LMFDB - Embedded newform 108.3.k.a.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	108.101
Dual form			108.3.k.a.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.31935	+	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	$-0.964407\pi$
$7$	−8.93347	−	7.49607i	−1.27621	−	1.07087i	−0.282455	−	0.959281i	$-0.591149\pi$
$8$		0			0
$9$	−5.51862	−	7.10949i	−0.613179	−	0.789944i
$10$		0			0
$11$	16.7592	+	2.95510i	1.52357	+	0.268646i	0.871833	−	0.489803i	$-0.162931\pi$
$11$	16.7592	+	2.95510i	1.52357	+	0.268646i	0.651733	+	0.758448i	$0.274042\pi$
$12$		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	$0.428898\pi$
$19$	−13.9412	+	24.1469i	−0.733749	+	1.27089i	−0.955270	+	0.295735i	$0.904435\pi$
$20$		0			0
$21$	31.9831	−	14.1796i	1.52301	−	0.675218i
$22$		0			0
$23$	6.09173	+	7.25984i	0.264858	+	0.315645i	0.882040	−	0.471175i	$-0.156170\pi$
$23$	6.09173	+	7.25984i	0.264858	+	0.315645i	−0.617182	+	0.786821i	$0.711726\pi$
$24$		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	−0.438667	−	0.898650i	$-0.644549\pi$
$31$	11.4748	−	9.62853i	0.370156	−	0.310598i	0.808823	+	0.588052i	$0.200105\pi$
$32$		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	$-0.734517\pi$
$43$	9.15032	−	51.8940i	0.212798	−	1.20684i	0.884687	−	0.466186i	$-0.154372\pi$
$44$		0			0
$45$	34.7925	+	31.5260i	0.773166	+	0.700579i
$46$		0			0
$47$	1.66892	−	1.98894i	0.0355088	−	0.0423178i	−0.747998	−	0.663701i	$-0.768985\pi$
$47$	1.66892	−	1.98894i	0.0355088	−	0.0423178i	0.783507	+	0.621383i	$0.213429\pi$
$48$		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	−0.314193	−	0.949359i	$-0.601734\pi$
$59$	−16.7995	+	2.96221i	−0.284738	+	0.0502070i	0.0294551	+	0.999566i	$0.490623\pi$
$60$		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	0.692438	−	0.721478i	$-0.256537\pi$
$67$	50.8610	+	18.5119i	0.759119	+	0.276297i	0.0666813	+	0.997774i	$0.478759\pi$
$68$		0			0
$69$	−27.5974	+	6.83472i	−0.399962	+	0.0990539i
$70$		0			0
$71$	−73.9041	+	42.6686i	−1.04090	+	0.600966i	−0.920089	−	0.391710i	$-0.871884\pi$
$71$	−73.9041	+	42.6686i	−1.04090	+	0.600966i	−0.120814	+	0.992675i	$0.538550\pi$
$72$		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	−0.436596	−	0.899658i	$-0.643816\pi$
$79$	−15.2280	+	5.54254i	−0.192759	+	0.0701587i	0.243837	+	0.969816i	$0.421594\pi$
$80$		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	$-0.924025\pi$
$83$	−31.4813	−	86.4941i	−0.379292	−	1.04210i	0.592358	−	0.805675i	$-0.298197\pi$
$84$		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	0.996255	−	0.0864583i	$-0.0275549\pi$
$103$	3.14264	+	17.8228i	0.0305111	+	0.173037i	−0.965744	+	0.259495i	$0.916444\pi$
$104$		0			0
$105$	−151.469	+	101.821i	−1.44257	+	0.969725i
$106$		0			0
$107$			184.373i			1.72311i	0.507661	+	0.861557i	$0.330510\pi$
$107$			184.373i			1.72311i	−0.507661	+	0.861557i	$0.669490\pi$
$108$		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	−0.994866	−	0.101201i	$-0.967731\pi$
$127$	−52.0434	+	90.1418i	−0.409790	+	0.709778i	0.585076	+	0.810979i	$0.301065\pi$
$128$		0			0
$129$	127.746	+	93.1203i	0.990280	+	0.721863i
$130$		0			0
$131$	29.7988	+	35.5129i	0.227472	+	0.271091i	0.867693	−	0.497100i	$-0.165602\pi$
$131$	29.7988	+	35.5129i	0.227472	+	0.271091i	−0.640221	+	0.768191i	$0.721157\pi$
$132$		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	−0.985136	−	0.171776i	$-0.945049\pi$
$139$	−137.198	+	115.123i	−0.987037	+	0.828222i	−0.00190072	+	0.999998i	$0.500605\pi$
$140$		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	$-0.865181\pi$
$151$	12.9241	−	73.2964i	0.0855903	−	0.485407i	0.997228	−	0.0744111i	$-0.0237077\pi$
$152$		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	$-0.400983\pi$
$163$	99.7820			0.612160			0.306080	+	0.952006i	$0.400983\pi$
$164$		0			0
$165$	117.130	−	239.196i	0.709877	−	1.44967i
$166$		0			0
$167$	−165.964	+	29.2639i	−0.993795	+	0.175233i	−0.646821	−	0.762642i	$-0.723902\pi$
$167$	−165.964	+	29.2639i	−0.993795	+	0.175233i	−0.346974	+	0.937875i	$0.612791\pi$
$168$		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	−0.256026	−	0.966670i	$-0.582413\pi$
$179$	81.1087	−	46.8281i	0.453121	−	0.261610i	0.709147	+	0.705060i	$0.249080\pi$
$180$		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	0.997221	−	0.0745008i	$-0.0237363\pi$
$191$	35.4147	+	97.3010i	0.185417	+	0.509430i	−0.811804	+	0.583930i	$0.801514\pi$
$192$		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	$-0.847864\pi$
$199$	−167.619	−	290.325i	−0.842306	−	1.45892i	0.0456336	−	0.998958i	$-0.485469\pi$
$200$		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	$-0.635685\pi$
$211$	−70.9699	−	402.490i	−0.336350	−	1.90754i	0.0771240	−	0.997022i	$-0.475426\pi$
$212$		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	0.872110	−	0.489310i	$-0.162751\pi$
$223$	120.793	+	101.358i	0.541674	+	0.454518i	−0.330436	+	0.943828i	$0.607196\pi$
$224$		0			0
$225$	−16.8718	−	10.6166i	−0.0749860	−	0.0471851i
$226$		0			0
$227$	277.370	+	48.9078i	1.22189	+	0.215453i	0.747141	−	0.664666i	$-0.231426\pi$
$227$	277.370	+	48.9078i	1.22189	+	0.215453i	0.474753	+	0.880119i	$0.342537\pi$
$228$		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	0.474569	−	0.880218i	$-0.342604\pi$
$239$	−113.450	−	135.204i	−0.474685	−	0.565707i	−0.949254	+	0.314511i	$0.898159\pi$
$240$		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	0.894618	−	0.446832i	$-0.147448\pi$
$251$	239.695	+	138.388i	0.954959	+	0.551346i	0.0603413	+	0.998178i	$0.480781\pi$
$252$		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	$0.470013\pi$
$263$	−237.412	+	282.937i	−0.902709	+	1.07581i	−0.996776	+	0.0802408i	$0.974431\pi$
$264$		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	$-0.267291\pi$
$271$	361.878			1.33534			0.667672	+	0.744455i	$0.267291\pi$
$272$		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	0.180604	−	0.983556i	$-0.442195\pi$
$283$	−88.6536	−	32.2673i	−0.313264	−	0.114019i	−0.493867	+	0.869537i	$0.664417\pi$
$284$		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	$0.154294\pi$
$307$	259.704	+	449.820i	0.845941	+	1.46521i	−0.0388611	+	0.999245i	$0.512373\pi$
$308$		0			0
$309$	−52.1664	−	15.0473i	−0.168823	−	0.0486968i
$310$		0			0
$311$	−23.9377	+	65.7684i	−0.0769702	+	0.211474i	−0.972210	−	0.234111i	$-0.924782\pi$
$311$	−23.9377	+	65.7684i	−0.0769702	+	0.211474i	0.895240	+	0.445585i	$0.147004\pi$
$312$		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	0.759729	−	0.650240i	$-0.225332\pi$
$331$	83.1781	+	69.7947i	0.251293	+	0.210860i	−0.508436	+	0.861100i	$0.669776\pi$
$332$		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	0.940620	−	0.339462i	$-0.110245\pi$
$347$	153.713	+	183.189i	0.442978	+	0.527921i	−0.497642	+	0.867383i	$0.665801\pi$
$348$		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	$-0.942687\pi$
$359$	−585.472	−	338.023i	−1.63084	−	0.941567i	−0.647008	−	0.762483i	$-0.723980\pi$
$360$		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	$-0.726068\pi$
$367$	80.7428	−	457.915i	0.220008	−	1.24772i	0.872002	−	0.489501i	$-0.162821\pi$
$368$		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	$-0.471973\pi$
$379$	66.6563			0.175874			0.0879371	+	0.996126i	$0.471973\pi$
$380$		0			0
$381$	−174.206	−	259.150i	−0.457234	−	0.680183i
$382$		0			0
$383$	82.5111	−	14.5489i	0.215434	−	0.0379868i	−0.0648895	−	0.997892i	$-0.520669\pi$
$383$	82.5111	−	14.5489i	0.215434	−	0.0379868i	0.280323	+	0.959906i	$0.409558\pi$
$384$		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	−0.942231	−	0.334963i	$-0.891276\pi$
$419$	−2.14955	+	5.90584i	−0.00513019	+	0.0140951i	0.937101	+	0.349058i	$0.113498\pi$
$420$		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	$0.247660\pi$
$431$			605.028i			1.40378i	−0.712287	+	0.701889i	$0.752340\pi$
$432$		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	0.119465	−	0.992838i	$-0.461882\pi$
$439$	−367.682	−	308.522i	−0.837545	−	0.702784i	−0.957010	+	0.290055i	$0.906326\pi$
$440$		0			0
$441$	525.744	−	580.217i	1.19216	−	1.31568i
$442$		0			0
$443$	478.290	+	84.3355i	1.07966	+	0.190373i	0.685066	−	0.728481i	$-0.259773\pi$
$443$	478.290	+	84.3355i	1.07966	+	0.190373i	0.394596	+	0.918855i	$0.370885\pi$
$444$		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	−0.0402729	−	0.999189i	$-0.512823\pi$
$463$	433.712	−	363.927i	0.936743	−	0.786020i	0.977015	+	0.213168i	$0.0683783\pi$
$464$		0			0
$465$	−95.0151	−	214.314i	−0.204334	−	0.460890i
$466$		0			0
$467$	−265.877	−	153.504i	−0.569330	−	0.328703i	0.187551	−	0.982255i	$-0.439945\pi$
$467$	−265.877	−	153.504i	−0.569330	−	0.328703i	−0.756882	+	0.653552i	$0.773278\pi$
$468$		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	−0.955875	−	0.293775i	$-0.905088\pi$
$479$	−239.776	+	285.754i	−0.500576	+	0.596564i	0.455298	+	0.890339i	$0.349533\pi$
$480$		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	$-0.290381\pi$
$487$	596.051			1.22392			0.611962	+	0.790887i	$0.290381\pi$
$488$		0			0
$489$	−131.648	+	268.844i	−0.269218	+	0.549783i
$490$		0			0
$491$	172.551	−	30.4253i	0.351427	−	0.0619660i	0.00485164	−	0.999988i	$-0.498456\pi$
$491$	172.551	−	30.4253i	0.351427	−	0.0619660i	0.346575	+	0.938022i	$0.387345\pi$
$492$		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	0.429560	−	0.903038i	$-0.358669\pi$
$499$	88.9017	+	32.3576i	0.178160	+	0.0648448i	−0.251400	+	0.967883i	$0.580891\pi$
$500$		0			0
$501$	140.119	−	485.767i	0.279678	−	0.969595i
$502$		0			0
$503$	−161.807	+	93.4192i	−0.321683	+	0.185724i	−0.652143	−	0.758096i	$-0.726130\pi$
$503$	−161.807	+	93.4192i	−0.321683	+	0.185724i	0.330459	+	0.943820i	$0.392796\pi$
$504$		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	0.803439	−	0.595388i	$-0.203001\pi$
$523$	−59.5704	−	103.179i	−0.113901	−	0.197283i	−0.917340	+	0.398104i	$0.869668\pi$
$524$		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	0.592608	−	0.805491i	$-0.298098\pi$
$547$	−53.4636	−	44.8613i	−0.0977397	−	0.0820133i	−0.690348	+	0.723477i	$0.742543\pi$
$548$		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	0.273208	−	0.961955i	$-0.411915\pi$
$563$	−406.246	−	484.146i	−0.721575	−	0.859939i	−0.994783	+	0.102016i	$0.967471\pi$
$564$		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	−0.967062	−	0.254541i	$-0.918076\pi$
$571$	−504.945	+	423.699i	−0.884317	+	0.742030i	0.0827453	+	0.996571i	$0.473631\pi$
$572$		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	−0.434925	−	0.900467i	$-0.643225\pi$
$587$	309.575	−	368.937i	0.527385	−	0.628513i	0.962310	+	0.271953i	$0.0876696\pi$
$588$		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	0.0511881	−	0.998689i	$-0.483699\pi$
$599$	264.076	−	46.5637i	0.440861	−	0.0777357i	0.389673	+	0.920953i	$0.372588\pi$
$600$		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	0.291971	−	0.956427i	$-0.405689\pi$
$607$	−60.1810	−	21.9041i	−0.0991449	−	0.0360858i	−0.391116	+	0.920341i	$0.627911\pi$
$608$		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	0.270448	−	0.962734i	$-0.412828\pi$
$619$	678.707	−	247.029i	1.09646	−	0.399078i	0.826009	+	0.563657i	$0.190606\pi$
$620$		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	0.787434	−	0.616399i	$-0.211409\pi$
$631$	−88.4036	−	153.120i	−0.140101	−	0.242662i	−0.927534	+	0.373738i	$0.878076\pi$
$632$		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	$0.0473716\pi$
$643$	70.9572	+	402.418i	0.110353	+	0.625844i	−0.878593	+	0.477571i	$0.841517\pi$
$644$		0			0
$645$	−740.657	−	362.686i	−1.14831	−	0.562303i
$646$		0			0
$647$			310.156i			0.479376i	0.970850	+	0.239688i	$0.0770451\pi$
$647$			310.156i			0.479376i	−0.970850	+	0.239688i	$0.922955\pi$
$648$		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	0.842315	−	0.538986i	$-0.181192\pi$
$659$	955.212	+	168.430i	1.44949	+	0.255584i	0.607173	+	0.794570i	$0.292304\pi$
$660$		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	−0.212196	−	0.977227i	$-0.568062\pi$
$683$	−795.421	−	459.236i	−1.16460	−	0.672381i	−0.952402	+	0.304846i	$0.901395\pi$
$684$		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	−0.952442	−	0.304719i	$-0.901438\pi$
$691$	32.3254	−	183.327i	0.0467806	−	0.265306i	0.999223	+	0.0394126i	$0.0125487\pi$
$692$		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	−0.455791	−	0.890087i	$-0.650643\pi$
$719$	62.6620	−	36.1779i	0.0871516	−	0.0503170i	0.542942	+	0.839770i	$0.317310\pi$
$720$		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	−0.572482	−	0.819917i	$-0.694019\pi$
$727$	−351.865	+	128.068i	−0.483995	+	0.176160i	0.0884863	+	0.996077i	$0.471797\pi$
$728$		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	$0.00663431\pi$
$739$	382.758	+	662.956i	0.517940	+	0.897098i	−0.481843	+	0.876258i	$0.660032\pi$
$740$		0			0
$741$	261.370	+	1055.37i	0.352726	+	1.42425i
$742$		0			0
$743$	111.257	−	305.675i	0.149740	−	0.411407i	−0.842032	−	0.539428i	$-0.818640\pi$
$743$	111.257	−	305.675i	0.149740	−	0.411407i	0.991771	+	0.128021i	$0.0408626\pi$
$744$		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	$-0.785714\pi$
$751$	−195.557	−	1109.06i	−0.260396	−	1.47678i	0.521436	−	0.853291i	$-0.325397\pi$
$752$		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	−0.759844	−	0.650105i	$-0.774725\pi$
$787$	−197.978	+	166.124i	−0.251561	+	0.211085i	0.508283	+	0.861190i	$0.330280\pi$
$788$		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	$-0.459166\pi$
$811$	207.504			0.255862			0.127931	+	0.991783i	$0.459166\pi$
$812$		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	$0.0482415\pi$
$823$	1516.66	+	552.020i	1.84285	+	0.670741i	0.854309	+	0.519766i	$0.173981\pi$
$824$		0			0
$825$	−31.3396	+	108.649i	−0.0379874	+	0.131696i
$826$		0			0
$827$	373.443	−	215.608i	0.451564	−	0.260710i	−0.256927	−	0.966431i	$-0.582710\pi$
$827$	373.443	−	215.608i	0.451564	−	0.260710i	0.708490	+	0.705720i	$0.249377\pi$
$828$		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	$-0.886275\pi$
$839$	−372.500	−	1023.43i	−0.443981	−	1.21983i	0.492872	−	0.870102i	$-0.335947\pi$
$840$		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	$0.281084\pi$
$859$	259.895	+	1473.94i	0.302555	+	1.71587i	−0.332242	+	0.943194i	$0.607805\pi$
$860$		0			0
$861$	4.62615	+	67.6868i	0.00537299	+	0.0786141i
$862$		0			0
$863$		−	867.837i		−	1.00561i	−0.864401	−	0.502803i	$-0.832302\pi$
$863$		−	867.837i		−	1.00561i	0.864401	−	0.502803i	$-0.167698\pi$
$864$		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	−0.563715	−	0.825969i	$-0.690628\pi$
$883$	382.739	−	662.923i	0.433453	−	0.750762i	0.997168	+	0.0752071i	$0.0239618\pi$
$884$		0			0
$885$	−28.3241	+	265.468i	−0.0320046	+	0.299964i
$886$		0			0
$887$	674.009	+	803.252i	0.759874	+	0.905583i	0.997840	−	0.0656906i	$-0.0209250\pi$
$887$	674.009	+	803.252i	0.759874	+	0.905583i	−0.237966	+	0.971274i	$0.576481\pi$
$888$		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	$0.179826\pi$
$907$	−119.877	+	679.859i	−0.132169	+	0.749569i	−0.976789	+	0.214203i	$0.931285\pi$
$908$		0			0
$909$	−58.1130	−	2.21241i	−0.0639306	−	0.00243389i
$910$		0			0
$911$	583.708	−	695.636i	0.640733	−	0.763596i	−0.343752	−	0.939060i	$-0.611698\pi$
$911$	583.708	−	695.636i	0.640733	−	0.763596i	0.984486	+	0.175464i	$0.0561426\pi$
$912$		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	$-0.670908\pi$
$919$	−940.127			−1.02299			−0.511494	+	0.859287i	$0.670908\pi$
$920$		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	0.999776	−	0.0211454i	$-0.00673130\pi$
$947$	208.635	+	573.219i	0.220311	+	0.605300i	−0.779465	+	0.626446i	$0.784509\pi$
$948$		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	$0.120519\pi$
$967$	176.440	+	1000.64i	0.182461	+	1.03479i	−0.746714	+	0.665145i	$0.768370\pi$
$968$		0			0
$969$	2130.74	+	1043.38i	2.19890	+	1.07676i
$970$		0			0
$971$			455.462i			0.469065i	0.972108	+	0.234532i	$0.0753559\pi$
$971$			455.462i			0.469065i	−0.972108	+	0.234532i	$0.924644\pi$
$972$		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	−0.775181	−	0.631739i	$-0.782341\pi$
$983$	−1690.45	−	298.071i	−1.71968	−	0.303226i	−0.944499	+	0.328513i	$0.893453\pi$
$984$		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	$0.542828\pi$
$991$	−916.942	+	1588.19i	−0.925270	+	1.60261i	−0.791127	+	0.611652i	$0.790505\pi$
$992$		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	108.3.k.a.101.3	yes	36
3.2	odd	2		324.3.k.a.305.5		36
4.3	odd	2		432.3.bc.b.209.4		36
27.2	odd	18		2916.3.c.b.1457.7		36
27.4	even	9		324.3.k.a.17.5		36
27.23	odd	18	inner	108.3.k.a.77.3	✓	36
27.25	even	9		2916.3.c.b.1457.30		36
108.23	even	18		432.3.bc.b.401.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.3	✓	36	27.23	odd	18	inner
108.3.k.a.101.3	yes	36	1.1	even	1	trivial
324.3.k.a.17.5		36	27.4	even	9
324.3.k.a.305.5		36	3.2	odd	2
432.3.bc.b.209.4		36	4.3	odd	2
432.3.bc.b.401.4		36	108.23	even	18
2916.3.c.b.1457.7		36	27.2	odd	18
2916.3.c.b.1457.30		36	27.25	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), 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

Properties

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