LMFDB - Embedded newform 1156.2.h.e.757.1

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			757.1
Root			$-2.12749 + 0.881234i$ of defining polynomial
Character	$\chi$	$=$	1156.757
Dual form			1156.2.h.e.733.1

$q$-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	$-0.985727\pi$
$3$	−3.00872	−	1.24625i	−1.73709	−	0.719525i	−0.738091	−	0.674701i	$-0.764273\pi$
$4$		0			0
$5$	−0.541196	+	1.30656i	−0.242030	+	0.584313i	−0.997484	−	0.0708890i	$-0.977416\pi$
$5$	−0.541196	+	1.30656i	−0.242030	+	0.584313i	0.755454	+	0.655202i	$0.227416\pi$
$6$		0			0
$7$	1.24625	+	3.00872i	0.471039	+	1.13719i	0.963705	+	0.266971i	$0.0860227\pi$
$7$	1.24625	+	3.00872i	0.471039	+	1.13719i	−0.492665	+	0.870219i	$0.663977\pi$
$8$		0			0
$9$	5.37794	+	5.37794i	1.79265	+	1.79265i
$10$		0			0
$11$	0.395595	−	0.163861i	0.119277	−	0.0494059i	−0.322247	−	0.946656i	$-0.604438\pi$
$11$	0.395595	−	0.163861i	0.119277	−	0.0494059i	0.441524	+	0.897250i	$0.354438\pi$
$12$		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	−0.881931	−	0.471378i	$-0.843757\pi$
$23$	−5.62185	+	2.32865i	−1.17224	+	0.485556i	−0.290305	+	0.956934i	$0.593757\pi$
$24$		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	−0.822438	−	0.568854i	$-0.807387\pi$
$29$	0.868918	−	2.09775i	0.161354	−	0.389543i	0.983792	+	0.179311i	$0.0573869\pi$
$30$		0			0
$31$	−5.62185	−	2.32865i	−1.00971	−	0.418237i	−0.184363	−	0.982858i	$-0.559022\pi$
$31$	−5.62185	−	2.32865i	−1.00971	−	0.418237i	−0.825350	+	0.564621i	$0.809022\pi$
$32$		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	0.680854	−	0.732419i	$-0.261609\pi$
$37$	3.91969	+	1.62359i	0.644393	+	0.266916i	−0.0364615	+	0.999335i	$0.511609\pi$
$38$		0			0
$39$	−3.24718	+	7.83938i	−0.519964	+	1.25531i
$40$		0			0
$41$	0.541196	+	1.30656i	0.0845206	+	0.204051i	0.960489	−	0.278317i	$-0.0897767\pi$
$41$	0.541196	+	1.30656i	0.0845206	+	0.204051i	−0.875969	+	0.482368i	$0.839777\pi$
$42$		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	$0.0650937\pi$
$61$	3.36142	+	8.11520i	0.430386	+	1.03904i	−0.548777	+	0.835969i	$0.684906\pi$
$62$		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	0.596594	−	0.802543i	$-0.296520\pi$
$71$	3.79991	+	1.57398i	0.450967	+	0.186796i	−0.145628	+	0.989339i	$0.546520\pi$
$72$		0			0
$73$	−3.78837	+	9.14594i	−0.443395	+	1.07045i	0.531354	+	0.847150i	$0.321683\pi$
$73$	−3.78837	+	9.14594i	−0.443395	+	1.07045i	−0.974749	+	0.223301i	$0.928317\pi$
$74$		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	−0.360318	−	0.932829i	$-0.617332\pi$
$79$	0.395595	−	0.163861i	0.0445080	−	0.0184358i	0.404826	+	0.914394i	$0.367332\pi$
$80$		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	$-0.691132\pi$
$97$	4.11609	−	9.93713i	0.417926	−	1.00896i	0.982947	−	0.183887i	$-0.0588679\pi$
$98$		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	$-0.747664\pi$
$107$	3.08332	−	7.44378i	0.298075	−	0.719618i	0.999973	−	0.00733983i	$-0.00233636\pi$
$108$		0			0
$109$	−3.36142	−	8.11520i	−0.321966	−	0.777295i	−0.999140	−	0.0414716i	$-0.986795\pi$
$109$	−3.36142	−	8.11520i	−0.321966	−	0.777295i	0.677174	−	0.735823i	$-0.263205\pi$
$110$		0			0
$111$	−9.76985	−	9.76985i	−0.927313	−	0.927313i
$112$		0			0
$113$	−12.5503	+	5.19849i	−1.18063	+	0.489033i	−0.884692	−	0.466175i	$-0.845632\pi$
$113$	−12.5503	+	5.19849i	−1.18063	+	0.489033i	−0.295936	+	0.955208i	$0.595632\pi$
$114$		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	$-0.747687\pi$
$131$	3.41104	−	8.23497i	0.298024	−	0.719493i	0.999974	−	0.00726659i	$-0.00231305\pi$
$132$		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	0.399397	−	0.916778i	$-0.369219\pi$
$139$	0.395595	+	0.163861i	0.0335540	+	0.0138985i	−0.365843	+	0.930676i	$0.619219\pi$
$140$		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	0.988459	−	0.151490i	$-0.0484070\pi$
$163$	2.32865	+	5.62185i	0.182394	+	0.440337i	−0.806065	+	0.591827i	$0.798407\pi$
$164$		0			0
$165$	0.754670	−	1.82194i	0.0587510	−	0.141837i
$166$		0			0
$167$	−19.4787	−	8.06833i	−1.50730	−	0.624346i	−0.532305	−	0.846553i	$-0.678674\pi$
$167$	−19.4787	−	8.06833i	−1.50730	−	0.624346i	−0.975000	+	0.222207i	$0.928674\pi$
$168$		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	−0.504554	−	0.863380i	$-0.668343\pi$
$173$	−19.3589	−	8.01872i	−1.47183	−	0.609652i	−0.967275	+	0.253729i	$0.918343\pi$
$174$		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	0.351830	−	0.936064i	$-0.385559\pi$
$181$	16.9853	−	7.03555i	1.26251	−	0.522948i	0.910679	+	0.413116i	$0.135559\pi$
$182$		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	−0.733780	−	0.679387i	$-0.762246\pi$
$193$	−10.7283	+	4.44382i	−0.772242	+	0.319873i	−0.0384615	+	0.999260i	$0.512246\pi$
$194$		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	$0.222184\pi$
$197$	9.52806	+	23.0028i	0.678846	+	1.63888i	−0.0872765	+	0.996184i	$0.527816\pi$
$198$		0			0
$199$	5.47660	−	13.2217i	0.388226	−	0.937259i	−0.602090	−	0.798428i	$-0.705665\pi$
$199$	5.47660	−	13.2217i	0.388226	−	0.937259i	0.990316	−	0.138832i	$-0.0443347\pi$
$200$		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	$0.147462\pi$
$211$	8.39605	+	20.2699i	0.578008	+	1.39543i	−0.316590	+	0.948563i	$0.602538\pi$
$212$		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	−0.395773	−	0.918348i	$-0.629523\pi$
$227$	−0.395595	+	0.163861i	−0.0262566	+	0.0108758i	0.369516	+	0.929224i	$0.379523\pi$
$228$		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	−0.991560	−	0.129650i	$-0.958614\pi$
$233$	−3.03370	+	7.32401i	−0.198744	+	0.479812i	0.792815	+	0.609462i	$0.208614\pi$
$234$		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	0.727785	−	0.685806i	$-0.240550\pi$
$241$	11.7591	+	4.87076i	0.757468	+	0.313754i	0.0296835	+	0.999559i	$0.490550\pi$
$242$		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	−0.441316	−	0.897352i	$-0.645488\pi$
$269$	−22.7632	−	9.42883i	−1.38790	−	0.574886i	−0.946581	+	0.322466i	$0.895488\pi$
$270$		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	−0.854354	−	0.519691i	$-0.826047\pi$
$277$	1.95131	−	4.71088i	0.117243	−	0.283049i	0.971597	+	0.236642i	$0.0760469\pi$
$278$		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	−0.463467	−	0.886114i	$-0.653395\pi$
$283$	−2.76917	+	1.14703i	−0.164610	+	0.0681837i	0.298857	+	0.954298i	$0.403395\pi$
$284$		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	$-0.601101\pi$
$311$	10.2331	−	24.7049i	0.580267	−	1.40089i	0.892572	−	0.450906i	$-0.148899\pi$
$312$		0			0
$313$	3.36142	+	8.11520i	0.189999	+	0.458698i	0.989959	−	0.141355i	$-0.0451460\pi$
$313$	3.36142	+	8.11520i	0.189999	+	0.458698i	−0.799960	+	0.600053i	$0.795146\pi$
$314$		0			0
$315$	−24.7684	−	24.7684i	−1.39554	−	1.39554i
$316$		0			0
$317$	−25.6159	+	10.6104i	−1.43873	+	0.595942i	−0.959490	−	0.281741i	$-0.909088\pi$
$317$	−25.6159	+	10.6104i	−1.43873	+	0.595942i	−0.479241	+	0.877683i	$0.659088\pi$
$318$		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	0.875804	−	0.482667i	$-0.160332\pi$
$337$	21.1808	+	8.77339i	1.15379	+	0.477917i	0.277989	+	0.960584i	$0.410332\pi$
$338$		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	0.823319	−	0.567579i	$-0.192120\pi$
$347$	−2.98409	−	7.20423i	−0.160194	−	0.386743i	−0.983513	+	0.180836i	$0.942120\pi$
$348$		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	0.990920	−	0.134452i	$-0.0429275\pi$
$367$	3.73876	+	9.02616i	0.195162	+	0.471162i	−0.795758	+	0.605614i	$0.792927\pi$
$368$		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	$0.396280\pi$
$379$	−11.2163	+	27.0785i	−0.576142	+	1.39093i	−0.896251	+	0.443548i	$0.853720\pi$
$380$		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	−0.657724	−	0.753259i	$-0.728481\pi$
$397$	−11.7591	+	4.87076i	−0.590171	+	0.244457i	0.0675534	+	0.997716i	$0.478481\pi$
$398$		0			0
$399$	−4.54118	−	4.54118i	−0.227344	−	0.227344i
$400$		0			0
$401$	3.78837	+	9.14594i	0.189182	+	0.456726i	0.989803	−	0.142445i	$-0.0454966\pi$
$401$	3.78837	+	9.14594i	0.189182	+	0.456726i	−0.800620	+	0.599172i	$0.795497\pi$
$402$		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	−0.454964	−	0.890510i	$-0.650348\pi$
$419$	−3.00872	+	1.24625i	−0.146986	+	0.0608835i	0.307978	+	0.951394i	$0.400348\pi$
$420$		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	−0.441074	−	0.897471i	$-0.645403\pi$
$431$	−2.45708	+	1.01776i	−0.118354	+	0.0490237i	0.322721	+	0.946494i	$0.395403\pi$
$432$		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	0.996319	−	0.0857193i	$-0.0273188\pi$
$439$	34.3662	+	14.2350i	1.64021	+	0.679398i	0.643891	+	0.765117i	$0.277319\pi$
$440$		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	$-0.935348\pi$
$449$	−9.10111	−	21.9720i	−0.429508	−	1.03692i	0.549936	−	0.835207i	$-0.314652\pi$
$450$		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	0.718382	−	0.695649i	$-0.244883\pi$
$479$	16.0744	+	6.65821i	0.734456	+	0.304222i	0.0160742	+	0.999871i	$0.494883\pi$
$480$		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	0.194779	−	0.980847i	$-0.437601\pi$
$487$	22.6434	−	9.37922i	1.02607	−	0.425013i	0.831293	+	0.555834i	$0.187601\pi$
$488$		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	−0.0604568	−	0.998171i	$-0.519256\pi$
$499$	13.4612	−	5.57582i	0.602607	−	0.249608i	0.663064	+	0.748563i	$0.269256\pi$
$500$		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	$-0.790747\pi$
$503$	−14.8904	−	35.9486i	−0.663930	−	1.60287i	0.127661	−	0.991818i	$-0.459253\pi$
$504$		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	−0.722348	−	0.691530i	$-0.756937\pi$
$521$	−16.9853	+	7.03555i	−0.744140	+	0.308233i	−0.0217921	+	0.999763i	$0.506937\pi$
$522$		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	0.296828	−	0.954931i	$-0.404071\pi$
$541$	−3.91969	−	1.62359i	−0.168521	−	0.0698035i	−0.465349	+	0.885127i	$0.654071\pi$
$542$		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	0.0371393	−	0.999310i	$-0.488175\pi$
$547$	−15.0436	−	6.23127i	−0.643218	−	0.266430i	−0.680357	+	0.732880i	$0.738175\pi$
$548$		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	0.895655	−	0.444749i	$-0.146707\pi$
$571$	−1.24625	−	3.00872i	−0.0521541	−	0.125911i	−0.947809	+	0.318838i	$0.896707\pi$
$572$		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	−0.492067	−	0.870557i	$-0.663759\pi$
$601$	−5.50207	+	2.27903i	−0.224434	+	0.0929637i	0.267633	+	0.963521i	$0.413759\pi$
$602$		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	−0.993264	−	0.115872i	$-0.963034\pi$
$607$	−5.14887	+	12.4305i	−0.208986	+	0.504538i	0.784278	+	0.620410i	$0.213034\pi$
$608$		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	−0.905423	−	0.424510i	$-0.860446\pi$
$617$	0.868918	−	2.09775i	0.0349813	−	0.0844524i	0.940405	+	0.340057i	$0.110446\pi$
$618$		0			0
$619$	7.83983	+	18.9270i	0.315109	+	0.760742i	0.999500	+	0.0316257i	$0.0100685\pi$
$619$	7.83983	+	18.9270i	0.315109	+	0.760742i	−0.684390	+	0.729116i	$0.739932\pi$
$620$		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	$0.454961\pi$
$641$	−16.6779	+	40.2639i	−0.658736	+	1.59033i	−0.799758	+	0.600322i	$0.795039\pi$
$642$		0			0
$643$	−5.38229	−	2.22942i	−0.212257	−	0.0879197i	0.274022	−	0.961724i	$-0.411646\pi$
$643$	−5.38229	−	2.22942i	−0.212257	−	0.0879197i	−0.486279	+	0.873804i	$0.661646\pi$
$644$		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	$0.115945\pi$
$653$	13.4307	+	32.4245i	0.525583	+	1.26887i	−0.408808	+	0.912620i	$0.634055\pi$
$654$		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	0.854562	−	0.519350i	$-0.173826\pi$
$673$	−3.03370	−	7.32401i	−0.116941	−	0.282320i	−0.971502	+	0.237030i	$0.923826\pi$
$674$		0			0
$675$	17.2190	−	41.5705i	0.662762	−	1.60005i
$676$		0			0
$677$	20.9413	+	8.67416i	0.804838	+	0.333375i	0.746893	−	0.664945i	$-0.231545\pi$
$677$	20.9413	+	8.67416i	0.804838	+	0.333375i	0.0579459	+	0.998320i	$0.481545\pi$
$678$		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	0.364487	−	0.931208i	$-0.381244\pi$
$683$	−0.947233	−	0.392357i	−0.0362449	−	0.0150131i	−0.400732	+	0.916195i	$0.631244\pi$
$684$		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	−0.241420	−	0.970421i	$-0.577613\pi$
$691$	7.20423	−	2.98409i	0.274062	−	0.113520i	0.515482	+	0.856901i	$0.327613\pi$
$692$		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	−1.00000		0.000460118i	$-0.999854\pi$
$709$	−7.79022	+	18.8073i	−0.292568	+	0.706321i	0.707432	+	0.706781i	$0.249854\pi$
$710$		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	−0.964362	−	0.264585i	$-0.914765\pi$
$719$	−2.55714	+	6.17348i	−0.0953653	+	0.230232i	0.868997	+	0.494817i	$0.164765\pi$
$720$		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	−1.00000		0.000756791i	$-0.999759\pi$
$743$	−7.96910	+	19.2391i	−0.292358	+	0.705815i	0.707642	+	0.706571i	$0.249759\pi$
$744$		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	0.422776	−	0.906234i	$-0.361056\pi$
$751$	2.21753	+	0.918531i	0.0809188	+	0.0335177i	−0.341857	+	0.939752i	$0.611056\pi$
$752$		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	−0.715855	−	0.698249i	$-0.753963\pi$
$787$	7.96910	−	19.2391i	0.284068	−	0.685800i	0.999923	+	0.0124489i	$0.00396271\pi$
$788$		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	$0.0481423\pi$
$809$	11.2659	+	27.1983i	0.396088	+	0.956240i	−0.592497	+	0.805573i	$0.701858\pi$
$810$		0			0
$811$	−5.80432	+	14.0129i	−0.203817	+	0.492058i	−0.992427	−	0.122836i	$-0.960801\pi$
$811$	−5.80432	+	14.0129i	−0.203817	+	0.492058i	0.788610	+	0.614894i	$0.210801\pi$
$812$		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	−0.755410	−	0.655253i	$-0.772562\pi$
$821$	6.93632	−	16.7458i	0.242079	−	0.584431i	0.997489	+	0.0708216i	$0.0225621\pi$
$822$		0			0
$823$	6.98594	+	16.8655i	0.243514	+	0.587896i	0.997627	−	0.0688493i	$-0.0219328\pi$
$823$	6.98594	+	16.8655i	0.243514	+	0.587896i	−0.754113	+	0.656745i	$0.771933\pi$
$824$		0			0
$825$	−2.95807	−	2.95807i	−0.102987	−	0.102987i
$826$		0			0
$827$	−8.23497	+	3.41104i	−0.286358	+	0.118613i	−0.521239	−	0.853411i	$-0.674530\pi$
$827$	−8.23497	+	3.41104i	−0.286358	+	0.118613i	0.234881	+	0.972024i	$0.424530\pi$
$828$		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	−0.692679	−	0.721246i	$-0.743570\pi$
$839$	−19.4787	+	8.06833i	−0.672478	+	0.278550i	0.0202004	+	0.999796i	$0.493570\pi$
$840$		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	0.926695	−	0.375813i	$-0.122637\pi$
$853$	38.4420	+	15.9232i	1.31623	+	0.545199i	0.389532	+	0.921013i	$0.372637\pi$
$854$		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	$-0.976397\pi$
$857$	−10.0843	−	24.3456i	−0.344472	−	0.831630i	0.652780	−	0.757548i	$-0.273603\pi$
$858$		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	0.906690	−	0.421797i	$-0.138600\pi$
$877$	−0.968144	−	2.33731i	−0.0326919	−	0.0789253i	−0.939382	+	0.342872i	$0.888600\pi$
$878$		0			0
$879$	−26.9606	+	65.0886i	−0.909358	+	2.19538i
$880$		0			0
$881$	31.6333	+	13.1030i	1.06575	+	0.441450i	0.845490	−	0.533991i	$-0.179308\pi$
$881$	31.6333	+	13.1030i	1.06575	+	0.441450i	0.220264	+	0.975440i	$0.429308\pi$
$882$		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	0.111050	−	0.993815i	$-0.464579\pi$
$887$	−15.2832	−	6.33049i	−0.513158	−	0.212557i	−0.624209	+	0.781258i	$0.714579\pi$
$888$		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	0.219587	−	0.975593i	$-0.429529\pi$
$907$	32.0652	−	13.2818i	1.06471	−	0.441016i	0.845120	+	0.534577i	$0.179529\pi$
$908$		0			0
$909$	−57.0360	−	57.0360i	−1.89176	−	1.89176i
$910$		0			0
$911$	−2.55714	−	6.17348i	−0.0847219	−	0.204537i	0.875841	−	0.482600i	$-0.160307\pi$
$911$	−2.55714	−	6.17348i	−0.0847219	−	0.204537i	−0.960563	+	0.278063i	$0.910307\pi$
$912$		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	−0.404014	−	0.914753i	$-0.632385\pi$
$929$	−1.30656	+	0.541196i	−0.0428669	+	0.0177561i	0.361147	+	0.932509i	$0.382385\pi$
$930$		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	−0.696941	−	0.717129i	$-0.745456\pi$
$941$	−20.9413	+	8.67416i	−0.682666	+	0.282770i	0.0142749	+	0.999898i	$0.495456\pi$
$942$		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	−0.821097	−	0.570789i	$-0.806637\pi$
$947$	5.01960	−	12.1184i	0.163115	−	0.393795i	0.984212	+	0.176994i	$0.0566374\pi$
$948$		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	0.207033	−	0.978334i	$-0.433619\pi$
$983$	−10.6085	−	4.39420i	−0.338360	−	0.140153i	−0.545393	+	0.838181i	$0.683619\pi$
$984$		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	$0.302121\pi$
$991$	−12.7256	+	30.7224i	−0.404243	+	0.975928i	−0.986624	+	0.163012i	$0.947879\pi$
$992$		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	−0.994502	−	0.104717i	$-0.966606\pi$
$997$	−51.2680	+	21.2359i	−1.62368	+	0.672548i	−0.629173	+	0.777265i	$0.716606\pi$
$998$		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.757.1		16
17.2	even	8	inner	1156.2.h.e.733.1		16
17.3	odd	16		68.2.e.a.13.1	✓	4
17.4	even	4	inner	1156.2.h.e.977.1		16
17.5	odd	16		1156.2.e.c.905.2		4
17.6	odd	16		1156.2.a.h.1.1		4
17.7	odd	16		1156.2.b.a.577.4		4
17.8	even	8	inner	1156.2.h.e.1001.4		16
17.9	even	8	inner	1156.2.h.e.1001.1		16
17.10	odd	16		1156.2.b.a.577.1		4
17.11	odd	16		1156.2.a.h.1.4		4
17.12	odd	16		68.2.e.a.21.1	yes	4
17.13	even	4	inner	1156.2.h.e.977.4		16
17.14	odd	16		1156.2.e.c.829.2		4
17.15	even	8	inner	1156.2.h.e.733.4		16
17.16	even	2	inner	1156.2.h.e.757.4		16
51.20	even	16		612.2.k.e.217.2		4
51.29	even	16		612.2.k.e.361.2		4
68.3	even	16		272.2.o.g.81.2		4
68.11	even	16		4624.2.a.bq.1.1		4
68.23	even	16		4624.2.a.bq.1.4		4
68.63	even	16		272.2.o.g.225.2		4
85.3	even	16		1700.2.m.b.149.2		4
85.12	even	16		1700.2.m.b.1449.2		4
85.29	odd	16		1700.2.o.c.701.2		4
85.37	even	16		1700.2.m.a.149.1		4
85.54	odd	16		1700.2.o.c.1101.2		4
85.63	even	16		1700.2.m.a.1449.1		4
136.3	even	16		1088.2.o.s.897.1		4
136.29	odd	16		1088.2.o.t.769.2		4
136.37	odd	16		1088.2.o.t.897.2		4
136.131	even	16		1088.2.o.s.769.1		4
204.71	odd	16		2448.2.be.u.1441.1		4
204.131	odd	16		2448.2.be.u.1585.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.e.a.13.1	✓	4	17.3	odd	16
68.2.e.a.21.1	yes	4	17.12	odd	16
272.2.o.g.81.2		4	68.3	even	16
272.2.o.g.225.2		4	68.63	even	16
612.2.k.e.217.2		4	51.20	even	16
612.2.k.e.361.2		4	51.29	even	16
1088.2.o.s.769.1		4	136.131	even	16
1088.2.o.s.897.1		4	136.3	even	16
1088.2.o.t.769.2		4	136.29	odd	16
1088.2.o.t.897.2		4	136.37	odd	16
1156.2.a.h.1.1		4	17.6	odd	16
1156.2.a.h.1.4		4	17.11	odd	16
1156.2.b.a.577.1		4	17.10	odd	16
1156.2.b.a.577.4		4	17.7	odd	16
1156.2.e.c.829.2		4	17.14	odd	16
1156.2.e.c.905.2		4	17.5	odd	16
1156.2.h.e.733.1		16	17.2	even	8	inner
1156.2.h.e.733.4		16	17.15	even	8	inner
1156.2.h.e.757.1		16	1.1	even	1	trivial
1156.2.h.e.757.4		16	17.16	even	2	inner
1156.2.h.e.977.1		16	17.4	even	4	inner
1156.2.h.e.977.4		16	17.13	even	4	inner
1156.2.h.e.1001.1		16	17.9	even	8	inner
1156.2.h.e.1001.4		16	17.8	even	8	inner
1700.2.m.a.149.1		4	85.37	even	16
1700.2.m.a.1449.1		4	85.63	even	16
1700.2.m.b.149.2		4	85.3	even	16
1700.2.m.b.1449.2		4	85.12	even	16
1700.2.o.c.701.2		4	85.29	odd	16
1700.2.o.c.1101.2		4	85.54	odd	16
2448.2.be.u.1441.1		4	204.71	odd	16
2448.2.be.u.1585.1		4	204.131	odd	16
4624.2.a.bq.1.1		4	68.11	even	16
4624.2.a.bq.1.4		4	68.23	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

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