LMFDB - Embedded newform 464.2.u.b.257.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [464,2,Mod(49,464)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("464.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(464, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 0, 12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			257.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	464.257
Dual form			464.2.u.b.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.240787i) q^{3} +(-0.0440730 + 0.193096i) q^{5} +(0.0990311 - 0.0476909i) q^{7} +(-1.67845 + 2.10471i) q^{9} +(0.832437 + 1.04384i) q^{11} +(2.45593 + 3.07964i) q^{13} +(-0.0244587 - 0.107160i) q^{15} -2.91185 q^{17} +(1.16756 + 0.562269i) q^{19} +(-0.0380322 + 0.0476909i) q^{21} +(1.73341 + 7.59455i) q^{23} +(4.46950 + 2.15240i) q^{25} +(0.702907 - 3.07964i) q^{27} +(-1.39493 - 5.20136i) q^{29} +(-2.07942 + 9.11052i) q^{31} +(-0.667563 - 0.321481i) q^{33} +(0.00484434 + 0.0212244i) q^{35} +(-1.88740 + 2.36672i) q^{37} +(-1.96950 - 0.948461i) q^{39} +3.76271 q^{41} +(-1.48307 - 6.49777i) q^{43} +(-0.332437 - 0.416863i) q^{45} +(-0.500000 - 0.626980i) q^{47} +(-4.35690 + 5.46337i) q^{49} +(1.45593 - 0.701137i) q^{51} +(-1.85474 + 8.12615i) q^{53} +(-0.238250 + 0.114735i) q^{55} -0.719169 q^{57} +5.08815 q^{59} +(9.96346 - 4.79815i) q^{61} +(-0.0658433 + 0.288478i) q^{63} +(-0.702907 + 0.338502i) q^{65} +(6.85839 - 8.60015i) q^{67} +(-2.69537 - 3.37989i) q^{69} +(-6.82640 - 8.56003i) q^{71} +(-1.76875 - 7.74940i) q^{73} -2.75302 q^{75} +(0.132219 + 0.0636733i) q^{77} +(-3.04892 + 3.82322i) q^{79} +(-1.40701 - 6.16451i) q^{81} +(-10.5184 - 5.06540i) q^{83} +(0.128334 - 0.562269i) q^{85} +(1.94989 + 2.26480i) q^{87} +(2.55765 - 11.2058i) q^{89} +(0.390084 + 0.187854i) q^{91} +(-1.15399 - 5.05596i) q^{93} +(-0.160030 + 0.200671i) q^{95} +(9.54288 + 4.59561i) q^{97} -3.59419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 4 q^{5} + 5 q^{7} - 6 q^{9} + 6 q^{11} + 11 q^{13} + 9 q^{15} - 10 q^{17} + 6 q^{19} + 15 q^{21} + 7 q^{23} + 17 q^{25} - 9 q^{27} + 15 q^{29} - 4 q^{31} - 3 q^{33} - 22 q^{35} - 13 q^{37}+ \cdots - 48 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 4 * q^5 + 5 * q^7 - 6 * q^9 + 6 * q^11 + 11 * q^13 + 9 * q^15 - 10 * q^17 + 6 * q^19 + 15 * q^21 + 7 * q^23 + 17 * q^25 - 9 * q^27 + 15 * q^29 - 4 * q^31 - 3 * q^33 - 22 * q^35 - 13 * q^37 - 2 * q^39 - 12 * q^41 + 7 * q^43 - 3 * q^45 - 3 * q^47 - 18 * q^49 + 5 * q^51 - 22 * q^53 + 24 * q^55 + 18 * q^57 + 38 * q^59 + 31 * q^61 + 2 * q^63 + 9 * q^65 - 11 * q^67 - 28 * q^69 - 23 * q^71 + 5 * q^73 - 26 * q^75 + 12 * q^77 - 23 * q^81 - 35 * q^83 - 26 * q^85 - 11 * q^87 + 13 * q^89 + q^91 - 12 * q^93 - 25 * q^95 + 20 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{7}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.240787i	−0.288675	+	0.139019i	−0.572617	−	0.819823i	$-0.694072\pi$
$3$	−0.500000	+	0.240787i	−0.288675	+	0.139019i	0.283942	+	0.958841i	$0.408358\pi$
$4$		0			0
$5$	−0.0440730	+	0.193096i	−0.0197100	+	0.0863553i	−0.983826	−	0.179125i	$-0.942673\pi$
$5$	−0.0440730	+	0.193096i	−0.0197100	+	0.0863553i	0.964116	+	0.265480i	$0.0855305\pi$
$6$		0			0
$7$	0.0990311	−	0.0476909i	0.0374302	−	0.0180255i	−0.415075	−	0.909787i	$-0.636245\pi$
$7$	0.0990311	−	0.0476909i	0.0374302	−	0.0180255i	0.452505	+	0.891762i	$0.350530\pi$
$8$		0			0
$9$	−1.67845	+	2.10471i	−0.559483	+	0.701569i
$10$		0			0
$11$	0.832437	+	1.04384i	0.250989	+	0.314731i	0.891325	−	0.453364i	$-0.149776\pi$
$11$	0.832437	+	1.04384i	0.250989	+	0.314731i	−0.640336	+	0.768095i	$0.721205\pi$
$12$		0			0
$13$	2.45593	+	3.07964i	0.681152	+	0.854137i	0.995460	−	0.0951839i	$-0.0303439\pi$
$13$	2.45593	+	3.07964i	0.681152	+	0.854137i	−0.314308	+	0.949321i	$0.601772\pi$
$14$		0			0
$15$	−0.0244587	−	0.107160i	−0.00631520	−	0.0276687i
$16$		0			0
$17$	−2.91185			−0.706228			−0.353114	−	0.935580i	$-0.614877\pi$
$17$	−2.91185			−0.706228			−0.353114	+	0.935580i	$0.614877\pi$
$18$		0			0
$19$	1.16756	+	0.562269i	0.267857	+	0.128993i	0.562992	−	0.826462i	$-0.309650\pi$
$19$	1.16756	+	0.562269i	0.267857	+	0.128993i	−0.295135	+	0.955456i	$0.595365\pi$
$20$		0			0
$21$	−0.0380322	+	0.0476909i	−0.00829931	+	0.0104070i
$22$		0			0
$23$	1.73341	+	7.59455i	0.361440	+	1.58357i	0.749542	+	0.661956i	$0.230274\pi$
$23$	1.73341	+	7.59455i	0.361440	+	1.58357i	−0.388102	+	0.921616i	$0.626869\pi$
$24$		0			0
$25$	4.46950	+	2.15240i	0.893900	+	0.430480i
$26$		0			0
$27$	0.702907	−	3.07964i	0.135274	−	0.592676i
$28$		0			0
$29$	−1.39493	−	5.20136i	−0.259032	−	0.965869i
$29$	−1.39493	−	5.20136i	−0.259032	−	0.965869i
$30$		0			0
$31$	−2.07942	+	9.11052i	−0.373474	+	1.63630i	0.343467	+	0.939165i	$0.388399\pi$
$31$	−2.07942	+	9.11052i	−0.373474	+	1.63630i	−0.716942	+	0.697133i	$0.754459\pi$
$32$		0			0
$33$	−0.667563	−	0.321481i	−0.116208	−	0.0559627i
$34$		0			0
$35$	0.00484434	+	0.0212244i	0.000818843	+	0.00358758i
$36$		0			0
$37$	−1.88740	+	2.36672i	−0.310286	+	0.389086i	−0.912384	−	0.409336i	$-0.865760\pi$
$37$	−1.88740	+	2.36672i	−0.310286	+	0.389086i	0.602098	+	0.798422i	$0.294332\pi$
$38$		0			0
$39$	−1.96950	−	0.948461i	−0.315372	−	0.151875i
$40$		0			0
$41$	3.76271			0.587636			0.293818	−	0.955861i	$-0.405074\pi$
$41$	3.76271			0.587636			0.293818	+	0.955861i	$0.405074\pi$
$42$		0			0
$43$	−1.48307	−	6.49777i	−0.226167	−	0.990901i	−0.952734	−	0.303806i	$-0.901743\pi$
$43$	−1.48307	−	6.49777i	−0.226167	−	0.990901i	0.726567	−	0.687095i	$-0.241115\pi$
$44$		0			0
$45$	−0.332437	−	0.416863i	−0.0495568	−	0.0621423i
$46$		0			0
$47$	−0.500000	−	0.626980i	−0.0729325	−	0.0914545i	0.744027	−	0.668150i	$-0.232913\pi$
$47$	−0.500000	−	0.626980i	−0.0729325	−	0.0914545i	−0.816959	+	0.576695i	$0.804342\pi$
$48$		0			0
$49$	−4.35690	+	5.46337i	−0.622414	+	0.780482i
$50$		0			0
$51$	1.45593	−	0.701137i	0.203871	−	0.0981789i
$52$		0			0
$53$	−1.85474	+	8.12615i	−0.254768	+	1.11621i	0.671992	+	0.740558i	$0.265439\pi$
$53$	−1.85474	+	8.12615i	−0.254768	+	1.11621i	−0.926760	+	0.375654i	$0.877418\pi$
$54$		0			0
$55$	−0.238250	+	0.114735i	−0.0321257	+	0.0154709i
$56$		0			0
$57$	−0.719169			−0.0952562
$58$		0			0
$59$	5.08815			0.662420			0.331210	−	0.943557i	$-0.392543\pi$
$59$	5.08815			0.662420			0.331210	+	0.943557i	$0.392543\pi$
$60$		0			0
$61$	9.96346	−	4.79815i	1.27569	−	0.614340i	0.331411	−	0.943486i	$-0.392475\pi$
$61$	9.96346	−	4.79815i	1.27569	−	0.614340i	0.944279	+	0.329146i	$0.106761\pi$
$62$		0			0
$63$	−0.0658433	+	0.288478i	−0.00829547	+	0.0363448i
$64$		0			0
$65$	−0.702907	+	0.338502i	−0.0871848	+	0.0419860i
$66$		0			0
$67$	6.85839	−	8.60015i	0.837885	−	1.05068i	−0.160092	−	0.987102i	$-0.551179\pi$
$67$	6.85839	−	8.60015i	0.837885	−	1.05068i	0.997977	−	0.0635730i	$-0.0202496\pi$
$68$		0			0
$69$	−2.69537	−	3.37989i	−0.324485	−	0.406891i
$70$		0			0
$71$	−6.82640	−	8.56003i	−0.810144	−	1.01589i	−0.999423	−	0.0339653i	$-0.989186\pi$
$71$	−6.82640	−	8.56003i	−0.810144	−	1.01589i	0.189279	−	0.981923i	$-0.439385\pi$
$72$		0			0
$73$	−1.76875	−	7.74940i	−0.207017	−	0.906999i	−0.966539	−	0.256518i	$-0.917425\pi$
$73$	−1.76875	−	7.74940i	−0.207017	−	0.906999i	0.759523	−	0.650481i	$-0.225432\pi$
$74$		0			0
$75$	−2.75302			−0.317891
$76$		0			0
$77$	0.132219	+	0.0636733i	0.0150678	+	0.00725625i
$78$		0			0
$79$	−3.04892	+	3.82322i	−0.343030	+	0.430146i	−0.923183	−	0.384362i	$-0.874422\pi$
$79$	−3.04892	+	3.82322i	−0.343030	+	0.430146i	0.580153	+	0.814508i	$0.302993\pi$
$80$		0			0
$81$	−1.40701	−	6.16451i	−0.156334	−	0.684946i
$82$		0			0
$83$	−10.5184	−	5.06540i	−1.15455	−	0.556000i	−0.244150	−	0.969737i	$-0.578509\pi$
$83$	−10.5184	−	5.06540i	−1.15455	−	0.556000i	−0.910396	+	0.413737i	$0.864223\pi$
$84$		0			0
$85$	0.128334	−	0.562269i	0.0139198	−	0.0609866i
$86$		0			0
$87$	1.94989	+	2.26480i	0.209050	+	0.242812i
$88$		0			0
$89$	2.55765	−	11.2058i	0.271110	−	1.18781i	−0.637595	−	0.770372i	$-0.720071\pi$
$89$	2.55765	−	11.2058i	0.271110	−	1.18781i	0.908705	−	0.417439i	$-0.137072\pi$
$90$		0			0
$91$	0.390084	+	0.187854i	0.0408919	+	0.0196925i
$92$		0			0
$93$	−1.15399	−	5.05596i	−0.119663	−	0.524278i
$94$		0			0
$95$	−0.160030	+	0.200671i	−0.0164187	+	0.0205884i
$96$		0			0
$97$	9.54288	+	4.59561i	0.968932	+	0.466613i	0.850285	−	0.526323i	$-0.176430\pi$
$97$	9.54288	+	4.59561i	0.968932	+	0.466613i	0.118648	+	0.992936i	$0.462144\pi$
$98$		0			0
$99$	−3.59419			−0.361229
$100$		0			0
$101$	−1.32908	−	5.82310i	−0.132249	−	0.579420i	−0.997012	−	0.0772410i	$-0.975389\pi$
$101$	−1.32908	−	5.82310i	−0.132249	−	0.579420i	0.864764	−	0.502179i	$-0.167468\pi$
$102$		0			0
$103$	8.97434	+	11.2535i	0.884268	+	1.10884i	0.993388	+	0.114809i	$0.0366256\pi$
$103$	8.97434	+	11.2535i	0.884268	+	1.10884i	−0.109119	+	0.994029i	$0.534803\pi$
$104$		0			0
$105$	−0.00753275	−	0.00944576i	−0.000735121	−	0.000921812i
$106$		0			0
$107$	10.2823	−	12.8936i	0.994030	−	1.24647i	0.0249596	−	0.999688i	$-0.492054\pi$
$107$	10.2823	−	12.8936i	0.994030	−	1.24647i	0.969070	−	0.246785i	$-0.0793743\pi$
$108$		0			0
$109$	−2.55980	+	1.23274i	−0.245185	+	0.118075i	−0.552441	−	0.833552i	$-0.686303\pi$
$109$	−2.55980	+	1.23274i	−0.245185	+	0.118075i	0.307256	+	0.951627i	$0.400589\pi$
$110$		0			0
$111$	0.373822	−	1.63782i	0.0354816	−	0.155455i
$112$		0			0
$113$	−14.1223	+	6.80094i	−1.32851	+	0.639778i	−0.957388	−	0.288804i	$-0.906742\pi$
$113$	−14.1223	+	6.80094i	−1.32851	+	0.639778i	−0.371125	+	0.928583i	$0.621028\pi$
$114$		0			0
$115$	−1.54288			−0.143874
$116$		0			0
$117$	−10.6039			−0.980329
$118$		0			0
$119$	−0.288364	+	0.138869i	−0.0264343	+	0.0127301i
$120$		0			0
$121$	2.05107	−	8.98634i	0.186461	−	0.816940i
$122$		0			0
$123$	−1.88135	+	0.906013i	−0.169636	+	0.0816924i
$124$		0			0
$125$	−1.23005	+	1.54244i	−0.110019	+	0.137960i
$126$		0			0
$127$	1.68867	+	2.11752i	0.149845	+	0.187900i	0.851089	−	0.525022i	$-0.175943\pi$
$127$	1.68867	+	2.11752i	0.149845	+	0.187900i	−0.701244	+	0.712922i	$0.747371\pi$
$128$		0			0
$129$	2.30612	+	2.89178i	0.203042	+	0.254607i
$130$		0			0
$131$	−3.25182	−	14.2472i	−0.284113	−	1.24478i	−0.892466	−	0.451115i	$-0.851027\pi$
$131$	−3.25182	−	14.2472i	−0.284113	−	1.24478i	0.608353	−	0.793667i	$-0.291831\pi$
$132$		0			0
$133$	0.142440			0.0123511
$134$		0			0
$135$	0.563687	+	0.271458i	0.0485145	+	0.0233633i
$136$		0			0
$137$	−0.993959	+	1.24639i	−0.0849197	+	0.106486i	−0.822476	−	0.568799i	$-0.807408\pi$
$137$	−0.993959	+	1.24639i	−0.0849197	+	0.106486i	0.737557	+	0.675285i	$0.235979\pi$
$138$		0			0
$139$	0.287168	+	1.25816i	0.0243573	+	0.106716i	0.985645	−	0.168829i	$-0.0539987\pi$
$139$	0.287168	+	1.25816i	0.0243573	+	0.106716i	−0.961288	+	0.275545i	$0.911142\pi$
$140$		0			0
$141$	0.400969	+	0.193096i	0.0337677	+	0.0162617i
$142$		0			0
$143$	−1.17025	+	5.12721i	−0.0978613	+	0.428758i
$144$		0			0
$145$	1.06584	−	0.0401160i	0.0885135	−	0.00333145i
$146$		0			0
$147$	0.862937	−	3.78077i	0.0711738	−	0.311833i
$148$		0			0
$149$	6.03415	+	2.90589i	0.494337	+	0.238060i	0.664406	−	0.747372i	$-0.268685\pi$
$149$	6.03415	+	2.90589i	0.494337	+	0.238060i	−0.170069	+	0.985432i	$0.554399\pi$
$150$		0			0
$151$	−2.11260	−	9.25593i	−0.171921	−	0.753237i	−0.985207	−	0.171371i	$-0.945180\pi$
$151$	−2.11260	−	9.25593i	−0.171921	−	0.753237i	0.813285	−	0.581865i	$-0.197677\pi$
$152$		0			0
$153$	4.88740	−	6.12860i	0.395122	−	0.495468i
$154$		0			0
$155$	−1.66756	−	0.803056i	−0.133942	−	0.0645030i
$156$		0			0
$157$	9.39373			0.749701			0.374851	−	0.927085i	$-0.377694\pi$
$157$	9.39373			0.749701			0.374851	+	0.927085i	$0.377694\pi$
$158$		0			0
$159$	−1.02930	−	4.50967i	−0.0816290	−	0.357640i
$160$		0			0
$161$	0.533852	+	0.669429i	0.0420734	+	0.0527584i
$162$		0			0
$163$	10.1434	+	12.7194i	0.794492	+	0.996262i	0.999846	+	0.0175740i	$0.00559426\pi$
$163$	10.1434	+	12.7194i	0.794492	+	0.996262i	−0.205353	+	0.978688i	$0.565834\pi$
$164$		0			0
$165$	0.0914984	−	0.114735i	0.00712314	−	0.00893213i
$166$		0			0
$167$	−12.3998	+	5.97142i	−0.959523	+	0.462082i	−0.847015	−	0.531569i	$-0.821603\pi$
$167$	−12.3998	+	5.97142i	−0.959523	+	0.462082i	−0.112508	+	0.993651i	$0.535888\pi$
$168$		0			0
$169$	−0.559802	+	2.45265i	−0.0430617	+	0.188666i
$170$		0			0
$171$	−3.14310	+	1.51364i	−0.240359	+	0.115751i
$172$		0			0
$173$	−0.119605			−0.00909340			−0.00454670	−	0.999990i	$-0.501447\pi$
$173$	−0.119605			−0.00909340			−0.00454670	+	0.999990i	$0.501447\pi$
$174$		0			0
$175$	0.545269			0.0412185
$176$		0			0
$177$	−2.54407	+	1.22516i	−0.191224	+	0.0920887i
$178$		0			0
$179$	−2.82155	+	12.3620i	−0.210893	+	0.923981i	0.753069	+	0.657941i	$0.228572\pi$
$179$	−2.82155	+	12.3620i	−0.210893	+	0.923981i	−0.963962	+	0.266040i	$0.914285\pi$
$180$		0			0
$181$	−6.42812	+	3.09562i	−0.477798	+	0.230095i	−0.657252	−	0.753671i	$-0.728281\pi$
$181$	−6.42812	+	3.09562i	−0.477798	+	0.230095i	0.179454	+	0.983766i	$0.442567\pi$
$182$		0			0
$183$	−3.82640	+	4.79815i	−0.282855	+	0.354689i
$184$		0			0
$185$	−0.373822	−	0.468758i	−0.0274839	−	0.0344638i
$186$		0			0
$187$	−2.42394	−	3.03952i	−0.177256	−	0.222272i
$188$		0			0
$189$	−0.0772609	−	0.338502i	−0.00561990	−	0.0246224i
$190$		0			0
$191$	−3.19806			−0.231404			−0.115702	−	0.993284i	$-0.536912\pi$
$191$	−3.19806			−0.231404			−0.115702	+	0.993284i	$0.536912\pi$
$192$		0			0
$193$	13.5782	+	6.53893i	0.977382	+	0.470682i	0.853204	−	0.521578i	$-0.174656\pi$
$193$	13.5782	+	6.53893i	0.977382	+	0.470682i	0.124178	+	0.992260i	$0.460371\pi$
$194$		0			0
$195$	0.269946	−	0.338502i	0.0193313	−	0.0242406i
$196$		0			0
$197$	3.23072	+	14.1547i	0.230179	+	1.00848i	0.949491	+	0.313794i	$0.101600\pi$
$197$	3.23072	+	14.1547i	0.230179	+	1.00848i	−0.719312	+	0.694687i	$0.755543\pi$
$198$		0			0
$199$	23.9013	+	11.5102i	1.69432	+	0.815939i	0.994860	+	0.101264i	$0.0322886\pi$
$199$	23.9013	+	11.5102i	1.69432	+	0.815939i	0.699456	+	0.714676i	$0.253426\pi$
$200$		0			0
$201$	−1.35839	+	5.95149i	−0.0958133	+	0.419785i
$202$		0			0
$203$	−0.386199	−	0.448572i	−0.0271058	−	0.0314835i
$204$		0			0
$205$	−0.165834	+	0.726566i	−0.0115823	+	0.0507455i
$206$		0			0
$207$	−18.8937	−	9.09874i	−1.31321	−	0.632406i
$208$		0			0
$209$	0.385002	+	1.68681i	0.0266312	+	0.116679i
$210$		0			0
$211$	10.4743	−	13.1344i	0.721084	−	0.904210i	−0.277315	−	0.960779i	$-0.589445\pi$
$211$	10.4743	−	13.1344i	0.721084	−	0.904210i	0.998399	+	0.0565688i	$0.0180160\pi$
$212$		0			0
$213$	5.47434	+	2.63631i	0.375096	+	0.180637i
$214$		0			0
$215$	1.32006			0.0900274
$216$		0			0
$217$	0.228562	+	1.00139i	0.0155158	+	0.0679791i
$218$		0			0
$219$	2.75033	+	3.44881i	0.185850	+	0.233049i
$220$		0			0
$221$	−7.15130	−	8.96745i	−0.481049	−	0.603216i
$222$		0			0
$223$	0.893436	−	1.12033i	0.0598289	−	0.0750231i	−0.751017	−	0.660283i	$-0.770436\pi$
$223$	0.893436	−	1.12033i	0.0598289	−	0.0750231i	0.810846	+	0.585260i	$0.199008\pi$
$224$		0			0
$225$	−12.0320	+	5.79430i	−0.802133	+	0.386287i
$226$		0			0
$227$	−2.98523	+	13.0791i	−0.198137	+	0.868093i	0.773908	+	0.633298i	$0.218299\pi$
$227$	−2.98523	+	13.0791i	−0.198137	+	0.868093i	−0.972045	+	0.234796i	$0.924558\pi$
$228$		0			0
$229$	−10.3693	+	4.99358i	−0.685221	+	0.329985i	−0.743899	−	0.668292i	$-0.767026\pi$
$229$	−10.3693	+	4.99358i	−0.685221	+	0.329985i	0.0586782	+	0.998277i	$0.481311\pi$
$230$		0			0
$231$	−0.0814412			−0.00535844
$232$		0			0
$233$	−0.735562			−0.0481883			−0.0240941	−	0.999710i	$-0.507670\pi$
$233$	−0.735562			−0.0481883			−0.0240941	+	0.999710i	$0.507670\pi$
$234$		0			0
$235$	0.143104	−	0.0689153i	0.00933508	−	0.00449554i
$236$		0			0
$237$	0.603875	−	2.64575i	0.0392259	−	0.171860i
$238$		0			0
$239$	0.0794168	−	0.0382451i	0.00513705	−	0.00247387i	−0.431313	−	0.902202i	$-0.641950\pi$
$239$	0.0794168	−	0.0382451i	0.00513705	−	0.00247387i	0.436450	+	0.899728i	$0.356235\pi$
$240$		0			0
$241$	−3.87382	+	4.85762i	−0.249535	+	0.312907i	−0.890785	−	0.454425i	$-0.849845\pi$
$241$	−3.87382	+	4.85762i	−0.249535	+	0.312907i	0.641250	+	0.767332i	$0.278416\pi$
$242$		0			0
$243$	8.09634	+	10.1525i	0.519381	+	0.651283i
$244$		0			0
$245$	−0.862937	−	1.08209i	−0.0551310	−	0.0691321i
$246$		0			0
$247$	1.13587	+	4.97656i	0.0722735	+	0.316651i
$248$		0			0
$249$	6.47889			0.410583
$250$		0			0
$251$	13.6869	+	6.59128i	0.863912	+	0.416038i	0.812723	−	0.582651i	$-0.197984\pi$
$251$	13.6869	+	6.59128i	0.863912	+	0.416038i	0.0511894	+	0.998689i	$0.483699\pi$
$252$		0			0
$253$	−6.48457	+	8.13139i	−0.407681	+	0.511216i
$254$		0			0
$255$	0.0712201	+	0.312036i	0.00445997	+	0.0195404i
$256$		0			0
$257$	−4.98307	−	2.39972i	−0.310836	−	0.149691i	0.271962	−	0.962308i	$-0.412328\pi$
$257$	−4.98307	−	2.39972i	−0.310836	−	0.149691i	−0.582797	+	0.812618i	$0.698042\pi$
$258$		0			0
$259$	−0.0740400	+	0.324390i	−0.00460062	+	0.0201566i
$260$		0			0
$261$	13.2887	+	5.79430i	0.822547	+	0.358658i
$262$		0			0
$263$	0.486959	−	2.13351i	0.0300272	−	0.131558i	−0.957693	−	0.287793i	$-0.907079\pi$
$263$	0.486959	−	2.13351i	0.0300272	−	0.131558i	0.987720	+	0.156235i	$0.0499357\pi$
$264$		0			0
$265$	−1.48739	−	0.716287i	−0.0913694	−	0.0440012i
$266$		0			0
$267$	1.41939	+	6.21874i	0.0868651	+	0.380581i
$268$		0			0
$269$	18.9901	−	23.8128i	1.15785	−	1.45189i	0.288642	−	0.957437i	$-0.406796\pi$
$269$	18.9901	−	23.8128i	1.15785	−	1.45189i	0.869203	−	0.494455i	$-0.164632\pi$
$270$		0			0
$271$	28.4218	+	13.6872i	1.72650	+	0.831440i	0.987477	+	0.157765i	$0.0504287\pi$
$271$	28.4218	+	13.6872i	1.72650	+	0.831440i	0.739027	+	0.673676i	$0.235286\pi$
$272$		0			0
$273$	−0.240275			−0.0145421
$274$		0			0
$275$	1.47381	+	6.45719i	0.0888742	+	0.389383i
$276$		0			0
$277$	8.85504	+	11.1039i	0.532048	+	0.667166i	0.973118	−	0.230306i	$-0.0739727\pi$
$277$	8.85504	+	11.1039i	0.532048	+	0.667166i	−0.441071	+	0.897472i	$0.645401\pi$
$278$		0			0
$279$	−15.6848	−	19.6681i	−0.939023	−	1.17750i
$280$		0			0
$281$	12.9453	−	16.2329i	0.772254	−	0.968376i	−0.227732	−	0.973724i	$-0.573131\pi$
$281$	12.9453	−	16.2329i	0.772254	−	0.968376i	0.999986	+	0.00534795i	$0.00170231\pi$
$282$		0			0
$283$	−15.6293	+	7.52667i	−0.929065	+	0.447414i	−0.836299	−	0.548274i	$-0.815285\pi$
$283$	−15.6293	+	7.52667i	−0.929065	+	0.447414i	−0.0927662	+	0.995688i	$0.529571\pi$
$284$		0			0
$285$	0.0316959	−	0.138869i	0.00187750	−	0.00822588i
$286$		0			0
$287$	0.372625	−	0.179447i	0.0219954	−	0.0105924i
$288$		0			0
$289$	−8.52111			−0.501242
$290$		0			0
$291$	−5.87800			−0.344575
$292$		0			0
$293$	−15.7920	+	7.60503i	−0.922579	+	0.444291i	−0.833991	−	0.551778i	$-0.813950\pi$
$293$	−15.7920	+	7.60503i	−0.922579	+	0.444291i	−0.0885879	+	0.996068i	$0.528235\pi$
$294$		0			0
$295$	−0.224250	+	0.982503i	−0.0130563	+	0.0572035i
$296$		0			0
$297$	3.79978	−	1.82988i	0.220486	−	0.106180i
$298$		0			0
$299$	−19.1313	+	23.9899i	−1.10639	+	1.38737i
$300$		0			0
$301$	−0.456755	−	0.572753i	−0.0263269	−	0.0330129i
$302$		0			0
$303$	2.06667	+	2.59152i	0.118727	+	0.148879i
$304$		0			0
$305$	0.487386	+	2.13538i	0.0279076	+	0.122271i
$306$		0			0
$307$	−30.3618			−1.73284			−0.866420	−	0.499316i	$-0.833585\pi$
$307$	−30.3618			−1.73284			−0.866420	+	0.499316i	$0.833585\pi$
$308$		0			0
$309$	−7.19687	−	3.46583i	−0.409415	−	0.197164i
$310$		0			0
$311$	14.8312	−	18.5978i	0.841003	−	1.05458i	−0.156754	−	0.987638i	$-0.550103\pi$
$311$	14.8312	−	18.5978i	0.841003	−	1.05458i	0.997757	−	0.0669461i	$-0.0213256\pi$
$312$		0			0
$313$	6.38069	+	27.9556i	0.360658	+	1.58015i	0.751529	+	0.659700i	$0.229317\pi$
$313$	6.38069	+	27.9556i	0.360658	+	1.58015i	−0.390871	+	0.920446i	$0.627826\pi$
$314$		0			0
$315$	−0.0528022	−	0.0254282i	−0.00297507	−	0.00143272i
$316$		0			0
$317$	1.68180	−	7.36845i	0.0944593	−	0.413853i	−0.905485	−	0.424378i	$-0.860493\pi$
$317$	1.68180	−	7.36845i	0.0944593	−	0.413853i	0.999945	+	0.0105243i	$0.00335006\pi$
$318$		0			0
$319$	4.26822	−	5.78589i	0.238974	−	0.323948i
$320$		0			0
$321$	−2.03654	+	8.92267i	−0.113669	+	0.498015i
$322$		0			0
$323$	−3.39977	−	1.63724i	−0.189168	−	0.0910987i
$324$		0			0
$325$	4.34817	+	19.0506i	0.241193	+	1.05674i
$326$		0			0
$327$	0.983074	−	1.23274i	0.0543641	−	0.0681705i
$328$		0			0
$329$	−0.0794168	−	0.0382451i	−0.00437839	−	0.00210852i
$330$		0			0
$331$	11.1860			0.614837			0.307419	−	0.951574i	$-0.400535\pi$
$331$	11.1860			0.614837			0.307419	+	0.951574i	$0.400535\pi$
$332$		0			0
$333$	−1.81336	−	7.94483i	−0.0993713	−	0.435374i
$334$		0			0
$335$	1.35839	+	1.70336i	0.0742167	+	0.0930647i
$336$		0			0
$337$	−12.9641	−	16.2565i	−0.706201	−	0.885548i	0.291269	−	0.956641i	$-0.405923\pi$
$337$	−12.9641	−	16.2565i	−0.706201	−	0.885548i	−0.997470	+	0.0710934i	$0.977351\pi$
$338$		0			0
$339$	5.42357	−	6.80094i	0.294568	−	0.369376i
$340$		0			0
$341$	−11.2409	+	5.41335i	−0.608731	+	0.293149i
$342$		0			0
$343$	−0.342126	+	1.49895i	−0.0184731	+	0.0809358i
$344$		0			0
$345$	0.771438	−	0.371505i	0.0415328	−	0.0200012i
$346$		0			0
$347$	−0.0193774			−0.00104023			−0.000520116	−	1.00000i	$-0.500166\pi$
$347$	−0.0193774			−0.00104023			−0.000520116		1.00000i	$0.500166\pi$
$348$		0			0
$349$	29.0315			1.55402			0.777009	−	0.629489i	$-0.216736\pi$
$349$	29.0315			1.55402			0.777009	+	0.629489i	$0.216736\pi$
$350$		0			0
$351$	11.2104	−	5.39866i	0.598369	−	0.288159i
$352$		0			0
$353$	−4.58761	+	20.0996i	−0.244174	+	1.06980i	0.693001	+	0.720937i	$0.256288\pi$
$353$	−4.58761	+	20.0996i	−0.244174	+	1.06980i	−0.937175	+	0.348860i	$0.886569\pi$
$354$		0			0
$355$	1.95377	−	0.940887i	0.103695	−	0.0499371i
$356$		0			0
$357$	0.110744	−	0.138869i	0.00586121	−	0.00734972i
$358$		0			0
$359$	−13.0248	−	16.3325i	−0.687420	−	0.861998i	0.308594	−	0.951194i	$-0.400142\pi$
$359$	−13.0248	−	16.3325i	−0.687420	−	0.861998i	−0.996014	+	0.0891962i	$0.971570\pi$
$360$		0			0
$361$	−10.7992	−	13.5418i	−0.568382	−	0.712728i
$362$		0			0
$363$	1.13826	+	4.98704i	0.0597431	+	0.261752i
$364$		0			0
$365$	1.57434			0.0824045
$366$		0			0
$367$	3.39008	+	1.63258i	0.176961	+	0.0852199i	0.520267	−	0.854004i	$-0.325832\pi$
$367$	3.39008	+	1.63258i	0.176961	+	0.0852199i	−0.343306	+	0.939224i	$0.611547\pi$
$368$		0			0
$369$	−6.31551	+	7.91940i	−0.328772	+	0.412268i
$370$		0			0
$371$	0.203866	+	0.893196i	0.0105842	+	0.0463724i
$372$		0			0
$373$	−13.5271	−	6.51433i	−0.700409	−	0.337299i	0.0495609	−	0.998771i	$-0.484218\pi$
$373$	−13.5271	−	6.51433i	−0.700409	−	0.337299i	−0.749970	+	0.661472i	$0.769932\pi$
$374$		0			0
$375$	0.243627	−	1.06740i	0.0125809	−	0.0551203i
$376$		0			0
$377$	12.5925	−	17.0700i	0.648545	−	0.879152i
$378$		0			0
$379$	5.24363	−	22.9738i	0.269347	−	1.18009i	−0.641428	−	0.767183i	$-0.721658\pi$
$379$	5.24363	−	22.9738i	0.269347	−	1.18009i	0.910775	−	0.412903i	$-0.135485\pi$
$380$		0			0
$381$	−1.35421	−	0.652152i	−0.0693781	−	0.0334108i
$382$		0			0
$383$	−5.96830	−	26.1488i	−0.304966	−	1.33614i	−0.862528	−	0.506009i	$-0.831120\pi$
$383$	−5.96830	−	26.1488i	−0.304966	−	1.33614i	0.557562	−	0.830135i	$-0.311737\pi$
$384$		0			0
$385$	−0.0181224	+	0.0227247i	−0.000923602	+	0.00115816i
$386$		0			0
$387$	16.1652	+	7.78474i	0.821722	+	0.395720i
$388$		0			0
$389$	−18.4034			−0.933090			−0.466545	−	0.884497i	$-0.654502\pi$
$389$	−18.4034			−0.933090			−0.466545	+	0.884497i	$0.654502\pi$
$390$		0			0
$391$	−5.04743	−	22.1142i	−0.255259	−	1.11836i
$392$		0			0
$393$	5.05645	+	6.34059i	0.255064	+	0.319840i
$394$		0			0
$395$	−0.603875	−	0.757236i	−0.0303843	−	0.0381007i
$396$		0			0
$397$	18.0233	−	22.6005i	0.904562	−	1.13428i	−0.0858736	−	0.996306i	$-0.527368\pi$
$397$	18.0233	−	22.6005i	0.904562	−	1.13428i	0.990435	−	0.137978i	$-0.0440604\pi$
$398$		0			0
$399$	−0.0712201	+	0.0342978i	−0.00356546	+	0.00171704i
$400$		0			0
$401$	−3.41281	+	14.9525i	−0.170428	+	0.746693i	0.815395	+	0.578905i	$0.196520\pi$
$401$	−3.41281	+	14.9525i	−0.170428	+	0.746693i	−0.985823	+	0.167788i	$0.946338\pi$
$402$		0			0
$403$	−33.1640	+	15.9709i	−1.65202	+	0.795569i
$404$		0			0
$405$	1.25236			0.0622301
$406$		0			0
$407$	−4.04162			−0.200336
$408$		0			0
$409$	31.2913	−	15.0691i	1.54726	−	0.745120i	0.551246	−	0.834343i	$-0.314153\pi$
$409$	31.2913	−	15.0691i	1.54726	−	0.745120i	0.996012	+	0.0892229i	$0.0284383\pi$
$410$		0			0
$411$	0.196866	−	0.862525i	0.00971067	−	0.0425452i
$412$		0			0
$413$	0.503885	−	0.242658i	0.0247946	−	0.0119404i
$414$		0			0
$415$	1.44169	−	1.80782i	0.0707698	−	0.0887425i
$416$		0			0
$417$	−0.446534	−	0.559936i	−0.0218669	−	0.0274202i
$418$		0			0
$419$	13.6935	+	17.1711i	0.668972	+	0.838864i	0.994287	−	0.106742i	$-0.0340417\pi$
$419$	13.6935	+	17.1711i	0.668972	+	0.838864i	−0.325315	+	0.945606i	$0.605470\pi$
$420$		0			0
$421$	−8.99761	−	39.4211i	−0.438517	−	1.92127i	−0.385596	−	0.922668i	$-0.626004\pi$
$421$	−8.99761	−	39.4211i	−0.438517	−	1.92127i	−0.0529206	−	0.998599i	$-0.516853\pi$
$422$		0			0
$423$	2.15883			0.104966
$424$		0			0
$425$	−13.0145	−	6.26747i	−0.631298	−	0.304017i
$426$		0			0
$427$	0.757865	−	0.950332i	0.0366756	−	0.0459898i
$428$		0			0
$429$	−0.649440	−	2.84538i	−0.0313553	−	0.137376i
$430$		0			0
$431$	−19.9121	−	9.58919i	−0.959134	−	0.461895i	−0.112255	−	0.993679i	$-0.535807\pi$
$431$	−19.9121	−	9.58919i	−0.959134	−	0.461895i	−0.846880	+	0.531785i	$0.821522\pi$
$432$		0			0
$433$	0.864961	−	3.78964i	0.0415674	−	0.182119i	−0.949882	−	0.312607i	$-0.898798\pi$
$433$	0.864961	−	3.78964i	0.0415674	−	0.182119i	0.991450	+	0.130489i	$0.0416547\pi$
$434$		0			0
$435$	−0.523262	+	0.276700i	−0.0250885	+	0.0132667i
$436$		0			0
$437$	−2.24632	+	9.84175i	−0.107456	+	0.470795i
$438$		0			0
$439$	9.15160	+	4.40718i	0.436782	+	0.210343i	0.639335	−	0.768928i	$-0.279210\pi$
$439$	9.15160	+	4.40718i	0.436782	+	0.210343i	−0.202553	+	0.979271i	$0.564924\pi$
$440$		0			0
$441$	−4.18598	−	18.3400i	−0.199332	−	0.873332i
$442$		0			0
$443$	−12.0312	+	15.0866i	−0.571618	+	0.716786i	−0.980658	−	0.195730i	$-0.937292\pi$
$443$	−12.0312	+	15.0866i	−0.571618	+	0.716786i	0.409040	+	0.912516i	$0.365864\pi$
$444$		0			0
$445$	2.05107	+	0.987745i	0.0972302	+	0.0468236i
$446$		0			0
$447$	−3.71678			−0.175797
$448$		0			0
$449$	−4.81522	−	21.0968i	−0.227244	−	0.995621i	−0.951876	−	0.306485i	$-0.900847\pi$
$449$	−4.81522	−	21.0968i	−0.227244	−	0.995621i	0.724631	−	0.689137i	$-0.242010\pi$
$450$		0			0
$451$	3.13222	+	3.92768i	0.147490	+	0.184947i
$452$		0			0
$453$	3.28501	+	4.11927i	0.154343	+	0.193540i
$454$		0			0
$455$	−0.0534662	+	0.0670445i	−0.00250653	+	0.00314309i
$456$		0			0
$457$	−2.28017	+	1.09807i	−0.106662	+	0.0513656i	−0.486454	−	0.873706i	$-0.661710\pi$
$457$	−2.28017	+	1.09807i	−0.106662	+	0.0513656i	0.379792	+	0.925072i	$0.375996\pi$
$458$		0			0
$459$	−2.04676	+	8.96745i	−0.0955346	+	0.418565i
$460$		0			0
$461$	−9.69687	+	4.66976i	−0.451628	+	0.217493i	−0.645849	−	0.763465i	$-0.723496\pi$
$461$	−9.69687	+	4.66976i	−0.451628	+	0.217493i	0.194221	+	0.980958i	$0.437782\pi$
$462$		0			0
$463$	6.12392			0.284603			0.142301	−	0.989823i	$-0.454550\pi$
$463$	6.12392			0.284603			0.142301	+	0.989823i	$0.454550\pi$
$464$		0			0
$465$	1.02715			0.0476328
$466$		0			0
$467$	31.5013	−	15.1702i	1.45770	−	0.701993i	0.473790	−	0.880638i	$-0.342885\pi$
$467$	31.5013	−	15.1702i	1.45770	−	0.701993i	0.983914	+	0.178644i	$0.0571711\pi$
$468$		0			0
$469$	0.269045	−	1.17876i	0.0124234	−	0.0544303i
$470$		0			0
$471$	−4.69687	+	2.26189i	−0.216420	+	0.104222i
$472$		0			0
$473$	5.54809	−	6.95708i	0.255101	−	0.319887i
$474$		0			0
$475$	4.00820	+	5.02612i	0.183909	+	0.230614i
$476$		0			0
$477$	−13.9901	−	17.5430i	−0.640562	−	0.803239i
$478$		0			0
$479$	−6.86994	−	30.0992i	−0.313895	−	1.37527i	−0.848067	−	0.529889i	$-0.822233\pi$
$479$	−6.86994	−	30.0992i	−0.313895	−	1.37527i	0.534171	−	0.845376i	$-0.320624\pi$
$480$		0			0
$481$	−11.9239			−0.543685
$482$		0			0
$483$	−0.428116	−	0.206170i	−0.0194799	−	0.00938105i
$484$		0			0
$485$	−1.30798	+	1.64015i	−0.0593922	+	0.0744755i
$486$		0			0
$487$	−0.0908344	−	0.397972i	−0.00411610	−	0.0180338i	0.972828	−	0.231528i	$-0.0743726\pi$
$487$	−0.0908344	−	0.397972i	−0.00411610	−	0.0180338i	−0.976944	+	0.213495i	$0.931515\pi$
$488$		0			0
$489$	−8.13437	−	3.91731i	−0.367849	−	0.177147i
$490$		0			0
$491$	4.48643	−	19.6563i	0.202470	−	0.887077i	−0.766958	−	0.641698i	$-0.778230\pi$
$491$	4.48643	−	19.6563i	0.202470	−	0.887077i	0.969427	−	0.245379i	$-0.0789125\pi$
$492$		0			0
$493$	4.06183	+	15.1456i	0.182935	+	0.682124i
$494$		0			0
$495$	0.158407	−	0.694025i	0.00711985	−	0.0311941i
$496$		0			0
$497$	−1.08426	−	0.522153i	−0.0486358	−	0.0234217i
$498$		0			0
$499$	−2.30947	−	10.1185i	−0.103386	−	0.452964i	−0.999950	−	0.0100487i	$-0.996801\pi$
$499$	−2.30947	−	10.1185i	−0.103386	−	0.452964i	0.896563	−	0.442915i	$-0.146056\pi$
$500$		0			0
$501$	4.76205	−	5.97142i	0.212752	−	0.266783i
$502$		0			0
$503$	20.7141	+	9.97538i	0.923596	+	0.444780i	0.834353	−	0.551230i	$-0.185841\pi$
$503$	20.7141	+	9.97538i	0.923596	+	0.444780i	0.0892420	+	0.996010i	$0.471556\pi$
$504$		0			0
$505$	1.18300			0.0526427
$506$		0			0
$507$	−0.310667	−	1.36112i	−0.0137972	−	0.0604495i
$508$		0			0
$509$	16.0262	+	20.0963i	0.710351	+	0.890752i	0.997749	−	0.0670594i	$-0.0213617\pi$
$509$	16.0262	+	20.0963i	0.710351	+	0.890752i	−0.287398	+	0.957811i	$0.592790\pi$
$510$		0			0
$511$	−0.544737	−	0.683079i	−0.0240977	−	0.0302176i
$512$		0			0
$513$	2.55227	−	3.20045i	0.112685	−	0.141303i
$514$		0			0
$515$	−2.56853	+	1.23694i	−0.113183	+	0.0545061i
$516$		0			0
$517$	0.238250	−	1.04384i	0.0104782	−	0.0459082i
$518$		0			0
$519$	0.0598025	−	0.0287994i	0.00262504	−	0.00126415i
$520$		0			0
$521$	17.1535			0.751507			0.375753	−	0.926720i	$-0.377384\pi$
$521$	17.1535			0.751507			0.375753	+	0.926720i	$0.377384\pi$
$522$		0			0
$523$	−22.4494			−0.981642			−0.490821	−	0.871261i	$-0.663303\pi$
$523$	−22.4494			−0.981642			−0.490821	+	0.871261i	$0.663303\pi$
$524$		0			0
$525$	−0.272635	+	0.131294i	−0.0118988	+	0.00573014i
$526$		0			0
$527$	6.05496	−	26.5285i	0.263758	−	1.15560i
$528$		0			0
$529$	−33.9502	+	16.3495i	−1.47609	+	0.710850i
$530$		0			0
$531$	−8.54019	+	10.7091i	−0.370613	+	0.464733i
$532$		0			0
$533$	9.24094	+	11.5878i	0.400269	+	0.501922i
$534$		0			0
$535$	2.03654	+	2.55374i	0.0880473	+	0.110408i
$536$		0			0
$537$	−1.56584	−	6.86041i	−0.0675711	−	0.296048i
$538$		0			0
$539$	−9.32975			−0.401861
$540$		0			0
$541$	11.2104	+	5.39866i	0.481974	+	0.232107i	0.659062	−	0.752088i	$-0.270953\pi$
$541$	11.2104	+	5.39866i	0.481974	+	0.232107i	−0.177088	+	0.984195i	$0.556668\pi$
$542$		0			0
$543$	2.46867	−	3.09562i	0.105941	−	0.132846i
$544$		0			0
$545$	−0.125219	−	0.548619i	−0.00536378	−	0.0235003i
$546$		0			0
$547$	−10.5988	−	5.10411i	−0.453172	−	0.218236i	0.193353	−	0.981129i	$-0.438064\pi$
$547$	−10.5988	−	5.10411i	−0.453172	−	0.218236i	−0.646524	+	0.762893i	$0.723778\pi$
$548$		0			0
$549$	−6.62445	+	29.0236i	−0.282725	+	1.23870i
$550$		0			0
$551$	1.29590	−	6.85724i	0.0552071	−	0.292128i
$552$		0			0
$553$	−0.119605	+	0.524023i	−0.00508612	+	0.0222837i
$554$		0			0
$555$	0.299782	+	0.144367i	0.0127250	+	0.00612805i
$556$		0			0
$557$	−7.28448	−	31.9154i	−0.308653	−	1.35230i	−0.856685	−	0.515841i	$-0.827480\pi$
$557$	−7.28448	−	31.9154i	−0.308653	−	1.35230i	0.548031	−	0.836458i	$-0.315377\pi$
$558$		0			0
$559$	16.3684	−	20.5254i	0.692311	−	0.868131i
$560$		0			0
$561$	1.94385	+	0.936107i	0.0820692	+	0.0395225i
$562$		0			0
$563$	30.1105			1.26901			0.634503	−	0.772920i	$-0.281205\pi$
$563$	30.1105			1.26901			0.634503	+	0.772920i	$0.281205\pi$
$564$		0			0
$565$	−0.690825	−	3.02670i	−0.0290632	−	0.127334i
$566$		0			0
$567$	−0.433329	−	0.543377i	−0.0181981	−	0.0228197i
$568$		0			0
$569$	9.71230	+	12.1788i	0.407161	+	0.510563i	0.942561	−	0.334035i	$-0.108410\pi$
$569$	9.71230	+	12.1788i	0.407161	+	0.510563i	−0.535400	+	0.844599i	$0.679839\pi$
$570$		0			0
$571$	−4.20589	+	5.27402i	−0.176011	+	0.220711i	−0.862009	−	0.506892i	$-0.830794\pi$
$571$	−4.20589	+	5.27402i	−0.176011	+	0.220711i	0.685998	+	0.727603i	$0.259366\pi$
$572$		0			0
$573$	1.59903	−	0.770053i	0.0668005	−	0.0321694i
$574$		0			0
$575$	−8.59903	+	37.6748i	−0.358604	+	1.57115i
$576$		0			0
$577$	16.8458	−	8.11250i	0.701299	−	0.337728i	−0.0490256	−	0.998798i	$-0.515612\pi$
$577$	16.8458	−	8.11250i	0.701299	−	0.337728i	0.750324	+	0.661070i	$0.229897\pi$
$578$		0			0
$579$	−8.36360			−0.347579
$580$		0			0
$581$	−1.28322			−0.0532371
$582$		0			0
$583$	−10.0264	+	4.82845i	−0.415250	+	0.199974i
$584$		0			0
$585$	0.467345	−	2.04757i	0.0193223	−	0.0846566i
$586$		0			0
$587$	−14.6407	+	7.05059i	−0.604287	+	0.291009i	−0.710902	−	0.703291i	$-0.751713\pi$
$587$	−14.6407	+	7.05059i	−0.604287	+	0.291009i	0.106615	+	0.994300i	$0.465999\pi$
$588$		0			0
$589$	−7.55041	+	9.46791i	−0.311109	+	0.390119i
$590$		0			0
$591$	−5.02363	−	6.29943i	−0.206645	−	0.259124i
$592$		0			0
$593$	19.4351	+	24.3709i	0.798105	+	1.00079i	0.999772	+	0.0213375i	$0.00679245\pi$
$593$	19.4351	+	24.3709i	0.798105	+	1.00079i	−0.201668	+	0.979454i	$0.564636\pi$
$594$		0			0
$595$	−0.0141060	−	0.0618025i	−0.000578290	−	0.00253365i
$596$		0			0
$597$	−14.7222			−0.602538
$598$		0			0
$599$	7.05280	+	3.39645i	0.288170	+	0.138775i	0.572384	−	0.819985i	$-0.306019\pi$
$599$	7.05280	+	3.39645i	0.288170	+	0.138775i	−0.284215	+	0.958761i	$0.591733\pi$
$600$		0			0
$601$	10.9566	−	13.7391i	0.446929	−	0.560431i	−0.506426	−	0.862283i	$-0.669034\pi$
$601$	10.9566	−	13.7391i	0.446929	−	0.560431i	0.953355	+	0.301853i	$0.0976051\pi$
$602$		0			0
$603$	6.58934	+	28.8698i	0.268339	+	1.17567i
$604$		0			0
$605$	1.64483	+	0.792110i	0.0668720	+	0.0322038i
$606$		0			0
$607$	−8.75504	+	38.3584i	−0.355356	+	1.55692i	0.409251	+	0.912422i	$0.365790\pi$
$607$	−8.75504	+	38.3584i	−0.355356	+	1.55692i	−0.764608	+	0.644496i	$0.777067\pi$
$608$		0			0
$609$	0.301110	+	0.131294i	0.0122016	+	0.00532030i
$610$		0			0
$611$	0.702907	−	3.07964i	0.0284366	−	0.124589i
$612$		0			0
$613$	−22.6429	−	10.9042i	−0.914537	−	0.440418i	−0.0834193	−	0.996515i	$-0.526584\pi$
$613$	−22.6429	−	10.9042i	−0.914537	−	0.440418i	−0.831118	+	0.556097i	$0.812298\pi$
$614$		0			0
$615$	−0.0920309	−	0.403214i	−0.00371104	−	0.0162591i
$616$		0			0
$617$	−7.87047	+	9.86926i	−0.316853	+	0.397321i	−0.914597	−	0.404366i	$-0.867492\pi$
$617$	−7.87047	+	9.86926i	−0.316853	+	0.397321i	0.597744	+	0.801687i	$0.296064\pi$
$618$		0			0
$619$	−19.5683	−	9.42359i	−0.786516	−	0.378766i	−0.00288757	−	0.999996i	$-0.500919\pi$
$619$	−19.5683	−	9.42359i	−0.786516	−	0.378766i	−0.783629	+	0.621230i	$0.786633\pi$
$620$		0			0
$621$	24.6069			0.987439
$622$		0			0
$623$	−0.281127	−	1.23170i	−0.0112631	−	0.0493469i
$624$		0			0
$625$	15.2213	+	19.0869i	0.608853	+	0.763477i
$626$		0			0
$627$	−0.598663	−	0.750699i	−0.0239083	−	0.0299800i
$628$		0			0
$629$	5.49582	−	6.89154i	0.219133	−	0.274784i
$630$		0			0
$631$	−35.4616	+	17.0774i	−1.41170	+	0.679841i	−0.975498	−	0.220006i	$-0.929392\pi$
$631$	−35.4616	+	17.0774i	−1.41170	+	0.679841i	−0.436206	+	0.899847i	$0.643678\pi$
$632$		0			0
$633$	−2.07457	+	9.08930i	−0.0824569	+	0.361267i
$634$		0			0
$635$	−0.483311	+	0.232750i	−0.0191796	+	0.00923642i
$636$		0			0
$637$	−27.5254			−1.09060
$638$		0			0
$639$	29.4741			1.16598
$640$		0			0
$641$	4.44020	−	2.13829i	0.175377	−	0.0844572i	−0.344135	−	0.938920i	$-0.611828\pi$
$641$	4.44020	−	2.13829i	0.175377	−	0.0844572i	0.519512	+	0.854463i	$0.326114\pi$
$642$		0			0
$643$	−1.56004	+	6.83498i	−0.0615220	+	0.269545i	−0.996329	−	0.0856119i	$-0.972715\pi$
$643$	−1.56004	+	6.83498i	−0.0615220	+	0.269545i	0.934807	+	0.355157i	$0.115573\pi$
$644$		0			0
$645$	−0.660030	+	0.317854i	−0.0259887	+	0.0125155i
$646$		0			0
$647$	9.18329	−	11.5155i	0.361032	−	0.452720i	−0.567830	−	0.823146i	$-0.692217\pi$
$647$	9.18329	−	11.5155i	0.361032	−	0.452720i	0.928862	+	0.370426i	$0.120788\pi$
$648$		0			0
$649$	4.23556	+	5.31123i	0.166260	+	0.208484i
$650$		0			0
$651$	−0.355404	−	0.445662i	−0.0139294	−	0.0174669i
$652$		0			0
$653$	5.56691	+	24.3902i	0.217850	+	0.954463i	0.959063	+	0.283193i	$0.0913937\pi$
$653$	5.56691	+	24.3902i	0.217850	+	0.954463i	−0.741213	+	0.671270i	$0.765749\pi$
$654$		0			0
$655$	2.89440			0.113093
$656$		0			0
$657$	19.2790	+	9.28426i	0.752144	+	0.362214i
$658$		0			0
$659$	−30.3384	+	38.0432i	−1.18182	+	1.48195i	−0.341477	+	0.939890i	$0.610927\pi$
$659$	−30.3384	+	38.0432i	−1.18182	+	1.48195i	−0.840339	+	0.542061i	$0.817644\pi$
$660$		0			0
$661$	6.40528	+	28.0634i	0.249137	+	1.09154i	0.932417	+	0.361383i	$0.117695\pi$
$661$	6.40528	+	28.0634i	0.249137	+	1.09154i	−0.683281	+	0.730156i	$0.739448\pi$
$662$		0			0
$663$	5.73490	+	2.76178i	0.222725	+	0.107259i
$664$		0			0
$665$	−0.00627776	+	0.0275047i	−0.000243441	+	0.00106659i
$666$		0			0
$667$	37.0840	−	19.6099i	1.43590	−	0.759299i
$668$		0			0
$669$	−0.176956	+	0.775295i	−0.00684151	+	0.0299746i
$670$		0			0
$671$	13.3025	+	6.40613i	0.513536	+	0.247306i
$672$		0			0
$673$	−5.14782	−	22.5541i	−0.198434	−	0.869395i	−0.971869	−	0.235520i	$-0.924321\pi$
$673$	−5.14782	−	22.5541i	−0.198434	−	0.869395i	0.773436	−	0.633875i	$-0.218537\pi$
$674$		0			0
$675$	9.77024	−	12.2515i	0.376057	−	0.471560i
$676$		0			0
$677$	16.2690	+	7.83476i	0.625270	+	0.301114i	0.719560	−	0.694431i	$-0.244344\pi$
$677$	16.2690	+	7.83476i	0.625270	+	0.301114i	−0.0942895	+	0.995545i	$0.530058\pi$
$678$		0			0
$679$	1.16421			0.0446783
$680$		0			0
$681$	−1.65668	−	7.25838i	−0.0634840	−	0.278142i
$682$		0			0
$683$	27.5127	+	34.4998i	1.05274	+	1.32010i	0.945413	+	0.325875i	$0.105659\pi$
$683$	27.5127	+	34.4998i	1.05274	+	1.32010i	0.107330	+	0.994223i	$0.465770\pi$
$684$		0			0
$685$	−0.196866	−	0.246862i	−0.00752186	−	0.00943211i
$686$		0			0
$687$	3.98225	−	4.99358i	0.151932	−	0.190517i
$688$		0			0
$689$	−29.5807	+	14.2453i	−1.12693	+	0.542703i
$690$		0			0
$691$	5.30702	−	23.2516i	0.201889	−	0.884531i	−0.767897	−	0.640573i	$-0.778697\pi$
$691$	5.30702	−	23.2516i	0.201889	−	0.884531i	0.969786	−	0.243958i	$-0.0784460\pi$
$692$		0			0
$693$	−0.355936	+	0.171410i	−0.0135209	+	0.00651132i
$694$		0			0
$695$	−0.255603			−0.00969559
$696$		0			0
$697$	−10.9565			−0.415005
$698$		0			0
$699$	0.367781	−	0.177114i	0.0139108	−	0.00669907i
$700$		0			0
$701$	−0.249668	+	1.09387i	−0.00942983	+	0.0413148i	−0.979424	−	0.201814i	$-0.935316\pi$
$701$	−0.249668	+	1.09387i	−0.00942983	+	0.0413148i	0.969994	+	0.243128i	$0.0781736\pi$
$702$		0			0
$703$	−3.53438	+	1.70207i	−0.133302	+	0.0641948i
$704$		0			0
$705$	−0.0549581	+	0.0689153i	−0.00206984	+	0.00259550i
$706$		0			0
$707$	−0.409330	−	0.513283i	−0.0153944	−	0.0193040i
$708$		0			0
$709$	2.54623	+	3.19287i	0.0956256	+	0.119911i	0.827342	−	0.561698i	$-0.189852\pi$
$709$	2.54623	+	3.19287i	0.0956256	+	0.119911i	−0.731716	+	0.681609i	$0.761280\pi$
$710$		0			0
$711$	−2.92931	−	12.8342i	−0.109858	−	0.481318i
$712$		0			0
$713$	−72.7948			−2.72619
$714$		0			0
$715$	−0.938469	−	0.451943i	−0.0350967	−	0.0169017i
$716$		0			0
$717$	−0.0304995	+	0.0382451i	−0.00113902	+	0.00142829i
$718$		0			0
$719$	6.48062	+	28.3935i	0.241686	+	1.05890i	0.939481	+	0.342600i	$0.111308\pi$
$719$	6.48062	+	28.3935i	0.241686	+	1.05890i	−0.697795	+	0.716298i	$0.745835\pi$
$720$		0			0
$721$	1.42543	+	0.686450i	0.0530857	+	0.0255647i
$722$		0			0
$723$	0.767258	−	3.36158i	0.0285346	−	0.125018i
$724$		0			0
$725$	4.96077	−	26.2499i	0.184238	−	0.974898i
$726$		0			0
$727$	−3.52888	+	15.4610i	−0.130879	+	0.573417i	0.866377	+	0.499390i	$0.166442\pi$
$727$	−3.52888	+	15.4610i	−0.130879	+	0.573417i	−0.997256	+	0.0740276i	$0.976415\pi$
$728$		0			0
$729$	10.5978	+	5.10365i	0.392512	+	0.189024i
$730$		0			0
$731$	4.31850	+	18.9206i	0.159725	+	0.699802i
$732$		0			0
$733$	−13.3490	+	16.7391i	−0.493056	+	0.618273i	−0.964647	−	0.263544i	$-0.915108\pi$
$733$	−13.3490	+	16.7391i	−0.493056	+	0.618273i	0.471591	+	0.881817i	$0.343680\pi$
$734$		0			0
$735$	0.692021	+	0.333260i	0.0255256	+	0.0122925i
$736$		0			0
$737$	14.6864			0.540980
$738$		0			0
$739$	−7.48547	−	32.7960i	−0.275357	−	1.20642i	−0.903592	−	0.428395i	$-0.859079\pi$
$739$	−7.48547	−	32.7960i	−0.275357	−	1.20642i	0.628234	−	0.778024i	$-0.283778\pi$
$740$		0			0
$741$	−1.76623	−	2.21478i	−0.0648839	−	0.0813619i
$742$		0			0
$743$	−3.38972	−	4.25057i	−0.124357	−	0.155938i	0.715756	−	0.698351i	$-0.246082\pi$
$743$	−3.38972	−	4.25057i	−0.124357	−	0.155938i	−0.840112	+	0.542413i	$0.817511\pi$
$744$		0			0
$745$	−0.827060	+	1.03710i	−0.0303011	+	0.0379964i
$746$		0			0
$747$	28.3158	−	13.6362i	1.03602	−	0.498922i
$748$		0			0
$749$	0.403362	−	1.76724i	0.0147385	−	0.0645737i
$750$		0			0
$751$	−15.1341	+	7.28822i	−0.552253	+	0.265951i	−0.689131	−	0.724637i	$-0.742007\pi$
$751$	−15.1341	+	7.28822i	−0.552253	+	0.265951i	0.136878	+	0.990588i	$0.456293\pi$
$752$		0			0
$753$	−8.43057			−0.307227
$754$		0			0
$755$	1.88040			0.0684346
$756$		0			0
$757$	−2.26271	+	1.08966i	−0.0822396	+	0.0396045i	−0.474551	−	0.880228i	$-0.657390\pi$
$757$	−2.26271	+	1.08966i	−0.0822396	+	0.0396045i	0.392312	+	0.919832i	$0.371675\pi$
$758$		0			0
$759$	1.28435	−	5.62710i	0.0466189	−	0.204251i
$760$		0			0
$761$	48.2367	−	23.2296i	1.74858	−	0.842071i	0.769484	−	0.638666i	$-0.220514\pi$
$761$	48.2367	−	23.2296i	1.74858	−	0.842071i	0.979095	−	0.203405i	$-0.0652007\pi$
$762$		0			0
$763$	−0.194710	+	0.244158i	−0.00704897	+	0.00883913i
$764$		0			0
$765$	0.968009	+	1.21384i	0.0349984	+	0.0438866i
$766$		0			0
$767$	12.4961	+	15.6696i	0.451209	+	0.565798i
$768$		0			0
$769$	−2.05658	−	9.01047i	−0.0741622	−	0.324926i	0.924215	−	0.381873i	$-0.124721\pi$
$769$	−2.05658	−	9.01047i	−0.0741622	−	0.324926i	−0.998377	+	0.0569466i	$0.981864\pi$
$770$		0			0
$771$	3.06936			0.110540
$772$		0			0
$773$	33.7298	+	16.2434i	1.21318	+	0.584235i	0.927404	−	0.374062i	$-0.122035\pi$
$773$	33.7298	+	16.2434i	1.21318	+	0.584235i	0.285773	+	0.958297i	$0.407750\pi$
$774$		0			0
$775$	−28.9034	+	36.2437i	−1.03824	+	1.30191i
$776$		0			0
$777$	−0.0410891	−	0.180023i	−0.00147406	−	0.00645829i
$778$		0			0
$779$	4.39320	+	2.11565i	0.157403	+	0.0758011i
$780$		0			0
$781$	3.25278	−	14.2514i	0.116394	−	0.509954i
$782$		0			0
$783$	−16.9988	+	0.639797i	−0.607488	+	0.0228645i
$784$		0			0
$785$	−0.414010	+	1.81390i	−0.0147766	+	0.0647407i
$786$		0			0
$787$	23.3686	+	11.2537i	0.833001	+	0.401152i	0.801240	−	0.598343i	$-0.204174\pi$
$787$	23.3686	+	11.2537i	0.833001	+	0.401152i	0.0317612	+	0.999495i	$0.489888\pi$
$788$		0			0
$789$	0.270242	+	1.18401i	0.00962086	+	0.0421518i
$790$		0			0
$791$	−1.07420	+	1.34701i	−0.0381943	+	0.0478941i
$792$		0			0
$793$	39.2461	+	18.8999i	1.39367	+	0.671156i
$794$		0			0
$795$	0.916166			0.0324931
$796$		0			0
$797$	−4.49300	−	19.6851i	−0.159150	−	0.697283i	−0.990033	−	0.140835i	$-0.955021\pi$
$797$	−4.49300	−	19.6851i	−0.159150	−	0.697283i	0.830883	−	0.556447i	$-0.187836\pi$
$798$		0			0
$799$	1.45593	+	1.82567i	0.0515070	+	0.0645877i
$800$		0			0
$801$	19.2920	+	24.1914i	0.681650	+	0.854762i
$802$		0			0
$803$	6.61679	−	8.29719i	0.233501	−	0.292801i
$804$		0			0
$805$	−0.152793	+	0.0735811i	−0.00538524	+	0.00259339i
$806$		0			0
$807$	−3.76122	+	16.4790i	−0.132401	+	0.580087i
$808$		0			0
$809$	−31.0306	+	14.9435i	−1.09098	+	0.525387i	−0.890810	−	0.454375i	$-0.849862\pi$
$809$	−31.0306	+	14.9435i	−1.09098	+	0.525387i	−0.200166	+	0.979762i	$0.564148\pi$
$810$		0			0
$811$	−32.7536			−1.15013			−0.575067	−	0.818106i	$-0.695024\pi$
$811$	−32.7536			−1.15013			−0.575067	+	0.818106i	$0.695024\pi$
$812$		0			0
$813$	−17.5066			−0.613984
$814$		0			0
$815$	−2.90312	+	1.39807i	−0.101692	+	0.0489723i
$816$		0			0
$817$	1.92191	−	8.42044i	0.0672392	−	0.294594i
$818$		0			0
$819$	−1.05011	+	0.505708i	−0.0366939	+	0.0176709i
$820$		0			0
$821$	2.70978	−	3.39795i	0.0945718	−	0.118589i	−0.732294	−	0.680989i	$-0.761550\pi$
$821$	2.70978	−	3.39795i	0.0945718	−	0.118589i	0.826866	+	0.562399i	$0.190122\pi$
$822$		0			0
$823$	−8.36108	−	10.4845i	−0.291449	−	0.365465i	0.614453	−	0.788954i	$-0.289377\pi$
$823$	−8.36108	−	10.4845i	−0.291449	−	0.365465i	−0.905902	+	0.423488i	$0.860805\pi$
$824$		0			0
$825$	−2.29172	−	2.87372i	−0.0797873	−	0.100050i
$826$		0			0
$827$	−5.86174	−	25.6820i	−0.203833	−	0.893049i	−0.968577	−	0.248715i	$-0.919992\pi$
$827$	−5.86174	−	25.6820i	−0.203833	−	0.893049i	0.764744	−	0.644334i	$-0.222865\pi$
$828$		0			0
$829$	−10.3618			−0.359880			−0.179940	−	0.983678i	$-0.557590\pi$
$829$	−10.3618			−0.359880			−0.179940	+	0.983678i	$0.557590\pi$
$830$		0			0
$831$	−7.10119	−	3.41975i	−0.246337	−	0.118630i
$832$		0			0
$833$	12.6866	−	15.9085i	0.439566	−	0.551199i
$834$		0			0
$835$	−0.606564	−	2.65753i	−0.0209910	−	0.0919676i
$836$		0			0
$837$	26.5954	+	12.8077i	0.919273	+	0.442699i
$838$		0			0
$839$	−5.93578	+	26.0064i	−0.204926	+	0.897839i	0.762959	+	0.646446i	$0.223746\pi$
$839$	−5.93578	+	26.0064i	−0.204926	+	0.897839i	−0.967885	+	0.251393i	$0.919112\pi$
$840$		0			0
$841$	−25.1084	+	14.5111i	−0.865805	+	0.500381i
$842$		0			0
$843$	−2.56398	+	11.2335i	−0.0883083	+	0.386904i
$844$		0			0
$845$	−0.448927	−	0.216192i	−0.0154435	−	0.00743722i
$846$		0			0
$847$	−0.225446	−	0.987745i	−0.00774643	−	0.0339393i
$848$		0			0
$849$	6.00232	−	7.52667i	0.205999	−	0.258315i
$850$		0			0
$851$	−21.2458	−	10.2314i	−0.728296	−	0.350729i
$852$		0			0
$853$	−19.7071			−0.674758			−0.337379	−	0.941369i	$-0.609540\pi$
$853$	−19.7071			−0.674758			−0.337379	+	0.941369i	$0.609540\pi$
$854$		0			0
$855$	−0.153752	−	0.673633i	−0.00525822	−	0.0230378i
$856$		0			0
$857$	1.34481	+	1.68634i	0.0459380	+	0.0576044i	0.804270	−	0.594264i	$-0.202557\pi$
$857$	1.34481	+	1.68634i	0.0459380	+	0.0576044i	−0.758332	+	0.651869i	$0.773985\pi$
$858$		0			0
$859$	−21.4799	−	26.9349i	−0.732883	−	0.919006i	0.266107	−	0.963944i	$-0.414263\pi$
$859$	−21.4799	−	26.9349i	−0.732883	−	0.919006i	−0.998990	+	0.0449372i	$0.985691\pi$
$860$		0			0
$861$	−0.143104	+	0.179447i	−0.00487698	+	0.00611553i
$862$		0			0
$863$	−8.63922	+	4.16043i	−0.294082	+	0.141623i	−0.575108	−	0.818078i	$-0.695040\pi$
$863$	−8.63922	+	4.16043i	−0.294082	+	0.141623i	0.281025	+	0.959700i	$0.409326\pi$
$864$		0			0
$865$	0.00527135	−	0.0230953i	0.000179231	−	0.000785263i
$866$		0			0
$867$	4.26055	−	2.05177i	0.144696	−	0.0696819i
$868$		0			0
$869$	−6.52888			−0.221477
$870$		0			0
$871$	43.3290			1.46815
$872$		0			0
$873$	−25.6896	+	12.3715i	−0.869462	+	0.418711i
$874$		0			0
$875$	−0.0482534	+	0.211412i	−0.00163126	+	0.00714702i
$876$		0			0
$877$	0.758824	−	0.365430i	0.0256237	−	0.0123397i	−0.421028	−	0.907048i	$-0.638331\pi$
$877$	0.758824	−	0.365430i	0.0256237	−	0.0123397i	0.446652	+	0.894708i	$0.352616\pi$
$878$		0			0
$879$	6.06481	−	7.60503i	0.204561	−	0.256511i
$880$		0			0
$881$	−5.13019	−	6.43306i	−0.172841	−	0.216735i	0.687864	−	0.725839i	$-0.258548\pi$
$881$	−5.13019	−	6.43306i	−0.172841	−	0.216735i	−0.860705	+	0.509104i	$0.829977\pi$
$882$		0			0
$883$	−33.8568	−	42.4551i	−1.13937	−	1.42873i	−0.887404	−	0.460993i	$-0.847493\pi$
$883$	−33.8568	−	42.4551i	−1.13937	−	1.42873i	−0.251969	−	0.967735i	$-0.581078\pi$
$884$		0			0
$885$	−0.124449	−	0.545248i	−0.00418332	−	0.0183283i
$886$		0			0
$887$	13.5013			0.453328			0.226664	−	0.973973i	$-0.427218\pi$
$887$	13.5013			0.453328			0.226664	+	0.973973i	$0.427218\pi$
$888$		0			0
$889$	0.268217	+	0.129167i	0.00899572	+	0.00433211i
$890$		0			0
$891$	5.26354	−	6.60027i	0.176335	−	0.221117i
$892$		0			0
$893$	−0.231250	−	1.01317i	−0.00773849	−	0.0339045i
$894$		0			0
$895$	−2.26271	−	1.08966i	−0.0756340	−	0.0364234i
$896$		0			0
$897$	3.78919	−	16.6015i	0.126517	−	0.554309i
$898$		0			0
$899$	50.2878	−	1.89272i	1.67719	−	0.0631257i
$900$		0			0
$901$	5.40073	−	23.6622i	0.179924	−	0.788301i
$902$		0			0
$903$	0.366289	+	0.176396i	0.0121893	+	0.00587007i
$904$		0			0
$905$	−0.314446	−	1.37768i	−0.0104525	−	0.0457956i
$906$		0			0
$907$	28.9795	−	36.3391i	0.962248	−	1.20662i	−0.0161456	−	0.999870i	$-0.505140\pi$
$907$	28.9795	−	36.3391i	0.962248	−	1.20662i	0.978394	−	0.206751i	$-0.0662891\pi$
$908$		0			0
$909$	14.4867	+	6.97644i	0.480494	+	0.231394i
$910$		0			0
$911$	−21.1685			−0.701344			−0.350672	−	0.936498i	$-0.614047\pi$
$911$	−21.1685			−0.701344			−0.350672	+	0.936498i	$0.614047\pi$
$912$		0			0
$913$	−3.46844	−	15.1962i	−0.114788	−	0.502921i
$914$		0			0
$915$	−0.757865	−	0.950332i	−0.0250542	−	0.0314170i
$916$		0			0
$917$	−1.00149	−	1.25583i	−0.0330722	−	0.0414712i
$918$		0			0
$919$	12.5699	−	15.7621i	0.414641	−	0.519944i	−0.530023	−	0.847984i	$-0.677817\pi$
$919$	12.5699	−	15.7621i	0.414641	−	0.519944i	0.944664	+	0.328040i	$0.106388\pi$
$920$		0			0
$921$	15.1809	−	7.31074i	0.500228	−	0.240897i
$922$		0			0
$923$	9.59664	−	42.0456i	0.315877	−	1.38395i
$924$		0			0
$925$	−13.5298	+	6.51563i	−0.444858	+	0.214232i
$926$		0			0
$927$	−38.7482			−1.27266
$928$		0			0
$929$	19.7952			0.649461			0.324730	−	0.945807i	$-0.394726\pi$
$929$	19.7952			0.649461			0.324730	+	0.945807i	$0.394726\pi$
$930$		0			0
$931$	−8.15883	+	3.92909i	−0.267395	+	0.128771i
$932$		0			0
$933$	−2.93751	+	12.8701i	−0.0961697	+	0.421347i
$934$		0			0
$935$	0.693750	−	0.334093i	0.0226881	−	0.0109260i
$936$		0			0
$937$	−34.9705	+	43.8516i	−1.14244	+	1.43257i	−0.257853	+	0.966184i	$0.583015\pi$
$937$	−34.9705	+	43.8516i	−1.14244	+	1.43257i	−0.884582	+	0.466384i	$0.845556\pi$
$938$		0			0
$939$	−9.92171	−	12.4414i	−0.323783	−	0.406011i
$940$		0			0
$941$	−1.50066	−	1.88177i	−0.0489202	−	0.0613441i	0.756769	−	0.653682i	$-0.226777\pi$
$941$	−1.50066	−	1.88177i	−0.0489202	−	0.0613441i	−0.805690	+	0.592338i	$0.798205\pi$
$942$		0			0
$943$	6.52230	+	28.5761i	0.212395	+	0.930565i
$944$		0			0
$945$	0.0687686			0.00223704
$946$		0			0
$947$	2.16003	+	1.04022i	0.0701915	+	0.0338025i	0.468650	−	0.883384i	$-0.344740\pi$
$947$	2.16003	+	1.04022i	0.0701915	+	0.0338025i	−0.398459	+	0.917186i	$0.630455\pi$
$948$		0			0
$949$	19.5214	−	24.4791i	0.633692	−	0.794624i
$950$		0			0
$951$	0.933329	+	4.08918i	0.0302653	+	0.132601i
$952$		0			0
$953$	30.1634	+	14.5259i	0.977090	+	0.470542i	0.853103	−	0.521742i	$-0.174718\pi$
$953$	30.1634	+	14.5259i	0.977090	+	0.470542i	0.123987	+	0.992284i	$0.460432\pi$
$954$		0			0
$955$	0.140948	−	0.617534i	0.00456098	−	0.0199829i
$956$		0			0
$957$	−0.740939	+	3.92068i	−0.0239512	+	0.126738i
$958$		0			0
$959$	−0.0389917	+	0.170834i	−0.00125911	+	0.00551651i
$960$		0			0
$961$	−50.7476	−	24.4387i	−1.63702	−	0.788347i
$962$		0			0
$963$	9.87896	+	43.2826i	0.318345	+	1.39476i
$964$		0			0
$965$	−1.86108	+	2.33372i	−0.0599102	+	0.0751250i
$966$		0			0
$967$	31.6906	+	15.2614i	1.01910	+	0.490773i	0.867378	−	0.497650i	$-0.165804\pi$
$967$	31.6906	+	15.2614i	1.01910	+	0.490773i	0.151723	+	0.988423i	$0.451518\pi$
$968$		0			0
$969$	2.09411			0.0672726
$970$		0			0
$971$	−6.12671	−	26.8429i	−0.196616	−	0.861429i	−0.972933	−	0.231087i	$-0.925772\pi$
$971$	−6.12671	−	26.8429i	−0.196616	−	0.861429i	0.776318	−	0.630342i	$-0.217085\pi$
$972$		0			0
$973$	0.0884415	+	0.110902i	0.00283530	+	0.00355536i
$974$		0			0
$975$	−6.76122	−	8.47830i	−0.216532	−	0.271523i
$976$		0			0
$977$	−7.08240	+	8.88105i	−0.226586	+	0.284130i	−0.882109	−	0.471045i	$-0.843877\pi$
$977$	−7.08240	+	8.88105i	−0.226586	+	0.284130i	0.655523	+	0.755175i	$0.272448\pi$
$978$		0			0
$979$	13.8262	−	6.65833i	0.441886	−	0.212801i
$980$		0			0
$981$	1.70195	−	7.45672i	0.0543390	−	0.238075i
$982$		0			0
$983$	−29.6589	+	14.2830i	−0.945972	+	0.455556i	−0.842272	−	0.539053i	$-0.818782\pi$
$983$	−29.6589	+	14.2830i	−0.945972	+	0.455556i	−0.103700	+	0.994609i	$0.533068\pi$
$984$		0			0
$985$	−2.87561			−0.0916245
$986$		0			0
$987$	0.0489173			0.00155706
$988$		0			0
$989$	46.7769	−	22.5266i	1.48742	−	0.716303i
$990$		0			0
$991$	5.00258	−	21.9177i	0.158912	−	0.696240i	−0.831201	−	0.555972i	$-0.812346\pi$
$991$	5.00258	−	21.9177i	0.158912	−	0.696240i	0.990114	−	0.140269i	$-0.0447966\pi$
$992$		0			0
$993$	−5.59299	+	2.69344i	−0.177488	+	0.0854738i
$994$		0			0
$995$	−3.27599	+	4.10796i	−0.103856	+	0.130231i
$996$		0			0
$997$	−13.7943	−	17.2975i	−0.436871	−	0.547819i	0.513845	−	0.857883i	$-0.328221\pi$
$997$	−13.7943	−	17.2975i	−0.436871	−	0.547819i	−0.950716	+	0.310065i	$0.899649\pi$
$998$		0			0
$999$	5.96197	+	7.47607i	0.188628	+	0.236532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.b.257.1		6
4.3	odd	2		58.2.d.a.25.1	yes	6
12.11	even	2		522.2.k.c.199.1		6
29.7	even	7	inner	464.2.u.b.65.1		6
116.7	odd	14		58.2.d.a.7.1	✓	6
116.15	even	28		1682.2.b.g.1681.2		6
116.23	odd	14		1682.2.a.m.1.2		3
116.35	odd	14		1682.2.a.n.1.2		3
116.43	even	28		1682.2.b.g.1681.5		6
348.239	even	14		522.2.k.c.181.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.a.7.1	✓	6	116.7	odd	14
58.2.d.a.25.1	yes	6	4.3	odd	2
464.2.u.b.65.1		6	29.7	even	7	inner
464.2.u.b.257.1		6	1.1	even	1	trivial
522.2.k.c.181.1		6	348.239	even	14
522.2.k.c.199.1		6	12.11	even	2
1682.2.a.m.1.2		3	116.23	odd	14
1682.2.a.n.1.2		3	116.35	odd	14
1682.2.b.g.1681.2		6	116.15	even	28
1682.2.b.g.1681.5		6	116.43	even	28

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.240787i) q^{3} +(-0.0440730 + 0.193096i) q^{5} +(0.0990311 - 0.0476909i) q^{7} +(-1.67845 + 2.10471i) q^{9} +(0.832437 + 1.04384i) q^{11} +(2.45593 + 3.07964i) q^{13} +(-0.0244587 - 0.107160i) q^{15} -2.91185 q^{17} +(1.16756 + 0.562269i) q^{19} +(-0.0380322 + 0.0476909i) q^{21} +(1.73341 + 7.59455i) q^{23} +(4.46950 + 2.15240i) q^{25} +(0.702907 - 3.07964i) q^{27} +(-1.39493 - 5.20136i) q^{29} +(-2.07942 + 9.11052i) q^{31} +(-0.667563 - 0.321481i) q^{33} +(0.00484434 + 0.0212244i) q^{35} +(-1.88740 + 2.36672i) q^{37} +(-1.96950 - 0.948461i) q^{39} +3.76271 q^{41} +(-1.48307 - 6.49777i) q^{43} +(-0.332437 - 0.416863i) q^{45} +(-0.500000 - 0.626980i) q^{47} +(-4.35690 + 5.46337i) q^{49} +(1.45593 - 0.701137i) q^{51} +(-1.85474 + 8.12615i) q^{53} +(-0.238250 + 0.114735i) q^{55} -0.719169 q^{57} +5.08815 q^{59} +(9.96346 - 4.79815i) q^{61} +(-0.0658433 + 0.288478i) q^{63} +(-0.702907 + 0.338502i) q^{65} +(6.85839 - 8.60015i) q^{67} +(-2.69537 - 3.37989i) q^{69} +(-6.82640 - 8.56003i) q^{71} +(-1.76875 - 7.74940i) q^{73} -2.75302 q^{75} +(0.132219 + 0.0636733i) q^{77} +(-3.04892 + 3.82322i) q^{79} +(-1.40701 - 6.16451i) q^{81} +(-10.5184 - 5.06540i) q^{83} +(0.128334 - 0.562269i) q^{85} +(1.94989 + 2.26480i) q^{87} +(2.55765 - 11.2058i) q^{89} +(0.390084 + 0.187854i) q^{91} +(-1.15399 - 5.05596i) q^{93} +(-0.160030 + 0.200671i) q^{95} +(9.54288 + 4.59561i) q^{97} -3.59419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 4 q^{5} + 5 q^{7} - 6 q^{9} + 6 q^{11} + 11 q^{13} + 9 q^{15} - 10 q^{17} + 6 q^{19} + 15 q^{21} + 7 q^{23} + 17 q^{25} - 9 q^{27} + 15 q^{29} - 4 q^{31} - 3 q^{33} - 22 q^{35} - 13 q^{37}+ \cdots - 48 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 4 * q^5 + 5 * q^7 - 6 * q^9 + 6 * q^11 + 11 * q^13 + 9 * q^15 - 10 * q^17 + 6 * q^19 + 15 * q^21 + 7 * q^23 + 17 * q^25 - 9 * q^27 + 15 * q^29 - 4 * q^31 - 3 * q^33 - 22 * q^35 - 13 * q^37 - 2 * q^39 - 12 * q^41 + 7 * q^43 - 3 * q^45 - 3 * q^47 - 18 * q^49 + 5 * q^51 - 22 * q^53 + 24 * q^55 + 18 * q^57 + 38 * q^59 + 31 * q^61 + 2 * q^63 + 9 * q^65 - 11 * q^67 - 28 * q^69 - 23 * q^71 + 5 * q^73 - 26 * q^75 + 12 * q^77 - 23 * q^81 - 35 * q^83 - 26 * q^85 - 11 * q^87 + 13 * q^89 + q^91 - 12 * q^93 - 25 * q^95 + 20 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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