LMFDB - Embedded newform 936.2.ed.e.739.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			739.10
Character	$\chi$	$=$	936.739
Dual form			936.2.ed.e.19.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.563514 + 1.29709i) q^{2} +(-1.36490 + 1.46186i) q^{4} +(0.00433170 - 0.00433170i) q^{5} +(-1.57369 + 0.421669i) q^{7} +(-2.66531 - 0.946628i) q^{8} +(0.00805959 + 0.00317764i) q^{10} +(-3.23180 - 0.865959i) q^{11} +(3.04585 + 1.92946i) q^{13} +(-1.43374 - 1.80361i) q^{14} +(-0.274077 - 3.99060i) q^{16} +(-4.80624 - 2.77488i) q^{17} +(-3.45861 + 0.926732i) q^{19} +(0.000419991 + 0.0122447i) q^{20} +(-0.697937 - 4.67993i) q^{22} +(-2.76176 - 4.78352i) q^{23} +4.99996i q^{25} +(-0.786312 + 5.03803i) q^{26} +(1.53152 - 2.87606i) q^{28} +(-1.51783 + 0.876322i) q^{29} +(-0.487954 + 0.487954i) q^{31} +(5.02173 - 2.60426i) q^{32} +(0.890900 - 7.79783i) q^{34} +(-0.00499021 + 0.00864330i) q^{35} +(3.01169 - 11.2398i) q^{37} +(-3.15103 - 3.96392i) q^{38} +(-0.0156458 + 0.00744482i) q^{40} +(-1.29226 + 4.82278i) q^{41} +(-9.33754 - 5.39103i) q^{43} +(5.67701 - 3.54250i) q^{44} +(4.64838 - 6.27785i) q^{46} +(2.87499 + 2.87499i) q^{47} +(-3.76348 + 2.17284i) q^{49} +(-6.48542 + 2.81755i) q^{50} +(-6.97789 + 1.81908i) q^{52} +3.71872i q^{53} +(-0.0177503 + 0.0102481i) q^{55} +(4.59355 + 0.365820i) q^{56} +(-1.99199 - 1.47495i) q^{58} +(-0.772342 - 2.88242i) q^{59} +(1.81829 + 1.04979i) q^{61} +(-0.907891 - 0.357953i) q^{62} +(6.20779 + 5.04612i) q^{64} +(0.0215515 - 0.00483585i) q^{65} +(0.133225 - 0.497203i) q^{67} +(10.6165 - 3.23861i) q^{68} +(-0.0140232 - 0.00160215i) q^{70} +(-0.569550 - 2.12559i) q^{71} +(-1.36174 + 1.36174i) q^{73} +(16.2762 - 2.42733i) q^{74} +(3.36592 - 6.32091i) q^{76} +5.45101 q^{77} +12.6705i q^{79} +(-0.0184733 - 0.0160988i) q^{80} +(-6.98380 + 1.04152i) q^{82} +(3.55694 + 3.55694i) q^{83} +(-0.0328391 + 0.00879922i) q^{85} +(1.73084 - 15.1496i) q^{86} +(7.79403 + 5.36737i) q^{88} +(-14.4893 - 3.88239i) q^{89} +(-5.60682 - 1.75203i) q^{91} +(10.7624 + 2.49172i) q^{92} +(-2.10903 + 5.34922i) q^{94} +(-0.0109673 + 0.0189960i) q^{95} +(4.71000 - 1.26204i) q^{97} +(-4.93916 - 3.65715i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) $ 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.563514	+	1.29709i	0.398465	+	0.917184i
$2$	0.563514	+	1.29709i	0.398465	+	0.917184i
$3$		0			0
$3$		0			0
$4$	−1.36490	+	1.46186i	−0.682452	+	0.730931i
$5$	0.00433170	−	0.00433170i	0.00193719	−	0.00193719i	−0.706138	−	0.708075i	$-0.749564\pi$
$5$	0.00433170	−	0.00433170i	0.00193719	−	0.00193719i	0.708075	+	0.706138i	$0.249564\pi$
$6$		0			0
$7$	−1.57369	+	0.421669i	−0.594800	+	0.159376i	−0.543646	−	0.839315i	$-0.682957\pi$
$7$	−1.57369	+	0.421669i	−0.594800	+	0.159376i	−0.0511537	+	0.998691i	$0.516290\pi$
$8$	−2.66531	−	0.946628i	−0.942331	−	0.334684i
$9$		0			0
$10$	0.00805959	+	0.00317764i	0.00254867	+	0.00100486i
$11$	−3.23180	−	0.865959i	−0.974426	−	0.261097i	−0.263730	−	0.964596i	$-0.584953\pi$
$11$	−3.23180	−	0.865959i	−0.974426	−	0.261097i	−0.710695	+	0.703500i	$0.751620\pi$
$12$		0			0
$13$	3.04585	+	1.92946i	0.844766	+	0.535136i
$13$	3.04585	+	1.92946i	0.844766	+	0.535136i
$14$	−1.43374	−	1.80361i	−0.383184	−	0.482035i
$15$		0			0
$16$	−0.274077	−	3.99060i	−0.0685191	−	0.997650i
$17$	−4.80624	−	2.77488i	−1.16568	−	0.673008i	−0.213025	−	0.977047i	$-0.568331\pi$
$17$	−4.80624	−	2.77488i	−1.16568	−	0.673008i	−0.952660	+	0.304039i	$0.901665\pi$
$18$		0			0
$19$	−3.45861	+	0.926732i	−0.793460	+	0.212607i	−0.632711	−	0.774388i	$-0.718058\pi$
$19$	−3.45861	+	0.926732i	−0.793460	+	0.212607i	−0.160749	+	0.986995i	$0.551391\pi$
$20$	0.000419991		0.0122447i	9.39129e−5		0.00273800i
$21$		0			0
$22$	−0.697937	−	4.67993i	−0.148801	−	0.997765i
$23$	−2.76176	−	4.78352i	−0.575868	−	0.997432i	−0.995947	−	0.0899447i	$-0.971331\pi$
$23$	−2.76176	−	4.78352i	−0.575868	−	0.997432i	0.420079	−	0.907488i	$-0.362002\pi$
$24$		0			0
$25$			4.99996i			0.999992i
$26$	−0.786312	+	5.03803i	−0.154208	+	0.988038i
$27$		0			0
$28$	1.53152	−	2.87606i	0.289429	−	0.543524i
$29$	−1.51783	+	0.876322i	−0.281855	+	0.162729i	−0.634263	−	0.773118i	$-0.718696\pi$
$29$	−1.51783	+	0.876322i	−0.281855	+	0.162729i	0.352408	+	0.935846i	$0.385363\pi$
$30$		0			0
$31$	−0.487954	+	0.487954i	−0.0876391	+	0.0876391i	−0.749567	−	0.661928i	$-0.769738\pi$
$31$	−0.487954	+	0.487954i	−0.0876391	+	0.0876391i	0.661928	+	0.749567i	$0.269738\pi$
$32$	5.02173	−	2.60426i	0.887726	−	0.460373i
$33$		0			0
$34$	0.890900	−	7.79783i	0.152788	−	1.33732i
$35$	−0.00499021	+	0.00864330i	−0.000843500	+	0.00146098i
$36$		0			0
$37$	3.01169	−	11.2398i	0.495119	−	1.84781i	−0.0342404	−	0.999414i	$-0.510901\pi$
$37$	3.01169	−	11.2398i	0.495119	−	1.84781i	0.529360	−	0.848397i	$-0.322432\pi$
$38$	−3.15103	−	3.96392i	−0.511165	−	0.643032i
$39$		0			0
$40$	−0.0156458	+	0.00744482i	−0.00247382	+	0.00117713i
$41$	−1.29226	+	4.82278i	−0.201817	+	0.753191i	0.788579	+	0.614933i	$0.210817\pi$
$41$	−1.29226	+	4.82278i	−0.201817	+	0.753191i	−0.990396	+	0.138258i	$0.955850\pi$
$42$		0			0
$43$	−9.33754	−	5.39103i	−1.42396	−	0.822125i	−0.427327	−	0.904097i	$-0.640545\pi$
$43$	−9.33754	−	5.39103i	−1.42396	−	0.822125i	−0.996635	+	0.0819721i	$0.973878\pi$
$44$	5.67701	−	3.54250i	0.855842	−	0.534052i
$45$		0			0
$46$	4.64838	−	6.27785i	0.685366	−	0.925618i
$47$	2.87499	+	2.87499i	0.419360	+	0.419360i	0.884983	−	0.465623i	$-0.154170\pi$
$47$	2.87499	+	2.87499i	0.419360	+	0.419360i	−0.465623	+	0.884983i	$0.654170\pi$
$48$		0			0
$49$	−3.76348	+	2.17284i	−0.537640	+	0.310406i
$50$	−6.48542	+	2.81755i	−0.917177	+	0.398462i
$51$		0			0
$52$	−6.97789	+	1.81908i	−0.967659	+	0.252261i
$53$			3.71872i			0.510805i	0.966835	+	0.255402i	$0.0822080\pi$
$53$			3.71872i			0.510805i	−0.966835	+	0.255402i	$0.917792\pi$
$54$		0			0
$55$	−0.0177503	+	0.0102481i	−0.00239345	+	0.00138186i
$56$	4.59355	+	0.365820i	0.613838	+	0.0488847i
$57$		0			0
$58$	−1.99199	−	1.47495i	−0.261561	−	0.193671i
$59$	−0.772342	−	2.88242i	−0.100550	−	0.375259i	0.897252	−	0.441519i	$-0.145560\pi$
$59$	−0.772342	−	2.88242i	−0.100550	−	0.375259i	−0.997802	+	0.0662595i	$0.978893\pi$
$60$		0			0
$61$	1.81829	+	1.04979i	0.232808	+	0.134412i	0.611867	−	0.790961i	$-0.290419\pi$
$61$	1.81829	+	1.04979i	0.232808	+	0.134412i	−0.379059	+	0.925373i	$0.623752\pi$
$62$	−0.907891	−	0.357953i	−0.115302	−	0.0454601i
$63$		0			0
$64$	6.20779	+	5.04612i	0.775974	+	0.630765i
$65$	0.0215515	−	0.00483585i	0.00267314	−	0.000599813i
$66$		0			0
$67$	0.133225	−	0.497203i	0.0162760	−	0.0607430i	−0.957310	−	0.289063i	$-0.906656\pi$
$67$	0.133225	−	0.497203i	0.0162760	−	0.0607430i	0.973586	+	0.228320i	$0.0733231\pi$
$68$	10.6165	−	3.23861i	1.28745	−	0.392739i
$69$		0			0
$70$	−0.0140232	−	0.00160215i	−0.00167610	−	0.000191493i
$71$	−0.569550	−	2.12559i	−0.0675932	−	0.252261i	0.923859	−	0.382734i	$-0.125017\pi$
$71$	−0.569550	−	2.12559i	−0.0675932	−	0.252261i	−0.991452	+	0.130472i	$0.958351\pi$
$72$		0			0
$73$	−1.36174	+	1.36174i	−0.159380	+	0.159380i	−0.782292	−	0.622912i	$-0.785949\pi$
$73$	−1.36174	+	1.36174i	−0.159380	+	0.159380i	0.622912	+	0.782292i	$0.285949\pi$
$74$	16.2762	−	2.42733i	1.89207	−	0.282172i
$75$		0			0
$76$	3.36592	−	6.32091i	0.386097	−	0.725058i
$77$	5.45101			0.621200
$78$		0			0
$79$			12.6705i			1.42555i	0.701394	+	0.712774i	$0.252561\pi$
$79$			12.6705i			1.42555i	−0.701394	+	0.712774i	$0.747439\pi$
$80$	−0.0184733	−	0.0160988i	−0.00206538	−	0.00179991i
$81$		0			0
$82$	−6.98380	+	1.04152i	−0.771232	+	0.115017i
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	0.874839	−	0.484414i	$-0.160967\pi$
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	−0.484414	+	0.874839i	$0.660967\pi$
$84$		0			0
$85$	−0.0328391	+	0.00879922i	−0.00356190	+	0.000954409i
$86$	1.73084	−	15.1496i	0.186641	−	1.63362i
$87$		0			0
$88$	7.79403	+	5.36737i	0.830846	+	0.572164i
$89$	−14.4893	−	3.88239i	−1.53586	−	0.411532i	−0.610934	−	0.791682i	$-0.709206\pi$
$89$	−14.4893	−	3.88239i	−1.53586	−	0.411532i	−0.924925	+	0.380149i	$0.875873\pi$
$90$		0			0
$91$	−5.60682	−	1.75203i	−0.587754	−	0.183663i
$92$	10.7624	+	2.49172i	1.12206	+	0.259780i
$93$		0			0
$94$	−2.10903	+	5.34922i	−0.217530	+	0.551730i
$95$	−0.0109673	+	0.0189960i	−0.00112522	+	0.00194895i
$96$		0			0
$97$	4.71000	−	1.26204i	0.478228	−	0.128141i	−0.0116495	−	0.999932i	$-0.503708\pi$
$97$	4.71000	−	1.26204i	0.478228	−	0.128141i	0.489877	+	0.871791i	$0.337042\pi$
$98$	−4.93916	−	3.65715i	−0.498930	−	0.369428i
$99$		0			0
$100$	−7.30925	−	6.82447i	−0.730925	−	0.682447i
$101$	7.89450	+	13.6737i	0.785532	+	1.36058i	0.928681	+	0.370880i	$0.120944\pi$
$101$	7.89450	+	13.6737i	0.785532	+	1.36058i	−0.143149	+	0.989701i	$0.545723\pi$
$102$		0			0
$103$	−14.3782			−1.41673			−0.708363	−	0.705848i	$-0.750566\pi$
$103$	−14.3782			−1.41673			−0.708363	+	0.705848i	$0.750566\pi$
$104$	−6.29166	−	8.02590i	−0.616948	−	0.787004i
$105$		0			0
$106$	−4.82352	+	2.09555i	−0.468502	+	0.203538i
$107$	2.19013	+	3.79342i	0.211728	+	0.366724i	0.952255	−	0.305302i	$-0.0987575\pi$
$107$	2.19013	+	3.79342i	0.211728	+	0.366724i	−0.740527	+	0.672026i	$0.765424\pi$
$108$		0			0
$109$	8.41638	−	8.41638i	0.806143	−	0.806143i	−0.177905	−	0.984048i	$-0.556932\pi$
$109$	8.41638	−	8.41638i	0.806143	−	0.806143i	0.984048	+	0.177905i	$0.0569319\pi$
$110$	−0.0232953	−	0.0172488i	−0.00222112	−	0.00164461i
$111$		0			0
$112$	2.11403	+	6.16440i	0.199757	+	0.582481i
$113$	−4.02349	+	6.96890i	−0.378498	+	0.655579i	−0.990844	−	0.135012i	$-0.956893\pi$
$113$	−4.02349	+	6.96890i	−0.378498	+	0.655579i	0.612346	+	0.790590i	$0.290226\pi$
$114$		0			0
$115$	−0.0326839	−	0.00875762i	−0.00304779	−	0.000816652i
$116$	0.790636	−	3.41496i	0.0734087	−	0.317071i
$117$		0			0
$118$	3.30354	−	2.62609i	0.304116	−	0.241751i
$119$	8.73362	+	2.34017i	0.800610	+	0.214523i
$120$		0			0
$121$	0.168393	+	0.0972215i	0.0153084	+	0.00883832i
$122$	−0.337043	+	2.95006i	−0.0305145	+	0.267086i
$123$		0			0
$124$	−0.0473109	−	1.37933i	−0.00424864	−	0.123868i
$125$	0.0433168	+	0.0433168i	0.00387437	+	0.00387437i
$126$		0			0
$127$	1.91208	+	3.31182i	0.169670	+	0.293877i	0.938304	−	0.345812i	$-0.112397\pi$
$127$	1.91208	+	3.31182i	0.169670	+	0.293877i	−0.768634	+	0.639689i	$0.779063\pi$
$128$	−3.04711	+	10.8956i	−0.269329	+	0.963048i
$129$		0			0
$130$	0.0184171	+	0.0252293i	0.00161529	+	0.00221275i
$131$	−10.1296			−0.885025			−0.442513	−	0.896762i	$-0.645913\pi$
$131$	−10.1296			−0.885025			−0.442513	+	0.896762i	$0.645913\pi$
$132$		0			0
$133$	5.05201	−	2.91678i	0.438065	−	0.252917i
$134$	0.719992	−	0.107375i	0.0621979	−	0.00927582i
$135$		0			0
$136$	10.1834	+	11.9457i	0.873215	+	1.02433i
$137$	4.42582	+	16.5174i	0.378123	+	1.41117i	0.848728	+	0.528830i	$0.177369\pi$
$137$	4.42582	+	16.5174i	0.378123	+	1.41117i	−0.470605	+	0.882344i	$0.655964\pi$
$138$		0			0
$139$	8.51425	−	14.7471i	0.722169	−	1.25083i	−0.237959	−	0.971275i	$-0.576478\pi$
$139$	8.51425	−	14.7471i	0.722169	−	1.25083i	0.960129	−	0.279559i	$-0.0901882\pi$
$140$	−0.00582415	−	0.0190923i	−0.000492230	−	0.00161359i
$141$		0			0
$142$	2.43614	−	1.93656i	0.204436	−	0.162513i
$143$	−8.17275	−	8.87322i	−0.683439	−	0.742016i
$144$		0			0
$145$	−0.00277884	+	0.0103708i	−0.000230770	+	0.000861245i
$146$	−2.53367	−	0.998946i	−0.209688	−	0.0826734i
$147$		0			0
$148$	12.3203	+	19.7439i	1.01273	+	1.62294i
$149$	−3.12545	−	11.6643i	−0.256047	−	0.955580i	−0.967505	−	0.252852i	$-0.918632\pi$
$149$	−3.12545	−	11.6643i	−0.256047	−	0.955580i	0.711458	−	0.702728i	$-0.248035\pi$
$150$		0			0
$151$	−1.75767	−	1.75767i	−0.143037	−	0.143037i	0.631962	−	0.774999i	$-0.282250\pi$
$151$	−1.75767	−	1.75767i	−0.143037	−	0.143037i	−0.774999	+	0.631962i	$0.782250\pi$
$152$	10.0956	+	0.803987i	0.818858	+	0.0652120i
$153$		0			0
$154$	3.07172	+	7.07047i	0.247526	+	0.569755i
$155$			0.00422734i			0.000339548i
$156$		0			0
$157$			23.1742i			1.84950i	0.380570	+	0.924752i	$0.375728\pi$
$157$			23.1742i			1.84950i	−0.380570	+	0.924752i	$0.624272\pi$
$158$	−16.4349	+	7.14003i	−1.30749	+	0.568030i
$159$		0			0
$160$	0.0104718	−	0.0330335i	0.000827865	−	0.00261153i
$161$	6.36323	+	6.36323i	0.501493	+	0.501493i
$162$		0			0
$163$	−2.24703	−	8.38602i	−0.176001	−	0.656844i	−0.996379	−	0.0850226i	$-0.972904\pi$
$163$	−2.24703	−	8.38602i	−0.176001	−	0.656844i	0.820378	−	0.571821i	$-0.193763\pi$
$164$	−5.28642	−	8.47173i	−0.412800	−	0.661531i
$165$		0			0
$166$	−2.60930	+	6.61808i	−0.202521	+	0.513662i
$167$	−6.23234	+	23.2594i	−0.482273	+	1.79987i	0.109764	+	0.993958i	$0.464990\pi$
$167$	−6.23234	+	23.2594i	−0.482273	+	1.79987i	−0.592037	+	0.805910i	$0.701676\pi$
$168$		0			0
$169$	5.55437	+	11.7537i	0.427259	+	0.904129i
$170$	−0.0299187	−	0.0376369i	−0.00229466	−	0.00288662i
$171$		0			0
$172$	20.6258	−	6.29195i	1.57270	−	0.479757i
$173$	5.71509	−	9.89883i	0.434510	−	0.752594i	−0.562745	−	0.826630i	$-0.690255\pi$
$173$	5.71509	−	9.89883i	0.434510	−	0.752594i	0.997256	+	0.0740365i	$0.0235881\pi$
$174$		0			0
$175$	−2.10833	−	7.86840i	−0.159375	−	0.594795i
$176$	−2.56993	+	13.1342i	−0.193716	+	0.990026i
$177$		0			0
$178$	−3.12909	−	20.9817i	−0.234535	−	1.57265i
$179$	−16.6433	+	9.60904i	−1.24398	+	0.718214i	−0.969903	−	0.243493i	$-0.921707\pi$
$179$	−16.6433	+	9.60904i	−1.24398	+	0.718214i	−0.274080	+	0.961707i	$0.588373\pi$
$180$		0			0
$181$	9.90437			0.736186			0.368093	−	0.929789i	$-0.380011\pi$
$181$	9.90437			0.736186			0.368093	+	0.929789i	$0.380011\pi$
$182$	−0.886969	−	8.25986i	−0.0657465	−	0.612262i
$183$		0			0
$184$	2.83276	+	15.3639i	0.208834	+	1.13264i
$185$	−0.0356416	−	0.0617331i	−0.00262043	−	0.00453871i
$186$		0			0
$187$	13.1299	+	13.1299i	0.960153	+	0.960153i
$188$	−8.12691	+	0.278752i	−0.592716	+	0.0203301i
$189$		0			0
$190$	−0.0308198	−	0.00352115i	−0.00223590	−	0.000255451i
$191$	−7.28556	−	4.20632i	−0.527165	−	0.304359i	0.212696	−	0.977118i	$-0.431775\pi$
$191$	−7.28556	−	4.20632i	−0.527165	−	0.304359i	−0.739861	+	0.672760i	$0.765109\pi$
$192$		0			0
$193$	−3.79409	−	1.01662i	−0.273105	−	0.0731782i	0.119667	−	0.992814i	$-0.461817\pi$
$193$	−3.79409	−	1.01662i	−0.273105	−	0.0731782i	−0.392772	+	0.919636i	$0.628484\pi$
$194$	4.29113	+	5.39813i	0.308085	+	0.387563i
$195$		0			0
$196$	1.96039	−	8.46740i	0.140028	−	0.604815i
$197$	15.3987	+	4.12608i	1.09711	+	0.293971i	0.761589	−	0.648060i	$-0.224420\pi$
$197$	15.3987	+	4.12608i	1.09711	+	0.293971i	0.335525	+	0.942031i	$0.391086\pi$
$198$		0			0
$199$	−6.41779	+	11.1159i	−0.454945	+	0.787988i	−0.998685	−	0.0512659i	$-0.983674\pi$
$199$	−6.41779	+	11.1159i	−0.454945	+	0.787988i	0.543740	+	0.839254i	$0.317008\pi$
$200$	4.73311	−	13.3265i	0.334681	−	0.942323i
$201$		0			0
$202$	−13.2874	+	17.9452i	−0.934896	+	1.26262i
$203$	2.01909	−	2.01909i	0.141712	−	0.141712i
$204$		0			0
$205$	0.0152931	+	0.0264885i	0.00106812	+	0.00185004i
$206$	−8.10232	−	18.6499i	−0.564515	−	1.29940i
$207$		0			0
$208$	6.86491	−	12.6836i	0.475996	−	0.879448i
$209$	11.9801			0.828679
$210$		0			0
$211$	−2.73940	−	4.74478i	−0.188588	−	0.326644i	0.756192	−	0.654350i	$-0.227058\pi$
$211$	−2.73940	−	4.74478i	−0.188588	−	0.326644i	−0.944780	+	0.327706i	$0.893724\pi$
$212$	−5.43625	−	5.07569i	−0.373363	−	0.348600i
$213$		0			0
$214$	−3.68625	+	4.97846i	−0.251987	+	0.340320i
$215$	−0.0637997	+	0.0170951i	−0.00435111	+	0.00116588i
$216$		0			0
$217$	0.562134	−	0.973645i	0.0381601	−	0.0660953i
$218$	15.6596	+	6.17408i	1.06060	+	0.418162i
$219$		0			0
$220$	0.00924607	−	0.0399361i	0.000623370	−	0.00269249i
$221$	−9.28504	−	17.7253i	−0.624580	−	1.19233i
$222$		0			0
$223$	−13.8516	−	3.71152i	−0.927572	−	0.248542i	−0.236753	−	0.971570i	$-0.576083\pi$
$223$	−13.8516	−	3.71152i	−0.927572	−	0.248542i	−0.690819	+	0.723028i	$0.742750\pi$
$224$	−6.80452	+	6.21582i	−0.454646	+	0.415312i
$225$		0			0
$226$	−11.3066	−	1.29178i	−0.752104	−	0.0859277i
$227$	9.25409	−	2.47963i	0.614215	−	0.164579i	0.0617186	−	0.998094i	$-0.480342\pi$
$227$	9.25409	−	2.47963i	0.614215	−	0.164579i	0.552497	+	0.833515i	$0.313675\pi$
$228$		0			0
$229$	−17.2631	−	17.2631i	−1.14078	−	1.14078i	−0.988309	−	0.152467i	$-0.951278\pi$
$229$	−17.2631	−	17.2631i	−1.14078	−	1.14078i	−0.152467	−	0.988309i	$-0.548722\pi$
$230$	−0.00705838	−	0.0473291i	−0.000465416	−	0.00312079i
$231$		0			0
$232$	4.87506	−	0.898848i	0.320063	−	0.0590123i
$233$			11.8549i			0.776641i	0.921524	+	0.388320i	$0.126945\pi$
$233$			11.8549i			0.776641i	−0.921524	+	0.388320i	$0.873055\pi$
$234$		0			0
$235$	0.0249071			0.00162476
$236$	5.26787	+	2.80517i	0.342909	+	0.182601i
$237$		0			0
$238$	1.88610	+	12.6470i	0.122258	+	0.819786i
$239$	−8.19428	+	8.19428i	−0.530044	+	0.530044i	−0.920585	−	0.390541i	$-0.872288\pi$
$239$	−8.19428	+	8.19428i	−0.530044	+	0.530044i	0.390541	+	0.920585i	$0.372288\pi$
$240$		0			0
$241$	5.54758	+	20.7038i	0.357351	+	1.33365i	0.877500	+	0.479576i	$0.159210\pi$
$241$	5.54758	+	20.7038i	0.357351	+	1.33365i	−0.520149	+	0.854075i	$0.674124\pi$
$242$	−0.0312138	+	0.273207i	−0.00200650	+	0.0175624i
$243$		0			0
$244$	−4.01643	+	1.22522i	−0.257126	+	0.0784369i
$245$	−0.00689014	+	0.0257143i	−0.000440195	+	0.00164283i
$246$		0			0
$247$	−12.3225	−	3.85057i	−0.784062	−	0.245006i
$248$	1.76246	−	0.838639i	0.111916	−	0.0532537i
$249$		0			0
$250$	−0.0317763	+	0.0805956i	−0.00200971	+	0.00509731i
$251$	−6.73491	−	3.88840i	−0.425104	−	0.245434i	0.272155	−	0.962254i	$-0.412264\pi$
$251$	−6.73491	−	3.88840i	−0.425104	−	0.245434i	−0.697259	+	0.716820i	$0.745597\pi$
$252$		0			0
$253$	4.78315	+	17.8510i	0.300714	+	1.12228i
$254$	−3.21826	+	4.34641i	−0.201932	+	0.272718i
$255$		0			0
$256$	−15.8498	+	2.18746i	−0.990610	+	0.136716i
$257$	13.3396	−	7.70163i	0.832103	−	0.480415i	−0.0224694	−	0.999748i	$-0.507153\pi$
$257$	13.3396	−	7.70163i	0.832103	−	0.480415i	0.854572	+	0.519333i	$0.173820\pi$
$258$		0			0
$259$			18.9579i			1.17799i
$260$	−0.0223464	+	0.0381058i	−0.00138587	+	0.00236322i
$261$		0			0
$262$	−5.70816	−	13.1390i	−0.352651	−	0.811731i
$263$	−17.8675	+	10.3158i	−1.10176	+	0.636101i	−0.936683	−	0.350180i	$-0.886120\pi$
$263$	−17.8675	+	10.3158i	−1.10176	+	0.636101i	−0.165077	+	0.986281i	$0.552787\pi$
$264$		0			0
$265$	0.0161084	+	0.0161084i	0.000989528	+	0.000989528i
$266$	6.63022	+	4.90929i	0.406525	+	0.301008i
$267$		0			0
$268$	0.545002	+	0.873390i	0.0332913	+	0.0533508i
$269$	−13.8319	−	7.98587i	−0.843348	−	0.486907i	0.0150527	−	0.999887i	$-0.495208\pi$
$269$	−13.8319	−	7.98587i	−0.843348	−	0.486907i	−0.858401	+	0.512979i	$0.828542\pi$
$270$		0			0
$271$	6.02478	−	22.4848i	0.365979	−	1.36585i	−0.500109	−	0.865962i	$-0.666707\pi$
$271$	6.02478	−	22.4848i	0.365979	−	1.36585i	0.866088	−	0.499891i	$-0.166627\pi$
$272$	−9.75617	+	19.9403i	−0.591555	+	1.20906i
$273$		0			0
$274$	−18.9306	+	15.0485i	−1.14364	+	0.909111i
$275$	4.32976	−	16.1589i	0.261095	−	0.974418i
$276$		0			0
$277$	3.01247	−	5.21776i	0.181002	−	0.313505i	−0.761220	−	0.648494i	$-0.775399\pi$
$277$	3.01247	−	5.21776i	0.181002	−	0.313505i	0.942222	+	0.334989i	$0.108733\pi$
$278$	23.9263	+	2.73357i	1.43500	+	0.163949i
$279$		0			0
$280$	0.0214825	−	0.0183132i	0.00128382	−	0.00109442i
$281$	20.3774	−	20.3774i	1.21561	−	1.21561i	0.246461	−	0.969153i	$-0.420732\pi$
$281$	20.3774	−	20.3774i	1.21561	−	1.21561i	0.969153	−	0.246461i	$-0.0792679\pi$
$282$		0			0
$283$	6.85490	−	3.95768i	0.407482	−	0.235260i	−0.282225	−	0.959348i	$-0.591073\pi$
$283$	6.85490	−	3.95768i	0.407482	−	0.235260i	0.689707	+	0.724088i	$0.257739\pi$
$284$	3.88470	+	2.06862i	0.230515	+	0.122750i
$285$		0			0
$286$	6.90393	−	15.6010i	0.408238	−	0.922507i
$287$		−	8.13447i		−	0.480163i
$288$		0			0
$289$	6.89996	+	11.9511i	0.405880	+	0.703005i
$290$	−0.0150178	+	0.00223966i	−0.000881873	+	0.000131517i
$291$		0			0
$292$	−0.132031	−	3.84932i	−0.00772655	−	0.225265i
$293$	−1.74094	+	0.466483i	−0.101707	+	0.0272522i	−0.309313	−	0.950960i	$-0.600099\pi$
$293$	−1.74094	+	0.466483i	−0.101707	+	0.0272522i	0.207607	+	0.978212i	$0.433433\pi$
$294$		0			0
$295$	−0.0158313	−	0.00914022i	−0.000921735	−	0.000532164i
$296$	−18.6670	+	27.1066i	−1.08500	+	1.57554i
$297$		0			0
$298$	13.3685	−	10.6270i	0.774417	−	0.615607i
$299$	0.817691	−	19.8986i	0.0472883	−	1.15076i
$300$		0			0
$301$	16.9676	+	4.54647i	0.977999	+	0.262054i
$302$	1.28939	−	3.27034i	0.0741962	−	0.188187i
$303$		0			0
$304$	4.64614	+	13.5479i	0.266474	+	0.777027i
$305$	0.0124236	−	0.00332890i	0.000711375	−	0.000190612i
$306$		0			0
$307$	14.6289	−	14.6289i	0.834914	−	0.834914i	−0.153270	−	0.988184i	$-0.548980\pi$
$307$	14.6289	−	14.6289i	0.834914	−	0.834914i	0.988184	+	0.153270i	$0.0489804\pi$
$308$	−7.44011	+	7.96862i	−0.423939	+	0.454054i
$309$		0			0
$310$	−0.00548325	+	0.00238216i	−0.000311428	+	0.000135298i
$311$	25.6430			1.45408			0.727040	−	0.686595i	$-0.240895\pi$
$311$	25.6430			1.45408			0.727040	+	0.686595i	$0.240895\pi$
$312$		0			0
$313$	−19.4022			−1.09668			−0.548340	−	0.836256i	$-0.684740\pi$
$313$	−19.4022			−1.09668			−0.548340	+	0.836256i	$0.684740\pi$
$314$	−30.0591	+	13.0590i	−1.69633	+	0.736962i
$315$		0			0
$316$	−18.5226	−	17.2941i	−1.04198	−	0.972867i
$317$	−11.2646	+	11.2646i	−0.632682	+	0.632682i	−0.948740	−	0.316058i	$-0.897641\pi$
$317$	−11.2646	+	11.2646i	−0.632682	+	0.632682i	0.316058	+	0.948740i	$0.397641\pi$
$318$		0			0
$319$	5.66420	−	1.51772i	0.317134	−	0.0849759i
$320$	0.0487485	−	0.00503200i	0.00272513	−	0.000281297i
$321$		0			0
$322$	−4.66793	+	11.8395i	−0.260134	+	0.659788i
$323$	19.1945	+	5.14315i	1.06801	+	0.286172i
$324$		0			0
$325$	−9.64723	+	15.2291i	−0.535132	+	0.844760i
$326$	9.61122	−	7.64025i	0.532316	−	0.423154i
$327$		0			0
$328$	8.00965	−	11.6309i	0.442259	−	0.642210i
$329$	−5.73663	−	3.31205i	−0.316271	−	0.182599i
$330$		0			0
$331$	−3.11057	+	0.833475i	−0.170972	+	0.0458119i	−0.343290	−	0.939230i	$-0.611541\pi$
$331$	−3.11057	+	0.833475i	−0.170972	+	0.0458119i	0.172317	+	0.985042i	$0.444875\pi$
$332$	−10.0546	+	0.344873i	−0.551820	+	0.0189274i
$333$		0			0
$334$	−33.6817	+	5.02308i	−1.84298	+	0.274851i
$335$	−0.00157664	−	0.00273082i	−8.61411e−5	−	0.000149201i
$336$		0			0
$337$		−	14.3103i		−	0.779534i	−0.920914	−	0.389767i	$-0.872556\pi$
$337$		−	14.3103i		−	0.779534i	0.920914	−	0.389767i	$-0.127444\pi$
$338$	−12.1157	+	13.8279i	−0.659005	+	0.752139i
$339$		0			0
$340$	0.0319590	−	0.0600163i	0.00173322	−	0.00325484i
$341$	1.99952	−	1.15442i	0.108280	−	0.0625155i
$342$		0			0
$343$	13.0705	−	13.0705i	0.705740	−	0.705740i
$344$	19.7842	+	23.2080i	1.06669	+	1.25129i
$345$		0			0
$346$	16.0602	+	1.83488i	0.863404	+	0.0986437i
$347$	−0.895267	+	1.55065i	−0.0480604	+	0.0832431i	−0.889055	−	0.457801i	$-0.848637\pi$
$347$	−0.895267	+	1.55065i	−0.0480604	+	0.0832431i	0.840994	+	0.541044i	$0.181971\pi$
$348$		0			0
$349$	−2.69383	+	10.0535i	−0.144197	+	0.538151i	0.855593	+	0.517650i	$0.173193\pi$
$349$	−2.69383	+	10.0535i	−0.144197	+	0.538151i	−0.999790	+	0.0205016i	$0.993474\pi$
$350$	9.01798	−	7.16866i	0.482031	−	0.383181i
$351$		0			0
$352$	−18.4844	+	4.06785i	−0.985224	+	0.216817i
$353$	2.28519	−	8.52844i	0.121628	−	0.453923i	−0.878069	−	0.478534i	$-0.841168\pi$
$353$	2.28519	−	8.52844i	0.121628	−	0.453923i	0.999697	+	0.0246115i	$0.00783486\pi$
$354$		0			0
$355$	−0.0116745	−	0.00674030i	−0.000619620	−	0.000357738i
$356$	25.4520	−	15.8822i	1.34895	−	0.841756i
$357$		0			0
$358$	−21.8426	−	16.1731i	−1.15442	−	0.854778i
$359$	−6.93284	−	6.93284i	−0.365901	−	0.365901i	0.500079	−	0.865980i	$-0.333304\pi$
$359$	−6.93284	−	6.93284i	−0.365901	−	0.365901i	−0.865980	+	0.500079i	$0.833304\pi$
$360$		0			0
$361$	−5.35132	+	3.08959i	−0.281648	+	0.162610i
$362$	5.58125	+	12.8469i	0.293344	+	0.675218i
$363$		0			0
$364$	10.2140	−	5.80503i	0.535359	−	0.304266i
$365$			0.0117973i			0.000617499i
$366$		0			0
$367$	12.8657	−	7.42801i	0.671583	−	0.387739i	−0.125093	−	0.992145i	$-0.539923\pi$
$367$	12.8657	−	7.42801i	0.671583	−	0.387739i	0.796676	+	0.604406i	$0.206590\pi$
$368$	−18.3322	+	12.3321i	−0.955630	+	0.642858i
$369$		0			0
$370$	0.0599891	−	0.0810180i	0.00311868	−	0.00421193i
$371$	−1.56807	−	5.85211i	−0.0814101	−	0.303827i
$372$		0			0
$373$	−18.4652	−	10.6609i	−0.956090	−	0.551999i	−0.0611226	−	0.998130i	$-0.519468\pi$
$373$	−18.4652	−	10.6609i	−0.956090	−	0.551999i	−0.894967	+	0.446131i	$0.852801\pi$
$374$	−9.63182	+	24.4296i	−0.498049	+	1.26322i
$375$		0			0
$376$	−4.94119	−	10.3843i	−0.254823	−	0.535528i
$377$	−6.31392	−	0.259458i	−0.325183	−	0.0133627i
$378$		0			0
$379$	−6.98578	+	26.0713i	−0.358835	+	1.33919i	0.516753	+	0.856134i	$0.327141\pi$
$379$	−6.98578	+	26.0713i	−0.358835	+	1.33919i	−0.875589	+	0.483058i	$0.839526\pi$
$380$	−0.0128001	−	0.0419604i	−0.000656633	−	0.00215252i
$381$		0			0
$382$	1.35047	−	11.8204i	0.0690963	−	0.604783i
$383$	−5.60173	−	20.9059i	−0.286235	−	1.06824i	−0.947932	−	0.318473i	$-0.896830\pi$
$383$	−5.60173	−	20.9059i	−0.286235	−	1.06824i	0.661697	−	0.749771i	$-0.269837\pi$
$384$		0			0
$385$	0.0236121	−	0.0236121i	0.00120339	−	0.00120339i
$386$	−0.819369	−	5.49418i	−0.0417048	−	0.279646i
$387$		0			0
$388$	−4.58376	+	8.60793i	−0.232705	+	0.437001i
$389$	25.5925			1.29759			0.648797	−	0.760962i	$-0.275273\pi$
$389$	25.5925			1.29759			0.648797	+	0.760962i	$0.275273\pi$
$390$		0			0
$391$			30.6543i			1.55025i
$392$	12.0877	−	2.22870i	0.610522	−	0.112566i
$393$		0			0
$394$	3.32549	+	22.2987i	0.167536	+	1.12339i
$395$	0.0548849	+	0.0548849i	0.00276156	+	0.00276156i
$396$		0			0
$397$	7.13276	−	1.91122i	0.357983	−	0.0959212i	−0.0753451	−	0.997158i	$-0.524006\pi$
$397$	7.13276	−	1.91122i	0.357983	−	0.0959212i	0.433328	+	0.901236i	$0.357339\pi$
$398$	−18.0349	−	2.06048i	−0.904009	−	0.103283i
$399$		0			0
$400$	19.9528	−	1.37037i	0.997642	−	0.0685186i
$401$	0.0510228	+	0.0136715i	0.00254796	+	0.000682723i	0.260093	−	0.965584i	$-0.416247\pi$
$401$	0.0510228	+	0.0136715i	0.00254796	+	0.000682723i	−0.257545	+	0.966266i	$0.582914\pi$
$402$		0			0
$403$	−2.42772	+	0.544746i	−0.120933	+	0.0271357i
$404$	−30.7642	−	7.12258i	−1.53058	−	0.354362i
$405$		0			0
$406$	3.75673	+	1.48116i	0.186443	+	0.0735087i
$407$	−19.4664	+	33.7168i	−0.964914	+	1.67128i
$408$		0			0
$409$	9.42392	−	2.52513i	0.465983	−	0.124860i	−0.0181853	−	0.999835i	$-0.505789\pi$
$409$	9.42392	−	2.52513i	0.465983	−	0.124860i	0.484168	+	0.874975i	$0.339122\pi$
$410$	−0.0257401	+	0.0347633i	−0.00127122	+	0.00171684i
$411$		0			0
$412$	19.6249	−	21.0189i	0.966847	−	1.03553i
$413$	2.43086	+	4.21037i	0.119615	+	0.207179i
$414$		0			0
$415$	0.0308152			0.00151266
$416$	20.3203	+	1.75705i	0.996282	+	0.0861465i
$417$		0			0
$418$	6.75094	+	15.5393i	0.330199	+	0.760050i
$419$	−4.74183	−	8.21309i	−0.231654	−	0.401236i	0.726641	−	0.687017i	$-0.241080\pi$
$419$	−4.74183	−	8.21309i	−0.231654	−	0.401236i	−0.958295	+	0.285781i	$0.907747\pi$
$420$		0			0
$421$	15.6320	−	15.6320i	0.761859	−	0.761859i	−0.214799	−	0.976658i	$-0.568910\pi$
$421$	15.6320	−	15.6320i	0.761859	−	0.761859i	0.976658	+	0.214799i	$0.0689097\pi$
$422$	4.61073	−	6.22701i	0.224447	−	0.303126i
$423$		0			0
$424$	3.52024	−	9.91154i	0.170958	−	0.481347i
$425$	13.8743	−	24.0310i	0.673003	−	1.16568i
$426$		0			0
$427$	−3.30409	−	0.885327i	−0.159896	−	0.0428440i
$428$	−8.53478	−	1.97598i	−0.412544	−	0.0955128i
$429$		0			0
$430$	−0.0581260	−	0.0731209i	−0.00280308	−	0.00352620i
$431$	37.8715	+	10.1476i	1.82421	+	0.488795i	0.997293	−	0.0735317i	$-0.0234270\pi$
$431$	37.8715	+	10.1476i	1.82421	+	0.488795i	0.826915	+	0.562327i	$0.190094\pi$
$432$		0			0
$433$	−5.12070	−	2.95644i	−0.246085	−	0.142077i	0.371885	−	0.928279i	$-0.378712\pi$
$433$	−5.12070	−	2.95644i	−0.246085	−	0.142077i	−0.617970	+	0.786201i	$0.712045\pi$
$434$	1.57968	+	0.180478i	0.0758270	+	0.00866321i
$435$		0			0
$436$	0.816033	+	23.7911i	0.0390809	+	1.13939i
$437$	13.9849	+	13.9849i	0.668989	+	0.668989i
$438$		0			0
$439$	3.69569	+	6.40112i	0.176385	+	0.305509i	0.940640	−	0.339406i	$-0.110226\pi$
$439$	3.69569	+	6.40112i	0.176385	+	0.305509i	−0.764254	+	0.644915i	$0.776893\pi$
$440$	0.0570112	−	0.0105116i	0.00271790	−	0.000501119i
$441$		0			0
$442$	17.7591	−	22.0320i	0.844716	−	1.04796i
$443$	27.3664			1.30022			0.650109	−	0.759841i	$-0.274723\pi$
$443$	27.3664			1.30022			0.650109	+	0.759841i	$0.274723\pi$
$444$		0			0
$445$	−0.0795804	+	0.0459458i	−0.00377247	+	0.00217804i
$446$	−2.99138	−	20.0583i	−0.141646	−	0.949789i
$447$		0			0
$448$	−11.8969	−	5.32340i	−0.562078	−	0.251507i
$449$	−4.34105	−	16.2010i	−0.204867	−	0.764573i	−0.989490	−	0.144600i	$-0.953810\pi$
$449$	−4.34105	−	16.2010i	−0.204867	−	0.764573i	0.784623	−	0.619973i	$-0.212856\pi$
$450$		0			0
$451$	8.35266	−	14.4672i	0.393311	−	0.681235i
$452$	−4.69588	−	15.3937i	−0.220875	−	0.724057i
$453$		0			0
$454$	8.43112	+	10.6061i	0.395692	+	0.497770i
$455$	−0.0318763	+	0.0166978i	−0.00149438	+	0.000782803i
$456$		0			0
$457$	7.41678	−	27.6798i	0.346942	−	1.29481i	−0.543385	−	0.839484i	$-0.682858\pi$
$457$	7.41678	−	27.6798i	0.346942	−	1.29481i	0.890327	−	0.455322i	$-0.150476\pi$
$458$	12.6638	−	32.1198i	0.591742	−	1.50086i
$459$		0			0
$460$	0.0574128	−	0.0358260i	0.00267688	−	0.00167040i
$461$	−9.47325	−	35.3546i	−0.441213	−	1.64663i	−0.725745	−	0.687963i	$-0.758505\pi$
$461$	−9.47325	−	35.3546i	−0.441213	−	1.64663i	0.284532	−	0.958666i	$-0.408162\pi$
$462$		0			0
$463$	−9.62736	−	9.62736i	−0.447422	−	0.447422i	0.447075	−	0.894497i	$-0.352466\pi$
$463$	−9.62736	−	9.62736i	−0.447422	−	0.447422i	−0.894497	+	0.447075i	$0.852466\pi$
$464$	3.91305	+	5.81689i	0.181659	+	0.270042i
$465$		0			0
$466$	−15.3769	+	6.68041i	−0.712322	+	0.309464i
$467$		−	26.0667i		−	1.20622i	−0.797658	−	0.603110i	$-0.793928\pi$
$467$		−	26.0667i		−	1.20622i	0.797658	−	0.603110i	$-0.206072\pi$
$468$		0			0
$469$			0.838620i			0.0387239i
$470$	0.0140355	+	0.0323069i	0.000647410	+	0.00149021i
$471$		0			0
$472$	−0.670046	+	8.41368i	−0.0308414	+	0.387271i
$473$	25.5087	+	25.5087i	1.17289	+	1.17289i
$474$		0			0
$475$	−4.63363	−	17.2929i	−0.212605	−	0.793454i
$476$	−15.3416	+	9.57324i	−0.703179	+	0.438789i
$477$		0			0
$478$	−15.2463	−	6.01116i	−0.697351	−	0.274944i
$479$	8.72017	−	32.5441i	0.398435	−	1.48698i	−0.417415	−	0.908716i	$-0.637064\pi$
$479$	8.72017	−	32.5441i	0.398435	−	1.48698i	0.815850	−	0.578263i	$-0.196269\pi$
$480$		0			0
$481$	30.8599	−	28.4238i	1.40709	−	1.29601i
$482$	−23.7287	+	18.8626i	−1.08081	+	0.859170i
$483$		0			0
$484$	−0.371964	+	0.113469i	−0.0169075	+	0.00515767i
$485$	0.0149355	−	0.0258691i	0.000678186	−	0.00117465i
$486$		0			0
$487$	6.44555	+	24.0551i	0.292076	+	1.09004i	0.943512	+	0.331338i	$0.107500\pi$
$487$	6.44555	+	24.0551i	0.292076	+	1.09004i	−0.651436	+	0.758703i	$0.725833\pi$
$488$	−3.85254	−	4.51926i	−0.174396	−	0.204577i
$489$		0			0
$490$	−0.0372366	+	0.00555324i	−0.00168218	+	0.000250870i
$491$	−31.9925	+	18.4709i	−1.44380	+	0.833578i	−0.998101	−	0.0616050i	$-0.980378\pi$
$491$	−31.9925	+	18.4709i	−1.44380	+	0.833578i	−0.445699	+	0.895183i	$0.647045\pi$
$492$		0			0
$493$	9.72677			0.438072
$494$	−1.94935	−	18.1533i	−0.0877056	−	0.816755i
$495$		0			0
$496$	2.08097	+	1.81349i	0.0934381	+	0.0814282i
$497$	1.79259	+	3.10486i	0.0804088	+	0.139272i
$498$		0			0
$499$	−15.6264	−	15.6264i	−0.699534	−	0.699534i	0.264776	−	0.964310i	$-0.414702\pi$
$499$	−15.6264	−	15.6264i	−0.699534	−	0.699534i	−0.964310	+	0.264776i	$0.914702\pi$
$500$	−0.122446	+	0.00419990i	−0.00547597	+	0.000187825i
$501$		0			0
$502$	1.24840	−	10.9270i	0.0557190	−	0.487695i
$503$	−29.7238	−	17.1610i	−1.32532	−	0.765173i	−0.340747	−	0.940155i	$-0.610680\pi$
$503$	−29.7238	−	17.1610i	−1.32532	−	0.765173i	−0.984572	+	0.174982i	$0.944013\pi$
$504$		0			0
$505$	0.0934268	+	0.0250336i	0.00415744	+	0.00111398i
$506$	−20.4590	+	16.2635i	−0.909513	+	0.722999i
$507$		0			0
$508$	−7.45124	−	1.72512i	−0.330595	−	0.0765399i
$509$	10.3675	+	2.77797i	0.459533	+	0.123131i	0.481156	−	0.876635i	$-0.340217\pi$
$509$	10.3675	+	2.77797i	0.459533	+	0.123131i	−0.0216237	+	0.999766i	$0.506884\pi$
$510$		0			0
$511$	1.56876	−	2.71717i	0.0693977	−	0.120200i
$512$	−11.7689	−	19.3260i	−0.520117	−	0.854095i
$513$		0			0
$514$	17.5068	+	12.9628i	0.772192	+	0.571763i
$515$	−0.0622820	+	0.0622820i	−0.00274447	+	0.00274447i
$516$		0			0
$517$	−6.80177	−	11.7810i	−0.299141	−	0.518128i
$518$	−24.5902	+	10.6831i	−1.08043	+	0.469386i
$519$		0			0
$520$	−0.0620193	−	0.00751222i	−0.00271973	−	0.000329433i
$521$	−36.1876			−1.58541			−0.792704	−	0.609607i	$-0.791327\pi$
$521$	−36.1876			−1.58541			−0.792704	+	0.609607i	$0.791327\pi$
$522$		0			0
$523$	5.07033	+	8.78207i	0.221710	+	0.384013i	0.955327	−	0.295550i	$-0.0955028\pi$
$523$	5.07033	+	8.78207i	0.221710	+	0.384013i	−0.733617	+	0.679563i	$0.762170\pi$
$524$	13.8259	−	14.8080i	0.603987	−	0.646892i
$525$		0			0
$526$	−23.4492	−	17.3627i	−1.02243	−	0.757052i
$527$	3.69924	−	0.991208i	0.161141	−	0.0431777i
$528$		0			0
$529$	−3.75469	+	6.50332i	−0.163247	+	0.282753i
$530$	−0.0118168	+	0.0299713i	−0.000513287	+	0.00130187i
$531$		0			0
$532$	−2.63158	+	11.3665i	−0.114094	+	0.492799i
$533$	−13.2414	+	12.1961i	−0.573548	+	0.528271i
$534$		0			0
$535$	0.0259190	+	0.00694496i	0.00112057	+	0.000300257i
$536$	−0.825752	+	1.19909i	−0.0356671	+	0.0517926i
$537$		0			0
$538$	2.56393	−	22.4415i	0.110539	−	0.967521i
$539$	14.0444	−	3.76319i	0.604936	−	0.162092i
$540$		0			0
$541$	−16.6100	−	16.6100i	−0.714119	−	0.714119i	0.253276	−	0.967394i	$-0.418492\pi$
$541$	−16.6100	−	16.6100i	−0.714119	−	0.714119i	−0.967394	+	0.253276i	$0.918492\pi$
$542$	32.5599	−	4.85579i	1.39857	−	0.208574i
$543$		0			0
$544$	−31.3622	−	1.41802i	−1.34464	−	0.0607972i
$545$		−	0.0729144i		−	0.00312331i
$546$		0			0
$547$	31.5052			1.34706			0.673532	−	0.739158i	$-0.264776\pi$
$547$	31.5052			1.34706			0.673532	+	0.739158i	$0.264776\pi$
$548$	−30.1869	−	16.0747i	−1.28952	−	0.686677i
$549$		0			0
$550$	23.3995	−	3.48966i	0.997758	−	0.148800i
$551$	4.43748	−	4.43748i	0.189043	−	0.189043i
$552$		0			0
$553$	−5.34278	−	19.9395i	−0.227198	−	0.847915i
$554$	8.46549	+	0.967180i	0.359664	+	0.0410915i
$555$		0			0
$556$	9.93711	+	32.5750i	0.421427	+	1.38149i
$557$	3.98647	−	14.8777i	0.168912	−	0.630389i	−0.828596	−	0.559846i	$-0.810860\pi$
$557$	3.98647	−	14.8777i	0.168912	−	0.630389i	0.997509	−	0.0705430i	$-0.0224732\pi$
$558$		0			0
$559$	−18.0389	−	34.4367i	−0.762966	−	1.45652i
$560$	0.0358596	+	0.0175450i	0.00151535	+	0.000741412i
$561$		0			0
$562$	37.9144	+	14.9484i	1.59932	+	0.630562i
$563$	36.0452	+	20.8107i	1.51912	+	0.877067i	0.999746	+	0.0225229i	$0.00716986\pi$
$563$	36.0452	+	20.8107i	1.51912	+	0.877067i	0.519379	+	0.854544i	$0.326163\pi$
$564$		0			0
$565$	0.0127586	+	0.0476157i	0.000536758	+	0.00200321i
$566$	8.99632	+	6.66124i	0.378143	+	0.279993i
$567$		0			0
$568$	−0.494114	+	6.20452i	−0.0207326	+	0.260336i
$569$	1.73040	−	0.999049i	0.0725423	−	0.0418823i	−0.463290	−	0.886207i	$-0.653331\pi$
$569$	1.73040	−	0.999049i	0.0725423	−	0.0418823i	0.535832	+	0.844324i	$0.319998\pi$
$570$		0			0
$571$		−	42.3453i		−	1.77210i	−0.463592	−	0.886049i	$-0.653440\pi$
$571$		−	42.3453i		−	1.77210i	0.463592	−	0.886049i	$-0.346560\pi$
$572$	24.1264	+	0.163662i	1.00878	+	0.00684304i
$573$		0			0
$574$	10.5512	−	4.58389i	0.440397	−	0.191328i
$575$	23.9174	−	13.8087i	0.997425	−	0.575863i
$576$		0			0
$577$	−17.1186	−	17.1186i	−0.712659	−	0.712659i	0.254432	−	0.967091i	$-0.418111\pi$
$577$	−17.1186	−	17.1186i	−0.712659	−	0.712659i	−0.967091	+	0.254432i	$0.918111\pi$
$578$	−11.6134	+	15.6845i	−0.483056	+	0.652389i
$579$		0			0
$580$	−0.0113678	−	0.0182174i	−0.000472021	−	0.000756435i
$581$	−7.09739	−	4.09768i	−0.294449	−	0.170000i
$582$		0			0
$583$	3.22026	−	12.0182i	0.133369	−	0.497741i
$584$	4.91853	−	2.34041i	0.203530	−	0.0968467i
$585$		0			0
$586$	−1.58611	−	1.99529i	−0.0655218	−	0.0824246i
$587$	−1.99421	+	7.44249i	−0.0823098	+	0.307185i	−0.994791	−	0.101934i	$-0.967497\pi$
$587$	−1.99421	+	7.44249i	−0.0823098	+	0.307185i	0.912481	+	0.409118i	$0.134164\pi$
$588$		0			0
$589$	1.23544	−	2.13985i	0.0509054	−	0.0881708i
$590$	0.00293454	−	0.0256854i	0.000120813	−	0.00105745i
$591$		0			0
$592$	−45.6790	−	8.93790i	−1.87739	−	0.367345i
$593$	−11.8828	+	11.8828i	−0.487967	+	0.487967i	−0.907664	−	0.419697i	$-0.862136\pi$
$593$	−11.8828	+	11.8828i	−0.487967	+	0.487967i	0.419697	+	0.907664i	$0.362136\pi$
$594$		0			0
$595$	0.0479683	−	0.0276945i	0.00196651	−	0.00113536i
$596$	21.3176	+	11.3517i	0.873202	+	0.464985i
$597$		0			0
$598$	26.2711	−	10.1525i	1.07431	−	0.415167i
$599$			45.8502i			1.87339i	0.350151	+	0.936693i	$0.386130\pi$
$599$			45.8502i			1.87339i	−0.350151	+	0.936693i	$0.613870\pi$
$600$		0			0
$601$	12.4138	+	21.5013i	0.506368	+	0.877056i	0.999973	+	0.00736919i	$0.00234571\pi$
$601$	12.4138	+	21.5013i	0.506368	+	0.877056i	−0.493605	+	0.869686i	$0.664321\pi$
$602$	3.66432	+	24.5706i	0.149346	+	1.00142i
$603$		0			0
$604$	4.96853	−	0.170420i	0.202167	−	0.00693429i
$605$	0.00115056		0.000308292i	4.67769e−5		1.25338e-5i
$606$		0			0
$607$	40.6484	+	23.4684i	1.64987	+	0.952551i	0.977123	+	0.212675i	$0.0682177\pi$
$607$	40.6484	+	23.4684i	1.64987	+	0.952551i	0.672744	+	0.739876i	$0.265116\pi$
$608$	−14.9548	+	13.6609i	−0.606496	+	0.554024i
$609$		0			0
$610$	0.0113188	+	0.0142387i	0.000458284	+	0.000576509i
$611$	3.20960	+	14.3039i	0.129846	+	0.578675i
$612$		0			0
$613$	7.13914	+	1.91293i	0.288347	+	0.0772624i	0.400093	−	0.916474i	$-0.368978\pi$
$613$	7.13914	+	1.91293i	0.288347	+	0.0772624i	−0.111746	+	0.993737i	$0.535644\pi$
$614$	27.2186	+	10.7314i	1.09845	+	0.433086i
$615$		0			0
$616$	−14.5287	−	5.16008i	−0.585376	−	0.207906i
$617$	3.43254	−	0.919746i	0.138189	−	0.0370276i	−0.189062	−	0.981965i	$-0.560545\pi$
$617$	3.43254	−	0.919746i	0.138189	−	0.0370276i	0.327250	+	0.944938i	$0.393878\pi$
$618$		0			0
$619$	−16.7707	+	16.7707i	−0.674072	+	0.674072i	−0.958652	−	0.284580i	$-0.908146\pi$
$619$	−16.7707	+	16.7707i	−0.674072	+	0.674072i	0.284580	+	0.958652i	$0.408146\pi$
$620$	−0.00617978	−	0.00576991i	−0.000248186	−	0.000231725i
$621$		0			0
$622$	14.4502	+	33.2614i	0.579400	+	1.33366i
$623$	24.4387			0.979117
$624$		0			0
$625$	−24.9994			−0.999977
$626$	−10.9334	−	25.1665i	−0.436988	−	1.00586i
$627$		0			0
$628$	−33.8775	−	31.6306i	−1.35186	−	1.26220i
$629$	−45.6641	+	45.6641i	−1.82074	+	1.82074i
$630$		0			0
$631$	−13.1022	+	3.51071i	−0.521589	+	0.139759i	−0.510001	−	0.860174i	$-0.670355\pi$
$631$	−13.1022	+	3.51071i	−0.521589	+	0.139759i	−0.0115873	+	0.999933i	$0.503688\pi$
$632$	11.9943	−	33.7710i	0.477107	−	1.34334i
$633$		0			0
$634$	−20.9590	−	8.26347i	−0.832388	−	0.328184i
$635$	0.0226284	+	0.00606326i	0.000897980	+	0.000240613i
$636$		0			0
$637$	−15.6554	−	0.643326i	−0.620289	−	0.0254895i
$638$	5.16048	+	6.49174i	0.204305	+	0.257011i
$639$		0			0
$640$	0.0339975	+	0.0603958i	0.00134387	+	0.00238735i
$641$	−19.1888	−	11.0787i	−0.757912	−	0.437581i	0.0706333	−	0.997502i	$-0.477498\pi$
$641$	−19.1888	−	11.0787i	−0.757912	−	0.437581i	−0.828546	+	0.559921i	$0.810831\pi$
$642$		0			0
$643$	−23.0119	+	6.16601i	−0.907499	+	0.243164i	−0.682234	−	0.731134i	$-0.738991\pi$
$643$	−23.0119	+	6.16601i	−0.907499	+	0.243164i	−0.225265	+	0.974298i	$0.572325\pi$
$644$	−17.9874	+	0.616964i	−0.708801	+	0.0243118i
$645$		0			0
$646$	4.14522	+	27.7953i	0.163092	+	1.09359i
$647$	−16.5037	−	28.5853i	−0.648829	−	1.12380i	−0.983403	−	0.181435i	$-0.941926\pi$
$647$	−16.5037	−	28.5853i	−0.648829	−	1.12380i	0.334574	−	0.942370i	$-0.391408\pi$
$648$		0			0
$649$			9.98424i			0.391916i
$650$	−25.1899	−	3.93153i	−0.988031	−	0.154207i
$651$		0			0
$652$	15.3262	+	8.16127i	0.600219	+	0.319620i
$653$	6.90829	−	3.98850i	0.270342	−	0.156082i	−0.358701	−	0.933453i	$-0.616780\pi$
$653$	6.90829	−	3.98850i	0.270342	−	0.156082i	0.629043	+	0.777370i	$0.283447\pi$
$654$		0			0
$655$	−0.0438783	+	0.0438783i	−0.00171447	+	0.00171447i
$656$	19.5999	+	3.83508i	0.765249	+	0.149735i
$657$		0			0
$658$	1.06336	−	9.30734i	0.0414541	−	0.362838i
$659$	−4.00689	+	6.94014i	−0.156086	+	0.270350i	−0.933454	−	0.358697i	$-0.883221\pi$
$659$	−4.00689	+	6.94014i	−0.156086	+	0.270350i	0.777368	+	0.629046i	$0.216554\pi$
$660$		0			0
$661$	4.42854	−	16.5276i	0.172250	−	0.642847i	−0.824753	−	0.565493i	$-0.808686\pi$
$661$	4.42854	−	16.5276i	0.172250	−	0.642847i	0.997004	−	0.0773545i	$-0.0246473\pi$
$662$	−2.83395	−	3.56503i	−0.110144	−	0.138559i
$663$		0			0
$664$	−6.11327	−	12.8475i	−0.237241	−	0.498578i
$665$	0.00924918	−	0.0345184i	0.000358668	−	0.00133857i
$666$		0			0
$667$	8.38380	+	4.84039i	0.324622	+	0.187421i
$668$	−25.4955	−	40.8577i	−0.986451	−	1.58083i
$669$		0			0
$670$	0.00265367	−	0.00358391i	0.000102520	−	0.000138458i
$671$	−4.96727	−	4.96727i	−0.191759	−	0.191759i
$672$		0			0
$673$	−40.8080	+	23.5605i	−1.57303	+	0.908190i	−0.577237	+	0.816576i	$0.695869\pi$
$673$	−40.8080	+	23.5605i	−1.57303	+	0.908190i	−0.995795	+	0.0916142i	$0.970797\pi$
$674$	18.5619	−	8.06408i	0.714976	−	0.310617i
$675$		0			0
$676$	−24.7634	−	7.92292i	−0.952439	−	0.304728i
$677$			29.4037i			1.13008i	0.825065	+	0.565038i	$0.191138\pi$
$677$			29.4037i			1.13008i	−0.825065	+	0.565038i	$0.808862\pi$
$678$		0			0
$679$	−6.87992	+	3.97212i	−0.264027	+	0.152436i
$680$	0.0958562	+	0.00763377i	0.00367592	+	0.000292742i
$681$		0			0
$682$	2.62415	+	1.94303i	0.100484	+	0.0744025i
$683$	6.46547	+	24.1295i	0.247394	+	0.923288i	0.972165	+	0.234298i	$0.0752791\pi$
$683$	6.46547	+	24.1295i	0.247394	+	0.923288i	−0.724771	+	0.688990i	$0.758054\pi$
$684$		0			0
$685$	0.0907195	+	0.0523769i	0.00346621	+	0.00200122i
$686$	24.3190	+	9.58824i	0.928506	+	0.366081i
$687$		0			0
$688$	−18.9543	+	38.7399i	−0.722624	+	1.47695i
$689$	−7.17511	+	11.3266i	−0.273350	+	0.431511i
$690$		0			0
$691$	−10.1307	+	37.8084i	−0.385391	+	1.43830i	0.452158	+	0.891938i	$0.350654\pi$
$691$	−10.1307	+	37.8084i	−0.385391	+	1.43830i	−0.837549	+	0.546362i	$0.816012\pi$
$692$	6.67016	+	21.8656i	0.253562	+	0.831206i
$693$		0			0
$694$	−2.51583	−	0.287433i	−0.0954996	−	0.0109108i
$695$	−0.0269989	−	0.100761i	−0.00102413	−	0.00382209i
$696$		0			0
$697$	19.5936	−	19.5936i	0.742159	−	0.742159i
$698$	−14.5583	+	2.17114i	−0.551041	+	0.0821790i
$699$		0			0
$700$	14.3802	+	7.65752i	0.543520	+	0.289427i
$701$	−43.6308			−1.64791			−0.823956	−	0.566654i	$-0.808238\pi$
$701$	−43.6308			−1.64791			−0.823956	+	0.566654i	$0.808238\pi$
$702$		0			0
$703$			41.6651i			1.57143i
$704$	−15.6926	−	21.6838i	−0.591438	−	0.817238i
$705$		0			0
$706$	12.3499	−	1.84179i	0.464795	−	0.0693168i
$707$	−18.1893	−	18.1893i	−0.684078	−	0.684078i
$708$		0			0
$709$	−47.8263	+	12.8150i	−1.79615	+	0.481278i	−0.993367	−	0.114987i	$-0.963317\pi$
$709$	−47.8263	+	12.8150i	−1.79615	+	0.481278i	−0.802787	+	0.596265i	$0.796651\pi$
$710$	0.00216403	−	0.0189412i	8.12146e−5	−	0.000710851i
$711$		0			0
$712$	34.9433	+	24.0637i	1.30955	+	0.901826i
$713$	3.68175	+	0.986522i	0.137883	+	0.0369455i
$714$		0			0
$715$	−0.0738379	−	0.00303422i	−0.00276138	−	0.000113473i
$716$	8.66948	−	37.4457i	0.323994	−	1.39941i
$717$		0			0
$718$	5.08579	−	12.8993i	0.189800	−	0.481397i
$719$	10.6542	−	18.4536i	0.397334	−	0.688202i	−0.596062	−	0.802938i	$-0.703269\pi$
$719$	10.6542	−	18.4536i	0.397334	−	0.688202i	0.993396	+	0.114736i	$0.0366022\pi$
$720$		0			0
$721$	22.6268	−	6.06285i	0.842668	−	0.225792i
$722$	−7.02303	−	5.20014i	−0.261370	−	0.193529i
$723$		0			0
$724$	−13.5185	+	14.4788i	−0.502411	+	0.538101i
$725$	−4.38158	−	7.58911i	−0.162728	−	0.281853i
$726$		0			0
$727$	38.5908			1.43125			0.715626	−	0.698484i	$-0.246141\pi$
$727$	38.5908			1.43125			0.715626	+	0.698484i	$0.246141\pi$
$728$	13.2854	+	9.97729i	0.492390	+	0.369783i
$729$		0			0
$730$	−0.0153022	+	0.00664795i	−0.000566360	+	0.000246052i
$731$	29.9190	+	51.8212i	1.10659	+	1.91668i
$732$		0			0
$733$	2.88135	−	2.88135i	0.106425	−	0.106425i	−0.651889	−	0.758314i	$-0.726023\pi$
$733$	2.88135	−	2.88135i	0.106425	−	0.106425i	0.758314	+	0.651889i	$0.226023\pi$
$734$	16.8848	+	12.5022i	0.623230	+	0.461465i
$735$		0			0
$736$	−26.3264	−	16.8292i	−0.970403	−	0.620332i
$737$	−0.861114	+	1.49149i	−0.0317196	+	0.0549399i
$738$		0			0
$739$	−25.1494	−	6.73876i	−0.925136	−	0.247889i	−0.235357	−	0.971909i	$-0.575626\pi$
$739$	−25.1494	−	6.73876i	−0.925136	−	0.247889i	−0.689779	+	0.724020i	$0.742292\pi$
$740$	0.138893	+	0.0321566i	0.00510580	+	0.00118210i
$741$		0			0
$742$	6.70711	−	5.33168i	0.246226	−	0.195732i
$743$	21.0093	+	5.62943i	0.770756	+	0.206524i	0.622706	−	0.782456i	$-0.286033\pi$
$743$	21.0093	+	5.62943i	0.770756	+	0.206524i	0.148051	+	0.988980i	$0.452700\pi$
$744$		0			0
$745$	−0.0640649	−	0.0369879i	−0.00234716	−	0.00135513i
$746$	3.42276	−	29.9586i	0.125316	−	1.09686i
$747$		0			0
$748$	−37.1151	+	1.27304i	−1.35706	+	0.0465471i
$749$	−5.04617	−	5.04617i	−0.184383	−	0.184383i
$750$		0			0
$751$	−2.57328	−	4.45706i	−0.0939004	−	0.162640i	0.815249	−	0.579111i	$-0.196600\pi$
$751$	−2.57328	−	4.45706i	−0.0939004	−	0.162640i	−0.909149	+	0.416471i	$0.863267\pi$
$752$	10.6849	−	12.2609i	0.389640	−	0.447108i
$753$		0			0
$754$	−3.22144	−	8.33595i	−0.117318	−	0.303577i
$755$	−0.0152274			−0.000554182
$756$		0			0
$757$	−44.0303	+	25.4209i	−1.60031	+	0.923939i	−0.608885	+	0.793259i	$0.708383\pi$
$757$	−44.0303	+	25.4209i	−1.60031	+	0.923939i	−0.991425	+	0.130680i	$0.958284\pi$
$758$	−37.7535	+	5.63033i	−1.37127	+	0.204503i
$759$		0			0
$760$	0.0472135	−	0.0402483i	0.00171261	−	0.00145996i
$761$	−9.04510	−	33.7568i	−0.327885	−	1.22368i	−0.911380	−	0.411565i	$-0.864982\pi$
$761$	−9.04510	−	33.7568i	−0.327885	−	1.22368i	0.583496	−	0.812116i	$-0.301685\pi$
$762$		0			0
$763$	−9.69586	+	16.7937i	−0.351014	+	0.607973i
$764$	16.0931	−	4.90926i	0.582230	−	0.177611i
$765$		0			0
$766$	23.9603	−	19.0468i	0.865721	−	0.688188i
$767$	3.20908	−	10.2696i	0.115873	−	0.370814i
$768$		0			0
$769$	11.4952	−	42.9007i	0.414528	−	1.54704i	−0.371251	−	0.928533i	$-0.621071\pi$
$769$	11.4952	−	42.9007i	0.414528	−	1.54704i	0.785779	−	0.618507i	$-0.212262\pi$
$770$	0.0439329	+	0.0173214i	0.00158323	+	0.000624219i
$771$		0			0
$772$	6.66474	−	4.15884i	0.239869	−	0.149680i
$773$	12.8446	+	47.9367i	0.461988	+	1.72416i	0.666687	+	0.745338i	$0.267712\pi$
$773$	12.8446	+	47.9367i	0.461988	+	1.72416i	−0.204699	+	0.978825i	$0.565621\pi$
$774$		0			0
$775$	−2.43975	−	2.43975i	−0.0876385	−	0.0876385i
$776$	−13.7483	−	1.09488i	−0.493535	−	0.0393040i
$777$		0			0
$778$	14.4218	+	33.1959i	0.517045	+	1.19013i
$779$		−	17.8777i		−	0.640535i
$780$		0			0
$781$			7.36270i			0.263458i
$782$	−39.7615	+	17.2741i	−1.42187	+	0.617722i
$783$		0			0
$784$	9.70243	+	14.4230i	0.346515	+	0.515107i
$785$	0.100384	+	0.100384i	0.00358285	+	0.00358285i
$786$		0			0
$787$	1.12108	+	4.18392i	0.0399621	+	0.149141i	0.983024	−	0.183476i	$-0.0587351\pi$
$787$	1.12108	+	4.18392i	0.0399621	+	0.149141i	−0.943062	+	0.332617i	$0.892068\pi$
$788$	−27.0495	+	16.8791i	−0.963600	+	0.601293i
$789$		0			0
$790$	−0.0402625	+	0.102119i	−0.00143247	+	0.00363324i
$791$	3.39317	−	12.6635i	0.120647	−	0.450261i
$792$		0			0
$793$	3.51270	+	6.70581i	0.124740	+	0.238130i
$794$	6.49844	+	8.17486i	0.230621	+	0.290115i
$795$		0			0
$796$	−7.49029	−	24.5541i	−0.265486	−	0.870297i
$797$	9.64544	−	16.7064i	0.341659	−	0.591771i	−0.643082	−	0.765797i	$-0.722345\pi$
$797$	9.64544	−	16.7064i	0.341659	−	0.591771i	0.984741	+	0.174027i	$0.0556779\pi$
$798$		0			0
$799$	−5.84012	−	21.7956i	−0.206609	−	0.771074i
$800$	13.0212	+	25.1085i	0.460369	+	0.887719i
$801$		0			0
$802$	0.0110188	+	0.0738854i	0.000389088	+	0.00260898i
$803$	5.58010	−	3.22167i	0.196917	−	0.113690i
$804$		0			0
$805$	0.0551272			0.00194298
$806$	−2.07464	−	2.84201i	−0.0730761	−	0.100106i
$807$		0			0
$808$	−8.09743	−	43.9178i	−0.284867	−	1.54502i
$809$	−14.4841	−	25.0872i	−0.509233	−	0.882018i	−0.999943	−	0.0106948i	$-0.996596\pi$
$809$	−14.4841	−	25.0872i	−0.509233	−	0.882018i	0.490709	−	0.871323i	$-0.336738\pi$
$810$		0			0
$811$	35.5730	+	35.5730i	1.24914	+	1.24914i	0.956102	+	0.293033i	$0.0946647\pi$
$811$	35.5730	+	35.5730i	1.24914	+	1.24914i	0.293033	+	0.956102i	$0.405335\pi$
$812$	0.195766	+	5.70748i	0.00687003	+	0.200293i
$813$		0			0
$814$	−54.7035	−	6.24985i	−1.91736	−	0.219057i
$815$	−0.0460591	−	0.0265923i	−0.00161338	−	0.000931486i
$816$		0			0
$817$	37.2910	+	9.99209i	1.30465	+	0.349579i
$818$	8.58585	+	10.8008i	0.300197	+	0.377640i
$819$		0			0
$820$	−0.0595961	−	0.0137978i	−0.00208119	−	0.000481840i
$821$	12.8376	+	3.43981i	0.448034	+	0.120050i	0.475779	−	0.879565i	$-0.342166\pi$
$821$	12.8376	+	3.43981i	0.448034	+	0.120050i	−0.0277455	+	0.999615i	$0.508833\pi$
$822$		0			0
$823$	11.2358	−	19.4610i	0.391656	−	0.678367i	−0.601013	−	0.799240i	$-0.705236\pi$
$823$	11.2358	−	19.4610i	0.391656	−	0.678367i	0.992668	+	0.120872i	$0.0385692\pi$
$824$	38.3224	+	13.6108i	1.33502	+	0.474155i
$825$		0			0
$826$	−4.09142	+	5.52565i	−0.142359	+	0.192262i
$827$	−2.97912	+	2.97912i	−0.103594	+	0.103594i	−0.757004	−	0.653410i	$-0.773338\pi$
$827$	−2.97912	+	2.97912i	−0.103594	+	0.103594i	0.653410	+	0.757004i	$0.273338\pi$
$828$		0			0
$829$	−7.48252	−	12.9601i	−0.259879	−	0.450123i	0.706331	−	0.707882i	$-0.250349\pi$
$829$	−7.48252	−	12.9601i	−0.259879	−	0.450123i	−0.966209	+	0.257759i	$0.917016\pi$
$830$	0.0173648	+	0.0399702i	0.000602741	+	0.00138739i
$831$		0			0
$832$	9.17169	+	27.3474i	0.317971	+	0.948100i
$833$	24.1176			0.835624
$834$		0			0
$835$	0.0737561	+	0.127749i	0.00255244	+	0.00442095i
$836$	−16.3516	+	17.5132i	−0.565533	+	0.605707i
$837$		0			0
$838$	7.98106	−	10.7788i	0.275701	−	0.372347i
$839$	−9.03430	+	2.42073i	−0.311899	+	0.0835730i	−0.411373	−	0.911467i	$-0.634951\pi$
$839$	−9.03430	+	2.42073i	−0.311899	+	0.0835730i	0.0994743	+	0.995040i	$0.468284\pi$
$840$		0			0
$841$	−12.9641	+	22.4545i	−0.447039	+	0.774294i
$842$	29.0851	+	11.4673i	1.00234	+	0.395191i
$843$		0			0
$844$	10.6752	+	2.47154i	0.367456	+	0.0850740i
$845$	0.0749732	+	0.0268535i	0.00257916	+	0.000923790i
$846$		0			0
$847$	−0.305993	−	0.0819907i	−0.0105141	−	0.00281723i
$848$	14.8399	−	1.01921i	0.509604	−	0.0349999i
$849$		0			0
$850$	38.9889	+	4.45447i	1.33731	+	0.152787i
$851$	−62.0833	+	16.6352i	−2.12819	+	0.570247i
$852$		0			0
$853$	7.92636	+	7.92636i	0.271393	+	0.271393i	0.829661	−	0.558268i	$-0.188534\pi$
$853$	7.92636	+	7.92636i	0.271393	+	0.271393i	−0.558268	+	0.829661i	$0.688534\pi$
$854$	−0.713547	−	4.78460i	−0.0244171	−	0.163726i
$855$		0			0
$856$	−2.24643	−	12.1839i	−0.0767815	−	0.416437i
$857$			38.4399i			1.31308i	0.754291	+	0.656541i	$0.227981\pi$
$857$			38.4399i			1.31308i	−0.754291	+	0.656541i	$0.772019\pi$
$858$		0			0
$859$	1.82343			0.0622145			0.0311072	−	0.999516i	$-0.490097\pi$
$859$	1.82343			0.0622145			0.0311072	+	0.999516i	$0.490097\pi$
$860$	0.0620898	−	0.116599i	0.00211725	−	0.00397601i
$861$		0			0
$862$	8.17870	+	54.8413i	0.278568	+	1.86790i
$863$	25.6067	−	25.6067i	0.871661	−	0.871661i	−0.120993	−	0.992653i	$-0.538608\pi$
$863$	25.6067	−	25.6067i	0.871661	−	0.871661i	0.992653	+	0.120993i	$0.0386078\pi$
$864$		0			0
$865$	−0.0181227	−	0.0676348i	−0.000616190	−	0.00229965i
$866$	0.949189	−	8.30802i	0.0322548	−	0.282318i
$867$		0			0
$868$	0.656075	+	2.15069i	0.0222686	+	0.0729993i
$869$	10.9722	−	40.9487i	0.372205	−	1.38909i
$870$		0			0
$871$	1.36512	−	1.25735i	0.0462552	−	0.0426037i
$872$	−30.3995	+	14.4651i	−1.02946	+	0.489850i
$873$		0			0
$874$	−10.2590	+	26.0204i	−0.347017	+	0.880154i
$875$	−0.0864327	−	0.0499019i	−0.00292196	−	0.00168699i
$876$		0			0
$877$	2.98286	+	11.1322i	0.100724	+	0.375907i	0.997825	−	0.0659183i	$-0.0209977\pi$
$877$	2.98286	+	11.1322i	0.100724	+	0.375907i	−0.897101	+	0.441826i	$0.854331\pi$
$878$	−6.22027	+	8.40077i	−0.209924	+	0.283512i
$879$		0			0
$880$	0.0457611	+	0.0680254i	0.00154261	+	0.00229314i
$881$	−11.9623	+	6.90643i	−0.403020	+	0.232684i	−0.687786	−	0.725913i	$-0.741417\pi$
$881$	−11.9623	+	6.90643i	−0.403020	+	0.232684i	0.284766	+	0.958597i	$0.408084\pi$
$882$		0			0
$883$			46.3198i			1.55879i	0.626536	+	0.779393i	$0.284472\pi$
$883$			46.3198i			1.55879i	−0.626536	+	0.779393i	$0.715528\pi$
$884$	38.5851	+	10.6199i	1.29776	+	0.357186i
$885$		0			0
$886$	15.4214	+	35.4968i	0.518091	+	1.19254i
$887$	−40.2976	+	23.2659i	−1.35306	+	0.781191i	−0.988677	−	0.150058i	$-0.952054\pi$
$887$	−40.2976	+	23.2659i	−1.35306	+	0.781191i	−0.364385	+	0.931248i	$0.618721\pi$
$888$		0			0
$889$	−4.40552	−	4.40552i	−0.147757	−	0.147757i
$890$	−0.104441	−	0.0773322i	−0.00350086	−	0.00259218i
$891$		0			0
$892$	24.3318	−	15.1832i	0.814690	−	0.508373i
$893$	−12.6078	−	7.27912i	−0.421904	−	0.243586i
$894$		0			0
$895$	−0.0304705	+	0.113717i	−0.00101852	+	0.00380115i
$896$	0.200856	−	18.4313i	0.00671014	−	0.615745i
$897$		0			0
$898$	18.5680	−	14.7602i	0.619622	−	0.492556i
$899$	0.313029	−	1.16824i	0.0104401	−	0.0389629i
$900$		0			0
$901$	10.3190	−	17.8730i	0.343776	−	0.595437i
$902$	23.4722	+	2.68169i	0.781538	+	0.0892905i
$903$		0			0
$904$	17.3208	−	14.7655i	0.576082	−	0.491094i
$905$	0.0429027	−	0.0429027i	0.00142613	−	0.00142613i
$906$		0			0
$907$	−23.2692	+	13.4345i	−0.772642	+	0.446085i	−0.833816	−	0.552042i	$-0.813849\pi$
$907$	−23.2692	+	13.4345i	−0.772642	+	0.446085i	0.0611745	+	0.998127i	$0.480515\pi$
$908$	−9.00607	+	16.9126i	−0.298877	+	0.561266i
$909$		0			0
$910$	−0.0396213	−	0.0319371i	−0.00131343	−	0.00105871i
$911$			34.1859i			1.13263i	0.824189	+	0.566315i	$0.191632\pi$
$911$			34.1859i			1.13263i	−0.824189	+	0.566315i	$0.808368\pi$
$912$		0			0
$913$	−8.41517	−	14.5755i	−0.278502	−	0.482379i
$914$	40.0827	−	5.97770i	1.32582	−	0.197725i
$915$		0			0
$916$	48.7986	−	1.67379i	1.61235	−	0.0553035i
$917$	15.9408	−	4.27133i	0.526413	−	0.141052i
$918$		0			0
$919$	12.0258	+	6.94309i	0.396694	+	0.229031i	0.685057	−	0.728490i	$-0.259777\pi$
$919$	12.0258	+	6.94309i	0.396694	+	0.229031i	−0.288362	+	0.957521i	$0.593111\pi$
$920$	0.0788226	+	0.0542813i	0.00259870	+	0.00178960i
$921$		0			0
$922$	40.5200	−	32.2105i	1.33445	−	1.06080i
$923$	2.36648	−	7.57315i	0.0778936	−	0.249273i
$924$		0			0
$925$	56.1986	+	15.0584i	1.84780	+	0.495116i
$926$	7.06244	−	17.9127i	0.232086	−	0.588649i
$927$		0			0
$928$	−5.33999	+	8.35350i	−0.175294	+	0.274217i
$929$	−26.6246	+	7.13405i	−0.873526	+	0.234061i	−0.667612	−	0.744510i	$-0.732683\pi$
$929$	−26.6246	+	7.13405i	−0.873526	+	0.234061i	−0.205914	+	0.978570i	$0.566017\pi$
$930$		0			0
$931$	11.0028	−	11.0028i	0.360601	−	0.360601i
$932$	−17.3302	−	16.1808i	−0.567670	−	0.530020i
$933$		0			0
$934$	33.8109	−	14.6889i	1.10633	−	0.480636i
$935$	0.113749			0.00372000
$936$		0			0
$937$	28.0766			0.917224			0.458612	−	0.888637i	$-0.348347\pi$
$937$	28.0766			0.917224			0.458612	+	0.888637i	$0.348347\pi$
$938$	−1.08777	+	0.472574i	−0.0355169	+	0.0154301i
$939$		0			0
$940$	−0.0339958	+	0.0364108i	−0.00110882	+	0.00118759i
$941$	−4.25969	+	4.25969i	−0.138862	+	0.138862i	−0.773121	−	0.634259i	$-0.781305\pi$
$941$	−4.25969	+	4.25969i	−0.138862	+	0.138862i	0.634259	+	0.773121i	$0.281305\pi$
$942$		0			0
$943$	26.6388	−	7.13783i	0.867477	−	0.232440i
$944$	−11.2909	+	3.87211i	−0.367488	+	0.126027i
$945$		0			0
$946$	−18.7127	+	47.4617i	−0.608401	+	1.54311i
$947$	−6.23584	−	1.67089i	−0.202637	−	0.0542965i	0.156073	−	0.987746i	$-0.450117\pi$
$947$	−6.23584	−	1.67089i	−0.202637	−	0.0542965i	−0.358710	+	0.933449i	$0.616783\pi$
$948$		0			0
$949$	−6.77508	+	1.52023i	−0.219929	+	0.0493488i
$950$	19.8194	−	15.7551i	0.643027	−	0.511162i
$951$		0			0
$952$	−21.0626	−	14.5048i	−0.682642	−	0.470102i
$953$	−14.7203	−	8.49878i	−0.476838	−	0.275302i	0.242260	−	0.970211i	$-0.422111\pi$
$953$	−14.7203	−	8.49878i	−0.476838	−	0.275302i	−0.719098	+	0.694909i	$0.755445\pi$
$954$		0			0
$955$	−0.0497794	+	0.0133383i	−0.00161082	+	0.000431618i
$956$	−0.794499	−	23.1633i	−0.0256959	−	0.749155i
$957$		0			0
$958$	47.1267	−	7.02820i	1.52260	−	0.227071i
$959$	−13.9297	−	24.1270i	−0.449815	−	0.779102i
$960$		0			0
$961$			30.5238i			0.984639i
$962$	54.2583	+	24.0110i	1.74936	+	0.774145i
$963$		0			0
$964$	−37.8381	−	20.1490i	−1.21868	−	0.648954i
$965$	−0.0208386	+	0.0120312i	−0.000670817	+	0.000387297i
$966$		0			0
$967$	−14.8731	+	14.8731i	−0.478288	+	0.478288i	−0.904584	−	0.426296i	$-0.859818\pi$
$967$	−14.8731	+	14.8731i	−0.478288	+	0.478288i	0.426296	+	0.904584i	$0.359818\pi$
$968$	−0.356786	−	0.418531i	−0.0114676	−	0.0134521i
$969$		0			0
$970$	0.0419710	+	0.00479517i	0.00134761	+	0.000153964i
$971$	7.95576	−	13.7798i	0.255313	−	0.442214i	−0.709668	−	0.704536i	$-0.751155\pi$
$971$	7.95576	−	13.7798i	0.255313	−	0.442214i	0.964980	+	0.262322i	$0.0844883\pi$
$972$		0			0
$973$	−7.18040	+	26.7976i	−0.230193	+	0.859092i
$974$	−27.5696	+	21.9159i	−0.883387	+	0.702230i
$975$		0			0
$976$	3.69093	−	7.54378i	0.118144	−	0.241470i
$977$	2.13713	−	7.97588i	0.0683729	−	0.255171i	−0.923276	−	0.384137i	$-0.874499\pi$
$977$	2.13713	−	7.97588i	0.0683729	−	0.255171i	0.991649	+	0.128966i	$0.0411658\pi$
$978$		0			0
$979$	43.4645	+	25.0942i	1.38913	+	0.802015i
$980$	−0.0281864	−	0.0451700i	−0.000900383	−	0.00144290i
$981$		0			0
$982$	−41.9866	−	31.0886i	−1.33985	−	0.992078i
$983$	30.1467	+	30.1467i	0.961530	+	0.961530i	0.999287	−	0.0377570i	$-0.0120213\pi$
$983$	30.1467	+	30.1467i	0.961530	+	0.961530i	−0.0377570	+	0.999287i	$0.512021\pi$
$984$		0			0
$985$	0.0845755	−	0.0488297i	0.00269480	−	0.00155584i
$986$	5.48117	+	12.6165i	0.174556	+	0.401792i
$987$		0			0
$988$	22.4480	−	12.7581i	0.714166	−	0.405890i
$989$			59.5551i			1.89374i
$990$		0			0
$991$	2.25938	−	1.30446i	0.0717717	−	0.0414374i	−0.463685	−	0.886000i	$-0.653473\pi$
$991$	2.25938	−	1.30446i	0.0717717	−	0.0414374i	0.535456	+	0.844563i	$0.320140\pi$
$992$	−1.17962	+	3.72114i	−0.0374528	+	0.118146i
$993$		0			0
$994$	−3.01715	+	4.07480i	−0.0956981	+	0.129245i
$995$	0.0203509	+	0.0759508i	0.000645168	+	0.00240780i
$996$		0			0
$997$	−21.3384	−	12.3197i	−0.675794	−	0.390170i	0.122475	−	0.992472i	$-0.460917\pi$
$997$	−21.3384	−	12.3197i	−0.675794	−	0.390170i	−0.798268	+	0.602302i	$0.794250\pi$
$998$	11.4632	−	29.0746i	0.362862	−	0.920341i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.e.739.10		56
3.2	odd	2		312.2.bt.d.115.5	yes	56
8.3	odd	2	inner	936.2.ed.e.739.4		56
13.6	odd	12	inner	936.2.ed.e.19.4		56
24.11	even	2		312.2.bt.d.115.11	yes	56
39.32	even	12		312.2.bt.d.19.11	yes	56
104.19	even	12	inner	936.2.ed.e.19.10		56
312.227	odd	12		312.2.bt.d.19.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.5	✓	56	312.227	odd	12
312.2.bt.d.19.11	yes	56	39.32	even	12
312.2.bt.d.115.5	yes	56	3.2	odd	2
312.2.bt.d.115.11	yes	56	24.11	even	2
936.2.ed.e.19.4		56	13.6	odd	12	inner
936.2.ed.e.19.10		56	104.19	even	12	inner
936.2.ed.e.739.4		56	8.3	odd	2	inner
936.2.ed.e.739.10		56	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563514 + 1.29709i) q^{2} +(-1.36490 + 1.46186i) q^{4} +(0.00433170 - 0.00433170i) q^{5} +(-1.57369 + 0.421669i) q^{7} +(-2.66531 - 0.946628i) q^{8} +(0.00805959 + 0.00317764i) q^{10} +(-3.23180 - 0.865959i) q^{11} +(3.04585 + 1.92946i) q^{13} +(-1.43374 - 1.80361i) q^{14} +(-0.274077 - 3.99060i) q^{16} +(-4.80624 - 2.77488i) q^{17} +(-3.45861 + 0.926732i) q^{19} +(0.000419991 + 0.0122447i) q^{20} +(-0.697937 - 4.67993i) q^{22} +(-2.76176 - 4.78352i) q^{23} +4.99996i q^{25} +(-0.786312 + 5.03803i) q^{26} +(1.53152 - 2.87606i) q^{28} +(-1.51783 + 0.876322i) q^{29} +(-0.487954 + 0.487954i) q^{31} +(5.02173 - 2.60426i) q^{32} +(0.890900 - 7.79783i) q^{34} +(-0.00499021 + 0.00864330i) q^{35} +(3.01169 - 11.2398i) q^{37} +(-3.15103 - 3.96392i) q^{38} +(-0.0156458 + 0.00744482i) q^{40} +(-1.29226 + 4.82278i) q^{41} +(-9.33754 - 5.39103i) q^{43} +(5.67701 - 3.54250i) q^{44} +(4.64838 - 6.27785i) q^{46} +(2.87499 + 2.87499i) q^{47} +(-3.76348 + 2.17284i) q^{49} +(-6.48542 + 2.81755i) q^{50} +(-6.97789 + 1.81908i) q^{52} +3.71872i q^{53} +(-0.0177503 + 0.0102481i) q^{55} +(4.59355 + 0.365820i) q^{56} +(-1.99199 - 1.47495i) q^{58} +(-0.772342 - 2.88242i) q^{59} +(1.81829 + 1.04979i) q^{61} +(-0.907891 - 0.357953i) q^{62} +(6.20779 + 5.04612i) q^{64} +(0.0215515 - 0.00483585i) q^{65} +(0.133225 - 0.497203i) q^{67} +(10.6165 - 3.23861i) q^{68} +(-0.0140232 - 0.00160215i) q^{70} +(-0.569550 - 2.12559i) q^{71} +(-1.36174 + 1.36174i) q^{73} +(16.2762 - 2.42733i) q^{74} +(3.36592 - 6.32091i) q^{76} +5.45101 q^{77} +12.6705i q^{79} +(-0.0184733 - 0.0160988i) q^{80} +(-6.98380 + 1.04152i) q^{82} +(3.55694 + 3.55694i) q^{83} +(-0.0328391 + 0.00879922i) q^{85} +(1.73084 - 15.1496i) q^{86} +(7.79403 + 5.36737i) q^{88} +(-14.4893 - 3.88239i) q^{89} +(-5.60682 - 1.75203i) q^{91} +(10.7624 + 2.49172i) q^{92} +(-2.10903 + 5.34922i) q^{94} +(-0.0109673 + 0.0189960i) q^{95} +(4.71000 - 1.26204i) q^{97} +(-4.93916 - 3.65715i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) \) 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Introduction

L-functions

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