LMFDB - Embedded newform 1456.2.cc.c.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.2
Root			$1.40744 + 0.138282i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.c.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.583963 - 1.01145i) q^{3} -1.81487i q^{5} +(0.866025 + 0.500000i) q^{7} +(0.817975 - 1.41677i) q^{9} +O(q^{10})$	\(q+(-0.583963 - 1.01145i) q^{3} -1.81487i q^{5} +(0.866025 + 0.500000i) q^{7} +(0.817975 - 1.41677i) q^{9} +(2.40625 - 1.38925i) q^{11} +(-3.58305 - 0.402155i) q^{13} +(-1.83566 + 1.05982i) q^{15} +(1.37198 - 2.37634i) q^{17} +(5.08351 + 2.93497i) q^{19} -1.16793i q^{21} +(-3.49955 - 6.06139i) q^{23} +1.70623 q^{25} -5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} -2.06697i q^{31} +(-2.81031 - 1.62254i) q^{33} +(0.907437 - 1.57173i) q^{35} +(1.50950 - 0.871512i) q^{37} +(1.68561 + 3.85893i) q^{39} +(5.51406 - 3.18355i) q^{41} +(-4.55195 + 7.88422i) q^{43} +(-2.57127 - 1.48452i) q^{45} -6.65932i q^{47} +(0.500000 + 0.866025i) q^{49} -3.20474 q^{51} -10.4879 q^{53} +(-2.52131 - 4.36703i) q^{55} -6.85564i q^{57} +(-2.66212 - 1.53698i) q^{59} +(-0.540892 + 0.936853i) q^{61} +(1.41677 - 0.817975i) q^{63} +(-0.729860 + 6.50279i) q^{65} +(-4.34568 + 2.50898i) q^{67} +(-4.08721 + 7.07925i) q^{69} +(-2.35453 - 1.35939i) q^{71} -7.67213i q^{73} +(-0.996377 - 1.72578i) q^{75} +2.77849 q^{77} +15.7399 q^{79} +(0.707906 + 1.22613i) q^{81} -7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} +(2.05328 - 3.55639i) q^{87} +(-13.9118 + 8.03198i) q^{89} +(-2.90194 - 2.13980i) q^{91} +(-2.09064 + 1.20703i) q^{93} +(5.32659 - 9.22592i) q^{95} +(-12.3209 - 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^9	$ 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	−0.583963	−	1.01145i	−0.337151	−	0.583963i	0.646745	−	0.762707i	$-0.276130\pi$
$3$	−0.583963	−	1.01145i	−0.337151	−	0.583963i	−0.983896	+	0.178744i	$0.942797\pi$
$4$		0			0
$5$		−	1.81487i		−	0.811636i	−0.913954	−	0.405818i	$-0.866987\pi$
$5$		−	1.81487i		−	0.811636i	0.913954	−	0.405818i	$-0.133013\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	0.817975	−	1.41677i	0.272658	−	0.472258i
$10$		0			0
$11$	2.40625	−	1.38925i	0.725510	−	0.418874i	−0.0912671	−	0.995826i	$-0.529092\pi$
$11$	2.40625	−	1.38925i	0.725510	−	0.418874i	0.816777	+	0.576953i	$0.195758\pi$
$12$		0			0
$13$	−3.58305	−	0.402155i	−0.993760	−	0.111538i
$13$	−3.58305	−	0.402155i	−0.993760	−	0.111538i
$14$		0			0
$15$	−1.83566	+	1.05982i	−0.473965	+	0.273644i
$16$		0			0
$17$	1.37198	−	2.37634i	0.332754	−	0.576347i	−0.650297	−	0.759680i	$-0.725355\pi$
$17$	1.37198	−	2.37634i	0.332754	−	0.576347i	0.983051	+	0.183334i	$0.0586888\pi$
$18$		0			0
$19$	5.08351	+	2.93497i	1.16624	+	0.673327i	0.952791	−	0.303628i	$-0.0981979\pi$
$19$	5.08351	+	2.93497i	1.16624	+	0.673327i	0.213446	+	0.976955i	$0.431531\pi$
$20$		0			0
$21$		−	1.16793i		−	0.254862i
$22$		0			0
$23$	−3.49955	−	6.06139i	−0.729706	−	1.26389i	−0.957007	−	0.290063i	$-0.906324\pi$
$23$	−3.49955	−	6.06139i	−0.729706	−	1.26389i	0.227302	−	0.973824i	$-0.427010\pi$
$24$		0			0
$25$	1.70623			0.341247
$26$		0			0
$27$	−5.41444			−1.04201
$28$		0			0
$29$	1.75806	+	3.04505i	0.326463	+	0.565451i	0.981807	−	0.189879i	$-0.0608097\pi$
$29$	1.75806	+	3.04505i	0.326463	+	0.565451i	−0.655344	+	0.755330i	$0.727476\pi$
$30$		0			0
$31$		−	2.06697i		−	0.371238i	−0.982622	−	0.185619i	$-0.940571\pi$
$31$		−	2.06697i		−	0.371238i	0.982622	−	0.185619i	$-0.0594290\pi$
$32$		0			0
$33$	−2.81031	−	1.62254i	−0.489213	−	0.282447i
$34$		0			0
$35$	0.907437	−	1.57173i	0.153385	−	0.265670i
$36$		0			0
$37$	1.50950	−	0.871512i	0.248161	−	0.143276i	−0.370761	−	0.928728i	$-0.620903\pi$
$37$	1.50950	−	0.871512i	0.248161	−	0.143276i	0.618922	+	0.785453i	$0.287570\pi$
$38$		0			0
$39$	1.68561	+	3.85893i	0.269913	+	0.617924i
$40$		0			0
$41$	5.51406	−	3.18355i	0.861152	−	0.497186i	−0.00324599	−	0.999995i	$-0.501033\pi$
$41$	5.51406	−	3.18355i	0.861152	−	0.497186i	0.864398	+	0.502808i	$0.167700\pi$
$42$		0			0
$43$	−4.55195	+	7.88422i	−0.694167	+	1.20233i	0.276294	+	0.961073i	$0.410894\pi$
$43$	−4.55195	+	7.88422i	−0.694167	+	1.20233i	−0.970461	+	0.241259i	$0.922440\pi$
$44$		0			0
$45$	−2.57127	−	1.48452i	−0.383302	−	0.221299i
$46$		0			0
$47$		−	6.65932i		−	0.971361i	−0.874136	−	0.485681i	$-0.838572\pi$
$47$		−	6.65932i		−	0.971361i	0.874136	−	0.485681i	$-0.161428\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−3.20474			−0.448753
$52$		0			0
$53$	−10.4879			−1.44063			−0.720313	−	0.693649i	$-0.756002\pi$
$53$	−10.4879			−1.44063			−0.720313	+	0.693649i	$0.756002\pi$
$54$		0			0
$55$	−2.52131	−	4.36703i	−0.339973	−	0.588850i
$56$		0			0
$57$		−	6.85564i		−	0.908052i
$58$		0			0
$59$	−2.66212	−	1.53698i	−0.346579	−	0.200097i	0.316598	−	0.948560i	$-0.397459\pi$
$59$	−2.66212	−	1.53698i	−0.346579	−	0.200097i	−0.663177	+	0.748462i	$0.730793\pi$
$60$		0			0
$61$	−0.540892	+	0.936853i	−0.0692541	+	0.119952i	−0.898573	−	0.438824i	$-0.855395\pi$
$61$	−0.540892	+	0.936853i	−0.0692541	+	0.119952i	0.829319	+	0.558775i	$0.188729\pi$
$62$		0			0
$63$	1.41677	−	0.817975i	0.178497	−	0.103055i
$64$		0			0
$65$	−0.729860	+	6.50279i	−0.0905280	+	0.806572i
$66$		0			0
$67$	−4.34568	+	2.50898i	−0.530910	+	0.306521i	−0.741387	−	0.671078i	$-0.765832\pi$
$67$	−4.34568	+	2.50898i	−0.530910	+	0.306521i	0.210477	+	0.977599i	$0.432498\pi$
$68$		0			0
$69$	−4.08721	+	7.07925i	−0.492042	+	0.852242i
$70$		0			0
$71$	−2.35453	−	1.35939i	−0.279431	−	0.161330i	0.353735	−	0.935346i	$-0.384912\pi$
$71$	−2.35453	−	1.35939i	−0.279431	−	0.161330i	−0.633166	+	0.774016i	$0.718245\pi$
$72$		0			0
$73$		−	7.67213i		−	0.897955i	−0.893543	−	0.448978i	$-0.851788\pi$
$73$		−	7.67213i		−	0.897955i	0.893543	−	0.448978i	$-0.148212\pi$
$74$		0			0
$75$	−0.996377	−	1.72578i	−0.115052	−	0.199275i
$76$		0			0
$77$	2.77849			0.316639
$78$		0			0
$79$	15.7399			1.77087			0.885436	−	0.464761i	$-0.153860\pi$
$79$	15.7399			1.77087			0.885436	+	0.464761i	$0.153860\pi$
$80$		0			0
$81$	0.707906	+	1.22613i	0.0786563	+	0.136237i
$82$		0			0
$83$		−	7.97408i		−	0.875269i	−0.899153	−	0.437635i	$-0.855816\pi$
$83$		−	7.97408i		−	0.875269i	0.899153	−	0.437635i	$-0.144184\pi$
$84$		0			0
$85$	−4.31275	−	2.48997i	−0.467784	−	0.270075i
$86$		0			0
$87$	2.05328	−	3.55639i	0.220135	−	0.381285i
$88$		0			0
$89$	−13.9118	+	8.03198i	−1.47465	+	0.851388i	−0.999592	−	0.0285683i	$-0.990905\pi$
$89$	−13.9118	+	8.03198i	−1.47465	+	0.851388i	−0.475055	+	0.879956i	$0.657572\pi$
$90$		0			0
$91$	−2.90194	−	2.13980i	−0.304206	−	0.224312i
$92$		0			0
$93$	−2.09064	+	1.20703i	−0.216789	+	0.125163i
$94$		0			0
$95$	5.32659	−	9.22592i	0.546497	−	0.946560i
$96$		0			0
$97$	−12.3209	−	7.11347i	−1.25100	−	0.722263i	−0.279689	−	0.960091i	$-0.590231\pi$
$97$	−12.3209	−	7.11347i	−1.25100	−	0.722263i	−0.971307	+	0.237827i	$0.923565\pi$
$98$		0			0
$99$		−	4.54548i		−	0.456838i
$100$		0			0
$101$	−0.0365612	−	0.0633259i	−0.00363798	−	0.00630117i	0.864201	−	0.503147i	$-0.167825\pi$
$101$	−0.0365612	−	0.0633259i	−0.00363798	−	0.00630117i	−0.867839	+	0.496846i	$0.834491\pi$
$102$		0			0
$103$	−12.9196			−1.27301			−0.636503	−	0.771275i	$-0.719620\pi$
$103$	−12.9196			−1.27301			−0.636503	+	0.771275i	$0.719620\pi$
$104$		0			0
$105$	−2.11964			−0.206855
$106$		0			0
$107$	2.00427	+	3.47150i	0.193761	+	0.335603i	0.946493	−	0.322723i	$-0.104598\pi$
$107$	2.00427	+	3.47150i	0.193761	+	0.335603i	−0.752733	+	0.658326i	$0.771265\pi$
$108$		0			0
$109$		−	1.98589i		−	0.190214i	−0.995467	−	0.0951071i	$-0.969681\pi$
$109$		−	1.98589i		−	0.190214i	0.995467	−	0.0951071i	$-0.0303194\pi$
$110$		0			0
$111$	−1.76299	−	1.01786i	−0.167335	−	0.0966110i
$112$		0			0
$113$	5.28711	−	9.15754i	0.497369	−	0.861469i	−0.502626	−	0.864504i	$-0.667633\pi$
$113$	5.28711	−	9.15754i	0.497369	−	0.861469i	0.999995	+	0.00303506i	$0.000966090\pi$
$114$		0			0
$115$	−11.0007	+	6.35123i	−1.02582	+	0.592256i
$116$		0			0
$117$	−3.50061	+	4.74743i	−0.323632	+	0.438900i
$118$		0			0
$119$	2.37634	−	1.37198i	0.217839	−	0.125769i
$120$		0			0
$121$	−1.63999	+	2.84054i	−0.149090	+	0.258231i
$122$		0			0
$123$	−6.44001	−	3.71814i	−0.580676	−	0.335254i
$124$		0			0
$125$		−	12.1710i		−	1.08860i
$126$		0			0
$127$	−5.63478	−	9.75972i	−0.500006	−	0.866035i	−1.00000		6.53271e-6i	$-0.999998\pi$
$127$	−5.63478	−	9.75972i	−0.500006	−	0.866035i	0.499994	−	0.866029i	$-0.333335\pi$
$128$		0			0
$129$	10.6327			0.936156
$130$		0			0
$131$	−3.06481			−0.267774			−0.133887	−	0.990997i	$-0.542746\pi$
$131$	−3.06481			−0.267774			−0.133887	+	0.990997i	$0.542746\pi$
$132$		0			0
$133$	2.93497	+	5.08351i	0.254494	+	0.440796i
$134$		0			0
$135$			9.82653i			0.845733i
$136$		0			0
$137$	18.9512	+	10.9415i	1.61911	+	0.934796i	0.987150	+	0.159799i	$0.0510845\pi$
$137$	18.9512	+	10.9415i	1.61911	+	0.934796i	0.631965	+	0.774997i	$0.282249\pi$
$138$		0			0
$139$	5.53535	−	9.58750i	0.469502	−	0.813201i	−0.529890	−	0.848066i	$-0.677767\pi$
$139$	5.53535	−	9.58750i	0.469502	−	0.813201i	0.999392	+	0.0348652i	$0.0111002\pi$
$140$		0			0
$141$	−6.73559	+	3.88879i	−0.567239	+	0.327495i
$142$		0			0
$143$	−9.18040	+	4.01006i	−0.767703	+	0.335338i
$144$		0			0
$145$	5.52637	−	3.19065i	0.458940	−	0.264969i
$146$		0			0
$147$	0.583963	−	1.01145i	0.0481644	−	0.0834232i
$148$		0			0
$149$	−1.99824	−	1.15369i	−0.163702	−	0.0945136i	0.415911	−	0.909406i	$-0.363463\pi$
$149$	−1.99824	−	1.15369i	−0.163702	−	0.0945136i	−0.579613	+	0.814892i	$0.696796\pi$
$150$		0			0
$151$			20.6158i			1.67769i	0.544371	+	0.838845i	$0.316768\pi$
$151$			20.6158i			1.67769i	−0.544371	+	0.838845i	$0.683232\pi$
$152$		0			0
$153$	−2.24449	−	3.88757i	−0.181456	−	0.314292i
$154$		0			0
$155$	−3.75128			−0.301310
$156$		0			0
$157$	2.89649			0.231165			0.115582	−	0.993298i	$-0.463127\pi$
$157$	2.89649			0.231165			0.115582	+	0.993298i	$0.463127\pi$
$158$		0			0
$159$	6.12455	+	10.6080i	0.485709	+	0.841272i
$160$		0			0
$161$		−	6.99909i		−	0.551606i
$162$		0			0
$163$	20.2944	+	11.7170i	1.58958	+	0.917743i	0.993376	+	0.114907i	$0.0366571\pi$
$163$	20.2944	+	11.7170i	1.58958	+	0.917743i	0.596201	+	0.802835i	$0.296676\pi$
$164$		0			0
$165$	−2.94470	+	5.10037i	−0.229244	+	0.397063i
$166$		0			0
$167$	−6.58349	+	3.80098i	−0.509446	+	0.294129i	−0.732606	−	0.680653i	$-0.761696\pi$
$167$	−6.58349	+	3.80098i	−0.509446	+	0.294129i	0.223160	+	0.974782i	$0.428363\pi$
$168$		0			0
$169$	12.6765	+	2.88188i	0.975119	+	0.221683i
$170$		0			0
$171$	8.31637	−	4.80146i	0.635969	−	0.367177i
$172$		0			0
$173$	2.69861	−	4.67412i	0.205171	−	0.355367i	−0.745016	−	0.667047i	$-0.767558\pi$
$173$	2.69861	−	4.67412i	0.205171	−	0.355367i	0.950187	+	0.311679i	$0.100892\pi$
$174$		0			0
$175$	1.47764	+	0.853117i	0.111699	+	0.0644896i
$176$		0			0
$177$			3.59015i			0.269852i
$178$		0			0
$179$	6.14571	+	10.6447i	0.459352	+	0.795621i	0.998927	−	0.0463168i	$-0.0147484\pi$
$179$	6.14571	+	10.6447i	0.459352	+	0.795621i	−0.539575	+	0.841938i	$0.681415\pi$
$180$		0			0
$181$	−21.8525			−1.62428			−0.812140	−	0.583463i	$-0.801697\pi$
$181$	−21.8525			−1.62428			−0.812140	+	0.583463i	$0.801697\pi$
$182$		0			0
$183$	1.26344			0.0933964
$184$		0			0
$185$	−1.58168	−	2.73956i	−0.116288	−	0.201416i
$186$		0			0
$187$		−	7.62407i		−	0.557527i
$188$		0			0
$189$	−4.68905	−	2.70722i	−0.341078	−	0.196921i
$190$		0			0
$191$	1.37858	−	2.38777i	0.0997507	−	0.172773i	−0.811831	−	0.583893i	$-0.801529\pi$
$191$	1.37858	−	2.38777i	0.0997507	−	0.172773i	0.911581	+	0.411120i	$0.134862\pi$
$192$		0			0
$193$	11.2491	−	6.49467i	0.809728	−	0.467497i	−0.0371334	−	0.999310i	$-0.511823\pi$
$193$	11.2491	−	6.49467i	0.809728	−	0.467497i	0.846861	+	0.531814i	$0.178489\pi$
$194$		0			0
$195$	7.00347	−	3.05917i	0.501529	−	0.219071i
$196$		0			0
$197$	16.4772	−	9.51312i	1.17395	−	0.677781i	0.219344	−	0.975648i	$-0.429608\pi$
$197$	16.4772	−	9.51312i	1.17395	−	0.677781i	0.954608	+	0.297866i	$0.0962749\pi$
$198$		0			0
$199$	10.0159	−	17.3480i	0.710006	−	1.22977i	−0.254848	−	0.966981i	$-0.582025\pi$
$199$	10.0159	−	17.3480i	0.710006	−	1.22977i	0.964854	−	0.262786i	$-0.0846412\pi$
$200$		0			0
$201$	5.07543	+	2.93030i	0.357993	+	0.206688i
$202$		0			0
$203$			3.51612i			0.246783i
$204$		0			0
$205$	−5.77773	−	10.0073i	−0.403534	−	0.698942i
$206$		0			0
$207$	−11.4502			−0.795842
$208$		0			0
$209$	16.3096			1.12816
$210$		0			0
$211$	5.00015	+	8.66052i	0.344225	+	0.596215i	0.985213	−	0.171336i	$-0.0548084\pi$
$211$	5.00015	+	8.66052i	0.344225	+	0.596215i	−0.640988	+	0.767551i	$0.721475\pi$
$212$		0			0
$213$			3.17532i			0.217570i
$214$		0			0
$215$	14.3089	+	8.26122i	0.975856	+	0.563411i
$216$		0			0
$217$	1.03348	−	1.79004i	0.0701574	−	0.121516i
$218$		0			0
$219$	−7.76000	+	4.48024i	−0.524372	+	0.302747i
$220$		0			0
$221$	−5.87153	+	7.96280i	−0.394962	+	0.535636i
$222$		0			0
$223$	−7.25954	+	4.19130i	−0.486135	+	0.280670i	−0.722970	−	0.690880i	$-0.757223\pi$
$223$	−7.25954	+	4.19130i	−0.486135	+	0.280670i	0.236835	+	0.971550i	$0.423890\pi$
$224$		0			0
$225$	1.39566	−	2.41735i	0.0930439	−	0.161157i
$226$		0			0
$227$	0.796500	+	0.459860i	0.0528656	+	0.0305220i	0.526200	−	0.850361i	$-0.323616\pi$
$227$	0.796500	+	0.459860i	0.0528656	+	0.0305220i	−0.473334	+	0.880883i	$0.656950\pi$
$228$		0			0
$229$			24.6208i			1.62699i	0.581574	+	0.813494i	$0.302437\pi$
$229$			24.6208i			1.62699i	−0.581574	+	0.813494i	$0.697563\pi$
$230$		0			0
$231$	−1.62254	−	2.81031i	−0.106755	−	0.184905i
$232$		0			0
$233$	17.2769			1.13185			0.565925	−	0.824457i	$-0.308519\pi$
$233$	17.2769			1.13185			0.565925	+	0.824457i	$0.308519\pi$
$234$		0			0
$235$	−12.0858			−0.788392
$236$		0			0
$237$	−9.19149	−	15.9201i	−0.597051	−	1.03412i
$238$		0			0
$239$		−	14.4828i		−	0.936816i	−0.883512	−	0.468408i	$-0.844828\pi$
$239$		−	14.4828i		−	0.936816i	0.883512	−	0.468408i	$-0.155172\pi$
$240$		0			0
$241$	−7.30441	−	4.21720i	−0.470518	−	0.271654i	0.245938	−	0.969285i	$-0.420904\pi$
$241$	−7.30441	−	4.21720i	−0.470518	−	0.271654i	−0.716457	+	0.697632i	$0.754237\pi$
$242$		0			0
$243$	−7.29488	+	12.6351i	−0.467967	+	0.810543i
$244$		0			0
$245$	1.57173	−	0.907437i	0.100414	−	0.0579740i
$246$		0			0
$247$	−17.0342	−	12.5605i	−1.08386	−	0.799205i
$248$		0			0
$249$	−8.06541	+	4.65657i	−0.511124	+	0.295098i
$250$		0			0
$251$	7.33631	−	12.7069i	0.463064	−	0.802050i	−0.536048	−	0.844188i	$-0.680083\pi$
$251$	7.33631	−	12.7069i	0.463064	−	0.802050i	0.999112	+	0.0421373i	$0.0134167\pi$
$252$		0			0
$253$	−16.8415	−	9.72346i	−1.05882	−	0.611309i
$254$		0			0
$255$			5.81620i			0.364224i
$256$		0			0
$257$	14.6643	+	25.3993i	0.914733	+	1.58436i	0.807292	+	0.590152i	$0.200932\pi$
$257$	14.6643	+	25.3993i	0.914733	+	1.58436i	0.107441	+	0.994211i	$0.465734\pi$
$258$		0			0
$259$	1.74302			0.108306
$260$		0			0
$261$	5.75219			0.356052
$262$		0			0
$263$	9.95747	+	17.2468i	0.614004	+	1.06349i	0.990558	+	0.137091i	$0.0437754\pi$
$263$	9.95747	+	17.2468i	0.614004	+	1.06349i	−0.376555	+	0.926394i	$0.622891\pi$
$264$		0			0
$265$			19.0342i			1.16926i
$266$		0			0
$267$	16.2479	+	9.38075i	0.994357	+	0.574092i
$268$		0			0
$269$	11.1625	−	19.3340i	0.680589	−	1.17881i	−0.294213	−	0.955740i	$-0.595057\pi$
$269$	11.1625	−	19.3340i	0.680589	−	1.17881i	0.974801	−	0.223074i	$-0.0716093\pi$
$270$		0			0
$271$	8.14054	−	4.69994i	0.494502	−	0.285501i	−0.231938	−	0.972731i	$-0.574507\pi$
$271$	8.14054	−	4.69994i	0.494502	−	0.285501i	0.726440	+	0.687230i	$0.241173\pi$
$272$		0			0
$273$	−0.469686	+	4.18474i	−0.0284267	+	0.253272i
$274$		0			0
$275$	4.10562	−	2.37038i	0.247578	−	0.142939i
$276$		0			0
$277$	−7.17133	+	12.4211i	−0.430883	+	0.746312i	−0.996950	−	0.0780478i	$-0.975131\pi$
$277$	−7.17133	+	12.4211i	−0.430883	+	0.746312i	0.566066	+	0.824360i	$0.308465\pi$
$278$		0			0
$279$	−2.92842	−	1.69073i	−0.175320	−	0.101221i
$280$		0			0
$281$			0.0988416i			0.00589640i	0.999996	+	0.00294820i	$0.000938442\pi$
$281$			0.0988416i			0.00589640i	−0.999996	+	0.00294820i	$0.999062\pi$
$282$		0			0
$283$	0.310336	+	0.537518i	0.0184476	+	0.0319521i	0.875102	−	0.483939i	$-0.160794\pi$
$283$	0.310336	+	0.537518i	0.0184476	+	0.0319521i	−0.856654	+	0.515891i	$0.827461\pi$
$284$		0			0
$285$	−12.4421			−0.737007
$286$		0			0
$287$	6.36709			0.375837
$288$		0			0
$289$	4.73534	+	8.20186i	0.278550	+	0.482462i
$290$		0			0
$291$			16.6160i			0.974047i
$292$		0			0
$293$	21.5586	+	12.4469i	1.25947	+	0.727153i	0.972971	−	0.230928i	$-0.0741762\pi$
$293$	21.5586	+	12.4469i	1.25947	+	0.727153i	0.286496	+	0.958082i	$0.407510\pi$
$294$		0			0
$295$	−2.78942	+	4.83142i	−0.162406	+	0.281296i
$296$		0			0
$297$	−13.0285	+	7.52200i	−0.755989	+	0.436471i
$298$		0			0
$299$	10.1014	+	23.1256i	0.584182	+	1.33739i
$300$		0			0
$301$	−7.88422	+	4.55195i	−0.454439	+	0.262370i
$302$		0			0
$303$	−0.0427008	+	0.0739599i	−0.00245310	+	0.00424889i
$304$		0			0
$305$	1.70027	+	0.981651i	0.0973571	+	0.0562091i
$306$		0			0
$307$		−	9.89767i		−	0.564890i	−0.959284	−	0.282445i	$-0.908855\pi$
$307$		−	9.89767i		−	0.564890i	0.959284	−	0.282445i	$-0.0911455\pi$
$308$		0			0
$309$	7.54456	+	13.0676i	0.429195	+	0.743387i
$310$		0			0
$311$	7.23790			0.410423			0.205212	−	0.978718i	$-0.434212\pi$
$311$	7.23790			0.410423			0.205212	+	0.978718i	$0.434212\pi$
$312$		0			0
$313$	32.6606			1.84609			0.923043	−	0.384696i	$-0.125694\pi$
$313$	32.6606			1.84609			0.923043	+	0.384696i	$0.125694\pi$
$314$		0			0
$315$	−1.48452	−	2.57127i	−0.0836433	−	0.144874i
$316$		0			0
$317$			17.1744i			0.964608i	0.876004	+	0.482304i	$0.160200\pi$
$317$			17.1744i			0.964608i	−0.876004	+	0.482304i	$0.839800\pi$
$318$		0			0
$319$	8.46064	+	4.88475i	0.473705	+	0.273494i
$320$		0			0
$321$	2.34084	−	4.05446i	0.130653	−	0.226298i
$322$		0			0
$323$	13.9489	−	8.05342i	0.776140	−	0.448105i
$324$		0			0
$325$	−6.11353	−	0.686170i	−0.339118	−	0.0380619i
$326$		0			0
$327$	−2.00864	+	1.15969i	−0.111078	+	0.0641309i
$328$		0			0
$329$	3.32966	−	5.76714i	0.183570	−	0.317953i
$330$		0			0
$331$	−17.2633	−	9.96698i	−0.948877	−	0.547835i	−0.0561454	−	0.998423i	$-0.517881\pi$
$331$	−17.2633	−	9.96698i	−0.948877	−	0.547835i	−0.892732	+	0.450588i	$0.851214\pi$
$332$		0			0
$333$		−	2.85150i		−	0.156261i
$334$		0			0
$335$	4.55348	+	7.88687i	0.248783	+	0.430905i
$336$		0			0
$337$	1.27189			0.0692842			0.0346421	−	0.999400i	$-0.488971\pi$
$337$	1.27189			0.0692842			0.0346421	+	0.999400i	$0.488971\pi$
$338$		0			0
$339$	−12.3499			−0.670754
$340$		0			0
$341$	−2.87152	−	4.97363i	−0.155502	−	0.269337i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	12.8479	+	7.41777i	0.691710	+	0.399359i
$346$		0			0
$347$	12.9417	−	22.4156i	0.694744	−	1.20333i	−0.275522	−	0.961295i	$-0.588851\pi$
$347$	12.9417	−	22.4156i	0.694744	−	1.20333i	0.970267	−	0.242038i	$-0.0778158\pi$
$348$		0			0
$349$	−14.9967	+	8.65837i	−0.802757	+	0.463472i	−0.844434	−	0.535659i	$-0.820063\pi$
$349$	−14.9967	+	8.65837i	−0.802757	+	0.463472i	0.0416774	+	0.999131i	$0.486730\pi$
$350$		0			0
$351$	19.4002	+	2.17744i	1.03551	+	0.116223i
$352$		0			0
$353$	−21.9533	+	12.6747i	−1.16846	+	0.674608i	−0.953316	−	0.301975i	$-0.902354\pi$
$353$	−21.9533	+	12.6747i	−1.16846	+	0.674608i	−0.215140	+	0.976583i	$0.569021\pi$
$354$		0			0
$355$	−2.46711	+	4.27317i	−0.130941	+	0.226796i
$356$		0			0
$357$	−2.77539	−	1.60237i	−0.146889	−	0.0848064i
$358$		0			0
$359$			5.27044i			0.278163i	0.990281	+	0.139082i	$0.0444151\pi$
$359$			5.27044i			0.278163i	−0.990281	+	0.139082i	$0.955585\pi$
$360$		0			0
$361$	7.72804	+	13.3854i	0.406739	+	0.704493i
$362$		0			0
$363$	3.83077			0.201063
$364$		0			0
$365$	−13.9240			−0.728813
$366$		0			0
$367$	12.6588	+	21.9257i	0.660783	+	1.14451i	0.980410	+	0.196967i	$0.0631092\pi$
$367$	12.6588	+	21.9257i	0.660783	+	1.14451i	−0.319627	+	0.947544i	$0.603557\pi$
$368$		0			0
$369$		−	10.4162i		−	0.542248i
$370$		0			0
$371$	−9.08280	−	5.24396i	−0.471556	−	0.272253i
$372$		0			0
$373$	3.39391	−	5.87842i	0.175730	−	0.304373i	−0.764684	−	0.644406i	$-0.777105\pi$
$373$	3.39391	−	5.87842i	0.175730	−	0.304373i	0.940414	+	0.340033i	$0.110438\pi$
$374$		0			0
$375$	−12.3104	+	7.10739i	−0.635704	+	0.367024i
$376$		0			0
$377$	−5.07464	−	11.6176i	−0.261357	−	0.598336i
$378$		0			0
$379$	−10.6717	+	6.16130i	−0.548168	+	0.316485i	−0.748383	−	0.663267i	$-0.769169\pi$
$379$	−10.6717	+	6.16130i	−0.548168	+	0.316485i	0.200215	+	0.979752i	$0.435836\pi$
$380$		0			0
$381$	−6.58100	+	11.3986i	−0.337155	+	0.583969i
$382$		0			0
$383$	6.28662	+	3.62958i	0.321232	+	0.185463i	0.651941	−	0.758269i	$-0.273955\pi$
$383$	6.28662	+	3.62958i	0.321232	+	0.185463i	−0.330710	+	0.943732i	$0.607288\pi$
$384$		0			0
$385$		−	5.04261i		−	0.256995i
$386$		0			0
$387$	7.44677	+	12.8982i	0.378541	+	0.655652i
$388$		0			0
$389$	7.14811			0.362424			0.181212	−	0.983444i	$-0.441998\pi$
$389$	7.14811			0.362424			0.181212	+	0.983444i	$0.441998\pi$
$390$		0			0
$391$	−19.2052			−0.971250
$392$		0			0
$393$	1.78974	+	3.09991i	0.0902802	+	0.156370i
$394$		0			0
$395$		−	28.5659i		−	1.43730i
$396$		0			0
$397$	−19.4520	−	11.2306i	−0.976266	−	0.563647i	−0.0751252	−	0.997174i	$-0.523936\pi$
$397$	−19.4520	−	11.2306i	−0.976266	−	0.563647i	−0.901141	+	0.433527i	$0.857269\pi$
$398$		0			0
$399$	3.42782	−	5.93716i	0.171606	−	0.297230i
$400$		0			0
$401$	−2.64547	+	1.52736i	−0.132108	+	0.0762729i	−0.564598	−	0.825366i	$-0.690969\pi$
$401$	−2.64547	+	1.52736i	−0.132108	+	0.0762729i	0.432489	+	0.901639i	$0.357635\pi$
$402$		0			0
$403$	−0.831240	+	7.40605i	−0.0414070	+	0.368921i
$404$		0			0
$405$	2.22527	−	1.28476i	0.110575	−	0.0638403i
$406$		0			0
$407$	2.42149	−	4.19414i	0.120029	−	0.207896i
$408$		0			0
$409$	4.85482	+	2.80293i	0.240055	+	0.138596i	0.615202	−	0.788369i	$-0.289074\pi$
$409$	4.85482	+	2.80293i	0.240055	+	0.138596i	−0.375147	+	0.926965i	$0.622408\pi$
$410$		0			0
$411$		−	25.5577i		−	1.26067i
$412$		0			0
$413$	−1.53698	−	2.66212i	−0.0756297	−	0.130995i
$414$		0			0
$415$	−14.4719			−0.710400
$416$		0			0
$417$	−12.9297			−0.633172
$418$		0			0
$419$	3.06969	+	5.31687i	0.149964	+	0.259746i	0.931214	−	0.364473i	$-0.118751\pi$
$419$	3.06969	+	5.31687i	0.149964	+	0.259746i	−0.781250	+	0.624219i	$0.785417\pi$
$420$		0			0
$421$		−	1.92589i		−	0.0938622i	−0.998898	−	0.0469311i	$-0.985056\pi$
$421$		−	1.92589i		−	0.0938622i	0.998898	−	0.0469311i	$-0.0149441\pi$
$422$		0			0
$423$	−9.43475	−	5.44716i	−0.458733	−	0.264850i
$424$		0			0
$425$	2.34092	−	4.05459i	0.113551	−	0.196677i
$426$		0			0
$427$	−0.936853	+	0.540892i	−0.0453375	+	0.0261756i
$428$		0			0
$429$	9.41700	+	6.94381i	0.454657	+	0.335250i
$430$		0			0
$431$	−9.30923	+	5.37469i	−0.448410	+	0.258890i	−0.707158	−	0.707055i	$-0.750023\pi$
$431$	−9.30923	+	5.37469i	−0.448410	+	0.258890i	0.258749	+	0.965945i	$0.416690\pi$
$432$		0			0
$433$	20.1328	−	34.8710i	0.967520	−	1.67579i	0.264835	−	0.964294i	$-0.414682\pi$
$433$	20.1328	−	34.8710i	0.967520	−	1.67579i	0.702685	−	0.711501i	$-0.251984\pi$
$434$		0			0
$435$	−6.45439	−	3.72644i	−0.309464	−	0.178669i
$436$		0			0
$437$		−	41.0842i		−	1.96532i
$438$		0			0
$439$	10.9754	+	19.0099i	0.523826	+	0.907294i	0.999615	+	0.0277345i	$0.00882930\pi$
$439$	10.9754	+	19.0099i	0.523826	+	0.907294i	−0.475789	+	0.879560i	$0.657837\pi$
$440$		0			0
$441$	1.63595			0.0779024
$442$		0			0
$443$	27.8963			1.32539			0.662697	−	0.748887i	$-0.269412\pi$
$443$	27.8963			1.32539			0.662697	+	0.748887i	$0.269412\pi$
$444$		0			0
$445$	14.5770	+	25.2481i	0.691017	+	1.19688i
$446$		0			0
$447$			2.69484i			0.127461i
$448$		0			0
$449$	19.1056	+	11.0306i	0.901648	+	0.520567i	0.877734	−	0.479147i	$-0.159054\pi$
$449$	19.1056	+	11.0306i	0.901648	+	0.520567i	0.0239134	+	0.999714i	$0.492387\pi$
$450$		0			0
$451$	8.84546	−	15.3208i	0.416516	−	0.721427i
$452$		0			0
$453$	20.8519	−	12.0389i	0.979708	−	0.565635i
$454$		0			0
$455$	−3.88347	+	5.26665i	−0.182060	+	0.246904i
$456$		0			0
$457$	4.77724	−	2.75814i	0.223470	−	0.129020i	−0.384086	−	0.923297i	$-0.625483\pi$
$457$	4.77724	−	2.75814i	0.223470	−	0.129020i	0.607556	+	0.794277i	$0.292150\pi$
$458$		0			0
$459$	−7.42851	+	12.8665i	−0.346733	+	0.600559i
$460$		0			0
$461$	25.0092	+	14.4391i	1.16479	+	0.672494i	0.952448	−	0.304700i	$-0.0985562\pi$
$461$	25.0092	+	14.4391i	1.16479	+	0.672494i	0.212346	+	0.977195i	$0.431890\pi$
$462$		0			0
$463$		−	14.2284i		−	0.661251i	−0.943762	−	0.330625i	$-0.892740\pi$
$463$		−	14.2284i		−	0.661251i	0.943762	−	0.330625i	$-0.107260\pi$
$464$		0			0
$465$	2.19061	+	3.79424i	0.101587	+	0.175954i
$466$		0			0
$467$	−4.54326			−0.210237			−0.105118	−	0.994460i	$-0.533522\pi$
$467$	−4.54326			−0.210237			−0.105118	+	0.994460i	$0.533522\pi$
$468$		0			0
$469$	−5.01796			−0.231708
$470$		0			0
$471$	−1.69144	−	2.92966i	−0.0779374	−	0.134992i
$472$		0			0
$473$			25.2951i			1.16307i
$474$		0			0
$475$	8.67366	+	5.00774i	0.397975	+	0.229771i
$476$		0			0
$477$	−8.57886	+	14.8590i	−0.392799	+	0.680348i
$478$		0			0
$479$	1.44239	−	0.832764i	0.0659044	−	0.0380499i	−0.466686	−	0.884423i	$-0.654552\pi$
$479$	1.44239	−	0.832764i	0.0659044	−	0.0380499i	0.532590	+	0.846373i	$0.321219\pi$
$480$		0			0
$481$	−5.75911	+	2.51562i	−0.262593	+	0.114702i
$482$		0			0
$483$	−7.07925	+	4.08721i	−0.322117	+	0.185974i
$484$		0			0
$485$	−12.9100	+	22.3608i	−0.586215	+	1.01535i
$486$		0			0
$487$	1.28598	+	0.742463i	0.0582735	+	0.0336442i	0.528854	−	0.848713i	$-0.322622\pi$
$487$	1.28598	+	0.742463i	0.0582735	+	0.0336442i	−0.470580	+	0.882357i	$0.655955\pi$
$488$		0			0
$489$		−	27.3691i		−	1.23767i
$490$		0			0
$491$	−7.99791	−	13.8528i	−0.360941	−	0.625167i	0.627175	−	0.778878i	$-0.284211\pi$
$491$	−7.99791	−	13.8528i	−0.360941	−	0.625167i	−0.988116	+	0.153711i	$0.950878\pi$
$492$		0			0
$493$	9.64808			0.434528
$494$		0			0
$495$	−8.24947			−0.370786
$496$		0			0
$497$	−1.35939	−	2.35453i	−0.0609768	−	0.105615i
$498$		0			0
$499$			17.7199i			0.793253i	0.917980	+	0.396627i	$0.129819\pi$
$499$			17.7199i			0.793253i	−0.917980	+	0.396627i	$0.870181\pi$
$500$		0			0
$501$	7.68902	+	4.43926i	0.343520	+	0.198331i
$502$		0			0
$503$	−0.598451	+	1.03655i	−0.0266836	+	0.0462174i	−0.879059	−	0.476713i	$-0.841828\pi$
$503$	−0.598451	+	1.03655i	−0.0266836	+	0.0462174i	0.852375	+	0.522931i	$0.175161\pi$
$504$		0			0
$505$	−0.114929	+	0.0663540i	−0.00511425	+	0.00295272i
$506$		0			0
$507$	−4.48774	−	14.5046i	−0.199307	−	0.644174i
$508$		0			0
$509$	5.44396	−	3.14307i	0.241299	−	0.139314i	−0.374474	−	0.927237i	$-0.622177\pi$
$509$	5.44396	−	3.14307i	0.241299	−	0.139314i	0.615774	+	0.787923i	$0.288844\pi$
$510$		0			0
$511$	3.83607	−	6.64426i	0.169698	−	0.293925i
$512$		0			0
$513$	−27.5244	−	15.8912i	−1.21523	−	0.701614i
$514$		0			0
$515$			23.4474i			1.03322i
$516$		0			0
$517$	−9.25143	−	16.0240i	−0.406878	−	0.704733i
$518$		0			0
$519$	−6.30354			−0.276695
$520$		0			0
$521$	−10.8473			−0.475230			−0.237615	−	0.971359i	$-0.576366\pi$
$521$	−10.8473			−0.475230			−0.237615	+	0.971359i	$0.576366\pi$
$522$		0			0
$523$	0.673629	+	1.16676i	0.0294557	+	0.0510188i	0.880377	−	0.474274i	$-0.157289\pi$
$523$	0.673629	+	1.16676i	0.0294557	+	0.0510188i	−0.850922	+	0.525292i	$0.823956\pi$
$524$		0			0
$525$		−	1.99275i		−	0.0869709i
$526$		0			0
$527$	−4.91181	−	2.83583i	−0.213962	−	0.123531i
$528$		0			0
$529$	−12.9936	+	22.5057i	−0.564941	+	0.978507i
$530$		0			0
$531$	−4.35510	+	2.51442i	−0.188995	+	0.109117i
$532$		0			0
$533$	−21.0375	+	9.18931i	−0.911233	+	0.398033i
$534$		0			0
$535$	6.30034	−	3.63750i	0.272388	−	0.157263i
$536$		0			0
$537$	7.17773	−	12.4322i	0.309742	−	0.536489i
$538$		0			0
$539$	2.40625	+	1.38925i	0.103644	+	0.0598391i
$540$		0			0
$541$		−	20.1571i		−	0.866621i	−0.901245	−	0.433310i	$-0.857345\pi$
$541$		−	20.1571i		−	0.866621i	0.901245	−	0.433310i	$-0.142655\pi$
$542$		0			0
$543$	12.7610	+	22.1027i	0.547628	+	0.948519i
$544$		0			0
$545$	−3.60415			−0.154385
$546$		0			0
$547$	3.42286			0.146351			0.0731755	−	0.997319i	$-0.476687\pi$
$547$	3.42286			0.146351			0.0731755	+	0.997319i	$0.476687\pi$
$548$		0			0
$549$	0.884873	+	1.53264i	0.0377654	+	0.0654117i
$550$		0			0
$551$			20.6394i			0.879266i
$552$		0			0
$553$	13.6311	+	7.86993i	0.579654	+	0.334663i
$554$		0			0
$555$	−1.84729	+	3.19960i	−0.0784130	+	0.135815i
$556$		0			0
$557$	−20.4948	+	11.8327i	−0.868394	+	0.501367i	−0.866814	−	0.498631i	$-0.833836\pi$
$557$	−20.4948	+	11.8327i	−0.868394	+	0.501367i	−0.00157977	+	0.999999i	$0.500503\pi$
$558$		0			0
$559$	19.4806	−	26.4190i	0.823940	−	1.11740i
$560$		0			0
$561$	−7.71139	+	4.45217i	−0.325575	+	0.187971i
$562$		0			0
$563$	−14.4037	+	24.9480i	−0.607045	+	1.05143i	0.384680	+	0.923050i	$0.374312\pi$
$563$	−14.4037	+	24.9480i	−0.607045	+	1.05143i	−0.991725	+	0.128382i	$0.959022\pi$
$564$		0			0
$565$	−16.6198	−	9.59543i	−0.699199	−	0.403683i
$566$		0			0
$567$			1.41581i			0.0594585i
$568$		0			0
$569$	−13.8361	−	23.9648i	−0.580040	−	1.00466i	−0.995474	−	0.0950353i	$-0.969704\pi$
$569$	−13.8361	−	23.9648i	−0.580040	−	1.00466i	0.415434	−	0.909623i	$-0.363630\pi$
$570$		0			0
$571$	12.9655			0.542588			0.271294	−	0.962497i	$-0.412548\pi$
$571$	12.9655			0.542588			0.271294	+	0.962497i	$0.412548\pi$
$572$		0			0
$573$	−3.22016			−0.134524
$574$		0			0
$575$	−5.97105	−	10.3422i	−0.249010	−	0.431298i
$576$		0			0
$577$		−	9.46047i		−	0.393844i	−0.980419	−	0.196922i	$-0.936905\pi$
$577$		−	9.46047i		−	0.393844i	0.980419	−	0.196922i	$-0.0630947\pi$
$578$		0			0
$579$	−13.1381	−	7.58529i	−0.546001	−	0.315234i
$580$		0			0
$581$	3.98704	−	6.90576i	0.165410	−	0.286499i
$582$		0			0
$583$	−25.2365	+	14.5703i	−1.04519	+	0.603440i
$584$		0			0
$585$	8.61598	+	6.35317i	0.356227	+	0.262671i
$586$		0			0
$587$	18.6673	−	10.7776i	0.770481	−	0.444837i	−0.0625654	−	0.998041i	$-0.519928\pi$
$587$	18.6673	−	10.7776i	0.770481	−	0.444837i	0.833046	+	0.553204i	$0.186595\pi$
$588$		0			0
$589$	6.06647	−	10.5074i	0.249965	−	0.432951i
$590$		0			0
$591$	−19.2441	−	11.1106i	−0.791598	−	0.457029i
$592$		0			0
$593$		−	3.97234i		−	0.163124i	−0.996668	−	0.0815622i	$-0.974009\pi$
$593$		−	3.97234i		−	0.163124i	0.996668	−	0.0815622i	$-0.0259909\pi$
$594$		0			0
$595$	−2.48997	−	4.31275i	−0.102079	−	0.176806i
$596$		0			0
$597$	−23.3956			−0.957517
$598$		0			0
$599$	19.5049			0.796950			0.398475	−	0.917179i	$-0.369540\pi$
$599$	19.5049			0.796950			0.398475	+	0.917179i	$0.369540\pi$
$600$		0			0
$601$	13.4368	+	23.2733i	0.548100	+	0.949336i	0.998405	+	0.0564616i	$0.0179818\pi$
$601$	13.4368	+	23.2733i	0.548100	+	0.949336i	−0.450305	+	0.892875i	$0.648685\pi$
$602$		0			0
$603$			8.20914i			0.334302i
$604$		0			0
$605$	5.15523	+	2.97637i	0.209590	+	0.121007i
$606$		0			0
$607$	12.5102	−	21.6682i	0.507772	−	0.879487i	−0.492187	−	0.870489i	$-0.663803\pi$
$607$	12.5102	−	21.6682i	0.507772	−	0.879487i	0.999960	−	0.00899773i	$-0.00286411\pi$
$608$		0			0
$609$	3.55639	−	2.05328i	0.144112	−	0.0832031i
$610$		0			0
$611$	−2.67808	+	23.8607i	−0.108343	+	0.965300i
$612$		0			0
$613$	−18.4970	+	10.6793i	−0.747088	+	0.431332i	−0.824641	−	0.565657i	$-0.808623\pi$
$613$	−18.4970	+	10.6793i	−0.747088	+	0.431332i	0.0775527	+	0.996988i	$0.475289\pi$
$614$		0			0
$615$	−6.74796	+	11.6878i	−0.272104	+	0.471298i
$616$		0			0
$617$	−28.5425	−	16.4790i	−1.14908	−	0.663420i	−0.200415	−	0.979711i	$-0.564229\pi$
$617$	−28.5425	−	16.4790i	−1.14908	−	0.663420i	−0.948662	+	0.316291i	$0.897562\pi$
$618$		0			0
$619$		−	48.9117i		−	1.96593i	−0.183795	−	0.982965i	$-0.558838\pi$
$619$		−	48.9117i		−	1.96593i	0.183795	−	0.982965i	$-0.441162\pi$
$620$		0			0
$621$	18.9481	+	32.8191i	0.760361	+	1.31698i
$622$		0			0
$623$	−16.0640			−0.643589
$624$		0			0
$625$	−13.5576			−0.542304
$626$		0			0
$627$	−9.52417	−	16.4964i	−0.380359	−	0.658801i
$628$		0			0
$629$		−	4.78278i		−	0.190702i
$630$		0			0
$631$	−4.65076	−	2.68512i	−0.185144	−	0.106893i	0.404563	−	0.914510i	$-0.367424\pi$
$631$	−4.65076	−	2.68512i	−0.185144	−	0.106893i	−0.589707	+	0.807617i	$0.700757\pi$
$632$		0			0
$633$	5.83981	−	10.1148i	0.232111	−	0.402029i
$634$		0			0
$635$	−17.7127	+	10.2264i	−0.702905	+	0.405823i
$636$		0			0
$637$	−1.44325	−	3.30409i	−0.0571837	−	0.130913i
$638$		0			0
$639$	−3.85189	+	2.22389i	−0.152378	+	0.0879757i
$640$		0			0
$641$	19.8510	−	34.3829i	0.784066	−	1.35804i	−0.145489	−	0.989360i	$-0.546475\pi$
$641$	19.8510	−	34.3829i	0.784066	−	1.35804i	0.929555	−	0.368683i	$-0.120191\pi$
$642$		0			0
$643$	−27.8388	−	16.0727i	−1.09785	−	0.633847i	−0.162198	−	0.986758i	$-0.551858\pi$
$643$	−27.8388	−	16.0727i	−1.09785	−	0.633847i	−0.935657	+	0.352911i	$0.885192\pi$
$644$		0			0
$645$		−	19.2970i		−	0.759818i
$646$		0			0
$647$	9.92502	+	17.1906i	0.390193	+	0.675833i	0.992475	−	0.122450i	$-0.0390751\pi$
$647$	9.92502	+	17.1906i	0.390193	+	0.675833i	−0.602282	+	0.798283i	$0.705742\pi$
$648$		0			0
$649$	−8.54096			−0.335262
$650$		0			0
$651$	−2.41406			−0.0946145
$652$		0			0
$653$	9.50024	+	16.4549i	0.371773	+	0.643930i	0.989838	−	0.142197i	$-0.0454165\pi$
$653$	9.50024	+	16.4549i	0.371773	+	0.643930i	−0.618065	+	0.786127i	$0.712083\pi$
$654$		0			0
$655$			5.56225i			0.217335i
$656$		0			0
$657$	−10.8697	−	6.27562i	−0.424067	−	0.244835i
$658$		0			0
$659$	−3.60729	+	6.24801i	−0.140520	+	0.243388i	−0.927693	−	0.373345i	$-0.878211\pi$
$659$	−3.60729	+	6.24801i	−0.140520	+	0.243388i	0.787173	+	0.616733i	$0.211544\pi$
$660$		0			0
$661$	14.5068	−	8.37548i	0.564248	−	0.325769i	−0.190601	−	0.981668i	$-0.561044\pi$
$661$	14.5068	−	8.37548i	0.564248	−	0.325769i	0.754849	+	0.655899i	$0.227710\pi$
$662$		0			0
$663$	11.4828	+	1.28880i	0.445953	+	0.0500529i
$664$		0			0
$665$	9.22592	−	5.32659i	0.357766	−	0.206556i
$666$		0			0
$667$	12.3048	−	21.3126i	0.476444	−	0.825226i
$668$		0			0
$669$	8.47860	+	4.89512i	0.327802	+	0.189256i
$670$		0			0
$671$			3.00573i			0.116035i
$672$		0			0
$673$	−18.6684	−	32.3346i	−0.719614	−	1.24641i	−0.961153	−	0.276016i	$-0.910986\pi$
$673$	−18.6684	−	32.3346i	−0.719614	−	1.24641i	0.241539	−	0.970391i	$-0.422348\pi$
$674$		0			0
$675$	−9.23831			−0.355583
$676$		0			0
$677$	28.1341			1.08128			0.540641	−	0.841253i	$-0.318182\pi$
$677$	28.1341			1.08128			0.540641	+	0.841253i	$0.318182\pi$
$678$		0			0
$679$	−7.11347	−	12.3209i	−0.272990	−	0.472832i
$680$		0			0
$681$		−	1.07416i		−	0.0411620i
$682$		0			0
$683$	1.79295	+	1.03516i	0.0686053	+	0.0396093i	0.533910	−	0.845541i	$-0.320722\pi$
$683$	1.79295	+	1.03516i	0.0686053	+	0.0396093i	−0.465305	+	0.885150i	$0.654055\pi$
$684$		0			0
$685$	19.8574	−	34.3941i	0.758714	−	1.31413i
$686$		0			0
$687$	24.9028	−	14.3776i	0.950100	−	0.548540i
$688$		0			0
$689$	37.5788	+	4.21776i	1.43164	+	0.160684i
$690$		0			0
$691$	−31.0542	+	17.9291i	−1.18136	+	0.682057i	−0.956328	−	0.292295i	$-0.905581\pi$
$691$	−31.0542	+	17.9291i	−1.18136	+	0.682057i	−0.225029	+	0.974352i	$0.572248\pi$
$692$		0			0
$693$	2.27274	−	3.93650i	0.0863342	−	0.149535i
$694$		0			0
$695$	−17.4001	−	10.0460i	−0.660023	−	0.381065i
$696$		0			0
$697$		−	17.4710i		−	0.661763i
$698$		0			0
$699$	−10.0891	−	17.4748i	−0.381604	−	0.660958i
$700$		0			0
$701$	−44.8940			−1.69562			−0.847812	−	0.530297i	$-0.822081\pi$
$701$	−44.8940			−1.69562			−0.847812	+	0.530297i	$0.822081\pi$
$702$		0			0
$703$	10.2314			0.385885
$704$		0			0
$705$	7.05767	+	12.2242i	0.265807	+	0.460391i
$706$		0			0
$707$		−	0.0731225i		−	0.00275005i
$708$		0			0
$709$	−14.0864	−	8.13279i	−0.529026	−	0.305433i	0.211594	−	0.977358i	$-0.432135\pi$
$709$	−14.0864	−	8.13279i	−0.529026	−	0.305433i	−0.740620	+	0.671924i	$0.765468\pi$
$710$		0			0
$711$	12.8748	−	22.2998i	0.482843	−	0.836309i
$712$		0			0
$713$	−12.5287	+	7.23344i	−0.469203	+	0.270894i
$714$		0			0
$715$	7.27775	+	16.6613i	0.272173	+	0.623096i
$716$		0			0
$717$	−14.6487	+	8.45743i	−0.547066	+	0.315849i
$718$		0			0
$719$	5.00744	−	8.67314i	0.186746	−	0.323454i	−0.757417	−	0.652931i	$-0.773539\pi$
$719$	5.00744	−	8.67314i	0.186746	−	0.323454i	0.944164	+	0.329477i	$0.106873\pi$
$720$		0			0
$721$	−11.1887	−	6.45980i	−0.416689	−	0.240575i
$722$		0			0
$723$			9.85076i			0.366354i
$724$		0			0
$725$	2.99966	+	5.19556i	0.111405	+	0.192958i
$726$		0			0
$727$	−34.5299			−1.28064			−0.640322	−	0.768106i	$-0.721199\pi$
$727$	−34.5299			−1.28064			−0.640322	+	0.768106i	$0.721199\pi$
$728$		0			0
$729$	21.2872			0.788415
$730$		0			0
$731$	12.4904	+	21.6340i	0.461973	+	0.800161i
$732$		0			0
$733$			33.1360i			1.22391i	0.790894	+	0.611953i	$0.209616\pi$
$733$			33.1360i			1.22391i	−0.790894	+	0.611953i	$0.790384\pi$
$734$		0			0
$735$	−1.83566	−	1.05982i	−0.0677093	−	0.0390920i
$736$		0			0
$737$	−6.97119	+	12.0745i	−0.256787	+	0.444768i
$738$		0			0
$739$	3.47767	−	2.00784i	0.127928	−	0.0738594i	−0.434670	−	0.900590i	$-0.643135\pi$
$739$	3.47767	−	2.00784i	0.127928	−	0.0738594i	0.562598	+	0.826730i	$0.309802\pi$
$740$		0			0
$741$	−2.75703	+	24.5641i	−0.101282	+	0.902386i
$742$		0			0
$743$	−10.8361	+	6.25622i	−0.397538	+	0.229519i	−0.685421	−	0.728147i	$-0.740382\pi$
$743$	−10.8361	+	6.25622i	−0.397538	+	0.229519i	0.287883	+	0.957666i	$0.407048\pi$
$744$		0			0
$745$	−2.09379	+	3.62656i	−0.0767107	+	0.132867i
$746$		0			0
$747$	−11.2975	−	6.52260i	−0.413353	−	0.238650i
$748$		0			0
$749$			4.00855i			0.146469i
$750$		0			0
$751$	−18.7579	−	32.4896i	−0.684486	−	1.18556i	−0.973598	−	0.228269i	$-0.926693\pi$
$751$	−18.7579	−	32.4896i	−0.684486	−	1.18556i	0.289112	−	0.957295i	$-0.406640\pi$
$752$		0			0
$753$	−17.1365			−0.624490
$754$		0			0
$755$	37.4150			1.36167
$756$		0			0
$757$	17.5223	+	30.3496i	0.636860	+	1.10307i	0.986118	+	0.166047i	$0.0531004\pi$
$757$	17.5223	+	30.3496i	0.636860	+	1.10307i	−0.349258	+	0.937027i	$0.613566\pi$
$758$		0			0
$759$			22.7126i			0.824414i
$760$		0			0
$761$	−3.72586	−	2.15113i	−0.135062	−	0.0779782i	0.430946	−	0.902378i	$-0.358180\pi$
$761$	−3.72586	−	2.15113i	−0.135062	−	0.0779782i	−0.566009	+	0.824399i	$0.691513\pi$
$762$		0			0
$763$	0.992947	−	1.71984i	0.0359471	−	0.0622622i
$764$		0			0
$765$	−7.05545	+	4.07347i	−0.255090	+	0.147277i
$766$		0			0
$767$	8.92043	+	6.57766i	0.322098	+	0.237506i
$768$		0			0
$769$	10.6146	−	6.12834i	0.382772	−	0.220994i	−0.296251	−	0.955110i	$-0.595737\pi$
$769$	10.6146	−	6.12834i	0.382772	−	0.220994i	0.679024	+	0.734116i	$0.262403\pi$
$770$		0			0
$771$	17.1268	−	29.6645i	0.616806	−	1.06834i
$772$		0			0
$773$	−3.29372	−	1.90163i	−0.118467	−	0.0683970i	0.439596	−	0.898196i	$-0.355122\pi$
$773$	−3.29372	−	1.90163i	−0.118467	−	0.0683970i	−0.558063	+	0.829799i	$0.688455\pi$
$774$		0			0
$775$		−	3.52673i		−	0.126684i
$776$		0			0
$777$	−1.01786	−	1.76299i	−0.0365155	−	0.0632468i
$778$		0			0
$779$	37.3744			1.33908
$780$		0			0
$781$	−7.55409			−0.270307
$782$		0			0
$783$	−9.51891	−	16.4872i	−0.340178	−	0.589206i
$784$		0			0
$785$		−	5.25675i		−	0.187622i
$786$		0			0
$787$	−15.0114	−	8.66684i	−0.535099	−	0.308940i	0.207991	−	0.978131i	$-0.433307\pi$
$787$	−15.0114	−	8.66684i	−0.535099	−	0.308940i	−0.743090	+	0.669191i	$0.766641\pi$
$788$		0			0
$789$	11.6296	−	20.1430i	0.414024	−	0.717110i
$790$		0			0
$791$	9.15754	−	5.28711i	0.325605	−	0.187988i
$792$		0			0
$793$	2.31480	−	3.13927i	0.0822011	−	0.111479i
$794$		0			0
$795$	19.2522	−	11.1153i	0.682807	−	0.394219i
$796$		0			0
$797$	25.1707	−	43.5969i	0.891592	−	1.54428i	0.0536245	−	0.998561i	$-0.482923\pi$
$797$	25.1707	−	43.5969i	0.891592	−	1.54428i	0.837967	−	0.545721i	$-0.183744\pi$
$798$		0			0
$799$	−15.8248	−	9.13645i	−0.559841	−	0.323224i
$800$		0			0
$801$			26.2798i			0.928552i
$802$		0			0
$803$	−10.6585	−	18.4610i	−0.376130	−	0.651476i
$804$		0			0
$805$	−12.7025			−0.447703
$806$		0			0
$807$	−26.0739			−0.917845
$808$		0			0
$809$	−8.03694	−	13.9204i	−0.282564	−	0.489415i	0.689452	−	0.724332i	$-0.257852\pi$
$809$	−8.03694	−	13.9204i	−0.282564	−	0.489415i	−0.972015	+	0.234917i	$0.924518\pi$
$810$		0			0
$811$			36.9875i			1.29881i	0.760443	+	0.649404i	$0.224982\pi$
$811$			36.9875i			1.29881i	−0.760443	+	0.649404i	$0.775018\pi$
$812$		0			0
$813$	−9.50754	−	5.48918i	−0.333444	−	0.192514i
$814$		0			0
$815$	21.2648	−	36.8317i	0.744873	−	1.29016i
$816$		0			0
$817$	−46.2798	+	26.7197i	−1.61913	+	0.934803i
$818$		0			0
$819$	−5.40533	+	2.36109i	−0.188878	+	0.0825031i
$820$		0			0
$821$	26.1021	−	15.0700i	0.910968	−	0.525948i	0.0302256	−	0.999543i	$-0.490377\pi$
$821$	26.1021	−	15.0700i	0.910968	−	0.525948i	0.880743	+	0.473595i	$0.157044\pi$
$822$		0			0
$823$	−20.8251	+	36.0702i	−0.725918	+	1.25733i	0.232677	+	0.972554i	$0.425251\pi$
$823$	−20.8251	+	36.0702i	−0.725918	+	1.25733i	−0.958595	+	0.284773i	$0.908082\pi$
$824$		0			0
$825$	−4.79506	−	2.76843i	−0.166942	−	0.0963842i
$826$		0			0
$827$		−	37.6524i		−	1.30930i	−0.755932	−	0.654651i	$-0.772816\pi$
$827$		−	37.6524i		−	1.30930i	0.755932	−	0.654651i	$-0.227184\pi$
$828$		0			0
$829$	−3.73737	−	6.47332i	−0.129804	−	0.224828i	0.793796	−	0.608184i	$-0.208102\pi$
$829$	−3.73737	−	6.47332i	−0.129804	−	0.224828i	−0.923601	+	0.383356i	$0.874768\pi$
$830$		0			0
$831$	16.7512			0.581091
$832$		0			0
$833$	2.74396			0.0950725
$834$		0			0
$835$	6.89829	+	11.9482i	0.238725	+	0.413484i
$836$		0			0
$837$			11.1915i			0.386834i
$838$		0			0
$839$	9.51957	+	5.49613i	0.328652	+	0.189747i	0.655242	−	0.755419i	$-0.272566\pi$
$839$	9.51957	+	5.49613i	0.328652	+	0.189747i	−0.326590	+	0.945166i	$0.605900\pi$
$840$		0			0
$841$	8.31846	−	14.4080i	0.286843	−	0.496827i
$842$		0			0
$843$	0.0999736	−	0.0577198i	0.00344328	−	0.00198798i
$844$		0			0
$845$	5.23025	−	23.0063i	0.179926	−	0.791442i
$846$		0			0
$847$	−2.84054	+	1.63999i	−0.0976022	+	0.0563507i
$848$		0			0
$849$	0.362450	−	0.627781i	0.0124392	−	0.0215454i
$850$		0			0
$851$	−10.5651	−	6.09979i	−0.362169	−	0.209098i
$852$		0			0
$853$			35.2031i			1.20533i	0.797994	+	0.602666i	$0.205895\pi$
$853$			35.2031i			1.20533i	−0.797994	+	0.602666i	$0.794105\pi$
$854$		0			0
$855$	−8.71404	−	15.0932i	−0.298014	−	0.516175i
$856$		0			0
$857$	−30.3681			−1.03736			−0.518678	−	0.854970i	$-0.673576\pi$
$857$	−30.3681			−1.03736			−0.518678	+	0.854970i	$0.673576\pi$
$858$		0			0
$859$	35.8306			1.22252			0.611262	−	0.791429i	$-0.290662\pi$
$859$	35.8306			1.22252			0.611262	+	0.791429i	$0.290662\pi$
$860$		0			0
$861$	−3.71814	−	6.44001i	−0.126714	−	0.219475i
$862$		0			0
$863$		−	32.3403i		−	1.10088i	−0.834876	−	0.550438i	$-0.814461\pi$
$863$		−	32.3403i		−	1.10088i	0.834876	−	0.550438i	$-0.185539\pi$
$864$		0			0
$865$	−8.48294	−	4.89763i	−0.288429	−	0.166524i
$866$		0			0
$867$	5.53053	−	9.57916i	0.187827	−	0.325325i
$868$		0			0
$869$	37.8740	−	21.8665i	1.28479	−	0.741772i
$870$		0			0
$871$	16.5798	−	7.24218i	0.561786	−	0.245392i
$872$		0			0
$873$	−20.1564	+	11.6373i	−0.682190	+	0.393862i
$874$		0			0
$875$	6.08548	−	10.5404i	0.205727	−	0.356329i
$876$		0			0
$877$	3.82446	+	2.20805i	0.129143	+	0.0745607i	0.563180	−	0.826334i	$-0.309578\pi$
$877$	3.82446	+	2.20805i	0.129143	+	0.0745607i	−0.434037	+	0.900895i	$0.642911\pi$
$878$		0			0
$879$		−	29.0740i		−	0.980642i
$880$		0			0
$881$	9.97753	+	17.2816i	0.336152	+	0.582232i	0.983705	−	0.179788i	$-0.0575412\pi$
$881$	9.97753	+	17.2816i	0.336152	+	0.582232i	−0.647554	+	0.762020i	$0.724208\pi$
$882$		0			0
$883$	12.9725			0.436559			0.218280	−	0.975886i	$-0.429955\pi$
$883$	12.9725			0.436559			0.218280	+	0.975886i	$0.429955\pi$
$884$		0			0
$885$	6.51567			0.219022
$886$		0			0
$887$	27.0862	+	46.9147i	0.909467	+	1.57524i	0.814806	+	0.579733i	$0.196843\pi$
$887$	27.0862	+	46.9147i	0.909467	+	1.57524i	0.0946605	+	0.995510i	$0.469823\pi$
$888$		0			0
$889$		−	11.2696i		−	0.377969i
$890$		0			0
$891$	3.40679	+	1.96691i	0.114132	+	0.0658941i
$892$		0			0
$893$	19.5449	−	33.8527i	0.654044	−	1.13284i
$894$		0			0
$895$	19.3187	−	11.1537i	0.645755	−	0.372827i
$896$		0			0
$897$	17.4916	−	23.7216i	0.584029	−	0.792043i
$898$		0			0
$899$	6.29401	−	3.63385i	0.209917	−	0.121196i
$900$		0			0
$901$	−14.3892	+	24.9228i	−0.479374	+	0.830300i
$902$		0			0
$903$	9.20818	+	5.31634i	0.306429	+	0.176917i
$904$		0			0
$905$			39.6594i			1.31832i
$906$		0			0
$907$	1.29570	+	2.24421i	0.0430229	+	0.0745178i	0.886735	−	0.462278i	$-0.152968\pi$
$907$	1.29570	+	2.24421i	0.0430229	+	0.0745178i	−0.843712	+	0.536796i	$0.819635\pi$
$908$		0			0
$909$	−0.119625			−0.00396770
$910$		0			0
$911$	−3.59896			−0.119239			−0.0596195	−	0.998221i	$-0.518989\pi$
$911$	−3.59896			−0.119239			−0.0596195	+	0.998221i	$0.518989\pi$
$912$		0			0
$913$	−11.0780	−	19.1876i	−0.366627	−	0.635017i
$914$		0			0
$915$		−	2.29299i		−	0.0758039i
$916$		0			0
$917$	−2.65421	−	1.53241i	−0.0876496	−	0.0506045i
$918$		0			0
$919$	−13.9624	+	24.1836i	−0.460578	+	0.797745i	−0.998990	−	0.0449372i	$-0.985691\pi$
$919$	−13.9624	+	24.1836i	−0.460578	+	0.797745i	0.538412	+	0.842682i	$0.319025\pi$
$920$		0			0
$921$	−10.0110	+	5.77987i	−0.329875	+	0.190453i
$922$		0			0
$923$	7.88971	+	5.81764i	0.259693	+	0.191490i
$924$		0			0
$925$	2.57557	−	1.48700i	0.0846841	−	0.0488924i
$926$		0			0
$927$	−10.5679	+	18.3042i	−0.347096	+	0.601187i
$928$		0			0
$929$	−23.0067	−	13.2830i	−0.754827	−	0.435800i	0.0726084	−	0.997361i	$-0.476868\pi$
$929$	−23.0067	−	13.2830i	−0.754827	−	0.435800i	−0.827435	+	0.561561i	$0.810201\pi$
$930$		0			0
$931$			5.86993i			0.192379i
$932$		0			0
$933$	−4.22666	−	7.32079i	−0.138375	−	0.239672i
$934$		0			0
$935$	−13.8367			−0.452509
$936$		0			0
$937$	3.02509			0.0988255			0.0494128	−	0.998778i	$-0.484265\pi$
$937$	3.02509			0.0988255			0.0494128	+	0.998778i	$0.484265\pi$
$938$		0			0
$939$	−19.0726	−	33.0347i	−0.622410	−	1.07805i
$940$		0			0
$941$		−	6.48465i		−	0.211394i	−0.994398	−	0.105697i	$-0.966293\pi$
$941$		−	6.48465i		−	0.211394i	0.994398	−	0.105697i	$-0.0337073\pi$
$942$		0			0
$943$	−38.5934	−	22.2819i	−1.25678	−	0.725599i
$944$		0			0
$945$	−4.91326	+	8.51002i	−0.159829	+	0.276831i
$946$		0			0
$947$	−18.3193	+	10.5767i	−0.595298	+	0.343695i	−0.767190	−	0.641420i	$-0.778345\pi$
$947$	−18.3193	+	10.5767i	−0.595298	+	0.343695i	0.171892	+	0.985116i	$0.445012\pi$
$948$		0			0
$949$	−3.08538	+	27.4897i	−0.100156	+	0.892352i
$950$		0			0
$951$	17.3711	−	10.0292i	0.563295	−	0.325219i
$952$		0			0
$953$	−18.1393	+	31.4182i	−0.587590	+	1.01774i	0.406957	+	0.913447i	$0.366590\pi$
$953$	−18.1393	+	31.4182i	−0.587590	+	1.01774i	−0.994547	+	0.104289i	$0.966743\pi$
$954$		0			0
$955$	−4.33351	−	2.50195i	−0.140229	−	0.0809613i
$956$		0			0
$957$		−	11.4101i		−	0.368835i
$958$		0			0
$959$	10.9415	+	18.9512i	0.353320	+	0.611968i
$960$		0			0
$961$	26.7277			0.862182
$962$		0			0
$963$	6.55779			0.211322
$964$		0			0
$965$	−11.7870	−	20.4157i	−0.379437	−	0.657204i
$966$		0			0
$967$			16.2828i			0.523621i	0.965119	+	0.261810i	$0.0843195\pi$
$967$			16.2828i			0.523621i	−0.965119	+	0.261810i	$0.915681\pi$
$968$		0			0
$969$	−16.2913	−	9.40580i	−0.523353	−	0.302158i
$970$		0			0
$971$	−12.2605	+	21.2358i	−0.393458	+	0.681489i	−0.992903	−	0.118927i	$-0.962055\pi$
$971$	−12.2605	+	21.2358i	−0.393458	+	0.681489i	0.599445	+	0.800416i	$0.295388\pi$
$972$		0			0
$973$	9.58750	−	5.53535i	0.307361	−	0.177455i
$974$		0			0
$975$	2.87604	+	6.58424i	0.0921071	+	0.210865i
$976$		0			0
$977$	9.45681	−	5.45989i	0.302550	−	0.174677i	−0.341038	−	0.940050i	$-0.610778\pi$
$977$	9.45681	−	5.45989i	0.302550	−	0.174677i	0.643588	+	0.765372i	$0.277445\pi$
$978$		0			0
$979$	−22.3168	+	38.6538i	−0.713248	+	1.23538i
$980$		0			0
$981$	−2.81357	−	1.62441i	−0.0898302	−	0.0518635i
$982$		0			0
$983$		−	19.6715i		−	0.627423i	−0.949518	−	0.313711i	$-0.898428\pi$
$983$		−	19.6715i		−	0.627423i	0.949518	−	0.313711i	$-0.101572\pi$
$984$		0			0
$985$	−17.2651	−	29.9040i	−0.550112	−	0.952822i
$986$		0			0
$987$	−7.77759			−0.247563
$988$		0			0
$989$	63.7191			2.02615
$990$		0			0
$991$	−0.869000	−	1.50515i	−0.0276047	−	0.0478127i	0.851893	−	0.523716i	$-0.175455\pi$
$991$	−0.869000	−	1.50515i	−0.0276047	−	0.0478127i	−0.879498	+	0.475903i	$0.842121\pi$
$992$		0			0
$993$			23.2814i			0.738812i
$994$		0			0
$995$	−31.4844	−	18.1775i	−0.998123	−	0.576267i
$996$		0			0
$997$	23.4768	−	40.6631i	0.743519	−	1.28781i	−0.207365	−	0.978264i	$-0.566489\pi$
$997$	23.4768	−	40.6631i	0.743519	−	1.28781i	0.950884	−	0.309549i	$-0.100178\pi$
$998$		0			0
$999$	−8.17312	+	4.71875i	−0.258586	+	0.149295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.c.673.2		12
4.3	odd	2		91.2.q.a.36.5	✓	12
12.11	even	2		819.2.ct.a.127.2		12
13.4	even	6	inner	1456.2.cc.c.225.2		12
28.3	even	6		637.2.k.g.569.5		12
28.11	odd	6		637.2.k.h.569.5		12
28.19	even	6		637.2.u.i.361.2		12
28.23	odd	6		637.2.u.h.361.2		12
28.27	even	2		637.2.q.h.491.5		12
52.3	odd	6		1183.2.c.i.337.9		12
52.11	even	12		1183.2.a.m.1.3		6
52.15	even	12		1183.2.a.p.1.4		6
52.23	odd	6		1183.2.c.i.337.4		12
52.43	odd	6		91.2.q.a.43.5	yes	12
156.95	even	6		819.2.ct.a.316.2		12
364.95	odd	6		637.2.u.h.30.2		12
364.167	odd	12		8281.2.a.by.1.3		6
364.199	even	6		637.2.u.i.30.2		12
364.223	odd	12		8281.2.a.ch.1.4		6
364.251	even	6		637.2.q.h.589.5		12
364.303	odd	6		637.2.k.h.459.2		12
364.355	even	6		637.2.k.g.459.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.5	✓	12	4.3	odd	2
91.2.q.a.43.5	yes	12	52.43	odd	6
637.2.k.g.459.2		12	364.355	even	6
637.2.k.g.569.5		12	28.3	even	6
637.2.k.h.459.2		12	364.303	odd	6
637.2.k.h.569.5		12	28.11	odd	6
637.2.q.h.491.5		12	28.27	even	2
637.2.q.h.589.5		12	364.251	even	6
637.2.u.h.30.2		12	364.95	odd	6
637.2.u.h.361.2		12	28.23	odd	6
637.2.u.i.30.2		12	364.199	even	6
637.2.u.i.361.2		12	28.19	even	6
819.2.ct.a.127.2		12	12.11	even	2
819.2.ct.a.316.2		12	156.95	even	6
1183.2.a.m.1.3		6	52.11	even	12
1183.2.a.p.1.4		6	52.15	even	12
1183.2.c.i.337.4		12	52.23	odd	6
1183.2.c.i.337.9		12	52.3	odd	6
1456.2.cc.c.225.2		12	13.4	even	6	inner
1456.2.cc.c.673.2		12	1.1	even	1	trivial
8281.2.a.by.1.3		6	364.167	odd	12
8281.2.a.ch.1.4		6	364.223	odd	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.583963 - 1.01145i) q^{3} -1.81487i q^{5} +(0.866025 + 0.500000i) q^{7} +(0.817975 - 1.41677i) q^{9} +O(q^{10})\)	\(q+(-0.583963 - 1.01145i) q^{3} -1.81487i q^{5} +(0.866025 + 0.500000i) q^{7} +(0.817975 - 1.41677i) q^{9} +(2.40625 - 1.38925i) q^{11} +(-3.58305 - 0.402155i) q^{13} +(-1.83566 + 1.05982i) q^{15} +(1.37198 - 2.37634i) q^{17} +(5.08351 + 2.93497i) q^{19} -1.16793i q^{21} +(-3.49955 - 6.06139i) q^{23} +1.70623 q^{25} -5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} -2.06697i q^{31} +(-2.81031 - 1.62254i) q^{33} +(0.907437 - 1.57173i) q^{35} +(1.50950 - 0.871512i) q^{37} +(1.68561 + 3.85893i) q^{39} +(5.51406 - 3.18355i) q^{41} +(-4.55195 + 7.88422i) q^{43} +(-2.57127 - 1.48452i) q^{45} -6.65932i q^{47} +(0.500000 + 0.866025i) q^{49} -3.20474 q^{51} -10.4879 q^{53} +(-2.52131 - 4.36703i) q^{55} -6.85564i q^{57} +(-2.66212 - 1.53698i) q^{59} +(-0.540892 + 0.936853i) q^{61} +(1.41677 - 0.817975i) q^{63} +(-0.729860 + 6.50279i) q^{65} +(-4.34568 + 2.50898i) q^{67} +(-4.08721 + 7.07925i) q^{69} +(-2.35453 - 1.35939i) q^{71} -7.67213i q^{73} +(-0.996377 - 1.72578i) q^{75} +2.77849 q^{77} +15.7399 q^{79} +(0.707906 + 1.22613i) q^{81} -7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} +(2.05328 - 3.55639i) q^{87} +(-13.9118 + 8.03198i) q^{89} +(-2.90194 - 2.13980i) q^{91} +(-2.09064 + 1.20703i) q^{93} +(5.32659 - 9.22592i) q^{95} +(-12.3209 - 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^9	\( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Introduction

L-functions

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