LMFDB - Embedded newform 936.2.ed.e.19.4

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			19.4
Character	$\chi$	$=$	936.19
Dual form			936.2.ed.e.739.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13656 - 0.841559i) q^{2} +(0.583557 + 1.91297i) q^{4} +(-0.00433170 - 0.00433170i) q^{5} +(1.57369 + 0.421669i) q^{7} +(0.946628 - 2.66531i) q^{8} +(0.00127787 + 0.00856863i) q^{10} +(-3.23180 + 0.865959i) q^{11} +(-3.04585 + 1.92946i) q^{13} +(-1.43374 - 1.80361i) q^{14} +(-3.31892 + 2.23266i) q^{16} +(-4.80624 + 2.77488i) q^{17} +(-3.45861 - 0.926732i) q^{19} +(0.00575862 - 0.0108142i) q^{20} +(4.40191 + 1.73554i) q^{22} +(2.76176 - 4.78352i) q^{23} -4.99996i q^{25} +(5.08556 + 0.370304i) q^{26} +(0.111697 + 3.25650i) q^{28} +(1.51783 + 0.876322i) q^{29} +(0.487954 + 0.487954i) q^{31} +(5.65108 + 0.255510i) q^{32} +(7.79783 + 0.890900i) q^{34} +(-0.00499021 - 0.00864330i) q^{35} +(-3.01169 - 11.2398i) q^{37} +(3.15103 + 3.96392i) q^{38} +(-0.0156458 + 0.00744482i) q^{40} +(-1.29226 - 4.82278i) q^{41} +(-9.33754 + 5.39103i) q^{43} +(-3.54250 - 5.67701i) q^{44} +(-7.16454 + 3.11259i) q^{46} +(-2.87499 + 2.87499i) q^{47} +(-3.76348 - 2.17284i) q^{49} +(-4.20776 + 5.68278i) q^{50} +(-5.46843 - 4.70067i) q^{52} +3.71872i q^{53} +(0.0177503 + 0.0102481i) q^{55} +(2.61358 - 3.79522i) q^{56} +(-0.987640 - 2.27334i) q^{58} +(-0.772342 + 2.88242i) q^{59} +(-1.81829 + 1.04979i) q^{61} +(-0.143949 - 0.965233i) q^{62} +(-6.20779 - 5.04612i) q^{64} +(0.0215515 + 0.00483585i) q^{65} +(0.133225 + 0.497203i) q^{67} +(-8.11299 - 7.57490i) q^{68} +(-0.00160215 + 0.0140232i) q^{70} +(0.569550 - 2.12559i) q^{71} +(-1.36174 - 1.36174i) q^{73} +(-6.03597 + 15.3093i) q^{74} +(-0.245485 - 7.15703i) q^{76} -5.45101 q^{77} +12.6705i q^{79} +(0.0240478 + 0.00470537i) q^{80} +(-2.58992 + 6.56891i) q^{82} +(3.55694 - 3.55694i) q^{83} +(0.0328391 + 0.00879922i) q^{85} +(15.1496 + 1.73084i) q^{86} +(-0.751264 + 9.43351i) q^{88} +(-14.4893 + 3.88239i) q^{89} +(-5.60682 + 1.75203i) q^{91} +(10.7624 + 2.49172i) q^{92} +(5.68708 - 0.848136i) q^{94} +(0.0109673 + 0.0189960i) q^{95} +(4.71000 + 1.26204i) q^{97} +(2.44886 + 5.63677i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.13656	−	0.841559i	−0.803672	−	0.595072i
$2$	−1.13656	−	0.841559i	−0.803672	−	0.595072i
$3$		0			0
$3$		0			0
$4$	0.583557	+	1.91297i	0.291779	+	0.956486i
$5$	−0.00433170	−	0.00433170i	−0.00193719	−	0.00193719i	0.706138	−	0.708075i	$-0.250436\pi$
$5$	−0.00433170	−	0.00433170i	−0.00193719	−	0.00193719i	−0.708075	+	0.706138i	$0.750436\pi$
$6$		0			0
$7$	1.57369	+	0.421669i	0.594800	+	0.159376i	0.543646	−	0.839315i	$-0.317043\pi$
$7$	1.57369	+	0.421669i	0.594800	+	0.159376i	0.0511537	+	0.998691i	$0.483710\pi$
$8$	0.946628	−	2.66531i	0.334684	−	0.942331i
$9$		0			0
$10$	0.00127787	+	0.00856863i	0.000404099	+	0.00270964i
$11$	−3.23180	+	0.865959i	−0.974426	+	0.261097i	−0.710695	−	0.703500i	$-0.751620\pi$
$11$	−3.23180	+	0.865959i	−0.974426	+	0.261097i	−0.263730	+	0.964596i	$0.584953\pi$
$12$		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
$16$	−3.31892	+	2.23266i	−0.829730	+	0.558164i
$17$	−4.80624	+	2.77488i	−1.16568	+	0.673008i	−0.952660	−	0.304039i	$-0.901665\pi$
$17$	−4.80624	+	2.77488i	−1.16568	+	0.673008i	−0.213025	+	0.977047i	$0.568331\pi$
$18$		0			0
$19$	−3.45861	−	0.926732i	−0.793460	−	0.212607i	−0.160749	−	0.986995i	$-0.551391\pi$
$19$	−3.45861	−	0.926732i	−0.793460	−	0.212607i	−0.632711	+	0.774388i	$0.718058\pi$
$20$	0.00575862	−	0.0108142i	0.00128767	−	0.00241813i
$21$		0			0
$22$	4.40191	+	1.73554i	0.938490	+	0.370017i
$23$	2.76176	−	4.78352i	0.575868	−	0.997432i	−0.420079	−	0.907488i	$-0.637998\pi$
$23$	2.76176	−	4.78352i	0.575868	−	0.997432i	0.995947	−	0.0899447i	$-0.0286690\pi$
$24$		0			0
$25$		−	4.99996i		−	0.999992i
$26$	5.08556	+	0.370304i	0.997359	+	0.0726227i
$27$		0			0
$28$	0.111697	+	3.25650i	0.0211088	+	0.615420i
$29$	1.51783	+	0.876322i	0.281855	+	0.162729i	0.634263	−	0.773118i	$-0.281304\pi$
$29$	1.51783	+	0.876322i	0.281855	+	0.162729i	−0.352408	+	0.935846i	$0.614637\pi$
$30$		0			0
$31$	0.487954	+	0.487954i	0.0876391	+	0.0876391i	0.749567	−	0.661928i	$-0.230262\pi$
$31$	0.487954	+	0.487954i	0.0876391	+	0.0876391i	−0.661928	+	0.749567i	$0.730262\pi$
$32$	5.65108	+	0.255510i	0.998979	+	0.0451682i
$33$		0			0
$34$	7.79783	+	0.890900i	1.33732	+	0.152788i
$35$	−0.00499021	−	0.00864330i	−0.000843500	−	0.00146098i
$36$		0			0
$37$	−3.01169	−	11.2398i	−0.495119	−	1.84781i	−0.529360	−	0.848397i	$-0.677568\pi$
$37$	−3.01169	−	11.2398i	−0.495119	−	1.84781i	0.0342404	−	0.999414i	$-0.489099\pi$
$38$	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	−0.990396	−	0.138258i	$-0.955850\pi$
$41$	−1.29226	−	4.82278i	−0.201817	−	0.753191i	0.788579	−	0.614933i	$-0.210817\pi$
$42$		0			0
$43$	−9.33754	+	5.39103i	−1.42396	+	0.822125i	−0.996635	−	0.0819721i	$-0.973878\pi$
$43$	−9.33754	+	5.39103i	−1.42396	+	0.822125i	−0.427327	+	0.904097i	$0.640545\pi$
$44$	−3.54250	−	5.67701i	−0.534052	−	0.855842i
$45$		0			0
$46$	−7.16454	+	3.11259i	−1.05635	+	0.458926i
$47$	−2.87499	+	2.87499i	−0.419360	+	0.419360i	−0.884983	−	0.465623i	$-0.845830\pi$
$47$	−2.87499	+	2.87499i	−0.419360	+	0.419360i	0.465623	+	0.884983i	$0.345830\pi$
$48$		0			0
$49$	−3.76348	−	2.17284i	−0.537640	−	0.310406i
$50$	−4.20776	+	5.68278i	−0.595068	+	0.803666i
$51$		0			0
$52$	−5.46843	−	4.70067i	−0.758335	−	0.651866i
$53$			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
$56$	2.61358	−	3.79522i	0.349255	−	0.507157i
$57$		0			0
$58$	−0.987640	−	2.27334i	−0.129683	−	0.298505i
$59$	−0.772342	+	2.88242i	−0.100550	+	0.375259i	−0.997802	−	0.0662595i	$-0.978893\pi$
$59$	−0.772342	+	2.88242i	−0.100550	+	0.375259i	0.897252	+	0.441519i	$0.145560\pi$
$60$		0			0
$61$	−1.81829	+	1.04979i	−0.232808	+	0.134412i	−0.611867	−	0.790961i	$-0.709581\pi$
$61$	−1.81829	+	1.04979i	−0.232808	+	0.134412i	0.379059	+	0.925373i	$0.376248\pi$
$62$	−0.143949	−	0.965233i	−0.0182816	−	0.122585i
$63$		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	0.973586	−	0.228320i	$-0.0733231\pi$
$67$	0.133225	+	0.497203i	0.0162760	+	0.0607430i	−0.957310	+	0.289063i	$0.906656\pi$
$68$	−8.11299	−	7.57490i	−0.983845	−	0.918591i
$69$		0			0
$70$	−0.00160215	+	0.0140232i	−0.000191493	+	0.00167610i
$71$	0.569550	−	2.12559i	0.0675932	−	0.252261i	−0.923859	−	0.382734i	$-0.874983\pi$
$71$	0.569550	−	2.12559i	0.0675932	−	0.252261i	0.991452	+	0.130472i	$0.0416494\pi$
$72$		0			0
$73$	−1.36174	−	1.36174i	−0.159380	−	0.159380i	0.622912	−	0.782292i	$-0.285949\pi$
$73$	−1.36174	−	1.36174i	−0.159380	−	0.159380i	−0.782292	+	0.622912i	$0.785949\pi$
$74$	−6.03597	+	15.3093i	−0.701667	+	1.77967i
$75$		0			0
$76$	−0.245485	−	7.15703i	−0.0281591	−	0.820967i
$77$	−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	$0.747439\pi$
$80$	0.0240478	+	0.00470537i	0.00268862	+	0.000526076i
$81$		0			0
$82$	−2.58992	+	6.56891i	−0.286008	+	0.725415i
$83$	3.55694	−	3.55694i	0.390425	−	0.390425i	−0.484414	−	0.874839i	$-0.660967\pi$
$83$	3.55694	−	3.55694i	0.390425	−	0.390425i	0.874839	+	0.484414i	$0.160967\pi$
$84$		0			0
$85$	0.0328391	+	0.00879922i	0.00356190	+	0.000954409i
$86$	15.1496	+	1.73084i	1.63362	+	0.186641i
$87$		0			0
$88$	−0.751264	+	9.43351i	−0.0800850	+	1.00562i
$89$	−14.4893	+	3.88239i	−1.53586	+	0.411532i	−0.924925	−	0.380149i	$-0.875873\pi$
$89$	−14.4893	+	3.88239i	−1.53586	+	0.411532i	−0.610934	+	0.791682i	$0.709206\pi$
$90$		0			0
$91$	−5.60682	+	1.75203i	−0.587754	+	0.183663i
$92$	10.7624	+	2.49172i	1.12206	+	0.259780i
$93$		0			0
$94$	5.68708	−	0.848136i	0.586577	−	0.0874786i
$95$	0.0109673	+	0.0189960i	0.00112522	+	0.00194895i
$96$		0			0
$97$	4.71000	+	1.26204i	0.478228	+	0.128141i	0.489877	−	0.871791i	$-0.337042\pi$
$97$	4.71000	+	1.26204i	0.478228	+	0.128141i	−0.0116495	+	0.999932i	$0.503708\pi$
$98$	2.44886	+	5.63677i	0.247372	+	0.569399i
$99$		0			0
$100$	9.56479	−	2.91776i	0.956479	−	0.291776i
$101$	−7.89450	+	13.6737i	−0.785532	+	1.36058i	0.143149	+	0.989701i	$0.454277\pi$
$101$	−7.89450	+	13.6737i	−0.785532	+	1.36058i	−0.928681	+	0.370880i	$0.879056\pi$
$102$		0			0
$103$	14.3782			1.41673			0.708363	−	0.705848i	$-0.249434\pi$
$103$	14.3782			1.41673			0.708363	+	0.705848i	$0.249434\pi$
$104$	2.25933	+	9.94462i	0.221546	+	0.975150i
$105$		0			0
$106$	3.12952	−	4.22656i	0.303966	−	0.410520i
$107$	2.19013	−	3.79342i	0.211728	−	0.366724i	−0.740527	−	0.672026i	$-0.765424\pi$
$107$	2.19013	−	3.79342i	0.211728	−	0.366724i	0.952255	+	0.305302i	$0.0987575\pi$
$108$		0			0
$109$	−8.41638	−	8.41638i	−0.806143	−	0.806143i	0.177905	−	0.984048i	$-0.443068\pi$
$109$	−8.41638	−	8.41638i	−0.806143	−	0.806143i	−0.984048	+	0.177905i	$0.943068\pi$
$110$	−0.0115499	−	0.0265855i	−0.00110124	−	0.00253483i
$111$		0			0
$112$	−6.16440	+	2.11403i	−0.582481	+	0.199757i
$113$	−4.02349	−	6.96890i	−0.378498	−	0.655579i	0.612346	−	0.790590i	$-0.290226\pi$
$113$	−4.02349	−	6.96890i	−0.378498	−	0.655579i	−0.990844	+	0.135012i	$0.956893\pi$
$114$		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
$122$	2.95006	+	0.337043i	0.267086	+	0.0305145i
$123$		0			0
$124$	−0.648693	+	1.21819i	−0.0582544	+	0.109397i
$125$	−0.0433168	+	0.0433168i	−0.00387437	+	0.00387437i
$126$		0			0
$127$	−1.91208	+	3.31182i	−0.169670	+	0.293877i	−0.938304	−	0.345812i	$-0.887603\pi$
$127$	−1.91208	+	3.31182i	−0.169670	+	0.293877i	0.768634	+	0.639689i	$0.220937\pi$
$128$	2.80895	+	10.9595i	0.248278	+	0.968689i
$129$		0			0
$130$	−0.0204250	−	0.0236331i	−0.00179139	−	0.00207276i
$131$	−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
$134$	0.267006	−	0.677219i	0.0230658	−	0.0585028i
$135$		0			0
$136$	2.84621	+	15.4369i	0.244061	+	1.32370i
$137$	4.42582	−	16.5174i	0.378123	−	1.41117i	−0.470605	−	0.882344i	$-0.655964\pi$
$137$	4.42582	−	16.5174i	0.378123	−	1.41117i	0.848728	−	0.528830i	$-0.177369\pi$
$138$		0			0
$139$	8.51425	+	14.7471i	0.722169	+	1.25083i	0.960129	+	0.279559i	$0.0901882\pi$
$139$	8.51425	+	14.7471i	0.722169	+	1.25083i	−0.237959	+	0.971275i	$0.576478\pi$
$140$	0.0136223	−	0.0145900i	0.00115130	−	0.00123308i
$141$		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
$146$	0.401721	+	2.69369i	0.0332467	+	0.222932i
$147$		0			0
$148$	19.7439	−	12.3203i	1.62294	−	1.01273i
$149$	3.12545	−	11.6643i	0.256047	−	0.955580i	−0.711458	−	0.702728i	$-0.751965\pi$
$149$	3.12545	−	11.6643i	0.256047	−	0.955580i	0.967505	−	0.252852i	$-0.0813685\pi$
$150$		0			0
$151$	1.75767	−	1.75767i	0.143037	−	0.143037i	−0.631962	−	0.774999i	$-0.717750\pi$
$151$	1.75767	−	1.75767i	0.143037	−	0.143037i	0.774999	+	0.631962i	$0.217750\pi$
$152$	−5.74405	+	8.34101i	−0.465904	+	0.676545i
$153$		0			0
$154$	6.19543	+	4.58735i	0.499242	+	0.369659i
$155$		−	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	$0.624272\pi$
$158$	10.6630	−	14.4009i	0.848303	−	1.14567i
$159$		0			0
$160$	−0.0233720	−	0.0255856i	−0.00184772	−	0.00202272i
$161$	6.36323	−	6.36323i	0.501493	−	0.501493i
$162$		0			0
$163$	−2.24703	+	8.38602i	−0.176001	+	0.656844i	0.820378	+	0.571821i	$0.193763\pi$
$163$	−2.24703	+	8.38602i	−0.176001	+	0.656844i	−0.996379	+	0.0850226i	$0.972904\pi$
$164$	8.47173	−	5.28642i	0.661531	−	0.412800i
$165$		0			0
$166$	−7.03607	+	1.04932i	−0.546105	+	0.0814428i
$167$	6.23234	+	23.2594i	0.482273	+	1.79987i	0.592037	+	0.805910i	$0.298324\pi$
$167$	6.23234	+	23.2594i	0.482273	+	1.79987i	−0.109764	+	0.993958i	$0.535010\pi$
$168$		0			0
$169$	5.55437	−	11.7537i	0.427259	−	0.904129i
$170$	−0.0299187	−	0.0376369i	−0.00229466	−	0.00288662i
$171$		0			0
$172$	−15.7619	−	14.7165i	−1.20183	−	1.12212i
$173$	−5.71509	−	9.89883i	−0.434510	−	0.752594i	0.562745	−	0.826630i	$-0.309745\pi$
$173$	−5.71509	−	9.89883i	−0.434510	−	0.752594i	−0.997256	+	0.0740365i	$0.976412\pi$
$174$		0			0
$175$	2.10833	−	7.86840i	0.159375	−	0.594795i
$176$	8.79272	−	10.0896i	0.662776	−	0.760529i
$177$		0			0
$178$	19.7352	+	7.78099i	1.47922	+	0.583210i
$179$	−16.6433	−	9.60904i	−1.24398	−	0.718214i	−0.274080	−	0.961707i	$-0.588373\pi$
$179$	−16.6433	−	9.60904i	−1.24398	−	0.718214i	−0.969903	+	0.243493i	$0.921707\pi$
$180$		0			0
$181$	−9.90437			−0.736186			−0.368093	−	0.929789i	$-0.619989\pi$
$181$	−9.90437			−0.736186			−0.368093	+	0.929789i	$0.619989\pi$
$182$	7.84695	+	2.72717i	0.581655	+	0.202151i
$183$		0			0
$184$	−10.1352	−	11.8892i	−0.747177	−	0.876482i
$185$	−0.0356416	+	0.0617331i	−0.00262043	+	0.00453871i
$186$		0			0
$187$	13.1299	−	13.1299i	0.960153	−	0.960153i
$188$	−7.17748	−	3.82205i	−0.523472	−	0.278751i
$189$		0			0
$190$	0.00352115	−	0.0308198i	0.000255451	−	0.00223590i
$191$	7.28556	−	4.20632i	0.527165	−	0.304359i	−0.212696	−	0.977118i	$-0.568225\pi$
$191$	7.28556	−	4.20632i	0.527165	−	0.304359i	0.739861	+	0.672760i	$0.234891\pi$
$192$		0			0
$193$	−3.79409	+	1.01662i	−0.273105	+	0.0731782i	−0.392772	−	0.919636i	$-0.628484\pi$
$193$	−3.79409	+	1.01662i	−0.273105	+	0.0731782i	0.119667	+	0.992814i	$0.461817\pi$
$194$	−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	$-0.775580\pi$
$197$	−15.3987	+	4.12608i	−1.09711	+	0.293971i	−0.335525	+	0.942031i	$0.608914\pi$
$198$		0			0
$199$	6.41779	+	11.1159i	0.454945	+	0.787988i	0.998685	−	0.0512659i	$-0.0163256\pi$
$199$	6.41779	+	11.1159i	0.454945	+	0.787988i	−0.543740	+	0.839254i	$0.682992\pi$
$200$	−13.3265	−	4.73311i	−0.942323	−	0.334681i
$201$		0			0
$202$	20.4798	−	8.89732i	1.44095	−	0.626013i
$203$	2.01909	+	2.01909i	0.141712	+	0.141712i
$204$		0			0
$205$	−0.0152931	+	0.0264885i	−0.00106812	+	0.00185004i
$206$	−16.3417	−	12.1001i	−1.13858	−	0.843054i
$207$		0			0
$208$	5.80111	−	13.2041i	0.402234	−	0.915537i
$209$	11.9801			0.828679
$210$		0			0
$211$	−2.73940	+	4.74478i	−0.188588	+	0.326644i	−0.944780	−	0.327706i	$-0.893724\pi$
$211$	−2.73940	+	4.74478i	−0.188588	+	0.326644i	0.756192	+	0.654350i	$0.227058\pi$
$212$	−7.11380	+	2.17008i	−0.488578	+	0.149042i
$213$		0			0
$214$	−5.68162	+	2.46834i	−0.388387	+	0.168732i
$215$	0.0637997	+	0.0170951i	0.00435111	+	0.00116588i
$216$		0			0
$217$	0.562134	+	0.973645i	0.0381601	+	0.0660953i
$218$	2.48288	+	16.6486i	0.168162	+	1.12759i
$219$		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	$-0.423917\pi$
$223$	13.8516	−	3.71152i	0.927572	−	0.248542i	0.690819	+	0.723028i	$0.257250\pi$
$224$	8.78532	+	2.78498i	0.586994	+	0.186079i
$225$		0			0
$226$	−1.29178	+	11.3066i	−0.0859277	+	0.752104i
$227$	9.25409	+	2.47963i	0.614215	+	0.164579i	0.552497	−	0.833515i	$-0.313675\pi$
$227$	9.25409	+	2.47963i	0.614215	+	0.164579i	0.0617186	+	0.998094i	$0.480342\pi$
$228$		0			0
$229$	17.2631	−	17.2631i	1.14078	−	1.14078i	0.152467	−	0.988309i	$-0.451278\pi$
$229$	17.2631	−	17.2631i	1.14078	−	1.14078i	0.988309	−	0.152467i	$-0.0487217\pi$
$230$	0.0445174	+	0.0175518i	0.00293539	+	0.00115733i
$231$		0			0
$232$	3.77250	−	3.21595i	0.247677	−	0.211138i
$233$		−	11.8549i		−	0.776641i	−0.921524	−	0.388320i	$-0.873055\pi$
$233$		−	11.8549i		−	0.776641i	0.921524	−	0.388320i	$-0.126945\pi$
$234$		0			0
$235$	0.0249071			0.00162476
$236$	−5.96470	+	0.204588i	−0.388269	+	0.0133176i
$237$		0			0
$238$	11.8957	+	4.69011i	0.771085	+	0.304015i
$239$	8.19428	+	8.19428i	0.530044	+	0.530044i	0.920585	−	0.390541i	$-0.127712\pi$
$239$	8.19428	+	8.19428i	0.530044	+	0.530044i	−0.390541	+	0.920585i	$0.627712\pi$
$240$		0			0
$241$	5.54758	−	20.7038i	0.357351	−	1.33365i	−0.520149	−	0.854075i	$-0.674124\pi$
$241$	5.54758	−	20.7038i	0.357351	−	1.33365i	0.877500	−	0.479576i	$-0.159210\pi$
$242$	−0.273207	−	0.0312138i	−0.0175624	−	0.00200650i
$243$		0			0
$244$	−3.06929	−	2.86572i	−0.196491	−	0.183459i
$245$	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
$250$	0.0856860	−	0.0127787i	0.00541926	−	0.000808196i
$251$	−6.73491	+	3.88840i	−0.425104	+	0.245434i	−0.697259	−	0.716820i	$-0.745597\pi$
$251$	−6.73491	+	3.88840i	−0.425104	+	0.245434i	0.272155	+	0.962254i	$0.412264\pi$
$252$		0			0
$253$	−4.78315	+	17.8510i	−0.300714	+	1.12228i
$254$	4.96030	−	2.15497i	0.311237	−	0.135215i
$255$		0			0
$256$	6.03049	−	14.8200i	0.376905	−	0.926252i
$257$	13.3396	+	7.70163i	0.832103	+	0.480415i	0.854572	−	0.519333i	$-0.173820\pi$
$257$	13.3396	+	7.70163i	0.832103	+	0.480415i	−0.0224694	+	0.999748i	$0.507153\pi$
$258$		0			0
$259$		−	18.9579i		−	1.17799i
$260$	0.00332570	+	0.0440494i	0.000206251	+	0.00273183i
$261$		0			0
$262$	11.5129	+	8.52464i	0.711271	+	0.526654i
$263$	17.8675	+	10.3158i	1.10176	+	0.636101i	0.936683	−	0.350180i	$-0.113880\pi$
$263$	17.8675	+	10.3158i	1.10176	+	0.636101i	0.165077	+	0.986281i	$0.447213\pi$
$264$		0			0
$265$	0.0161084	−	0.0161084i	0.000989528	−	0.000989528i
$266$	3.28730	+	7.56668i	0.201557	+	0.463943i
$267$		0			0
$268$	−0.873390	+	0.545002i	−0.0533508	+	0.0332913i
$269$	13.8319	−	7.98587i	0.843348	−	0.486907i	−0.0150527	−	0.999887i	$-0.504792\pi$
$269$	13.8319	−	7.98587i	0.843348	−	0.486907i	0.858401	+	0.512979i	$0.171458\pi$
$270$		0			0
$271$	−6.02478	−	22.4848i	−0.365979	−	1.36585i	−0.866088	−	0.499891i	$-0.833373\pi$
$271$	−6.02478	−	22.4848i	−0.365979	−	1.36585i	0.500109	−	0.865962i	$-0.333293\pi$
$272$	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	$-0.224601\pi$
$277$	−3.01247	−	5.21776i	−0.181002	−	0.313505i	−0.942222	+	0.334989i	$0.891267\pi$
$278$	2.73357	−	23.9263i	0.163949	−	1.43500i
$279$		0			0
$280$	−0.0277610	+	0.00511849i	−0.00165904	+	0.000305888i
$281$	20.3774	+	20.3774i	1.21561	+	1.21561i	0.969153	+	0.246461i	$0.0792679\pi$
$281$	20.3774	+	20.3774i	1.21561	+	1.21561i	0.246461	+	0.969153i	$0.420732\pi$
$282$		0			0
$283$	6.85490	+	3.95768i	0.407482	+	0.235260i	0.689707	−	0.724088i	$-0.257739\pi$
$283$	6.85490	+	3.95768i	0.407482	+	0.235260i	−0.282225	+	0.959348i	$0.591073\pi$
$284$	4.39856	−	0.150870i	0.261007	−	0.00895250i
$285$		0			0
$286$	−16.7562	+	3.20713i	−0.990814	+	0.189642i
$287$		−	8.13447i		−	0.480163i
$288$		0			0
$289$	6.89996	−	11.9511i	0.405880	−	0.703005i
$290$	−0.00556928	+	0.0141256i	−0.000327039	+	0.000829483i
$291$		0			0
$292$	1.81032	−	3.39963i	0.105941	−	0.198948i
$293$	1.74094	+	0.466483i	0.101707	+	0.0272522i	0.309313	−	0.950960i	$-0.399901\pi$
$293$	1.74094	+	0.466483i	0.101707	+	0.0272522i	−0.207607	+	0.978212i	$0.566567\pi$
$294$		0			0
$295$	0.0158313	−	0.00914022i	0.000921735	−	0.000532164i
$296$	−32.8085	−	2.61280i	−1.90696	−	0.151866i
$297$		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
$302$	−3.47689	+	0.518523i	−0.200073	+	0.0298377i
$303$		0			0
$304$	13.5479	−	4.64614i	0.777027	−	0.266474i
$305$	0.0124236	+	0.00332890i	0.000711375	+	0.000190612i
$306$		0			0
$307$	14.6289	+	14.6289i	0.834914	+	0.834914i	0.988184	−	0.153270i	$-0.0489804\pi$
$307$	14.6289	+	14.6289i	0.834914	+	0.834914i	−0.153270	+	0.988184i	$0.548980\pi$
$308$	−3.18098	−	10.4276i	−0.181253	−	0.594169i
$309$		0			0
$310$	−0.00355755	+	0.00480464i	−0.000202055	+	0.000272885i
$311$	−25.6430			−1.45408			−0.727040	−	0.686595i	$-0.759105\pi$
$311$	−25.6430			−1.45408			−0.727040	+	0.686595i	$0.759105\pi$
$312$		0			0
$313$	−19.4022			−1.09668			−0.548340	−	0.836256i	$-0.684740\pi$
$313$	−19.4022			−1.09668			−0.548340	+	0.836256i	$0.684740\pi$
$314$	19.5025	−	26.3390i	1.10059	−	1.48640i
$315$		0			0
$316$	−24.2384	+	7.39399i	−1.36352	+	0.415944i
$317$	11.2646	+	11.2646i	0.632682	+	0.632682i	0.948740	−	0.316058i	$-0.102359\pi$
$317$	11.2646	+	11.2646i	0.632682	+	0.632682i	−0.316058	+	0.948740i	$0.602359\pi$
$318$		0			0
$319$	−5.66420	−	1.51772i	−0.317134	−	0.0849759i
$320$	0.00503200	+	0.0487485i	0.000281297	+	0.00272513i
$321$		0			0
$322$	−12.5873	+	1.87719i	−0.701460	+	0.104612i
$323$	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
$328$	−14.0775	−	1.12110i	−0.777300	−	0.0619024i
$329$	−5.73663	+	3.31205i	−0.316271	+	0.182599i
$330$		0			0
$331$	−3.11057	−	0.833475i	−0.170972	−	0.0458119i	0.172317	−	0.985042i	$-0.444875\pi$
$331$	−3.11057	−	0.833475i	−0.170972	−	0.0458119i	−0.343290	+	0.939230i	$0.611541\pi$
$332$	8.88001	+	4.72865i	0.487354	+	0.259518i
$333$		0			0
$334$	12.4907	−	31.6807i	0.683461	−	1.73349i
$335$	0.00157664	−	0.00273082i	8.61411e−5	−	0.000149201i
$336$		0			0
$337$			14.3103i			0.779534i	0.920914	+	0.389767i	$0.127444\pi$
$337$			14.3103i			0.779534i	−0.920914	+	0.389767i	$0.872556\pi$
$338$	−16.2043	+	8.68449i	−0.881398	+	0.472374i
$339$		0			0
$340$	0.00233085	+	0.0679552i	0.000126408	+	0.00368539i
$341$	−1.99952	−	1.15442i	−0.108280	−	0.0625155i
$342$		0			0
$343$	−13.0705	−	13.0705i	−0.705740	−	0.705740i
$344$	5.52961	+	29.9908i	0.298137	+	1.61699i
$345$		0			0
$346$	−1.83488	+	16.0602i	−0.0986437	+	0.863404i
$347$	−0.895267	−	1.55065i	−0.0480604	−	0.0832431i	0.840994	−	0.541044i	$-0.181971\pi$
$347$	−0.895267	−	1.55065i	−0.0480604	−	0.0832431i	−0.889055	+	0.457801i	$0.848637\pi$
$348$		0			0
$349$	2.69383	+	10.0535i	0.144197	+	0.538151i	0.999790	+	0.0205016i	$0.00652631\pi$
$349$	2.69383	+	10.0535i	0.144197	+	0.538151i	−0.855593	+	0.517650i	$0.826807\pi$
$350$	−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	0.999697	−	0.0246115i	$-0.00783486\pi$
$353$	2.28519	+	8.52844i	0.121628	+	0.453923i	−0.878069	+	0.478534i	$0.841168\pi$
$354$		0			0
$355$	−0.0116745	+	0.00674030i	−0.000619620	+	0.000357738i
$356$	−15.8822	−	25.4520i	−0.841756	−	1.34895i
$357$		0			0
$358$	10.8297	+	24.9277i	0.572365	+	1.31747i
$359$	6.93284	−	6.93284i	0.365901	−	0.365901i	−0.500079	−	0.865980i	$-0.666696\pi$
$359$	6.93284	−	6.93284i	0.365901	−	0.365901i	0.865980	+	0.500079i	$0.166696\pi$
$360$		0			0
$361$	−5.35132	−	3.08959i	−0.281648	−	0.162610i
$362$	11.2570	+	8.33511i	0.591652	+	0.438084i
$363$		0			0
$364$	−6.62349	−	9.70327i	−0.347165	−	0.508590i
$365$			0.0117973i			0.000617499i
$366$		0			0
$367$	−12.8657	−	7.42801i	−0.671583	−	0.387739i	0.125093	−	0.992145i	$-0.460077\pi$
$367$	−12.8657	−	7.42801i	−0.671583	−	0.387739i	−0.796676	+	0.604406i	$0.793410\pi$
$368$	1.51387	+	22.0422i	0.0789159	+	1.14903i
$369$		0			0
$370$	0.0924611	−	0.0401691i	0.00480682	−	0.00208829i
$371$	−1.56807	+	5.85211i	−0.0814101	+	0.303827i
$372$		0			0
$373$	18.4652	−	10.6609i	0.956090	−	0.551999i	0.0611226	−	0.998130i	$-0.480532\pi$
$373$	18.4652	−	10.6609i	0.956090	−	0.551999i	0.894967	+	0.446131i	$0.147199\pi$
$374$	−25.9725	+	3.87339i	−1.34301	+	0.200288i
$375$		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	−0.875589	−	0.483058i	$-0.839526\pi$
$379$	−6.98578	−	26.0713i	−0.358835	−	1.33919i	0.516753	−	0.856134i	$-0.327141\pi$
$380$	−0.0299387	+	0.0320654i	−0.00153582	+	0.00164492i
$381$		0			0
$382$	−11.8204	−	1.35047i	−0.604783	−	0.0690963i
$383$	5.60173	−	20.9059i	0.286235	−	1.06824i	−0.661697	−	0.749771i	$-0.730163\pi$
$383$	5.60173	−	20.9059i	0.286235	−	1.06824i	0.947932	−	0.318473i	$-0.103170\pi$
$384$		0			0
$385$	0.0236121	+	0.0236121i	0.00120339	+	0.00120339i
$386$	5.16778	+	2.03749i	0.263033	+	0.103706i
$387$		0			0
$388$	0.334306	+	9.74656i	0.0169718	+	0.494807i
$389$	−25.5925			−1.29759			−0.648797	−	0.760962i	$-0.724727\pi$
$389$	−25.5925			−1.29759			−0.648797	+	0.760962i	$0.724727\pi$
$390$		0			0
$391$			30.6543i			1.55025i
$392$	−9.35392	+	7.97397i	−0.472445	+	0.402746i
$393$		0			0
$394$	20.9740	+	8.26939i	1.05665	+	0.416606i
$395$	0.0548849	−	0.0548849i	0.00276156	−	0.00276156i
$396$		0			0
$397$	−7.13276	−	1.91122i	−0.357983	−	0.0959212i	0.0753451	−	0.997158i	$-0.475994\pi$
$397$	−7.13276	−	1.91122i	−0.357983	−	0.0959212i	−0.433328	+	0.901236i	$0.642661\pi$
$398$	2.06048	−	18.0349i	0.103283	−	0.904009i
$399$		0			0
$400$	11.1632	+	16.5945i	0.558160	+	0.829724i
$401$	0.0510228	−	0.0136715i	0.00254796	−	0.000682723i	−0.257545	−	0.966266i	$-0.582914\pi$
$401$	0.0510228	−	0.0136715i	0.00254796	−	0.000682723i	0.260093	+	0.965584i	$0.416247\pi$
$402$		0			0
$403$	−2.42772	−	0.544746i	−0.120933	−	0.0271357i
$404$	−30.7642	−	7.12258i	−1.53058	−	0.354362i
$405$		0			0
$406$	−0.595641	−	3.99400i	−0.0295612	−	0.198219i
$407$	19.4664	+	33.7168i	0.964914	+	1.67128i
$408$		0			0
$409$	9.42392	+	2.52513i	0.465983	+	0.124860i	0.484168	−	0.874975i	$-0.339122\pi$
$409$	9.42392	+	2.52513i	0.465983	+	0.124860i	−0.0181853	+	0.999835i	$0.505789\pi$
$410$	0.0396733	−	0.0172358i	0.00195932	−	0.000851215i
$411$		0			0
$412$	8.39050	+	27.5051i	0.413370	+	1.35508i
$413$	−2.43086	+	4.21037i	−0.119615	+	0.207179i
$414$		0			0
$415$	−0.0308152			−0.00151266
$416$	−17.7053	+	10.1253i	−0.868075	+	0.496433i
$417$		0			0
$418$	−13.6161	−	10.0819i	−0.665986	−	0.493123i
$419$	−4.74183	+	8.21309i	−0.231654	+	0.401236i	−0.958295	−	0.285781i	$-0.907747\pi$
$419$	−4.74183	+	8.21309i	−0.231654	+	0.401236i	0.726641	+	0.687017i	$0.241080\pi$
$420$		0			0
$421$	−15.6320	−	15.6320i	−0.761859	−	0.761859i	0.214799	−	0.976658i	$-0.431090\pi$
$421$	−15.6320	−	15.6320i	−0.761859	−	0.761859i	−0.976658	+	0.214799i	$0.931090\pi$
$422$	7.10651	−	3.08738i	0.345940	−	0.150291i
$423$		0			0
$424$	9.91154	+	3.52024i	0.481347	+	0.170958i
$425$	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	$-0.976573\pi$
$431$	−37.8715	+	10.1476i	−1.82421	+	0.488795i	−0.826915	+	0.562327i	$0.809906\pi$
$432$		0			0
$433$	−5.12070	+	2.95644i	−0.246085	+	0.142077i	−0.617970	−	0.786201i	$-0.712045\pi$
$433$	−5.12070	+	2.95644i	−0.246085	+	0.142077i	0.371885	+	0.928279i	$0.378712\pi$
$434$	0.180478	−	1.57968i	0.00866321	−	0.0758270i
$435$		0			0
$436$	11.1889	−	21.0117i	0.535849	−	1.00628i
$437$	−13.9849	+	13.9849i	−0.668989	+	0.668989i
$438$		0			0
$439$	−3.69569	+	6.40112i	−0.176385	+	0.305509i	−0.940640	−	0.339406i	$-0.889774\pi$
$439$	−3.69569	+	6.40112i	−0.176385	+	0.305509i	0.764254	+	0.644915i	$0.223107\pi$
$440$	0.0441174	−	0.0376089i	0.00210321	−	0.00179293i
$441$		0			0
$442$	−25.4700	+	12.3321i	−1.21148	+	0.586576i
$443$	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
$446$	−18.8667	−	7.43855i	−0.893364	−	0.352226i
$447$		0			0
$448$	−7.64135	−	10.5587i	−0.361020	−	0.498850i
$449$	−4.34105	+	16.2010i	−0.204867	+	0.764573i	0.784623	+	0.619973i	$0.212856\pi$
$449$	−4.34105	+	16.2010i	−0.204867	+	0.764573i	−0.989490	+	0.144600i	$0.953810\pi$
$450$		0			0
$451$	8.35266	+	14.4672i	0.393311	+	0.681235i
$452$	10.9834	−	11.7636i	0.516614	−	0.553312i
$453$		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	0.890327	+	0.455322i	$0.150476\pi$
$457$	7.41678	+	27.6798i	0.346942	+	1.29481i	−0.543385	+	0.839484i	$0.682858\pi$
$458$	−34.1485	+	5.09270i	−1.59565	+	0.237966i
$459$		0			0
$460$	−0.0358260	−	0.0574128i	−0.00167040	−	0.00267688i
$461$	9.47325	−	35.3546i	0.441213	−	1.64663i	−0.284532	−	0.958666i	$-0.591838\pi$
$461$	9.47325	−	35.3546i	0.441213	−	1.64663i	0.725745	−	0.687963i	$-0.241495\pi$
$462$		0			0
$463$	9.62736	−	9.62736i	0.447422	−	0.447422i	−0.447075	−	0.894497i	$-0.647534\pi$
$463$	9.62736	−	9.62736i	0.447422	−	0.447422i	0.894497	+	0.447075i	$0.147534\pi$
$464$	−6.99410	+	0.480359i	−0.324693	+	0.0223001i
$465$		0			0
$466$	−9.97660	+	13.4739i	−0.462157	+	0.624165i
$467$			26.0667i			1.20622i	0.797658	+	0.603110i	$0.206072\pi$
$467$			26.0667i			1.20622i	−0.797658	+	0.603110i	$0.793928\pi$
$468$		0			0
$469$			0.838620i			0.0387239i
$470$	−0.0283086	−	0.0209608i	−0.00130578	−	0.000966850i
$471$		0			0
$472$	6.95143	+	4.78711i	0.319966	+	0.220345i
$473$	25.5087	−	25.5087i	1.17289	−	1.17289i
$474$		0			0
$475$	−4.63363	+	17.2929i	−0.212605	+	0.793454i
$476$	−9.57324	−	15.3416i	−0.438789	−	0.703179i
$477$		0			0
$478$	−2.41736	−	16.2093i	−0.110567	−	0.741396i
$479$	−8.72017	−	32.5441i	−0.398435	−	1.48698i	−0.815850	−	0.578263i	$-0.803731\pi$
$479$	−8.72017	−	32.5441i	−0.398435	−	1.48698i	0.417415	−	0.908716i	$-0.362936\pi$
$480$		0			0
$481$	30.8599	+	28.4238i	1.40709	+	1.29601i
$482$	−23.7287	+	18.8626i	−1.08081	+	0.859170i
$483$		0			0
$484$	0.284249	+	0.265396i	0.0129204	+	0.0120635i
$485$	−0.0149355	−	0.0258691i	−0.000678186	−	0.00117465i
$486$		0			0
$487$	−6.44555	+	24.0551i	−0.292076	+	1.09004i	0.651436	+	0.758703i	$0.274167\pi$
$487$	−6.44555	+	24.0551i	−0.292076	+	1.09004i	−0.943512	+	0.331338i	$0.892500\pi$
$488$	1.07677	+	5.84006i	0.0487432	+	0.264367i
$489$		0			0
$490$	0.0138091	−	0.0350245i	0.000623829	−	0.00158224i
$491$	−31.9925	−	18.4709i	−1.44380	−	0.833578i	−0.445699	−	0.895183i	$-0.647045\pi$
$491$	−31.9925	−	18.4709i	−1.44380	−	0.833578i	−0.998101	+	0.0616050i	$0.980378\pi$
$492$		0			0
$493$	−9.72677			−0.438072
$494$	−17.2458	−	5.99369i	−0.775925	−	0.269669i
$495$		0			0
$496$	−2.70892	−	0.530047i	−0.121634	−	0.0237998i
$497$	1.79259	−	3.10486i	0.0804088	−	0.139272i
$498$		0			0
$499$	−15.6264	+	15.6264i	−0.699534	+	0.699534i	−0.964310	−	0.264776i	$-0.914702\pi$
$499$	−15.6264	+	15.6264i	−0.699534	+	0.699534i	0.264776	+	0.964310i	$0.414702\pi$
$500$	−0.108142	−	0.0575860i	−0.00483624	−	0.00257532i
$501$		0			0
$502$	10.9270	+	1.24840i	0.487695	+	0.0557190i
$503$	29.7238	−	17.1610i	1.32532	−	0.765173i	0.340747	−	0.940155i	$-0.389320\pi$
$503$	29.7238	−	17.1610i	1.32532	−	0.765173i	0.984572	+	0.174982i	$0.0559866\pi$
$504$		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	$-0.659783\pi$
$509$	−10.3675	+	2.77797i	−0.459533	+	0.123131i	0.0216237	+	0.999766i	$0.493116\pi$
$510$		0			0
$511$	−1.56876	−	2.71717i	−0.0693977	−	0.120200i
$512$	−19.3260	+	11.7689i	−0.854095	+	0.520117i
$513$		0			0
$514$	−8.67996	−	19.9795i	−0.382857	−	0.881257i
$515$	−0.0622820	−	0.0622820i	−0.00274447	−	0.00274447i
$516$		0			0
$517$	6.80177	−	11.7810i	0.299141	−	0.518128i
$518$	−15.9542	+	21.5469i	−0.700987	+	0.946716i
$519$		0			0
$520$	0.0332903	−	0.0528638i	0.00145988	−	0.00231823i
$521$	−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	−0.733617	−	0.679563i	$-0.762170\pi$
$523$	5.07033	−	8.78207i	0.221710	−	0.384013i	0.955327	+	0.295550i	$0.0955028\pi$
$524$	−5.91119	−	19.3776i	−0.258231	−	0.846514i
$525$		0			0
$526$	−11.6262	−	26.7612i	−0.506928	−	1.16684i
$527$	−3.69924	−	0.991208i	−0.161141	−	0.0431777i
$528$		0			0
$529$	−3.75469	−	6.50332i	−0.163247	−	0.282753i
$530$	−0.0318643	+	0.00475205i	−0.00138410	+	0.000206416i
$531$		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
$536$	1.45132	+	0.115579i	0.0626873	+	0.00499227i
$537$		0			0
$538$	−22.4415	−	2.56393i	−0.967521	−	0.110539i
$539$	14.0444	+	3.76319i	0.604936	+	0.162092i
$540$		0			0
$541$	16.6100	−	16.6100i	0.714119	−	0.714119i	−0.253276	−	0.967394i	$-0.581508\pi$
$541$	16.6100	−	16.6100i	0.714119	−	0.714119i	0.967394	+	0.253276i	$0.0815079\pi$
$542$	−12.0747	+	30.6256i	−0.518654	+	1.31548i
$543$		0			0
$544$	−27.8695	+	14.4531i	−1.19489	+	0.619669i
$545$			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	$0.264776\pi$
$548$	34.1800	−	1.17237i	1.46010	−	0.0500811i
$549$		0			0
$550$	8.67761	−	22.0094i	0.370015	−	0.938483i
$551$	−4.43748	−	4.43748i	−0.189043	−	0.189043i
$552$		0			0
$553$	−5.34278	+	19.9395i	−0.227198	+	0.847915i
$554$	−0.967180	+	8.46549i	−0.0410915	+	0.359664i
$555$		0			0
$556$	−23.2423	+	24.8933i	−0.985692	+	1.05571i
$557$	−3.98647	−	14.8777i	−0.168912	−	0.630389i	−0.997509	−	0.0705430i	$-0.977527\pi$
$557$	−3.98647	−	14.8777i	−0.168912	−	0.630389i	0.828596	−	0.559846i	$-0.189140\pi$
$558$		0			0
$559$	18.0389	−	34.4367i	0.762966	−	1.45652i
$560$	0.0358596	+	0.0175450i	0.00151535	+	0.000741412i
$561$		0			0
$562$	−6.01145	−	40.3090i	−0.253578	−	1.70033i
$563$	36.0452	−	20.8107i	1.51912	−	0.877067i	0.519379	−	0.854544i	$-0.326163\pi$
$563$	36.0452	−	20.8107i	1.51912	−	0.877067i	0.999746	−	0.0225229i	$-0.00716986\pi$
$564$		0			0
$565$	−0.0127586	+	0.0476157i	−0.000536758	+	0.00200321i
$566$	−4.46042	−	10.2670i	−0.187485	−	0.431553i
$567$		0			0
$568$	−5.12621	−	3.53017i	−0.215091	−	0.148123i
$569$	1.73040	+	0.999049i	0.0725423	+	0.0418823i	0.535832	−	0.844324i	$-0.319998\pi$
$569$	1.73040	+	0.999049i	0.0725423	+	0.0418823i	−0.463290	+	0.886207i	$0.653331\pi$
$570$		0			0
$571$			42.3453i			1.77210i	0.463592	+	0.886049i	$0.346560\pi$
$571$			42.3453i			1.77210i	−0.463592	+	0.886049i	$0.653440\pi$
$572$	21.7435	+	10.4562i	0.909140	+	0.437196i
$573$		0			0
$574$	−6.84564	+	9.24535i	−0.285731	+	0.385893i
$575$	−23.9174	−	13.8087i	−0.997425	−	0.575863i
$576$		0			0
$577$	−17.1186	+	17.1186i	−0.712659	+	0.712659i	−0.967091	−	0.254432i	$-0.918111\pi$
$577$	−17.1186	+	17.1186i	−0.712659	+	0.712659i	0.254432	+	0.967091i	$0.418111\pi$
$578$	−17.8998	+	7.77645i	−0.744533	+	0.323458i
$579$		0			0
$580$	0.0182174	−	0.0113678i	0.000756435	−	0.000472021i
$581$	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	0.912481	−	0.409118i	$-0.134164\pi$
$587$	−1.99421	−	7.44249i	−0.0823098	−	0.307185i	−0.994791	+	0.101934i	$0.967497\pi$
$588$		0			0
$589$	−1.23544	−	2.13985i	−0.0509054	−	0.0881708i
$590$	−0.0256854	−	0.00293454i	−0.00105745	−	0.000120813i
$591$		0			0
$592$	35.0902	+	30.5799i	1.44220	+	1.25683i
$593$	−11.8828	−	11.8828i	−0.487967	−	0.487967i	0.419697	−	0.907664i	$-0.362136\pi$
$593$	−11.8828	−	11.8828i	−0.487967	−	0.487967i	−0.907664	+	0.419697i	$0.862136\pi$
$594$		0			0
$595$	0.0479683	+	0.0276945i	0.00196651	+	0.00113536i
$596$	24.1374	−	0.827911i	0.988708	−	0.0339126i
$597$		0			0
$598$	15.8165	−	23.3041i	0.646783	−	0.952978i
$599$			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	−0.493605	−	0.869686i	$-0.664321\pi$
$601$	12.4138	−	21.5013i	0.506368	−	0.877056i	0.999973	−	0.00736919i	$-0.00234571\pi$
$602$	23.1109	+	9.11192i	0.941932	+	0.371374i
$603$		0			0
$604$	4.38808	+	2.33668i	0.178549	+	0.0950780i
$605$	−0.00115056		0.000308292i	−4.67769e−5		1.25338e-5i
$606$		0			0
$607$	−40.6484	+	23.4684i	−1.64987	+	0.952551i	−0.672744	+	0.739876i	$0.734884\pi$
$607$	−40.6484	+	23.4684i	−1.64987	+	0.952551i	−0.977123	+	0.212675i	$0.931782\pi$
$608$	−19.3081	−	6.12075i	−0.783047	−	0.248229i
$609$		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	$-0.631022\pi$
$613$	−7.13914	+	1.91293i	−0.288347	+	0.0772624i	0.111746	+	0.993737i	$0.464356\pi$
$614$	−4.31560	−	28.9377i	−0.174163	−	1.16783i
$615$		0			0
$616$	−5.16008	+	14.5287i	−0.207906	+	0.585376i
$617$	3.43254	+	0.919746i	0.138189	+	0.0370276i	0.327250	−	0.944938i	$-0.393878\pi$
$617$	3.43254	+	0.919746i	0.138189	+	0.0370276i	−0.189062	+	0.981965i	$0.560545\pi$
$618$		0			0
$619$	−16.7707	−	16.7707i	−0.674072	−	0.674072i	0.284580	−	0.958652i	$-0.408146\pi$
$619$	−16.7707	−	16.7707i	−0.674072	−	0.674072i	−0.958652	+	0.284580i	$0.908146\pi$
$620$	0.00808678	−	0.00246689i	0.000324773	−	9.90728e-5i
$621$		0			0
$622$	29.1449	+	21.5801i	1.16860	+	0.865283i
$623$	−24.4387			−0.979117
$624$		0			0
$625$	−24.9994			−0.999977
$626$	22.0519	+	16.3281i	0.881371	+	0.652603i
$627$		0			0
$628$	−44.3316	+	13.5235i	−1.76902	+	0.539646i
$629$	45.6641	+	45.6641i	1.82074	+	1.82074i
$630$		0			0
$631$	13.1022	+	3.51071i	0.521589	+	0.139759i	0.510001	−	0.860174i	$-0.329645\pi$
$631$	13.1022	+	3.51071i	0.521589	+	0.139759i	0.0115873	+	0.999933i	$0.496312\pi$
$632$	33.7710	+	11.9943i	1.34334	+	0.477107i
$633$		0			0
$634$	−3.32312	−	22.2828i	−0.131978	−	0.884961i
$635$	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
$640$	0.0353056	−	0.0596406i	0.00139558	−	0.00235750i
$641$	−19.1888	+	11.0787i	−0.757912	+	0.437581i	−0.828546	−	0.559921i	$-0.810831\pi$
$641$	−19.1888	+	11.0787i	−0.757912	+	0.437581i	0.0706333	+	0.997502i	$0.477498\pi$
$642$		0			0
$643$	−23.0119	−	6.16601i	−0.907499	−	0.243164i	−0.225265	−	0.974298i	$-0.572325\pi$
$643$	−23.0119	−	6.16601i	−0.907499	−	0.243164i	−0.682234	+	0.731134i	$0.738991\pi$
$644$	15.8860	+	8.45937i	0.625996	+	0.333346i
$645$		0			0
$646$	−26.1440	−	10.3078i	−1.02862	−	0.405554i
$647$	16.5037	−	28.5853i	0.648829	−	1.12380i	−0.334574	−	0.942370i	$-0.608592\pi$
$647$	16.5037	−	28.5853i	0.648829	−	1.12380i	0.983403	−	0.181435i	$-0.0580743\pi$
$648$		0			0
$649$		−	9.98424i		−	0.391916i
$650$	1.85151	−	25.4276i	0.0726221	−	0.997352i
$651$		0			0
$652$	−17.3535	+	0.595223i	−0.679615	+	0.0233107i
$653$	−6.90829	−	3.98850i	−0.270342	−	0.156082i	0.358701	−	0.933453i	$-0.383220\pi$
$653$	−6.90829	−	3.98850i	−0.270342	−	0.156082i	−0.629043	+	0.777370i	$0.716553\pi$
$654$		0			0
$655$	0.0438783	+	0.0438783i	0.00171447	+	0.00171447i
$656$	15.0565	+	13.1213i	0.587858	+	0.512299i
$657$		0			0
$658$	9.30734	+	1.06336i	0.362838	+	0.0414541i
$659$	−4.00689	−	6.94014i	−0.156086	−	0.270350i	0.777368	−	0.629046i	$-0.216554\pi$
$659$	−4.00689	−	6.94014i	−0.156086	−	0.270350i	−0.933454	+	0.358697i	$0.883221\pi$
$660$		0			0
$661$	−4.42854	−	16.5276i	−0.172250	−	0.642847i	−0.997004	−	0.0773545i	$-0.975353\pi$
$661$	−4.42854	−	16.5276i	−0.172250	−	0.642847i	0.824753	−	0.565493i	$-0.191314\pi$
$662$	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
$668$	−40.8577	+	25.4955i	−1.58083	+	0.986451i
$669$		0			0
$670$	−0.00409010	+	0.00177692i	−0.000158014	+	6.86483e-5i
$671$	4.96727	−	4.96727i	0.191759	−	0.191759i
$672$		0			0
$673$	−40.8080	−	23.5605i	−1.57303	−	0.908190i	−0.995795	−	0.0916142i	$-0.970797\pi$
$673$	−40.8080	−	23.5605i	−1.57303	−	0.908190i	−0.577237	−	0.816576i	$-0.695869\pi$
$674$	12.0430	−	16.2646i	0.463879	−	0.626490i
$675$		0			0
$676$	25.7257	+	3.76641i	0.989452	+	0.144862i
$677$			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
$680$	0.0545391	−	0.0791970i	0.00209148	−	0.00303707i
$681$		0			0
$682$	1.30107	+	2.99479i	0.0498205	+	0.114676i
$683$	6.46547	−	24.1295i	0.247394	−	0.923288i	−0.724771	−	0.688990i	$-0.758054\pi$
$683$	6.46547	−	24.1295i	0.247394	−	0.923288i	0.972165	−	0.234298i	$-0.0752791\pi$
$684$		0			0
$685$	−0.0907195	+	0.0523769i	−0.00346621	+	0.00200122i
$686$	3.85587	+	25.8550i	0.147218	+	0.987150i
$687$		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	−0.837549	−	0.546362i	$-0.816012\pi$
$691$	−10.1307	−	37.8084i	−0.385391	−	1.43830i	0.452158	−	0.891938i	$-0.350654\pi$
$692$	15.6011	−	16.7093i	0.593065	−	0.635194i
$693$		0			0
$694$	−0.287433	+	2.51583i	−0.0109108	+	0.0954996i
$695$	0.0269989	−	0.100761i	0.00102413	−	0.00382209i
$696$		0			0
$697$	19.5936	+	19.5936i	0.742159	+	0.742159i
$698$	5.39890	−	13.6935i	0.204351	−	0.518305i
$699$		0			0
$700$	16.2824	−	0.558483i	0.615415	−	0.0211087i
$701$	43.6308			1.64791			0.823956	−	0.566654i	$-0.191762\pi$
$701$	43.6308			1.64791			0.823956	+	0.566654i	$0.191762\pi$
$702$		0			0
$703$			41.6651i			1.57143i
$704$	24.4321	+	10.9324i	0.920819	+	0.412030i
$705$		0			0
$706$	4.57992	−	11.6162i	0.172368	−	0.437183i
$707$	−18.1893	+	18.1893i	−0.684078	+	0.684078i
$708$		0			0
$709$	47.8263	+	12.8150i	1.79615	+	0.481278i	0.993367	−	0.114987i	$-0.0366827\pi$
$709$	47.8263	+	12.8150i	1.79615	+	0.481278i	0.802787	+	0.596265i	$0.203349\pi$
$710$	0.0189412	+	0.00216403i	0.000710851	+	8.12146e-5i
$711$		0			0
$712$	−3.36817	+	42.2936i	−0.126227	+	1.58502i
$713$	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
$718$	−13.7140	+	2.04523i	−0.511802	+	0.0763271i
$719$	−10.6542	−	18.4536i	−0.397334	−	0.688202i	0.596062	−	0.802938i	$-0.296731\pi$
$719$	−10.6542	−	18.4536i	−0.397334	−	0.688202i	−0.993396	+	0.114736i	$0.963398\pi$
$720$		0			0
$721$	22.6268	+	6.06285i	0.842668	+	0.225792i
$722$	3.48205	+	8.01497i	0.129589	+	0.298286i
$723$		0			0
$724$	−5.77976	−	18.9468i	−0.214803	−	0.704151i
$725$	4.38158	−	7.58911i	0.162728	−	0.281853i
$726$		0			0
$727$	−38.5908			−1.43125			−0.715626	−	0.698484i	$-0.753859\pi$
$727$	−38.5908			−1.43125			−0.715626	+	0.698484i	$0.753859\pi$
$728$	−0.637851	+	16.6025i	−0.0236403	+	0.615328i
$729$		0			0
$730$	0.00992813	−	0.0134084i	0.000367457	−	0.000496267i
$731$	29.9190	−	51.8212i	1.10659	−	1.91668i
$732$		0			0
$733$	−2.88135	−	2.88135i	−0.106425	−	0.106425i	0.651889	−	0.758314i	$-0.273977\pi$
$733$	−2.88135	−	2.88135i	−0.106425	−	0.106425i	−0.758314	+	0.651889i	$0.773977\pi$
$734$	8.37157	+	19.2696i	0.309000	+	0.711255i
$735$		0			0
$736$	16.8292	−	26.3264i	0.620332	−	0.970403i
$737$	−0.861114	−	1.49149i	−0.0317196	−	0.0549399i
$738$		0			0
$739$	−25.1494	+	6.73876i	−0.925136	+	0.247889i	−0.689779	−	0.724020i	$-0.742292\pi$
$739$	−25.1494	+	6.73876i	−0.925136	+	0.247889i	−0.235357	+	0.971909i	$0.575626\pi$
$740$	−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	$-0.713967\pi$
$743$	−21.0093	+	5.62943i	−0.770756	+	0.206524i	−0.148051	+	0.988980i	$0.547300\pi$
$744$		0			0
$745$	−0.0640649	+	0.0369879i	−0.00234716	+	0.00135513i
$746$	−29.9586	−	3.42276i	−1.09686	−	0.125316i
$747$		0			0
$748$	32.7791	+	17.4551i	1.19852	+	0.638220i
$749$	5.04617	−	5.04617i	0.184383	−	0.184383i
$750$		0			0
$751$	2.57328	−	4.45706i	0.0939004	−	0.162640i	−0.815249	−	0.579111i	$-0.803400\pi$
$751$	2.57328	−	4.45706i	0.0939004	−	0.162640i	0.909149	+	0.416471i	$0.136733\pi$
$752$	3.12300	−	15.9607i	0.113884	−	0.582027i
$753$		0			0
$754$	7.39453	+	5.01865i	0.269293	+	0.182768i
$755$	−0.0152274			−0.000554182
$756$		0			0
$757$	44.0303	+	25.4209i	1.60031	+	0.923939i	0.991425	+	0.130680i	$0.0417162\pi$
$757$	44.0303	+	25.4209i	1.60031	+	0.923939i	0.608885	+	0.793259i	$0.291617\pi$
$758$	−14.0007	+	35.5106i	−0.508530	+	1.28980i
$759$		0			0
$760$	0.0610122	−	0.0112493i	0.00221315	−	0.000408053i
$761$	−9.04510	+	33.7568i	−0.327885	+	1.22368i	0.583496	+	0.812116i	$0.301685\pi$
$761$	−9.04510	+	33.7568i	−0.327885	+	1.22368i	−0.911380	+	0.411565i	$0.864982\pi$
$762$		0			0
$763$	−9.69586	−	16.7937i	−0.351014	−	0.607973i
$764$	12.2981	+	11.4824i	0.444930	+	0.415420i
$765$		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	0.785779	+	0.618507i	$0.212262\pi$
$769$	11.4952	+	42.9007i	0.414528	+	1.54704i	−0.371251	+	0.928533i	$0.621071\pi$
$770$	−0.00696571	−	0.0467077i	−0.000251027	−	0.00168323i
$771$		0			0
$772$	−4.15884	−	6.66474i	−0.149680	−	0.239869i
$773$	−12.8446	+	47.9367i	−0.461988	+	1.72416i	0.204699	+	0.978825i	$0.434379\pi$
$773$	−12.8446	+	47.9367i	−0.461988	+	1.72416i	−0.666687	+	0.745338i	$0.732288\pi$
$774$		0			0
$775$	2.43975	−	2.43975i	0.0876385	−	0.0876385i
$776$	7.82235	−	11.3589i	0.280806	−	0.407762i
$777$		0			0
$778$	29.0876	+	21.5376i	1.04284	+	0.772161i
$779$			17.8777i			0.640535i
$780$		0			0
$781$			7.36270i			0.263458i
$782$	25.7974	−	34.8406i	0.922513	−	1.24590i
$783$		0			0
$784$	17.3419	−	1.19105i	0.619354	−	0.0425376i
$785$	0.100384	−	0.100384i	0.00358285	−	0.00358285i
$786$		0			0
$787$	1.12108	−	4.18392i	0.0399621	−	0.149141i	−0.943062	−	0.332617i	$-0.892068\pi$
$787$	1.12108	−	4.18392i	0.0399621	−	0.149141i	0.983024	+	0.183476i	$0.0587351\pi$
$788$	−16.8791	−	27.0495i	−0.601293	−	0.963600i
$789$		0			0
$790$	−0.108569	+	0.0161914i	−0.00386272	+	0.000576063i
$791$	−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
$796$	−17.5193	+	18.7638i	−0.620956	+	0.665066i
$797$	−9.64544	−	16.7064i	−0.341659	−	0.591771i	0.643082	−	0.765797i	$-0.277655\pi$
$797$	−9.64544	−	16.7064i	−0.341659	−	0.591771i	−0.984741	+	0.174027i	$0.944322\pi$
$798$		0			0
$799$	5.84012	−	21.7956i	0.206609	−	0.771074i
$800$	1.27754	−	28.2552i	0.0451679	−	0.998972i
$801$		0			0
$802$	−0.0694961	−	0.0274001i	−0.00245399	−	0.000967532i
$803$	5.58010	+	3.22167i	0.196917	+	0.113690i
$804$		0			0
$805$	−0.0551272			−0.00194298
$806$	2.30083	+	2.66221i	0.0810431	+	0.0937723i
$807$		0			0
$808$	28.9715	+	33.9852i	1.01921	+	1.19559i
$809$	−14.4841	+	25.0872i	−0.509233	+	0.882018i	0.490709	+	0.871323i	$0.336738\pi$
$809$	−14.4841	+	25.0872i	−0.509233	+	0.882018i	−0.999943	+	0.0106948i	$0.996596\pi$
$810$		0			0
$811$	35.5730	−	35.5730i	1.24914	−	1.24914i	0.293033	−	0.956102i	$-0.405335\pi$
$811$	35.5730	−	35.5730i	1.24914	−	1.24914i	0.956102	−	0.293033i	$-0.0946647\pi$
$812$	−2.68420	+	5.04070i	−0.0941970	+	0.176894i
$813$		0			0
$814$	6.24985	−	54.7035i	0.219057	−	1.91736i
$815$	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	$-0.657834\pi$
$821$	−12.8376	+	3.43981i	−0.448034	+	0.120050i	0.0277455	+	0.999615i	$0.491167\pi$
$822$		0			0
$823$	−11.2358	−	19.4610i	−0.391656	−	0.678367i	0.601013	−	0.799240i	$-0.294764\pi$
$823$	−11.2358	−	19.4610i	−0.391656	−	0.678367i	−0.992668	+	0.120872i	$0.961431\pi$
$824$	13.6108	−	38.3224i	0.474155	−	1.33502i
$825$		0			0
$826$	6.30610	−	2.73965i	0.219417	−	0.0953245i
$827$	−2.97912	−	2.97912i	−0.103594	−	0.103594i	0.653410	−	0.757004i	$-0.273338\pi$
$827$	−2.97912	−	2.97912i	−0.103594	−	0.103594i	−0.757004	+	0.653410i	$0.773338\pi$
$828$		0			0
$829$	7.48252	−	12.9601i	0.259879	−	0.450123i	−0.706331	−	0.707882i	$-0.749651\pi$
$829$	7.48252	−	12.9601i	0.259879	−	0.450123i	0.966209	+	0.257759i	$0.0829841\pi$
$830$	0.0350235	+	0.0259328i	0.00121568	+	0.000900141i
$831$		0			0
$832$	28.6443	+	3.39203i	0.993061	+	0.117597i
$833$	24.1176			0.835624
$834$		0			0
$835$	0.0737561	−	0.127749i	0.00255244	−	0.00442095i
$836$	6.99105	+	22.9175i	0.241791	+	0.792619i
$837$		0			0
$838$	12.3012	−	5.34418i	0.424938	−	0.184612i
$839$	9.03430	+	2.42073i	0.311899	+	0.0835730i	0.411373	−	0.911467i	$-0.365049\pi$
$839$	9.03430	+	2.42073i	0.311899	+	0.0835730i	−0.0994743	+	0.995040i	$0.531716\pi$
$840$		0			0
$841$	−12.9641	−	22.4545i	−0.447039	−	0.774294i
$842$	4.61154	+	30.9221i	0.158924	+	1.06565i
$843$		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
$848$	−8.30262	−	12.3421i	−0.285113	−	0.423830i
$849$		0			0
$850$	4.45447	−	38.9889i	0.152787	−	1.33731i
$851$	−62.0833	−	16.6352i	−2.12819	−	0.570247i
$852$		0			0
$853$	−7.92636	+	7.92636i	−0.271393	+	0.271393i	−0.829661	−	0.558268i	$-0.811466\pi$
$853$	−7.92636	+	7.92636i	−0.271393	+	0.271393i	0.558268	+	0.829661i	$0.311466\pi$
$854$	4.50036	+	1.77435i	0.153999	+	0.0607171i
$855$		0			0
$856$	−8.03742	−	9.42835i	−0.274713	−	0.322254i
$857$		−	38.4399i		−	1.31308i	−0.754291	−	0.656541i	$-0.772019\pi$
$857$		−	38.4399i		−	1.31308i	0.754291	−	0.656541i	$-0.227981\pi$
$858$		0			0
$859$	1.82343			0.0622145			0.0311072	−	0.999516i	$-0.490097\pi$
$859$	1.82343			0.0622145			0.0311072	+	0.999516i	$0.490097\pi$
$860$	0.00452837	+	0.132023i	0.000154416	+	0.00450195i
$861$		0			0
$862$	51.5833	+	20.3377i	1.75693	+	0.692704i
$863$	−25.6067	−	25.6067i	−0.871661	−	0.871661i	0.120993	−	0.992653i	$-0.461392\pi$
$863$	−25.6067	−	25.6067i	−0.871661	−	0.871661i	−0.992653	+	0.120993i	$0.961392\pi$
$864$		0			0
$865$	−0.0181227	+	0.0676348i	−0.000616190	+	0.00229965i
$866$	8.30802	+	0.949189i	0.282318	+	0.0322548i
$867$		0			0
$868$	−1.53452	+	1.64352i	−0.0520849	+	0.0557848i
$869$	−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
$874$	27.6639	−	4.12563i	0.935745	−	0.139551i
$875$	−0.0864327	+	0.0499019i	−0.00292196	+	0.00168699i
$876$		0			0
$877$	−2.98286	+	11.1322i	−0.100724	+	0.375907i	−0.997825	−	0.0659183i	$-0.979002\pi$
$877$	−2.98286	+	11.1322i	−0.100724	+	0.375907i	0.897101	+	0.441826i	$0.145669\pi$
$878$	9.58730	−	4.16514i	0.323556	−	0.140567i
$879$		0			0
$880$	−0.0817923	+	0.00561754i	−0.00275722	+	0.000189367i
$881$	−11.9623	−	6.90643i	−0.403020	−	0.232684i	0.284766	−	0.958597i	$-0.408084\pi$
$881$	−11.9623	−	6.90643i	−0.403020	−	0.232684i	−0.687786	+	0.725913i	$0.741417\pi$
$882$		0			0
$883$		−	46.3198i		−	1.55879i	−0.626536	−	0.779393i	$-0.715528\pi$
$883$		−	46.3198i		−	1.55879i	0.626536	−	0.779393i	$-0.284472\pi$
$884$	39.3264	+	7.41829i	1.32269	+	0.249504i
$885$		0			0
$886$	−31.1037	−	23.0305i	−1.04495	−	0.773723i
$887$	40.2976	+	23.2659i	1.35306	+	0.781191i	0.988677	−	0.150058i	$-0.0479459\pi$
$887$	40.2976	+	23.2659i	1.35306	+	0.781191i	0.364385	+	0.931248i	$0.381279\pi$
$888$		0			0
$889$	−4.40552	+	4.40552i	−0.147757	+	0.147757i
$890$	−0.0517822	−	0.119192i	−0.00173574	−	0.00399532i
$891$		0			0
$892$	15.1832	+	24.3318i	0.508373	+	0.814690i
$893$	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
$902$	2.68169	−	23.4722i	0.0892905	−	0.781538i
$903$		0			0
$904$	−22.3830	+	4.12692i	−0.744449	+	0.137259i
$905$	0.0429027	+	0.0429027i	0.00142613	+	0.00142613i
$906$		0			0
$907$	−23.2692	−	13.4345i	−0.772642	−	0.446085i	0.0611745	−	0.998127i	$-0.480515\pi$
$907$	−23.2692	−	13.4345i	−0.772642	−	0.446085i	−0.833816	+	0.552042i	$0.813849\pi$
$908$	0.656836	+	19.1498i	0.0217979	+	0.635509i
$909$		0			0
$910$	−0.0221773	−	0.0458039i	−0.000735172	−	0.00151838i
$911$			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
$914$	14.8645	−	37.7015i	0.491675	−	1.24706i
$915$		0			0
$916$	43.0977	+	22.9498i	1.42399	+	0.758282i
$917$	−15.9408	−	4.27133i	−0.526413	−	0.141052i
$918$		0			0
$919$	−12.0258	+	6.94309i	−0.396694	+	0.229031i	−0.685057	−	0.728490i	$-0.740223\pi$
$919$	−12.0258	+	6.94309i	−0.396694	+	0.229031i	0.288362	+	0.957521i	$0.406889\pi$
$920$	−0.00759768	+	0.0954030i	−0.000250488	+	0.00314534i
$921$		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
$926$	−19.0441	+	2.84013i	−0.625828	+	0.0933323i
$927$		0			0
$928$	8.35350	+	5.33999i	0.274217	+	0.175294i
$929$	−26.6246	−	7.13405i	−0.873526	−	0.234061i	−0.205914	−	0.978570i	$-0.566017\pi$
$929$	−26.6246	−	7.13405i	−0.873526	−	0.234061i	−0.667612	+	0.744510i	$0.732683\pi$
$930$		0			0
$931$	11.0028	+	11.0028i	0.360601	+	0.360601i
$932$	22.6781	−	6.91802i	0.742846	−	0.226607i
$933$		0			0
$934$	21.9366	−	29.6264i	0.717788	−	0.969406i
$935$	−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	$0.348347\pi$
$938$	0.705748	−	0.953146i	0.0230435	−	0.0311213i
$939$		0			0
$940$	0.0145347	+	0.0476466i	0.000474071	+	0.00155406i
$941$	4.25969	+	4.25969i	0.138862	+	0.138862i	0.773121	−	0.634259i	$-0.218695\pi$
$941$	4.25969	+	4.25969i	0.138862	+	0.138862i	−0.634259	+	0.773121i	$0.718695\pi$
$942$		0			0
$943$	−26.6388	−	7.13783i	−0.867477	−	0.232440i
$944$	−3.87211	−	11.2909i	−0.126027	−	0.367488i
$945$		0			0
$946$	−50.4593	+	7.52520i	−1.64057	+	0.244666i
$947$	−6.23584	+	1.67089i	−0.202637	+	0.0542965i	−0.358710	−	0.933449i	$-0.616783\pi$
$947$	−6.23584	+	1.67089i	−0.202637	+	0.0542965i	0.156073	+	0.987746i	$0.450117\pi$
$948$		0			0
$949$	6.77508	+	1.52023i	0.219929	+	0.0493488i
$950$	19.8194	−	15.7551i	0.643027	−	0.511162i
$951$		0			0
$952$	−2.03021	+	25.4931i	−0.0657996	+	0.826236i
$953$	−14.7203	+	8.49878i	−0.476838	+	0.275302i	−0.719098	−	0.694909i	$-0.755445\pi$
$953$	−14.7203	+	8.49878i	−0.476838	+	0.275302i	0.242260	+	0.970211i	$0.422111\pi$
$954$		0			0
$955$	−0.0497794	−	0.0133383i	−0.00161082	−	0.000431618i
$956$	−10.8936	+	20.4573i	−0.352324	+	0.661635i
$957$		0			0
$958$	−17.4768	+	44.3270i	−0.564649	+	1.43214i
$959$	13.9297	−	24.1270i	0.449815	−	0.779102i
$960$		0			0
$961$		−	30.5238i		−	0.984639i
$962$	−11.1540	−	58.2758i	−0.359619	−	1.87889i
$963$		0			0
$964$	42.8432	−	1.46952i	1.37989	−	0.0473299i
$965$	0.0208386	+	0.0120312i	0.000670817	+	0.000387297i
$966$		0			0
$967$	14.8731	+	14.8731i	0.478288	+	0.478288i	0.904584	−	0.426296i	$-0.140182\pi$
$967$	14.8731	+	14.8731i	0.478288	+	0.478288i	−0.426296	+	0.904584i	$0.640182\pi$
$968$	−0.0997206	−	0.540852i	−0.00320514	−	0.0173836i
$969$		0			0
$970$	−0.00479517	+	0.0419710i	−0.000153964	+	0.00134761i
$971$	7.95576	+	13.7798i	0.255313	+	0.442214i	0.964980	−	0.262322i	$-0.0844883\pi$
$971$	7.95576	+	13.7798i	0.255313	+	0.442214i	−0.709668	+	0.704536i	$0.751155\pi$
$972$		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	0.991649	−	0.128966i	$-0.0411658\pi$
$977$	2.13713	+	7.97588i	0.0683729	+	0.255171i	−0.923276	+	0.384137i	$0.874499\pi$
$978$		0			0
$979$	43.4645	−	25.0942i	1.38913	−	0.802015i
$980$	−0.0451700	+	0.0281864i	−0.00144290	+	0.000900383i
$981$		0			0
$982$	20.8172	+	47.9169i	0.664303	+	1.52909i
$983$	−30.1467	+	30.1467i	−0.961530	+	0.961530i	−0.999287	−	0.0377570i	$-0.987979\pi$
$983$	−30.1467	+	30.1467i	−0.961530	+	0.961530i	0.0377570	+	0.999287i	$0.487979\pi$
$984$		0			0
$985$	0.0845755	+	0.0488297i	0.00269480	+	0.00155584i
$986$	11.0551	+	8.18565i	0.352066	+	0.260684i
$987$		0			0
$988$	14.5569	+	21.3256i	0.463117	+	0.678456i
$989$			59.5551i			1.89374i
$990$		0			0
$991$	−2.25938	−	1.30446i	−0.0717717	−	0.0414374i	0.463685	−	0.886000i	$-0.346527\pi$
$991$	−2.25938	−	1.30446i	−0.0717717	−	0.0414374i	−0.535456	+	0.844563i	$0.679860\pi$
$992$	2.63279	+	2.88214i	0.0835912	+	0.0915082i
$993$		0			0
$994$	−4.65032	+	2.02030i	−0.147499	+	0.0640802i
$995$	0.0203509	−	0.0759508i	0.000645168	−	0.00240780i
$996$		0			0
$997$	21.3384	−	12.3197i	0.675794	−	0.390170i	−0.122475	−	0.992472i	$-0.539083\pi$
$997$	21.3384	−	12.3197i	0.675794	−	0.390170i	0.798268	+	0.602302i	$0.205750\pi$
$998$	30.9110	−	4.60988i	0.978469	−	0.145923i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.5	✓	56	24.11	even	2
312.2.bt.d.19.11	yes	56	3.2	odd	2
312.2.bt.d.115.5	yes	56	39.11	even	12
312.2.bt.d.115.11	yes	56	312.11	odd	12
936.2.ed.e.19.4		56	1.1	even	1	trivial
936.2.ed.e.19.10		56	8.3	odd	2	inner
936.2.ed.e.739.4		56	104.11	even	12	inner
936.2.ed.e.739.10		56	13.11	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.13656 - 0.841559i) q^{2} +(0.583557 + 1.91297i) q^{4} +(-0.00433170 - 0.00433170i) q^{5} +(1.57369 + 0.421669i) q^{7} +(0.946628 - 2.66531i) q^{8} +(0.00127787 + 0.00856863i) q^{10} +(-3.23180 + 0.865959i) q^{11} +(-3.04585 + 1.92946i) q^{13} +(-1.43374 - 1.80361i) q^{14} +(-3.31892 + 2.23266i) q^{16} +(-4.80624 + 2.77488i) q^{17} +(-3.45861 - 0.926732i) q^{19} +(0.00575862 - 0.0108142i) q^{20} +(4.40191 + 1.73554i) q^{22} +(2.76176 - 4.78352i) q^{23} -4.99996i q^{25} +(5.08556 + 0.370304i) q^{26} +(0.111697 + 3.25650i) q^{28} +(1.51783 + 0.876322i) q^{29} +(0.487954 + 0.487954i) q^{31} +(5.65108 + 0.255510i) q^{32} +(7.79783 + 0.890900i) q^{34} +(-0.00499021 - 0.00864330i) q^{35} +(-3.01169 - 11.2398i) q^{37} +(3.15103 + 3.96392i) q^{38} +(-0.0156458 + 0.00744482i) q^{40} +(-1.29226 - 4.82278i) q^{41} +(-9.33754 + 5.39103i) q^{43} +(-3.54250 - 5.67701i) q^{44} +(-7.16454 + 3.11259i) q^{46} +(-2.87499 + 2.87499i) q^{47} +(-3.76348 - 2.17284i) q^{49} +(-4.20776 + 5.68278i) q^{50} +(-5.46843 - 4.70067i) q^{52} +3.71872i q^{53} +(0.0177503 + 0.0102481i) q^{55} +(2.61358 - 3.79522i) q^{56} +(-0.987640 - 2.27334i) q^{58} +(-0.772342 + 2.88242i) q^{59} +(-1.81829 + 1.04979i) q^{61} +(-0.143949 - 0.965233i) q^{62} +(-6.20779 - 5.04612i) q^{64} +(0.0215515 + 0.00483585i) q^{65} +(0.133225 + 0.497203i) q^{67} +(-8.11299 - 7.57490i) q^{68} +(-0.00160215 + 0.0140232i) q^{70} +(0.569550 - 2.12559i) q^{71} +(-1.36174 - 1.36174i) q^{73} +(-6.03597 + 15.3093i) q^{74} +(-0.245485 - 7.15703i) q^{76} -5.45101 q^{77} +12.6705i q^{79} +(0.0240478 + 0.00470537i) q^{80} +(-2.58992 + 6.56891i) q^{82} +(3.55694 - 3.55694i) q^{83} +(0.0328391 + 0.00879922i) q^{85} +(15.1496 + 1.73084i) q^{86} +(-0.751264 + 9.43351i) q^{88} +(-14.4893 + 3.88239i) q^{89} +(-5.60682 + 1.75203i) q^{91} +(10.7624 + 2.49172i) q^{92} +(5.68708 - 0.848136i) q^{94} +(0.0109673 + 0.0189960i) q^{95} +(4.71000 + 1.26204i) q^{97} +(2.44886 + 5.63677i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) \) 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

Modular forms

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Database

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