LMFDB - Embedded newform 572.2.i.b.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, degree $2$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	572.529
Dual form			572.2.i.b.133.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.849814 - 1.47192i) q^{3} +1.11126 q^{5} +(1.14400 + 1.98146i) q^{7} +(0.0556321 + 0.0963576i) q^{9} +O(q^{10})$	\(q+(0.849814 - 1.47192i) q^{3} +1.11126 q^{5} +(1.14400 + 1.98146i) q^{7} +(0.0556321 + 0.0963576i) q^{9} +(0.500000 - 0.866025i) q^{11} +(2.50000 - 2.59808i) q^{13} +(0.944368 - 1.63569i) q^{15} +(1.73855 + 3.01126i) q^{17} +(0.349814 + 0.605896i) q^{19} +3.88874 q^{21} +(-0.961078 + 1.66464i) q^{23} -3.76509 q^{25} +5.28799 q^{27} +(3.34362 - 5.79133i) q^{29} -5.79851 q^{31} +(-0.849814 - 1.47192i) q^{33} +(1.27128 + 2.20192i) q^{35} +(-0.532732 + 0.922719i) q^{37} +(-1.69963 - 5.88768i) q^{39} +(1.73855 - 3.01126i) q^{41} +(-5.12110 - 8.87000i) q^{43} +(0.0618219 + 0.107079i) q^{45} -3.98762 q^{47} +(0.882546 - 1.52861i) q^{49} +5.90978 q^{51} -0.510520 q^{53} +(0.555632 - 0.962383i) q^{55} +1.18911 q^{57} +(0.343624 + 0.595175i) q^{59} +(2.10507 + 3.64610i) q^{61} +(-0.127286 + 0.220465i) q^{63} +(2.77816 - 2.88715i) q^{65} +(-6.08217 + 10.5346i) q^{67} +(1.63348 + 2.82926i) q^{69} +(3.01671 + 5.22510i) q^{71} +8.35346 q^{73} +(-3.19963 + 5.54192i) q^{75} +2.28799 q^{77} -14.1309 q^{79} +(4.32691 - 7.49443i) q^{81} -3.51052 q^{83} +(1.93199 + 3.34630i) q^{85} +(-5.68292 - 9.84310i) q^{87} +(-4.66690 + 8.08330i) q^{89} +(8.00797 + 1.98146i) q^{91} +(-4.92766 + 8.53495i) q^{93} +(0.388736 + 0.673310i) q^{95} +(2.89926 + 5.02166i) q^{97} +0.111264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 6 q^{5} - 5 q^{7}+O(q^{10}) $ 6 * q - q^3 + 6 * q^5 - 5 * q^7	$ 6 q - q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{11} + 15 q^{13} + 6 q^{15} + 5 q^{17} - 4 q^{19} + 24 q^{21} + q^{23} + 12 q^{25} + 8 q^{27} - 4 q^{29} + 14 q^{31} + q^{33} - 9 q^{35} + 8 q^{37} + 2 q^{39} + 5 q^{41} - 8 q^{43} + 18 q^{45} + 12 q^{47} - 12 q^{49} - 14 q^{51} + 22 q^{53} + 3 q^{55} + 20 q^{57} - 22 q^{59} - 6 q^{61} + 4 q^{63} + 15 q^{65} - 7 q^{67} + 23 q^{69} + 11 q^{71} + 4 q^{73} - 7 q^{75} - 10 q^{77} - 40 q^{79} + 9 q^{81} + 4 q^{83} - 24 q^{85} - 29 q^{87} - 27 q^{89} - 35 q^{91} - 37 q^{93} + 3 q^{95} - 7 q^{97}+O(q^{100}) $ 6 * q - q^3 + 6 * q^5 - 5 * q^7 + 3 * q^11 + 15 * q^13 + 6 * q^15 + 5 * q^17 - 4 * q^19 + 24 * q^21 + q^23 + 12 * q^25 + 8 * q^27 - 4 * q^29 + 14 * q^31 + q^33 - 9 * q^35 + 8 * q^37 + 2 * q^39 + 5 * q^41 - 8 * q^43 + 18 * q^45 + 12 * q^47 - 12 * q^49 - 14 * q^51 + 22 * q^53 + 3 * q^55 + 20 * q^57 - 22 * q^59 - 6 * q^61 + 4 * q^63 + 15 * q^65 - 7 * q^67 + 23 * q^69 + 11 * q^71 + 4 * q^73 - 7 * q^75 - 10 * q^77 - 40 * q^79 + 9 * q^81 + 4 * q^83 - 24 * q^85 - 29 * q^87 - 27 * q^89 - 35 * q^91 - 37 * q^93 + 3 * q^95 - 7 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.849814	−	1.47192i	0.490640	−	0.849814i	−0.509302	−	0.860588i	$-0.670096\pi$
$3$	0.849814	−	1.47192i	0.490640	−	0.849814i	0.999942	+	0.0107740i	$0.00342955\pi$
$4$		0			0
$5$	1.11126			0.496972			0.248486	−	0.968635i	$-0.420067\pi$
$5$	1.11126			0.496972			0.248486	+	0.968635i	$0.420067\pi$
$6$		0			0
$7$	1.14400	+	1.98146i	0.432390	+	0.748921i	0.997079	−	0.0763828i	$-0.0243371\pi$
$7$	1.14400	+	1.98146i	0.432390	+	0.748921i	−0.564689	+	0.825304i	$0.691004\pi$
$8$		0			0
$9$	0.0556321	+	0.0963576i	0.0185440	+	0.0321192i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	0.944368	−	1.63569i	0.243835	−	0.422334i
$16$		0			0
$17$	1.73855	+	3.01126i	0.421660	+	0.730337i	0.996102	−	0.0882084i	$-0.0281141\pi$
$17$	1.73855	+	3.01126i	0.421660	+	0.730337i	−0.574442	+	0.818545i	$0.694781\pi$
$18$		0			0
$19$	0.349814	+	0.605896i	0.0802529	+	0.139002i	0.903358	−	0.428886i	$-0.141094\pi$
$19$	0.349814	+	0.605896i	0.0802529	+	0.139002i	−0.823106	+	0.567888i	$0.807761\pi$
$20$		0			0
$21$	3.88874			0.848592
$22$		0			0
$23$	−0.961078	+	1.66464i	−0.200399	+	0.347101i	−0.948657	−	0.316307i	$-0.897557\pi$
$23$	−0.961078	+	1.66464i	−0.200399	+	0.347101i	0.748258	+	0.663408i	$0.230890\pi$
$24$		0			0
$25$	−3.76509			−0.753018
$26$		0			0
$27$	5.28799			1.01767
$28$		0			0
$29$	3.34362	−	5.79133i	0.620895	−	1.07542i	−0.368424	−	0.929658i	$-0.620102\pi$
$29$	3.34362	−	5.79133i	0.620895	−	1.07542i	0.989319	−	0.145765i	$-0.0465642\pi$
$30$		0			0
$31$	−5.79851			−1.04144			−0.520722	−	0.853726i	$-0.674337\pi$
$31$	−5.79851			−1.04144			−0.520722	+	0.853726i	$0.674337\pi$
$32$		0			0
$33$	−0.849814	−	1.47192i	−0.147934	−	0.256229i
$34$		0			0
$35$	1.27128	+	2.20192i	0.214886	+	0.372193i
$36$		0			0
$37$	−0.532732	+	0.922719i	−0.0875806	+	0.151694i	−0.906488	−	0.422232i	$-0.861247\pi$
$37$	−0.532732	+	0.922719i	−0.0875806	+	0.151694i	0.818907	+	0.573926i	$0.194580\pi$
$38$		0			0
$39$	−1.69963	−	5.88768i	−0.272158	−	0.942784i
$40$		0			0
$41$	1.73855	−	3.01126i	0.271516	−	0.470279i	−0.697734	−	0.716357i	$-0.745808\pi$
$41$	1.73855	−	3.01126i	0.271516	−	0.470279i	0.969250	+	0.246077i	$0.0791417\pi$
$42$		0			0
$43$	−5.12110	−	8.87000i	−0.780960	−	1.35266i	−0.931383	−	0.364040i	$-0.881397\pi$
$43$	−5.12110	−	8.87000i	−0.780960	−	1.35266i	0.150423	−	0.988622i	$-0.451936\pi$
$44$		0			0
$45$	0.0618219	+	0.107079i	0.00921587	+	0.0159624i
$46$		0			0
$47$	−3.98762			−0.581654			−0.290827	−	0.956776i	$-0.593930\pi$
$47$	−3.98762			−0.581654			−0.290827	+	0.956776i	$0.593930\pi$
$48$		0			0
$49$	0.882546	−	1.52861i	0.126078	−	0.218373i
$50$		0			0
$51$	5.90978			0.827534
$52$		0			0
$53$	−0.510520			−0.0701254			−0.0350627	−	0.999385i	$-0.511163\pi$
$53$	−0.510520			−0.0701254			−0.0350627	+	0.999385i	$0.511163\pi$
$54$		0			0
$55$	0.555632	−	0.962383i	0.0749214	−	0.129768i
$56$		0			0
$57$	1.18911			0.157501
$58$		0			0
$59$	0.343624	+	0.595175i	0.0447361	+	0.0774851i	0.887526	−	0.460757i	$-0.152422\pi$
$59$	0.343624	+	0.595175i	0.0447361	+	0.0774851i	−0.842790	+	0.538242i	$0.819089\pi$
$60$		0			0
$61$	2.10507	+	3.64610i	0.269527	+	0.466835i	0.968740	−	0.248079i	$-0.0797993\pi$
$61$	2.10507	+	3.64610i	0.269527	+	0.466835i	−0.699213	+	0.714914i	$0.746466\pi$
$62$		0			0
$63$	−0.127286	+	0.220465i	−0.0160365	+	0.0277760i
$64$		0			0
$65$	2.77816	−	2.88715i	0.344588	−	0.358107i
$66$		0			0
$67$	−6.08217	+	10.5346i	−0.743056	+	1.28701i	0.208042	+	0.978120i	$0.433291\pi$
$67$	−6.08217	+	10.5346i	−0.743056	+	1.28701i	−0.951098	+	0.308891i	$0.900042\pi$
$68$		0			0
$69$	1.63348	+	2.82926i	0.196647	+	0.340603i
$70$		0			0
$71$	3.01671	+	5.22510i	0.358018	+	0.620105i	0.987630	−	0.156805i	$-0.0501194\pi$
$71$	3.01671	+	5.22510i	0.358018	+	0.620105i	−0.629612	+	0.776910i	$0.716786\pi$
$72$		0			0
$73$	8.35346			0.977698			0.488849	−	0.872368i	$-0.337417\pi$
$73$	8.35346			0.977698			0.488849	+	0.872368i	$0.337417\pi$
$74$		0			0
$75$	−3.19963	+	5.54192i	−0.369461	+	0.639926i
$76$		0			0
$77$	2.28799			0.260741
$78$		0			0
$79$	−14.1309			−1.58985			−0.794927	−	0.606705i	$-0.792491\pi$
$79$	−14.1309			−1.58985			−0.794927	+	0.606705i	$0.792491\pi$
$80$		0			0
$81$	4.32691	−	7.49443i	0.480768	−	0.832715i
$82$		0			0
$83$	−3.51052			−0.385330			−0.192665	−	0.981265i	$-0.561713\pi$
$83$	−3.51052			−0.385330			−0.192665	+	0.981265i	$0.561713\pi$
$84$		0			0
$85$	1.93199	+	3.34630i	0.209554	+	0.362957i
$86$		0			0
$87$	−5.68292	−	9.84310i	−0.609273	−	1.05529i
$88$		0			0
$89$	−4.66690	+	8.08330i	−0.494690	+	0.856828i	−0.999981	−	0.00612063i	$-0.998052\pi$
$89$	−4.66690	+	8.08330i	−0.494690	+	0.856828i	0.505291	+	0.862949i	$0.331385\pi$
$90$		0			0
$91$	8.00797	+	1.98146i	0.839464	+	0.207713i
$92$		0			0
$93$	−4.92766	+	8.53495i	−0.510974	+	0.885033i
$94$		0			0
$95$	0.388736	+	0.673310i	0.0398835	+	0.0690802i
$96$		0			0
$97$	2.89926	+	5.02166i	0.294375	+	0.509872i	0.974839	−	0.222909i	$-0.0715552\pi$
$97$	2.89926	+	5.02166i	0.294375	+	0.509872i	−0.680464	+	0.732781i	$0.738222\pi$
$98$		0			0
$99$	0.111264			0.0111825
$100$		0			0
$101$	−6.49381	+	11.2476i	−0.646158	+	1.11918i	0.337874	+	0.941191i	$0.390292\pi$
$101$	−6.49381	+	11.2476i	−0.646158	+	1.11918i	−0.984033	+	0.177988i	$0.943041\pi$
$102$		0			0
$103$	−12.4327			−1.22503			−0.612514	−	0.790460i	$-0.709842\pi$
$103$	−12.4327			−1.22503			−0.612514	+	0.790460i	$0.709842\pi$
$104$		0			0
$105$	4.32141			0.421727
$106$		0			0
$107$	6.43199	−	11.1405i	0.621804	−	1.07700i	−0.367346	−	0.930084i	$-0.619733\pi$
$107$	6.43199	−	11.1405i	0.621804	−	1.07700i	0.989150	−	0.146911i	$-0.0469332\pi$
$108$		0			0
$109$	−0.346172			−0.0331573			−0.0165786	−	0.999863i	$-0.505277\pi$
$109$	−0.346172			−0.0331573			−0.0165786	+	0.999863i	$0.505277\pi$
$110$		0			0
$111$	0.905446	+	1.56828i	0.0859411	+	0.148854i
$112$		0			0
$113$	−2.93818	−	5.08907i	−0.276401	−	0.478740i	0.694087	−	0.719891i	$-0.255808\pi$
$113$	−2.93818	−	5.08907i	−0.276401	−	0.478740i	−0.970488	+	0.241151i	$0.922475\pi$
$114$		0			0
$115$	−1.06801	+	1.84985i	−0.0995926	+	0.172499i
$116$		0			0
$117$	0.389425	+	0.0963576i	0.0360023	+	0.00890826i
$118$		0			0
$119$	−3.97779	+	6.88973i	−0.364643	+	0.631581i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−2.95489	−	5.11802i	−0.266433	−	0.461476i
$124$		0			0
$125$	−9.74033			−0.871202
$126$		0			0
$127$	−4.94437	+	8.56390i	−0.438742	+	0.759923i	−0.997593	−	0.0693451i	$-0.977909\pi$
$127$	−4.94437	+	8.56390i	−0.438742	+	0.759923i	0.558851	+	0.829268i	$0.311242\pi$
$128$		0			0
$129$	−17.4079			−1.53268
$130$		0			0
$131$	15.2632			1.33355			0.666777	−	0.745257i	$-0.267673\pi$
$131$	15.2632			1.33355			0.666777	+	0.745257i	$0.267673\pi$
$132$		0			0
$133$	−0.800372	+	1.38628i	−0.0694010	+	0.120206i
$134$		0			0
$135$	5.87636			0.505756
$136$		0			0
$137$	9.75890	+	16.9029i	0.833759	+	1.44411i	0.895037	+	0.445993i	$0.147149\pi$
$137$	9.75890	+	16.9029i	0.833759	+	1.44411i	−0.0612773	+	0.998121i	$0.519517\pi$
$138$		0			0
$139$	−8.28799	−	14.3552i	−0.702978	−	1.21759i	−0.967416	−	0.253191i	$-0.918520\pi$
$139$	−8.28799	−	14.3552i	−0.702978	−	1.21759i	0.264438	−	0.964403i	$-0.414814\pi$
$140$		0			0
$141$	−3.38874	+	5.86946i	−0.285383	+	0.494298i
$142$		0			0
$143$	−1.00000	−	3.46410i	−0.0836242	−	0.289683i
$144$		0			0
$145$	3.71565	−	6.43569i	0.308568	−	0.534455i
$146$		0			0
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$		0			0
$149$	7.75526	+	13.4325i	0.635336	+	1.10043i	0.986444	+	0.164099i	$0.0524716\pi$
$149$	7.75526	+	13.4325i	0.635336	+	1.10043i	−0.351108	+	0.936335i	$0.614195\pi$
$150$		0			0
$151$	−2.76509			−0.225020			−0.112510	−	0.993651i	$-0.535889\pi$
$151$	−2.76509			−0.225020			−0.112510	+	0.993651i	$0.535889\pi$
$152$		0			0
$153$	−0.193438	+	0.335045i	−0.0156386	+	0.0270868i
$154$		0			0
$155$	−6.44368			−0.517569
$156$		0			0
$157$	−0.0123797			−0.000988009			−0.000494004	−	1.00000i	$-0.500157\pi$
$157$	−0.0123797			−0.000988009			−0.000494004		1.00000i	$0.500157\pi$
$158$		0			0
$159$	−0.433847	+	0.751446i	−0.0344063	+	0.0595935i
$160$		0			0
$161$	−4.39788			−0.346601
$162$		0			0
$163$	−11.7200	−	20.2996i	−0.917980	−	1.58999i	−0.802479	−	0.596680i	$-0.796486\pi$
$163$	−11.7200	−	20.2996i	−0.917980	−	1.58999i	−0.115500	−	0.993307i	$-0.536847\pi$
$164$		0			0
$165$	−0.944368	−	1.63569i	−0.0735189	−	0.127339i
$166$		0			0
$167$	−5.16071	+	8.93861i	−0.399347	+	0.691690i	−0.993646	−	0.112555i	$-0.964097\pi$
$167$	−5.16071	+	8.93861i	−0.399347	+	0.691690i	0.594298	+	0.804245i	$0.297430\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−0.0389218	+	0.0674145i	−0.00297642	+	0.00515531i
$172$		0			0
$173$	−0.193438	−	0.335045i	−0.0147068	−	0.0254730i	0.858578	−	0.512682i	$-0.171348\pi$
$173$	−0.193438	−	0.335045i	−0.0147068	−	0.0254730i	−0.873285	+	0.487209i	$0.838015\pi$
$174$		0			0
$175$	−4.30725	−	7.46038i	−0.325598	−	0.563951i
$176$		0			0
$177$	1.16807			0.0877973
$178$		0			0
$179$	−12.8207	+	22.2061i	−0.958266	+	1.65977i	−0.231555	+	0.972822i	$0.574381\pi$
$179$	−12.8207	+	22.2061i	−0.958266	+	1.65977i	−0.726711	+	0.686943i	$0.758952\pi$
$180$		0			0
$181$	−19.5970			−1.45664			−0.728318	−	0.685240i	$-0.759697\pi$
$181$	−19.5970			−1.45664			−0.728318	+	0.685240i	$0.759697\pi$
$182$		0			0
$183$	7.15569			0.528964
$184$		0			0
$185$	−0.592006	+	1.02538i	−0.0435251	+	0.0753878i
$186$		0			0
$187$	3.47710			0.254271
$188$		0			0
$189$	6.04944	+	10.4779i	0.440032	+	0.762158i
$190$		0			0
$191$	−5.46108	−	9.45886i	−0.395150	−	0.684419i	0.597971	−	0.801518i	$-0.295974\pi$
$191$	−5.46108	−	9.45886i	−0.395150	−	0.684419i	−0.993120	+	0.117099i	$0.962641\pi$
$192$		0			0
$193$	−1.68911	+	2.92562i	−0.121585	+	0.210591i	−0.920393	−	0.390995i	$-0.872131\pi$
$193$	−1.68911	+	2.92562i	−0.121585	+	0.210591i	0.798808	+	0.601586i	$0.205464\pi$
$194$		0			0
$195$	−1.88874	−	6.54277i	−0.135255	−	0.468538i
$196$		0			0
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	−0.660003	−	0.751263i	$-0.729445\pi$
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	0.980614	+	0.195947i	$0.0627782\pi$
$198$		0			0
$199$	2.86584	+	4.96377i	0.203154	+	0.351873i	0.949543	−	0.313637i	$-0.101548\pi$
$199$	2.86584	+	4.96377i	0.203154	+	0.351873i	−0.746389	+	0.665510i	$0.768214\pi$
$200$		0			0
$201$	10.3374	+	17.9050i	0.729146	+	1.26292i
$202$		0			0
$203$	15.3004			1.07388
$204$		0			0
$205$	1.93199	−	3.34630i	0.134936	−	0.233716i
$206$		0			0
$207$	−0.213867			−0.0148648
$208$		0			0
$209$	0.699628			0.0483943
$210$		0			0
$211$	3.04944	−	5.28179i	0.209932	−	0.363613i	−0.741761	−	0.670665i	$-0.766009\pi$
$211$	3.04944	−	5.28179i	0.209932	−	0.363613i	0.951693	+	0.307051i	$0.0993423\pi$
$212$		0			0
$213$	10.2546			0.702632
$214$		0			0
$215$	−5.69089	−	9.85691i	−0.388115	−	0.672236i
$216$		0			0
$217$	−6.63348	−	11.4895i	−0.450310	−	0.779959i
$218$		0			0
$219$	7.09888	−	12.2956i	0.479698	−	0.830862i
$220$		0			0
$221$	12.1698	+	3.01126i	0.818633	+	0.202559i
$222$		0			0
$223$	−4.76578	+	8.25457i	−0.319140	+	0.552767i	−0.980309	−	0.197470i	$-0.936727\pi$
$223$	−4.76578	+	8.25457i	−0.319140	+	0.552767i	0.661169	+	0.750237i	$0.270061\pi$
$224$		0			0
$225$	−0.209460	−	0.362795i	−0.0139640	−	0.0241863i
$226$		0			0
$227$	−6.83743	−	11.8428i	−0.453816	−	0.786033i	0.544803	−	0.838564i	$-0.316604\pi$
$227$	−6.83743	−	11.8428i	−0.453816	−	0.786033i	−0.998619	+	0.0525310i	$0.983271\pi$
$228$		0			0
$229$	8.72067			0.576278			0.288139	−	0.957589i	$-0.406963\pi$
$229$	8.72067			0.576278			0.288139	+	0.957589i	$0.406963\pi$
$230$		0			0
$231$	1.94437	−	3.36774i	0.127930	−	0.221581i
$232$		0			0
$233$	−0.353456			−0.0231557			−0.0115778	−	0.999933i	$-0.503685\pi$
$233$	−0.353456			−0.0231557			−0.0115778	+	0.999933i	$0.503685\pi$
$234$		0			0
$235$	−4.43130			−0.289066
$236$		0			0
$237$	−12.0087	+	20.7996i	−0.780046	+	1.35108i
$238$		0			0
$239$	11.6094			0.750950			0.375475	−	0.926833i	$-0.377480\pi$
$239$	11.6094			0.750950			0.375475	+	0.926833i	$0.377480\pi$
$240$		0			0
$241$	−10.2385	−	17.7337i	−0.659523	−	1.14233i	−0.980739	−	0.195321i	$-0.937425\pi$
$241$	−10.2385	−	17.7337i	−0.659523	−	1.14233i	0.321216	−	0.947006i	$-0.395908\pi$
$242$		0			0
$243$	0.577844	+	1.00085i	0.0370687	+	0.0642048i
$244$		0			0
$245$	0.980742	−	1.69869i	0.0626573	−	0.108526i
$246$		0			0
$247$	2.44870	+	0.605896i	0.155807	+	0.0385522i
$248$		0			0
$249$	−2.98329	+	5.16721i	−0.189058	+	0.327459i
$250$		0			0
$251$	3.38874	+	5.86946i	0.213895	+	0.370477i	0.952930	−	0.303190i	$-0.0980516\pi$
$251$	3.38874	+	5.86946i	0.213895	+	0.370477i	−0.739035	+	0.673667i	$0.764718\pi$
$252$		0			0
$253$	0.961078	+	1.66464i	0.0604225	+	0.104655i
$254$		0			0
$255$	6.56732			0.411262
$256$		0			0
$257$	11.8931	−	20.5994i	0.741869	−	1.28495i	−0.209774	−	0.977750i	$-0.567273\pi$
$257$	11.8931	−	20.5994i	0.741869	−	1.28495i	0.951643	−	0.307205i	$-0.0993938\pi$
$258$		0			0
$259$	−2.43777			−0.151476
$260$		0			0
$261$	0.744051			0.0460556
$262$		0			0
$263$	7.86219	−	13.6177i	0.484804	−	0.839705i	−0.515044	−	0.857164i	$-0.672224\pi$
$263$	7.86219	−	13.6177i	0.484804	−	0.839705i	0.999848	+	0.0174592i	$0.00555773\pi$
$264$		0			0
$265$	−0.567323			−0.0348504
$266$		0			0
$267$	7.93199	+	13.7386i	0.485430	+	0.840789i
$268$		0			0
$269$	1.66690	+	2.88715i	0.101632	+	0.176033i	0.912357	−	0.409395i	$-0.134260\pi$
$269$	1.66690	+	2.88715i	0.101632	+	0.176033i	−0.810725	+	0.585427i	$0.800927\pi$
$270$		0			0
$271$	−4.52723	+	7.84139i	−0.275010	+	0.476331i	−0.970138	−	0.242555i	$-0.922014\pi$
$271$	−4.52723	+	7.84139i	−0.275010	+	0.476331i	0.695128	+	0.718886i	$0.255348\pi$
$272$		0			0
$273$	9.72184	−	10.1032i	0.588392	−	0.611475i
$274$		0			0
$275$	−1.88255	+	3.26067i	−0.113522	+	0.196626i
$276$		0			0
$277$	3.42835	+	5.93807i	0.205989	+	0.356784i	0.950448	−	0.310885i	$-0.100625\pi$
$277$	3.42835	+	5.93807i	0.205989	+	0.356784i	−0.744458	+	0.667669i	$0.767292\pi$
$278$		0			0
$279$	−0.322583	−	0.558731i	−0.0193126	−	0.0334503i
$280$		0			0
$281$	25.2509			1.50634			0.753170	−	0.657826i	$-0.228524\pi$
$281$	25.2509			1.50634			0.753170	+	0.657826i	$0.228524\pi$
$282$		0			0
$283$	4.13416	−	7.16058i	0.245751	−	0.425652i	−0.716592	−	0.697493i	$-0.754299\pi$
$283$	4.13416	−	7.16058i	0.245751	−	0.425652i	0.962342	+	0.271840i	$0.0876323\pi$
$284$		0			0
$285$	1.32141			0.0782737
$286$		0			0
$287$	7.95558			0.469603
$288$		0			0
$289$	2.45489	−	4.25199i	0.144405	−	0.250117i
$290$		0			0
$291$	9.85532			0.577729
$292$		0			0
$293$	1.88874	+	3.27139i	0.110341	+	0.191116i	0.915908	−	0.401389i	$-0.131472\pi$
$293$	1.88874	+	3.27139i	0.110341	+	0.191116i	−0.805567	+	0.592505i	$0.798139\pi$
$294$		0			0
$295$	0.381857	+	0.661396i	0.0222326	+	0.0385080i
$296$		0			0
$297$	2.64400	−	4.57954i	0.153420	−	0.265732i
$298$		0			0
$299$	1.92216	+	6.65855i	0.111161	+	0.385074i
$300$		0			0
$301$	11.7170	−	20.2945i	0.675358	−	1.16975i
$302$		0			0
$303$	11.0371	+	19.1168i	0.634063	+	1.09823i
$304$		0			0
$305$	2.33929	+	4.05178i	0.133948	+	0.232004i
$306$		0			0
$307$	9.53528			0.544207			0.272104	−	0.962268i	$-0.412281\pi$
$307$	9.53528			0.544207			0.272104	+	0.962268i	$0.412281\pi$
$308$		0			0
$309$	−10.5655	+	18.2999i	−0.601048	+	1.04105i
$310$		0			0
$311$	8.00866			0.454130			0.227065	−	0.973880i	$-0.427087\pi$
$311$	8.00866			0.454130			0.227065	+	0.973880i	$0.427087\pi$
$312$		0			0
$313$	−4.33379			−0.244960			−0.122480	−	0.992471i	$-0.539085\pi$
$313$	−4.33379			−0.244960			−0.122480	+	0.992471i	$0.539085\pi$
$314$		0			0
$315$	−0.141448	+	0.244995i	−0.00796970	+	0.0138039i
$316$		0			0
$317$	30.1396			1.69281			0.846404	−	0.532541i	$-0.178763\pi$
$317$	30.1396			1.69281			0.846404	+	0.532541i	$0.178763\pi$
$318$		0			0
$319$	−3.34362	−	5.79133i	−0.187207	−	0.324252i
$320$		0			0
$321$	−10.9320	−	18.9348i	−0.610164	−	1.05684i
$322$		0			0
$323$	−1.21634	+	2.10676i	−0.0676789	+	0.117223i
$324$		0			0
$325$	−9.41273	+	9.78200i	−0.522124	+	0.542608i
$326$		0			0
$327$	−0.294182	+	0.509538i	−0.0162683	+	0.0281775i
$328$		0			0
$329$	−4.56182	−	7.90131i	−0.251501	−	0.435613i
$330$		0			0
$331$	4.39926	+	7.61974i	0.241805	+	0.418819i	0.961228	−	0.275753i	$-0.0889272\pi$
$331$	4.39926	+	7.61974i	0.241805	+	0.418819i	−0.719423	+	0.694572i	$0.755594\pi$
$332$		0			0
$333$	−0.118548			−0.00649639
$334$		0			0
$335$	−6.75890	+	11.7068i	−0.369278	+	0.639609i
$336$		0			0
$337$	−23.4079			−1.27511			−0.637555	−	0.770405i	$-0.720054\pi$
$337$	−23.4079			−1.27511			−0.637555	+	0.770405i	$0.720054\pi$
$338$		0			0
$339$	−9.98762			−0.542453
$340$		0			0
$341$	−2.89926	+	5.02166i	−0.157004	+	0.271938i
$342$		0			0
$343$	20.0545			1.08284
$344$		0			0
$345$	1.81522	+	3.14406i	0.0977283	+	0.169270i
$346$		0			0
$347$	−6.20327	−	10.7444i	−0.333009	−	0.576788i	0.650091	−	0.759856i	$-0.274731\pi$
$347$	−6.20327	−	10.7444i	−0.333009	−	0.576788i	−0.983100	+	0.183068i	$0.941397\pi$
$348$		0			0
$349$	0.0327319	−	0.0566933i	0.00175210	−	0.00303472i	−0.865148	−	0.501517i	$-0.832776\pi$
$349$	0.0327319	−	0.0566933i	0.00175210	−	0.00303472i	0.866900	+	0.498482i	$0.166109\pi$
$350$		0			0
$351$	13.2200	−	13.7386i	0.705630	−	0.733313i
$352$		0			0
$353$	16.4981	−	28.5756i	0.878107	−	1.52093i	0.0246921	−	0.999695i	$-0.492139\pi$
$353$	16.4981	−	28.5756i	0.878107	−	1.52093i	0.853415	−	0.521232i	$-0.174527\pi$
$354$		0			0
$355$	3.35236	+	5.80646i	0.177925	+	0.308175i
$356$		0			0
$357$	6.76076	+	11.7100i	0.357817	+	0.619758i
$358$		0			0
$359$	11.6328			0.613955			0.306978	−	0.951717i	$-0.400682\pi$
$359$	11.6328			0.613955			0.306978	+	0.951717i	$0.400682\pi$
$360$		0			0
$361$	9.25526	−	16.0306i	0.487119	−	0.843715i
$362$		0			0
$363$	−1.69963			−0.0892073
$364$		0			0
$365$	9.28290			0.485889
$366$		0			0
$367$	10.1971	−	17.6619i	0.532283	−	0.921942i	−0.467006	−	0.884254i	$-0.654667\pi$
$367$	10.1971	−	17.6619i	0.532283	−	0.921942i	0.999290	−	0.0376877i	$-0.0119992\pi$
$368$		0			0
$369$	0.386877			0.0201400
$370$		0			0
$371$	−0.584033	−	1.01158i	−0.0303215	−	0.0525184i
$372$		0			0
$373$	−12.0723	−	20.9099i	−0.625082	−	1.08267i	−0.988525	−	0.151058i	$-0.951732\pi$
$373$	−12.0723	−	20.9099i	−0.625082	−	1.08267i	0.363443	−	0.931617i	$-0.381601\pi$
$374$		0			0
$375$	−8.27747	+	14.3370i	−0.427447	+	0.740360i
$376$		0			0
$377$	−6.68725	−	23.1653i	−0.344411	−	1.19307i
$378$		0			0
$379$	−12.9814	+	22.4845i	−0.666811	+	1.15495i	0.311980	+	0.950089i	$0.399008\pi$
$379$	−12.9814	+	22.4845i	−0.666811	+	1.15495i	−0.978791	+	0.204862i	$0.934325\pi$
$380$		0			0
$381$	8.40359	+	14.5554i	0.430529	+	0.745698i
$382$		0			0
$383$	−2.03706	−	3.52830i	−0.104089	−	0.180287i	0.809277	−	0.587428i	$-0.199859\pi$
$383$	−2.03706	−	3.52830i	−0.104089	−	0.180287i	−0.913366	+	0.407140i	$0.866526\pi$
$384$		0			0
$385$	2.54256			0.129581
$386$		0			0
$387$	0.569794	−	0.986913i	0.0289643	−	0.0501676i
$388$		0			0
$389$	−20.5192			−1.04036			−0.520182	−	0.854055i	$-0.674136\pi$
$389$	−20.5192			−1.04036			−0.520182	+	0.854055i	$0.674136\pi$
$390$		0			0
$391$	−6.68353			−0.338001
$392$		0			0
$393$	12.9709	−	22.4663i	0.654296	−	1.13327i
$394$		0			0
$395$	−15.7032			−0.790113
$396$		0			0
$397$	−8.49126	−	14.7073i	−0.426164	−	0.738138i	0.570364	−	0.821392i	$-0.306802\pi$
$397$	−8.49126	−	14.7073i	−0.426164	−	0.738138i	−0.996528	+	0.0832539i	$0.973469\pi$
$398$		0			0
$399$	1.36033	+	2.35617i	0.0681019	+	0.117956i
$400$		0			0
$401$	−16.8633	+	29.2081i	−0.842112	+	1.45858i	0.0459931	+	0.998942i	$0.485355\pi$
$401$	−16.8633	+	29.2081i	−0.842112	+	1.45858i	−0.888105	+	0.459640i	$0.847979\pi$
$402$		0			0
$403$	−14.4963	+	15.0650i	−0.722111	+	0.750440i
$404$		0			0
$405$	4.80834	−	8.32830i	0.238929	−	0.413836i
$406$		0			0
$407$	0.532732	+	0.922719i	0.0264065	+	0.0457375i
$408$		0			0
$409$	−3.68980	−	6.39091i	−0.182449	−	0.316010i	0.760265	−	0.649613i	$-0.225069\pi$
$409$	−3.68980	−	6.39091i	−0.182449	−	0.316010i	−0.942714	+	0.333602i	$0.891736\pi$
$410$		0			0
$411$	33.1730			1.63630
$412$		0			0
$413$	−0.786210	+	1.36175i	−0.0386868	+	0.0670076i
$414$		0			0
$415$	−3.90112			−0.191498
$416$		0			0
$417$	−28.1730			−1.37964
$418$		0			0
$419$	−3.42216	+	5.92735i	−0.167183	+	0.289570i	−0.937428	−	0.348178i	$-0.886800\pi$
$419$	−3.42216	+	5.92735i	−0.167183	+	0.289570i	0.770245	+	0.637748i	$0.220134\pi$
$420$		0			0
$421$	−30.5017			−1.48656			−0.743281	−	0.668979i	$-0.766731\pi$
$421$	−30.5017			−1.48656			−0.743281	+	0.668979i	$0.766731\pi$
$422$		0			0
$423$	−0.221840	−	0.384237i	−0.0107862	−	0.0186823i
$424$		0			0
$425$	−6.54580	−	11.3377i	−0.317518	−	0.549957i
$426$		0			0
$427$	−4.81639	+	8.34224i	−0.233082	+	0.403709i
$428$		0			0
$429$	−5.94870	−	1.47192i	−0.287206	−	0.0710650i
$430$		0			0
$431$	−8.89493	+	15.4065i	−0.428453	+	0.742103i	−0.996736	−	0.0807303i	$-0.974275\pi$
$431$	−8.89493	+	15.4065i	−0.428453	+	0.742103i	0.568282	+	0.822834i	$0.307608\pi$
$432$		0			0
$433$	−9.41597	−	16.3089i	−0.452502	−	0.783757i	0.546038	−	0.837760i	$-0.316135\pi$
$433$	−9.41597	−	16.3089i	−0.452502	−	0.783757i	−0.998541	+	0.0540029i	$0.982802\pi$
$434$		0			0
$435$	−6.31522	−	10.9383i	−0.302792	−	0.524451i
$436$		0			0
$437$	−1.34479			−0.0643303
$438$		0			0
$439$	−12.2491	+	21.2160i	−0.584616	+	1.01259i	0.410307	+	0.911947i	$0.365422\pi$
$439$	−12.2491	+	21.2160i	−0.584616	+	1.01259i	−0.994923	+	0.100638i	$0.967912\pi$
$440$		0			0
$441$	0.196391			0.00935197
$442$		0			0
$443$	16.6414			0.790659			0.395330	−	0.918539i	$-0.370630\pi$
$443$	16.6414			0.790659			0.395330	+	0.918539i	$0.370630\pi$
$444$		0			0
$445$	−5.18615	+	8.98268i	−0.245847	+	0.425820i
$446$		0			0
$447$	26.3621			1.24689
$448$		0			0
$449$	−11.6192	−	20.1251i	−0.548346	−	0.949763i	−0.998388	−	0.0567554i	$-0.981924\pi$
$449$	−11.6192	−	20.1251i	−0.548346	−	0.949763i	0.450042	−	0.893007i	$-0.351409\pi$
$450$		0			0
$451$	−1.73855	−	3.01126i	−0.0818651	−	0.141795i
$452$		0			0
$453$	−2.34981	+	4.07000i	−0.110404	+	0.191225i
$454$		0			0
$455$	8.89897	+	2.20192i	0.417190	+	0.103228i
$456$		0			0
$457$	6.69344	−	11.5934i	0.313106	−	0.542315i	−0.665927	−	0.746017i	$-0.731964\pi$
$457$	6.69344	−	11.5934i	0.313106	−	0.542315i	0.979033	+	0.203702i	$0.0652972\pi$
$458$		0			0
$459$	9.19344	+	15.9235i	0.429113	+	0.743245i
$460$		0			0
$461$	−7.74838	−	13.4206i	−0.360878	−	0.625059i	0.627227	−	0.778836i	$-0.284190\pi$
$461$	−7.74838	−	13.4206i	−0.360878	−	0.625059i	−0.988106	+	0.153777i	$0.950856\pi$
$462$		0			0
$463$	24.7751			1.15140			0.575699	−	0.817662i	$-0.304730\pi$
$463$	24.7751			1.15140			0.575699	+	0.817662i	$0.304730\pi$
$464$		0			0
$465$	−5.47593	+	9.48459i	−0.253940	+	0.439837i
$466$		0			0
$467$	2.54256			0.117656			0.0588279	−	0.998268i	$-0.481264\pi$
$467$	2.54256			0.117656			0.0588279	+	0.998268i	$0.481264\pi$
$468$		0			0
$469$	−27.8319			−1.28516
$470$		0			0
$471$	−0.0105205	+	0.0182220i	−0.000484757	+	0.000839624i
$472$		0			0
$473$	−10.2422			−0.470936
$474$		0			0
$475$	−1.31708	−	2.28125i	−0.0604319	−	0.104671i
$476$		0			0
$477$	−0.0284013	−	0.0491925i	−0.00130041	−	0.00225237i
$478$		0			0
$479$	−11.9913	+	20.7695i	−0.547895	+	0.948982i	0.450524	+	0.892764i	$0.351237\pi$
$479$	−11.9913	+	20.7695i	−0.547895	+	0.948982i	−0.998419	+	0.0562171i	$0.982096\pi$
$480$		0			0
$481$	1.06546	+	3.69087i	0.0485810	+	0.168289i
$482$		0			0
$483$	−3.73738	+	6.47333i	−0.170057	+	0.294547i
$484$		0			0
$485$	3.22184	+	5.58039i	0.146296	+	0.253392i
$486$		0			0
$487$	−0.189108	−	0.327544i	−0.00856929	−	0.0148424i	0.861709	−	0.507403i	$-0.169394\pi$
$487$	−0.189108	−	0.327544i	−0.00856929	−	0.0148424i	−0.870278	+	0.492560i	$0.836061\pi$
$488$		0			0
$489$	−39.8392			−1.80159
$490$		0			0
$491$	12.1749	−	21.0875i	0.549444	−	0.951665i	−0.448869	−	0.893598i	$-0.648173\pi$
$491$	12.1749	−	21.0875i	0.549444	−	0.951665i	0.998313	−	0.0580673i	$-0.0184938\pi$
$492$		0			0
$493$	23.2522			1.04723
$494$		0			0
$495$	0.123644			0.00555738
$496$		0			0
$497$	−6.90221	+	11.9550i	−0.309606	+	0.536254i
$498$		0			0
$499$	−1.23353			−0.0552204			−0.0276102	−	0.999619i	$-0.508790\pi$
$499$	−1.23353			−0.0552204			−0.0276102	+	0.999619i	$0.508790\pi$
$500$		0			0
$501$	8.77128	+	15.1923i	0.391872	+	0.678742i
$502$		0			0
$503$	−0.228718	−	0.396151i	−0.0101980	−	0.0176635i	0.860881	−	0.508806i	$-0.169913\pi$
$503$	−0.228718	−	0.396151i	−0.0101980	−	0.0176635i	−0.871079	+	0.491142i	$0.836580\pi$
$504$		0			0
$505$	−7.21634	+	12.4991i	−0.321123	+	0.556201i
$506$		0			0
$507$	−19.5457	−	10.3034i	−0.868056	−	0.457592i
$508$		0			0
$509$	−20.9746	+	36.3290i	−0.929681	+	1.61025i	−0.145826	+	0.989310i	$0.546584\pi$
$509$	−20.9746	+	36.3290i	−0.929681	+	1.61025i	−0.783855	+	0.620944i	$0.786749\pi$
$510$		0			0
$511$	9.55632	+	16.5520i	0.422747	+	0.732219i
$512$		0			0
$513$	1.84981	+	3.20397i	0.0816713	+	0.141459i
$514$		0			0
$515$	−13.8160			−0.608805
$516$		0			0
$517$	−1.99381	+	3.45338i	−0.0876877	+	0.151879i
$518$		0			0
$519$	−0.657546			−0.0288631
$520$		0			0
$521$	10.5316			0.461396			0.230698	−	0.973025i	$-0.425899\pi$
$521$	10.5316			0.461396			0.230698	+	0.973025i	$0.425899\pi$
$522$		0			0
$523$	−6.89307	+	11.9391i	−0.301413	+	0.522062i	−0.976456	−	0.215716i	$-0.930792\pi$
$523$	−6.89307	+	11.9391i	−0.301413	+	0.522062i	0.675043	+	0.737778i	$0.264125\pi$
$524$		0			0
$525$	−14.6414			−0.639005
$526$		0			0
$527$	−10.0810	−	17.4608i	−0.439135	−	0.760605i
$528$		0			0
$529$	9.65266	+	16.7189i	0.419681	+	0.726908i
$530$		0			0
$531$	−0.0382331	+	0.0662216i	−0.00165917	+	0.00287377i
$532$		0			0
$533$	−3.47710	−	12.0450i	−0.150610	−	0.521728i
$534$		0			0
$535$	7.14764	−	12.3801i	0.309019	−	0.535237i
$536$		0			0
$537$	21.7905	+	37.7422i	0.940328	+	1.62870i
$538$		0			0
$539$	−0.882546	−	1.52861i	−0.0380139	−	0.0658421i
$540$		0			0
$541$	41.4028			1.78005			0.890023	−	0.455915i	$-0.150688\pi$
$541$	41.4028			1.78005			0.890023	+	0.455915i	$0.150688\pi$
$542$		0			0
$543$	−16.6538	+	28.8453i	−0.714684	+	1.23787i
$544$		0			0
$545$	−0.384689			−0.0164783
$546$		0			0
$547$	16.9629			0.725280			0.362640	−	0.931929i	$-0.381876\pi$
$547$	16.9629			0.725280			0.362640	+	0.931929i	$0.381876\pi$
$548$		0			0
$549$	−0.234219	+	0.405680i	−0.00999624	+	0.0173140i
$550$		0			0
$551$	4.67859			0.199315
$552$		0			0
$553$	−16.1657	−	27.9999i	−0.687437	−	1.19068i
$554$		0			0
$555$	1.00619	+	1.74277i	0.0427104	+	0.0739765i
$556$		0			0
$557$	−18.3319	+	31.7518i	−0.776749	+	1.34537i	0.157057	+	0.987589i	$0.449799\pi$
$557$	−18.3319	+	31.7518i	−0.776749	+	1.34537i	−0.933806	+	0.357779i	$0.883534\pi$
$558$		0			0
$559$	−35.8477	−	8.87000i	−1.51619	−	0.375161i
$560$		0			0
$561$	2.95489	−	5.11802i	0.124755	−	0.216083i
$562$		0			0
$563$	4.52468	+	7.83698i	0.190693	+	0.330289i	0.945480	−	0.325680i	$-0.105593\pi$
$563$	4.52468	+	7.83698i	0.190693	+	0.330289i	−0.754787	+	0.655970i	$0.772260\pi$
$564$		0			0
$565$	−3.26509	−	5.65531i	−0.137363	−	0.237920i
$566$		0			0
$567$	19.7999			0.831517
$568$		0			0
$569$	10.0760	−	17.4521i	0.422407	−	0.731631i	−0.573767	−	0.819018i	$-0.694519\pi$
$569$	10.0760	−	17.4521i	0.422407	−	0.731631i	0.996174	+	0.0873877i	$0.0278519\pi$
$570$		0			0
$571$	36.0507			1.50868			0.754338	−	0.656486i	$-0.227958\pi$
$571$	36.0507			1.50868			0.754338	+	0.656486i	$0.227958\pi$
$572$		0			0
$573$	−18.5636			−0.775506
$574$		0			0
$575$	3.61855	−	6.26751i	0.150904	−	0.261373i
$576$		0			0
$577$	−14.9890			−0.624000			−0.312000	−	0.950082i	$-0.600999\pi$
$577$	−14.9890			−0.624000			−0.312000	+	0.950082i	$0.600999\pi$
$578$		0			0
$579$	2.87085	+	4.97247i	0.119309	+	0.206649i
$580$		0			0
$581$	−4.01602	−	6.95595i	−0.166613	−	0.288582i
$582$		0			0
$583$	−0.255260	+	0.442124i	−0.0105718	+	0.0183109i
$584$		0			0
$585$	0.432754	+	0.107079i	0.0178922	+	0.00442716i
$586$		0			0
$587$	8.94506	−	15.4933i	0.369202	−	0.639477i	−0.620239	−	0.784413i	$-0.712964\pi$
$587$	8.94506	−	15.4933i	0.369202	−	0.639477i	0.989441	+	0.144936i	$0.0462977\pi$
$588$		0			0
$589$	−2.02840	−	3.51329i	−0.0835788	−	0.144763i
$590$		0			0
$591$	−7.64833	−	13.2473i	−0.314610	−	0.544921i
$592$		0			0
$593$	23.7193			0.974035			0.487017	−	0.873392i	$-0.338085\pi$
$593$	23.7193			0.974035			0.487017	+	0.873392i	$0.338085\pi$
$594$		0			0
$595$	−4.42037	+	7.65631i	−0.181218	+	0.313878i
$596$		0			0
$597$	9.74171			0.398702
$598$		0			0
$599$	4.71201			0.192527			0.0962637	−	0.995356i	$-0.469311\pi$
$599$	4.71201			0.192527			0.0962637	+	0.995356i	$0.469311\pi$
$600$		0			0
$601$	−15.6025	+	27.0244i	−0.636440	+	1.10235i	0.349768	+	0.936836i	$0.386261\pi$
$601$	−15.6025	+	27.0244i	−0.636440	+	1.10235i	−0.986208	+	0.165511i	$0.947073\pi$
$602$		0			0
$603$	−1.35346			−0.0551170
$604$		0			0
$605$	−0.555632	−	0.962383i	−0.0225897	−	0.0391264i
$606$		0			0
$607$	−4.93268	−	8.54365i	−0.200211	−	0.346776i	0.748385	−	0.663264i	$-0.230829\pi$
$607$	−4.93268	−	8.54365i	−0.200211	−	0.346776i	−0.948596	+	0.316488i	$0.897496\pi$
$608$		0			0
$609$	13.0025	−	22.5209i	0.526887	−	0.912595i
$610$		0			0
$611$	−9.96905	+	10.3601i	−0.403305	+	0.419126i
$612$		0			0
$613$	1.68292	−	2.91490i	0.0679724	−	0.117732i	−0.830036	−	0.557709i	$-0.811680\pi$
$613$	1.68292	−	2.91490i	0.0679724	−	0.117732i	0.898009	+	0.439978i	$0.145014\pi$
$614$		0			0
$615$	−3.28366	−	5.68747i	−0.132410	−	0.229341i
$616$		0			0
$617$	11.2992	+	19.5708i	0.454889	+	0.787890i	0.998682	−	0.0513290i	$-0.0163457\pi$
$617$	11.2992	+	19.5708i	0.454889	+	0.787890i	−0.543793	+	0.839219i	$0.683012\pi$
$618$		0			0
$619$	9.52152			0.382702			0.191351	−	0.981522i	$-0.438713\pi$
$619$	9.52152			0.382702			0.191351	+	0.981522i	$0.438713\pi$
$620$		0			0
$621$	−5.08217	+	8.80258i	−0.203941	+	0.353236i
$622$		0			0
$623$	−21.3556			−0.855596
$624$		0			0
$625$	8.00138			0.320055
$626$		0			0
$627$	0.594554	−	1.02980i	0.0237442	−	0.0411261i
$628$		0			0
$629$	−3.70472			−0.147717
$630$		0			0
$631$	3.35965	+	5.81908i	0.133745	+	0.231654i	0.925117	−	0.379681i	$-0.123966\pi$
$631$	3.35965	+	5.81908i	0.133745	+	0.231654i	−0.791372	+	0.611335i	$0.790633\pi$
$632$		0			0
$633$	−5.18292	−	8.97708i	−0.206002	−	0.356807i
$634$		0			0
$635$	−5.49450	+	9.51675i	−0.218043	+	0.377661i
$636$		0			0
$637$	−1.76509	−	6.11446i	−0.0699355	−	0.242264i
$638$		0			0
$639$	−0.335652	+	0.581366i	−0.0132782	+	0.0229985i
$640$		0			0
$641$	−19.7348	−	34.1817i	−0.779479	−	1.35010i	−0.932242	−	0.361834i	$-0.882151\pi$
$641$	−19.7348	−	34.1817i	−0.779479	−	1.35010i	0.152763	−	0.988263i	$-0.451183\pi$
$642$		0			0
$643$	6.53637	+	11.3213i	0.257769	+	0.446470i	0.965644	−	0.259868i	$-0.0836792\pi$
$643$	6.53637	+	11.3213i	0.257769	+	0.446470i	−0.707875	+	0.706338i	$0.750346\pi$
$644$		0			0
$645$	−19.3448			−0.761701
$646$		0			0
$647$	12.0080	−	20.7984i	0.472082	−	0.817670i	−0.527408	−	0.849612i	$-0.676836\pi$
$647$	12.0080	−	20.7984i	0.472082	−	0.817670i	0.999490	+	0.0319422i	$0.0101692\pi$
$648$		0			0
$649$	0.687248			0.0269769
$650$		0			0
$651$	−22.5489			−0.883760
$652$		0			0
$653$	−18.4920	+	32.0290i	−0.723646	+	1.25339i	0.235883	+	0.971781i	$0.424202\pi$
$653$	−18.4920	+	32.0290i	−0.723646	+	1.25339i	−0.959529	+	0.281610i	$0.909132\pi$
$654$		0			0
$655$	16.9615			0.662740
$656$		0			0
$657$	0.464720	+	0.804919i	0.0181305	+	0.0314029i
$658$		0			0
$659$	12.7403	+	22.0669i	0.496293	+	0.859605i	0.999991	−	0.00427532i	$-0.00136088\pi$
$659$	12.7403	+	22.0669i	0.496293	+	0.859605i	−0.503698	+	0.863880i	$0.668028\pi$
$660$		0			0
$661$	7.42766	−	12.8651i	0.288902	−	0.500394i	−0.684646	−	0.728876i	$-0.740043\pi$
$661$	7.42766	−	12.8651i	0.288902	−	0.500394i	0.973548	+	0.228482i	$0.0733764\pi$
$662$		0			0
$663$	14.7744	−	15.3541i	0.573792	−	0.596302i
$664$		0			0
$665$	−0.889425	+	1.54053i	−0.0344904	+	0.0597391i
$666$		0			0
$667$	6.42697	+	11.1318i	0.248853	+	0.431026i
$668$		0			0
$669$	8.10005	+	14.0297i	0.313166	+	0.542420i
$670$		0			0
$671$	4.21015			0.162531
$672$		0			0
$673$	23.0483	−	39.9208i	0.888446	−	1.53883i	0.0467327	−	0.998907i	$-0.485119\pi$
$673$	23.0483	−	39.9208i	0.888446	−	1.53883i	0.841713	−	0.539925i	$-0.181548\pi$
$674$		0			0
$675$	−19.9098			−0.766328
$676$		0			0
$677$	−24.8502			−0.955072			−0.477536	−	0.878612i	$-0.658470\pi$
$677$	−24.8502			−0.955072			−0.477536	+	0.878612i	$0.658470\pi$
$678$		0			0
$679$	−6.63348	+	11.4895i	−0.254569	+	0.440927i
$680$		0			0
$681$	−23.2422			−0.890643
$682$		0			0
$683$	16.8015	+	29.1010i	0.642890	+	1.11352i	0.984784	+	0.173780i	$0.0555982\pi$
$683$	16.8015	+	29.1010i	0.642890	+	1.11352i	−0.341894	+	0.939738i	$0.611068\pi$
$684$		0			0
$685$	10.8447	+	18.7836i	0.414355	+	0.717685i
$686$		0			0
$687$	7.41095	−	12.8361i	0.282745	−	0.489729i
$688$		0			0
$689$	−1.27630	+	1.32637i	−0.0486232	+	0.0505307i
$690$		0			0
$691$	−16.7225	+	28.9643i	−0.636155	+	1.10185i	0.350114	+	0.936707i	$0.386143\pi$
$691$	−16.7225	+	28.9643i	−0.636155	+	1.10185i	−0.986269	+	0.165146i	$0.947191\pi$
$692$		0			0
$693$	0.127286	+	0.220465i	0.00483519	+	0.00837479i
$694$		0			0
$695$	−9.21015	−	15.9524i	−0.349361	−	0.605111i
$696$		0			0
$697$	12.0902			0.457950
$698$		0			0
$699$	−0.300372	+	0.520259i	−0.0113611	+	0.0196780i
$700$		0			0
$701$	−21.1396			−0.798431			−0.399216	−	0.916857i	$-0.630718\pi$
$701$	−21.1396			−0.798431			−0.399216	+	0.916857i	$0.630718\pi$
$702$		0			0
$703$	−0.745428			−0.0281144
$704$		0			0
$705$	−3.76578	+	6.52252i	−0.141828	+	0.245652i
$706$		0			0
$707$	−29.7156			−1.11757
$708$		0			0
$709$	−8.24288	−	14.2771i	−0.309568	−	0.536187i	0.668700	−	0.743532i	$-0.266851\pi$
$709$	−8.24288	−	14.2771i	−0.309568	−	0.536187i	−0.978268	+	0.207345i	$0.933518\pi$
$710$		0			0
$711$	−0.786133	−	1.36162i	−0.0294823	−	0.0510648i
$712$		0			0
$713$	5.57282	−	9.65241i	0.208704	−	0.361486i
$714$		0			0
$715$	−1.11126	−	3.84953i	−0.0415589	−	0.143964i
$716$		0			0
$717$	9.86584	−	17.0881i	0.368446	−	0.638168i
$718$		0			0
$719$	−6.01671	−	10.4212i	−0.224385	−	0.388647i	0.731749	−	0.681574i	$-0.238704\pi$
$719$	−6.01671	−	10.4212i	−0.224385	−	0.388647i	−0.956135	+	0.292927i	$0.905371\pi$
$720$		0			0
$721$	−14.2229	−	24.6348i	−0.529690	−	0.917450i
$722$		0			0
$723$	−34.8035			−1.29435
$724$		0			0
$725$	−12.5891	+	21.8049i	−0.467546	+	0.809813i
$726$		0			0
$727$	−11.5846			−0.429651			−0.214825	−	0.976652i	$-0.568918\pi$
$727$	−11.5846			−0.429651			−0.214825	+	0.976652i	$0.568918\pi$
$728$		0			0
$729$	27.9257			1.03429
$730$		0			0
$731$	17.8066	−	30.8419i	0.658599	−	1.14073i
$732$		0			0
$733$	19.2051			0.709355			0.354677	−	0.934989i	$-0.384591\pi$
$733$	19.2051			0.709355			0.354677	+	0.934989i	$0.384591\pi$
$734$		0			0
$735$	−1.66690	−	2.88715i	−0.0614844	−	0.106494i
$736$		0			0
$737$	6.08217	+	10.5346i	0.224040	+	0.388048i
$738$		0			0
$739$	−7.23855	+	12.5375i	−0.266274	+	0.461201i	−0.967897	−	0.251348i	$-0.919126\pi$
$739$	−7.23855	+	12.5375i	−0.266274	+	0.461201i	0.701622	+	0.712549i	$0.252459\pi$
$740$		0			0
$741$	2.97277	−	3.08939i	0.109207	−	0.113492i
$742$		0			0
$743$	11.1774	−	19.3599i	0.410060	−	0.710244i	−0.584836	−	0.811151i	$-0.698841\pi$
$743$	11.1774	−	19.3599i	0.410060	−	0.710244i	0.994896	+	0.100907i	$0.0321745\pi$
$744$		0			0
$745$	8.61814	+	14.9271i	0.315744	+	0.546885i
$746$		0			0
$747$	−0.195298	−	0.338265i	−0.00714556	−	0.0123765i
$748$		0			0
$749$	29.4327			1.07545
$750$		0			0
$751$	−8.07413	+	13.9848i	−0.294629	+	0.510312i	−0.974899	−	0.222650i	$-0.928529\pi$
$751$	−8.07413	+	13.9848i	−0.294629	+	0.510312i	0.680270	+	0.732962i	$0.261863\pi$
$752$		0			0
$753$	11.5192			0.419782
$754$		0			0
$755$	−3.07275			−0.111829
$756$		0			0
$757$	9.88874	−	17.1278i	0.359412	−	0.622520i	−0.628451	−	0.777850i	$-0.716311\pi$
$757$	9.88874	−	17.1278i	0.359412	−	0.622520i	0.987863	+	0.155329i	$0.0496439\pi$
$758$		0			0
$759$	3.26695			0.118583
$760$		0			0
$761$	−1.72184	−	2.98231i	−0.0624166	−	0.108109i	0.833128	−	0.553079i	$-0.186547\pi$
$761$	−1.72184	−	2.98231i	−0.0624166	−	0.108109i	−0.895545	+	0.444971i	$0.853214\pi$
$762$		0			0
$763$	−0.396020	−	0.685926i	−0.0143369	−	0.0248322i
$764$		0			0
$765$	−0.214961	+	0.372323i	−0.00777193	+	0.0134614i
$766$		0			0
$767$	2.40537	+	0.595175i	0.0868529	+	0.0214905i
$768$		0			0
$769$	−12.0254	+	20.8286i	−0.433646	+	0.751097i	−0.997184	−	0.0749932i	$-0.976106\pi$
$769$	−12.0254	+	20.8286i	−0.433646	+	0.751097i	0.563538	+	0.826090i	$0.309440\pi$
$770$		0			0
$771$	−20.2138	−	35.0113i	−0.727982	−	1.26090i
$772$		0			0
$773$	27.5883	+	47.7843i	0.992282	+	1.71868i	0.603531	+	0.797339i	$0.293760\pi$
$773$	27.5883	+	47.7843i	0.992282	+	1.71868i	0.388750	+	0.921343i	$0.372907\pi$
$774$		0			0
$775$	21.8319			0.784226
$776$		0			0
$777$	−2.07165	+	3.58821i	−0.0743202	+	0.128726i
$778$		0			0
$779$	2.43268			0.0871597
$780$		0			0
$781$	6.03342			0.215893
$782$		0			0
$783$	17.6811	−	30.6245i	0.631869	−	1.09443i
$784$		0			0
$785$	−0.0137571			−0.000491013
$786$		0			0
$787$	−16.8640	−	29.2093i	−0.601136	−	1.04120i	−0.992649	−	0.121025i	$-0.961382\pi$
$787$	−16.8640	−	29.2093i	−0.601136	−	1.04120i	0.391514	−	0.920172i	$-0.371952\pi$
$788$		0			0
$789$	−13.3628	−	23.1451i	−0.475728	−	0.823986i
$790$		0			0
$791$	6.72253	−	11.6438i	0.239026	−	0.414004i
$792$		0			0
$793$	14.7355	+	3.64610i	0.523274	+	0.129477i
$794$		0			0
$795$	−0.482119	+	0.835055i	−0.0170990	+	0.0296163i
$796$		0			0
$797$	2.33242	+	4.03986i	0.0826184	+	0.143099i	0.904374	−	0.426741i	$-0.140338\pi$
$797$	2.33242	+	4.03986i	0.0826184	+	0.143099i	−0.821755	+	0.569840i	$0.807005\pi$
$798$		0			0
$799$	−6.93268	−	12.0077i	−0.245260	−	0.424804i
$800$		0			0
$801$	−1.03852			−0.0366942
$802$		0			0
$803$	4.17673	−	7.23431i	0.147394	−	0.255293i
$804$		0			0
$805$	−4.88721			−0.172251
$806$		0			0
$807$	5.66621			0.199460
$808$		0			0
$809$	−7.72184	+	13.3746i	−0.271485	+	0.470227i	−0.969242	−	0.246108i	$-0.920848\pi$
$809$	−7.72184	+	13.3746i	−0.271485	+	0.470227i	0.697757	+	0.716335i	$0.254182\pi$
$810$		0			0
$811$	54.6945			1.92058			0.960292	−	0.278996i	$-0.0900015\pi$
$811$	54.6945			1.92058			0.960292	+	0.278996i	$0.0900015\pi$
$812$		0			0
$813$	7.69461	+	13.3275i	0.269862	+	0.467414i
$814$		0			0
$815$	−13.0240	−	22.5582i	−0.456211	−	0.790180i
$816$		0			0
$817$	3.58286	−	6.20570i	0.125349	−	0.217110i
$818$		0			0
$819$	0.254572	+	0.881862i	0.00889545	+	0.0308147i
$820$		0			0
$821$	11.9010	−	20.6132i	0.415349	−	0.719406i	−0.580116	−	0.814534i	$-0.696993\pi$
$821$	11.9010	−	20.6132i	0.415349	−	0.719406i	0.995465	+	0.0951282i	$0.0303261\pi$
$822$		0			0
$823$	26.2818	+	45.5214i	0.916126	+	1.58678i	0.805244	+	0.592943i	$0.202034\pi$
$823$	26.2818	+	45.5214i	0.916126	+	1.58678i	0.110882	+	0.993834i	$0.464633\pi$
$824$		0			0
$825$	3.19963	+	5.54192i	0.111397	+	0.192945i
$826$		0			0
$827$	−43.3236			−1.50651			−0.753255	−	0.657729i	$-0.771517\pi$
$827$	−43.3236			−1.50651			−0.753255	+	0.657729i	$0.771517\pi$
$828$		0			0
$829$	6.28985	−	10.8943i	0.218456	−	0.378376i	−0.735880	−	0.677112i	$-0.763231\pi$
$829$	6.28985	−	10.8943i	0.218456	−	0.378376i	0.954336	+	0.298735i	$0.0965648\pi$
$830$		0			0
$831$	11.6538			0.404267
$832$		0			0
$833$	6.13740			0.212648
$834$		0			0
$835$	−5.73491	+	9.93315i	−0.198465	+	0.343751i
$836$		0			0
$837$	−30.6625			−1.05985
$838$		0			0
$839$	−25.2145	−	43.6728i	−0.870500	−	1.50775i	−0.861480	−	0.507792i	$-0.830462\pi$
$839$	−25.2145	−	43.6728i	−0.870500	−	1.50775i	−0.00902065	−	0.999959i	$-0.502871\pi$
$840$		0			0
$841$	−7.85965	−	13.6133i	−0.271022	−	0.469424i
$842$		0			0
$843$	21.4585	−	37.1673i	0.739071	−	1.28011i
$844$		0			0
$845$	−0.555632	−	14.4357i	−0.0191143	−	0.496605i
$846$		0			0
$847$	1.14400	−	1.98146i	0.0393082	−	0.0680837i
$848$		0			0
$849$	−7.02654	−	12.1703i	−0.241150	−	0.417685i
$850$		0			0
$851$	−1.02399	−	1.77361i	−0.0351021	−	0.0607986i
$852$		0			0
$853$	53.4930			1.83157			0.915783	−	0.401672i	$-0.131571\pi$
$853$	53.4930			1.83157			0.915783	+	0.401672i	$0.131571\pi$
$854$		0			0
$855$	−0.0432524	+	0.0749153i	−0.00147920	+	0.00256205i
$856$		0			0
$857$	38.2522			1.30667			0.653336	−	0.757068i	$-0.273369\pi$
$857$	38.2522			1.30667			0.653336	+	0.757068i	$0.273369\pi$
$858$		0			0
$859$	−1.79495			−0.0612428			−0.0306214	−	0.999531i	$-0.509749\pi$
$859$	−1.79495			−0.0612428			−0.0306214	+	0.999531i	$0.509749\pi$
$860$		0			0
$861$	6.76076	−	11.7100i	0.230406	−	0.399075i
$862$		0			0
$863$	31.5984			1.07562			0.537811	−	0.843065i	$-0.319251\pi$
$863$	31.5984			1.07562			0.537811	+	0.843065i	$0.319251\pi$
$864$		0			0
$865$	−0.214961	−	0.372323i	−0.00730889	−	0.0126594i
$866$		0			0
$867$	−4.17240	−	7.22680i	−0.141702	−	0.245435i
$868$		0			0
$869$	−7.06546	+	12.2377i	−0.239679	+	0.415137i
$870$		0			0
$871$	12.1643	+	42.1385i	0.412173	+	1.42781i
$872$		0			0
$873$	−0.322583	+	0.558731i	−0.0109178	+	0.0189102i
$874$		0			0
$875$	−11.1429	−	19.3001i	−0.376699	−	0.652462i
$876$		0			0
$877$	19.9294	+	34.5188i	0.672969	+	1.16562i	0.977058	+	0.212973i	$0.0683148\pi$
$877$	19.9294	+	34.5188i	0.672969	+	1.16562i	−0.304089	+	0.952644i	$0.598352\pi$
$878$		0			0
$879$	6.42030			0.216551
$880$		0			0
$881$	−2.10686	+	3.64918i	−0.0709818	+	0.122944i	−0.899332	−	0.437267i	$-0.855947\pi$
$881$	−2.10686	+	3.64918i	−0.0709818	+	0.122944i	0.828350	+	0.560211i	$0.189280\pi$
$882$		0			0
$883$	52.6588			1.77211			0.886054	−	0.463581i	$-0.153436\pi$
$883$	52.6588			1.77211			0.886054	+	0.463581i	$0.153436\pi$
$884$		0			0
$885$	1.29803			0.0436328
$886$		0			0
$887$	24.7923	−	42.9416i	0.832445	−	1.44184i	−0.0636493	−	0.997972i	$-0.520274\pi$
$887$	24.7923	−	42.9416i	0.832445	−	1.44184i	0.896094	−	0.443864i	$-0.146393\pi$
$888$		0			0
$889$	−22.6253			−0.758830
$890$		0			0
$891$	−4.32691	−	7.49443i	−0.144957	−	0.251073i
$892$		0			0
$893$	−1.39493	−	2.41608i	−0.0466794	−	0.0808511i
$894$		0			0
$895$	−14.2472	+	24.6769i	−0.476232	+	0.824858i
$896$		0			0
$897$	11.4343	+	2.82926i	0.381781	+	0.0944663i
$898$		0			0
$899$	−19.3880	+	33.5811i	−0.646628	+	1.11999i
$900$		0			0
$901$	−0.887565	−	1.53731i	−0.0295691	−	0.0512152i
$902$		0			0
$903$	−19.9146	−	34.4931i	−0.662716	−	1.14786i
$904$		0			0
$905$	−21.7775			−0.723908
$906$		0			0
$907$	5.73236	−	9.92874i	0.190340	−	0.329678i	−0.755023	−	0.655698i	$-0.772374\pi$
$907$	5.73236	−	9.92874i	0.190340	−	0.329678i	0.945363	+	0.326020i	$0.105708\pi$
$908$		0			0
$909$	−1.44506			−0.0479295
$910$		0			0
$911$	27.7971			0.920960			0.460480	−	0.887670i	$-0.347677\pi$
$911$	27.7971			0.920960			0.460480	+	0.887670i	$0.347677\pi$
$912$		0			0
$913$	−1.75526	+	3.04020i	−0.0580906	+	0.100616i
$914$		0			0
$915$	7.95186			0.262880
$916$		0			0
$917$	17.4611	+	30.2435i	0.576616	+	0.998728i
$918$		0			0
$919$	23.0316	+	39.8918i	0.759741	+	1.31591i	0.942983	+	0.332842i	$0.108008\pi$
$919$	23.0316	+	39.8918i	0.759741	+	1.31591i	−0.183241	+	0.983068i	$0.558659\pi$
$920$		0			0
$921$	8.10322	−	14.0352i	0.267010	−	0.462475i
$922$		0			0
$923$	21.1170	+	5.22510i	0.695074	+	0.171986i
$924$		0			0
$925$	2.00578	−	3.47412i	0.0659498	−	0.114228i
$926$		0			0
$927$	−0.691656	−	1.19798i	−0.0227170	−	0.0393469i
$928$		0			0
$929$	−10.5462	−	18.2666i	−0.346010	−	0.599307i	0.639527	−	0.768769i	$-0.279130\pi$
$929$	−10.5462	−	18.2666i	−0.346010	−	0.599307i	−0.985537	+	0.169462i	$0.945797\pi$
$930$		0			0
$931$	1.23491			0.0404725
$932$		0			0
$933$	6.80587	−	11.7881i	0.222814	−	0.385926i
$934$		0			0
$935$	3.86398			0.126366
$936$		0			0
$937$	13.4561			0.439590			0.219795	−	0.975546i	$-0.429461\pi$
$937$	13.4561			0.439590			0.219795	+	0.975546i	$0.429461\pi$
$938$		0			0
$939$	−3.68292	+	6.37900i	−0.120187	+	0.208171i
$940$		0			0
$941$	−32.6428			−1.06413			−0.532063	−	0.846705i	$-0.678583\pi$
$941$	−32.6428			−1.06413			−0.532063	+	0.846705i	$0.678583\pi$
$942$		0			0
$943$	3.34176	+	5.78811i	0.108823	+	0.188487i
$944$		0			0
$945$	6.72253	+	11.6438i	0.218684	+	0.378772i
$946$		0			0
$947$	23.3473	−	40.4387i	0.758684	−	1.31408i	−0.184838	−	0.982769i	$-0.559176\pi$
$947$	23.3473	−	40.4387i	0.758684	−	1.31408i	0.943522	−	0.331311i	$-0.107491\pi$
$948$		0			0
$949$	20.8836	−	21.7029i	0.677912	−	0.704506i
$950$		0			0
$951$	25.6130	−	44.3631i	0.830560	−	1.43857i
$952$		0			0
$953$	7.09957	+	12.2968i	0.229978	+	0.398333i	0.957801	−	0.287431i	$-0.0928013\pi$
$953$	7.09957	+	12.2968i	0.229978	+	0.398333i	−0.727823	+	0.685765i	$0.759468\pi$
$954$		0			0
$955$	−6.06870	−	10.5113i	−0.196379	−	0.340138i
$956$		0			0
$957$	−11.3658			−0.367405
$958$		0			0
$959$	−22.3283	+	38.6737i	−0.721018	+	1.24884i
$960$		0			0
$961$	2.62275			0.0846048
$962$		0			0
$963$	1.43130			0.0461230
$964$		0			0
$965$	−1.87704	+	3.25114i	−0.0604242	+	0.104658i
$966$		0			0
$967$	−3.83703			−0.123391			−0.0616953	−	0.998095i	$-0.519651\pi$
$967$	−3.83703			−0.123391			−0.0616953	+	0.998095i	$0.519651\pi$
$968$		0			0
$969$	2.06732	+	3.58071i	0.0664120	+	0.115029i
$970$		0			0
$971$	12.0167	+	20.8136i	0.385635	+	0.667939i	0.991857	−	0.127356i	$-0.0406492\pi$
$971$	12.0167	+	20.8136i	0.385635	+	0.667939i	−0.606222	+	0.795295i	$0.707316\pi$
$972$		0			0
$973$	18.9629	−	32.8446i	0.607921	−	1.05295i
$974$		0			0
$975$	6.39926	+	22.1677i	0.204940	+	0.709934i
$976$		0			0
$977$	−28.4610	+	49.2959i	−0.910548	+	1.57712i	−0.0972565	+	0.995259i	$0.531007\pi$
$977$	−28.4610	+	49.2959i	−0.910548	+	1.57712i	−0.813292	+	0.581856i	$0.802327\pi$
$978$		0			0
$979$	4.66690	+	8.08330i	0.149155	+	0.258343i
$980$		0			0
$981$	−0.0192583	−	0.0333563i	−0.000614870	−	0.00106499i
$982$		0			0
$983$	−37.5571			−1.19789			−0.598943	−	0.800791i	$-0.704412\pi$
$983$	−37.5571			−1.19789			−0.598943	+	0.800791i	$0.704412\pi$
$984$		0			0
$985$	5.00069	−	8.66145i	0.159335	−	0.275977i
$986$		0			0
$987$	−15.5068			−0.493587
$988$		0			0
$989$	19.6871			0.626013
$990$		0			0
$991$	−23.8633	+	41.3324i	−0.758042	+	1.31297i	0.185805	+	0.982587i	$0.440511\pi$
$991$	−23.8633	+	41.3324i	−0.758042	+	1.31297i	−0.943848	+	0.330381i	$0.892823\pi$
$992$		0			0
$993$	14.9542			0.474557
$994$		0			0
$995$	3.18470	+	5.51606i	0.100962	+	0.174871i
$996$		0			0
$997$	0.182918	+	0.316823i	0.00579307	+	0.0100339i	0.868907	−	0.494975i	$-0.164823\pi$
$997$	0.182918	+	0.316823i	0.00579307	+	0.0100339i	−0.863114	+	0.505009i	$0.831489\pi$
$998$		0			0
$999$	−2.81708	+	4.87933i	−0.0891285	+	0.154375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.b.529.3	yes	6
13.3	even	3	inner	572.2.i.b.133.3	✓	6
13.4	even	6		7436.2.a.m.1.1		3
13.9	even	3		7436.2.a.n.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.b.133.3	✓	6	13.3	even	3	inner
572.2.i.b.529.3	yes	6	1.1	even	1	trivial
7436.2.a.m.1.1		3	13.4	even	6
7436.2.a.n.1.1		3	13.9	even	3

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.849814 - 1.47192i) q^{3} +1.11126 q^{5} +(1.14400 + 1.98146i) q^{7} +(0.0556321 + 0.0963576i) q^{9} +O(q^{10})\)	\(q+(0.849814 - 1.47192i) q^{3} +1.11126 q^{5} +(1.14400 + 1.98146i) q^{7} +(0.0556321 + 0.0963576i) q^{9} +(0.500000 - 0.866025i) q^{11} +(2.50000 - 2.59808i) q^{13} +(0.944368 - 1.63569i) q^{15} +(1.73855 + 3.01126i) q^{17} +(0.349814 + 0.605896i) q^{19} +3.88874 q^{21} +(-0.961078 + 1.66464i) q^{23} -3.76509 q^{25} +5.28799 q^{27} +(3.34362 - 5.79133i) q^{29} -5.79851 q^{31} +(-0.849814 - 1.47192i) q^{33} +(1.27128 + 2.20192i) q^{35} +(-0.532732 + 0.922719i) q^{37} +(-1.69963 - 5.88768i) q^{39} +(1.73855 - 3.01126i) q^{41} +(-5.12110 - 8.87000i) q^{43} +(0.0618219 + 0.107079i) q^{45} -3.98762 q^{47} +(0.882546 - 1.52861i) q^{49} +5.90978 q^{51} -0.510520 q^{53} +(0.555632 - 0.962383i) q^{55} +1.18911 q^{57} +(0.343624 + 0.595175i) q^{59} +(2.10507 + 3.64610i) q^{61} +(-0.127286 + 0.220465i) q^{63} +(2.77816 - 2.88715i) q^{65} +(-6.08217 + 10.5346i) q^{67} +(1.63348 + 2.82926i) q^{69} +(3.01671 + 5.22510i) q^{71} +8.35346 q^{73} +(-3.19963 + 5.54192i) q^{75} +2.28799 q^{77} -14.1309 q^{79} +(4.32691 - 7.49443i) q^{81} -3.51052 q^{83} +(1.93199 + 3.34630i) q^{85} +(-5.68292 - 9.84310i) q^{87} +(-4.66690 + 8.08330i) q^{89} +(8.00797 + 1.98146i) q^{91} +(-4.92766 + 8.53495i) q^{93} +(0.388736 + 0.673310i) q^{95} +(2.89926 + 5.02166i) q^{97} +0.111264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 6 q^{5} - 5 q^{7}+O(q^{10}) \) 6 * q - q^3 + 6 * q^5 - 5 * q^7	\( 6 q - q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{11} + 15 q^{13} + 6 q^{15} + 5 q^{17} - 4 q^{19} + 24 q^{21} + q^{23} + 12 q^{25} + 8 q^{27} - 4 q^{29} + 14 q^{31} + q^{33} - 9 q^{35} + 8 q^{37} + 2 q^{39} + 5 q^{41} - 8 q^{43} + 18 q^{45} + 12 q^{47} - 12 q^{49} - 14 q^{51} + 22 q^{53} + 3 q^{55} + 20 q^{57} - 22 q^{59} - 6 q^{61} + 4 q^{63} + 15 q^{65} - 7 q^{67} + 23 q^{69} + 11 q^{71} + 4 q^{73} - 7 q^{75} - 10 q^{77} - 40 q^{79} + 9 q^{81} + 4 q^{83} - 24 q^{85} - 29 q^{87} - 27 q^{89} - 35 q^{91} - 37 q^{93} + 3 q^{95} - 7 q^{97}+O(q^{100}) \) 6 * q - q^3 + 6 * q^5 - 5 * q^7 + 3 * q^11 + 15 * q^13 + 6 * q^15 + 5 * q^17 - 4 * q^19 + 24 * q^21 + q^23 + 12 * q^25 + 8 * q^27 - 4 * q^29 + 14 * q^31 + q^33 - 9 * q^35 + 8 * q^37 + 2 * q^39 + 5 * q^41 - 8 * q^43 + 18 * q^45 + 12 * q^47 - 12 * q^49 - 14 * q^51 + 22 * q^53 + 3 * q^55 + 20 * q^57 - 22 * q^59 - 6 * q^61 + 4 * q^63 + 15 * q^65 - 7 * q^67 + 23 * q^69 + 11 * q^71 + 4 * q^73 - 7 * q^75 - 10 * q^77 - 40 * q^79 + 9 * q^81 + 4 * q^83 - 24 * q^85 - 29 * q^87 - 27 * q^89 - 35 * q^91 - 37 * q^93 + 3 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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