LMFDB - Embedded newform 512.2.i.b.417.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(33,512)] 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("512.33"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			417.6
Character	$\chi$	$=$	512.417
Dual form			512.2.i.b.97.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.435353 - 2.18867i) q^{3} +(-0.649649 - 0.434082i) q^{5} +(-3.64486 + 1.50975i) q^{7} +(-1.82909 - 0.757635i) q^{9} +(-5.80194 + 1.15408i) q^{11} +(-2.03484 + 1.35963i) q^{13} +(-1.23289 + 1.23289i) q^{15} +(0.960477 + 0.960477i) q^{17} +(-0.435978 - 0.652487i) q^{19} +(1.71754 + 8.63465i) q^{21} +(0.421603 - 1.01784i) q^{23} +(-1.67980 - 4.05540i) q^{25} +(1.26483 - 1.89295i) q^{27} +(1.43977 + 0.286388i) q^{29} -6.88004i q^{31} +13.2009i q^{33} +(3.02323 + 0.601358i) q^{35} +(1.07856 - 1.61417i) q^{37} +(2.08991 + 5.04550i) q^{39} +(-2.79324 + 6.74347i) q^{41} +(1.20307 + 6.04824i) q^{43} +(0.859393 + 1.28617i) q^{45} +(-6.30014 - 6.30014i) q^{47} +(6.05588 - 6.05588i) q^{49} +(2.52031 - 1.68402i) q^{51} +(-10.2655 + 2.04194i) q^{53} +(4.27019 + 1.76877i) q^{55} +(-1.61788 + 0.670148i) q^{57} +(-4.21278 - 2.81489i) q^{59} +(2.08276 - 10.4707i) q^{61} +7.81061 q^{63} +1.91212 q^{65} +(-1.42195 + 7.14864i) q^{67} +(-2.04417 - 1.36587i) q^{69} +(2.49385 - 1.03299i) q^{71} +(-1.90488 - 0.789026i) q^{73} +(-9.60722 + 1.91099i) q^{75} +(19.4049 - 12.9659i) q^{77} +(-6.20432 + 6.20432i) q^{79} +(-7.79217 - 7.79217i) q^{81} +(-1.13685 - 1.70141i) q^{83} +(-0.207047 - 1.04090i) q^{85} +(1.25361 - 3.02649i) q^{87} +(1.15743 + 2.79429i) q^{89} +(5.36398 - 8.02776i) q^{91} +(-15.0581 - 2.99524i) q^{93} +0.613137i q^{95} -13.1193i q^{97} +(11.4867 + 2.28484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.435353	−	2.18867i	0.251351	−	1.26363i	−0.624492	−	0.781031i	$-0.714694\pi$
$3$	0.435353	−	2.18867i	0.251351	−	1.26363i	0.875843	−	0.482596i	$-0.160306\pi$
$4$		0			0
$5$	−0.649649	−	0.434082i	−0.290532	−	0.194127i	0.401760	−	0.915745i	$-0.368399\pi$
$5$	−0.649649	−	0.434082i	−0.290532	−	0.194127i	−0.692292	+	0.721618i	$0.743399\pi$
$6$		0			0
$7$	−3.64486	+	1.50975i	−1.37763	+	0.570631i	−0.943845	−	0.330387i	$-0.892821\pi$
$7$	−3.64486	+	1.50975i	−1.37763	+	0.570631i	−0.433780	+	0.901019i	$0.642821\pi$
$8$		0			0
$9$	−1.82909	−	0.757635i	−0.609697	−	0.252545i
$10$		0			0
$11$	−5.80194	+	1.15408i	−1.74935	+	0.347968i	−0.962936	−	0.269730i	$-0.913065\pi$
$11$	−5.80194	+	1.15408i	−1.74935	+	0.347968i	−0.786415	+	0.617698i	$0.788065\pi$
$12$		0			0
$13$	−2.03484	+	1.35963i	−0.564362	+	0.377095i	−0.804779	−	0.593575i	$-0.797716\pi$
$13$	−2.03484	+	1.35963i	−0.564362	+	0.377095i	0.240417	+	0.970670i	$0.422716\pi$
$14$		0			0
$15$	−1.23289	+	1.23289i	−0.318330	+	0.318330i
$16$		0			0
$17$	0.960477	+	0.960477i	0.232950	+	0.232950i	0.813923	−	0.580973i	$-0.197328\pi$
$17$	0.960477	+	0.960477i	0.232950	+	0.232950i	−0.580973	+	0.813923i	$0.697328\pi$
$18$		0			0
$19$	−0.435978	−	0.652487i	−0.100020	−	0.149691i	0.778084	−	0.628160i	$-0.216192\pi$
$19$	−0.435978	−	0.652487i	−0.100020	−	0.149691i	−0.878104	+	0.478469i	$0.841192\pi$
$20$		0			0
$21$	1.71754	+	8.63465i	0.374798	+	1.88423i
$22$		0			0
$23$	0.421603	−	1.01784i	0.0879104	−	0.212234i	−0.873810	−	0.486268i	$-0.838358\pi$
$23$	0.421603	−	1.01784i	0.0879104	−	0.212234i	0.961720	+	0.274033i	$0.0883579\pi$
$24$		0			0
$25$	−1.67980	−	4.05540i	−0.335960	−	0.811079i
$26$		0			0
$27$	1.26483	−	1.89295i	0.243417	−	0.364299i
$28$		0			0
$29$	1.43977	+	0.286388i	0.267358	+	0.0531809i	0.326949	−	0.945042i	$-0.393980\pi$
$29$	1.43977	+	0.286388i	0.267358	+	0.0531809i	−0.0595906	+	0.998223i	$0.518980\pi$
$30$		0			0
$31$		−	6.88004i		−	1.23569i	−0.786300	−	0.617845i	$-0.788006\pi$
$31$		−	6.88004i		−	1.23569i	0.786300	−	0.617845i	$-0.211994\pi$
$32$		0			0
$33$			13.2009i			2.29799i
$34$		0			0
$35$	3.02323	+	0.601358i	0.511019	+	0.101648i
$36$		0			0
$37$	1.07856	−	1.61417i	0.177313	−	0.265368i	−0.732158	−	0.681135i	$-0.761487\pi$
$37$	1.07856	−	1.61417i	0.177313	−	0.265368i	0.909471	+	0.415767i	$0.136487\pi$
$38$		0			0
$39$	2.08991	+	5.04550i	0.334654	+	0.807926i
$40$		0			0
$41$	−2.79324	+	6.74347i	−0.436230	+	1.05315i	0.541010	+	0.841016i	$0.318042\pi$
$41$	−2.79324	+	6.74347i	−0.436230	+	1.05315i	−0.977240	+	0.212136i	$0.931958\pi$
$42$		0			0
$43$	1.20307	+	6.04824i	0.183467	+	0.922349i	0.957330	+	0.288996i	$0.0933215\pi$
$43$	1.20307	+	6.04824i	0.183467	+	0.922349i	−0.773864	+	0.633352i	$0.781678\pi$
$44$		0			0
$45$	0.859393	+	1.28617i	0.128111	+	0.191731i
$46$		0			0
$47$	−6.30014	−	6.30014i	−0.918970	−	0.918970i	0.0779845	−	0.996955i	$-0.475152\pi$
$47$	−6.30014	−	6.30014i	−0.918970	−	0.918970i	−0.996955	+	0.0779845i	$0.975152\pi$
$48$		0			0
$49$	6.05588	−	6.05588i	0.865126	−	0.865126i
$50$		0			0
$51$	2.52031	−	1.68402i	0.352914	−	0.235810i
$52$		0			0
$53$	−10.2655	+	2.04194i	−1.41008	+	0.280482i	−0.840660	−	0.541564i	$-0.817832\pi$
$53$	−10.2655	+	2.04194i	−1.41008	+	0.280482i	−0.569421	+	0.822046i	$0.692832\pi$
$54$		0			0
$55$	4.27019	+	1.76877i	0.575792	+	0.238501i
$56$		0			0
$57$	−1.61788	+	0.670148i	−0.214293	+	0.0887632i
$58$		0			0
$59$	−4.21278	−	2.81489i	−0.548458	−	0.366468i	0.250255	−	0.968180i	$-0.419485\pi$
$59$	−4.21278	−	2.81489i	−0.548458	−	0.366468i	−0.798713	+	0.601712i	$0.794485\pi$
$60$		0			0
$61$	2.08276	−	10.4707i	0.266670	−	1.34064i	−0.582633	−	0.812736i	$-0.697977\pi$
$61$	2.08276	−	10.4707i	0.266670	−	1.34064i	0.849303	−	0.527906i	$-0.177023\pi$
$62$		0			0
$63$	7.81061			0.984045
$64$		0			0
$65$	1.91212			0.237169
$66$		0			0
$67$	−1.42195	+	7.14864i	−0.173719	+	0.873345i	0.791353	+	0.611360i	$0.209377\pi$
$67$	−1.42195	+	7.14864i	−0.173719	+	0.873345i	−0.965072	+	0.261985i	$0.915623\pi$
$68$		0			0
$69$	−2.04417	−	1.36587i	−0.246089	−	0.164431i
$70$		0			0
$71$	2.49385	−	1.03299i	0.295965	−	0.122593i	−0.229760	−	0.973247i	$-0.573794\pi$
$71$	2.49385	−	1.03299i	0.295965	−	0.122593i	0.525725	+	0.850655i	$0.323794\pi$
$72$		0			0
$73$	−1.90488	−	0.789026i	−0.222949	−	0.0923485i	0.268413	−	0.963304i	$-0.413501\pi$
$73$	−1.90488	−	0.789026i	−0.222949	−	0.0923485i	−0.491362	+	0.870955i	$0.663501\pi$
$74$		0			0
$75$	−9.60722	+	1.91099i	−1.10935	+	0.220663i
$76$		0			0
$77$	19.4049	−	12.9659i	2.21139	−	1.47760i
$78$		0			0
$79$	−6.20432	+	6.20432i	−0.698040	+	0.698040i	−0.963988	−	0.265947i	$-0.914315\pi$
$79$	−6.20432	+	6.20432i	−0.698040	+	0.698040i	0.265947	+	0.963988i	$0.414315\pi$
$80$		0			0
$81$	−7.79217	−	7.79217i	−0.865797	−	0.865797i
$82$		0			0
$83$	−1.13685	−	1.70141i	−0.124785	−	0.186755i	0.763817	−	0.645433i	$-0.223323\pi$
$83$	−1.13685	−	1.70141i	−0.124785	−	0.186755i	−0.888602	+	0.458678i	$0.848323\pi$
$84$		0			0
$85$	−0.207047	−	1.04090i	−0.0224575	−	0.112901i
$86$		0			0
$87$	1.25361	−	3.02649i	0.134402	−	0.324474i
$88$		0			0
$89$	1.15743	+	2.79429i	0.122688	+	0.296194i	0.973276	−	0.229638i	$-0.0737541\pi$
$89$	1.15743	+	2.79429i	0.122688	+	0.296194i	−0.850589	+	0.525832i	$0.823754\pi$
$90$		0			0
$91$	5.36398	−	8.02776i	0.562298	−	0.841538i
$92$		0			0
$93$	−15.0581	−	2.99524i	−1.56145	−	0.310592i
$94$		0			0
$95$			0.613137i			0.0629066i
$96$		0			0
$97$		−	13.1193i		−	1.33207i	−0.745922	−	0.666034i	$-0.767991\pi$
$97$		−	13.1193i		−	1.33207i	0.745922	−	0.666034i	$-0.232009\pi$
$98$		0			0
$99$	11.4867	+	2.28484i	1.15445	+	0.229635i
$100$		0			0
$101$	2.49376	−	3.73217i	0.248138	−	0.371365i	−0.686402	−	0.727222i	$-0.740811\pi$
$101$	2.49376	−	3.73217i	0.248138	−	0.371365i	0.934540	+	0.355857i	$0.115811\pi$
$102$		0			0
$103$	4.09230	+	9.87970i	0.403227	+	0.973476i	0.986878	+	0.161471i	$0.0516237\pi$
$103$	4.09230	+	9.87970i	0.403227	+	0.973476i	−0.583651	+	0.812005i	$0.698376\pi$
$104$		0			0
$105$	2.63235	−	6.35504i	0.256891	−	0.620189i
$106$		0			0
$107$	−0.745466	−	3.74771i	−0.0720669	−	0.362305i	0.927877	−	0.372886i	$-0.121632\pi$
$107$	−0.745466	−	3.74771i	−0.0720669	−	0.362305i	−0.999944	+	0.0105812i	$0.996632\pi$
$108$		0			0
$109$	5.47688	+	8.19674i	0.524590	+	0.785105i	0.995265	−	0.0972021i	$-0.0309893\pi$
$109$	5.47688	+	8.19674i	0.524590	+	0.785105i	−0.470674	+	0.882307i	$0.655989\pi$
$110$		0			0
$111$	−3.06333	−	3.06333i	−0.290759	−	0.290759i
$112$		0			0
$113$	−3.26239	+	3.26239i	−0.306900	+	0.306900i	−0.843706	−	0.536806i	$-0.819631\pi$
$113$	−3.26239	+	3.26239i	−0.306900	+	0.306900i	0.536806	+	0.843706i	$0.319631\pi$
$114$		0			0
$115$	−0.715720	+	0.478229i	−0.0667412	+	0.0445951i
$116$		0			0
$117$	4.75201	−	0.945233i	0.439323	−	0.0873868i
$118$		0			0
$119$	−4.95088	−	2.05072i	−0.453846	−	0.187989i
$120$		0			0
$121$	22.1680	−	9.18227i	2.01527	−	0.834752i
$122$		0			0
$123$	13.5432	+	9.04925i	1.22115	+	0.815943i
$124$		0			0
$125$	−1.43124	+	7.19532i	−0.128014	+	0.643569i
$126$		0			0
$127$	6.57619			0.583543			0.291771	−	0.956488i	$-0.405755\pi$
$127$	6.57619			0.583543			0.291771	+	0.956488i	$0.405755\pi$
$128$		0			0
$129$	13.7614			1.21162
$130$		0			0
$131$	−0.948444	+	4.76815i	−0.0828659	+	0.416595i	0.916978	+	0.398937i	$0.130621\pi$
$131$	−0.948444	+	4.76815i	−0.0828659	+	0.416595i	−0.999844	+	0.0176578i	$0.994379\pi$
$132$		0			0
$133$	2.57417	+	1.72000i	0.223209	+	0.149143i
$134$		0			0
$135$	−1.64339	+	0.680715i	−0.141441	+	0.0585866i
$136$		0			0
$137$	−19.4588	−	8.06010i	−1.66248	−	0.688621i	−0.664214	−	0.747542i	$-0.731234\pi$
$137$	−19.4588	−	8.06010i	−1.66248	−	0.688621i	−0.998263	+	0.0589215i	$0.981234\pi$
$138$		0			0
$139$	18.8196	−	3.74344i	1.59625	−	0.317515i	0.684741	−	0.728786i	$-0.259915\pi$
$139$	18.8196	−	3.74344i	1.59625	−	0.317515i	0.911513	+	0.411272i	$0.134915\pi$
$140$		0			0
$141$	−16.5317	+	11.0461i	−1.39222	+	0.930252i
$142$		0			0
$143$	10.2369	−	10.2369i	0.856050	−	0.856050i
$144$		0			0
$145$	−0.811028	−	0.811028i	−0.0673522	−	0.0673522i
$146$		0			0
$147$	−10.6179	−	15.8908i	−0.875747	−	1.31065i
$148$		0			0
$149$	−0.183778	−	0.923914i	−0.0150557	−	0.0756900i	0.972527	−	0.232790i	$-0.0747855\pi$
$149$	−0.183778	−	0.923914i	−0.0150557	−	0.0756900i	−0.987583	+	0.157100i	$0.949785\pi$
$150$		0			0
$151$	4.16374	−	10.0522i	0.338841	−	0.818034i	−0.658987	−	0.752154i	$-0.729015\pi$
$151$	4.16374	−	10.0522i	0.338841	−	0.818034i	0.997828	−	0.0658792i	$-0.0209852\pi$
$152$		0			0
$153$	−1.02911	−	2.48449i	−0.0831986	−	0.200859i
$154$		0			0
$155$	−2.98650	+	4.46961i	−0.239881	+	0.359008i
$156$		0			0
$157$	−2.16776	−	0.431195i	−0.173006	−	0.0344131i	0.107827	−	0.994170i	$-0.465611\pi$
$157$	−2.16776	−	0.431195i	−0.173006	−	0.0344131i	−0.280833	+	0.959757i	$0.590611\pi$
$158$		0			0
$159$			23.3568i			1.85232i
$160$		0			0
$161$			4.34640i			0.342544i
$162$		0			0
$163$	10.1978	+	2.02847i	0.798753	+	0.158882i	0.577560	−	0.816348i	$-0.304005\pi$
$163$	10.1978	+	2.02847i	0.798753	+	0.158882i	0.221193	+	0.975230i	$0.429005\pi$
$164$		0			0
$165$	5.73029	−	8.57598i	0.446102	−	0.667640i
$166$		0			0
$167$	5.67541	+	13.7016i	0.439176	+	1.06027i	0.976234	+	0.216720i	$0.0695358\pi$
$167$	5.67541	+	13.7016i	0.439176	+	1.06027i	−0.537058	+	0.843546i	$0.680464\pi$
$168$		0			0
$169$	−2.68293	+	6.47717i	−0.206379	+	0.498244i
$170$		0			0
$171$	0.303097	+	1.52377i	0.0231784	+	0.116526i
$172$		0			0
$173$	−2.81628	−	4.21486i	−0.214118	−	0.320450i	0.708827	−	0.705382i	$-0.249225\pi$
$173$	−2.81628	−	4.21486i	−0.214118	−	0.320450i	−0.922945	+	0.384933i	$0.874225\pi$
$174$		0			0
$175$	12.2453	+	12.2453i	0.925654	+	0.925654i
$176$		0			0
$177$	−7.99491	+	7.99491i	−0.600934	+	0.600934i
$178$		0			0
$179$	−2.53753	+	1.69552i	−0.189664	+	0.126729i	−0.646777	−	0.762679i	$-0.723883\pi$
$179$	−2.53753	+	1.69552i	−0.189664	+	0.126729i	0.457113	+	0.889409i	$0.348883\pi$
$180$		0			0
$181$	6.51424	−	1.29576i	0.484200	−	0.0963133i	0.0530464	−	0.998592i	$-0.483107\pi$
$181$	6.51424	−	1.29576i	0.484200	−	0.0963133i	0.431153	+	0.902279i	$0.358107\pi$
$182$		0			0
$183$	−22.0102	−	9.11694i	−1.62704	−	0.673943i
$184$		0			0
$185$	−1.40136	+	0.580464i	−0.103030	+	0.0426766i
$186$		0			0
$187$	−6.68109	−	4.46416i	−0.488570	−	0.326452i
$188$		0			0
$189$	−1.75224	+	8.80912i	−0.127457	+	0.640769i
$190$		0			0
$191$	−1.58154			−0.114436			−0.0572181	−	0.998362i	$-0.518223\pi$
$191$	−1.58154			−0.114436			−0.0572181	+	0.998362i	$0.518223\pi$
$192$		0			0
$193$	−16.3932			−1.18001			−0.590004	−	0.807401i	$-0.700874\pi$
$193$	−16.3932			−1.18001			−0.590004	+	0.807401i	$0.700874\pi$
$194$		0			0
$195$	0.832448	−	4.18500i	0.0596128	−	0.299694i
$196$		0			0
$197$	2.24425	+	1.49956i	0.159896	+	0.106839i	0.632944	−	0.774197i	$-0.281846\pi$
$197$	2.24425	+	1.49956i	0.159896	+	0.106839i	−0.473048	+	0.881037i	$0.656846\pi$
$198$		0			0
$199$	12.1675	−	5.03992i	0.862528	−	0.357271i	0.0928322	−	0.995682i	$-0.470408\pi$
$199$	12.1675	−	5.03992i	0.862528	−	0.357271i	0.769696	+	0.638411i	$0.220408\pi$
$200$		0			0
$201$	15.0269	+	6.22436i	1.05992	+	0.439032i
$202$		0			0
$203$	−5.68012	+	1.12985i	−0.398666	+	0.0792996i
$204$		0			0
$205$	4.74184	−	3.16839i	0.331184	−	0.221290i
$206$		0			0
$207$	−1.54230	+	1.54230i	−0.107197	+	0.107197i
$208$		0			0
$209$	3.28254	+	3.28254i	0.227058	+	0.227058i
$210$		0			0
$211$	−3.81684	−	5.71230i	−0.262762	−	0.393251i	0.676505	−	0.736438i	$-0.263494\pi$
$211$	−3.81684	−	5.71230i	−0.262762	−	0.393251i	−0.939267	+	0.343187i	$0.888494\pi$
$212$		0			0
$213$	−1.17516	−	5.90791i	−0.0805205	−	0.404804i
$214$		0			0
$215$	1.84386	−	4.45147i	0.125750	−	0.303588i
$216$		0			0
$217$	10.3871	+	25.0767i	0.705124	+	1.70232i
$218$		0			0
$219$	−2.55621	+	3.82564i	−0.172733	+	0.258512i
$220$		0			0
$221$	−3.26031	−	0.648516i	−0.219312	−	0.0436239i
$222$		0			0
$223$			3.88311i			0.260032i	0.991512	+	0.130016i	$0.0415029\pi$
$223$			3.88311i			0.260032i	−0.991512	+	0.130016i	$0.958497\pi$
$224$		0			0
$225$			8.69037i			0.579358i
$226$		0			0
$227$	−22.5337	−	4.48224i	−1.49562	−	0.297497i	−0.621577	−	0.783353i	$-0.713508\pi$
$227$	−22.5337	−	4.48224i	−1.49562	−	0.297497i	−0.874039	+	0.485856i	$0.838508\pi$
$228$		0			0
$229$	3.41606	−	5.11250i	0.225740	−	0.337844i	−0.701260	−	0.712906i	$-0.747379\pi$
$229$	3.41606	−	5.11250i	0.225740	−	0.337844i	0.927000	+	0.375062i	$0.122379\pi$
$230$		0			0
$231$	−19.9301	−	48.1156i	−1.31131	−	3.16577i
$232$		0			0
$233$	0.733834	−	1.77163i	0.0480751	−	0.116064i	−0.898018	−	0.439960i	$-0.854993\pi$
$233$	0.733834	−	1.77163i	0.0480751	−	0.116064i	0.946093	+	0.323896i	$0.104993\pi$
$234$		0			0
$235$	1.35811	+	6.82766i	0.0885930	+	0.445387i
$236$		0			0
$237$	10.8781	+	16.2803i	0.706610	+	1.05752i
$238$		0			0
$239$	−6.09870	−	6.09870i	−0.394492	−	0.394492i	0.481793	−	0.876285i	$-0.339986\pi$
$239$	−6.09870	−	6.09870i	−0.394492	−	0.394492i	−0.876285	+	0.481793i	$0.839986\pi$
$240$		0			0
$241$	5.21549	−	5.21549i	0.335959	−	0.335959i	−0.518885	−	0.854844i	$-0.673653\pi$
$241$	5.21549	−	5.21549i	0.335959	−	0.335959i	0.854844	+	0.518885i	$0.173653\pi$
$242$		0			0
$243$	−14.7680	+	9.86763i	−0.947365	+	0.633009i
$244$		0			0
$245$	−6.56295	+	1.30545i	−0.419291	+	0.0834022i
$246$		0			0
$247$	1.77429	+	0.734933i	0.112895	+	0.0467627i
$248$		0			0
$249$	−4.21876	+	1.74747i	−0.267353	+	0.110741i
$250$		0			0
$251$	−3.73150	−	2.49331i	−0.235530	−	0.157376i	0.432204	−	0.901776i	$-0.357736\pi$
$251$	−3.73150	−	2.49331i	−0.235530	−	0.157376i	−0.667735	+	0.744399i	$0.732736\pi$
$252$		0			0
$253$	−1.27145	+	6.39201i	−0.0799354	+	0.401862i
$254$		0			0
$255$	−2.36832			−0.148310
$256$		0			0
$257$	−5.86891			−0.366092			−0.183046	−	0.983104i	$-0.558596\pi$
$257$	−5.86891			−0.366092			−0.183046	+	0.983104i	$0.558596\pi$
$258$		0			0
$259$	−1.49418	+	7.51177i	−0.0928441	+	0.466759i
$260$		0			0
$261$	−2.41649	−	1.61465i	−0.149577	−	0.0999442i
$262$		0			0
$263$	−27.1667	+	11.2528i	−1.67517	+	0.693877i	−0.999078	−	0.0429417i	$-0.986327\pi$
$263$	−27.1667	+	11.2528i	−1.67517	+	0.693877i	−0.676090	+	0.736819i	$0.736327\pi$
$264$		0			0
$265$	7.55537	+	3.12954i	0.464123	+	0.192246i
$266$		0			0
$267$	6.61966	−	1.31673i	0.405117	−	0.0805827i
$268$		0			0
$269$	−9.18707	+	6.13860i	−0.560145	+	0.374277i	−0.803176	−	0.595741i	$-0.796858\pi$
$269$	−9.18707	+	6.13860i	−0.560145	+	0.374277i	0.243031	+	0.970019i	$0.421858\pi$
$270$		0			0
$271$	−17.2217	+	17.2217i	−1.04614	+	1.04614i	−0.0472600	+	0.998883i	$0.515049\pi$
$271$	−17.2217	+	17.2217i	−1.04614	+	1.04614i	−0.998883	+	0.0472600i	$0.984951\pi$
$272$		0			0
$273$	−15.2349	−	15.2349i	−0.922056	−	0.922056i
$274$		0			0
$275$	14.4263	+	21.5906i	0.869941	+	1.30196i
$276$		0			0
$277$	−5.36979	−	26.9957i	−0.322639	−	1.62202i	−0.712868	−	0.701299i	$-0.752604\pi$
$277$	−5.36979	−	26.9957i	−0.322639	−	1.62202i	0.390228	−	0.920718i	$-0.372396\pi$
$278$		0			0
$279$	−5.21255	+	12.5842i	−0.312067	+	0.753397i
$280$		0			0
$281$	−6.20216	−	14.9733i	−0.369990	−	0.893234i	−0.993751	−	0.111619i	$-0.964396\pi$
$281$	−6.20216	−	14.9733i	−0.369990	−	0.893234i	0.623762	−	0.781615i	$-0.285604\pi$
$282$		0			0
$283$	4.95606	−	7.41727i	0.294607	−	0.440911i	−0.654408	−	0.756142i	$-0.727082\pi$
$283$	4.95606	−	7.41727i	0.294607	−	0.440911i	0.949015	+	0.315231i	$0.102082\pi$
$284$		0			0
$285$	1.34195	+	0.266931i	0.0794904	+	0.0158116i
$286$		0			0
$287$		−	28.7960i		−	1.69978i
$288$		0			0
$289$		−	15.1550i		−	0.891469i
$290$		0			0
$291$	−28.7139	−	5.71155i	−1.68324	−	0.334817i
$292$		0			0
$293$	−13.5525	+	20.2828i	−0.791747	+	1.18493i	0.187500	+	0.982265i	$0.439961\pi$
$293$	−13.5525	+	20.2828i	−0.791747	+	1.18493i	−0.979247	+	0.202669i	$0.935039\pi$
$294$		0			0
$295$	1.51494	+	3.65738i	0.0882031	+	0.212941i
$296$		0			0
$297$	−5.15386	+	12.4425i	−0.299057	+	0.721988i
$298$		0			0
$299$	0.525997	+	2.64436i	0.0304192	+	0.152928i
$300$		0			0
$301$	−13.5163	−	20.2286i	−0.779069	−	1.16596i
$302$		0			0
$303$	−7.08281	−	7.08281i	−0.406897	−	0.406897i
$304$		0			0
$305$	−5.89822	+	5.89822i	−0.337731	+	0.337731i
$306$		0			0
$307$	−8.15880	+	5.45154i	−0.465647	+	0.311136i	−0.766169	−	0.642639i	$-0.777839\pi$
$307$	−8.15880	+	5.45154i	−0.465647	+	0.311136i	0.300521	+	0.953775i	$0.402839\pi$
$308$		0			0
$309$	23.4050	−	4.65554i	1.33146	−	0.264844i
$310$		0			0
$311$	28.3647	+	11.7490i	1.60842	+	0.666227i	0.992574	−	0.121643i	$-0.0388163\pi$
$311$	28.3647	+	11.7490i	1.60842	+	0.666227i	0.615841	+	0.787870i	$0.288816\pi$
$312$		0			0
$313$	−22.4586	+	9.30264i	−1.26943	+	0.525816i	−0.912792	−	0.408425i	$-0.866078\pi$
$313$	−22.4586	+	9.30264i	−1.26943	+	0.525816i	−0.356641	+	0.934242i	$0.616078\pi$
$314$		0			0
$315$	−5.07416	−	3.39044i	−0.285896	−	0.191030i
$316$		0			0
$317$	−1.29802	+	6.52557i	−0.0729039	+	0.366513i	−0.999965	−	0.00839833i	$-0.997327\pi$
$317$	−1.29802	+	6.52557i	−0.0729039	+	0.366513i	0.927061	+	0.374911i	$0.122327\pi$
$318$		0			0
$319$	−8.68396			−0.486209
$320$		0			0
$321$	−8.52703			−0.475933
$322$		0			0
$323$	0.207952	−	1.04544i	0.0115707	−	0.0581701i
$324$		0			0
$325$	8.93197	+	5.96815i	0.495457	+	0.331054i
$326$		0			0
$327$	20.3243	−	8.41860i	1.12394	−	0.465550i
$328$		0			0
$329$	32.4747	+	13.4515i	1.79039	+	0.741604i
$330$		0			0
$331$	−3.84304	+	0.764428i	−0.211233	+	0.0420168i	−0.299572	−	0.954074i	$-0.596844\pi$
$331$	−3.84304	+	0.764428i	−0.211233	+	0.0420168i	0.0883396	+	0.996090i	$0.471844\pi$
$332$		0			0
$333$	−3.19573	+	2.13532i	−0.175125	+	0.117015i
$334$		0			0
$335$	4.02686	−	4.02686i	0.220011	−	0.220011i
$336$		0			0
$337$	13.8621	+	13.8621i	0.755119	+	0.755119i	0.975430	−	0.220311i	$-0.0707072\pi$
$337$	13.8621	+	13.8621i	0.755119	+	0.755119i	−0.220311	+	0.975430i	$0.570707\pi$
$338$		0			0
$339$	5.72000	+	8.56058i	0.310668	+	0.464947i
$340$		0			0
$341$	7.94010	+	39.9176i	0.429980	+	2.16166i
$342$		0			0
$343$	−2.36172	+	5.70170i	−0.127521	+	0.307863i
$344$		0			0
$345$	0.735093	+	1.77467i	0.0395761	+	0.0955451i
$346$		0			0
$347$	13.7444	−	20.5699i	0.737836	−	1.10425i	−0.252773	−	0.967526i	$-0.581343\pi$
$347$	13.7444	−	20.5699i	0.737836	−	1.10425i	0.990609	−	0.136724i	$-0.0436574\pi$
$348$		0			0
$349$	34.6278	+	6.88789i	1.85358	+	0.368700i	0.990628	−	0.136584i	$-0.0436124\pi$
$349$	34.6278	+	6.88789i	1.85358	+	0.368700i	0.862953	+	0.505284i	$0.168612\pi$
$350$		0			0
$351$			5.57155i			0.297388i
$352$		0			0
$353$			16.3511i			0.870283i	0.900362	+	0.435141i	$0.143302\pi$
$353$			16.3511i			0.870283i	−0.900362	+	0.435141i	$0.856698\pi$
$354$		0			0
$355$	−2.06853	−	0.411455i	−0.109786	−	0.0218378i
$356$		0			0
$357$	−6.64372	+	9.94303i	−0.351623	+	0.526241i
$358$		0			0
$359$	−0.837827	−	2.02269i	−0.0442188	−	0.106754i	0.900227	−	0.435421i	$-0.143401\pi$
$359$	−0.837827	−	2.02269i	−0.0442188	−	0.106754i	−0.944446	+	0.328667i	$0.893401\pi$
$360$		0			0
$361$	7.03532	−	16.9848i	0.370280	−	0.893935i
$362$		0			0
$363$	−10.4460	−	52.5158i	−0.548275	−	2.75636i
$364$		0			0
$365$	0.895000	+	1.33946i	0.0468464	+	0.0701106i
$366$		0			0
$367$	20.9060	+	20.9060i	1.09129	+	1.09129i	0.995392	+	0.0958935i	$0.0305708\pi$
$367$	20.9060	+	20.9060i	1.09129	+	1.09129i	0.0958935	+	0.995392i	$0.469429\pi$
$368$		0			0
$369$	10.2182	−	10.2182i	0.531936	−	0.531936i
$370$		0			0
$371$	34.3336	−	22.9410i	1.78251	−	1.19104i
$372$		0			0
$373$	−23.8329	+	4.74066i	−1.23402	+	0.245462i	−0.768659	−	0.639659i	$-0.779076\pi$
$373$	−23.8329	+	4.74066i	−1.23402	+	0.245462i	−0.465362	+	0.885121i	$0.654076\pi$
$374$		0			0
$375$	15.1251	+	6.26501i	0.781055	+	0.323524i
$376$		0			0
$377$	−3.31907	+	1.37481i	−0.170941	+	0.0708061i
$378$		0			0
$379$	20.7596	+	13.8712i	1.06635	+	0.712513i	0.959485	−	0.281760i	$-0.0909182\pi$
$379$	20.7596	+	13.8712i	1.06635	+	0.712513i	0.106867	+	0.994273i	$0.465918\pi$
$380$		0			0
$381$	2.86296	−	14.3931i	0.146674	−	0.737381i
$382$		0			0
$383$	−24.5463			−1.25426			−0.627128	−	0.778916i	$-0.715770\pi$
$383$	−24.5463			−1.25426			−0.627128	+	0.778916i	$0.715770\pi$
$384$		0			0
$385$	−18.2346			−0.929323
$386$		0			0
$387$	2.38183	−	11.9743i	0.121075	−	0.608687i
$388$		0			0
$389$	−19.0280	−	12.7141i	−0.964758	−	0.644630i	−0.0298624	−	0.999554i	$-0.509507\pi$
$389$	−19.0280	−	12.7141i	−0.964758	−	0.644630i	−0.934895	+	0.354924i	$0.884507\pi$
$390$		0			0
$391$	1.38255	−	0.572672i	0.0699187	−	0.0289613i
$392$		0			0
$393$	10.0230	+	4.15166i	0.505593	+	0.209423i
$394$		0			0
$395$	6.72381	−	1.33745i	0.338312	−	0.0672944i
$396$		0			0
$397$	−20.2490	+	13.5300i	−1.01627	+	0.679050i	−0.947886	−	0.318609i	$-0.896784\pi$
$397$	−20.2490	+	13.5300i	−1.01627	+	0.679050i	−0.0683838	+	0.997659i	$0.521784\pi$
$398$		0			0
$399$	4.88518	−	4.88518i	0.244565	−	0.244565i
$400$		0			0
$401$	13.4688	+	13.4688i	0.672599	+	0.672599i	0.958314	−	0.285716i	$-0.0922312\pi$
$401$	13.4688	+	13.4688i	0.672599	+	0.672599i	−0.285716	+	0.958314i	$0.592231\pi$
$402$		0			0
$403$	9.35433	+	13.9997i	0.465972	+	0.697377i
$404$		0			0
$405$	1.67974	+	8.44462i	0.0834669	+	0.419616i
$406$		0			0
$407$	−4.39483	+	10.6101i	−0.217844	+	0.525922i
$408$		0			0
$409$	−3.05166	−	7.36736i	−0.150895	−	0.364293i	0.830299	−	0.557319i	$-0.188170\pi$
$409$	−3.05166	−	7.36736i	−0.150895	−	0.364293i	−0.981194	+	0.193026i	$0.938170\pi$
$410$		0			0
$411$	−26.1123	+	39.0798i	−1.28803	+	1.92767i
$412$		0			0
$413$	19.6048	+	3.89963i	0.964688	+	0.191888i
$414$		0			0
$415$			1.59881i			0.0784824i
$416$		0			0
$417$		−	42.8195i		−	2.09688i
$418$		0			0
$419$	12.5395	+	2.49426i	0.612593	+	0.121852i	0.491629	−	0.870805i	$-0.336402\pi$
$419$	12.5395	+	2.49426i	0.612593	+	0.121852i	0.120964	+	0.992657i	$0.461402\pi$
$420$		0			0
$421$	10.8903	−	16.2984i	0.530759	−	0.794337i	−0.465099	−	0.885259i	$-0.653981\pi$
$421$	10.8903	−	16.2984i	0.530759	−	0.794337i	0.995858	+	0.0909215i	$0.0289812\pi$
$422$		0			0
$423$	6.75033	+	16.2967i	0.328212	+	0.792375i
$424$		0			0
$425$	2.28170	−	5.50852i	0.110679	−	0.267203i
$426$		0			0
$427$	8.21683	+	41.3088i	0.397640	+	1.99907i
$428$		0			0
$429$	−17.9485	−	26.8618i	−0.866560	−	1.29690i
$430$		0			0
$431$	18.4810	+	18.4810i	0.890199	+	0.890199i	0.994541	−	0.104343i	$-0.0332739\pi$
$431$	18.4810	+	18.4810i	0.890199	+	0.890199i	−0.104343	+	0.994541i	$0.533274\pi$
$432$		0			0
$433$	6.00332	−	6.00332i	0.288501	−	0.288501i	−0.547986	−	0.836487i	$-0.684605\pi$
$433$	6.00332	−	6.00332i	0.288501	−	0.288501i	0.836487	+	0.547986i	$0.184605\pi$
$434$		0			0
$435$	−2.12815	+	1.42199i	−0.102037	+	0.0681791i
$436$		0			0
$437$	−0.847937	+	0.168665i	−0.0405623	+	0.00806835i
$438$		0			0
$439$	−19.8680	−	8.22958i	−0.948246	−	0.392777i	−0.145675	−	0.989333i	$-0.546535\pi$
$439$	−19.8680	−	8.22958i	−0.948246	−	0.392777i	−0.802571	+	0.596556i	$0.796535\pi$
$440$		0			0
$441$	−15.6649	+	6.48862i	−0.745948	+	0.308982i
$442$		0			0
$443$	−15.5336	−	10.3792i	−0.738023	−	0.493131i	0.128848	−	0.991664i	$-0.458872\pi$
$443$	−15.5336	−	10.3792i	−0.738023	−	0.493131i	−0.866871	+	0.498533i	$0.833872\pi$
$444$		0			0
$445$	0.461025	−	2.31773i	0.0218547	−	0.109871i
$446$		0			0
$447$	−2.10215			−0.0994282
$448$		0			0
$449$	32.6778			1.54216			0.771081	−	0.636737i	$-0.219716\pi$
$449$	32.6778			1.54216			0.771081	+	0.636737i	$0.219716\pi$
$450$		0			0
$451$	8.42370	−	42.3488i	0.396657	−	1.99413i
$452$		0			0
$453$	−20.1881	−	13.4893i	−0.948522	−	0.633782i
$454$		0			0
$455$	−6.96941	+	2.88682i	−0.326731	+	0.135336i
$456$		0			0
$457$	−23.3834	−	9.68573i	−1.09383	−	0.453079i	−0.238489	−	0.971145i	$-0.576652\pi$
$457$	−23.3834	−	9.68573i	−1.09383	−	0.453079i	−0.855341	+	0.518066i	$0.826652\pi$
$458$		0			0
$459$	3.03298	−	0.603297i	0.141567	−	0.0281595i
$460$		0			0
$461$	−2.39596	+	1.60093i	−0.111591	+	0.0745627i	−0.610113	−	0.792314i	$-0.708876\pi$
$461$	−2.39596	+	1.60093i	−0.111591	+	0.0745627i	0.498522	+	0.866877i	$0.333876\pi$
$462$		0			0
$463$	24.5897	−	24.5897i	1.14278	−	1.14278i	0.154840	−	0.987940i	$-0.450514\pi$
$463$	24.5897	−	24.5897i	1.14278	−	1.14278i	0.987940	−	0.154840i	$-0.0494863\pi$
$464$		0			0
$465$	8.48230	+	8.48230i	0.393357	+	0.393357i
$466$		0			0
$467$	7.08500	+	10.6035i	0.327855	+	0.490670i	0.958379	−	0.285500i	$-0.0921598\pi$
$467$	7.08500	+	10.6035i	0.327855	+	0.490670i	−0.630524	+	0.776170i	$0.717160\pi$
$468$		0			0
$469$	−5.60983	−	28.2025i	−0.259038	−	1.30227i
$470$		0			0
$471$	−1.88748	+	4.55679i	−0.0869707	+	0.209966i
$472$		0			0
$473$	−13.9603	−	33.7031i	−0.641895	−	1.54967i
$474$		0			0
$475$	−1.91374	+	2.86411i	−0.0878082	+	0.131414i
$476$		0			0
$477$	20.3237	+	4.04263i	0.930556	+	0.185099i
$478$		0			0
$479$		−	8.39981i		−	0.383797i	−0.981415	−	0.191899i	$-0.938536\pi$
$479$		−	8.39981i		−	0.383797i	0.981415	−	0.191899i	$-0.0614644\pi$
$480$		0			0
$481$			4.75101i			0.216628i
$482$		0			0
$483$	9.51281	+	1.89222i	0.432848	+	0.0860988i
$484$		0			0
$485$	−5.69487	+	8.52297i	−0.258591	+	0.387008i
$486$		0			0
$487$	−6.40268	−	15.4574i	−0.290133	−	0.700443i	0.709859	−	0.704343i	$-0.248758\pi$
$487$	−6.40268	−	15.4574i	−0.290133	−	0.700443i	−0.999992	+	0.00390038i	$0.998758\pi$
$488$		0			0
$489$	8.87928	−	21.4365i	0.401535	−	0.969391i
$490$		0			0
$491$	−1.85105	−	9.30587i	−0.0835368	−	0.419968i	−0.999811	−	0.0194174i	$-0.993819\pi$
$491$	−1.85105	−	9.30587i	−0.0835368	−	0.419968i	0.916275	−	0.400551i	$-0.131181\pi$
$492$		0			0
$493$	1.10779	+	1.65793i	0.0498926	+	0.0746695i
$494$		0			0
$495$	−6.47049	−	6.47049i	−0.290827	−	0.290827i
$496$		0			0
$497$	−7.53017	+	7.53017i	−0.337774	+	0.337774i
$498$		0			0
$499$	−12.4453	+	8.31569i	−0.557129	+	0.372261i	−0.802027	−	0.597287i	$-0.796245\pi$
$499$	−12.4453	+	8.31569i	−0.557129	+	0.372261i	0.244899	+	0.969549i	$0.421245\pi$
$500$		0			0
$501$	32.4591	−	6.45653i	1.45017	−	0.288456i
$502$		0			0
$503$	7.01440	+	2.90546i	0.312757	+	0.129548i	0.533540	−	0.845775i	$-0.320861\pi$
$503$	7.01440	+	2.90546i	0.312757	+	0.129548i	−0.220783	+	0.975323i	$0.570861\pi$
$504$		0			0
$505$	−3.24013	+	1.34211i	−0.144184	+	0.0597230i
$506$		0			0
$507$	13.0083	+	8.69190i	0.577721	+	0.386021i
$508$		0			0
$509$	6.73996	−	33.8841i	0.298743	−	1.50188i	−0.481521	−	0.876435i	$-0.659915\pi$
$509$	6.73996	−	33.8841i	0.298743	−	1.50188i	0.780264	−	0.625450i	$-0.215085\pi$
$510$		0			0
$511$	8.13423			0.359837
$512$		0			0
$513$	−1.78656			−0.0788787
$514$		0			0
$515$	1.63003	−	8.19473i	0.0718279	−	0.361103i
$516$		0			0
$517$	43.8239	+	29.2822i	1.92737	+	1.28783i
$518$		0			0
$519$	−10.4510	+	4.32894i	−0.458748	+	0.190020i
$520$		0			0
$521$	−35.4201	−	14.6715i	−1.55178	−	0.642770i	−0.568146	−	0.822928i	$-0.692339\pi$
$521$	−35.4201	−	14.6715i	−1.55178	−	0.642770i	−0.983638	+	0.180158i	$0.942339\pi$
$522$		0			0
$523$	3.91974	−	0.779685i	0.171398	−	0.0340933i	−0.108645	−	0.994081i	$-0.534651\pi$
$523$	3.91974	−	0.779685i	0.171398	−	0.0340933i	0.280043	+	0.959987i	$0.409651\pi$
$524$		0			0
$525$	32.1318	−	21.4698i	1.40235	−	0.937018i
$526$		0			0
$527$	6.60811	−	6.60811i	0.287854	−	0.287854i
$528$		0			0
$529$	15.4052	+	15.4052i	0.669792	+	0.669792i
$530$		0			0
$531$	5.57291	+	8.34045i	0.241844	+	0.361945i
$532$		0			0
$533$	−3.48487	−	17.5196i	−0.150946	−	0.758859i
$534$		0			0
$535$	−1.14252	+	2.75829i	−0.0493955	+	0.119251i
$536$		0			0
$537$	2.60621	+	6.29195i	0.112466	+	0.271518i
$538$		0			0
$539$	−28.1469	+	42.1248i	−1.21237	+	1.81445i
$540$		0			0
$541$	−37.1103	−	7.38169i	−1.59550	−	0.317364i	−0.684256	−	0.729242i	$-0.739873\pi$
$541$	−37.1103	−	7.38169i	−1.59550	−	0.317364i	−0.911239	+	0.411878i	$0.864873\pi$
$542$		0			0
$543$		−	14.8216i		−	0.636056i
$544$		0			0
$545$		−	7.70242i		−	0.329935i
$546$		0			0
$547$	−6.05489	−	1.20439i	−0.258888	−	0.0514961i	0.0639395	−	0.997954i	$-0.479634\pi$
$547$	−6.05489	−	1.20439i	−0.258888	−	0.0514961i	−0.322828	+	0.946458i	$0.604634\pi$
$548$		0			0
$549$	−11.7426	+	17.5740i	−0.501160	+	0.750039i
$550$		0			0
$551$	−0.440842	−	1.06429i	−0.0187805	−	0.0453402i
$552$		0			0
$553$	13.2469	−	31.9808i	0.563315	−	1.35996i
$554$		0			0
$555$	0.660355	+	3.31983i	0.0280305	+	0.140919i
$556$		0			0
$557$	−10.4706	−	15.6704i	−0.443653	−	0.663974i	0.540490	−	0.841351i	$-0.318239\pi$
$557$	−10.4706	−	15.6704i	−0.443653	−	0.663974i	−0.984143	+	0.177377i	$0.943239\pi$
$558$		0			0
$559$	−10.6714	−	10.6714i	−0.451354	−	0.451354i
$560$		0			0
$561$	−12.6792	+	12.6792i	−0.535316	+	0.535316i
$562$		0			0
$563$	31.7318	−	21.2025i	1.33733	−	0.893578i	0.338458	−	0.940981i	$-0.390095\pi$
$563$	31.7318	−	21.2025i	1.33733	−	0.893578i	0.998876	+	0.0474033i	$0.0150946\pi$
$564$		0			0
$565$	3.53555	−	0.703266i	0.148742	−	0.0295866i
$566$		0			0
$567$	40.1656	+	16.6371i	1.68680	+	0.698694i
$568$		0			0
$569$	5.70005	−	2.36104i	0.238958	−	0.0989798i	−0.259991	−	0.965611i	$-0.583719\pi$
$569$	5.70005	−	2.36104i	0.238958	−	0.0989798i	0.498949	+	0.866631i	$0.333719\pi$
$570$		0			0
$571$	−25.4415	−	16.9994i	−1.06469	−	0.711405i	−0.105574	−	0.994411i	$-0.533668\pi$
$571$	−25.4415	−	16.9994i	−1.06469	−	0.711405i	−0.959118	+	0.283007i	$0.908668\pi$
$572$		0			0
$573$	−0.688527	+	3.46146i	−0.0287636	+	0.144605i
$574$		0			0
$575$	−4.83596			−0.201673
$576$		0			0
$577$	13.1957			0.549345			0.274673	−	0.961538i	$-0.411431\pi$
$577$	13.1957			0.549345			0.274673	+	0.961538i	$0.411431\pi$
$578$		0			0
$579$	−7.13682	+	35.8792i	−0.296596	+	1.49109i
$580$		0			0
$581$	6.71236	+	4.48506i	0.278476	+	0.186071i
$582$		0			0
$583$	57.2035	−	23.6945i	2.36913	−	0.981324i
$584$		0			0
$585$	−3.49745	−	1.44869i	−0.144602	−	0.0598959i
$586$		0			0
$587$	−28.1626	+	5.60188i	−1.16239	+	0.231215i	−0.738344	−	0.674424i	$-0.764392\pi$
$587$	−28.1626	+	5.60188i	−1.16239	+	0.231215i	−0.424050	+	0.905639i	$0.639392\pi$
$588$		0			0
$589$	−4.48913	+	2.99954i	−0.184971	+	0.123594i
$590$		0			0
$591$	4.25908	−	4.25908i	0.175195	−	0.175195i
$592$		0			0
$593$	8.50593	+	8.50593i	0.349297	+	0.349297i	0.859848	−	0.510551i	$-0.170559\pi$
$593$	8.50593	+	8.50593i	0.349297	+	0.349297i	−0.510551	+	0.859848i	$0.670559\pi$
$594$		0			0
$595$	2.32615	+	3.48133i	0.0953630	+	0.142721i
$596$		0			0
$597$	−5.73358	−	28.8246i	−0.234660	−	1.17971i
$598$		0			0
$599$	−17.7398	+	42.8278i	−0.724831	+	1.74990i	−0.0657345	+	0.997837i	$0.520939\pi$
$599$	−17.7398	+	42.8278i	−0.724831	+	1.74990i	−0.659096	+	0.752059i	$0.729061\pi$
$600$		0			0
$601$	9.36011	+	22.5973i	0.381807	+	0.921763i	0.991617	+	0.129215i	$0.0412459\pi$
$601$	9.36011	+	22.5973i	0.381807	+	0.921763i	−0.609810	+	0.792548i	$0.708754\pi$
$602$		0			0
$603$	8.01693	−	11.9982i	0.326475	−	0.488604i
$604$		0			0
$605$	−18.3872	−	3.65745i	−0.747548	−	0.148697i
$606$		0			0
$607$		−	19.9552i		−	0.809956i	−0.914326	−	0.404978i	$-0.867279\pi$
$607$		−	19.9552i		−	0.809956i	0.914326	−	0.404978i	$-0.132721\pi$
$608$		0			0
$609$			12.9238i			0.523698i
$610$		0			0
$611$	21.3856	+	4.25387i	0.865170	+	0.172093i
$612$		0			0
$613$	−15.7066	+	23.5066i	−0.634384	+	0.949423i	0.365443	+	0.930834i	$0.380917\pi$
$613$	−15.7066	+	23.5066i	−0.634384	+	0.949423i	−0.999827	+	0.0185890i	$0.994083\pi$
$614$		0			0
$615$	−4.87019	−	11.7577i	−0.196385	−	0.474115i
$616$		0			0
$617$	−7.93425	+	19.1550i	−0.319421	+	0.771150i	0.679864	+	0.733338i	$0.262039\pi$
$617$	−7.93425	+	19.1550i	−0.319421	+	0.771150i	−0.999285	+	0.0378118i	$0.987961\pi$
$618$		0			0
$619$	1.06040	+	5.33101i	0.0426212	+	0.214271i	0.996227	−	0.0867872i	$-0.0276600\pi$
$619$	1.06040	+	5.33101i	0.0426212	+	0.214271i	−0.953606	+	0.301059i	$0.902660\pi$
$620$		0			0
$621$	−1.39347	−	2.08547i	−0.0559179	−	0.0836871i
$622$		0			0
$623$	−8.43735	−	8.43735i	−0.338035	−	0.338035i
$624$		0			0
$625$	−11.4662	+	11.4662i	−0.458647	+	0.458647i
$626$		0			0
$627$	8.61344	−	5.75532i	0.343988	−	0.229845i
$628$		0			0
$629$	2.58630	−	0.514447i	0.103123	−	0.0205124i
$630$		0			0
$631$	−35.9213	−	14.8791i	−1.43000	−	0.592327i	−0.472652	−	0.881249i	$-0.656703\pi$
$631$	−35.9213	−	14.8791i	−1.43000	−	0.592327i	−0.957353	+	0.288922i	$0.906703\pi$
$632$		0			0
$633$	−14.1640	+	5.86692i	−0.562968	+	0.233189i
$634$		0			0
$635$	−4.27222	−	2.85460i	−0.169538	−	0.113282i
$636$		0			0
$637$	−4.08894	+	20.5565i	−0.162010	+	0.814479i
$638$		0			0
$639$	−5.34410			−0.211409
$640$		0			0
$641$	2.72233			0.107526			0.0537629	−	0.998554i	$-0.482878\pi$
$641$	2.72233			0.107526			0.0537629	+	0.998554i	$0.482878\pi$
$642$		0			0
$643$	−0.135549	+	0.681448i	−0.00534551	+	0.0268737i	−0.983366	−	0.181635i	$-0.941861\pi$
$643$	−0.135549	+	0.681448i	−0.00534551	+	0.0268737i	0.978020	+	0.208509i	$0.0668610\pi$
$644$		0			0
$645$	−8.94005	−	5.97355i	−0.352014	−	0.235208i
$646$		0			0
$647$	−29.4862	+	12.2136i	−1.15922	+	0.480165i	−0.877616	−	0.479365i	$-0.840867\pi$
$647$	−29.4862	+	12.2136i	−1.15922	+	0.480165i	−0.281606	+	0.959530i	$0.590867\pi$
$648$		0			0
$649$	27.6909	+	11.4700i	1.08696	+	0.450235i
$650$		0			0
$651$	59.4067	−	11.8167i	2.32833	−	0.463134i
$652$		0			0
$653$	35.6443	−	23.8167i	1.39487	−	0.932021i	0.394956	−	0.918700i	$-0.370760\pi$
$653$	35.6443	−	23.8167i	1.39487	−	0.932021i	0.999911	−	0.0133207i	$-0.00424022\pi$
$654$		0			0
$655$	2.68592	−	2.68592i	0.104948	−	0.104948i
$656$		0			0
$657$	2.88640	+	2.88640i	0.112609	+	0.112609i
$658$		0			0
$659$	−19.0570	−	28.5207i	−0.742354	−	1.11101i	−0.989849	−	0.142122i	$-0.954608\pi$
$659$	−19.0570	−	28.5207i	−0.742354	−	1.11101i	0.247496	−	0.968889i	$-0.420392\pi$
$660$		0			0
$661$	2.62496	+	13.1966i	0.102099	+	0.513287i	0.997661	+	0.0683508i	$0.0217737\pi$
$661$	2.62496	+	13.1966i	0.102099	+	0.513287i	−0.895562	+	0.444936i	$0.853226\pi$
$662$		0			0
$663$	−2.83877	+	6.85340i	−0.110249	+	0.266164i
$664$		0			0
$665$	−0.925683	−	2.23480i	−0.0358965	−	0.0866617i
$666$		0			0
$667$	0.898508	−	1.34471i	0.0347904	−	0.0520675i
$668$		0			0
$669$	8.49882	+	1.69052i	0.328584	+	0.0653593i
$670$		0			0
$671$			63.1543i			2.43805i
$672$		0			0
$673$			23.6665i			0.912275i	0.889909	+	0.456137i	$0.150767\pi$
$673$			23.6665i			0.912275i	−0.889909	+	0.456137i	$0.849233\pi$
$674$		0			0
$675$	−9.80133	−	1.94961i	−0.377254	−	0.0750404i
$676$		0			0
$677$	−14.9427	+	22.3633i	−0.574294	+	0.859491i	−0.998948	−	0.0458647i	$-0.985396\pi$
$677$	−14.9427	+	22.3633i	−0.574294	+	0.859491i	0.424654	+	0.905356i	$0.360396\pi$
$678$		0			0
$679$	19.8069	+	47.8181i	0.760120	+	1.83509i
$680$		0			0
$681$	−19.6203	+	47.3675i	−0.751850	+	1.81513i
$682$		0			0
$683$	−4.84474	−	24.3562i	−0.185379	−	0.931963i	−0.955708	−	0.294316i	$-0.904908\pi$
$683$	−4.84474	−	24.3562i	−0.185379	−	0.931963i	0.770329	−	0.637647i	$-0.220092\pi$
$684$		0			0
$685$	9.14265	+	13.6829i	0.349323	+	0.522798i
$686$		0			0
$687$	−9.70237	−	9.70237i	−0.370168	−	0.370168i
$688$		0			0
$689$	18.1124	−	18.1124i	0.690027	−	0.690027i
$690$		0			0
$691$	−11.5361	+	7.70819i	−0.438855	+	0.293233i	−0.755302	−	0.655377i	$-0.772510\pi$
$691$	−11.5361	+	7.70819i	−0.438855	+	0.293233i	0.316448	+	0.948610i	$0.397510\pi$
$692$		0			0
$693$	−45.3167	+	9.01406i	−1.72144	+	0.342416i
$694$		0			0
$695$	−13.8511	−	5.73730i	−0.525401	−	0.217628i
$696$		0			0
$697$	−9.15978	+	3.79410i	−0.346951	+	0.143712i
$698$		0			0
$699$	−3.55804	−	2.37740i	−0.134577	−	0.0899217i
$700$		0			0
$701$	−7.20549	+	36.2244i	−0.272148	+	1.36818i	0.566750	+	0.823890i	$0.308200\pi$
$701$	−7.20549	+	36.2244i	−0.272148	+	1.36818i	−0.838898	+	0.544289i	$0.816800\pi$
$702$		0			0
$703$	−1.52345			−0.0574581
$704$		0			0
$705$	15.5347			0.585072
$706$		0			0
$707$	−3.45474	+	17.3682i	−0.129929	+	0.653197i
$708$		0			0
$709$	20.0441	+	13.3930i	0.752770	+	0.502985i	0.871774	−	0.489909i	$-0.162970\pi$
$709$	20.0441	+	13.3930i	0.752770	+	0.502985i	−0.119003	+	0.992894i	$0.537970\pi$
$710$		0			0
$711$	16.0489	−	6.64766i	0.601880	−	0.249307i
$712$		0			0
$713$	−7.00278	−	2.90065i	−0.262256	−	0.108630i
$714$		0			0
$715$	−11.0940	+	2.20674i	−0.414893	+	0.0825273i
$716$		0			0
$717$	−16.0031	+	10.6929i	−0.597647	+	0.399335i
$718$		0			0
$719$	5.08606	−	5.08606i	0.189678	−	0.189678i	−0.605879	−	0.795557i	$-0.707178\pi$
$719$	5.08606	−	5.08606i	0.189678	−	0.189678i	0.795557	+	0.605879i	$0.207178\pi$
$720$		0			0
$721$	−29.8317	−	29.8317i	−1.11099	−	1.11099i
$722$		0			0
$723$	−9.14439	−	13.6855i	−0.340084	−	0.508971i
$724$		0			0
$725$	−1.25711	−	6.31990i	−0.0466878	−	0.234715i
$726$		0			0
$727$	16.1339	−	38.9506i	0.598372	−	1.44460i	−0.276867	−	0.960908i	$-0.589296\pi$
$727$	16.1339	−	38.9506i	0.598372	−	1.44460i	0.875240	−	0.483690i	$-0.160704\pi$
$728$		0			0
$729$	2.51641	+	6.07515i	0.0932003	+	0.225006i
$730$		0			0
$731$	−4.65368	+	6.96472i	−0.172122	+	0.257599i
$732$		0			0
$733$	32.2035	+	6.40567i	1.18946	+	0.236599i	0.749862	−	0.661595i	$-0.230120\pi$
$733$	32.2035	+	6.40567i	1.18946	+	0.236599i	0.439601	+	0.898193i	$0.355120\pi$
$734$		0			0
$735$			14.9324i			0.550791i
$736$		0			0
$737$		−	43.1170i		−	1.58824i
$738$		0			0
$739$	1.11174	+	0.221139i	0.0408961	+	0.00813474i	0.215496	−	0.976505i	$-0.430863\pi$
$739$	1.11174	+	0.221139i	0.0408961	+	0.00813474i	−0.174600	+	0.984639i	$0.555863\pi$
$740$		0			0
$741$	2.38096	−	3.56336i	0.0874669	−	0.130903i
$742$		0			0
$743$	−11.1248	−	26.8577i	−0.408130	−	0.985313i	−0.985629	−	0.168922i	$-0.945972\pi$
$743$	−11.1248	−	26.8577i	−0.408130	−	0.985313i	0.577500	−	0.816391i	$-0.304028\pi$
$744$		0			0
$745$	−0.281663	+	0.679995i	−0.0103193	+	0.0249131i
$746$		0			0
$747$	0.790350	+	3.97336i	0.0289174	+	0.145378i
$748$		0			0
$749$	8.37522	+	12.5344i	0.306024	+	0.457997i
$750$		0			0
$751$	−19.2670	−	19.2670i	−0.703061	−	0.703061i	0.262005	−	0.965066i	$-0.415616\pi$
$751$	−19.2670	−	19.2670i	−0.703061	−	0.703061i	−0.965066	+	0.262005i	$0.915616\pi$
$752$		0			0
$753$	−7.08155	+	7.08155i	−0.258066	+	0.258066i
$754$		0			0
$755$	−7.06843	+	4.72298i	−0.257247	+	0.171887i
$756$		0			0
$757$	−3.81457	+	0.758766i	−0.138643	+	0.0275778i	−0.263924	−	0.964544i	$-0.585017\pi$
$757$	−3.81457	+	0.758766i	−0.138643	+	0.0275778i	0.125281	+	0.992121i	$0.460017\pi$
$758$		0			0
$759$	13.4365	+	5.56556i	0.487713	+	0.202017i
$760$		0			0
$761$	14.1327	−	5.85394i	0.512309	−	0.212205i	−0.111526	−	0.993762i	$-0.535574\pi$
$761$	14.1327	−	5.85394i	0.512309	−	0.212205i	0.623835	+	0.781556i	$0.285574\pi$
$762$		0			0
$763$	−32.3375	−	21.6072i	−1.17069	−	0.782233i
$764$		0			0
$765$	−0.409911	+	2.06076i	−0.0148204	+	0.0745071i
$766$		0			0
$767$	12.3995			0.447722
$768$		0			0
$769$	−47.4209			−1.71004			−0.855020	−	0.518595i	$-0.826455\pi$
$769$	−47.4209			−1.71004			−0.855020	+	0.518595i	$0.826455\pi$
$770$		0			0
$771$	−2.55505	+	12.8451i	−0.0920178	+	0.462604i
$772$		0			0
$773$	−18.9615	−	12.6697i	−0.681998	−	0.455697i	0.165699	−	0.986176i	$-0.447012\pi$
$773$	−18.9615	−	12.6697i	−0.681998	−	0.455697i	−0.847698	+	0.530480i	$0.822012\pi$
$774$		0			0
$775$	−27.9013	+	11.5571i	−1.00224	+	0.415143i
$776$		0			0
$777$	15.7903	+	6.54054i	0.566473	+	0.234641i
$778$		0			0
$779$	5.61781	−	1.11745i	0.201279	−	0.0400369i
$780$		0			0
$781$	−13.2770	+	8.87142i	−0.475089	+	0.317444i
$782$		0			0
$783$	2.36318	−	2.36318i	0.0844532	−	0.0844532i
$784$		0			0
$785$	1.22111	+	1.22111i	0.0435833	+	0.0435833i
$786$		0			0
$787$	−8.45960	−	12.6607i	−0.301552	−	0.451305i	0.649488	−	0.760372i	$-0.274983\pi$
$787$	−8.45960	−	12.6607i	−0.301552	−	0.451305i	−0.951040	+	0.309067i	$0.899983\pi$
$788$		0			0
$789$	12.8015	+	64.3577i	0.455747	+	2.29119i
$790$		0			0
$791$	6.96556	−	16.8163i	0.247667	−	0.597920i
$792$		0			0
$793$	9.99830	+	24.1380i	0.355050	+	0.857167i
$794$		0			0
$795$	10.1388	−	15.1737i	0.359585	−	0.538157i
$796$		0			0
$797$	−1.21865	−	0.242404i	−0.0431668	−	0.00858640i	0.173460	−	0.984841i	$-0.444505\pi$
$797$	−1.21865	−	0.242404i	−0.0431668	−	0.00858640i	−0.216626	+	0.976255i	$0.569505\pi$
$798$		0			0
$799$		−	12.1023i		−	0.428148i
$800$		0			0
$801$		−	5.98792i		−	0.211573i
$802$		0			0
$803$	11.9626	+	2.37950i	0.422150	+	0.0839709i
$804$		0			0
$805$	1.88669	−	2.82363i	0.0664971	−	0.0995200i
$806$		0			0
$807$	9.43574	+	22.7799i	0.332154	+	0.801890i
$808$		0			0
$809$	11.5600	−	27.9083i	0.406428	−	0.981203i	−0.579642	−	0.814871i	$-0.696808\pi$
$809$	11.5600	−	27.9083i	0.406428	−	0.981203i	0.986070	−	0.166332i	$-0.0531923\pi$
$810$		0			0
$811$	−1.27743	−	6.42210i	−0.0448568	−	0.225510i	0.951854	−	0.306552i	$-0.0991753\pi$
$811$	−1.27743	−	6.42210i	−0.0448568	−	0.225510i	−0.996711	+	0.0810417i	$0.974175\pi$
$812$		0			0
$813$	30.1950	+	45.1900i	1.05899	+	1.58488i
$814$		0			0
$815$	−5.74447	−	5.74447i	−0.201220	−	0.201220i
$816$		0			0
$817$	3.42189	−	3.42189i	0.119717	−	0.119717i
$818$		0			0
$819$	−15.8933	+	10.6196i	−0.555357	+	0.371078i
$820$		0			0
$821$	−0.732994	+	0.145802i	−0.0255817	+	0.00508851i	−0.207865	−	0.978158i	$-0.566651\pi$
$821$	−0.732994	+	0.145802i	−0.0255817	+	0.00508851i	0.182283	+	0.983246i	$0.441651\pi$
$822$		0			0
$823$	−40.6921	−	16.8552i	−1.41844	−	0.587535i	−0.463969	−	0.885852i	$-0.653575\pi$
$823$	−40.6921	−	16.8552i	−1.41844	−	0.587535i	−0.954467	+	0.298316i	$0.903575\pi$
$824$		0			0
$825$	53.5351	−	22.1750i	1.86385	−	0.772033i
$826$		0			0
$827$	17.5797	+	11.7464i	0.611308	+	0.408463i	0.822324	−	0.569020i	$-0.192677\pi$
$827$	17.5797	+	11.7464i	0.611308	+	0.408463i	−0.211016	+	0.977483i	$0.567677\pi$
$828$		0			0
$829$	8.12158	−	40.8299i	0.282074	−	1.41808i	−0.536607	−	0.843833i	$-0.680294\pi$
$829$	8.12158	−	40.8299i	0.282074	−	1.41808i	0.818681	−	0.574249i	$-0.194706\pi$
$830$		0			0
$831$	−61.4224			−2.13072
$832$		0			0
$833$	11.6331			0.403062
$834$		0			0
$835$	2.26061	−	11.3649i	0.0782316	−	0.393297i
$836$		0			0
$837$	−13.0236	−	8.70208i	−0.450161	−	0.300788i
$838$		0			0
$839$	33.4505	−	13.8556i	1.15484	−	0.478350i	0.278686	−	0.960382i	$-0.410101\pi$
$839$	33.4505	−	13.8556i	1.15484	−	0.478350i	0.876154	+	0.482032i	$0.160101\pi$
$840$		0			0
$841$	−24.8016	−	10.2732i	−0.855227	−	0.354247i
$842$		0			0
$843$	−35.4718	+	7.05577i	−1.22171	+	0.243014i
$844$		0			0
$845$	4.55459	−	3.04328i	0.156683	−	0.104692i
$846$		0			0
$847$	−66.9361	+	66.9361i	−2.29995	+	2.29995i
$848$		0			0
$849$	−14.0763	−	14.0763i	−0.483097	−	0.483097i
$850$		0			0
$851$	−1.18825	−	1.77834i	−0.0407326	−	0.0609606i
$852$		0			0
$853$	2.29019	+	11.5136i	0.0784145	+	0.394217i	0.999982	+	0.00599829i	$0.00190933\pi$
$853$	2.29019	+	11.5136i	0.0784145	+	0.394217i	−0.921567	+	0.388218i	$0.873091\pi$
$854$		0			0
$855$	0.464534	−	1.12148i	0.0158867	−	0.0383540i
$856$		0			0
$857$	−3.96261	−	9.56660i	−0.135360	−	0.326789i	0.841636	−	0.540045i	$-0.181593\pi$
$857$	−3.96261	−	9.56660i	−0.135360	−	0.326789i	−0.976996	+	0.213257i	$0.931593\pi$
$858$		0			0
$859$	22.7757	−	34.0863i	0.777098	−	1.16301i	−0.205753	−	0.978604i	$-0.565964\pi$
$859$	22.7757	−	34.0863i	0.777098	−	1.16301i	0.982850	−	0.184405i	$-0.0590357\pi$
$860$		0			0
$861$	−63.0249	−	12.5364i	−2.14788	−	0.427241i
$862$		0			0
$863$		−	22.4117i		−	0.762902i	−0.924389	−	0.381451i	$-0.875424\pi$
$863$		−	22.4117i		−	0.762902i	0.924389	−	0.381451i	$-0.124576\pi$
$864$		0			0
$865$			3.96067i			0.134667i
$866$		0			0
$867$	−33.1692	−	6.59776i	−1.12648	−	0.224072i
$868$		0			0
$869$	28.8368	−	43.1574i	0.978223	−	1.46401i
$870$		0			0
$871$	−6.82609	−	16.4796i	−0.231293	−	0.558391i
$872$		0			0
$873$	−9.93967	+	23.9965i	−0.336407	+	0.812158i
$874$		0			0
$875$	−5.64647	−	28.3867i	−0.190886	−	0.959646i
$876$		0			0
$877$	−22.8368	−	34.1777i	−0.771145	−	1.15410i	−0.984200	−	0.177060i	$-0.943341\pi$
$877$	−22.8368	−	34.1777i	−0.771145	−	1.15410i	0.213055	−	0.977040i	$-0.431659\pi$
$878$		0			0
$879$	38.4921	+	38.4921i	1.29831	+	1.29831i
$880$		0			0
$881$	−19.2835	+	19.2835i	−0.649677	+	0.649677i	−0.952915	−	0.303238i	$-0.901932\pi$
$881$	−19.2835	+	19.2835i	−0.649677	+	0.649677i	0.303238	+	0.952915i	$0.401932\pi$
$882$		0			0
$883$	−43.0348	+	28.7549i	−1.44824	+	0.967681i	−0.451068	+	0.892490i	$0.648957\pi$
$883$	−43.0348	+	28.7549i	−1.44824	+	0.967681i	−0.997169	+	0.0751915i	$0.976043\pi$
$884$		0			0
$885$	8.66433	−	1.72344i	0.291248	−	0.0579329i
$886$		0			0
$887$	−2.36214	−	0.978431i	−0.0793129	−	0.0328525i	0.342674	−	0.939454i	$-0.388667\pi$
$887$	−2.36214	−	0.978431i	−0.0793129	−	0.0328525i	−0.421987	+	0.906602i	$0.638667\pi$
$888$		0			0
$889$	−23.9693	+	9.92840i	−0.803904	+	0.332988i
$890$		0			0
$891$	54.2025	+	36.2170i	1.81585	+	1.21331i
$892$		0			0
$893$	−1.36404	+	6.85748i	−0.0456458	+	0.229477i
$894$		0			0
$895$	2.38450			0.0797049
$896$		0			0
$897$	6.01663			0.200889
$898$		0			0
$899$	1.97036	−	9.90565i	0.0657151	−	0.330372i
$900$		0			0
$901$	−11.8210	−	7.89857i	−0.393816	−	0.263140i
$902$		0			0
$903$	−50.1581	+	20.7762i	−1.66916	+	0.691388i
$904$		0			0
$905$	−4.79444	−	1.98592i	−0.159372	−	0.0660142i
$906$		0			0
$907$	−21.3347	+	4.24373i	−0.708405	+	0.140911i	−0.536127	−	0.844138i	$-0.680113\pi$
$907$	−21.3347	+	4.24373i	−0.708405	+	0.140911i	−0.172279	+	0.985048i	$0.555113\pi$
$908$		0			0
$909$	−7.38893	+	4.93712i	−0.245075	+	0.163754i
$910$		0			0
$911$	1.38797	−	1.38797i	0.0459856	−	0.0459856i	−0.683740	−	0.729726i	$-0.739648\pi$
$911$	1.38797	−	1.38797i	0.0459856	−	0.0459856i	0.729726	+	0.683740i	$0.239648\pi$
$912$		0			0
$913$	8.55950	+	8.55950i	0.283278	+	0.283278i
$914$		0			0
$915$	10.3414	+	15.4771i	0.341877	+	0.511655i
$916$		0			0
$917$	−3.74177	−	18.8111i	−0.123564	−	0.621198i
$918$		0			0
$919$	1.63873	−	3.95625i	0.0540568	−	0.130505i	−0.894544	−	0.446980i	$-0.852499\pi$
$919$	1.63873	−	3.95625i	0.0540568	−	0.130505i	0.948601	+	0.316475i	$0.102499\pi$
$920$		0			0
$921$	8.37964	+	20.2302i	0.276119	+	0.666609i
$922$		0			0
$923$	−3.67009	+	5.49268i	−0.120802	+	0.180794i
$924$		0			0
$925$	−8.35786	−	1.66248i	−0.274805	−	0.0546621i
$926$		0			0
$927$		−	21.1713i		−	0.695358i
$928$		0			0
$929$			53.4969i			1.75518i	0.479415	+	0.877589i	$0.340849\pi$
$929$			53.4969i			1.75518i	−0.479415	+	0.877589i	$0.659151\pi$
$930$		0			0
$931$	−6.59161	−	1.31115i	−0.216031	−	0.0429713i
$932$		0			0
$933$	38.0634	−	56.9659i	1.24614	−	1.86498i
$934$		0			0
$935$	2.40255	+	5.80028i	0.0785719	+	0.189689i
$936$		0			0
$937$	9.69070	−	23.3954i	0.316582	−	0.764295i	−0.682849	−	0.730559i	$-0.739259\pi$
$937$	9.69070	−	23.3954i	0.316582	−	0.764295i	0.999431	−	0.0337361i	$-0.0107406\pi$
$938$		0			0
$939$	10.5830	+	53.2042i	0.345362	+	1.73625i
$940$		0			0
$941$	14.9326	+	22.3482i	0.486788	+	0.728529i	0.990825	−	0.135153i	$-0.0431525\pi$
$941$	14.9326	+	22.3482i	0.486788	+	0.728529i	−0.504037	+	0.863682i	$0.668153\pi$
$942$		0			0
$943$	5.68614	+	5.68614i	0.185166	+	0.185166i
$944$		0			0
$945$	4.96222	−	4.96222i	0.161421	−	0.161421i
$946$		0			0
$947$	−15.6970	+	10.4884i	−0.510083	+	0.340827i	−0.783830	−	0.620975i	$-0.786737\pi$
$947$	−15.6970	+	10.4884i	−0.510083	+	0.340827i	0.273747	+	0.961802i	$0.411737\pi$
$948$		0			0
$949$	4.94890	−	0.984397i	0.160648	−	0.0319549i
$950$		0			0
$951$	13.7172	+	5.68185i	0.444811	+	0.184247i
$952$		0			0
$953$	31.0836	−	12.8753i	1.00690	−	0.417070i	0.182575	−	0.983192i	$-0.441557\pi$
$953$	31.0836	−	12.8753i	1.00690	−	0.417070i	0.824322	+	0.566122i	$0.191557\pi$
$954$		0			0
$955$	1.02745	+	0.686517i	0.0332473	+	0.0222152i
$956$		0			0
$957$	−3.78059	+	19.0063i	−0.122209	+	0.614387i
$958$		0			0
$959$	83.0932			2.68322
$960$		0			0
$961$	−16.3349			−0.526932
$962$		0			0
$963$	−1.47587	+	7.41970i	−0.0475592	+	0.239096i
$964$		0			0
$965$	10.6498	+	7.11598i	0.342830	+	0.229072i
$966$		0			0
$967$	−39.0826	+	16.1886i	−1.25681	+	0.520589i	−0.908930	−	0.416949i	$-0.863099\pi$
$967$	−39.0826	+	16.1886i	−1.25681	+	0.520589i	−0.347883	+	0.937538i	$0.613099\pi$
$968$		0			0
$969$	−2.19760	−	0.910274i	−0.0705970	−	0.0292422i
$970$		0			0
$971$	−15.9123	+	3.16514i	−0.510649	+	0.101574i	−0.443688	−	0.896181i	$-0.646330\pi$
$971$	−15.9123	+	3.16514i	−0.510649	+	0.101574i	−0.0669606	+	0.997756i	$0.521330\pi$
$972$		0			0
$973$	−62.9429	+	42.0571i	−2.01786	+	1.34829i
$974$		0			0
$975$	16.9509	−	16.9509i	0.542862	−	0.542862i
$976$		0			0
$977$	−14.4085	−	14.4085i	−0.460970	−	0.460970i	0.438004	−	0.898973i	$-0.355686\pi$
$977$	−14.4085	−	14.4085i	−0.460970	−	0.460970i	−0.898973	+	0.438004i	$0.855686\pi$
$978$		0			0
$979$	−9.94018	−	14.8765i	−0.317690	−	0.475456i
$980$		0			0
$981$	−3.80759	−	19.1421i	−0.121567	−	0.611159i
$982$		0			0
$983$	14.2810	−	34.4773i	0.455492	−	1.09966i	−0.514711	−	0.857364i	$-0.672101\pi$
$983$	14.2810	−	34.4773i	0.455492	−	1.09966i	0.970203	−	0.242292i	$-0.0778991\pi$
$984$		0			0
$985$	−0.807045	−	1.94838i	−0.0257146	−	0.0620805i
$986$		0			0
$987$	43.5788	−	65.2202i	1.38713	−	2.07598i
$988$		0			0
$989$	6.66337	+	1.32543i	0.211883	+	0.0421461i
$990$		0			0
$991$			5.17247i			0.164309i	0.996620	+	0.0821544i	$0.0261801\pi$
$991$			5.17247i			0.164309i	−0.996620	+	0.0821544i	$0.973820\pi$
$992$		0			0
$993$			8.74393i			0.277480i
$994$		0			0
$995$	−10.0923	−	2.00749i	−0.319948	−	0.0636416i
$996$		0			0
$997$	11.3818	−	17.0341i	0.360466	−	0.539476i	−0.606267	−	0.795261i	$-0.707334\pi$
$997$	11.3818	−	17.0341i	0.360466	−	0.539476i	0.966734	+	0.255785i	$0.0823338\pi$
$998$		0			0
$999$	−1.69136	−	4.08331i	−0.0535123	−	0.129190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.417.6		56
4.3	odd	2		512.2.i.a.417.2		56
8.3	odd	2		256.2.i.a.81.6		56
8.5	even	2		64.2.i.a.61.3	yes	56
24.5	odd	2		576.2.bd.a.253.5		56
64.11	odd	16		256.2.i.a.177.6		56
64.21	even	16	inner	512.2.i.b.97.6		56
64.43	odd	16		512.2.i.a.97.2		56
64.53	even	16		64.2.i.a.21.3	✓	56
192.53	odd	16		576.2.bd.a.469.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.3	✓	56	64.53	even	16
64.2.i.a.61.3	yes	56	8.5	even	2
256.2.i.a.81.6		56	8.3	odd	2
256.2.i.a.177.6		56	64.11	odd	16
512.2.i.a.97.2		56	64.43	odd	16
512.2.i.a.417.2		56	4.3	odd	2
512.2.i.b.97.6		56	64.21	even	16	inner
512.2.i.b.417.6		56	1.1	even	1	trivial
576.2.bd.a.253.5		56	24.5	odd	2
576.2.bd.a.469.5		56	192.53	odd	16

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.435353 - 2.18867i) q^{3} +(-0.649649 - 0.434082i) q^{5} +(-3.64486 + 1.50975i) q^{7} +(-1.82909 - 0.757635i) q^{9} +(-5.80194 + 1.15408i) q^{11} +(-2.03484 + 1.35963i) q^{13} +(-1.23289 + 1.23289i) q^{15} +(0.960477 + 0.960477i) q^{17} +(-0.435978 - 0.652487i) q^{19} +(1.71754 + 8.63465i) q^{21} +(0.421603 - 1.01784i) q^{23} +(-1.67980 - 4.05540i) q^{25} +(1.26483 - 1.89295i) q^{27} +(1.43977 + 0.286388i) q^{29} -6.88004i q^{31} +13.2009i q^{33} +(3.02323 + 0.601358i) q^{35} +(1.07856 - 1.61417i) q^{37} +(2.08991 + 5.04550i) q^{39} +(-2.79324 + 6.74347i) q^{41} +(1.20307 + 6.04824i) q^{43} +(0.859393 + 1.28617i) q^{45} +(-6.30014 - 6.30014i) q^{47} +(6.05588 - 6.05588i) q^{49} +(2.52031 - 1.68402i) q^{51} +(-10.2655 + 2.04194i) q^{53} +(4.27019 + 1.76877i) q^{55} +(-1.61788 + 0.670148i) q^{57} +(-4.21278 - 2.81489i) q^{59} +(2.08276 - 10.4707i) q^{61} +7.81061 q^{63} +1.91212 q^{65} +(-1.42195 + 7.14864i) q^{67} +(-2.04417 - 1.36587i) q^{69} +(2.49385 - 1.03299i) q^{71} +(-1.90488 - 0.789026i) q^{73} +(-9.60722 + 1.91099i) q^{75} +(19.4049 - 12.9659i) q^{77} +(-6.20432 + 6.20432i) q^{79} +(-7.79217 - 7.79217i) q^{81} +(-1.13685 - 1.70141i) q^{83} +(-0.207047 - 1.04090i) q^{85} +(1.25361 - 3.02649i) q^{87} +(1.15743 + 2.79429i) q^{89} +(5.36398 - 8.02776i) q^{91} +(-15.0581 - 2.99524i) q^{93} +0.613137i q^{95} -13.1193i q^{97} +(11.4867 + 2.28484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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