LMFDB - Embedded newform 912.2.cc.d.641.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(257,912)] 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("912.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,0,0,0,0,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			641.1
Root			$-0.396613 + 1.68603i$ of defining polynomial
Character	$\chi$	$=$	912.641
Dual form			912.2.cc.d.737.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26184 + 1.18649i) q^{3} +(-1.86241 + 2.21954i) q^{5} +(-0.562083 - 0.973556i) q^{7} +(0.184473 - 2.99432i) q^{9} +(2.70920 + 1.56416i) q^{11} +(-5.18404 + 0.914087i) q^{13} +(-0.283400 - 5.01044i) q^{15} +(0.880484 + 2.41911i) q^{17} +(-4.13617 + 1.37554i) q^{19} +(1.86437 + 0.561563i) q^{21} +(-4.31710 - 5.14492i) q^{23} +(-0.589524 - 3.34336i) q^{25} +(3.31997 + 3.99723i) q^{27} +(1.09635 + 0.399039i) q^{29} +(3.90801 - 2.25629i) q^{31} +(-5.27443 + 1.24073i) q^{33} +(3.20767 + 0.565599i) q^{35} -12.0703i q^{37} +(5.45687 - 7.30426i) q^{39} +(1.06170 - 6.02118i) q^{41} +(-2.21295 - 1.85688i) q^{43} +(6.30245 + 5.98611i) q^{45} +(0.377793 - 1.03798i) q^{47} +(2.86813 - 4.96774i) q^{49} +(-3.98128 - 2.00784i) q^{51} +(5.66806 - 4.75606i) q^{53} +(-8.51736 + 3.10007i) q^{55} +(3.58710 - 6.64324i) q^{57} +(6.41833 - 2.33608i) q^{59} +(-5.58223 + 4.68405i) q^{61} +(-3.01883 + 1.50346i) q^{63} +(7.62598 - 13.2086i) q^{65} +(2.42040 - 6.64999i) q^{67} +(11.5519 + 1.36985i) q^{69} +(3.31294 + 2.77989i) q^{71} +(-1.30735 + 7.41438i) q^{73} +(4.71075 + 3.51931i) q^{75} -3.51674i q^{77} +(-4.30920 - 0.759829i) q^{79} +(-8.93194 - 1.10474i) q^{81} +(-12.5112 + 7.22333i) q^{83} +(-7.00913 - 2.55111i) q^{85} +(-1.85688 + 0.797290i) q^{87} +(2.38095 + 13.5030i) q^{89} +(3.80378 + 4.53316i) q^{91} +(-2.25420 + 7.48389i) q^{93} +(4.65018 - 11.7422i) q^{95} +(-1.47287 - 4.04669i) q^{97} +(5.18337 - 7.82368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53}+ \cdots + 30 q^{99}+O(q^{100}) $ 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.26184	+	1.18649i	−0.728523	+	0.685022i
$3$	−1.26184	+	1.18649i	−0.728523	+	0.685022i
$4$		0			0
$5$	−1.86241	+	2.21954i	−0.832897	+	0.992608i	0.167081	+	0.985943i	$0.446566\pi$
$5$	−1.86241	+	2.21954i	−0.832897	+	0.992608i	−0.999978	+	0.00666440i	$0.997879\pi$
$6$		0			0
$7$	−0.562083	−	0.973556i	−0.212447	−	0.367969i	0.740033	−	0.672571i	$-0.234810\pi$
$7$	−0.562083	−	0.973556i	−0.212447	−	0.367969i	−0.952480	+	0.304602i	$0.901477\pi$
$8$		0			0
$9$	0.184473	−	2.99432i	0.0614909	−	0.998108i
$10$		0			0
$11$	2.70920	+	1.56416i	0.816855	+	0.471611i	0.849331	−	0.527861i	$-0.177006\pi$
$11$	2.70920	+	1.56416i	0.816855	+	0.471611i	−0.0324759	+	0.999473i	$0.510339\pi$
$12$		0			0
$13$	−5.18404	+	0.914087i	−1.43780	+	0.253522i	−0.837579	−	0.546316i	$-0.816030\pi$
$13$	−5.18404	+	0.914087i	−1.43780	+	0.253522i	−0.600216	+	0.799838i	$0.704919\pi$
$14$		0			0
$15$	−0.283400	−	5.01044i	−0.0731734	−	1.29369i
$16$		0			0
$17$	0.880484	+	2.41911i	0.213549	+	0.586720i	0.999502	−	0.0315662i	$-0.0100495\pi$
$17$	0.880484	+	2.41911i	0.213549	+	0.586720i	−0.785953	+	0.618286i	$0.787827\pi$
$18$		0			0
$19$	−4.13617	+	1.37554i	−0.948902	+	0.315571i
$19$	−4.13617	+	1.37554i	−0.948902	+	0.315571i
$20$		0			0
$21$	1.86437	+	0.561563i	0.406840	+	0.122543i
$22$		0			0
$23$	−4.31710	−	5.14492i	−0.900178	−	1.07279i	−0.996993	−	0.0774881i	$-0.975310\pi$
$23$	−4.31710	−	5.14492i	−0.900178	−	1.07279i	0.0968152	−	0.995302i	$-0.469134\pi$
$24$		0			0
$25$	−0.589524	−	3.34336i	−0.117905	−	0.668671i
$26$		0			0
$27$	3.31997	+	3.99723i	0.638928	+	0.769267i
$28$		0			0
$29$	1.09635	+	0.399039i	0.203587	+	0.0740998i	0.441801	−	0.897113i	$-0.354340\pi$
$29$	1.09635	+	0.399039i	0.203587	+	0.0740998i	−0.238214	+	0.971213i	$0.576562\pi$
$30$		0			0
$31$	3.90801	−	2.25629i	0.701899	−	0.405241i	−0.106155	−	0.994350i	$-0.533854\pi$
$31$	3.90801	−	2.25629i	0.701899	−	0.405241i	0.808054	+	0.589108i	$0.200521\pi$
$32$		0			0
$33$	−5.27443	+	1.24073i	−0.918161	+	0.215984i
$34$		0			0
$35$	3.20767	+	0.565599i	0.542196	+	0.0956038i
$36$		0			0
$37$		−	12.0703i		−	1.98435i	−0.124859	−	0.992174i	$-0.539848\pi$
$37$		−	12.0703i		−	1.98435i	0.124859	−	0.992174i	$-0.460152\pi$
$38$		0			0
$39$	5.45687	−	7.30426i	0.873799	−	1.16962i
$40$		0			0
$41$	1.06170	−	6.02118i	0.165809	−	0.940350i	−0.782417	−	0.622755i	$-0.786014\pi$
$41$	1.06170	−	6.02118i	0.165809	−	0.940350i	0.948226	−	0.317595i	$-0.102875\pi$
$42$		0			0
$43$	−2.21295	−	1.85688i	−0.337471	−	0.283172i	0.458265	−	0.888816i	$-0.348471\pi$
$43$	−2.21295	−	1.85688i	−0.337471	−	0.283172i	−0.795736	+	0.605644i	$0.792916\pi$
$44$		0			0
$45$	6.30245	+	5.98611i	0.939514	+	0.892357i
$46$		0			0
$47$	0.377793	−	1.03798i	0.0551068	−	0.151405i	−0.909085	−	0.416611i	$-0.863218\pi$
$47$	0.377793	−	1.03798i	0.0551068	−	0.151405i	0.964192	+	0.265206i	$0.0854400\pi$
$48$		0			0
$49$	2.86813	−	4.96774i	0.409732	−	0.709677i
$50$		0			0
$51$	−3.98128	−	2.00784i	−0.557491	−	0.281153i
$52$		0			0
$53$	5.66806	−	4.75606i	0.778568	−	0.653296i	−0.164320	−	0.986407i	$-0.552543\pi$
$53$	5.66806	−	4.75606i	0.778568	−	0.653296i	0.942887	+	0.333111i	$0.108099\pi$
$54$		0			0
$55$	−8.51736	+	3.10007i	−1.14848	+	0.418013i
$56$		0			0
$57$	3.58710	−	6.64324i	0.475123	−	0.879919i
$58$		0			0
$59$	6.41833	−	2.33608i	0.835596	−	0.304132i	0.111442	−	0.993771i	$-0.464453\pi$
$59$	6.41833	−	2.33608i	0.835596	−	0.304132i	0.724153	+	0.689639i	$0.242231\pi$
$60$		0			0
$61$	−5.58223	+	4.68405i	−0.714732	+	0.599731i	−0.925922	−	0.377714i	$-0.876710\pi$
$61$	−5.58223	+	4.68405i	−0.714732	+	0.599731i	0.211191	+	0.977445i	$0.432266\pi$
$62$		0			0
$63$	−3.01883	+	1.50346i	−0.380337	+	0.189418i
$64$		0			0
$65$	7.62598	−	13.2086i	0.945887	−	1.63832i
$66$		0			0
$67$	2.42040	−	6.64999i	0.295699	−	0.812425i	−0.699508	−	0.714625i	$-0.746597\pi$
$67$	2.42040	−	6.64999i	0.295699	−	0.812425i	0.995206	−	0.0977999i	$-0.0311805\pi$
$68$		0			0
$69$	11.5519	+	1.36985i	1.39068	+	0.164911i
$70$		0			0
$71$	3.31294	+	2.77989i	0.393174	+	0.329912i	0.817848	−	0.575434i	$-0.195167\pi$
$71$	3.31294	+	2.77989i	0.393174	+	0.329912i	−0.424674	+	0.905346i	$0.639611\pi$
$72$		0			0
$73$	−1.30735	+	7.41438i	−0.153014	+	0.867787i	0.807565	+	0.589779i	$0.200785\pi$
$73$	−1.30735	+	7.41438i	−0.153014	+	0.867787i	−0.960579	+	0.278008i	$0.910326\pi$
$74$		0			0
$75$	4.71075	+	3.51931i	0.543950	+	0.406375i
$76$		0			0
$77$		−	3.51674i		−	0.400770i
$78$		0			0
$79$	−4.30920	−	0.759829i	−0.484823	−	0.0854874i	−0.0741064	−	0.997250i	$-0.523610\pi$
$79$	−4.30920	−	0.759829i	−0.484823	−	0.0854874i	−0.410717	+	0.911763i	$0.634722\pi$
$80$		0			0
$81$	−8.93194	−	1.10474i	−0.992438	−	0.122749i
$82$		0			0
$83$	−12.5112	+	7.22333i	−1.37328	+	0.792863i	−0.991340	−	0.131324i	$-0.958077\pi$
$83$	−12.5112	+	7.22333i	−1.37328	+	0.792863i	−0.381940	+	0.924187i	$0.624744\pi$
$84$		0			0
$85$	−7.00913	−	2.55111i	−0.760247	−	0.276707i
$86$		0			0
$87$	−1.85688	+	0.797290i	−0.199078	+	0.0854784i
$88$		0			0
$89$	2.38095	+	13.5030i	0.252380	+	1.43132i	0.802710	+	0.596369i	$0.203391\pi$
$89$	2.38095	+	13.5030i	0.252380	+	1.43132i	−0.550331	+	0.834947i	$0.685498\pi$
$90$		0			0
$91$	3.80378	+	4.53316i	0.398744	+	0.475205i
$92$		0			0
$93$	−2.25420	+	7.48389i	−0.233750	+	0.776043i
$94$		0			0
$95$	4.65018	−	11.7422i	0.477098	−	1.20473i
$96$		0			0
$97$	−1.47287	−	4.04669i	−0.149548	−	0.410879i	0.842187	−	0.539186i	$-0.181268\pi$
$97$	−1.47287	−	4.04669i	−0.149548	−	0.410879i	−0.991735	+	0.128307i	$0.959046\pi$
$98$		0			0
$99$	5.18337	−	7.82368i	0.520948	−	0.786309i
$100$		0			0
$101$	−5.82418	+	1.02696i	−0.579528	+	0.102186i	−0.455725	−	0.890121i	$-0.650620\pi$
$101$	−5.82418	+	1.02696i	−0.579528	+	0.102186i	−0.123802	+	0.992307i	$0.539509\pi$
$102$		0			0
$103$	−17.2614	−	9.96588i	−1.70082	−	0.981967i	−0.944934	−	0.327261i	$-0.893874\pi$
$103$	−17.2614	−	9.96588i	−1.70082	−	0.981967i	−0.755884	−	0.654706i	$-0.772792\pi$
$104$		0			0
$105$	−4.71865	+	3.09218i	−0.460493	+	0.301766i
$106$		0			0
$107$	2.39183	+	4.14277i	0.231227	+	0.400496i	0.958169	−	0.286202i	$-0.0923927\pi$
$107$	2.39183	+	4.14277i	0.231227	+	0.400496i	−0.726943	+	0.686698i	$0.759059\pi$
$108$		0			0
$109$	−5.52889	+	6.58908i	−0.529572	+	0.631119i	−0.962816	−	0.270157i	$-0.912924\pi$
$109$	−5.52889	+	6.58908i	−0.529572	+	0.631119i	0.433244	+	0.901276i	$0.357369\pi$
$110$		0			0
$111$	14.3213	+	15.2308i	1.35932	+	1.44564i
$112$		0			0
$113$	−16.1668			−1.52085			−0.760424	−	0.649427i	$-0.775009\pi$
$113$	−16.1668			−1.52085			−0.760424	+	0.649427i	$0.775009\pi$
$114$		0			0
$115$	19.4596			1.81462
$116$		0			0
$117$	1.78076	+	15.6913i	0.164631	+	1.45066i
$118$		0			0
$119$	1.86023	−	2.21694i	0.170527	−	0.203226i
$120$		0			0
$121$	−0.606822	−	1.05105i	−0.0551656	−	0.0955496i
$122$		0			0
$123$	5.80439	+	8.85745i	0.523364	+	0.798649i
$124$		0			0
$125$	−4.02747	−	2.32526i	−0.360228	−	0.207978i
$126$		0			0
$127$	−7.59392	+	1.33901i	−0.673852	+	0.118818i	−0.500095	−	0.865970i	$-0.666702\pi$
$127$	−7.59392	+	1.33901i	−0.673852	+	0.118818i	−0.173756	+	0.984789i	$0.555591\pi$
$128$		0			0
$129$	4.99556	−	0.282558i	0.439834	−	0.0248778i
$130$		0			0
$131$	−0.757267	−	2.08057i	−0.0661627	−	0.181781i	0.902205	−	0.431307i	$-0.141947\pi$
$131$	−0.757267	−	2.08057i	−0.0661627	−	0.181781i	−0.968368	+	0.249526i	$0.919725\pi$
$132$		0			0
$133$	3.66404	+	3.25362i	0.317712	+	0.282125i
$134$		0			0
$135$	−15.0551	−	0.0756985i	−1.29574	−	0.00651509i
$136$		0			0
$137$	−0.138747	−	0.165352i	−0.0118540	−	0.0141270i	0.760085	−	0.649824i	$-0.225157\pi$
$137$	−0.138747	−	0.165352i	−0.0118540	−	0.0141270i	−0.771939	+	0.635697i	$0.780713\pi$
$138$		0			0
$139$	−3.25695	−	18.4711i	−0.276251	−	1.56670i	−0.734961	−	0.678110i	$-0.762799\pi$
$139$	−3.25695	−	18.4711i	−0.276251	−	1.56670i	0.458710	−	0.888586i	$-0.348312\pi$
$140$		0			0
$141$	0.754839	+	1.75801i	0.0635689	+	0.148051i
$142$		0			0
$143$	−15.4744	−	5.63222i	−1.29403	−	0.470990i
$144$		0			0
$145$	−2.92754	+	1.69022i	−0.243119	+	0.140365i
$146$		0			0
$147$	2.27507	+	9.67150i	0.187645	+	0.797692i
$148$		0			0
$149$	−4.18590	−	0.738088i	−0.342923	−	0.0604665i	−0.000465272	−	1.00000i	$-0.500148\pi$
$149$	−4.18590	−	0.738088i	−0.342923	−	0.0604665i	−0.342457	+	0.939533i	$0.611259\pi$
$150$		0			0
$151$			8.94139i			0.727640i	0.931469	+	0.363820i	$0.118528\pi$
$151$			8.94139i			0.727640i	−0.931469	+	0.363820i	$0.881472\pi$
$152$		0			0
$153$	7.40602	−	2.19019i	0.598741	−	0.177067i
$154$		0			0
$155$	−2.27041	+	12.8761i	−0.182363	+	1.03423i
$156$		0			0
$157$	1.55311	+	1.30322i	0.123952	+	0.104008i	0.702656	−	0.711529i	$-0.251997\pi$
$157$	1.55311	+	1.30322i	0.123952	+	0.104008i	−0.578705	+	0.815537i	$0.696442\pi$
$158$		0			0
$159$	−1.50914	+	12.7265i	−0.119682	+	1.00928i
$160$		0			0
$161$	−2.58230	+	7.09481i	−0.203514	+	0.559149i
$162$		0			0
$163$	4.66573	−	8.08128i	0.365448	−	0.632975i	−0.623400	−	0.781903i	$-0.714249\pi$
$163$	4.66573	−	8.08128i	0.365448	−	0.632975i	0.988848	+	0.148929i	$0.0475825\pi$
$164$		0			0
$165$	7.06933	−	14.0176i	0.550346	−	1.09127i
$166$		0			0
$167$	9.70512	−	8.14356i	0.751005	−	0.630168i	−0.184764	−	0.982783i	$-0.559152\pi$
$167$	9.70512	−	8.14356i	0.751005	−	0.630168i	0.935768	+	0.352615i	$0.114708\pi$
$168$		0			0
$169$	13.8228	−	5.03107i	1.06329	−	0.387006i
$170$		0			0
$171$	3.35581	+	12.6388i	0.256626	+	0.966511i
$172$		0			0
$173$	8.86150	−	3.22532i	0.673727	−	0.245217i	0.0175755	−	0.999846i	$-0.494405\pi$
$173$	8.86150	−	3.22532i	0.673727	−	0.245217i	0.656152	+	0.754629i	$0.272183\pi$
$174$		0			0
$175$	−2.92358	+	2.45318i	−0.221002	+	0.185443i
$176$		0			0
$177$	−5.32716	+	10.5631i	−0.400414	+	0.793968i
$178$		0			0
$179$	−3.74454	+	6.48573i	−0.279880	+	0.484766i	−0.971355	−	0.237634i	$-0.923628\pi$
$179$	−3.74454	+	6.48573i	−0.279880	+	0.484766i	0.691475	+	0.722401i	$0.256961\pi$
$180$		0			0
$181$	5.46326	−	15.0102i	0.406081	−	1.11570i	−0.553151	−	0.833081i	$-0.686575\pi$
$181$	5.46326	−	15.0102i	0.406081	−	1.11570i	0.959232	−	0.282618i	$-0.0912030\pi$
$182$		0			0
$183$	1.48629	−	12.5338i	0.109870	−	0.926524i
$184$		0			0
$185$	26.7905	+	22.4799i	1.96968	+	1.65276i
$186$		0			0
$187$	−1.39846	+	7.93107i	−0.102266	+	0.579977i
$188$		0			0
$189$	2.02543	−	5.47894i	0.147328	−	0.398534i
$190$		0			0
$191$			7.61751i			0.551184i	0.961275	+	0.275592i	$0.0888738\pi$
$191$			7.61751i			0.551184i	−0.961275	+	0.275592i	$0.911126\pi$
$192$		0			0
$193$	11.8171	+	2.08368i	0.850616	+	0.149987i	0.581928	−	0.813241i	$-0.302299\pi$
$193$	11.8171	+	2.08368i	0.850616	+	0.149987i	0.268688	+	0.963227i	$0.413410\pi$
$194$		0			0
$195$	6.04913	+	25.7153i	0.433187	+	1.84151i
$196$		0			0
$197$	−15.2618	+	8.81139i	−1.08736	+	0.627786i	−0.932871	−	0.360210i	$-0.882705\pi$
$197$	−15.2618	+	8.81139i	−1.08736	+	0.627786i	−0.154485	+	0.987995i	$0.549372\pi$
$198$		0			0
$199$	2.12679	+	0.774087i	0.150764	+	0.0548736i	0.416300	−	0.909227i	$-0.363327\pi$
$199$	2.12679	+	0.774087i	0.150764	+	0.0548736i	−0.265536	+	0.964101i	$0.585549\pi$
$200$		0			0
$201$	4.83601	+	11.2630i	0.341106	+	0.794430i
$202$		0			0
$203$	−0.227753	−	1.29165i	−0.0159851	−	0.0906562i
$204$		0			0
$205$	11.3869	+	13.5704i	0.795297	+	0.947798i
$206$		0			0
$207$	−16.2019	+	11.9777i	−1.12611	+	0.832508i
$208$		0			0
$209$	−13.3573	−	2.74299i	−0.923942	−	0.189737i
$210$		0			0
$211$	1.31716	+	3.61886i	0.0906769	+	0.249133i	0.976738	−	0.214435i	$-0.0687911\pi$
$211$	1.31716	+	3.61886i	0.0906769	+	0.249133i	−0.886061	+	0.463568i	$0.846569\pi$
$212$		0			0
$213$	−7.47872	+	0.423010i	−0.512433	+	0.0289842i
$214$		0			0
$215$	8.24284	−	1.45344i	0.562157	−	0.0991235i
$216$		0			0
$217$	−4.39325	−	2.53644i	−0.298233	−	0.172185i
$218$		0			0
$219$	−7.14743	−	10.9069i	−0.482979	−	0.737021i
$220$		0			0
$221$	−6.77574	−	11.7359i	−0.455786	−	0.789444i
$222$		0			0
$223$	3.57822	−	4.26435i	0.239615	−	0.285562i	−0.632813	−	0.774305i	$-0.718100\pi$
$223$	3.57822	−	4.26435i	0.239615	−	0.285562i	0.872428	+	0.488743i	$0.162544\pi$
$224$		0			0
$225$	−10.1198	+	1.14847i	−0.674656	+	0.0765645i
$226$		0			0
$227$	−24.7738			−1.64430			−0.822148	−	0.569274i	$-0.807224\pi$
$227$	−24.7738			−1.64430			−0.822148	+	0.569274i	$0.807224\pi$
$228$		0			0
$229$	−24.7947			−1.63848			−0.819241	−	0.573449i	$-0.805605\pi$
$229$	−24.7947			−1.63848			−0.819241	+	0.573449i	$0.805605\pi$
$230$		0			0
$231$	4.17259	+	4.43756i	0.274536	+	0.291970i
$232$		0			0
$233$	−13.8205	+	16.4706i	−0.905410	+	1.07903i	0.0911239	+	0.995840i	$0.470954\pi$
$233$	−13.8205	+	16.4706i	−0.905410	+	1.07903i	−0.996534	+	0.0831862i	$0.973490\pi$
$234$		0			0
$235$	1.60022	+	2.77167i	0.104387	+	0.180804i
$236$		0			0
$237$	6.33905	−	4.15406i	0.411766	−	0.269835i
$238$		0			0
$239$	10.5128	+	6.06955i	0.680015	+	0.392607i	0.799861	−	0.600186i	$-0.204907\pi$
$239$	10.5128	+	6.06955i	0.680015	+	0.392607i	−0.119846	+	0.992793i	$0.538240\pi$
$240$		0			0
$241$	−21.4162	+	3.77626i	−1.37954	+	0.243250i	−0.813709	−	0.581272i	$-0.802555\pi$
$241$	−21.4162	+	3.77626i	−1.37954	+	0.243250i	−0.565830	+	0.824522i	$0.691444\pi$
$242$		0			0
$243$	12.5814	−	9.20367i	0.807099	−	0.590416i
$244$		0			0
$245$	5.68445	+	15.6179i	0.363166	+	0.997791i
$246$		0			0
$247$	20.1847	−	10.9117i	1.28432	−	0.694295i
$248$		0			0
$249$	7.21666	−	23.9591i	0.457337	−	1.51835i
$250$		0			0
$251$	12.5021	+	14.8994i	0.789127	+	0.940445i	0.999307	−	0.0372181i	$-0.0118496\pi$
$251$	12.5021	+	14.8994i	0.789127	+	0.940445i	−0.210181	+	0.977663i	$0.567405\pi$
$252$		0			0
$253$	−3.64843	−	20.6913i	−0.229375	−	1.30085i
$254$		0			0
$255$	11.8713	−	5.09718i	0.743407	−	0.319198i
$256$		0			0
$257$	10.1861	+	3.70746i	0.635395	+	0.231265i	0.639578	−	0.768727i	$-0.279109\pi$
$257$	10.1861	+	3.70746i	0.635395	+	0.231265i	−0.00418306	+	0.999991i	$0.501332\pi$
$258$		0			0
$259$	−11.7511	+	6.78452i	−0.730180	+	0.421569i
$260$		0			0
$261$	1.39710	−	3.20922i	0.0864783	−	0.198646i
$262$		0			0
$263$	−30.4663	−	5.37204i	−1.87863	−	0.331254i	−0.887150	−	0.461481i	$-0.847318\pi$
$263$	−30.4663	−	5.37204i	−1.87863	−	0.331254i	−0.991484	+	0.130227i	$0.958429\pi$
$264$		0			0
$265$			21.4382i			1.31694i
$266$		0			0
$267$	−19.0256	−	14.2136i	−1.16435	−	0.869861i
$268$		0			0
$269$	−0.880210	+	4.99192i	−0.0536673	+	0.304363i	−0.999812	−	0.0193811i	$-0.993830\pi$
$269$	−0.880210	+	4.99192i	−0.0536673	+	0.304363i	0.946145	+	0.323744i	$0.104942\pi$
$270$		0			0
$271$	−4.01481	−	3.36882i	−0.243882	−	0.204641i	0.512650	−	0.858597i	$-0.328664\pi$
$271$	−4.01481	−	3.36882i	−0.243882	−	0.204641i	−0.756533	+	0.653956i	$0.773108\pi$
$272$		0			0
$273$	−10.1783	−	1.20697i	−0.616020	−	0.0730491i
$274$		0			0
$275$	3.63240	−	9.97993i	0.219042	−	0.601812i
$276$		0			0
$277$	2.15677	−	3.73563i	0.129588	−	0.224453i	−0.793929	−	0.608010i	$-0.791968\pi$
$277$	2.15677	−	3.73563i	0.129588	−	0.224453i	0.923517	+	0.383558i	$0.125301\pi$
$278$		0			0
$279$	−6.03514	−	12.1181i	−0.361314	−	0.725489i
$280$		0			0
$281$	8.43804	−	7.08036i	0.503371	−	0.422379i	−0.355418	−	0.934707i	$-0.615661\pi$
$281$	8.43804	−	7.08036i	0.503371	−	0.422379i	0.858789	+	0.512329i	$0.171217\pi$
$282$		0			0
$283$	3.71261	−	1.35128i	0.220691	−	0.0803251i	−0.229308	−	0.973354i	$-0.573646\pi$
$283$	3.71261	−	1.35128i	0.220691	−	0.0803251i	0.450000	+	0.893029i	$0.351424\pi$
$284$		0			0
$285$	8.06427	+	20.3342i	0.477686	+	1.20449i
$286$		0			0
$287$	−6.45871	+	2.35078i	−0.381246	+	0.138762i
$288$		0			0
$289$	7.94592	−	6.66742i	0.467407	−	0.392201i
$290$		0			0
$291$	6.65990	+	3.35871i	0.390410	+	0.196891i
$292$		0			0
$293$	10.0719	−	17.4450i	0.588406	−	1.01915i	−0.406036	−	0.913857i	$-0.633089\pi$
$293$	10.0719	−	17.4450i	0.588406	−	1.01915i	0.994441	−	0.105291i	$-0.0335775\pi$
$294$		0			0
$295$	−6.76857	+	18.5965i	−0.394081	+	1.08273i
$296$		0			0
$297$	2.74216	+	16.0222i	0.159116	+	0.929705i
$298$		0			0
$299$	27.0830	+	22.7253i	1.56625	+	1.31424i
$300$		0			0
$301$	−0.563920	+	3.19815i	−0.0325038	+	0.184338i
$302$		0			0
$303$	6.13070	−	8.20620i	0.352199	−	0.471434i
$304$		0			0
$305$		−	21.1136i		−	1.20896i
$306$		0			0
$307$	6.45677	+	1.13850i	0.368508	+	0.0649778i	0.354836	−	0.934929i	$-0.384537\pi$
$307$	6.45677	+	1.13850i	0.368508	+	0.0649778i	0.0136720	+	0.999907i	$0.495648\pi$
$308$		0			0
$309$	33.6056	−	7.90520i	1.91175	−	0.449711i
$310$		0			0
$311$	1.86672	−	1.07775i	0.105852	−	0.0611137i	−0.446139	−	0.894963i	$-0.647201\pi$
$311$	1.86672	−	1.07775i	0.105852	−	0.0611137i	0.551991	+	0.833850i	$0.313868\pi$
$312$		0			0
$313$	15.9106	+	5.79098i	0.899320	+	0.327326i	0.749980	−	0.661460i	$-0.230063\pi$
$313$	15.9106	+	5.79098i	0.899320	+	0.327326i	0.149340	+	0.988786i	$0.452285\pi$
$314$		0			0
$315$	2.28532	−	9.50047i	0.128763	−	0.535291i
$316$		0			0
$317$	−0.961500	−	5.45293i	−0.0540032	−	0.306267i	0.945827	−	0.324670i	$-0.105253\pi$
$317$	−0.961500	−	5.45293i	−0.0540032	−	0.306267i	−0.999831	+	0.0184023i	$0.994142\pi$
$318$		0			0
$319$	2.34608	+	2.79595i	0.131355	+	0.156543i
$320$		0			0
$321$	−7.93346	−	2.38962i	−0.442803	−	0.133375i
$322$		0			0
$323$	−6.96942	−	8.79469i	−0.387789	−	0.489350i
$324$		0			0
$325$	6.11224	+	16.7932i	0.339046	+	0.931521i
$326$		0			0
$327$	−0.841320	−	14.8743i	−0.0465251	−	0.822553i
$328$		0			0
$329$	−1.22288	+	0.215627i	−0.0674195	+	0.0118879i
$330$		0			0
$331$	6.67525	+	3.85396i	0.366905	+	0.211833i	0.672106	−	0.740455i	$-0.265390\pi$
$331$	6.67525	+	3.85396i	0.366905	+	0.211833i	−0.305200	+	0.952288i	$0.598723\pi$
$332$		0			0
$333$	−36.1424	−	2.22664i	−1.98059	−	0.122019i
$334$		0			0
$335$	10.2521	+	17.7572i	0.560133	+	0.970179i
$336$		0			0
$337$	8.14195	−	9.70320i	0.443520	−	0.528567i	−0.497252	−	0.867606i	$-0.665657\pi$
$337$	8.14195	−	9.70320i	0.443520	−	0.528567i	0.940772	+	0.339039i	$0.110102\pi$
$338$		0			0
$339$	20.3999	−	19.1818i	1.10797	−	1.04181i
$340$		0			0
$341$	14.1168			0.764466
$342$		0			0
$343$	−14.3177			−0.773081
$344$		0			0
$345$	−24.5548	+	23.0886i	−1.32199	+	1.24305i
$346$		0			0
$347$	−2.93143	+	3.49354i	−0.157367	+	0.187543i	−0.838967	−	0.544182i	$-0.816840\pi$
$347$	−2.93143	+	3.49354i	−0.157367	+	0.187543i	0.681600	+	0.731725i	$0.261284\pi$
$348$		0			0
$349$	0.809906	+	1.40280i	0.0433533	+	0.0750901i	0.886888	−	0.461985i	$-0.152863\pi$
$349$	0.809906	+	1.40280i	0.0433533	+	0.0750901i	−0.843535	+	0.537075i	$0.819529\pi$
$350$		0			0
$351$	−20.8647	−	17.6871i	−1.11367	−	0.944066i
$352$		0			0
$353$	−5.92549	−	3.42108i	−0.315382	−	0.182086i	0.333950	−	0.942591i	$-0.391618\pi$
$353$	−5.92549	−	3.42108i	−0.315382	−	0.182086i	−0.649332	+	0.760505i	$0.724952\pi$
$354$		0			0
$355$	−12.3401	+	2.17590i	−0.654947	+	0.115485i
$356$		0			0
$357$	0.283068	+	5.00457i	0.0149815	+	0.264870i
$358$		0			0
$359$	1.39824	+	3.84165i	0.0737965	+	0.202754i	0.971106	−	0.238647i	$-0.0767038\pi$
$359$	1.39824	+	3.84165i	0.0737965	+	0.202754i	−0.897310	+	0.441401i	$0.854482\pi$
$360$		0			0
$361$	15.2158	−	11.3790i	0.800829	−	0.598893i
$362$		0			0
$363$	2.01277	+	0.606261i	0.105643	+	0.0318205i
$364$		0			0
$365$	−14.0217	−	16.7104i	−0.733927	−	0.874660i
$366$		0			0
$367$	1.71891	+	9.74845i	0.0897266	+	0.508865i	0.996236	+	0.0866798i	$0.0276257\pi$
$367$	1.71891	+	9.74845i	0.0897266	+	0.508865i	−0.906510	+	0.422185i	$0.861263\pi$
$368$		0			0
$369$	−17.8335	−	4.28980i	−0.928375	−	0.223318i
$370$		0			0
$371$	−7.81621	−	2.84487i	−0.405797	−	0.147698i
$372$		0			0
$373$	6.90673	−	3.98760i	0.357617	−	0.206470i	−0.310418	−	0.950600i	$-0.600469\pi$
$373$	6.90673	−	3.98760i	0.357617	−	0.206470i	0.668035	+	0.744130i	$0.267136\pi$
$374$		0			0
$375$	7.84092	−	1.84446i	0.404904	−	0.0952475i
$376$		0			0
$377$	−6.04829	−	1.06648i	−0.311503	−	0.0549264i
$378$		0			0
$379$			10.7490i			0.552141i	0.961137	+	0.276071i	$0.0890323\pi$
$379$			10.7490i			0.552141i	−0.961137	+	0.276071i	$0.910968\pi$
$380$		0			0
$381$	7.99358	−	10.6997i	0.409523	−	0.548165i
$382$		0			0
$383$	0.913805	−	5.18245i	0.0466933	−	0.264811i	−0.952520	−	0.304477i	$-0.901518\pi$
$383$	0.913805	−	5.18245i	0.0466933	−	0.264811i	0.999213	+	0.0396663i	$0.0126295\pi$
$384$		0			0
$385$	7.80554	+	6.54963i	0.397807	+	0.333800i
$386$		0			0
$387$	−5.96833	+	6.28373i	−0.303387	+	0.319420i
$388$		0			0
$389$	−5.43196	+	14.9242i	−0.275411	+	0.756686i	0.722457	+	0.691416i	$0.243013\pi$
$389$	−5.43196	+	14.9242i	−0.275411	+	0.756686i	−0.997868	+	0.0652695i	$0.979209\pi$
$390$		0			0
$391$	8.64499	−	14.9736i	0.437196	−	0.757245i
$392$		0			0
$393$	3.42413	+	1.72686i	0.172725	+	0.0871084i
$394$		0			0
$395$	9.71199	−	8.14933i	0.488663	−	0.410037i
$396$		0			0
$397$	−33.6599	+	12.2512i	−1.68934	+	0.614870i	−0.994542	−	0.104334i	$-0.966729\pi$
$397$	−33.6599	+	12.2512i	−1.68934	+	0.614870i	−0.694799	+	0.719204i	$0.744507\pi$
$398$		0			0
$399$	−8.48382	+	0.241809i	−0.424722	+	0.0121056i
$400$		0			0
$401$	−5.57564	+	2.02937i	−0.278434	+	0.101342i	−0.477463	−	0.878652i	$-0.658443\pi$
$401$	−5.57564	+	2.02937i	−0.278434	+	0.101342i	0.199029	+	0.979994i	$0.436221\pi$
$402$		0			0
$403$	−18.1968	+	15.2690i	−0.906449	+	0.760601i
$404$		0			0
$405$	19.0870	−	17.7673i	0.948440	−	0.882864i
$406$		0			0
$407$	18.8799	−	32.7009i	0.935841	−	1.62092i
$408$		0			0
$409$	9.06715	−	24.9118i	0.448342	−	1.23181i	−0.485536	−	0.874217i	$-0.661375\pi$
$409$	9.06715	−	24.9118i	0.448342	−	1.23181i	0.933878	−	0.357592i	$-0.116402\pi$
$410$		0			0
$411$	0.371266	+	0.0440256i	0.0183132	+	0.00217162i
$412$		0			0
$413$	−5.88194	−	4.93553i	−0.289431	−	0.242862i
$414$		0			0
$415$	7.26852	−	41.2218i	0.356798	−	2.02350i
$416$		0			0
$417$	26.0255	+	19.4432i	1.27448	+	0.952136i
$418$		0			0
$419$			8.21543i			0.401350i	0.979658	+	0.200675i	$0.0643135\pi$
$419$			8.21543i			0.401350i	−0.979658	+	0.200675i	$0.935686\pi$
$420$		0			0
$421$	−16.5911	−	2.92547i	−0.808603	−	0.142578i	−0.245961	−	0.969280i	$-0.579104\pi$
$421$	−16.5911	−	2.92547i	−0.808603	−	0.142578i	−0.562641	+	0.826701i	$0.690215\pi$
$422$		0			0
$423$	−3.03835	−	1.32271i	−0.147730	−	0.0643125i
$424$		0			0
$425$	7.56888	−	4.36989i	0.367144	−	0.211971i
$426$		0			0
$427$	7.69786	+	2.80179i	0.372526	+	0.135588i
$428$		0			0
$429$	26.2088	−	11.2533i	1.26537	−	0.543314i
$430$		0			0
$431$	−5.03223	−	28.5392i	−0.242394	−	1.37469i	−0.826467	−	0.562985i	$-0.809653\pi$
$431$	−5.03223	−	28.5392i	−0.242394	−	1.37469i	0.584073	−	0.811701i	$-0.301458\pi$
$432$		0			0
$433$	−17.6845	−	21.0756i	−0.849863	−	1.01283i	−0.999709	−	0.0241176i	$-0.992322\pi$
$433$	−17.6845	−	21.0756i	−0.849863	−	1.01283i	0.149846	−	0.988709i	$-0.452122\pi$
$434$		0			0
$435$	1.68866	−	5.60629i	0.0809649	−	0.268801i
$436$		0			0
$437$	24.9333	+	15.3419i	1.19272	+	0.733902i
$438$		0			0
$439$	5.19707	+	14.2788i	0.248042	+	0.681491i	0.999758	+	0.0220034i	$0.00700448\pi$
$439$	5.19707	+	14.2788i	0.248042	+	0.681491i	−0.751715	+	0.659488i	$0.770773\pi$
$440$		0			0
$441$	−14.3459	−	9.50451i	−0.683139	−	0.452596i
$442$		0			0
$443$	4.75117	−	0.837760i	0.225735	−	0.0398032i	−0.0596365	−	0.998220i	$-0.518994\pi$
$443$	4.75117	−	0.837760i	0.225735	−	0.0398032i	0.285371	+	0.958417i	$0.407883\pi$
$444$		0			0
$445$	−34.4047	−	19.8636i	−1.63094	−	0.941624i
$446$		0			0
$447$	6.15767	−	4.03519i	0.291248	−	0.190858i
$448$		0			0
$449$	−1.78666	−	3.09458i	−0.0843176	−	0.146042i	0.820783	−	0.571241i	$-0.193538\pi$
$449$	−1.78666	−	3.09458i	−0.0843176	−	0.146042i	−0.905100	+	0.425198i	$0.860204\pi$
$450$		0			0
$451$	12.2944	−	14.6519i	0.578921	−	0.689932i
$452$		0			0
$453$	−10.6089	−	11.2826i	−0.498449	−	0.530103i
$454$		0			0
$455$	−17.1457			−0.803804
$456$		0			0
$457$	26.0709			1.21955			0.609774	−	0.792576i	$-0.291260\pi$
$457$	26.0709			1.21955			0.609774	+	0.792576i	$0.291260\pi$
$458$		0			0
$459$	−6.74655	+	11.5509i	−0.314902	+	0.539148i
$460$		0			0
$461$	−8.46456	+	10.0877i	−0.394234	+	0.469830i	−0.926253	−	0.376903i	$-0.876989\pi$
$461$	−8.46456	+	10.0877i	−0.394234	+	0.469830i	0.532019	+	0.846732i	$0.321433\pi$
$462$		0			0
$463$	10.6868	+	18.5101i	0.496659	+	0.860238i	0.999993	−	0.00385369i	$-0.00122667\pi$
$463$	10.6868	+	18.5101i	0.496659	+	0.860238i	−0.503334	+	0.864092i	$0.667893\pi$
$464$		0			0
$465$	−12.4125	−	18.9414i	−0.575617	−	0.878386i
$466$		0			0
$467$	−8.01942	−	4.63001i	−0.371094	−	0.214251i	0.302842	−	0.953041i	$-0.402065\pi$
$467$	−8.01942	−	4.63001i	−0.371094	−	0.214251i	−0.673936	+	0.738789i	$0.735398\pi$
$468$		0			0
$469$	−7.83459	+	1.38145i	−0.361768	+	0.0637894i
$470$		0			0
$471$	−3.50603	+	0.198308i	−0.161549	+	0.00913753i
$472$		0			0
$473$	−3.09086	−	8.49206i	−0.142118	−	0.390465i
$474$		0			0
$475$	7.03730	+	13.0178i	0.322894	+	0.597296i
$476$		0			0
$477$	−13.1956	−	17.8494i	−0.604185	−	0.817266i
$478$		0			0
$479$	−3.61743	−	4.31108i	−0.165284	−	0.196978i	0.677045	−	0.735942i	$-0.263260\pi$
$479$	−3.61743	−	4.31108i	−0.165284	−	0.196978i	−0.842329	+	0.538964i	$0.818816\pi$
$480$		0			0
$481$	11.0333	+	62.5731i	0.503076	+	2.85309i
$482$		0			0
$483$	−5.15949	−	12.0164i	−0.234765	−	0.546764i
$484$		0			0
$485$	11.7249	+	4.26751i	0.532400	+	0.193778i
$486$		0			0
$487$	−17.7438	+	10.2444i	−0.804048	+	0.464217i	−0.844885	−	0.534948i	$-0.820331\pi$
$487$	−17.7438	+	10.2444i	−0.804048	+	0.464217i	0.0408365	+	0.999166i	$0.486998\pi$
$488$		0			0
$489$	3.70098	+	15.7331i	0.167364	+	0.711476i
$490$		0			0
$491$	−32.2309	−	5.68317i	−1.45456	−	0.256478i	−0.610196	−	0.792250i	$-0.708909\pi$
$491$	−32.2309	−	5.68317i	−1.45456	−	0.256478i	−0.844363	+	0.535772i	$0.820021\pi$
$492$		0			0
$493$			3.00354i			0.135273i
$494$		0			0
$495$	7.71138	+	26.0756i	0.346601	+	1.17201i
$496$		0			0
$497$	0.844229	−	4.78786i	0.0378689	−	0.214765i
$498$		0			0
$499$	−15.7157	−	13.1871i	−0.703533	−	0.590334i	0.219243	−	0.975670i	$-0.429641\pi$
$499$	−15.7157	−	13.1871i	−0.703533	−	0.590334i	−0.922776	+	0.385336i	$0.874086\pi$
$500$		0			0
$501$	−2.58402	+	21.7909i	−0.115446	+	0.973546i
$502$		0			0
$503$	−7.95923	+	21.8678i	−0.354885	+	0.975037i	0.625893	+	0.779909i	$0.284735\pi$
$503$	−7.95923	+	21.8678i	−0.354885	+	0.975037i	−0.980778	+	0.195128i	$0.937488\pi$
$504$		0			0
$505$	8.56766	−	14.8396i	0.381256	−	0.660354i
$506$		0			0
$507$	−11.4728	+	22.7490i	−0.509523	+	1.01032i
$508$		0			0
$509$	16.6553	−	13.9754i	0.738232	−	0.619450i	−0.194130	−	0.980976i	$-0.562188\pi$
$509$	16.6553	−	13.9754i	0.738232	−	0.619450i	0.932362	+	0.361525i	$0.117744\pi$
$510$		0			0
$511$	7.95315	−	2.89471i	0.351827	−	0.128054i
$512$		0			0
$513$	−19.2303	−	11.9664i	−0.849038	−	0.528331i
$514$		0			0
$515$	54.2675	−	19.7518i	2.39131	−	0.870367i
$516$		0			0
$517$	2.64708	−	2.22116i	0.116418	−	0.0976866i
$518$		0			0
$519$	−7.35496	+	14.5839i	−0.322847	+	0.640164i
$520$		0			0
$521$	7.53777	−	13.0558i	0.330236	−	0.571985i	−0.652322	−	0.757942i	$-0.726205\pi$
$521$	7.53777	−	13.0558i	0.330236	−	0.571985i	0.982558	+	0.185957i	$0.0595384\pi$
$522$		0			0
$523$	−2.38040	+	6.54010i	−0.104088	+	0.285979i	−0.980794	−	0.195048i	$-0.937514\pi$
$523$	−2.38040	+	6.54010i	−0.104088	+	0.285979i	0.876706	+	0.481027i	$0.159736\pi$
$524$		0			0
$525$	0.778413	−	6.56432i	0.0339727	−	0.286490i
$526$		0			0
$527$	8.89914	+	7.46727i	0.387653	+	0.325279i
$528$		0			0
$529$	−3.83894	+	21.7717i	−0.166911	+	0.946597i
$530$		0			0
$531$	−5.81098	−	19.6495i	−0.252175	−	0.852716i
$532$		0			0
$533$			32.1845i			1.39407i
$534$		0			0
$535$	−13.6496	−	2.40679i	−0.590124	−	0.104055i
$536$		0			0
$537$	−2.97027	−	12.6268i	−0.128176	−	0.544887i
$538$		0			0
$539$	15.5407	−	8.97240i	0.669384	−	0.386469i
$540$		0			0
$541$	−4.63626	−	1.68746i	−0.199328	−	0.0725495i	0.240427	−	0.970667i	$-0.422713\pi$
$541$	−4.63626	−	1.68746i	−0.199328	−	0.0725495i	−0.439755	+	0.898118i	$0.644935\pi$
$542$		0			0
$543$	10.9157	+	25.4226i	0.468439	+	1.09099i
$544$		0			0
$545$	−4.32762	−	24.5432i	−0.185375	−	1.05131i
$546$		0			0
$547$	−9.08478	−	10.8268i	−0.388437	−	0.462922i	0.536021	−	0.844205i	$-0.319927\pi$
$547$	−9.08478	−	10.8268i	−0.388437	−	0.462922i	−0.924458	+	0.381283i	$0.875482\pi$
$548$		0			0
$549$	12.9958	+	17.5791i	0.554647	+	0.750257i
$550$		0			0
$551$	−5.08359	−	0.142413i	−0.216568	−	0.00606701i
$552$		0			0
$553$	1.68239	+	4.62234i	0.0715426	+	0.196562i
$554$		0			0
$555$	−60.4776	+	3.42072i	−2.56713	+	0.145202i
$556$		0			0
$557$	−0.424076	+	0.0747760i	−0.0179687	+	0.00316836i	−0.182625	−	0.983183i	$-0.558460\pi$
$557$	−0.424076	+	0.0747760i	−0.0179687	+	0.00316836i	0.164657	+	0.986351i	$0.447348\pi$
$558$		0			0
$559$	13.1694	+	7.60334i	0.557005	+	0.321587i
$560$		0			0
$561$	−7.64552	−	11.6670i	−0.322794	−	0.492581i
$562$		0			0
$563$	−2.44919	−	4.24212i	−0.103221	−	0.178784i	0.809789	−	0.586721i	$-0.199582\pi$
$563$	−2.44919	−	4.24212i	−0.103221	−	0.178784i	−0.913010	+	0.407937i	$0.866248\pi$
$564$		0			0
$565$	30.1093	−	35.8829i	1.26671	−	1.50961i
$566$		0			0
$567$	3.94496	+	9.31670i	0.165673	+	0.391264i
$568$		0			0
$569$	−9.33523			−0.391353			−0.195677	−	0.980668i	$-0.562690\pi$
$569$	−9.33523			−0.391353			−0.195677	+	0.980668i	$0.562690\pi$
$570$		0			0
$571$	−23.4478			−0.981260			−0.490630	−	0.871368i	$-0.663233\pi$
$571$	−23.4478			−0.981260			−0.490630	+	0.871368i	$0.663233\pi$
$572$		0			0
$573$	−9.03812	−	9.61207i	−0.377573	−	0.401550i
$574$		0			0
$575$	−14.6563	+	17.4667i	−0.611209	+	0.728410i
$576$		0			0
$577$	−1.23938	−	2.14667i	−0.0515960	−	0.0893669i	0.839074	−	0.544017i	$-0.183097\pi$
$577$	−1.23938	−	2.14667i	−0.0515960	−	0.0893669i	−0.890670	+	0.454651i	$0.849764\pi$
$578$		0			0
$579$	−17.3836	+	11.3917i	−0.722437	+	0.473422i
$580$		0			0
$581$	14.0646	+	8.12021i	0.583499	+	0.336883i
$582$		0			0
$583$	22.7951	−	4.01940i	0.944078	−	0.166466i
$584$		0			0
$585$	−38.1440	−	25.2713i	−1.57706	−	1.04484i
$586$		0			0
$587$	−13.2139	−	36.3050i	−0.545398	−	1.49847i	−0.839859	−	0.542804i	$-0.817363\pi$
$587$	−13.2139	−	36.3050i	−0.545398	−	1.49847i	0.294462	−	0.955663i	$-0.404860\pi$
$588$		0			0
$589$	−13.0605	+	14.7080i	−0.538150	+	0.606034i
$590$		0			0
$591$	8.80325	−	29.2265i	0.362117	−	1.20222i
$592$		0			0
$593$	−2.81505	−	3.35484i	−0.115600	−	0.137767i	0.705141	−	0.709067i	$-0.250884\pi$
$593$	−2.81505	−	3.35484i	−0.115600	−	0.137767i	−0.820741	+	0.571300i	$0.806439\pi$
$594$		0			0
$595$	1.45606	+	8.25771i	0.0596925	+	0.338533i
$596$		0			0
$597$	−3.60211	+	1.54664i	−0.147424	+	0.0632999i
$598$		0			0
$599$	40.2689	+	14.6567i	1.64534	+	0.598855i	0.987961	−	0.154704i	$-0.0494423\pi$
$599$	40.2689	+	14.6567i	1.64534	+	0.598855i	0.657380	+	0.753559i	$0.271665\pi$
$600$		0			0
$601$	−24.0390	+	13.8789i	−0.980571	+	0.566133i	−0.902443	−	0.430810i	$-0.858228\pi$
$601$	−24.0390	+	13.8789i	−0.980571	+	0.566133i	−0.0781288	+	0.996943i	$0.524895\pi$
$602$		0			0
$603$	−19.4657	−	8.47419i	−0.792705	−	0.345096i
$604$		0			0
$605$	3.46299	+	0.610618i	0.140791	+	0.0248252i
$606$		0			0
$607$		−	16.1090i		−	0.653844i	−0.945051	−	0.326922i	$-0.893989\pi$
$607$		−	16.1090i		−	0.653844i	0.945051	−	0.326922i	$-0.106011\pi$
$608$		0			0
$609$	1.81992	+	1.35963i	0.0737470	+	0.0550950i
$610$		0			0
$611$	−1.00969	+	5.72626i	−0.0408478	+	0.231660i
$612$		0			0
$613$	17.2068	+	14.4382i	0.694975	+	0.583154i	0.920339	−	0.391121i	$-0.127913\pi$
$613$	17.2068	+	14.4382i	0.694975	+	0.583154i	−0.225364	+	0.974275i	$0.572357\pi$
$614$		0			0
$615$	−30.4696	−	3.61316i	−1.22865	−	0.145697i
$616$		0			0
$617$	15.8059	−	43.4264i	0.636322	−	1.74828i	−0.0266596	−	0.999645i	$-0.508487\pi$
$617$	15.8059	−	43.4264i	0.636322	−	1.74828i	0.662982	−	0.748636i	$-0.269291\pi$
$618$		0			0
$619$	20.8534	−	36.1192i	0.838170	−	1.45175i	−0.0532532	−	0.998581i	$-0.516959\pi$
$619$	20.8534	−	36.1192i	0.838170	−	1.45175i	0.891423	−	0.453172i	$-0.149708\pi$
$620$		0			0
$621$	6.23279	−	34.3374i	0.250113	−	1.37791i
$622$		0			0
$623$	11.8076	−	9.90779i	0.473063	−	0.396947i
$624$		0			0
$625$	28.6128	−	10.4142i	1.14451	−	0.416568i
$626$		0			0
$627$	20.1093	−	12.3871i	0.803087	−	0.494693i
$628$		0			0
$629$	29.1994	−	10.6277i	1.16426	−	0.423755i
$630$		0			0
$631$	3.34686	−	2.80835i	0.133236	−	0.111799i	−0.573734	−	0.819042i	$-0.694506\pi$
$631$	3.34686	−	2.80835i	0.133236	−	0.111799i	0.706971	+	0.707243i	$0.250061\pi$
$632$		0			0
$633$	−5.95579	−	3.00362i	−0.236722	−	0.119383i
$634$		0			0
$635$	11.1710	−	19.3488i	0.443309	−	0.767834i
$636$		0			0
$637$	−10.3275	+	28.3747i	−0.409192	+	1.12425i
$638$		0			0
$639$	8.93504	−	9.40721i	0.353465	−	0.372144i
$640$		0			0
$641$	−2.18494	−	1.83339i	−0.0863001	−	0.0724144i	0.598617	−	0.801035i	$-0.295717\pi$
$641$	−2.18494	−	1.83339i	−0.0863001	−	0.0724144i	−0.684917	+	0.728621i	$0.740162\pi$
$642$		0			0
$643$	−7.65253	+	43.3997i	−0.301786	+	1.71152i	0.336471	+	0.941694i	$0.390766\pi$
$643$	−7.65253	+	43.3997i	−0.301786	+	1.71152i	−0.638258	+	0.769823i	$0.720345\pi$
$644$		0			0
$645$	−8.67664	+	11.6141i	−0.341643	+	0.457303i
$646$		0			0
$647$			20.3269i			0.799131i	0.916705	+	0.399566i	$0.130839\pi$
$647$			20.3269i			0.799131i	−0.916705	+	0.399566i	$0.869161\pi$
$648$		0			0
$649$	21.0426	+	3.71037i	0.825992	+	0.145645i
$650$		0			0
$651$	8.55303	−	2.01197i	0.335220	−	0.0788554i
$652$		0			0
$653$	−35.1702	+	20.3055i	−1.37632	+	0.794617i	−0.991714	−	0.128465i	$-0.958995\pi$
$653$	−35.1702	+	20.3055i	−1.37632	+	0.794617i	−0.384603	+	0.923082i	$0.625662\pi$
$654$		0			0
$655$	6.02826	+	2.19411i	0.235543	+	0.0857308i
$656$		0			0
$657$	21.9599	+	5.28239i	0.856736	+	0.206086i
$658$		0			0
$659$	−6.33474	−	35.9261i	−0.246766	−	1.39948i	−0.816354	−	0.577552i	$-0.804008\pi$
$659$	−6.33474	−	35.9261i	−0.246766	−	1.39948i	0.569588	−	0.821930i	$-0.307103\pi$
$660$		0			0
$661$	−2.71797	−	3.23916i	−0.105717	−	0.125989i	0.710591	−	0.703605i	$-0.248427\pi$
$661$	−2.71797	−	3.23916i	−0.105717	−	0.125989i	−0.816308	+	0.577616i	$0.803983\pi$
$662$		0			0
$663$	22.4745	+	6.76948i	0.872837	+	0.262905i
$664$		0			0
$665$	−14.0455	+	2.07288i	−0.544660	+	0.0803830i
$666$		0			0
$667$	−2.68004	−	7.36334i	−0.103771	−	0.285110i
$668$		0			0
$669$	0.544490	+	9.62645i	0.0210512	+	0.372180i
$670$		0			0
$671$	−22.4500	+	3.95854i	−0.866672	+	0.152818i
$672$		0			0
$673$	22.4627	+	12.9688i	0.865874	+	0.499912i	0.865975	−	0.500088i	$-0.166699\pi$
$673$	22.4627	+	12.9688i	0.865874	+	0.499912i	−0.000101249		1.00000i	$0.500032\pi$
$674$		0			0
$675$	11.4070	−	13.4563i	0.439054	−	0.517933i
$676$		0			0
$677$	16.1874	+	28.0374i	0.622132	+	1.07756i	0.989088	+	0.147326i	$0.0470665\pi$
$677$	16.1874	+	28.0374i	0.622132	+	1.07756i	−0.366956	+	0.930238i	$0.619600\pi$
$678$		0			0
$679$	−3.11180	+	3.70850i	−0.119420	+	0.142319i
$680$		0			0
$681$	31.2605	−	29.3939i	1.19791	−	1.12638i
$682$		0			0
$683$	−12.5635			−0.480728			−0.240364	−	0.970683i	$-0.577267\pi$
$683$	−12.5635			−0.480728			−0.240364	+	0.970683i	$0.577267\pi$
$684$		0			0
$685$	0.625411			0.0238957
$686$		0			0
$687$	31.2869	−	29.4188i	1.19367	−	1.12240i
$688$		0			0
$689$	−25.0360	+	29.8367i	−0.953796	+	1.13669i
$690$		0			0
$691$	7.86815	+	13.6280i	0.299319	+	0.518435i	0.975980	−	0.217859i	$-0.0699073\pi$
$691$	7.86815	+	13.6280i	0.299319	+	0.518435i	−0.676662	+	0.736294i	$0.736574\pi$
$692$		0			0
$693$	−10.5303	−	0.648743i	−0.400012	−	0.0246437i
$694$		0			0
$695$	47.0630	+	27.1719i	1.78520	+	1.03069i
$696$		0			0
$697$	15.5007	−	2.73319i	0.587130	−	0.103527i
$698$		0			0
$699$	−2.10303	−	37.1812i	−0.0795441	−	1.40632i
$700$		0			0
$701$	−10.8602	−	29.8381i	−0.410183	−	1.12697i	−0.957094	−	0.289777i	$-0.906419\pi$
$701$	−10.8602	−	29.8381i	−0.410183	−	1.12697i	0.546911	−	0.837191i	$-0.315803\pi$
$702$		0			0
$703$	16.6033	+	49.9249i	0.626204	+	1.88295i
$704$		0			0
$705$	−5.30779	−	1.59875i	−0.199903	−	0.0602122i
$706$		0			0
$707$	4.27347	+	5.09293i	0.160721	+	0.191539i
$708$		0			0
$709$	6.11366	+	34.6723i	0.229603	+	1.30214i	0.853687	+	0.520787i	$0.174361\pi$
$709$	6.11366	+	34.6723i	0.229603	+	1.30214i	−0.624084	+	0.781358i	$0.714528\pi$
$710$		0			0
$711$	−3.07010	+	12.7630i	−0.115138	+	0.478649i
$712$		0			0
$713$	−28.4797	−	10.3658i	−1.06657	−	0.388201i
$714$		0			0
$715$	41.3206	−	23.8565i	1.54530	−	0.892182i
$716$		0			0
$717$	−20.4669	+	4.81453i	−0.764350	+	0.179802i
$718$		0			0
$719$	−14.7056	−	2.59299i	−0.548426	−	0.0967023i	−0.107432	−	0.994212i	$-0.534263\pi$
$719$	−14.7056	−	2.59299i	−0.548426	−	0.0967023i	−0.440994	+	0.897510i	$0.645374\pi$
$720$		0			0
$721$			22.4066i			0.834465i
$722$		0			0
$723$	22.5433	−	30.1752i	0.838394	−	1.12223i
$724$		0			0
$725$	0.687805	−	3.90074i	0.0255444	−	0.144870i
$726$		0			0
$727$	22.7799	+	19.1146i	0.844860	+	0.708922i	0.958651	−	0.284583i	$-0.0918551\pi$
$727$	22.7799	+	19.1146i	0.844860	+	0.708922i	−0.113791	+	0.993505i	$0.536300\pi$
$728$		0			0
$729$	−4.95565	+	26.5413i	−0.183543	+	0.983012i
$730$		0			0
$731$	2.54354	−	6.98831i	0.0940761	−	0.258472i
$732$		0			0
$733$	1.63062	−	2.82432i	0.0602284	−	0.104319i	−0.834339	−	0.551252i	$-0.814150\pi$
$733$	1.63062	−	2.82432i	0.0602284	−	0.104319i	0.894567	+	0.446933i	$0.147484\pi$
$734$		0			0
$735$	−25.7034	−	12.9627i	−0.948083	−	0.478137i
$736$		0			0
$737$	16.9590	−	14.2303i	0.624692	−	0.524178i
$738$		0			0
$739$	5.54154	−	2.01696i	0.203849	−	0.0741950i	−0.238078	−	0.971246i	$-0.576517\pi$
$739$	5.54154	−	2.01696i	0.203849	−	0.0741950i	0.441927	+	0.897051i	$0.354295\pi$
$740$		0			0
$741$	−12.5232	+	37.7178i	−0.460051	+	1.38560i
$742$		0			0
$743$	−27.7676	+	10.1066i	−1.01870	+	0.370775i	−0.796766	−	0.604288i	$-0.793458\pi$
$743$	−27.7676	+	10.1066i	−1.01870	+	0.370775i	−0.221930	+	0.975063i	$0.571236\pi$
$744$		0			0
$745$	9.43410	−	7.91615i	0.345639	−	0.290025i
$746$		0			0
$747$	19.3210	+	38.7950i	0.706919	+	1.41943i
$748$		0			0
$749$	2.68881	−	4.65716i	0.0982470	−	0.170169i
$750$		0			0
$751$	6.20481	−	17.0476i	0.226417	−	0.622074i	−0.773515	−	0.633778i	$-0.781503\pi$
$751$	6.20481	−	17.0476i	0.226417	−	0.622074i	0.999932	+	0.0117037i	$0.00372548\pi$
$752$		0			0
$753$	−33.4537	−	3.96703i	−1.21912	−	0.144566i
$754$		0			0
$755$	−19.8458	−	16.6526i	−0.722261	−	0.606049i
$756$		0			0
$757$	−3.70068	+	20.9876i	−0.134504	+	0.762807i	0.840701	+	0.541500i	$0.182143\pi$
$757$	−3.70068	+	20.9876i	−0.134504	+	0.762807i	−0.975204	+	0.221307i	$0.928968\pi$
$758$		0			0
$759$	29.1537	+	21.7802i	1.05821	+	0.790571i
$760$		0			0
$761$			29.1728i			1.05751i	0.848774	+	0.528757i	$0.177342\pi$
$761$			29.1728i			1.05751i	−0.848774	+	0.528757i	$0.822658\pi$
$762$		0			0
$763$	9.52252	+	1.67908i	0.344739	+	0.0607867i
$764$		0			0
$765$	−8.93185	+	20.5170i	−0.322932	+	0.741793i
$766$		0			0
$767$	−31.1375	+	17.9773i	−1.12431	+	0.649122i
$768$		0			0
$769$	−25.9596	−	9.44854i	−0.936129	−	0.340723i	−0.171493	−	0.985185i	$-0.554859\pi$
$769$	−25.9596	−	9.44854i	−0.936129	−	0.340723i	−0.764636	+	0.644462i	$0.777081\pi$
$770$		0			0
$771$	−17.2521	+	7.40758i	−0.621321	+	0.266777i
$772$		0			0
$773$	−7.60654	−	43.1388i	−0.273588	−	1.55160i	−0.743411	−	0.668835i	$-0.766793\pi$
$773$	−7.60654	−	43.1388i	−0.273588	−	1.55160i	0.469823	−	0.882761i	$-0.344318\pi$
$774$		0			0
$775$	−9.84744	−	11.7357i	−0.353731	−	0.421560i
$776$		0			0
$777$	6.77825	−	22.5036i	0.243168	−	0.807312i
$778$		0			0
$779$	3.89104	+	26.3650i	0.139411	+	0.944624i
$780$		0			0
$781$	4.62724	+	12.7132i	0.165576	+	0.454916i
$782$		0			0
$783$	2.04480	+	5.70716i	0.0730752	+	0.203957i
$784$		0			0
$785$	−5.78507	+	1.02006i	−0.206478	+	0.0364077i
$786$		0			0
$787$	−31.9379	−	18.4393i	−1.13846	−	0.657291i	−0.192412	−	0.981314i	$-0.561631\pi$
$787$	−31.9379	−	18.4393i	−1.13846	−	0.657291i	−0.946049	+	0.324023i	$0.894964\pi$
$788$		0			0
$789$	44.8175	−	29.3694i	1.59554	−	1.04558i
$790$		0			0
$791$	9.08710	+	15.7393i	0.323100	+	0.559626i
$792$		0			0
$793$	24.6569	−	29.3850i	0.875593	−	1.04349i
$794$		0			0
$795$	−25.4363	−	27.0516i	−0.902132	−	0.959421i
$796$		0			0
$797$	−47.4368			−1.68030			−0.840148	−	0.542357i	$-0.817532\pi$
$797$	−47.4368			−1.68030			−0.840148	+	0.542357i	$0.817532\pi$
$798$		0			0
$799$	2.84362			0.100600
$800$		0			0
$801$	40.8716	−	4.63838i	1.44413	−	0.163889i
$802$		0			0
$803$	−15.1391	+	18.0421i	−0.534249	+	0.636693i
$804$		0			0
$805$	−10.9379	−	18.9450i	−0.385510	−	0.667723i
$806$		0			0
$807$	−4.81219	−	7.34335i	−0.169397	−	0.258498i
$808$		0			0
$809$	46.6699	+	26.9449i	1.64083	+	0.947331i	0.980540	+	0.196317i	$0.0628981\pi$
$809$	46.6699	+	26.9449i	1.64083	+	0.947331i	0.660286	+	0.751015i	$0.270435\pi$
$810$		0			0
$811$	−5.26849	+	0.928977i	−0.185002	+	0.0326208i	−0.265381	−	0.964144i	$-0.585498\pi$
$811$	−5.26849	+	0.928977i	−0.185002	+	0.0326208i	0.0803796	+	0.996764i	$0.474387\pi$
$812$		0			0
$813$	9.06312	−	0.512626i	0.317857	−	0.0179786i
$814$		0			0
$815$	9.24719	+	25.4064i	0.323915	+	0.889949i
$816$		0			0
$817$	11.7073	+	4.63637i	0.409588	+	0.162206i
$818$		0			0
$819$	14.2754	−	10.5535i	0.498825	−	0.368769i
$820$		0			0
$821$	14.7984	+	17.6360i	0.516468	+	0.615502i	0.959742	−	0.280884i	$-0.0906276\pi$
$821$	14.7984	+	17.6360i	0.516468	+	0.615502i	−0.443274	+	0.896386i	$0.646183\pi$
$822$		0			0
$823$	−1.89577	−	10.7514i	−0.0660824	−	0.374772i	−0.999857	−	0.0169103i	$-0.994617\pi$
$823$	−1.89577	−	10.7514i	−0.0660824	−	0.374772i	0.933775	−	0.357862i	$-0.116494\pi$
$824$		0			0
$825$	7.25761	+	16.9029i	0.252678	+	0.588482i
$826$		0			0
$827$	0.866657	+	0.315437i	0.0301366	+	0.0109688i	0.357044	−	0.934087i	$-0.383784\pi$
$827$	0.866657	+	0.315437i	0.0301366	+	0.0109688i	−0.326908	+	0.945056i	$0.606007\pi$
$828$		0			0
$829$	36.7431	−	21.2136i	1.27614	−	0.736780i	0.300004	−	0.953938i	$-0.403012\pi$
$829$	36.7431	−	21.2136i	1.27614	−	0.736780i	0.976137	+	0.217158i	$0.0696786\pi$
$830$		0			0
$831$	1.71081	+	7.27276i	0.0593472	+	0.252289i
$832$		0			0
$833$	14.5428	+	2.56430i	0.503880	+	0.0888476i
$834$		0			0
$835$			36.7076i			1.27032i
$836$		0			0
$837$	21.9934	+	8.13039i	0.760201	+	0.281027i
$838$		0			0
$839$	−2.73490	+	15.5104i	−0.0944194	+	0.535479i	0.900504	+	0.434847i	$0.143198\pi$
$839$	−2.73490	+	15.5104i	−0.0944194	+	0.535479i	−0.994924	+	0.100632i	$0.967914\pi$
$840$		0			0
$841$	−21.1725	−	17.7659i	−0.730087	−	0.612616i
$842$		0			0
$843$	−2.24666	+	18.9459i	−0.0773790	+	0.652533i
$844$		0			0
$845$	−14.5770	+	40.0501i	−0.501465	+	1.37776i
$846$		0			0
$847$	−0.682168	+	1.18155i	−0.0234396	+	0.0405985i
$848$		0			0
$849$	−3.08143	+	6.11007i	−0.105754	+	0.209697i
$850$		0			0
$851$	−62.1009	+	52.1088i	−2.12879	+	1.78627i
$852$		0			0
$853$	−30.2008	+	10.9922i	−1.03405	+	0.376365i	−0.802623	−	0.596486i	$-0.796563\pi$
$853$	−30.2008	+	10.9922i	−1.03405	+	0.376365i	−0.231431	+	0.972851i	$0.574341\pi$
$854$		0			0
$855$	−34.3021	−	16.0903i	−1.17311	−	0.550275i
$856$		0			0
$857$	−23.1422	+	8.42308i	−0.790524	+	0.287727i	−0.705554	−	0.708656i	$-0.749302\pi$
$857$	−23.1422	+	8.42308i	−0.790524	+	0.287727i	−0.0849699	+	0.996384i	$0.527079\pi$
$858$		0			0
$859$	11.9557	−	10.0320i	0.407923	−	0.342288i	−0.415623	−	0.909537i	$-0.636437\pi$
$859$	11.9557	−	10.0320i	0.407923	−	0.342288i	0.823547	+	0.567248i	$0.191992\pi$
$860$		0			0
$861$	5.36067	−	10.6295i	0.182691	−	0.362253i
$862$		0			0
$863$	7.05542	−	12.2203i	0.240169	−	0.415985i	−0.720593	−	0.693358i	$-0.756130\pi$
$863$	7.05542	−	12.2203i	0.240169	−	0.415985i	0.960762	+	0.277373i	$0.0894637\pi$
$864$		0			0
$865$	−9.34505	+	25.6753i	−0.317741	+	0.872987i
$866$		0			0
$867$	−2.11563	+	17.8410i	−0.0718505	+	0.605911i
$868$		0			0
$869$	−10.4860	−	8.79880i	−0.355713	−	0.298479i
$870$		0			0
$871$	−6.46878	+	36.6863i	−0.219186	+	1.24307i
$872$		0			0
$873$	−12.3888	+	3.66376i	−0.419297	+	0.123999i
$874$		0			0
$875$			5.22796i			0.176737i
$876$		0			0
$877$	17.9817	+	3.17067i	0.607200	+	0.107066i	0.468791	−	0.883309i	$-0.344690\pi$
$877$	17.9817	+	3.17067i	0.607200	+	0.107066i	0.138410	+	0.990375i	$0.455801\pi$
$878$		0			0
$879$	7.98928	+	33.9630i	0.269472	+	1.14554i
$880$		0			0
$881$	5.32331	−	3.07342i	0.179347	−	0.103546i	−0.407639	−	0.913143i	$-0.633648\pi$
$881$	5.32331	−	3.07342i	0.179347	−	0.103546i	0.586986	+	0.809597i	$0.300314\pi$
$882$		0			0
$883$	−51.4745	−	18.7352i	−1.73225	−	0.630489i	−0.733468	−	0.679724i	$-0.762099\pi$
$883$	−51.4745	−	18.7352i	−1.73225	−	0.630489i	−0.998787	+	0.0492352i	$0.984322\pi$
$884$		0			0
$885$	−13.5237	−	31.4966i	−0.454596	−	1.05875i
$886$		0			0
$887$	7.62578	+	43.2479i	0.256049	+	1.45212i	0.793367	+	0.608744i	$0.208326\pi$
$887$	7.62578	+	43.2479i	0.256049	+	1.45212i	−0.537318	+	0.843379i	$0.680563\pi$
$888$		0			0
$889$	5.57202	+	6.64047i	0.186879	+	0.222714i
$890$		0			0
$891$	−22.4704	−	16.9639i	−0.752788	−	0.568313i
$892$		0			0
$893$	−0.134831	+	4.81292i	−0.00451194	+	0.161058i
$894$		0			0
$895$	−7.42145	−	20.3903i	−0.248072	−	0.681571i
$896$		0			0
$897$	−61.1377	+	3.45806i	−2.04133	+	0.115461i
$898$		0			0
$899$	5.18490	−	0.914238i	0.172926	−	0.0304915i
$900$		0			0
$901$	16.4961	+	9.52401i	0.549564	+	0.317291i
$902$		0			0
$903$	−3.08300	−	4.70463i	−0.102596	−	0.156560i
$904$		0			0
$905$	23.1408	+	40.0811i	0.769228	+	1.33234i
$906$		0			0
$907$	21.7940	−	25.9730i	0.723656	−	0.862420i	−0.271324	−	0.962488i	$-0.587462\pi$
$907$	21.7940	−	25.9730i	0.723656	−	0.862420i	0.994981	+	0.100068i	$0.0319060\pi$
$908$		0			0
$909$	2.00065	+	17.6289i	0.0663573	+	0.584715i
$910$		0			0
$911$	15.3654			0.509077			0.254539	−	0.967063i	$-0.418076\pi$
$911$	15.3654			0.509077			0.254539	+	0.967063i	$0.418076\pi$
$912$		0			0
$913$	−45.1937			−1.49569
$914$		0			0
$915$	25.0511	+	26.6420i	0.828165	+	0.880756i
$916$		0			0
$917$	−1.59991	+	1.90670i	−0.0528336	+	0.0629646i
$918$		0			0
$919$	6.10344	+	10.5715i	0.201334	+	0.348720i	0.948958	−	0.315401i	$-0.102139\pi$
$919$	6.10344	+	10.5715i	0.201334	+	0.348720i	−0.747625	+	0.664121i	$0.768806\pi$
$920$		0			0
$921$	−9.49823	+	6.22431i	−0.312977	+	0.205098i
$922$		0			0
$923$	−19.7155	−	11.3828i	−0.648944	−	0.374668i
$924$		0			0
$925$	−40.3554	+	7.11574i	−1.32688	+	0.233964i
$926$		0			0
$927$	−33.0253	+	49.8478i	−1.08469	+	1.63722i
$928$		0			0
$929$	−6.30750	−	17.3297i	−0.206942	−	0.568569i	0.792188	−	0.610278i	$-0.208942\pi$
$929$	−6.30750	−	17.3297i	−0.206942	−	0.568569i	−0.999130	+	0.0417085i	$0.986720\pi$
$930$		0			0
$931$	−5.02970	+	24.4926i	−0.164842	+	0.802714i
$932$		0			0
$933$	−1.07676	+	3.57480i	−0.0352514	+	0.117034i
$934$		0			0
$935$	−14.9988	−	17.8749i	−0.490513	−	0.584570i
$936$		0			0
$937$	−4.35606	−	24.7045i	−0.142306	−	0.807060i	−0.969491	−	0.245129i	$-0.921170\pi$
$937$	−4.35606	−	24.7045i	−0.142306	−	0.807060i	0.827184	−	0.561931i	$-0.189941\pi$
$938$		0			0
$939$	−26.9476	+	11.5705i	−0.879400	+	0.377589i
$940$		0			0
$941$	43.7853	+	15.9365i	1.42736	+	0.519517i	0.936174	−	0.351538i	$-0.114341\pi$
$941$	43.7853	+	15.9365i	1.42736	+	0.519517i	0.491187	+	0.871054i	$0.336563\pi$
$942$		0			0
$943$	−35.5619	+	20.5317i	−1.15806	+	0.668604i
$944$		0			0
$945$	8.38854	+	14.6996i	0.272879	+	0.478177i
$946$		0			0
$947$	54.8110	+	9.66466i	1.78112	+	0.314059i	0.964690	−	0.263387i	$-0.0848397\pi$
$947$	54.8110	+	9.66466i	1.78112	+	0.314059i	0.816429	+	0.577446i	$0.195951\pi$
$948$		0			0
$949$		−	39.6315i		−	1.28649i
$950$		0			0
$951$	7.68312	+	5.73991i	0.249142	+	0.186129i
$952$		0			0
$953$	−3.28854	+	18.6502i	−0.106526	+	0.604140i	0.884074	+	0.467348i	$0.154790\pi$
$953$	−3.28854	+	18.6502i	−0.106526	+	0.604140i	−0.990600	+	0.136792i	$0.956321\pi$
$954$		0			0
$955$	−16.9074	−	14.1870i	−0.547109	−	0.459079i
$956$		0			0
$957$	−6.27774	−	0.744430i	−0.202930	−	0.0240640i
$958$		0			0
$959$	−0.0829924	+	0.228020i	−0.00267997	+	0.00736314i
$960$		0			0
$961$	−5.31832	+	9.21160i	−0.171559	+	0.297148i
$962$		0			0
$963$	12.8460	−	6.39768i	0.413957	−	0.206162i
$964$		0			0
$965$	−26.6332	+	22.3479i	−0.857353	+	0.719405i
$966$		0			0
$967$	23.9285	−	8.70925i	0.769488	−	0.280071i	0.0727056	−	0.997353i	$-0.476837\pi$
$967$	23.9285	−	8.70925i	0.769488	−	0.280071i	0.696782	+	0.717283i	$0.254614\pi$
$968$		0			0
$969$	19.2291	+	2.82832i	0.617728	+	0.0908588i
$970$		0			0
$971$	14.6975	−	5.34944i	0.471664	−	0.171672i	−0.0952419	−	0.995454i	$-0.530362\pi$
$971$	14.6975	−	5.34944i	0.471664	−	0.171672i	0.566906	+	0.823782i	$0.308140\pi$
$972$		0			0
$973$	−16.1519	+	13.5531i	−0.517807	+	0.434492i
$974$		0			0
$975$	−27.6377	−	13.9382i	−0.885115	−	0.446380i
$976$		0			0
$977$	−10.2781	+	17.8022i	−0.328827	+	0.569544i	−0.982279	−	0.187423i	$-0.939986\pi$
$977$	−10.2781	+	17.8022i	−0.328827	+	0.569544i	0.653453	+	0.756967i	$0.273320\pi$
$978$		0			0
$979$	−14.6704	+	40.3065i	−0.468867	+	1.28820i
$980$		0			0
$981$	18.7099	+	17.7708i	0.597361	+	0.567378i
$982$		0			0
$983$	−14.5443	−	12.2041i	−0.463890	−	0.389250i	0.380670	−	0.924711i	$-0.375693\pi$
$983$	−14.5443	−	12.2041i	−0.463890	−	0.389250i	−0.844560	+	0.535461i	$0.820138\pi$
$984$		0			0
$985$	8.86652	−	50.2845i	0.282511	−	1.60220i
$986$		0			0
$987$	1.28724	−	1.72302i	0.0409732	−	0.0548444i
$988$		0			0
$989$			19.4018i			0.616941i
$990$		0			0
$991$	41.2131	+	7.26698i	1.30918	+	0.230843i	0.784325	−	0.620350i	$-0.213009\pi$
$991$	41.2131	+	7.26698i	1.30918	+	0.230843i	0.524852	+	0.851193i	$0.324121\pi$
$992$		0			0
$993$	−12.9958	+	3.05706i	−0.412409	+	0.0970129i
$994$		0			0
$995$	−5.67907	+	3.27881i	−0.180039	+	0.103945i
$996$		0			0
$997$	14.4637	+	5.26435i	0.458069	+	0.166724i	0.560740	−	0.827992i	$-0.310517\pi$
$997$	14.4637	+	5.26435i	0.458069	+	0.166724i	−0.102671	+	0.994715i	$0.532739\pi$
$998$		0			0
$999$	48.2478	−	40.0731i	1.52649	−	1.26786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.d.641.1		18
3.2	odd	2		912.2.cc.c.641.2		18
4.3	odd	2		114.2.l.a.71.3	yes	18
12.11	even	2		114.2.l.b.71.2	yes	18
19.15	odd	18		912.2.cc.c.737.2		18
57.53	even	18	inner	912.2.cc.d.737.1		18
76.15	even	18		114.2.l.b.53.2	yes	18
228.167	odd	18		114.2.l.a.53.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.3	✓	18	228.167	odd	18
114.2.l.a.71.3	yes	18	4.3	odd	2
114.2.l.b.53.2	yes	18	76.15	even	18
114.2.l.b.71.2	yes	18	12.11	even	2
912.2.cc.c.641.2		18	3.2	odd	2
912.2.cc.c.737.2		18	19.15	odd	18
912.2.cc.d.641.1		18	1.1	even	1	trivial
912.2.cc.d.737.1		18	57.53	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26184 + 1.18649i) q^{3} +(-1.86241 + 2.21954i) q^{5} +(-0.562083 - 0.973556i) q^{7} +(0.184473 - 2.99432i) q^{9} +(2.70920 + 1.56416i) q^{11} +(-5.18404 + 0.914087i) q^{13} +(-0.283400 - 5.01044i) q^{15} +(0.880484 + 2.41911i) q^{17} +(-4.13617 + 1.37554i) q^{19} +(1.86437 + 0.561563i) q^{21} +(-4.31710 - 5.14492i) q^{23} +(-0.589524 - 3.34336i) q^{25} +(3.31997 + 3.99723i) q^{27} +(1.09635 + 0.399039i) q^{29} +(3.90801 - 2.25629i) q^{31} +(-5.27443 + 1.24073i) q^{33} +(3.20767 + 0.565599i) q^{35} -12.0703i q^{37} +(5.45687 - 7.30426i) q^{39} +(1.06170 - 6.02118i) q^{41} +(-2.21295 - 1.85688i) q^{43} +(6.30245 + 5.98611i) q^{45} +(0.377793 - 1.03798i) q^{47} +(2.86813 - 4.96774i) q^{49} +(-3.98128 - 2.00784i) q^{51} +(5.66806 - 4.75606i) q^{53} +(-8.51736 + 3.10007i) q^{55} +(3.58710 - 6.64324i) q^{57} +(6.41833 - 2.33608i) q^{59} +(-5.58223 + 4.68405i) q^{61} +(-3.01883 + 1.50346i) q^{63} +(7.62598 - 13.2086i) q^{65} +(2.42040 - 6.64999i) q^{67} +(11.5519 + 1.36985i) q^{69} +(3.31294 + 2.77989i) q^{71} +(-1.30735 + 7.41438i) q^{73} +(4.71075 + 3.51931i) q^{75} -3.51674i q^{77} +(-4.30920 - 0.759829i) q^{79} +(-8.93194 - 1.10474i) q^{81} +(-12.5112 + 7.22333i) q^{83} +(-7.00913 - 2.55111i) q^{85} +(-1.85688 + 0.797290i) q^{87} +(2.38095 + 13.5030i) q^{89} +(3.80378 + 4.53316i) q^{91} +(-2.25420 + 7.48389i) q^{93} +(4.65018 - 11.7422i) q^{95} +(-1.47287 - 4.04669i) q^{97} +(5.18337 - 7.82368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53}+ \cdots + 30 q^{99}+O(q^{100}) \) 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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