LMFDB - Embedded newform 234.2.y.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.36513 + 1.06603i) q^{3} -1.00000i q^{4} +(-3.36565 - 0.901822i) q^{5} +(-0.211491 + 1.71909i) q^{6} +(0.0541850 + 0.0145188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.727143 - 2.91054i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.36513 + 1.06603i) q^{3} -1.00000i q^{4} +(-3.36565 - 0.901822i) q^{5} +(-0.211491 + 1.71909i) q^{6} +(0.0541850 + 0.0145188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.727143 - 2.91054i) q^{9} +(-3.01756 + 1.74219i) q^{10} +(-3.65076 - 3.65076i) q^{11} +(1.06603 + 1.36513i) q^{12} +(-3.37979 + 1.25580i) q^{13} +(0.0485810 - 0.0280482i) q^{14} +(5.55591 - 2.35679i) q^{15} -1.00000 q^{16} +(-1.83057 + 3.17065i) q^{17} +(-1.54390 - 2.57223i) q^{18} +(0.677531 - 0.181544i) q^{19} +(-0.901822 + 3.36565i) q^{20} +(-0.0894470 + 0.0379430i) q^{21} -5.16296 q^{22} +(2.89347 - 5.01164i) q^{23} +(1.71909 + 0.211491i) q^{24} +(6.18416 + 3.57043i) q^{25} +(-1.50189 + 3.27785i) q^{26} +(2.11009 + 4.74842i) q^{27} +(0.0145188 - 0.0541850i) q^{28} +3.45319i q^{29} +(2.26212 - 5.59512i) q^{30} +(1.54108 - 5.75138i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.87559 + 1.09192i) q^{33} +(0.947575 + 3.53640i) q^{34} +(-0.169274 - 0.0977305i) q^{35} +(-2.91054 - 0.727143i) q^{36} +(7.28892 + 1.95306i) q^{37} +(0.350716 - 0.607458i) q^{38} +(3.27512 - 5.31729i) q^{39} +(1.74219 + 3.01756i) q^{40} +(-0.780112 - 2.91142i) q^{41} +(-0.0364188 + 0.0900783i) q^{42} +(-4.70232 + 2.71489i) q^{43} +(-3.65076 + 3.65076i) q^{44} +(-5.07210 + 9.14010i) q^{45} +(-1.49777 - 5.58976i) q^{46} +(-4.82793 + 1.29364i) q^{47} +(1.36513 - 1.06603i) q^{48} +(-6.05945 - 3.49843i) q^{49} +(6.89754 - 1.84819i) q^{50} +(-0.881051 - 6.27979i) q^{51} +(1.25580 + 3.37979i) q^{52} -3.89525i q^{53} +(4.84970 + 1.86558i) q^{54} +(8.99483 + 15.5795i) q^{55} +(-0.0280482 - 0.0485810i) q^{56} +(-0.731384 + 0.970102i) q^{57} +(2.44178 + 2.44178i) q^{58} +(0.745519 + 0.745519i) q^{59} +(-2.35679 - 5.55591i) q^{60} +(1.50195 + 2.60145i) q^{61} +(-2.97713 - 5.15654i) q^{62} +(0.0816580 - 0.147151i) q^{63} +1.00000i q^{64} +(12.5077 - 1.17860i) q^{65} +(7.04809 - 5.50389i) q^{66} +(-10.5121 + 2.81672i) q^{67} +(3.17065 + 1.83057i) q^{68} +(1.39262 + 9.92606i) q^{69} +(-0.188801 + 0.0505890i) q^{70} +(-3.98742 - 14.8813i) q^{71} +(-2.57223 + 1.54390i) q^{72} +(5.86521 - 5.86521i) q^{73} +(6.53507 - 3.77302i) q^{74} +(-12.2484 + 1.71844i) q^{75} +(-0.181544 - 0.677531i) q^{76} +(-0.144812 - 0.250821i) q^{77} +(-1.44403 - 6.07575i) q^{78} +(2.76723 - 4.79298i) q^{79} +(3.36565 + 0.901822i) q^{80} +(-7.94252 - 4.23277i) q^{81} +(-2.61030 - 1.50706i) q^{82} +(-4.13340 - 15.4261i) q^{83} +(0.0379430 + 0.0894470i) q^{84} +(9.02042 - 9.02042i) q^{85} +(-1.40533 + 5.24476i) q^{86} +(-3.68122 - 4.71405i) q^{87} +5.16296i q^{88} +(-4.41179 + 16.4650i) q^{89} +(2.87651 + 10.0495i) q^{90} +(-0.201367 + 0.0189747i) q^{91} +(-5.01164 - 2.89347i) q^{92} +(4.02740 + 9.49420i) q^{93} +(-2.49912 + 4.32861i) q^{94} -2.44405 q^{95} +(0.211491 - 1.71909i) q^{96} +(-0.595628 + 2.22292i) q^{97} +(-6.75844 + 1.81092i) q^{98} +(-13.2803 + 7.97107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.36513	+	1.06603i	−0.788156	+	0.615475i
$3$	−1.36513	+	1.06603i	−0.788156	+	0.615475i
$4$		−	1.00000i		−	0.500000i
$5$	−3.36565	−	0.901822i	−1.50516	−	0.403307i	−0.590337	−	0.807157i	$-0.701005\pi$
$5$	−3.36565	−	0.901822i	−1.50516	−	0.403307i	−0.914825	+	0.403850i	$0.867672\pi$
$6$	−0.211491	+	1.71909i	−0.0863407	+	0.701816i
$7$	0.0541850	+	0.0145188i	0.0204800	+	0.00548760i	0.269045	−	0.963128i	$-0.413292\pi$
$7$	0.0541850	+	0.0145188i	0.0204800	+	0.00548760i	−0.248564	+	0.968615i	$0.579959\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.727143	−	2.91054i	0.242381	−	0.970181i
$10$	−3.01756	+	1.74219i	−0.954235	+	0.550928i
$11$	−3.65076	−	3.65076i	−1.10075	−	1.10075i	−0.994321	−	0.106426i	$-0.966059\pi$
$11$	−3.65076	−	3.65076i	−1.10075	−	1.10075i	−0.106426	−	0.994321i	$-0.533941\pi$
$12$	1.06603	+	1.36513i	0.307737	+	0.394078i
$13$	−3.37979	+	1.25580i	−0.937385	+	0.348295i
$13$	−3.37979	+	1.25580i	−0.937385	+	0.348295i
$14$	0.0485810	−	0.0280482i	0.0129838	−	0.00749621i
$15$	5.55591	−	2.35679i	1.43453	−	0.608521i
$16$	−1.00000			−0.250000
$17$	−1.83057	+	3.17065i	−0.443979	+	0.768995i	−0.997980	−	0.0635211i	$-0.979767\pi$
$17$	−1.83057	+	3.17065i	−0.443979	+	0.768995i	0.554001	+	0.832516i	$0.313100\pi$
$18$	−1.54390	−	2.57223i	−0.363900	−	0.606281i
$19$	0.677531	−	0.181544i	0.155436	−	0.0416491i	−0.180262	−	0.983619i	$-0.557694\pi$
$19$	0.677531	−	0.181544i	0.155436	−	0.0416491i	0.335698	+	0.941970i	$0.391028\pi$
$20$	−0.901822	+	3.36565i	−0.201654	+	0.752581i
$21$	−0.0894470	+	0.0379430i	−0.0195189	+	0.00827985i
$22$	−5.16296			−1.10075
$23$	2.89347	−	5.01164i	0.603330	−	1.04500i	−0.388982	−	0.921245i	$-0.627173\pi$
$23$	2.89347	−	5.01164i	0.603330	−	1.04500i	0.992313	−	0.123754i	$-0.0394933\pi$
$24$	1.71909	+	0.211491i	0.350908	+	0.0431704i
$25$	6.18416	+	3.57043i	1.23683	+	0.714085i
$26$	−1.50189	+	3.27785i	−0.294545	+	0.642840i
$27$	2.11009	+	4.74842i	0.406088	+	0.913834i
$28$	0.0145188	−	0.0541850i	0.00274380	−	0.0102400i
$29$			3.45319i			0.641242i	0.947208	+	0.320621i	$0.103892\pi$
$29$			3.45319i			0.641242i	−0.947208	+	0.320621i	$0.896108\pi$
$30$	2.26212	−	5.59512i	0.413004	−	1.02152i
$31$	1.54108	−	5.75138i	0.276786	−	1.03298i	−0.677850	−	0.735201i	$-0.737088\pi$
$31$	1.54108	−	5.75138i	0.276786	−	1.03298i	0.954635	−	0.297778i	$-0.0962454\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	8.87559	+	1.09192i	1.54504	+	0.190079i
$34$	0.947575	+	3.53640i	0.162508	+	0.606487i
$35$	−0.169274	−	0.0977305i	−0.0286126	−	0.0165195i
$36$	−2.91054	−	0.727143i	−0.485091	−	0.121191i
$37$	7.28892	+	1.95306i	1.19829	+	0.321081i	0.802158	−	0.597112i	$-0.203685\pi$
$37$	7.28892	+	1.95306i	1.19829	+	0.321081i	0.396134	+	0.918193i	$0.370352\pi$
$38$	0.350716	−	0.607458i	0.0568937	−	0.0985427i
$39$	3.27512	−	5.31729i	0.524439	−	0.851448i
$40$	1.74219	+	3.01756i	0.275464	+	0.477117i
$41$	−0.780112	−	2.91142i	−0.121833	−	0.454687i	0.877874	−	0.478892i	$-0.158961\pi$
$41$	−0.780112	−	2.91142i	−0.121833	−	0.454687i	−0.999707	+	0.0242048i	$0.992295\pi$
$42$	−0.0364188	+	0.0900783i	−0.00561955	+	0.0138994i
$43$	−4.70232	+	2.71489i	−0.717097	+	0.414016i	−0.813683	−	0.581309i	$-0.802541\pi$
$43$	−4.70232	+	2.71489i	−0.717097	+	0.414016i	0.0965863	+	0.995325i	$0.469208\pi$
$44$	−3.65076	+	3.65076i	−0.550373	+	0.550373i
$45$	−5.07210	+	9.14010i	−0.756104	+	1.36253i
$46$	−1.49777	−	5.58976i	−0.220834	−	0.824165i
$47$	−4.82793	+	1.29364i	−0.704226	+	0.188697i	−0.593123	−	0.805112i	$-0.702105\pi$
$47$	−4.82793	+	1.29364i	−0.704226	+	0.188697i	−0.111103	+	0.993809i	$0.535439\pi$
$48$	1.36513	−	1.06603i	0.197039	−	0.153869i
$49$	−6.05945	−	3.49843i	−0.865636	−	0.499775i
$50$	6.89754	−	1.84819i	0.975459	−	0.261373i
$51$	−0.881051	−	6.27979i	−0.123372	−	0.879346i
$52$	1.25580	+	3.37979i	0.174148	+	0.468692i
$53$		−	3.89525i		−	0.535053i	−0.963550	−	0.267527i	$-0.913794\pi$
$53$		−	3.89525i		−	0.535053i	0.963550	−	0.267527i	$-0.0862064\pi$
$54$	4.84970	+	1.86558i	0.659961	+	0.253873i
$55$	8.99483	+	15.5795i	1.21286	+	2.10074i
$56$	−0.0280482	−	0.0485810i	−0.00374810	−	0.00649190i
$57$	−0.731384	+	0.970102i	−0.0968742	+	0.128493i
$58$	2.44178	+	2.44178i	0.320621	+	0.320621i
$59$	0.745519	+	0.745519i	0.0970583	+	0.0970583i	0.753969	−	0.656910i	$-0.228137\pi$
$59$	0.745519	+	0.745519i	0.0970583	+	0.0970583i	−0.656910	+	0.753969i	$0.728137\pi$
$60$	−2.35679	−	5.55591i	−0.304260	−	0.717264i
$61$	1.50195	+	2.60145i	0.192305	+	0.333082i	0.946014	−	0.324127i	$-0.105070\pi$
$61$	1.50195	+	2.60145i	0.192305	+	0.333082i	−0.753709	+	0.657209i	$0.771737\pi$
$62$	−2.97713	−	5.15654i	−0.378096	−	0.654882i
$63$	0.0816580	−	0.147151i	0.0102879	−	0.0185392i
$64$			1.00000i			0.125000i
$65$	12.5077	−	1.17860i	1.55139	−	0.146187i
$66$	7.04809	−	5.50389i	0.867560	−	0.677482i
$67$	−10.5121	+	2.81672i	−1.28426	+	0.344117i	−0.835478	−	0.549524i	$-0.814809\pi$
$67$	−10.5121	+	2.81672i	−1.28426	+	0.344117i	−0.448784	+	0.893640i	$0.648143\pi$
$68$	3.17065	+	1.83057i	0.384497	+	0.221990i
$69$	1.39262	+	9.92606i	0.167652	+	1.19496i
$70$	−0.188801	+	0.0505890i	−0.0225660	+	0.00604655i
$71$	−3.98742	−	14.8813i	−0.473220	−	1.76608i	−0.628085	−	0.778145i	$-0.716161\pi$
$71$	−3.98742	−	14.8813i	−0.473220	−	1.76608i	0.154865	−	0.987936i	$-0.450506\pi$
$72$	−2.57223	+	1.54390i	−0.303141	+	0.181950i
$73$	5.86521	−	5.86521i	0.686471	−	0.686471i	−0.274979	−	0.961450i	$-0.588671\pi$
$73$	5.86521	−	5.86521i	0.686471	−	0.686471i	0.961450	+	0.274979i	$0.0886710\pi$
$74$	6.53507	−	3.77302i	0.759687	−	0.438605i
$75$	−12.2484	+	1.71844i	−1.41432	+	0.198428i
$76$	−0.181544	−	0.677531i	−0.0208245	−	0.0777182i
$77$	−0.144812	−	0.250821i	−0.0165028	−	0.0285838i
$78$	−1.44403	−	6.07575i	−0.163504	−	0.687944i
$79$	2.76723	−	4.79298i	0.311338	−	0.539253i	−0.667314	−	0.744776i	$-0.732556\pi$
$79$	2.76723	−	4.79298i	0.311338	−	0.539253i	0.978652	+	0.205523i	$0.0658896\pi$
$80$	3.36565	+	0.901822i	0.376291	+	0.100827i
$81$	−7.94252	−	4.23277i	−0.882503	−	0.470307i
$82$	−2.61030	−	1.50706i	−0.288260	−	0.166427i
$83$	−4.13340	−	15.4261i	−0.453699	−	1.69323i	−0.691883	−	0.722009i	$-0.743219\pi$
$83$	−4.13340	−	15.4261i	−0.453699	−	1.69323i	0.238184	−	0.971220i	$-0.423448\pi$
$84$	0.0379430	+	0.0894470i	0.00413992	+	0.00975947i
$85$	9.02042	−	9.02042i	0.978402	−	0.978402i
$86$	−1.40533	+	5.24476i	−0.151540	+	0.565556i
$87$	−3.68122	−	4.71405i	−0.394668	−	0.505399i
$88$			5.16296i			0.550373i
$89$	−4.41179	+	16.4650i	−0.467649	+	1.74529i	0.180306	+	0.983611i	$0.442291\pi$
$89$	−4.41179	+	16.4650i	−0.467649	+	1.74529i	−0.647955	+	0.761679i	$0.724375\pi$
$90$	2.87651	+	10.0495i	0.303211	+	1.05932i
$91$	−0.201367	+	0.0189747i	−0.0211090	+	0.00198909i
$92$	−5.01164	−	2.89347i	−0.522500	−	0.301665i
$93$	4.02740	+	9.49420i	0.417622	+	0.984503i
$94$	−2.49912	+	4.32861i	−0.257765	+	0.446462i
$95$	−2.44405			−0.250754
$96$	0.211491	−	1.71909i	0.0215852	−	0.175454i
$97$	−0.595628	+	2.22292i	−0.0604769	+	0.225703i	−0.989549	−	0.144195i	$-0.953941\pi$
$97$	−0.595628	+	2.22292i	−0.0604769	+	0.225703i	0.929072	+	0.369898i	$0.120607\pi$
$98$	−6.75844	+	1.81092i	−0.682706	+	0.182930i
$99$	−13.2803	+	7.97107i	−1.33472	+	0.801123i
$100$	3.57043	−	6.18416i	0.357043	−	0.618416i
$101$	−3.52328			−0.350580			−0.175290	−	0.984517i	$-0.556086\pi$
$101$	−3.52328			−0.350580			−0.175290	+	0.984517i	$0.556086\pi$
$102$	−5.06348	−	3.81748i	−0.501359	−	0.377987i
$103$	5.20698	−	3.00625i	0.513059	−	0.296215i	−0.221031	−	0.975267i	$-0.570942\pi$
$103$	5.20698	−	3.00625i	0.513059	−	0.296215i	0.734090	+	0.679052i	$0.237609\pi$
$104$	3.27785	+	1.50189i	0.321420	+	0.147272i
$105$	0.335265	−	0.0470375i	0.0327185	−	0.00459039i
$106$	−2.75436	−	2.75436i	−0.267527	−	0.267527i
$107$	14.5555	−	8.40363i	1.40714	−	0.812410i	0.412024	−	0.911173i	$-0.364822\pi$
$107$	14.5555	−	8.40363i	1.40714	−	0.812410i	0.995111	+	0.0987630i	$0.0314886\pi$
$108$	4.74842	−	2.11009i	0.456917	−	0.203044i
$109$	−14.0667	−	14.0667i	−1.34734	−	1.34734i	−0.888537	−	0.458806i	$-0.848277\pi$
$109$	−14.0667	−	14.0667i	−1.34734	−	1.34734i	−0.458806	−	0.888537i	$-0.651723\pi$
$110$	17.3767	+	4.65607i	1.65680	+	0.443939i
$111$	−12.0323	+	5.10406i	−1.14206	+	0.484456i
$112$	−0.0541850	−	0.0145188i	−0.00512000	−	0.00137190i
$113$			19.5681i			1.84082i	0.390960	+	0.920408i	$0.372143\pi$
$113$			19.5681i			1.84082i	−0.390960	+	0.920408i	$0.627857\pi$
$114$	0.168799	+	1.20313i	0.0158095	+	0.112684i
$115$	−14.2580	+	14.2580i	−1.32957	+	1.32957i
$116$	3.45319			0.320621
$117$	1.19746	+	10.7502i	0.110705	+	0.993853i
$118$	1.05432			0.0970583
$119$	−0.145224	+	0.145224i	−0.0133126	+	0.0133126i
$120$	−5.59512	−	2.26212i	−0.510762	−	0.206502i
$121$			15.6561i			1.42328i
$122$	2.90154	+	0.777466i	0.262693	+	0.0703885i
$123$	4.16862	+	3.14283i	0.375872	+	0.283379i
$124$	−5.75138	−	1.54108i	−0.516489	−	0.138393i
$125$	−5.27469	−	5.27469i	−0.471782	−	0.471782i
$126$	−0.0463103	−	0.161792i	−0.00412565	−	0.0144136i
$127$	−0.00248320	+	0.00143368i	−0.000220349	+	0.000127218i	−0.500110	−	0.865962i	$-0.666707\pi$
$127$	−0.00248320	+	0.00143368i	−0.000220349	+	0.000127218i	0.499890	+	0.866089i	$0.333374\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	3.52510	−	8.71899i	0.310368	−	0.767665i
$130$	8.01087	−	9.67766i	0.702600	−	0.848787i
$131$	−10.8797	+	6.28138i	−0.950562	+	0.548807i	−0.893255	−	0.449550i	$-0.851584\pi$
$131$	−10.8797	+	6.28138i	−0.950562	+	0.548807i	−0.0573063	+	0.998357i	$0.518251\pi$
$132$	1.09192	−	8.87559i	0.0950393	−	0.772521i
$133$	0.0393479			0.00341189
$134$	−5.44148	+	9.42492i	−0.470072	+	0.814189i
$135$	−2.81960	−	17.8844i	−0.242673	−	1.53925i
$136$	3.53640	−	0.947575i	0.303244	−	0.0812539i
$137$	−3.63959	+	13.5832i	−0.310952	+	1.16049i	0.616748	+	0.787160i	$0.288450\pi$
$137$	−3.63959	+	13.5832i	−0.310952	+	1.16049i	−0.927700	+	0.373327i	$0.878217\pi$
$138$	8.00352	+	6.03405i	0.681305	+	0.513653i
$139$	0.313887			0.0266236			0.0133118	−	0.999911i	$-0.495763\pi$
$139$	0.313887			0.0266236			0.0133118	+	0.999911i	$0.495763\pi$
$140$	−0.0977305	+	0.169274i	−0.00825973	+	0.0143063i
$141$	5.21168	−	6.91272i	0.438902	−	0.582156i
$142$	−13.3422	−	7.70311i	−1.11965	−	0.646430i
$143$	16.9234	+	7.75420i	1.41521	+	0.648438i
$144$	−0.727143	+	2.91054i	−0.0605953	+	0.242545i
$145$	3.11417	−	11.6222i	0.258617	−	0.965173i
$146$		−	8.29466i		−	0.686471i
$147$	12.0014	−	1.68379i	0.989856	−	0.138876i
$148$	1.95306	−	7.28892i	0.160541	−	0.599146i
$149$	4.31299	−	4.31299i	0.353334	−	0.353334i	−0.508014	−	0.861349i	$-0.669620\pi$
$149$	4.31299	−	4.31299i	0.353334	−	0.353334i	0.861349	+	0.508014i	$0.169620\pi$
$150$	−7.44578	+	9.87602i	−0.607945	+	0.806374i
$151$	−2.90331	−	10.8353i	−0.236268	−	0.881766i	−0.977573	−	0.210597i	$-0.932459\pi$
$151$	−2.90331	−	10.8353i	−0.236268	−	0.881766i	0.741305	−	0.671169i	$-0.234207\pi$
$152$	−0.607458	−	0.350716i	−0.0492714	−	0.0284468i
$153$	7.89721	+	7.63348i	0.638452	+	0.617130i
$154$	−0.279755	−	0.0749601i	−0.0225433	−	0.00604046i
$155$	−10.3734	+	17.9673i	−0.833215	+	1.44317i
$156$	−5.31729	−	3.27512i	−0.425724	−	0.262220i
$157$	−6.52002	−	11.2930i	−0.520354	−	0.901280i	−0.999720	−	0.0236645i	$-0.992467\pi$
$157$	−6.52002	−	11.2930i	−0.520354	−	0.901280i	0.479366	−	0.877615i	$-0.340867\pi$
$158$	−1.43242	−	5.34588i	−0.113958	−	0.425295i
$159$	4.15247	+	5.31751i	0.329312	+	0.421706i
$160$	3.01756	−	1.74219i	0.238559	−	0.137732i
$161$	0.229546	−	0.229546i	0.0180908	−	0.0180908i
$162$	−8.60923	+	2.62320i	−0.676405	+	0.206098i
$163$	−1.44937	−	5.40913i	−0.113524	−	0.423676i	0.885649	−	0.464356i	$-0.153714\pi$
$163$	−1.44937	−	5.40913i	−0.113524	−	0.423676i	−0.999172	+	0.0406802i	$0.987048\pi$
$164$	−2.91142	+	0.780112i	−0.227343	+	0.0609165i
$165$	−28.8874	−	11.6792i	−2.24888	−	0.909225i
$166$	−13.8306	−	7.98511i	−1.07346	−	0.619765i
$167$	8.94898	−	2.39787i	0.692493	−	0.185553i	0.104627	−	0.994512i	$-0.466635\pi$
$167$	8.94898	−	2.39787i	0.692493	−	0.185553i	0.587866	+	0.808959i	$0.299968\pi$
$168$	0.0900783	+	0.0364188i	0.00694970	+	0.00280977i
$169$	9.84595	−	8.48865i	0.757381	−	0.652973i
$170$		−	12.7568i		−	0.978402i
$171$	−0.0357291	−	2.10399i	−0.00273228	−	0.160896i
$172$	2.71489	+	4.70232i	0.207008	+	0.358548i
$173$	−4.92325	−	8.52731i	−0.374307	−	0.648319i	0.615916	−	0.787812i	$-0.288786\pi$
$173$	−4.92325	−	8.52731i	−0.374307	−	0.648319i	−0.990223	+	0.139493i	$0.955453\pi$
$174$	−5.93635	−	0.730318i	−0.450034	−	0.0553653i
$175$	0.283250	+	0.283250i	0.0214117	+	0.0214117i
$176$	3.65076	+	3.65076i	0.275187	+	0.275187i
$177$	−1.81248	−	0.222980i	−0.136234	−	0.0167602i
$178$	8.52292	+	14.7621i	0.638820	+	1.10647i
$179$	7.69779	+	13.3330i	0.575360	+	0.996553i	0.996002	+	0.0893264i	$0.0284714\pi$
$179$	7.69779	+	13.3330i	0.575360	+	0.996553i	−0.420642	+	0.907227i	$0.638195\pi$
$180$	9.14010	+	5.07210i	0.681263	+	0.378052i
$181$		−	17.1903i		−	1.27774i	−0.769314	−	0.638871i	$-0.779402\pi$
$181$		−	17.1903i		−	1.27774i	0.769314	−	0.638871i	$-0.220598\pi$
$182$	−0.128971	+	0.155805i	−0.00955993	+	0.0115490i
$183$	−4.82359	−	1.95018i	−0.356570	−	0.144162i
$184$	−5.58976	+	1.49777i	−0.412082	+	0.110417i
$185$	−22.7706	−	13.1466i	−1.67413	−	0.966559i
$186$	9.56122	+	3.86561i	0.701062	+	0.283441i
$187$	18.2583	−	4.89229i	1.33518	−	0.357760i
$188$	1.29364	+	4.82793i	0.0943484	+	0.352113i
$189$	0.0453940	+	0.287929i	0.00330193	+	0.0209438i
$190$	−1.72821	+	1.72821i	−0.125377	+	0.125377i
$191$	−7.39988	+	4.27232i	−0.535436	+	0.309134i	−0.743227	−	0.669039i	$-0.766706\pi$
$191$	−7.39988	+	4.27232i	−0.535436	+	0.309134i	0.207791	+	0.978173i	$0.433373\pi$
$192$	−1.06603	−	1.36513i	−0.0769344	−	0.0985196i
$193$	0.157908	+	0.589319i	0.0113664	+	0.0424201i	0.971376	−	0.237547i	$-0.0763432\pi$
$193$	0.157908	+	0.589319i	0.0113664	+	0.0424201i	−0.960010	+	0.279967i	$0.909677\pi$
$194$	1.15067	+	1.99301i	0.0826130	+	0.143090i
$195$	−15.8181	+	14.9425i	−1.13276	+	1.07006i
$196$	−3.49843	+	6.05945i	−0.249888	+	0.432818i
$197$	17.3239	+	4.64193i	1.23428	+	0.330724i	0.816244	−	0.577707i	$-0.196052\pi$
$197$	17.3239	+	4.64193i	1.23428	+	0.330724i	0.418035	+	0.908431i	$0.362719\pi$
$198$	−3.75421	+	15.0270i	−0.266800	+	1.06792i
$199$	17.2644	+	9.96763i	1.22384	+	0.706586i	0.965735	−	0.259530i	$-0.0835675\pi$
$199$	17.2644	+	9.96763i	1.22384	+	0.706586i	0.258108	+	0.966116i	$0.416901\pi$
$200$	−1.84819	−	6.89754i	−0.130687	−	0.487729i
$201$	11.3477	−	15.0515i	0.800404	−	1.06165i
$202$	−2.49134	+	2.49134i	−0.175290	+	0.175290i
$203$	−0.0501363	+	0.187111i	−0.00351888	+	0.0131326i
$204$	−6.27979	+	0.881051i	−0.439673	+	0.0616859i
$205$			10.5023i			0.733514i
$206$	1.55615	−	5.80763i	0.108422	−	0.404637i
$207$	−12.4826	−	12.0658i	−0.867602	−	0.838628i
$208$	3.37979	−	1.25580i	0.234346	−	0.0870738i
$209$	−3.13628	−	1.81073i	−0.216941	−	0.125251i
$210$	0.203807	−	0.270329i	0.0140641	−	0.0186544i
$211$	−0.727198	+	1.25954i	−0.0500623	+	0.0867105i	−0.889971	−	0.456018i	$-0.849275\pi$
$211$	−0.727198	+	1.25954i	−0.0500623	+	0.0867105i	0.839908	+	0.542728i	$0.182609\pi$
$212$	−3.89525			−0.267527
$213$	21.3073	+	16.0641i	1.45995	+	1.10069i
$214$	4.35004	−	16.2346i	0.297363	−	1.10977i
$215$	18.2747	−	4.89669i	1.24632	−	0.333951i
$216$	1.86558	−	4.84970i	0.126937	−	0.329980i
$217$	0.167007	−	0.289264i	0.0113371	−	0.0196365i
$218$	−19.8933			−1.34734
$219$	−1.75424	+	14.2593i	−0.118541	+	0.963552i
$220$	15.5795	−	8.99483i	1.05037	−	0.606432i
$221$	2.20527	−	13.0149i	0.148342	−	0.875480i
$222$	−4.89903	+	12.1173i	−0.328801	+	0.813258i
$223$	−3.00391	−	3.00391i	−0.201157	−	0.201157i	0.599339	−	0.800496i	$-0.295430\pi$
$223$	−3.00391	−	3.00391i	−0.201157	−	0.201157i	−0.800496	+	0.599339i	$0.795430\pi$
$224$	−0.0485810	+	0.0280482i	−0.00324595	+	0.00187405i
$225$	14.8887	−	15.4031i	0.992577	−	1.02687i
$226$	13.8368	+	13.8368i	0.920408	+	0.920408i
$227$	22.5667	+	6.04673i	1.49780	+	0.401335i	0.912364	−	0.409380i	$-0.134255\pi$
$227$	22.5667	+	6.04673i	1.49780	+	0.401335i	0.585440	+	0.810716i	$0.300922\pi$
$228$	0.970102	+	0.731384i	0.0642466	+	0.0484371i
$229$	5.96935	+	1.59948i	0.394466	+	0.105697i	0.450599	−	0.892727i	$-0.351210\pi$
$229$	5.96935	+	1.59948i	0.394466	+	0.105697i	−0.0561332	+	0.998423i	$0.517877\pi$
$230$			20.1639i			1.32957i
$231$	0.465071	+	0.188029i	0.0305994	+	0.0123714i
$232$	2.44178	−	2.44178i	0.160310	−	0.160310i
$233$	1.20969			0.0792497			0.0396249	−	0.999215i	$-0.487384\pi$
$233$	1.20969			0.0792497			0.0396249	+	0.999215i	$0.487384\pi$
$234$	8.44825	+	6.75479i	0.552279	+	0.441574i
$235$	17.4157			1.13608
$236$	0.745519	−	0.745519i	0.0485292	−	0.0485292i
$237$	1.33186	+	9.49299i	0.0865138	+	0.616636i
$238$			0.205377i			0.0133126i
$239$	13.1345	+	3.51937i	0.849599	+	0.227649i	0.657246	−	0.753676i	$-0.271721\pi$
$239$	13.1345	+	3.51937i	0.849599	+	0.227649i	0.192353	+	0.981326i	$0.438388\pi$
$240$	−5.55591	+	2.35679i	−0.358632	+	0.152130i
$241$	−6.88614	−	1.84513i	−0.443575	−	0.118856i	0.0301165	−	0.999546i	$-0.490412\pi$
$241$	−6.88614	−	1.84513i	−0.443575	−	0.118856i	−0.473692	+	0.880691i	$0.657079\pi$
$242$	11.0706	+	11.0706i	0.711642	+	0.711642i
$243$	15.3548	−	2.68874i	0.985013	−	0.172483i
$244$	2.60145	−	1.50195i	0.166541	−	0.0961524i
$245$	17.2390	+	17.2390i	1.10136	+	1.10136i
$246$	5.16997	−	0.725345i	0.329625	−	0.0462463i
$247$	−2.06193	+	1.46442i	−0.131198	+	0.0931789i
$248$	−5.15654	+	2.97713i	−0.327441	+	0.189048i
$249$	22.0873	+	16.6522i	1.39973	+	1.05529i
$250$	−7.45953			−0.471782
$251$	2.50999	−	4.34744i	0.158429	−	0.274408i	−0.775873	−	0.630889i	$-0.782690\pi$
$251$	2.50999	−	4.34744i	0.158429	−	0.274408i	0.934302	+	0.356481i	$0.116024\pi$
$252$	−0.147151	−	0.0816580i	−0.00926962	−	0.00514397i
$253$	−28.8597	+	7.73293i	−1.81439	+	0.486165i
$254$	−0.000742127		0.00276966i	−4.65652e−5		0.000173784i
$255$	−2.69795	+	21.9301i	−0.168952	+	1.37332i
$256$	1.00000			0.0625000
$257$	2.47055	−	4.27912i	0.154109	−	0.266924i	−0.778625	−	0.627489i	$-0.784083\pi$
$257$	2.47055	−	4.27912i	0.154109	−	0.266924i	0.932734	+	0.360565i	$0.117416\pi$
$258$	−3.67264	−	8.65788i	−0.228648	−	0.539016i
$259$	0.366594	+	0.211653i	0.0227791	+	0.0131515i
$260$	−1.17860	−	12.5077i	−0.0730934	−	0.775693i
$261$	10.0507	+	2.51097i	0.622121	+	0.155425i
$262$	−3.25148	+	12.1347i	−0.200877	+	0.749684i
$263$			12.9065i			0.795849i	0.917418	+	0.397925i	$0.130269\pi$
$263$			12.9065i			0.795849i	−0.917418	+	0.397925i	$0.869731\pi$
$264$	−5.50389	−	7.04809i	−0.338741	−	0.433780i
$265$	−3.51282	+	13.1100i	−0.215791	+	0.805342i
$266$	0.0278231	−	0.0278231i	0.00170595	−	0.00170595i
$267$	−11.5296	−	27.1800i	−0.705601	−	1.66339i
$268$	2.81672	+	10.5121i	0.172058	+	0.642131i
$269$	−22.4600	−	12.9673i	−1.36941	−	0.790630i	−0.378558	−	0.925577i	$-0.623580\pi$
$269$	−22.4600	−	12.9673i	−1.36941	−	0.790630i	−0.990853	+	0.134948i	$0.956913\pi$
$270$	−14.6400	−	10.6524i	−0.890960	−	0.648287i
$271$	−15.7870	−	4.23012i	−0.958992	−	0.256961i	−0.254819	−	0.966989i	$-0.582016\pi$
$271$	−15.7870	−	4.23012i	−0.958992	−	0.256961i	−0.704174	+	0.710028i	$0.748682\pi$
$272$	1.83057	−	3.17065i	0.110995	−	0.192249i
$273$	0.254663	−	0.240567i	0.0154129	−	0.0145598i
$274$	7.03116	+	12.1783i	0.424768	+	0.735719i
$275$	−9.54212	−	35.6117i	−0.575412	−	2.14747i
$276$	9.92606	−	1.39262i	0.597479	−	0.0838260i
$277$	−14.7653	+	8.52472i	−0.887158	+	0.512201i	−0.873012	−	0.487699i	$-0.837836\pi$
$277$	−14.7653	+	8.52472i	−0.887158	+	0.512201i	−0.0141462	+	0.999900i	$0.504503\pi$
$278$	0.221952	−	0.221952i	0.0133118	−	0.0133118i
$279$	−15.6191	−	8.66745i	−0.935088	−	0.518907i
$280$	0.0505890	+	0.188801i	0.00302327	+	0.0112830i
$281$	−3.85082	+	1.03182i	−0.229721	+	0.0615535i	−0.371843	−	0.928296i	$-0.621274\pi$
$281$	−3.85082	+	1.03182i	−0.229721	+	0.0615535i	0.142122	+	0.989849i	$0.454607\pi$
$282$	−1.20282	−	8.57325i	−0.0716270	−	0.510529i
$283$	−15.7258	−	9.07928i	−0.934801	−	0.539707i	−0.0464740	−	0.998920i	$-0.514798\pi$
$283$	−15.7258	−	9.07928i	−0.934801	−	0.539707i	−0.888327	+	0.459212i	$0.848132\pi$
$284$	−14.8813	+	3.98742i	−0.883040	+	0.236610i
$285$	3.33644	−	2.60544i	0.197634	−	0.154333i
$286$	17.4497	−	6.48362i	1.03182	−	0.383385i
$287$		−	0.169081i		−	0.00998056i
$288$	1.54390	+	2.57223i	0.0909750	+	0.151570i
$289$	1.79800	+	3.11423i	0.105765	+	0.183190i
$290$	−6.01611	−	10.4202i	−0.353278	−	0.611895i
$291$	−1.55659	−	3.66952i	−0.0912492	−	0.215111i
$292$	−5.86521	−	5.86521i	−0.343235	−	0.343235i
$293$	14.4630	+	14.4630i	0.844940	+	0.844940i	0.989497	−	0.144557i	$-0.0461756\pi$
$293$	14.4630	+	14.4630i	0.844940	+	0.844940i	−0.144557	+	0.989497i	$0.546176\pi$
$294$	7.29563	−	9.67686i	0.425490	−	0.564366i
$295$	−1.83683	−	3.18148i	−0.106944	−	0.185233i
$296$	−3.77302	−	6.53507i	−0.219303	−	0.379843i
$297$	9.63190	−	25.0388i	0.558900	−	1.45290i
$298$		−	6.09950i		−	0.353334i
$299$	−3.48573	+	20.5719i	−0.201585	+	1.18970i
$300$	1.71844	+	12.2484i	0.0992141	+	0.707159i
$301$	−0.294212	+	0.0788339i	−0.0169581	+	0.00454391i
$302$	−9.71468	−	5.60877i	−0.559017	−	0.322749i
$303$	4.80973	−	3.75594i	0.276312	−	0.215773i
$304$	−0.677531	+	0.181544i	−0.0388591	+	0.0104123i
$305$	−2.70898	−	10.1101i	−0.155116	−	0.578900i
$306$	10.9819	−	0.186489i	0.627791	−	0.0106609i
$307$	−6.72055	+	6.72055i	−0.383562	+	0.383562i	−0.872384	−	0.488822i	$-0.837427\pi$
$307$	−6.72055	+	6.72055i	−0.383562	+	0.383562i	0.488822	+	0.872384i	$0.337427\pi$
$308$	−0.250821	+	0.144812i	−0.0142919	+	0.00825142i
$309$	−3.90342	+	9.65473i	−0.222058	+	0.549238i
$310$	5.36969	+	20.0399i	0.304978	+	1.13819i
$311$	−1.80968	−	3.13446i	−0.102618	−	0.177739i	0.810145	−	0.586230i	$-0.199388\pi$
$311$	−1.80968	−	3.13446i	−0.102618	−	0.177739i	−0.912762	+	0.408491i	$0.866055\pi$
$312$	−6.07575	+	1.44403i	−0.343972	+	0.0817522i
$313$	−9.03947	+	15.6568i	−0.510941	+	0.884975i	0.488979	+	0.872296i	$0.337370\pi$
$313$	−9.03947	+	15.6568i	−0.510941	+	0.884975i	−0.999920	+	0.0126797i	$0.995964\pi$
$314$	−12.5957	−	3.37501i	−0.710817	−	0.190463i
$315$	−0.407535	+	0.421616i	−0.0229620	+	0.0237554i
$316$	−4.79298	−	2.76723i	−0.269626	−	0.155669i
$317$	−2.76420	−	10.3161i	−0.155253	−	0.579412i	−0.999084	−	0.0428025i	$-0.986371\pi$
$317$	−2.76420	−	10.3161i	−0.155253	−	0.579412i	0.843830	−	0.536610i	$-0.180295\pi$
$318$	6.69628	+	0.823809i	0.375509	+	0.0461969i
$319$	12.6068	−	12.6068i	0.705845	−	0.705845i
$320$	0.901822	−	3.36565i	0.0504134	−	0.188145i
$321$	−10.9116	+	26.9887i	−0.609025	+	1.50636i
$322$		−	0.324627i		−	0.0180908i
$323$	−0.664659	+	2.48054i	−0.0369826	+	0.138021i
$324$	−4.23277	+	7.94252i	−0.235154	+	0.441251i
$325$	−25.3849	−	4.30125i	−1.40810	−	0.238590i
$326$	−4.84969	−	2.79997i	−0.268600	−	0.155076i
$327$	34.1983	+	4.20724i	1.89117	+	0.232661i
$328$	−1.50706	+	2.61030i	−0.0832135	+	0.144130i
$329$	−0.280384			−0.0154581
$330$	−28.6849	+	12.1680i	−1.57905	+	0.669827i
$331$	−0.861097	+	3.21366i	−0.0473301	+	0.176639i	−0.985545	−	0.169416i	$-0.945812\pi$
$331$	−0.861097	+	3.21366i	−0.0473301	+	0.176639i	0.938215	+	0.346054i	$0.112479\pi$
$332$	−15.4261	+	4.13340i	−0.846615	+	0.226850i
$333$	10.9846	−	19.7946i	0.601950	−	1.08474i
$334$	4.63233	−	8.02344i	0.253470	−	0.439023i
$335$	37.9203			2.07181
$336$	0.0894470	−	0.0379430i	0.00487973	−	0.00206996i
$337$	2.50494	−	1.44623i	0.136453	−	0.0787811i	−0.430220	−	0.902724i	$-0.641564\pi$
$337$	2.50494	−	1.44623i	0.136453	−	0.0787811i	0.566672	+	0.823943i	$0.308231\pi$
$338$	0.959757	−	12.9645i	0.0522039	−	0.705177i
$339$	−20.8603	−	26.7130i	−1.13298	−	1.45085i
$340$	−9.02042	−	9.02042i	−0.489201	−	0.489201i
$341$	−26.6230	+	15.3708i	−1.44172	+	0.832376i
$342$	−1.51301	−	1.46248i	−0.0818143	−	0.0790821i
$343$	−0.555202	−	0.555202i	−0.0299781	−	0.0299781i
$344$	5.24476	+	1.40533i	0.282778	+	0.0757702i
$345$	4.26447	−	34.6635i	0.229591	−	1.86622i
$346$	−9.51098	−	2.54846i	−0.511313	−	0.137006i
$347$		−	17.9932i		−	0.965923i	−0.875642	−	0.482962i	$-0.839561\pi$
$347$		−	17.9932i		−	0.965923i	0.875642	−	0.482962i	$-0.160439\pi$
$348$	−4.71405	+	3.68122i	−0.252699	+	0.197334i
$349$	18.3144	−	18.3144i	0.980348	−	0.980348i	−0.0194630	−	0.999811i	$-0.506196\pi$
$349$	18.3144	−	18.3144i	0.980348	−	0.980348i	0.999811	+	0.0194630i	$0.00619566\pi$
$350$	0.400577			0.0214117
$351$	−13.0947	−	13.3988i	−0.698945	−	0.715176i
$352$	5.16296			0.275187
$353$	−2.10008	+	2.10008i	−0.111776	+	0.111776i	−0.760783	−	0.649007i	$-0.775185\pi$
$353$	−2.10008	+	2.10008i	−0.111776	+	0.111776i	0.649007	+	0.760783i	$0.275185\pi$
$354$	−1.43929	+	1.12394i	−0.0764971	+	0.0597370i
$355$			53.6810i			2.84909i
$356$	16.4650	+	4.41179i	0.872645	+	0.233824i
$357$	0.0434354	−	0.353062i	0.00229885	−	0.0186860i
$358$	14.8710	+	3.98467i	0.785957	+	0.210596i
$359$	0.0334095	+	0.0334095i	0.00176329	+	0.00176329i	0.707988	−	0.706225i	$-0.249603\pi$
$359$	0.0334095	+	0.0334095i	0.00176329	+	0.00176329i	−0.706225	+	0.707988i	$0.749603\pi$
$360$	10.0495	−	2.87651i	0.529658	−	0.151606i
$361$	−16.0284	+	9.25400i	−0.843600	+	0.487052i
$362$	−12.1554	−	12.1554i	−0.638871	−	0.638871i
$363$	−16.6900	−	21.3726i	−0.875996	−	1.12177i
$364$	0.0189747	+	0.201367i	0.000994546	+	0.0105545i
$365$	−25.0296	+	14.4508i	−1.31011	+	0.756392i
$366$	−4.78978	+	2.03180i	−0.250366	+	0.106204i
$367$	−9.50010			−0.495901			−0.247951	−	0.968773i	$-0.579757\pi$
$367$	−9.50010			−0.495901			−0.247951	+	0.968773i	$0.579757\pi$
$368$	−2.89347	+	5.01164i	−0.150833	+	0.261250i
$369$	−9.04106	+	0.153531i	−0.470659	+	0.00799253i
$370$	−25.3973	+	6.80519i	−1.32034	+	0.353785i
$371$	0.0565545	−	0.211064i	0.00293616	−	0.0109579i
$372$	9.49420	−	4.02740i	0.492251	−	0.208811i
$373$	26.8580			1.39066			0.695328	−	0.718693i	$-0.255259\pi$
$373$	26.8580			1.39066			0.695328	+	0.718693i	$0.255259\pi$
$374$	9.45117	−	16.3699i	0.488709	−	0.846468i
$375$	12.8236	+	1.57762i	0.662208	+	0.0814681i
$376$	4.32861	+	2.49912i	0.223231	+	0.128882i
$377$	−4.33651	−	11.6711i	−0.223341	−	0.601090i
$378$	0.235695	+	0.171498i	0.0121229	+	0.00882093i
$379$	4.93097	−	18.4026i	0.253287	−	0.945279i	−0.715749	−	0.698358i	$-0.753914\pi$
$379$	4.93097	−	18.4026i	0.253287	−	0.945279i	0.969036	−	0.246921i	$-0.0794189\pi$
$380$			2.44405i			0.125377i
$381$	0.00186154	−	0.00460433i	9.53696e−5	−	0.000235887i
$382$	−2.21152	+	8.25349i	−0.113151	+	0.422285i
$383$	−6.76886	+	6.76886i	−0.345873	+	0.345873i	−0.858570	−	0.512697i	$-0.828646\pi$
$383$	−6.76886	+	6.76886i	−0.345873	+	0.345873i	0.512697	+	0.858570i	$0.328646\pi$
$384$	−1.71909	−	0.211491i	−0.0877270	−	0.0107926i
$385$	0.261189	+	0.974771i	0.0133114	+	0.0496789i
$386$	0.528369	+	0.305054i	0.0268933	+	0.0155268i
$387$	4.48253	+	15.6604i	0.227860	+	0.796064i
$388$	2.22292	+	0.595628i	0.112851	+	0.0302384i
$389$	4.60612	−	7.97804i	0.233540	−	0.404502i	−0.725308	−	0.688425i	$-0.758302\pi$
$389$	4.60612	−	7.97804i	0.233540	−	0.404502i	0.958847	+	0.283922i	$0.0916358\pi$
$390$	−0.619146	+	21.7511i	−0.0313517	+	1.10141i
$391$	10.5934	+	18.3484i	0.535733	+	0.927916i
$392$	1.81092	+	6.75844i	0.0914652	+	0.341353i
$393$	8.15597	−	20.1730i	0.411414	−	1.01759i
$394$	15.5322	−	8.96753i	0.782502	−	0.451777i
$395$	−13.6359	+	13.6359i	−0.686098	+	0.686098i
$396$	7.97107	+	13.2803i	0.400562	+	0.667362i
$397$	7.23488	+	27.0009i	0.363108	+	1.35514i	0.869967	+	0.493110i	$0.164140\pi$
$397$	7.23488	+	27.0009i	0.363108	+	1.35514i	−0.506859	+	0.862029i	$0.669194\pi$
$398$	19.2560	−	5.15962i	0.965215	−	0.258629i
$399$	−0.0537148	+	0.0419462i	−0.00268910	+	0.00209993i
$400$	−6.18416	−	3.57043i	−0.309208	−	0.178521i
$401$	−8.59039	+	2.30179i	−0.428984	+	0.114946i	−0.466849	−	0.884337i	$-0.654611\pi$
$401$	−8.59039	+	2.30179i	−0.428984	+	0.114946i	0.0378654	+	0.999283i	$0.487944\pi$
$402$	−2.61897	−	18.6670i	−0.130623	−	0.931026i
$403$	2.01404	+	21.3737i	0.100327	+	1.06470i
$404$			3.52328i			0.175290i
$405$	22.9145	+	21.4087i	1.13863	+	1.06381i
$406$	0.0968559	+	0.167759i	0.00480688	+	0.00832576i
$407$	−19.4800	−	33.7403i	−0.965586	−	1.67244i
$408$	−3.81748	+	5.06348i	−0.188994	+	0.250680i
$409$	−24.6479	−	24.6479i	−1.21876	−	1.21876i	−0.968067	−	0.250692i	$-0.919342\pi$
$409$	−24.6479	−	24.6479i	−1.21876	−	1.21876i	−0.250692	−	0.968067i	$-0.580658\pi$
$410$	7.42626	+	7.42626i	0.366757	+	0.366757i
$411$	−9.51159	−	22.4227i	−0.469172	−	1.10603i
$412$	−3.00625	−	5.20698i	−0.148107	−	0.256529i
$413$	0.0295719	+	0.0512200i	0.00145514	+	0.00252037i
$414$	−17.3583	+	0.294772i	−0.853115	+	0.0144872i
$415$			55.6462i			2.73157i
$416$	1.50189	−	3.27785i	0.0736362	−	0.160710i
$417$	−0.428496	+	0.334614i	−0.0209835	+	0.0163861i
$418$	−3.49807	+	0.937304i	−0.171096	+	0.0458450i
$419$	14.9055	+	8.60570i	0.728182	+	0.420416i	0.817757	−	0.575564i	$-0.195217\pi$
$419$	14.9055	+	8.60570i	0.728182	+	0.420416i	−0.0895746	+	0.995980i	$0.528551\pi$
$420$	−0.0470375	−	0.335265i	−0.00229519	−	0.0163592i
$421$	3.68017	−	0.986098i	0.179360	−	0.0480595i	−0.168021	−	0.985783i	$-0.553738\pi$
$421$	3.68017	−	0.986098i	0.179360	−	0.0480595i	0.347381	+	0.937724i	$0.387071\pi$
$422$	0.376425	+	1.40484i	0.0183241	+	0.0683864i
$423$	0.254598	+	14.9926i	0.0123790	+	0.728964i
$424$	−2.75436	+	2.75436i	−0.133763	+	0.133763i
$425$	−22.6411	+	13.0719i	−1.09826	+	0.634078i
$426$	26.4255	−	3.70749i	1.28032	−	0.179628i
$427$	0.0436131	+	0.162766i	0.00211059	+	0.00787681i
$428$	−8.40363	−	14.5555i	−0.406205	−	0.703568i
$429$	−31.3689	+	7.45548i	−1.51450	+	0.359954i
$430$	9.45967	−	16.3846i	0.456186	−	0.790137i
$431$	−20.9081	−	5.60231i	−1.00711	−	0.269854i	−0.282687	−	0.959212i	$-0.591226\pi$
$431$	−20.9081	−	5.60231i	−1.00711	−	0.269854i	−0.724420	+	0.689358i	$0.757893\pi$
$432$	−2.11009	−	4.74842i	−0.101522	−	0.228459i
$433$	15.1421	+	8.74227i	0.727681	+	0.420127i	0.817573	−	0.575825i	$-0.195319\pi$
$433$	15.1421	+	8.74227i	0.727681	+	0.420127i	−0.0898923	+	0.995951i	$0.528652\pi$
$434$	−0.0864490	−	0.322632i	−0.00414968	−	0.0154868i
$435$	8.13845	+	19.1856i	0.390209	+	0.919880i
$436$	−14.0667	+	14.0667i	−0.673671	+	0.673671i
$437$	1.05058	−	3.92084i	0.0502563	−	0.187559i
$438$	8.84239	+	11.3233i	0.422506	+	0.541046i
$439$		−	6.29999i		−	0.300682i	−0.988634	−	0.150341i	$-0.951963\pi$
$439$		−	6.29999i		−	0.300682i	0.988634	−	0.150341i	$-0.0480372\pi$
$440$	4.65607	−	17.3767i	0.221969	−	0.828401i
$441$	−14.5884	+	15.0924i	−0.694686	+	0.718688i
$442$	−7.64360	−	10.7623i	−0.363569	−	0.511911i
$443$	−13.9547	−	8.05675i	−0.663007	−	0.382788i	0.130414	−	0.991460i	$-0.458369\pi$
$443$	−13.9547	−	8.05675i	−0.663007	−	0.382788i	−0.793422	+	0.608672i	$0.791703\pi$
$444$	5.10406	+	12.0323i	0.242228	+	0.571029i
$445$	29.6970	−	51.4368i	1.40778	−	2.43834i
$446$	−4.24818			−0.201157
$447$	−1.28999	+	10.4856i	−0.0610143	+	0.495951i
$448$	−0.0145188	+	0.0541850i	−0.000685950	+	0.00256000i
$449$	−18.3173	+	4.90811i	−0.864447	+	0.231628i	−0.663685	−	0.748012i	$-0.731009\pi$
$449$	−18.3173	+	4.90811i	−0.864447	+	0.231628i	−0.200762	+	0.979640i	$0.564342\pi$
$450$	−0.363737	−	21.4195i	−0.0171467	−	1.00972i
$451$	−7.78089	+	13.4769i	−0.366388	+	0.634602i
$452$	19.5681			0.920408
$453$	15.5142	+	11.6966i	0.728921	+	0.549552i
$454$	20.2327	−	11.6814i	0.949570	−	0.548234i
$455$	0.694841	+	0.117735i	0.0325746	+	0.00551949i
$456$	1.20313	−	0.168799i	0.0563418	−	0.00790473i
$457$	−11.9721	−	11.9721i	−0.560032	−	0.560032i	0.369285	−	0.929316i	$-0.379603\pi$
$457$	−11.9721	−	11.9721i	−0.560032	−	0.560032i	−0.929316	+	0.369285i	$0.879603\pi$
$458$	5.35197	−	3.08996i	0.250081	−	0.144384i
$459$	−18.9182	−	2.00197i	−0.883028	−	0.0934439i
$460$	14.2580	+	14.2580i	0.664783	+	0.664783i
$461$	12.5113	+	3.35240i	0.582711	+	0.156137i	0.538120	−	0.842868i	$-0.319135\pi$
$461$	12.5113	+	3.35240i	0.582711	+	0.156137i	0.0445913	+	0.999005i	$0.485801\pi$
$462$	0.461811	−	0.195898i	0.0214854	−	0.00911401i
$463$	17.0527	+	4.56925i	0.792505	+	0.212351i	0.632291	−	0.774731i	$-0.282115\pi$
$463$	17.0527	+	4.56925i	0.792505	+	0.212351i	0.160214	+	0.987082i	$0.448782\pi$
$464$		−	3.45319i		−	0.160310i
$465$	−4.99271	−	35.5861i	−0.231532	−	1.65027i
$466$	0.855383	−	0.855383i	0.0396249	−	0.0396249i
$467$	21.1177			0.977210			0.488605	−	0.872505i	$-0.337506\pi$
$467$	21.1177			0.977210			0.488605	+	0.872505i	$0.337506\pi$
$468$	10.7502	−	1.19746i	0.496927	−	0.0553524i
$469$	−0.610496			−0.0281901
$470$	12.3148	−	12.3148i	0.568039	−	0.568039i
$471$	20.9394	+	8.46582i	0.964835	+	0.390084i
$472$		−	1.05432i		−	0.0485292i
$473$	27.0784	+	7.25565i	1.24507	+	0.333615i
$474$	7.65433	+	5.77079i	0.351575	+	0.265061i
$475$	4.83815	+	1.29638i	0.221990	+	0.0594820i
$476$	0.145224	+	0.145224i	0.00665632	+	0.00665632i
$477$	−11.3373	−	2.83240i	−0.519099	−	0.129687i
$478$	11.7761	−	6.79891i	0.538624	−	0.310975i
$479$	−10.8748	−	10.8748i	−0.496883	−	0.496883i	0.413583	−	0.910466i	$-0.364277\pi$
$479$	−10.8748	−	10.8748i	−0.496883	−	0.496883i	−0.910466	+	0.413583i	$0.864277\pi$
$480$	−2.26212	+	5.59512i	−0.103251	+	0.255381i
$481$	−27.0877	+	2.55246i	−1.23509	+	0.116382i
$482$	−6.17394	+	3.56453i	−0.281215	+	0.162360i
$483$	−0.0686556	+	0.558063i	−0.00312394	+	0.0253928i
$484$	15.6561			0.711642
$485$	4.00935	−	6.94439i	0.182055	−	0.315329i
$486$	8.95628	−	12.7587i	0.406265	−	0.578748i
$487$	−15.1707	+	4.06498i	−0.687450	+	0.184202i	−0.585603	−	0.810598i	$-0.699142\pi$
$487$	−15.1707	+	4.06498i	−0.687450	+	0.184202i	−0.101848	+	0.994800i	$0.532475\pi$
$488$	0.777466	−	2.90154i	0.0351942	−	0.131347i
$489$	7.74489	+	5.83907i	0.350236	+	0.264052i
$490$	24.3796			1.10136
$491$	−3.19734	+	5.53796i	−0.144294	+	0.249925i	−0.929109	−	0.369805i	$-0.879424\pi$
$491$	−3.19734	+	5.53796i	−0.144294	+	0.249925i	0.784815	+	0.619730i	$0.212758\pi$
$492$	3.14283	−	4.16862i	0.141690	−	0.187936i
$493$	−10.9489	−	6.32132i	−0.493112	−	0.284698i
$494$	−0.422503	+	2.49351i	−0.0190093	+	0.112188i
$495$	51.8854	−	14.8513i	2.33207	−	0.667517i
$496$	−1.54108	+	5.75138i	−0.0691964	+	0.258245i
$497$		−	0.864234i		−	0.0387662i
$498$	27.3930	−	3.84322i	1.22751	−	0.172219i
$499$	−1.98095	+	7.39299i	−0.0886794	+	0.330956i	−0.995985	−	0.0895148i	$-0.971468\pi$
$499$	−1.98095	+	7.39299i	−0.0886794	+	0.330956i	0.907306	+	0.420471i	$0.138135\pi$
$500$	−5.27469	+	5.27469i	−0.235891	+	0.235891i
$501$	−9.66028	+	12.8133i	−0.431590	+	0.572457i
$502$	−1.29927	−	4.84894i	−0.0579892	−	0.216419i
$503$	6.97222	+	4.02541i	0.310876	+	0.179484i	0.647318	−	0.762220i	$-0.275890\pi$
$503$	6.97222	+	4.02541i	0.310876	+	0.179484i	−0.336442	+	0.941704i	$0.609224\pi$
$504$	−0.161792	+	0.0463103i	−0.00720679	+	0.00206282i
$505$	11.8581	+	3.17737i	0.527679	+	0.141391i
$506$	−14.9389	+	25.8749i	−0.664114	+	1.15028i
$507$	−4.39179	+	22.0842i	−0.195046	+	0.980794i
$508$	0.00143368	+	0.00248320i	6.36092e−5	+	0.000110174i
$509$	−8.37966	−	31.2733i	−0.371422	−	1.38617i	−0.858503	−	0.512809i	$-0.828605\pi$
$509$	−8.37966	−	31.2733i	−0.371422	−	1.38617i	0.487081	−	0.873357i	$-0.338062\pi$
$510$	13.5992	+	17.4147i	0.602182	+	0.771134i
$511$	0.402962	−	0.232651i	0.0178260	−	0.0102919i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	2.29170	+	2.83413i	0.101181	+	0.125130i
$514$	−1.27885	−	4.77274i	−0.0564077	−	0.210517i
$515$	−20.2359	+	5.42221i	−0.891702	+	0.238931i
$516$	−8.71899	−	3.52510i	−0.383832	−	0.155184i
$517$	22.3484	+	12.9029i	0.982882	+	0.567467i
$518$	0.408883	−	0.109560i	0.0179653	−	0.00481378i
$519$	15.8113	+	6.39252i	0.694037	+	0.280600i
$520$	−9.67766	−	8.01087i	−0.424393	−	0.351300i
$521$			3.95332i			0.173198i	0.996243	+	0.0865990i	$0.0275999\pi$
$521$			3.95332i			0.173198i	−0.996243	+	0.0865990i	$0.972400\pi$
$522$	8.88242	−	5.33137i	0.388773	−	0.233348i
$523$	−19.7397	−	34.1901i	−0.863155	−	1.49503i	−0.868868	−	0.495044i	$-0.835152\pi$
$523$	−19.7397	−	34.1901i	−0.863155	−	1.49503i	0.00571276	−	0.999984i	$-0.498182\pi$
$524$	6.28138	+	10.8797i	0.274403	+	0.475281i
$525$	−0.688627	−	0.0847183i	−0.0300542	−	0.00369741i
$526$	9.12628	+	9.12628i	0.397925	+	0.397925i
$527$	15.4145	+	15.4145i	0.671468	+	0.671468i
$528$	−8.87559	−	1.09192i	−0.386261	−	0.0475196i
$529$	−5.24435	−	9.08349i	−0.228015	−	0.394934i
$530$	6.78625	+	11.7541i	0.294776	+	0.510567i
$531$	2.71197	−	1.62777i	0.117689	−	0.0706390i
$532$		−	0.0393479i		−	0.00170595i
$533$	6.29276	+	8.86031i	0.272570	+	0.383783i
$534$	−27.3718	−	11.0665i	−1.18449	−	0.478893i
$535$	−56.5673	+	15.1572i	−2.44562	+	0.655301i
$536$	9.42492	+	5.44148i	0.407095	+	0.235036i
$537$	−24.7219	−	9.99509i	−1.06683	−	0.431320i
$538$	−25.0509	+	6.71236i	−1.08002	+	0.289391i
$539$	9.34970	+	34.8935i	0.402720	+	1.50297i
$540$	−17.8844	+	2.81960i	−0.769623	+	0.121336i
$541$	8.65093	−	8.65093i	0.371933	−	0.371933i	−0.496248	−	0.868181i	$-0.665289\pi$
$541$	8.65093	−	8.65093i	0.371933	−	0.371933i	0.868181	+	0.496248i	$0.165289\pi$
$542$	−14.1542	+	8.17196i	−0.607977	+	0.351016i
$543$	18.3254	+	23.4669i	0.786419	+	1.00706i
$544$	−0.947575	−	3.53640i	−0.0406269	−	0.151622i
$545$	34.6578	+	60.0291i	1.48458	+	2.57136i
$546$	0.00996791	−	0.350180i	0.000426587	−	0.0149863i
$547$	12.5519	−	21.7406i	0.536681	−	0.929559i	−0.462399	−	0.886672i	$-0.653011\pi$
$547$	12.5519	−	21.7406i	0.536681	−	0.929559i	0.999080	−	0.0428870i	$-0.0136556\pi$
$548$	13.5832	+	3.63959i	0.580243	+	0.155476i
$549$	8.66377	−	2.47986i	0.369761	−	0.105838i
$550$	−31.9286	−	18.4340i	−1.36144	−	0.786027i
$551$	0.626906	+	2.33965i	0.0267071	+	0.0996723i
$552$	6.03405	−	8.00352i	0.256826	−	0.340652i
$553$	0.219531	−	0.219531i	0.00933541	−	0.00933541i
$554$	−4.41272	+	16.4685i	−0.187479	+	0.699680i
$555$	45.0995	−	6.32744i	1.91437	−	0.268585i
$556$		−	0.313887i		−	0.0133118i
$557$	−2.76078	+	10.3034i	−0.116978	+	0.436567i	−0.999427	−	0.0338399i	$-0.989226\pi$
$557$	−2.76078	+	10.3034i	−0.116978	+	0.436567i	0.882449	+	0.470407i	$0.155893\pi$
$558$	−17.1731	+	4.91553i	−0.726997	+	0.208091i
$559$	12.4835	−	15.0809i	0.527996	−	0.637854i
$560$	0.169274	+	0.0977305i	0.00715314	+	0.00412987i
$561$	−19.7095	+	26.1425i	−0.832136	+	1.10374i
$562$	−1.99333	+	3.45255i	−0.0840836	+	0.145637i
$563$	−29.8646			−1.25864			−0.629322	−	0.777144i	$-0.716667\pi$
$563$	−29.8646			−1.25864			−0.629322	+	0.777144i	$0.716667\pi$
$564$	−6.91272	−	5.21168i	−0.291078	−	0.219451i
$565$	17.6470	−	65.8594i	0.742414	−	2.77073i
$566$	−17.5398	+	4.69978i	−0.737254	+	0.197547i
$567$	−0.368911	−	0.344669i	−0.0154928	−	0.0144747i
$568$	−7.70311	+	13.3422i	−0.323215	+	0.559825i
$569$	45.0588			1.88896			0.944482	−	0.328563i	$-0.106564\pi$
$569$	45.0588			1.88896			0.944482	+	0.328563i	$0.106564\pi$
$570$	0.516894	−	4.20154i	0.0216503	−	0.175983i
$571$	23.2043	−	13.3970i	0.971071	−	0.560648i	0.0715081	−	0.997440i	$-0.477219\pi$
$571$	23.2043	−	13.3970i	0.971071	−	0.560648i	0.899562	+	0.436792i	$0.143885\pi$
$572$	7.75420	−	16.9234i	0.324219	−	0.707604i
$573$	5.54733	−	13.7208i	0.231743	−	0.573194i
$574$	−0.119559	−	0.119559i	−0.00499028	−	0.00499028i
$575$	35.7874	−	20.6619i	1.49244	−	0.861659i
$576$	2.91054	+	0.727143i	0.121273	+	0.0302976i
$577$	−20.9051	−	20.9051i	−0.870292	−	0.870292i	0.122212	−	0.992504i	$-0.461001\pi$
$577$	−20.9051	−	20.9051i	−0.870292	−	0.870292i	−0.992504	+	0.122212i	$0.961001\pi$
$578$	3.47347	+	0.930713i	0.144477	+	0.0387126i
$579$	−0.843798	−	0.636160i	−0.0350670	−	0.0264379i
$580$	−11.6222	−	3.11417i	−0.482587	−	0.129309i
$581$		−	0.895873i		−	0.0371671i
$582$	−3.69542	−	1.49406i	−0.153180	−	0.0619310i
$583$	−14.2206	+	14.2206i	−0.588958	+	0.588958i
$584$	−8.29466			−0.343235
$585$	5.66452	−	37.2611i	0.234199	−	1.54056i
$586$	20.4538			0.844940
$587$	−17.7153	+	17.7153i	−0.731190	+	0.731190i	−0.970856	−	0.239665i	$-0.922962\pi$
$587$	−17.7153	+	17.7153i	−0.731190	+	0.731190i	0.239665	+	0.970856i	$0.422962\pi$
$588$	−1.68379	−	12.0014i	−0.0694381	−	0.494928i
$589$		−	4.17651i		−	0.172090i
$590$	−3.54848	−	0.950812i	−0.146089	−	0.0391443i
$591$	−28.5978	+	12.1311i	−1.17636	+	0.499005i
$592$	−7.28892	−	1.95306i	−0.299573	−	0.0802703i
$593$	−13.5809	−	13.5809i	−0.557700	−	0.557700i	0.370952	−	0.928652i	$-0.379031\pi$
$593$	−13.5809	−	13.5809i	−0.557700	−	0.557700i	−0.928652	+	0.370952i	$0.879031\pi$
$594$	−10.8943	−	24.5159i	−0.447000	−	1.00590i
$595$	0.619738	−	0.357806i	0.0254068	−	0.0146686i
$596$	−4.31299	−	4.31299i	−0.176667	−	0.176667i
$597$	−34.1940	+	4.79740i	−1.39947	+	0.196344i
$598$	12.0817	+	17.0113i	0.494059	+	0.695644i
$599$	12.8779	−	7.43506i	0.526176	−	0.303788i	−0.213282	−	0.976991i	$-0.568415\pi$
$599$	12.8779	−	7.43506i	0.526176	−	0.303788i	0.739458	+	0.673203i	$0.235082\pi$
$600$	9.87602	+	7.44578i	0.403187	+	0.303973i
$601$	−23.1090			−0.942636			−0.471318	−	0.881963i	$-0.656222\pi$
$601$	−23.1090			−0.942636			−0.471318	+	0.881963i	$0.656222\pi$
$602$	−0.152295	+	0.263783i	−0.00620710	+	0.0107510i
$603$	0.554350	+	32.6442i	0.0225749	+	1.32937i
$604$	−10.8353	+	2.90331i	−0.440883	+	0.118134i
$605$	14.1190	−	52.6930i	0.574021	−	2.14228i
$606$	0.745142	−	6.05684i	0.0302693	−	0.246042i
$607$	29.8697			1.21238			0.606188	−	0.795322i	$-0.292698\pi$
$607$	29.8697			1.21238			0.606188	+	0.795322i	$0.292698\pi$
$608$	−0.350716	+	0.607458i	−0.0142234	+	0.0246357i
$609$	−0.131025	−	0.308878i	−0.00530938	−	0.0125164i
$610$	−9.06443	−	5.23335i	−0.367008	−	0.211892i
$611$	14.6928	−	10.4351i	0.594409	−	0.422160i
$612$	7.63348	−	7.89721i	0.308565	−	0.319226i
$613$	−8.88349	+	33.1536i	−0.358801	+	1.33906i	0.516832	+	0.856087i	$0.327111\pi$
$613$	−8.88349	+	33.1536i	−0.358801	+	1.33906i	−0.875633	+	0.482977i	$0.839556\pi$
$614$			9.50429i			0.383562i
$615$	−11.1958	−	14.3370i	−0.451459	−	0.578124i
$616$	−0.0749601	+	0.279755i	−0.00302023	+	0.0112716i
$617$	1.94352	−	1.94352i	0.0782432	−	0.0782432i	−0.666902	−	0.745145i	$-0.732380\pi$
$617$	1.94352	−	1.94352i	0.0782432	−	0.0782432i	0.745145	+	0.666902i	$0.232380\pi$
$618$	4.06679	+	9.58706i	0.163590	+	0.385648i
$619$	4.73494	+	17.6710i	0.190313	+	0.710259i	0.993430	+	0.114438i	$0.0365066\pi$
$619$	4.73494	+	17.6710i	0.190313	+	0.710259i	−0.803117	+	0.595821i	$0.796827\pi$
$620$	17.9673	+	10.3734i	0.721585	+	0.416607i
$621$	29.9029	+	3.16439i	1.19996	+	0.126982i
$622$	−3.49603	−	0.936759i	−0.140178	−	0.0375606i
$623$	−0.478106	+	0.828104i	−0.0191549	+	0.0331773i
$624$	−3.27512	+	5.31729i	−0.131110	+	0.212862i
$625$	−4.85624	−	8.41125i	−0.194250	−	0.336450i
$626$	4.67917	+	17.4629i	0.187017	+	0.697958i
$627$	6.21172	−	0.871502i	0.248072	−	0.0348044i
$628$	−11.2930	+	6.52002i	−0.450640	+	0.260177i
$629$	−19.5354	+	19.5354i	−0.778927	+	0.778927i
$630$	0.00995627	+	0.586298i	0.000396667	+	0.0233587i
$631$	−8.90171	−	33.2216i	−0.354371	−	1.32253i	−0.881274	−	0.472606i	$-0.843313\pi$
$631$	−8.90171	−	33.2216i	−0.354371	−	1.32253i	0.526902	−	0.849926i	$-0.323353\pi$
$632$	−5.34588	+	1.43242i	−0.212648	+	0.0569788i
$633$	−0.349999	−	2.49465i	−0.0139112	−	0.0991536i
$634$	−9.24920	−	5.34003i	−0.367333	−	0.212080i
$635$	0.00965051	−	0.00258585i	0.000382969	−	0.000102616i
$636$	5.31751	−	4.15247i	0.210853	−	0.164656i
$637$	24.8730	+	4.21451i	0.985503	+	0.166985i
$638$		−	17.8287i		−	0.705845i
$639$	−46.2120	+	0.784753i	−1.82812	+	0.0310443i
$640$	−1.74219	−	3.01756i	−0.0688660	−	0.119279i
$641$	−6.77781	−	11.7395i	−0.267707	−	0.463683i	0.700562	−	0.713592i	$-0.252933\pi$
$641$	−6.77781	−	11.7395i	−0.267707	−	0.463683i	−0.968269	+	0.249909i	$0.919599\pi$
$642$	11.3682	+	26.7995i	0.448669	+	1.05769i
$643$	28.1744	+	28.1744i	1.11109	+	1.11109i	0.993003	+	0.118088i	$0.0376765\pi$
$643$	28.1744	+	28.1744i	1.11109	+	1.11109i	0.118088	+	0.993003i	$0.462324\pi$
$644$	−0.229546	−	0.229546i	−0.00904538	−	0.00904538i
$645$	−19.7272	+	26.1660i	−0.776759	+	1.03029i
$646$	1.28402	+	2.22399i	0.0505192	+	0.0875019i
$647$	−11.0797	−	19.1906i	−0.435588	−	0.754460i	0.561756	−	0.827303i	$-0.310126\pi$
$647$	−11.0797	−	19.1906i	−0.435588	−	0.754460i	−0.997343	+	0.0728432i	$0.976793\pi$
$648$	2.62320	+	8.60923i	0.103049	+	0.338202i
$649$		−	5.44343i		−	0.213673i
$650$	−20.9913	+	14.9084i	−0.823345	+	0.584755i
$651$	0.0803799	+	0.572917i	0.00315034	+	0.0224544i
$652$	−5.40913	+	1.44937i	−0.211838	+	0.0567618i
$653$	−29.5307	−	17.0495i	−1.15562	−	0.667200i	−0.205372	−	0.978684i	$-0.565841\pi$
$653$	−29.5307	−	17.0495i	−1.15562	−	0.667200i	−0.950251	+	0.311484i	$0.899174\pi$
$654$	27.1568	−	21.2069i	1.06192	−	0.829256i
$655$	42.2818	−	11.3294i	1.65209	−	0.442675i
$656$	0.780112	+	2.91142i	0.0304582	+	0.113672i
$657$	−12.8061	−	21.3358i	−0.499613	−	0.832389i
$658$	−0.198261	+	0.198261i	−0.00772903	+	0.00772903i
$659$	4.93704	−	2.85040i	0.192320	−	0.111036i	−0.400748	−	0.916188i	$-0.631250\pi$
$659$	4.93704	−	2.85040i	0.192320	−	0.111036i	0.593068	+	0.805152i	$0.297916\pi$
$660$	−11.6792	+	28.8874i	−0.454613	+	1.12444i
$661$	2.37504	+	8.86377i	0.0923783	+	0.344761i	0.996609	−	0.0822839i	$-0.0262214\pi$
$661$	2.37504	+	8.86377i	0.0923783	+	0.344761i	−0.904231	+	0.427044i	$0.859555\pi$
$662$	1.66351	+	2.88129i	0.0646542	+	0.111984i
$663$	10.8639	+	20.1179i	0.421919	+	0.781316i
$664$	−7.98511	+	13.8306i	−0.309882	+	0.536732i
$665$	−0.132431	−	0.0354848i	−0.00513545	−	0.00137604i
$666$	−6.22962	−	21.7641i	−0.241393	−	0.843343i
$667$	17.3062	+	9.99171i	0.670097	+	0.386881i
$668$	−2.39787	−	8.94898i	−0.0927765	−	0.346246i
$669$	7.30300	+	0.898450i	0.282350	+	0.0347361i
$670$	26.8137	−	26.8137i	1.03590	−	1.03590i
$671$	4.01402	−	14.9805i	0.154960	−	0.578318i
$672$	0.0364188	−	0.0900783i	0.00140489	−	0.00347485i
$673$		−	30.8722i		−	1.19004i	−0.803713	−	0.595018i	$-0.797145\pi$
$673$		−	30.8722i		−	1.19004i	0.803713	−	0.595018i	$-0.202855\pi$
$674$	0.748623	−	2.79390i	0.0288359	−	0.107617i
$675$	−3.90472	+	36.8989i	−0.150293	+	1.42024i
$676$	−8.48865	−	9.84595i	−0.326487	−	0.378691i
$677$	−3.80387	−	2.19617i	−0.146195	−	0.0844055i	0.425118	−	0.905138i	$-0.360232\pi$
$677$	−3.80387	−	2.19617i	−0.146195	−	0.0844055i	−0.571313	+	0.820732i	$0.693566\pi$
$678$	−33.6394	−	4.13848i	−1.29191	−	0.158937i
$679$	−0.0645483	+	0.111801i	−0.00247714	+	0.00429052i
$680$	−12.7568			−0.489201
$681$	−37.2524	+	15.8023i	−1.42752	+	0.605546i
$682$	−7.95652	+	29.6941i	−0.304671	+	1.13705i
$683$	11.2191	−	3.00615i	0.429287	−	0.115027i	−0.0377045	−	0.999289i	$-0.512005\pi$
$683$	11.2191	−	3.00615i	0.429287	−	0.115027i	0.466991	+	0.884262i	$0.345338\pi$
$684$	−2.10399	+	0.0357291i	−0.0804482	+	0.00136614i
$685$	24.4992	−	42.4338i	0.936065	−	1.62131i
$686$	−0.785174			−0.0299781
$687$	−9.85402	+	4.18003i	−0.375954	+	0.159478i
$688$	4.70232	−	2.71489i	0.179274	−	0.103504i
$689$	4.89164	+	13.1651i	0.186356	+	0.501551i
$690$	−21.4954	−	27.5262i	−0.818315	−	1.04791i
$691$	7.51539	+	7.51539i	0.285899	+	0.285899i	0.835456	−	0.549557i	$-0.185204\pi$
$691$	7.51539	+	7.51539i	0.285899	+	0.285899i	−0.549557	+	0.835456i	$0.685204\pi$
$692$	−8.52731	+	4.92325i	−0.324160	+	0.187154i
$693$	−0.835326	+	0.239098i	−0.0317314	+	0.00908258i
$694$	−12.7231	−	12.7231i	−0.482962	−	0.482962i
$695$	−1.05643	−	0.283070i	−0.0400728	−	0.0107375i
$696$	−0.730318	+	5.93635i	−0.0276826	+	0.225017i
$697$	10.6591	+	2.85610i	0.403743	+	0.108183i
$698$		−	25.9005i		−	0.980348i
$699$	−1.65139	+	1.28958i	−0.0624612	+	0.0487762i
$700$	0.283250	−	0.283250i	0.0107059	−	0.0107059i
$701$	10.2778			0.388185			0.194093	−	0.980983i	$-0.437824\pi$
$701$	10.2778			0.388185			0.194093	+	0.980983i	$0.437824\pi$
$702$	−18.7338	−	0.215025i	−0.707060	−	0.00811560i
$703$	5.29304			0.199631
$704$	3.65076	−	3.65076i	0.137593	−	0.137593i
$705$	−23.7747	+	18.5658i	−0.895407	+	0.699227i
$706$			2.96995i			0.111776i
$707$	−0.190909	−	0.0511539i	−0.00717988	−	0.00192384i
$708$	−0.222980	+	1.81248i	−0.00838009	+	0.0681171i
$709$	35.0211	+	9.38387i	1.31524	+	0.352419i	0.847194	−	0.531283i	$-0.178290\pi$
$709$	35.0211	+	9.38387i	1.31524	+	0.352419i	0.468050	+	0.883702i	$0.344957\pi$
$710$	37.9582	+	37.9582i	1.42455	+	1.42455i
$711$	−11.9380	−	11.5393i	−0.447711	−	0.432759i
$712$	14.7621	−	8.52292i	0.553235	−	0.319410i
$713$	−24.3648	−	24.3648i	−0.912468	−	0.912468i
$714$	−0.218939	−	0.280366i	−0.00819360	−	0.0104924i
$715$	−49.9653	−	41.3598i	−1.86860	−	1.54677i
$716$	13.3330	−	7.69779i	0.498276	−	0.287680i
$717$	−21.6820	+	9.19741i	−0.809729	+	0.343484i
$718$	0.0472482			0.00176329
$719$	0.703567	−	1.21861i	0.0262386	−	0.0454466i	−0.852608	−	0.522551i	$-0.824980\pi$
$719$	0.703567	−	1.21861i	0.0262386	−	0.0454466i	0.878847	+	0.477105i	$0.158314\pi$
$720$	5.07210	−	9.14010i	0.189026	−	0.340632i
$721$	0.325787	−	0.0872945i	0.0121330	−	0.00325102i
$722$	−4.79022	+	17.8773i	−0.178274	+	0.665326i
$723$	11.3674	−	4.82201i	0.422759	−	0.179333i
$724$	−17.1903			−0.638871
$725$	−12.3294	+	21.3551i	−0.457901	+	0.793108i
$726$	−26.9143	−	3.31113i	−0.998884	−	0.122887i
$727$	−32.7077	−	18.8838i	−1.21306	−	0.700361i	−0.249636	−	0.968340i	$-0.580311\pi$
$727$	−32.7077	−	18.8838i	−1.21306	−	0.700361i	−0.963425	+	0.267978i	$0.913644\pi$
$728$	0.155805	+	0.128971i	0.00577451	+	0.00477997i
$729$	−18.0950	+	20.0392i	−0.670185	+	0.742194i
$730$	−7.48031	+	27.9169i	−0.276859	+	1.03325i
$731$		−	19.8792i		−	0.735258i
$732$	−1.95018	+	4.82359i	−0.0720809	+	0.178285i
$733$	−8.62288	+	32.1810i	−0.318493	+	1.18863i	0.602199	+	0.798346i	$0.294291\pi$
$733$	−8.62288	+	32.1810i	−0.318493	+	1.18863i	−0.920693	+	0.390288i	$0.872375\pi$
$734$	−6.71759	+	6.71759i	−0.247951	+	0.247951i
$735$	−41.9108	−	5.15607i	−1.54590	−	0.190184i
$736$	1.49777	+	5.58976i	0.0552086	+	0.206041i
$737$	48.6605	+	28.0941i	1.79243	+	1.03486i
$738$	−6.28443	+	6.50156i	−0.231333	+	0.239326i
$739$	−23.0630	−	6.17972i	−0.848388	−	0.227325i	−0.191668	−	0.981460i	$-0.561390\pi$
$739$	−23.0630	−	6.17972i	−0.848388	−	0.227325i	−0.656719	+	0.754135i	$0.728056\pi$
$740$	−13.1466	+	22.7706i	−0.483280	+	0.837065i
$741$	1.25368	−	4.19721i	0.0460549	−	0.154188i
$742$	−0.109255	−	0.189235i	−0.00401087	−	0.00694703i
$743$	−3.12072	−	11.6467i	−0.114488	−	0.427275i	0.884760	−	0.466047i	$-0.154322\pi$
$743$	−3.12072	−	11.6467i	−0.114488	−	0.427275i	−0.999248	+	0.0387716i	$0.987656\pi$
$744$	3.86561	−	9.56122i	0.141720	−	0.350531i
$745$	−18.4056	+	10.6265i	−0.674328	+	0.389323i
$746$	18.9915	−	18.9915i	0.695328	−	0.695328i
$747$	−47.9038	+	0.813482i	−1.75271	+	0.0297637i
$748$	−4.89229	−	18.2583i	−0.178880	−	0.667588i
$749$	0.910702	−	0.244022i	0.0332763	−	0.00891637i
$750$	10.1832	−	7.95212i	0.371838	−	0.290370i
$751$	26.0668	+	15.0497i	0.951192	+	0.549171i	0.893451	−	0.449161i	$-0.148277\pi$
$751$	26.0668	+	15.0497i	0.951192	+	0.549171i	0.0577408	+	0.998332i	$0.481610\pi$
$752$	4.82793	−	1.29364i	0.176057	−	0.0471742i
$753$	1.20805	+	8.61054i	0.0440240	+	0.313786i
$754$	−11.3191	−	5.18632i	−0.412216	−	0.188875i
$755$			39.0861i			1.42249i
$756$	0.287929	−	0.0453940i	0.0104719	−	0.00165096i
$757$	25.3503	+	43.9080i	0.921371	+	1.59586i	0.797296	+	0.603589i	$0.206263\pi$
$757$	25.3503	+	43.9080i	0.921371	+	1.59586i	0.124076	+	0.992273i	$0.460403\pi$
$758$	−9.52590	−	16.4993i	−0.345996	−	0.599283i
$759$	31.1536	−	41.3218i	1.13080	−	1.49989i
$760$	1.72821	+	1.72821i	0.0626886	+	0.0626886i
$761$	10.5364	+	10.5364i	0.381943	+	0.381943i	0.871802	−	0.489859i	$-0.162952\pi$
$761$	10.5364	+	10.5364i	0.381943	+	0.381943i	−0.489859	+	0.871802i	$0.662952\pi$
$762$	−0.00193945	−	0.00457206i	−7.02588e−5	−	0.000165628i
$763$	−0.557971	−	0.966434i	−0.0201999	−	0.0349873i
$764$	4.27232	+	7.39988i	0.154567	+	0.267718i
$765$	−19.6952	−	32.8135i	−0.712081	−	1.18637i
$766$			9.57262i			0.345873i
$767$	−3.45592	−	1.58348i	−0.124786	−	0.0571761i
$768$	−1.36513	+	1.06603i	−0.0492598	+	0.0384672i
$769$	25.6571

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.36513 + 1.06603i) q^{3} -1.00000i q^{4} +(-3.36565 - 0.901822i) q^{5} +(-0.211491 + 1.71909i) q^{6} +(0.0541850 + 0.0145188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.727143 - 2.91054i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.36513 + 1.06603i) q^{3} -1.00000i q^{4} +(-3.36565 - 0.901822i) q^{5} +(-0.211491 + 1.71909i) q^{6} +(0.0541850 + 0.0145188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.727143 - 2.91054i) q^{9} +(-3.01756 + 1.74219i) q^{10} +(-3.65076 - 3.65076i) q^{11} +(1.06603 + 1.36513i) q^{12} +(-3.37979 + 1.25580i) q^{13} +(0.0485810 - 0.0280482i) q^{14} +(5.55591 - 2.35679i) q^{15} -1.00000 q^{16} +(-1.83057 + 3.17065i) q^{17} +(-1.54390 - 2.57223i) q^{18} +(0.677531 - 0.181544i) q^{19} +(-0.901822 + 3.36565i) q^{20} +(-0.0894470 + 0.0379430i) q^{21} -5.16296 q^{22} +(2.89347 - 5.01164i) q^{23} +(1.71909 + 0.211491i) q^{24} +(6.18416 + 3.57043i) q^{25} +(-1.50189 + 3.27785i) q^{26} +(2.11009 + 4.74842i) q^{27} +(0.0145188 - 0.0541850i) q^{28} +3.45319i q^{29} +(2.26212 - 5.59512i) q^{30} +(1.54108 - 5.75138i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.87559 + 1.09192i) q^{33} +(0.947575 + 3.53640i) q^{34} +(-0.169274 - 0.0977305i) q^{35} +(-2.91054 - 0.727143i) q^{36} +(7.28892 + 1.95306i) q^{37} +(0.350716 - 0.607458i) q^{38} +(3.27512 - 5.31729i) q^{39} +(1.74219 + 3.01756i) q^{40} +(-0.780112 - 2.91142i) q^{41} +(-0.0364188 + 0.0900783i) q^{42} +(-4.70232 + 2.71489i) q^{43} +(-3.65076 + 3.65076i) q^{44} +(-5.07210 + 9.14010i) q^{45} +(-1.49777 - 5.58976i) q^{46} +(-4.82793 + 1.29364i) q^{47} +(1.36513 - 1.06603i) q^{48} +(-6.05945 - 3.49843i) q^{49} +(6.89754 - 1.84819i) q^{50} +(-0.881051 - 6.27979i) q^{51} +(1.25580 + 3.37979i) q^{52} -3.89525i q^{53} +(4.84970 + 1.86558i) q^{54} +(8.99483 + 15.5795i) q^{55} +(-0.0280482 - 0.0485810i) q^{56} +(-0.731384 + 0.970102i) q^{57} +(2.44178 + 2.44178i) q^{58} +(0.745519 + 0.745519i) q^{59} +(-2.35679 - 5.55591i) q^{60} +(1.50195 + 2.60145i) q^{61} +(-2.97713 - 5.15654i) q^{62} +(0.0816580 - 0.147151i) q^{63} +1.00000i q^{64} +(12.5077 - 1.17860i) q^{65} +(7.04809 - 5.50389i) q^{66} +(-10.5121 + 2.81672i) q^{67} +(3.17065 + 1.83057i) q^{68} +(1.39262 + 9.92606i) q^{69} +(-0.188801 + 0.0505890i) q^{70} +(-3.98742 - 14.8813i) q^{71} +(-2.57223 + 1.54390i) q^{72} +(5.86521 - 5.86521i) q^{73} +(6.53507 - 3.77302i) q^{74} +(-12.2484 + 1.71844i) q^{75} +(-0.181544 - 0.677531i) q^{76} +(-0.144812 - 0.250821i) q^{77} +(-1.44403 - 6.07575i) q^{78} +(2.76723 - 4.79298i) q^{79} +(3.36565 + 0.901822i) q^{80} +(-7.94252 - 4.23277i) q^{81} +(-2.61030 - 1.50706i) q^{82} +(-4.13340 - 15.4261i) q^{83} +(0.0379430 + 0.0894470i) q^{84} +(9.02042 - 9.02042i) q^{85} +(-1.40533 + 5.24476i) q^{86} +(-3.68122 - 4.71405i) q^{87} +5.16296i q^{88} +(-4.41179 + 16.4650i) q^{89} +(2.87651 + 10.0495i) q^{90} +(-0.201367 + 0.0189747i) q^{91} +(-5.01164 - 2.89347i) q^{92} +(4.02740 + 9.49420i) q^{93} +(-2.49912 + 4.32861i) q^{94} -2.44405 q^{95} +(0.211491 - 1.71909i) q^{96} +(-0.595628 + 2.22292i) q^{97} +(-6.75844 + 1.81092i) q^{98} +(-13.2803 + 7.97107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Introduction

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