LMFDB - Embedded newform 912.2.cc.c.737.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			737.2
Root			$-0.396613 + 1.68603i$ of defining polynomial
Character	$\chi$	$=$	912.737
Dual form			912.2.cc.c.641.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.779936 + 1.54651i) q^{3} +(1.86241 + 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(-1.78340 - 2.41236i) q^{9} +O(q^{10})$	\(q+(-0.779936 + 1.54651i) q^{3} +(1.86241 + 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(-1.78340 - 2.41236i) q^{9} +(-2.70920 + 1.56416i) q^{11} +(-5.18404 - 0.914087i) q^{13} +(-4.88511 + 1.14915i) q^{15} +(-0.880484 + 2.41911i) q^{17} +(-4.13617 - 1.37554i) q^{19} +(-1.06723 - 1.62858i) q^{21} +(4.31710 - 5.14492i) q^{23} +(-0.589524 + 3.34336i) q^{25} +(5.12168 - 0.876562i) q^{27} +(-1.09635 + 0.399039i) q^{29} +(3.90801 + 2.25629i) q^{31} +(-0.305986 - 5.40975i) q^{33} +(-3.20767 + 0.565599i) q^{35} +12.0703i q^{37} +(5.45687 - 7.30426i) q^{39} +(-1.06170 - 6.02118i) q^{41} +(-2.21295 + 1.85688i) q^{43} +(2.03290 - 8.45114i) q^{45} +(-0.377793 - 1.03798i) q^{47} +(2.86813 + 4.96774i) q^{49} +(-3.05446 - 3.24843i) q^{51} +(-5.66806 - 4.75606i) q^{53} +(-8.51736 - 3.10007i) q^{55} +(5.35324 - 5.32380i) q^{57} +(-6.41833 - 2.33608i) q^{59} +(-5.58223 - 4.68405i) q^{61} +(3.35099 - 0.380292i) q^{63} +(-7.62598 - 13.2086i) q^{65} +(2.42040 + 6.64999i) q^{67} +(4.58962 + 10.6892i) q^{69} +(-3.31294 + 2.77989i) q^{71} +(-1.30735 - 7.41438i) q^{73} +(-4.71075 - 3.51931i) q^{75} -3.51674i q^{77} +(-4.30920 + 0.759829i) q^{79} +(-2.63897 + 8.60441i) q^{81} +(12.5112 + 7.22333i) q^{83} +(-7.00913 + 2.55111i) q^{85} +(0.237965 - 2.00675i) q^{87} +(-2.38095 + 13.5030i) q^{89} +(3.80378 - 4.53316i) q^{91} +(-6.53737 + 4.28402i) q^{93} +(-4.65018 - 11.7422i) q^{95} +(-1.47287 + 4.04669i) q^{97} +(8.60490 + 3.74605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 - 3 * q^9	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$-1$	$1$

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
$3$	−0.779936	+	1.54651i	−0.450296	+	0.892879i
$3$	−0.779936	+	1.54651i	−0.450296	+	0.892879i
$4$		0			0
$5$	1.86241	+	2.21954i	0.832897	+	0.992608i	0.999978	+	0.00666440i	$0.00212136\pi$
$5$	1.86241	+	2.21954i	0.832897	+	0.992608i	−0.167081	+	0.985943i	$0.553434\pi$
$6$		0			0
$7$	−0.562083	+	0.973556i	−0.212447	+	0.367969i	−0.952480	−	0.304602i	$-0.901477\pi$
$7$	−0.562083	+	0.973556i	−0.212447	+	0.367969i	0.740033	+	0.672571i	$0.234810\pi$
$8$		0			0
$9$	−1.78340	−	2.41236i	−0.594467	−	0.804120i
$10$		0			0
$11$	−2.70920	+	1.56416i	−0.816855	+	0.471611i	−0.849331	−	0.527861i	$-0.822994\pi$
$11$	−2.70920	+	1.56416i	−0.816855	+	0.471611i	0.0324759	+	0.999473i	$0.489661\pi$
$12$		0			0
$13$	−5.18404	−	0.914087i	−1.43780	−	0.253522i	−0.600216	−	0.799838i	$-0.704919\pi$
$13$	−5.18404	−	0.914087i	−1.43780	−	0.253522i	−0.837579	+	0.546316i	$0.816030\pi$
$14$		0			0
$15$	−4.88511	+	1.14915i	−1.26133	+	0.296709i
$16$		0			0
$17$	−0.880484	+	2.41911i	−0.213549	+	0.586720i	−0.999502	−	0.0315662i	$-0.989951\pi$
$17$	−0.880484	+	2.41911i	−0.213549	+	0.586720i	0.785953	+	0.618286i	$0.212173\pi$
$18$		0			0
$19$	−4.13617	−	1.37554i	−0.948902	−	0.315571i
$19$	−4.13617	−	1.37554i	−0.948902	−	0.315571i
$20$		0			0
$21$	−1.06723	−	1.62858i	−0.232888	−	0.355385i
$22$		0			0
$23$	4.31710	−	5.14492i	0.900178	−	1.07279i	−0.0968152	−	0.995302i	$-0.530866\pi$
$23$	4.31710	−	5.14492i	0.900178	−	1.07279i	0.996993	−	0.0774881i	$-0.0246900\pi$
$24$		0			0
$25$	−0.589524	+	3.34336i	−0.117905	+	0.668671i
$26$		0			0
$27$	5.12168	−	0.876562i	0.985668	−	0.168694i
$28$		0			0
$29$	−1.09635	+	0.399039i	−0.203587	+	0.0740998i	−0.441801	−	0.897113i	$-0.645660\pi$
$29$	−1.09635	+	0.399039i	−0.203587	+	0.0740998i	0.238214	+	0.971213i	$0.423438\pi$
$30$		0			0
$31$	3.90801	+	2.25629i	0.701899	+	0.405241i	0.808054	−	0.589108i	$-0.200521\pi$
$31$	3.90801	+	2.25629i	0.701899	+	0.405241i	−0.106155	+	0.994350i	$0.533854\pi$
$32$		0			0
$33$	−0.305986	−	5.40975i	−0.0532653	−	0.941717i
$34$		0			0
$35$	−3.20767	+	0.565599i	−0.542196	+	0.0956038i
$36$		0			0
$37$			12.0703i			1.98435i	0.124859	+	0.992174i	$0.460152\pi$
$37$			12.0703i			1.98435i	−0.124859	+	0.992174i	$0.539848\pi$
$38$		0			0
$39$	5.45687	−	7.30426i	0.873799	−	1.16962i
$40$		0			0
$41$	−1.06170	−	6.02118i	−0.165809	−	0.940350i	−0.948226	−	0.317595i	$-0.897125\pi$
$41$	−1.06170	−	6.02118i	−0.165809	−	0.940350i	0.782417	−	0.622755i	$-0.213986\pi$
$42$		0			0
$43$	−2.21295	+	1.85688i	−0.337471	+	0.283172i	−0.795736	−	0.605644i	$-0.792916\pi$
$43$	−2.21295	+	1.85688i	−0.337471	+	0.283172i	0.458265	+	0.888816i	$0.348471\pi$
$44$		0			0
$45$	2.03290	−	8.45114i	0.303047	−	1.25982i
$46$		0			0
$47$	−0.377793	−	1.03798i	−0.0551068	−	0.151405i	0.909085	−	0.416611i	$-0.136782\pi$
$47$	−0.377793	−	1.03798i	−0.0551068	−	0.151405i	−0.964192	+	0.265206i	$0.914560\pi$
$48$		0			0
$49$	2.86813	+	4.96774i	0.409732	+	0.709677i
$50$		0			0
$51$	−3.05446	−	3.24843i	−0.427710	−	0.454871i
$52$		0			0
$53$	−5.66806	−	4.75606i	−0.778568	−	0.653296i	0.164320	−	0.986407i	$-0.447457\pi$
$53$	−5.66806	−	4.75606i	−0.778568	−	0.653296i	−0.942887	+	0.333111i	$0.891901\pi$
$54$		0			0
$55$	−8.51736	−	3.10007i	−1.14848	−	0.418013i
$56$		0			0
$57$	5.35324	−	5.32380i	0.709054	−	0.705154i
$58$		0			0
$59$	−6.41833	−	2.33608i	−0.835596	−	0.304132i	−0.111442	−	0.993771i	$-0.535547\pi$
$59$	−6.41833	−	2.33608i	−0.835596	−	0.304132i	−0.724153	+	0.689639i	$0.757769\pi$
$60$		0			0
$61$	−5.58223	−	4.68405i	−0.714732	−	0.599731i	0.211191	−	0.977445i	$-0.432266\pi$
$61$	−5.58223	−	4.68405i	−0.714732	−	0.599731i	−0.925922	+	0.377714i	$0.876710\pi$
$62$		0			0
$63$	3.35099	−	0.380292i	0.422184	−	0.0479123i
$64$		0			0
$65$	−7.62598	−	13.2086i	−0.945887	−	1.63832i
$66$		0			0
$67$	2.42040	+	6.64999i	0.295699	+	0.812425i	0.995206	+	0.0977999i	$0.0311805\pi$
$67$	2.42040	+	6.64999i	0.295699	+	0.812425i	−0.699508	+	0.714625i	$0.746597\pi$
$68$		0			0
$69$	4.58962	+	10.6892i	0.552525	+	1.28682i
$70$		0			0
$71$	−3.31294	+	2.77989i	−0.393174	+	0.329912i	−0.817848	−	0.575434i	$-0.804833\pi$
$71$	−3.31294	+	2.77989i	−0.393174	+	0.329912i	0.424674	+	0.905346i	$0.360389\pi$
$72$		0			0
$73$	−1.30735	−	7.41438i	−0.153014	−	0.867787i	−0.960579	−	0.278008i	$-0.910326\pi$
$73$	−1.30735	−	7.41438i	−0.153014	−	0.867787i	0.807565	−	0.589779i	$-0.200785\pi$
$74$		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	−0.410717	−	0.911763i	$-0.634722\pi$
$79$	−4.30920	+	0.759829i	−0.484823	+	0.0854874i	−0.0741064	+	0.997250i	$0.523610\pi$
$80$		0			0
$81$	−2.63897	+	8.60441i	−0.293219	+	0.956045i
$82$		0			0
$83$	12.5112	+	7.22333i	1.37328	+	0.792863i	0.991340	−	0.131324i	$-0.0419227\pi$
$83$	12.5112	+	7.22333i	1.37328	+	0.792863i	0.381940	+	0.924187i	$0.375256\pi$
$84$		0			0
$85$	−7.00913	+	2.55111i	−0.760247	+	0.276707i
$86$		0			0
$87$	0.237965	−	2.00675i	0.0255125	−	0.215146i
$88$		0			0
$89$	−2.38095	+	13.5030i	−0.252380	+	1.43132i	0.550331	+	0.834947i	$0.314502\pi$
$89$	−2.38095	+	13.5030i	−0.252380	+	1.43132i	−0.802710	+	0.596369i	$0.796609\pi$
$90$		0			0
$91$	3.80378	−	4.53316i	0.398744	−	0.475205i
$92$		0			0
$93$	−6.53737	+	4.28402i	−0.677894	+	0.444232i
$94$		0			0
$95$	−4.65018	−	11.7422i	−0.477098	−	1.20473i
$96$		0			0
$97$	−1.47287	+	4.04669i	−0.149548	+	0.410879i	−0.991735	−	0.128307i	$-0.959046\pi$
$97$	−1.47287	+	4.04669i	−0.149548	+	0.410879i	0.842187	+	0.539186i	$0.181268\pi$
$98$		0			0
$99$	8.60490	+	3.74605i	0.864825	+	0.376492i
$100$		0			0
$101$	5.82418	+	1.02696i	0.579528	+	0.102186i	0.455725	−	0.890121i	$-0.349380\pi$
$101$	5.82418	+	1.02696i	0.579528	+	0.102186i	0.123802	+	0.992307i	$0.460491\pi$
$102$		0			0
$103$	−17.2614	+	9.96588i	−1.70082	+	0.981967i	−0.755884	+	0.654706i	$0.772792\pi$
$103$	−17.2614	+	9.96588i	−1.70082	+	0.981967i	−0.944934	+	0.327261i	$0.893874\pi$
$104$		0			0
$105$	1.62707	−	5.40184i	0.158786	−	0.527165i
$106$		0			0
$107$	−2.39183	+	4.14277i	−0.231227	+	0.400496i	−0.958169	−	0.286202i	$-0.907607\pi$
$107$	−2.39183	+	4.14277i	−0.231227	+	0.400496i	0.726943	+	0.686698i	$0.240941\pi$
$108$		0			0
$109$	−5.52889	−	6.58908i	−0.529572	−	0.631119i	0.433244	−	0.901276i	$-0.357369\pi$
$109$	−5.52889	−	6.58908i	−0.529572	−	0.631119i	−0.962816	+	0.270157i	$0.912924\pi$
$110$		0			0
$111$	−18.6669	−	9.41408i	−1.77178	−	0.893545i
$112$		0			0
$113$	16.1668			1.52085			0.760424	−	0.649427i	$-0.224991\pi$
$113$	16.1668			1.52085			0.760424	+	0.649427i	$0.224991\pi$
$114$		0			0
$115$	19.4596			1.81462
$116$		0			0
$117$	7.04012	+	14.1360i	0.650859	+	1.30687i
$118$		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
$123$	10.1399	+	3.05421i	0.914282	+	0.275389i
$124$		0			0
$125$	4.02747	−	2.32526i	0.360228	−	0.207978i
$126$		0			0
$127$	−7.59392	−	1.33901i	−0.673852	−	0.118818i	−0.173756	−	0.984789i	$-0.555591\pi$
$127$	−7.59392	−	1.33901i	−0.673852	−	0.118818i	−0.500095	+	0.865970i	$0.666702\pi$
$128$		0			0
$129$	−1.14573	−	4.87060i	−0.100876	−	0.428832i
$130$		0			0
$131$	0.757267	−	2.08057i	0.0661627	−	0.181781i	−0.902205	−	0.431307i	$-0.858053\pi$
$131$	0.757267	−	2.08057i	0.0661627	−	0.181781i	0.968368	+	0.249526i	$0.0802749\pi$
$132$		0			0
$133$	3.66404	−	3.25362i	0.317712	−	0.282125i
$134$		0			0
$135$	11.4843	+	9.73525i	0.988407	+	0.837877i
$136$		0			0
$137$	0.138747	−	0.165352i	0.0118540	−	0.0141270i	−0.760085	−	0.649824i	$-0.774843\pi$
$137$	0.138747	−	0.165352i	0.0118540	−	0.0141270i	0.771939	+	0.635697i	$0.219287\pi$
$138$		0			0
$139$	−3.25695	+	18.4711i	−0.276251	+	1.56670i	0.458710	+	0.888586i	$0.348312\pi$
$139$	−3.25695	+	18.4711i	−0.276251	+	1.56670i	−0.734961	+	0.678110i	$0.762799\pi$
$140$		0			0
$141$	1.89990	+	0.225295i	0.160000	+	0.0189732i
$142$		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
$147$	−9.91963	+	0.561072i	−0.818157	+	0.0462765i
$148$		0			0
$149$	4.18590	−	0.738088i	0.342923	−	0.0604665i	0.000465272	−	1.00000i	$-0.499852\pi$
$149$	4.18590	−	0.738088i	0.342923	−	0.0604665i	0.342457	+	0.939533i	$0.388741\pi$
$150$		0			0
$151$		−	8.94139i		−	0.727640i	−0.931469	−	0.363820i	$-0.881472\pi$
$151$		−	8.94139i		−	0.727640i	0.931469	−	0.363820i	$-0.118528\pi$
$152$		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	−0.578705	−	0.815537i	$-0.696442\pi$
$157$	1.55311	−	1.30322i	0.123952	−	0.104008i	0.702656	+	0.711529i	$0.251997\pi$
$158$		0			0
$159$	11.7760	−	5.05629i	0.933900	−	0.400990i
$160$		0			0
$161$	2.58230	+	7.09481i	0.203514	+	0.559149i
$162$		0			0
$163$	4.66573	+	8.08128i	0.365448	+	0.632975i	0.988848	−	0.148929i	$-0.0475825\pi$
$163$	4.66573	+	8.08128i	0.365448	+	0.632975i	−0.623400	+	0.781903i	$0.714249\pi$
$164$		0			0
$165$	11.4373	−	10.7543i	0.890391	−	0.837225i
$166$		0			0
$167$	−9.70512	−	8.14356i	−0.751005	−	0.630168i	0.184764	−	0.982783i	$-0.440848\pi$
$167$	−9.70512	−	8.14356i	−0.751005	−	0.630168i	−0.935768	+	0.352615i	$0.885292\pi$
$168$		0			0
$169$	13.8228	+	5.03107i	1.06329	+	0.387006i
$170$		0			0
$171$	4.05813	+	12.4311i	0.310333	+	0.950628i
$172$		0			0
$173$	−8.86150	−	3.22532i	−0.673727	−	0.245217i	−0.0175755	−	0.999846i	$-0.505595\pi$
$173$	−8.86150	−	3.22532i	−0.673727	−	0.245217i	−0.656152	+	0.754629i	$0.727817\pi$
$174$		0			0
$175$	−2.92358	−	2.45318i	−0.221002	−	0.185443i
$176$		0			0
$177$	8.61867	−	8.10403i	0.647819	−	0.609137i
$178$		0			0
$179$	3.74454	+	6.48573i	0.279880	+	0.484766i	0.971355	−	0.237634i	$-0.0763720\pi$
$179$	3.74454	+	6.48573i	0.279880	+	0.484766i	−0.691475	+	0.722401i	$0.743039\pi$
$180$		0			0
$181$	5.46326	+	15.0102i	0.406081	+	1.11570i	0.959232	+	0.282618i	$0.0912030\pi$
$181$	5.46326	+	15.0102i	0.406081	+	1.11570i	−0.553151	+	0.833081i	$0.686575\pi$
$182$		0			0
$183$	11.5977	−	4.97973i	0.857329	−	0.368112i
$184$		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	0.268688	−	0.963227i	$-0.413410\pi$
$193$	11.8171	−	2.08368i	0.850616	−	0.149987i	0.581928	+	0.813241i	$0.302299\pi$
$194$		0			0
$195$	26.3750	−	1.49182i	1.88875	−	0.106831i
$196$		0			0
$197$	15.2618	+	8.81139i	1.08736	+	0.627786i	0.932871	−	0.360210i	$-0.117295\pi$
$197$	15.2618	+	8.81139i	1.08736	+	0.627786i	0.154485	+	0.987995i	$0.450628\pi$
$198$		0			0
$199$	2.12679	−	0.774087i	0.150764	−	0.0548736i	−0.265536	−	0.964101i	$-0.585549\pi$
$199$	2.12679	−	0.774087i	0.150764	−	0.0548736i	0.416300	+	0.909227i	$0.363327\pi$
$200$		0			0
$201$	−12.1720	−	1.44339i	−0.858549	−	0.101809i
$202$		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
$207$	−20.1105	−	1.23896i	−1.39778	−	0.0861135i
$208$		0			0
$209$	13.3573	−	2.74299i	0.923942	−	0.189737i
$210$		0			0
$211$	1.31716	−	3.61886i	0.0906769	−	0.249133i	−0.886061	−	0.463568i	$-0.846569\pi$
$211$	1.31716	−	3.61886i	0.0906769	−	0.249133i	0.976738	+	0.214435i	$0.0687911\pi$
$212$		0			0
$213$	−1.71525	−	7.29164i	−0.117527	−	0.499615i
$214$		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
$219$	12.4861	+	3.76090i	0.843731	+	0.254138i
$220$		0			0
$221$	6.77574	−	11.7359i	0.455786	−	0.789444i
$222$		0			0
$223$	3.57822	+	4.26435i	0.239615	+	0.285562i	0.872428	−	0.488743i	$-0.162544\pi$
$223$	3.57822	+	4.26435i	0.239615	+	0.285562i	−0.632813	+	0.774305i	$0.718100\pi$
$224$		0			0
$225$	9.11674	−	4.54039i	0.607783	−	0.302693i
$226$		0			0
$227$	24.7738			1.64430			0.822148	−	0.569274i	$-0.192776\pi$
$227$	24.7738			1.64430			0.822148	+	0.569274i	$0.192776\pi$
$228$		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
$231$	5.43869	+	2.74283i	0.357839	+	0.180465i
$232$		0			0
$233$	13.8205	+	16.4706i	0.905410	+	1.07903i	0.996534	+	0.0831862i	$0.0265096\pi$
$233$	13.8205	+	16.4706i	0.905410	+	1.07903i	−0.0911239	+	0.995840i	$0.529046\pi$
$234$		0			0
$235$	1.60022	−	2.77167i	0.104387	−	0.180804i
$236$		0			0
$237$	2.18582	−	7.25685i	0.141984	−	0.471383i
$238$		0			0
$239$	−10.5128	+	6.06955i	−0.680015	+	0.392607i	−0.799861	−	0.600186i	$-0.795093\pi$
$239$	−10.5128	+	6.06955i	−0.680015	+	0.392607i	0.119846	+	0.992793i	$0.461760\pi$
$240$		0			0
$241$	−21.4162	−	3.77626i	−1.37954	−	0.243250i	−0.565830	−	0.824522i	$-0.691444\pi$
$241$	−21.4162	−	3.77626i	−1.37954	−	0.243250i	−0.813709	+	0.581272i	$0.802555\pi$
$242$		0			0
$243$	−11.2486	−	10.7921i	−0.721597	−	0.692313i
$244$		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
$249$	−20.9289	+	13.7149i	−1.32631	+	0.869149i
$250$		0			0
$251$	−12.5021	+	14.8994i	−0.789127	+	0.940445i	−0.999307	−	0.0372181i	$-0.988150\pi$
$251$	−12.5021	+	14.8994i	−0.789127	+	0.940445i	0.210181	+	0.977663i	$0.432595\pi$
$252$		0			0
$253$	−3.64843	+	20.6913i	−0.229375	+	1.30085i
$254$		0			0
$255$	1.52134	−	12.8294i	0.0952702	−	0.803409i
$256$		0			0
$257$	−10.1861	+	3.70746i	−0.635395	+	0.231265i	−0.639578	−	0.768727i	$-0.720891\pi$
$257$	−10.1861	+	3.70746i	−0.635395	+	0.231265i	0.00418306	+	0.999991i	$0.498668\pi$
$258$		0			0
$259$	−11.7511	−	6.78452i	−0.730180	−	0.421569i
$260$		0			0
$261$	2.91786	+	1.93315i	0.180611	+	0.119659i
$262$		0			0
$263$	30.4663	−	5.37204i	1.87863	−	0.331254i	0.887150	−	0.461481i	$-0.152682\pi$
$263$	30.4663	−	5.37204i	1.87863	−	0.331254i	0.991484	+	0.130227i	$0.0415706\pi$
$264$		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	$-0.00616958\pi$
$269$	0.880210	+	4.99192i	0.0536673	+	0.304363i	−0.946145	+	0.323744i	$0.895058\pi$
$270$		0			0
$271$	−4.01481	+	3.36882i	−0.243882	+	0.204641i	−0.756533	−	0.653956i	$-0.773108\pi$
$271$	−4.01481	+	3.36882i	−0.243882	+	0.204641i	0.512650	+	0.858597i	$0.328664\pi$
$272$		0			0
$273$	4.04389	+	9.41816i	0.244747	+	0.570013i
$274$		0			0
$275$	−3.63240	−	9.97993i	−0.219042	−	0.601812i
$276$		0			0
$277$	2.15677	+	3.73563i	0.129588	+	0.224453i	0.923517	−	0.383558i	$-0.125301\pi$
$277$	2.15677	+	3.73563i	0.129588	+	0.224453i	−0.793929	+	0.608010i	$0.791968\pi$
$278$		0			0
$279$	−1.52655	−	13.4514i	−0.0913924	−	0.805314i
$280$		0			0
$281$	−8.43804	−	7.08036i	−0.503371	−	0.422379i	0.355418	−	0.934707i	$-0.384339\pi$
$281$	−8.43804	−	7.08036i	−0.503371	−	0.422379i	−0.858789	+	0.512329i	$0.828783\pi$
$282$		0			0
$283$	3.71261	+	1.35128i	0.220691	+	0.0803251i	0.450000	−	0.893029i	$-0.351424\pi$
$283$	3.71261	+	1.35128i	0.220691	+	0.0803251i	−0.229308	+	0.973354i	$0.573646\pi$
$284$		0			0
$285$	21.7863	+	1.96661i	1.29051	+	0.116492i
$286$		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
$291$	−5.10951	−	5.43398i	−0.299525	−	0.318545i
$292$		0			0
$293$	−10.0719	−	17.4450i	−0.588406	−	1.01915i	−0.994441	−	0.105291i	$-0.966422\pi$
$293$	−10.0719	−	17.4450i	−0.588406	−	1.01915i	0.406036	−	0.913857i	$-0.366911\pi$
$294$		0			0
$295$	−6.76857	−	18.5965i	−0.394081	−	1.08273i
$296$		0			0
$297$	−12.5046	+	10.3859i	−0.725590	+	0.602651i
$298$		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	0.0136720	−	0.999907i	$-0.495648\pi$
$307$	6.45677	−	1.13850i	0.368508	−	0.0649778i	0.354836	+	0.934929i	$0.384537\pi$
$308$		0			0
$309$	−1.94956	−	34.4677i	−0.110906	−	1.96080i
$310$		0			0
$311$	−1.86672	−	1.07775i	−0.105852	−	0.0611137i	0.446139	−	0.894963i	$-0.352799\pi$
$311$	−1.86672	−	1.07775i	−0.105852	−	0.0611137i	−0.551991	+	0.833850i	$0.686132\pi$
$312$		0			0
$313$	15.9106	−	5.79098i	0.899320	−	0.327326i	0.149340	−	0.988786i	$-0.452285\pi$
$313$	15.9106	−	5.79098i	0.899320	−	0.327326i	0.749980	+	0.661460i	$0.230063\pi$
$314$		0			0
$315$	7.08499	+	6.72938i	0.399194	+	0.379157i
$316$		0			0
$317$	0.961500	−	5.45293i	0.0540032	−	0.306267i	−0.945827	−	0.324670i	$-0.894747\pi$
$317$	0.961500	−	5.45293i	0.0540032	−	0.306267i	0.999831	+	0.0184023i	$0.00585798\pi$
$318$		0			0
$319$	2.34608	−	2.79595i	0.131355	−	0.156543i
$320$		0			0
$321$	−4.54137	−	6.93009i	−0.253474	−	0.386800i
$322$		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
$327$	14.5023	−	3.41144i	0.801977	−	0.188653i
$328$		0			0
$329$	1.22288	+	0.215627i	0.0674195	+	0.0118879i
$330$		0			0
$331$	6.67525	−	3.85396i	0.366905	−	0.211833i	−0.305200	−	0.952288i	$-0.598723\pi$
$331$	6.67525	−	3.85396i	0.366905	−	0.211833i	0.672106	+	0.740455i	$0.265390\pi$
$332$		0			0
$333$	29.1180	−	21.5262i	1.59566	−	1.17963i
$334$		0			0
$335$	−10.2521	+	17.7572i	−0.560133	+	0.970179i
$336$		0			0
$337$	8.14195	+	9.70320i	0.443520	+	0.528567i	0.940772	−	0.339039i	$-0.110102\pi$
$337$	8.14195	+	9.70320i	0.443520	+	0.528567i	−0.497252	+	0.867606i	$0.665657\pi$
$338$		0			0
$339$	−12.6091	+	25.0022i	−0.684832	+	1.35793i
$340$		0			0
$341$	−14.1168			−0.764466
$342$		0			0
$343$	−14.3177			−0.773081
$344$		0			0
$345$	−15.1772	+	30.0945i	−0.817115	+	1.62023i
$346$		0			0
$347$	2.93143	+	3.49354i	0.157367	+	0.187543i	0.838967	−	0.544182i	$-0.183160\pi$
$347$	2.93143	+	3.49354i	0.157367	+	0.187543i	−0.681600	+	0.731725i	$0.738716\pi$
$348$		0			0
$349$	0.809906	−	1.40280i	0.0433533	−	0.0750901i	−0.843535	−	0.537075i	$-0.819529\pi$
$349$	0.809906	−	1.40280i	0.0433533	−	0.0750901i	0.886888	+	0.461985i	$0.152863\pi$
$350$		0			0
$351$	−27.3523	−	0.137530i	−1.45996	−	0.00734079i
$352$		0			0
$353$	5.92549	−	3.42108i	0.315382	−	0.182086i	−0.333950	−	0.942591i	$-0.608382\pi$
$353$	5.92549	−	3.42108i	0.315382	−	0.182086i	0.649332	+	0.760505i	$0.275048\pi$
$354$		0			0
$355$	−12.3401	−	2.17590i	−0.654947	−	0.115485i
$356$		0			0
$357$	4.87938	−	1.14780i	0.258244	−	0.0607481i
$358$		0			0
$359$	−1.39824	+	3.84165i	−0.0737965	+	0.202754i	−0.971106	−	0.238647i	$-0.923296\pi$
$359$	−1.39824	+	3.84165i	−0.0737965	+	0.202754i	0.897310	+	0.441401i	$0.145518\pi$
$360$		0			0
$361$	15.2158	+	11.3790i	0.800829	+	0.598893i
$362$		0			0
$363$	−1.15217	−	1.75821i	−0.0604734	−	0.0922819i
$364$		0			0
$365$	14.0217	−	16.7104i	0.733927	−	0.874660i
$366$		0			0
$367$	1.71891	−	9.74845i	0.0897266	−	0.508865i	−0.906510	−	0.422185i	$-0.861263\pi$
$367$	1.71891	−	9.74845i	0.0897266	−	0.508865i	0.996236	−	0.0866798i	$-0.0276257\pi$
$368$		0			0
$369$	−12.6318	+	13.2994i	−0.657587	+	0.692337i
$370$		0			0
$371$	7.81621	−	2.84487i	0.405797	−	0.147698i
$372$		0			0
$373$	6.90673	+	3.98760i	0.357617	+	0.206470i	0.668035	−	0.744130i	$-0.267136\pi$
$373$	6.90673	+	3.98760i	0.357617	+	0.206470i	−0.310418	+	0.950600i	$0.600469\pi$
$374$		0			0
$375$	0.454875	+	8.04209i	0.0234897	+	0.415292i
$376$		0			0
$377$	6.04829	−	1.06648i	0.311503	−	0.0549264i
$378$		0			0
$379$		−	10.7490i		−	0.552141i	−0.961137	−	0.276071i	$-0.910968\pi$
$379$		−	10.7490i		−	0.552141i	0.961137	−	0.276071i	$-0.0890323\pi$
$380$		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	$-0.0984816\pi$
$383$	−0.913805	−	5.18245i	−0.0466933	−	0.264811i	−0.999213	+	0.0396663i	$0.987371\pi$
$384$		0			0
$385$	7.80554	−	6.54963i	0.397807	−	0.333800i
$386$		0			0
$387$	8.42604	+	2.02686i	0.428320	+	0.103031i
$388$		0			0
$389$	5.43196	+	14.9242i	0.275411	+	0.756686i	0.997868	+	0.0652695i	$0.0207907\pi$
$389$	5.43196	+	14.9242i	0.275411	+	0.756686i	−0.722457	+	0.691416i	$0.756987\pi$
$390$		0			0
$391$	8.64499	+	14.9736i	0.437196	+	0.757245i
$392$		0			0
$393$	2.62701	+	2.79384i	0.132515	+	0.140930i
$394$		0			0
$395$	−9.71199	−	8.14933i	−0.488663	−	0.410037i
$396$		0			0
$397$	−33.6599	−	12.2512i	−1.68934	−	0.614870i	−0.694799	−	0.719204i	$-0.744507\pi$
$397$	−33.6599	−	12.2512i	−1.68934	−	0.614870i	−0.994542	+	0.104334i	$0.966729\pi$
$398$		0			0
$399$	2.17405	+	8.20409i	0.108839	+	0.410718i
$400$		0			0
$401$	5.57564	+	2.02937i	0.278434	+	0.101342i	0.477463	−	0.878652i	$-0.341557\pi$
$401$	5.57564	+	2.02937i	0.278434	+	0.101342i	−0.199029	+	0.979994i	$0.563779\pi$
$402$		0			0
$403$	−18.1968	−	15.2690i	−0.906449	−	0.760601i
$404$		0			0
$405$	−24.0127	+	10.1677i	−1.19320	+	0.505235i
$406$		0			0
$407$	−18.8799	−	32.7009i	−0.935841	−	1.62092i
$408$		0			0
$409$	9.06715	+	24.9118i	0.448342	+	1.23181i	0.933878	+	0.357592i	$0.116402\pi$
$409$	9.06715	+	24.9118i	0.448342	+	1.23181i	−0.485536	+	0.874217i	$0.661375\pi$
$410$		0			0
$411$	0.147506	+	0.343539i	0.00727592	+	0.0169455i
$412$		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	−0.562641	−	0.826701i	$-0.690215\pi$
$421$	−16.5911	+	2.92547i	−0.808603	+	0.142578i	−0.245961	+	0.969280i	$0.579104\pi$
$422$		0			0
$423$	−1.83022	+	2.76250i	−0.0889884	+	0.134317i
$424$		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
$429$	−3.35874	+	28.3241i	−0.162162	+	1.36750i
$430$		0			0
$431$	5.03223	−	28.5392i	0.242394	−	1.37469i	−0.584073	−	0.811701i	$-0.698542\pi$
$431$	5.03223	−	28.5392i	0.242394	−	1.37469i	0.826467	−	0.562985i	$-0.190347\pi$
$432$		0			0
$433$	−17.6845	+	21.0756i	−0.849863	+	1.01283i	0.149846	+	0.988709i	$0.452122\pi$
$433$	−17.6845	+	21.0756i	−0.849863	+	1.01283i	−0.999709	+	0.0241176i	$0.992322\pi$
$434$		0			0
$435$	4.89724	−	3.20922i	0.234805	−	0.153870i
$436$		0			0
$437$	−24.9333	+	15.3419i	−1.19272	+	0.733902i
$438$		0			0
$439$	5.19707	−	14.2788i	0.248042	−	0.681491i	−0.751715	−	0.659488i	$-0.770773\pi$
$439$	5.19707	−	14.2788i	0.248042	−	0.681491i	0.999758	−	0.0220034i	$-0.00700448\pi$
$440$		0			0
$441$	6.86897	−	15.7784i	0.327094	−	0.751353i
$442$		0			0
$443$	−4.75117	−	0.837760i	−0.225735	−	0.0398032i	0.0596365	−	0.998220i	$-0.481006\pi$
$443$	−4.75117	−	0.837760i	−0.225735	−	0.0398032i	−0.285371	+	0.958417i	$0.592117\pi$
$444$		0			0
$445$	−34.4047	+	19.8636i	−1.63094	+	0.941624i
$446$		0			0
$447$	−2.12328	+	7.04921i	−0.100427	+	0.333416i
$448$		0			0
$449$	1.78666	−	3.09458i	0.0843176	−	0.146042i	−0.820783	−	0.571241i	$-0.806462\pi$
$449$	1.78666	−	3.09458i	0.0843176	−	0.146042i	0.905100	+	0.425198i	$0.139796\pi$
$450$		0			0
$451$	12.2944	+	14.6519i	0.578921	+	0.689932i
$452$		0			0
$453$	13.8280	+	6.97372i	0.649695	+	0.327654i
$454$		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
$459$	−2.38906	+	13.1617i	−0.111512	+	0.614336i
$460$		0			0
$461$	8.46456	+	10.0877i	0.394234	+	0.469830i	0.926253	−	0.376903i	$-0.123011\pi$
$461$	8.46456	+	10.0877i	0.394234	+	0.469830i	−0.532019	+	0.846732i	$0.678567\pi$
$462$		0			0
$463$	10.6868	−	18.5101i	0.496659	−	0.860238i	−0.503334	−	0.864092i	$-0.667893\pi$
$463$	10.6868	−	18.5101i	0.496659	−	0.860238i	0.999993	+	0.00385369i	$0.00122667\pi$
$464$		0			0
$465$	−21.6838	−	6.53133i	−1.00556	−	0.302883i
$466$		0			0
$467$	8.01942	−	4.63001i	0.371094	−	0.214251i	−0.302842	−	0.953041i	$-0.597935\pi$
$467$	8.01942	−	4.63001i	0.371094	−	0.214251i	0.673936	+	0.738789i	$0.264602\pi$
$468$		0			0
$469$	−7.83459	−	1.38145i	−0.361768	−	0.0637894i
$470$		0			0
$471$	0.804111	+	3.41833i	0.0370515	+	0.157508i
$472$		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
$477$	−1.36494	+	22.1554i	−0.0624961	+	1.01442i
$478$		0			0
$479$	3.61743	−	4.31108i	0.165284	−	0.196978i	−0.677045	−	0.735942i	$-0.736740\pi$
$479$	3.61743	−	4.31108i	0.165284	−	0.196978i	0.842329	+	0.538964i	$0.181184\pi$
$480$		0			0
$481$	11.0333	−	62.5731i	0.503076	−	2.85309i
$482$		0			0
$483$	−12.9862	−	1.53994i	−0.590894	−	0.0700697i
$484$		0			0
$485$	−11.7249	+	4.26751i	−0.532400	+	0.193778i
$486$		0			0
$487$	−17.7438	−	10.2444i	−0.804048	−	0.464217i	0.0408365	−	0.999166i	$-0.486998\pi$
$487$	−17.7438	−	10.2444i	−0.804048	−	0.464217i	−0.844885	+	0.534948i	$0.820331\pi$
$488$		0			0
$489$	−16.1368	+	0.912725i	−0.729730	+	0.0412748i
$490$		0			0
$491$	32.2309	−	5.68317i	1.45456	−	0.256478i	0.610196	−	0.792250i	$-0.291091\pi$
$491$	32.2309	−	5.68317i	1.45456	−	0.256478i	0.844363	+	0.535772i	$0.179979\pi$
$492$		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	−0.922776	−	0.385336i	$-0.874086\pi$
$499$	−15.7157	+	13.1871i	−0.703533	+	0.590334i	0.219243	+	0.975670i	$0.429641\pi$
$500$		0			0
$501$	20.1635	−	8.65763i	0.900838	−	0.386794i
$502$		0			0
$503$	7.95923	+	21.8678i	0.354885	+	0.975037i	0.980778	+	0.195128i	$0.0625124\pi$
$503$	7.95923	+	21.8678i	0.354885	+	0.975037i	−0.625893	+	0.779909i	$0.715265\pi$
$504$		0			0
$505$	8.56766	+	14.8396i	0.381256	+	0.660354i
$506$		0			0
$507$	−18.5615	+	17.4532i	−0.824345	+	0.775122i
$508$		0			0
$509$	−16.6553	−	13.9754i	−0.738232	−	0.619450i	0.194130	−	0.980976i	$-0.437812\pi$
$509$	−16.6553	−	13.9754i	−0.738232	−	0.619450i	−0.932362	+	0.361525i	$0.882256\pi$
$510$		0			0
$511$	7.95315	+	2.89471i	0.351827	+	0.128054i
$512$		0			0
$513$	−22.3899	−	3.41950i	−0.988538	−	0.150974i
$514$		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
$519$	11.8994	−	11.1889i	0.522326	−	0.491137i
$520$		0			0
$521$	−7.53777	−	13.0558i	−0.330236	−	0.571985i	0.652322	−	0.757942i	$-0.273795\pi$
$521$	−7.53777	−	13.0558i	−0.330236	−	0.571985i	−0.982558	+	0.185957i	$0.940462\pi$
$522$		0			0
$523$	−2.38040	−	6.54010i	−0.104088	−	0.285979i	0.876706	−	0.481027i	$-0.159736\pi$
$523$	−2.38040	−	6.54010i	−0.104088	−	0.285979i	−0.980794	+	0.195048i	$0.937514\pi$
$524$		0			0
$525$	6.07407	−	2.60803i	0.265094	−	0.113824i
$526$		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
$537$	−12.9508	+	0.732519i	−0.558867	+	0.0316105i
$538$		0			0
$539$	−15.5407	−	8.97240i	−0.669384	−	0.386469i
$540$		0			0
$541$	−4.63626	+	1.68746i	−0.199328	+	0.0725495i	−0.439755	−	0.898118i	$-0.644935\pi$
$541$	−4.63626	+	1.68746i	−0.199328	+	0.0725495i	0.240427	+	0.970667i	$0.422713\pi$
$542$		0			0
$543$	−27.4744	−	3.25799i	−1.17904	−	0.139814i
$544$		0			0
$545$	4.32762	−	24.5432i	0.185375	−	1.05131i
$546$		0			0
$547$	−9.08478	+	10.8268i	−0.388437	+	0.462922i	−0.924458	−	0.381283i	$-0.875482\pi$
$547$	−9.08478	+	10.8268i	−0.388437	+	0.462922i	0.536021	+	0.844205i	$0.319927\pi$
$548$		0			0
$549$	−1.34427	+	21.8199i	−0.0573720	+	0.931250i
$550$		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
$555$	−13.8706	−	58.9648i	−0.588773	−	2.50292i
$556$		0			0
$557$	0.424076	+	0.0747760i	0.0179687	+	0.00316836i	0.182625	−	0.983183i	$-0.441540\pi$
$557$	0.424076	+	0.0747760i	0.0179687	+	0.00316836i	−0.164657	+	0.986351i	$0.552652\pi$
$558$		0			0
$559$	13.1694	−	7.60334i	0.557005	−	0.321587i
$560$		0			0
$561$	13.3562	+	4.02299i	0.563899	+	0.169851i
$562$		0			0
$563$	2.44919	−	4.24212i	0.103221	−	0.178784i	−0.809789	−	0.586721i	$-0.800418\pi$
$563$	2.44919	−	4.24212i	0.103221	−	0.178784i	0.913010	+	0.407937i	$0.133752\pi$
$564$		0			0
$565$	30.1093	+	35.8829i	1.26671	+	1.50961i
$566$		0			0
$567$	−6.89355	−	7.40557i	−0.289502	−	0.311005i
$568$		0			0
$569$	9.33523			0.391353			0.195677	−	0.980668i	$-0.437310\pi$
$569$	9.33523			0.391353			0.195677	+	0.980668i	$0.437310\pi$
$570$		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
$573$	−11.7806	−	5.94117i	−0.492141	−	0.248196i
$574$		0			0
$575$	14.6563	+	17.4667i	0.611209	+	0.728410i
$576$		0			0
$577$	−1.23938	+	2.14667i	−0.0515960	+	0.0893669i	−0.890670	−	0.454651i	$-0.849764\pi$
$577$	−1.23938	+	2.14667i	−0.0515960	+	0.0893669i	0.839074	+	0.544017i	$0.183097\pi$
$578$		0			0
$579$	−5.99417	+	19.9005i	−0.249109	+	0.827036i
$580$		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
$585$	−18.2637	+	41.9528i	−0.755112	+	1.73454i
$586$		0			0
$587$	13.2139	−	36.3050i	0.545398	−	1.49847i	−0.294462	−	0.955663i	$-0.595140\pi$
$587$	13.2139	−	36.3050i	0.545398	−	1.49847i	0.839859	−	0.542804i	$-0.182637\pi$
$588$		0			0
$589$	−13.0605	−	14.7080i	−0.538150	−	0.606034i
$590$		0			0
$591$	−25.5301	+	16.7302i	−1.05017	+	0.688188i
$592$		0			0
$593$	2.81505	−	3.35484i	0.115600	−	0.137767i	−0.705141	−	0.709067i	$-0.749116\pi$
$593$	2.81505	−	3.35484i	0.115600	−	0.137767i	0.820741	+	0.571300i	$0.193561\pi$
$594$		0			0
$595$	1.45606	−	8.25771i	0.0596925	−	0.338533i
$596$		0			0
$597$	−0.461622	+	3.89284i	−0.0188929	+	0.159323i
$598$		0			0
$599$	−40.2689	+	14.6567i	−1.64534	+	0.598855i	−0.987961	−	0.154704i	$-0.950558\pi$
$599$	−40.2689	+	14.6567i	−1.64534	+	0.598855i	−0.657380	+	0.753559i	$0.728335\pi$
$600$		0			0
$601$	−24.0390	−	13.8789i	−0.980571	−	0.566133i	−0.0781288	−	0.996943i	$-0.524895\pi$
$601$	−24.0390	−	13.8789i	−0.980571	−	0.566133i	−0.902443	+	0.430810i	$0.858228\pi$
$602$		0			0
$603$	11.7256	−	17.6985i	0.477505	−	0.720737i
$604$		0			0
$605$	−3.46299	+	0.610618i	−0.140791	+	0.0248252i
$606$		0			0
$607$			16.1090i			0.653844i	0.945051	+	0.326922i	$0.106011\pi$
$607$			16.1090i			0.653844i	−0.945051	+	0.326922i	$0.893989\pi$
$608$		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	−0.225364	−	0.974275i	$-0.572357\pi$
$613$	17.2068	−	14.4382i	0.694975	−	0.583154i	0.920339	+	0.391121i	$0.127913\pi$
$614$		0			0
$615$	12.1057	+	28.1940i	0.488150	+	1.13689i
$616$		0			0
$617$	−15.8059	−	43.4264i	−0.636322	−	1.74828i	−0.662982	−	0.748636i	$-0.730709\pi$
$617$	−15.8059	−	43.4264i	−0.636322	−	1.74828i	0.0266596	−	0.999645i	$-0.491513\pi$
$618$		0			0
$619$	20.8534	+	36.1192i	0.838170	+	1.45175i	0.891423	+	0.453172i	$0.149708\pi$
$619$	20.8534	+	36.1192i	0.838170	+	1.45175i	−0.0532532	+	0.998581i	$0.516959\pi$
$620$		0			0
$621$	17.6010	−	30.1349i	0.706303	−	1.20927i
$622$		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
$627$	−6.17575	+	22.7965i	−0.246636	+	0.910406i
$628$		0			0
$629$	−29.1994	−	10.6277i	−1.16426	−	0.423755i
$630$		0			0
$631$	3.34686	+	2.80835i	0.133236	+	0.111799i	0.706971	−	0.707243i	$-0.250061\pi$
$631$	3.34686	+	2.80835i	0.133236	+	0.111799i	−0.573734	+	0.819042i	$0.694506\pi$
$632$		0			0
$633$	4.56932	+	4.85948i	0.181614	+	0.193147i
$634$		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
$639$	12.6144	+	3.03436i	0.499018	+	0.120038i
$640$		0			0
$641$	2.18494	−	1.83339i	0.0863001	−	0.0724144i	−0.598617	−	0.801035i	$-0.704283\pi$
$641$	2.18494	−	1.83339i	0.0863001	−	0.0724144i	0.684917	+	0.728621i	$0.259838\pi$
$642$		0			0
$643$	−7.65253	−	43.3997i	−0.301786	−	1.71152i	−0.638258	−	0.769823i	$-0.720345\pi$
$643$	−7.65253	−	43.3997i	−0.301786	−	1.71152i	0.336471	−	0.941694i	$-0.390766\pi$
$644$		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
$651$	−0.496187	−	8.77247i	−0.0194471	−	0.343820i
$652$		0			0
$653$	35.1702	+	20.3055i	1.37632	+	0.794617i	0.991714	−	0.128465i	$-0.0410051\pi$
$653$	35.1702	+	20.3055i	1.37632	+	0.794617i	0.384603	+	0.923082i	$0.374338\pi$
$654$		0			0
$655$	6.02826	−	2.19411i	0.235543	−	0.0857308i
$656$		0			0
$657$	−15.5546	+	16.3766i	−0.606843	+	0.638912i
$658$		0			0
$659$	6.33474	−	35.9261i	0.246766	−	1.39948i	−0.569588	−	0.821930i	$-0.692897\pi$
$659$	6.33474	−	35.9261i	0.246766	−	1.39948i	0.816354	−	0.577552i	$-0.195992\pi$
$660$		0			0
$661$	−2.71797	+	3.23916i	−0.105717	+	0.125989i	−0.816308	−	0.577616i	$-0.803983\pi$
$661$	−2.71797	+	3.23916i	−0.105717	+	0.125989i	0.710591	+	0.703605i	$0.248427\pi$
$662$		0			0
$663$	12.8651	+	19.6320i	0.499640	+	0.762445i
$664$		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
$669$	−9.38565	+	2.20783i	−0.362870	+	0.0853598i
$670$		0			0
$671$	22.4500	+	3.95854i	0.866672	+	0.152818i
$672$		0			0
$673$	22.4627	−	12.9688i	0.865874	−	0.499912i	−0.000101249	−	1.00000i	$-0.500032\pi$
$673$	22.4627	−	12.9688i	0.865874	−	0.499912i	0.865975	+	0.500088i	$0.166699\pi$
$674$		0			0
$675$	−0.0886972	+	17.6404i	−0.00341396	+	0.678978i
$676$		0			0
$677$	−16.1874	+	28.0374i	−0.622132	+	1.07756i	0.366956	+	0.930238i	$0.380400\pi$
$677$	−16.1874	+	28.0374i	−0.622132	+	1.07756i	−0.989088	+	0.147326i	$0.952934\pi$
$678$		0			0
$679$	−3.11180	−	3.70850i	−0.119420	−	0.142319i
$680$		0			0
$681$	−19.3220	+	38.3130i	−0.740420	+	1.46816i
$682$		0			0
$683$	12.5635			0.480728			0.240364	−	0.970683i	$-0.422733\pi$
$683$	12.5635			0.480728			0.240364	+	0.970683i	$0.422733\pi$
$684$		0			0
$685$	0.625411			0.0238957
$686$		0			0
$687$	19.3383	−	38.3454i	0.737802	−	1.46297i
$688$		0			0
$689$	25.0360	+	29.8367i	0.953796	+	1.13669i
$690$		0			0
$691$	7.86815	−	13.6280i	0.299319	−	0.518435i	−0.676662	−	0.736294i	$-0.736574\pi$
$691$	7.86815	−	13.6280i	0.299319	−	0.518435i	0.975980	+	0.217859i	$0.0699073\pi$
$692$		0			0
$693$	−8.48365	+	6.27176i	−0.322267	+	0.238244i
$694$		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
$699$	−36.2511	+	8.52752i	−1.37114	+	0.322541i
$700$		0			0
$701$	10.8602	−	29.8381i	0.410183	−	1.12697i	−0.546911	−	0.837191i	$-0.684197\pi$
$701$	10.8602	−	29.8381i	0.410183	−	1.12697i	0.957094	−	0.289777i	$-0.0935812\pi$
$702$		0			0
$703$	16.6033	−	49.9249i	0.626204	−	1.88295i
$704$		0			0
$705$	3.03835	+	4.63649i	0.114431	+	0.174620i
$706$		0			0
$707$	−4.27347	+	5.09293i	−0.160721	+	0.191539i
$708$		0			0
$709$	6.11366	−	34.6723i	0.229603	−	1.30214i	−0.624084	−	0.781358i	$-0.714528\pi$
$709$	6.11366	−	34.6723i	0.229603	−	1.30214i	0.853687	−	0.520787i	$-0.174361\pi$
$710$		0			0
$711$	9.51801	+	9.04028i	0.356953	+	0.339037i
$712$		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
$717$	−1.18735	−	20.9920i	−0.0443422	−	0.783961i
$718$		0			0
$719$	14.7056	−	2.59299i	0.548426	−	0.0967023i	0.107432	−	0.994212i	$-0.465737\pi$
$719$	14.7056	−	2.59299i	0.548426	−	0.0967023i	0.440994	+	0.897510i	$0.354626\pi$
$720$		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	−0.113791	−	0.993505i	$-0.536300\pi$
$727$	22.7799	−	19.1146i	0.844860	−	0.708922i	0.958651	+	0.284583i	$0.0918551\pi$
$728$		0			0
$729$	25.4633	−	8.97894i	0.943084	−	0.332553i
$730$		0			0
$731$	−2.54354	−	6.98831i	−0.0940761	−	0.258472i
$732$		0			0
$733$	1.63062	+	2.82432i	0.0602284	+	0.104319i	0.894567	−	0.446933i	$-0.147484\pi$
$733$	1.63062	+	2.82432i	0.0602284	+	0.104319i	−0.834339	+	0.551252i	$0.814150\pi$
$734$		0			0
$735$	−19.7198	−	20.9720i	−0.727375	−	0.773565i
$736$		0			0
$737$	−16.9590	−	14.2303i	−0.624692	−	0.524178i
$738$		0			0
$739$	5.54154	+	2.01696i	0.203849	+	0.0741950i	0.441927	−	0.897051i	$-0.354295\pi$
$739$	5.54154	+	2.01696i	0.203849	+	0.0741950i	−0.238078	+	0.971246i	$0.576517\pi$
$740$		0			0
$741$	−32.6179	+	22.7055i	−1.19825	+	0.834106i
$742$		0			0
$743$	27.7676	+	10.1066i	1.01870	+	0.370775i	0.796766	−	0.604288i	$-0.206542\pi$
$743$	27.7676	+	10.1066i	1.01870	+	0.370775i	0.221930	+	0.975063i	$0.428764\pi$
$744$		0			0
$745$	9.43410	+	7.91615i	0.345639	+	0.290025i
$746$		0			0
$747$	−4.88714	−	43.0635i	−0.178811	−	1.57561i
$748$		0			0
$749$	−2.68881	−	4.65716i	−0.0982470	−	0.170169i
$750$		0			0
$751$	6.20481	+	17.0476i	0.226417	+	0.622074i	0.999932	−	0.0117037i	$-0.00372548\pi$
$751$	6.20481	+	17.0476i	0.226417	+	0.622074i	−0.773515	+	0.633778i	$0.781503\pi$
$752$		0			0
$753$	−13.2913	−	30.9553i	−0.484363	−	1.12807i
$754$		0			0
$755$	19.8458	−	16.6526i	0.722261	−	0.606049i
$756$		0			0
$757$	−3.70068	−	20.9876i	−0.134504	−	0.762807i	−0.975204	−	0.221307i	$-0.928968\pi$
$757$	−3.70068	−	20.9876i	−0.134504	−	0.762807i	0.840701	−	0.541500i	$-0.182143\pi$
$758$		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
$765$	18.6543	+	12.3589i	0.674447	+	0.446837i
$766$		0			0
$767$	31.1375	+	17.9773i	1.12431	+	0.649122i
$768$		0			0
$769$	−25.9596	+	9.44854i	−0.936129	+	0.340723i	−0.764636	−	0.644462i	$-0.777081\pi$
$769$	−25.9596	+	9.44854i	−0.936129	+	0.340723i	−0.171493	+	0.985185i	$0.554859\pi$
$770$		0			0
$771$	2.21092	−	18.6446i	0.0796244	−	0.671468i
$772$		0			0
$773$	7.60654	−	43.1388i	0.273588	−	1.55160i	−0.469823	−	0.882761i	$-0.655682\pi$
$773$	7.60654	−	43.1388i	0.273588	−	1.55160i	0.743411	−	0.668835i	$-0.233207\pi$
$774$		0			0
$775$	−9.84744	+	11.7357i	−0.353731	+	0.421560i
$776$		0			0
$777$	19.6575	−	12.8818i	0.705208	−	0.462131i
$778$		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
$783$	−5.26538	+	3.00477i	−0.188169	+	0.107382i
$784$		0			0
$785$	5.78507	+	1.02006i	0.206478	+	0.0364077i
$786$		0			0
$787$	−31.9379	+	18.4393i	−1.13846	+	0.657291i	−0.946049	−	0.324023i	$-0.894964\pi$
$787$	−31.9379	+	18.4393i	−1.13846	+	0.657291i	−0.192412	+	0.981314i	$0.561631\pi$
$788$		0			0
$789$	−15.4539	+	51.3064i	−0.550172	+	1.82656i
$790$		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
$795$	33.1545	+	16.7204i	1.17587	+	0.593013i
$796$		0			0
$797$	47.4368			1.68030			0.840148	−	0.542357i	$-0.182468\pi$
$797$	47.4368			1.68030			0.840148	+	0.542357i	$0.182468\pi$
$798$		0			0
$799$	2.84362			0.100600
$800$		0			0
$801$	36.8203	−	18.3376i	1.30098	−	0.647926i
$802$		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
$807$	−8.40657	−	2.53212i	−0.295925	−	0.0891349i
$808$		0			0
$809$	−46.6699	+	26.9449i	−1.64083	+	0.947331i	−0.660286	+	0.751015i	$0.729565\pi$
$809$	−46.6699	+	26.9449i	−1.64083	+	0.947331i	−0.980540	+	0.196317i	$0.937102\pi$
$810$		0			0
$811$	−5.26849	−	0.928977i	−0.185002	−	0.0326208i	0.0803796	−	0.996764i	$-0.474387\pi$
$811$	−5.26849	−	0.928977i	−0.185002	−	0.0326208i	−0.265381	+	0.964144i	$0.585498\pi$
$812$		0			0
$813$	−2.07863	−	8.83641i	−0.0729008	−	0.309906i
$814$		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
$819$	−17.7193	−	1.09164i	−0.619162	−	0.0381450i
$820$		0			0
$821$	−14.7984	+	17.6360i	−0.516468	+	0.615502i	−0.959742	−	0.280884i	$-0.909372\pi$
$821$	−14.7984	+	17.6360i	−0.516468	+	0.615502i	0.443274	+	0.896386i	$0.353817\pi$
$822$		0			0
$823$	−1.89577	+	10.7514i	−0.0660824	+	0.374772i	0.933775	+	0.357862i	$0.116494\pi$
$823$	−1.89577	+	10.7514i	−0.0660824	+	0.374772i	−0.999857	+	0.0169103i	$0.994617\pi$
$824$		0			0
$825$	18.2671	+	2.16616i	0.635979	+	0.0754160i
$826$		0			0
$827$	−0.866657	+	0.315437i	−0.0301366	+	0.0109688i	−0.357044	−	0.934087i	$-0.616216\pi$
$827$	−0.866657	+	0.315437i	−0.0301366	+	0.0109688i	0.326908	+	0.945056i	$0.393993\pi$
$828$		0			0
$829$	36.7431	+	21.2136i	1.27614	+	0.736780i	0.976137	−	0.217158i	$-0.0696786\pi$
$829$	36.7431	+	21.2136i	1.27614	+	0.736780i	0.300004	+	0.953938i	$0.403012\pi$
$830$		0			0
$831$	−7.45935	+	0.421914i	−0.258762	+	0.0146360i
$832$		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	0.994924	+	0.100632i	$0.0320864\pi$
$839$	2.73490	+	15.5104i	0.0944194	+	0.535479i	−0.900504	+	0.434847i	$0.856802\pi$
$840$		0			0
$841$	−21.1725	+	17.7659i	−0.730087	+	0.612616i
$842$		0			0
$843$	17.5310	−	7.52731i	0.603799	−	0.259254i
$844$		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
$849$	−4.98536	+	4.68768i	−0.171097	+	0.160881i
$850$		0			0
$851$	62.1009	+	52.1088i	2.12879	+	1.78627i
$852$		0			0
$853$	−30.2008	−	10.9922i	−1.03405	−	0.376365i	−0.231431	−	0.972851i	$-0.574341\pi$
$853$	−30.2008	−	10.9922i	−1.03405	−	0.376365i	−0.802623	+	0.596486i	$0.796563\pi$
$854$		0			0
$855$	−20.0333	+	32.1590i	−0.685125	+	1.09981i
$856$		0			0
$857$	23.1422	+	8.42308i	0.790524	+	0.287727i	0.705554	−	0.708656i	$-0.250698\pi$
$857$	23.1422	+	8.42308i	0.790524	+	0.287727i	0.0849699	+	0.996384i	$0.472921\pi$
$858$		0			0
$859$	11.9557	+	10.0320i	0.407923	+	0.342288i	0.823547	−	0.567248i	$-0.191992\pi$
$859$	11.9557	+	10.0320i	0.407923	+	0.342288i	−0.415623	+	0.909537i	$0.636437\pi$
$860$		0			0
$861$	−8.67289	+	8.15502i	−0.295571	+	0.277922i
$862$		0			0
$863$	−7.05542	−	12.2203i	−0.240169	−	0.415985i	0.720593	−	0.693358i	$-0.243870\pi$
$863$	−7.05542	−	12.2203i	−0.240169	−	0.415985i	−0.960762	+	0.277373i	$0.910536\pi$
$864$		0			0
$865$	−9.34505	−	25.6753i	−0.317741	−	0.872987i
$866$		0			0
$867$	−16.5086	+	7.08830i	−0.560660	+	0.240731i
$868$		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	0.138410	−	0.990375i	$-0.455801\pi$
$877$	17.9817	−	3.17067i	0.607200	−	0.107066i	0.468791	+	0.883309i	$0.344690\pi$
$878$		0			0
$879$	34.8344	−	1.97029i	1.17493	−	0.0664564i
$880$		0			0
$881$	−5.32331	−	3.07342i	−0.179347	−	0.103546i	0.407639	−	0.913143i	$-0.366352\pi$
$881$	−5.32331	−	3.07342i	−0.179347	−	0.103546i	−0.586986	+	0.809597i	$0.699686\pi$
$882$		0			0
$883$	−51.4745	+	18.7352i	−1.73225	+	0.630489i	−0.998787	−	0.0492352i	$-0.984322\pi$
$883$	−51.4745	+	18.7352i	−1.73225	+	0.630489i	−0.733468	+	0.679724i	$0.762099\pi$
$884$		0			0
$885$	34.0387	+	4.03640i	1.14420	+	0.135682i
$886$		0			0
$887$	−7.62578	+	43.2479i	−0.256049	+	1.45212i	0.537318	+	0.843379i	$0.319437\pi$
$887$	−7.62578	+	43.2479i	−0.256049	+	1.45212i	−0.793367	+	0.608744i	$0.791674\pi$
$888$		0			0
$889$	5.57202	−	6.64047i	0.186879	−	0.222714i
$890$		0			0
$891$	−6.30914	−	27.4388i	−0.211364	−	0.919236i
$892$		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
$897$	−14.0220	−	59.6084i	−0.468180	−	1.99027i
$898$		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
$903$	5.38579	+	1.62224i	0.179228	+	0.0539848i
$904$		0			0
$905$	−23.1408	+	40.0811i	−0.769228	+	1.33234i
$906$		0			0
$907$	21.7940	+	25.9730i	0.723656	+	0.862420i	0.994981	−	0.100068i	$-0.0319060\pi$
$907$	21.7940	+	25.9730i	0.723656	+	0.862420i	−0.271324	+	0.962488i	$0.587462\pi$
$908$		0			0
$909$	−7.90944	−	15.8815i	−0.262340	−	0.526756i
$910$		0			0
$911$	−15.3654			−0.509077			−0.254539	−	0.967063i	$-0.581924\pi$
$911$	−15.3654			−0.509077			−0.254539	+	0.967063i	$0.581924\pi$
$912$		0			0
$913$	−45.1937			−1.49569
$914$		0			0
$915$	32.6525	+	16.4673i	1.07946	+	0.544391i
$916$		0			0
$917$	1.59991	+	1.90670i	0.0528336	+	0.0629646i
$918$		0			0
$919$	6.10344	−	10.5715i	0.201334	−	0.348720i	−0.747625	−	0.664121i	$-0.768806\pi$
$919$	6.10344	−	10.5715i	0.201334	−	0.348720i	0.948958	+	0.315401i	$0.102139\pi$
$920$		0			0
$921$	−3.27516	+	10.8734i	−0.107920	+	0.358292i
$922$		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
$927$	54.8253	+	23.8676i	1.80070	+	0.783915i
$928$		0			0
$929$	6.30750	−	17.3297i	0.206942	−	0.568569i	−0.792188	−	0.610278i	$-0.791058\pi$
$929$	6.30750	−	17.3297i	0.206942	−	0.568569i	0.999130	+	0.0417085i	$0.0132801\pi$
$930$		0			0
$931$	−5.02970	−	24.4926i	−0.164842	−	0.802714i
$932$		0			0
$933$	3.12268	−	2.04633i	0.102232	−	0.0669938i
$934$		0			0
$935$	14.9988	−	17.8749i	0.490513	−	0.584570i
$936$		0			0
$937$	−4.35606	+	24.7045i	−0.142306	+	0.807060i	0.827184	+	0.561931i	$0.189941\pi$
$937$	−4.35606	+	24.7045i	−0.142306	+	0.807060i	−0.969491	+	0.245129i	$0.921170\pi$
$938$		0			0
$939$	−3.45342	+	29.1225i	−0.112698	+	0.950378i
$940$		0			0
$941$	−43.7853	+	15.9365i	−1.42736	+	0.519517i	−0.936174	−	0.351538i	$-0.885659\pi$
$941$	−43.7853	+	15.9365i	−1.42736	+	0.519517i	−0.491187	+	0.871054i	$0.663437\pi$
$942$		0			0
$943$	−35.5619	−	20.5317i	−1.15806	−	0.668604i
$944$		0			0
$945$	−15.9329	+	5.70854i	−0.518297	+	0.185699i
$946$		0			0
$947$	−54.8110	+	9.66466i	−1.78112	+	0.314059i	−0.964690	−	0.263387i	$-0.915160\pi$
$947$	−54.8110	+	9.66466i	−1.78112	+	0.314059i	−0.816429	+	0.577446i	$0.804049\pi$
$948$		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	0.990600	+	0.136792i	$0.0436792\pi$
$953$	3.28854	+	18.6502i	0.106526	+	0.604140i	−0.884074	+	0.467348i	$0.845210\pi$
$954$		0			0
$955$	−16.9074	+	14.1870i	−0.547109	+	0.459079i
$956$		0			0
$957$	2.49417	+	5.80889i	0.0806252	+	0.187775i
$958$		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
$963$	14.2594	−	1.61826i	0.459504	−	0.0521476i
$964$		0			0
$965$	26.6332	+	22.3479i	0.857353	+	0.719405i
$966$		0			0
$967$	23.9285	+	8.70925i	0.769488	+	0.280071i	0.696782	−	0.717283i	$-0.254614\pi$
$967$	23.9285	+	8.70925i	0.769488	+	0.280071i	0.0727056	+	0.997353i	$0.476837\pi$
$968$		0			0
$969$	8.16540	+	17.6376i	0.262310	+	0.566601i
$970$		0			0
$971$	−14.6975	−	5.34944i	−0.471664	−	0.171672i	0.0952419	−	0.995454i	$-0.469638\pi$
$971$	−14.6975	−	5.34944i	−0.471664	−	0.171672i	−0.566906	+	0.823782i	$0.691860\pi$
$972$		0			0
$973$	−16.1519	−	13.5531i	−0.517807	−	0.434492i
$974$		0			0
$975$	21.2038	+	22.5503i	0.679064	+	0.722187i
$976$		0			0
$977$	10.2781	+	17.8022i	0.328827	+	0.569544i	0.982279	−	0.187423i	$-0.0600135\pi$
$977$	10.2781	+	17.8022i	0.328827	+	0.569544i	−0.653453	+	0.756967i	$0.726680\pi$
$978$		0			0
$979$	−14.6704	−	40.3065i	−0.468867	−	1.28820i
$980$		0			0
$981$	−6.03501	+	25.0886i	−0.192683	+	0.801018i
$982$		0			0
$983$	14.5443	−	12.2041i	0.463890	−	0.389250i	−0.380670	−	0.924711i	$-0.624307\pi$
$983$	14.5443	−	12.2041i	0.463890	−	0.389250i	0.844560	+	0.535461i	$0.179862\pi$
$984$		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	0.524852	−	0.851193i	$-0.324121\pi$
$991$	41.2131	−	7.26698i	1.30918	−	0.230843i	0.784325	+	0.620350i	$0.213009\pi$
$992$		0			0
$993$	0.753924	+	13.3292i	0.0239251	+	0.422989i
$994$		0			0
$995$	5.67907	+	3.27881i	0.180039	+	0.103945i
$996$		0			0
$997$	14.4637	−	5.26435i	0.458069	−	0.166724i	−0.102671	−	0.994715i	$-0.532739\pi$
$997$	14.4637	−	5.26435i	0.458069	−	0.166724i	0.560740	+	0.827992i	$0.310517\pi$
$998$		0			0
$999$	10.5804	+	61.8204i	0.334748	+	1.95591i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.3	✓	18	12.11	even	2
114.2.l.a.71.3	yes	18	76.71	even	18
114.2.l.b.53.2	yes	18	4.3	odd	2
114.2.l.b.71.2	yes	18	228.71	odd	18
912.2.cc.c.641.2		18	57.14	even	18	inner
912.2.cc.c.737.2		18	1.1	even	1	trivial
912.2.cc.d.641.1		18	19.14	odd	18
912.2.cc.d.737.1		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.779936 + 1.54651i) q^{3} +(1.86241 + 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(-1.78340 - 2.41236i) q^{9} +O(q^{10})\)	\(q+(-0.779936 + 1.54651i) q^{3} +(1.86241 + 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(-1.78340 - 2.41236i) q^{9} +(-2.70920 + 1.56416i) q^{11} +(-5.18404 - 0.914087i) q^{13} +(-4.88511 + 1.14915i) q^{15} +(-0.880484 + 2.41911i) q^{17} +(-4.13617 - 1.37554i) q^{19} +(-1.06723 - 1.62858i) q^{21} +(4.31710 - 5.14492i) q^{23} +(-0.589524 + 3.34336i) q^{25} +(5.12168 - 0.876562i) q^{27} +(-1.09635 + 0.399039i) q^{29} +(3.90801 + 2.25629i) q^{31} +(-0.305986 - 5.40975i) q^{33} +(-3.20767 + 0.565599i) q^{35} +12.0703i q^{37} +(5.45687 - 7.30426i) q^{39} +(-1.06170 - 6.02118i) q^{41} +(-2.21295 + 1.85688i) q^{43} +(2.03290 - 8.45114i) q^{45} +(-0.377793 - 1.03798i) q^{47} +(2.86813 + 4.96774i) q^{49} +(-3.05446 - 3.24843i) q^{51} +(-5.66806 - 4.75606i) q^{53} +(-8.51736 - 3.10007i) q^{55} +(5.35324 - 5.32380i) q^{57} +(-6.41833 - 2.33608i) q^{59} +(-5.58223 - 4.68405i) q^{61} +(3.35099 - 0.380292i) q^{63} +(-7.62598 - 13.2086i) q^{65} +(2.42040 + 6.64999i) q^{67} +(4.58962 + 10.6892i) q^{69} +(-3.31294 + 2.77989i) q^{71} +(-1.30735 - 7.41438i) q^{73} +(-4.71075 - 3.51931i) q^{75} -3.51674i q^{77} +(-4.30920 + 0.759829i) q^{79} +(-2.63897 + 8.60441i) q^{81} +(12.5112 + 7.22333i) q^{83} +(-7.00913 + 2.55111i) q^{85} +(0.237965 - 2.00675i) q^{87} +(-2.38095 + 13.5030i) q^{89} +(3.80378 - 4.53316i) q^{91} +(-6.53737 + 4.28402i) q^{93} +(-4.65018 - 11.7422i) q^{95} +(-1.47287 + 4.04669i) q^{97} +(8.60490 + 3.74605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 - 3 * q^9	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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