LMFDB - Embedded newform 496.2.i.h.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [496,2,Mod(129,496)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(496, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("496.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 496 = 2^{4} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	496.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.96057994026$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			129.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	496.129
Dual form			496.2.i.h.273.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.207107 + 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.207107 + 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(1.62132 + 2.80821i) q^{11} +(1.91421 + 3.31552i) q^{13} -0.414214 q^{15} +(2.91421 - 5.04757i) q^{17} +(2.20711 - 3.82282i) q^{19} +(0.0857864 + 0.148586i) q^{21} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +2.41421 q^{27} -6.82843 q^{29} +(5.00000 - 2.44949i) q^{31} +1.34315 q^{33} +0.414214 q^{35} +(-0.500000 + 0.866025i) q^{37} +1.58579 q^{39} +(3.74264 + 6.48244i) q^{41} +(-5.44975 + 9.43924i) q^{43} +(1.41421 - 2.44949i) q^{45} -9.65685 q^{47} +(3.41421 + 5.91359i) q^{49} +(-1.20711 - 2.09077i) q^{51} +(-2.91421 - 5.04757i) q^{53} +(1.62132 - 2.80821i) q^{55} +(-0.914214 - 1.58346i) q^{57} +(2.03553 - 3.52565i) q^{59} -2.82843 q^{61} -1.17157 q^{63} +(1.91421 - 3.31552i) q^{65} +(1.62132 + 2.80821i) q^{67} +(0.828427 - 1.43488i) q^{69} +(0.0355339 + 0.0615465i) q^{71} +(0.914214 + 1.58346i) q^{73} +(-0.828427 - 1.43488i) q^{75} -1.34315 q^{77} +(-3.37868 + 5.85204i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(-5.03553 - 8.72180i) q^{83} -5.82843 q^{85} +(-1.41421 + 2.44949i) q^{87} +4.48528 q^{89} -1.58579 q^{91} +(0.156854 - 2.30090i) q^{93} -4.41421 q^{95} +5.17157 q^{97} +(-4.58579 + 7.94282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 + 2 * q^7	$ 4 q - 2 q^{3} - 2 q^{5} + 2 q^{7} - 2 q^{11} + 2 q^{13} + 4 q^{15} + 6 q^{17} + 6 q^{19} + 6 q^{21} + 16 q^{23} + 8 q^{25} + 4 q^{27} - 16 q^{29} + 20 q^{31} + 28 q^{33} - 4 q^{35} - 2 q^{37} + 12 q^{39} - 2 q^{41} - 2 q^{43} - 16 q^{47} + 8 q^{49} - 2 q^{51} - 6 q^{53} - 2 q^{55} + 2 q^{57} - 6 q^{59} - 16 q^{63} + 2 q^{65} - 2 q^{67} - 8 q^{69} - 14 q^{71} - 2 q^{73} + 8 q^{75} - 28 q^{77} - 22 q^{79} + 2 q^{81} - 6 q^{83} - 12 q^{85} - 16 q^{89} - 12 q^{91} - 22 q^{93} - 12 q^{95} + 32 q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 + 2 * q^7 - 2 * q^11 + 2 * q^13 + 4 * q^15 + 6 * q^17 + 6 * q^19 + 6 * q^21 + 16 * q^23 + 8 * q^25 + 4 * q^27 - 16 * q^29 + 20 * q^31 + 28 * q^33 - 4 * q^35 - 2 * q^37 + 12 * q^39 - 2 * q^41 - 2 * q^43 - 16 * q^47 + 8 * q^49 - 2 * q^51 - 6 * q^53 - 2 * q^55 + 2 * q^57 - 6 * q^59 - 16 * q^63 + 2 * q^65 - 2 * q^67 - 8 * q^69 - 14 * q^71 - 2 * q^73 + 8 * q^75 - 28 * q^77 - 22 * q^79 + 2 * q^81 - 6 * q^83 - 12 * q^85 - 16 * q^89 - 12 * q^91 - 22 * q^93 - 12 * q^95 + 32 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/496\mathbb{Z}\right)^\times$.

$n$	$63$	$65$	$373$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−0.207107	+	0.358719i	−0.0782790	+	0.135583i	−0.902507	−	0.430674i	$-0.858276\pi$
$7$	−0.207107	+	0.358719i	−0.0782790	+	0.135583i	0.824228	+	0.566257i	$0.191609\pi$
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	1.62132	+	2.80821i	0.488846	+	0.846707i	0.999918	−	0.0128314i	$-0.00408449\pi$
$11$	1.62132	+	2.80821i	0.488846	+	0.846707i	−0.511071	+	0.859538i	$0.670751\pi$
$12$		0			0
$13$	1.91421	+	3.31552i	0.530907	+	0.919558i	0.999349	+	0.0360643i	$0.0114821\pi$
$13$	1.91421	+	3.31552i	0.530907	+	0.919558i	−0.468442	+	0.883494i	$0.655185\pi$
$14$		0			0
$15$	−0.414214			−0.106949
$16$		0			0
$17$	2.91421	−	5.04757i	0.706801	−	1.22421i	−0.259237	−	0.965814i	$-0.583471\pi$
$17$	2.91421	−	5.04757i	0.706801	−	1.22421i	0.966038	−	0.258401i	$-0.0831955\pi$
$18$		0			0
$19$	2.20711	−	3.82282i	0.506345	−	0.877015i	−0.493628	−	0.869673i	$-0.664330\pi$
$19$	2.20711	−	3.82282i	0.506345	−	0.877015i	0.999973	−	0.00734216i	$-0.00233710\pi$
$20$		0			0
$21$	0.0857864	+	0.148586i	0.0187201	+	0.0324242i
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$		0			0
$31$	5.00000	−	2.44949i	0.898027	−	0.439941i
$31$	5.00000	−	2.44949i	0.898027	−	0.439941i
$32$		0			0
$33$	1.34315			0.233812
$34$		0			0
$35$	0.414214			0.0700149
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	1.58579			0.253929
$40$		0			0
$41$	3.74264	+	6.48244i	0.584502	+	1.01239i	0.994937	+	0.100498i	$0.0320435\pi$
$41$	3.74264	+	6.48244i	0.584502	+	1.01239i	−0.410435	+	0.911890i	$0.634623\pi$
$42$		0			0
$43$	−5.44975	+	9.43924i	−0.831079	+	1.43947i	0.0661049	+	0.997813i	$0.478943\pi$
$43$	−5.44975	+	9.43924i	−0.831079	+	1.43947i	−0.897184	+	0.441658i	$0.854391\pi$
$44$		0			0
$45$	1.41421	−	2.44949i	0.210819	−	0.365148i
$46$		0			0
$47$	−9.65685			−1.40860			−0.704298	−	0.709904i	$-0.748738\pi$
$47$	−9.65685			−1.40860			−0.704298	+	0.709904i	$0.748738\pi$
$48$		0			0
$49$	3.41421	+	5.91359i	0.487745	+	0.844799i
$50$		0			0
$51$	−1.20711	−	2.09077i	−0.169029	−	0.292766i
$52$		0			0
$53$	−2.91421	−	5.04757i	−0.400298	−	0.693337i	0.593464	−	0.804861i	$-0.297760\pi$
$53$	−2.91421	−	5.04757i	−0.400298	−	0.693337i	−0.993762	+	0.111524i	$0.964427\pi$
$54$		0			0
$55$	1.62132	−	2.80821i	0.218619	−	0.378659i
$56$		0			0
$57$	−0.914214	−	1.58346i	−0.121091	−	0.209735i
$58$		0			0
$59$	2.03553	−	3.52565i	0.265004	−	0.459000i	−0.702561	−	0.711624i	$-0.747960\pi$
$59$	2.03553	−	3.52565i	0.265004	−	0.459000i	0.967565	+	0.252624i	$0.0812934\pi$
$60$		0			0
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$		0			0
$63$	−1.17157			−0.147604
$64$		0			0
$65$	1.91421	−	3.31552i	0.237429	−	0.411239i
$66$		0			0
$67$	1.62132	+	2.80821i	0.198076	+	0.343077i	0.947904	−	0.318555i	$-0.103197\pi$
$67$	1.62132	+	2.80821i	0.198076	+	0.343077i	−0.749829	+	0.661632i	$0.769864\pi$
$68$		0			0
$69$	0.828427	−	1.43488i	0.0997309	−	0.172739i
$70$		0			0
$71$	0.0355339	+	0.0615465i	0.00421710	+	0.00730423i	0.868126	−	0.496343i	$-0.165324\pi$
$71$	0.0355339	+	0.0615465i	0.00421710	+	0.00730423i	−0.863909	+	0.503648i	$0.831991\pi$
$72$		0			0
$73$	0.914214	+	1.58346i	0.107001	+	0.185330i	0.914554	−	0.404464i	$-0.132542\pi$
$73$	0.914214	+	1.58346i	0.107001	+	0.185330i	−0.807553	+	0.589795i	$0.799209\pi$
$74$		0			0
$75$	−0.828427	−	1.43488i	−0.0956585	−	0.165685i
$76$		0			0
$77$	−1.34315			−0.153066
$78$		0			0
$79$	−3.37868	+	5.85204i	−0.380131	+	0.658406i	−0.991081	−	0.133263i	$-0.957454\pi$
$79$	−3.37868	+	5.85204i	−0.380131	+	0.658406i	0.610950	+	0.791670i	$0.290788\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	−5.03553	−	8.72180i	−0.552722	−	0.957342i	−0.998077	−	0.0619880i	$-0.980256\pi$
$83$	−5.03553	−	8.72180i	−0.552722	−	0.957342i	0.445355	−	0.895354i	$-0.353077\pi$
$84$		0			0
$85$	−5.82843			−0.632182
$86$		0			0
$87$	−1.41421	+	2.44949i	−0.151620	+	0.262613i
$88$		0			0
$89$	4.48528			0.475439			0.237719	−	0.971334i	$-0.423600\pi$
$89$	4.48528			0.475439			0.237719	+	0.971334i	$0.423600\pi$
$90$		0			0
$91$	−1.58579			−0.166236
$92$		0			0
$93$	0.156854	−	2.30090i	0.0162650	−	0.238593i
$94$		0			0
$95$	−4.41421			−0.452889
$96$		0			0
$97$	5.17157			0.525094			0.262547	−	0.964919i	$-0.415438\pi$
$97$	5.17157			0.525094			0.262547	+	0.964919i	$0.415438\pi$
$98$		0			0
$99$	−4.58579	+	7.94282i	−0.460889	+	0.798283i
$100$		0			0
$101$	−8.48528			−0.844317			−0.422159	−	0.906522i	$-0.638727\pi$
$101$	−8.48528			−0.844317			−0.422159	+	0.906522i	$0.638727\pi$
$102$		0			0
$103$	1.03553	+	1.79360i	0.102034	+	0.176728i	0.912523	−	0.409026i	$-0.134132\pi$
$103$	1.03553	+	1.79360i	0.102034	+	0.176728i	−0.810488	+	0.585755i	$0.800798\pi$
$104$		0			0
$105$	0.0857864	−	0.148586i	0.00837190	−	0.0145006i
$106$		0			0
$107$	6.20711	−	10.7510i	0.600064	−	1.03934i	−0.392747	−	0.919646i	$-0.628475\pi$
$107$	6.20711	−	10.7510i	0.600064	−	1.03934i	0.992811	−	0.119694i	$-0.0381914\pi$
$108$		0			0
$109$	−10.8284			−1.03718			−0.518588	−	0.855024i	$-0.673542\pi$
$109$	−10.8284			−1.03718			−0.518588	+	0.855024i	$0.673542\pi$
$110$		0			0
$111$	0.207107	+	0.358719i	0.0196577	+	0.0340481i
$112$		0			0
$113$	−8.32843	−	14.4253i	−0.783473	−	1.35701i	−0.929907	−	0.367794i	$-0.880113\pi$
$113$	−8.32843	−	14.4253i	−0.783473	−	1.35701i	0.146435	−	0.989220i	$-0.453220\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	−5.41421	+	9.37769i	−0.500544	+	0.866968i
$118$		0			0
$119$	1.20711	+	2.09077i	0.110655	+	0.191661i
$120$		0			0
$121$	0.242641	−	0.420266i	0.0220582	−	0.0382060i
$122$		0			0
$123$	3.10051			0.279563
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	4.44975	−	7.70719i	0.394851	−	0.683902i	−0.598231	−	0.801324i	$-0.704129\pi$
$127$	4.44975	−	7.70719i	0.394851	−	0.683902i	0.993082	+	0.117421i	$0.0374628\pi$
$128$		0			0
$129$	2.25736	+	3.90986i	0.198749	+	0.344244i
$130$		0			0
$131$	−6.62132	+	11.4685i	−0.578507	+	1.00200i	0.417143	+	0.908841i	$0.363031\pi$
$131$	−6.62132	+	11.4685i	−0.578507	+	1.00200i	−0.995651	+	0.0931636i	$0.970302\pi$
$132$		0			0
$133$	0.914214	+	1.58346i	0.0792724	+	0.137304i
$134$		0			0
$135$	−1.20711	−	2.09077i	−0.103891	−	0.179945i
$136$		0			0
$137$	−4.74264	−	8.21449i	−0.405191	−	0.701812i	0.589153	−	0.808022i	$-0.299462\pi$
$137$	−4.74264	−	8.21449i	−0.405191	−	0.701812i	−0.994344	+	0.106210i	$0.966128\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$		0			0
$143$	−6.20711	+	10.7510i	−0.519064	+	0.899046i
$144$		0			0
$145$	3.41421	+	5.91359i	0.283535	+	0.491097i
$146$		0			0
$147$	2.82843			0.233285
$148$		0			0
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	−5.31371			−0.432423			−0.216212	−	0.976346i	$-0.569370\pi$
$151$	−5.31371			−0.432423			−0.216212	+	0.976346i	$0.569370\pi$
$152$		0			0
$153$	16.4853			1.33276
$154$		0			0
$155$	−4.62132	−	3.10538i	−0.371193	−	0.249430i
$156$		0			0
$157$	9.17157			0.731971			0.365986	−	0.930621i	$-0.380732\pi$
$157$	9.17157			0.731971			0.365986	+	0.930621i	$0.380732\pi$
$158$		0			0
$159$	−2.41421			−0.191460
$160$		0			0
$161$	−0.828427	+	1.43488i	−0.0652892	+	0.113084i
$162$		0			0
$163$	−20.9706			−1.64254			−0.821271	−	0.570539i	$-0.806734\pi$
$163$	−20.9706			−1.64254			−0.821271	+	0.570539i	$0.806734\pi$
$164$		0			0
$165$	−0.671573	−	1.16320i	−0.0522819	−	0.0905549i
$166$		0			0
$167$	11.2782	−	19.5344i	0.872731	−	1.51162i	0.0135714	−	0.999908i	$-0.495680\pi$
$167$	11.2782	−	19.5344i	0.872731	−	1.51162i	0.859160	−	0.511707i	$-0.170987\pi$
$168$		0			0
$169$	−0.828427	+	1.43488i	−0.0637252	+	0.110375i
$170$		0			0
$171$	12.4853			0.954773
$172$		0			0
$173$	−4.15685	−	7.19988i	−0.316040	−	0.547397i	0.663618	−	0.748071i	$-0.269020\pi$
$173$	−4.15685	−	7.19988i	−0.316040	−	0.547397i	−0.979658	+	0.200674i	$0.935687\pi$
$174$		0			0
$175$	0.828427	+	1.43488i	0.0626232	+	0.108467i
$176$		0			0
$177$	−0.843146	−	1.46037i	−0.0633747	−	0.109768i
$178$		0			0
$179$	−7.62132	+	13.2005i	−0.569644	+	0.986653i	0.426957	+	0.904272i	$0.359586\pi$
$179$	−7.62132	+	13.2005i	−0.569644	+	0.986653i	−0.996601	+	0.0823807i	$0.973748\pi$
$180$		0			0
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	0.541200	−	0.840894i	$-0.317970\pi$
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	−0.998835	+	0.0482461i	$0.984637\pi$
$182$		0			0
$183$	−0.585786	+	1.01461i	−0.0433026	+	0.0750023i
$184$		0			0
$185$	1.00000			0.0735215
$186$		0			0
$187$	18.8995			1.38207
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	−10.4497	−	18.0995i	−0.756117	−	1.30963i	−0.944817	−	0.327599i	$-0.893761\pi$
$191$	−10.4497	−	18.0995i	−0.756117	−	1.30963i	0.188700	−	0.982035i	$-0.439573\pi$
$192$		0			0
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	−0.965451	−	0.260586i	$-0.916084\pi$
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	0.708400	+	0.705812i	$0.249418\pi$
$194$		0			0
$195$	−0.792893	−	1.37333i	−0.0567803	−	0.0983463i
$196$		0			0
$197$	6.74264	+	11.6786i	0.480393	+	0.832066i	0.999747	−	0.0224938i	$-0.00716061\pi$
$197$	6.74264	+	11.6786i	0.480393	+	0.832066i	−0.519354	+	0.854559i	$0.673827\pi$
$198$		0			0
$199$	9.20711	+	15.9472i	0.652674	+	1.13047i	0.982471	+	0.186413i	$0.0596864\pi$
$199$	9.20711	+	15.9472i	0.652674	+	1.13047i	−0.329797	+	0.944052i	$0.606980\pi$
$200$		0			0
$201$	1.34315			0.0947382
$202$		0			0
$203$	1.41421	−	2.44949i	0.0992583	−	0.171920i
$204$		0			0
$205$	3.74264	−	6.48244i	0.261397	−	0.452754i
$206$		0			0
$207$	5.65685	+	9.79796i	0.393179	+	0.681005i
$208$		0			0
$209$	14.3137			0.990100
$210$		0			0
$211$	5.20711	−	9.01897i	0.358472	−	0.620892i	−0.629234	−	0.777216i	$-0.716631\pi$
$211$	5.20711	−	9.01897i	0.358472	−	0.620892i	0.987706	+	0.156324i	$0.0499645\pi$
$212$		0			0
$213$	0.0294373			0.00201701
$214$		0			0
$215$	10.8995			0.743339
$216$		0			0
$217$	−0.156854	+	2.30090i	−0.0106480	+	0.156195i
$218$		0			0
$219$	0.757359			0.0511776
$220$		0			0
$221$	22.3137			1.50098
$222$		0			0
$223$	−11.8640	+	20.5490i	−0.794470	+	1.37606i	0.128706	+	0.991683i	$0.458918\pi$
$223$	−11.8640	+	20.5490i	−0.794470	+	1.37606i	−0.923175	+	0.384379i	$0.874416\pi$
$224$		0			0
$225$	11.3137			0.754247
$226$		0			0
$227$	−9.20711	−	15.9472i	−0.611097	−	1.05845i	−0.991056	−	0.133448i	$-0.957395\pi$
$227$	−9.20711	−	15.9472i	−0.611097	−	1.05845i	0.379959	−	0.925003i	$-0.375938\pi$
$228$		0			0
$229$	2.74264	−	4.75039i	0.181239	−	0.313915i	−0.761064	−	0.648677i	$-0.775323\pi$
$229$	2.74264	−	4.75039i	0.181239	−	0.313915i	0.942303	+	0.334762i	$0.108656\pi$
$230$		0			0
$231$	−0.278175	+	0.481813i	−0.0183025	+	0.0317009i
$232$		0			0
$233$	−9.17157			−0.600850			−0.300425	−	0.953805i	$-0.597128\pi$
$233$	−9.17157			−0.600850			−0.300425	+	0.953805i	$0.597128\pi$
$234$		0			0
$235$	4.82843	+	8.36308i	0.314972	+	0.545547i
$236$		0			0
$237$	1.39949	+	2.42400i	0.0909070	+	0.157455i
$238$		0			0
$239$	−10.6213	−	18.3967i	−0.687036	−	1.18998i	−0.972792	−	0.231679i	$-0.925578\pi$
$239$	−10.6213	−	18.3967i	−0.687036	−	1.18998i	0.285756	−	0.958302i	$-0.407755\pi$
$240$		0			0
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	−0.996851	−	0.0792954i	$-0.974733\pi$
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	0.567097	+	0.823651i	$0.308066\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$	3.41421	−	5.91359i	0.218126	−	0.377805i
$246$		0			0
$247$	16.8995			1.07529
$248$		0			0
$249$	−4.17157			−0.264363
$250$		0			0
$251$	3.20711	−	5.55487i	0.202431	−	0.350620i	−0.746880	−	0.664958i	$-0.768449\pi$
$251$	3.20711	−	5.55487i	0.202431	−	0.350620i	0.949311	+	0.314338i	$0.101783\pi$
$252$		0			0
$253$	6.48528	+	11.2328i	0.407726	+	0.706202i
$254$		0			0
$255$	−1.20711	+	2.09077i	−0.0755920	+	0.130929i
$256$		0			0
$257$	−11.1569	−	19.3242i	−0.695945	−	1.20541i	−0.969861	−	0.243659i	$-0.921652\pi$
$257$	−11.1569	−	19.3242i	−0.695945	−	1.20541i	0.273915	−	0.961754i	$-0.411681\pi$
$258$		0			0
$259$	−0.207107	−	0.358719i	−0.0128690	−	0.0222897i
$260$		0			0
$261$	−9.65685	−	16.7262i	−0.597744	−	1.03532i
$262$		0			0
$263$	23.3137			1.43758			0.718792	−	0.695225i	$-0.244695\pi$
$263$	23.3137			1.43758			0.718792	+	0.695225i	$0.244695\pi$
$264$		0			0
$265$	−2.91421	+	5.04757i	−0.179019	+	0.310070i
$266$		0			0
$267$	0.928932	−	1.60896i	0.0568497	−	0.0984666i
$268$		0			0
$269$	13.0858	+	22.6652i	0.797854	+	1.38192i	0.921011	+	0.389537i	$0.127365\pi$
$269$	13.0858	+	22.6652i	0.797854	+	1.38192i	−0.123156	+	0.992387i	$0.539302\pi$
$270$		0			0
$271$	0.686292			0.0416892			0.0208446	−	0.999783i	$-0.493364\pi$
$271$	0.686292			0.0416892			0.0208446	+	0.999783i	$0.493364\pi$
$272$		0			0
$273$	−0.328427	+	0.568852i	−0.0198773	+	0.0344285i
$274$		0			0
$275$	12.9706			0.782154
$276$		0			0
$277$	14.1421			0.849719			0.424859	−	0.905259i	$-0.360324\pi$
$277$	14.1421			0.849719			0.424859	+	0.905259i	$0.360324\pi$
$278$		0			0
$279$	13.0711	+	8.78335i	0.782544	+	0.525845i
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$		0			0
$283$	13.6569			0.811816			0.405908	−	0.913914i	$-0.366955\pi$
$283$	13.6569			0.811816			0.405908	+	0.913914i	$0.366955\pi$
$284$		0			0
$285$	−0.914214	+	1.58346i	−0.0541533	+	0.0937963i
$286$		0			0
$287$	−3.10051			−0.183017
$288$		0			0
$289$	−8.48528	−	14.6969i	−0.499134	−	0.864526i
$290$		0			0
$291$	1.07107	−	1.85514i	0.0627871	−	0.108750i
$292$		0			0
$293$	−7.39949	+	12.8163i	−0.432283	+	0.748736i	−0.997070	−	0.0765008i	$-0.975625\pi$
$293$	−7.39949	+	12.8163i	−0.432283	+	0.748736i	0.564786	+	0.825237i	$0.308959\pi$
$294$		0			0
$295$	−4.07107			−0.237027
$296$		0			0
$297$	3.91421	+	6.77962i	0.227126	+	0.393393i
$298$		0			0
$299$	7.65685	+	13.2621i	0.442807	+	0.766965i
$300$		0			0
$301$	−2.25736	−	3.90986i	−0.130112	−	0.225361i
$302$		0			0
$303$	−1.75736	+	3.04384i	−0.100958	+	0.174864i
$304$		0			0
$305$	1.41421	+	2.44949i	0.0809776	+	0.140257i
$306$		0			0
$307$	−5.62132	+	9.73641i	−0.320826	+	0.555686i	−0.980659	−	0.195726i	$-0.937294\pi$
$307$	−5.62132	+	9.73641i	−0.320826	+	0.555686i	0.659833	+	0.751412i	$0.270627\pi$
$308$		0			0
$309$	0.857864			0.0488022
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$		0			0
$313$	0.914214	−	1.58346i	0.0516744	−	0.0895027i	−0.839031	−	0.544083i	$-0.816878\pi$
$313$	0.914214	−	1.58346i	0.0516744	−	0.0895027i	0.890706	+	0.454581i	$0.150211\pi$
$314$		0			0
$315$	0.585786	+	1.01461i	0.0330053	+	0.0571669i
$316$		0			0
$317$	3.91421	−	6.77962i	0.219844	−	0.380781i	−0.734916	−	0.678158i	$-0.762778\pi$
$317$	3.91421	−	6.77962i	0.219844	−	0.380781i	0.954760	+	0.297377i	$0.0961118\pi$
$318$		0			0
$319$	−11.0711	−	19.1757i	−0.619861	−	1.07363i
$320$		0			0
$321$	−2.57107	−	4.45322i	−0.143503	−	0.248555i
$322$		0			0
$323$	−12.8640	−	22.2810i	−0.715770	−	1.23975i
$324$		0			0
$325$	15.3137			0.849452
$326$		0			0
$327$	−2.24264	+	3.88437i	−0.124018	+	0.214806i
$328$		0			0
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$		0			0
$331$	4.62132	+	8.00436i	0.254011	+	0.439960i	0.964626	−	0.263621i	$-0.0849168\pi$
$331$	4.62132	+	8.00436i	0.254011	+	0.439960i	−0.710616	+	0.703580i	$0.751583\pi$
$332$		0			0
$333$	−2.82843			−0.154997
$334$		0			0
$335$	1.62132	−	2.80821i	0.0885822	−	0.153429i
$336$		0			0
$337$	9.31371			0.507350			0.253675	−	0.967290i	$-0.418361\pi$
$337$	9.31371			0.507350			0.253675	+	0.967290i	$0.418361\pi$
$338$		0			0
$339$	−6.89949			−0.374729
$340$		0			0
$341$	14.9853	+	10.0696i	0.811498	+	0.545301i
$342$		0			0
$343$	−5.72792			−0.309279
$344$		0			0
$345$	−1.65685			−0.0892020
$346$		0			0
$347$	−4.27817	+	7.41002i	−0.229664	+	0.397790i	−0.957709	−	0.287740i	$-0.907096\pi$
$347$	−4.27817	+	7.41002i	−0.229664	+	0.397790i	0.728044	+	0.685530i	$0.240430\pi$
$348$		0			0
$349$	−27.1127			−1.45131			−0.725655	−	0.688059i	$-0.758463\pi$
$349$	−27.1127			−1.45131			−0.725655	+	0.688059i	$0.758463\pi$
$350$		0			0
$351$	4.62132	+	8.00436i	0.246668	+	0.427241i
$352$		0			0
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$		0			0
$355$	0.0355339	−	0.0615465i	0.00188594	−	0.00326655i
$356$		0			0
$357$	1.00000			0.0529256
$358$		0			0
$359$	3.55025	+	6.14922i	0.187375	+	0.324543i	0.944374	−	0.328873i	$-0.106669\pi$
$359$	3.55025	+	6.14922i	0.187375	+	0.324543i	−0.756999	+	0.653416i	$0.773335\pi$
$360$		0			0
$361$	−0.242641	−	0.420266i	−0.0127706	−	0.0221193i
$362$		0			0
$363$	−0.100505	−	0.174080i	−0.00527515	−	0.00913682i
$364$		0			0
$365$	0.914214	−	1.58346i	0.0478521	−	0.0828823i
$366$		0			0
$367$	−12.1066	−	20.9692i	−0.631959	−	1.09459i	−0.987151	−	0.159792i	$-0.948918\pi$
$367$	−12.1066	−	20.9692i	−0.631959	−	1.09459i	0.355191	−	0.934794i	$-0.384416\pi$
$368$		0			0
$369$	−10.5858	+	18.3351i	−0.551074	+	0.954488i
$370$		0			0
$371$	2.41421			0.125340
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$		0			0
$375$	−1.86396	+	3.22848i	−0.0962545	+	0.166718i
$376$		0			0
$377$	−13.0711	−	22.6398i	−0.673194	−	1.16601i
$378$		0			0
$379$	3.69239	−	6.39540i	0.189665	−	0.328510i	−0.755473	−	0.655179i	$-0.772593\pi$
$379$	3.69239	−	6.39540i	0.189665	−	0.328510i	0.945139	+	0.326669i	$0.105926\pi$
$380$		0			0
$381$	−1.84315	−	3.19242i	−0.0944272	−	0.163553i
$382$		0			0
$383$	2.55025	+	4.41717i	0.130312	+	0.225707i	0.923797	−	0.382883i	$-0.125069\pi$
$383$	2.55025	+	4.41717i	0.130312	+	0.225707i	−0.793485	+	0.608590i	$0.791735\pi$
$384$		0			0
$385$	0.671573	+	1.16320i	0.0342265	+	0.0592821i
$386$		0			0
$387$	−30.8284			−1.56710
$388$		0			0
$389$	5.57107	−	9.64937i	0.282464	−	0.489243i	−0.689527	−	0.724260i	$-0.742181\pi$
$389$	5.57107	−	9.64937i	0.282464	−	0.489243i	0.971991	+	0.235018i	$0.0755148\pi$
$390$		0			0
$391$	11.6569	−	20.1903i	0.589512	−	1.02107i
$392$		0			0
$393$	2.74264	+	4.75039i	0.138348	+	0.239626i
$394$		0			0
$395$	6.75736			0.340000
$396$		0			0
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	−0.0493613	−	0.998781i	$-0.515719\pi$
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	0.889650	−	0.456642i	$-0.150948\pi$
$398$		0			0
$399$	0.757359			0.0379154
$400$		0			0
$401$	−26.8284			−1.33975			−0.669874	−	0.742475i	$-0.733652\pi$
$401$	−26.8284			−1.33975			−0.669874	+	0.742475i	$0.733652\pi$
$402$		0			0
$403$	17.6924	+	11.8887i	0.881321	+	0.592220i
$404$		0			0
$405$	7.48528			0.371947
$406$		0			0
$407$	−3.24264			−0.160732
$408$		0			0
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	0.489215	+	0.872163i	$0.337283\pi$
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	−0.999923	+	0.0124088i	$0.996050\pi$
$410$		0			0
$411$	−3.92893			−0.193800
$412$		0			0
$413$	0.843146	+	1.46037i	0.0414885	+	0.0718602i
$414$		0			0
$415$	−5.03553	+	8.72180i	−0.247185	+	0.428136i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	0.943418	+	0.331605i	$0.107590\pi$
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	−0.184531	+	0.982827i	$0.559077\pi$
$422$		0			0
$423$	−13.6569	−	23.6544i	−0.664019	−	1.15011i
$424$		0			0
$425$	−11.6569	−	20.1903i	−0.565440	−	0.979372i
$426$		0			0
$427$	0.585786	−	1.01461i	0.0283482	−	0.0491005i
$428$		0			0
$429$	2.57107	+	4.45322i	0.124132	+	0.215003i
$430$		0			0
$431$	−8.37868	+	14.5123i	−0.403587	+	0.699033i	−0.994156	−	0.107954i	$-0.965570\pi$
$431$	−8.37868	+	14.5123i	−0.403587	+	0.699033i	0.590569	+	0.806987i	$0.298903\pi$
$432$		0			0
$433$	27.1127			1.30295			0.651477	−	0.758669i	$-0.274150\pi$
$433$	27.1127			1.30295			0.651477	+	0.758669i	$0.274150\pi$
$434$		0			0
$435$	2.82843			0.135613
$436$		0			0
$437$	8.82843	−	15.2913i	0.422321	−	0.731481i
$438$		0			0
$439$	1.03553	+	1.79360i	0.0494233	+	0.0856037i	0.889679	−	0.456587i	$-0.150928\pi$
$439$	1.03553	+	1.79360i	0.0494233	+	0.0856037i	−0.840255	+	0.542191i	$0.817595\pi$
$440$		0			0
$441$	−9.65685	+	16.7262i	−0.459850	+	0.796484i
$442$		0			0
$443$	−2.37868	−	4.11999i	−0.113014	−	0.195747i	0.803970	−	0.594670i	$-0.202717\pi$
$443$	−2.37868	−	4.11999i	−0.113014	−	0.195747i	−0.916984	+	0.398923i	$0.869384\pi$
$444$		0			0
$445$	−2.24264	−	3.88437i	−0.106311	−	0.184137i
$446$		0			0
$447$	0.207107	+	0.358719i	0.00979581	+	0.0169668i
$448$		0			0
$449$	−40.6274			−1.91733			−0.958663	−	0.284543i	$-0.908158\pi$
$449$	−40.6274			−1.91733			−0.958663	+	0.284543i	$0.908158\pi$
$450$		0			0
$451$	−12.1360	+	21.0202i	−0.571464	+	0.989804i
$452$		0			0
$453$	−1.10051	+	1.90613i	−0.0517062	+	0.0895578i
$454$		0			0
$455$	0.792893	+	1.37333i	0.0371714	+	0.0643828i
$456$		0			0
$457$	−31.1127			−1.45539			−0.727695	−	0.685901i	$-0.759409\pi$
$457$	−31.1127			−1.45539			−0.727695	+	0.685901i	$0.759409\pi$
$458$		0			0
$459$	7.03553	−	12.1859i	0.328391	−	0.568789i
$460$		0			0
$461$	−2.14214			−0.0997692			−0.0498846	−	0.998755i	$-0.515885\pi$
$461$	−2.14214			−0.0997692			−0.0498846	+	0.998755i	$0.515885\pi$
$462$		0			0
$463$	8.97056			0.416897			0.208449	−	0.978033i	$-0.433159\pi$
$463$	8.97056			0.416897			0.208449	+	0.978033i	$0.433159\pi$
$464$		0			0
$465$	−2.07107	+	1.01461i	−0.0960435	+	0.0470515i
$466$		0			0
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	−1.34315			−0.0620207
$470$		0			0
$471$	1.89949	−	3.29002i	0.0875241	−	0.151596i
$472$		0			0
$473$	−35.3431			−1.62508
$474$		0			0
$475$	−8.82843	−	15.2913i	−0.405076	−	0.701612i
$476$		0			0
$477$	8.24264	−	14.2767i	0.377405	−	0.653684i
$478$		0			0
$479$	−7.86396	+	13.6208i	−0.359314	+	0.622349i	−0.987846	−	0.155434i	$-0.950322\pi$
$479$	−7.86396	+	13.6208i	−0.359314	+	0.622349i	0.628533	+	0.777783i	$0.283656\pi$
$480$		0			0
$481$	−3.82843			−0.174561
$482$		0			0
$483$	0.343146	+	0.594346i	0.0156137	+	0.0270437i
$484$		0			0
$485$	−2.58579	−	4.47871i	−0.117415	−	0.203368i
$486$		0			0
$487$	9.69239	+	16.7877i	0.439204	+	0.760724i	0.997628	−	0.0688318i	$-0.0219272\pi$
$487$	9.69239	+	16.7877i	0.439204	+	0.760724i	−0.558424	+	0.829556i	$0.688594\pi$
$488$		0			0
$489$	−4.34315	+	7.52255i	−0.196404	+	0.340181i
$490$		0			0
$491$	0.792893	+	1.37333i	0.0357828	+	0.0619776i	0.883362	−	0.468691i	$-0.155274\pi$
$491$	0.792893	+	1.37333i	0.0357828	+	0.0619776i	−0.847579	+	0.530669i	$0.821941\pi$
$492$		0			0
$493$	−19.8995	+	34.4669i	−0.896228	+	1.55231i
$494$		0			0
$495$	9.17157			0.412232
$496$		0			0
$497$	−0.0294373			−0.00132044
$498$		0			0
$499$	−1.10660	+	1.91669i	−0.0495383	+	0.0858028i	−0.889731	−	0.456485i	$-0.849108\pi$
$499$	−1.10660	+	1.91669i	−0.0495383	+	0.0858028i	0.840193	+	0.542288i	$0.182442\pi$
$500$		0			0
$501$	−4.67157	−	8.09140i	−0.208710	−	0.361497i
$502$		0			0
$503$	−6.69239	+	11.5916i	−0.298399	+	0.516842i	−0.975770	−	0.218800i	$-0.929786\pi$
$503$	−6.69239	+	11.5916i	−0.298399	+	0.516842i	0.677371	+	0.735642i	$0.263119\pi$
$504$		0			0
$505$	4.24264	+	7.34847i	0.188795	+	0.327003i
$506$		0			0
$507$	0.343146	+	0.594346i	0.0152396	+	0.0263958i
$508$		0			0
$509$	16.3995	+	28.4048i	0.726895	+	1.25902i	0.958189	+	0.286135i	$0.0923706\pi$
$509$	16.3995	+	28.4048i	0.726895	+	1.25902i	−0.231294	+	0.972884i	$0.574296\pi$
$510$		0			0
$511$	−0.757359			−0.0335036
$512$		0			0
$513$	5.32843	−	9.22911i	0.235256	−	0.407475i
$514$		0			0
$515$	1.03553	−	1.79360i	0.0456311	−	0.0790353i
$516$		0			0
$517$	−15.6569	−	27.1185i	−0.688588	−	1.19267i
$518$		0			0
$519$	−3.44365			−0.151159
$520$		0			0
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	−0.550169	−	0.835054i	$-0.685437\pi$
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	0.998262	+	0.0589331i	$0.0187699\pi$
$522$		0			0
$523$	8.00000			0.349816			0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000			0.349816			0.174908	+	0.984585i	$0.444037\pi$
$524$		0			0
$525$	0.686292			0.0299522
$526$		0			0
$527$	2.20711	−	32.3762i	0.0961431	−	1.41033i
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	11.5147			0.499696
$532$		0			0
$533$	−14.3284	+	24.8176i	−0.620633	+	1.07497i
$534$		0			0
$535$	−12.4142			−0.536713
$536$		0			0
$537$	3.15685	+	5.46783i	0.136228	+	0.235954i
$538$		0			0
$539$	−11.0711	+	19.1757i	−0.476865	+	0.825954i
$540$		0			0
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	−0.304683	−	0.952454i	$-0.598550\pi$
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	0.977191	−	0.212364i	$-0.0681162\pi$
$542$		0			0
$543$	−5.10051			−0.218884
$544$		0			0
$545$	5.41421	+	9.37769i	0.231919	+	0.401696i
$546$		0			0
$547$	−9.86396	−	17.0849i	−0.421753	−	0.730497i	0.574358	−	0.818604i	$-0.305252\pi$
$547$	−9.86396	−	17.0849i	−0.421753	−	0.730497i	−0.996111	+	0.0881071i	$0.971918\pi$
$548$		0			0
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$		0			0
$551$	−15.0711	+	26.1039i	−0.642049	+	1.11206i
$552$		0			0
$553$	−1.39949	−	2.42400i	−0.0595126	−	0.103079i
$554$		0			0
$555$	0.207107	−	0.358719i	0.00879119	−	0.0152268i
$556$		0			0
$557$	27.5147			1.16584			0.582918	−	0.812531i	$-0.301911\pi$
$557$	27.5147			1.16584			0.582918	+	0.812531i	$0.301911\pi$
$558$		0			0
$559$	−41.7279			−1.76490
$560$		0			0
$561$	3.91421	−	6.77962i	0.165258	−	0.286236i
$562$		0			0
$563$	6.62132	+	11.4685i	0.279055	+	0.483338i	0.971150	−	0.238468i	$-0.0766454\pi$
$563$	6.62132	+	11.4685i	0.279055	+	0.483338i	−0.692095	+	0.721807i	$0.743312\pi$
$564$		0			0
$565$	−8.32843	+	14.4253i	−0.350380	+	0.606875i
$566$		0			0
$567$	−1.55025	−	2.68512i	−0.0651045	−	0.112764i
$568$		0			0
$569$	6.57107	+	11.3814i	0.275473	+	0.477134i	0.970254	−	0.242087i	$-0.0778320\pi$
$569$	6.57107	+	11.3814i	0.275473	+	0.477134i	−0.694781	+	0.719221i	$0.744499\pi$
$570$		0			0
$571$	−10.5503	−	18.2736i	−0.441514	−	0.764725i	0.556288	−	0.830990i	$-0.312225\pi$
$571$	−10.5503	−	18.2736i	−0.441514	−	0.764725i	−0.997802	+	0.0662645i	$0.978892\pi$
$572$		0			0
$573$	−8.65685			−0.361645
$574$		0			0
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$		0			0
$577$	0.0147186	−	0.0254934i	0.000612744	−	0.00106130i	−0.865719	−	0.500531i	$-0.833138\pi$
$577$	0.0147186	−	0.0254934i	0.000612744	−	0.00106130i	0.866332	+	0.499469i	$0.166472\pi$
$578$		0			0
$579$	1.47918	+	2.56202i	0.0614728	+	0.106474i
$580$		0			0
$581$	4.17157			0.173066
$582$		0			0
$583$	9.44975	−	16.3674i	0.391369	−	0.677870i
$584$		0			0
$585$	10.8284			0.447700
$586$		0			0
$587$	31.6569			1.30662			0.653309	−	0.757091i	$-0.273380\pi$
$587$	31.6569			1.30662			0.653309	+	0.757091i	$0.273380\pi$
$588$		0			0
$589$	1.67157	−	24.5204i	0.0688760	−	1.01035i
$590$		0			0
$591$	5.58579			0.229769
$592$		0			0
$593$	−1.31371			−0.0539475			−0.0269738	−	0.999636i	$-0.508587\pi$
$593$	−1.31371			−0.0539475			−0.0269738	+	0.999636i	$0.508587\pi$
$594$		0			0
$595$	1.20711	−	2.09077i	0.0494866	−	0.0857132i
$596$		0			0
$597$	7.62742			0.312169
$598$		0			0
$599$	7.55025	+	13.0774i	0.308495	+	0.534329i	0.978033	−	0.208449i	$-0.0668414\pi$
$599$	7.55025	+	13.0774i	0.308495	+	0.534329i	−0.669538	+	0.742777i	$0.733508\pi$
$600$		0			0
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	−0.791911	−	0.610636i	$-0.790914\pi$
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	0.924782	+	0.380498i	$0.124247\pi$
$602$		0			0
$603$	−4.58579	+	7.94282i	−0.186748	+	0.323456i
$604$		0			0
$605$	−0.485281			−0.0197295
$606$		0			0
$607$	−0.792893	−	1.37333i	−0.0321825	−	0.0557418i	0.849486	−	0.527612i	$-0.176912\pi$
$607$	−0.792893	−	1.37333i	−0.0321825	−	0.0557418i	−0.881668	+	0.471870i	$0.843579\pi$
$608$		0			0
$609$	−0.585786	−	1.01461i	−0.0237373	−	0.0411141i
$610$		0			0
$611$	−18.4853	−	32.0174i	−0.747834	−	1.29529i
$612$		0			0
$613$	−6.15685	+	10.6640i	−0.248673	+	0.430714i	−0.963158	−	0.268937i	$-0.913328\pi$
$613$	−6.15685	+	10.6640i	−0.248673	+	0.430714i	0.714485	+	0.699651i	$0.246661\pi$
$614$		0			0
$615$	−1.55025	−	2.68512i	−0.0625122	−	0.108274i
$616$		0			0
$617$	16.6421	−	28.8250i	0.669987	−	1.16045i	−0.307920	−	0.951412i	$-0.599633\pi$
$617$	16.6421	−	28.8250i	0.669987	−	1.16045i	0.977907	−	0.209040i	$-0.0670337\pi$
$618$		0			0
$619$	20.3431			0.817660			0.408830	−	0.912611i	$-0.365937\pi$
$619$	20.3431			0.817660			0.408830	+	0.912611i	$0.365937\pi$
$620$		0			0
$621$	9.65685			0.387516
$622$		0			0
$623$	−0.928932	+	1.60896i	−0.0372169	+	0.0644615i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	2.96447	−	5.13461i	0.118389	−	0.205056i
$628$		0			0
$629$	2.91421	+	5.04757i	0.116197	+	0.201260i
$630$		0			0
$631$	25.0061	+	43.3118i	0.995477	+	1.72422i	0.580013	+	0.814607i	$0.303047\pi$
$631$	25.0061	+	43.3118i	0.995477	+	1.72422i	0.415464	+	0.909610i	$0.363619\pi$
$632$		0			0
$633$	−2.15685	−	3.73578i	−0.0857273	−	0.148484i
$634$		0			0
$635$	−8.89949			−0.353166
$636$		0			0
$637$	−13.0711	+	22.6398i	−0.517895	+	0.897020i
$638$		0			0
$639$	−0.100505	+	0.174080i	−0.00397592	+	0.00688649i
$640$		0			0
$641$	6.98528	+	12.0989i	0.275902	+	0.477876i	0.970362	−	0.241655i	$-0.0776901\pi$
$641$	6.98528	+	12.0989i	0.275902	+	0.477876i	−0.694460	+	0.719531i	$0.744357\pi$
$642$		0			0
$643$	−35.3137			−1.39264			−0.696318	−	0.717733i	$-0.745180\pi$
$643$	−35.3137			−1.39264			−0.696318	+	0.717733i	$0.745180\pi$
$644$		0			0
$645$	2.25736	−	3.90986i	0.0888834	−	0.153951i
$646$		0			0
$647$	45.3137			1.78147			0.890733	−	0.454527i	$-0.150192\pi$
$647$	45.3137			1.78147			0.890733	+	0.454527i	$0.150192\pi$
$648$		0			0
$649$	13.2010			0.518185
$650$		0			0
$651$	0.792893	+	0.532799i	0.0310759	+	0.0208821i
$652$		0			0
$653$	−6.14214			−0.240360			−0.120180	−	0.992752i	$-0.538347\pi$
$653$	−6.14214			−0.240360			−0.120180	+	0.992752i	$0.538347\pi$
$654$		0			0
$655$	13.2426			0.517433
$656$		0			0
$657$	−2.58579	+	4.47871i	−0.100881	+	0.174731i
$658$		0			0
$659$	1.65685			0.0645419			0.0322709	−	0.999479i	$-0.489726\pi$
$659$	1.65685			0.0645419			0.0322709	+	0.999479i	$0.489726\pi$
$660$		0			0
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	0.814915	−	0.579581i	$-0.196784\pi$
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	−0.909389	+	0.415946i	$0.863450\pi$
$662$		0			0
$663$	4.62132	−	8.00436i	0.179477	−	0.310864i
$664$		0			0
$665$	0.914214	−	1.58346i	0.0354517	−	0.0614041i
$666$		0			0
$667$	−27.3137			−1.05759
$668$		0			0
$669$	4.91421	+	8.51167i	0.189994	+	0.329080i
$670$		0			0
$671$	−4.58579	−	7.94282i	−0.177032	−	0.306629i
$672$		0			0
$673$	−4.67157	−	8.09140i	−0.180076	−	0.311901i	0.761830	−	0.647777i	$-0.224301\pi$
$673$	−4.67157	−	8.09140i	−0.180076	−	0.311901i	−0.941906	+	0.335876i	$0.890968\pi$
$674$		0			0
$675$	4.82843	−	8.36308i	0.185846	−	0.321895i
$676$		0			0
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	0.951711	+	0.306994i	$0.0993232\pi$
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	−0.209991	+	0.977703i	$0.567343\pi$
$678$		0			0
$679$	−1.07107	+	1.85514i	−0.0411038	+	0.0711939i
$680$		0			0
$681$	−7.62742			−0.292283
$682$		0			0
$683$	1.37258			0.0525204			0.0262602	−	0.999655i	$-0.491640\pi$
$683$	1.37258			0.0525204			0.0262602	+	0.999655i	$0.491640\pi$
$684$		0			0
$685$	−4.74264	+	8.21449i	−0.181207	+	0.313860i
$686$		0			0
$687$	−1.13604	−	1.96768i	−0.0433426	−	0.0750716i
$688$		0			0
$689$	11.1569	−	19.3242i	0.425042	−	0.736195i
$690$		0			0
$691$	−0.0355339	−	0.0615465i	−0.00135177	−	0.00234134i	0.865349	−	0.501170i	$-0.167097\pi$
$691$	−0.0355339	−	0.0615465i	−0.00135177	−	0.00234134i	−0.866700	+	0.498829i	$0.833764\pi$
$692$		0			0
$693$	−1.89949	−	3.29002i	−0.0721558	−	0.124978i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	43.6274			1.65251
$698$		0			0
$699$	−1.89949	+	3.29002i	−0.0718455	+	0.124440i
$700$		0			0
$701$	6.74264	−	11.6786i	0.254666	−	0.441094i	−0.710139	−	0.704062i	$-0.751368\pi$
$701$	6.74264	−	11.6786i	0.254666	−	0.441094i	0.964805	+	0.262967i	$0.0847011\pi$
$702$		0			0
$703$	2.20711	+	3.82282i	0.0832426	+	0.144180i
$704$		0			0
$705$	4.00000			0.150649
$706$		0			0
$707$	1.75736	−	3.04384i	0.0660923	−	0.114475i
$708$		0			0
$709$	17.3137			0.650230			0.325115	−	0.945674i	$-0.394597\pi$
$709$	17.3137			0.650230			0.325115	+	0.945674i	$0.394597\pi$
$710$		0			0
$711$	−19.1127			−0.716782
$712$		0			0
$713$	20.0000	−	9.79796i	0.749006	−	0.366936i
$714$		0			0
$715$	12.4142			0.464265
$716$		0			0
$717$	−8.79899			−0.328604
$718$		0			0
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	−0.931411	−	0.363968i	$-0.881422\pi$
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	0.780911	+	0.624642i	$0.214755\pi$
$720$		0			0
$721$	−0.857864			−0.0319485
$722$		0			0
$723$	2.76346	+	4.78645i	0.102774	+	0.178010i
$724$		0			0
$725$	−13.6569	+	23.6544i	−0.507203	+	0.878501i
$726$		0			0
$727$	20.4203	−	35.3690i	0.757347	−	1.31176i	−0.186851	−	0.982388i	$-0.559828\pi$
$727$	20.4203	−	35.3690i	0.757347	−	1.31176i	0.944199	−	0.329376i	$-0.106838\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	31.7635	+	55.0159i	1.17481	+	2.03484i
$732$		0			0
$733$	−7.81371	−	13.5337i	−0.288606	−	0.499880i	0.684871	−	0.728664i	$-0.259858\pi$
$733$	−7.81371	−	13.5337i	−0.288606	−	0.499880i	−0.973477	+	0.228784i	$0.926525\pi$
$734$		0			0
$735$	−1.41421	−	2.44949i	−0.0521641	−	0.0903508i
$736$		0			0
$737$	−5.25736	+	9.10601i	−0.193657	+	0.335424i
$738$		0			0
$739$	22.9350	+	39.7246i	0.843679	+	1.46129i	0.886764	+	0.462223i	$0.152948\pi$
$739$	22.9350	+	39.7246i	0.843679	+	1.46129i	−0.0430851	+	0.999071i	$0.513719\pi$
$740$		0			0
$741$	3.50000	−	6.06218i	0.128576	−	0.222700i
$742$		0			0
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$		0			0
$747$	14.2426	−	24.6690i	0.521111	−	0.902591i
$748$		0			0
$749$	2.57107	+	4.45322i	0.0939448	+	0.162717i
$750$		0			0
$751$	3.62132	−	6.27231i	0.132144	−	0.228880i	−0.792359	−	0.610055i	$-0.791147\pi$
$751$	3.62132	−	6.27231i	0.132144	−	0.228880i	0.924503	+	0.381175i	$0.124481\pi$
$752$		0			0
$753$	−1.32843	−	2.30090i	−0.0484106	−	0.0838496i
$754$		0			0
$755$	2.65685	+	4.60181i	0.0966928	+	0.167477i
$756$		0			0
$757$	−11.6716	−	20.2158i	−0.424211	−	0.734754i	0.572136	−	0.820159i	$-0.306115\pi$
$757$	−11.6716	−	20.2158i	−0.424211	−	0.734754i	−0.996346	+	0.0854047i	$0.972782\pi$
$758$		0			0
$759$	5.37258			0.195012
$760$		0			0
$761$	−15.2279	+	26.3755i	−0.552012	+	0.956112i	0.446118	+	0.894974i	$0.352806\pi$
$761$	−15.2279	+	26.3755i	−0.552012	+	0.956112i	−0.998129	+	0.0611380i	$0.980527\pi$
$762$		0			0
$763$	2.24264	−	3.88437i	0.0811890	−	0.140624i
$764$		0			0
$765$	−8.24264	−	14.2767i	−0.298013	−	0.516174i
$766$		0			0
$767$	15.5858			0.562770
$768$		0			0
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$770$		0			0
$771$	−9.24264			−0.332866
$772$		0			0
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$		0			0
$775$	1.51472	−	22.2195i	0.0544103	−	0.798148i
$776$		0			0
$777$	−0.171573			−0.00615514
$778$		0			0
$779$	33.0416			1.18384
$780$		0			0
$781$	−0.115224	+	0.199573i	−0.00412303	+	0.00714129i
$782$		0			0
$783$	−16.4853			−0.589136
$784$		0			0
$785$	−4.58579	−	7.94282i	−0.163674	−	0.283491i
$786$		0			0
$787$	21.2071	−	36.7318i	0.755952	−	1.30935i	−0.188948	−	0.981987i	$-0.560508\pi$
$787$	21.2071	−	36.7318i	0.755952	−	1.30935i	0.944900	−	0.327360i	$-0.106159\pi$
$788$		0			0
$789$	4.82843	−	8.36308i	0.171897	−	0.297734i
$790$		0			0
$791$	6.89949			0.245318
$792$		0			0
$793$	−5.41421	−	9.37769i	−0.192264	−	0.333012i
$794$		0			0
$795$	1.20711	+	2.09077i	0.0428117	+	0.0741520i
$796$		0			0
$797$	−14.2279	−	24.6435i	−0.503979	−	0.872917i	−0.999989	−	0.00460050i	$-0.998536\pi$
$797$	−14.2279	−	24.6435i	−0.503979	−	0.872917i	0.496011	−	0.868316i	$-0.334798\pi$
$798$		0			0
$799$	−28.1421	+	48.7436i	−0.995597	+	1.72442i
$800$		0			0
$801$	6.34315	+	10.9867i	0.224124	+	0.388194i
$802$		0			0
$803$	−2.96447	+	5.13461i	−0.104614	+	0.181196i
$804$		0			0
$805$	1.65685			0.0583964
$806$		0			0
$807$	10.8406			0.381608
$808$		0			0
$809$	6.01472	−	10.4178i	0.211466	−	0.366270i	−0.740707	−	0.671828i	$-0.765509\pi$
$809$	6.01472	−	10.4178i	0.211466	−	0.366270i	0.952174	+	0.305558i	$0.0988428\pi$
$810$		0			0
$811$	−6.86396	−	11.8887i	−0.241026	−	0.417470i	0.719981	−	0.693994i	$-0.244151\pi$
$811$	−6.86396	−	11.8887i	−0.241026	−	0.417470i	−0.961007	+	0.276524i	$0.910817\pi$
$812$		0			0
$813$	0.142136	−	0.246186i	0.00498491	−	0.00863412i
$814$		0			0
$815$	10.4853	+	18.1610i	0.367283	+	0.636153i
$816$		0			0
$817$	24.0563	+	41.6668i	0.841625	+	1.45774i
$818$		0			0
$819$	−2.24264	−	3.88437i	−0.0783642	−	0.135731i
$820$		0			0
$821$	8.48528			0.296138			0.148069	−	0.988977i	$-0.452694\pi$
$821$	8.48528			0.296138			0.148069	+	0.988977i	$0.452694\pi$
$822$		0			0
$823$	18.1066	−	31.3616i	0.631156	−	1.09320i	−0.356159	−	0.934425i	$-0.615914\pi$
$823$	18.1066	−	31.3616i	0.631156	−	1.09320i	0.987316	−	0.158770i	$-0.0507528\pi$
$824$		0			0
$825$	2.68629	−	4.65279i	0.0935247	−	0.161989i
$826$		0			0
$827$	18.4497	+	31.9559i	0.641561	+	1.11122i	0.985084	+	0.172072i	$0.0550460\pi$
$827$	18.4497	+	31.9559i	0.641561	+	1.11122i	−0.343524	+	0.939144i	$0.611621\pi$
$828$		0			0
$829$	38.4264			1.33460			0.667302	−	0.744787i	$-0.267449\pi$
$829$	38.4264			1.33460			0.667302	+	0.744787i	$0.267449\pi$
$830$		0			0
$831$	2.92893	−	5.07306i	0.101604	−	0.175982i
$832$		0			0
$833$	39.7990			1.37895
$834$		0			0
$835$	−22.5563			−0.780595
$836$		0			0
$837$	12.0711	−	5.91359i	0.417237	−	0.204404i
$838$		0			0
$839$	14.6274			0.504995			0.252497	−	0.967598i	$-0.418748\pi$
$839$	14.6274			0.504995			0.252497	+	0.967598i	$0.418748\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$		0			0
$843$	0.414214	−	0.717439i	0.0142663	−	0.0247099i
$844$		0			0
$845$	1.65685			0.0569975
$846$		0			0
$847$	0.100505	+	0.174080i	0.00345339	+	0.00598146i
$848$		0			0
$849$	2.82843	−	4.89898i	0.0970714	−	0.168133i
$850$		0			0
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$		0			0
$853$	−15.5147			−0.531214			−0.265607	−	0.964081i	$-0.585572\pi$
$853$	−15.5147			−0.531214			−0.265607	+	0.964081i	$0.585572\pi$
$854$		0			0
$855$	−6.24264	−	10.8126i	−0.213494	−	0.369782i
$856$		0			0
$857$	9.74264	+	16.8747i	0.332802	+	0.576430i	0.983060	−	0.183283i	$-0.0586725\pi$
$857$	9.74264	+	16.8747i	0.332802	+	0.576430i	−0.650258	+	0.759714i	$0.725339\pi$
$858$		0			0
$859$	−24.6924	−	42.7685i	−0.842493	−	1.45924i	−0.887780	−	0.460267i	$-0.847754\pi$
$859$	−24.6924	−	42.7685i	−0.842493	−	1.45924i	0.0452869	−	0.998974i	$-0.485580\pi$
$860$		0			0
$861$	−0.642136	+	1.11221i	−0.0218839	+	0.0379041i
$862$		0			0
$863$	−1.30761	−	2.26485i	−0.0445116	−	0.0770964i	0.842911	−	0.538053i	$-0.180840\pi$
$863$	−1.30761	−	2.26485i	−0.0445116	−	0.0770964i	−0.887423	+	0.460956i	$0.847507\pi$
$864$		0			0
$865$	−4.15685	+	7.19988i	−0.141337	+	0.244803i
$866$		0			0
$867$	−7.02944			−0.238732
$868$		0			0
$869$	−21.9117			−0.743303
$870$		0			0
$871$	−6.20711	+	10.7510i	−0.210320	+	0.364285i
$872$		0			0
$873$	7.31371	+	12.6677i	0.247532	+	0.428737i
$874$		0			0
$875$	1.86396	−	3.22848i	0.0630134	−	0.109142i
$876$		0			0
$877$	−26.9142	−	46.6168i	−0.908828	−	1.57414i	−0.815694	−	0.578483i	$-0.803645\pi$
$877$	−26.9142	−	46.6168i	−0.908828	−	1.57414i	−0.0931343	−	0.995654i	$-0.529689\pi$
$878$		0			0
$879$	3.06497	+	5.30869i	0.103379	+	0.179058i
$880$		0			0
$881$	−5.84315	−	10.1206i	−0.196861	−	0.340973i	0.750648	−	0.660702i	$-0.229741\pi$
$881$	−5.84315	−	10.1206i	−0.196861	−	0.340973i	−0.947509	+	0.319729i	$0.896408\pi$
$882$		0			0
$883$	30.2843			1.01915			0.509573	−	0.860427i	$-0.329803\pi$
$883$	30.2843			1.01915			0.509573	+	0.860427i	$0.329803\pi$
$884$		0			0
$885$	−0.843146	+	1.46037i	−0.0283420	+	0.0490898i
$886$		0			0
$887$	−25.6630	+	44.4495i	−0.861678	+	1.49247i	0.00863117	+	0.999963i	$0.497253\pi$
$887$	−25.6630	+	44.4495i	−0.861678	+	1.49247i	−0.870309	+	0.492507i	$0.836081\pi$
$888$		0			0
$889$	1.84315	+	3.19242i	0.0618171	+	0.107070i
$890$		0			0
$891$	−24.2721			−0.813145
$892$		0			0
$893$	−21.3137	+	36.9164i	−0.713236	+	1.23536i
$894$		0			0
$895$	15.2426			0.509505
$896$		0			0
$897$	6.34315			0.211791
$898$		0			0
$899$	−34.1421	+	16.7262i	−1.13870	+	0.557849i
$900$		0			0
$901$	−33.9706			−1.13172
$902$		0			0
$903$	−1.87006			−0.0622316
$904$		0			0
$905$	−6.15685	+	10.6640i	−0.204661	+	0.354483i
$906$		0			0
$907$	−32.6863			−1.08533			−0.542665	−	0.839949i	$-0.682585\pi$
$907$	−32.6863			−1.08533			−0.542665	+	0.839949i	$0.682585\pi$
$908$		0			0
$909$	−12.0000	−	20.7846i	−0.398015	−	0.689382i
$910$		0			0
$911$	0.479185	−	0.829972i	0.0158761	−	0.0274982i	−0.857978	−	0.513686i	$-0.828280\pi$
$911$	0.479185	−	0.829972i	0.0158761	−	0.0274982i	0.873854	+	0.486188i	$0.161613\pi$
$912$		0			0
$913$	16.3284	−	28.2817i	0.540392	−	0.935987i
$914$		0			0
$915$	1.17157			0.0387310
$916$		0			0
$917$	−2.74264	−	4.75039i	−0.0905700	−	0.156872i
$918$		0			0
$919$	−17.4497	−	30.2238i	−0.575614	−	0.996993i	−0.995975	−	0.0896356i	$-0.971430\pi$
$919$	−17.4497	−	30.2238i	−0.575614	−	0.996993i	0.420361	−	0.907357i	$-0.361904\pi$
$920$		0			0
$921$	2.32843	+	4.03295i	0.0767243	+	0.132890i
$922$		0			0
$923$	−0.136039	+	0.235626i	−0.00447778	+	0.00775574i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$		0			0
$927$	−2.92893	+	5.07306i	−0.0961988	+	0.166621i
$928$		0			0
$929$	7.51472			0.246550			0.123275	−	0.992373i	$-0.460660\pi$
$929$	7.51472			0.246550			0.123275	+	0.992373i	$0.460660\pi$
$930$		0			0
$931$	30.1421			0.987869
$932$		0			0
$933$	−2.34315	+	4.05845i	−0.0767111	+	0.132868i
$934$		0			0
$935$	−9.44975	−	16.3674i	−0.309040	−	0.535273i
$936$		0			0
$937$	−7.84315	+	13.5847i	−0.256224	+	0.443794i	−0.965227	−	0.261412i	$-0.915812\pi$
$937$	−7.84315	+	13.5847i	−0.256224	+	0.443794i	0.709003	+	0.705206i	$0.249145\pi$
$938$		0			0
$939$	−0.378680	−	0.655892i	−0.0123577	−	0.0214042i
$940$		0			0
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	0.996516	+	0.0833989i	$0.0265776\pi$
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	−0.426033	+	0.904708i	$0.640089\pi$
$942$		0			0
$943$	14.9706	+	25.9298i	0.487509	+	0.844390i
$944$		0			0
$945$	1.00000			0.0325300
$946$		0			0
$947$	9.55025	−	16.5415i	0.310342	−	0.537527i	−0.668095	−	0.744076i	$-0.732890\pi$
$947$	9.55025	−	16.5415i	0.310342	−	0.537527i	0.978436	+	0.206549i	$0.0662233\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$		0			0
$951$	−1.62132	−	2.80821i	−0.0525749	−	0.0910624i
$952$		0			0
$953$	3.51472			0.113853			0.0569265	−	0.998378i	$-0.481870\pi$
$953$	3.51472			0.113853			0.0569265	+	0.998378i	$0.481870\pi$
$954$		0			0
$955$	−10.4497	+	18.0995i	−0.338146	+	0.585686i
$956$		0			0
$957$	−9.17157			−0.296475
$958$		0			0
$959$	3.92893			0.126872
$960$		0			0
$961$	19.0000	−	24.4949i	0.612903	−	0.790158i
$962$		0			0
$963$	35.1127			1.13149
$964$		0			0
$965$	7.14214			0.229913
$966$		0			0
$967$	−7.72183	+	13.3746i	−0.248317	+	0.430098i	−0.963059	−	0.269290i	$-0.913211\pi$
$967$	−7.72183	+	13.3746i	−0.248317	+	0.430098i	0.714742	+	0.699388i	$0.246544\pi$
$968$		0			0
$969$	−10.6569			−0.342347
$970$		0			0
$971$	−0.349242	−	0.604906i	−0.0112077	−	0.0194123i	0.860367	−	0.509675i	$-0.170234\pi$
$971$	−0.349242	−	0.604906i	−0.0112077	−	0.0194123i	−0.871575	+	0.490262i	$0.836901\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.17157	−	5.49333i	0.101572	−	0.175927i
$976$		0			0
$977$	−0.485281			−0.0155255			−0.00776276	−	0.999970i	$-0.502471\pi$
$977$	−0.485281			−0.0155255			−0.00776276	+	0.999970i	$0.502471\pi$
$978$		0			0
$979$	7.27208	+	12.5956i	0.232417	+	0.402557i
$980$		0			0
$981$	−15.3137	−	26.5241i	−0.488929	−	0.846850i
$982$		0			0
$983$	−19.4203	−	33.6370i	−0.619412	−	1.07285i	−0.989593	−	0.143893i	$-0.954038\pi$
$983$	−19.4203	−	33.6370i	−0.619412	−	1.07285i	0.370182	−	0.928959i	$-0.379295\pi$
$984$		0			0
$985$	6.74264	−	11.6786i	0.214838	−	0.372111i
$986$		0			0
$987$	−0.828427	−	1.43488i	−0.0263691	−	0.0456727i
$988$		0			0
$989$	−21.7990	+	37.7570i	−0.693168	+	1.20060i
$990$		0			0
$991$	−47.9411			−1.52290			−0.761450	−	0.648224i	$-0.775512\pi$
$991$	−47.9411			−1.52290			−0.761450	+	0.648224i	$0.775512\pi$
$992$		0			0
$993$	3.82843			0.121491
$994$		0			0
$995$	9.20711	−	15.9472i	0.291885	−	0.505559i
$996$		0			0
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	−0.999823	−	0.0188015i	$-0.994015\pi$
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	0.483629	−	0.875273i	$-0.339318\pi$
$998$		0			0
$999$	−1.20711	+	2.09077i	−0.0381912	+	0.0661490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	496.2.i.h.129.2		4
4.3	odd	2		31.2.c.a.5.2	✓	4
12.11	even	2		279.2.h.c.253.1		4
20.3	even	4		775.2.o.d.749.2		8
20.7	even	4		775.2.o.d.749.3		8
20.19	odd	2		775.2.e.e.501.1		4
31.25	even	3	inner	496.2.i.h.273.2		4
124.3	even	30		961.2.g.r.448.2		16
124.7	odd	30		961.2.g.o.338.1		16
124.11	even	30		961.2.d.i.388.1		8
124.15	even	10		961.2.g.r.846.2		16
124.19	odd	30		961.2.g.o.844.2		16
124.23	even	10		961.2.g.r.816.1		16
124.27	even	10		961.2.g.r.235.1		16
124.35	odd	10		961.2.g.o.235.1		16
124.39	odd	10		961.2.g.o.816.1		16
124.43	even	30		961.2.g.r.844.2		16
124.47	odd	10		961.2.g.o.846.2		16
124.51	odd	30		961.2.d.l.388.1		8
124.55	even	30		961.2.g.r.338.1		16
124.59	odd	30		961.2.g.o.448.2		16
124.67	odd	6		961.2.a.a.1.2		2
124.71	odd	30		961.2.d.l.374.1		8
124.75	even	30		961.2.d.i.628.2		8
124.79	even	30		961.2.g.r.732.1		16
124.83	even	30		961.2.d.i.531.2		8
124.87	odd	6		31.2.c.a.25.2	yes	4
124.91	even	10		961.2.g.r.547.2		16
124.95	odd	10		961.2.g.o.547.2		16
124.99	even	6		961.2.c.a.521.2		4
124.103	odd	30		961.2.d.l.531.2		8
124.107	odd	30		961.2.g.o.732.1		16
124.111	odd	30		961.2.d.l.628.2		8
124.115	even	30		961.2.d.i.374.1		8
124.119	even	6		961.2.a.c.1.2		2
124.123	even	2		961.2.c.a.439.2		4
372.119	odd	6		8649.2.a.k.1.1		2
372.191	even	6		8649.2.a.l.1.1		2
372.335	even	6		279.2.h.c.118.1		4
620.87	even	12		775.2.o.d.149.3		8
620.459	odd	6		775.2.e.e.676.1		4
620.583	even	12		775.2.o.d.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	4.3	odd	2
31.2.c.a.25.2	yes	4	124.87	odd	6
279.2.h.c.118.1		4	372.335	even	6
279.2.h.c.253.1		4	12.11	even	2
496.2.i.h.129.2		4	1.1	even	1	trivial
496.2.i.h.273.2		4	31.25	even	3	inner
775.2.e.e.501.1		4	20.19	odd	2
775.2.e.e.676.1		4	620.459	odd	6
775.2.o.d.149.2		8	620.583	even	12
775.2.o.d.149.3		8	620.87	even	12
775.2.o.d.749.2		8	20.3	even	4
775.2.o.d.749.3		8	20.7	even	4
961.2.a.a.1.2		2	124.67	odd	6
961.2.a.c.1.2		2	124.119	even	6
961.2.c.a.439.2		4	124.123	even	2
961.2.c.a.521.2		4	124.99	even	6
961.2.d.i.374.1		8	124.115	even	30
961.2.d.i.388.1		8	124.11	even	30
961.2.d.i.531.2		8	124.83	even	30
961.2.d.i.628.2		8	124.75	even	30
961.2.d.l.374.1		8	124.71	odd	30
961.2.d.l.388.1		8	124.51	odd	30
961.2.d.l.531.2		8	124.103	odd	30
961.2.d.l.628.2		8	124.111	odd	30
961.2.g.o.235.1		16	124.35	odd	10
961.2.g.o.338.1		16	124.7	odd	30
961.2.g.o.448.2		16	124.59	odd	30
961.2.g.o.547.2		16	124.95	odd	10
961.2.g.o.732.1		16	124.107	odd	30
961.2.g.o.816.1		16	124.39	odd	10
961.2.g.o.844.2		16	124.19	odd	30
961.2.g.o.846.2		16	124.47	odd	10
961.2.g.r.235.1		16	124.27	even	10
961.2.g.r.338.1		16	124.55	even	30
961.2.g.r.448.2		16	124.3	even	30
961.2.g.r.547.2		16	124.91	even	10
961.2.g.r.732.1		16	124.79	even	30
961.2.g.r.816.1		16	124.23	even	10
961.2.g.r.844.2		16	124.43	even	30
961.2.g.r.846.2		16	124.15	even	10
8649.2.a.k.1.1		2	372.119	odd	6
8649.2.a.l.1.1		2	372.191	even	6

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:	\( N \)	\(=\)	\( 496 = 2^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	496.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.207107 + 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.207107 + 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(1.62132 + 2.80821i) q^{11} +(1.91421 + 3.31552i) q^{13} -0.414214 q^{15} +(2.91421 - 5.04757i) q^{17} +(2.20711 - 3.82282i) q^{19} +(0.0857864 + 0.148586i) q^{21} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +2.41421 q^{27} -6.82843 q^{29} +(5.00000 - 2.44949i) q^{31} +1.34315 q^{33} +0.414214 q^{35} +(-0.500000 + 0.866025i) q^{37} +1.58579 q^{39} +(3.74264 + 6.48244i) q^{41} +(-5.44975 + 9.43924i) q^{43} +(1.41421 - 2.44949i) q^{45} -9.65685 q^{47} +(3.41421 + 5.91359i) q^{49} +(-1.20711 - 2.09077i) q^{51} +(-2.91421 - 5.04757i) q^{53} +(1.62132 - 2.80821i) q^{55} +(-0.914214 - 1.58346i) q^{57} +(2.03553 - 3.52565i) q^{59} -2.82843 q^{61} -1.17157 q^{63} +(1.91421 - 3.31552i) q^{65} +(1.62132 + 2.80821i) q^{67} +(0.828427 - 1.43488i) q^{69} +(0.0355339 + 0.0615465i) q^{71} +(0.914214 + 1.58346i) q^{73} +(-0.828427 - 1.43488i) q^{75} -1.34315 q^{77} +(-3.37868 + 5.85204i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(-5.03553 - 8.72180i) q^{83} -5.82843 q^{85} +(-1.41421 + 2.44949i) q^{87} +4.48528 q^{89} -1.58579 q^{91} +(0.156854 - 2.30090i) q^{93} -4.41421 q^{95} +5.17157 q^{97} +(-4.58579 + 7.94282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 + 2 * q^7	\( 4 q - 2 q^{3} - 2 q^{5} + 2 q^{7} - 2 q^{11} + 2 q^{13} + 4 q^{15} + 6 q^{17} + 6 q^{19} + 6 q^{21} + 16 q^{23} + 8 q^{25} + 4 q^{27} - 16 q^{29} + 20 q^{31} + 28 q^{33} - 4 q^{35} - 2 q^{37} + 12 q^{39} - 2 q^{41} - 2 q^{43} - 16 q^{47} + 8 q^{49} - 2 q^{51} - 6 q^{53} - 2 q^{55} + 2 q^{57} - 6 q^{59} - 16 q^{63} + 2 q^{65} - 2 q^{67} - 8 q^{69} - 14 q^{71} - 2 q^{73} + 8 q^{75} - 28 q^{77} - 22 q^{79} + 2 q^{81} - 6 q^{83} - 12 q^{85} - 16 q^{89} - 12 q^{91} - 22 q^{93} - 12 q^{95} + 32 q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 + 2 * q^7 - 2 * q^11 + 2 * q^13 + 4 * q^15 + 6 * q^17 + 6 * q^19 + 6 * q^21 + 16 * q^23 + 8 * q^25 + 4 * q^27 - 16 * q^29 + 20 * q^31 + 28 * q^33 - 4 * q^35 - 2 * q^37 + 12 * q^39 - 2 * q^41 - 2 * q^43 - 16 * q^47 + 8 * q^49 - 2 * q^51 - 6 * q^53 - 2 * q^55 + 2 * q^57 - 6 * q^59 - 16 * q^63 + 2 * q^65 - 2 * q^67 - 8 * q^69 - 14 * q^71 - 2 * q^73 + 8 * q^75 - 28 * q^77 - 22 * q^79 + 2 * q^81 - 6 * q^83 - 12 * q^85 - 16 * q^89 - 12 * q^91 - 22 * q^93 - 12 * q^95 + 32 * q^97 - 24 * q^99

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