LMFDB - Embedded newform 432.3.bc.c.209.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			209.3
Character	$\chi$	$=$	432.209
Dual form			432.3.bc.c.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.391734 - 2.97431i) q^{3} +(7.52350 - 1.32660i) q^{5} +(-4.40811 - 3.69885i) q^{7} +(-8.69309 - 2.33028i) q^{9} +O(q^{10})$	\(q+(0.391734 - 2.97431i) q^{3} +(7.52350 - 1.32660i) q^{5} +(-4.40811 - 3.69885i) q^{7} +(-8.69309 - 2.33028i) q^{9} +(-8.02644 - 1.41528i) q^{11} +(-22.0464 - 8.02423i) q^{13} +(-0.998502 - 22.8969i) q^{15} +(6.39327 - 3.69115i) q^{17} +(7.80130 - 13.5122i) q^{19} +(-12.7283 + 11.6622i) q^{21} +(19.9755 + 23.8059i) q^{23} +(31.3510 - 11.4108i) q^{25} +(-10.3364 + 24.9431i) q^{27} +(-9.68546 - 26.6106i) q^{29} +(-12.2601 + 10.2874i) q^{31} +(-7.35371 + 23.3187i) q^{33} +(-38.0714 - 21.9805i) q^{35} +(5.99046 + 10.3758i) q^{37} +(-32.5029 + 62.4295i) q^{39} +(2.82625 - 7.76505i) q^{41} +(7.82854 - 44.3978i) q^{43} +(-68.4938 - 5.99965i) q^{45} +(43.4592 - 51.7927i) q^{47} +(-2.75876 - 15.6457i) q^{49} +(-8.47419 - 20.4615i) q^{51} -16.4115i q^{53} -62.2645 q^{55} +(-37.1336 - 28.4967i) q^{57} +(-57.3592 + 10.1140i) q^{59} +(54.6605 + 45.8656i) q^{61} +(29.7008 + 42.4266i) q^{63} +(-176.511 - 31.1237i) q^{65} +(47.1688 + 17.1680i) q^{67} +(78.6313 - 50.0879i) q^{69} +(-35.4363 + 20.4592i) q^{71} +(-49.7692 + 86.2028i) q^{73} +(-21.6581 - 97.7176i) q^{75} +(30.1466 + 35.9273i) q^{77} +(72.4061 - 26.3537i) q^{79} +(70.1396 + 40.5147i) q^{81} +(-36.0769 - 99.1205i) q^{83} +(43.2031 - 36.2517i) q^{85} +(-82.9423 + 18.3833i) q^{87} +(-0.302200 - 0.174475i) q^{89} +(67.5026 + 116.918i) q^{91} +(25.7954 + 40.4953i) q^{93} +(40.7678 - 112.009i) q^{95} +(11.1076 - 62.9944i) q^{97} +(66.4766 + 31.0070i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 - 12 * q^9	$ 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45} + 378 q^{47} + 72 q^{49} + 54 q^{51} + 72 q^{57} - 252 q^{59} - 144 q^{61} - 318 q^{63} + 18 q^{65} + 594 q^{67} - 522 q^{69} + 648 q^{71} + 126 q^{73} + 438 q^{75} - 342 q^{77} + 72 q^{79} + 324 q^{81} - 594 q^{83} + 360 q^{85} - 1062 q^{87} + 648 q^{89} + 198 q^{91} + 462 q^{93} - 252 q^{95} + 702 q^{97} - 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{18}\right)$

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
$3$	0.391734	−	2.97431i	0.130578	−	0.991438i
$3$	0.391734	−	2.97431i	0.130578	−	0.991438i
$4$		0			0
$5$	7.52350	−	1.32660i	1.50470	−	0.265319i	0.640301	−	0.768124i	$-0.278810\pi$
$5$	7.52350	−	1.32660i	1.50470	−	0.265319i	0.864400	+	0.502805i	$0.167699\pi$
$6$		0			0
$7$	−4.40811	−	3.69885i	−0.629731	−	0.528407i	0.271115	−	0.962547i	$-0.412608\pi$
$7$	−4.40811	−	3.69885i	−0.629731	−	0.528407i	−0.900845	+	0.434140i	$0.857052\pi$
$8$		0			0
$9$	−8.69309	−	2.33028i	−0.965899	−	0.258920i
$10$		0			0
$11$	−8.02644	−	1.41528i	−0.729677	−	0.128662i	−0.203546	−	0.979065i	$-0.565247\pi$
$11$	−8.02644	−	1.41528i	−0.729677	−	0.128662i	−0.526131	+	0.850404i	$0.676358\pi$
$12$		0			0
$13$	−22.0464	−	8.02423i	−1.69588	−	0.617248i	−0.700531	−	0.713622i	$-0.747053\pi$
$13$	−22.0464	−	8.02423i	−1.69588	−	0.617248i	−0.995345	+	0.0963739i	$0.969276\pi$
$14$		0			0
$15$	−0.998502	−	22.8969i	−0.0665668	−	1.52646i
$16$		0			0
$17$	6.39327	−	3.69115i	0.376075	−	0.217127i	−0.300034	−	0.953928i	$-0.596998\pi$
$17$	6.39327	−	3.69115i	0.376075	−	0.217127i	0.676109	+	0.736802i	$0.263665\pi$
$18$		0			0
$19$	7.80130	−	13.5122i	0.410595	−	0.711171i	−0.584360	−	0.811494i	$-0.698654\pi$
$19$	7.80130	−	13.5122i	0.410595	−	0.711171i	0.994955	+	0.100324i	$0.0319878\pi$
$20$		0			0
$21$	−12.7283	+	11.6622i	−0.606112	+	0.555341i
$22$		0			0
$23$	19.9755	+	23.8059i	0.868500	+	1.03504i	0.999049	+	0.0435964i	$0.0138816\pi$
$23$	19.9755	+	23.8059i	0.868500	+	1.03504i	−0.130549	+	0.991442i	$0.541674\pi$
$24$		0			0
$25$	31.3510	−	11.4108i	1.25404	−	0.456433i
$26$		0			0
$27$	−10.3364	+	24.9431i	−0.382828	+	0.923819i
$28$		0			0
$29$	−9.68546	−	26.6106i	−0.333981	−	0.917606i	−0.987065	−	0.160320i	$-0.948747\pi$
$29$	−9.68546	−	26.6106i	−0.333981	−	0.917606i	0.653084	−	0.757286i	$-0.273475\pi$
$30$		0			0
$31$	−12.2601	+	10.2874i	−0.395487	+	0.331853i	−0.818746	−	0.574156i	$-0.805330\pi$
$31$	−12.2601	+	10.2874i	−0.395487	+	0.331853i	0.423259	+	0.906009i	$0.360886\pi$
$32$		0			0
$33$	−7.35371	+	23.3187i	−0.222840	+	0.706629i
$34$		0			0
$35$	−38.0714	−	21.9805i	−1.08775	−	0.628014i
$36$		0			0
$37$	5.99046	+	10.3758i	0.161904	+	0.280427i	0.935552	−	0.353190i	$-0.114903\pi$
$37$	5.99046	+	10.3758i	0.161904	+	0.280427i	−0.773647	+	0.633617i	$0.781570\pi$
$38$		0			0
$39$	−32.5029	+	62.4295i	−0.833408	+	1.60076i
$40$		0			0
$41$	2.82625	−	7.76505i	0.0689329	−	0.189391i	−0.900443	−	0.434975i	$-0.856757\pi$
$41$	2.82625	−	7.76505i	0.0689329	−	0.189391i	0.969375	+	0.245583i	$0.0789795\pi$
$42$		0			0
$43$	7.82854	−	44.3978i	0.182059	−	1.03251i	−0.747617	−	0.664130i	$-0.768802\pi$
$43$	7.82854	−	44.3978i	0.182059	−	1.03251i	0.929676	−	0.368378i	$-0.120087\pi$
$44$		0			0
$45$	−68.4938	−	5.99965i	−1.52209	−	0.133326i
$46$		0			0
$47$	43.4592	−	51.7927i	0.924664	−	1.10197i	−0.0698695	−	0.997556i	$-0.522258\pi$
$47$	43.4592	−	51.7927i	0.924664	−	1.10197i	0.994534	−	0.104416i	$-0.0332973\pi$
$48$		0			0
$49$	−2.75876	−	15.6457i	−0.0563012	−	0.319300i
$50$		0			0
$51$	−8.47419	−	20.4615i	−0.166161	−	0.401207i
$52$		0			0
$53$		−	16.4115i		−	0.309652i	−0.987942	−	0.154826i	$-0.950518\pi$
$53$		−	16.4115i		−	0.309652i	0.987942	−	0.154826i	$-0.0494816\pi$
$54$		0			0
$55$	−62.2645			−1.13208
$56$		0			0
$57$	−37.1336	−	28.4967i	−0.651467	−	0.499943i
$58$		0			0
$59$	−57.3592	+	10.1140i	−0.972190	+	0.171423i	−0.637115	−	0.770768i	$-0.719873\pi$
$59$	−57.3592	+	10.1140i	−0.972190	+	0.171423i	−0.335074	+	0.942192i	$0.608761\pi$
$60$		0			0
$61$	54.6605	+	45.8656i	0.896073	+	0.751895i	0.969419	−	0.245412i	$-0.0789231\pi$
$61$	54.6605	+	45.8656i	0.896073	+	0.751895i	−0.0733455	+	0.997307i	$0.523368\pi$
$62$		0			0
$63$	29.7008	+	42.4266i	0.471441	+	0.673437i
$64$		0			0
$65$	−176.511	−	31.1237i	−2.71555	−	0.478825i
$66$		0			0
$67$	47.1688	+	17.1680i	0.704012	+	0.256239i	0.669123	−	0.743152i	$-0.266670\pi$
$67$	47.1688	+	17.1680i	0.704012	+	0.256239i	0.0348888	+	0.999391i	$0.488892\pi$
$68$		0			0
$69$	78.6313	−	50.0879i	1.13958	−	0.725911i
$70$		0			0
$71$	−35.4363	+	20.4592i	−0.499103	+	0.288157i	−0.728343	−	0.685213i	$-0.759709\pi$
$71$	−35.4363	+	20.4592i	−0.499103	+	0.288157i	0.229240	+	0.973370i	$0.426376\pi$
$72$		0			0
$73$	−49.7692	+	86.2028i	−0.681770	+	1.18086i	0.292670	+	0.956213i	$0.405456\pi$
$73$	−49.7692	+	86.2028i	−0.681770	+	1.18086i	−0.974440	+	0.224647i	$0.927877\pi$
$74$		0			0
$75$	−21.6581	−	97.7176i	−0.288775	−	1.30290i
$76$		0			0
$77$	30.1466	+	35.9273i	0.391514	+	0.466588i
$78$		0			0
$79$	72.4061	−	26.3537i	0.916533	−	0.333591i	0.159674	−	0.987170i	$-0.448956\pi$
$79$	72.4061	−	26.3537i	0.916533	−	0.333591i	0.756858	+	0.653579i	$0.226733\pi$
$80$		0			0
$81$	70.1396	+	40.5147i	0.865921	+	0.500181i
$82$		0			0
$83$	−36.0769	−	99.1205i	−0.434662	−	1.19422i	−0.942920	−	0.333018i	$-0.891933\pi$
$83$	−36.0769	−	99.1205i	−0.434662	−	1.19422i	0.508259	−	0.861204i	$-0.330289\pi$
$84$		0			0
$85$	43.2031	−	36.2517i	0.508272	−	0.426491i
$86$		0			0
$87$	−82.9423	+	18.3833i	−0.953360	+	0.211303i
$88$		0			0
$89$	−0.302200	−	0.174475i	−0.00339551	−	0.00196040i	0.498301	−	0.867004i	$-0.333957\pi$
$89$	−0.302200	−	0.174475i	−0.00339551	−	0.00196040i	−0.501697	+	0.865044i	$0.667291\pi$
$90$		0			0
$91$	67.5026	+	116.918i	0.741787	+	1.28481i
$92$		0			0
$93$	25.7954	+	40.4953i	0.277370	+	0.435434i
$94$		0			0
$95$	40.7678	−	112.009i	0.429135	−	1.17904i
$96$		0			0
$97$	11.1076	−	62.9944i	0.114511	−	0.649427i	−0.872479	−	0.488651i	$-0.837489\pi$
$97$	11.1076	−	62.9944i	0.114511	−	0.649427i	0.986991	−	0.160776i	$-0.0513997\pi$
$98$		0			0
$99$	66.4766	+	31.0070i	0.671481	+	0.313202i
$100$		0			0
$101$	107.169	−	127.719i	1.06107	−	1.26454i	0.0980344	−	0.995183i	$-0.468744\pi$
$101$	107.169	−	127.719i	1.06107	−	1.26454i	0.963040	−	0.269357i	$-0.0868111\pi$
$102$		0			0
$103$	17.4708	+	99.0819i	0.169620	+	0.961960i	0.944173	+	0.329451i	$0.106864\pi$
$103$	17.4708	+	99.0819i	0.169620	+	0.961960i	−0.774553	+	0.632509i	$0.782025\pi$
$104$		0			0
$105$	−80.2908	+	104.626i	−0.764674	+	0.996435i
$106$		0			0
$107$		−	6.57806i		−	0.0614772i	−0.999527	−	0.0307386i	$-0.990214\pi$
$107$		−	6.57806i		−	0.0614772i	0.999527	−	0.0307386i	$-0.00978594\pi$
$108$		0			0
$109$	198.876			1.82455			0.912276	−	0.409576i	$-0.134323\pi$
$109$	198.876			1.82455			0.912276	+	0.409576i	$0.134323\pi$
$110$		0			0
$111$	33.2075	−	13.7530i	0.299167	−	0.123901i
$112$		0			0
$113$	−5.16749	+	0.911168i	−0.0457300	+	0.00806344i	−0.196466	−	0.980511i	$-0.562947\pi$
$113$	−5.16749	+	0.911168i	−0.0457300	+	0.00806344i	0.150736	+	0.988574i	$0.451836\pi$
$114$		0			0
$115$	181.867	+	152.604i	1.58145	+	1.32699i
$116$		0			0
$117$	172.952	+	121.130i	1.47823	+	1.03530i
$118$		0			0
$119$	−41.8353	−	7.37669i	−0.351557	−	0.0619890i
$120$		0			0
$121$	−51.2820	−	18.6651i	−0.423819	−	0.154257i
$122$		0			0
$123$	−21.9886	−	11.4480i	−0.178769	−	0.0930730i
$124$		0			0
$125$	55.3300	−	31.9448i	0.442640	−	0.255558i
$126$		0			0
$127$	22.2191	−	38.4846i	0.174954	−	0.303029i	−0.765192	−	0.643803i	$-0.777356\pi$
$127$	22.2191	−	38.4846i	0.174954	−	0.303029i	0.940145	+	0.340774i	$0.110689\pi$
$128$		0			0
$129$	−128.986	−	40.6767i	−0.999895	−	0.315323i
$130$		0			0
$131$	−25.8274	−	30.7798i	−0.197155	−	0.234961i	0.658405	−	0.752664i	$-0.271232\pi$
$131$	−25.8274	−	30.7798i	−0.197155	−	0.234961i	−0.855560	+	0.517703i	$0.826787\pi$
$132$		0			0
$133$	−84.3688	+	30.7077i	−0.634352	+	0.230885i
$134$		0			0
$135$	−44.6762	+	201.372i	−0.330935	+	1.49164i
$136$		0			0
$137$	17.6267	+	48.4289i	0.128662	+	0.353495i	0.987252	−	0.159168i	$-0.0508811\pi$
$137$	17.6267	+	48.4289i	0.128662	+	0.353495i	−0.858590	+	0.512663i	$0.828659\pi$
$138$		0			0
$139$	82.4641	−	69.1956i	0.593267	−	0.497810i	−0.296006	−	0.955186i	$-0.595655\pi$
$139$	82.4641	−	69.1956i	0.593267	−	0.497810i	0.889274	+	0.457376i	$0.151211\pi$
$140$		0			0
$141$	−137.023	−	149.550i	−0.971796	−	1.06064i
$142$		0			0
$143$	165.598	+	95.6078i	1.15802	+	0.668586i
$144$		0			0
$145$	−108.170	−	187.356i	−0.746001	−	1.29211i
$146$		0			0
$147$	−47.6159	+	2.07646i	−0.323918	+	0.0141256i
$148$		0			0
$149$	−48.2594	+	132.592i	−0.323888	+	0.889876i	0.665735	+	0.746189i	$0.268118\pi$
$149$	−48.2594	+	132.592i	−0.323888	+	0.889876i	−0.989623	+	0.143688i	$0.954104\pi$
$150$		0			0
$151$	22.7795	−	129.189i	0.150858	−	0.855557i	−0.811618	−	0.584189i	$-0.801413\pi$
$151$	22.7795	−	129.189i	0.150858	−	0.855557i	0.962476	−	0.271368i	$-0.0874761\pi$
$152$		0			0
$153$	−64.1787	+	17.1894i	−0.419468	+	0.112349i
$154$		0			0
$155$	−78.5916	+	93.6618i	−0.507043	+	0.604270i
$156$		0			0
$157$	33.4745	+	189.844i	0.213214	+	1.20919i	0.883980	+	0.467526i	$0.154854\pi$
$157$	33.4745	+	189.844i	0.213214	+	1.20919i	−0.670766	+	0.741669i	$0.734034\pi$
$158$		0			0
$159$	−48.8131	−	6.42896i	−0.307000	−	0.0404337i
$160$		0			0
$161$		−	178.825i		−	1.11072i
$162$		0			0
$163$	−80.4819			−0.493754			−0.246877	−	0.969047i	$-0.579404\pi$
$163$	−80.4819			−0.493754			−0.246877	+	0.969047i	$0.579404\pi$
$164$		0			0
$165$	−24.3911	+	185.194i	−0.147825	+	1.12239i
$166$		0			0
$167$	106.625	−	18.8008i	0.638472	−	0.112580i	0.154964	−	0.987920i	$-0.450474\pi$
$167$	106.625	−	18.8008i	0.638472	−	0.112580i	0.483508	+	0.875340i	$0.339363\pi$
$168$		0			0
$169$	292.193	+	245.179i	1.72896	+	1.45077i
$170$		0			0
$171$	−99.3047	+	99.2839i	−0.580729	+	0.580608i
$172$		0			0
$173$	83.3770	+	14.7016i	0.481948	+	0.0849804i	0.409343	−	0.912380i	$-0.365758\pi$
$173$	83.3770	+	14.7016i	0.481948	+	0.0849804i	0.0726044	+	0.997361i	$0.476869\pi$
$174$		0			0
$175$	−180.405	−	65.6622i	−1.03089	−	0.375213i
$176$		0			0
$177$	7.61258	+	174.566i	0.0430089	+	0.986250i
$178$		0			0
$179$	145.291	−	83.8837i	0.811681	−	0.468624i	−0.0358583	−	0.999357i	$-0.511417\pi$
$179$	145.291	−	83.8837i	0.811681	−	0.468624i	0.847539	+	0.530733i	$0.178083\pi$
$180$		0			0
$181$	144.733	−	250.684i	0.799627	−	1.38500i	−0.120232	−	0.992746i	$-0.538364\pi$
$181$	144.733	−	250.684i	0.799627	−	1.38500i	0.919859	−	0.392249i	$-0.128303\pi$
$182$		0			0
$183$	157.831	−	144.610i	0.862465	−	0.790220i
$184$		0			0
$185$	58.8338	+	70.1154i	0.318020	+	0.379002i
$186$		0			0
$187$	−56.5392	+	20.5786i	−0.302349	+	0.110046i
$188$		0			0
$189$	137.825	−	71.7195i	0.729231	−	0.379468i
$190$		0			0
$191$	13.7963	+	37.9051i	0.0722320	+	0.198456i	0.970555	−	0.240880i	$-0.0774360\pi$
$191$	13.7963	+	37.9051i	0.0722320	+	0.198456i	−0.898323	+	0.439336i	$0.855214\pi$
$192$		0			0
$193$	−185.784	+	155.891i	−0.962610	+	0.807726i	−0.981376	−	0.192098i	$-0.938471\pi$
$193$	−185.784	+	155.891i	−0.962610	+	0.807726i	0.0187656	+	0.999824i	$0.494026\pi$
$194$		0			0
$195$	−161.717	+	512.807i	−0.829318	+	2.62978i
$196$		0			0
$197$	−4.72432	−	2.72758i	−0.0239813	−	0.0138456i	0.487961	−	0.872865i	$-0.337741\pi$
$197$	−4.72432	−	2.72758i	−0.0239813	−	0.0138456i	−0.511943	+	0.859020i	$0.671074\pi$
$198$		0			0
$199$	−71.5073	−	123.854i	−0.359333	−	0.622383i	0.628516	−	0.777796i	$-0.283663\pi$
$199$	−71.5073	−	123.854i	−0.359333	−	0.622383i	−0.987850	+	0.155413i	$0.950329\pi$
$200$		0			0
$201$	69.5407	−	133.569i	0.345974	−	0.664525i
$202$		0			0
$203$	−55.7339	+	153.127i	−0.274551	+	0.754323i
$204$		0			0
$205$	10.9622	−	62.1697i	0.0534741	−	0.303267i
$206$		0			0
$207$	−118.174	−	253.495i	−0.570891	−	1.22461i
$208$		0			0
$209$	−81.7403	+	97.4143i	−0.391102	+	0.466097i
$210$		0			0
$211$	1.49994	+	8.50659i	0.00710873	+	0.0403156i	0.988156	−	0.153454i	$-0.0490397\pi$
$211$	1.49994	+	8.50659i	0.00710873	+	0.0403156i	−0.981047	+	0.193770i	$0.937929\pi$
$212$		0			0
$213$	46.9704	+	113.413i	0.220518	+	0.532457i
$214$		0			0
$215$		−	344.413i		−	1.60192i
$216$		0			0
$217$	92.0956			0.424404
$218$		0			0
$219$	236.898	+	181.798i	1.08173	+	0.830127i
$220$		0			0
$221$	−170.567	+	30.0756i	−0.771797	+	0.136089i
$222$		0			0
$223$	235.030	+	197.214i	1.05395	+	0.884367i	0.993503	−	0.113805i	$-0.0363039\pi$
$223$	235.030	+	197.214i	1.05395	+	0.884367i	0.0604441	+	0.998172i	$0.480748\pi$
$224$		0			0
$225$	−299.127	+	26.1387i	−1.32945	+	0.116172i
$226$		0			0
$227$	−11.7174	−	2.06609i	−0.0516185	−	0.00910173i	0.147779	−	0.989020i	$-0.452787\pi$
$227$	−11.7174	−	2.06609i	−0.0516185	−	0.00910173i	−0.199398	+	0.979919i	$0.563899\pi$
$228$		0			0
$229$	362.125	+	131.803i	1.58133	+	0.575558i	0.975493	−	0.220029i	$-0.0706153\pi$
$229$	362.125	+	131.803i	1.58133	+	0.575558i	0.605839	+	0.795587i	$0.292837\pi$
$230$		0			0
$231$	118.668	−	75.5914i	0.513716	−	0.327236i
$232$		0			0
$233$	−8.31951	+	4.80327i	−0.0357060	+	0.0206149i	−0.517747	−	0.855534i	$-0.673229\pi$
$233$	−8.31951	+	4.80327i	−0.0357060	+	0.0206149i	0.482041	+	0.876149i	$0.339896\pi$
$234$		0			0
$235$	258.258	−	447.315i	1.09897	−	1.90347i
$236$		0			0
$237$	−50.0201	−	225.682i	−0.211055	−	0.952245i
$238$		0			0
$239$	66.1793	+	78.8695i	0.276901	+	0.329998i	0.886514	−	0.462701i	$-0.153120\pi$
$239$	66.1793	+	78.8695i	0.276901	+	0.329998i	−0.609613	+	0.792699i	$0.708675\pi$
$240$		0			0
$241$	−100.052	+	36.4160i	−0.415154	+	0.151104i	−0.541148	−	0.840927i	$-0.682010\pi$
$241$	−100.052	+	36.4160i	−0.415154	+	0.151104i	0.125994	+	0.992031i	$0.459788\pi$
$242$		0			0
$243$	147.979	−	192.746i	0.608969	−	0.793194i
$244$		0			0
$245$	−41.5111	−	114.051i	−0.169433	−	0.465513i
$246$		0			0
$247$	−280.416	+	235.297i	−1.13529	+	0.952619i
$248$		0			0
$249$	−308.948	+	68.4752i	−1.24076	+	0.275001i
$250$		0			0
$251$	−70.6683	−	40.8004i	−0.281547	−	0.162551i	0.352577	−	0.935783i	$-0.385306\pi$
$251$	−70.6683	−	40.8004i	−0.281547	−	0.162551i	−0.634124	+	0.773232i	$0.718639\pi$
$252$		0			0
$253$	−126.640	−	219.347i	−0.500555	−	0.866986i
$254$		0			0
$255$	−90.8998	−	142.701i	−0.356470	−	0.559610i
$256$		0			0
$257$	150.247	−	412.801i	0.584620	−	1.60623i	−0.195572	−	0.980689i	$-0.562656\pi$
$257$	150.247	−	412.801i	0.584620	−	1.60623i	0.780192	−	0.625541i	$-0.215122\pi$
$258$		0			0
$259$	11.9718	−	67.8955i	0.0462232	−	0.262145i
$260$		0			0
$261$	22.1864	+	253.898i	0.0850055	+	0.972789i
$262$		0			0
$263$	−289.840	+	345.418i	−1.10205	+	1.31338i	−0.156584	+	0.987665i	$0.550048\pi$
$263$	−289.840	+	345.418i	−1.10205	+	1.31338i	−0.945469	+	0.325711i	$0.894396\pi$
$264$		0			0
$265$	−21.7715	−	123.472i	−0.0821566	−	0.465933i
$266$		0			0
$267$	−0.637327	+	0.830491i	−0.00238699	+	0.00311045i
$268$		0			0
$269$		−	363.566i		−	1.35155i	−0.737110	−	0.675773i	$-0.763810\pi$
$269$		−	363.566i		−	1.35155i	0.737110	−	0.675773i	$-0.236190\pi$
$270$		0			0
$271$	70.6655			0.260758			0.130379	−	0.991464i	$-0.458381\pi$
$271$	70.6655			0.260758			0.130379	+	0.991464i	$0.458381\pi$
$272$		0			0
$273$	374.194	−	154.973i	1.37067	−	0.567667i
$274$		0			0
$275$	−267.786	+	47.2179i	−0.973768	+	0.171701i
$276$		0			0
$277$	−178.872	−	150.091i	−0.645746	−	0.541845i	0.260031	−	0.965600i	$-0.416267\pi$
$277$	−178.872	−	150.091i	−0.645746	−	0.541845i	−0.905777	+	0.423755i	$0.860712\pi$
$278$		0			0
$279$	130.551	−	60.8602i	0.467924	−	0.218137i
$280$		0			0
$281$	−284.922	−	50.2394i	−1.01396	−	0.178788i	−0.358108	−	0.933680i	$-0.616578\pi$
$281$	−284.922	−	50.2394i	−1.01396	−	0.178788i	−0.655849	+	0.754892i	$0.727689\pi$
$282$		0			0
$283$	144.152	+	52.4669i	0.509370	+	0.185395i	0.583903	−	0.811823i	$-0.301525\pi$
$283$	144.152	+	52.4669i	0.509370	+	0.185395i	−0.0745339	+	0.997218i	$0.523747\pi$
$284$		0			0
$285$	−317.179	−	165.134i	−1.11291	−	0.579417i
$286$		0			0
$287$	−41.1802	+	23.7754i	−0.143485	+	0.0828410i
$288$		0			0
$289$	−117.251	+	203.084i	−0.405712	+	0.702714i
$290$		0			0
$291$	−183.014	−	57.7146i	−0.628914	−	0.198332i
$292$		0			0
$293$	104.985	+	125.117i	0.358311	+	0.427019i	0.914844	−	0.403807i	$-0.132313\pi$
$293$	104.985	+	125.117i	0.358311	+	0.427019i	−0.556533	+	0.830826i	$0.687869\pi$
$294$		0			0
$295$	−418.125	+	152.185i	−1.41737	+	0.515882i
$296$		0			0
$297$	118.266	−	185.576i	0.398201	−	0.624834i
$298$		0			0
$299$	−249.364	−	685.122i	−0.833993	−	2.29138i
$300$		0			0
$301$	−198.730	+	166.754i	−0.660232	+	0.554001i
$302$		0			0
$303$	−337.893	−	368.785i	−1.11516	−	1.21711i
$304$		0			0
$305$	472.084	+	272.558i	1.54781	+	0.893631i
$306$		0			0
$307$	−163.324	−	282.886i	−0.532000	−	0.921452i	−0.999302	−	0.0373539i	$-0.988107\pi$
$307$	−163.324	−	282.886i	−0.532000	−	0.921452i	0.467302	−	0.884098i	$-0.345226\pi$
$308$		0			0
$309$	301.545	−	13.1499i	0.975873	−	0.0425564i
$310$		0			0
$311$	−159.228	+	437.476i	−0.511988	+	1.40668i	0.367173	+	0.930152i	$0.380326\pi$
$311$	−159.228	+	437.476i	−0.511988	+	1.40668i	−0.879162	+	0.476524i	$0.841897\pi$
$312$		0			0
$313$	38.0827	−	215.978i	0.121670	−	0.690025i	−0.861560	−	0.507655i	$-0.830512\pi$
$313$	38.0827	−	215.978i	0.121670	−	0.690025i	0.983230	−	0.182369i	$-0.0583766\pi$
$314$		0			0
$315$	279.737	+	279.795i	0.888054	+	0.888239i
$316$		0			0
$317$	−81.8800	+	97.5807i	−0.258296	+	0.307826i	−0.879571	−	0.475767i	$-0.842171\pi$
$317$	−81.8800	+	97.5807i	−0.258296	+	0.307826i	0.621275	+	0.783593i	$0.286615\pi$
$318$		0			0
$319$	40.0784	+	227.296i	0.125638	+	0.712526i
$320$		0			0
$321$	−19.5652	−	2.57685i	−0.0609508	−	0.00802757i
$322$		0			0
$323$		−	115.183i		−	0.356604i
$324$		0			0
$325$	−782.738			−2.40843
$326$		0			0
$327$	77.9066	−	591.520i	0.238246	−	1.80893i
$328$		0			0
$329$	−383.146	+	67.5591i	−1.16458	+	0.205347i
$330$		0			0
$331$	−208.107	−	174.623i	−0.628723	−	0.527561i	0.271809	−	0.962351i	$-0.412378\pi$
$331$	−208.107	−	174.623i	−0.628723	−	0.527561i	−0.900532	+	0.434790i	$0.856823\pi$
$332$		0			0
$333$	−27.8971	−	104.157i	−0.0837752	−	0.312784i
$334$		0			0
$335$	377.650	+	66.5898i	1.12731	+	0.198776i
$336$		0			0
$337$	−482.379	−	175.572i	−1.43139	−	0.520984i	−0.494061	−	0.869427i	$-0.664488\pi$
$337$	−482.379	−	175.572i	−1.43139	−	0.520984i	−0.937330	+	0.348443i	$0.886710\pi$
$338$		0			0
$339$	0.685818	+	15.7267i	0.00202306	+	0.0463914i
$340$		0			0
$341$	112.965	−	65.2201i	0.331274	−	0.191261i
$342$		0			0
$343$	−186.693	+	323.361i	−0.544293	+	0.942743i
$344$		0			0
$345$	525.136	−	481.148i	1.52213	−	1.39463i
$346$		0			0
$347$	115.155	+	137.237i	0.331859	+	0.395494i	0.906011	−	0.423255i	$-0.139112\pi$
$347$	115.155	+	137.237i	0.331859	+	0.395494i	−0.574152	+	0.818749i	$0.694668\pi$
$348$		0			0
$349$	324.668	−	118.170i	0.930281	−	0.338595i	0.167960	−	0.985794i	$-0.446282\pi$
$349$	324.668	−	118.170i	0.930281	−	0.338595i	0.762321	+	0.647199i	$0.224060\pi$
$350$		0			0
$351$	428.029	−	466.964i	1.21946	−	1.33038i
$352$		0			0
$353$	84.0412	+	230.901i	0.238077	+	0.654112i	0.999979	+	0.00641959i	$0.00204343\pi$
$353$	84.0412	+	230.901i	0.238077	+	0.654112i	−0.761902	+	0.647692i	$0.775734\pi$
$354$		0			0
$355$	−239.464	+	200.934i	−0.674547	+	0.566012i
$356$		0			0
$357$	−38.3289	+	121.542i	−0.107364	+	0.340452i
$358$		0			0
$359$	481.215	+	277.830i	1.34043	+	0.773899i	0.986871	−	0.161512i	$-0.0516371\pi$
$359$	481.215	+	277.830i	1.34043	+	0.773899i	0.353562	+	0.935411i	$0.384970\pi$
$360$		0			0
$361$	58.7794	+	101.809i	0.162824	+	0.282019i
$362$		0			0
$363$	−75.6049	+	145.217i	−0.208278	+	0.400047i
$364$		0			0
$365$	−260.082	+	714.571i	−0.712555	+	1.95773i
$366$		0			0
$367$	−69.2101	+	392.510i	−0.188583	+	1.06951i	0.732681	+	0.680572i	$0.238269\pi$
$367$	−69.2101	+	392.510i	−0.188583	+	1.06951i	−0.921264	+	0.388937i	$0.872842\pi$
$368$		0			0
$369$	−42.6636	+	60.9163i	−0.115619	+	0.165085i
$370$		0			0
$371$	−60.7038	+	72.3439i	−0.163622	+	0.194997i
$372$		0			0
$373$	71.1393	+	403.451i	0.190722	+	1.08164i	0.918381	+	0.395698i	$0.129497\pi$
$373$	71.1393	+	403.451i	0.190722	+	1.08164i	−0.727659	+	0.685939i	$0.759392\pi$
$374$		0			0
$375$	−73.3392	−	177.083i	−0.195571	−	0.472220i
$376$		0			0
$377$			664.385i			1.76230i
$378$		0			0
$379$	61.5139			0.162306			0.0811529	−	0.996702i	$-0.474140\pi$
$379$	61.5139			0.162306			0.0811529	+	0.996702i	$0.474140\pi$
$380$		0			0
$381$	−105.761	−	81.1623i	−0.277589	−	0.213025i
$382$		0			0
$383$	−200.252	+	35.3098i	−0.522851	+	0.0921927i	−0.428844	−	0.903379i	$-0.641079\pi$
$383$	−200.252	+	35.3098i	−0.522851	+	0.0921927i	−0.0940074	+	0.995572i	$0.529968\pi$
$384$		0			0
$385$	274.469	+	230.307i	0.712906	+	0.598199i
$386$		0			0
$387$	−171.514	+	367.712i	−0.443188	+	0.950159i
$388$		0			0
$389$	−251.130	−	44.2810i	−0.645579	−	0.113833i	−0.158734	−	0.987321i	$-0.550741\pi$
$389$	−251.130	−	44.2810i	−0.645579	−	0.113833i	−0.486845	+	0.873488i	$0.661852\pi$
$390$		0			0
$391$	215.580	+	78.4647i	0.551355	+	0.200677i
$392$		0			0
$393$	−101.666	+	64.7612i	−0.258693	+	0.164787i
$394$		0			0
$395$	509.787	−	294.326i	1.29060	−	0.745128i
$396$		0			0
$397$	13.8139	−	23.9264i	0.0347957	−	0.0602679i	−0.848103	−	0.529831i	$-0.822255\pi$
$397$	13.8139	−	23.9264i	0.0347957	−	0.0602679i	0.882899	+	0.469563i	$0.155589\pi$
$398$		0			0
$399$	58.2843	+	262.968i	0.146076	+	0.659069i
$400$		0			0
$401$	−240.702	−	286.857i	−0.600254	−	0.715354i	0.377288	−	0.926096i	$-0.376857\pi$
$401$	−240.702	−	286.857i	−0.600254	−	0.715354i	−0.977542	+	0.210741i	$0.932412\pi$
$402$		0			0
$403$	352.840	−	128.423i	0.875533	−	0.318668i
$404$		0			0
$405$	581.442	+	211.765i	1.43566	+	0.522878i
$406$		0			0
$407$	−33.3975	−	91.7588i	−0.0820577	−	0.225452i
$408$		0			0
$409$	156.992	−	131.732i	0.383843	−	0.322082i	−0.430366	−	0.902654i	$-0.641616\pi$
$409$	156.992	−	131.732i	0.383843	−	0.322082i	0.814209	+	0.580572i	$0.197171\pi$
$410$		0			0
$411$	150.948	−	33.4560i	0.367269	−	0.0814015i
$412$		0			0
$413$	290.256	+	167.579i	0.702799	+	0.405761i
$414$		0			0
$415$	−402.918	−	697.874i	−0.970886	−	1.68162i
$416$		0			0
$417$	−173.505	−	272.380i	−0.416080	−	0.653191i
$418$		0			0
$419$	−81.7427	+	224.586i	−0.195090	+	0.536005i	−0.998210	−	0.0598126i	$-0.980950\pi$
$419$	−81.7427	+	224.586i	−0.195090	+	0.536005i	0.803120	+	0.595818i	$0.203172\pi$
$420$		0			0
$421$	34.6408	−	196.458i	0.0822821	−	0.466645i	−0.915628	−	0.402027i	$-0.868306\pi$
$421$	34.6408	−	196.458i	0.0822821	−	0.466645i	0.997910	−	0.0646183i	$-0.0205830\pi$
$422$		0			0
$423$	−498.486	+	348.966i	−1.17845	+	0.824979i
$424$		0			0
$425$	158.316	−	188.674i	0.372508	−	0.443938i
$426$		0			0
$427$	−71.2998	−	404.362i	−0.166979	−	0.946983i
$428$		0			0
$429$	349.238	−	455.086i	0.814074	−	1.06081i
$430$		0			0
$431$		−	235.094i		−	0.545461i	−0.962090	−	0.272731i	$-0.912073\pi$
$431$		−	235.094i		−	0.545461i	0.962090	−	0.272731i	$-0.0879267\pi$
$432$		0			0
$433$	−391.650			−0.904504			−0.452252	−	0.891890i	$-0.649379\pi$
$433$	−391.650			−0.904504			−0.452252	+	0.891890i	$0.649379\pi$
$434$		0			0
$435$	−599.630	+	248.338i	−1.37846	+	0.570892i
$436$		0			0
$437$	477.506	−	84.1972i	1.09269	−	0.192671i
$438$		0			0
$439$	−62.2561	−	52.2391i	−0.141813	−	0.118996i	0.569121	−	0.822254i	$-0.307283\pi$
$439$	−62.2561	−	52.2391i	−0.141813	−	0.118996i	−0.710935	+	0.703258i	$0.751728\pi$
$440$		0			0
$441$	−12.4767	+	142.438i	−0.0282919	+	0.322989i
$442$		0			0
$443$	−519.689	−	91.6352i	−1.17311	−	0.206851i	−0.447069	−	0.894500i	$-0.647532\pi$
$443$	−519.689	−	91.6352i	−1.17311	−	0.206851i	−0.726044	+	0.687648i	$0.758643\pi$
$444$		0			0
$445$	−2.50506	−	0.911769i	−0.00562936	−	0.00204892i
$446$		0			0
$447$	375.464	+	195.479i	0.839965	+	0.437314i
$448$		0			0
$449$	−104.119	+	60.1132i	−0.231891	+	0.133882i	−0.611444	−	0.791288i	$-0.709411\pi$
$449$	−104.119	+	60.1132i	−0.231891	+	0.133882i	0.379553	+	0.925170i	$0.376078\pi$
$450$		0			0
$451$	−33.6744	+	58.3258i	−0.0746661	+	0.129326i
$452$		0			0
$453$	−375.325	−	118.361i	−0.828533	−	0.261283i
$454$		0			0
$455$	662.959	+	790.084i	1.45705	+	1.73645i
$456$		0			0
$457$	134.507	−	48.9566i	0.294326	−	0.107126i	−0.190637	−	0.981661i	$-0.561055\pi$
$457$	134.507	−	48.9566i	0.294326	−	0.107126i	0.484963	+	0.874535i	$0.338833\pi$
$458$		0			0
$459$	25.9858	+	197.621i	0.0566139	+	0.430547i
$460$		0			0
$461$	−80.7643	−	221.898i	−0.175194	−	0.481341i	0.820753	−	0.571283i	$-0.193554\pi$
$461$	−80.7643	−	221.898i	−0.175194	−	0.481341i	−0.995947	+	0.0899422i	$0.971332\pi$
$462$		0			0
$463$	−113.622	+	95.3405i	−0.245405	+	0.205919i	−0.757191	−	0.653194i	$-0.773429\pi$
$463$	−113.622	+	95.3405i	−0.245405	+	0.205919i	0.511786	+	0.859113i	$0.328984\pi$
$464$		0			0
$465$	247.793	+	270.447i	0.532888	+	0.581606i
$466$		0			0
$467$	78.1166	+	45.1006i	0.167273	+	0.0965752i	0.581299	−	0.813690i	$-0.302544\pi$
$467$	78.1166	+	45.1006i	0.167273	+	0.0965752i	−0.414026	+	0.910265i	$0.635878\pi$
$468$		0			0
$469$	−144.423	−	250.149i	−0.307939	−	0.533366i
$470$		0			0
$471$	577.767	−	25.1956i	1.22668	−	0.0534938i
$472$		0			0
$473$	−125.671	+	345.277i	−0.265688	+	0.729973i
$474$		0			0
$475$	90.3924	−	512.641i	0.190300	−	1.07924i
$476$		0			0
$477$	−38.2435	+	142.667i	−0.0801750	+	0.299092i
$478$		0			0
$479$	165.915	−	197.730i	0.346378	−	0.412797i	−0.564526	−	0.825415i	$-0.690941\pi$
$479$	165.915	−	197.730i	0.346378	−	0.412797i	0.910904	+	0.412618i	$0.135386\pi$
$480$		0			0
$481$	−48.8104	−	276.818i	−0.101477	−	0.575504i
$482$		0			0
$483$	−531.883	−	70.0520i	−1.10121	−	0.145035i
$484$		0			0
$485$		−	488.674i		−	1.00758i
$486$		0			0
$487$	103.107			0.211718			0.105859	−	0.994381i	$-0.466241\pi$
$487$	103.107			0.211718			0.105859	+	0.994381i	$0.466241\pi$
$488$		0			0
$489$	−31.5275	+	239.378i	−0.0644734	+	0.489526i
$490$		0			0
$491$	753.133	−	132.798i	1.53388	−	0.270464i	0.658007	−	0.753012i	$-0.271400\pi$
$491$	753.133	−	132.798i	1.53388	−	0.270464i	0.875870	+	0.482548i	$0.160289\pi$
$492$		0			0
$493$	−160.145	−	134.378i	−0.324839	−	0.272572i
$494$		0			0
$495$	541.271	+	145.094i	1.09348	+	0.293119i
$496$		0			0
$497$	231.883	+	40.8872i	0.466565	+	0.0822679i
$498$		0			0
$499$	−675.618	−	245.905i	−1.35394	−	0.492795i	−0.439767	−	0.898112i	$-0.644939\pi$
$499$	−675.618	−	245.905i	−1.35394	−	0.492795i	−0.914176	+	0.405317i	$0.867161\pi$
$500$		0			0
$501$	−14.1510	−	324.501i	−0.0282455	−	0.647706i
$502$		0			0
$503$	−506.649	+	292.514i	−1.00725	+	0.581538i	−0.910386	−	0.413759i	$-0.864216\pi$
$503$	−506.649	+	292.514i	−1.00725	+	0.581538i	−0.0968675	+	0.995297i	$0.530882\pi$
$504$		0			0
$505$	636.852	−	1103.06i	1.26109	−	2.18428i
$506$		0			0
$507$	843.703	−	773.030i	1.66411	−	1.52471i
$508$		0			0
$509$	567.862	+	676.751i	1.11564	+	1.32957i	0.938458	+	0.345393i	$0.112254\pi$
$509$	567.862	+	676.751i	1.11564	+	1.32957i	0.177184	+	0.984178i	$0.443301\pi$
$510$		0			0
$511$	538.239	−	195.903i	1.05331	−	0.383372i
$512$		0			0
$513$	256.401	+	334.256i	0.499806	+	0.651572i
$514$		0			0
$515$	262.884	+	722.266i	0.510453	+	1.40246i
$516$		0			0
$517$	−422.124	+	354.204i	−0.816487	+	0.685114i
$518$		0			0
$519$	76.3888	−	242.230i	0.147185	−	0.466725i
$520$		0			0
$521$	22.5511	+	13.0199i	0.0432843	+	0.0249902i	0.521486	−	0.853260i	$-0.325378\pi$
$521$	22.5511	+	13.0199i	0.0432843	+	0.0249902i	−0.478202	+	0.878250i	$0.658711\pi$
$522$		0			0
$523$	289.411	+	501.274i	0.553366	+	0.958458i	0.998029	+	0.0627602i	$0.0199903\pi$
$523$	289.411	+	501.274i	0.553366	+	0.958458i	−0.444662	+	0.895698i	$0.646676\pi$
$524$		0			0
$525$	−265.971	+	510.860i	−0.506611	+	0.973067i
$526$		0			0
$527$	−40.4095	+	111.024i	−0.0766784	+	0.210672i
$528$		0			0
$529$	−75.8392	+	430.106i	−0.143363	+	0.813054i
$530$		0			0
$531$	522.197	+	45.7414i	0.983422	+	0.0861419i
$532$		0			0
$533$	−124.617	+	148.513i	−0.233803	+	0.278636i
$534$		0			0
$535$	−8.72643	−	49.4901i	−0.0163111	−	0.0925048i
$536$		0			0
$537$	−192.581	−	465.001i	−0.358624	−	0.865923i
$538$		0			0
$539$			129.484i			0.240229i
$540$		0			0
$541$	−84.9565			−0.157036			−0.0785180	−	0.996913i	$-0.525019\pi$
$541$	−84.9565			−0.157036			−0.0785180	+	0.996913i	$0.525019\pi$
$542$		0			0
$543$	−688.917	−	528.682i	−1.26872	−	0.973631i
$544$		0			0
$545$	1496.25	−	263.828i	2.74540	−	0.484089i
$546$		0			0
$547$	662.004	+	555.487i	1.21025	+	1.01552i	0.999277	+	0.0380234i	$0.0121062\pi$
$547$	662.004	+	555.487i	1.21025	+	1.01552i	0.210968	+	0.977493i	$0.432338\pi$
$548$		0			0
$549$	−368.289	−	526.088i	−0.670836	−	0.958266i
$550$		0			0
$551$	−435.128	−	76.7248i	−0.789706	−	0.139246i
$552$		0			0
$553$	−416.652	−	151.649i	−0.753440	−	0.274230i
$554$		0			0
$555$	231.592	−	147.524i	0.417283	−	0.265808i
$556$		0			0
$557$	−226.376	+	130.698i	−0.406420	+	0.234647i	−0.689250	−	0.724523i	$-0.742060\pi$
$557$	−226.376	+	130.698i	−0.406420	+	0.234647i	0.282830	+	0.959170i	$0.408727\pi$
$558$		0			0
$559$	−528.849	+	915.994i	−0.946063	+	1.63863i
$560$		0			0
$561$	39.0588	+	176.227i	0.0696236	+	0.314130i
$562$		0			0
$563$	−505.895	−	602.902i	−0.898570	−	1.07087i	−0.997127	−	0.0757425i	$-0.975867\pi$
$563$	−505.895	−	602.902i	−0.898570	−	1.07087i	0.0985575	−	0.995131i	$-0.468577\pi$
$564$		0			0
$565$	−37.6689	+	13.7104i	−0.0666706	+	0.0242661i
$566$		0			0
$567$	−159.326	−	438.029i	−0.280998	−	0.772538i
$568$		0			0
$569$	90.4364	+	248.472i	0.158939	+	0.436682i	0.993444	−	0.114319i	$-0.0364684\pi$
$569$	90.4364	+	248.472i	0.158939	+	0.436682i	−0.834505	+	0.551001i	$0.814246\pi$
$570$		0			0
$571$	48.7960	−	40.9447i	0.0854572	−	0.0717071i	−0.599058	−	0.800705i	$-0.704458\pi$
$571$	48.7960	−	40.9447i	0.0854572	−	0.0717071i	0.684515	+	0.728998i	$0.260014\pi$
$572$		0			0
$573$	118.146	−	26.1859i	0.206189	−	0.0456996i
$574$		0			0
$575$	897.896	+	518.400i	1.56156	+	0.901566i
$576$		0			0
$577$	485.361	+	840.670i	0.841180	+	1.45697i	0.888898	+	0.458106i	$0.151472\pi$
$577$	485.361	+	840.670i	0.841180	+	1.45697i	−0.0477175	+	0.998861i	$0.515195\pi$
$578$		0			0
$579$	390.891	+	613.647i	0.675114	+	1.05984i
$580$		0			0
$581$	−207.600	+	570.377i	−0.357316	+	0.981717i
$582$		0			0
$583$	−23.2269	+	131.726i	−0.0398403	+	0.225946i
$584$		0			0
$585$	1461.90	+	681.881i	2.49897	+	1.16561i
$586$		0			0
$587$	−65.3472	+	77.8778i	−0.111324	+	0.132671i	−0.818829	−	0.574038i	$-0.805376\pi$
$587$	−65.3472	+	77.8778i	−0.111324	+	0.132671i	0.707505	+	0.706708i	$0.249821\pi$
$588$		0			0
$589$	43.3618	+	245.917i	0.0736193	+	0.417516i
$590$		0			0
$591$	−9.96337	+	12.9831i	−0.0168585	+	0.0219680i
$592$		0			0
$593$		−	926.755i		−	1.56282i	−0.624016	−	0.781412i	$-0.714500\pi$
$593$		−	926.755i		−	1.56282i	0.624016	−	0.781412i	$-0.285500\pi$
$594$		0			0
$595$	−324.534			−0.545435
$596$		0			0
$597$	−396.393	+	164.167i	−0.663976	+	0.274987i
$598$		0			0
$599$	553.736	−	97.6386i	0.924434	−	0.163003i	0.308883	−	0.951100i	$-0.400045\pi$
$599$	553.736	−	97.6386i	0.924434	−	0.163003i	0.615551	+	0.788097i	$0.288934\pi$
$600$		0			0
$601$	291.320	+	244.447i	0.484726	+	0.406733i	0.852132	−	0.523327i	$-0.175310\pi$
$601$	291.320	+	244.447i	0.484726	+	0.406733i	−0.367406	+	0.930061i	$0.619754\pi$
$602$		0			0
$603$	−370.036	−	259.160i	−0.613658	−	0.429784i
$604$		0			0
$605$	−410.582	−	72.3967i	−0.678648	−	0.119664i
$606$		0			0
$607$	−1056.66	−	384.593i	−1.74079	−	0.633597i	−0.741492	−	0.670962i	$-0.765881\pi$
$607$	−1056.66	−	384.593i	−1.74079	−	0.633597i	−0.999302	+	0.0373651i	$0.988104\pi$
$608$		0			0
$609$	433.616	+	225.755i	0.712014	+	0.370698i
$610$		0			0
$611$	−1373.72	+	793.115i	−2.24831	+	1.29806i
$612$		0			0
$613$	−313.409	+	542.840i	−0.511270	+	0.885546i	0.488644	+	0.872483i	$0.337492\pi$
$613$	−313.409	+	542.840i	−0.511270	+	0.885546i	−0.999915	+	0.0130631i	$0.995842\pi$
$614$		0			0
$615$	−180.618	−	56.9590i	−0.293688	−	0.0926163i
$616$		0			0
$617$	113.319	+	135.049i	0.183662	+	0.218880i	0.850018	−	0.526754i	$-0.176591\pi$
$617$	113.319	+	135.049i	0.183662	+	0.218880i	−0.666356	+	0.745634i	$0.732147\pi$
$618$		0			0
$619$	873.825	−	318.046i	1.41167	−	0.513807i	0.480052	−	0.877240i	$-0.340618\pi$
$619$	873.825	−	318.046i	1.41167	−	0.513807i	0.931620	+	0.363434i	$0.118396\pi$
$620$		0			0
$621$	−800.267	+	252.185i	−1.28868	+	0.406095i
$622$		0			0
$623$	0.686776	+	1.88690i	0.00110237	+	0.00302873i
$624$		0			0
$625$	−265.041	+	222.395i	−0.424065	+	0.355833i
$626$		0			0
$627$	257.720	+	281.282i	0.411037	+	0.448615i
$628$		0			0
$629$	76.5973	+	44.2235i	0.121776	+	0.0703076i
$630$		0			0
$631$	−327.053	−	566.473i	−0.518309	−	0.897738i	−0.999774	−	0.0212724i	$-0.993228\pi$
$631$	−327.053	−	566.473i	−0.518309	−	0.897738i	0.481464	−	0.876466i	$-0.340105\pi$
$632$		0			0
$633$	25.8889	−	1.12898i	0.0408987	−	0.00178353i
$634$		0			0
$635$	116.112	−	319.015i	0.182854	−	0.502386i
$636$		0			0
$637$	−64.7240	+	367.068i	−0.101608	+	0.576245i
$638$		0			0
$639$	355.727	−	95.2768i	0.556693	−	0.149103i
$640$		0			0
$641$	473.126	−	563.850i	0.738106	−	0.879641i	−0.258149	−	0.966105i	$-0.583112\pi$
$641$	473.126	−	563.850i	0.738106	−	0.879641i	0.996255	+	0.0864644i	$0.0275569\pi$
$642$		0			0
$643$	123.683	+	701.440i	0.192353	+	1.09089i	0.916139	+	0.400862i	$0.131289\pi$
$643$	123.683	+	701.440i	0.192353	+	1.09089i	−0.723786	+	0.690025i	$0.757600\pi$
$644$		0			0
$645$	−1024.39	−	134.918i	−1.58820	−	0.209176i
$646$		0			0
$647$			291.136i			0.449978i	0.974361	+	0.224989i	$0.0722346\pi$
$647$			291.136i			0.449978i	−0.974361	+	0.224989i	$0.927765\pi$
$648$		0			0
$649$	474.704			0.731440
$650$		0			0
$651$	36.0770	−	273.921i	0.0554178	−	0.420770i
$652$		0			0
$653$	−1145.26	+	201.940i	−1.75384	+	0.309250i	−0.955946	−	0.293542i	$-0.905166\pi$
$653$	−1145.26	+	201.940i	−1.75384	+	0.309250i	−0.797898	+	0.602792i	$0.794055\pi$
$654$		0			0
$655$	−235.145	−	197.310i	−0.359000	−	0.301236i
$656$		0			0
$657$	633.525	−	633.392i	0.964269	−	0.964067i
$658$		0			0
$659$	−521.251	−	91.9106i	−0.790972	−	0.139470i	−0.236455	−	0.971642i	$-0.575986\pi$
$659$	−521.251	−	91.9106i	−0.790972	−	0.139470i	−0.554517	+	0.832173i	$0.687097\pi$
$660$		0			0
$661$	−3.61822	−	1.31693i	−0.00547386	−	0.00199232i	0.339282	−	0.940685i	$-0.389816\pi$
$661$	−3.61822	−	1.31693i	−0.00547386	−	0.00199232i	−0.344756	+	0.938692i	$0.612038\pi$
$662$		0			0
$663$	22.6373	+	519.102i	0.0341437	+	0.782959i
$664$		0			0
$665$	−594.012	+	342.953i	−0.893251	+	0.515719i
$666$		0			0
$667$	440.016	−	762.131i	0.659695	−	1.14262i
$668$		0			0
$669$	678.645	−	621.798i	1.01442	−	0.929444i
$670$		0			0
$671$	−373.817	−	445.497i	−0.557104	−	0.663930i
$672$		0			0
$673$	389.797	−	141.874i	0.579193	−	0.210809i	−0.0357768	−	0.999360i	$-0.511391\pi$
$673$	389.797	−	141.874i	0.579193	−	0.210809i	0.614970	+	0.788551i	$0.289168\pi$
$674$		0			0
$675$	−39.4336	+	899.937i	−0.0584201	+	1.33324i
$676$		0			0
$677$	−406.146	−	1115.88i	−0.599921	−	1.64827i	−0.751430	−	0.659813i	$-0.770636\pi$
$677$	−406.146	−	1115.88i	−0.599921	−	1.64827i	0.151509	−	0.988456i	$-0.451587\pi$
$678$		0			0
$679$	−281.970	+	236.601i	−0.415273	+	0.348455i
$680$		0			0
$681$	−10.7353	+	34.0419i	−0.0157640	+	0.0499881i
$682$		0			0
$683$	−444.994	−	256.917i	−0.651528	−	0.376160i	0.137513	−	0.990500i	$-0.456089\pi$
$683$	−444.994	−	256.917i	−0.651528	−	0.376160i	−0.789041	+	0.614340i	$0.789422\pi$
$684$		0			0
$685$	196.860	+	340.971i	0.287387	+	0.497768i
$686$		0			0
$687$	533.880	−	1025.44i	0.777117	−	1.49264i
$688$		0			0
$689$	−131.690	+	361.815i	−0.191132	+	0.525131i
$690$		0			0
$691$	−91.9225	+	521.318i	−0.133028	+	0.754440i	0.843184	+	0.537625i	$0.180678\pi$
$691$	−91.9225	+	521.318i	−0.133028	+	0.754440i	−0.976213	+	0.216816i	$0.930433\pi$
$692$		0			0
$693$	−178.346	−	382.569i	−0.257354	−	0.552048i
$694$		0			0
$695$	528.625	−	629.990i	0.760611	−	0.906461i
$696$		0			0
$697$	−10.5930	−	60.0762i	−0.0151981	−	0.0861925i
$698$		0			0
$699$	11.0274	+	26.6264i	0.0157760	+	0.0380922i
$700$		0			0
$701$		−	13.0718i		−	0.0186474i	−0.999957	−	0.00932369i	$-0.997032\pi$
$701$		−	13.0718i		−	0.0186474i	0.999957	−	0.00932369i	$-0.00296787\pi$
$702$		0			0
$703$	186.934			0.265908
$704$		0			0
$705$	−1229.29	−	943.368i	−1.74367	−	1.33811i
$706$		0			0
$707$	−944.823	+	166.598i	−1.33638	+	0.235640i
$708$		0			0
$709$	−584.480	−	490.437i	−0.824372	−	0.691730i	0.129620	−	0.991564i	$-0.458624\pi$
$709$	−584.480	−	490.437i	−0.824372	−	0.691730i	−0.953992	+	0.299834i	$0.903069\pi$
$710$		0			0
$711$	−690.844	+	60.3682i	−0.971651	+	0.0849060i
$712$		0			0
$713$	−489.803	−	86.3655i	−0.686961	−	0.121130i
$714$		0			0
$715$	1372.71	+	499.624i	1.91987	+	0.698775i
$716$		0			0
$717$	260.507	−	165.942i	0.363330	−	0.231440i
$718$		0			0
$719$	782.468	−	451.758i	1.08827	−	0.628315i	0.155157	−	0.987890i	$-0.450412\pi$
$719$	782.468	−	451.758i	1.08827	−	0.628315i	0.933116	+	0.359575i	$0.117078\pi$
$720$		0			0
$721$	289.476	−	501.386i	0.401492	−	0.695404i
$722$		0			0
$723$	69.1188	+	311.852i	0.0955999	+	0.431330i
$724$		0			0
$725$	−607.297	−	723.748i	−0.837650	−	0.998273i
$726$		0			0
$727$	−906.427	+	329.912i	−1.24680	+	0.453800i	−0.879321	−	0.476230i	$-0.842003\pi$
$727$	−906.427	+	329.912i	−1.24680	+	0.453800i	−0.367484	+	0.930030i	$0.619781\pi$
$728$		0			0
$729$	−515.319	−	515.643i	−0.706885	−	0.707329i
$730$		0			0
$731$	−113.829	−	312.744i	−0.155717	−	0.427830i
$732$		0			0
$733$	421.118	−	353.360i	0.574513	−	0.482074i	−0.308627	−	0.951183i	$-0.599869\pi$
$733$	421.118	−	353.360i	0.574513	−	0.482074i	0.883140	+	0.469109i	$0.155425\pi$
$734$		0			0
$735$	−355.484	+	78.7894i	−0.483652	+	0.107196i
$736$		0			0
$737$	−354.300	−	204.555i	−0.480733	−	0.277551i
$738$		0			0
$739$	261.308	+	452.598i	0.353596	+	0.612446i	0.986877	−	0.161476i	$-0.0516254\pi$
$739$	261.308	+	452.598i	0.353596	+	0.612446i	−0.633281	+	0.773922i	$0.718292\pi$
$740$		0			0
$741$	589.998	+	926.219i	0.796219	+	1.24996i
$742$		0			0
$743$	170.432	−	468.259i	0.229384	−	0.630227i	−0.770591	−	0.637330i	$-0.780039\pi$
$743$	170.432	−	468.259i	0.229384	−	0.630227i	0.999975	+	0.00710282i	$0.00226092\pi$
$744$		0			0
$745$	−187.184	+	1061.57i	−0.251254	+	1.42493i
$746$		0			0
$747$	82.6412	+	945.733i	0.110631	+	1.26604i
$748$		0			0
$749$	−24.3312	+	28.9968i	−0.0324850	+	0.0387141i
$750$		0			0
$751$	−69.7868	−	395.781i	−0.0929252	−	0.527005i	−0.995363	−	0.0961857i	$-0.969336\pi$
$751$	−69.7868	−	395.781i	−0.0929252	−	0.527005i	0.902438	−	0.430819i	$-0.141775\pi$
$752$		0			0
$753$	−149.036	+	194.207i	−0.197923	+	0.257911i
$754$		0			0
$755$		−	1002.17i		−	1.32738i
$756$		0			0
$757$	564.958			0.746312			0.373156	−	0.927769i	$-0.378276\pi$
$757$	564.958			0.746312			0.373156	+	0.927769i	$0.378276\pi$
$758$		0			0
$759$	−702.017	+	290.742i	−0.924924	+	0.383059i
$760$		0			0
$761$	−353.849	+	62.3930i	−0.464978	+	0.0819882i	−0.401229	−	0.915978i	$-0.631417\pi$
$761$	−353.849	+	62.3930i	−0.464978	+	0.0819882i	−0.0637492	+	0.997966i	$0.520306\pi$
$762$		0			0
$763$	−876.669	−	735.612i	−1.14898	−	0.964105i
$764$		0			0
$765$	−460.045	+	214.464i	−0.601366	+	0.280345i
$766$		0			0
$767$	1345.72	+	237.287i	1.75452	+	0.309370i
$768$		0			0
$769$	564.254	+	205.372i	0.733751	+	0.267063i	0.681752	−	0.731584i	$-0.261219\pi$
$769$	564.254	+	205.372i	0.733751	+	0.267063i	0.0519990	+	0.998647i	$0.483441\pi$
$770$		0			0
$771$	−1168.94	−	608.591i	−1.51614	−	0.789353i
$772$		0			0
$773$	−198.839	+	114.799i	−0.257230	+	0.148512i	−0.623070	−	0.782166i	$-0.714115\pi$
$773$	−198.839	+	114.799i	−0.257230	+	0.148512i	0.365840	+	0.930678i	$0.380782\pi$
$774$		0			0
$775$	−266.978	+	462.419i	−0.344487	+	0.596669i
$776$		0			0
$777$	−197.253	−	62.2049i	−0.253865	−	0.0800578i
$778$		0			0
$779$	−82.8749	−	98.7664i	−0.106386	−	0.126786i
$780$		0			0
$781$	313.383	−	114.062i	0.401259	−	0.146046i
$782$		0			0
$783$	763.863	+	33.4711i	0.975560	+	0.0427472i
$784$		0			0
$785$	503.692	+	1383.88i	0.641646	+	1.76291i
$786$		0			0
$787$	803.701	−	674.385i	1.02122	−	0.856906i	0.0314403	−	0.999506i	$-0.489991\pi$
$787$	803.701	−	674.385i	1.02122	−	0.856906i	0.989780	+	0.142600i	$0.0455462\pi$
$788$		0			0
$789$	913.841	+	997.387i	1.15823	+	1.26412i
$790$		0			0
$791$	26.1492	+	15.0972i	0.0330584	+	0.0190863i
$792$		0			0
$793$	−837.030	−	1449.78i	−1.05552	−	1.82822i
$794$		0			0
$795$	−375.774	+	16.3870i	−0.472672	+	0.0206125i
$796$		0			0
$797$	509.637	−	1400.22i	0.639444	−	1.75686i	−0.0140206	−	0.999902i	$-0.504463\pi$
$797$	509.637	−	1400.22i	0.639444	−	1.75686i	0.653465	−	0.756957i	$-0.273315\pi$
$798$		0			0
$799$	86.6716	−	491.539i	0.108475	−	0.615193i
$800$		0			0
$801$	2.22048	+	2.22094i	0.00277213	+	0.00277271i
$802$		0			0
$803$	521.471	−	621.464i	0.649403	−	0.773928i
$804$		0			0
$805$	−237.229	−	1345.39i	−0.294695	−	1.67130i
$806$		0			0
$807$	−1081.36	−	142.421i	−1.33997	−	0.176482i
$808$		0			0
$809$		−	1326.92i		−	1.64020i	−0.572222	−	0.820099i	$-0.693918\pi$
$809$		−	1326.92i		−	1.64020i	0.572222	−	0.820099i	$-0.306082\pi$
$810$		0			0
$811$	−412.746			−0.508935			−0.254467	−	0.967081i	$-0.581900\pi$
$811$	−412.746			−0.508935			−0.254467	+	0.967081i	$0.581900\pi$
$812$		0			0
$813$	27.6821	−	210.181i	0.0340493	−	0.258526i
$814$		0			0
$815$	−605.506	+	106.767i	−0.742952	+	0.131002i
$816$		0			0
$817$	−538.842	−	452.142i	−0.659537	−	0.553417i
$818$		0			0
$819$	−314.354	−	1173.68i	−0.383827	−	1.43306i
$820$		0			0
$821$	266.832	+	47.0497i	0.325008	+	0.0573078i	0.333772	−	0.942654i	$-0.391678\pi$
$821$	266.832	+	47.0497i	0.325008	+	0.0573078i	−0.00876353	+	0.999962i	$0.502790\pi$
$822$		0			0
$823$	674.756	+	245.591i	0.819874	+	0.298410i	0.717696	−	0.696357i	$-0.245197\pi$
$823$	674.756	+	245.591i	0.819874	+	0.298410i	0.102178	+	0.994766i	$0.467419\pi$
$824$		0			0
$825$	35.5399	+	814.977i	0.0430787	+	0.987851i
$826$		0			0
$827$	−966.321	+	557.906i	−1.16847	+	0.674614i	−0.953318	−	0.301968i	$-0.902356\pi$
$827$	−966.321	+	557.906i	−1.16847	+	0.674614i	−0.215147	+	0.976582i	$0.569023\pi$
$828$		0			0
$829$	−561.875	+	973.195i	−0.677774	+	1.17394i	0.297876	+	0.954605i	$0.403722\pi$
$829$	−561.875	+	973.195i	−0.677774	+	1.17394i	−0.975650	+	0.219334i	$0.929611\pi$
$830$		0			0
$831$	−516.488	+	473.225i	−0.621526	+	0.569464i
$832$		0			0
$833$	−75.3882	−	89.8441i	−0.0905020	−	0.107856i
$834$		0			0
$835$	777.251	−	282.896i	0.930840	−	0.338798i
$836$		0			0
$837$	−129.876	−	412.140i	−0.155169	−	0.492401i
$838$		0			0
$839$	86.6527	+	238.076i	0.103281	+	0.283762i	0.980560	−	0.196218i	$-0.0628660\pi$
$839$	86.6527	+	238.076i	0.103281	+	0.283762i	−0.877279	+	0.479980i	$0.840644\pi$
$840$		0			0
$841$	29.9287	−	25.1132i	0.0355870	−	0.0298611i
$842$		0			0
$843$	−261.041	+	827.767i	−0.309658	+	0.981930i
$844$		0			0
$845$	2523.57	+	1456.99i	2.98648	+	1.72424i
$846$		0			0
$847$	157.018	+	271.963i	0.185381	+	0.321089i
$848$		0			0
$849$	212.522	−	408.199i	0.250320	−	0.480800i
$850$		0			0
$851$	−127.342	+	349.870i	−0.149638	+	0.411128i
$852$		0			0
$853$	138.485	−	785.388i	0.162351	−	0.920736i	−0.789403	−	0.613875i	$-0.789610\pi$
$853$	138.485	−	785.388i	0.162351	−	0.920736i	0.951754	−	0.306862i	$-0.0992789\pi$
$854$		0			0
$855$	−615.410	+	878.701i	−0.719778	+	1.02772i
$856$		0			0
$857$	−718.626	+	856.426i	−0.838537	+	0.999330i	0.161385	+	0.986891i	$0.448404\pi$
$857$	−718.626	+	856.426i	−0.838537	+	0.999330i	−0.999923	+	0.0124382i	$0.996041\pi$
$858$		0			0
$859$	177.886	+	1008.84i	0.207085	+	1.17444i	0.894125	+	0.447817i	$0.147798\pi$
$859$	177.886	+	1008.84i	0.207085	+	1.17444i	−0.687041	+	0.726619i	$0.741091\pi$
$860$		0			0
$861$	54.5838	+	131.796i	0.0633958	+	0.153074i
$862$		0			0
$863$		−	1691.86i		−	1.96044i	−0.197921	−	0.980218i	$-0.563419\pi$
$863$		−	1691.86i		−	1.96044i	0.197921	−	0.980218i	$-0.436581\pi$
$864$		0			0
$865$	646.790			0.747734
$866$		0			0
$867$	558.105	+	428.296i	0.643720	+	0.493997i
$868$		0			0
$869$	−618.461	+	109.051i	−0.711693	+	0.125491i
$870$		0			0
$871$	−902.141	−	756.986i	−1.03575	−	0.869100i
$872$		0			0
$873$	−243.354	+	521.732i	−0.278756	+	0.597631i
$874$		0			0
$875$	−362.060	−	63.8409i	−0.413783	−	0.0729611i
$876$		0			0
$877$	−197.694	−	71.9546i	−0.225420	−	0.0820463i	0.226841	−	0.973932i	$-0.427160\pi$
$877$	−197.694	−	71.9546i	−0.225420	−	0.0820463i	−0.452261	+	0.891886i	$0.649383\pi$
$878$		0			0
$879$	413.262	−	263.247i	0.470150	−	0.299484i
$880$		0			0
$881$	−654.815	+	378.058i	−0.743263	+	0.429123i	−0.823255	−	0.567672i	$-0.807844\pi$
$881$	−654.815	+	378.058i	−0.743263	+	0.429123i	0.0799913	+	0.996796i	$0.474511\pi$
$882$		0			0
$883$	641.960	−	1111.91i	0.727021	−	1.25924i	−0.231116	−	0.972926i	$-0.574238\pi$
$883$	641.960	−	1111.91i	0.727021	−	1.25924i	0.958137	−	0.286311i	$-0.0924291\pi$
$884$		0			0
$885$	288.852	+	1303.25i	0.326387	+	1.47260i
$886$		0			0
$887$	−292.453	−	348.533i	−0.329711	−	0.392934i	0.575567	−	0.817755i	$-0.304782\pi$
$887$	−292.453	−	348.533i	−0.329711	−	0.392934i	−0.905277	+	0.424821i	$0.860337\pi$
$888$		0			0
$889$	−240.293	+	87.4595i	−0.270296	+	0.0983797i
$890$		0			0
$891$	−505.632	−	424.456i	−0.567488	−	0.476381i
$892$		0			0
$893$	−360.797	−	991.282i	−0.404028	−	1.11006i
$894$		0			0
$895$	981.817	−	823.842i	1.09700	−	0.920494i
$896$		0			0
$897$	−2135.45	+	473.301i	−2.38066	+	0.527649i
$898$		0			0
$899$	392.499	+	226.610i	0.436596	+	0.252069i
$900$		0			0
$901$	−60.5775	−	104.923i	−0.0672337	−	0.116452i
$902$		0			0
$903$	418.130	+	656.409i	0.463045	+	0.726920i
$904$		0			0
$905$	756.339	−	2078.02i	0.835734	−	2.29616i
$906$		0			0
$907$	−271.826	+	1541.60i	−0.299698	+	1.69967i	0.347771	+	0.937580i	$0.386939\pi$
$907$	−271.826	+	1541.60i	−0.299698	+	1.69967i	−0.647469	+	0.762092i	$0.724172\pi$
$908$		0			0
$909$	−1229.25	+	860.536i	−1.35231	+	0.946684i
$910$		0			0
$911$	−618.498	+	737.097i	−0.678922	+	0.809108i	−0.989969	−	0.141287i	$-0.954876\pi$
$911$	−618.498	+	737.097i	−0.678922	+	0.809108i	0.311047	+	0.950395i	$0.399320\pi$
$912$		0			0
$913$	149.286	+	846.644i	0.163512	+	0.927321i
$914$		0			0
$915$	995.603	−	1297.35i	1.08809	−	1.41787i
$916$		0			0
$917$			231.213i			0.252140i
$918$		0			0
$919$	1645.52			1.79055			0.895277	−	0.445509i	$-0.146977\pi$
$919$	1645.52			1.79055			0.895277	+	0.445509i	$0.146977\pi$
$920$		0			0
$921$	−905.371	+	374.961i	−0.983030	+	0.407124i
$922$		0			0
$923$	945.412	−	166.702i	1.02428	−	0.180608i
$924$		0			0
$925$	306.203	+	256.935i	0.331030	+	0.277767i
$926$		0			0
$927$	79.0133	−	902.040i	0.0852355	−	0.973074i
$928$		0			0
$929$	1341.86	+	236.606i	1.44441	+	0.254689i	0.840262	−	0.542180i	$-0.182401\pi$
$929$	1341.86	+	236.606i	1.44441	+	0.254689i	0.604151	+	0.796869i	$0.293512\pi$
$930$		0			0
$931$	−232.930	−	84.7797i	−0.250194	−	0.0910631i
$932$		0			0
$933$	1238.82	+	644.969i	1.32778	+	0.691286i
$934$		0			0
$935$	−398.073	+	229.828i	−0.425747	+	0.245805i
$936$		0			0
$937$	−175.293	+	303.616i	−0.187079	+	0.324030i	−0.944275	−	0.329158i	$-0.893235\pi$
$937$	−175.293	+	303.616i	−0.187079	+	0.324030i	0.757196	+	0.653187i	$0.226569\pi$
$938$		0			0
$939$	−627.467	−	197.876i	−0.668229	−	0.210730i
$940$		0			0
$941$	−195.237	−	232.674i	−0.207478	−	0.247263i	0.652263	−	0.757992i	$-0.273820\pi$
$941$	−195.237	−	232.674i	−0.207478	−	0.247263i	−0.859741	+	0.510730i	$0.829375\pi$
$942$		0			0
$943$	241.310	−	87.8295i	0.255896	−	0.0931384i
$944$		0			0
$945$	941.782	−	722.420i	0.996595	−	0.764466i
$946$		0			0
$947$	487.225	+	1338.64i	0.514493	+	1.41356i	0.876508	+	0.481387i	$0.159867\pi$
$947$	487.225	+	1338.64i	0.514493	+	1.41356i	−0.362015	+	0.932172i	$0.617911\pi$
$948$		0			0
$949$	1788.94	−	1501.10i	1.88508	−	1.58177i
$950$		0			0
$951$	258.161	+	281.762i	0.271462	+	0.296280i
$952$		0			0
$953$	−551.558	−	318.442i	−0.578760	−	0.334147i	0.181880	−	0.983321i	$-0.441782\pi$
$953$	−551.558	−	318.442i	−0.578760	−	0.334147i	−0.760640	+	0.649173i	$0.775115\pi$
$954$		0			0
$955$	154.081	+	266.877i	0.161342	+	0.279452i
$956$		0			0
$957$	691.749	−	30.1662i	0.722831	−	0.0315216i
$958$		0			0
$959$	101.431	−	278.678i	0.105767	−	0.290593i
$960$		0			0
$961$	−122.397	+	694.150i	−0.127365	+	0.722321i
$962$		0			0
$963$	−15.3287	+	57.1837i	−0.0159177	+	0.0593807i
$964$		0			0
$965$	−1190.94	+	1419.31i	−1.23414	+	1.47078i
$966$		0			0
$967$	107.436	+	609.298i	0.111102	+	0.630091i	0.988607	+	0.150522i	$0.0480956\pi$
$967$	107.436	+	609.298i	0.111102	+	0.630091i	−0.877505	+	0.479568i	$0.840793\pi$
$968$		0			0
$969$	−342.591	−	45.1212i	−0.353551	−	0.0465647i
$970$		0			0
$971$		−	1356.90i		−	1.39743i	−0.715402	−	0.698713i	$-0.753756\pi$
$971$		−	1356.90i		−	1.39743i	0.715402	−	0.698713i	$-0.246244\pi$
$972$		0			0
$973$	−619.455			−0.636645
$974$		0			0
$975$	−306.625	+	2328.11i	−0.314487	+	2.38780i
$976$		0			0
$977$	−179.599	+	31.6681i	−0.183827	+	0.0324136i	−0.264804	−	0.964302i	$-0.585307\pi$
$977$	−179.599	+	31.6681i	−0.183827	+	0.0324136i	0.0809768	+	0.996716i	$0.474196\pi$
$978$		0			0
$979$	2.17866	+	1.82811i	0.00222540	+	0.00186733i
$980$		0			0
$981$	−1728.85	−	463.437i	−1.76233	−	0.472413i
$982$		0			0
$983$	−1251.09	−	220.600i	−1.27272	−	0.224415i	−0.503835	−	0.863800i	$-0.668078\pi$
$983$	−1251.09	−	220.600i	−1.27272	−	0.224415i	−0.768887	+	0.639385i	$0.779189\pi$
$984$		0			0
$985$	−39.1618	−	14.2537i	−0.0397582	−	0.0144708i
$986$		0			0
$987$	50.8503	+	1166.06i	0.0515201	+	1.18142i
$988$		0			0
$989$	1213.31	−	700.504i	1.22680	−	0.708295i
$990$		0			0
$991$	274.584	−	475.593i	0.277078	−	0.479912i	−0.693580	−	0.720380i	$-0.743967\pi$
$991$	274.584	−	475.593i	0.277078	−	0.479912i	0.970657	+	0.240468i	$0.0773008\pi$
$992$		0			0
$993$	−600.906	+	550.571i	−0.605142	+	0.554452i
$994$		0			0
$995$	−702.290	−	836.957i	−0.705820	−	0.841163i
$996$		0			0
$997$	1295.37	−	471.475i	1.29927	−	0.472894i	0.402508	−	0.915416i	$-0.368138\pi$
$997$	1295.37	−	471.475i	1.29927	−	0.472894i	0.896758	+	0.442522i	$0.145916\pi$
$998$		0			0
$999$	−320.724	+	42.1729i	−0.321045	+	0.0422152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.c.209.3		36
4.3	odd	2		54.3.f.a.47.3	yes	36
12.11	even	2		162.3.f.a.143.4		36
27.23	odd	18	inner	432.3.bc.c.401.3		36
108.23	even	18		54.3.f.a.23.3	✓	36
108.31	odd	18		162.3.f.a.17.4		36
108.79	odd	18		1458.3.b.c.1457.21		36
108.83	even	18		1458.3.b.c.1457.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.3	✓	36	108.23	even	18
54.3.f.a.47.3	yes	36	4.3	odd	2
162.3.f.a.17.4		36	108.31	odd	18
162.3.f.a.143.4		36	12.11	even	2
432.3.bc.c.209.3		36	1.1	even	1	trivial
432.3.bc.c.401.3		36	27.23	odd	18	inner
1458.3.b.c.1457.16		36	108.83	even	18
1458.3.b.c.1457.21		36	108.79	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.391734 - 2.97431i) q^{3} +(7.52350 - 1.32660i) q^{5} +(-4.40811 - 3.69885i) q^{7} +(-8.69309 - 2.33028i) q^{9} +O(q^{10})\)	\(q+(0.391734 - 2.97431i) q^{3} +(7.52350 - 1.32660i) q^{5} +(-4.40811 - 3.69885i) q^{7} +(-8.69309 - 2.33028i) q^{9} +(-8.02644 - 1.41528i) q^{11} +(-22.0464 - 8.02423i) q^{13} +(-0.998502 - 22.8969i) q^{15} +(6.39327 - 3.69115i) q^{17} +(7.80130 - 13.5122i) q^{19} +(-12.7283 + 11.6622i) q^{21} +(19.9755 + 23.8059i) q^{23} +(31.3510 - 11.4108i) q^{25} +(-10.3364 + 24.9431i) q^{27} +(-9.68546 - 26.6106i) q^{29} +(-12.2601 + 10.2874i) q^{31} +(-7.35371 + 23.3187i) q^{33} +(-38.0714 - 21.9805i) q^{35} +(5.99046 + 10.3758i) q^{37} +(-32.5029 + 62.4295i) q^{39} +(2.82625 - 7.76505i) q^{41} +(7.82854 - 44.3978i) q^{43} +(-68.4938 - 5.99965i) q^{45} +(43.4592 - 51.7927i) q^{47} +(-2.75876 - 15.6457i) q^{49} +(-8.47419 - 20.4615i) q^{51} -16.4115i q^{53} -62.2645 q^{55} +(-37.1336 - 28.4967i) q^{57} +(-57.3592 + 10.1140i) q^{59} +(54.6605 + 45.8656i) q^{61} +(29.7008 + 42.4266i) q^{63} +(-176.511 - 31.1237i) q^{65} +(47.1688 + 17.1680i) q^{67} +(78.6313 - 50.0879i) q^{69} +(-35.4363 + 20.4592i) q^{71} +(-49.7692 + 86.2028i) q^{73} +(-21.6581 - 97.7176i) q^{75} +(30.1466 + 35.9273i) q^{77} +(72.4061 - 26.3537i) q^{79} +(70.1396 + 40.5147i) q^{81} +(-36.0769 - 99.1205i) q^{83} +(43.2031 - 36.2517i) q^{85} +(-82.9423 + 18.3833i) q^{87} +(-0.302200 - 0.174475i) q^{89} +(67.5026 + 116.918i) q^{91} +(25.7954 + 40.4953i) q^{93} +(40.7678 - 112.009i) q^{95} +(11.1076 - 62.9944i) q^{97} +(66.4766 + 31.0070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q + 18 * q^5 - 12 * q^9	\( 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45} + 378 q^{47} + 72 q^{49} + 54 q^{51} + 72 q^{57} - 252 q^{59} - 144 q^{61} - 318 q^{63} + 18 q^{65} + 594 q^{67} - 522 q^{69} + 648 q^{71} + 126 q^{73} + 438 q^{75} - 342 q^{77} + 72 q^{79} + 324 q^{81} - 594 q^{83} + 360 q^{85} - 1062 q^{87} + 648 q^{89} + 198 q^{91} + 462 q^{93} - 252 q^{95} + 702 q^{97} - 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

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