LMFDB - Embedded newform 637.2.x.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	637.19
Dual form			637.2.x.b.570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28713 - 0.612835i) q^{2} +1.20226i q^{3} +(3.12335 + 1.80327i) q^{4} +(-3.08075 + 0.825486i) q^{5} +(0.736784 - 2.74971i) q^{6} +(-2.68981 - 2.68981i) q^{8} +1.55458 q^{9} +O(q^{10})$	\(q+(-2.28713 - 0.612835i) q^{2} +1.20226i q^{3} +(3.12335 + 1.80327i) q^{4} +(-3.08075 + 0.825486i) q^{5} +(0.736784 - 2.74971i) q^{6} +(-2.68981 - 2.68981i) q^{8} +1.55458 q^{9} +7.55197 q^{10} +(-3.00989 - 3.00989i) q^{11} +(-2.16799 + 3.75506i) q^{12} +(3.48609 - 0.920440i) q^{13} +(-0.992444 - 3.70385i) q^{15} +(0.897005 + 1.55366i) q^{16} +(0.721872 - 1.25032i) q^{17} +(-3.55553 - 0.952702i) q^{18} +(1.77447 + 1.77447i) q^{19} +(-11.1108 - 2.97714i) q^{20} +(5.03945 + 8.72858i) q^{22} +(4.52952 - 2.61512i) q^{23} +(3.23384 - 3.23384i) q^{24} +(4.47949 - 2.58624i) q^{25} +(-8.53721 - 0.0312285i) q^{26} +5.47577i q^{27} +(1.34350 - 2.32701i) q^{29} +9.07940i q^{30} +(-1.37793 + 5.14250i) q^{31} +(0.869646 + 3.24556i) q^{32} +(3.61866 - 3.61866i) q^{33} +(-2.41725 + 2.41725i) q^{34} +(4.85550 + 2.80333i) q^{36} +(0.160626 - 0.599466i) q^{37} +(-2.97099 - 5.14591i) q^{38} +(1.10660 + 4.19116i) q^{39} +(10.5070 + 6.06624i) q^{40} +(-5.04879 + 1.35282i) q^{41} +(-5.46143 + 3.15316i) q^{43} +(-3.97331 - 14.8286i) q^{44} +(-4.78929 + 1.28329i) q^{45} +(-11.9622 + 3.20527i) q^{46} +(1.71303 + 6.39313i) q^{47} +(-1.86789 + 1.07843i) q^{48} +(-11.8301 + 3.16987i) q^{50} +(1.50320 + 0.867874i) q^{51} +(12.5481 + 3.41149i) q^{52} +(3.79264 + 6.56904i) q^{53} +(3.35574 - 12.5238i) q^{54} +(11.7574 + 6.78811i) q^{55} +(-2.13337 + 2.13337i) q^{57} +(-4.49884 + 4.49884i) q^{58} +(0.525675 + 1.96185i) q^{59} +(3.57928 - 13.3581i) q^{60} +5.24062i q^{61} +(6.30300 - 10.9171i) q^{62} -11.5440i q^{64} +(-9.97996 + 5.71336i) q^{65} +(-10.4940 + 6.05870i) q^{66} +(6.19777 - 6.19777i) q^{67} +(4.50931 - 2.60345i) q^{68} +(3.14404 + 5.44564i) q^{69} +(8.31929 + 2.22915i) q^{71} +(-4.18153 - 4.18153i) q^{72} +(15.2724 + 4.09222i) q^{73} +(-0.734747 + 1.27262i) q^{74} +(3.10932 + 5.38549i) q^{75} +(2.34245 + 8.74214i) q^{76} +(0.0375447 - 10.2639i) q^{78} +(-1.00643 + 1.74319i) q^{79} +(-4.04597 - 4.04597i) q^{80} -1.91953 q^{81} +12.3763 q^{82} +(5.11623 + 5.11623i) q^{83} +(-1.19179 + 4.44782i) q^{85} +(14.4234 - 3.86473i) q^{86} +(2.79766 + 1.61523i) q^{87} +16.1921i q^{88} +(6.76189 + 1.81184i) q^{89} +11.7402 q^{90} +18.8630 q^{92} +(-6.18260 - 1.65662i) q^{93} -15.6717i q^{94} +(-6.93151 - 4.00191i) q^{95} +(-3.90200 + 1.04554i) q^{96} +(1.62618 - 6.06897i) q^{97} +(-4.67912 - 4.67912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.28713	−	0.612835i	−1.61725	−	0.433340i	−0.667055	−	0.745009i	$-0.732445\pi$
$2$	−2.28713	−	0.612835i	−1.61725	−	0.433340i	−0.950191	+	0.311669i	$0.899112\pi$
$3$			1.20226i			0.694122i	0.937842	+	0.347061i	$0.112820\pi$
$3$			1.20226i			0.694122i	−0.937842	+	0.347061i	$0.887180\pi$
$4$	3.12335	+	1.80327i	1.56167	+	0.901633i
$5$	−3.08075	+	0.825486i	−1.37776	+	0.369168i	−0.870305	−	0.492513i	$-0.836078\pi$
$5$	−3.08075	+	0.825486i	−1.37776	+	0.369168i	−0.507450	+	0.861681i	$0.669412\pi$
$6$	0.736784	−	2.74971i	0.300791	−	1.12257i
$7$		0			0
$7$		0			0
$8$	−2.68981	−	2.68981i	−0.950991	−	0.950991i
$9$	1.55458			0.518194
$10$	7.55197			2.38814
$11$	−3.00989	−	3.00989i	−0.907517	−	0.907517i	0.0885547	−	0.996071i	$-0.471775\pi$
$11$	−3.00989	−	3.00989i	−0.907517	−	0.907517i	−0.996071	+	0.0885547i	$0.971775\pi$
$12$	−2.16799	+	3.75506i	−0.625844	+	1.08399i
$13$	3.48609	−	0.920440i	0.966866	−	0.255284i
$13$	3.48609	−	0.920440i	0.966866	−	0.255284i
$14$		0			0
$15$	−0.992444	−	3.70385i	−0.256248	−	0.956331i
$16$	0.897005	+	1.55366i	0.224251	+	0.388414i
$17$	0.721872	−	1.25032i	0.175080	−	0.303247i	−0.765109	−	0.643901i	$-0.777315\pi$
$17$	0.721872	−	1.25032i	0.175080	−	0.303247i	0.940189	+	0.340654i	$0.110648\pi$
$18$	−3.55553	−	0.952702i	−0.838047	−	0.224554i
$19$	1.77447	+	1.77447i	0.407092	+	0.407092i	0.880723	−	0.473631i	$-0.157057\pi$
$19$	1.77447	+	1.77447i	0.407092	+	0.407092i	−0.473631	+	0.880723i	$0.657057\pi$
$20$	−11.1108	−	2.97714i	−2.48446	−	0.665709i
$21$		0			0
$22$	5.03945	+	8.72858i	1.07441	+	1.86094i
$23$	4.52952	−	2.61512i	0.944470	−	0.545290i	0.0531111	−	0.998589i	$-0.483086\pi$
$23$	4.52952	−	2.61512i	0.944470	−	0.545290i	0.891359	+	0.453299i	$0.149753\pi$
$24$	3.23384	−	3.23384i	0.660104	−	0.660104i
$25$	4.47949	−	2.58624i	0.895898	−	0.517247i
$26$	−8.53721	−	0.0312285i	−1.67428	−	0.00612442i
$27$			5.47577i			1.05381i
$28$		0			0
$29$	1.34350	−	2.32701i	0.249482	−	0.432116i	−0.713900	−	0.700248i	$-0.753073\pi$
$29$	1.34350	−	2.32701i	0.249482	−	0.432116i	0.963382	+	0.268132i	$0.0864063\pi$
$30$			9.07940i			1.65766i
$31$	−1.37793	+	5.14250i	−0.247483	+	0.923620i	0.724636	+	0.689132i	$0.242008\pi$
$31$	−1.37793	+	5.14250i	−0.247483	+	0.923620i	−0.972119	+	0.234488i	$0.924659\pi$
$32$	0.869646	+	3.24556i	0.153733	+	0.573740i
$33$	3.61866	−	3.61866i	0.629928	−	0.629928i
$34$	−2.41725	+	2.41725i	−0.414555	+	0.414555i
$35$		0			0
$36$	4.85550	+	2.80333i	0.809250	+	0.467221i
$37$	0.160626	−	0.599466i	0.0264068	−	0.0985516i	−0.951465	−	0.307758i	$-0.900421\pi$
$37$	0.160626	−	0.599466i	0.0264068	−	0.0985516i	0.977872	+	0.209206i	$0.0670880\pi$
$38$	−2.97099	−	5.14591i	−0.481958	−	0.834776i
$39$	1.10660	+	4.19116i	0.177198	+	0.671123i
$40$	10.5070	+	6.06624i	1.66131	+	0.959157i
$41$	−5.04879	+	1.35282i	−0.788488	+	0.211275i	−0.630524	−	0.776170i	$-0.717160\pi$
$41$	−5.04879	+	1.35282i	−0.788488	+	0.211275i	−0.157965	+	0.987445i	$0.550493\pi$
$42$		0			0
$43$	−5.46143	+	3.15316i	−0.832860	+	0.480852i	−0.854831	−	0.518907i	$-0.826339\pi$
$43$	−5.46143	+	3.15316i	−0.832860	+	0.480852i	0.0219711	+	0.999759i	$0.493006\pi$
$44$	−3.97331	−	14.8286i	−0.598998	−	2.23549i
$45$	−4.78929	+	1.28329i	−0.713944	+	0.191301i
$46$	−11.9622	+	3.20527i	−1.76374	+	0.472591i
$47$	1.71303	+	6.39313i	0.249872	+	0.932533i	0.970872	+	0.239599i	$0.0770159\pi$
$47$	1.71303	+	6.39313i	0.249872	+	0.932533i	−0.721000	+	0.692935i	$0.756317\pi$
$48$	−1.86789	+	1.07843i	−0.269607	+	0.155658i
$49$		0			0
$50$	−11.8301	+	3.16987i	−1.67303	+	0.448287i
$51$	1.50320	+	0.867874i	0.210490	+	0.121527i
$52$	12.5481	+	3.41149i	1.74010	+	0.473088i
$53$	3.79264	+	6.56904i	0.520959	+	0.902328i	0.999703	+	0.0243730i	$0.00775895\pi$
$53$	3.79264	+	6.56904i	0.520959	+	0.902328i	−0.478744	+	0.877955i	$0.658908\pi$
$54$	3.35574	−	12.5238i	0.456659	−	1.70427i
$55$	11.7574	+	6.78811i	1.58536	+	0.915309i
$56$		0			0
$57$	−2.13337	+	2.13337i	−0.282571	+	0.282571i
$58$	−4.49884	+	4.49884i	−0.590727	+	0.590727i
$59$	0.525675	+	1.96185i	0.0684370	+	0.255410i	0.991665	−	0.128842i	$-0.0411259\pi$
$59$	0.525675	+	1.96185i	0.0684370	+	0.255410i	−0.923228	+	0.384252i	$0.874459\pi$
$60$	3.57928	−	13.3581i	0.462083	−	1.72452i
$61$			5.24062i			0.670993i	0.942041	+	0.335496i	$0.108904\pi$
$61$			5.24062i			0.670993i	−0.942041	+	0.335496i	$0.891096\pi$
$62$	6.30300	−	10.9171i	0.800482	−	1.38648i
$63$		0			0
$64$		−	11.5440i		−	1.44300i
$65$	−9.97996	+	5.71336i	−1.23786	+	0.708655i
$66$	−10.4940	+	6.05870i	−1.29172	+	0.745775i
$67$	6.19777	−	6.19777i	0.757178	−	0.757178i	−0.218630	−	0.975808i	$-0.570159\pi$
$67$	6.19777	−	6.19777i	0.757178	−	0.757178i	0.975808	+	0.218630i	$0.0701586\pi$
$68$	4.50931	−	2.60345i	0.546835	−	0.315715i
$69$	3.14404	+	5.44564i	0.378498	+	0.655578i
$70$		0			0
$71$	8.31929	+	2.22915i	0.987318	+	0.264551i	0.716124	−	0.697974i	$-0.245915\pi$
$71$	8.31929	+	2.22915i	0.987318	+	0.264551i	0.271194	+	0.962525i	$0.412581\pi$
$72$	−4.18153	−	4.18153i	−0.492798	−	0.492798i
$73$	15.2724	+	4.09222i	1.78749	+	0.478958i	0.991916	−	0.126894i	$-0.0405008\pi$
$73$	15.2724	+	4.09222i	1.78749	+	0.478958i	0.795578	+	0.605852i	$0.207167\pi$
$74$	−0.734747	+	1.27262i	−0.0854126	+	0.147939i
$75$	3.10932	+	5.38549i	0.359033	+	0.621863i
$76$	2.34245	+	8.74214i	0.268697	+	1.00279i
$77$		0			0
$78$	0.0375447	−	10.2639i	0.00425110	−	1.16216i
$79$	−1.00643	+	1.74319i	−0.113233	+	0.196125i	−0.917072	−	0.398722i	$-0.869454\pi$
$79$	−1.00643	+	1.74319i	−0.113233	+	0.196125i	0.803839	+	0.594847i	$0.202787\pi$
$80$	−4.04597	−	4.04597i	−0.452353	−	0.452353i
$81$	−1.91953			−0.213281
$82$	12.3763			1.36673
$83$	5.11623	+	5.11623i	0.561579	+	0.561579i	0.929756	−	0.368177i	$-0.120018\pi$
$83$	5.11623	+	5.11623i	0.561579	+	0.561579i	−0.368177	+	0.929756i	$0.620018\pi$
$84$		0			0
$85$	−1.19179	+	4.44782i	−0.129268	+	0.482434i
$86$	14.4234	−	3.86473i	1.55531	−	0.416744i
$87$	2.79766	+	1.61523i	0.299941	+	0.173171i
$88$			16.1921i			1.72608i
$89$	6.76189	+	1.81184i	0.716759	+	0.192055i	0.598725	−	0.800955i	$-0.295674\pi$
$89$	6.76189	+	1.81184i	0.716759	+	0.192055i	0.118034	+	0.993010i	$0.462341\pi$
$90$	11.7402			1.23752
$91$		0			0
$92$	18.8630			1.96661
$93$	−6.18260	−	1.65662i	−0.641105	−	0.171784i
$94$		−	15.6717i		−	1.61641i
$95$	−6.93151	−	4.00191i	−0.711158	−	0.410587i
$96$	−3.90200	+	1.04554i	−0.398246	+	0.106710i
$97$	1.62618	−	6.06897i	0.165113	−	0.616211i	−0.832913	−	0.553405i	$-0.813328\pi$
$97$	1.62618	−	6.06897i	0.165113	−	0.616211i	0.998026	−	0.0628062i	$-0.0200050\pi$
$98$		0			0
$99$	−4.67912	−	4.67912i	−0.470270	−	0.470270i
$100$	18.6547			1.86547
$101$	−13.3392			−1.32730			−0.663649	−	0.748044i	$-0.730993\pi$
$101$	−13.3392			−1.32730			−0.663649	+	0.748044i	$0.730993\pi$
$102$	−2.90616	−	2.90616i	−0.287752	−	0.287752i
$103$	3.08727	−	5.34730i	0.304197	−	0.526885i	−0.672885	−	0.739747i	$-0.734945\pi$
$103$	3.08727	−	5.34730i	0.304197	−	0.526885i	0.977082	+	0.212862i	$0.0682785\pi$
$104$	−11.8527	−	6.90110i	−1.16225	−	0.676708i
$105$		0			0
$106$	−4.64852	−	17.3485i	−0.451504	−	1.68504i
$107$	4.27353	+	7.40196i	0.413137	+	0.715575i	0.995231	−	0.0975469i	$-0.0310996\pi$
$107$	4.27353	+	7.40196i	0.413137	+	0.715575i	−0.582094	+	0.813122i	$0.697766\pi$
$108$	−9.87427	+	17.1027i	−0.950152	+	1.64571i
$109$	−4.50957	−	1.20834i	−0.431939	−	0.115738i	0.0362973	−	0.999341i	$-0.488444\pi$
$109$	−4.50957	−	1.20834i	−0.431939	−	0.115738i	−0.468236	+	0.883603i	$0.655110\pi$
$110$	−22.7306	−	22.7306i	−2.16728	−	2.16728i
$111$	0.720711	+	0.193114i	0.0684069	+	0.0183296i
$112$		0			0
$113$	9.80118	+	16.9761i	0.922018	+	1.59698i	0.796289	+	0.604917i	$0.206794\pi$
$113$	9.80118	+	16.9761i	0.922018	+	1.59698i	0.125729	+	0.992065i	$0.459873\pi$
$114$	6.18669	−	3.57189i	0.579437	−	0.334538i
$115$	−11.7956	+	11.7956i	−1.09994	+	1.09994i
$116$	8.39245	−	4.84538i	0.779219	−	0.449883i
$117$	5.41941	−	1.43090i	0.501024	−	0.132287i
$118$		−	4.80915i		−	0.442718i
$119$		0			0
$120$	−7.29317	+	12.6321i	−0.665773	+	1.15315i
$121$			7.11890i			0.647173i
$122$	3.21164	−	11.9860i	0.290768	−	1.08516i
$123$	−1.62643	−	6.06993i	−0.146651	−	0.547308i
$124$	−13.5770	+	13.5770i	−1.21925	+	1.21925i
$125$	−0.388969	+	0.388969i	−0.0347904	+	0.0347904i
$126$		0			0
$127$	1.02476	+	0.591646i	0.0909329	+	0.0525001i	0.544777	−	0.838581i	$-0.316614\pi$
$127$	1.02476	+	0.591646i	0.0909329	+	0.0525001i	−0.453844	+	0.891081i	$0.649948\pi$
$128$	−5.33527	+	19.9115i	−0.471576	+	1.75994i
$129$	−3.79090	−	6.56603i	−0.333770	−	0.578107i
$130$	26.3268	−	6.95114i	2.30901	−	0.609655i
$131$	−8.37536	−	4.83552i	−0.731758	−	0.422481i	0.0873067	−	0.996181i	$-0.472174\pi$
$131$	−8.37536	−	4.83552i	−0.731758	−	0.422481i	−0.819065	+	0.573701i	$0.805507\pi$
$132$	17.8277	−	4.77693i	1.55171	−	0.415778i
$133$		0			0
$134$	−17.9733	+	10.3769i	−1.55266	+	0.896428i
$135$	−4.52017	−	16.8695i	−0.389034	−	1.45190i
$136$	−5.30482	+	1.42142i	−0.454884	+	0.121886i
$137$	−6.37069	+	1.70702i	−0.544285	+	0.145841i	−0.520477	−	0.853876i	$-0.674246\pi$
$137$	−6.37069	+	1.70702i	−0.544285	+	0.145841i	−0.0238082	+	0.999717i	$0.507579\pi$
$138$	−3.85355	−	14.3817i	−0.328036	−	1.22425i
$139$	−19.6752	+	11.3595i	−1.66883	+	0.963500i	−0.700562	+	0.713591i	$0.747067\pi$
$139$	−19.6752	+	11.3595i	−1.66883	+	0.963500i	−0.968269	+	0.249909i	$0.919599\pi$
$140$		0			0
$141$	−7.68617	+	2.05950i	−0.647292	+	0.173441i
$142$	−17.6612	−	10.1967i	−1.48210	−	0.855688i
$143$	−13.2632	−	7.72232i	−1.10912	−	0.645773i
$144$	1.39447	+	2.41529i	0.116206	+	0.201274i
$145$	−2.21808	+	8.27800i	−0.184202	+	0.687450i
$146$	−32.4220	−	18.7189i	−2.68327	−	1.54918i
$147$		0			0
$148$	1.58269	−	1.58269i	0.130096	−	0.130096i
$149$	10.7410	−	10.7410i	0.879936	−	0.879936i	−0.113591	−	0.993528i	$-0.536235\pi$
$149$	10.7410	−	10.7410i	0.879936	−	0.879936i	0.993528	+	0.113591i	$0.0362354\pi$
$150$	−3.81099	−	14.2228i	−0.311166	−	1.16129i
$151$	−1.86148	+	6.94712i	−0.151485	+	0.565349i	0.847896	+	0.530163i	$0.177869\pi$
$151$	−1.86148	+	6.94712i	−0.151485	+	0.565349i	−0.999381	+	0.0351862i	$0.988798\pi$
$152$		−	9.54598i		−	0.774281i
$153$	1.12221	−	1.94372i	0.0907252	−	0.157141i
$154$		0			0
$155$		−	16.9802i		−	1.36389i
$156$	−4.10148	+	15.0860i	−0.328381	+	1.20784i
$157$	16.4569	−	9.50142i	1.31341	−	0.758296i	0.330748	−	0.943719i	$-0.392699\pi$
$157$	16.4569	−	9.50142i	1.31341	−	0.758296i	0.982659	+	0.185423i	$0.0593656\pi$
$158$	3.37014	−	3.37014i	0.268114	−	0.268114i
$159$	−7.89767	+	4.55972i	−0.626326	+	0.361609i
$160$	−5.35833	−	9.28090i	−0.423613	−	0.733720i
$161$		0			0
$162$	4.39021	+	1.17635i	0.344928	+	0.0924231i
$163$	−0.717062	−	0.717062i	−0.0561646	−	0.0561646i	0.678467	−	0.734631i	$-0.262645\pi$
$163$	−0.717062	−	0.717062i	−0.0561646	−	0.0561646i	−0.734631	+	0.678467i	$0.762645\pi$
$164$	−18.2086	−	4.87899i	−1.42185	−	0.380985i
$165$	−8.16105	+	14.1353i	−0.635337	+	1.10044i
$166$	−8.56608	−	14.8369i	−0.664857	−	1.15157i
$167$	0.522634	+	1.95050i	0.0404426	+	0.150934i	0.983195	−	0.182561i	$-0.0584387\pi$
$167$	0.522634	+	1.95050i	0.0404426	+	0.150934i	−0.942752	+	0.333495i	$0.891772\pi$
$168$		0			0
$169$	11.3056	−	6.41746i	0.869660	−	0.493651i
$170$	5.45155	−	9.44237i	0.418115	−	0.724197i
$171$	2.75856	+	2.75856i	0.210952	+	0.210952i
$172$	−22.7439			−1.73421
$173$	2.45048			0.186307			0.0931533	−	0.995652i	$-0.470305\pi$
$173$	2.45048			0.186307			0.0931533	+	0.995652i	$0.470305\pi$
$174$	−5.40875	−	5.40875i	−0.410037	−	0.410037i
$175$		0			0
$176$	1.97645	−	7.37623i	0.148981	−	0.556004i
$177$	−2.35864	+	0.631995i	−0.177286	+	0.0475037i
$178$	−14.3550	−	8.28784i	−1.07595	−	0.621200i
$179$			7.50965i			0.561298i	0.959811	+	0.280649i	$0.0905496\pi$
$179$			7.50965i			0.561298i	−0.959811	+	0.280649i	$0.909450\pi$
$180$	−17.2727	−	4.62821i	−1.28743	−	0.344966i
$181$	−4.93320			−0.366682			−0.183341	−	0.983049i	$-0.558691\pi$
$181$	−4.93320			−0.366682			−0.183341	+	0.983049i	$0.558691\pi$
$182$		0			0
$183$	−6.30057			−0.465751
$184$	−19.2177	−	5.14937i	−1.41675	−	0.379617i
$185$			1.97940i			0.145528i
$186$	13.1252	+	7.57782i	0.962384	+	0.555633i
$187$	−5.93608	+	1.59057i	−0.434089	+	0.116314i
$188$	−6.17811	+	23.0570i	−0.450585	+	1.68161i
$189$		0			0
$190$	13.4008	+	13.4008i	0.972193	+	0.972193i
$191$	−6.08863			−0.440558			−0.220279	−	0.975437i	$-0.570697\pi$
$191$	−6.08863			−0.440558			−0.220279	+	0.975437i	$0.570697\pi$
$192$	13.8788			1.00162
$193$	10.2443	+	10.2443i	0.737402	+	0.737402i	0.972074	−	0.234672i	$-0.0754018\pi$
$193$	10.2443	+	10.2443i	0.737402	+	0.737402i	−0.234672	+	0.972074i	$0.575402\pi$
$194$	−7.43855	+	12.8840i	−0.534057	+	0.925014i
$195$	−6.86892	−	11.9985i	−0.491894	−	0.859228i
$196$		0			0
$197$	−4.33340	−	16.1725i	−0.308742	−	1.15224i	−0.929676	−	0.368379i	$-0.879913\pi$
$197$	−4.33340	−	16.1725i	−0.308742	−	1.15224i	0.620934	−	0.783863i	$-0.286754\pi$
$198$	7.83424	+	13.5693i	0.556755	+	0.964328i
$199$	9.90747	−	17.1602i	0.702322	−	1.21646i	−0.265328	−	0.964158i	$-0.585480\pi$
$199$	9.90747	−	17.1602i	0.702322	−	1.21646i	0.967649	−	0.252298i	$-0.0811865\pi$
$200$	−19.0055	−	5.09250i	−1.34389	−	0.360094i
$201$	7.45130	+	7.45130i	0.525574	+	0.525574i
$202$	30.5084	+	8.17471i	2.14657	+	0.575171i
$203$		0			0
$204$	3.13002	+	5.42135i	0.219145	+	0.379570i
$205$	14.4373	−	8.33541i	1.00835	−	0.582170i
$206$	−10.3380	+	10.3380i	−0.720282	+	0.720282i
$207$	7.04151	−	4.06542i	0.489419	−	0.282566i
$208$	4.55708	+	4.59054i	0.315977	+	0.318297i
$209$		−	10.6819i		−	0.738885i
$210$		0			0
$211$	−9.56393	+	16.5652i	−0.658408	+	1.14040i	0.322619	+	0.946529i	$0.395437\pi$
$211$	−9.56393	+	16.5652i	−0.658408	+	1.14040i	−0.981028	+	0.193868i	$0.937897\pi$
$212$			27.3566i			1.87886i
$213$	−2.68000	+	10.0019i	−0.183631	+	0.685320i
$214$	−5.23793	−	19.5482i	−0.358058	−	1.33629i
$215$	14.2224	−	14.2224i	0.969961	−	0.969961i
$216$	14.7288	−	14.7288i	1.00217	−	1.00217i
$217$		0			0
$218$	9.57347	+	5.52725i	0.648397	+	0.374352i
$219$	−4.91989	+	18.3613i	−0.332455	+	1.24074i
$220$	24.4816	+	42.4033i	1.65055	+	2.85883i
$221$	1.36566	−	5.02316i	0.0918645	−	0.337894i
$222$	−1.53001	−	0.883353i	−0.102688	−	0.0592868i
$223$	−0.670621	+	0.179692i	−0.0449081	+	0.0120331i	−0.281203	−	0.959648i	$-0.590733\pi$
$223$	−0.670621	+	0.179692i	−0.0449081	+	0.0120331i	0.236295	+	0.971681i	$0.424067\pi$
$224$		0			0
$225$	6.96374	−	4.02052i	0.464249	−	0.268034i
$226$	−12.0130	−	44.8332i	−0.799094	−	2.98226i
$227$	5.03400	−	1.34886i	0.334118	−	0.0895267i	−0.0878596	−	0.996133i	$-0.528003\pi$
$227$	5.03400	−	1.34886i	0.334118	−	0.0895267i	0.421978	+	0.906606i	$0.361336\pi$
$228$	−10.5103	+	2.81622i	−0.696060	+	0.186509i
$229$	0.274163	+	1.02319i	0.0181172	+	0.0676142i	0.974393	−	0.224853i	$-0.0721903\pi$
$229$	0.274163	+	1.02319i	0.0181172	+	0.0676142i	−0.956275	+	0.292468i	$0.905524\pi$
$230$	34.2068	−	19.7493i	2.25553	−	1.30223i
$231$		0			0
$232$	−9.87299	+	2.64546i	−0.648193	+	0.173683i
$233$	1.14405	+	0.660517i	0.0749492	+	0.0432719i	0.537006	−	0.843578i	$-0.319555\pi$
$233$	1.14405	+	0.660517i	0.0749492	+	0.0432719i	−0.462057	+	0.886850i	$0.652888\pi$
$234$	−13.2718	−	0.0485473i	−0.867604	−	0.00317364i
$235$	−10.5549	−	18.2816i	−0.688524	−	1.19256i
$236$	−1.89586	+	7.07546i	−0.123410	+	0.460573i
$237$	−2.09577	−	1.20999i	−0.136135	−	0.0785973i
$238$		0			0
$239$	15.2273	−	15.2273i	0.984972	−	0.984972i	−0.0149168	−	0.999889i	$-0.504748\pi$
$239$	15.2273	−	15.2273i	0.984972	−	0.984972i	0.999889	+	0.0149168i	$0.00474835\pi$
$240$	4.86429	−	4.86429i	0.313989	−	0.313989i
$241$	−0.908152	−	3.38927i	−0.0584992	−	0.218322i	0.930488	−	0.366322i	$-0.119383\pi$
$241$	−0.908152	−	3.38927i	−0.0584992	−	0.218322i	−0.988987	+	0.148000i	$0.952716\pi$
$242$	4.36271	−	16.2819i	0.280446	−	1.04664i
$243$			14.1195i			0.905769i
$244$	−9.45024	+	16.3683i	−0.604989	+	1.04787i
$245$		0			0
$246$			14.8795i			0.948680i
$247$	7.81925	+	4.55266i	0.497527	+	0.289679i
$248$	17.5387	−	10.1260i	1.11371	−	0.643000i
$249$	−6.15101	+	6.15101i	−0.389805	+	0.389805i
$250$	1.12800	−	0.651249i	0.0713407	−	0.0411886i
$251$	8.75834	+	15.1699i	0.552822	+	0.957515i	0.998069	+	0.0621079i	$0.0197823\pi$
$251$	8.75834	+	15.1699i	0.552822	+	0.957515i	−0.445248	+	0.895407i	$0.646884\pi$
$252$		0			0
$253$	−21.5046	−	5.76214i	−1.35198	−	0.362262i
$254$	−1.98118	−	1.98118i	−0.124310	−	0.124310i
$255$	−5.34741	−	1.43283i	−0.334868	−	0.0897276i
$256$	12.8609	−	22.2758i	0.803807	−	1.39224i
$257$	3.42559	+	5.93330i	0.213683	+	0.370109i	0.952864	−	0.303397i	$-0.0981208\pi$
$257$	3.42559	+	5.93330i	0.213683	+	0.370109i	−0.739182	+	0.673506i	$0.764788\pi$
$258$	4.64639	+	17.3406i	0.289272	+	1.07958i
$259$		0			0
$260$	−41.4736	−	0.151708i	−2.57208	−	0.00940850i
$261$	2.08858	−	3.61753i	0.129280	−	0.223920i
$262$	16.1922	+	16.1922i	1.00036	+	1.00036i
$263$	17.4170			1.07398			0.536989	−	0.843589i	$-0.319562\pi$
$263$	17.4170			1.07398			0.536989	+	0.843589i	$0.319562\pi$
$264$	−19.4670			−1.19811
$265$	−17.1068	−	17.1068i	−1.05086	−	1.05086i
$266$		0			0
$267$	−2.17830	+	8.12952i	−0.133310	+	0.497518i
$268$	30.5340	−	8.18157i	1.86516	−	0.499769i
$269$	0.145276	+	0.0838752i	0.00885764	+	0.00511396i	0.504422	−	0.863457i	$-0.331706\pi$
$269$	0.145276	+	0.0838752i	0.00885764	+	0.00511396i	−0.495565	+	0.868571i	$0.665039\pi$
$270$			41.3529i			2.51666i
$271$	2.40913	+	0.645525i	0.146344	+	0.0392128i	0.331248	−	0.943544i	$-0.392530\pi$
$271$	2.40913	+	0.645525i	0.146344	+	0.0392128i	−0.184903	+	0.982757i	$0.559197\pi$
$272$	2.59009			0.157047
$273$		0			0
$274$	15.6167			0.943441
$275$	−21.2671	−	5.69850i	−1.28245	−	0.343632i
$276$			22.6782i			1.36506i
$277$	7.38731	+	4.26506i	0.443860	+	0.256263i	0.705234	−	0.708975i	$-0.250842\pi$
$277$	7.38731	+	4.26506i	0.443860	+	0.256263i	−0.261373	+	0.965238i	$0.584175\pi$
$278$	51.9613	−	13.9230i	3.11643	−	0.835046i
$279$	−2.14210	+	7.99444i	−0.128244	+	0.478614i
$280$		0			0
$281$	15.7936	+	15.7936i	0.942166	+	0.942166i	0.998417	−	0.0562508i	$-0.0179146\pi$
$281$	15.7936	+	15.7936i	0.942166	+	0.942166i	−0.0562508	+	0.998417i	$0.517915\pi$
$282$	18.8414			1.12199
$283$	−9.58097			−0.569530			−0.284765	−	0.958597i	$-0.591915\pi$
$283$	−9.58097			−0.569530			−0.284765	+	0.958597i	$0.591915\pi$
$284$	21.9643	+	21.9643i	1.30334	+	1.30334i
$285$	4.81132	−	8.33345i	0.284998	−	0.493631i
$286$	25.6021	+	25.7901i	1.51388	+	1.52500i
$287$		0			0
$288$	1.35194	+	5.04550i	0.0796636	+	0.297309i
$289$	7.45780	+	12.9173i	0.438694	+	0.759841i
$290$	10.1461	−	17.5735i	0.595799	−	1.03195i
$291$	7.29645	+	1.95508i	0.427726	+	0.114609i
$292$	40.3215	+	40.3215i	2.35964	+	2.35964i
$293$	−14.5286	−	3.89292i	−0.848769	−	0.227427i	−0.191884	−	0.981418i	$-0.561460\pi$
$293$	−14.5286	−	3.89292i	−0.848769	−	0.227427i	−0.656885	+	0.753991i	$0.728126\pi$
$294$		0			0
$295$	−3.23895	−	5.61003i	−0.188579	−	0.326628i
$296$	−2.04450	+	1.18039i	−0.118834	+	0.0686090i
$297$	16.4815	−	16.4815i	0.956352	−	0.956352i
$298$	−31.1485	+	17.9836i	−1.80438	+	1.04176i
$299$	13.3832	−	13.2857i	0.773972	−	0.768330i
$300$			22.4277i			1.29486i
$301$		0			0
$302$	8.51488	−	14.7482i	0.489976	−	0.848663i
$303$		−	16.0371i		−	0.921307i
$304$	−1.16521	+	4.34863i	−0.0668295	+	0.249411i
$305$	−4.32606	−	16.1451i	−0.247709	−	0.924464i
$306$	−3.75782	+	3.75782i	−0.214820	+	0.214820i
$307$	15.7439	−	15.7439i	0.898552	−	0.898552i	−0.0967560	−	0.995308i	$-0.530847\pi$
$307$	15.7439	−	15.7439i	0.898552	−	0.898552i	0.995308	+	0.0967560i	$0.0308467\pi$
$308$		0			0
$309$	6.42882	+	3.71168i	0.365723	+	0.211150i
$310$	−10.4061	+	38.8360i	−0.591025	+	2.20574i
$311$	1.94686	+	3.37206i	0.110396	+	0.191212i	0.915930	−	0.401338i	$-0.131455\pi$
$311$	1.94686	+	3.37206i	0.110396	+	0.191212i	−0.805534	+	0.592550i	$0.798121\pi$
$312$	8.29688	−	14.2500i	0.469718	−	0.806747i
$313$	−8.63858	−	4.98749i	−0.488282	−	0.281910i	0.235580	−	0.971855i	$-0.424301\pi$
$313$	−8.63858	−	4.98749i	−0.488282	−	0.281910i	−0.723861	+	0.689946i	$0.757634\pi$
$314$	−43.4620	+	11.6456i	−2.45270	+	0.657199i
$315$		0			0
$316$	−6.28689	+	3.62974i	−0.353665	+	0.204189i
$317$	4.01848	+	14.9972i	0.225701	+	0.842326i	0.982123	+	0.188242i	$0.0602790\pi$
$317$	4.01848	+	14.9972i	0.225701	+	0.842326i	−0.756422	+	0.654084i	$0.773054\pi$
$318$	20.8574	−	5.58871i	1.16962	−	0.313399i
$319$	−11.0479	+	2.96026i	−0.618561	+	0.165743i
$320$	9.52940	+	35.5642i	0.532710	+	1.98810i
$321$	−8.89905	+	5.13787i	−0.496697	+	0.286768i
$322$		0			0
$323$	3.49959	−	0.937714i	0.194723	−	0.0521758i
$324$	−5.99535	−	3.46142i	−0.333075	−	0.192301i
$325$	13.2354	−	13.1389i	0.734169	−	0.728817i
$326$	1.20057	+	2.07946i	0.0664936	+	0.115170i
$327$	1.45273	−	5.42166i	0.0803361	−	0.299818i
$328$	17.2191	+	9.94146i	0.950766	+	0.548925i
$329$		0			0
$330$	27.3280	−	27.3280i	1.50436	−	1.50436i
$331$	−10.3551	+	10.3551i	−0.569166	+	0.569166i	−0.931895	−	0.362729i	$-0.881845\pi$
$331$	−10.3551	+	10.3551i	−0.569166	+	0.569166i	0.362729	+	0.931895i	$0.381845\pi$
$332$	6.75384	+	25.2057i	0.370665	+	1.38334i
$333$	0.249707	−	0.931919i	0.0136839	−	0.0510688i
$334$		−	4.78133i		−	0.261622i
$335$	−13.9776	+	24.2100i	−0.763680	+	1.32273i
$336$		0			0
$337$		−	11.8235i		−	0.644066i	−0.946728	−	0.322033i	$-0.895634\pi$
$337$		−	11.8235i		−	0.644066i	0.946728	−	0.322033i	$-0.104366\pi$
$338$	−29.7902	+	7.74912i	−1.62037	+	0.421497i
$339$	−20.4097	+	11.7835i	−1.10850	+	0.639993i
$340$	−11.7430	+	11.7430i	−0.636852	+	0.636852i
$341$	19.6258	−	11.3309i	1.06280	−	0.613605i
$342$	−4.61865	−	7.99973i	−0.249748	−	0.432576i
$343$		0			0
$344$	23.1716	+	6.20881i	1.24933	+	0.334756i
$345$	−14.1813	−	14.1813i	−0.763496	−	0.763496i
$346$	−5.60457	−	1.50174i	−0.301303	−	0.0807340i
$347$	5.00685	−	8.67212i	0.268782	−	0.465544i	−0.699766	−	0.714372i	$-0.746712\pi$
$347$	5.00685	−	8.67212i	0.268782	−	0.465544i	0.968548	+	0.248829i	$0.0800456\pi$
$348$	5.82539	+	10.0899i	0.312274	+	0.540874i
$349$	−4.39634	−	16.4073i	−0.235330	−	0.878265i	−0.978000	−	0.208607i	$-0.933107\pi$
$349$	−4.39634	−	16.4073i	−0.235330	−	0.878265i	0.742669	−	0.669658i	$-0.233559\pi$
$350$		0			0
$351$	5.04012	+	19.0890i	0.269022	+	1.01890i
$352$	7.15125	−	12.3863i	0.381163	−	0.660194i
$353$	−25.5124	−	25.5124i	−1.35789	−	1.35789i	−0.876520	−	0.481366i	$-0.840141\pi$
$353$	−25.5124	−	25.5124i	−1.35789	−	1.35789i	−0.481366	−	0.876520i	$-0.659859\pi$
$354$	5.78182			0.307300
$355$	−27.4698			−1.45795
$356$	17.8525	+	17.8525i	0.946181	+	0.946181i
$357$		0			0
$358$	4.60217	−	17.1755i	0.243232	−	0.907756i
$359$	3.34645	−	0.896679i	0.176619	−	0.0473249i	−0.169426	−	0.985543i	$-0.554191\pi$
$359$	3.34645	−	0.896679i	0.176619	−	0.0473249i	0.346045	+	0.938218i	$0.387525\pi$
$360$	16.3341	+	9.43047i	0.860880	+	0.497030i
$361$		−	12.7025i		−	0.668553i
$362$	11.2829	+	3.02324i	0.593014	+	0.158898i
$363$	−8.55873			−0.449217
$364$		0			0
$365$	−50.4284			−2.63954
$366$	14.4102	+	3.86121i	0.753234	+	0.201828i
$367$			12.6820i			0.661994i	0.943632	+	0.330997i	$0.107385\pi$
$367$			12.6820i			0.661994i	−0.943632	+	0.330997i	$0.892615\pi$
$368$	8.12600	+	4.69155i	0.423597	+	0.244564i
$369$	−7.84876	+	2.10307i	−0.408590	+	0.109481i
$370$	1.21305	−	4.52715i	0.0630633	−	0.235355i
$371$		0			0
$372$	−16.3231	−	16.3231i	−0.846312	−	0.846312i
$373$	30.0385			1.55533			0.777667	−	0.628677i	$-0.216403\pi$
$373$	30.0385			1.55533			0.777667	+	0.628677i	$0.216403\pi$
$374$	14.5513			0.752432
$375$	−0.467640	−	0.467640i	−0.0241488	−	0.0241488i
$376$	12.5886	−	21.8040i	0.649206	−	1.12446i
$377$	2.54169	−	9.34878i	0.130904	−	0.481487i
$378$		0			0
$379$	3.10882	+	11.6023i	0.159689	+	0.595969i	0.998658	+	0.0517891i	$0.0164924\pi$
$379$	3.10882	+	11.6023i	0.159689	+	0.595969i	−0.838969	+	0.544180i	$0.816841\pi$
$380$	−14.4330	−	24.9987i	−0.740398	−	1.28241i
$381$	−0.711310	+	1.23202i	−0.0364415	+	0.0631185i
$382$	13.9255	+	3.73133i	0.712490	+	0.190911i
$383$	4.04719	+	4.04719i	0.206802	+	0.206802i	0.802907	−	0.596105i	$-0.203286\pi$
$383$	4.04719	+	4.04719i	0.206802	+	0.206802i	−0.596105	+	0.802907i	$0.703286\pi$
$384$	−23.9387	−	6.41436i	−1.22162	−	0.327331i
$385$		0			0
$386$	−17.1520	−	29.7082i	−0.873015	−	1.51211i
$387$	−8.49024	+	4.90184i	−0.431583	+	0.249175i
$388$	16.0231	−	16.0231i	0.813449	−	0.813449i
$389$	14.2446	−	8.22413i	0.722231	−	0.416980i	−0.0933424	−	0.995634i	$-0.529755\pi$
$389$	14.2446	−	8.22413i	0.722231	−	0.416980i	0.815573	+	0.578654i	$0.196422\pi$
$390$	8.35704	+	31.6516i	0.423175	+	1.60274i
$391$		−	7.55112i		−	0.381877i
$392$		0			0
$393$	5.81352	−	10.0693i	0.293253	−	0.507930i
$394$			39.6442i			1.99725i
$395$	1.66159	−	6.20115i	0.0836038	−	0.312014i
$396$	−6.17683	−	23.0522i	−0.310397	−	1.15842i
$397$	−7.98783	+	7.98783i	−0.400898	+	0.400898i	−0.878549	−	0.477652i	$-0.841488\pi$
$397$	−7.98783	+	7.98783i	−0.400898	+	0.400898i	0.477652	+	0.878549i	$0.341488\pi$
$398$	−33.1761	+	33.1761i	−1.66297	+	1.66297i
$399$		0			0
$400$	8.03625	+	4.63973i	0.401812	+	0.231987i
$401$	6.26544	−	23.3830i	0.312881	−	1.16769i	−0.613064	−	0.790033i	$-0.710063\pi$
$401$	6.26544	−	23.3830i	0.312881	−	1.16769i	0.925946	−	0.377656i	$-0.123270\pi$
$402$	−12.4757	−	21.6085i	−0.622231	−	1.07774i
$403$	−0.0702158	+	19.1955i	−0.00349770	+	0.956195i
$404$	−41.6629	−	24.0541i	−2.07281	−	1.19674i
$405$	5.91359	−	1.58454i	0.293849	−	0.0787366i
$406$		0			0
$407$	−2.28780	+	1.32086i	−0.113402	+	0.0654726i
$408$	−1.70891	−	6.37774i	−0.0846037	−	0.315745i
$409$	−0.348508	+	0.0933824i	−0.0172326	+	0.00461746i	−0.267425	−	0.963579i	$-0.586173\pi$
$409$	−0.348508	+	0.0933824i	−0.0172326	+	0.00461746i	0.250192	+	0.968196i	$0.419506\pi$
$410$	−38.1283	+	10.2165i	−1.88302	+	0.504555i
$411$	−2.05228	−	7.65920i	−0.101231	−	0.377800i
$412$	19.2852	−	11.1343i	0.950114	−	0.548549i
$413$		0			0
$414$	−18.5963	+	4.98286i	−0.913957	+	0.244894i
$415$	−19.9852	−	11.5385i	−0.981036	−	0.566401i
$416$	6.01901	+	10.5139i	0.295106	+	0.515484i
$417$	−13.6570	−	23.6547i	−0.668787	−	1.15837i
$418$	−6.54626	+	24.4310i	−0.320188	+	1.19496i
$419$	15.9181	+	9.19033i	0.777651	+	0.448977i	0.835597	−	0.549343i	$-0.185122\pi$
$419$	15.9181	+	9.19033i	0.777651	+	0.448977i	−0.0579460	+	0.998320i	$0.518455\pi$
$420$		0			0
$421$	20.7439	−	20.7439i	1.01099	−	1.01099i	0.0110561	−	0.999939i	$-0.496481\pi$
$421$	20.7439	−	20.7439i	1.01099	−	1.01099i	0.999939	−	0.0110561i	$-0.00351933\pi$
$422$	32.0257	−	32.0257i	1.55899	−	1.55899i
$423$	2.66305	+	9.93864i	0.129482	+	0.483233i
$424$	7.46800	−	27.8710i	0.362678	−	1.35353i
$425$		−	7.46772i		−	0.362238i
$426$	12.2590	−	21.2333i	0.593952	−	1.02876i
$427$		0			0
$428$			30.8252i			1.48999i
$429$	9.28420	−	15.9457i	0.448245	−	0.769866i
$430$	−41.2445	+	23.8125i	−1.98899	+	1.14834i
$431$	−6.82413	+	6.82413i	−0.328707	+	0.328707i	−0.852095	−	0.523388i	$-0.824668\pi$
$431$	−6.82413	+	6.82413i	−0.328707	+	0.328707i	0.523388	+	0.852095i	$0.324668\pi$
$432$	−8.50747	+	4.91179i	−0.409316	+	0.236319i
$433$	−13.6960	−	23.7221i	−0.658186	−	1.14001i	−0.981085	−	0.193578i	$-0.937991\pi$
$433$	−13.6960	−	23.7221i	−0.658186	−	1.14001i	0.322899	−	0.946433i	$-0.395343\pi$
$434$		0			0
$435$	−9.95227	−	2.66670i	−0.477175	−	0.127859i
$436$	−11.9060	−	11.9060i	−0.570195	−	0.570195i
$437$	12.6780	+	3.39705i	0.606469	+	0.162503i
$438$	22.5048	−	38.9795i	1.07532	−	1.86251i
$439$	−17.2958	−	29.9571i	−0.825481	−	1.42978i	−0.901551	−	0.432673i	$-0.857570\pi$
$439$	−17.2958	−	29.9571i	−0.825481	−	1.42978i	0.0760695	−	0.997103i	$-0.475763\pi$
$440$	−13.3663	−	49.8838i	−0.637214	−	2.37812i
$441$		0			0
$442$	−6.20181	+	10.6517i	−0.294990	+	0.506649i
$443$	−3.98607	+	6.90408i	−0.189384	+	0.328023i	−0.945045	−	0.326940i	$-0.893982\pi$
$443$	−3.98607	+	6.90408i	−0.189384	+	0.328023i	0.755661	+	0.654963i	$0.227316\pi$
$444$	1.90280	+	1.90280i	0.0903027	+	0.0903027i
$445$	−22.3274			−1.05842
$446$	1.64392			0.0778418
$447$	12.9134	+	12.9134i	0.610784	+	0.610784i
$448$		0			0
$449$	−5.25579	+	19.6149i	−0.248036	+	0.925683i	0.723797	+	0.690013i	$0.242395\pi$
$449$	−5.25579	+	19.6149i	−0.248036	+	0.925683i	−0.971833	+	0.235670i	$0.924271\pi$
$450$	−18.3909	+	4.92782i	−0.866955	+	0.232300i
$451$	19.2682	+	11.1245i	0.907302	+	0.523831i
$452$			70.6966i			3.32529i
$453$	−8.35221	−	2.23797i	−0.392421	−	0.105149i
$454$	−12.3400			−0.579146
$455$		0			0
$456$	11.4767			0.537446
$457$	−1.35752	−	0.363747i	−0.0635022	−	0.0170154i	0.226928	−	0.973912i	$-0.427132\pi$
$457$	−1.35752	−	0.363747i	−0.0635022	−	0.0170154i	−0.290430	+	0.956896i	$0.593798\pi$
$458$		−	2.50818i		−	0.117200i
$459$	6.84646	+	3.95280i	0.319565	+	0.184501i
$460$	−58.1123	+	15.5711i	−2.70950	+	0.726009i
$461$	4.89285	−	18.2604i	0.227883	−	0.850469i	−0.753347	−	0.657624i	$-0.771562\pi$
$461$	4.89285	−	18.2604i	0.227883	−	0.850469i	0.981229	−	0.192846i	$-0.0617717\pi$
$462$		0			0
$463$	22.4573	+	22.4573i	1.04368	+	1.04368i	0.999002	+	0.0446754i	$0.0142253\pi$
$463$	22.4573	+	22.4573i	1.04368	+	1.04368i	0.0446754	+	0.999002i	$0.485775\pi$
$464$	4.82051			0.223787
$465$	20.4146			0.946703
$466$	−2.21180	−	2.21180i	−0.102460	−	0.102460i
$467$	−14.1945	+	24.5855i	−0.656841	+	1.13768i	0.324588	+	0.945855i	$0.394774\pi$
$467$	−14.1945	+	24.5855i	−0.656841	+	1.13768i	−0.981429	+	0.191826i	$0.938559\pi$
$468$	19.5070	+	5.30343i	0.901711	+	0.245151i
$469$		0			0
$470$	12.9368	+	48.2807i	0.596729	+	2.22702i
$471$	11.4231	+	19.7854i	0.526350	+	0.911665i
$472$	3.86302	−	6.69096i	0.177810	−	0.307976i
$473$	25.9290	+	6.94764i	1.19221	+	0.319453i
$474$	4.05176	+	4.05176i	0.186104	+	0.186104i
$475$	12.5379	+	3.35953i	0.575280	+	0.154146i
$476$		0			0
$477$	5.89597	+	10.2121i	0.269958	+	0.467581i
$478$	−44.1586	+	25.4950i	−2.01977	+	1.16611i
$479$	−2.47311	+	2.47311i	−0.112999	+	0.112999i	−0.761346	−	0.648346i	$-0.775461\pi$
$479$	−2.47311	+	2.47311i	−0.112999	+	0.112999i	0.648346	+	0.761346i	$0.275461\pi$
$480$	11.1580	−	6.44208i	0.509291	−	0.294039i
$481$	0.00818512	−	2.23764i	0.000373209	−	0.102027i
$482$			8.30825i			0.378430i
$483$		0			0
$484$	−12.8373	+	22.2348i	−0.583512	+	1.01067i
$485$			20.0394i			0.909942i
$486$	8.65295	−	32.2933i	0.392506	−	1.46485i
$487$	6.29214	+	23.4826i	0.285124	+	1.06410i	0.948749	+	0.316032i	$0.102351\pi$
$487$	6.29214	+	23.4826i	0.285124	+	1.06410i	−0.663625	+	0.748066i	$0.730983\pi$
$488$	14.0963	−	14.0963i	0.638108	−	0.638108i
$489$	0.862092	−	0.862092i	0.0389851	−	0.0389851i
$490$		0			0
$491$	−5.24444	−	3.02788i	−0.236678	−	0.136646i	0.376971	−	0.926225i	$-0.376966\pi$
$491$	−5.24444	−	3.02788i	−0.236678	−	0.136646i	−0.613649	+	0.789579i	$0.710299\pi$
$492$	5.86579	−	21.8914i	0.264450	−	0.986941i
$493$	−1.93967	−	3.35961i	−0.0873584	−	0.151309i
$494$	−15.0936	−	15.2044i	−0.679094	−	0.684080i
$495$	18.2778	+	10.5527i	0.821525	+	0.474308i
$496$	−9.22569	+	2.47202i	−0.414246	+	0.110997i
$497$		0			0
$498$	17.8377	−	10.2986i	0.799328	−	0.461492i
$499$	4.73497	+	17.6712i	0.211967	+	0.791070i	0.987212	+	0.159410i	$0.0509593\pi$
$499$	4.73497	+	17.6712i	0.211967	+	0.791070i	−0.775246	+	0.631660i	$0.782374\pi$
$500$	−1.91630	+	0.513471i	−0.0856995	+	0.0229631i
$501$	−2.34499	+	0.628339i	−0.104767	+	0.0280721i
$502$	−10.7348	−	40.0629i	−0.479119	−	1.78810i
$503$	7.01237	−	4.04859i	0.312666	−	0.180518i	−0.335453	−	0.942057i	$-0.608889\pi$
$503$	7.01237	−	4.04859i	0.312666	−	0.180518i	0.648119	+	0.761539i	$0.275556\pi$
$504$		0			0
$505$	41.0947	−	11.0113i	1.82869	−	0.489996i
$506$	45.6526	+	26.3575i	2.02950	+	1.17173i
$507$	7.71543	+	13.5922i	0.342654	+	0.603651i
$508$	2.13379	+	3.69583i	0.0946717	+	0.163976i
$509$	−4.18077	+	15.6029i	−0.185309	+	0.691584i	0.809255	+	0.587458i	$0.199871\pi$
$509$	−4.18077	+	15.6029i	−0.185309	+	0.691584i	−0.994564	+	0.104126i	$0.966795\pi$
$510$	11.3521	+	6.55416i	0.502681	+	0.290223i
$511$		0			0
$512$	−13.9135	+	13.9135i	−0.614896	+	0.614896i
$513$	−9.71660	+	9.71660i	−0.428998	+	0.428998i
$514$	−4.19864	−	15.6696i	−0.185194	−	0.691154i
$515$	−5.09699	+	19.0222i	−0.224600	+	0.838219i
$516$		−	27.3440i		−	1.20375i
$517$	14.0866	−	24.3987i	0.619527	−	1.07305i
$518$		0			0
$519$			2.94610i			0.129320i
$520$	42.2121	+	11.4763i	1.85112	+	0.503271i
$521$	28.0133	−	16.1735i	1.22729	−	0.708574i	0.260825	−	0.965386i	$-0.416005\pi$
$521$	28.0133	−	16.1735i	1.22729	−	0.708574i	0.966461	+	0.256812i	$0.0826721\pi$
$522$	−6.99382	+	6.99382i	−0.306111	+	0.306111i
$523$	−18.4602	+	10.6580i	−0.807210	+	0.466043i	−0.845986	−	0.533205i	$-0.820987\pi$
$523$	−18.4602	+	10.6580i	−0.807210	+	0.466043i	0.0387760	+	0.999248i	$0.487654\pi$
$524$	−17.4394	−	30.2060i	−0.761845	−	1.31956i
$525$		0			0
$526$	−39.8349	−	10.6737i	−1.73688	−	0.465397i
$527$	5.43507	+	5.43507i	0.236755	+	0.236755i
$528$	8.86811	+	2.37620i	0.385935	+	0.103411i
$529$	2.17769	−	3.77187i	0.0946821	−	0.163994i
$530$	28.6419	+	49.6092i	1.24413	+	2.15489i
$531$	0.817205	+	3.04985i	0.0354637	+	0.132352i
$532$		0			0
$533$	−16.3553	+	9.36315i	−0.708428	+	0.405563i
$534$	9.96410	−	17.2583i	0.431189	−	0.746841i
$535$	−19.2759	−	19.2759i	−0.833370	−	0.833370i
$536$	−33.3417			−1.44014
$537$	−9.02852			−0.389609
$538$	−0.280864	−	0.280864i	−0.0121089	−	0.0121089i
$539$		0			0
$540$	16.3021	−	60.8404i	0.701532	−	2.61815i
$541$	−17.8879	+	4.79305i	−0.769061	+	0.206069i	−0.621957	−	0.783052i	$-0.713662\pi$
$541$	−17.8879	+	4.79305i	−0.769061	+	0.206069i	−0.147104	+	0.989121i	$0.546995\pi$
$542$	−5.11440	−	2.95280i	−0.219682	−	0.126834i
$543$		−	5.93096i		−	0.254522i
$544$	4.68576	+	1.25555i	0.200900	+	0.0538311i
$545$	14.8904			0.637833
$546$		0			0
$547$	−35.0943			−1.50053			−0.750263	−	0.661140i	$-0.770073\pi$
$547$	−35.0943			−1.50053			−0.750263	+	0.661140i	$0.770073\pi$
$548$	−22.9761	−	6.15643i	−0.981490	−	0.262990i
$549$			8.14698i			0.347705i
$550$	45.1483	+	26.0664i	1.92513	+	1.11148i
$551$	6.51323	−	1.74521i	0.277473	−	0.0743486i
$552$	6.19086	−	23.1046i	0.263500	−	0.983397i
$553$		0			0
$554$	−14.2820	−	14.2820i	−0.606782	−	0.606782i
$555$	−2.37975			−0.101015
$556$	−81.9368			−3.47490
$557$	−6.70621	−	6.70621i	−0.284151	−	0.284151i	0.550611	−	0.834762i	$-0.314395\pi$
$557$	−6.70621	−	6.70621i	−0.284151	−	0.284151i	−0.834762	+	0.550611i	$0.814395\pi$
$558$	9.79854	−	16.9716i	0.414805	−	0.718464i
$559$	−16.1367	+	16.0191i	−0.682510	+	0.677535i
$560$		0			0
$561$	−1.91227	−	7.13668i	−0.0807360	−	0.301311i
$562$	−26.4431	−	45.8008i	−1.11544	−	1.93199i
$563$	−15.8351	+	27.4272i	−0.667369	+	1.15592i	0.311268	+	0.950322i	$0.399246\pi$
$563$	−15.8351	+	27.4272i	−0.667369	+	1.15592i	−0.978637	+	0.205595i	$0.934087\pi$
$564$	−27.7204	−	7.42767i	−1.16724	−	0.312761i
$565$	−44.2086	−	44.2086i	−1.85987	−	1.85987i
$566$	21.9129	+	5.87155i	0.921069	+	0.246800i
$567$		0			0
$568$	−16.3813	−	28.3733i	−0.687345	−	1.19052i
$569$	6.05848	−	3.49787i	0.253985	−	0.146638i	−0.367603	−	0.929983i	$-0.619821\pi$
$569$	6.05848	−	3.49787i	0.253985	−	0.146638i	0.621587	+	0.783345i	$0.286488\pi$
$570$	−16.1111	+	16.1111i	−0.674821	+	0.674821i
$571$	−13.2500	+	7.64990i	−0.554496	+	0.320139i	−0.750933	−	0.660378i	$-0.770396\pi$
$571$	−13.2500	+	7.64990i	−0.554496	+	0.320139i	0.196437	+	0.980516i	$0.437063\pi$
$572$	−27.5001	−	48.0365i	−1.14984	−	2.00851i
$573$		−	7.32009i		−	0.305801i
$574$		0			0
$575$	13.5266	−	23.4288i	0.564099	−	0.977049i
$576$		−	17.9461i		−	0.747754i
$577$	−10.8175	+	40.3714i	−0.450338	+	1.68068i	0.251106	+	0.967960i	$0.419206\pi$
$577$	−10.8175	+	40.3714i	−0.450338	+	1.68068i	−0.701444	+	0.712725i	$0.747461\pi$
$578$	−9.14080	−	34.1139i	−0.380207	−	1.41895i
$579$	−12.3163	+	12.3163i	−0.511847	+	0.511847i
$580$	−21.8553	+	21.8553i	−0.907491	+	0.907491i
$581$		0			0
$582$	−15.4898	−	8.94304i	−0.642073	−	0.370701i
$583$	8.35668	−	31.1876i	0.346098	−	1.29166i
$584$	−30.0724	−	52.0870i	−1.24441	−	2.15538i
$585$	−15.5147	+	8.88189i	−0.641453	+	0.367221i
$586$	30.8431	+	17.8073i	1.27412	+	0.735611i
$587$	0.941084	−	0.252163i	0.0388427	−	0.0104079i	−0.239345	−	0.970934i	$-0.576933\pi$
$587$	0.941084	−	0.252163i	0.0388427	−	0.0104079i	0.278188	+	0.960527i	$0.410266\pi$
$588$		0			0
$589$	−11.5703	+	6.68012i	−0.476746	+	0.275250i
$590$	3.96988	+	14.8158i	0.163437	+	0.609957i
$591$	19.4435	−	5.20986i	0.799797	−	0.214305i
$592$	1.07545	−	0.288165i	0.0442006	−	0.0118435i
$593$	−10.2197	−	38.1404i	−0.419673	−	1.56624i	−0.775288	−	0.631608i	$-0.782395\pi$
$593$	−10.2197	−	38.1404i	−0.419673	−	1.56624i	0.355616	−	0.934632i	$-0.384271\pi$
$594$	−47.7957	+	27.5949i	−1.96108	+	1.13223i
$595$		0			0
$596$	52.9167	−	14.1790i	2.16755	−	0.580794i
$597$	20.6310	+	11.9113i	0.844370	+	0.487497i
$598$	−38.7511	+	22.1844i	−1.58465	+	0.907186i
$599$	−8.27438	−	14.3316i	−0.338082	−	0.585575i	0.645990	−	0.763346i	$-0.276445\pi$
$599$	−8.27438	−	14.3316i	−0.338082	−	0.585575i	−0.984072	+	0.177771i	$0.943111\pi$
$600$	6.12248	−	22.8494i	0.249949	−	0.932824i
$601$	−9.99562	−	5.77097i	−0.407730	−	0.235403i	0.282084	−	0.959390i	$-0.408974\pi$
$601$	−9.99562	−	5.77097i	−0.407730	−	0.235403i	−0.689814	+	0.723987i	$0.742308\pi$
$602$		0			0
$603$	9.63495	−	9.63495i	0.392365	−	0.392365i
$604$	−18.3415	+	18.3415i	−0.746307	+	0.746307i
$605$	−5.87655	−	21.9316i	−0.238916	−	0.891645i
$606$	−9.82809	+	36.6789i	−0.399239	+	1.48998i
$607$		−	21.3778i		−	0.867696i	−0.900986	−	0.433848i	$-0.857155\pi$
$607$		−	21.3778i		−	0.867696i	0.900986	−	0.433848i	$-0.142845\pi$
$608$	−4.21600	+	7.30232i	−0.170981	+	0.296148i
$609$		0			0
$610$			39.5770i			1.60243i
$611$	11.8563	+	20.7102i	0.479653	+	0.837847i
$612$	7.01010	−	4.04728i	0.283366	−	0.163602i
$613$	22.0693	−	22.0693i	0.891372	−	0.891372i	−0.103281	−	0.994652i	$-0.532934\pi$
$613$	22.0693	−	22.0693i	0.891372	−	0.891372i	0.994652	+	0.103281i	$0.0329340\pi$
$614$	−45.6568	+	26.3600i	−1.84256	+	1.06380i
$615$	10.0213	+	17.3574i	0.404097	+	0.699917i
$616$		0			0
$617$	26.9421	+	7.21911i	1.08465	+	0.290630i	0.756498	−	0.653996i	$-0.226909\pi$
$617$	26.9421	+	7.21911i	1.08465	+	0.290630i	0.328149	+	0.944626i	$0.393575\pi$
$618$	−12.4289	−	12.4289i	−0.499964	−	0.499964i
$619$	−46.5004	−	12.4597i	−1.86901	−	0.500799i	−0.999982	−	0.00603119i	$-0.998080\pi$
$619$	−46.5004	−	12.4597i	−1.86901	−	0.500799i	−0.869025	−	0.494768i	$-0.835253\pi$
$620$	30.6199	−	53.0352i	1.22972	−	2.12994i
$621$	14.3198	+	24.8026i	0.574633	+	0.995294i
$622$	−2.38621	−	8.90546i	−0.0956783	−	0.357076i
$623$		0			0
$624$	−5.51901	+	5.47878i	−0.220937	+	0.219327i
$625$	−12.0539	+	20.8781i	−0.482158	+	0.835122i
$626$	16.7011	+	16.7011i	0.667509	+	0.667509i
$627$	12.8424			0.512877
$628$	68.5343			2.73482
$629$	−0.633571	−	0.633571i	−0.0252621	−	0.0252621i
$630$		0			0
$631$	−2.94853	+	11.0041i	−0.117379	+	0.438064i	−0.999454	−	0.0330448i	$-0.989480\pi$
$631$	−2.94853	+	11.0041i	−0.117379	+	0.438064i	0.882075	+	0.471109i	$0.156146\pi$
$632$	7.39598	−	1.98175i	0.294196	−	0.0788296i
$633$	−19.9156	−	11.4983i	−0.791575	−	0.457016i
$634$		−	36.7632i		−	1.46005i
$635$	−3.64543	−	0.976791i	−0.144665	−	0.0387628i
$636$	−32.8896			−1.30416
$637$		0			0
$638$	27.0820			1.07219
$639$	12.9330	+	3.46539i	0.511622	+	0.137089i
$640$		−	65.7466i		−	2.59886i
$641$	16.9100	+	9.76301i	0.667906	+	0.385616i	0.795283	−	0.606239i	$-0.207322\pi$
$641$	16.9100	+	9.76301i	0.667906	+	0.385616i	−0.127377	+	0.991854i	$0.540656\pi$
$642$	23.5020	−	6.29733i	0.927548	−	0.248536i
$643$	−9.35047	+	34.8964i	−0.368747	+	1.37618i	0.493524	+	0.869732i	$0.335709\pi$
$643$	−9.35047	+	34.8964i	−0.368747	+	1.37618i	−0.862270	+	0.506449i	$0.830958\pi$
$644$		0			0
$645$	17.0990	+	17.0990i	0.673272	+	0.673272i
$646$	−8.57869			−0.337524
$647$	−5.79390			−0.227782			−0.113891	−	0.993493i	$-0.536331\pi$
$647$	−5.79390			−0.227782			−0.113891	+	0.993493i	$0.536331\pi$
$648$	5.16316	+	5.16316i	0.202828	+	0.202828i
$649$	4.32272	−	7.48717i	0.169682	−	0.293897i
$650$	−38.3231	+	21.9393i	−1.50316	+	0.860532i
$651$		0			0
$652$	−0.946581	−	3.53269i	−0.0370710	−	0.138351i
$653$	−18.1035	−	31.3562i	−0.708445	−	1.22706i	−0.965434	−	0.260648i	$-0.916064\pi$
$653$	−18.1035	−	31.3562i	−0.708445	−	1.22706i	0.256989	−	0.966414i	$-0.417270\pi$
$654$	−6.64516	+	11.5098i	−0.259846	+	0.450067i
$655$	29.7941	+	7.98330i	1.16415	+	0.311933i
$656$	−6.63060	−	6.63060i	−0.258882	−	0.258882i
$657$	23.7421	+	6.36168i	0.926269	+	0.248193i
$658$		0			0
$659$	−10.3685	−	17.9588i	−0.403901	−	0.699576i	0.590292	−	0.807190i	$-0.299013\pi$
$659$	−10.3685	−	17.9588i	−0.403901	−	0.699576i	−0.994193	+	0.107613i	$0.965679\pi$
$660$	−50.9796	+	29.4331i	−1.98438	+	1.14568i
$661$	23.9986	−	23.9986i	0.933438	−	0.933438i	−0.0644808	−	0.997919i	$-0.520539\pi$
$661$	23.9986	−	23.9986i	0.933438	−	0.933438i	0.997919	+	0.0644808i	$0.0205391\pi$
$662$	30.0293	−	17.3374i	1.16712	−	0.673838i
$663$	6.03912	+	1.64188i	0.234540	+	0.0637652i
$664$		−	27.5234i		−	1.06811i
$665$		0			0
$666$	−1.14222	+	1.97839i	−0.0442603	+	0.0766611i
$667$		−	14.0537i		−	0.544160i
$668$	−1.88490	+	7.03452i	−0.0729288	+	0.272174i
$669$	−0.216036	−	0.806257i	−0.00835243	−	0.0311717i
$670$	46.8054	−	46.8054i	1.80825	−	1.80825i
$671$	15.7737	−	15.7737i	0.608937	−	0.608937i
$672$		0			0
$673$	−35.7571	−	20.6444i	−1.37834	−	0.795783i	−0.386377	−	0.922341i	$-0.626274\pi$
$673$	−35.7571	−	20.6444i	−1.37834	−	0.795783i	−0.991959	+	0.126558i	$0.959607\pi$
$674$	−7.24584	+	27.0419i	−0.279099	+	1.04161i
$675$	14.1616	+	24.5287i	0.545082	+	0.944109i
$676$	46.8837	+	0.342999i	1.80322	+	0.0131923i
$677$	39.1750	+	22.6177i	1.50562	+	0.869268i	0.999979	+	0.00652270i	$0.00207626\pi$
$677$	39.1750	+	22.6177i	1.50562	+	0.869268i	0.505638	+	0.862746i	$0.331257\pi$
$678$	53.9009	−	14.4427i	2.07005	−	0.554669i
$679$		0			0
$680$	15.1695	−	8.75810i	0.581723	−	0.335858i
$681$	1.62167	+	6.05215i	0.0621425	+	0.231919i
$682$	−51.8307	+	13.8880i	−1.98470	+	0.531799i
$683$	−42.0091	+	11.2563i	−1.60743	+	0.430710i	−0.947276	−	0.320419i	$-0.896176\pi$
$683$	−42.0091	+	11.2563i	−1.60743	+	0.430710i	−0.660156	+	0.751129i	$0.729510\pi$
$684$	3.64153	+	13.5904i	0.139237	+	0.519641i
$685$	18.2174	−	10.5178i	0.696051	−	0.401866i
$686$		0			0
$687$	−1.23013	+	0.329613i	−0.0469325	+	0.0125755i
$688$	−9.79785	−	5.65679i	−0.373539	−	0.215663i
$689$	19.2679	+	19.4094i	0.734048	+	0.739438i
$690$	23.7437	+	41.1253i	0.903907	+	1.56561i
$691$	5.57267	−	20.7975i	0.211994	−	0.791174i	−0.775209	−	0.631705i	$-0.782355\pi$
$691$	5.57267	−	20.7975i	0.211994	−	0.791174i	0.987203	−	0.159468i	$-0.0509780\pi$
$692$	7.65370	+	4.41887i	0.290950	+	0.167980i
$693$		0			0
$694$	−16.7659	+	16.7659i	−0.636425	+	0.636425i
$695$	51.2375	−	51.2375i	1.94355	−	1.94355i
$696$	−3.18052	−	11.8699i	−0.120557	−	0.449926i
$697$	−1.95312	+	7.28916i	−0.0739798	+	0.276096i
$698$			40.2200i			1.52235i
$699$	−0.794111	+	1.37544i	−0.0300360	+	0.0520239i
$700$		0			0
$701$		−	8.77295i		−	0.331350i	−0.986180	−	0.165675i	$-0.947020\pi$
$701$		−	8.77295i		−	0.331350i	0.986180	−	0.165675i	$-0.0529803\pi$
$702$	0.171000	−	46.7478i	0.00645399	−	1.76438i
$703$	1.34876	−	0.778708i	0.0508695	−	0.0293695i
$704$	−34.7462	+	34.7462i	−1.30955	+	1.30955i
$705$	21.9791	−	12.6896i	0.827781	−	0.477920i
$706$	42.7152	+	73.9850i	1.60761	+	2.78446i
$707$		0			0
$708$	−8.50651	−	2.27931i	−0.319694	−	0.0856618i
$709$	−29.9934	−	29.9934i	−1.12643	−	1.12643i	−0.990754	−	0.135672i	$-0.956681\pi$
$709$	−29.9934	−	29.9934i	−1.12643	−	1.12643i	−0.135672	−	0.990754i	$-0.543319\pi$
$710$	62.8270	+	16.8345i	2.35786	+	0.631786i
$711$	−1.56458	+	2.70994i	−0.0586765	+	0.101631i
$712$	−13.3147	−	23.0617i	−0.498989	−	0.864274i
$713$	7.20689	+	26.8965i	0.269900	+	1.00728i
$714$		0			0
$715$	47.2352	+	12.8420i	1.76650	+	0.480264i
$716$	−13.5419	+	23.4553i	−0.506084	+	0.876564i
$717$	18.3071	+	18.3071i	0.683691	+	0.683691i
$718$	−8.20329			−0.306144
$719$	−5.60019			−0.208852			−0.104426	−	0.994533i	$-0.533301\pi$
$719$	−5.60019			−0.208852			−0.104426	+	0.994533i	$0.533301\pi$
$720$	−6.28980	−	6.28980i	−0.234407	−	0.234407i
$721$		0			0
$722$	−7.78453	+	29.0523i	−0.289710	+	1.08121i
$723$	4.07477	−	1.09183i	0.151542	−	0.0406056i
$724$	−15.4081	−	8.89587i	−0.572637	−	0.330612i
$725$		−	13.8985i		−	0.516176i
$726$	19.5749	+	5.24509i	0.726494	+	0.194664i
$727$	32.0200			1.18756			0.593778	−	0.804629i	$-0.297636\pi$
$727$	32.0200			1.18756			0.593778	+	0.804629i	$0.297636\pi$
$728$		0			0
$729$	−22.7339			−0.841996
$730$	115.336	+	30.9043i	4.26879	+	1.14382i
$731$			9.10469i			0.336749i
$732$	−19.6789	−	11.3616i	−0.727352	−	0.419937i
$733$	−0.884660	+	0.237044i	−0.0326757	+	0.00875542i	−0.275120	−	0.961410i	$-0.588718\pi$
$733$	−0.884660	+	0.237044i	−0.0326757	+	0.00875542i	0.242444	+	0.970165i	$0.422051\pi$
$734$	7.77195	−	29.0053i	0.286868	−	1.07061i
$735$		0			0
$736$	12.4266	+	12.4266i	0.458051	+	0.458051i
$737$	−37.3092			−1.37430
$738$	19.2400			0.708233
$739$	6.20218	+	6.20218i	0.228151	+	0.228151i	0.811920	−	0.583769i	$-0.198423\pi$
$739$	6.20218	+	6.20218i	0.228151	+	0.228151i	−0.583769	+	0.811920i	$0.698423\pi$
$740$	−3.56939	+	6.18236i	−0.131213	+	0.227268i
$741$	−5.47347	+	9.40074i	−0.201073	+	0.345345i
$742$		0			0
$743$	−9.56609	−	35.7011i	−0.350946	−	1.30975i	−0.885510	−	0.464620i	$-0.846191\pi$
$743$	−9.56609	−	35.7011i	−0.350946	−	1.30975i	0.534564	−	0.845128i	$-0.320476\pi$
$744$	12.1740	+	21.0860i	0.446321	+	0.773050i
$745$	−24.2238	+	41.9569i	−0.887492	+	1.53718i
$746$	−68.7019	−	18.4086i	−2.51536	−	0.673988i
$747$	7.95360	+	7.95360i	0.291007	+	0.291007i
$748$	−21.4087	−	5.73643i	−0.782778	−	0.209745i
$749$		0			0
$750$	0.782967	+	1.35614i	0.0285899	+	0.0495192i
$751$	10.7508	−	6.20698i	0.392303	−	0.226496i	−0.290855	−	0.956767i	$-0.593940\pi$
$751$	10.7508	−	6.20698i	0.392303	−	0.226496i	0.683157	+	0.730271i	$0.260606\pi$
$752$	−8.39613	+	8.39613i	−0.306175	+	0.306175i
$753$	−18.2381	+	10.5298i	−0.664633	+	0.383726i
$754$	−11.5424	+	19.8242i	−0.420350	+	0.721957i
$755$		−	22.9390i		−	0.834835i
$756$		0			0
$757$	11.7793	−	20.4023i	0.428124	−	0.741533i	−0.568582	−	0.822626i	$-0.692508\pi$
$757$	11.7793	−	20.4023i	0.428124	−	0.741533i	0.996707	+	0.0810934i	$0.0258412\pi$
$758$		−	28.4411i		−	1.03303i
$759$	6.92756	−	25.8540i	0.251454	−	0.938441i
$760$	7.88007	+	29.4088i	0.285840	+	1.06677i
$761$	−9.57799	+	9.57799i	−0.347202	+	0.347202i	−0.859066	−	0.511864i	$-0.828955\pi$
$761$	−9.57799	+	9.57799i	−0.347202	+	0.347202i	0.511864	+	0.859066i	$0.328955\pi$
$762$	2.38189	−	2.38189i	0.0862866	−	0.0862866i
$763$		0			0
$764$	−19.0169	−	10.9794i	−0.688008	−	0.397222i
$765$	−1.85273	+	6.91450i	−0.0669857	+	0.249994i
$766$	−6.77619	−	11.7367i	−0.244834	−	0.424064i
$767$	3.63831	+	6.35531i	0.131372	+	0.229477i
$768$	26.7812	+	15.4621i	0.966382	+	0.557941i
$769$	29.8604	−	8.00107i	1.07679	−	0.288526i	0.323512	−	0.946224i	$-0.395136\pi$
$769$	29.8604	−	8.00107i	1.07679	−	0.288526i	0.753282	+	0.657698i	$0.228470\pi$
$770$		0			0
$771$	−7.13334	+	4.11844i	−0.256901	+	0.148322i
$772$	13.5233	+	50.4698i	0.486716	+	1.81645i
$773$	−19.2999	+	5.17138i	−0.694167	+	0.186002i	−0.588617	−	0.808412i	$-0.700327\pi$
$773$	−19.2999	+	5.17138i	−0.694167	+	0.186002i	−0.105551	+	0.994414i	$0.533661\pi$
$774$	22.4223	−	6.00804i	0.805953	−	0.215954i
$775$	7.12729	+	26.5994i	0.256020	+	0.955480i
$776$	−20.6985	+	11.9503i	−0.743032	+	0.428990i
$777$		0			0
$778$	−37.6193	+	10.0801i	−1.34872	+	0.361388i
$779$	−11.3595	−	6.55839i	−0.406995	−	0.234979i
$780$	0.182391	−	49.8619i	0.00653065	−	1.78534i
$781$	−18.3307	−	31.7497i	−0.655923	−	1.13609i
$782$	−4.62759	+	17.2704i	−0.165482	+	0.617588i
$783$	12.7422	+	7.35671i	0.455369	+	0.262907i
$784$		0			0
$785$	−42.8565	+	42.8565i	−1.52961	+	1.52961i
$786$	−19.4671	+	19.4671i	−0.694369	+	0.694369i
$787$	12.8359	+	47.9041i	0.457549	+	1.70760i	0.680483	+	0.732764i	$0.261770\pi$
$787$	12.8359	+	47.9041i	0.457549	+	1.70760i	−0.222934	+	0.974834i	$0.571563\pi$
$788$	15.6286	−	58.3266i	0.556744	−	2.07780i
$789$			20.9397i			0.745472i
$790$	−7.60056	+	13.1646i	−0.270416	+	0.468374i
$791$		0			0
$792$			25.1719i			0.894445i
$793$	4.82368	+	18.2693i	0.171294	+	0.648760i
$794$	23.1644	−	13.3740i	0.822075	−	0.474625i
$795$	20.5668	−	20.5668i	0.729429	−	0.729429i
$796$	61.8889	−	35.7316i	2.19360	−	1.26647i
$797$	−3.67854	−	6.37141i	−0.130300	−	0.225687i	0.793492	−	0.608581i	$-0.208261\pi$
$797$	−3.67854	−	6.37141i	−0.130300	−	0.225687i	−0.923792	+	0.382894i	$0.874928\pi$
$798$		0			0
$799$	9.23003	+	2.47318i	0.326535	+	0.0874948i
$800$	12.2894	+	12.2894i	0.434495	+	0.434495i
$801$	10.5119	+	2.81666i	0.371420	+	0.0995217i
$802$	−28.6598	+	49.6402i	−1.01201	+	1.75286i
$803$	−33.6510	−	58.2853i	−1.18752	−	2.05684i
$804$	9.83634	+	36.7097i	0.346901	+	1.29465i
$805$		0			0
$806$	11.9243	−	43.8596i	0.420014	−	1.54489i
$807$	−0.100839	+	0.174659i	−0.00354972	+	0.00614829i
$808$	35.8798	+	35.8798i	1.26225	+	1.26225i
$809$	40.7796			1.43373			0.716867	−	0.697210i	$-0.245575\pi$
$809$	40.7796			1.43373			0.716867	+	0.697210i	$0.245575\pi$
$810$	−14.4962			−0.509345
$811$	−2.15658	−	2.15658i	−0.0757278	−	0.0757278i	0.668228	−	0.743956i	$-0.267053\pi$
$811$	−2.15658	−	2.15658i	−0.0757278	−	0.0757278i	−0.743956	+	0.668228i	$0.767053\pi$
$812$		0			0
$813$	−0.776086	+	2.89639i	−0.0272185	+	0.101581i
$814$	6.04195	−	1.61894i	0.211770	−	0.0567437i
$815$	2.80102	+	1.61717i	0.0981153	+	0.0566469i
$816$			3.11395i			0.109010i
$817$	−15.2863	−	4.09596i	−0.534801	−	0.143299i
$818$	0.854311			0.0298703
$819$		0			0
$820$	60.1238			2.09961
$821$	−36.0893	−	9.67009i	−1.25952	−	0.337488i	−0.433516	−	0.901146i	$-0.642727\pi$
$821$	−36.0893	−	9.67009i	−1.25952	−	0.337488i	−0.826009	+	0.563658i	$0.809394\pi$
$822$			18.7753i			0.654863i
$823$	−31.8883	−	18.4107i	−1.11156	−	0.641757i	−0.172324	−	0.985040i	$-0.555128\pi$
$823$	−31.8883	−	18.4107i	−1.11156	−	0.641757i	−0.939232	+	0.343283i	$0.888461\pi$
$824$	−22.6874	+	6.07906i	−0.790352	+	0.211774i
$825$	6.85105	−	25.5685i	0.238523	−	0.890179i
$826$		0			0
$827$	−16.2525	−	16.2525i	−0.565154	−	0.565154i	0.365613	−	0.930767i	$-0.380859\pi$
$827$	−16.2525	−	16.2525i	−0.565154	−	0.565154i	−0.930767	+	0.365613i	$0.880859\pi$
$828$	29.3241			1.01908
$829$	13.7217			0.476575			0.238287	−	0.971195i	$-0.423414\pi$
$829$	13.7217			0.476575			0.238287	+	0.971195i	$0.423414\pi$
$830$	38.6376	+	38.6376i	1.34113	+	1.34113i
$831$	−5.12770	+	8.88143i	−0.177878	+	0.308093i
$832$	−10.6256	−	40.2434i	−0.368375	−	1.39519i
$833$		0			0
$834$	16.7390	+	62.4708i	0.579624	+	2.16319i
$835$	−3.22021	−	5.57757i	−0.111440	−	0.193020i
$836$	19.2624	−	33.3634i	0.666203	−	1.15390i
$837$	−28.1591	−	7.54522i	−0.973322	−	0.260801i
$838$	−30.7747	−	30.7747i	−1.06309	−	1.06309i
$839$	−4.02716	−	1.07907i	−0.139033	−	0.0372537i	0.188631	−	0.982048i	$-0.439595\pi$
$839$	−4.02716	−	1.07907i	−0.139033	−	0.0372537i	−0.327664	+	0.944794i	$0.606262\pi$
$840$		0			0
$841$	10.8900	+	18.8620i	0.375517	+	0.650415i
$842$	−60.1565	+	34.7314i	−2.07313	+	1.19692i
$843$	−18.9879	+	18.9879i	−0.653978	+	0.653978i
$844$	−59.7430	+	34.4926i	−2.05644	+	1.18729i
$845$	−29.5322	+	29.1032i	−1.01594	+	1.00118i
$846$		−	24.3630i		−	0.837617i
$847$		0			0
$848$	−6.80403	+	11.7849i	−0.233651	+	0.404696i
$849$		−	11.5188i		−	0.395323i
$850$	−4.57648	+	17.0796i	−0.156972	+	0.585827i
$851$	−0.840114	−	3.13535i	−0.0287987	−	0.107478i
$852$	−26.4067	+	26.4067i	−0.904678	+	0.904678i
$853$	−3.44436	+	3.44436i	−0.117933	+	0.117933i	−0.763610	−	0.645678i	$-0.776575\pi$
$853$	−3.44436	+	3.44436i	−0.117933	+	0.117933i	0.645678	+	0.763610i	$0.276575\pi$
$854$		0			0
$855$	−10.7756	−	6.22130i	−0.368518	−	0.212764i
$856$	8.41490	−	31.4048i	0.287615	−	1.07340i
$857$	−24.3123	−	42.1101i	−0.830491	−	1.43845i	−0.897650	−	0.440710i	$-0.854727\pi$
$857$	−24.3123	−	42.1101i	−0.830491	−	1.43845i	0.0671586	−	0.997742i	$-0.478607\pi$
$858$	−31.0063	+	30.7802i	−1.05854	+	1.05082i
$859$	−21.7355	−	12.5490i	−0.741606	−	0.428167i	0.0810468	−	0.996710i	$-0.474174\pi$
$859$	−21.7355	−	12.5490i	−0.741606	−	0.428167i	−0.822653	+	0.568544i	$0.807507\pi$
$860$	70.0684	−	18.7748i	2.38931	−	0.640214i
$861$		0			0
$862$	19.7898	−	11.4256i	0.674042	−	0.389158i
$863$	13.4540	+	50.2112i	0.457981	+	1.70921i	0.679173	+	0.733978i	$0.262338\pi$
$863$	13.4540	+	50.2112i	0.457981	+	1.70921i	−0.221192	+	0.975230i	$0.570995\pi$
$864$	−17.7720	+	4.76198i	−0.604614	+	0.162006i
$865$	−7.54933	+	2.02284i	−0.256685	+	0.0687785i
$866$	16.7867	+	62.6489i	0.570436	+	2.12890i
$867$	−15.5299	+	8.96618i	−0.527423	+	0.304508i
$868$		0			0
$869$	8.27609	−	2.21757i	0.280747	−	0.0752259i
$870$	21.1279	+	12.1982i	0.716302	+	0.413557i
$871$	15.9013	−	27.3106i	0.538795	−	0.925386i
$872$	8.87970	+	15.3801i	0.300705	+	0.520836i
$873$	2.52802	−	9.43472i	0.0855607	−	0.319317i
$874$	−26.9143	−	15.5390i	−0.910390	−	0.525614i
$875$		0			0
$876$	−48.4768	+	48.4768i	−1.63788	+	1.63788i
$877$	−23.6690	+	23.6690i	−0.799246	+	0.799246i	−0.982977	−	0.183731i	$-0.941183\pi$
$877$	−23.6690	+	23.6690i	−0.799246	+	0.799246i	0.183731	+	0.982977i	$0.441183\pi$
$878$	21.1989	+	79.1153i	0.715428	+	2.67001i
$879$	4.68029	−	17.4671i	0.157862	−	0.589150i
$880$			24.3559i			0.821037i
$881$	−26.0483	+	45.1170i	−0.877590	+	1.52003i	−0.0236116	+	0.999721i	$0.507517\pi$
$881$	−26.0483	+	45.1170i	−0.877590	+	1.52003i	−0.853978	+	0.520309i	$0.825817\pi$
$882$		0			0
$883$		−	22.4598i		−	0.755831i	−0.925840	−	0.377916i	$-0.876641\pi$
$883$		−	22.4598i		−	0.755831i	0.925840	−	0.377916i	$-0.123359\pi$
$884$	13.3235	−	13.2264i	0.448119	−	0.444852i
$885$	6.74468	−	3.89404i	0.226720	−	0.130897i
$886$	13.3477	−	13.3477i	0.448426	−	0.448426i
$887$	−10.3759	+	5.99053i	−0.348389	+	0.201142i	−0.663975	−	0.747754i	$-0.731132\pi$
$887$	−10.3759	+	5.99053i	−0.348389	+	0.201142i	0.315587	+	0.948897i	$0.397799\pi$
$888$	−1.41914	−	2.45801i	−0.0476231	−	0.0824856i
$889$		0			0
$890$	51.0656	+	13.6830i	1.71172	+	0.458655i
$891$	5.77757	+	5.77757i	0.193556	+	0.193556i
$892$	−2.41861	−	0.648066i	−0.0809812	−	0.0216989i
$893$	−8.30469	+	14.3842i	−0.277906	+	0.481347i
$894$	−21.6209	−	37.4485i	−0.723110	−	1.25246i
$895$	−6.19911	−	23.1354i	−0.207213	−	0.773330i
$896$		0			0
$897$	15.9728	+	16.0901i	0.533315	+	0.537231i
$898$	24.0414	−	41.6409i	0.802271	−	1.38957i
$899$	10.1154	+	10.1154i	0.337368	+	0.337368i
$900$	29.0002			0.966675
$901$	10.9512			0.364837
$902$	−37.2513	−	37.2513i	−1.24033	−	1.24033i
$903$		0			0
$904$	19.2993	−	72.0259i	0.641885	−	2.39555i
$905$	15.1980	−	4.07228i	0.505198	−	0.135367i
$906$	17.7311	+	10.2371i	0.589076	+	0.340103i
$907$			0.531924i			0.0176622i	0.999961	+	0.00883112i	$0.00281107\pi$
$907$			0.531924i			0.0176622i	−0.999961	+	0.00883112i	$0.997189\pi$
$908$	18.1553	+	4.86469i	0.602504	+	0.161440i
$909$	−20.7368			−0.687798
$910$		0			0
$911$	2.16430			0.0717065			0.0358532	−	0.999357i	$-0.488585\pi$
$911$	2.16430			0.0717065			0.0358532	+	0.999357i	$0.488585\pi$
$912$	−5.22816	−	1.40088i	−0.173122	−	0.0463878i
$913$		−	30.7986i		−	1.01928i
$914$	2.88191	+	1.66387i	0.0953252	+	0.0550360i
$915$	19.4105	−	5.20103i	0.641691	−	0.171941i
$916$	−0.988776	+	3.69016i	−0.0326701	+	0.121926i
$917$		0			0
$918$	−13.2363	−	13.2363i	−0.436864	−	0.436864i
$919$	−25.8041			−0.851197			−0.425599	−	0.904912i	$-0.639936\pi$
$919$	−25.8041			−0.851197			−0.425599	+	0.904912i	$0.639936\pi$
$920$	63.4558			2.09207
$921$	18.9282	+	18.9282i	0.623705	+	0.623705i
$922$	−22.3812	+	38.7653i	−0.737084	+	1.27667i
$923$	31.0535	+	0.113592i	1.02214	+	0.00373892i
$924$		0			0
$925$	−0.830835	−	3.10072i	−0.0273177	−	0.101951i
$926$	−37.6001	−	65.1252i	−1.23562	−	2.14015i
$927$	4.79941	−	8.31282i	0.157633	−	0.273029i
$928$	8.72084	+	2.33674i	0.286276	+	0.0767073i
$929$	14.6922	+	14.6922i	0.482034	+	0.482034i	0.905781	−	0.423747i	$-0.139285\pi$
$929$	14.6922	+	14.6922i	0.482034	+	0.482034i	−0.423747	+	0.905781i	$0.639285\pi$
$930$	−46.6908	−	12.5108i	−1.53105	−	0.410244i
$931$		0			0
$932$	2.38218	+	4.12605i	0.0780308	+	0.135153i
$933$	−4.05408	+	2.34063i	−0.132725	+	0.0766286i
$934$	47.5314	−	47.5314i	1.55528	−	1.55528i
$935$	16.9746	−	9.80029i	0.555129	−	0.320504i
$936$	−18.4260	−	10.7283i	−0.602273	−	0.350666i
$937$			37.2049i			1.21543i	0.794154	+	0.607716i	$0.207914\pi$
$937$			37.2049i			1.21543i	−0.794154	+	0.607716i	$0.792086\pi$
$938$		0			0
$939$	5.99623	−	10.3858i	0.195680	−	0.338927i
$940$		−	76.1329i		−	2.48318i
$941$	11.5462	−	43.0912i	0.376397	−	1.40473i	−0.474897	−	0.880042i	$-0.657515\pi$
$941$	11.5462	−	43.0912i	0.376397	−	1.40473i	0.851293	−	0.524690i	$-0.175819\pi$
$942$	−14.0010	−	52.2524i	−0.456177	−	1.70247i
$943$	−19.3308	+	19.3308i	−0.629497	+	0.629497i
$944$	−2.57650	+	2.57650i	−0.0838580	+	0.0838580i
$945$		0			0
$946$	−55.0452	−	31.7803i	−1.78967	−	1.03327i
$947$	2.03021	−	7.57686i	0.0659731	−	0.246215i	−0.925062	−	0.379816i	$-0.875987\pi$
$947$	2.03021	−	7.57686i	0.0659731	−	0.246215i	0.991035	+	0.133601i	$0.0426540\pi$
$948$	−4.36387	−	7.55844i	−0.141732	−	0.245487i
$949$	57.0074	+	0.208529i	1.85054	+	0.00676914i
$950$	−26.6170	−	15.3674i	−0.863571	−	0.498583i
$951$	−18.0304	+	4.83124i	−0.584677	+	0.156664i
$952$		0			0
$953$	28.7075	−	16.5743i	0.929926	−	0.536893i	0.0431379	−	0.999069i	$-0.486265\pi$
$953$	28.7075	−	16.5743i	0.929926	−	0.536893i	0.886788	+	0.462176i	$0.152931\pi$
$954$	−7.22651	−	26.9697i	−0.233967	−	0.873176i
$955$	18.7576	−	5.02608i	0.606981	−	0.162640i
$956$	75.0190	−	20.1013i	2.42629	−	0.650122i
$957$	−3.55899	−	13.2823i	−0.115046	−	0.429357i
$958$	7.17194	−	4.14072i	0.231715	−	0.133781i
$959$		0			0
$960$	−42.7573	+	11.4568i	−1.37998	+	0.369766i
$961$	2.30019	+	1.32801i	0.0741995	+	0.0428391i
$962$	−1.39002	+	5.11275i	−0.0448161	+	0.164842i
$963$	6.64355	+	11.5070i	0.214085	+	0.370807i
$964$	3.27528	−	12.2235i	0.105490	−	0.393693i
$965$	−40.0168	−	23.1037i	−1.28818	−	0.743734i
$966$		0			0
$967$	−21.9068	+	21.9068i	−0.704477	+	0.704477i	−0.965368	−	0.260892i	$-0.915984\pi$
$967$	−21.9068	+	21.9068i	−0.704477	+	0.704477i	0.260892	+	0.965368i	$0.415984\pi$
$968$	19.1485	−	19.1485i	0.615456	−	0.615456i
$969$	1.12737	+	4.20741i	0.0362164	+	0.135161i
$970$	12.2808	−	45.8327i	0.394314	−	1.47160i
$971$			20.7070i			0.664518i	0.943188	+	0.332259i	$0.107811\pi$
$971$			20.7070i			0.664518i	−0.943188	+	0.332259i	$0.892189\pi$
$972$	−25.4613	+	44.1003i	−0.816672	+	1.41452i
$973$		0			0
$974$		−	57.5638i		−	1.84446i
$975$	15.7964	+	15.9123i	0.505888	+	0.509603i
$976$	−8.14213	+	4.70086i	−0.260623	+	0.150471i
$977$	−12.6510	+	12.6510i	−0.404740	+	0.404740i	−0.879900	−	0.475159i	$-0.842390\pi$
$977$	−12.6510	+	12.6510i	−0.404740	+	0.404740i	0.475159	+	0.879900i	$0.342390\pi$
$978$	−2.50004	+	1.44340i	−0.0799423	+	0.0461547i
$979$	−14.8991	−	25.8060i	−0.476177	−	0.824763i
$980$		0			0
$981$	−7.01050	−	1.87846i	−0.223828	−	0.0599746i
$982$	10.1391	+	10.1391i	0.323553	+	0.323553i
$983$	−43.2530	−	11.5896i	−1.37955	−	0.369651i	−0.508596	−	0.861006i	$-0.669835\pi$
$983$	−43.2530	−	11.5896i	−1.37955	−	0.369651i	−0.870959	+	0.491355i	$0.836502\pi$
$984$	−11.9522	+	20.7018i	−0.381021	+	0.659948i
$985$	26.7003	+	46.2463i	0.850742	+	1.47353i
$986$	2.37740	+	8.87257i	0.0757117	+	0.282560i
$987$		0			0
$988$	16.2126	+	28.3198i	0.515791	+	0.900971i
$989$	−16.4918	+	28.5646i	−0.524407	+	0.908300i
$990$	−35.3366	−	35.3366i	−1.12307	−	1.12307i
$991$	−25.1560			−0.799105			−0.399553	−	0.916710i	$-0.630835\pi$
$991$	−25.1560			−0.799105			−0.399553	+	0.916710i	$0.630835\pi$
$992$	−17.8886			−0.567964
$993$	−12.4494	−	12.4494i	−0.395071	−	0.395071i
$994$		0			0
$995$	−16.3569	+	61.0449i	−0.518550	+	1.93525i
$996$	−30.3037	+	8.11985i	−0.960209	+	0.257287i
$997$	10.3336	+	5.96610i	0.327268	+	0.188948i	0.654628	−	0.755952i	$-0.272825\pi$
$997$	10.3336	+	5.96610i	0.327268	+	0.188948i	−0.327359	+	0.944900i	$0.606159\pi$
$998$		−	43.3180i		−	1.37121i
$999$	3.28254	+	0.879553i	0.103855	+	0.0278278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.19.2		32
7.2	even	3		91.2.bc.a.6.7	✓	32
7.3	odd	6		637.2.bb.b.227.7		32
7.4	even	3		637.2.bb.b.227.8		32
7.5	odd	6		91.2.bc.a.6.8	yes	32
7.6	odd	2	inner	637.2.x.b.19.1		32
13.11	odd	12		637.2.bb.b.362.7		32
21.2	odd	6		819.2.fm.g.370.1		32
21.5	even	6		819.2.fm.g.370.2		32
91.11	odd	12	inner	637.2.x.b.570.2		32
91.24	even	12	inner	637.2.x.b.570.1		32
91.37	odd	12		91.2.bc.a.76.8	yes	32
91.76	even	12		637.2.bb.b.362.8		32
91.89	even	12		91.2.bc.a.76.7	yes	32
273.89	odd	12		819.2.fm.g.622.1		32
273.128	even	12		819.2.fm.g.622.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.7	✓	32	7.2	even	3
91.2.bc.a.6.8	yes	32	7.5	odd	6
91.2.bc.a.76.7	yes	32	91.89	even	12
91.2.bc.a.76.8	yes	32	91.37	odd	12
637.2.x.b.19.1		32	7.6	odd	2	inner
637.2.x.b.19.2		32	1.1	even	1	trivial
637.2.x.b.570.1		32	91.24	even	12	inner
637.2.x.b.570.2		32	91.11	odd	12	inner
637.2.bb.b.227.7		32	7.3	odd	6
637.2.bb.b.227.8		32	7.4	even	3
637.2.bb.b.362.7		32	13.11	odd	12
637.2.bb.b.362.8		32	91.76	even	12
819.2.fm.g.370.1		32	21.2	odd	6
819.2.fm.g.370.2		32	21.5	even	6
819.2.fm.g.622.1		32	273.89	odd	12
819.2.fm.g.622.2		32	273.128	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.28713 - 0.612835i) q^{2} +1.20226i q^{3} +(3.12335 + 1.80327i) q^{4} +(-3.08075 + 0.825486i) q^{5} +(0.736784 - 2.74971i) q^{6} +(-2.68981 - 2.68981i) q^{8} +1.55458 q^{9} +O(q^{10})\)	\(q+(-2.28713 - 0.612835i) q^{2} +1.20226i q^{3} +(3.12335 + 1.80327i) q^{4} +(-3.08075 + 0.825486i) q^{5} +(0.736784 - 2.74971i) q^{6} +(-2.68981 - 2.68981i) q^{8} +1.55458 q^{9} +7.55197 q^{10} +(-3.00989 - 3.00989i) q^{11} +(-2.16799 + 3.75506i) q^{12} +(3.48609 - 0.920440i) q^{13} +(-0.992444 - 3.70385i) q^{15} +(0.897005 + 1.55366i) q^{16} +(0.721872 - 1.25032i) q^{17} +(-3.55553 - 0.952702i) q^{18} +(1.77447 + 1.77447i) q^{19} +(-11.1108 - 2.97714i) q^{20} +(5.03945 + 8.72858i) q^{22} +(4.52952 - 2.61512i) q^{23} +(3.23384 - 3.23384i) q^{24} +(4.47949 - 2.58624i) q^{25} +(-8.53721 - 0.0312285i) q^{26} +5.47577i q^{27} +(1.34350 - 2.32701i) q^{29} +9.07940i q^{30} +(-1.37793 + 5.14250i) q^{31} +(0.869646 + 3.24556i) q^{32} +(3.61866 - 3.61866i) q^{33} +(-2.41725 + 2.41725i) q^{34} +(4.85550 + 2.80333i) q^{36} +(0.160626 - 0.599466i) q^{37} +(-2.97099 - 5.14591i) q^{38} +(1.10660 + 4.19116i) q^{39} +(10.5070 + 6.06624i) q^{40} +(-5.04879 + 1.35282i) q^{41} +(-5.46143 + 3.15316i) q^{43} +(-3.97331 - 14.8286i) q^{44} +(-4.78929 + 1.28329i) q^{45} +(-11.9622 + 3.20527i) q^{46} +(1.71303 + 6.39313i) q^{47} +(-1.86789 + 1.07843i) q^{48} +(-11.8301 + 3.16987i) q^{50} +(1.50320 + 0.867874i) q^{51} +(12.5481 + 3.41149i) q^{52} +(3.79264 + 6.56904i) q^{53} +(3.35574 - 12.5238i) q^{54} +(11.7574 + 6.78811i) q^{55} +(-2.13337 + 2.13337i) q^{57} +(-4.49884 + 4.49884i) q^{58} +(0.525675 + 1.96185i) q^{59} +(3.57928 - 13.3581i) q^{60} +5.24062i q^{61} +(6.30300 - 10.9171i) q^{62} -11.5440i q^{64} +(-9.97996 + 5.71336i) q^{65} +(-10.4940 + 6.05870i) q^{66} +(6.19777 - 6.19777i) q^{67} +(4.50931 - 2.60345i) q^{68} +(3.14404 + 5.44564i) q^{69} +(8.31929 + 2.22915i) q^{71} +(-4.18153 - 4.18153i) q^{72} +(15.2724 + 4.09222i) q^{73} +(-0.734747 + 1.27262i) q^{74} +(3.10932 + 5.38549i) q^{75} +(2.34245 + 8.74214i) q^{76} +(0.0375447 - 10.2639i) q^{78} +(-1.00643 + 1.74319i) q^{79} +(-4.04597 - 4.04597i) q^{80} -1.91953 q^{81} +12.3763 q^{82} +(5.11623 + 5.11623i) q^{83} +(-1.19179 + 4.44782i) q^{85} +(14.4234 - 3.86473i) q^{86} +(2.79766 + 1.61523i) q^{87} +16.1921i q^{88} +(6.76189 + 1.81184i) q^{89} +11.7402 q^{90} +18.8630 q^{92} +(-6.18260 - 1.65662i) q^{93} -15.6717i q^{94} +(-6.93151 - 4.00191i) q^{95} +(-3.90200 + 1.04554i) q^{96} +(1.62618 - 6.06897i) q^{97} +(-4.67912 - 4.67912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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