LMFDB - Embedded newform 464.2.y.e.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(33,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([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("464.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.y (of order $14$, degree $6$, 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 232)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	464.33
Dual form			464.2.y.e.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42415 - 2.95728i) q^{3} +(-0.136467 + 0.597901i) q^{5} +(-0.294470 + 0.141809i) q^{7} +(-4.84685 + 6.07775i) q^{9} +O(q^{10})$	\(q+(-1.42415 - 2.95728i) q^{3} +(-0.136467 + 0.597901i) q^{5} +(-0.294470 + 0.141809i) q^{7} +(-4.84685 + 6.07775i) q^{9} +(-3.71818 + 2.96515i) q^{11} +(-2.63087 - 3.29900i) q^{13} +(1.96251 - 0.447931i) q^{15} +1.72036i q^{17} +(0.863022 - 1.79208i) q^{19} +(0.838739 + 0.668872i) q^{21} +(1.12584 + 4.93263i) q^{23} +(4.16598 + 2.00623i) q^{25} +(15.2762 + 3.48668i) q^{27} +(-5.38071 - 0.218958i) q^{29} +(-8.88354 - 2.02761i) q^{31} +(14.0640 + 6.77289i) q^{33} +(-0.0446024 - 0.195416i) q^{35} +(4.28644 + 3.41832i) q^{37} +(-6.00933 + 12.4785i) q^{39} -6.90110i q^{41} +(-7.25565 + 1.65605i) q^{43} +(-2.97246 - 3.72735i) q^{45} +(-2.73445 + 2.18065i) q^{47} +(-4.29783 + 5.38930i) q^{49} +(5.08758 - 2.45005i) q^{51} +(0.145980 - 0.639579i) q^{53} +(-1.26546 - 2.62775i) q^{55} -6.52877 q^{57} +10.3221 q^{59} +(-6.65192 - 13.8129i) q^{61} +(0.565368 - 2.47704i) q^{63} +(2.33151 - 1.12279i) q^{65} +(-0.567230 + 0.711284i) q^{67} +(12.9838 - 10.3543i) q^{69} +(2.65263 + 3.32630i) q^{71} +(-5.98816 + 1.36676i) q^{73} -15.1772i q^{75} +(0.674406 - 1.40042i) q^{77} +(-3.37455 - 2.69112i) q^{79} +(-6.25501 - 27.4050i) q^{81} +(-6.50740 - 3.13380i) q^{83} +(-1.02860 - 0.234772i) q^{85} +(7.01544 + 16.2241i) q^{87} +(-4.11167 - 0.938463i) q^{89} +(1.24254 + 0.598375i) q^{91} +(6.65530 + 29.1588i) q^{93} +(0.953715 + 0.760562i) q^{95} +(-0.123789 + 0.257051i) q^{97} -36.9698i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9	$ 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9} + 10 q^{13} - 14 q^{15} + 14 q^{21} - 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} - 8 q^{35} - 38 q^{45} + 14 q^{47} - 18 q^{49} + 56 q^{51} - 48 q^{53} + 28 q^{55} - 12 q^{57} + 128 q^{59} - 28 q^{61} - 42 q^{63} - 28 q^{65} + 4 q^{67} + 28 q^{69} + 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} - 80 q^{83} + 112 q^{87} + 42 q^{89} + 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) $ 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9 + 10 * q^13 - 14 * q^15 + 14 * q^21 - 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 - 8 * q^35 - 38 * q^45 + 14 * q^47 - 18 * q^49 + 56 * q^51 - 48 * q^53 + 28 * q^55 - 12 * q^57 + 128 * q^59 - 28 * q^61 - 42 * q^63 - 28 * q^65 + 4 * q^67 + 28 * q^69 + 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 - 80 * q^83 + 112 * q^87 + 42 * q^89 + 28 * q^91 + 6 * q^93 + 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.42415	−	2.95728i	−0.822235	−	1.70739i	−0.699130	−	0.714995i	$-0.746429\pi$
$3$	−1.42415	−	2.95728i	−0.822235	−	1.70739i	−0.123105	−	0.992394i	$-0.539285\pi$
$4$		0			0
$5$	−0.136467	+	0.597901i	−0.0610299	+	0.267390i	−0.996232	−	0.0867239i	$-0.972360\pi$
$5$	−0.136467	+	0.597901i	−0.0610299	+	0.267390i	0.935202	+	0.354114i	$0.115217\pi$
$6$		0			0
$7$	−0.294470	+	0.141809i	−0.111299	+	0.0535988i	−0.488705	−	0.872449i	$-0.662530\pi$
$7$	−0.294470	+	0.141809i	−0.111299	+	0.0535988i	0.377406	+	0.926048i	$0.376816\pi$
$8$		0			0
$9$	−4.84685	+	6.07775i	−1.61562	+	2.02592i
$10$		0			0
$11$	−3.71818	+	2.96515i	−1.12107	+	0.894026i	−0.995185	−	0.0980183i	$-0.968750\pi$
$11$	−3.71818	+	2.96515i	−1.12107	+	0.894026i	−0.125889	+	0.992044i	$0.540178\pi$
$12$		0			0
$13$	−2.63087	−	3.29900i	−0.729671	−	0.914979i	0.269171	−	0.963093i	$-0.413250\pi$
$13$	−2.63087	−	3.29900i	−0.729671	−	0.914979i	−0.998842	+	0.0481137i	$0.984679\pi$
$14$		0			0
$15$	1.96251	−	0.447931i	0.506719	−	0.115655i
$16$		0			0
$17$			1.72036i			0.417248i	0.977996	+	0.208624i	$0.0668984\pi$
$17$			1.72036i			0.417248i	−0.977996	+	0.208624i	$0.933102\pi$
$18$		0			0
$19$	0.863022	−	1.79208i	0.197991	−	0.411132i	−0.778209	−	0.628005i	$-0.783872\pi$
$19$	0.863022	−	1.79208i	0.197991	−	0.411132i	0.976200	+	0.216873i	$0.0695859\pi$
$20$		0			0
$21$	0.838739	+	0.668872i	0.183028	+	0.145960i
$22$		0			0
$23$	1.12584	+	4.93263i	0.234754	+	1.02853i	0.945639	+	0.325217i	$0.105437\pi$
$23$	1.12584	+	4.93263i	0.234754	+	1.02853i	−0.710885	+	0.703308i	$0.751705\pi$
$24$		0			0
$25$	4.16598	+	2.00623i	0.833196	+	0.401246i
$26$		0			0
$27$	15.2762	+	3.48668i	2.93990	+	0.671013i
$28$		0			0
$29$	−5.38071	−	0.218958i	−0.999173	−	0.0406594i
$29$	−5.38071	−	0.218958i	−0.999173	−	0.0406594i
$30$		0			0
$31$	−8.88354	−	2.02761i	−1.59553	−	0.364169i	−0.669856	−	0.742491i	$-0.733644\pi$
$31$	−8.88354	−	2.02761i	−1.59553	−	0.364169i	−0.925674	+	0.378322i	$0.876501\pi$
$32$		0			0
$33$	14.0640	+	6.77289i	2.44824	+	1.17901i
$34$		0			0
$35$	−0.0446024	−	0.195416i	−0.00753919	−	0.0330313i
$36$		0			0
$37$	4.28644	+	3.41832i	0.704686	+	0.561968i	0.908929	−	0.416952i	$-0.136902\pi$
$37$	4.28644	+	3.41832i	0.704686	+	0.561968i	−0.204242	+	0.978920i	$0.565473\pi$
$38$		0			0
$39$	−6.00933	+	12.4785i	−0.962263	+	1.99816i
$40$		0			0
$41$		−	6.90110i		−	1.07777i	−0.842379	−	0.538885i	$-0.818846\pi$
$41$		−	6.90110i		−	1.07777i	0.842379	−	0.538885i	$-0.181154\pi$
$42$		0			0
$43$	−7.25565	+	1.65605i	−1.10648	+	0.252546i	−0.736461	−	0.676480i	$-0.763505\pi$
$43$	−7.25565	+	1.65605i	−1.10648	+	0.252546i	−0.370015	+	0.929026i	$0.620647\pi$
$44$		0			0
$45$	−2.97246	−	3.72735i	−0.443108	−	0.555640i
$46$		0			0
$47$	−2.73445	+	2.18065i	−0.398860	+	0.318080i	−0.802295	−	0.596928i	$-0.796388\pi$
$47$	−2.73445	+	2.18065i	−0.398860	+	0.318080i	0.403434	+	0.915009i	$0.367816\pi$
$48$		0			0
$49$	−4.29783	+	5.38930i	−0.613975	+	0.769900i
$50$		0			0
$51$	5.08758	−	2.45005i	0.712404	−	0.343076i
$52$		0			0
$53$	0.145980	−	0.639579i	0.0200519	−	0.0878530i	−0.963912	−	0.266221i	$-0.914225\pi$
$53$	0.145980	−	0.639579i	0.0200519	−	0.0878530i	0.983964	+	0.178368i	$0.0570819\pi$
$54$		0			0
$55$	−1.26546	−	2.62775i	−0.170634	−	0.354326i
$56$		0			0
$57$	−6.52877			−0.864757
$58$		0			0
$59$	10.3221			1.34383			0.671915	−	0.740629i	$-0.265472\pi$
$59$	10.3221			1.34383			0.671915	+	0.740629i	$0.265472\pi$
$60$		0			0
$61$	−6.65192	−	13.8129i	−0.851691	−	1.76856i	−0.598467	−	0.801148i	$-0.704223\pi$
$61$	−6.65192	−	13.8129i	−0.851691	−	1.76856i	−0.253224	−	0.967408i	$-0.581491\pi$
$62$		0			0
$63$	0.565368	−	2.47704i	0.0712297	−	0.312078i
$64$		0			0
$65$	2.33151	−	1.12279i	0.289188	−	0.139265i
$66$		0			0
$67$	−0.567230	+	0.711284i	−0.0692982	+	0.0868971i	−0.815272	−	0.579078i	$-0.803413\pi$
$67$	−0.567230	+	0.711284i	−0.0692982	+	0.0868971i	0.745974	+	0.665975i	$0.231984\pi$
$68$		0			0
$69$	12.9838	−	10.3543i	1.56307	−	1.24651i
$70$		0			0
$71$	2.65263	+	3.32630i	0.314810	+	0.394759i	0.913911	−	0.405914i	$-0.133047\pi$
$71$	2.65263	+	3.32630i	0.314810	+	0.394759i	−0.599102	+	0.800673i	$0.704475\pi$
$72$		0			0
$73$	−5.98816	+	1.36676i	−0.700861	+	0.159967i	−0.558080	−	0.829787i	$-0.688462\pi$
$73$	−5.98816	+	1.36676i	−0.700861	+	0.159967i	−0.142781	+	0.989754i	$0.545605\pi$
$74$		0			0
$75$		−	15.1772i		−	1.75251i
$76$		0			0
$77$	0.674406	−	1.40042i	0.0768557	−	0.159592i
$78$		0			0
$79$	−3.37455	−	2.69112i	−0.379667	−	0.302774i	0.414998	−	0.909822i	$-0.363782\pi$
$79$	−3.37455	−	2.69112i	−0.379667	−	0.302774i	−0.794665	+	0.607048i	$0.792354\pi$
$80$		0			0
$81$	−6.25501	−	27.4050i	−0.695001	−	3.04500i
$82$		0			0
$83$	−6.50740	−	3.13380i	−0.714280	−	0.343979i	0.0412002	−	0.999151i	$-0.486882\pi$
$83$	−6.50740	−	3.13380i	−0.714280	−	0.343979i	−0.755480	+	0.655172i	$0.772596\pi$
$84$		0			0
$85$	−1.02860	−	0.234772i	−0.111568	−	0.0254646i
$86$		0			0
$87$	7.01544	+	16.2241i	0.752134	+	1.73941i
$88$		0			0
$89$	−4.11167	−	0.938463i	−0.435837	−	0.0994769i	−0.00102740	−	0.999999i	$-0.500327\pi$
$89$	−4.11167	−	0.938463i	−0.435837	−	0.0994769i	−0.434809	+	0.900523i	$0.643184\pi$
$90$		0			0
$91$	1.24254	+	0.598375i	0.130253	+	0.0627268i
$92$		0			0
$93$	6.65530	+	29.1588i	0.690122	+	3.02362i
$94$		0			0
$95$	0.953715	+	0.760562i	0.0978491	+	0.0780321i
$96$		0			0
$97$	−0.123789	+	0.257051i	−0.0125689	+	0.0260996i	−0.907159	−	0.420788i	$-0.861753\pi$
$97$	−0.123789	+	0.257051i	−0.0125689	+	0.0260996i	0.894590	+	0.446888i	$0.147468\pi$
$98$		0			0
$99$		−	36.9698i		−	3.71560i
$100$		0			0
$101$	−17.2186	+	3.93003i	−1.71331	+	0.391053i	−0.962888	−	0.269902i	$-0.913009\pi$
$101$	−17.2186	+	3.93003i	−1.71331	+	0.391053i	−0.750426	+	0.660955i	$0.770151\pi$
$102$		0			0
$103$	−9.54887	−	11.9739i	−0.940878	−	1.17982i	−0.983532	−	0.180734i	$-0.942153\pi$
$103$	−9.54887	−	11.9739i	−0.940878	−	1.17982i	0.0426537	−	0.999090i	$-0.486419\pi$
$104$		0			0
$105$	−0.514380	+	0.410204i	−0.0501984	+	0.0400318i
$106$		0			0
$107$	−6.82377	+	8.55673i	−0.659678	+	0.827210i	−0.993308	−	0.115494i	$-0.963155\pi$
$107$	−6.82377	+	8.55673i	−0.659678	+	0.827210i	0.333630	+	0.942704i	$0.391726\pi$
$108$		0			0
$109$	−4.21128	+	2.02805i	−0.403368	+	0.194252i	−0.624557	−	0.780979i	$-0.714720\pi$
$109$	−4.21128	+	2.02805i	−0.403368	+	0.194252i	0.221189	+	0.975231i	$0.429006\pi$
$110$		0			0
$111$	4.00440	−	17.5444i	0.380081	−	1.66524i
$112$		0			0
$113$	−2.63131	−	5.46397i	−0.247533	−	0.514007i	0.739770	−	0.672860i	$-0.234935\pi$
$113$	−2.63131	−	5.46397i	−0.247533	−	0.514007i	−0.987302	+	0.158854i	$0.949220\pi$
$114$		0			0
$115$	−3.10287			−0.289344
$116$		0			0
$117$	32.8019			3.03254
$118$		0			0
$119$	−0.243962	−	0.506592i	−0.0223640	−	0.0464393i
$120$		0			0
$121$	2.58502	−	11.3257i	0.235002	−	1.02961i
$122$		0			0
$123$	−20.4085	+	9.82822i	−1.84017	+	0.886181i
$124$		0			0
$125$	−3.67991	+	4.61446i	−0.329141	+	0.412730i
$126$		0			0
$127$	3.03189	−	2.41785i	0.269037	−	0.214550i	−0.479673	−	0.877447i	$-0.659245\pi$
$127$	3.03189	−	2.41785i	0.269037	−	0.214550i	0.748710	+	0.662897i	$0.230673\pi$
$128$		0			0
$129$	15.2306	+	19.0985i	1.34098	+	1.68153i
$130$		0			0
$131$	18.4841	−	4.21888i	1.61497	−	0.368606i	0.682791	−	0.730613i	$-0.260766\pi$
$131$	18.4841	−	4.21888i	1.61497	−	0.368606i	0.932175	+	0.362008i	$0.117909\pi$
$132$		0			0
$133$			0.650098i			0.0563707i
$134$		0			0
$135$	−4.16939	+	8.65782i	−0.358844	+	0.745147i
$136$		0			0
$137$	11.3927	+	9.08538i	0.973345	+	0.776217i	0.974639	−	0.223783i	$-0.0718405\pi$
$137$	11.3927	+	9.08538i	0.973345	+	0.776217i	−0.00129423	+	0.999999i	$0.500412\pi$
$138$		0			0
$139$	1.68524	+	7.38350i	0.142940	+	0.626260i	0.994743	+	0.102399i	$0.0326519\pi$
$139$	1.68524	+	7.38350i	0.142940	+	0.626260i	−0.851804	+	0.523861i	$0.824491\pi$
$140$		0			0
$141$	10.3431	+	4.98096i	0.871044	+	0.419473i
$142$		0			0
$143$	19.5641	+	4.46537i	1.63603	+	0.373413i
$144$		0			0
$145$	0.865205	−	3.18725i	0.0718514	−	0.264687i
$146$		0			0
$147$	22.0585	+	5.03470i	1.81935	+	0.415255i
$148$		0			0
$149$	−9.13720	−	4.40025i	−0.748549	−	0.360482i	0.0204004	−	0.999792i	$-0.493506\pi$
$149$	−9.13720	−	4.40025i	−0.748549	−	0.360482i	−0.768949	+	0.639310i	$0.779220\pi$
$150$		0			0
$151$	−2.17697	−	9.53793i	−0.177159	−	0.776186i	−0.982933	−	0.183963i	$-0.941107\pi$
$151$	−2.17697	−	9.53793i	−0.177159	−	0.776186i	0.805774	−	0.592223i	$-0.201750\pi$
$152$		0			0
$153$	−10.4559	−	8.33830i	−0.845309	−	0.674112i
$154$		0			0
$155$	2.42462	−	5.03478i	0.194750	−	0.404403i
$156$		0			0
$157$			10.8273i			0.864114i	0.901846	+	0.432057i	$0.142212\pi$
$157$			10.8273i			0.864114i	−0.901846	+	0.432057i	$0.857788\pi$
$158$		0			0
$159$	−2.09932	+	0.479155i	−0.166487	+	0.0379995i
$160$		0			0
$161$	−1.03102	−	1.29286i	−0.0812556	−	0.101891i
$162$		0			0
$163$	15.7944	−	12.5956i	1.23711	−	0.986566i	0.237229	−	0.971454i	$-0.423761\pi$
$163$	15.7944	−	12.5956i	1.23711	−	0.986566i	0.999886	−	0.0151123i	$-0.00481058\pi$
$164$		0			0
$165$	−5.96880	+	7.48463i	−0.464670	+	0.582678i
$166$		0			0
$167$	4.77190	−	2.29802i	0.369260	−	0.177826i	−0.240046	−	0.970762i	$-0.577162\pi$
$167$	4.77190	−	2.29802i	0.369260	−	0.177826i	0.609306	+	0.792935i	$0.291448\pi$
$168$		0			0
$169$	−1.06919	+	4.68441i	−0.0822452	+	0.360340i
$170$		0			0
$171$	6.70890	+	13.9312i	0.513043	+	1.06534i
$172$		0			0
$173$	4.33809			0.329819			0.164909	−	0.986309i	$-0.447267\pi$
$173$	4.33809			0.329819			0.164909	+	0.986309i	$0.447267\pi$
$174$		0			0
$175$	−1.51126			−0.114240
$176$		0			0
$177$	−14.7003	−	30.5255i	−1.10494	−	2.29444i
$178$		0			0
$179$	−3.81909	+	16.7325i	−0.285452	+	1.25065i	0.605242	+	0.796042i	$0.293077\pi$
$179$	−3.81909	+	16.7325i	−0.285452	+	1.25065i	−0.890693	+	0.454604i	$0.849781\pi$
$180$		0			0
$181$	−11.3770	+	5.47888i	−0.845646	+	0.407242i	−0.805960	−	0.591970i	$-0.798350\pi$
$181$	−11.3770	+	5.47888i	−0.845646	+	0.407242i	−0.0396867	+	0.999212i	$0.512636\pi$
$182$		0			0
$183$	−31.3752	+	39.3432i	−2.31932	+	2.90834i
$184$		0			0
$185$	−2.62878	+	2.09638i	−0.193271	+	0.154129i
$186$		0			0
$187$	−5.10111	−	6.39659i	−0.373030	−	0.467765i
$188$		0			0
$189$	−4.99281	+	1.13958i	−0.363173	+	0.0828919i
$190$		0			0
$191$			13.6103i			0.984808i	0.870367	+	0.492404i	$0.163882\pi$
$191$			13.6103i			0.984808i	−0.870367	+	0.492404i	$0.836118\pi$
$192$		0			0
$193$	5.40424	−	11.2220i	0.389005	−	0.807778i	−0.610866	−	0.791734i	$-0.709179\pi$
$193$	5.40424	−	11.2220i	0.389005	−	0.807778i	0.999871	−	0.0160440i	$-0.00510718\pi$
$194$		0			0
$195$	−6.64084	−	5.29589i	−0.475560	−	0.379247i
$196$		0			0
$197$	−0.330554	−	1.44825i	−0.0235510	−	0.103184i	0.961786	−	0.273801i	$-0.0882810\pi$
$197$	−0.330554	−	1.44825i	−0.0235510	−	0.103184i	−0.985337	+	0.170617i	$0.945424\pi$
$198$		0			0
$199$	8.93699	+	4.30383i	0.633526	+	0.305090i	0.722947	−	0.690904i	$-0.242787\pi$
$199$	8.93699	+	4.30383i	0.633526	+	0.305090i	−0.0894203	+	0.995994i	$0.528501\pi$
$200$		0			0
$201$	2.91129	+	0.664483i	0.205347	+	0.0468690i
$202$		0			0
$203$	1.61551	−	0.698557i	0.113386	−	0.0490291i
$204$		0			0
$205$	4.12618	+	0.941773i	0.288185	+	0.0657763i
$206$		0			0
$207$	−35.4361	−	17.0651i	−2.46298	−	1.18611i
$208$		0			0
$209$	2.10492	+	9.22227i	0.145601	+	0.637918i
$210$		0			0
$211$	−7.72880	−	6.16351i	−0.532072	−	0.424314i	0.320248	−	0.947334i	$-0.396234\pi$
$211$	−7.72880	−	6.16351i	−0.532072	−	0.424314i	−0.852320	+	0.523020i	$0.824805\pi$
$212$		0			0
$213$	6.05905	−	12.5817i	0.415159	−	0.862087i
$214$		0			0
$215$		−	4.56416i		−	0.311273i
$216$		0			0
$217$	2.90346	−	0.662697i	0.197100	−	0.0449868i
$218$		0			0
$219$	12.5699	+	15.7622i	0.849398	+	1.06511i
$220$		0			0
$221$	5.67546	−	4.52603i	0.381773	−	0.304454i
$222$		0			0
$223$	10.5864	−	13.2749i	0.708917	−	0.888953i	−0.288738	−	0.957408i	$-0.593236\pi$
$223$	10.5864	−	13.2749i	0.708917	−	0.888953i	0.997654	+	0.0684550i	$0.0218070\pi$
$224$		0			0
$225$	−32.3852	+	15.5959i	−2.15902	+	1.03973i
$226$		0			0
$227$	−0.736755	+	3.22794i	−0.0489002	+	0.214246i	−0.993475	−	0.114051i	$-0.963617\pi$
$227$	−0.736755	+	3.22794i	−0.0489002	+	0.214246i	0.944575	+	0.328296i	$0.106474\pi$
$228$		0			0
$229$	−2.23936	−	4.65008i	−0.147981	−	0.307286i	0.813781	−	0.581171i	$-0.197405\pi$
$229$	−2.23936	−	4.65008i	−0.147981	−	0.307286i	−0.961762	+	0.273885i	$0.911691\pi$
$230$		0			0
$231$	−5.10189			−0.335680
$232$		0			0
$233$	10.6512			0.697783			0.348892	−	0.937163i	$-0.386558\pi$
$233$	10.6512			0.697783			0.348892	+	0.937163i	$0.386558\pi$
$234$		0			0
$235$	−0.930652	−	1.93252i	−0.0607090	−	0.126064i
$236$		0			0
$237$	−3.15252	+	13.8121i	−0.204778	+	0.897191i
$238$		0			0
$239$	−9.59472	+	4.62057i	−0.620631	+	0.298880i	−0.717652	−	0.696402i	$-0.754783\pi$
$239$	−9.59472	+	4.62057i	−0.620631	+	0.298880i	0.0970209	+	0.995282i	$0.469069\pi$
$240$		0			0
$241$	1.82979	−	2.29448i	0.117867	−	0.147801i	−0.719398	−	0.694599i	$-0.755582\pi$
$241$	1.82979	−	2.29448i	0.117867	−	0.147801i	0.837265	+	0.546798i	$0.184153\pi$
$242$		0			0
$243$	−35.3847	+	28.2183i	−2.26993	+	1.81021i
$244$		0			0
$245$	−2.63576	−	3.30514i	−0.168393	−	0.211158i
$246$		0			0
$247$	−8.18258	+	1.86762i	−0.520645	+	0.118834i
$248$		0			0
$249$			23.7072i			1.50238i
$250$		0			0
$251$	7.85981	−	16.3211i	0.496107	−	1.03018i	−0.491155	−	0.871072i	$-0.663425\pi$
$251$	7.85981	−	16.3211i	0.496107	−	1.03018i	0.987262	−	0.159104i	$-0.0508605\pi$
$252$		0			0
$253$	−18.8121	−	15.0021i	−1.18271	−	0.943176i
$254$		0			0
$255$	0.770601	+	3.37622i	0.0482569	+	0.211427i
$256$		0			0
$257$	17.0262	+	8.19937i	1.06206	+	0.511462i	0.881540	−	0.472108i	$-0.156507\pi$
$257$	17.0262	+	8.19937i	1.06206	+	0.511462i	0.180522	+	0.983571i	$0.442221\pi$
$258$		0			0
$259$	−1.74697	−	0.398735i	−0.108552	−	0.0247762i
$260$		0			0
$261$	27.4102	−	31.6414i	1.69665	−	1.95855i
$262$		0			0
$263$	13.2676	+	3.02824i	0.818116	+	0.186730i	0.611044	−	0.791596i	$-0.290750\pi$
$263$	13.2676	+	3.02824i	0.818116	+	0.186730i	0.207071	+	0.978326i	$0.433607\pi$
$264$		0			0
$265$	0.362484	+	0.174563i	0.0222672	+	0.0107233i
$266$		0			0
$267$	3.08035	+	13.4959i	0.188514	+	0.825936i
$268$		0			0
$269$	−1.94346	−	1.54986i	−0.118495	−	0.0944967i	0.562449	−	0.826832i	$-0.309859\pi$
$269$	−1.94346	−	1.54986i	−0.118495	−	0.0944967i	−0.680945	+	0.732335i	$0.738431\pi$
$270$		0			0
$271$	−4.42198	+	9.18233i	−0.268616	+	0.557787i	−0.991025	−	0.133679i	$-0.957321\pi$
$271$	−4.42198	+	9.18233i	−0.268616	+	0.557787i	0.722409	+	0.691467i	$0.243035\pi$
$272$		0			0
$273$		−	4.52672i		−	0.273969i
$274$		0			0
$275$	−21.4386	+	4.89323i	−1.29280	+	0.295073i
$276$		0			0
$277$	−14.4508	−	18.1207i	−0.868263	−	1.08877i	−0.995297	−	0.0968690i	$-0.969117\pi$
$277$	−14.4508	−	18.1207i	−0.868263	−	1.08877i	0.127034	−	0.991898i	$-0.459454\pi$
$278$		0			0
$279$	55.3804	−	44.1644i	3.31554	−	2.64405i
$280$		0			0
$281$	0.775063	−	0.971899i	0.0462364	−	0.0579786i	−0.758176	−	0.652050i	$-0.773909\pi$
$281$	0.775063	−	0.971899i	0.0462364	−	0.0579786i	0.804412	+	0.594072i	$0.202480\pi$
$282$		0			0
$283$	−15.0202	+	7.23333i	−0.892856	+	0.429977i	−0.823303	−	0.567602i	$-0.807871\pi$
$283$	−15.0202	+	7.23333i	−0.892856	+	0.429977i	−0.0695523	+	0.997578i	$0.522157\pi$
$284$		0			0
$285$	0.890963	−	3.90356i	0.0527761	−	0.231227i
$286$		0			0
$287$	0.978639	+	2.03216i	0.0577672	+	0.119955i
$288$		0			0
$289$	14.0404			0.825904
$290$		0			0
$291$	0.936468			0.0548967
$292$		0			0
$293$	11.5967	+	24.0807i	0.677484	+	1.40681i	0.901740	+	0.432279i	$0.142290\pi$
$293$	11.5967	+	24.0807i	0.677484	+	1.40681i	−0.224256	+	0.974530i	$0.571995\pi$
$294$		0			0
$295$	−1.40863	+	6.17163i	−0.0820138	+	0.359326i
$296$		0			0
$297$	−67.1380	+	32.3320i	−3.89574	+	1.87609i
$298$		0			0
$299$	13.3108	−	16.6913i	0.769785	−	0.965280i
$300$		0			0
$301$	1.90172	−	1.51657i	0.109614	−	0.0874139i
$302$		0			0
$303$	36.1441	+	45.3233i	2.07642	+	2.60375i
$304$		0			0
$305$	9.16650	−	2.09219i	0.524872	−	0.119799i
$306$		0			0
$307$			14.4465i			0.824506i	0.911069	+	0.412253i	$0.135258\pi$
$307$			14.4465i			0.824506i	−0.911069	+	0.412253i	$0.864742\pi$
$308$		0			0
$309$	−21.8112	+	45.2914i	−1.24079	+	2.57654i
$310$		0			0
$311$	−17.5399	−	13.9876i	−0.994599	−	0.793166i	−0.0161948	−	0.999869i	$-0.505155\pi$
$311$	−17.5399	−	13.9876i	−0.994599	−	0.793166i	−0.978404	+	0.206703i	$0.933727\pi$
$312$		0			0
$313$	3.38107	+	14.8134i	0.191109	+	0.837304i	0.976017	+	0.217692i	$0.0698529\pi$
$313$	3.38107	+	14.8134i	0.191109	+	0.837304i	−0.784908	+	0.619612i	$0.787290\pi$
$314$		0			0
$315$	1.40387	+	0.676069i	0.0790992	+	0.0380922i
$316$		0			0
$317$	−7.06457	−	1.61244i	−0.396786	−	0.0905638i	0.0194720	−	0.999810i	$-0.493801\pi$
$317$	−7.06457	−	1.61244i	−0.396786	−	0.0905638i	−0.416258	+	0.909247i	$0.636659\pi$
$318$		0			0
$319$	20.6557	−	15.1405i	1.15650	−	0.847705i
$320$		0			0
$321$	35.0228	+	7.99372i	1.95478	+	0.446166i
$322$		0			0
$323$	3.08302	+	1.48470i	0.171544	+	0.0826112i
$324$		0			0
$325$	−4.34158	−	19.0217i	−0.240828	−	1.05513i
$326$		0			0
$327$	11.9950	+	9.56571i	0.663326	+	0.528985i
$328$		0			0
$329$	0.495976	−	1.02990i	0.0273440	−	0.0567805i
$330$		0			0
$331$			4.85090i			0.266630i	0.991074	+	0.133315i	$0.0425621\pi$
$331$			4.85090i			0.266630i	−0.991074	+	0.133315i	$0.957438\pi$
$332$		0			0
$333$	−41.5514	+	9.48384i	−2.27700	+	0.519711i
$334$		0			0
$335$	−0.347869	−	0.436214i	−0.0190061	−	0.0238329i
$336$		0			0
$337$	20.0284	−	15.9721i	1.09101	−	0.870055i	0.0988633	−	0.995101i	$-0.468479\pi$
$337$	20.0284	−	15.9721i	1.09101	−	0.870055i	0.992151	+	0.125046i	$0.0399079\pi$
$338$		0			0
$339$	−12.4111	+	15.5630i	−0.674079	+	0.845269i
$340$		0			0
$341$	39.0427	−	18.8020i	2.11428	−	1.01818i
$342$		0			0
$343$	1.01042	−	4.42695i	0.0545577	−	0.239033i
$344$		0			0
$345$	4.41896	+	9.17606i	0.237909	+	0.494023i
$346$		0			0
$347$	−10.9788			−0.589370			−0.294685	−	0.955594i	$-0.595215\pi$
$347$	−10.9788			−0.589370			−0.294685	+	0.955594i	$0.595215\pi$
$348$		0			0
$349$	0.685139			0.0366747			0.0183373	−	0.999832i	$-0.494163\pi$
$349$	0.685139			0.0366747			0.0183373	+	0.999832i	$0.494163\pi$
$350$		0			0
$351$	−28.6870	−	59.5691i	−1.53120	−	3.17956i
$352$		0			0
$353$	1.19318	−	5.22766i	0.0635065	−	0.278240i	−0.933198	−	0.359364i	$-0.882994\pi$
$353$	1.19318	−	5.22766i	0.0635065	−	0.278240i	0.996704	+	0.0811236i	$0.0258509\pi$
$354$		0			0
$355$	−2.35079	+	1.13208i	−0.124767	+	0.0600847i
$356$		0			0
$357$	−1.15070	+	1.44293i	−0.0609014	+	0.0763680i
$358$		0			0
$359$	19.8673	−	15.8437i	1.04856	−	0.836197i	0.0617494	−	0.998092i	$-0.480332\pi$
$359$	19.8673	−	15.8437i	1.04856	−	0.836197i	0.986808	+	0.161895i	$0.0517606\pi$
$360$		0			0
$361$	9.37955	+	11.7616i	0.493661	+	0.619031i
$362$		0			0
$363$	−37.1748	+	8.48490i	−1.95117	+	0.445342i
$364$		0			0
$365$		−	3.76685i		−	0.197166i
$366$		0			0
$367$	8.23285	−	17.0957i	0.429751	−	0.892388i	−0.567848	−	0.823134i	$-0.692224\pi$
$367$	8.23285	−	17.0957i	0.429751	−	0.892388i	0.997599	−	0.0692544i	$-0.0220620\pi$
$368$		0			0
$369$	41.9432	+	33.4486i	2.18347	+	1.74126i
$370$		0			0
$371$	0.0477116	+	0.209038i	0.00247706	+	0.0108527i
$372$		0			0
$373$	22.3441	+	10.7604i	1.15693	+	0.557150i	0.911110	−	0.412164i	$-0.135227\pi$
$373$	22.3441	+	10.7604i	1.15693	+	0.557150i	0.245825	+	0.969314i	$0.420941\pi$
$374$		0			0
$375$	18.8870	+	4.31084i	0.975322	+	0.222611i
$376$		0			0
$377$	13.4336	+	18.3270i	0.691865	+	0.943890i
$378$		0			0
$379$	−4.82824	−	1.10202i	−0.248010	−	0.0566067i	0.0967085	−	0.995313i	$-0.469169\pi$
$379$	−4.82824	−	1.10202i	−0.248010	−	0.0566067i	−0.344719	+	0.938706i	$0.612026\pi$
$380$		0			0
$381$	−11.4682	−	5.52277i	−0.587531	−	0.282940i
$382$		0			0
$383$	5.17194	+	22.6597i	0.264274	+	1.15786i	0.916564	+	0.399889i	$0.130951\pi$
$383$	5.17194	+	22.6597i	0.264274	+	1.15786i	−0.652290	+	0.757970i	$0.726192\pi$
$384$		0			0
$385$	0.745278	+	0.594339i	0.0379829	+	0.0302903i
$386$		0			0
$387$	25.1019	−	52.1247i	1.27600	−	2.64965i
$388$		0			0
$389$		−	26.6484i		−	1.35113i	−0.737301	−	0.675565i	$-0.763900\pi$
$389$		−	26.6484i		−	1.35113i	0.737301	−	0.675565i	$-0.236100\pi$
$390$		0			0
$391$	−8.48589	+	1.93685i	−0.429150	+	0.0979506i
$392$		0			0
$393$	−38.8007	−	48.6545i	−1.95723	−	2.45429i
$394$		0			0
$395$	2.06954	−	1.65040i	0.104130	−	0.0830407i
$396$		0			0
$397$	−10.4670	+	13.1252i	−0.525325	+	0.658737i	−0.971730	−	0.236094i	$-0.924133\pi$
$397$	−10.4670	+	13.1252i	−0.525325	+	0.658737i	0.446405	+	0.894831i	$0.352704\pi$
$398$		0			0
$399$	1.92252	−	0.925839i	0.0962466	−	0.0463499i
$400$		0			0
$401$	−8.15340	+	35.7224i	−0.407161	+	1.78389i	0.190015	+	0.981781i	$0.439146\pi$
$401$	−8.15340	+	35.7224i	−0.407161	+	1.78389i	−0.597176	+	0.802110i	$0.703711\pi$
$402$		0			0
$403$	16.6823	+	34.6412i	0.831005	+	1.72560i
$404$		0			0
$405$	17.2391			0.856618
$406$		0			0
$407$	−26.0736			−1.29242
$408$		0			0
$409$	0.556937	+	1.15649i	0.0275388	+	0.0571848i	0.914284	−	0.405073i	$-0.132754\pi$
$409$	0.556937	+	1.15649i	0.0275388	+	0.0571848i	−0.886746	+	0.462258i	$0.847040\pi$
$410$		0			0
$411$	10.6431	−	46.6304i	0.524985	−	2.30011i
$412$		0			0
$413$	−3.03956	+	1.46377i	−0.149567	+	0.0720276i
$414$		0			0
$415$	2.76175	−	3.46312i	0.135569	−	0.169998i
$416$		0			0
$417$	19.4351	−	15.4990i	0.951740	−	0.758987i
$418$		0			0
$419$	−11.5704	−	14.5088i	−0.565250	−	0.708802i	0.414268	−	0.910155i	$-0.364038\pi$
$419$	−11.5704	−	14.5088i	−0.565250	−	0.708802i	−0.979519	+	0.201353i	$0.935466\pi$
$420$		0			0
$421$	9.76598	−	2.22902i	0.475965	−	0.108636i	0.0221929	−	0.999754i	$-0.492935\pi$
$421$	9.76598	−	2.22902i	0.475965	−	0.108636i	0.453772	+	0.891118i	$0.350078\pi$
$422$		0			0
$423$		−	27.1886i		−	1.32195i
$424$		0			0
$425$	−3.45143	+	7.16697i	−0.167419	+	0.347649i
$426$		0			0
$427$	3.91758	+	3.12416i	0.189585	+	0.151189i
$428$		0			0
$429$	−14.6569	−	64.2159i	−0.707640	−	3.10037i
$430$		0			0
$431$	−8.26153	−	3.97854i	−0.397944	−	0.191640i	0.224199	−	0.974543i	$-0.428023\pi$
$431$	−8.26153	−	3.97854i	−0.397944	−	0.191640i	−0.622143	+	0.782904i	$0.713738\pi$
$432$		0			0
$433$	−20.7331	−	4.73219i	−0.996368	−	0.227415i	−0.306909	−	0.951739i	$-0.599295\pi$
$433$	−20.7331	−	4.73219i	−0.996368	−	0.227415i	−0.689459	+	0.724324i	$0.742152\pi$
$434$		0			0
$435$	−10.6578	+	1.98048i	−0.511002	+	0.0949568i
$436$		0			0
$437$	9.81132	+	2.23937i	0.469339	+	0.107124i
$438$		0			0
$439$	−17.8377	−	8.59017i	−0.851345	−	0.409986i	−0.0432686	−	0.999063i	$-0.513777\pi$
$439$	−17.8377	−	8.59017i	−0.851345	−	0.409986i	−0.808077	+	0.589077i	$0.799491\pi$
$440$		0			0
$441$	−11.9240	−	52.2422i	−0.567807	−	2.48773i
$442$		0			0
$443$	−5.05031	−	4.02749i	−0.239947	−	0.191352i	0.496132	−	0.868247i	$-0.334753\pi$
$443$	−5.05031	−	4.02749i	−0.239947	−	0.191352i	−0.736079	+	0.676896i	$0.763325\pi$
$444$		0			0
$445$	1.12222	−	2.33031i	0.0531982	−	0.110467i
$446$		0			0
$447$			33.2879i			1.57446i
$448$		0			0
$449$	−0.869120	+	0.198371i	−0.0410163	+	0.00936170i	−0.242980	−	0.970031i	$-0.578125\pi$
$449$	−0.869120	+	0.198371i	−0.0410163	+	0.00936170i	0.201964	+	0.979393i	$0.435268\pi$
$450$		0			0
$451$	20.4628	+	25.6595i	0.963555	+	1.20826i
$452$		0			0
$453$	−25.1060	+	20.0214i	−1.17958	+	0.940687i
$454$		0			0
$455$	−0.527335	+	0.661257i	−0.0247219	+	0.0310002i
$456$		0			0
$457$	−6.76281	+	3.25680i	−0.316351	+	0.152347i	−0.585320	−	0.810802i	$-0.699031\pi$
$457$	−6.76281	+	3.25680i	−0.316351	+	0.152347i	0.268969	+	0.963149i	$0.413317\pi$
$458$		0			0
$459$	−5.99834	+	26.2804i	−0.279978	+	1.22667i
$460$		0			0
$461$	2.02120	+	4.19706i	0.0941364	+	0.195476i	0.942720	−	0.333585i	$-0.108258\pi$
$461$	2.02120	+	4.19706i	0.0941364	+	0.195476i	−0.848584	+	0.529061i	$0.822544\pi$
$462$		0			0
$463$	−16.5581			−0.769520			−0.384760	−	0.923017i	$-0.625716\pi$
$463$	−16.5581			−0.769520			−0.384760	+	0.923017i	$0.625716\pi$
$464$		0			0
$465$	−18.3423			−0.850603
$466$		0			0
$467$	5.93783	+	12.3300i	0.274770	+	0.570565i	0.991995	−	0.126276i	$-0.0403025\pi$
$467$	5.93783	+	12.3300i	0.274770	+	0.570565i	−0.717225	+	0.696841i	$0.754588\pi$
$468$		0			0
$469$	0.0661654	−	0.289890i	0.00305524	−	0.0133859i
$470$		0			0
$471$	32.0195	−	15.4198i	1.47538	−	0.710505i
$472$		0			0
$473$	22.0674	−	27.6716i	1.01466	−	1.27234i
$474$		0			0
$475$	7.19067	−	5.73436i	0.329930	−	0.263111i
$476$		0			0
$477$	3.17966	+	3.98717i	0.145587	+	0.182560i
$478$		0			0
$479$	−30.9396	+	7.06176i	−1.41367	+	0.322660i	−0.860091	−	0.510140i	$-0.829594\pi$
$479$	−30.9396	+	7.06176i	−1.41367	+	0.322660i	−0.553574	+	0.832800i	$0.686736\pi$
$480$		0			0
$481$		−	23.1341i		−	1.05482i
$482$		0			0
$483$	−2.35501	+	4.89024i	−0.107157	+	0.222514i
$484$		0			0
$485$	−0.136798	−	0.109093i	−0.00621168	−	0.00495365i
$486$		0			0
$487$	−7.81891	−	34.2569i	−0.354309	−	1.55233i	−0.767115	−	0.641509i	$-0.778309\pi$
$487$	−7.81891	−	34.2569i	−0.354309	−	1.55233i	0.412806	−	0.910819i	$-0.364549\pi$
$488$		0			0
$489$	−59.7425	−	28.7705i	−2.70165	−	1.30105i
$490$		0			0
$491$	−12.4972	−	2.85240i	−0.563990	−	0.128727i	−0.0689858	−	0.997618i	$-0.521976\pi$
$491$	−12.4972	−	2.85240i	−0.563990	−	0.128727i	−0.495004	+	0.868891i	$0.664833\pi$
$492$		0			0
$493$	0.376685	−	9.25674i	0.0169650	−	0.416903i
$494$		0			0
$495$	22.1043	+	5.04516i	0.993514	+	0.226763i
$496$		0			0
$497$	−1.25282	−	0.603326i	−0.0561966	−	0.0270628i
$498$		0			0
$499$	4.08484	+	17.8969i	0.182863	+	0.801173i	0.980259	+	0.197718i	$0.0633529\pi$
$499$	4.08484	+	17.8969i	0.182863	+	0.801173i	−0.797396	+	0.603456i	$0.793790\pi$
$500$		0			0
$501$	−13.5918	−	10.8391i	−0.607238	−	0.484256i
$502$		0			0
$503$	3.07138	−	6.37779i	0.136946	−	0.284371i	−0.821206	−	0.570632i	$-0.806698\pi$
$503$	3.07138	−	6.37779i	0.136946	−	0.284371i	0.958152	+	0.286261i	$0.0924124\pi$
$504$		0			0
$505$		−	10.8313i		−	0.481988i
$506$		0			0
$507$	15.3758	−	3.50943i	0.682864	−	0.155859i
$508$		0			0
$509$	0.104264	+	0.130743i	0.00462142	+	0.00579507i	0.784137	−	0.620588i	$-0.213106\pi$
$509$	0.104264	+	0.130743i	0.00462142	+	0.00579507i	−0.779515	+	0.626383i	$0.784535\pi$
$510$		0			0
$511$	1.56951	−	1.25164i	0.0694311	−	0.0553695i
$512$		0			0
$513$	19.4321	−	24.3671i	0.857947	−	1.07583i
$514$		0			0
$515$	8.46232	−	4.07524i	0.372895	−	0.179577i
$516$		0			0
$517$	3.70122	−	16.2161i	0.162779	−	0.713183i
$518$		0			0
$519$	−6.17810	−	12.8290i	−0.271188	−	0.563129i
$520$		0			0
$521$	−8.16492			−0.357712			−0.178856	−	0.983875i	$-0.557240\pi$
$521$	−8.16492			−0.357712			−0.178856	+	0.983875i	$0.557240\pi$
$522$		0			0
$523$	22.6967			0.992459			0.496230	−	0.868191i	$-0.334717\pi$
$523$	22.6967			0.992459			0.496230	+	0.868191i	$0.334717\pi$
$524$		0			0
$525$	2.15226	+	4.46921i	0.0939323	+	0.195052i
$526$		0			0
$527$	3.48821	−	15.2828i	0.151949	−	0.665731i
$528$		0			0
$529$	−2.34108	+	1.12740i	−0.101786	+	0.0490175i
$530$		0			0
$531$	−50.0299	+	62.7355i	−2.17111	+	2.72249i
$532$		0			0
$533$	−22.7668	+	18.1559i	−0.986137	+	0.786418i
$534$		0			0
$535$	−4.18486	−	5.24765i	−0.180927	−	0.226876i
$536$		0			0
$537$	54.9217	−	12.5355i	2.37005	−	0.540948i
$538$		0			0
$539$		−	32.7821i		−	1.41202i
$540$		0			0
$541$	−19.0092	+	39.4729i	−0.817268	+	1.69707i	−0.105764	+	0.994391i	$0.533729\pi$
$541$	−19.0092	+	39.4729i	−0.817268	+	1.69707i	−0.711503	+	0.702683i	$0.751985\pi$
$542$		0			0
$543$	32.4052	+	25.8423i	1.39064	+	1.10900i
$544$		0			0
$545$	−0.637870	−	2.79469i	−0.0273234	−	0.119711i
$546$		0			0
$547$	−14.3354	−	6.90356i	−0.612937	−	0.295175i	0.101542	−	0.994831i	$-0.467622\pi$
$547$	−14.3354	−	6.90356i	−0.612937	−	0.295175i	−0.714480	+	0.699656i	$0.753337\pi$
$548$		0			0
$549$	116.192	+	26.5201i	4.95895	+	1.13185i
$550$		0			0
$551$	−5.03606	+	9.45372i	−0.214543	+	0.402742i
$552$		0			0
$553$	1.37533	+	0.313910i	0.0584849	+	0.0133488i
$554$		0			0
$555$	9.94337	+	4.78847i	0.422072	+	0.203259i
$556$		0			0
$557$	5.54172	+	24.2799i	0.234810	+	1.02877i	0.945591	+	0.325358i	$0.105485\pi$
$557$	5.54172	+	24.2799i	0.234810	+	1.02877i	−0.710781	+	0.703414i	$0.751658\pi$
$558$		0			0
$559$	24.5520	+	19.5796i	1.03844	+	0.828127i
$560$		0			0
$561$	−11.6518	+	24.1952i	−0.491938	+	1.02152i
$562$		0			0
$563$		−	8.56468i		−	0.360958i	−0.983579	−	0.180479i	$-0.942235\pi$
$563$		−	8.56468i		−	0.360958i	0.983579	−	0.180479i	$-0.0577648\pi$
$564$		0			0
$565$	3.62600	−	0.827611i	0.152547	−	0.0348179i
$566$		0			0
$567$	5.72819	+	7.18292i	0.240561	+	0.301654i
$568$		0			0
$569$	−20.8516	+	16.6286i	−0.874146	+	0.697108i	−0.954035	−	0.299696i	$-0.903115\pi$
$569$	−20.8516	+	16.6286i	−0.874146	+	0.697108i	0.0798889	+	0.996804i	$0.474543\pi$
$570$		0			0
$571$	8.91957	−	11.1848i	0.373273	−	0.468069i	−0.559345	−	0.828935i	$-0.688947\pi$
$571$	8.91957	−	11.1848i	0.373273	−	0.468069i	0.932618	+	0.360866i	$0.117519\pi$
$572$		0			0
$573$	40.2496	−	19.3832i	1.68145	−	0.809744i
$574$		0			0
$575$	−5.20577	+	22.8080i	−0.217096	+	0.951158i
$576$		0			0
$577$	−16.0183	−	33.2624i	−0.666851	−	1.38473i	−0.909945	−	0.414728i	$-0.863877\pi$
$577$	−16.0183	−	33.2624i	−0.666851	−	1.38473i	0.243094	−	0.970003i	$-0.421838\pi$
$578$		0			0
$579$	−40.8831			−1.69904
$580$		0			0
$581$	2.36063			0.0979355
$582$		0			0
$583$	1.35367	+	2.81092i	0.0560633	+	0.116417i
$584$		0			0
$585$	−4.47638	+	19.6123i	−0.185076	+	0.810870i
$586$		0			0
$587$	−22.2992	+	10.7388i	−0.920388	+	0.443236i	−0.833210	−	0.552957i	$-0.813499\pi$
$587$	−22.2992	+	10.7388i	−0.920388	+	0.443236i	−0.0871786	+	0.996193i	$0.527785\pi$
$588$		0			0
$589$	−11.3003	+	14.1702i	−0.465622	+	0.583871i
$590$		0			0
$591$	−3.81214	+	3.04008i	−0.156810	+	0.125052i
$592$		0			0
$593$	15.5202	+	19.4617i	0.637338	+	0.799197i	0.990667	−	0.136302i	$-0.0435218\pi$
$593$	15.5202	+	19.4617i	0.637338	+	0.799197i	−0.353329	+	0.935499i	$0.614950\pi$
$594$		0			0
$595$	0.336185	−	0.0767321i	0.0137822	−	0.00314571i
$596$		0			0
$597$		−	32.5585i		−	1.33253i
$598$		0			0
$599$	6.73699	−	13.9895i	0.275266	−	0.571596i	−0.716805	−	0.697273i	$-0.754396\pi$
$599$	6.73699	−	13.9895i	0.275266	−	0.571596i	0.992071	+	0.125678i	$0.0401106\pi$
$600$		0			0
$601$	5.66301	+	4.51610i	0.230999	+	0.184216i	0.732148	−	0.681145i	$-0.238518\pi$
$601$	5.66301	+	4.51610i	0.230999	+	0.184216i	−0.501149	+	0.865361i	$0.667089\pi$
$602$		0			0
$603$	−1.57373	−	6.89496i	−0.0640873	−	0.280785i
$604$		0			0
$605$	6.41888	+	3.09117i	0.260965	+	0.125674i
$606$		0			0
$607$	2.32851	+	0.531467i	0.0945113	+	0.0215716i	0.269515	−	0.962996i	$-0.413137\pi$
$607$	2.32851	+	0.531467i	0.0945113	+	0.0215716i	−0.175004	+	0.984568i	$0.555994\pi$
$608$		0			0
$609$	−4.36656	−	3.78266i	−0.176942	−	0.153281i
$610$		0			0
$611$	14.3879	+	3.28395i	0.582074	+	0.132855i
$612$		0			0
$613$	−18.7899	−	9.04876i	−0.758919	−	0.365476i	0.0140655	−	0.999901i	$-0.495523\pi$
$613$	−18.7899	−	9.04876i	−0.758919	−	0.365476i	−0.772984	+	0.634425i	$0.781237\pi$
$614$		0			0
$615$	−3.09122	−	13.5435i	−0.124650	−	0.546127i
$616$		0			0
$617$	7.07139	+	5.63924i	0.284683	+	0.227027i	0.755411	−	0.655251i	$-0.227437\pi$
$617$	7.07139	+	5.63924i	0.284683	+	0.227027i	−0.470728	+	0.882278i	$0.656009\pi$
$618$		0			0
$619$	−13.9169	+	28.8986i	−0.559365	+	1.16153i	0.409124	+	0.912479i	$0.365834\pi$
$619$	−13.9169	+	28.8986i	−0.559365	+	1.16153i	−0.968489	+	0.249055i	$0.919880\pi$
$620$		0			0
$621$			79.2772i			3.18128i
$622$		0			0
$623$	1.34385	−	0.306724i	0.0538400	−	0.0122886i
$624$		0			0
$625$	12.1579	+	15.2456i	0.486317	+	0.609823i
$626$		0			0
$627$	24.2751	−	19.3588i	0.969456	−	0.773115i
$628$		0			0
$629$	−5.88073	+	7.37420i	−0.234480	+	0.294029i
$630$		0			0
$631$	32.7801	−	15.7861i	1.30496	−	0.628434i	0.353274	−	0.935520i	$-0.385068\pi$
$631$	32.7801	−	15.7861i	1.30496	−	0.628434i	0.951682	+	0.307086i	$0.0993540\pi$
$632$		0			0
$633$	−7.22026	+	31.6340i	−0.286980	+	1.25734i
$634$		0			0
$635$	1.03188	+	2.14273i	0.0409491	+	0.0850316i
$636$		0			0
$637$	29.0863			1.15244
$638$		0			0
$639$	−33.0733			−1.30836
$640$		0			0
$641$	−12.7518	−	26.4795i	−0.503667	−	1.04588i	−0.985510	−	0.169618i	$-0.945747\pi$
$641$	−12.7518	−	26.4795i	−0.503667	−	1.04588i	0.481843	−	0.876258i	$-0.339968\pi$
$642$		0			0
$643$	−10.4747	+	45.8928i	−0.413083	+	1.80983i	0.156238	+	0.987719i	$0.450063\pi$
$643$	−10.4747	+	45.8928i	−0.413083	+	1.80983i	−0.569321	+	0.822115i	$0.692794\pi$
$644$		0			0
$645$	−13.4975	+	6.50006i	−0.531464	+	0.255940i
$646$		0			0
$647$	−10.4549	+	13.1101i	−0.411026	+	0.515411i	−0.943652	−	0.330940i	$-0.892634\pi$
$647$	−10.4549	+	13.1101i	−0.411026	+	0.515411i	0.532625	+	0.846351i	$0.321206\pi$
$648$		0			0
$649$	−38.3796	+	30.6067i	−1.50653	+	1.20142i
$650$		0			0
$651$	−6.09476	−	7.64259i	−0.238872	−	0.299537i
$652$		0			0
$653$	−43.8382	+	10.0058i	−1.71552	+	0.391556i	−0.963526	−	0.267614i	$-0.913765\pi$
$653$	−43.8382	+	10.0058i	−1.71552	+	0.391556i	−0.751994	+	0.659170i	$0.770908\pi$
$654$		0			0
$655$			11.6274i			0.454321i
$656$		0			0
$657$	20.7169	−	43.0190i	0.808242	−	1.67833i
$658$		0			0
$659$	−11.1071	−	8.85762i	−0.432671	−	0.345044i	0.382810	−	0.923827i	$-0.374956\pi$
$659$	−11.1071	−	8.85762i	−0.432671	−	0.345044i	−0.815482	+	0.578783i	$0.803528\pi$
$660$		0			0
$661$	9.49854	+	41.6158i	0.369450	+	1.61867i	0.728290	+	0.685269i	$0.240315\pi$
$661$	9.49854	+	41.6158i	0.369450	+	1.61867i	−0.358840	+	0.933399i	$0.616828\pi$
$662$		0			0
$663$	−21.4675	−	10.3382i	−0.833727	−	0.401502i
$664$		0			0
$665$	−0.388695	−	0.0887170i	−0.0150729	−	0.00344030i
$666$		0			0
$667$	−4.97779	−	26.7876i	−0.192741	−	1.03722i
$668$		0			0
$669$	−54.3343	−	12.4014i	−2.10068	−	0.479468i
$670$		0			0
$671$	65.6902	+	31.6347i	2.53594	+	1.22125i
$672$		0			0
$673$	2.34591	+	10.2781i	0.0904282	+	0.396192i	0.999804	−	0.0197831i	$-0.00629758\pi$
$673$	2.34591	+	10.2781i	0.0904282	+	0.396192i	−0.909376	+	0.415975i	$0.863440\pi$
$674$		0			0
$675$	56.6451	+	45.1730i	2.18027	+	1.73871i
$676$		0			0
$677$	−13.7605	+	28.5740i	−0.528860	+	1.09819i	0.449881	+	0.893089i	$0.351467\pi$
$677$	−13.7605	+	28.5740i	−0.528860	+	1.09819i	−0.978741	+	0.205101i	$0.934248\pi$
$678$		0			0
$679$		−	0.0932482i		−	0.00357854i
$680$		0			0
$681$	10.5952	−	2.41828i	0.406008	−	0.0926686i
$682$		0			0
$683$	−15.4538	−	19.3784i	−0.591323	−	0.741495i	0.392675	−	0.919677i	$-0.371550\pi$
$683$	−15.4538	−	19.3784i	−0.591323	−	0.741495i	−0.983998	+	0.178182i	$0.942978\pi$
$684$		0			0
$685$	−6.98689	+	5.57186i	−0.266955	+	0.212890i
$686$		0			0
$687$	−10.5624	+	13.2448i	−0.402981	+	0.505323i
$688$		0			0
$689$	−2.49403	+	1.20106i	−0.0950149	+	0.0457568i
$690$		0			0
$691$	0.116466	−	0.510271i	0.00443058	−	0.0194116i	−0.972664	−	0.232216i	$-0.925402\pi$
$691$	0.116466	−	0.510271i	0.00443058	−	0.0194116i	0.977095	+	0.212804i	$0.0682596\pi$
$692$		0			0
$693$	5.24265	+	10.8865i	0.199152	+	0.413543i
$694$		0			0
$695$	−4.64459			−0.176179
$696$		0			0
$697$	11.8723			0.449697
$698$		0			0
$699$	−15.1689	−	31.4986i	−0.573742	−	1.19139i
$700$		0			0
$701$	6.44928	−	28.2561i	0.243586	−	1.06722i	−0.694139	−	0.719841i	$-0.744215\pi$
$701$	6.44928	−	28.2561i	0.243586	−	1.06722i	0.937725	−	0.347379i	$-0.112928\pi$
$702$		0			0
$703$	9.82520	−	4.73157i	0.370565	−	0.178454i
$704$		0			0
$705$	−4.38961	+	5.50440i	−0.165322	+	0.207308i
$706$		0			0
$707$	4.51304	−	3.59903i	0.169730	−	0.135355i
$708$		0			0
$709$	−30.0136	−	37.6359i	−1.12718	−	1.41344i	−0.897963	−	0.440070i	$-0.854954\pi$
$709$	−30.0136	−	37.6359i	−1.12718	−	1.41344i	−0.229221	−	0.973374i	$-0.573618\pi$
$710$		0			0
$711$	32.7119	−	7.46628i	1.22679	−	0.280007i
$712$		0			0
$713$		−	46.1020i		−	1.72653i
$714$		0			0
$715$	−5.33970	+	11.0880i	−0.199694	+	0.414668i
$716$		0			0
$717$	27.3287	+	21.7939i	1.02061	+	0.813908i
$718$		0			0
$719$	−4.06492	−	17.8096i	−0.151596	−	0.664185i	−0.992422	−	0.122879i	$-0.960787\pi$
$719$	−4.06492	−	17.8096i	−0.151596	−	0.664185i	0.840826	−	0.541306i	$-0.182070\pi$
$720$		0			0
$721$	4.50986	+	2.17183i	0.167956	+	0.0808833i
$722$		0			0
$723$	−9.39134	−	2.14351i	−0.349268	−	0.0797180i
$724$		0			0
$725$	−21.9767	−	11.7071i	−0.816193	−	0.434792i
$726$		0			0
$727$	−14.7545	−	3.36761i	−0.547213	−	0.124898i	−0.0600281	−	0.998197i	$-0.519119\pi$
$727$	−14.7545	−	3.36761i	−0.547213	−	0.124898i	−0.487185	+	0.873299i	$0.661976\pi$
$728$		0			0
$729$	57.8648	+	27.8662i	2.14314	+	1.03208i
$730$		0			0
$731$	−2.84900	−	12.4823i	−0.105374	−	0.461675i
$732$		0			0
$733$	36.1552	+	28.8328i	1.33542	+	1.06496i	0.992061	+	0.125761i	$0.0401372\pi$
$733$	36.1552	+	28.8328i	1.33542	+	1.06496i	0.343362	+	0.939203i	$0.388434\pi$
$734$		0			0
$735$	−6.02051	+	12.5017i	−0.222070	+	0.461133i
$736$		0			0
$737$		−	4.32660i		−	0.159372i
$738$		0			0
$739$	22.4926	−	5.13380i	0.827405	−	0.188850i	0.212209	−	0.977224i	$-0.431934\pi$
$739$	22.4926	−	5.13380i	0.827405	−	0.188850i	0.615196	+	0.788374i	$0.289077\pi$
$740$		0			0
$741$	17.1763	+	21.5384i	0.630988	+	0.791234i
$742$		0			0
$743$	−14.1975	+	11.3221i	−0.520855	+	0.415368i	−0.848311	−	0.529499i	$-0.822380\pi$
$743$	−14.1975	+	11.3221i	−0.520855	+	0.415368i	0.327456	+	0.944866i	$0.393809\pi$
$744$		0			0
$745$	3.87784	−	4.86266i	0.142073	−	0.178154i
$746$		0			0
$747$	50.5868	−	24.3613i	1.85087	−	0.891334i
$748$		0			0
$749$	0.795969	−	3.48737i	0.0290841	−	0.127426i
$750$		0			0
$751$	−2.05070	−	4.25832i	−0.0748311	−	0.155388i	0.860197	−	0.509962i	$-0.170340\pi$
$751$	−2.05070	−	4.25832i	−0.0748311	−	0.155388i	−0.935028	+	0.354573i	$0.884626\pi$
$752$		0			0
$753$	−59.4596			−2.16683
$754$		0			0
$755$	5.99983			0.218356
$756$		0			0
$757$	−3.41186	−	7.08479i	−0.124006	−	0.257501i	0.829719	−	0.558181i	$-0.188501\pi$
$757$	−3.41186	−	7.08479i	−0.124006	−	0.257501i	−0.953725	+	0.300680i	$0.902786\pi$
$758$		0			0
$759$	−17.5743	+	76.9980i	−0.637906	+	2.79485i
$760$		0			0
$761$	−6.24291	+	3.00643i	−0.226305	+	0.108983i	−0.543601	−	0.839344i	$-0.682940\pi$
$761$	−6.24291	+	3.00643i	−0.226305	+	0.108983i	0.317296	+	0.948327i	$0.397225\pi$
$762$		0			0
$763$	0.952499	−	1.19440i	0.0344828	−	0.0432400i
$764$		0			0
$765$	6.41237	−	5.11369i	0.231840	−	0.184886i
$766$		0			0
$767$	−27.1562	−	34.0528i	−0.980554	−	1.22958i
$768$		0			0
$769$	−49.9097	+	11.3916i	−1.79979	+	0.410790i	−0.985501	−	0.169671i	$-0.945730\pi$
$769$	−49.9097	+	11.3916i	−1.79979	+	0.410790i	−0.814288	+	0.580461i	$0.802873\pi$
$770$		0			0
$771$		−	62.0283i		−	2.23390i
$772$		0			0
$773$	−5.94886	+	12.3529i	−0.213966	+	0.444304i	−0.980134	−	0.198335i	$-0.936446\pi$
$773$	−5.94886	+	12.3529i	−0.213966	+	0.444304i	0.766169	+	0.642640i	$0.222161\pi$
$774$		0			0
$775$	−32.9408	−	26.2694i	−1.18327	−	0.943625i
$776$		0			0
$777$	1.30878	+	5.73416i	0.0469524	+	0.205712i
$778$		0			0
$779$	−12.3673	−	5.95580i	−0.443106	−	0.213389i
$780$		0			0
$781$	−19.7259	−	4.50231i	−0.705849	−	0.161105i
$782$		0			0
$783$	−81.4332	−	22.1057i	−2.91018	−	0.789992i
$784$		0			0
$785$	−6.47367	−	1.47757i	−0.231055	−	0.0527368i
$786$		0			0
$787$	9.61605	+	4.63085i	0.342775	+	0.165072i	0.597349	−	0.801982i	$-0.296221\pi$
$787$	9.61605	+	4.63085i	0.342775	+	0.165072i	−0.254574	+	0.967053i	$0.581935\pi$
$788$		0			0
$789$	−9.93972	−	43.5488i	−0.353863	−	1.55038i
$790$		0			0
$791$	1.54968	+	1.23583i	0.0551003	+	0.0439410i
$792$		0			0
$793$	−28.0683	+	58.2845i	−0.996736	+	2.06974i
$794$		0			0
$795$		−	1.32057i		−	0.0468359i
$796$		0			0
$797$	22.7143	−	5.18439i	0.804581	−	0.183640i	0.199597	−	0.979878i	$-0.436037\pi$
$797$	22.7143	−	5.18439i	0.804581	−	0.183640i	0.604984	+	0.796238i	$0.293180\pi$
$798$		0			0
$799$	−3.75149	−	4.70422i	−0.132718	−	0.166423i
$800$		0			0
$801$	25.6324	−	20.4412i	0.905676	−	0.722253i
$802$		0			0
$803$	18.2124	−	22.8376i	0.642702	−	0.805923i
$804$		0			0
$805$	0.913701	−	0.440015i	0.0322037	−	0.0155085i
$806$		0			0
$807$	−1.81559	+	7.95461i	−0.0639118	+	0.280016i
$808$		0			0
$809$	−16.7192	−	34.7177i	−0.587815	−	1.22061i	−0.956684	−	0.291129i	$-0.905969\pi$
$809$	−16.7192	−	34.7177i	−0.587815	−	1.22061i	0.368869	−	0.929482i	$-0.379745\pi$
$810$		0			0
$811$	−12.4473			−0.437084			−0.218542	−	0.975828i	$-0.570130\pi$
$811$	−12.4473			−0.437084			−0.218542	+	0.975828i	$0.570130\pi$
$812$		0			0
$813$	33.4523			1.17322
$814$		0			0
$815$	5.37553	+	11.1624i	0.188297	+	0.391002i
$816$		0			0
$817$	−3.29400	+	14.4319i	−0.115242	+	0.504910i
$818$		0			0
$819$	−9.65917	+	4.65161i	−0.337519	+	0.162540i
$820$		0			0
$821$	6.52179	−	8.17806i	0.227612	−	0.285416i	−0.654891	−	0.755723i	$-0.727285\pi$
$821$	6.52179	−	8.17806i	0.227612	−	0.285416i	0.882503	+	0.470307i	$0.155857\pi$
$822$		0			0
$823$	−32.7667	+	26.1306i	−1.14217	+	0.910854i	−0.996911	−	0.0785392i	$-0.974974\pi$
$823$	−32.7667	+	26.1306i	−1.14217	+	0.910854i	−0.145264	+	0.989393i	$0.546403\pi$
$824$		0			0
$825$	45.0026	+	56.4314i	1.56679	+	1.96469i
$826$		0			0
$827$	−18.3395	+	4.18586i	−0.637725	+	0.145557i	−0.529146	−	0.848531i	$-0.677487\pi$
$827$	−18.3395	+	4.18586i	−0.637725	+	0.145557i	−0.108580	+	0.994088i	$0.534630\pi$
$828$		0			0
$829$		−	33.0460i		−	1.14773i	−0.818948	−	0.573867i	$-0.805443\pi$
$829$		−	33.0460i		−	1.14773i	0.818948	−	0.573867i	$-0.194557\pi$
$830$		0			0
$831$	−33.0079	+	68.5417i	−1.14503	+	2.37768i
$832$		0			0
$833$	−9.27152	−	7.39379i	−0.321239	−	0.256180i
$834$		0			0
$835$	0.722785	+	3.16673i	0.0250130	+	0.109589i
$836$		0			0
$837$	−128.637	−	61.9482i	−4.44633	−	2.14124i
$838$		0			0
$839$	−8.34515	−	1.90473i	−0.288106	−	0.0657584i	0.0760252	−	0.997106i	$-0.475777\pi$
$839$	−8.34515	−	1.90473i	−0.288106	−	0.0657584i	−0.364132	+	0.931347i	$0.618634\pi$
$840$		0			0
$841$	28.9041	+	2.35630i	0.996694	+	0.0812516i
$842$		0			0
$843$	−3.97799	−	0.907950i	−0.137009	−	0.0312715i
$844$		0			0
$845$	−2.65491	−	1.27854i	−0.0913317	−	0.0439830i
$846$		0			0
$847$	0.844878	+	3.70165i	0.0290304	+	0.127190i
$848$		0			0
$849$	42.7820	+	34.1175i	1.46827	+	1.17091i
$850$		0			0
$851$	−12.0355	+	24.9919i	−0.412571	+	0.856712i
$852$		0			0
$853$			22.1666i			0.758969i	0.925198	+	0.379484i	$0.123899\pi$
$853$			22.1666i			0.758969i	−0.925198	+	0.379484i	$0.876101\pi$
$854$		0			0
$855$	−9.24502	+	2.11012i	−0.316173	+	0.0721644i
$856$		0			0
$857$	2.03964	+	2.55763i	0.0696728	+	0.0873670i	0.815447	−	0.578832i	$-0.196491\pi$
$857$	2.03964	+	2.55763i	0.0696728	+	0.0873670i	−0.745774	+	0.666199i	$0.767920\pi$
$858$		0			0
$859$	−28.5801	+	22.7918i	−0.975139	+	0.777647i	−0.974966	−	0.222353i	$-0.928626\pi$
$859$	−28.5801	+	22.7918i	−0.975139	+	0.777647i	−0.000172584		1.00000i	$0.500055\pi$
$860$		0			0
$861$	4.61595	−	5.78822i	0.157311	−	0.197262i
$862$		0			0
$863$	−4.39516	+	2.11660i	−0.149613	+	0.0720498i	−0.507192	−	0.861833i	$-0.669317\pi$
$863$	−4.39516	+	2.11660i	−0.149613	+	0.0720498i	0.357579	+	0.933883i	$0.383602\pi$
$864$		0			0
$865$	−0.592006	+	2.59375i	−0.0201288	+	0.0881901i
$866$		0			0
$867$	−19.9956	−	41.5214i	−0.679088	−	1.41014i
$868$		0			0
$869$	20.5268			0.696323
$870$		0			0
$871$	3.83883			0.130074
$872$		0			0
$873$	−0.962305	−	1.99825i	−0.0325691	−	0.0676304i
$874$		0			0
$875$	0.429249	−	1.88066i	0.0145113	−	0.0635780i
$876$		0			0
$877$	41.5923	−	20.0298i	1.40447	−	0.676358i	0.430408	−	0.902634i	$-0.358370\pi$
$877$	41.5923	−	20.0298i	1.40447	−	0.676358i	0.974063	+	0.226277i	$0.0726554\pi$
$878$		0			0
$879$	54.6980	−	68.5892i	1.84492	−	2.31346i
$880$		0			0
$881$	3.25429	−	2.59521i	0.109640	−	0.0874348i	−0.567135	−	0.823625i	$-0.691948\pi$
$881$	3.25429	−	2.59521i	0.109640	−	0.0874348i	0.676775	+	0.736190i	$0.263377\pi$
$882$		0			0
$883$	27.7771	+	34.8313i	0.934772	+	1.17217i	0.984848	+	0.173422i	$0.0554824\pi$
$883$	27.7771	+	34.8313i	0.934772	+	1.17217i	−0.0500753	+	0.998745i	$0.515946\pi$
$884$		0			0
$885$	20.2574	−	4.62361i	0.680944	−	0.155421i
$886$		0			0
$887$		−	14.9134i		−	0.500744i	−0.968150	−	0.250372i	$-0.919447\pi$
$887$		−	14.9134i		−	0.500744i	0.968150	−	0.250372i	$-0.0805529\pi$
$888$		0			0
$889$	−0.549926	+	1.14193i	−0.0184439	+	0.0382992i
$890$		0			0
$891$	104.517	+	83.3497i	3.50146	+	2.79232i
$892$		0			0
$893$	1.54802	+	6.78231i	0.0518024	+	0.226961i
$894$		0			0
$895$	−9.48321	−	4.56687i	−0.316989	−	0.152654i
$896$		0			0
$897$	−68.3175	−	15.5930i	−2.28105	−	0.520636i
$898$		0			0
$899$	47.3558	+	12.8551i	1.57940	+	0.428741i
$900$		0			0
$901$	1.10030	+	0.251137i	0.0366565	+	0.00836660i
$902$		0			0
$903$	−7.19329	−	3.46410i	−0.239378	−	0.115278i
$904$		0			0
$905$	−1.72324	−	7.55002i	−0.0572825	−	0.250971i
$906$		0			0
$907$	33.9941	+	27.1094i	1.12876	+	0.900153i	0.995853	−	0.0909764i	$-0.0289988\pi$
$907$	33.9941	+	27.1094i	1.12876	+	0.900153i	0.132903	+	0.991129i	$0.457570\pi$
$908$		0			0
$909$	59.5701	−	123.699i	1.97582	−	4.10282i
$910$		0			0
$911$			49.5298i			1.64100i	0.571650	+	0.820498i	$0.306304\pi$
$911$			49.5298i			1.64100i	−0.571650	+	0.820498i	$0.693696\pi$
$912$		0			0
$913$	33.4878	−	7.64338i	1.10829	−	0.252959i
$914$		0			0
$915$	−19.2417	−	24.1283i	−0.636111	−	0.797658i
$916$		0			0
$917$	−4.84474	+	3.86355i	−0.159987	+	0.127586i
$918$		0			0
$919$	8.10530	−	10.1637i	0.267369	−	0.335270i	−0.629964	−	0.776625i	$-0.716930\pi$
$919$	8.10530	−	10.1637i	0.267369	−	0.335270i	0.897333	+	0.441354i	$0.145502\pi$
$920$		0			0
$921$	42.7224	−	20.5740i	1.40775	−	0.677937i
$922$		0			0
$923$	3.99474	−	17.5021i	0.131488	−	0.576088i
$924$		0			0
$925$	10.9993	+	22.8402i	0.361654	+	0.750983i
$926$		0			0
$927$	119.056			3.91032
$928$		0			0
$929$	−50.4564			−1.65542			−0.827710	−	0.561156i	$-0.810357\pi$
$929$	−50.4564			−1.65542			−0.827710	+	0.561156i	$0.810357\pi$
$930$		0			0
$931$	5.94896	+	12.3531i	0.194969	+	0.404858i
$932$		0			0
$933$	−16.3858	+	71.7911i	−0.536449	+	2.35033i
$934$		0			0
$935$	4.52067	−	2.17704i	0.147842	−	0.0711967i
$936$		0			0
$937$	11.5802	−	14.5211i	0.378309	−	0.474384i	−0.555829	−	0.831297i	$-0.687599\pi$
$937$	11.5802	−	14.5211i	0.378309	−	0.474384i	0.934138	+	0.356912i	$0.116171\pi$
$938$		0			0
$939$	38.9923	−	31.0953i	1.27247	−	1.01476i
$940$		0			0
$941$	−29.1245	−	36.5209i	−0.949430	−	1.19055i	−0.981578	−	0.191064i	$-0.938806\pi$
$941$	−29.1245	−	36.5209i	−0.949430	−	1.19055i	0.0321475	−	0.999483i	$-0.489765\pi$
$942$		0			0
$943$	34.0406	−	7.76955i	1.10851	−	0.253011i
$944$		0			0
$945$		−	3.14072i		−	0.102168i
$946$		0			0
$947$	5.27851	−	10.9609i	0.171529	−	0.356183i	−0.797428	−	0.603414i	$-0.793807\pi$
$947$	5.27851	−	10.9609i	0.171529	−	0.356183i	0.968956	+	0.247232i	$0.0795209\pi$
$948$		0			0
$949$	20.2630	+	16.1592i	0.657765	+	0.524550i
$950$		0			0
$951$	5.29258	+	23.1883i	0.171624	+	0.751932i
$952$		0			0
$953$	8.24999	+	3.97299i	0.267243	+	0.128698i	0.562707	−	0.826656i	$-0.309760\pi$
$953$	8.24999	+	3.97299i	0.267243	+	0.128698i	−0.295464	+	0.955354i	$0.595474\pi$
$954$		0			0
$955$	−8.13763	−	1.85736i	−0.263328	−	0.0601028i
$956$		0			0
$957$	−74.1916	−	39.5224i	−2.39827	−	1.27758i
$958$		0			0
$959$	−4.64320	−	1.05978i	−0.149937	−	0.0342221i
$960$		0			0
$961$	46.8760	+	22.5743i	1.51213	+	0.728202i
$962$		0			0
$963$	−18.9320	−	82.9463i	−0.610074	−	2.67291i
$964$		0			0
$965$	5.97216	+	4.76264i	0.192251	+	0.153315i
$966$		0			0
$967$	−10.5663	+	21.9412i	−0.339790	+	0.705581i	−0.998921	−	0.0464476i	$-0.985210\pi$
$967$	−10.5663	+	21.9412i	−0.339790	+	0.705581i	0.659131	+	0.752028i	$0.270924\pi$
$968$		0			0
$969$		−	11.2318i		−	0.360818i
$970$		0			0
$971$	−0.649386	+	0.148218i	−0.0208398	+	0.00475655i	−0.232928	−	0.972494i	$-0.574831\pi$
$971$	−0.649386	+	0.148218i	−0.0208398	+	0.00475655i	0.212088	+	0.977251i	$0.431974\pi$
$972$		0			0
$973$	−1.54330	−	1.93523i	−0.0494759	−	0.0620408i
$974$		0			0
$975$	−50.0695	+	39.9291i	−1.60351	+	1.27875i
$976$		0			0
$977$	−13.4359	+	16.8480i	−0.429851	+	0.539016i	−0.948837	−	0.315767i	$-0.897738\pi$
$977$	−13.4359	+	16.8480i	−0.429851	+	0.539016i	0.518986	+	0.854783i	$0.326310\pi$
$978$		0			0
$979$	18.0706	−	8.70235i	0.577540	−	0.278128i
$980$		0			0
$981$	8.08547	−	35.4248i	0.258149	−	1.13103i
$982$		0			0
$983$	−5.28115	−	10.9664i	−0.168443	−	0.349775i	0.799611	−	0.600518i	$-0.205039\pi$
$983$	−5.28115	−	10.9664i	−0.168443	−	0.349775i	−0.968053	+	0.250744i	$0.919325\pi$
$984$		0			0
$985$	0.911023			0.0290276
$986$		0			0
$987$	−3.75207			−0.119430
$988$		0			0
$989$	−16.3374	−	33.9250i	−0.519500	−	1.07875i
$990$		0			0
$991$	−6.40285	+	28.0527i	−0.203393	+	0.891125i	0.765459	+	0.643485i	$0.222512\pi$
$991$	−6.40285	+	28.0527i	−0.203393	+	0.891125i	−0.968852	+	0.247640i	$0.920345\pi$
$992$		0			0
$993$	14.3455	−	6.90842i	0.455240	−	0.219232i
$994$		0			0
$995$	−3.79287	+	4.75611i	−0.120242	+	0.150779i
$996$		0			0
$997$	46.0909	−	36.7562i	1.45971	−	1.16408i	0.506321	−	0.862345i	$-0.331005\pi$
$997$	46.0909	−	36.7562i	1.45971	−	1.16408i	0.953391	−	0.301736i	$-0.0975663\pi$
$998$		0			0
$999$	53.5617	+	67.1643i	1.69462	+	2.12498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.y.e.33.1		48
4.3	odd	2		232.2.q.a.33.8	✓	48
29.22	even	14	inner	464.2.y.e.225.1		48
116.15	even	28		6728.2.a.bf.1.23		24
116.43	even	28		6728.2.a.be.1.2		24
116.51	odd	14		232.2.q.a.225.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.33.8	✓	48	4.3	odd	2
232.2.q.a.225.8	yes	48	116.51	odd	14
464.2.y.e.33.1		48	1.1	even	1	trivial
464.2.y.e.225.1		48	29.22	even	14	inner
6728.2.a.be.1.2		24	116.43	even	28
6728.2.a.bf.1.23		24	116.15	even	28

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.y (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42415 - 2.95728i) q^{3} +(-0.136467 + 0.597901i) q^{5} +(-0.294470 + 0.141809i) q^{7} +(-4.84685 + 6.07775i) q^{9} +O(q^{10})\)	\(q+(-1.42415 - 2.95728i) q^{3} +(-0.136467 + 0.597901i) q^{5} +(-0.294470 + 0.141809i) q^{7} +(-4.84685 + 6.07775i) q^{9} +(-3.71818 + 2.96515i) q^{11} +(-2.63087 - 3.29900i) q^{13} +(1.96251 - 0.447931i) q^{15} +1.72036i q^{17} +(0.863022 - 1.79208i) q^{19} +(0.838739 + 0.668872i) q^{21} +(1.12584 + 4.93263i) q^{23} +(4.16598 + 2.00623i) q^{25} +(15.2762 + 3.48668i) q^{27} +(-5.38071 - 0.218958i) q^{29} +(-8.88354 - 2.02761i) q^{31} +(14.0640 + 6.77289i) q^{33} +(-0.0446024 - 0.195416i) q^{35} +(4.28644 + 3.41832i) q^{37} +(-6.00933 + 12.4785i) q^{39} -6.90110i q^{41} +(-7.25565 + 1.65605i) q^{43} +(-2.97246 - 3.72735i) q^{45} +(-2.73445 + 2.18065i) q^{47} +(-4.29783 + 5.38930i) q^{49} +(5.08758 - 2.45005i) q^{51} +(0.145980 - 0.639579i) q^{53} +(-1.26546 - 2.62775i) q^{55} -6.52877 q^{57} +10.3221 q^{59} +(-6.65192 - 13.8129i) q^{61} +(0.565368 - 2.47704i) q^{63} +(2.33151 - 1.12279i) q^{65} +(-0.567230 + 0.711284i) q^{67} +(12.9838 - 10.3543i) q^{69} +(2.65263 + 3.32630i) q^{71} +(-5.98816 + 1.36676i) q^{73} -15.1772i q^{75} +(0.674406 - 1.40042i) q^{77} +(-3.37455 - 2.69112i) q^{79} +(-6.25501 - 27.4050i) q^{81} +(-6.50740 - 3.13380i) q^{83} +(-1.02860 - 0.234772i) q^{85} +(7.01544 + 16.2241i) q^{87} +(-4.11167 - 0.938463i) q^{89} +(1.24254 + 0.598375i) q^{91} +(6.65530 + 29.1588i) q^{93} +(0.953715 + 0.760562i) q^{95} +(-0.123789 + 0.257051i) q^{97} -36.9698i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9	\( 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9} + 10 q^{13} - 14 q^{15} + 14 q^{21} - 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} - 8 q^{35} - 38 q^{45} + 14 q^{47} - 18 q^{49} + 56 q^{51} - 48 q^{53} + 28 q^{55} - 12 q^{57} + 128 q^{59} - 28 q^{61} - 42 q^{63} - 28 q^{65} + 4 q^{67} + 28 q^{69} + 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} - 80 q^{83} + 112 q^{87} + 42 q^{89} + 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) \) 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9 + 10 * q^13 - 14 * q^15 + 14 * q^21 - 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 - 8 * q^35 - 38 * q^45 + 14 * q^47 - 18 * q^49 + 56 * q^51 - 48 * q^53 + 28 * q^55 - 12 * q^57 + 128 * q^59 - 28 * q^61 - 42 * q^63 - 28 * q^65 + 4 * q^67 + 28 * q^69 + 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 - 80 * q^83 + 112 * q^87 + 42 * q^89 + 28 * q^91 + 6 * q^93 + 70 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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