LMFDB - Embedded newform 1156.2.h.e.733.1

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			733.1
Root			$-2.12749 - 0.881234i$ of defining polynomial
Character	$\chi$	$=$	1156.733
Dual form			1156.2.h.e.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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	−0.738091	+	0.674701i	$0.764273\pi$
$3$	−3.00872	+	1.24625i	−1.73709	+	0.719525i	−0.998995	+	0.0448236i	$0.985727\pi$
$4$		0			0
$5$	−0.541196	−	1.30656i	−0.242030	−	0.584313i	0.755454	−	0.655202i	$-0.227416\pi$
$5$	−0.541196	−	1.30656i	−0.242030	−	0.584313i	−0.997484	+	0.0708890i	$0.977416\pi$
$6$		0			0
$7$	1.24625	−	3.00872i	0.471039	−	1.13719i	−0.492665	−	0.870219i	$-0.663977\pi$
$7$	1.24625	−	3.00872i	0.471039	−	1.13719i	0.963705	−	0.266971i	$-0.0860227\pi$
$8$		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	$-0.354438\pi$
$11$	0.395595	+	0.163861i	0.119277	+	0.0494059i	−0.322247	+	0.946656i	$0.604438\pi$
$12$		0			0
$13$			2.60555i			0.722650i	0.932440	+	0.361325i	$0.117675\pi$
$13$			2.60555i			0.722650i	−0.932440	+	0.361325i	$0.882325\pi$
$14$		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	0.754516	−	0.656282i	$-0.227872\pi$
$19$	0.428189	+	0.428189i	0.0982334	+	0.0982334i	−0.656282	+	0.754516i	$0.727872\pi$
$20$		0			0
$21$			10.6056i			2.31432i
$22$		0			0
$23$	−5.62185	−	2.32865i	−1.17224	−	0.485556i	−0.290305	−	0.956934i	$-0.593757\pi$
$23$	−5.62185	−	2.32865i	−1.17224	−	0.485556i	−0.881931	+	0.471378i	$0.843757\pi$
$24$		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	$-0.0573869\pi$
$29$	0.868918	+	2.09775i	0.161354	+	0.389543i	−0.822438	+	0.568854i	$0.807387\pi$
$30$		0			0
$31$	−5.62185	+	2.32865i	−1.00971	+	0.418237i	−0.825350	−	0.564621i	$-0.809022\pi$
$31$	−5.62185	+	2.32865i	−1.00971	+	0.418237i	−0.184363	+	0.982858i	$0.559022\pi$
$32$		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	$-0.511609\pi$
$37$	3.91969	−	1.62359i	0.644393	−	0.266916i	0.680854	+	0.732419i	$0.261609\pi$
$38$		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	$-0.839777\pi$
$41$	0.541196	−	1.30656i	0.0845206	−	0.204051i	0.960489	+	0.278317i	$0.0897767\pi$
$42$		0			0
$43$	2.40024	−	2.40024i	0.366033	−	0.366033i	−0.499995	−	0.866028i	$-0.666665\pi$
$43$	2.40024	−	2.40024i	0.366033	−	0.366033i	0.866028	+	0.499995i	$0.166665\pi$
$44$		0			0
$45$	−9.93713	−	4.11609i	−1.48134	−	0.613591i
$46$		0			0
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$		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	0.407194	−	0.913341i	$-0.366507\pi$
$53$	−3.68481	−	3.68481i	−0.506147	−	0.506147i	−0.913341	+	0.407194i	$0.866507\pi$
$54$		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	−0.981852	−	0.189647i	$-0.939266\pi$
$59$	−6.08504	+	6.08504i	−0.792205	+	0.792205i	0.189647	+	0.981852i	$0.439266\pi$
$60$		0			0
$61$	3.36142	−	8.11520i	0.430386	−	1.03904i	−0.548777	−	0.835969i	$-0.684906\pi$
$61$	3.36142	−	8.11520i	0.430386	−	1.03904i	0.979163	−	0.203076i	$-0.0650937\pi$
$62$		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	$-0.546520\pi$
$71$	3.79991	−	1.57398i	0.450967	−	0.186796i	0.596594	+	0.802543i	$0.296520\pi$
$72$		0			0
$73$	−3.78837	−	9.14594i	−0.443395	−	1.07045i	−0.974749	−	0.223301i	$-0.928317\pi$
$73$	−3.78837	−	9.14594i	−0.443395	−	1.07045i	0.531354	−	0.847150i	$-0.321683\pi$
$74$		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	$-0.367332\pi$
$79$	0.395595	+	0.163861i	0.0445080	+	0.0184358i	−0.360318	+	0.932829i	$0.617332\pi$
$80$		0			0
$81$		−	26.0278i		−	2.89197i
$82$		0			0
$83$	−12.5983	−	12.5983i	−1.38284	−	1.38284i	−0.839535	−	0.543305i	$-0.817173\pi$
$83$	−12.5983	−	12.5983i	−1.38284	−	1.38284i	−0.543305	−	0.839535i	$-0.682827\pi$
$84$		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	$-0.864033\pi$
$89$		−	7.81665i		−	0.828564i	0.910149	−	0.414282i	$-0.135967\pi$
$90$		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	0.982947	+	0.183887i	$0.0588679\pi$
$97$	4.11609	+	9.93713i	0.417926	+	1.00896i	−0.565021	+	0.825076i	$0.691132\pi$
$98$		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	0.999973	+	0.00733983i	$0.00233636\pi$
$107$	3.08332	+	7.44378i	0.298075	+	0.719618i	−0.701898	+	0.712278i	$0.747664\pi$
$108$		0			0
$109$	−3.36142	+	8.11520i	−0.321966	+	0.777295i	0.677174	+	0.735823i	$0.263205\pi$
$109$	−3.36142	+	8.11520i	−0.321966	+	0.777295i	−0.999140	+	0.0414716i	$0.986795\pi$
$110$		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	$-0.595632\pi$
$113$	−12.5503	−	5.19849i	−1.18063	−	0.489033i	−0.884692	+	0.466175i	$0.845632\pi$
$114$		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	−0.725849	−	0.687854i	$-0.758553\pi$
$127$	−0.428189	+	0.428189i	−0.0379957	+	0.0379957i	0.687854	+	0.725849i	$0.258553\pi$
$128$		0			0
$129$	−4.23034	+	10.2130i	−0.372461	+	0.899200i
$130$		0			0
$131$	3.41104	+	8.23497i	0.298024	+	0.719493i	0.999974	+	0.00726659i	$0.00231305\pi$
$131$	3.41104	+	8.23497i	0.298024	+	0.719493i	−0.701950	+	0.712226i	$0.747687\pi$
$132$		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	$-0.619219\pi$
$139$	0.395595	−	0.163861i	0.0335540	−	0.0138985i	0.399397	+	0.916778i	$0.369219\pi$
$140$		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	$0.112117\pi$
$149$			8.42221i			0.689974i	−0.938607	+	0.344987i	$0.887883\pi$
$150$		0			0
$151$	−3.25662	−	3.25662i	−0.265020	−	0.265020i	0.562070	−	0.827090i	$-0.310005\pi$
$151$	−3.25662	−	3.25662i	−0.265020	−	0.265020i	−0.827090	+	0.562070i	$0.810005\pi$
$152$		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	$0.109102\pi$
$157$			8.42221i			0.672165i	−0.941833	+	0.336083i	$0.890898\pi$
$158$		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	$-0.798407\pi$
$163$	2.32865	−	5.62185i	0.182394	−	0.440337i	0.988459	+	0.151490i	$0.0484070\pi$
$164$		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	$-0.928674\pi$
$167$	−19.4787	+	8.06833i	−1.50730	+	0.624346i	−0.532305	+	0.846553i	$0.678674\pi$
$168$		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	$-0.918343\pi$
$173$	−19.3589	+	8.01872i	−1.47183	+	0.609652i	−0.504554	+	0.863380i	$0.668343\pi$
$174$		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	−0.187939	−	0.982181i	$-0.560181\pi$
$179$	10.6262	−	10.6262i	0.794242	−	0.794242i	0.982181	+	0.187939i	$0.0601808\pi$
$180$		0			0
$181$	16.9853	+	7.03555i	1.26251	+	0.522948i	0.910679	−	0.413116i	$-0.135559\pi$
$181$	16.9853	+	7.03555i	1.26251	+	0.522948i	0.351830	+	0.936064i	$0.385559\pi$
$182$		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	$-0.921011\pi$
$191$		−	6.78890i		−	0.491227i	0.969368	−	0.245614i	$-0.0789895\pi$
$192$		0			0
$193$	−10.7283	−	4.44382i	−0.772242	−	0.319873i	−0.0384615	−	0.999260i	$-0.512246\pi$
$193$	−10.7283	−	4.44382i	−0.772242	−	0.319873i	−0.733780	+	0.679387i	$0.762246\pi$
$194$		0			0
$195$	−8.48528	+	8.48528i	−0.607644	+	0.607644i
$196$		0			0
$197$	9.52806	−	23.0028i	0.678846	−	1.63888i	−0.0872765	−	0.996184i	$-0.527816\pi$
$197$	9.52806	−	23.0028i	0.678846	−	1.63888i	0.766122	−	0.642695i	$-0.222184\pi$
$198$		0			0
$199$	5.47660	+	13.2217i	0.388226	+	0.937259i	0.990316	+	0.138832i	$0.0443347\pi$
$199$	5.47660	+	13.2217i	0.388226	+	0.937259i	−0.602090	+	0.798428i	$0.705665\pi$
$200$		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	−0.316590	−	0.948563i	$-0.602538\pi$
$211$	8.39605	−	20.2699i	0.578008	−	1.39543i	0.894598	−	0.446872i	$-0.147462\pi$
$212$		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	0.145688	−	0.989331i	$-0.453461\pi$
$223$	−12.5983	−	12.5983i	−0.843643	−	0.843643i	−0.989331	+	0.145688i	$0.953461\pi$
$224$		0			0
$225$		−	22.8167i		−	1.52111i
$226$		0			0
$227$	−0.395595	−	0.163861i	−0.0262566	−	0.0108758i	0.369516	−	0.929224i	$-0.379523\pi$
$227$	−0.395595	−	0.163861i	−0.0262566	−	0.0108758i	−0.395773	+	0.918348i	$0.629523\pi$
$228$		0			0
$229$	3.25662	−	3.25662i	0.215203	−	0.215203i	−0.591270	−	0.806474i	$-0.701373\pi$
$229$	3.25662	−	3.25662i	0.215203	−	0.215203i	0.806474	+	0.591270i	$0.201373\pi$
$230$		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	$-0.208614\pi$
$233$	−3.03370	−	7.32401i	−0.198744	−	0.479812i	−0.991560	+	0.129650i	$0.958614\pi$
$234$		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	$-0.490550\pi$
$241$	11.7591	−	4.87076i	0.757468	−	0.313754i	0.727785	+	0.685806i	$0.240550\pi$
$242$		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	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$		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	0.990798	−	0.135346i	$-0.0432146\pi$
$257$	13.7139	+	13.7139i	0.855452	+	0.855452i	−0.135346	+	0.990798i	$0.543215\pi$
$258$		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	0.00406616	−	0.999992i	$-0.498706\pi$
$263$	16.2831	−	16.2831i	1.00406	−	1.00406i	0.999992	−	0.00406616i	$-0.00129430\pi$
$264$		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	$-0.895488\pi$
$269$	−22.7632	+	9.42883i	−1.38790	+	0.574886i	−0.441316	+	0.897352i	$0.645488\pi$
$270$		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	$-0.0760469\pi$
$277$	1.95131	+	4.71088i	0.117243	+	0.283049i	−0.854354	+	0.519691i	$0.826047\pi$
$278$		0			0
$279$	−17.7106	+	42.7572i	−1.06031	+	2.55981i
$280$		0			0
$281$	−13.0265	+	13.0265i	−0.777094	+	0.777094i	−0.979336	−	0.202242i	$-0.935177\pi$
$281$	−13.0265	+	13.0265i	−0.777094	+	0.777094i	0.202242	+	0.979336i	$0.435177\pi$
$282$		0			0
$283$	−2.76917	−	1.14703i	−0.164610	−	0.0681837i	0.298857	−	0.954298i	$-0.403395\pi$
$283$	−2.76917	−	1.14703i	−0.164610	−	0.0681837i	−0.463467	+	0.886114i	$0.653395\pi$
$284$		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	$0.217731\pi$
$293$			21.6333i			1.26383i	−0.775037	+	0.631916i	$0.782269\pi$
$294$		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	0.892572	+	0.450906i	$0.148899\pi$
$311$	10.2331	+	24.7049i	0.580267	+	1.40089i	−0.312305	+	0.949982i	$0.601101\pi$
$312$		0			0
$313$	3.36142	−	8.11520i	0.189999	−	0.458698i	−0.799960	−	0.600053i	$-0.795146\pi$
$313$	3.36142	−	8.11520i	0.189999	−	0.458698i	0.989959	+	0.141355i	$0.0451460\pi$
$314$		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	$-0.659088\pi$
$317$	−25.6159	−	10.6104i	−1.43873	−	0.595942i	−0.959490	+	0.281741i	$0.909088\pi$
$318$		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	−0.769988	−	0.638059i	$-0.779738\pi$
$331$	−2.40024	+	2.40024i	−0.131929	+	0.131929i	0.638059	+	0.769988i	$0.279738\pi$
$332$		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	$-0.410332\pi$
$337$	21.1808	−	8.77339i	1.15379	−	0.477917i	0.875804	+	0.482667i	$0.160332\pi$
$338$		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	$-0.942120\pi$
$347$	−2.98409	+	7.20423i	−0.160194	+	0.386743i	0.823319	+	0.567579i	$0.192120\pi$
$348$		0			0
$349$	−16.7113	+	16.7113i	−0.894534	+	0.894534i	−0.994946	−	0.100412i	$-0.967984\pi$
$349$	−16.7113	+	16.7113i	−0.894534	+	0.894534i	0.100412	+	0.994946i	$0.467984\pi$
$350$		0			0
$351$	−36.1047	−	14.9550i	−1.92712	−	0.798241i
$352$		0			0
$353$		−	31.2111i		−	1.66120i	−0.556870	−	0.830600i	$-0.687998\pi$
$353$		−	31.2111i		−	1.66120i	0.556870	−	0.830600i	$-0.312002\pi$
$354$		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	0.945458	−	0.325744i	$-0.105615\pi$
$359$	11.7419	+	11.7419i	0.619714	+	0.619714i	−0.325744	+	0.945458i	$0.605615\pi$
$360$		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	$-0.792927\pi$
$367$	3.73876	−	9.02616i	0.195162	−	0.471162i	0.990920	+	0.134452i	$0.0429275\pi$
$368$		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	−0.896251	−	0.443548i	$-0.853720\pi$
$379$	−11.2163	−	27.0785i	−0.576142	−	1.39093i	0.320109	−	0.947381i	$-0.396280\pi$
$380$		0			0
$381$	0.754670	−	1.82194i	0.0386629	−	0.0933406i
$382$		0			0
$383$	13.7139	−	13.7139i	0.700750	−	0.700750i	−0.263822	−	0.964571i	$-0.584983\pi$
$383$	13.7139	−	13.7139i	0.700750	−	0.700750i	0.964571	+	0.263822i	$0.0849830\pi$
$384$		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	0.500592	−	0.865683i	$-0.333116\pi$
$389$	−7.20071	−	7.20071i	−0.365091	−	0.365091i	−0.865683	+	0.500592i	$0.833116\pi$
$390$		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	$-0.478481\pi$
$397$	−11.7591	−	4.87076i	−0.590171	−	0.244457i	−0.657724	+	0.753259i	$0.728481\pi$
$398$		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	$-0.795497\pi$
$401$	3.78837	−	9.14594i	0.189182	−	0.456726i	0.989803	+	0.142445i	$0.0454966\pi$
$402$		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	$-0.400348\pi$
$419$	−3.00872	−	1.24625i	−0.146986	−	0.0608835i	−0.454964	+	0.890510i	$0.650348\pi$
$420$		0			0
$421$			18.6056i			0.906779i	0.891312	+	0.453390i	$0.149785\pi$
$421$			18.6056i			0.906779i	−0.891312	+	0.453390i	$0.850215\pi$
$422$		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	$-0.395403\pi$
$431$	−2.45708	−	1.01776i	−0.118354	−	0.0490237i	−0.441074	+	0.897471i	$0.645403\pi$
$432$		0			0
$433$	−10.6262	+	10.6262i	−0.510664	+	0.510664i	−0.914730	−	0.404066i	$-0.867597\pi$
$433$	−10.6262	+	10.6262i	−0.510664	+	0.510664i	0.404066	+	0.914730i	$0.367597\pi$
$434$		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	$-0.277319\pi$
$439$	34.3662	−	14.2350i	1.64021	−	0.679398i	0.996319	+	0.0857193i	$0.0273188\pi$
$440$		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	0.549936	+	0.835207i	$0.314652\pi$
$449$	−9.10111	+	21.9720i	−0.429508	+	1.03692i	−0.979444	+	0.201717i	$0.935348\pi$
$450$		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	0.970763	+	0.240041i	$0.0771610\pi$
$457$	25.8840	+	25.8840i	1.21080	+	1.21080i	0.240041	+	0.970763i	$0.422839\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.6554	+	20.6554i	0.962016	+	0.962016i	0.999305	−	0.0372881i	$-0.0118719\pi$
$461$	20.6554	+	20.6554i	0.962016	+	0.962016i	−0.0372881	+	0.999305i	$0.511872\pi$
$462$		0			0
$463$			39.6333i			1.84192i	0.389662	+	0.920958i	$0.372592\pi$
$463$			39.6333i			1.84192i	−0.389662	+	0.920958i	$0.627408\pi$
$464$		0			0
$465$	−25.8917	−	10.7247i	−1.20070	−	0.497346i
$466$		0			0
$467$	11.4826	−	11.4826i	0.531352	−	0.531352i	−0.389623	−	0.920975i	$-0.627395\pi$
$467$	11.4826	−	11.4826i	0.531352	−	0.531352i	0.920975	+	0.389623i	$0.127395\pi$
$468$		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	$-0.494883\pi$
$479$	16.0744	−	6.65821i	0.734456	−	0.304222i	0.718382	+	0.695649i	$0.244883\pi$
$480$		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	$-0.187601\pi$
$487$	22.6434	+	9.37922i	1.02607	+	0.425013i	0.194779	+	0.980847i	$0.437601\pi$
$488$		0			0
$489$			19.8167i			0.896140i
$490$		0			0
$491$	6.94142	+	6.94142i	0.313262	+	0.313262i	0.846172	−	0.532910i	$-0.178902\pi$
$491$	6.94142	+	6.94142i	0.313262	+	0.313262i	−0.532910	+	0.846172i	$0.678902\pi$
$492$		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	$-0.269256\pi$
$499$	13.4612	+	5.57582i	0.602607	+	0.249608i	−0.0604568	+	0.998171i	$0.519256\pi$
$500$		0			0
$501$	48.5507	−	48.5507i	2.16909	−	2.16909i
$502$		0			0
$503$	−14.8904	+	35.9486i	−0.663930	+	1.60287i	0.127661	+	0.991818i	$0.459253\pi$
$503$	−14.8904	+	35.9486i	−0.663930	+	1.60287i	−0.791591	+	0.611052i	$0.790747\pi$
$504$		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	$-0.506937\pi$
$521$	−16.9853	−	7.03555i	−0.744140	−	0.308233i	−0.722348	+	0.691530i	$0.756937\pi$
$522$		0			0
$523$		−	12.0000i		−	0.524723i	−0.964970	−	0.262362i	$-0.915499\pi$
$523$		−	12.0000i		−	0.524723i	0.964970	−	0.262362i	$-0.0845013\pi$
$524$		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	$-0.654071\pi$
$541$	−3.91969	+	1.62359i	−0.168521	+	0.0698035i	0.296828	+	0.954931i	$0.404071\pi$
$542$		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	$-0.738175\pi$
$547$	−15.0436	+	6.23127i	−0.643218	+	0.266430i	0.0371393	+	0.999310i	$0.488175\pi$
$548$		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	$-0.850262\pi$
$557$		−	21.3944i		−	0.906512i	0.891380	−	0.453256i	$-0.149738\pi$
$558$		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	0.944003	−	0.329937i	$-0.107028\pi$
$563$	14.5703	+	14.5703i	0.614066	+	0.614066i	−0.329937	+	0.944003i	$0.607028\pi$
$564$		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	−0.995593	−	0.0937741i	$-0.970107\pi$
$569$	−21.5117	+	21.5117i	−0.901819	+	0.901819i	0.0937741	+	0.995593i	$0.470107\pi$
$570$		0			0
$571$	−1.24625	+	3.00872i	−0.0521541	+	0.125911i	−0.947809	−	0.318838i	$-0.896707\pi$
$571$	−1.24625	+	3.00872i	−0.0521541	+	0.125911i	0.895655	+	0.444749i	$0.146707\pi$
$572$		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	−0.636698	−	0.771113i	$-0.719700\pi$
$587$	3.25662	−	3.25662i	0.134415	−	0.134415i	0.771113	+	0.636698i	$0.219700\pi$
$588$		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	0.683828	−	0.729643i	$-0.260314\pi$
$593$	−1.11567	−	1.11567i	−0.0458151	−	0.0458151i	−0.729643	+	0.683828i	$0.760314\pi$
$594$		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	$-0.821328\pi$
$599$		−	26.0555i		−	1.06460i	0.846556	−	0.532300i	$-0.178672\pi$
$600$		0			0
$601$	−5.50207	−	2.27903i	−0.224434	−	0.0929637i	0.267633	−	0.963521i	$-0.413759\pi$
$601$	−5.50207	−	2.27903i	−0.224434	−	0.0929637i	−0.492067	+	0.870557i	$0.663759\pi$
$602$		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	$-0.213034\pi$
$607$	−5.14887	−	12.4305i	−0.208986	−	0.504538i	−0.993264	+	0.115872i	$0.963034\pi$
$608$		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	$-0.110446\pi$
$617$	0.868918	+	2.09775i	0.0349813	+	0.0844524i	−0.905423	+	0.424510i	$0.860446\pi$
$618$		0			0
$619$	7.83983	−	18.9270i	0.315109	−	0.760742i	−0.684390	−	0.729116i	$-0.739932\pi$
$619$	7.83983	−	18.9270i	0.315109	−	0.760742i	0.999500	−	0.0316257i	$-0.0100685\pi$
$620$		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	0.960520	−	0.278209i	$-0.0897409\pi$
$631$	17.1395	+	17.1395i	0.682311	+	0.682311i	−0.278209	+	0.960520i	$0.589741\pi$
$632$		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	−0.799758	−	0.600322i	$-0.795039\pi$
$641$	−16.6779	−	40.2639i	−0.658736	−	1.59033i	0.141023	−	0.990006i	$-0.454961\pi$
$642$		0			0
$643$	−5.38229	+	2.22942i	−0.212257	+	0.0879197i	−0.486279	−	0.873804i	$-0.661646\pi$
$643$	−5.38229	+	2.22942i	−0.212257	+	0.0879197i	0.274022	+	0.961724i	$0.411646\pi$
$644$		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	−0.408808	−	0.912620i	$-0.634055\pi$
$653$	13.4307	−	32.4245i	0.525583	−	1.26887i	0.934391	−	0.356249i	$-0.115945\pi$
$654$		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	$-0.785803\pi$
$659$		−	32.0000i		−	1.24654i	0.782006	−	0.623272i	$-0.214197\pi$
$660$		0			0
$661$	0.856379	+	0.856379i	0.0333093	+	0.0333093i	0.723565	−	0.690256i	$-0.242502\pi$
$661$	0.856379	+	0.856379i	0.0333093	+	0.0333093i	−0.690256	+	0.723565i	$0.742502\pi$
$662$		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	$-0.923826\pi$
$673$	−3.03370	+	7.32401i	−0.116941	+	0.282320i	0.854562	+	0.519350i	$0.173826\pi$
$674$		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	$-0.481545\pi$
$677$	20.9413	−	8.67416i	0.804838	−	0.333375i	0.746893	+	0.664945i	$0.231545\pi$
$678$		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	$-0.631244\pi$
$683$	−0.947233	+	0.392357i	−0.0362449	+	0.0150131i	0.364487	+	0.931208i	$0.381244\pi$
$684$		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	$-0.327613\pi$
$691$	7.20423	+	2.98409i	0.274062	+	0.113520i	−0.241420	+	0.970421i	$0.577613\pi$
$692$		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	$0.0471598\pi$
$701$			7.81665i			0.295231i	−0.989045	+	0.147615i	$0.952840\pi$
$702$		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	$-0.249854\pi$
$709$	−7.79022	−	18.8073i	−0.292568	−	0.706321i	−1.00000		0.000460118i	$0.999854\pi$
$710$		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	$-0.164765\pi$
$719$	−2.55714	−	6.17348i	−0.0953653	−	0.230232i	−0.964362	+	0.264585i	$0.914765\pi$
$720$		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	$-0.962001\pi$
$727$		−	6.42221i		−	0.238186i	0.992883	−	0.119093i	$-0.0379987\pi$
$728$		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	−0.973293	−	0.229566i	$-0.926269\pi$
$733$	−32.5662	−	32.5662i	−1.20286	−	1.20286i	−0.229566	−	0.973293i	$-0.573731\pi$
$734$		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	−0.0939921	−	0.995573i	$-0.529963\pi$
$739$	24.5091	−	24.5091i	0.901581	−	0.901581i	0.995573	+	0.0939921i	$0.0299628\pi$
$740$		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	$-0.249759\pi$
$743$	−7.96910	−	19.2391i	−0.292358	−	0.705815i	−1.00000		0.000756791i	$0.999759\pi$
$744$		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	$-0.611056\pi$
$751$	2.21753	−	0.918531i	0.0809188	−	0.0335177i	0.422776	+	0.906234i	$0.361056\pi$
$752$		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	−0.00302702	+	0.999995i	$0.500964\pi$
$757$	−27.5968	+	27.5968i	−1.00302	+	1.00302i	−0.999995	+	0.00302702i	$0.999036\pi$
$758$		0			0
$759$	7.83938	+	3.24718i	0.284551	+	0.117865i
$760$		0			0
$761$		−	31.4500i		−	1.14006i	−0.821624	−	0.570030i	$-0.806932\pi$
$761$		−	31.4500i		−	1.14006i	0.821624	−	0.570030i	$-0.193068\pi$
$762$		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	$0.108894\pi$
$769$			18.6056i			0.670933i	−0.942052	+	0.335467i	$0.891106\pi$
$770$		0			0
$771$	−58.3525	−	24.1704i	−2.10151	−	0.870475i
$772$		0			0
$773$	−20.2272	+	20.2272i	−0.727521	+	0.727521i	−0.970125	−	0.242604i	$-0.921998\pi$
$773$	−20.2272	+	20.2272i	−0.727521	+	0.727521i	0.242604	+	0.970125i	$0.421998\pi$
$774$		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	$-0.00396271\pi$
$787$	7.96910	+	19.2391i	0.284068	+	0.685800i	−0.715855	+	0.698249i	$0.753963\pi$
$788$		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	0.660140	−	0.751143i	$-0.270497\pi$
$797$	−2.56914	−	2.56914i	−0.0910035	−	0.0910035i	−0.751143	+	0.660140i	$0.770497\pi$
$798$		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	−0.592497	−	0.805573i	$-0.701858\pi$
$809$	11.2659	−	27.1983i	0.396088	−	0.956240i	0.988585	−	0.150667i	$-0.0481423\pi$
$810$		0			0
$811$	−5.80432	−	14.0129i	−0.203817	−	0.492058i	0.788610	−	0.614894i	$-0.210801\pi$
$811$	−5.80432	−	14.0129i	−0.203817	−	0.492058i	−0.992427	+	0.122836i	$0.960801\pi$
$812$		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	$-0.0225621\pi$
$821$	6.93632	+	16.7458i	0.242079	+	0.584431i	−0.755410	+	0.655253i	$0.772562\pi$
$822$		0			0
$823$	6.98594	−	16.8655i	0.243514	−	0.587896i	−0.754113	−	0.656745i	$-0.771933\pi$
$823$	6.98594	−	16.8655i	0.243514	−	0.587896i	0.997627	+	0.0688493i	$0.0219328\pi$
$824$		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	$-0.424530\pi$
$827$	−8.23497	−	3.41104i	−0.286358	−	0.118613i	−0.521239	+	0.853411i	$0.674530\pi$
$828$		0			0
$829$		−	18.8444i		−	0.654493i	−0.944939	−	0.327247i	$-0.893879\pi$
$829$		−	18.8444i		−	0.654493i	0.944939	−	0.327247i	$-0.106121\pi$
$830$		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	$-0.493570\pi$
$839$	−19.4787	−	8.06833i	−0.672478	−	0.278550i	−0.692679	+	0.721246i	$0.743570\pi$
$840$		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	$-0.372637\pi$
$853$	38.4420	−	15.9232i	1.31623	−	0.545199i	0.926695	+	0.375813i	$0.122637\pi$
$854$		0			0
$855$	−2.49251	−	6.01744i	−0.0852419	−	0.205792i
$856$		0			0
$857$	−10.0843	+	24.3456i	−0.344472	+	0.831630i	0.652780	+	0.757548i	$0.273603\pi$
$857$	−10.0843	+	24.3456i	−0.344472	+	0.831630i	−0.997252	+	0.0740819i	$0.976397\pi$
$858$		0			0
$859$	−1.28457	+	1.28457i	−0.0438289	+	0.0438289i	−0.728682	−	0.684853i	$-0.759867\pi$
$859$	−1.28457	+	1.28457i	−0.0438289	+	0.0438289i	0.684853	+	0.728682i	$0.259867\pi$
$860$		0			0
$861$	13.8568	+	5.73968i	0.472239	+	0.195608i
$862$		0			0
$863$		−	52.4777i		−	1.78636i	−0.449697	−	0.893181i	$-0.648468\pi$
$863$		−	52.4777i		−	1.78636i	0.449697	−	0.893181i	$-0.351532\pi$
$864$		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	$-0.888600\pi$
$877$	−0.968144	+	2.33731i	−0.0326919	+	0.0789253i	0.906690	+	0.421797i	$0.138600\pi$
$878$		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	$-0.429308\pi$
$881$	31.6333	−	13.1030i	1.06575	−	0.441450i	0.845490	+	0.533991i	$0.179308\pi$
$882$		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	$-0.714579\pi$
$887$	−15.2832	+	6.33049i	−0.513158	+	0.212557i	0.111050	+	0.993815i	$0.464579\pi$
$888$		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	$-0.179529\pi$
$907$	32.0652	+	13.2818i	1.06471	+	0.441016i	0.219587	+	0.975593i	$0.429529\pi$
$908$		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	$-0.910307\pi$
$911$	−2.55714	+	6.17348i	−0.0847219	+	0.204537i	0.875841	+	0.482600i	$0.160307\pi$
$912$		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	$-0.382385\pi$
$929$	−1.30656	−	0.541196i	−0.0428669	−	0.0177561i	−0.404014	+	0.914753i	$0.632385\pi$
$930$		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	0.777382	−	0.629028i	$-0.216547\pi$
$937$	4.54118	+	4.54118i	0.148354	+	0.148354i	−0.629028	+	0.777382i	$0.716547\pi$
$938$		0			0
$939$			28.6056i			0.933507i
$940$		0			0
$941$	−20.9413	−	8.67416i	−0.682666	−	0.282770i	0.0142749	−	0.999898i	$-0.495456\pi$
$941$	−20.9413	−	8.67416i	−0.682666	−	0.282770i	−0.696941	+	0.717129i	$0.745456\pi$
$942$		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	$-0.0566374\pi$
$947$	5.01960	+	12.1184i	0.163115	+	0.393795i	−0.821097	+	0.570789i	$0.806637\pi$
$948$		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	0.414129	−	0.910218i	$-0.364086\pi$
$967$	−15.4267	−	15.4267i	−0.496089	−	0.496089i	−0.910218	+	0.414129i	$0.864086\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	38.9105	+	38.9105i	1.24870	+	1.24870i	0.956296	+	0.292402i	$0.0944545\pi$
$971$	38.9105	+	38.9105i	1.24870	+	1.24870i	0.292402	+	0.956296i	$0.405546\pi$
$972$		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	−0.490424	−	0.871484i	$-0.663158\pi$
$977$	11.9108	−	11.9108i	0.381060	−	0.381060i	0.871484	+	0.490424i	$0.163158\pi$
$978$		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	$-0.683619\pi$
$983$	−10.6085	+	4.39420i	−0.338360	+	0.140153i	0.207033	+	0.978334i	$0.433619\pi$
$984$		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	−0.986624	−	0.163012i	$-0.947879\pi$
$991$	−12.7256	−	30.7224i	−0.404243	−	0.975928i	0.582381	−	0.812916i	$-0.302121\pi$
$992$		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	$-0.716606\pi$
$997$	−51.2680	−	21.2359i	−1.62368	−	0.672548i	−0.994502	+	0.104717i	$0.966606\pi$
$998$		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.733.1		16
17.2	even	8	inner	1156.2.h.e.977.1		16
17.3	odd	16		1156.2.a.h.1.1		4
17.4	even	4	inner	1156.2.h.e.1001.4		16
17.5	odd	16		1156.2.b.a.577.1		4
17.6	odd	16		68.2.e.a.21.1	yes	4
17.7	odd	16		1156.2.e.c.829.2		4
17.8	even	8	inner	1156.2.h.e.757.4		16
17.9	even	8	inner	1156.2.h.e.757.1		16
17.10	odd	16		68.2.e.a.13.1	✓	4
17.11	odd	16		1156.2.e.c.905.2		4
17.12	odd	16		1156.2.b.a.577.4		4
17.13	even	4	inner	1156.2.h.e.1001.1		16
17.14	odd	16		1156.2.a.h.1.4		4
17.15	even	8	inner	1156.2.h.e.977.4		16
17.16	even	2	inner	1156.2.h.e.733.4		16
51.23	even	16		612.2.k.e.361.2		4
51.44	even	16		612.2.k.e.217.2		4
68.3	even	16		4624.2.a.bq.1.4		4
68.23	even	16		272.2.o.g.225.2		4
68.27	even	16		272.2.o.g.81.2		4
68.31	even	16		4624.2.a.bq.1.1		4
85.23	even	16		1700.2.m.a.1449.1		4
85.27	even	16		1700.2.m.a.149.1		4
85.44	odd	16		1700.2.o.c.1101.2		4
85.57	even	16		1700.2.m.b.1449.2		4
85.74	odd	16		1700.2.o.c.701.2		4
85.78	even	16		1700.2.m.b.149.2		4
136.27	even	16		1088.2.o.s.897.1		4
136.61	odd	16		1088.2.o.t.897.2		4
136.91	even	16		1088.2.o.s.769.1		4
136.125	odd	16		1088.2.o.t.769.2		4
204.23	odd	16		2448.2.be.u.1585.1		4
204.95	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	17.10	odd	16
68.2.e.a.21.1	yes	4	17.6	odd	16
272.2.o.g.81.2		4	68.27	even	16
272.2.o.g.225.2		4	68.23	even	16
612.2.k.e.217.2		4	51.44	even	16
612.2.k.e.361.2		4	51.23	even	16
1088.2.o.s.769.1		4	136.91	even	16
1088.2.o.s.897.1		4	136.27	even	16
1088.2.o.t.769.2		4	136.125	odd	16
1088.2.o.t.897.2		4	136.61	odd	16
1156.2.a.h.1.1		4	17.3	odd	16
1156.2.a.h.1.4		4	17.14	odd	16
1156.2.b.a.577.1		4	17.5	odd	16
1156.2.b.a.577.4		4	17.12	odd	16
1156.2.e.c.829.2		4	17.7	odd	16
1156.2.e.c.905.2		4	17.11	odd	16
1156.2.h.e.733.1		16	1.1	even	1	trivial
1156.2.h.e.733.4		16	17.16	even	2	inner
1156.2.h.e.757.1		16	17.9	even	8	inner
1156.2.h.e.757.4		16	17.8	even	8	inner
1156.2.h.e.977.1		16	17.2	even	8	inner
1156.2.h.e.977.4		16	17.15	even	8	inner
1156.2.h.e.1001.1		16	17.13	even	4	inner
1156.2.h.e.1001.4		16	17.4	even	4	inner
1700.2.m.a.149.1		4	85.27	even	16
1700.2.m.a.1449.1		4	85.23	even	16
1700.2.m.b.149.2		4	85.78	even	16
1700.2.m.b.1449.2		4	85.57	even	16
1700.2.o.c.701.2		4	85.74	odd	16
1700.2.o.c.1101.2		4	85.44	odd	16
2448.2.be.u.1441.1		4	204.95	odd	16
2448.2.be.u.1585.1		4	204.23	odd	16
4624.2.a.bq.1.1		4	68.31	even	16
4624.2.a.bq.1.4		4	68.3	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)

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