LMFDB - Embedded newform 1792.2.m.g.1345.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.8
Root			$0.117630 + 0.893490i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.g.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41958 + 2.41958i) q^{3} +(-2.54136 + 2.54136i) q^{5} +1.00000i q^{7} +8.70871i q^{9} +O(q^{10})$	\(q+(2.41958 + 2.41958i) q^{3} +(-2.54136 + 2.54136i) q^{5} +1.00000i q^{7} +8.70871i q^{9} +(-0.764739 + 0.764739i) q^{11} +(-1.26582 - 1.26582i) q^{13} -12.2980 q^{15} +5.65390 q^{17} +(-0.0445673 - 0.0445673i) q^{19} +(-2.41958 + 2.41958i) q^{21} -1.46467i q^{23} -7.91700i q^{25} +(-13.8127 + 13.8127i) q^{27} +(3.56633 + 3.56633i) q^{29} +4.75455 q^{31} -3.70069 q^{33} +(-2.54136 - 2.54136i) q^{35} +(-5.09082 + 5.09082i) q^{37} -6.12551i q^{39} -7.50243i q^{41} +(-3.22558 + 3.22558i) q^{43} +(-22.1320 - 22.1320i) q^{45} -1.52393 q^{47} -1.00000 q^{49} +(13.6800 + 13.6800i) q^{51} +(4.66114 - 4.66114i) q^{53} -3.88695i q^{55} -0.215668i q^{57} +(5.38865 - 5.38865i) q^{59} +(-6.80717 - 6.80717i) q^{61} -8.70871 q^{63} +6.43381 q^{65} +(-4.92858 - 4.92858i) q^{67} +(3.54387 - 3.54387i) q^{69} -6.19187i q^{71} +8.59924i q^{73} +(19.1558 - 19.1558i) q^{75} +(-0.764739 - 0.764739i) q^{77} +7.84435 q^{79} -40.7155 q^{81} +(7.43857 + 7.43857i) q^{83} +(-14.3686 + 14.3686i) q^{85} +17.2580i q^{87} -9.32780i q^{89} +(1.26582 - 1.26582i) q^{91} +(11.5040 + 11.5040i) q^{93} +0.226523 q^{95} +0.485578 q^{97} +(-6.65990 - 6.65990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 - 4 * q^5	$ 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.41958	+	2.41958i	1.39694	+	1.39694i	0.808640	+	0.588304i	$0.200204\pi$
$3$	2.41958	+	2.41958i	1.39694	+	1.39694i	0.588304	+	0.808640i	$0.299796\pi$
$4$		0			0
$5$	−2.54136	+	2.54136i	−1.13653	+	1.13653i	−0.147462	+	0.989068i	$0.547110\pi$
$5$	−2.54136	+	2.54136i	−1.13653	+	1.13653i	−0.989068	+	0.147462i	$0.952890\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			8.70871i			2.90290i
$10$		0			0
$11$	−0.764739	+	0.764739i	−0.230578	+	0.230578i	−0.812934	−	0.582356i	$-0.802131\pi$
$11$	−0.764739	+	0.764739i	−0.230578	+	0.230578i	0.582356	+	0.812934i	$0.302131\pi$
$12$		0			0
$13$	−1.26582	−	1.26582i	−0.351076	−	0.351076i	0.509434	−	0.860510i	$-0.329855\pi$
$13$	−1.26582	−	1.26582i	−0.351076	−	0.351076i	−0.860510	+	0.509434i	$0.829855\pi$
$14$		0			0
$15$	−12.2980			−3.17534
$16$		0			0
$17$	5.65390			1.37127			0.685636	−	0.727945i	$-0.259524\pi$
$17$	5.65390			1.37127			0.685636	+	0.727945i	$0.259524\pi$
$18$		0			0
$19$	−0.0445673	−	0.0445673i	−0.0102244	−	0.0102244i	0.701976	−	0.712201i	$-0.252301\pi$
$19$	−0.0445673	−	0.0445673i	−0.0102244	−	0.0102244i	−0.712201	+	0.701976i	$0.752301\pi$
$20$		0			0
$21$	−2.41958	+	2.41958i	−0.527995	+	0.527995i
$22$		0			0
$23$		−	1.46467i		−	0.305404i	−0.988272	−	0.152702i	$-0.951203\pi$
$23$		−	1.46467i		−	0.305404i	0.988272	−	0.152702i	$-0.0487975\pi$
$24$		0			0
$25$		−	7.91700i		−	1.58340i
$26$		0			0
$27$	−13.8127	+	13.8127i	−2.65825	+	2.65825i
$28$		0			0
$29$	3.56633	+	3.56633i	0.662251	+	0.662251i	0.955910	−	0.293659i	$-0.0948730\pi$
$29$	3.56633	+	3.56633i	0.662251	+	0.662251i	−0.293659	+	0.955910i	$0.594873\pi$
$30$		0			0
$31$	4.75455			0.853943			0.426971	−	0.904265i	$-0.359581\pi$
$31$	4.75455			0.853943			0.426971	+	0.904265i	$0.359581\pi$
$32$		0			0
$33$	−3.70069			−0.644208
$34$		0			0
$35$	−2.54136	−	2.54136i	−0.429568	−	0.429568i
$36$		0			0
$37$	−5.09082	+	5.09082i	−0.836926	+	0.836926i	−0.988453	−	0.151527i	$-0.951581\pi$
$37$	−5.09082	+	5.09082i	−0.836926	+	0.836926i	0.151527	+	0.988453i	$0.451581\pi$
$38$		0			0
$39$		−	6.12551i		−	0.980867i
$40$		0			0
$41$		−	7.50243i		−	1.17168i	−0.810426	−	0.585841i	$-0.800764\pi$
$41$		−	7.50243i		−	1.17168i	0.810426	−	0.585841i	$-0.199236\pi$
$42$		0			0
$43$	−3.22558	+	3.22558i	−0.491897	+	0.491897i	−0.908903	−	0.417007i	$-0.863079\pi$
$43$	−3.22558	+	3.22558i	−0.491897	+	0.491897i	0.417007	+	0.908903i	$0.363079\pi$
$44$		0			0
$45$	−22.1320	−	22.1320i	−3.29924	−	3.29924i
$46$		0			0
$47$	−1.52393			−0.222287			−0.111144	−	0.993804i	$-0.535451\pi$
$47$	−1.52393			−0.222287			−0.111144	+	0.993804i	$0.535451\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	13.6800	+	13.6800i	1.91559	+	1.91559i
$52$		0			0
$53$	4.66114	−	4.66114i	0.640257	−	0.640257i	−0.310362	−	0.950619i	$-0.600450\pi$
$53$	4.66114	−	4.66114i	0.640257	−	0.640257i	0.950619	+	0.310362i	$0.100450\pi$
$54$		0			0
$55$		−	3.88695i		−	0.524117i
$56$		0			0
$57$		−	0.215668i		−	0.0285659i
$58$		0			0
$59$	5.38865	−	5.38865i	0.701543	−	0.701543i	−0.263199	−	0.964742i	$-0.584777\pi$
$59$	5.38865	−	5.38865i	0.701543	−	0.701543i	0.964742	+	0.263199i	$0.0847775\pi$
$60$		0			0
$61$	−6.80717	−	6.80717i	−0.871569	−	0.871569i	0.121074	−	0.992643i	$-0.461366\pi$
$61$	−6.80717	−	6.80717i	−0.871569	−	0.871569i	−0.992643	+	0.121074i	$0.961366\pi$
$62$		0			0
$63$	−8.70871			−1.09719
$64$		0			0
$65$	6.43381			0.798016
$66$		0			0
$67$	−4.92858	−	4.92858i	−0.602122	−	0.602122i	0.338754	−	0.940875i	$-0.389995\pi$
$67$	−4.92858	−	4.92858i	−0.602122	−	0.602122i	−0.940875	+	0.338754i	$0.889995\pi$
$68$		0			0
$69$	3.54387	−	3.54387i	0.426632	−	0.426632i
$70$		0			0
$71$		−	6.19187i		−	0.734839i	−0.930055	−	0.367420i	$-0.880241\pi$
$71$		−	6.19187i		−	0.734839i	0.930055	−	0.367420i	$-0.119759\pi$
$72$		0			0
$73$			8.59924i			1.00647i	0.864151	+	0.503233i	$0.167856\pi$
$73$			8.59924i			1.00647i	−0.864151	+	0.503233i	$0.832144\pi$
$74$		0			0
$75$	19.1558	−	19.1558i	2.21192	−	2.21192i
$76$		0			0
$77$	−0.764739	−	0.764739i	−0.0871502	−	0.0871502i
$78$		0			0
$79$	7.84435			0.882558			0.441279	−	0.897370i	$-0.354525\pi$
$79$	7.84435			0.882558			0.441279	+	0.897370i	$0.354525\pi$
$80$		0			0
$81$	−40.7155			−4.52395
$82$		0			0
$83$	7.43857	+	7.43857i	0.816489	+	0.816489i	0.985598	−	0.169108i	$-0.0540887\pi$
$83$	7.43857	+	7.43857i	0.816489	+	0.816489i	−0.169108	+	0.985598i	$0.554089\pi$
$84$		0			0
$85$	−14.3686	+	14.3686i	−1.55849	+	1.55849i
$86$		0			0
$87$			17.2580i			1.85026i
$88$		0			0
$89$		−	9.32780i		−	0.988745i	−0.869250	−	0.494373i	$-0.835398\pi$
$89$		−	9.32780i		−	0.988745i	0.869250	−	0.494373i	$-0.164602\pi$
$90$		0			0
$91$	1.26582	−	1.26582i	0.132694	−	0.132694i
$92$		0			0
$93$	11.5040	+	11.5040i	1.19291	+	1.19291i
$94$		0			0
$95$	0.226523			0.0232407
$96$		0			0
$97$	0.485578			0.0493030			0.0246515	−	0.999696i	$-0.492152\pi$
$97$	0.485578			0.0493030			0.0246515	+	0.999696i	$0.492152\pi$
$98$		0			0
$99$	−6.65990	−	6.65990i	−0.669345	−	0.669345i
$100$		0			0
$101$	−4.55780	+	4.55780i	−0.453518	+	0.453518i	−0.896521	−	0.443002i	$-0.853913\pi$
$101$	−4.55780	+	4.55780i	−0.453518	+	0.453518i	0.443002	+	0.896521i	$0.353913\pi$
$102$		0			0
$103$			4.26862i			0.420599i	0.977637	+	0.210300i	$0.0674440\pi$
$103$			4.26862i			0.420599i	−0.977637	+	0.210300i	$0.932556\pi$
$104$		0			0
$105$		−	12.2980i		−	1.20016i
$106$		0			0
$107$	−1.80860	+	1.80860i	−0.174844	+	0.174844i	−0.789104	−	0.614260i	$-0.789455\pi$
$107$	−1.80860	+	1.80860i	−0.174844	+	0.174844i	0.614260	+	0.789104i	$0.289455\pi$
$108$		0			0
$109$	11.0153	+	11.0153i	1.05507	+	1.05507i	0.998392	+	0.0566812i	$0.0180519\pi$
$109$	11.0153	+	11.0153i	1.05507	+	1.05507i	0.0566812	+	0.998392i	$0.481948\pi$
$110$		0			0
$111$	−24.6353			−2.33828
$112$		0			0
$113$	−11.6345			−1.09449			−0.547243	−	0.836974i	$-0.684323\pi$
$113$	−11.6345			−1.09449			−0.547243	+	0.836974i	$0.684323\pi$
$114$		0			0
$115$	3.72224	+	3.72224i	0.347101	+	0.347101i
$116$		0			0
$117$	11.0237	−	11.0237i	1.01914	−	1.01914i
$118$		0			0
$119$			5.65390i			0.518292i
$120$		0			0
$121$			9.83035i			0.893668i
$122$		0			0
$123$	18.1527	−	18.1527i	1.63677	−	1.63677i
$124$		0			0
$125$	7.41313	+	7.41313i	0.663051	+	0.663051i
$126$		0			0
$127$	11.7630			1.04380			0.521899	−	0.853007i	$-0.325224\pi$
$127$	11.7630			1.04380			0.521899	+	0.853007i	$0.325224\pi$
$128$		0			0
$129$	−15.6091			−1.37430
$130$		0			0
$131$	11.0924	+	11.0924i	0.969152	+	0.969152i	0.999538	−	0.0303864i	$-0.00967378\pi$
$131$	11.0924	+	11.0924i	0.969152	+	0.969152i	−0.0303864	+	0.999538i	$0.509674\pi$
$132$		0			0
$133$	0.0445673	−	0.0445673i	0.00386447	−	0.00386447i
$134$		0			0
$135$		−	70.2059i		−	6.04236i
$136$		0			0
$137$		−	7.47159i		−	0.638341i	−0.947697	−	0.319170i	$-0.896596\pi$
$137$		−	7.47159i		−	0.638341i	0.947697	−	0.319170i	$-0.103404\pi$
$138$		0			0
$139$	−0.249091	+	0.249091i	−0.0211277	+	0.0211277i	−0.717592	−	0.696464i	$-0.754756\pi$
$139$	−0.249091	+	0.249091i	−0.0211277	+	0.0211277i	0.696464	+	0.717592i	$0.254756\pi$
$140$		0			0
$141$	−3.68726	−	3.68726i	−0.310523	−	0.310523i
$142$		0			0
$143$	1.93605			0.161901
$144$		0			0
$145$	−18.1267			−1.50534
$146$		0			0
$147$	−2.41958	−	2.41958i	−0.199563	−	0.199563i
$148$		0			0
$149$	4.43030	−	4.43030i	0.362944	−	0.362944i	−0.501951	−	0.864896i	$-0.667384\pi$
$149$	4.43030	−	4.43030i	0.362944	−	0.362944i	0.864896	+	0.501951i	$0.167384\pi$
$150$		0			0
$151$			12.4475i			1.01297i	0.862250	+	0.506483i	$0.169055\pi$
$151$			12.4475i			1.01297i	−0.862250	+	0.506483i	$0.830945\pi$
$152$		0			0
$153$			49.2382i			3.98067i
$154$		0			0
$155$	−12.0830	+	12.0830i	−0.970531	+	0.970531i
$156$		0			0
$157$	3.71095	+	3.71095i	0.296166	+	0.296166i	0.839510	−	0.543344i	$-0.182842\pi$
$157$	3.71095	+	3.71095i	0.296166	+	0.296166i	−0.543344	+	0.839510i	$0.682842\pi$
$158$		0			0
$159$	22.5560			1.78881
$160$		0			0
$161$	1.46467			0.115432
$162$		0			0
$163$	−5.46072	−	5.46072i	−0.427717	−	0.427717i	0.460133	−	0.887850i	$-0.347802\pi$
$163$	−5.46072	−	5.46072i	−0.427717	−	0.427717i	−0.887850	+	0.460133i	$0.847802\pi$
$164$		0			0
$165$	9.40479	−	9.40479i	0.732162	−	0.732162i
$166$		0			0
$167$			8.39368i			0.649523i	0.945796	+	0.324761i	$0.105284\pi$
$167$			8.39368i			0.649523i	−0.945796	+	0.324761i	$0.894716\pi$
$168$		0			0
$169$		−	9.79539i		−	0.753491i
$170$		0			0
$171$	0.388124	−	0.388124i	0.0296806	−	0.0296806i
$172$		0			0
$173$	−8.17036	−	8.17036i	−0.621181	−	0.621181i	0.324653	−	0.945833i	$-0.394753\pi$
$173$	−8.17036	−	8.17036i	−0.621181	−	0.621181i	−0.945833	+	0.324653i	$0.894753\pi$
$174$		0			0
$175$	7.91700			0.598469
$176$		0			0
$177$	26.0765			1.96003
$178$		0			0
$179$	13.7656	+	13.7656i	1.02889	+	1.02889i	0.999570	+	0.0293209i	$0.00933448\pi$
$179$	13.7656	+	13.7656i	1.02889	+	1.02889i	0.0293209	+	0.999570i	$0.490666\pi$
$180$		0			0
$181$	−8.11694	+	8.11694i	−0.603327	+	0.603327i	−0.941194	−	0.337867i	$-0.890295\pi$
$181$	−8.11694	+	8.11694i	−0.603327	+	0.603327i	0.337867	+	0.941194i	$0.390295\pi$
$182$		0			0
$183$		−	32.9410i		−	2.43507i
$184$		0			0
$185$		−	25.8752i		−	1.90238i
$186$		0			0
$187$	−4.32376	+	4.32376i	−0.316185	+	0.316185i
$188$		0			0
$189$	−13.8127	−	13.8127i	−1.00472	−	1.00472i
$190$		0			0
$191$	16.5900			1.20041			0.600206	−	0.799846i	$-0.295085\pi$
$191$	16.5900			1.20041			0.600206	+	0.799846i	$0.295085\pi$
$192$		0			0
$193$	−1.32261			−0.0952033			−0.0476016	−	0.998866i	$-0.515158\pi$
$193$	−1.32261			−0.0952033			−0.0476016	+	0.998866i	$0.515158\pi$
$194$		0			0
$195$	15.5671	+	15.5671i	1.11478	+	1.11478i
$196$		0			0
$197$	11.5578	−	11.5578i	0.823457	−	0.823457i	−0.163145	−	0.986602i	$-0.552164\pi$
$197$	11.5578	−	11.5578i	0.823457	−	0.823457i	0.986602	+	0.163145i	$0.0521637\pi$
$198$		0			0
$199$			26.1422i			1.85317i	0.376081	+	0.926587i	$0.377272\pi$
$199$			26.1422i			1.85317i	−0.376081	+	0.926587i	$0.622728\pi$
$200$		0			0
$201$		−	23.8502i		−	1.68226i
$202$		0			0
$203$	−3.56633	+	3.56633i	−0.250307	+	0.250307i
$204$		0			0
$205$	19.0664	+	19.0664i	1.33165	+	1.33165i
$206$		0			0
$207$	12.7554			0.886559
$208$		0			0
$209$	0.0681647			0.00471505
$210$		0			0
$211$	17.4835	+	17.4835i	1.20361	+	1.20361i	0.973060	+	0.230551i	$0.0740527\pi$
$211$	17.4835	+	17.4835i	1.20361	+	1.20361i	0.230551	+	0.973060i	$0.425947\pi$
$212$		0			0
$213$	14.9817	−	14.9817i	1.02653	−	1.02653i
$214$		0			0
$215$		−	16.3947i		−	1.11811i
$216$		0			0
$217$			4.75455i			0.322760i
$218$		0			0
$219$	−20.8065	+	20.8065i	−1.40598	+	1.40598i
$220$		0			0
$221$	−7.15683	−	7.15683i	−0.481420	−	0.481420i
$222$		0			0
$223$	9.70637			0.649987			0.324993	−	0.945716i	$-0.394638\pi$
$223$	9.70637			0.649987			0.324993	+	0.945716i	$0.394638\pi$
$224$		0			0
$225$	68.9469			4.59646
$226$		0			0
$227$	−16.7964	−	16.7964i	−1.11481	−	1.11481i	−0.992490	−	0.122323i	$-0.960966\pi$
$227$	−16.7964	−	16.7964i	−1.11481	−	1.11481i	−0.122323	−	0.992490i	$-0.539034\pi$
$228$		0			0
$229$	−13.1587	+	13.1587i	−0.869555	+	0.869555i	−0.992423	−	0.122868i	$-0.960791\pi$
$229$	−13.1587	+	13.1587i	−0.869555	+	0.869555i	0.122868	+	0.992423i	$0.460791\pi$
$230$		0			0
$231$		−	3.70069i		−	0.243488i
$232$		0			0
$233$		−	10.7832i		−	0.706431i	−0.935542	−	0.353216i	$-0.885088\pi$
$233$		−	10.7832i		−	0.706431i	0.935542	−	0.353216i	$-0.114912\pi$
$234$		0			0
$235$	3.87284	−	3.87284i	0.252636	−	0.252636i
$236$		0			0
$237$	18.9800	+	18.9800i	1.23288	+	1.23288i
$238$		0			0
$239$	−2.08310			−0.134745			−0.0673724	−	0.997728i	$-0.521462\pi$
$239$	−2.08310			−0.134745			−0.0673724	+	0.997728i	$0.521462\pi$
$240$		0			0
$241$	−15.8817			−1.02303			−0.511516	−	0.859274i	$-0.670916\pi$
$241$	−15.8817			−1.02303			−0.511516	+	0.859274i	$0.670916\pi$
$242$		0			0
$243$	−57.0764	−	57.0764i	−3.66145	−	3.66145i
$244$		0			0
$245$	2.54136	−	2.54136i	0.162361	−	0.162361i
$246$		0			0
$247$			0.112828i			0.00717911i
$248$		0			0
$249$			35.9964i			2.28118i
$250$		0			0
$251$	−17.1226	+	17.1226i	−1.08077	+	1.08077i	−0.0843330	+	0.996438i	$0.526876\pi$
$251$	−17.1226	+	17.1226i	−1.08077	+	1.08077i	−0.996438	+	0.0843330i	$0.973124\pi$
$252$		0			0
$253$	1.12009	+	1.12009i	0.0704194	+	0.0704194i
$254$		0			0
$255$	−69.5318			−4.35425
$256$		0			0
$257$	−16.3998			−1.02299			−0.511497	−	0.859285i	$-0.670909\pi$
$257$	−16.3998			−1.02299			−0.511497	+	0.859285i	$0.670909\pi$
$258$		0			0
$259$	−5.09082	−	5.09082i	−0.316328	−	0.316328i
$260$		0			0
$261$	−31.0582	+	31.0582i	−1.92245	+	1.92245i
$262$		0			0
$263$			24.4978i			1.51060i	0.655379	+	0.755300i	$0.272509\pi$
$263$			24.4978i			1.51060i	−0.655379	+	0.755300i	$0.727491\pi$
$264$		0			0
$265$			23.6912i			1.45534i
$266$		0			0
$267$	22.5693	−	22.5693i	1.38122	−	1.38122i
$268$		0			0
$269$	−1.05278	−	1.05278i	−0.0641889	−	0.0641889i	0.674284	−	0.738472i	$-0.264453\pi$
$269$	−1.05278	−	1.05278i	−0.0641889	−	0.0641889i	−0.738472	+	0.674284i	$0.764453\pi$
$270$		0			0
$271$	−28.0458			−1.70366			−0.851829	−	0.523820i	$-0.824507\pi$
$271$	−28.0458			−1.70366			−0.851829	+	0.523820i	$0.824507\pi$
$272$		0			0
$273$	6.12551			0.370733
$274$		0			0
$275$	6.05444	+	6.05444i	0.365096	+	0.365096i
$276$		0			0
$277$	3.59707	−	3.59707i	0.216127	−	0.216127i	−0.590737	−	0.806864i	$-0.701163\pi$
$277$	3.59707	−	3.59707i	0.216127	−	0.216127i	0.806864	+	0.590737i	$0.201163\pi$
$278$		0			0
$279$			41.4060i			2.47891i
$280$		0			0
$281$		−	2.33236i		−	0.139137i	−0.997577	−	0.0695683i	$-0.977838\pi$
$281$		−	2.33236i		−	0.139137i	0.997577	−	0.0695683i	$-0.0221622\pi$
$282$		0			0
$283$	−4.49397	+	4.49397i	−0.267139	+	0.267139i	−0.827946	−	0.560807i	$-0.810491\pi$
$283$	−4.49397	+	4.49397i	−0.267139	+	0.267139i	0.560807	+	0.827946i	$0.310491\pi$
$284$		0			0
$285$	0.548089	+	0.548089i	0.0324660	+	0.0324660i
$286$		0			0
$287$	7.50243			0.442854
$288$		0			0
$289$	14.9666			0.880386
$290$		0			0
$291$	1.17489	+	1.17489i	0.0688736	+	0.0688736i
$292$		0			0
$293$	1.02932	−	1.02932i	0.0601334	−	0.0601334i	−0.676401	−	0.736534i	$-0.736461\pi$
$293$	1.02932	−	1.02932i	0.0601334	−	0.0601334i	0.736534	+	0.676401i	$0.236461\pi$
$294$		0			0
$295$			27.3890i			1.59465i
$296$		0			0
$297$		−	21.1262i		−	1.22587i
$298$		0			0
$299$	−1.85401	+	1.85401i	−0.107220	+	0.107220i
$300$		0			0
$301$	−3.22558	−	3.22558i	−0.185920	−	0.185920i
$302$		0			0
$303$	−22.0559			−1.26708
$304$		0			0
$305$	34.5989			1.98113
$306$		0			0
$307$	5.26150	+	5.26150i	0.300290	+	0.300290i	0.841127	−	0.540837i	$-0.181893\pi$
$307$	5.26150	+	5.26150i	0.300290	+	0.300290i	−0.540837	+	0.841127i	$0.681893\pi$
$308$		0			0
$309$	−10.3282	+	10.3282i	−0.587554	+	0.587554i
$310$		0			0
$311$			8.74660i			0.495974i	0.968763	+	0.247987i	$0.0797690\pi$
$311$			8.74660i			0.495974i	−0.968763	+	0.247987i	$0.920231\pi$
$312$		0			0
$313$			8.77036i			0.495730i	0.968795	+	0.247865i	$0.0797289\pi$
$313$			8.77036i			0.495730i	−0.968795	+	0.247865i	$0.920271\pi$
$314$		0			0
$315$	22.1320	−	22.1320i	1.24699	−	1.24699i
$316$		0			0
$317$	15.2046	+	15.2046i	0.853975	+	0.853975i	0.990620	−	0.136645i	$-0.0436320\pi$
$317$	15.2046	+	15.2046i	0.853975	+	0.853975i	−0.136645	+	0.990620i	$0.543632\pi$
$318$		0			0
$319$	−5.45463			−0.305401
$320$		0			0
$321$	−8.75210			−0.488495
$322$		0			0
$323$	−0.251979	−	0.251979i	−0.0140205	−	0.0140205i
$324$		0			0
$325$	−10.0215	+	10.0215i	−0.555893	+	0.555893i
$326$		0			0
$327$			53.3047i			2.94776i
$328$		0			0
$329$		−	1.52393i		−	0.0840167i
$330$		0			0
$331$	−4.92777	+	4.92777i	−0.270854	+	0.270854i	−0.829444	−	0.558590i	$-0.811343\pi$
$331$	−4.92777	+	4.92777i	−0.270854	+	0.270854i	0.558590	+	0.829444i	$0.311343\pi$
$332$		0			0
$333$	−44.3345	−	44.3345i	−2.42952	−	2.42952i
$334$		0			0
$335$	25.0506			1.36866
$336$		0			0
$337$	−12.5793			−0.685237			−0.342619	−	0.939475i	$-0.611314\pi$
$337$	−12.5793			−0.685237			−0.342619	+	0.939475i	$0.611314\pi$
$338$		0			0
$339$	−28.1507	−	28.1507i	−1.52893	−	1.52893i
$340$		0			0
$341$	−3.63599	+	3.63599i	−0.196900	+	0.196900i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			18.0125i			0.969761i
$346$		0			0
$347$	3.38504	−	3.38504i	0.181718	−	0.181718i	−0.610386	−	0.792104i	$-0.708986\pi$
$347$	3.38504	−	3.38504i	0.181718	−	0.181718i	0.792104	+	0.610386i	$0.208986\pi$
$348$		0			0
$349$	−24.8531	−	24.8531i	−1.33035	−	1.33035i	−0.905051	−	0.425303i	$-0.860168\pi$
$349$	−24.8531	−	24.8531i	−1.33035	−	1.33035i	−0.425303	−	0.905051i	$-0.639832\pi$
$350$		0			0
$351$	34.9688			1.86650
$352$		0			0
$353$	8.70479			0.463309			0.231655	−	0.972798i	$-0.425586\pi$
$353$	8.70479			0.463309			0.231655	+	0.972798i	$0.425586\pi$
$354$		0			0
$355$	15.7357	+	15.7357i	0.835167	+	0.835167i
$356$		0			0
$357$	−13.6800	+	13.6800i	−0.724025	+	0.724025i
$358$		0			0
$359$		−	4.04735i		−	0.213611i	−0.994280	−	0.106805i	$-0.965938\pi$
$359$		−	4.04735i		−	0.213611i	0.994280	−	0.106805i	$-0.0340622\pi$
$360$		0			0
$361$		−	18.9960i		−	0.999791i
$362$		0			0
$363$	−23.7853	+	23.7853i	−1.24840	+	1.24840i
$364$		0			0
$365$	−21.8537	−	21.8537i	−1.14388	−	1.14388i
$366$		0			0
$367$	31.6904			1.65423			0.827113	−	0.562036i	$-0.189982\pi$
$367$	31.6904			1.65423			0.827113	+	0.562036i	$0.189982\pi$
$368$		0			0
$369$	65.3365			3.40128
$370$		0			0
$371$	4.66114	+	4.66114i	0.241994	+	0.241994i
$372$		0			0
$373$	15.1383	−	15.1383i	0.783830	−	0.783830i	−0.196645	−	0.980475i	$-0.563005\pi$
$373$	15.1383	−	15.1383i	0.783830	−	0.783830i	0.980475	+	0.196645i	$0.0630046\pi$
$374$		0			0
$375$			35.8733i			1.85249i
$376$		0			0
$377$		−	9.02869i		−	0.465001i
$378$		0			0
$379$	13.8140	−	13.8140i	0.709580	−	0.709580i	−0.256867	−	0.966447i	$-0.582690\pi$
$379$	13.8140	−	13.8140i	0.709580	−	0.709580i	0.966447	+	0.256867i	$0.0826903\pi$
$380$		0			0
$381$	28.4615	+	28.4615i	1.45813	+	1.45813i
$382$		0			0
$383$	−17.3513			−0.886610			−0.443305	−	0.896371i	$-0.646194\pi$
$383$	−17.3513			−0.886610			−0.443305	+	0.896371i	$0.646194\pi$
$384$		0			0
$385$	3.88695			0.198097
$386$		0			0
$387$	−28.0907	−	28.0907i	−1.42793	−	1.42793i
$388$		0			0
$389$	17.8880	−	17.8880i	0.906958	−	0.906958i	−0.0890675	−	0.996026i	$-0.528389\pi$
$389$	17.8880	−	17.8880i	0.906958	−	0.906958i	0.996026	+	0.0890675i	$0.0283887\pi$
$390$		0			0
$391$		−	8.28108i		−	0.418792i
$392$		0			0
$393$			53.6781i			2.70770i
$394$		0			0
$395$	−19.9353	+	19.9353i	−1.00305	+	1.00305i
$396$		0			0
$397$	4.35521	+	4.35521i	0.218582	+	0.218582i	0.807900	−	0.589319i	$-0.200604\pi$
$397$	4.35521	+	4.35521i	0.218582	+	0.218582i	−0.589319	+	0.807900i	$0.700604\pi$
$398$		0			0
$399$	0.215668			0.0107969
$400$		0			0
$401$	17.6318			0.880492			0.440246	−	0.897877i	$-0.354891\pi$
$401$	17.6318			0.880492			0.440246	+	0.897877i	$0.354891\pi$
$402$		0			0
$403$	−6.01842	−	6.01842i	−0.299799	−	0.299799i
$404$		0			0
$405$	103.473	−	103.473i	5.14160	−	5.14160i
$406$		0			0
$407$		−	7.78631i		−	0.385953i
$408$		0			0
$409$		−	24.7264i		−	1.22264i	−0.791383	−	0.611320i	$-0.790639\pi$
$409$		−	24.7264i		−	1.22264i	0.791383	−	0.611320i	$-0.209361\pi$
$410$		0			0
$411$	18.0781	−	18.0781i	0.891726	−	0.891726i
$412$		0			0
$413$	5.38865	+	5.38865i	0.265158	+	0.265158i
$414$		0			0
$415$	−37.8081			−1.85593
$416$		0			0
$417$	−1.20539			−0.0590283
$418$		0			0
$419$	−1.67364	−	1.67364i	−0.0817626	−	0.0817626i	0.665043	−	0.746805i	$-0.268413\pi$
$419$	−1.67364	−	1.67364i	−0.0817626	−	0.0817626i	−0.746805	+	0.665043i	$0.768413\pi$
$420$		0			0
$421$	−22.2705	+	22.2705i	−1.08540	+	1.08540i	−0.0894016	+	0.995996i	$0.528495\pi$
$421$	−22.2705	+	22.2705i	−1.08540	+	1.08540i	−0.995996	+	0.0894016i	$0.971505\pi$
$422$		0			0
$423$		−	13.2714i		−	0.645279i
$424$		0			0
$425$		−	44.7619i		−	2.17127i
$426$		0			0
$427$	6.80717	−	6.80717i	0.329422	−	0.329422i
$428$		0			0
$429$	4.68442	+	4.68442i	0.226166	+	0.226166i
$430$		0			0
$431$	23.0028			1.10800			0.554002	−	0.832515i	$-0.313100\pi$
$431$	23.0028			1.10800			0.554002	+	0.832515i	$0.313100\pi$
$432$		0			0
$433$	−1.31078			−0.0629921			−0.0314960	−	0.999504i	$-0.510027\pi$
$433$	−1.31078			−0.0629921			−0.0314960	+	0.999504i	$0.510027\pi$
$434$		0			0
$435$	−43.8588	−	43.8588i	−2.10287	−	2.10287i
$436$		0			0
$437$	−0.0652762	+	0.0652762i	−0.00312258	+	0.00312258i
$438$		0			0
$439$		−	36.2799i		−	1.73155i	−0.500437	−	0.865773i	$-0.666827\pi$
$439$		−	36.2799i		−	1.73155i	0.500437	−	0.865773i	$-0.333173\pi$
$440$		0			0
$441$		−	8.70871i		−	0.414701i
$442$		0			0
$443$	9.57493	−	9.57493i	0.454918	−	0.454918i	−0.442065	−	0.896983i	$-0.645754\pi$
$443$	9.57493	−	9.57493i	0.454918	−	0.454918i	0.896983	+	0.442065i	$0.145754\pi$
$444$		0			0
$445$	23.7053	+	23.7053i	1.12374	+	1.12374i
$446$		0			0
$447$	21.4389			1.01403
$448$		0			0
$449$	−3.60363			−0.170066			−0.0850329	−	0.996378i	$-0.527100\pi$
$449$	−3.60363			−0.170066			−0.0850329	+	0.996378i	$0.527100\pi$
$450$		0			0
$451$	5.73740	+	5.73740i	0.270164	+	0.270164i
$452$		0			0
$453$	−30.1178	+	30.1178i	−1.41506	+	1.41506i
$454$		0			0
$455$			6.43381i			0.301622i
$456$		0			0
$457$		−	6.35277i		−	0.297170i	−0.988900	−	0.148585i	$-0.952528\pi$
$457$		−	6.35277i		−	0.297170i	0.988900	−	0.148585i	$-0.0474719\pi$
$458$		0			0
$459$	−78.0955	+	78.0955i	−3.64518	+	3.64518i
$460$		0			0
$461$	4.16339	+	4.16339i	0.193908	+	0.193908i	0.797383	−	0.603474i	$-0.206217\pi$
$461$	4.16339	+	4.16339i	0.193908	+	0.193908i	−0.603474	+	0.797383i	$0.706217\pi$
$462$		0			0
$463$	12.7205			0.591171			0.295585	−	0.955316i	$-0.404485\pi$
$463$	12.7205			0.591171			0.295585	+	0.955316i	$0.404485\pi$
$464$		0			0
$465$	−58.4716			−2.71156
$466$		0			0
$467$	15.4085	+	15.4085i	0.713022	+	0.713022i	0.967166	−	0.254145i	$-0.0817939\pi$
$467$	15.4085	+	15.4085i	0.713022	+	0.713022i	−0.254145	+	0.967166i	$0.581794\pi$
$468$		0			0
$469$	4.92858	−	4.92858i	0.227581	−	0.227581i
$470$		0			0
$471$			17.9579i			0.827455i
$472$		0			0
$473$		−	4.93346i		−	0.226841i
$474$		0			0
$475$	−0.352839	+	0.352839i	−0.0161894	+	0.0161894i
$476$		0			0
$477$	40.5925	+	40.5925i	1.85860	+	1.85860i
$478$		0			0
$479$	26.3235			1.20275			0.601375	−	0.798967i	$-0.294620\pi$
$479$	26.3235			1.20275			0.601375	+	0.798967i	$0.294620\pi$
$480$		0			0
$481$	12.8882			0.587649
$482$		0			0
$483$	3.54387	+	3.54387i	0.161252	+	0.161252i
$484$		0			0
$485$	−1.23403	+	1.23403i	−0.0560343	+	0.0560343i
$486$		0			0
$487$			4.62575i			0.209613i	0.994493	+	0.104806i	$0.0334223\pi$
$487$			4.62575i			0.209613i	−0.994493	+	0.104806i	$0.966578\pi$
$488$		0			0
$489$		−	26.4253i		−	1.19499i
$490$		0			0
$491$	2.74222	−	2.74222i	0.123754	−	0.123754i	−0.642517	−	0.766271i	$-0.722110\pi$
$491$	2.74222	−	2.74222i	0.123754	−	0.123754i	0.766271	+	0.642517i	$0.222110\pi$
$492$		0			0
$493$	20.1637	+	20.1637i	0.908126	+	0.908126i
$494$		0			0
$495$	33.8504			1.52146
$496$		0			0
$497$	6.19187			0.277743
$498$		0			0
$499$	0.703246	+	0.703246i	0.0314816	+	0.0314816i	0.722672	−	0.691191i	$-0.242914\pi$
$499$	0.703246	+	0.703246i	0.0314816	+	0.0314816i	−0.691191	+	0.722672i	$0.742914\pi$
$500$		0			0
$501$	−20.3092	+	20.3092i	−0.907347	+	0.907347i
$502$		0			0
$503$		−	23.3204i		−	1.03980i	−0.854226	−	0.519902i	$-0.825968\pi$
$503$		−	23.3204i		−	1.03980i	0.854226	−	0.519902i	$-0.174032\pi$
$504$		0			0
$505$		−	23.1660i		−	1.03087i
$506$		0			0
$507$	23.7007	−	23.7007i	1.05259	−	1.05259i
$508$		0			0
$509$	−4.80305	−	4.80305i	−0.212891	−	0.212891i	0.592603	−	0.805495i	$-0.298100\pi$
$509$	−4.80305	−	4.80305i	−0.212891	−	0.212891i	−0.805495	+	0.592603i	$0.798100\pi$
$510$		0			0
$511$	−8.59924			−0.380408
$512$		0			0
$513$	1.23119			0.0543582
$514$		0			0
$515$	−10.8481	−	10.8481i	−0.478024	−	0.478024i
$516$		0			0
$517$	1.16541	−	1.16541i	0.0512545	−	0.0512545i
$518$		0			0
$519$		−	39.5376i		−	1.73551i
$520$		0			0
$521$			33.2330i			1.45596i	0.685596	+	0.727982i	$0.259542\pi$
$521$			33.2330i			1.45596i	−0.685596	+	0.727982i	$0.740458\pi$
$522$		0			0
$523$	20.4284	−	20.4284i	0.893271	−	0.893271i	−0.101559	−	0.994830i	$-0.532383\pi$
$523$	20.4284	−	20.4284i	0.893271	−	0.893271i	0.994830	+	0.101559i	$0.0323830\pi$
$524$		0			0
$525$	19.1558	+	19.1558i	0.836027	+	0.836027i
$526$		0			0
$527$	26.8818			1.17099
$528$		0			0
$529$	20.8548			0.906728
$530$		0			0
$531$	46.9282	+	46.9282i	2.03651	+	2.03651i
$532$		0			0
$533$	−9.49674	+	9.49674i	−0.411350	+	0.411350i
$534$		0			0
$535$		−	9.19260i		−	0.397431i
$536$		0			0
$537$			66.6140i			2.87461i
$538$		0			0
$539$	0.764739	−	0.764739i	0.0329397	−	0.0329397i
$540$		0			0
$541$	−3.50325	−	3.50325i	−0.150617	−	0.150617i	0.627777	−	0.778393i	$-0.283965\pi$
$541$	−3.50325	−	3.50325i	−0.150617	−	0.150617i	−0.778393	+	0.627777i	$0.783965\pi$
$542$		0			0
$543$	−39.2791			−1.68563
$544$		0			0
$545$	−55.9876			−2.39824
$546$		0			0
$547$	21.9766	+	21.9766i	0.939652	+	0.939652i	0.998280	−	0.0586277i	$-0.0186725\pi$
$547$	21.9766	+	21.9766i	0.939652	+	0.939652i	−0.0586277	+	0.998280i	$0.518672\pi$
$548$		0			0
$549$	59.2817	−	59.2817i	2.53008	−	2.53008i
$550$		0			0
$551$		−	0.317883i		−	0.0135423i
$552$		0			0
$553$			7.84435i			0.333576i
$554$		0			0
$555$	62.6071	−	62.6071i	2.65752	−	2.65752i
$556$		0			0
$557$	−4.25629	−	4.25629i	−0.180345	−	0.180345i	0.611161	−	0.791506i	$-0.290703\pi$
$557$	−4.25629	−	4.25629i	−0.180345	−	0.180345i	−0.791506	+	0.611161i	$0.790703\pi$
$558$		0			0
$559$	8.16603			0.345386
$560$		0			0
$561$	−20.9233			−0.883384
$562$		0			0
$563$	−8.97634	−	8.97634i	−0.378307	−	0.378307i	0.492184	−	0.870491i	$-0.336199\pi$
$563$	−8.97634	−	8.97634i	−0.378307	−	0.378307i	−0.870491	+	0.492184i	$0.836199\pi$
$564$		0			0
$565$	29.5675	−	29.5675i	1.24392	−	1.24392i
$566$		0			0
$567$		−	40.7155i		−	1.70989i
$568$		0			0
$569$		−	12.3968i		−	0.519701i	−0.965649	−	0.259851i	$-0.916327\pi$
$569$		−	12.3968i		−	0.519701i	0.965649	−	0.259851i	$-0.0836733\pi$
$570$		0			0
$571$	5.24097	−	5.24097i	0.219328	−	0.219328i	−0.588887	−	0.808215i	$-0.700434\pi$
$571$	5.24097	−	5.24097i	0.219328	−	0.219328i	0.808215	+	0.588887i	$0.200434\pi$
$572$		0			0
$573$	40.1408	+	40.1408i	1.67691	+	1.67691i
$574$		0			0
$575$	−11.5958			−0.483577
$576$		0			0
$577$	43.5232			1.81189			0.905947	−	0.423390i	$-0.139160\pi$
$577$	43.5232			1.81189			0.905947	+	0.423390i	$0.139160\pi$
$578$		0			0
$579$	−3.20015	−	3.20015i	−0.132994	−	0.132994i
$580$		0			0
$581$	−7.43857	+	7.43857i	−0.308604	+	0.308604i
$582$		0			0
$583$			7.12912i			0.295258i
$584$		0			0
$585$			56.0302i			2.31657i
$586$		0			0
$587$	−2.64923	+	2.64923i	−0.109346	+	0.109346i	−0.759663	−	0.650317i	$-0.774636\pi$
$587$	−2.64923	+	2.64923i	−0.109346	+	0.109346i	0.650317	+	0.759663i	$0.274636\pi$
$588$		0			0
$589$	−0.211897	−	0.211897i	−0.00873108	−	0.00873108i
$590$		0			0
$591$	55.9299			2.30065
$592$		0			0
$593$	5.12318			0.210384			0.105192	−	0.994452i	$-0.466454\pi$
$593$	5.12318			0.210384			0.105192	+	0.994452i	$0.466454\pi$
$594$		0			0
$595$	−14.3686	−	14.3686i	−0.589054	−	0.589054i
$596$		0			0
$597$	−63.2532	+	63.2532i	−2.58878	+	2.58878i
$598$		0			0
$599$		−	39.6945i		−	1.62187i	−0.585135	−	0.810936i	$-0.698959\pi$
$599$		−	39.6945i		−	1.62187i	0.585135	−	0.810936i	$-0.301041\pi$
$600$		0			0
$601$			19.6274i			0.800620i	0.916380	+	0.400310i	$0.131097\pi$
$601$			19.6274i			0.800620i	−0.916380	+	0.400310i	$0.868903\pi$
$602$		0			0
$603$	42.9216	−	42.9216i	1.74790	−	1.74790i
$604$		0			0
$605$	−24.9824	−	24.9824i	−1.01568	−	1.01568i
$606$		0			0
$607$	−25.7837			−1.04653			−0.523264	−	0.852170i	$-0.675286\pi$
$607$	−25.7837			−1.04653			−0.523264	+	0.852170i	$0.675286\pi$
$608$		0			0
$609$	−17.2580			−0.699331
$610$		0			0
$611$	1.92902	+	1.92902i	0.0780397	+	0.0780397i
$612$		0			0
$613$	4.09160	−	4.09160i	0.165258	−	0.165258i	−0.619633	−	0.784891i	$-0.712719\pi$
$613$	4.09160	−	4.09160i	0.165258	−	0.165258i	0.784891	+	0.619633i	$0.212719\pi$
$614$		0			0
$615$			92.2651i			3.72049i
$616$		0			0
$617$		−	10.4658i		−	0.421337i	−0.977558	−	0.210668i	$-0.932436\pi$
$617$		−	10.4658i		−	0.421337i	0.977558	−	0.210668i	$-0.0675640\pi$
$618$		0			0
$619$	21.5251	−	21.5251i	0.865166	−	0.865166i	−0.126766	−	0.991933i	$-0.540460\pi$
$619$	21.5251	−	21.5251i	0.865166	−	0.865166i	0.991933	+	0.126766i	$0.0404599\pi$
$620$		0			0
$621$	20.2310	+	20.2310i	0.811841	+	0.811841i
$622$		0			0
$623$	9.32780			0.373711
$624$		0			0
$625$	1.90615			0.0762459
$626$		0			0
$627$	0.164930	+	0.164930i	0.00658666	+	0.00658666i
$628$		0			0
$629$	−28.7830	+	28.7830i	−1.14765	+	1.14765i
$630$		0			0
$631$			0.948167i			0.0377459i	0.999822	+	0.0188730i	$0.00600781\pi$
$631$			0.948167i			0.0377459i	−0.999822	+	0.0188730i	$0.993992\pi$
$632$		0			0
$633$			84.6052i			3.36275i
$634$		0			0
$635$	−29.8940	+	29.8940i	−1.18631	+	1.18631i
$636$		0			0
$637$	1.26582	+	1.26582i	0.0501537	+	0.0501537i
$638$		0			0
$639$	53.9232			2.13317
$640$		0			0
$641$	12.1984			0.481808			0.240904	−	0.970549i	$-0.422556\pi$
$641$	12.1984			0.481808			0.240904	+	0.970549i	$0.422556\pi$
$642$		0			0
$643$	−35.6860	−	35.6860i	−1.40732	−	1.40732i	−0.773402	−	0.633916i	$-0.781446\pi$
$643$	−35.6860	−	35.6860i	−1.40732	−	1.40732i	−0.633916	−	0.773402i	$-0.718554\pi$
$644$		0			0
$645$	39.6683	−	39.6683i	1.56194	−	1.56194i
$646$		0			0
$647$		−	29.4906i		−	1.15939i	−0.814832	−	0.579697i	$-0.803171\pi$
$647$		−	29.4906i		−	1.15939i	0.814832	−	0.579697i	$-0.196829\pi$
$648$		0			0
$649$			8.24183i			0.323520i
$650$		0			0
$651$	−11.5040	+	11.5040i	−0.450878	+	0.450878i
$652$		0			0
$653$	−30.8952	−	30.8952i	−1.20902	−	1.20902i	−0.971344	−	0.237679i	$-0.923613\pi$
$653$	−30.8952	−	30.8952i	−1.20902	−	1.20902i	−0.237679	−	0.971344i	$-0.576387\pi$
$654$		0			0
$655$	−56.3798			−2.20294
$656$		0			0
$657$	−74.8883			−2.92167
$658$		0			0
$659$	−12.6158	−	12.6158i	−0.491443	−	0.491443i	0.417317	−	0.908761i	$-0.362970\pi$
$659$	−12.6158	−	12.6158i	−0.491443	−	0.491443i	−0.908761	+	0.417317i	$0.862970\pi$
$660$		0			0
$661$	−20.5214	+	20.5214i	−0.798189	+	0.798189i	−0.982810	−	0.184621i	$-0.940894\pi$
$661$	−20.5214	+	20.5214i	−0.798189	+	0.798189i	0.184621	+	0.982810i	$0.440894\pi$
$662$		0			0
$663$		−	34.6330i		−	1.34503i
$664$		0			0
$665$			0.226523i			0.00878418i
$666$		0			0
$667$	5.22349	−	5.22349i	0.202254	−	0.202254i
$668$		0			0
$669$	23.4853	+	23.4853i	0.907995	+	0.907995i
$670$		0			0
$671$	10.4114			0.401929
$672$		0			0
$673$	19.4620			0.750205			0.375103	−	0.926983i	$-0.377607\pi$
$673$	19.4620			0.750205			0.375103	+	0.926983i	$0.377607\pi$
$674$		0			0
$675$	109.355	+	109.355i	4.20907	+	4.20907i
$676$		0			0
$677$	−3.68505	+	3.68505i	−0.141628	+	0.141628i	−0.774366	−	0.632738i	$-0.781931\pi$
$677$	−3.68505	+	3.68505i	−0.141628	+	0.141628i	0.632738	+	0.774366i	$0.281931\pi$
$678$		0			0
$679$			0.485578i			0.0186348i
$680$		0			0
$681$		−	81.2802i		−	3.11466i
$682$		0			0
$683$	0.819191	−	0.819191i	0.0313455	−	0.0313455i	−0.691260	−	0.722606i	$-0.742944\pi$
$683$	0.819191	−	0.819191i	0.0313455	−	0.0313455i	0.722606	+	0.691260i	$0.242944\pi$
$684$		0			0
$685$	18.9880	+	18.9880i	0.725493	+	0.725493i
$686$		0			0
$687$	−63.6772			−2.42944
$688$		0			0
$689$	−11.8003			−0.449558
$690$		0			0
$691$	−9.07535	−	9.07535i	−0.345243	−	0.345243i	0.513091	−	0.858334i	$-0.328500\pi$
$691$	−9.07535	−	9.07535i	−0.345243	−	0.345243i	−0.858334	+	0.513091i	$0.828500\pi$
$692$		0			0
$693$	6.65990	−	6.65990i	0.252989	−	0.252989i
$694$		0			0
$695$		−	1.26606i		−	0.0480244i
$696$		0			0
$697$		−	42.4180i		−	1.60670i
$698$		0			0
$699$	26.0908	−	26.0908i	0.986845	−	0.986845i
$700$		0			0
$701$	22.5919	+	22.5919i	0.853286	+	0.853286i	0.990536	−	0.137250i	$-0.0438265\pi$
$701$	22.5919	+	22.5919i	0.853286	+	0.853286i	−0.137250	+	0.990536i	$0.543827\pi$
$702$		0			0
$703$	0.453768			0.0171142
$704$		0			0
$705$	18.7413			0.705837
$706$		0			0
$707$	−4.55780	−	4.55780i	−0.171414	−	0.171414i
$708$		0			0
$709$	13.6206	−	13.6206i	0.511532	−	0.511532i	−0.403464	−	0.914996i	$-0.632194\pi$
$709$	13.6206	−	13.6206i	0.511532	−	0.511532i	0.914996	+	0.403464i	$0.132194\pi$
$710$		0			0
$711$			68.3142i			2.56198i
$712$		0			0
$713$		−	6.96383i		−	0.260798i
$714$		0			0
$715$	−4.92019	+	4.92019i	−0.184005	+	0.184005i
$716$		0			0
$717$	−5.04023	−	5.04023i	−0.188231	−	0.188231i
$718$		0			0
$719$	25.9785			0.968836			0.484418	−	0.874837i	$-0.339031\pi$
$719$	25.9785			0.968836			0.484418	+	0.874837i	$0.339031\pi$
$720$		0			0
$721$	−4.26862			−0.158972
$722$		0			0
$723$	−38.4271	−	38.4271i	−1.42912	−	1.42912i
$724$		0			0
$725$	28.2346	−	28.2346i	1.04861	−	1.04861i
$726$		0			0
$727$			27.5763i			1.02275i	0.859358	+	0.511375i	$0.170864\pi$
$727$			27.5763i			1.02275i	−0.859358	+	0.511375i	$0.829136\pi$
$728$		0			0
$729$		−	154.055i		−	5.70574i
$730$		0			0
$731$	−18.2371	+	18.2371i	−0.674524	+	0.674524i
$732$		0			0
$733$	−30.1992	−	30.1992i	−1.11543	−	1.11543i	−0.992403	−	0.123029i	$-0.960739\pi$
$733$	−30.1992	−	30.1992i	−1.11543	−	1.11543i	−0.123029	−	0.992403i	$-0.539261\pi$
$734$		0			0
$735$	12.2980			0.453619
$736$		0			0
$737$	7.53816			0.277672
$738$		0			0
$739$	36.5445	+	36.5445i	1.34431	+	1.34431i	0.891718	+	0.452592i	$0.149501\pi$
$739$	36.5445	+	36.5445i	1.34431	+	1.34431i	0.452592	+	0.891718i	$0.350499\pi$
$740$		0			0
$741$	−0.272997	+	0.272997i	−0.0100288	+	0.0100288i
$742$		0			0
$743$		−	43.1375i		−	1.58256i	−0.611452	−	0.791281i	$-0.709414\pi$
$743$		−	43.1375i		−	1.58256i	0.611452	−	0.791281i	$-0.290586\pi$
$744$		0			0
$745$			22.5180i			0.824994i
$746$		0			0
$747$	−64.7804	+	64.7804i	−2.37019	+	2.37019i
$748$		0			0
$749$	−1.80860	−	1.80860i	−0.0660848	−	0.0660848i
$750$		0			0
$751$	−9.04305			−0.329986			−0.164993	−	0.986295i	$-0.552760\pi$
$751$	−9.04305			−0.329986			−0.164993	+	0.986295i	$0.552760\pi$
$752$		0			0
$753$	−82.8591			−3.01955
$754$		0			0
$755$	−31.6336	−	31.6336i	−1.15126	−	1.15126i
$756$		0			0
$757$	−1.07442	+	1.07442i	−0.0390505	+	0.0390505i	−0.726362	−	0.687312i	$-0.758791\pi$
$757$	−1.07442	+	1.07442i	−0.0390505	+	0.0390505i	0.687312	+	0.726362i	$0.258791\pi$
$758$		0			0
$759$			5.42028i			0.196744i
$760$		0			0
$761$		−	34.1138i		−	1.23662i	−0.785932	−	0.618312i	$-0.787817\pi$
$761$		−	34.1138i		−	1.23662i	0.785932	−	0.618312i	$-0.212183\pi$
$762$		0			0
$763$	−11.0153	+	11.0153i	−0.398780	+	0.398780i
$764$		0			0
$765$	−125.132	−	125.132i	−4.52415	−	4.52415i
$766$		0			0
$767$	−13.6422			−0.492590
$768$		0			0
$769$	−54.2612			−1.95671			−0.978354	−	0.206939i	$-0.933650\pi$
$769$	−54.2612			−1.95671			−0.978354	+	0.206939i	$0.933650\pi$
$770$		0			0
$771$	−39.6807	−	39.6807i	−1.42906	−	1.42906i
$772$		0			0
$773$	25.6779	−	25.6779i	0.923571	−	0.923571i	−0.0737087	−	0.997280i	$-0.523484\pi$
$773$	25.6779	−	25.6779i	0.923571	−	0.923571i	0.997280	+	0.0737087i	$0.0234835\pi$
$774$		0			0
$775$		−	37.6418i		−	1.35213i
$776$		0			0
$777$		−	24.6353i		−	0.883786i
$778$		0			0
$779$	−0.334363	+	0.334363i	−0.0119798	+	0.0119798i
$780$		0			0
$781$	4.73517	+	4.73517i	0.169438	+	0.169438i
$782$		0			0
$783$	−98.5212			−3.52086
$784$		0			0
$785$	−18.8617			−0.673203
$786$		0			0
$787$	16.3479	+	16.3479i	0.582741	+	0.582741i	0.935656	−	0.352914i	$-0.114809\pi$
$787$	16.3479	+	16.3479i	0.582741	+	0.582741i	−0.352914	+	0.935656i	$0.614809\pi$
$788$		0			0
$789$	−59.2744	+	59.2744i	−2.11022	+	2.11022i
$790$		0			0
$791$		−	11.6345i		−	0.413677i
$792$		0			0
$793$			17.2333i			0.611974i
$794$		0			0
$795$	−57.3228	+	57.3228i	−2.03303	+	2.03303i
$796$		0			0
$797$	−29.8211	−	29.8211i	−1.05632	−	1.05632i	−0.998317	−	0.0580002i	$-0.981528\pi$
$797$	−29.8211	−	29.8211i	−1.05632	−	1.05632i	−0.0580002	−	0.998317i	$-0.518472\pi$
$798$		0			0
$799$	−8.61612			−0.304816
$800$		0			0
$801$	81.2332			2.87023
$802$		0			0
$803$	−6.57618	−	6.57618i	−0.232068	−	0.232068i
$804$		0			0
$805$	−3.72224	+	3.72224i	−0.131192	+	0.131192i
$806$		0			0
$807$		−	5.09455i		−	0.179337i
$808$		0			0
$809$			33.6378i			1.18264i	0.806437	+	0.591320i	$0.201393\pi$
$809$			33.6378i			1.18264i	−0.806437	+	0.591320i	$0.798607\pi$
$810$		0			0
$811$	20.1583	−	20.1583i	0.707854	−	0.707854i	−0.258230	−	0.966084i	$-0.583139\pi$
$811$	20.1583	−	20.1583i	0.707854	−	0.707854i	0.966084	+	0.258230i	$0.0831391\pi$
$812$		0			0
$813$	−67.8589	−	67.8589i	−2.37991	−	2.37991i
$814$		0			0
$815$	27.7553			0.972226
$816$		0			0
$817$	0.287511			0.0100587
$818$		0			0
$819$	11.0237	+	11.0237i	0.385199	+	0.385199i
$820$		0			0
$821$	39.5171	−	39.5171i	1.37915	−	1.37915i	0.533107	−	0.846048i	$-0.321024\pi$
$821$	39.5171	−	39.5171i	1.37915	−	1.37915i	0.846048	−	0.533107i	$-0.178976\pi$
$822$		0			0
$823$			9.35542i			0.326109i	0.986617	+	0.163055i	$0.0521347\pi$
$823$			9.35542i			0.326109i	−0.986617	+	0.163055i	$0.947865\pi$
$824$		0			0
$825$			29.2984i			1.02004i
$826$		0			0
$827$	−32.3120	+	32.3120i	−1.12360	+	1.12360i	−0.132402	+	0.991196i	$0.542269\pi$
$827$	−32.3120	+	32.3120i	−1.12360	+	1.12360i	−0.991196	+	0.132402i	$0.957731\pi$
$828$		0			0
$829$	−5.08302	−	5.08302i	−0.176541	−	0.176541i	0.613305	−	0.789846i	$-0.289840\pi$
$829$	−5.08302	−	5.08302i	−0.176541	−	0.176541i	−0.789846	+	0.613305i	$0.789840\pi$
$830$		0			0
$831$	17.4068			0.603834
$832$		0			0
$833$	−5.65390			−0.195896
$834$		0			0
$835$	−21.3313	−	21.3313i	−0.738202	−	0.738202i
$836$		0			0
$837$	−65.6731	+	65.6731i	−2.26999	+	2.26999i
$838$		0			0
$839$		−	1.28514i		−	0.0443681i	−0.999754	−	0.0221841i	$-0.992938\pi$
$839$		−	1.28514i		−	0.0443681i	0.999754	−	0.0221841i	$-0.00706199\pi$
$840$		0			0
$841$		−	3.56255i		−	0.122846i
$842$		0			0
$843$	5.64331	−	5.64331i	0.194366	−	0.194366i
$844$		0			0
$845$	24.8936	+	24.8936i	0.856365	+	0.856365i
$846$		0			0
$847$	−9.83035			−0.337775
$848$		0			0
$849$	−21.7470			−0.746356
$850$		0			0
$851$	7.45636	+	7.45636i	0.255601	+	0.255601i
$852$		0			0
$853$	9.60791	−	9.60791i	0.328969	−	0.328969i	−0.523226	−	0.852194i	$-0.675271\pi$
$853$	9.60791	−	9.60791i	0.328969	−	0.328969i	0.852194	+	0.523226i	$0.175271\pi$
$854$		0			0
$855$			1.97272i			0.0674657i
$856$		0			0
$857$			35.7439i			1.22099i	0.792021	+	0.610494i	$0.209029\pi$
$857$			35.7439i			1.22099i	−0.792021	+	0.610494i	$0.790971\pi$
$858$		0			0
$859$	25.0570	−	25.0570i	0.854933	−	0.854933i	−0.135803	−	0.990736i	$-0.543361\pi$
$859$	25.0570	−	25.0570i	0.854933	−	0.854933i	0.990736	+	0.135803i	$0.0433614\pi$
$860$		0			0
$861$	18.1527	+	18.1527i	0.618643	+	0.618643i
$862$		0			0
$863$	18.5689			0.632092			0.316046	−	0.948744i	$-0.397645\pi$
$863$	18.5689			0.632092			0.316046	+	0.948744i	$0.397645\pi$
$864$		0			0
$865$	41.5276			1.41198
$866$		0			0
$867$	36.2128	+	36.2128i	1.22985	+	1.22985i
$868$		0			0
$869$	−5.99888	+	5.99888i	−0.203498	+	0.203498i
$870$		0			0
$871$			12.4774i			0.422781i
$872$		0			0
$873$			4.22876i			0.143122i
$874$		0			0
$875$	−7.41313	+	7.41313i	−0.250610	+	0.250610i
$876$		0			0
$877$	−39.9442	−	39.9442i	−1.34882	−	1.34882i	−0.886946	−	0.461873i	$-0.847177\pi$
$877$	−39.9442	−	39.9442i	−1.34882	−	1.34882i	−0.461873	−	0.886946i	$-0.652823\pi$
$878$		0			0
$879$	4.98103			0.168006
$880$		0			0
$881$	41.1798			1.38738			0.693691	−	0.720273i	$-0.255983\pi$
$881$	41.1798			1.38738			0.693691	+	0.720273i	$0.255983\pi$
$882$		0			0
$883$	26.9999	+	26.9999i	0.908618	+	0.908618i	0.996161	−	0.0875424i	$-0.0279013\pi$
$883$	26.9999	+	26.9999i	0.908618	+	0.908618i	−0.0875424	+	0.996161i	$0.527901\pi$
$884$		0			0
$885$	−66.2698	+	66.2698i	−2.22763	+	2.22763i
$886$		0			0
$887$			47.5720i			1.59731i	0.601788	+	0.798656i	$0.294455\pi$
$887$			47.5720i			1.59731i	−0.601788	+	0.798656i	$0.705545\pi$
$888$		0			0
$889$			11.7630i			0.394519i
$890$		0			0
$891$	31.1368	−	31.1368i	1.04312	−	1.04312i
$892$		0			0
$893$	0.0679172	+	0.0679172i	0.00227276	+	0.00227276i
$894$		0			0
$895$	−69.9667			−2.33873
$896$		0			0
$897$	−8.97183			−0.299561
$898$		0			0
$899$	16.9563	+	16.9563i	0.565525	+	0.565525i
$900$		0			0
$901$	26.3536	−	26.3536i	0.877966	−	0.877966i
$902$		0			0
$903$		−	15.6091i		−	0.519438i
$904$		0			0
$905$		−	41.2561i		−	1.37140i
$906$		0			0
$907$	23.3827	−	23.3827i	0.776408	−	0.776408i	−0.202810	−	0.979218i	$-0.565007\pi$
$907$	23.3827	−	23.3827i	0.776408	−	0.776408i	0.979218	+	0.202810i	$0.0650073\pi$
$908$		0			0
$909$	−39.6926	−	39.6926i	−1.31652	−	1.31652i
$910$		0			0
$911$	36.5816			1.21200			0.606002	−	0.795463i	$-0.292772\pi$
$911$	36.5816			1.21200			0.606002	+	0.795463i	$0.292772\pi$
$912$		0			0
$913$	−11.3771			−0.376528
$914$		0			0
$915$	83.7148	+	83.7148i	2.76753	+	2.76753i
$916$		0			0
$917$	−11.0924	+	11.0924i	−0.366305	+	0.366305i
$918$		0			0
$919$			16.2676i			0.536618i	0.963333	+	0.268309i	$0.0864648\pi$
$919$			16.2676i			0.536618i	−0.963333	+	0.268309i	$0.913535\pi$
$920$		0			0
$921$			25.4612i			0.838976i
$922$		0			0
$923$	−7.83780	+	7.83780i	−0.257984	+	0.257984i
$924$		0			0
$925$	40.3040	+	40.3040i	1.32519	+	1.32519i
$926$		0			0
$927$	−37.1742			−1.22096
$928$		0			0
$929$	11.1820			0.366871			0.183435	−	0.983032i	$-0.441278\pi$
$929$	11.1820			0.366871			0.183435	+	0.983032i	$0.441278\pi$
$930$		0			0
$931$	0.0445673	+	0.0445673i	0.00146063	+	0.00146063i
$932$		0			0
$933$	−21.1631	+	21.1631i	−0.692848	+	0.692848i
$934$		0			0
$935$		−	21.9764i		−	0.718706i
$936$		0			0
$937$			37.5933i			1.22812i	0.789260	+	0.614059i	$0.210464\pi$
$937$			37.5933i			1.22812i	−0.789260	+	0.614059i	$0.789536\pi$
$938$		0			0
$939$	−21.2206	+	21.2206i	−0.692507	+	0.692507i
$940$		0			0
$941$	−14.0965	−	14.0965i	−0.459532	−	0.459532i	0.438970	−	0.898502i	$-0.355344\pi$
$941$	−14.0965	−	14.0965i	−0.459532	−	0.459532i	−0.898502	+	0.438970i	$0.855344\pi$
$942$		0			0
$943$	−10.9886			−0.357837
$944$		0			0
$945$	70.2059			2.28380
$946$		0			0
$947$	7.95369	+	7.95369i	0.258460	+	0.258460i	0.824428	−	0.565967i	$-0.191497\pi$
$947$	7.95369	+	7.95369i	0.258460	+	0.258460i	−0.565967	+	0.824428i	$0.691497\pi$
$948$		0			0
$949$	10.8851	−	10.8851i	0.353346	−	0.353346i
$950$		0			0
$951$			73.5774i			2.38591i
$952$		0			0
$953$			29.7695i			0.964329i	0.876081	+	0.482164i	$0.160149\pi$
$953$			29.7695i			0.964329i	−0.876081	+	0.482164i	$0.839851\pi$
$954$		0			0
$955$	−42.1612	+	42.1612i	−1.36430	+	1.36430i
$956$		0			0
$957$	−13.1979	−	13.1979i	−0.426628	−	0.426628i
$958$		0			0
$959$	7.47159			0.241270
$960$		0			0
$961$	−8.39424			−0.270782
$962$		0			0
$963$	−15.7506	−	15.7506i	−0.507555	−	0.507555i
$964$		0			0
$965$	3.36122	−	3.36122i	0.108201	−	0.108201i
$966$		0			0
$967$			55.3211i			1.77901i	0.456927	+	0.889504i	$0.348950\pi$
$967$			55.3211i			1.77901i	−0.456927	+	0.889504i	$0.651050\pi$
$968$		0			0
$969$		−	1.21936i		−	0.0391716i
$970$		0			0
$971$	−8.46733	+	8.46733i	−0.271730	+	0.271730i	−0.829796	−	0.558067i	$-0.811543\pi$
$971$	−8.46733	+	8.46733i	−0.271730	+	0.271730i	0.558067	+	0.829796i	$0.311543\pi$
$972$		0			0
$973$	−0.249091	−	0.249091i	−0.00798551	−	0.00798551i
$974$		0			0
$975$	−48.4956			−1.55310
$976$		0			0
$977$	39.7381			1.27133			0.635667	−	0.771963i	$-0.280725\pi$
$977$	39.7381			1.27133			0.635667	+	0.771963i	$0.280725\pi$
$978$		0			0
$979$	7.13334	+	7.13334i	0.227983	+	0.227983i
$980$		0			0
$981$	−95.9290	+	95.9290i	−3.06278	+	3.06278i
$982$		0			0
$983$		−	5.03380i		−	0.160553i	−0.996773	−	0.0802766i	$-0.974420\pi$
$983$		−	5.03380i		−	0.160553i	0.996773	−	0.0802766i	$-0.0255804\pi$
$984$		0			0
$985$			58.7449i			1.87177i
$986$		0			0
$987$	3.68726	−	3.68726i	0.117367	−	0.117367i
$988$		0			0
$989$	4.72441	+	4.72441i	0.150227	+	0.150227i
$990$		0			0
$991$	−28.5560			−0.907110			−0.453555	−	0.891228i	$-0.649844\pi$
$991$	−28.5560			−0.907110			−0.453555	+	0.891228i	$0.649844\pi$
$992$		0			0
$993$	−23.8462			−0.756737
$994$		0			0
$995$	−66.4368	−	66.4368i	−2.10619	−	2.10619i
$996$		0			0
$997$	−18.6687	+	18.6687i	−0.591243	+	0.591243i	−0.937967	−	0.346724i	$-0.887294\pi$
$997$	−18.6687	+	18.6687i	−0.591243	+	0.591243i	0.346724	+	0.937967i	$0.387294\pi$
$998$		0			0
$999$		−	140.636i		−	4.44952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.g.1345.8	yes	16
4.3	odd	2		1792.2.m.e.1345.1	yes	16
8.3	odd	2		1792.2.m.h.1345.8	yes	16
8.5	even	2		1792.2.m.f.1345.1	yes	16
16.3	odd	4		1792.2.m.h.449.8	yes	16
16.5	even	4	inner	1792.2.m.g.449.8	yes	16
16.11	odd	4		1792.2.m.e.449.1	✓	16
16.13	even	4		1792.2.m.f.449.1	yes	16
32.5	even	8		7168.2.a.ba.1.1		8
32.11	odd	8		7168.2.a.bf.1.1		8
32.21	even	8		7168.2.a.be.1.8		8
32.27	odd	8		7168.2.a.bb.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.1	✓	16	16.11	odd	4
1792.2.m.e.1345.1	yes	16	4.3	odd	2
1792.2.m.f.449.1	yes	16	16.13	even	4
1792.2.m.f.1345.1	yes	16	8.5	even	2
1792.2.m.g.449.8	yes	16	16.5	even	4	inner
1792.2.m.g.1345.8	yes	16	1.1	even	1	trivial
1792.2.m.h.449.8	yes	16	16.3	odd	4
1792.2.m.h.1345.8	yes	16	8.3	odd	2
7168.2.a.ba.1.1		8	32.5	even	8
7168.2.a.bb.1.8		8	32.27	odd	8
7168.2.a.be.1.8		8	32.21	even	8
7168.2.a.bf.1.1		8	32.11	odd	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.41958 + 2.41958i) q^{3} +(-2.54136 + 2.54136i) q^{5} +1.00000i q^{7} +8.70871i q^{9} +O(q^{10})\)	\(q+(2.41958 + 2.41958i) q^{3} +(-2.54136 + 2.54136i) q^{5} +1.00000i q^{7} +8.70871i q^{9} +(-0.764739 + 0.764739i) q^{11} +(-1.26582 - 1.26582i) q^{13} -12.2980 q^{15} +5.65390 q^{17} +(-0.0445673 - 0.0445673i) q^{19} +(-2.41958 + 2.41958i) q^{21} -1.46467i q^{23} -7.91700i q^{25} +(-13.8127 + 13.8127i) q^{27} +(3.56633 + 3.56633i) q^{29} +4.75455 q^{31} -3.70069 q^{33} +(-2.54136 - 2.54136i) q^{35} +(-5.09082 + 5.09082i) q^{37} -6.12551i q^{39} -7.50243i q^{41} +(-3.22558 + 3.22558i) q^{43} +(-22.1320 - 22.1320i) q^{45} -1.52393 q^{47} -1.00000 q^{49} +(13.6800 + 13.6800i) q^{51} +(4.66114 - 4.66114i) q^{53} -3.88695i q^{55} -0.215668i q^{57} +(5.38865 - 5.38865i) q^{59} +(-6.80717 - 6.80717i) q^{61} -8.70871 q^{63} +6.43381 q^{65} +(-4.92858 - 4.92858i) q^{67} +(3.54387 - 3.54387i) q^{69} -6.19187i q^{71} +8.59924i q^{73} +(19.1558 - 19.1558i) q^{75} +(-0.764739 - 0.764739i) q^{77} +7.84435 q^{79} -40.7155 q^{81} +(7.43857 + 7.43857i) q^{83} +(-14.3686 + 14.3686i) q^{85} +17.2580i q^{87} -9.32780i q^{89} +(1.26582 - 1.26582i) q^{91} +(11.5040 + 11.5040i) q^{93} +0.226523 q^{95} +0.485578 q^{97} +(-6.65990 - 6.65990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 - 4 * q^5	\( 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Introduction

L-functions

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