LMFDB - Embedded newform 1792.2.m.f.1345.1

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			1345.1
Root			$0.117630 + 0.893490i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.f.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41958 - 2.41958i) q^{3} +(2.54136 - 2.54136i) q^{5} +1.00000i q^{7} +8.70871i q^{9} +O(q^{10})$	\(q+(-2.41958 - 2.41958i) q^{3} +(2.54136 - 2.54136i) q^{5} +1.00000i q^{7} +8.70871i q^{9} +(0.764739 - 0.764739i) q^{11} +(1.26582 + 1.26582i) q^{13} -12.2980 q^{15} +5.65390 q^{17} +(0.0445673 + 0.0445673i) q^{19} +(2.41958 - 2.41958i) q^{21} -1.46467i q^{23} -7.91700i q^{25} +(13.8127 - 13.8127i) q^{27} +(-3.56633 - 3.56633i) q^{29} +4.75455 q^{31} -3.70069 q^{33} +(2.54136 + 2.54136i) q^{35} +(5.09082 - 5.09082i) q^{37} -6.12551i q^{39} -7.50243i q^{41} +(3.22558 - 3.22558i) q^{43} +(22.1320 + 22.1320i) q^{45} -1.52393 q^{47} -1.00000 q^{49} +(-13.6800 - 13.6800i) q^{51} +(-4.66114 + 4.66114i) q^{53} -3.88695i q^{55} -0.215668i q^{57} +(-5.38865 + 5.38865i) q^{59} +(6.80717 + 6.80717i) q^{61} -8.70871 q^{63} +6.43381 q^{65} +(4.92858 + 4.92858i) q^{67} +(-3.54387 + 3.54387i) q^{69} -6.19187i q^{71} +8.59924i q^{73} +(-19.1558 + 19.1558i) q^{75} +(0.764739 + 0.764739i) q^{77} +7.84435 q^{79} -40.7155 q^{81} +(-7.43857 - 7.43857i) q^{83} +(14.3686 - 14.3686i) q^{85} +17.2580i q^{87} -9.32780i q^{89} +(-1.26582 + 1.26582i) q^{91} +(-11.5040 - 11.5040i) q^{93} +0.226523 q^{95} +0.485578 q^{97} +(6.65990 + 6.65990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.799796\pi$
$3$	−2.41958	−	2.41958i	−1.39694	−	1.39694i	−0.588304	−	0.808640i	$-0.700204\pi$
$4$		0			0
$5$	2.54136	−	2.54136i	1.13653	−	1.13653i	0.147462	−	0.989068i	$-0.452890\pi$
$5$	2.54136	−	2.54136i	1.13653	−	1.13653i	0.989068	−	0.147462i	$-0.0471104\pi$
$6$		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	−0.582356	−	0.812934i	$-0.697869\pi$
$11$	0.764739	−	0.764739i	0.230578	−	0.230578i	0.812934	+	0.582356i	$0.197869\pi$
$12$		0			0
$13$	1.26582	+	1.26582i	0.351076	+	0.351076i	0.860510	−	0.509434i	$-0.170145\pi$
$13$	1.26582	+	1.26582i	0.351076	+	0.351076i	−0.509434	+	0.860510i	$0.670145\pi$
$14$		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	0.712201	−	0.701976i	$-0.247699\pi$
$19$	0.0445673	+	0.0445673i	0.0102244	+	0.0102244i	−0.701976	+	0.712201i	$0.747699\pi$
$20$		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	0.293659	−	0.955910i	$-0.405127\pi$
$29$	−3.56633	−	3.56633i	−0.662251	−	0.662251i	−0.955910	+	0.293659i	$0.905127\pi$
$30$		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	−0.151527	−	0.988453i	$-0.548419\pi$
$37$	5.09082	−	5.09082i	0.836926	−	0.836926i	0.988453	+	0.151527i	$0.0484190\pi$
$38$		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	−0.417007	−	0.908903i	$-0.636921\pi$
$43$	3.22558	−	3.22558i	0.491897	−	0.491897i	0.908903	+	0.417007i	$0.136921\pi$
$44$		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	−0.950619	−	0.310362i	$-0.899550\pi$
$53$	−4.66114	+	4.66114i	−0.640257	+	0.640257i	0.310362	+	0.950619i	$0.399550\pi$
$54$		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	−0.964742	−	0.263199i	$-0.915223\pi$
$59$	−5.38865	+	5.38865i	−0.701543	+	0.701543i	0.263199	+	0.964742i	$0.415223\pi$
$60$		0			0
$61$	6.80717	+	6.80717i	0.871569	+	0.871569i	0.992643	−	0.121074i	$-0.0386339\pi$
$61$	6.80717	+	6.80717i	0.871569	+	0.871569i	−0.121074	+	0.992643i	$0.538634\pi$
$62$		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	0.940875	−	0.338754i	$-0.110005\pi$
$67$	4.92858	+	4.92858i	0.602122	+	0.602122i	−0.338754	+	0.940875i	$0.610005\pi$
$68$		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	0.169108	−	0.985598i	$-0.445911\pi$
$83$	−7.43857	−	7.43857i	−0.816489	−	0.816489i	−0.985598	+	0.169108i	$0.945911\pi$
$84$		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	−0.443002	−	0.896521i	$-0.646087\pi$
$101$	4.55780	−	4.55780i	0.453518	−	0.453518i	0.896521	+	0.443002i	$0.146087\pi$
$102$		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	−0.614260	−	0.789104i	$-0.710545\pi$
$107$	1.80860	−	1.80860i	0.174844	−	0.174844i	0.789104	+	0.614260i	$0.210545\pi$
$108$		0			0
$109$	−11.0153	−	11.0153i	−1.05507	−	1.05507i	−0.998392	−	0.0566812i	$-0.981948\pi$
$109$	−11.0153	−	11.0153i	−1.05507	−	1.05507i	−0.0566812	−	0.998392i	$-0.518052\pi$
$110$		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	0.0303864	−	0.999538i	$-0.490326\pi$
$131$	−11.0924	−	11.0924i	−0.969152	−	0.969152i	−0.999538	+	0.0303864i	$0.990326\pi$
$132$		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	−0.696464	−	0.717592i	$-0.745244\pi$
$139$	0.249091	−	0.249091i	0.0211277	−	0.0211277i	0.717592	+	0.696464i	$0.245244\pi$
$140$		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	−0.864896	−	0.501951i	$-0.832616\pi$
$149$	−4.43030	+	4.43030i	−0.362944	+	0.362944i	0.501951	+	0.864896i	$0.332616\pi$
$150$		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	0.543344	−	0.839510i	$-0.317158\pi$
$157$	−3.71095	−	3.71095i	−0.296166	−	0.296166i	−0.839510	+	0.543344i	$0.817158\pi$
$158$		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	0.887850	−	0.460133i	$-0.152198\pi$
$163$	5.46072	+	5.46072i	0.427717	+	0.427717i	−0.460133	+	0.887850i	$0.652198\pi$
$164$		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	0.945833	−	0.324653i	$-0.105247\pi$
$173$	8.17036	+	8.17036i	0.621181	+	0.621181i	−0.324653	+	0.945833i	$0.605247\pi$
$174$		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	$-0.990666\pi$
$179$	−13.7656	−	13.7656i	−1.02889	−	1.02889i	−0.0293209	−	0.999570i	$-0.509334\pi$
$180$		0			0
$181$	8.11694	−	8.11694i	0.603327	−	0.603327i	−0.337867	−	0.941194i	$-0.609705\pi$
$181$	8.11694	−	8.11694i	0.603327	−	0.603327i	0.941194	+	0.337867i	$0.109705\pi$
$182$		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	−0.986602	−	0.163145i	$-0.947836\pi$
$197$	−11.5578	+	11.5578i	−0.823457	+	0.823457i	0.163145	+	0.986602i	$0.447836\pi$
$198$		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	$-0.925947\pi$
$211$	−17.4835	−	17.4835i	−1.20361	−	1.20361i	−0.230551	−	0.973060i	$-0.574053\pi$
$212$		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	$0.0390343\pi$
$227$	16.7964	+	16.7964i	1.11481	+	1.11481i	0.122323	+	0.992490i	$0.460966\pi$
$228$		0			0
$229$	13.1587	−	13.1587i	0.869555	−	0.869555i	−0.122868	−	0.992423i	$-0.539209\pi$
$229$	13.1587	−	13.1587i	0.869555	−	0.869555i	0.992423	+	0.122868i	$0.0392093\pi$
$230$		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	$-0.473124\pi$
$251$	17.1226	−	17.1226i	1.08077	−	1.08077i	0.996438	−	0.0843330i	$-0.0268759\pi$
$252$		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	0.738472	−	0.674284i	$-0.235547\pi$
$269$	1.05278	+	1.05278i	0.0641889	+	0.0641889i	−0.674284	+	0.738472i	$0.735547\pi$
$270$		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	−0.806864	−	0.590737i	$-0.798837\pi$
$277$	−3.59707	+	3.59707i	−0.216127	+	0.216127i	0.590737	+	0.806864i	$0.298837\pi$
$278$		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	−0.560807	−	0.827946i	$-0.689509\pi$
$283$	4.49397	−	4.49397i	0.267139	−	0.267139i	0.827946	+	0.560807i	$0.189509\pi$
$284$		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	−0.736534	−	0.676401i	$-0.763539\pi$
$293$	−1.02932	+	1.02932i	−0.0601334	+	0.0601334i	0.676401	+	0.736534i	$0.263539\pi$
$294$		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	0.540837	−	0.841127i	$-0.318107\pi$
$307$	−5.26150	−	5.26150i	−0.300290	−	0.300290i	−0.841127	+	0.540837i	$0.818107\pi$
$308$		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	0.136645	−	0.990620i	$-0.456368\pi$
$317$	−15.2046	−	15.2046i	−0.853975	−	0.853975i	−0.990620	+	0.136645i	$0.956368\pi$
$318$		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	−0.558590	−	0.829444i	$-0.688657\pi$
$331$	4.92777	−	4.92777i	0.270854	−	0.270854i	0.829444	+	0.558590i	$0.188657\pi$
$332$		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	−0.792104	−	0.610386i	$-0.791014\pi$
$347$	−3.38504	+	3.38504i	−0.181718	+	0.181718i	0.610386	+	0.792104i	$0.291014\pi$
$348$		0			0
$349$	24.8531	+	24.8531i	1.33035	+	1.33035i	0.905051	+	0.425303i	$0.139832\pi$
$349$	24.8531	+	24.8531i	1.33035	+	1.33035i	0.425303	+	0.905051i	$0.360168\pi$
$350$		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	−0.980475	−	0.196645i	$-0.936995\pi$
$373$	−15.1383	+	15.1383i	−0.783830	+	0.783830i	0.196645	+	0.980475i	$0.436995\pi$
$374$		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	−0.966447	−	0.256867i	$-0.917310\pi$
$379$	−13.8140	+	13.8140i	−0.709580	+	0.709580i	0.256867	+	0.966447i	$0.417310\pi$
$380$		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	−0.996026	−	0.0890675i	$-0.971611\pi$
$389$	−17.8880	+	17.8880i	−0.906958	+	0.906958i	0.0890675	+	0.996026i	$0.471611\pi$
$390$		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	0.589319	−	0.807900i	$-0.299396\pi$
$397$	−4.35521	−	4.35521i	−0.218582	−	0.218582i	−0.807900	+	0.589319i	$0.799396\pi$
$398$		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	0.746805	−	0.665043i	$-0.231587\pi$
$419$	1.67364	+	1.67364i	0.0817626	+	0.0817626i	−0.665043	+	0.746805i	$0.731587\pi$
$420$		0			0
$421$	22.2705	−	22.2705i	1.08540	−	1.08540i	0.0894016	−	0.995996i	$-0.471505\pi$
$421$	22.2705	−	22.2705i	1.08540	−	1.08540i	0.995996	−	0.0894016i	$-0.0284955\pi$
$422$		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	−0.896983	−	0.442065i	$-0.854246\pi$
$443$	−9.57493	+	9.57493i	−0.454918	+	0.454918i	0.442065	+	0.896983i	$0.354246\pi$
$444$		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	0.603474	−	0.797383i	$-0.293783\pi$
$461$	−4.16339	−	4.16339i	−0.193908	−	0.193908i	−0.797383	+	0.603474i	$0.793783\pi$
$462$		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	0.254145	−	0.967166i	$-0.418206\pi$
$467$	−15.4085	−	15.4085i	−0.713022	−	0.713022i	−0.967166	+	0.254145i	$0.918206\pi$
$468$		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	−0.766271	−	0.642517i	$-0.777890\pi$
$491$	−2.74222	+	2.74222i	−0.123754	+	0.123754i	0.642517	+	0.766271i	$0.277890\pi$
$492$		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	0.691191	−	0.722672i	$-0.257086\pi$
$499$	−0.703246	−	0.703246i	−0.0314816	−	0.0314816i	−0.722672	+	0.691191i	$0.757086\pi$
$500$		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	0.805495	−	0.592603i	$-0.201900\pi$
$509$	4.80305	+	4.80305i	0.212891	+	0.212891i	−0.592603	+	0.805495i	$0.701900\pi$
$510$		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	−0.994830	−	0.101559i	$-0.967617\pi$
$523$	−20.4284	+	20.4284i	−0.893271	+	0.893271i	0.101559	+	0.994830i	$0.467617\pi$
$524$		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	0.778393	−	0.627777i	$-0.216035\pi$
$541$	3.50325	+	3.50325i	0.150617	+	0.150617i	−0.627777	+	0.778393i	$0.716035\pi$
$542$		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	0.0586277	−	0.998280i	$-0.481328\pi$
$547$	−21.9766	−	21.9766i	−0.939652	−	0.939652i	−0.998280	+	0.0586277i	$0.981328\pi$
$548$		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	0.791506	−	0.611161i	$-0.209297\pi$
$557$	4.25629	+	4.25629i	0.180345	+	0.180345i	−0.611161	+	0.791506i	$0.709297\pi$
$558$		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	0.870491	−	0.492184i	$-0.163801\pi$
$563$	8.97634	+	8.97634i	0.378307	+	0.378307i	−0.492184	+	0.870491i	$0.663801\pi$
$564$		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	−0.808215	−	0.588887i	$-0.799566\pi$
$571$	−5.24097	+	5.24097i	−0.219328	+	0.219328i	0.588887	+	0.808215i	$0.299566\pi$
$572$		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	−0.650317	−	0.759663i	$-0.725364\pi$
$587$	2.64923	−	2.64923i	0.109346	−	0.109346i	0.759663	+	0.650317i	$0.225364\pi$
$588$		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	−0.784891	−	0.619633i	$-0.787281\pi$
$613$	−4.09160	+	4.09160i	−0.165258	+	0.165258i	0.619633	+	0.784891i	$0.287281\pi$
$614$		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	−0.991933	−	0.126766i	$-0.959540\pi$
$619$	−21.5251	+	21.5251i	−0.865166	+	0.865166i	0.126766	+	0.991933i	$0.459540\pi$
$620$		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	$0.218554\pi$
$643$	35.6860	+	35.6860i	1.40732	+	1.40732i	0.633916	+	0.773402i	$0.281446\pi$
$644$		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	$0.0763868\pi$
$653$	30.8952	+	30.8952i	1.20902	+	1.20902i	0.237679	+	0.971344i	$0.423613\pi$
$654$		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	0.908761	−	0.417317i	$-0.137030\pi$
$659$	12.6158	+	12.6158i	0.491443	+	0.491443i	−0.417317	+	0.908761i	$0.637030\pi$
$660$		0			0
$661$	20.5214	−	20.5214i	0.798189	−	0.798189i	−0.184621	−	0.982810i	$-0.559106\pi$
$661$	20.5214	−	20.5214i	0.798189	−	0.798189i	0.982810	+	0.184621i	$0.0591057\pi$
$662$		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	−0.632738	−	0.774366i	$-0.718069\pi$
$677$	3.68505	−	3.68505i	0.141628	−	0.141628i	0.774366	+	0.632738i	$0.218069\pi$
$678$		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	−0.722606	−	0.691260i	$-0.757056\pi$
$683$	−0.819191	+	0.819191i	−0.0313455	+	0.0313455i	0.691260	+	0.722606i	$0.257056\pi$
$684$		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	0.858334	−	0.513091i	$-0.171500\pi$
$691$	9.07535	+	9.07535i	0.345243	+	0.345243i	−0.513091	+	0.858334i	$0.671500\pi$
$692$		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	0.137250	−	0.990536i	$-0.456173\pi$
$701$	−22.5919	−	22.5919i	−0.853286	−	0.853286i	−0.990536	+	0.137250i	$0.956173\pi$
$702$		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	−0.914996	−	0.403464i	$-0.867806\pi$
$709$	−13.6206	+	13.6206i	−0.511532	+	0.511532i	0.403464	+	0.914996i	$0.367806\pi$
$710$		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	$0.0392609\pi$
$733$	30.1992	+	30.1992i	1.11543	+	1.11543i	0.123029	+	0.992403i	$0.460739\pi$
$734$		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	$-0.850499\pi$
$739$	−36.5445	−	36.5445i	−1.34431	−	1.34431i	−0.452592	−	0.891718i	$-0.649501\pi$
$740$		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	−0.687312	−	0.726362i	$-0.741209\pi$
$757$	1.07442	−	1.07442i	0.0390505	−	0.0390505i	0.726362	+	0.687312i	$0.241209\pi$
$758$		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	−0.997280	−	0.0737087i	$-0.976516\pi$
$773$	−25.6779	+	25.6779i	−0.923571	+	0.923571i	0.0737087	+	0.997280i	$0.476516\pi$
$774$		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	0.352914	−	0.935656i	$-0.385191\pi$
$787$	−16.3479	−	16.3479i	−0.582741	−	0.582741i	−0.935656	+	0.352914i	$0.885191\pi$
$788$		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	$0.0184724\pi$
$797$	29.8211	+	29.8211i	1.05632	+	1.05632i	0.0580002	+	0.998317i	$0.481528\pi$
$798$		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	−0.966084	−	0.258230i	$-0.916861\pi$
$811$	−20.1583	+	20.1583i	−0.707854	+	0.707854i	0.258230	+	0.966084i	$0.416861\pi$
$812$		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	$0.678976\pi$
$821$	−39.5171	+	39.5171i	−1.37915	+	1.37915i	−0.846048	+	0.533107i	$0.821024\pi$
$822$		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	$-0.457731\pi$
$827$	32.3120	−	32.3120i	1.12360	−	1.12360i	0.991196	−	0.132402i	$-0.0422690\pi$
$828$		0			0
$829$	5.08302	+	5.08302i	0.176541	+	0.176541i	0.789846	−	0.613305i	$-0.210160\pi$
$829$	5.08302	+	5.08302i	0.176541	+	0.176541i	−0.613305	+	0.789846i	$0.710160\pi$
$830$		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	−0.852194	−	0.523226i	$-0.824729\pi$
$853$	−9.60791	+	9.60791i	−0.328969	+	0.328969i	0.523226	+	0.852194i	$0.324729\pi$
$854$		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	−0.990736	−	0.135803i	$-0.956639\pi$
$859$	−25.0570	+	25.0570i	−0.854933	+	0.854933i	0.135803	+	0.990736i	$0.456639\pi$
$860$		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	$0.152823\pi$
$877$	39.9442	+	39.9442i	1.34882	+	1.34882i	0.461873	+	0.886946i	$0.347177\pi$
$878$		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	0.0875424	−	0.996161i	$-0.472099\pi$
$883$	−26.9999	−	26.9999i	−0.908618	−	0.908618i	−0.996161	+	0.0875424i	$0.972099\pi$
$884$		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	−0.979218	−	0.202810i	$-0.934993\pi$
$907$	−23.3827	+	23.3827i	−0.776408	+	0.776408i	0.202810	+	0.979218i	$0.434993\pi$
$908$		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	0.898502	−	0.438970i	$-0.144656\pi$
$941$	14.0965	+	14.0965i	0.459532	+	0.459532i	−0.438970	+	0.898502i	$0.644656\pi$
$942$		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	0.565967	−	0.824428i	$-0.308503\pi$
$947$	−7.95369	−	7.95369i	−0.258460	−	0.258460i	−0.824428	+	0.565967i	$0.808503\pi$
$948$		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	−0.558067	−	0.829796i	$-0.688457\pi$
$971$	8.46733	−	8.46733i	0.271730	−	0.271730i	0.829796	+	0.558067i	$0.188457\pi$
$972$		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	−0.346724	−	0.937967i	$-0.612706\pi$
$997$	18.6687	−	18.6687i	0.591243	−	0.591243i	0.937967	+	0.346724i	$0.112706\pi$
$998$		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.f.1345.1	yes	16
4.3	odd	2		1792.2.m.h.1345.8	yes	16
8.3	odd	2		1792.2.m.e.1345.1	yes	16
8.5	even	2		1792.2.m.g.1345.8	yes	16
16.3	odd	4		1792.2.m.e.449.1	✓	16
16.5	even	4	inner	1792.2.m.f.449.1	yes	16
16.11	odd	4		1792.2.m.h.449.8	yes	16
16.13	even	4		1792.2.m.g.449.8	yes	16
32.5	even	8		7168.2.a.be.1.8		8
32.11	odd	8		7168.2.a.bb.1.8		8
32.21	even	8		7168.2.a.ba.1.1		8
32.27	odd	8		7168.2.a.bf.1.1		8

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