LMFDB - Embedded newform 850.2.h.k.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(251,850)]

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

lf = mfeigenbasis(mf)

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")

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

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.k.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(0.292893 - 0.292893i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(0.292893 - 0.292893i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +(-1.58579 + 1.58579i) q^{11} +(-0.292893 - 0.292893i) q^{12} +3.00000 q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(3.53553 - 2.12132i) q^{17} -2.82843 q^{18} -7.24264i q^{19} -0.585786 q^{21} +(1.58579 + 1.58579i) q^{22} +(2.82843 - 2.82843i) q^{23} +(-0.292893 + 0.292893i) q^{24} -3.00000i q^{26} +(1.70711 - 1.70711i) q^{27} +(1.00000 - 1.00000i) q^{28} +(-0.707107 - 0.707107i) q^{29} +(-5.36396 - 5.36396i) q^{31} -1.00000i q^{32} -0.928932 q^{33} +(-2.12132 - 3.53553i) q^{34} +2.82843i q^{36} +(5.24264 + 5.24264i) q^{37} -7.24264 q^{38} +(0.878680 + 0.878680i) q^{39} +(4.41421 - 4.41421i) q^{41} +0.585786i q^{42} -3.75736i q^{43} +(1.58579 - 1.58579i) q^{44} +(-2.82843 - 2.82843i) q^{46} +1.58579 q^{47} +(0.292893 + 0.292893i) q^{48} +5.00000i q^{49} +(1.65685 + 0.414214i) q^{51} -3.00000 q^{52} +3.00000i q^{53} +(-1.70711 - 1.70711i) q^{54} +(-1.00000 - 1.00000i) q^{56} +(2.12132 - 2.12132i) q^{57} +(-0.707107 + 0.707107i) q^{58} -12.8995i q^{59} +(6.12132 - 6.12132i) q^{61} +(-5.36396 + 5.36396i) q^{62} +(2.82843 + 2.82843i) q^{63} -1.00000 q^{64} +0.928932i q^{66} -14.4853 q^{67} +(-3.53553 + 2.12132i) q^{68} +1.65685 q^{69} +(3.70711 + 3.70711i) q^{71} +2.82843 q^{72} +(8.36396 + 8.36396i) q^{73} +(5.24264 - 5.24264i) q^{74} +7.24264i q^{76} -3.17157i q^{77} +(0.878680 - 0.878680i) q^{78} +(0.242641 - 0.242641i) q^{79} -7.48528 q^{81} +(-4.41421 - 4.41421i) q^{82} -4.24264i q^{83} +0.585786 q^{84} -3.75736 q^{86} -0.414214i q^{87} +(-1.58579 - 1.58579i) q^{88} -11.4853 q^{89} +(-3.00000 + 3.00000i) q^{91} +(-2.82843 + 2.82843i) q^{92} -3.14214i q^{93} -1.58579i q^{94} +(0.292893 - 0.292893i) q^{96} +(0.121320 + 0.121320i) q^{97} +5.00000 q^{98} +(4.48528 + 4.48528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} - 4 q^{7}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 - 4 * q^7	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} - 4 q^{7} - 12 q^{11} - 4 q^{12} + 12 q^{13} + 4 q^{14} + 4 q^{16} - 8 q^{21} + 12 q^{22} - 4 q^{24} + 4 q^{27} + 4 q^{28} + 4 q^{31} - 32 q^{33} + 4 q^{37} - 12 q^{38} + 12 q^{39} + 12 q^{41} + 12 q^{44} + 12 q^{47} + 4 q^{48} - 16 q^{51} - 12 q^{52} - 4 q^{54} - 4 q^{56} + 16 q^{61} + 4 q^{62} - 4 q^{64} - 24 q^{67} - 16 q^{69} + 12 q^{71} + 8 q^{73} + 4 q^{74} + 12 q^{78} - 16 q^{79} + 4 q^{81} - 12 q^{82} + 8 q^{84} - 32 q^{86} - 12 q^{88} - 12 q^{89} - 12 q^{91} + 4 q^{96} - 8 q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 - 4 * q^7 - 12 * q^11 - 4 * q^12 + 12 * q^13 + 4 * q^14 + 4 * q^16 - 8 * q^21 + 12 * q^22 - 4 * q^24 + 4 * q^27 + 4 * q^28 + 4 * q^31 - 32 * q^33 + 4 * q^37 - 12 * q^38 + 12 * q^39 + 12 * q^41 + 12 * q^44 + 12 * q^47 + 4 * q^48 - 16 * q^51 - 12 * q^52 - 4 * q^54 - 4 * q^56 + 16 * q^61 + 4 * q^62 - 4 * q^64 - 24 * q^67 - 16 * q^69 + 12 * q^71 + 8 * q^73 + 4 * q^74 + 12 * q^78 - 16 * q^79 + 4 * q^81 - 12 * q^82 + 8 * q^84 - 32 * q^86 - 12 * q^88 - 12 * q^89 - 12 * q^91 + 4 * q^96 - 8 * q^97 + 20 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

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
$3$	0.292893	+	0.292893i	0.169102	+	0.169102i	0.786585	−	0.617483i	$-0.211847\pi$
$3$	0.292893	+	0.292893i	0.169102	+	0.169102i	−0.617483	+	0.786585i	$0.711847\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	0.292893	−	0.292893i	0.119573	−	0.119573i
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$			1.00000i			0.353553i
$9$		−	2.82843i		−	0.942809i
$10$		0			0
$11$	−1.58579	+	1.58579i	−0.478133	+	0.478133i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−1.58579	+	1.58579i	−0.478133	+	0.478133i	0.426401	+	0.904534i	$0.359781\pi$
$12$	−0.292893	−	0.292893i	−0.0845510	−	0.0845510i
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.53553	−	2.12132i	0.857493	−	0.514496i
$17$	3.53553	−	2.12132i	0.857493	−	0.514496i
$18$	−2.82843			−0.666667
$19$		−	7.24264i		−	1.66158i	−0.556589	−	0.830788i	$-0.687890\pi$
$19$		−	7.24264i		−	1.66158i	0.556589	−	0.830788i	$-0.312110\pi$
$20$		0			0
$21$	−0.585786			−0.127829
$22$	1.58579	+	1.58579i	0.338091	+	0.338091i
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	−0.347801	−	0.937568i	$-0.613071\pi$
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	0.937568	+	0.347801i	$0.113071\pi$
$24$	−0.292893	+	0.292893i	−0.0597866	+	0.0597866i
$25$		0			0
$26$		−	3.00000i		−	0.588348i
$27$	1.70711	−	1.70711i	0.328533	−	0.328533i
$28$	1.00000	−	1.00000i	0.188982	−	0.188982i
$29$	−0.707107	−	0.707107i	−0.131306	−	0.131306i	0.638399	−	0.769706i	$-0.279597\pi$
$29$	−0.707107	−	0.707107i	−0.131306	−	0.131306i	−0.769706	+	0.638399i	$0.779597\pi$
$30$		0			0
$31$	−5.36396	−	5.36396i	−0.963396	−	0.963396i	0.0359575	−	0.999353i	$-0.488552\pi$
$31$	−5.36396	−	5.36396i	−0.963396	−	0.963396i	−0.999353	+	0.0359575i	$0.988552\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.928932			−0.161706
$34$	−2.12132	−	3.53553i	−0.363803	−	0.606339i
$35$		0			0
$36$			2.82843i			0.471405i
$37$	5.24264	+	5.24264i	0.861885	+	0.861885i	0.991557	−	0.129672i	$-0.0413925\pi$
$37$	5.24264	+	5.24264i	0.861885	+	0.861885i	−0.129672	+	0.991557i	$0.541392\pi$
$38$	−7.24264			−1.17491
$39$	0.878680	+	0.878680i	0.140701	+	0.140701i
$40$		0			0
$41$	4.41421	−	4.41421i	0.689384	−	0.689384i	−0.272712	−	0.962096i	$-0.587920\pi$
$41$	4.41421	−	4.41421i	0.689384	−	0.689384i	0.962096	+	0.272712i	$0.0879205\pi$
$42$			0.585786i			0.0903888i
$43$		−	3.75736i		−	0.572992i	−0.958081	−	0.286496i	$-0.907509\pi$
$43$		−	3.75736i		−	0.572992i	0.958081	−	0.286496i	$-0.0924905\pi$
$44$	1.58579	−	1.58579i	0.239066	−	0.239066i
$45$		0			0
$46$	−2.82843	−	2.82843i	−0.417029	−	0.417029i
$47$	1.58579			0.231311			0.115655	−	0.993289i	$-0.463103\pi$
$47$	1.58579			0.231311			0.115655	+	0.993289i	$0.463103\pi$
$48$	0.292893	+	0.292893i	0.0422755	+	0.0422755i
$49$			5.00000i			0.714286i
$50$		0			0
$51$	1.65685	+	0.414214i	0.232006	+	0.0580015i
$52$	−3.00000			−0.416025
$53$			3.00000i			0.412082i	0.978543	+	0.206041i	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$	−1.70711	−	1.70711i	−0.232308	−	0.232308i
$55$		0			0
$56$	−1.00000	−	1.00000i	−0.133631	−	0.133631i
$57$	2.12132	−	2.12132i	0.280976	−	0.280976i
$58$	−0.707107	+	0.707107i	−0.0928477	+	0.0928477i
$59$		−	12.8995i		−	1.67937i	−0.543073	−	0.839686i	$-0.682739\pi$
$59$		−	12.8995i		−	1.67937i	0.543073	−	0.839686i	$-0.317261\pi$
$60$		0			0
$61$	6.12132	−	6.12132i	0.783755	−	0.783755i	−0.196707	−	0.980462i	$-0.563025\pi$
$61$	6.12132	−	6.12132i	0.783755	−	0.783755i	0.980462	+	0.196707i	$0.0630249\pi$
$62$	−5.36396	+	5.36396i	−0.681224	+	0.681224i
$63$	2.82843	+	2.82843i	0.356348	+	0.356348i
$64$	−1.00000			−0.125000
$65$		0			0
$66$			0.928932i			0.114344i
$67$	−14.4853			−1.76966			−0.884829	−	0.465915i	$-0.845725\pi$
$67$	−14.4853			−1.76966			−0.884829	+	0.465915i	$0.845725\pi$
$68$	−3.53553	+	2.12132i	−0.428746	+	0.257248i
$69$	1.65685			0.199462
$70$		0			0
$71$	3.70711	+	3.70711i	0.439953	+	0.439953i	0.891996	−	0.452043i	$-0.149305\pi$
$71$	3.70711	+	3.70711i	0.439953	+	0.439953i	−0.452043	+	0.891996i	$0.649305\pi$
$72$	2.82843			0.333333
$73$	8.36396	+	8.36396i	0.978928	+	0.978928i	0.999783	−	0.0208549i	$-0.00663881\pi$
$73$	8.36396	+	8.36396i	0.978928	+	0.978928i	−0.0208549	+	0.999783i	$0.506639\pi$
$74$	5.24264	−	5.24264i	0.609445	−	0.609445i
$75$		0			0
$76$			7.24264i			0.830788i
$77$		−	3.17157i		−	0.361434i
$78$	0.878680	−	0.878680i	0.0994909	−	0.0994909i
$79$	0.242641	−	0.242641i	0.0272992	−	0.0272992i	−0.693325	−	0.720625i	$-0.743855\pi$
$79$	0.242641	−	0.242641i	0.0272992	−	0.0272992i	0.720625	+	0.693325i	$0.243855\pi$
$80$		0			0
$81$	−7.48528			−0.831698
$82$	−4.41421	−	4.41421i	−0.487468	−	0.487468i
$83$		−	4.24264i		−	0.465690i	−0.972514	−	0.232845i	$-0.925196\pi$
$83$		−	4.24264i		−	0.465690i	0.972514	−	0.232845i	$-0.0748035\pi$
$84$	0.585786			0.0639145
$85$		0			0
$86$	−3.75736			−0.405166
$87$		−	0.414214i		−	0.0444084i
$88$	−1.58579	−	1.58579i	−0.169045	−	0.169045i
$89$	−11.4853			−1.21744			−0.608719	−	0.793386i	$-0.708316\pi$
$89$	−11.4853			−1.21744			−0.608719	+	0.793386i	$0.708316\pi$
$90$		0			0
$91$	−3.00000	+	3.00000i	−0.314485	+	0.314485i
$92$	−2.82843	+	2.82843i	−0.294884	+	0.294884i
$93$		−	3.14214i		−	0.325824i
$94$		−	1.58579i		−	0.163561i
$95$		0			0
$96$	0.292893	−	0.292893i	0.0298933	−	0.0298933i
$97$	0.121320	+	0.121320i	0.0123182	+	0.0123182i	0.713239	−	0.700921i	$-0.247227\pi$
$97$	0.121320	+	0.121320i	0.0123182	+	0.0123182i	−0.700921	+	0.713239i	$0.747227\pi$
$98$	5.00000			0.505076
$99$	4.48528	+	4.48528i	0.450788	+	0.450788i
$100$		0			0
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	0.414214	−	1.65685i	0.0410133	−	0.164053i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$			3.00000i			0.294174i
$105$		0			0
$106$	3.00000			0.291386
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	0.557047	−	0.830481i	$-0.311934\pi$
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	−0.830481	+	0.557047i	$0.811934\pi$
$108$	−1.70711	+	1.70711i	−0.164266	+	0.164266i
$109$	−8.60660	+	8.60660i	−0.824363	+	0.824363i	−0.986730	−	0.162367i	$-0.948087\pi$
$109$	−8.60660	+	8.60660i	−0.824363	+	0.824363i	0.162367	+	0.986730i	$0.448087\pi$
$110$		0			0
$111$			3.07107i			0.291493i
$112$	−1.00000	+	1.00000i	−0.0944911	+	0.0944911i
$113$	2.46447	−	2.46447i	0.231837	−	0.231837i	−0.581622	−	0.813459i	$-0.697582\pi$
$113$	2.46447	−	2.46447i	0.231837	−	0.231837i	0.813459	+	0.581622i	$0.197582\pi$
$114$	−2.12132	−	2.12132i	−0.198680	−	0.198680i
$115$		0			0
$116$	0.707107	+	0.707107i	0.0656532	+	0.0656532i
$117$		−	8.48528i		−	0.784465i
$118$	−12.8995			−1.18749
$119$	−1.41421	+	5.65685i	−0.129641	+	0.518563i
$120$		0			0
$121$			5.97056i			0.542778i
$122$	−6.12132	−	6.12132i	−0.554198	−	0.554198i
$123$	2.58579			0.233153
$124$	5.36396	+	5.36396i	0.481698	+	0.481698i
$125$		0			0
$126$	2.82843	−	2.82843i	0.251976	−	0.251976i
$127$			17.7279i			1.57310i	0.617527	+	0.786549i	$0.288134\pi$
$127$			17.7279i			1.57310i	−0.617527	+	0.786549i	$0.711866\pi$
$128$			1.00000i			0.0883883i
$129$	1.10051	−	1.10051i	0.0968941	−	0.0968941i
$130$		0			0
$131$	7.58579	+	7.58579i	0.662773	+	0.662773i	0.956033	−	0.293260i	$-0.0947400\pi$
$131$	7.58579	+	7.58579i	0.662773	+	0.662773i	−0.293260	+	0.956033i	$0.594740\pi$
$132$	0.928932			0.0808532
$133$	7.24264	+	7.24264i	0.628017	+	0.628017i
$134$			14.4853i			1.25134i
$135$		0			0
$136$	2.12132	+	3.53553i	0.181902	+	0.303170i
$137$	4.58579			0.391790			0.195895	−	0.980625i	$-0.437239\pi$
$137$	4.58579			0.391790			0.195895	+	0.980625i	$0.437239\pi$
$138$		−	1.65685i		−	0.141041i
$139$	11.0000	+	11.0000i	0.933008	+	0.933008i	0.997893	−	0.0648849i	$-0.0206680\pi$
$139$	11.0000	+	11.0000i	0.933008	+	0.933008i	−0.0648849	+	0.997893i	$0.520668\pi$
$140$		0			0
$141$	0.464466	+	0.464466i	0.0391151	+	0.0391151i
$142$	3.70711	−	3.70711i	0.311093	−	0.311093i
$143$	−4.75736	+	4.75736i	−0.397830	+	0.397830i
$144$		−	2.82843i		−	0.235702i
$145$		0			0
$146$	8.36396	−	8.36396i	0.692206	−	0.692206i
$147$	−1.46447	+	1.46447i	−0.120787	+	0.120787i
$148$	−5.24264	−	5.24264i	−0.430942	−	0.430942i
$149$	12.7279			1.04271			0.521356	−	0.853339i	$-0.325426\pi$
$149$	12.7279			1.04271			0.521356	+	0.853339i	$0.325426\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	7.24264			0.587456
$153$	−6.00000	−	10.0000i	−0.485071	−	0.808452i
$154$	−3.17157			−0.255573
$155$		0			0
$156$	−0.878680	−	0.878680i	−0.0703507	−	0.0703507i
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$	−0.242641	−	0.242641i	−0.0193035	−	0.0193035i
$159$	−0.878680	+	0.878680i	−0.0696838	+	0.0696838i
$160$		0			0
$161$			5.65685i			0.445823i
$162$			7.48528i			0.588099i
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	−0.860598	−	0.509284i	$-0.829910\pi$
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	0.509284	+	0.860598i	$0.329910\pi$
$164$	−4.41421	+	4.41421i	−0.344692	+	0.344692i
$165$		0			0
$166$	−4.24264			−0.329293
$167$	−1.07107	−	1.07107i	−0.0828817	−	0.0828817i	0.664451	−	0.747332i	$-0.268666\pi$
$167$	−1.07107	−	1.07107i	−0.0828817	−	0.0828817i	−0.747332	+	0.664451i	$0.768666\pi$
$168$		−	0.585786i		−	0.0451944i
$169$	−4.00000			−0.307692
$170$		0			0
$171$	−20.4853			−1.56655
$172$			3.75736i			0.286496i
$173$	−17.6569	−	17.6569i	−1.34243	−	1.34243i	−0.893639	−	0.448787i	$-0.851856\pi$
$173$	−17.6569	−	17.6569i	−1.34243	−	1.34243i	−0.448787	−	0.893639i	$-0.648144\pi$
$174$	−0.414214			−0.0314014
$175$		0			0
$176$	−1.58579	+	1.58579i	−0.119533	+	0.119533i
$177$	3.77817	−	3.77817i	0.283985	−	0.283985i
$178$			11.4853i			0.860858i
$179$		−	0.686292i		−	0.0512958i	−0.999671	−	0.0256479i	$-0.991835\pi$
$179$		−	0.686292i		−	0.0512958i	0.999671	−	0.0256479i	$-0.00816488\pi$
$180$		0			0
$181$	−14.0000	+	14.0000i	−1.04061	+	1.04061i	−0.0414721	+	0.999140i	$0.513205\pi$
$181$	−14.0000	+	14.0000i	−1.04061	+	1.04061i	−0.999140	+	0.0414721i	$0.986795\pi$
$182$	3.00000	+	3.00000i	0.222375	+	0.222375i
$183$	3.58579			0.265069
$184$	2.82843	+	2.82843i	0.208514	+	0.208514i
$185$		0			0
$186$	−3.14214			−0.230393
$187$	−2.24264	+	8.97056i	−0.163998	+	0.655993i
$188$	−1.58579			−0.115655
$189$			3.41421i			0.248347i
$190$		0			0
$191$	21.2132			1.53493			0.767467	−	0.641089i	$-0.221517\pi$
$191$	21.2132			1.53493			0.767467	+	0.641089i	$0.221517\pi$
$192$	−0.292893	−	0.292893i	−0.0211377	−	0.0211377i
$193$	18.4853	−	18.4853i	1.33060	−	1.33060i	0.425767	−	0.904833i	$-0.360004\pi$
$193$	18.4853	−	18.4853i	1.33060	−	1.33060i	0.904833	−	0.425767i	$-0.139996\pi$
$194$	0.121320	−	0.121320i	0.00871029	−	0.00871029i
$195$		0			0
$196$		−	5.00000i		−	0.357143i
$197$	−3.34315	+	3.34315i	−0.238189	+	0.238189i	−0.816100	−	0.577911i	$-0.803868\pi$
$197$	−3.34315	+	3.34315i	−0.238189	+	0.238189i	0.577911	+	0.816100i	$0.303868\pi$
$198$	4.48528	−	4.48528i	0.318755	−	0.318755i
$199$	7.12132	+	7.12132i	0.504817	+	0.504817i	0.912931	−	0.408114i	$-0.133813\pi$
$199$	7.12132	+	7.12132i	0.504817	+	0.504817i	−0.408114	+	0.912931i	$0.633813\pi$
$200$		0			0
$201$	−4.24264	−	4.24264i	−0.299253	−	0.299253i
$202$		0			0
$203$	1.41421			0.0992583
$204$	−1.65685	−	0.414214i	−0.116003	−	0.0290008i
$205$		0			0
$206$		0			0
$207$	−8.00000	−	8.00000i	−0.556038	−	0.556038i
$208$	3.00000			0.208013
$209$	11.4853	+	11.4853i	0.794454	+	0.794454i
$210$		0			0
$211$	−8.00000	+	8.00000i	−0.550743	+	0.550743i	−0.926655	−	0.375912i	$-0.877329\pi$
$211$	−8.00000	+	8.00000i	−0.550743	+	0.550743i	0.375912	+	0.926655i	$0.377329\pi$
$212$		−	3.00000i		−	0.206041i
$213$			2.17157i			0.148794i
$214$	−2.82843	+	2.82843i	−0.193347	+	0.193347i
$215$		0			0
$216$	1.70711	+	1.70711i	0.116154	+	0.116154i
$217$	10.7279			0.728259
$218$	8.60660	+	8.60660i	0.582913	+	0.582913i
$219$			4.89949i			0.331077i
$220$		0			0
$221$	10.6066	−	6.36396i	0.713477	−	0.428086i
$222$	3.07107			0.206117
$223$			23.2426i			1.55644i	0.627990	+	0.778221i	$0.283878\pi$
$223$			23.2426i			1.55644i	−0.627990	+	0.778221i	$0.716122\pi$
$224$	1.00000	+	1.00000i	0.0668153	+	0.0668153i
$225$		0			0
$226$	−2.46447	−	2.46447i	−0.163934	−	0.163934i
$227$	4.05025	−	4.05025i	0.268825	−	0.268825i	−0.559802	−	0.828627i	$-0.689123\pi$
$227$	4.05025	−	4.05025i	0.268825	−	0.268825i	0.828627	+	0.559802i	$0.189123\pi$
$228$	−2.12132	+	2.12132i	−0.140488	+	0.140488i
$229$		−	7.75736i		−	0.512621i	−0.966595	−	0.256310i	$-0.917493\pi$
$229$		−	7.75736i		−	0.512621i	0.966595	−	0.256310i	$-0.0825069\pi$
$230$		0			0
$231$	0.928932	−	0.928932i	0.0611193	−	0.0611193i
$232$	0.707107	−	0.707107i	0.0464238	−	0.0464238i
$233$	10.9497	+	10.9497i	0.717342	+	0.717342i	0.968060	−	0.250718i	$-0.0806668\pi$
$233$	10.9497	+	10.9497i	0.717342	+	0.717342i	−0.250718	+	0.968060i	$0.580667\pi$
$234$	−8.48528			−0.554700
$235$		0			0
$236$			12.8995i			0.839686i
$237$	0.142136			0.00923270
$238$	5.65685	+	1.41421i	0.366679	+	0.0916698i
$239$	−22.2426			−1.43876			−0.719378	−	0.694618i	$-0.755573\pi$
$239$	−22.2426			−1.43876			−0.719378	+	0.694618i	$0.755573\pi$
$240$		0			0
$241$	2.75736	+	2.75736i	0.177617	+	0.177617i	0.790316	−	0.612699i	$-0.209916\pi$
$241$	2.75736	+	2.75736i	0.177617	+	0.177617i	−0.612699	+	0.790316i	$0.709916\pi$
$242$	5.97056			0.383802
$243$	−7.31371	−	7.31371i	−0.469175	−	0.469175i
$244$	−6.12132	+	6.12132i	−0.391877	+	0.391877i
$245$		0			0
$246$		−	2.58579i		−	0.164864i
$247$		−	21.7279i		−	1.38251i
$248$	5.36396	−	5.36396i	0.340612	−	0.340612i
$249$	1.24264	−	1.24264i	0.0787492	−	0.0787492i
$250$		0			0
$251$	20.4853			1.29302			0.646510	−	0.762906i	$-0.276228\pi$
$251$	20.4853			1.29302			0.646510	+	0.762906i	$0.276228\pi$
$252$	−2.82843	−	2.82843i	−0.178174	−	0.178174i
$253$			8.97056i			0.563974i
$254$	17.7279			1.11235
$255$		0			0
$256$	1.00000			0.0625000
$257$			6.72792i			0.419676i	0.977736	+	0.209838i	$0.0672937\pi$
$257$			6.72792i			0.419676i	−0.977736	+	0.209838i	$0.932706\pi$
$258$	−1.10051	−	1.10051i	−0.0685145	−	0.0685145i
$259$	−10.4853			−0.651524
$260$		0			0
$261$	−2.00000	+	2.00000i	−0.123797	+	0.123797i
$262$	7.58579	−	7.58579i	0.468651	−	0.468651i
$263$		−	4.75736i		−	0.293351i	−0.989185	−	0.146676i	$-0.953143\pi$
$263$		−	4.75736i		−	0.293351i	0.989185	−	0.146676i	$-0.0468574\pi$
$264$		−	0.928932i		−	0.0571718i
$265$		0			0
$266$	7.24264	−	7.24264i	0.444075	−	0.444075i
$267$	−3.36396	−	3.36396i	−0.205871	−	0.205871i
$268$	14.4853			0.884829
$269$	11.2929	+	11.2929i	0.688540	+	0.688540i	0.961909	−	0.273369i	$-0.0881381\pi$
$269$	11.2929	+	11.2929i	0.688540	+	0.688540i	−0.273369	+	0.961909i	$0.588138\pi$
$270$		0			0
$271$	−6.48528			−0.393953			−0.196976	−	0.980408i	$-0.563112\pi$
$271$	−6.48528			−0.393953			−0.196976	+	0.980408i	$0.563112\pi$
$272$	3.53553	−	2.12132i	0.214373	−	0.128624i
$273$	−1.75736			−0.106360
$274$		−	4.58579i		−	0.277037i
$275$		0			0
$276$	−1.65685			−0.0997309
$277$	8.24264	+	8.24264i	0.495252	+	0.495252i	0.909956	−	0.414704i	$-0.136115\pi$
$277$	8.24264	+	8.24264i	0.495252	+	0.495252i	−0.414704	+	0.909956i	$0.636115\pi$
$278$	11.0000	−	11.0000i	0.659736	−	0.659736i
$279$	−15.1716	+	15.1716i	−0.908298	+	0.908298i
$280$		0			0
$281$		−	3.34315i		−	0.199435i	−0.995016	−	0.0997177i	$-0.968206\pi$
$281$		−	3.34315i		−	0.199435i	0.995016	−	0.0997177i	$-0.0317940\pi$
$282$	0.464466	−	0.464466i	0.0276586	−	0.0276586i
$283$	−19.1213	+	19.1213i	−1.13664	+	1.13664i	−0.147597	+	0.989048i	$0.547154\pi$
$283$	−19.1213	+	19.1213i	−1.13664	+	1.13664i	−0.989048	+	0.147597i	$0.952846\pi$
$284$	−3.70711	−	3.70711i	−0.219976	−	0.219976i
$285$		0			0
$286$	4.75736	+	4.75736i	0.281309	+	0.281309i
$287$			8.82843i			0.521126i
$288$	−2.82843			−0.166667
$289$	8.00000	−	15.0000i	0.470588	−	0.882353i
$290$		0			0
$291$			0.0710678i			0.00416607i
$292$	−8.36396	−	8.36396i	−0.489464	−	0.489464i
$293$	20.6569			1.20679			0.603393	−	0.797444i	$-0.293815\pi$
$293$	20.6569			1.20679			0.603393	+	0.797444i	$0.293815\pi$
$294$	1.46447	+	1.46447i	0.0854094	+	0.0854094i
$295$		0			0
$296$	−5.24264	+	5.24264i	−0.304722	+	0.304722i
$297$			5.41421i			0.314165i
$298$		−	12.7279i		−	0.737309i
$299$	8.48528	−	8.48528i	0.490716	−	0.490716i
$300$		0			0
$301$	3.75736	+	3.75736i	0.216571	+	0.216571i
$302$	−12.0000			−0.690522
$303$		0			0
$304$		−	7.24264i		−	0.415394i
$305$		0			0
$306$	−10.0000	+	6.00000i	−0.571662	+	0.342997i
$307$	−33.2132			−1.89558			−0.947789	−	0.318899i	$-0.896687\pi$
$307$	−33.2132			−1.89558			−0.947789	+	0.318899i	$0.896687\pi$
$308$			3.17157i			0.180717i
$309$		0			0
$310$		0			0
$311$	−1.41421	−	1.41421i	−0.0801927	−	0.0801927i	0.665873	−	0.746065i	$-0.268059\pi$
$311$	−1.41421	−	1.41421i	−0.0801927	−	0.0801927i	−0.746065	+	0.665873i	$0.768059\pi$
$312$	−0.878680	+	0.878680i	−0.0497454	+	0.0497454i
$313$	−22.4853	+	22.4853i	−1.27094	+	1.27094i	−0.325349	+	0.945594i	$0.605482\pi$
$313$	−22.4853	+	22.4853i	−1.27094	+	1.27094i	−0.945594	+	0.325349i	$0.894518\pi$
$314$		−	12.0000i		−	0.677199i
$315$		0			0
$316$	−0.242641	+	0.242641i	−0.0136496	+	0.0136496i
$317$	14.1421	−	14.1421i	0.794301	−	0.794301i	−0.187889	−	0.982190i	$-0.560164\pi$
$317$	14.1421	−	14.1421i	0.794301	−	0.794301i	0.982190	+	0.187889i	$0.0601645\pi$
$318$	0.878680	+	0.878680i	0.0492739	+	0.0492739i
$319$	2.24264			0.125564
$320$		0			0
$321$		−	1.65685i		−	0.0924766i
$322$	5.65685			0.315244
$323$	−15.3640	−	25.6066i	−0.854874	−	1.42479i
$324$	7.48528			0.415849
$325$		0			0
$326$	4.48528	+	4.48528i	0.248417	+	0.248417i
$327$	−5.04163			−0.278803
$328$	4.41421	+	4.41421i	0.243734	+	0.243734i
$329$	−1.58579	+	1.58579i	−0.0874272	+	0.0874272i
$330$		0			0
$331$		−	15.7279i		−	0.864485i	−0.901757	−	0.432242i	$-0.857722\pi$
$331$		−	15.7279i		−	0.864485i	0.901757	−	0.432242i	$-0.142278\pi$
$332$			4.24264i			0.232845i
$333$	14.8284	−	14.8284i	0.812593	−	0.812593i
$334$	−1.07107	+	1.07107i	−0.0586062	+	0.0586062i
$335$		0			0
$336$	−0.585786			−0.0319573
$337$	12.8492	+	12.8492i	0.699943	+	0.699943i	0.964398	−	0.264455i	$-0.0851921\pi$
$337$	12.8492	+	12.8492i	0.699943	+	0.699943i	−0.264455	+	0.964398i	$0.585192\pi$
$338$			4.00000i			0.217571i
$339$	1.44365			0.0784083
$340$		0			0
$341$	17.0122			0.921262
$342$			20.4853i			1.10772i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	3.75736			0.202583
$345$		0			0
$346$	−17.6569	+	17.6569i	−0.949238	+	0.949238i
$347$	−15.7071	+	15.7071i	−0.843202	+	0.843202i	−0.989274	−	0.146072i	$-0.953337\pi$
$347$	−15.7071	+	15.7071i	−0.843202	+	0.843202i	0.146072	+	0.989274i	$0.453337\pi$
$348$			0.414214i			0.0222042i
$349$		−	10.9706i		−	0.587241i	−0.955922	−	0.293620i	$-0.905140\pi$
$349$		−	10.9706i		−	0.587241i	0.955922	−	0.293620i	$-0.0948602\pi$
$350$		0			0
$351$	5.12132	−	5.12132i	0.273356	−	0.273356i
$352$	1.58579	+	1.58579i	0.0845227	+	0.0845227i
$353$	−11.3137			−0.602168			−0.301084	−	0.953598i	$-0.597348\pi$
$353$	−11.3137			−0.602168			−0.301084	+	0.953598i	$0.597348\pi$
$354$	−3.77817	−	3.77817i	−0.200808	−	0.200808i
$355$		0			0
$356$	11.4853			0.608719
$357$	−2.07107	+	1.24264i	−0.109613	+	0.0657675i
$358$	−0.686292			−0.0362716
$359$			7.07107i			0.373197i	0.982436	+	0.186598i	$0.0597463\pi$
$359$			7.07107i			0.373197i	−0.982436	+	0.186598i	$0.940254\pi$
$360$		0			0
$361$	−33.4558			−1.76083
$362$	14.0000	+	14.0000i	0.735824	+	0.735824i
$363$	−1.74874	+	1.74874i	−0.0917849	+	0.0917849i
$364$	3.00000	−	3.00000i	0.157243	−	0.157243i
$365$		0			0
$366$		−	3.58579i		−	0.187432i
$367$	18.2426	−	18.2426i	0.952258	−	0.952258i	−0.0466531	−	0.998911i	$-0.514856\pi$
$367$	18.2426	−	18.2426i	0.952258	−	0.952258i	0.998911	+	0.0466531i	$0.0148555\pi$
$368$	2.82843	−	2.82843i	0.147442	−	0.147442i
$369$	−12.4853	−	12.4853i	−0.649958	−	0.649958i
$370$		0			0
$371$	−3.00000	−	3.00000i	−0.155752	−	0.155752i
$372$			3.14214i			0.162912i
$373$	−32.4853			−1.68202			−0.841012	−	0.541016i	$-0.818040\pi$
$373$	−32.4853			−1.68202			−0.841012	+	0.541016i	$0.818040\pi$
$374$	8.97056	+	2.24264i	0.463857	+	0.115964i
$375$		0			0
$376$			1.58579i			0.0817807i
$377$	−2.12132	−	2.12132i	−0.109254	−	0.109254i
$378$	3.41421			0.175608
$379$	−0.485281	−	0.485281i	−0.0249272	−	0.0249272i	0.694533	−	0.719461i	$-0.255611\pi$
$379$	−0.485281	−	0.485281i	−0.0249272	−	0.0249272i	−0.719461	+	0.694533i	$0.755611\pi$
$380$		0			0
$381$	−5.19239	+	5.19239i	−0.266014	+	0.266014i
$382$		−	21.2132i		−	1.08536i
$383$			13.2426i			0.676667i	0.941026	+	0.338334i	$0.109863\pi$
$383$			13.2426i			0.676667i	−0.941026	+	0.338334i	$0.890137\pi$
$384$	−0.292893	+	0.292893i	−0.0149466	+	0.0149466i
$385$		0			0
$386$	−18.4853	−	18.4853i	−0.940876	−	0.940876i
$387$	−10.6274			−0.540222
$388$	−0.121320	−	0.121320i	−0.00615911	−	0.00615911i
$389$		−	16.6274i		−	0.843044i	−0.906818	−	0.421522i	$-0.861496\pi$
$389$		−	16.6274i		−	0.843044i	0.906818	−	0.421522i	$-0.138504\pi$
$390$		0			0
$391$	4.00000	−	16.0000i	0.202289	−	0.809155i
$392$	−5.00000			−0.252538
$393$			4.44365i			0.224153i
$394$	3.34315	+	3.34315i	0.168425	+	0.168425i
$395$		0			0
$396$	−4.48528	−	4.48528i	−0.225394	−	0.225394i
$397$	−4.72792	+	4.72792i	−0.237288	+	0.237288i	−0.815726	−	0.578438i	$-0.803662\pi$
$397$	−4.72792	+	4.72792i	−0.237288	+	0.237288i	0.578438	+	0.815726i	$0.303662\pi$
$398$	7.12132	−	7.12132i	0.356960	−	0.356960i
$399$			4.24264i			0.212398i
$400$		0			0
$401$	−2.10051	+	2.10051i	−0.104894	+	0.104894i	−0.757606	−	0.652712i	$-0.773631\pi$
$401$	−2.10051	+	2.10051i	−0.104894	+	0.104894i	0.652712	+	0.757606i	$0.273631\pi$
$402$	−4.24264	+	4.24264i	−0.211604	+	0.211604i
$403$	−16.0919	−	16.0919i	−0.801594	−	0.801594i
$404$		0			0
$405$		0			0
$406$		−	1.41421i		−	0.0701862i
$407$	−16.6274			−0.824190
$408$	−0.414214	+	1.65685i	−0.0205066	+	0.0820265i
$409$	−25.4853			−1.26017			−0.630083	−	0.776528i	$-0.716979\pi$
$409$	−25.4853			−1.26017			−0.630083	+	0.776528i	$0.716979\pi$
$410$		0			0
$411$	1.34315	+	1.34315i	0.0662525	+	0.0662525i
$412$		0			0
$413$	12.8995	+	12.8995i	0.634743	+	0.634743i
$414$	−8.00000	+	8.00000i	−0.393179	+	0.393179i
$415$		0			0
$416$		−	3.00000i		−	0.147087i
$417$			6.44365i			0.315547i
$418$	11.4853	−	11.4853i	0.561763	−	0.561763i
$419$	11.3137	−	11.3137i	0.552711	−	0.552711i	−0.374511	−	0.927222i	$-0.622190\pi$
$419$	11.3137	−	11.3137i	0.552711	−	0.552711i	0.927222	+	0.374511i	$0.122190\pi$
$420$		0			0
$421$	−19.2132			−0.936394			−0.468197	−	0.883624i	$-0.655096\pi$
$421$	−19.2132			−0.936394			−0.468197	+	0.883624i	$0.655096\pi$
$422$	8.00000	+	8.00000i	0.389434	+	0.389434i
$423$		−	4.48528i		−	0.218082i
$424$	−3.00000			−0.145693
$425$		0			0
$426$	2.17157			0.105213
$427$			12.2426i			0.592463i
$428$	2.82843	+	2.82843i	0.136717	+	0.136717i
$429$	−2.78680			−0.134548
$430$		0			0
$431$	17.6569	−	17.6569i	0.850501	−	0.850501i	−0.139694	−	0.990195i	$-0.544612\pi$
$431$	17.6569	−	17.6569i	0.850501	−	0.850501i	0.990195	+	0.139694i	$0.0446119\pi$
$432$	1.70711	−	1.70711i	0.0821332	−	0.0821332i
$433$			5.75736i			0.276681i	0.990385	+	0.138341i	$0.0441768\pi$
$433$			5.75736i			0.276681i	−0.990385	+	0.138341i	$0.955823\pi$
$434$		−	10.7279i		−	0.514957i
$435$		0			0
$436$	8.60660	−	8.60660i	0.412181	−	0.412181i
$437$	−20.4853	−	20.4853i	−0.979944	−	0.979944i
$438$	4.89949			0.234107
$439$	−20.9706	−	20.9706i	−1.00087	−	1.00087i	−1.00000		0.000870732i	$-0.999723\pi$
$439$	−20.9706	−	20.9706i	−1.00087	−	1.00087i	−0.000870732	−	1.00000i	$-0.500277\pi$
$440$		0			0
$441$	14.1421			0.673435
$442$	−6.36396	−	10.6066i	−0.302703	−	0.504505i
$443$	−37.7990			−1.79588			−0.897942	−	0.440114i	$-0.854938\pi$
$443$	−37.7990			−1.79588			−0.897942	+	0.440114i	$0.854938\pi$
$444$		−	3.07107i		−	0.145746i
$445$		0			0
$446$	23.2426			1.10057
$447$	3.72792	+	3.72792i	0.176325	+	0.176325i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	28.7990	−	28.7990i	1.35911	−	1.35911i	0.484090	−	0.875018i	$-0.339151\pi$
$449$	28.7990	−	28.7990i	1.35911	−	1.35911i	0.875018	−	0.484090i	$-0.160849\pi$
$450$		0			0
$451$			14.0000i			0.659234i
$452$	−2.46447	+	2.46447i	−0.115919	+	0.115919i
$453$	3.51472	−	3.51472i	0.165136	−	0.165136i
$454$	−4.05025	−	4.05025i	−0.190088	−	0.190088i
$455$		0			0
$456$	2.12132	+	2.12132i	0.0993399	+	0.0993399i
$457$		−	2.24264i		−	0.104906i	−0.998623	−	0.0524532i	$-0.983296\pi$
$457$		−	2.24264i		−	0.104906i	0.998623	−	0.0524532i	$-0.0167040\pi$
$458$	−7.75736			−0.362478
$459$	2.41421	−	9.65685i	0.112686	−	0.450743i
$460$		0			0
$461$		−	40.2843i		−	1.87623i	−0.346330	−	0.938113i	$-0.612572\pi$
$461$		−	40.2843i		−	1.87623i	0.346330	−	0.938113i	$-0.387428\pi$
$462$	−0.928932	−	0.928932i	−0.0432178	−	0.0432178i
$463$	25.2426			1.17312			0.586562	−	0.809904i	$-0.300481\pi$
$463$	25.2426			1.17312			0.586562	+	0.809904i	$0.300481\pi$
$464$	−0.707107	−	0.707107i	−0.0328266	−	0.0328266i
$465$		0			0
$466$	10.9497	−	10.9497i	0.507237	−	0.507237i
$467$		−	18.7279i		−	0.866625i	−0.901244	−	0.433312i	$-0.857345\pi$
$467$		−	18.7279i		−	0.866625i	0.901244	−	0.433312i	$-0.142655\pi$
$468$			8.48528i			0.392232i
$469$	14.4853	−	14.4853i	0.668868	−	0.668868i
$470$		0			0
$471$	3.51472	+	3.51472i	0.161950	+	0.161950i
$472$	12.8995			0.593747
$473$	5.95837	+	5.95837i	0.273966	+	0.273966i
$474$		−	0.142136i		−	0.00652851i
$475$		0			0
$476$	1.41421	−	5.65685i	0.0648204	−	0.259281i
$477$	8.48528			0.388514
$478$			22.2426i			1.01735i
$479$	10.0503	+	10.0503i	0.459208	+	0.459208i	0.898395	−	0.439188i	$-0.144734\pi$
$479$	10.0503	+	10.0503i	0.459208	+	0.459208i	−0.439188	+	0.898395i	$0.644734\pi$
$480$		0			0
$481$	15.7279	+	15.7279i	0.717132	+	0.717132i
$482$	2.75736	−	2.75736i	0.125594	−	0.125594i
$483$	−1.65685	+	1.65685i	−0.0753895	+	0.0753895i
$484$		−	5.97056i		−	0.271389i
$485$		0			0
$486$	−7.31371	+	7.31371i	−0.331757	+	0.331757i
$487$	−11.2426	+	11.2426i	−0.509453	+	0.509453i	−0.914358	−	0.404906i	$-0.867304\pi$
$487$	−11.2426	+	11.2426i	−0.509453	+	0.509453i	0.404906	+	0.914358i	$0.367304\pi$
$488$	6.12132	+	6.12132i	0.277099	+	0.277099i
$489$	−2.62742			−0.118816
$490$		0			0
$491$			6.89949i			0.311370i	0.987807	+	0.155685i	$0.0497585\pi$
$491$			6.89949i			0.311370i	−0.987807	+	0.155685i	$0.950242\pi$
$492$	−2.58579			−0.116576
$493$	−4.00000	−	1.00000i	−0.180151	−	0.0450377i
$494$	−21.7279			−0.977585
$495$		0			0
$496$	−5.36396	−	5.36396i	−0.240849	−	0.240849i
$497$	−7.41421			−0.332573
$498$	−1.24264	−	1.24264i	−0.0556841	−	0.0556841i
$499$	8.51472	−	8.51472i	0.381171	−	0.381171i	−0.490353	−	0.871524i	$-0.663132\pi$
$499$	8.51472	−	8.51472i	0.381171	−	0.381171i	0.871524	+	0.490353i	$0.163132\pi$
$500$		0			0
$501$		−	0.627417i		−	0.0280309i
$502$		−	20.4853i		−	0.914303i
$503$	13.0711	−	13.0711i	0.582810	−	0.582810i	−0.352864	−	0.935674i	$-0.614792\pi$
$503$	13.0711	−	13.0711i	0.582810	−	0.582810i	0.935674	+	0.352864i	$0.114792\pi$
$504$	−2.82843	+	2.82843i	−0.125988	+	0.125988i
$505$		0			0
$506$	8.97056			0.398790
$507$	−1.17157	−	1.17157i	−0.0520314	−	0.0520314i
$508$		−	17.7279i		−	0.786549i
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$	−16.7279			−0.740000
$512$		−	1.00000i		−	0.0441942i
$513$	−12.3640	−	12.3640i	−0.545882	−	0.545882i
$514$	6.72792			0.296756
$515$		0			0
$516$	−1.10051	+	1.10051i	−0.0484470	+	0.0484470i
$517$	−2.51472	+	2.51472i	−0.110597	+	0.110597i
$518$			10.4853i			0.460697i
$519$		−	10.3431i		−	0.454014i
$520$		0			0
$521$	−11.3137	+	11.3137i	−0.495663	+	0.495663i	−0.910085	−	0.414422i	$-0.863984\pi$
$521$	−11.3137	+	11.3137i	−0.495663	+	0.495663i	0.414422	+	0.910085i	$0.363984\pi$
$522$	2.00000	+	2.00000i	0.0875376	+	0.0875376i
$523$	26.4853			1.15812			0.579060	−	0.815285i	$-0.303420\pi$
$523$	26.4853			1.15812			0.579060	+	0.815285i	$0.303420\pi$
$524$	−7.58579	−	7.58579i	−0.331387	−	0.331387i
$525$		0			0
$526$	−4.75736			−0.207431
$527$	−30.3431	−	7.58579i	−1.32177	−	0.330442i
$528$	−0.928932			−0.0404266
$529$			7.00000i			0.304348i
$530$		0			0
$531$	−36.4853			−1.58333
$532$	−7.24264	−	7.24264i	−0.314008	−	0.314008i
$533$	13.2426	−	13.2426i	0.573602	−	0.573602i
$534$	−3.36396	+	3.36396i	−0.145573	+	0.145573i
$535$		0			0
$536$		−	14.4853i		−	0.625669i
$537$	0.201010	−	0.201010i	0.00867423	−	0.00867423i
$538$	11.2929	−	11.2929i	0.486871	−	0.486871i
$539$	−7.92893	−	7.92893i	−0.341523	−	0.341523i
$540$		0			0
$541$	20.9706	+	20.9706i	0.901595	+	0.901595i	0.995574	−	0.0939792i	$-0.0299587\pi$
$541$	20.9706	+	20.9706i	0.901595	+	0.901595i	−0.0939792	+	0.995574i	$0.529959\pi$
$542$			6.48528i			0.278567i
$543$	−8.20101			−0.351939
$544$	−2.12132	−	3.53553i	−0.0909509	−	0.151585i
$545$		0			0
$546$			1.75736i			0.0752080i
$547$	2.39340	+	2.39340i	0.102334	+	0.102334i	0.756420	−	0.654086i	$-0.226947\pi$
$547$	2.39340	+	2.39340i	0.102334	+	0.102334i	−0.654086	+	0.756420i	$0.726947\pi$
$548$	−4.58579			−0.195895
$549$	−17.3137	−	17.3137i	−0.738931	−	0.738931i
$550$		0			0
$551$	−5.12132	+	5.12132i	−0.218176	+	0.218176i
$552$			1.65685i			0.0705204i
$553$			0.485281i			0.0206363i
$554$	8.24264	−	8.24264i	0.350196	−	0.350196i
$555$		0			0
$556$	−11.0000	−	11.0000i	−0.466504	−	0.466504i
$557$	34.7990			1.47448			0.737240	−	0.675631i	$-0.236129\pi$
$557$	34.7990			1.47448			0.737240	+	0.675631i	$0.236129\pi$
$558$	15.1716	+	15.1716i	0.642264	+	0.642264i
$559$		−	11.2721i		−	0.476758i
$560$		0			0
$561$	−3.28427	+	1.97056i	−0.138662	+	0.0831972i
$562$	−3.34315			−0.141022
$563$			45.9411i			1.93619i	0.250588	+	0.968094i	$0.419376\pi$
$563$			45.9411i			1.93619i	−0.250588	+	0.968094i	$0.580624\pi$
$564$	−0.464466	−	0.464466i	−0.0195576	−	0.0195576i
$565$		0			0
$566$	19.1213	+	19.1213i	0.803729	+	0.803729i
$567$	7.48528	−	7.48528i	0.314352	−	0.314352i
$568$	−3.70711	+	3.70711i	−0.155547	+	0.155547i
$569$			20.3137i			0.851595i	0.904818	+	0.425797i	$0.140006\pi$
$569$			20.3137i			0.851595i	−0.904818	+	0.425797i	$0.859994\pi$
$570$		0			0
$571$	−20.2132	+	20.2132i	−0.845896	+	0.845896i	−0.989618	−	0.143722i	$-0.954093\pi$
$571$	−20.2132	+	20.2132i	−0.845896	+	0.845896i	0.143722	+	0.989618i	$0.454093\pi$
$572$	4.75736	−	4.75736i	0.198915	−	0.198915i
$573$	6.21320	+	6.21320i	0.259560	+	0.259560i
$574$	8.82843			0.368491
$575$		0			0
$576$			2.82843i			0.117851i
$577$	4.97056			0.206927			0.103464	−	0.994633i	$-0.467007\pi$
$577$	4.97056			0.206927			0.103464	+	0.994633i	$0.467007\pi$
$578$	−15.0000	−	8.00000i	−0.623918	−	0.332756i
$579$	10.8284			0.450014
$580$		0			0
$581$	4.24264	+	4.24264i	0.176014	+	0.176014i
$582$	0.0710678			0.00294586
$583$	−4.75736	−	4.75736i	−0.197030	−	0.197030i
$584$	−8.36396	+	8.36396i	−0.346103	+	0.346103i
$585$		0			0
$586$		−	20.6569i		−	0.853327i
$587$			24.0000i			0.990586i	0.868726	+	0.495293i	$0.164939\pi$
$587$			24.0000i			0.990586i	−0.868726	+	0.495293i	$0.835061\pi$
$588$	1.46447	−	1.46447i	0.0603936	−	0.0603936i
$589$	−38.8492	+	38.8492i	−1.60076	+	1.60076i
$590$		0			0
$591$	−1.95837			−0.0805566
$592$	5.24264	+	5.24264i	0.215471	+	0.215471i
$593$		−	18.0000i		−	0.739171i	−0.929197	−	0.369586i	$-0.879500\pi$
$593$		−	18.0000i		−	0.739171i	0.929197	−	0.369586i	$-0.120500\pi$
$594$	5.41421			0.222148
$595$		0			0
$596$	−12.7279			−0.521356
$597$			4.17157i			0.170731i
$598$	−8.48528	−	8.48528i	−0.346989	−	0.346989i
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	28.7279	−	28.7279i	1.17184	−	1.17184i	0.190065	−	0.981772i	$-0.439130\pi$
$601$	28.7279	−	28.7279i	1.17184	−	1.17184i	0.981772	−	0.190065i	$-0.0608698\pi$
$602$	3.75736	−	3.75736i	0.153139	−	0.153139i
$603$			40.9706i			1.66845i
$604$			12.0000i			0.488273i
$605$		0			0
$606$		0			0
$607$	26.4558	+	26.4558i	1.07381	+	1.07381i	0.997050	+	0.0767600i	$0.0244575\pi$
$607$	26.4558	+	26.4558i	1.07381	+	1.07381i	0.0767600	+	0.997050i	$0.475542\pi$
$608$	−7.24264			−0.293728
$609$	0.414214	+	0.414214i	0.0167848	+	0.0167848i
$610$		0			0
$611$	4.75736			0.192462
$612$	6.00000	+	10.0000i	0.242536	+	0.404226i
$613$	−4.02944			−0.162747			−0.0813737	−	0.996684i	$-0.525931\pi$
$613$	−4.02944			−0.162747			−0.0813737	+	0.996684i	$0.525931\pi$
$614$			33.2132i			1.34038i
$615$		0			0
$616$	3.17157			0.127786
$617$	−19.4350	−	19.4350i	−0.782425	−	0.782425i	0.197815	−	0.980239i	$-0.436616\pi$
$617$	−19.4350	−	19.4350i	−0.782425	−	0.782425i	−0.980239	+	0.197815i	$0.936616\pi$
$618$		0			0
$619$	−5.75736	+	5.75736i	−0.231408	+	0.231408i	−0.813280	−	0.581872i	$-0.802320\pi$
$619$	−5.75736	+	5.75736i	−0.231408	+	0.231408i	0.581872	+	0.813280i	$0.302320\pi$
$620$		0			0
$621$		−	9.65685i		−	0.387516i
$622$	−1.41421	+	1.41421i	−0.0567048	+	0.0567048i
$623$	11.4853	−	11.4853i	0.460148	−	0.460148i
$624$	0.878680	+	0.878680i	0.0351753	+	0.0351753i
$625$		0			0
$626$	22.4853	+	22.4853i	0.898693	+	0.898693i
$627$			6.72792i			0.268687i
$628$	−12.0000			−0.478852
$629$	29.6569	+	7.41421i	1.18250	+	0.295624i
$630$		0			0
$631$		−	2.48528i		−	0.0989375i	−0.998776	−	0.0494687i	$-0.984247\pi$
$631$		−	2.48528i		−	0.0989375i	0.998776	−	0.0494687i	$-0.0157528\pi$
$632$	0.242641	+	0.242641i	0.00965173	+	0.00965173i
$633$	−4.68629			−0.186263
$634$	−14.1421	−	14.1421i	−0.561656	−	0.561656i
$635$		0			0
$636$	0.878680	−	0.878680i	0.0348419	−	0.0348419i
$637$			15.0000i			0.594322i
$638$		−	2.24264i		−	0.0887870i
$639$	10.4853	−	10.4853i	0.414791	−	0.414791i
$640$		0			0
$641$	3.55635	+	3.55635i	0.140467	+	0.140467i	0.773844	−	0.633376i	$-0.218332\pi$
$641$	3.55635	+	3.55635i	0.140467	+	0.140467i	−0.633376	+	0.773844i	$0.718332\pi$
$642$	−1.65685			−0.0653908
$643$	3.75736	+	3.75736i	0.148176	+	0.148176i	0.777303	−	0.629127i	$-0.216587\pi$
$643$	3.75736	+	3.75736i	0.148176	+	0.148176i	−0.629127	+	0.777303i	$0.716587\pi$
$644$		−	5.65685i		−	0.222911i
$645$		0			0
$646$	−25.6066	+	15.3640i	−1.00748	+	0.604487i
$647$	47.5269			1.86848			0.934238	−	0.356651i	$-0.116081\pi$
$647$	47.5269			1.86848			0.934238	+	0.356651i	$0.116081\pi$
$648$		−	7.48528i		−	0.294050i
$649$	20.4558	+	20.4558i	0.802962	+	0.802962i
$650$		0			0
$651$	3.14214	+	3.14214i	0.123150	+	0.123150i
$652$	4.48528	−	4.48528i	0.175657	−	0.175657i
$653$	4.79899	−	4.79899i	0.187799	−	0.187799i	−0.606945	−	0.794744i	$-0.707605\pi$
$653$	4.79899	−	4.79899i	0.187799	−	0.187799i	0.794744	+	0.606945i	$0.207605\pi$
$654$			5.04163i			0.197143i
$655$		0			0
$656$	4.41421	−	4.41421i	0.172346	−	0.172346i
$657$	23.6569	−	23.6569i	0.922942	−	0.922942i
$658$	1.58579	+	1.58579i	0.0618204	+	0.0618204i
$659$	−30.2132			−1.17694			−0.588470	−	0.808519i	$-0.700269\pi$
$659$	−30.2132			−1.17694			−0.588470	+	0.808519i	$0.700269\pi$
$660$		0			0
$661$		−	12.0000i		−	0.466746i	−0.972387	−	0.233373i	$-0.925024\pi$
$661$		−	12.0000i		−	0.466746i	0.972387	−	0.233373i	$-0.0749763\pi$
$662$	−15.7279			−0.611283
$663$	4.97056	+	1.24264i	0.193041	+	0.0482602i
$664$	4.24264			0.164646
$665$		0			0
$666$	−14.8284	−	14.8284i	−0.574590	−	0.574590i
$667$	−4.00000			−0.154881
$668$	1.07107	+	1.07107i	0.0414409	+	0.0414409i
$669$	−6.80761	+	6.80761i	−0.263197	+	0.263197i
$670$		0			0
$671$			19.4142i			0.749477i
$672$			0.585786i			0.0225972i
$673$	25.8787	−	25.8787i	0.997550	−	0.997550i	−0.00244721	−	0.999997i	$-0.500779\pi$
$673$	25.8787	−	25.8787i	0.997550	−	0.997550i	0.999997	+	0.00244721i	$0.000778973\pi$
$674$	12.8492	−	12.8492i	0.494934	−	0.494934i
$675$		0			0
$676$	4.00000			0.153846
$677$	22.4142	+	22.4142i	0.861448	+	0.861448i	0.991506	−	0.130058i	$-0.0415164\pi$
$677$	22.4142	+	22.4142i	0.861448	+	0.861448i	−0.130058	+	0.991506i	$0.541516\pi$
$678$		−	1.44365i		−	0.0554431i
$679$	−0.242641			−0.00931169
$680$		0			0
$681$	2.37258			0.0909176
$682$		−	17.0122i		−	0.651431i
$683$	−24.5355	−	24.5355i	−0.938826	−	0.938826i	0.0594077	−	0.998234i	$-0.481079\pi$
$683$	−24.5355	−	24.5355i	−0.938826	−	0.938826i	−0.998234	+	0.0594077i	$0.981079\pi$
$684$	20.4853			0.783274
$685$		0			0
$686$	−12.0000	+	12.0000i	−0.458162	+	0.458162i
$687$	2.27208	−	2.27208i	0.0866852	−	0.0866852i
$688$		−	3.75736i		−	0.143248i
$689$			9.00000i			0.342873i
$690$		0			0
$691$	9.48528	−	9.48528i	0.360837	−	0.360837i	−0.503284	−	0.864121i	$-0.667875\pi$
$691$	9.48528	−	9.48528i	0.360837	−	0.360837i	0.864121	+	0.503284i	$0.167875\pi$
$692$	17.6569	+	17.6569i	0.671213	+	0.671213i
$693$	−8.97056			−0.340764
$694$	15.7071	+	15.7071i	0.596234	+	0.596234i
$695$		0			0
$696$	0.414214			0.0157007
$697$	6.24264	−	24.9706i	0.236457	−	0.945828i
$698$	−10.9706			−0.415242
$699$			6.41421i			0.242608i
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$	−5.12132	−	5.12132i	−0.193292	−	0.193292i
$703$	37.9706	−	37.9706i	1.43209	−	1.43209i
$704$	1.58579	−	1.58579i	0.0597666	−	0.0597666i
$705$		0			0
$706$			11.3137i			0.425797i
$707$		0			0
$708$	−3.77817	+	3.77817i	−0.141992	+	0.141992i
$709$	−2.60660	−	2.60660i	−0.0978930	−	0.0978930i	0.656464	−	0.754357i	$-0.272051\pi$
$709$	−2.60660	−	2.60660i	−0.0978930	−	0.0978930i	−0.754357	+	0.656464i	$0.772051\pi$
$710$		0			0
$711$	−0.686292	−	0.686292i	−0.0257379	−	0.0257379i
$712$		−	11.4853i		−	0.430429i
$713$	−30.3431			−1.13636
$714$	1.24264	+	2.07107i	0.0465047	+	0.0775078i
$715$		0			0
$716$			0.686292i			0.0256479i
$717$	−6.51472	−	6.51472i	−0.243297	−	0.243297i
$718$	7.07107			0.263890
$719$	27.7487	+	27.7487i	1.03485	+	1.03485i	0.999370	+	0.0354830i	$0.0112970\pi$
$719$	27.7487	+	27.7487i	1.03485	+	1.03485i	0.0354830	+	0.999370i	$0.488703\pi$
$720$		0			0
$721$		0			0
$722$			33.4558i			1.24510i
$723$			1.61522i			0.0600708i
$724$	14.0000	−	14.0000i	0.520306	−	0.520306i
$725$		0			0
$726$	1.74874	+	1.74874i	0.0649017	+	0.0649017i
$727$	−16.7574			−0.621496			−0.310748	−	0.950492i	$-0.600580\pi$
$727$	−16.7574			−0.621496			−0.310748	+	0.950492i	$0.600580\pi$
$728$	−3.00000	−	3.00000i	−0.111187	−	0.111187i
$729$			18.1716i			0.673021i
$730$		0			0
$731$	−7.97056	−	13.2843i	−0.294802	−	0.491337i
$732$	−3.58579			−0.132534
$733$			32.9706i			1.21780i	0.793249	+	0.608898i	$0.208388\pi$
$733$			32.9706i			1.21780i	−0.793249	+	0.608898i	$0.791612\pi$
$734$	−18.2426	−	18.2426i	−0.673348	−	0.673348i
$735$		0			0
$736$	−2.82843	−	2.82843i	−0.104257	−	0.104257i
$737$	22.9706	−	22.9706i	0.846132	−	0.846132i
$738$	−12.4853	+	12.4853i	−0.459590	+	0.459590i
$739$			35.1838i			1.29426i	0.762381	+	0.647128i	$0.224030\pi$
$739$			35.1838i			1.29426i	−0.762381	+	0.647128i	$0.775970\pi$
$740$		0			0
$741$	6.36396	−	6.36396i	0.233786	−	0.233786i
$742$	−3.00000	+	3.00000i	−0.110133	+	0.110133i
$743$	17.8284	+	17.8284i	0.654062	+	0.654062i	0.953968	−	0.299907i	$-0.0969556\pi$
$743$	17.8284	+	17.8284i	0.654062	+	0.654062i	−0.299907	+	0.953968i	$0.596956\pi$
$744$	3.14214			0.115196
$745$		0			0
$746$			32.4853i			1.18937i
$747$	−12.0000			−0.439057
$748$	2.24264	−	8.97056i	0.0819991	−	0.327996i
$749$	5.65685			0.206697
$750$		0			0
$751$	19.3640	+	19.3640i	0.706601	+	0.706601i	0.965819	−	0.259218i	$-0.0834648\pi$
$751$	19.3640	+	19.3640i	0.706601	+	0.706601i	−0.259218	+	0.965819i	$0.583465\pi$
$752$	1.58579			0.0578277
$753$	6.00000	+	6.00000i	0.218652	+	0.218652i
$754$	−2.12132	+	2.12132i	−0.0772539	+	0.0772539i
$755$		0			0
$756$		−	3.41421i		−	0.124174i
$757$			32.9411i			1.19727i	0.801024	+	0.598633i	$0.204289\pi$
$757$			32.9411i			1.19727i	−0.801024	+	0.598633i	$0.795711\pi$
$758$	−0.485281	+	0.485281i	−0.0176262	+	0.0176262i
$759$	−2.62742	+	2.62742i	−0.0953692	+	0.0953692i
$760$		0			0
$761$	20.4853			0.742591			0.371295	−	0.928515i	$-0.378914\pi$
$761$	20.4853			0.742591			0.371295	+	0.928515i	$0.378914\pi$
$762$	5.19239	+	5.19239i	0.188100	+	0.188100i
$763$		−	17.2132i		−	0.623160i
$764$	−21.2132			−0.767467
$765$		0			0
$766$	13.2426			0.478476
$767$		−	38.6985i		−	1.39732i
$768$	0.292893	+	0.292893i	0.0105689	+	0.0105689i
$769$	14.4558			0.521291			0.260646	−	0.965435i	$-0.416065\pi$
$769$	14.4558			0.521291			0.260646	+	0.965435i	$0.416065\pi$
$770$		0			0
$771$	−1.97056	+	1.97056i	−0.0709681	+	0.0709681i
$772$	−18.4853	+	18.4853i	−0.665300	+	0.665300i
$773$			32.4853i			1.16841i	0.811605	+	0.584207i	$0.198594\pi$
$773$			32.4853i			1.16841i	−0.811605	+	0.584207i	$0.801406\pi$
$774$			10.6274i			0.381995i
$775$		0			0
$776$	−0.121320	+	0.121320i	−0.00435515	+	0.00435515i
$777$	−3.07107	−	3.07107i	−0.110174	−	0.110174i
$778$	−16.6274			−0.596122
$779$	−31.9706	−	31.9706i	−1.14546	−	1.14546i
$780$		0			0
$781$	−11.7574			−0.420711
$782$	−16.0000	−	4.00000i	−0.572159	−	0.143040i
$783$	−2.41421			−0.0862770
$784$			5.00000i			0.178571i
$785$		0			0
$786$	4.44365			0.158500
$787$	1.36396	+	1.36396i	0.0486200	+	0.0486200i	0.730999	−	0.682379i	$-0.239055\pi$
$787$	1.36396	+	1.36396i	0.0486200	+	0.0486200i	−0.682379	+	0.730999i	$0.739055\pi$
$788$	3.34315	−	3.34315i	0.119095	−	0.119095i
$789$	1.39340	−	1.39340i	0.0496063	−	0.0496063i
$790$		0			0
$791$			4.92893i			0.175253i
$792$	−4.48528	+	4.48528i	−0.159378	+	0.159378i
$793$	18.3640	−	18.3640i	0.652123	−	0.652123i
$794$	4.72792	+	4.72792i	0.167788	+	0.167788i
$795$		0			0
$796$	−7.12132	−	7.12132i	−0.252409	−	0.252409i
$797$		−	28.9706i		−	1.02619i	−0.858332	−	0.513095i	$-0.828499\pi$
$797$		−	28.9706i		−	1.02619i	0.858332	−	0.513095i	$-0.171501\pi$
$798$	4.24264			0.150188
$799$	5.60660	−	3.36396i	0.198347	−	0.119008i
$800$		0			0
$801$			32.4853i			1.14781i
$802$	2.10051	+	2.10051i	0.0741714	+	0.0741714i
$803$	−26.5269			−0.936114
$804$	4.24264	+	4.24264i	0.149626	+	0.149626i
$805$		0			0
$806$	−16.0919	+	16.0919i	−0.566812	+	0.566812i
$807$			6.61522i			0.232867i
$808$		0			0
$809$	−35.1421	+	35.1421i	−1.23553	+	1.23553i	−0.273723	+	0.961809i	$0.588255\pi$
$809$	−35.1421	+	35.1421i	−1.23553	+	1.23553i	−0.961809	+	0.273723i	$0.911745\pi$
$810$		0			0
$811$	9.48528	+	9.48528i	0.333073	+	0.333073i	0.853752	−	0.520679i	$-0.174321\pi$
$811$	9.48528	+	9.48528i	0.333073	+	0.333073i	−0.520679	+	0.853752i	$0.674321\pi$
$812$	−1.41421			−0.0496292
$813$	−1.89949	−	1.89949i	−0.0666182	−	0.0666182i
$814$			16.6274i			0.582791i
$815$		0			0
$816$	1.65685	+	0.414214i	0.0580015	+	0.0145004i
$817$	−27.2132			−0.952069
$818$			25.4853i			0.891072i
$819$	8.48528	+	8.48528i	0.296500	+	0.296500i
$820$		0			0
$821$	−18.0208	−	18.0208i	−0.628931	−	0.628931i	0.318868	−	0.947799i	$-0.396697\pi$
$821$	−18.0208	−	18.0208i	−0.628931	−	0.628931i	−0.947799	+	0.318868i	$0.896697\pi$
$822$	1.34315	−	1.34315i	0.0468476	−	0.0468476i
$823$	10.7279	−	10.7279i	0.373952	−	0.373952i	−0.494962	−	0.868914i	$-0.664818\pi$
$823$	10.7279	−	10.7279i	0.373952	−	0.373952i	0.868914	+	0.494962i	$0.164818\pi$
$824$		0			0
$825$		0			0
$826$	12.8995	−	12.8995i	0.448831	−	0.448831i
$827$	−5.31371	+	5.31371i	−0.184776	+	0.184776i	−0.793433	−	0.608657i	$-0.791708\pi$
$827$	−5.31371	+	5.31371i	−0.184776	+	0.184776i	0.608657	+	0.793433i	$0.291708\pi$
$828$	8.00000	+	8.00000i	0.278019	+	0.278019i
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$		0			0
$831$			4.82843i			0.167496i
$832$	−3.00000			−0.104006
$833$	10.6066	+	17.6777i	0.367497	+	0.612495i
$834$	6.44365			0.223125
$835$		0			0
$836$	−11.4853	−	11.4853i	−0.397227	−	0.397227i
$837$	−18.3137			−0.633014
$838$	−11.3137	−	11.3137i	−0.390826	−	0.390826i
$839$	2.97918	−	2.97918i	0.102853	−	0.102853i	−0.653808	−	0.756661i	$-0.726830\pi$
$839$	2.97918	−	2.97918i	0.102853	−	0.102853i	0.756661	+	0.653808i	$0.226830\pi$
$840$		0			0
$841$		−	28.0000i		−	0.965517i
$842$			19.2132i			0.662131i
$843$	0.979185	−	0.979185i	0.0337249	−	0.0337249i
$844$	8.00000	−	8.00000i	0.275371	−	0.275371i
$845$		0			0
$846$	−4.48528			−0.154207
$847$	−5.97056	−	5.97056i	−0.205151	−	0.205151i
$848$			3.00000i			0.103020i
$849$	−11.2010			−0.384418
$850$		0			0
$851$	29.6569			1.01662
$852$		−	2.17157i		−	0.0743969i
$853$	8.51472	+	8.51472i	0.291538	+	0.291538i	0.837688	−	0.546149i	$-0.183907\pi$
$853$	8.51472	+	8.51472i	0.291538	+	0.291538i	−0.546149	+	0.837688i	$0.683907\pi$
$854$	12.2426			0.418935
$855$		0			0
$856$	2.82843	−	2.82843i	0.0966736	−	0.0966736i
$857$	−25.4350	+	25.4350i	−0.868844	+	0.868844i	−0.992345	−	0.123500i	$-0.960588\pi$
$857$	−25.4350	+	25.4350i	−0.868844	+	0.868844i	0.123500	+	0.992345i	$0.460588\pi$
$858$			2.78680i			0.0951397i
$859$			45.7279i			1.56022i	0.625645	+	0.780108i	$0.284836\pi$
$859$			45.7279i			1.56022i	−0.625645	+	0.780108i	$0.715164\pi$
$860$		0			0
$861$	−2.58579	+	2.58579i	−0.0881234	+	0.0881234i
$862$	−17.6569	−	17.6569i	−0.601395	−	0.601395i
$863$	55.1127			1.87606			0.938029	−	0.346557i	$-0.112649\pi$
$863$	55.1127			1.87606			0.938029	+	0.346557i	$0.112649\pi$
$864$	−1.70711	−	1.70711i	−0.0580770	−	0.0580770i
$865$		0			0
$866$	5.75736			0.195643
$867$	6.73654	−	2.05025i	0.228785	−	0.0696302i
$868$	−10.7279			−0.364129
$869$			0.769553i			0.0261053i
$870$		0			0
$871$	−43.4558			−1.47245
$872$	−8.60660	−	8.60660i	−0.291456	−	0.291456i
$873$	0.343146	−	0.343146i	0.0116137	−	0.0116137i
$874$	−20.4853	+	20.4853i	−0.692925	+	0.692925i
$875$		0			0
$876$		−	4.89949i		−	0.165539i
$877$	8.51472	−	8.51472i	0.287522	−	0.287522i	−0.548578	−	0.836099i	$-0.684831\pi$
$877$	8.51472	−	8.51472i	0.287522	−	0.287522i	0.836099	+	0.548578i	$0.184831\pi$
$878$	−20.9706	+	20.9706i	−0.707722	+	0.707722i
$879$	6.05025	+	6.05025i	0.204070	+	0.204070i
$880$		0			0
$881$	−8.44365	−	8.44365i	−0.284474	−	0.284474i	0.550416	−	0.834890i	$-0.314469\pi$
$881$	−8.44365	−	8.44365i	−0.284474	−	0.284474i	−0.834890	+	0.550416i	$0.814469\pi$
$882$		−	14.1421i		−	0.476190i
$883$	−18.7279			−0.630245			−0.315122	−	0.949051i	$-0.602046\pi$
$883$	−18.7279			−0.630245			−0.315122	+	0.949051i	$0.602046\pi$
$884$	−10.6066	+	6.36396i	−0.356739	+	0.214043i
$885$		0			0
$886$			37.7990i			1.26988i
$887$	−19.5858	−	19.5858i	−0.657626	−	0.657626i	0.297192	−	0.954818i	$-0.403950\pi$
$887$	−19.5858	−	19.5858i	−0.657626	−	0.657626i	−0.954818	+	0.297192i	$0.903950\pi$
$888$	−3.07107			−0.103058
$889$	−17.7279	−	17.7279i	−0.594575	−	0.594575i
$890$		0			0
$891$	11.8701	−	11.8701i	0.397662	−	0.397662i
$892$		−	23.2426i		−	0.778221i
$893$		−	11.4853i		−	0.384340i
$894$	3.72792	−	3.72792i	0.124680	−	0.124680i
$895$		0			0
$896$	−1.00000	−	1.00000i	−0.0334077	−	0.0334077i
$897$	4.97056			0.165962
$898$	−28.7990	−	28.7990i	−0.961035	−	0.961035i
$899$			7.58579i			0.253000i
$900$		0			0
$901$	6.36396	+	10.6066i	0.212014	+	0.353357i
$902$	14.0000			0.466149
$903$			2.20101i			0.0732450i
$904$	2.46447	+	2.46447i	0.0819669	+	0.0819669i
$905$		0			0
$906$	−3.51472	−	3.51472i	−0.116769	−	0.116769i
$907$	7.84924	−	7.84924i	0.260630	−	0.260630i	−0.564680	−	0.825310i	$-0.691000\pi$
$907$	7.84924	−	7.84924i	0.260630	−	0.260630i	0.825310	+	0.564680i	$0.191000\pi$
$908$	−4.05025	+	4.05025i	−0.134412	+	0.134412i
$909$		0			0
$910$		0			0
$911$	−35.3137	+	35.3137i	−1.17000	+	1.17000i	−0.187785	+	0.982210i	$0.560131\pi$
$911$	−35.3137	+	35.3137i	−1.17000	+	1.17000i	−0.982210	+	0.187785i	$0.939869\pi$
$912$	2.12132	−	2.12132i	0.0702439	−	0.0702439i
$913$	6.72792	+	6.72792i	0.222662	+	0.222662i
$914$	−2.24264			−0.0741800
$915$		0			0
$916$			7.75736i			0.256310i
$917$	−15.1716			−0.501009
$918$	−9.65685	−	2.41421i	−0.318724	−	0.0796809i
$919$	31.2132			1.02963			0.514814	−	0.857302i	$-0.327861\pi$
$919$	31.2132			1.02963			0.514814	+	0.857302i	$0.327861\pi$
$920$		0			0
$921$	−9.72792	−	9.72792i	−0.320546	−	0.320546i
$922$	−40.2843			−1.32669
$923$	11.1213	+	11.1213i	0.366063	+	0.366063i
$924$	−0.928932	+	0.928932i	−0.0305596	+	0.0305596i
$925$		0			0
$926$		−	25.2426i		−	0.829525i
$927$		0			0
$928$	−0.707107	+	0.707107i	−0.0232119	+	0.0232119i
$929$	15.3431	−	15.3431i	0.503392	−	0.503392i	−0.409098	−	0.912490i	$-0.634157\pi$
$929$	15.3431	−	15.3431i	0.503392	−	0.503392i	0.912490	+	0.409098i	$0.134157\pi$
$930$		0			0
$931$	36.2132			1.18684
$932$	−10.9497	−	10.9497i	−0.358671	−	0.358671i
$933$		−	0.828427i		−	0.0271215i
$934$	−18.7279			−0.612796
$935$		0			0
$936$	8.48528			0.277350
$937$			47.2132i			1.54239i	0.636600	+	0.771194i	$0.280340\pi$
$937$			47.2132i			1.54239i	−0.636600	+	0.771194i	$0.719660\pi$
$938$	−14.4853	−	14.4853i	−0.472961	−	0.472961i
$939$	−13.1716			−0.429838
$940$		0			0
$941$	14.8076	−	14.8076i	0.482714	−	0.482714i	−0.423283	−	0.905997i	$-0.639122\pi$
$941$	14.8076	−	14.8076i	0.482714	−	0.482714i	0.905997	+	0.423283i	$0.139122\pi$
$942$	3.51472	−	3.51472i	0.114516	−	0.114516i
$943$		−	24.9706i		−	0.813153i
$944$		−	12.8995i		−	0.419843i
$945$		0			0
$946$	5.95837	−	5.95837i	0.193723	−	0.193723i
$947$	26.2929	+	26.2929i	0.854404	+	0.854404i	0.990672	−	0.136268i	$-0.0435108\pi$
$947$	26.2929	+	26.2929i	0.854404	+	0.854404i	−0.136268	+	0.990672i	$0.543511\pi$
$948$	−0.142136			−0.00461635
$949$	25.0919	+	25.0919i	0.814517	+	0.814517i
$950$		0			0
$951$	8.28427			0.268636
$952$	−5.65685	−	1.41421i	−0.183340	−	0.0458349i
$953$	−4.58579			−0.148548			−0.0742741	−	0.997238i	$-0.523664\pi$
$953$	−4.58579			−0.148548			−0.0742741	+	0.997238i	$0.523664\pi$
$954$		−	8.48528i		−	0.274721i
$955$		0			0
$956$	22.2426			0.719378
$957$	0.656854	+	0.656854i	0.0212331	+	0.0212331i
$958$	10.0503	−	10.0503i	0.324709	−	0.324709i
$959$	−4.58579	+	4.58579i	−0.148083	+	0.148083i
$960$		0			0
$961$			26.5442i			0.856263i
$962$	15.7279	−	15.7279i	0.507089	−	0.507089i
$963$	−8.00000	+	8.00000i	−0.257796	+	0.257796i
$964$	−2.75736	−	2.75736i	−0.0888086	−	0.0888086i
$965$		0			0
$966$	1.65685	+	1.65685i	0.0533084	+	0.0533084i
$967$			30.9706i			0.995946i	0.867192	+	0.497973i	$0.165922\pi$
$967$			30.9706i			0.995946i	−0.867192	+	0.497973i	$0.834078\pi$
$968$	−5.97056			−0.191901
$969$	3.00000	−	12.0000i	0.0963739	−	0.385496i
$970$		0			0
$971$		−	30.5563i		−	0.980600i	−0.871554	−	0.490300i	$-0.836887\pi$
$971$		−	30.5563i		−	0.980600i	0.871554	−	0.490300i	$-0.163113\pi$
$972$	7.31371	+	7.31371i	0.234587	+	0.234587i
$973$	−22.0000			−0.705288
$974$	11.2426	+	11.2426i	0.360237	+	0.360237i
$975$		0			0
$976$	6.12132	−	6.12132i	0.195939	−	0.195939i
$977$			0.727922i			0.0232883i	0.999932	+	0.0116441i	$0.00370653\pi$
$977$			0.727922i			0.0232883i	−0.999932	+	0.0116441i	$0.996293\pi$
$978$			2.62742i			0.0840155i
$979$	18.2132	−	18.2132i	0.582097	−	0.582097i
$980$		0			0
$981$	24.3431	+	24.3431i	0.777217	+	0.777217i
$982$	6.89949			0.220172
$983$	44.0122	+	44.0122i	1.40377	+	1.40377i	0.787657	+	0.616114i	$0.211294\pi$
$983$	44.0122	+	44.0122i	1.40377	+	1.40377i	0.616114	+	0.787657i	$0.288706\pi$
$984$			2.58579i			0.0824319i
$985$		0			0
$986$	−1.00000	+	4.00000i	−0.0318465	+	0.127386i
$987$	−0.928932			−0.0295682
$988$			21.7279i			0.691257i
$989$	−10.6274	−	10.6274i	−0.337932	−	0.337932i
$990$		0			0
$991$	21.1213	+	21.1213i	0.670941	+	0.670941i	0.957933	−	0.286992i	$-0.0926553\pi$
$991$	21.1213	+	21.1213i	0.670941	+	0.670941i	−0.286992	+	0.957933i	$0.592655\pi$
$992$	−5.36396	+	5.36396i	−0.170306	+	0.170306i
$993$	4.60660	−	4.60660i	0.146186	−	0.146186i
$994$			7.41421i			0.235165i
$995$		0			0
$996$	−1.24264	+	1.24264i	−0.0393746	+	0.0393746i
$997$	−30.6985	+	30.6985i	−0.972231	+	0.972231i	−0.999625	−	0.0273939i	$-0.991279\pi$
$997$	−30.6985	+	30.6985i	−0.972231	+	0.972231i	0.0273939	+	0.999625i	$0.491279\pi$
$998$	−8.51472	−	8.51472i	−0.269529	−	0.269529i
$999$	17.8995			0.566315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.k.251.1		4
5.2	odd	4		170.2.g.f.149.1	yes	4
5.3	odd	4		170.2.g.e.149.2	yes	4
5.4	even	2		850.2.h.h.251.2		4
15.2	even	4		1530.2.n.j.829.1		4
15.8	even	4		1530.2.n.o.829.2		4
17.4	even	4	inner	850.2.h.k.701.1		4
85.4	even	4		850.2.h.h.701.2		4
85.38	odd	4		170.2.g.f.89.1	yes	4
85.72	odd	4		170.2.g.e.89.2	✓	4
255.38	even	4		1530.2.n.j.1279.1		4
255.242	even	4		1530.2.n.o.1279.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.g.e.89.2	✓	4	85.72	odd	4
170.2.g.e.149.2	yes	4	5.3	odd	4
170.2.g.f.89.1	yes	4	85.38	odd	4
170.2.g.f.149.1	yes	4	5.2	odd	4
850.2.h.h.251.2		4	5.4	even	2
850.2.h.h.701.2		4	85.4	even	4
850.2.h.k.251.1		4	1.1	even	1	trivial
850.2.h.k.701.1		4	17.4	even	4	inner
1530.2.n.j.829.1		4	15.2	even	4
1530.2.n.j.1279.1		4	255.38	even	4
1530.2.n.o.829.2		4	15.8	even	4
1530.2.n.o.1279.2		4	255.242	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(0.292893 - 0.292893i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(0.292893 - 0.292893i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +(-1.58579 + 1.58579i) q^{11} +(-0.292893 - 0.292893i) q^{12} +3.00000 q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(3.53553 - 2.12132i) q^{17} -2.82843 q^{18} -7.24264i q^{19} -0.585786 q^{21} +(1.58579 + 1.58579i) q^{22} +(2.82843 - 2.82843i) q^{23} +(-0.292893 + 0.292893i) q^{24} -3.00000i q^{26} +(1.70711 - 1.70711i) q^{27} +(1.00000 - 1.00000i) q^{28} +(-0.707107 - 0.707107i) q^{29} +(-5.36396 - 5.36396i) q^{31} -1.00000i q^{32} -0.928932 q^{33} +(-2.12132 - 3.53553i) q^{34} +2.82843i q^{36} +(5.24264 + 5.24264i) q^{37} -7.24264 q^{38} +(0.878680 + 0.878680i) q^{39} +(4.41421 - 4.41421i) q^{41} +0.585786i q^{42} -3.75736i q^{43} +(1.58579 - 1.58579i) q^{44} +(-2.82843 - 2.82843i) q^{46} +1.58579 q^{47} +(0.292893 + 0.292893i) q^{48} +5.00000i q^{49} +(1.65685 + 0.414214i) q^{51} -3.00000 q^{52} +3.00000i q^{53} +(-1.70711 - 1.70711i) q^{54} +(-1.00000 - 1.00000i) q^{56} +(2.12132 - 2.12132i) q^{57} +(-0.707107 + 0.707107i) q^{58} -12.8995i q^{59} +(6.12132 - 6.12132i) q^{61} +(-5.36396 + 5.36396i) q^{62} +(2.82843 + 2.82843i) q^{63} -1.00000 q^{64} +0.928932i q^{66} -14.4853 q^{67} +(-3.53553 + 2.12132i) q^{68} +1.65685 q^{69} +(3.70711 + 3.70711i) q^{71} +2.82843 q^{72} +(8.36396 + 8.36396i) q^{73} +(5.24264 - 5.24264i) q^{74} +7.24264i q^{76} -3.17157i q^{77} +(0.878680 - 0.878680i) q^{78} +(0.242641 - 0.242641i) q^{79} -7.48528 q^{81} +(-4.41421 - 4.41421i) q^{82} -4.24264i q^{83} +0.585786 q^{84} -3.75736 q^{86} -0.414214i q^{87} +(-1.58579 - 1.58579i) q^{88} -11.4853 q^{89} +(-3.00000 + 3.00000i) q^{91} +(-2.82843 + 2.82843i) q^{92} -3.14214i q^{93} -1.58579i q^{94} +(0.292893 - 0.292893i) q^{96} +(0.121320 + 0.121320i) q^{97} +5.00000 q^{98} +(4.48528 + 4.48528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} - 4 q^{7}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 - 4 * q^7	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} - 4 q^{7} - 12 q^{11} - 4 q^{12} + 12 q^{13} + 4 q^{14} + 4 q^{16} - 8 q^{21} + 12 q^{22} - 4 q^{24} + 4 q^{27} + 4 q^{28} + 4 q^{31} - 32 q^{33} + 4 q^{37} - 12 q^{38} + 12 q^{39} + 12 q^{41} + 12 q^{44} + 12 q^{47} + 4 q^{48} - 16 q^{51} - 12 q^{52} - 4 q^{54} - 4 q^{56} + 16 q^{61} + 4 q^{62} - 4 q^{64} - 24 q^{67} - 16 q^{69} + 12 q^{71} + 8 q^{73} + 4 q^{74} + 12 q^{78} - 16 q^{79} + 4 q^{81} - 12 q^{82} + 8 q^{84} - 32 q^{86} - 12 q^{88} - 12 q^{89} - 12 q^{91} + 4 q^{96} - 8 q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 - 4 * q^7 - 12 * q^11 - 4 * q^12 + 12 * q^13 + 4 * q^14 + 4 * q^16 - 8 * q^21 + 12 * q^22 - 4 * q^24 + 4 * q^27 + 4 * q^28 + 4 * q^31 - 32 * q^33 + 4 * q^37 - 12 * q^38 + 12 * q^39 + 12 * q^41 + 12 * q^44 + 12 * q^47 + 4 * q^48 - 16 * q^51 - 12 * q^52 - 4 * q^54 - 4 * q^56 + 16 * q^61 + 4 * q^62 - 4 * q^64 - 24 * q^67 - 16 * q^69 + 12 * q^71 + 8 * q^73 + 4 * q^74 + 12 * q^78 - 16 * q^79 + 4 * q^81 - 12 * q^82 + 8 * q^84 - 32 * q^86 - 12 * q^88 - 12 * q^89 - 12 * q^91 + 4 * q^96 - 8 * q^97 + 20 * q^98 - 16 * q^99

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