LMFDB - Embedded newform 60.7.k.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(13,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.k (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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 66x^{10} + 1601x^{8} + 17520x^{6} + 84208x^{4} + 136704x^{2} + 14400 $ x^12 + 66x^10 + 1601x^8 + 17520x^6 + 84208x^4 + 136704*x^2 + 14400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{10}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.6
Root			$0.336188i$ of defining polynomial
Character	$\chi$	$=$	60.13
Dual form			60.7.k.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 + 11.0227i) q^{3} +(124.791 + 7.22440i) q^{5} +(-434.591 + 434.591i) q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(11.0227 + 11.0227i) q^{3} +(124.791 + 7.22440i) q^{5} +(-434.591 + 434.591i) q^{7} +243.000i q^{9} +1741.85 q^{11} +(-1546.05 - 1546.05i) q^{13} +(1295.90 + 1455.17i) q^{15} +(-4012.73 + 4012.73i) q^{17} +13222.1i q^{19} -9580.74 q^{21} +(-104.299 - 104.299i) q^{23} +(15520.6 + 1803.08i) q^{25} +(-2678.52 + 2678.52i) q^{27} +25650.1i q^{29} +2115.55 q^{31} +(19199.9 + 19199.9i) q^{33} +(-57372.8 + 51093.4i) q^{35} +(7053.23 - 7053.23i) q^{37} -34083.4i q^{39} +5999.41 q^{41} +(-4978.68 - 4978.68i) q^{43} +(-1755.53 + 30324.2i) q^{45} +(133244. - 133244. i) q^{47} -260090. i q^{49} -88462.3 q^{51} +(-163796. - 163796. i) q^{53} +(217367. + 12583.8i) q^{55} +(-145743. + 145743. i) q^{57} +242915. i q^{59} +290038. q^{61} +(-105606. - 105606. i) q^{63} +(-181764. - 204103. i) q^{65} +(282135. - 282135. i) q^{67} -2299.30i q^{69} +340961. q^{71} +(-76398.2 - 76398.2i) q^{73} +(151204. + 190954. i) q^{75} +(-756992. + 756992. i) q^{77} -532850. i q^{79} -59049.0 q^{81} +(-71723.3 - 71723.3i) q^{83} +(-529743. + 471764. i) q^{85} +(-282733. + 282733. i) q^{87} -196530. i q^{89} +1.34380e6 q^{91} +(23319.1 + 23319.1i) q^{93} +(-95521.4 + 1.64999e6i) q^{95} +(-94622.0 + 94622.0i) q^{97} +423269. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) $ 12 * q + 312 * q^5 + 120 * q^7	$ 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) $ 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$4$		0			0
$5$	124.791	+	7.22440i	0.998328	+	0.0577952i
$5$	124.791	+	7.22440i	0.998328	+	0.0577952i
$6$		0			0
$7$	−434.591	+	434.591i	−1.26703	+	1.26703i	−0.319415	+	0.947615i	$0.603486\pi$
$7$	−434.591	+	434.591i	−1.26703	+	1.26703i	−0.947615	+	0.319415i	$0.896514\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	1741.85			1.30868			0.654338	−	0.756202i	$-0.272947\pi$
$11$	1741.85			1.30868			0.654338	+	0.756202i	$0.272947\pi$
$12$		0			0
$13$	−1546.05	−	1546.05i	−0.703711	−	0.703711i	0.261494	−	0.965205i	$-0.415785\pi$
$13$	−1546.05	−	1546.05i	−0.703711	−	0.703711i	−0.965205	+	0.261494i	$0.915785\pi$
$14$		0			0
$15$	1295.90	+	1455.17i	0.383971	+	0.431161i
$16$		0			0
$17$	−4012.73	+	4012.73i	−0.816758	+	0.816758i	−0.985637	−	0.168879i	$-0.945985\pi$
$17$	−4012.73	+	4012.73i	−0.816758	+	0.816758i	0.168879	+	0.985637i	$0.445985\pi$
$18$		0			0
$19$			13222.1i			1.92769i	0.266456	+	0.963847i	$0.414147\pi$
$19$			13222.1i			1.92769i	−0.266456	+	0.963847i	$0.585853\pi$
$20$		0			0
$21$	−9580.74			−1.03453
$22$		0			0
$23$	−104.299	−	104.299i	−0.00857225	−	0.00857225i	0.702808	−	0.711380i	$-0.251929\pi$
$23$	−104.299	−	104.299i	−0.00857225	−	0.00857225i	−0.711380	+	0.702808i	$0.751929\pi$
$24$		0			0
$25$	15520.6	+	1803.08i	0.993319	+	0.115397i
$26$		0			0
$27$	−2678.52	+	2678.52i	−0.136083	+	0.136083i
$28$		0			0
$29$			25650.1i			1.05171i	0.850575	+	0.525853i	$0.176254\pi$
$29$			25650.1i			1.05171i	−0.850575	+	0.525853i	$0.823746\pi$
$30$		0			0
$31$	2115.55			0.0710130			0.0355065	−	0.999369i	$-0.488696\pi$
$31$	2115.55			0.0710130			0.0355065	+	0.999369i	$0.488696\pi$
$32$		0			0
$33$	19199.9	+	19199.9i	0.534265	+	0.534265i
$34$		0			0
$35$	−57372.8	+	51093.4i	−1.33814	+	1.19168i
$36$		0			0
$37$	7053.23	−	7053.23i	0.139246	−	0.139246i	−0.634048	−	0.773294i	$-0.718608\pi$
$37$	7053.23	−	7053.23i	0.139246	−	0.139246i	0.773294	+	0.634048i	$0.218608\pi$
$38$		0			0
$39$		−	34083.4i		−	0.574578i
$40$		0			0
$41$	5999.41			0.0870476			0.0435238	−	0.999052i	$-0.486142\pi$
$41$	5999.41			0.0870476			0.0435238	+	0.999052i	$0.486142\pi$
$42$		0			0
$43$	−4978.68	−	4978.68i	−0.0626194	−	0.0626194i	0.675104	−	0.737723i	$-0.264099\pi$
$43$	−4978.68	−	4978.68i	−0.0626194	−	0.0626194i	−0.737723	+	0.675104i	$0.764099\pi$
$44$		0			0
$45$	−1755.53	+	30324.2i	−0.0192651	+	0.332776i
$46$		0			0
$47$	133244.	−	133244.i	1.28338	−	1.28338i	0.344642	−	0.938734i	$-0.388000\pi$
$47$	133244.	−	133244.i	1.28338	−	1.28338i	0.938734	−	0.344642i	$-0.112000\pi$
$48$		0			0
$49$		−	260090.i		−	2.21073i
$50$		0			0
$51$	−88462.3			−0.666880
$52$		0			0
$53$	−163796.	−	163796.i	−1.10021	−	1.10021i	−0.994385	−	0.105823i	$-0.966252\pi$
$53$	−163796.	−	163796.i	−1.10021	−	1.10021i	−0.105823	−	0.994385i	$-0.533748\pi$
$54$		0			0
$55$	217367.	+	12583.8i	1.30649	+	0.0756352i
$56$		0			0
$57$	−145743.	+	145743.i	−0.786978	+	0.786978i
$58$		0			0
$59$			242915.i			1.18276i	0.806392	+	0.591381i	$0.201417\pi$
$59$			242915.i			1.18276i	−0.806392	+	0.591381i	$0.798583\pi$
$60$		0			0
$61$	290038.			1.27781			0.638904	−	0.769286i	$-0.279388\pi$
$61$	290038.			1.27781			0.638904	+	0.769286i	$0.279388\pi$
$62$		0			0
$63$	−105606.	−	105606.i	−0.422343	−	0.422343i
$64$		0			0
$65$	−181764.	−	204103.i	−0.661864	−	0.743206i
$66$		0			0
$67$	282135.	−	282135.i	0.938063	−	0.938063i	−0.0601272	−	0.998191i	$-0.519151\pi$
$67$	282135.	−	282135.i	0.938063	−	0.938063i	0.998191	+	0.0601272i	$0.0191506\pi$
$68$		0			0
$69$		−	2299.30i		−	0.00699921i
$70$		0			0
$71$	340961.			0.952642			0.476321	−	0.879271i	$-0.341970\pi$
$71$	340961.			0.952642			0.476321	+	0.879271i	$0.341970\pi$
$72$		0			0
$73$	−76398.2	−	76398.2i	−0.196388	−	0.196388i	0.602062	−	0.798450i	$-0.294346\pi$
$73$	−76398.2	−	76398.2i	−0.196388	−	0.196388i	−0.798450	+	0.602062i	$0.794346\pi$
$74$		0			0
$75$	151204.	+	190954.i	0.358410	+	0.452632i
$76$		0			0
$77$	−756992.	+	756992.i	−1.65813	+	1.65813i
$78$		0			0
$79$		−	532850.i		−	1.08075i	−0.841426	−	0.540373i	$-0.818283\pi$
$79$		−	532850.i		−	1.08075i	0.841426	−	0.540373i	$-0.181717\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−71723.3	−	71723.3i	−0.125437	−	0.125437i	0.641601	−	0.767038i	$-0.278270\pi$
$83$	−71723.3	−	71723.3i	−0.125437	−	0.125437i	−0.767038	+	0.641601i	$0.778270\pi$
$84$		0			0
$85$	−529743.	+	471764.i	−0.862598	+	0.768188i
$86$		0			0
$87$	−282733.	+	282733.i	−0.429357	+	0.429357i
$88$		0			0
$89$		−	196530.i		−	0.278778i	−0.990238	−	0.139389i	$-0.955486\pi$
$89$		−	196530.i		−	0.278778i	0.990238	−	0.139389i	$-0.0445139\pi$
$90$		0			0
$91$	1.34380e6			1.78325
$92$		0			0
$93$	23319.1	+	23319.1i	0.0289909	+	0.0289909i
$94$		0			0
$95$	−95521.4	+	1.64999e6i	−0.111411	+	1.92447i
$96$		0			0
$97$	−94622.0	+	94622.0i	−0.103676	+	0.103676i	−0.757042	−	0.653366i	$-0.773356\pi$
$97$	−94622.0	+	94622.0i	−0.103676	+	0.103676i	0.653366	+	0.757042i	$0.273356\pi$
$98$		0			0
$99$			423269.i			0.436226i
$100$		0			0
$101$	−37899.3			−0.0367847			−0.0183924	−	0.999831i	$-0.505855\pi$
$101$	−37899.3			−0.0367847			−0.0183924	+	0.999831i	$0.505855\pi$
$102$		0			0
$103$	745060.	+	745060.i	0.681836	+	0.681836i	0.960414	−	0.278578i	$-0.0898631\pi$
$103$	745060.	+	745060.i	0.681836	+	0.681836i	−0.278578	+	0.960414i	$0.589863\pi$
$104$		0			0
$105$	−1.19559e6	−	69215.1i	−1.03280	−	0.0597906i
$106$		0			0
$107$	−519132.	+	519132.i	−0.423767	+	0.423767i	−0.886498	−	0.462732i	$-0.846869\pi$
$107$	−519132.	+	519132.i	−0.423767	+	0.423767i	0.462732	+	0.886498i	$0.346869\pi$
$108$		0			0
$109$		−	156462.i		−	0.120817i	−0.998174	−	0.0604085i	$-0.980760\pi$
$109$		−	156462.i		−	0.120817i	0.998174	−	0.0604085i	$-0.0192403\pi$
$110$		0			0
$111$	155491.			0.113694
$112$		0			0
$113$	−421885.	−	421885.i	−0.292387	−	0.292387i	0.545635	−	0.838023i	$-0.316288\pi$
$113$	−421885.	−	421885.i	−0.292387	−	0.292387i	−0.838023	+	0.545635i	$0.816288\pi$
$114$		0			0
$115$	−12262.0	−	13769.0i	−0.00806248	−	0.00905335i
$116$		0			0
$117$	375691.	−	375691.i	0.234570	−	0.234570i
$118$		0			0
$119$		−	3.48780e6i		−	2.06971i
$120$		0			0
$121$	1.26248e6			0.712635
$122$		0			0
$123$	66129.7	+	66129.7i	0.0355370	+	0.0355370i
$124$		0			0
$125$	1.92381e6	+	337136.i	0.984990	+	0.172613i
$126$		0			0
$127$	−1.15775e6	+	1.15775e6i	−0.565203	+	0.565203i	−0.930781	−	0.365578i	$-0.880871\pi$
$127$	−1.15775e6	+	1.15775e6i	−0.565203	+	0.565203i	0.365578	+	0.930781i	$0.380871\pi$
$128$		0			0
$129$		−	109757.i		−	0.0511286i
$130$		0			0
$131$	3.27380e6			1.45626			0.728129	−	0.685441i	$-0.240390\pi$
$131$	3.27380e6			1.45626			0.728129	+	0.685441i	$0.240390\pi$
$132$		0			0
$133$	−5.74619e6	−	5.74619e6i	−2.44245	−	2.44245i
$134$		0			0
$135$	−353606.	+	314904.i	−0.143720	+	0.127990i
$136$		0			0
$137$	−610909.	+	610909.i	−0.237583	+	0.237583i	−0.815848	−	0.578266i	$-0.803730\pi$
$137$	−610909.	+	610909.i	−0.237583	+	0.237583i	0.578266	+	0.815848i	$0.303730\pi$
$138$		0			0
$139$			51237.3i			0.0190784i	0.999955	+	0.00953919i	$0.00303647\pi$
$139$			51237.3i			0.0190784i	−0.999955	+	0.00953919i	$0.996964\pi$
$140$		0			0
$141$	2.93742e6			1.04787
$142$		0			0
$143$	−2.69299e6	−	2.69299e6i	−0.920930	−	0.920930i
$144$		0			0
$145$	−185306.	+	3.20090e6i	−0.0607836	+	1.04995i
$146$		0			0
$147$	2.86690e6	−	2.86690e6i	0.902526	−	0.902526i
$148$		0			0
$149$		−	408073.i		−	0.123361i	−0.998096	−	0.0616806i	$-0.980354\pi$
$149$		−	408073.i		−	0.123361i	0.998096	−	0.0616806i	$-0.0196460\pi$
$150$		0			0
$151$	706336.			0.205154			0.102577	−	0.994725i	$-0.467291\pi$
$151$	706336.			0.205154			0.102577	+	0.994725i	$0.467291\pi$
$152$		0			0
$153$	−975094.	−	975094.i	−0.272253	−	0.272253i
$154$		0			0
$155$	264002.	+	15283.6i	0.0708943	+	0.00410421i
$156$		0			0
$157$	619055.	−	619055.i	0.159967	−	0.159967i	−0.622585	−	0.782552i	$-0.713918\pi$
$157$	619055.	−	619055.i	0.159967	−	0.159967i	0.782552	+	0.622585i	$0.213918\pi$
$158$		0			0
$159$		−	3.61094e6i		−	0.898316i
$160$		0			0
$161$	90654.5			0.0217226
$162$		0			0
$163$	4.36371e6	+	4.36371e6i	1.00761	+	1.00761i	0.999971	+	0.00764160i	$0.00243242\pi$
$163$	4.36371e6	+	4.36371e6i	1.00761	+	1.00761i	0.00764160	+	0.999971i	$0.497568\pi$
$164$		0			0
$165$	2.25727e6	+	2.53468e6i	0.502494	+	0.564250i
$166$		0			0
$167$	681741.	−	681741.i	0.146376	−	0.146376i	−0.630121	−	0.776497i	$-0.716995\pi$
$167$	681741.	−	681741.i	0.146376	−	0.146376i	0.776497	+	0.630121i	$0.216995\pi$
$168$		0			0
$169$		−	46246.4i		−	0.00958115i
$170$		0			0
$171$	−3.21296e6			−0.642565
$172$		0			0
$173$	1.82817e6	+	1.82817e6i	0.353083	+	0.353083i	0.861255	−	0.508172i	$-0.169679\pi$
$173$	1.82817e6	+	1.82817e6i	0.353083	+	0.353083i	−0.508172	+	0.861255i	$0.669679\pi$
$174$		0			0
$175$	−7.52873e6	+	5.96152e6i	−1.40478	+	1.11235i
$176$		0			0
$177$	−2.67758e6	+	2.67758e6i	−0.482861	+	0.482861i
$178$		0			0
$179$			3.53033e6i			0.615539i	0.951461	+	0.307770i	$0.0995826\pi$
$179$			3.53033e6i			0.615539i	−0.951461	+	0.307770i	$0.900417\pi$
$180$		0			0
$181$	−8.33482e6			−1.40560			−0.702798	−	0.711390i	$-0.748066\pi$
$181$	−8.33482e6			−1.40560			−0.702798	+	0.711390i	$0.748066\pi$
$182$		0			0
$183$	3.19700e6	+	3.19700e6i	0.521663	+	0.521663i
$184$		0			0
$185$	931135.	−	829225.i	0.147061	−	0.130966i
$186$		0			0
$187$	−6.98957e6	+	6.98957e6i	−1.06887	+	1.06887i
$188$		0			0
$189$		−	2.32812e6i		−	0.344842i
$190$		0			0
$191$	7.56249e6			1.08534			0.542669	−	0.839947i	$-0.317414\pi$
$191$	7.56249e6			1.08534			0.542669	+	0.839947i	$0.317414\pi$
$192$		0			0
$193$	4.08318e6	+	4.08318e6i	0.567971	+	0.567971i	0.931560	−	0.363588i	$-0.118449\pi$
$193$	4.08318e6	+	4.08318e6i	0.567971	+	0.567971i	−0.363588	+	0.931560i	$0.618449\pi$
$194$		0			0
$195$	246232.	−	4.25330e6i	0.0332078	−	0.573617i
$196$		0			0
$197$	5.88513e6	−	5.88513e6i	0.769763	−	0.769763i	−0.208301	−	0.978065i	$-0.566793\pi$
$197$	5.88513e6	−	5.88513e6i	0.769763	−	0.769763i	0.978065	+	0.208301i	$0.0667935\pi$
$198$		0			0
$199$		−	1.95912e6i		−	0.248600i	−0.992245	−	0.124300i	$-0.960331\pi$
$199$		−	1.95912e6i		−	0.248600i	0.992245	−	0.124300i	$-0.0396685\pi$
$200$		0			0
$201$	6.21978e6			0.765926
$202$		0			0
$203$	−1.11473e7	−	1.11473e7i	−1.33254	−	1.33254i
$204$		0			0
$205$	748672.	+	43342.1i	0.0869021	+	0.00503093i
$206$		0			0
$207$	25344.5	−	25344.5i	0.00285742	−	0.00285742i
$208$		0			0
$209$			2.30308e7i			2.52273i
$210$		0			0
$211$	−9.61679e6			−1.02372			−0.511862	−	0.859068i	$-0.671044\pi$
$211$	−9.61679e6			−1.02372			−0.511862	+	0.859068i	$0.671044\pi$
$212$		0			0
$213$	3.75831e6	+	3.75831e6i	0.388915	+	0.388915i
$214$		0			0
$215$	−585327.	−	657263.i	−0.0588957	−	0.0661339i
$216$		0			0
$217$	−919399.	+	919399.i	−0.0899756	+	0.0899756i
$218$		0			0
$219$		−	1.68423e6i		−	0.160350i
$220$		0			0
$221$	1.24078e7			1.14952
$222$		0			0
$223$	4.72258e6	+	4.72258e6i	0.425858	+	0.425858i	0.887215	−	0.461357i	$-0.152637\pi$
$223$	4.72258e6	+	4.72258e6i	0.425858	+	0.425858i	−0.461357	+	0.887215i	$0.652637\pi$
$224$		0			0
$225$	−438149.	+	3.77151e6i	−0.0384657	+	0.331106i
$226$		0			0
$227$	−1.39551e7	+	1.39551e7i	−1.19304	+	1.19304i	−0.216832	+	0.976209i	$0.569572\pi$
$227$	−1.39551e7	+	1.39551e7i	−1.19304	+	1.19304i	−0.976209	+	0.216832i	$0.930428\pi$
$228$		0			0
$229$		−	8.51729e6i		−	0.709243i	−0.935010	−	0.354621i	$-0.884610\pi$
$229$		−	8.51729e6i		−	0.709243i	0.935010	−	0.354621i	$-0.115390\pi$
$230$		0			0
$231$	−1.66882e7			−1.35386
$232$		0			0
$233$	−3.61223e6	−	3.61223e6i	−0.285567	−	0.285567i	0.549758	−	0.835324i	$-0.314720\pi$
$233$	−3.61223e6	−	3.61223e6i	−0.285567	−	0.285567i	−0.835324	+	0.549758i	$0.814720\pi$
$234$		0			0
$235$	1.75903e7	−	1.56650e7i	1.35540	−	1.20706i
$236$		0			0
$237$	5.87345e6	−	5.87345e6i	0.441213	−	0.441213i
$238$		0			0
$239$		−	1.17894e7i		−	0.863573i	−0.901976	−	0.431787i	$-0.857883\pi$
$239$		−	1.17894e7i		−	0.863573i	0.901976	−	0.431787i	$-0.142117\pi$
$240$		0			0
$241$	1.80995e7			1.29305			0.646527	−	0.762891i	$-0.276221\pi$
$241$	1.80995e7			1.29305			0.646527	+	0.762891i	$0.276221\pi$
$242$		0			0
$243$	−650880.	−	650880.i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	1.87899e6	−	3.24569e7i	0.127770	−	2.20703i
$246$		0			0
$247$	2.04420e7	−	2.04420e7i	1.35654	−	1.35654i
$248$		0			0
$249$		−	1.58117e6i		−	0.102419i
$250$		0			0
$251$	−2.50841e7			−1.58627			−0.793136	−	0.609045i	$-0.791553\pi$
$251$	−2.50841e7			−1.58627			−0.793136	+	0.609045i	$0.791553\pi$
$252$		0			0
$253$	−181672.	−	181672.i	−0.0112183	−	0.0112183i
$254$		0			0
$255$	−1.10393e7	−	639087.i	−0.665766	−	0.0385425i
$256$		0			0
$257$	−1.37054e6	+	1.37054e6i	−0.0807409	+	0.0807409i	−0.746324	−	0.665583i	$-0.768183\pi$
$257$	−1.37054e6	+	1.37054e6i	−0.0807409	+	0.0807409i	0.665583	+	0.746324i	$0.268183\pi$
$258$		0			0
$259$			6.13054e6i			0.352858i
$260$		0			0
$261$	−6.23297e6			−0.350569
$262$		0			0
$263$	9.00140e6	+	9.00140e6i	0.494815	+	0.494815i	0.909819	−	0.415005i	$-0.136220\pi$
$263$	9.00140e6	+	9.00140e6i	0.494815	+	0.494815i	−0.415005	+	0.909819i	$0.636220\pi$
$264$		0			0
$265$	−1.92569e7	−	2.16236e7i	−1.03478	−	1.16196i
$266$		0			0
$267$	2.16629e6	−	2.16629e6i	0.113811	−	0.113811i
$268$		0			0
$269$			1.32739e7i			0.681934i	0.940075	+	0.340967i	$0.110754\pi$
$269$			1.32739e7i			0.681934i	−0.940075	+	0.340967i	$0.889246\pi$
$270$		0			0
$271$	−2.09347e7			−1.05186			−0.525931	−	0.850527i	$-0.676283\pi$
$271$	−2.09347e7			−1.05186			−0.525931	+	0.850527i	$0.676283\pi$
$272$		0			0
$273$	1.48123e7	+	1.48123e7i	0.728007	+	0.728007i
$274$		0			0
$275$	2.70346e7	+	3.14069e6i	1.29993	+	0.151018i
$276$		0			0
$277$	2.07887e7	−	2.07887e7i	0.978110	−	0.978110i	−0.0216554	−	0.999765i	$-0.506894\pi$
$277$	2.07887e7	−	2.07887e7i	0.978110	−	0.978110i	0.999765	+	0.0216554i	$0.00689365\pi$
$278$		0			0
$279$			514078.i			0.0236710i
$280$		0			0
$281$	−2.31495e7			−1.04333			−0.521666	−	0.853150i	$-0.674689\pi$
$281$	−2.31495e7			−1.04333			−0.521666	+	0.853150i	$0.674689\pi$
$282$		0			0
$283$	1.72171e7	+	1.72171e7i	0.759626	+	0.759626i	0.976254	−	0.216629i	$-0.0695060\pi$
$283$	1.72171e7	+	1.72171e7i	0.759626	+	0.759626i	−0.216629	+	0.976254i	$0.569506\pi$
$284$		0			0
$285$	−1.92403e7	+	1.71345e7i	−0.831146	+	0.740179i
$286$		0			0
$287$	−2.60729e6	+	2.60729e6i	−0.110292	+	0.110292i
$288$		0			0
$289$		−	8.06648e6i		−	0.334188i
$290$		0			0
$291$	−2.08598e6			−0.0846509
$292$		0			0
$293$	1.22374e7	+	1.22374e7i	0.486504	+	0.486504i	0.907201	−	0.420697i	$-0.138215\pi$
$293$	1.22374e7	+	1.22374e7i	0.486504	+	0.486504i	−0.420697	+	0.907201i	$0.638215\pi$
$294$		0			0
$295$	−1.75491e6	+	3.03136e7i	−0.0683580	+	1.18079i
$296$		0			0
$297$	−4.66557e6	+	4.66557e6i	−0.178088	+	0.178088i
$298$		0			0
$299$			322502.i			0.0120648i
$300$		0			0
$301$	4.32738e6			0.158681
$302$		0			0
$303$	−417753.	−	417753.i	−0.0150173	−	0.0150173i
$304$		0			0
$305$	3.61942e7	+	2.09535e6i	1.27567	+	0.0738512i
$306$		0			0
$307$	1.77106e7	−	1.77106e7i	0.612095	−	0.612095i	−0.331397	−	0.943492i	$-0.607520\pi$
$307$	1.77106e7	−	1.77106e7i	0.612095	−	0.612095i	0.943492	+	0.331397i	$0.107520\pi$
$308$		0			0
$309$			1.64252e7i			0.556717i
$310$		0			0
$311$	−3.27320e7			−1.08816			−0.544078	−	0.839035i	$-0.683120\pi$
$311$	−3.27320e7			−1.08816			−0.544078	+	0.839035i	$0.683120\pi$
$312$		0			0
$313$	6.21365e6	+	6.21365e6i	0.202635	+	0.202635i	0.801128	−	0.598493i	$-0.204234\pi$
$313$	6.21365e6	+	6.21365e6i	0.202635	+	0.202635i	−0.598493	+	0.801128i	$0.704234\pi$
$314$		0			0
$315$	−1.24157e7	−	1.39416e7i	−0.397228	−	0.446047i
$316$		0			0
$317$	−2.97274e7	+	2.97274e7i	−0.933209	+	0.933209i	−0.997905	−	0.0646964i	$-0.979392\pi$
$317$	−2.97274e7	+	2.97274e7i	−0.933209	+	0.933209i	0.0646964	+	0.997905i	$0.479392\pi$
$318$		0			0
$319$			4.46785e7i			1.37634i
$320$		0			0
$321$	−1.14445e7			−0.346004
$322$		0			0
$323$	−5.30566e7	−	5.30566e7i	−1.57446	−	1.57446i
$324$		0			0
$325$	−2.12080e7	−	2.67834e7i	−0.617804	−	0.780216i
$326$		0			0
$327$	1.72463e6	−	1.72463e6i	0.0493233	−	0.0493233i
$328$		0			0
$329$			1.15813e8i			3.25215i
$330$		0			0
$331$	1.83615e7			0.506319			0.253160	−	0.967425i	$-0.418530\pi$
$331$	1.83615e7			0.506319			0.253160	+	0.967425i	$0.418530\pi$
$332$		0			0
$333$	1.71393e6	+	1.71393e6i	0.0464153	+	0.0464153i
$334$		0			0
$335$	3.72462e7	−	3.31696e7i	0.990711	−	0.882280i
$336$		0			0
$337$	6.12610e6	−	6.12610e6i	0.160064	−	0.160064i	−0.622531	−	0.782595i	$-0.713896\pi$
$337$	6.12610e6	−	6.12610e6i	0.160064	−	0.160064i	0.782595	+	0.622531i	$0.213896\pi$
$338$		0			0
$339$		−	9.30063e6i		−	0.238733i
$340$		0			0
$341$	3.68497e6			0.0929331
$342$		0			0
$343$	6.19036e7	+	6.19036e7i	1.53403	+	1.53403i
$344$		0			0
$345$	16611.1	−	286933.i	0.000404521	−	0.00698751i
$346$		0			0
$347$	−3.34832e7	+	3.34832e7i	−0.801381	+	0.801381i	−0.983311	−	0.181931i	$-0.941765\pi$
$347$	−3.34832e7	+	3.34832e7i	−0.801381	+	0.801381i	0.181931	+	0.983311i	$0.441765\pi$
$348$		0			0
$349$		−	6.34970e7i		−	1.49375i	−0.664966	−	0.746873i	$-0.731554\pi$
$349$		−	6.34970e7i		−	1.49375i	0.664966	−	0.746873i	$-0.268446\pi$
$350$		0			0
$351$	8.28226e6			0.191526
$352$		0			0
$353$	−3.69832e7	−	3.69832e7i	−0.840776	−	0.840776i	0.148184	−	0.988960i	$-0.452657\pi$
$353$	−3.69832e7	−	3.69832e7i	−0.840776	−	0.840776i	−0.988960	+	0.148184i	$0.952657\pi$
$354$		0			0
$355$	4.25489e7	+	2.46324e6i	0.951050	+	0.0550581i
$356$		0			0
$357$	3.84450e7	−	3.84450e7i	0.844957	−	0.844957i
$358$		0			0
$359$		−	2.07094e7i		−	0.447593i	−0.974636	−	0.223797i	$-0.928155\pi$
$359$		−	2.07094e7i		−	0.447593i	0.974636	−	0.223797i	$-0.0718451\pi$
$360$		0			0
$361$	−1.27777e8			−2.71600
$362$		0			0
$363$	1.39159e7	+	1.39159e7i	0.290932	+	0.290932i
$364$		0			0
$365$	−8.98188e6	−	1.00857e7i	−0.184709	−	0.207410i
$366$		0			0
$367$	−2.49832e7	+	2.49832e7i	−0.505416	+	0.505416i	−0.913116	−	0.407700i	$-0.866331\pi$
$367$	−2.49832e7	+	2.49832e7i	−0.505416	+	0.505416i	0.407700	+	0.913116i	$0.366331\pi$
$368$		0			0
$369$			1.45786e6i			0.0290159i
$370$		0			0
$371$	1.42368e8			2.78799
$372$		0			0
$373$	−4.40738e7	−	4.40738e7i	−0.849285	−	0.849285i	0.140759	−	0.990044i	$-0.455046\pi$
$373$	−4.40738e7	−	4.40738e7i	−0.849285	−	0.849285i	−0.990044	+	0.140759i	$0.955046\pi$
$374$		0			0
$375$	1.74894e7	+	2.49217e7i	0.331651	+	0.472589i
$376$		0			0
$377$	3.96564e7	−	3.96564e7i	0.740098	−	0.740098i
$378$		0			0
$379$		−	4.46118e7i		−	0.819468i	−0.912205	−	0.409734i	$-0.865622\pi$
$379$		−	4.46118e7i		−	0.819468i	0.912205	−	0.409734i	$-0.134378\pi$
$380$		0			0
$381$	−2.55231e7			−0.461487
$382$		0			0
$383$	1.25472e7	+	1.25472e7i	0.223332	+	0.223332i	0.809900	−	0.586568i	$-0.199521\pi$
$383$	1.25472e7	+	1.25472e7i	0.223332	+	0.223332i	−0.586568	+	0.809900i	$0.699521\pi$
$384$		0			0
$385$	−9.99347e7	+	8.89970e7i	−1.75119	+	1.55953i
$386$		0			0
$387$	1.20982e6	−	1.20982e6i	0.0208731	−	0.0208731i
$388$		0			0
$389$		−	8.26003e7i		−	1.40324i	−0.712550	−	0.701622i	$-0.752460\pi$
$389$		−	8.26003e7i		−	1.40324i	0.712550	−	0.701622i	$-0.247540\pi$
$390$		0			0
$391$	837044.			0.0140029
$392$		0			0
$393$	3.60861e7	+	3.60861e7i	0.594514	+	0.594514i
$394$		0			0
$395$	3.84952e6	−	6.64949e7i	0.0624619	−	1.07894i
$396$		0			0
$397$	3.16157e7	−	3.16157e7i	0.505280	−	0.505280i	−0.407794	−	0.913074i	$-0.633702\pi$
$397$	3.16157e7	−	3.16157e7i	0.505280	−	0.505280i	0.913074	+	0.407794i	$0.133702\pi$
$398$		0			0
$399$		−	1.26677e8i		−	1.99425i
$400$		0			0
$401$	1.16278e8			1.80329			0.901645	−	0.432476i	$-0.142360\pi$
$401$	1.16278e8			1.80329			0.901645	+	0.432476i	$0.142360\pi$
$402$		0			0
$403$	−3.27075e6	−	3.27075e6i	−0.0499727	−	0.0499727i
$404$		0			0
$405$	−7.36879e6	−	426594.i	−0.110925	−	0.00642169i
$406$		0			0
$407$	1.22857e7	−	1.22857e7i	0.182228	−	0.182228i
$408$		0			0
$409$			4.33273e7i			0.633274i	0.948547	+	0.316637i	$0.102554\pi$
$409$			4.33273e7i			0.633274i	−0.948547	+	0.316637i	$0.897446\pi$
$410$		0			0
$411$	−1.34677e7			−0.193985
$412$		0			0
$413$	−1.05569e8	−	1.05569e8i	−1.49860	−	1.49860i
$414$		0			0
$415$	−8.43227e6	−	9.46859e6i	−0.117978	−	0.132477i
$416$		0			0
$417$	−564773.	+	564773.i	−0.00778872	+	0.00778872i
$418$		0			0
$419$			9.71526e7i			1.32073i	0.750947	+	0.660363i	$0.229597\pi$
$419$			9.71526e7i			1.32073i	−0.750947	+	0.660363i	$0.770403\pi$
$420$		0			0
$421$	1.00395e8			1.34545			0.672723	−	0.739895i	$-0.265125\pi$
$421$	1.00395e8			1.34545			0.672723	+	0.739895i	$0.265125\pi$
$422$		0			0
$423$	3.23783e7	+	3.23783e7i	0.427792	+	0.427792i
$424$		0			0
$425$	−6.95154e7	+	5.50448e7i	−0.905553	+	0.717050i
$426$		0			0
$427$	−1.26048e8	+	1.26048e8i	−1.61902	+	1.61902i
$428$		0			0
$429$		−	5.93681e7i		−	0.751937i
$430$		0			0
$431$	−7.69779e7			−0.961467			−0.480733	−	0.876867i	$-0.659629\pi$
$431$	−7.69779e7			−0.961467			−0.480733	+	0.876867i	$0.659629\pi$
$432$		0			0
$433$	3.09209e7	+	3.09209e7i	0.380880	+	0.380880i	0.871419	−	0.490539i	$-0.163200\pi$
$433$	3.09209e7	+	3.09209e7i	0.380880	+	0.380880i	−0.490539	+	0.871419i	$0.663200\pi$
$434$		0			0
$435$	−3.73251e7	+	3.32400e7i	−0.453454	+	0.403825i
$436$		0			0
$437$	1.37904e6	−	1.37904e6i	0.0165247	−	0.0165247i
$438$		0			0
$439$		−	1.59163e8i		−	1.88126i	−0.339429	−	0.940632i	$-0.610234\pi$
$439$		−	1.59163e8i		−	1.88126i	0.339429	−	0.940632i	$-0.389766\pi$
$440$		0			0
$441$	6.32019e7			0.736910
$442$		0			0
$443$	−1.73843e7	−	1.73843e7i	−0.199961	−	0.199961i	0.600022	−	0.799983i	$-0.295158\pi$
$443$	−1.73843e7	−	1.73843e7i	−0.199961	−	0.199961i	−0.799983	+	0.600022i	$0.795158\pi$
$444$		0			0
$445$	1.41981e6	−	2.45252e7i	0.0161120	−	0.278312i
$446$		0			0
$447$	4.49807e6	−	4.49807e6i	0.0503620	−	0.0503620i
$448$		0			0
$449$			4.63392e7i			0.511928i	0.966686	+	0.255964i	$0.0823929\pi$
$449$			4.63392e7i			0.511928i	−0.966686	+	0.255964i	$0.917607\pi$
$450$		0			0
$451$	1.04501e7			0.113917
$452$		0			0
$453$	7.78574e6	+	7.78574e6i	0.0837539	+	0.0837539i
$454$		0			0
$455$	1.67695e8	+	9.70817e6i	1.78027	+	0.103063i
$456$		0			0
$457$	−6.61841e7	+	6.61841e7i	−0.693433	+	0.693433i	−0.962986	−	0.269552i	$-0.913124\pi$
$457$	−6.61841e7	+	6.61841e7i	−0.693433	+	0.693433i	0.269552	+	0.962986i	$0.413124\pi$
$458$		0			0
$459$		−	2.14963e7i		−	0.222293i
$460$		0			0
$461$	1.27007e8			1.29636			0.648180	−	0.761487i	$-0.275530\pi$
$461$	1.27007e8			1.29636			0.648180	+	0.761487i	$0.275530\pi$
$462$		0			0
$463$	−3.12465e7	−	3.12465e7i	−0.314817	−	0.314817i	0.531955	−	0.846772i	$-0.321457\pi$
$463$	−3.12465e7	−	3.12465e7i	−0.314817	−	0.314817i	−0.846772	+	0.531955i	$0.821457\pi$
$464$		0			0
$465$	2.74155e6	+	3.07848e6i	0.0272670	+	0.0306180i
$466$		0			0
$467$	−7.46043e7	+	7.46043e7i	−0.732509	+	0.732509i	−0.971116	−	0.238607i	$-0.923309\pi$
$467$	−7.46043e7	+	7.46043e7i	−0.732509	+	0.732509i	0.238607	+	0.971116i	$0.423309\pi$
$468$		0			0
$469$			2.45227e8i			2.37711i
$470$		0			0
$471$	1.36473e7			0.130613
$472$		0			0
$473$	−8.67211e6	−	8.67211e6i	−0.0819486	−	0.0819486i
$474$		0			0
$475$	−2.38404e7	+	2.05214e8i	−0.222450	+	1.91482i
$476$		0			0
$477$	3.98023e7	−	3.98023e7i	0.366736	−	0.366736i
$478$		0			0
$479$			1.25186e8i			1.13907i	0.821967	+	0.569535i	$0.192877\pi$
$479$			1.25186e8i			1.13907i	−0.821967	+	0.569535i	$0.807123\pi$
$480$		0			0
$481$	−2.18093e7			−0.195978
$482$		0			0
$483$	999257.	+	999257.i	0.00886821	+	0.00886821i
$484$		0			0
$485$	−1.24916e7	+	1.11244e7i	−0.109494	+	0.0975105i
$486$		0			0
$487$	−1.78483e7	+	1.78483e7i	−0.154529	+	0.154529i	−0.780137	−	0.625608i	$-0.784851\pi$
$487$	−1.78483e7	+	1.78483e7i	−0.154529	+	0.154529i	0.625608	+	0.780137i	$0.284851\pi$
$488$		0			0
$489$			9.61999e7i			0.822712i
$490$		0			0
$491$	−7.87160e6			−0.0664996			−0.0332498	−	0.999447i	$-0.510586\pi$
$491$	−7.87160e6			−0.0664996			−0.0332498	+	0.999447i	$0.510586\pi$
$492$		0			0
$493$	−1.02927e8	−	1.02927e8i	−0.858990	−	0.858990i
$494$		0			0
$495$	−3.05787e6	+	5.28202e7i	−0.0252117	+	0.435496i
$496$		0			0
$497$	−1.48179e8	+	1.48179e8i	−1.20703	+	1.20703i
$498$		0			0
$499$		−	2.04122e8i		−	1.64282i	−0.570341	−	0.821408i	$-0.693189\pi$
$499$		−	2.04122e8i		−	1.64282i	0.570341	−	0.821408i	$-0.306811\pi$
$500$		0			0
$501$	1.50293e7			0.119516
$502$		0			0
$503$	−1.31448e8	−	1.31448e8i	−1.03288	−	1.03288i	−0.999441	−	0.0334411i	$-0.989353\pi$
$503$	−1.31448e8	−	1.31448e8i	−1.03288	−	1.03288i	−0.0334411	−	0.999441i	$-0.510647\pi$
$504$		0			0
$505$	−4.72950e6	−	273800.i	−0.0367232	−	0.00212598i
$506$		0			0
$507$	509760.	−	509760.i	0.00391149	−	0.00391149i
$508$		0			0
$509$		−	1.09172e8i		−	0.827864i	−0.910308	−	0.413932i	$-0.864155\pi$
$509$		−	1.09172e8i		−	0.827864i	0.910308	−	0.413932i	$-0.135845\pi$
$510$		0			0
$511$	6.64040e7			0.497658
$512$		0			0
$513$	−3.54155e7	−	3.54155e7i	−0.262326	−	0.262326i
$514$		0			0
$515$	8.75942e7	+	9.83595e7i	0.641289	+	0.720103i
$516$		0			0
$517$	2.32091e8	−	2.32091e8i	1.67952	−	1.67952i
$518$		0			0
$519$			4.03026e7i			0.288291i
$520$		0			0
$521$	2.04975e8			1.44940			0.724699	−	0.689065i	$-0.241979\pi$
$521$	2.04975e8			1.44940			0.724699	+	0.689065i	$0.241979\pi$
$522$		0			0
$523$	8.95018e7	+	8.95018e7i	0.625643	+	0.625643i	0.946969	−	0.321325i	$-0.104128\pi$
$523$	8.95018e7	+	8.95018e7i	0.625643	+	0.625643i	−0.321325	+	0.946969i	$0.604128\pi$
$524$		0			0
$525$	−1.48699e8	−	1.72749e7i	−1.02761	−	0.119381i
$526$		0			0
$527$	−8.48913e6	+	8.48913e6i	−0.0580005	+	0.0580005i
$528$		0			0
$529$		−	1.48014e8i		−	0.999853i
$530$		0			0
$531$	−5.90282e7			−0.394254
$532$		0			0
$533$	−9.27540e6	−	9.27540e6i	−0.0612564	−	0.0612564i
$534$		0			0
$535$	−6.85335e7	+	6.10327e7i	−0.447550	+	0.398567i
$536$		0			0
$537$	−3.89138e7	+	3.89138e7i	−0.251293	+	0.251293i
$538$		0			0
$539$		−	4.53037e8i		−	2.89313i
$540$		0			0
$541$	8.89006e7			0.561452			0.280726	−	0.959788i	$-0.409425\pi$
$541$	8.89006e7			0.561452			0.280726	+	0.959788i	$0.409425\pi$
$542$		0			0
$543$	−9.18722e7	−	9.18722e7i	−0.573832	−	0.573832i
$544$		0			0
$545$	1.13034e6	−	1.95250e7i	0.00698264	−	0.120615i
$546$		0			0
$547$	1.51070e8	−	1.51070e8i	0.923032	−	0.923032i	−0.0742109	−	0.997243i	$-0.523644\pi$
$547$	1.51070e8	−	1.51070e8i	0.923032	−	0.923032i	0.997243	+	0.0742109i	$0.0236438\pi$
$548$		0			0
$549$			7.04793e7i			0.425936i
$550$		0			0
$551$	−3.39147e8			−2.02737
$552$		0			0
$553$	2.31572e8	+	2.31572e8i	1.36934	+	1.36934i
$554$		0			0
$555$	1.94039e7	+	1.12333e6i	0.113504	+	0.00657096i
$556$		0			0
$557$	−4.19535e7	+	4.19535e7i	−0.242774	+	0.242774i	−0.817997	−	0.575223i	$-0.804915\pi$
$557$	−4.19535e7	+	4.19535e7i	−0.242774	+	0.242774i	0.575223	+	0.817997i	$0.304915\pi$
$558$		0			0
$559$			1.53946e7i			0.0881320i
$560$		0			0
$561$	−1.54088e8			−0.872731
$562$		0			0
$563$	1.45051e8	+	1.45051e8i	0.812821	+	0.812821i	0.985056	−	0.172235i	$-0.0550987\pi$
$563$	1.45051e8	+	1.45051e8i	0.812821	+	0.812821i	−0.172235	+	0.985056i	$0.555099\pi$
$564$		0			0
$565$	−4.95996e7	−	5.56953e7i	−0.275000	−	0.308797i
$566$		0			0
$567$	2.56622e7	−	2.56622e7i	0.140781	−	0.140781i
$568$		0			0
$569$			2.03261e8i			1.10336i	0.834055	+	0.551681i	$0.186013\pi$
$569$			2.03261e8i			1.10336i	−0.834055	+	0.551681i	$0.813987\pi$
$570$		0			0
$571$	−4.99009e7			−0.268040			−0.134020	−	0.990979i	$-0.542789\pi$
$571$	−4.99009e7			−0.268040			−0.134020	+	0.990979i	$0.542789\pi$
$572$		0			0
$573$	8.33591e7	+	8.33591e7i	0.443087	+	0.443087i
$574$		0			0
$575$	−1.43072e6	−	1.80684e6i	−0.00752577	−	0.00950419i
$576$		0			0
$577$	2.44010e8	−	2.44010e8i	1.27023	−	1.27023i	0.324257	−	0.945969i	$-0.394886\pi$
$577$	2.44010e8	−	2.44010e8i	1.27023	−	1.27023i	0.945969	−	0.324257i	$-0.105114\pi$
$578$		0			0
$579$			9.00153e7i			0.463747i
$580$		0			0
$581$	6.23406e7			0.317865
$582$		0			0
$583$	−2.85307e8	−	2.85307e8i	−1.43982	−	1.43982i
$584$		0			0
$585$	4.95970e7	−	4.41687e7i	0.247735	−	0.220621i
$586$		0			0
$587$	8.15126e7	−	8.15126e7i	0.403005	−	0.403005i	−0.476286	−	0.879291i	$-0.658017\pi$
$587$	8.15126e7	−	8.15126e7i	0.403005	−	0.403005i	0.879291	+	0.476286i	$0.158017\pi$
$588$		0			0
$589$			2.79719e7i			0.136891i
$590$		0			0
$591$	1.29740e8			0.628509
$592$		0			0
$593$	−2.02160e8	−	2.02160e8i	−0.969461	−	0.969461i	0.0300859	−	0.999547i	$-0.490422\pi$
$593$	−2.02160e8	−	2.02160e8i	−0.969461	−	0.969461i	−0.999547	+	0.0300859i	$0.990422\pi$
$594$		0			0
$595$	2.51972e7	−	4.35246e8i	0.119620	−	2.06625i
$596$		0			0
$597$	2.15948e7	−	2.15948e7i	0.101491	−	0.101491i
$598$		0			0
$599$			2.48856e8i			1.15789i	0.815366	+	0.578946i	$0.196536\pi$
$599$			2.48856e8i			1.15789i	−0.815366	+	0.578946i	$0.803464\pi$
$600$		0			0
$601$	3.83838e8			1.76817			0.884087	−	0.467323i	$-0.154782\pi$
$601$	3.83838e8			1.76817			0.884087	+	0.467323i	$0.154782\pi$
$602$		0			0
$603$	6.85588e7	+	6.85588e7i	0.312688	+	0.312688i
$604$		0			0
$605$	1.57546e8	+	9.12063e6i	0.711443	+	0.0411869i
$606$		0			0
$607$	−1.68146e8	+	1.68146e8i	−0.751833	+	0.751833i	−0.974821	−	0.222989i	$-0.928419\pi$
$607$	−1.68146e8	+	1.68146e8i	−0.751833	+	0.751833i	0.222989	+	0.974821i	$0.428419\pi$
$608$		0			0
$609$		−	2.45747e8i		−	1.08802i
$610$		0			0
$611$	−4.12005e8			−1.80625
$612$		0			0
$613$	−4.09111e7	−	4.09111e7i	−0.177607	−	0.177607i	0.612705	−	0.790312i	$-0.290081\pi$
$613$	−4.09111e7	−	4.09111e7i	−0.177607	−	0.177607i	−0.790312	+	0.612705i	$0.790081\pi$
$614$		0			0
$615$	7.77465e6	+	8.73014e6i	0.0334238	+	0.0375315i
$616$		0			0
$617$	−1.33390e7	+	1.33390e7i	−0.0567896	+	0.0567896i	−0.734931	−	0.678142i	$-0.762786\pi$
$617$	−1.33390e7	+	1.33390e7i	−0.0567896	+	0.0567896i	0.678142	+	0.734931i	$0.262786\pi$
$618$		0			0
$619$		−	5.99503e7i		−	0.252766i	−0.991981	−	0.126383i	$-0.959663\pi$
$619$		−	5.99503e7i		−	0.252766i	0.991981	−	0.126383i	$-0.0403369\pi$
$620$		0			0
$621$	558731.			0.00233307
$622$		0			0
$623$	8.54102e7	+	8.54102e7i	0.353220	+	0.353220i
$624$		0			0
$625$	2.37638e8	+	5.59699e7i	0.973367	+	0.229253i
$626$		0			0
$627$	−2.53862e8	+	2.53862e8i	−1.02990	+	1.02990i
$628$		0			0
$629$			5.66054e7i			0.227461i
$630$		0			0
$631$	−2.38090e8			−0.947661			−0.473830	−	0.880616i	$-0.657129\pi$
$631$	−2.38090e8			−0.947661			−0.473830	+	0.880616i	$0.657129\pi$
$632$		0			0
$633$	−1.06003e8	−	1.06003e8i	−0.417933	−	0.417933i
$634$		0			0
$635$	−1.52841e8	+	1.36113e8i	−0.596925	+	0.531593i
$636$		0			0
$637$	−4.02113e8	+	4.02113e8i	−1.55571	+	1.55571i
$638$		0			0
$639$			8.28536e7i			0.317547i
$640$		0			0
$641$	1.12702e7			0.0427915			0.0213958	−	0.999771i	$-0.493189\pi$
$641$	1.12702e7			0.0427915			0.0213958	+	0.999771i	$0.493189\pi$
$642$		0			0
$643$	1.76168e8	+	1.76168e8i	0.662665	+	0.662665i	0.956007	−	0.293342i	$-0.0947676\pi$
$643$	1.76168e8	+	1.76168e8i	0.662665	+	0.662665i	−0.293342	+	0.956007i	$0.594768\pi$
$644$		0			0
$645$	792929.	−	1.36967e7i	0.00295498	−	0.0510431i
$646$		0			0
$647$	−3.55627e7	+	3.55627e7i	−0.131305	+	0.131305i	−0.769705	−	0.638400i	$-0.779597\pi$
$647$	−3.55627e7	+	3.55627e7i	−0.131305	+	0.131305i	0.638400	+	0.769705i	$0.279597\pi$
$648$		0			0
$649$			4.23120e8i			1.54785i
$650$		0			0
$651$	−2.02685e7			−0.0734648
$652$		0			0
$653$	3.39695e8	+	3.39695e8i	1.21997	+	1.21997i	0.967641	+	0.252330i	$0.0811968\pi$
$653$	3.39695e8	+	3.39695e8i	1.21997	+	1.21997i	0.252330	+	0.967641i	$0.418803\pi$
$654$		0			0
$655$	4.08541e8	+	2.36512e7i	1.45382	+	0.0841647i
$656$		0			0
$657$	1.85648e7	−	1.85648e7i	0.0654626	−	0.0654626i
$658$		0			0
$659$			1.47250e8i			0.514516i	0.966343	+	0.257258i	$0.0828191\pi$
$659$			1.47250e8i			0.514516i	−0.966343	+	0.257258i	$0.917181\pi$
$660$		0			0
$661$	−1.50035e8			−0.519504			−0.259752	−	0.965675i	$-0.583641\pi$
$661$	−1.50035e8			−0.519504			−0.259752	+	0.965675i	$0.583641\pi$
$662$		0			0
$663$	1.36767e8	+	1.36767e8i	0.469291	+	0.469291i
$664$		0			0
$665$	−6.75560e8	−	7.58586e8i	−2.29720	−	2.57952i
$666$		0			0
$667$	2.67526e6	−	2.67526e6i	0.00901549	−	0.00901549i
$668$		0			0
$669$			1.04111e8i			0.347711i
$670$		0			0
$671$	5.05203e8			1.67224
$672$		0			0
$673$	1.00799e8	+	1.00799e8i	0.330683	+	0.330683i	0.852846	−	0.522163i	$-0.174875\pi$
$673$	1.00799e8	+	1.00799e8i	0.330683	+	0.330683i	−0.522163	+	0.852846i	$0.674875\pi$
$674$		0			0
$675$	−4.64018e7	+	3.67427e7i	−0.150877	+	0.119470i
$676$		0			0
$677$	4.27340e8	−	4.27340e8i	1.37723	−	1.37723i	0.527973	−	0.849261i	$-0.322952\pi$
$677$	4.27340e8	−	4.27340e8i	1.37723	−	1.37723i	0.849261	−	0.527973i	$-0.177048\pi$
$678$		0			0
$679$		−	8.22438e7i		−	0.262720i
$680$		0			0
$681$	−3.07646e8			−0.974114
$682$		0			0
$683$	3.87402e8	+	3.87402e8i	1.21590	+	1.21590i	0.969053	+	0.246851i	$0.0793958\pi$
$683$	3.87402e8	+	3.87402e8i	1.21590	+	1.21590i	0.246851	+	0.969053i	$0.420604\pi$
$684$		0			0
$685$	−8.06494e7	+	7.18225e7i	−0.250917	+	0.223454i
$686$		0			0
$687$	9.38835e7	−	9.38835e7i	0.289547	−	0.289547i
$688$		0			0
$689$			5.06474e8i			1.54846i
$690$		0			0
$691$	−3.37766e8			−1.02372			−0.511861	−	0.859068i	$-0.671044\pi$
$691$	−3.37766e8			−1.02372			−0.511861	+	0.859068i	$0.671044\pi$
$692$		0			0
$693$	−1.83949e8	−	1.83949e8i	−0.552711	−	0.552711i
$694$		0			0
$695$	−370159.	+	6.39395e6i	−0.00110264	+	0.0190465i
$696$		0			0
$697$	−2.40740e7	+	2.40740e7i	−0.0710968	+	0.0710968i
$698$		0			0
$699$		−	7.96330e7i		−	0.233164i
$700$		0			0
$701$	−6.25787e8			−1.81666			−0.908328	−	0.418259i	$-0.862641\pi$
$701$	−6.25787e8			−1.81666			−0.908328	+	0.418259i	$0.862641\pi$
$702$		0			0
$703$	9.32582e7	+	9.32582e7i	0.268424	+	0.268424i
$704$		0			0
$705$	3.66563e8	+	2.12211e7i	1.04612	+	0.0605620i
$706$		0			0
$707$	1.64707e7	−	1.64707e7i	0.0466074	−	0.0466074i
$708$		0			0
$709$			4.87624e8i			1.36819i	0.729393	+	0.684094i	$0.239802\pi$
$709$			4.87624e8i			1.36819i	−0.729393	+	0.684094i	$0.760198\pi$
$710$		0			0
$711$	1.29482e8			0.360249
$712$		0			0
$713$	−220649.	−	220649.i	−0.000608741	−	0.000608741i
$714$		0			0
$715$	−3.16606e8	−	3.55516e8i	−0.866166	−	0.972616i
$716$		0			0
$717$	1.29951e8	−	1.29951e8i	0.352552	−	0.352552i
$718$		0			0
$719$		−	6.52599e8i		−	1.75574i	−0.478901	−	0.877869i	$-0.658965\pi$
$719$		−	6.52599e8i		−	1.75574i	0.478901	−	0.877869i	$-0.341035\pi$
$720$		0			0
$721$	−6.47593e8			−1.72781
$722$		0			0
$723$	1.99506e8	+	1.99506e8i	0.527887	+	0.527887i
$724$		0			0
$725$	−4.62492e7	+	3.98105e8i	−0.121364	+	1.04468i
$726$		0			0
$727$	−3.39087e6	+	3.39087e6i	−0.00882486	+	0.00882486i	−0.711505	−	0.702681i	$-0.751986\pi$
$727$	−3.39087e6	+	3.39087e6i	−0.00882486	+	0.00882486i	0.702681	+	0.711505i	$0.251986\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	3.99563e7			0.102290
$732$		0			0
$733$	−1.36080e8	−	1.36080e8i	−0.345528	−	0.345528i	0.512913	−	0.858441i	$-0.328566\pi$
$733$	−1.36080e8	−	1.36080e8i	−0.345528	−	0.345528i	−0.858441	+	0.512913i	$0.828566\pi$
$734$		0			0
$735$	3.78475e8	−	3.37051e8i	0.953179	−	0.848856i
$736$		0			0
$737$	4.91436e8	−	4.91436e8i	1.22762	−	1.22762i
$738$		0			0
$739$		−	3.76720e8i		−	0.933438i	−0.884406	−	0.466719i	$-0.845436\pi$
$739$		−	3.76720e8i		−	0.933438i	0.884406	−	0.466719i	$-0.154564\pi$
$740$		0			0
$741$	4.50652e8			1.10761
$742$		0			0
$743$	2.11364e8	+	2.11364e8i	0.515305	+	0.515305i	0.916147	−	0.400842i	$-0.131282\pi$
$743$	2.11364e8	+	2.11364e8i	0.515305	+	0.515305i	−0.400842	+	0.916147i	$0.631282\pi$
$744$		0			0
$745$	2.94808e6	−	5.09238e7i	0.00712969	−	0.123155i
$746$		0			0
$747$	1.74288e7	−	1.74288e7i	0.0418124	−	0.0418124i
$748$		0			0
$749$		−	4.51221e8i		−	1.07385i
$750$		0			0
$751$	−4.42340e8			−1.04433			−0.522164	−	0.852845i	$-0.674875\pi$
$751$	−4.42340e8			−1.04433			−0.522164	+	0.852845i	$0.674875\pi$
$752$		0			0
$753$	−2.76495e8	−	2.76495e8i	−0.647593	−	0.647593i
$754$		0			0
$755$	8.81445e7	+	5.10286e6i	0.204811	+	0.0118569i
$756$		0			0
$757$	−1.29598e8	+	1.29598e8i	−0.298752	+	0.298752i	−0.840525	−	0.541773i	$-0.817753\pi$
$757$	−1.29598e8	+	1.29598e8i	−0.298752	+	0.298752i	0.541773	+	0.840525i	$0.317753\pi$
$758$		0			0
$759$		−	4.00504e6i		−	0.00915970i
$760$		0			0
$761$	−2.09659e8			−0.475730			−0.237865	−	0.971298i	$-0.576448\pi$
$761$	−2.09659e8			−0.475730			−0.237865	+	0.971298i	$0.576448\pi$
$762$		0			0
$763$	6.79968e7	+	6.79968e7i	0.153079	+	0.153079i
$764$		0			0
$765$	−1.14639e8	−	1.28727e8i	−0.256063	−	0.287533i
$766$		0			0
$767$	3.75559e8	−	3.75559e8i	0.832323	−	0.832323i
$768$		0			0
$769$		−	4.36243e7i		−	0.0959290i	−0.998849	−	0.0479645i	$-0.984727\pi$
$769$		−	4.36243e7i		−	0.0959290i	0.998849	−	0.0479645i	$-0.0152734\pi$
$770$		0			0
$771$	−3.02142e7			−0.0659247
$772$		0			0
$773$	−3.19290e8	−	3.19290e8i	−0.691269	−	0.691269i	0.271242	−	0.962511i	$-0.412565\pi$
$773$	−3.19290e8	−	3.19290e8i	−0.691269	−	0.691269i	−0.962511	+	0.271242i	$0.912565\pi$
$774$		0			0
$775$	3.28346e7	+	3.81451e6i	0.0705386	+	0.00819470i
$776$		0			0
$777$	−6.75752e7	+	6.75752e7i	−0.144054	+	0.144054i
$778$		0			0
$779$			7.93245e7i			0.167801i
$780$		0			0
$781$	5.93903e8			1.24670
$782$		0			0
$783$	−6.87041e7	−	6.87041e7i	−0.143119	−	0.143119i
$784$		0			0
$785$	8.17248e7	−	7.27802e7i	0.168945	−	0.150454i
$786$		0			0
$787$	2.36623e8	−	2.36623e8i	0.485437	−	0.485437i	−0.421426	−	0.906863i	$-0.638470\pi$
$787$	2.36623e8	−	2.36623e8i	0.485437	−	0.485437i	0.906863	+	0.421426i	$0.138470\pi$
$788$		0			0
$789$			1.98439e8i			0.404015i
$790$		0			0
$791$	3.66695e8			0.740927
$792$		0			0
$793$	−4.48414e8	−	4.48414e8i	−0.899208	−	0.899208i
$794$		0			0
$795$	2.60869e7	−	4.50613e8i	0.0519183	−	0.896814i
$796$		0			0
$797$	−5.07717e8	+	5.07717e8i	−1.00288	+	1.00288i	−0.00287989	+	0.999996i	$0.500917\pi$
$797$	−5.07717e8	+	5.07717e8i	−1.00288	+	1.00288i	−0.999996	+	0.00287989i	$0.999083\pi$
$798$		0			0
$799$			1.06934e9i			2.09642i
$800$		0			0
$801$	4.77568e7			0.0929260
$802$		0			0
$803$	−1.33074e8	−	1.33074e8i	−0.257008	−	0.257008i
$804$		0			0
$805$	1.13129e7	+	654924.i	0.0216863	+	0.00125546i
$806$		0			0
$807$	−1.46314e8	+	1.46314e8i	−0.278398	+	0.278398i
$808$		0			0
$809$		−	9.66993e8i		−	1.82632i	−0.407598	−	0.913162i	$-0.633633\pi$
$809$		−	9.66993e8i		−	1.82632i	0.407598	−	0.913162i	$-0.366367\pi$
$810$		0			0
$811$	6.56148e8			1.23010			0.615049	−	0.788489i	$-0.289136\pi$
$811$	6.56148e8			1.23010			0.615049	+	0.788489i	$0.289136\pi$
$812$		0			0
$813$	−2.30757e8	−	2.30757e8i	−0.429421	−	0.429421i
$814$		0			0
$815$	5.13027e8	+	5.76078e8i	0.947693	+	1.06416i
$816$		0			0
$817$	6.58284e7	−	6.58284e7i	0.120711	−	0.120711i
$818$		0			0
$819$			3.26544e8i			0.594415i
$820$		0			0
$821$	−1.05035e9			−1.89804			−0.949020	−	0.315217i	$-0.897923\pi$
$821$	−1.05035e9			−1.89804			−0.949020	+	0.315217i	$0.897923\pi$
$822$		0			0
$823$	−3.29658e8	−	3.29658e8i	−0.591376	−	0.591376i	0.346627	−	0.938003i	$-0.387327\pi$
$823$	−3.29658e8	−	3.29658e8i	−0.591376	−	0.591376i	−0.938003	+	0.346627i	$0.887327\pi$
$824$		0			0
$825$	2.63375e8	+	3.32613e8i	0.469043	+	0.592348i
$826$		0			0
$827$	5.78384e7	−	5.78384e7i	0.102259	−	0.102259i	−0.654127	−	0.756385i	$-0.726964\pi$
$827$	5.78384e7	−	5.78384e7i	0.102259	−	0.102259i	0.756385	+	0.654127i	$0.226964\pi$
$828$		0			0
$829$			2.45886e8i			0.431589i	0.976439	+	0.215794i	$0.0692341\pi$
$829$			2.45886e8i			0.431589i	−0.976439	+	0.215794i	$0.930766\pi$
$830$		0			0
$831$	4.58295e8			0.798624
$832$		0			0
$833$	1.04367e9	+	1.04367e9i	1.80563	+	1.80563i
$834$		0			0
$835$	9.00003e7	−	8.01500e7i	0.154591	−	0.137672i
$836$		0			0
$837$	−5.66653e6	+	5.66653e6i	−0.00966365	+	0.00966365i
$838$		0			0
$839$			1.95702e8i			0.331368i	0.986179	+	0.165684i	$0.0529831\pi$
$839$			1.95702e8i			0.331368i	−0.986179	+	0.165684i	$0.947017\pi$
$840$		0			0
$841$	−6.31027e7			−0.106086
$842$		0			0
$843$	−2.55170e8	−	2.55170e8i	−0.425938	−	0.425938i
$844$		0			0
$845$	334102.	−	5.77114e6i	0.000553745	−	0.00956514i
$846$		0			0
$847$	−5.48661e8	+	5.48661e8i	−0.902929	+	0.902929i
$848$		0			0
$849$			3.79557e8i			0.620232i
$850$		0			0
$851$	−1.47128e6			−0.00238730
$852$		0			0
$853$	1.45641e8	+	1.45641e8i	0.234659	+	0.234659i	0.814634	−	0.579975i	$-0.196938\pi$
$853$	1.45641e8	+	1.45641e8i	0.234659	+	0.234659i	−0.579975	+	0.814634i	$0.696938\pi$
$854$		0			0
$855$	−4.00949e8	−	2.32117e7i	−0.641491	−	0.0371372i
$856$		0			0
$857$	1.48350e8	−	1.48350e8i	0.235693	−	0.235693i	−0.579371	−	0.815064i	$-0.696702\pi$
$857$	1.48350e8	−	1.48350e8i	0.235693	−	0.235693i	0.815064	+	0.579371i	$0.196702\pi$
$858$		0			0
$859$			4.59801e8i			0.725421i	0.931902	+	0.362710i	$0.118149\pi$
$859$			4.59801e8i			0.725421i	−0.931902	+	0.362710i	$0.881851\pi$
$860$		0			0
$861$	−5.74788e7			−0.0900530
$862$		0			0
$863$	−2.17602e8	−	2.17602e8i	−0.338555	−	0.338555i	0.517268	−	0.855823i	$-0.326949\pi$
$863$	−2.17602e8	−	2.17602e8i	−0.338555	−	0.338555i	−0.855823	+	0.517268i	$0.826949\pi$
$864$		0			0
$865$	2.14931e8	+	2.41346e8i	0.332087	+	0.372900i
$866$		0			0
$867$	8.89144e7	−	8.89144e7i	0.136432	−	0.136432i
$868$		0			0
$869$		−	9.28144e8i		−	1.41435i
$870$		0			0
$871$	−8.72391e8			−1.32025
$872$		0			0
$873$	−2.29932e7	−	2.29932e7i	−0.0345586	−	0.0345586i
$874$		0			0
$875$	−9.82586e8	+	6.89554e8i	−1.46672	+	1.02930i
$876$		0			0
$877$	−4.49643e8	+	4.49643e8i	−0.666606	+	0.666606i	−0.956929	−	0.290323i	$-0.906237\pi$
$877$	−4.49643e8	+	4.49643e8i	−0.666606	+	0.666606i	0.290323	+	0.956929i	$0.406237\pi$
$878$		0			0
$879$			2.69778e8i			0.397228i
$880$		0			0
$881$	1.14586e8			0.167573			0.0837867	−	0.996484i	$-0.473299\pi$
$881$	1.14586e8			0.167573			0.0837867	+	0.996484i	$0.473299\pi$
$882$		0			0
$883$	−5.17599e8	−	5.17599e8i	−0.751815	−	0.751815i	0.223003	−	0.974818i	$-0.428414\pi$
$883$	−5.17599e8	−	5.17599e8i	−0.751815	−	0.751815i	−0.974818	+	0.223003i	$0.928414\pi$
$884$		0			0
$885$	−3.53481e8	+	3.14794e8i	−0.509961	+	0.454147i
$886$		0			0
$887$	4.33717e8	−	4.33717e8i	0.621492	−	0.621492i	−0.324421	−	0.945913i	$-0.605169\pi$
$887$	4.33717e8	−	4.33717e8i	0.621492	−	0.621492i	0.945913	+	0.324421i	$0.105169\pi$
$888$		0			0
$889$		−	1.00630e9i		−	1.43226i
$890$		0			0
$891$	−1.02854e8			−0.145409
$892$		0			0
$893$	1.76176e9	+	1.76176e9i	2.47396	+	2.47396i
$894$		0			0
$895$	−2.55045e7	+	4.40553e8i	−0.0355752	+	0.614511i
$896$		0			0
$897$	−3.55485e6	+	3.55485e6i	−0.00492542	+	0.00492542i
$898$		0			0
$899$			5.42640e7i			0.0746849i
$900$		0			0
$901$	1.31454e9			1.79721
$902$		0			0
$903$	4.76995e7	+	4.76995e7i	0.0647814	+	0.0647814i
$904$		0			0
$905$	−1.04011e9	−	6.02140e7i	−1.40325	−	0.0812367i
$906$		0			0
$907$	4.61918e8	−	4.61918e8i	0.619075	−	0.619075i	−0.326219	−	0.945294i	$-0.605775\pi$
$907$	4.61918e8	−	4.61918e8i	0.619075	−	0.619075i	0.945294	+	0.326219i	$0.105775\pi$
$908$		0			0
$909$		−	9.20954e6i		−	0.0122616i
$910$		0			0
$911$	−1.99604e8			−0.264006			−0.132003	−	0.991249i	$-0.542141\pi$
$911$	−1.99604e8			−0.264006			−0.132003	+	0.991249i	$0.542141\pi$
$912$		0			0
$913$	−1.24931e8	−	1.24931e8i	−0.164157	−	0.164157i
$914$		0			0
$915$	3.75861e8	+	4.22054e8i	0.490641	+	0.550941i
$916$		0			0
$917$	−1.42276e9	+	1.42276e9i	−1.84512	+	1.84512i
$918$		0			0
$919$		−	8.33200e8i		−	1.07350i	−0.843741	−	0.536751i	$-0.819652\pi$
$919$		−	8.33200e8i		−	1.07350i	0.843741	−	0.536751i	$-0.180348\pi$
$920$		0			0
$921$	3.90438e8			0.499774
$922$		0			0
$923$	−5.27144e8	−	5.27144e8i	−0.670385	−	0.670385i
$924$		0			0
$925$	1.22188e8	−	9.67529e7i	0.154384	−	0.122247i
$926$		0			0
$927$	−1.81050e8	+	1.81050e8i	−0.227279	+	0.227279i
$928$		0			0
$929$		−	3.02246e8i		−	0.376975i	−0.982076	−	0.188488i	$-0.939641\pi$
$929$		−	3.02246e8i		−	0.376975i	0.982076	−	0.188488i	$-0.0603585\pi$
$930$		0			0
$931$	3.43892e9			4.26161
$932$		0			0
$933$	−3.60795e8	−	3.60795e8i	−0.444238	−	0.444238i
$934$		0			0
$935$	−9.22732e8	+	8.21741e8i	−1.12886	+	1.00531i
$936$		0			0
$937$	1.06881e8	−	1.06881e8i	0.129922	−	0.129922i	−0.639156	−	0.769077i	$-0.720716\pi$
$937$	1.06881e8	−	1.06881e8i	0.129922	−	0.129922i	0.769077	+	0.639156i	$0.220716\pi$
$938$		0			0
$939$			1.36982e8i			0.165451i
$940$		0			0
$941$	1.02554e9			1.23079			0.615393	−	0.788220i	$-0.288997\pi$
$941$	1.02554e9			1.23079			0.615393	+	0.788220i	$0.288997\pi$
$942$		0			0
$943$	−625729.	−	625729.i	−0.000746194	−	0.000746194i
$944$		0			0
$945$	1.68193e7	−	2.90529e8i	0.0199302	−	0.344265i
$946$		0			0
$947$	−5.66359e8	+	5.66359e8i	−0.666871	+	0.666871i	−0.956990	−	0.290120i	$-0.906305\pi$
$947$	−5.66359e8	+	5.66359e8i	−0.666871	+	0.666871i	0.290120	+	0.956990i	$0.406305\pi$
$948$		0			0
$949$			2.36231e8i			0.276401i
$950$		0			0
$951$	−6.55352e8			−0.761962
$952$		0			0
$953$	−6.58594e8	−	6.58594e8i	−0.760920	−	0.760920i	0.215569	−	0.976489i	$-0.430839\pi$
$953$	−6.58594e8	−	6.58594e8i	−0.760920	−	0.760920i	−0.976489	+	0.215569i	$0.930839\pi$
$954$		0			0
$955$	9.43732e8	+	5.46345e7i	1.08352	+	0.0627273i
$956$		0			0
$957$	−4.92478e8	+	4.92478e8i	−0.561890	+	0.561890i
$958$		0			0
$959$		−	5.30991e8i		−	0.602048i
$960$		0			0
$961$	−8.83028e8			−0.994957
$962$		0			0
$963$	−1.26149e8	−	1.26149e8i	−0.141256	−	0.141256i
$964$		0			0
$965$	4.80046e8	+	5.39043e8i	0.534196	+	0.599848i
$966$		0			0
$967$	−3.62176e8	+	3.62176e8i	−0.400535	+	0.400535i	−0.878421	−	0.477887i	$-0.841403\pi$
$967$	−3.62176e8	+	3.62176e8i	−0.400535	+	0.400535i	0.477887	+	0.878421i	$0.341403\pi$
$968$		0			0
$969$		−	1.16965e9i		−	1.28554i
$970$		0			0
$971$	−1.35916e9			−1.48461			−0.742306	−	0.670061i	$-0.766268\pi$
$971$	−1.35916e9			−1.48461			−0.742306	+	0.670061i	$0.766268\pi$
$972$		0			0
$973$	−2.22673e7	−	2.22673e7i	−0.0241729	−	0.0241729i
$974$		0			0
$975$	6.14551e7	−	5.28995e8i	0.0663047	−	0.570739i
$976$		0			0
$977$	9.67638e8	−	9.67638e8i	1.03760	−	1.03760i	0.0383333	−	0.999265i	$-0.487795\pi$
$977$	9.67638e8	−	9.67638e8i	1.03760	−	1.03760i	0.999265	−	0.0383333i	$-0.0122048\pi$
$978$		0			0
$979$		−	3.42325e8i		−	0.364830i
$980$		0			0
$981$	3.80202e7			0.0402723
$982$		0			0
$983$	−9.02083e8	−	9.02083e8i	−0.949699	−	0.949699i	0.0490952	−	0.998794i	$-0.484366\pi$
$983$	−9.02083e8	−	9.02083e8i	−0.949699	−	0.949699i	−0.998794	+	0.0490952i	$0.984366\pi$
$984$		0			0
$985$	7.76928e8	−	6.91895e8i	0.812965	−	0.723988i
$986$		0			0
$987$	−1.27658e9	+	1.27658e9i	−1.32769	+	1.32769i
$988$		0			0
$989$			1.03854e6i			0.00107358i
$990$		0			0
$991$	2.83531e8			0.291326			0.145663	−	0.989334i	$-0.453468\pi$
$991$	2.83531e8			0.291326			0.145663	+	0.989334i	$0.453468\pi$
$992$		0			0
$993$	2.02394e8	+	2.02394e8i	0.206704	+	0.206704i
$994$		0			0
$995$	1.41534e7	−	2.44480e8i	0.0143679	−	0.248185i
$996$		0			0
$997$	1.24098e9	−	1.24098e9i	1.25222	−	1.25222i	0.297498	−	0.954723i	$-0.403848\pi$
$997$	1.24098e9	−	1.24098e9i	1.25222	−	1.25222i	0.954723	−	0.297498i	$-0.0961521\pi$
$998$		0			0
$999$			3.77844e7i			0.0378980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.k.a.13.6	✓	12
3.2	odd	2		180.7.l.b.73.1		12
4.3	odd	2		240.7.bg.d.193.3		12
5.2	odd	4	inner	60.7.k.a.37.6	yes	12
5.3	odd	4		300.7.k.d.157.3		12
5.4	even	2		300.7.k.d.193.3		12
15.2	even	4		180.7.l.b.37.1		12
20.7	even	4		240.7.bg.d.97.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.k.a.13.6	✓	12	1.1	even	1	trivial
60.7.k.a.37.6	yes	12	5.2	odd	4	inner
180.7.l.b.37.1		12	15.2	even	4
180.7.l.b.73.1		12	3.2	odd	2
240.7.bg.d.97.3		12	20.7	even	4
240.7.bg.d.193.3		12	4.3	odd	2
300.7.k.d.157.3		12	5.3	odd	4
300.7.k.d.193.3		12	5.4	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.0227 + 11.0227i) q^{3} +(124.791 + 7.22440i) q^{5} +(-434.591 + 434.591i) q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 + 11.0227i) q^{3} +(124.791 + 7.22440i) q^{5} +(-434.591 + 434.591i) q^{7} +243.000i q^{9} +1741.85 q^{11} +(-1546.05 - 1546.05i) q^{13} +(1295.90 + 1455.17i) q^{15} +(-4012.73 + 4012.73i) q^{17} +13222.1i q^{19} -9580.74 q^{21} +(-104.299 - 104.299i) q^{23} +(15520.6 + 1803.08i) q^{25} +(-2678.52 + 2678.52i) q^{27} +25650.1i q^{29} +2115.55 q^{31} +(19199.9 + 19199.9i) q^{33} +(-57372.8 + 51093.4i) q^{35} +(7053.23 - 7053.23i) q^{37} -34083.4i q^{39} +5999.41 q^{41} +(-4978.68 - 4978.68i) q^{43} +(-1755.53 + 30324.2i) q^{45} +(133244. - 133244. i) q^{47} -260090. i q^{49} -88462.3 q^{51} +(-163796. - 163796. i) q^{53} +(217367. + 12583.8i) q^{55} +(-145743. + 145743. i) q^{57} +242915. i q^{59} +290038. q^{61} +(-105606. - 105606. i) q^{63} +(-181764. - 204103. i) q^{65} +(282135. - 282135. i) q^{67} -2299.30i q^{69} +340961. q^{71} +(-76398.2 - 76398.2i) q^{73} +(151204. + 190954. i) q^{75} +(-756992. + 756992. i) q^{77} -532850. i q^{79} -59049.0 q^{81} +(-71723.3 - 71723.3i) q^{83} +(-529743. + 471764. i) q^{85} +(-282733. + 282733. i) q^{87} -196530. i q^{89} +1.34380e6 q^{91} +(23319.1 + 23319.1i) q^{93} +(-95521.4 + 1.64999e6i) q^{95} +(-94622.0 + 94622.0i) q^{97} +423269. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) \) 12 * q + 312 * q^5 + 120 * q^7	\( 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) \) 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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