10111	+	21.9720i	0.429508	+	1.03692i	−0.549936	+	0.835207i	$0.685348\pi$
$450$		0			0
$451$	0.428189	+	0.428189i	0.0201627	+	0.0201627i
$452$		0			0
$453$	−13.8568	+	5.73968i	−0.651050	+	0.269674i
$454$		0			0
$455$			12.0000i			0.562569i
$456$		0			0
$457$	25.8840	−	25.8840i	1.21080	−	1.21080i	0.240041	−	0.970763i	$-0.422839\pi$
$457$	25.8840	−	25.8840i	1.21080	−	1.21080i	0.970763	−	0.240041i	$-0.0771610\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.6554	−	20.6554i	0.962016	−	0.962016i	−0.0372881	−	0.999305i	$-0.511872\pi$
$461$	20.6554	−	20.6554i	0.962016	−	0.962016i	0.999305	+	0.0372881i	$0.0118719\pi$
$462$		0			0
$463$		−	39.6333i		−	1.84192i	−0.389662	−	0.920958i	$-0.627408\pi$
$463$		−	39.6333i		−	1.84192i	0.389662	−	0.920958i	$-0.372592\pi$
$464$		0			0
$465$	25.8917	−	10.7247i	1.20070	−	0.497346i
$466$		0			0
$467$	11.4826	+	11.4826i	0.531352	+	0.531352i	0.920975	−	0.389623i	$-0.127395\pi$
$467$	11.4826	+	11.4826i	0.531352	+	0.531352i	−0.389623	+	0.920975i	$0.627395\pi$
$468$		0			0
$469$	11.4794	+	27.7136i	0.530068	+	1.27970i
$470$		0			0
$471$	10.4962	−	25.3401i	0.483639	−	1.16761i
$472$		0			0
$473$	−1.34283	−	0.556218i	−0.0617433	−	0.0255749i
$474$		0			0
$475$	1.81665			0.0833538
$476$		0			0
$477$	−39.6333			−1.81468
$478$		0			0
$479$	−16.0744	−	6.65821i	−0.734456	−	0.304222i	−0.0160742	−	0.999871i	$-0.505117\pi$
$479$	−16.0744	−	6.65821i	−0.734456	−	0.304222i	−0.718382	+	0.695649i	$0.755117\pi$
$480$		0			0
$481$	−4.23034	+	10.2130i	−0.192887	+	0.465670i
$482$		0			0
$483$	−24.6966	−	59.6228i	−1.12373	−	2.71293i
$484$		0			0
$485$	10.7559	+	10.7559i	0.488399	+	0.488399i
$486$		0			0
$487$	−22.6434	+	9.37922i	−1.02607	+	0.425013i	−0.831293	−	0.555834i	$-0.812399\pi$
$487$	−22.6434	+	9.37922i	−1.02607	+	0.425013i	−0.194779	+	0.980847i	$0.562399\pi$
$488$		0			0
$489$		−	19.8167i		−	0.896140i
$490$		0			0
$491$	6.94142	−	6.94142i	0.313262	−	0.313262i	−0.532910	−	0.846172i	$-0.678902\pi$
$491$	6.94142	−	6.94142i	0.313262	−	0.313262i	0.846172	+	0.532910i	$0.178902\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−3.25662	+	3.25662i	−0.146374	+	0.146374i
$496$		0			0
$497$			13.3944i			0.600823i
$498$		0			0
$499$	−13.4612	+	5.57582i	−0.602607	+	0.249608i	−0.663064	−	0.748563i	$-0.730744\pi$
$499$	−13.4612	+	5.57582i	−0.602607	+	0.249608i	0.0604568	+	0.998171i	$0.480744\pi$
$500$		0			0
$501$	48.5507	+	48.5507i	2.16909	+	2.16909i
$502$		0			0
$503$	14.8904	+	35.9486i	0.663930	+	1.60287i	0.791591	+	0.611052i	$0.209253\pi$
$503$	14.8904	+	35.9486i	0.663930	+	1.60287i	−0.127661	+	0.991818i	$0.540747\pi$
$504$		0			0
$505$	−5.73968	+	13.8568i	−0.255413	+	0.616620i
$506$		0			0
$507$	18.6875	+	7.74061i	0.829940	+	0.343772i
$508$		0			0
$509$	3.21110			0.142330			0.0711648	−	0.997465i	$-0.477328\pi$
$509$	3.21110			0.142330			0.0711648	+	0.997465i	$0.477328\pi$
$510$		0			0
$511$	−32.2389			−1.42616
$512$		0			0
$513$	8.39102	+	3.47567i	0.370472	+	0.153455i
$514$		0			0
$515$	−7.14980	+	17.2611i	−0.315058	+	0.760617i
$516$		0			0
$517$	−0.655444	−	1.58238i	−0.0288264	−	0.0695931i
$518$		0			0
$519$	48.2522	+	48.2522i	2.11803	+	2.11803i
$520$		0			0
$521$	16.9853	−	7.03555i	0.744140	−	0.308233i	0.0217921	−	0.999763i	$-0.493063\pi$
$521$	16.9853	−	7.03555i	0.744140	−	0.308233i	0.722348	+	0.691530i	$0.243063\pi$
$522$		0			0
$523$			12.0000i			0.524723i	0.964970	+	0.262362i	$0.0845013\pi$
$523$			12.0000i			0.524723i	−0.964970	+	0.262362i	$0.915499\pi$
$524$		0			0
$525$	22.4978	−	22.4978i	0.981883	−	0.981883i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	9.91912	−	9.91912i	0.431266	−	0.431266i
$530$		0			0
$531$		−	65.4500i		−	2.84029i
$532$		0			0
$533$	−3.40432	+	1.41011i	−0.147457	+	0.0610788i
$534$		0			0
$535$	8.05709	+	8.05709i	0.348338	+	0.348338i
$536$		0			0
$537$	18.7284	+	45.2143i	0.808190	+	1.95114i
$538$		0			0
$539$	0.590809	−	1.42634i	0.0254480	−	0.0614368i
$540$		0			0
$541$	3.91969	+	1.62359i	0.168521	+	0.0698035i	0.465349	−	0.885127i	$-0.345929\pi$
$541$	3.91969	+	1.62359i	0.168521	+	0.0698035i	−0.296828	+	0.954931i	$0.595929\pi$
$542$		0			0
$543$	−59.8722			−2.56936
$544$		0			0
$545$	12.4222			0.532109
$546$		0			0
$547$	15.0436	+	6.23127i	0.643218	+	0.266430i	0.680357	−	0.732880i	$-0.261825\pi$
$547$	15.0436	+	6.23127i	0.643218	+	0.266430i	−0.0371393	+	0.999310i	$0.511825\pi$
$548$		0			0
$549$	25.5655	−	61.7205i	1.09111	−	2.63417i
$550$		0			0
$551$	0.526174	+	1.27030i	0.0224158	+	0.0541165i
$552$		0			0
$553$	0.986024	+	0.986024i	0.0419300	+	0.0419300i
$554$		0			0
$555$	−18.0523	+	7.47752i	−0.766279	+	0.317403i
$556$		0			0
$557$			21.3944i			0.906512i	0.891380	+	0.453256i	$0.149738\pi$
$557$			21.3944i			0.906512i	−0.891380	+	0.453256i	$0.850262\pi$
$558$		0			0
$559$	6.25394	−	6.25394i	0.264514	−	0.264514i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.5703	−	14.5703i	0.614066	−	0.614066i	−0.329937	−	0.944003i	$-0.607028\pi$
$563$	14.5703	−	14.5703i	0.614066	−	0.614066i	0.944003	+	0.329937i	$0.107028\pi$
$564$		0			0
$565$		−	19.2111i		−	0.808217i
$566$		0			0
$567$	78.3103	−	32.4372i	3.28872	−	1.36223i
$568$		0			0
$569$	−21.5117	−	21.5117i	−0.901819	−	0.901819i	0.0937741	−	0.995593i	$-0.470107\pi$
$569$	−21.5117	−	21.5117i	−0.901819	−	0.901819i	−0.995593	+	0.0937741i	$0.970107\pi$
$570$		0			0
$571$	1.24625	+	3.00872i	0.0521541	+	0.125911i	0.947809	−	0.318838i	$-0.103293\pi$
$571$	1.24625	+	3.00872i	0.0521541	+	0.125911i	−0.895655	+	0.444749i	$0.853293\pi$
$572$		0			0
$573$	−8.46069	+	20.4259i	−0.353450	+	0.853304i
$574$		0			0
$575$	16.8655	+	6.98594i	0.703342	+	0.291334i
$576$		0			0
$577$	31.4500			1.30928			0.654640	−	0.755941i	$-0.272820\pi$
$577$	31.4500			1.30928			0.654640	+	0.755941i	$0.272820\pi$
$578$		0			0
$579$	37.8167			1.57161
$580$		0			0
$581$	53.6053	+	22.2041i	2.22392	+	0.921180i
$582$		0			0
$583$	0.853896	−	2.06149i	0.0353648	−	0.0853781i
$584$		0			0
$585$	−10.7247	−	25.8917i	−0.443412	−	1.07049i
$586$		0			0
$587$	3.25662	+	3.25662i	0.134415	+	0.134415i	0.771113	−	0.636698i	$-0.219700\pi$
$587$	3.25662	+	3.25662i	0.134415	+	0.134415i	−0.636698	+	0.771113i	$0.719700\pi$
$588$		0			0
$589$	3.40432	−	1.41011i	0.140272	−	0.0581027i
$590$		0			0
$591$		−	81.0833i		−	3.33532i
$592$		0			0
$593$	−1.11567	+	1.11567i	−0.0458151	+	0.0458151i	−0.729643	−	0.683828i	$-0.760314\pi$
$593$	−1.11567	+	1.11567i	−0.0458151	+	0.0458151i	0.683828	+	0.729643i	$0.260314\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−32.9551	+	32.9551i	−1.34876	+	1.34876i
$598$		0			0
$599$			26.0555i			1.06460i	0.846556	+	0.532300i	$0.178672\pi$
$599$			26.0555i			1.06460i	−0.846556	+	0.532300i	$0.821328\pi$
$600$		0			0
$601$	5.50207	−	2.27903i	0.224434	−	0.0929637i	−0.267633	−	0.963521i	$-0.586241\pi$
$601$	5.50207	−	2.27903i	0.224434	−	0.0929637i	0.492067	+	0.870557i	$0.336241\pi$
$602$		0			0
$603$	−49.5367	−	49.5367i	−2.01729	−	2.01729i
$604$		0			0
$605$	5.85393	+	14.1326i	0.237996	+	0.574573i
$606$		0			0
$607$	5.14887	−	12.4305i	0.208986	−	0.504538i	−0.784278	−	0.620410i	$-0.786966\pi$
$607$	5.14887	−	12.4305i	0.208986	−	0.504538i	0.993264	+	0.115872i	$0.0369663\pi$
$608$		0			0
$609$	22.2478	+	9.21536i	0.901528	+	0.373425i
$610$		0			0
$611$	10.4222			0.421637
$612$		0			0
$613$	40.4222			1.63264			0.816319	−	0.577602i	$-0.196011\pi$
$613$	40.4222			1.63264			0.816319	+	0.577602i	$0.196011\pi$
$614$		0			0
$615$	−6.01744	−	2.49251i	−0.242647	−	0.100508i
$616$		0			0
$617$	−0.868918	+	2.09775i	−0.0349813	+	0.0844524i	−0.940405	−	0.340057i	$-0.889554\pi$
$617$	−0.868918	+	2.09775i	−0.0349813	+	0.0844524i	0.905423	+	0.424510i	$0.139554\pi$
$618$		0			0
$619$	−7.83983	−	18.9270i	−0.315109	−	0.760742i	−0.999500	−	0.0316257i	$-0.989932\pi$
$619$	−7.83983	−	18.9270i	−0.315109	−	0.760742i	0.684390	−	0.729116i	$-0.260068\pi$
$620$		0			0
$621$	64.5352	+	64.5352i	2.58971	+	2.58971i
$622$		0			0
$623$	23.5181	−	9.74153i	0.942234	−	0.390286i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−0.597088	+	0.597088i	−0.0238454	+	0.0238454i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	17.1395	−	17.1395i	0.682311	−	0.682311i	−0.278209	−	0.960520i	$-0.589741\pi$
$631$	17.1395	−	17.1395i	0.682311	−	0.682311i	0.960520	+	0.278209i	$0.0897409\pi$
$632$		0			0
$633$		−	71.4500i		−	2.83988i
$634$		0			0
$635$	−0.791191	+	0.327722i	−0.0313975	+	0.0130053i
$636$		0			0
$637$	6.64288	+	6.64288i	0.263200	+	0.263200i
$638$		0			0
$639$	−11.9709	−	28.9004i	−0.473563	−	1.14328i
$640$		0			0
$641$	16.6779	−	40.2639i	0.658736	−	1.59033i	−0.141023	−	0.990006i	$-0.545039\pi$
$641$	16.6779	−	40.2639i	0.658736	−	1.59033i	0.799758	−	0.600322i	$-0.204961\pi$
$642$		0			0
$643$	5.38229	+	2.22942i	0.212257	+	0.0879197i	0.486279	−	0.873804i	$-0.338354\pi$
$643$	5.38229	+	2.22942i	0.212257	+	0.0879197i	−0.274022	+	0.961724i	$0.588354\pi$
$644$		0			0
$645$	15.6333			0.615561
$646$		0			0
$647$	−17.2111			−0.676638			−0.338319	−	0.941031i	$-0.609858\pi$
$647$	−17.2111			−0.676638			−0.338319	+	0.941031i	$0.609858\pi$
$648$		0			0
$649$	3.40432	+	1.41011i	0.133631	+	0.0553518i
$650$		0			0
$651$	24.6966	−	59.6228i	0.967935	−	2.33680i
$652$		0			0
$653$	−13.4307	−	32.4245i	−0.525583	−	1.26887i	−0.934391	−	0.356249i	$-0.884055\pi$
$653$	−13.4307	−	32.4245i	−0.525583	−	1.26887i	0.408808	−	0.912620i	$-0.365945\pi$
$654$		0			0
$655$	8.91347	+	8.91347i	0.348278	+	0.348278i
$656$		0			0
$657$	69.5599	−	28.8127i	2.71379	−	1.12409i
$658$		0			0
$659$			32.0000i			1.24654i	0.782006	+	0.623272i	$0.214197\pi$
$659$			32.0000i			1.24654i	−0.782006	+	0.623272i	$0.785803\pi$
$660$		0			0
$661$	0.856379	−	0.856379i	0.0333093	−	0.0333093i	−0.690256	−	0.723565i	$-0.742502\pi$
$661$	0.856379	−	0.856379i	0.0333093	−	0.0333093i	0.723565	+	0.690256i	$0.242502\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.97205	+	1.97205i	−0.0764728	+	0.0764728i
$666$		0			0
$667$			13.8167i			0.534983i
$668$		0			0
$669$	−53.6053	+	22.2041i	−2.07250	+	0.858459i
$670$		0			0
$671$	2.65953	+	2.65953i	0.102670	+	0.102670i
$672$		0			0
$673$	3.03370	+	7.32401i	0.116941	+	0.282320i	0.971502	−	0.237030i	$-0.0761741\pi$
$673$	3.03370	+	7.32401i	0.116941	+	0.282320i	−0.854562	+	0.519350i	$0.826174\pi$
$674$		0			0
$675$	−17.2190	+	41.5705i	−0.662762	+	1.60005i
$676$		0			0
$677$	−20.9413	−	8.67416i	−0.804838	−	0.333375i	−0.0579459	−	0.998320i	$-0.518455\pi$
$677$	−20.9413	−	8.67416i	−0.804838	−	0.333375i	−0.746893	+	0.664945i	$0.768455\pi$
$678$		0			0
$679$	35.0278			1.34424
$680$		0			0
$681$	1.39445			0.0534354
$682$		0			0
$683$	0.947233	+	0.392357i	0.0362449	+	0.0150131i	0.400732	−	0.916195i	$-0.368756\pi$
$683$	0.947233	+	0.392357i	0.0362449	+	0.0150131i	−0.364487	+	0.931208i	$0.618756\pi$
$684$		0			0
$685$	−1.41011	+	3.40432i	−0.0538777	+	0.130072i
$686$		0			0
$687$	5.73968	+	13.8568i	0.218983	+	0.528671i
$688$		0			0
$689$	9.60095	+	9.60095i	0.365767	+	0.365767i
$690$		0			0
$691$	−7.20423	+	2.98409i	−0.274062	+	0.113520i	−0.515482	−	0.856901i	$-0.672387\pi$
$691$	−7.20423	+	2.98409i	−0.274062	+	0.113520i	0.241420	+	0.970421i	$0.422387\pi$
$692$		0			0
$693$			10.6056i			0.402872i
$694$		0			0
$695$	−0.428189	+	0.428189i	−0.0162422	+	0.0162422i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	18.2551	−	18.2551i	0.690472	−	0.690472i
$700$		0			0
$701$		−	7.81665i		−	0.295231i	−0.989045	−	0.147615i	$-0.952840\pi$
$701$		−	7.81665i		−	0.295231i	0.989045	−	0.147615i	$-0.0471598\pi$
$702$		0			0
$703$	−2.37357	+	0.983166i	−0.0895210	+	0.0370808i
$704$		0			0
$705$	13.0265	+	13.0265i	0.490605	+	0.490605i
$706$		0			0
$707$	13.2172	+	31.9091i	0.497084	+	1.20007i
$708$		0			0
$709$	7.79022	−	18.8073i	0.292568	−	0.706321i	−0.707432	−	0.706781i	$-0.750146\pi$
$709$	7.79022	−	18.8073i	0.292568	−	0.706321i	1.00000		0.000460118i	$0.000146460\pi$
$710$		0			0
$711$	−3.00872	−	1.24625i	−0.112836	−	0.0467381i
$712$		0			0
$713$	37.0278			1.38670
$714$		0			0
$715$	1.57779			0.0590062
$716$		0			0
$717$	−44.4957	−	18.4307i	−1.66172	−	0.688308i
$718$		0			0
$719$	2.55714	−	6.17348i	0.0953653	−	0.230232i	−0.868997	−	0.494817i	$-0.835235\pi$
$719$	2.55714	−	6.17348i	0.0953653	−	0.230232i	0.964362	+	0.264585i	$0.0852350\pi$
$720$		0			0
$721$	16.4644	+	39.7485i	0.613166	+	1.48031i
$722$		0			0
$723$	−29.3095	−	29.3095i	−1.09003	−	1.09003i
$724$		0			0
$725$	−6.29326	+	2.60675i	−0.233726	+	0.0968124i
$726$		0			0
$727$			6.42221i			0.238186i	0.992883	+	0.119093i	$0.0379987\pi$
$727$			6.42221i			0.238186i	−0.992883	+	0.119093i	$0.962001\pi$
$728$		0			0
$729$	−36.3610	+	36.3610i	−1.34670	+	1.34670i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−32.5662	+	32.5662i	−1.20286	+	1.20286i	−0.229566	+	0.973293i	$0.573731\pi$
$733$	−32.5662	+	32.5662i	−1.20286	+	1.20286i	−0.973293	+	0.229566i	$0.926269\pi$
$734$		0			0
$735$			16.6056i			0.612505i
$736$		0			0
$737$	3.64387	−	1.50934i	0.134224	−	0.0555973i
$738$		0			0
$739$	24.5091	+	24.5091i	0.901581	+	0.901581i	0.995573	−	0.0939921i	$-0.0299628\pi$
$739$	24.5091	+	24.5091i	0.901581	+	0.901581i	−0.0939921	+	0.995573i	$0.529963\pi$
$740$		0			0
$741$	−1.96633	−	4.74715i	−0.0722350	−	0.174391i
$742$		0			0
$743$	7.96910	−	19.2391i	0.292358	−	0.705815i	−0.707642	−	0.706571i	$-0.750241\pi$
$743$	7.96910	−	19.2391i	0.292358	−	0.705815i	1.00000		0.000756791i	$0.000240894\pi$
$744$		0			0
$745$	−11.0041	−	4.55806i	−0.403161	−	0.166995i
$746$		0			0
$747$	−135.505			−4.95789
$748$		0			0
$749$	26.2389			0.958747
$750$		0			0
$751$	−2.21753	−	0.918531i	−0.0809188	−	0.0335177i	0.341857	−	0.939752i	$-0.388944\pi$
$751$	−2.21753	−	0.918531i	−0.0809188	−	0.0335177i	−0.422776	+	0.906234i	$0.638944\pi$
$752$		0			0
$753$	−14.9550	+	36.1047i	−0.544992	+	1.31573i
$754$		0			0
$755$	2.49251	+	6.01744i	0.0907116	+	0.218997i
$756$		0			0
$757$	−27.5968	−	27.5968i	−1.00302	−	1.00302i	−0.999995	−	0.00302702i	$-0.999036\pi$
$757$	−27.5968	−	27.5968i	−1.00302	−	1.00302i	−0.00302702	−	0.999995i	$-0.500964\pi$
$758$		0			0
$759$	−7.83938	+	3.24718i	−0.284551	+	0.117865i
$760$		0			0
$761$			31.4500i			1.14006i	0.821624	+	0.570030i	$0.193068\pi$
$761$			31.4500i			1.14006i	−0.821624	+	0.570030i	$0.806932\pi$
$762$		0			0
$763$	20.2272	−	20.2272i	0.732273	−	0.732273i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.8549	+	15.8549i	−0.572487	+	0.572487i
$768$		0			0
$769$		−	18.6056i		−	0.670933i	−0.942052	−	0.335467i	$-0.891106\pi$
$769$		−	18.6056i		−	0.670933i	0.942052	−	0.335467i	$-0.108894\pi$
$770$		0			0
$771$	58.3525	−	24.1704i	2.10151	−	0.870475i
$772$		0			0
$773$	−20.2272	−	20.2272i	−0.727521	−	0.727521i	0.242604	−	0.970125i	$-0.421998\pi$
$773$	−20.2272	−	20.2272i	−0.727521	−	0.727521i	−0.970125	+	0.242604i	$0.921998\pi$
$774$		0			0
$775$	6.98594	+	16.8655i	0.250942	+	0.605828i
$776$		0			0
$777$	−17.2190	+	41.5705i	−0.617730	+	1.49133i
$778$		0			0
$779$	−0.791191	−	0.327722i	−0.0283474	−	0.0117419i
$780$		0			0
$781$	1.76114			0.0630186
$782$		0			0
$783$	−34.0555			−1.21704
$784$		0			0
$785$	−11.0041	−	4.55806i	−0.392755	−	0.162684i
$786$		0			0
$787$	−7.96910	+	19.2391i	−0.284068	+	0.685800i	−0.999923	−	0.0124489i	$-0.996037\pi$
$787$	−7.96910	+	19.2391i	−0.284068	+	0.685800i	0.715855	+	0.698249i	$0.246037\pi$
$788$		0			0
$789$	28.6984	+	69.2841i	1.02169	+	2.46658i
$790$		0			0
$791$	−31.2816	−	31.2816i	−1.11225	−	1.11225i
$792$		0			0
$793$	−21.1446	+	8.75836i	−0.750865	+	0.311019i
$794$		0			0
$795$			24.0000i			0.851192i
$796$		0			0
$797$	−2.56914	+	2.56914i	−0.0910035	+	0.0910035i	−0.751143	−	0.660140i	$-0.770497\pi$
$797$	−2.56914	+	2.56914i	−0.0910035	+	0.0910035i	0.660140	+	0.751143i	$0.270497\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−42.0375	+	42.0375i	−1.48532	+	1.48532i
$802$		0			0
$803$			4.23886i			0.149586i
$804$		0			0
$805$	−25.8917	+	10.7247i	−0.912563	+	0.377996i
$806$		0			0
$807$	56.7374	+	56.7374i	1.99725	+	1.99725i
$808$		0			0
$809$	−11.2659	−	27.1983i	−0.396088	−	0.956240i	−0.988585	−	0.150667i	$-0.951858\pi$
$809$	−11.2659	−	27.1983i	−0.396088	−	0.956240i	0.592497	−	0.805573i	$-0.298142\pi$
$810$		0			0
$811$	5.80432	−	14.0129i	0.203817	−	0.492058i	−0.788610	−	0.614894i	$-0.789199\pi$
$811$	5.80432	−	14.0129i	0.203817	−	0.492058i	0.992427	+	0.122836i	$0.0391988\pi$
$812$		0			0
$813$	−3.64387	−	1.50934i	−0.127796	−	0.0529349i
$814$		0			0
$815$	−8.60555			−0.301439
$816$		0			0
$817$	2.05551			0.0719133
$818$		0			0
$819$	−59.6228	−	24.6966i	−2.08339	−	0.862968i
$820$		0			0
$821$	−6.93632	+	16.7458i	−0.242079	+	0.584431i	−0.997489	−	0.0708216i	$-0.977438\pi$
$821$	−6.93632	+	16.7458i	−0.242079	+	0.584431i	0.755410	+	0.655253i	$0.227438\pi$
$822$		0			0
$823$	−6.98594	−	16.8655i	−0.243514	−	0.587896i	0.754113	−	0.656745i	$-0.228067\pi$
$823$	−6.98594	−	16.8655i	−0.243514	−	0.587896i	−0.997627	+	0.0688493i	$0.978067\pi$
$824$		0			0
$825$	−2.95807	−	2.95807i	−0.102987	−	0.102987i
$826$		0			0
$827$	8.23497	−	3.41104i	0.286358	−	0.118613i	−0.234881	−	0.972024i	$-0.575470\pi$
$827$	8.23497	−	3.41104i	0.286358	−	0.118613i	0.521239	+	0.853411i	$0.325470\pi$
$828$		0			0
$829$			18.8444i			0.654493i	0.944939	+	0.327247i	$0.106121\pi$
$829$			18.8444i			0.654493i	−0.944939	+	0.327247i	$0.893879\pi$
$830$		0			0
$831$	−11.7419	+	11.7419i	−0.407322	+	0.407322i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	21.0836	−	21.0836i	0.729627	−	0.729627i
$836$		0			0
$837$			91.2666i			3.15464i
$838$		0			0
$839$	19.4787	−	8.06833i	0.672478	−	0.278550i	−0.0202004	−	0.999796i	$-0.506430\pi$
$839$	19.4787	−	8.06833i	0.672478	−	0.278550i	0.692679	+	0.721246i	$0.256430\pi$
$840$		0			0
$841$	16.8605	+	16.8605i	0.581398	+	0.581398i
$842$		0			0
$843$	−22.9587	−	55.4273i	−0.790741	−	1.90902i
$844$		0			0
$845$	3.36142	−	8.11520i	0.115637	−	0.279171i
$846$		0			0
$847$	32.5443	+	13.4803i	1.11824	+	0.463188i
$848$		0			0
$849$	9.76114			0.335001
$850$		0			0
$851$	−25.8167			−0.884983
$852$		0			0
$853$	−38.4420	−	15.9232i	−1.31623	−	0.545199i	−0.389532	−	0.921013i	$-0.627363\pi$
$853$	−38.4420	−	15.9232i	−1.31623	−	0.545199i	−0.926695	+	0.375813i	$0.877363\pi$
$854$		0			0
$855$	2.49251	−	6.01744i	0.0852419	−	0.205792i
$856$		0			0
$857$	10.0843	+	24.3456i	0.344472	+	0.831630i	0.997252	+	0.0740819i	$0.0236026\pi$
$857$	10.0843	+	24.3456i	0.344472	+	0.831630i	−0.652780	+	0.757548i	$0.726397\pi$
$858$		0			0
$859$	−1.28457	−	1.28457i	−0.0438289	−	0.0438289i	0.684853	−	0.728682i	$-0.259867\pi$
$859$	−1.28457	−	1.28457i	−0.0438289	−	0.0438289i	−0.728682	+	0.684853i	$0.759867\pi$
$860$		0			0
$861$	−13.8568	+	5.73968i	−0.472239	+	0.195608i
$862$		0			0
$863$			52.4777i			1.78636i	0.449697	+	0.893181i	$0.351532\pi$
$863$			52.4777i			1.78636i	−0.449697	+	0.893181i	$0.648468\pi$
$864$		0			0
$865$	20.9539	−	20.9539i	0.712454	−	0.712454i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.129645	−	0.129645i	0.00439792	−	0.00439792i
$870$		0			0
$871$			24.0000i			0.813209i
$872$		0			0
$873$	−75.5774	+	31.3052i	−2.55791	+	1.05952i
$874$		0			0
$875$	−26.0529	−	26.0529i	−0.880750	−	0.880750i
$876$		0			0
$877$	0.968144	+	2.33731i	0.0326919	+	0.0789253i	0.939382	−	0.342872i	$-0.111400\pi$
$877$	0.968144	+	2.33731i	0.0326919	+	0.0789253i	−0.906690	+	0.421797i	$0.861400\pi$
$878$		0			0
$879$	26.9606	−	65.0886i	0.909358	−	2.19538i
$880$		0			0
$881$	−31.6333	−	13.1030i	−1.06575	−	0.441450i	−0.220264	−	0.975440i	$-0.570692\pi$
$881$	−31.6333	−	13.1030i	−1.06575	−	0.441450i	−0.845490	+	0.533991i	$0.820692\pi$
$882$		0			0
$883$	−25.5778			−0.860761			−0.430381	−	0.902647i	$-0.641621\pi$
$883$	−25.5778			−0.860761			−0.430381	+	0.902647i	$0.641621\pi$
$884$		0			0
$885$	−39.6333			−1.33226
$886$		0			0
$887$	15.2832	+	6.33049i	0.513158	+	0.212557i	0.624209	−	0.781258i	$-0.285421\pi$
$887$	15.2832	+	6.33049i	0.513158	+	0.212557i	−0.111050	+	0.993815i	$0.535421\pi$
$888$		0			0
$889$	−0.754670	+	1.82194i	−0.0253108	+	0.0611057i
$890$		0			0
$891$	−4.26493	−	10.2965i	−0.142881	−	0.344944i
$892$		0			0
$893$	1.71276	+	1.71276i	0.0573152	+	0.0573152i
$894$		0			0
$895$	19.6347	−	8.13296i	0.656316	−	0.271855i
$896$		0			0
$897$		−	51.6333i		−	1.72399i
$898$		0			0
$899$	−9.76985	+	9.76985i	−0.325843	+	0.325843i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	25.4558	−	25.4558i	0.847117	−	0.847117i
$904$		0			0
$905$			26.0000i			0.864269i
$906$		0			0
$907$	−32.0652	+	13.2818i	−1.06471	+	0.441016i	−0.845120	−	0.534577i	$-0.820471\pi$
$907$	−32.0652	+	13.2818i	−1.06471	+	0.441016i	−0.219587	+	0.975593i	$0.570471\pi$
$908$		0			0
$909$	−57.0360	−	57.0360i	−1.89176	−	1.89176i
$910$		0			0
$911$	2.55714	+	6.17348i	0.0847219	+	0.204537i	0.960563	−	0.278063i	$-0.0896925\pi$
$911$	2.55714	+	6.17348i	0.0847219	+	0.204537i	−0.875841	+	0.482600i	$0.839693\pi$
$912$		0			0
$913$	2.91945	−	7.04819i	0.0966198	−	0.233261i
$914$		0			0
$915$	−37.3750	−	15.4812i	−1.23558	−	0.511793i
$916$		0			0
$917$	29.0278			0.958581
$918$		0			0
$919$	40.8444			1.34733			0.673666	−	0.739036i	$-0.264718\pi$
$919$	40.8444			1.34733			0.673666	+	0.739036i	$0.264718\pi$
$920$		0			0
$921$	63.8183	+	26.4344i	2.10288	+	0.871043i
$922$		0			0
$923$	−4.10107	+	9.90087i	−0.134988	+	0.325891i
$924$		0			0
$925$	−4.87076	−	11.7591i	−0.160150	−	0.386636i
$926$		0			0
$927$	−71.0485	−	71.0485i	−2.33354	−	2.33354i
$928$		0			0
$929$	1.30656	−	0.541196i	0.0428669	−	0.0177561i	−0.361147	−	0.932509i	$-0.617615\pi$
$929$	1.30656	−	0.541196i	0.0428669	−	0.0177561i	0.404014	+	0.914753i	$0.367615\pi$
$930$		0			0
$931$			2.18335i			0.0715563i
$932$		0			0
$933$	−61.5772	+	61.5772i	−2.01595	+	2.01595i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.54118	−	4.54118i	0.148354	−	0.148354i	−0.629028	−	0.777382i	$-0.716547\pi$
$937$	4.54118	−	4.54118i	0.148354	−	0.148354i	0.777382	+	0.629028i	$0.216547\pi$
$938$		0			0
$939$		−	28.6056i		−	0.933507i
$940$		0			0
$941$	20.9413	−	8.67416i	0.682666	−	0.282770i	−0.0142749	−	0.999898i	$-0.504544\pi$
$941$	20.9413	−	8.67416i	0.682666	−	0.282770i	0.696941	+	0.717129i	$0.254544\pi$
$942$		0			0
$943$	−6.08504	−	6.08504i	−0.198156	−	0.198156i
$944$		0			0
$945$	−26.4344	−	63.8183i	−0.859911	−	2.07601i
$946$		0			0
$947$	−5.01960	+	12.1184i	−0.163115	+	0.393795i	−0.984212	−	0.176994i	$-0.943363\pi$
$947$	−5.01960	+	12.1184i	−0.163115	+	0.393795i	0.821097	+	0.570789i	$0.193363\pi$
$948$		0			0
$949$	−23.8302	−	9.87080i	−0.773562	−	0.320420i
$950$		0			0
$951$	90.2944			2.92800
$952$		0			0
$953$	50.2389			1.62740			0.813698	−	0.581288i	$-0.197451\pi$
$953$	50.2389			1.62740			0.813698	+	0.581288i	$0.197451\pi$
$954$		0			0
$955$	8.87012	+	3.67412i	0.287030	+	0.118892i
$956$		0			0
$957$	1.21166	−	2.92521i	0.0391675	−	0.0945586i
$958$		0			0
$959$	3.24718	+	7.83938i	0.104857	+	0.253147i
$960$		0			0
$961$	4.26227	+	4.26227i	0.137492	+	0.137492i
$962$		0			0
$963$	−56.6141	+	23.4503i	−1.82436	+	0.755676i
$964$		0			0
$965$		−	16.4222i		−	0.528649i
$966$		0			0
$967$	−15.4267	+	15.4267i	−0.496089	+	0.496089i	−0.910218	−	0.414129i	$-0.864086\pi$
$967$	−15.4267	+	15.4267i	−0.496089	+	0.496089i	0.414129	+	0.910218i	$0.364086\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	38.9105	−	38.9105i	1.24870	−	1.24870i	0.292402	−	0.956296i	$-0.405546\pi$
$971$	38.9105	−	38.9105i	1.24870	−	1.24870i	0.956296	−	0.292402i	$-0.0944545\pi$
$972$		0			0
$973$			1.39445i			0.0447040i
$974$		0			0
$975$	23.5181	−	9.74153i	0.753183	−	0.311979i
$976$		0			0
$977$	11.9108	+	11.9108i	0.381060	+	0.381060i	0.871484	−	0.490424i	$-0.163158\pi$
$977$	11.9108	+	11.9108i	0.381060	+	0.381060i	−0.490424	+	0.871484i	$0.663158\pi$
$978$		0			0
$979$	−1.28084	−	3.09223i	−0.0409360	−	0.0988282i
$980$		0			0
$981$	−25.5655	+	61.7205i	−0.816243	+	1.97059i
$982$		0			0
$983$	10.6085	+	4.39420i	0.338360	+	0.140153i	0.545393	−	0.838181i	$-0.316381\pi$
$983$	10.6085	+	4.39420i	0.338360	+	0.140153i	−0.207033	+	0.978334i	$0.566381\pi$
$984$		0			0
$985$	−35.2111			−1.12192
$986$		0			0
$987$	42.4222			1.35031
$988$		0			0
$989$	19.0831	+	7.90447i	0.606806	+	0.251347i
$990$		0			0
$991$	12.7256	−	30.7224i	0.404243	−	0.975928i	−0.582381	−	0.812916i	$-0.697879\pi$
$991$	12.7256	−	30.7224i	0.404243	−	0.975928i	0.986624	−	0.163012i	$-0.0521210\pi$
$992$		0			0
$993$	−4.23034	−	10.2130i	−0.134246	−	0.324098i
$994$		0			0
$995$	14.3110	+	14.3110i	0.453690	+	0.453690i
$996$		0			0
$997$	51.2680	−	21.2359i	1.62368	−	0.672548i	0.629173	−	0.777265i	$-0.283394\pi$
$997$	51.2680	−	21.2359i	1.62368	−	0.672548i	0.994502	+	0.104717i	$0.0333937\pi$
$998$		0			0
$999$		−	63.6333i		−	2.01327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.h.e.757.4		16
17.2	even	8	inner	1156.2.h.e.733.4		16
17.3	odd	16		1156.2.e.c.829.2		4
17.4	even	4	inner	1156.2.h.e.977.4		16
17.5	odd	16		68.2.e.a.21.1	yes	4
17.6	odd	16		1156.2.a.h.1.4		4
17.7	odd	16		1156.2.b.a.577.1		4
17.8	even	8	inner	1156.2.h.e.1001.1		16
17.9	even	8	inner	1156.2.h.e.1001.4		16
17.10	odd	16		1156.2.b.a.577.4		4
17.11	odd	16		1156.2.a.h.1.1		4
17.12	odd	16		1156.2.e.c.905.2		4
17.13	even	4	inner	1156.2.h.e.977.1		16
17.14	odd	16		68.2.e.a.13.1	✓	4
17.15	even	8	inner	1156.2.h.e.733.1		16
17.16	even	2	inner	1156.2.h.e.757.1		16
51.5	even	16		612.2.k.e.361.2		4
51.14	even	16		612.2.k.e.217.2		4
68.11	even	16		4624.2.a.bq.1.4		4
68.23	even	16		4624.2.a.bq.1.1		4
68.31	even	16		272.2.o.g.81.2		4
68.39	even	16		272.2.o.g.225.2		4
85.14	odd	16		1700.2.o.c.1101.2		4
85.22	even	16		1700.2.m.b.1449.2		4
85.39	odd	16		1700.2.o.c.701.2		4
85.48	even	16		1700.2.m.b.149.2		4
85.73	even	16		1700.2.m.a.1449.1		4
85.82	even	16		1700.2.m.a.149.1		4
136.5	odd	16		1088.2.o.t.769.2		4
136.99	even	16		1088.2.o.s.897.1		4
136.107	even	16		1088.2.o.s.769.1		4
136.133	odd	16		1088.2.o.t.897.2		4
204.107	odd	16		2448.2.be.u.1585.1		4
204.167	odd	16		2448.2.be.u.1441.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.e.a.13.1	✓	4	17.14	odd	16
68.2.e.a.21.1	yes	4	17.5	odd	16
272.2.o.g.81.2		4	68.31	even	16
272.2.o.g.225.2		4	68.39	even	16
612.2.k.e.217.2		4	51.14	even	16
612.2.k.e.361.2		4	51.5	even	16
1088.2.o.s.769.1		4	136.107	even	16
1088.2.o.s.897.1		4	136.99	even	16
1088.2.o.t.769.2		4	136.5	odd	16
1088.2.o.t.897.2		4	136.133	odd	16
1156.2.a.h.1.1		4	17.11	odd	16
1156.2.a.h.1.4		4	17.6	odd	16
1156.2.b.a.577.1		4	17.7	odd	16
1156.2.b.a.577.4		4	17.10	odd	16
1156.2.e.c.829.2		4	17.3	odd	16
1156.2.e.c.905.2		4	17.12	odd	16
1156.2.h.e.733.1		16	17.15	even	8	inner
1156.2.h.e.733.4		16	17.2	even	8	inner
1156.2.h.e.757.1		16	17.16	even	2	inner
1156.2.h.e.757.4		16	1.1	even	1	trivial
1156.2.h.e.977.1		16	17.13	even	4	inner
1156.2.h.e.977.4		16	17.4	even	4	inner
1156.2.h.e.1001.1		16	17.8	even	8	inner
1156.2.h.e.1001.4		16	17.9	even	8	inner
1700.2.m.a.149.1		4	85.82	even	16
1700.2.m.a.1449.1		4	85.73	even	16
1700.2.m.b.149.2		4	85.48	even	16
1700.2.m.b.1449.2		4	85.22	even	16
1700.2.o.c.701.2		4	85.39	odd	16
1700.2.o.c.1101.2		4	85.14	odd	16
2448.2.be.u.1441.1		4	204.167	odd	16
2448.2.be.u.1585.1		4	204.107	odd	16
4624.2.a.bq.1.1		4	68.23	even	16
4624.2.a.bq.1.4		4	68.11	even	16

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:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00872 + 1.24625i) q^{3} +(0.541196 - 1.30656i) q^{5} +(-1.24625 - 3.00872i) q^{7} +(5.37794 + 5.37794i) q^{9} +O(q^{10})\)	\(q+(3.00872 + 1.24625i) q^{3} +(0.541196 - 1.30656i) q^{5} +(-1.24625 - 3.00872i) q^{7} +(5.37794 + 5.37794i) q^{9} +(-0.395595 + 0.163861i) q^{11} -2.60555i q^{13} +(3.25662 - 3.25662i) q^{15} +(0.428189 - 0.428189i) q^{19} -10.6056i q^{21} +(5.62185 - 2.32865i) q^{23} +(2.12132 + 2.12132i) q^{25} +(5.73968 + 13.8568i) q^{27} +(-0.868918 + 2.09775i) q^{29} +(5.62185 + 2.32865i) q^{31} -1.39445 q^{33} -4.60555 q^{35} +(-3.91969 - 1.62359i) q^{37} +(3.24718 - 7.83938i) q^{39} +(-0.541196 - 1.30656i) q^{41} +(2.40024 + 2.40024i) q^{43} +(9.93713 - 4.11609i) q^{45} +4.00000i q^{47} +(-2.54951 + 2.54951i) q^{49} +(-3.68481 + 3.68481i) q^{53} +0.605551i q^{55} +(1.82194 - 0.754670i) q^{57} +(-6.08504 - 6.08504i) q^{59} +(-3.36142 - 8.11520i) q^{61} +(9.47844 - 22.8830i) q^{63} +(-3.40432 - 1.41011i) q^{65} -9.21110 q^{67} +19.8167 q^{69} +(-3.79991 - 1.57398i) q^{71} +(3.78837 - 9.14594i) q^{73} +(3.73876 + 9.02616i) q^{75} +(0.986024 + 0.986024i) q^{77} +(-0.395595 + 0.163861i) q^{79} +26.0278i q^{81} +(-12.5983 + 12.5983i) q^{83} +(-5.22866 + 5.22866i) q^{87} +7.81665i q^{89} +(-7.83938 + 3.24718i) q^{91} +(14.0125 + 14.0125i) q^{93} +(-0.327722 - 0.791191i) q^{95} +(-4.11609 + 9.93713i) q^{97} +(-3.00872 - 1.24625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 80 q^{33} - 16 q^{35} - 32 q^{67} + 144 q^{69}+O(q^{100}) \) 16 * q - 80 * q^33 - 16 * q^35 - 32 * q^67 + 144 * q^69

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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