LMFDB - Embedded newform 232.2.q.a.33.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(9,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("232.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.q (of order $14$, degree $6$, 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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.8
Character	$\chi$	$=$	232.33
Dual form			232.2.q.a.225.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42415 + 2.95728i) q^{3} +(-0.136467 + 0.597901i) q^{5} +(0.294470 - 0.141809i) q^{7} +(-4.84685 + 6.07775i) q^{9} +O(q^{10})$	\(q+(1.42415 + 2.95728i) q^{3} +(-0.136467 + 0.597901i) q^{5} +(0.294470 - 0.141809i) q^{7} +(-4.84685 + 6.07775i) q^{9} +(3.71818 - 2.96515i) q^{11} +(-2.63087 - 3.29900i) q^{13} +(-1.96251 + 0.447931i) q^{15} +1.72036i q^{17} +(-0.863022 + 1.79208i) q^{19} +(0.838739 + 0.668872i) q^{21} +(-1.12584 - 4.93263i) q^{23} +(4.16598 + 2.00623i) q^{25} +(-15.2762 - 3.48668i) q^{27} +(-5.38071 - 0.218958i) q^{29} +(8.88354 + 2.02761i) q^{31} +(14.0640 + 6.77289i) q^{33} +(0.0446024 + 0.195416i) q^{35} +(4.28644 + 3.41832i) q^{37} +(6.00933 - 12.4785i) q^{39} -6.90110i q^{41} +(7.25565 - 1.65605i) q^{43} +(-2.97246 - 3.72735i) q^{45} +(2.73445 - 2.18065i) q^{47} +(-4.29783 + 5.38930i) q^{49} +(-5.08758 + 2.45005i) q^{51} +(0.145980 - 0.639579i) q^{53} +(1.26546 + 2.62775i) q^{55} -6.52877 q^{57} -10.3221 q^{59} +(-6.65192 - 13.8129i) q^{61} +(-0.565368 + 2.47704i) q^{63} +(2.33151 - 1.12279i) q^{65} +(0.567230 - 0.711284i) q^{67} +(12.9838 - 10.3543i) q^{69} +(-2.65263 - 3.32630i) q^{71} +(-5.98816 + 1.36676i) q^{73} +15.1772i q^{75} +(0.674406 - 1.40042i) q^{77} +(3.37455 + 2.69112i) q^{79} +(-6.25501 - 27.4050i) q^{81} +(6.50740 + 3.13380i) q^{83} +(-1.02860 - 0.234772i) q^{85} +(-7.01544 - 16.2241i) q^{87} +(-4.11167 - 0.938463i) q^{89} +(-1.24254 - 0.598375i) q^{91} +(6.65530 + 29.1588i) q^{93} +(-0.953715 - 0.760562i) q^{95} +(-0.123789 + 0.257051i) q^{97} +36.9698i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$1$	$1$

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
$3$	1.42415	+	2.95728i	0.822235	+	1.70739i	0.699130	+	0.714995i	$0.253571\pi$
$3$	1.42415	+	2.95728i	0.822235	+	1.70739i	0.123105	+	0.992394i	$0.460715\pi$
$4$		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	−0.377406	−	0.926048i	$-0.623184\pi$
$7$	0.294470	−	0.141809i	0.111299	−	0.0535988i	0.488705	+	0.872449i	$0.337470\pi$
$8$		0			0
$9$	−4.84685	+	6.07775i	−1.61562	+	2.02592i
$10$		0			0
$11$	3.71818	−	2.96515i	1.12107	−	0.894026i	0.125889	−	0.992044i	$-0.459822\pi$
$11$	3.71818	−	2.96515i	1.12107	−	0.894026i	0.995185	+	0.0980183i	$0.0312504\pi$
$12$		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	−0.976200	−	0.216873i	$-0.930414\pi$
$19$	−0.863022	+	1.79208i	−0.197991	+	0.411132i	0.778209	+	0.628005i	$0.216128\pi$
$20$		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	$-0.894563\pi$
$23$	−1.12584	−	4.93263i	−0.234754	−	1.02853i	0.710885	−	0.703308i	$-0.248295\pi$
$24$		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	0.925674	−	0.378322i	$-0.123499\pi$
$31$	8.88354	+	2.02761i	1.59553	+	0.364169i	0.669856	+	0.742491i	$0.266356\pi$
$32$		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	0.370015	−	0.929026i	$-0.379353\pi$
$43$	7.25565	−	1.65605i	1.10648	−	0.252546i	0.736461	+	0.676480i	$0.236495\pi$
$44$		0			0
$45$	−2.97246	−	3.72735i	−0.443108	−	0.555640i
$46$		0			0
$47$	2.73445	−	2.18065i	0.398860	−	0.318080i	−0.403434	−	0.915009i	$-0.632184\pi$
$47$	2.73445	−	2.18065i	0.398860	−	0.318080i	0.802295	+	0.596928i	$0.203612\pi$
$48$		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	$-0.734528\pi$
$59$	−10.3221			−1.34383			−0.671915	+	0.740629i	$0.734528\pi$
$60$		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	−0.745974	−	0.665975i	$-0.768016\pi$
$67$	0.567230	−	0.711284i	0.0692982	−	0.0868971i	0.815272	+	0.579078i	$0.196587\pi$
$68$		0			0
$69$	12.9838	−	10.3543i	1.56307	−	1.24651i
$70$		0			0
$71$	−2.65263	−	3.32630i	−0.314810	−	0.394759i	0.599102	−	0.800673i	$-0.295525\pi$
$71$	−2.65263	−	3.32630i	−0.314810	−	0.394759i	−0.913911	+	0.405914i	$0.866953\pi$
$72$		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	0.794665	−	0.607048i	$-0.207646\pi$
$79$	3.37455	+	2.69112i	0.379667	+	0.302774i	−0.414998	+	0.909822i	$0.636218\pi$
$80$		0			0
$81$	−6.25501	−	27.4050i	−0.695001	−	3.04500i
$82$		0			0
$83$	6.50740	+	3.13380i	0.714280	+	0.343979i	0.755480	−	0.655172i	$-0.227404\pi$
$83$	6.50740	+	3.13380i	0.714280	+	0.343979i	−0.0412002	+	0.999151i	$0.513118\pi$
$84$		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	$0.0578473\pi$
$103$	9.54887	+	11.9739i	0.940878	+	1.17982i	−0.0426537	+	0.999090i	$0.513581\pi$
$104$		0			0
$105$	−0.514380	+	0.410204i	−0.0501984	+	0.0400318i
$106$		0			0
$107$	6.82377	−	8.55673i	0.659678	−	0.827210i	−0.333630	−	0.942704i	$-0.608274\pi$
$107$	6.82377	−	8.55673i	0.659678	−	0.827210i	0.993308	+	0.115494i	$0.0368450\pi$
$108$		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	−0.748710	−	0.662897i	$-0.769327\pi$
$127$	−3.03189	+	2.41785i	−0.269037	+	0.214550i	0.479673	+	0.877447i	$0.340755\pi$
$128$		0			0
$129$	15.2306	+	19.0985i	1.34098	+	1.68153i
$130$		0			0
$131$	−18.4841	+	4.21888i	−1.61497	+	0.368606i	−0.932175	−	0.362008i	$-0.882091\pi$
$131$	−18.4841	+	4.21888i	−1.61497	+	0.368606i	−0.682791	+	0.730613i	$0.739234\pi$
$132$		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	$-0.967348\pi$
$139$	−1.68524	−	7.38350i	−0.142940	−	0.626260i	0.851804	−	0.523861i	$-0.175509\pi$
$140$		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	$0.0588926\pi$
$151$	2.17697	+	9.53793i	0.177159	+	0.776186i	−0.805774	+	0.592223i	$0.798250\pi$
$152$		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	$0.576239\pi$
$163$	−15.7944	+	12.5956i	−1.23711	+	0.986566i	−0.999886	+	0.0151123i	$0.995189\pi$
$164$		0			0
$165$	−5.96880	+	7.48463i	−0.464670	+	0.582678i
$166$		0			0
$167$	−4.77190	+	2.29802i	−0.369260	+	0.177826i	−0.609306	−	0.792935i	$-0.708552\pi$
$167$	−4.77190	+	2.29802i	−0.369260	+	0.177826i	0.240046	+	0.970762i	$0.422838\pi$
$168$		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	$-0.706923\pi$
$179$	3.81909	−	16.7325i	0.285452	−	1.25065i	0.890693	−	0.454604i	$-0.150219\pi$
$180$		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	$-0.836118\pi$
$191$		−	13.6103i		−	0.984808i	0.870367	−	0.492404i	$-0.163882\pi$
$192$		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	0.0894203	−	0.995994i	$-0.471499\pi$
$199$	−8.93699	−	4.30383i	−0.633526	−	0.305090i	−0.722947	+	0.690904i	$0.757213\pi$
$200$		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	0.852320	−	0.523020i	$-0.175195\pi$
$211$	7.72880	+	6.16351i	0.532072	+	0.424314i	−0.320248	+	0.947334i	$0.603766\pi$
$212$		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	−0.997654	−	0.0684550i	$-0.978193\pi$
$223$	−10.5864	+	13.2749i	−0.708917	+	0.888953i	0.288738	+	0.957408i	$0.406764\pi$
$224$		0			0
$225$	−32.3852	+	15.5959i	−2.15902	+	1.03973i
$226$		0			0
$227$	0.736755	−	3.22794i	0.0489002	−	0.214246i	−0.944575	−	0.328296i	$-0.893526\pi$
$227$	0.736755	−	3.22794i	0.0489002	−	0.214246i	0.993475	+	0.114051i	$0.0363827\pi$
$228$		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	−0.0970209	−	0.995282i	$-0.530931\pi$
$239$	9.59472	−	4.62057i	0.620631	−	0.298880i	0.717652	+	0.696402i	$0.245217\pi$
$240$		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	$0.336575\pi$
$251$	−7.85981	+	16.3211i	−0.496107	+	1.03018i	−0.987262	+	0.159104i	$0.949139\pi$
$252$		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	−0.207071	−	0.978326i	$-0.566393\pi$
$263$	−13.2676	−	3.02824i	−0.818116	−	0.186730i	−0.611044	+	0.791596i	$0.709250\pi$
$264$		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	−0.722409	−	0.691467i	$-0.756965\pi$
$271$	4.42198	−	9.18233i	0.268616	−	0.557787i	0.991025	+	0.133679i	$0.0426792\pi$
$272$		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	0.0695523	−	0.997578i	$-0.477843\pi$
$283$	15.0202	−	7.23333i	0.892856	−	0.429977i	0.823303	+	0.567602i	$0.192129\pi$
$284$		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	$-0.864742\pi$
$307$		−	14.4465i		−	0.824506i	0.911069	−	0.412253i	$-0.135258\pi$
$308$		0			0
$309$	−21.8112	+	45.2914i	−1.24079	+	2.57654i
$310$		0			0
$311$	17.5399	+	13.9876i	0.994599	+	0.793166i	0.978404	−	0.206703i	$-0.0662734\pi$
$311$	17.5399	+	13.9876i	0.994599	+	0.793166i	0.0161948	+	0.999869i	$0.494845\pi$
$312$		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	$-0.957438\pi$
$331$		−	4.85090i		−	0.266630i	0.991074	−	0.133315i	$-0.0425621\pi$
$332$		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	$-0.404785\pi$
$347$	10.9788			0.589370			0.294685	+	0.955594i	$0.404785\pi$
$348$		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	−0.986808	−	0.161895i	$-0.948239\pi$
$359$	−19.8673	+	15.8437i	−1.04856	+	0.836197i	−0.0617494	+	0.998092i	$0.519668\pi$
$360$		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	$0.307776\pi$
$367$	−8.23285	+	17.0957i	−0.429751	+	0.892388i	−0.997599	+	0.0692544i	$0.977938\pi$
$368$		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	0.344719	−	0.938706i	$-0.387974\pi$
$379$	4.82824	+	1.10202i	0.248010	+	0.0566067i	−0.0967085	+	0.995313i	$0.530831\pi$
$380$		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	$-0.869049\pi$
$383$	−5.17194	−	22.6597i	−0.264274	−	1.15786i	0.652290	−	0.757970i	$-0.273808\pi$
$384$		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	0.979519	−	0.201353i	$-0.0645339\pi$
$419$	11.5704	+	14.5088i	0.565250	+	0.708802i	−0.414268	+	0.910155i	$0.635962\pi$
$420$		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	0.622143	−	0.782904i	$-0.286262\pi$
$431$	8.26153	+	3.97854i	0.397944	+	0.191640i	−0.224199	+	0.974543i	$0.571977\pi$
$432$		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	0.808077	−	0.589077i	$-0.200509\pi$
$439$	17.8377	+	8.59017i	0.851345	+	0.409986i	0.0432686	+	0.999063i	$0.486223\pi$
$440$		0			0
$441$	−11.9240	−	52.2422i	−0.567807	−	2.48773i
$442$		0			0
$443$	5.05031	+	4.02749i	0.239947	+	0.191352i	0.736079	−	0.676896i	$-0.236675\pi$
$443$	5.05031	+	4.02749i	0.239947	+	0.191352i	−0.496132	+	0.868247i	$0.665247\pi$
$444$		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	$-0.374284\pi$
$463$	16.5581			0.769520			0.384760	+	0.923017i	$0.374284\pi$
$464$		0			0
$465$	−18.3423			−0.850603
$466$		0			0
$467$	−5.93783	−	12.3300i	−0.274770	−	0.570565i	0.717225	−	0.696841i	$-0.245412\pi$
$467$	−5.93783	−	12.3300i	−0.274770	−	0.570565i	−0.991995	+	0.126276i	$0.959698\pi$
$468$		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	0.553574	−	0.832800i	$-0.313264\pi$
$479$	30.9396	−	7.06176i	1.41367	−	0.322660i	0.860091	+	0.510140i	$0.170406\pi$
$480$		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	$0.221691\pi$
$487$	7.81891	+	34.2569i	0.354309	+	1.55233i	−0.412806	+	0.910819i	$0.635451\pi$
$488$		0			0
$489$	−59.7425	−	28.7705i	−2.70165	−	1.30105i
$490$		0			0
$491$	12.4972	+	2.85240i	0.563990	+	0.128727i	0.495004	−	0.868891i	$-0.335167\pi$
$491$	12.4972	+	2.85240i	0.563990	+	0.128727i	0.0689858	+	0.997618i	$0.478024\pi$
$492$		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	$-0.936647\pi$
$499$	−4.08484	−	17.8969i	−0.182863	−	0.801173i	0.797396	−	0.603456i	$-0.206210\pi$
$500$		0			0
$501$	−13.5918	−	10.8391i	−0.607238	−	0.484256i
$502$		0			0
$503$	−3.07138	+	6.37779i	−0.136946	+	0.284371i	−0.958152	−	0.286261i	$-0.907588\pi$
$503$	−3.07138	+	6.37779i	−0.136946	+	0.284371i	0.821206	+	0.570632i	$0.193302\pi$
$504$		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	$-0.665283\pi$
$523$	−22.6967			−0.992459			−0.496230	+	0.868191i	$0.665283\pi$
$524$		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	0.714480	−	0.699656i	$-0.246663\pi$
$547$	14.3354	+	6.90356i	0.612937	+	0.295175i	−0.101542	+	0.994831i	$0.532378\pi$
$548$		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	$0.0577648\pi$
$563$			8.56468i			0.360958i	−0.983579	+	0.180479i	$0.942235\pi$
$564$		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	−0.932618	−	0.360866i	$-0.882481\pi$
$571$	−8.91957	+	11.1848i	−0.373273	+	0.468069i	0.559345	+	0.828935i	$0.311053\pi$
$572$		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	0.0871786	−	0.996193i	$-0.472215\pi$
$587$	22.2992	−	10.7388i	0.920388	−	0.443236i	0.833210	+	0.552957i	$0.186501\pi$
$588$		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	−0.992071	−	0.125678i	$-0.959889\pi$
$599$	−6.73699	+	13.9895i	−0.275266	+	0.571596i	0.716805	+	0.697273i	$0.245604\pi$
$600$		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	0.175004	−	0.984568i	$-0.444006\pi$
$607$	−2.32851	−	0.531467i	−0.0945113	−	0.0215716i	−0.269515	+	0.962996i	$0.586863\pi$
$608$		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	$-0.634166\pi$
$619$	13.9169	−	28.8986i	0.559365	−	1.16153i	0.968489	−	0.249055i	$-0.0801201\pi$
$620$		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	−0.951682	−	0.307086i	$-0.900646\pi$
$631$	−32.7801	+	15.7861i	−1.30496	+	0.628434i	−0.353274	+	0.935520i	$0.614932\pi$
$632$		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	$-0.549937\pi$
$643$	10.4747	−	45.8928i	0.413083	−	1.80983i	0.569321	−	0.822115i	$-0.307206\pi$
$644$		0			0
$645$	−13.4975	+	6.50006i	−0.531464	+	0.255940i
$646$		0			0
$647$	10.4549	−	13.1101i	0.411026	−	0.515411i	−0.532625	−	0.846351i	$-0.678794\pi$
$647$	10.4549	−	13.1101i	0.411026	−	0.515411i	0.943652	+	0.330940i	$0.107366\pi$
$648$		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	0.815482	−	0.578783i	$-0.196472\pi$
$659$	11.1071	+	8.85762i	0.432671	+	0.345044i	−0.382810	+	0.923827i	$0.625044\pi$
$660$		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	0.983998	−	0.178182i	$-0.0570216\pi$
$683$	15.4538	+	19.3784i	0.591323	+	0.741495i	−0.392675	+	0.919677i	$0.628450\pi$
$684$		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	−0.977095	−	0.212804i	$-0.931740\pi$
$691$	−0.116466	+	0.510271i	−0.00443058	+	0.0194116i	0.972664	+	0.232216i	$0.0745975\pi$
$692$		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	$0.0392128\pi$
$719$	4.06492	+	17.8096i	0.151596	+	0.664185i	−0.840826	+	0.541306i	$0.817930\pi$
$720$		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	0.487185	−	0.873299i	$-0.338024\pi$
$727$	14.7545	+	3.36761i	0.547213	+	0.124898i	0.0600281	+	0.998197i	$0.480881\pi$
$728$		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	−0.615196	−	0.788374i	$-0.710923\pi$
$739$	−22.4926	+	5.13380i	−0.827405	+	0.188850i	−0.212209	+	0.977224i	$0.568066\pi$
$740$		0			0
$741$	17.1763	+	21.5384i	0.630988	+	0.791234i
$742$		0			0
$743$	14.1975	−	11.3221i	0.520855	−	0.415368i	−0.327456	−	0.944866i	$-0.606191\pi$
$743$	14.1975	−	11.3221i	0.520855	−	0.415368i	0.848311	+	0.529499i	$0.177620\pi$
$744$		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	0.935028	−	0.354573i	$-0.115374\pi$
$751$	2.05070	+	4.25832i	0.0748311	+	0.155388i	−0.860197	+	0.509962i	$0.829660\pi$
$752$		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	0.254574	−	0.967053i	$-0.418065\pi$
$787$	−9.61605	−	4.63085i	−0.342775	−	0.165072i	−0.597349	+	0.801982i	$0.703779\pi$
$788$		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	$-0.429870\pi$
$811$	12.4473			0.437084			0.218542	+	0.975828i	$0.429870\pi$
$812$		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	0.145264	−	0.989393i	$-0.453597\pi$
$823$	32.7667	−	26.1306i	1.14217	−	0.910854i	0.996911	+	0.0785392i	$0.0250256\pi$
$824$		0			0
$825$	45.0026	+	56.4314i	1.56679	+	1.96469i
$826$		0			0
$827$	18.3395	−	4.18586i	0.637725	−	0.145557i	0.108580	−	0.994088i	$-0.465370\pi$
$827$	18.3395	−	4.18586i	0.637725	−	0.145557i	0.529146	+	0.848531i	$0.322513\pi$
$828$		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	0.364132	−	0.931347i	$-0.381366\pi$
$839$	8.34515	+	1.90473i	0.288106	+	0.0657584i	−0.0760252	+	0.997106i	$0.524223\pi$
$840$		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	0.000172584	−	1.00000i	$-0.499945\pi$
$859$	28.5801	−	22.7918i	0.975139	−	0.777647i	0.974966	+	0.222353i	$0.0713736\pi$
$860$		0			0
$861$	4.61595	−	5.78822i	0.157311	−	0.197262i
$862$		0			0
$863$	4.39516	−	2.11660i	0.149613	−	0.0720498i	−0.357579	−	0.933883i	$-0.616398\pi$
$863$	4.39516	−	2.11660i	0.149613	−	0.0720498i	0.507192	+	0.861833i	$0.330683\pi$
$864$		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	$-0.944518\pi$
$883$	−27.7771	−	34.8313i	−0.934772	−	1.17217i	0.0500753	−	0.998745i	$-0.484054\pi$
$884$		0			0
$885$	20.2574	−	4.62361i	0.680944	−	0.155421i
$886$		0			0
$887$			14.9134i			0.500744i	0.968150	+	0.250372i	$0.0805529\pi$
$887$			14.9134i			0.500744i	−0.968150	+	0.250372i	$0.919447\pi$
$888$		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	−0.132903	−	0.991129i	$-0.542430\pi$
$907$	−33.9941	−	27.1094i	−1.12876	−	0.900153i	−0.995853	+	0.0909764i	$0.971001\pi$
$908$		0			0
$909$	59.5701	−	123.699i	1.97582	−	4.10282i
$910$		0			0
$911$		−	49.5298i		−	1.64100i	−0.571650	−	0.820498i	$-0.693696\pi$
$911$		−	49.5298i		−	1.64100i	0.571650	−	0.820498i	$-0.306304\pi$
$912$		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	−0.897333	−	0.441354i	$-0.854498\pi$
$919$	−8.10530	+	10.1637i	−0.267369	+	0.335270i	0.629964	+	0.776625i	$0.283070\pi$
$920$		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	−0.968956	−	0.247232i	$-0.920479\pi$
$947$	−5.27851	+	10.9609i	−0.171529	+	0.356183i	0.797428	+	0.603414i	$0.206193\pi$
$948$		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	−0.659131	−	0.752028i	$-0.729076\pi$
$967$	10.5663	−	21.9412i	0.339790	−	0.705581i	0.998921	+	0.0464476i	$0.0147900\pi$
$968$		0			0
$969$		−	11.2318i		−	0.360818i
$970$		0			0
$971$	0.649386	−	0.148218i	0.0208398	−	0.00475655i	−0.212088	−	0.977251i	$-0.568026\pi$
$971$	0.649386	−	0.148218i	0.0208398	−	0.00475655i	0.232928	+	0.972494i	$0.425169\pi$
$972$		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	0.968053	−	0.250744i	$-0.0806752\pi$
$983$	5.28115	+	10.9664i	0.168443	+	0.349775i	−0.799611	+	0.600518i	$0.794961\pi$
$984$		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	$-0.777488\pi$
$991$	6.40285	−	28.0527i	0.203393	−	0.891125i	0.968852	−	0.247640i	$-0.0796549\pi$
$992$		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	232.2.q.a.33.8	✓	48
4.3	odd	2		464.2.y.e.33.1		48
29.14	odd	28		6728.2.a.be.1.2		24
29.15	odd	28		6728.2.a.bf.1.23		24
29.22	even	14	inner	232.2.q.a.225.8	yes	48
116.51	odd	14		464.2.y.e.225.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.33.8	✓	48	1.1	even	1	trivial
232.2.q.a.225.8	yes	48	29.22	even	14	inner
464.2.y.e.33.1		48	4.3	odd	2
464.2.y.e.225.1		48	116.51	odd	14
6728.2.a.be.1.2		24	29.14	odd	28
6728.2.a.bf.1.23		24	29.15	odd	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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.q (of order \(14\), degree \(6\), 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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