LMFDB - Embedded newform 360.2.b.d.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(251,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("360.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.b (of order $2$, degree $1$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.2580992.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + x^{4} + 2x^{2} - 8x + 8 $ x^6 - 2x^5 + x^4 + 2x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Root			$-1.06244 - 0.933389i$ of defining polynomial
Character	$\chi$	$=$	360.251
Dual form			360.2.b.d.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06244 + 0.933389i) q^{2} +(0.257569 - 1.98335i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(1.57758 + 2.34760i) q^{8} +O(q^{10})$	\(q+(-1.06244 + 0.933389i) q^{2} +(0.257569 - 1.98335i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(1.57758 + 2.34760i) q^{8} +(-1.06244 + 0.933389i) q^{10} +2.31934i q^{11} -5.14777i q^{13} +(1.32001 + 1.50252i) q^{14} +(-3.86732 - 1.02170i) q^{16} -5.10495i q^{17} +8.24977 q^{19} +(0.257569 - 1.98335i) q^{20} +(-2.16485 - 2.46417i) q^{22} +0.969724 q^{23} +1.00000 q^{25} +(4.80487 + 5.46921i) q^{26} +(-2.80487 - 0.364258i) q^{28} +3.28005 q^{29} +5.10495i q^{31} +(5.06244 - 2.52422i) q^{32} +(4.76491 + 5.42372i) q^{34} -1.41421i q^{35} +3.69074i q^{37} +(-8.76491 + 7.70025i) q^{38} +(1.57758 + 2.34760i) q^{40} -4.59587i q^{41} +3.21949 q^{43} +(4.60006 + 0.597391i) q^{44} +(-1.03028 + 0.905130i) q^{46} -9.52982 q^{47} +5.00000 q^{49} +(-1.06244 + 0.933389i) q^{50} +(-10.2098 - 1.32591i) q^{52} +7.21949 q^{53} +2.31934i q^{55} +(3.32001 - 2.23104i) q^{56} +(-3.48486 + 3.06156i) q^{58} +0.862313i q^{59} -4.63869i q^{61} +(-4.76491 - 5.42372i) q^{62} +(-3.02248 + 7.40707i) q^{64} -5.14777i q^{65} +5.28005 q^{67} +(-10.1249 - 1.31488i) q^{68} +(1.32001 + 1.50252i) q^{70} -13.2800 q^{71} -12.5601 q^{73} +(-3.44490 - 3.92120i) q^{74} +(2.12489 - 16.3621i) q^{76} +3.28005 q^{77} +8.01901i q^{79} +(-3.86732 - 1.02170i) q^{80} +(4.28974 + 4.88285i) q^{82} +7.38148i q^{83} -5.10495i q^{85} +(-3.42053 + 3.00504i) q^{86} +(-5.44490 + 3.65895i) q^{88} -10.2527i q^{89} -7.28005 q^{91} +(0.249771 - 1.92330i) q^{92} +(10.1249 - 8.89503i) q^{94} +8.24977 q^{95} -15.7796 q^{97} +(-5.31221 + 4.66695i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8} + 2 q^{10} - 6 q^{16} + 16 q^{19} + 2 q^{20} - 20 q^{22} + 4 q^{23} + 6 q^{25} + 20 q^{26} - 8 q^{28} - 12 q^{29} + 22 q^{32} - 4 q^{34} - 20 q^{38} + 2 q^{40} - 16 q^{43} - 12 q^{44} - 8 q^{46} + 8 q^{47} + 30 q^{49} + 2 q^{50} - 4 q^{52} + 8 q^{53} + 12 q^{56} - 20 q^{58} + 4 q^{62} + 14 q^{64} - 44 q^{68} - 48 q^{71} - 12 q^{73} + 4 q^{74} - 4 q^{76} - 12 q^{77} - 6 q^{80} + 16 q^{82} - 40 q^{86} - 8 q^{88} - 12 q^{91} - 32 q^{92} + 44 q^{94} + 16 q^{95} + 4 q^{97} + 10 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8 + 2 * q^10 - 6 * q^16 + 16 * q^19 + 2 * q^20 - 20 * q^22 + 4 * q^23 + 6 * q^25 + 20 * q^26 - 8 * q^28 - 12 * q^29 + 22 * q^32 - 4 * q^34 - 20 * q^38 + 2 * q^40 - 16 * q^43 - 12 * q^44 - 8 * q^46 + 8 * q^47 + 30 * q^49 + 2 * q^50 - 4 * q^52 + 8 * q^53 + 12 * q^56 - 20 * q^58 + 4 * q^62 + 14 * q^64 - 44 * q^68 - 48 * q^71 - 12 * q^73 + 4 * q^74 - 4 * q^76 - 12 * q^77 - 6 * q^80 + 16 * q^82 - 40 * q^86 - 8 * q^88 - 12 * q^91 - 32 * q^92 + 44 * q^94 + 16 * q^95 + 4 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.06244	+	0.933389i	−0.751260	+	0.660006i
$2$	−1.06244	+	0.933389i	−0.751260	+	0.660006i
$3$		0			0
$3$		0			0
$4$	0.257569	−	1.98335i	0.128785	−	0.991673i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$		−	1.41421i		−	0.534522i	−0.963624	−	0.267261i	$-0.913881\pi$
$7$		−	1.41421i		−	0.534522i	0.963624	−	0.267261i	$-0.0861187\pi$
$8$	1.57758	+	2.34760i	0.557759	+	0.830003i
$9$		0			0
$10$	−1.06244	+	0.933389i	−0.335974	+	0.295164i
$11$			2.31934i			0.699308i	0.936879	+	0.349654i	$0.113701\pi$
$11$			2.31934i			0.699308i	−0.936879	+	0.349654i	$0.886299\pi$
$12$		0			0
$13$		−	5.14777i		−	1.42773i	−0.700281	−	0.713867i	$-0.746942\pi$
$13$		−	5.14777i		−	1.42773i	0.700281	−	0.713867i	$-0.253058\pi$
$14$	1.32001	+	1.50252i	0.352788	+	0.401566i
$15$		0			0
$16$	−3.86732	−	1.02170i	−0.966829	−	0.255424i
$17$		−	5.10495i		−	1.23813i	−0.785339	−	0.619067i	$-0.787511\pi$
$17$		−	5.10495i		−	1.23813i	0.785339	−	0.619067i	$-0.212489\pi$
$18$		0			0
$19$	8.24977			1.89263			0.946314	−	0.323250i	$-0.104775\pi$
$19$	8.24977			1.89263			0.946314	+	0.323250i	$0.104775\pi$
$20$	0.257569	−	1.98335i	0.0575942	−	0.443489i
$21$		0			0
$22$	−2.16485	−	2.46417i	−0.461548	−	0.525363i
$23$	0.969724			0.202201			0.101101	−	0.994876i	$-0.467764\pi$
$23$	0.969724			0.202201			0.101101	+	0.994876i	$0.467764\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	4.80487	+	5.46921i	0.942313	+	1.07260i
$27$		0			0
$28$	−2.80487	−	0.364258i	−0.530071	−	0.0688382i
$29$	3.28005			0.609089			0.304545	−	0.952498i	$-0.401496\pi$
$29$	3.28005			0.609089			0.304545	+	0.952498i	$0.401496\pi$
$30$		0			0
$31$			5.10495i			0.916877i	0.888726	+	0.458438i	$0.151591\pi$
$31$			5.10495i			0.916877i	−0.888726	+	0.458438i	$0.848409\pi$
$32$	5.06244	−	2.52422i	0.894922	−	0.446223i
$33$		0			0
$34$	4.76491	+	5.42372i	0.817175	+	0.930160i
$35$		−	1.41421i		−	0.239046i
$36$		0			0
$37$			3.69074i			0.606754i	0.952871	+	0.303377i	$0.0981141\pi$
$37$			3.69074i			0.606754i	−0.952871	+	0.303377i	$0.901886\pi$
$38$	−8.76491	+	7.70025i	−1.42186	+	1.24915i
$39$		0			0
$40$	1.57758	+	2.34760i	0.249437	+	0.371189i
$41$		−	4.59587i		−	0.717754i	−0.933385	−	0.358877i	$-0.883160\pi$
$41$		−	4.59587i		−	0.717754i	0.933385	−	0.358877i	$-0.116840\pi$
$42$		0			0
$43$	3.21949			0.490968			0.245484	−	0.969401i	$-0.421053\pi$
$43$	3.21949			0.490968			0.245484	+	0.969401i	$0.421053\pi$
$44$	4.60006	+	0.597391i	0.693485	+	0.0900601i
$45$		0			0
$46$	−1.03028	+	0.905130i	−0.151906	+	0.133454i
$47$	−9.52982			−1.39007			−0.695033	−	0.718977i	$-0.744610\pi$
$47$	−9.52982			−1.39007			−0.695033	+	0.718977i	$0.744610\pi$
$48$		0			0
$49$	5.00000			0.714286
$50$	−1.06244	+	0.933389i	−0.150252	+	0.132001i
$51$		0			0
$52$	−10.2098	−	1.32591i	−1.41585	−	0.183870i
$53$	7.21949			0.991674			0.495837	−	0.868416i	$-0.334861\pi$
$53$	7.21949			0.991674			0.495837	+	0.868416i	$0.334861\pi$
$54$		0			0
$55$			2.31934i			0.312740i
$56$	3.32001	−	2.23104i	0.443655	−	0.298135i
$57$		0			0
$58$	−3.48486	+	3.06156i	−0.457585	+	0.402003i
$59$			0.862313i			0.112264i	0.998423	+	0.0561318i	$0.0178767\pi$
$59$			0.862313i			0.112264i	−0.998423	+	0.0561318i	$0.982123\pi$
$60$		0			0
$61$		−	4.63869i		−	0.593923i	−0.954889	−	0.296961i	$-0.904027\pi$
$61$		−	4.63869i		−	0.593923i	0.954889	−	0.296961i	$-0.0959733\pi$
$62$	−4.76491	−	5.42372i	−0.605144	−	0.688813i
$63$		0			0
$64$	−3.02248	+	7.40707i	−0.377810	+	0.925883i
$65$		−	5.14777i		−	0.638502i
$66$		0			0
$67$	5.28005			0.645060			0.322530	−	0.946559i	$-0.395467\pi$
$67$	5.28005			0.645060			0.322530	+	0.946559i	$0.395467\pi$
$68$	−10.1249	−	1.31488i	−1.22782	−	0.159452i
$69$		0			0
$70$	1.32001	+	1.50252i	0.157772	+	0.179586i
$71$	−13.2800			−1.57605			−0.788026	−	0.615642i	$-0.788897\pi$
$71$	−13.2800			−1.57605			−0.788026	+	0.615642i	$0.788897\pi$
$72$		0			0
$73$	−12.5601			−1.47005			−0.735024	−	0.678041i	$-0.762829\pi$
$73$	−12.5601			−1.47005			−0.735024	+	0.678041i	$0.762829\pi$
$74$	−3.44490	−	3.92120i	−0.400461	−	0.455830i
$75$		0			0
$76$	2.12489	−	16.3621i	0.243741	−	1.87687i
$77$	3.28005			0.373796
$78$		0			0
$79$			8.01901i			0.902210i	0.892471	+	0.451105i	$0.148970\pi$
$79$			8.01901i			0.902210i	−0.892471	+	0.451105i	$0.851030\pi$
$80$	−3.86732	−	1.02170i	−0.432379	−	0.114229i
$81$		0			0
$82$	4.28974	+	4.88285i	0.473722	+	0.539220i
$83$			7.38148i			0.810223i	0.914267	+	0.405111i	$0.132767\pi$
$83$			7.38148i			0.810223i	−0.914267	+	0.405111i	$0.867233\pi$
$84$		0			0
$85$		−	5.10495i		−	0.553710i
$86$	−3.42053	+	3.00504i	−0.368845	+	0.324042i
$87$		0			0
$88$	−5.44490	+	3.65895i	−0.580428	+	0.390046i
$89$		−	10.2527i		−	1.08679i	−0.839478	−	0.543393i	$-0.817139\pi$
$89$		−	10.2527i		−	1.08679i	0.839478	−	0.543393i	$-0.182861\pi$
$90$		0			0
$91$	−7.28005			−0.763156
$92$	0.249771	−	1.92330i	0.0260404	−	0.200518i
$93$		0			0
$94$	10.1249	−	8.89503i	1.04430	−	0.917452i
$95$	8.24977			0.846409
$96$		0			0
$97$	−15.7796			−1.60217			−0.801087	−	0.598548i	$-0.795745\pi$
$97$	−15.7796			−1.60217			−0.801087	+	0.598548i	$0.795745\pi$
$98$	−5.31221	+	4.66695i	−0.536615	+	0.471433i
$99$		0			0
$100$	0.257569	−	1.98335i	0.0257569	−	0.198335i
$101$	−16.4390			−1.63574			−0.817870	−	0.575403i	$-0.804845\pi$
$101$	−16.4390			−1.63574			−0.817870	+	0.575403i	$0.804845\pi$
$102$		0			0
$103$		−	15.9096i		−	1.56762i	−0.621002	−	0.783809i	$-0.713274\pi$
$103$		−	15.9096i		−	1.56762i	0.621002	−	0.783809i	$-0.286726\pi$
$104$	12.0849	−	8.12102i	1.18502	−	0.796332i
$105$		0			0
$106$	−7.67030	+	6.73860i	−0.745005	+	0.654511i
$107$		−	2.82843i		−	0.273434i	−0.990610	−	0.136717i	$-0.956345\pi$
$107$		−	2.82843i		−	0.273434i	0.990610	−	0.136717i	$-0.0436552\pi$
$108$		0			0
$109$			10.2955i			0.986134i	0.869991	+	0.493067i	$0.164124\pi$
$109$			10.2955i			0.986134i	−0.869991	+	0.493067i	$0.835876\pi$
$110$	−2.16485	−	2.46417i	−0.206410	−	0.234949i
$111$		0			0
$112$	−1.44490	+	5.46921i	−0.136530	+	0.516792i
$113$			0.466267i			0.0438627i	0.999759	+	0.0219313i	$0.00698152\pi$
$113$			0.466267i			0.0438627i	−0.999759	+	0.0219313i	$0.993018\pi$
$114$		0			0
$115$	0.969724			0.0904272
$116$	0.844838	−	6.50547i	0.0784413	−	0.604017i
$117$		0			0
$118$	−0.804874	−	0.916158i	−0.0740946	−	0.0843392i
$119$	−7.21949			−0.661810
$120$		0			0
$121$	5.62065			0.510968
$122$	4.32970	+	4.92834i	0.391993	+	0.446191i
$123$		0			0
$124$	10.1249	+	1.31488i	0.909242	+	0.118080i
$125$	1.00000			0.0894427
$126$		0			0
$127$			6.71784i			0.596112i	0.954548	+	0.298056i	$0.0963382\pi$
$127$			6.71784i			0.596112i	−0.954548	+	0.298056i	$0.903662\pi$
$128$	−3.70247	−	10.6907i	−0.327255	−	0.944936i
$129$		0			0
$130$	4.80487	+	5.46921i	0.421415	+	0.479682i
$131$			21.1002i			1.84353i	0.387749	+	0.921765i	$0.373253\pi$
$131$			21.1002i			1.84353i	−0.387749	+	0.921765i	$0.626747\pi$
$132$		0			0
$133$		−	11.6669i		−	1.01165i
$134$	−5.60975	+	4.92834i	−0.484608	+	0.425744i
$135$		0			0
$136$	11.9844	−	8.05348i	1.02765	−	0.690580i
$137$			21.0573i			1.79905i	0.436869	+	0.899525i	$0.356087\pi$
$137$			21.0573i			1.79905i	−0.436869	+	0.899525i	$0.643913\pi$
$138$		0			0
$139$	−2.90917			−0.246753			−0.123376	−	0.992360i	$-0.539372\pi$
$139$	−2.90917			−0.246753			−0.123376	+	0.992360i	$0.539372\pi$
$140$	−2.80487	−	0.364258i	−0.237055	−	0.0307854i
$141$		0			0
$142$	14.1093	−	12.3955i	1.18403	−	1.04020i
$143$	11.9394			0.998427
$144$		0			0
$145$	3.28005			0.272393
$146$	13.3444	−	11.7235i	1.10439	−	0.970240i
$147$		0			0
$148$	7.32001	+	0.950620i	0.601701	+	0.0781405i
$149$	11.2800			0.924097			0.462049	−	0.886855i	$-0.347115\pi$
$149$	11.2800			0.924097			0.462049	+	0.886855i	$0.347115\pi$
$150$		0			0
$151$			21.7638i			1.77111i	0.464531	+	0.885557i	$0.346223\pi$
$151$			21.7638i			1.77111i	−0.464531	+	0.885557i	$0.653777\pi$
$152$	13.0147	+	19.3672i	1.05563	+	1.57089i
$153$		0			0
$154$	−3.48486	+	3.06156i	−0.280818	+	0.246708i
$155$			5.10495i			0.410040i
$156$		0			0
$157$			8.32943i			0.664761i	0.943145	+	0.332380i	$0.107852\pi$
$157$			8.32943i			0.664761i	−0.943145	+	0.332380i	$0.892148\pi$
$158$	−7.48486	−	8.51974i	−0.595464	−	0.677794i
$159$		0			0
$160$	5.06244	−	2.52422i	0.400221	−	0.199557i
$161$		−	1.37140i		−	0.108081i
$162$		0			0
$163$	−20.4995			−1.60565			−0.802824	−	0.596216i	$-0.796670\pi$
$163$	−20.4995			−1.60565			−0.802824	+	0.596216i	$0.796670\pi$
$164$	−9.11520	−	1.18375i	−0.711777	−	0.0924356i
$165$		0			0
$166$	−6.88979	−	7.84240i	−0.534752	−	0.608688i
$167$	−6.90917			−0.534648			−0.267324	−	0.963607i	$-0.586139\pi$
$167$	−6.90917			−0.534648			−0.267324	+	0.963607i	$0.586139\pi$
$168$		0			0
$169$	−13.4995			−1.03843
$170$	4.76491	+	5.42372i	0.365452	+	0.415980i
$171$		0			0
$172$	0.829242	−	6.38537i	0.0632291	−	0.486880i
$173$	19.2195			1.46123			0.730616	−	0.682789i	$-0.239233\pi$
$173$	19.2195			1.46123			0.730616	+	0.682789i	$0.239233\pi$
$174$		0			0
$175$		−	1.41421i		−	0.106904i
$176$	2.36967	−	8.96963i	0.178620	−	0.676112i
$177$		0			0
$178$	9.56978	+	10.8929i	0.717286	+	0.816460i
$179$		−	12.5293i		−	0.936480i	−0.883601	−	0.468240i	$-0.844888\pi$
$179$		−	12.5293i		−	0.936480i	0.883601	−	0.468240i	$-0.155112\pi$
$180$		0			0
$181$		−	3.53489i		−	0.262746i	−0.991333	−	0.131373i	$-0.958061\pi$
$181$		−	3.53489i		−	0.262746i	0.991333	−	0.131373i	$-0.0419386\pi$
$182$	7.73463	−	6.79512i	0.573329	−	0.503688i
$183$		0			0
$184$	1.52982	+	2.27653i	0.112780	+	0.167828i
$185$			3.69074i			0.271349i
$186$		0			0
$187$	11.8401			0.865837
$188$	−2.45459	+	18.9009i	−0.179019	+	1.37849i
$189$		0			0
$190$	−8.76491	+	7.70025i	−0.635873	+	0.558635i
$191$	25.1202			1.81763			0.908816	−	0.417196i	$-0.136987\pi$
$191$	25.1202			1.81763			0.908816	+	0.417196i	$0.136987\pi$
$192$		0			0
$193$	7.77959			0.559987			0.279994	−	0.960002i	$-0.409668\pi$
$193$	7.77959			0.559987			0.279994	+	0.960002i	$0.409668\pi$
$194$	16.7649	−	14.7285i	1.20365	−	1.05744i
$195$		0			0
$196$	1.28785	−	9.91673i	0.0919889	−	0.708338i
$197$	2.49954			0.178085			0.0890425	−	0.996028i	$-0.471619\pi$
$197$	2.49954			0.178085			0.0890425	+	0.996028i	$0.471619\pi$
$198$		0			0
$199$		−	21.0573i		−	1.49272i	−0.665545	−	0.746358i	$-0.731801\pi$
$199$		−	21.0573i		−	1.49272i	0.665545	−	0.746358i	$-0.268199\pi$
$200$	1.57758	+	2.34760i	0.111552	+	0.166001i
$201$		0			0
$202$	17.4655	−	15.3440i	1.22887	−	1.07960i
$203$		−	4.63869i		−	0.325572i
$204$		0			0
$205$		−	4.59587i		−	0.320989i
$206$	14.8498	+	16.9030i	1.03464	+	1.17769i
$207$		0			0
$208$	−5.25946	+	19.9081i	−0.364678	+	1.38038i
$209$			19.1341i			1.32353i
$210$		0			0
$211$	−16.0294			−1.10351			−0.551753	−	0.834007i	$-0.686041\pi$
$211$	−16.0294			−1.10351			−0.551753	+	0.834007i	$0.686041\pi$
$212$	1.85952	−	14.3188i	0.127712	−	0.983416i
$213$		0			0
$214$	2.64002	+	3.00504i	0.180468	+	0.205420i
$215$	3.21949			0.219568
$216$		0			0
$217$	7.21949			0.490091
$218$	−9.60975	−	10.9384i	−0.650854	−	0.740843i
$219$		0			0
$220$	4.60006	+	0.597391i	0.310136	+	0.0402761i
$221$	−26.2791			−1.76773
$222$		0			0
$223$		−	0.310412i		−	0.0207868i	−0.999946	−	0.0103934i	$-0.996692\pi$
$223$		−	0.310412i		−	0.0207868i	0.999946	−	0.0103934i	$-0.00330837\pi$
$224$	−3.56978	−	7.15938i	−0.238516	−	0.478356i
$225$		0			0
$226$	−0.435208	−	0.495382i	−0.0289496	−	0.0329523i
$227$			3.84659i			0.255307i	0.991819	+	0.127654i	$0.0407446\pi$
$227$			3.84659i			0.255307i	−0.991819	+	0.127654i	$0.959255\pi$
$228$		0			0
$229$			6.36331i			0.420500i	0.977648	+	0.210250i	$0.0674277\pi$
$229$			6.36331i			0.420500i	−0.977648	+	0.210250i	$0.932572\pi$
$230$	−1.03028	+	0.905130i	−0.0679344	+	0.0596825i
$231$		0			0
$232$	5.17454	+	7.70025i	0.339725	+	0.505546i
$233$			1.25836i			0.0824379i	0.999150	+	0.0412189i	$0.0131241\pi$
$233$			1.25836i			0.0824379i	−0.999150	+	0.0412189i	$0.986876\pi$
$234$		0			0
$235$	−9.52982			−0.621657
$236$	1.71026	+	0.222105i	0.111329	+	0.0144578i
$237$		0			0
$238$	7.67030	−	6.73860i	0.497192	−	0.436798i
$239$	−0.499542			−0.0323127			−0.0161563	−	0.999869i	$-0.505143\pi$
$239$	−0.499542			−0.0323127			−0.0161563	+	0.999869i	$0.505143\pi$
$240$		0			0
$241$	6.06055			0.390394			0.195197	−	0.980764i	$-0.437465\pi$
$241$	6.06055			0.390394			0.195197	+	0.980764i	$0.437465\pi$
$242$	−5.97161	+	5.24625i	−0.383870	+	0.337242i
$243$		0			0
$244$	−9.20012	−	1.19478i	−0.588977	−	0.0764881i
$245$	5.00000			0.319438
$246$		0			0
$247$		−	42.4679i		−	2.70217i
$248$	−11.9844	+	8.05348i	−0.761010	+	0.511396i
$249$		0			0
$250$	−1.06244	+	0.933389i	−0.0671948	+	0.0590327i
$251$		−	12.0904i		−	0.763139i	−0.924340	−	0.381569i	$-0.875384\pi$
$251$		−	12.0904i		−	0.763139i	0.924340	−	0.381569i	$-0.124616\pi$
$252$		0			0
$253$			2.24912i			0.141401i
$254$	−6.27036	−	7.13732i	−0.393437	−	0.447835i
$255$		0			0
$256$	13.9123	+	7.90245i	0.869517	+	0.493903i
$257$			11.5539i			0.720712i	0.932815	+	0.360356i	$0.117345\pi$
$257$			11.5539i			0.720712i	−0.932815	+	0.360356i	$0.882655\pi$
$258$		0			0
$259$	5.21949			0.324324
$260$	−10.2098	−	1.32591i	−0.633185	−	0.0822292i
$261$		0			0
$262$	−19.6947	−	22.4177i	−1.21674	−	1.38497i
$263$	7.52982			0.464308			0.232154	−	0.972679i	$-0.425423\pi$
$263$	7.52982			0.464308			0.232154	+	0.972679i	$0.425423\pi$
$264$		0			0
$265$	7.21949			0.443490
$266$	10.8898	+	12.3955i	0.667696	+	0.760014i
$267$		0			0
$268$	1.35998	−	10.4722i	0.0830738	−	0.639689i
$269$	−25.8401			−1.57550			−0.787751	−	0.615994i	$-0.788754\pi$
$269$	−25.8401			−1.57550			−0.787751	+	0.615994i	$0.788754\pi$
$270$		0			0
$271$			23.8001i			1.44576i	0.690976	+	0.722878i	$0.257181\pi$
$271$			23.8001i			1.44576i	−0.690976	+	0.722878i	$0.742819\pi$
$272$	−5.21571	+	19.7425i	−0.316249	+	1.19706i
$273$		0			0
$274$	−19.6547	−	22.3722i	−1.18738	−	1.35156i
$275$			2.31934i			0.139862i
$276$		0			0
$277$			24.1962i			1.45381i	0.686739	+	0.726904i	$0.259042\pi$
$277$			24.1962i			1.45381i	−0.686739	+	0.726904i	$0.740958\pi$
$278$	3.09083	−	2.71539i	0.185376	−	0.162858i
$279$		0			0
$280$	3.32001	−	2.23104i	0.198409	−	0.133330i
$281$		−	8.96696i		−	0.534924i	−0.963568	−	0.267462i	$-0.913815\pi$
$281$		−	8.96696i		−	0.534924i	0.963568	−	0.267462i	$-0.0861850\pi$
$282$		0			0
$283$	14.7200			0.875010			0.437505	−	0.899216i	$-0.355862\pi$
$283$	14.7200			0.875010			0.437505	+	0.899216i	$0.355862\pi$
$284$	−3.42053	+	26.3389i	−0.202971	+	1.56293i
$285$		0			0
$286$	−12.6850	+	11.1442i	−0.750079	+	0.658968i
$287$	−6.49954			−0.383656
$288$		0			0
$289$	−9.06055			−0.532974
$290$	−3.48486	+	3.06156i	−0.204638	+	0.179781i
$291$		0			0
$292$	−3.23509	+	24.9110i	−0.189319	+	1.45781i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$			0.862313i			0.0502058i
$296$	−8.66439	+	5.82244i	−0.503608	+	0.338422i
$297$		0			0
$298$	−11.9844	+	10.5287i	−0.694238	+	0.609910i
$299$		−	4.99192i		−	0.288690i
$300$		0			0
$301$		−	4.55305i		−	0.262434i
$302$	−20.3141	−	23.1228i	−1.16895	−	1.33057i
$303$		0			0
$304$	−31.9045	−	8.42876i	−1.82985	−	0.483423i
$305$		−	4.63869i		−	0.265610i
$306$		0			0
$307$	10.0606			0.574186			0.287093	−	0.957903i	$-0.407311\pi$
$307$	10.0606			0.574186			0.287093	+	0.957903i	$0.407311\pi$
$308$	0.844838	−	6.50547i	0.0481391	−	0.370683i
$309$		0			0
$310$	−4.76491	−	5.42372i	−0.270629	−	0.308047i
$311$	−11.5005			−0.652131			−0.326066	−	0.945347i	$-0.605723\pi$
$311$	−11.5005			−0.652131			−0.326066	+	0.945347i	$0.605723\pi$
$312$		0			0
$313$	6.65940			0.376412			0.188206	−	0.982130i	$-0.439733\pi$
$313$	6.65940			0.376412			0.188206	+	0.982130i	$0.439733\pi$
$314$	−7.77460	−	8.84954i	−0.438746	−	0.499408i
$315$		0			0
$316$	15.9045	+	2.06545i	0.894697	+	0.116191i
$317$	−4.06055			−0.228063			−0.114032	−	0.993477i	$-0.536377\pi$
$317$	−4.06055			−0.228063			−0.114032	+	0.993477i	$0.536377\pi$
$318$		0			0
$319$			7.60756i			0.425941i
$320$	−3.02248	+	7.40707i	−0.168962	+	0.414068i
$321$		0			0
$322$	1.28005	+	1.45703i	0.0713342	+	0.0811971i
$323$		−	42.1147i		−	2.34332i
$324$		0			0
$325$		−	5.14777i		−	0.285547i
$326$	21.7796	−	19.1341i	1.20626	−	1.05974i
$327$		0			0
$328$	10.7893	−	7.25036i	0.595738	−	0.400334i
$329$			13.4772i			0.743022i
$330$		0			0
$331$	−10.3103			−0.566707			−0.283353	−	0.959016i	$-0.591447\pi$
$331$	−10.3103			−0.566707			−0.283353	+	0.959016i	$0.591447\pi$
$332$	14.6400	+	1.90124i	0.803476	+	0.104344i
$333$		0			0
$334$	7.34060	−	6.44895i	0.401660	−	0.352871i
$335$	5.28005			0.288480
$336$		0			0
$337$	−2.12110			−0.115544			−0.0577720	−	0.998330i	$-0.518400\pi$
$337$	−2.12110			−0.115544			−0.0577720	+	0.998330i	$0.518400\pi$
$338$	14.3425	−	12.6003i	0.780129	−	0.685367i
$339$		0			0
$340$	−10.1249	−	1.31488i	−0.549099	−	0.0713093i
$341$	−11.8401			−0.641180
$342$		0			0
$343$		−	16.9706i		−	0.916324i
$344$	5.07901	+	7.55809i	0.273842	+	0.407505i
$345$		0			0
$346$	−20.4196	+	17.9393i	−1.09777	+	0.964421i
$347$		−	32.6112i		−	1.75066i	−0.483523	−	0.875332i	$-0.660643\pi$
$347$		−	32.6112i		−	1.75066i	0.483523	−	0.875332i	$-0.339357\pi$
$348$		0			0
$349$		−	7.55275i		−	0.404289i	−0.979356	−	0.202145i	$-0.935209\pi$
$349$		−	7.55275i		−	0.404289i	0.979356	−	0.202145i	$-0.0647911\pi$
$350$	1.32001	+	1.50252i	0.0705576	+	0.0803131i
$351$		0			0
$352$	5.85453	+	11.7415i	0.312047	+	0.625826i
$353$		−	8.01901i		−	0.426809i	−0.976964	−	0.213405i	$-0.931545\pi$
$353$		−	8.01901i		−	0.426809i	0.976964	−	0.213405i	$-0.0684552\pi$
$354$		0			0
$355$	−13.2800			−0.704832
$356$	−20.3347	−	2.64078i	−1.07774	−	0.139961i
$357$		0			0
$358$	11.6947	+	13.3116i	0.618082	+	0.703541i
$359$	3.71904			0.196283			0.0981416	−	0.995172i	$-0.468710\pi$
$359$	3.71904			0.196283			0.0981416	+	0.995172i	$0.468710\pi$
$360$		0			0
$361$	49.0587			2.58204
$362$	3.29942	+	3.75561i	0.173414	+	0.197391i
$363$		0			0
$364$	−1.87511	+	14.4388i	−0.0982827	+	0.756801i
$365$	−12.5601			−0.657425
$366$		0			0
$367$			14.1850i			0.740448i	0.928942	+	0.370224i	$0.120719\pi$
$367$			14.1850i			0.740448i	−0.928942	+	0.370224i	$0.879281\pi$
$368$	−3.75023	−	0.990764i	−0.195494	−	0.0516471i
$369$		0			0
$370$	−3.44490	−	3.92120i	−0.179092	−	0.203853i
$371$		−	10.2099i		−	0.530072i
$372$		0			0
$373$			35.5955i			1.84307i	0.388299	+	0.921533i	$0.373063\pi$
$373$			35.5955i			1.84307i	−0.388299	+	0.921533i	$0.626937\pi$
$374$	−12.5795	+	11.0515i	−0.650469	+	0.571457i
$375$		0			0
$376$	−15.0341	−	22.3722i	−0.775322	−	1.15376i
$377$		−	16.8849i		−	0.869618i
$378$		0			0
$379$	−9.59037			−0.492624			−0.246312	−	0.969191i	$-0.579219\pi$
$379$	−9.59037			−0.492624			−0.246312	+	0.969191i	$0.579219\pi$
$380$	2.12489	−	16.3621i	0.109004	−	0.839360i
$381$		0			0
$382$	−26.6888	+	23.4469i	−1.36552	+	1.19965i
$383$	19.5904			1.00102			0.500511	−	0.865730i	$-0.333146\pi$
$383$	19.5904			1.00102			0.500511	+	0.865730i	$0.333146\pi$
$384$		0			0
$385$	3.28005			0.167167
$386$	−8.26537	+	7.26138i	−0.420696	+	0.369595i
$387$		0			0
$388$	−4.06433	+	31.2964i	−0.206335	+	1.58883i
$389$	−2.12110			−0.107544			−0.0537721	−	0.998553i	$-0.517124\pi$
$389$	−2.12110			−0.107544			−0.0537721	+	0.998553i	$0.517124\pi$
$390$		0			0
$391$		−	4.95040i		−	0.250352i
$392$	7.88790	+	11.7380i	0.398399	+	0.592859i
$393$		0			0
$394$	−2.65562	+	2.33305i	−0.133788	+	0.117537i
$395$			8.01901i			0.403480i
$396$		0			0
$397$			27.3778i			1.37405i	0.726632	+	0.687027i	$0.241085\pi$
$397$			27.3778i			1.37405i	−0.726632	+	0.687027i	$0.758915\pi$
$398$	19.6547	+	22.3722i	0.985201	+	1.12142i
$399$		0			0
$400$	−3.86732	−	1.02170i	−0.193366	−	0.0510848i
$401$			2.78561i			0.139107i	0.997578	+	0.0695534i	$0.0221574\pi$
$401$			2.78561i			0.139107i	−0.997578	+	0.0695534i	$0.977843\pi$
$402$		0			0
$403$	26.2791			1.30906
$404$	−4.23417	+	32.6042i	−0.210658	+	1.62212i
$405$		0			0
$406$	4.32970	+	4.92834i	0.214879	+	0.244589i
$407$	−8.56009			−0.424308
$408$		0			0
$409$	12.4390			0.615068			0.307534	−	0.951537i	$-0.400496\pi$
$409$	12.4390			0.615068			0.307534	+	0.951537i	$0.400496\pi$
$410$	4.28974	+	4.88285i	0.211855	+	0.241147i
$411$		0			0
$412$	−31.5542	−	4.09781i	−1.55456	−	0.201885i
$413$	1.21949			0.0600074
$414$		0			0
$415$			7.38148i			0.362343i
$416$	−12.9941	−	26.0603i	−0.637088	−	1.27771i
$417$		0			0
$418$	−17.8595	−	20.3288i	−0.873538	−	0.994316i
$419$			9.34759i			0.456660i	0.973584	+	0.228330i	$0.0733265\pi$
$419$			9.34759i			0.456660i	−0.973584	+	0.228330i	$0.926674\pi$
$420$		0			0
$421$		−	23.3339i		−	1.13722i	−0.822606	−	0.568612i	$-0.807481\pi$
$421$		−	23.3339i		−	1.13722i	0.822606	−	0.568612i	$-0.192519\pi$
$422$	17.0303	−	14.9616i	0.829021	−	0.728321i
$423$		0			0
$424$	11.3893	+	16.9485i	0.553115	+	0.823092i
$425$		−	5.10495i		−	0.247627i
$426$		0			0
$427$	−6.56009			−0.317465
$428$	−5.60975	−	0.728515i	−0.271157	−	0.0352141i
$429$		0			0
$430$	−3.42053	+	3.00504i	−0.164953	+	0.144916i
$431$	23.7190			1.14251			0.571253	−	0.820774i	$-0.306458\pi$
$431$	23.7190			1.14251			0.571253	+	0.820774i	$0.306458\pi$
$432$		0			0
$433$	16.5601			0.795827			0.397914	−	0.917423i	$-0.369734\pi$
$433$	16.5601			0.795827			0.397914	+	0.917423i	$0.369734\pi$
$434$	−7.67030	+	6.73860i	−0.368186	+	0.323463i
$435$		0			0
$436$	20.4196	+	2.65181i	0.977922	+	0.126999i
$437$	8.00000			0.382692
$438$		0			0
$439$		−	32.3711i		−	1.54499i	−0.635023	−	0.772493i	$-0.719009\pi$
$439$		−	32.3711i		−	1.54499i	0.635023	−	0.772493i	$-0.280991\pi$
$440$	−5.44490	+	3.65895i	−0.259575	+	0.174434i
$441$		0			0
$442$	27.9201	−	24.5287i	1.32802	−	1.16671i
$443$			30.0945i			1.42983i	0.699209	+	0.714917i	$0.253536\pi$
$443$			30.0945i			1.42983i	−0.699209	+	0.714917i	$0.746464\pi$
$444$		0			0
$445$		−	10.2527i		−	0.486026i
$446$	0.289736	+	0.329795i	0.0137194	+	0.0156163i
$447$		0			0
$448$	10.4752	+	4.27443i	0.494905	+	0.201948i
$449$		−	4.24264i		−	0.200223i	−0.994976	−	0.100111i	$-0.968080\pi$
$449$		−	4.24264i		−	0.200223i	0.994976	−	0.100111i	$-0.0319199\pi$
$450$		0			0
$451$	10.6594			0.501932
$452$	0.924768	+	0.120096i	0.0434974	+	0.00564884i
$453$		0			0
$454$	−3.59037	−	4.08679i	−0.168504	−	0.191802i
$455$	−7.28005			−0.341294
$456$		0			0
$457$	−26.2186			−1.22645			−0.613227	−	0.789907i	$-0.710129\pi$
$457$	−26.2186			−1.22645			−0.613227	+	0.789907i	$0.710129\pi$
$458$	−5.93945	−	6.76066i	−0.277532	−	0.315905i
$459$		0			0
$460$	0.249771	−	1.92330i	0.0116456	−	0.0896742i
$461$	15.4012			0.717303			0.358652	−	0.933472i	$-0.383237\pi$
$461$	15.4012			0.717303			0.358652	+	0.933472i	$0.383237\pi$
$462$		0			0
$463$			25.4130i			1.18104i	0.807022	+	0.590522i	$0.201078\pi$
$463$			25.4130i			1.18104i	−0.807022	+	0.590522i	$0.798922\pi$
$464$	−12.6850	−	3.35121i	−0.588885	−	0.155576i
$465$		0			0
$466$	−1.17454	−	1.33693i	−0.0544095	−	0.0619323i
$467$		−	26.1623i		−	1.21065i	−0.795980	−	0.605323i	$-0.793044\pi$
$467$		−	26.1623i		−	1.21065i	0.795980	−	0.605323i	$-0.206956\pi$
$468$		0			0
$469$		−	7.46711i		−	0.344799i
$470$	10.1249	−	8.89503i	0.467026	−	0.410297i
$471$		0			0
$472$	−2.02437	+	1.36037i	−0.0931791	+	0.0626160i
$473$			7.46711i			0.343338i
$474$		0			0
$475$	8.24977			0.378525
$476$	−1.85952	+	14.3188i	−0.0852309	+	0.656299i
$477$		0			0
$478$	0.530734	−	0.466267i	0.0242752	−	0.0213265i
$479$	−7.84014			−0.358225			−0.179113	−	0.983829i	$-0.557323\pi$
$479$	−7.84014			−0.358225			−0.179113	+	0.983829i	$0.557323\pi$
$480$		0			0
$481$	18.9991			0.866284
$482$	−6.43899	+	5.65685i	−0.293288	+	0.257663i
$483$		0			0
$484$	1.44770	−	11.1477i	0.0658047	−	0.506713i
$485$	−15.7796			−0.716514
$486$		0			0
$487$		−	13.1668i		−	0.596644i	−0.954465	−	0.298322i	$-0.903573\pi$
$487$		−	13.1668i		−	0.596644i	0.954465	−	0.298322i	$-0.0964269\pi$
$488$	10.8898	−	7.31790i	0.492958	−	0.331266i
$489$		0			0
$490$	−5.31221	+	4.66695i	−0.239981	+	0.210831i
$491$			12.8825i			0.581378i	0.956818	+	0.290689i	$0.0938845\pi$
$491$			12.8825i			0.581378i	−0.956818	+	0.290689i	$0.906115\pi$
$492$		0			0
$493$		−	16.7445i		−	0.754134i
$494$	39.6391	+	45.1197i	1.78345	+	2.03003i
$495$		0			0
$496$	5.21571	−	19.7425i	0.234192	−	0.886463i
$497$			18.7808i			0.842435i
$498$		0			0
$499$	−12.1287			−0.542954			−0.271477	−	0.962445i	$-0.587512\pi$
$499$	−12.1287			−0.542954			−0.271477	+	0.962445i	$0.587512\pi$
$500$	0.257569	−	1.98335i	0.0115188	−	0.0886979i
$501$		0			0
$502$	11.2850	+	12.8453i	0.503676	+	0.573316i
$503$	−29.4087			−1.31127			−0.655635	−	0.755078i	$-0.727599\pi$
$503$	−29.4087			−1.31127			−0.655635	+	0.755078i	$0.727599\pi$
$504$		0			0
$505$	−16.4390			−0.731525
$506$	−2.09931	−	2.38956i	−0.0933256	−	0.106229i
$507$		0			0
$508$	13.3238	+	1.73031i	0.591148	+	0.0767700i
$509$	25.5592			1.13289			0.566445	−	0.824099i	$-0.308318\pi$
$509$	25.5592			1.13289			0.566445	+	0.824099i	$0.308318\pi$
$510$		0			0
$511$			17.7627i			0.785774i
$512$	−22.1571	+	4.58967i	−0.979213	+	0.202837i
$513$		0			0
$514$	−10.7843	−	12.2754i	−0.475674	−	0.541443i
$515$		−	15.9096i		−	0.701060i
$516$		0			0
$517$		−	22.1029i		−	0.972085i
$518$	−5.54541	+	4.87182i	−0.243652	+	0.214055i
$519$		0			0
$520$	12.0849	−	8.12102i	0.529959	−	0.356130i
$521$		−	19.0912i		−	0.836402i	−0.908354	−	0.418201i	$-0.862661\pi$
$521$		−	19.0912i		−	0.836402i	0.908354	−	0.418201i	$-0.137339\pi$
$522$		0			0
$523$	8.12110			0.355111			0.177556	−	0.984111i	$-0.443181\pi$
$523$	8.12110			0.355111			0.177556	+	0.984111i	$0.443181\pi$
$524$	41.8489	+	5.43475i	1.82818	+	0.237418i
$525$		0			0
$526$	−8.00000	+	7.02825i	−0.348817	+	0.306446i
$527$	26.0606			1.13522
$528$		0			0
$529$	−22.0596			−0.959115
$530$	−7.67030	+	6.73860i	−0.333177	+	0.292706i
$531$		0			0
$532$	−23.1396	−	3.00504i	−1.00323	−	0.130285i
$533$	−23.6585			−1.02476
$534$		0			0
$535$		−	2.82843i		−	0.122284i
$536$	8.32970	+	12.3955i	0.359788	+	0.535402i
$537$		0			0
$538$	27.4537	−	24.1189i	1.18361	−	1.03984i
$539$			11.5967i			0.499506i
$540$		0			0
$541$		−	17.5914i		−	0.756313i	−0.925742	−	0.378156i	$-0.876558\pi$
$541$		−	17.5914i		−	0.756313i	0.925742	−	0.378156i	$-0.123442\pi$
$542$	−22.2148	−	25.2863i	−0.954207	−	1.08614i
$543$		0			0
$544$	−12.8860	−	25.8435i	−0.552483	−	1.10803i
$545$			10.2955i			0.441013i
$546$		0			0
$547$	20.3397			0.869662			0.434831	−	0.900512i	$-0.356808\pi$
$547$	20.3397			0.869662			0.434831	+	0.900512i	$0.356808\pi$
$548$	41.7640	+	5.42372i	1.78407	+	0.231690i
$549$		0			0
$550$	−2.16485	−	2.46417i	−0.0923095	−	0.105073i
$551$	27.0596			1.15278
$552$		0			0
$553$	11.3406			0.482251
$554$	−22.5845	−	25.7071i	−0.959522	−	1.09219i
$555$		0			0
$556$	−0.749313	+	5.76989i	−0.0317779	+	0.244698i
$557$	25.7796			1.09232			0.546158	−	0.837682i	$-0.316090\pi$
$557$	25.7796			1.09232			0.546158	+	0.837682i	$0.316090\pi$
$558$		0			0
$559$		−	16.5732i		−	0.700973i
$560$	−1.44490	+	5.46921i	−0.0610580	+	0.231116i
$561$		0			0
$562$	8.36967	+	9.52688i	0.353053	+	0.401867i
$563$		−	2.03633i		−	0.0858213i	−0.999079	−	0.0429106i	$-0.986337\pi$
$563$		−	2.03633i		−	0.0858213i	0.999079	−	0.0429106i	$-0.0136631\pi$
$564$		0			0
$565$			0.466267i			0.0196160i
$566$	−15.6391	+	13.7394i	−0.657361	+	0.577512i
$567$		0			0
$568$	−20.9503	−	31.1763i	−0.879057	−	1.30813i
$569$			34.6904i			1.45430i	0.686480	+	0.727149i	$0.259155\pi$
$569$			34.6904i			1.45430i	−0.686480	+	0.727149i	$0.740845\pi$
$570$		0			0
$571$	−35.3094			−1.47765			−0.738826	−	0.673896i	$-0.764620\pi$
$571$	−35.3094			−1.47765			−0.738826	+	0.673896i	$0.764620\pi$
$572$	3.07523	−	23.6800i	0.128582	−	0.990112i
$573$		0			0
$574$	6.90539	−	6.06660i	0.288225	−	0.253215i
$575$	0.969724			0.0404403
$576$		0			0
$577$	−1.21949			−0.0507682			−0.0253841	−	0.999678i	$-0.508081\pi$
$577$	−1.21949			−0.0507682			−0.0253841	+	0.999678i	$0.508081\pi$
$578$	9.62632	−	8.45702i	0.400402	−	0.351766i
$579$		0			0
$580$	0.844838	−	6.50547i	0.0350800	−	0.270125i
$581$	10.4390			0.433082
$582$		0			0
$583$			16.7445i			0.693486i
$584$	−19.8146	−	29.4861i	−0.819932	−	1.22014i
$585$		0			0
$586$	6.37466	−	5.60034i	0.263335	−	0.231348i
$587$			24.1260i			0.995785i	0.867239	+	0.497893i	$0.165893\pi$
$587$			24.1260i			0.995785i	−0.867239	+	0.497893i	$0.834107\pi$
$588$		0			0
$589$			42.1147i			1.73531i
$590$	−0.804874	−	0.916158i	−0.0331361	−	0.0377176i
$591$		0			0
$592$	3.77082	−	14.2733i	0.154980	−	0.586627i
$593$			8.10465i			0.332818i	0.986057	+	0.166409i	$0.0532172\pi$
$593$			8.10465i			0.332818i	−0.986057	+	0.166409i	$0.946783\pi$
$594$		0			0
$595$	−7.21949			−0.295970
$596$	2.90539	−	22.3722i	0.119009	−	0.916402i
$597$		0			0
$598$	4.65940	+	5.30362i	0.190537	+	0.216881i
$599$	−31.7190			−1.29600			−0.648002	−	0.761638i	$-0.724395\pi$
$599$	−31.7190			−1.29600			−0.648002	+	0.761638i	$0.724395\pi$
$600$		0			0
$601$	−39.4381			−1.60871			−0.804356	−	0.594147i	$-0.797490\pi$
$601$	−39.4381			−1.60871			−0.804356	+	0.594147i	$0.797490\pi$
$602$	4.24977	+	4.83736i	0.173208	+	0.197156i
$603$		0			0
$604$	43.1651	+	5.60568i	1.75636	+	0.228092i
$605$	5.62065			0.228512
$606$		0			0
$607$		−	10.5203i		−	0.427007i	−0.976942	−	0.213503i	$-0.931513\pi$
$607$		−	10.5203i		−	0.427007i	0.976942	−	0.213503i	$-0.0684874\pi$
$608$	41.7640	−	20.8242i	1.69375	−	0.844533i
$609$		0			0
$610$	4.32970	+	4.92834i	0.175304	+	0.199543i
$611$			49.0573i			1.98465i
$612$		0			0
$613$		−	6.25157i		−	0.252499i	−0.991999	−	0.126249i	$-0.959706\pi$
$613$		−	6.25157i		−	0.252499i	0.991999	−	0.126249i	$-0.0402939\pi$
$614$	−10.6888	+	9.39041i	−0.431363	+	0.378966i
$615$		0			0
$616$	5.17454	+	7.70025i	0.208488	+	0.310252i
$617$		−	11.6395i		−	0.468590i	−0.972166	−	0.234295i	$-0.924722\pi$
$617$		−	11.6395i		−	0.468590i	0.972166	−	0.234295i	$-0.0752782\pi$
$618$		0			0
$619$	33.0284			1.32753			0.663763	−	0.747943i	$-0.268959\pi$
$619$	33.0284			1.32753			0.663763	+	0.747943i	$0.268959\pi$
$620$	10.1249	+	1.31488i	0.406625	+	0.0528068i
$621$		0			0
$622$	12.2186	−	10.7344i	0.489920	−	0.430410i
$623$	−14.4995			−0.580912
$624$		0			0
$625$	1.00000			0.0400000
$626$	−7.07523	+	6.21581i	−0.282783	+	0.248434i
$627$		0			0
$628$	16.5201	+	2.14540i	0.659225	+	0.0856109i
$629$	18.8411			0.751242
$630$		0			0
$631$		−	39.7525i		−	1.58252i	−0.611478	−	0.791262i	$-0.709425\pi$
$631$		−	39.7525i		−	1.58252i	0.611478	−	0.791262i	$-0.290575\pi$
$632$	−18.8255	+	12.6506i	−0.748837	+	0.503216i
$633$		0			0
$634$	4.31410	−	3.79008i	0.171335	−	0.150523i
$635$			6.71784i			0.266589i
$636$		0			0
$637$		−	25.7389i		−	1.01981i
$638$	−7.10081	−	8.08259i	−0.281124	−	0.319993i
$639$		0			0
$640$	−3.70247	−	10.6907i	−0.146353	−	0.422588i
$641$		−	37.9577i		−	1.49924i	−0.661869	−	0.749619i	$-0.730237\pi$
$641$		−	37.9577i		−	1.49924i	0.661869	−	0.749619i	$-0.269763\pi$
$642$		0			0
$643$	−32.4995			−1.28166			−0.640828	−	0.767684i	$-0.721409\pi$
$643$	−32.4995			−1.28166			−0.640828	+	0.767684i	$0.721409\pi$
$644$	−2.71995	−	0.353229i	−0.107181	−	0.0139192i
$645$		0			0
$646$	39.3094	+	44.7445i	1.54661	+	1.76045i
$647$	−36.0899			−1.41884			−0.709420	−	0.704786i	$-0.751043\pi$
$647$	−36.0899			−1.41884			−0.709420	+	0.704786i	$0.751043\pi$
$648$		0			0
$649$	−2.00000			−0.0785069
$650$	4.80487	+	5.46921i	0.188463	+	0.214520i
$651$		0			0
$652$	−5.28005	+	40.6577i	−0.206783	+	1.59228i
$653$	4.18166			0.163641			0.0818204	−	0.996647i	$-0.473927\pi$
$653$	4.18166			0.163641			0.0818204	+	0.996647i	$0.473927\pi$
$654$		0			0
$655$			21.1002i			0.824452i
$656$	−4.69558	+	17.7737i	−0.183332	+	0.693946i
$657$		0			0
$658$	−12.5795	−	14.3188i	−0.490399	−	0.558203i
$659$			16.6434i			0.648336i	0.945999	+	0.324168i	$0.105084\pi$
$659$			16.6434i			0.648336i	−0.945999	+	0.324168i	$0.894916\pi$
$660$		0			0
$661$			19.7990i			0.770091i	0.922897	+	0.385046i	$0.125814\pi$
$661$			19.7990i			0.770091i	−0.922897	+	0.385046i	$0.874186\pi$
$662$	10.9541	−	9.62354i	0.425744	−	0.374030i
$663$		0			0
$664$	−17.3288	+	11.6449i	−0.672487	+	0.451909i
$665$		−	11.6669i		−	0.452424i
$666$		0			0
$667$	3.18074			0.123159
$668$	−1.77959	+	13.7033i	−0.0688544	+	0.530196i
$669$		0			0
$670$	−5.60975	+	4.92834i	−0.216723	+	0.190398i
$671$	10.7587			0.415335
$672$		0			0
$673$	−43.9982			−1.69600			−0.848002	−	0.529992i	$-0.822195\pi$
$673$	−43.9982			−1.69600			−0.848002	+	0.529992i	$0.822195\pi$
$674$	2.25355	−	1.97982i	0.0868036	−	0.0762597i
$675$		0			0
$676$	−3.47706	+	26.7743i	−0.133733	+	1.02978i
$677$	2.49954			0.0960652			0.0480326	−	0.998846i	$-0.484705\pi$
$677$	2.49954			0.0960652			0.0480326	+	0.998846i	$0.484705\pi$
$678$		0			0
$679$			22.3157i			0.856398i
$680$	11.9844	−	8.05348i	0.459581	−	0.308837i
$681$		0			0
$682$	12.5795	−	11.0515i	0.481693	−	0.423182i
$683$			23.6456i			0.904773i	0.891822	+	0.452387i	$0.149427\pi$
$683$			23.6456i			0.904773i	−0.891822	+	0.452387i	$0.850573\pi$
$684$		0			0
$685$			21.0573i			0.804560i
$686$	15.8401	+	18.0303i	0.604779	+	0.688398i
$687$		0			0
$688$	−12.4508	−	3.28935i	−0.474682	−	0.125405i
$689$		−	37.1643i		−	1.41585i
$690$		0			0
$691$	14.6888			0.558787			0.279393	−	0.960177i	$-0.409867\pi$
$691$	14.6888			0.558787			0.279393	+	0.960177i	$0.409867\pi$
$692$	4.95035	−	38.1189i	0.188184	−	1.44906i
$693$		0			0
$694$	30.4390	+	34.6476i	1.15545	+	1.31520i
$695$	−2.90917			−0.110351
$696$		0			0
$697$	−23.4617			−0.888675
$698$	7.04965	+	8.02436i	0.266833	+	0.303727i
$699$		0			0
$700$	−2.80487	−	0.364258i	−0.106014	−	0.0137676i
$701$	8.43899			0.318736			0.159368	−	0.987219i	$-0.449054\pi$
$701$	8.43899			0.318736			0.159368	+	0.987219i	$0.449054\pi$
$702$		0			0
$703$			30.4478i			1.14836i
$704$	−17.1795	−	7.01016i	−0.647478	−	0.264206i
$705$		0			0
$706$	7.48486	+	8.51974i	0.281696	+	0.320645i
$707$			23.2482i			0.874340i
$708$		0			0
$709$		−	37.3904i		−	1.40423i	−0.712066	−	0.702113i	$-0.752240\pi$
$709$		−	37.3904i		−	1.40423i	0.712066	−	0.702113i	$-0.247760\pi$
$710$	14.1093	−	12.3955i	0.529512	−	0.465193i
$711$		0			0
$712$	24.0693	−	16.1745i	0.902036	−	0.606165i
$713$			4.95040i			0.185394i
$714$		0			0
$715$	11.9394			0.446510
$716$	−24.8498	−	3.22715i	−0.928682	−	0.120604i
$717$		0			0
$718$	−3.95126	+	3.47131i	−0.147460	+	0.129548i
$719$	40.3397			1.50442			0.752208	−	0.658926i	$-0.228989\pi$
$719$	40.3397			1.50442			0.752208	+	0.658926i	$0.228989\pi$
$720$		0			0
$721$	−22.4995			−0.837927
$722$	−52.1221	+	45.7909i	−1.93978	+	1.70416i
$723$		0			0
$724$	−7.01090	−	0.910477i	−0.260558	−	0.0338376i
$725$	3.28005			0.121818
$726$		0			0
$727$			11.1305i			0.412806i	0.978467	+	0.206403i	$0.0661757\pi$
$727$			11.1305i			0.412806i	−0.978467	+	0.206403i	$0.933824\pi$
$728$	−11.4849	−	17.0907i	−0.425657	−	0.633422i
$729$		0			0
$730$	13.3444	−	11.7235i	0.493898	−	0.433905i
$731$		−	16.4354i		−	0.607884i
$732$		0			0
$733$			29.8530i			1.10265i	0.834291	+	0.551324i	$0.185877\pi$
$733$			29.8530i			1.10265i	−0.834291	+	0.551324i	$0.814123\pi$
$734$	−13.2401	−	15.0707i	−0.488700	−	0.556270i
$735$		0			0
$736$	4.90917	−	2.44779i	0.180954	−	0.0902269i
$737$			12.2462i			0.451096i
$738$		0			0
$739$	−16.7493			−0.616133			−0.308067	−	0.951365i	$-0.599682\pi$
$739$	−16.7493			−0.616133			−0.308067	+	0.951365i	$0.599682\pi$
$740$	7.32001	+	0.950620i	0.269089	+	0.0349455i
$741$		0			0
$742$	9.52982	+	10.8474i	0.349851	+	0.398222i
$743$	−44.0899			−1.61750			−0.808751	−	0.588151i	$-0.799856\pi$
$743$	−44.0899			−1.61750			−0.808751	+	0.588151i	$0.799856\pi$
$744$		0			0
$745$	11.2800			0.413269
$746$	−33.2245	−	37.8182i	−1.21643	−	1.38462i
$747$		0			0
$748$	3.04965	−	23.4831i	0.111506	−	0.858627i
$749$	−4.00000			−0.146157
$750$		0			0
$751$			24.9896i			0.911883i	0.890010	+	0.455941i	$0.150697\pi$
$751$			24.9896i			0.911883i	−0.890010	+	0.455941i	$0.849303\pi$
$752$	36.8548	+	9.73658i	1.34396	+	0.355057i
$753$		0			0
$754$	15.7602	+	17.9393i	0.573953	+	0.653310i
$755$			21.7638i			0.792066i
$756$		0			0
$757$			22.7833i			0.828072i	0.910260	+	0.414036i	$0.135881\pi$
$757$			22.7833i			0.828072i	−0.910260	+	0.414036i	$0.864119\pi$
$758$	10.1892	−	8.95155i	0.370089	−	0.325135i
$759$		0			0
$760$	13.0147	+	19.3672i	0.472092	+	0.702522i
$761$			30.4049i			1.10218i	0.834446	+	0.551089i	$0.185788\pi$
$761$			30.4049i			1.10218i	−0.834446	+	0.551089i	$0.814212\pi$
$762$		0			0
$763$	14.5601			0.527111
$764$	6.47018	−	49.8220i	0.234083	−	1.80250i
$765$		0			0
$766$	−20.8136	+	18.2854i	−0.752028	+	0.660680i
$767$	4.43899			0.160283
$768$		0			0
$769$	−10.3179			−0.372072			−0.186036	−	0.982543i	$-0.559564\pi$
$769$	−10.3179			−0.372072			−0.186036	+	0.982543i	$0.559564\pi$
$770$	−3.48486	+	3.06156i	−0.125586	+	0.110331i
$771$		0			0
$772$	2.00378	−	15.4296i	0.0721177	−	0.555324i
$773$	−2.94036			−0.105758			−0.0528788	−	0.998601i	$-0.516840\pi$
$773$	−2.94036			−0.105758			−0.0528788	+	0.998601i	$0.516840\pi$
$774$		0			0
$775$			5.10495i			0.183375i
$776$	−24.8936	−	37.0442i	−0.893627	−	1.32981i
$777$		0			0
$778$	2.25355	−	1.97982i	0.0807937	−	0.0709798i
$779$		−	37.9149i		−	1.35844i
$780$		0			0
$781$		−	30.8010i		−	1.10215i
$782$	4.62065	+	5.25951i	0.165234	+	0.188080i
$783$		0			0
$784$	−19.3366	−	5.10848i	−0.690592	−	0.182446i
$785$			8.32943i			0.297290i
$786$		0			0
$787$	−25.2413			−0.899755			−0.449877	−	0.893090i	$-0.648532\pi$
$787$	−25.2413			−0.899755			−0.449877	+	0.893090i	$0.648532\pi$
$788$	0.643805	−	4.95745i	0.0229346	−	0.176602i
$789$		0			0
$790$	−7.48486	−	8.51974i	−0.266299	−	0.303119i
$791$	0.659401			0.0234456
$792$		0			0
$793$	−23.8789			−0.847964
$794$	−25.5542	−	29.0874i	−0.906884	−	1.03227i
$795$		0			0
$796$	−41.7640	−	5.42372i	−1.48029	−	0.192239i
$797$	13.7796			0.488098			0.244049	−	0.969763i	$-0.421524\pi$
$797$	13.7796			0.488098			0.244049	+	0.969763i	$0.421524\pi$
$798$		0			0
$799$			48.6493i			1.72109i
$800$	5.06244	−	2.52422i	0.178984	−	0.0892446i
$801$		0			0
$802$	−2.60006	−	2.95955i	−0.0918113	−	0.104505i
$803$		−	29.1312i		−	1.02802i
$804$		0			0
$805$		−	1.37140i		−	0.0483354i
$806$	−27.9201	+	24.5287i	−0.983443	+	0.863985i
$807$		0			0
$808$	−25.9338	−	38.5922i	−0.912349	−	1.35767i
$809$		−	32.3865i		−	1.13865i	−0.822113	−	0.569324i	$-0.807205\pi$
$809$		−	32.3865i		−	1.13865i	0.822113	−	0.569324i	$-0.192795\pi$
$810$		0			0
$811$	−12.4702			−0.437887			−0.218944	−	0.975738i	$-0.570261\pi$
$811$	−12.4702			−0.437887			−0.218944	+	0.975738i	$0.570261\pi$
$812$	−9.20012	−	1.19478i	−0.322861	−	0.0419286i
$813$		0			0
$814$	9.09461	−	7.98990i	0.318766	−	0.280046i
$815$	−20.4995			−0.718068
$816$		0			0
$817$	26.5601			0.929220
$818$	−13.2157	+	11.6104i	−0.462077	+	0.405949i
$819$		0			0
$820$	−9.11520	−	1.18375i	−0.318316	−	0.0413385i
$821$	41.8401			1.46023			0.730115	−	0.683324i	$-0.239466\pi$
$821$	41.8401			1.46023			0.730115	+	0.683324i	$0.239466\pi$
$822$		0			0
$823$		−	3.39574i		−	0.118368i	−0.998247	−	0.0591840i	$-0.981150\pi$
$823$		−	3.39574i		−	0.118368i	0.998247	−	0.0591840i	$-0.0188499\pi$
$824$	37.3494	−	25.0986i	1.30113	−	0.874353i
$825$		0			0
$826$	−1.29564	+	1.13826i	−0.0450812	+	0.0396052i
$827$			4.38179i			0.152370i	0.997094	+	0.0761848i	$0.0242739\pi$
$827$			4.38179i			0.152370i	−0.997094	+	0.0761848i	$0.975726\pi$
$828$		0			0
$829$		−	45.8757i		−	1.59333i	−0.604423	−	0.796664i	$-0.706596\pi$
$829$		−	45.8757i		−	1.59333i	0.604423	−	0.796664i	$-0.293404\pi$
$830$	−6.88979	−	7.84240i	−0.239148	−	0.272214i
$831$		0			0
$832$	38.1299	+	15.5590i	1.32192	+	0.539412i
$833$		−	25.5248i		−	0.884381i
$834$		0			0
$835$	−6.90917			−0.239102
$836$	37.9494	+	4.92834i	1.31251	+	0.170450i
$837$		0			0
$838$	−8.72494	−	9.93128i	−0.301398	−	0.343070i
$839$	−24.8392			−0.857545			−0.428773	−	0.903412i	$-0.641054\pi$
$839$	−24.8392			−0.857545			−0.428773	+	0.903412i	$0.641054\pi$
$840$		0			0
$841$	−18.2413			−0.629010
$842$	21.7796	+	24.7909i	0.750574	+	0.854351i
$843$		0			0
$844$	−4.12867	+	31.7918i	−0.142115	+	1.09432i
$845$	−13.4995			−0.464398
$846$		0			0
$847$		−	7.94879i		−	0.273124i
$848$	−27.9201	−	7.37613i	−0.958779	−	0.253297i
$849$		0			0
$850$	4.76491	+	5.42372i	0.163435	+	0.186032i
$851$			3.57900i			0.122687i
$852$		0			0
$853$			10.0125i			0.342823i	0.985200	+	0.171411i	$0.0548327\pi$
$853$			10.0125i			0.342823i	−0.985200	+	0.171411i	$0.945167\pi$
$854$	6.96972	−	6.12312i	0.238499	−	0.209529i
$855$		0			0
$856$	6.64002	−	4.46207i	0.226951	−	0.152510i
$857$		−	26.6286i		−	0.909615i	−0.890590	−	0.454807i	$-0.849708\pi$
$857$		−	26.6286i		−	0.909615i	0.890590	−	0.454807i	$-0.150292\pi$
$858$		0			0
$859$	14.4096			0.491650			0.245825	−	0.969314i	$-0.420941\pi$
$859$	14.4096			0.491650			0.245825	+	0.969314i	$0.420941\pi$
$860$	0.829242	−	6.38537i	0.0282769	−	0.217739i
$861$		0			0
$862$	−25.2001	+	22.1391i	−0.858319	+	0.754061i
$863$	−49.5280			−1.68595			−0.842976	−	0.537951i	$-0.819199\pi$
$863$	−49.5280			−1.68595			−0.842976	+	0.537951i	$0.819199\pi$
$864$		0			0
$865$	19.2195			0.653482
$866$	−17.5942	+	15.4570i	−0.597874	+	0.525251i
$867$		0			0
$868$	1.85952	−	14.3188i	0.0631162	−	0.486010i
$869$	−18.5988			−0.630923
$870$		0			0
$871$		−	27.1805i		−	0.920975i
$872$	−24.1698	+	16.2420i	−0.818494	+	0.550025i
$873$		0			0
$874$	−8.49954	+	7.46711i	−0.287501	+	0.252579i
$875$		−	1.41421i		−	0.0478091i
$876$		0			0
$877$		−	23.0924i		−	0.779775i	−0.920863	−	0.389887i	$-0.872514\pi$
$877$		−	23.0924i		−	0.779775i	0.920863	−	0.389887i	$-0.127486\pi$
$878$	30.2148	+	34.3924i	1.01970	+	1.16069i
$879$		0			0
$880$	2.36967	−	8.96963i	0.0798814	−	0.302366i
$881$			24.3092i			0.818999i	0.912310	+	0.409499i	$0.134297\pi$
$881$			24.3092i			0.818999i	−0.912310	+	0.409499i	$0.865703\pi$
$882$		0			0
$883$	−14.0606			−0.473175			−0.236588	−	0.971610i	$-0.576029\pi$
$883$	−14.0606			−0.473175			−0.236588	+	0.971610i	$0.576029\pi$
$884$	−6.76869	+	52.1206i	−0.227656	+	1.75301i
$885$		0			0
$886$	−28.0899	−	31.9737i	−0.943699	−	1.07418i
$887$	5.96881			0.200413			0.100206	−	0.994967i	$-0.468050\pi$
$887$	5.96881			0.200413			0.100206	+	0.994967i	$0.468050\pi$
$888$		0			0
$889$	9.50046			0.318635
$890$	9.56978	+	10.8929i	0.320780	+	0.365132i
$891$		0			0
$892$	−0.615655	−	0.0799526i	−0.0206137	−	0.00267701i
$893$	−78.6188			−2.63088
$894$		0			0
$895$		−	12.5293i		−	0.418807i
$896$	−15.1190	+	5.23608i	−0.505090	+	0.174925i
$897$		0			0
$898$	3.96004	+	4.50756i	0.132148	+	0.150419i
$899$			16.7445i			0.558460i
$900$		0			0
$901$		−	36.8552i		−	1.22782i
$902$	−11.3250	+	9.94937i	−0.377081	+	0.331278i
$903$		0			0
$904$	−1.09461	+	0.735574i	−0.0364062	+	0.0244648i
$905$		−	3.53489i		−	0.117504i
$906$		0			0
$907$	−7.96125			−0.264349			−0.132174	−	0.991226i	$-0.542196\pi$
$907$	−7.96125			−0.264349			−0.132174	+	0.991226i	$0.542196\pi$
$908$	7.62912	+	0.990764i	0.253181	+	0.0328796i
$909$		0			0
$910$	7.73463	−	6.79512i	0.256401	−	0.225256i
$911$	−40.4995			−1.34181			−0.670905	−	0.741543i	$-0.734094\pi$
$911$	−40.4995			−1.34181			−0.670905	+	0.741543i	$0.734094\pi$
$912$		0			0
$913$	−17.1202			−0.566596
$914$	27.8557	−	24.4721i	0.921386	−	0.809466i
$915$		0			0
$916$	12.6206	+	1.63899i	0.416998	+	0.0541538i
$917$	29.8401			0.985408
$918$		0			0
$919$			11.6395i			0.383953i	0.981400	+	0.191976i	$0.0614897\pi$
$919$			11.6395i			0.383953i	−0.981400	+	0.191976i	$0.938510\pi$
$920$	1.52982	+	2.27653i	0.0504366	+	0.0750549i
$921$		0			0
$922$	−16.3628	+	14.3753i	−0.538881	+	0.473424i
$923$			68.3626i			2.25018i
$924$		0			0
$925$			3.69074i			0.121351i
$926$	−23.7202	−	26.9999i	−0.779496	−	0.887271i
$927$		0			0
$928$	16.6050	−	8.27955i	0.545087	−	0.271790i
$929$		−	23.9560i		−	0.785971i	−0.919545	−	0.392985i	$-0.871442\pi$
$929$		−	23.9560i		−	0.785971i	0.919545	−	0.392985i	$-0.128558\pi$
$930$		0			0
$931$	41.2489			1.35188
$932$	2.49576	+	0.324114i	0.0817514	+	0.0106167i
$933$		0			0
$934$	24.4196	+	27.7959i	0.799034	+	0.909511i
$935$	11.8401			0.387214
$936$		0			0
$937$	10.1211			0.330642			0.165321	−	0.986240i	$-0.447134\pi$
$937$	10.1211			0.330642			0.165321	+	0.986240i	$0.447134\pi$
$938$	6.96972	+	7.93338i	0.227570	+	0.259034i
$939$		0			0
$940$	−2.45459	+	18.9009i	−0.0800598	+	0.616480i
$941$	28.3179			0.923137			0.461568	−	0.887105i	$-0.347287\pi$
$941$	28.3179			0.923137			0.461568	+	0.887105i	$0.347287\pi$
$942$		0			0
$943$		−	4.45673i		−	0.145131i
$944$	0.881022	−	3.33484i	0.0286748	−	0.108540i
$945$		0			0
$946$	−6.96972	−	7.93338i	−0.226605	−	0.257936i
$947$			53.4284i			1.73619i	0.496398	+	0.868095i	$0.334656\pi$
$947$			53.4284i			1.73619i	−0.496398	+	0.868095i	$0.665344\pi$
$948$		0			0
$949$			64.6565i			2.09884i
$950$	−8.76491	+	7.70025i	−0.284371	+	0.249829i
$951$		0			0
$952$	−11.3893	−	16.9485i	−0.369130	−	0.549304i
$953$			4.48413i			0.145255i	0.997359	+	0.0726276i	$0.0231385\pi$
$953$			4.48413i			0.145255i	−0.997359	+	0.0726276i	$0.976862\pi$
$954$		0			0
$955$	25.1202			0.812870
$956$	−0.128666	+	0.990764i	−0.00416137	+	0.0320436i
$957$		0			0
$958$	8.32970	−	7.31790i	0.269120	−	0.236431i
$959$	29.7796			0.961633
$960$		0			0
$961$	4.93945			0.159337
$962$	−20.1854	+	17.7335i	−0.650805	+	0.571752i
$963$		0			0
$964$	1.56101	−	12.0202i	0.0502768	−	0.387144i
$965$	7.77959			0.250434
$966$		0			0
$967$		−	13.5748i		−	0.436537i	−0.975889	−	0.218268i	$-0.929959\pi$
$967$		−	13.5748i		−	0.436537i	0.975889	−	0.218268i	$-0.0700408\pi$
$968$	8.86702	+	13.1950i	0.284997	+	0.424105i
$969$		0			0
$970$	16.7649	−	14.7285i	0.538289	−	0.472904i
$971$		−	54.2907i		−	1.74227i	−0.491042	−	0.871136i	$-0.663384\pi$
$971$		−	54.2907i		−	1.74227i	0.491042	−	0.871136i	$-0.336616\pi$
$972$		0			0
$973$			4.11419i			0.131895i
$974$	12.2897	+	13.9890i	0.393789	+	0.448235i
$975$		0			0
$976$	−4.73933	+	17.9393i	−0.151702	+	0.574222i
$977$		−	15.7122i		−	0.502678i	−0.967899	−	0.251339i	$-0.919129\pi$
$977$		−	15.7122i		−	0.502678i	0.967899	−	0.251339i	$-0.0808709\pi$
$978$		0			0
$979$	23.7796			0.759999
$980$	1.28785	−	9.91673i	0.0411387	−	0.316778i
$981$		0			0
$982$	−12.0244	−	13.6869i	−0.383713	−	0.436766i
$983$	13.4087			0.427672			0.213836	−	0.976870i	$-0.431404\pi$
$983$	13.4087			0.427672			0.213836	+	0.976870i	$0.431404\pi$
$984$		0			0
$985$	2.49954			0.0796420
$986$	15.6291	+	17.7901i	0.497733	+	0.566551i
$987$		0			0
$988$	−84.2286	−	10.9384i	−2.67967	−	0.347998i
$989$	3.12202			0.0992745
$990$		0			0
$991$		−	18.1433i		−	0.576341i	−0.957579	−	0.288170i	$-0.906953\pi$
$991$		−	18.1433i		−	0.576341i	0.957579	−	0.288170i	$-0.0930469\pi$
$992$	12.8860	+	25.8435i	0.409131	+	0.820533i
$993$		0			0
$994$	−17.5298	−	19.9535i	−0.556012	−	0.632888i
$995$		−	21.0573i		−	0.667563i
$996$		0			0
$997$		−	28.7385i		−	0.910159i	−0.890451	−	0.455079i	$-0.849611\pi$
$997$		−	28.7385i		−	0.910159i	0.890451	−	0.455079i	$-0.150389\pi$
$998$	12.8860	−	11.3208i	0.407900	−	0.358353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.b.d.251.2	yes	6
3.2	odd	2		360.2.b.c.251.5	✓	6
4.3	odd	2		1440.2.b.d.431.4		6
5.2	odd	4		1800.2.m.e.899.3		12
5.3	odd	4		1800.2.m.e.899.10		12
5.4	even	2		1800.2.b.d.251.5		6
8.3	odd	2		360.2.b.c.251.6	yes	6
8.5	even	2		1440.2.b.c.431.1		6
12.11	even	2		1440.2.b.c.431.6		6
15.2	even	4		1800.2.m.d.899.10		12
15.8	even	4		1800.2.m.d.899.3		12
15.14	odd	2		1800.2.b.e.251.2		6
20.3	even	4		7200.2.m.e.3599.8		12
20.7	even	4		7200.2.m.e.3599.2		12
20.19	odd	2		7200.2.b.e.4751.1		6
24.5	odd	2		1440.2.b.d.431.3		6
24.11	even	2	inner	360.2.b.d.251.1	yes	6
40.3	even	4		1800.2.m.d.899.9		12
40.13	odd	4		7200.2.m.d.3599.2		12
40.19	odd	2		1800.2.b.e.251.1		6
40.27	even	4		1800.2.m.d.899.4		12
40.29	even	2		7200.2.b.d.4751.4		6
40.37	odd	4		7200.2.m.d.3599.8		12
60.23	odd	4		7200.2.m.d.3599.11		12
60.47	odd	4		7200.2.m.d.3599.5		12
60.59	even	2		7200.2.b.d.4751.3		6
120.29	odd	2		7200.2.b.e.4751.6		6
120.53	even	4		7200.2.m.e.3599.5		12
120.59	even	2		1800.2.b.d.251.6		6
120.77	even	4		7200.2.m.e.3599.11		12
120.83	odd	4		1800.2.m.e.899.4		12
120.107	odd	4		1800.2.m.e.899.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.b.c.251.5	✓	6	3.2	odd	2
360.2.b.c.251.6	yes	6	8.3	odd	2
360.2.b.d.251.1	yes	6	24.11	even	2	inner
360.2.b.d.251.2	yes	6	1.1	even	1	trivial
1440.2.b.c.431.1		6	8.5	even	2
1440.2.b.c.431.6		6	12.11	even	2
1440.2.b.d.431.3		6	24.5	odd	2
1440.2.b.d.431.4		6	4.3	odd	2
1800.2.b.d.251.5		6	5.4	even	2
1800.2.b.d.251.6		6	120.59	even	2
1800.2.b.e.251.1		6	40.19	odd	2
1800.2.b.e.251.2		6	15.14	odd	2
1800.2.m.d.899.3		12	15.8	even	4
1800.2.m.d.899.4		12	40.27	even	4
1800.2.m.d.899.9		12	40.3	even	4
1800.2.m.d.899.10		12	15.2	even	4
1800.2.m.e.899.3		12	5.2	odd	4
1800.2.m.e.899.4		12	120.83	odd	4
1800.2.m.e.899.9		12	120.107	odd	4
1800.2.m.e.899.10		12	5.3	odd	4
7200.2.b.d.4751.3		6	60.59	even	2
7200.2.b.d.4751.4		6	40.29	even	2
7200.2.b.e.4751.1		6	20.19	odd	2
7200.2.b.e.4751.6		6	120.29	odd	2
7200.2.m.d.3599.2		12	40.13	odd	4
7200.2.m.d.3599.5		12	60.47	odd	4
7200.2.m.d.3599.8		12	40.37	odd	4
7200.2.m.d.3599.11		12	60.23	odd	4
7200.2.m.e.3599.2		12	20.7	even	4
7200.2.m.e.3599.5		12	120.53	even	4
7200.2.m.e.3599.8		12	20.3	even	4
7200.2.m.e.3599.11		12	120.77	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06244 + 0.933389i) q^{2} +(0.257569 - 1.98335i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(1.57758 + 2.34760i) q^{8} +O(q^{10})\)	\(q+(-1.06244 + 0.933389i) q^{2} +(0.257569 - 1.98335i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(1.57758 + 2.34760i) q^{8} +(-1.06244 + 0.933389i) q^{10} +2.31934i q^{11} -5.14777i q^{13} +(1.32001 + 1.50252i) q^{14} +(-3.86732 - 1.02170i) q^{16} -5.10495i q^{17} +8.24977 q^{19} +(0.257569 - 1.98335i) q^{20} +(-2.16485 - 2.46417i) q^{22} +0.969724 q^{23} +1.00000 q^{25} +(4.80487 + 5.46921i) q^{26} +(-2.80487 - 0.364258i) q^{28} +3.28005 q^{29} +5.10495i q^{31} +(5.06244 - 2.52422i) q^{32} +(4.76491 + 5.42372i) q^{34} -1.41421i q^{35} +3.69074i q^{37} +(-8.76491 + 7.70025i) q^{38} +(1.57758 + 2.34760i) q^{40} -4.59587i q^{41} +3.21949 q^{43} +(4.60006 + 0.597391i) q^{44} +(-1.03028 + 0.905130i) q^{46} -9.52982 q^{47} +5.00000 q^{49} +(-1.06244 + 0.933389i) q^{50} +(-10.2098 - 1.32591i) q^{52} +7.21949 q^{53} +2.31934i q^{55} +(3.32001 - 2.23104i) q^{56} +(-3.48486 + 3.06156i) q^{58} +0.862313i q^{59} -4.63869i q^{61} +(-4.76491 - 5.42372i) q^{62} +(-3.02248 + 7.40707i) q^{64} -5.14777i q^{65} +5.28005 q^{67} +(-10.1249 - 1.31488i) q^{68} +(1.32001 + 1.50252i) q^{70} -13.2800 q^{71} -12.5601 q^{73} +(-3.44490 - 3.92120i) q^{74} +(2.12489 - 16.3621i) q^{76} +3.28005 q^{77} +8.01901i q^{79} +(-3.86732 - 1.02170i) q^{80} +(4.28974 + 4.88285i) q^{82} +7.38148i q^{83} -5.10495i q^{85} +(-3.42053 + 3.00504i) q^{86} +(-5.44490 + 3.65895i) q^{88} -10.2527i q^{89} -7.28005 q^{91} +(0.249771 - 1.92330i) q^{92} +(10.1249 - 8.89503i) q^{94} +8.24977 q^{95} -15.7796 q^{97} +(-5.31221 + 4.66695i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8} + 2 q^{10} - 6 q^{16} + 16 q^{19} + 2 q^{20} - 20 q^{22} + 4 q^{23} + 6 q^{25} + 20 q^{26} - 8 q^{28} - 12 q^{29} + 22 q^{32} - 4 q^{34} - 20 q^{38} + 2 q^{40} - 16 q^{43} - 12 q^{44} - 8 q^{46} + 8 q^{47} + 30 q^{49} + 2 q^{50} - 4 q^{52} + 8 q^{53} + 12 q^{56} - 20 q^{58} + 4 q^{62} + 14 q^{64} - 44 q^{68} - 48 q^{71} - 12 q^{73} + 4 q^{74} - 4 q^{76} - 12 q^{77} - 6 q^{80} + 16 q^{82} - 40 q^{86} - 8 q^{88} - 12 q^{91} - 32 q^{92} + 44 q^{94} + 16 q^{95} + 4 q^{97} + 10 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8 + 2 * q^10 - 6 * q^16 + 16 * q^19 + 2 * q^20 - 20 * q^22 + 4 * q^23 + 6 * q^25 + 20 * q^26 - 8 * q^28 - 12 * q^29 + 22 * q^32 - 4 * q^34 - 20 * q^38 + 2 * q^40 - 16 * q^43 - 12 * q^44 - 8 * q^46 + 8 * q^47 + 30 * q^49 + 2 * q^50 - 4 * q^52 + 8 * q^53 + 12 * q^56 - 20 * q^58 + 4 * q^62 + 14 * q^64 - 44 * q^68 - 48 * q^71 - 12 * q^73 + 4 * q^74 - 4 * q^76 - 12 * q^77 - 6 * q^80 + 16 * q^82 - 40 * q^86 - 8 * q^88 - 12 * q^91 - 32 * q^92 + 44 * q^94 + 16 * q^95 + 4 * q^97 + 10 * q^98

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