LMFDB - Embedded newform 105.2.m.a.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.m (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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.8
Root			$0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	105.97
Dual form			105.2.m.a.13.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48838 + 1.48838i) q^{2} +(0.707107 + 0.707107i) q^{3} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +2.10489i q^{6} +(-1.97552 - 1.75993i) q^{7} +(-0.640825 + 0.640825i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.48838 + 1.48838i) q^{2} +(0.707107 + 0.707107i) q^{3} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +2.10489i q^{6} +(-1.97552 - 1.75993i) q^{7} +(-0.640825 + 0.640825i) q^{8} +1.00000i q^{9} +(0.798469 - 4.63845i) q^{10} -2.67187 q^{11} +(-1.71866 + 1.71866i) q^{12} +(1.22714 + 1.22714i) q^{13} +(-0.320879 - 5.55976i) q^{14} +(0.379340 - 2.20366i) q^{15} +2.95352 q^{16} +(-4.74624 + 4.74624i) q^{17} +(-1.48838 + 1.48838i) q^{18} +6.01729 q^{19} +(4.43929 - 3.13538i) q^{20} +(-0.152445 - 2.64136i) q^{21} +(-3.97676 - 3.97676i) q^{22} +(-0.175684 + 0.175684i) q^{23} -0.906263 q^{24} +(-1.67187 + 4.71220i) q^{25} +3.65291i q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.27759 - 4.80159i) q^{28} -0.304889i q^{29} +(3.84448 - 2.71528i) q^{30} -7.25379i q^{31} +(5.67761 + 5.67761i) q^{32} +(-1.88930 - 1.88930i) q^{33} -14.1284 q^{34} +(-0.666037 + 5.87847i) q^{35} -2.43055 q^{36} +(-0.735441 - 0.735441i) q^{37} +(8.95602 + 8.95602i) q^{38} +1.73544i q^{39} +(1.99709 + 0.343782i) q^{40} -7.05736i q^{41} +(3.70445 - 4.15824i) q^{42} +(0.304889 - 0.304889i) q^{43} -6.49412i q^{44} +(1.82645 - 1.28999i) q^{45} -0.522969 q^{46} +(0.556866 - 0.556866i) q^{47} +(2.08845 + 2.08845i) q^{48} +(0.805321 + 6.95352i) q^{49} +(-9.50193 + 4.52517i) q^{50} -6.71220 q^{51} +(-2.98263 + 2.98263i) q^{52} +(-4.99031 + 4.99031i) q^{53} -2.10489 q^{54} +(3.44668 + 4.88005i) q^{55} +(2.39376 - 0.138155i) q^{56} +(4.25487 + 4.25487i) q^{57} +(0.453791 - 0.453791i) q^{58} -7.98837 q^{59} +(5.35610 + 0.922006i) q^{60} +5.53409i q^{61} +(10.7964 - 10.7964i) q^{62} +(1.75993 - 1.97552i) q^{63} +10.9939i q^{64} +(0.658323 - 3.82432i) q^{65} -5.62399i q^{66} +(-3.43055 - 3.43055i) q^{67} +(-11.5360 - 11.5360i) q^{68} -0.248455 q^{69} +(-9.74071 + 7.75808i) q^{70} +15.3087 q^{71} +(-0.640825 - 0.640825i) q^{72} +(10.0208 + 10.0208i) q^{73} -2.18923i q^{74} +(-4.51422 + 2.14984i) q^{75} +14.6253i q^{76} +(5.27832 + 4.70230i) q^{77} +(-2.58300 + 2.58300i) q^{78} -11.2973i q^{79} +(-3.81000 - 5.39447i) q^{80} -1.00000 q^{81} +(10.5040 - 10.5040i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(6.41995 - 0.370525i) q^{84} +(14.7914 + 2.54621i) q^{85} +0.907583 q^{86} +(0.215589 - 0.215589i) q^{87} +(1.71220 - 1.71220i) q^{88} +6.91251 q^{89} +(4.63845 + 0.798469i) q^{90} +(-0.264559 - 4.58392i) q^{91} +(-0.427009 - 0.427009i) q^{92} +(5.12921 - 5.12921i) q^{93} +1.65766 q^{94} +(-7.76222 - 10.9903i) q^{95} +8.02936i q^{96} +(-8.84137 + 8.84137i) q^{97} +(-9.15086 + 11.5481i) q^{98} -2.67187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 16 * q - 8 * q^7 + 24 * q^8	$ 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	1.48838	+	1.48838i	1.05244	+	1.05244i	0.998546	+	0.0538973i	$0.0171644\pi$
$2$	1.48838	+	1.48838i	1.05244	+	1.05244i	0.0538973	+	0.998546i	$0.482836\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			2.43055i			1.21528i
$5$	−1.28999	−	1.82645i	−0.576899	−	0.816815i
$5$	−1.28999	−	1.82645i	−0.576899	−	0.816815i
$6$			2.10489i			0.859317i
$7$	−1.97552	−	1.75993i	−0.746675	−	0.665189i
$7$	−1.97552	−	1.75993i	−0.746675	−	0.665189i
$8$	−0.640825	+	0.640825i	−0.226566	+	0.226566i
$9$			1.00000i			0.333333i
$10$	0.798469	−	4.63845i	0.252498	−	1.46681i
$11$	−2.67187			−0.805600			−0.402800	−	0.915288i	$-0.631963\pi$
$11$	−2.67187			−0.805600			−0.402800	+	0.915288i	$0.631963\pi$
$12$	−1.71866	+	1.71866i	−0.496134	+	0.496134i
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	0.856498	−	0.516150i	$-0.172635\pi$
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	−0.516150	+	0.856498i	$0.672635\pi$
$14$	−0.320879	−	5.55976i	−0.0857585	−	1.48591i
$15$	0.379340	−	2.20366i	0.0979452	−	0.568982i
$16$	2.95352			0.738380
$17$	−4.74624	+	4.74624i	−1.15113	+	1.15113i	−0.164807	+	0.986326i	$0.552700\pi$
$17$	−4.74624	+	4.74624i	−1.15113	+	1.15113i	−0.986326	+	0.164807i	$0.947300\pi$
$18$	−1.48838	+	1.48838i	−0.350815	+	0.350815i
$19$	6.01729			1.38046			0.690231	−	0.723589i	$-0.257509\pi$
$19$	6.01729			1.38046			0.690231	+	0.723589i	$0.257509\pi$
$20$	4.43929	−	3.13538i	0.992656	−	0.701092i
$21$	−0.152445	−	2.64136i	−0.0332662	−	0.576391i
$22$	−3.97676	−	3.97676i	−0.847848	−	0.847848i
$23$	−0.175684	+	0.175684i	−0.0366327	+	0.0366327i	−0.725186	−	0.688553i	$-0.758246\pi$
$23$	−0.175684	+	0.175684i	−0.0366327	+	0.0366327i	0.688553	+	0.725186i	$0.258246\pi$
$24$	−0.906263			−0.184990
$25$	−1.67187	+	4.71220i	−0.334374	+	0.942440i
$26$			3.65291i			0.716394i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.27759	−	4.80159i	0.808389	−	0.907416i
$29$		−	0.304889i		−	0.0566165i	−0.999599	−	0.0283083i	$-0.990988\pi$
$29$		−	0.304889i		−	0.0566165i	0.999599	−	0.0283083i	$-0.00901200\pi$
$30$	3.84448	−	2.71528i	0.701903	−	0.495739i
$31$		−	7.25379i		−	1.30282i	−0.758726	−	0.651410i	$-0.774178\pi$
$31$		−	7.25379i		−	1.30282i	0.758726	−	0.651410i	$-0.225822\pi$
$32$	5.67761	+	5.67761i	1.00367	+	1.00367i
$33$	−1.88930	−	1.88930i	−0.328885	−	0.328885i
$34$	−14.1284			−2.42301
$35$	−0.666037	+	5.87847i	−0.112581	+	0.993643i
$36$	−2.43055			−0.405092
$37$	−0.735441	−	0.735441i	−0.120906	−	0.120906i	0.644065	−	0.764971i	$-0.277247\pi$
$37$	−0.735441	−	0.735441i	−0.120906	−	0.120906i	−0.764971	+	0.644065i	$0.777247\pi$
$38$	8.95602	+	8.95602i	1.45286	+	1.45286i
$39$			1.73544i			0.277893i
$40$	1.99709	+	0.343782i	0.315768	+	0.0543567i
$41$		−	7.05736i		−	1.10217i	−0.834447	−	0.551087i	$-0.814213\pi$
$41$		−	7.05736i		−	1.10217i	0.834447	−	0.551087i	$-0.185787\pi$
$42$	3.70445	−	4.15824i	0.571608	−	0.641630i
$43$	0.304889	−	0.304889i	0.0464952	−	0.0464952i	−0.683477	−	0.729972i	$-0.739533\pi$
$43$	0.304889	−	0.304889i	0.0464952	−	0.0464952i	0.729972	+	0.683477i	$0.239533\pi$
$44$		−	6.49412i		−	0.979026i
$45$	1.82645	−	1.28999i	0.272272	−	0.192300i
$46$	−0.522969			−0.0771076
$47$	0.556866	−	0.556866i	0.0812273	−	0.0812273i	−0.665326	−	0.746553i	$-0.731707\pi$
$47$	0.556866	−	0.556866i	0.0812273	−	0.0812273i	0.746553	+	0.665326i	$0.231707\pi$
$48$	2.08845	+	2.08845i	0.301442	+	0.301442i
$49$	0.805321	+	6.95352i	0.115046	+	0.993360i
$50$	−9.50193	+	4.52517i	−1.34378	+	0.639955i
$51$	−6.71220			−0.939896
$52$	−2.98263	+	2.98263i	−0.413617	+	0.413617i
$53$	−4.99031	+	4.99031i	−0.685472	+	0.685472i	−0.961228	−	0.275756i	$-0.911072\pi$
$53$	−4.99031	+	4.99031i	−0.685472	+	0.685472i	0.275756	+	0.961228i	$0.411072\pi$
$54$	−2.10489			−0.286439
$55$	3.44668	+	4.88005i	0.464750	+	0.658026i
$56$	2.39376	−	0.138155i	0.319880	−	0.0184617i
$57$	4.25487	+	4.25487i	0.563571	+	0.563571i
$58$	0.453791	−	0.453791i	0.0595857	−	0.0595857i
$59$	−7.98837			−1.04000			−0.519999	−	0.854167i	$-0.674068\pi$
$59$	−7.98837			−1.04000			−0.519999	+	0.854167i	$0.674068\pi$
$60$	5.35610	+	0.922006i	0.691470	+	0.119031i
$61$			5.53409i			0.708567i	0.935138	+	0.354284i	$0.115275\pi$
$61$			5.53409i			0.708567i	−0.935138	+	0.354284i	$0.884725\pi$
$62$	10.7964	−	10.7964i	1.37114	−	1.37114i
$63$	1.75993	−	1.97552i	0.221730	−	0.248892i
$64$			10.9939i			1.37423i
$65$	0.658323	−	3.82432i	0.0816549	−	0.474348i
$66$		−	5.62399i		−	0.692265i
$67$	−3.43055	−	3.43055i	−0.419109	−	0.419109i	0.465788	−	0.884896i	$-0.345771\pi$
$67$	−3.43055	−	3.43055i	−0.419109	−	0.419109i	−0.884896	+	0.465788i	$0.845771\pi$
$68$	−11.5360	−	11.5360i	−1.39894	−	1.39894i
$69$	−0.248455			−0.0299104
$70$	−9.74071	+	7.75808i	−1.16424	+	0.927268i
$71$	15.3087			1.81681			0.908407	−	0.418087i	$-0.137299\pi$
$71$	15.3087			1.81681			0.908407	+	0.418087i	$0.137299\pi$
$72$	−0.640825	−	0.640825i	−0.0755219	−	0.0755219i
$73$	10.0208	+	10.0208i	1.17285	+	1.17285i	0.981527	+	0.191323i	$0.0612778\pi$
$73$	10.0208	+	10.0208i	1.17285	+	1.17285i	0.191323	+	0.981527i	$0.438722\pi$
$74$		−	2.18923i		−	0.254493i
$75$	−4.51422	+	2.14984i	−0.521257	+	0.248242i
$76$			14.6253i			1.67764i
$77$	5.27832	+	4.70230i	0.601521	+	0.535876i
$78$	−2.58300	+	2.58300i	−0.292467	+	0.292467i
$79$		−	11.2973i		−	1.27104i	−0.772084	−	0.635521i	$-0.780785\pi$
$79$		−	11.2973i		−	1.27104i	0.772084	−	0.635521i	$-0.219215\pi$
$80$	−3.81000	−	5.39447i	−0.425971	−	0.603120i
$81$	−1.00000			−0.111111
$82$	10.5040	−	10.5040i	1.15998	−	1.15998i
$83$	−4.88941	−	4.88941i	−0.536682	−	0.536682i	0.385871	−	0.922553i	$-0.373901\pi$
$83$	−4.88941	−	4.88941i	−0.536682	−	0.536682i	−0.922553	+	0.385871i	$0.873901\pi$
$84$	6.41995	−	0.370525i	0.700474	−	0.0404276i
$85$	14.7914	+	2.54621i	1.60435	+	0.276175i
$86$	0.907583			0.0978671
$87$	0.215589	−	0.215589i	0.0231136	−	0.0231136i
$88$	1.71220	−	1.71220i	0.182521	−	0.182521i
$89$	6.91251			0.732725			0.366363	−	0.930472i	$-0.380603\pi$
$89$	6.91251			0.732725			0.366363	+	0.930472i	$0.380603\pi$
$90$	4.63845	+	0.798469i	0.488935	+	0.0841660i
$91$	−0.264559	−	4.58392i	−0.0277333	−	0.480525i
$92$	−0.427009	−	0.427009i	−0.0445188	−	0.0445188i
$93$	5.12921	−	5.12921i	0.531874	−	0.531874i
$94$	1.65766			0.170974
$95$	−7.76222	−	10.9903i	−0.796387	−	1.12758i
$96$			8.02936i			0.819493i
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	−0.995233	−	0.0975276i	$-0.968907\pi$
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	0.0975276	+	0.995233i	$0.468907\pi$
$98$	−9.15086	+	11.5481i	−0.924376	+	1.16654i
$99$		−	2.67187i		−	0.268533i
$100$	−11.4533	−	4.06357i	−1.14533	−	0.406357i
$101$		−	7.22962i		−	0.719374i	−0.933073	−	0.359687i	$-0.882883\pi$
$101$		−	7.22962i		−	0.719374i	0.933073	−	0.359687i	$-0.117117\pi$
$102$	−9.99031	−	9.99031i	−0.989188	−	0.989188i
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	0.276628	−	0.960977i	$-0.410783\pi$
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	−0.960977	+	0.276628i	$0.910783\pi$
$104$	−1.57277			−0.154222
$105$	−4.62766	+	3.68575i	−0.451614	+	0.359692i
$106$	−14.8550			−1.44284
$107$	−7.47295	−	7.47295i	−0.722437	−	0.722437i	0.246664	−	0.969101i	$-0.420666\pi$
$107$	−7.47295	−	7.47295i	−0.722437	−	0.722437i	−0.969101	+	0.246664i	$0.920666\pi$
$108$	−1.71866	−	1.71866i	−0.165378	−	0.165378i
$109$		−	5.95352i		−	0.570244i	−0.958491	−	0.285122i	$-0.907966\pi$
$109$		−	5.95352i		−	0.570244i	0.958491	−	0.285122i	$-0.0920341\pi$
$110$	−2.13341	+	12.3933i	−0.203412	+	1.18166i
$111$		−	1.04007i		−	0.0987192i
$112$	−5.83473	−	5.19798i	−0.551330	−	0.491163i
$113$	6.99031	−	6.99031i	0.657593	−	0.657593i	−0.297217	−	0.954810i	$-0.596058\pi$
$113$	6.99031	−	6.99031i	0.657593	−	0.657593i	0.954810	+	0.297217i	$0.0960585\pi$
$114$			12.6657i			1.18625i
$115$	0.547509	+	0.0942489i	0.0510555	+	0.00878876i
$116$	0.741049			0.0688047
$117$	−1.22714	+	1.22714i	−0.113449	+	0.113449i
$118$	−11.8897	−	11.8897i	−1.09454	−	1.09454i
$119$	17.7293	−	1.02324i	1.62524	−	0.0938002i
$120$	1.16907	+	1.65525i	0.106721	+	0.151103i
$121$	−3.86110			−0.351009
$122$	−8.23683	+	8.23683i	−0.745727	+	0.745727i
$123$	4.99031	−	4.99031i	0.449961	−	0.449961i
$124$	17.6307			1.58329
$125$	10.7633	−	3.02508i	0.962700	−	0.270571i
$126$	5.55976	−	0.320879i	0.495303	−	0.0285862i
$127$	2.86110	+	2.86110i	0.253882	+	0.253882i	0.822560	−	0.568678i	$-0.192545\pi$
$127$	2.86110	+	2.86110i	0.253882	+	0.253882i	−0.568678	+	0.822560i	$0.692545\pi$
$128$	−5.00781	+	5.00781i	−0.442632	+	0.442632i
$129$	0.431179			0.0379632
$130$	6.67187	−	4.71220i	0.585162	−	0.413287i
$131$			9.34764i			0.816707i	0.912824	+	0.408353i	$0.133897\pi$
$131$			9.34764i			0.816707i	−0.912824	+	0.408353i	$0.866103\pi$
$132$	4.59204	−	4.59204i	0.399686	−	0.399686i
$133$	−11.8873	−	10.5900i	−1.03076	−	0.918268i
$134$		−	10.2119i		−	0.882177i
$135$	2.20366	+	0.379340i	0.189661	+	0.0326484i
$136$		−	6.08302i		−	0.521615i
$137$	7.51943	+	7.51943i	0.642428	+	0.642428i	0.951152	−	0.308724i	$-0.0999019\pi$
$137$	7.51943	+	7.51943i	0.642428	+	0.642428i	−0.308724	+	0.951152i	$0.599902\pi$
$138$	−0.369795	−	0.369795i	−0.0314791	−	0.0314791i
$139$	7.78902			0.660656			0.330328	−	0.943866i	$-0.392841\pi$
$139$	7.78902			0.660656			0.330328	+	0.943866i	$0.392841\pi$
$140$	−14.2879	−	1.61884i	−1.20755	−	0.136817i
$141$	0.787528			0.0663218
$142$	22.7852	+	22.7852i	1.91209	+	1.91209i
$143$	−3.27877	−	3.27877i	−0.274184	−	0.274184i
$144$			2.95352i			0.246127i
$145$	−0.556866	+	0.393303i	−0.0462452	+	0.0326620i
$146$			29.8296i			2.46872i
$147$	−4.34743	+	5.48633i	−0.358570	+	0.452505i
$148$	1.78753	−	1.78753i	0.146934	−	0.146934i
$149$			14.2855i			1.17031i	0.810920	+	0.585157i	$0.198967\pi$
$149$			14.2855i			1.17031i	−0.810920	+	0.585157i	$0.801033\pi$
$150$	−9.91866	−	3.51910i	−0.809855	−	0.287333i
$151$	9.77990			0.795877			0.397939	−	0.917412i	$-0.369726\pi$
$151$	9.77990			0.795877			0.397939	+	0.917412i	$0.369726\pi$
$152$	−3.85603	+	3.85603i	−0.312765	+	0.312765i
$153$	−4.74624	−	4.74624i	−0.383711	−	0.383711i
$154$	0.857347	+	14.8550i	0.0690870	+	1.19705i
$155$	−13.2487	+	9.35729i	−1.06416	+	0.751596i
$156$	−4.21808			−0.337717
$157$	2.17731	−	2.17731i	0.173768	−	0.173768i	−0.614864	−	0.788633i	$-0.710789\pi$
$157$	2.17731	−	2.17731i	0.173768	−	0.173768i	0.788633	+	0.614864i	$0.210789\pi$
$158$	16.8146	−	16.8146i	1.33770	−	1.33770i
$159$	−7.05736			−0.559685
$160$	3.04586	−	17.6939i	0.240796	−	1.39883i
$161$	0.656257	−	0.0378756i	0.0517203	−	0.00298502i
$162$	−1.48838	−	1.48838i	−0.116938	−	0.116938i
$163$	−13.6757	+	13.6757i	−1.07117	+	1.07117i	−0.0739001	+	0.997266i	$0.523545\pi$
$163$	−13.6757	+	13.6757i	−1.07117	+	1.07117i	−0.997266	+	0.0739001i	$0.976455\pi$
$164$	17.1533			1.33945
$165$	−1.01355	+	5.88789i	−0.0789046	+	0.458371i
$166$		−	14.5546i		−	1.12966i
$167$	−6.23288	+	6.23288i	−0.482315	+	0.482315i	−0.905870	−	0.423555i	$-0.860782\pi$
$167$	−6.23288	+	6.23288i	−0.482315	+	0.482315i	0.423555	+	0.905870i	$0.360782\pi$
$168$	1.79034	+	1.59496i	0.138128	+	0.123054i
$169$		−	9.98824i		−	0.768326i
$170$	18.2255	+	25.8049i	1.39783	+	1.97915i
$171$			6.01729i			0.460154i
$172$	0.741049	+	0.741049i	0.0565045	+	0.0565045i
$173$	6.76935	+	6.76935i	0.514664	+	0.514664i	0.915952	−	0.401288i	$-0.131437\pi$
$173$	6.76935	+	6.76935i	0.514664	+	0.514664i	−0.401288	+	0.915952i	$0.631437\pi$
$174$	0.641758			0.0486515
$175$	11.5959	−	6.36666i	0.876570	−	0.481274i
$176$	−7.89143			−0.594839
$177$	−5.64863	−	5.64863i	−0.424577	−	0.424577i
$178$	10.2885	+	10.2885i	0.771152	+	0.771152i
$179$			1.30103i			0.0972437i	0.998817	+	0.0486218i	$0.0154829\pi$
$179$			1.30103i			0.0972437i	−0.998817	+	0.0486218i	$0.984517\pi$
$180$	3.13538	+	4.43929i	0.233697	+	0.330885i
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	6.42885	−	7.21638i	0.476538	−	0.534913i
$183$	−3.91319	+	3.91319i	−0.289271	+	0.289271i
$184$		−	0.225165i		−	0.0165994i
$185$	−0.394541	+	2.29196i	−0.0290072	+	0.168508i
$186$	15.2684			1.11953
$187$	12.6814	−	12.6814i	0.927352	−	0.927352i
$188$	1.35349	+	1.35349i	0.0987136	+	0.0987136i
$189$	2.64136	−	0.152445i	0.192130	−	0.0110887i
$190$	4.80462	−	27.9109i	0.348564	−	2.02487i
$191$	1.93791			0.140222			0.0701110	−	0.997539i	$-0.477665\pi$
$191$	1.93791			0.140222			0.0701110	+	0.997539i	$0.477665\pi$
$192$	−7.77383	+	7.77383i	−0.561028	+	0.561028i
$193$	−7.82786	+	7.82786i	−0.563462	+	0.563462i	−0.930289	−	0.366827i	$-0.880444\pi$
$193$	−7.82786	+	7.82786i	−0.563462	+	0.563462i	0.366827	+	0.930289i	$0.380444\pi$
$194$	−26.3186			−1.88957
$195$	3.16970	−	2.23870i	0.226987	−	0.160316i
$196$	−16.9009	+	1.95738i	−1.20721	+	0.139813i
$197$	−8.50767	−	8.50767i	−0.606146	−	0.606146i	0.335790	−	0.941937i	$-0.390997\pi$
$197$	−8.50767	−	8.50767i	−0.606146	−	0.606146i	−0.941937	+	0.335790i	$0.890997\pi$
$198$	3.97676	−	3.97676i	0.282616	−	0.282616i
$199$	−3.25460			−0.230712			−0.115356	−	0.993324i	$-0.536801\pi$
$199$	−3.25460			−0.230712			−0.115356	+	0.993324i	$0.536801\pi$
$200$	−1.94832	−	4.09107i	−0.137767	−	0.289283i
$201$		−	4.85153i		−	0.342201i
$202$	10.7604	−	10.7604i	0.757101	−	0.757101i
$203$	−0.536583	+	0.602314i	−0.0376607	+	0.0422741i
$204$		−	16.3144i		−	1.14223i
$205$	−12.8900	+	9.10390i	−0.900273	+	0.635844i
$206$		−	20.6747i		−	1.44048i
$207$	−0.175684	−	0.175684i	−0.0122109	−	0.0122109i
$208$	3.62439	+	3.62439i	0.251306	+	0.251306i
$209$	−16.0774			−1.11210
$210$	−12.3735	−	1.40193i	−0.853854	−	0.0967426i
$211$	−17.2508			−1.18759			−0.593797	−	0.804615i	$-0.702372\pi$
$211$	−17.2508			−1.18759			−0.593797	+	0.804615i	$0.702372\pi$
$212$	−12.1292	−	12.1292i	−0.833037	−	0.833037i
$213$	10.8249	+	10.8249i	0.741711	+	0.741711i
$214$		−	22.2452i		−	1.52065i
$215$	−0.950169	−	0.163563i	−0.0648010	−	0.0111549i
$216$		−	0.906263i		−	0.0616634i
$217$	−12.7661	+	14.3300i	−0.866622	+	0.972782i
$218$	8.86110	−	8.86110i	0.600150	−	0.600150i
$219$			14.1716i			0.957628i
$220$	−11.8612	+	8.37733i	−0.799683	+	0.564799i
$221$	−11.6486			−0.783572
$222$	1.54802	−	1.54802i	0.103896	−	0.103896i
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	0.536768	−	0.843730i	$-0.319645\pi$
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	−0.843730	+	0.536768i	$0.819645\pi$
$224$	−1.22403	−	21.2084i	−0.0817841	−	1.41705i
$225$	−4.71220	−	1.67187i	−0.314147	−	0.111458i
$226$	20.8085			1.38416
$227$	14.1613	−	14.1613i	0.939918	−	0.939918i	−0.0583764	−	0.998295i	$-0.518592\pi$
$227$	14.1613	−	14.1613i	0.939918	−	0.939918i	0.998295	+	0.0583764i	$0.0185924\pi$
$228$	−10.3417	+	10.3417i	−0.684894	+	0.684894i
$229$	−28.9307			−1.91180			−0.955898	−	0.293699i	$-0.905114\pi$
$229$	−28.9307			−1.91180			−0.955898	+	0.293699i	$0.905114\pi$
$230$	0.674623	+	0.955180i	0.0444833	+	0.0629827i
$231$	0.407313	+	7.05736i	0.0267992	+	0.464340i
$232$	0.195381	+	0.195381i	0.0128274	+	0.0128274i
$233$	−4.78546	+	4.78546i	−0.313506	+	0.313506i	−0.846266	−	0.532760i	$-0.821155\pi$
$233$	−4.78546	+	4.78546i	−0.313506	+	0.313506i	0.532760	+	0.846266i	$0.321155\pi$
$234$	−3.65291			−0.238798
$235$	−1.73544	−	0.298741i	−0.113208	−	0.0194877i
$236$		−	19.4162i		−	1.26388i
$237$	7.98837	−	7.98837i	0.518901	−	0.518901i
$238$	27.9109	+	24.8650i	1.80920	+	1.61176i
$239$			16.1769i			1.04640i	0.852210	+	0.523200i	$0.175262\pi$
$239$			16.1769i			1.04640i	−0.852210	+	0.523200i	$0.824738\pi$
$240$	1.12039	−	6.50855i	0.0723208	−	0.420125i
$241$		−	11.3707i		−	0.732454i	−0.930526	−	0.366227i	$-0.880649\pi$
$241$		−	11.3707i		−	0.732454i	0.930526	−	0.366227i	$-0.119351\pi$
$242$	−5.74679	−	5.74679i	−0.369418	−	0.369418i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−13.4509			−0.861105
$245$	11.6614	−	10.4408i	0.745022	−	0.667040i
$246$	14.8550			0.947117
$247$	7.38407	+	7.38407i	0.469837	+	0.469837i
$248$	4.64841	+	4.64841i	0.295174	+	0.295174i
$249$		−	6.91467i		−	0.438199i
$250$	20.5224	+	11.5174i	1.29795	+	0.728427i
$251$			6.95039i			0.438705i	0.975646	+	0.219352i	$0.0703944\pi$
$251$			6.95039i			0.438705i	−0.975646	+	0.219352i	$0.929606\pi$
$252$	4.80159	+	4.27759i	0.302472	+	0.269463i
$253$	0.469405	−	0.469405i	0.0295112	−	0.0295112i
$254$			8.51682i			0.534393i
$255$	8.65865	+	12.2595i	0.542226	+	0.767722i
$256$	7.08066			0.442541
$257$	10.0889	−	10.0889i	0.629329	−	0.629329i	−0.318570	−	0.947899i	$-0.603203\pi$
$257$	10.0889	−	10.0889i	0.629329	−	0.629329i	0.947899	+	0.318570i	$0.103203\pi$
$258$	0.641758	+	0.641758i	0.0399541	+	0.0399541i
$259$	0.158553	+	2.74720i	0.00985202	+	0.170703i
$260$	9.29520	+	1.60009i	0.576464	+	0.0992332i
$261$	0.304889			0.0188722
$262$	−13.9128	+	13.9128i	−0.859538	+	0.859538i
$263$	18.1984	−	18.1984i	1.12216	−	1.12216i	0.130744	−	0.991416i	$-0.458263\pi$
$263$	18.1984	−	18.1984i	1.12216	−	1.12216i	0.991416	−	0.130744i	$-0.0417367\pi$
$264$	2.42142			0.149028
$265$	15.5520	+	2.67714i	0.955352	+	0.164456i
$266$	−1.93082	−	33.4547i	−0.118386	−	2.05124i
$267$	4.88789	+	4.88789i	0.299134	+	0.299134i
$268$	8.33813	−	8.33813i	0.509333	−	0.509333i
$269$	−15.5119			−0.945775			−0.472888	−	0.881123i	$-0.656788\pi$
$269$	−15.5119			−0.945775			−0.472888	+	0.881123i	$0.656788\pi$
$270$	2.71528	+	3.84448i	0.165246	+	0.233968i
$271$			13.3418i			0.810458i	0.914215	+	0.405229i	$0.132808\pi$
$271$			13.3418i			0.810458i	−0.914215	+	0.405229i	$0.867192\pi$
$272$	−14.0181	+	14.0181i	−0.849974	+	0.849974i
$273$	3.05425	−	3.42839i	0.184852	−	0.207496i
$274$			22.3835i			1.35224i
$275$	4.46702	−	12.5904i	0.269372	−	0.759229i
$276$		−	0.603882i		−	0.0363494i
$277$	−2.00561	−	2.00561i	−0.120505	−	0.120505i	0.644282	−	0.764788i	$-0.277156\pi$
$277$	−2.00561	−	2.00561i	−0.120505	−	0.120505i	−0.764788	+	0.644282i	$0.777156\pi$
$278$	11.5930	+	11.5930i	0.695304	+	0.695304i
$279$	7.25379			0.434273
$280$	−3.34026	−	4.19388i	−0.199619	−	0.250632i
$281$	13.5557			0.808664			0.404332	−	0.914612i	$-0.367504\pi$
$281$	13.5557			0.808664			0.404332	+	0.914612i	$0.367504\pi$
$282$	1.17214	+	1.17214i	0.0698000	+	0.0698000i
$283$	−16.2444	−	16.2444i	−0.965627	−	0.965627i	0.0338017	−	0.999429i	$-0.489239\pi$
$283$	−16.2444	−	16.2444i	−0.965627	−	0.965627i	−0.999429	+	0.0338017i	$0.989239\pi$
$284$			37.2087i			2.20793i
$285$	2.28260	−	13.2600i	0.135210	−	0.785457i
$286$		−	9.76010i		−	0.577127i
$287$	−12.4204	+	13.9419i	−0.733155	+	0.822966i
$288$	−5.67761	+	5.67761i	−0.334557	+	0.334557i
$289$		−	28.0537i		−	1.65021i
$290$	−1.41421	−	0.243445i	−0.0830455	−	0.0142956i
$291$	−12.5036			−0.732973
$292$	−24.3562	+	24.3562i	−1.42534	+	1.42534i
$293$	−2.41765	−	2.41765i	−0.141240	−	0.141240i	0.632951	−	0.774192i	$-0.281843\pi$
$293$	−2.41765	−	2.41765i	−0.141240	−	0.141240i	−0.774192	+	0.632951i	$0.781843\pi$
$294$	−14.6364	+	1.69511i	−0.853611	+	0.0988609i
$295$	10.3049	+	14.5904i	0.599974	+	0.849486i
$296$	0.942578			0.0547862
$297$	1.88930	−	1.88930i	0.109628	−	0.109628i
$298$	−21.2623	+	21.2623i	−1.23169	+	1.23169i
$299$	−0.431179			−0.0249357
$300$	−5.22529	−	10.9720i	−0.301682	−	0.633472i
$301$	−1.13890	+	0.0657309i	−0.0656449	+	0.00378867i
$302$	14.5562	+	14.5562i	0.837616	+	0.837616i
$303$	5.11211	−	5.11211i	0.293683	−	0.293683i
$304$	17.7722			1.01931
$305$	10.1078	−	7.13890i	0.578769	−	0.408772i
$306$		−	14.1284i		−	0.807669i
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	−0.470652	−	0.882319i	$-0.655981\pi$
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	0.882319	+	0.470652i	$0.155981\pi$
$308$	−11.4292	+	12.8292i	−0.651238	+	0.731014i
$309$		−	9.82225i		−	0.558768i
$310$	−33.6463	−	5.79193i	−1.91098	−	0.328959i
$311$			10.2542i			0.581460i	0.956805	+	0.290730i	$0.0938981\pi$
$311$			10.2542i			0.581460i	−0.956805	+	0.290730i	$0.906102\pi$
$312$	−1.11211	−	1.11211i	−0.0629611	−	0.0629611i
$313$	22.0904	+	22.0904i	1.24862	+	1.24862i	0.956329	+	0.292293i	$0.0944182\pi$
$313$	22.0904	+	22.0904i	1.24862	+	1.24862i	0.292293	+	0.956329i	$0.405582\pi$
$314$	6.48134			0.365763
$315$	−5.87847	−	0.666037i	−0.331214	−	0.0375269i
$316$	27.4586			1.54467
$317$	−12.2563	−	12.2563i	−0.688385	−	0.688385i	0.273490	−	0.961875i	$-0.411822\pi$
$317$	−12.2563	−	12.2563i	−0.688385	−	0.688385i	−0.961875	+	0.273490i	$0.911822\pi$
$318$	−10.5040	−	10.5040i	−0.589037	−	0.589037i
$319$			0.814625i			0.0456102i
$320$	20.0798	−	14.1819i	1.12249	−	0.792793i
$321$		−	10.5683i		−	0.589867i
$322$	1.03313	+	0.920387i	0.0575743	+	0.0512912i
$323$	−28.5595	+	28.5595i	−1.58909	+	1.58909i
$324$		−	2.43055i		−	0.135031i
$325$	−7.83417	+	3.73092i	−0.434561	+	0.206954i
$326$	−40.7094			−2.25468
$327$	4.20978	−	4.20978i	0.232801	−	0.232801i
$328$	4.52253	+	4.52253i	0.249715	+	0.249715i
$329$	−2.08014	+	0.120054i	−0.114682	+	0.00661882i
$330$	−10.2720	+	7.25487i	−0.565453	+	0.399367i
$331$	1.26308			0.0694252			0.0347126	−	0.999397i	$-0.488948\pi$
$331$	1.26308			0.0694252			0.0347126	+	0.999397i	$0.488948\pi$
$332$	11.8840	−	11.8840i	0.652217	−	0.652217i
$333$	0.735441	−	0.735441i	0.0403019	−	0.0403019i
$334$	−18.5538			−1.01522
$335$	−1.84038	+	10.6911i	−0.100551	+	0.584118i
$336$	−0.450249	−	7.80130i	−0.0245631	−	0.425596i
$337$	−9.55621	−	9.55621i	−0.520560	−	0.520560i	0.397180	−	0.917741i	$-0.369989\pi$
$337$	−9.55621	−	9.55621i	−0.520560	−	0.520560i	−0.917741	+	0.397180i	$0.869989\pi$
$338$	14.8663	−	14.8663i	0.808620	−	0.808620i
$339$	9.88579			0.536922
$340$	−6.18869	+	35.9512i	−0.335629	+	1.94973i
$341$			19.3812i			1.04955i
$342$	−8.95602	+	8.95602i	−0.484286	+	0.484286i
$343$	10.6468	−	15.1541i	0.574871	−	0.818244i
$344$			0.390761i			0.0210684i
$345$	0.320503	+	0.453791i	0.0172553	+	0.0244313i
$346$			20.1507i			1.08331i
$347$	6.54975	+	6.54975i	0.351609	+	0.351609i	0.860708	−	0.509099i	$-0.170021\pi$
$347$	6.54975	+	6.54975i	0.351609	+	0.351609i	−0.509099	+	0.860708i	$0.670021\pi$
$348$	0.524001	+	0.524001i	0.0280894	+	0.0280894i
$349$	−2.77139			−0.148349			−0.0741746	−	0.997245i	$-0.523632\pi$
$349$	−2.77139			−0.148349			−0.0741746	+	0.997245i	$0.523632\pi$
$350$	26.7352	+	7.78315i	1.42905	+	0.416027i
$351$	−1.73544			−0.0926310
$352$	−15.1699	−	15.1699i	−0.808556	−	0.808556i
$353$	−0.970568	−	0.970568i	−0.0516581	−	0.0516581i	0.680806	−	0.732464i	$-0.261630\pi$
$353$	−0.970568	−	0.970568i	−0.0516581	−	0.0516581i	−0.732464	+	0.680806i	$0.761630\pi$
$354$		−	16.8146i		−	0.893687i
$355$	−19.7481	−	27.9607i	−1.04812	−	1.48400i
$356$			16.8012i			0.890463i
$357$	13.2601	+	11.8130i	0.701797	+	0.625209i
$358$	−1.93643	+	1.93643i	−0.102344	+	0.102344i
$359$		−	9.32813i		−	0.492320i	−0.969229	−	0.246160i	$-0.920831\pi$
$359$		−	9.32813i		−	0.492320i	0.969229	−	0.246160i	$-0.0791688\pi$
$360$	−0.343782	+	1.99709i	−0.0181189	+	0.105256i
$361$	17.2078			0.905674
$362$	−12.6293	+	12.6293i	−0.663783	+	0.663783i
$363$	−2.73021	−	2.73021i	−0.143299	−	0.143299i
$364$	11.1415	−	0.643024i	0.583971	−	0.0337036i
$365$	5.37586	−	31.2293i	0.281385	−	1.63462i
$366$	−11.6486			−0.608884
$367$	13.0035	−	13.0035i	0.678776	−	0.678776i	−0.280948	−	0.959723i	$-0.590649\pi$
$367$	13.0035	−	13.0035i	0.678776	−	0.678776i	0.959723	+	0.280948i	$0.0906487\pi$
$368$	−0.518887	+	0.518887i	−0.0270488	+	0.0270488i
$369$	7.05736			0.367392
$370$	−3.99853	+	2.82408i	−0.207874	+	0.146817i
$371$	18.6410	−	1.07586i	0.967793	−	0.0558557i
$372$	12.4668	+	12.4668i	0.646373	+	0.646373i
$373$	20.6757	−	20.6757i	1.07055	−	1.07055i	0.0732339	−	0.997315i	$-0.476668\pi$
$373$	20.6757	−	20.6757i	1.07055	−	1.07055i	0.997315	−	0.0732339i	$-0.0233320\pi$
$374$	37.7493			1.95197
$375$	9.74986	+	5.47176i	0.503481	+	0.282560i
$376$			0.713708i			0.0368067i
$377$	0.374143	−	0.374143i	0.0192693	−	0.0192693i
$378$	4.15824	+	3.70445i	0.213877	+	0.190536i
$379$			22.0077i			1.13046i	0.824933	+	0.565230i	$0.191213\pi$
$379$			22.0077i			1.13046i	−0.824933	+	0.565230i	$0.808787\pi$
$380$	26.7125	−	18.8665i	1.37032	−	0.967830i
$381$			4.04621i			0.207294i
$382$	2.88434	+	2.88434i	0.147576	+	0.147576i
$383$	−0.390382	−	0.390382i	−0.0199476	−	0.0199476i	0.697063	−	0.717010i	$-0.254490\pi$
$383$	−0.390382	−	0.390382i	−0.0199476	−	0.0199476i	−0.717010	+	0.697063i	$0.754490\pi$
$384$	−7.08211			−0.361407
$385$	1.77957	−	15.7065i	0.0906950	−	0.800478i
$386$	−23.3017			−1.18602
$387$	0.304889	+	0.304889i	0.0154984	+	0.0154984i
$388$	−21.4894	−	21.4894i	−1.09096	−	1.09096i
$389$			25.9300i			1.31470i	0.753584	+	0.657352i	$0.228323\pi$
$389$			25.9300i			1.31470i	−0.753584	+	0.657352i	$0.771677\pi$
$390$	8.04976	+	1.38570i	0.407615	+	0.0701674i
$391$		−	1.66768i		−	0.0843381i
$392$	−4.97206	−	3.93992i	−0.251127	−	0.198996i
$393$	−6.60978	+	6.60978i	−0.333419	+	0.333419i
$394$		−	25.3253i		−	1.27587i
$395$	−20.6339	+	14.5733i	−1.03821	+	0.733263i
$396$	6.49412			0.326342
$397$	−17.1631	+	17.1631i	−0.861391	+	0.861391i	−0.991500	−	0.130109i	$-0.958467\pi$
$397$	−17.1631	+	17.1631i	−0.861391	+	0.861391i	0.130109	+	0.991500i	$0.458467\pi$
$398$	−4.84408	−	4.84408i	−0.242812	−	0.242812i
$399$	−0.917304	−	15.8938i	−0.0459226	−	0.795686i
$400$	−4.93791	+	13.9176i	−0.246895	+	0.695879i
$401$	−12.9418			−0.646281			−0.323140	−	0.946351i	$-0.604739\pi$
$401$	−12.9418			−0.646281			−0.323140	+	0.946351i	$0.604739\pi$
$402$	7.22093	−	7.22093i	0.360147	−	0.360147i
$403$	8.90143	−	8.90143i	0.443412	−	0.443412i
$404$	17.5720			0.874238
$405$	1.28999	+	1.82645i	0.0640999	+	0.0907572i
$406$	−1.69511	+	0.0978326i	−0.0841269	+	0.00485535i
$407$	1.96500	+	1.96500i	0.0974016	+	0.0974016i
$408$	4.30135	−	4.30135i	0.212948	−	0.212948i
$409$	−2.64278			−0.130677			−0.0653386	−	0.997863i	$-0.520813\pi$
$409$	−2.64278			−0.130677			−0.0653386	+	0.997863i	$0.520813\pi$
$410$	−32.7352	−	5.63508i	−1.61668	−	0.278297i
$411$			10.6341i			0.524540i
$412$	16.8811	−	16.8811i	0.831672	−	0.831672i
$413$	15.7812	+	14.0589i	0.776540	+	0.691795i
$414$		−	0.522969i		−	0.0257025i
$415$	−2.62301	+	15.2376i	−0.128759	+	0.747982i
$416$			13.9345i			0.683194i
$417$	5.50767	+	5.50767i	0.269712	+	0.269712i
$418$	−23.9293	−	23.9293i	−1.17042	−	1.17042i
$419$	10.0302			0.490007			0.245003	−	0.969522i	$-0.421211\pi$
$419$	10.0302			0.490007			0.245003	+	0.969522i	$0.421211\pi$
$420$	−8.95840	−	11.2478i	−0.437125	−	0.548835i
$421$	−26.6440			−1.29855			−0.649274	−	0.760555i	$-0.724927\pi$
$421$	−26.6440			−1.29855			−0.649274	+	0.760555i	$0.724927\pi$
$422$	−25.6757	−	25.6757i	−1.24987	−	1.24987i
$423$	0.556866	+	0.556866i	0.0270758	+	0.0270758i
$424$		−	6.39583i		−	0.310609i
$425$	−14.4301	−	30.3004i	−0.699965	−	1.46978i
$426$			32.2232i			1.56122i
$427$	9.73958	−	10.9327i	0.471332	−	0.529069i
$428$	18.1634	−	18.1634i	0.877960	−	0.877960i
$429$		−	4.63688i		−	0.223870i
$430$	−1.17077	−	1.65766i	−0.0564595	−	0.0799394i
$431$	22.3747			1.07775			0.538876	−	0.842385i	$-0.318849\pi$
$431$	22.3747			1.07775			0.538876	+	0.842385i	$0.318849\pi$
$432$	−2.08845	+	2.08845i	−0.100481	+	0.100481i
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	0.952373	−	0.304935i	$-0.0986349\pi$
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	−0.304935	+	0.952373i	$0.598635\pi$
$434$	−40.3293	+	2.32759i	−1.93587	+	0.111728i
$435$	−0.671871	−	0.115657i	−0.0322138	−	0.00554532i
$436$	14.4703			0.693004
$437$	−1.05714	+	1.05714i	−0.0505700	+	0.0505700i
$438$	−21.0927	+	21.0927i	−1.00785	+	1.00785i
$439$	25.6790			1.22559			0.612795	−	0.790242i	$-0.290045\pi$
$439$	25.6790			1.22559			0.612795	+	0.790242i	$0.290045\pi$
$440$	−5.33598	−	0.918542i	−0.254383	−	0.0437898i
$441$	−6.95352	+	0.805321i	−0.331120	+	0.0383486i
$442$	−17.3376	−	17.3376i	−0.824665	−	0.824665i
$443$	−15.6351	+	15.6351i	−0.742845	+	0.742845i	−0.973125	−	0.230279i	$-0.926036\pi$
$443$	−15.6351	+	15.6351i	−0.742845	+	0.742845i	0.230279	+	0.973125i	$0.426036\pi$
$444$	2.52795			0.119971
$445$	−8.91705	−	12.6254i	−0.422709	−	0.598501i
$446$		−	13.6452i		−	0.646120i
$447$	−10.1014	+	10.1014i	−0.477779	+	0.477779i
$448$	19.3484	−	21.7185i	0.914124	−	1.02610i
$449$		−	7.01947i		−	0.331269i	−0.986187	−	0.165635i	$-0.947033\pi$
$449$		−	7.01947i		−	0.331269i	0.986187	−	0.165635i	$-0.0529673\pi$
$450$	−4.52517	−	9.50193i	−0.213318	−	0.447925i
$451$			18.8564i			0.887912i
$452$	16.9903	+	16.9903i	0.799157	+	0.799157i
$453$	6.91544	+	6.91544i	0.324916	+	0.324916i
$454$	42.1548			1.97842
$455$	−8.03104	+	6.39640i	−0.376501	+	0.299868i
$456$	−5.45325			−0.255372
$457$	11.2119	+	11.2119i	0.524472	+	0.524472i	0.918919	−	0.394447i	$-0.129064\pi$
$457$	11.2119	+	11.2119i	0.524472	+	0.524472i	−0.394447	+	0.918919i	$0.629064\pi$
$458$	−43.0599	−	43.0599i	−2.01206	−	2.01206i
$459$		−	6.71220i		−	0.313299i
$460$	−0.229077	+	1.33075i	−0.0106808	+	0.0620465i
$461$		−	29.9845i		−	1.39652i	−0.715846	−	0.698259i	$-0.753959\pi$
$461$		−	29.9845i		−	1.39652i	0.715846	−	0.698259i	$-0.246041\pi$
$462$	−9.89780	+	11.1103i	−0.460488	+	0.516897i
$463$	7.70220	−	7.70220i	0.357951	−	0.357951i	−0.505106	−	0.863057i	$-0.668547\pi$
$463$	7.70220	−	7.70220i	0.357951	−	0.357951i	0.863057	+	0.505106i	$0.168547\pi$
$464$		−	0.900497i		−	0.0418045i
$465$	−15.9849	−	2.75166i	−0.741280	−	0.127605i
$466$	−14.2452			−0.659895
$467$	1.80961	−	1.80961i	0.0837386	−	0.0837386i	−0.663997	−	0.747735i	$-0.731141\pi$
$467$	1.80961	−	1.80961i	0.0837386	−	0.0837386i	0.747735	+	0.663997i	$0.231141\pi$
$468$	−2.98263	−	2.98263i	−0.137872	−	0.137872i
$469$	0.739590	+	12.8146i	0.0341511	+	0.591724i
$470$	−2.13836	−	3.02764i	−0.0986350	−	0.139654i
$471$	3.07918			0.141881
$472$	5.11915	−	5.11915i	0.235628	−	0.235628i
$473$	−0.814625	+	0.814625i	−0.0374565	+	0.0374565i
$474$	23.7795			1.09223
$475$	−10.0601	+	28.3547i	−0.461591	+	1.30100i
$476$	2.48704	+	43.0920i	0.113993	+	1.97512i
$477$	−4.99031	−	4.99031i	−0.228491	−	0.228491i
$478$	−24.0774	+	24.0774i	−1.10128	+	1.10128i
$479$	4.09455			0.187085			0.0935425	−	0.995615i	$-0.470181\pi$
$479$	4.09455			0.187085			0.0935425	+	0.995615i	$0.470181\pi$
$480$	14.6653	−	10.3578i	0.669374	−	0.472765i
$481$		−	1.80498i		−	0.0823001i
$482$	16.9240	−	16.9240i	0.770867	−	0.770867i
$483$	0.490826	+	0.437262i	0.0223334	+	0.0198961i
$484$		−	9.38461i		−	0.426573i
$485$	27.5536	+	4.74311i	1.25114	+	0.215374i
$486$		−	2.10489i		−	0.0954796i
$487$	−10.3049	−	10.3049i	−0.466959	−	0.466959i	0.433969	−	0.900928i	$-0.357113\pi$
$487$	−10.3049	−	10.3049i	−0.466959	−	0.466959i	−0.900928	+	0.433969i	$0.857113\pi$
$488$	−3.54638	−	3.54638i	−0.160537	−	0.160537i
$489$	−19.3404			−0.874603
$490$	32.8966	+	1.81673i	1.48612	+	0.0820714i
$491$	−8.55953			−0.386286			−0.193143	−	0.981171i	$-0.561868\pi$
$491$	−8.55953			−0.386286			−0.193143	+	0.981171i	$0.561868\pi$
$492$	12.1292	+	12.1292i	0.546827	+	0.546827i
$493$	1.44708	+	1.44708i	0.0651732	+	0.0651732i
$494$			21.9806i			0.988955i
$495$	−4.88005	+	3.44668i	−0.219342	+	0.154917i
$496$		−	21.4242i		−	0.961976i
$497$	−30.2427	−	26.9423i	−1.35657	−	1.20853i
$498$	10.2917	−	10.2917i	0.461180	−	0.461180i
$499$			23.7564i			1.06348i	0.846907	+	0.531741i	$0.178462\pi$
$499$			23.7564i			1.06348i	−0.846907	+	0.531741i	$0.821538\pi$
$500$	7.35261	+	26.1608i	0.328819	+	1.16995i
$501$	−8.81463			−0.393808
$502$	−10.3448	+	10.3448i	−0.461712	+	0.461712i
$503$	−17.9504	−	17.9504i	−0.800367	−	0.800367i	0.182786	−	0.983153i	$-0.441489\pi$
$503$	−17.9504	−	17.9504i	−0.800367	−	0.800367i	−0.983153	+	0.182786i	$0.941489\pi$
$504$	0.138155	+	2.39376i	0.00615391	+	0.106627i
$505$	−13.2046	+	9.32611i	−0.587596	+	0.415007i
$506$	1.39731			0.0621179
$507$	7.06275	−	7.06275i	0.313668	−	0.313668i
$508$	−6.95406	+	6.95406i	−0.308537	+	0.308537i
$509$	16.8977			0.748979			0.374489	−	0.927231i	$-0.377818\pi$
$509$	16.8977			0.748979			0.374489	+	0.927231i	$0.377818\pi$
$510$	−5.35948	+	31.1342i	−0.237322	+	1.37865i
$511$	−2.16039	−	37.4322i	−0.0955698	−	1.65590i
$512$	20.5543	+	20.5543i	0.908382	+	0.908382i
$513$	−4.25487	+	4.25487i	−0.187857	+	0.187857i
$514$	30.0323			1.32467
$515$	−3.72598	+	21.6449i	−0.164186	+	0.953787i
$516$			1.04800i			0.0461357i
$517$	−1.48788	+	1.48788i	−0.0654367	+	0.0654367i
$518$	−3.85289	+	4.32486i	−0.169286	+	0.190024i
$519$			9.57331i			0.420221i
$520$	2.02885	+	2.87259i	0.0889708	+	0.125971i
$521$		−	7.88477i		−	0.345438i	−0.984971	−	0.172719i	$-0.944745\pi$
$521$		−	7.88477i		−	0.345438i	0.984971	−	0.172719i	$-0.0552552\pi$
$522$	0.453791	+	0.453791i	0.0198619	+	0.0198619i
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	0.679669	−	0.733519i	$-0.262123\pi$
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	−0.733519	+	0.679669i	$0.762123\pi$
$524$	−22.7199			−0.992524
$525$	12.7015	+	3.69766i	0.554338	+	0.161379i
$526$	54.1722			2.36202
$527$	34.4283	+	34.4283i	1.49972	+	1.49972i
$528$	−5.58008	−	5.58008i	−0.242842	−	0.242842i
$529$			22.9383i			0.997316i
$530$	19.1627	+	27.1319i	0.832374	+	1.17853i
$531$		−	7.98837i		−	0.346666i
$532$	25.7395	−	28.8926i	1.11595	−	1.25265i
$533$	8.66039	−	8.66039i	0.375123	−	0.375123i
$534$			14.5501i			0.629643i
$535$	−4.00900	+	23.2890i	−0.173324	+	1.00687i
$536$	4.39677			0.189911
$537$	−0.919968	+	0.919968i	−0.0396996	+	0.0396996i
$538$	−23.0876	−	23.0876i	−0.995375	−	0.995375i
$539$	−2.15171	−	18.5789i	−0.0926809	−	0.800250i
$540$	−0.922006	+	5.35610i	−0.0396768	+	0.230490i
$541$	34.9495			1.50260			0.751298	−	0.659963i	$-0.229428\pi$
$541$	34.9495			1.50260			0.751298	+	0.659963i	$0.229428\pi$
$542$	−19.8577	+	19.8577i	−0.852962	+	0.852962i
$543$	−6.00000	+	6.00000i	−0.257485	+	0.257485i
$544$	−53.8947			−2.31071
$545$	−10.8738	+	7.67996i	−0.465784	+	0.328973i
$546$	9.64863	−	0.556866i	0.412923	−	0.0238317i
$547$	3.83548	+	3.83548i	0.163993	+	0.163993i	0.784333	−	0.620340i	$-0.213005\pi$
$547$	3.83548	+	3.83548i	0.163993	+	0.163993i	−0.620340	+	0.784333i	$0.713005\pi$
$548$	−18.2764	+	18.2764i	−0.780727	+	0.780727i
$549$	−5.53409			−0.236189
$550$	25.3879	−	12.0907i	1.08255	−	0.515548i
$551$		−	1.83461i		−	0.0781569i
$552$	0.159216	−	0.159216i	0.00677668	−	0.00677668i
$553$	−19.8823	+	22.3179i	−0.845483	+	0.949054i
$554$		−	5.97022i		−	0.253650i
$555$	−1.89964	+	1.34168i	−0.0806353	+	0.0569510i
$556$			18.9316i			0.802880i
$557$	−16.3147	−	16.3147i	−0.691275	−	0.691275i	0.271238	−	0.962512i	$-0.412567\pi$
$557$	−16.3147	−	16.3147i	−0.691275	−	0.691275i	−0.962512	+	0.271238i	$0.912567\pi$
$558$	10.7964	+	10.7964i	0.457048	+	0.457048i
$559$	0.748285			0.0316491
$560$	−1.96715	+	17.3622i	−0.0831275	+	0.733686i
$561$	17.9341			0.757180
$562$	20.1760	+	20.1760i	0.851073	+	0.851073i
$563$	23.7521	+	23.7521i	1.00103	+	1.00103i	0.999999	+	0.00103054i	$0.000328032\pi$
$563$	23.7521	+	23.7521i	1.00103	+	1.00103i	0.00103054	+	0.999999i	$0.499672\pi$
$564$			1.91413i			0.0805993i
$565$	−21.7849	−	3.75008i	−0.916497	−	0.157767i
$566$		−	48.3556i		−	2.03254i
$567$	1.97552	+	1.75993i	0.0829638	+	0.0739099i
$568$	−9.81023	+	9.81023i	−0.411628	+	0.411628i
$569$		−	0.277792i		−	0.0116457i	−0.999983	−	0.00582283i	$-0.998147\pi$
$569$		−	0.277792i		−	0.0116457i	0.999983	−	0.00582283i	$-0.00185348\pi$
$570$	23.1334	−	16.3386i	0.968950	−	0.684349i
$571$	−3.11538			−0.130375			−0.0651874	−	0.997873i	$-0.520765\pi$
$571$	−3.11538			−0.130375			−0.0651874	+	0.997873i	$0.520765\pi$
$572$	7.96921	−	7.96921i	0.333209	−	0.333209i
$573$	1.37031	+	1.37031i	0.0572454	+	0.0572454i
$574$	−39.2372	+	2.26456i	−1.63773	+	0.0945209i
$575$	−0.534138	−	1.12158i	−0.0222751	−	0.0467731i
$576$	−10.9939			−0.458077
$577$	29.5905	−	29.5905i	1.23187	−	1.23187i	0.268625	−	0.963245i	$-0.413431\pi$
$577$	29.5905	−	29.5905i	1.23187	−	1.23187i	0.963245	−	0.268625i	$-0.0865693\pi$
$578$	41.7545	−	41.7545i	1.73676	−	1.73676i
$579$	−11.0703			−0.460064
$580$	−0.955943	−	1.35349i	−0.0396934	−	0.0562007i
$581$	1.05410	+	18.2641i	0.0437316	+	0.757722i
$582$	−18.6101	−	18.6101i	−0.771413	−	0.771413i
$583$	13.3335	−	13.3335i	0.552216	−	0.552216i
$584$	−12.8432			−0.531456
$585$	3.82432	+	0.658323i	0.158116	+	0.0272183i
$586$		−	7.19676i		−	0.297295i
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.105375	−	0.994433i	$-0.466396\pi$
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.994433	−	0.105375i	$-0.0336041\pi$
$588$	−13.3348	−	10.5667i	−0.549918	−	0.435762i
$589$		−	43.6482i		−	1.79849i
$590$	−6.37847	+	37.0537i	−0.262597	+	1.52547i
$591$		−	12.0317i		−	0.494916i
$592$	−2.17214	−	2.17214i	−0.0892745	−	0.0892745i
$593$	15.1889	+	15.1889i	0.623733	+	0.623733i	0.946484	−	0.322751i	$-0.104608\pi$
$593$	15.1889	+	15.1889i	0.623733	+	0.623733i	−0.322751	+	0.946484i	$0.604608\pi$
$594$	5.62399			0.230755
$595$	−24.7395	−	31.0618i	−1.01422	−	1.27341i
$596$	−34.7217			−1.42225
$597$	−2.30135	−	2.30135i	−0.0941878	−	0.0941878i
$598$	−0.641758	−	0.641758i	−0.0262434	−	0.0262434i
$599$		−	22.2776i		−	0.910238i	−0.890431	−	0.455119i	$-0.849597\pi$
$599$		−	22.2776i		−	0.910238i	0.890431	−	0.455119i	$-0.150403\pi$
$600$	1.51516	−	4.27050i	0.0618560	−	0.174342i
$601$			22.3458i			0.911503i	0.890107	+	0.455752i	$0.150629\pi$
$601$			22.3458i			0.911503i	−0.890107	+	0.455752i	$0.849371\pi$
$602$	−1.79294	−	1.59728i	−0.0730749	−	0.0651002i
$603$	3.43055	−	3.43055i	0.139703	−	0.139703i
$604$			23.7706i			0.967210i
$605$	4.98077	+	7.05213i	0.202497	+	0.286710i
$606$	15.2175			0.618170
$607$	−0.576027	+	0.576027i	−0.0233802	+	0.0233802i	−0.718700	−	0.695320i	$-0.755263\pi$
$607$	−0.576027	+	0.576027i	−0.0233802	+	0.0233802i	0.695320	+	0.718700i	$0.255263\pi$
$608$	34.1639	+	34.1639i	1.38553	+	1.38553i
$609$	−0.805321	+	0.0464788i	−0.0326333	+	0.00188341i
$610$	25.6696	+	4.41880i	1.03933	+	0.178912i
$611$	1.36671			0.0552911
$612$	11.5360	−	11.5360i	0.466315	−	0.466315i
$613$	−16.4709	+	16.4709i	−0.665253	+	0.665253i	−0.956613	−	0.291361i	$-0.905892\pi$
$613$	−16.4709	+	16.4709i	−0.665253	+	0.665253i	0.291361	+	0.956613i	$0.405892\pi$
$614$	21.4714			0.866514
$615$	−15.5520	−	2.67714i	−0.627117	−	0.107953i
$616$	−6.39583	+	0.369132i	−0.257695	+	0.0148728i
$617$	−3.70013	−	3.70013i	−0.148962	−	0.148962i	0.628692	−	0.777654i	$-0.283590\pi$
$617$	−3.70013	−	3.70013i	−0.148962	−	0.148962i	−0.777654	+	0.628692i	$0.783590\pi$
$618$	14.6192	−	14.6192i	0.588072	−	0.588072i
$619$	−39.8840			−1.60307			−0.801536	−	0.597946i	$-0.795984\pi$
$619$	−39.8840			−1.60307			−0.801536	+	0.597946i	$0.795984\pi$
$620$	−22.7434	−	32.2017i	−0.913396	−	1.29325i
$621$		−	0.248455i		−	0.00997015i
$622$	−15.2621	+	15.2621i	−0.611954	+	0.611954i
$623$	−13.6558	−	12.1655i	−0.547107	−	0.487401i
$624$			5.12566i			0.205191i
$625$	−19.4097	−	15.7564i	−0.776388	−	0.630256i
$626$			65.7578i			2.62821i
$627$	−11.3685	−	11.3685i	−0.454013	−	0.454013i
$628$	5.29207	+	5.29207i	0.211177	+	0.211177i
$629$	6.98117			0.278357
$630$	−7.75808	−	9.74071i	−0.309089	−	0.388079i
$631$	−33.9725			−1.35242			−0.676211	−	0.736708i	$-0.736379\pi$
$631$	−33.9725			−1.35242			−0.676211	+	0.736708i	$0.736379\pi$
$632$	7.23957	+	7.23957i	0.287975	+	0.287975i
$633$	−12.1981	−	12.1981i	−0.484833	−	0.484833i
$634$		−	36.4842i		−	1.44897i
$635$	1.53489	−	8.91646i	0.0609103	−	0.353839i
$636$		−	17.1533i		−	0.680172i
$637$	−7.54472	+	9.52120i	−0.298933	+	0.377244i
$638$	−1.21247	+	1.21247i	−0.0480022	+	0.0480022i
$639$			15.3087i			0.605605i
$640$	15.6065	+	2.68653i	0.616902	+	0.106194i
$641$	−18.1113			−0.715352			−0.357676	−	0.933846i	$-0.616431\pi$
$641$	−18.1113			−0.715352			−0.357676	+	0.933846i	$0.616431\pi$
$642$	15.7297	−	15.7297i	0.620802	−	0.620802i
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.948063	+	0.318082i	$0.103039\pi$
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.318082	+	0.948063i	$0.396961\pi$
$644$	0.0920586	+	1.59507i	0.00362762	+	0.0628545i
$645$	−0.556214	−	0.787528i	−0.0219009	−	0.0310089i
$646$	−85.0149			−3.34487
$647$	12.9277	−	12.9277i	0.508241	−	0.508241i	−0.405745	−	0.913986i	$-0.632988\pi$
$647$	12.9277	−	12.9277i	0.508241	−	0.508241i	0.913986	+	0.405745i	$0.132988\pi$
$648$	0.640825	−	0.640825i	0.0251740	−	0.0251740i
$649$	21.3439			0.837821
$650$	−17.2132	−	6.10719i	−0.675159	−	0.239544i
$651$	−19.1598	+	1.10580i	−0.750934	+	0.0433398i
$652$	−33.2396	−	33.2396i	−1.30176	−	1.30176i
$653$	−9.39937	+	9.39937i	−0.367826	+	0.367826i	−0.866684	−	0.498858i	$-0.833753\pi$
$653$	−9.39937	+	9.39937i	−0.367826	+	0.367826i	0.498858	+	0.866684i	$0.333753\pi$
$654$	12.5315			0.490020
$655$	17.0730	−	12.0583i	0.667099	−	0.471158i
$656$		−	20.8441i		−	0.813824i
$657$	−10.0208	+	10.0208i	−0.390950	+	0.390950i
$658$	−3.27473	−	2.91736i	−0.127662	−	0.113730i
$659$		−	9.13808i		−	0.355969i	−0.984033	−	0.177985i	$-0.943042\pi$
$659$		−	9.13808i		−	0.355969i	0.984033	−	0.177985i	$-0.0569577\pi$
$660$	−14.3108	−	2.46348i	−0.557048	−	0.0958909i
$661$		−	28.4837i		−	1.10789i	−0.832554	−	0.553943i	$-0.813122\pi$
$661$		−	28.4837i		−	1.10789i	0.832554	−	0.553943i	$-0.186878\pi$
$662$	1.87995	+	1.87995i	0.0730662	+	0.0730662i
$663$	−8.23683	−	8.23683i	−0.319892	−	0.319892i
$664$	6.26651			0.243188
$665$	−4.00774	+	35.3725i	−0.155413	+	1.37169i
$666$	2.18923			0.0848310
$667$	0.0535642	+	0.0535642i	0.00207401	+	0.00207401i
$668$	−15.1493	−	15.1493i	−0.586146	−	0.586146i
$669$		−	6.48264i		−	0.250633i
$670$	−18.6516	+	13.1733i	−0.720575	+	0.508927i
$671$		−	14.7864i		−	0.570821i
$672$	14.1311	−	15.8621i	0.545118	−	0.611894i
$673$	26.8815	−	26.8815i	1.03621	−	1.03621i	0.0368867	−	0.999319i	$-0.488256\pi$
$673$	26.8815	−	26.8815i	1.03621	−	1.03621i	0.999319	−	0.0368867i	$-0.0117441\pi$
$674$		−	28.4466i		−	1.09572i
$675$	−2.14984	−	4.51422i	−0.0827473	−	0.173752i
$676$	24.2769			0.933729
$677$	−1.19694	+	1.19694i	−0.0460022	+	0.0460022i	−0.729734	−	0.683731i	$-0.760356\pi$
$677$	−1.19694	+	1.19694i	−0.0460022	+	0.0460022i	0.683731	+	0.729734i	$0.260356\pi$
$678$	14.7138	+	14.7138i	0.565081	+	0.565081i
$679$	33.0264	−	1.90611i	1.26744	−	0.0731496i
$680$	−11.1104	+	7.84702i	−0.426063	+	0.300919i
$681$	20.0271			0.767440
$682$	−28.8466	+	28.8466i	−1.10459	+	1.10459i
$683$	2.41553	−	2.41553i	0.0924275	−	0.0924275i	−0.659381	−	0.751809i	$-0.729182\pi$
$683$	2.41553	−	2.41553i	0.0924275	−	0.0924275i	0.751809	+	0.659381i	$0.229182\pi$
$684$	−14.6253			−0.559214
$685$	4.03393	−	23.4338i	0.154129	−	0.895361i
$686$	38.4015	−	6.70863i	1.46618	−	0.256137i
$687$	−20.4571	−	20.4571i	−0.780487	−	0.780487i
$688$	0.900497	−	0.900497i	0.0343311	−	0.0343311i
$689$	−12.2476			−0.466598
$690$	−0.198383	+	1.15244i	−0.00755233	+	0.0438728i
$691$			41.6703i			1.58521i	0.609735	+	0.792606i	$0.291276\pi$
$691$			41.6703i			1.58521i	−0.609735	+	0.792606i	$0.708724\pi$
$692$	−16.4533	+	16.4533i	−0.625459	+	0.625459i
$693$	−4.70230	+	5.27832i	−0.178625	+	0.200507i
$694$			19.4970i			0.740098i
$695$	−10.0477	−	14.2263i	−0.381132	−	0.539634i
$696$			0.276310i			0.0104735i
$697$	33.4960	+	33.4960i	1.26875	+	1.26875i
$698$	−4.12488	−	4.12488i	−0.156129	−	0.156129i
$699$	−6.76767			−0.255977
$700$	15.4745	+	28.1845i	0.584881	+	1.06527i
$701$	13.7870			0.520727			0.260364	−	0.965511i	$-0.416158\pi$
$701$	13.7870			0.520727			0.260364	+	0.965511i	$0.416158\pi$
$702$	−2.58300	−	2.58300i	−0.0974889	−	0.0974889i
$703$	−4.42536	−	4.42536i	−0.166906	−	0.166906i
$704$		−	29.3742i		−	1.10708i
$705$	−1.01590	−	1.43838i	−0.0382610	−	0.0541727i
$706$		−	2.88915i		−	0.108735i
$707$	−12.7236	+	14.2822i	−0.478520	+	0.537138i
$708$	13.7293	−	13.7293i	0.515978	−	0.515978i
$709$			24.6722i			0.926585i	0.886205	+	0.463293i	$0.153332\pi$
$709$			24.6722i			0.926585i	−0.886205	+	0.463293i	$0.846668\pi$
$710$	12.2236	−	71.0088i	0.458742	−	2.66491i
$711$	11.2973			0.423680
$712$	−4.42971	+	4.42971i	−0.166010	+	0.166010i
$713$	1.27438	+	1.27438i	0.0477257	+	0.0477257i
$714$	2.15380	+	37.3182i	0.0806041	+	1.39660i
$715$	−1.75895	+	10.2181i	−0.0657811	+	0.382135i
$716$	−3.16223			−0.118178
$717$	−11.4388	+	11.4388i	−0.427191	+	0.427191i
$718$	13.8838	−	13.8838i	0.518139	−	0.518139i
$719$	−29.9117			−1.11552			−0.557758	−	0.830003i	$-0.688338\pi$
$719$	−29.9117			−1.11552			−0.557758	+	0.830003i	$0.688338\pi$
$720$	5.39447	−	3.81000i	0.201040	−	0.141990i
$721$	1.49735	+	25.9441i	0.0557642	+	0.966207i
$722$	25.6118	+	25.6118i	0.953171	+	0.953171i
$723$	8.04033	−	8.04033i	0.299023	−	0.299023i
$724$	−20.6239			−0.766482
$725$	1.43670	+	0.509736i	0.0533577	+	0.0189311i
$726$		−	8.12719i		−	0.301628i
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.113491	+	0.993539i	$0.536203\pi$
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.993539	+	0.113491i	$0.963797\pi$
$728$	3.10702	+	2.76795i	0.115154	+	0.102587i
$729$		−	1.00000i		−	0.0370370i
$730$	54.4825	−	38.4798i	2.01649	−	1.42420i
$731$			2.89416i			0.107044i
$732$	−9.51121	−	9.51121i	−0.351545	−	0.351545i
$733$	−3.86707	−	3.86707i	−0.142834	−	0.142834i	0.632074	−	0.774908i	$-0.282204\pi$
$733$	−3.86707	−	3.86707i	−0.142834	−	0.142834i	−0.774908	+	0.632074i	$0.782204\pi$
$734$	38.7082			1.42875
$735$	15.6287	+	0.863100i	0.576472	+	0.0318359i
$736$	−1.99493			−0.0735342
$737$	9.16599	+	9.16599i	0.337634	+	0.337634i
$738$	10.5040	+	10.5040i	0.386659	+	0.386659i
$739$		−	11.9735i		−	0.440454i	−0.975449	−	0.220227i	$-0.929320\pi$
$739$		−	11.9735i		−	0.440454i	0.975449	−	0.220227i	$-0.0706797\pi$
$740$	−5.57073	−	0.958952i	−0.204784	−	0.0352518i
$741$			10.4427i			0.383621i
$742$	29.3462	+	26.1436i	1.07733	+	0.959763i
$743$	−12.0406	+	12.0406i	−0.441728	+	0.441728i	−0.892593	−	0.450864i	$-0.851116\pi$
$743$	−12.0406	+	12.0406i	−0.441728	+	0.441728i	0.450864	+	0.892593i	$0.351116\pi$
$744$			6.57385i			0.241009i
$745$	26.0918	−	18.4281i	0.955931	−	0.675154i
$746$	61.5467			2.25338
$747$	4.88941	−	4.88941i	0.178894	−	0.178894i
$748$	30.8227	+	30.8227i	1.12699	+	1.12699i
$749$	1.61109	+	27.9148i	0.0588679	+	1.01998i
$750$	6.36745	+	22.6556i	0.232506	+	0.827264i
$751$	−24.1119			−0.879855			−0.439928	−	0.898033i	$-0.644996\pi$
$751$	−24.1119			−0.879855			−0.439928	+	0.898033i	$0.644996\pi$
$752$	1.64472	−	1.64472i	0.0599767	−	0.0599767i
$753$	−4.91467	+	4.91467i	−0.179100	+	0.179100i
$754$	1.11373			0.0405598
$755$	−12.6159	−	17.8625i	−0.459141	−	0.650085i
$756$	0.370525	+	6.41995i	0.0134759	+	0.233491i
$757$	29.2896	+	29.2896i	1.06455	+	1.06455i	0.997768	+	0.0667825i	$0.0212733\pi$
$757$	29.2896	+	29.2896i	1.06455	+	1.06455i	0.0667825	+	0.997768i	$0.478727\pi$
$758$	−32.7558	+	32.7558i	−1.18975	+	1.18975i
$759$	0.663839			0.0240958
$760$	12.0171	+	2.06864i	0.435906	+	0.0750374i
$761$		−	32.3002i		−	1.17088i	−0.810716	−	0.585440i	$-0.800922\pi$
$761$		−	32.3002i		−	1.17088i	0.810716	−	0.585440i	$-0.199078\pi$
$762$	−6.02230	+	6.02230i	−0.218165	+	0.218165i
$763$	−10.4778	+	11.7613i	−0.379320	+	0.425787i
$764$			4.71018i			0.170408i
$765$	−2.54621	+	14.7914i	−0.0920584	+	0.534784i
$766$		−	1.16207i		−	0.0419874i
$767$	−9.80287	−	9.80287i	−0.353961	−	0.353961i
$768$	5.00678	+	5.00678i	0.180667	+	0.180667i
$769$	18.4310			0.664640			0.332320	−	0.943167i	$-0.392169\pi$
$769$	18.4310			0.664640			0.332320	+	0.943167i	$0.392169\pi$
$770$	26.0259	−	20.7286i	0.937910	−	0.747007i
$771$	14.2679			0.513845
$772$	−19.0260	−	19.0260i	−0.684761	−	0.684761i
$773$	17.7963	+	17.7963i	0.640088	+	0.640088i	0.950577	−	0.310489i	$-0.100493\pi$
$773$	17.7963	+	17.7963i	0.640088	+	0.640088i	−0.310489	+	0.950577i	$0.600493\pi$
$774$			0.907583i			0.0326224i
$775$	34.1813	+	12.1274i	1.22783	+	0.435629i
$776$		−	11.3315i		−	0.406779i
$777$	−1.83045	+	2.05468i	−0.0656670	+	0.0737111i
$778$	−38.5937	+	38.5937i	−1.38365	+	1.38365i
$779$		−	42.4662i		−	1.52151i
$780$	5.44126	+	7.70413i	0.194829	+	0.275852i
$781$	−40.9030			−1.46362
$782$	2.48214	−	2.48214i	0.0887611	−	0.0887611i
$783$	0.215589	+	0.215589i	0.00770453	+	0.00770453i
$784$	2.37853	+	20.5374i	0.0849476	+	0.733478i
$785$	−6.78546	−	1.16806i	−0.242184	−	0.0416898i
$786$	−19.6757			−0.701810
$787$	−16.0671	+	16.0671i	−0.572730	+	0.572730i	−0.932890	−	0.360160i	$-0.882722\pi$
$787$	−16.0671	+	16.0671i	−0.572730	+	0.572730i	0.360160	+	0.932890i	$0.382722\pi$
$788$	20.6783	−	20.6783i	0.736635	−	0.736635i
$789$	25.7364			0.916240
$790$	−52.4018	−	9.02051i	−1.86437	−	0.320935i
$791$	−26.1119	+	1.50704i	−0.928432	+	0.0535840i
$792$	1.71220	+	1.71220i	0.0608404	+	0.0608404i
$793$	−6.79111	+	6.79111i	−0.241159	+	0.241159i
$794$	−51.0904			−1.81313
$795$	9.10390	+	12.8900i	0.322882	+	0.457159i
$796$		−	7.91046i		−	0.280379i
$797$	−25.5337	+	25.5337i	−0.904451	+	0.904451i	−0.995817	−	0.0913664i	$-0.970877\pi$
$797$	−25.5337	+	25.5337i	−0.904451	+	0.904451i	0.0913664	+	0.995817i	$0.470877\pi$
$798$	22.2907	−	25.0213i	0.789083	−	0.885745i
$799$			5.28605i			0.187007i
$800$	−36.2463	+	17.2618i	−1.28150	+	0.610297i
$801$			6.91251i			0.244242i
$802$	−19.2623	−	19.2623i	−0.680174	−	0.680174i
$803$	−26.7744	−	26.7744i	−0.944847	−	0.944847i
$804$	11.7919			0.415868
$805$	−0.915741	−	1.14977i	−0.0322756	−	0.0405239i
$806$	26.4974			0.933332
$807$	−10.9685	−	10.9685i	−0.386111	−	0.386111i
$808$	4.63292	+	4.63292i	0.162986	+	0.162986i
$809$			27.5404i			0.968270i	0.874993	+	0.484135i	$0.160866\pi$
$809$			27.5404i			0.968270i	−0.874993	+	0.484135i	$0.839134\pi$
$810$	−0.798469	+	4.63845i	−0.0280553	+	0.162978i
$811$		−	34.2545i		−	1.20284i	−0.798933	−	0.601420i	$-0.794602\pi$
$811$		−	34.2545i		−	1.20284i	0.798933	−	0.601420i	$-0.205398\pi$
$812$	−1.46395	−	1.30419i	−0.0513747	−	0.0457682i
$813$	−9.43409	+	9.43409i	−0.330868	+	0.330868i
$814$			5.84935i			0.205020i
$815$	42.6196	+	7.33659i	1.49290	+	0.256990i
$816$	−19.8246			−0.694001
$817$	1.83461	−	1.83461i	0.0641848	−	0.0641848i
$818$	−3.93347	−	3.93347i	−0.137530	−	0.137530i
$819$	4.58392	−	0.264559i	0.160175	−	0.00924443i
$820$	−22.1275	−	31.3297i	−0.772726	−	1.09408i
$821$	49.7482			1.73623			0.868113	−	0.496367i	$-0.165333\pi$
$821$	49.7482			1.73623			0.868113	+	0.496367i	$0.165333\pi$
$822$	−15.8275	+	15.8275i	−0.552049	+	0.552049i
$823$	−6.10417	+	6.10417i	−0.212778	+	0.212778i	−0.805447	−	0.592668i	$-0.798074\pi$
$823$	−6.10417	+	6.10417i	−0.212778	+	0.212778i	0.592668	+	0.805447i	$0.298074\pi$
$824$	8.90155			0.310100
$825$	12.0614	−	5.74409i	0.419925	−	0.199984i
$826$	2.56330	+	44.4134i	0.0891886	+	1.54534i
$827$	−4.96734	−	4.96734i	−0.172731	−	0.172731i	0.615447	−	0.788178i	$-0.288976\pi$
$827$	−4.96734	−	4.96734i	−0.172731	−	0.172731i	−0.788178	+	0.615447i	$0.788976\pi$
$828$	0.427009	−	0.427009i	0.0148396	−	0.0148396i
$829$	−28.3500			−0.984636			−0.492318	−	0.870415i	$-0.663850\pi$
$829$	−28.3500			−0.984636			−0.492318	+	0.870415i	$0.663850\pi$
$830$	−26.5833	+	18.7752i	−0.922720	+	0.651698i
$831$		−	2.83636i		−	0.0983922i
$832$	−13.4910	+	13.4910i	−0.467717	+	0.467717i
$833$	−36.8254	−	29.1809i	−1.27592	−	1.01106i
$834$			16.3950i			0.567713i
$835$	19.4244	+	3.34374i	0.672209	+	0.115715i
$836$		−	39.0770i		−	1.35151i
$837$	5.12921	+	5.12921i	0.177291	+	0.177291i
$838$	14.9287	+	14.9287i	0.515705	+	0.515705i
$839$	32.8100			1.13273			0.566364	−	0.824156i	$-0.308350\pi$
$839$	32.8100			1.13273			0.566364	+	0.824156i	$0.308350\pi$
$840$	0.603605	−	5.32744i	0.0208264	−	0.183814i
$841$	28.9070			0.996795
$842$	−39.6563	−	39.6563i	−1.36665	−	1.36665i
$843$	9.58531	+	9.58531i	0.330136	+	0.330136i
$844$		−	41.9289i		−	1.44325i
$845$	−18.2431	+	12.8847i	−0.627581	+	0.443247i
$846$			1.65766i			0.0569915i
$847$	7.62767	+	6.79526i	0.262090	+	0.233488i
$848$	−14.7390	+	14.7390i	−0.506139	+	0.506139i
$849$		−	22.9730i		−	0.788431i
$850$	23.6209	−	66.5760i	0.810191	−	2.28354i
$851$	0.258411			0.00885820
$852$	−26.3105	+	26.3105i	−0.901384	+	0.901384i
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	0.390184	−	0.920737i	$-0.372411\pi$
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	−0.920737	+	0.390184i	$0.872411\pi$
$854$	30.7682	−	1.77577i	1.05287	−	0.0607657i
$855$	10.9903	−	7.76222i	0.375861	−	0.265462i
$856$	9.57770			0.327359
$857$	−17.8346	+	17.8346i	−0.609218	+	0.609218i	−0.942742	−	0.333523i	$-0.891762\pi$
$857$	−17.8346	+	17.8346i	−0.609218	+	0.609218i	0.333523	+	0.942742i	$0.391762\pi$
$858$	6.90143	−	6.90143i	0.235611	−	0.235611i
$859$	17.2711			0.589283			0.294641	−	0.955608i	$-0.404800\pi$
$859$	17.2711			0.589283			0.294641	+	0.955608i	$0.404800\pi$
$860$	0.397549	−	2.30944i	0.0135563	−	0.0787511i
$861$	−18.6410	+	1.07586i	−0.635284	+	0.0366651i
$862$	33.3021	+	33.3021i	1.13427	+	1.13427i
$863$	2.94383	−	2.94383i	0.100209	−	0.100209i	−0.655225	−	0.755434i	$-0.727426\pi$
$863$	2.94383	−	2.94383i	0.100209	−	0.100209i	0.755434	+	0.655225i	$0.227426\pi$
$864$	−8.02936			−0.273164
$865$	3.63154	−	21.0963i	0.123476	−	0.717295i
$866$			40.1038i			1.36278i
$867$	19.8369	−	19.8369i	0.673697	−	0.673697i
$868$	−34.8298	−	31.0288i	−1.18220	−	1.05318i
$869$			30.1848i			1.02395i
$870$	−0.827859	−	1.17214i	−0.0280670	−	0.0397393i
$871$		−	8.41955i		−	0.285286i
$872$	3.81517	+	3.81517i	0.129198	+	0.129198i
$873$	−8.84137	−	8.84137i	−0.299235	−	0.299235i
$874$	−3.14686			−0.106444
$875$	−26.5870	−	12.9665i	−0.898805	−	0.438349i
$876$	−34.4448			−1.16378
$877$	−8.49735	−	8.49735i	−0.286935	−	0.286935i	0.548932	−	0.835867i	$-0.315035\pi$
$877$	−8.49735	−	8.49735i	−0.286935	−	0.286935i	−0.835867	+	0.548932i	$0.815035\pi$
$878$	38.2201	+	38.2201i	1.28987	+	1.28987i
$879$		−	3.41907i		−	0.115322i
$880$	10.1798	+	14.4133i	0.343162	+	0.485873i
$881$			35.7762i			1.20533i	0.797994	+	0.602665i	$0.205894\pi$
$881$			35.7762i			1.20533i	−0.797994	+	0.602665i	$0.794106\pi$
$882$	−11.5481	−	9.15086i	−0.388845	−	0.308125i
$883$	24.6278	−	24.6278i	0.828791	−	0.828791i	−0.158559	−	0.987350i	$-0.550685\pi$
$883$	24.6278	−	24.6278i	0.828791	−	0.828791i	0.987350	+	0.158559i	$0.0506848\pi$
$884$		−	28.3126i		−	0.952256i
$885$	−3.03031	+	17.6036i	−0.101863	+	0.591739i
$886$	−46.5419			−1.56361
$887$	0.732491	−	0.732491i	0.0245946	−	0.0245946i	−0.694703	−	0.719297i	$-0.744464\pi$
$887$	0.732491	−	0.732491i	0.0245946	−	0.0245946i	0.719297	+	0.694703i	$0.244464\pi$
$888$	0.666503	+	0.666503i	0.0223664	+	0.0223664i
$889$	−0.616823	−	10.6875i	−0.0206876	−	0.358447i
$890$	5.51943	−	32.0633i	0.185012	−	1.07477i
$891$	2.67187			0.0895111
$892$	11.1415	−	11.1415i	0.373043	−	0.373043i
$893$	3.35083	−	3.35083i	0.112131	−	0.112131i
$894$	−30.0694			−1.00567
$895$	2.37628	−	1.67831i	0.0794301	−	0.0560998i
$896$	18.7064	−	1.07963i	0.624936	−	0.0360679i
$897$	−0.304889	−	0.304889i	−0.0101800	−	0.0101800i
$898$	10.4476	−	10.4476i	0.348642	−	0.348642i
$899$	−2.21160			−0.0737611
$900$	4.06357	−	11.4533i	0.135452	−	0.381775i
$901$		−	47.3704i		−	1.57814i
$902$	−28.0654	+	28.0654i	−0.934477	+	0.934477i
$903$	−0.851800	−	0.758842i	−0.0283461	−	0.0252527i
$904$			8.95913i			0.297976i
$905$	15.4980	−	10.9459i	0.515170	−	0.363854i
$906$			20.5856i			0.683911i
$907$	−22.8743	−	22.8743i	−0.759530	−	0.759530i	0.216707	−	0.976237i	$-0.430468\pi$
$907$	−22.8743	−	22.8743i	−0.759530	−	0.759530i	−0.976237	+	0.216707i	$0.930468\pi$
$908$	34.4198	+	34.4198i	1.14226	+	1.14226i
$909$	7.22962			0.239791
$910$	−21.4735	−	2.43297i	−0.711840	−	0.0806523i
$911$	24.7867			0.821220			0.410610	−	0.911811i	$-0.365316\pi$
$911$	24.7867			0.821220			0.410610	+	0.911811i	$0.365316\pi$
$912$	12.5668	+	12.5668i	0.416130	+	0.416130i
$913$	13.0639	+	13.0639i	0.432351	+	0.432351i
$914$			33.3752i			1.10395i
$915$	12.1952	+	2.09930i	0.403162	+	0.0694008i
$916$		−	70.3176i		−	2.32336i
$917$	16.4512	−	18.4664i	0.543265	−	0.609814i
$918$	9.99031	−	9.99031i	0.329729	−	0.329729i
$919$			14.5898i			0.481272i	0.970615	+	0.240636i	$0.0773560\pi$
$919$			14.5898i			0.481272i	−0.970615	+	0.240636i	$0.922644\pi$
$920$	−0.411254	+	0.290460i	−0.0135587	+	0.00957619i
$921$	10.2007			0.336125
$922$	44.6283	−	44.6283i	1.46976	−	1.46976i
$923$	18.7860	+	18.7860i	0.618349	+	0.618349i
$924$	−17.1533	+	0.989994i	−0.564302	+	0.0325684i
$925$	4.69511	−	2.23598i	0.154374	−	0.0735187i
$926$	22.9276			0.753447
$927$	6.94538	−	6.94538i	0.228116	−	0.228116i
$928$	1.73104	−	1.73104i	0.0568243	−	0.0568243i
$929$	−25.1526			−0.825229			−0.412615	−	0.910906i	$-0.635384\pi$
$929$	−25.1526			−0.825229			−0.412615	+	0.910906i	$0.635384\pi$
$930$	−19.6960	−	27.8871i	−0.645859	−	0.914453i
$931$	4.84585	+	41.8414i	0.158816	+	1.37130i
$932$	−11.6313	−	11.6313i	−0.380996	−	0.380996i
$933$	−7.25079	+	7.25079i	−0.237380	+	0.237380i
$934$	5.38676			0.176260
$935$	−39.5207	−	6.80314i	−1.29246	−	0.222487i
$936$		−	1.57277i		−	0.0514075i
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	−0.0711778	−	0.997464i	$-0.522676\pi$
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	0.997464	+	0.0711778i	$0.0226758\pi$
$938$	−17.9722	+	20.1738i	−0.586815	+	0.658699i
$939$			31.2405i			1.01950i
$940$	0.726106	−	4.21808i	0.0236830	−	0.137579i
$941$			0.106973i			0.00348721i	0.999998	+	0.00174360i	$0.000555007\pi$
$941$			0.106973i			0.00348721i	−0.999998	+	0.00174360i	$0.999445\pi$
$942$	4.58300	+	4.58300i	0.149322	+	0.149322i
$943$	1.23987	+	1.23987i	0.0403756	+	0.0403756i
$944$	−23.5938			−0.767914
$945$	−3.68575	−	4.62766i	−0.119897	−	0.150538i
$946$	−2.42494			−0.0788417
$947$	17.9671	+	17.9671i	0.583851	+	0.583851i	0.935959	−	0.352108i	$-0.114535\pi$
$947$	17.9671	+	17.9671i	0.583851	+	0.583851i	−0.352108	+	0.935959i	$0.614535\pi$
$948$	19.4162	+	19.4162i	0.630607	+	0.630607i
$949$			24.5940i			0.798354i
$950$	−57.1759	+	27.2293i	−1.85503	+	0.883434i
$951$		−	17.3331i		−	0.562064i
$952$	−10.7057	+	12.0171i	−0.346973	+	0.389477i
$953$	31.8008	−	31.8008i	1.03013	−	1.03013i	0.0305973	−	0.999532i	$-0.490259\pi$
$953$	31.8008	−	31.8008i	1.03013	−	1.03013i	0.999532	−	0.0305973i	$-0.00974093\pi$
$954$		−	14.8550i		−	0.480947i
$955$	−2.49987	−	3.53950i	−0.0808940	−	0.114536i
$956$	−39.3189			−1.27166
$957$	−0.576027	+	0.576027i	−0.0186203	+	0.0186203i
$958$	6.09425	+	6.09425i	0.196896	+	0.196896i
$959$	−1.62111	−	28.0884i	−0.0523483	−	0.907021i
$960$	24.2267	+	4.17041i	0.781912	+	0.134599i
$961$	−21.6175			−0.697339
$962$	2.68650	−	2.68650i	0.0866162	−	0.0866162i
$963$	7.47295	−	7.47295i	0.240812	−	0.240812i
$964$	27.6372			0.890134
$965$	24.3951	+	4.19940i	0.785305	+	0.135183i
$966$	0.0797239	+	1.38135i	0.00256507	+	0.0444441i
$967$	0.210995	+	0.210995i	0.00678513	+	0.00678513i	0.710491	−	0.703706i	$-0.248473\pi$
$967$	0.210995	+	0.210995i	0.00678513	+	0.00678513i	−0.703706	+	0.710491i	$0.748473\pi$
$968$	2.47429	−	2.47429i	0.0795267	−	0.0795267i
$969$	−40.3893			−1.29749
$970$	33.9507	+	48.0698i	1.09009	+	1.54343i
$971$			54.1165i			1.73668i	0.495969	+	0.868340i	$0.334813\pi$
$971$			54.1165i			1.73668i	−0.495969	+	0.868340i	$0.665187\pi$
$972$	1.71866	−	1.71866i	0.0551260	−	0.0551260i
$973$	−15.3873	−	13.7081i	−0.493295	−	0.439462i
$974$		−	30.6752i		−	0.982896i
$975$	−8.17775	−	2.90143i	−0.261898	−	0.0929203i
$976$			16.3450i			0.523192i
$977$	25.0981	+	25.0981i	0.802958	+	0.802958i	0.983557	−	0.180599i	$-0.0578035\pi$
$977$	25.0981	+	25.0981i	0.802958	+	0.802958i	−0.180599	+	0.983557i	$0.557803\pi$
$978$	−28.7859	−	28.7859i	−0.920471	−	0.920471i
$979$	−18.4693			−0.590283
$980$	25.3770	+	28.3437i	0.810638	+	0.905407i
$981$	5.95352			0.190081
$982$	−12.7398	−	12.7398i	−0.406545	−	0.406545i
$983$	−1.23358	−	1.23358i	−0.0393451	−	0.0393451i	0.687161	−	0.726506i	$-0.258857\pi$
$983$	−1.23358	−	1.23358i	−0.0393451	−	0.0393451i	−0.726506	+	0.687161i	$0.758857\pi$
$984$			6.39583i			0.203892i
$985$	−4.56409	+	26.5136i	−0.145424	+	0.844795i
$986$			4.30761i			0.137182i
$987$	−1.55577	−	1.38599i	−0.0495208	−	0.0441166i
$988$	−17.9474	+	17.9474i	−0.570982	+	0.570982i
$989$			0.107128i			0.00340648i
$990$	−12.3933	−	2.13341i	−0.393886	−	0.0678041i
$991$	48.9637			1.55538			0.777691	−	0.628647i	$-0.216391\pi$
$991$	48.9637			1.55538			0.777691	+	0.628647i	$0.216391\pi$
$992$	41.1842	−	41.1842i	1.30760	−	1.30760i
$993$	0.893133	+	0.893133i	0.0283427	+	0.0283427i
$994$	−4.91225	−	85.1129i	−0.155807	−	2.69962i
$995$	4.19838	+	5.94437i	0.133098	+	0.188449i
$996$	16.8065			0.532533
$997$	11.9844	−	11.9844i	0.379551	−	0.379551i	−0.491389	−	0.870940i	$-0.663511\pi$
$997$	11.9844	−	11.9844i	0.379551	−	0.379551i	0.870940	+	0.491389i	$0.163511\pi$
$998$	−35.3585	+	35.3585i	−1.11926	+	1.11926i
$999$	1.04007			0.0329064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.m.a.97.8	yes	16
3.2	odd	2		315.2.p.e.307.2		16
4.3	odd	2		1680.2.cz.d.97.1		16
5.2	odd	4		525.2.m.b.118.2		16
5.3	odd	4	inner	105.2.m.a.13.7	✓	16
5.4	even	2		525.2.m.b.307.1		16
7.2	even	3		735.2.v.a.472.7		32
7.3	odd	6		735.2.v.a.607.1		32
7.4	even	3		735.2.v.a.607.2		32
7.5	odd	6		735.2.v.a.472.8		32
7.6	odd	2	inner	105.2.m.a.97.7	yes	16
15.8	even	4		315.2.p.e.118.1		16
20.3	even	4		1680.2.cz.d.433.8		16
21.20	even	2		315.2.p.e.307.1		16
28.27	even	2		1680.2.cz.d.97.8		16
35.3	even	12		735.2.v.a.313.7		32
35.13	even	4	inner	105.2.m.a.13.8	yes	16
35.18	odd	12		735.2.v.a.313.8		32
35.23	odd	12		735.2.v.a.178.1		32
35.27	even	4		525.2.m.b.118.1		16
35.33	even	12		735.2.v.a.178.2		32
35.34	odd	2		525.2.m.b.307.2		16
105.83	odd	4		315.2.p.e.118.2		16
140.83	odd	4		1680.2.cz.d.433.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	5.3	odd	4	inner
105.2.m.a.13.8	yes	16	35.13	even	4	inner
105.2.m.a.97.7	yes	16	7.6	odd	2	inner
105.2.m.a.97.8	yes	16	1.1	even	1	trivial
315.2.p.e.118.1		16	15.8	even	4
315.2.p.e.118.2		16	105.83	odd	4
315.2.p.e.307.1		16	21.20	even	2
315.2.p.e.307.2		16	3.2	odd	2
525.2.m.b.118.1		16	35.27	even	4
525.2.m.b.118.2		16	5.2	odd	4
525.2.m.b.307.1		16	5.4	even	2
525.2.m.b.307.2		16	35.34	odd	2
735.2.v.a.178.1		32	35.23	odd	12
735.2.v.a.178.2		32	35.33	even	12
735.2.v.a.313.7		32	35.3	even	12
735.2.v.a.313.8		32	35.18	odd	12
735.2.v.a.472.7		32	7.2	even	3
735.2.v.a.472.8		32	7.5	odd	6
735.2.v.a.607.1		32	7.3	odd	6
735.2.v.a.607.2		32	7.4	even	3
1680.2.cz.d.97.1		16	4.3	odd	2
1680.2.cz.d.97.8		16	28.27	even	2
1680.2.cz.d.433.1		16	140.83	odd	4
1680.2.cz.d.433.8		16	20.3	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48838 + 1.48838i) q^{2} +(0.707107 + 0.707107i) q^{3} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +2.10489i q^{6} +(-1.97552 - 1.75993i) q^{7} +(-0.640825 + 0.640825i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.48838 + 1.48838i) q^{2} +(0.707107 + 0.707107i) q^{3} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +2.10489i q^{6} +(-1.97552 - 1.75993i) q^{7} +(-0.640825 + 0.640825i) q^{8} +1.00000i q^{9} +(0.798469 - 4.63845i) q^{10} -2.67187 q^{11} +(-1.71866 + 1.71866i) q^{12} +(1.22714 + 1.22714i) q^{13} +(-0.320879 - 5.55976i) q^{14} +(0.379340 - 2.20366i) q^{15} +2.95352 q^{16} +(-4.74624 + 4.74624i) q^{17} +(-1.48838 + 1.48838i) q^{18} +6.01729 q^{19} +(4.43929 - 3.13538i) q^{20} +(-0.152445 - 2.64136i) q^{21} +(-3.97676 - 3.97676i) q^{22} +(-0.175684 + 0.175684i) q^{23} -0.906263 q^{24} +(-1.67187 + 4.71220i) q^{25} +3.65291i q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.27759 - 4.80159i) q^{28} -0.304889i q^{29} +(3.84448 - 2.71528i) q^{30} -7.25379i q^{31} +(5.67761 + 5.67761i) q^{32} +(-1.88930 - 1.88930i) q^{33} -14.1284 q^{34} +(-0.666037 + 5.87847i) q^{35} -2.43055 q^{36} +(-0.735441 - 0.735441i) q^{37} +(8.95602 + 8.95602i) q^{38} +1.73544i q^{39} +(1.99709 + 0.343782i) q^{40} -7.05736i q^{41} +(3.70445 - 4.15824i) q^{42} +(0.304889 - 0.304889i) q^{43} -6.49412i q^{44} +(1.82645 - 1.28999i) q^{45} -0.522969 q^{46} +(0.556866 - 0.556866i) q^{47} +(2.08845 + 2.08845i) q^{48} +(0.805321 + 6.95352i) q^{49} +(-9.50193 + 4.52517i) q^{50} -6.71220 q^{51} +(-2.98263 + 2.98263i) q^{52} +(-4.99031 + 4.99031i) q^{53} -2.10489 q^{54} +(3.44668 + 4.88005i) q^{55} +(2.39376 - 0.138155i) q^{56} +(4.25487 + 4.25487i) q^{57} +(0.453791 - 0.453791i) q^{58} -7.98837 q^{59} +(5.35610 + 0.922006i) q^{60} +5.53409i q^{61} +(10.7964 - 10.7964i) q^{62} +(1.75993 - 1.97552i) q^{63} +10.9939i q^{64} +(0.658323 - 3.82432i) q^{65} -5.62399i q^{66} +(-3.43055 - 3.43055i) q^{67} +(-11.5360 - 11.5360i) q^{68} -0.248455 q^{69} +(-9.74071 + 7.75808i) q^{70} +15.3087 q^{71} +(-0.640825 - 0.640825i) q^{72} +(10.0208 + 10.0208i) q^{73} -2.18923i q^{74} +(-4.51422 + 2.14984i) q^{75} +14.6253i q^{76} +(5.27832 + 4.70230i) q^{77} +(-2.58300 + 2.58300i) q^{78} -11.2973i q^{79} +(-3.81000 - 5.39447i) q^{80} -1.00000 q^{81} +(10.5040 - 10.5040i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(6.41995 - 0.370525i) q^{84} +(14.7914 + 2.54621i) q^{85} +0.907583 q^{86} +(0.215589 - 0.215589i) q^{87} +(1.71220 - 1.71220i) q^{88} +6.91251 q^{89} +(4.63845 + 0.798469i) q^{90} +(-0.264559 - 4.58392i) q^{91} +(-0.427009 - 0.427009i) q^{92} +(5.12921 - 5.12921i) q^{93} +1.65766 q^{94} +(-7.76222 - 10.9903i) q^{95} +8.02936i q^{96} +(-8.84137 + 8.84137i) q^{97} +(-9.15086 + 11.5481i) q^{98} -2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 + 24 * q^8	\( 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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