LMFDB - Embedded newform 525.2.r.g.499.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(424,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.424"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.g.424.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.41421 q^{6} +(-0.358719 + 2.62132i) q^{7} +2.82843i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.292893 - 0.507306i) q^{11} -4.41421i q^{13} +(2.29289 - 2.95680i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-1.94218 + 1.12132i) q^{17} +(-1.22474 + 0.707107i) q^{18} +(2.32843 - 4.03295i) q^{19} +(-1.00000 - 2.44949i) q^{21} +0.828427i q^{22} +(-1.94218 - 1.12132i) q^{23} +(-1.41421 - 2.44949i) q^{24} +(-3.12132 + 5.40629i) q^{26} +1.00000i q^{27} -8.24264 q^{29} +(2.91421 + 5.04757i) q^{31} +(0.507306 + 0.292893i) q^{33} +3.17157 q^{34} +(-7.28692 - 4.20711i) q^{37} +(-5.70346 + 3.29289i) q^{38} +(2.20711 + 3.82282i) q^{39} -6.24264 q^{41} +(-0.507306 + 3.70711i) q^{42} -7.58579i q^{43} +(1.58579 + 2.74666i) q^{46} +(-11.5300 - 6.65685i) q^{47} +4.00000i q^{48} +(-6.74264 - 1.88064i) q^{49} +(1.12132 - 1.94218i) q^{51} +(5.91359 - 3.41421i) q^{53} +(0.707107 - 1.22474i) q^{54} +(-7.41421 - 1.01461i) q^{56} +4.65685i q^{57} +(10.0951 + 5.82843i) q^{58} +(-0.707107 - 1.22474i) q^{59} +(2.24264 - 3.88437i) q^{61} -8.24264i q^{62} +(2.09077 + 1.62132i) q^{63} -8.00000 q^{64} +(-0.414214 - 0.717439i) q^{66} +(11.8887 - 6.86396i) q^{67} +2.24264 q^{69} -0.585786 q^{71} +(2.44949 + 1.41421i) q^{72} +(-10.4539 + 6.03553i) q^{73} +(5.94975 + 10.3053i) q^{74} +(1.43488 - 0.585786i) q^{77} -6.24264i q^{78} +(3.32843 - 5.76500i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.64564 + 4.41421i) q^{82} +2.58579i q^{83} +(-5.36396 + 9.29065i) q^{86} +(7.13834 - 4.12132i) q^{87} +(1.43488 - 0.828427i) q^{88} +(-6.12132 + 10.6024i) q^{89} +(11.5711 + 1.58346i) q^{91} +(-5.04757 - 2.91421i) q^{93} +(9.41421 + 16.3059i) q^{94} +5.17157i q^{97} +(6.92820 + 7.07107i) q^{98} -0.585786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9} - 8 q^{11} + 24 q^{14} + 16 q^{16} - 4 q^{19} - 8 q^{21} - 8 q^{26} - 32 q^{29} + 12 q^{31} + 48 q^{34} + 12 q^{39} - 16 q^{41} + 24 q^{46} - 20 q^{49} - 8 q^{51} - 48 q^{56} - 16 q^{61} - 64 q^{64}+ \cdots - 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 - 8 * q^11 + 24 * q^14 + 16 * q^16 - 4 * q^19 - 8 * q^21 - 8 * q^26 - 32 * q^29 + 12 * q^31 + 48 * q^34 + 12 * q^39 - 16 * q^41 + 24 * q^46 - 20 * q^49 - 8 * q^51 - 48 * q^56 - 16 * q^61 - 64 * q^64 + 8 * q^66 - 16 * q^69 - 16 * q^71 + 8 * q^74 + 4 * q^79 - 4 * q^81 + 8 * q^86 - 32 * q^89 + 36 * q^91 + 64 * q^94 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	1.41421			0.577350
$7$	−0.358719	+	2.62132i	−0.135583	+	0.990766i
$7$	−0.358719	+	2.62132i	−0.135583	+	0.990766i
$8$			2.82843i			1.00000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	0.818487	−	0.574526i	$-0.194813\pi$
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	−0.906797	+	0.421567i	$0.861480\pi$
$12$		0			0
$13$		−	4.41421i		−	1.22428i	−0.790748	−	0.612141i	$-0.790308\pi$
$13$		−	4.41421i		−	1.22428i	0.790748	−	0.612141i	$-0.209692\pi$
$14$	2.29289	−	2.95680i	0.612801	−	0.790237i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.94218	+	1.12132i	−0.471049	+	0.271960i	−0.716679	−	0.697404i	$-0.754339\pi$
$17$	−1.94218	+	1.12132i	−0.471049	+	0.271960i	0.245630	+	0.969364i	$0.421005\pi$
$18$	−1.22474	+	0.707107i	−0.288675	+	0.166667i
$19$	2.32843	−	4.03295i	0.534178	−	0.925223i	−0.465025	−	0.885298i	$-0.653955\pi$
$19$	2.32843	−	4.03295i	0.534178	−	0.925223i	0.999203	−	0.0399255i	$-0.0127121\pi$
$20$		0			0
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$			0.828427i			0.176621i
$23$	−1.94218	−	1.12132i	−0.404973	−	0.233811i	0.283654	−	0.958927i	$-0.408453\pi$
$23$	−1.94218	−	1.12132i	−0.404973	−	0.233811i	−0.688628	+	0.725115i	$0.741787\pi$
$24$	−1.41421	−	2.44949i	−0.288675	−	0.500000i
$25$		0			0
$26$	−3.12132	+	5.40629i	−0.612141	+	1.06026i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−8.24264			−1.53062			−0.765310	−	0.643662i	$-0.777414\pi$
$29$	−8.24264			−1.53062			−0.765310	+	0.643662i	$0.777414\pi$
$30$		0			0
$31$	2.91421	+	5.04757i	0.523408	+	0.906570i	0.999629	+	0.0272438i	$0.00867303\pi$
$31$	2.91421	+	5.04757i	0.523408	+	0.906570i	−0.476221	+	0.879326i	$0.657994\pi$
$32$		0			0
$33$	0.507306	+	0.292893i	0.0883106	+	0.0509862i
$34$	3.17157			0.543920
$35$		0			0
$36$		0			0
$37$	−7.28692	−	4.20711i	−1.19796	−	0.691644i	−0.237862	−	0.971299i	$-0.576447\pi$
$37$	−7.28692	−	4.20711i	−1.19796	−	0.691644i	−0.960101	+	0.279655i	$0.909780\pi$
$38$	−5.70346	+	3.29289i	−0.925223	+	0.534178i
$39$	2.20711	+	3.82282i	0.353420	+	0.612141i
$40$		0			0
$41$	−6.24264			−0.974937			−0.487468	−	0.873141i	$-0.662080\pi$
$41$	−6.24264			−0.974937			−0.487468	+	0.873141i	$0.662080\pi$
$42$	−0.507306	+	3.70711i	−0.0782790	+	0.572019i
$43$		−	7.58579i		−	1.15682i	−0.815746	−	0.578411i	$-0.803673\pi$
$43$		−	7.58579i		−	1.15682i	0.815746	−	0.578411i	$-0.196327\pi$
$44$		0			0
$45$		0			0
$46$	1.58579	+	2.74666i	0.233811	+	0.404973i
$47$	−11.5300	−	6.65685i	−1.68182	−	0.971002i	−0.960448	−	0.278459i	$-0.910176\pi$
$47$	−11.5300	−	6.65685i	−1.68182	−	0.971002i	−0.721377	−	0.692543i	$-0.756490\pi$
$48$			4.00000i			0.577350i
$49$	−6.74264	−	1.88064i	−0.963234	−	0.268662i
$50$		0			0
$51$	1.12132	−	1.94218i	0.157016	−	0.271960i
$52$		0			0
$53$	5.91359	−	3.41421i	0.812294	−	0.468978i	−0.0354577	−	0.999371i	$-0.511289\pi$
$53$	5.91359	−	3.41421i	0.812294	−	0.468978i	0.847752	+	0.530393i	$0.177956\pi$
$54$	0.707107	−	1.22474i	0.0962250	−	0.166667i
$55$		0			0
$56$	−7.41421	−	1.01461i	−0.990766	−	0.135583i
$57$			4.65685i			0.616815i
$58$	10.0951	+	5.82843i	1.32556	+	0.765310i
$59$	−0.707107	−	1.22474i	−0.0920575	−	0.159448i	0.816319	−	0.577601i	$-0.196011\pi$
$59$	−0.707107	−	1.22474i	−0.0920575	−	0.159448i	−0.908377	+	0.418153i	$0.862678\pi$
$60$		0			0
$61$	2.24264	−	3.88437i	0.287141	−	0.497342i	−0.685985	−	0.727615i	$-0.740629\pi$
$61$	2.24264	−	3.88437i	0.287141	−	0.497342i	0.973126	+	0.230273i	$0.0739619\pi$
$62$		−	8.24264i		−	1.04682i
$63$	2.09077	+	1.62132i	0.263412	+	0.204267i
$64$	−8.00000			−1.00000
$65$		0			0
$66$	−0.414214	−	0.717439i	−0.0509862	−	0.0883106i
$67$	11.8887	−	6.86396i	1.45244	−	0.838566i	0.453820	−	0.891093i	$-0.350061\pi$
$67$	11.8887	−	6.86396i	1.45244	−	0.838566i	0.998619	+	0.0525271i	$0.0167276\pi$
$68$		0			0
$69$	2.24264			0.269982
$70$		0			0
$71$	−0.585786			−0.0695201			−0.0347600	−	0.999396i	$-0.511067\pi$
$71$	−0.585786			−0.0695201			−0.0347600	+	0.999396i	$0.511067\pi$
$72$	2.44949	+	1.41421i	0.288675	+	0.166667i
$73$	−10.4539	+	6.03553i	−1.22353	+	0.706406i	−0.965669	−	0.259776i	$-0.916351\pi$
$73$	−10.4539	+	6.03553i	−1.22353	+	0.706406i	−0.257862	+	0.966182i	$0.583018\pi$
$74$	5.94975	+	10.3053i	0.691644	+	1.19796i
$75$		0			0
$76$		0			0
$77$	1.43488	−	0.585786i	0.163520	−	0.0667566i
$78$		−	6.24264i		−	0.706840i
$79$	3.32843	−	5.76500i	0.374477	−	0.648614i	−0.615771	−	0.787925i	$-0.711155\pi$
$79$	3.32843	−	5.76500i	0.374477	−	0.648614i	0.990249	+	0.139311i	$0.0444888\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.64564	+	4.41421i	0.844320	+	0.487468i
$83$			2.58579i			0.283827i	0.989879	+	0.141913i	$0.0453255\pi$
$83$			2.58579i			0.283827i	−0.989879	+	0.141913i	$0.954675\pi$
$84$		0			0
$85$		0			0
$86$	−5.36396	+	9.29065i	−0.578411	+	1.00184i
$87$	7.13834	−	4.12132i	0.765310	−	0.441852i
$88$	1.43488	−	0.828427i	0.152958	−	0.0883106i
$89$	−6.12132	+	10.6024i	−0.648859	+	1.12386i	0.334537	+	0.942383i	$0.391420\pi$
$89$	−6.12132	+	10.6024i	−0.648859	+	1.12386i	−0.983396	+	0.181474i	$0.941913\pi$
$90$		0			0
$91$	11.5711	+	1.58346i	1.21298	+	0.165992i
$92$		0			0
$93$	−5.04757	−	2.91421i	−0.523408	−	0.302190i
$94$	9.41421	+	16.3059i	0.971002	+	1.68182i
$95$		0			0
$96$		0			0
$97$			5.17157i			0.525094i	0.964919	+	0.262547i	$0.0845624\pi$
$97$			5.17157i			0.525094i	−0.964919	+	0.262547i	$0.915438\pi$
$98$	6.92820	+	7.07107i	0.699854	+	0.714286i
$99$	−0.585786			−0.0588738
$100$		0			0
$101$	−1.12132	−	1.94218i	−0.111576	−	0.193255i	0.804830	−	0.593505i	$-0.202256\pi$
$101$	−1.12132	−	1.94218i	−0.111576	−	0.193255i	−0.916406	+	0.400251i	$0.868923\pi$
$102$	−2.74666	+	1.58579i	−0.271960	+	0.157016i
$103$	−6.27231	−	3.62132i	−0.618029	−	0.356819i	0.158072	−	0.987428i	$-0.449472\pi$
$103$	−6.27231	−	3.62132i	−0.618029	−	0.356819i	−0.776101	+	0.630608i	$0.782805\pi$
$104$	12.4853			1.22428
$105$		0			0
$106$	−9.65685			−0.937957
$107$	10.8996	+	6.29289i	1.05371	+	0.608357i	0.923684	−	0.383154i	$-0.125162\pi$
$107$	10.8996	+	6.29289i	1.05371	+	0.608357i	0.130021	+	0.991511i	$0.458496\pi$
$108$		0			0
$109$	1.74264	+	3.01834i	0.166915	+	0.289105i	0.937334	−	0.348433i	$-0.113286\pi$
$109$	1.74264	+	3.01834i	0.166915	+	0.289105i	−0.770419	+	0.637538i	$0.779953\pi$
$110$		0			0
$111$	8.41421			0.798642
$112$	8.36308	+	6.48528i	0.790237	+	0.612801i
$113$		−	15.6569i		−	1.47287i	−0.676507	−	0.736436i	$-0.736507\pi$
$113$		−	15.6569i		−	1.47287i	0.676507	−	0.736436i	$-0.263493\pi$
$114$	3.29289	−	5.70346i	0.308408	−	0.534178i
$115$		0			0
$116$		0			0
$117$	−3.82282	−	2.20711i	−0.353420	−	0.204047i
$118$			2.00000i			0.184115i
$119$	−2.24264	−	5.49333i	−0.205583	−	0.503572i
$120$		0			0
$121$	5.32843	−	9.22911i	0.484402	−	0.839010i
$122$	−5.49333	+	3.17157i	−0.497342	+	0.287141i
$123$	5.40629	−	3.12132i	0.487468	−	0.281440i
$124$		0			0
$125$		0			0
$126$	−1.41421	−	3.46410i	−0.125988	−	0.308607i
$127$			3.92893i			0.348636i	0.984689	+	0.174318i	$0.0557721\pi$
$127$			3.92893i			0.348636i	−0.984689	+	0.174318i	$0.944228\pi$
$128$	9.79796	+	5.65685i	0.866025	+	0.500000i
$129$	3.79289	+	6.56948i	0.333946	+	0.578411i
$130$		0			0
$131$	−3.24264	+	5.61642i	−0.283311	+	0.490709i	−0.972198	−	0.234160i	$-0.924766\pi$
$131$	−3.24264	+	5.61642i	−0.283311	+	0.490709i	0.688887	+	0.724868i	$0.258099\pi$
$132$		0			0
$133$	9.73641	+	7.55025i	0.844254	+	0.654690i
$134$	−19.4142			−1.67713
$135$		0			0
$136$	−3.17157	−	5.49333i	−0.271960	−	0.471049i
$137$	14.7840	−	8.53553i	1.26308	−	0.729240i	0.289411	−	0.957205i	$-0.406541\pi$
$137$	14.7840	−	8.53553i	1.26308	−	0.729240i	0.973669	+	0.227965i	$0.0732072\pi$
$138$	−2.74666	−	1.58579i	−0.233811	−	0.134991i
$139$	5.48528			0.465255			0.232628	−	0.972566i	$-0.425268\pi$
$139$	5.48528			0.465255			0.232628	+	0.972566i	$0.425268\pi$
$140$		0			0
$141$	13.3137			1.12122
$142$	0.717439	+	0.414214i	0.0602061	+	0.0347600i
$143$	−2.23936	+	1.29289i	−0.187264	+	0.108117i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$		0			0
$146$	17.0711			1.41281
$147$	6.77962	−	1.74264i	0.559173	−	0.143731i
$148$		0			0
$149$	3.17157	−	5.49333i	0.259825	−	0.450031i	−0.706370	−	0.707843i	$-0.749668\pi$
$149$	3.17157	−	5.49333i	0.259825	−	0.450031i	0.966195	+	0.257812i	$0.0830017\pi$
$150$		0			0
$151$	−5.24264	−	9.08052i	−0.426640	−	0.738962i	0.569932	−	0.821692i	$-0.306970\pi$
$151$	−5.24264	−	9.08052i	−0.426640	−	0.738962i	−0.996572	+	0.0827296i	$0.973636\pi$
$152$	11.4069	+	6.58579i	0.925223	+	0.534178i
$153$			2.24264i			0.181307i
$154$	−2.17157	−	0.297173i	−0.174990	−	0.0239469i
$155$		0			0
$156$		0			0
$157$	−10.5154	+	6.07107i	−0.839220	+	0.484524i	−0.856999	−	0.515318i	$-0.827674\pi$
$157$	−10.5154	+	6.07107i	−0.839220	+	0.484524i	0.0177789	+	0.999842i	$0.494340\pi$
$158$	−8.15295	+	4.70711i	−0.648614	+	0.374477i
$159$	−3.41421	+	5.91359i	−0.270765	+	0.468978i
$160$		0			0
$161$	3.63604	−	4.68885i	0.286560	−	0.369533i
$162$			1.41421i			0.111111i
$163$	−2.86976	−	1.65685i	−0.224777	−	0.129775i	0.383383	−	0.923589i	$-0.374759\pi$
$163$	−2.86976	−	1.65685i	−0.224777	−	0.129775i	−0.608160	+	0.793814i	$0.708092\pi$
$164$		0			0
$165$		0			0
$166$	1.82843	−	3.16693i	0.141913	−	0.245801i
$167$		−	20.2426i		−	1.56642i	−0.621756	−	0.783211i	$-0.713580\pi$
$167$		−	20.2426i		−	1.56642i	0.621756	−	0.783211i	$-0.286420\pi$
$168$	6.92820	−	2.82843i	0.534522	−	0.218218i
$169$	−6.48528			−0.498868
$170$		0			0
$171$	−2.32843	−	4.03295i	−0.178059	−	0.308408i
$172$		0			0
$173$	−2.44949	−	1.41421i	−0.186231	−	0.107521i	0.403986	−	0.914765i	$-0.367625\pi$
$173$	−2.44949	−	1.41421i	−0.186231	−	0.107521i	−0.590217	+	0.807245i	$0.700958\pi$
$174$	−11.6569			−0.883704
$175$		0			0
$176$	−2.34315			−0.176621
$177$	1.22474	+	0.707107i	0.0920575	+	0.0531494i
$178$	14.9941	−	8.65685i	1.12386	−	0.648859i
$179$	4.17157	+	7.22538i	0.311798	+	0.540050i	0.978752	−	0.205049i	$-0.0657354\pi$
$179$	4.17157	+	7.22538i	0.311798	+	0.540050i	−0.666954	+	0.745099i	$0.732402\pi$
$180$		0			0
$181$	−10.6569			−0.792118			−0.396059	−	0.918225i	$-0.629622\pi$
$181$	−10.6569			−0.792118			−0.396059	+	0.918225i	$0.629622\pi$
$182$	−13.0519	−	10.1213i	−0.967473	−	0.750242i
$183$			4.48528i			0.331562i
$184$	3.17157	−	5.49333i	0.233811	−	0.404973i
$185$		0			0
$186$	4.12132	+	7.13834i	0.302190	+	0.523408i
$187$	1.13770	+	0.656854i	0.0831972	+	0.0480339i
$188$		0			0
$189$	−2.62132	−	0.358719i	−0.190673	−	0.0260930i
$190$		0			0
$191$	7.48528	−	12.9649i	0.541616	−	0.938106i	−0.457196	−	0.889366i	$-0.651146\pi$
$191$	7.48528	−	12.9649i	0.541616	−	0.938106i	0.998811	−	0.0487401i	$-0.0155206\pi$
$192$	6.92820	−	4.00000i	0.500000	−	0.288675i
$193$	−13.2005	+	7.62132i	−0.950194	+	0.548595i	−0.893141	−	0.449777i	$-0.851504\pi$
$193$	−13.2005	+	7.62132i	−0.950194	+	0.548595i	−0.0570527	+	0.998371i	$0.518170\pi$
$194$	3.65685	−	6.33386i	0.262547	−	0.454744i
$195$		0			0
$196$		0			0
$197$			25.5563i			1.82081i	0.413713	+	0.910407i	$0.364232\pi$
$197$			25.5563i			1.82081i	−0.413713	+	0.910407i	$0.635768\pi$
$198$	0.717439	+	0.414214i	0.0509862	+	0.0294369i
$199$	11.2426	+	19.4728i	0.796970	+	1.38039i	0.921581	+	0.388186i	$0.126898\pi$
$199$	11.2426	+	19.4728i	0.796970	+	1.38039i	−0.124611	+	0.992206i	$0.539768\pi$
$200$		0			0
$201$	−6.86396	+	11.8887i	−0.484146	+	0.838566i
$202$			3.17157i			0.223151i
$203$	2.95680	−	21.6066i	0.207526	−	1.51649i
$204$		0			0
$205$		0			0
$206$	5.12132	+	8.87039i	0.356819	+	0.618029i
$207$	−1.94218	+	1.12132i	−0.134991	+	0.0779372i
$208$	−15.2913	−	8.82843i	−1.06026	−	0.612141i
$209$	−2.72792			−0.188694
$210$		0			0
$211$	−28.1421			−1.93738			−0.968692	−	0.248265i	$-0.920140\pi$
$211$	−28.1421			−1.93738			−0.968692	+	0.248265i	$0.920140\pi$
$212$		0			0
$213$	0.507306	−	0.292893i	0.0347600	−	0.0200687i
$214$	−8.89949	−	15.4144i	−0.608357	−	1.05371i
$215$		0			0
$216$	−2.82843			−0.192450
$217$	−14.2767	+	5.82843i	−0.969164	+	0.395659i
$218$		−	4.92893i		−	0.333829i
$219$	6.03553	−	10.4539i	0.407844	−	0.706406i
$220$		0			0
$221$	4.94975	+	8.57321i	0.332956	+	0.576697i
$222$	−10.3053	−	5.94975i	−0.691644	−	0.399321i
$223$			22.8284i			1.52870i	0.644799	+	0.764352i	$0.276941\pi$
$223$			22.8284i			1.52870i	−0.644799	+	0.764352i	$0.723059\pi$
$224$		0			0
$225$		0			0
$226$	−11.0711	+	19.1757i	−0.736436	+	1.27555i
$227$	−7.73268	+	4.46447i	−0.513236	+	0.296317i	−0.734163	−	0.678973i	$-0.762425\pi$
$227$	−7.73268	+	4.46447i	−0.513236	+	0.296317i	0.220927	+	0.975290i	$0.429092\pi$
$228$		0			0
$229$	4.15685	−	7.19988i	0.274693	−	0.475782i	−0.695365	−	0.718657i	$-0.744757\pi$
$229$	4.15685	−	7.19988i	0.274693	−	0.475782i	0.970058	+	0.242875i	$0.0780906\pi$
$230$		0			0
$231$	−0.949747	+	1.22474i	−0.0624888	+	0.0805823i
$232$		−	23.3137i		−	1.53062i
$233$	4.77589	+	2.75736i	0.312879	+	0.180641i	0.648214	−	0.761458i	$-0.275516\pi$
$233$	4.77589	+	2.75736i	0.312879	+	0.180641i	−0.335335	+	0.942099i	$0.608850\pi$
$234$	3.12132	+	5.40629i	0.204047	+	0.353420i
$235$		0			0
$236$		0			0
$237$			6.65685i			0.432409i
$238$	−1.13770	+	8.31371i	−0.0737465	+	0.538898i
$239$	5.31371			0.343715			0.171858	−	0.985122i	$-0.445023\pi$
$239$	5.31371			0.343715			0.171858	+	0.985122i	$0.445023\pi$
$240$		0			0
$241$	10.8284	+	18.7554i	0.697520	+	1.20814i	0.969324	+	0.245788i	$0.0790466\pi$
$241$	10.8284	+	18.7554i	0.697520	+	1.20814i	−0.271803	+	0.962353i	$0.587620\pi$
$242$	−13.0519	+	7.53553i	−0.839010	+	0.484402i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$	−8.82843			−0.562880
$247$	−17.8023	−	10.2782i	−1.13273	−	0.653985i
$248$	−14.2767	+	8.24264i	−0.906570	+	0.523408i
$249$	−1.29289	−	2.23936i	−0.0819338	−	0.141913i
$250$		0			0
$251$	−2.58579			−0.163213			−0.0816067	−	0.996665i	$-0.526005\pi$
$251$	−2.58579			−0.163213			−0.0816067	+	0.996665i	$0.526005\pi$
$252$		0			0
$253$			1.31371i			0.0825921i
$254$	2.77817	−	4.81194i	0.174318	−	0.301928i
$255$		0			0
$256$		0			0
$257$	−8.74729	−	5.05025i	−0.545641	−	0.315026i	0.201721	−	0.979443i	$-0.435347\pi$
$257$	−8.74729	−	5.05025i	−0.545641	−	0.315026i	−0.747362	+	0.664417i	$0.768680\pi$
$258$		−	10.7279i		−	0.667891i
$259$	13.6421	−	17.5922i	0.847681	−	1.09313i
$260$		0			0
$261$	−4.12132	+	7.13834i	−0.255103	+	0.441852i
$262$	7.94282	−	4.58579i	0.490709	−	0.283311i
$263$	5.91359	−	3.41421i	0.364648	−	0.210529i	−0.306470	−	0.951880i	$-0.599148\pi$
$263$	5.91359	−	3.41421i	0.364648	−	0.210529i	0.671118	+	0.741351i	$0.265815\pi$
$264$	−0.828427	+	1.43488i	−0.0509862	+	0.0883106i
$265$		0			0
$266$	−6.58579	−	16.1318i	−0.403800	−	0.989105i
$267$		−	12.2426i		−	0.749237i
$268$		0			0
$269$	−10.0711	−	17.4436i	−0.614044	−	1.06356i	−0.990551	−	0.137142i	$-0.956208\pi$
$269$	−10.0711	−	17.4436i	−0.614044	−	1.06356i	0.376508	−	0.926414i	$-0.377125\pi$
$270$		0			0
$271$	4.07107	−	7.05130i	0.247300	−	0.428336i	−0.715476	−	0.698637i	$-0.753790\pi$
$271$	4.07107	−	7.05130i	0.247300	−	0.428336i	0.962776	+	0.270302i	$0.0871234\pi$
$272$			8.97056i			0.543920i
$273$	−10.8126	+	4.41421i	−0.654407	+	0.267160i
$274$	−24.1421			−1.45848
$275$		0			0
$276$		0			0
$277$	−11.5916	+	6.69239i	−0.696469	+	0.402107i	−0.806031	−	0.591873i	$-0.798389\pi$
$277$	−11.5916	+	6.69239i	−0.696469	+	0.402107i	0.109562	+	0.993980i	$0.465055\pi$
$278$	−6.71807	−	3.87868i	−0.402923	−	0.232628i
$279$	5.82843			0.348939
$280$		0			0
$281$	−1.65685			−0.0988396			−0.0494198	−	0.998778i	$-0.515737\pi$
$281$	−1.65685			−0.0988396			−0.0494198	+	0.998778i	$0.515737\pi$
$282$	−16.3059	−	9.41421i	−0.971002	−	0.560608i
$283$	−4.11999	+	2.37868i	−0.244908	+	0.141398i	−0.617431	−	0.786625i	$-0.711826\pi$
$283$	−4.11999	+	2.37868i	−0.244908	+	0.141398i	0.372522	+	0.928023i	$0.378493\pi$
$284$		0			0
$285$		0			0
$286$	3.65685			0.216234
$287$	2.23936	−	16.3640i	0.132185	−	0.965934i
$288$		0			0
$289$	−5.98528	+	10.3668i	−0.352075	+	0.609812i
$290$		0			0
$291$	−2.58579	−	4.47871i	−0.151581	−	0.262547i
$292$		0			0
$293$			7.31371i			0.427271i	0.976913	+	0.213636i	$0.0685306\pi$
$293$			7.31371i			0.427271i	−0.976913	+	0.213636i	$0.931469\pi$
$294$	−9.53553	−	2.65962i	−0.556124	−	0.155112i
$295$		0			0
$296$	11.8995	−	20.6105i	0.691644	−	1.19796i
$297$	0.507306	−	0.292893i	0.0294369	−	0.0169954i
$298$	−7.76874	+	4.48528i	−0.450031	+	0.259825i
$299$	−4.94975	+	8.57321i	−0.286251	+	0.495802i
$300$		0			0
$301$	19.8848	+	2.72117i	1.14614	+	0.156846i
$302$			14.8284i			0.853280i
$303$	1.94218	+	1.12132i	0.111576	+	0.0644182i
$304$	−9.31371	−	16.1318i	−0.534178	−	0.925223i
$305$		0			0
$306$	1.58579	−	2.74666i	0.0906534	−	0.157016i
$307$		−	4.41421i		−	0.251932i	−0.992035	−	0.125966i	$-0.959797\pi$
$307$		−	4.41421i		−	0.251932i	0.992035	−	0.125966i	$-0.0402031\pi$
$308$		0			0
$309$	7.24264			0.412019
$310$		0			0
$311$	1.46447	+	2.53653i	0.0830423	+	0.143833i	0.904555	−	0.426356i	$-0.140203\pi$
$311$	1.46447	+	2.53653i	0.0830423	+	0.143833i	−0.821513	+	0.570190i	$0.806870\pi$
$312$	−10.8126	+	6.24264i	−0.612141	+	0.353420i
$313$	14.0410	+	8.10660i	0.793647	+	0.458212i	0.841245	−	0.540654i	$-0.181823\pi$
$313$	14.0410	+	8.10660i	0.793647	+	0.458212i	−0.0475980	+	0.998867i	$0.515157\pi$
$314$	17.1716			0.969048
$315$		0			0
$316$		0			0
$317$	17.2335	+	9.94975i	0.967928	+	0.558833i	0.898604	−	0.438761i	$-0.144582\pi$
$317$	17.2335	+	9.94975i	0.967928	+	0.558833i	0.0693241	+	0.997594i	$0.477916\pi$
$318$	8.36308	−	4.82843i	0.468978	−	0.270765i
$319$	2.41421	+	4.18154i	0.135170	+	0.234121i
$320$		0			0
$321$	−12.5858			−0.702470
$322$	−7.76874	+	3.17157i	−0.432935	+	0.176745i
$323$			10.4437i			0.581100i
$324$		0			0
$325$		0			0
$326$	2.34315	+	4.05845i	0.129775	+	0.224777i
$327$	−3.01834	−	1.74264i	−0.166915	−	0.0963683i
$328$		−	17.6569i		−	0.974937i
$329$	21.5858	−	27.8359i	1.19006	−	1.53464i
$330$		0			0
$331$	−8.81371	+	15.2658i	−0.484445	+	0.839084i	−0.999840	−	0.0178689i	$-0.994312\pi$
$331$	−8.81371	+	15.2658i	−0.484445	+	0.839084i	0.515395	+	0.856953i	$0.327645\pi$
$332$		0			0
$333$	−7.28692	+	4.20711i	−0.399321	+	0.230548i
$334$	−14.3137	+	24.7921i	−0.783211	+	1.35656i
$335$		0			0
$336$	−10.4853	−	1.43488i	−0.572019	−	0.0782790i
$337$		−	18.8995i		−	1.02952i	−0.857334	−	0.514761i	$-0.827881\pi$
$337$		−	18.8995i		−	1.02952i	0.857334	−	0.514761i	$-0.172119\pi$
$338$	7.94282	+	4.58579i	0.432032	+	0.249434i
$339$	7.82843	+	13.5592i	0.425182	+	0.736436i
$340$		0			0
$341$	1.70711	−	2.95680i	0.0924450	−	0.160119i
$342$			6.58579i			0.356119i
$343$	7.34847	−	17.0000i	0.396780	−	0.917914i
$344$	21.4558			1.15682
$345$		0			0
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	−7.76874	+	4.48528i	−0.417048	+	0.240783i	−0.693813	−	0.720155i	$-0.744071\pi$
$347$	−7.76874	+	4.48528i	−0.417048	+	0.240783i	0.276766	+	0.960937i	$0.410737\pi$
$348$		0			0
$349$	−28.6274			−1.53239			−0.766195	−	0.642608i	$-0.777852\pi$
$349$	−28.6274			−1.53239			−0.766195	+	0.642608i	$0.777852\pi$
$350$		0			0
$351$	4.41421			0.235613
$352$		0			0
$353$	−12.0373	+	6.94975i	−0.640682	+	0.369898i	−0.784877	−	0.619651i	$-0.787274\pi$
$353$	−12.0373	+	6.94975i	−0.640682	+	0.369898i	0.144195	+	0.989549i	$0.453941\pi$
$354$	−1.00000	−	1.73205i	−0.0531494	−	0.0920575i
$355$		0			0
$356$		0			0
$357$	4.68885	+	3.63604i	0.248160	+	0.192440i
$358$		−	11.7990i		−	0.623596i
$359$	−14.7071	+	25.4735i	−0.776211	+	1.34444i	0.157900	+	0.987455i	$0.449528\pi$
$359$	−14.7071	+	25.4735i	−0.776211	+	1.34444i	−0.934111	+	0.356982i	$0.883806\pi$
$360$		0			0
$361$	−1.34315	−	2.32640i	−0.0706919	−	0.122442i
$362$	13.0519	+	7.53553i	0.685994	+	0.396059i
$363$			10.6569i			0.559340i
$364$		0			0
$365$		0			0
$366$	3.17157	−	5.49333i	0.165781	−	0.287141i
$367$	19.4113	−	11.2071i	1.01326	−	0.585006i	0.101116	−	0.994875i	$-0.467759\pi$
$367$	19.4113	−	11.2071i	1.01326	−	0.585006i	0.912145	+	0.409868i	$0.134425\pi$
$368$	−7.76874	+	4.48528i	−0.404973	+	0.233811i
$369$	−3.12132	+	5.40629i	−0.162489	+	0.281440i
$370$		0			0
$371$	6.82843	+	16.7262i	0.354514	+	0.868379i
$372$		0			0
$373$	−9.31615	−	5.37868i	−0.482372	−	0.278497i	0.239033	−	0.971012i	$-0.423170\pi$
$373$	−9.31615	−	5.37868i	−0.482372	−	0.278497i	−0.721404	+	0.692514i	$0.756503\pi$
$374$	−0.928932	−	1.60896i	−0.0480339	−	0.0831972i
$375$		0			0
$376$	18.8284	−	32.6118i	0.971002	−	1.68182i
$377$			36.3848i			1.87391i
$378$	2.95680	+	2.29289i	0.152081	+	0.117934i
$379$	24.7990			1.27384			0.636919	−	0.770931i	$-0.280208\pi$
$379$	24.7990			1.27384			0.636919	+	0.770931i	$0.280208\pi$
$380$		0			0
$381$	−1.96447	−	3.40256i	−0.100643	−	0.174318i
$382$	−18.3351	+	10.5858i	−0.938106	+	0.541616i
$383$	3.88437	+	2.24264i	0.198482	+	0.114594i	0.595947	−	0.803024i	$-0.296777\pi$
$383$	3.88437	+	2.24264i	0.198482	+	0.114594i	−0.397465	+	0.917617i	$0.630110\pi$
$384$	−11.3137			−0.577350
$385$		0			0
$386$	21.5563			1.09719
$387$	−6.56948	−	3.79289i	−0.333946	−	0.192804i
$388$		0			0
$389$	−18.4350	−	31.9304i	−0.934693	−	1.61894i	−0.775180	−	0.631740i	$-0.782341\pi$
$389$	−18.4350	−	31.9304i	−0.934693	−	1.61894i	−0.159513	−	0.987196i	$-0.550992\pi$
$390$		0			0
$391$	5.02944			0.254350
$392$	5.31925	−	19.0711i	0.268662	−	0.963234i
$393$		−	6.48528i		−	0.327139i
$394$	18.0711	−	31.3000i	0.910407	−	1.57687i
$395$		0			0
$396$		0			0
$397$	15.7731	+	9.10660i	0.791629	+	0.457047i	0.840536	−	0.541756i	$-0.182240\pi$
$397$	15.7731	+	9.10660i	0.791629	+	0.457047i	−0.0489067	+	0.998803i	$0.515574\pi$
$398$		−	31.7990i		−	1.59394i
$399$	−12.2071	−	1.67050i	−0.611120	−	0.0836298i
$400$		0			0
$401$	8.24264	−	14.2767i	0.411618	−	0.712943i	−0.583449	−	0.812150i	$-0.698297\pi$
$401$	8.24264	−	14.2767i	0.411618	−	0.712943i	0.995067	+	0.0992068i	$0.0316305\pi$
$402$	16.8132	−	9.70711i	0.838566	−	0.484146i
$403$	22.2810	−	12.8640i	1.10990	−	0.640800i
$404$		0			0
$405$		0			0
$406$	−18.8995	+	24.3718i	−0.937966	+	1.20955i
$407$			4.92893i			0.244318i
$408$	5.49333	+	3.17157i	0.271960	+	0.157016i
$409$	−1.84315	−	3.19242i	−0.0911377	−	0.157855i	0.816852	−	0.576847i	$-0.195717\pi$
$409$	−1.84315	−	3.19242i	−0.0911377	−	0.157855i	−0.907990	+	0.418992i	$0.862384\pi$
$410$		0			0
$411$	−8.53553	+	14.7840i	−0.421027	+	0.729240i
$412$		0			0
$413$	3.46410	−	1.41421i	0.170457	−	0.0695889i
$414$	3.17157			0.155874
$415$		0			0
$416$		0			0
$417$	−4.75039	+	2.74264i	−0.232628	+	0.134308i
$418$	3.34101	+	1.92893i	0.163414	+	0.0943472i
$419$	8.82843			0.431297			0.215648	−	0.976471i	$-0.430813\pi$
$419$	8.82843			0.431297			0.215648	+	0.976471i	$0.430813\pi$
$420$		0			0
$421$	10.5147			0.512456			0.256228	−	0.966616i	$-0.417520\pi$
$421$	10.5147			0.512456			0.256228	+	0.966616i	$0.417520\pi$
$422$	34.4669	+	19.8995i	1.67782	+	0.968692i
$423$	−11.5300	+	6.65685i	−0.560608	+	0.323667i
$424$	9.65685	+	16.7262i	0.468978	+	0.812294i
$425$		0			0
$426$	−0.828427			−0.0401374
$427$	9.37769	+	7.27208i	0.453818	+	0.351921i
$428$		0			0
$429$	1.29289	−	2.23936i	0.0624215	−	0.108117i
$430$		0			0
$431$	−15.5858	−	26.9954i	−0.750741	−	1.30032i	−0.947464	−	0.319862i	$-0.896363\pi$
$431$	−15.5858	−	26.9954i	−0.750741	−	1.30032i	0.196723	−	0.980459i	$-0.436970\pi$
$432$	3.46410	+	2.00000i	0.166667	+	0.0962250i
$433$			6.55635i			0.315078i	0.987513	+	0.157539i	$0.0503560\pi$
$433$			6.55635i			0.315078i	−0.987513	+	0.157539i	$0.949644\pi$
$434$	21.6066	+	2.95680i	1.03715	+	0.141931i
$435$		0			0
$436$		0			0
$437$	−9.04447	+	5.22183i	−0.432656	+	0.249794i
$438$	−14.7840	+	8.53553i	−0.706406	+	0.407844i
$439$	5.82843	−	10.0951i	0.278176	−	0.481814i	−0.692756	−	0.721172i	$-0.743604\pi$
$439$	5.82843	−	10.0951i	0.278176	−	0.481814i	0.970931	+	0.239358i	$0.0769369\pi$
$440$		0			0
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$		−	14.0000i		−	0.665912i
$443$	14.2767	+	8.24264i	0.678305	+	0.391620i	0.799216	−	0.601044i	$-0.205248\pi$
$443$	14.2767	+	8.24264i	0.678305	+	0.391620i	−0.120911	+	0.992663i	$0.538582\pi$
$444$		0			0
$445$		0			0
$446$	16.1421	−	27.9590i	0.764352	−	1.32390i
$447$			6.34315i			0.300020i
$448$	2.86976	−	20.9706i	0.135583	−	0.990766i
$449$	−26.9706			−1.27282			−0.636410	−	0.771351i	$-0.719581\pi$
$449$	−26.9706			−1.27282			−0.636410	+	0.771351i	$0.719581\pi$
$450$		0			0
$451$	1.82843	+	3.16693i	0.0860973	+	0.149125i
$452$		0			0
$453$	9.08052	+	5.24264i	0.426640	+	0.246321i
$454$	12.6274			0.592634
$455$		0			0
$456$	−13.1716			−0.616815
$457$	−0.953065	−	0.550253i	−0.0445825	−	0.0257397i	0.477543	−	0.878608i	$-0.341527\pi$
$457$	−0.953065	−	0.550253i	−0.0445825	−	0.0257397i	−0.522126	+	0.852869i	$0.674861\pi$
$458$	−10.1822	+	5.87868i	−0.475782	+	0.274693i
$459$	−1.12132	−	1.94218i	−0.0523388	−	0.0906534i
$460$		0			0
$461$	−12.9289			−0.602160			−0.301080	−	0.953599i	$-0.597347\pi$
$461$	−12.9289			−0.602160			−0.301080	+	0.953599i	$0.597347\pi$
$462$	2.02922	−	0.828427i	0.0944080	−	0.0385419i
$463$		−	7.58579i		−	0.352541i	−0.984342	−	0.176271i	$-0.943597\pi$
$463$		−	7.58579i		−	0.352541i	0.984342	−	0.176271i	$-0.0564034\pi$
$464$	−16.4853	+	28.5533i	−0.765310	+	1.32556i
$465$		0			0
$466$	−3.89949	−	6.75412i	−0.180641	−	0.312879i
$467$	25.3864	+	14.6569i	1.17474	+	0.678238i	0.954793	−	0.297273i	$-0.0960770\pi$
$467$	25.3864	+	14.6569i	1.17474	+	0.678238i	0.219951	+	0.975511i	$0.429410\pi$
$468$		0			0
$469$	13.7279	+	33.6264i	0.633897	+	1.55272i
$470$		0			0
$471$	6.07107	−	10.5154i	0.279740	−	0.484524i
$472$	3.46410	−	2.00000i	0.159448	−	0.0920575i
$473$	−3.84831	+	2.22183i	−0.176946	+	0.102160i
$474$	4.70711	−	8.15295i	0.216205	−	0.374477i
$475$		0			0
$476$		0			0
$477$		−	6.82843i		−	0.312652i
$478$	−6.50794	−	3.75736i	−0.297666	−	0.171858i
$479$	5.31371	+	9.20361i	0.242790	+	0.420524i	0.961508	−	0.274778i	$-0.0886042\pi$
$479$	5.31371	+	9.20361i	0.242790	+	0.420524i	−0.718718	+	0.695301i	$0.755271\pi$
$480$		0			0
$481$	−18.5711	+	32.1660i	−0.846768	+	1.46664i
$482$		−	30.6274i		−	1.39504i
$483$	−0.804479	+	5.87868i	−0.0366051	+	0.267489i
$484$		0			0
$485$		0			0
$486$	−0.707107	−	1.22474i	−0.0320750	−	0.0555556i
$487$	16.3674	−	9.44975i	0.741680	−	0.428209i	−0.0810001	−	0.996714i	$-0.525811\pi$
$487$	16.3674	−	9.44975i	0.741680	−	0.428209i	0.822680	+	0.568505i	$0.192478\pi$
$488$	10.9867	+	6.34315i	0.497342	+	0.287141i
$489$	3.31371			0.149851
$490$		0			0
$491$	18.1421			0.818743			0.409372	−	0.912368i	$-0.365748\pi$
$491$	18.1421			0.818743			0.409372	+	0.912368i	$0.365748\pi$
$492$		0			0
$493$	16.0087	−	9.24264i	0.720997	−	0.416268i
$494$	14.5355	+	25.1763i	0.653985	+	1.13273i
$495$		0			0
$496$	23.3137			1.04682
$497$	0.210133	−	1.53553i	0.00942575	−	0.0688781i
$498$			3.65685i			0.163868i
$499$	−15.3995	+	26.6727i	−0.689376	+	1.19403i	0.282664	+	0.959219i	$0.408782\pi$
$499$	−15.3995	+	26.6727i	−0.689376	+	1.19403i	−0.972040	+	0.234815i	$0.924551\pi$
$500$		0			0
$501$	10.1213	+	17.5306i	0.452187	+	0.783211i
$502$	3.16693	+	1.82843i	0.141347	+	0.0816067i
$503$		−	1.51472i		−	0.0675380i	−0.999430	−	0.0337690i	$-0.989249\pi$
$503$		−	1.51472i		−	0.0675380i	0.999430	−	0.0337690i	$-0.0107510\pi$
$504$	−4.58579	+	5.91359i	−0.204267	+	0.263412i
$505$		0			0
$506$	0.928932	−	1.60896i	0.0412961	−	0.0715269i
$507$	5.61642	−	3.24264i	0.249434	−	0.144011i
$508$		0			0
$509$	−12.8995	+	22.3426i	−0.571760	+	0.990317i	0.424625	+	0.905369i	$0.360406\pi$
$509$	−12.8995	+	22.3426i	−0.571760	+	0.990317i	−0.996385	+	0.0849483i	$0.972927\pi$
$510$		0			0
$511$	−12.0711	−	29.5680i	−0.533993	−	1.30801i
$512$		−	22.6274i		−	1.00000i
$513$	4.03295	+	2.32843i	0.178059	+	0.102803i
$514$	7.14214	+	12.3705i	0.315026	+	0.545641i
$515$		0			0
$516$		0			0
$517$			7.79899i			0.342999i
$518$	−29.1477	+	11.8995i	−1.28068	+	0.522834i
$519$	2.82843			0.124154
$520$		0			0
$521$	−11.5563	−	20.0162i	−0.506293	−	0.876925i	−0.999973	−	0.00728166i	$-0.997682\pi$
$521$	−11.5563	−	20.0162i	−0.506293	−	0.876925i	0.493681	−	0.869643i	$-0.335651\pi$
$522$	10.0951	−	5.82843i	0.441852	−	0.255103i
$523$	9.01897	+	5.20711i	0.394372	+	0.227691i	0.684053	−	0.729432i	$-0.260216\pi$
$523$	9.01897	+	5.20711i	0.394372	+	0.227691i	−0.289681	+	0.957123i	$0.593549\pi$
$524$		0			0
$525$		0			0
$526$	−9.65685			−0.421059
$527$	−11.3199	−	6.53553i	−0.493102	−	0.284692i
$528$	2.02922	−	1.17157i	0.0883106	−	0.0509862i
$529$	−8.98528	−	15.5630i	−0.390664	−	0.676651i
$530$		0			0
$531$	−1.41421			−0.0613716
$532$		0			0
$533$			27.5563i			1.19360i
$534$	−8.65685	+	14.9941i	−0.374619	+	0.648859i
$535$		0			0
$536$	19.4142	+	33.6264i	0.838566	+	1.45244i
$537$	−7.22538	−	4.17157i	−0.311798	−	0.180017i
$538$			28.4853i			1.22809i
$539$	1.02082	+	3.97141i	0.0439696	+	0.171061i
$540$		0			0
$541$	−4.84315	+	8.38857i	−0.208223	+	0.360653i	−0.951155	−	0.308714i	$-0.900101\pi$
$541$	−4.84315	+	8.38857i	−0.208223	+	0.360653i	0.742932	+	0.669367i	$0.233435\pi$
$542$	−9.97204	+	5.75736i	−0.428336	+	0.247300i
$543$	9.22911	−	5.32843i	0.396059	−	0.228665i
$544$		0			0
$545$		0			0
$546$	16.3640	+	2.23936i	0.700313	+	0.0958356i
$547$		−	7.79899i		−	0.333461i	−0.986003	−	0.166730i	$-0.946679\pi$
$547$		−	7.79899i		−	0.333461i	0.986003	−	0.166730i	$-0.0533209\pi$
$548$		0			0
$549$	−2.24264	−	3.88437i	−0.0957136	−	0.165781i
$550$		0			0
$551$	−19.1924	+	33.2422i	−0.817623	+	1.41616i
$552$			6.34315i			0.269982i
$553$	13.9180	+	10.7929i	0.591852	+	0.458961i
$554$	18.9289			0.804213
$555$		0			0
$556$		0			0
$557$	17.0233	−	9.82843i	0.721302	−	0.416444i	−0.0939298	−	0.995579i	$-0.529943\pi$
$557$	17.0233	−	9.82843i	0.721302	−	0.416444i	0.815232	+	0.579135i	$0.196610\pi$
$558$	−7.13834	−	4.12132i	−0.302190	−	0.174469i
$559$	−33.4853			−1.41628
$560$		0			0
$561$	−1.31371			−0.0554648
$562$	2.02922	+	1.17157i	0.0855976	+	0.0494198i
$563$	36.6193	−	21.1421i	1.54332	−	0.891035i	0.544691	−	0.838637i	$-0.316647\pi$
$563$	36.6193	−	21.1421i	1.54332	−	0.891035i	0.998626	−	0.0523981i	$-0.0166865\pi$
$564$		0			0
$565$		0			0
$566$	6.72792			0.282796
$567$	2.44949	−	1.00000i	0.102869	−	0.0419961i
$568$		−	1.65685i		−	0.0695201i
$569$	8.43503	−	14.6099i	0.353615	−	0.612479i	−0.633265	−	0.773935i	$-0.718286\pi$
$569$	8.43503	−	14.6099i	0.353615	−	0.612479i	0.986880	+	0.161456i	$0.0516190\pi$
$570$		0			0
$571$	2.98528	+	5.17066i	0.124930	+	0.216385i	0.921706	−	0.387890i	$-0.126796\pi$
$571$	2.98528	+	5.17066i	0.124930	+	0.216385i	−0.796775	+	0.604275i	$0.793463\pi$
$572$		0			0
$573$			14.9706i			0.625404i
$574$	−14.3137	+	18.4582i	−0.597443	+	0.770431i
$575$		0			0
$576$	−4.00000	+	6.92820i	−0.166667	+	0.288675i
$577$	21.2664	−	12.2782i	0.885333	−	0.511147i	0.0129197	−	0.999917i	$-0.495887\pi$
$577$	21.2664	−	12.2782i	0.885333	−	0.511147i	0.872413	+	0.488769i	$0.162554\pi$
$578$	14.6609	−	8.46447i	0.609812	−	0.352075i
$579$	7.62132	−	13.2005i	0.316731	−	0.548595i
$580$		0			0
$581$	−6.77817	−	0.927572i	−0.281206	−	0.0384822i
$582$			7.31371i			0.303163i
$583$	−3.46410	−	2.00000i	−0.143468	−	0.0828315i
$584$	−17.0711	−	29.5680i	−0.706406	−	1.22353i
$585$		0			0
$586$	5.17157	−	8.95743i	0.213636	−	0.370028i
$587$		−	21.7574i		−	0.898022i	−0.893526	−	0.449011i	$-0.851776\pi$
$587$		−	21.7574i		−	0.898022i	0.893526	−	0.449011i	$-0.148224\pi$
$588$		0			0
$589$	27.1421			1.11837
$590$		0			0
$591$	−12.7782	−	22.1324i	−0.525624	−	0.910407i
$592$	−29.1477	+	16.8284i	−1.19796	+	0.691644i
$593$	−9.16756	−	5.29289i	−0.376467	−	0.217353i	0.299813	−	0.953998i	$-0.403076\pi$
$593$	−9.16756	−	5.29289i	−0.376467	−	0.217353i	−0.676280	+	0.736645i	$0.736409\pi$
$594$	−0.828427			−0.0339908
$595$		0			0
$596$		0			0
$597$	−19.4728	−	11.2426i	−0.796970	−	0.460131i
$598$	12.1244	−	7.00000i	0.495802	−	0.286251i
$599$	−6.92893	−	12.0013i	−0.283108	−	0.490358i	0.689040	−	0.724723i	$-0.258032\pi$
$599$	−6.92893	−	12.0013i	−0.283108	−	0.490358i	−0.972149	+	0.234365i	$0.924699\pi$
$600$		0			0
$601$	−29.8284			−1.21673			−0.608363	−	0.793659i	$-0.708174\pi$
$601$	−29.8284			−1.21673			−0.608363	+	0.793659i	$0.708174\pi$
$602$	−22.4296	−	17.3934i	−0.914163	−	0.708902i
$603$		−	13.7279i		−	0.559044i
$604$		0			0
$605$		0			0
$606$	−1.58579	−	2.74666i	−0.0644182	−	0.111576i
$607$	6.27231	+	3.62132i	0.254585	+	0.146985i	0.621862	−	0.783127i	$-0.286376\pi$
$607$	6.27231	+	3.62132i	0.254585	+	0.146985i	−0.367277	+	0.930112i	$0.619710\pi$
$608$		0			0
$609$	8.24264	+	20.1903i	0.334009	+	0.818151i
$610$		0			0
$611$	−29.3848	+	50.8959i	−1.18878	+	2.05903i
$612$		0			0
$613$	−15.7116	+	9.07107i	−0.634584	+	0.366377i	−0.782525	−	0.622619i	$-0.786069\pi$
$613$	−15.7116	+	9.07107i	−0.634584	+	0.366377i	0.147941	+	0.988996i	$0.452735\pi$
$614$	−3.12132	+	5.40629i	−0.125966	+	0.218180i
$615$		0			0
$616$	1.65685	+	4.05845i	0.0667566	+	0.163520i
$617$			3.17157i			0.127683i	0.997960	+	0.0638414i	$0.0203352\pi$
$617$			3.17157i			0.127683i	−0.997960	+	0.0638414i	$0.979665\pi$
$618$	−8.87039	−	5.12132i	−0.356819	−	0.206010i
$619$	3.01472	+	5.22165i	0.121172	+	0.209876i	0.920230	−	0.391378i	$-0.128001\pi$
$619$	3.01472	+	5.22165i	0.121172	+	0.209876i	−0.799058	+	0.601254i	$0.794668\pi$
$620$		0			0
$621$	1.12132	−	1.94218i	0.0449970	−	0.0779372i
$622$		−	4.14214i		−	0.166085i
$623$	−25.5965	−	19.8492i	−1.02550	−	0.795243i
$624$	17.6569			0.706840
$625$		0			0
$626$	−11.4645	−	19.8570i	−0.458212	−	0.793647i
$627$	2.36245	−	1.36396i	0.0943472	−	0.0544714i
$628$		0			0
$629$	18.8701			0.752398
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	16.3059	+	9.41421i	0.648614	+	0.374477i
$633$	24.3718	−	14.0711i	0.968692	−	0.559275i
$634$	−14.0711	−	24.3718i	−0.558833	−	0.967928i
$635$		0			0
$636$		0			0
$637$	−8.30153	+	29.7635i	−0.328919	+	1.17927i
$638$		−	6.82843i		−	0.270340i
$639$	−0.292893	+	0.507306i	−0.0115867	+	0.0200687i
$640$		0			0
$641$	−14.6066	−	25.2994i	−0.576926	−	0.999265i	−0.995829	−	0.0912345i	$-0.970919\pi$
$641$	−14.6066	−	25.2994i	−0.576926	−	0.999265i	0.418903	−	0.908031i	$-0.362415\pi$
$642$	15.4144	+	8.89949i	0.608357	+	0.351235i
$643$		−	6.55635i		−	0.258557i	−0.991608	−	0.129279i	$-0.958734\pi$
$643$		−	6.55635i		−	0.258557i	0.991608	−	0.129279i	$-0.0412661\pi$
$644$		0			0
$645$		0			0
$646$	7.38478	−	12.7908i	0.290550	−	0.503248i
$647$	−40.1704	+	23.1924i	−1.57926	+	0.911787i	−0.584299	+	0.811539i	$0.698630\pi$
$647$	−40.1704	+	23.1924i	−1.57926	+	0.911787i	−0.994962	+	0.100248i	$0.968036\pi$
$648$	2.44949	−	1.41421i	0.0962250	−	0.0555556i
$649$	−0.414214	+	0.717439i	−0.0162593	+	0.0281619i
$650$		0			0
$651$	9.44975	−	12.1859i	0.370365	−	0.477603i
$652$		0			0
$653$	−14.0665	−	8.12132i	−0.550466	−	0.317812i	0.198844	−	0.980031i	$-0.436281\pi$
$653$	−14.0665	−	8.12132i	−0.550466	−	0.317812i	−0.749310	+	0.662219i	$0.769615\pi$
$654$	2.46447	+	4.26858i	0.0963683	+	0.166915i
$655$		0			0
$656$	−12.4853	+	21.6251i	−0.487468	+	0.844320i
$657$			12.0711i			0.470937i
$658$	−46.1200	+	18.8284i	−1.79795	+	0.734009i
$659$	4.68629			0.182552			0.0912760	−	0.995826i	$-0.470905\pi$
$659$	4.68629			0.182552			0.0912760	+	0.995826i	$0.470905\pi$
$660$		0			0
$661$	−4.84315	−	8.38857i	−0.188377	−	0.326278i	0.756333	−	0.654187i	$-0.226989\pi$
$661$	−4.84315	−	8.38857i	−0.188377	−	0.326278i	−0.944709	+	0.327910i	$0.893656\pi$
$662$	21.5891	−	12.4645i	0.839084	−	0.484445i
$663$	−8.57321	−	4.94975i	−0.332956	−	0.192232i
$664$	−7.31371			−0.283827
$665$		0			0
$666$	11.8995			0.461096
$667$	16.0087	+	9.24264i	0.619860	+	0.357876i
$668$		0			0
$669$	−11.4142	−	19.7700i	−0.441299	−	0.764352i
$670$		0			0
$671$	−2.62742			−0.101430
$672$		0			0
$673$			27.7279i			1.06883i	0.845221	+	0.534416i	$0.179469\pi$
$673$			27.7279i			1.06883i	−0.845221	+	0.534416i	$0.820531\pi$
$674$	−13.3640	+	23.1471i	−0.514761	+	0.891591i
$675$		0			0
$676$		0			0
$677$	−13.7694	−	7.94975i	−0.529200	−	0.305534i	0.211491	−	0.977380i	$-0.432168\pi$
$677$	−13.7694	−	7.94975i	−0.529200	−	0.305534i	−0.740691	+	0.671846i	$0.765502\pi$
$678$		−	22.1421i		−	0.850364i
$679$	−13.5563	−	1.85514i	−0.520245	−	0.0711939i
$680$		0			0
$681$	4.46447	−	7.73268i	0.171079	−	0.296317i
$682$	−4.18154	+	2.41421i	−0.160119	+	0.0924450i
$683$	20.2773	−	11.7071i	0.775889	−	0.447960i	−0.0590821	−	0.998253i	$-0.518817\pi$
$683$	20.2773	−	11.7071i	0.775889	−	0.447960i	0.834972	+	0.550293i	$0.185484\pi$
$684$		0			0
$685$		0			0
$686$	−21.0208	+	15.6245i	−0.802578	+	0.596547i
$687$			8.31371i			0.317188i
$688$	−26.2779	−	15.1716i	−1.00184	−	0.578411i
$689$	−15.0711	−	26.1039i	−0.574162	−	0.994478i
$690$		0			0
$691$	−3.84315	+	6.65652i	−0.146200	+	0.253226i	−0.929820	−	0.368014i	$-0.880038\pi$
$691$	−3.84315	+	6.65652i	−0.146200	+	0.253226i	0.783620	+	0.621241i	$0.213371\pi$
$692$		0			0
$693$	0.210133	−	1.53553i	0.00798229	−	0.0583301i
$694$	12.6863			0.481565
$695$		0			0
$696$	11.6569	+	20.1903i	0.441852	+	0.765310i
$697$	12.1244	−	7.00000i	0.459243	−	0.265144i
$698$	35.0613	+	20.2426i	1.32709	+	0.766195i
$699$	−5.51472			−0.208586
$700$		0			0
$701$	−1.21320			−0.0458221			−0.0229110	−	0.999738i	$-0.507293\pi$
$701$	−1.21320			−0.0458221			−0.0229110	+	0.999738i	$0.507293\pi$
$702$	−5.40629	−	3.12132i	−0.204047	−	0.117807i
$703$	−33.9341	+	19.5919i	−1.27985	+	0.738922i
$704$	2.34315	+	4.05845i	0.0883106	+	0.152958i
$705$		0			0
$706$	19.6569			0.739795
$707$	5.49333	−	2.24264i	0.206598	−	0.0843432i
$708$		0			0
$709$	25.5563	−	44.2649i	0.959789	−	1.66240i	0.236781	−	0.971563i	$-0.423908\pi$
$709$	25.5563	−	44.2649i	0.959789	−	1.66240i	0.723008	−	0.690840i	$-0.242759\pi$
$710$		0			0
$711$	−3.32843	−	5.76500i	−0.124826	−	0.216205i
$712$	−29.9882	−	17.3137i	−1.12386	−	0.648859i
$713$		−	13.0711i		−	0.489515i
$714$	−3.17157	−	7.76874i	−0.118693	−	0.290738i
$715$		0			0
$716$		0			0
$717$	−4.60181	+	2.65685i	−0.171858	+	0.0992220i
$718$	36.0249	−	20.7990i	1.34444	−	0.776211i
$719$	17.2426	−	29.8651i	0.643042	−	1.11378i	−0.341708	−	0.939806i	$-0.611005\pi$
$719$	17.2426	−	29.8651i	0.643042	−	1.11378i	0.984750	−	0.173975i	$-0.0556613\pi$
$720$		0			0
$721$	11.7426	−	15.1427i	0.437319	−	0.563944i
$722$			3.79899i			0.141384i
$723$	−18.7554	−	10.8284i	−0.697520	−	0.402714i
$724$		0			0
$725$		0			0
$726$	7.53553	−	13.0519i	0.279670	−	0.484402i
$727$		−	13.2426i		−	0.491142i	−0.969379	−	0.245571i	$-0.921024\pi$
$727$		−	13.2426i		−	0.491142i	0.969379	−	0.245571i	$-0.0789755\pi$
$728$	−4.47871	+	32.7279i	−0.165992	+	1.21298i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.50610	+	14.7330i	0.314609	+	0.544919i
$732$		0			0
$733$	16.6646	+	9.62132i	0.615522	+	0.355372i	0.775123	−	0.631810i	$-0.217688\pi$
$733$	16.6646	+	9.62132i	0.615522	+	0.355372i	−0.159602	+	0.987181i	$0.551021\pi$
$734$	−31.6985			−1.17001
$735$		0			0
$736$		0			0
$737$	−6.96426	−	4.02082i	−0.256532	−	0.148109i
$738$	7.64564	−	4.41421i	0.281440	−	0.162489i
$739$	−3.42893	−	5.93908i	−0.126135	−	0.218473i	0.796041	−	0.605243i	$-0.206924\pi$
$739$	−3.42893	−	5.93908i	−0.126135	−	0.218473i	−0.922176	+	0.386770i	$0.873591\pi$
$740$		0			0
$741$	20.5563			0.755156
$742$	3.46410	−	25.3137i	0.127171	−	0.929295i
$743$			20.7279i			0.760434i	0.924897	+	0.380217i	$0.124151\pi$
$743$			20.7279i			0.760434i	−0.924897	+	0.380217i	$0.875849\pi$
$744$	8.24264	−	14.2767i	0.302190	−	0.523408i
$745$		0			0
$746$	7.60660	+	13.1750i	0.278497	+	0.482372i
$747$	2.23936	+	1.29289i	0.0819338	+	0.0473045i
$748$		0			0
$749$	−20.4056	+	26.3140i	−0.745604	+	0.961492i
$750$		0			0
$751$	12.8137	−	22.1940i	0.467579	−	0.809870i	−0.531735	−	0.846911i	$-0.678460\pi$
$751$	12.8137	−	22.1940i	0.467579	−	0.809870i	0.999314	+	0.0370405i	$0.0117931\pi$
$752$	−46.1200	+	26.6274i	−1.68182	+	0.971002i
$753$	2.23936	−	1.29289i	0.0816067	−	0.0471156i
$754$	25.7279	−	44.5621i	0.936956	−	1.62285i
$755$		0			0
$756$		0			0
$757$			37.5980i			1.36652i	0.730174	+	0.683261i	$0.239439\pi$
$757$			37.5980i			1.36652i	−0.730174	+	0.683261i	$0.760561\pi$
$758$	−30.3724	−	17.5355i	−1.10318	−	0.636919i
$759$	−0.656854	−	1.13770i	−0.0238423	−	0.0412961i
$760$		0			0
$761$	17.5355	−	30.3724i	0.635663	−	1.10100i	−0.350712	−	0.936483i	$-0.614060\pi$
$761$	17.5355	−	30.3724i	0.635663	−	1.10100i	0.986374	−	0.164516i	$-0.0526064\pi$
$762$			5.55635i			0.201285i
$763$	−8.53716	+	3.48528i	−0.309066	+	0.126176i
$764$		0			0
$765$		0			0
$766$	−3.17157	−	5.49333i	−0.114594	−	0.198482i
$767$	−5.40629	+	3.12132i	−0.195210	+	0.112704i
$768$		0			0
$769$	−17.9706			−0.648035			−0.324018	−	0.946051i	$-0.605034\pi$
$769$	−17.9706			−0.648035			−0.324018	+	0.946051i	$0.605034\pi$
$770$		0			0
$771$	10.1005			0.363761
$772$		0			0
$773$	33.8365	−	19.5355i	1.21702	−	0.702644i	0.252737	−	0.967535i	$-0.418669\pi$
$773$	33.8365	−	19.5355i	1.21702	−	0.702644i	0.964278	+	0.264891i	$0.0853359\pi$
$774$	5.36396	+	9.29065i	0.192804	+	0.333946i
$775$		0			0
$776$	−14.6274			−0.525094
$777$	−3.01834	+	22.0563i	−0.108282	+	0.791267i
$778$			52.1421i			1.86939i
$779$	−14.5355	+	25.1763i	−0.520790	+	0.902034i
$780$		0			0
$781$	0.171573	+	0.297173i	0.00613936	+	0.0106337i
$782$	−6.15978	−	3.55635i	−0.220273	−	0.127175i
$783$		−	8.24264i		−	0.294568i
$784$	−20.0000	+	19.5959i	−0.714286	+	0.699854i
$785$		0			0
$786$	−4.58579	+	7.94282i	−0.163570	+	0.283311i
$787$	−16.3059	+	9.41421i	−0.581242	+	0.335580i	−0.761627	−	0.648016i	$-0.775599\pi$
$787$	−16.3059	+	9.41421i	−0.581242	+	0.335580i	0.180385	+	0.983596i	$0.442266\pi$
$788$		0			0
$789$	−3.41421	+	5.91359i	−0.121549	+	0.210529i
$790$		0			0
$791$	41.0416	+	5.61642i	1.45927	+	0.199697i
$792$		−	1.65685i		−	0.0588738i
$793$	−17.1464	−	9.89949i	−0.608888	−	0.351541i
$794$	−12.8787	−	22.3065i	−0.457047	−	0.791629i
$795$		0			0
$796$		0			0
$797$		−	41.5563i		−	1.47200i	−0.676981	−	0.736001i	$-0.736712\pi$
$797$		−	41.5563i		−	1.47200i	0.676981	−	0.736001i	$-0.263288\pi$
$798$	13.7694	+	10.6777i	0.487430	+	0.377985i
$799$	29.8579			1.05630
$800$		0			0
$801$	6.12132	+	10.6024i	0.216286	+	0.374619i
$802$	−20.1903	+	11.6569i	−0.712943	+	0.411618i
$803$	6.12372	+	3.53553i	0.216102	+	0.124766i
$804$		0			0
$805$		0			0
$806$	−36.3848			−1.28160
$807$	17.4436	+	10.0711i	0.614044	+	0.354518i
$808$	5.49333	−	3.17157i	0.193255	−	0.111576i
$809$	20.3137	+	35.1844i	0.714192	+	1.23702i	0.963270	+	0.268533i	$0.0865390\pi$
$809$	20.3137	+	35.1844i	0.714192	+	1.23702i	−0.249078	+	0.968483i	$0.580128\pi$
$810$		0			0
$811$	10.9706			0.385229			0.192614	−	0.981275i	$-0.438303\pi$
$811$	10.9706			0.385229			0.192614	+	0.981275i	$0.438303\pi$
$812$		0			0
$813$			8.14214i			0.285557i
$814$	3.48528	−	6.03668i	0.122159	−	0.211586i
$815$		0			0
$816$	−4.48528	−	7.76874i	−0.157016	−	0.271960i
$817$	−30.5931	−	17.6630i	−1.07032	−	0.617948i
$818$			5.21320i			0.182275i
$819$	7.15685	−	9.22911i	0.250081	−	0.322491i
$820$		0			0
$821$	8.77817	−	15.2042i	0.306360	−	0.530632i	−0.671203	−	0.741274i	$-0.734222\pi$
$821$	8.77817	−	15.2042i	0.306360	−	0.530632i	0.977563	+	0.210642i	$0.0675554\pi$
$822$	20.9077	−	12.0711i	0.729240	−	0.421027i
$823$	−29.6910	+	17.1421i	−1.03496	+	0.597537i	−0.918403	−	0.395646i	$-0.870521\pi$
$823$	−29.6910	+	17.1421i	−1.03496	+	0.597537i	−0.116562	+	0.993183i	$0.537187\pi$
$824$	10.2426	−	17.7408i	0.356819	−	0.618029i
$825$		0			0
$826$	−5.24264	−	0.717439i	−0.182415	−	0.0249629i
$827$		−	7.17157i		−	0.249380i	−0.992196	−	0.124690i	$-0.960206\pi$
$827$		−	7.17157i		−	0.249380i	0.992196	−	0.124690i	$-0.0397936\pi$
$828$		0			0
$829$	−3.67157	−	6.35935i	−0.127519	−	0.220869i	0.795196	−	0.606353i	$-0.207368\pi$
$829$	−3.67157	−	6.35935i	−0.127519	−	0.220869i	−0.922715	+	0.385483i	$0.874035\pi$
$830$		0			0
$831$	6.69239	−	11.5916i	0.232156	−	0.402107i
$832$			35.3137i			1.22428i
$833$	15.2042	−	3.90812i	0.526796	−	0.135408i
$834$	7.75736			0.268615
$835$		0			0
$836$		0			0
$837$	−5.04757	+	2.91421i	−0.174469	+	0.100730i
$838$	−10.8126	−	6.24264i	−0.373514	−	0.215648i
$839$	32.7279			1.12989			0.564947	−	0.825127i	$-0.308897\pi$
$839$	32.7279			1.12989			0.564947	+	0.825127i	$0.308897\pi$
$840$		0			0
$841$	38.9411			1.34280
$842$	−12.8778	−	7.43503i	−0.443800	−	0.256228i
$843$	1.43488	−	0.828427i	0.0494198	−	0.0285325i
$844$		0			0
$845$		0			0
$846$	18.8284			0.647335
$847$	22.2810	+	17.2782i	0.765585	+	0.593685i
$848$		−	27.3137i		−	0.937957i
$849$	2.37868	−	4.11999i	0.0816361	−	0.141398i
$850$		0			0
$851$	9.43503	+	16.3419i	0.323429	+	0.560195i
$852$		0			0
$853$		−	44.0122i		−	1.50695i	−0.657477	−	0.753474i	$-0.728376\pi$
$853$		−	44.0122i		−	1.50695i	0.657477	−	0.753474i	$-0.271624\pi$
$854$	−6.34315	−	15.5375i	−0.217058	−	0.531681i
$855$		0			0
$856$	−17.7990	+	30.8288i	−0.608357	+	1.05371i
$857$	−1.94218	+	1.12132i	−0.0663437	+	0.0383036i	−0.532805	−	0.846238i	$-0.678862\pi$
$857$	−1.94218	+	1.12132i	−0.0663437	+	0.0383036i	0.466461	+	0.884542i	$0.345529\pi$
$858$	−3.16693	+	1.82843i	−0.108117	+	0.0624215i
$859$	2.17157	−	3.76127i	0.0740931	−	0.128333i	−0.826598	−	0.562792i	$-0.809727\pi$
$859$	2.17157	−	3.76127i	0.0740931	−	0.128333i	0.900692	+	0.434459i	$0.143060\pi$
$860$		0			0
$861$	6.24264	+	15.2913i	0.212749	+	0.521126i
$862$			44.0833i			1.50148i
$863$	−25.8067	−	14.8995i	−0.878470	−	0.507185i	−0.00831615	−	0.999965i	$-0.502647\pi$
$863$	−25.8067	−	14.8995i	−0.878470	−	0.507185i	−0.870154	+	0.492781i	$0.835980\pi$
$864$		0			0
$865$		0			0
$866$	4.63604	−	8.02986i	0.157539	−	0.272866i
$867$		−	11.9706i		−	0.406542i
$868$		0			0
$869$	−3.89949			−0.132281
$870$		0			0
$871$	−30.2990	−	52.4794i	−1.02664	−	1.77820i
$872$	−8.53716	+	4.92893i	−0.289105	+	0.166915i
$873$	4.47871	+	2.58579i	0.151581	+	0.0875156i
$874$	14.7696			0.499588
$875$		0			0
$876$		0			0
$877$	−15.5885	−	9.00000i	−0.526385	−	0.303908i	0.213158	−	0.977018i	$-0.431625\pi$
$877$	−15.5885	−	9.00000i	−0.526385	−	0.303908i	−0.739543	+	0.673109i	$0.764958\pi$
$878$	−14.2767	+	8.24264i	−0.481814	+	0.278176i
$879$	−3.65685	−	6.33386i	−0.123343	−	0.213636i
$880$		0			0
$881$	−10.3431			−0.348469			−0.174235	−	0.984704i	$-0.555745\pi$
$881$	−10.3431			−0.348469			−0.174235	+	0.984704i	$0.555745\pi$
$882$	9.58783	−	2.46447i	0.322839	−	0.0829829i
$883$		−	6.07107i		−	0.204308i	−0.994769	−	0.102154i	$-0.967427\pi$
$883$		−	6.07107i		−	0.204308i	0.994769	−	0.102154i	$-0.0325734\pi$
$884$		0			0
$885$		0			0
$886$	−11.6569	−	20.1903i	−0.391620	−	0.678305i
$887$	−32.2276	−	18.6066i	−1.08210	−	0.624749i	−0.150635	−	0.988589i	$-0.548132\pi$
$887$	−32.2276	−	18.6066i	−1.08210	−	0.624749i	−0.931461	+	0.363841i	$0.881465\pi$
$888$			23.7990i			0.798642i
$889$	−10.2990	−	1.40938i	−0.345417	−	0.0472692i
$890$		0			0
$891$	−0.292893	+	0.507306i	−0.00981229	+	0.0169954i
$892$		0			0
$893$	−53.6936	+	31.0000i	−1.79679	+	1.03738i
$894$	4.48528	−	7.76874i	0.150010	−	0.259825i
$895$		0			0
$896$	−18.3431	+	23.6544i	−0.612801	+	0.790237i
$897$		−	9.89949i		−	0.330535i
$898$	33.0321	+	19.0711i	1.10229	+	0.636410i
$899$	−24.0208	−	41.6053i	−0.801139	−	1.38761i
$900$		0			0
$901$	−7.65685	+	13.2621i	−0.255087	+	0.441823i
$902$		−	5.17157i		−	0.172195i
$903$	−18.5813	+	7.58579i	−0.618347	+	0.252439i
$904$	44.2843			1.47287
$905$		0			0
$906$	−7.41421	−	12.8418i	−0.246321	−	0.426640i
$907$	39.3044	−	22.6924i	1.30508	−	0.753488i	0.323809	−	0.946122i	$-0.395036\pi$
$907$	39.3044	−	22.6924i	1.30508	−	0.753488i	0.981271	+	0.192634i	$0.0617030\pi$
$908$		0			0
$909$	−2.24264			−0.0743837
$910$		0			0
$911$	−4.24264			−0.140565			−0.0702825	−	0.997527i	$-0.522390\pi$
$911$	−4.24264			−0.140565			−0.0702825	+	0.997527i	$0.522390\pi$
$912$	16.1318	+	9.31371i	0.534178	+	0.308408i
$913$	1.31178	−	0.757359i	0.0434137	−	0.0250649i
$914$	0.778175	+	1.34784i	0.0257397	+	0.0445825i
$915$		0			0
$916$		0			0
$917$	−13.5592	−	10.5147i	−0.447765	−	0.347227i
$918$			3.17157i			0.104678i
$919$	−17.6716	+	30.6081i	−0.582931	+	1.00967i	0.412198	+	0.911094i	$0.364761\pi$
$919$	−17.6716	+	30.6081i	−0.582931	+	1.00967i	−0.995130	+	0.0985727i	$0.968572\pi$
$920$		0			0
$921$	2.20711	+	3.82282i	0.0727266	+	0.125966i
$922$	15.8346	+	9.14214i	0.521486	+	0.301080i
$923$			2.58579i			0.0851122i
$924$		0			0
$925$		0			0
$926$	−5.36396	+	9.29065i	−0.176271	+	0.305310i
$927$	−6.27231	+	3.62132i	−0.206010	+	0.118940i
$928$		0			0
$929$	15.5061	−	26.8573i	0.508739	−	0.881161i	−0.491210	−	0.871041i	$-0.663445\pi$
$929$	15.5061	−	26.8573i	0.508739	−	0.881161i	0.999949	−	0.0101199i	$-0.00322133\pi$
$930$		0			0
$931$	−23.2843	+	22.8138i	−0.763111	+	0.747693i
$932$		0			0
$933$	−2.53653	−	1.46447i	−0.0830423	−	0.0479445i
$934$	−20.7279	−	35.9018i	−0.678238	−	1.17474i
$935$		0			0
$936$	6.24264	−	10.8126i	0.204047	−	0.353420i
$937$			22.0711i			0.721030i	0.932753	+	0.360515i	$0.117399\pi$
$937$			22.0711i			0.721030i	−0.932753	+	0.360515i	$0.882601\pi$
$938$	6.96426	−	50.8909i	0.227391	−	1.66165i
$939$	−16.2132			−0.529098
$940$		0			0
$941$	18.3640	+	31.8073i	0.598648	+	1.03689i	0.993021	+	0.117938i	$0.0376285\pi$
$941$	18.3640	+	31.8073i	0.598648	+	1.03689i	−0.394373	+	0.918950i	$0.629038\pi$
$942$	−14.8710	+	8.58579i	−0.484524	+	0.279740i
$943$	12.1244	+	7.00000i	0.394823	+	0.227951i
$944$	−5.65685			−0.184115
$945$		0			0
$946$	6.28427			0.204319
$947$	−16.5160	−	9.53553i	−0.536699	−	0.309863i	0.207041	−	0.978332i	$-0.433617\pi$
$947$	−16.5160	−	9.53553i	−0.536699	−	0.309863i	−0.743740	+	0.668469i	$0.766950\pi$
$948$		0			0
$949$	26.6421	+	46.1455i	0.864840	+	1.49795i
$950$		0			0
$951$	−19.8995			−0.645285
$952$	15.5375	−	6.34315i	0.503572	−	0.205583i
$953$			31.5147i			1.02086i	0.859919	+	0.510431i	$0.170514\pi$
$953$			31.5147i			1.02086i	−0.859919	+	0.510431i	$0.829486\pi$
$954$	−4.82843	+	8.36308i	−0.156326	+	0.270765i
$955$		0			0
$956$		0			0
$957$	−4.18154	−	2.41421i	−0.135170	−	0.0780404i
$958$		−	15.0294i		−	0.485579i
$959$	17.0711	+	41.8154i	0.551254	+	1.35029i
$960$		0			0
$961$	−1.48528	+	2.57258i	−0.0479123	+	0.0829865i
$962$	45.4896	−	26.2635i	1.46664	−	0.846768i
$963$	10.8996	−	6.29289i	0.351235	−	0.202786i
$964$		0			0
$965$		0			0
$966$	5.14214	−	6.63103i	0.165446	−	0.213350i
$967$			13.3848i			0.430425i	0.976567	+	0.215213i	$0.0690445\pi$
$967$			13.3848i			0.430425i	−0.976567	+	0.215213i	$0.930956\pi$
$968$	26.1039	+	15.0711i	0.839010	+	0.484402i
$969$	−5.22183	−	9.04447i	−0.167749	−	0.290550i
$970$		0			0
$971$	−12.8284	+	22.2195i	−0.411684	+	0.713057i	−0.995074	−	0.0991347i	$-0.968393\pi$
$971$	−12.8284	+	22.2195i	−0.411684	+	0.713057i	0.583390	+	0.812192i	$0.301726\pi$
$972$		0			0
$973$	−1.96768	+	14.3787i	−0.0630808	+	0.460959i
$974$	−26.7279			−0.856418
$975$		0			0
$976$	−8.97056	−	15.5375i	−0.287141	−	0.497342i
$977$	39.5760	−	22.8492i	1.26615	−	0.731012i	0.291893	−	0.956451i	$-0.405715\pi$
$977$	39.5760	−	22.8492i	1.26615	−	0.731012i	0.974257	+	0.225439i	$0.0723816\pi$
$978$	−4.05845	−	2.34315i	−0.129775	−	0.0749255i
$979$	7.17157			0.229204
$980$		0			0
$981$	3.48528			0.111276
$982$	−22.2195	−	12.8284i	−0.709052	−	0.409372i
$983$	−49.4971	+	28.5772i	−1.57871	+	0.911470i	−0.583673	+	0.811989i	$0.698385\pi$
$983$	−49.4971	+	28.5772i	−1.57871	+	0.911470i	−0.995039	+	0.0994811i	$0.968282\pi$
$984$	8.82843	+	15.2913i	0.281440	+	0.487468i
$985$		0			0
$986$	−26.1421			−0.832535
$987$	−4.77589	+	34.8995i	−0.152018	+	1.11086i
$988$		0			0
$989$	−8.50610	+	14.7330i	−0.270478	+	0.468482i
$990$		0			0
$991$	9.67157	+	16.7517i	0.307228	+	0.532134i	0.977755	−	0.209751i	$-0.0672654\pi$
$991$	9.67157	+	16.7517i	0.307228	+	0.532134i	−0.670527	+	0.741885i	$0.733932\pi$
$992$		0			0
$993$		−	17.6274i		−	0.559389i
$994$	−1.34315	+	1.73205i	−0.0426020	+	0.0549373i
$995$		0			0
$996$		0			0
$997$	−8.00436	+	4.62132i	−0.253501	+	0.146359i	−0.621366	−	0.783520i	$-0.713422\pi$
$997$	−8.00436	+	4.62132i	−0.253501	+	0.146359i	0.367865	+	0.929879i	$0.380089\pi$
$998$	37.7209	−	21.7782i	1.19403	−	0.689376i
$999$	4.20711	−	7.28692i	0.133107	−	0.230548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.g.499.1		8
5.2	odd	4		105.2.i.c.16.2	✓	4
5.3	odd	4		525.2.i.g.226.1		4
5.4	even	2	inner	525.2.r.g.499.4		8
7.4	even	3	inner	525.2.r.g.424.4		8
15.2	even	4		315.2.j.d.226.1		4
20.7	even	4		1680.2.bg.p.961.2		4
35.2	odd	12		735.2.a.i.1.1		2
35.4	even	6	inner	525.2.r.g.424.1		8
35.12	even	12		735.2.a.j.1.1		2
35.17	even	12		735.2.i.j.361.2		4
35.18	odd	12		525.2.i.g.151.1		4
35.23	odd	12		3675.2.a.z.1.2		2
35.27	even	4		735.2.i.j.226.2		4
35.32	odd	12		105.2.i.c.46.2	yes	4
35.33	even	12		3675.2.a.x.1.2		2
105.2	even	12		2205.2.a.u.1.2		2
105.32	even	12		315.2.j.d.46.1		4
105.47	odd	12		2205.2.a.s.1.2		2
140.67	even	12		1680.2.bg.p.1201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.c.16.2	✓	4	5.2	odd	4
105.2.i.c.46.2	yes	4	35.32	odd	12
315.2.j.d.46.1		4	105.32	even	12
315.2.j.d.226.1		4	15.2	even	4
525.2.i.g.151.1		4	35.18	odd	12
525.2.i.g.226.1		4	5.3	odd	4
525.2.r.g.424.1		8	35.4	even	6	inner
525.2.r.g.424.4		8	7.4	even	3	inner
525.2.r.g.499.1		8	1.1	even	1	trivial
525.2.r.g.499.4		8	5.4	even	2	inner
735.2.a.i.1.1		2	35.2	odd	12
735.2.a.j.1.1		2	35.12	even	12
735.2.i.j.226.2		4	35.27	even	4
735.2.i.j.361.2		4	35.17	even	12
1680.2.bg.p.961.2		4	20.7	even	4
1680.2.bg.p.1201.2		4	140.67	even	12
2205.2.a.s.1.2		2	105.47	odd	12
2205.2.a.u.1.2		2	105.2	even	12
3675.2.a.x.1.2		2	35.33	even	12
3675.2.a.z.1.2		2	35.23	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.41421 q^{6} +(-0.358719 + 2.62132i) q^{7} +2.82843i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.292893 - 0.507306i) q^{11} -4.41421i q^{13} +(2.29289 - 2.95680i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-1.94218 + 1.12132i) q^{17} +(-1.22474 + 0.707107i) q^{18} +(2.32843 - 4.03295i) q^{19} +(-1.00000 - 2.44949i) q^{21} +0.828427i q^{22} +(-1.94218 - 1.12132i) q^{23} +(-1.41421 - 2.44949i) q^{24} +(-3.12132 + 5.40629i) q^{26} +1.00000i q^{27} -8.24264 q^{29} +(2.91421 + 5.04757i) q^{31} +(0.507306 + 0.292893i) q^{33} +3.17157 q^{34} +(-7.28692 - 4.20711i) q^{37} +(-5.70346 + 3.29289i) q^{38} +(2.20711 + 3.82282i) q^{39} -6.24264 q^{41} +(-0.507306 + 3.70711i) q^{42} -7.58579i q^{43} +(1.58579 + 2.74666i) q^{46} +(-11.5300 - 6.65685i) q^{47} +4.00000i q^{48} +(-6.74264 - 1.88064i) q^{49} +(1.12132 - 1.94218i) q^{51} +(5.91359 - 3.41421i) q^{53} +(0.707107 - 1.22474i) q^{54} +(-7.41421 - 1.01461i) q^{56} +4.65685i q^{57} +(10.0951 + 5.82843i) q^{58} +(-0.707107 - 1.22474i) q^{59} +(2.24264 - 3.88437i) q^{61} -8.24264i q^{62} +(2.09077 + 1.62132i) q^{63} -8.00000 q^{64} +(-0.414214 - 0.717439i) q^{66} +(11.8887 - 6.86396i) q^{67} +2.24264 q^{69} -0.585786 q^{71} +(2.44949 + 1.41421i) q^{72} +(-10.4539 + 6.03553i) q^{73} +(5.94975 + 10.3053i) q^{74} +(1.43488 - 0.585786i) q^{77} -6.24264i q^{78} +(3.32843 - 5.76500i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.64564 + 4.41421i) q^{82} +2.58579i q^{83} +(-5.36396 + 9.29065i) q^{86} +(7.13834 - 4.12132i) q^{87} +(1.43488 - 0.828427i) q^{88} +(-6.12132 + 10.6024i) q^{89} +(11.5711 + 1.58346i) q^{91} +(-5.04757 - 2.91421i) q^{93} +(9.41421 + 16.3059i) q^{94} +5.17157i q^{97} +(6.92820 + 7.07107i) q^{98} -0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9} - 8 q^{11} + 24 q^{14} + 16 q^{16} - 4 q^{19} - 8 q^{21} - 8 q^{26} - 32 q^{29} + 12 q^{31} + 48 q^{34} + 12 q^{39} - 16 q^{41} + 24 q^{46} - 20 q^{49} - 8 q^{51} - 48 q^{56} - 16 q^{61} - 64 q^{64}+ \cdots - 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 - 8 * q^11 + 24 * q^14 + 16 * q^16 - 4 * q^19 - 8 * q^21 - 8 * q^26 - 32 * q^29 + 12 * q^31 + 48 * q^34 + 12 * q^39 - 16 * q^41 + 24 * q^46 - 20 * q^49 - 8 * q^51 - 48 * q^56 - 16 * q^61 - 64 * q^64 + 8 * q^66 - 16 * q^69 - 16 * q^71 + 8 * q^74 + 4 * q^79 - 4 * q^81 + 8 * q^86 - 32 * q^89 + 36 * q^91 + 64 * q^94 - 16 * q^99

Introduction

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