LMFDB - Embedded newform 560.2.x.a.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(127,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1, 0]))

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

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

chi := DirichletCharacter("560.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.x (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$-0.394157 - 1.35818i$ of defining polynomial
Character	$\chi$	$=$	560.127
Dual form			560.2.x.a.463.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.964019 - 0.964019i) q^{3} +(-1.75233 - 1.38900i) q^{5} +(-0.707107 + 0.707107i) q^{7} -1.14134i q^{9} +O(q^{10})$	\(q+(-0.964019 - 0.964019i) q^{3} +(-1.75233 - 1.38900i) q^{5} +(-0.707107 + 0.707107i) q^{7} -1.14134i q^{9} +3.37856i q^{11} +(0.610996 - 0.610996i) q^{13} +(0.350255 + 3.02831i) q^{15} +(-2.11566 - 2.11566i) q^{17} -7.98465 q^{19} +1.36333 q^{21} +(3.02831 + 3.02831i) q^{23} +(1.14134 + 4.86799i) q^{25} +(-3.99233 + 3.99233i) q^{27} +9.15066i q^{29} +8.68516i q^{31} +(3.25700 - 3.25700i) q^{33} +(2.22126 - 0.256912i) q^{35} +(-4.36333 - 4.36333i) q^{37} -1.17802 q^{39} +2.23132 q^{41} +(-8.33491 - 8.33491i) q^{43} +(-1.58532 + 2.00000i) q^{45} +(1.66453 - 1.66453i) q^{47} -1.00000i q^{49} +4.07907i q^{51} +(0.221992 - 0.221992i) q^{53} +(4.69284 - 5.92036i) q^{55} +(7.69735 + 7.69735i) q^{57} +1.22753 q^{59} -5.55602 q^{61} +(0.807047 + 0.807047i) q^{63} +(-1.91934 + 0.221992i) q^{65} +(3.50582 - 3.50582i) q^{67} -5.83869i q^{69} +3.85607i q^{71} +(-3.86799 + 3.86799i) q^{73} +(3.59257 - 5.79310i) q^{75} +(-2.38900 - 2.38900i) q^{77} -7.93515 q^{79} +4.27334 q^{81} +(-5.65685 - 5.65685i) q^{83} +(0.768679 + 6.64600i) q^{85} +(8.82141 - 8.82141i) q^{87} -15.0093i q^{89} +0.864079i q^{91} +(8.37266 - 8.37266i) q^{93} +(13.9918 + 11.0907i) q^{95} +(-9.17634 - 9.17634i) q^{97} +3.85607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 20 q^{13} + 4 q^{17} + 8 q^{21} - 20 q^{25} - 24 q^{33} - 44 q^{37} - 32 q^{41} - 36 q^{45} + 28 q^{53} + 8 q^{57} - 16 q^{61} + 36 q^{65} + 4 q^{73} - 16 q^{77} + 68 q^{81} + 68 q^{85} + 8 q^{93} + 12 q^{97}+O(q^{100}) $ 12 * q + 20 * q^13 + 4 * q^17 + 8 * q^21 - 20 * q^25 - 24 * q^33 - 44 * q^37 - 32 * q^41 - 36 * q^45 + 28 * q^53 + 8 * q^57 - 16 * q^61 + 36 * q^65 + 4 * q^73 - 16 * q^77 + 68 * q^81 + 68 * q^85 + 8 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.964019	−	0.964019i	−0.556576	−	0.556576i	0.371755	−	0.928331i	$-0.378756\pi$
$3$	−0.964019	−	0.964019i	−0.556576	−	0.556576i	−0.928331	+	0.371755i	$0.878756\pi$
$4$		0			0
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$		−	1.14134i		−	0.380445i
$10$		0			0
$11$			3.37856i			1.01867i	0.860567	+	0.509337i	$0.170109\pi$
$11$			3.37856i			1.01867i	−0.860567	+	0.509337i	$0.829891\pi$
$12$		0			0
$13$	0.610996	−	0.610996i	0.169460	−	0.169460i	−0.617282	−	0.786742i	$-0.711766\pi$
$13$	0.610996	−	0.610996i	0.169460	−	0.169460i	0.786742	+	0.617282i	$0.211766\pi$
$14$		0			0
$15$	0.350255	+	3.02831i	0.0904355	+	0.781905i
$16$		0			0
$17$	−2.11566	−	2.11566i	−0.513123	−	0.513123i	0.402359	−	0.915482i	$-0.368190\pi$
$17$	−2.11566	−	2.11566i	−0.513123	−	0.513123i	−0.915482	+	0.402359i	$0.868190\pi$
$18$		0			0
$19$	−7.98465			−1.83180			−0.915902	−	0.401401i	$-0.868523\pi$
$19$	−7.98465			−1.83180			−0.915902	+	0.401401i	$0.868523\pi$
$20$		0			0
$21$	1.36333			0.297503
$22$		0			0
$23$	3.02831	+	3.02831i	0.631446	+	0.631446i	0.948431	−	0.316985i	$-0.102670\pi$
$23$	3.02831	+	3.02831i	0.631446	+	0.631446i	−0.316985	+	0.948431i	$0.602670\pi$
$24$		0			0
$25$	1.14134	+	4.86799i	0.228267	+	0.973599i
$26$		0			0
$27$	−3.99233	+	3.99233i	−0.768323	+	0.768323i
$28$		0			0
$29$			9.15066i			1.69924i	0.527399	+	0.849618i	$0.323167\pi$
$29$			9.15066i			1.69924i	−0.527399	+	0.849618i	$0.676833\pi$
$30$		0			0
$31$			8.68516i			1.55990i	0.625841	+	0.779950i	$0.284756\pi$
$31$			8.68516i			1.55990i	−0.625841	+	0.779950i	$0.715244\pi$
$32$		0			0
$33$	3.25700	−	3.25700i	0.566970	−	0.566970i
$34$		0			0
$35$	2.22126	−	0.256912i	0.375461	−	0.0434260i
$36$		0			0
$37$	−4.36333	−	4.36333i	−0.717327	−	0.717327i	0.250730	−	0.968057i	$-0.419329\pi$
$37$	−4.36333	−	4.36333i	−0.717327	−	0.717327i	−0.968057	+	0.250730i	$0.919329\pi$
$38$		0			0
$39$	−1.17802			−0.188635
$40$		0			0
$41$	2.23132			0.348474			0.174237	−	0.984704i	$-0.444254\pi$
$41$	2.23132			0.348474			0.174237	+	0.984704i	$0.444254\pi$
$42$		0			0
$43$	−8.33491	−	8.33491i	−1.27106	−	1.27106i	−0.945532	−	0.325529i	$-0.894458\pi$
$43$	−8.33491	−	8.33491i	−1.27106	−	1.27106i	−0.325529	−	0.945532i	$-0.605542\pi$
$44$		0			0
$45$	−1.58532	+	2.00000i	−0.236326	+	0.298142i
$46$		0			0
$47$	1.66453	−	1.66453i	0.242797	−	0.242797i	−0.575210	−	0.818006i	$-0.695079\pi$
$47$	1.66453	−	1.66453i	0.242797	−	0.242797i	0.818006	+	0.575210i	$0.195079\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$			4.07907i			0.571184i
$52$		0			0
$53$	0.221992	−	0.221992i	0.0304930	−	0.0304930i	−0.691696	−	0.722189i	$-0.743136\pi$
$53$	0.221992	−	0.221992i	0.0304930	−	0.0304930i	0.722189	+	0.691696i	$0.243136\pi$
$54$		0			0
$55$	4.69284	−	5.92036i	0.632782	−	0.798302i
$56$		0			0
$57$	7.69735	+	7.69735i	1.01954	+	1.01954i
$58$		0			0
$59$	1.22753			0.159810			0.0799052	−	0.996802i	$-0.474538\pi$
$59$	1.22753			0.159810			0.0799052	+	0.996802i	$0.474538\pi$
$60$		0			0
$61$	−5.55602			−0.711375			−0.355687	−	0.934605i	$-0.615753\pi$
$61$	−5.55602			−0.711375			−0.355687	+	0.934605i	$0.615753\pi$
$62$		0			0
$63$	0.807047	+	0.807047i	0.101678	+	0.101678i
$64$		0			0
$65$	−1.91934	+	0.221992i	−0.238065	+	0.0275347i
$66$		0			0
$67$	3.50582	−	3.50582i	0.428304	−	0.428304i	−0.459746	−	0.888050i	$-0.652060\pi$
$67$	3.50582	−	3.50582i	0.428304	−	0.428304i	0.888050	+	0.459746i	$0.152060\pi$
$68$		0			0
$69$		−	5.83869i		−	0.702895i
$70$		0			0
$71$			3.85607i			0.457632i	0.973470	+	0.228816i	$0.0734854\pi$
$71$			3.85607i			0.457632i	−0.973470	+	0.228816i	$0.926515\pi$
$72$		0			0
$73$	−3.86799	+	3.86799i	−0.452714	+	0.452714i	−0.896254	−	0.443540i	$-0.853722\pi$
$73$	−3.86799	+	3.86799i	−0.452714	+	0.452714i	0.443540	+	0.896254i	$0.353722\pi$
$74$		0			0
$75$	3.59257	−	5.79310i	0.414834	−	0.668930i
$76$		0			0
$77$	−2.38900	−	2.38900i	−0.272252	−	0.272252i
$78$		0			0
$79$	−7.93515			−0.892774			−0.446387	−	0.894840i	$-0.647289\pi$
$79$	−7.93515			−0.892774			−0.446387	+	0.894840i	$0.647289\pi$
$80$		0			0
$81$	4.27334			0.474816
$82$		0			0
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$		0			0
$85$	0.768679	+	6.64600i	0.0833750	+	0.720860i
$86$		0			0
$87$	8.82141	−	8.82141i	0.945755	−	0.945755i
$88$		0			0
$89$		−	15.0093i		−	1.59099i	−0.605963	−	0.795493i	$-0.707212\pi$
$89$		−	15.0093i		−	1.59099i	0.605963	−	0.795493i	$-0.292788\pi$
$90$		0			0
$91$			0.864079i			0.0905801i
$92$		0			0
$93$	8.37266	−	8.37266i	0.868204	−	0.868204i
$94$		0			0
$95$	13.9918	+	11.0907i	1.43552	+	1.13788i
$96$		0			0
$97$	−9.17634	−	9.17634i	−0.931716	−	0.931716i	0.0660970	−	0.997813i	$-0.478945\pi$
$97$	−9.17634	−	9.17634i	−0.931716	−	0.931716i	−0.997813	+	0.0660970i	$0.978945\pi$
$98$		0			0
$99$	3.85607			0.387550
$100$		0			0
$101$	6.77801			0.674437			0.337218	−	0.941426i	$-0.390514\pi$
$101$	6.77801			0.674437			0.337218	+	0.941426i	$0.390514\pi$
$102$		0			0
$103$	−5.79310	−	5.79310i	−0.570812	−	0.570812i	0.361544	−	0.932355i	$-0.382250\pi$
$103$	−5.79310	−	5.79310i	−0.570812	−	0.570812i	−0.932355	+	0.361544i	$0.882250\pi$
$104$		0			0
$105$	−2.38900	−	1.89367i	−0.233143	−	0.184803i
$106$		0			0
$107$	8.33491	−	8.33491i	0.805766	−	0.805766i	−0.178224	−	0.983990i	$-0.557035\pi$
$107$	8.33491	−	8.33491i	0.805766	−	0.805766i	0.983990	+	0.178224i	$0.0570352\pi$
$108$		0			0
$109$			5.41468i			0.518632i	0.965792	+	0.259316i	$0.0834972\pi$
$109$			5.41468i			0.518632i	−0.965792	+	0.259316i	$0.916503\pi$
$110$		0			0
$111$			8.41266i			0.798494i
$112$		0			0
$113$	−12.0993	+	12.0993i	−1.13821	+	1.13821i	−0.149436	+	0.988771i	$0.547746\pi$
$113$	−12.0993	+	12.0993i	−1.13821	+	1.13821i	−0.988771	+	0.149436i	$0.952254\pi$
$114$		0			0
$115$	−1.10027	−	9.51293i	−0.102601	−	0.887085i
$116$		0			0
$117$	−0.697352	−	0.697352i	−0.0644702	−	0.0644702i
$118$		0			0
$119$	2.99200			0.274276
$120$		0			0
$121$	−0.414680			−0.0376981
$122$		0			0
$123$	−2.15103	−	2.15103i	−0.193952	−	0.193952i
$124$		0			0
$125$	4.76166	−	10.1157i	0.425896	−	0.904772i
$126$		0			0
$127$	0.350255	−	0.350255i	0.0310801	−	0.0310801i	−0.691396	−	0.722476i	$-0.743004\pi$
$127$	0.350255	−	0.350255i	0.0310801	−	0.0310801i	0.722476	+	0.691396i	$0.243004\pi$
$128$		0			0
$129$			16.0700i			1.41489i
$130$		0			0
$131$			0.700510i			0.0612039i	0.999532	+	0.0306019i	$0.00974242\pi$
$131$			0.700510i			0.0612039i	−0.999532	+	0.0306019i	$0.990258\pi$
$132$		0			0
$133$	5.64600	−	5.64600i	0.489570	−	0.489570i
$134$		0			0
$135$	12.5412	−	1.45052i	1.07938	−	0.124841i
$136$		0			0
$137$	−0.858664	−	0.858664i	−0.0733606	−	0.0733606i	0.669474	−	0.742835i	$-0.266519\pi$
$137$	−0.858664	−	0.858664i	−0.0733606	−	0.0733606i	−0.742835	+	0.669474i	$0.766519\pi$
$138$		0			0
$139$	0.955026			0.0810042			0.0405021	−	0.999179i	$-0.487104\pi$
$139$	0.955026			0.0810042			0.0405021	+	0.999179i	$0.487104\pi$
$140$		0			0
$141$	−3.20927			−0.270270
$142$		0			0
$143$	2.06429	+	2.06429i	0.172624	+	0.172624i
$144$		0			0
$145$	12.7103	−	16.0350i	1.05553	−	1.33163i
$146$		0			0
$147$	−0.964019	+	0.964019i	−0.0795109	+	0.0795109i
$148$		0			0
$149$			0.726656i			0.0595300i	0.999557	+	0.0297650i	$0.00947590\pi$
$149$			0.726656i			0.0595300i	−0.999557	+	0.0297650i	$0.990524\pi$
$150$		0			0
$151$		−	16.4468i		−	1.33842i	−0.743072	−	0.669211i	$-0.766632\pi$
$151$		−	16.4468i		−	1.33842i	0.743072	−	0.669211i	$-0.233368\pi$
$152$		0			0
$153$	−2.41468	+	2.41468i	−0.195215	+	0.195215i
$154$		0			0
$155$	12.0637	−	15.2193i	0.968982	−	1.22244i
$156$		0			0
$157$	15.1600	+	15.1600i	1.20990	+	1.20990i	0.971059	+	0.238840i	$0.0767673\pi$
$157$	15.1600	+	15.1600i	1.20990	+	1.20990i	0.238840	+	0.971059i	$0.423233\pi$
$158$		0			0
$159$	−0.428009			−0.0339433
$160$		0			0
$161$	−4.28267			−0.337522
$162$		0			0
$163$	−9.78543	−	9.78543i	−0.766454	−	0.766454i	0.211026	−	0.977480i	$-0.432319\pi$
$163$	−9.78543	−	9.78543i	−0.766454	−	0.766454i	−0.977480	+	0.211026i	$0.932319\pi$
$164$		0			0
$165$	−10.2313	+	1.18336i	−0.796507	+	0.0921244i
$166$		0			0
$167$	11.8497	−	11.8497i	0.916959	−	0.916959i	−0.0798483	−	0.996807i	$-0.525444\pi$
$167$	11.8497	−	11.8497i	0.916959	−	0.916959i	0.996807	+	0.0798483i	$0.0254436\pi$
$168$		0			0
$169$			12.2534i			0.942567i
$170$		0			0
$171$			9.11317i			0.696902i
$172$		0			0
$173$	−9.38900	+	9.38900i	−0.713833	+	0.713833i	−0.967335	−	0.253502i	$-0.918418\pi$
$173$	−9.38900	+	9.38900i	−0.713833	+	0.713833i	0.253502	+	0.967335i	$0.418418\pi$
$174$		0			0
$175$	−4.24924	−	2.63514i	−0.321212	−	0.199198i
$176$		0			0
$177$	−1.18336	−	1.18336i	−0.0889467	−	0.0889467i
$178$		0			0
$179$	−21.4809			−1.60556			−0.802779	−	0.596276i	$-0.796646\pi$
$179$	−21.4809			−1.60556			−0.802779	+	0.596276i	$0.796646\pi$
$180$		0			0
$181$	−9.50466			−0.706476			−0.353238	−	0.935533i	$-0.614919\pi$
$181$	−9.50466			−0.706476			−0.353238	+	0.935533i	$0.614919\pi$
$182$		0			0
$183$	5.35610	+	5.35610i	0.395935	+	0.395935i
$184$		0			0
$185$	1.58532	+	13.7067i	0.116555	+	1.00774i
$186$		0			0
$187$	7.14789	−	7.14789i	0.522705	−	0.522705i
$188$		0			0
$189$		−	5.64600i		−	0.410686i
$190$		0			0
$191$			12.5907i			0.911034i	0.890227	+	0.455517i	$0.150546\pi$
$191$			12.5907i			0.911034i	−0.890227	+	0.455517i	$0.849454\pi$
$192$		0			0
$193$	0.961367	−	0.961367i	0.0692007	−	0.0692007i	−0.671659	−	0.740860i	$-0.734418\pi$
$193$	0.961367	−	0.961367i	0.0692007	−	0.0692007i	0.740860	+	0.671659i	$0.234418\pi$
$194$		0			0
$195$	2.06429	+	1.63628i	0.147827	+	0.117176i
$196$		0			0
$197$	18.0607	+	18.0607i	1.28677	+	1.28677i	0.936737	+	0.350033i	$0.113830\pi$
$197$	18.0607	+	18.0607i	1.28677	+	1.28677i	0.350033	+	0.936737i	$0.386170\pi$
$198$		0			0
$199$	−7.02962			−0.498317			−0.249158	−	0.968463i	$-0.580154\pi$
$199$	−7.02962			−0.498317			−0.249158	+	0.968463i	$0.580154\pi$
$200$		0			0
$201$	−6.75935			−0.476768
$202$		0			0
$203$	−6.47050	−	6.47050i	−0.454140	−	0.454140i
$204$		0			0
$205$	−3.91002	−	3.09931i	−0.273087	−	0.216465i
$206$		0			0
$207$	3.45632	−	3.45632i	0.240231	−	0.240231i
$208$		0			0
$209$		−	26.9766i		−	1.86601i
$210$		0			0
$211$			8.63566i			0.594503i	0.954799	+	0.297252i	$0.0960700\pi$
$211$			8.63566i			0.594503i	−0.954799	+	0.297252i	$0.903930\pi$
$212$		0			0
$213$	3.71733	−	3.71733i	0.254707	−	0.254707i
$214$		0			0
$215$	3.02831	+	26.1827i	0.206529	+	1.78565i
$216$		0			0
$217$	−6.14134	−	6.14134i	−0.416901	−	0.416901i
$218$		0			0
$219$	7.45763			0.503940
$220$		0			0
$221$	−2.58532			−0.173907
$222$		0			0
$223$	−4.11958	−	4.11958i	−0.275868	−	0.275868i	0.555589	−	0.831457i	$-0.312493\pi$
$223$	−4.11958	−	4.11958i	−0.275868	−	0.275868i	−0.831457	+	0.555589i	$0.812493\pi$
$224$		0			0
$225$	5.55602	−	1.30265i	0.370401	−	0.0868432i
$226$		0			0
$227$	−16.9333	+	16.9333i	−1.12390	+	1.12390i	−0.132755	+	0.991149i	$0.542382\pi$
$227$	−16.9333	+	16.9333i	−1.12390	+	1.12390i	−0.991149	+	0.132755i	$0.957618\pi$
$228$		0			0
$229$		−	17.3434i		−	1.14608i	−0.819527	−	0.573040i	$-0.805764\pi$
$229$		−	17.3434i		−	1.14608i	0.819527	−	0.573040i	$-0.194236\pi$
$230$		0			0
$231$			4.60609i			0.303058i
$232$		0			0
$233$	3.68802	−	3.68802i	0.241610	−	0.241610i	−0.575906	−	0.817516i	$-0.695350\pi$
$233$	3.68802	−	3.68802i	0.241610	−	0.241610i	0.817516	+	0.575906i	$0.195350\pi$
$234$		0			0
$235$	−5.22885	+	0.604770i	−0.341092	+	0.0394509i
$236$		0			0
$237$	7.64963	+	7.64963i	0.496897	+	0.496897i
$238$		0			0
$239$	−14.6923			−0.950364			−0.475182	−	0.879888i	$-0.657618\pi$
$239$	−14.6923			−0.950364			−0.475182	+	0.879888i	$0.657618\pi$
$240$		0			0
$241$	−0.179969			−0.0115928			−0.00579642	−	0.999983i	$-0.501845\pi$
$241$	−0.179969			−0.0115928			−0.00579642	+	0.999983i	$0.501845\pi$
$242$		0			0
$243$	7.85739	+	7.85739i	0.504052	+	0.504052i
$244$		0			0
$245$	−1.38900	+	1.75233i	−0.0887402	+	0.111952i
$246$		0			0
$247$	−4.87859	+	4.87859i	−0.310417	+	0.310417i
$248$		0			0
$249$			10.9066i			0.691179i
$250$		0			0
$251$			16.6698i			1.05219i	0.850426	+	0.526095i	$0.176344\pi$
$251$			16.6698i			1.05219i	−0.850426	+	0.526095i	$0.823656\pi$
$252$		0			0
$253$	−10.2313	+	10.2313i	−0.643238	+	0.643238i
$254$		0			0
$255$	5.66585	−	7.14789i	0.354809	−	0.447618i
$256$		0			0
$257$	11.5853	+	11.5853i	0.722672	+	0.722672i	0.969149	−	0.246476i	$-0.0792728\pi$
$257$	11.5853	+	11.5853i	0.722672	+	0.722672i	−0.246476	+	0.969149i	$0.579273\pi$
$258$		0			0
$259$	6.17068			0.383427
$260$		0			0
$261$	10.4440			0.646466
$262$		0			0
$263$	6.83488	+	6.83488i	0.421457	+	0.421457i	0.885705	−	0.464248i	$-0.153676\pi$
$263$	6.83488	+	6.83488i	0.421457	+	0.421457i	−0.464248	+	0.885705i	$0.653676\pi$
$264$		0			0
$265$	−0.697352	+	0.0806560i	−0.0428380	+	0.00495466i
$266$		0			0
$267$	−14.4693	+	14.4693i	−0.885505	+	0.885505i
$268$		0			0
$269$			6.00000i			0.365826i	0.983129	+	0.182913i	$0.0585527\pi$
$269$			6.00000i			0.365826i	−0.983129	+	0.182913i	$0.941447\pi$
$270$		0			0
$271$			11.8587i			0.720365i	0.932882	+	0.360183i	$0.117286\pi$
$271$			11.8587i			0.720365i	−0.932882	+	0.360183i	$0.882714\pi$
$272$		0			0
$273$	0.832988	−	0.832988i	0.0504147	−	0.0504147i
$274$		0			0
$275$	−16.4468	+	3.85607i	−0.991780	+	0.232530i
$276$		0			0
$277$	−13.3727	−	13.3727i	−0.803485	−	0.803485i	0.180153	−	0.983639i	$-0.442341\pi$
$277$	−13.3727	−	13.3727i	−0.803485	−	0.803485i	−0.983639	+	0.180153i	$0.942341\pi$
$278$		0			0
$279$	9.91269			0.593457
$280$		0			0
$281$	−14.8867			−0.888063			−0.444032	−	0.896011i	$-0.646452\pi$
$281$	−14.8867			−0.888063			−0.444032	+	0.896011i	$0.646452\pi$
$282$		0			0
$283$	−14.2058	−	14.2058i	−0.844445	−	0.844445i	0.144988	−	0.989433i	$-0.453686\pi$
$283$	−14.2058	−	14.2058i	−0.844445	−	0.844445i	−0.989433	+	0.144988i	$0.953686\pi$
$284$		0			0
$285$	−2.79667	−	24.1800i	−0.165660	−	1.43230i
$286$		0			0
$287$	−1.57778	+	1.57778i	−0.0931335	+	0.0931335i
$288$		0			0
$289$		−	8.04796i		−	0.473410i
$290$		0			0
$291$			17.6923i			1.03714i
$292$		0			0
$293$	16.9637	−	16.9637i	0.991029	−	0.991029i	−0.00893151	−	0.999960i	$-0.502843\pi$
$293$	16.9637	−	16.9637i	0.991029	−	0.991029i	0.999960	+	0.00893151i	$0.00284303\pi$
$294$		0			0
$295$	−2.15103	−	1.70504i	−0.125238	−	0.0992712i
$296$		0			0
$297$	−13.4883	−	13.4883i	−0.782672	−	0.782672i
$298$		0			0
$299$	3.70057			0.214009
$300$		0			0
$301$	11.7873			0.679411
$302$		0			0
$303$	−6.53413	−	6.53413i	−0.375376	−	0.375376i
$304$		0			0
$305$	9.73599	+	7.71733i	0.557481	+	0.441893i
$306$		0			0
$307$	−22.1904	+	22.1904i	−1.26647	+	1.26647i	−0.318577	+	0.947897i	$0.603205\pi$
$307$	−22.1904	+	22.1904i	−1.26647	+	1.26647i	−0.947897	+	0.318577i	$0.896795\pi$
$308$		0			0
$309$			11.1693i			0.635401i
$310$		0			0
$311$		−	16.8433i		−	0.955096i	−0.878606	−	0.477548i	$-0.841526\pi$
$311$		−	16.8433i		−	0.955096i	0.878606	−	0.477548i	$-0.158474\pi$
$312$		0			0
$313$	5.17634	−	5.17634i	0.292584	−	0.292584i	−0.545516	−	0.838100i	$-0.683666\pi$
$313$	5.17634	−	5.17634i	0.292584	−	0.292584i	0.838100	+	0.545516i	$0.183666\pi$
$314$		0			0
$315$	−0.293223	−	2.53520i	−0.0165212	−	0.142843i
$316$		0			0
$317$	−17.5653	−	17.5653i	−0.986568	−	0.986568i	0.0133429	−	0.999911i	$-0.495753\pi$
$317$	−17.5653	−	17.5653i	−0.986568	−	0.986568i	−0.999911	+	0.0133429i	$0.995753\pi$
$318$		0			0
$319$	−30.9161			−1.73097
$320$		0			0
$321$	−16.0700			−0.896940
$322$		0			0
$323$	16.8928	+	16.8928i	0.939941	+	0.939941i
$324$		0			0
$325$	3.67168	+	2.27697i	0.203668	+	0.126304i
$326$		0			0
$327$	5.21985	−	5.21985i	0.288658	−	0.288658i
$328$		0			0
$329$			2.35400i			0.129780i
$330$		0			0
$331$		−	23.6815i		−	1.30165i	−0.759228	−	0.650825i	$-0.774423\pi$
$331$		−	23.6815i		−	1.30165i	0.759228	−	0.650825i	$-0.225577\pi$
$332$		0			0
$333$	−4.98002	+	4.98002i	−0.272904	+	0.272904i
$334$		0			0
$335$	−11.0130	+	1.27376i	−0.601702	+	0.0695931i
$336$		0			0
$337$	11.9193	+	11.9193i	0.649288	+	0.649288i	0.952821	−	0.303533i	$-0.0981662\pi$
$337$	11.9193	+	11.9193i	0.649288	+	0.649288i	−0.303533	+	0.952821i	$0.598166\pi$
$338$		0			0
$339$	23.3279			1.26700
$340$		0			0
$341$	−29.3434			−1.58903
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	−8.10996	+	10.2313i	−0.436626	+	0.550836i
$346$		0			0
$347$	18.1981	−	18.1981i	0.976925	−	0.976925i	−0.0228151	−	0.999740i	$-0.507263\pi$
$347$	18.1981	−	18.1981i	0.976925	−	0.976925i	0.999740	+	0.0228151i	$0.00726289\pi$
$348$		0			0
$349$			9.52332i			0.509772i	0.966971	+	0.254886i	$0.0820379\pi$
$349$			9.52332i			0.509772i	−0.966971	+	0.254886i	$0.917962\pi$
$350$		0			0
$351$			4.87859i			0.260400i
$352$		0			0
$353$	−5.10633	+	5.10633i	−0.271783	+	0.271783i	−0.829817	−	0.558035i	$-0.811556\pi$
$353$	−5.10633	+	5.10633i	−0.271783	+	0.271783i	0.558035	+	0.829817i	$0.311556\pi$
$354$		0			0
$355$	5.35610	−	6.75712i	0.284272	−	0.358631i
$356$		0			0
$357$	−2.88434	−	2.88434i	−0.152655	−	0.152655i
$358$		0			0
$359$	−31.1391			−1.64346			−0.821729	−	0.569878i	$-0.806990\pi$
$359$	−31.1391			−1.64346			−0.821729	+	0.569878i	$0.806990\pi$
$360$		0			0
$361$	44.7546			2.35551
$362$		0			0
$363$	0.399759	+	0.399759i	0.0209819	+	0.0209819i
$364$		0			0
$365$	12.1507	−	1.40535i	0.635995	−	0.0735594i
$366$		0			0
$367$	−16.4063	+	16.4063i	−0.856402	+	0.856402i	−0.990912	−	0.134510i	$-0.957054\pi$
$367$	−16.4063	+	16.4063i	−0.856402	+	0.856402i	0.134510	+	0.990912i	$0.457054\pi$
$368$		0			0
$369$		−	2.54669i		−	0.132575i
$370$		0			0
$371$			0.313944i			0.0162992i
$372$		0			0
$373$	−10.9800	+	10.9800i	−0.568524	+	0.568524i	−0.931715	−	0.363191i	$-0.881687\pi$
$373$	−10.9800	+	10.9800i	−0.568524	+	0.568524i	0.363191	+	0.931715i	$0.381687\pi$
$374$		0			0
$375$	−14.3420	+	5.16136i	−0.740618	+	0.266531i
$376$		0			0
$377$	5.59102	+	5.59102i	0.287952	+	0.287952i
$378$		0			0
$379$	25.7830			1.32438			0.662191	−	0.749335i	$-0.269627\pi$
$379$	25.7830			1.32438			0.662191	+	0.749335i	$0.269627\pi$
$380$		0			0
$381$	−0.675305			−0.0345969
$382$		0			0
$383$	8.81242	+	8.81242i	0.450294	+	0.450294i	0.895452	−	0.445158i	$-0.146853\pi$
$383$	8.81242	+	8.81242i	0.450294	+	0.450294i	−0.445158	+	0.895452i	$0.646853\pi$
$384$		0			0
$385$	0.867993	+	7.50466i	0.0442370	+	0.382473i
$386$		0			0
$387$	−9.51293	+	9.51293i	−0.483569	+	0.483569i
$388$		0			0
$389$			13.8001i			0.699691i	0.936807	+	0.349845i	$0.113766\pi$
$389$			13.8001i			0.699691i	−0.936807	+	0.349845i	$0.886234\pi$
$390$		0			0
$391$		−	12.8137i		−	0.648019i
$392$		0			0
$393$	0.675305	−	0.675305i	0.0340646	−	0.0340646i
$394$		0			0
$395$	13.9050	+	11.0220i	0.699637	+	0.554574i
$396$		0			0
$397$	17.7230	+	17.7230i	0.889493	+	0.889493i	0.994474	−	0.104981i	$-0.0334782\pi$
$397$	17.7230	+	17.7230i	0.889493	+	0.889493i	−0.104981	+	0.994474i	$0.533478\pi$
$398$		0			0
$399$	−10.8857			−0.544967
$400$		0			0
$401$	26.4427			1.32048			0.660242	−	0.751053i	$-0.270454\pi$
$401$	26.4427			1.32048			0.660242	+	0.751053i	$0.270454\pi$
$402$		0			0
$403$	5.30660	+	5.30660i	0.264341	+	0.264341i
$404$		0			0
$405$	−7.48832	−	5.93569i	−0.372097	−	0.294947i
$406$		0			0
$407$	14.7418	−	14.7418i	0.730723	−	0.730723i
$408$		0			0
$409$		−	8.79667i		−	0.434967i	−0.976064	−	0.217484i	$-0.930215\pi$
$409$		−	8.79667i		−	0.434967i	0.976064	−	0.217484i	$-0.0697848\pi$
$410$		0			0
$411$			1.65554i			0.0816616i
$412$		0			0
$413$	−0.867993	+	0.867993i	−0.0427111	+	0.0427111i
$414$		0			0
$415$	2.05529	+	17.7701i	0.100890	+	0.872299i
$416$		0			0
$417$	−0.920662	−	0.920662i	−0.0450850	−	0.0450850i
$418$		0			0
$419$	26.3100			1.28533			0.642664	−	0.766148i	$-0.277829\pi$
$419$	26.3100			1.28533			0.642664	+	0.766148i	$0.277829\pi$
$420$		0			0
$421$	12.6226			0.615190			0.307595	−	0.951517i	$-0.400476\pi$
$421$	12.6226			0.615190			0.307595	+	0.951517i	$0.400476\pi$
$422$		0			0
$423$	−1.89979	−	1.89979i	−0.0923708	−	0.0923708i
$424$		0			0
$425$	7.88434	−	12.7137i	0.382447	−	0.616705i
$426$		0			0
$427$	3.92870	−	3.92870i	0.190123	−	0.190123i
$428$		0			0
$429$		−	3.98002i		−	0.192157i
$430$		0			0
$431$		−	32.3171i		−	1.55666i	−0.627855	−	0.778330i	$-0.716067\pi$
$431$		−	32.3171i		−	1.55666i	0.627855	−	0.778330i	$-0.283933\pi$
$432$		0			0
$433$	−21.9193	+	21.9193i	−1.05338	+	1.05338i	−0.0548837	+	0.998493i	$0.517479\pi$
$433$	−21.9193	+	21.9193i	−1.05338	+	1.05338i	−0.998493	+	0.0548837i	$0.982521\pi$
$434$		0			0
$435$	−27.7110	+	3.20507i	−1.32864	+	0.153671i
$436$		0			0
$437$	−24.1800	−	24.1800i	−1.15668	−	1.15668i
$438$		0			0
$439$	−5.35610			−0.255633			−0.127816	−	0.991798i	$-0.540797\pi$
$439$	−5.35610			−0.255633			−0.127816	+	0.991798i	$0.540797\pi$
$440$		0			0
$441$	−1.14134			−0.0543493
$442$		0			0
$443$	25.9597	+	25.9597i	1.23338	+	1.23338i	0.962656	+	0.270729i	$0.0872647\pi$
$443$	25.9597	+	25.9597i	1.23338	+	1.23338i	0.270729	+	0.962656i	$0.412735\pi$
$444$		0			0
$445$	−20.8480	+	26.3013i	−0.988291	+	1.24680i
$446$		0			0
$447$	0.700510	−	0.700510i	0.0331330	−	0.0331330i
$448$		0			0
$449$		−	3.25337i		−	0.153536i	−0.997049	−	0.0767680i	$-0.975540\pi$
$449$		−	3.25337i		−	0.153536i	0.997049	−	0.0767680i	$-0.0244601\pi$
$450$		0			0
$451$			7.53866i			0.354981i
$452$		0			0
$453$	−15.8550	+	15.8550i	−0.744935	+	0.744935i
$454$		0			0
$455$	1.20021	−	1.51415i	0.0562667	−	0.0709846i
$456$		0			0
$457$	−19.9766	−	19.9766i	−0.934468	−	0.934468i	0.0635134	−	0.997981i	$-0.479769\pi$
$457$	−19.9766	−	19.9766i	−0.934468	−	0.934468i	−0.997981	+	0.0635134i	$0.979769\pi$
$458$		0			0
$459$	16.8928			0.788489
$460$		0			0
$461$	31.2080			1.45350			0.726750	−	0.686902i	$-0.241030\pi$
$461$	31.2080			1.45350			0.726750	+	0.686902i	$0.241030\pi$
$462$		0			0
$463$	−20.9256	−	20.9256i	−0.972497	−	0.972497i	0.0271346	−	0.999632i	$-0.491362\pi$
$463$	−20.9256	−	20.9256i	−0.972497	−	0.972497i	−0.999632	+	0.0271346i	$0.991362\pi$
$464$		0			0
$465$	−26.3013	+	3.04202i	−1.21969	+	0.141070i
$466$		0			0
$467$	−13.7778	+	13.7778i	−0.637558	+	0.637558i	−0.949953	−	0.312394i	$-0.898869\pi$
$467$	−13.7778	+	13.7778i	−0.637558	+	0.637558i	0.312394	+	0.949953i	$0.398869\pi$
$468$		0			0
$469$			4.95798i			0.228938i
$470$		0			0
$471$		−	29.2290i		−	1.34680i
$472$		0			0
$473$	28.1600	−	28.1600i	1.29480	−	1.29480i
$474$		0			0
$475$	−9.11317	−	38.8692i	−0.418141	−	1.78344i
$476$		0			0
$477$	−0.253368	−	0.253368i	−0.0116009	−	0.0116009i
$478$		0			0
$479$	7.81116			0.356901			0.178450	−	0.983949i	$-0.442892\pi$
$479$	7.81116			0.356901			0.178450	+	0.983949i	$0.442892\pi$
$480$		0			0
$481$	−5.33195			−0.243116
$482$		0			0
$483$	4.12858	+	4.12858i	0.187857	+	0.187857i
$484$		0			0
$485$	3.33402	+	28.8260i	0.151390	+	1.30892i
$486$		0			0
$487$	6.18387	−	6.18387i	0.280218	−	0.280218i	−0.552978	−	0.833196i	$-0.686509\pi$
$487$	6.18387	−	6.18387i	0.280218	−	0.280218i	0.833196	+	0.552978i	$0.186509\pi$
$488$		0			0
$489$			18.8667i			0.853180i
$490$		0			0
$491$		−	13.0367i		−	0.588340i	−0.955753	−	0.294170i	$-0.904957\pi$
$491$		−	13.0367i		−	0.588340i	0.955753	−	0.294170i	$-0.0950431\pi$
$492$		0			0
$493$	19.3597	−	19.3597i	0.871917	−	0.871917i
$494$		0			0
$495$	−6.75712	−	5.35610i	−0.303710	−	0.240739i
$496$		0			0
$497$	−2.72666	−	2.72666i	−0.122307	−	0.122307i
$498$		0			0
$499$	39.7747			1.78056			0.890281	−	0.455412i	$-0.150508\pi$
$499$	39.7747			1.78056			0.890281	+	0.455412i	$0.150508\pi$
$500$		0			0
$501$	−22.8467			−1.02072
$502$		0			0
$503$	12.2777	+	12.2777i	0.547437	+	0.547437i	0.925699	−	0.378262i	$-0.123478\pi$
$503$	12.2777	+	12.2777i	0.547437	+	0.547437i	−0.378262	+	0.925699i	$0.623478\pi$
$504$		0			0
$505$	−11.8773	−	9.41468i	−0.528534	−	0.418948i
$506$		0			0
$507$	11.8125	−	11.8125i	0.524610	−	0.524610i
$508$		0			0
$509$		−	10.6240i		−	0.470898i	−0.971887	−	0.235449i	$-0.924344\pi$
$509$		−	10.6240i		−	0.470898i	0.971887	−	0.235449i	$-0.0756561\pi$
$510$		0			0
$511$		−	5.47017i		−	0.241986i
$512$		0			0
$513$	31.8773	−	31.8773i	1.40742	−	1.40742i
$514$		0			0
$515$	2.10480	+	18.1981i	0.0927485	+	0.801904i
$516$		0			0
$517$	5.62371	+	5.62371i	0.247331	+	0.247331i
$518$		0			0
$519$	18.1023			0.794605
$520$		0			0
$521$	3.56327			0.156110			0.0780549	−	0.996949i	$-0.475129\pi$
$521$	3.56327			0.156110			0.0780549	+	0.996949i	$0.475129\pi$
$522$		0			0
$523$	0.827768	+	0.827768i	0.0361958	+	0.0361958i	0.724973	−	0.688777i	$-0.241852\pi$
$523$	0.827768	+	0.827768i	0.0361958	+	0.0361958i	−0.688777	+	0.724973i	$0.741852\pi$
$524$		0			0
$525$	1.55602	+	6.63667i	0.0679101	+	0.289648i
$526$		0			0
$527$	18.3749	−	18.3749i	0.800421	−	0.800421i
$528$		0			0
$529$		−	4.65872i		−	0.202553i
$530$		0			0
$531$		−	1.40102i		−	0.0607991i
$532$		0			0
$533$	1.36333	−	1.36333i	0.0590523	−	0.0590523i
$534$		0			0
$535$	−26.1827	+	3.02831i	−1.13198	+	0.130925i
$536$		0			0
$537$	20.7080	+	20.7080i	0.893616	+	0.893616i
$538$		0			0
$539$	3.37856			0.145525
$540$		0			0
$541$	−25.7347			−1.10642			−0.553210	−	0.833042i	$-0.686597\pi$
$541$	−25.7347			−1.10642			−0.553210	+	0.833042i	$0.686597\pi$
$542$		0			0
$543$	9.16267	+	9.16267i	0.393208	+	0.393208i
$544$		0			0
$545$	7.52101	−	9.48832i	0.322165	−	0.406435i
$546$		0			0
$547$	17.0696	−	17.0696i	0.729842	−	0.729842i	−0.240746	−	0.970588i	$-0.577392\pi$
$547$	17.0696	−	17.0696i	0.729842	−	0.729842i	0.970588	+	0.240746i	$0.0773921\pi$
$548$		0			0
$549$			6.34128i			0.270639i
$550$		0			0
$551$		−	73.0649i		−	3.11267i
$552$		0			0
$553$	5.61100	−	5.61100i	0.238604	−	0.238604i
$554$		0			0
$555$	11.6852	−	14.7418i	0.496010	−	0.625753i
$556$		0			0
$557$	−23.1600	−	23.1600i	−0.981320	−	0.981320i	0.0185083	−	0.999829i	$-0.494108\pi$
$557$	−23.1600	−	23.1600i	−0.981320	−	0.981320i	−0.999829	+	0.0185083i	$0.994108\pi$
$558$		0			0
$559$	−10.1852			−0.430788
$560$		0			0
$561$	−13.7814			−0.581851
$562$		0			0
$563$	−4.95634	−	4.95634i	−0.208885	−	0.208885i	0.594908	−	0.803793i	$-0.297188\pi$
$563$	−4.95634	−	4.95634i	−0.208885	−	0.208885i	−0.803793	+	0.594908i	$0.797188\pi$
$564$		0			0
$565$	38.0080	−	4.39602i	1.59901	−	0.184942i
$566$		0			0
$567$	−3.02171	+	3.02171i	−0.126900	+	0.126900i
$568$		0			0
$569$			28.1986i			1.18215i	0.806617	+	0.591074i	$0.201296\pi$
$569$			28.1986i			1.18215i	−0.806617	+	0.591074i	$0.798704\pi$
$570$		0			0
$571$		−	8.25715i		−	0.345551i	−0.984961	−	0.172776i	$-0.944726\pi$
$571$		−	8.25715i		−	0.345551i	0.984961	−	0.172776i	$-0.0552735\pi$
$572$		0			0
$573$	12.1377	−	12.1377i	0.507060	−	0.507060i
$574$		0			0
$575$	−11.2855	+	18.1981i	−0.470636	+	0.758913i
$576$		0			0
$577$	−5.44036	−	5.44036i	−0.226485	−	0.226485i	0.584738	−	0.811223i	$-0.301197\pi$
$577$	−5.44036	−	5.44036i	−0.226485	−	0.226485i	−0.811223	+	0.584738i	$0.801197\pi$
$578$		0			0
$579$	−1.85355			−0.0770309
$580$		0			0
$581$	8.00000			0.331896
$582$		0			0
$583$	0.750014	+	0.750014i	0.0310624	+	0.0310624i
$584$		0			0
$585$	0.253368	+	2.19062i	0.0104755	+	0.0905709i
$586$		0			0
$587$	8.55790	−	8.55790i	0.353222	−	0.353222i	−0.508085	−	0.861307i	$-0.669646\pi$
$587$	8.55790	−	8.55790i	0.353222	−	0.353222i	0.861307	+	0.508085i	$0.169646\pi$
$588$		0			0
$589$		−	69.3480i		−	2.85743i
$590$		0			0
$591$		−	34.8217i		−	1.43237i
$592$		0			0
$593$	−29.9217	+	29.9217i	−1.22874	+	1.22874i	−0.264293	+	0.964443i	$0.585138\pi$
$593$	−29.9217	+	29.9217i	−1.22874	+	1.22874i	−0.964443	+	0.264293i	$0.914862\pi$
$594$		0			0
$595$	−5.24297	−	4.15589i	−0.214941	−	0.170375i
$596$		0			0
$597$	6.77669	+	6.77669i	0.277351	+	0.277351i
$598$		0			0
$599$	17.2463			0.704666			0.352333	−	0.935875i	$-0.385388\pi$
$599$	17.2463			0.704666			0.352333	+	0.935875i	$0.385388\pi$
$600$		0			0
$601$	−29.0980			−1.18693			−0.593466	−	0.804859i	$-0.702241\pi$
$601$	−29.0980			−1.18693			−0.593466	+	0.804859i	$0.702241\pi$
$602$		0			0
$603$	−4.00132	−	4.00132i	−0.162946	−	0.162946i
$604$		0			0
$605$	0.726656	+	0.575992i	0.0295428	+	0.0234174i
$606$		0			0
$607$	−3.41907	+	3.41907i	−0.138776	+	0.138776i	−0.773082	−	0.634306i	$-0.781286\pi$
$607$	−3.41907	+	3.41907i	−0.138776	+	0.138776i	0.634306	+	0.773082i	$0.281286\pi$
$608$		0			0
$609$			12.4754i			0.505527i
$610$		0			0
$611$		−	2.03404i		−	0.0822885i
$612$		0			0
$613$	13.3013	−	13.3013i	0.537236	−	0.537236i	−0.385480	−	0.922716i	$-0.625964\pi$
$613$	13.3013	−	13.3013i	0.537236	−	0.537236i	0.922716	+	0.385480i	$0.125964\pi$
$614$		0			0
$615$	0.781532	+	6.75712i	0.0315144	+	0.272474i
$616$		0			0
$617$	−13.9380	−	13.9380i	−0.561123	−	0.561123i	0.368504	−	0.929626i	$-0.379870\pi$
$617$	−13.9380	−	13.9380i	−0.561123	−	0.561123i	−0.929626	+	0.368504i	$0.879870\pi$
$618$		0			0
$619$	22.7264			0.913452			0.456726	−	0.889607i	$-0.349022\pi$
$619$	22.7264			0.913452			0.456726	+	0.889607i	$0.349022\pi$
$620$		0			0
$621$	−24.1800			−0.970309
$622$		0			0
$623$	10.6132	+	10.6132i	0.425209	+	0.425209i
$624$		0			0
$625$	−22.3947	+	11.1120i	−0.895788	+	0.444481i
$626$		0			0
$627$	−26.0060	+	26.0060i	−1.03858	+	1.03858i
$628$		0			0
$629$			18.4626i			0.736154i
$630$		0			0
$631$			2.93257i			0.116744i	0.998295	+	0.0583718i	$0.0185909\pi$
$631$			2.93257i			0.116744i	−0.998295	+	0.0583718i	$0.981409\pi$
$632$		0			0
$633$	8.32493	−	8.32493i	0.330886	−	0.330886i
$634$		0			0
$635$	−1.10027	+	0.127258i	−0.0436629	+	0.00505006i
$636$		0			0
$637$	−0.610996	−	0.610996i	−0.0242085	−	0.0242085i
$638$		0			0
$639$	4.40108			0.174104
$640$		0			0
$641$	14.2241			0.561817			0.280908	−	0.959735i	$-0.409364\pi$
$641$	14.2241			0.561817			0.280908	+	0.959735i	$0.409364\pi$
$642$		0			0
$643$	22.8909	+	22.8909i	0.902730	+	0.902730i	0.995672	−	0.0929416i	$-0.0296270\pi$
$643$	22.8909	+	22.8909i	0.902730	+	0.902730i	−0.0929416	+	0.995672i	$0.529627\pi$
$644$		0			0
$645$	22.3213	−	28.1600i	0.878901	−	1.10880i
$646$		0			0
$647$	−1.62729	+	1.62729i	−0.0639752	+	0.0639752i	−0.738370	−	0.674395i	$-0.764404\pi$
$647$	−1.62729	+	1.62729i	−0.0639752	+	0.0639752i	0.674395	+	0.738370i	$0.264404\pi$
$648$		0			0
$649$			4.14728i			0.162795i
$650$		0			0
$651$			11.8407i			0.464075i
$652$		0			0
$653$	−7.46264	+	7.46264i	−0.292036	+	0.292036i	−0.837884	−	0.545848i	$-0.816207\pi$
$653$	−7.46264	+	7.46264i	−0.292036	+	0.292036i	0.545848	+	0.837884i	$0.316207\pi$
$654$		0			0
$655$	0.973012	−	1.22753i	0.0380187	−	0.0479634i
$656$		0			0
$657$	4.41468	+	4.41468i	0.172233	+	0.172233i
$658$		0			0
$659$	−10.3902			−0.404745			−0.202372	−	0.979309i	$-0.564865\pi$
$659$	−10.3902			−0.404745			−0.202372	+	0.979309i	$0.564865\pi$
$660$		0			0
$661$	48.3973			1.88243			0.941217	−	0.337801i	$-0.109683\pi$
$661$	48.3973			1.88243			0.941217	+	0.337801i	$0.109683\pi$
$662$		0			0
$663$	2.49230	+	2.49230i	0.0967928	+	0.0967928i
$664$		0			0
$665$	−17.7360	+	2.05135i	−0.687772	+	0.0795480i
$666$		0			0
$667$	−27.7110	+	27.7110i	−1.07297	+	1.07297i
$668$		0			0
$669$			7.94271i			0.307083i
$670$		0			0
$671$		−	18.7713i		−	0.724660i
$672$		0			0
$673$	−7.97070	+	7.97070i	−0.307248	+	0.307248i	−0.843841	−	0.536593i	$-0.819711\pi$
$673$	−7.97070	+	7.97070i	−0.307248	+	0.307248i	0.536593	+	0.843841i	$0.319711\pi$
$674$		0			0
$675$	−23.9912	−	14.8780i	−0.923422	−	0.572655i
$676$		0			0
$677$	18.7137	+	18.7137i	0.719226	+	0.719226i	0.968447	−	0.249221i	$-0.0801745\pi$
$677$	18.7137	+	18.7137i	0.719226	+	0.719226i	−0.249221	+	0.968447i	$0.580174\pi$
$678$		0			0
$679$	12.9773			0.498023
$680$		0			0
$681$	32.6481			1.25108
$682$		0			0
$683$	−8.81242	−	8.81242i	−0.337198	−	0.337198i	0.518114	−	0.855312i	$-0.326634\pi$
$683$	−8.81242	−	8.81242i	−0.337198	−	0.337198i	−0.855312	+	0.518114i	$0.826634\pi$
$684$		0			0
$685$	0.311977	+	2.69735i	0.0119200	+	0.103061i
$686$		0			0
$687$	−16.7193	+	16.7193i	−0.637882	+	0.637882i
$688$		0			0
$689$		−	0.271273i		−	0.0103347i
$690$		0			0
$691$		−	5.00258i		−	0.190307i	−0.995463	−	0.0951536i	$-0.969666\pi$
$691$		−	5.00258i		−	0.190307i	0.995463	−	0.0951536i	$-0.0303342\pi$
$692$		0			0
$693$	−2.72666	+	2.72666i	−0.103577	+	0.103577i
$694$		0			0
$695$	−1.67352	−	1.32653i	−0.0634803	−	0.0503183i
$696$		0			0
$697$	−4.72072	−	4.72072i	−0.178810	−	0.178810i
$698$		0			0
$699$	−7.11065			−0.268949
$700$		0			0
$701$	−7.23471			−0.273251			−0.136626	−	0.990623i	$-0.543626\pi$
$701$	−7.23471			−0.273251			−0.136626	+	0.990623i	$0.543626\pi$
$702$		0			0
$703$	34.8397	+	34.8397i	1.31400	+	1.31400i
$704$		0			0
$705$	5.62371	+	4.45769i	0.211801	+	0.167886i
$706$		0			0
$707$	−4.79278	+	4.79278i	−0.180251	+	0.180251i
$708$		0			0
$709$			37.6387i			1.41355i	0.707437	+	0.706776i	$0.249851\pi$
$709$			37.6387i			1.41355i	−0.707437	+	0.706776i	$0.750149\pi$
$710$		0			0
$711$			9.05667i			0.339652i
$712$		0			0
$713$	−26.3013	+	26.3013i	−0.984993	+	0.984993i
$714$		0			0
$715$	−0.750014	−	6.48462i	−0.0280489	−	0.242511i
$716$		0			0
$717$	14.1636	+	14.1636i	0.528950	+	0.528950i
$718$		0			0
$719$	−28.5285			−1.06393			−0.531967	−	0.846765i	$-0.678547\pi$
$719$	−28.5285			−1.06393			−0.531967	+	0.846765i	$0.678547\pi$
$720$		0			0
$721$	8.19269			0.305112
$722$		0			0
$723$	0.173494	+	0.173494i	0.00645231	+	0.00645231i
$724$		0			0
$725$	−44.5454	+	10.4440i	−1.65437	+	0.387880i
$726$		0			0
$727$	−8.55790	+	8.55790i	−0.317395	+	0.317395i	−0.847766	−	0.530371i	$-0.822053\pi$
$727$	−8.55790	+	8.55790i	−0.317395	+	0.317395i	0.530371	+	0.847766i	$0.322053\pi$
$728$		0			0
$729$		−	27.9694i		−	1.03590i
$730$		0			0
$731$			35.2677i			1.30442i
$732$		0			0
$733$	−28.2956	+	28.2956i	−1.04512	+	1.04512i	−0.0461903	+	0.998933i	$0.514708\pi$
$733$	−28.2956	+	28.2956i	−1.04512	+	1.04512i	−0.998933	+	0.0461903i	$0.985292\pi$
$734$		0			0
$735$	3.02831	−	0.350255i	0.111701	−	0.0129194i
$736$		0			0
$737$	11.8446	+	11.8446i	0.436302	+	0.436302i
$738$		0			0
$739$	44.1758			1.62503			0.812517	−	0.582938i	$-0.198097\pi$
$739$	44.1758			1.62503			0.812517	+	0.582938i	$0.198097\pi$
$740$		0			0
$741$	9.40610			0.345542
$742$		0			0
$743$	2.45179	+	2.45179i	0.0899473	+	0.0899473i	0.750649	−	0.660701i	$-0.229741\pi$
$743$	2.45179	+	2.45179i	0.0899473	+	0.0899473i	−0.660701	+	0.750649i	$0.729741\pi$
$744$		0			0
$745$	1.00933	−	1.27334i	0.0369789	−	0.0466517i
$746$		0			0
$747$	−6.45637	+	6.45637i	−0.236226	+	0.236226i
$748$		0			0
$749$			11.7873i			0.430700i
$750$		0			0
$751$			45.8314i			1.67241i	0.548417	+	0.836205i	$0.315231\pi$
$751$			45.8314i			1.67241i	−0.548417	+	0.836205i	$0.684769\pi$
$752$		0			0
$753$	16.0700	−	16.0700i	0.585624	−	0.585624i
$754$		0			0
$755$	−22.8447	+	28.8203i	−0.831403	+	1.04888i
$756$		0			0
$757$	−16.9800	−	16.9800i	−0.617149	−	0.617149i	0.327650	−	0.944799i	$-0.393743\pi$
$757$	−16.9800	−	16.9800i	−0.617149	−	0.617149i	−0.944799	+	0.327650i	$0.893743\pi$
$758$		0			0
$759$	19.7264			0.716022
$760$		0			0
$761$	−21.0093			−0.761588			−0.380794	−	0.924660i	$-0.624349\pi$
$761$	−21.0093			−0.761588			−0.380794	+	0.924660i	$0.624349\pi$
$762$		0			0
$763$	−3.82876	−	3.82876i	−0.138610	−	0.138610i
$764$		0			0
$765$	7.58532	−	0.877321i	0.274248	−	0.0317196i
$766$		0			0
$767$	0.750014	−	0.750014i	0.0270814	−	0.0270814i
$768$		0			0
$769$		−	10.4113i		−	0.375441i	−0.982223	−	0.187720i	$-0.939890\pi$
$769$		−	10.4113i		−	0.375441i	0.982223	−	0.187720i	$-0.0601099\pi$
$770$		0			0
$771$		−	22.3369i		−	0.804445i
$772$		0			0
$773$	1.67168	−	1.67168i	0.0601260	−	0.0601260i	−0.676404	−	0.736530i	$-0.736463\pi$
$773$	1.67168	−	1.67168i	0.0601260	−	0.0601260i	0.736530	+	0.676404i	$0.236463\pi$
$774$		0			0
$775$	−42.2793	+	9.91269i	−1.51872	+	0.356074i
$776$		0			0
$777$	−5.94865	−	5.94865i	−0.213407	−	0.213407i
$778$		0			0
$779$	−17.8163			−0.638336
$780$		0			0
$781$	−13.0280			−0.466178
$782$		0			0
$783$	−36.5324	−	36.5324i	−1.30556	−	1.30556i
$784$		0			0
$785$	−5.50805	−	47.6226i	−0.196591	−	1.69972i
$786$		0			0
$787$	6.74813	−	6.74813i	0.240545	−	0.240545i	−0.576531	−	0.817076i	$-0.695594\pi$
$787$	6.74813	−	6.74813i	0.240545	−	0.240545i	0.817076	+	0.576531i	$0.195594\pi$
$788$		0			0
$789$		−	13.1779i		−	0.469146i
$790$		0			0
$791$		−	17.1110i		−	0.608398i
$792$		0			0
$793$	−3.39470	+	3.39470i	−0.120549	+	0.120549i
$794$		0			0
$795$	0.750014	+	0.594506i	0.0266003	+	0.0210850i
$796$		0			0
$797$	30.9123	+	30.9123i	1.09497	+	1.09497i	0.994989	+	0.0999815i	$0.0318783\pi$
$797$	30.9123	+	30.9123i	1.09497	+	1.09497i	0.0999815	+	0.994989i	$0.468122\pi$
$798$		0			0
$799$	−7.04316			−0.249169
$800$		0			0
$801$	−17.1307			−0.605283
$802$		0			0
$803$	−13.0683	−	13.0683i	−0.461169	−	0.461169i
$804$		0			0
$805$	7.50466	+	5.94865i	0.264505	+	0.209662i
$806$		0			0
$807$	5.78411	−	5.78411i	0.203610	−	0.203610i
$808$		0			0
$809$		−	26.6040i		−	0.935346i	−0.883902	−	0.467673i	$-0.845092\pi$
$809$		−	26.6040i		−	0.935346i	0.883902	−	0.467673i	$-0.154908\pi$
$810$		0			0
$811$		−	22.9809i		−	0.806970i	−0.914986	−	0.403485i	$-0.867799\pi$
$811$		−	22.9809i		−	0.806970i	0.914986	−	0.403485i	$-0.132201\pi$
$812$		0			0
$813$	11.4320	−	11.4320i	0.400938	−	0.400938i
$814$		0			0
$815$	3.55532	+	30.7393i	0.124538	+	1.07675i
$816$		0			0
$817$	66.5513	+	66.5513i	2.32834	+	2.32834i
$818$		0			0
$819$	0.986204			0.0344608
$820$		0			0
$821$	41.5360			1.44962			0.724809	−	0.688950i	$-0.241928\pi$
$821$	41.5360			1.44962			0.724809	+	0.688950i	$0.241928\pi$
$822$		0			0
$823$	29.8338	+	29.8338i	1.03994	+	1.03994i	0.999168	+	0.0407725i	$0.0129819\pi$
$823$	29.8338	+	29.8338i	1.03994	+	1.03994i	0.0407725	+	0.999168i	$0.487018\pi$
$824$		0			0
$825$	19.5724	+	12.1377i	0.681422	+	0.422581i
$826$		0			0
$827$	−21.8987	+	21.8987i	−0.761491	+	0.761491i	−0.976592	−	0.215101i	$-0.930992\pi$
$827$	−21.8987	+	21.8987i	−0.761491	+	0.761491i	0.215101	+	0.976592i	$0.430992\pi$
$828$		0			0
$829$			1.96731i			0.0683274i	0.999416	+	0.0341637i	$0.0108768\pi$
$829$			1.96731i			0.0683274i	−0.999416	+	0.0341637i	$0.989123\pi$
$830$		0			0
$831$			25.7830i			0.894402i
$832$		0			0
$833$	−2.11566	+	2.11566i	−0.0733033	+	0.0733033i
$834$		0			0
$835$	−37.2239	+	4.30534i	−1.28819	+	0.148992i
$836$		0			0
$837$	−34.6740	−	34.6740i	−1.19851	−	1.19851i
$838$		0			0
$839$	−39.5517			−1.36548			−0.682739	−	0.730662i	$-0.739211\pi$
$839$	−39.5517			−1.36548			−0.682739	+	0.730662i	$0.739211\pi$
$840$		0			0
$841$	−54.7347			−1.88740
$842$		0			0
$843$	14.3510	+	14.3510i	0.494275	+	0.494275i
$844$		0			0
$845$	17.0200	−	21.4720i	0.585505	−	0.738658i
$846$		0			0
$847$	0.293223	−	0.293223i	0.0100753	−	0.0100753i
$848$		0			0
$849$			27.3892i			0.939996i
$850$		0			0
$851$		−	26.4270i		−	0.905906i
$852$		0			0
$853$	−8.16932	+	8.16932i	−0.279712	+	0.279712i	−0.832994	−	0.553282i	$-0.813375\pi$
$853$	−8.16932	+	8.16932i	−0.279712	+	0.279712i	0.553282	+	0.832994i	$0.313375\pi$
$854$		0			0
$855$	12.6582	−	15.9693i	0.432902	−	0.546139i
$856$		0			0
$857$	−25.8094	−	25.8094i	−0.881632	−	0.881632i	0.112069	−	0.993700i	$-0.464252\pi$
$857$	−25.8094	−	25.8094i	−0.881632	−	0.881632i	−0.993700	+	0.112069i	$0.964252\pi$
$858$		0			0
$859$	33.3396			1.13753			0.568767	−	0.822499i	$-0.307421\pi$
$859$	33.3396			1.13753			0.568767	+	0.822499i	$0.307421\pi$
$860$		0			0
$861$	3.04202			0.103672
$862$		0			0
$863$	2.29628	+	2.29628i	0.0781662	+	0.0781662i	0.745109	−	0.666943i	$-0.232397\pi$
$863$	2.29628	+	2.29628i	0.0781662	+	0.0781662i	−0.666943	+	0.745109i	$0.732397\pi$
$864$		0			0
$865$	29.4940	−	3.41129i	1.00283	−	0.115987i
$866$		0			0
$867$	−7.75839	+	7.75839i	−0.263489	+	0.263489i
$868$		0			0
$869$		−	26.8094i		−	0.909446i
$870$		0			0
$871$		−	4.28408i		−	0.145161i
$872$		0			0
$873$	−10.4733	+	10.4733i	−0.354467	+	0.354467i
$874$		0			0
$875$	3.78585	+	10.5199i	0.127985	+	0.355636i
$876$		0			0
$877$	−29.7453	−	29.7453i	−1.00443	−	1.00443i	−0.999990	−	0.00443773i	$-0.998587\pi$
$877$	−29.7453	−	29.7453i	−1.00443	−	1.00443i	−0.00443773	−	0.999990i	$-0.501413\pi$
$878$		0			0
$879$	−32.7066			−1.10317
$880$		0			0
$881$	−30.3786			−1.02348			−0.511740	−	0.859140i	$-0.670999\pi$
$881$	−30.3786			−1.02348			−0.511740	+	0.859140i	$0.670999\pi$
$882$		0			0
$883$	9.61194	+	9.61194i	0.323467	+	0.323467i	0.850096	−	0.526628i	$-0.176544\pi$
$883$	9.61194	+	9.61194i	0.323467	+	0.323467i	−0.526628	+	0.850096i	$0.676544\pi$
$884$		0			0
$885$	0.429948	+	3.71733i	0.0144525	+	0.124957i
$886$		0			0
$887$	12.4140	−	12.4140i	0.416821	−	0.416821i	−0.467286	−	0.884106i	$-0.654768\pi$
$887$	12.4140	−	12.4140i	0.416821	−	0.416821i	0.884106	+	0.467286i	$0.154768\pi$
$888$		0			0
$889$			0.495336i			0.0166130i
$890$		0			0
$891$			14.4378i			0.483683i
$892$		0			0
$893$	−13.2907	+	13.2907i	−0.444756	+	0.444756i
$894$		0			0
$895$	37.6417	+	29.8371i	1.25822	+	0.997343i
$896$		0			0
$897$	−3.56742	−	3.56742i	−0.119113	−	0.119113i
$898$		0			0
$899$	−79.4750			−2.65064
$900$		0			0
$901$	−0.939320			−0.0312933
$902$		0			0
$903$	−11.3632	−	11.3632i	−0.378144	−	0.378144i
$904$		0			0
$905$	16.6553	+	13.2020i	0.553642	+	0.438850i
$906$		0			0
$907$	−16.7971	+	16.7971i	−0.557738	+	0.557738i	−0.928663	−	0.370925i	$-0.879041\pi$
$907$	−16.7971	+	16.7971i	−0.557738	+	0.557738i	0.370925	+	0.928663i	$0.379041\pi$
$908$		0			0
$909$		−	7.73599i		−	0.256586i
$910$		0			0
$911$		−	25.6275i		−	0.849076i	−0.905410	−	0.424538i	$-0.860437\pi$
$911$		−	25.6275i		−	0.849076i	0.905410	−	0.424538i	$-0.139563\pi$
$912$		0			0
$913$	19.1120	−	19.1120i	0.632516	−	0.632516i
$914$		0			0
$915$	−1.94602	−	16.8253i	−0.0643335	−	0.556228i
$916$		0			0
$917$	−0.495336	−	0.495336i	−0.0163574	−	0.0163574i
$918$		0			0
$919$	20.4944			0.676047			0.338023	−	0.941138i	$-0.390242\pi$
$919$	20.4944			0.676047			0.338023	+	0.941138i	$0.390242\pi$
$920$		0			0
$921$	42.7839			1.40978
$922$		0			0
$923$	2.35605	+	2.35605i	0.0775502	+	0.0775502i
$924$		0			0
$925$	16.2606	−	26.2207i	0.534646	−	0.862130i
$926$		0			0
$927$	−6.61188	+	6.61188i	−0.217163	+	0.217163i
$928$		0			0
$929$			26.6354i			0.873878i	0.899491	+	0.436939i	$0.143937\pi$
$929$			26.6354i			0.873878i	−0.899491	+	0.436939i	$0.856063\pi$
$930$		0			0
$931$			7.98465i			0.261686i
$932$		0			0
$933$	−16.2373	+	16.2373i	−0.531584	+	0.531584i
$934$		0			0
$935$	−22.4539	+	2.59703i	−0.734322	+	0.0849320i
$936$		0			0
$937$	2.66235	+	2.66235i	0.0869751	+	0.0869751i	0.749256	−	0.662281i	$-0.230411\pi$
$937$	2.66235	+	2.66235i	0.0869751	+	0.0869751i	−0.662281	+	0.749256i	$0.730411\pi$
$938$		0			0
$939$	−9.98018			−0.325691
$940$		0			0
$941$	−8.76397			−0.285697			−0.142849	−	0.989745i	$-0.545626\pi$
$941$	−8.76397			−0.285697			−0.142849	+	0.989745i	$0.545626\pi$
$942$		0			0
$943$	6.75712	+	6.75712i	0.220042	+	0.220042i
$944$		0			0
$945$	−7.84232	+	9.89367i	−0.255111	+	0.321841i
$946$		0			0
$947$	8.50840	−	8.50840i	0.276486	−	0.276486i	−0.555219	−	0.831704i	$-0.687365\pi$
$947$	8.50840	−	8.50840i	0.276486	−	0.276486i	0.831704	+	0.555219i	$0.187365\pi$
$948$		0			0
$949$			4.72666i			0.153434i
$950$		0			0
$951$			33.8666i			1.09820i
$952$		0			0
$953$	34.5420	−	34.5420i	1.11892	−	1.11892i	0.127025	−	0.991900i	$-0.459457\pi$
$953$	34.5420	−	34.5420i	1.11892	−	1.11892i	0.991900	−	0.127025i	$-0.0405428\pi$
$954$		0			0
$955$	17.4886	−	22.0632i	0.565917	−	0.713947i
$956$		0			0
$957$	29.8037	+	29.8037i	0.963416	+	0.963416i
$958$		0			0
$959$	1.21433			0.0392129
$960$		0			0
$961$	−44.4320			−1.43329
$962$		0			0
$963$	−9.51293	−	9.51293i	−0.306550	−	0.306550i
$964$		0			0
$965$	−3.01998	+	0.349292i	−0.0972165	+	0.0112441i
$966$		0			0
$967$	−26.4057	+	26.4057i	−0.849151	+	0.849151i	−0.990027	−	0.140876i	$-0.955008\pi$
$967$	−26.4057	+	26.4057i	−0.849151	+	0.849151i	0.140876	+	0.990027i	$0.455008\pi$
$968$		0			0
$969$		−	32.5700i		−	1.04630i
$970$		0			0
$971$			51.6830i			1.65858i	0.558815	+	0.829292i	$0.311256\pi$
$971$			51.6830i			1.65858i	−0.558815	+	0.829292i	$0.688744\pi$
$972$		0			0
$973$	−0.675305	+	0.675305i	−0.0216493	+	0.0216493i
$974$		0			0
$975$	−1.34452	−	5.73461i	−0.0430591	−	0.183654i
$976$		0			0
$977$	−6.11203	−	6.11203i	−0.195541	−	0.195541i	0.602544	−	0.798085i	$-0.294154\pi$
$977$	−6.11203	−	6.11203i	−0.195541	−	0.195541i	−0.798085	+	0.602544i	$0.794154\pi$
$978$		0			0
$979$	50.7099			1.62070
$980$		0			0
$981$	6.17997			0.197311
$982$		0			0
$983$	−9.92168	−	9.92168i	−0.316452	−	0.316452i	0.530950	−	0.847403i	$-0.321835\pi$
$983$	−9.92168	−	9.92168i	−0.316452	−	0.316452i	−0.847403	+	0.530950i	$0.821835\pi$
$984$		0			0
$985$	−6.56196	−	56.7347i	−0.209081	−	1.80772i
$986$		0			0
$987$	2.26930	−	2.26930i	0.0722326	−	0.0722326i
$988$		0			0
$989$		−	50.4813i		−	1.60521i
$990$		0			0
$991$			54.1200i			1.71918i	0.510985	+	0.859590i	$0.329281\pi$
$991$			54.1200i			1.71918i	−0.510985	+	0.859590i	$0.670719\pi$
$992$		0			0
$993$	−22.8294	+	22.8294i	−0.724468	+	0.724468i
$994$		0			0
$995$	12.3182	+	9.76418i	0.390514	+	0.309545i
$996$		0			0
$997$	−18.7837	−	18.7837i	−0.594886	−	0.594886i	0.344061	−	0.938947i	$-0.388197\pi$
$997$	−18.7837	−	18.7837i	−0.594886	−	0.594886i	−0.938947	+	0.344061i	$0.888197\pi$
$998$		0			0
$999$	34.8397			1.10228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.x.a.127.3	✓	12
4.3	odd	2	inner	560.2.x.a.127.4	yes	12
5.3	odd	4	inner	560.2.x.a.463.4	yes	12
20.3	even	4	inner	560.2.x.a.463.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.x.a.127.3	✓	12	1.1	even	1	trivial
560.2.x.a.127.4	yes	12	4.3	odd	2	inner
560.2.x.a.463.3	yes	12	20.3	even	4	inner
560.2.x.a.463.4	yes	12	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.964019 - 0.964019i) q^{3} +(-1.75233 - 1.38900i) q^{5} +(-0.707107 + 0.707107i) q^{7} -1.14134i q^{9} +O(q^{10})\)	\(q+(-0.964019 - 0.964019i) q^{3} +(-1.75233 - 1.38900i) q^{5} +(-0.707107 + 0.707107i) q^{7} -1.14134i q^{9} +3.37856i q^{11} +(0.610996 - 0.610996i) q^{13} +(0.350255 + 3.02831i) q^{15} +(-2.11566 - 2.11566i) q^{17} -7.98465 q^{19} +1.36333 q^{21} +(3.02831 + 3.02831i) q^{23} +(1.14134 + 4.86799i) q^{25} +(-3.99233 + 3.99233i) q^{27} +9.15066i q^{29} +8.68516i q^{31} +(3.25700 - 3.25700i) q^{33} +(2.22126 - 0.256912i) q^{35} +(-4.36333 - 4.36333i) q^{37} -1.17802 q^{39} +2.23132 q^{41} +(-8.33491 - 8.33491i) q^{43} +(-1.58532 + 2.00000i) q^{45} +(1.66453 - 1.66453i) q^{47} -1.00000i q^{49} +4.07907i q^{51} +(0.221992 - 0.221992i) q^{53} +(4.69284 - 5.92036i) q^{55} +(7.69735 + 7.69735i) q^{57} +1.22753 q^{59} -5.55602 q^{61} +(0.807047 + 0.807047i) q^{63} +(-1.91934 + 0.221992i) q^{65} +(3.50582 - 3.50582i) q^{67} -5.83869i q^{69} +3.85607i q^{71} +(-3.86799 + 3.86799i) q^{73} +(3.59257 - 5.79310i) q^{75} +(-2.38900 - 2.38900i) q^{77} -7.93515 q^{79} +4.27334 q^{81} +(-5.65685 - 5.65685i) q^{83} +(0.768679 + 6.64600i) q^{85} +(8.82141 - 8.82141i) q^{87} -15.0093i q^{89} +0.864079i q^{91} +(8.37266 - 8.37266i) q^{93} +(13.9918 + 11.0907i) q^{95} +(-9.17634 - 9.17634i) q^{97} +3.85607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 20 q^{13} + 4 q^{17} + 8 q^{21} - 20 q^{25} - 24 q^{33} - 44 q^{37} - 32 q^{41} - 36 q^{45} + 28 q^{53} + 8 q^{57} - 16 q^{61} + 36 q^{65} + 4 q^{73} - 16 q^{77} + 68 q^{81} + 68 q^{85} + 8 q^{93} + 12 q^{97}+O(q^{100}) \) 12 * q + 20 * q^13 + 4 * q^17 + 8 * q^21 - 20 * q^25 - 24 * q^33 - 44 * q^37 - 32 * q^41 - 36 * q^45 + 28 * q^53 + 8 * q^57 - 16 * q^61 + 36 * q^65 + 4 * q^73 - 16 * q^77 + 68 * q^81 + 68 * q^85 + 8 * q^93 + 12 * q^97

Introduction

L-functions

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