LMFDB - Embedded newform 850.2.h.g.251.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [850,2,Mod(251,850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(850, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("850.251"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.h (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,-4,0,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.g.701.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-1.70711 - 1.70711i) q^{3} -1.00000 q^{4} +(1.70711 - 1.70711i) q^{6} +(0.414214 - 0.414214i) q^{7} -1.00000i q^{8} +2.82843i q^{9} +(1.00000 - 1.00000i) q^{11} +(1.70711 + 1.70711i) q^{12} -1.00000 q^{13} +(0.414214 + 0.414214i) q^{14} +1.00000 q^{16} +(4.12132 + 0.121320i) q^{17} -2.82843 q^{18} -2.41421i q^{19} -1.41421 q^{21} +(1.00000 + 1.00000i) q^{22} +(-2.24264 + 2.24264i) q^{23} +(-1.70711 + 1.70711i) q^{24} -1.00000i q^{26} +(-0.292893 + 0.292893i) q^{27} +(-0.414214 + 0.414214i) q^{28} +(-6.94975 - 6.94975i) q^{29} +(-3.70711 - 3.70711i) q^{31} +1.00000i q^{32} -3.41421 q^{33} +(-0.121320 + 4.12132i) q^{34} -2.82843i q^{36} +(-1.58579 - 1.58579i) q^{37} +2.41421 q^{38} +(1.70711 + 1.70711i) q^{39} +(-6.65685 + 6.65685i) q^{41} -1.41421i q^{42} -10.2426i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-2.24264 - 2.24264i) q^{46} -3.24264 q^{47} +(-1.70711 - 1.70711i) q^{48} +6.65685i q^{49} +(-6.82843 - 7.24264i) q^{51} +1.00000 q^{52} +3.48528i q^{53} +(-0.292893 - 0.292893i) q^{54} +(-0.414214 - 0.414214i) q^{56} +(-4.12132 + 4.12132i) q^{57} +(6.94975 - 6.94975i) q^{58} -10.8995i q^{59} +(-5.77817 + 5.77817i) q^{61} +(3.70711 - 3.70711i) q^{62} +(1.17157 + 1.17157i) q^{63} -1.00000 q^{64} -3.41421i q^{66} -8.82843 q^{67} +(-4.12132 - 0.121320i) q^{68} +7.65685 q^{69} +(-8.29289 - 8.29289i) q^{71} +2.82843 q^{72} +(-5.53553 - 5.53553i) q^{73} +(1.58579 - 1.58579i) q^{74} +2.41421i q^{76} -0.828427i q^{77} +(-1.70711 + 1.70711i) q^{78} +(8.24264 - 8.24264i) q^{79} +9.48528 q^{81} +(-6.65685 - 6.65685i) q^{82} -9.89949i q^{83} +1.41421 q^{84} +10.2426 q^{86} +23.7279i q^{87} +(-1.00000 - 1.00000i) q^{88} +14.6569 q^{89} +(-0.414214 + 0.414214i) q^{91} +(2.24264 - 2.24264i) q^{92} +12.6569i q^{93} -3.24264i q^{94} +(1.70711 - 1.70711i) q^{96} +(-10.1213 - 10.1213i) q^{97} -6.65685 q^{98} +(2.82843 + 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{4} + 4 q^{6} - 4 q^{7} + 4 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{14} + 4 q^{16} + 8 q^{17} + 4 q^{22} + 8 q^{23} - 4 q^{24} - 4 q^{27} + 4 q^{28} - 8 q^{29} - 12 q^{31} - 8 q^{33} + 8 q^{34}+ \cdots - 4 q^{98}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^6 - 4 * q^7 + 4 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^14 + 4 * q^16 + 8 * q^17 + 4 * q^22 + 8 * q^23 - 4 * q^24 - 4 * q^27 + 4 * q^28 - 8 * q^29 - 12 * q^31 - 8 * q^33 + 8 * q^34 - 12 * q^37 + 4 * q^38 + 4 * q^39 - 4 * q^41 - 4 * q^44 + 8 * q^46 + 4 * q^47 - 4 * q^48 - 16 * q^51 + 4 * q^52 - 4 * q^54 + 4 * q^56 - 8 * q^57 + 8 * q^58 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 4 * q^64 - 24 * q^67 - 8 * q^68 + 8 * q^69 - 36 * q^71 - 8 * q^73 + 12 * q^74 - 4 * q^78 + 16 * q^79 + 4 * q^81 - 4 * q^82 + 24 * q^86 - 4 * q^88 + 36 * q^89 + 4 * q^91 - 8 * q^92 + 4 * q^96 - 32 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.70711	−	1.70711i	−0.985599	−	0.985599i	0.0142992	−	0.999898i	$-0.495448\pi$
$3$	−1.70711	−	1.70711i	−0.985599	−	0.985599i	−0.999898	+	0.0142992i	$0.995448\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	1.70711	−	1.70711i	0.696923	−	0.696923i
$7$	0.414214	−	0.414214i	0.156558	−	0.156558i	−0.624482	−	0.781040i	$-0.714690\pi$
$7$	0.414214	−	0.414214i	0.156558	−	0.156558i	0.781040	+	0.624482i	$0.214690\pi$
$8$		−	1.00000i		−	0.353553i
$9$			2.82843i			0.942809i
$10$		0			0
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$	1.70711	+	1.70711i	0.492799	+	0.492799i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	0.414214	+	0.414214i	0.110703	+	0.110703i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.12132	+	0.121320i	0.999567	+	0.0294245i
$17$	4.12132	+	0.121320i	0.999567	+	0.0294245i
$18$	−2.82843			−0.666667
$19$		−	2.41421i		−	0.553859i	−0.960890	−	0.276929i	$-0.910683\pi$
$19$		−	2.41421i		−	0.553859i	0.960890	−	0.276929i	$-0.0893168\pi$
$20$		0			0
$21$	−1.41421			−0.308607
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−2.24264	+	2.24264i	−0.467623	+	0.467623i	−0.901144	−	0.433521i	$-0.857271\pi$
$23$	−2.24264	+	2.24264i	−0.467623	+	0.467623i	0.433521	+	0.901144i	$0.357271\pi$
$24$	−1.70711	+	1.70711i	−0.348462	+	0.348462i
$25$		0			0
$26$		−	1.00000i		−	0.196116i
$27$	−0.292893	+	0.292893i	−0.0563673	+	0.0563673i
$28$	−0.414214	+	0.414214i	−0.0782790	+	0.0782790i
$29$	−6.94975	−	6.94975i	−1.29054	−	1.29054i	−0.934455	−	0.356080i	$-0.884113\pi$
$29$	−6.94975	−	6.94975i	−1.29054	−	1.29054i	−0.356080	−	0.934455i	$-0.615887\pi$
$30$		0			0
$31$	−3.70711	−	3.70711i	−0.665816	−	0.665816i	0.290929	−	0.956745i	$-0.406036\pi$
$31$	−3.70711	−	3.70711i	−0.665816	−	0.665816i	−0.956745	+	0.290929i	$0.906036\pi$
$32$			1.00000i			0.176777i
$33$	−3.41421			−0.594338
$34$	−0.121320	+	4.12132i	−0.0208063	+	0.706801i
$35$		0			0
$36$		−	2.82843i		−	0.471405i
$37$	−1.58579	−	1.58579i	−0.260702	−	0.260702i	0.564637	−	0.825339i	$-0.309016\pi$
$37$	−1.58579	−	1.58579i	−0.260702	−	0.260702i	−0.825339	+	0.564637i	$0.809016\pi$
$38$	2.41421			0.391637
$39$	1.70711	+	1.70711i	0.273356	+	0.273356i
$40$		0			0
$41$	−6.65685	+	6.65685i	−1.03963	+	1.03963i	−0.0404442	+	0.999182i	$0.512877\pi$
$41$	−6.65685	+	6.65685i	−1.03963	+	1.03963i	−0.999182	+	0.0404442i	$0.987123\pi$
$42$		−	1.41421i		−	0.218218i
$43$		−	10.2426i		−	1.56199i	−0.624538	−	0.780994i	$-0.714713\pi$
$43$		−	10.2426i		−	1.56199i	0.624538	−	0.780994i	$-0.285287\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$		0			0
$46$	−2.24264	−	2.24264i	−0.330659	−	0.330659i
$47$	−3.24264			−0.472988			−0.236494	−	0.971633i	$-0.575998\pi$
$47$	−3.24264			−0.472988			−0.236494	+	0.971633i	$0.575998\pi$
$48$	−1.70711	−	1.70711i	−0.246400	−	0.246400i
$49$			6.65685i			0.950979i
$50$		0			0
$51$	−6.82843	−	7.24264i	−0.956171	−	1.01417i
$52$	1.00000			0.138675
$53$			3.48528i			0.478740i	0.970928	+	0.239370i	$0.0769409\pi$
$53$			3.48528i			0.478740i	−0.970928	+	0.239370i	$0.923059\pi$
$54$	−0.292893	−	0.292893i	−0.0398577	−	0.0398577i
$55$		0			0
$56$	−0.414214	−	0.414214i	−0.0553516	−	0.0553516i
$57$	−4.12132	+	4.12132i	−0.545882	+	0.545882i
$58$	6.94975	−	6.94975i	0.912547	−	0.912547i
$59$		−	10.8995i		−	1.41899i	−0.704709	−	0.709497i	$-0.748922\pi$
$59$		−	10.8995i		−	1.41899i	0.704709	−	0.709497i	$-0.251078\pi$
$60$		0			0
$61$	−5.77817	+	5.77817i	−0.739819	+	0.739819i	−0.972543	−	0.232723i	$-0.925236\pi$
$61$	−5.77817	+	5.77817i	−0.739819	+	0.739819i	0.232723	+	0.972543i	$0.425236\pi$
$62$	3.70711	−	3.70711i	0.470803	−	0.470803i
$63$	1.17157	+	1.17157i	0.147604	+	0.147604i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	3.41421i		−	0.420261i
$67$	−8.82843			−1.07856			−0.539282	−	0.842125i	$-0.681304\pi$
$67$	−8.82843			−1.07856			−0.539282	+	0.842125i	$0.681304\pi$
$68$	−4.12132	−	0.121320i	−0.499784	−	0.0147123i
$69$	7.65685			0.921777
$70$		0			0
$71$	−8.29289	−	8.29289i	−0.984185	−	0.984185i	0.0156915	−	0.999877i	$-0.495005\pi$
$71$	−8.29289	−	8.29289i	−0.984185	−	0.984185i	−0.999877	+	0.0156915i	$0.995005\pi$
$72$	2.82843			0.333333
$73$	−5.53553	−	5.53553i	−0.647885	−	0.647885i	0.304596	−	0.952482i	$-0.401478\pi$
$73$	−5.53553	−	5.53553i	−0.647885	−	0.647885i	−0.952482	+	0.304596i	$0.901478\pi$
$74$	1.58579	−	1.58579i	0.184344	−	0.184344i
$75$		0			0
$76$			2.41421i			0.276929i
$77$		−	0.828427i		−	0.0944080i
$78$	−1.70711	+	1.70711i	−0.193292	+	0.193292i
$79$	8.24264	−	8.24264i	0.927370	−	0.927370i	−0.0701658	−	0.997535i	$-0.522353\pi$
$79$	8.24264	−	8.24264i	0.927370	−	0.927370i	0.997535	+	0.0701658i	$0.0223528\pi$
$80$		0			0
$81$	9.48528			1.05392
$82$	−6.65685	−	6.65685i	−0.735127	−	0.735127i
$83$		−	9.89949i		−	1.08661i	−0.839535	−	0.543305i	$-0.817173\pi$
$83$		−	9.89949i		−	1.08661i	0.839535	−	0.543305i	$-0.182827\pi$
$84$	1.41421			0.154303
$85$		0			0
$86$	10.2426			1.10449
$87$			23.7279i			2.54390i
$88$	−1.00000	−	1.00000i	−0.106600	−	0.106600i
$89$	14.6569			1.55362			0.776812	−	0.629733i	$-0.216836\pi$
$89$	14.6569			1.55362			0.776812	+	0.629733i	$0.216836\pi$
$90$		0			0
$91$	−0.414214	+	0.414214i	−0.0434214	+	0.0434214i
$92$	2.24264	−	2.24264i	0.233811	−	0.233811i
$93$			12.6569i			1.31245i
$94$		−	3.24264i		−	0.334453i
$95$		0			0
$96$	1.70711	−	1.70711i	0.174231	−	0.174231i
$97$	−10.1213	−	10.1213i	−1.02766	−	1.02766i	−0.999606	−	0.0280581i	$-0.991068\pi$
$97$	−10.1213	−	10.1213i	−1.02766	−	1.02766i	−0.0280581	−	0.999606i	$-0.508932\pi$
$98$	−6.65685			−0.672444
$99$	2.82843	+	2.82843i	0.284268	+	0.284268i
$100$		0			0
$101$	−4.34315			−0.432159			−0.216080	−	0.976376i	$-0.569327\pi$
$101$	−4.34315			−0.432159			−0.216080	+	0.976376i	$0.569327\pi$
$102$	7.24264	−	6.82843i	0.717128	−	0.676115i
$103$	2.34315			0.230877			0.115439	−	0.993315i	$-0.463173\pi$
$103$	2.34315			0.230877			0.115439	+	0.993315i	$0.463173\pi$
$104$			1.00000i			0.0980581i
$105$		0			0
$106$	−3.48528			−0.338520
$107$	8.82843	+	8.82843i	0.853476	+	0.853476i	0.990560	−	0.137083i	$-0.0437728\pi$
$107$	8.82843	+	8.82843i	0.853476	+	0.853476i	−0.137083	+	0.990560i	$0.543773\pi$
$108$	0.292893	−	0.292893i	0.0281837	−	0.0281837i
$109$	−8.36396	+	8.36396i	−0.801122	+	0.801122i	−0.983271	−	0.182149i	$-0.941695\pi$
$109$	−8.36396	+	8.36396i	−0.801122	+	0.801122i	0.182149	+	0.983271i	$0.441695\pi$
$110$		0			0
$111$			5.41421i			0.513894i
$112$	0.414214	−	0.414214i	0.0391395	−	0.0391395i
$113$	−2.46447	+	2.46447i	−0.231837	+	0.231837i	−0.813459	−	0.581622i	$-0.802418\pi$
$113$	−2.46447	+	2.46447i	−0.231837	+	0.231837i	0.581622	+	0.813459i	$0.302418\pi$
$114$	−4.12132	−	4.12132i	−0.385997	−	0.385997i
$115$		0			0
$116$	6.94975	+	6.94975i	0.645268	+	0.645268i
$117$		−	2.82843i		−	0.261488i
$118$	10.8995			1.00338
$119$	1.75736	−	1.65685i	0.161097	−	0.151884i
$120$		0			0
$121$			9.00000i			0.818182i
$122$	−5.77817	−	5.77817i	−0.523131	−	0.523131i
$123$	22.7279			2.04931
$124$	3.70711	+	3.70711i	0.332908	+	0.332908i
$125$		0			0
$126$	−1.17157	+	1.17157i	−0.104372	+	0.104372i
$127$			7.72792i			0.685742i	0.939382	+	0.342871i	$0.111399\pi$
$127$			7.72792i			0.685742i	−0.939382	+	0.342871i	$0.888601\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−17.4853	+	17.4853i	−1.53949	+	1.53949i
$130$		0			0
$131$	14.0711	+	14.0711i	1.22939	+	1.22939i	0.964193	+	0.265202i	$0.0854387\pi$
$131$	14.0711	+	14.0711i	1.22939	+	1.22939i	0.265202	+	0.964193i	$0.414561\pi$
$132$	3.41421			0.297169
$133$	−1.00000	−	1.00000i	−0.0867110	−	0.0867110i
$134$		−	8.82843i		−	0.762660i
$135$		0			0
$136$	0.121320	−	4.12132i	0.0104031	−	0.353400i
$137$	16.7279			1.42916			0.714581	−	0.699552i	$-0.246617\pi$
$137$	16.7279			1.42916			0.714581	+	0.699552i	$0.246617\pi$
$138$			7.65685i			0.651795i
$139$	−0.656854	−	0.656854i	−0.0557137	−	0.0557137i	0.678701	−	0.734415i	$-0.262543\pi$
$139$	−0.656854	−	0.656854i	−0.0557137	−	0.0557137i	−0.734415	+	0.678701i	$0.762543\pi$
$140$		0			0
$141$	5.53553	+	5.53553i	0.466176	+	0.466176i
$142$	8.29289	−	8.29289i	0.695924	−	0.695924i
$143$	−1.00000	+	1.00000i	−0.0836242	+	0.0836242i
$144$			2.82843i			0.235702i
$145$		0			0
$146$	5.53553	−	5.53553i	0.458124	−	0.458124i
$147$	11.3640	−	11.3640i	0.937284	−	0.937284i
$148$	1.58579	+	1.58579i	0.130351	+	0.130351i
$149$	−1.75736			−0.143968			−0.0719842	−	0.997406i	$-0.522933\pi$
$149$	−1.75736			−0.143968			−0.0719842	+	0.997406i	$0.522933\pi$
$150$		0			0
$151$			4.82843i			0.392932i	0.980511	+	0.196466i	$0.0629465\pi$
$151$			4.82843i			0.392932i	−0.980511	+	0.196466i	$0.937053\pi$
$152$	−2.41421			−0.195819
$153$	−0.343146	+	11.6569i	−0.0277417	+	0.942401i
$154$	0.828427			0.0667566
$155$		0			0
$156$	−1.70711	−	1.70711i	−0.136678	−	0.136678i
$157$	−2.82843			−0.225733			−0.112867	−	0.993610i	$-0.536003\pi$
$157$	−2.82843			−0.225733			−0.112867	+	0.993610i	$0.536003\pi$
$158$	8.24264	+	8.24264i	0.655749	+	0.655749i
$159$	5.94975	−	5.94975i	0.471846	−	0.471846i
$160$		0			0
$161$			1.85786i			0.146420i
$162$			9.48528i			0.745234i
$163$	−0.343146	+	0.343146i	−0.0268772	+	0.0268772i	−0.720418	−	0.693540i	$-0.756050\pi$
$163$	−0.343146	+	0.343146i	−0.0268772	+	0.0268772i	0.693540	+	0.720418i	$0.256050\pi$
$164$	6.65685	−	6.65685i	0.519813	−	0.519813i
$165$		0			0
$166$	9.89949			0.768350
$167$	−10.7279	−	10.7279i	−0.830152	−	0.830152i	0.157386	−	0.987537i	$-0.449693\pi$
$167$	−10.7279	−	10.7279i	−0.830152	−	0.830152i	−0.987537	+	0.157386i	$0.949693\pi$
$168$			1.41421i			0.109109i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	6.82843			0.522183
$172$			10.2426i			0.780994i
$173$	−0.928932	−	0.928932i	−0.0706254	−	0.0706254i	0.670912	−	0.741537i	$-0.265903\pi$
$173$	−0.928932	−	0.928932i	−0.0706254	−	0.0706254i	−0.741537	+	0.670912i	$0.765903\pi$
$174$	−23.7279			−1.79881
$175$		0			0
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	−18.6066	+	18.6066i	−1.39856	+	1.39856i
$178$			14.6569i			1.09858i
$179$			6.82843i			0.510381i	0.966891	+	0.255190i	$0.0821381\pi$
$179$			6.82843i			0.510381i	−0.966891	+	0.255190i	$0.917862\pi$
$180$		0			0
$181$	6.82843	−	6.82843i	0.507553	−	0.507553i	−0.406222	−	0.913775i	$-0.633154\pi$
$181$	6.82843	−	6.82843i	0.507553	−	0.507553i	0.913775	+	0.406222i	$0.133154\pi$
$182$	−0.414214	−	0.414214i	−0.0307036	−	0.0307036i
$183$	19.7279			1.45833
$184$	2.24264	+	2.24264i	0.165330	+	0.165330i
$185$		0			0
$186$	−12.6569			−0.928046
$187$	4.24264	−	4.00000i	0.310253	−	0.292509i
$188$	3.24264			0.236494
$189$			0.242641i			0.0176495i
$190$		0			0
$191$	0.242641			0.0175569			0.00877843	−	0.999961i	$-0.497206\pi$
$191$	0.242641			0.0175569			0.00877843	+	0.999961i	$0.497206\pi$
$192$	1.70711	+	1.70711i	0.123200	+	0.123200i
$193$	−2.82843	+	2.82843i	−0.203595	+	0.203595i	−0.801538	−	0.597944i	$-0.795985\pi$
$193$	−2.82843	+	2.82843i	−0.203595	+	0.203595i	0.597944	+	0.801538i	$0.295985\pi$
$194$	10.1213	−	10.1213i	0.726668	−	0.726668i
$195$		0			0
$196$		−	6.65685i		−	0.475490i
$197$	18.0711	−	18.0711i	1.28751	−	1.28751i	0.351216	−	0.936295i	$-0.385768\pi$
$197$	18.0711	−	18.0711i	1.28751	−	1.28751i	0.936295	−	0.351216i	$-0.114232\pi$
$198$	−2.82843	+	2.82843i	−0.201008	+	0.201008i
$199$	−8.05025	−	8.05025i	−0.570667	−	0.570667i	0.361648	−	0.932315i	$-0.382214\pi$
$199$	−8.05025	−	8.05025i	−0.570667	−	0.570667i	−0.932315	+	0.361648i	$0.882214\pi$
$200$		0			0
$201$	15.0711	+	15.0711i	1.06303	+	1.06303i
$202$		−	4.34315i		−	0.305583i
$203$	−5.75736			−0.404087
$204$	6.82843	+	7.24264i	0.478086	+	0.507086i
$205$		0			0
$206$			2.34315i			0.163255i
$207$	−6.34315	−	6.34315i	−0.440879	−	0.440879i
$208$	−1.00000			−0.0693375
$209$	−2.41421	−	2.41421i	−0.166995	−	0.166995i
$210$		0			0
$211$	3.41421	−	3.41421i	0.235044	−	0.235044i	−0.579750	−	0.814794i	$-0.696850\pi$
$211$	3.41421	−	3.41421i	0.235044	−	0.235044i	0.814794	+	0.579750i	$0.196850\pi$
$212$		−	3.48528i		−	0.239370i
$213$			28.3137i			1.94002i
$214$	−8.82843	+	8.82843i	−0.603499	+	0.603499i
$215$		0			0
$216$	0.292893	+	0.292893i	0.0199289	+	0.0199289i
$217$	−3.07107			−0.208478
$218$	−8.36396	−	8.36396i	−0.566479	−	0.566479i
$219$			18.8995i			1.27711i
$220$		0			0
$221$	−4.12132	−	0.121320i	−0.277230	−	0.00816089i
$222$	−5.41421			−0.363378
$223$		−	25.3848i		−	1.69989i	−0.526871	−	0.849945i	$-0.676635\pi$
$223$		−	25.3848i		−	1.69989i	0.526871	−	0.849945i	$-0.323365\pi$
$224$	0.414214	+	0.414214i	0.0276758	+	0.0276758i
$225$		0			0
$226$	−2.46447	−	2.46447i	−0.163934	−	0.163934i
$227$	14.5355	−	14.5355i	0.964757	−	0.964757i	−0.0346425	−	0.999400i	$-0.511029\pi$
$227$	14.5355	−	14.5355i	0.964757	−	0.964757i	0.999400	+	0.0346425i	$0.0110293\pi$
$228$	4.12132	−	4.12132i	0.272941	−	0.272941i
$229$		−	16.2426i		−	1.07334i	−0.843791	−	0.536672i	$-0.819681\pi$
$229$		−	16.2426i		−	1.07334i	0.843791	−	0.536672i	$-0.180319\pi$
$230$		0			0
$231$	−1.41421	+	1.41421i	−0.0930484	+	0.0930484i
$232$	−6.94975	+	6.94975i	−0.456273	+	0.456273i
$233$	8.36396	+	8.36396i	0.547941	+	0.547941i	0.925845	−	0.377904i	$-0.123355\pi$
$233$	8.36396	+	8.36396i	0.547941	+	0.547941i	−0.377904	+	0.925845i	$0.623355\pi$
$234$	2.82843			0.184900
$235$		0			0
$236$			10.8995i			0.709497i
$237$	−28.1421			−1.82803
$238$	1.65685	+	1.75736i	0.107398	+	0.113913i
$239$	27.4142			1.77328			0.886639	−	0.462462i	$-0.153034\pi$
$239$	27.4142			1.77328			0.886639	+	0.462462i	$0.153034\pi$
$240$		0			0
$241$	−19.8284	−	19.8284i	−1.27726	−	1.27726i	−0.942194	−	0.335067i	$-0.891241\pi$
$241$	−19.8284	−	19.8284i	−1.27726	−	1.27726i	−0.335067	−	0.942194i	$-0.608759\pi$
$242$	−9.00000			−0.578542
$243$	−15.3137	−	15.3137i	−0.982375	−	0.982375i
$244$	5.77817	−	5.77817i	0.369910	−	0.369910i
$245$		0			0
$246$			22.7279i			1.44908i
$247$			2.41421i			0.153613i
$248$	−3.70711	+	3.70711i	−0.235402	+	0.235402i
$249$	−16.8995	+	16.8995i	−1.07096	+	1.07096i
$250$		0			0
$251$	−2.14214			−0.135210			−0.0676052	−	0.997712i	$-0.521536\pi$
$251$	−2.14214			−0.135210			−0.0676052	+	0.997712i	$0.521536\pi$
$252$	−1.17157	−	1.17157i	−0.0738022	−	0.0738022i
$253$			4.48528i			0.281987i
$254$	−7.72792			−0.484893
$255$		0			0
$256$	1.00000			0.0625000
$257$			22.5858i			1.40886i	0.709772	+	0.704431i	$0.248798\pi$
$257$			22.5858i			1.40886i	−0.709772	+	0.704431i	$0.751202\pi$
$258$	−17.4853	−	17.4853i	−1.08859	−	1.08859i
$259$	−1.31371			−0.0816299
$260$		0			0
$261$	19.6569	−	19.6569i	1.21673	−	1.21673i
$262$	−14.0711	+	14.0711i	−0.869313	+	0.869313i
$263$			29.7279i			1.83310i	0.399918	+	0.916551i	$0.369039\pi$
$263$			29.7279i			1.83310i	−0.399918	+	0.916551i	$0.630961\pi$
$264$			3.41421i			0.210130i
$265$		0			0
$266$	1.00000	−	1.00000i	0.0613139	−	0.0613139i
$267$	−25.0208	−	25.0208i	−1.53125	−	1.53125i
$268$	8.82843			0.539282
$269$	−2.46447	−	2.46447i	−0.150261	−	0.150261i	0.627974	−	0.778235i	$-0.283885\pi$
$269$	−2.46447	−	2.46447i	−0.150261	−	0.150261i	−0.778235	+	0.627974i	$0.783885\pi$
$270$		0			0
$271$	−6.34315			−0.385319			−0.192659	−	0.981266i	$-0.561711\pi$
$271$	−6.34315			−0.385319			−0.192659	+	0.981266i	$0.561711\pi$
$272$	4.12132	+	0.121320i	0.249892	+	0.00735613i
$273$	1.41421			0.0855921
$274$			16.7279i			1.01057i
$275$		0			0
$276$	−7.65685			−0.460888
$277$	−5.89949	−	5.89949i	−0.354466	−	0.354466i	0.507302	−	0.861768i	$-0.330643\pi$
$277$	−5.89949	−	5.89949i	−0.354466	−	0.354466i	−0.861768	+	0.507302i	$0.830643\pi$
$278$	0.656854	−	0.656854i	0.0393955	−	0.0393955i
$279$	10.4853	−	10.4853i	0.627737	−	0.627737i
$280$		0			0
$281$		−	1.48528i		−	0.0886045i	−0.999018	−	0.0443022i	$-0.985894\pi$
$281$		−	1.48528i		−	0.0886045i	0.999018	−	0.0443022i	$-0.0141065\pi$
$282$	−5.53553	+	5.53553i	−0.329636	+	0.329636i
$283$	−6.77817	+	6.77817i	−0.402921	+	0.402921i	−0.879261	−	0.476340i	$-0.841963\pi$
$283$	−6.77817	+	6.77817i	−0.402921	+	0.402921i	0.476340	+	0.879261i	$0.341963\pi$
$284$	8.29289	+	8.29289i	0.492093	+	0.492093i
$285$		0			0
$286$	−1.00000	−	1.00000i	−0.0591312	−	0.0591312i
$287$			5.51472i			0.325524i
$288$	−2.82843			−0.166667
$289$	16.9706	+	1.00000i	0.998268	+	0.0588235i
$290$		0			0
$291$			34.5563i			2.02573i
$292$	5.53553	+	5.53553i	0.323943	+	0.323943i
$293$	−5.48528			−0.320454			−0.160227	−	0.987080i	$-0.551223\pi$
$293$	−5.48528			−0.320454			−0.160227	+	0.987080i	$0.551223\pi$
$294$	11.3640	+	11.3640i	0.662760	+	0.662760i
$295$		0			0
$296$	−1.58579	+	1.58579i	−0.0921720	+	0.0921720i
$297$			0.585786i			0.0339908i
$298$		−	1.75736i		−	0.101801i
$299$	2.24264	−	2.24264i	0.129695	−	0.129695i
$300$		0			0
$301$	−4.24264	−	4.24264i	−0.244542	−	0.244542i
$302$	−4.82843			−0.277845
$303$	7.41421	+	7.41421i	0.425935	+	0.425935i
$304$		−	2.41421i		−	0.138465i
$305$		0			0
$306$	−11.6569	−	0.343146i	−0.666378	−	0.0196163i
$307$	−9.89949			−0.564994			−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949			−0.564994			−0.282497	+	0.959268i	$0.591163\pi$
$308$			0.828427i			0.0472040i
$309$	−4.00000	−	4.00000i	−0.227552	−	0.227552i
$310$		0			0
$311$	−2.58579	−	2.58579i	−0.146626	−	0.146626i	0.629983	−	0.776609i	$-0.283062\pi$
$311$	−2.58579	−	2.58579i	−0.146626	−	0.146626i	−0.776609	+	0.629983i	$0.783062\pi$
$312$	1.70711	−	1.70711i	0.0966459	−	0.0966459i
$313$	−6.48528	+	6.48528i	−0.366570	+	0.366570i	−0.866225	−	0.499655i	$-0.833460\pi$
$313$	−6.48528	+	6.48528i	−0.366570	+	0.366570i	0.499655	+	0.866225i	$0.333460\pi$
$314$		−	2.82843i		−	0.159617i
$315$		0			0
$316$	−8.24264	+	8.24264i	−0.463685	+	0.463685i
$317$	24.4853	−	24.4853i	1.37523	−	1.37523i	0.522735	−	0.852495i	$-0.324912\pi$
$317$	24.4853	−	24.4853i	1.37523	−	1.37523i	0.852495	−	0.522735i	$-0.175088\pi$
$318$	5.94975	+	5.94975i	0.333645	+	0.333645i
$319$	−13.8995			−0.778222
$320$		0			0
$321$		−	30.1421i		−	1.68237i
$322$	−1.85786			−0.103535
$323$	0.292893	−	9.94975i	0.0162970	−	0.553619i
$324$	−9.48528			−0.526960
$325$		0			0
$326$	−0.343146	−	0.343146i	−0.0190051	−	0.0190051i
$327$	28.5563			1.57917
$328$	6.65685	+	6.65685i	0.367563	+	0.367563i
$329$	−1.34315	+	1.34315i	−0.0740500	+	0.0740500i
$330$		0			0
$331$		−	8.55635i		−	0.470299i	−0.971959	−	0.235150i	$-0.924442\pi$
$331$		−	8.55635i		−	0.470299i	0.971959	−	0.235150i	$-0.0755581\pi$
$332$			9.89949i			0.543305i
$333$	4.48528	−	4.48528i	0.245792	−	0.245792i
$334$	10.7279	−	10.7279i	0.587006	−	0.587006i
$335$		0			0
$336$	−1.41421			−0.0771517
$337$	21.4350	+	21.4350i	1.16764	+	1.16764i	0.982761	+	0.184879i	$0.0591894\pi$
$337$	21.4350	+	21.4350i	1.16764	+	1.16764i	0.184879	+	0.982761i	$0.440811\pi$
$338$		−	12.0000i		−	0.652714i
$339$	8.41421			0.456997
$340$		0			0
$341$	−7.41421			−0.401502
$342$			6.82843i			0.369239i
$343$	5.65685	+	5.65685i	0.305441	+	0.305441i
$344$	−10.2426			−0.552246
$345$		0			0
$346$	0.928932	−	0.928932i	0.0499397	−	0.0499397i
$347$	10.4350	−	10.4350i	0.560182	−	0.560182i	−0.369177	−	0.929359i	$-0.620360\pi$
$347$	10.4350	−	10.4350i	0.560182	−	0.560182i	0.929359	+	0.369177i	$0.120360\pi$
$348$		−	23.7279i		−	1.27195i
$349$			8.97056i			0.480183i	0.970750	+	0.240092i	$0.0771775\pi$
$349$			8.97056i			0.480183i	−0.970750	+	0.240092i	$0.922823\pi$
$350$		0			0
$351$	0.292893	−	0.292893i	0.0156335	−	0.0156335i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−5.31371			−0.282820			−0.141410	−	0.989951i	$-0.545164\pi$
$353$	−5.31371			−0.282820			−0.141410	+	0.989951i	$0.545164\pi$
$354$	−18.6066	−	18.6066i	−0.988930	−	0.988930i
$355$		0			0
$356$	−14.6569			−0.776812
$357$	−5.82843	−	0.171573i	−0.308473	−	0.00908060i
$358$	−6.82843			−0.360894
$359$		−	12.3848i		−	0.653643i	−0.945086	−	0.326822i	$-0.894022\pi$
$359$		−	12.3848i		−	0.653643i	0.945086	−	0.326822i	$-0.105978\pi$
$360$		0			0
$361$	13.1716			0.693241
$362$	6.82843	+	6.82843i	0.358894	+	0.358894i
$363$	15.3640	−	15.3640i	0.806399	−	0.806399i
$364$	0.414214	−	0.414214i	0.0217107	−	0.0217107i
$365$		0			0
$366$			19.7279i			1.03120i
$367$	−5.55635	+	5.55635i	−0.290039	+	0.290039i	−0.837096	−	0.547057i	$-0.815748\pi$
$367$	−5.55635	+	5.55635i	−0.290039	+	0.290039i	0.547057	+	0.837096i	$0.315748\pi$
$368$	−2.24264	+	2.24264i	−0.116906	+	0.116906i
$369$	−18.8284	−	18.8284i	−0.980169	−	0.980169i
$370$		0			0
$371$	1.44365	+	1.44365i	0.0749506	+	0.0749506i
$372$		−	12.6569i		−	0.656227i
$373$	−24.2843			−1.25739			−0.628696	−	0.777651i	$-0.716411\pi$
$373$	−24.2843			−1.25739			−0.628696	+	0.777651i	$0.716411\pi$
$374$	4.00000	+	4.24264i	0.206835	+	0.219382i
$375$		0			0
$376$			3.24264i			0.167226i
$377$	6.94975	+	6.94975i	0.357930	+	0.357930i
$378$	−0.242641			−0.0124801
$379$	−4.00000	−	4.00000i	−0.205466	−	0.205466i	0.596871	−	0.802337i	$-0.296410\pi$
$379$	−4.00000	−	4.00000i	−0.205466	−	0.205466i	−0.802337	+	0.596871i	$0.796410\pi$
$380$		0			0
$381$	13.1924	−	13.1924i	0.675867	−	0.675867i
$382$			0.242641i			0.0124146i
$383$		−	22.2132i		−	1.13504i	−0.823359	−	0.567521i	$-0.807903\pi$
$383$		−	22.2132i		−	1.13504i	0.823359	−	0.567521i	$-0.192097\pi$
$384$	−1.70711	+	1.70711i	−0.0871154	+	0.0871154i
$385$		0			0
$386$	−2.82843	−	2.82843i	−0.143963	−	0.143963i
$387$	28.9706			1.47266
$388$	10.1213	+	10.1213i	0.513832	+	0.513832i
$389$		−	10.6274i		−	0.538831i	−0.963024	−	0.269416i	$-0.913169\pi$
$389$		−	10.6274i		−	0.538831i	0.963024	−	0.269416i	$-0.0868306\pi$
$390$		0			0
$391$	−9.51472	+	8.97056i	−0.481180	+	0.453661i
$392$	6.65685			0.336222
$393$		−	48.0416i		−	2.42338i
$394$	18.0711	+	18.0711i	0.910407	+	0.910407i
$395$		0			0
$396$	−2.82843	−	2.82843i	−0.142134	−	0.142134i
$397$	16.4853	−	16.4853i	0.827373	−	0.827373i	−0.159780	−	0.987153i	$-0.551079\pi$
$397$	16.4853	−	16.4853i	0.827373	−	0.827373i	0.987153	+	0.159780i	$0.0510785\pi$
$398$	8.05025	−	8.05025i	0.403523	−	0.403523i
$399$			3.41421i			0.170924i
$400$		0			0
$401$	14.8284	−	14.8284i	0.740496	−	0.740496i	−0.232177	−	0.972674i	$-0.574585\pi$
$401$	14.8284	−	14.8284i	0.740496	−	0.740496i	0.972674	+	0.232177i	$0.0745849\pi$
$402$	−15.0711	+	15.0711i	−0.751677	+	0.751677i
$403$	3.70711	+	3.70711i	0.184664	+	0.184664i
$404$	4.34315			0.216080
$405$		0			0
$406$		−	5.75736i		−	0.285733i
$407$	−3.17157			−0.157209
$408$	−7.24264	+	6.82843i	−0.358564	+	0.338058i
$409$	11.4853			0.567911			0.283955	−	0.958838i	$-0.408353\pi$
$409$	11.4853			0.567911			0.283955	+	0.958838i	$0.408353\pi$
$410$		0			0
$411$	−28.5563	−	28.5563i	−1.40858	−	1.40858i
$412$	−2.34315			−0.115439
$413$	−4.51472	−	4.51472i	−0.222155	−	0.222155i
$414$	6.34315	−	6.34315i	0.311749	−	0.311749i
$415$		0			0
$416$		−	1.00000i		−	0.0490290i
$417$			2.24264i			0.109823i
$418$	2.41421	−	2.41421i	0.118083	−	0.118083i
$419$	9.75736	−	9.75736i	0.476678	−	0.476678i	−0.427389	−	0.904068i	$-0.640567\pi$
$419$	9.75736	−	9.75736i	0.476678	−	0.476678i	0.904068	+	0.427389i	$0.140567\pi$
$420$		0			0
$421$	22.9289			1.11749			0.558744	−	0.829340i	$-0.311283\pi$
$421$	22.9289			1.11749			0.558744	+	0.829340i	$0.311283\pi$
$422$	3.41421	+	3.41421i	0.166201	+	0.166201i
$423$		−	9.17157i		−	0.445937i
$424$	3.48528			0.169260
$425$		0			0
$426$	−28.3137			−1.37180
$427$			4.78680i			0.231649i
$428$	−8.82843	−	8.82843i	−0.426738	−	0.426738i
$429$	3.41421			0.164840
$430$		0			0
$431$	16.0000	−	16.0000i	0.770693	−	0.770693i	−0.207535	−	0.978228i	$-0.566544\pi$
$431$	16.0000	−	16.0000i	0.770693	−	0.770693i	0.978228	+	0.207535i	$0.0665440\pi$
$432$	−0.292893	+	0.292893i	−0.0140918	+	0.0140918i
$433$			0.928932i			0.0446416i	0.999751	+	0.0223208i	$0.00710553\pi$
$433$			0.928932i			0.0446416i	−0.999751	+	0.0223208i	$0.992894\pi$
$434$		−	3.07107i		−	0.147416i
$435$		0			0
$436$	8.36396	−	8.36396i	0.400561	−	0.400561i
$437$	5.41421	+	5.41421i	0.258997	+	0.258997i
$438$	−18.8995			−0.903053
$439$	−22.6274	−	22.6274i	−1.07995	−	1.07995i	−0.996513	−	0.0834344i	$-0.973411\pi$
$439$	−22.6274	−	22.6274i	−1.07995	−	1.07995i	−0.0834344	−	0.996513i	$-0.526589\pi$
$440$		0			0
$441$	−18.8284			−0.896592
$442$	0.121320	−	4.12132i	0.00577062	−	0.196031i
$443$	20.0000			0.950229			0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000			0.950229			0.475114	+	0.879924i	$0.342407\pi$
$444$		−	5.41421i		−	0.256947i
$445$		0			0
$446$	25.3848			1.20200
$447$	3.00000	+	3.00000i	0.141895	+	0.141895i
$448$	−0.414214	+	0.414214i	−0.0195698	+	0.0195698i
$449$	−29.3848	+	29.3848i	−1.38675	+	1.38675i	−0.554709	+	0.832045i	$0.687170\pi$
$449$	−29.3848	+	29.3848i	−1.38675	+	1.38675i	−0.832045	+	0.554709i	$0.812830\pi$
$450$		0			0
$451$			13.3137i			0.626918i
$452$	2.46447	−	2.46447i	0.115919	−	0.115919i
$453$	8.24264	−	8.24264i	0.387273	−	0.387273i
$454$	14.5355	+	14.5355i	0.682186	+	0.682186i
$455$		0			0
$456$	4.12132	+	4.12132i	0.192999	+	0.192999i
$457$			27.5563i			1.28903i	0.764591	+	0.644516i	$0.222941\pi$
$457$			27.5563i			1.28903i	−0.764591	+	0.644516i	$0.777059\pi$
$458$	16.2426			0.758969
$459$	−1.24264	+	1.17157i	−0.0580015	+	0.0546843i
$460$		0			0
$461$		−	6.97056i		−	0.324651i	−0.986737	−	0.162326i	$-0.948100\pi$
$461$		−	6.97056i		−	0.324651i	0.986737	−	0.162326i	$-0.0518995\pi$
$462$	−1.41421	−	1.41421i	−0.0657952	−	0.0657952i
$463$	1.10051			0.0511448			0.0255724	−	0.999673i	$-0.491859\pi$
$463$	1.10051			0.0511448			0.0255724	+	0.999673i	$0.491859\pi$
$464$	−6.94975	−	6.94975i	−0.322634	−	0.322634i
$465$		0			0
$466$	−8.36396	+	8.36396i	−0.387453	+	0.387453i
$467$		−	25.2132i		−	1.16673i	−0.812211	−	0.583364i	$-0.801736\pi$
$467$		−	25.2132i		−	1.16673i	0.812211	−	0.583364i	$-0.198264\pi$
$468$			2.82843i			0.130744i
$469$	−3.65685	+	3.65685i	−0.168858	+	0.168858i
$470$		0			0
$471$	4.82843	+	4.82843i	0.222482	+	0.222482i
$472$	−10.8995			−0.501690
$473$	−10.2426	−	10.2426i	−0.470957	−	0.470957i
$474$		−	28.1421i		−	1.29261i
$475$		0			0
$476$	−1.75736	+	1.65685i	−0.0805484	+	0.0759418i
$477$	−9.85786			−0.451361
$478$			27.4142i			1.25390i
$479$	19.0208	+	19.0208i	0.869083	+	0.869083i	0.992371	−	0.123288i	$-0.0393438\pi$
$479$	19.0208	+	19.0208i	0.869083	+	0.869083i	−0.123288	+	0.992371i	$0.539344\pi$
$480$		0			0
$481$	1.58579	+	1.58579i	0.0723056	+	0.0723056i
$482$	19.8284	−	19.8284i	0.903160	−	0.903160i
$483$	3.17157	−	3.17157i	0.144312	−	0.144312i
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$	15.3137	−	15.3137i	0.694644	−	0.694644i
$487$	−14.4142	+	14.4142i	−0.653170	+	0.653170i	−0.953755	−	0.300585i	$-0.902818\pi$
$487$	−14.4142	+	14.4142i	−0.653170	+	0.653170i	0.300585	+	0.953755i	$0.402818\pi$
$488$	5.77817	+	5.77817i	0.261566	+	0.261566i
$489$	1.17157			0.0529804
$490$		0			0
$491$		−	8.27208i		−	0.373314i	−0.982425	−	0.186657i	$-0.940235\pi$
$491$		−	8.27208i		−	0.373314i	0.982425	−	0.186657i	$-0.0597652\pi$
$492$	−22.7279			−1.02465
$493$	−27.7990	−	29.4853i	−1.25200	−	1.32795i
$494$	−2.41421			−0.108621
$495$		0			0
$496$	−3.70711	−	3.70711i	−0.166454	−	0.166454i
$497$	−6.87006			−0.308164
$498$	−16.8995	−	16.8995i	−0.757284	−	0.757284i
$499$	−19.2426	+	19.2426i	−0.861419	+	0.861419i	−0.991503	−	0.130084i	$-0.958475\pi$
$499$	−19.2426	+	19.2426i	−0.861419	+	0.861419i	0.130084	+	0.991503i	$0.458475\pi$
$500$		0			0
$501$			36.6274i			1.63639i
$502$		−	2.14214i		−	0.0956082i
$503$	−26.1421	+	26.1421i	−1.16562	+	1.16562i	−0.182395	+	0.983225i	$0.558385\pi$
$503$	−26.1421	+	26.1421i	−1.16562	+	1.16562i	−0.983225	+	0.182395i	$0.941615\pi$
$504$	1.17157	−	1.17157i	0.0521860	−	0.0521860i
$505$		0			0
$506$	−4.48528			−0.199395
$507$	20.4853	+	20.4853i	0.909783	+	0.909783i
$508$		−	7.72792i		−	0.342871i
$509$	32.0000			1.41838			0.709188	−	0.705020i	$-0.249062\pi$
$509$	32.0000			1.41838			0.709188	+	0.705020i	$0.249062\pi$
$510$		0			0
$511$	−4.58579			−0.202863
$512$			1.00000i			0.0441942i
$513$	0.707107	+	0.707107i	0.0312195	+	0.0312195i
$514$	−22.5858			−0.996216
$515$		0			0
$516$	17.4853	−	17.4853i	0.769747	−	0.769747i
$517$	−3.24264	+	3.24264i	−0.142611	+	0.142611i
$518$		−	1.31371i		−	0.0577210i
$519$			3.17157i			0.139217i
$520$		0			0
$521$	4.68629	−	4.68629i	0.205310	−	0.205310i	−0.596960	−	0.802271i	$-0.703625\pi$
$521$	4.68629	−	4.68629i	0.205310	−	0.205310i	0.802271	+	0.596960i	$0.203625\pi$
$522$	19.6569	+	19.6569i	0.860357	+	0.860357i
$523$	−4.82843			−0.211132			−0.105566	−	0.994412i	$-0.533665\pi$
$523$	−4.82843			−0.211132			−0.105566	+	0.994412i	$0.533665\pi$
$524$	−14.0711	−	14.0711i	−0.614697	−	0.614697i
$525$		0			0
$526$	−29.7279			−1.29620
$527$	−14.8284	−	15.7279i	−0.645936	−	0.685119i
$528$	−3.41421			−0.148585
$529$			12.9411i			0.562658i
$530$		0			0
$531$	30.8284			1.33784
$532$	1.00000	+	1.00000i	0.0433555	+	0.0433555i
$533$	6.65685	−	6.65685i	0.288340	−	0.288340i
$534$	25.0208	−	25.0208i	1.08276	−	1.08276i
$535$		0			0
$536$			8.82843i			0.381330i
$537$	11.6569	−	11.6569i	0.503030	−	0.503030i
$538$	2.46447	−	2.46447i	0.106251	−	0.106251i
$539$	6.65685	+	6.65685i	0.286731	+	0.286731i
$540$		0			0
$541$	−11.3137	−	11.3137i	−0.486414	−	0.486414i	0.420758	−	0.907173i	$-0.361764\pi$
$541$	−11.3137	−	11.3137i	−0.486414	−	0.486414i	−0.907173	+	0.420758i	$0.861764\pi$
$542$		−	6.34315i		−	0.272461i
$543$	−23.3137			−1.00049
$544$	−0.121320	+	4.12132i	−0.00520157	+	0.176700i
$545$		0			0
$546$			1.41421i			0.0605228i
$547$	−11.4645	−	11.4645i	−0.490185	−	0.490185i	0.418179	−	0.908364i	$-0.362668\pi$
$547$	−11.4645	−	11.4645i	−0.490185	−	0.490185i	−0.908364	+	0.418179i	$0.862668\pi$
$548$	−16.7279			−0.714581
$549$	−16.3431	−	16.3431i	−0.697508	−	0.697508i
$550$		0			0
$551$	−16.7782	+	16.7782i	−0.714774	+	0.714774i
$552$		−	7.65685i		−	0.325897i
$553$		−	6.82843i		−	0.290374i
$554$	5.89949	−	5.89949i	0.250646	−	0.250646i
$555$		0			0
$556$	0.656854	+	0.656854i	0.0278568	+	0.0278568i
$557$	−7.82843			−0.331701			−0.165851	−	0.986151i	$-0.553037\pi$
$557$	−7.82843			−0.331701			−0.165851	+	0.986151i	$0.553037\pi$
$558$	10.4853	+	10.4853i	0.443877	+	0.443877i
$559$			10.2426i			0.433218i
$560$		0			0
$561$	−14.0711	−	0.414214i	−0.594081	−	0.0174881i
$562$	1.48528			0.0626528
$563$			32.1421i			1.35463i	0.735693	+	0.677315i	$0.236856\pi$
$563$			32.1421i			1.35463i	−0.735693	+	0.677315i	$0.763144\pi$
$564$	−5.53553	−	5.53553i	−0.233088	−	0.233088i
$565$		0			0
$566$	−6.77817	−	6.77817i	−0.284908	−	0.284908i
$567$	3.92893	−	3.92893i	0.165000	−	0.165000i
$568$	−8.29289	+	8.29289i	−0.347962	+	0.347962i
$569$			25.9706i			1.08874i	0.838844	+	0.544371i	$0.183232\pi$
$569$			25.9706i			1.08874i	−0.838844	+	0.544371i	$0.816768\pi$
$570$		0			0
$571$	23.0416	−	23.0416i	0.964262	−	0.964262i	−0.0351208	−	0.999383i	$-0.511182\pi$
$571$	23.0416	−	23.0416i	0.964262	−	0.964262i	0.999383	+	0.0351208i	$0.0111816\pi$
$572$	1.00000	−	1.00000i	0.0418121	−	0.0418121i
$573$	−0.414214	−	0.414214i	−0.0173040	−	0.0173040i
$574$	−5.51472			−0.230180
$575$		0			0
$576$		−	2.82843i		−	0.117851i
$577$	−18.3431			−0.763635			−0.381818	−	0.924238i	$-0.624702\pi$
$577$	−18.3431			−0.763635			−0.381818	+	0.924238i	$0.624702\pi$
$578$	−1.00000	+	16.9706i	−0.0415945	+	0.705882i
$579$	9.65685			0.401325
$580$		0			0
$581$	−4.10051	−	4.10051i	−0.170118	−	0.170118i
$582$	−34.5563			−1.43241
$583$	3.48528	+	3.48528i	0.144346	+	0.144346i
$584$	−5.53553	+	5.53553i	−0.229062	+	0.229062i
$585$		0			0
$586$		−	5.48528i		−	0.226595i
$587$			3.17157i			0.130905i	0.997856	+	0.0654524i	$0.0208491\pi$
$587$			3.17157i			0.130905i	−0.997856	+	0.0654524i	$0.979151\pi$
$588$	−11.3640	+	11.3640i	−0.468642	+	0.468642i
$589$	−8.94975	+	8.94975i	−0.368768	+	0.368768i
$590$		0			0
$591$	−61.6985			−2.53794
$592$	−1.58579	−	1.58579i	−0.0651754	−	0.0651754i
$593$			14.2843i			0.586585i	0.956023	+	0.293292i	$0.0947509\pi$
$593$			14.2843i			0.586585i	−0.956023	+	0.293292i	$0.905249\pi$
$594$	−0.585786			−0.0240351
$595$		0			0
$596$	1.75736			0.0719842
$597$			27.4853i			1.12490i
$598$	2.24264	+	2.24264i	0.0917084	+	0.0917084i
$599$	42.7696			1.74752			0.873758	−	0.486360i	$-0.161676\pi$
$599$	42.7696			1.74752			0.873758	+	0.486360i	$0.161676\pi$
$600$		0			0
$601$	13.1716	−	13.1716i	0.537280	−	0.537280i	−0.385449	−	0.922729i	$-0.625954\pi$
$601$	13.1716	−	13.1716i	0.537280	−	0.537280i	0.922729	+	0.385449i	$0.125954\pi$
$602$	4.24264	−	4.24264i	0.172917	−	0.172917i
$603$		−	24.9706i		−	1.01688i
$604$		−	4.82843i		−	0.196466i
$605$		0			0
$606$	−7.41421	+	7.41421i	−0.301182	+	0.301182i
$607$	4.07107	+	4.07107i	0.165240	+	0.165240i	0.784883	−	0.619644i	$-0.212723\pi$
$607$	4.07107	+	4.07107i	0.165240	+	0.165240i	−0.619644	+	0.784883i	$0.712723\pi$
$608$	2.41421			0.0979093
$609$	9.82843	+	9.82843i	0.398268	+	0.398268i
$610$		0			0
$611$	3.24264			0.131183
$612$	0.343146	−	11.6569i	0.0138708	−	0.471200i
$613$	23.2843			0.940443			0.470221	−	0.882548i	$-0.344174\pi$
$613$	23.2843			0.940443			0.470221	+	0.882548i	$0.344174\pi$
$614$		−	9.89949i		−	0.399511i
$615$		0			0
$616$	−0.828427			−0.0333783
$617$	−0.564971	−	0.564971i	−0.0227449	−	0.0227449i	0.695643	−	0.718388i	$-0.255120\pi$
$617$	−0.564971	−	0.564971i	−0.0227449	−	0.0227449i	−0.718388	+	0.695643i	$0.755120\pi$
$618$	4.00000	−	4.00000i	0.160904	−	0.160904i
$619$	−10.2426	+	10.2426i	−0.411686	+	0.411686i	−0.882326	−	0.470639i	$-0.844023\pi$
$619$	−10.2426	+	10.2426i	−0.411686	+	0.411686i	0.470639	+	0.882326i	$0.344023\pi$
$620$		0			0
$621$		−	1.31371i		−	0.0527173i
$622$	2.58579	−	2.58579i	0.103681	−	0.103681i
$623$	6.07107	−	6.07107i	0.243232	−	0.243232i
$624$	1.70711	+	1.70711i	0.0683390	+	0.0683390i
$625$		0			0
$626$	−6.48528	−	6.48528i	−0.259204	−	0.259204i
$627$			8.24264i			0.329179i
$628$	2.82843			0.112867
$629$	−6.34315	−	6.72792i	−0.252918	−	0.268260i
$630$		0			0
$631$			49.6569i			1.97681i	0.151847	+	0.988404i	$0.451478\pi$
$631$			49.6569i			1.97681i	−0.151847	+	0.988404i	$0.548522\pi$
$632$	−8.24264	−	8.24264i	−0.327875	−	0.327875i
$633$	−11.6569			−0.463318
$634$	24.4853	+	24.4853i	0.972435	+	0.972435i
$635$		0			0
$636$	−5.94975	+	5.94975i	−0.235923	+	0.235923i
$637$		−	6.65685i		−	0.263754i
$638$		−	13.8995i		−	0.550286i
$639$	23.4558	−	23.4558i	0.927899	−	0.927899i
$640$		0			0
$641$	−11.0711	−	11.0711i	−0.437281	−	0.437281i	0.453815	−	0.891096i	$-0.350063\pi$
$641$	−11.0711	−	11.0711i	−0.437281	−	0.437281i	−0.891096	+	0.453815i	$0.850063\pi$
$642$	30.1421			1.18962
$643$	18.3848	+	18.3848i	0.725025	+	0.725025i	0.969624	−	0.244599i	$-0.0786565\pi$
$643$	18.3848	+	18.3848i	0.725025	+	0.725025i	−0.244599	+	0.969624i	$0.578656\pi$
$644$		−	1.85786i		−	0.0732101i
$645$		0			0
$646$	9.94975	+	0.292893i	0.391468	+	0.0115237i
$647$	−48.2132			−1.89546			−0.947728	−	0.319078i	$-0.896627\pi$
$647$	−48.2132			−1.89546			−0.947728	+	0.319078i	$0.896627\pi$
$648$		−	9.48528i		−	0.372617i
$649$	−10.8995	−	10.8995i	−0.427843	−	0.427843i
$650$		0			0
$651$	5.24264	+	5.24264i	0.205475	+	0.205475i
$652$	0.343146	−	0.343146i	0.0134386	−	0.0134386i
$653$	−6.51472	+	6.51472i	−0.254941	+	0.254941i	−0.822993	−	0.568052i	$-0.807697\pi$
$653$	−6.51472	+	6.51472i	−0.254941	+	0.254941i	0.568052	+	0.822993i	$0.307697\pi$
$654$			28.5563i			1.11664i
$655$		0			0
$656$	−6.65685	+	6.65685i	−0.259906	+	0.259906i
$657$	15.6569	−	15.6569i	0.610832	−	0.610832i
$658$	−1.34315	−	1.34315i	−0.0523613	−	0.0523613i
$659$	−10.7574			−0.419047			−0.209524	−	0.977804i	$-0.567191\pi$
$659$	−10.7574			−0.419047			−0.209524	+	0.977804i	$0.567191\pi$
$660$		0			0
$661$		−	11.3137i		−	0.440052i	−0.975494	−	0.220026i	$-0.929386\pi$
$661$		−	11.3137i		−	0.440052i	0.975494	−	0.220026i	$-0.0706143\pi$
$662$	8.55635			0.332552
$663$	6.82843	+	7.24264i	0.265194	+	0.281281i
$664$	−9.89949			−0.384175
$665$		0			0
$666$	4.48528	+	4.48528i	0.173801	+	0.173801i
$667$	31.1716			1.20697
$668$	10.7279	+	10.7279i	0.415076	+	0.415076i
$669$	−43.3345	+	43.3345i	−1.67541	+	1.67541i
$670$		0			0
$671$			11.5563i			0.446128i
$672$		−	1.41421i		−	0.0545545i
$673$	8.46447	−	8.46447i	0.326281	−	0.326281i	−0.524889	−	0.851170i	$-0.675893\pi$
$673$	8.46447	−	8.46447i	0.326281	−	0.326281i	0.851170	+	0.524889i	$0.175893\pi$
$674$	−21.4350	+	21.4350i	−0.825646	+	0.825646i
$675$		0			0
$676$	12.0000			0.461538
$677$	31.8284	+	31.8284i	1.22327	+	1.22327i	0.966464	+	0.256802i	$0.0826687\pi$
$677$	31.8284	+	31.8284i	1.22327	+	1.22327i	0.256802	+	0.966464i	$0.417331\pi$
$678$			8.41421i			0.323146i
$679$	−8.38478			−0.321778
$680$		0			0
$681$	−49.6274			−1.90173
$682$		−	7.41421i		−	0.283905i
$683$	−8.19239	−	8.19239i	−0.313473	−	0.313473i	0.532780	−	0.846253i	$-0.321147\pi$
$683$	−8.19239	−	8.19239i	−0.313473	−	0.313473i	−0.846253	+	0.532780i	$0.821147\pi$
$684$	−6.82843			−0.261091
$685$		0			0
$686$	−5.65685	+	5.65685i	−0.215980	+	0.215980i
$687$	−27.7279	+	27.7279i	−1.05789	+	1.05789i
$688$		−	10.2426i		−	0.390497i
$689$		−	3.48528i		−	0.132779i
$690$		0			0
$691$	−23.8284	+	23.8284i	−0.906476	+	0.906476i	−0.995986	−	0.0895098i	$-0.971470\pi$
$691$	−23.8284	+	23.8284i	−0.906476	+	0.906476i	0.0895098	+	0.995986i	$0.471470\pi$
$692$	0.928932	+	0.928932i	0.0353127	+	0.0353127i
$693$	2.34315			0.0890087
$694$	10.4350	+	10.4350i	0.396108	+	0.396108i
$695$		0			0
$696$	23.7279			0.899405
$697$	−28.2426	+	26.6274i	−1.06977	+	1.00859i
$698$	−8.97056			−0.339541
$699$		−	28.5563i		−	1.08010i
$700$		0			0
$701$	8.97056			0.338813			0.169407	−	0.985546i	$-0.445815\pi$
$701$	8.97056			0.338813			0.169407	+	0.985546i	$0.445815\pi$
$702$	0.292893	+	0.292893i	0.0110545	+	0.0110545i
$703$	−3.82843	+	3.82843i	−0.144392	+	0.144392i
$704$	−1.00000	+	1.00000i	−0.0376889	+	0.0376889i
$705$		0			0
$706$		−	5.31371i		−	0.199984i
$707$	−1.79899	+	1.79899i	−0.0676580	+	0.0676580i
$708$	18.6066	−	18.6066i	0.699279	−	0.699279i
$709$	−16.5061	−	16.5061i	−0.619899	−	0.619899i	0.325606	−	0.945506i	$-0.394432\pi$
$709$	−16.5061	−	16.5061i	−0.619899	−	0.619899i	−0.945506	+	0.325606i	$0.894432\pi$
$710$		0			0
$711$	23.3137	+	23.3137i	0.874332	+	0.874332i
$712$		−	14.6569i		−	0.549289i
$713$	16.6274			0.622702
$714$	0.171573	−	5.82843i	0.00642095	−	0.218123i
$715$		0			0
$716$		−	6.82843i		−	0.255190i
$717$	−46.7990	−	46.7990i	−1.74774	−	1.74774i
$718$	12.3848			0.462196
$719$	−36.6777	−	36.6777i	−1.36785	−	1.36785i	−0.863504	−	0.504343i	$-0.831735\pi$
$719$	−36.6777	−	36.6777i	−1.36785	−	1.36785i	−0.504343	−	0.863504i	$-0.668265\pi$
$720$		0			0
$721$	0.970563	−	0.970563i	0.0361456	−	0.0361456i
$722$			13.1716i			0.490195i
$723$			67.6985i			2.51773i
$724$	−6.82843	+	6.82843i	−0.253776	+	0.253776i
$725$		0			0
$726$	15.3640	+	15.3640i	0.570210	+	0.570210i
$727$	22.2132			0.823842			0.411921	−	0.911220i	$-0.364858\pi$
$727$	22.2132			0.823842			0.411921	+	0.911220i	$0.364858\pi$
$728$	0.414214	+	0.414214i	0.0153518	+	0.0153518i
$729$			23.8284i			0.882534i
$730$		0			0
$731$	1.24264	−	42.2132i	0.0459607	−	1.56131i
$732$	−19.7279			−0.729165
$733$			10.8284i			0.399957i	0.979800	+	0.199979i	$0.0640872\pi$
$733$			10.8284i			0.399957i	−0.979800	+	0.199979i	$0.935913\pi$
$734$	−5.55635	−	5.55635i	−0.205089	−	0.205089i
$735$		0			0
$736$	−2.24264	−	2.24264i	−0.0826648	−	0.0826648i
$737$	−8.82843	+	8.82843i	−0.325199	+	0.325199i
$738$	18.8284	−	18.8284i	0.693084	−	0.693084i
$739$			5.87006i			0.215934i	0.994155	+	0.107967i	$0.0344340\pi$
$739$			5.87006i			0.215934i	−0.994155	+	0.107967i	$0.965566\pi$
$740$		0			0
$741$	4.12132	−	4.12132i	0.151400	−	0.151400i
$742$	−1.44365	+	1.44365i	−0.0529981	+	0.0529981i
$743$	−4.55635	−	4.55635i	−0.167156	−	0.167156i	0.618572	−	0.785728i	$-0.287712\pi$
$743$	−4.55635	−	4.55635i	−0.167156	−	0.167156i	−0.785728	+	0.618572i	$0.787712\pi$
$744$	12.6569			0.464023
$745$		0			0
$746$		−	24.2843i		−	0.889110i
$747$	28.0000			1.02447
$748$	−4.24264	+	4.00000i	−0.155126	+	0.146254i
$749$	7.31371			0.267237
$750$		0			0
$751$	−2.15076	−	2.15076i	−0.0784823	−	0.0784823i	0.666776	−	0.745258i	$-0.267674\pi$
$751$	−2.15076	−	2.15076i	−0.0784823	−	0.0784823i	−0.745258	+	0.666776i	$0.767674\pi$
$752$	−3.24264			−0.118247
$753$	3.65685	+	3.65685i	0.133263	+	0.133263i
$754$	−6.94975	+	6.94975i	−0.253095	+	0.253095i
$755$		0			0
$756$		−	0.242641i		−	0.00882476i
$757$		−	39.8284i		−	1.44759i	−0.690016	−	0.723794i	$-0.742396\pi$
$757$		−	39.8284i		−	1.44759i	0.690016	−	0.723794i	$-0.257604\pi$
$758$	4.00000	−	4.00000i	0.145287	−	0.145287i
$759$	7.65685	−	7.65685i	0.277926	−	0.277926i
$760$		0			0
$761$	43.1127			1.56283			0.781417	−	0.624009i	$-0.214497\pi$
$761$	43.1127			1.56283			0.781417	+	0.624009i	$0.214497\pi$
$762$	13.1924	+	13.1924i	0.477910	+	0.477910i
$763$			6.92893i			0.250844i
$764$	−0.242641			−0.00877843
$765$		0			0
$766$	22.2132			0.802596
$767$			10.8995i			0.393558i
$768$	−1.70711	−	1.70711i	−0.0615999	−	0.0615999i
$769$	23.1421			0.834527			0.417263	−	0.908786i	$-0.362989\pi$
$769$	23.1421			0.834527			0.417263	+	0.908786i	$0.362989\pi$
$770$		0			0
$771$	38.5563	−	38.5563i	1.38857	−	1.38857i
$772$	2.82843	−	2.82843i	0.101797	−	0.101797i
$773$			23.5147i			0.845766i	0.906184	+	0.422883i	$0.138982\pi$
$773$			23.5147i			0.845766i	−0.906184	+	0.422883i	$0.861018\pi$
$774$			28.9706i			1.04133i
$775$		0			0
$776$	−10.1213	+	10.1213i	−0.363334	+	0.363334i
$777$	2.24264	+	2.24264i	0.0804543	+	0.0804543i
$778$	10.6274			0.381011
$779$	16.0711	+	16.0711i	0.575806	+	0.575806i
$780$		0			0
$781$	−16.5858			−0.593486
$782$	−8.97056	−	9.51472i	−0.320787	−	0.340246i
$783$	4.07107			0.145488
$784$			6.65685i			0.237745i
$785$		0			0
$786$	48.0416			1.71359
$787$	0.393398	+	0.393398i	0.0140231	+	0.0140231i	0.714084	−	0.700060i	$-0.246844\pi$
$787$	0.393398	+	0.393398i	0.0140231	+	0.0140231i	−0.700060	+	0.714084i	$0.746844\pi$
$788$	−18.0711	+	18.0711i	−0.643755	+	0.643755i
$789$	50.7487	−	50.7487i	1.80670	−	1.80670i
$790$		0			0
$791$			2.04163i			0.0725920i
$792$	2.82843	−	2.82843i	0.100504	−	0.100504i
$793$	5.77817	−	5.77817i	0.205189	−	0.205189i
$794$	16.4853	+	16.4853i	0.585041	+	0.585041i
$795$		0			0
$796$	8.05025	+	8.05025i	0.285334	+	0.285334i
$797$		−	26.6274i		−	0.943192i	−0.881815	−	0.471596i	$-0.843678\pi$
$797$		−	26.6274i		−	0.943192i	0.881815	−	0.471596i	$-0.156322\pi$
$798$	−3.41421			−0.120862
$799$	−13.3640	−	0.393398i	−0.472783	−	0.0139174i
$800$		0			0
$801$			41.4558i			1.46477i
$802$	14.8284	+	14.8284i	0.523610	+	0.523610i
$803$	−11.0711			−0.390689
$804$	−15.0711	−	15.0711i	−0.531516	−	0.531516i
$805$		0			0
$806$	−3.70711	+	3.70711i	−0.130577	+	0.130577i
$807$			8.41421i			0.296194i
$808$			4.34315i			0.152791i
$809$	25.8284	−	25.8284i	0.908079	−	0.908079i	−0.0880380	−	0.996117i	$-0.528060\pi$
$809$	25.8284	−	25.8284i	0.908079	−	0.908079i	0.996117	+	0.0880380i	$0.0280597\pi$
$810$		0			0
$811$	36.0711	+	36.0711i	1.26663	+	1.26663i	0.947820	+	0.318807i	$0.103282\pi$
$811$	36.0711	+	36.0711i	1.26663	+	1.26663i	0.318807	+	0.947820i	$0.396718\pi$
$812$	5.75736			0.202044
$813$	10.8284	+	10.8284i	0.379770	+	0.379770i
$814$		−	3.17157i		−	0.111164i
$815$		0			0
$816$	−6.82843	−	7.24264i	−0.239043	−	0.253543i
$817$	−24.7279			−0.865120
$818$			11.4853i			0.401573i
$819$	−1.17157	−	1.17157i	−0.0409381	−	0.0409381i
$820$		0			0
$821$	−3.92031	−	3.92031i	−0.136820	−	0.136820i	0.635380	−	0.772200i	$-0.280844\pi$
$821$	−3.92031	−	3.92031i	−0.136820	−	0.136820i	−0.772200	+	0.635380i	$0.780844\pi$
$822$	28.5563	−	28.5563i	0.996017	−	0.996017i
$823$	−8.58579	+	8.58579i	−0.299282	+	0.299282i	−0.840732	−	0.541451i	$-0.817875\pi$
$823$	−8.58579	+	8.58579i	−0.299282	+	0.299282i	0.541451	+	0.840732i	$0.317875\pi$
$824$		−	2.34315i		−	0.0816274i
$825$		0			0
$826$	4.51472	−	4.51472i	0.157087	−	0.157087i
$827$	−10.1421	+	10.1421i	−0.352677	+	0.352677i	−0.861105	−	0.508428i	$-0.830227\pi$
$827$	−10.1421	+	10.1421i	−0.352677	+	0.352677i	0.508428	+	0.861105i	$0.330227\pi$
$828$	6.34315	+	6.34315i	0.220440	+	0.220440i
$829$	−11.3137			−0.392941			−0.196471	−	0.980510i	$-0.562948\pi$
$829$	−11.3137			−0.392941			−0.196471	+	0.980510i	$0.562948\pi$
$830$		0			0
$831$			20.1421i			0.698723i
$832$	1.00000			0.0346688
$833$	−0.807612	+	27.4350i	−0.0279821	+	0.950567i
$834$	−2.24264			−0.0776563
$835$		0			0
$836$	2.41421	+	2.41421i	0.0834973	+	0.0834973i
$837$	2.17157			0.0750605
$838$	9.75736	+	9.75736i	0.337062	+	0.337062i
$839$	−8.87868	+	8.87868i	−0.306526	+	0.306526i	−0.843560	−	0.537034i	$-0.819545\pi$
$839$	−8.87868	+	8.87868i	−0.306526	+	0.306526i	0.537034	+	0.843560i	$0.319545\pi$
$840$		0			0
$841$			67.5980i			2.33096i
$842$			22.9289i			0.790183i
$843$	−2.53553	+	2.53553i	−0.0873284	+	0.0873284i
$844$	−3.41421	+	3.41421i	−0.117522	+	0.117522i
$845$		0			0
$846$	9.17157			0.315325
$847$	3.72792	+	3.72792i	0.128093	+	0.128093i
$848$			3.48528i			0.119685i
$849$	23.1421			0.794236
$850$		0			0
$851$	7.11270			0.243820
$852$		−	28.3137i		−	0.970012i
$853$	0.514719	+	0.514719i	0.0176236	+	0.0176236i	0.715864	−	0.698240i	$-0.246033\pi$
$853$	0.514719	+	0.514719i	0.0176236	+	0.0176236i	−0.698240	+	0.715864i	$0.746033\pi$
$854$	−4.78680			−0.163801
$855$		0			0
$856$	8.82843	−	8.82843i	0.301749	−	0.301749i
$857$	15.4350	−	15.4350i	0.527251	−	0.527251i	−0.392501	−	0.919752i	$-0.628390\pi$
$857$	15.4350	−	15.4350i	0.527251	−	0.527251i	0.919752	+	0.392501i	$0.128390\pi$
$858$			3.41421i			0.116559i
$859$		−	47.8701i		−	1.63331i	−0.577129	−	0.816653i	$-0.695827\pi$
$859$		−	47.8701i		−	1.63331i	0.577129	−	0.816653i	$-0.304173\pi$
$860$		0			0
$861$	9.41421	−	9.41421i	0.320836	−	0.320836i
$862$	16.0000	+	16.0000i	0.544962	+	0.544962i
$863$	1.45584			0.0495575			0.0247788	−	0.999693i	$-0.492112\pi$
$863$	1.45584			0.0495575			0.0247788	+	0.999693i	$0.492112\pi$
$864$	−0.292893	−	0.292893i	−0.00996443	−	0.00996443i
$865$		0			0
$866$	−0.928932			−0.0315664
$867$	−27.2635	−	30.6777i	−0.925916	−	1.04187i
$868$	3.07107			0.104239
$869$		−	16.4853i		−	0.559225i
$870$		0			0
$871$	8.82843			0.299140
$872$	8.36396	+	8.36396i	0.283239	+	0.283239i
$873$	28.6274	−	28.6274i	0.968891	−	0.968891i
$874$	−5.41421	+	5.41421i	−0.183139	+	0.183139i
$875$		0			0
$876$		−	18.8995i		−	0.638555i
$877$	34.2132	−	34.2132i	1.15530	−	1.15530i	0.169823	−	0.985475i	$-0.445680\pi$
$877$	34.2132	−	34.2132i	1.15530	−	1.15530i	0.985475	−	0.169823i	$-0.0543197\pi$
$878$	22.6274	−	22.6274i	0.763638	−	0.763638i
$879$	9.36396	+	9.36396i	0.315839	+	0.315839i
$880$		0			0
$881$	28.0416	+	28.0416i	0.944747	+	0.944747i	0.998551	−	0.0538049i	$-0.0171349\pi$
$881$	28.0416	+	28.0416i	0.944747	+	0.944747i	−0.0538049	+	0.998551i	$0.517135\pi$
$882$		−	18.8284i		−	0.633986i
$883$	55.4975			1.86764			0.933819	−	0.357745i	$-0.116454\pi$
$883$	55.4975			1.86764			0.933819	+	0.357745i	$0.116454\pi$
$884$	4.12132	+	0.121320i	0.138615	+	0.00408044i
$885$		0			0
$886$			20.0000i			0.671913i
$887$	−36.8995	−	36.8995i	−1.23896	−	1.23896i	−0.960425	−	0.278539i	$-0.910150\pi$
$887$	−36.8995	−	36.8995i	−1.23896	−	1.23896i	−0.278539	−	0.960425i	$-0.589850\pi$
$888$	5.41421			0.181689
$889$	3.20101	+	3.20101i	0.107358	+	0.107358i
$890$		0			0
$891$	9.48528	−	9.48528i	0.317769	−	0.317769i
$892$			25.3848i			0.849945i
$893$			7.82843i			0.261968i
$894$	−3.00000	+	3.00000i	−0.100335	+	0.100335i
$895$		0			0
$896$	−0.414214	−	0.414214i	−0.0138379	−	0.0138379i
$897$	−7.65685			−0.255655
$898$	−29.3848	−	29.3848i	−0.980583	−	0.980583i
$899$			51.5269i			1.71852i
$900$		0			0
$901$	−0.422836	+	14.3640i	−0.0140867	+	0.478533i
$902$	−13.3137			−0.443298
$903$			14.4853i			0.482040i
$904$	2.46447	+	2.46447i	0.0819669	+	0.0819669i
$905$		0			0
$906$	8.24264	+	8.24264i	0.273843	+	0.273843i
$907$	−2.97918	+	2.97918i	−0.0989222	+	0.0989222i	−0.754836	−	0.655914i	$-0.772284\pi$
$907$	−2.97918	+	2.97918i	−0.0989222	+	0.0989222i	0.655914	+	0.754836i	$0.272284\pi$
$908$	−14.5355	+	14.5355i	−0.482379	+	0.482379i
$909$		−	12.2843i		−	0.407444i
$910$		0			0
$911$	−3.31371	+	3.31371i	−0.109788	+	0.109788i	−0.759867	−	0.650079i	$-0.774736\pi$
$911$	−3.31371	+	3.31371i	−0.109788	+	0.109788i	0.650079	+	0.759867i	$0.274736\pi$
$912$	−4.12132	+	4.12132i	−0.136471	+	0.136471i
$913$	−9.89949	−	9.89949i	−0.327625	−	0.327625i
$914$	−27.5563			−0.911483
$915$		0			0
$916$			16.2426i			0.536672i
$917$	11.6569			0.384943
$918$	−1.17157	−	1.24264i	−0.0386677	−	0.0410133i
$919$	−43.0122			−1.41884			−0.709421	−	0.704785i	$-0.751043\pi$
$919$	−43.0122			−1.41884			−0.709421	+	0.704785i	$0.751043\pi$
$920$		0			0
$921$	16.8995	+	16.8995i	0.556857	+	0.556857i
$922$	6.97056			0.229563
$923$	8.29289	+	8.29289i	0.272964	+	0.272964i
$924$	1.41421	−	1.41421i	0.0465242	−	0.0465242i
$925$		0			0
$926$			1.10051i			0.0361648i
$927$			6.62742i			0.217673i
$928$	6.94975	−	6.94975i	0.228137	−	0.228137i
$929$	13.4853	−	13.4853i	0.442438	−	0.442438i	−0.450393	−	0.892831i	$-0.648716\pi$
$929$	13.4853	−	13.4853i	0.442438	−	0.442438i	0.892831	+	0.450393i	$0.148716\pi$
$930$		0			0
$931$	16.0711			0.526708
$932$	−8.36396	−	8.36396i	−0.273971	−	0.273971i
$933$			8.82843i			0.289030i
$934$	25.2132			0.825001
$935$		0			0
$936$	−2.82843			−0.0924500
$937$		−	45.8406i		−	1.49755i	−0.662826	−	0.748774i	$-0.730643\pi$
$937$		−	45.8406i		−	1.49755i	0.662826	−	0.748774i	$-0.269357\pi$
$938$	−3.65685	−	3.65685i	−0.119401	−	0.119401i
$939$	22.1421			0.722581
$940$		0			0
$941$	−38.4056	+	38.4056i	−1.25199	+	1.25199i	−0.297158	+	0.954828i	$0.596039\pi$
$941$	−38.4056	+	38.4056i	−1.25199	+	1.25199i	−0.954828	+	0.297158i	$0.903961\pi$
$942$	−4.82843	+	4.82843i	−0.157319	+	0.157319i
$943$		−	29.8579i		−	0.972306i
$944$		−	10.8995i		−	0.354748i
$945$		0			0
$946$	10.2426	−	10.2426i	0.333017	−	0.333017i
$947$	14.7782	+	14.7782i	0.480226	+	0.480226i	0.905204	−	0.424978i	$-0.139718\pi$
$947$	14.7782	+	14.7782i	0.480226	+	0.480226i	−0.424978	+	0.905204i	$0.639718\pi$
$948$	28.1421			0.914014
$949$	5.53553	+	5.53553i	0.179691	+	0.179691i
$950$		0			0
$951$	−83.5980			−2.71085
$952$	−1.65685	−	1.75736i	−0.0536990	−	0.0569563i
$953$	20.5858			0.666839			0.333420	−	0.942779i	$-0.391797\pi$
$953$	20.5858			0.666839			0.333420	+	0.942779i	$0.391797\pi$
$954$		−	9.85786i		−	0.319160i
$955$		0			0
$956$	−27.4142			−0.886639
$957$	23.7279	+	23.7279i	0.767015	+	0.767015i
$958$	−19.0208	+	19.0208i	−0.614535	+	0.614535i
$959$	6.92893	−	6.92893i	0.223747	−	0.223747i
$960$		0			0
$961$		−	3.51472i		−	0.113378i
$962$	−1.58579	+	1.58579i	−0.0511278	+	0.0511278i
$963$	−24.9706	+	24.9706i	−0.804665	+	0.804665i
$964$	19.8284	+	19.8284i	0.638631	+	0.638631i
$965$		0			0
$966$	3.17157	+	3.17157i	0.102044	+	0.102044i
$967$			33.5980i			1.08044i	0.841524	+	0.540219i	$0.181659\pi$
$967$			33.5980i			1.08044i	−0.841524	+	0.540219i	$0.818341\pi$
$968$	9.00000			0.289271
$969$	−17.4853	+	16.4853i	−0.561708	+	0.529584i
$970$		0			0
$971$		−	22.0122i		−	0.706405i	−0.935547	−	0.353202i	$-0.885093\pi$
$971$		−	22.0122i		−	0.706405i	0.935547	−	0.353202i	$-0.114907\pi$
$972$	15.3137	+	15.3137i	0.491187	+	0.491187i
$973$	−0.544156			−0.0174448
$974$	−14.4142	−	14.4142i	−0.461861	−	0.461861i
$975$		0			0
$976$	−5.77817	+	5.77817i	−0.184955	+	0.184955i
$977$			34.2426i			1.09552i	0.836636	+	0.547760i	$0.184519\pi$
$977$			34.2426i			1.09552i	−0.836636	+	0.547760i	$0.815481\pi$
$978$			1.17157i			0.0374628i
$979$	14.6569	−	14.6569i	0.468435	−	0.468435i
$980$		0			0
$981$	−23.6569	−	23.6569i	−0.755305	−	0.755305i
$982$	8.27208			0.263973
$983$	8.07107	+	8.07107i	0.257427	+	0.257427i	0.824007	−	0.566580i	$-0.191734\pi$
$983$	8.07107	+	8.07107i	0.257427	+	0.257427i	−0.566580	+	0.824007i	$0.691734\pi$
$984$		−	22.7279i		−	0.724540i
$985$		0			0
$986$	29.4853	−	27.7990i	0.939003	−	0.885300i
$987$	4.58579			0.145967
$988$		−	2.41421i		−	0.0768064i
$989$	22.9706	+	22.9706i	0.730421	+	0.730421i
$990$		0			0
$991$	22.0919	+	22.0919i	0.701772	+	0.701772i	0.964791	−	0.263019i	$-0.0847182\pi$
$991$	22.0919	+	22.0919i	0.701772	+	0.701772i	−0.263019	+	0.964791i	$0.584718\pi$
$992$	3.70711	−	3.70711i	0.117701	−	0.117701i
$993$	−14.6066	+	14.6066i	−0.463526	+	0.463526i
$994$		−	6.87006i		−	0.217905i
$995$		0			0
$996$	16.8995	−	16.8995i	0.535481	−	0.535481i
$997$	−33.2843	+	33.2843i	−1.05412	+	1.05412i	−0.0556745	+	0.998449i	$0.517731\pi$
$997$	−33.2843	+	33.2843i	−1.05412	+	1.05412i	−0.998449	+	0.0556745i	$0.982269\pi$
$998$	−19.2426	−	19.2426i	−0.609115	−	0.609115i
$999$	0.928932			0.0293901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.g.251.1		4
5.2	odd	4		850.2.g.e.149.1		4
5.3	odd	4		850.2.g.h.149.2		4
5.4	even	2		170.2.h.a.81.2	yes	4
15.14	odd	2		1530.2.q.c.1441.1		4
17.4	even	4	inner	850.2.h.g.701.1		4
20.19	odd	2		1360.2.bt.a.81.1		4
85.4	even	4		170.2.h.a.21.2	✓	4
85.9	even	8		2890.2.b.j.2311.4		4
85.19	even	8		2890.2.a.v.1.2		2
85.38	odd	4		850.2.g.e.599.1		4
85.49	even	8		2890.2.a.t.1.1		2
85.59	even	8		2890.2.b.j.2311.1		4
85.72	odd	4		850.2.g.h.599.2		4
255.89	odd	4		1530.2.q.c.361.1		4
340.259	odd	4		1360.2.bt.a.1041.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.a.21.2	✓	4	85.4	even	4
170.2.h.a.81.2	yes	4	5.4	even	2
850.2.g.e.149.1		4	5.2	odd	4
850.2.g.e.599.1		4	85.38	odd	4
850.2.g.h.149.2		4	5.3	odd	4
850.2.g.h.599.2		4	85.72	odd	4
850.2.h.g.251.1		4	1.1	even	1	trivial
850.2.h.g.701.1		4	17.4	even	4	inner
1360.2.bt.a.81.1		4	20.19	odd	2
1360.2.bt.a.1041.1		4	340.259	odd	4
1530.2.q.c.361.1		4	255.89	odd	4
1530.2.q.c.1441.1		4	15.14	odd	2
2890.2.a.t.1.1		2	85.49	even	8
2890.2.a.v.1.2		2	85.19	even	8
2890.2.b.j.2311.1		4	85.59	even	8
2890.2.b.j.2311.4		4	85.9	even	8

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.70711 - 1.70711i) q^{3} -1.00000 q^{4} +(1.70711 - 1.70711i) q^{6} +(0.414214 - 0.414214i) q^{7} -1.00000i q^{8} +2.82843i q^{9} +(1.00000 - 1.00000i) q^{11} +(1.70711 + 1.70711i) q^{12} -1.00000 q^{13} +(0.414214 + 0.414214i) q^{14} +1.00000 q^{16} +(4.12132 + 0.121320i) q^{17} -2.82843 q^{18} -2.41421i q^{19} -1.41421 q^{21} +(1.00000 + 1.00000i) q^{22} +(-2.24264 + 2.24264i) q^{23} +(-1.70711 + 1.70711i) q^{24} -1.00000i q^{26} +(-0.292893 + 0.292893i) q^{27} +(-0.414214 + 0.414214i) q^{28} +(-6.94975 - 6.94975i) q^{29} +(-3.70711 - 3.70711i) q^{31} +1.00000i q^{32} -3.41421 q^{33} +(-0.121320 + 4.12132i) q^{34} -2.82843i q^{36} +(-1.58579 - 1.58579i) q^{37} +2.41421 q^{38} +(1.70711 + 1.70711i) q^{39} +(-6.65685 + 6.65685i) q^{41} -1.41421i q^{42} -10.2426i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-2.24264 - 2.24264i) q^{46} -3.24264 q^{47} +(-1.70711 - 1.70711i) q^{48} +6.65685i q^{49} +(-6.82843 - 7.24264i) q^{51} +1.00000 q^{52} +3.48528i q^{53} +(-0.292893 - 0.292893i) q^{54} +(-0.414214 - 0.414214i) q^{56} +(-4.12132 + 4.12132i) q^{57} +(6.94975 - 6.94975i) q^{58} -10.8995i q^{59} +(-5.77817 + 5.77817i) q^{61} +(3.70711 - 3.70711i) q^{62} +(1.17157 + 1.17157i) q^{63} -1.00000 q^{64} -3.41421i q^{66} -8.82843 q^{67} +(-4.12132 - 0.121320i) q^{68} +7.65685 q^{69} +(-8.29289 - 8.29289i) q^{71} +2.82843 q^{72} +(-5.53553 - 5.53553i) q^{73} +(1.58579 - 1.58579i) q^{74} +2.41421i q^{76} -0.828427i q^{77} +(-1.70711 + 1.70711i) q^{78} +(8.24264 - 8.24264i) q^{79} +9.48528 q^{81} +(-6.65685 - 6.65685i) q^{82} -9.89949i q^{83} +1.41421 q^{84} +10.2426 q^{86} +23.7279i q^{87} +(-1.00000 - 1.00000i) q^{88} +14.6569 q^{89} +(-0.414214 + 0.414214i) q^{91} +(2.24264 - 2.24264i) q^{92} +12.6569i q^{93} -3.24264i q^{94} +(1.70711 - 1.70711i) q^{96} +(-10.1213 - 10.1213i) q^{97} -6.65685 q^{98} +(2.82843 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{4} + 4 q^{6} - 4 q^{7} + 4 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{14} + 4 q^{16} + 8 q^{17} + 4 q^{22} + 8 q^{23} - 4 q^{24} - 4 q^{27} + 4 q^{28} - 8 q^{29} - 12 q^{31} - 8 q^{33} + 8 q^{34}+ \cdots - 4 q^{98}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^6 - 4 * q^7 + 4 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^14 + 4 * q^16 + 8 * q^17 + 4 * q^22 + 8 * q^23 - 4 * q^24 - 4 * q^27 + 4 * q^28 - 8 * q^29 - 12 * q^31 - 8 * q^33 + 8 * q^34 - 12 * q^37 + 4 * q^38 + 4 * q^39 - 4 * q^41 - 4 * q^44 + 8 * q^46 + 4 * q^47 - 4 * q^48 - 16 * q^51 + 4 * q^52 - 4 * q^54 + 4 * q^56 - 8 * q^57 + 8 * q^58 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 4 * q^64 - 24 * q^67 - 8 * q^68 + 8 * q^69 - 36 * q^71 - 8 * q^73 + 12 * q^74 - 4 * q^78 + 16 * q^79 + 4 * q^81 - 4 * q^82 + 24 * q^86 - 4 * q^88 + 36 * q^89 + 4 * q^91 - 8 * q^92 + 4 * q^96 - 32 * q^97 - 4 * q^98

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