LMFDB - Embedded newform 1156.2.h.e.977.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1156.733");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			977.4
Root			$-0.881234 - 2.12749i$ of defining polynomial
Character	$\chi$	$=$	1156.977
Dual form			1156.2.h.e.1001.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24625 - 3.00872i) q^{3} +(-1.30656 - 0.541196i) q^{5} +(3.00872 - 1.24625i) q^{7} +(-5.37794 - 5.37794i) q^{9} +O(q^{10})$	\(q+(1.24625 - 3.00872i) q^{3} +(-1.30656 - 0.541196i) q^{5} +(3.00872 - 1.24625i) q^{7} +(-5.37794 - 5.37794i) q^{9} +(-0.163861 - 0.395595i) q^{11} -2.60555i q^{13} +(-3.25662 + 3.25662i) q^{15} +(-0.428189 + 0.428189i) q^{19} -10.6056i q^{21} +(2.32865 + 5.62185i) q^{23} +(-2.12132 - 2.12132i) q^{25} +(-13.8568 + 5.73968i) q^{27} +(2.09775 + 0.868918i) q^{29} +(2.32865 - 5.62185i) q^{31} -1.39445 q^{33} -4.60555 q^{35} +(-1.62359 + 3.91969i) q^{37} +(-7.83938 - 3.24718i) q^{39} +(1.30656 - 0.541196i) q^{41} +(-2.40024 - 2.40024i) q^{43} +(4.11609 + 9.93713i) q^{45} +4.00000i q^{47} +(2.54951 - 2.54951i) q^{49} +(3.68481 - 3.68481i) q^{53} +0.605551i q^{55} +(0.754670 + 1.82194i) q^{57} +(6.08504 + 6.08504i) q^{59} +(8.11520 - 3.36142i) q^{61} +(-22.8830 - 9.47844i) q^{63} +(-1.41011 + 3.40432i) q^{65} -9.21110 q^{67} +19.8167 q^{69} +(-1.57398 + 3.79991i) q^{71} +(-9.14594 - 3.78837i) q^{73} +(-9.02616 + 3.73876i) q^{75} +(-0.986024 - 0.986024i) q^{77} +(-0.163861 - 0.395595i) q^{79} +26.0278i q^{81} +(12.5983 - 12.5983i) q^{83} +(5.22866 - 5.22866i) q^{87} +7.81665i q^{89} +(-3.24718 - 7.83938i) q^{91} +(-14.0125 - 14.0125i) q^{93} +(0.791191 - 0.327722i) q^{95} +(9.93713 + 4.11609i) q^{97} +(-1.24625 + 3.00872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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
$3$	1.24625	−	3.00872i	0.719525	−	1.73709i	0.0448236	−	0.998995i	$-0.485727\pi$
$3$	1.24625	−	3.00872i	0.719525	−	1.73709i	0.674701	−	0.738091i	$-0.264273\pi$
$4$		0			0
$5$	−1.30656	−	0.541196i	−0.584313	−	0.242030i	0.0708890	−	0.997484i	$-0.477416\pi$
$5$	−1.30656	−	0.541196i	−0.584313	−	0.242030i	−0.655202	+	0.755454i	$0.727416\pi$
$6$		0			0
$7$	3.00872	−	1.24625i	1.13719	−	0.471039i	0.266971	−	0.963705i	$-0.413977\pi$
$7$	3.00872	−	1.24625i	1.13719	−	0.471039i	0.870219	+	0.492665i	$0.163977\pi$
$8$		0			0
$9$	−5.37794	−	5.37794i	−1.79265	−	1.79265i
$10$		0			0
$11$	−0.163861	−	0.395595i	−0.0494059	−	0.119277i	0.897250	−	0.441524i	$-0.145562\pi$
$11$	−0.163861	−	0.395595i	−0.0494059	−	0.119277i	−0.946656	+	0.322247i	$0.895562\pi$
$12$		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	−0.754516	−	0.656282i	$-0.772128\pi$
$19$	−0.428189	+	0.428189i	−0.0982334	+	0.0982334i	0.656282	+	0.754516i	$0.272128\pi$
$20$		0			0
$21$		−	10.6056i		−	2.31432i
$22$		0			0
$23$	2.32865	+	5.62185i	0.485556	+	1.17224i	0.956934	+	0.290305i	$0.0937567\pi$
$23$	2.32865	+	5.62185i	0.485556	+	1.17224i	−0.471378	+	0.881931i	$0.656243\pi$
$24$		0			0
$25$	−2.12132	−	2.12132i	−0.424264	−	0.424264i
$26$		0			0
$27$	−13.8568	+	5.73968i	−2.66675	+	1.10460i
$28$		0			0
$29$	2.09775	+	0.868918i	0.389543	+	0.161354i	0.568854	−	0.822438i	$-0.307387\pi$
$29$	2.09775	+	0.868918i	0.389543	+	0.161354i	−0.179311	+	0.983792i	$0.557387\pi$
$30$		0			0
$31$	2.32865	−	5.62185i	0.418237	−	1.00971i	−0.564621	−	0.825350i	$-0.690978\pi$
$31$	2.32865	−	5.62185i	0.418237	−	1.00971i	0.982858	−	0.184363i	$-0.0590223\pi$
$32$		0			0
$33$	−1.39445			−0.242742
$34$		0			0
$35$	−4.60555			−0.778480
$36$		0			0
$37$	−1.62359	+	3.91969i	−0.266916	+	0.644393i	−0.999335	−	0.0364615i	$-0.988391\pi$
$37$	−1.62359	+	3.91969i	−0.266916	+	0.644393i	0.732419	+	0.680854i	$0.238391\pi$
$38$		0			0
$39$	−7.83938	−	3.24718i	−1.25531	−	0.519964i
$40$		0			0
$41$	1.30656	−	0.541196i	0.204051	−	0.0845206i	−0.278317	−	0.960489i	$-0.589777\pi$
$41$	1.30656	−	0.541196i	0.204051	−	0.0845206i	0.482368	+	0.875969i	$0.339777\pi$
$42$		0			0
$43$	−2.40024	−	2.40024i	−0.366033	−	0.366033i	0.499995	−	0.866028i	$-0.333335\pi$
$43$	−2.40024	−	2.40024i	−0.366033	−	0.366033i	−0.866028	+	0.499995i	$0.833335\pi$
$44$		0			0
$45$	4.11609	+	9.93713i	0.613591	+	1.48134i
$46$		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	−0.407194	−	0.913341i	$-0.633493\pi$
$53$	3.68481	−	3.68481i	0.506147	−	0.506147i	0.913341	+	0.407194i	$0.133493\pi$
$54$		0			0
$55$			0.605551i			0.0816525i
$56$		0			0
$57$	0.754670	+	1.82194i	0.0999585	+	0.241321i
$58$		0			0
$59$	6.08504	+	6.08504i	0.792205	+	0.792205i	0.981852	−	0.189647i	$-0.0607344\pi$
$59$	6.08504	+	6.08504i	0.792205	+	0.792205i	−0.189647	+	0.981852i	$0.560734\pi$
$60$		0			0
$61$	8.11520	−	3.36142i	1.03904	−	0.430386i	0.203076	−	0.979163i	$-0.434906\pi$
$61$	8.11520	−	3.36142i	1.03904	−	0.430386i	0.835969	+	0.548777i	$0.184906\pi$
$62$		0			0
$63$	−22.8830	−	9.47844i	−2.88299	−	1.19417i
$64$		0			0
$65$	−1.41011	+	3.40432i	−0.174903	+	0.422254i
$66$		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
$71$	−1.57398	+	3.79991i	−0.186796	+	0.450967i	−0.989339	−	0.145628i	$-0.953480\pi$
$71$	−1.57398	+	3.79991i	−0.186796	+	0.450967i	0.802543	+	0.596594i	$0.203480\pi$
$72$		0			0
$73$	−9.14594	−	3.78837i	−1.07045	−	0.443395i	−0.223301	−	0.974749i	$-0.571683\pi$
$73$	−9.14594	−	3.78837i	−1.07045	−	0.443395i	−0.847150	+	0.531354i	$0.821683\pi$
$74$		0			0
$75$	−9.02616	+	3.73876i	−1.04225	+	0.431715i
$76$		0			0
$77$	−0.986024	−	0.986024i	−0.112368	−	0.112368i
$78$		0			0
$79$	−0.163861	−	0.395595i	−0.0184358	−	0.0445080i	0.914394	−	0.404826i	$-0.132668\pi$
$79$	−0.163861	−	0.395595i	−0.0184358	−	0.0445080i	−0.932829	+	0.360318i	$0.882668\pi$
$80$		0			0
$81$			26.0278i			2.89197i
$82$		0			0
$83$	12.5983	−	12.5983i	1.38284	−	1.38284i	0.543305	−	0.839535i	$-0.317173\pi$
$83$	12.5983	−	12.5983i	1.38284	−	1.38284i	0.839535	−	0.543305i	$-0.182827\pi$
$84$		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
$91$	−3.24718	−	7.83938i	−0.340397	−	0.821790i
$92$		0			0
$93$	−14.0125	−	14.0125i	−1.45303	−	1.45303i
$94$		0			0
$95$	0.791191	−	0.327722i	0.0811745	−	0.0336236i
$96$		0			0
$97$	9.93713	+	4.11609i	1.00896	+	0.417926i	0.825076	−	0.565021i	$-0.191132\pi$
$97$	9.93713	+	4.11609i	1.00896	+	0.417926i	0.183887	+	0.982947i	$0.441132\pi$
$98$		0			0
$99$	−1.24625	+	3.00872i	−0.125253	+	0.302388i
$100$		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
$105$	−5.73968	+	13.8568i	−0.560136	+	1.35229i
$106$		0			0
$107$	7.44378	+	3.08332i	0.719618	+	0.298075i	0.712278	−	0.701898i	$-0.247664\pi$
$107$	7.44378	+	3.08332i	0.719618	+	0.298075i	0.00733983	+	0.999973i	$0.497664\pi$
$108$		0			0
$109$	−8.11520	+	3.36142i	−0.777295	+	0.321966i	−0.735823	−	0.677174i	$-0.763205\pi$
$109$	−8.11520	+	3.36142i	−0.777295	+	0.321966i	−0.0414716	+	0.999140i	$0.513205\pi$
$110$		0			0
$111$	9.76985	+	9.76985i	0.927313	+	0.927313i
$112$		0			0
$113$	5.19849	+	12.5503i	0.489033	+	1.18063i	0.955208	+	0.295936i	$0.0956317\pi$
$113$	5.19849	+	12.5503i	0.489033	+	1.18063i	−0.466175	+	0.884692i	$0.654368\pi$
$114$		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
$125$	4.32957	+	10.4525i	0.387248	+	0.934900i
$126$		0			0
$127$	0.428189	+	0.428189i	0.0379957	+	0.0379957i	0.725849	−	0.687854i	$-0.241447\pi$
$127$	0.428189	+	0.428189i	0.0379957	+	0.0379957i	−0.687854	+	0.725849i	$0.741447\pi$
$128$		0			0
$129$	−10.2130	+	4.23034i	−0.899200	+	0.372461i
$130$		0			0
$131$	8.23497	+	3.41104i	0.719493	+	0.298024i	0.712226	−	0.701950i	$-0.247687\pi$
$131$	8.23497	+	3.41104i	0.719493	+	0.298024i	0.00726659	+	0.999974i	$0.497687\pi$
$132$		0			0
$133$	−0.754670	+	1.82194i	−0.0654382	+	0.157982i
$134$		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
$139$	−0.163861	+	0.395595i	−0.0138985	+	0.0335540i	−0.930676	−	0.365843i	$-0.880781\pi$
$139$	−0.163861	+	0.395595i	−0.0138985	+	0.0335540i	0.916778	+	0.399397i	$0.130781\pi$
$140$		0			0
$141$	12.0349	+	4.98501i	1.01352	+	0.419814i
$142$		0			0
$143$	−1.03074	+	0.426948i	−0.0861952	+	0.0357032i
$144$		0			0
$145$	−2.27059	−	2.27059i	−0.188562	−	0.188562i
$146$		0			0
$147$	−4.49343	−	10.8481i	−0.370612	−	0.894736i
$148$		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	−0.562070	−	0.827090i	$-0.689995\pi$
$151$	3.25662	−	3.25662i	0.265020	−	0.265020i	0.827090	+	0.562070i	$0.189995\pi$
$152$		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
$159$	−6.49435	−	15.6788i	−0.515036	−	1.24341i
$160$		0			0
$161$	14.0125	+	14.0125i	1.10434	+	1.10434i
$162$		0			0
$163$	5.62185	−	2.32865i	0.440337	−	0.182394i	−0.151490	−	0.988459i	$-0.548407\pi$
$163$	5.62185	−	2.32865i	0.440337	−	0.182394i	0.591827	+	0.806065i	$0.298407\pi$
$164$		0			0
$165$	1.82194	+	0.754670i	0.141837	+	0.0587510i
$166$		0			0
$167$	8.06833	−	19.4787i	0.624346	−	1.50730i	−0.222207	−	0.975000i	$-0.571326\pi$
$167$	8.06833	−	19.4787i	0.624346	−	1.50730i	0.846553	−	0.532305i	$-0.178674\pi$
$168$		0			0
$169$	6.21110			0.477777
$170$		0			0
$171$	4.60555			0.352195
$172$		0			0
$173$	8.01872	−	19.3589i	0.609652	−	1.47183i	−0.253729	−	0.967275i	$-0.581657\pi$
$173$	8.01872	−	19.3589i	0.609652	−	1.47183i	0.863380	−	0.504554i	$-0.168343\pi$
$174$		0			0
$175$	−9.02616	−	3.73876i	−0.682314	−	0.282624i
$176$		0			0
$177$	25.8917	−	10.7247i	1.94614	−	0.806117i
$178$		0			0
$179$	−10.6262	−	10.6262i	−0.794242	−	0.794242i	0.187939	−	0.982181i	$-0.439819\pi$
$179$	−10.6262	−	10.6262i	−0.794242	−	0.794242i	−0.982181	+	0.187939i	$0.939819\pi$
$180$		0			0
$181$	−7.03555	−	16.9853i	−0.522948	−	1.26251i	−0.936064	−	0.351830i	$-0.885559\pi$
$181$	−7.03555	−	16.9853i	−0.522948	−	1.26251i	0.413116	−	0.910679i	$-0.364441\pi$
$182$		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
$193$	4.44382	+	10.7283i	0.319873	+	0.772242i	0.999260	+	0.0384615i	$0.0122457\pi$
$193$	4.44382	+	10.7283i	0.319873	+	0.772242i	−0.679387	+	0.733780i	$0.737754\pi$
$194$		0			0
$195$	8.48528	+	8.48528i	0.607644	+	0.607644i
$196$		0			0
$197$	23.0028	−	9.52806i	1.63888	−	0.678846i	0.642695	−	0.766122i	$-0.277816\pi$
$197$	23.0028	−	9.52806i	1.63888	−	0.678846i	0.996184	+	0.0872765i	$0.0278164\pi$
$198$		0			0
$199$	13.2217	+	5.47660i	0.937259	+	0.388226i	0.798428	−	0.602090i	$-0.205665\pi$
$199$	13.2217	+	5.47660i	0.937259	+	0.388226i	0.138832	+	0.990316i	$0.455665\pi$
$200$		0			0
$201$	−11.4794	+	27.7136i	−0.809692	+	1.95477i
$202$		0			0
$203$	7.39445			0.518989
$204$		0			0
$205$	−2.00000			−0.139686
$206$		0			0
$207$	17.7106	−	42.7572i	1.23097	−	2.97183i
$208$		0			0
$209$	0.239553	+	0.0992262i	0.0165702	+	0.00686362i
$210$		0			0
$211$	20.2699	−	8.39605i	1.39543	−	0.578008i	0.446872	−	0.894598i	$-0.352538\pi$
$211$	20.2699	−	8.39605i	1.39543	−	0.578008i	0.948563	+	0.316590i	$0.102538\pi$
$212$		0			0
$213$	9.47131	+	9.47131i	0.648963	+	0.648963i
$214$		0			0
$215$	1.83706	+	4.43506i	0.125287	+	0.302469i
$216$		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	$-0.546539\pi$
$223$	12.5983	−	12.5983i	0.843643	−	0.843643i	0.989331	+	0.145688i	$0.0465394\pi$
$224$		0			0
$225$			22.8167i			1.52111i
$226$		0			0
$227$	0.163861	+	0.395595i	0.0108758	+	0.0262566i	0.929224	−	0.369516i	$-0.120477\pi$
$227$	0.163861	+	0.395595i	0.0108758	+	0.0262566i	−0.918348	+	0.395773i	$0.870477\pi$
$228$		0			0
$229$	−3.25662	−	3.25662i	−0.215203	−	0.215203i	0.591270	−	0.806474i	$-0.298627\pi$
$229$	−3.25662	−	3.25662i	−0.215203	−	0.215203i	−0.806474	+	0.591270i	$0.798627\pi$
$230$		0			0
$231$	−4.19551	+	1.73784i	−0.276044	+	0.114341i
$232$		0			0
$233$	−7.32401	−	3.03370i	−0.479812	−	0.198744i	0.129650	−	0.991560i	$-0.458614\pi$
$233$	−7.32401	−	3.03370i	−0.479812	−	0.198744i	−0.609462	+	0.792815i	$0.708614\pi$
$234$		0			0
$235$	2.16478	−	5.22625i	0.141215	−	0.340923i
$236$		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
$241$	−4.87076	+	11.7591i	−0.313754	+	0.757468i	0.685806	+	0.727785i	$0.259450\pi$
$241$	−4.87076	+	11.7591i	−0.313754	+	0.757468i	−0.999559	+	0.0296835i	$0.990550\pi$
$242$		0			0
$243$	36.7398	+	15.2181i	2.35686	+	0.976243i
$244$		0			0
$245$	−4.71088	+	1.95131i	−0.300967	+	0.124665i
$246$		0			0
$247$	1.11567	+	1.11567i	0.0709883	+	0.0709883i
$248$		0			0
$249$	−22.2041	−	53.6053i	−1.40713	−	3.39710i
$250$		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	−0.990798	−	0.135346i	$-0.956785\pi$
$257$	−13.7139	+	13.7139i	−0.855452	+	0.855452i	0.135346	+	0.990798i	$0.456785\pi$
$258$		0			0
$259$			13.8167i			0.858525i
$260$		0			0
$261$	−6.60860	−	15.9546i	−0.409062	−	0.987563i
$262$		0			0
$263$	−16.2831	−	16.2831i	−1.00406	−	1.00406i	−0.999992	−	0.00406616i	$-0.998706\pi$
$263$	−16.2831	−	16.2831i	−1.00406	−	1.00406i	−0.00406616	−	0.999992i	$-0.501294\pi$
$264$		0			0
$265$	−6.80863	+	2.82023i	−0.418251	+	0.173245i
$266$		0			0
$267$	23.5181	+	9.74153i	1.43929	+	0.596172i
$268$		0			0
$269$	9.42883	−	22.7632i	0.574886	−	1.38790i	−0.322466	−	0.946581i	$-0.604512\pi$
$269$	9.42883	−	22.7632i	0.574886	−	1.38790i	0.897352	−	0.441316i	$-0.145488\pi$
$270$		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
$275$	−0.491583	+	1.18679i	−0.0296436	+	0.0715659i
$276$		0			0
$277$	4.71088	+	1.95131i	0.283049	+	0.117243i	0.519691	−	0.854354i	$-0.326047\pi$
$277$	4.71088	+	1.95131i	0.283049	+	0.117243i	−0.236642	+	0.971597i	$0.576047\pi$
$278$		0			0
$279$	−42.7572	+	17.7106i	−2.55981	+	1.06031i
$280$		0			0
$281$	13.0265	+	13.0265i	0.777094	+	0.777094i	0.979336	−	0.202242i	$-0.0648227\pi$
$281$	13.0265	+	13.0265i	0.777094	+	0.777094i	−0.202242	+	0.979336i	$0.564823\pi$
$282$		0			0
$283$	1.14703	+	2.76917i	0.0681837	+	0.164610i	0.954298	−	0.298857i	$-0.0966053\pi$
$283$	1.14703	+	2.76917i	0.0681837	+	0.164610i	−0.886114	+	0.463467i	$0.846605\pi$
$284$		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
$295$	−4.65729	−	11.2437i	−0.271158	−	0.654633i
$296$		0			0
$297$	4.54118	+	4.54118i	0.263506	+	0.263506i
$298$		0			0
$299$	14.6480	−	6.06740i	0.847116	−	0.350887i
$300$		0			0
$301$	−10.2130	−	4.23034i	−0.588665	−	0.243833i
$302$		0			0
$303$	−13.2172	+	31.9091i	−0.759308	+	1.83313i
$304$		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
$309$	−16.4644	+	39.7485i	−0.936626	+	2.26121i
$310$		0			0
$311$	24.7049	+	10.2331i	1.40089	+	0.580267i	0.949982	−	0.312305i	$-0.101101\pi$
$311$	24.7049	+	10.2331i	1.40089	+	0.580267i	0.450906	+	0.892572i	$0.351101\pi$
$312$		0			0
$313$	8.11520	−	3.36142i	0.458698	−	0.189999i	−0.141355	−	0.989959i	$-0.545146\pi$
$313$	8.11520	−	3.36142i	0.458698	−	0.189999i	0.600053	+	0.799960i	$0.295146\pi$
$314$		0			0
$315$	24.7684	+	24.7684i	1.39554	+	1.39554i
$316$		0			0
$317$	10.6104	+	25.6159i	0.595942	+	1.43873i	0.877683	+	0.479241i	$0.159088\pi$
$317$	10.6104	+	25.6159i	0.595942	+	1.43873i	−0.281741	+	0.959490i	$0.590912\pi$
$318$		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
$329$	4.98501	+	12.0349i	0.274833	+	0.663505i
$330$		0			0
$331$	2.40024	+	2.40024i	0.131929	+	0.131929i	0.769988	−	0.638059i	$-0.220262\pi$
$331$	2.40024	+	2.40024i	0.131929	+	0.131929i	−0.638059	+	0.769988i	$0.720262\pi$
$332$		0			0
$333$	29.8114	−	12.3483i	1.63365	−	0.676682i
$334$		0			0
$335$	12.0349	+	4.98501i	0.657536	+	0.272360i
$336$		0			0
$337$	−8.77339	+	21.1808i	−0.477917	+	1.15379i	0.482667	+	0.875804i	$0.339668\pi$
$337$	−8.77339	+	21.1808i	−0.477917	+	1.15379i	−0.960584	+	0.277989i	$0.910332\pi$
$338$		0			0
$339$	44.2389			2.40273
$340$		0			0
$341$	−2.60555			−0.141099
$342$		0			0
$343$	−4.23034	+	10.2130i	−0.228417	+	0.551447i
$344$		0			0
$345$	−25.8917	−	10.7247i	−1.39396	−	0.577398i
$346$		0			0
$347$	−7.20423	+	2.98409i	−0.386743	+	0.160194i	−0.567579	−	0.823319i	$-0.692120\pi$
$347$	−7.20423	+	2.98409i	−0.386743	+	0.160194i	0.180836	+	0.983513i	$0.442120\pi$
$348$		0			0
$349$	16.7113	+	16.7113i	0.894534	+	0.894534i	0.994946	−	0.100412i	$-0.0320161\pi$
$349$	16.7113	+	16.7113i	0.894534	+	0.894534i	−0.100412	+	0.994946i	$0.532016\pi$
$350$		0			0
$351$	14.9550	+	36.1047i	0.798241	+	1.92712i
$352$		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	−0.945458	−	0.325744i	$-0.894385\pi$
$359$	−11.7419	+	11.7419i	−0.619714	+	0.619714i	0.325744	+	0.945458i	$0.394385\pi$
$360$		0			0
$361$			18.6333i			0.980700i
$362$		0			0
$363$	−13.4803	−	32.5443i	−0.707532	−	1.70813i
$364$		0			0
$365$	9.89949	+	9.89949i	0.518163	+	0.518163i
$366$		0			0
$367$	9.02616	−	3.73876i	0.471162	−	0.195162i	−0.134452	−	0.990920i	$-0.542927\pi$
$367$	9.02616	−	3.73876i	0.471162	−	0.195162i	0.605614	+	0.795758i	$0.292927\pi$
$368$		0			0
$369$	−9.93713	−	4.11609i	−0.517306	−	0.214275i
$370$		0			0
$371$	6.49435	−	15.6788i	0.337170	−	0.814000i
$372$		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
$377$	2.26401	−	5.46581i	0.116602	−	0.281503i
$378$		0			0
$379$	−27.0785	−	11.2163i	−1.39093	−	0.576142i	−0.443548	−	0.896251i	$-0.646280\pi$
$379$	−27.0785	−	11.2163i	−1.39093	−	0.576142i	−0.947381	+	0.320109i	$0.896280\pi$
$380$		0			0
$381$	1.82194	−	0.754670i	0.0933406	−	0.0386629i
$382$		0			0
$383$	−13.7139	−	13.7139i	−0.700750	−	0.700750i	0.263822	−	0.964571i	$-0.415017\pi$
$383$	−13.7139	−	13.7139i	−0.700750	−	0.700750i	−0.964571	+	0.263822i	$0.915017\pi$
$384$		0			0
$385$	0.754670	+	1.82194i	0.0384616	+	0.0928544i
$386$		0			0
$387$			25.8167i			1.31233i
$388$		0			0
$389$	7.20071	−	7.20071i	0.365091	−	0.365091i	−0.500592	−	0.865683i	$-0.666884\pi$
$389$	7.20071	−	7.20071i	0.365091	−	0.365091i	0.865683	+	0.500592i	$0.166884\pi$
$390$		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
$397$	4.87076	+	11.7591i	0.244457	+	0.590171i	0.997716	−	0.0675534i	$-0.0215193\pi$
$397$	4.87076	+	11.7591i	0.244457	+	0.590171i	−0.753259	+	0.657724i	$0.771519\pi$
$398$		0			0
$399$	4.54118	+	4.54118i	0.227344	+	0.227344i
$400$		0			0
$401$	9.14594	−	3.78837i	0.456726	−	0.189182i	−0.142445	−	0.989803i	$-0.545497\pi$
$401$	9.14594	−	3.78837i	0.456726	−	0.189182i	0.599172	+	0.800620i	$0.295497\pi$
$402$		0			0
$403$	−14.6480	−	6.06740i	−0.729669	−	0.302239i
$404$		0			0
$405$	14.0861	−	34.0069i	0.699945	−	1.68982i
$406$		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
$411$	−3.24718	+	7.83938i	−0.160171	+	0.386688i
$412$		0			0
$413$	25.8917	+	10.7247i	1.27405	+	0.527728i
$414$		0			0
$415$	−23.2786	+	9.64230i	−1.14270	+	0.473322i
$416$		0			0
$417$	0.986024	+	0.986024i	0.0482858	+	0.0482858i
$418$		0			0
$419$	1.24625	+	3.00872i	0.0608835	+	0.146986i	0.951394	−	0.307978i	$-0.0996523\pi$
$419$	1.24625	+	3.00872i	0.0608835	+	0.146986i	−0.890510	+	0.454964i	$0.849652\pi$
$420$		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
$431$	1.01776	+	2.45708i	0.0490237	+	0.118354i	0.946494	−	0.322721i	$-0.104597\pi$
$431$	1.01776	+	2.45708i	0.0490237	+	0.118354i	−0.897471	+	0.441074i	$0.854597\pi$
$432$		0			0
$433$	10.6262	+	10.6262i	0.510664	+	0.510664i	0.914730	−	0.404066i	$-0.132403\pi$
$433$	10.6262	+	10.6262i	0.510664	+	0.510664i	−0.404066	+	0.914730i	$0.632403\pi$
$434$		0			0
$435$	−9.66131	+	4.00185i	−0.463224	+	0.191874i
$436$		0			0
$437$	−3.40432	−	1.41011i	−0.162851	−	0.0674549i
$438$		0			0
$439$	−14.2350	+	34.3662i	−0.679398	+	1.64021i	0.0857193	+	0.996319i	$0.472681\pi$
$439$	−14.2350	+	34.3662i	−0.679398	+	1.64021i	−0.765117	+	0.643891i	$0.777319\pi$
$440$		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
$445$	4.23034	−	10.2130i	0.200537	−	0.484140i
$446$		0			0
$447$	−25.3401	−	10.4962i	−1.19854	−	0.496453i
$448$		0			0
$449$	−21.9720	+	9.10111i	−1.03692	+	0.429508i	−0.835207	−	0.549936i	$-0.814652\pi$
$449$	−21.9720	+	9.10111i	−1.03692	+	0.429508i	−0.201717	+	0.979444i	$0.564652\pi$
$450$		0			0
$451$	−0.428189	−	0.428189i	−0.0201627	−	0.0201627i
$452$		0			0
$453$	−5.73968	−	13.8568i	−0.269674	−	0.651050i
$454$		0			0
$455$			12.0000i			0.562569i
$456$		0			0
$457$	−25.8840	+	25.8840i	−1.21080	+	1.21080i	−0.240041	+	0.970763i	$0.577161\pi$
$457$	−25.8840	+	25.8840i	−1.21080	+	1.21080i	−0.970763	+	0.240041i	$0.922839\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−20.6554	+	20.6554i	−0.962016	+	0.962016i	−0.999305	−	0.0372881i	$-0.988128\pi$
$461$	−20.6554	+	20.6554i	−0.962016	+	0.962016i	0.0372881	+	0.999305i	$0.488128\pi$
$462$		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
$465$	10.7247	+	25.8917i	0.497346	+	1.20070i
$466$		0			0
$467$	−11.4826	−	11.4826i	−0.531352	−	0.531352i	0.389623	−	0.920975i	$-0.372605\pi$
$467$	−11.4826	−	11.4826i	−0.531352	−	0.531352i	−0.920975	+	0.389623i	$0.872605\pi$
$468$		0			0
$469$	−27.7136	+	11.4794i	−1.27970	+	0.530068i
$470$		0			0
$471$	−25.3401	−	10.4962i	−1.16761	−	0.483639i
$472$		0			0
$473$	−0.556218	+	1.34283i	−0.0255749	+	0.0617433i
$474$		0			0
$475$	1.81665			0.0833538
$476$		0			0
$477$	−39.6333			−1.81468
$478$		0			0
$479$	−6.65821	+	16.0744i	−0.304222	+	0.734456i	0.695649	+	0.718382i	$0.255117\pi$
$479$	−6.65821	+	16.0744i	−0.304222	+	0.734456i	−0.999871	+	0.0160742i	$0.994883\pi$
$480$		0			0
$481$	10.2130	+	4.23034i	0.465670	+	0.192887i
$482$		0			0
$483$	59.6228	−	24.6966i	2.71293	−	1.12373i
$484$		0			0
$485$	−10.7559	−	10.7559i	−0.488399	−	0.488399i
$486$		0			0
$487$	−9.37922	−	22.6434i	−0.425013	−	1.02607i	−0.980847	−	0.194779i	$-0.937601\pi$
$487$	−9.37922	−	22.6434i	−0.425013	−	1.02607i	0.555834	−	0.831293i	$-0.312399\pi$
$488$		0			0
$489$		−	19.8167i		−	0.896140i
$490$		0			0
$491$	−6.94142	+	6.94142i	−0.313262	+	0.313262i	−0.846172	−	0.532910i	$-0.821098\pi$
$491$	−6.94142	+	6.94142i	−0.313262	+	0.313262i	0.532910	+	0.846172i	$0.321098\pi$
$492$		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
$499$	−5.57582	−	13.4612i	−0.249608	−	0.602607i	0.748563	−	0.663064i	$-0.230744\pi$
$499$	−5.57582	−	13.4612i	−0.249608	−	0.602607i	−0.998171	+	0.0604568i	$0.980744\pi$
$500$		0			0
$501$	−48.5507	−	48.5507i	−2.16909	−	2.16909i
$502$		0			0
$503$	−35.9486	+	14.8904i	−1.60287	+	0.663930i	−0.991818	−	0.127661i	$-0.959253\pi$
$503$	−35.9486	+	14.8904i	−1.60287	+	0.663930i	−0.611052	+	0.791591i	$0.709253\pi$
$504$		0			0
$505$	13.8568	+	5.73968i	0.616620	+	0.255413i
$506$		0			0
$507$	7.74061	−	18.6875i	0.343772	−	0.829940i
$508$		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
$513$	3.47567	−	8.39102i	0.153455	−	0.370472i
$514$		0			0
$515$	17.2611	+	7.14980i	0.760617	+	0.315058i
$516$		0			0
$517$	1.58238	−	0.655444i	0.0695931	−	0.0288264i
$518$		0			0
$519$	−48.2522	−	48.2522i	−2.11803	−	2.11803i
$520$		0			0
$521$	7.03555	+	16.9853i	0.308233	+	0.744140i	0.999763	+	0.0217921i	$0.00693719\pi$
$521$	7.03555	+	16.9853i	0.308233	+	0.744140i	−0.691530	+	0.722348i	$0.743063\pi$
$522$		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
$533$	−1.41011	−	3.40432i	−0.0610788	−	0.147457i
$534$		0			0
$535$	−8.05709	−	8.05709i	−0.348338	−	0.348338i
$536$		0			0
$537$	−45.2143	+	18.7284i	−1.95114	+	0.808190i
$538$		0			0
$539$	−1.42634	−	0.590809i	−0.0614368	−	0.0254480i
$540$		0			0
$541$	1.62359	−	3.91969i	0.0698035	−	0.168521i	−0.885127	−	0.465349i	$-0.845929\pi$
$541$	1.62359	−	3.91969i	0.0698035	−	0.168521i	0.954931	+	0.296828i	$0.0959289\pi$
$542$		0			0
$543$	−59.8722			−2.56936
$544$		0			0
$545$	12.4222			0.532109
$546$		0			0
$547$	6.23127	−	15.0436i	0.266430	−	0.643218i	−0.732880	−	0.680357i	$-0.761825\pi$
$547$	6.23127	−	15.0436i	0.266430	−	0.643218i	0.999310	+	0.0371393i	$0.0118245\pi$
$548$		0			0
$549$	−61.7205	−	25.5655i	−2.63417	−	1.09111i
$550$		0			0
$551$	−1.27030	+	0.526174i	−0.0541165	+	0.0224158i
$552$		0			0
$553$	−0.986024	−	0.986024i	−0.0419300	−	0.0419300i
$554$		0			0
$555$	−7.47752	−	18.0523i	−0.317403	−	0.766279i
$556$		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	−0.944003	−	0.329937i	$-0.892972\pi$
$563$	−14.5703	+	14.5703i	−0.614066	+	0.614066i	0.329937	+	0.944003i	$0.392972\pi$
$564$		0			0
$565$		−	19.2111i		−	0.808217i
$566$		0			0
$567$	32.4372	+	78.3103i	1.36223	+	3.28872i
$568$		0			0
$569$	21.5117	+	21.5117i	0.901819	+	0.901819i	0.995593	−	0.0937741i	$-0.0298932\pi$
$569$	21.5117	+	21.5117i	0.901819	+	0.901819i	−0.0937741	+	0.995593i	$0.529893\pi$
$570$		0			0
$571$	−3.00872	+	1.24625i	−0.125911	+	0.0521541i	−0.444749	−	0.895655i	$-0.646707\pi$
$571$	−3.00872	+	1.24625i	−0.125911	+	0.0521541i	0.318838	+	0.947809i	$0.396707\pi$
$572$		0			0
$573$	20.4259	+	8.46069i	0.853304	+	0.353450i
$574$		0			0
$575$	6.98594	−	16.8655i	0.291334	−	0.703342i
$576$		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
$581$	22.2041	−	53.6053i	0.921180	−	2.22392i
$582$		0			0
$583$	−2.06149	−	0.853896i	−0.0853781	−	0.0353648i
$584$		0			0
$585$	25.8917	−	10.7247i	1.07049	−	0.443412i
$586$		0			0
$587$	−3.25662	−	3.25662i	−0.134415	−	0.134415i	0.636698	−	0.771113i	$-0.280300\pi$
$587$	−3.25662	−	3.25662i	−0.134415	−	0.134415i	−0.771113	+	0.636698i	$0.780300\pi$
$588$		0			0
$589$	1.41011	+	3.40432i	0.0581027	+	0.140272i
$590$		0			0
$591$		−	81.0833i		−	3.33532i
$592$		0			0
$593$	1.11567	−	1.11567i	0.0458151	−	0.0458151i	−0.683828	−	0.729643i	$-0.739686\pi$
$593$	1.11567	−	1.11567i	0.0458151	−	0.0458151i	0.729643	+	0.683828i	$0.239686\pi$
$594$		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
$601$	2.27903	+	5.50207i	0.0929637	+	0.224434i	0.963521	−	0.267633i	$-0.0862415\pi$
$601$	2.27903	+	5.50207i	0.0929637	+	0.224434i	−0.870557	+	0.492067i	$0.836241\pi$
$602$		0			0
$603$	49.5367	+	49.5367i	2.01729	+	2.01729i
$604$		0			0
$605$	−14.1326	+	5.85393i	−0.574573	+	0.237996i
$606$		0			0
$607$	−12.4305	−	5.14887i	−0.504538	−	0.208986i	0.115872	−	0.993264i	$-0.463034\pi$
$607$	−12.4305	−	5.14887i	−0.504538	−	0.208986i	−0.620410	+	0.784278i	$0.713034\pi$
$608$		0			0
$609$	9.21536	−	22.2478i	0.373425	−	0.901528i
$610$		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
$615$	−2.49251	+	6.01744i	−0.100508	+	0.242647i
$616$		0			0
$617$	2.09775	+	0.868918i	0.0844524	+	0.0349813i	0.424510	−	0.905423i	$-0.360446\pi$
$617$	2.09775	+	0.868918i	0.0844524	+	0.0349813i	−0.340057	+	0.940405i	$0.610446\pi$
$618$		0			0
$619$	18.9270	−	7.83983i	0.760742	−	0.315109i	0.0316257	−	0.999500i	$-0.489932\pi$
$619$	18.9270	−	7.83983i	0.760742	−	0.315109i	0.729116	+	0.684390i	$0.239932\pi$
$620$		0			0
$621$	−64.5352	−	64.5352i	−2.58971	−	2.58971i
$622$		0			0
$623$	9.74153	+	23.5181i	0.390286	+	0.942234i
$624$		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	$-0.910259\pi$
$631$	−17.1395	+	17.1395i	−0.682311	+	0.682311i	0.278209	+	0.960520i	$0.410259\pi$
$632$		0			0
$633$		−	71.4500i		−	2.83988i
$634$		0			0
$635$	−0.327722	−	0.791191i	−0.0130053	−	0.0313975i
$636$		0			0
$637$	−6.64288	−	6.64288i	−0.263200	−	0.263200i
$638$		0			0
$639$	28.9004	−	11.9709i	1.14328	−	0.473563i
$640$		0			0
$641$	−40.2639	−	16.6779i	−1.59033	−	0.658736i	−0.600322	−	0.799758i	$-0.704961\pi$
$641$	−40.2639	−	16.6779i	−1.59033	−	0.658736i	−0.990006	+	0.141023i	$0.954961\pi$
$642$		0			0
$643$	2.22942	−	5.38229i	0.0879197	−	0.212257i	−0.873804	−	0.486279i	$-0.838354\pi$
$643$	2.22942	−	5.38229i	0.0879197	−	0.212257i	0.961724	+	0.274022i	$0.0883540\pi$
$644$		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
$649$	1.41011	−	3.40432i	0.0553518	−	0.133631i
$650$		0			0
$651$	−59.6228	−	24.6966i	−2.33680	−	0.967935i
$652$		0			0
$653$	32.4245	−	13.4307i	1.26887	−	0.525583i	0.356249	−	0.934391i	$-0.384055\pi$
$653$	32.4245	−	13.4307i	1.26887	−	0.525583i	0.912620	+	0.408808i	$0.134055\pi$
$654$		0			0
$655$	−8.91347	−	8.91347i	−0.348278	−	0.348278i
$656$		0			0
$657$	28.8127	+	69.5599i	1.12409	+	2.71379i
$658$		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	−0.723565	−	0.690256i	$-0.757498\pi$
$661$	−0.856379	+	0.856379i	−0.0333093	+	0.0333093i	0.690256	+	0.723565i	$0.257498\pi$
$662$		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
$669$	−22.2041	−	53.6053i	−0.858459	−	2.07250i
$670$		0			0
$671$	−2.65953	−	2.65953i	−0.102670	−	0.102670i
$672$		0			0
$673$	−7.32401	+	3.03370i	−0.282320	+	0.116941i	−0.519350	−	0.854562i	$-0.673826\pi$
$673$	−7.32401	+	3.03370i	−0.282320	+	0.116941i	0.237030	+	0.971502i	$0.423826\pi$
$674$		0			0
$675$	41.5705	+	17.2190i	1.60005	+	0.662762i
$676$		0			0
$677$	−8.67416	+	20.9413i	−0.333375	+	0.804838i	0.664945	+	0.746893i	$0.268455\pi$
$677$	−8.67416	+	20.9413i	−0.333375	+	0.804838i	−0.998320	+	0.0579459i	$0.981545\pi$
$678$		0			0
$679$	35.0278			1.34424
$680$		0			0
$681$	1.39445			0.0534354
$682$		0			0
$683$	0.392357	−	0.947233i	0.0150131	−	0.0362449i	−0.916195	−	0.400732i	$-0.868756\pi$
$683$	0.392357	−	0.947233i	0.0150131	−	0.0362449i	0.931208	+	0.364487i	$0.118756\pi$
$684$		0			0
$685$	3.40432	+	1.41011i	0.130072	+	0.0538777i
$686$		0			0
$687$	−13.8568	+	5.73968i	−0.528671	+	0.218983i
$688$		0			0
$689$	−9.60095	−	9.60095i	−0.365767	−	0.365767i
$690$		0			0
$691$	−2.98409	−	7.20423i	−0.113520	−	0.274062i	0.856901	−	0.515482i	$-0.172387\pi$
$691$	−2.98409	−	7.20423i	−0.113520	−	0.274062i	−0.970421	+	0.241420i	$0.922387\pi$
$692$		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
$703$	−0.983166	−	2.37357i	−0.0370808	−	0.0895210i
$704$		0			0
$705$	−13.0265	−	13.0265i	−0.490605	−	0.490605i
$706$		0			0
$707$	−31.9091	+	13.2172i	−1.20007	+	0.497084i
$708$		0			0
$709$	−18.8073	−	7.79022i	−0.706321	−	0.292568i	0.000460118	−	1.00000i	$-0.499854\pi$
$709$	−18.8073	−	7.79022i	−0.706321	−	0.292568i	−0.706781	+	0.707432i	$0.749854\pi$
$710$		0			0
$711$	−1.24625	+	3.00872i	−0.0467381	+	0.112836i
$712$		0			0
$713$	37.0278			1.38670
$714$		0			0
$715$	1.57779			0.0590062
$716$		0			0
$717$	−18.4307	+	44.4957i	−0.688308	+	1.66172i
$718$		0			0
$719$	−6.17348	−	2.55714i	−0.230232	−	0.0953653i	0.264585	−	0.964362i	$-0.414765\pi$
$719$	−6.17348	−	2.55714i	−0.230232	−	0.0953653i	−0.494817	+	0.868997i	$0.664765\pi$
$720$		0			0
$721$	−39.7485	+	16.4644i	−1.48031	+	0.613166i
$722$		0			0
$723$	29.3095	+	29.3095i	1.09003	+	1.09003i
$724$		0			0
$725$	−2.60675	−	6.29326i	−0.0968124	−	0.233726i
$726$		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	$-0.426269\pi$
$733$	32.5662	−	32.5662i	1.20286	−	1.20286i	0.973293	−	0.229566i	$-0.0737305\pi$
$734$		0			0
$735$			16.6056i			0.612505i
$736$		0			0
$737$	1.50934	+	3.64387i	0.0555973	+	0.134224i
$738$		0			0
$739$	−24.5091	−	24.5091i	−0.901581	−	0.901581i	0.0939921	−	0.995573i	$-0.470037\pi$
$739$	−24.5091	−	24.5091i	−0.901581	−	0.901581i	−0.995573	+	0.0939921i	$0.970037\pi$
$740$		0			0
$741$	4.74715	−	1.96633i	0.174391	−	0.0722350i
$742$		0			0
$743$	−19.2391	−	7.96910i	−0.705815	−	0.292358i	0.000756791	−	1.00000i	$-0.499759\pi$
$743$	−19.2391	−	7.96910i	−0.705815	−	0.292358i	−0.706571	+	0.707642i	$0.749759\pi$
$744$		0			0
$745$	−4.55806	+	11.0041i	−0.166995	+	0.403161i
$746$		0			0
$747$	−135.505			−4.95789
$748$		0			0
$749$	26.2389			0.958747
$750$		0			0
$751$	−0.918531	+	2.21753i	−0.0335177	+	0.0809188i	−0.939752	−	0.341857i	$-0.888944\pi$
$751$	−0.918531	+	2.21753i	−0.0335177	+	0.0809188i	0.906234	+	0.422776i	$0.138944\pi$
$752$		0			0
$753$	36.1047	+	14.9550i	1.31573	+	0.544992i
$754$		0			0
$755$	−6.01744	+	2.49251i	−0.218997	+	0.0907116i
$756$		0			0
$757$	27.5968	+	27.5968i	1.00302	+	1.00302i	0.999995	+	0.00302702i	$0.000963531\pi$
$757$	27.5968	+	27.5968i	1.00302	+	1.00302i	0.00302702	+	0.999995i	$0.499036\pi$
$758$		0			0
$759$	−3.24718	−	7.83938i	−0.117865	−	0.284551i
$760$		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
$771$	24.1704	+	58.3525i	0.870475	+	2.10151i
$772$		0			0
$773$	20.2272	+	20.2272i	0.727521	+	0.727521i	0.970125	−	0.242604i	$-0.0780017\pi$
$773$	20.2272	+	20.2272i	0.727521	+	0.727521i	−0.242604	+	0.970125i	$0.578002\pi$
$774$		0			0
$775$	−16.8655	+	6.98594i	−0.605828	+	0.250942i
$776$		0			0
$777$	41.5705	+	17.2190i	1.49133	+	0.617730i
$778$		0			0
$779$	−0.327722	+	0.791191i	−0.0117419	+	0.0283474i
$780$		0			0
$781$	1.76114			0.0630186
$782$		0			0
$783$	−34.0555			−1.21704
$784$		0			0
$785$	−4.55806	+	11.0041i	−0.162684	+	0.392755i
$786$		0			0
$787$	19.2391	+	7.96910i	0.685800	+	0.284068i	0.698249	−	0.715855i	$-0.253963\pi$
$787$	19.2391	+	7.96910i	0.685800	+	0.284068i	−0.0124489	+	0.999923i	$0.503963\pi$
$788$		0			0
$789$	−69.2841	+	28.6984i	−2.46658	+	1.02169i
$790$		0			0
$791$	31.2816	+	31.2816i	1.11225	+	1.11225i
$792$		0			0
$793$	−8.75836	−	21.1446i	−0.311019	−	0.750865i
$794$		0			0
$795$			24.0000i			0.851192i
$796$		0			0
$797$	2.56914	−	2.56914i	0.0910035	−	0.0910035i	−0.660140	−	0.751143i	$-0.729503\pi$
$797$	2.56914	−	2.56914i	0.0910035	−	0.0910035i	0.751143	+	0.660140i	$0.229503\pi$
$798$		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
$805$	−10.7247	−	25.8917i	−0.377996	−	0.912563i
$806$		0			0
$807$	−56.7374	−	56.7374i	−1.99725	−	1.99725i
$808$		0			0
$809$	27.1983	−	11.2659i	0.956240	−	0.396088i	0.150667	−	0.988585i	$-0.451858\pi$
$809$	27.1983	−	11.2659i	0.956240	−	0.396088i	0.805573	+	0.592497i	$0.201858\pi$
$810$		0			0
$811$	−14.0129	−	5.80432i	−0.492058	−	0.203817i	0.122836	−	0.992427i	$-0.460801\pi$
$811$	−14.0129	−	5.80432i	−0.492058	−	0.203817i	−0.614894	+	0.788610i	$0.710801\pi$
$812$		0			0
$813$	−1.50934	+	3.64387i	−0.0529349	+	0.127796i
$814$		0			0
$815$	−8.60555			−0.301439
$816$		0			0
$817$	2.05551			0.0719133
$818$		0			0
$819$	−24.6966	+	59.6228i	−0.862968	+	2.08339i
$820$		0			0
$821$	16.7458	+	6.93632i	0.584431	+	0.242079i	0.655253	−	0.755410i	$-0.272562\pi$
$821$	16.7458	+	6.93632i	0.584431	+	0.242079i	−0.0708216	+	0.997489i	$0.522562\pi$
$822$		0			0
$823$	16.8655	−	6.98594i	0.587896	−	0.243514i	−0.0688493	−	0.997627i	$-0.521933\pi$
$823$	16.8655	−	6.98594i	0.587896	−	0.243514i	0.656745	+	0.754113i	$0.271933\pi$
$824$		0			0
$825$	2.95807	+	2.95807i	0.102987	+	0.102987i
$826$		0			0
$827$	3.41104	+	8.23497i	0.118613	+	0.286358i	0.972024	−	0.234881i	$-0.0754700\pi$
$827$	3.41104	+	8.23497i	0.118613	+	0.286358i	−0.853411	+	0.521239i	$0.825470\pi$
$828$		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
$839$	8.06833	+	19.4787i	0.278550	+	0.672478i	0.999796	−	0.0202004i	$-0.00643042\pi$
$839$	8.06833	+	19.4787i	0.278550	+	0.672478i	−0.721246	+	0.692679i	$0.756430\pi$
$840$		0			0
$841$	−16.8605	−	16.8605i	−0.581398	−	0.581398i
$842$		0			0
$843$	55.4273	−	22.9587i	1.90902	−	0.790741i
$844$		0			0
$845$	−8.11520	−	3.36142i	−0.279171	−	0.115637i
$846$		0			0
$847$	13.4803	−	32.5443i	0.463188	−	1.11824i
$848$		0			0
$849$	9.76114			0.335001
$850$		0			0
$851$	−25.8167			−0.884983
$852$		0			0
$853$	−15.9232	+	38.4420i	−0.545199	+	1.31623i	0.375813	+	0.926695i	$0.377363\pi$
$853$	−15.9232	+	38.4420i	−0.545199	+	1.31623i	−0.921013	+	0.389532i	$0.872637\pi$
$854$		0			0
$855$	−6.01744	−	2.49251i	−0.205792	−	0.0852419i
$856$		0			0
$857$	−24.3456	+	10.0843i	−0.831630	+	0.344472i	−0.757548	−	0.652780i	$-0.773603\pi$
$857$	−24.3456	+	10.0843i	−0.831630	+	0.344472i	−0.0740819	+	0.997252i	$0.523603\pi$
$858$		0			0
$859$	1.28457	+	1.28457i	0.0438289	+	0.0438289i	0.728682	−	0.684853i	$-0.240133\pi$
$859$	1.28457	+	1.28457i	0.0438289	+	0.0438289i	−0.684853	+	0.728682i	$0.740133\pi$
$860$		0			0
$861$	−5.73968	−	13.8568i	−0.195608	−	0.472239i
$862$		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
$873$	−31.3052	−	75.5774i	−1.05952	−	2.55791i
$874$		0			0
$875$	26.0529	+	26.0529i	0.880750	+	0.880750i
$876$		0			0
$877$	−2.33731	+	0.968144i	−0.0789253	+	0.0326919i	−0.421797	−	0.906690i	$-0.638600\pi$
$877$	−2.33731	+	0.968144i	−0.0789253	+	0.0326919i	0.342872	+	0.939382i	$0.388600\pi$
$878$		0			0
$879$	−65.0886	−	26.9606i	−2.19538	−	0.909358i
$880$		0			0
$881$	−13.1030	+	31.6333i	−0.441450	+	1.06575i	0.533991	+	0.845490i	$0.320692\pi$
$881$	−13.1030	+	31.6333i	−0.441450	+	1.06575i	−0.975440	+	0.220264i	$0.929308\pi$
$882$		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
$887$	6.33049	−	15.2832i	0.212557	−	0.513158i	−0.781258	−	0.624209i	$-0.785421\pi$
$887$	6.33049	−	15.2832i	0.212557	−	0.513158i	0.993815	+	0.111050i	$0.0354215\pi$
$888$		0			0
$889$	1.82194	+	0.754670i	0.0611057	+	0.0253108i
$890$		0			0
$891$	10.2965	−	4.26493i	0.344944	−	0.142881i
$892$		0			0
$893$	−1.71276	−	1.71276i	−0.0573152	−	0.0573152i
$894$		0			0
$895$	8.13296	+	19.6347i	0.271855	+	0.656316i
$896$		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
$907$	−13.2818	−	32.0652i	−0.441016	−	1.06471i	−0.975593	−	0.219587i	$-0.929529\pi$
$907$	−13.2818	−	32.0652i	−0.441016	−	1.06471i	0.534577	−	0.845120i	$-0.320471\pi$
$908$		0			0
$909$	57.0360	+	57.0360i	1.89176	+	1.89176i
$910$		0			0
$911$	−6.17348	+	2.55714i	−0.204537	+	0.0847219i	−0.482600	−	0.875841i	$-0.660307\pi$
$911$	−6.17348	+	2.55714i	−0.204537	+	0.0847219i	0.278063	+	0.960563i	$0.410307\pi$
$912$		0			0
$913$	−7.04819	−	2.91945i	−0.233261	−	0.0966198i
$914$		0			0
$915$	−15.4812	+	37.3750i	−0.511793	+	1.23558i
$916$		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
$921$	26.4344	−	63.8183i	0.871043	−	2.10288i
$922$		0			0
$923$	9.90087	+	4.10107i	0.325891	+	0.134988i
$924$		0			0
$925$	11.7591	−	4.87076i	0.386636	−	0.160150i
$926$		0			0
$927$	71.0485	+	71.0485i	2.33354	+	2.33354i
$928$		0			0
$929$	0.541196	+	1.30656i	0.0177561	+	0.0428669i	0.932509	−	0.361147i	$-0.117615\pi$
$929$	0.541196	+	1.30656i	0.0177561	+	0.0428669i	−0.914753	+	0.404014i	$0.867615\pi$
$930$		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	$-0.783453\pi$
$937$	−4.54118	+	4.54118i	−0.148354	+	0.148354i	0.629028	+	0.777382i	$0.283453\pi$
$938$		0			0
$939$		−	28.6056i		−	0.933507i
$940$		0			0
$941$	8.67416	+	20.9413i	0.282770	+	0.682666i	0.999898	−	0.0142749i	$-0.00454399\pi$
$941$	8.67416	+	20.9413i	0.282770	+	0.682666i	−0.717129	+	0.696941i	$0.754544\pi$
$942$		0			0
$943$	6.08504	+	6.08504i	0.198156	+	0.198156i
$944$		0			0
$945$	63.8183	−	26.4344i	2.07601	−	0.859911i
$946$		0			0
$947$	12.1184	+	5.01960i	0.393795	+	0.163115i	0.570789	−	0.821097i	$-0.306637\pi$
$947$	12.1184	+	5.01960i	0.393795	+	0.163115i	−0.176994	+	0.984212i	$0.556637\pi$
$948$		0			0
$949$	−9.87080	+	23.8302i	−0.320420	+	0.773562i
$950$		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
$955$	3.67412	−	8.87012i	0.118892	−	0.287030i
$956$		0			0
$957$	−2.92521	−	1.21166i	−0.0945586	−	0.0391675i
$958$		0			0
$959$	−7.83938	+	3.24718i	−0.253147	+	0.104857i
$960$		0			0
$961$	−4.26227	−	4.26227i	−0.137492	−	0.137492i
$962$		0			0
$963$	−23.4503	−	56.6141i	−0.755676	−	1.82436i
$964$		0			0
$965$		−	16.4222i		−	0.528649i
$966$		0			0
$967$	15.4267	−	15.4267i	0.496089	−	0.496089i	−0.414129	−	0.910218i	$-0.635914\pi$
$967$	15.4267	−	15.4267i	0.496089	−	0.496089i	0.910218	+	0.414129i	$0.135914\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−38.9105	+	38.9105i	−1.24870	+	1.24870i	−0.292402	+	0.956296i	$0.594454\pi$
$971$	−38.9105	+	38.9105i	−1.24870	+	1.24870i	−0.956296	+	0.292402i	$0.905546\pi$
$972$		0			0
$973$			1.39445i			0.0447040i
$974$		0			0
$975$	9.74153	+	23.5181i	0.311979	+	0.753183i
$976$		0			0
$977$	−11.9108	−	11.9108i	−0.381060	−	0.381060i	0.490424	−	0.871484i	$-0.336842\pi$
$977$	−11.9108	−	11.9108i	−0.381060	−	0.381060i	−0.871484	+	0.490424i	$0.836842\pi$
$978$		0			0
$979$	3.09223	−	1.28084i	0.0988282	−	0.0409360i
$980$		0			0
$981$	61.7205	+	25.5655i	1.97059	+	0.816243i
$982$		0			0
$983$	4.39420	−	10.6085i	0.140153	−	0.338360i	−0.838181	−	0.545393i	$-0.816381\pi$
$983$	4.39420	−	10.6085i	0.140153	−	0.338360i	0.978334	+	0.207033i	$0.0663806\pi$
$984$		0			0
$985$	−35.2111			−1.12192
$986$		0			0
$987$	42.4222			1.35031
$988$		0			0
$989$	7.90447	−	19.0831i	0.251347	−	0.606806i
$990$		0			0
$991$	−30.7224	−	12.7256i	−0.975928	−	0.404243i	−0.163012	−	0.986624i	$-0.552121\pi$
$991$	−30.7224	−	12.7256i	−0.975928	−	0.404243i	−0.812916	+	0.582381i	$0.802121\pi$
$992$		0			0
$993$	10.2130	−	4.23034i	0.324098	−	0.134246i
$994$		0			0
$995$	−14.3110	−	14.3110i	−0.453690	−	0.453690i
$996$		0			0
$997$	21.2359	+	51.2680i	0.672548	+	1.62368i	0.777265	+	0.629173i	$0.216606\pi$
$997$	21.2359	+	51.2680i	0.672548	+	1.62368i	−0.104717	+	0.994502i	$0.533394\pi$
$998$		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.977.4		16
17.2	even	8	inner	1156.2.h.e.1001.1		16
17.3	odd	16		1156.2.e.c.905.2		4
17.4	even	4	inner	1156.2.h.e.757.1		16
17.5	odd	16		1156.2.e.c.829.2		4
17.6	odd	16		1156.2.b.a.577.1		4
17.7	odd	16		1156.2.a.h.1.1		4
17.8	even	8	inner	1156.2.h.e.733.1		16
17.9	even	8	inner	1156.2.h.e.733.4		16
17.10	odd	16		1156.2.a.h.1.4		4
17.11	odd	16		1156.2.b.a.577.4		4
17.12	odd	16		68.2.e.a.13.1	✓	4
17.13	even	4	inner	1156.2.h.e.757.4		16
17.14	odd	16		68.2.e.a.21.1	yes	4
17.15	even	8	inner	1156.2.h.e.1001.4		16
17.16	even	2	inner	1156.2.h.e.977.1		16
51.14	even	16		612.2.k.e.361.2		4
51.29	even	16		612.2.k.e.217.2		4
68.7	even	16		4624.2.a.bq.1.4		4
68.27	even	16		4624.2.a.bq.1.1		4
68.31	even	16		272.2.o.g.225.2		4
68.63	even	16		272.2.o.g.81.2		4
85.12	even	16		1700.2.m.a.149.1		4
85.14	odd	16		1700.2.o.c.701.2		4
85.29	odd	16		1700.2.o.c.1101.2		4
85.48	even	16		1700.2.m.a.1449.1		4
85.63	even	16		1700.2.m.b.149.2		4
85.82	even	16		1700.2.m.b.1449.2		4
136.29	odd	16		1088.2.o.t.897.2		4
136.99	even	16		1088.2.o.s.769.1		4
136.131	even	16		1088.2.o.s.897.1		4
136.133	odd	16		1088.2.o.t.769.2		4
204.131	odd	16		2448.2.be.u.1441.1		4
204.167	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	17.12	odd	16
68.2.e.a.21.1	yes	4	17.14	odd	16
272.2.o.g.81.2		4	68.63	even	16
272.2.o.g.225.2		4	68.31	even	16
612.2.k.e.217.2		4	51.29	even	16
612.2.k.e.361.2		4	51.14	even	16
1088.2.o.s.769.1		4	136.99	even	16
1088.2.o.s.897.1		4	136.131	even	16
1088.2.o.t.769.2		4	136.133	odd	16
1088.2.o.t.897.2		4	136.29	odd	16
1156.2.a.h.1.1		4	17.7	odd	16
1156.2.a.h.1.4		4	17.10	odd	16
1156.2.b.a.577.1		4	17.6	odd	16
1156.2.b.a.577.4		4	17.11	odd	16
1156.2.e.c.829.2		4	17.5	odd	16
1156.2.e.c.905.2		4	17.3	odd	16
1156.2.h.e.733.1		16	17.8	even	8	inner
1156.2.h.e.733.4		16	17.9	even	8	inner
1156.2.h.e.757.1		16	17.4	even	4	inner
1156.2.h.e.757.4		16	17.13	even	4	inner
1156.2.h.e.977.1		16	17.16	even	2	inner
1156.2.h.e.977.4		16	1.1	even	1	trivial
1156.2.h.e.1001.1		16	17.2	even	8	inner
1156.2.h.e.1001.4		16	17.15	even	8	inner
1700.2.m.a.149.1		4	85.12	even	16
1700.2.m.a.1449.1		4	85.48	even	16
1700.2.m.b.149.2		4	85.63	even	16
1700.2.m.b.1449.2		4	85.82	even	16
1700.2.o.c.701.2		4	85.14	odd	16
1700.2.o.c.1101.2		4	85.29	odd	16
2448.2.be.u.1441.1		4	204.131	odd	16
2448.2.be.u.1585.1		4	204.167	odd	16
4624.2.a.bq.1.1		4	68.27	even	16
4624.2.a.bq.1.4		4	68.7	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)

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