LMFDB - Embedded newform 432.3.bc.b.209.4

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 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			209.4
Character	$\chi$	$=$	432.209
Dual form			432.3.bc.b.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31935 - 2.69431i) q^{3} +(-5.13754 + 0.905886i) q^{5} +(8.93347 + 7.49607i) q^{7} +(-5.51862 - 7.10949i) q^{9} +O(q^{10})$	\(q+(1.31935 - 2.69431i) q^{3} +(-5.13754 + 0.905886i) q^{5} +(8.93347 + 7.49607i) q^{7} +(-5.51862 - 7.10949i) q^{9} +(-16.7592 - 2.95510i) q^{11} +(-12.2141 - 4.44559i) q^{13} +(-4.33749 + 15.0373i) q^{15} +(-24.5630 + 14.1815i) q^{17} +(13.9412 - 24.1469i) q^{19} +(31.9831 - 14.1796i) q^{21} +(-6.09173 - 7.25984i) q^{23} +(2.08134 - 0.757544i) q^{25} +(-26.4362 + 5.48893i) q^{27} +(4.43920 + 12.1966i) q^{29} +(-11.4748 + 9.62853i) q^{31} +(-30.0733 + 41.2557i) q^{33} +(-52.6866 - 30.4186i) q^{35} +(-19.3390 - 33.4961i) q^{37} +(-28.0926 + 27.0434i) q^{39} +(-0.663254 + 1.82228i) q^{41} +(-9.15032 + 51.8940i) q^{43} +(34.7925 + 31.5260i) q^{45} +(-1.66892 + 1.98894i) q^{47} +(15.1070 + 85.6762i) q^{49} +(5.80197 + 84.8907i) q^{51} +14.7096i q^{53} +88.7782 q^{55} +(-46.6659 - 69.4203i) q^{57} +(16.7995 - 2.96221i) q^{59} +(-17.6298 - 14.7932i) q^{61} +(3.99288 - 104.880i) q^{63} +(66.7778 + 11.7747i) q^{65} +(-50.8610 - 18.5119i) q^{67} +(-27.5974 + 6.83472i) q^{69} +(73.9041 - 42.6686i) q^{71} +(-1.73700 + 3.00857i) q^{73} +(0.704957 - 6.60723i) q^{75} +(-127.566 - 152.028i) q^{77} +(15.2280 - 5.54254i) q^{79} +(-20.0898 + 78.4691i) q^{81} +(31.4813 + 86.4941i) q^{83} +(113.347 - 95.1090i) q^{85} +(38.7183 + 4.13104i) q^{87} +(-55.7558 - 32.1906i) q^{89} +(-75.7903 - 131.273i) q^{91} +(10.8029 + 43.6202i) q^{93} +(-49.7492 + 136.685i) q^{95} +(7.70330 - 43.6876i) q^{97} +(71.4785 + 135.458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * 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
$3$	1.31935	−	2.69431i	0.439784	−	0.898103i
$3$	1.31935	−	2.69431i	0.439784	−	0.898103i
$4$		0			0
$5$	−5.13754	+	0.905886i	−1.02751	+	0.181177i	−0.661900	−	0.749592i	$-0.730250\pi$
$5$	−5.13754	+	0.905886i	−1.02751	+	0.181177i	−0.365607	+	0.930769i	$0.619139\pi$
$6$		0			0
$7$	8.93347	+	7.49607i	1.27621	+	1.07087i	0.993755	+	0.111586i	$0.0355931\pi$
$7$	8.93347	+	7.49607i	1.27621	+	1.07087i	0.282455	+	0.959281i	$0.408851\pi$
$8$		0			0
$9$	−5.51862	−	7.10949i	−0.613179	−	0.789944i
$10$		0			0
$11$	−16.7592	−	2.95510i	−1.52357	−	0.268646i	−0.651733	−	0.758448i	$-0.725958\pi$
$11$	−16.7592	−	2.95510i	−1.52357	−	0.268646i	−0.871833	+	0.489803i	$0.837069\pi$
$12$		0			0
$13$	−12.2141	−	4.44559i	−0.939550	−	0.341968i	−0.173562	−	0.984823i	$-0.555528\pi$
$13$	−12.2141	−	4.44559i	−0.939550	−	0.341968i	−0.765988	+	0.642855i	$0.777750\pi$
$14$		0			0
$15$	−4.33749	+	15.0373i	−0.289166	+	1.00249i
$16$		0			0
$17$	−24.5630	+	14.1815i	−1.44488	+	0.834203i	−0.998170	−	0.0604744i	$-0.980739\pi$
$17$	−24.5630	+	14.1815i	−1.44488	+	0.834203i	−0.446713	+	0.894678i	$0.647405\pi$
$18$		0			0
$19$	13.9412	−	24.1469i	0.733749	−	1.27089i	−0.221521	−	0.975156i	$-0.571102\pi$
$19$	13.9412	−	24.1469i	0.733749	−	1.27089i	0.955270	−	0.295735i	$-0.0955646\pi$
$20$		0			0
$21$	31.9831	−	14.1796i	1.52301	−	0.675218i
$22$		0			0
$23$	−6.09173	−	7.25984i	−0.264858	−	0.315645i	0.617182	−	0.786821i	$-0.288274\pi$
$23$	−6.09173	−	7.25984i	−0.264858	−	0.315645i	−0.882040	+	0.471175i	$0.843830\pi$
$24$		0			0
$25$	2.08134	−	0.757544i	0.0832534	−	0.0303018i
$26$		0			0
$27$	−26.4362	+	5.48893i	−0.979118	+	0.203294i
$28$		0			0
$29$	4.43920	+	12.1966i	0.153076	+	0.420573i	0.992399	−	0.123060i	$-0.0392707\pi$
$29$	4.43920	+	12.1966i	0.153076	+	0.420573i	−0.839323	+	0.543633i	$0.817049\pi$
$30$		0			0
$31$	−11.4748	+	9.62853i	−0.370156	+	0.310598i	−0.808823	−	0.588052i	$-0.799895\pi$
$31$	−11.4748	+	9.62853i	−0.370156	+	0.310598i	0.438667	+	0.898650i	$0.355451\pi$
$32$		0			0
$33$	−30.0733	+	41.2557i	−0.911312	+	1.25017i
$34$		0			0
$35$	−52.6866	−	30.4186i	−1.50533	−	0.869103i
$36$		0			0
$37$	−19.3390	−	33.4961i	−0.522676	−	0.905301i	−0.999652	−	0.0263844i	$-0.991601\pi$
$37$	−19.3390	−	33.4961i	−0.522676	−	0.905301i	0.476976	−	0.878916i	$-0.341733\pi$
$38$		0			0
$39$	−28.0926	+	27.0434i	−0.720322	+	0.693421i
$40$		0			0
$41$	−0.663254	+	1.82228i	−0.0161769	+	0.0444458i	−0.947518	−	0.319702i	$-0.896417\pi$
$41$	−0.663254	+	1.82228i	−0.0161769	+	0.0444458i	0.931341	+	0.364147i	$0.118640\pi$
$42$		0			0
$43$	−9.15032	+	51.8940i	−0.212798	+	1.20684i	0.671889	+	0.740652i	$0.265483\pi$
$43$	−9.15032	+	51.8940i	−0.212798	+	1.20684i	−0.884687	+	0.466186i	$0.845628\pi$
$44$		0			0
$45$	34.7925	+	31.5260i	0.773166	+	0.700579i
$46$		0			0
$47$	−1.66892	+	1.98894i	−0.0355088	+	0.0423178i	−0.783507	−	0.621383i	$-0.786571\pi$
$47$	−1.66892	+	1.98894i	−0.0355088	+	0.0423178i	0.747998	+	0.663701i	$0.231015\pi$
$48$		0			0
$49$	15.1070	+	85.6762i	0.308306	+	1.74849i
$50$		0			0
$51$	5.80197	+	84.8907i	0.113764	+	1.66452i
$52$		0			0
$53$			14.7096i			0.277539i	0.990325	+	0.138770i	$0.0443147\pi$
$53$			14.7096i			0.277539i	−0.990325	+	0.138770i	$0.955685\pi$
$54$		0			0
$55$	88.7782			1.61415
$56$		0			0
$57$	−46.6659	−	69.4203i	−0.818700	−	1.21790i
$58$		0			0
$59$	16.7995	−	2.96221i	0.284738	−	0.0502070i	−0.0294551	−	0.999566i	$-0.509377\pi$
$59$	16.7995	−	2.96221i	0.284738	−	0.0502070i	0.314193	+	0.949359i	$0.398266\pi$
$60$		0			0
$61$	−17.6298	−	14.7932i	−0.289013	−	0.242511i	0.486741	−	0.873547i	$-0.338186\pi$
$61$	−17.6298	−	14.7932i	−0.289013	−	0.242511i	−0.775754	+	0.631036i	$0.782630\pi$
$62$		0			0
$63$	3.99288	−	104.880i	0.0633790	−	1.66477i
$64$		0			0
$65$	66.7778	+	11.7747i	1.02735	+	0.181150i
$66$		0			0
$67$	−50.8610	−	18.5119i	−0.759119	−	0.276297i	−0.0666813	−	0.997774i	$-0.521241\pi$
$67$	−50.8610	−	18.5119i	−0.759119	−	0.276297i	−0.692438	+	0.721478i	$0.743463\pi$
$68$		0			0
$69$	−27.5974	+	6.83472i	−0.399962	+	0.0990539i
$70$		0			0
$71$	73.9041	−	42.6686i	1.04090	−	0.600966i	0.120814	−	0.992675i	$-0.461450\pi$
$71$	73.9041	−	42.6686i	1.04090	−	0.600966i	0.920089	+	0.391710i	$0.128116\pi$
$72$		0			0
$73$	−1.73700	+	3.00857i	−0.0237945	+	0.0412132i	−0.877677	−	0.479252i	$-0.840908\pi$
$73$	−1.73700	+	3.00857i	−0.0237945	+	0.0412132i	0.853883	+	0.520465i	$0.174241\pi$
$74$		0			0
$75$	0.704957	−	6.60723i	0.00939943	−	0.0880964i
$76$		0			0
$77$	−127.566	−	152.028i	−1.65671	−	1.97439i
$78$		0			0
$79$	15.2280	−	5.54254i	0.192759	−	0.0701587i	−0.243837	−	0.969816i	$-0.578406\pi$
$79$	15.2280	−	5.54254i	0.192759	−	0.0701587i	0.436596	+	0.899658i	$0.356184\pi$
$80$		0			0
$81$	−20.0898	+	78.4691i	−0.248022	+	0.968754i
$82$		0			0
$83$	31.4813	+	86.4941i	0.379292	+	1.04210i	0.971650	+	0.236422i	$0.0759749\pi$
$83$	31.4813	+	86.4941i	0.379292	+	1.04210i	−0.592358	+	0.805675i	$0.701803\pi$
$84$		0			0
$85$	113.347	−	95.1090i	1.33349	−	1.11893i
$86$		0			0
$87$	38.7183	+	4.13104i	0.445038	+	0.0474833i
$88$		0			0
$89$	−55.7558	−	32.1906i	−0.626469	−	0.361692i	0.152914	−	0.988239i	$-0.451134\pi$
$89$	−55.7558	−	32.1906i	−0.626469	−	0.361692i	−0.779383	+	0.626547i	$0.784468\pi$
$90$		0			0
$91$	−75.7903	−	131.273i	−0.832860	−	1.44256i
$92$		0			0
$93$	10.8029	+	43.6202i	0.116160	+	0.469034i
$94$		0			0
$95$	−49.7492	+	136.685i	−0.523676	+	1.43879i
$96$		0			0
$97$	7.70330	−	43.6876i	0.0794154	−	0.450387i	−0.919007	−	0.394241i	$-0.871008\pi$
$97$	7.70330	−	43.6876i	0.0794154	−	0.450387i	0.998423	−	0.0561463i	$-0.0178813\pi$
$98$		0			0
$99$	71.4785	+	135.458i	0.722005	+	1.36826i
$100$		0			0
$101$	4.15348	−	4.94993i	0.0411236	−	0.0490092i	−0.745091	−	0.666963i	$-0.767594\pi$
$101$	4.15348	−	4.94993i	0.0411236	−	0.0490092i	0.786214	+	0.617954i	$0.212038\pi$
$102$		0			0
$103$	−3.14264	−	17.8228i	−0.0305111	−	0.173037i	0.965744	−	0.259495i	$-0.0835562\pi$
$103$	−3.14264	−	17.8228i	−0.0305111	−	0.173037i	−0.996255	+	0.0864583i	$0.972445\pi$
$104$		0			0
$105$	−151.469	+	101.821i	−1.44257	+	0.969725i
$106$		0			0
$107$		−	184.373i		−	1.72311i	−0.507661	−	0.861557i	$-0.669490\pi$
$107$		−	184.373i		−	1.72311i	0.507661	−	0.861557i	$-0.330510\pi$
$108$		0			0
$109$	−13.0774			−0.119976			−0.0599882	−	0.998199i	$-0.519106\pi$
$109$	−13.0774			−0.119976			−0.0599882	+	0.998199i	$0.519106\pi$
$110$		0			0
$111$	−115.764	+	7.91204i	−1.04292	+	0.0712797i
$112$		0			0
$113$	−30.9310	+	5.45397i	−0.273726	+	0.0482652i	−0.308826	−	0.951119i	$-0.599936\pi$
$113$	−30.9310	+	5.45397i	−0.273726	+	0.0482652i	0.0351002	+	0.999384i	$0.488825\pi$
$114$		0			0
$115$	37.8731	+	31.7793i	0.329331	+	0.276342i
$116$		0			0
$117$	35.7993	+	111.370i	0.305977	+	0.951879i
$118$		0			0
$119$	−325.738	−	57.4364i	−2.73729	−	0.482659i
$120$		0			0
$121$	158.436	+	57.6661i	1.30939	+	0.476580i
$122$		0			0
$123$	4.03471	+	4.19124i	0.0328025	+	0.0340751i
$124$		0			0
$125$	102.940	−	59.4325i	0.823521	−	0.475460i
$126$		0			0
$127$	52.0434	−	90.1418i	0.409790	−	0.709778i	−0.585076	−	0.810979i	$-0.698935\pi$
$127$	52.0434	−	90.1418i	0.409790	−	0.709778i	0.994866	+	0.101201i	$0.0322685\pi$
$128$		0			0
$129$	127.746	+	93.1203i	0.990280	+	0.721863i
$130$		0			0
$131$	−29.7988	−	35.5129i	−0.227472	−	0.271091i	0.640221	−	0.768191i	$-0.278843\pi$
$131$	−29.7988	−	35.5129i	−0.227472	−	0.271091i	−0.867693	+	0.497100i	$0.834398\pi$
$132$		0			0
$133$	305.551	−	111.211i	2.29737	−	0.836175i
$134$		0			0
$135$	130.844	−	52.1478i	0.969218	−	0.386280i
$136$		0			0
$137$	−75.3084	−	206.908i	−0.549697	−	1.51028i	−0.834121	−	0.551581i	$-0.814025\pi$
$137$	−75.3084	−	206.908i	−0.549697	−	1.51028i	0.284425	−	0.958698i	$-0.408197\pi$
$138$		0			0
$139$	137.198	−	115.123i	0.987037	−	0.828222i	0.00190072	−	0.999998i	$-0.499395\pi$
$139$	137.198	−	115.123i	0.987037	−	0.828222i	0.985136	+	0.171776i	$0.0549505\pi$
$140$		0			0
$141$	3.15692	+	7.12068i	0.0223895	+	0.0505013i
$142$		0			0
$143$	191.563	+	110.599i	1.33960	+	0.773417i
$144$		0			0
$145$	−33.8553	−	58.6391i	−0.233485	−	0.404408i
$146$		0			0
$147$	250.770	+	72.3341i	1.70592	+	0.492069i
$148$		0			0
$149$	−48.9623	+	134.523i	−0.328606	+	0.902837i	0.659859	+	0.751389i	$0.270616\pi$
$149$	−48.9623	+	134.523i	−0.328606	+	0.902837i	−0.988465	+	0.151448i	$0.951606\pi$
$150$		0			0
$151$	−12.9241	+	73.2964i	−0.0855903	+	0.485407i	0.911637	+	0.410995i	$0.134819\pi$
$151$	−12.9241	+	73.2964i	−0.0855903	+	0.485407i	−0.997228	+	0.0744111i	$0.976292\pi$
$152$		0			0
$153$	236.377	+	96.3685i	1.54495	+	0.629859i
$154$		0			0
$155$	50.2300	−	59.8618i	0.324065	−	0.386205i
$156$		0			0
$157$	5.61396	+	31.8383i	0.0357577	+	0.202792i	0.997453	−	0.0713294i	$-0.0227241\pi$
$157$	5.61396	+	31.8383i	0.0357577	+	0.202792i	−0.961695	+	0.274121i	$0.911613\pi$
$158$		0			0
$159$	39.6322	+	19.4071i	0.249259	+	0.122057i
$160$		0			0
$161$		−	110.520i		−	0.686457i
$162$		0			0
$163$	−99.7820			−0.612160			−0.306080	−	0.952006i	$-0.599017\pi$
$163$	−99.7820			−0.612160			−0.306080	+	0.952006i	$0.599017\pi$
$164$		0			0
$165$	117.130	−	239.196i	0.709877	−	1.44967i
$166$		0			0
$167$	165.964	−	29.2639i	0.993795	−	0.175233i	0.346974	−	0.937875i	$-0.387209\pi$
$167$	165.964	−	29.2639i	0.993795	−	0.175233i	0.646821	+	0.762642i	$0.276098\pi$
$168$		0			0
$169$	−0.0393605	−	0.0330274i	−0.000232903	−	0.000195428i
$170$		0			0
$171$	−248.609	+	34.1425i	−1.45385	+	0.199664i
$172$		0			0
$173$	−134.040	−	23.6349i	−0.774800	−	0.136618i	−0.227752	−	0.973719i	$-0.573137\pi$
$173$	−134.040	−	23.6349i	−0.774800	−	0.136618i	−0.547048	+	0.837101i	$0.684249\pi$
$174$		0			0
$175$	24.2721	+	8.83434i	0.138698	+	0.0504819i
$176$		0			0
$177$	14.1834	−	49.1713i	0.0801322	−	0.277804i
$178$		0			0
$179$	−81.1087	+	46.8281i	−0.453121	+	0.261610i	−0.709147	−	0.705060i	$-0.750920\pi$
$179$	−81.1087	+	46.8281i	−0.453121	+	0.261610i	0.256026	+	0.966670i	$0.417587\pi$
$180$		0			0
$181$	−8.38226	+	14.5185i	−0.0463108	+	0.0802127i	−0.888252	−	0.459357i	$-0.848080\pi$
$181$	−8.38226	+	14.5185i	−0.0463108	+	0.0802127i	0.841941	+	0.539570i	$0.181413\pi$
$182$		0			0
$183$	−63.1173	+	27.9827i	−0.344903	+	0.152911i
$184$		0			0
$185$	129.698	+	154.569i	0.701073	+	0.835506i
$186$		0			0
$187$	453.565	−	165.084i	2.42548	−	0.882802i
$188$		0			0
$189$	−277.312	−	149.132i	−1.46726	−	0.789059i
$190$		0			0
$191$	−35.4147	−	97.3010i	−0.185417	−	0.509430i	0.811804	−	0.583930i	$-0.198486\pi$
$191$	−35.4147	−	97.3010i	−0.185417	−	0.509430i	−0.997221	+	0.0745008i	$0.976264\pi$
$192$		0			0
$193$	−179.148	+	150.323i	−0.928228	+	0.778876i	−0.975498	−	0.220006i	$-0.929392\pi$
$193$	−179.148	+	150.323i	−0.928228	+	0.778876i	0.0472702	+	0.998882i	$0.484948\pi$
$194$		0			0
$195$	119.828	−	164.385i	0.614504	−	0.843001i
$196$		0			0
$197$	193.515	+	111.726i	0.982309	+	0.567136i	0.902966	−	0.429711i	$-0.141385\pi$
$197$	193.515	+	111.726i	0.982309	+	0.567136i	0.0793425	+	0.996847i	$0.474718\pi$
$198$		0			0
$199$	167.619	+	290.325i	0.842306	+	1.45892i	0.887940	+	0.459959i	$0.152136\pi$
$199$	167.619	+	290.325i	0.842306	+	1.45892i	−0.0456336	+	0.998958i	$0.514531\pi$
$200$		0			0
$201$	−116.980	+	112.612i	−0.581992	+	0.560256i
$202$		0			0
$203$	−51.7691	+	142.235i	−0.255020	+	0.700663i
$204$		0			0
$205$	1.75672	−	9.96284i	0.00856936	−	0.0485992i
$206$		0			0
$207$	−17.9959	+	83.3734i	−0.0869366	+	0.402770i
$208$		0			0
$209$	−305.001	+	363.486i	−1.45934	+	1.73917i
$210$		0			0
$211$	70.9699	+	402.490i	0.336350	+	1.90754i	0.413474	+	0.910516i	$0.364315\pi$
$211$	70.9699	+	402.490i	0.336350	+	1.90754i	−0.0771240	+	0.997022i	$0.524574\pi$
$212$		0			0
$213$	−17.4567	−	255.415i	−0.0819565	−	1.19913i
$214$		0			0
$215$		−	274.897i		−	1.27859i
$216$		0			0
$217$	−174.686			−0.805005
$218$		0			0
$219$	5.81430	+	8.64937i	0.0265493	+	0.0394948i
$220$		0			0
$221$	363.061	−	64.0174i	1.64281	−	0.289672i
$222$		0			0
$223$	−120.793	−	101.358i	−0.541674	−	0.454518i	0.330436	−	0.943828i	$-0.392804\pi$
$223$	−120.793	−	101.358i	−0.541674	−	0.454518i	−0.872110	+	0.489310i	$0.837249\pi$
$224$		0			0
$225$	−16.8718	−	10.6166i	−0.0749860	−	0.0471851i
$226$		0			0
$227$	−277.370	−	48.9078i	−1.22189	−	0.215453i	−0.474753	−	0.880119i	$-0.657463\pi$
$227$	−277.370	−	48.9078i	−1.22189	−	0.215453i	−0.747141	+	0.664666i	$0.768574\pi$
$228$		0			0
$229$	−108.465	−	39.4779i	−0.473645	−	0.172393i	0.0941577	−	0.995557i	$-0.469984\pi$
$229$	−108.465	−	39.4779i	−0.473645	−	0.172393i	−0.567803	+	0.823165i	$0.692206\pi$
$230$		0			0
$231$	−577.915	+	143.125i	−2.50180	+	0.619590i
$232$		0			0
$233$	−195.583	+	112.920i	−0.839414	+	0.484636i	−0.857065	−	0.515208i	$-0.827715\pi$
$233$	−195.583	+	112.920i	−0.839414	+	0.484636i	0.0176510	+	0.999844i	$0.494381\pi$
$234$		0			0
$235$	6.77236	−	11.7301i	0.0288186	−	0.0499152i
$236$		0			0
$237$	5.15779	−	48.3415i	0.0217628	−	0.203973i
$238$		0			0
$239$	113.450	+	135.204i	0.474685	+	0.565707i	0.949254	−	0.314511i	$-0.101841\pi$
$239$	113.450	+	135.204i	0.474685	+	0.565707i	−0.474569	+	0.880218i	$0.657396\pi$
$240$		0			0
$241$	−66.1775	+	24.0866i	−0.274596	+	0.0999446i	−0.475647	−	0.879636i	$-0.657786\pi$
$241$	−66.1775	+	24.0866i	−0.274596	+	0.0999446i	0.201052	+	0.979581i	$0.435564\pi$
$242$		0			0
$243$	184.915	+	157.657i	0.760966	+	0.648792i
$244$		0			0
$245$	−155.226	−	426.479i	−0.633574	−	1.74073i
$246$		0			0
$247$	−277.628	+	232.957i	−1.12400	+	0.943146i
$248$		0			0
$249$	274.577	+	29.2959i	1.10272	+	0.117654i
$250$		0			0
$251$	−239.695	−	138.388i	−0.954959	−	0.551346i	−0.0603413	−	0.998178i	$-0.519219\pi$
$251$	−239.695	−	138.388i	−0.954959	−	0.551346i	−0.894618	+	0.446832i	$0.852552\pi$
$252$		0			0
$253$	80.6391	+	139.671i	0.318732	+	0.552060i
$254$		0			0
$255$	−106.709	−	430.873i	−0.418467	−	1.68970i
$256$		0			0
$257$	−125.873	+	345.834i	−0.489780	+	1.34566i	0.411100	+	0.911590i	$0.365145\pi$
$257$	−125.873	+	345.834i	−0.489780	+	1.34566i	−0.900880	+	0.434069i	$0.857077\pi$
$258$		0			0
$259$	78.3250	−	444.203i	0.302413	−	1.71507i
$260$		0			0
$261$	62.2134	−	98.8689i	0.238366	−	0.378808i
$262$		0			0
$263$	237.412	−	282.937i	0.902709	−	1.07581i	−0.0940665	−	0.995566i	$-0.529987\pi$
$263$	237.412	−	282.937i	0.902709	−	1.07581i	0.996776	−	0.0802408i	$-0.0255689\pi$
$264$		0			0
$265$	−13.3252	−	75.5710i	−0.0502838	−	0.285173i
$266$		0			0
$267$	−160.293	+	107.753i	−0.600348	+	0.403568i
$268$		0			0
$269$		−	484.753i		−	1.80205i	−0.433762	−	0.901027i	$-0.642814\pi$
$269$		−	484.753i		−	1.80205i	0.433762	−	0.901027i	$-0.357186\pi$
$270$		0			0
$271$	−361.878			−1.33534			−0.667672	−	0.744455i	$-0.732709\pi$
$271$	−361.878			−1.33534			−0.667672	+	0.744455i	$0.732709\pi$
$272$		0			0
$273$	−453.683	+	31.0076i	−1.66184	+	0.113581i
$274$		0			0
$275$	−37.1202	+	6.54529i	−0.134983	+	0.0238011i
$276$		0			0
$277$	−158.794	−	133.244i	−0.573263	−	0.481024i	0.309464	−	0.950911i	$-0.399850\pi$
$277$	−158.794	−	133.244i	−0.573263	−	0.481024i	−0.882727	+	0.469887i	$0.844295\pi$
$278$		0			0
$279$	131.779	+	28.4441i	0.472327	+	0.101950i
$280$		0			0
$281$	323.449	+	57.0328i	1.15106	+	0.202964i	0.716440	−	0.697648i	$-0.245770\pi$
$281$	323.449	+	57.0328i	1.15106	+	0.202964i	0.434624	+	0.900612i	$0.356881\pi$
$282$		0			0
$283$	88.6536	+	32.2673i	0.313264	+	0.114019i	0.493867	−	0.869537i	$-0.335583\pi$
$283$	88.6536	+	32.2673i	0.313264	+	0.114019i	−0.180604	+	0.983556i	$0.557805\pi$
$284$		0			0
$285$	302.635	+	314.375i	1.06188	+	1.10307i
$286$		0			0
$287$	−19.5851	+	11.3074i	−0.0682407	+	0.0393988i
$288$		0			0
$289$	257.727	−	446.397i	0.891790	−	1.54463i
$290$		0			0
$291$	−107.544	−	78.3944i	−0.369569	−	0.269397i
$292$		0			0
$293$	267.257	+	318.504i	0.912139	+	1.08704i	0.995891	+	0.0905579i	$0.0288650\pi$
$293$	267.257	+	318.504i	0.912139	+	1.08704i	−0.0837526	+	0.996487i	$0.526691\pi$
$294$		0			0
$295$	−83.6248	+	30.4369i	−0.283474	+	0.103176i
$296$		0			0
$297$	459.270	−	13.8686i	1.54637	−	0.0466956i
$298$		0			0
$299$	42.1310	+	115.754i	0.140907	+	0.387137i
$300$		0			0
$301$	−470.745	+	395.002i	−1.56394	+	1.31230i
$302$		0			0
$303$	−7.85673	−	17.7215i	−0.0259298	−	0.0584867i
$304$		0			0
$305$	103.975	+	60.0298i	0.340900	+	0.196819i
$306$		0			0
$307$	−259.704	−	449.820i	−0.845941	−	1.46521i	−0.884802	−	0.465968i	$-0.845706\pi$
$307$	−259.704	−	449.820i	−0.845941	−	1.46521i	0.0388611	−	0.999245i	$-0.487627\pi$
$308$		0			0
$309$	−52.1664	−	15.0473i	−0.168823	−	0.0486968i
$310$		0			0
$311$	23.9377	−	65.7684i	0.0769702	−	0.211474i	−0.895240	−	0.445585i	$-0.852996\pi$
$311$	23.9377	−	65.7684i	0.0769702	−	0.211474i	0.972210	+	0.234111i	$0.0752179\pi$
$312$		0			0
$313$	−52.1791	+	295.923i	−0.166706	+	0.945439i	0.780581	+	0.625055i	$0.214923\pi$
$313$	−52.1791	+	295.923i	−0.166706	+	0.945439i	−0.947287	+	0.320385i	$0.896188\pi$
$314$		0			0
$315$	74.4961	+	542.444i	0.236496	+	1.72204i
$316$		0			0
$317$	−281.650	+	335.657i	−0.888485	+	1.05886i	0.109409	+	0.993997i	$0.465104\pi$
$317$	−281.650	+	335.657i	−0.888485	+	1.05886i	−0.997894	+	0.0648589i	$0.979340\pi$
$318$		0			0
$319$	−38.3554	−	217.524i	−0.120236	−	0.681894i
$320$		0			0
$321$	−496.758	−	243.253i	−1.54753	−	0.757798i
$322$		0			0
$323$			790.828i			2.44838i
$324$		0			0
$325$	−28.7895			−0.0885830
$326$		0			0
$327$	−17.2537	+	35.2346i	−0.0527637	+	0.107751i
$328$		0			0
$329$	−29.8184	+	5.25779i	−0.0906334	+	0.0159811i
$330$		0			0
$331$	−83.1781	−	69.7947i	−0.251293	−	0.210860i	0.508436	−	0.861100i	$-0.330224\pi$
$331$	−83.1781	−	69.7947i	−0.251293	−	0.210860i	−0.759729	+	0.650240i	$0.774668\pi$
$332$		0			0
$333$	−131.416	+	322.343i	−0.394642	+	0.967996i
$334$		0			0
$335$	278.070	+	49.0312i	0.830059	+	0.146362i
$336$		0			0
$337$	−515.109	−	187.484i	−1.52851	−	0.556334i	−0.565257	−	0.824915i	$-0.691223\pi$
$337$	−515.109	−	187.484i	−1.52851	−	0.556334i	−0.963257	+	0.268581i	$0.913445\pi$
$338$		0			0
$339$	−26.1142	+	90.5335i	−0.0770331	+	0.267060i
$340$		0			0
$341$	220.763	−	127.457i	0.647398	−	0.373775i
$342$		0			0
$343$	−221.562	+	383.756i	−0.645953	+	1.11882i
$344$		0			0
$345$	135.591	−	60.1137i	0.393018	−	0.174243i
$346$		0			0
$347$	−153.713	−	183.189i	−0.442978	−	0.527921i	0.497642	−	0.867383i	$-0.334199\pi$
$347$	−153.713	−	183.189i	−0.442978	−	0.527921i	−0.940620	+	0.339462i	$0.889755\pi$
$348$		0			0
$349$	431.921	−	157.206i	1.23760	−	0.450448i	0.361403	−	0.932410i	$-0.382298\pi$
$349$	431.921	−	157.206i	1.23760	−	0.450448i	0.876192	+	0.481962i	$0.160076\pi$
$350$		0			0
$351$	347.297	+	50.4817i	0.989450	+	0.143822i
$352$		0			0
$353$	−144.709	−	397.585i	−0.409940	−	1.12630i	−0.957222	−	0.289354i	$-0.906560\pi$
$353$	−144.709	−	397.585i	−0.409940	−	1.12630i	0.547282	−	0.836948i	$-0.315663\pi$
$354$		0			0
$355$	−341.032	+	286.160i	−0.960654	+	0.806084i
$356$		0			0
$357$	−584.515	+	801.860i	−1.63730	+	2.24611i
$358$		0			0
$359$	585.472	+	338.023i	1.63084	+	0.941567i	0.983834	+	0.179084i	$0.0573134\pi$
$359$	585.472	+	338.023i	1.63084	+	0.941567i	0.647008	+	0.762483i	$0.276020\pi$
$360$		0			0
$361$	−208.216	−	360.641i	−0.576776	−	0.999005i
$362$		0			0
$363$	364.404	−	350.795i	1.00387	−	0.966377i
$364$		0			0
$365$	6.19846	−	17.0301i	0.0169821	−	0.0466579i
$366$		0			0
$367$	−80.7428	+	457.915i	−0.220008	+	1.24772i	0.651995	+	0.758223i	$0.273932\pi$
$367$	−80.7428	+	457.915i	−0.220008	+	1.24772i	−0.872002	+	0.489501i	$0.837179\pi$
$368$		0			0
$369$	16.6157	−	5.34104i	0.0450290	−	0.0144744i
$370$		0			0
$371$	−110.264	+	131.407i	−0.297207	+	0.354198i
$372$		0			0
$373$	−13.5537	−	76.8670i	−0.0363371	−	0.206078i	0.961234	−	0.275734i	$-0.0889209\pi$
$373$	−13.5537	−	76.8670i	−0.0363371	−	0.206078i	−0.997571	+	0.0696562i	$0.977810\pi$
$374$		0			0
$375$	−24.3153	−	355.765i	−0.0648407	−	0.948707i
$376$		0			0
$377$		−	168.706i		−	0.447496i
$378$		0			0
$379$	−66.6563			−0.175874			−0.0879371	−	0.996126i	$-0.528027\pi$
$379$	−66.6563			−0.175874			−0.0879371	+	0.996126i	$0.528027\pi$
$380$		0			0
$381$	−174.206	−	259.150i	−0.457234	−	0.680183i
$382$		0			0
$383$	−82.5111	+	14.5489i	−0.215434	+	0.0379868i	−0.280323	−	0.959906i	$-0.590442\pi$
$383$	−82.5111	+	14.5489i	−0.215434	+	0.0379868i	0.0648895	+	0.997892i	$0.479331\pi$
$384$		0			0
$385$	793.097	+	665.487i	2.05999	+	1.72854i
$386$		0			0
$387$	419.437	−	221.329i	1.08382	−	0.571910i
$388$		0			0
$389$	−523.234	−	92.2603i	−1.34507	−	0.237173i	−0.545687	−	0.837989i	$-0.683731\pi$
$389$	−523.234	−	92.2603i	−1.34507	−	0.237173i	−0.799387	+	0.600816i	$0.794842\pi$
$390$		0			0
$391$	252.586	+	91.9339i	0.646001	+	0.235125i
$392$		0			0
$393$	−134.998	+	33.4333i	−0.343506	+	0.0850720i
$394$		0			0
$395$	−73.2135	+	42.2698i	−0.185351	+	0.107012i
$396$		0			0
$397$	−230.531	+	399.291i	−0.580682	+	1.00577i	0.414717	+	0.909950i	$0.363881\pi$
$397$	−230.531	+	399.291i	−0.580682	+	1.00577i	−0.995399	+	0.0958197i	$0.969453\pi$
$398$		0			0
$399$	103.491	−	969.975i	0.259377	−	2.43101i
$400$		0			0
$401$	127.933	+	152.465i	0.319036	+	0.380212i	0.901599	−	0.432574i	$-0.142394\pi$
$401$	127.933	+	152.465i	0.319036	+	0.380212i	−0.582563	+	0.812786i	$0.697950\pi$
$402$		0			0
$403$	182.960	−	66.5919i	0.453994	−	0.165240i
$404$		0			0
$405$	32.1278	−	421.337i	0.0793280	−	1.04034i
$406$		0			0
$407$	225.122	+	618.518i	0.553126	+	1.51970i
$408$		0			0
$409$	95.6855	−	80.2897i	0.233950	−	0.196307i	−0.518274	−	0.855214i	$-0.673425\pi$
$409$	95.6855	−	80.2897i	0.233950	−	0.196307i	0.752224	+	0.658907i	$0.228981\pi$
$410$		0			0
$411$	−656.833	−	70.0807i	−1.59813	−	0.170513i
$412$		0			0
$413$	172.283	+	99.4676i	0.417150	+	0.240842i
$414$		0			0
$415$	−240.090	−	415.848i	−0.578530	−	1.00204i
$416$		0			0
$417$	−129.164	−	521.542i	−0.309746	−	1.25070i
$418$		0			0
$419$	2.14955	−	5.90584i	0.00513019	−	0.0140951i	−0.937101	−	0.349058i	$-0.886502\pi$
$419$	2.14955	−	5.90584i	0.00513019	−	0.0140951i	0.942231	+	0.334963i	$0.108724\pi$
$420$		0			0
$421$	−70.5491	+	400.104i	−0.167575	+	0.950365i	0.778795	+	0.627279i	$0.215831\pi$
$421$	−70.5491	+	400.104i	−0.167575	+	0.950365i	−0.946370	+	0.323086i	$0.895280\pi$
$422$		0			0
$423$	23.3504	+	0.888969i	0.0552020	+	0.00210158i
$424$		0			0
$425$	−40.3808	+	48.1239i	−0.0950136	+	0.113233i
$426$		0			0
$427$	−46.6047	−	264.308i	−0.109144	−	0.618989i
$428$		0			0
$429$	550.726	−	370.210i	1.28374	−	0.862961i
$430$		0			0
$431$		−	605.028i		−	1.40378i	−0.712287	−	0.701889i	$-0.752340\pi$
$431$		−	605.028i		−	1.40378i	0.712287	−	0.701889i	$-0.247660\pi$
$432$		0			0
$433$	535.568			1.23688			0.618439	−	0.785833i	$-0.287766\pi$
$433$	535.568			1.23688			0.618439	+	0.785833i	$0.287766\pi$
$434$		0			0
$435$	−202.659	+	13.8510i	−0.465883	+	0.0318414i
$436$		0			0
$437$	−260.229	+	45.8854i	−0.595490	+	0.105001i
$438$		0			0
$439$	367.682	+	308.522i	0.837545	+	0.702784i	0.957010	−	0.290055i	$-0.0936735\pi$
$439$	367.682	+	308.522i	0.837545	+	0.702784i	−0.119465	+	0.992838i	$0.538118\pi$
$440$		0			0
$441$	525.744	−	580.217i	1.19216	−	1.31568i
$442$		0			0
$443$	−478.290	−	84.3355i	−1.07966	−	0.190373i	−0.394596	−	0.918855i	$-0.629115\pi$
$443$	−478.290	−	84.3355i	−1.07966	−	0.190373i	−0.685066	+	0.728481i	$0.740227\pi$
$444$		0			0
$445$	315.608	+	114.872i	0.709232	+	0.258139i
$446$		0			0
$447$	297.847	+	309.403i	0.666325	+	0.692176i
$448$		0			0
$449$	423.011	−	244.226i	0.942118	−	0.543932i	0.0514944	−	0.998673i	$-0.483602\pi$
$449$	423.011	−	244.226i	0.942118	−	0.543932i	0.890624	+	0.454741i	$0.150268\pi$
$450$		0			0
$451$	16.5007	−	28.5800i	0.0365868	−	0.0633702i
$452$		0			0
$453$	180.432	+	131.525i	0.398304	+	0.290343i
$454$		0			0
$455$	508.293	+	605.760i	1.11713	+	1.33134i
$456$		0			0
$457$	−561.056	+	204.208i	−1.22769	+	0.446844i	−0.872807	−	0.488065i	$-0.837703\pi$
$457$	−561.056	+	204.208i	−1.22769	+	0.446844i	−0.354887	+	0.934909i	$0.615481\pi$
$458$		0			0
$459$	571.511	−	509.728i	1.24512	−	1.11052i
$460$		0			0
$461$	289.819	+	796.271i	0.628675	+	1.72727i	0.684685	+	0.728839i	$0.259940\pi$
$461$	289.819	+	796.271i	0.628675	+	1.72727i	−0.0560100	+	0.998430i	$0.517838\pi$
$462$		0			0
$463$	−433.712	+	363.927i	−0.936743	+	0.786020i	−0.977015	−	0.213168i	$-0.931622\pi$
$463$	−433.712	+	363.927i	−0.936743	+	0.786020i	0.0402729	+	0.999189i	$0.487177\pi$
$464$		0			0
$465$	−95.0151	−	214.314i	−0.204334	−	0.460890i
$466$		0			0
$467$	265.877	+	153.504i	0.569330	+	0.328703i	0.756882	−	0.653552i	$-0.226722\pi$
$467$	265.877	+	153.504i	0.569330	+	0.328703i	−0.187551	+	0.982255i	$0.560055\pi$
$468$		0			0
$469$	−315.599	−	546.633i	−0.672918	−	1.16553i
$470$		0			0
$471$	93.1891	+	26.8803i	0.197854	+	0.0570706i
$472$		0			0
$473$	306.705	−	842.664i	0.648424	−	1.78153i
$474$		0			0
$475$	10.7240	−	60.8190i	0.0225769	−	0.128040i
$476$		0			0
$477$	104.578	−	81.1765i	0.219240	−	0.170181i
$478$		0			0
$479$	239.776	−	285.754i	0.500576	−	0.596564i	−0.455298	−	0.890339i	$-0.650467\pi$
$479$	239.776	−	285.754i	0.500576	−	0.596564i	0.955875	+	0.293775i	$0.0949117\pi$
$480$		0			0
$481$	87.2994	+	495.100i	0.181496	+	1.02931i
$482$		0			0
$483$	−297.774	−	145.814i	−0.616509	−	0.301893i
$484$		0			0
$485$			231.425i			0.477164i
$486$		0			0
$487$	−596.051			−1.22392			−0.611962	−	0.790887i	$-0.709619\pi$
$487$	−596.051			−1.22392			−0.611962	+	0.790887i	$0.709619\pi$
$488$		0			0
$489$	−131.648	+	268.844i	−0.269218	+	0.549783i
$490$		0			0
$491$	−172.551	+	30.4253i	−0.351427	+	0.0619660i	−0.346575	−	0.938022i	$-0.612655\pi$
$491$	−172.551	+	30.4253i	−0.351427	+	0.0619660i	−0.00485164	+	0.999988i	$0.501544\pi$
$492$		0			0
$493$	−282.006	−	236.631i	−0.572020	−	0.479982i
$494$		0			0
$495$	−489.932	−	631.168i	−0.989763	−	1.27509i
$496$		0			0
$497$	980.066	+	172.812i	1.97196	+	0.347711i
$498$		0			0
$499$	−88.9017	−	32.3576i	−0.178160	−	0.0648448i	0.251400	−	0.967883i	$-0.419109\pi$
$499$	−88.9017	−	32.3576i	−0.178160	−	0.0648448i	−0.429560	+	0.903038i	$0.641331\pi$
$500$		0			0
$501$	140.119	−	485.767i	0.279678	−	0.969595i
$502$		0			0
$503$	161.807	−	93.4192i	0.321683	−	0.185724i	−0.330459	−	0.943820i	$-0.607204\pi$
$503$	161.807	−	93.4192i	0.321683	−	0.185724i	0.652143	+	0.758096i	$0.273870\pi$
$504$		0			0
$505$	−16.8546	+	29.1930i	−0.0333754	+	0.0578080i
$506$		0			0
$507$	−0.140917	+	0.0624747i	−0.000277942	+	0.000123224i
$508$		0			0
$509$	289.843	+	345.421i	0.569435	+	0.678627i	0.971515	−	0.236978i	$-0.0761569\pi$
$509$	289.843	+	345.421i	0.569435	+	0.678627i	−0.402080	+	0.915605i	$0.631712\pi$
$510$		0			0
$511$	−38.0698	+	13.8563i	−0.0745006	+	0.0271160i
$512$		0			0
$513$	−236.012	+	714.875i	−0.460063	+	1.39352i
$514$		0			0
$515$	32.2909	+	88.7185i	0.0627007	+	0.172269i
$516$		0			0
$517$	33.8473	−	28.4012i	0.0654686	−	0.0549347i
$518$		0			0
$519$	−240.526	+	329.964i	−0.463442	+	0.635768i
$520$		0			0
$521$	−96.0094	−	55.4311i	−0.184279	−	0.106394i	0.405022	−	0.914307i	$-0.367264\pi$
$521$	−96.0094	−	55.4311i	−0.184279	−	0.106394i	−0.589302	+	0.807913i	$0.700597\pi$
$522$		0			0
$523$	59.5704	+	103.179i	0.113901	+	0.197283i	0.917340	−	0.398104i	$-0.130332\pi$
$523$	59.5704	+	103.179i	0.113901	+	0.197283i	−0.803439	+	0.595388i	$0.796999\pi$
$524$		0			0
$525$	55.8260	−	53.7411i	0.106335	−	0.102364i
$526$		0			0
$527$	145.310	−	399.235i	0.275730	−	0.757562i
$528$		0			0
$529$	76.2638	−	432.513i	0.144166	−	0.817605i
$530$		0			0
$531$	−113.770	−	103.089i	−0.214256	−	0.194141i
$532$		0			0
$533$	16.2022	−	19.3090i	0.0303981	−	0.0362270i
$534$		0			0
$535$	167.021	+	947.224i	0.312189	+	1.77051i
$536$		0			0
$537$	19.1585	+	280.315i	0.0356769	+	0.522001i
$538$		0			0
$539$		−	1480.51i		−	2.74677i
$540$		0			0
$541$	−967.717			−1.78876			−0.894378	−	0.447312i	$-0.852381\pi$
$541$	−967.717			−1.78876			−0.894378	+	0.447312i	$0.852381\pi$
$542$		0			0
$543$	28.0582	+	41.7394i	0.0516725	+	0.0768682i
$544$		0			0
$545$	67.1857	−	11.8467i	0.123277	−	0.0217370i
$546$		0			0
$547$	53.4636	+	44.8613i	0.0977397	+	0.0820133i	0.690348	−	0.723477i	$-0.257457\pi$
$547$	53.4636	+	44.8613i	0.0977397	+	0.0820133i	−0.592608	+	0.805491i	$0.701902\pi$
$548$		0			0
$549$	−7.87976	+	206.977i	−0.0143529	+	0.377007i
$550$		0			0
$551$	356.399	+	62.8427i	0.646821	+	0.114052i
$552$		0			0
$553$	177.586	+	64.6360i	0.321132	+	0.116882i
$554$		0			0
$555$	587.574	−	145.517i	1.05869	−	0.262193i
$556$		0			0
$557$	67.9974	−	39.2583i	0.122078	−	0.0704818i	−0.437718	−	0.899113i	$-0.644213\pi$
$557$	67.9974	−	39.2583i	0.122078	−	0.0704818i	0.559796	+	0.828631i	$0.310880\pi$
$558$		0			0
$559$	342.463	−	593.163i	0.612635	−	1.06111i
$560$		0			0
$561$	153.624	−	1439.85i	0.273840	−	2.56657i
$562$		0			0
$563$	406.246	+	484.146i	0.721575	+	0.859939i	0.994783	−	0.102016i	$-0.0325293\pi$
$563$	406.246	+	484.146i	0.721575	+	0.859939i	−0.273208	+	0.961955i	$0.588085\pi$
$564$		0			0
$565$	153.969	−	56.0400i	0.272511	−	0.0991858i
$566$		0			0
$567$	−767.681	+	550.407i	−1.35393	+	0.970735i
$568$		0			0
$569$	−50.9515	−	139.988i	−0.0895457	−	0.246025i	0.886833	−	0.462089i	$-0.152900\pi$
$569$	−50.9515	−	139.988i	−0.0895457	−	0.246025i	−0.976379	+	0.216065i	$0.930678\pi$
$570$		0			0
$571$	504.945	−	423.699i	0.884317	−	0.742030i	−0.0827453	−	0.996571i	$-0.526369\pi$
$571$	504.945	−	423.699i	0.884317	−	0.742030i	0.967062	+	0.254541i	$0.0819243\pi$
$572$		0			0
$573$	−308.884	−	32.9563i	−0.539064	−	0.0575153i
$574$		0			0
$575$	−18.1786	−	10.4954i	−0.0316149	−	0.0182529i
$576$		0			0
$577$	−125.956	−	218.162i	−0.218295	−	0.378098i	0.735992	−	0.676990i	$-0.236716\pi$
$577$	−125.956	−	218.162i	−0.218295	−	0.378098i	−0.954287	+	0.298893i	$0.903383\pi$
$578$		0			0
$579$	168.657	+	681.010i	0.291291	+	1.17618i
$580$		0			0
$581$	−367.129	+	1008.68i	−0.631891	+	1.73611i
$582$		0			0
$583$	43.4683	−	246.521i	0.0745597	−	0.422849i
$584$		0			0
$585$	−284.809	−	539.737i	−0.486853	−	0.922627i
$586$		0			0
$587$	−309.575	+	368.937i	−0.527385	+	0.628513i	−0.962310	−	0.271953i	$-0.912330\pi$
$587$	−309.575	+	368.937i	−0.527385	+	0.628513i	0.434925	+	0.900467i	$0.356775\pi$
$588$		0			0
$589$	72.5260	+	411.315i	0.123134	+	0.698328i
$590$		0			0
$591$	556.339	−	373.983i	0.941351	−	0.632797i
$592$		0			0
$593$		−	458.703i		−	0.773529i	−0.922178	−	0.386765i	$-0.873593\pi$
$593$		−	458.703i		−	0.773529i	0.922178	−	0.386765i	$-0.126407\pi$
$594$		0			0
$595$	1725.52			2.90004
$596$		0			0
$597$	1003.37	−	68.5769i	1.68069	−	0.114869i
$598$		0			0
$599$	−264.076	+	46.5637i	−0.440861	+	0.0777357i	−0.389673	−	0.920953i	$-0.627412\pi$
$599$	−264.076	+	46.5637i	−0.440861	+	0.0777357i	−0.0511881	+	0.998689i	$0.516301\pi$
$600$		0			0
$601$	−596.139	−	500.220i	−0.991913	−	0.832314i	−0.00606910	−	0.999982i	$-0.501932\pi$
$601$	−596.139	−	500.220i	−0.991913	−	0.832314i	−0.985844	+	0.167668i	$0.946376\pi$
$602$		0			0
$603$	149.072	+	463.756i	0.247217	+	0.769081i
$604$		0			0
$605$	−866.212	−	152.736i	−1.43175	−	0.252457i
$606$		0			0
$607$	60.1810	+	21.9041i	0.0991449	+	0.0360858i	0.391116	−	0.920341i	$-0.372089\pi$
$607$	60.1810	+	21.9041i	0.0991449	+	0.0360858i	−0.291971	+	0.956427i	$0.594311\pi$
$608$		0			0
$609$	314.922	+	327.140i	0.517114	+	0.537175i
$610$		0			0
$611$	29.2264	−	16.8738i	0.0478337	−	0.0276168i
$612$		0			0
$613$	6.41301	−	11.1077i	0.0104617	−	0.0181202i	−0.860747	−	0.509033i	$-0.830003\pi$
$613$	6.41301	−	11.1077i	0.0104617	−	0.0181202i	0.871209	+	0.490913i	$0.163337\pi$
$614$		0			0
$615$	−24.5253	−	17.8777i	−0.0398785	−	0.0290694i
$616$		0			0
$617$	109.778	+	130.829i	0.177923	+	0.212040i	0.847634	−	0.530582i	$-0.178026\pi$
$617$	109.778	+	130.829i	0.177923	+	0.212040i	−0.669711	+	0.742622i	$0.733582\pi$
$618$		0			0
$619$	−678.707	+	247.029i	−1.09646	+	0.399078i	−0.826009	−	0.563657i	$-0.809394\pi$
$619$	−678.707	+	247.029i	−1.09646	+	0.399078i	−0.270448	+	0.962734i	$0.587172\pi$
$620$		0			0
$621$	200.891	+	158.485i	0.323496	+	0.255210i
$622$		0			0
$623$	−256.789	−	705.523i	−0.412182	−	1.13246i
$624$		0			0
$625$	−517.438	+	434.182i	−0.827900	+	0.694691i
$626$		0			0
$627$	576.940	+	1301.33i	0.920160	+	2.07549i
$628$		0			0
$629$	950.047	+	548.510i	1.51041	+	0.872035i
$630$		0			0
$631$	88.4036	+	153.120i	0.140101	+	0.242662i	0.927534	−	0.373738i	$-0.121924\pi$
$631$	88.4036	+	153.120i	0.140101	+	0.242662i	−0.787434	+	0.616399i	$0.788591\pi$
$632$		0			0
$633$	1178.07	+	339.812i	1.86109	+	0.536828i
$634$		0			0
$635$	−185.717	+	510.252i	−0.292467	+	0.803546i
$636$		0			0
$637$	196.361	−	1113.62i	0.308260	−	1.74823i
$638$		0			0
$639$	−711.200	−	289.949i	−1.11299	−	0.453755i
$640$		0			0
$641$	335.280	−	399.571i	0.523057	−	0.623355i	−0.438244	−	0.898856i	$-0.644399\pi$
$641$	335.280	−	399.571i	0.523057	−	0.623355i	0.961301	+	0.275501i	$0.0888438\pi$
$642$		0			0
$643$	−70.9572	−	402.418i	−0.110353	−	0.625844i	−0.988946	−	0.148273i	$-0.952628\pi$
$643$	−70.9572	−	402.418i	−0.110353	−	0.625844i	0.878593	−	0.477571i	$-0.158483\pi$
$644$		0			0
$645$	−740.657	−	362.686i	−1.14831	−	0.562303i
$646$		0			0
$647$		−	310.156i		−	0.479376i	−0.970850	−	0.239688i	$-0.922955\pi$
$647$		−	310.156i		−	0.479376i	0.970850	−	0.239688i	$-0.0770451\pi$
$648$		0			0
$649$	−290.301			−0.447305
$650$		0			0
$651$	−230.473	+	470.659i	−0.354029	+	0.722978i
$652$		0			0
$653$	−1016.19	+	179.182i	−1.55619	+	0.274398i	−0.884537	−	0.466471i	$-0.845525\pi$
$653$	−1016.19	+	179.182i	−1.55619	+	0.274398i	−0.671650	+	0.740869i	$0.734414\pi$
$654$		0			0
$655$	185.263	+	155.454i	0.282845	+	0.237335i
$656$		0			0
$657$	30.9752	−	4.25396i	0.0471464	−	0.00647482i
$658$		0			0
$659$	−955.212	−	168.430i	−1.44949	−	0.255584i	−0.607173	−	0.794570i	$-0.707696\pi$
$659$	−955.212	−	168.430i	−1.44949	−	0.255584i	−0.842315	+	0.538986i	$0.818808\pi$
$660$		0			0
$661$	658.521	+	239.682i	0.996250	+	0.362605i	0.788137	−	0.615500i	$-0.211046\pi$
$661$	658.521	+	239.682i	0.996250	+	0.362605i	0.208113	+	0.978105i	$0.433268\pi$
$662$		0			0
$663$	306.523	−	1062.66i	0.462327	−	1.60281i
$664$		0			0
$665$	−1469.03	+	848.146i	−2.20907	+	1.27541i
$666$		0			0
$667$	61.5030	−	106.526i	0.0922084	−	0.159710i
$668$		0			0
$669$	−432.458	+	191.728i	−0.646424	+	0.286589i
$670$		0			0
$671$	251.747	+	300.020i	0.375181	+	0.447123i
$672$		0			0
$673$	409.377	−	149.001i	0.608287	−	0.221398i	−0.0194664	−	0.999811i	$-0.506197\pi$
$673$	409.377	−	149.001i	0.608287	−	0.221398i	0.627754	+	0.778412i	$0.283975\pi$
$674$		0			0
$675$	−50.8645	+	31.4509i	−0.0753547	+	0.0465939i
$676$		0			0
$677$	138.700	+	381.074i	0.204874	+	0.562887i	0.998993	−	0.0448762i	$-0.0142893\pi$
$677$	138.700	+	381.074i	0.204874	+	0.562887i	−0.794119	+	0.607763i	$0.792067\pi$
$678$		0			0
$679$	396.302	−	332.537i	0.583656	−	0.489745i
$680$		0			0
$681$	−497.722	+	682.794i	−0.730869	+	1.00263i
$682$		0			0
$683$	795.421	+	459.236i	1.16460	+	0.672381i	0.952402	−	0.304846i	$-0.0986050\pi$
$683$	795.421	+	459.236i	1.16460	+	0.672381i	0.212196	+	0.977227i	$0.431938\pi$
$684$		0			0
$685$	574.335	+	994.778i	0.838446	+	1.45223i
$686$		0			0
$687$	−249.469	+	240.152i	−0.363128	+	0.349567i
$688$		0			0
$689$	65.3927	−	179.665i	0.0949095	−	0.260762i
$690$		0			0
$691$	−32.3254	+	183.327i	−0.0467806	+	0.265306i	−0.999223	−	0.0394126i	$-0.987451\pi$
$691$	−32.3254	+	183.327i	−0.0467806	+	0.265306i	0.952442	+	0.304719i	$0.0985624\pi$
$692$		0			0
$693$	−376.850	+	1745.91i	−0.543795	+	2.51936i
$694$		0			0
$695$	−600.572	+	715.734i	−0.864132	+	1.02983i
$696$		0			0
$697$	−9.55101	−	54.1665i	−0.0137030	−	0.0777138i
$698$		0			0
$699$	46.1983	+	675.944i	0.0660920	+	0.967016i
$700$		0			0
$701$		−	1096.71i		−	1.56449i	−0.622970	−	0.782246i	$-0.714074\pi$
$701$		−	1096.71i		−	1.56449i	0.622970	−	0.782246i	$-0.285926\pi$
$702$		0			0
$703$	−1078.44			−1.53405
$704$		0			0
$705$	−22.6693	−	33.7230i	−0.0321551	−	0.0478340i
$706$		0			0
$707$	74.2100	−	13.0852i	0.104965	−	0.0185081i
$708$		0			0
$709$	−28.7772	−	24.1469i	−0.0405884	−	0.0340577i	0.622268	−	0.782804i	$-0.286211\pi$
$709$	−28.7772	−	24.1469i	−0.0405884	−	0.0340577i	−0.662856	+	0.748747i	$0.730656\pi$
$710$		0			0
$711$	−123.442	−	77.6762i	−0.173618	−	0.109249i
$712$		0			0
$713$	139.803	+	24.6511i	0.196077	+	0.0345737i
$714$		0			0
$715$	−1084.35	−	394.671i	−1.51657	−	0.551987i
$716$		0			0
$717$	513.962	−	127.287i	0.716823	−	0.177527i
$718$		0			0
$719$	−62.6620	+	36.1779i	−0.0871516	+	0.0503170i	−0.542942	−	0.839770i	$-0.682690\pi$
$719$	−62.6620	+	36.1779i	−0.0871516	+	0.0503170i	0.455791	+	0.890087i	$0.349357\pi$
$720$		0			0
$721$	105.526	−	182.777i	0.146361	−	0.253505i
$722$		0			0
$723$	−22.4146	+	210.082i	−0.0310022	+	0.290569i
$724$		0			0
$725$	18.4789	+	22.0223i	0.0254882	+	0.0303756i
$726$		0			0
$727$	351.865	−	128.068i	0.483995	−	0.176160i	−0.0884863	−	0.996077i	$-0.528203\pi$
$727$	351.865	−	128.068i	0.483995	−	0.176160i	0.572482	+	0.819917i	$0.305981\pi$
$728$		0			0
$729$	668.743	−	290.213i	0.917343	−	0.398097i
$730$		0			0
$731$	−511.174	−	1404.44i	−0.699280	−	1.92126i
$732$		0			0
$733$	1086.12	−	911.363i	1.48175	−	1.24333i	0.577451	−	0.816425i	$-0.304047\pi$
$733$	1086.12	−	911.363i	1.48175	−	1.24333i	0.904295	−	0.426908i	$-0.140397\pi$
$734$		0			0
$735$	−1353.86	−	144.450i	−1.84199	−	0.196531i
$736$		0			0
$737$	797.686	+	460.544i	1.08234	+	0.624891i
$738$		0			0
$739$	−382.758	−	662.956i	−0.517940	−	0.897098i	−0.999783	−	0.0208408i	$-0.993366\pi$
$739$	−382.758	−	662.956i	−0.517940	−	0.897098i	0.481843	−	0.876258i	$-0.339968\pi$
$740$		0			0
$741$	261.370	+	1055.37i	0.352726	+	1.42425i
$742$		0			0
$743$	−111.257	+	305.675i	−0.149740	+	0.411407i	−0.991771	−	0.128021i	$-0.959137\pi$
$743$	−111.257	+	305.675i	−0.149740	+	0.411407i	0.842032	+	0.539428i	$0.181360\pi$
$744$		0			0
$745$	129.683	−	735.470i	0.174071	−	0.987208i
$746$		0			0
$747$	441.196	−	701.143i	0.590624	−	0.938612i
$748$		0			0
$749$	1382.07	−	1647.09i	1.84523	−	2.19905i
$750$		0			0
$751$	195.557	+	1109.06i	0.260396	+	1.47678i	0.781832	+	0.623489i	$0.214286\pi$
$751$	195.557	+	1109.06i	0.260396	+	1.47678i	−0.521436	+	0.853291i	$0.674603\pi$
$752$		0			0
$753$	−689.102	+	463.230i	−0.915142	+	0.615179i
$754$		0			0
$755$		−	388.271i		−	0.514266i
$756$		0			0
$757$	−543.494			−0.717957			−0.358979	−	0.933346i	$-0.616875\pi$
$757$	−543.494			−0.717957			−0.358979	+	0.933346i	$0.616875\pi$
$758$		0			0
$759$	482.709	−	32.9914i	0.635980	−	0.0434669i
$760$		0			0
$761$	109.050	−	19.2284i	0.143298	−	0.0252673i	−0.101539	−	0.994832i	$-0.532377\pi$
$761$	109.050	−	19.2284i	0.143298	−	0.0252673i	0.244837	+	0.969564i	$0.421266\pi$
$762$		0			0
$763$	−116.827	−	98.0293i	−0.153115	−	0.128479i
$764$		0			0
$765$	−1301.69	−	280.966i	−1.70156	−	0.367276i
$766$		0			0
$767$	−218.361	−	38.5029i	−0.284695	−	0.0501993i
$768$		0			0
$769$	−291.156	−	105.972i	−0.378617	−	0.137805i	0.145699	−	0.989329i	$-0.453457\pi$
$769$	−291.156	−	105.972i	−0.378617	−	0.137805i	−0.524316	+	0.851524i	$0.675679\pi$
$770$		0			0
$771$	765.714	+	795.420i	0.993144	+	1.03167i
$772$		0			0
$773$	−886.108	+	511.595i	−1.14632	+	0.661830i	−0.947989	−	0.318304i	$-0.896887\pi$
$773$	−886.108	+	511.595i	−1.14632	+	0.661830i	−0.198335	+	0.980134i	$0.563553\pi$
$774$		0			0
$775$	−16.5889	+	28.7329i	−0.0214051	+	0.0370747i
$776$		0			0
$777$	−1093.48	−	797.092i	−1.40731	−	1.02586i
$778$		0			0
$779$	34.7558	+	41.4203i	0.0446159	+	0.0531712i
$780$		0			0
$781$	−1364.67	+	496.698i	−1.74733	+	0.635977i
$782$		0			0
$783$	−184.302	−	298.065i	−0.235379	−	0.380671i
$784$		0			0
$785$	−57.6838	−	158.485i	−0.0734826	−	0.201892i
$786$		0			0
$787$	197.978	−	166.124i	0.251561	−	0.211085i	−0.508283	−	0.861190i	$-0.669720\pi$
$787$	197.978	−	166.124i	0.251561	−	0.211085i	0.759844	+	0.650105i	$0.225275\pi$
$788$		0			0
$789$	−449.090	−	1012.96i	−0.569188	−	1.28385i
$790$		0			0
$791$	−317.205	−	183.138i	−0.401017	−	0.231527i
$792$		0			0
$793$	149.569	+	259.061i	0.188611	+	0.326684i
$794$		0			0
$795$	−221.192	−	63.8026i	−0.278229	−	0.0802548i
$796$		0			0
$797$	517.692	−	1422.35i	0.649551	−	1.78463i	0.0301573	−	0.999545i	$-0.490399\pi$
$797$	517.692	−	1422.35i	0.649551	−	1.78463i	0.619393	−	0.785081i	$-0.287379\pi$
$798$		0			0
$799$	12.7876	−	72.5219i	0.0160045	−	0.0907658i
$800$		0			0
$801$	78.8358	+	574.043i	0.0984217	+	0.716658i
$802$		0			0
$803$	38.0014	−	45.2882i	0.0473242	−	0.0563988i
$804$		0			0
$805$	100.118	+	567.798i	0.124370	+	0.705340i
$806$		0			0
$807$	−1306.07	−	639.560i	−1.61843	−	0.792516i
$808$		0			0
$809$			434.934i			0.537619i	0.963193	+	0.268810i	$0.0866303\pi$
$809$			434.934i			0.537619i	−0.963193	+	0.268810i	$0.913370\pi$
$810$		0			0
$811$	−207.504			−0.255862			−0.127931	−	0.991783i	$-0.540834\pi$
$811$	−207.504			−0.255862			−0.127931	+	0.991783i	$0.540834\pi$
$812$		0			0
$813$	−477.445	+	975.013i	−0.587264	+	1.19928i
$814$		0			0
$815$	512.634	−	90.3912i	0.628998	−	0.110909i
$816$		0			0
$817$	1125.51	+	944.419i	1.37762	+	1.15596i
$818$		0			0
$819$	−515.024	+	1263.27i	−0.628845	+	1.54246i
$820$		0			0
$821$	−1587.42	−	279.904i	−1.93351	−	0.340931i	−0.933663	−	0.358154i	$-0.883406\pi$
$821$	−1587.42	−	279.904i	−1.93351	−	0.340931i	−0.999852	+	0.0172230i	$0.994517\pi$
$822$		0			0
$823$	−1516.66	−	552.020i	−1.84285	−	0.670741i	−0.988537	−	0.150976i	$-0.951759\pi$
$823$	−1516.66	−	552.020i	−1.84285	−	0.670741i	−0.854309	−	0.519766i	$-0.826019\pi$
$824$		0			0
$825$	−31.3396	+	108.649i	−0.0379874	+	0.131696i
$826$		0			0
$827$	−373.443	+	215.608i	−0.451564	+	0.260710i	−0.708490	−	0.705720i	$-0.750623\pi$
$827$	−373.443	+	215.608i	−0.451564	+	0.260710i	0.256927	+	0.966431i	$0.417290\pi$
$828$		0			0
$829$	−731.702	+	1267.35i	−0.882633	+	1.52876i	−0.0342292	+	0.999414i	$0.510898\pi$
$829$	−731.702	+	1267.35i	−0.882633	+	1.52876i	−0.848403	+	0.529350i	$0.822436\pi$
$830$		0			0
$831$	−568.505	+	252.044i	−0.684122	+	0.303302i
$832$		0			0
$833$	−1586.09	−	1890.22i	−1.90407	−	2.26918i
$834$		0			0
$835$	−826.135	+	300.688i	−0.989383	+	0.360106i
$836$		0			0
$837$	250.500	−	317.526i	0.299284	−	0.379362i
$838$		0			0
$839$	372.500	+	1023.43i	0.443981	+	1.21983i	0.936852	+	0.349725i	$0.113725\pi$
$839$	372.500	+	1023.43i	0.443981	+	1.21983i	−0.492872	+	0.870102i	$0.664053\pi$
$840$		0			0
$841$	515.193	−	432.298i	0.612595	−	0.514028i
$842$		0			0
$843$	580.408	−	796.226i	0.688502	−	0.944515i
$844$		0			0
$845$	0.232135	+	0.134023i	0.000274716	+	0.000158608i
$846$		0			0
$847$	983.117	+	1702.81i	1.16070	+	2.01040i
$848$		0			0
$849$	203.904	−	196.288i	0.240169	−	0.231200i
$850$		0			0
$851$	−125.369	+	344.447i	−0.147319	+	0.404756i
$852$		0			0
$853$	−95.8295	+	543.476i	−0.112344	+	0.637135i	0.875687	+	0.482879i	$0.160409\pi$
$853$	−95.8295	+	543.476i	−0.112344	+	0.637135i	−0.988031	+	0.154256i	$0.950702\pi$
$854$		0			0
$855$	1246.31	−	400.620i	1.45767	−	0.468561i
$856$		0			0
$857$	−1054.84	+	1257.11i	−1.23085	+	1.46687i	−0.394300	+	0.918982i	$0.629013\pi$
$857$	−1054.84	+	1257.11i	−1.23085	+	1.46687i	−0.836551	+	0.547889i	$0.815431\pi$
$858$		0			0
$859$	−259.895	−	1473.94i	−0.302555	−	1.71587i	−0.634797	−	0.772679i	$-0.718916\pi$
$859$	−259.895	−	1473.94i	−0.302555	−	1.71587i	0.332242	−	0.943194i	$-0.392195\pi$
$860$		0			0
$861$	4.62615	+	67.6868i	0.00537299	+	0.0786141i
$862$		0			0
$863$			867.837i			1.00561i	0.864401	+	0.502803i	$0.167698\pi$
$863$			867.837i			1.00561i	−0.864401	+	0.502803i	$0.832302\pi$
$864$		0			0
$865$	710.048			0.820865
$866$		0			0
$867$	−862.698	−	1283.35i	−0.995038	−	1.48022i
$868$		0			0
$869$	−271.588	+	47.8883i	−0.312530	+	0.0551074i
$870$		0			0
$871$	538.927	+	452.214i	0.618745	+	0.519189i
$872$		0			0
$873$	−353.108	+	186.328i	−0.404476	+	0.213435i
$874$		0			0
$875$	1365.12	+	240.708i	1.56014	+	0.275095i
$876$		0			0
$877$	451.456	+	164.316i	0.514773	+	0.187362i	0.586327	−	0.810075i	$-0.300574\pi$
$877$	451.456	+	164.316i	0.514773	+	0.187362i	−0.0715539	+	0.997437i	$0.522796\pi$
$878$		0			0
$879$	1210.75	−	299.853i	1.37742	−	0.341130i
$880$		0			0
$881$	−716.751	+	413.816i	−0.813565	+	0.469712i	−0.848192	−	0.529688i	$-0.822309\pi$
$881$	−716.751	+	413.816i	−0.813565	+	0.469712i	0.0346271	+	0.999400i	$0.488976\pi$
$882$		0			0
$883$	−382.739	+	662.923i	−0.433453	+	0.750762i	−0.997168	−	0.0752071i	$-0.976038\pi$
$883$	−382.739	+	662.923i	−0.433453	+	0.750762i	0.563715	+	0.825969i	$0.309372\pi$
$884$		0			0
$885$	−28.3241	+	265.468i	−0.0320046	+	0.299964i
$886$		0			0
$887$	−674.009	−	803.252i	−0.759874	−	0.905583i	0.237966	−	0.971274i	$-0.423519\pi$
$887$	−674.009	−	803.252i	−0.759874	−	0.905583i	−0.997840	+	0.0656906i	$0.979075\pi$
$888$		0			0
$889$	1140.64	−	415.158i	1.28306	−	0.466994i
$890$		0			0
$891$	568.573	−	1255.71i	0.638130	−	1.40933i
$892$		0			0
$893$	24.7599	+	68.0274i	0.0277267	+	0.0761785i
$894$		0			0
$895$	374.278	−	314.056i	0.418188	−	0.350901i
$896$		0			0
$897$	367.463	+	39.2064i	0.409658	+	0.0437084i
$898$		0			0
$899$	−168.374	−	97.2110i	−0.187291	−	0.108132i
$900$		0			0
$901$	−208.603	−	361.311i	−0.231524	−	0.401011i
$902$		0			0
$903$	443.179	+	1789.48i	0.490785	+	1.98171i
$904$		0			0
$905$	29.9121	−	82.1827i	0.0330520	−	0.0908096i
$906$		0			0
$907$	119.877	−	679.859i	0.132169	−	0.749569i	−0.844620	−	0.535366i	$-0.820174\pi$
$907$	119.877	−	679.859i	0.132169	−	0.749569i	0.976789	−	0.214203i	$-0.0687153\pi$
$908$		0			0
$909$	−58.1130	−	2.21241i	−0.0639306	−	0.00243389i
$910$		0			0
$911$	−583.708	+	695.636i	−0.640733	+	0.763596i	−0.984486	−	0.175464i	$-0.943857\pi$
$911$	−583.708	+	695.636i	−0.640733	+	0.763596i	0.343752	+	0.939060i	$0.388302\pi$
$912$		0			0
$913$	−272.003	−	1542.60i	−0.297922	−	1.68960i
$914$		0			0
$915$	298.918	−	200.939i	0.326686	−	0.219606i
$916$		0			0
$917$		−	540.627i		−	0.589561i
$918$		0			0
$919$	940.127			1.02299			0.511494	−	0.859287i	$-0.329092\pi$
$919$	940.127			1.02299			0.511494	+	0.859287i	$0.329092\pi$
$920$		0			0
$921$	−1554.60	+	106.251i	−1.68794	+	0.115365i
$922$		0			0
$923$	−1092.36	+	192.613i	−1.18349	+	0.208681i
$924$		0			0
$925$	−65.6257	−	55.0665i	−0.0709467	−	0.0595314i
$926$		0			0
$927$	−109.368	+	120.700i	−0.117981	+	0.130205i
$928$		0			0
$929$	−272.955	−	48.1294i	−0.293816	−	0.0518078i	0.0247970	−	0.999693i	$-0.492106\pi$
$929$	−272.955	−	48.1294i	−0.293816	−	0.0518078i	−0.318613	+	0.947885i	$0.603217\pi$
$930$		0			0
$931$	2279.43	+	829.643i	2.44836	+	0.891131i
$932$		0			0
$933$	−145.618	−	151.267i	−0.156075	−	0.162130i
$934$		0			0
$935$	−2180.66	+	1259.00i	−2.33225	+	1.34653i
$936$		0			0
$937$	468.807	−	811.997i	0.500327	−	0.866592i	−0.499673	−	0.866214i	$-0.666546\pi$
$937$	468.807	−	811.997i	0.500327	−	0.866592i	1.00000		0.000378066i	$-0.000120342\pi$
$938$		0			0
$939$	728.464	+	531.013i	0.775787	+	0.565509i
$940$		0			0
$941$	579.952	+	691.160i	0.616315	+	0.734495i	0.980432	−	0.196858i	$-0.0630737\pi$
$941$	579.952	+	691.160i	0.616315	+	0.734495i	−0.364117	+	0.931353i	$0.618629\pi$
$942$		0			0
$943$	17.2698	−	6.28570i	0.0183137	−	0.00666564i
$944$		0			0
$945$	1559.80	+	514.959i	1.65058	+	0.544930i
$946$		0			0
$947$	−208.635	−	573.219i	−0.220311	−	0.605300i	0.779465	−	0.626446i	$-0.215491\pi$
$947$	−208.635	−	573.219i	−0.220311	−	0.605300i	−0.999776	+	0.0211454i	$0.993269\pi$
$948$		0			0
$949$	34.5908	−	29.0251i	0.0364497	−	0.0305849i
$950$		0			0
$951$	532.769	+	1201.70i	0.560220	+	1.26362i
$952$		0			0
$953$	−1125.59	−	649.858i	−1.18110	−	0.681908i	−0.224830	−	0.974398i	$-0.572183\pi$
$953$	−1125.59	−	649.858i	−1.18110	−	0.681908i	−0.956269	+	0.292490i	$0.905516\pi$
$954$		0			0
$955$	270.088	+	467.806i	0.282815	+	0.489849i
$956$		0			0
$957$	−636.682	−	183.650i	−0.665289	−	0.191902i
$958$		0			0
$959$	878.233	−	2412.93i	0.915780	−	2.51608i
$960$		0			0
$961$	−127.913	+	725.429i	−0.133104	+	0.754869i
$962$		0			0
$963$	−1310.80	+	1017.48i	−1.36116	+	1.05658i
$964$		0			0
$965$	784.204	−	934.578i	0.812647	−	0.968475i
$966$		0			0
$967$	−176.440	−	1000.64i	−0.182461	−	1.03479i	−0.929175	−	0.369641i	$-0.879481\pi$
$967$	−176.440	−	1000.64i	−0.182461	−	1.03479i	0.746714	−	0.665145i	$-0.231630\pi$
$968$		0			0
$969$	2130.74	+	1043.38i	2.19890	+	1.07676i
$970$		0			0
$971$		−	455.462i		−	0.469065i	−0.972108	−	0.234532i	$-0.924644\pi$
$971$		−	455.462i		−	0.469065i	0.972108	−	0.234532i	$-0.0753559\pi$
$972$		0			0
$973$	2088.62			2.14658
$974$		0			0
$975$	−37.9835	+	77.5677i	−0.0389574	+	0.0795567i
$976$		0			0
$977$	1060.32	−	186.964i	1.08529	−	0.191365i	0.397734	−	0.917501i	$-0.369797\pi$
$977$	1060.32	−	186.964i	1.08529	−	0.191365i	0.687551	+	0.726136i	$0.258686\pi$
$978$		0			0
$979$	839.297	+	704.254i	0.857300	+	0.719361i
$980$		0			0
$981$	72.1693	+	92.9738i	0.0735670	+	0.0947746i
$982$		0			0
$983$	1690.45	+	298.071i	1.71968	+	0.303226i	0.944499	−	0.328513i	$-0.106547\pi$
$983$	1690.45	+	298.071i	1.71968	+	0.303226i	0.775181	+	0.631739i	$0.217659\pi$
$984$		0			0
$985$	−1095.40	−	398.693i	−1.11208	−	0.404765i
$986$		0			0
$987$	−25.1749	+	87.2769i	−0.0255065	+	0.0884264i
$988$		0			0
$989$	432.484	−	249.695i	0.437294	−	0.252472i
$990$		0			0
$991$	916.942	−	1588.19i	0.925270	−	1.60261i	0.134143	−	0.990962i	$-0.457172\pi$
$991$	916.942	−	1588.19i	0.925270	−	1.60261i	0.791127	−	0.611652i	$-0.209495\pi$
$992$		0			0
$993$	−297.790	+	132.024i	−0.299889	+	0.132954i
$994$		0			0
$995$	−1124.15	−	1339.71i	−1.12980	−	1.34644i
$996$		0			0
$997$	464.326	−	169.001i	0.465723	−	0.169509i	−0.0984911	−	0.995138i	$-0.531402\pi$
$997$	464.326	−	169.001i	0.465723	−	0.169509i	0.564214	+	0.825629i	$0.309179\pi$
$998$		0			0
$999$	695.107	+	779.359i	0.695803	+	0.780139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.b.209.4		36
4.3	odd	2		108.3.k.a.101.3	yes	36
12.11	even	2		324.3.k.a.305.5		36
27.23	odd	18	inner	432.3.bc.b.401.4		36
108.23	even	18		108.3.k.a.77.3	✓	36
108.31	odd	18		324.3.k.a.17.5		36
108.79	odd	18		2916.3.c.b.1457.30		36
108.83	even	18		2916.3.c.b.1457.7		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.3	✓	36	108.23	even	18
108.3.k.a.101.3	yes	36	4.3	odd	2
324.3.k.a.17.5		36	108.31	odd	18
324.3.k.a.305.5		36	12.11	even	2
432.3.bc.b.209.4		36	1.1	even	1	trivial
432.3.bc.b.401.4		36	27.23	odd	18	inner
2916.3.c.b.1457.7		36	108.83	even	18
2916.3.c.b.1457.30		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)

\(f(q)\)	\(=\)	\(q+(1.31935 - 2.69431i) q^{3} +(-5.13754 + 0.905886i) q^{5} +(8.93347 + 7.49607i) q^{7} +(-5.51862 - 7.10949i) q^{9} +O(q^{10})\)	\(q+(1.31935 - 2.69431i) q^{3} +(-5.13754 + 0.905886i) q^{5} +(8.93347 + 7.49607i) q^{7} +(-5.51862 - 7.10949i) q^{9} +(-16.7592 - 2.95510i) q^{11} +(-12.2141 - 4.44559i) q^{13} +(-4.33749 + 15.0373i) q^{15} +(-24.5630 + 14.1815i) q^{17} +(13.9412 - 24.1469i) q^{19} +(31.9831 - 14.1796i) q^{21} +(-6.09173 - 7.25984i) q^{23} +(2.08134 - 0.757544i) q^{25} +(-26.4362 + 5.48893i) q^{27} +(4.43920 + 12.1966i) q^{29} +(-11.4748 + 9.62853i) q^{31} +(-30.0733 + 41.2557i) q^{33} +(-52.6866 - 30.4186i) q^{35} +(-19.3390 - 33.4961i) q^{37} +(-28.0926 + 27.0434i) q^{39} +(-0.663254 + 1.82228i) q^{41} +(-9.15032 + 51.8940i) q^{43} +(34.7925 + 31.5260i) q^{45} +(-1.66892 + 1.98894i) q^{47} +(15.1070 + 85.6762i) q^{49} +(5.80197 + 84.8907i) q^{51} +14.7096i q^{53} +88.7782 q^{55} +(-46.6659 - 69.4203i) q^{57} +(16.7995 - 2.96221i) q^{59} +(-17.6298 - 14.7932i) q^{61} +(3.99288 - 104.880i) q^{63} +(66.7778 + 11.7747i) q^{65} +(-50.8610 - 18.5119i) q^{67} +(-27.5974 + 6.83472i) q^{69} +(73.9041 - 42.6686i) q^{71} +(-1.73700 + 3.00857i) q^{73} +(0.704957 - 6.60723i) q^{75} +(-127.566 - 152.028i) q^{77} +(15.2280 - 5.54254i) q^{79} +(-20.0898 + 78.4691i) q^{81} +(31.4813 + 86.4941i) q^{83} +(113.347 - 95.1090i) q^{85} +(38.7183 + 4.13104i) q^{87} +(-55.7558 - 32.1906i) q^{89} +(-75.7903 - 131.273i) q^{91} +(10.8029 + 43.6202i) q^{93} +(-49.7492 + 136.685i) q^{95} +(7.70330 - 43.6876i) q^{97} +(71.4785 + 135.458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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