LMFDB - Embedded newform 912.2.cc.d.737.1

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			737.1
Root			$-0.396613 - 1.68603i$ of defining polynomial
Character	$\chi$	$=$	912.737
Dual form			912.2.cc.d.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26184 - 1.18649i) q^{3} +(-1.86241 - 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(0.184473 + 2.99432i) q^{9} +O(q^{10})$	\(q+(-1.26184 - 1.18649i) q^{3} +(-1.86241 - 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(0.184473 + 2.99432i) q^{9} +(2.70920 - 1.56416i) q^{11} +(-5.18404 - 0.914087i) q^{13} +(-0.283400 + 5.01044i) q^{15} +(0.880484 - 2.41911i) q^{17} +(-4.13617 - 1.37554i) q^{19} +(1.86437 - 0.561563i) q^{21} +(-4.31710 + 5.14492i) q^{23} +(-0.589524 + 3.34336i) q^{25} +(3.31997 - 3.99723i) q^{27} +(1.09635 - 0.399039i) q^{29} +(3.90801 + 2.25629i) q^{31} +(-5.27443 - 1.24073i) q^{33} +(3.20767 - 0.565599i) q^{35} +12.0703i q^{37} +(5.45687 + 7.30426i) q^{39} +(1.06170 + 6.02118i) q^{41} +(-2.21295 + 1.85688i) q^{43} +(6.30245 - 5.98611i) q^{45} +(0.377793 + 1.03798i) q^{47} +(2.86813 + 4.96774i) q^{49} +(-3.98128 + 2.00784i) q^{51} +(5.66806 + 4.75606i) q^{53} +(-8.51736 - 3.10007i) q^{55} +(3.58710 + 6.64324i) q^{57} +(6.41833 + 2.33608i) q^{59} +(-5.58223 - 4.68405i) q^{61} +(-3.01883 - 1.50346i) q^{63} +(7.62598 + 13.2086i) q^{65} +(2.42040 + 6.64999i) q^{67} +(11.5519 - 1.36985i) q^{69} +(3.31294 - 2.77989i) q^{71} +(-1.30735 - 7.41438i) q^{73} +(4.71075 - 3.51931i) q^{75} +3.51674i q^{77} +(-4.30920 + 0.759829i) q^{79} +(-8.93194 + 1.10474i) q^{81} +(-12.5112 - 7.22333i) q^{83} +(-7.00913 + 2.55111i) q^{85} +(-1.85688 - 0.797290i) q^{87} +(2.38095 - 13.5030i) q^{89} +(3.80378 - 4.53316i) q^{91} +(-2.25420 - 7.48389i) q^{93} +(4.65018 + 11.7422i) q^{95} +(-1.47287 + 4.04669i) q^{97} +(5.18337 + 7.82368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * 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} - 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}+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

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
$3$	−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	−0.999978	−	0.00666440i	$-0.997879\pi$
$5$	−1.86241	−	2.21954i	−0.832897	−	0.992608i	0.167081	−	0.985943i	$-0.446566\pi$
$6$		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
$9$	0.184473	+	2.99432i	0.0614909	+	0.998108i
$10$		0			0
$11$	2.70920	−	1.56416i	0.816855	−	0.471611i	−0.0324759	−	0.999473i	$-0.510339\pi$
$11$	2.70920	−	1.56416i	0.816855	−	0.471611i	0.849331	+	0.527861i	$0.177006\pi$
$12$		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
$15$	−0.283400	+	5.01044i	−0.0731734	+	1.29369i
$16$		0			0
$17$	0.880484	−	2.41911i	0.213549	−	0.586720i	−0.785953	−	0.618286i	$-0.787827\pi$
$17$	0.880484	−	2.41911i	0.213549	−	0.586720i	0.999502	+	0.0315662i	$0.0100495\pi$
$18$		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	0.0968152	+	0.995302i	$0.469134\pi$
$23$	−4.31710	+	5.14492i	−0.900178	+	1.07279i	−0.996993	+	0.0774881i	$0.975310\pi$
$24$		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	−0.238214	−	0.971213i	$-0.576562\pi$
$29$	1.09635	−	0.399039i	0.203587	−	0.0740998i	0.441801	+	0.897113i	$0.354340\pi$
$30$		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
$33$	−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	$0.460152\pi$
$37$			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	$0.102875\pi$
$41$	1.06170	+	6.02118i	0.165809	+	0.940350i	−0.782417	+	0.622755i	$0.786014\pi$
$42$		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
$45$	6.30245	−	5.98611i	0.939514	−	0.892357i
$46$		0			0
$47$	0.377793	+	1.03798i	0.0551068	+	0.151405i	0.964192	−	0.265206i	$-0.0854400\pi$
$47$	0.377793	+	1.03798i	0.0551068	+	0.151405i	−0.909085	+	0.416611i	$0.863218\pi$
$48$		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	0.942887	−	0.333111i	$-0.108099\pi$
$53$	5.66806	+	4.75606i	0.778568	+	0.653296i	−0.164320	+	0.986407i	$0.552543\pi$
$54$		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	0.724153	−	0.689639i	$-0.242231\pi$
$59$	6.41833	+	2.33608i	0.835596	+	0.304132i	0.111442	+	0.993771i	$0.464453\pi$
$60$		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
$63$	−3.01883	−	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	0.995206	+	0.0977999i	$0.0311805\pi$
$67$	2.42040	+	6.64999i	0.295699	+	0.812425i	−0.699508	+	0.714625i	$0.746597\pi$
$68$		0			0
$69$	11.5519	−	1.36985i	1.39068	−	0.164911i
$70$		0			0
$71$	3.31294	−	2.77989i	0.393174	−	0.329912i	−0.424674	−	0.905346i	$-0.639611\pi$
$71$	3.31294	−	2.77989i	0.393174	−	0.329912i	0.817848	+	0.575434i	$0.195167\pi$
$72$		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
$81$	−8.93194	+	1.10474i	−0.992438	+	0.122749i
$82$		0			0
$83$	−12.5112	−	7.22333i	−1.37328	−	0.792863i	−0.381940	−	0.924187i	$-0.624744\pi$
$83$	−12.5112	−	7.22333i	−1.37328	−	0.792863i	−0.991340	+	0.131324i	$0.958077\pi$
$84$		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	−0.550331	−	0.834947i	$-0.685498\pi$
$89$	2.38095	−	13.5030i	0.252380	−	1.43132i	0.802710	−	0.596369i	$-0.203391\pi$
$90$		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	−0.991735	−	0.128307i	$-0.959046\pi$
$97$	−1.47287	+	4.04669i	−0.149548	+	0.410879i	0.842187	+	0.539186i	$0.181268\pi$
$98$		0			0
$99$	5.18337	+	7.82368i	0.520948	+	0.786309i
$100$		0			0
$101$	−5.82418	−	1.02696i	−0.579528	−	0.102186i	−0.123802	−	0.992307i	$-0.539509\pi$
$101$	−5.82418	−	1.02696i	−0.579528	−	0.102186i	−0.455725	+	0.890121i	$0.650620\pi$
$102$		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
$105$	−4.71865	−	3.09218i	−0.460493	−	0.301766i
$106$		0			0
$107$	2.39183	−	4.14277i	0.231227	−	0.400496i	−0.726943	−	0.686698i	$-0.759059\pi$
$107$	2.39183	−	4.14277i	0.231227	−	0.400496i	0.958169	+	0.286202i	$0.0923927\pi$
$108$		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
$111$	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	−0.173756	−	0.984789i	$-0.555591\pi$
$127$	−7.59392	−	1.33901i	−0.673852	−	0.118818i	−0.500095	+	0.865970i	$0.666702\pi$
$128$		0			0
$129$	4.99556	+	0.282558i	0.439834	+	0.0248778i
$130$		0			0
$131$	−0.757267	+	2.08057i	−0.0661627	+	0.181781i	−0.968368	−	0.249526i	$-0.919725\pi$
$131$	−0.757267	+	2.08057i	−0.0661627	+	0.181781i	0.902205	+	0.431307i	$0.141947\pi$
$132$		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	−0.771939	−	0.635697i	$-0.780713\pi$
$137$	−0.138747	+	0.165352i	−0.0118540	+	0.0141270i	0.760085	+	0.649824i	$0.225157\pi$
$138$		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
$141$	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	−0.342457	−	0.939533i	$-0.611259\pi$
$149$	−4.18590	+	0.738088i	−0.342923	+	0.0604665i	−0.000465272		1.00000i	$0.500148\pi$
$150$		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
$159$	−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	0.988848	−	0.148929i	$-0.0475825\pi$
$163$	4.66573	+	8.08128i	0.365448	+	0.632975i	−0.623400	+	0.781903i	$0.714249\pi$
$164$		0			0
$165$	7.06933	+	14.0176i	0.550346	+	1.09127i
$166$		0			0
$167$	9.70512	+	8.14356i	0.751005	+	0.630168i	0.935768	−	0.352615i	$-0.114708\pi$
$167$	9.70512	+	8.14356i	0.751005	+	0.630168i	−0.184764	+	0.982783i	$0.559152\pi$
$168$		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	0.656152	−	0.754629i	$-0.272183\pi$
$173$	8.86150	+	3.22532i	0.673727	+	0.245217i	0.0175755	+	0.999846i	$0.494405\pi$
$174$		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	0.691475	−	0.722401i	$-0.256961\pi$
$179$	−3.74454	−	6.48573i	−0.279880	−	0.484766i	−0.971355	+	0.237634i	$0.923628\pi$
$180$		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
$183$	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	$-0.911126\pi$
$191$		−	7.61751i		−	0.551184i	0.961275	−	0.275592i	$-0.0888738\pi$
$192$		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
$195$	6.04913	−	25.7153i	0.433187	−	1.84151i
$196$		0			0
$197$	−15.2618	−	8.81139i	−1.08736	−	0.627786i	−0.154485	−	0.987995i	$-0.549372\pi$
$197$	−15.2618	−	8.81139i	−1.08736	−	0.627786i	−0.932871	+	0.360210i	$0.882705\pi$
$198$		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
$201$	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	−0.886061	−	0.463568i	$-0.846569\pi$
$211$	1.31716	−	3.61886i	0.0906769	−	0.249133i	0.976738	+	0.214435i	$0.0687911\pi$
$212$		0			0
$213$	−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	0.872428	−	0.488743i	$-0.162544\pi$
$223$	3.57822	+	4.26435i	0.239615	+	0.285562i	−0.632813	+	0.774305i	$0.718100\pi$
$224$		0			0
$225$	−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	−0.996534	−	0.0831862i	$-0.973490\pi$
$233$	−13.8205	−	16.4706i	−0.905410	−	1.07903i	0.0911239	−	0.995840i	$-0.470954\pi$
$234$		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	−0.119846	−	0.992793i	$-0.538240\pi$
$239$	10.5128	−	6.06955i	0.680015	−	0.392607i	0.799861	+	0.600186i	$0.204907\pi$
$240$		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
$243$	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	−0.210181	−	0.977663i	$-0.567405\pi$
$251$	12.5021	−	14.8994i	0.789127	−	0.940445i	0.999307	+	0.0372181i	$0.0118496\pi$
$252$		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	−0.00418306	−	0.999991i	$-0.501332\pi$
$257$	10.1861	−	3.70746i	0.635395	−	0.231265i	0.639578	+	0.768727i	$0.279109\pi$
$258$		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	−0.991484	−	0.130227i	$-0.958429\pi$
$263$	−30.4663	+	5.37204i	−1.87863	+	0.331254i	−0.887150	+	0.461481i	$0.847318\pi$
$264$		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	0.946145	−	0.323744i	$-0.104942\pi$
$269$	−0.880210	−	4.99192i	−0.0536673	−	0.304363i	−0.999812	+	0.0193811i	$0.993830\pi$
$270$		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
$273$	−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	0.923517	−	0.383558i	$-0.125301\pi$
$277$	2.15677	+	3.73563i	0.129588	+	0.224453i	−0.793929	+	0.608010i	$0.791968\pi$
$278$		0			0
$279$	−6.03514	+	12.1181i	−0.361314	+	0.725489i
$280$		0			0
$281$	8.43804	+	7.08036i	0.503371	+	0.422379i	0.858789	−	0.512329i	$-0.171217\pi$
$281$	8.43804	+	7.08036i	0.503371	+	0.422379i	−0.355418	+	0.934707i	$0.615661\pi$
$282$		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
$285$	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	0.994441	+	0.105291i	$0.0335775\pi$
$293$	10.0719	+	17.4450i	0.588406	+	1.01915i	−0.406036	+	0.913857i	$0.633089\pi$
$294$		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	0.0136720	−	0.999907i	$-0.495648\pi$
$307$	6.45677	−	1.13850i	0.368508	−	0.0649778i	0.354836	+	0.934929i	$0.384537\pi$
$308$		0			0
$309$	33.6056	+	7.90520i	1.91175	+	0.449711i
$310$		0			0
$311$	1.86672	+	1.07775i	0.105852	+	0.0611137i	0.551991	−	0.833850i	$-0.313868\pi$
$311$	1.86672	+	1.07775i	0.105852	+	0.0611137i	−0.446139	+	0.894963i	$0.647201\pi$
$312$		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
$315$	2.28532	+	9.50047i	0.128763	+	0.535291i
$316$		0			0
$317$	−0.961500	+	5.45293i	−0.0540032	+	0.306267i	−0.999831	−	0.0184023i	$-0.994142\pi$
$317$	−0.961500	+	5.45293i	−0.0540032	+	0.306267i	0.945827	+	0.324670i	$0.105253\pi$
$318$		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	−0.305200	−	0.952288i	$-0.598723\pi$
$331$	6.67525	−	3.85396i	0.366905	−	0.211833i	0.672106	+	0.740455i	$0.265390\pi$
$332$		0			0
$333$	−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	0.940772	−	0.339039i	$-0.110102\pi$
$337$	8.14195	+	9.70320i	0.443520	+	0.528567i	−0.497252	+	0.867606i	$0.665657\pi$
$338$		0			0
$339$	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	0.681600	−	0.731725i	$-0.261284\pi$
$347$	−2.93143	−	3.49354i	−0.157367	−	0.187543i	−0.838967	+	0.544182i	$0.816840\pi$
$348$		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
$351$	−20.8647	+	17.6871i	−1.11367	+	0.944066i
$352$		0			0
$353$	−5.92549	+	3.42108i	−0.315382	+	0.182086i	−0.649332	−	0.760505i	$-0.724952\pi$
$353$	−5.92549	+	3.42108i	−0.315382	+	0.182086i	0.333950	+	0.942591i	$0.391618\pi$
$354$		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	−0.897310	−	0.441401i	$-0.854482\pi$
$359$	1.39824	−	3.84165i	0.0737965	−	0.202754i	0.971106	+	0.238647i	$0.0767038\pi$
$360$		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	−0.906510	−	0.422185i	$-0.861263\pi$
$367$	1.71891	−	9.74845i	0.0897266	−	0.508865i	0.996236	−	0.0866798i	$-0.0276257\pi$
$368$		0			0
$369$	−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	0.668035	−	0.744130i	$-0.267136\pi$
$373$	6.90673	+	3.98760i	0.357617	+	0.206470i	−0.310418	+	0.950600i	$0.600469\pi$
$374$		0			0
$375$	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	$-0.910968\pi$
$379$		−	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	0.999213	−	0.0396663i	$-0.0126295\pi$
$383$	0.913805	+	5.18245i	0.0466933	+	0.264811i	−0.952520	+	0.304477i	$0.901518\pi$
$384$		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	−0.997868	−	0.0652695i	$-0.979209\pi$
$389$	−5.43196	−	14.9242i	−0.275411	−	0.756686i	0.722457	−	0.691416i	$-0.243013\pi$
$390$		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	−0.694799	−	0.719204i	$-0.744507\pi$
$397$	−33.6599	−	12.2512i	−1.68934	−	0.614870i	−0.994542	+	0.104334i	$0.966729\pi$
$398$		0			0
$399$	−8.48382	−	0.241809i	−0.424722	−	0.0121056i
$400$		0			0
$401$	−5.57564	−	2.02937i	−0.278434	−	0.101342i	0.199029	−	0.979994i	$-0.436221\pi$
$401$	−5.57564	−	2.02937i	−0.278434	−	0.101342i	−0.477463	+	0.878652i	$0.658443\pi$
$402$		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	0.933878	+	0.357592i	$0.116402\pi$
$409$	9.06715	+	24.9118i	0.448342	+	1.23181i	−0.485536	+	0.874217i	$0.661375\pi$
$410$		0			0
$411$	0.371266	−	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	$-0.935686\pi$
$419$		−	8.21543i		−	0.401350i	0.979658	−	0.200675i	$-0.0643135\pi$
$420$		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
$423$	−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	0.584073	+	0.811701i	$0.301458\pi$
$431$	−5.03223	+	28.5392i	−0.242394	+	1.37469i	−0.826467	+	0.562985i	$0.809653\pi$
$432$		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
$435$	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	−0.751715	−	0.659488i	$-0.770773\pi$
$439$	5.19707	−	14.2788i	0.248042	−	0.681491i	0.999758	−	0.0220034i	$-0.00700448\pi$
$440$		0			0
$441$	−14.3459	+	9.50451i	−0.683139	+	0.452596i
$442$		0			0
$443$	4.75117	+	0.837760i	0.225735	+	0.0398032i	0.285371	−	0.958417i	$-0.407883\pi$
$443$	4.75117	+	0.837760i	0.225735	+	0.0398032i	−0.0596365	+	0.998220i	$0.518994\pi$
$444$		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	−0.905100	−	0.425198i	$-0.860204\pi$
$449$	−1.78666	+	3.09458i	−0.0843176	+	0.146042i	0.820783	+	0.571241i	$0.193538\pi$
$450$		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	0.532019	−	0.846732i	$-0.321433\pi$
$461$	−8.46456	−	10.0877i	−0.394234	−	0.469830i	−0.926253	+	0.376903i	$0.876989\pi$
$462$		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
$465$	−12.4125	+	18.9414i	−0.575617	+	0.878386i
$466$		0			0
$467$	−8.01942	+	4.63001i	−0.371094	+	0.214251i	−0.673936	−	0.738789i	$-0.735398\pi$
$467$	−8.01942	+	4.63001i	−0.371094	+	0.214251i	0.302842	+	0.953041i	$0.402065\pi$
$468$		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	−0.842329	−	0.538964i	$-0.818816\pi$
$479$	−3.61743	+	4.31108i	−0.165284	+	0.196978i	0.677045	+	0.735942i	$0.263260\pi$
$480$		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	0.0408365	−	0.999166i	$-0.486998\pi$
$487$	−17.7438	−	10.2444i	−0.804048	−	0.464217i	−0.844885	+	0.534948i	$0.820331\pi$
$488$		0			0
$489$	3.70098	−	15.7331i	0.167364	−	0.711476i
$490$		0			0
$491$	−32.2309	+	5.68317i	−1.45456	+	0.256478i	−0.844363	−	0.535772i	$-0.820021\pi$
$491$	−32.2309	+	5.68317i	−1.45456	+	0.256478i	−0.610196	+	0.792250i	$0.708909\pi$
$492$		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
$501$	−2.58402	−	21.7909i	−0.115446	−	0.973546i
$502$		0			0
$503$	−7.95923	−	21.8678i	−0.354885	−	0.975037i	−0.980778	−	0.195128i	$-0.937488\pi$
$503$	−7.95923	−	21.8678i	−0.354885	−	0.975037i	0.625893	−	0.779909i	$-0.284735\pi$
$504$		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	0.932362	−	0.361525i	$-0.117744\pi$
$509$	16.6553	+	13.9754i	0.738232	+	0.619450i	−0.194130	+	0.980976i	$0.562188\pi$
$510$		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	0.982558	−	0.185957i	$-0.0595384\pi$
$521$	7.53777	+	13.0558i	0.330236	+	0.571985i	−0.652322	+	0.757942i	$0.726205\pi$
$522$		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
$525$	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	−0.439755	−	0.898118i	$-0.644935\pi$
$541$	−4.63626	+	1.68746i	−0.199328	+	0.0725495i	0.240427	+	0.970667i	$0.422713\pi$
$542$		0			0
$543$	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	−0.924458	−	0.381283i	$-0.875482\pi$
$547$	−9.08478	+	10.8268i	−0.388437	+	0.462922i	0.536021	+	0.844205i	$0.319927\pi$
$548$		0			0
$549$	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	0.164657	−	0.986351i	$-0.447348\pi$
$557$	−0.424076	−	0.0747760i	−0.0179687	−	0.00316836i	−0.182625	+	0.983183i	$0.558460\pi$
$558$		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	−0.913010	−	0.407937i	$-0.866248\pi$
$563$	−2.44919	+	4.24212i	−0.103221	+	0.178784i	0.809789	+	0.586721i	$0.199582\pi$
$564$		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	−0.890670	−	0.454651i	$-0.849764\pi$
$577$	−1.23938	+	2.14667i	−0.0515960	+	0.0893669i	0.839074	+	0.544017i	$0.183097\pi$
$578$		0			0
$579$	−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	0.294462	+	0.955663i	$0.404860\pi$
$587$	−13.2139	+	36.3050i	−0.545398	+	1.49847i	−0.839859	+	0.542804i	$0.817363\pi$
$588$		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	−0.820741	−	0.571300i	$-0.806439\pi$
$593$	−2.81505	+	3.35484i	−0.115600	+	0.137767i	0.705141	+	0.709067i	$0.250884\pi$
$594$		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	0.657380	−	0.753559i	$-0.271665\pi$
$599$	40.2689	−	14.6567i	1.64534	−	0.598855i	0.987961	+	0.154704i	$0.0494423\pi$
$600$		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
$603$	−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	$0.106011\pi$
$607$			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
$615$	−30.4696	+	3.61316i	−1.22865	+	0.145697i
$616$		0			0
$617$	15.8059	+	43.4264i	0.636322	+	1.74828i	0.662982	+	0.748636i	$0.269291\pi$
$617$	15.8059	+	43.4264i	0.636322	+	1.74828i	−0.0266596	+	0.999645i	$0.508487\pi$
$618$		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
$621$	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	0.706971	−	0.707243i	$-0.250061\pi$
$631$	3.34686	+	2.80835i	0.133236	+	0.111799i	−0.573734	+	0.819042i	$0.694506\pi$
$632$		0			0
$633$	−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	−0.684917	−	0.728621i	$-0.740162\pi$
$641$	−2.18494	+	1.83339i	−0.0863001	+	0.0724144i	0.598617	+	0.801035i	$0.295717\pi$
$642$		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	$-0.869161\pi$
$647$		−	20.3269i		−	0.799131i	0.916705	−	0.399566i	$-0.130839\pi$
$648$		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	−0.384603	−	0.923082i	$-0.625662\pi$
$653$	−35.1702	−	20.3055i	−1.37632	−	0.794617i	−0.991714	+	0.128465i	$0.958995\pi$
$654$		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	0.569588	+	0.821930i	$0.307103\pi$
$659$	−6.33474	+	35.9261i	−0.246766	+	1.39948i	−0.816354	+	0.577552i	$0.804008\pi$
$660$		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
$663$	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	−0.000101249	−	1.00000i	$-0.500032\pi$
$673$	22.4627	−	12.9688i	0.865874	−	0.499912i	0.865975	+	0.500088i	$0.166699\pi$
$674$		0			0
$675$	11.4070	+	13.4563i	0.439054	+	0.517933i
$676$		0			0
$677$	16.1874	−	28.0374i	0.622132	−	1.07756i	−0.366956	−	0.930238i	$-0.619600\pi$
$677$	16.1874	−	28.0374i	0.622132	−	1.07756i	0.989088	−	0.147326i	$-0.0470665\pi$
$678$		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	−0.676662	−	0.736294i	$-0.736574\pi$
$691$	7.86815	−	13.6280i	0.299319	−	0.518435i	0.975980	+	0.217859i	$0.0699073\pi$
$692$		0			0
$693$	−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	0.546911	+	0.837191i	$0.315803\pi$
$701$	−10.8602	+	29.8381i	−0.410183	+	1.12697i	−0.957094	+	0.289777i	$0.906419\pi$
$702$		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	−0.624084	−	0.781358i	$-0.714528\pi$
$709$	6.11366	−	34.6723i	0.229603	−	1.30214i	0.853687	−	0.520787i	$-0.174361\pi$
$710$		0			0
$711$	−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	−0.440994	−	0.897510i	$-0.645374\pi$
$719$	−14.7056	+	2.59299i	−0.548426	+	0.0967023i	−0.107432	+	0.994212i	$0.534263\pi$
$720$		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
$729$	−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	0.894567	−	0.446933i	$-0.147484\pi$
$733$	1.63062	+	2.82432i	0.0602284	+	0.104319i	−0.834339	+	0.551252i	$0.814150\pi$
$734$		0			0
$735$	−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	0.441927	−	0.897051i	$-0.354295\pi$
$739$	5.54154	+	2.01696i	0.203849	+	0.0741950i	−0.238078	+	0.971246i	$0.576517\pi$
$740$		0			0
$741$	−12.5232	−	37.7178i	−0.460051	−	1.38560i
$742$		0			0
$743$	−27.7676	−	10.1066i	−1.01870	−	0.370775i	−0.221930	−	0.975063i	$-0.571236\pi$
$743$	−27.7676	−	10.1066i	−1.01870	−	0.370775i	−0.796766	+	0.604288i	$0.793458\pi$
$744$		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	0.999932	−	0.0117037i	$-0.00372548\pi$
$751$	6.20481	+	17.0476i	0.226417	+	0.622074i	−0.773515	+	0.633778i	$0.781503\pi$
$752$		0			0
$753$	−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	−0.975204	−	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	$-0.822658\pi$
$761$		−	29.1728i		−	1.05751i	0.848774	−	0.528757i	$-0.177342\pi$
$762$		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	−0.764636	−	0.644462i	$-0.777081\pi$
$769$	−25.9596	+	9.44854i	−0.936129	+	0.340723i	−0.171493	+	0.985185i	$0.554859\pi$
$770$		0			0
$771$	−17.2521	−	7.40758i	−0.621321	−	0.266777i
$772$		0			0
$773$	−7.60654	+	43.1388i	−0.273588	+	1.55160i	0.469823	+	0.882761i	$0.344318\pi$
$773$	−7.60654	+	43.1388i	−0.273588	+	1.55160i	−0.743411	+	0.668835i	$0.766793\pi$
$774$		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	−0.946049	−	0.324023i	$-0.894964\pi$
$787$	−31.9379	+	18.4393i	−1.13846	+	0.657291i	−0.192412	+	0.981314i	$0.561631\pi$
$788$		0			0
$789$	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	0.660286	−	0.751015i	$-0.270435\pi$
$809$	46.6699	−	26.9449i	1.64083	−	0.947331i	0.980540	−	0.196317i	$-0.0628981\pi$
$810$		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
$813$	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	−0.443274	−	0.896386i	$-0.646183\pi$
$821$	14.7984	−	17.6360i	0.516468	−	0.615502i	0.959742	+	0.280884i	$0.0906276\pi$
$822$		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
$825$	7.25761	−	16.9029i	0.252678	−	0.588482i
$826$		0			0
$827$	0.866657	−	0.315437i	0.0301366	−	0.0109688i	−0.326908	−	0.945056i	$-0.606007\pi$
$827$	0.866657	−	0.315437i	0.0301366	−	0.0109688i	0.357044	+	0.934087i	$0.383784\pi$
$828$		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
$831$	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	−0.994924	−	0.100632i	$-0.967914\pi$
$839$	−2.73490	−	15.5104i	−0.0944194	−	0.535479i	0.900504	−	0.434847i	$-0.143198\pi$
$840$		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	−0.231431	−	0.972851i	$-0.574341\pi$
$853$	−30.2008	−	10.9922i	−1.03405	−	0.376365i	−0.802623	+	0.596486i	$0.796563\pi$
$854$		0			0
$855$	−34.3021	+	16.0903i	−1.17311	+	0.550275i
$856$		0			0
$857$	−23.1422	−	8.42308i	−0.790524	−	0.287727i	−0.0849699	−	0.996384i	$-0.527079\pi$
$857$	−23.1422	−	8.42308i	−0.790524	−	0.287727i	−0.705554	+	0.708656i	$0.749302\pi$
$858$		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
$861$	5.36067	+	10.6295i	0.182691	+	0.362253i
$862$		0			0
$863$	7.05542	+	12.2203i	0.240169	+	0.415985i	0.960762	−	0.277373i	$-0.0894637\pi$
$863$	7.05542	+	12.2203i	0.240169	+	0.415985i	−0.720593	+	0.693358i	$0.756130\pi$
$864$		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	0.138410	−	0.990375i	$-0.455801\pi$
$877$	17.9817	−	3.17067i	0.607200	−	0.107066i	0.468791	+	0.883309i	$0.344690\pi$
$878$		0			0
$879$	7.98928	−	33.9630i	0.269472	−	1.14554i
$880$		0			0
$881$	5.32331	+	3.07342i	0.179347	+	0.103546i	0.586986	−	0.809597i	$-0.300314\pi$
$881$	5.32331	+	3.07342i	0.179347	+	0.103546i	−0.407639	+	0.913143i	$0.633648\pi$
$882$		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
$885$	−13.5237	+	31.4966i	−0.454596	+	1.05875i
$886$		0			0
$887$	7.62578	−	43.2479i	0.256049	−	1.45212i	−0.537318	−	0.843379i	$-0.680563\pi$
$887$	7.62578	−	43.2479i	0.256049	−	1.45212i	0.793367	−	0.608744i	$-0.208326\pi$
$888$		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	0.994981	−	0.100068i	$-0.0319060\pi$
$907$	21.7940	+	25.9730i	0.723656	+	0.862420i	−0.271324	+	0.962488i	$0.587462\pi$
$908$		0			0
$909$	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	−0.747625	−	0.664121i	$-0.768806\pi$
$919$	6.10344	−	10.5715i	0.201334	−	0.348720i	0.948958	+	0.315401i	$0.102139\pi$
$920$		0			0
$921$	−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	−0.999130	−	0.0417085i	$-0.986720\pi$
$929$	−6.30750	+	17.3297i	−0.206942	+	0.568569i	0.792188	+	0.610278i	$0.208942\pi$
$930$		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	0.827184	+	0.561931i	$0.189941\pi$
$937$	−4.35606	+	24.7045i	−0.142306	+	0.807060i	−0.969491	+	0.245129i	$0.921170\pi$
$938$		0			0
$939$	−26.9476	−	11.5705i	−0.879400	−	0.377589i
$940$		0			0
$941$	43.7853	−	15.9365i	1.42736	−	0.519517i	0.491187	−	0.871054i	$-0.336563\pi$
$941$	43.7853	−	15.9365i	1.42736	−	0.519517i	0.936174	+	0.351538i	$0.114341\pi$
$942$		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	0.816429	−	0.577446i	$-0.195951\pi$
$947$	54.8110	−	9.66466i	1.78112	−	0.314059i	0.964690	+	0.263387i	$0.0848397\pi$
$948$		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	$-0.956321\pi$
$953$	−3.28854	−	18.6502i	−0.106526	−	0.604140i	0.884074	−	0.467348i	$-0.154790\pi$
$954$		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	0.696782	−	0.717283i	$-0.254614\pi$
$967$	23.9285	+	8.70925i	0.769488	+	0.280071i	0.0727056	+	0.997353i	$0.476837\pi$
$968$		0			0
$969$	19.2291	−	2.82832i	0.617728	−	0.0908588i
$970$		0			0
$971$	14.6975	+	5.34944i	0.471664	+	0.171672i	0.566906	−	0.823782i	$-0.308140\pi$
$971$	14.6975	+	5.34944i	0.471664	+	0.171672i	−0.0952419	+	0.995454i	$0.530362\pi$
$972$		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	0.653453	−	0.756967i	$-0.273320\pi$
$977$	−10.2781	−	17.8022i	−0.328827	−	0.569544i	−0.982279	+	0.187423i	$0.939986\pi$
$978$		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	−0.844560	−	0.535461i	$-0.820138\pi$
$983$	−14.5443	+	12.2041i	−0.463890	+	0.389250i	0.380670	+	0.924711i	$0.375693\pi$
$984$		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
$993$	−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	−0.102671	−	0.994715i	$-0.532739\pi$
$997$	14.4637	−	5.26435i	0.458069	−	0.166724i	0.560740	+	0.827992i	$0.310517\pi$
$998$		0			0
$999$	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.737.1		18
3.2	odd	2		912.2.cc.c.737.2		18
4.3	odd	2		114.2.l.a.53.3	✓	18
12.11	even	2		114.2.l.b.53.2	yes	18
19.14	odd	18		912.2.cc.c.641.2		18
57.14	even	18	inner	912.2.cc.d.641.1		18
76.71	even	18		114.2.l.b.71.2	yes	18
228.71	odd	18		114.2.l.a.71.3	yes	18

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

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)

\(f(q)\)	\(=\)	\(q+(-1.26184 - 1.18649i) q^{3} +(-1.86241 - 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(0.184473 + 2.99432i) q^{9} +O(q^{10})\)	\(q+(-1.26184 - 1.18649i) q^{3} +(-1.86241 - 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(0.184473 + 2.99432i) q^{9} +(2.70920 - 1.56416i) q^{11} +(-5.18404 - 0.914087i) q^{13} +(-0.283400 + 5.01044i) q^{15} +(0.880484 - 2.41911i) q^{17} +(-4.13617 - 1.37554i) q^{19} +(1.86437 - 0.561563i) q^{21} +(-4.31710 + 5.14492i) q^{23} +(-0.589524 + 3.34336i) q^{25} +(3.31997 - 3.99723i) q^{27} +(1.09635 - 0.399039i) q^{29} +(3.90801 + 2.25629i) q^{31} +(-5.27443 - 1.24073i) q^{33} +(3.20767 - 0.565599i) q^{35} +12.0703i q^{37} +(5.45687 + 7.30426i) q^{39} +(1.06170 + 6.02118i) q^{41} +(-2.21295 + 1.85688i) q^{43} +(6.30245 - 5.98611i) q^{45} +(0.377793 + 1.03798i) q^{47} +(2.86813 + 4.96774i) q^{49} +(-3.98128 + 2.00784i) q^{51} +(5.66806 + 4.75606i) q^{53} +(-8.51736 - 3.10007i) q^{55} +(3.58710 + 6.64324i) q^{57} +(6.41833 + 2.33608i) q^{59} +(-5.58223 - 4.68405i) q^{61} +(-3.01883 - 1.50346i) q^{63} +(7.62598 + 13.2086i) q^{65} +(2.42040 + 6.64999i) q^{67} +(11.5519 - 1.36985i) q^{69} +(3.31294 - 2.77989i) q^{71} +(-1.30735 - 7.41438i) q^{73} +(4.71075 - 3.51931i) q^{75} +3.51674i q^{77} +(-4.30920 + 0.759829i) q^{79} +(-8.93194 + 1.10474i) q^{81} +(-12.5112 - 7.22333i) q^{83} +(-7.00913 + 2.55111i) q^{85} +(-1.85688 - 0.797290i) q^{87} +(2.38095 - 13.5030i) q^{89} +(3.80378 - 4.53316i) q^{91} +(-2.25420 - 7.48389i) q^{93} +(4.65018 + 11.7422i) q^{95} +(-1.47287 + 4.04669i) q^{97} +(5.18337 + 7.82368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) \) 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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